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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_79.53', 'a10': [0.5680647467311558, 0.8229838658936564], 'a2': [0.9485364419471455, -0.3166679938014725], 'a3': [0.99675730813421, -0.08046656871672588], 'a4': [0.7994427634035012, -0.6007422642379789], 'a5': [0.27821746391645263, 0.9605181116313724], 'a6': [0.9199794436588242, -0.3919666098600751], 'a7': [-0.4286925614030542, 0.9034504346103823], 'a8': [0.5680647467311558, -0.8229838658936564], 'a9': [0.9870502626379128, -0.16041128085776024], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.53', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^74', 'a^77', 'a^70', 'a^16', 'a^73', 'a^25', 'a^66', 'a^76', 'a^12', 'a^10', 'a^69', 'a^44', 'a^21', 'a^15', 'a^62', 'a^57', 'a^72', 'a^46', 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'184.82728197263859495634232328231', '185.59381904209652641270568398035', '186.259706173853445088339954617780', '186.82160920385110760287738463857', '187.31912440739653281440085242142', '188.56747388849185293800472449467', '189.72138507178044933394145748011', '190.53157910690691381712110730169', '191.07743308918554082166462641184', '192.12793634285586709509418763817', '192.95261569527219882288403282772', '193.43138565654590220939723260934', '194.12736883420345384758396709581', '195.4075691508372117435618522200', '195.81541334313384637459430994703', '196.89895063773812177012937174801', '197.1267442105882360598865758479', '198.49656548850444967486605197379', '198.57623747303315128154708899512'], 'prelabel': '1-79-79.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.018018781694492145, 'root_number': '0.998398213526892030752850729697-0.0565774445014133421774499201934*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00900939084725', 'prec': 57}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.49537943793128191870431161885-0.127970329213371926054461074085*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.23933403024', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.90763838053', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.50510319127', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.53', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/53'], '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': '1-79-79.53-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': '1-79-79.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.009009390847246073, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23933403024', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_79.53', 'Lhash_array': ['dirichlet_L_79.53'], 'label': '1-79-79.53-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/53'}