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lfunc_lfunctions • Show schema
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{'Lhash': '595087992295768231133879942266,1627402209781895199041251805865', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -22, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 150.34712629336104, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 2], [1], [1], [1, 22, 219, 1078, 2401], [1, 0, -224, 0, 14641], [1, -14, 387, -2366, 28561], [1, 0, -416, 0, 83521], [1, -58, 1563, -20938, 130321], [1, 0, 400, 0, 279841], [1, 0, 496, 0, 707281], [1, -58, 2763, -55738, 923521], [1, 112, 5874, 153328, 1874161], [1, 0, 1246, 0, 2825761], [1, 10, 3723, 18490, 3418801], [1, 0, -368, 0, 4879681], [1, 0, -1010, 0, 7890481], [1, 0, -6080, 0, 12117361], [1, 110, 10467, 409310, 13845841], [1, -74, 10347, -332186, 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'10.93750925732094331592233578921677'], 'prelabel': '4-450e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5016584493941383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 1959430282647309326, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46944165228859422603865026333', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.28379398036722079984577032314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79452488949178472009365443193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 150.34712629336104, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, -22, 0, 0, 0, 0, 0, 14, 0, 0, 4, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 58, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 265, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, -110, 0, 0, -8, 0, 0, 74, 0, 0, 0, 0, 0, 32, 0, 0, -116, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, -82, 0, 0, 0], 'euler11': [1, 0, -224, 0, 14641], 'euler13': [1, -14, 387, -2366, 28561], 'euler17': [1, 0, -416, 0, 83521], 'euler19': [1, -58, 1563, -20938, 130321], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 0, 400, 0, 279841], 'euler29': [1, 0, 496, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -58, 2763, -55738, 923521], 'euler37': [1, 112, 5874, 153328, 1874161], 'euler41': [1, 0, 1246, 0, 2825761], 'euler43': [1, 10, 3723, 18490, 3418801], 'euler47': [1, 0, -368, 0, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -1010, 0, 7890481], 'euler59': [1, 0, -6080, 0, 12117361], 'euler61': [1, 110, 10467, 409310, 13845841], 'euler67': [1, -74, 10347, -332186, 20151121], 'euler7': [1, 22, 219, 1078, 2401], 'euler71': [1, 0, -8930, 0, 25411681], 'euler73': [1, -32, 10914, -170528, 28398241], 'euler79': [1, -208, 23298, -1298128, 38950081], 'euler83': [1, 0, -12896, 0, 47458321], 'euler89': [1, 0, 2590, 0, 62742241], 'euler97': [1, 82, 20499, 771538, 88529281], 'euler_factors': [[1, 0, 2, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 22, 219, 1078, 2401], [1, 0, -224, 0, 14641], [1, -14, 387, -2366, 28561], [1, 0, -416, 0, 83521], [1, -58, 1563, -20938, 130321], [1, 0, 400, 0, 279841], [1, 0, 496, 0, 707281], [1, -58, 2763, -55738, 923521], [1, 112, 5874, 153328, 1874161], [1, 0, 1246, 0, 2825761], [1, 10, 3723, 18490, 3418801], [1, 0, -368, 0, 4879681], [1, 0, -1010, 0, 7890481], [1, 0, -6080, 0, 12117361], [1, 110, 10467, 409310, 13845841], [1, -74, 10347, -332186, 20151121], [1, 0, -8930, 0, 25411681], [1, -32, 10914, -170528, 28398241], [1, -208, 23298, -1298128, 38950081], [1, 0, -12896, 0, 47458321], [1, 0, 2590, 0, 62742241], [1, 82, 20499, 771538, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/3/d/a'], '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': '4-450e2-1.1-c2e2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-450e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5016584493941383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1959430282647309326, 'z1': {'__RealLiteral__': 0, 'data': '0.46944165228859422603865026333', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '595087992295768231133879942266,1627402209781895199041251805865', 'Lhash_array': ['595087992295768231133879942266', '1627402209781895199041251805865'], 'factors': ['2-450-3.2-c2-0-1', '2-450-3.2-c2-0-9'], 'label': '4-450e2-1.1-c2e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/3/d/a'}