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  • lfunc_lfunctions • Show schema
    {'Lhash': '826350482304987073988455592645,829210899120496311693715975987,898183771003938794526946554917', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 380137.2649529088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': '1.1.1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1], [1, -3, 15, -29, 75, -75, 125], [1, 3, 3, 1], [1, 0, 24, -9, 264, 0, 1331], [1, 3, 30, 75, 390, 507, 2197], [1, 6, 54, 203, 918, 1734, 4913], [1, -9, 63, -323, 1197, -3249, 6859], [1, -6, 24, -7, 552, -3174, 12167], [1, -3, 51, -155, 1479, -2523, 24389], [1, -9, 99, -485, 3069, -8649, 29791], [1, 15, 165, 1167, 6105, 20535, 50653], [1, 6, 108, 473, 4428, 10086, 68921], [1, -15, 183, -1273, 7869, -27735, 79507], 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2.057140047787853, 2.825583569433044, 3.62743670675145, 4.4266508783017, 5.1860789408266115, 5.869518974213843, 6.4452216557495845, 6.886331843428412, 7.172001534531393, 7.289493986471124, 7.233723366117224, 7.008246257750967, 6.628341692101993, 6.116220982675409, 5.496800907308052, 4.792432858676859, 4.0285395471739776, 3.240575273319033, 2.4836376274376146], 'positive_zeros': ['0.65187558950093180119691289059027', '0.65413206049932382237357048378506', '0.70854206264898913283623119668212', '1.65389287250209917126837319312081', '1.76392028998598566113426962755820', '2.09257618724218220383161314607114', '2.34069707002746933547932828638809', '2.56820976122091824400830153550249', '2.89644965119238528042385376950020', '3.27068266268950213905337288966458', '3.30281685730568073087897900672759', '3.58656676249718544358578802658960', '4.09774645952002925146413941287063', '4.20041969951546270606649997049722', '4.38489505943158945544014373528157', '4.95735880251478022352499483326654', '5.10401249935893826809905281049922', '5.10808174913628658183882527390272', '5.54581193989269308545396616499515', '5.56467107358535976174956455476567', '5.92677626236596525643964033194983', '6.20589568053361955392840618345853', '6.42428192542730361503269565275724', '6.52420132860505270256062507958161', '6.84265023592385566260119570533698', '7.01293988909348912508957273053067', '7.14714694552327799355863953810611', '7.61560058896578302344334582407084', '7.61853898542556140028033956548232', '7.74198363819550306211886689393962'], 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 158474791456444760, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65187558950093180119691289059', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.65413206049932382237357048379', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.70854206264898913283623119668', 'prec': 97}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 380137.2649529088, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, 9, 0, 0, 0, 6, 0, -6, 0, 0, 0, 3, 0, 9, 0, 0, 0, -9, 0, -15, 0, 0, 0, -6, 0, 15, 0, 0, 0, 9, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 3, 0, -12, 0, 0, 0, -9, 0, 12, 0, 0, 0, 21, 0, 3, 0, 0, 0, 0, 0, 15, 0, 0, 0, -6, 0, -18, 0, 0, 0, 18, 0, 9, 0, 0, 0, 27, 0, 15, 0, 0, 0], 'euler11': [1, 0, 24, -9, 264, 0, 1331], 'euler13': [1, 3, 30, 75, 390, 507, 2197], 'euler17': [1, 6, 54, 203, 918, 1734, 4913], 'euler19': [1, -9, 63, -323, 1197, -3249, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -6, 24, -7, 552, -3174, 12167], 'euler29': [1, -3, 51, -155, 1479, -2523, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -9, 99, -485, 3069, -8649, 29791], 'euler37': [1, 15, 165, 1167, 6105, 20535, 50653], 'euler41': [1, 6, 108, 473, 4428, 10086, 68921], 'euler43': [1, -15, 183, -1273, 7869, -27735, 79507], 'euler47': [1, -9, 147, -847, 6909, -19881, 103823], 'euler5': [1, -3, 15, -29, 75, -75, 125], 'euler53': [1, -6, 162, -617, 8586, -16854, 148877], 'euler59': [1, -3, 33, 135, 1947, -10443, 205379], 'euler61': [1, 12, 192, 1391, 11712, 44652, 226981], 'euler67': [1, -12, 156, -1281, 10452, -53868, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, -21, 249, -2115, 17679, -105861, 357911], 'euler73': [1, -3, 105, -475, 7665, -15987, 389017], 'euler79': [1, -15, 195, -1433, 15405, -93615, 493039], 'euler83': [1, 6, 78, 1539, 6474, 41334, 571787], 'euler89': [1, -18, 318, -3241, 28302, -142578, 704969], 'euler97': [1, -15, 57, 311, 5529, -141135, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -3, 15, -29, 75, -75, 125], [1, 3, 3, 1, 0, 0, 0], [1, 0, 24, -9, 264, 0, 1331], [1, 3, 30, 75, 390, 507, 2197], [1, 6, 54, 203, 918, 1734, 4913], [1, -9, 63, -323, 1197, -3249, 6859], [1, -6, 24, -7, 552, -3174, 12167], [1, -3, 51, -155, 1479, -2523, 24389], [1, -9, 99, -485, 3069, -8649, 29791], [1, 15, 165, 1167, 6105, 20535, 50653], [1, 6, 108, 473, 4428, 10086, 68921], [1, -15, 183, -1273, 7869, -27735, 79507], [1, -9, 147, -847, 6909, -19881, 103823], [1, -6, 162, -617, 8586, -16854, 148877], [1, -3, 33, 135, 1947, -10443, 205379], [1, 12, 192, 1391, 11712, 44652, 226981], [1, -12, 156, -1281, 10452, -53868, 300763], [1, -21, 249, -2115, 17679, -105861, 357911], [1, -3, 105, -475, 7665, -15987, 389017], [1, -15, 195, -1433, 15405, -93615, 493039], [1, 6, 78, 1539, 6474, 41334, 571787], [1, -18, 318, -3241, 28302, -142578, 704969], [1, -15, 57, 311, 5529, -141135, 912673]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/cc'], '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': '6-9072e3-1.1-c1e3-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 158474791456444760, 'z1': {'__RealLiteral__': 0, 'data': '0.65187558950093180119691289059', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '826350482304987073988455592645,829210899120496311693715975987,898183771003938794526946554917', 'Lhash_array': ['826350482304987073988455592645', '829210899120496311693715975987', '898183771003938794526946554917'], 'factors': ['2-9072-1.1-c1-0-31', '2-9072-1.1-c1-0-32', '2-9072-1.1-c1-0-38'], 'label': '6-9072e3-1.1-c1e3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/cc'}