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lfunc_lfunctions • Show schema
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{'Lhash': '1961216118898580441235073064167,2479568866242782888235996860280', 'a10': -6, 'a2': -1, 'a3': -3, 'a4': 0, 'a5': 6, 'a6': 3, 'a7': 2, 'a8': 1, 'a9': 6, '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, 3, 3]], [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, 3, 3], [1, -6, 17, -30, 25], [1, -2, 15, -14, 49], [1, 0, -10, 0, 121], [1, -9, 40, -117, 169], [1, 6, 29, 102, 289], [1, 8, 19], [1, 0, 23, 0, 529], [1, 6, 7, 174, 841], [1, 0, -59, 0, 961], [1, 0, -47, 0, 1369], [1, 12, 103, 492, 1681], [1, -1, -42, -43, 1849], [1, -12, 95, -564, 2209], [1, 12, 91, 636, 2809], [1, 0, -59, 0, 3481], [1, 7, -12, 427, 3721], [1, -15, 142, -1005, 4489], [1, 6, -35, 426, 5041], [1, -7, -24, -511, 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'root_analytic_conductor': 0.9540935923915415, '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': 1347171742466172929, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54712672288837368532835762924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95603494038211965070339268295', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03354411211094901129353740907', '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, -3, 0, 6, 3, 2, 1, 6, -6, 0, 0, 9, -2, -18, -1, -6, -6, -8, 0, -6, 0, 0, -3, 19, -9, -9, 0, -6, 18, 0, 0, 0, 6, 12, 0, 0, 8, -27, 6, -12, 6, 1, 0, 36, 0, 12, 3, -11, -19, 18, 0, -12, 9, 0, 2, 24, 6, 0, 0, -7, 0, 12, 1, 54, 0, 15, 0, 0, -12, -6, 6, 7, 0, -57, 0, 0, 27, 9, -6, 9, 12, 0, 0, -36, -1, 18, 0, 0, -36, 18, 0, 0, -12, -48, 0, 12, 11, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, -9, 40, -117, 169], 'euler17': [1, 6, 29, 102, 289], 'euler19': [1, 8, 19, 0, 0], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, 0, 23, 0, 529], 'euler29': [1, 6, 7, 174, 841], 'euler3': [1, 3, 3, 0, 0], 'euler31': [1, 0, -59, 0, 961], 'euler37': [1, 0, -47, 0, 1369], 'euler41': [1, 12, 103, 492, 1681], 'euler43': [1, -1, -42, -43, 1849], 'euler47': [1, -12, 95, -564, 2209], 'euler5': [1, -6, 17, -30, 25], 'euler53': [1, 12, 91, 636, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 7, -12, 427, 3721], 'euler67': [1, -15, 142, -1005, 4489], 'euler7': [1, -2, 15, -14, 49], 'euler71': [1, 6, -35, 426, 5041], 'euler73': [1, -7, -24, -511, 5329], 'euler79': [1, -9, 106, -711, 6241], 'euler83': [1, 0, -58, 0, 6889], 'euler89': [1, 0, -89, 0, 7921], 'euler97': [1, -12, 145, -1164, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, 3, 3, 0, 0], [1, -6, 17, -30, 25], [1, -2, 15, -14, 49], [1, 0, -10, 0, 121], [1, -9, 40, -117, 169], [1, 6, 29, 102, 289], [1, 8, 19, 0, 0], [1, 0, 23, 0, 529], [1, 6, 7, 174, 841], [1, 0, -59, 0, 961], [1, 0, -47, 0, 1369], [1, 12, 103, 492, 1681], [1, -1, -42, -43, 1849], [1, -12, 95, -564, 2209], [1, 12, 91, 636, 2809], [1, 0, -59, 0, 3481], [1, 7, -12, 427, 3721], [1, -15, 142, -1005, 4489], [1, 6, -35, 426, 5041], [1, -7, -24, -511, 5329], [1, -9, 106, -711, 6241], [1, 0, -58, 0, 6889], [1, 0, -89, 0, 7921], [1, -12, 145, -1164, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/h/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-c1e2-0-2', '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': 1347171742466172929, 'z1': {'__RealLiteral__': 0, 'data': '1.54712672288837368532835762924', 'prec': 103}}
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{'Lhash': '1961216118898580441235073064167,2479568866242782888235996860280', 'Lhash_array': ['1961216118898580441235073064167', '2479568866242782888235996860280'], 'label': '4-114e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/h/b'}