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lfunc_lfunctions • Show schema
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{'Lhash': '796853153817462110928579021030', 'a10': [-0.1635934225331807, -0.09445070653718407], 'a2': [0.5, -0.8660254037844386], 'a3': [0.3779989480064389, 1.6903008002441535], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, -0.18890141307436814], 'a6': [1.6528429070518222, 0.5177937085447074], 'a7': [-2.53047176485212, 0.7724717776632328], 'a8': [-1.0, 0.0], 'a9': [-2.714233590612051, 1.2778638486134637], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.3779989480064389, -1.6903008002441535]]], [7, [[1.0, 0], [2.53047176485212, -0.7724717776632328]]], [13, [[1.0, 0], [-3.59702657169448, -0.2477899161060785]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.251', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '2662355668337553321736755673369', 'degree': 2, 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[2.9195362534853033, -1.6855950418586112], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-546-273.251-c1-0-4', '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/546/2/q/j/251/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2725372773262806, 1.0634055669009603, 0.8405278530888439, 0.5955023278841993, 0.32040862324430636, 0.009531782592545463, -0.33926740404715616, -0.7236049093052385, -1.1360452585006642, -1.5639884068149468, -1.9899933584854876, -2.392575644616349, -2.747505500955264, -3.0295970383293, -3.21492209885776, -3.283314670134098, -3.220962749661253, -3.0228252479730373, -2.6945729244039, -2.253744685851371, -1.7298418550879153, -1.1631574485897374, -0.6022540510144464, -0.10015518727781526, 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'7.02842537020320630278646042914798', '7.64858574084794672663628408323756', '8.698186345523038145815933866918242', '9.336423186735802257378776782970412', '10.86538939083258391384446032909945'], 'prelabel': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.4798628218754715, 'root_number': '0.06322062107662707 - 0.997999575686626*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.239931410938', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62860630024866131980355638431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90334179035796415696362628920', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50129958880979770275393517345', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.251', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/j/251/7'], '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': '2-546-273.251-c1-0-4', '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': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.23993141093773576, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62860630024866131980355638431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '796853153817462110928579021030', 'Lhash_array': ['796853153817462110928579021030'], 'label': '2-546-273.251-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/j/251/7'}