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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_41.7', 'a10': [0.30901699437494745, -0.9510565162951535], 'a2': [-0.5877852522924731, 0.8090169943749475], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [-0.30901699437494745, -0.9510565162951535], 'a5': [-0.9510565162951535, 0.30901699437494745], 'a6': [0.9876883405951378, -0.15643446504023087], 'a7': [0.9876883405951378, 0.15643446504023087], 'a8': [0.9510565162951535, 0.30901699437494745], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 4.406061916579626, 'analytic_normalization': 0, 'bad_lfactors': [[41, [1]]], 'bad_primes': [41], 'central_character': '41.7', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 41, 'conductor_radical': 41, 'conjugate': 'dirichlet_L_41.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^25', 'a^28', 'a^18', 'a^39', 'a^1', 'a^2', 'a^10', 'a^32', 'a^37', 'a^13', 'a^9', 'a^15', 'a^3', 'a^16', 'a^7', 'a^24', 'a^31', 'a^6', 'a^26', 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'199.80466611021210550237941865578'], 'prelabel': '1-41-41.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.406061916579626, 'root_angle': 0.30528241313780774, 'root_number': '0.574279141273299967652557464676+0.818659555553101192535222546790*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.152641206569', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.649260490932499006252731143485+0.180036933200298001252504976839*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.24944840552', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.66650029732', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.35801007816', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.406061916579626, 'bad_primes': [41], 'central_character': '41.7', 'conductor': 41, 'conductor_radical': 41, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/41/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-41-41.7-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-41-41.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.406061916579626, 'root_angle': 0.15264120656890387, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24944840552', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_41.7', 'Lhash_array': ['dirichlet_L_41.7'], 'label': '1-41-41.7-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/41/7'}