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lfunc_lfunctions • Show schema
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{'Lhash': '641901955793631420432915575886', 'a10': [0.8138593383654928, 3.786506698443208], 'a2': [0, 1.7320508075688772], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [2.186140661634507, -0.469881908087808], 'a6': [0, 0], 'a7': [0, 1.5845739827865226], 'a8': [0, 1.7320508075688772], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.420477463777095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.186140661634507, 0.469881908087808]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 29], 'central_character': '1305.784', 'coefficient_field': 'CDF', 'conductor': 1305, 'conductor_radical': 435, 'conjugate': '2520947211106884714669690815857', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.7320508075688772], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.186140661634507, 0.469881908087808]], [[1.0, 0], [0, -1.5845739827865226], [-7.0, 0]], [[1.0, 0], [6.372281323269014, 0], [11.0, 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'positive_zeros': ['0.50637135791050198570641533202775', '2.05895958927615268588247061141799', '2.65395071942177938444270968473943', '3.65493315569520899609632918763916', '4.92019331034461521528071545332781', '5.63567115529696747756206491348125', '6.86927819880008607321345877625315', '7.49744995121491811356411280125898', '8.666165626059160603391485510425560', '9.642844749200554176990629068723933'], 'prelabel': '2-1305-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.4663044034406484, 'root_number': '-0.97767182555822490546722097419168845628946037951974205216 + 0.21013757757632938534131993792732428857594303983886354405*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4663044034406484', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50637135791050198570641533203', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05895958927615268588247061142', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.65395071942177938444270968474', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.420477463777095, 'bad_primes': [3, 5, 29], 'central_character': '5.4', 'conductor': 1305, 'conductor_radical': 435, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1305/2/c/e/784/4'], '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': '2-1305-5.4-c1-0-12', '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': '2-1305-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.4663044034406484, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50637135791050198570641533203', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '641901955793631420432915575886', 'Lhash_array': ['641901955793631420432915575886'], 'factors': ['2-1305-5.4-c1-0-12'], 'label': '2-1305-5.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1305/2/c/e/784/4'}