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lfunc_lfunctions • Show schema
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{'Lhash': '250118283574887807267022743989,1198274671007544071191859137410', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, -1, 10, 25], [1, 6, 23, 42, 49], [1, 4, 26, 44, 121], [1, -1, -12, -13, 169], [1, 6, 19, 102, 289], [1, -8, 19], [1, 4, -7, 92, 529], [1, -2, -25, -58, 841], [1, 14, 111, 434, 961], [1, -2, 75, -74, 1369], [1, -8, 23, -328, 1681], [1, -7, 6, -301, 1849], [1, -8, 17, -376, 2209], [1, 8, 11, 424, 2809], [1, 12, 85, 708, 3481], [1, 5, -36, 305, 3721], [1, 9, 14, 603, 4489], [1, -2, -67, -142, 5041], [1, -15, 152, -1095, 5329], [1, -11, 42, 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'3.34086295204750639435431510326972', '3.63887174160624148002397516596514', '4.26378358551390660447476156966158', '4.60653433172373397212413852645042', '5.14007424707999011979484774011707', '5.78598780566470540757099855451928', '5.85158369645341203304735718995523', '6.36477781932498180868876626301544', '6.77330127275235764807102755319608', '7.17833761686351194720418511255706', '7.58383624909787730661035929683874', '7.68297041940295429103608388901959', '8.153649840448480367314574553022153', '8.784259842871944441195996534682652', '9.254588465403944963934804538997809'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 498187303506663051, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19730853559321172433349778748', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, -6, 0, 0, 0, -4, 0, 1, 0, 0, 0, -6, 0, 8, 0, 0, 0, -4, 0, 5, 0, 0, 0, 2, 0, -14, 0, 0, 0, 12, 0, 2, 0, 0, 0, 8, 0, 7, 0, 0, 0, 8, 0, 13, 0, 0, 0, -8, 0, 8, 0, 0, 0, -12, 0, -5, 0, 0, 0, -2, 0, -9, 0, 0, 0, 2, 0, 15, 0, 0, 0, 24, 0, 11, 0, 0, 0, -12, 0, 12, 0, 0, 0, 0, 0, -6, 0, 0, 0, -16, 0, 14, 0, 0, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, -1, -12, -13, 169], 'euler17': [1, 6, 19, 102, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, -7, 92, 529], 'euler29': [1, -2, -25, -58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 14, 111, 434, 961], 'euler37': [1, -2, 75, -74, 1369], 'euler41': [1, -8, 23, -328, 1681], 'euler43': [1, -7, 6, -301, 1849], 'euler47': [1, -8, 17, -376, 2209], 'euler5': [1, 2, -1, 10, 25], 'euler53': [1, 8, 11, 424, 2809], 'euler59': [1, 12, 85, 708, 3481], 'euler61': [1, 5, -36, 305, 3721], 'euler67': [1, 9, 14, 603, 4489], 'euler7': [1, 6, 23, 42, 49], 'euler71': [1, -2, -67, -142, 5041], 'euler73': [1, -15, 152, -1095, 5329], 'euler79': [1, -11, 42, -869, 6241], 'euler83': [1, 12, 202, 996, 6889], 'euler89': [1, 0, -89, 0, 7921], 'euler97': [1, -14, 99, -1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, -1, 10, 25], [1, 6, 23, 42, 49], [1, 4, 26, 44, 121], [1, -1, -12, -13, 169], [1, 6, 19, 102, 289], [1, -8, 19, 0, 0], [1, 4, -7, 92, 529], [1, -2, -25, -58, 841], [1, 14, 111, 434, 961], [1, -2, 75, -74, 1369], [1, -8, 23, -328, 1681], [1, -7, 6, -301, 1849], [1, -8, 17, -376, 2209], [1, 8, 11, 424, 2809], [1, 12, 85, 708, 3481], [1, 5, -36, 305, 3721], [1, 9, 14, 603, 4489], [1, -2, -67, -142, 5041], [1, -15, 152, -1095, 5329], [1, -11, 42, -869, 6241], [1, 12, 202, 996, 6889], [1, 0, -89, 0, 7921], [1, -14, 99, -1358, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/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': '4-2736e2-1.1-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': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 498187303506663051, 'z1': {'__RealLiteral__': 0, 'data': '0.19730853559321172433349778748', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '250118283574887807267022743989,1198274671007544071191859137410', 'Lhash_array': ['250118283574887807267022743989', '1198274671007544071191859137410'], 'label': '4-2736e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/d'}