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lfunc_lfunctions • Show schema
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{'Lhash': '612840990013899062032861538046,1785617339119278581026513251827', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, 8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -5, 0, 25], [1, -2, 15, -14, 49], [1, 0, 22, 0, 121], [1, -7, 36, -91, 169], [1, 0, -17, 0, 289], [1, 8, 19], [1, 0, -23, 0, 529], [1, 0, -29, 0, 841], [1, 22, 183, 682, 961], [1, 2, 75, 74, 1369], [1, 0, -41, 0, 1681], [1, -5, -18, -215, 1849], [1, 0, -47, 0, 2209], [1, 0, -53, 0, 2809], [1, 0, -59, 0, 3481], [1, -13, 108, -793, 3721], [1, -5, -42, -335, 4489], [1, 0, -71, 0, 5041], [1, -7, -24, -511, 5329], [1, 13, 90, 1027, 6241], [1, 0, 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'4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1335980907801655149, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48344629813890547028717724100', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40860371051596851626892960750', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.78167645699854059480313143426', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -14, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -7, 36, -91, 169], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, 8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, 0, -29, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 22, 183, 682, 961], 'euler37': [1, 2, 75, 74, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, -5, -18, -215, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, 0, -53, 0, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, -13, 108, -793, 3721], 'euler67': [1, -5, -42, -335, 4489], 'euler7': [1, -2, 15, -14, 49], 'euler71': [1, 0, -71, 0, 5041], 'euler73': [1, -7, -24, -511, 5329], 'euler79': [1, 13, 90, 1027, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, -89, 0, 7921], 'euler97': [1, 14, 99, 1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 25], [1, -2, 15, -14, 49], [1, 0, 22, 0, 121], [1, -7, 36, -91, 169], [1, 0, -17, 0, 289], [1, 8, 19, 0, 0], [1, 0, -23, 0, 529], [1, 0, -29, 0, 841], [1, 22, 183, 682, 961], [1, 2, 75, 74, 1369], [1, 0, -41, 0, 1681], [1, -5, -18, -215, 1849], [1, 0, -47, 0, 2209], [1, 0, -53, 0, 2809], [1, 0, -59, 0, 3481], [1, -13, 108, -793, 3721], [1, -5, -42, -335, 4489], [1, 0, -71, 0, 5041], [1, -7, -24, -511, 5329], [1, 13, 90, 1027, 6241], [1, 0, 166, 0, 6889], [1, 0, -89, 0, 7921], [1, 14, 99, 1358, 9409]], 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/l'], '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': '4-2736e2-1.1-c1e2-0-18', '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': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1335980907801655149, 'z1': {'__RealLiteral__': 0, 'data': '0.48344629813890547028717724100', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '612840990013899062032861538046,1785617339119278581026513251827', 'Lhash_array': ['612840990013899062032861538046', '1785617339119278581026513251827'], 'label': '4-2736e2-1.1-c1e2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/l'}