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lfunc_lfunctions • Show schema
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{'Lhash': '471167435573437832849891251319', 'a10': [0.0, 0.0], 'a2': [-0.11262492128989265, 0.19507208587253982], 'a3': [-2.067546248353325, 4.767101059440642], 'a4': [3.974631254208891, 6.884263273641009], 'a5': [0.0, 0.0], 'a6': [-0.6970711137462744, -0.9402149409046936], 'a7': [-15.597008339265834, 27.0148108896839], 'a8': [-3.5925688692847775, 0.0], 'a9': [-18.45050502184018, -19.71240382193532], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.067546248353325, -4.767101059440642]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.151', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3436098971061329936174442719094', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.11262492128989265, -0.19507208587253982], [-4.0, -6.928203230275509]], [[1.0, 0], [2.067546248353325, 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[-864.3964432149435, -1497.178557530108], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-15e2-9.7-c3-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/e/d/151/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8647314497621292, 0.5484873492306286, 0.2560052599645662, -0.006521747352572159, -0.2328771916286154, -0.41681909606428574, -0.5522175846110254, -0.6333398633636675, -0.6552737686989013, -0.6144648060793173, -0.5093264913594917, -0.34087056592153836, -0.11329304868068363, 0.16555495802841505, 0.48388516066964565, 0.8259486190115272, 1.172330471435826, 1.500604335449757, 1.786362188983027, 2.004602997236275, 2.131425748455717, 2.1459327144346507, 2.0322104000189323, 1.7812232217127866, 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'6.25945539000631164637649471337919', '7.03778075061073782829134848367773', '7.82845398708889823929794301566496', '9.633626570328707259968291779205102', '10.28098206056054409700995679415981', '11.26253549655335775302633540092914'], 'prelabel': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.8160769906041113, 'root_number': '-0.8376601736454252 + 0.5461917552364884*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.408038495302', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37168556973712492837050373942', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55333102184869040779465892175', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29516059918888976725107807043', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/e/d/151/4'], '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': '2-15e2-9.7-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.40803849530205566, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37168556973712492837050373942', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '471167435573437832849891251319', 'Lhash_array': ['471167435573437832849891251319'], 'label': '2-15e2-9.7-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/e/d/151/4'}