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lfunc_lfunctions • Show schema
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{'Lhash': '501660137095702546561482748100', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.449489742783178, 2.449489742783178], 'a6': [0.0, 0.0], 'a7': [1.0, -2.449489742783178], 'a8': [0.0, 0.0], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.577298010553363, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 2.449489742783178]]]], 'bad_primes': [2, 7], 'central_character': '448.335', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '2745862848214933355606127937737', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -3.0]], [[1.0, 0], [2.449489742783178, -2.449489742783178], [0, -5.0]], [[1.0, 0], [-1.0, 2.449489742783178]], [[1.0, 0], [1.0, -1.0], [0, -11.0]], [[1.0, 0], [2.449489742783178, 2.449489742783178], [0, 13.0]], [[1.0, 0], [0, -4.898979485566356], [-17.0, 0]], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-448-112.27-c1-0-1', '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/448/2/j/b/335/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6588283900159205, 0.46066764909961616, 0.2555238695855622, 0.03769701495655244, -0.19703964371539642, -0.4502867729278369, -0.7202488833043803, -1.0013431257974765, -1.2841495493951955, -1.5556811954866332, -1.7999770365702203, -1.999029594223025, -2.134045815848874, -2.1870080051488885, -2.14245812625668, -1.9893811243302597, -1.7230185907191762, -1.346410688939925, -0.8714489496536724, -0.31923153452814257, 0.28044987139829375, 0.8905949122105419, 1.4694596230560735, 1.9738946284926022, 2.3633244210269795, 2.6040161538440056, 2.673189647279103, 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'8.122338433040946297856386497582973', '9.094963027553661249744154547067518', '9.373919491995049782927842159919848', '11.16206859475083615479126115834468'], 'prelabel': '2-448-112.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8913746351670688, 'root_angle': -0.37581207139278755, 'root_number': '-0.7107054991241843 - 0.7034896541631895*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375812071393', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39574006986261279509391240487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44230968382041748701932054782', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03973201023045790626887351144', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.577298010553363, 'bad_primes': [2, 7], 'central_character': '112.27', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/2/j/b/335/1'], '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': '2-448-112.27-c1-0-1', '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': '2-448-112.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8913746351670688, 'root_angle': -0.37581207139278755, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39574006986261279509391240487', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '501660137095702546561482748100', 'Lhash_array': ['501660137095702546561482748100'], 'factors': ['2-448-112.27-c1-0-1'], 'label': '2-448-112.27-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/2/j/b/335/1'}