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lfunc_lfunctions • Show schema
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{'Lhash': '716798567588878447841400837342', 'a10': [1.0, 0.0], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [1.4142135623730951, 1.4142135623730951], 'a4': [0.0, -1.0], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [-2.0, 0.0], 'a7': [-1.0, 1.0], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.058017826781965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [53, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 5, 53], 'central_character': '2120.2013', 'coefficient_field': 'CDF', 'conductor': 2120, 'conductor_radical': 530, 'conjugate': '2698022014057096118484649984229', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.4142135623730951, 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[[1.0, 0], [-1.0, -1.0], [0, 1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2120-2120.2013-c0-0-1', 'leading_term': '0.79526287821000339527422896419972', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2120/1/z/a/2013/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.7952628782100034, 0.7219334629173564, 0.6544928519166165, 0.59068239783116, 0.5283152618377651, 0.4654236741713649, 0.400363308153914, 0.3318714054060121, 0.2590859671859791, 0.18153773475134694, 0.09912616085150178, 0.01208768925216323, -0.07903857999839602, -0.1734453602011765, -0.27009101874244507, -0.36773298036764507, -0.4649613023654092, -0.5602331134833807, -0.6519085013319756, -0.7382882301828458, -0.8176534282573737, -0.8883071324884804, -0.9486173368761669, 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'3.53493539102465213501285410024863', '4.04441103460826966468444003424966', '6.41394819026063945697705695300748', '6.97216199951321295894392588031342', '7.35826364912308788768364755015338', '8.142750001128152825995822956202391', '8.673932609696716651455362840083730'], 'prelabel': '2-2120-2120.2013-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0285999352430297, 'root_angle': 0.9262081911747834, 'root_number': '-0.97324898946773016378805774830813 + 0.22975292054736118352393736938184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4631040955873917', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56545436688928726583852173053', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94181342104305409998969935241', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84728174454495703162073545608', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.058017826781965, 'bad_primes': [2, 5, 53], 'central_character': '2120.2013', 'conductor': 2120, 'conductor_radical': 530, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2120/1/z/a/2013/1'], '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': '2-2120-2120.2013-c0-0-1', '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': '2-2120-2120.2013-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0285999352430297, 'root_angle': 0.4631040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56545436688928726583852173053', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '716798567588878447841400837342', 'Lhash_array': ['716798567588878447841400837342'], 'label': '2-2120-2120.2013-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2120/1/z/a/2013/1'}