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lfunc_lfunctions • Show schema
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{'Lhash': '2407922519116303621772634803655', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.7320508075688772], 'a4': [0.0, 0.0], 'a5': [3.0, -1.7320508075688772], 'a6': [0.0, 0.0], 'a7': [2.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.7320508075688772]]], [19, [[1.0, 0], [0.5, -4.330127018922194]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.449', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '1301631298215083026340505726607', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772]], [[1.0, 0], [-3.0, 1.7320508075688772], [2.5, -4.330127018922194]], [[1.0, 0], [-2.0, 0], [7.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-11.0, 0]], [[1.0, 0], [3.0, 1.7320508075688772], [6.5, 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6.463741477749767, 5.821459525613552, 4.318309332173606, 2.4149935639022826, 0.6634320786715049, -0.4846582729985877], 'positive_zeros': ['1.89951593813214637856779014792966', '2.84529555653443883205991713069128', '4.13354026037681857881857609658659', '5.17220262981596176209381566042698', '5.76972056195236193060375975629448', '6.84471438265028161356410146148580', '7.81588038446192400424350943867604', '8.988892667303114962930770324534926', '9.622196553332809591683249842154275', '10.31248576050724156465789401278201'], 'prelabel': '2-912-57.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.5677532880622769, 'root_number': '-0.21124959666651258 + 0.9774321500279372*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.283876644031', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89951593813214637856779014793', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '57.50', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bn/b/449/1'], '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': '2-912-57.50-c1-0-34', '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': '2-912-57.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.28387664403113844, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89951593813214637856779014793', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2407922519116303621772634803655', 'Lhash_array': ['2407922519116303621772634803655'], 'label': '2-912-57.50-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bn/b/449/1'}