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lfunc_lfunctions • Show schema
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{'Lhash': '2209317902553619822535421784437', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, -0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.235185906266681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, 0.5]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.274', 'coefficient_field': 'CDF', 'conductor': 2475, 'conductor_radical': 165, 'conjugate': '673313787996354737293098122973', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], 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'2.90835925064399848199713132426007', '3.95710386230969074382491729595176', '4.53069524800404915178777638017881', '5.62088639152425492222226990585929', '6.25186879635549421369336562786451', '7.26415791938763102600590165139145', '7.62895125750952989987674137708552', '8.671557563247609180192398313553439', '9.528327767847837080065683623843867'], 'prelabel': '2-2475-495.274-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.111389178580879, 'root_angle': 0.7968608267940113, 'root_number': '-0.80318100631520478081327964289353 + 0.59573506787371093788410164186078*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3984304133970056', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74284452052943568260306113996', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90835925064399848199713132426', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95710386230969074382491729595', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.235185906266681, 'bad_primes': [3, 5, 11], 'central_character': '495.274', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/1/t/a/274/1'], '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': '2-2475-495.274-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2475-495.274-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.111389178580879, 'root_angle': 0.39843041339700563, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74284452052943568260306113996', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2209317902553619822535421784437', 'Lhash_array': ['2209317902553619822535421784437'], 'label': '2-2475-495.274-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/1/t/a/274/1'}