Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(101,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1000.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.t (of order \(10\), degree \(4\), 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: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(56\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 101.48 | ||
Character | \(\chi\) | \(=\) | 1000.101 |
Dual form | 1000.2.t.b.901.48 |
$q$-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 \(\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times\).
\(n\) | \(377\) | \(501\) | \(751\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25131 | − | 0.658957i | 0.884810 | − | 0.465953i | ||||
\(3\) | 1.48079 | − | 2.03813i | 0.854932 | − | 1.17671i | −0.127822 | − | 0.991797i | \(-0.540799\pi\) |
0.982754 | − | 0.184916i | \(-0.0592014\pi\) | |||||||
\(4\) | 1.13155 | − | 1.64912i | 0.565776 | − | 0.824559i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.509884 | − | 3.52610i | 0.208159 | − | 1.43953i | ||||
\(7\) | 3.58786 | 1.35608 | 0.678042 | − | 0.735024i | \(-0.262829\pi\) | ||||
0.678042 | + | 0.735024i | \(0.262829\pi\) | |||||||
\(8\) | 0.329223 | − | 2.80920i | 0.116398 | − | 0.993203i | ||||
\(9\) | −1.03418 | − | 3.18289i | −0.344728 | − | 1.06096i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.49567 | + | 0.810891i | 0.752472 | + | 0.244493i | 0.660044 | − | 0.751227i | \(-0.270537\pi\) |
0.0924272 | + | 0.995719i | \(0.470537\pi\) | |||||||
\(12\) | −1.68553 | − | 4.74824i | −0.486570 | − | 1.37070i | ||||
\(13\) | −6.50757 | + | 2.11444i | −1.80488 | + | 0.586440i | −0.999976 | − | 0.00697033i | \(-0.997781\pi\) |
−0.804900 | + | 0.593410i | \(0.797781\pi\) | |||||||
\(14\) | 4.48952 | − | 2.36424i | 1.19988 | − | 0.631871i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.43918 | − | 3.73212i | −0.359796 | − | 0.933031i | ||||
\(17\) | −1.57369 | + | 1.14335i | −0.381677 | + | 0.277304i | −0.762036 | − | 0.647534i | \(-0.775800\pi\) |
0.380360 | + | 0.924839i | \(0.375800\pi\) | |||||||
\(18\) | −3.39148 | − | 3.30130i | −0.799378 | − | 0.778124i | ||||
\(19\) | 3.00859 | + | 4.14097i | 0.690218 | + | 0.950003i | 1.00000 | 0.000804663i | \(-0.000256132\pi\) | |
−0.309782 | + | 0.950808i | \(0.600256\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.31285 | − | 7.31251i | 1.15936 | − | 1.59572i | ||||
\(22\) | 3.65719 | − | 0.629861i | 0.779716 | − | 0.134287i | ||||
\(23\) | 0.239759 | − | 0.737902i | 0.0499932 | − | 0.153863i | −0.922943 | − | 0.384936i | \(-0.874224\pi\) |
0.972936 | + | 0.231073i | \(0.0742236\pi\) | |||||||
\(24\) | −5.23800 | − | 4.83083i | −1.06920 | − | 0.986088i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.74966 | + | 6.93403i | −1.32372 | + | 1.35987i | ||||
\(27\) | −0.830663 | − | 0.269899i | −0.159861 | − | 0.0519421i | ||||
\(28\) | 4.05985 | − | 5.91680i | 0.767239 | − | 1.11817i | ||||
\(29\) | −3.28631 | + | 4.52322i | −0.610252 | + | 0.839940i | −0.996598 | − | 0.0824137i | \(-0.973737\pi\) |
0.386346 | + | 0.922354i | \(0.373737\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.72253 | − | 1.25149i | 0.309376 | − | 0.224775i | −0.422253 | − | 0.906478i | \(-0.638761\pi\) |
0.731629 | + | 0.681704i | \(0.238761\pi\) | |||||||
\(32\) | −4.26017 | − | 3.72168i | −0.753099 | − | 0.657907i | ||||
\(33\) | 5.34825 | − | 3.88573i | 0.931010 | − | 0.676419i | ||||
\(34\) | −1.21576 | + | 2.46769i | −0.208500 | + | 0.423205i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.41920 | − | 1.89612i | −1.06987 | − | 0.316019i | ||||
\(37\) | −8.43241 | + | 2.73986i | −1.38628 | + | 0.450430i | −0.904729 | − | 0.425988i | \(-0.859926\pi\) |
−0.481551 | + | 0.876418i | \(0.659926\pi\) | |||||||
\(38\) | 6.49339 | + | 3.19910i | 1.05337 | + | 0.518963i | ||||
\(39\) | −5.32683 | + | 16.3943i | −0.852975 | + | 2.62519i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.12308 | + | 3.45647i | 0.175395 | + | 0.539811i | 0.999651 | − | 0.0264065i | \(-0.00840642\pi\) |
−0.824256 | + | 0.566217i | \(0.808406\pi\) | |||||||
\(42\) | 1.82939 | − | 12.6512i | 0.282281 | − | 1.95212i | ||||
\(43\) | 0.652170i | 0.0994550i | 0.998763 | + | 0.0497275i | \(0.0158353\pi\) | ||||
−0.998763 | + | 0.0497275i | \(0.984165\pi\) | |||||||
\(44\) | 4.16123 | − | 3.19808i | 0.627329 | − | 0.482129i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.186233 | − | 1.08133i | −0.0274585 | − | 0.159434i | ||||
\(47\) | −0.745059 | − | 0.541317i | −0.108678 | − | 0.0789592i | 0.532119 | − | 0.846670i | \(-0.321396\pi\) |
−0.640797 | + | 0.767710i | \(0.721396\pi\) | |||||||
\(48\) | −9.73767 | − | 2.59324i | −1.40551 | − | 0.374302i | ||||
\(49\) | 5.87273 | 0.838962 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.90045i | 0.686201i | ||||||||
\(52\) | −3.87669 | + | 13.1244i | −0.537601 | + | 1.82002i | ||||
\(53\) | −1.07913 | + | 1.48529i | −0.148229 | + | 0.204020i | −0.876675 | − | 0.481084i | \(-0.840243\pi\) |
0.728445 | + | 0.685104i | \(0.240243\pi\) | |||||||
\(54\) | −1.21727 | + | 0.209644i | −0.165649 | + | 0.0285290i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.18121 | − | 10.0790i | 0.157845 | − | 1.34687i | ||||
\(57\) | 12.8949 | 1.70797 | ||||||||
\(58\) | −1.13159 | + | 7.82548i | −0.148584 | + | 1.02754i | ||||
\(59\) | −3.74706 | + | 1.21749i | −0.487826 | + | 0.158504i | −0.542594 | − | 0.839995i | \(-0.682558\pi\) |
0.0547685 | + | 0.998499i | \(0.482558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.21266 | − | 2.01862i | −0.795449 | − | 0.258457i | −0.117027 | − | 0.993129i | \(-0.537336\pi\) |
−0.678423 | + | 0.734672i | \(0.737336\pi\) | |||||||
\(62\) | 1.33074 | − | 2.70108i | 0.169004 | − | 0.343037i | ||||
\(63\) | −3.71051 | − | 11.4198i | −0.467480 | − | 1.43876i | ||||
\(64\) | −7.78322 | − | 1.84971i | −0.972903 | − | 0.231214i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.13179 | − | 8.38651i | 0.508588 | − | 1.03231i | ||||
\(67\) | −2.89052 | − | 3.97847i | −0.353134 | − | 0.486047i | 0.595086 | − | 0.803662i | \(-0.297118\pi\) |
−0.948220 | + | 0.317615i | \(0.897118\pi\) | |||||||
\(68\) | 0.104813 | + | 3.88897i | 0.0127104 | + | 0.471607i | ||||
\(69\) | −1.14891 | − | 1.58133i | −0.138312 | − | 0.190370i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48762 | + | 3.26045i | 0.532582 | + | 0.386944i | 0.821323 | − | 0.570464i | \(-0.193236\pi\) |
−0.288740 | + | 0.957407i | \(0.593236\pi\) | |||||||
\(72\) | −9.28187 | + | 1.85735i | −1.09388 | + | 0.218891i | ||||
\(73\) | 4.58222 | − | 14.1026i | 0.536309 | − | 1.65059i | −0.204496 | − | 0.978868i | \(-0.565555\pi\) |
0.740804 | − | 0.671721i | \(-0.234445\pi\) | |||||||
\(74\) | −8.74611 | + | 8.98500i | −1.01671 | + | 1.04449i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.2333 | − | 0.275801i | 1.17384 | − | 0.0316365i | ||||
\(77\) | 8.95410 | + | 2.90936i | 1.02041 | + | 0.331553i | ||||
\(78\) | 4.13762 | + | 24.0245i | 0.468493 | + | 2.72024i | ||||
\(79\) | −7.65406 | − | 5.56100i | −0.861148 | − | 0.625661i | 0.0670487 | − | 0.997750i | \(-0.478642\pi\) |
−0.928197 | + | 0.372089i | \(0.878642\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.34247 | − | 4.60807i | 0.704719 | − | 0.512008i | ||||
\(82\) | 3.68298 | + | 3.58506i | 0.406718 | + | 0.395904i | ||||
\(83\) | −4.72884 | − | 6.50869i | −0.519058 | − | 0.714422i | 0.466356 | − | 0.884597i | \(-0.345567\pi\) |
−0.985414 | + | 0.170176i | \(0.945567\pi\) | |||||||
\(84\) | −6.04743 | − | 17.0360i | −0.659829 | − | 1.85878i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.429752 | + | 0.816067i | 0.0463414 | + | 0.0879988i | ||||
\(87\) | 4.35257 | + | 13.3958i | 0.466645 | + | 1.43618i | ||||
\(88\) | 3.09959 | − | 6.74386i | 0.330417 | − | 0.718898i | ||||
\(89\) | −3.35636 | + | 10.3298i | −0.355773 | + | 1.09496i | 0.599787 | + | 0.800160i | \(0.295252\pi\) |
−0.955560 | + | 0.294797i | \(0.904748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.3483 | + | 7.58631i | −2.44756 | + | 0.795261i | ||||
\(92\) | −0.945588 | − | 1.23036i | −0.0985843 | − | 0.128274i | ||||
\(93\) | − | 5.36393i | − | 0.556213i | ||||||
\(94\) | −1.28900 | − | 0.186393i | −0.132951 | − | 0.0192250i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −13.8937 | + | 3.17175i | −1.41802 | + | 0.323716i | ||||
\(97\) | 4.56353 | + | 3.31560i | 0.463356 | + | 0.336648i | 0.794846 | − | 0.606811i | \(-0.207551\pi\) |
−0.331490 | + | 0.943459i | \(0.607551\pi\) | |||||||
\(98\) | 7.34861 | − | 3.86988i | 0.742321 | − | 0.390917i | ||||
\(99\) | − | 8.78205i | − | 0.882629i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.202935i | 0.0201928i | 0.999949 | + | 0.0100964i | \(0.00321383\pi\) | ||||
−0.999949 | + | 0.0100964i | \(0.996786\pi\) | |||||||
\(102\) | 3.22919 | + | 6.13198i | 0.319737 | + | 0.607157i | ||||
\(103\) | 10.6807 | + | 7.76000i | 1.05240 | + | 0.764616i | 0.972668 | − | 0.232201i | \(-0.0745926\pi\) |
0.0797351 | + | 0.996816i | \(0.474593\pi\) | |||||||
\(104\) | 3.79744 | + | 18.9772i | 0.372369 | + | 1.86087i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.371579 | + | 2.56966i | −0.0360910 | + | 0.249587i | ||||
\(107\) | − | 14.9185i | − | 1.44222i | −0.692819 | − | 0.721111i | \(-0.743632\pi\) | ||
0.692819 | − | 0.721111i | \(-0.256368\pi\) | |||||||
\(108\) | −1.38503 | + | 1.06446i | −0.133275 | + | 0.102427i | ||||
\(109\) | 8.22423 | − | 2.67221i | 0.787738 | − | 0.255952i | 0.112598 | − | 0.993641i | \(-0.464083\pi\) |
0.675141 | + | 0.737689i | \(0.264083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.90242 | + | 21.2435i | −0.655149 | + | 2.01634i | ||||
\(112\) | −5.16358 | − | 13.3903i | −0.487913 | − | 1.26527i | ||||
\(113\) | 1.82593 | + | 5.61964i | 0.171769 | + | 0.528652i | 0.999471 | − | 0.0325164i | \(-0.0103521\pi\) |
−0.827702 | + | 0.561168i | \(0.810352\pi\) | |||||||
\(114\) | 16.1355 | − | 8.49718i | 1.51123 | − | 0.795834i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.74069 | + | 10.5378i | 0.347314 | + | 0.978407i | ||||
\(117\) | 13.4601 | + | 18.5262i | 1.24438 | + | 1.71275i | ||||
\(118\) | −3.88646 | + | 3.99261i | −0.357778 | + | 0.367550i | ||||
\(119\) | −5.64619 | + | 4.10220i | −0.517585 | + | 0.376048i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.32838 | − | 2.41821i | −0.302580 | − | 0.219837i | ||||
\(122\) | −9.10414 | + | 1.56796i | −0.824250 | + | 0.141957i | ||||
\(123\) | 8.70777 | + | 2.82933i | 0.785153 | + | 0.255112i | ||||
\(124\) | −0.114726 | − | 4.25678i | −0.0103027 | − | 0.382270i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.1681 | − | 11.8446i | −1.08402 | − | 1.05520i | ||||
\(127\) | 1.09193 | − | 3.36061i | 0.0968930 | − | 0.298206i | −0.890849 | − | 0.454299i | \(-0.849890\pi\) |
0.987742 | + | 0.156093i | \(0.0498899\pi\) | |||||||
\(128\) | −10.9581 | + | 2.81425i | −0.968569 | + | 0.248747i | ||||
\(129\) | 1.32921 | + | 0.965725i | 0.117030 | + | 0.0850273i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.96559 | + | 5.45817i | 0.346475 | + | 0.476883i | 0.946319 | − | 0.323235i | \(-0.104770\pi\) |
−0.599843 | + | 0.800118i | \(0.704770\pi\) | |||||||
\(132\) | −0.356209 | − | 13.2168i | −0.0310040 | − | 1.15037i | ||||
\(133\) | 10.7944 | + | 14.8572i | 0.935992 | + | 1.28828i | ||||
\(134\) | −6.23858 | − | 3.07356i | −0.538931 | − | 0.265515i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.69382 | + | 4.79724i | 0.230993 | + | 0.411360i | ||||
\(137\) | −2.54696 | − | 7.83872i | −0.217601 | − | 0.669707i | −0.998959 | − | 0.0456237i | \(-0.985472\pi\) |
0.781358 | − | 0.624084i | \(-0.214528\pi\) | |||||||
\(138\) | −2.47967 | − | 1.22166i | −0.211083 | − | 0.103994i | ||||
\(139\) | 1.29543 | + | 0.420910i | 0.109877 | + | 0.0357011i | 0.363439 | − | 0.931618i | \(-0.381602\pi\) |
−0.253563 | + | 0.967319i | \(0.581602\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.20655 | + | 0.716950i | −0.185825 | + | 0.0603781i | ||||
\(142\) | 7.76389 | + | 1.12268i | 0.651531 | + | 0.0942132i | ||||
\(143\) | −17.9553 | −1.50150 | ||||||||
\(144\) | −10.3906 | + | 8.44047i | −0.865881 | + | 0.703373i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.55925 | − | 20.6663i | −0.294565 | − | 1.71035i | ||||
\(147\) | 8.69626 | − | 11.9694i | 0.717256 | − | 0.987218i | ||||
\(148\) | −5.02336 | + | 17.0063i | −0.412918 | + | 1.39791i | ||||
\(149\) | 9.46274i | 0.775218i | 0.921824 | + | 0.387609i | \(0.126699\pi\) | ||||
−0.921824 | + | 0.387609i | \(0.873301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.99542 | 0.650658 | 0.325329 | − | 0.945601i | \(-0.394525\pi\) | ||||
0.325329 | + | 0.945601i | \(0.394525\pi\) | |||||||
\(152\) | 12.6233 | − | 7.08843i | 1.02389 | − | 0.574947i | ||||
\(153\) | 5.26667 | + | 3.82646i | 0.425785 | + | 0.309351i | ||||
\(154\) | 13.1215 | − | 2.25985i | 1.05736 | − | 0.182104i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.0086 | + | 27.3356i | 1.68203 | + | 2.18860i | ||||
\(157\) | − | 7.78075i | − | 0.620971i | −0.950578 | − | 0.310486i | \(-0.899508\pi\) | ||
0.950578 | − | 0.310486i | \(-0.100492\pi\) | |||||||
\(158\) | −13.2421 | − | 1.91484i | −1.05348 | − | 0.152336i | ||||
\(159\) | 1.42926 | + | 4.39880i | 0.113347 | + | 0.348847i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.860221 | − | 2.64749i | 0.0677949 | − | 0.208651i | ||||
\(162\) | 4.89987 | − | 9.94554i | 0.384970 | − | 0.781396i | ||||
\(163\) | 21.8518 | − | 7.10008i | 1.71157 | − | 0.556121i | 0.720973 | − | 0.692964i | \(-0.243695\pi\) |
0.990593 | + | 0.136842i | \(0.0436953\pi\) | |||||||
\(164\) | 6.97095 | + | 2.05909i | 0.544340 | + | 0.160788i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.2062 | − | 5.02828i | −0.792154 | − | 0.390271i | ||||
\(167\) | −9.78464 | + | 7.10896i | −0.757158 | + | 0.550108i | −0.898037 | − | 0.439919i | \(-0.855007\pi\) |
0.140879 | + | 0.990027i | \(0.455007\pi\) | |||||||
\(168\) | −18.7932 | − | 17.3323i | −1.44993 | − | 1.33722i | ||||
\(169\) | 27.3604 | − | 19.8785i | 2.10465 | − | 1.52912i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.0688 | − | 13.8585i | 0.769982 | − | 1.05979i | ||||
\(172\) | 1.07551 | + | 0.737964i | 0.0820065 | + | 0.0562692i | ||||
\(173\) | −15.0391 | − | 4.88649i | −1.14340 | − | 0.371513i | −0.324747 | − | 0.945801i | \(-0.605279\pi\) |
−0.818653 | + | 0.574288i | \(0.805279\pi\) | |||||||
\(174\) | 14.2737 | + | 13.8942i | 1.08209 | + | 1.05332i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.565371 | − | 10.4812i | −0.0426165 | − | 0.790047i | ||||
\(177\) | −3.06719 | + | 9.43984i | −0.230544 | + | 0.709542i | ||||
\(178\) | 2.60705 | + | 15.1375i | 0.195407 | + | 1.13460i | ||||
\(179\) | 8.68076 | − | 11.9480i | 0.648830 | − | 0.893038i | −0.350217 | − | 0.936668i | \(-0.613892\pi\) |
0.999048 | + | 0.0436301i | \(0.0138923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.16443 | + | 4.35546i | 0.235210 | + | 0.323739i | 0.910263 | − | 0.414030i | \(-0.135879\pi\) |
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(182\) | −24.2168 | + | 24.8783i | −1.79507 | + | 1.84410i | ||||
\(183\) | −13.3138 | + | 9.67305i | −0.984186 | + | 0.715053i | ||||
\(184\) | −1.99398 | − | 0.916465i | −0.146998 | − | 0.0675627i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.53460 | − | 6.71194i | −0.259169 | − | 0.492143i | ||||
\(187\) | −4.85455 | + | 1.57734i | −0.355000 | + | 0.115346i | ||||
\(188\) | −1.73577 | + | 0.616162i | −0.126594 | + | 0.0449382i | ||||
\(189\) | −2.98030 | − | 0.968359i | −0.216785 | − | 0.0704378i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.20367 | + | 9.85988i | 0.231809 | + | 0.713436i | 0.997529 | + | 0.0702610i | \(0.0223832\pi\) |
−0.765719 | + | 0.643175i | \(0.777617\pi\) | |||||||
\(192\) | −15.2952 | + | 13.1242i | −1.10384 | + | 0.947156i | ||||
\(193\) | 0.720451 | 0.0518592 | 0.0259296 | − | 0.999664i | \(-0.491745\pi\) | ||||
0.0259296 | + | 0.999664i | \(0.491745\pi\) | |||||||
\(194\) | 7.89523 | + | 1.14167i | 0.566844 | + | 0.0819672i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.64530 | − | 9.68483i | 0.474664 | − | 0.691774i | ||||
\(197\) | 3.51179 | − | 4.83357i | 0.250205 | − | 0.344377i | −0.665378 | − | 0.746506i | \(-0.731730\pi\) |
0.915583 | + | 0.402129i | \(0.131730\pi\) | |||||||
\(198\) | −5.78699 | − | 10.9891i | −0.411264 | − | 0.780959i | ||||
\(199\) | 13.1660 | 0.933311 | 0.466655 | − | 0.884439i | \(-0.345459\pi\) | ||||
0.466655 | + | 0.884439i | \(0.345459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.3889 | −0.873843 | ||||||||
\(202\) | 0.133725 | + | 0.253934i | 0.00940888 | + | 0.0178668i | ||||
\(203\) | −11.7908 | + | 16.2287i | −0.827553 | + | 1.13903i | ||||
\(204\) | 8.08142 | + | 5.54511i | 0.565813 | + | 0.388236i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.4784 | + | 2.67203i | 1.28745 | + | 0.186169i | ||||
\(207\) | −2.59662 | −0.180477 | ||||||||
\(208\) | 17.2569 | + | 21.2440i | 1.19655 | + | 1.47301i | ||||
\(209\) | 4.15056 | + | 12.7741i | 0.287100 | + | 0.883603i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.22662 | + | 1.69823i | 0.359816 | + | 0.116911i | 0.483346 | − | 0.875430i | \(-0.339421\pi\) |
−0.123530 | + | 0.992341i | \(0.539421\pi\) | |||||||
\(212\) | 1.22833 | + | 3.46029i | 0.0843622 | + | 0.237654i | ||||
\(213\) | 13.2904 | − | 4.31832i | 0.910644 | − | 0.295886i | ||||
\(214\) | −9.83063 | − | 18.6676i | −0.672008 | − | 1.27609i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.03167 | + | 2.24464i | −0.0701965 | + | 0.152729i | ||||
\(217\) | 6.18020 | − | 4.49018i | 0.419539 | − | 0.304813i | ||||
\(218\) | 8.53018 | − | 8.76318i | 0.577737 | − | 0.593517i | ||||
\(219\) | −21.9577 | − | 30.2221i | −1.48376 | − | 2.04222i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.82337 | − | 10.7679i | 0.526257 | − | 0.724330i | ||||
\(222\) | 5.36147 | + | 31.1306i | 0.359838 | + | 2.08935i | ||||
\(223\) | 6.29390 | − | 19.3706i | 0.421471 | − | 1.29715i | −0.484862 | − | 0.874590i | \(-0.661130\pi\) |
0.906333 | − | 0.422564i | \(-0.138870\pi\) | |||||||
\(224\) | −15.2849 | − | 13.3529i | −1.02127 | − | 0.892177i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.98791 | + | 5.82870i | 0.398310 | + | 0.387720i | ||||
\(227\) | −15.0541 | − | 4.89137i | −0.999175 | − | 0.324652i | −0.236639 | − | 0.971598i | \(-0.576046\pi\) |
−0.762536 | + | 0.646946i | \(0.776046\pi\) | |||||||
\(228\) | 14.5912 | − | 21.2652i | 0.966328 | − | 1.40832i | ||||
\(229\) | 3.76598 | − | 5.18342i | 0.248863 | − | 0.342530i | −0.666250 | − | 0.745729i | \(-0.732102\pi\) |
0.915113 | + | 0.403198i | \(0.132102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.1888 | − | 13.9414i | 1.26253 | − | 0.917280i | ||||
\(232\) | 11.6247 | + | 10.7211i | 0.763199 | + | 0.703872i | ||||
\(233\) | 14.2284 | − | 10.3375i | 0.932133 | − | 0.677234i | −0.0143813 | − | 0.999897i | \(-0.504578\pi\) |
0.946514 | + | 0.322662i | \(0.104578\pi\) | |||||||
\(234\) | 29.0507 | + | 14.3124i | 1.89910 | + | 0.935631i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.23220 | + | 7.55701i | −0.145304 | + | 0.491919i | ||||
\(237\) | −22.6680 | + | 7.36529i | −1.47245 | + | 0.478427i | ||||
\(238\) | −4.36196 | + | 8.85371i | −0.282744 | + | 0.573901i | ||||
\(239\) | 2.60748 | − | 8.02498i | 0.168664 | − | 0.519093i | −0.830624 | − | 0.556834i | \(-0.812016\pi\) |
0.999288 | + | 0.0377406i | \(0.0120161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.07674 | + | 3.31387i | 0.0693591 | + | 0.213465i | 0.979728 | − | 0.200332i | \(-0.0642022\pi\) |
−0.910369 | + | 0.413797i | \(0.864202\pi\) | |||||||
\(242\) | −5.75834 | − | 0.832671i | −0.370160 | − | 0.0535261i | ||||
\(243\) | − | 22.3706i | − | 1.43507i | ||||||
\(244\) | −10.3589 | + | 7.96124i | −0.663159 | + | 0.509666i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.7605 | − | 2.19768i | 0.813581 | − | 0.140119i | ||||
\(247\) | −28.3344 | − | 20.5862i | −1.80288 | − | 1.30987i | ||||
\(248\) | −2.94859 | − | 5.25096i | −0.187236 | − | 0.333436i | ||||
\(249\) | −20.2679 | −1.28443 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.8769i | 1.06526i | 0.846347 | + | 0.532632i | \(0.178797\pi\) | ||||
−0.846347 | + | 0.532632i | \(0.821203\pi\) | |||||||
\(252\) | −23.0312 | − | 6.80299i | −1.45083 | − | 0.428548i | ||||
\(253\) | 1.19672 | − | 1.64714i | 0.0752369 | − | 0.103555i | ||||
\(254\) | −0.848157 | − | 4.92470i | −0.0532181 | − | 0.309003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.8575 | + | 10.7424i | −0.741094 | + | 0.671401i | ||||
\(257\) | 4.42621 | 0.276099 | 0.138050 | − | 0.990425i | \(-0.455917\pi\) | ||||
0.138050 | + | 0.990425i | \(0.455917\pi\) | |||||||
\(258\) | 2.29962 | + | 0.332531i | 0.143168 | + | 0.0207025i | ||||
\(259\) | −30.2543 | + | 9.83022i | −1.87991 | + | 0.610820i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.7956 | + | 5.78213i | 1.10152 | + | 0.357905i | ||||
\(262\) | 8.55888 | + | 4.21671i | 0.528770 | + | 0.260509i | ||||
\(263\) | −3.79412 | − | 11.6771i | −0.233956 | − | 0.720041i | −0.997258 | − | 0.0740002i | \(-0.976423\pi\) |
0.763303 | − | 0.646041i | \(-0.223577\pi\) | |||||||
\(264\) | −9.15503 | − | 16.3036i | −0.563453 | − | 1.00342i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 23.2974 | + | 11.4779i | 1.42845 | + | 0.703757i | ||||
\(267\) | 16.0834 | + | 22.1369i | 0.984289 | + | 1.35476i | ||||
\(268\) | −9.83174 | + | 0.264978i | −0.600569 | + | 0.0161861i | ||||
\(269\) | 16.8702 | + | 23.2198i | 1.02859 | + | 1.41573i | 0.906000 | + | 0.423277i | \(0.139120\pi\) |
0.122591 | + | 0.992457i | \(0.460880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.96640 | − | 2.15522i | −0.180196 | − | 0.130920i | 0.494031 | − | 0.869444i | \(-0.335523\pi\) |
−0.674227 | + | 0.738524i | \(0.735523\pi\) | |||||||
\(272\) | 6.53197 | + | 4.22772i | 0.396059 | + | 0.256343i | ||||
\(273\) | −19.1119 | + | 58.8204i | −1.15671 | + | 3.55997i | ||||
\(274\) | −8.35241 | − | 8.13034i | −0.504588 | − | 0.491172i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.90785 | + | 0.105322i | −0.235225 | + | 0.00633961i | ||||
\(277\) | −3.79042 | − | 1.23158i | −0.227744 | − | 0.0739986i | 0.192922 | − | 0.981214i | \(-0.438204\pi\) |
−0.420666 | + | 0.907216i | \(0.638204\pi\) | |||||||
\(278\) | 1.89834 | − | 0.326942i | 0.113855 | − | 0.0196087i | ||||
\(279\) | −5.76478 | − | 4.18836i | −0.345128 | − | 0.250750i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.0045 | + | 16.7138i | −1.37234 | + | 0.997060i | −0.374785 | + | 0.927112i | \(0.622283\pi\) |
−0.997551 | + | 0.0699483i | \(0.977717\pi\) | |||||||
\(282\) | −2.28863 | + | 2.35115i | −0.136286 | + | 0.140009i | ||||
\(283\) | −7.67233 | − | 10.5601i | −0.456073 | − | 0.627730i | 0.517616 | − | 0.855613i | \(-0.326820\pi\) |
−0.973689 | + | 0.227883i | \(0.926820\pi\) | |||||||
\(284\) | 10.4548 | − | 3.71125i | 0.620380 | − | 0.220222i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.4676 | + | 11.8318i | −1.32854 | + | 0.699627i | ||||
\(287\) | 4.02944 | + | 12.4013i | 0.237850 | + | 0.732028i | ||||
\(288\) | −7.43992 | + | 17.4086i | −0.438402 | + | 1.02581i | ||||
\(289\) | −4.08404 | + | 12.5694i | −0.240238 | + | 0.739375i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.5152 | − | 4.39136i | 0.792277 | − | 0.257426i | ||||
\(292\) | −18.0719 | − | 23.5145i | −1.05758 | − | 1.37608i | ||||
\(293\) | 27.0373i | 1.57954i | 0.613404 | + | 0.789769i | \(0.289800\pi\) | ||||
−0.613404 | + | 0.789769i | \(0.710200\pi\) | |||||||
\(294\) | 2.99441 | − | 20.7079i | 0.174638 | − | 1.20771i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.92066 | + | 24.5904i | 0.286008 | + | 1.42929i | ||||
\(297\) | −1.85420 | − | 1.34715i | −0.107592 | − | 0.0781698i | ||||
\(298\) | 6.23554 | + | 11.8408i | 0.361215 | + | 0.685920i | ||||
\(299\) | 5.30890i | 0.307022i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.33989i | 0.134869i | ||||||||
\(302\) | 10.0047 | − | 5.26864i | 0.575708 | − | 0.303176i | ||||
\(303\) | 0.413607 | + | 0.300503i | 0.0237611 | + | 0.0172635i | ||||
\(304\) | 11.1247 | − | 17.1880i | 0.638045 | − | 0.985801i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.11170 | + | 1.31758i | 0.520881 | + | 0.0753208i | ||||
\(307\) | 23.1194i | 1.31949i | 0.751488 | + | 0.659747i | \(0.229336\pi\) | ||||
−0.751488 | + | 0.659747i | \(0.770664\pi\) | |||||||
\(308\) | 14.9299 | − | 11.4743i | 0.850710 | − | 0.653807i | ||||
\(309\) | 31.6317 | − | 10.2778i | 1.79947 | − | 0.584682i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.30515 | − | 10.1722i | 0.187418 | − | 0.576813i | −0.812564 | − | 0.582872i | \(-0.801929\pi\) |
0.999982 | + | 0.00605932i | \(0.00192875\pi\) | |||||||
\(312\) | 44.3012 | + | 20.3615i | 2.50806 | + | 1.15274i | ||||
\(313\) | 2.15115 | + | 6.62056i | 0.121590 | + | 0.374216i | 0.993264 | − | 0.115870i | \(-0.0369655\pi\) |
−0.871674 | + | 0.490086i | \(0.836965\pi\) | |||||||
\(314\) | −5.12718 | − | 9.73613i | −0.289343 | − | 0.549441i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.8317 | + | 6.32989i | −1.00311 | + | 0.356084i | ||||
\(317\) | −1.64686 | − | 2.26671i | −0.0924971 | − | 0.127311i | 0.760260 | − | 0.649619i | \(-0.225071\pi\) |
−0.852757 | + | 0.522307i | \(0.825071\pi\) | |||||||
\(318\) | 4.68706 | + | 4.56244i | 0.262837 | + | 0.255849i | ||||
\(319\) | −11.8694 | + | 8.62360i | −0.664557 | + | 0.482829i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.4057 | − | 22.0911i | −1.69708 | − | 1.23300i | ||||
\(322\) | −0.668177 | − | 3.87967i | −0.0372361 | − | 0.216206i | ||||
\(323\) | −9.46919 | − | 3.07673i | −0.526880 | − | 0.171194i | ||||
\(324\) | −0.422428 | − | 15.6738i | −0.0234682 | − | 0.870764i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.6647 | − | 23.2838i | 1.25528 | − | 1.28957i | ||||
\(327\) | 6.73201 | − | 20.7190i | 0.372281 | − | 1.14576i | ||||
\(328\) | 10.0797 | − | 2.01700i | 0.556557 | − | 0.111370i | ||||
\(329\) | −2.67317 | − | 1.94217i | −0.147376 | − | 0.107075i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6066 | − | 21.4807i | −0.857819 | − | 1.18069i | −0.982085 | − | 0.188437i | \(-0.939658\pi\) |
0.124266 | − | 0.992249i | \(-0.460342\pi\) | |||||||
\(332\) | −16.0845 | + | 0.433498i | −0.882753 | + | 0.0237913i | ||||
\(333\) | 17.4413 | + | 24.0060i | 0.955780 | + | 1.31552i | ||||
\(334\) | −7.55912 | + | 15.3432i | −0.413616 | + | 0.839540i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −34.9374 | − | 9.30419i | −1.90599 | − | 0.507585i | ||||
\(337\) | 5.89820 | + | 18.1528i | 0.321295 | + | 0.988845i | 0.973085 | + | 0.230446i | \(0.0740184\pi\) |
−0.651790 | + | 0.758400i | \(0.725982\pi\) | |||||||
\(338\) | 21.1373 | − | 42.9035i | 1.14972 | − | 2.33364i | ||||
\(339\) | 14.1574 | + | 4.60001i | 0.768923 | + | 0.249838i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.31368 | − | 1.72652i | 0.287752 | − | 0.0934963i | ||||
\(342\) | 3.46703 | − | 23.9762i | 0.187475 | − | 1.29649i | ||||
\(343\) | −4.04448 | −0.218381 | ||||||||
\(344\) | 1.83208 | + | 0.214710i | 0.0987790 | + | 0.0115764i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.0385 | + | 3.79559i | −1.18480 | + | 0.204052i | ||||
\(347\) | −11.3134 | + | 15.5716i | −0.607336 | + | 0.835926i | −0.996355 | − | 0.0853039i | \(-0.972814\pi\) |
0.389019 | + | 0.921230i | \(0.372814\pi\) | |||||||
\(348\) | 27.0165 | + | 7.98018i | 1.44824 | + | 0.427782i | ||||
\(349\) | 0.0595710i | 0.00318876i | 0.999999 | + | 0.00159438i | \(0.000507507\pi\) | ||||
−0.999999 | + | 0.00159438i | \(0.999492\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.97629 | 0.318991 | ||||||||
\(352\) | −7.61408 | − | 12.7426i | −0.405832 | − | 0.679184i | ||||
\(353\) | −15.7539 | − | 11.4459i | −0.838497 | − | 0.609203i | 0.0834537 | − | 0.996512i | \(-0.473405\pi\) |
−0.921950 | + | 0.387308i | \(0.873405\pi\) | |||||||
\(354\) | 2.38244 | + | 13.8333i | 0.126625 | + | 0.735232i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.2372 | + | 17.2237i | 0.701569 | + | 0.912856i | ||||
\(357\) | 17.5821i | 0.930545i | ||||||||
\(358\) | 2.98907 | − | 20.6709i | 0.157977 | − | 1.09249i | ||||
\(359\) | −7.90364 | − | 24.3249i | −0.417138 | − | 1.28382i | −0.910324 | − | 0.413896i | \(-0.864168\pi\) |
0.493186 | − | 0.869924i | \(-0.335832\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.22468 | + | 6.84685i | −0.117088 | + | 0.360361i | ||||
\(362\) | 6.82974 | + | 3.36481i | 0.358963 | + | 0.176850i | ||||
\(363\) | −9.85725 | + | 3.20281i | −0.517371 | + | 0.168104i | ||||
\(364\) | −13.9090 | + | 47.0883i | −0.729032 | + | 2.46810i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.2856 | + | 20.8772i | −0.537636 | + | 1.09127i | ||||
\(367\) | −23.3737 | + | 16.9820i | −1.22010 | + | 0.886453i | −0.996108 | − | 0.0881385i | \(-0.971908\pi\) |
−0.223990 | + | 0.974592i | \(0.571908\pi\) | |||||||
\(368\) | −3.09900 | + | 0.167165i | −0.161546 | + | 0.00871409i | ||||
\(369\) | 9.84012 | − | 7.14927i | 0.512256 | − | 0.372176i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.87175 | + | 5.32901i | −0.201011 | + | 0.276669i | ||||
\(372\) | −8.84575 | − | 6.06956i | −0.458631 | − | 0.314692i | ||||
\(373\) | −23.6625 | − | 7.68840i | −1.22520 | − | 0.398090i | −0.376224 | − | 0.926529i | \(-0.622778\pi\) |
−0.848972 | + | 0.528438i | \(0.822778\pi\) | |||||||
\(374\) | −5.03514 | + | 5.17268i | −0.260361 | + | 0.267473i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.76596 | + | 1.91481i | −0.0910724 | + | 0.0987486i | ||||
\(377\) | 11.8218 | − | 36.3839i | 0.608855 | − | 1.87386i | ||||
\(378\) | −4.36739 | + | 0.752174i | −0.224634 | + | 0.0386877i | ||||
\(379\) | 3.80553 | − | 5.23786i | 0.195477 | − | 0.269051i | −0.700016 | − | 0.714128i | \(-0.746824\pi\) |
0.895492 | + | 0.445077i | \(0.146824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.23244 | − | 7.20183i | −0.268066 | − | 0.368961i | ||||
\(382\) | 10.5060 | + | 10.2267i | 0.537535 | + | 0.523243i | ||||
\(383\) | −2.47525 | + | 1.79838i | −0.126480 | + | 0.0918928i | −0.649227 | − | 0.760595i | \(-0.724907\pi\) |
0.522747 | + | 0.852488i | \(0.324907\pi\) | |||||||
\(384\) | −10.4908 | + | 26.5013i | −0.535357 | + | 1.35239i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.901508 | − | 0.474746i | 0.0458855 | − | 0.0241640i | ||||
\(387\) | 2.07579 | − | 0.674465i | 0.105518 | − | 0.0342850i | ||||
\(388\) | 10.6317 | − | 3.77403i | 0.539742 | − | 0.191597i | ||||
\(389\) | −26.7250 | − | 8.68349i | −1.35501 | − | 0.440270i | −0.460637 | − | 0.887588i | \(-0.652379\pi\) |
−0.894375 | + | 0.447318i | \(0.852379\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.466377 | + | 1.43536i | 0.0235857 | + | 0.0725893i | ||||
\(392\) | 1.93344 | − | 16.4977i | 0.0976535 | − | 0.833259i | ||||
\(393\) | 16.9966 | 0.857367 | ||||||||
\(394\) | 1.20923 | − | 8.36241i | 0.0609200 | − | 0.421292i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.4826 | − | 9.93734i | −0.727780 | − | 0.499370i | ||||
\(397\) | 20.5622 | − | 28.3014i | 1.03199 | − | 1.42041i | 0.128539 | − | 0.991704i | \(-0.458971\pi\) |
0.903446 | − | 0.428701i | \(-0.141029\pi\) | |||||||
\(398\) | 16.4747 | − | 8.67581i | 0.825802 | − | 0.434879i | ||||
\(399\) | 46.2651 | 2.31615 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3727 | 0.667799 | 0.333900 | − | 0.942609i | \(-0.391635\pi\) | ||||
0.333900 | + | 0.942609i | \(0.391635\pi\) | |||||||
\(402\) | −15.5023 | + | 8.16373i | −0.773185 | + | 0.407170i | ||||
\(403\) | −8.56329 | + | 11.7864i | −0.426568 | + | 0.587120i | ||||
\(404\) | 0.334663 | + | 0.229631i | 0.0166501 | + | 0.0114246i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.05997 | + | 28.0767i | −0.201493 | + | 1.39342i | ||||
\(407\) | −23.2662 | −1.15326 | ||||||||
\(408\) | 13.7664 | + | 1.61334i | 0.681536 | + | 0.0798724i | ||||
\(409\) | −8.50186 | − | 26.1660i | −0.420390 | − | 1.29383i | −0.907340 | − | 0.420397i | \(-0.861891\pi\) |
0.486950 | − | 0.873430i | \(-0.338109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.7478 | − | 6.41645i | −0.974088 | − | 0.316500i | ||||
\(412\) | 24.8829 | − | 8.83294i | 1.22589 | − | 0.435168i | ||||
\(413\) | −13.4439 | + | 4.36820i | −0.661533 | + | 0.214945i | ||||
\(414\) | −3.24917 | + | 1.71106i | −0.159688 | + | 0.0840940i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.5927 | + | 15.2113i | 1.74507 | + | 0.745793i | ||||
\(417\) | 2.77612 | − | 2.01697i | 0.135947 | − | 0.0987713i | ||||
\(418\) | 13.6112 | + | 13.2493i | 0.665746 | + | 0.648046i | ||||
\(419\) | 23.3551 | + | 32.1455i | 1.14097 | + | 1.57041i | 0.765321 | + | 0.643648i | \(0.222580\pi\) |
0.375649 | + | 0.926762i | \(0.377420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.75042 | − | 3.78563i | 0.134047 | − | 0.184500i | −0.736717 | − | 0.676202i | \(-0.763625\pi\) |
0.870764 | + | 0.491701i | \(0.163625\pi\) | |||||||
\(422\) | 7.65919 | − | 1.31910i | 0.372843 | − | 0.0642130i | ||||
\(423\) | −0.952426 | + | 2.93127i | −0.0463085 | + | 0.142523i | ||||
\(424\) | 3.81721 | + | 3.52048i | 0.185380 | + | 0.170969i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.7848 | − | 14.1614i | 0.667877 | − | 0.686120i | ||||
\(427\) | −22.2901 | − | 7.24251i | −1.07870 | − | 0.350489i | ||||
\(428\) | −24.6023 | − | 16.8810i | −1.18920 | − | 0.815975i | ||||
\(429\) | −26.5880 | + | 36.5952i | −1.28368 | + | 1.76683i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.2735 | + | 11.8234i | −0.783869 | + | 0.569514i | −0.906138 | − | 0.422983i | \(-0.860983\pi\) |
0.122269 | + | 0.992497i | \(0.460983\pi\) | |||||||
\(432\) | 0.188180 | + | 3.48857i | 0.00905379 | + | 0.167844i | ||||
\(433\) | 1.13838 | − | 0.827085i | 0.0547073 | − | 0.0397472i | −0.560096 | − | 0.828428i | \(-0.689236\pi\) |
0.614803 | + | 0.788681i | \(0.289236\pi\) | |||||||
\(434\) | 4.77451 | − | 9.69108i | 0.229184 | − | 0.465187i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.89934 | − | 16.5865i | 0.234636 | − | 0.794348i | ||||
\(437\) | 3.77696 | − | 1.22721i | 0.180677 | − | 0.0587054i | ||||
\(438\) | −47.3909 | − | 23.3481i | −2.26443 | − | 1.11562i | ||||
\(439\) | 4.33963 | − | 13.3560i | 0.207119 | − | 0.637447i | −0.792500 | − | 0.609871i | \(-0.791221\pi\) |
0.999620 | − | 0.0275762i | \(-0.00877888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.07349 | − | 18.6923i | −0.289214 | − | 0.890109i | ||||
\(442\) | 2.69385 | − | 18.6293i | 0.128133 | − | 0.886105i | ||||
\(443\) | − | 9.37158i | − | 0.445257i | −0.974903 | − | 0.222629i | \(-0.928536\pi\) | ||
0.974903 | − | 0.222629i | \(-0.0714637\pi\) | |||||||
\(444\) | 27.2226 | + | 35.4210i | 1.29193 | + | 1.68101i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.88880 | − | 28.3861i | −0.231491 | − | 1.34412i | ||||
\(447\) | 19.2863 | + | 14.0123i | 0.912210 | + | 0.662759i | ||||
\(448\) | −27.9251 | − | 6.63650i | −1.31934 | − | 0.313545i | ||||
\(449\) | −27.0993 | −1.27889 | −0.639447 | − | 0.768835i | \(-0.720837\pi\) | ||||
−0.639447 | + | 0.768835i | \(0.720837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.53690i | 0.449075i | ||||||||
\(452\) | 11.3336 | + | 3.34774i | 0.533088 | + | 0.157464i | ||||
\(453\) | 11.8395 | − | 16.2957i | 0.556269 | − | 0.765638i | ||||
\(454\) | −22.0605 | + | 3.79938i | −1.03535 | + | 0.178314i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.24530 | − | 36.2244i | 0.198804 | − | 1.69636i | ||||
\(457\) | −32.1890 | −1.50574 | −0.752869 | − | 0.658170i | \(-0.771331\pi\) | ||||
−0.752869 | + | 0.658170i | \(0.771331\pi\) | |||||||
\(458\) | 1.29675 | − | 8.96768i | 0.0605932 | − | 0.419032i | ||||
\(459\) | 1.61580 | − | 0.525005i | 0.0754190 | − | 0.0245051i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.49963 | + | 0.812178i | 0.116419 | + | 0.0378269i | 0.366647 | − | 0.930360i | \(-0.380506\pi\) |
−0.250228 | + | 0.968187i | \(0.580506\pi\) | |||||||
\(462\) | 14.8243 | − | 30.0896i | 0.689687 | − | 1.39990i | ||||
\(463\) | 9.34875 | + | 28.7725i | 0.434473 | + | 1.33717i | 0.893625 | + | 0.448814i | \(0.148153\pi\) |
−0.459152 | + | 0.888358i | \(0.651847\pi\) | |||||||
\(464\) | 21.6108 | + | 5.75518i | 1.00326 | + | 0.267178i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.9921 | − | 22.3113i | 0.509201 | − | 1.03355i | ||||
\(467\) | 24.2441 | + | 33.3692i | 1.12188 | + | 1.54414i | 0.802635 | + | 0.596471i | \(0.203431\pi\) |
0.319250 | + | 0.947671i | \(0.396569\pi\) | |||||||
\(468\) | 45.7826 | − | 1.23390i | 2.11630 | − | 0.0570371i | ||||
\(469\) | −10.3708 | − | 14.2742i | −0.478879 | − | 0.659120i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.8582 | − | 11.5216i | −0.730705 | − | 0.530889i | ||||
\(472\) | 2.18657 | + | 10.9271i | 0.100645 | + | 0.502960i | ||||
\(473\) | −0.528839 | + | 1.62760i | −0.0243160 | + | 0.0748371i | ||||
\(474\) | −23.5113 | + | 24.1535i | −1.07991 | + | 1.10941i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.376053 | + | 13.9531i | 0.0172364 | + | 0.639538i | ||||
\(477\) | 5.84354 | + | 1.89868i | 0.267557 | + | 0.0869346i | ||||
\(478\) | −2.02536 | − | 11.7600i | −0.0926378 | − | 0.537888i | ||||
\(479\) | −12.7715 | − | 9.27902i | −0.583544 | − | 0.423969i | 0.256456 | − | 0.966556i | \(-0.417445\pi\) |
−0.840000 | + | 0.542586i | \(0.817445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.0813 | − | 35.6596i | 2.23791 | − | 1.62594i | ||||
\(482\) | 3.53104 | + | 3.43715i | 0.160834 | + | 0.156558i | ||||
\(483\) | −4.12211 | − | 5.67360i | −0.187563 | − | 0.258158i | ||||
\(484\) | −7.75416 | + | 2.75257i | −0.352462 | + | 0.125117i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.7412 | − | 27.9925i | −0.668676 | − | 1.26977i | ||||
\(487\) | −11.0724 | − | 34.0773i | −0.501738 | − | 1.54419i | −0.806187 | − | 0.591661i | \(-0.798472\pi\) |
0.304449 | − | 0.952529i | \(-0.401528\pi\) | |||||||
\(488\) | −7.71605 | + | 16.7880i | −0.349289 | + | 0.759959i | ||||
\(489\) | 17.8870 | − | 55.0505i | 0.808877 | − | 2.48947i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.10672 | + | 2.30911i | −0.320722 | + | 0.104209i | −0.464954 | − | 0.885335i | \(-0.653929\pi\) |
0.144232 | + | 0.989544i | \(0.453929\pi\) | |||||||
\(492\) | 14.5192 | − | 11.1586i | 0.654575 | − | 0.503069i | ||||
\(493\) | − | 10.8756i | − | 0.489811i | ||||||
\(494\) | −49.0205 | − | 7.08850i | −2.20554 | − | 0.318927i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.14976 | − | 4.62757i | −0.321034 | − | 0.207784i | ||||
\(497\) | 16.1009 | + | 11.6980i | 0.722226 | + | 0.524728i | ||||
\(498\) | −25.3615 | + | 13.3557i | −1.13647 | + | 0.598483i | ||||
\(499\) | − | 1.61567i | − | 0.0723272i | −0.999346 | − | 0.0361636i | \(-0.988486\pi\) | ||
0.999346 | − | 0.0361636i | \(-0.0115137\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.4692i | 1.36126i | ||||||||
\(502\) | 11.1212 | + | 21.1183i | 0.496363 | + | 0.942555i | ||||
\(503\) | 24.0283 | + | 17.4576i | 1.07137 | + | 0.778395i | 0.976158 | − | 0.217062i | \(-0.0696473\pi\) |
0.0952114 | + | 0.995457i | \(0.469647\pi\) | |||||||
\(504\) | −33.3020 | + | 6.66391i | −1.48339 | + | 0.296834i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.412069 | − | 2.84966i | 0.0183187 | − | 0.126683i | ||||
\(507\) | − | 85.1999i | − | 3.78386i | ||||||
\(508\) | −4.30647 | − | 5.60342i | −0.191069 | − | 0.248612i | ||||
\(509\) | 1.21315 | − | 0.394177i | 0.0537721 | − | 0.0174716i | −0.282007 | − | 0.959412i | \(-0.591000\pi\) |
0.335780 | + | 0.941941i | \(0.391000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.4404 | − | 50.5983i | 0.727279 | − | 2.23834i | ||||
\(512\) | −7.75863 | + | 21.2557i | −0.342886 | + | 0.939377i | ||||
\(513\) | −1.38148 | − | 4.25176i | −0.0609939 | − | 0.187720i | ||||
\(514\) | 5.53856 | − | 2.91668i | 0.244295 | − | 0.128649i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.09666 | − | 1.09925i | 0.136323 | − | 0.0483918i | ||||
\(517\) | −1.42047 | − | 1.95511i | −0.0624722 | − | 0.0859855i | ||||
\(518\) | −31.3798 | + | 32.2369i | −1.37875 | + | 1.41641i | ||||
\(519\) | −32.2290 | + | 23.4157i | −1.41469 | + | 1.02784i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.44563 | + | 6.86265i | 0.413821 | + | 0.300658i | 0.775147 | − | 0.631781i | \(-0.217676\pi\) |
−0.361326 | + | 0.932440i | \(0.617676\pi\) | |||||||
\(522\) | 26.0779 | − | 4.49128i | 1.14140 | − | 0.196578i | ||||
\(523\) | 19.1314 | + | 6.21617i | 0.836558 | + | 0.271814i | 0.695805 | − | 0.718230i | \(-0.255048\pi\) |
0.140753 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(524\) | 13.4884 | − | 0.363531i | 0.589245 | − | 0.0158809i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.4423 | − | 12.1115i | −0.542512 | − | 0.528087i | ||||
\(527\) | −1.27984 | + | 3.93893i | −0.0557505 | + | 0.171582i | ||||
\(528\) | −22.1991 | − | 14.3681i | −0.966093 | − | 0.625289i | ||||
\(529\) | 18.1204 | + | 13.1652i | 0.787842 | + | 0.572401i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.75031 | + | 10.6674i | 0.336335 | + | 0.462925i | ||||
\(532\) | 36.7157 | − | 0.989534i | 1.59183 | − | 0.0429018i | ||||
\(533\) | −14.6170 | − | 20.1186i | −0.633133 | − | 0.871432i | ||||
\(534\) | 34.7126 | + | 17.1019i | 1.50216 | + | 0.740070i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.1279 | + | 6.81026i | −0.523847 | + | 0.294158i | ||||
\(537\) | −11.4973 | − | 35.3850i | −0.496144 | − | 1.52697i | ||||
\(538\) | 36.4106 | + | 17.9384i | 1.56977 | + | 0.773380i | ||||
\(539\) | 14.6564 | + | 4.76215i | 0.631295 | + | 0.205120i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0637 | + | 6.19417i | −0.819612 | + | 0.266308i | −0.688664 | − | 0.725081i | \(-0.741802\pi\) |
−0.130949 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(542\) | −5.13208 | − | 0.742113i | −0.220442 | − | 0.0318765i | ||||
\(543\) | 13.5628 | 0.582036 | ||||||||
\(544\) | 10.9594 | + | 0.985901i | 0.469881 | + | 0.0422701i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.8452 | + | 86.1965i | 0.635316 | + | 3.68887i | ||||
\(547\) | 22.5997 | − | 31.1058i | 0.966293 | − | 1.32999i | 0.0223953 | − | 0.999749i | \(-0.492871\pi\) |
0.943897 | − | 0.330239i | \(-0.107129\pi\) | |||||||
\(548\) | −15.8090 | − | 4.66969i | −0.675327 | − | 0.199479i | ||||
\(549\) | 21.8619i | 0.933041i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.6176 | −1.21915 | ||||||||
\(552\) | −4.82053 | + | 2.70690i | −0.205175 | + | 0.115213i | ||||
\(553\) | −27.4617 | − | 19.9521i | −1.16779 | − | 0.848448i | ||||
\(554\) | −5.55455 | + | 0.956633i | −0.235990 | + | 0.0406434i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.15997 | − | 1.66003i | 0.0916032 | − | 0.0704010i | ||||
\(557\) | 10.9707i | 0.464844i | 0.972615 | + | 0.232422i | \(0.0746650\pi\) | ||||
−0.972615 | + | 0.232422i | \(0.925335\pi\) | |||||||
\(558\) | −9.97347 | − | 1.44219i | −0.422211 | − | 0.0610528i | ||||
\(559\) | −1.37897 | − | 4.24405i | −0.0583244 | − | 0.179504i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.97373 | + | 12.2299i | −0.167771 | + | 0.516346i | ||||
\(562\) | −17.7721 | + | 36.0731i | −0.749672 | + | 1.52165i | ||||
\(563\) | −1.00145 | + | 0.325391i | −0.0422061 | + | 0.0137136i | −0.330044 | − | 0.943966i | \(-0.607064\pi\) |
0.287838 | + | 0.957679i | \(0.407064\pi\) | |||||||
\(564\) | −1.31448 | + | 4.45012i | −0.0553498 | + | 0.187384i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.5591 | − | 8.15816i | −0.696030 | − | 0.342913i | ||||
\(567\) | 22.7559 | − | 16.5331i | 0.955658 | − | 0.694326i | ||||
\(568\) | 10.6367 | − | 11.5332i | 0.446305 | − | 0.483923i | ||||
\(569\) | −16.4403 | + | 11.9446i | −0.689213 | + | 0.500743i | −0.876401 | − | 0.481581i | \(-0.840063\pi\) |
0.187188 | + | 0.982324i | \(0.440063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.81803 | − | 12.1370i | 0.369023 | − | 0.507917i | −0.583612 | − | 0.812033i | \(-0.698361\pi\) |
0.952635 | + | 0.304116i | \(0.0983610\pi\) | |||||||
\(572\) | −20.3174 | + | 29.6104i | −0.849511 | + | 1.23807i | ||||
\(573\) | 24.8396 | + | 8.07089i | 1.03769 | + | 0.337166i | ||||
\(574\) | 13.2140 | + | 12.8627i | 0.551543 | + | 0.536878i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.16186 | + | 26.6861i | 0.0900776 | + | 1.11192i | ||||
\(577\) | −8.80026 | + | 27.0844i | −0.366360 | + | 1.12754i | 0.582765 | + | 0.812640i | \(0.301971\pi\) |
−0.949125 | + | 0.314899i | \(0.898029\pi\) | |||||||
\(578\) | 3.17228 | + | 18.4194i | 0.131950 | + | 0.766146i | ||||
\(579\) | 1.06683 | − | 1.46837i | 0.0443361 | − | 0.0610235i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.9664 | − | 23.3523i | −0.703885 | − | 0.968815i | ||||
\(582\) | 14.0180 | − | 14.4009i | 0.581065 | − | 0.596937i | ||||
\(583\) | −3.89755 | + | 2.83173i | −0.161420 | + | 0.117278i | ||||
\(584\) | −38.1086 | − | 17.5153i | −1.57694 | − | 0.724789i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.8164 | + | 33.8321i | 0.735990 | + | 1.39759i | ||||
\(587\) | −32.9333 | + | 10.7007i | −1.35930 | + | 0.441664i | −0.895810 | − | 0.444438i | \(-0.853403\pi\) |
−0.463491 | + | 0.886101i | \(0.653403\pi\) | |||||||
\(588\) | −9.89865 | − | 27.8851i | −0.408213 | − | 1.14996i | ||||
\(589\) | 10.3648 | + | 3.36772i | 0.427073 | + | 0.138764i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.65121 | − | 14.3150i | −0.191325 | − | 0.588839i | ||||
\(592\) | 22.3613 | + | 27.5277i | 0.919042 | + | 1.13138i | ||||
\(593\) | −34.9925 | −1.43697 | −0.718484 | − | 0.695543i | \(-0.755164\pi\) | ||||
−0.718484 | + | 0.695543i | \(0.755164\pi\) | |||||||
\(594\) | −3.20789 | − | 0.463870i | −0.131621 | − | 0.0190328i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.6052 | + | 10.7076i | 0.639213 | + | 0.438600i | ||||
\(597\) | 19.4960 | − | 26.8339i | 0.797918 | − | 1.09824i | ||||
\(598\) | 3.49834 | + | 6.64308i | 0.143058 | + | 0.271656i | ||||
\(599\) | −17.7341 | −0.724596 | −0.362298 | − | 0.932062i | \(-0.618008\pi\) | ||||
−0.362298 | + | 0.932062i | \(0.618008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.01505 | −0.0821957 | −0.0410979 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410979 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(602\) | 1.54189 | + | 2.92793i | 0.0628427 | + | 0.119334i | ||||
\(603\) | −9.67370 | + | 13.3147i | −0.393943 | + | 0.542217i | ||||
\(604\) | 9.04723 | − | 13.1854i | 0.368127 | − | 0.536506i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.715569 | + | 0.103473i | 0.0290680 | + | 0.00420331i | ||||
\(607\) | 39.1971 | 1.59096 | 0.795481 | − | 0.605979i | \(-0.207218\pi\) | ||||
0.795481 | + | 0.605979i | \(0.207218\pi\) | |||||||
\(608\) | 2.59427 | − | 28.8382i | 0.105211 | − | 1.16955i | ||||
\(609\) | 15.6164 | + | 48.0624i | 0.632809 | + | 1.94759i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.99311 | + | 1.94728i | 0.242455 | + | 0.0787785i | ||||
\(612\) | 12.2698 | − | 4.35552i | 0.495977 | − | 0.176062i | ||||
\(613\) | −20.4908 | + | 6.65786i | −0.827615 | + | 0.268909i | −0.692041 | − | 0.721859i | \(-0.743288\pi\) |
−0.135575 | + | 0.990767i | \(0.543288\pi\) | |||||||
\(614\) | 15.2347 | + | 28.9295i | 0.614822 | + | 1.16750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1209 | − | 24.1960i | 0.448073 | − | 0.974886i | ||||
\(617\) | 24.1235 | − | 17.5267i | 0.971175 | − | 0.705600i | 0.0154563 | − | 0.999881i | \(-0.495080\pi\) |
0.955719 | + | 0.294280i | \(0.0950799\pi\) | |||||||
\(618\) | 32.8085 | − | 33.7046i | 1.31975 | − | 1.35580i | ||||
\(619\) | −2.86875 | − | 3.94849i | −0.115305 | − | 0.158703i | 0.747464 | − | 0.664303i | \(-0.231271\pi\) |
−0.862768 | + | 0.505599i | \(0.831271\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.398318 | + | 0.548237i | −0.0159839 | + | 0.0220000i | ||||
\(622\) | −2.56728 | − | 14.9065i | −0.102939 | − | 0.597698i | ||||
\(623\) | −12.0421 | + | 37.0619i | −0.482458 | + | 1.48485i | ||||
\(624\) | 68.8518 | − | 3.71399i | 2.75628 | − | 0.148678i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.05442 | + | 6.86685i | 0.281951 | + | 0.274455i | ||||
\(627\) | 32.1813 | + | 10.4564i | 1.28520 | + | 0.417587i | ||||
\(628\) | −12.8314 | − | 8.80432i | −0.512028 | − | 0.351331i | ||||
\(629\) | 10.1374 | − | 13.9529i | 0.404205 | − | 0.556340i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.3860 | + | 8.99897i | −0.493080 | + | 0.358243i | −0.806367 | − | 0.591415i | \(-0.798570\pi\) |
0.313288 | + | 0.949658i | \(0.398570\pi\) | |||||||
\(632\) | −18.1419 | + | 19.6710i | −0.721644 | + | 0.782469i | ||||
\(633\) | 11.2007 | − | 8.13781i | 0.445189 | − | 0.323449i | ||||
\(634\) | −3.55441 | − | 1.75115i | −0.141163 | − | 0.0695470i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.87141 | + | 2.62045i | 0.351774 | + | 0.103908i | ||||
\(637\) | −38.2172 | + | 12.4175i | −1.51422 | + | 0.492001i | ||||
\(638\) | −9.16967 | + | 18.6122i | −0.363031 | + | 0.736864i | ||||
\(639\) | 5.73663 | − | 17.6555i | 0.226937 | − | 0.698442i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.46226 | − | 7.57805i | −0.0972533 | − | 0.299315i | 0.890581 | − | 0.454825i | \(-0.150298\pi\) |
−0.987834 | + | 0.155510i | \(0.950298\pi\) | |||||||
\(642\) | −52.6041 | − | 7.60669i | −2.07612 | − | 0.300212i | ||||
\(643\) | 6.46830i | 0.255085i | 0.991833 | + | 0.127542i | \(0.0407089\pi\) | ||||
−0.991833 | + | 0.127542i | \(0.959291\pi\) | |||||||
\(644\) | −3.39263 | − | 4.41437i | −0.133689 | − | 0.173951i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.8763 | + | 2.38985i | −0.545956 | + | 0.0940274i | ||||
\(647\) | 12.1303 | + | 8.81321i | 0.476893 | + | 0.346483i | 0.800122 | − | 0.599838i | \(-0.204768\pi\) |
−0.323229 | + | 0.946321i | \(0.604768\pi\) | |||||||
\(648\) | −10.8569 | − | 19.3344i | −0.426500 | − | 0.759526i | ||||
\(649\) | −10.3387 | −0.405828 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 19.2450i | − | 0.754272i | ||||||
\(652\) | 13.0176 | − | 44.0703i | 0.509807 | − | 1.72593i | ||||
\(653\) | 22.6975 | − | 31.2404i | 0.888220 | − | 1.22253i | −0.0858552 | − | 0.996308i | \(-0.527362\pi\) |
0.974076 | − | 0.226223i | \(-0.0726378\pi\) | |||||||
\(654\) | −5.22910 | − | 30.3620i | −0.204474 | − | 1.18725i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.2837 | − | 9.16596i | 0.440554 | − | 0.357870i | ||||
\(657\) | −49.6261 | −1.93610 | ||||||||
\(658\) | −4.62476 | − | 0.668753i | −0.180292 | − | 0.0260707i | ||||
\(659\) | −32.1885 | + | 10.4587i | −1.25389 | + | 0.407412i | −0.859312 | − | 0.511452i | \(-0.829108\pi\) |
−0.394574 | + | 0.918864i | \(0.629108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.06103 | − | 0.344750i | −0.0412693 | − | 0.0134092i | 0.288310 | − | 0.957537i | \(-0.406907\pi\) |
−0.329579 | + | 0.944128i | \(0.606907\pi\) | |||||||
\(662\) | −33.6836 | − | 16.5949i | −1.30915 | − | 0.644979i | ||||
\(663\) | −10.3617 | − | 31.8900i | −0.402415 | − | 1.23851i | ||||
\(664\) | −19.8411 | + | 11.1415i | −0.769983 | + | 0.432372i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 37.6434 | + | 18.5458i | 1.45865 | + | 0.718635i | ||||
\(667\) | 2.54977 | + | 3.50945i | 0.0987274 | + | 0.135887i | ||||
\(668\) | 0.651686 | + | 24.1802i | 0.0252145 | + | 0.935559i | ||||
\(669\) | −30.1599 | − | 41.5116i | −1.16605 | − | 1.60493i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8678 | − | 10.0756i | −0.535362 | − | 0.388963i | ||||
\(672\) | −49.8485 | + | 11.3798i | −1.92295 | + | 0.438986i | ||||
\(673\) | 8.12719 | − | 25.0129i | 0.313280 | − | 0.964177i | −0.663177 | − | 0.748463i | \(-0.730792\pi\) |
0.976457 | − | 0.215714i | \(-0.0692079\pi\) | |||||||
\(674\) | 19.3424 | + | 18.8281i | 0.745040 | + | 0.725231i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.82229 | − | 67.6142i | −0.0700880 | − | 2.60054i | ||||
\(677\) | −16.8361 | − | 5.47038i | −0.647064 | − | 0.210244i | −0.0329450 | − | 0.999457i | \(-0.510489\pi\) |
−0.614119 | + | 0.789213i | \(0.710489\pi\) | |||||||
\(678\) | 20.7465 | − | 3.57306i | 0.796763 | − | 0.137223i | ||||
\(679\) | 16.3733 | + | 11.8959i | 0.628350 | + | 0.456523i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.2611 | + | 23.4391i | −1.23625 | + | 0.898188i | ||||
\(682\) | 5.51136 | − | 5.66190i | 0.211041 | − | 0.216805i | ||||
\(683\) | 26.8971 | + | 37.0207i | 1.02919 | + | 1.41656i | 0.905554 | + | 0.424230i | \(0.139455\pi\) |
0.123635 | + | 0.992328i | \(0.460545\pi\) | |||||||
\(684\) | −11.4610 | − | 32.2863i | −0.438222 | − | 1.23450i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.06089 | + | 2.66514i | −0.193226 | + | 0.101755i | ||||
\(687\) | −4.98787 | − | 15.3511i | −0.190299 | − | 0.585680i | ||||
\(688\) | 2.43398 | − | 0.938592i | 0.0927946 | − | 0.0357835i | ||||
\(689\) | 3.88194 | − | 11.9474i | 0.147890 | − | 0.455159i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.90130 | + | 1.91745i | −0.224496 | + | 0.0729432i | −0.419105 | − | 0.907938i | \(-0.637656\pi\) |
0.194609 | + | 0.980881i | \(0.437656\pi\) | |||||||
\(692\) | −25.0759 | + | 19.2719i | −0.953243 | + | 0.732608i | ||||
\(693\) | − | 31.5088i | − | 1.19692i | ||||||
\(694\) | −3.89558 | + | 26.9399i | −0.147874 | + | 1.02262i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 39.0646 | − | 7.81702i | 1.48074 | − | 0.296304i | ||||
\(697\) | −5.71935 | − | 4.15535i | −0.216636 | − | 0.157395i | ||||
\(698\) | 0.0392547 | + | 0.0745417i | 0.00148581 | + | 0.00282145i | ||||
\(699\) | − | 44.3069i | − | 1.67584i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.2933i | − | 0.804238i | −0.915587 | − | 0.402119i | \(-0.868274\pi\) | ||
0.915587 | − | 0.402119i | \(-0.131726\pi\) | |||||||
\(702\) | 7.47818 | − | 3.93812i | 0.282246 | − | 0.148635i | ||||
\(703\) | −36.7153 | − | 26.6752i | −1.38474 | − | 1.00608i | ||||
\(704\) | −17.9244 | − | 10.9276i | −0.675552 | − | 0.411850i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.2554 | − | 3.94120i | −1.02577 | − | 0.148329i | ||||
\(707\) | 0.728101i | 0.0273831i | ||||||||
\(708\) | 12.0967 | + | 15.7398i | 0.454623 | + | 0.591539i | ||||
\(709\) | 10.0050 | − | 3.25084i | 0.375747 | − | 0.122088i | −0.115054 | − | 0.993359i | \(-0.536704\pi\) |
0.490801 | + | 0.871272i | \(0.336704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.78435 | + | 30.1131i | −0.366942 | + | 1.12933i | ||||
\(712\) | 27.9135 | + | 12.8295i | 1.04610 | + | 0.480806i | ||||
\(713\) | −0.510486 | − | 1.57111i | −0.0191178 | − | 0.0588387i | ||||
\(714\) | 11.5859 | + | 22.0007i | 0.433590 | + | 0.823355i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.88100 | − | 27.8354i | −0.369270 | − | 1.04026i | ||||
\(717\) | −12.4948 | − | 17.1977i | −0.466628 | − | 0.642258i | ||||
\(718\) | −25.9190 | − | 25.2298i | −0.967287 | − | 0.941569i | ||||
\(719\) | −5.42565 | + | 3.94197i | −0.202343 | + | 0.147011i | −0.684342 | − | 0.729161i | \(-0.739911\pi\) |
0.482000 | + | 0.876171i | \(0.339911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.3209 | + | 27.8418i | 1.42715 | + | 1.03688i | ||||
\(722\) | 1.72802 | + | 10.0335i | 0.0643103 | + | 0.373408i | ||||
\(723\) | 8.34852 | + | 2.71260i | 0.310485 | + | 0.100883i | ||||
\(724\) | 10.7634 | − | 0.290087i | 0.400018 | − | 0.0107810i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.2240 | + | 10.5032i | −0.379447 | + | 0.389811i | ||||
\(727\) | −13.0656 | + | 40.2119i | −0.484578 | + | 1.49138i | 0.348013 | + | 0.937490i | \(0.386857\pi\) |
−0.832591 | + | 0.553888i | \(0.813143\pi\) | |||||||
\(728\) | 13.6247 | + | 68.0875i | 0.504964 | + | 2.52349i | ||||
\(729\) | −26.5667 | − | 19.3018i | −0.983951 | − | 0.714882i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.745662 | − | 1.02632i | −0.0275793 | − | 0.0379597i | ||||
\(732\) | 0.886740 | + | 32.9016i | 0.0327749 | + | 1.21608i | ||||
\(733\) | −15.7936 | − | 21.7381i | −0.583351 | − | 0.802914i | 0.410707 | − | 0.911768i | \(-0.365282\pi\) |
−0.994058 | + | 0.108854i | \(0.965282\pi\) | |||||||
\(734\) | −18.0573 | + | 36.6520i | −0.666509 | + | 1.35285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.76765 | + | 2.25128i | −0.138877 | + | 0.0829833i | ||||
\(737\) | −3.98768 | − | 12.2728i | −0.146888 | − | 0.452075i | ||||
\(738\) | 7.60198 | − | 15.4302i | 0.279833 | − | 0.567992i | ||||
\(739\) | 13.3854 | + | 4.34919i | 0.492391 | + | 0.159988i | 0.544679 | − | 0.838644i | \(-0.316651\pi\) |
−0.0522881 | + | 0.998632i | \(0.516651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −83.9145 | + | 27.2655i | −3.08268 | + | 1.00162i | ||||
\(742\) | −1.33317 | + | 9.21956i | −0.0489423 | + | 0.338461i | ||||
\(743\) | 43.2190 | 1.58555 | 0.792776 | − | 0.609513i | \(-0.208635\pi\) | ||||
0.792776 | + | 0.609513i | \(0.208635\pi\) | |||||||
\(744\) | −15.0684 | − | 1.76593i | −0.552433 | − | 0.0647422i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.6754 | + | 5.97197i | −1.26956 | + | 0.218650i | ||||
\(747\) | −15.8260 | + | 21.7826i | −0.579042 | + | 0.796983i | ||||
\(748\) | −2.89195 | + | 9.79056i | −0.105740 | + | 0.357978i | ||||
\(749\) | − | 53.5254i | − | 1.95577i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.24240 | −0.118317 | −0.0591584 | − | 0.998249i | \(-0.518842\pi\) | ||||
−0.0591584 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(752\) | −0.947987 | + | 3.55971i | −0.0345695 | + | 0.129809i | ||||
\(753\) | 34.3974 | + | 24.9912i | 1.25351 | + | 0.910728i | ||||
\(754\) | −9.18262 | − | 53.3176i | −0.334411 | − | 1.94171i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.96930 | + | 3.81912i | −0.180732 | + | 0.138900i | ||||
\(757\) | − | 25.4279i | − | 0.924193i | −0.886830 | − | 0.462096i | \(-0.847097\pi\) | ||
0.886830 | − | 0.462096i | \(-0.152903\pi\) | |||||||
\(758\) | 1.31037 | − | 9.06187i | 0.0475948 | − | 0.329142i | ||||
\(759\) | −1.58500 | − | 4.87812i | −0.0575317 | − | 0.177064i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.54324 | − | 17.0603i | 0.200942 | − | 0.618437i | −0.798913 | − | 0.601446i | \(-0.794591\pi\) |
0.999856 | − | 0.0169909i | \(-0.00540862\pi\) | |||||||
\(762\) | −11.2931 | − | 5.56377i | −0.409106 | − | 0.201554i | ||||
\(763\) | 29.5074 | − | 9.58753i | 1.06824 | − | 0.347092i | ||||
\(764\) | 19.8852 | + | 5.87373i | 0.719422 | + | 0.212504i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.91226 | + | 3.88141i | −0.0690926 | + | 0.140241i | ||||
\(767\) | 21.8100 | − | 15.8459i | 0.787512 | − | 0.572161i | ||||
\(768\) | 4.33597 | + | 40.0743i | 0.156461 | + | 1.44606i | ||||
\(769\) | 9.85987 | − | 7.16362i | 0.355556 | − | 0.258327i | −0.395640 | − | 0.918406i | \(-0.629477\pi\) |
0.751196 | + | 0.660079i | \(0.229477\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.55427 | − | 9.02118i | 0.236046 | − | 0.324890i | ||||
\(772\) | 0.815228 | − | 1.18811i | 0.0293407 | − | 0.0427610i | ||||
\(773\) | 19.3807 | + | 6.29718i | 0.697076 | + | 0.226494i | 0.636056 | − | 0.771643i | \(-0.280565\pi\) |
0.0610199 | + | 0.998137i | \(0.480565\pi\) | |||||||
\(774\) | 2.15301 | − | 2.21182i | 0.0773884 | − | 0.0795022i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.8166 | − | 11.7283i | 0.388294 | − | 0.421022i | ||||
\(777\) | −24.7649 | + | 76.2186i | −0.888437 | + | 2.73433i | ||||
\(778\) | −39.1633 | + | 6.74491i | −1.40407 | + | 0.241817i | ||||
\(779\) | −10.9343 | + | 15.0497i | −0.391761 | + | 0.539213i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.55573 | + | 11.7760i | 0.306148 | + | 0.421377i | ||||
\(782\) | 1.52942 | + | 1.48876i | 0.0546920 | + | 0.0532379i | ||||
\(783\) | 3.95063 | − | 2.87030i | 0.141184 | − | 0.102576i | ||||
\(784\) | −8.45193 | − | 21.9178i | −0.301855 | − | 0.782777i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.2681 | − | 11.2001i | 0.758607 | − | 0.399493i | ||||
\(787\) | 1.87380 | − | 0.608835i | 0.0667938 | − | 0.0217026i | −0.275430 | − | 0.961321i | \(-0.588820\pi\) |
0.342223 | + | 0.939619i | \(0.388820\pi\) | |||||||
\(788\) | −3.99735 | − | 11.2608i | −0.142400 | − | 0.401149i | ||||
\(789\) | −29.4177 | − | 9.55840i | −1.04730 | − | 0.340288i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.55119 | + | 20.1625i | 0.232934 | + | 0.716896i | ||||
\(792\) | −24.6705 | − | 2.89126i | −0.876630 | − | 0.102736i | ||||
\(793\) | 44.6976 | 1.58726 | ||||||||
\(794\) | 7.08024 | − | 48.9634i | 0.251268 | − | 1.73765i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.8980 | − | 21.7122i | 0.528045 | − | 0.769570i | ||||
\(797\) | −13.3592 | + | 18.3873i | −0.473206 | + | 0.651313i | −0.977182 | − | 0.212405i | \(-0.931870\pi\) |
0.503975 | + | 0.863718i | \(0.331870\pi\) | |||||||
\(798\) | 57.8919 | − | 30.4867i | 2.04935 | − | 1.07922i | ||||
\(799\) | 1.79141 | 0.0633756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.3498 | 1.28436 | ||||||||
\(802\) | 16.7334 | − | 8.81201i | 0.590875 | − | 0.311163i | ||||
\(803\) | 22.8714 | − | 31.4798i | 0.807114 | − | 1.11090i | ||||
\(804\) | −14.0186 | + | 20.4307i | −0.494399 | + | 0.720536i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.94863 | + | 20.3912i | −0.103861 | + | 0.718250i | ||||
\(807\) | 72.3059 | 2.54529 | ||||||||
\(808\) | 0.570085 | + | 0.0668109i | 0.0200555 | + | 0.00235040i | ||||
\(809\) | 15.7618 | + | 48.5099i | 0.554156 | + | 1.70552i | 0.698163 | + | 0.715939i | \(0.254001\pi\) |
−0.144007 | + | 0.989577i | \(0.545999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.6096 | + | 13.8447i | 1.49622 | + | 0.486153i | 0.938914 | − | 0.344152i | \(-0.111834\pi\) |
0.557310 | + | 0.830305i | \(0.311834\pi\) | |||||||
\(812\) | 13.4211 | + | 37.8080i | 0.470987 | + | 1.32680i | ||||
\(813\) | −8.78521 | + | 2.85449i | −0.308111 | + | 0.100111i | ||||
\(814\) | −29.1132 | + | 15.3314i | −1.02042 | + | 0.537366i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18.2891 | − | 7.05264i | 0.640246 | − | 0.246892i | ||||
\(817\) | −2.70061 | + | 1.96211i | −0.0944826 | + | 0.0686456i | ||||
\(818\) | −27.8808 | − | 27.1395i | −0.974828 | − | 0.948909i | ||||
\(819\) | 48.2928 | + | 66.4694i | 1.68749 | + | 2.32263i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5666 | − | 22.8020i | 0.578180 | − | 0.795796i | −0.415314 | − | 0.909678i | \(-0.636328\pi\) |
0.993494 | + | 0.113881i | \(0.0363284\pi\) | |||||||
\(822\) | −28.9388 | + | 4.98399i | −1.00936 | + | 0.173837i | ||||
\(823\) | 1.11758 | − | 3.43957i | 0.0389565 | − | 0.119896i | −0.929687 | − | 0.368350i | \(-0.879923\pi\) |
0.968644 | + | 0.248455i | \(0.0799227\pi\) | |||||||
\(824\) | 25.3157 | − | 27.4495i | 0.881916 | − | 0.956250i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.9441 | + | 14.3249i | −0.485176 | + | 0.498428i | ||||
\(827\) | −26.8330 | − | 8.71857i | −0.933075 | − | 0.303174i | −0.197255 | − | 0.980352i | \(-0.563203\pi\) |
−0.735819 | + | 0.677178i | \(0.763203\pi\) | |||||||
\(828\) | −2.93821 | + | 4.28213i | −0.102110 | + | 0.148814i | ||||
\(829\) | 31.0042 | − | 42.6736i | 1.07682 | − | 1.48212i | 0.213846 | − | 0.976867i | \(-0.431401\pi\) |
0.862974 | − | 0.505248i | \(-0.168599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.12292 | + | 5.90165i | −0.281781 | + | 0.204726i | ||||
\(832\) | 54.5610 | − | 4.42003i | 1.89156 | − | 0.153237i | ||||
\(833\) | −9.24188 | + | 6.71462i | −0.320212 | + | 0.232648i | ||||
\(834\) | 2.14469 | − | 4.35319i | 0.0742645 | − | 0.150739i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 25.7626 | + | 7.60980i | 0.891018 | + | 0.263190i | ||||
\(837\) | −1.76862 | + | 0.574659i | −0.0611324 | + | 0.0198631i | ||||
\(838\) | 50.4069 | + | 24.8340i | 1.74128 | + | 0.857876i | ||||
\(839\) | −2.76644 | + | 8.51422i | −0.0955081 | + | 0.293944i | −0.987386 | − | 0.158333i | \(-0.949388\pi\) |
0.891878 | + | 0.452277i | \(0.149388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.698169 | − | 2.14874i | −0.0240748 | − | 0.0740946i | ||||
\(842\) | 0.947061 | − | 6.54940i | 0.0326379 | − | 0.225707i | ||||
\(843\) | 71.6357i | 2.46726i | ||||||||
\(844\) | 8.71478 | − | 6.69768i | 0.299975 | − | 0.230544i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.739798 | + | 4.29553i | 0.0254348 | + | 0.147683i | ||||
\(847\) | −11.9418 | − | 8.67620i | −0.410324 | − | 0.298118i | ||||
\(848\) | 7.09635 | + | 1.88983i | 0.243690 | + | 0.0648971i | ||||
\(849\) | −32.8838 | −1.12857 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.87919i | 0.235816i | ||||||||
\(852\) | 7.91737 | − | 26.8039i | 0.271245 | − | 0.918285i | ||||
\(853\) | −18.5100 | + | 25.4769i | −0.633772 | + | 0.872312i | −0.998264 | − | 0.0588942i | \(-0.981243\pi\) |
0.364492 | + | 0.931206i | \(0.381243\pi\) | |||||||
\(854\) | −32.6644 | + | 5.62563i | −1.11775 | + | 0.192505i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41.9090 | − | 4.91151i | −1.43242 | − | 0.167872i | ||||
\(857\) | −47.9238 | −1.63705 | −0.818523 | − | 0.574473i | \(-0.805207\pi\) | ||||
−0.818523 | + | 0.574473i | \(0.805207\pi\) | |||||||
\(858\) | −9.15512 | + | 63.3123i | −0.312551 | + | 2.16145i | ||||
\(859\) | 25.9430 | − | 8.42940i | 0.885164 | − | 0.287607i | 0.169064 | − | 0.985605i | \(-0.445925\pi\) |
0.716100 | + | 0.697998i | \(0.245925\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.2423 | + | 10.1512i | 1.06473 | + | 0.345953i | ||||
\(862\) | −12.5721 | + | 25.5183i | −0.428208 | + | 0.869157i | ||||
\(863\) | 13.2070 | + | 40.6471i | 0.449573 | + | 1.38364i | 0.877390 | + | 0.479778i | \(0.159283\pi\) |
−0.427817 | + | 0.903865i | \(0.640717\pi\) | |||||||
\(864\) | 2.53429 | + | 4.24128i | 0.0862183 | + | 0.144291i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.879458 | − | 1.78509i | 0.0298852 | − | 0.0606597i | ||||
\(867\) | 19.5704 | + | 26.9364i | 0.664646 | + | 0.914807i | ||||
\(868\) | −0.411620 | − | 15.2727i | −0.0139713 | − | 0.518391i | ||||
\(869\) | −14.5926 | − | 20.0850i | −0.495020 | − | 0.681337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.2225 | + | 19.7783i | 0.922400 | + | 0.670163i | ||||
\(872\) | −4.79918 | − | 23.9833i | −0.162521 | − | 0.812176i | ||||
\(873\) | 5.83367 | − | 17.9542i | 0.197440 | − | 0.607657i | ||||
\(874\) | 3.91747 | − | 4.02447i | 0.132510 | − | 0.136130i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −74.6861 | + | 2.01289i | −2.52341 | + | 0.0680091i | ||||
\(877\) | 55.1526 | + | 17.9202i | 1.86237 | + | 0.605121i | 0.994023 | + | 0.109168i | \(0.0348187\pi\) |
0.868349 | + | 0.495953i | \(0.165181\pi\) | |||||||
\(878\) | −3.37081 | − | 19.5721i | −0.113759 | − | 0.660527i | ||||
\(879\) | 55.1055 | + | 40.0365i | 1.85866 | + | 1.35040i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.3649 | − | 10.4367i | 0.483965 | − | 0.351621i | −0.318894 | − | 0.947790i | \(-0.603311\pi\) |
0.802859 | + | 0.596169i | \(0.203311\pi\) | |||||||
\(882\) | −19.9172 | − | 19.3877i | −0.670648 | − | 0.652817i | ||||
\(883\) | −25.0162 | − | 34.4318i | −0.841861 | − | 1.15872i | −0.985598 | − | 0.169107i | \(-0.945912\pi\) |
0.143736 | − | 0.989616i | \(-0.454088\pi\) | |||||||
\(884\) | −8.90507 | − | 25.0861i | −0.299510 | − | 0.843738i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.17547 | − | 11.7267i | −0.207469 | − | 0.393968i | ||||
\(887\) | 12.2612 | + | 37.7360i | 0.411689 | + | 1.26705i | 0.915179 | + | 0.403048i | \(0.132049\pi\) |
−0.503489 | + | 0.864001i | \(0.667951\pi\) | |||||||
\(888\) | 57.4047 | + | 26.3841i | 1.92638 | + | 0.885394i | ||||
\(889\) | 3.91768 | − | 12.0574i | 0.131395 | − | 0.404392i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.5653 | − | 6.35716i | 0.655463 | − | 0.212973i | ||||
\(892\) | −24.8226 | − | 32.2983i | −0.831122 | − | 1.08143i | ||||
\(893\) | − | 4.71386i | − | 0.157743i | ||||||
\(894\) | 33.3666 | + | 4.82490i | 1.11595 | + | 0.161369i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −39.3161 | + | 10.0971i | −1.31346 | + | 0.337321i | ||||
\(897\) | 10.8202 | + | 7.86135i | 0.361277 | + | 0.262483i | ||||
\(898\) | −33.9096 | + | 17.8573i | −1.13158 | + | 0.595904i | ||||
\(899\) | 11.9042i | 0.397026i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.57122i | − | 0.118974i | ||||||
\(902\) | 6.28440 | + | 11.9336i | 0.209248 | + | 0.397346i | ||||
\(903\) | 4.76900 | + | 3.46488i | 0.158703 | + | 0.115304i | ||||
\(904\) | 16.3879 | − | 3.27930i | 0.545052 | − | 0.109068i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.07674 | − | 28.1927i | 0.135440 | − | 0.936639i | ||||
\(907\) | 34.9093i | 1.15914i | 0.814921 | + | 0.579571i | \(0.196780\pi\) | ||||
−0.814921 | + | 0.579571i | \(0.803220\pi\) | |||||||
\(908\) | −25.1009 | + | 19.2911i | −0.833004 | + | 0.640199i | ||||
\(909\) | 0.645920 | − | 0.209872i | 0.0214238 | − | 0.00696102i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.05588 | + | 21.7158i | −0.233772 | + | 0.719476i | 0.763510 | + | 0.645796i | \(0.223474\pi\) |
−0.997282 | + | 0.0736799i | \(0.976526\pi\) | |||||||
\(912\) | −18.5581 | − | 48.1254i | −0.614520 | − | 1.59359i | ||||
\(913\) | −6.52377 | − | 20.0781i | −0.215905 | − | 0.664488i | ||||
\(914\) | −40.2784 | + | 21.2112i | −1.33229 | + | 0.701603i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.28668 | − | 12.0758i | −0.141636 | − | 0.398997i | ||||
\(917\) | 14.2280 | + | 19.5831i | 0.469850 | + | 0.646692i | ||||
\(918\) | 1.67591 | − | 1.72169i | 0.0553133 | − | 0.0568241i | ||||
\(919\) | 44.3337 | − | 32.2104i | 1.46244 | − | 1.06252i | 0.479715 | − | 0.877424i | \(-0.340740\pi\) |
0.982720 | − | 0.185097i | \(-0.0592600\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 47.1203 | + | 34.2349i | 1.55267 | + | 1.12808i | ||||
\(922\) | 3.66300 | − | 0.630861i | 0.120634 | − | 0.0207763i | ||||
\(923\) | −36.0975 | − | 11.7288i | −1.18816 | − | 0.386058i | ||||
\(924\) | −1.27803 | − | 47.4200i | −0.0420441 | − | 1.56000i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.6580 | + | 29.8429i | 1.00748 | + | 0.980698i | ||||
\(927\) | 13.6534 | − | 42.0209i | 0.448437 | − | 1.38015i | ||||
\(928\) | 30.8342 | − | 7.03907i | 1.01218 | − | 0.231069i | ||||
\(929\) | 26.3740 | + | 19.1618i | 0.865301 | + | 0.628678i | 0.929322 | − | 0.369270i | \(-0.120392\pi\) |
−0.0640206 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.6686 | + | 24.3188i | 0.579066 | + | 0.797016i | ||||
\(932\) | −0.947653 | − | 35.1617i | −0.0310414 | − | 1.15176i | ||||
\(933\) | −15.8380 | − | 21.7992i | −0.518514 | − | 0.713673i | ||||
\(934\) | 52.3258 | + | 25.7793i | 1.71215 | + | 0.843526i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 56.4752 | − | 31.7128i | 1.84595 | − | 1.03656i | ||||
\(937\) | −2.49974 | − | 7.69340i | −0.0816628 | − | 0.251332i | 0.901886 | − | 0.431974i | \(-0.142183\pi\) |
−0.983549 | + | 0.180641i | \(0.942183\pi\) | |||||||
\(938\) | −22.3831 | − | 11.0275i | −0.730835 | − | 0.360061i | ||||
\(939\) | 16.6789 | + | 5.41932i | 0.544297 | + | 0.176853i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.7042 | − | 11.2761i | 1.13133 | − | 0.367590i | 0.317246 | − | 0.948343i | \(-0.397242\pi\) |
0.814080 | + | 0.580753i | \(0.197242\pi\) | |||||||
\(942\) | −27.4357 | − | 3.96728i | −0.893904 | − | 0.129261i | ||||
\(943\) | 2.81981 | 0.0918255 | ||||||||
\(944\) | 9.93655 | + | 12.2323i | 0.323407 | + | 0.398128i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.410776 | + | 2.38511i | 0.0133555 | + | 0.0775467i | ||||
\(947\) | −8.90757 | + | 12.2602i | −0.289457 | + | 0.398404i | −0.928838 | − | 0.370487i | \(-0.879191\pi\) |
0.639380 | + | 0.768890i | \(0.279191\pi\) | |||||||
\(948\) | −13.5038 | + | 45.7165i | −0.438584 | + | 1.48480i | ||||
\(949\) | 101.463i | 3.29362i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.05851 | −0.228888 | ||||||||
\(952\) | 9.66504 | + | 17.2118i | 0.313246 | + | 0.557838i | ||||
\(953\) | −44.0685 | − | 32.0176i | −1.42752 | − | 1.03715i | −0.990472 | − | 0.137714i | \(-0.956024\pi\) |
−0.437047 | − | 0.899439i | \(-0.643976\pi\) | |||||||
\(954\) | 8.56323 | − | 1.47480i | 0.277245 | − | 0.0477485i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.2837 | − | 13.3807i | −0.332597 | − | 0.432763i | ||||
\(957\) | 36.9610i | 1.19478i | ||||||||
\(958\) | −22.0956 | − | 3.19508i | −0.713875 | − | 0.103228i | ||||
\(959\) | −9.13812 | − | 28.1242i | −0.295085 | − | 0.908179i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.17865 | + | 25.1713i | −0.263827 | + | 0.811977i | ||||
\(962\) | 37.9177 | − | 76.9637i | 1.22252 | − | 2.48141i | ||||
\(963\) | −47.4839 | + | 15.4285i | −1.53015 | + | 0.497175i | ||||
\(964\) | 6.68335 | + | 1.97414i | 0.215256 | + | 0.0635828i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.89670 | − | 4.38314i | −0.286247 | − | 0.141025i | ||||
\(967\) | −17.8627 | + | 12.9780i | −0.574424 | + | 0.417344i | −0.836710 | − | 0.547647i | \(-0.815524\pi\) |
0.262285 | + | 0.964990i | \(0.415524\pi\) | |||||||
\(968\) | −7.88903 | + | 8.55397i | −0.253563 | + | 0.274935i | ||||
\(969\) | −20.2926 | + | 14.7434i | −0.651892 | + | 0.473628i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.05516 | + | 6.95783i | −0.162228 | + | 0.223287i | −0.882390 | − | 0.470518i | \(-0.844067\pi\) |
0.720163 | + | 0.693805i | \(0.244067\pi\) | |||||||
\(972\) | −36.8917 | − | 25.3135i | −1.18330 | − | 0.811930i | ||||
\(973\) | 4.64781 | + | 1.51016i | 0.149002 | + | 0.0484137i | ||||
\(974\) | −36.3105 | − | 35.3450i | −1.16346 | − | 1.13253i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.40742 | + | 26.0916i | 0.0450505 | + | 0.835171i | ||||
\(977\) | −5.88484 | + | 18.1117i | −0.188273 | + | 0.579444i | −0.999989 | − | 0.00460737i | \(-0.998533\pi\) |
0.811717 | + | 0.584052i | \(0.198533\pi\) | |||||||
\(978\) | −13.8937 | − | 80.6719i | −0.444273 | − | 2.57960i | ||||
\(979\) | −16.7527 | + | 23.0581i | −0.535418 | + | 0.736940i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0107 | − | 23.4133i | −0.543111 | − | 0.747529i | ||||
\(982\) | −7.37111 | + | 7.57244i | −0.235221 | + | 0.241646i | ||||
\(983\) | −16.6333 | + | 12.0848i | −0.530521 | + | 0.385446i | −0.820553 | − | 0.571571i | \(-0.806334\pi\) |
0.290032 | + | 0.957017i | \(0.406334\pi\) | |||||||
\(984\) | 10.8150 | − | 23.5304i | 0.344768 | − | 0.750122i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.16653 | − | 13.6087i | −0.228229 | − | 0.433390i | ||||
\(987\) | −7.91678 | + | 2.57232i | −0.251994 | + | 0.0818777i | ||||
\(988\) | −66.0109 | + | 23.4325i | −2.10009 | + | 0.745488i | ||||
\(989\) | 0.481237 | + | 0.156364i | 0.0153025 | + | 0.00497207i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.98983 | − | 24.5902i | −0.253805 | − | 0.781132i | −0.994063 | − | 0.108809i | \(-0.965296\pi\) |
0.740258 | − | 0.672323i | \(-0.234704\pi\) | |||||||
\(992\) | −11.9959 | − | 1.07915i | −0.380871 | − | 0.0342629i | ||||
\(993\) | −66.8905 | −2.12271 | ||||||||
\(994\) | 27.8558 | + | 4.02802i | 0.883531 | + | 0.127761i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −22.9342 | + | 33.4242i | −0.726699 | + | 1.05909i | ||||
\(997\) | −11.2686 | + | 15.5099i | −0.356881 | + | 0.491204i | −0.949276 | − | 0.314443i | \(-0.898182\pi\) |
0.592396 | + | 0.805647i | \(0.298182\pi\) | |||||||
\(998\) | −1.06466 | − | 2.02170i | −0.0337011 | − | 0.0639958i | ||||
\(999\) | 7.74398 | 0.245009 |
(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 | 1000.2.t.b.101.48 | 224 | ||
5.2 | odd | 4 | 200.2.o.a.29.19 | ✓ | 112 | ||
5.3 | odd | 4 | 1000.2.o.a.149.10 | 112 | |||
5.4 | even | 2 | inner | 1000.2.t.b.101.9 | 224 | ||
8.5 | even | 2 | inner | 1000.2.t.b.101.20 | 224 | ||
20.7 | even | 4 | 800.2.be.a.529.25 | 112 | |||
25.6 | even | 5 | inner | 1000.2.t.b.901.20 | 224 | ||
25.8 | odd | 20 | 200.2.o.a.69.24 | yes | 112 | ||
25.17 | odd | 20 | 1000.2.o.a.349.5 | 112 | |||
25.19 | even | 10 | inner | 1000.2.t.b.901.37 | 224 | ||
40.13 | odd | 4 | 1000.2.o.a.149.5 | 112 | |||
40.27 | even | 4 | 800.2.be.a.529.4 | 112 | |||
40.29 | even | 2 | inner | 1000.2.t.b.101.37 | 224 | ||
40.37 | odd | 4 | 200.2.o.a.29.24 | yes | 112 | ||
100.83 | even | 20 | 800.2.be.a.369.4 | 112 | |||
200.69 | even | 10 | inner | 1000.2.t.b.901.9 | 224 | ||
200.83 | even | 20 | 800.2.be.a.369.25 | 112 | |||
200.117 | odd | 20 | 1000.2.o.a.349.10 | 112 | |||
200.133 | odd | 20 | 200.2.o.a.69.19 | yes | 112 | ||
200.181 | even | 10 | inner | 1000.2.t.b.901.48 | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.o.a.29.19 | ✓ | 112 | 5.2 | odd | 4 | ||
200.2.o.a.29.24 | yes | 112 | 40.37 | odd | 4 | ||
200.2.o.a.69.19 | yes | 112 | 200.133 | odd | 20 | ||
200.2.o.a.69.24 | yes | 112 | 25.8 | odd | 20 | ||
800.2.be.a.369.4 | 112 | 100.83 | even | 20 | |||
800.2.be.a.369.25 | 112 | 200.83 | even | 20 | |||
800.2.be.a.529.4 | 112 | 40.27 | even | 4 | |||
800.2.be.a.529.25 | 112 | 20.7 | even | 4 | |||
1000.2.o.a.149.5 | 112 | 40.13 | odd | 4 | |||
1000.2.o.a.149.10 | 112 | 5.3 | odd | 4 | |||
1000.2.o.a.349.5 | 112 | 25.17 | odd | 20 | |||
1000.2.o.a.349.10 | 112 | 200.117 | odd | 20 | |||
1000.2.t.b.101.9 | 224 | 5.4 | even | 2 | inner | ||
1000.2.t.b.101.20 | 224 | 8.5 | even | 2 | inner | ||
1000.2.t.b.101.37 | 224 | 40.29 | even | 2 | inner | ||
1000.2.t.b.101.48 | 224 | 1.1 | even | 1 | trivial | ||
1000.2.t.b.901.9 | 224 | 200.69 | even | 10 | inner | ||
1000.2.t.b.901.20 | 224 | 25.6 | even | 5 | inner | ||
1000.2.t.b.901.37 | 224 | 25.19 | even | 10 | inner | ||
1000.2.t.b.901.48 | 224 | 200.181 | even | 10 | inner |