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lfunc_lfunctions • Show schema
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{'Lhash': '890247016692623955493374216413,1004755676124466807078909406948', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1216.520616665379, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [7, [1, 0, 1]], [13, [1, -4, 13]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '4368.1', 'coefficient_field': '1.1.1.1', 'conductor': 19079424, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 0, -6, 0, 25], [1, 0, 1], [1, 0, -22, 0, 121], [1, -4, 13], [1, 4, 38, 68, 289], [1, 0, -22, 0, 361], [1, -12, 82, -276, 529], [1, 0, 58, 0, 841], [1, 0, -62, 0, 961], [1, 0, -70, 0, 1369], [1, 0, -82, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -30, 0, 2209], [1, -8, 122, -424, 2809], [1, 0, -82, 0, 3481], [1, -24, 266, -1464, 3721], [1, 0, -130, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, 50, 0, 5329], [1, 0, 158, 0, 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'0.792612472193496644052679307863572', '1.59124711584340676922929112786814', '2.04964569977334677336367017866309', '2.86142006283351617578994245020201', '3.03487274458277689145393711937603', '3.82060605220317077412457362246867', '3.91137816516967560657369713802360', '4.71698001294601351326983741524574', '4.77054409279933922656430640471866', '5.30241383272797543260989484947090', '5.49132057618226255564145175109790', '5.99044672383959295725746431397266', '6.54389110651510098374254399382399', '6.73312554614171988020941052096484', '6.83033136682861410790766180889835', '7.39419611348063201568599122663609', '7.63078502487664671856029875240856', '8.452700606269748405984881845755071', '8.544881459057269762140229875293417'], 'prelabel': '4-4368e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.905815405419923, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1994076201534892678, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70228106745844854077682498338', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.792612472193496644052679307864', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.59124711584340676922929112787', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1216.520616665379, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 19079424, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 12, 0, 6, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -1, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, -4, 13, 0, 0], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 0, -22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -12, 82, -276, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, -62, 0, 961], 'euler37': [1, 0, -70, 0, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, -8, 122, -424, 2809], 'euler59': [1, 0, -82, 0, 3481], 'euler61': [1, -24, 266, -1464, 3721], 'euler67': [1, 0, -130, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, 50, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 30, 0, 6889], 'euler89': [1, 0, -162, 0, 7921], 'euler97': [1, 0, -190, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, -6, 0, 25], [1, 0, 1, 0, 0], [1, 0, -22, 0, 121], [1, -4, 13, 0, 0], [1, 4, 38, 68, 289], [1, 0, -22, 0, 361], [1, -12, 82, -276, 529], [1, 0, 58, 0, 841], [1, 0, -62, 0, 961], [1, 0, -70, 0, 1369], [1, 0, -82, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -30, 0, 2209], [1, -8, 122, -424, 2809], [1, 0, -82, 0, 3481], [1, -24, 266, -1464, 3721], [1, 0, -130, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, 50, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, 30, 0, 6889], [1, 0, -162, 0, 7921], [1, 0, -190, 0, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4368/2/h/f'], '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': '4-4368e2-1.1-c1e2-0-13', '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': '4-4368e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.905815405419923, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1994076201534892678, 'z1': {'__RealLiteral__': 0, 'data': '0.70228106745844854077682498338', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '890247016692623955493374216413,1004755676124466807078909406948', 'Lhash_array': ['890247016692623955493374216413', '1004755676124466807078909406948'], 'label': '4-4368e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4368/2/h/f'}