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lfunc_lfunctions • Show schema
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{'Lhash': '2174376808301711466988156790478,2317424923886172641785683158174', 'a10': 8, 'a2': 1, 'a3': 0, 'a4': 2, 'a5': 8, 'a6': 0, 'a7': 1, 'a8': 5, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.498417380479413, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, -1, 7]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': '1.1.1.1', 'conductor': 321489, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, -1, -1, -2, 4], [1], [1, -8, 26, -40, 25], [1, -1, 7], [1, 4, 26, 44, 121], [1, 1, -12, 13, 169], [1, 6, 19, 102, 289], [1, 4, -3, 76, 361], [1, 12, 82, 276, 529], [1, -2, -25, -58, 841], [1, 3, -22, 93, 961], [1, 3, -28, 111, 1369], [1, 2, -37, 82, 1681], [1, -1, -42, -43, 1849], [1, -6, -11, -282, 2209], [1, 6, -17, 318, 2809], [1, -6, -23, -354, 3481], [1, -5, -36, -305, 3721], [1, 7, -18, 469, 4489], [1, 0, 142, 0, 5041], [1, -6, -37, -438, 5329], [1, 11, 42, 869, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1071682725337076915, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71528085728846256494530826959', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82812592323858053351951550137', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46872887508172216304132251587', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.498417380479413, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 321489, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 2, 8, 0, 1, 5, 0, 8, -4, 0, -1, 1, 0, 5, -6, 0, -4, 16, 0, -4, -12, 0, 38, -1, 0, 2, 2, 0, -3, 10, 0, -6, 8, 0, -3, -4, 0, 40, -2, 0, 1, -8, 0, -12, 6, 0, -6, 38, 0, -2, -6, 0, -32, 5, 0, 2, 6, 0, 5, -3, 0, 17, -8, 0, -7, -12, 0, 8, 0, 0, 6, -3, 0, -8, -4, 0, -11, 40, 0, -2, 6, 0, -48, 1, 0, -20, -4, 0, -1, -24, 0, 6, -32, 0, -9, -6, 0, 76], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 1, -12, 13, 169], 'euler17': [1, 6, 19, 102, 289], 'euler19': [1, 4, -3, 76, 361], 'euler2': [1, -1, -1, -2, 4], 'euler23': [1, 12, 82, 276, 529], 'euler29': [1, -2, -25, -58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 3, -22, 93, 961], 'euler37': [1, 3, -28, 111, 1369], 'euler41': [1, 2, -37, 82, 1681], 'euler43': [1, -1, -42, -43, 1849], 'euler47': [1, -6, -11, -282, 2209], 'euler5': [1, -8, 26, -40, 25], 'euler53': [1, 6, -17, 318, 2809], 'euler59': [1, -6, -23, -354, 3481], 'euler61': [1, -5, -36, -305, 3721], 'euler67': [1, 7, -18, 469, 4489], 'euler7': [1, -1, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -6, -37, -438, 5329], 'euler79': [1, 11, 42, 869, 6241], 'euler83': [1, -6, -47, -498, 6889], 'euler89': [1, 4, -73, 356, 7921], 'euler97': [1, 9, -16, 873, 9409], 'euler_factors': [[1, -1, -1, -2, 4], [1, 0, 0, 0, 0], [1, -8, 26, -40, 25], [1, -1, 7, 0, 0], [1, 4, 26, 44, 121], [1, 1, -12, 13, 169], [1, 6, 19, 102, 289], [1, 4, -3, 76, 361], [1, 12, 82, 276, 529], [1, -2, -25, -58, 841], [1, 3, -22, 93, 961], [1, 3, -28, 111, 1369], [1, 2, -37, 82, 1681], [1, -1, -42, -43, 1849], [1, -6, -11, -282, 2209], [1, 6, -17, 318, 2809], [1, -6, -23, -354, 3481], [1, -5, -36, -305, 3721], [1, 7, -18, 469, 4489], [1, 0, 142, 0, 5041], [1, -6, -37, -438, 5329], [1, 11, 42, 869, 6241], [1, -6, -47, -498, 6889], [1, 4, -73, 356, 7921], [1, 9, -16, 873, 9409]], 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/g/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': '4-567e2-1.1-c1e2-0-35', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-567e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1071682725337076915, 'z1': {'__RealLiteral__': 0, 'data': '1.71528085728846256494530826959', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2174376808301711466988156790478,2317424923886172641785683158174', 'Lhash_array': ['2174376808301711466988156790478', '2317424923886172641785683158174'], 'label': '4-567e2-1.1-c1e2-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/g/e'}