Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(122,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.122");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.j (of order \(4\), degree \(2\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 122.8 | ||
Character | \(\chi\) | \(=\) | 429.122 |
Dual form | 429.2.j.a.320.8 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.43577 | − | 1.43577i | −1.01524 | − | 1.01524i | −0.999882 | − | 0.0153578i | \(-0.995111\pi\) |
−0.0153578 | − | 0.999882i | \(-0.504889\pi\) | |||||||
\(3\) | −1.73083 | − | 0.0650121i | −0.999295 | − | 0.0375347i | ||||
\(4\) | 2.12285i | 1.06142i | ||||||||
\(5\) | −1.59194 | − | 1.59194i | −0.711937 | − | 0.711937i | 0.255004 | − | 0.966940i | \(-0.417923\pi\) |
−0.966940 | + | 0.255004i | \(0.917923\pi\) | |||||||
\(6\) | 2.39173 | + | 2.57841i | 0.976418 | + | 1.05263i | ||||
\(7\) | 1.33791 | + | 1.33791i | 0.505683 | + | 0.505683i | 0.913198 | − | 0.407515i | \(-0.133605\pi\) |
−0.407515 | + | 0.913198i | \(0.633605\pi\) | |||||||
\(8\) | 0.176380 | − | 0.176380i | 0.0623599 | − | 0.0623599i | ||||
\(9\) | 2.99155 | + | 0.225050i | 0.997182 | + | 0.0750166i | ||||
\(10\) | 4.57130i | 1.44557i | ||||||||
\(11\) | −0.707107 | + | 0.707107i | −0.213201 | + | 0.213201i | ||||
\(12\) | 0.138011 | − | 3.67429i | 0.0398403 | − | 1.06068i | ||||
\(13\) | −2.05741 | + | 2.96092i | −0.570623 | + | 0.821212i | ||||
\(14\) | − | 3.84185i | − | 1.02678i | ||||||
\(15\) | 2.65188 | + | 2.85887i | 0.684713 | + | 0.738157i | ||||
\(16\) | 3.73921 | 0.934803 | ||||||||
\(17\) | 5.94126 | 1.44097 | 0.720484 | − | 0.693471i | \(-0.243920\pi\) | ||||
0.720484 | + | 0.693471i | \(0.243920\pi\) | |||||||
\(18\) | −3.97204 | − | 4.61828i | −0.936219 | − | 1.08854i | ||||
\(19\) | −2.46772 | + | 2.46772i | −0.566134 | + | 0.566134i | −0.931043 | − | 0.364909i | \(-0.881100\pi\) |
0.364909 | + | 0.931043i | \(0.381100\pi\) | |||||||
\(20\) | 3.37944 | − | 3.37944i | 0.755666 | − | 0.755666i | ||||
\(21\) | −2.22872 | − | 2.40268i | −0.486346 | − | 0.524307i | ||||
\(22\) | 2.03048 | 0.432900 | ||||||||
\(23\) | −0.808524 | −0.168589 | −0.0842944 | − | 0.996441i | \(-0.526864\pi\) | ||||
−0.0842944 | + | 0.996441i | \(0.526864\pi\) | |||||||
\(24\) | −0.316751 | + | 0.293818i | −0.0646566 | + | 0.0599752i | ||||
\(25\) | 0.0685372i | 0.0137074i | ||||||||
\(26\) | 7.20515 | − | 1.29723i | 1.41305 | − | 0.254407i | ||||
\(27\) | −5.16323 | − | 0.584009i | −0.993664 | − | 0.112393i | ||||
\(28\) | −2.84018 | + | 2.84018i | −0.536744 | + | 0.536744i | ||||
\(29\) | − | 5.12953i | − | 0.952529i | −0.879302 | − | 0.476265i | \(-0.841990\pi\) | ||
0.879302 | − | 0.476265i | \(-0.158010\pi\) | |||||||
\(30\) | 0.297190 | − | 7.91215i | 0.0542592 | − | 1.44455i | ||||
\(31\) | 6.56068 | − | 6.56068i | 1.17833 | − | 1.17833i | 0.198163 | − | 0.980169i | \(-0.436502\pi\) |
0.980169 | − | 0.198163i | \(-0.0634975\pi\) | |||||||
\(32\) | −5.72140 | − | 5.72140i | −1.01141 | − | 1.01141i | ||||
\(33\) | 1.26985 | − | 1.17791i | 0.221053 | − | 0.205048i | ||||
\(34\) | −8.53026 | − | 8.53026i | −1.46293 | − | 1.46293i | ||||
\(35\) | − | 4.25974i | − | 0.720028i | ||||||
\(36\) | −0.477746 | + | 6.35060i | −0.0796244 | + | 1.05843i | ||||
\(37\) | 5.17706 | + | 5.17706i | 0.851104 | + | 0.851104i | 0.990269 | − | 0.139166i | \(-0.0444420\pi\) |
−0.139166 | + | 0.990269i | \(0.544442\pi\) | |||||||
\(38\) | 7.08614 | 1.14952 | ||||||||
\(39\) | 3.75353 | − | 4.99110i | 0.601045 | − | 0.799215i | ||||
\(40\) | −0.561573 | −0.0887925 | ||||||||
\(41\) | 5.79232 | + | 5.79232i | 0.904609 | + | 0.904609i | 0.995831 | − | 0.0912219i | \(-0.0290773\pi\) |
−0.0912219 | + | 0.995831i | \(0.529077\pi\) | |||||||
\(42\) | −0.249767 | + | 6.64960i | −0.0385399 | + | 1.02606i | ||||
\(43\) | − | 6.08422i | − | 0.927835i | −0.885878 | − | 0.463917i | \(-0.846443\pi\) | ||
0.885878 | − | 0.463917i | \(-0.153557\pi\) | |||||||
\(44\) | −1.50108 | − | 1.50108i | −0.226296 | − | 0.226296i | ||||
\(45\) | −4.40409 | − | 5.12062i | −0.656524 | − | 0.763338i | ||||
\(46\) | 1.16085 | + | 1.16085i | 0.171158 | + | 0.171158i | ||||
\(47\) | −6.46036 | + | 6.46036i | −0.942340 | + | 0.942340i | −0.998426 | − | 0.0560856i | \(-0.982138\pi\) |
0.0560856 | + | 0.998426i | \(0.482138\pi\) | |||||||
\(48\) | −6.47194 | − | 0.243094i | −0.934145 | − | 0.0350876i | ||||
\(49\) | − | 3.41999i | − | 0.488570i | ||||||
\(50\) | 0.0984033 | − | 0.0984033i | 0.0139163 | − | 0.0139163i | ||||
\(51\) | −10.2833 | − | 0.386254i | −1.43995 | − | 0.0540864i | ||||
\(52\) | −6.28558 | − | 4.36757i | −0.871654 | − | 0.605673i | ||||
\(53\) | − | 4.64016i | − | 0.637376i | −0.947860 | − | 0.318688i | \(-0.896758\pi\) | ||
0.947860 | − | 0.318688i | \(-0.103242\pi\) | |||||||
\(54\) | 6.57469 | + | 8.25169i | 0.894702 | + | 1.12291i | ||||
\(55\) | 2.25134 | 0.303571 | ||||||||
\(56\) | 0.471962 | 0.0630686 | ||||||||
\(57\) | 4.43164 | − | 4.11077i | 0.586984 | − | 0.544485i | ||||
\(58\) | −7.36480 | + | 7.36480i | −0.967046 | + | 0.967046i | ||||
\(59\) | −1.07306 | + | 1.07306i | −0.139701 | + | 0.139701i | −0.773499 | − | 0.633798i | \(-0.781495\pi\) |
0.633798 | + | 0.773499i | \(0.281495\pi\) | |||||||
\(60\) | −6.06895 | + | 5.62954i | −0.783498 | + | 0.726770i | ||||
\(61\) | 8.34079 | 1.06793 | 0.533964 | − | 0.845507i | \(-0.320702\pi\) | ||||
0.533964 | + | 0.845507i | \(0.320702\pi\) | |||||||
\(62\) | −18.8392 | −2.39258 | ||||||||
\(63\) | 3.70133 | + | 4.30352i | 0.466323 | + | 0.542193i | ||||
\(64\) | 8.95074i | 1.11884i | ||||||||
\(65\) | 7.98888 | − | 1.43833i | 0.990898 | − | 0.178403i | ||||
\(66\) | −3.51442 | − | 0.132006i | −0.432595 | − | 0.0162488i | ||||
\(67\) | 2.38684 | − | 2.38684i | 0.291600 | − | 0.291600i | −0.546112 | − | 0.837712i | \(-0.683893\pi\) |
0.837712 | + | 0.546112i | \(0.183893\pi\) | |||||||
\(68\) | 12.6124i | 1.52948i | ||||||||
\(69\) | 1.39942 | + | 0.0525638i | 0.168470 | + | 0.00632794i | ||||
\(70\) | −6.11600 | + | 6.11600i | −0.731001 | + | 0.731001i | ||||
\(71\) | 7.67850 | + | 7.67850i | 0.911270 | + | 0.911270i | 0.996372 | − | 0.0851021i | \(-0.0271216\pi\) |
−0.0851021 | + | 0.996372i | \(0.527122\pi\) | |||||||
\(72\) | 0.567344 | − | 0.487956i | 0.0668622 | − | 0.0575061i | ||||
\(73\) | 2.21842 | + | 2.21842i | 0.259647 | + | 0.259647i | 0.824910 | − | 0.565264i | \(-0.191226\pi\) |
−0.565264 | + | 0.824910i | \(0.691226\pi\) | |||||||
\(74\) | − | 14.8661i | − | 1.72815i | ||||||
\(75\) | 0.00445574 | − | 0.118626i | 0.000514505 | − | 0.0136978i | ||||
\(76\) | −5.23859 | − | 5.23859i | −0.600908 | − | 0.600908i | ||||
\(77\) | −1.89209 | −0.215624 | ||||||||
\(78\) | −12.5552 | + | 1.77686i | −1.42160 | + | 0.201190i | ||||
\(79\) | 8.33607 | 0.937881 | 0.468941 | − | 0.883230i | \(-0.344636\pi\) | ||||
0.468941 | + | 0.883230i | \(0.344636\pi\) | |||||||
\(80\) | −5.95260 | − | 5.95260i | −0.665521 | − | 0.665521i | ||||
\(81\) | 8.89871 | + | 1.34649i | 0.988745 | + | 0.149610i | ||||
\(82\) | − | 16.6328i | − | 1.83679i | ||||||
\(83\) | 7.81391 | + | 7.81391i | 0.857688 | + | 0.857688i | 0.991065 | − | 0.133377i | \(-0.0425822\pi\) |
−0.133377 | + | 0.991065i | \(0.542582\pi\) | |||||||
\(84\) | 5.10052 | − | 4.73123i | 0.556512 | − | 0.516219i | ||||
\(85\) | −9.45813 | − | 9.45813i | −1.02588 | − | 1.02588i | ||||
\(86\) | −8.73551 | + | 8.73551i | −0.941975 | + | 0.941975i | ||||
\(87\) | −0.333481 | + | 8.87834i | −0.0357529 | + | 0.951858i | ||||
\(88\) | 0.249439i | 0.0265903i | ||||||||
\(89\) | 1.90101 | − | 1.90101i | 0.201506 | − | 0.201506i | −0.599139 | − | 0.800645i | \(-0.704490\pi\) |
0.800645 | + | 0.599139i | \(0.204490\pi\) | |||||||
\(90\) | −1.02877 | + | 13.6753i | −0.108442 | + | 1.44150i | ||||
\(91\) | −6.71408 | + | 1.20882i | −0.703827 | + | 0.126718i | ||||
\(92\) | − | 1.71637i | − | 0.178944i | ||||||
\(93\) | −11.7819 | + | 10.9289i | −1.22173 | + | 1.13327i | ||||
\(94\) | 18.5511 | 1.91340 | ||||||||
\(95\) | 7.85692 | 0.806103 | ||||||||
\(96\) | 9.53081 | + | 10.2747i | 0.972734 | + | 1.04866i | ||||
\(97\) | −8.73321 | + | 8.73321i | −0.886723 | + | 0.886723i | −0.994207 | − | 0.107484i | \(-0.965721\pi\) |
0.107484 | + | 0.994207i | \(0.465721\pi\) | |||||||
\(98\) | −4.91030 | + | 4.91030i | −0.496015 | + | 0.496015i | ||||
\(99\) | −2.27448 | + | 1.95621i | −0.228594 | + | 0.196606i | ||||
\(100\) | −0.145494 | −0.0145494 | ||||||||
\(101\) | 12.3057 | 1.22446 | 0.612230 | − | 0.790680i | \(-0.290273\pi\) | ||||
0.612230 | + | 0.790680i | \(0.290273\pi\) | |||||||
\(102\) | 14.2099 | + | 15.3190i | 1.40699 | + | 1.51681i | ||||
\(103\) | 0.219707i | 0.0216484i | 0.999941 | + | 0.0108242i | \(0.00344552\pi\) | ||||
−0.999941 | + | 0.0108242i | \(0.996554\pi\) | |||||||
\(104\) | 0.159361 | + | 0.885135i | 0.0156267 | + | 0.0867946i | ||||
\(105\) | −0.276935 | + | 7.37290i | −0.0270261 | + | 0.719521i | ||||
\(106\) | −6.66219 | + | 6.66219i | −0.647089 | + | 0.647089i | ||||
\(107\) | 19.3508i | 1.87071i | 0.353712 | + | 0.935354i | \(0.384919\pi\) | ||||
−0.353712 | + | 0.935354i | \(0.615081\pi\) | |||||||
\(108\) | 1.23976 | − | 10.9607i | 0.119296 | − | 1.05470i | ||||
\(109\) | 8.98090 | − | 8.98090i | 0.860214 | − | 0.860214i | −0.131149 | − | 0.991363i | \(-0.541867\pi\) |
0.991363 | + | 0.131149i | \(0.0418665\pi\) | |||||||
\(110\) | −3.23240 | − | 3.23240i | −0.308197 | − | 0.308197i | ||||
\(111\) | −8.62404 | − | 9.29718i | −0.818558 | − | 0.882450i | ||||
\(112\) | 5.00274 | + | 5.00274i | 0.472714 | + | 0.472714i | ||||
\(113\) | − | 7.35849i | − | 0.692228i | −0.938192 | − | 0.346114i | \(-0.887501\pi\) | ||
0.938192 | − | 0.346114i | \(-0.112499\pi\) | |||||||
\(114\) | −12.2649 | − | 0.460684i | −1.14871 | − | 0.0431470i | ||||
\(115\) | 1.28712 | + | 1.28712i | 0.120025 | + | 0.120025i | ||||
\(116\) | 10.8892 | 1.01104 | ||||||||
\(117\) | −6.82120 | + | 8.39472i | −0.630620 | + | 0.776092i | ||||
\(118\) | 3.08134 | 0.283660 | ||||||||
\(119\) | 7.94888 | + | 7.94888i | 0.728673 | + | 0.728673i | ||||
\(120\) | 0.971988 | + | 0.0365090i | 0.0887299 | + | 0.00333280i | ||||
\(121\) | − | 1.00000i | − | 0.0909091i | ||||||
\(122\) | −11.9754 | − | 11.9754i | −1.08420 | − | 1.08420i | ||||
\(123\) | −9.64895 | − | 10.4021i | −0.870017 | − | 0.937925i | ||||
\(124\) | 13.9273 | + | 13.9273i | 1.25071 | + | 1.25071i | ||||
\(125\) | −7.85059 | + | 7.85059i | −0.702178 | + | 0.702178i | ||||
\(126\) | 0.864608 | − | 11.4931i | 0.0770254 | − | 1.02389i | ||||
\(127\) | 16.6392i | 1.47649i | 0.674533 | + | 0.738245i | \(0.264345\pi\) | ||||
−0.674533 | + | 0.738245i | \(0.735655\pi\) | |||||||
\(128\) | 1.40838 | − | 1.40838i | 0.124484 | − | 0.124484i | ||||
\(129\) | −0.395548 | + | 10.5308i | −0.0348260 | + | 0.927181i | ||||
\(130\) | −13.5353 | − | 9.40505i | −1.18712 | − | 0.824878i | ||||
\(131\) | − | 9.24333i | − | 0.807593i | −0.914849 | − | 0.403797i | \(-0.867690\pi\) | ||
0.914849 | − | 0.403797i | \(-0.132310\pi\) | |||||||
\(132\) | 2.50053 | + | 2.69570i | 0.217643 | + | 0.234631i | ||||
\(133\) | −6.60318 | −0.572568 | ||||||||
\(134\) | −6.85390 | −0.592087 | ||||||||
\(135\) | 7.28984 | + | 9.14925i | 0.627409 | + | 0.787442i | ||||
\(136\) | 1.04792 | − | 1.04792i | 0.0898586 | − | 0.0898586i | ||||
\(137\) | 10.7552 | − | 10.7552i | 0.918877 | − | 0.918877i | −0.0780704 | − | 0.996948i | \(-0.524876\pi\) |
0.996948 | + | 0.0780704i | \(0.0248759\pi\) | |||||||
\(138\) | −1.93377 | − | 2.08471i | −0.164613 | − | 0.177462i | ||||
\(139\) | 10.3460 | 0.877534 | 0.438767 | − | 0.898601i | \(-0.355415\pi\) | ||||
0.438767 | + | 0.898601i | \(0.355415\pi\) | |||||||
\(140\) | 9.04279 | 0.764255 | ||||||||
\(141\) | 11.6018 | − | 10.7618i | 0.977047 | − | 0.906306i | ||||
\(142\) | − | 22.0491i | − | 1.85032i | ||||||
\(143\) | −0.638878 | − | 3.54850i | −0.0534256 | − | 0.296740i | ||||
\(144\) | 11.1860 | + | 0.841509i | 0.932169 | + | 0.0701257i | ||||
\(145\) | −8.16589 | + | 8.16589i | −0.678141 | + | 0.678141i | ||||
\(146\) | − | 6.37027i | − | 0.527207i | ||||||
\(147\) | −0.222340 | + | 5.91942i | −0.0183383 | + | 0.488225i | ||||
\(148\) | −10.9901 | + | 10.9901i | −0.903381 | + | 0.903381i | ||||
\(149\) | −2.11903 | − | 2.11903i | −0.173597 | − | 0.173597i | 0.614960 | − | 0.788558i | \(-0.289172\pi\) |
−0.788558 | + | 0.614960i | \(0.789172\pi\) | |||||||
\(150\) | −0.176717 | + | 0.163922i | −0.0144289 | + | 0.0133842i | ||||
\(151\) | −0.534299 | − | 0.534299i | −0.0434806 | − | 0.0434806i | 0.685032 | − | 0.728513i | \(-0.259788\pi\) |
−0.728513 | + | 0.685032i | \(0.759788\pi\) | |||||||
\(152\) | 0.870514i | 0.0706080i | ||||||||
\(153\) | 17.7736 | + | 1.33708i | 1.43691 | + | 0.108096i | ||||
\(154\) | 2.71660 | + | 2.71660i | 0.218910 | + | 0.218910i | ||||
\(155\) | −20.8884 | −1.67780 | ||||||||
\(156\) | 10.5953 | + | 7.96816i | 0.848306 | + | 0.637964i | ||||
\(157\) | 14.0635 | 1.12239 | 0.561194 | − | 0.827684i | \(-0.310342\pi\) | ||||
0.561194 | + | 0.827684i | \(0.310342\pi\) | |||||||
\(158\) | −11.9686 | − | 11.9686i | −0.952174 | − | 0.952174i | ||||
\(159\) | −0.301667 | + | 8.03134i | −0.0239237 | + | 0.636926i | ||||
\(160\) | 18.2162i | 1.44012i | ||||||||
\(161\) | −1.08173 | − | 1.08173i | −0.0852525 | − | 0.0852525i | ||||
\(162\) | −10.8432 | − | 14.7097i | −0.851923 | − | 1.15570i | ||||
\(163\) | −9.22582 | − | 9.22582i | −0.722622 | − | 0.722622i | 0.246517 | − | 0.969139i | \(-0.420714\pi\) |
−0.969139 | + | 0.246517i | \(0.920714\pi\) | |||||||
\(164\) | −12.2962 | + | 12.2962i | −0.960173 | + | 0.960173i | ||||
\(165\) | −3.89669 | − | 0.146364i | −0.303357 | − | 0.0113944i | ||||
\(166\) | − | 22.4379i | − | 1.74152i | ||||||
\(167\) | 7.87009 | − | 7.87009i | 0.609006 | − | 0.609006i | −0.333680 | − | 0.942686i | \(-0.608291\pi\) |
0.942686 | + | 0.333680i | \(0.108291\pi\) | |||||||
\(168\) | −0.816887 | − | 0.0306832i | −0.0630242 | − | 0.00236726i | ||||
\(169\) | −4.53411 | − | 12.1837i | −0.348778 | − | 0.937205i | ||||
\(170\) | 27.1593i | 2.08302i | ||||||||
\(171\) | −7.93766 | + | 6.82694i | −0.607008 | + | 0.522069i | ||||
\(172\) | 12.9159 | 0.984826 | ||||||||
\(173\) | 4.50776 | 0.342719 | 0.171359 | − | 0.985209i | \(-0.445184\pi\) | ||||
0.171359 | + | 0.985209i | \(0.445184\pi\) | |||||||
\(174\) | 13.2260 | − | 12.2684i | 1.00266 | − | 0.930067i | ||||
\(175\) | −0.0916966 | + | 0.0916966i | −0.00693161 | + | 0.00693161i | ||||
\(176\) | −2.64402 | + | 2.64402i | −0.199301 | + | 0.199301i | ||||
\(177\) | 1.92706 | − | 1.78753i | 0.144846 | − | 0.134359i | ||||
\(178\) | −5.45880 | −0.409154 | ||||||||
\(179\) | −19.9301 | −1.48964 | −0.744821 | − | 0.667264i | \(-0.767465\pi\) | ||||
−0.744821 | + | 0.667264i | \(0.767465\pi\) | |||||||
\(180\) | 10.8703 | − | 9.34922i | 0.810225 | − | 0.696850i | ||||
\(181\) | − | 0.659700i | − | 0.0490351i | −0.999699 | − | 0.0245176i | \(-0.992195\pi\) | ||
0.999699 | − | 0.0245176i | \(-0.00780497\pi\) | |||||||
\(182\) | 11.3754 | + | 7.90428i | 0.843203 | + | 0.585904i | ||||
\(183\) | −14.4365 | − | 0.542252i | −1.06718 | − | 0.0400844i | ||||
\(184\) | −0.142608 | + | 0.142608i | −0.0105132 | + | 0.0105132i | ||||
\(185\) | − | 16.4831i | − | 1.21186i | ||||||
\(186\) | 32.6074 | + | 1.22477i | 2.39089 | + | 0.0898048i | ||||
\(187\) | −4.20111 | + | 4.20111i | −0.307215 | + | 0.307215i | ||||
\(188\) | −13.7144 | − | 13.7144i | −1.00022 | − | 1.00022i | ||||
\(189\) | −6.12659 | − | 7.68929i | −0.445644 | − | 0.559314i | ||||
\(190\) | −11.2807 | − | 11.2807i | −0.818387 | − | 0.818387i | ||||
\(191\) | 9.84556i | 0.712399i | 0.934410 | + | 0.356200i | \(0.115928\pi\) | ||||
−0.934410 | + | 0.356200i | \(0.884072\pi\) | |||||||
\(192\) | 0.581906 | − | 15.4922i | 0.0419955 | − | 1.11805i | ||||
\(193\) | −16.1341 | − | 16.1341i | −1.16136 | − | 1.16136i | −0.984179 | − | 0.177176i | \(-0.943304\pi\) |
−0.177176 | − | 0.984179i | \(-0.556696\pi\) | |||||||
\(194\) | 25.0777 | 1.80047 | ||||||||
\(195\) | −13.9209 | + | 1.97013i | −0.996897 | + | 0.141084i | ||||
\(196\) | 7.26011 | 0.518579 | ||||||||
\(197\) | −0.879493 | − | 0.879493i | −0.0626613 | − | 0.0626613i | 0.675082 | − | 0.737743i | \(-0.264108\pi\) |
−0.737743 | + | 0.675082i | \(0.764108\pi\) | |||||||
\(198\) | 6.07427 | + | 0.456959i | 0.431680 | + | 0.0324746i | ||||
\(199\) | − | 6.49836i | − | 0.460657i | −0.973113 | − | 0.230328i | \(-0.926020\pi\) | ||
0.973113 | − | 0.230328i | \(-0.0739800\pi\) | |||||||
\(200\) | 0.0120886 | + | 0.0120886i | 0.000854793 | + | 0.000854793i | ||||
\(201\) | −4.28640 | + | 3.97605i | −0.302339 | + | 0.280449i | ||||
\(202\) | −17.6681 | − | 17.6681i | −1.24312 | − | 1.24312i | ||||
\(203\) | 6.86285 | − | 6.86285i | 0.481678 | − | 0.481678i | ||||
\(204\) | 0.819958 | − | 21.8299i | 0.0574085 | − | 1.52840i | ||||
\(205\) | − | 18.4420i | − | 1.28805i | ||||||
\(206\) | 0.315449 | − | 0.315449i | 0.0219783 | − | 0.0219783i | ||||
\(207\) | −2.41874 | − | 0.181958i | −0.168114 | − | 0.0126470i | ||||
\(208\) | −7.69310 | + | 11.0715i | −0.533421 | + | 0.767672i | ||||
\(209\) | − | 3.48988i | − | 0.241400i | ||||||
\(210\) | 10.9834 | − | 10.1881i | 0.757924 | − | 0.703048i | ||||
\(211\) | −21.8200 | −1.50215 | −0.751076 | − | 0.660216i | \(-0.770465\pi\) | ||||
−0.751076 | + | 0.660216i | \(0.770465\pi\) | |||||||
\(212\) | 9.85036 | 0.676526 | ||||||||
\(213\) | −12.7910 | − | 13.7894i | −0.876424 | − | 0.944832i | ||||
\(214\) | 27.7832 | − | 27.7832i | 1.89922 | − | 1.89922i | ||||
\(215\) | −9.68570 | + | 9.68570i | −0.660560 | + | 0.660560i | ||||
\(216\) | −1.01370 | + | 0.807684i | −0.0689735 | + | 0.0549559i | ||||
\(217\) | 17.5552 | 1.19172 | ||||||||
\(218\) | −25.7889 | −1.74665 | ||||||||
\(219\) | −3.69549 | − | 3.98393i | −0.249718 | − | 0.269209i | ||||
\(220\) | 4.77925i | 0.322217i | ||||||||
\(221\) | −12.2236 | + | 17.5916i | −0.822250 | + | 1.18334i | ||||
\(222\) | −0.966475 | + | 25.7307i | −0.0648656 | + | 1.72693i | ||||
\(223\) | −4.85663 | + | 4.85663i | −0.325224 | + | 0.325224i | −0.850767 | − | 0.525543i | \(-0.823862\pi\) |
0.525543 | + | 0.850767i | \(0.323862\pi\) | |||||||
\(224\) | − | 15.3094i | − | 1.02290i | ||||||
\(225\) | −0.0154243 | + | 0.205032i | −0.00102828 | + | 0.0136688i | ||||
\(226\) | −10.5651 | + | 10.5651i | −0.702778 | + | 0.702778i | ||||
\(227\) | 8.99284 | + | 8.99284i | 0.596876 | + | 0.596876i | 0.939480 | − | 0.342604i | \(-0.111309\pi\) |
−0.342604 | + | 0.939480i | \(0.611309\pi\) | |||||||
\(228\) | 8.72654 | + | 9.40769i | 0.577929 | + | 0.623039i | ||||
\(229\) | −0.967793 | − | 0.967793i | −0.0639536 | − | 0.0639536i | 0.674407 | − | 0.738360i | \(-0.264400\pi\) |
−0.738360 | + | 0.674407i | \(0.764400\pi\) | |||||||
\(230\) | − | 3.69601i | − | 0.243707i | ||||||
\(231\) | 3.27489 | + | 0.123009i | 0.215472 | + | 0.00809339i | ||||
\(232\) | −0.904748 | − | 0.904748i | −0.0593996 | − | 0.0593996i | ||||
\(233\) | 18.1180 | 1.18695 | 0.593473 | − | 0.804854i | \(-0.297756\pi\) | ||||
0.593473 | + | 0.804854i | \(0.297756\pi\) | |||||||
\(234\) | 21.8465 | − | 2.25920i | 1.42815 | − | 0.147689i | ||||
\(235\) | 20.5690 | 1.34177 | ||||||||
\(236\) | −2.27795 | − | 2.27795i | −0.148282 | − | 0.148282i | ||||
\(237\) | −14.4283 | − | 0.541945i | −0.937220 | − | 0.0352031i | ||||
\(238\) | − | 22.8255i | − | 1.47956i | ||||||
\(239\) | 1.80992 | + | 1.80992i | 0.117074 | + | 0.117074i | 0.763217 | − | 0.646143i | \(-0.223619\pi\) |
−0.646143 | + | 0.763217i | \(0.723619\pi\) | |||||||
\(240\) | 9.91595 | + | 10.6899i | 0.640072 | + | 0.690032i | ||||
\(241\) | −0.298552 | − | 0.298552i | −0.0192314 | − | 0.0192314i | 0.697426 | − | 0.716657i | \(-0.254329\pi\) |
−0.716657 | + | 0.697426i | \(0.754329\pi\) | |||||||
\(242\) | −1.43577 | + | 1.43577i | −0.0922945 | + | 0.0922945i | ||||
\(243\) | −15.3146 | − | 2.90907i | −0.982433 | − | 0.186617i | ||||
\(244\) | 17.7062i | 1.13352i | ||||||||
\(245\) | −5.44441 | + | 5.44441i | −0.347831 | + | 0.347831i | ||||
\(246\) | −1.08133 | + | 28.7886i | −0.0689434 | + | 1.83550i | ||||
\(247\) | −2.22961 | − | 12.3838i | −0.141867 | − | 0.787965i | ||||
\(248\) | − | 2.31435i | − | 0.146961i | ||||||
\(249\) | −13.0166 | − | 14.0326i | −0.824891 | − | 0.889277i | ||||
\(250\) | 22.5432 | 1.42576 | ||||||||
\(251\) | 19.7624 | 1.24739 | 0.623695 | − | 0.781667i | \(-0.285631\pi\) | ||||
0.623695 | + | 0.781667i | \(0.285631\pi\) | |||||||
\(252\) | −9.13572 | + | 7.85735i | −0.575496 | + | 0.494967i | ||||
\(253\) | 0.571713 | − | 0.571713i | 0.0359433 | − | 0.0359433i | ||||
\(254\) | 23.8900 | − | 23.8900i | 1.49899 | − | 1.49899i | ||||
\(255\) | 15.7555 | + | 16.9853i | 0.986649 | + | 1.06366i | ||||
\(256\) | 13.8573 | 0.866080 | ||||||||
\(257\) | −5.28192 | −0.329477 | −0.164739 | − | 0.986337i | \(-0.552678\pi\) | ||||
−0.164739 | + | 0.986337i | \(0.552678\pi\) | |||||||
\(258\) | 15.6876 | − | 14.5518i | 0.976668 | − | 0.905954i | ||||
\(259\) | 13.8529i | 0.860777i | ||||||||
\(260\) | 3.05336 | + | 16.9592i | 0.189361 | + | 1.05176i | ||||
\(261\) | 1.15440 | − | 15.3452i | 0.0714555 | − | 0.949845i | ||||
\(262\) | −13.2713 | + | 13.2713i | −0.819901 | + | 0.819901i | ||||
\(263\) | − | 1.25809i | − | 0.0775772i | −0.999247 | − | 0.0387886i | \(-0.987650\pi\) | ||
0.999247 | − | 0.0387886i | \(-0.0123499\pi\) | |||||||
\(264\) | 0.0162166 | − | 0.431737i | 0.000998061 | − | 0.0265716i | ||||
\(265\) | −7.38686 | + | 7.38686i | −0.453771 | + | 0.453771i | ||||
\(266\) | 9.48062 | + | 9.48062i | 0.581294 | + | 0.581294i | ||||
\(267\) | −3.41391 | + | 3.16673i | −0.208928 | + | 0.193801i | ||||
\(268\) | 5.06691 | + | 5.06691i | 0.309511 | + | 0.309511i | ||||
\(269\) | 10.7370i | 0.654648i | 0.944912 | + | 0.327324i | \(0.106147\pi\) | ||||
−0.944912 | + | 0.327324i | \(0.893853\pi\) | |||||||
\(270\) | 2.66968 | − | 23.6027i | 0.162472 | − | 1.43641i | ||||
\(271\) | 12.4997 | + | 12.4997i | 0.759306 | + | 0.759306i | 0.976196 | − | 0.216890i | \(-0.0695914\pi\) |
−0.216890 | + | 0.976196i | \(0.569591\pi\) | |||||||
\(272\) | 22.2157 | 1.34702 | ||||||||
\(273\) | 11.6995 | − | 1.65576i | 0.708088 | − | 0.100211i | ||||
\(274\) | −30.8839 | −1.86576 | ||||||||
\(275\) | −0.0484631 | − | 0.0484631i | −0.00292243 | − | 0.00292243i | ||||
\(276\) | −0.111585 | + | 2.97075i | −0.00671662 | + | 0.178818i | ||||
\(277\) | 28.1615i | 1.69206i | 0.533136 | + | 0.846030i | \(0.321014\pi\) | ||||
−0.533136 | + | 0.846030i | \(0.678986\pi\) | |||||||
\(278\) | −14.8544 | − | 14.8544i | −0.890908 | − | 0.890908i | ||||
\(279\) | 21.1030 | − | 18.1501i | 1.26341 | − | 1.08662i | ||||
\(280\) | −0.751335 | − | 0.751335i | −0.0449009 | − | 0.0449009i | ||||
\(281\) | −1.96439 | + | 1.96439i | −0.117185 | + | 0.117185i | −0.763268 | − | 0.646082i | \(-0.776406\pi\) |
0.646082 | + | 0.763268i | \(0.276406\pi\) | |||||||
\(282\) | −32.1089 | − | 1.20605i | −1.91205 | − | 0.0718191i | ||||
\(283\) | 12.6405i | 0.751399i | 0.926741 | + | 0.375700i | \(0.122598\pi\) | ||||
−0.926741 | + | 0.375700i | \(0.877402\pi\) | |||||||
\(284\) | −16.3003 | + | 16.3003i | −0.967244 | + | 0.967244i | ||||
\(285\) | −13.5990 | − | 0.510794i | −0.805535 | − | 0.0302568i | ||||
\(286\) | −4.17753 | + | 6.01209i | −0.247023 | + | 0.355502i | ||||
\(287\) | 15.4992i | 0.914890i | ||||||||
\(288\) | −15.8282 | − | 18.4034i | −0.932687 | − | 1.08443i | ||||
\(289\) | 18.2986 | 1.07639 | ||||||||
\(290\) | 23.4486 | 1.37695 | ||||||||
\(291\) | 15.6835 | − | 14.5479i | 0.919381 | − | 0.852815i | ||||
\(292\) | −4.70937 | + | 4.70937i | −0.275595 | + | 0.275595i | ||||
\(293\) | 5.21608 | − | 5.21608i | 0.304727 | − | 0.304727i | −0.538133 | − | 0.842860i | \(-0.680870\pi\) |
0.842860 | + | 0.538133i | \(0.180870\pi\) | |||||||
\(294\) | 8.81813 | − | 8.17967i | 0.514284 | − | 0.477048i | ||||
\(295\) | 3.41651 | 0.198917 | ||||||||
\(296\) | 1.82626 | 0.106149 | ||||||||
\(297\) | 4.06391 | − | 3.23800i | 0.235812 | − | 0.187888i | ||||
\(298\) | 6.08485i | 0.352486i | ||||||||
\(299\) | 1.66347 | − | 2.39398i | 0.0962008 | − | 0.138447i | ||||
\(300\) | 0.251825 | + | 0.00945886i | 0.0145391 | + | 0.000546108i | ||||
\(301\) | 8.14014 | − | 8.14014i | 0.469190 | − | 0.469190i | ||||
\(302\) | 1.53426i | 0.0882865i | ||||||||
\(303\) | −21.2990 | − | 0.800017i | −1.22360 | − | 0.0459598i | ||||
\(304\) | −9.22733 | + | 9.22733i | −0.529224 | + | 0.529224i | ||||
\(305\) | −13.2780 | − | 13.2780i | −0.760297 | − | 0.760297i | ||||
\(306\) | −23.5990 | − | 27.4384i | −1.34906 | − | 1.56855i | ||||
\(307\) | 17.3917 | + | 17.3917i | 0.992595 | + | 0.992595i | 0.999973 | − | 0.00737737i | \(-0.00234831\pi\) |
−0.00737737 | + | 0.999973i | \(0.502348\pi\) | |||||||
\(308\) | − | 4.01662i | − | 0.228868i | ||||||
\(309\) | 0.0142836 | − | 0.380276i | 0.000812568 | − | 0.0216332i | ||||
\(310\) | 29.9908 | + | 29.9908i | 1.70336 | + | 1.70336i | ||||
\(311\) | 4.35195 | 0.246776 | 0.123388 | − | 0.992358i | \(-0.460624\pi\) | ||||
0.123388 | + | 0.992358i | \(0.460624\pi\) | |||||||
\(312\) | −0.218283 | − | 1.54238i | −0.0123578 | − | 0.0873200i | ||||
\(313\) | −14.1848 | −0.801771 | −0.400885 | − | 0.916128i | \(-0.631297\pi\) | ||||
−0.400885 | + | 0.916128i | \(0.631297\pi\) | |||||||
\(314\) | −20.1919 | − | 20.1919i | −1.13949 | − | 1.13949i | ||||
\(315\) | 0.958654 | − | 12.7432i | 0.0540140 | − | 0.717999i | ||||
\(316\) | 17.6962i | 0.995490i | ||||||||
\(317\) | −22.1988 | − | 22.1988i | −1.24681 | − | 1.24681i | −0.957120 | − | 0.289691i | \(-0.906447\pi\) |
−0.289691 | − | 0.957120i | \(-0.593553\pi\) | |||||||
\(318\) | 11.9642 | − | 11.0980i | 0.670921 | − | 0.622345i | ||||
\(319\) | 3.62712 | + | 3.62712i | 0.203080 | + | 0.203080i | ||||
\(320\) | 14.2490 | − | 14.2490i | 0.796545 | − | 0.796545i | ||||
\(321\) | 1.25803 | − | 33.4929i | 0.0702165 | − | 1.86939i | ||||
\(322\) | 3.10623i | 0.173103i | ||||||||
\(323\) | −14.6614 | + | 14.6614i | −0.815781 | + | 0.815781i | ||||
\(324\) | −2.85840 | + | 18.8906i | −0.158800 | + | 1.04948i | ||||
\(325\) | −0.202933 | − | 0.141009i | −0.0112567 | − | 0.00782178i | ||||
\(326\) | 26.4922i | 1.46727i | ||||||||
\(327\) | −16.1283 | + | 14.9605i | −0.891896 | + | 0.827320i | ||||
\(328\) | 2.04330 | 0.112823 | ||||||||
\(329\) | −17.2868 | −0.953051 | ||||||||
\(330\) | 5.38459 | + | 5.80488i | 0.296412 | + | 0.319548i | ||||
\(331\) | −20.1546 | + | 20.1546i | −1.10780 | + | 1.10780i | −0.114359 | + | 0.993439i | \(0.536481\pi\) |
−0.993439 | + | 0.114359i | \(0.963519\pi\) | |||||||
\(332\) | −16.5877 | + | 16.5877i | −0.910371 | + | 0.910371i | ||||
\(333\) | 14.3223 | + | 16.6525i | 0.784858 | + | 0.912552i | ||||
\(334\) | −22.5992 | −1.23657 | ||||||||
\(335\) | −7.59942 | −0.415201 | ||||||||
\(336\) | −8.33365 | − | 8.98412i | −0.454638 | − | 0.490124i | ||||
\(337\) | − | 25.4303i | − | 1.38528i | −0.721284 | − | 0.692639i | \(-0.756448\pi\) | ||
0.721284 | − | 0.692639i | \(-0.243552\pi\) | |||||||
\(338\) | −10.9830 | + | 24.0028i | −0.597395 | + | 1.30558i | ||||
\(339\) | −0.478390 | + | 12.7363i | −0.0259826 | + | 0.691740i | ||||
\(340\) | 20.0782 | − | 20.0782i | 1.08889 | − | 1.08889i | ||||
\(341\) | 9.27820i | 0.502442i | ||||||||
\(342\) | 21.1985 | + | 1.59473i | 1.14628 | + | 0.0862333i | ||||
\(343\) | 13.9410 | − | 13.9410i | 0.752744 | − | 0.752744i | ||||
\(344\) | −1.07314 | − | 1.07314i | −0.0578596 | − | 0.0578596i | ||||
\(345\) | −2.14411 | − | 2.31147i | −0.115435 | − | 0.124445i | ||||
\(346\) | −6.47209 | − | 6.47209i | −0.347942 | − | 0.347942i | ||||
\(347\) | − | 10.5051i | − | 0.563942i | −0.959423 | − | 0.281971i | \(-0.909012\pi\) | ||
0.959423 | − | 0.281971i | \(-0.0909882\pi\) | |||||||
\(348\) | −18.8474 | − | 0.707930i | −1.01032 | − | 0.0379490i | ||||
\(349\) | −11.1101 | − | 11.1101i | −0.594709 | − | 0.594709i | 0.344191 | − | 0.938900i | \(-0.388153\pi\) |
−0.938900 | + | 0.344191i | \(0.888153\pi\) | |||||||
\(350\) | 0.263310 | 0.0140745 | ||||||||
\(351\) | 12.3521 | − | 14.0864i | 0.659306 | − | 0.751875i | ||||
\(352\) | 8.09128 | 0.431266 | ||||||||
\(353\) | 12.9257 | + | 12.9257i | 0.687967 | + | 0.687967i | 0.961782 | − | 0.273815i | \(-0.0882857\pi\) |
−0.273815 | + | 0.961782i | \(0.588286\pi\) | |||||||
\(354\) | −5.33328 | − | 0.200324i | −0.283460 | − | 0.0106471i | ||||
\(355\) | − | 24.4474i | − | 1.29753i | ||||||
\(356\) | 4.03555 | + | 4.03555i | 0.213884 | + | 0.213884i | ||||
\(357\) | −13.2414 | − | 14.2749i | −0.700809 | − | 0.755510i | ||||
\(358\) | 28.6149 | + | 28.6149i | 1.51234 | + | 1.51234i | ||||
\(359\) | 5.05627 | − | 5.05627i | 0.266860 | − | 0.266860i | −0.560974 | − | 0.827834i | \(-0.689573\pi\) |
0.827834 | + | 0.560974i | \(0.189573\pi\) | |||||||
\(360\) | −1.67997 | − | 0.126382i | −0.0885423 | − | 0.00666091i | ||||
\(361\) | 6.82072i | 0.358985i | ||||||||
\(362\) | −0.947175 | + | 0.947175i | −0.0497824 | + | 0.0497824i | ||||
\(363\) | −0.0650121 | + | 1.73083i | −0.00341225 | + | 0.0908450i | ||||
\(364\) | −2.56613 | − | 14.2530i | −0.134502 | − | 0.747059i | ||||
\(365\) | − | 7.06318i | − | 0.369704i | ||||||
\(366\) | 19.9489 | + | 21.5060i | 1.04274 | + | 1.12413i | ||||
\(367\) | −11.3223 | −0.591019 | −0.295510 | − | 0.955340i | \(-0.595489\pi\) | ||||
−0.295510 | + | 0.955340i | \(0.595489\pi\) | |||||||
\(368\) | −3.02324 | −0.157597 | ||||||||
\(369\) | 16.0244 | + | 18.6316i | 0.834199 | + | 0.969920i | ||||
\(370\) | −23.6659 | + | 23.6659i | −1.23033 | + | 1.23033i | ||||
\(371\) | 6.20813 | − | 6.20813i | 0.322310 | − | 0.322310i | ||||
\(372\) | −23.2004 | − | 25.0113i | −1.20288 | − | 1.29677i | ||||
\(373\) | 20.7274 | 1.07322 | 0.536612 | − | 0.843829i | \(-0.319704\pi\) | ||||
0.536612 | + | 0.843829i | \(0.319704\pi\) | |||||||
\(374\) | 12.0636 | 0.623795 | ||||||||
\(375\) | 14.0984 | − | 13.0776i | 0.728039 | − | 0.675327i | ||||
\(376\) | 2.27896i | 0.117528i | ||||||||
\(377\) | 15.1881 | + | 10.5536i | 0.782228 | + | 0.543536i | ||||
\(378\) | −2.24368 | + | 19.8364i | −0.115402 | + | 1.02027i | ||||
\(379\) | −9.54285 | + | 9.54285i | −0.490183 | + | 0.490183i | −0.908364 | − | 0.418181i | \(-0.862668\pi\) |
0.418181 | + | 0.908364i | \(0.362668\pi\) | |||||||
\(380\) | 16.6790i | 0.855616i | ||||||||
\(381\) | 1.08175 | − | 28.7996i | 0.0554196 | − | 1.47545i | ||||
\(382\) | 14.1359 | − | 14.1359i | 0.723256 | − | 0.723256i | ||||
\(383\) | −11.0397 | − | 11.0397i | −0.564105 | − | 0.564105i | 0.366366 | − | 0.930471i | \(-0.380602\pi\) |
−0.930471 | + | 0.366366i | \(0.880602\pi\) | |||||||
\(384\) | −2.52923 | + | 2.34611i | −0.129069 | + | 0.119724i | ||||
\(385\) | 3.01209 | + | 3.01209i | 0.153511 | + | 0.153511i | ||||
\(386\) | 46.3295i | 2.35811i | ||||||||
\(387\) | 1.36925 | − | 18.2012i | 0.0696030 | − | 0.925220i | ||||
\(388\) | −18.5393 | − | 18.5393i | −0.941189 | − | 0.941189i | ||||
\(389\) | 29.8511 | 1.51351 | 0.756757 | − | 0.653697i | \(-0.226783\pi\) | ||||
0.756757 | + | 0.653697i | \(0.226783\pi\) | |||||||
\(390\) | 22.8158 | + | 17.1585i | 1.15532 | + | 0.868855i | ||||
\(391\) | −4.80365 | −0.242931 | ||||||||
\(392\) | −0.603218 | − | 0.603218i | −0.0304671 | − | 0.0304671i | ||||
\(393\) | −0.600928 | + | 15.9986i | −0.0303128 | + | 0.807024i | ||||
\(394\) | 2.52549i | 0.127232i | ||||||||
\(395\) | −13.2705 | − | 13.2705i | −0.667712 | − | 0.667712i | ||||
\(396\) | −4.15273 | − | 4.82837i | −0.208683 | − | 0.242635i | ||||
\(397\) | 18.0127 | + | 18.0127i | 0.904030 | + | 0.904030i | 0.995782 | − | 0.0917522i | \(-0.0292468\pi\) |
−0.0917522 | + | 0.995782i | \(0.529247\pi\) | |||||||
\(398\) | −9.33013 | + | 9.33013i | −0.467677 | + | 0.467677i | ||||
\(399\) | 11.4290 | + | 0.429286i | 0.572165 | + | 0.0214912i | ||||
\(400\) | 0.256275i | 0.0128138i | ||||||||
\(401\) | 0.856457 | − | 0.856457i | 0.0427694 | − | 0.0427694i | −0.685399 | − | 0.728168i | \(-0.740372\pi\) |
0.728168 | + | 0.685399i | \(0.240372\pi\) | |||||||
\(402\) | 11.8629 | + | 0.445586i | 0.591670 | + | 0.0222238i | ||||
\(403\) | 5.92763 | + | 32.9237i | 0.295276 | + | 1.64004i | ||||
\(404\) | 26.1231i | 1.29967i | ||||||||
\(405\) | −12.0227 | − | 16.3097i | −0.597411 | − | 0.810437i | ||||
\(406\) | −19.7069 | −0.978037 | ||||||||
\(407\) | −7.32147 | −0.362912 | ||||||||
\(408\) | −1.88190 | + | 1.74565i | −0.0931681 | + | 0.0864224i | ||||
\(409\) | −12.7740 | + | 12.7740i | −0.631635 | + | 0.631635i | −0.948478 | − | 0.316843i | \(-0.897377\pi\) |
0.316843 | + | 0.948478i | \(0.397377\pi\) | |||||||
\(410\) | −26.4785 | + | 26.4785i | −1.30768 | + | 1.30768i | ||||
\(411\) | −19.3146 | + | 17.9162i | −0.952720 | + | 0.883740i | ||||
\(412\) | −0.466405 | −0.0229781 | ||||||||
\(413\) | −2.87133 | −0.141289 | ||||||||
\(414\) | 3.21149 | + | 3.73399i | 0.157836 | + | 0.183516i | ||||
\(415\) | − | 24.8785i | − | 1.22124i | ||||||
\(416\) | 28.7119 | − | 5.16934i | 1.40772 | − | 0.253448i | ||||
\(417\) | −17.9071 | − | 0.672613i | −0.876916 | − | 0.0329380i | ||||
\(418\) | −5.01065 | + | 5.01065i | −0.245079 | + | 0.245079i | ||||
\(419\) | 29.8330i | 1.45744i | 0.684814 | + | 0.728718i | \(0.259883\pi\) | ||||
−0.684814 | + | 0.728718i | \(0.740117\pi\) | |||||||
\(420\) | −15.6515 | − | 0.587890i | −0.763717 | − | 0.0286861i | ||||
\(421\) | −13.5610 | + | 13.5610i | −0.660923 | + | 0.660923i | −0.955598 | − | 0.294674i | \(-0.904789\pi\) |
0.294674 | + | 0.955598i | \(0.404789\pi\) | |||||||
\(422\) | 31.3284 | + | 31.3284i | 1.52504 | + | 1.52504i | ||||
\(423\) | −20.7804 | + | 17.8726i | −1.01038 | + | 0.868994i | ||||
\(424\) | −0.818434 | − | 0.818434i | −0.0397466 | − | 0.0397466i | ||||
\(425\) | 0.407197i | 0.0197520i | ||||||||
\(426\) | −1.43345 | + | 38.1632i | −0.0694511 | + | 1.84901i | ||||
\(427\) | 11.1592 | + | 11.1592i | 0.540033 | + | 0.540033i | ||||
\(428\) | −41.0787 | −1.98561 | ||||||||
\(429\) | 0.875094 | + | 6.18338i | 0.0422499 | + | 0.298536i | ||||
\(430\) | 27.8128 | 1.34125 | ||||||||
\(431\) | −8.09111 | − | 8.09111i | −0.389735 | − | 0.389735i | 0.484858 | − | 0.874593i | \(-0.338871\pi\) |
−0.874593 | + | 0.484858i | \(0.838871\pi\) | |||||||
\(432\) | −19.3064 | − | 2.18374i | −0.928880 | − | 0.105065i | ||||
\(433\) | 2.38252i | 0.114497i | 0.998360 | + | 0.0572484i | \(0.0182327\pi\) | ||||
−0.998360 | + | 0.0572484i | \(0.981767\pi\) | |||||||
\(434\) | −25.2052 | − | 25.2052i | −1.20989 | − | 1.20989i | ||||
\(435\) | 14.6647 | − | 13.6029i | 0.703116 | − | 0.652209i | ||||
\(436\) | 19.0651 | + | 19.0651i | 0.913052 | + | 0.913052i | ||||
\(437\) | 1.99521 | − | 1.99521i | 0.0954438 | − | 0.0954438i | ||||
\(438\) | −0.414144 | + | 11.0259i | −0.0197886 | + | 0.526836i | ||||
\(439\) | 23.3582i | 1.11483i | 0.830236 | + | 0.557413i | \(0.188206\pi\) | ||||
−0.830236 | + | 0.557413i | \(0.811794\pi\) | |||||||
\(440\) | 0.397092 | − | 0.397092i | 0.0189306 | − | 0.0189306i | ||||
\(441\) | 0.769667 | − | 10.2311i | 0.0366508 | − | 0.487193i | ||||
\(442\) | 42.8077 | − | 7.70717i | 2.03616 | − | 0.366593i | ||||
\(443\) | − | 32.6213i | − | 1.54989i | −0.632032 | − | 0.774943i | \(-0.717779\pi\) | ||
0.632032 | − | 0.774943i | \(-0.282221\pi\) | |||||||
\(444\) | 19.7365 | − | 18.3075i | 0.936653 | − | 0.868837i | ||||
\(445\) | −6.05257 | −0.286919 | ||||||||
\(446\) | 13.9460 | 0.660360 | ||||||||
\(447\) | 3.52991 | + | 3.80544i | 0.166959 | + | 0.179991i | ||||
\(448\) | −11.9753 | + | 11.9753i | −0.565780 | + | 0.565780i | ||||
\(449\) | −14.7169 | + | 14.7169i | −0.694534 | + | 0.694534i | −0.963226 | − | 0.268692i | \(-0.913409\pi\) |
0.268692 | + | 0.963226i | \(0.413409\pi\) | |||||||
\(450\) | 0.316524 | − | 0.272232i | 0.0149211 | − | 0.0128332i | ||||
\(451\) | −8.19158 | −0.385726 | ||||||||
\(452\) | 15.6209 | 0.734748 | ||||||||
\(453\) | 0.890045 | + | 0.959516i | 0.0418179 | + | 0.0450820i | ||||
\(454\) | − | 25.8232i | − | 1.21194i | ||||||
\(455\) | 12.6128 | + | 8.76405i | 0.591296 | + | 0.410865i | ||||
\(456\) | 0.0565939 | − | 1.50671i | 0.00265025 | − | 0.0705583i | ||||
\(457\) | 21.8413 | − | 21.8413i | 1.02169 | − | 1.02169i | 0.0219331 | − | 0.999759i | \(-0.493018\pi\) |
0.999759 | − | 0.0219331i | \(-0.00698209\pi\) | |||||||
\(458\) | 2.77905i | 0.129856i | ||||||||
\(459\) | −30.6761 | − | 3.46975i | −1.43184 | − | 0.161954i | ||||
\(460\) | −2.73236 | + | 2.73236i | −0.127397 | + | 0.127397i | ||||
\(461\) | −26.2030 | − | 26.2030i | −1.22039 | − | 1.22039i | −0.967492 | − | 0.252901i | \(-0.918615\pi\) |
−0.252901 | − | 0.967492i | \(-0.581385\pi\) | |||||||
\(462\) | −4.52536 | − | 4.87859i | −0.210539 | − | 0.226972i | ||||
\(463\) | −18.0526 | − | 18.0526i | −0.838976 | − | 0.838976i | 0.149748 | − | 0.988724i | \(-0.452154\pi\) |
−0.988724 | + | 0.149748i | \(0.952154\pi\) | |||||||
\(464\) | − | 19.1804i | − | 0.890428i | ||||||
\(465\) | 36.1542 | + | 1.35800i | 1.67661 | + | 0.0629756i | ||||
\(466\) | −26.0131 | − | 26.0131i | −1.20504 | − | 1.20504i | ||||
\(467\) | −9.23398 | −0.427298 | −0.213649 | − | 0.976911i | \(-0.568535\pi\) | ||||
−0.213649 | + | 0.976911i | \(0.568535\pi\) | |||||||
\(468\) | −17.8207 | − | 14.4804i | −0.823762 | − | 0.669355i | ||||
\(469\) | 6.38677 | 0.294914 | ||||||||
\(470\) | −29.5323 | − | 29.5323i | −1.36222 | − | 1.36222i | ||||
\(471\) | −24.3415 | − | 0.914297i | −1.12160 | − | 0.0421286i | ||||
\(472\) | 0.378535i | 0.0174235i | ||||||||
\(473\) | 4.30219 | + | 4.30219i | 0.197815 | + | 0.197815i | ||||
\(474\) | 19.9376 | + | 21.4938i | 0.915764 | + | 0.987243i | ||||
\(475\) | −0.169130 | − | 0.169130i | −0.00776024 | − | 0.00776024i | ||||
\(476\) | −16.8743 | + | 16.8743i | −0.773431 | + | 0.773431i | ||||
\(477\) | 1.04427 | − | 13.8813i | 0.0478137 | − | 0.635580i | ||||
\(478\) | − | 5.19725i | − | 0.237717i | ||||||
\(479\) | −7.27499 | + | 7.27499i | −0.332403 | + | 0.332403i | −0.853498 | − | 0.521096i | \(-0.825523\pi\) |
0.521096 | + | 0.853498i | \(0.325523\pi\) | |||||||
\(480\) | 1.18427 | − | 31.5292i | 0.0540545 | − | 1.43910i | ||||
\(481\) | −25.9802 | + | 4.67752i | −1.18460 | + | 0.213277i | ||||
\(482\) | 0.857302i | 0.0390490i | ||||||||
\(483\) | 1.80197 | + | 1.94262i | 0.0819925 | + | 0.0883924i | ||||
\(484\) | 2.12285 | 0.0964931 | ||||||||
\(485\) | 27.8055 | 1.26258 | ||||||||
\(486\) | 17.8114 | + | 26.1649i | 0.807944 | + | 1.18687i | ||||
\(487\) | −3.72175 | + | 3.72175i | −0.168648 | + | 0.168648i | −0.786385 | − | 0.617737i | \(-0.788050\pi\) |
0.617737 | + | 0.786385i | \(0.288050\pi\) | |||||||
\(488\) | 1.47115 | − | 1.47115i | 0.0665959 | − | 0.0665959i | ||||
\(489\) | 15.3685 | + | 16.5681i | 0.694989 | + | 0.749236i | ||||
\(490\) | 15.6338 | 0.706263 | ||||||||
\(491\) | 17.5271 | 0.790985 | 0.395493 | − | 0.918469i | \(-0.370574\pi\) | ||||
0.395493 | + | 0.918469i | \(0.370574\pi\) | |||||||
\(492\) | 22.0821 | − | 20.4833i | 0.995536 | − | 0.923457i | ||||
\(493\) | − | 30.4759i | − | 1.37256i | ||||||
\(494\) | −14.5791 | + | 20.9815i | −0.655945 | + | 0.944002i | ||||
\(495\) | 6.73499 | + | 0.506664i | 0.302715 | + | 0.0227728i | ||||
\(496\) | 24.5318 | − | 24.5318i | 1.10151 | − | 1.10151i | ||||
\(497\) | 20.5463i | 0.921627i | ||||||||
\(498\) | −1.45873 | + | 38.8362i | −0.0653674 | + | 1.74029i | ||||
\(499\) | 16.8825 | − | 16.8825i | 0.755763 | − | 0.755763i | −0.219786 | − | 0.975548i | \(-0.570536\pi\) |
0.975548 | + | 0.219786i | \(0.0705358\pi\) | |||||||
\(500\) | −16.6656 | − | 16.6656i | −0.745308 | − | 0.745308i | ||||
\(501\) | −14.1334 | + | 13.1101i | −0.631436 | + | 0.585718i | ||||
\(502\) | −28.3742 | − | 28.3742i | −1.26640 | − | 1.26640i | ||||
\(503\) | − | 4.61727i | − | 0.205874i | −0.994688 | − | 0.102937i | \(-0.967176\pi\) | ||
0.994688 | − | 0.102937i | \(-0.0328240\pi\) | |||||||
\(504\) | 1.41190 | + | 0.106215i | 0.0628909 | + | 0.00473119i | ||||
\(505\) | −19.5899 | − | 19.5899i | −0.871738 | − | 0.871738i | ||||
\(506\) | −1.64169 | −0.0729821 | ||||||||
\(507\) | 7.05569 | + | 21.3826i | 0.313354 | + | 0.949636i | ||||
\(508\) | −35.3225 | −1.56718 | ||||||||
\(509\) | −9.55041 | − | 9.55041i | −0.423315 | − | 0.423315i | 0.463029 | − | 0.886343i | \(-0.346763\pi\) |
−0.886343 | + | 0.463029i | \(0.846763\pi\) | |||||||
\(510\) | 1.76568 | − | 47.0082i | 0.0781858 | − | 2.08156i | ||||
\(511\) | 5.93610i | 0.262598i | ||||||||
\(512\) | −22.7126 | − | 22.7126i | −1.00376 | − | 1.00376i | ||||
\(513\) | 14.1826 | − | 11.3002i | 0.626176 | − | 0.498917i | ||||
\(514\) | 7.58360 | + | 7.58360i | 0.334498 | + | 0.334498i | ||||
\(515\) | 0.349761 | − | 0.349761i | 0.0154123 | − | 0.0154123i | ||||
\(516\) | −22.3552 | − | 0.839687i | −0.984132 | − | 0.0369652i | ||||
\(517\) | − | 9.13633i | − | 0.401815i | ||||||
\(518\) | 19.8895 | − | 19.8895i | 0.873895 | − | 0.873895i | ||||
\(519\) | −7.80217 | − | 0.293059i | −0.342477 | − | 0.0128639i | ||||
\(520\) | 1.15539 | − | 1.66277i | 0.0506671 | − | 0.0729175i | ||||
\(521\) | 41.1736i | 1.80385i | 0.431894 | + | 0.901925i | \(0.357846\pi\) | ||||
−0.431894 | + | 0.901925i | \(0.642154\pi\) | |||||||
\(522\) | −23.6896 | + | 20.3747i | −1.03687 | + | 0.891776i | ||||
\(523\) | −14.0362 | −0.613760 | −0.306880 | − | 0.951748i | \(-0.599285\pi\) | ||||
−0.306880 | + | 0.951748i | \(0.599285\pi\) | |||||||
\(524\) | 19.6222 | 0.857199 | ||||||||
\(525\) | 0.164673 | − | 0.152750i | 0.00718691 | − | 0.00666655i | ||||
\(526\) | −1.80632 | + | 1.80632i | −0.0787595 | + | 0.0787595i | ||||
\(527\) | 38.9787 | − | 38.9787i | 1.69794 | − | 1.69794i | ||||
\(528\) | 4.74825 | − | 4.40446i | 0.206641 | − | 0.191680i | ||||
\(529\) | −22.3463 | −0.971578 | ||||||||
\(530\) | 21.2116 | 0.921373 | ||||||||
\(531\) | −3.45162 | + | 2.96863i | −0.149787 | + | 0.128828i | ||||
\(532\) | − | 14.0175i | − | 0.607738i | ||||||
\(533\) | −29.0678 | + | 5.23342i | −1.25907 | + | 0.226684i | ||||
\(534\) | 9.44826 | + | 0.354888i | 0.408866 | + | 0.0153575i | ||||
\(535\) | 30.8052 | − | 30.8052i | 1.33183 | − | 1.33183i | ||||
\(536\) | − | 0.841985i | − | 0.0363682i | ||||||
\(537\) | 34.4955 | + | 1.29569i | 1.48859 | + | 0.0559133i | ||||
\(538\) | 15.4159 | − | 15.4159i | 0.664625 | − | 0.664625i | ||||
\(539\) | 2.41830 | + | 2.41830i | 0.104163 | + | 0.104163i | ||||
\(540\) | −19.4225 | + | 15.4752i | −0.835810 | + | 0.665947i | ||||
\(541\) | −6.96858 | − | 6.96858i | −0.299602 | − | 0.299602i | 0.541256 | − | 0.840858i | \(-0.317949\pi\) |
−0.840858 | + | 0.541256i | \(0.817949\pi\) | |||||||
\(542\) | − | 35.8934i | − | 1.54175i | ||||||
\(543\) | −0.0428885 | + | 1.14183i | −0.00184052 | + | 0.0490006i | ||||
\(544\) | −33.9923 | − | 33.9923i | −1.45741 | − | 1.45741i | ||||
\(545\) | −28.5941 | −1.22484 | ||||||||
\(546\) | −19.1751 | − | 14.4205i | −0.820617 | − | 0.617141i | ||||
\(547\) | −11.2135 | −0.479454 | −0.239727 | − | 0.970840i | \(-0.577058\pi\) | ||||
−0.239727 | + | 0.970840i | \(0.577058\pi\) | |||||||
\(548\) | 22.8316 | + | 22.8316i | 0.975318 | + | 0.975318i | ||||
\(549\) | 24.9519 | + | 1.87709i | 1.06492 | + | 0.0801123i | ||||
\(550\) | 0.139163i | 0.00593394i | ||||||||
\(551\) | 12.6582 | + | 12.6582i | 0.539259 | + | 0.539259i | ||||
\(552\) | 0.256101 | − | 0.237558i | 0.0109004 | − | 0.0101112i | ||||
\(553\) | 11.1529 | + | 11.1529i | 0.474271 | + | 0.474271i | ||||
\(554\) | 40.4333 | − | 40.4333i | 1.71785 | − | 1.71785i | ||||
\(555\) | −1.07160 | + | 28.5295i | −0.0454870 | + | 1.21101i | ||||
\(556\) | 21.9629i | 0.931436i | ||||||||
\(557\) | 5.09175 | − | 5.09175i | 0.215745 | − | 0.215745i | −0.590958 | − | 0.806702i | \(-0.701250\pi\) |
0.806702 | + | 0.590958i | \(0.201250\pi\) | |||||||
\(558\) | −56.3583 | − | 4.23975i | −2.38584 | − | 0.179483i | ||||
\(559\) | 18.0149 | + | 12.5177i | 0.761949 | + | 0.529444i | ||||
\(560\) | − | 15.9281i | − | 0.673085i | ||||||
\(561\) | 7.54453 | − | 6.99828i | 0.318530 | − | 0.295468i | ||||
\(562\) | 5.64080 | 0.237943 | ||||||||
\(563\) | −36.2204 | −1.52651 | −0.763255 | − | 0.646098i | \(-0.776400\pi\) | ||||
−0.763255 | + | 0.646098i | \(0.776400\pi\) | |||||||
\(564\) | 22.8456 | + | 24.6288i | 0.961975 | + | 1.03706i | ||||
\(565\) | −11.7143 | + | 11.7143i | −0.492823 | + | 0.492823i | ||||
\(566\) | 18.1488 | − | 18.1488i | 0.762851 | − | 0.762851i | ||||
\(567\) | 10.1042 | + | 13.7072i | 0.424336 | + | 0.575647i | ||||
\(568\) | 2.70867 | 0.113653 | ||||||||
\(569\) | 19.6747 | 0.824807 | 0.412404 | − | 0.911001i | \(-0.364689\pi\) | ||||
0.412404 | + | 0.911001i | \(0.364689\pi\) | |||||||
\(570\) | 18.7916 | + | 20.2583i | 0.787093 | + | 0.848529i | ||||
\(571\) | − | 10.1981i | − | 0.426779i | −0.976967 | − | 0.213389i | \(-0.931550\pi\) | ||
0.976967 | − | 0.213389i | \(-0.0684503\pi\) | |||||||
\(572\) | 7.53292 | − | 1.35624i | 0.314967 | − | 0.0567072i | ||||
\(573\) | 0.640080 | − | 17.0410i | 0.0267397 | − | 0.711897i | ||||
\(574\) | 22.2533 | − | 22.2533i | 0.928833 | − | 0.928833i | ||||
\(575\) | − | 0.0554139i | − | 0.00231092i | ||||||
\(576\) | −2.01436 | + | 26.7766i | −0.0839318 | + | 1.11569i | ||||
\(577\) | 0.128356 | − | 0.128356i | 0.00534353 | − | 0.00534353i | −0.704430 | − | 0.709773i | \(-0.748797\pi\) |
0.709773 | + | 0.704430i | \(0.248797\pi\) | |||||||
\(578\) | −26.2725 | − | 26.2725i | −1.09279 | − | 1.09279i | ||||
\(579\) | 26.8764 | + | 28.9742i | 1.11695 | + | 1.20413i | ||||
\(580\) | −17.3349 | − | 17.3349i | −0.719794 | − | 0.719794i | ||||
\(581\) | 20.9086i | 0.867436i | ||||||||
\(582\) | −43.4052 | − | 1.63035i | −1.79920 | − | 0.0675803i | ||||
\(583\) | 3.28109 | + | 3.28109i | 0.135889 | + | 0.135889i | ||||
\(584\) | 0.782572 | 0.0323830 | ||||||||
\(585\) | 24.2228 | − | 2.50494i | 1.00149 | − | 0.103567i | ||||
\(586\) | −14.9781 | −0.618741 | ||||||||
\(587\) | −10.3530 | − | 10.3530i | −0.427313 | − | 0.427313i | 0.460399 | − | 0.887712i | \(-0.347706\pi\) |
−0.887712 | + | 0.460399i | \(0.847706\pi\) | |||||||
\(588\) | −12.5660 | − | 0.471995i | −0.518214 | − | 0.0194647i | ||||
\(589\) | 32.3798i | 1.33419i | ||||||||
\(590\) | −4.90530 | − | 4.90530i | −0.201948 | − | 0.201948i | ||||
\(591\) | 1.46508 | + | 1.57943i | 0.0602651 | + | 0.0649691i | ||||
\(592\) | 19.3581 | + | 19.3581i | 0.795614 | + | 0.795614i | ||||
\(593\) | 10.7607 | − | 10.7607i | 0.441889 | − | 0.441889i | −0.450757 | − | 0.892647i | \(-0.648846\pi\) |
0.892647 | + | 0.450757i | \(0.148846\pi\) | |||||||
\(594\) | −10.4838 | − | 1.18582i | −0.430157 | − | 0.0486548i | ||||
\(595\) | − | 25.3083i | − | 1.03754i | ||||||
\(596\) | 4.49837 | − | 4.49837i | 0.184261 | − | 0.184261i | ||||
\(597\) | −0.422472 | + | 11.2476i | −0.0172906 | + | 0.460332i | ||||
\(598\) | −5.82554 | + | 1.04884i | −0.238224 | + | 0.0428902i | ||||
\(599\) | − | 36.9829i | − | 1.51108i | −0.655101 | − | 0.755541i | \(-0.727374\pi\) | ||
0.655101 | − | 0.755541i | \(-0.272626\pi\) | |||||||
\(600\) | −0.0201374 | − | 0.0217092i | −0.000822107 | − | 0.000886275i | ||||
\(601\) | −26.5895 | −1.08461 | −0.542304 | − | 0.840182i | \(-0.682448\pi\) | ||||
−0.542304 | + | 0.840182i | \(0.682448\pi\) | |||||||
\(602\) | −23.3747 | −0.952681 | ||||||||
\(603\) | 7.67752 | − | 6.60320i | 0.312653 | − | 0.268903i | ||||
\(604\) | 1.13423 | − | 1.13423i | 0.0461514 | − | 0.0461514i | ||||
\(605\) | −1.59194 | + | 1.59194i | −0.0647215 | + | 0.0647215i | ||||
\(606\) | 29.4318 | + | 31.7290i | 1.19558 | + | 1.28890i | ||||
\(607\) | −18.9328 | −0.768458 | −0.384229 | − | 0.923238i | \(-0.625533\pi\) | ||||
−0.384229 | + | 0.923238i | \(0.625533\pi\) | |||||||
\(608\) | 28.2376 | 1.14519 | ||||||||
\(609\) | −12.3246 | + | 11.4323i | −0.499418 | + | 0.463259i | ||||
\(610\) | 38.1283i | 1.54377i | ||||||||
\(611\) | −5.83700 | − | 32.4202i | −0.236140 | − | 1.31158i | ||||
\(612\) | −2.83842 | + | 37.7306i | −0.114736 | + | 1.52517i | ||||
\(613\) | −6.30253 | + | 6.30253i | −0.254557 | + | 0.254557i | −0.822836 | − | 0.568279i | \(-0.807609\pi\) |
0.568279 | + | 0.822836i | \(0.307609\pi\) | |||||||
\(614\) | − | 49.9408i | − | 2.01544i | ||||||
\(615\) | −1.19896 | + | 31.9200i | −0.0483465 | + | 1.28714i | ||||
\(616\) | −0.333728 | + | 0.333728i | −0.0134463 | + | 0.0134463i | ||||
\(617\) | −28.2292 | − | 28.2292i | −1.13647 | − | 1.13647i | −0.989079 | − | 0.147386i | \(-0.952914\pi\) |
−0.147386 | − | 0.989079i | \(-0.547086\pi\) | |||||||
\(618\) | −0.566496 | + | 0.525480i | −0.0227878 | + | 0.0211379i | ||||
\(619\) | −21.2163 | − | 21.2163i | −0.852756 | − | 0.852756i | 0.137716 | − | 0.990472i | \(-0.456024\pi\) |
−0.990472 | + | 0.137716i | \(0.956024\pi\) | |||||||
\(620\) | − | 44.3429i | − | 1.78085i | ||||||
\(621\) | 4.17459 | + | 0.472186i | 0.167521 | + | 0.0189482i | ||||
\(622\) | −6.24838 | − | 6.24838i | −0.250537 | − | 0.250537i | ||||
\(623\) | 5.08675 | 0.203797 | ||||||||
\(624\) | 14.0352 | − | 18.6628i | 0.561859 | − | 0.747109i | ||||
\(625\) | 25.3380 | 1.01352 | ||||||||
\(626\) | 20.3660 | + | 20.3660i | 0.813990 | + | 0.813990i | ||||
\(627\) | −0.226884 | + | 6.04039i | −0.00906089 | + | 0.241230i | ||||
\(628\) | 29.8546i | 1.19133i | ||||||||
\(629\) | 30.7583 | + | 30.7583i | 1.22641 | + | 1.22641i | ||||
\(630\) | −19.6727 | + | 16.9199i | −0.783779 | + | 0.674104i | ||||
\(631\) | −9.80024 | − | 9.80024i | −0.390141 | − | 0.390141i | 0.484597 | − | 0.874738i | \(-0.338966\pi\) |
−0.874738 | + | 0.484597i | \(0.838966\pi\) | |||||||
\(632\) | 1.47032 | − | 1.47032i | 0.0584861 | − | 0.0584861i | ||||
\(633\) | 37.7667 | + | 1.41856i | 1.50109 | + | 0.0563828i | ||||
\(634\) | 63.7447i | 2.53163i | ||||||||
\(635\) | 26.4886 | − | 26.4886i | 1.05117 | − | 1.05117i | ||||
\(636\) | −17.0493 | − | 0.640392i | −0.676049 | − | 0.0253932i | ||||
\(637\) | 10.1263 | + | 7.03632i | 0.401219 | + | 0.278789i | ||||
\(638\) | − | 10.4154i | − | 0.412350i | ||||||
\(639\) | 21.2425 | + | 24.6986i | 0.840342 | + | 0.977063i | ||||
\(640\) | −4.48411 | −0.177250 | ||||||||
\(641\) | 1.46545 | 0.0578817 | 0.0289409 | − | 0.999581i | \(-0.490787\pi\) | ||||
0.0289409 | + | 0.999581i | \(0.490787\pi\) | |||||||
\(642\) | −49.8942 | + | 46.2817i | −1.96917 | + | 1.82659i | ||||
\(643\) | 6.81498 | − | 6.81498i | 0.268757 | − | 0.268757i | −0.559842 | − | 0.828599i | \(-0.689138\pi\) |
0.828599 | + | 0.559842i | \(0.189138\pi\) | |||||||
\(644\) | 2.29635 | − | 2.29635i | 0.0904890 | − | 0.0904890i | ||||
\(645\) | 17.3940 | − | 16.1346i | 0.684888 | − | 0.635300i | ||||
\(646\) | 42.1006 | 1.65643 | ||||||||
\(647\) | 30.3672 | 1.19386 | 0.596928 | − | 0.802295i | \(-0.296388\pi\) | ||||
0.596928 | + | 0.802295i | \(0.296388\pi\) | |||||||
\(648\) | 1.80705 | − | 1.33206i | 0.0709877 | − | 0.0523283i | ||||
\(649\) | − | 1.51754i | − | 0.0595688i | ||||||
\(650\) | 0.0889083 | + | 0.493821i | 0.00348727 | + | 0.0193692i | ||||
\(651\) | −30.3851 | − | 1.14130i | −1.19088 | − | 0.0447311i | ||||
\(652\) | 19.5850 | − | 19.5850i | 0.767008 | − | 0.767008i | ||||
\(653\) | 32.7119i | 1.28012i | 0.768326 | + | 0.640058i | \(0.221090\pi\) | ||||
−0.768326 | + | 0.640058i | \(0.778910\pi\) | |||||||
\(654\) | 44.6363 | + | 1.67659i | 1.74542 | + | 0.0655599i | ||||
\(655\) | −14.7148 | + | 14.7148i | −0.574955 | + | 0.574955i | ||||
\(656\) | 21.6587 | + | 21.6587i | 0.845631 | + | 0.845631i | ||||
\(657\) | 6.13726 | + | 7.13577i | 0.239437 | + | 0.278393i | ||||
\(658\) | 24.8198 | + | 24.8198i | 0.967575 | + | 0.967575i | ||||
\(659\) | 38.9430i | 1.51700i | 0.651672 | + | 0.758501i | \(0.274068\pi\) | ||||
−0.651672 | + | 0.758501i | \(0.725932\pi\) | |||||||
\(660\) | 0.310709 | − | 8.27208i | 0.0120943 | − | 0.321990i | ||||
\(661\) | 28.7697 | + | 28.7697i | 1.11901 | + | 1.11901i | 0.991887 | + | 0.127126i | \(0.0405753\pi\) |
0.127126 | + | 0.991887i | \(0.459425\pi\) | |||||||
\(662\) | 57.8747 | 2.24936 | ||||||||
\(663\) | 22.3007 | − | 29.6534i | 0.866087 | − | 1.15164i | ||||
\(664\) | 2.75644 | 0.106971 | ||||||||
\(665\) | 10.5119 | + | 10.5119i | 0.407632 | + | 0.407632i | ||||
\(666\) | 3.34561 | − | 44.4726i | 0.129640 | − | 1.72328i | ||||
\(667\) | 4.14735i | 0.160586i | ||||||||
\(668\) | 16.7070 | + | 16.7070i | 0.646413 | + | 0.646413i | ||||
\(669\) | 8.72174 | − | 8.09026i | 0.337202 | − | 0.312787i | ||||
\(670\) | 10.9110 | + | 10.9110i | 0.421528 | + | 0.421528i | ||||
\(671\) | −5.89783 | + | 5.89783i | −0.227683 | + | 0.227683i | ||||
\(672\) | −0.995298 | + | 26.4980i | −0.0383945 | + | 1.02218i | ||||
\(673\) | 9.94571i | 0.383379i | 0.981456 | + | 0.191690i | \(0.0613967\pi\) | ||||
−0.981456 | + | 0.191690i | \(0.938603\pi\) | |||||||
\(674\) | −36.5120 | + | 36.5120i | −1.40639 | + | 1.40639i | ||||
\(675\) | 0.0400263 | − | 0.353873i | 0.00154061 | − | 0.0136206i | ||||
\(676\) | 25.8641 | − | 9.62523i | 0.994772 | − | 0.370201i | ||||
\(677\) | − | 40.8169i | − | 1.56872i | −0.620305 | − | 0.784360i | \(-0.712991\pi\) | ||
0.620305 | − | 0.784360i | \(-0.287009\pi\) | |||||||
\(678\) | 18.9732 | − | 17.5995i | 0.728661 | − | 0.675904i | ||||
\(679\) | −23.3685 | −0.896801 | ||||||||
\(680\) | −3.33645 | −0.127947 | ||||||||
\(681\) | −14.9804 | − | 16.1497i | −0.574051 | − | 0.618859i | ||||
\(682\) | 13.3213 | − | 13.3213i | 0.510100 | − | 0.510100i | ||||
\(683\) | 36.2434 | − | 36.2434i | 1.38681 | − | 1.38681i | 0.554890 | − | 0.831924i | \(-0.312760\pi\) |
0.831924 | − | 0.554890i | \(-0.187240\pi\) | |||||||
\(684\) | −14.4926 | − | 16.8504i | −0.554137 | − | 0.644293i | ||||
\(685\) | −34.2432 | −1.30836 | ||||||||
\(686\) | −40.0321 | −1.52843 | ||||||||
\(687\) | 1.61217 | + | 1.73800i | 0.0615080 | + | 0.0663090i | ||||
\(688\) | − | 22.7502i | − | 0.867343i | ||||||
\(689\) | 13.7392 | + | 9.54673i | 0.523420 | + | 0.363701i | ||||
\(690\) | −0.240285 | + | 6.39716i | −0.00914749 | + | 0.243536i | ||||
\(691\) | 15.4886 | − | 15.4886i | 0.589214 | − | 0.589214i | −0.348205 | − | 0.937419i | \(-0.613209\pi\) |
0.937419 | + | 0.348205i | \(0.113209\pi\) | |||||||
\(692\) | 9.56929i | 0.363770i | ||||||||
\(693\) | −5.66028 | − | 0.425815i | −0.215016 | − | 0.0161754i | ||||
\(694\) | −15.0828 | + | 15.0828i | −0.572536 | + | 0.572536i | ||||
\(695\) | −16.4702 | − | 16.4702i | −0.624749 | − | 0.624749i | ||||
\(696\) | 1.50715 | + | 1.62478i | 0.0571282 | + | 0.0615873i | ||||
\(697\) | 34.4137 | + | 34.4137i | 1.30351 | + | 1.30351i | ||||
\(698\) | 31.9029i | 1.20754i | ||||||||
\(699\) | −31.3591 | − | 1.17789i | −1.18611 | − | 0.0445517i | ||||
\(700\) | −0.194658 | − | 0.194658i | −0.00735738 | − | 0.00735738i | ||||
\(701\) | 0.523590 | 0.0197757 | 0.00988785 | − | 0.999951i | \(-0.496853\pi\) | ||||
0.00988785 | + | 0.999951i | \(0.496853\pi\) | |||||||
\(702\) | −37.9594 | + | 2.49001i | −1.43269 | + | 0.0939793i | ||||
\(703\) | −25.5511 | −0.963677 | ||||||||
\(704\) | −6.32913 | − | 6.32913i | −0.238538 | − | 0.238538i | ||||
\(705\) | −35.6014 | − | 1.33723i | −1.34083 | − | 0.0503631i | ||||
\(706\) | − | 37.1166i | − | 1.39690i | ||||||
\(707\) | 16.4639 | + | 16.4639i | 0.619188 | + | 0.619188i | ||||
\(708\) | 3.79466 | + | 4.09085i | 0.142612 | + | 0.153743i | ||||
\(709\) | −8.56339 | − | 8.56339i | −0.321605 | − | 0.321605i | 0.527778 | − | 0.849383i | \(-0.323025\pi\) |
−0.849383 | + | 0.527778i | \(0.823025\pi\) | |||||||
\(710\) | −35.1007 | + | 35.1007i | −1.31731 | + | 1.31731i | ||||
\(711\) | 24.9377 | + | 1.87603i | 0.935239 | + | 0.0703566i | ||||
\(712\) | − | 0.670600i | − | 0.0251318i | ||||||
\(713\) | −5.30446 | + | 5.30446i | −0.198654 | + | 0.198654i | ||||
\(714\) | −1.48393 | + | 39.5070i | −0.0555347 | + | 1.47851i | ||||
\(715\) | −4.63194 | + | 6.66604i | −0.173225 | + | 0.249296i | ||||
\(716\) | − | 42.3085i | − | 1.58114i | ||||||
\(717\) | −3.01500 | − | 3.25034i | −0.112597 | − | 0.121386i | ||||
\(718\) | −14.5192 | −0.541853 | ||||||||
\(719\) | −11.5025 | −0.428972 | −0.214486 | − | 0.976727i | \(-0.568808\pi\) | ||||
−0.214486 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(720\) | −16.4678 | − | 19.1471i | −0.613720 | − | 0.713571i | ||||
\(721\) | −0.293949 | + | 0.293949i | −0.0109472 | + | 0.0109472i | ||||
\(722\) | 9.79296 | − | 9.79296i | 0.364456 | − | 0.364456i | ||||
\(723\) | 0.497334 | + | 0.536152i | 0.0184960 | + | 0.0199397i | ||||
\(724\) | 1.40044 | 0.0520471 | ||||||||
\(725\) | 0.351563 | 0.0130567 | ||||||||
\(726\) | 2.57841 | − | 2.39173i | 0.0956937 | − | 0.0887652i | ||||
\(727\) | − | 27.3315i | − | 1.01367i | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||
0.862044 | − | 0.506834i | \(-0.169184\pi\) | |||||||
\(728\) | −0.971021 | + | 1.39744i | −0.0359884 | + | 0.0517927i | ||||
\(729\) | 26.3179 | + | 6.03075i | 0.974736 | + | 0.223361i | ||||
\(730\) | −10.1411 | + | 10.1411i | −0.375338 | + | 0.375338i | ||||
\(731\) | − | 36.1480i | − | 1.33698i | ||||||
\(732\) | 1.15112 | − | 30.6465i | 0.0425466 | − | 1.13273i | ||||
\(733\) | 9.41825 | − | 9.41825i | 0.347871 | − | 0.347871i | −0.511445 | − | 0.859316i | \(-0.670890\pi\) |
0.859316 | + | 0.511445i | \(0.170890\pi\) | |||||||
\(734\) | 16.2562 | + | 16.2562i | 0.600026 | + | 0.600026i | ||||
\(735\) | 9.77730 | − | 9.06940i | 0.360641 | − | 0.334530i | ||||
\(736\) | 4.62588 | + | 4.62588i | 0.170512 | + | 0.170512i | ||||
\(737\) | 3.37551i | 0.124338i | ||||||||
\(738\) | 3.74321 | − | 49.7579i | 0.137790 | − | 1.83161i | ||||
\(739\) | −19.9099 | − | 19.9099i | −0.732399 | − | 0.732399i | 0.238696 | − | 0.971094i | \(-0.423280\pi\) |
−0.971094 | + | 0.238696i | \(0.923280\pi\) | |||||||
\(740\) | 34.9912 | 1.28630 | ||||||||
\(741\) | 3.05397 | + | 21.5793i | 0.112191 | + | 0.792735i | ||||
\(742\) | −17.8268 | −0.654444 | ||||||||
\(743\) | 27.2359 | + | 27.2359i | 0.999187 | + | 0.999187i | 1.00000 | 0.000812252i | \(-0.000258548\pi\) | |
−0.000812252 | 1.00000i | \(0.500259\pi\) | ||||||||
\(744\) | −0.150461 | + | 4.00574i | −0.00551615 | + | 0.146858i | ||||
\(745\) | 6.74672i | 0.247181i | ||||||||
\(746\) | −29.7597 | − | 29.7597i | −1.08958 | − | 1.08958i | ||||
\(747\) | 21.6172 | + | 25.1342i | 0.790931 | + | 0.919612i | ||||
\(748\) | −8.91831 | − | 8.91831i | −0.326086 | − | 0.326086i | ||||
\(749\) | −25.8896 | + | 25.8896i | −0.945985 | + | 0.945985i | ||||
\(750\) | −39.0185 | − | 1.46558i | −1.42475 | − | 0.0535154i | ||||
\(751\) | − | 42.4363i | − | 1.54852i | −0.632866 | − | 0.774261i | \(-0.718122\pi\) | ||
0.632866 | − | 0.774261i | \(-0.281878\pi\) | |||||||
\(752\) | −24.1567 | + | 24.1567i | −0.880903 | + | 0.880903i | ||||
\(753\) | −34.2053 | − | 1.28479i | −1.24651 | − | 0.0468205i | ||||
\(754\) | −6.65417 | − | 36.9590i | −0.242330 | − | 1.34597i | ||||
\(755\) | 1.70114i | 0.0619109i | ||||||||
\(756\) | 16.3232 | − | 13.0058i | 0.593669 | − | 0.473017i | ||||
\(757\) | 19.0517 | 0.692447 | 0.346224 | − | 0.938152i | \(-0.387464\pi\) | ||||
0.346224 | + | 0.938152i | \(0.387464\pi\) | |||||||
\(758\) | 27.4026 | 0.995307 | ||||||||
\(759\) | −1.02671 | + | 0.952369i | −0.0372671 | + | 0.0345688i | ||||
\(760\) | 1.38581 | − | 1.38581i | 0.0502684 | − | 0.0502684i | ||||
\(761\) | −20.7318 | + | 20.7318i | −0.751526 | + | 0.751526i | −0.974764 | − | 0.223238i | \(-0.928337\pi\) |
0.223238 | + | 0.974764i | \(0.428337\pi\) | |||||||
\(762\) | −42.9026 | + | 39.7964i | −1.55420 | + | 1.44167i | ||||
\(763\) | 24.0313 | 0.869991 | ||||||||
\(764\) | −20.9006 | −0.756158 | ||||||||
\(765\) | −26.1659 | − | 30.4230i | −0.946030 | − | 1.09995i | ||||
\(766\) | 31.7010i | 1.14540i | ||||||||
\(767\) | −0.969524 | − | 5.38500i | −0.0350075 | − | 0.194441i | ||||
\(768\) | −23.9846 | − | 0.900890i | −0.865470 | − | 0.0325081i | ||||
\(769\) | −22.9142 | + | 22.9142i | −0.826306 | + | 0.826306i | −0.987004 | − | 0.160698i | \(-0.948626\pi\) |
0.160698 | + | 0.987004i | \(0.448626\pi\) | |||||||
\(770\) | − | 8.64932i | − | 0.311700i | ||||||
\(771\) | 9.14211 | + | 0.343389i | 0.329245 | + | 0.0123668i | ||||
\(772\) | 34.2502 | − | 34.2502i | 1.23269 | − | 1.23269i | ||||
\(773\) | −7.44427 | − | 7.44427i | −0.267752 | − | 0.267752i | 0.560442 | − | 0.828194i | \(-0.310631\pi\) |
−0.828194 | + | 0.560442i | \(0.810631\pi\) | |||||||
\(774\) | −28.0986 | + | 24.1668i | −1.00998 | + | 0.868657i | ||||
\(775\) | 0.449650 | + | 0.449650i | 0.0161519 | + | 0.0161519i | ||||
\(776\) | 3.08073i | 0.110592i | ||||||||
\(777\) | 0.900605 | − | 23.9770i | 0.0323090 | − | 0.860170i | ||||
\(778\) | −42.8593 | − | 42.8593i | −1.53658 | − | 1.53658i | ||||
\(779\) | −28.5877 | −1.02426 | ||||||||
\(780\) | −4.18229 | − | 29.5520i | −0.149750 | − | 1.05813i | ||||
\(781\) | −10.8590 | −0.388567 | ||||||||
\(782\) | 6.89692 | + | 6.89692i | 0.246633 | + | 0.246633i | ||||
\(783\) | −2.99569 | + | 26.4849i | −0.107057 | + | 0.946494i | ||||
\(784\) | − | 12.7881i | − | 0.456717i | ||||||
\(785\) | −22.3882 | − | 22.3882i | −0.799070 | − | 0.799070i | ||||
\(786\) | 23.8331 | − | 22.1075i | 0.850098 | − | 0.788548i | ||||
\(787\) | 2.70791 | + | 2.70791i | 0.0965264 | + | 0.0965264i | 0.753721 | − | 0.657195i | \(-0.228257\pi\) |
−0.657195 | + | 0.753721i | \(0.728257\pi\) | |||||||
\(788\) | 1.86703 | − | 1.86703i | 0.0665102 | − | 0.0665102i | ||||
\(789\) | −0.0817911 | + | 2.17754i | −0.00291184 | + | 0.0775225i | ||||
\(790\) | 38.1067i | 1.35578i | ||||||||
\(791\) | 9.84500 | − | 9.84500i | 0.350048 | − | 0.350048i | ||||
\(792\) | −0.0561363 | + | 0.746210i | −0.00199472 | + | 0.0265154i | ||||
\(793\) | −17.1604 | + | 24.6964i | −0.609385 | + | 0.876996i | ||||
\(794\) | − | 51.7239i | − | 1.83561i | ||||||
\(795\) | 13.2656 | − | 12.3052i | 0.470483 | − | 0.436419i | ||||
\(796\) | 13.7950 | 0.488952 | ||||||||
\(797\) | 3.00031 | 0.106277 | 0.0531383 | − | 0.998587i | \(-0.483078\pi\) | ||||
0.0531383 | + | 0.998587i | \(0.483078\pi\) | |||||||
\(798\) | −15.7930 | − | 17.0257i | −0.559066 | − | 0.602703i | ||||
\(799\) | −38.3827 | + | 38.3827i | −1.35788 | + | 1.35788i | ||||
\(800\) | 0.392128 | − | 0.392128i | 0.0138638 | − | 0.0138638i | ||||
\(801\) | 6.11477 | − | 5.25913i | 0.216055 | − | 0.185822i | ||||
\(802\) | −2.45934 | −0.0868424 | ||||||||
\(803\) | −3.13732 | −0.110714 | ||||||||
\(804\) | −8.44055 | − | 9.09937i | −0.297675 | − | 0.320910i | ||||
\(805\) | 3.44411i | 0.121389i | ||||||||
\(806\) | 38.7600 | − | 55.7814i | 1.36526 | − | 1.96481i | ||||
\(807\) | 0.698037 | − | 18.5840i | 0.0245721 | − | 0.654187i | ||||
\(808\) | 2.17048 | − | 2.17048i | 0.0763571 | − | 0.0763571i | ||||
\(809\) | 16.1882i | 0.569148i | 0.958654 | + | 0.284574i | \(0.0918521\pi\) | ||||
−0.958654 | + | 0.284574i | \(0.908148\pi\) | |||||||
\(810\) | −6.15523 | + | 40.6787i | −0.216273 | + | 1.42930i | ||||
\(811\) | 4.02134 | − | 4.02134i | 0.141208 | − | 0.141208i | −0.632969 | − | 0.774177i | \(-0.718164\pi\) |
0.774177 | + | 0.632969i | \(0.218164\pi\) | |||||||
\(812\) | 14.5688 | + | 14.5688i | 0.511264 | + | 0.511264i | ||||
\(813\) | −20.8223 | − | 22.4476i | −0.730270 | − | 0.787271i | ||||
\(814\) | 10.5119 | + | 10.5119i | 0.368442 | + | 0.368442i | ||||
\(815\) | 29.3739i | 1.02892i | ||||||||
\(816\) | −38.4515 | − | 1.44429i | −1.34607 | − | 0.0505601i | ||||
\(817\) | 15.0141 | + | 15.0141i | 0.525279 | + | 0.525279i | ||||
\(818\) | 36.6810 | 1.28252 | ||||||||
\(819\) | −20.3575 | + | 2.10523i | −0.711350 | + | 0.0735625i | ||||
\(820\) | 39.1496 | 1.36716 | ||||||||
\(821\) | 20.8379 | + | 20.8379i | 0.727249 | + | 0.727249i | 0.970071 | − | 0.242822i | \(-0.0780730\pi\) |
−0.242822 | + | 0.970071i | \(0.578073\pi\) | |||||||
\(822\) | 53.4547 | + | 2.00782i | 1.86445 | + | 0.0700309i | ||||
\(823\) | − | 3.89412i | − | 0.135741i | −0.997694 | − | 0.0678703i | \(-0.978380\pi\) | ||
0.997694 | − | 0.0678703i | \(-0.0216204\pi\) | |||||||
\(824\) | 0.0387521 | + | 0.0387521i | 0.00134999 | + | 0.00134999i | ||||
\(825\) | 0.0807307 | + | 0.0870321i | 0.00281068 | + | 0.00303007i | ||||
\(826\) | 4.12256 | + | 4.12256i | 0.143442 | + | 0.143442i | ||||
\(827\) | 12.6103 | − | 12.6103i | 0.438502 | − | 0.438502i | −0.453005 | − | 0.891508i | \(-0.649648\pi\) |
0.891508 | + | 0.453005i | \(0.149648\pi\) | |||||||
\(828\) | 0.386269 | − | 5.13461i | 0.0134238 | − | 0.178440i | ||||
\(829\) | − | 47.1893i | − | 1.63895i | −0.573113 | − | 0.819476i | \(-0.694264\pi\) | ||
0.573113 | − | 0.819476i | \(-0.305736\pi\) | |||||||
\(830\) | −35.7197 | + | 35.7197i | −1.23985 | + | 1.23985i | ||||
\(831\) | 1.83084 | − | 48.7427i | 0.0635110 | − | 1.69087i | ||||
\(832\) | −26.5024 | − | 18.4154i | −0.918807 | − | 0.638438i | ||||
\(833\) | − | 20.3190i | − | 0.704013i | ||||||
\(834\) | 24.7447 | + | 26.6762i | 0.856840 | + | 0.923720i | ||||
\(835\) | −25.0574 | −0.867147 | ||||||||
\(836\) | 7.40849 | 0.256228 | ||||||||
\(837\) | −37.7058 | + | 30.0428i | −1.30330 | + | 1.03843i | ||||
\(838\) | 42.8331 | − | 42.8331i | 1.47965 | − | 1.47965i | ||||
\(839\) | −36.9591 | + | 36.9591i | −1.27597 | + | 1.27597i | −0.333064 | + | 0.942904i | \(0.608083\pi\) |
−0.942904 | + | 0.333064i | \(0.891917\pi\) | |||||||
\(840\) | 1.25159 | + | 1.34928i | 0.0431839 | + | 0.0465546i | ||||
\(841\) | 2.68794 | 0.0926877 | ||||||||
\(842\) | 38.9409 | 1.34199 | ||||||||
\(843\) | 3.52773 | − | 3.27231i | 0.121501 | − | 0.112704i | ||||
\(844\) | − | 46.3205i | − | 1.59442i | ||||||
\(845\) | −12.1776 | + | 26.6137i | −0.418923 | + | 0.915539i | ||||
\(846\) | 55.4966 | + | 4.17493i | 1.90801 | + | 0.143537i | ||||
\(847\) | 1.33791 | − | 1.33791i | 0.0459712 | − | 0.0459712i | ||||
\(848\) | − | 17.3506i | − | 0.595821i | ||||||
\(849\) | 0.821785 | − | 21.8785i | 0.0282036 | − | 0.750870i | ||||
\(850\) | 0.584640 | − | 0.584640i | 0.0200530 | − | 0.0200530i | ||||
\(851\) | −4.18578 | − | 4.18578i | −0.143487 | − | 0.143487i | ||||
\(852\) | 29.2727 | − | 27.1533i | 1.00287 | − | 0.930257i | ||||
\(853\) | 31.2710 | + | 31.2710i | 1.07070 | + | 1.07070i | 0.997303 | + | 0.0733967i | \(0.0233839\pi\) |
0.0733967 | + | 0.997303i | \(0.476616\pi\) | |||||||
\(854\) | − | 32.0441i | − | 1.09653i | ||||||
\(855\) | 23.5043 | + | 1.76820i | 0.803831 | + | 0.0604710i | ||||
\(856\) | 3.41309 | + | 3.41309i | 0.116657 | + | 0.116657i | ||||
\(857\) | 35.8252 | 1.22377 | 0.611883 | − | 0.790948i | \(-0.290412\pi\) | ||||
0.611883 | + | 0.790948i | \(0.290412\pi\) | |||||||
\(858\) | 7.62146 | − | 10.1343i | 0.260192 | − | 0.345980i | ||||
\(859\) | −7.65699 | −0.261253 | −0.130627 | − | 0.991432i | \(-0.541699\pi\) | ||||
−0.130627 | + | 0.991432i | \(0.541699\pi\) | |||||||
\(860\) | −20.5613 | − | 20.5613i | −0.701134 | − | 0.701134i | ||||
\(861\) | 1.00764 | − | 26.8265i | 0.0343402 | − | 0.914245i | ||||
\(862\) | 23.2339i | 0.791349i | ||||||||
\(863\) | 26.4363 | + | 26.4363i | 0.899901 | + | 0.899901i | 0.995427 | − | 0.0955257i | \(-0.0304532\pi\) |
−0.0955257 | + | 0.995427i | \(0.530453\pi\) | |||||||
\(864\) | 26.1995 | + | 32.8822i | 0.891326 | + | 1.11868i | ||||
\(865\) | −7.17608 | − | 7.17608i | −0.243994 | − | 0.243994i | ||||
\(866\) | 3.42075 | − | 3.42075i | 0.116242 | − | 0.116242i | ||||
\(867\) | −31.6718 | − | 1.18963i | −1.07563 | − | 0.0404020i | ||||
\(868\) | 37.2670i | 1.26492i | ||||||||
\(869\) | −5.89449 | + | 5.89449i | −0.199957 | + | 0.199957i | ||||
\(870\) | −40.5856 | − | 1.52444i | −1.37598 | − | 0.0516835i | ||||
\(871\) | 2.15654 | + | 11.9780i | 0.0730715 | + | 0.405858i | ||||
\(872\) | − | 3.16811i | − | 0.107286i | ||||||
\(873\) | −28.0912 | + | 24.1604i | −0.950744 | + | 0.817706i | ||||
\(874\) | −5.72931 | −0.193797 | ||||||||
\(875\) | −21.0068 | −0.710159 | ||||||||
\(876\) | 8.45729 | − | 7.84495i | 0.285745 | − | 0.265056i | ||||
\(877\) | −26.7626 | + | 26.7626i | −0.903708 | + | 0.903708i | −0.995755 | − | 0.0920467i | \(-0.970659\pi\) |
0.0920467 | + | 0.995755i | \(0.470659\pi\) | |||||||
\(878\) | 33.5369 | − | 33.5369i | 1.13182 | − | 1.13182i | ||||
\(879\) | −9.36726 | + | 8.68904i | −0.315950 | + | 0.293074i | ||||
\(880\) | 8.41825 | 0.283779 | ||||||||
\(881\) | −35.8635 | −1.20827 | −0.604136 | − | 0.796882i | \(-0.706481\pi\) | ||||
−0.604136 | + | 0.796882i | \(0.706481\pi\) | |||||||
\(882\) | −15.7945 | + | 13.5843i | −0.531827 | + | 0.457408i | ||||
\(883\) | − | 1.32600i | − | 0.0446234i | −0.999751 | − | 0.0223117i | \(-0.992897\pi\) | ||
0.999751 | − | 0.0223117i | \(-0.00710263\pi\) | |||||||
\(884\) | −37.3443 | − | 25.9489i | −1.25603 | − | 0.872756i | ||||
\(885\) | −5.91339 | − | 0.222114i | −0.198777 | − | 0.00746629i | ||||
\(886\) | −46.8366 | + | 46.8366i | −1.57351 | + | 1.57351i | ||||
\(887\) | − | 4.04050i | − | 0.135667i | −0.997697 | − | 0.0678333i | \(-0.978391\pi\) | ||
0.997697 | − | 0.0678333i | \(-0.0216086\pi\) | |||||||
\(888\) | −3.16095 | − | 0.118729i | −0.106075 | − | 0.00398429i | ||||
\(889\) | −22.2618 | + | 22.2618i | −0.746635 | + | 0.746635i | ||||
\(890\) | 8.69007 | + | 8.69007i | 0.291292 | + | 0.291292i | ||||
\(891\) | −7.24445 | + | 5.34022i | −0.242698 | + | 0.178904i | ||||
\(892\) | −10.3099 | − | 10.3099i | −0.345200 | − | 0.345200i | ||||
\(893\) | − | 31.8847i | − | 1.06698i | ||||||
\(894\) | 0.395589 | − | 10.5319i | 0.0132305 | − | 0.352238i | ||||
\(895\) | 31.7274 | + | 31.7274i | 1.06053 | + | 1.06053i | ||||
\(896\) | 3.76858 | 0.125899 | ||||||||
\(897\) | −3.03482 | + | 4.03542i | −0.101330 | + | 0.134739i | ||||
\(898\) | 42.2601 | 1.41024 | ||||||||
\(899\) | −33.6532 | − | 33.6532i | −1.12240 | − | 1.12240i | ||||
\(900\) | −0.435252 | − | 0.0327434i | −0.0145084 | − | 0.00109145i | ||||
\(901\) | − | 27.5684i | − | 0.918438i | ||||||
\(902\) | 11.7612 | + | 11.7612i | 0.391605 | + | 0.391605i | ||||
\(903\) | −14.6184 | + | 13.5600i | −0.486470 | + | 0.451249i | ||||
\(904\) | −1.29789 | − | 1.29789i | −0.0431673 | − | 0.0431673i | ||||
\(905\) | −1.05020 | + | 1.05020i | −0.0349099 | + | 0.0349099i | ||||
\(906\) | 0.0997451 | − | 2.65554i | 0.00331381 | − | 0.0882243i | ||||
\(907\) | − | 17.6046i | − | 0.584552i | −0.956334 | − | 0.292276i | \(-0.905587\pi\) | ||
0.956334 | − | 0.292276i | \(-0.0944126\pi\) | |||||||
\(908\) | −19.0904 | + | 19.0904i | −0.633538 | + | 0.633538i | ||||
\(909\) | 36.8130 | + | 2.76939i | 1.22101 | + | 0.0918548i | ||||
\(910\) | −5.52586 | − | 30.6921i | −0.183180 | − | 1.01743i | ||||
\(911\) | − | 10.6654i | − | 0.353359i | −0.984268 | − | 0.176680i | \(-0.943464\pi\) | ||
0.984268 | − | 0.176680i | \(-0.0565357\pi\) | |||||||
\(912\) | 16.5708 | − | 15.3711i | 0.548715 | − | 0.508986i | ||||
\(913\) | −11.0505 | −0.365719 | ||||||||
\(914\) | −62.7180 | −2.07453 | ||||||||
\(915\) | 22.1188 | + | 23.8452i | 0.731224 | + | 0.788299i | ||||
\(916\) | 2.05448 | − | 2.05448i | 0.0678818 | − | 0.0678818i | ||||
\(917\) | 12.3667 | − | 12.3667i | 0.408386 | − | 0.408386i | ||||
\(918\) | 39.0620 | + | 49.0255i | 1.28924 | + | 1.61808i | ||||
\(919\) | 24.9929 | 0.824440 | 0.412220 | − | 0.911084i | \(-0.364753\pi\) | ||||
0.412220 | + | 0.911084i | \(0.364753\pi\) | |||||||
\(920\) | 0.454045 | 0.0149694 | ||||||||
\(921\) | −28.9714 | − | 31.2327i | −0.954639 | − | 1.02915i | ||||
\(922\) | 75.2426i | 2.47798i | ||||||||
\(923\) | −38.5333 | + | 6.93760i | −1.26834 | + | 0.228354i | ||||
\(924\) | −0.261129 | + | 6.95209i | −0.00859051 | + | 0.228707i | ||||
\(925\) | −0.354821 | + | 0.354821i | −0.0116664 | + | 0.0116664i | ||||
\(926\) | 51.8386i | 1.70352i | ||||||||
\(927\) | −0.0494451 | + | 0.657265i | −0.00162399 | + | 0.0215874i | ||||
\(928\) | −29.3481 | + | 29.3481i | −0.963397 | + | 0.963397i | ||||
\(929\) | 15.3186 | + | 15.3186i | 0.502588 | + | 0.502588i | 0.912241 | − | 0.409653i | \(-0.134350\pi\) |
−0.409653 | + | 0.912241i | \(0.634350\pi\) | |||||||
\(930\) | −49.9593 | − | 53.8588i | −1.63823 | − | 1.76610i | ||||
\(931\) | 8.43957 | + | 8.43957i | 0.276596 | + | 0.276596i | ||||
\(932\) | 38.4617i | 1.25985i | ||||||||
\(933\) | −7.53248 | − | 0.282929i | −0.246602 | − | 0.00926269i | ||||
\(934\) | 13.2578 | + | 13.2578i | 0.433810 | + | 0.433810i | ||||
\(935\) | 13.3758 | 0.437436 | ||||||||
\(936\) | 0.277537 | + | 2.68379i | 0.00907159 | + | 0.0877223i | ||||
\(937\) | 15.3687 | 0.502073 | 0.251036 | − | 0.967978i | \(-0.419229\pi\) | ||||
0.251036 | + | 0.967978i | \(0.419229\pi\) | |||||||
\(938\) | −9.16991 | − | 9.16991i | −0.299408 | − | 0.299408i | ||||
\(939\) | 24.5514 | + | 0.922181i | 0.801206 | + | 0.0300942i | ||||
\(940\) | 43.6648i | 1.42419i | ||||||||
\(941\) | 26.5102 | + | 26.5102i | 0.864207 | + | 0.864207i | 0.991824 | − | 0.127617i | \(-0.0407327\pi\) |
−0.127617 | + | 0.991824i | \(0.540733\pi\) | |||||||
\(942\) | 33.6360 | + | 36.2614i | 1.09592 | + | 1.18146i | ||||
\(943\) | −4.68323 | − | 4.68323i | −0.152507 | − | 0.152507i | ||||
\(944\) | −4.01242 | + | 4.01242i | −0.130593 | + | 0.130593i | ||||
\(945\) | −2.48773 | + | 21.9940i | −0.0809259 | + | 0.715466i | ||||
\(946\) | − | 12.3539i | − | 0.401659i | ||||||
\(947\) | 5.05234 | − | 5.05234i | 0.164179 | − | 0.164179i | −0.620236 | − | 0.784415i | \(-0.712963\pi\) |
0.784415 | + | 0.620236i | \(0.212963\pi\) | |||||||
\(948\) | 1.15047 | − | 30.6291i | 0.0373654 | − | 0.994788i | ||||
\(949\) | −11.1328 | + | 2.00436i | −0.361385 | + | 0.0650644i | ||||
\(950\) | 0.485664i | 0.0157570i | ||||||||
\(951\) | 36.9792 | + | 39.8656i | 1.19913 | + | 1.29273i | ||||
\(952\) | 2.80405 | 0.0908799 | ||||||||
\(953\) | −42.4331 | −1.37454 | −0.687271 | − | 0.726401i | \(-0.741191\pi\) | ||||
−0.687271 | + | 0.726401i | \(0.741191\pi\) | |||||||
\(954\) | −21.4296 | + | 18.4309i | −0.693808 | + | 0.596723i | ||||
\(955\) | 15.6735 | − | 15.6735i | 0.507183 | − | 0.507183i | ||||
\(956\) | −3.84219 | + | 3.84219i | −0.124265 | + | 0.124265i | ||||
\(957\) | −6.04213 | − | 6.51374i | −0.195314 | − | 0.210559i | ||||
\(958\) | 20.8904 | 0.674937 | ||||||||
\(959\) | 28.7790 | 0.929321 | ||||||||
\(960\) | −25.5890 | + | 23.7363i | −0.825882 | + | 0.766086i | ||||
\(961\) | − | 55.0849i | − | 1.77693i | ||||||
\(962\) | 44.0173 | + | 30.5857i | 1.41918 | + | 0.986122i | ||||
\(963\) | −4.35488 | + | 57.8887i | −0.140334 | + | 1.86544i | ||||
\(964\) | 0.633781 | − | 0.633781i | 0.0204127 | − | 0.0204127i | ||||
\(965\) | 51.3689i | 1.65362i | ||||||||
\(966\) | 0.201942 | − | 5.37636i | 0.00649739 | − | 0.172981i | ||||
\(967\) | 0.0403125 | − | 0.0403125i | 0.00129636 | − | 0.00129636i | −0.706458 | − | 0.707755i | \(-0.749708\pi\) |
0.707755 | + | 0.706458i | \(0.249708\pi\) | |||||||
\(968\) | −0.176380 | − | 0.176380i | −0.00566908 | − | 0.00566908i | ||||
\(969\) | 26.3295 | − | 24.4232i | 0.845826 | − | 0.784586i | ||||
\(970\) | −39.9221 | − | 39.9221i | −1.28182 | − | 1.28182i | ||||
\(971\) | − | 41.5020i | − | 1.33186i | −0.746012 | − | 0.665932i | \(-0.768034\pi\) | ||
0.746012 | − | 0.665932i | \(-0.231966\pi\) | |||||||
\(972\) | 6.17552 | − | 32.5106i | 0.198080 | − | 1.04278i | ||||
\(973\) | 13.8420 | + | 13.8420i | 0.443754 | + | 0.443754i | ||||
\(974\) | 10.6871 | 0.342437 | ||||||||
\(975\) | 0.342076 | + | 0.257256i | 0.0109552 | + | 0.00823879i | ||||
\(976\) | 31.1880 | 0.998303 | ||||||||
\(977\) | −0.505411 | − | 0.505411i | −0.0161695 | − | 0.0161695i | 0.698976 | − | 0.715145i | \(-0.253640\pi\) |
−0.715145 | + | 0.698976i | \(0.753640\pi\) | |||||||
\(978\) | 1.72231 | − | 45.8535i | 0.0550735 | − | 1.46623i | ||||
\(979\) | 2.68843i | 0.0859226i | ||||||||
\(980\) | −11.5577 | − | 11.5577i | −0.369196 | − | 0.369196i | ||||
\(981\) | 28.8879 | − | 24.8456i | 0.922321 | − | 0.793260i | ||||
\(982\) | −25.1648 | − | 25.1648i | −0.803040 | − | 0.803040i | ||||
\(983\) | 14.7864 | − | 14.7864i | 0.471613 | − | 0.471613i | −0.430823 | − | 0.902436i | \(-0.641777\pi\) |
0.902436 | + | 0.430823i | \(0.141777\pi\) | |||||||
\(984\) | −3.53661 | − | 0.132839i | −0.112743 | − | 0.00423476i | ||||
\(985\) | 2.80020i | 0.0892217i | ||||||||
\(986\) | −43.7562 | + | 43.7562i | −1.39348 | + | 1.39348i | ||||
\(987\) | 29.9205 | + | 1.12385i | 0.952379 | + | 0.0357725i | ||||
\(988\) | 26.2890 | − | 4.73312i | 0.836365 | − | 0.150581i | ||||
\(989\) | 4.91924i | 0.156423i | ||||||||
\(990\) | −8.94242 | − | 10.3973i | −0.284209 | − | 0.330449i | ||||
\(991\) | 53.9383 | 1.71341 | 0.856703 | − | 0.515809i | \(-0.172509\pi\) | ||||
0.856703 | + | 0.515809i | \(0.172509\pi\) | |||||||
\(992\) | −75.0724 | −2.38355 | ||||||||
\(993\) | 36.1945 | − | 33.5739i | 1.14860 | − | 1.06544i | ||||
\(994\) | 29.4997 | − | 29.4997i | 0.935673 | − | 0.935673i | ||||
\(995\) | −10.3450 | + | 10.3450i | −0.327958 | + | 0.327958i | ||||
\(996\) | 29.7890 | − | 27.6322i | 0.943900 | − | 0.875559i | ||||
\(997\) | −52.5725 | −1.66499 | −0.832495 | − | 0.554033i | \(-0.813088\pi\) | ||||
−0.832495 | + | 0.554033i | \(0.813088\pi\) | |||||||
\(998\) | −48.4785 | −1.53456 | ||||||||
\(999\) | −23.7069 | − | 29.7538i | −0.750053 | − | 0.941369i |
(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 | 429.2.j.a.122.8 | ✓ | 96 | |
3.2 | odd | 2 | inner | 429.2.j.a.122.41 | yes | 96 | |
13.8 | odd | 4 | inner | 429.2.j.a.320.41 | yes | 96 | |
39.8 | even | 4 | inner | 429.2.j.a.320.8 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.j.a.122.8 | ✓ | 96 | 1.1 | even | 1 | trivial | |
429.2.j.a.122.41 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.j.a.320.8 | yes | 96 | 39.8 | even | 4 | inner | |
429.2.j.a.320.41 | yes | 96 | 13.8 | odd | 4 | inner |