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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.116', 'a10': [-0.9906859460363308, 0.1361666490962466], 'a2': [-0.7757112907044198, 0.6310879443260528], 'a3': [-0.7757112907044198, 0.6310879443260528], 'a4': [0.20345601305263378, -0.9790840876823229], 'a5': [0.8544194045464886, 0.5195839500354336], 'a6': [0.20345601305263378, -0.9790840876823229], 'a7': [0.20345601305263378, 0.9790840876823229], 'a8': [0.46006503773115215, 0.8878852184023752], 'a9': [0.20345601305263378, -0.9790840876823229], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.116', 'coeff_info': ['x^23 - 1', '0.962917287347799 + 0.269796771157024*I', '\\\\zeta_{23}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.415', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^9', 'a^18', 'a^2', 'a^18', 'a^5', 'a^4', 'a^18', 'a^11', 'a^1', 'a^4', 'a^12', 'a^14', 'a^11', 'a^13', 'a^12', 'a^4', 'a^9', 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False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.9943289224952742, 'root_number': '-0.999841295431967510093553059117+0.0178152729118884236551720756515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.497164461248', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(23)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.469095666713146049640033369877+0.433381478417246361734679469844*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.54708501271', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.64573493331', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.522987003', 'prec': 37}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.116', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/116'], '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': '1-23e2-529.116-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': '1-23e2-529.116-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.4971644612476371, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54708501271', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.116', 'Lhash_array': ['dirichlet_L_529.116'], 'label': '1-23e2-529.116-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/116'}