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lfunc_lfunctions • Show schema
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{'Lhash': '1728063796959060565726045439440,2058417798261955842808449644352', 'a10': 2, 'a2': 2, 'a3': 1, 'a4': 3, 'a5': 1, 'a6': 2, 'a7': 3, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, -1, 1]], [5, [1, -1, 1]], [31, [1, -11, 31]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -1, 1], [1, -1, 1], [1, -3, 2, -21, 49], [1, -3, -2, -33, 121], [1, -2, -9, -26, 169], [1, -4, -1, -68, 289], [1, 0, -19, 0, 361], [1, 8, 62, 184, 529], [1, 10, 83, 290, 841], [1, -11, 31], [1, -6, -1, -222, 1369], [1, -2, -37, -82, 1681], [1, -8, 21, -344, 1849], [1, 16, 158, 752, 2209], [1, -3, -44, -159, 2809], [1, 3, -50, 177, 3481], [1, 16, 186, 976, 3721], [1, -10, 33, -670, 4489], [1, -8, -7, -568, 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0.21879614574138606], 'positive_zeros': ['1.36320197114878326546102890200227', '1.62380532765996854711342145857079', '2.46838012742712737135329819440929', '2.87811219297513495013808418306221', '3.76954057489232609354877021191390', '3.87030646276061031301297979427689', '4.50015076232325173498030338144756', '4.86889098220833586022263647803929', '5.68280636162624683313065548242360', '5.75902762572781259140433119921025', '6.26054626222910571322493439985124', '6.69896880412838919509821790879479', '7.31338212734660411489206356736662', '7.929063340094521089099421073307337', '7.976943537951356950966702021411006', '8.355019401360742023099072822766006', '9.259186178159370207996579597283969', '9.291772934936483037937818557627691', '10.06313336648752984205782750849562', '10.15490639733422592398993750235905'], 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, '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': 1111163704572958184, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36320197114878326546102890200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62380532765996854711342145857', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46838012742712737135329819441', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 2, 1, 3, 1, 2, 3, 4, 0, 2, 3, 3, 2, 6, 1, 5, 4, 0, 0, 3, 3, 6, -8, 4, 0, 4, -1, 9, -10, 2, 11, 6, 3, 8, 3, 0, 6, 0, 2, 4, 2, 6, 8, 9, 0, -16, -16, 5, 7, 0, 4, 6, 3, -2, 3, 12, 0, -20, -3, 3, -16, 22, 0, 7, 2, 6, 10, 12, -8, 6, 8, 0, -14, 12, 0, 0, 9, 4, -8, 5, -1, 4, 9, 9, 4, 16, -10, 12, -16, 0, 6, -24, 11, -32, 0, 6, -14, 14, 0, 0], 'euler11': [1, -3, -2, -33, 121], 'euler13': [1, -2, -9, -26, 169], 'euler17': [1, -4, -1, -68, 289], 'euler19': [1, 0, -19, 0, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 10, 83, 290, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, -11, 31, 0, 0], 'euler37': [1, -6, -1, -222, 1369], 'euler41': [1, -2, -37, -82, 1681], 'euler43': [1, -8, 21, -344, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, -3, -44, -159, 2809], 'euler59': [1, 3, -50, 177, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, -10, 33, -670, 4489], 'euler7': [1, -3, 2, -21, 49], 'euler71': [1, -8, -7, -568, 5041], 'euler73': [1, 14, 123, 1022, 5329], 'euler79': [1, 8, -15, 632, 6241], 'euler83': [1, -9, -2, -747, 6889], 'euler89': [1, 16, 242, 1424, 7921], 'euler97': [1, 14, 243, 1358, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -1, 1, 0, 0], [1, -1, 1, 0, 0], [1, -3, 2, -21, 49], [1, -3, -2, -33, 121], [1, -2, -9, -26, 169], [1, -4, -1, -68, 289], [1, 0, -19, 0, 361], [1, 8, 62, 184, 529], [1, 10, 83, 290, 841], [1, -11, 31, 0, 0], [1, -6, -1, -222, 1369], [1, -2, -37, -82, 1681], [1, -8, 21, -344, 1849], [1, 16, 158, 752, 2209], [1, -3, -44, -159, 2809], [1, 3, -50, 177, 3481], [1, 16, 186, 976, 3721], [1, -10, 33, -670, 4489], [1, -8, -7, -568, 5041], [1, 14, 123, 1022, 5329], [1, 8, -15, 632, 6241], [1, -9, -2, -747, 6889], [1, 16, 242, 1424, 7921], [1, 14, 243, 1358, 9409]], 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/i/i'], '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': '4-930e2-1.1-c1e2-0-19', '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': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1111163704572958184, 'z1': {'__RealLiteral__': 0, 'data': '1.36320197114878326546102890200', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1728063796959060565726045439440,2058417798261955842808449644352', 'Lhash_array': ['1728063796959060565726045439440', '2058417798261955842808449644352'], 'label': '4-930e2-1.1-c1e2-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/i/i'}