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lfunc_lfunctions • Show schema
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{'Lhash': '555090823671297689652283137887', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -32, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 5], [1, 32, 343], [1, 60, 1331], [1, 34, 2197], [1, 42, 4913], [1, -76, 6859], [1, 0, 12167], [1, 6, 24389], [1, -232, 29791], [1, -134, 50653], [1, 234, 68921], [1, -412, 79507], [1, 360, 103823], [1, 222, 148877], [1, -660, 205379], [1, 490, 226981], [1, 812, 300763], [1, -120, 357911], [1, -746, 389017], [1, 152, 493039], [1, 804, 571787], [1, -678, 704969], [1, -194, 912673], [1, 798, 1030301], [1, 1088, 1092727], [1, -1716, 1225043], [1, 970, 1295029], [1, 426, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 5], 1]], [[[1, 32, 343], 1]], [[[1, 60, 1331], 1]], [[[1, 34, 2197], 1]], [[[1, 42, 4913], 1]], [[[1, -76, 6859], 1]], [[[1, 0, 12167], 1]], [[[1, 6, 24389], 1]], [[[1, -232, 29791], 1]], [[[1, -134, 50653], 1]], [[[1, 234, 68921], 1]], [[[1, -412, 79507], 1]], [[[1, 360, 103823], 1]], [[[1, 222, 148877], 1]], [[[1, -660, 205379], 1]], [[[1, 490, 226981], 1]], [[[1, 812, 300763], 1]], [[[1, -120, 357911], 1]], [[[1, -746, 389017], 1]], [[[1, 152, 493039], 1]], [[[1, 804, 571787], 1]], [[[1, -678, 704969], 1]], [[[1, -194, 912673], 1]], [[[1, 798, 1030301], 1]], [[[1, 1088, 1092727], 1]], [[[1, -1716, 1225043], 1]], [[[1, 970, 1295029], 1]], [[[1, 426, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-720-1.1-c3-0-0', 'leading_term': '0.672181280914369684543914036756720000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6721812809143697, 0.6596251624207068, 0.6220696276469996, 0.5598538453651468, 0.4735453693006894, 0.3639432595225027, 0.23208189009810534, 0.07923490874710502, -0.09308129976859797, -0.28310538207129743, -0.48883080893540487, -0.708008509061851, -0.9381531504341261, -1.1765538311768782, -1.4202898632725514, -1.666252221563529, -1.9111710895292742, -2.151649765456198, -2.384205001547856, -2.6053136386013613, -2.8114651750248187, -2.999219676656871, -3.1652701990490204, -3.3065086630211153, -3.420093904228104, -3.5035204153027526, -3.5546861221489356, -3.5719573914376346, -3.554229361391837, -3.500979629206062, -3.4123133219334867, -3.288997628462329, -3.1324839821715456, -2.944916259425928, -2.7291235989637683, -2.488596750253427, 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'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 947410445386869324, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43788944964121694309058618898', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58703497053564748485326602717', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20985699988465287320024599894', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, -32, 0, 0, 0, -60, 0, -34, 0, 0, 0, -42, 0, 76, 0, 0, 0, 0, 0, 25, 0, 0, 0, -6, 0, 232, 0, 0, 0, 160, 0, 134, 0, 0, 0, -234, 0, 412, 0, 0, 0, -360, 0, 681, 0, 0, 0, -222, 0, 300, 0, 0, 0, 660, 0, -490, 0, 0, 0, 170, 0, -812, 0, 0, 0, 120, 0, 746, 0, 0, 0, 1920, 0, -152, 0, 0, 0, -804, 0, 210, 0, 0, 0, 678, 0, 1088, 0, 0, 0, -380, 0, 194, 0, 0, 0], 'euler11': [1, 60, 1331], 'euler13': [1, 34, 2197], 'euler17': [1, 42, 4913], 'euler19': [1, -76, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 0, 12167], 'euler29': [1, 6, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -232, 29791], 'euler37': [1, -134, 50653], 'euler41': [1, 234, 68921], 'euler43': [1, -412, 79507], 'euler47': [1, 360, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 222, 148877], 'euler59': [1, -660, 205379], 'euler61': [1, 490, 226981], 'euler67': [1, 812, 300763], 'euler7': [1, 32, 343], 'euler71': [1, -120, 357911], 'euler73': [1, -746, 389017], 'euler79': [1, 152, 493039], 'euler83': [1, 804, 571787], 'euler89': [1, -678, 704969], 'euler97': [1, -194, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, 32, 343], [1, 60, 1331], [1, 34, 2197], [1, 42, 4913], [1, -76, 6859], [1, 0, 12167], [1, 6, 24389], [1, -232, 29791], [1, -134, 50653], [1, 234, 68921], [1, -412, 79507], [1, 360, 103823], [1, 222, 148877], [1, -660, 205379], [1, 490, 226981], [1, 812, 300763], [1, -120, 357911], [1, -746, 389017], [1, 152, 493039], [1, 804, 571787], [1, -678, 704969], [1, -194, 912673]], 'index': 0, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/b'], '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': '2-720-1.1-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 947410445386869324, 'z1': {'__RealLiteral__': 0, 'data': '0.43788944964121694309058618898', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20219508
{'Lhash': '555090823671297689652283137887', 'Lhash_array': ['555090823671297689652283137887'], 'label': '2-720-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/b'}
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id: 24569809
{'Lhash': '555090823671297689652283137887', 'Lhash_array': ['555090823671297689652283137887'], 'label': '2-720-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/b/1/1'}