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lfunc_lfunctions • Show schema
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{'Lhash': '1704952945932220345575781725660', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1738009097128217, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2352.1391', 'coefficient_field': 'CDF', 'conductor': 2352, 'conductor_radical': 42, 'conjugate': '952713416172806847979262265422', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, 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'5.37530197767016374525331139885486', '6.11391631326066834002344188923872', '6.90610897171116143590507148111096', '7.958411572793768958225092059464788', '8.643294438049273805902338103224415', '9.517379058209313772826750562946697'], 'prelabel': '2-2352-84.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0834209291465722, 'root_angle': 0.4798270469460539, 'root_number': '0.063332786104344676563637747749200 + 0.99799246400173850503495435029375*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.23991352347302694', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34497072428732213919284917472', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96026680797038438561041820804', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69852074162922439106140613861', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1738009097128217, 'bad_primes': [2, 3, 7], 'central_character': '84.47', 'conductor': 2352, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2352/1/z/b/1391/1'], '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': '2-2352-84.47-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2352-84.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0834209291465722, 'root_angle': 0.23991352347302694, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34497072428732213919284917472', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1704952945932220345575781725660', 'Lhash_array': ['1704952945932220345575781725660'], 'label': '2-2352-84.47-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2352/1/z/b/1391/1'}