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lfunc_lfunctions • Show schema
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{'Lhash': '2392313279781413011734040264988,3853216520094758759367504954208', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 1, 'a7': 2, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1, -1, 1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, -1, 1], [1, 0, -5, 0, 25], [1, -2, 15, -14, 49], [1, 4, 26, 44, 121], [1, -3, -4, -39, 169], [1, 4, -1, 68, 289], [1, -8, 19], [1, 4, -7, 92, 529], [1, 0, -29, 0, 841], [1, 6, 71, 186, 961], [1, 10, 99, 370, 1369], [1, 4, -25, 164, 1681], [1, -9, 38, -387, 1849], [1, 10, 53, 470, 2209], [1, -4, -37, -212, 2809], [1, -14, 137, -826, 3481], [1, 11, 60, 671, 3721], [1, 3, -58, 201, 4489], [1, 14, 125, 994, 5041], [1, -11, 48, -803, 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1300489487693078999, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88720241946061314769023443231', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03965187205450842041976789976', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61870851811828748658304663038', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, 0, 0, 1, 2, -1, 0, 0, -4, 0, 3, 2, 0, -1, -4, 0, 8, 0, 2, -4, -4, -1, 5, 3, -1, 0, 0, 0, -6, 0, -4, -4, 0, 0, -10, 8, 3, 0, -4, 2, 9, 0, 0, -4, -10, -1, -11, 5, -4, 0, 4, -1, 0, -2, 8, 0, 14, 0, -11, -6, 0, 1, 0, -4, -3, 0, -4, 0, -14, 0, 11, -10, 5, 0, -8, 3, -1, 0, -1, -4, 16, 0, 0, 9, 0, 4, 14, 0, 6, 0, -6, -10, 0, 0, -2, -11, 0, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, -3, -4, -39, 169], 'euler17': [1, 4, -1, 68, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 4, -7, 92, 529], 'euler29': [1, 0, -29, 0, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, 6, 71, 186, 961], 'euler37': [1, 10, 99, 370, 1369], 'euler41': [1, 4, -25, 164, 1681], 'euler43': [1, -9, 38, -387, 1849], 'euler47': [1, 10, 53, 470, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, -4, -37, -212, 2809], 'euler59': [1, -14, 137, -826, 3481], 'euler61': [1, 11, 60, 671, 3721], 'euler67': [1, 3, -58, 201, 4489], 'euler7': [1, -2, 15, -14, 49], 'euler71': [1, 14, 125, 994, 5041], 'euler73': [1, -11, 48, -803, 5329], 'euler79': [1, 1, -78, 79, 6241], 'euler83': [1, -16, 230, -1328, 6889], 'euler89': [1, -14, 107, -1246, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, -1, 1, 0, 0], [1, 0, -5, 0, 25], [1, -2, 15, -14, 49], [1, 4, 26, 44, 121], [1, -3, -4, -39, 169], [1, 4, -1, 68, 289], [1, -8, 19, 0, 0], [1, 4, -7, 92, 529], [1, 0, -29, 0, 841], [1, 6, 71, 186, 961], [1, 10, 99, 370, 1369], [1, 4, -25, 164, 1681], [1, -9, 38, -387, 1849], [1, 10, 53, 470, 2209], [1, -4, -37, -212, 2809], [1, -14, 137, -826, 3481], [1, 11, 60, 671, 3721], [1, 3, -58, 201, 4489], [1, 14, 125, 994, 5041], [1, -11, 48, -803, 5329], [1, 1, -78, 79, 6241], [1, -16, 230, -1328, 6889], [1, -14, 107, -1246, 7921], [1, 2, -93, 194, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/e/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': '4-114e2-1.1-c1e2-0-7', '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': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1300489487693078999, 'z1': {'__RealLiteral__': 0, 'data': '1.88720241946061314769023443231', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2392313279781413011734040264988,3853216520094758759367504954208', 'Lhash_array': ['2392313279781413011734040264988', '3853216520094758759367504954208'], 'label': '4-114e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/e/b'}