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lfunc_lfunctions • Show schema
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{'Lhash': '1470277360488155022513212775675', 'a10': [9.17642980026145, 1.828205919214448e-60], 'a2': [-1.56177874283944, 1.56177874283944], 'a3': [-1.3386866988778399, 3.2318755841993485], 'a4': [0.0, -0.8783056831702838], 'a5': [-2.9378136443251748, -2.9378136443251748], 'a6': [-2.956742157275027, -7.138207016533652], 'a7': [1.012485192902634, -2.444355484407478], 'a8': [-4.875395825667339, -4.875395825667339], 'a9': [-2.288976683312505, -2.288976683312505], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.820183587140522, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.012485192902634, 2.444355484407478]]], [41, [[1.0, 0], [-40.74382637438555, 4.576091386098468]]]], 'bad_primes': [7, 41], 'central_character': '287.85', 'coefficient_field': 'CDF', 'conductor': 287, 'conductor_radical': 287, 'conjugate': '670738568308011777952555702532', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.56177874283944, 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[[1.0, 0], [93.48344947037971, 93.48344947037971], [0, 10609.0]], [[1.0, 0], [0, -45.46485493426751], [-11449.0, 0]], [[1.0, 0], [-143.86143225623925, 59.58935634295255], [8401.13566727737, -8401.13566727737]], [[1.0, 0], [0, 103.50831583835654], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-287-41.3-c2-0-18', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/287/3/m/a/85/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6457966293745842, 0.6955331814488581, 0.711962500822823, 0.69674594885098, 0.6511653680162196, 0.5765577277624834, 0.47483265908349376, 0.3490031379201056, 0.20366069960123528, 0.045331690107295965, -0.11734199051449463, -0.2736457081212275, -0.4110953828135471, -0.5160227843158398, -0.5744436729403911, 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'2.30248264822906143352531053661421', '3.95198310813745292502441727229830', '5.89598106859437421378900530854721', '6.62715355946259164787226839497530', '7.77273322630735548258548743076448', '8.707744038834190906898459532898276', '9.719231873695147081489801594308967', '10.85095867021227445129809746280063', '11.55715008525139722153065582141176'], 'prelabel': '2-287-41.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7964591159429673, 'root_angle': -0.13668901938153274, 'root_number': '0.909206874267209 - 0.41634464063471693*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0683445096908', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15984432952064586673754641552', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30248264822906143352531053661', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95198310813745292502441727230', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.820183587140522, 'bad_primes': [7, 41], 'central_character': '41.3', 'conductor': 287, 'conductor_radical': 287, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/287/3/m/a/85/11'], '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': '2-287-41.3-c2-0-18', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-287-41.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7964591159429673, 'root_angle': -0.06834450969076637, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15984432952064586673754641552', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1470277360488155022513212775675', 'Lhash_array': ['1470277360488155022513212775675'], 'label': '2-287-41.3-c2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/287/3/m/a/85/11'}