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lfunc_lfunctions • Show schema
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{'Lhash': '1252894502735443604704461160618', 'a10': [1.9692067477088253, 7.396099022399371e-61], 'a2': [0.9846033738544127, 1.7053830688195766], 'a3': [-1.6049463093154912, 0.6512659550556774], 'a4': [-0.9388876076109847, 1.6262010389790171], 'a5': [0.5, -0.8660254037844386], 'a6': [-2.690893484057784, -2.0958096056467697], 'a7': [1.5141381900213373, 2.6225642747973357], 'a8': [0.240685870922157, 0.0], 'a9': [2.1517053115708324, -2.0904937818988762], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6049463093154912, -0.6512659550556774]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.391', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2350862332746141343430071539360', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'6.58495635636726968403472151201018', '7.45742434656417465252846311196129', '8.674588460365161963995009767232705', '10.14546085032234942624428014961516', '10.74625892046088372644149536473477'], 'prelabel': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.8009629179717522, 'root_number': '-0.8107913967561184 - 0.5853352124605716*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.400481458986', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.988359491574311493623613773316', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.15926971738357951998811209019', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73134254836445658753717810415', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.4', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/e/391/7'], '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': '2-585-9.4-c1-0-9', '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': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.4004814589858761, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.988359491574311493623613773316', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1252894502735443604704461160618', 'Lhash_array': ['1252894502735443604704461160618'], 'label': '2-585-9.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/e/391/7'}