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lfunc_lfunctions • Show schema
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{'Lhash': '1361738837787295056336794796728', 'a10': [-6.967187438350306, 4.022507543026129], 'a2': [0.0, 2.600899882330192], 'a3': [0.20672695665829002, 1.7196697256714155], 'a4': [-4.764680197905207, 0.0], 'a5': [1.5465830001200558, 2.6787603343302395], 'a6': [-4.472688787145578, 0.5376761172470252], 'a7': [1.098774161092756, -2.406801891081796], 'a8': [0.0, -7.190656401412265], 'a9': [-2.914527930781603, 0.7110041776908964], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.20672695665829002, -1.7196697256714155]]], [7, [[1.0, 0], [-1.098774161092756, 2.406801891081796]]], [13, [[1.0, 0], [-3.572481815172607, 0.4872100986853967]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.269', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '4228216515905594197790424244084', 'degree': 2, 'euler_factors': [[[1.0, 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[-54.5, -94.39676901250381]], [[1.0, 0], [7.816950612608877, -4.513118540431745], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-273-273.269-c1-0-3', '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/273/2/r/b/269/31', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2456455669477404, 1.063306957300241, 0.9005557778576171, 0.7503673837241567, 0.6072226444334328, 0.4676736826487218, 0.3305771427453524, 0.1970512759921318, 0.07023254425445766, -0.04511375867608112, -0.1431019319367591, -0.2173417023156506, -0.2616497217460573, -0.27083344201968373, -0.2415064724089467, -0.17287553569757627, -0.06742260075848333, 0.06860507859603962, 0.2249866754651683, 0.38768261437741763, 0.5394134819248729, 0.6606912402541577, 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'5.15053335278366911759557530901442', '5.71852461914253214035334457072102', '7.982971113111677331881258521065566', '8.796500447620864097818949291604227', '9.313227682103274206325581509913198', '10.62551468226769594212717915262145', '11.57254837646526417289472136100228'], 'prelabel': '2-273-273.269-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.7667908066860692, 'root_number': '-0.743405728134032 + 0.668840730949835*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.383395403343', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07422253225149413468250899259', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06495504543050942589733704613', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31513896217154287414618283214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.269', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/b/269/31'], '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': '2-273-273.269-c1-0-3', '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': '2-273-273.269-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.3833954033430346, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07422253225149413468250899259', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1361738837787295056336794796728', 'Lhash_array': ['1361738837787295056336794796728'], 'label': '2-273-273.269-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/269/31'}