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lfunc_lfunctions • Show schema
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{'Lhash': '1865645035202147425871105486140', 'a10': [0.0, 0.0], 'a2': [-1.2281016272920902, -2.127134415327917], 'a3': [-0.7805223727225773, -1.3519044059997163], 'a4': [-2.0164672139149595, 3.4926236662975696], 'a5': [0.0, 0.0], 'a6': [-1.9171215921569609, 3.320552001903196], 'a7': [4.505274079010705, 0.0], 'a8': [4.993300157992075, 0.0], 'a9': [0.2815696513590363, -0.487692942023306], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.7980368652739958, -2.1389053204898247]]]], 'bad_primes': [5, 19], 'central_character': '475.26', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1316854791439170046942455244696', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2281016272920902, 2.127134415327917], [-1.0, 1.7320508075688772]], [[1.0, 0], [0.7805223727225773, 1.3519044059997163], [-1.5, 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'9.384894082490634637930547433904821', '10.27493059575800871664701003151968', '11.24470638426130826436757725979972'], 'prelabel': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.8976783131621969, 'root_number': '-0.9487773321604139 + 0.3159455237514334*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.448839156581', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47173443129065245380355518329', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.28755976434492210579899386278', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95791070482832818390299263301', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.7', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/g/26/1'], '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': '2-475-19.7-c1-0-10', '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': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.44883915658109846, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47173443129065245380355518329', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1865645035202147425871105486140', 'Lhash_array': ['1865645035202147425871105486140'], 'label': '2-475-19.7-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/g/26/1'}