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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_683.32', 'a10': [0.41541501300188644, -0.9096319953545183], 'a2': [0.14231483827328514, 0.9898214418809327], 'a3': [1.0, 0.0], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [-0.8412535328311812, -0.5406408174555976], 'a6': [0.14231483827328514, 0.9898214418809327], 'a7': [-0.8412535328311812, -0.5406408174555976], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 73.3985436347289, 'analytic_normalization': 0, 'bad_lfactors': [[683, [1]]], 'bad_primes': [683], 'central_character': '683.32', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 683, 'conductor_radical': 683, 'conjugate': 'dirichlet_L_683.619', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^0', 'a^10', 'a^13', 'a^5', 'a^13', 'a^15', 'a^0', 'a^18', 'a^5', 'a^10', 'a^7', 'a^18', 'a^13', 'a^20', 'a^5', 'a^5', 'a^12', 'a^1', 'a^13', 'a^10', 'a^17', 'a^15', 'a^4', 'a^12', 'a^0', 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'195.24678016044117973539933384894', '196.168948976847851678836771506372', '196.36887866598395498620902726551', '196.9466399587380130849664951348', '197.72061202793402808663742913434', '198.30930949730049593852182647064', '198.66925475777042511340839402685', '199.30779811287704445320347639956'], 'prelabel': '1-683-683.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 73.3985436347289, 'root_angle': 0.062319970906144516, 'root_number': '0.980895462340755696370055647097+0.194535580188599749743056709569*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0311599854531', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.00771715364957050583484111142+0.389132618359858838344615516547*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.433777586654', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.06501621074', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.66274607694', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.3985436347289, 'bad_primes': [683], 'central_character': '683.32', 'conductor': 683, 'conductor_radical': 683, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/683/32'], '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': '1-683-683.32-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': '1-683-683.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 73.3985436347289, 'root_angle': 0.031159985453072258, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.433777586654', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_683.32', 'Lhash_array': ['dirichlet_L_683.32'], 'label': '1-683-683.32-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/683/32'}