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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2415.398', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9898214418809327, -0.14231483827328514], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9594929736144974, -0.28173255684142967], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9096319953545183, -0.41541501300188644], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 11.21521285025812, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 5, 7, 23], 'central_character': '2415.398', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 2415, 'conductor_radical': 2415, 'conjugate': 'dirichlet_L_2415.2057', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 0, 'a^42', 0, 0, 0, 'a^41', 0, 0, 'a^12', 0, 'a^37', 0, 0, 'a^40', 'a^35', 0, 'a^42', 0, 0, 'a^11', 0, 0, 0, 'a^36', 0, 0, 'a^24', 0, 'a^30', 'a^39', 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'data': '0.843031765875', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.93551727939', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.76000416645', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 11.21521285025812, 'bad_primes': [3, 5, 7, 23], 'central_character': '2415.398', 'conductor': 2415, 'conductor_radical': 2415, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2415/398'], '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': '1-2415-2415.398-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2415-2415.398-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.21521285025812, 'root_angle': -0.13753750394443567, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.843031765875', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2415.398', 'Lhash_array': ['dirichlet_L_2415.398'], 'factors': ['1-2415-2415.398-r0-0-0'], 'label': '1-2415-2415.398-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2415/398'}
Lfunction data - 1-2415-2415.398-r0-0-0