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lfunc_lfunctions • Show schema
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{'Lhash': '2336774111408756006128583303768', 'a10': -10, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': 5, 'a6': 0, 'a7': -4, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.930515701549973, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '270.1', 'coefficient_field': '1.1.1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, 2], [1], [1, -5], [1, 4, 343], [1, 42, 1331], [1, -20, 2197], [1, 93, 4913], [1, -59, 6859], [1, 9, 12167], [1, 120, 24389], [1, -47, 29791], [1, 262, 50653], [1, 126, 68921], [1, 178, 79507], [1, 144, 103823], [1, 741, 148877], [1, -444, 205379], [1, -221, 226981], [1, 538, 300763], [1, 690, 357911], [1, 1126, 389017], [1, -665, 493039], [1, 75, 571787], [1, -1086, 704969], [1, -1544, 912673], [1, -132, 1030301], [1, 892, 1092727], [1, -1140, 1225043], [1, 1735, 1295029], [1, -1434, 1442897]], 'euler_factors_factorization': [[[[1, 2], 1]], [1], [[[1, -5], 1]], [[[1, 4, 343], 1]], [[[1, 42, 1331], 1]], [[[1, -20, 2197], 1]], [[[1, 93, 4913], 1]], [[[1, -59, 6859], 1]], [[[1, 9, 12167], 1]], [[[1, 120, 24389], 1]], [[[1, -47, 29791], 1]], [[[1, 262, 50653], 1]], [[[1, 126, 68921], 1]], [[[1, 178, 79507], 1]], [[[1, 144, 103823], 1]], [[[1, 741, 148877], 1]], [[[1, -444, 205379], 1]], [[[1, -221, 226981], 1]], [[[1, 538, 300763], 1]], [[[1, 690, 357911], 1]], [[[1, 1126, 389017], 1]], [[[1, -665, 493039], 1]], [[[1, 75, 571787], 1]], [[[1, -1086, 704969], 1]], [[[1, -1544, 912673], 1]], [[[1, -132, 1030301], 1]], [[[1, 892, 1092727], 1]], [[[1, -1140, 1225043], 1]], [[[1, 1735, 1295029], 1]], [[[1, -1434, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-270-1.1-c3-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': 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'0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 27054900829264453, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84338974082293675312061668138', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16781717532362284854674510984', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94045888314730274073260402257', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.930515701549973, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, 5, 0, -4, -8, 0, -10, -42, 0, 20, 8, 0, 16, -93, 0, 59, 20, 0, 84, -9, 0, 25, -40, 0, -16, -120, 0, 47, -32, 0, 186, -20, 0, -262, -118, 0, -40, -126, 0, -178, -168, 0, 18, -144, 0, -327, -50, 0, 80, -741, 0, -210, 32, 0, 240, 444, 0, 221, -94, 0, 64, 100, 0, -538, -372, 0, 40, -690, 0, -1126, 524, 0, 236, 168, 0, 665, 80, 0, 252, -75, 0, -465, 356, 0, 336, 1086, 0, -80, -36, 0, 288, 295, 0, 1544, 654, 0, 100], 'euler11': [1, 42, 1331], 'euler13': [1, -20, 2197], 'euler17': [1, 93, 4913], 'euler19': [1, -59, 6859], 'euler2': [1, 2, 0], 'euler23': [1, 9, 12167], 'euler29': [1, 120, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -47, 29791], 'euler37': [1, 262, 50653], 'euler41': [1, 126, 68921], 'euler43': [1, 178, 79507], 'euler47': [1, 144, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 741, 148877], 'euler59': [1, -444, 205379], 'euler61': [1, -221, 226981], 'euler67': [1, 538, 300763], 'euler7': [1, 4, 343], 'euler71': [1, 690, 357911], 'euler73': [1, 1126, 389017], 'euler79': [1, -665, 493039], 'euler83': [1, 75, 571787], 'euler89': [1, -1086, 704969], 'euler97': [1, -1544, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, -5, 0], [1, 4, 343], [1, 42, 1331], [1, -20, 2197], [1, 93, 4913], [1, -59, 6859], [1, 9, 12167], [1, 120, 24389], [1, -47, 29791], [1, 262, 50653], [1, 126, 68921], [1, 178, 79507], [1, 144, 103823], [1, 741, 148877], [1, -444, 205379], [1, -221, 226981], [1, 538, 300763], [1, 690, 357911], [1, 1126, 389017], [1, -665, 493039], [1, 75, 571787], [1, -1086, 704969], [1, -1544, 912673]], 'index': 12, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/270/4/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/270/4/a/e'], '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': '2-270-1.1-c3-0-12', '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': '2-270-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.991305012342451, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 27054900829264453, 'z1': {'__RealLiteral__': 0, 'data': '1.84338974082293675312061668138', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20699571
{'Lhash': '2336774111408756006128583303768', 'Lhash_array': ['2336774111408756006128583303768'], 'label': '2-270-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/e'}
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id: 24555405
{'Lhash': '2336774111408756006128583303768', 'Lhash_array': ['2336774111408756006128583303768'], 'label': '2-270-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/e/1/1'}