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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3744.3035', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.25881904510252074, -0.9659258262890683], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 402.3486784310761, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '3744.3035', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 3744, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_3744.3443', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^17', 0, 'a^0', 0, 0, 0, 'a^5', 0, 0, 0, 0, 0, 'a^20', 0, 'a^11', 0, 0, 0, 'a^6', 0, 'a^10', 0, 0, 0, 'a^29', 0, 'a^14', 0, 0, 0, 'a^41', 0, 'a^25', 0, 0, 0, 'a^0', 0, 'a^15', 0, 0, 0, 'a^10', 0, 'a^0', 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'prelabel': '1-3744-3744.3035-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 402.3486784310761, 'root_angle': 0.9946533054797118, 'root_number': '-0.999858931424152455776303350346+0.0167963463691362590647462991392*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.00762887846325242113396729283-0.0969856117125427126977483171689*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0331067571248', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.22173573588', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.68301991661', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 402.3486784310761, 'bad_primes': [2, 3, 13], 'central_character': '3744.3035', 'conductor': 3744, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3744/3035'], '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': '1-3744-3744.3035-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': '1-3744-3744.3035-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 402.3486784310761, 'root_angle': 0.4973266527398559, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0331067571248', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3744.3035', 'Lhash_array': ['dirichlet_L_3744.3035'], 'label': '1-3744-3744.3035-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3744/3035'}