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lfunc_lfunctions • Show schema
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{'Lhash': '3664111864981363959703499811390', 'a10': [-2.188036243406275, 2.283089441423738], 'a2': [0.43330352039743586, -1.3461976300718959], 'a3': [0.49788246593955554, 0.49788246593955554], 'a4': [-1.6244961184223778, -1.166624344521675], 'a5': [-2.010786701155962, -0.9781292565169102], 'a6': [0.8859824209379469, -0.4545139704664152], 'a7': [-2.9184889625509784, 2.9184889625509784], 'a8': [-2.274406814763644, 1.681390389218606], 'a9': [0.0, -2.5042261002198947], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.43330352039743586, 1.3461976300718959]]], [5, [[1.0, 0], [2.010786701155962, 0.9781292565169102]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.267', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '269376674091225235421153404069', 'degree': 2, 'euler_factors': 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'root_number': '-0.8668396750617804 - 0.49858698111642175*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.416926223966', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.89047460264024855989615345418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.05682173374237597568648836963', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94318815832860417289725973586', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '20.7', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/k/d/267/15'], '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': '2-380-20.7-c1-0-52', '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': '2-380-20.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': -0.41692622396619905, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.89047460264024855989615345418', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3664111864981363959703499811390', 'Lhash_array': ['3664111864981363959703499811390'], 'label': '2-380-20.7-c1-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/k/d/267/15'}