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lfunc_lfunctions • Show schema
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{'Lhash': '633390608143892026521990669208,2077856330344711907874297866708', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -2, '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, 2, 99, 98, 2401], [1, 0, -224, 0, 14641], [1, -34, 627, -5746, 28561], [1, 0, 304, 0, 83521], [1, 62, 1683, 22382, 130321], [1, 0, -1040, 0, 279841], [1, 0, -224, 0, 707281], [1, 62, 2883, 59582, 923521], [1, 32, 2994, 43808, 1874161], [1, 0, -3074, 0, 2825761], [1, -130, 7923, -240370, 3418801], [1, 0, -3968, 0, 4879681], [1, 0, -5330, 0, 7890481], [1, 0, 6160, 0, 12117361], [1, 110, 10467, 409310, 13845841], [1, 146, 14307, 655394, 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'9.105631289517625272778830482989415', '9.623703901323081708092429389040889', '10.52058960513546600597722482348034', '10.78278328174507392435443954746864', '10.88841961777572520168006882496315'], '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': 39396914710336424, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49965708849887783610113584457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.63913962567493917656566909809', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.16285690686954947771582296698', '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, -2, 0, 0, 0, 0, 0, 34, 0, 0, 4, 0, 0, -62, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -62, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 130, 0, 0, 0, 0, 0, -95, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 0, -110, 0, 0, -8, 0, 0, -146, 0, 0, 0, 0, 0, 112, 0, 0, 124, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 178, 0, 0, 0], 'euler11': [1, 0, -224, 0, 14641], 'euler13': [1, -34, 627, -5746, 28561], 'euler17': [1, 0, 304, 0, 83521], 'euler19': [1, 62, 1683, 22382, 130321], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 0, -1040, 0, 279841], 'euler29': [1, 0, -224, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 62, 2883, 59582, 923521], 'euler37': [1, 32, 2994, 43808, 1874161], 'euler41': [1, 0, -3074, 0, 2825761], 'euler43': [1, -130, 7923, -240370, 3418801], 'euler47': [1, 0, -3968, 0, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -5330, 0, 7890481], 'euler59': [1, 0, 6160, 0, 12117361], 'euler61': [1, 110, 10467, 409310, 13845841], 'euler67': [1, 146, 14307, 655394, 20151121], 'euler7': [1, 2, 99, 98, 2401], 'euler71': [1, 0, 4030, 0, 25411681], 'euler73': [1, -112, 13794, -596848, 28398241], 'euler79': [1, -208, 23298, -1298128, 38950081], 'euler83': [1, 0, -13616, 0, 47458321], 'euler89': [1, 0, -14690, 0, 62742241], 'euler97': [1, -178, 26739, -1674802, 88529281], 'euler_factors': [[1, 0, 2, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, 99, 98, 2401], [1, 0, -224, 0, 14641], [1, -34, 627, -5746, 28561], [1, 0, 304, 0, 83521], [1, 62, 1683, 22382, 130321], [1, 0, -1040, 0, 279841], [1, 0, -224, 0, 707281], [1, 62, 2883, 59582, 923521], [1, 32, 2994, 43808, 1874161], [1, 0, -3074, 0, 2825761], [1, -130, 7923, -240370, 3418801], [1, 0, -3968, 0, 4879681], [1, 0, -5330, 0, 7890481], [1, 0, 6160, 0, 12117361], [1, 110, 10467, 409310, 13845841], [1, 146, 14307, 655394, 20151121], [1, 0, 4030, 0, 25411681], [1, -112, 13794, -596848, 28398241], [1, -208, 23298, -1298128, 38950081], [1, 0, -13616, 0, 47458321], [1, 0, -14690, 0, 62742241], [1, -178, 26739, -1674802, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/3/d/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': '4-450e2-1.1-c2e2-0-5', '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': 39396914710336424, 'z1': {'__RealLiteral__': 0, 'data': '0.49965708849887783610113584457', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '633390608143892026521990669208,2077856330344711907874297866708', 'Lhash_array': ['633390608143892026521990669208', '2077856330344711907874297866708'], 'factors': ['2-450-3.2-c2-0-2', '2-450-3.2-c2-0-11'], 'label': '4-450e2-1.1-c2e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/3/d/c'}