Formats: - HTML - YAML - JSON - 2026-09-21T17:28:17.719709
  • lfunc_lfunctions • Show schema
    {'Lhash': '2717594518825378505932163544831', 'a10': [0.0, 0.0], 'a2': [1.3027756377319946, 0.0], 'a3': [2.302775637731995, 0.0], 'a4': [-0.3027756377319947, 0.0], 'a5': [0.0, 0.0], 'a6': [3.0, 0.0], 'a7': [-0.6972243622680053, 0.0], 'a8': [-3.0, 0.0], 'a9': [2.302775637731995, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.15474661143733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '3025.1', 'coefficient_field': 'CDF', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3027756377319946, 0], [2.0, 0]], [[1.0, 0], [-2.302775637731995, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.6972243622680053, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0], [13.0, 0]], [[1.0, 0], [6.908326913195984, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0], [19.0, 0]], [[1.0, 0], [7.302775637731995, 0], [23.0, 0]], [[1.0, 0], [0.9083269131959839, 0], [29.0, 0]], [[1.0, 0], [-10.21110255092798, 0], [31.0, 0]], [[1.0, 0], [-2.394448724536011, 0], [37.0, 0]], [[1.0, 0], [-5.60555127546399, 0], [41.0, 0]], [[1.0, 0], [7.211102550927978, 0], [43.0, 0]], [[1.0, 0], [3.0, 0], [47.0, 0]], [[1.0, 0], [1.3027756377319946, 0], [53.0, 0]], [[1.0, 0], [14.21110255092798, 0], [59.0, 0]], [[1.0, 0], [-7.908326913195984, 0], [61.0, 0]], [[1.0, 0], [4.0, 0], [67.0, 0]], [[1.0, 0], [2.605551275463989, 0], [71.0, 0]], [[1.0, 0], [-7.908326913195984, 0], [73.0, 0]], [[1.0, 0], [-10.908326913195983, 0], [79.0, 0]], [[1.0, 0], [-3.513878188659973, 0], [83.0, 0]], [[1.0, 0], [-1.6972243622680054, 0], [89.0, 0]], [[1.0, 0], [-15.302775637731994, 0], [97.0, 0]], [[1.0, 0], [-0.5138781886599733, 0], [101.0, 0]], [[1.0, 0], [-2.908326913195984, 0], [103.0, 0]], [[1.0, 0], [-3.0, 0], [107.0, 0]], [[1.0, 0], [11.513878188659973, 0], [109.0, 0]], [[1.0, 0], [10.816653826391969, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 154, 'label': '2-55e2-1.1-c1-0-154', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3025/2/a/h/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [1.648661492871478e-58, 0.3076249739449546, 0.6153349021063873, 0.9231400787327003, 1.2309055376231435, 1.5382882333630257, 1.8446851078625326, 2.1491943426366276, 2.4505912232058398, 2.7473192019923616, 3.037496017531891, 3.3189341520677376, 3.5891744936560013, 3.845531794160486, 4.085150348089581, 4.305068222597631, 4.50228831363809, 4.673854463000435, 4.816930831177299, 4.928882675984336, 5.007356638006219, 5.050358587670233, 5.0563270544168155, 5.0242002466625895, 4.95347469258928, 4.844253595764929, 4.6972831140297275, 4.513974940613742, 4.29641379629695, 4.0473487311385306, 3.770167481738968, 3.468853530277043, 3.147925957148355, 2.812362659870438, 2.4675080146601673, 2.1189665693770463, 1.7724848613776951, 1.433823934083004, 1.1086255639082485, 0.8022755867702946, 0.5197680133562773, 0.26557382864255114, 0.04351846963410814, -0.1433280456219715, -0.2927445133727942, -0.4034319204912294, -0.47506367214340584, -0.5083100832148064, -0.5048352072659534, -0.46726484338922214, -0.39912541440240884, -0.30475432608565606, -0.18918336942097078, -0.05799768552328646, 0.0828262567563671, 0.22709935201757117, 0.36861012743852367, 0.5013208563977618, 0.61956330134714, 0.7182275770866193, 0.7929375425494886, 0.840206272895213, 0.8575655430226267, 0.8436638693296948, 0.7983285006975728, 0.7225878052637065, 0.6186517405441444, 0.48984948618906377, 0.34052481851257493, 0.1758913645195279, 0.0018514356852361435, -0.17521635014506462, -0.34869405662552894, -0.5119782043367954, -0.6587415213556864, -0.7831931470587236, -0.8803273814947735, -0.9461510436822391, -0.9778798510841972, -0.974094966859699, -0.9348519741613426, -0.8617360053031904, -0.7578585402331949, -0.6277934407710761, -0.47745203827216876, -0.3138994647456376, -0.1451168236706851, 0.02028385683806033, 0.17338275582250204, 0.3053024055542154, 0.40757218615632, 0.47249333294296453, 0.4934899448138527, 0.4654313534733568, 0.38491166549593137, 0.25047333394876165, 0.06276324135924534, -0.17538805527047294, -0.4589706148452747, -0.7808865846618479, -1.1321291570620302, -1.5020457964165117, -1.878678971546914, -2.2491741870683883, -2.6002419223316298, -2.91865730278945, -3.191779080285982, -3.4080679047770235, -3.557583027504949, -3.6324365549328186, -3.6271852127654185, -3.5391412845806967, -3.3685869279179634, -3.1188793731523705, -2.796438472381143, -2.4106125490913954, -1.9734233381413562, -1.4991958102986014, -1.0040836412631269, -0.5055057992489781, -0.021513976675895594, 0.4298858201245801, 0.8314314645663997, 1.1672948788536843, 1.4237357314138634, 1.5896907585141107, 1.6572725533764794, 1.6221545895313432, 1.4838232629372285, 1.2456827166344, 0.9150039718199594, 0.5027162080456422, 0.02304465713053045, -0.5069937786223885, -1.068219693967992, -1.6400218212984787, -2.2011608412822428, -2.730614151803276, -3.208426765718663, -3.6165323404169896, -3.9395087242817577, -4.165234369899125, -4.285415473597615, -4.2959586465651345, -4.197170126088719, -3.9937697546278135, -3.6947158930168675, -3.3128457527284123, -2.864343962737495, -2.3680601484433277, -1.8447035173886626, -1.315948565731148, -0.8034907269872588, -0.3280938229049751, 0.09132764209520096, 0.4385490828490507, 0.7007598331391263, 0.8691357102871395, 0.9392317136686509, 0.9111743086105196, 0.789641776509178, 0.5836308901063799, 0.3060182539204636, -0.027065439493593135, -0.39702072545133504, -0.7836885927812608, -1.1663413384574517, -1.5247080433933893, -1.8399851032876204, -2.095782038879436, -2.27895501967903, -2.380285118400068, -2.3949651065877906, -2.3228673288471073, -2.1685754743027084, -1.9411744329273841, -1.6538043479123457, -1.322996877861552, -0.9678229739549551, -0.6088915811441982, -0.2672470560031758, 0.03678070467805212, 0.2847157764658673, 0.46100685430884614, 0.5539725787025049, 0.5565700189192031, 0.466942432689585, 0.2887124570200659, 0.03099887078561999, -0.2918515467734063, -0.6608113945578921, -1.0529793885363479, -1.4426130226131673, -1.8023414982186834, -2.104503050799483, -2.322543142943586, -2.43240534364995, -2.413845377485781, -2.25160095123048, -1.9363555217004131, -1.4654429539999374, -0.8432516623980075, -0.08130080011582122, 0.8020232875322315, 1.7820655670289522, 2.828814336065967, 3.908089400950807, 4.9829547061799575, 6.015291687821234, 6.967460579233269, 7.803971347034481, 8.493084220107473, 9.008262046408944, 9.329402920046755, 9.443791408852059, 9.346719830205021, 9.04174674522111, 8.540577398682256, 7.862569347439604, 7.033885053966124, 6.086330820800358, 5.05593718844678, 3.98134898183764, 2.9021028674182396, 1.8568760429438265, 0.8817911944770672, 0.008860010190899678, -0.7353595414607885, -1.3308279344978384, -1.7647608814075346, -2.0320051765292995, -2.135039173571694, -2.0836028249923424, -1.89398125218944, -1.5879835385942116, -1.1916738902387836, -0.7339246562831889, -0.24486927705236924, 0.24566243491620626, 0.7096444073699462, 1.1222121297553744, 1.4628092840325255, 1.7160667719355884, 1.87237321074563, 1.928113580286296, 1.8855714458289516, 1.7525089949422719, 1.5414569455426659, 1.2687621974841359, 0.9534540148701641, 0.615998811084242, 0.27701874307210517, -0.04394997360076246, -0.32958686259824815, -0.5657408860574074, -0.7421555090173201, -0.8529272785554637], 'positive_zeros': ['2.14380407214424809613980907824400', '2.71261568446308868884804894398528', '3.55521969568218248454933003356239', '4.41159056032614430486774950379700', '4.88943947770883126725106922733148', '6.09607495494088206138081319698971', '6.70542394417216571655570705990078', '7.80854250451670877484888967795354', '8.273454019913271568335971180774479'], 'prelabel': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14380407214424809613980907824', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.71261568446308868884804894399', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.55521969568218248454933003356', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.15474661143733, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'index': 154, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3025/2/a/h/1/2'], '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': '2-55e2-1.1-c1-0-154', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14380407214424809613980907824', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2717594518825378505932163544831', 'Lhash_array': ['2717594518825378505932163544831'], 'factors': ['2-55e2-1.1-c1-0-154'], 'label': '2-55e2-1.1-c1-0-154', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3025/2/a/h/1/2'}