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lfunc_lfunctions • Show schema
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{'Lhash': '4954554345174357422915729095612', 'a10': [-0.24587775369195192, 0.173703324489602], 'a2': [-0.1346318793594891, 0.0], 'a3': [-2.155577581549734, -2.155577581549734], 'a4': [-1.981874257060132, 0.0], 'a5': [1.826296675510398, -1.290209460909223], 'a6': [0.29020946090922306, 0.29020946090922306], 'a7': [0.0, -1.9096998278577821], 'a8': [0.5360872146011749, 0.0], 'a9': [0.0, 6.2930294201596], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5190276131383228, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.826296675510398, 1.290209460909223]]], [13, [[1.0, 0], [-3.601364624008691, -0.173703324489602]]]], 'bad_primes': [5, 13], 'central_character': '65.8', 'coefficient_field': 'CDF', 'conductor': 65, 'conductor_radical': 65, 'conjugate': '1377227425356986430053874595914', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.1346318793594891, 0], [2.0, 0]], [[1.0, 0], [2.155577581549734, 2.155577581549734], [0, 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'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.90845422570094098027227911901', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.41496974358630568270895729773', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.13441084724006496807754619305', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5190276131383228, 'bad_primes': [5, 13], 'central_character': '65.8', 'conductor': 65, 'conductor_radical': 65, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/65/2/k/b/8/3'], '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': '2-65-65.8-c1-0-4', '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': '2-65-65.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7204357106212342, 'root_angle': 0.29467815579266127, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.90845422570094098027227911901', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4954554345174357422915729095612', 'Lhash_array': ['4954554345174357422915729095612'], 'label': '2-65-65.8-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/65/2/k/b/8/3'}