Formats: - HTML - YAML - JSON - 2026-07-18T18:43:45.230498
  • lfunc_lfunctions • Show schema
    {'Lhash': '2031244957357504160723073582297', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 12, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '960.1', 'coefficient_field': '1.1.1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -3], [1, 5], [1, -12, 343], [1, 24, 1331], [1, 38, 2197], [1, 6, 4913], [1, -104, 6859], [1, 100, 12167], [1, 230, 24389], [1, -56, 29791], [1, 190, 50653], [1, -202, 68921], [1, 148, 79507], [1, 124, 103823], [1, 206, 148877], [1, 128, 205379], [1, 190, 226981], [1, 204, 300763], [1, -440, 357911], [1, -1210, 389017], [1, 816, 493039], [1, 1412, 571787], [1, 214, 704969], [1, -1202, 912673], [1, 1342, 1030301], [1, 908, 1092727], [1, 876, 1225043], [1, 302, 1295029], [1, 998, 1442897]], 'euler_factors_factorization': [[1], [[[1, -3], 1]], [[[1, 5], 1]], [[[1, -12, 343], 1]], [[[1, 24, 1331], 1]], [[[1, 38, 2197], 1]], [[[1, 6, 4913], 1]], [[[1, -104, 6859], 1]], [[[1, 100, 12167], 1]], [[[1, 230, 24389], 1]], [[[1, -56, 29791], 1]], [[[1, 190, 50653], 1]], [[[1, -202, 68921], 1]], [[[1, 148, 79507], 1]], [[[1, 124, 103823], 1]], [[[1, 206, 148877], 1]], [[[1, 128, 205379], 1]], [[[1, 190, 226981], 1]], [[[1, 204, 300763], 1]], [[[1, -440, 357911], 1]], [[[1, -1210, 389017], 1]], [[[1, 816, 493039], 1]], [[[1, 1412, 571787], 1]], [[[1, 214, 704969], 1]], [[[1, -1202, 912673], 1]], [[[1, 1342, 1030301], 1]], [[[1, 908, 1092727], 1]], [[[1, 876, 1225043], 1]], [[[1, 302, 1295029], 1]], [[[1, 998, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 42, 'label': '2-960-1.1-c3-0-42', '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/960/4/a/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.9228144862453762e-60, 0.2697681320504909, 0.5363421727980839, 0.796549177213665, 1.04725924562729, 1.2854088789218, 1.5080263962979272, 1.7122598821879582, 1.8954079520495963, 2.0549534205606856, 2.1885997288707317, 2.2943097494765, 2.370346347737142, 2.415313847771367, 2.42819933691082, 2.408412555886754, 2.3558229696179755, 2.27079250306163, 2.1542023642724457, 2.0074723676380297, 1.8325712180136553, 1.6320163235974965, 1.4088618728028681, 1.1666741374169813, 0.9094932485667007, 0.6417810291781232, 0.368354850536742, 0.09430790309508123, -0.1750832772261529, -0.4344627182362537, -0.6785085763057203, -0.90205411798555, -1.1002134485273714, -1.2685089310233106, -1.4029969150094386, -1.5003881464840565, -1.5581590778220704, -1.5746502497854291, -1.549147990167919, -1.4819458730185178, -1.3743827137200477, 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1.5014166509740896, 1.111506872151605, 0.6988863319449138, 0.2913269377254517, -0.08422030491810266, -0.40333056982071336, -0.6456496913457812, -0.7961791489151677, -0.8462184040159361, -0.7939024433548836, -0.6442975936165382, -0.4090465554487412, -0.1055824235795627, 0.24404060699494098, 0.6146269010133126, 0.979535558115453, 1.312484104029046, 1.589342372406435, 1.789798395116077, 1.8987849096965645, 1.9075692196679899], 'positive_zeros': ['1.60236973578665625602832087739952', '2.71379767898427593977972690360650', '3.74610531081243546386164291762739', '4.79146062091131050526406040296281', '5.56385271295564639586285409180289', '6.94980187619923034078811211793818', '7.75684730155721592930073376063672', '8.142363929842809234706105463883273', '9.282296051467975522125667996069631'], 'prelabel': '2-960-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.526076906696543, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 874512395819769686, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60236973578665625602832087740', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71379767898427593977972690361', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74610531081243546386164291763', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, -5, 0, 12, 0, 9, 0, -24, 0, -38, 0, -15, 0, -6, 0, 104, 0, 36, 0, -100, 0, 25, 0, 27, 0, -230, 0, 56, 0, -72, 0, -60, 0, -190, 0, -114, 0, 202, 0, -148, 0, -45, 0, -124, 0, -199, 0, -18, 0, -206, 0, 120, 0, 312, 0, -128, 0, -190, 0, 108, 0, 190, 0, -204, 0, -300, 0, 440, 0, 1210, 0, 75, 0, -288, 0, -816, 0, 81, 0, -1412, 0, 30, 0, -690, 0, -214, 0, -456, 0, 168, 0, -520, 0, 1202, 0, -216, 0], 'euler11': [1, 24, 1331], 'euler13': [1, 38, 2197], 'euler17': [1, 6, 4913], 'euler19': [1, -104, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 100, 12167], 'euler29': [1, 230, 24389], 'euler3': [1, -3, 0], 'euler31': [1, -56, 29791], 'euler37': [1, 190, 50653], 'euler41': [1, -202, 68921], 'euler43': [1, 148, 79507], 'euler47': [1, 124, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 206, 148877], 'euler59': [1, 128, 205379], 'euler61': [1, 190, 226981], 'euler67': [1, 204, 300763], 'euler7': [1, -12, 343], 'euler71': [1, -440, 357911], 'euler73': [1, -1210, 389017], 'euler79': [1, 816, 493039], 'euler83': [1, 1412, 571787], 'euler89': [1, 214, 704969], 'euler97': [1, -1202, 912673], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, 5, 0], [1, -12, 343], [1, 24, 1331], [1, 38, 2197], [1, 6, 4913], [1, -104, 6859], [1, 100, 12167], [1, 230, 24389], [1, -56, 29791], [1, 190, 50653], [1, -202, 68921], [1, 148, 79507], [1, 124, 103823], [1, 206, 148877], [1, 128, 205379], [1, 190, 226981], [1, 204, 300763], [1, -440, 357911], [1, -1210, 389017], [1, 816, 493039], [1, 1412, 571787], [1, 214, 704969], [1, -1202, 912673]], 'index': 42, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/a/y/1/1', 'ModularForm/GL2/Q/holomorphic/960/4/a/y'], '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': '2-960-1.1-c3-0-42', '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': '2-960-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.526076906696543, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 874512395819769686, 'z1': {'__RealLiteral__': 0, 'data': '1.60236973578665625602832087740', 'prec': 103}}
  • lfunc_instances • Show schema
    • id: 20107930
      {'Lhash': '2031244957357504160723073582297', 'Lhash_array': ['2031244957357504160723073582297'], 'factors': ['2-960-1.1-c3-0-42'], 'label': '2-960-1.1-c3-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/a/y'}
    • id: 24578101
      {'Lhash': '2031244957357504160723073582297', 'Lhash_array': ['2031244957357504160723073582297'], 'factors': ['2-960-1.1-c3-0-42'], 'label': '2-960-1.1-c3-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/a/y/1/1'}