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lfunc_lfunctions • Show schema
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{'Lhash': '397730889173386631328567085037,1605875951996211998284095013260', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': -5, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.66888685406058, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [31, [1, 4, 31]]], 'bad_primes': [3, 31], 'central_character': '837.1', 'coefficient_field': '1.1.1.1', 'conductor': 700569, 'conductor_radical': 93, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1], [1, 0, -5, 0, 25], [1, 5, 18, 35, 49], [1, 0, -11, 0, 121], [1, 5, 12, 65, 169], [1, 0, -17, 0, 289], [1, -7, 30, -133, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 4, 31], [1, 11, 84, 407, 1369], [1, 0, -41, 0, 1681], [1, -13, 126, -559, 1849], [1, 0, 94, 0, 2209], [1, 0, -53, 0, 2809], [1, 0, -59, 0, 3481], [1, 26, 291, 1586, 3721], [1, 11, 54, 737, 4489], [1, 0, -71, 0, 5041], [1, -10, 27, -730, 5329], [1, -13, 90, -1027, 6241], [1, 0, -83, 0, 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2.5852424739627753, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1198852006922864223, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31375434926767570178897708878', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.26681275716438589695621080791', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.57154021486041601091222152967', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.66888685406058, 'bad_primes': [3, 31], 'central_character': '1.1', 'conductor': 700569, 'conductor_radical': 93, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, -5, 0, 0, 0, 0, 0, -5, 0, 0, 12, 0, 0, 7, 0, 0, 0, 0, 0, 5, 0, 0, 20, 0, 0, -4, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 7, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, -32, 0, 0, -11, 0, 0, 0, 0, 0, 10, 0, 0, -28, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 28, 0, 0, -20], 'euler11': [1, 0, -11, 0, 121], 'euler13': [1, 5, 12, 65, 169], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, -7, 30, -133, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, 31, 0, 0], 'euler37': [1, 11, 84, 407, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, -13, 126, -559, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, 0, -53, 0, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 26, 291, 1586, 3721], 'euler67': [1, 11, 54, 737, 4489], 'euler7': [1, 5, 18, 35, 49], 'euler71': [1, 0, -71, 0, 5041], 'euler73': [1, -10, 27, -730, 5329], 'euler79': [1, -13, 90, -1027, 6241], 'euler83': [1, 0, -83, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, -28, 390, -2716, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 0, 0, 0], [1, 0, -5, 0, 25], [1, 5, 18, 35, 49], [1, 0, -11, 0, 121], [1, 5, 12, 65, 169], [1, 0, -17, 0, 289], [1, -7, 30, -133, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 4, 31, 0, 0], [1, 11, 84, 407, 1369], [1, 0, -41, 0, 1681], [1, -13, 126, -559, 1849], [1, 0, 94, 0, 2209], [1, 0, -53, 0, 2809], [1, 0, -59, 0, 3481], [1, 26, 291, 1586, 3721], [1, 11, 54, 737, 4489], [1, 0, -71, 0, 5041], [1, -10, 27, -730, 5329], [1, -13, 90, -1027, 6241], [1, 0, -83, 0, 6889], [1, 0, 178, 0, 7921], [1, -28, 390, -2716, 9409]], 'index': 1, 'instance_types': ['ECNF', 'ECNF', 'CMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/77841.1/CMa', 'EllipticCurve/2.0.3.1/77841.3/CMa', 'ModularForm/GL2/Q/holomorphic/837/2/h/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-837e2-1.1-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': '4-837e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5852424739627753, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1198852006922864223, 'z1': {'__RealLiteral__': 0, 'data': '0.31375434926767570178897708878', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15720862
{'Lhash': '397730889173386631328567085037,1605875951996211998284095013260', 'Lhash_array': ['397730889173386631328567085037', '1605875951996211998284095013260'], 'label': '4-837e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/837/2/h/a'}
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id: 9800344
{'Lhash': '_397730889173386631328567085037', 'Lhash_array': ['_397730889173386631328567085037'], 'label': '4-837e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/77841.3/CMa'}
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id: 9799742
{'Lhash': '_397730889173386631328567085037', 'Lhash_array': ['_397730889173386631328567085037'], 'label': '4-837e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/77841.1/CMa'}