# Identifications: Torus 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, 0.0003112650688600338
# 2, 0.0008691073914722791
# 3, 0.0008691073914720571
# 4, 0.0006181836074257152
# 5, 0.002541301941148988
# 6, 0.004649913969036912
# 7, 0.004649913969036579
# 8, 0.002804239465901137
# 9, 0.0008895272340454508
# 10, 0.017489625328879987
# 11, 0.0073455809501703495
# 12, 0.0073455809501700164
# 13, 0.010739287809013676
# 14, 0.010739287809012787
# 15, 0.0136542351530623
# 16, 0.0
# 17, 0.004999943466274859
# 18, 0.10067165746102669
# 19, 0.026635378676363786
# 20, 0.24179489926886255
# 21, 0.2417948992688641
# 22, 0.11164533654344821
# 23, 0.21514801739009481
# 24, 0.21514801739009815
# 25, 0.007208422818863469
# 26, 0.007208422818863469
# 27, 0.09414370149475604
# 28, 0.04160711004409934
# 29, 2.220446049250313e-16
# 30, 0.08688381031666326
# 31, 0.08688381031666315
# 32, 0.13296595339252149
# 33, 0.19119663186931746
# 34, 0.1911966318693178
# 35, 0.1356552069159137
# 36, 0.2007061238296961
# 37, 0.2532504421684575
# 38, 0.14912272891031464
# 39, 0.14912272891031475
# 40, 0.1895316388037156
# 41, 0.021455528622870923
# 42, 0.04753936739267817
# 43, 0.04753936739267994
# 44, 0.05002080551582844
# 45, 0.21601224910660233
# 46, 0.0777456721277694
# 47, 0.1405915402398772
# 48, 0.1405915402398772
# 49, 0.08778470355655521
# 50, 0.08778470355655277
# 51, 0.013670569702209812
# 52, 0.23660096511950057
# 53, 0.32610062451893007
# 54, 0.32610062451891986
# 55, 0.0
# 56, 0.01290626341264356
# 57, 0.3890103035159026
# 58, 0.2021774508230667
# 59, 0.08916117818499336
# 60, 0.08916117818499225
# 61, 0.0
# 62, 0.4086668983241988
# 63, 0.18782194981002198
# 64, 0.15902086893926926
# 65, 0.15902086893927747
# 66, 0.1850096111451881
# 67, 0.38451150978697757
# 68, 0.38451150978698234
# 69, 1.1102230246251565e-16
# 70, 0.18042018558937634
# 71, 0.36383795123211193
# 72, 0.3638379512321075
# 73, 0.44320190236242385
# 74, 0.44320190236242085
# 75, 0.20618040631850454
# 76, 0.28806237030453297
# 77, 0.33160284705466614
# 78, 0.3316028470547069
# 79, 0.13671647268235076
# 80, 0.17634222450748693
# 81, 0.06446832319032991
# 82, 0.0
# 83, 0.11312368070719858
# 84, 0.11312368070719592
# 85, 0.28385441281445767
# 86, 0.48449267518850947
# 87, 0.4844926751885118
# 88, 0.12081639629330843
# 89, 0.28946164039226274
# 90, 0.2646600692833917
# 91, 0.26466006928339747
# 92, 0.3381443581011352
# 93, 0.22413464832315655
# 94, 0.3032358382404954
# 95, 2
# 96, 0.11735730928401822
# 97, 0.4116516475148321
# 98, 0.4116516475148304
# 99, 0.16410341957356278
# 100, 0.37905712371340894
# 101, 0.52147061736122
# 102, 0.5214706173612043
# 103, 0.4276244967401124
# 104, 0.29308358151857883
# 105, 0.29308358151858693
# 106, 0.38061445528256077
# 107, 0.24165795015115898
# 108, 0.32828272622951415
# 109, 0.32828272622951993
# 110, 0.4771318891549776
# 111, 0.4771318891549884
# 112, 0.08486962059472325
# 113, 0.23057693375417443
# 114, 0.2789820387668619
# 115, 0.2622422145619987
# 116, 0.2622422145619857
# 117, 0.419382160783907
# 118, 0.3114606670199669
# 119, 0.36987355376075104
# 120, 0.28845241234581565
# 121, 0.28845241234581576
# 122, 0.1694249910116301
# 123, 0.5037673660506381
# 124, 0.503767366050631
# 125, 0.05099872962467267
# 126, 0.0
# 127, 0.3462163107241297
# 128, 0.4241657792782907
# 129, 0.4241657792782906
# 130, 0.011440672902887195
# 131, 0.011440672902887083
# 132, 0.3254834576952824
# 133, 0.38001585960907525
# 134, 0.5313859424037267
# 135, 0.5313859424037277
# 136, 2
# 137, 0.24488389800479504
# 138, 0.11622944484108466
# 139, 0.21626405005701943
# 140, 0.2708091925551809
# 141, 0.2708091925551792
# 142, 0.21409640789049234
# 143, 0.21409640789049456
# 144, 0.0
# 145, 0.30647292528006087
# 146, 0.39842477065624005
# 147, 0.31464588415287476
# 148, 0.3361795684172051
# 149, 0.48056072387882043
# 150, 0.4805607238788099
# 151, 0.37771891097022936
# 152, 0.21594841869994197
# 153, 0.392102070278849
# 154, 0.39210207027882393
# 155, 0.3388630245166455
# 156, 0.16924647372472934
# 157, 0.5253243323842449
# 158, 0.525324332384253
# 159, 0.33990547682682315
# 160, 0.3862817674095622
# 161, 0.3334735227752387
# 162, 0.3334735227752692
# 163, 0.2922995657661792
# 164, 0.5362345704528007
# 165, 0.536234570452838
# 166, 0.22985127509977865
# 167, 0.007550097877228823
# 168, 0.007550097877229489
# 169, 0.20676928451892262
# 170, 0.6928400757630253
# 171, 0.6411678214650853
# 172, 0.6411678214650818
# 173, 0.6728310375386006
# 174, 0.6728310375385858
# 175, 0.17335816582812036
# 176, 0.1714185920893191
# 177, 0.2646966642791967
# 178, 0.3437537586624403
# 179, 0.3437537586624412
# 180, 2.220446049250313e-16
# 181, 0.5554509725695547
# 182, 0.20779845346607784
# 183, 0.2919961646446735
# 184, 0.2919961646446698
# 185, 0.46653299541729665
# 186, 0.2517205833509739
# 187, 0.0
# 188, 0.409293770911209
# 189, 0.4092937709112211
# 190, 0.2525140921584239
# 191, 0.23629174172774825
# 192, 2
# 193, 2
# 194, 0.13441847571728038
# 195, 0.11896502548246268
# 196, 0.1189650254824578
# 197, 0.21178282108806568
# 198, 0.21591186291598208
# 199, 0.37438344547744007
# 200, 0.3743834454774473
# 201, 0.44143700671569064
# 202, 0.4414370067162796
# 203, 0.15590252213512534
# 204, 0.1559025221351027
# 205, 0.07097059231857639
# 206, 0.11325083644853351
# 207, 0.3198602892068
# 208, 0.021125970899165236
# 209, 0.021125970899165236
# 210, 0.3369081606903417
# 211, 0.4637835437555523
# 212, 0.4637835437555444
# 213, 0.2545210661969678
# 214, 0.4190683905752053
# 215, 0.2934536803387148
# 216, 0.2530345335095787
# 217, 0.34459276926365867
# 218, 0.3445927692636488
# 219, 0.29775308490842023
# 220, 0.37621498130010533
# 221, 0.3430173172675153
# 222, 0.34301731726755313
# 223, 0.2905719131871938
# 224, 0.31219888788487293
# 225, 0.3121988878848746
# 226, 0.27473190156827887
# 227, 0.21607836060409313
# 228, 0.1549653108110579
# 229, 0.3268342947989059
# 230, 0.35970207738643023
# 231, 0.359702077386435
# 232, 0.3014879212477112
# 233, 0.3054222725983319
# 234, 0.3054222725983513
# 235, 0.2193580336926051
# 236, 0.0
# 237, 2
# 238, 0.18077791317069825
# 239, 0.46377588448538587
# 240, 0.46377588448538
# 241, 0.3826102156439377
# 242, 0.38261021564393116
# 243, 0.12722477881484762
# 244, 0.02873650859487653
# 245, 0.02873650859487975
# 246, 0.40089876747992403
# 247, 0.40089876747990594
# 248, 0.1310312050637824
# 249, 0.057019369976645806
# 250, 0.08754815732229204
# 251, 0.0875481573222946
# 252, 0.12237814007263448
# 253, 0.1380137300825649
# 254, 0.16600156599761606
# 255, 0.16600156599761007
# 256, 0.4292523321297832
# 257, 0.0
# 258, 0.1805252737426145
# 259, 2
# 260, 0.2318631012090976
# 261, 0.33473454822132
# 262, 0.3347345482213262
# 263, 0.40805403650031846
# 264, 0.32088909998848403
# 265, 0.3740175054627083
# 266, 0.37401750546270196
# 267, 0.4587680892767956
# 268, 0.28681660058583114
# 269, 0.18281194601342976
# 270, 0.5131280127720317
# 271, 0.5131280127720451
# 272, 0.7285314426169179
# 273, 0.7285314426168639
# 274, 0.40043347452997957
# 275, 0.4004334745299992
# 276, 0.05183555166835241
# 277, 0.04418076152882
# 278, 2
# 279, 0.22499226853470244
# 280, 0.10543260876102711
# 281, 0.14954373868463988
# 282, 0.3167610574551275
# 283, 0.3167610574551426
# 284, 0.40817666404291564
# 285, 0.40817666404288033
# 286, 0.016618135558440494
# 287, 0.24482231901981488
# 288, 0.09829393511839357
# 289, 0.13261508617204942
# 290, 0.5180472341961767
# 291, 0.5180472341961463
# 292, 0.3234599756060773
# 293, 0.0
# 294, 0.12099605207587372
# 295, 0.3296222382676691
# 296, 0.3296222382676802
# 297, 0.39374048636645076
# 298, 0.3937404863664432
# 299, 0.29257557391554967
# 300, 0.37898838176118255
# 301, 0.35180400276212975
# 302, 0.22856738470823668
# 303, 0.22856738470816584
# 304, 0.5216086605170818
# 305, 0.521608660517132
# 306, 0.4292934665435536
# 307, 0.12686532513677906
# 308, 0.01662479804878325
# 309, 0.2633246397307355
# 310, 0.26332463973073494
# 311, 0.32294956417853105
# 312, 0.3604832565268309
# 313, 0.36048325652681046
# 314, 0.0
# 315, 0.13515846625280403
# 316, 0.34345140301345123
# 317, 0.34345140301345856
# 318, 0.35557303171330945
# 319, 0.3555730317132385
# 320, 0.039427399494065485
# 321, 0.1852286047854268
# 322, 0.2603720566124017
# 323, 0.12105397913411275
# 324, 0.39062921541944895
# 325, 0.0
# 326, 0.27600915594502606
# 327, 0.27600915594504405
# 328, 0.23566805464866025
# 329, 0.3873809483913443
# 330, 0.31006658380766583
# 331, 0.31006658380767216
# 332, 0.11919793065129991
# 333, 0.1191979306512988
# 334, 0.24590417199813475
# 335, 0.4173373320945377
# 336, 0.41733733209454515
# 337, 0.3790007603861344
# 338, 0.14917855379607203
# 339, 0.3513581053014192
# 340, 0.22805836423861892
# 341, 0.2471860283871682
# 342, 0.28847534028181954
# 343, 0.2884753402818341
# 344, 0.2740760315180192
# 345, 0.37273833820902436
# 346, 0.3591897286845446
# 347, 0.3591897286846002
# 348, 2.220446049250313e-16
# 349, 0.3883825653714831
# 350, 0.3883825653714682
# 351, 0.50535519756877
# 352, 0.5053551975687935
# 353, 2.220446049250313e-16
# 354, 0.4005604581466127
# 355, 0.17586162815314887
# 356, 0.14096924152909862
# 357, 2
# 358, 0.3189339468565535
# 359, 0.44897075695285804
# 360, 0.4489707569529434
# 361, 0.2727419085168964
# 362, 0.27274190851703983
# 363, 0.28628005392754496
# 364, 0.30315211913353246
# 365, 0.17245822118744725
# 366, 0.32008095522504576
# 367, 0.32008095522503166
# 368, 0.28501087731560515
# 369, 2.220446049250313e-16
# 370, 0.3399356330870622
# 371, 0.12511487295520218
# 372, 0.17047091345468435
# 373, 0.6524417308931779
# 374, 0.6524417308931668
# 375, 0.3349603364986091
# 376, 0.4690364060646043
# 377, 0.46903640606461094
# 378, 0.26276747557655333
# 379, 0.07287216215147108
# 380, 0.40950866664064844
# 381, 0.40950866664062113
# 382, 0.2111208715897973
# 383, 0.29059717590619016
# 384, 0.29059717590621137
# 385, 0.2787785206915212
# 386, 0.31294378113637134
# 387, 0.008885431644712893
# 388, 0.008885431644714226
# 389, 0.2144599883768692
# 390, 0.21445998837687208
# 391, 0.08192105368822
# 392, 0.20207988592821668
# 393, 0.0715397887452075
# 394, 0.29173105225841456
# 395, 0.291731052258434
# 396, 0.1636264038610119
# 397, 0.16362640386101102
# 398, 0.12723497726610955
# 399, 0.30112636309850105
# 400, 0.22804995117386484
# 401, 0.2960450584740777
# 402, 0.2960450584740697
# 403, 0.12939448358222794
# 404, 0.14872895161344857
# 405, 0.1773806730624905
# 406, 0.0
# 407, 0.27160706140793023
# 408, 0.2503422764129486
# 409, 0.3950059204148483
# 410, 0.39500592041484806
# 411, 2
# 412, 0.2577807445168646
# 413, 0.25778074451683197
# 414, 2
# 415, 0.22446773742832526
# 416, 0.10934138289741946
# 417, 0.10934138289741258
# 418, 0.18170733525269045
# 419, 0.1559780697527159
# 420, 0.31865047357514165
# 421, 0.3186504735750897
# 422, 0.1020393833466654
# 423, 0.19090679441512848
# 424, 0.2803499162680865
# 425, 0.2803499162681232
# 426, 0.2200982897803947
# 427, 0.22009828978038548
# 428, 0.3525430194467928
# 429, 0.26391597841508607
# 430, 2.220446049250313e-16
# 431, 0.14144681331835762
# 432, 0.19255387317135964
# 433, 0.19255387317137174
# 434, 0.2719915883654821
# 435, 0.12089801295489033
# 436, 0.3094937779656275
# 437, 0.2808700138948992
# 438, 0.2808700138949072
# 439, 0.2853207987117483
# 440, 0.3911289425797684
# 441, 0.3911289425797818
# 442, 0.25107738105845956
# 443, 0.1797961215917453
# 444, 0.39977875726306855
# 445, 0.3997787572630874
# 446, 0.2159841639124277
# 447, 2
# 448, 2
# 449, 0.25231153404483186
# 450, 0.252311534044835
# 451, 0.42861300067897523
# 452, 0.36439152884585224
# 453, 0.3301243786355048
# 454, 0.33012437863550514
# 455, 0.2292386610525159
# 456, 0.1135711174783478
# 457, 0.4651288017536266
# 458, 0.09931675241156179
# 459, 0.12585952681753887
# 460, 0.1258595268175362
# 461, 0.37185591596177825
# 462, 0.21730499354825417
# 463, 0.19149374452960666
# 464, 0.191493744529581
# 465, 0.1914266619928351
# 466, 0.1962239696999566
# 467, 0.35287993895752223
# 468, 0.35287993895747105
# 469, 0.2805724960744327
# 470, 0.2957761915749586
# 471, 0.2957761915749576
# 472, 0.0006700670542104659
# 473, 0.0006700670542102438
# 474, 0.19622799340252306
# 475, 0.03541007439355348
# 476, 0.029904060369544627
# 477, 0.16451165776670407
# 478, 0.16451165776679944
# 479, 0.1817177337910847
# 480, 0.1817177337910426
# 481, 0.1105980773004751
# 482, 0.09409605458943138
# 483, 0.028231978595627427
# 484, 0.14179061361716738
# 485, 0.0
# 486, 0.37106271432893345
# 487, 0.37106271432906723
# 488, 0.15796149501679657
# 489, 0.15796149501677503
# 490, 0.2264684811908575
# 491, 0.20347848365088494
# 492, 0.12576570808282794
# 493, 0.008519342893784199
# 494, 0.008519342893783644
# 495, 0.28752694420638125
# 496, 0.3398746208207981
# 497, 0.3398746208207959
# 498, 0.13165273292983126
# 499, 0.4259975824779805
# 500, 0.4259975824779554
# 501, 0.3041879027846345
# 502, 0.37715753031476296
# 503, 2
# 504, 0.47015768696724125
# 505, 0.470157686967263
# 506, 0.35011622124337993
# 507, 0.07259791232944846
# 508, 0.07259791232945512
# 509, 0.0
# 510, 0.02175637356531135
# 511, 0.03611197552812906

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