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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2015.1918', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9135454576426009, 0.4067366430758002], 'a3': [0.9945218953682733, 0.10452846326765347], 'a4': [0.6691306063588582, 0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.8660254037844386, 0.5], 'a7': [-0.6691306063588582, -0.7431448254773942], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 216.54182346116943, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [13, [1]], [31, [1]]], 'bad_primes': [5, 13, 31], 'central_character': '2015.1918', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 2015, 'conductor_radical': 2015, 'conjugate': 'dirichlet_L_2015.457', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^1', 'a^8', 0, 'a^5', 'a^38', 'a^12', 'a^2', 0, 'a^43', 'a^9', 0, 'a^42', 0, 'a^16', 'a^17', 'a^6', 'a^29', 0, 'a^39', 'a^47', 'a^7', 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'193.47638777390009039355229253016', '193.728613225425224743994029555133', '194.54402579639420268748721255802', '194.84479826046320179381465184921', '195.587082651507666305927354913995', '196.27874226984066159458291351858', '196.79354994645247847573132862800', '197.08097148301654014565191318610', '197.6586839624854694195457682549', '198.06204955365953174055377468711', '198.795341250831025688265122665871', '199.24989023122621808626140569279'], 'prelabel': '1-2015-2015.1918-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 216.54182346116943, 'root_angle': 0.5153962492738713, 'root_number': '-0.0483498857533760125174839787447+0.998830460362335709689500055657*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.257698124637', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.25967960979306169599372459934+0.857663621639402811082232529236*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.0801042787', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.27762167914', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.09779088406', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 216.54182346116943, 'bad_primes': [5, 13, 31], 'central_character': '2015.1918', 'conductor': 2015, 'conductor_radical': 2015, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2015/1918'], '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': '1-2015-2015.1918-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': '1-2015-2015.1918-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 216.54182346116943, 'root_angle': 0.25769812463693564, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0801042787', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2015.1918', 'Lhash_array': ['dirichlet_L_2015.1918'], 'label': '1-2015-2015.1918-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2015/1918'}