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lfunc_lfunctions • Show schema
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{'Lhash': '869689407702274143005466537318,1622473820388829259362100954321', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5193.362470102899, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '9025.1', 'coefficient_field': '1.1.1.1', 'conductor': 81450625, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, -4, 10, -12, 9], [1], [1, -2, 10, -14, 49], [1, -6, 26, -66, 121], [1, -3, 17, -39, 169], [1, -1, 33, -17, 289], [1], [1, 0, 26, 0, 529], [1, 3, 29, 87, 841], [1, -12, 98, -372, 961], [1, -11, 93, -407, 1369], [1, -3, 53, -123, 1681], [1, 8, 82, 344, 1849], [1, 14, 138, 658, 2209], [1, -11, 105, -583, 2809], [1, 2, 114, 118, 3481], [1, -13, 153, -793, 3721], [1, -8, 130, -536, 4489], [1, -2, 138, -142, 5041], [1, -9, 65, -657, 5329], [1, 4, 162, 316, 6241], 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'6.11765142509953107341377678579720', '6.17022431635392131465161080426736', '6.71736474138147691284895078985586', '6.89461646952033672066651631671934', '7.27023676897772042536200799631576', '7.84567053183210594336980460417337', '8.006320665930130547081588906133252'], 'prelabel': '4-95e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1993131179966894183, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68606397342114157715312823560', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.27990616664932516970826645625', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.65689531816417491680861591721', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5193.362470102899, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 81450625, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 0, 4, 1, 0, 0, 2, 0, 6, 0, 6, 4, 3, 0, 0, -3, 1, 0, 0, 0, 8, 0, 0, 0, 0, 0, -4, 2, -3, 0, 12, 0, 24, 0, 0, 6, 11, 0, 12, 0, 3, 0, -8, 6, 0, 0, -14, -12, -6, 0, 4, 3, 11, 0, 0, 0, 0, 0, -2, 0, 13, 0, 12, -7, 0, 0, 8, 1, 0, 0, 2, 0, 9, 0, 0, 0, 12, 0, -4, 0, -37, 0, 6, 8, 0, 0, -12, 0, -1, 0, 6, 0, 48, 0, 0, 0, -11, 0, 36, 0], 'euler11': [1, -6, 26, -66, 121], 'euler13': [1, -3, 17, -39, 169], 'euler17': [1, -1, 33, -17, 289], 'euler19': [1, 0, 0, 0, 0], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, 26, 0, 529], 'euler29': [1, 3, 29, 87, 841], 'euler3': [1, -4, 10, -12, 9], 'euler31': [1, -12, 98, -372, 961], 'euler37': [1, -11, 93, -407, 1369], 'euler41': [1, -3, 53, -123, 1681], 'euler43': [1, 8, 82, 344, 1849], 'euler47': [1, 14, 138, 658, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -11, 105, -583, 2809], 'euler59': [1, 2, 114, 118, 3481], 'euler61': [1, -13, 153, -793, 3721], 'euler67': [1, -8, 130, -536, 4489], 'euler7': [1, -2, 10, -14, 49], 'euler71': [1, -2, 138, -142, 5041], 'euler73': [1, -9, 65, -657, 5329], 'euler79': [1, 4, 162, 316, 6241], 'euler83': [1, -6, 130, -498, 6889], 'euler89': [1, 1, 117, 89, 7921], 'euler97': [1, 11, 193, 1067, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, -4, 10, -12, 9], [1, 0, 0, 0, 0], [1, -2, 10, -14, 49], [1, -6, 26, -66, 121], [1, -3, 17, -39, 169], [1, -1, 33, -17, 289], [1, 0, 0, 0, 0], [1, 0, 26, 0, 529], [1, 3, 29, 87, 841], [1, -12, 98, -372, 961], [1, -11, 93, -407, 1369], [1, -3, 53, -123, 1681], [1, 8, 82, 344, 1849], [1, 14, 138, 658, 2209], [1, -11, 105, -583, 2809], [1, 2, 114, 118, 3481], [1, -13, 153, -793, 3721], [1, -8, 130, -536, 4489], [1, -2, 138, -142, 5041], [1, -9, 65, -657, 5329], [1, 4, 162, 316, 6241], [1, -6, 130, -498, 6889], [1, 1, 117, 89, 7921], [1, 11, 193, 1067, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9025/2/a/r'], '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': '4-95e4-1.1-c1e2-0-6', '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': '4-95e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1993131179966894183, 'z1': {'__RealLiteral__': 0, 'data': '0.68606397342114157715312823560', 'prec': 103}}
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{'Lhash': '869689407702274143005466537318,1622473820388829259362100954321', 'Lhash_array': ['869689407702274143005466537318', '1622473820388829259362100954321'], 'label': '4-95e4-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9025/2/a/r'}