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lfunc_lfunctions • Show schema
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{'Lhash': '97374527730753228470195754479,1489154104134728740204214425092', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9136.127898623889, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5, 25]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1', 'coefficient_field': '1.1.1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 5, 25], [1, 2, -339, 686, 117649], [1, 30, -431, 39930, 1771561], [1, -4, -2181, -8788, 4826809], [1, -180, 17926, -884340, 24137569], [1, 56, 14502, 384104, 47045881], [1, 120, 2233, 1460040, 148035889], [1, 210, 19711, 5121690, 594823321], [1, -4, -29775, -119164, 887503681], [1, -400, 141306, -20261200, 2565726409], [1, 240, -11321, 16541040, 4750104241], [1, -136, -61011, -10812952, 6321363049], [1, -120, -89423, -12458760, 10779215329], [1, 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{'__RealLiteral__': 0, 'data': '1.37232588779270444710161745246', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9136.127898623889, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, -2, 0, 0, 0, -30, 0, 4, 0, 0, 0, 180, 0, -56, 0, 0, 0, -120, 0, 0, 0, 0, 0, -210, 0, 4, 0, 0, 0, 10, 0, 400, 0, 0, 0, -240, 0, 136, 0, 0, 0, 120, 0, 343, 0, 0, 0, -60, 0, 150, 0, 0, 0, 450, 0, 166, 0, 0, 0, -20, 0, -908, 0, 0, 0, -2040, 0, -500, 0, 0, 0, 60, 0, 916, 0, 0, 0, 1140, 0, -900, 0, 0, 0, -840, 0, -8, 0, 0, 0, 280, 0, -1538, 0, 0, 0], 'euler11': [1, 30, -431, 39930, 1771561], 'euler13': [1, -4, -2181, -8788, 4826809], 'euler17': [1, -180, 17926, -884340, 24137569], 'euler19': [1, 56, 14502, 384104, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 120, 2233, 1460040, 148035889], 'euler29': [1, 210, 19711, 5121690, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, -29775, -119164, 887503681], 'euler37': [1, -400, 141306, -20261200, 2565726409], 'euler41': [1, 240, -11321, 16541040, 4750104241], 'euler43': [1, -136, -61011, -10812952, 6321363049], 'euler47': [1, -120, -89423, -12458760, 10779215329], 'euler5': [1, 5, 25, 0, 0], 'euler53': [1, 60, 298654, 8932620, 22164361129], 'euler59': [1, -450, -2879, -92420550, 42180533641], 'euler61': [1, -166, -199425, -37678846, 51520374361], 'euler67': [1, 908, 523701, 273092804, 90458382169], 'euler7': [1, 2, -339, 686, 117649], 'euler71': [1, 2040, 1756222, 730138440, 128100283921], 'euler73': [1, 500, 840534, 194508500, 151334226289], 'euler79': [1, -916, 346017, -451623724, 243087455521], 'euler83': [1, -1140, 727813, -651837180, 326940373369], 'euler89': [1, 840, 1586338, 592173960, 496981290961], 'euler97': [1, 1538, 1452771, 1403691074, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 5, 25, 0, 0], [1, 2, -339, 686, 117649], [1, 30, -431, 39930, 1771561], [1, -4, -2181, -8788, 4826809], [1, -180, 17926, -884340, 24137569], [1, 56, 14502, 384104, 47045881], [1, 120, 2233, 1460040, 148035889], [1, 210, 19711, 5121690, 594823321], [1, -4, -29775, -119164, 887503681], [1, -400, 141306, -20261200, 2565726409], [1, 240, -11321, 16541040, 4750104241], [1, -136, -61011, -10812952, 6321363049], [1, -120, -89423, -12458760, 10779215329], [1, 60, 298654, 8932620, 22164361129], [1, -450, -2879, -92420550, 42180533641], [1, -166, -199425, -37678846, 51520374361], [1, 908, 523701, 273092804, 90458382169], [1, 2040, 1756222, 730138440, 128100283921], [1, 500, 840534, 194508500, 151334226289], [1, -916, 346017, -451623724, 243087455521], [1, -1140, 727813, -651837180, 326940373369], [1, 840, 1586338, 592173960, 496981290961], [1, 1538, 1452771, 1403691074, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/4/i/c'], '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': '4-1620e2-1.1-c3e2-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-1620e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.77666068805192, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1978372657772219838, 'z1': {'__RealLiteral__': 0, 'data': '0.07681495809115050831755858804', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '97374527730753228470195754479,1489154104134728740204214425092', 'Lhash_array': ['97374527730753228470195754479', '1489154104134728740204214425092'], 'label': '4-1620e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/4/i/c'}