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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2009.272', 'a10': [-0.4738686624729987, 0.880595531856738], 'a2': [0.8345732537213026, -0.5508969814521025], 'a3': [-0.9438833303083676, 0.3302790619551671], 'a4': [0.3930250316539236, -0.9195277725514507], 'a5': [-0.880595531856738, 0.4738686624729987], 'a6': [-0.6057900438408199, 0.795624548881781], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.17855689479863665, -0.9839295885986297], 'a9': [0.7818314824680298, -0.6234898018587335], 'algebraic': True, 'analytic_conductor': 9.329756776881393, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '2009.272', 'coeff_info': ['x^280 - 1', '0.999748234942507 + 0.0224380642958049*I', '\\\\zeta_{280}'], 'conductor': 2009, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_2009.1588', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^254', 'a^125', 'a^228', 'a^118', 'a^99', 0, 'a^202', 'a^250', 'a^92', 'a^37', 'a^73', 'a^149', 0, 'a^243', 'a^176', 'a^227', 'a^224', 'a^91', 'a^66', 0, 'a^11', 'a^4', 'a^47', 'a^236', 'a^123', 'a^95', 0, 'a^73', 'a^217', 'a^112', 'a^150', 'a^162', 'a^201', 0, 'a^198', 'a^248', 'a^65', 'a^274', 'a^40', 0, 0, 'a^134', 'a^265', 'a^88', 'a^258', 'a^219', 'a^21', 0, 'a^210', 'a^72', 'a^97', 'a^53', 'a^69', 'a^155', 0, 'a^216', 'a^47', 'a^204', 'a^191', 'a^66', 'a^86', 0, 'a^124', 'a^267', 'a^136', 'a^63', 'a^175', 'a^129', 0, 'a^137', 'a^172', 'a^250', 'a^222', 'a^81', 'a^39', 0, 'a^248', 'a^245', 'a^14', 'a^220', 0, 'a^180', 0, 'a^65', 'a^108', 'a^198', 'a^239', 'a^61', 'a^62', 0, 'a^232', 'a^237', 'a^193', 'a^209', 'a^275', 'a^63', 0, 'a^7', 'a^184'], 'euler_factors': [[1, 'a^254'], [1, 'a^125'], [1, 'a^118'], [0], [1, 'a^37'], [1, 'a^149'], [1, 'a^227'], [1, 'a^91'], [1, 'a^4'], [1, 'a^73'], [1, 'a^112'], [1, 'a^248'], [0], [1, 'a^134'], [1, 'a^219'], [1, 'a^53'], [1, 'a^204'], [1, 'a^66'], [1, 'a^63'], [1, 'a^137'], [1, 'a^250'], [1, 'a^245'], [1, 'a^180'], [1, 'a^61'], [1, 'a^63'], [1, 'a^251']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2009-2009.272-r0-0-0', 'leading_term': '1.41793123784576700395976169707-0.137564153831378768082039312618*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/2009/272', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.424588674557738, 1.3910972874501748, 0.6313480154364064, -0.936151332613572, -2.264441211559144, -2.074365601037874, -0.18939602047841111, 2.0479951984012628, 2.859457257500593, 1.7098840747750046, -0.13276657643195927, -0.886760254915952, -0.11938557241783317, 0.8938203391832348, 0.7969386363080595, -0.1332860851315181, -0.362005436295495, 0.7745098640902623, 1.9102099845587992, 1.2320092063386037, -0.977609712626521, -2.3121073575062843, -1.3204664116745277, 0.019145053238061583, -1.872035460296838, 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'190.53734342553618081631272828178', '191.09601144940623468525344174686', '191.777709378859532465593964801386', '192.06627276368433066197711329680', '193.05279026557983850795178906715', '193.46191846305889435447910300358', '193.86206546905687420972046527946', '194.22608246557874923897574065165', '195.1067090868487655719578178465', '195.526283010526272648451103899593', '195.72016627147723398439111182203', '196.2425991469580239414513007232', '197.411909614134918401166043191', '197.851014684181858006192658863394', '198.49737887009100431769935155066', '199.02450444324059289377120005995', '199.62509639800839440874932781021'], 'prelabel': '1-2009-2009.272-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': -0.061570570185138875, 'root_number': '0.981350740884953573293109443014-0.192225709426581935513138484001*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0307852850926', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(280)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.06303826393086908789331660006-0.192505442794045540560186838734*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.762659174761', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.89973596712', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.09877522732', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.329756776881393, 'bad_primes': [7, 41], 'central_character': '2009.272', 'conductor': 2009, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2009/272'], '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': '1-2009-2009.272-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': '1-2009-2009.272-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': -0.030785285092569437, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.762659174761', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2009.272', 'Lhash_array': ['dirichlet_L_2009.272'], 'label': '1-2009-2009.272-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2009/272'}
Lfunction data - 1-2009-2009.272-r0-0-0