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lfunc_lfunctions • Show schema
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{'Lhash': '1124365781372090397951432853221,1541539875003221657748191052860', 'a10': 0, 'a2': 2, 'a3': 2, 'a4': -1, 'a5': 0, 'a6': 4, 'a7': 0, 'a8': -8, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 224.1592981509412, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': '1.1.1.1', 'conductor': 3515625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, -2, 5, -4, 4], [1, -2, 1], [1], [1, 0, -6, 0, 49], [1, -2, 18, -22, 121], [1, -9, 45, -117, 169], [1, -1, 23, -17, 289], [1, 2, 34, 38, 361], [1, 0, 26, 0, 529], [1, -11, 87, -319, 841], [1, -10, 82, -310, 961], [1, -5, 49, -185, 1369], [1, 5, 87, 205, 1681], [1, -2, 42, -86, 1849], [1, 6, 98, 282, 2209], [1, -5, 111, -265, 2809], [1, 8, 134, 472, 3481], [1, -1, 121, -61, 3721], [1, -6, 138, -402, 4489], [1, 6, 146, 426, 5041], [1, 5, 121, 365, 5329], [1, 0, 158, 0, 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'9.058052298791271090132899876654720'], 'prelabel': '4-1875e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1486920194659764480, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.886968208092717484353992052130', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.21606054122932682573547065653', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.32725131854991977661984969121', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 224.1592981509412, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 3515625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 2, 2, -1, 0, 4, 0, -8, 3, 0, 2, -2, 9, 0, 0, -7, 1, 6, -2, 0, 0, 4, 0, -16, 0, 18, 4, 0, 11, 0, 10, 14, 4, 2, 0, -3, 5, -4, 18, 0, -5, 0, 2, -2, 0, 0, -6, -14, 6, 0, 2, -9, 5, 8, 0, 0, -4, 22, -8, 0, 1, 20, 0, 35, 0, 8, 6, -1, 0, 0, -6, -24, -5, 10, 0, 2, 0, 36, 0, 0, 5, -10, 16, 0, 0, 4, 22, -16, 13, 0, 0, 0, 20, -12, 0, 28, 11, 12, 6, 0], 'euler11': [1, -2, 18, -22, 121], 'euler13': [1, -9, 45, -117, 169], 'euler17': [1, -1, 23, -17, 289], 'euler19': [1, 2, 34, 38, 361], 'euler2': [1, -2, 5, -4, 4], 'euler23': [1, 0, 26, 0, 529], 'euler29': [1, -11, 87, -319, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, -10, 82, -310, 961], 'euler37': [1, -5, 49, -185, 1369], 'euler41': [1, 5, 87, 205, 1681], 'euler43': [1, -2, 42, -86, 1849], 'euler47': [1, 6, 98, 282, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -5, 111, -265, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, -1, 121, -61, 3721], 'euler67': [1, -6, 138, -402, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 6, 146, 426, 5041], 'euler73': [1, 5, 121, 365, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, -16, 210, -1328, 6889], 'euler89': [1, -13, 219, -1157, 7921], 'euler97': [1, -11, 213, -1067, 9409], 'euler_factors': [[1, -2, 5, -4, 4], [1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -6, 0, 49], [1, -2, 18, -22, 121], [1, -9, 45, -117, 169], [1, -1, 23, -17, 289], [1, 2, 34, 38, 361], [1, 0, 26, 0, 529], [1, -11, 87, -319, 841], [1, -10, 82, -310, 961], [1, -5, 49, -185, 1369], [1, 5, 87, 205, 1681], [1, -2, 42, -86, 1849], [1, 6, 98, 282, 2209], [1, -5, 111, -265, 2809], [1, 8, 134, 472, 3481], [1, -1, 121, -61, 3721], [1, -6, 138, -402, 4489], [1, 6, 146, 426, 5041], [1, 5, 121, 365, 5329], [1, 0, 158, 0, 6241], [1, -16, 210, -1328, 6889], [1, -13, 219, -1157, 7921], [1, -11, 213, -1067, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/d'], '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': '4-1875e2-1.1-c1e2-0-0', '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': '4-1875e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1486920194659764480, 'z1': {'__RealLiteral__': 0, 'data': '0.886968208092717484353992052130', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1124365781372090397951432853221,1541539875003221657748191052860', 'Lhash_array': ['1124365781372090397951432853221', '1541539875003221657748191052860'], 'label': '4-1875e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/d'}