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lfunc_lfunctions • Show schema
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{'Lhash': '1900510374804637091455105972288', 'a10': [-35.133098786817605, 0.0], 'a2': [-2.1647277744081275, 0.0], 'a3': [9.141328046956966, 0.0], 'a4': [-3.313953662706036, 0.0], 'a5': [16.229799978624833, 0.0], 'a6': [-19.788486718223748, 0.0], 'a7': [12.22457032404499, 0.0], 'a8': [24.49162973202632, 0.0], 'a9': [56.563878462082066, 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], [2.1647277744081275, 0], [8.0, 0]], [[1.0, 0], [-9.141328046956966, 0], [27.0, 0]], [[1.0, 0], [-16.229799978624833, 0], [125.0, 0]], [[1.0, 0], [-12.22457032404499, 0], [343.0, 0]], [[1.0, 0], [11.176106641123434, 0], [1331.0, 0]], [[1.0, 0], [-28.899984855326423, 0], [2197.0, 0]], [[1.0, 0], 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'2.29929516347426127831644346677952', '3.88501664806996189253614872456904', '5.17636498002881724781946133170710', '6.77332377360380800406156412236112', '8.120068912494754485503792789981917', '8.488434159587181295653221589465248', '9.388693851775112223697830677177153', '9.988855277190082740388463912366243', '10.81217535844956751247945212966290'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49923833465031044330113644005', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29929516347426127831644346678', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88501664806996189253614872457', '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': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/i/1/4'], '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': '2-17e2-1.1-c3-0-30', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49923833465031044330113644005', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1900510374804637091455105972288', 'Lhash_array': ['1900510374804637091455105972288'], 'label': '2-17e2-1.1-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/i/1/4'}