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lfunc_lfunctions • Show schema
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{'Lhash': '1866641421288792696721306599526', 'a10': [1.6184407500101492, -2.8032216080574583], 'a2': [-0.8660254037844386, 0.5], 'a3': [1.6002062903825311, 0.9238795325112867], 'a4': [0.5, -0.8660254037844386], 'a5': [-2.8032216080574583, 1.6184407500101492], 'a6': [-1.8477590650225735, 0], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [0.20710678118654752, 0.3587194676071504], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.2360395200945005, -3.077694966166166]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1011', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '141507635010924345774028612462', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [-1.6002062903825311, -0.9238795325112867], [1.5, 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'7.88456814855701435270935344357030', '8.401171339862733670421997638478814', '8.856242593587960732581197749082336', '10.17320384163914191867267176133293'], 'prelabel': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.5152620747581143, 'root_number': '-0.0479288527837311824821238391303064559404372814660699172 + 0.9988507521501074705389478290300542713186696885197763509*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2576310373790571', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47252044132091306366831155134', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73977976798393516786393396490', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62784049868317650608160360263', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.10', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/1011/4'], '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': '2-1078-77.10-c1-0-21', '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': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.2576310373790571, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47252044132091306366831155134', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1866641421288792696721306599526', 'Lhash_array': ['1866641421288792696721306599526'], 'label': '2-1078-77.10-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/1011/4'}