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lfunc_lfunctions • Show schema
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{'Lhash': '1761214871106158261918469660025,2734108352902042413856832650120', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.5070039818273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1], [1, 0, 10, 0, 25], [1, 4, 18, 28, 49], [1, 0, 10, 0, 121], [1], [1, 0, -14, 0, 289], [1, 4, 42, 76, 361], [1, 0, -2, 0, 529], [1, 0, 10, 0, 841], [1, 4, 66, 124, 961], [1, 4, 78, 148, 1369], [1, 0, 34, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -14, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 106, 0, 3481], [1, 20, 222, 1220, 3721], [1, 28, 330, 1876, 4489], [1, 0, 130, 0, 5041], [1, -20, 246, -1460, 5329], [1, 8, 174, 632, 6241], [1, 0, 58, 0, 6889], [1, 0, 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'8.019660782712146266296032753363226', '8.717394945817194771911214024179399', '8.939932819757655947582294898696435', '9.258486323625683228056617943448421'], 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, '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': 429928283265998105, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38935355750951163595138786834', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15683119024263477820965343635', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61946421446322524837121717635', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.5070039818273, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 7, 0, 0, -28, 0, 0, 0, 0, 0, 20, 0, 0, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 10], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 0, -14, 0, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, 10, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, 66, 124, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, 34, 0, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 0, -14, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, 106, 0, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 28, 330, 1876, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, 0, 130, 0, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, 0, 58, 0, 6889], 'euler89': [1, 0, 130, 0, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, 4, 18, 28, 49], [1, 0, 10, 0, 121], [1, 0, 0, 0, 0], [1, 0, -14, 0, 289], [1, 4, 42, 76, 361], [1, 0, -2, 0, 529], [1, 0, 10, 0, 841], [1, 4, 66, 124, 961], [1, 4, 78, 148, 1369], [1, 0, 34, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -14, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 106, 0, 3481], [1, 20, 222, 1220, 3721], [1, 28, 330, 1876, 4489], [1, 0, 130, 0, 5041], [1, -20, 246, -1460, 5329], [1, 8, 174, 632, 6241], [1, 0, 58, 0, 6889], [1, 0, 130, 0, 7921], [1, -20, 294, -1940, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/a/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': '4-39e4-1.1-c1e2-0-10', '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': 2, 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 429928283265998105, 'z1': {'__RealLiteral__': 0, 'data': '1.38935355750951163595138786834', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1761214871106158261918469660025,2734108352902042413856832650120', 'Lhash_array': ['1761214871106158261918469660025', '2734108352902042413856832650120'], 'label': '4-39e4-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/a/j'}