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lfunc_lfunctions • Show schema
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{'Lhash': '1799645457151027022552931850121', 'a10': [-6.6109426079280595, -3.816829494284432], 'a2': [1.1392130673908192, 1.9731749133672862], 'a3': [0.0, 0.0], 'a4': [-1.5956128258279982, 2.763682483542643], 'a5': [-2.9015391401142105, 1.6752044036091749], 'a6': [0.0, 0.0], 'a7': [3.546967923006458, 0.0], 'a8': [-2.714119657155311, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-4.1595875107496, -1.3030087261472747]]]], 'bad_primes': [3, 19], 'central_character': '171.107', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '4219641589267495758118355169564', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1392130673908192, -1.9731749133672862], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.9015391401142105, -1.6752044036091749], [2.5, 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'11.63334069844174737593427247681901', '12.18032290203935155778558536918890'], 'prelabel': '2-171-57.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.7347899076874903, 'root_number': '-0.6725241923340577 - 0.7400751385673102*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.367394953844', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41966994440504079027652531164', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25386922790423552262060965944', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75781177852137440189233310067', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '57.50', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/m/a/107/7'], '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': '2-171-57.50-c1-0-1', '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': '2-171-57.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.36739495384374515, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41966994440504079027652531164', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1799645457151027022552931850121', 'Lhash_array': ['1799645457151027022552931850121'], 'label': '2-171-57.50-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/m/a/107/7'}