-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2410088589966513898739267585356', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-3.0, -1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.348612101957944, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.431', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'conjugate': '2136005720201220712655357265075', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [2.5, -4.330127018922194]], [[1.0, 0], [3.0, 1.7320508075688772], [3.5, 6.06217782649107]], [[1.0, 0], [0, 0], [-5.5, -9.526279441628825]], [[1.0, 0], [-1.0, -1.7320508075688772], [-6.5, 11.258330249197702]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-19.0, 0]], [[1.0, 0], [0, 0], [-11.5, 19.91858428704209]], [[1.0, 0], [0, 0], [14.5, 25.11473670974872]], [[1.0, 0], [9.0, -5.196152422706632], [15.5, -26.846787517317598]], [[1.0, 0], [10.0, 0], [37.0, 0]], [[1.0, 0], [0, 0], [20.5, -35.50704155516198]], [[1.0, 0], [9.0, 5.196152422706632], [21.5, 37.239092362730865]], [[1.0, 0], [0, 0], [-23.5, -40.703193977868615]], [[1.0, 0], [0, 0], [-53.0, 0]], [[1.0, 0], [0, 0], [-29.5, 51.09549882328188]], [[1.0, 0], [7.0, -12.12435565298214], [-30.5, -52.827549630850754]], [[1.0, 0], [3.0, -1.7320508075688772], [33.5, -58.023702053557386]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [-10.0, 0], [73.0, 0]], [[1.0, 0], [15.0, 8.660254037844387], [39.5, 68.41600689897065]], [[1.0, 0], [0, 0], [-41.5, -71.88010851410841]], [[1.0, 0], [0, 0], [-89.0, 0]], [[1.0, 0], [-7.0, 12.12435565298214], [-48.5, -84.00446416709055]], [[1.0, 0], [0, 0], [50.5, 87.4685657822283]], [[1.0, 0], [-3.0, 1.7320508075688772], [51.5, -89.20061658979718]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [2.0, 0], [109.0, 0]], [[1.0, 0], [0, 0], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-6e4-36.11-c1-0-21', 'leading_term': '2.5405533243493051050264194398070063120398465', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1296/2/s/b/431/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-2.4733675041445293e-60, -0.149570913400893, -0.30064808120238545, -0.45331144638965826, -0.6075248205721446, -0.7630773491880035, -0.9195348572397236, -1.076203275015442, -1.232105378611358, -1.385971230321946, -1.5362420537125212, -1.6810868468318374, -1.8184307938642557, -1.9459944231282416, -2.0613424152501416, -2.1619409368382754, -2.245222325869837, -2.308655866434493, -2.349823258242155, -2.3664972168474896, -2.3567214471137583, -2.318890031942216, -2.2518240890409245, -2.1548433886857787, -2.0278305121049733, -1.871285078581085, -1.6863655926327374, -1.474916571073514, -1.2394788107021848, -0.9832809548694496, -0.7102109115693169, -0.42476616350914725, -0.13198258425166742, 0.16265797770934914, 0.4533403789680472, 0.734047412568622, 0.9987071177043981, 1.2413529452024408, 1.4562928458745725, 1.638282707504523, 1.7826990242545413, 1.8857052691234257, 1.9444061832857353, 1.9569841199193019, 1.922811704143259, 1.8425354087926995, 1.7181252048693805, 1.5528862246681603, 1.351429365217131, 1.1195989411704927, 0.8643568418869907, 0.5936241204492315, 0.3160824979285895, 0.04093985219963944, -0.2223346807324233, -0.46429889527073687, -0.6758405797199457, -0.8484859375161428, -0.9747030209008409, -1.0481893310399402, -1.0641326095736725, -1.0194341221895027, -0.9128844342589687, -0.7452828054567248, -0.5194928711101274, -0.24042920146265426, 0.08502841325599797, 0.44819358073129834, 0.8388027487850858, 1.2453105978474088, 1.6552437328692422, 2.0556023792728824, 2.433297391027307, 2.775607844127739, 3.070642921896959, 3.307790793368184, 3.478136818876859, 3.574833742219915, 3.5934075747862333, 3.5319846434463793, 3.3914277293497297, 3.1753723061430734, 2.8901574995733066, 2.544650413188325, 2.149966748818553, 1.7190950272588017, 1.2664360014776983, 0.8072728622888894, 0.35719137646413973, -0.06852800873209997, -0.4555219726859725, -0.790934769698386, -1.0639619370731854, -1.2663228664493436, -1.3926399333248998, -1.4407050399923058, -1.411618567517509, -1.3097907150006691, -1.142800845457082, -0.9211165337817668, -0.6576802683895325, -0.3673779178964992, -0.06640885176657854, 0.2284172832040448, 0.5004279457128903, 0.7338470390523941, 0.9145323415473191, 1.0306569944955337, 1.0733024104827806, 1.0369329289100904, 0.9197270038749356, 0.7237455144391618, 0.4549247196908175, 0.1228891575503002, -0.2594119298238337, -0.6762326462849982, -1.1097028233206359, -1.5406171142506881, -1.949306767974366, -2.3165550481133605, -2.6245139735879643, -2.8575787043435326, -3.003176620676424, -3.0524309884186427, -3.000664003161591, -2.847710797310544, -2.598024405063029, -2.260561351095181, -1.848448019683025, -1.3784387743615076, -0.8701874006038988, -0.3453632923166999, 0.17334762788523725, 0.6633104537836967, 1.1030258590939237, 1.473178060826854, 1.7575930595044682, 1.9440572574393553, 2.0249524302950683, 1.9976713309452812, 1.8647885830820583, 1.633973498421829, 1.317644448271952, 0.9323777863965329, 0.4980973625544296, 0.03708268563066406, -0.4271558759743841, -0.8710784306322323, -1.2723317585797247, -1.6109165850889908, -1.8702434010281508, -2.038018931910683, -2.1069132160383424, -2.074968004770043, -1.9457203398577916, -1.7280300440655705, -1.4356157160737744, -1.0863198059102903, -0.7011385868353323, -0.30306647251140373, 0.08418464342979183, 0.4375222123251919, 0.7357926984020734, 0.9610102350813252, 1.099423991922233, 1.1423615682544621, 1.086797017645848, 0.9356065486791, 0.6974918064720089, 0.3865690218906957, 0.021641215223764478, -0.37481100585020627, -0.7778677702098962, -1.161570969772523, -1.5004109183645986, -1.7708151060256048, -1.9525537048057768, -2.029979553266967, -1.9930282365861802, -1.8379162453099325, -1.5674914257284238, -1.191209173502511, -0.7247290156965434, -0.18914817863199576, 0.39008982153411376, 0.984553875442433, 1.5643769073810367, 2.0999134473284085, 2.563408412565521, 2.9305800583994714, 3.182023455230911, 3.3043498707918557, 3.2909916637060554, 3.142620986152123, 2.8671527210757795, 2.479326382937355, 1.999886768980481, 1.4544074603111992, 0.8718233494255931, 0.2827568263209235, -0.28226410788507317, -0.7945896412745468, -1.229126160533247, -1.565805780439597, -1.7907561011738808, -1.8970960988641041, -1.8853061012470875, -1.7631454215119322, -1.5451188952145047, -1.251521602889735, -0.9071177211503578, -0.5395330335619364, -0.1774596125983145, 0.15121572339959294, 0.42124130323702996, 0.6116720434097512, 0.7072741175884706, 0.6995700298518117, 0.587452913326373, 0.37732541009223297, 0.0827483054371377, -0.27638465747089713, -0.6750986446182976, -1.0849409536313073, -1.4758364602936247, -1.8180783502053066, -2.0843266461281336, -2.251484562425927, -2.3023286174954825, -2.226782482063622, -2.0227459696823966, -1.6964181233266133, -1.2620853319662986, -0.7413798138055318, -0.1620484212911569, 0.44369570695213756, 1.0411377730837035, 1.5952191598464998, 2.0727509490457767, 2.44453992607285, 2.68728755216298, 2.785135307506113, 2.7307512757087613, 2.5258815711996814, 2.1813244167027768, 1.7163221711842263, 1.1574049443212842, 0.5367560664996661, -0.1097978618819203, -0.745043579352607, -1.3327378903326497, -1.8399097725227047, -2.2389552051096087, -2.509384423062625, -2.6391032691318204, -2.625140534230701, -2.47376971638391], 'positive_zeros': ['1.90122466674381610432524343009038', '3.11435795830023942203295875344424', '3.85258078133306121299589384488794', '5.20509341476204425358857392739069', '5.98953758786361121439203569905346', '6.64067407637014960138314739604081', '7.71455632940894528481633771734219', '8.500749533110170567923410202696747', '9.361937964888382320503327288223750'], 'prelabel': '2-6e4-36.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': -0.9444444444444445, 'root_number': '-0.98480775301220805936674302458952301367064325171984241879 - 0.1736481776669303488517166267693147960003756771840693873*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47222222222222227', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90122466674381610432524343009', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11435795830023942203295875344', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85258078133306121299589384489', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.348612101957944, 'bad_primes': [2, 3], 'central_character': '36.11', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/2/s/b/431/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-6e4-36.11-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6e4-36.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': -0.47222222222222227, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90122466674381610432524343009', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2410088589966513898739267585356', 'Lhash_array': ['2410088589966513898739267585356'], 'label': '2-6e4-36.11-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/2/s/b/431/1'}