# Identifications: Projective Plane Glued
# Comparison of Eigenfunctions on Level 3 to Eigenfunctions on Level 2
# Looking at K = 20 eigenvalues to either side of the closest level-2 eigenvalue.

# Dot value closer to zero means closer comparison.

# Eigenvalue Index, Dot Value
# 0, 0.0
# 1, 0.00017225677959220587
# 2, 0.00019085106911675975
# 3, 0.0014215263537862288
# 4, 0.0014332152551934652
# 5, 0.0014332152551935762
# 6, 0.0003283457785615562
# 7, 0.0024135566193831393
# 8, 0.011862172098631052
# 9, 0.0006826703997200312
# 10, 1.1102230246251565e-16
# 11, 0.029416001032016248
# 12, 0.010935030837211812
# 13, 0.01093503083721159
# 14, 0.007310975902898864
# 15, 0.0114455486965932
# 16, 0.0
# 17, 0.13241666911770067
# 18, 0.13936823348128213
# 19, 0.020649452413137426
# 20, 0.10727115593082526
# 21, 0.10727115593083258
# 22, 0.1462234558282004
# 23, 0.14622345582819962
# 24, 0.15199842905627303
# 25, 0.09744720526326123
# 26, 0.012681577596699856
# 27, 0.17245953861599883
# 28, 0.0
# 29, 0.30870546429789125
# 30, 0.3087054642978896
# 31, 0.2954368270613493
# 32, 0.2954368270613271
# 33, 0.03233281594177728
# 34, 0.1406970871980564
# 35, 0.18662940620748614
# 36, 0.18662940620749024
# 37, 0.25785727730529673
# 38, 0.08347280612342267
# 39, 0.18336585417922457
# 40, 0.18336585417922457
# 41, 0.09278219317442538
# 42, 0.19535037200805416
# 43, 0.12542904916261732
# 44, 0.1254290491626212
# 45, 0.0006505301638105587
# 46, 0.0006505301638103367
# 47, 0.1306412151169133
# 48, 0.09999860002487682
# 49, 0.04335567486896852
# 50, 0.1199105458179065
# 51, 0.04554051756117905
# 52, 0.04554051756117905
# 53, 2.220446049250313e-16
# 54, 0.08949904161103861
# 55, 2
# 56, 0.40218584221689535
# 57, 0.38227003632157686
# 58, 0.23651928851896276
# 59, 0.23651928851895532
# 60, 0.24629670924209435
# 61, 0.24629670924209135
# 62, 2.220446049250313e-16
# 63, 0.36554596070839407
# 64, 0.4059355012585302
# 65, 0.17716550190725022
# 66, 1.1102230246251565e-16
# 67, 0.10969442174125965
# 68, 0.28669511702143546
# 69, 0.2866951170214319
# 70, 0.4563569234466117
# 71, 0.14996624711657192
# 72, 0.12400492594907986
# 73, 0.30894529212355704
# 74, 0.2571849976203482
# 75, 0.35179929573462276
# 76, 0.25481977542280865
# 77, 0.254819775422926
# 78, 0.34341394116269497
# 79, 0.3491229521143736
# 80, 0.34912295211437216
# 81, 0.30410155906748726
# 82, 0.1690069008156737
# 83, 0.0
# 84, 0.27648904303214206
# 85, 0.3481892886969452
# 86, 0.34818928869694077
# 87, 0.38970843263391786
# 88, 0.3748323788862906
# 89, 0.08920561505468683
# 90, 2
# 91, 2
# 92, 0.2686074263136293
# 93, 0.3276381930192762
# 94, 0.28024593779748774
# 95, 0.4105852070345878
# 96, 0.4105852070348346
# 97, 0.2956332476273248
# 98, 0.0017108198585332746
# 99, 0.0017108198585331635
# 100, 0.2231085764775964
# 101, 0.05397313337891407
# 102, 0.35124162631759803
# 103, 0.2990335838239834
# 104, 0.4343075963268249
# 105, 0.4343075963268489
# 106, 0.1331497120044084
# 107, 0.13314971200433845
# 108, 0.31805119235322277
# 109, 0.20612425364085596
# 110, 0.2453253434413427
# 111, 2
# 112, 0.04929695354159502
# 113, 0.04929695354161101
# 114, 0.200417306554719
# 115, 0.1646341733414829
# 116, 0.16463417334152608
# 117, 0.12928064901028413
# 118, 0.07591395135006518
# 119, 0.119820643948503
# 120, 0.11982064394850289
# 121, 0.15906872237364877
# 122, 0.235642406282922
# 123, 0.0
# 124, 0.23684131172816103
# 125, 0.22291385057650626
# 126, 0.2229138505764956
# 127, 0.4365670469378792
# 128, 0.43656704693793014
# 129, 0.3304678113817242
# 130, 0.10115447488738427
# 131, 0.3464993092115435
# 132, 0.1560090006047059
# 133, 0.1560090006047079
# 134, 0.3495370617211323
# 135, 0.37629969537839925
# 136, 0.03988523435788616
# 137, 0.09630369421987162
# 138, 0.1423564162680755
# 139, 0.1423564162680837
# 140, 0.47270830302271405
# 141, 0.47270830302297395
# 142, 0.28510868419131663
# 143, 0.10712408036477084
# 144, 0.23140142707582367
# 145, 0.1418919065690848
# 146, 2
# 147, 0.0
# 148, 0.18627874251696963
# 149, 0.1862787425170419
# 150, 0.4704657031100512
# 151, 0.10690471481621788
# 152, 0.10690471481621555
# 153, 0.17917916470328465
# 154, 0.24071223967015676
# 155, 0.33754459016243143
# 156, 0.3375445901624362
# 157, 0.1984153441407821
# 158, 0.0
# 159, 0.3479216585802525
# 160, 0.3390461369422363
# 161, 0.6242521927165923
# 162, 0.6242521927165983
# 163, 0.008815596088504463
# 164, 0.008815596088503685
# 165, 0.20341217186293536
# 166, 0.48050985540995494
# 167, 0.1649436975518287
# 168, 0.42624283632121607
# 169, 0.39054086471461247
# 170, 0.3905408647148896
# 171, 0.4604009245247278
# 172, 0.4604009245247308
# 173, 0.20379939135569713
# 174, 0.40897955880438486
# 175, 0.4089795588044064
# 176, 0.30746370752189967
# 177, 0.49967476930420496
# 178, 0.4996747693042125
# 179, 0.4405220725238125
# 180, 0.4405220725237978
# 181, 0.3433667765406161
# 182, 0.5130112037246596
# 183, 0.5130112037246535
# 184, 0.26026227977110705
# 185, 0.2602622797711064
# 186, 0.25153195747364876
# 187, 0.3937605810071825
# 188, 0.3179530820287363
# 189, 0.18986422328869168
# 190, 0.4636771645257851
# 191, 0.4636771645257607
# 192, 0.16588391126249646
# 193, 0.2797754675316204
# 194, 2.220446049250313e-16
# 195, 0.38563744889270146
# 196, 0.3856374488926614
# 197, 0.40932046182419546
# 198, 0.3731901567275636
# 199, 0.38370721793281415
# 200, 0.38370721793281404
# 201, 0.3804601952485611
# 202, 0.23048272888501586
# 203, 0.17662317308536546
# 204, 0.3565831185024697
# 205, 0.4412891080393866
# 206, 0.4412891080393907
# 207, 0.08943702276983112
# 208, 0.45449428990810936
# 209, 0.43617620531470047
# 210, 0.43617620531462287
# 211, 0.3982345526447324
# 212, 0.48185520489999156
# 213, 0.48185520489997336
# 214, 0.46539009746369064
# 215, 0.2830274999404855
# 216, 0.37400971478112854
# 217, 0.37400971478112544
# 218, 0.1082814275338776
# 219, 0.21201594892352416
# 220, 2
# 221, 0.19617600407097935
# 222, 0.19617600407096403
# 223, 0.4077787343977868
# 224, 0.19366955004331865
# 225, 0.19366955004331865
# 226, 0.13756553237444336
# 227, 0.20534810047866148
# 228, 0.3875154067864758
# 229, 0.4359217933039168
# 230, 0.4359217933039019
# 231, 0.25066161339702375
# 232, 0.25066161339701243
# 233, 1.1102230246251565e-16
# 234, 0.24922555023695303
# 235, 0.3057432882288146
# 236, 0.30574328822879127
# 237, 0.38359559648220753
# 238, 0.3835955964822336
# 239, 0.16325414711359276
# 240, 0.29215666707314014
# 241, 0.3936236506186631
# 242, 0.36264028357599365
# 243, 0.24465282520932574
# 244, 0.021663047229855015
# 245, 0.021663047229855015
# 246, 0.3950547736366945
# 247, 0.39505477363670005
# 248, 0.06239672058478618
# 249, 0.4047526897910094
# 250, 0.40475268979101986
# 251, 0.2565916057583829
# 252, 0.25659160575838635
# 253, 0.3682912208866824
# 254, 0.3682912208866953
# 255, 0.3284418708953559
# 256, 0.32604822918209964
# 257, 0.3260482291821003
# 258, 0.3059407475836985
# 259, 0.11467013435710804
# 260, 0.1146701343571036
# 261, 0.22224213348495225
# 262, 2
# 263, 0.3355360210295081
# 264, 0.2480332849695539
# 265, 0.2430919931590596
# 266, 0.2430919931590504
# 267, 0.4948782892097576
# 268, 0.2850243612337259
# 269, 0.4961335952074176
# 270, 0.4961335952072574
# 271, 0.4046078097068019
# 272, 1.1102230246251565e-16
# 273, 0.3806015933022039
# 274, 0.38060159330220356
# 275, 0.1631665373433696
# 276, 0.39813184902874044
# 277, 0.39813184902873877
# 278, 0.11093607558580754
# 279, 0.1776806316647338
# 280, 0.4513435843487923
# 281, 0.4513435843487309
# 282, 0.10814245939061795
# 283, 0.5706870172859366
# 284, 0.1455714477008191
# 285, 0.13229875896193943
# 286, 0.25261068434492506
# 287, 0.42680113199049563
# 288, 0.4268011319904953
# 289, 0.1803121477827383
# 290, 0.1803121477827414
# 291, 0.36045761983643965
# 292, 0.0
# 293, 0.33419039533218464
# 294, 0.09741416012753146
# 295, 0.35929635114206315
# 296, 0.35929635114205083
# 297, 0.11711948212574363
# 298, 2.220446049250313e-16
# 299, 0.1444982205634966
# 300, 0.14449822056344463
# 301, 0.31029323983735546
# 302, 0.06378851177678102
# 303, 2
# 304, 2
# 305, 0.05664447845238474
# 306, 0.32461853305775157
# 307, 0.32461853305776867
# 308, 0.3699266153277969
# 309, 0.15854849594864828
# 310, 0.2778560384671268
# 311, 0.21105347071187008
# 312, 0.21105347071188263
# 313, 0.2730089849842574
# 314, 0.0
# 315, 0.26513802365831673
# 316, 0.4404366516084727
# 317, 0.4404366516084719
# 318, 0.0815363154289559
# 319, 0.006646834343965846
# 320, 0.3272835128727547
# 321, 0.32728351287279167
# 322, 0.2977537814404462
# 323, 0.18756118497731278
# 324, 0.5351890379720419
# 325, 0.535189037972025
# 326, 0.009074624468261128
# 327, 0.009074624468260684
# 328, 2
# 329, 0.1208258569900067
# 330, 0.35563439140692577
# 331, 0.35563439140692144
# 332, 0.24084068340936915
# 333, 0.4257420941786436
# 334, 0.32090659592078696
# 335, 0.34950426570544313
# 336, 0.3495042657054306
# 337, 0.3413687037300197
# 338, 0.09906692453713883
# 339, 0.1927904072465665
# 340, 0.3353944841504811
# 341, 0.144428534245019
# 342, 0.3161576004982901
# 343, 0.18921591998591036
# 344, 0.527393907080991
# 345, 0.5273939070809803
# 346, 2.220446049250313e-16
# 347, 0.0
# 348, 0.33445430759765815
# 349, 0.3344543075976648
# 350, 0.33464779528028876
# 351, 0.34632793981930143
# 352, 0.23085112387074125
# 353, 0.23085112387076168
# 354, 0.28010543590059467
# 355, 0.1656214420923663
# 356, 0.3449389751977545
# 357, 0.34493897519772165
# 358, 0.48019184711771323
# 359, 0.4687546434517542
# 360, 0.46875464345173934
# 361, 0.30056173895250093
# 362, 0.3066804075014419
# 363, 0.10707757037592425
# 364, 0.6132301882997937
# 365, 0.613230188299835
# 366, 0.0951672109552616
# 367, 0.09516721095526692
# 368, 0.22062686783862073
# 369, 0.3805956464424457
# 370, 0.3805956464424637
# 371, 0.292773286658385
# 372, 0.2689539544374896
# 373, 0.0
# 374, 0.37825214939967466
# 375, 0.37825214939967167
# 376, 0.28024760137641636
# 377, 0.5004610911968179
# 378, 0.5004610911968128
# 379, 0.33080115449170344
# 380, 0.3554390774295846
# 381, 0.5270834979353431
# 382, 0.5270834979353498
# 383, 0.13565032263317367
# 384, 0.43028247035336664
# 385, 0.25148549981911794
# 386, 0.5765834655665619
# 387, 0.5765834655665585
# 388, 0.34756225493873005
# 389, 0.34756225493872506
# 390, 0.24220143855511977
# 391, 0.242201438555101
# 392, 0.2930638640790506
# 393, 0.4505258494785258
# 394, 0.45052584947853025
# 395, 0.0604300461179782
# 396, 0.14072504399995445
# 397, 0.140725043999946
# 398, 0.2740168899727239
# 399, 0.16363295642772047
# 400, 0.16363295642774467
# 401, 0.3600532190869008
# 402, 0.36005321908692767
# 403, 0.23161787189024707
# 404, 0.273644680310537
# 405, 0.18215162833550136
# 406, 0.16609194282173467
# 407, 0.19087379750525868
# 408, 1.1102230246251565e-16
# 409, 0.1458121298153494
# 410, 0.294908863315715
# 411, 0.29490886331568733
# 412, 0.08730280659994727
# 413, 0.18510190066999654
# 414, 0.185101900669998
# 415, 0.5300981930202857
# 416, 0.5300981930202631
# 417, 0.1013301270407686
# 418, 0.18602286999721196
# 419, 0.18602286999720263
# 420, 0.22767120147176212
# 421, 0.11744167872571354
# 422, 0.1309538525285402
# 423, 0.35872025945573394
# 424, 0.35872025945574737
# 425, 0.03452828705996047
# 426, 0.3011383063976123
# 427, 0.30113830639760986
# 428, 0.1775429438727898
# 429, 0.1775429438729227
# 430, 0.2737604769004748
# 431, 2
# 432, 2.220446049250313e-16
# 433, 0.30394058137967783
# 434, 0.087188060963444
# 435, 0.36525531637191977
# 436, 0.3043232339676185
# 437, 0.3043232339674331
# 438, 0.061938516373562735
# 439, 0.06994440016393044
# 440, 0.038273366343332005
# 441, 0.023577187020793033
# 442, 0.341024494017823
# 443, 0.3410244940178324
# 444, 0.2979879830259474
# 445, 0.30565715386200554
# 446, 2.220446049250313e-16
# 447, 0.028616369636030314
# 448, 0.11241380378148136
# 449, 0.31317578915952815
# 450, 0.18817155973249988
# 451, 0.18817155973254196
# 452, 0.36719659870849997
# 453, 0.3016593118167342
# 454, 0.30165931181668837
# 455, 0.08740296889584098
# 456, 0.00155522412983089
# 457, 0.001555224129830668
# 458, 0.3867212002525249
# 459, 0.38672120025253875
# 460, 0.46629016383012833
# 461, 0.46629016383020094
# 462, 0.08834989036867502
# 463, 0.26422133386981395
# 464, 0.06084800266746948
# 465, 0.06511495032410664
# 466, 0.06511495032416748
# 467, 0.23229218548753394
# 468, 0.23229218548739883
# 469, 0.25386900078885744
# 470, 0.3391608737960624
# 471, 0.3391608737959776
# 472, 0.20252656941109604
# 473, 0.37729596724040515
# 474, 0.37729596724037384
# 475, 0.2651455362421309
# 476, 0.06576335769440123
# 477, 0.0818931199419638
# 478, 0.2177559215027376
# 479, 0.21775592150259948
# 480, 0.08285083983879427
# 481, 0.1979053408566681
# 482, 0.26602091302376807
# 483, 0.26602091302364383
# 484, 0.2753081422739879
# 485, 0.27530814227277867
# 486, 0.14424193820500752
# 487, 0.025723692140210086
# 488, 0.025723692140196208
# 489, 0.11891687734677758
# 490, 0.11891687734672252
# 491, 0.06495380898645153
# 492, 0.40951105585266856
# 493, 0.4095110558528291
# 494, 0.26176628210193464
# 495, 0.2617662821019061
# 496, 0.18060513764205866
# 497, 0.18060513764198194
# 498, 0.25524810110242835
# 499, 0.3822998268021466
# 500, 0.10587259954266048
# 501, 0.25632743395169244
# 502, 0.25632743395170665
# 503, 0.16609031161676902
# 504, 0.35834532839987376
# 505, 0.3583453283998348
# 506, 0.4716384737418342
# 507, 0.4716384737417937
# 508, 0.38503374380309385
# 509, 0.38503374380305355
# 510, 2
# 511, 2

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