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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_85.59', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.7071067811865476, 0.7071067811865476], 'a7': [-0.7071067811865476, 0.7071067811865476], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 0.39473834048527545, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [17, [1]]], 'bad_primes': [5, 17], 'central_character': '85.59', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 85, 'conductor_radical': 85, 'conjugate': 'dirichlet_L_85.49', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^1', 'a^4', 0, 'a^3', 'a^3', 'a^6', 'a^2', 0, 'a^3', 'a^5', 'a^0', 'a^5', 0, 'a^0', 0, 'a^4', 'a^6', 0, 'a^4', 'a^5', 'a^7', 'a^7', 0, 'a^2', 'a^3', 'a^7', 'a^1', 0, 'a^5', 'a^2', 'a^4', 0, 0, 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'186.8419066427015639830991968616', '187.325320934688704732919333985190', '188.072945686534142537657361150991', '188.88165193754236054670877506641', '189.92877695762975700088435316341', '190.59466280944173914783228612011', '191.20234230774154182000488176839', '192.274977293452326362009809109320', '193.12758348552699934347125434441', '193.83251722171078743902204764973', '194.66138629912614816601559869163', '195.74460269467891676733968576147', '196.531689856030723579295637755992', '197.04534700522119463925729047436', '197.64473050884947939464119861694', '198.70825364789805207369599986432', '199.22357425798434580778047438679', '199.70741937263384194682393950967'], 'prelabel': '1-85-85.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.39473834048527545, 'root_angle': 0.7741785140991118, 'root_number': '-0.758727356476261289179969185973+0.651408319362398323341418504665*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38708925705', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.724723403576384985025150424262+0.780598320874480650146287384408*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.85299293783', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.36653930812', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.63105648181', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.39473834048527545, 'bad_primes': [5, 17], 'central_character': '85.59', 'conductor': 85, 'conductor_radical': 85, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/85/59'], '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': '1-85-85.59-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': '1-85-85.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.39473834048527545, 'root_angle': 0.3870892570495559, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.85299293783', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_85.59', 'Lhash_array': ['dirichlet_L_85.59'], 'label': '1-85-85.59-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/85/59'}