# Identifications: Klein Bottle Horizontal 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, 0.0004106827796719337
# 2, 0.0008467422239333278
# 3, 0.001213690430604375
# 4, 0.001695495860162266
# 5, 0.0013315311553242504
# 6, 0.003761623212570231
# 7, 0.014718189368639667
# 8, 0.011905936095741754
# 9, 0.08498327717138932
# 10, 0.024030335828698846
# 11, 0.011037897483484604
# 12, 0.004090726671721723
# 13, 0.08910903449335483
# 14, 0.005514441531876635
# 15, 0.013337646831422134
# 16, 1.1102230246251565e-16
# 17, 0.006241499711309606
# 18, 0.11830647910249703
# 19, 0.13082409185296662
# 20, 0.25247824050527956
# 21, 0.15402010369246466
# 22, 0.061781236190881494
# 23, 0.1350729871903632
# 24, 0.23316645227194455
# 25, 0.007208422818863469
# 26, 0.10046186052377393
# 27, 0.019977467290337114
# 28, 0.09871017803940663
# 29, 0.0
# 30, 0.0
# 31, 0.37599425933930164
# 32, 0.37998690472455043
# 33, 0.19248424337543024
# 34, 0.11199410507997432
# 35, 0.16409481134191473
# 36, 0.18684722051624647
# 37, 0.2726867736389439
# 38, 0.1834840592926278
# 39, 0.22084566563423513
# 40, 0.09879751700644401
# 41, 0.19302480660366017
# 42, 0.07007729698159326
# 43, 0.0006505301638103367
# 44, 0.2958935896209792
# 45, 0.18000713951216196
# 46, 0.1297109917508924
# 47, 0.13102095348176845
# 48, 0.2703801922201232
# 49, 0.10435968304780596
# 50, 0.05412759182955551
# 51, 0.06431850210077272
# 52, 0.22552843633891662
# 53, 0.24335434177897874
# 54, 0.36401385947399667
# 55, 0.3020706740344563
# 56, 0.3699258451199551
# 57, 0.29288977156531604
# 58, 0.3180573866513199
# 59, 0.08916117818499214
# 60, 0.48233411110929336
# 61, 2.220446049250313e-16
# 62, 0.2369032207635885
# 63, 0.44297902501702946
# 64, 0.41711841336066924
# 65, 0.17795721330945014
# 66, 0.1921782256821204
# 67, 0.0
# 68, 0.27133128611520296
# 69, 0.3099140151454426
# 70, 0.33104198111943617
# 71, 0.28260724888583166
# 72, 0.19711271874641978
# 73, 0.17720432525860041
# 74, 0.29656722301699656
# 75, 0.35617904239986686
# 76, 0.3946114640238394
# 77, 0.40590363943881425
# 78, 0.20365202952588635
# 79, 0.05471357365990914
# 80, 0.36963905145376375
# 81, 0.42837500067982714
# 82, 0.0
# 83, 2.220446049250313e-16
# 84, 0.1131236807071877
# 85, 0.42316907141149374
# 86, 0.5388353506197976
# 87, 0.0
# 88, 0.32747259870684253
# 89, 0.2847592280148472
# 90, 0.5268369081847544
# 91, 0.269598320889046
# 92, 0.23863900621499734
# 93, 0.5104284160935966
# 94, 2
# 95, 0.4525207479979455
# 96, 0.2786193239792307
# 97, 0.359409009233972
# 98, 0.5493487157983998
# 99, 0.0017108198585333856
# 100, 0.4911859568560668
# 101, 0.3700175288632037
# 102, 0.3651437694767886
# 103, 0.3964938006953268
# 104, 0.5825305796459691
# 105, 0.3735691922308576
# 106, 0.32135406431464786
# 107, 0.348299905695193
# 108, 0.47041846106467444
# 109, 0.2717676960570785
# 110, 0.41179307630053885
# 111, 0.508164131162447
# 112, 0.5060054879258207
# 113, 0.41795312925718586
# 114, 0.46124592015462784
# 115, 0.42082876646795675
# 116, 0.49103019390917513
# 117, 0.3883365675779792
# 118, 0.31822354484543913
# 119, 0.46226216059330993
# 120, 0.3572913234255721
# 121, 0.4401670981515956
# 122, 0.5294219860945326
# 123, 0.3322033675994438
# 124, 1.1102230246251565e-16
# 125, 0.37247301262776855
# 126, 0.2510433393000855
# 127, 0.12385086320486172
# 128, 0.3946890653005306
# 129, 0.2551095289678029
# 130, 0.011440672902887639
# 131, 0.4789538942939531
# 132, 0.5220985892896857
# 133, 0.46807199559314705
# 134, 0.1430173019390647
# 135, 0.0526000656521749
# 136, 0.35084014041006273
# 137, 0.25406226619885486
# 138, 0.3340349438377168
# 139, 0.25104058339701396
# 140, 0.09808883394953816
# 141, 0.27497284663653754
# 142, 0.2487592287138587
# 143, 1.1102230246251565e-16
# 144, 0.20904162213424915
# 145, 0.13753054338875959
# 146, 0.3721420507782657
# 147, 0.2763740700589934
# 148, 0.30754421870124726
# 149, 0.3178859928073874
# 150, 0.18624648649910458
# 151, 0.4456240721505613
# 152, 0.38686585839859644
# 153, 0.3723293858112878
# 154, 0.4666743738466653
# 155, 0.4505426778683729
# 156, 0.5182093267998477
# 157, 0.0
# 158, 0.4973530673952854
# 159, 0.583018925880185
# 160, 0.5221192541352789
# 161, 0.008815596088503352
# 162, 0.24292255500296622
# 163, 0.5709654289694552
# 164, 0.4461969843297453
# 165, 0.36663423052644806
# 166, 0.3773829493719375
# 167, 0.0075500978772296
# 168, 0.43332353309294946
# 169, 0.26099702689788173
# 170, 0.23904541424991188
# 171, 0.2502042441676908
# 172, 0.0
# 173, 0.5252424362743662
# 174, 0.5351959105878377
# 175, 0.4786912570118744
# 176, 0.5534250452986944
# 177, 0.08843018173423145
# 178, 0.34908461875987595
# 179, 0.22684412999108927
# 180, 0.5183791425327438
# 181, 0.26026227977110905
# 182, 0.40117446728867157
# 183, 0.28193180890342373
# 184, 0.33317277502138576
# 185, 0.421261582583635
# 186, 0.25109908916070267
# 187, 0.44850861063911796
# 188, 0.19007685055713663
# 189, 0.4210630942000938
# 190, 2.220446049250313e-16
# 191, 0.42763366902522926
# 192, 0.36840658585136166
# 193, 2
# 194, 0.32414835161230005
# 195, 0.3863639985515843
# 196, 0.10442045822227708
# 197, 0.384025529845875
# 198, 0.3076455126905888
# 199, 0.20016302761742777
# 200, 0.1562662623402602
# 201, 0.40597194541388526
# 202, 0.23636484391238033
# 203, 0.2763099177727466
# 204, 0.44941416017640745
# 205, 0.39791842631582486
# 206, 0.3855726177528238
# 207, 0.0
# 208, 0.02112597089916557
# 209, 0.3734192857090134
# 210, 0.3725609782632251
# 211, 0.48389992557563954
# 212, 0.4760495490320549
# 213, 0.23732575307557346
# 214, 0.32159094402308896
# 215, 0.3598253864827199
# 216, 0.402073624557313
# 217, 0.24887285070776188
# 218, 0.38099874095801034
# 219, 0.3777901088719141
# 220, 0.5641320420205074
# 221, 0.24492274891794552
# 222, 0.19617600407097313
# 223, 0.4223157622171061
# 224, 0.33744287916015636
# 225, 0.28951739467503745
# 226, 0.47869526026828524
# 227, 0.41624217980543543
# 228, 0.35612885332938127
# 229, 0.46120655424603585
# 230, 0.35587971716225963
# 231, 0.18442843922507302
# 232, 0.4491125385497756
# 233, 0.5232151306497417
# 234, 0.4747040718325999
# 235, 2.220446049250313e-16
# 236, 0.27116330381568765
# 237, 0.2113983011681656
# 238, 0.29519439978971906
# 239, 0.5199124157310878
# 240, 0.5120591230694314
# 241, 0.4087557009163362
# 242, 0.3416836761187221
# 243, 0.42444455973668593
# 244, 0.3968999292890374
# 245, 0.028736508594877863
# 246, 0.49580194619827656
# 247, 0.391325533144135
# 248, 0.4382975802100284
# 249, 0.021663047229854793
# 250, 0.3413877362895503
# 251, 0.4837613627112014
# 252, 0.21672805645857096
# 253, 0.41235885355787283
# 254, 0.35517353417851616
# 255, 0.08754815732229326
# 256, 0.2758759666544147
# 257, 0.2440621657031301
# 258, 0.23207966784808576
# 259, 0.3630168441763908
# 260, 0.4323268865065888
# 261, 0.11467013435710827
# 262, 2
# 263, 2
# 264, 0.3470832908956769
# 265, 0.33751834823899785
# 266, 0.41738463982554075
# 267, 0.21856062573888102
# 268, 0.05452025595133203
# 269, 0.37726501698763837
# 270, 0.42288359682639176
# 271, 0.14990781833640787
# 272, 0.6443810476397804
# 273, 0.2794077582074468
# 274, 0.4193302219174512
# 275, 0.3710990015142037
# 276, 0.40864789176068206
# 277, 0.0
# 278, 0.3121900803027474
# 279, 0.3597306665288631
# 280, 0.4596098114960001
# 281, 0.3703755399627231
# 282, 0.4163065922410899
# 283, 0.5380523714891075
# 284, 0.27590151978398203
# 285, 0.13280127766850136
# 286, 0.507831082486953
# 287, 0.11563093680646597
# 288, 0.43052011351149155
# 289, 0.3514032816808331
# 290, 0.5363787307249448
# 291, 0.3005541431995904
# 292, 2.220446049250313e-16
# 293, 0.2686519400307186
# 294, 0.20036997336598206
# 295, 0.22174004182674756
# 296, 0.41882691611092904
# 297, 0.24889040036432386
# 298, 0.34301135948555816
# 299, 0.328719607995022
# 300, 0.5695520450299871
# 301, 0.45786131513989425
# 302, 0.4550569399343948
# 303, 0.41363014236833584
# 304, 0.18965472375736647
# 305, 0.028656582746368953
# 306, 2
# 307, 0.24256853817956703
# 308, 0.4497585136511598
# 309, 0.12423493157472765
# 310, 0.4312722707300688
# 311, 0.26332463973073217
# 312, 0.48252225022122985
# 313, 0.46521216284608113
# 314, 0.0
# 315, 0.32851953424126634
# 316, 0.25587802452066233
# 317, 0.2951591368489519
# 318, 0.4067462519598425
# 319, 0.3917417768379763
# 320, 2.220446049250313e-16
# 321, 0.45504299542570725
# 322, 0.38210995309125484
# 323, 0.12679493195400993
# 324, 0.38597087911767103
# 325, 0.4076994111488558
# 326, 0.009074624468260795
# 327, 0.5141318511541876
# 328, 0.2891610328996047
# 329, 0.29801933587808216
# 330, 0.3623079847515248
# 331, 0.35528749166477647
# 332, 0.11919793065129458
# 333, 0.3849930935873369
# 334, 0.4317882756857707
# 335, 0.502571056917428
# 336, 0.281640132835974
# 337, 0.42995510297365014
# 338, 0.420009290827128
# 339, 0.396307618022689
# 340, 0.25213410718253404
# 341, 0.46909953884798916
# 342, 0.24517305698385916
# 343, 0.20356191997220996
# 344, 0.35571477027110077
# 345, 0.0
# 346, 0.47149039198435594
# 347, 0.4510134485844344
# 348, 0.4919196838174612
# 349, 0.4364544754044015
# 350, 0.3630344822780547
# 351, 0.22812614830272493
# 352, 0.39733404118267857
# 353, 0.2934066279194971
# 354, 0.47359385780636487
# 355, 0.18903016027117314
# 356, 0.2429357629741058
# 357, 0.45349302850221695
# 358, 0.4132931664666898
# 359, 0.47647064184030896
# 360, 0.3454208939622029
# 361, 0.49194347782032144
# 362, 0.36071132696065034
# 363, 0.18656663077779434
# 364, 0.3564082285834165
# 365, 0.09516721095526393
# 366, 0.35328825030943045
# 367, 0.7391371974150446
# 368, 0.5244007176774861
# 369, 0.39490893875014965
# 370, 0.0
# 371, 0.5284743541518739
# 372, 0.4910955471996137
# 373, 0.6667990134599202
# 374, 1.1102230246251565e-16
# 375, 0.5105125820662569
# 376, 0.3506484971066638
# 377, 0.4103041463907887
# 378, 0.47275524462039986
# 379, 0.21641813708577007
# 380, 0.49776018812949197
# 381, 0.3957740152541346
# 382, 0.38274353901152847
# 383, 0.36820622856782215
# 384, 0.1895928128906501
# 385, 0.44207525043686124
# 386, 0.0
# 387, 0.008885431644713337
# 388, 0.5851692767834121
# 389, 0.501068958033011
# 390, 0.44976188621360935
# 391, 0.28327422896793486
# 392, 0.21485556888670543
# 393, 0.36649533723336214
# 394, 0.06520371954377058
# 395, 0.14072504399995378
# 396, 0.22341633913496484
# 397, 0.16271329924893674
# 398, 0.2718794664579576
# 399, 0.07326607902688653
# 400, 0.28889804612015424
# 401, 0.35354051453738544
# 402, 0.2827387177891171
# 403, 0.16785808965620364
# 404, 0.4371371338461312
# 405, 0.29678283363675295
# 406, 0.25540677331513895
# 407, 0.0
# 408, 0.3926707798220793
# 409, 0.2577807445168542
# 410, 0.42972007317799576
# 411, 0.2817616234438458
# 412, 0.27317123032197455
# 413, 0.4034392372202602
# 414, 0.0
# 415, 0.3238390555294617
# 416, 0.18510190066999532
# 417, 0.19082587001866547
# 418, 0.29034430464109506
# 419, 0.33803026678785475
# 420, 0.20548673336179824
# 421, 0.08306144612191313
# 422, 0.24977810083880492
# 423, 0.23487565974216706
# 424, 0.21862426332861284
# 425, 0.4998281986153258
# 426, 0.2222627757269907
# 427, 0.2953461060033813
# 428, 0.1344496701482789
# 429, 0.19133264502261205
# 430, 0.14433771338361256
# 431, 0.16382439979136953
# 432, 0.0
# 433, 0.37671422152687617
# 434, 0.2647475952011601
# 435, 0.3016335046276164
# 436, 0.38047871908768793
# 437, 0.41495419615977724
# 438, 0.3351842759757655
# 439, 0.31505063400244626
# 440, 0.3254141729476019
# 441, 0.25888819645637484
# 442, 0.42578153795119134
# 443, 0.4074681896162424
# 444, 0.3260596493757021
# 445, 0.2965011324527195
# 446, 2
# 447, 0.39824455731824737
# 448, 0.013799298653344838
# 449, 0.13616709075508848
# 450, 0.28346807406660457
# 451, 0.2784430770648689
# 452, 2.220446049250313e-16
# 453, 0.28074073340825423
# 454, 0.4312689954627036
# 455, 0.40571174730259996
# 456, 0.2951595542889758
# 457, 0.0015552241298286695
# 458, 0.46210507147904034
# 459, 0.30621301304293136
# 460, 0.17380387259877295
# 461, 0.25168544197941844
# 462, 0.2273237791664604
# 463, 0.1398825746561314
# 464, 0.43975271627311063
# 465, 0.18680599615061733
# 466, 0.2101321558736331
# 467, 0.27787318190994603
# 468, 0.15634848303038063
# 469, 0.0006700670542103548
# 470, 0.37592897542277426
# 471, 0.33481560283919753
# 472, 0.13558274110073898
# 473, 0.05122620063790129
# 474, 0.27728260583795206
# 475, 0.2081963863201307
# 476, 0.04478596220086828
# 477, 0.3324130129670041
# 478, 0.35001415073929
# 479, 0.22278279959451663
# 480, 0.14034218611110594
# 481, 0.16540183897974658
# 482, 0.2779880787327921
# 483, 0.3722740498331025
# 484, 0.15392259921022067
# 485, 0.08311921967759506
# 486, 0.0853651746103179
# 487, 0.4066511466135132
# 488, 0.12748110280871994
# 489, 0.44120106228173306
# 490, 0.27530814227237155
# 491, 0.025723692140127485
# 492, 0.2552043262039665
# 493, 0.22644222568975947
# 494, 0.27470254381154924
# 495, 0.0
# 496, 0.249760315705004
# 497, 0.008519342893784643
# 498, 0.18055734307806992
# 499, 0.1300140495405786
# 500, 0.367048490358
# 501, 0.2651839544252399
# 502, 0.3893463383084722
# 503, 0.3315945169051445
# 504, 0.3964667127268182
# 505, 0.348148859624958
# 506, 0.13226265639437074
# 507, 0.36901590487506997
# 508, 0.11536077474973583
# 509, 0.05143449752667539
# 510, 0.4778227511198103
# 511, 2

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