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lfunc_lfunctions • Show schema
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{'Lhash': '2460902424534104640599974700716', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [1.6374586088176875, -1.5227374377773877], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.6374586088176875, 1.5227374377773877]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '980.569', 'coefficient_field': 'CDF', 'conductor': 980, 'conductor_radical': 70, 'conjugate': '1198250299807695871194933140724', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386], [1.5, -2.598076211353316]], [[1.0, 0], [-1.6374586088176875, 1.5227374377773877]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.1374586088176875, 1.9701361019788473], [-5.5, 9.526279441628825]], [[1.0, 0], 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'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.4685627595435391, 'root_number': '0.09860252407656615 + 0.9951268975591656*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.234281379772', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94130971427855647793677836062', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74579446592009931401234472719', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87633730315401775075689056968', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'bad_primes': [2, 5, 7], 'central_character': '35.9', 'conductor': 980, 'conductor_radical': 70, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/980/2/q/g/569/2'], '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': '2-980-35.9-c1-0-18', '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': '2-980-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.23428137977176955, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94130971427855647793677836062', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2460902424534104640599974700716', 'Lhash_array': ['2460902424534104640599974700716'], 'label': '2-980-35.9-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/980/2/q/g/569/2'}