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lfunc_lfunctions • Show schema
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{'Lhash': '1511407887935017222020676476729', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 4, 'a5': -5, 'a6': 0, 'a7': -7, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.583128327349353, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 5]], [7, [1, 7]]], 'bad_primes': [3, 5, 7], 'central_character': '315.244', 'coefficient_field': '1.1.1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[1, 0, -4], [1], [1, 5], [1, 7], [1, -13, 121], [1, -19, 169], [1, -29, 289], [1, 0, -361], [1, 0, -529], [1, 23, 841], [1, 0, -961], [1, 0, -1369], [1, 0, -1681], [1, 0, -1849], [1, 31, 2209], [1, 0, -2809], [1, 0, -3481], [1, 0, -3721], [1, 0, -4489], [1, 2, 5041], [1, -34, 5329], [1, 157, 6241], [1, -86, 6889], [1, 0, -7921], [1, 149, 9409], [1, 0, -10201], [1, -199, 10609], [1, 0, -11449], [1, 97, 11881], [1, 0, -12769]], 'euler_factors_factorization': [[[[1, -2], 1], [[1, 2], 1]], [1], 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2.4962308979761247, 1.5104090218991166, 0.38233186981847395, -0.5839913706644337, -1.1493901906549724, -1.2116678836596957, -0.8355952136572108, -0.2311418454398983, 0.31394899559843126, 0.5270258737175862, 0.24045401887049397, -0.5493941814718053, -1.6730968105770507, -2.833111050060938, -3.6901688074053283, -3.9656088713304345, -3.528655305241784, -2.44158622504067, -0.9480458721590126, 0.5931778247508617, 1.8099077474352836, 2.4237009186293683, 2.3300650391327955], 'positive_zeros': ['1.19229059463459525297986245434610', '3.24380662599066294345935222613306', '3.81242820160127633922274281554200', '5.78598926920184600444775710632800', '6.60451494626098115725564219985123', '7.48630701906346438116537150418035', '8.500550253919827948579538127353771', '9.636233618004979992010515391986887', '10.69010714352588202670322378226830', '11.53909938078069870630499054907760'], 'prelabel': '2-315-35.34-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.92969765118337, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2-0', 'trace_hash': 1117921665860808861, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19229059463459525297986245435', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.24380662599066294345935222613', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81242820160127633922274281554', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.583128327349353, 'bad_primes': [3, 5, 7], 'central_character': '35.34', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 4, -5, 0, -7, 0, 0, 0, 13, 0, 19, 0, 0, 16, 29, 0, 0, -20, 0, 0, 0, 0, 25, 0, 0, -28, -23, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, -31, 0, 49, 0, 0, 76, 0, 0, -65, 0, 0, 0, 0, 0, 0, 0, 0, 64, -95, 0, 0, 116, 0, 0, -2, 0, 34, 0, 0, 0, -91, 0, -157, -80, 0, 0, 86, 0, -145, 0, 0, 0, 0, 0, -133, 0, 0, 0, 0, 0, -149, 0, 0, 100], 'euler11': [1, -13, 121], 'euler13': [1, -19, 169], 'euler17': [1, -29, 289], 'euler19': [1, 0, -361], 'euler2': [1, 0, -4], 'euler23': [1, 0, -529], 'euler29': [1, 23, 841], 'euler3': [1, 0, 0], 'euler31': [1, 0, -961], 'euler37': [1, 0, -1369], 'euler41': [1, 0, -1681], 'euler43': [1, 0, -1849], 'euler47': [1, 31, 2209], 'euler5': [1, 5, 0], 'euler53': [1, 0, -2809], 'euler59': [1, 0, -3481], 'euler61': [1, 0, -3721], 'euler67': [1, 0, -4489], 'euler7': [1, 7, 0], 'euler71': [1, 2, 5041], 'euler73': [1, -34, 5329], 'euler79': [1, 157, 6241], 'euler83': [1, -86, 6889], 'euler89': [1, 0, -7921], 'euler97': [1, 149, 9409], 'euler_factors': [[1, 0, -4], [1, 0, 0], [1, 5, 0], [1, 7, 0], [1, -13, 121], [1, -19, 169], [1, -29, 289], [1, 0, -361], [1, 0, -529], [1, 23, 841], [1, 0, -961], [1, 0, -1369], [1, 0, -1681], [1, 0, -1849], [1, 31, 2209], [1, 0, -2809], [1, 0, -3481], [1, 0, -3721], [1, 0, -4489], [1, 2, 5041], [1, -34, 5329], [1, 157, 6241], [1, -86, 6889], [1, 0, -7921], [1, 149, 9409]], 'index': 15, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/3/e/a/244/1', 'ModularForm/GL2/Q/holomorphic/315/3/e/a'], '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': '2-315-35.34-c2-0-15', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-315-35.34-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.92969765118337, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2-0', 'trace_hash': 1117921665860808861, 'z1': {'__RealLiteral__': 0, 'data': '1.19229059463459525297986245435', 'prec': 103}}
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lfunc_instances • Show schema
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id: 13432018
{'Lhash': '1511407887935017222020676476729', 'Lhash_array': ['1511407887935017222020676476729'], 'label': '2-315-35.34-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/3/e/a'}
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id: 24551648
{'Lhash': '1511407887935017222020676476729', 'Lhash_array': ['1511407887935017222020676476729'], 'label': '2-315-35.34-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/3/e/a/244/1'}