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lfunc_lfunctions • Show schema
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{'Lhash': '934986449190897156858022516793,1771319443133792134283909239576', 'a10': 0, 'a2': 3, 'a3': 3, 'a4': 4, 'a5': 0, 'a6': 9, 'a7': 4, 'a8': 3, 'a9': 2, '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, -3, 5, -6, 4], [1, -3, 7, -9, 9], [1], [1, -4, 13, -28, 49], [1, 7, 33, 77, 121], [1, -10, 51, -130, 169], [1, -12, 70, -204, 289], [1], [1, -1, 45, -23, 529], [1, 3, 49, 87, 841], [1, 15, 107, 465, 961], [1, -3, 65, -111, 1369], [1, 0, -43, 0, 1681], [1, 1, 75, 43, 1849], [1, -16, 153, -752, 2209], [1, -9, 125, -477, 2809], [1, -11, 117, -649, 3481], [1, 6, 131, 366, 3721], [1, -4, 93, -268, 4489], [1, 12, 173, 852, 5041], [1, -2, 147, -146, 5329], [1, 16, 222, 1264, 6241], 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'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': 2248495162894077034, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73757425667811069209212819860', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.39732465934610180722098323874', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.68113756773508305348519639633', '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, 3, 3, 4, 0, 9, 4, 3, 2, 0, -7, 12, 10, 12, 0, 3, 12, 6, 0, 0, 12, -21, 1, 9, 0, 30, -6, 16, -3, 0, -15, 6, -21, 36, 0, 8, 3, 0, 30, 0, 0, 36, -1, -28, 0, 3, 16, 9, 3, 0, 36, 40, 9, -18, 0, 12, 0, -9, 11, 0, -6, -45, 8, 5, 0, -63, 4, 48, 3, 0, -12, 6, 2, 9, 0, 0, -28, 90, -16, 0, -14, 0, 0, 48, 0, -3, -9, -21, 0, 0, 40, 4, -45, 48, 0, 18, 1, 9, -14, 0], 'euler11': [1, 7, 33, 77, 121], 'euler13': [1, -10, 51, -130, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, 0, 0, 0], 'euler2': [1, -3, 5, -6, 4], 'euler23': [1, -1, 45, -23, 529], 'euler29': [1, 3, 49, 87, 841], 'euler3': [1, -3, 7, -9, 9], 'euler31': [1, 15, 107, 465, 961], 'euler37': [1, -3, 65, -111, 1369], 'euler41': [1, 0, -43, 0, 1681], 'euler43': [1, 1, 75, 43, 1849], 'euler47': [1, -16, 153, -752, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -9, 125, -477, 2809], 'euler59': [1, -11, 117, -649, 3481], 'euler61': [1, 6, 131, 366, 3721], 'euler67': [1, -4, 93, -268, 4489], 'euler7': [1, -4, 13, -28, 49], 'euler71': [1, 12, 173, 852, 5041], 'euler73': [1, -2, 147, -146, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, 146, 0, 6889], 'euler89': [1, 0, 133, 0, 7921], 'euler97': [1, -1, 163, -97, 9409], 'euler_factors': [[1, -3, 5, -6, 4], [1, -3, 7, -9, 9], [1, 0, 0, 0, 0], [1, -4, 13, -28, 49], [1, 7, 33, 77, 121], [1, -10, 51, -130, 169], [1, -12, 70, -204, 289], [1, 0, 0, 0, 0], [1, -1, 45, -23, 529], [1, 3, 49, 87, 841], [1, 15, 107, 465, 961], [1, -3, 65, -111, 1369], [1, 0, -43, 0, 1681], [1, 1, 75, 43, 1849], [1, -16, 153, -752, 2209], [1, -9, 125, -477, 2809], [1, -11, 117, -649, 3481], [1, 6, 131, 366, 3721], [1, -4, 93, -268, 4489], [1, 12, 173, 852, 5041], [1, -2, 147, -146, 5329], [1, 16, 222, 1264, 6241], [1, 0, 146, 0, 6889], [1, 0, 133, 0, 7921], [1, -1, 163, -97, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9025/2/a/v'], '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-c1e2-0-7', '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': 2248495162894077034, 'z1': {'__RealLiteral__': 0, 'data': '0.73757425667811069209212819860', 'prec': 103}}
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{'Lhash': '934986449190897156858022516793,1771319443133792134283909239576', 'Lhash_array': ['934986449190897156858022516793', '1771319443133792134283909239576'], 'label': '4-95e4-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9025/2/a/v'}