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lfunc_lfunctions • Show schema
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{'Lhash': '735463312232004479266766945668', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.6873995617361737, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [4.222116404419777, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.065546335746074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '3640.1', 'coefficient_field': 'CDF', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.6873995617361737, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.2221164044197774, 0], [17.0, 0]], [[1.0, 0], [0.7778835955802227, 0], [19.0, 0]], [[1.0, 0], [-7.819031932311901, 0], [23.0, 0]], [[1.0, 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[0]], 'group': 'GL2', 'index': 6, 'label': '2-3640-1.1-c1-0-6', 'leading_term': '0.80062211698356816994182685379462', '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/3640/2/a/p/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.8006221169835682, 0.7944113361295356, 0.7757651415296586, 0.7446477144230207, 0.7010180869262297, 0.6448568984295391, 0.5762013194699419, 0.49518591109157695, 0.40208691760412907, 0.29736740272057616, 0.1817207028730822, 0.05610984570888469, -0.078199175263983, -0.21961210138694917, -0.3661906274253971, -0.5156473918094151, -0.665352706518625, -0.8123537082501233, -0.9534063194869318, -1.085020102089738, -1.2035157625145152, -1.3050947249889744, -1.3859198285335896, -1.442205830473018, -1.4703180209718822, -1.4668768806463315, 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'6.27671680147623795093464811241921', '7.02563063596333029396700723541561', '7.54312165642481378372799501941141', '8.524292984173163514023410396298020'], 'prelabel': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58017825424418269792892065228', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.68587159636540516011195790087', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11323311213912354113152463034', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.065546335746074, 'bad_primes': [2, 5, 7, 13], 'central_character': '1.1', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3640/2/a/p/1/1'], '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': '2-3640-1.1-c1-0-6', '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': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58017825424418269792892065228', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '735463312232004479266766945668', 'Lhash_array': ['735463312232004479266766945668'], 'label': '2-3640-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3640/2/a/p/1/1'}