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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1001.207', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.9135454576426009, 0.4067366430758002], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [0.10452846326765347, 0.9945218953682733], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.207', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.324', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^14', 'a^26', 'a^7', 'a^27', 0, 'a^9', 'a^28', 'a^20', 0, 'a^10', 0, 0, 'a^21', 'a^22', 'a^2', 'a^11', 'a^19', 'a^3', 0, 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'189.47385935964598715698831917286', '190.07017022828881036820112571322', '190.518775722935469813195204049819', '191.154831128867332569046212048326', '192.01396159342447378946687692922', '192.53969132114151972810771745449', '193.137402525376923421565350998', '193.97197518031430534165681783583', '194.30685652734403536088853189533', '194.89769146321293831758882450388', '195.85292908676186288072913169993', '196.11622942316674751657560190948', '196.99438670919159892838618386991', '197.65901491412552166230646506954', '198.2711813401103681181522733324', '198.603595390179055382630419164593', '199.334297638084588171597826643997', '199.61921812062395688278916234682'], 'prelabel': '1-1001-1001.207-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.7943927868068403, 'root_number': '-0.798537832622824636851849383619+0.601944623590942711857357980804*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.397196393403', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.471650806226243702106824135141+0.252223414045588066127191010096*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.1051837204', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.26622276056', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.49696277548', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.207', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/207'], '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': '1-1001-1001.207-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': '1-1001-1001.207-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.39719639340342017, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.1051837204', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1001.207', 'Lhash_array': ['dirichlet_L_1001.207'], 'label': '1-1001-1001.207-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/207'}