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lfunc_lfunctions • Show schema
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{'Lhash': '1796233052984517850529373463903', 'a10': [-90.24886820814073, 0.0], 'a2': [-4.861663367367383, 0.0], 'a3': [-5.065538004949329, 0.0], 'a4': [15.635770697601963, 0.0], 'a5': [18.563372530873313, 0.0], 'a6': [24.62694055466941, 0.0], 'a7': [-14.021016490038978, 0.0], 'a8': [-37.122546682148744, 0.0], 'a9': [-1.3403247204139737, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0, 0]]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': 'CDF', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.861663367367383, 0], [8.0, 0]], [[1.0, 0], [5.065538004949329, 0], [27.0, 0]], [[1.0, 0], [-18.563372530873313, 0], [125.0, 0]], [[1.0, 0], [14.021016490038978, 0], [343.0, 0]], [[1.0, 0], [19.47906335245184, 0], [1331.0, 0]], [[1.0, 0], [-29.905968567347198, 0], [2197.0, 0]], [[1.0, 0], 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'5.32340549503406808511212071405639', '6.22907983840361446796642802277299', '6.79530610942899082938959039771955', '8.280247688443618612949452240452484', '9.299798087978079145846850056019753', '9.820847124462820235234877256151900', '10.77451631596123964724994294089060'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41697803216526841253758566484', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72257208992771570984289301690', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.32340549503406808511212071406', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/g/1/1'], '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': '2-17e2-1.1-c3-0-28', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41697803216526841253758566484', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1796233052984517850529373463903', 'Lhash_array': ['1796233052984517850529373463903'], 'label': '2-17e2-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/g/1/1'}