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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_43.39', 'a10': [0.6234898018587335, -0.7818314824680298], 'a2': [0.2225209339563144, 0.9749279121818236], 'a3': [0.2225209339563144, -0.9749279121818236], 'a4': [-0.9009688679024191, 0.4338837391175581], 'a5': [-0.6234898018587335, -0.7818314824680298], 'a6': [1.0, 0.0], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [-0.6234898018587335, -0.7818314824680298], 'a9': [-0.9009688679024191, -0.4338837391175581], 'algebraic': True, 'analytic_conductor': 4.620991766168876, 'analytic_normalization': 0, 'bad_lfactors': [[43, [1]]], 'bad_primes': [43], 'central_character': '43.39', 'coeff_info': ['x^14 - 1', '0.900968867902419 + 0.433883739117558*I', '\\\\zeta_{14}'], 'conductor': 43, 'conductor_radical': 43, 'conjugate': 'dirichlet_L_43.32', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^11', 'a^6', 'a^9', 'a^0', 'a^7', 'a^9', 'a^8', 'a^12', 'a^8', 'a^3', 'a^2', 'a^10', 'a^6', 'a^12', 'a^12', 'a^11', 'a^13', 'a^1', 'a^4', 'a^11', 'a^8', 'a^6', 'a^4', 'a^5', 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'199.97759819393624970689995116914'], 'prelabel': '1-43-43.39-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.620991766168876, 'root_angle': -0.6090587029649038, 'root_number': '-0.335954097068381210833532599173-0.941878359801821062690811261160*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.304529351482', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(14)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.763034943443155201768804559008-0.0906274663281204984402900411094*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.368654505307', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.42809008015', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.44267966817', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.620991766168876, 'bad_primes': [43], 'central_character': '43.39', 'conductor': 43, 'conductor_radical': 43, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/43/39'], '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': '1-43-43.39-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': '1-43-43.39-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.620991766168876, 'root_angle': -0.3045293514824519, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.368654505307', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_43.39', 'Lhash_array': ['dirichlet_L_43.39'], 'label': '1-43-43.39-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/43/39'}