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lfunc_lfunctions • Show schema
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{'Lhash': '3270269280210541371107415784630', 'a10': 0, 'a2': 3, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': -20, 'a8': -21, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -3, 8], [1], [1], [1, 20, 343], [1, -24, 1331], [1, 74, 2197], [1, -54, 4913], [1, 124, 6859], [1, 120, 12167], [1, -78, 24389], [1, -200, 29791], [1, -70, 50653], [1, 330, 68921], [1, 92, 79507], [1, 24, 103823], [1, -450, 148877], [1, 24, 205379], [1, 322, 226981], [1, -196, 300763], [1, -288, 357911], [1, -430, 389017], [1, 520, 493039], [1, -156, 571787], [1, 1026, 704969], [1, -286, 912673], [1, -1734, 1030301], [1, 452, 1092727], [1, 1404, 1225043], [1, 1474, 1295029], [1, -1086, 1442897]], 'euler_factors_factorization': [[[[1, -3, 8], 1]], [1], [1], [[[1, 20, 343], 1]], [[[1, -24, 1331], 1]], [[[1, 74, 2197], 1]], [[[1, -54, 4913], 1]], [[[1, 124, 6859], 1]], [[[1, 120, 12167], 1]], [[[1, -78, 24389], 1]], [[[1, -200, 29791], 1]], [[[1, -70, 50653], 1]], [[[1, 330, 68921], 1]], [[[1, 92, 79507], 1]], [[[1, 24, 103823], 1]], [[[1, -450, 148877], 1]], [[[1, 24, 205379], 1]], [[[1, 322, 226981], 1]], [[[1, -196, 300763], 1]], [[[1, -288, 357911], 1]], [[[1, -430, 389017], 1]], [[[1, 520, 493039], 1]], [[[1, -156, 571787], 1]], [[[1, 1026, 704969], 1]], [[[1, -286, 912673], 1]], [[[1, -1734, 1030301], 1]], [[[1, 452, 1092727], 1]], [[[1, 1404, 1225043], 1]], [[[1, 1474, 1295029], 1]], [[[1, -1086, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-15e2-1.1-c3-0-19', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 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'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1709780090063613729, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.57978758470335437435358267536', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78677782881581625327031002249', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80750741579903131949499602018', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 3, 0, 1, 0, 0, -20, -21, 0, 0, 24, 0, -74, -60, 0, -71, 54, 0, -124, 0, 0, 72, -120, 0, 0, -222, 0, -20, 78, 0, 200, -45, 0, 162, 0, 0, 70, -372, 0, 0, -330, 0, -92, 24, 0, -360, -24, 0, 57, 0, 0, -74, 450, 0, 0, 420, 0, 234, -24, 0, -322, 600, 0, 433, 0, 0, 196, 54, 0, 0, 288, 0, 430, 210, 0, -124, -480, 0, -520, 0, 0, -990, 156, 0, 0, -276, 0, -504, -1026, 0, 1480, -120, 0, -72, 0, 0, 286, 171, 0, 0], 'euler11': [1, -24, 1331], 'euler13': [1, 74, 2197], 'euler17': [1, -54, 4913], 'euler19': [1, 124, 6859], 'euler2': [1, -3, 8], 'euler23': [1, 120, 12167], 'euler29': [1, -78, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -200, 29791], 'euler37': [1, -70, 50653], 'euler41': [1, 330, 68921], 'euler43': [1, 92, 79507], 'euler47': [1, 24, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -450, 148877], 'euler59': [1, 24, 205379], 'euler61': [1, 322, 226981], 'euler67': [1, -196, 300763], 'euler7': [1, 20, 343], 'euler71': [1, -288, 357911], 'euler73': [1, -430, 389017], 'euler79': [1, 520, 493039], 'euler83': [1, -156, 571787], 'euler89': [1, 1026, 704969], 'euler97': [1, -286, 912673], 'euler_factors': [[1, -3, 8], [1, 0, 0], [1, 0, 0], [1, 20, 343], [1, -24, 1331], [1, 74, 2197], [1, -54, 4913], [1, 124, 6859], [1, 120, 12167], [1, -78, 24389], [1, -200, 29791], [1, -70, 50653], [1, 330, 68921], [1, 92, 79507], [1, 24, 103823], [1, -450, 148877], [1, 24, 205379], [1, 322, 226981], [1, -196, 300763], [1, -288, 357911], [1, -430, 389017], [1, 520, 493039], [1, -156, 571787], [1, 1026, 704969], [1, -286, 912673]], 'index': 19, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/225/4/a/g'], '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': '2-15e2-1.1-c3-0-19', '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': '2-15e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1709780090063613729, 'z1': {'__RealLiteral__': 0, 'data': '2.57978758470335437435358267536', 'prec': 103}}
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lfunc_instances • Show schema
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id: 17108797
{'Lhash': '3270269280210541371107415784630', 'Lhash_array': ['3270269280210541371107415784630'], 'label': '2-15e2-1.1-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/a/g'}
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id: 24554000
{'Lhash': '3270269280210541371107415784630', 'Lhash_array': ['3270269280210541371107415784630'], 'label': '2-15e2-1.1-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/a/g/1/1'}