Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.5 | ||
Root | \(1.04641 - 1.81243i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.471 |
Dual form | 637.2.h.m.165.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.579810 | −0.409988 | −0.204994 | − | 0.978763i | \(-0.565717\pi\) | ||||
−0.204994 | + | 0.978763i | \(0.565717\pi\) | |||||||
\(3\) | −0.946019 | + | 1.63855i | −0.546185 | + | 0.946019i | 0.452347 | + | 0.891842i | \(0.350587\pi\) |
−0.998531 | + | 0.0541772i | \(0.982746\pi\) | |||||||
\(4\) | −1.66382 | −0.831910 | ||||||||
\(5\) | 0.736809 | − | 1.27619i | 0.329511 | − | 0.570729i | −0.652904 | − | 0.757441i | \(-0.726450\pi\) |
0.982415 | + | 0.186711i | \(0.0597828\pi\) | |||||||
\(6\) | 0.548512 | − | 0.950050i | 0.223929 | − | 0.387856i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.12432 | 0.751061 | ||||||||
\(9\) | −0.289905 | − | 0.502131i | −0.0966351 | − | 0.167377i | ||||
\(10\) | −0.427209 | + | 0.739948i | −0.135095 | + | 0.233992i | ||||
\(11\) | −0.289905 | + | 0.502131i | −0.0874097 | + | 0.151398i | −0.906415 | − | 0.422387i | \(-0.861192\pi\) |
0.819006 | + | 0.573785i | \(0.194526\pi\) | |||||||
\(12\) | 1.57401 | − | 2.72626i | 0.454376 | − | 0.787003i | ||||
\(13\) | 0.128893 | − | 3.60325i | 0.0357485 | − | 0.999361i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.39407 | + | 2.41460i | 0.359947 | + | 0.623447i | ||||
\(16\) | 2.09594 | 0.523984 | ||||||||
\(17\) | 1.19657 | 0.290211 | 0.145105 | − | 0.989416i | \(-0.453648\pi\) | ||||
0.145105 | + | 0.989416i | \(0.453648\pi\) | |||||||
\(18\) | 0.168090 | + | 0.291141i | 0.0396192 | + | 0.0686225i | ||||
\(19\) | −0.230479 | − | 0.399201i | −0.0528755 | − | 0.0915831i | 0.838376 | − | 0.545092i | \(-0.183505\pi\) |
−0.891252 | + | 0.453509i | \(0.850172\pi\) | |||||||
\(20\) | −1.22592 | + | 2.12335i | −0.274123 | + | 0.474796i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.168090 | − | 0.291141i | 0.0358369 | − | 0.0620714i | ||||
\(23\) | 2.36795 | 0.493752 | 0.246876 | − | 0.969047i | \(-0.420596\pi\) | ||||
0.246876 | + | 0.969047i | \(0.420596\pi\) | |||||||
\(24\) | −2.00965 | + | 3.48081i | −0.410218 | + | 0.710518i | ||||
\(25\) | 1.41423 | + | 2.44951i | 0.282845 | + | 0.489902i | ||||
\(26\) | −0.0747335 | + | 2.08920i | −0.0146565 | + | 0.409726i | ||||
\(27\) | −4.57909 | −0.881247 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.44550 | + | 5.96777i | 0.639813 | + | 1.10819i | 0.985474 | + | 0.169828i | \(0.0543214\pi\) |
−0.345661 | + | 0.938359i | \(0.612345\pi\) | |||||||
\(30\) | −0.808297 | − | 1.40001i | −0.147574 | − | 0.255606i | ||||
\(31\) | 2.22171 | + | 3.84811i | 0.399031 | + | 0.691141i | 0.993607 | − | 0.112898i | \(-0.0360134\pi\) |
−0.594576 | + | 0.804040i | \(0.702680\pi\) | |||||||
\(32\) | −5.46389 | −0.965888 | ||||||||
\(33\) | −0.548512 | − | 0.950050i | −0.0954837 | − | 0.165383i | ||||
\(34\) | −0.693783 | −0.118983 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.482350 | + | 0.835455i | 0.0803917 | + | 0.139242i | ||||
\(37\) | 9.16301 | 1.50639 | 0.753195 | − | 0.657798i | \(-0.228512\pi\) | ||||
0.753195 | + | 0.657798i | \(0.228512\pi\) | |||||||
\(38\) | 0.133634 | + | 0.231461i | 0.0216783 | + | 0.0375479i | ||||
\(39\) | 5.78218 | + | 3.61994i | 0.925889 | + | 0.579654i | ||||
\(40\) | 1.56522 | − | 2.71104i | 0.247483 | − | 0.428653i | ||||
\(41\) | −2.00845 | − | 3.47874i | −0.313667 | − | 0.543288i | 0.665486 | − | 0.746410i | \(-0.268224\pi\) |
−0.979153 | + | 0.203123i | \(0.934891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.02951 | + | 6.97931i | −0.614494 | + | 1.06433i | 0.375979 | + | 0.926628i | \(0.377306\pi\) |
−0.990473 | + | 0.137706i | \(0.956027\pi\) | |||||||
\(44\) | 0.482350 | − | 0.835455i | 0.0727170 | − | 0.125950i | ||||
\(45\) | −0.854419 | −0.127369 | ||||||||
\(46\) | −1.37296 | −0.202432 | ||||||||
\(47\) | −5.75964 | + | 9.97598i | −0.840129 | + | 1.45515i | 0.0496552 | + | 0.998766i | \(0.484188\pi\) |
−0.889785 | + | 0.456381i | \(0.849146\pi\) | |||||||
\(48\) | −1.98280 | + | 3.43430i | −0.286192 | + | 0.495699i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.819983 | − | 1.42025i | −0.115963 | − | 0.200854i | ||||
\(51\) | −1.13198 | + | 1.96064i | −0.158509 | + | 0.274545i | ||||
\(52\) | −0.214455 | + | 5.99515i | −0.0297395 | + | 0.831378i | ||||
\(53\) | 4.69760 | + | 8.13647i | 0.645264 | + | 1.11763i | 0.984240 | + | 0.176836i | \(0.0565861\pi\) |
−0.338976 | + | 0.940795i | \(0.610081\pi\) | |||||||
\(54\) | 2.65501 | 0.361300 | ||||||||
\(55\) | 0.427209 | + | 0.739948i | 0.0576049 | + | 0.0997746i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.872150 | 0.115519 | ||||||||
\(58\) | −1.99773 | − | 3.46018i | −0.262315 | − | 0.454344i | ||||
\(59\) | −0.240919 | −0.0313650 | −0.0156825 | − | 0.999877i | \(-0.504992\pi\) | ||||
−0.0156825 | + | 0.999877i | \(0.504992\pi\) | |||||||
\(60\) | −2.31948 | − | 4.01746i | −0.299444 | − | 0.518652i | ||||
\(61\) | 3.86355 | + | 6.69187i | 0.494677 | + | 0.856806i | 0.999981 | − | 0.00613544i | \(-0.00195298\pi\) |
−0.505304 | + | 0.862941i | \(0.668620\pi\) | |||||||
\(62\) | −1.28817 | − | 2.23118i | −0.163598 | − | 0.283360i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.02385 | −0.127982 | ||||||||
\(65\) | −4.50346 | − | 2.81940i | −0.558585 | − | 0.349703i | ||||
\(66\) | 0.318033 | + | 0.550849i | 0.0391471 | + | 0.0678048i | ||||
\(67\) | 0.724287 | − | 1.25450i | 0.0884857 | − | 0.153262i | −0.818385 | − | 0.574670i | \(-0.805131\pi\) |
0.906871 | + | 0.421408i | \(0.138464\pi\) | |||||||
\(68\) | −1.99088 | −0.241429 | ||||||||
\(69\) | −2.24013 | + | 3.88001i | −0.269680 | + | 0.467099i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.25725 | − | 10.8379i | 0.742599 | − | 1.28622i | −0.208709 | − | 0.977978i | \(-0.566926\pi\) |
0.951308 | − | 0.308241i | \(-0.0997405\pi\) | |||||||
\(72\) | −0.615852 | − | 1.06669i | −0.0725788 | − | 0.125710i | ||||
\(73\) | −1.84701 | − | 3.19911i | −0.216176 | − | 0.374427i | 0.737460 | − | 0.675391i | \(-0.236025\pi\) |
−0.953636 | + | 0.300963i | \(0.902692\pi\) | |||||||
\(74\) | −5.31281 | −0.617601 | ||||||||
\(75\) | −5.35154 | −0.617943 | ||||||||
\(76\) | 0.383476 | + | 0.664199i | 0.0439877 | + | 0.0761889i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.35257 | − | 2.09888i | −0.379603 | − | 0.237651i | ||||
\(79\) | −8.03967 | + | 13.9251i | −0.904533 | + | 1.56670i | −0.0829909 | + | 0.996550i | \(0.526447\pi\) |
−0.821542 | + | 0.570147i | \(0.806886\pi\) | |||||||
\(80\) | 1.54430 | − | 2.67481i | 0.172658 | − | 0.299053i | ||||
\(81\) | 5.20163 | − | 9.00948i | 0.577958 | − | 1.00105i | ||||
\(82\) | 1.16452 | + | 2.01701i | 0.128600 | + | 0.222741i | ||||
\(83\) | 15.4005 | 1.69042 | 0.845212 | − | 0.534431i | \(-0.179474\pi\) | ||||
0.845212 | + | 0.534431i | \(0.179474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.881643 | − | 1.52705i | 0.0956276 | − | 0.165632i | ||||
\(86\) | 2.33635 | − | 4.04668i | 0.251935 | − | 0.436364i | ||||
\(87\) | −13.0380 | −1.39782 | ||||||||
\(88\) | −0.615852 | + | 1.06669i | −0.0656500 | + | 0.113709i | ||||
\(89\) | −2.49107 | −0.264052 | −0.132026 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132026 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(90\) | 0.495401 | 0.0522198 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.93984 | −0.410757 | ||||||||
\(93\) | −8.40712 | −0.871778 | ||||||||
\(94\) | 3.33950 | − | 5.78418i | 0.344443 | − | 0.596593i | ||||
\(95\) | −0.679276 | −0.0696922 | ||||||||
\(96\) | 5.16894 | − | 8.95287i | 0.527553 | − | 0.913749i | ||||
\(97\) | 7.82275 | − | 13.5494i | 0.794280 | − | 1.37573i | −0.129015 | − | 0.991643i | \(-0.541182\pi\) |
0.923295 | − | 0.384091i | \(-0.125485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.336180 | 0.0337874 | ||||||||
\(100\) | −2.35302 | − | 4.07555i | −0.235302 | − | 0.407555i | ||||
\(101\) | 7.00682 | − | 12.1362i | 0.697205 | − | 1.20759i | −0.272227 | − | 0.962233i | \(-0.587760\pi\) |
0.969432 | − | 0.245361i | \(-0.0789066\pi\) | |||||||
\(102\) | 0.656332 | − | 1.13680i | 0.0649866 | − | 0.112560i | ||||
\(103\) | 5.37461 | − | 9.30910i | 0.529576 | − | 0.917253i | −0.469829 | − | 0.882758i | \(-0.655684\pi\) |
0.999405 | − | 0.0344951i | \(-0.0109823\pi\) | |||||||
\(104\) | 0.273810 | − | 7.65445i | 0.0268493 | − | 0.750581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.72371 | − | 4.71761i | −0.264551 | − | 0.458215i | ||||
\(107\) | 3.75523 | 0.363031 | 0.181516 | − | 0.983388i | \(-0.441900\pi\) | ||||
0.181516 | + | 0.983388i | \(0.441900\pi\) | |||||||
\(108\) | 7.61878 | 0.733118 | ||||||||
\(109\) | 4.10417 | + | 7.10862i | 0.393108 | + | 0.680883i | 0.992858 | − | 0.119305i | \(-0.0380666\pi\) |
−0.599750 | + | 0.800187i | \(0.704733\pi\) | |||||||
\(110\) | −0.247700 | − | 0.429030i | −0.0236173 | − | 0.0409064i | ||||
\(111\) | −8.66838 | + | 15.0141i | −0.822766 | + | 1.42507i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.90423 | − | 6.76233i | 0.367279 | − | 0.636146i | −0.621860 | − | 0.783129i | \(-0.713623\pi\) |
0.989139 | + | 0.146982i | \(0.0469560\pi\) | |||||||
\(114\) | −0.505682 | −0.0473614 | ||||||||
\(115\) | 1.74473 | − | 3.02196i | 0.162697 | − | 0.281799i | ||||
\(116\) | −5.73269 | − | 9.92930i | −0.532266 | − | 0.921913i | ||||
\(117\) | −1.84667 | + | 0.979879i | −0.170724 | + | 0.0905898i | ||||
\(118\) | 0.139687 | 0.0128593 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.96145 | + | 5.12939i | 0.270342 | + | 0.468247i | ||||
\(121\) | 5.33191 | + | 9.23514i | 0.484719 | + | 0.839558i | ||||
\(122\) | −2.24013 | − | 3.88001i | −0.202812 | − | 0.351280i | ||||
\(123\) | 7.60014 | 0.685281 | ||||||||
\(124\) | −3.69652 | − | 6.40257i | −0.331958 | − | 0.574967i | ||||
\(125\) | 11.5361 | 1.03182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.469682 | + | 0.813513i | 0.0416775 | + | 0.0721876i | 0.886112 | − | 0.463472i | \(-0.153396\pi\) |
−0.844434 | + | 0.535659i | \(0.820063\pi\) | |||||||
\(128\) | 11.5214 | 1.01836 | ||||||||
\(129\) | −7.62398 | − | 13.2051i | −0.671254 | − | 1.16265i | ||||
\(130\) | 2.61115 | + | 1.63471i | 0.229013 | + | 0.143374i | ||||
\(131\) | −0.568583 | + | 0.984814i | −0.0496773 | + | 0.0860436i | −0.889795 | − | 0.456361i | \(-0.849153\pi\) |
0.840117 | + | 0.542404i | \(0.182486\pi\) | |||||||
\(132\) | 0.912625 | + | 1.58071i | 0.0794338 | + | 0.137583i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.419949 | + | 0.727373i | −0.0362781 | + | 0.0628355i | ||||
\(135\) | −3.37391 | + | 5.84379i | −0.290380 | + | 0.502954i | ||||
\(136\) | 2.54190 | 0.217966 | ||||||||
\(137\) | −8.63997 | −0.738162 | −0.369081 | − | 0.929397i | \(-0.620328\pi\) | ||||
−0.369081 | + | 0.929397i | \(0.620328\pi\) | |||||||
\(138\) | 1.29885 | − | 2.24967i | 0.110565 | − | 0.191505i | ||||
\(139\) | −7.27709 | + | 12.6043i | −0.617235 | + | 1.06908i | 0.372753 | + | 0.927930i | \(0.378414\pi\) |
−0.989988 | + | 0.141151i | \(0.954920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.8975 | − | 18.8749i | −0.917731 | − | 1.58956i | ||||
\(142\) | −3.62802 | + | 6.28391i | −0.304457 | + | 0.527334i | ||||
\(143\) | 1.77193 | + | 1.10932i | 0.148177 | + | 0.0927661i | ||||
\(144\) | −0.607623 | − | 1.05243i | −0.0506352 | − | 0.0877028i | ||||
\(145\) | 10.1547 | 0.843301 | ||||||||
\(146\) | 1.07091 | + | 1.85488i | 0.0886295 | + | 0.153511i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.2456 | −1.25318 | ||||||||
\(149\) | −6.69011 | − | 11.5876i | −0.548075 | − | 0.949294i | −0.998406 | − | 0.0564323i | \(-0.982027\pi\) |
0.450331 | − | 0.892861i | \(-0.351306\pi\) | |||||||
\(150\) | 3.10288 | 0.253349 | ||||||||
\(151\) | −8.06958 | − | 13.9769i | −0.656693 | − | 1.13743i | −0.981467 | − | 0.191634i | \(-0.938621\pi\) |
0.324774 | − | 0.945792i | \(-0.394712\pi\) | |||||||
\(152\) | −0.489611 | − | 0.848032i | −0.0397127 | − | 0.0687845i | ||||
\(153\) | −0.346892 | − | 0.600834i | −0.0280445 | − | 0.0485745i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.54790 | 0.525940 | ||||||||
\(156\) | −9.62050 | − | 6.02293i | −0.770257 | − | 0.482220i | ||||
\(157\) | −0.314340 | − | 0.544453i | −0.0250871 | − | 0.0434521i | 0.853209 | − | 0.521569i | \(-0.174653\pi\) |
−0.878296 | + | 0.478117i | \(0.841320\pi\) | |||||||
\(158\) | 4.66148 | − | 8.07393i | 0.370848 | − | 0.642327i | ||||
\(159\) | −17.7761 | −1.40973 | ||||||||
\(160\) | −4.02584 | + | 6.97296i | −0.318271 | + | 0.551261i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.01596 | + | 5.22379i | −0.236956 | + | 0.410420i | ||||
\(163\) | 5.84207 | + | 10.1188i | 0.457586 | + | 0.792563i | 0.998833 | − | 0.0483011i | \(-0.0153807\pi\) |
−0.541246 | + | 0.840864i | \(0.682047\pi\) | |||||||
\(164\) | 3.34170 | + | 5.78800i | 0.260943 | + | 0.451967i | ||||
\(165\) | −1.61659 | −0.125852 | ||||||||
\(166\) | −8.92937 | −0.693054 | ||||||||
\(167\) | 11.0293 | + | 19.1033i | 0.853474 | + | 1.47826i | 0.878054 | + | 0.478562i | \(0.158842\pi\) |
−0.0245803 | + | 0.999698i | \(0.507825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9668 | − | 0.928867i | −0.997444 | − | 0.0714513i | ||||
\(170\) | −0.511186 | + | 0.885399i | −0.0392061 | + | 0.0679070i | ||||
\(171\) | −0.133634 | + | 0.231461i | −0.0102193 | + | 0.0177003i | ||||
\(172\) | 6.70437 | − | 11.6123i | 0.511204 | − | 0.885431i | ||||
\(173\) | 5.69534 | + | 9.86463i | 0.433009 | + | 0.749994i | 0.997131 | − | 0.0756980i | \(-0.0241185\pi\) |
−0.564122 | + | 0.825692i | \(0.690785\pi\) | |||||||
\(174\) | 7.55958 | 0.573090 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.607623 | + | 1.05243i | −0.0458013 | + | 0.0793302i | ||||
\(177\) | 0.227914 | − | 0.394759i | 0.0171311 | − | 0.0296719i | ||||
\(178\) | 1.44435 | 0.108258 | ||||||||
\(179\) | 1.73621 | − | 3.00721i | 0.129771 | − | 0.224769i | −0.793817 | − | 0.608157i | \(-0.791909\pi\) |
0.923588 | + | 0.383387i | \(0.125243\pi\) | |||||||
\(180\) | 1.42160 | 0.105960 | ||||||||
\(181\) | −21.0992 | −1.56829 | −0.784145 | − | 0.620578i | \(-0.786898\pi\) | ||||
−0.784145 | + | 0.620578i | \(0.786898\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.6200 | −1.08074 | ||||||||
\(184\) | 5.03029 | 0.370838 | ||||||||
\(185\) | 6.75138 | − | 11.6937i | 0.496372 | − | 0.859741i | ||||
\(186\) | 4.87453 | 0.357418 | ||||||||
\(187\) | −0.346892 | + | 0.600834i | −0.0253672 | + | 0.0439373i | ||||
\(188\) | 9.58300 | − | 16.5982i | 0.698912 | − | 1.21055i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.393851 | 0.0285730 | ||||||||
\(191\) | −5.95945 | − | 10.3221i | −0.431211 | − | 0.746879i | 0.565767 | − | 0.824565i | \(-0.308580\pi\) |
−0.996978 | + | 0.0776864i | \(0.975247\pi\) | |||||||
\(192\) | 0.968585 | − | 1.67764i | 0.0699016 | − | 0.121073i | ||||
\(193\) | −7.18970 | + | 12.4529i | −0.517526 | + | 0.896381i | 0.482267 | + | 0.876024i | \(0.339814\pi\) |
−0.999793 | + | 0.0203567i | \(0.993520\pi\) | |||||||
\(194\) | −4.53571 | + | 7.85608i | −0.325645 | + | 0.564034i | ||||
\(195\) | 8.88009 | − | 4.71195i | 0.635916 | − | 0.337430i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.48462 | − | 6.03553i | −0.248269 | − | 0.430014i | 0.714777 | − | 0.699353i | \(-0.246528\pi\) |
−0.963046 | + | 0.269339i | \(0.913195\pi\) | |||||||
\(198\) | −0.194921 | −0.0138524 | ||||||||
\(199\) | −3.57352 | −0.253320 | −0.126660 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126660 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(200\) | 3.00427 | + | 5.20355i | 0.212434 | + | 0.367946i | ||||
\(201\) | 1.37038 | + | 2.37357i | 0.0966591 | + | 0.167418i | ||||
\(202\) | −4.06263 | + | 7.03668i | −0.285846 | + | 0.495099i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.88341 | − | 3.26216i | 0.131865 | − | 0.228397i | ||||
\(205\) | −5.91938 | −0.413427 | ||||||||
\(206\) | −3.11626 | + | 5.39751i | −0.217120 | + | 0.376062i | ||||
\(207\) | −0.686481 | − | 1.18902i | −0.0477138 | − | 0.0826426i | ||||
\(208\) | 0.270152 | − | 7.55218i | 0.0187316 | − | 0.523649i | ||||
\(209\) | 0.267268 | 0.0184873 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.05694 | + | 12.2230i | 0.485820 | + | 0.841464i | 0.999867 | − | 0.0162974i | \(-0.00518784\pi\) |
−0.514048 | + | 0.857762i | \(0.671855\pi\) | |||||||
\(212\) | −7.81595 | − | 13.5376i | −0.536802 | − | 0.929768i | ||||
\(213\) | 11.8390 | + | 20.5057i | 0.811192 | + | 1.40503i | ||||
\(214\) | −2.17732 | −0.148838 | ||||||||
\(215\) | 5.93795 | + | 10.2848i | 0.404965 | + | 0.701420i | ||||
\(216\) | −9.72746 | −0.661870 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.37964 | − | 4.12165i | −0.161169 | − | 0.279154i | ||||
\(219\) | 6.98922 | 0.472288 | ||||||||
\(220\) | −0.710799 | − | 1.23114i | −0.0479221 | − | 0.0830035i | ||||
\(221\) | 0.154229 | − | 4.31153i | 0.0103746 | − | 0.290025i | ||||
\(222\) | 5.02602 | − | 8.70532i | 0.337324 | − | 0.584263i | ||||
\(223\) | −0.454565 | − | 0.787329i | −0.0304399 | − | 0.0527235i | 0.850404 | − | 0.526130i | \(-0.176357\pi\) |
−0.880844 | + | 0.473407i | \(0.843024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.819983 | − | 1.42025i | 0.0546655 | − | 0.0946835i | ||||
\(226\) | −2.26371 | + | 3.92087i | −0.150580 | + | 0.260812i | ||||
\(227\) | 2.33512 | 0.154988 | 0.0774938 | − | 0.996993i | \(-0.475308\pi\) | ||||
0.0774938 | + | 0.996993i | \(0.475308\pi\) | |||||||
\(228\) | −1.45110 | −0.0961015 | ||||||||
\(229\) | −8.34036 | + | 14.4459i | −0.551147 | + | 0.954614i | 0.447045 | + | 0.894511i | \(0.352476\pi\) |
−0.998192 | + | 0.0601030i | \(0.980857\pi\) | |||||||
\(230\) | −1.01161 | + | 1.75216i | −0.0667036 | + | 0.115534i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.31934 | + | 12.6775i | 0.480538 | + | 0.832317i | ||||
\(233\) | 8.26321 | − | 14.3123i | 0.541341 | − | 0.937630i | −0.457486 | − | 0.889217i | \(-0.651250\pi\) |
0.998827 | − | 0.0484137i | \(-0.0154166\pi\) | |||||||
\(234\) | 1.07072 | − | 0.568144i | 0.0699949 | − | 0.0371407i | ||||
\(235\) | 8.48750 | + | 14.7008i | 0.553664 | + | 0.958973i | ||||
\(236\) | 0.400846 | 0.0260928 | ||||||||
\(237\) | −15.2114 | − | 26.3469i | −0.988084 | − | 1.71141i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.18043 | 0.205725 | 0.102862 | − | 0.994696i | \(-0.467200\pi\) | ||||
0.102862 | + | 0.994696i | \(0.467200\pi\) | |||||||
\(240\) | 2.92188 | + | 5.06085i | 0.188607 | + | 0.326676i | ||||
\(241\) | −15.8598 | −1.02162 | −0.510811 | − | 0.859693i | \(-0.670655\pi\) | ||||
−0.510811 | + | 0.859693i | \(0.670655\pi\) | |||||||
\(242\) | −3.09150 | − | 5.35463i | −0.198729 | − | 0.344209i | ||||
\(243\) | 2.97304 | + | 5.14945i | 0.190720 | + | 0.330338i | ||||
\(244\) | −6.42825 | − | 11.1341i | −0.411527 | − | 0.712785i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.40664 | −0.280957 | ||||||||
\(247\) | −1.46813 | + | 0.779018i | −0.0934147 | + | 0.0495677i | ||||
\(248\) | 4.71962 | + | 8.17463i | 0.299696 | + | 0.519089i | ||||
\(249\) | −14.5692 | + | 25.2345i | −0.923284 | + | 1.59917i | ||||
\(250\) | −6.68878 | −0.423035 | ||||||||
\(251\) | −1.24788 | + | 2.16139i | −0.0787654 | + | 0.136426i | −0.902718 | − | 0.430234i | \(-0.858431\pi\) |
0.823952 | + | 0.566659i | \(0.191764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.686481 | + | 1.18902i | −0.0431587 | + | 0.0747531i | ||||
\(254\) | −0.272326 | − | 0.471683i | −0.0170873 | − | 0.0295960i | ||||
\(255\) | 1.66810 | + | 2.88924i | 0.104461 | + | 0.180931i | ||||
\(256\) | −4.63253 | −0.289533 | ||||||||
\(257\) | 10.5204 | 0.656245 | 0.328123 | − | 0.944635i | \(-0.393584\pi\) | ||||
0.328123 | + | 0.944635i | \(0.393584\pi\) | |||||||
\(258\) | 4.42046 | + | 7.65647i | 0.275206 | + | 0.476671i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.49294 | + | 4.69097i | 0.464693 | + | 0.290921i | ||||
\(261\) | 1.99773 | − | 3.46018i | 0.123657 | − | 0.214180i | ||||
\(262\) | 0.329670 | − | 0.571006i | 0.0203671 | − | 0.0352768i | ||||
\(263\) | 15.6749 | − | 27.1498i | 0.966558 | − | 1.67413i | 0.261188 | − | 0.965288i | \(-0.415886\pi\) |
0.705370 | − | 0.708839i | \(-0.250781\pi\) | |||||||
\(264\) | −1.16522 | − | 2.01821i | −0.0717140 | − | 0.124212i | ||||
\(265\) | 13.8449 | 0.850486 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.35660 | − | 4.08174i | 0.144221 | − | 0.249799i | ||||
\(268\) | −1.20508 | + | 2.08727i | −0.0736122 | + | 0.127500i | ||||
\(269\) | −21.1265 | −1.28811 | −0.644054 | − | 0.764980i | \(-0.722749\pi\) | ||||
−0.644054 | + | 0.764980i | \(0.722749\pi\) | |||||||
\(270\) | 1.95623 | − | 3.38829i | 0.119052 | − | 0.206205i | ||||
\(271\) | 6.52007 | 0.396066 | 0.198033 | − | 0.980195i | \(-0.436545\pi\) | ||||
0.198033 | + | 0.980195i | \(0.436545\pi\) | |||||||
\(272\) | 2.50793 | 0.152066 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.00954 | 0.302638 | ||||||||
\(275\) | −1.63997 | −0.0988937 | ||||||||
\(276\) | 3.72717 | − | 6.45565i | 0.224349 | − | 0.388584i | ||||
\(277\) | −14.5310 | −0.873081 | −0.436540 | − | 0.899685i | \(-0.643796\pi\) | ||||
−0.436540 | + | 0.899685i | \(0.643796\pi\) | |||||||
\(278\) | 4.21933 | − | 7.30810i | 0.253059 | − | 0.438311i | ||||
\(279\) | 1.28817 | − | 2.23118i | 0.0771207 | − | 0.133577i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1832 | 1.62161 | 0.810807 | − | 0.585314i | \(-0.199029\pi\) | ||||
0.810807 | + | 0.585314i | \(0.199029\pi\) | |||||||
\(282\) | 6.31846 | + | 10.9439i | 0.376259 | + | 0.651699i | ||||
\(283\) | −4.28791 | + | 7.42688i | −0.254890 | + | 0.441482i | −0.964866 | − | 0.262744i | \(-0.915373\pi\) |
0.709976 | + | 0.704226i | \(0.248706\pi\) | |||||||
\(284\) | −10.4109 | + | 18.0323i | −0.617775 | + | 1.07002i | ||||
\(285\) | 0.642608 | − | 1.11303i | 0.0380648 | − | 0.0659302i | ||||
\(286\) | −1.02739 | − | 0.643196i | −0.0607506 | − | 0.0380330i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.58401 | + | 2.74358i | 0.0933387 | + | 0.161667i | ||||
\(289\) | −15.5682 | −0.915778 | ||||||||
\(290\) | −5.88779 | −0.345743 | ||||||||
\(291\) | 14.8009 | + | 25.6360i | 0.867647 | + | 1.50281i | ||||
\(292\) | 3.07309 | + | 5.32274i | 0.179839 | + | 0.311490i | ||||
\(293\) | 5.24356 | − | 9.08212i | 0.306332 | − | 0.530583i | −0.671225 | − | 0.741254i | \(-0.734232\pi\) |
0.977557 | + | 0.210671i | \(0.0675648\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.177511 | + | 0.307458i | −0.0103351 | + | 0.0179009i | ||||
\(296\) | 19.4652 | 1.13139 | ||||||||
\(297\) | 1.32750 | − | 2.29930i | 0.0770295 | − | 0.133419i | ||||
\(298\) | 3.87899 | + | 6.71862i | 0.224704 | + | 0.389199i | ||||
\(299\) | 0.305213 | − | 8.53231i | 0.0176509 | − | 0.493436i | ||||
\(300\) | 8.90400 | 0.514073 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.67882 | + | 8.10396i | 0.269236 | + | 0.466331i | ||||
\(303\) | 13.2572 | + | 22.9621i | 0.761605 | + | 1.31914i | ||||
\(304\) | −0.483069 | − | 0.836701i | −0.0277059 | − | 0.0479881i | ||||
\(305\) | 11.3868 | 0.652006 | ||||||||
\(306\) | 0.201131 | + | 0.348370i | 0.0114979 | + | 0.0199150i | ||||
\(307\) | −19.1751 | −1.09438 | −0.547190 | − | 0.837008i | \(-0.684303\pi\) | ||||
−0.547190 | + | 0.837008i | \(0.684303\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1690 | + | 17.6132i | 0.578493 | + | 1.00198i | ||||
\(310\) | −3.79654 | −0.215629 | ||||||||
\(311\) | 1.74427 | + | 3.02117i | 0.0989086 | + | 0.171315i | 0.911233 | − | 0.411891i | \(-0.135132\pi\) |
−0.812325 | + | 0.583206i | \(0.801798\pi\) | |||||||
\(312\) | 12.2832 | + | 7.68991i | 0.695399 | + | 0.435356i | ||||
\(313\) | 10.1607 | − | 17.5989i | 0.574318 | − | 0.994748i | −0.421797 | − | 0.906690i | \(-0.638601\pi\) |
0.996115 | − | 0.0880579i | \(-0.0280661\pi\) | |||||||
\(314\) | 0.182258 | + | 0.315680i | 0.0102854 | + | 0.0178148i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.3766 | − | 23.1689i | 0.752490 | − | 1.30335i | ||||
\(317\) | 13.9110 | − | 24.0946i | 0.781320 | − | 1.35329i | −0.149853 | − | 0.988708i | \(-0.547880\pi\) |
0.931173 | − | 0.364578i | \(-0.118787\pi\) | |||||||
\(318\) | 10.3067 | 0.577974 | ||||||||
\(319\) | −3.99547 | −0.223703 | ||||||||
\(320\) | −0.754384 | + | 1.30663i | −0.0421714 | + | 0.0730429i | ||||
\(321\) | −3.55252 | + | 6.15314i | −0.198282 | + | 0.343435i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.275784 | − | 0.477672i | −0.0153450 | − | 0.0265784i | ||||
\(324\) | −8.65457 | + | 14.9902i | −0.480809 | + | 0.832786i | ||||
\(325\) | 9.00848 | − | 4.78008i | 0.499700 | − | 0.265151i | ||||
\(326\) | −3.38729 | − | 5.86697i | −0.187605 | − | 0.324941i | ||||
\(327\) | −15.5305 | −0.858837 | ||||||||
\(328\) | −4.26660 | − | 7.38996i | −0.235583 | − | 0.408042i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.937318 | 0.0515976 | ||||||||
\(331\) | 4.67148 | + | 8.09123i | 0.256768 | + | 0.444734i | 0.965374 | − | 0.260869i | \(-0.0840092\pi\) |
−0.708607 | + | 0.705604i | \(0.750676\pi\) | |||||||
\(332\) | −25.6237 | −1.40628 | ||||||||
\(333\) | −2.65640 | − | 4.60103i | −0.145570 | − | 0.252135i | ||||
\(334\) | −6.39491 | − | 11.0763i | −0.349914 | − | 0.606069i | ||||
\(335\) | −1.06732 | − | 1.84866i | −0.0583140 | − | 0.101003i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.9182 | 1.24844 | 0.624218 | − | 0.781250i | \(-0.285418\pi\) | ||||
0.624218 | + | 0.781250i | \(0.285418\pi\) | |||||||
\(338\) | 7.51827 | + | 0.538567i | 0.408940 | + | 0.0292942i | ||||
\(339\) | 7.38696 | + | 12.7946i | 0.401205 | + | 0.694907i | ||||
\(340\) | −1.46689 | + | 2.54074i | −0.0795535 | + | 0.137791i | ||||
\(341\) | −2.57634 | −0.139517 | ||||||||
\(342\) | 0.0774824 | − | 0.134204i | 0.00418977 | − | 0.00725690i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.55996 | + | 14.8263i | −0.461522 | + | 0.799380i | ||||
\(345\) | 3.30109 | + | 5.71766i | 0.177725 | + | 0.307828i | ||||
\(346\) | −3.30222 | − | 5.71961i | −0.177528 | − | 0.307488i | ||||
\(347\) | −26.6711 | −1.43178 | −0.715889 | − | 0.698214i | \(-0.753978\pi\) | ||||
−0.715889 | + | 0.698214i | \(0.753978\pi\) | |||||||
\(348\) | 21.6929 | 1.16286 | ||||||||
\(349\) | 7.61723 | + | 13.1934i | 0.407741 | + | 0.706228i | 0.994636 | − | 0.103435i | \(-0.0329832\pi\) |
−0.586895 | + | 0.809663i | \(0.699650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.590213 | + | 16.4996i | −0.0315033 | + | 0.880683i | ||||
\(352\) | 1.58401 | − | 2.74358i | 0.0844280 | − | 0.146234i | ||||
\(353\) | −11.2044 | + | 19.4066i | −0.596352 | + | 1.03291i | 0.397003 | + | 0.917817i | \(0.370050\pi\) |
−0.993355 | + | 0.115094i | \(0.963283\pi\) | |||||||
\(354\) | −0.132147 | + | 0.228885i | −0.00702353 | + | 0.0121651i | ||||
\(355\) | −9.22079 | − | 15.9709i | −0.489389 | − | 0.847646i | ||||
\(356\) | 4.14468 | 0.219668 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.00667 | + | 1.74361i | −0.0532044 | + | 0.0921528i | ||||
\(359\) | −8.01927 | + | 13.8898i | −0.423241 | + | 0.733075i | −0.996254 | − | 0.0864711i | \(-0.972441\pi\) |
0.573013 | + | 0.819546i | \(0.305774\pi\) | |||||||
\(360\) | −1.81506 | −0.0956620 | ||||||||
\(361\) | 9.39376 | − | 16.2705i | 0.494408 | − | 0.856340i | ||||
\(362\) | 12.2335 | 0.642980 | ||||||||
\(363\) | −20.1764 | −1.05898 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.44356 | −0.284929 | ||||||||
\(366\) | 8.47682 | 0.443090 | ||||||||
\(367\) | −3.45002 | + | 5.97561i | −0.180090 | + | 0.311924i | −0.941911 | − | 0.335863i | \(-0.890972\pi\) |
0.761821 | + | 0.647787i | \(0.224305\pi\) | |||||||
\(368\) | 4.96308 | 0.258718 | ||||||||
\(369\) | −1.16452 | + | 2.01701i | −0.0606225 | + | 0.105001i | ||||
\(370\) | −3.91452 | + | 6.78015i | −0.203506 | + | 0.352483i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13.9879 | 0.725240 | ||||||||
\(373\) | −3.84264 | − | 6.65566i | −0.198965 | − | 0.344617i | 0.749228 | − | 0.662312i | \(-0.230425\pi\) |
−0.948193 | + | 0.317695i | \(0.897091\pi\) | |||||||
\(374\) | 0.201131 | − | 0.348370i | 0.0104003 | − | 0.0180138i | ||||
\(375\) | −10.9134 | + | 18.9026i | −0.563566 | + | 0.976125i | ||||
\(376\) | −12.2353 | + | 21.1922i | −0.630988 | + | 1.09290i | ||||
\(377\) | 21.9475 | − | 11.6458i | 1.13035 | − | 0.599788i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.5817 | + | 21.7922i | 0.646281 | + | 1.11939i | 0.984004 | + | 0.178146i | \(0.0570098\pi\) |
−0.337723 | + | 0.941245i | \(0.609657\pi\) | |||||||
\(380\) | 1.13019 | 0.0579776 | ||||||||
\(381\) | −1.77731 | −0.0910545 | ||||||||
\(382\) | 3.45535 | + | 5.98484i | 0.176791 | + | 0.306211i | ||||
\(383\) | −11.0218 | − | 19.0904i | −0.563189 | − | 0.975473i | −0.997216 | − | 0.0745724i | \(-0.976241\pi\) |
0.434026 | − | 0.900900i | \(-0.357093\pi\) | |||||||
\(384\) | −10.8995 | + | 18.8785i | −0.556212 | + | 0.963387i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.16866 | − | 7.22033i | 0.212179 | − | 0.367505i | ||||
\(387\) | 4.67270 | 0.237527 | ||||||||
\(388\) | −13.0156 | + | 22.5438i | −0.660769 | + | 1.14449i | ||||
\(389\) | 5.49058 | + | 9.50996i | 0.278383 | + | 0.482174i | 0.970983 | − | 0.239148i | \(-0.0768681\pi\) |
−0.692600 | + | 0.721322i | \(0.743535\pi\) | |||||||
\(390\) | −5.14877 | + | 2.73204i | −0.260718 | + | 0.138342i | ||||
\(391\) | 2.83342 | 0.143292 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.07578 | − | 1.86331i | −0.0542660 | − | 0.0939914i | ||||
\(394\) | 2.02042 | + | 3.49946i | 0.101787 | + | 0.176300i | ||||
\(395\) | 11.8474 | + | 20.5203i | 0.596107 | + | 1.03249i | ||||
\(396\) | −0.559343 | −0.0281081 | ||||||||
\(397\) | 12.5382 | + | 21.7168i | 0.629275 | + | 1.08994i | 0.987698 | + | 0.156377i | \(0.0499813\pi\) |
−0.358423 | + | 0.933559i | \(0.616685\pi\) | |||||||
\(398\) | 2.07196 | 0.103858 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.96413 | + | 5.13402i | 0.148206 | + | 0.256701i | ||||
\(401\) | −22.6601 | −1.13159 | −0.565797 | − | 0.824545i | \(-0.691431\pi\) | ||||
−0.565797 | + | 0.824545i | \(0.691431\pi\) | |||||||
\(402\) | −0.794560 | − | 1.37622i | −0.0396291 | − | 0.0686395i | ||||
\(403\) | 14.1521 | − | 7.50937i | 0.704964 | − | 0.374068i | ||||
\(404\) | −11.6581 | + | 20.1924i | −0.580012 | + | 1.00461i | ||||
\(405\) | −7.66521 | − | 13.2765i | −0.380887 | − | 0.659716i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.65640 | + | 4.60103i | −0.131673 | + | 0.228064i | ||||
\(408\) | −2.40468 | + | 4.16503i | −0.119050 | + | 0.206200i | ||||
\(409\) | 17.1465 | 0.847839 | 0.423919 | − | 0.905700i | \(-0.360654\pi\) | ||||
0.423919 | + | 0.905700i | \(0.360654\pi\) | |||||||
\(410\) | 3.43212 | 0.169500 | ||||||||
\(411\) | 8.17358 | − | 14.1570i | 0.403173 | − | 0.698316i | ||||
\(412\) | −8.94238 | + | 15.4887i | −0.440560 | + | 0.763072i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.398029 | + | 0.689407i | 0.0195621 | + | 0.0338825i | ||||
\(415\) | 11.3472 | − | 19.6540i | 0.557013 | − | 0.964775i | ||||
\(416\) | −0.704257 | + | 19.6877i | −0.0345291 | + | 0.965271i | ||||
\(417\) | −13.7685 | − | 23.8478i | −0.674248 | − | 1.16783i | ||||
\(418\) | −0.154965 | −0.00757958 | ||||||||
\(419\) | −16.9902 | − | 29.4279i | −0.830027 | − | 1.43765i | −0.898016 | − | 0.439963i | \(-0.854992\pi\) |
0.0679891 | − | 0.997686i | \(-0.478342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.3623 | −1.57724 | −0.788621 | − | 0.614879i | \(-0.789205\pi\) | ||||
−0.788621 | + | 0.614879i | \(0.789205\pi\) | |||||||
\(422\) | −4.09169 | − | 7.08701i | −0.199180 | − | 0.344990i | ||||
\(423\) | 6.67900 | 0.324744 | ||||||||
\(424\) | 9.97920 | + | 17.2845i | 0.484633 | + | 0.839409i | ||||
\(425\) | 1.69222 | + | 2.93101i | 0.0820847 | + | 0.142175i | ||||
\(426\) | −6.86435 | − | 11.8894i | −0.332579 | − | 0.576044i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.24802 | −0.302009 | ||||||||
\(429\) | −3.49397 | + | 1.85397i | −0.168690 | + | 0.0895104i | ||||
\(430\) | −3.44288 | − | 5.96325i | −0.166031 | − | 0.287574i | ||||
\(431\) | 9.45640 | − | 16.3790i | 0.455499 | − | 0.788947i | −0.543218 | − | 0.839592i | \(-0.682794\pi\) |
0.998717 | + | 0.0506447i | \(0.0161276\pi\) | |||||||
\(432\) | −9.59749 | −0.461759 | ||||||||
\(433\) | 9.57006 | − | 16.5758i | 0.459908 | − | 0.796584i | −0.539048 | − | 0.842275i | \(-0.681216\pi\) |
0.998956 | + | 0.0456914i | \(0.0145491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.60653 | + | 16.6390i | −0.460598 | + | 0.797779i | ||||
\(436\) | −6.82859 | − | 11.8275i | −0.327030 | − | 0.566433i | ||||
\(437\) | −0.545763 | − | 0.945289i | −0.0261074 | − | 0.0452193i | ||||
\(438\) | −4.05242 | −0.193632 | ||||||||
\(439\) | −9.60289 | −0.458321 | −0.229160 | − | 0.973389i | \(-0.573598\pi\) | ||||
−0.229160 | + | 0.973389i | \(0.573598\pi\) | |||||||
\(440\) | 0.907530 | + | 1.57189i | 0.0432648 | + | 0.0749368i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0894239 | + | 2.49987i | −0.00425346 | + | 0.118907i | ||||
\(443\) | 20.1998 | − | 34.9871i | 0.959721 | − | 1.66229i | 0.236546 | − | 0.971620i | \(-0.423984\pi\) |
0.723175 | − | 0.690665i | \(-0.242682\pi\) | |||||||
\(444\) | 14.4226 | − | 24.9807i | 0.684468 | − | 1.18553i | ||||
\(445\) | −1.83544 | + | 3.17907i | −0.0870081 | + | 0.150703i | ||||
\(446\) | 0.263561 | + | 0.456502i | 0.0124800 | + | 0.0216160i | ||||
\(447\) | 25.3159 | 1.19740 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.3112 | − | 23.0556i | 0.628194 | − | 1.08806i | −0.359720 | − | 0.933060i | \(-0.617128\pi\) |
0.987914 | − | 0.155003i | \(-0.0495387\pi\) | |||||||
\(450\) | −0.475435 | + | 0.823477i | −0.0224122 | + | 0.0388191i | ||||
\(451\) | 2.32904 | 0.109670 | ||||||||
\(452\) | −6.49594 | + | 11.2513i | −0.305543 | + | 0.529217i | ||||
\(453\) | 30.5359 | 1.43470 | ||||||||
\(454\) | −1.35393 | −0.0635430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.85273 | 0.0867619 | ||||||||
\(457\) | −1.61287 | −0.0754468 | −0.0377234 | − | 0.999288i | \(-0.512011\pi\) | ||||
−0.0377234 | + | 0.999288i | \(0.512011\pi\) | |||||||
\(458\) | 4.83583 | − | 8.37590i | 0.225963 | − | 0.391380i | ||||
\(459\) | −5.47920 | −0.255747 | ||||||||
\(460\) | −2.90291 | + | 5.02799i | −0.135349 | + | 0.234431i | ||||
\(461\) | −7.96032 | + | 13.7877i | −0.370749 | + | 0.642156i | −0.989681 | − | 0.143289i | \(-0.954232\pi\) |
0.618932 | + | 0.785445i | \(0.287566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.8475 | −1.34066 | −0.670328 | − | 0.742065i | \(-0.733847\pi\) | ||||
−0.670328 | + | 0.742065i | \(0.733847\pi\) | |||||||
\(464\) | 7.22154 | + | 12.5081i | 0.335252 | + | 0.580673i | ||||
\(465\) | −6.19444 | + | 10.7291i | −0.287260 | + | 0.497549i | ||||
\(466\) | −4.79110 | + | 8.29842i | −0.221943 | + | 0.384417i | ||||
\(467\) | −3.72268 | + | 6.44787i | −0.172265 | + | 0.298372i | −0.939211 | − | 0.343339i | \(-0.888442\pi\) |
0.766946 | + | 0.641711i | \(0.221775\pi\) | |||||||
\(468\) | 3.07252 | − | 1.63034i | 0.142027 | − | 0.0753626i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.92114 | − | 8.52367i | −0.226995 | − | 0.393167i | ||||
\(471\) | 1.18949 | 0.0548087 | ||||||||
\(472\) | −0.511789 | −0.0235570 | ||||||||
\(473\) | −2.33635 | − | 4.04668i | −0.107425 | − | 0.186066i | ||||
\(474\) | 8.81971 | + | 15.2762i | 0.405103 | + | 0.701658i | ||||
\(475\) | 0.651899 | − | 1.12912i | 0.0299112 | − | 0.0518077i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.72371 | − | 4.71761i | 0.124710 | − | 0.216005i | ||||
\(478\) | −1.84404 | −0.0843446 | ||||||||
\(479\) | 18.6263 | − | 32.2617i | 0.851058 | − | 1.47408i | −0.0291956 | − | 0.999574i | \(-0.509295\pi\) |
0.880254 | − | 0.474503i | \(-0.157372\pi\) | |||||||
\(480\) | −7.61704 | − | 13.1931i | −0.347669 | − | 0.602180i | ||||
\(481\) | 1.18105 | − | 33.0166i | 0.0538512 | − | 1.50543i | ||||
\(482\) | 9.19570 | 0.418853 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.87134 | − | 15.3656i | −0.403243 | − | 0.698437i | ||||
\(485\) | −11.5277 | − | 19.9666i | −0.523448 | − | 0.906638i | ||||
\(486\) | −1.72380 | − | 2.98571i | −0.0781931 | − | 0.135434i | ||||
\(487\) | 24.1726 | 1.09537 | 0.547684 | − | 0.836686i | \(-0.315510\pi\) | ||||
0.547684 | + | 0.836686i | \(0.315510\pi\) | |||||||
\(488\) | 8.20742 | + | 14.2157i | 0.371533 | + | 0.643513i | ||||
\(489\) | −22.1069 | −0.999707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.03571 | − | 5.25800i | −0.137000 | − | 0.237290i | 0.789360 | − | 0.613931i | \(-0.210413\pi\) |
−0.926360 | + | 0.376640i | \(0.877079\pi\) | |||||||
\(492\) | −12.6453 | −0.570092 | ||||||||
\(493\) | 4.12277 | + | 7.14086i | 0.185680 | + | 0.321608i | ||||
\(494\) | 0.851236 | − | 0.451683i | 0.0382989 | − | 0.0203222i | ||||
\(495\) | 0.247700 | − | 0.429030i | 0.0111333 | − | 0.0192835i | ||||
\(496\) | 4.65656 | + | 8.06540i | 0.209086 | + | 0.362147i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.44736 | − | 14.6313i | 0.378535 | − | 0.655642i | ||||
\(499\) | 1.25782 | − | 2.17861i | 0.0563079 | − | 0.0975281i | −0.836497 | − | 0.547971i | \(-0.815400\pi\) |
0.892805 | + | 0.450443i | \(0.148734\pi\) | |||||||
\(500\) | −19.1941 | −0.858385 | ||||||||
\(501\) | −41.7358 | −1.86462 | ||||||||
\(502\) | 0.723533 | − | 1.25320i | 0.0322929 | − | 0.0559329i | ||||
\(503\) | −17.0026 | + | 29.4493i | −0.758107 | + | 1.31308i | 0.185708 | + | 0.982605i | \(0.440542\pi\) |
−0.943815 | + | 0.330474i | \(0.892791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3254 | − | 17.8841i | −0.459473 | − | 0.795831i | ||||
\(506\) | 0.398029 | − | 0.689407i | 0.0176946 | − | 0.0306479i | ||||
\(507\) | 13.7888 | − | 20.3680i | 0.612383 | − | 0.904576i | ||||
\(508\) | −0.781466 | − | 1.35354i | −0.0346719 | − | 0.0600536i | ||||
\(509\) | −29.3048 | −1.29891 | −0.649457 | − | 0.760399i | \(-0.725004\pi\) | ||||
−0.649457 | + | 0.760399i | \(0.725004\pi\) | |||||||
\(510\) | −0.967183 | − | 1.67521i | −0.0428276 | − | 0.0741795i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.3568 | −0.899654 | ||||||||
\(513\) | 1.05538 | + | 1.82798i | 0.0465964 | + | 0.0807073i | ||||
\(514\) | −6.09984 | −0.269053 | ||||||||
\(515\) | −7.92012 | − | 13.7180i | −0.349002 | − | 0.604489i | ||||
\(516\) | 12.6849 | + | 21.9709i | 0.558423 | + | 0.967217i | ||||
\(517\) | −3.33950 | − | 5.78418i | −0.146871 | − | 0.254388i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.5516 | −0.946011 | ||||||||
\(520\) | −9.56679 | − | 5.98930i | −0.419531 | − | 0.262648i | ||||
\(521\) | −4.57386 | − | 7.92216i | −0.200385 | − | 0.347076i | 0.748268 | − | 0.663397i | \(-0.230886\pi\) |
−0.948652 | + | 0.316321i | \(0.897552\pi\) | |||||||
\(522\) | −1.15831 | + | 2.00625i | −0.0506977 | + | 0.0878111i | ||||
\(523\) | 14.1075 | 0.616876 | 0.308438 | − | 0.951244i | \(-0.400194\pi\) | ||||
0.308438 | + | 0.951244i | \(0.400194\pi\) | |||||||
\(524\) | 0.946019 | − | 1.63855i | 0.0413270 | − | 0.0715805i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.08849 | + | 15.7417i | −0.396277 | + | 0.686372i | ||||
\(527\) | 2.65843 | + | 4.60453i | 0.115803 | + | 0.200577i | ||||
\(528\) | −1.14965 | − | 1.99125i | −0.0500319 | − | 0.0866578i | ||||
\(529\) | −17.3928 | −0.756209 | ||||||||
\(530\) | −8.02743 | −0.348689 | ||||||||
\(531\) | 0.0698437 | + | 0.120973i | 0.00303096 | + | 0.00524977i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7936 | + | 6.78856i | −0.554154 | + | 0.294045i | ||||
\(534\) | −1.36638 | + | 2.36664i | −0.0591290 | + | 0.102414i | ||||
\(535\) | 2.76688 | − | 4.79238i | 0.119623 | − | 0.207193i | ||||
\(536\) | 1.53862 | − | 2.66496i | 0.0664582 | − | 0.115109i | ||||
\(537\) | 3.28498 | + | 5.68976i | 0.141758 | + | 0.245531i | ||||
\(538\) | 12.2494 | 0.528109 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.61359 | − | 9.72302i | 0.241570 | − | 0.418412i | ||||
\(541\) | −3.90147 | + | 6.75754i | −0.167737 | + | 0.290529i | −0.937624 | − | 0.347651i | \(-0.886979\pi\) |
0.769887 | + | 0.638181i | \(0.220313\pi\) | |||||||
\(542\) | −3.78041 | −0.162382 | ||||||||
\(543\) | 19.9602 | − | 34.5721i | 0.856576 | − | 1.48363i | ||||
\(544\) | −6.53792 | −0.280311 | ||||||||
\(545\) | 12.0959 | 0.518133 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.99390 | 0.299038 | 0.149519 | − | 0.988759i | \(-0.452228\pi\) | ||||
0.149519 | + | 0.988759i | \(0.452228\pi\) | |||||||
\(548\) | 14.3753 | 0.614084 | ||||||||
\(549\) | 2.24013 | − | 3.88001i | 0.0956063 | − | 0.165595i | ||||
\(550\) | 0.950869 | 0.0405452 | ||||||||
\(551\) | 1.58823 | − | 2.75089i | 0.0676608 | − | 0.117192i | ||||
\(552\) | −4.75875 | + | 8.24240i | −0.202546 | + | 0.350820i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.42520 | 0.357952 | ||||||||
\(555\) | 12.7739 | + | 22.1250i | 0.542221 | + | 0.939154i | ||||
\(556\) | 12.1078 | − | 20.9713i | 0.513484 | − | 0.889380i | ||||
\(557\) | 3.62124 | − | 6.27218i | 0.153437 | − | 0.265761i | −0.779052 | − | 0.626960i | \(-0.784299\pi\) |
0.932489 | + | 0.361199i | \(0.117632\pi\) | |||||||
\(558\) | −0.746894 | + | 1.29366i | −0.0316186 | + | 0.0547650i | ||||
\(559\) | 24.6288 | + | 15.4189i | 1.04169 | + | 0.652149i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.656332 | − | 1.13680i | −0.0277104 | − | 0.0479958i | ||||
\(562\) | −15.7611 | −0.664842 | ||||||||
\(563\) | −15.9321 | −0.671459 | −0.335730 | − | 0.941958i | \(-0.608983\pi\) | ||||
−0.335730 | + | 0.941958i | \(0.608983\pi\) | |||||||
\(564\) | 18.1314 | + | 31.4045i | 0.763470 | + | 1.32237i | ||||
\(565\) | −5.75334 | − | 9.96509i | −0.242045 | − | 0.419234i | ||||
\(566\) | 2.48618 | − | 4.30618i | 0.104502 | − | 0.181002i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2924 | − | 23.0231i | 0.557737 | − | 0.966029i | ||||
\(569\) | −42.2759 | −1.77230 | −0.886149 | − | 0.463401i | \(-0.846629\pi\) | ||||
−0.886149 | + | 0.463401i | \(0.846629\pi\) | |||||||
\(570\) | −0.372591 | + | 0.645346i | −0.0156061 | + | 0.0270306i | ||||
\(571\) | −6.81247 | − | 11.7995i | −0.285093 | − | 0.493795i | 0.687539 | − | 0.726148i | \(-0.258691\pi\) |
−0.972632 | + | 0.232352i | \(0.925358\pi\) | |||||||
\(572\) | −2.94818 | − | 1.84571i | −0.123270 | − | 0.0771730i | ||||
\(573\) | 22.5510 | 0.942082 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.34882 | + | 5.80032i | 0.139655 | + | 0.241890i | ||||
\(576\) | 0.296821 | + | 0.514108i | 0.0123675 | + | 0.0214212i | ||||
\(577\) | 13.1925 | + | 22.8500i | 0.549209 | + | 0.951258i | 0.998329 | + | 0.0577867i | \(0.0184043\pi\) |
−0.449120 | + | 0.893472i | \(0.648262\pi\) | |||||||
\(578\) | 9.02662 | 0.375458 | ||||||||
\(579\) | −13.6032 | − | 23.5614i | −0.565329 | − | 0.979179i | ||||
\(580\) | −16.8956 | −0.701550 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.58174 | − | 14.8640i | −0.355725 | − | 0.616133i | ||||
\(583\) | −5.44743 | −0.225609 | ||||||||
\(584\) | −3.92364 | − | 6.79594i | −0.162361 | − | 0.281218i | ||||
\(585\) | −0.110129 | + | 3.07868i | −0.00455326 | + | 0.127288i | ||||
\(586\) | −3.04027 | + | 5.26591i | −0.125592 | + | 0.217533i | ||||
\(587\) | 11.0720 | + | 19.1773i | 0.456990 | + | 0.791530i | 0.998800 | − | 0.0489708i | \(-0.0155941\pi\) |
−0.541810 | + | 0.840501i | \(0.682261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.02411 | − | 1.77382i | 0.0421979 | − | 0.0730889i | ||||
\(590\) | 0.102923 | − | 0.178268i | 0.00423727 | − | 0.00733916i | ||||
\(591\) | 13.1861 | 0.542402 | ||||||||
\(592\) | 19.2051 | 0.789324 | ||||||||
\(593\) | 13.0419 | − | 22.5893i | 0.535568 | − | 0.927630i | −0.463568 | − | 0.886061i | \(-0.653431\pi\) |
0.999136 | − | 0.0415689i | \(-0.0132356\pi\) | |||||||
\(594\) | −0.769700 | + | 1.33316i | −0.0315812 | + | 0.0547002i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.1311 | + | 19.2797i | 0.455949 | + | 0.789727i | ||||
\(597\) | 3.38062 | − | 5.85540i | 0.138360 | − | 0.239646i | ||||
\(598\) | −0.176965 | + | 4.94712i | −0.00723665 | + | 0.202303i | ||||
\(599\) | 8.42202 | + | 14.5874i | 0.344114 | + | 0.596024i | 0.985192 | − | 0.171452i | \(-0.0548458\pi\) |
−0.641078 | + | 0.767476i | \(0.721512\pi\) | |||||||
\(600\) | −11.3684 | −0.464113 | ||||||||
\(601\) | −4.31691 | − | 7.47710i | −0.176090 | − | 0.304997i | 0.764448 | − | 0.644686i | \(-0.223012\pi\) |
−0.940538 | + | 0.339688i | \(0.889678\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.839898 | −0.0342033 | ||||||||
\(604\) | 13.4263 | + | 23.2551i | 0.546309 | + | 0.946235i | ||||
\(605\) | 15.7144 | 0.638881 | ||||||||
\(606\) | −7.68665 | − | 13.3137i | −0.312249 | − | 0.540831i | ||||
\(607\) | −10.9181 | − | 18.9107i | −0.443153 | − | 0.767564i | 0.554768 | − | 0.832005i | \(-0.312807\pi\) |
−0.997922 | + | 0.0644411i | \(0.979474\pi\) | |||||||
\(608\) | 1.25931 | + | 2.18119i | 0.0510718 | + | 0.0884590i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.60218 | −0.267315 | ||||||||
\(611\) | 35.2036 | + | 22.0392i | 1.42418 | + | 0.891612i | ||||
\(612\) | 0.577165 | + | 0.999680i | 0.0233305 | + | 0.0404096i | ||||
\(613\) | 24.0244 | − | 41.6114i | 0.970334 | − | 1.68067i | 0.275791 | − | 0.961218i | \(-0.411060\pi\) |
0.694543 | − | 0.719451i | \(-0.255607\pi\) | |||||||
\(614\) | 11.1179 | 0.448683 | ||||||||
\(615\) | 5.59985 | − | 9.69922i | 0.225808 | − | 0.391110i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.23709 | − | 14.2671i | 0.331613 | − | 0.574370i | −0.651215 | − | 0.758893i | \(-0.725741\pi\) |
0.982828 | + | 0.184523i | \(0.0590739\pi\) | |||||||
\(618\) | −5.89608 | − | 10.2123i | −0.237175 | − | 0.410799i | ||||
\(619\) | −21.0267 | − | 36.4192i | −0.845133 | − | 1.46381i | −0.885506 | − | 0.464628i | \(-0.846188\pi\) |
0.0403733 | − | 0.999185i | \(-0.487145\pi\) | |||||||
\(620\) | −10.8945 | −0.437535 | ||||||||
\(621\) | −10.8431 | −0.435117 | ||||||||
\(622\) | −1.01135 | − | 1.75170i | −0.0405513 | − | 0.0702370i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.1191 | + | 7.58716i | 0.485151 | + | 0.303730i | ||||
\(625\) | 1.42880 | − | 2.47475i | 0.0571519 | − | 0.0989900i | ||||
\(626\) | −5.89129 | + | 10.2040i | −0.235463 | + | 0.407835i | ||||
\(627\) | −0.252841 | + | 0.437933i | −0.0100975 | + | 0.0174894i | ||||
\(628\) | 0.523006 | + | 0.905872i | 0.0208702 | + | 0.0361482i | ||||
\(629\) | 10.9642 | 0.437170 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.06667 | − | 10.5078i | 0.241510 | − | 0.418308i | −0.719634 | − | 0.694353i | \(-0.755691\pi\) |
0.961145 | + | 0.276045i | \(0.0890239\pi\) | |||||||
\(632\) | −17.0788 | + | 29.5814i | −0.679360 | + | 1.17669i | ||||
\(633\) | −26.7040 | −1.06139 | ||||||||
\(634\) | −8.06575 | + | 13.9703i | −0.320332 | + | 0.554831i | ||||
\(635\) | 1.38426 | 0.0549328 | ||||||||
\(636\) | 29.5762 | 1.17277 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.31661 | 0.0917157 | ||||||||
\(639\) | −7.25604 | −0.287044 | ||||||||
\(640\) | 8.48908 | − | 14.7035i | 0.335560 | − | 0.581207i | ||||
\(641\) | −0.404355 | −0.0159711 | −0.00798553 | − | 0.999968i | \(-0.502542\pi\) | ||||
−0.00798553 | + | 0.999968i | \(0.502542\pi\) | |||||||
\(642\) | 2.05979 | − | 3.56765i | 0.0812933 | − | 0.140804i | ||||
\(643\) | −14.1741 | + | 24.5503i | −0.558973 | + | 0.968169i | 0.438610 | + | 0.898678i | \(0.355471\pi\) |
−0.997583 | + | 0.0694914i | \(0.977862\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.4697 | −0.884742 | ||||||||
\(646\) | 0.159902 | + | 0.276959i | 0.00629128 | + | 0.0108968i | ||||
\(647\) | 17.4045 | − | 30.1455i | 0.684242 | − | 1.18514i | −0.289433 | − | 0.957198i | \(-0.593467\pi\) |
0.973675 | − | 0.227943i | \(-0.0731999\pi\) | |||||||
\(648\) | 11.0499 | − | 19.1390i | 0.434082 | − | 0.751852i | ||||
\(649\) | 0.0698437 | − | 0.120973i | 0.00274160 | − | 0.00474860i | ||||
\(650\) | −5.22321 | + | 2.77154i | −0.204871 | + | 0.108709i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.72016 | − | 16.8358i | −0.380671 | − | 0.659341i | ||||
\(653\) | −25.1500 | −0.984195 | −0.492098 | − | 0.870540i | \(-0.663770\pi\) | ||||
−0.492098 | + | 0.870540i | \(0.663770\pi\) | |||||||
\(654\) | 9.00473 | 0.352113 | ||||||||
\(655\) | 0.837873 | + | 1.45124i | 0.0327384 | + | 0.0567046i | ||||
\(656\) | −4.20959 | − | 7.29122i | −0.164357 | − | 0.284674i | ||||
\(657\) | −1.07091 | + | 1.85488i | −0.0417803 | + | 0.0723657i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.33723 | + | 7.51230i | −0.168954 | + | 0.292638i | −0.938053 | − | 0.346493i | \(-0.887372\pi\) |
0.769098 | + | 0.639131i | \(0.220706\pi\) | |||||||
\(660\) | 2.68972 | 0.104697 | ||||||||
\(661\) | −9.50000 | + | 16.4545i | −0.369507 | + | 0.640005i | −0.989489 | − | 0.144612i | \(-0.953807\pi\) |
0.619982 | + | 0.784616i | \(0.287140\pi\) | |||||||
\(662\) | −2.70857 | − | 4.69138i | −0.105272 | − | 0.182336i | ||||
\(663\) | 6.91878 | + | 4.33151i | 0.268703 | + | 0.168222i | ||||
\(664\) | 32.7156 | 1.26961 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.54021 | + | 2.66772i | 0.0596819 | + | 0.103372i | ||||
\(667\) | 8.15877 | + | 14.1314i | 0.315909 | + | 0.547170i | ||||
\(668\) | −18.3508 | − | 31.7845i | −0.710013 | − | 1.22978i | ||||
\(669\) | 1.72011 | 0.0665032 | ||||||||
\(670\) | 0.618844 | + | 1.07187i | 0.0239080 | + | 0.0414099i | ||||
\(671\) | −4.48026 | −0.172958 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.284273 | + | 0.492376i | 0.0109579 | + | 0.0189797i | 0.871452 | − | 0.490480i | \(-0.163179\pi\) |
−0.860494 | + | 0.509460i | \(0.829845\pi\) | |||||||
\(674\) | −13.2882 | −0.511843 | ||||||||
\(675\) | −6.47587 | − | 11.2165i | −0.249256 | − | 0.431725i | ||||
\(676\) | 21.5744 | + | 1.54547i | 0.829784 | + | 0.0594411i | ||||
\(677\) | −13.8398 | + | 23.9713i | −0.531908 | + | 0.921292i | 0.467398 | + | 0.884047i | \(0.345191\pi\) |
−0.999306 | + | 0.0372449i | \(0.988142\pi\) | |||||||
\(678\) | −4.28304 | − | 7.41844i | −0.164489 | − | 0.284903i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.87289 | − | 3.24394i | 0.0718221 | − | 0.124400i | ||||
\(681\) | −2.20907 | + | 3.82622i | −0.0846518 | + | 0.146621i | ||||
\(682\) | 1.49379 | 0.0572001 | ||||||||
\(683\) | −23.7917 | −0.910363 | −0.455181 | − | 0.890399i | \(-0.650426\pi\) | ||||
−0.455181 | + | 0.890399i | \(0.650426\pi\) | |||||||
\(684\) | 0.222343 | − | 0.385110i | 0.00850150 | − | 0.0147250i | ||||
\(685\) | −6.36600 | + | 11.0262i | −0.243232 | + | 0.421291i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.7803 | − | 27.3323i | −0.602056 | − | 1.04279i | ||||
\(688\) | −8.44559 | + | 14.6282i | −0.321985 | + | 0.557694i | ||||
\(689\) | 29.9232 | − | 15.8779i | 1.13998 | − | 0.604898i | ||||
\(690\) | −1.91401 | − | 3.31516i | −0.0728650 | − | 0.126206i | ||||
\(691\) | 36.8433 | 1.40159 | 0.700793 | − | 0.713365i | \(-0.252830\pi\) | ||||
0.700793 | + | 0.713365i | \(0.252830\pi\) | |||||||
\(692\) | −9.47603 | − | 16.4130i | −0.360224 | − | 0.623927i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.4642 | 0.587012 | ||||||||
\(695\) | 10.7236 | + | 18.5739i | 0.406771 | + | 0.704548i | ||||
\(696\) | −27.6969 | −1.04985 | ||||||||
\(697\) | −2.40325 | − | 4.16255i | −0.0910296 | − | 0.157668i | ||||
\(698\) | −4.41655 | − | 7.64969i | −0.167169 | − | 0.289545i | ||||
\(699\) | 15.6343 | + | 27.0794i | 0.591344 | + | 1.02424i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.34987 | 0.0887533 | 0.0443767 | − | 0.999015i | \(-0.485870\pi\) | ||||
0.0443767 | + | 0.999015i | \(0.485870\pi\) | |||||||
\(702\) | 0.342212 | − | 9.56664i | 0.0129160 | − | 0.361070i | ||||
\(703\) | −2.11188 | − | 3.65788i | −0.0796511 | − | 0.137960i | ||||
\(704\) | 0.296821 | − | 0.514108i | 0.0111868 | − | 0.0193762i | ||||
\(705\) | −32.1174 | −1.20961 | ||||||||
\(706\) | 6.49645 | − | 11.2522i | 0.244497 | − | 0.423481i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.379208 | + | 0.656807i | −0.0142515 | + | 0.0246843i | ||||
\(709\) | −5.04160 | − | 8.73231i | −0.189341 | − | 0.327949i | 0.755689 | − | 0.654930i | \(-0.227302\pi\) |
−0.945031 | + | 0.326981i | \(0.893969\pi\) | |||||||
\(710\) | 5.34631 | + | 9.26008i | 0.200643 | + | 0.347525i | ||||
\(711\) | 9.32297 | 0.349639 | ||||||||
\(712\) | −5.29182 | −0.198319 | ||||||||
\(713\) | 5.26090 | + | 9.11214i | 0.197022 | + | 0.341252i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.72128 | − | 1.44397i | 0.101770 | − | 0.0540013i | ||||
\(716\) | −2.88875 | + | 5.00346i | −0.107958 | + | 0.186988i | ||||
\(717\) | −3.00875 | + | 5.21130i | −0.112364 | + | 0.194620i | ||||
\(718\) | 4.64966 | − | 8.05344i | 0.173524 | − | 0.300552i | ||||
\(719\) | −3.25113 | − | 5.63113i | −0.121247 | − | 0.210006i | 0.799013 | − | 0.601314i | \(-0.205356\pi\) |
−0.920260 | + | 0.391308i | \(0.872023\pi\) | |||||||
\(720\) | −1.79081 | −0.0667394 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.44660 | + | 9.43379i | −0.202701 | + | 0.351089i | ||||
\(723\) | 15.0037 | − | 25.9872i | 0.557994 | − | 0.966474i | ||||
\(724\) | 35.1052 | 1.30468 | ||||||||
\(725\) | −9.74542 | + | 16.8796i | −0.361936 | + | 0.626891i | ||||
\(726\) | 11.6985 | 0.434171 | ||||||||
\(727\) | −3.12636 | −0.115950 | −0.0579750 | − | 0.998318i | \(-0.518464\pi\) | ||||
−0.0579750 | + | 0.998318i | \(0.518464\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.9595 | 0.739242 | ||||||||
\(730\) | 3.15623 | 0.116817 | ||||||||
\(731\) | −4.82158 | + | 8.35123i | −0.178333 | + | 0.308881i | ||||
\(732\) | 24.3250 | 0.899078 | ||||||||
\(733\) | 3.83220 | − | 6.63756i | 0.141545 | − | 0.245164i | −0.786533 | − | 0.617548i | \(-0.788126\pi\) |
0.928079 | + | 0.372384i | \(0.121460\pi\) | |||||||
\(734\) | 2.00036 | − | 3.46472i | 0.0738346 | − | 0.127885i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.9382 | −0.476909 | ||||||||
\(737\) | 0.419949 | + | 0.727373i | 0.0154690 | + | 0.0267931i | ||||
\(738\) | 0.675201 | − | 1.16948i | 0.0248545 | − | 0.0430493i | ||||
\(739\) | −10.2162 | + | 17.6950i | −0.375810 | + | 0.650922i | −0.990448 | − | 0.137887i | \(-0.955969\pi\) |
0.614638 | + | 0.788809i | \(0.289302\pi\) | |||||||
\(740\) | −11.2331 | + | 19.4563i | −0.412936 | + | 0.715227i | ||||
\(741\) | 0.112414 | − | 3.14257i | 0.00412964 | − | 0.115445i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.07080 | − | 8.78288i | −0.186030 | − | 0.322213i | 0.757893 | − | 0.652378i | \(-0.226229\pi\) |
−0.943923 | + | 0.330166i | \(0.892895\pi\) | |||||||
\(744\) | −17.8594 | −0.654758 | ||||||||
\(745\) | −19.7173 | −0.722387 | ||||||||
\(746\) | 2.22801 | + | 3.85902i | 0.0815731 | + | 0.141289i | ||||
\(747\) | −4.46469 | − | 7.73306i | −0.163354 | − | 0.282938i | ||||
\(748\) | 0.577165 | − | 0.999680i | 0.0211033 | − | 0.0365519i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.32771 | − | 10.9599i | 0.231055 | − | 0.400200i | ||||
\(751\) | −22.2961 | −0.813598 | −0.406799 | − | 0.913518i | \(-0.633355\pi\) | ||||
−0.406799 | + | 0.913518i | \(0.633355\pi\) | |||||||
\(752\) | −12.0718 | + | 20.9090i | −0.440214 | + | 0.762474i | ||||
\(753\) | −2.36104 | − | 4.08943i | −0.0860409 | − | 0.149027i | ||||
\(754\) | −12.7254 | + | 6.75234i | −0.463431 | + | 0.245906i | ||||
\(755\) | −23.7829 | −0.865550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.2909 | − | 21.2884i | −0.446720 | − | 0.773741i | 0.551451 | − | 0.834207i | \(-0.314074\pi\) |
−0.998170 | + | 0.0604666i | \(0.980741\pi\) | |||||||
\(758\) | −7.29503 | − | 12.6354i | −0.264967 | − | 0.458937i | ||||
\(759\) | −1.29885 | − | 2.24967i | −0.0471452 | − | 0.0816580i | ||||
\(760\) | −1.44300 | −0.0523431 | ||||||||
\(761\) | 17.6167 | + | 30.5130i | 0.638603 | + | 1.10609i | 0.985739 | + | 0.168279i | \(0.0538209\pi\) |
−0.347136 | + | 0.937815i | \(0.612846\pi\) | |||||||
\(762\) | 1.03050 | 0.0373312 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.91545 | + | 17.1741i | 0.358728 | + | 0.621336i | ||||
\(765\) | −1.02237 | −0.0369639 | ||||||||
\(766\) | 6.39057 | + | 11.0688i | 0.230901 | + | 0.399932i | ||||
\(767\) | −0.0310528 | + | 0.868091i | −0.00112125 | + | 0.0313449i | ||||
\(768\) | 4.38246 | − | 7.59065i | 0.158138 | − | 0.273904i | ||||
\(769\) | −4.62257 | − | 8.00653i | −0.166694 | − | 0.288723i | 0.770561 | − | 0.637366i | \(-0.219976\pi\) |
−0.937256 | + | 0.348643i | \(0.886643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.95251 | + | 17.2383i | −0.358431 | + | 0.620821i | ||||
\(772\) | 11.9624 | − | 20.7194i | 0.430535 | − | 0.745708i | ||||
\(773\) | −6.32671 | −0.227556 | −0.113778 | − | 0.993506i | \(-0.536295\pi\) | ||||
−0.113778 | + | 0.993506i | \(0.536295\pi\) | |||||||
\(774\) | −2.70928 | −0.0973830 | ||||||||
\(775\) | −6.28400 | + | 10.8842i | −0.225728 | + | 0.390972i | ||||
\(776\) | 16.6180 | − | 28.7833i | 0.596553 | − | 1.03326i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.18349 | − | 5.51397i | −0.114134 | − | 0.197686i | ||||
\(779\) | −0.925812 | + | 1.60355i | −0.0331706 | + | 0.0574532i | ||||
\(780\) | −14.7749 | + | 7.83984i | −0.529025 | + | 0.280711i | ||||
\(781\) | 3.62802 | + | 6.28391i | 0.129821 | + | 0.224856i | ||||
\(782\) | −1.64285 | −0.0587480 | ||||||||
\(783\) | −15.7772 | − | 27.3270i | −0.563833 | − | 0.976587i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.926435 | −0.0330659 | ||||||||
\(786\) | 0.623749 | + | 1.08036i | 0.0222484 | + | 0.0385353i | ||||
\(787\) | 46.0057 | 1.63993 | 0.819963 | − | 0.572416i | \(-0.193994\pi\) | ||||
0.819963 | + | 0.572416i | \(0.193994\pi\) | |||||||
\(788\) | 5.79777 | + | 10.0420i | 0.206537 | + | 0.357733i | ||||
\(789\) | 29.6576 | + | 51.3684i | 1.05584 | + | 1.82876i | ||||
\(790\) | −6.86924 | − | 11.8979i | −0.244397 | − | 0.423307i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.714154 | 0.0253764 | ||||||||
\(793\) | 24.6104 | − | 13.0588i | 0.873942 | − | 0.463731i | ||||
\(794\) | −7.26979 | − | 12.5916i | −0.257995 | − | 0.446861i | ||||
\(795\) | −13.0976 | + | 22.6856i | −0.464523 | + | 0.804577i | ||||
\(796\) | 5.94569 | 0.210740 | ||||||||
\(797\) | −12.3745 | + | 21.4333i | −0.438327 | + | 0.759205i | −0.997561 | − | 0.0698051i | \(-0.977762\pi\) |
0.559233 | + | 0.829010i | \(0.311096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.89181 | + | 11.9370i | −0.243815 | + | 0.422299i | ||||
\(800\) | −7.72717 | − | 13.3839i | −0.273197 | − | 0.473191i | ||||
\(801\) | 0.722173 | + | 1.25084i | 0.0255167 | + | 0.0441963i | ||||
\(802\) | 13.1386 | 0.463940 | ||||||||
\(803\) | 2.14183 | 0.0755835 | ||||||||
\(804\) | −2.28006 | − | 3.94919i | −0.0804117 | − | 0.139277i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.20551 | + | 4.35401i | −0.289027 | + | 0.153363i | ||||
\(807\) | 19.9861 | − | 34.6170i | 0.703545 | − | 1.21858i | ||||
\(808\) | 14.8847 | − | 25.7811i | 0.523643 | − | 0.906977i | ||||
\(809\) | −15.0174 | + | 26.0109i | −0.527983 | + | 0.914494i | 0.471485 | + | 0.881874i | \(0.343718\pi\) |
−0.999468 | + | 0.0326194i | \(0.989615\pi\) | |||||||
\(810\) | 4.44437 | + | 7.69787i | 0.156159 | + | 0.270475i | ||||
\(811\) | −13.4160 | −0.471101 | −0.235550 | − | 0.971862i | \(-0.575689\pi\) | ||||
−0.235550 | + | 0.971862i | \(0.575689\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.16812 | + | 10.6835i | −0.216325 | + | 0.374686i | ||||
\(814\) | 1.54021 | − | 2.66772i | 0.0539843 | − | 0.0935036i | ||||
\(815\) | 17.2180 | 0.603119 | ||||||||
\(816\) | −2.37255 | + | 4.10938i | −0.0830560 | + | 0.143857i | ||||
\(817\) | 3.71487 | 0.129967 | ||||||||
\(818\) | −9.94171 | −0.347604 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.84878 | 0.343934 | ||||||||
\(821\) | 10.1506 | 0.354257 | 0.177128 | − | 0.984188i | \(-0.443319\pi\) | ||||
0.177128 | + | 0.984188i | \(0.443319\pi\) | |||||||
\(822\) | −4.73912 | + | 8.20840i | −0.165296 | + | 0.286301i | ||||
\(823\) | −48.0434 | −1.67469 | −0.837344 | − | 0.546676i | \(-0.815893\pi\) | ||||
−0.837344 | + | 0.546676i | \(0.815893\pi\) | |||||||
\(824\) | 11.4174 | − | 19.7755i | 0.397744 | − | 0.688913i | ||||
\(825\) | 1.55144 | − | 2.68717i | 0.0540142 | − | 0.0935553i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.41781 | 0.292716 | 0.146358 | − | 0.989232i | \(-0.453245\pi\) | ||||
0.146358 | + | 0.989232i | \(0.453245\pi\) | |||||||
\(828\) | 1.14218 | + | 1.97832i | 0.0396935 | + | 0.0687512i | ||||
\(829\) | −28.0821 | + | 48.6396i | −0.975331 | + | 1.68932i | −0.296495 | + | 0.955034i | \(0.595818\pi\) |
−0.678837 | + | 0.734289i | \(0.737516\pi\) | |||||||
\(830\) | −6.57924 | + | 11.3956i | −0.228369 | + | 0.395546i | ||||
\(831\) | 13.7466 | − | 23.8098i | 0.476863 | − | 0.825951i | ||||
\(832\) | −0.131968 | + | 3.68920i | −0.00457516 | + | 0.127900i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.98314 | + | 13.8272i | 0.276434 | + | 0.478797i | ||||
\(835\) | 32.5060 | 1.12492 | ||||||||
\(836\) | −0.444686 | −0.0153798 | ||||||||
\(837\) | −10.1734 | − | 17.6209i | −0.351645 | − | 0.609066i | ||||
\(838\) | 9.85111 | + | 17.0626i | 0.340301 | + | 0.589419i | ||||
\(839\) | −13.0690 | + | 22.6362i | −0.451192 | + | 0.781488i | −0.998460 | − | 0.0554692i | \(-0.982335\pi\) |
0.547268 | + | 0.836957i | \(0.315668\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.24289 | + | 16.0092i | −0.318720 | + | 0.552040i | ||||
\(842\) | 18.7640 | 0.646650 | ||||||||
\(843\) | −25.7158 | + | 44.5411i | −0.885700 | + | 1.53408i | ||||
\(844\) | −11.7415 | − | 20.3368i | −0.404158 | − | 0.700023i | ||||
\(845\) | −10.7394 | + | 15.8637i | −0.369448 | + | 0.545727i | ||||
\(846\) | −3.87255 | −0.133141 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.84586 | + | 17.0535i | 0.338108 | + | 0.585621i | ||||
\(849\) | −8.11290 | − | 14.0519i | −0.278434 | − | 0.482262i | ||||
\(850\) | −0.981166 | − | 1.69943i | −0.0336537 | − | 0.0582900i | ||||
\(851\) | 21.6976 | 0.743783 | ||||||||
\(852\) | −19.6979 | − | 34.1178i | −0.674839 | − | 1.16886i | ||||
\(853\) | −9.56236 | −0.327409 | −0.163705 | − | 0.986509i | \(-0.552344\pi\) | ||||
−0.163705 | + | 0.986509i | \(0.552344\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.196926 | + | 0.341085i | 0.00673471 | + | 0.0116649i | ||||
\(856\) | 7.97730 | 0.272659 | ||||||||
\(857\) | 2.83687 | + | 4.91361i | 0.0969058 | + | 0.167846i | 0.910402 | − | 0.413724i | \(-0.135772\pi\) |
−0.813497 | + | 0.581570i | \(0.802439\pi\) | |||||||
\(858\) | 2.02584 | − | 1.07495i | 0.0691610 | − | 0.0366982i | ||||
\(859\) | −13.2675 | + | 22.9801i | −0.452683 | + | 0.784070i | −0.998552 | − | 0.0538010i | \(-0.982866\pi\) |
0.545869 | + | 0.837871i | \(0.316200\pi\) | |||||||
\(860\) | −9.87968 | − | 17.1121i | −0.336894 | − | 0.583518i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.48292 | + | 9.49669i | −0.186749 | + | 0.323459i | ||||
\(863\) | −9.52402 | + | 16.4961i | −0.324202 | + | 0.561533i | −0.981350 | − | 0.192227i | \(-0.938429\pi\) |
0.657149 | + | 0.753761i | \(0.271762\pi\) | |||||||
\(864\) | 25.0196 | 0.851186 | ||||||||
\(865\) | 16.7855 | 0.570725 | ||||||||
\(866\) | −5.54882 | + | 9.61084i | −0.188557 | + | 0.326590i | ||||
\(867\) | 14.7278 | − | 25.5094i | 0.500184 | − | 0.866343i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.66148 | − | 8.07393i | −0.158130 | − | 0.273889i | ||||
\(870\) | 5.56997 | − | 9.64746i | 0.188840 | − | 0.327080i | ||||
\(871\) | −4.42692 | − | 2.77148i | −0.150001 | − | 0.0939081i | ||||
\(872\) | 8.71856 | + | 15.1010i | 0.295248 | + | 0.511384i | ||||
\(873\) | −9.07143 | −0.307021 | ||||||||
\(874\) | 0.316439 | + | 0.548089i | 0.0107037 | + | 0.0185394i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.6288 | −0.392901 | ||||||||
\(877\) | −13.2586 | − | 22.9645i | −0.447710 | − | 0.775456i | 0.550527 | − | 0.834818i | \(-0.314427\pi\) |
−0.998237 | + | 0.0593613i | \(0.981094\pi\) | |||||||
\(878\) | 5.56785 | 0.187906 | ||||||||
\(879\) | 9.92102 | + | 17.1837i | 0.334628 | + | 0.579592i | ||||
\(880\) | 0.895404 | + | 1.55088i | 0.0301840 | + | 0.0522803i | ||||
\(881\) | −2.02357 | − | 3.50492i | −0.0681757 | − | 0.118084i | 0.829923 | − | 0.557879i | \(-0.188385\pi\) |
−0.898098 | + | 0.439795i | \(0.855051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.7968 | 1.50753 | 0.753766 | − | 0.657142i | \(-0.228235\pi\) | ||||
0.753766 | + | 0.657142i | \(0.228235\pi\) | |||||||
\(884\) | −0.256610 | + | 7.17362i | −0.00863073 | + | 0.241275i | ||||
\(885\) | −0.335858 | − | 0.581723i | −0.0112897 | − | 0.0195544i | ||||
\(886\) | −11.7120 | + | 20.2859i | −0.393474 | + | 0.681517i | ||||
\(887\) | 50.1066 | 1.68241 | 0.841207 | − | 0.540714i | \(-0.181846\pi\) | ||||
0.841207 | + | 0.540714i | \(0.181846\pi\) | |||||||
\(888\) | −18.4144 | + | 31.8947i | −0.617948 | + | 1.07032i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.06421 | − | 1.84326i | 0.0356723 | − | 0.0617862i | ||||
\(891\) | 3.01596 | + | 5.22379i | 0.101038 | + | 0.175004i | ||||
\(892\) | 0.756314 | + | 1.30997i | 0.0253233 | + | 0.0438612i | ||||
\(893\) | 5.30990 | 0.177689 | ||||||||
\(894\) | −14.6784 | −0.490920 | ||||||||
\(895\) | −2.55851 | − | 4.43148i | −0.0855217 | − | 0.148128i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.6919 | + | 8.57184i | 0.457160 | + | 0.286205i | ||||
\(898\) | −7.71796 | + | 13.3679i | −0.257552 | + | 0.446093i | ||||
\(899\) | −15.3098 | + | 26.5173i | −0.510610 | + | 0.884402i | ||||
\(900\) | −1.36430 | + | 2.36304i | −0.0454768 | + | 0.0787681i | ||||
\(901\) | 5.62100 | + | 9.73586i | 0.187263 | + | 0.324348i | ||||
\(902\) | −1.35040 | −0.0449635 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.29384 | − | 14.3654i | 0.275849 | − | 0.477785i | ||||
\(905\) | −15.5461 | + | 26.9266i | −0.516769 | + | 0.895069i | ||||
\(906\) | −17.7050 | −0.588210 | ||||||||
\(907\) | −2.77789 | + | 4.81144i | −0.0922382 | + | 0.159761i | −0.908453 | − | 0.417988i | \(-0.862735\pi\) |
0.816214 | + | 0.577749i | \(0.196069\pi\) | |||||||
\(908\) | −3.88522 | −0.128936 | ||||||||
\(909\) | −8.12526 | −0.269498 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.5845 | −0.483205 | −0.241603 | − | 0.970375i | \(-0.577673\pi\) | ||||
−0.241603 | + | 0.970375i | \(0.577673\pi\) | |||||||
\(912\) | 1.82797 | 0.0605302 | ||||||||
\(913\) | −4.46469 | + | 7.73306i | −0.147760 | + | 0.255927i | ||||
\(914\) | 0.935158 | 0.0309323 | ||||||||
\(915\) | −10.7721 | + | 18.6579i | −0.356116 | + | 0.616810i | ||||
\(916\) | 13.8769 | − | 24.0354i | 0.458504 | − | 0.794153i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.17690 | 0.104853 | ||||||||
\(919\) | 3.50823 | + | 6.07643i | 0.115726 | + | 0.200443i | 0.918070 | − | 0.396419i | \(-0.129747\pi\) |
−0.802344 | + | 0.596862i | \(0.796414\pi\) | |||||||
\(920\) | 3.70636 | − | 6.41960i | 0.122195 | − | 0.211648i | ||||
\(921\) | 18.1400 | − | 31.4194i | 0.597734 | − | 1.03531i | ||||
\(922\) | 4.61548 | − | 7.99424i | 0.152003 | − | 0.263276i | ||||
\(923\) | −38.2450 | − | 23.9433i | −1.25885 | − | 0.788105i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.9586 | + | 22.4449i | 0.426075 | + | 0.737984i | ||||
\(926\) | 16.7261 | 0.549653 | ||||||||
\(927\) | −6.23251 | −0.204702 | ||||||||
\(928\) | −18.8258 | − | 32.6072i | −0.617987 | − | 1.07039i | ||||
\(929\) | −29.8098 | − | 51.6321i | −0.978028 | − | 1.69399i | −0.669558 | − | 0.742760i | \(-0.733517\pi\) |
−0.308469 | − | 0.951234i | \(-0.599817\pi\) | |||||||
\(930\) | 3.59160 | − | 6.22083i | 0.117773 | − | 0.203989i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.7485 | + | 23.8131i | −0.450347 | + | 0.780024i | ||||
\(933\) | −6.60046 | −0.216089 | ||||||||
\(934\) | 2.15845 | − | 3.73854i | 0.0706266 | − | 0.122329i | ||||
\(935\) | 0.511186 | + | 0.885399i | 0.0167176 | + | 0.0289557i | ||||
\(936\) | −3.92291 | + | 2.08158i | −0.128224 | + | 0.0680385i | ||||
\(937\) | 14.5256 | 0.474531 | 0.237266 | − | 0.971445i | \(-0.423749\pi\) | ||||
0.237266 | + | 0.971445i | \(0.423749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.2245 | + | 33.2978i | 0.627367 | + | 1.08663i | ||||
\(940\) | −14.1217 | − | 24.4595i | −0.460598 | − | 0.797779i | ||||
\(941\) | 15.1230 | + | 26.1937i | 0.492994 | + | 0.853891i | 0.999967 | − | 0.00807086i | \(-0.00256906\pi\) |
−0.506973 | + | 0.861962i | \(0.669236\pi\) | |||||||
\(942\) | −0.689678 | −0.0224709 | ||||||||
\(943\) | −4.75591 | − | 8.23749i | −0.154874 | − | 0.268249i | ||||
\(944\) | −0.504951 | −0.0164348 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.35464 | + | 2.34630i | 0.0440431 | + | 0.0762849i | ||||
\(947\) | 15.5278 | 0.504585 | 0.252292 | − | 0.967651i | \(-0.418816\pi\) | ||||
0.252292 | + | 0.967651i | \(0.418816\pi\) | |||||||
\(948\) | 25.3090 | + | 43.8364i | 0.821997 | + | 1.42374i | ||||
\(949\) | −11.7652 | + | 6.24288i | −0.381916 | + | 0.202652i | ||||
\(950\) | −0.377978 | + | 0.654677i | −0.0122632 | + | 0.0212405i | ||||
\(951\) | 26.3202 | + | 45.5879i | 0.853490 | + | 1.47829i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.8527 | + | 18.7974i | −0.351554 | + | 0.608909i | −0.986522 | − | 0.163629i | \(-0.947680\pi\) |
0.634968 | + | 0.772538i | \(0.281013\pi\) | |||||||
\(954\) | −1.57924 | + | 2.73532i | −0.0511297 | + | 0.0885593i | ||||
\(955\) | −17.5639 | −0.568354 | ||||||||
\(956\) | −5.29166 | −0.171144 | ||||||||
\(957\) | 3.77979 | − | 6.54679i | 0.122183 | − | 0.211628i | ||||
\(958\) | −10.7997 | + | 18.7057i | −0.348924 | + | 0.604353i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.42732 | − | 2.47220i | −0.0460667 | − | 0.0797899i | ||||
\(961\) | 5.62802 | − | 9.74801i | 0.181549 | − | 0.314452i | ||||
\(962\) | −0.684784 | + | 19.1434i | −0.0220783 | + | 0.617207i | ||||
\(963\) | −1.08866 | − | 1.88561i | −0.0350816 | − | 0.0607630i | ||||
\(964\) | 26.3879 | 0.849898 | ||||||||
\(965\) | 10.5949 | + | 18.3508i | 0.341061 | + | 0.590735i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.7524 | 0.731667 | 0.365833 | − | 0.930680i | \(-0.380784\pi\) | ||||
0.365833 | + | 0.930680i | \(0.380784\pi\) | |||||||
\(968\) | 11.3267 | + | 19.6184i | 0.364054 | + | 0.630559i | ||||
\(969\) | 1.04359 | 0.0335249 | ||||||||
\(970\) | 6.68390 | + | 11.5769i | 0.214607 | + | 0.371711i | ||||
\(971\) | −26.5064 | − | 45.9105i | −0.850632 | − | 1.47334i | −0.880639 | − | 0.473787i | \(-0.842886\pi\) |
0.0300076 | − | 0.999550i | \(-0.490447\pi\) | |||||||
\(972\) | −4.94660 | − | 8.56776i | −0.158662 | − | 0.274811i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.0156 | −0.449087 | ||||||||
\(975\) | −0.689777 | + | 19.2829i | −0.0220905 | + | 0.617548i | ||||
\(976\) | 8.09776 | + | 14.0257i | 0.259203 | + | 0.448953i | ||||
\(977\) | 2.32294 | − | 4.02345i | 0.0743174 | − | 0.128722i | −0.826472 | − | 0.562978i | \(-0.809656\pi\) |
0.900789 | + | 0.434257i | \(0.142989\pi\) | |||||||
\(978\) | 12.8178 | 0.409868 | ||||||||
\(979\) | 0.722173 | − | 1.25084i | 0.0230807 | − | 0.0399770i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.37964 | − | 4.12165i | 0.0759760 | − | 0.131594i | ||||
\(982\) | 1.76014 | + | 3.04865i | 0.0561682 | + | 0.0972862i | ||||
\(983\) | 3.91896 | + | 6.78783i | 0.124995 | + | 0.216498i | 0.921731 | − | 0.387830i | \(-0.126775\pi\) |
−0.796736 | + | 0.604328i | \(0.793442\pi\) | |||||||
\(984\) | 16.1451 | 0.514688 | ||||||||
\(985\) | −10.2700 | −0.327229 | ||||||||
\(986\) | −2.39043 | − | 4.14034i | −0.0761267 | − | 0.131855i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.44270 | − | 1.29615i | 0.0777127 | − | 0.0412359i | ||||
\(989\) | −9.54167 | + | 16.5267i | −0.303408 | + | 0.525517i | ||||
\(990\) | −0.143619 | + | 0.248756i | −0.00456452 | + | 0.00790598i | ||||
\(991\) | 8.87507 | − | 15.3721i | 0.281926 | − | 0.488310i | −0.689933 | − | 0.723873i | \(-0.742360\pi\) |
0.971859 | + | 0.235563i | \(0.0756935\pi\) | |||||||
\(992\) | −12.1392 | − | 21.0257i | −0.385419 | − | 0.667565i | ||||
\(993\) | −17.6772 | −0.560970 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.63300 | + | 4.56049i | −0.0834717 | + | 0.144577i | ||||
\(996\) | 24.2405 | − | 41.9857i | 0.768089 | − | 1.33037i | ||||
\(997\) | 35.3203 | 1.11861 | 0.559303 | − | 0.828963i | \(-0.311069\pi\) | ||||
0.559303 | + | 0.828963i | \(0.311069\pi\) | |||||||
\(998\) | −0.729299 | + | 1.26318i | −0.0230855 | + | 0.0399853i | ||||
\(999\) | −41.9583 | −1.32750 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.h.m.471.5 | 16 | ||
7.2 | even | 3 | 637.2.f.l.393.3 | yes | 16 | ||
7.3 | odd | 6 | 637.2.g.m.263.3 | 16 | |||
7.4 | even | 3 | 637.2.g.m.263.4 | 16 | |||
7.5 | odd | 6 | 637.2.f.l.393.4 | yes | 16 | ||
7.6 | odd | 2 | inner | 637.2.h.m.471.6 | 16 | ||
13.9 | even | 3 | 637.2.g.m.373.4 | 16 | |||
91.9 | even | 3 | 637.2.f.l.295.3 | ✓ | 16 | ||
91.16 | even | 3 | 8281.2.a.ci.1.6 | 8 | |||
91.23 | even | 6 | 8281.2.a.cl.1.4 | 8 | |||
91.48 | odd | 6 | 637.2.g.m.373.3 | 16 | |||
91.61 | odd | 6 | 637.2.f.l.295.4 | yes | 16 | ||
91.68 | odd | 6 | 8281.2.a.ci.1.5 | 8 | |||
91.74 | even | 3 | inner | 637.2.h.m.165.5 | 16 | ||
91.75 | odd | 6 | 8281.2.a.cl.1.3 | 8 | |||
91.87 | odd | 6 | inner | 637.2.h.m.165.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.l.295.3 | ✓ | 16 | 91.9 | even | 3 | ||
637.2.f.l.295.4 | yes | 16 | 91.61 | odd | 6 | ||
637.2.f.l.393.3 | yes | 16 | 7.2 | even | 3 | ||
637.2.f.l.393.4 | yes | 16 | 7.5 | odd | 6 | ||
637.2.g.m.263.3 | 16 | 7.3 | odd | 6 | |||
637.2.g.m.263.4 | 16 | 7.4 | even | 3 | |||
637.2.g.m.373.3 | 16 | 91.48 | odd | 6 | |||
637.2.g.m.373.4 | 16 | 13.9 | even | 3 | |||
637.2.h.m.165.5 | 16 | 91.74 | even | 3 | inner | ||
637.2.h.m.165.6 | 16 | 91.87 | odd | 6 | inner | ||
637.2.h.m.471.5 | 16 | 1.1 | even | 1 | trivial | ||
637.2.h.m.471.6 | 16 | 7.6 | odd | 2 | inner | ||
8281.2.a.ci.1.5 | 8 | 91.68 | odd | 6 | |||
8281.2.a.ci.1.6 | 8 | 91.16 | even | 3 | |||
8281.2.a.cl.1.3 | 8 | 91.75 | odd | 6 | |||
8281.2.a.cl.1.4 | 8 | 91.23 | even | 6 |