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lfunc_lfunctions • Show schema
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{'Lhash': '1051392672953337139748738907960', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.459954113745018], 'a4': [0, 0], 'a5': [0, 1.4859799055295422], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-3.051374241731037, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.52054303693677, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '1568.785', 'coefficient_field': 'CDF', 'conductor': 1568, 'conductor_radical': 14, 'conjugate': '1385910674745762817323510462037', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.459954113745018], [-3.0, 0]], [[1.0, 0], [0, -1.4859799055295422], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.046286504776832], [-11.0, 0]], [[1.0, 0], [0, 2.5863323910318137], [-13.0, 0]], [[1.0, 0], [-1.2595105213686244, 0], [17.0, 0]], [[1.0, 0], [0, -3.0983380883458804], [-19.0, 0]], [[1.0, 0], 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'4.40812564271274973122998706571898', '5.23818183498140904327994253980997', '5.91914120158057155549930496577490', '7.04182010534688018909918942680749', '8.237196770136636773676231423690092', '8.968527671793300274738851524132225', '9.259520885232498960748371819648314'], 'prelabel': '2-1568-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.538437937414866, 'root_angle': 0.11190131869423584, 'root_number': '0.93884065752202041929767754087573145083339447147994089266 + 0.3443518836649806448765684572661214940351284159131218687*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.055950659347117924', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.829402575728708751678381766355', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.68467510947674333899622454794', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.70265016527142071570211140206', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.52054303693677, 'bad_primes': [2, 7], 'central_character': '8.5', 'conductor': 1568, 'conductor_radical': 14, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1568/2/b/f/785/1'], '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': '2-1568-8.5-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1568-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.538437937414866, 'root_angle': 0.05595065934711792, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.829402575728708751678381766355', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1051392672953337139748738907960', 'Lhash_array': ['1051392672953337139748738907960'], 'label': '2-1568-8.5-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1568/2/b/f/785/1'}