-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1849508009754289157563136346427', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [9.740939025454006, 0.0], 'a4': [0.0, 0.0], 'a5': [-17.54830009201737, 0.0], 'a6': [0.0, 0.0], 'a7': [-10.73914389617162, 0.0], 'a8': [0.0, 0.0], 'a9': [67.88589309761284, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 109.50754497065464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-29.0, 0]]]], 'bad_primes': [2, 29], 'central_character': '1856.1', 'coefficient_field': 'CDF', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-9.740939025454006, 0], [27.0, 0]], [[1.0, 0], [17.54830009201737, 0], [125.0, 0]], [[1.0, 0], [10.73914389617162, 0], [343.0, 0]], [[1.0, 0], [-5.601960833382562, 0], [1331.0, 0]], [[1.0, 0], [17.104697673135203, 0], [2197.0, 0]], [[1.0, 0], [100.38805864141237, 0], [4913.0, 0]], [[1.0, 0], [-76.51281167907798, 0], [6859.0, 0]], [[1.0, 0], [-76.57644160216545, 0], [12167.0, 0]], [[1.0, 0], [-29.0, 0]], [[1.0, 0], [-181.08161353321225, 0], [29791.0, 0]], [[1.0, 0], [-175.74958466817654, 0], [50653.0, 0]], [[1.0, 0], [-153.95321233628283, 0], [68921.0, 0]], [[1.0, 0], [441.3379095372532, 0], [79507.0, 0]], [[1.0, 0], [431.27675584449065, 0], [103823.0, 0]], [[1.0, 0], [-178.30260833729756, 0], [148877.0, 0]], [[1.0, 0], [765.3426120850443, 0], [205379.0, 0]], [[1.0, 0], [611.248353749723, 0], [226981.0, 0]], [[1.0, 0], [729.6465769306362, 0], [300763.0, 0]], [[1.0, 0], [552.2287374743055, 0], [357911.0, 0]], [[1.0, 0], [753.0422633704992, 0], [389017.0, 0]], [[1.0, 0], [917.4658679638385, 0], [493039.0, 0]], [[1.0, 0], [-225.3551637792028, 0], [571787.0, 0]], [[1.0, 0], [-86.6665055173858, 0], [704969.0, 0]], [[1.0, 0], [1674.0979248598235, 0], [912673.0, 0]], [[1.0, 0], [-852.3958768475402, 0], [1030301.0, 0]], [[1.0, 0], [547.7896766546429, 0], [1092727.0, 0]], [[1.0, 0], [313.4071296458108, 0], [1225043.0, 0]], [[1.0, 0], [990.7393918469143, 0], [1295029.0, 0]], [[1.0, 0], [619.6593771248084, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 139, 'label': '2-1856-1.1-c3-0-139', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1856/4/a/bg/1/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1765388259706221e-60, 0.32923083402685566, 0.6547650962170566, 0.9729370371877158, 1.2801428276812896, 1.5728721788515594, 1.8477406781306025, 2.1015229549740417, 2.331186691293583, 2.533927375399674, 2.7072035708318336, 2.8487723381016523, 2.95672431396424, 3.029517825304367, 3.0660112988927937, 3.065493129652006, 3.027708093715343, 2.9528793429034477, 2.8417249979774506, 2.6954683720253496, 2.5158409045465646, 2.3050769721887274, 2.0658998635998636, 1.8014983623647527, 1.5154935712931423, 1.2118958301371952, 0.8950518227957485, 0.5695822338591215, 0.24031059166144486, -0.08781578130769659, -0.40981150758806356, -0.7207441082090471, -1.0158284415362622, -1.290522672698529, -1.5406236293719309, -1.7623592552655338, -1.952475781048397, -2.108317200587336, -2.2278946739138186, -2.309943581488649, -2.353966129507365, -2.360257653624562, -2.329915086839945, -2.2648264423516125, -2.1676406075444956, -2.041717242180951, -1.8910571112483048, -1.7202137476237418, -1.5341879166913182, -1.3383069276904889, -1.1380913871495386, -0.9391124998573591, -0.7468434739294251, -0.5665089605756858, -0.4029367392217265, -0.26041602944631903, -0.14256685992141488, -0.05222484128840347, 0.008654531686470585, 0.039068285628212206, 0.03901181967307691, 0.00949557314196158, -0.04746936564359833, -0.12891772669311496, -0.23100867719120627, -0.3491356663321376, -0.4780655392520616, -0.6121039327192475, -0.7452829692057855, -0.8715663389134538, -0.9850660358295974, -1.0802643273296142, -1.152234018201015, -1.1968497465947086, -1.2109829438606798, -1.1926732191451321, -1.141269302797906, -1.0575333021942277, -0.9437028834221818, -0.803507077793031, -0.6421327000816486, -0.4661398242687242, -0.2833263530658241, -0.10254339354128643, 0.066535139043913, 0.2136835794930429, 0.32842951636728274, 0.40038455711505705, 0.41959140039536885, 0.37687674209219985, 0.264198821371012, 0.07497803245179227, -0.1956009827444561, -0.5503269668953664, -0.989749835030878, -1.5120278834791672, -2.1128421524229597, -2.785383807609419, -3.520418254904515, -4.306427325676272, -5.129828343542286, -5.975266284875758, -6.8259726641268905, -7.664182301556946, -8.471596856899746, -9.229882026348678, -9.921183684395052, -10.52864707904614, -11.036922518665536, -11.432640865327697, -11.704842599401921, -11.845345249528865, -11.849035576746159, -11.714075025454559, -11.442009550461101, -11.03777792205507, -10.509615905859263, -9.868857202086245, -9.129635589502552, -8.308496225311458, -7.423927373093792, -6.495826838901891, -5.5449199698145835, -4.592148101125855, -3.6580477360857477, -2.7621414350068716, -1.9223613324464606, -1.1545253732269682, -0.4718847704662677, 0.11524111855451846, 0.5997292608732364, 0.9778070349959204, 1.2490901561105452, 1.4165028950129024, 1.4860834163823138, 1.4666813984951674, 1.3695592286605187, 1.2079118292511162, 0.9963234010997916, 0.7501819341526867, 0.4850741128123604, 0.21618414737107702, -0.04227996132673134, -0.27761018736254345, -0.4790516349971276, -0.6381672060355904, -0.7490994339395018, -0.8087193098031559, -0.8166565724981802, -0.7752108735920015, -0.6891482545352949, -0.565392277778223, -0.4126237236106922, -0.24080679842032668, -0.060663113605031876, 0.11688286996236684, 0.2812618025584043, 0.42279533143542397, 0.5331852027257472, 0.605932751375481, 0.6366688822276639, 0.6233785184023379, 0.5665081551805057, 0.468950416772815, 0.33590514607013633, 0.17462231759628533, -0.005962306888587772, -0.19568262153879828, -0.3836679590568244, -0.558914717353583, -0.7108766558107665, -0.8300452146368912, -0.9084910441052814, -0.940339110428532, -0.9221522521341993, -0.8532018137869835, -0.7356088416104982, -0.5743450916832133, -0.3770895318323603, -0.1539428311156087, 0.08299078215004267, 0.3201382719808137, 0.5430870578942174, 0.7372814815650791, 0.888755094994355, 0.9848646753440026, 1.0149906875694092, 0.971169361998232, 0.848623657809601, 0.6461640957078961, 0.3664356376565895, 0.01599326856342902, -0.3948035718018292, -0.8520793705090199, -1.3389068824944566, -1.8359321187912532, -2.3221366716689156, -2.7757069173270628, -3.174973697685221, -3.4993816679605776, -3.730444857596228, -3.8526443035586824, -3.854224964789216, -3.727852508559093, -3.4710958712919604, -3.0867085416105127, -2.5826900080518493, -1.9721183978525796, -1.27275558493519, -0.5064365004058876, 0.301735448630789, 1.1243555415972468, 1.9328080025449919, 2.698433336088158, 3.393722181266979, 3.9934828312008697, 4.475929683180381, 4.823642457627554, 5.024350986898514, 5.07150754227542, 4.964617746177614, 4.709311715131507, 4.317148724620739, 3.805160846639934, 3.195153115977074, 2.5127892545301025, 1.7865022660317602, 1.046277794891886, 0.3223645836879696, -0.3560296789286853, -0.9619975831032606, -1.4720883264256448, -1.867307523270486, -2.1339138247349974, -2.26397493774028, -2.2556567769021316, -2.1132319956919683, -1.8468074304732907, -1.4717834115208952, -1.0080707926097394, -0.47910328545437125, 0.08930733346529837, 0.6702178594434742, 1.236841807595088, 1.763816637988309, 2.228388597325961, 2.611457744992052, 2.898432637594075, 3.079853606117951, 3.151755115851412, 3.1157507819334582, 2.978838569277297, 2.7529378296217035, 2.454183399620516, 2.102014302407892, 1.7181050189853375, 1.325195275000949], 'positive_zeros': ['1.45900456278828047682619166542091', '2.93624279897876652459736183687630', '3.10803653125865008567545667264924', '4.24502392065890446520270319641902', '4.63683039190104491527944744913904', '6.54009265649579301822220097468077', '7.20237587827492080033620163324333', '7.83742606651996775966762446949330', '8.428066444271966622823681662279942'], 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45900456278828047682619166542', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93624279897876652459736183688', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10803653125865008567545667265', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 109.50754497065464, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'index': 139, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1856/4/a/bg/1/9'], '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': '2-1856-1.1-c3-0-139', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45900456278828047682619166542', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1849508009754289157563136346427', 'Lhash_array': ['1849508009754289157563136346427'], 'label': '2-1856-1.1-c3-0-139', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1856/4/a/bg/1/9'}