-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1306084587827808543968233134433', 'a10': [-290.23352491562025, 502.6992112136619], 'a2': [3.9075364531836625, 6.768051669341589], 'a3': [-11.759288876305739, 20.367685794641073], 'a4': [-14.537682265918312, 25.18000430886356], 'a5': [37.137660568611295, 64.32431497908203], 'a6': [-183.79939979072728, -7.022658575883846e-60], 'a7': [0.0, 0.0], 'a8': [22.85623940824452, 0.0], 'a9': [-155.06174975281579, -268.57482888240776], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8588071708360525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]]], 'bad_primes': [7], 'central_character': '49.18', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '4511346672478672160696203294996', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.9075364531836625, -6.768051669341589], [-16.0, 27.712812921102035]], [[1.0, 0], [11.759288876305739, -20.367685794641073], [-121.5, -210.4441731196186]], [[1.0, 0], [-37.137660568611295, -64.32431497908203], [-1562.5, 2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [-212.10956256179605, 367.38453912824014], [-80525.5, -139474.25730488764]], [[1.0, 0], [252.2333570951518, 0], [371293.0, 0]], [[1.0, 0], [-552.1733792861337, 956.3923475105839], [-709928.5, -1229632.2317411618]], [[1.0, 0], [-3.235499091787226, -5.604048814818435], [-1238049.5, 2144364.636285245]], [[1.0, 0], [-1806.1925398951798, -3128.4172473503277], [-3218171.5, 5574036.5454701455]], [[1.0, 0], [5005.0171585919825, 0], [20511149.0, 0]], [[1.0, 0], [1410.8451062847291, -2443.6554056950636], [-14314575.5, -24793572.054780666]], [[1.0, 0], [-1023.4382502471842, -1772.647047837514], [-34671978.5, 60053628.36093575]], [[1.0, 0], [-9393.805639690689, 0], [115856201.0, 0]], [[1.0, 0], [-10320.771448239979, 0], [147008443.0, 0]], [[1.0, 0], [8517.794043676364, 14753.25205205502], [-114672503.5, 198618602.2931199]], [[1.0, 0], [-19753.334486652053, 34213.778949783846], [-209097746.5, -362167920.6861574]], [[1.0, 0], [16974.891973791677, -29401.375351600323], [-357462149.5, -619142604.7167817]], [[1.0, 0], [14147.616000865231, 24504.389719472994], [-422298150.5, 731441852.6083683]], [[1.0, 0], [28050.46402343236, -48584.82886446776], [-675062553.5, -1169242640.9491835]], [[1.0, 0], [15537.405627744096, 0], [1804229351.0, 0]], [[1.0, 0], [-39109.77226914357, 67740.112642605], [-1036535796.5, -1795332663.4018745]], [[1.0, 0], [-22667.735436375136, -39261.66946833121], [-1538528199.5, 2664809010.4114656]], [[1.0, 0], [-1381.822122667201, 0], [3939040643.0, 0]], [[1.0, 0], [-34439.71643939016, -59651.33867128887], [-2792029724.5, 4835937339.076535]], [[1.0, 0], [-108857.19816950361, 0], [8587340257.0, 0]], [[1.0, 0], [8986.13433938204, -15564.441239449085], [-5255050250.5, -9102014030.193556]], [[1.0, 0], [15886.8303719503, 27516.797375446287], [-5796370371.5, 10039607982.924889]], [[1.0, 0], [4114.681859896694, 7126.838038323079], [-7012758653.5, 12146454289.080307]], [[1.0, 0], [-5534.3353692896935, 9585.750045735214], [-7693119774.5, -13324874318.146824]], [[1.0, 0], [-65184.34317183965, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-7e2-7.4-c5-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/49/6/c/h/18/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0526474416056133, 1.7445493961267247, 1.4459245062529584, 1.1601214500051011, 0.8904321289284517, 0.640112987344258, 0.4123878581429741, 0.2104286306053863, 0.03731124947542268, -0.10405404439712151, -0.21101776218640367, -0.2813093508575185, -0.31317459374404977, -0.3055265145407712, -0.2581023161141867, -0.17161725529314234, -0.04790495298158927, 0.10996741519404715, 0.2976211788124721, 0.5093375797303391, 0.7380898520743406, 0.9756456888842077, 1.2127472853852859, 1.4393726919468601, 1.645077860866731, 1.8194136454342635, 1.9524063042516155, 2.035084059866833, 2.0600263201493543, 2.0219067242167656, 1.917996702040183, 1.7485932393021122, 1.5173335034614264, 1.2313603439253074, 0.9013067575781721, 0.5410743914845366, 0.16739102720711443, -0.20085548046861054, -0.5434946388475725, -0.8401338261734619, -1.0713569947913977, -1.2200008434026242, -1.2724339419702508, -1.2197539321719815, -1.0588123198243766, -0.7929766750208153, -0.43254711477088326, 0.005241802931040823, 0.4966812829759625, 1.0125303207549314, 1.519426392110482, 1.9817155873368584, 2.3636162194364467, 2.6315953715383364, 2.756808562933365, 2.7174317723243546, 2.5007052211608367, 2.1045117576407466, 1.538330694054245, 0.8234407361328785, -0.007707863227850315, -0.9129739923385527, -1.8428158553212064, -2.743279029597003, -3.5595053304491184, -4.239528691530212, -4.738082162588681, -5.020117779340212, -5.063742363645955, -4.862299374270501, -4.425379679098296, -3.7786200764147897, -2.9622426422096066, -2.028393400143134, -1.0374465400167663, -0.05354054906289768, 0.8603048895172315, 1.6470867560361033, 2.260305458825493, 2.667632110616354, 2.8534053094698226, 2.8197008715540783, 2.5858426222083217, 2.186366704077976, 1.6676025359042324, 1.0831754962645213, 0.48885434051036725, -0.06275357017523085, -0.5271247532819271, -0.8718489359827692, -1.0793337487799353, -1.147883136159296, -1.0910168204740105, -0.9350897762379206, -0.7154647003238596, -0.47166496650276424, -0.2420692982392678, -0.05878437830326066, 0.056664571524128876, 0.09625747237134638, 0.06659414589855926, -0.012018804944415835, -0.10848480742800731, -0.18555855219391965, -0.2056957172904011, -0.13740737174333462, 0.038697247408664336, 0.3250137138603551, 0.7039394233044334, 1.137326586939308, 1.5686823163573758, 1.928079272466737, 2.1393928265074096, 2.1291554298668616, 1.8360584068574923, 1.21997314674122, 0.269334997833782, -0.9941530172588628, -2.5142874285919943, -4.203024858299902, -5.947011914076608, -7.617487117078452, -9.082614957812035, -10.220958100193082, -10.934578399250604, -11.160216423527224, -10.877148105934918, -10.1106480533086, -8.930470078383488, -7.444333601291058, -5.787011071383111, -4.10617041588721, -2.5465638397046173, -1.2344082860688526, -0.263832708146488, 0.3129402572374162, 0.49043805698477894, 0.3091670700509502, -0.15071423633039543, -0.780508229690351, -1.4574803689196103, -2.060896629248347, -2.4875208539224007, -2.6645487762208564, -2.5582809368125923, -2.177398285436535, -1.5704303682199825, -0.8177997642530577, -0.01957836739471805, 0.7193056897055847, 1.3043060759091103, 1.664766231390093, 1.763762912316544, 1.6028745010868546, 1.2211990234222871, 0.6887908961581535, 0.09551506530352741, -0.4629915840194353, -0.9001154095521716, -1.151552805421801, -1.185038367322461, -1.0049968709308668, -0.6513768758596092, -0.19282693866153136, 0.28473161214420567, 0.6923389521020116, 0.9527705043744836, 1.0134639469556117, 0.8554749395612021, 0.4969467363175749, -0.009552517656726144, -0.5854771816103747, -1.139227895332472, -1.5814740170582027, -1.8403510306187225, -1.8739702396896116, -1.6780653986857537, -1.287364005841496, -0.7702949088849813, -0.21776592852162144, 0.2722199867527403, 0.6115719761313938, 0.7378398070054026, 0.6258810124109684, 0.2932854960993972, -0.20162253548057962, -0.769139497581024, -1.303540444466553, -1.7019757327155, -1.8837074116814903, -1.806271942249872, -1.475522838773619, -0.9474200876983956, -0.3207622475596977, 0.2784059793713435, 0.7184867542709888, 0.8867112572121146, 0.7121341776708058, 0.1831601071152195, -0.643787109653444, -1.64653799119325, -2.6507569426474142, -3.4533193099825783, -3.8522668269708227, -3.6788671000185884, -2.8267333136353754, -1.2732001610773465, 0.9108072943067088, 3.5644774465481985, 6.454359430407056, 9.302968001616662, 11.824698027009278, 13.763749906230542, 14.928350236150893, 15.216055556815105, 14.626284137822202, 13.25821852009403, 11.2945343881601, 8.97365514048464, 6.555028919588509, 4.282971102047887, 2.354732443950695, 0.8976231068019093, -0.0416076178607648, -0.49407958633760746, -0.5540003676029012, -0.35502822204228063, -0.04240538028578572, 0.2539813440126897, 0.440868251834987, 0.4737327630226184, 0.3581561302405395, 0.14094411248176336, -0.10652042994191056, -0.30878965734429087, -0.4061965658511991, -0.3697925632770426, -0.20827682672962106, 0.034419743418342384, 0.2902060040837479, 0.48398814444062427, 0.5529992051887868, 0.4638598975442801, 0.22334373901493504, -0.1198947194658288, -0.4834605946634757, -0.7679110826530162, -0.8787370277090015, -0.7490454181291346, -0.35795034190039066, 0.25968060474233257, 1.014882984421608, 1.7781536363107737, 2.4029214118351567, 2.754731692368194, 2.7404827402315033, 2.3316736807958245], 'positive_zeros': ['1.03031907024905714493777001066095', '2.04075490907682545513325787181272', '4.55618893221208174406971048280697', '5.87360222460017352265734089575420', '7.49889964007213940707466960142179', '9.381993051123879888130872564287316', '10.85990767642170353774269852146665', '12.17877900957590538010028864274094', '12.60869044177866024989671828475399', '13.22827555724588715841668644050967'], 'prelabel': '2-7e2-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8033564116672807, 'root_angle': 0.8967970958395212, 'root_number': '-0.9478990257184787 + 0.31857092937359927*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.44839854792', 'prec': 44}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03031907024905714493777001066', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04075490907682545513325787181', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55618893221208174406971048281', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.8588071708360525, 'bad_primes': [7], 'central_character': '7.4', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/6/c/h/18/3'], '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': '2-7e2-7.4-c5-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-7e2-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8033564116672807, 'root_angle': 0.4483985479197606, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03031907024905714493777001066', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1306084587827808543968233134433', 'Lhash_array': ['1306084587827808543968233134433'], 'label': '2-7e2-7.4-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/6/c/h/18/3'}