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lfunc_lfunctions • Show schema
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{'Lhash': '2172606341444918008651978857521', 'a10': [0.15443747695460017, 0.2674935566781151], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.09856314879997632, 0.1707163814755304], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.15443747695460017, -0.2674935566781151], 'a6': [-0.19712629759995265, -2.5850163036148697e-62], 'a7': [-1.710311805109224, -2.0186216904868597], 'a8': [1.0, 0.0], 'a9': [1.4805706113972674, -2.5644235231333834], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [1.710311805109224, 2.0186216904868597]]], [23, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 7, 23], 'central_character': '322.93', 'coefficient_field': 'CDF', 'conductor': 322, 'conductor_radical': 322, 'conjugate': '1232603214728230864804225456428', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 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94.39676901250381]], [[1.0, 0], [-7.5707457845645445, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-322-7.2-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/322/2/e/a/93/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0762384544540342, 1.1311371744093366, 1.1814883166080208, 1.2255572957149397, 1.2592066202707737, 1.2765810102761024, 1.2709217782765134, 1.23540347369475, 1.1639484939886735, 1.052007836380939, 0.8972959890646723, 0.7004499459359671, 0.46556089320517086, 0.20051104640900644, -0.08295826758282368, -0.3695159712469792, -0.6408992544186332, -0.8769820628930391, -1.057235985561256, -1.162517879663716, -1.177067509580355, -1.0905495105817928, -0.8999337004689365, -0.6109831182675138, -0.23911670536810245, 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'8.273169652071912158831778202102094', '8.749844388179610188492143088917343', '9.981313409834506102251417882072602', '10.68698167565940446474581331069834', '11.52037162524675570010138417778112'], 'prelabel': '2-322-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': 0.08941865804048113, 'root_number': '0.9608016163696079 + 0.2772368193107633*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0447093290202', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71388420520114867792770960064', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07104739073207130633112884700', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34395857203823037259302264529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'bad_primes': [2, 7, 23], 'central_character': '7.2', 'conductor': 322, 'conductor_radical': 322, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/322/2/e/a/93/3'], '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': '2-322-7.2-c1-0-8', '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': '2-322-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': 0.044709329020240565, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71388420520114867792770960064', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2172606341444918008651978857521', 'Lhash_array': ['2172606341444918008651978857521'], 'label': '2-322-7.2-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/322/2/e/a/93/3'}