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lfunc_lfunctions • Show schema
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{'Lhash': '1699213969498661704705543063367', 'a10': [0.0, 0.0], 'a2': [-0.20905692653530694, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.9562952014676114, 0.0], 'a5': [0.0, 0.0], 'a6': [0.20905692653530694, 0.0], 'a7': [0.591022937785412, 0.0], 'a8': [0.8270909152852018, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.20905692653530694, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.591022937785412, 0], [7.0, 0]], [[1.0, 0], [0.8707957138175905, 0], [11.0, 0]], [[1.0, 0], [-1.150568489849769, 0], [13.0, 0]], [[1.0, 0], [4.933954606602582, 0], [17.0, 0]], [[1.0, 0], [2.849431510150231, 0], [19.0, 0]], [[1.0, 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'7.36852667471047721159185492280127', '8.076325453989171989904704369344259', '9.104420090777818617354725582030638'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34044347014290301584258655770', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81598929201090046958090229333', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19831349910687715367917400501', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/g/1/2'], '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': '2-1875-1.1-c1-0-41', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34044347014290301584258655770', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1699213969498661704705543063367', 'Lhash_array': ['1699213969498661704705543063367'], 'label': '2-1875-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/g/1/2'}