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lfunc_lfunctions • Show schema
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{'Lhash': '605908569694908813526471906560,1297214683501433174637446452223', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, '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, 2, 3, 4, 4], [1], [1, 0, 2, 0, 25], [1, 0, 6, 0, 49], [1, 4, 26, 44, 121], [1], [1, 4, 6, 68, 289], [1, 0, 30, 0, 361], [1, -8, 62, -184, 529], [1, 4, 62, 116, 841], [1, -8, 70, -248, 961], [1, -4, 46, -148, 1369], [1, -16, 138, -656, 1681], [1, -8, 70, -344, 1849], [1, 12, 98, 564, 2209], [1, -4, 110, -212, 2809], [1, -4, 90, -236, 3481], [1, -4, -2, -244, 3721], [1, 8, 142, 536, 4489], [1, -4, 146, -284, 5041], [1, 12, 150, 876, 5329], [1, 0, 30, 0, 6241], [1, 4, 138, 332, 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3.4850030340642104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 170556409705346138, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47797758277069428743367883195', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.02332194949292890214877486170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.94348077187133837272790771925', '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, -2, 0, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 8, 8, 0, -2, 0, 0, 0, -4, 0, 8, 2, 0, 8, 0, 0, 4, 0, 0, 0, 16, 0, 8, -4, 0, -16, -12, 0, -6, 4, 0, 0, 4, 0, 0, 0, 0, 8, 4, 0, 4, -16, 0, -11, 0, 0, -8, -4, 0, 0, 4, 0, -12, -8, 0, 0, 0, 0, 0, 0, 0, -32, -4, 0, 0, -16, 0, 0, 24, 0, 0, 8, 0, 24, 0, 0, 4, 12, 0, -2], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 4, 6, 68, 289], 'euler19': [1, 0, 30, 0, 361], 'euler2': [1, 2, 3, 4, 4], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -8, 70, -248, 961], 'euler37': [1, -4, 46, -148, 1369], 'euler41': [1, -16, 138, -656, 1681], 'euler43': [1, -8, 70, -344, 1849], 'euler47': [1, 12, 98, 564, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, -4, 110, -212, 2809], 'euler59': [1, -4, 90, -236, 3481], 'euler61': [1, -4, -2, -244, 3721], 'euler67': [1, 8, 142, 536, 4489], 'euler7': [1, 0, 6, 0, 49], 'euler71': [1, -4, 146, -284, 5041], 'euler73': [1, 12, 150, 876, 5329], 'euler79': [1, 0, 30, 0, 6241], 'euler83': [1, 4, 138, 332, 6889], 'euler89': [1, -24, 314, -2136, 7921], 'euler97': [1, -4, 166, -388, 9409], 'euler_factors': [[1, 2, 3, 4, 4], [1, 0, 0, 0, 0], [1, 0, 2, 0, 25], [1, 0, 6, 0, 49], [1, 4, 26, 44, 121], [1, 0, 0, 0, 0], [1, 4, 6, 68, 289], [1, 0, 30, 0, 361], [1, -8, 62, -184, 529], [1, 4, 62, 116, 841], [1, -8, 70, -248, 961], [1, -4, 46, -148, 1369], [1, -16, 138, -656, 1681], [1, -8, 70, -344, 1849], [1, 12, 98, 564, 2209], [1, -4, 110, -212, 2809], [1, -4, 90, -236, 3481], [1, -4, -2, -244, 3721], [1, 8, 142, 536, 4489], [1, -4, 146, -284, 5041], [1, 12, 150, 876, 5329], [1, 0, 30, 0, 6241], [1, 4, 138, 332, 6889], [1, -24, 314, -2136, 7921], [1, -4, 166, -388, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/a/f'], '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-c1e2-0-1', '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': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 170556409705346138, 'z1': {'__RealLiteral__': 0, 'data': '0.47797758277069428743367883195', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '605908569694908813526471906560,1297214683501433174637446452223', 'Lhash_array': ['605908569694908813526471906560', '1297214683501433174637446452223'], 'label': '4-39e4-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/a/f'}