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lfunc_lfunctions • Show schema
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{'Lhash': '2631607627776204069046241763615', 'a10': [0.2031874032484531, 7.230723380506971e-61], 'a2': [0.10423472237634492, 0.06017994502288864], 'a3': [-0.5822920240977583, 0.0], 'a4': [-0.9927567484340842, -1.7195051278447082], 'a5': [1.4619941317263336, -0.844082705505852], 'a6': [-0.060695047473789766, -0.03504230199746964], 'a7': [0.0, 0.0], 'a8': [0.0, -0.47969596625901406], 'a9': [-2.660935998672136, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.8012432279477526, 3.1233832351750177]]]], 'bad_primes': [7, 13], 'central_character': '637.361', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '553530054793240337642879232557', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.10423472237634492, -0.06017994502288864], [1.0, 1.7320508075688772]], [[1.0, 0], [0.5822920240977583, 0], 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'8.837528465479733513914382839333069', '10.17488738792584712503252112775922', '10.92042356572745127521299243673850'], 'prelabel': '2-637-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.7969131371283146, 'root_number': '-0.8032788972368217 + 0.5956030668608043*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.398456568564', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07597237543405583232259579481', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33491408374266540928933268194', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35958716397527796243396616314', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.88', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/u/h/361/4'], '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': '2-637-91.88-c1-0-37', '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': '2-637-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.3984565685641573, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07597237543405583232259579481', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2631607627776204069046241763615', 'Lhash_array': ['2631607627776204069046241763615'], 'label': '2-637-91.88-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/u/h/361/4'}