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lfunc_lfunctions • Show schema
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{'Lhash': '1422448504291849811651030164187', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.7320508075688772], 'a4': [0.0, 0.0], 'a5': [4.292528739883945, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 2.757874763926024], 'a8': [0.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.463242151435402, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.7320508075688772]]]], 'bad_primes': [2, 3], 'central_character': '384.127', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1761263961502794668636810349194', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772]], [[1.0, 0], [-4.292528739883945, 0], [25.0, 0]], [[1.0, 0], [0, -2.757874763926024], [-49.0, 0]], [[1.0, 0], [0, -13.797958971132712], [-121.0, 0]], [[1.0, 0], [-14.526609990349584, 0], [169.0, 0]], [[1.0, 0], [-22.867266923048554, 0], [289.0, 0]], 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'5.97427377794655409872599685751723', '7.39944984429357637506618429263500', '8.576676593134577514414986737327102', '9.313832192147454381200353453627522', '10.27008066450660363353974428717763', '10.96320376534683458486274071570170'], 'prelabel': '2-384-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2346935173885334, 'root_angle': 1.140244383243981e-61, 'root_number': '1.0 + 3.582183377696315e-61*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0000000000000000000000000000000000000000000000000000000000000570122191622', 'prec': 250}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12211401472594293858186585503', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98617778780051879919517157990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99476278487736800343135389777', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.463242151435402, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/3/g/a/127/4'], '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': '2-384-4.3-c2-0-8', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-384-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2346935173885334, 'root_angle': 5.701221916219905e-62, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12211401472594293858186585503', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1422448504291849811651030164187', 'Lhash_array': ['1422448504291849811651030164187'], 'label': '2-384-4.3-c2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/3/g/a/127/4'}