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lfunc_lfunctions • Show schema
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{'Lhash': '1179581330806735136551052237891,1463092746984658074222685042527', 'a10': -1, 'a2': -1, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': -1, 'a7': 0, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 137.78085756426492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1, -1, 1]], [5, [1, -1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1470.1', 'coefficient_field': '1.1.1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1, 1, 1], [1, -1, 1], [1, -1, 1], [1], [1, -4, 5, -44, 121], [1, -4, 30, -52, 169], [1, -2, -13, -34, 289], [1, -4, -3, -76, 361], [1, -8, 41, -184, 529], [1, 4, 62, 116, 841], [1, 0, -31, 0, 961], [1, 6, -1, 222, 1369], [1, -12, 118, -492, 1681], [1, 8, 102, 344, 1849], [1, 0, -47, 0, 2209], [1, -10, 47, -530, 2809], [1, -12, 85, -708, 3481], [1, -14, 135, -854, 3721], [1, -12, 77, -804, 4489], [1, 16, 206, 1136, 5041], [1, -10, 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False, 'rational': True, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 273393708851931401, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.930525596402006859466527614738', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.15417666880861415904274916006', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.98312152670810907756760744300', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 137.78085756426492, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, -1, 1, 0, 1, -1, 0, 1, 0, -1, 4, 0, 4, 0, 1, -1, 2, 0, 4, 0, 0, -4, 8, 1, 0, -4, -1, 0, -4, -1, 0, 0, 4, -2, 0, 0, -6, -4, 4, 1, 12, 0, -8, 0, 0, -8, 0, -1, 0, 0, 2, 0, 10, 1, 4, 0, 4, 4, 12, 0, 14, 0, 0, 1, 4, -4, 12, 0, 8, 0, -16, 0, 10, 6, 0, 0, 0, -4, -16, -1, -1, -12, 24, 0, 2, 8, -4, 4, 10, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0], 'euler11': [1, -4, 5, -44, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -2, -13, -34, 289], 'euler19': [1, -4, -3, -76, 361], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, -8, 41, -184, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, 0, -31, 0, 961], 'euler37': [1, 6, -1, 222, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, -10, 47, -530, 2809], 'euler59': [1, -12, 85, -708, 3481], 'euler61': [1, -14, 135, -854, 3721], 'euler67': [1, -12, 77, -804, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, -10, 27, -730, 5329], 'euler79': [1, 16, 177, 1264, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, -10, 11, -890, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, -1, 1, 0, 0], [1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, -4, 5, -44, 121], [1, -4, 30, -52, 169], [1, -2, -13, -34, 289], [1, -4, -3, -76, 361], [1, -8, 41, -184, 529], [1, 4, 62, 116, 841], [1, 0, -31, 0, 961], [1, 6, -1, 222, 1369], [1, -12, 118, -492, 1681], [1, 8, 102, 344, 1849], [1, 0, -47, 0, 2209], [1, -10, 47, -530, 2809], [1, -12, 85, -708, 3481], [1, -14, 135, -854, 3721], [1, -12, 77, -804, 4489], [1, 16, 206, 1136, 5041], [1, -10, 27, -730, 5329], [1, 16, 177, 1264, 6241], [1, -24, 310, -1992, 6889], [1, -10, 11, -890, 7921], [1, 4, 198, 388, 9409]], 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1470/2/i/j'], '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': '4-1470e2-1.1-c1e2-0-24', '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': '4-1470e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 273393708851931401, 'z1': {'__RealLiteral__': 0, 'data': '0.930525596402006859466527614738', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1179581330806735136551052237891,1463092746984658074222685042527', 'Lhash_array': ['1179581330806735136551052237891', '1463092746984658074222685042527'], 'label': '4-1470e2-1.1-c1e2-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/2/i/j'}