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lfunc_lfunctions • Show schema
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{'Lhash': '2264589260650084289274947954203', 'a10': [-30.515098779427458, 0.0], 'a2': [-3.4997082504100745, 0.0], 'a3': [2.825394264636364, 0.0], 'a4': [4.247957837988345, 0.0], 'a5': [8.71932646838544, 0.0], 'a6': [-9.888055618609188, 0.0], 'a7': [6.855007379415726, 0.0], 'a8': [13.131052910278644, 0.0], 'a9': [-19.01714724935994, 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], [3.4997082504100745, 0], [8.0, 0]], [[1.0, 0], [-2.825394264636364, 0], [27.0, 0]], [[1.0, 0], [-8.71932646838544, 0], [125.0, 0]], [[1.0, 0], [-6.855007379415726, 0], [343.0, 0]], [[1.0, 0], [61.792837192893955, 0], [1331.0, 0]], [[1.0, 0], [5.373625532754265, 0], [2197.0, 0]], [[1.0, 0], [0, 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'4.88241583511897246230111794510284', '5.93515997089198698656219694695032', '7.62254390422517999633803313092318', '8.020616493494238205893149361169782', '9.034161845977013174098686193286229', '9.830838973530026818363442928988718', '10.52222021554070720145036682072125'], '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': '1.78644593411020734177600392640', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90195107330070120662980348654', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88241583511897246230111794510', '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': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/g/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-c3-0-37', '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': '1.78644593411020734177600392640', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2264589260650084289274947954203', 'Lhash_array': ['2264589260650084289274947954203'], 'label': '2-17e2-1.1-c3-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/g/1/4'}