Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 221.8 | ||
Character | \(\chi\) | \(=\) | 570.221 |
Dual form | 570.2.s.a.521.8 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.691758 | − | 1.58791i | 0.399387 | − | 0.916782i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | −1.72105 | + | 0.194877i | −0.702617 | + | 0.0795580i | ||||
\(7\) | −1.96058 | −0.741028 | −0.370514 | − | 0.928827i | \(-0.620818\pi\) | ||||
−0.370514 | + | 0.928827i | \(0.620818\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.04294 | − | 2.19691i | −0.680980 | − | 0.732302i | ||||
\(10\) | 0.866025 | + | 0.500000i | 0.273861 | + | 0.158114i | ||||
\(11\) | − | 4.91222i | − | 1.48109i | −0.672007 | − | 0.740545i | \(-0.734568\pi\) | ||
0.672007 | − | 0.740545i | \(-0.265432\pi\) | |||||||
\(12\) | 1.02929 | + | 1.39304i | 0.297132 | + | 0.402135i | ||||
\(13\) | 1.73616 | + | 1.00237i | 0.481524 | + | 0.278008i | 0.721051 | − | 0.692881i | \(-0.243659\pi\) |
−0.239527 | + | 0.970890i | \(0.576992\pi\) | |||||||
\(14\) | 0.980288 | + | 1.69791i | 0.261993 | + | 0.453785i | ||||
\(15\) | 0.194877 | + | 1.72105i | 0.0503169 | + | 0.444374i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.39530 | + | 1.96028i | −0.823481 | + | 0.475437i | −0.851615 | − | 0.524167i | \(-0.824377\pi\) |
0.0281343 | + | 0.999604i | \(0.491043\pi\) | |||||||
\(18\) | −0.881106 | + | 2.86769i | −0.207679 | + | 0.675921i | ||||
\(19\) | −3.86720 | + | 2.01117i | −0.887195 | + | 0.461394i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | −1.35624 | + | 3.11322i | −0.295957 | + | 0.679361i | ||||
\(22\) | −4.25411 | + | 2.45611i | −0.906978 | + | 0.523644i | ||||
\(23\) | −5.91161 | − | 3.41307i | −1.23266 | − | 0.711674i | −0.265073 | − | 0.964228i | \(-0.585396\pi\) |
−0.967583 | + | 0.252554i | \(0.918729\pi\) | |||||||
\(24\) | 0.691758 | − | 1.58791i | 0.141205 | − | 0.324132i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | − | 2.00475i | − | 0.393163i | ||||||
\(27\) | −4.90172 | + | 1.72429i | −0.943336 | + | 0.331839i | ||||
\(28\) | 0.980288 | − | 1.69791i | 0.185257 | − | 0.320874i | ||||
\(29\) | −2.51673 | + | 4.35910i | −0.467344 | + | 0.809464i | −0.999304 | − | 0.0373055i | \(-0.988123\pi\) |
0.531959 | + | 0.846770i | \(0.321456\pi\) | |||||||
\(30\) | 1.39304 | − | 1.02929i | 0.254333 | − | 0.187923i | ||||
\(31\) | − | 0.233588i | − | 0.0419536i | −0.999780 | − | 0.0209768i | \(-0.993322\pi\) | ||
0.999780 | − | 0.0209768i | \(-0.00667761\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −7.80018 | − | 3.39807i | −1.35784 | − | 0.591528i | ||||
\(34\) | 3.39530 | + | 1.96028i | 0.582289 | + | 0.336185i | ||||
\(35\) | 1.69791 | − | 0.980288i | 0.286999 | − | 0.165699i | ||||
\(36\) | 2.92405 | − | 0.670786i | 0.487341 | − | 0.111798i | ||||
\(37\) | − | 7.19430i | − | 1.18274i | −0.806402 | − | 0.591368i | \(-0.798588\pi\) | ||
0.806402 | − | 0.591368i | \(-0.201412\pi\) | |||||||
\(38\) | 3.67532 | + | 2.34350i | 0.596216 | + | 0.380167i | ||||
\(39\) | 2.79269 | − | 2.06347i | 0.447188 | − | 0.330420i | ||||
\(40\) | −0.866025 | + | 0.500000i | −0.136931 | + | 0.0790569i | ||||
\(41\) | 5.88249 | + | 10.1888i | 0.918690 | + | 1.59122i | 0.801407 | + | 0.598119i | \(0.204085\pi\) |
0.117282 | + | 0.993099i | \(0.462582\pi\) | |||||||
\(42\) | 3.37425 | − | 0.382070i | 0.520659 | − | 0.0589547i | ||||
\(43\) | −2.94487 | − | 5.10067i | −0.449089 | − | 0.777845i | 0.549238 | − | 0.835666i | \(-0.314918\pi\) |
−0.998327 | + | 0.0578212i | \(0.981585\pi\) | |||||||
\(44\) | 4.25411 | + | 2.45611i | 0.641331 | + | 0.370272i | ||||
\(45\) | 2.86769 | + | 0.881106i | 0.427490 | + | 0.131347i | ||||
\(46\) | 6.82614i | 1.00646i | ||||||||
\(47\) | 1.60922 | + | 0.929084i | 0.234729 | + | 0.135521i | 0.612752 | − | 0.790275i | \(-0.290063\pi\) |
−0.378023 | + | 0.925796i | \(0.623396\pi\) | |||||||
\(48\) | −1.72105 | + | 0.194877i | −0.248413 | + | 0.0281280i | ||||
\(49\) | −3.15615 | −0.450878 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0.764024 | + | 6.74748i | 0.106985 | + | 0.944836i | ||||
\(52\) | −1.73616 | + | 1.00237i | −0.240762 | + | 0.139004i | ||||
\(53\) | 5.29044 | − | 9.16331i | 0.726698 | − | 1.25868i | −0.231573 | − | 0.972817i | \(-0.574387\pi\) |
0.958271 | − | 0.285861i | \(-0.0922794\pi\) | |||||||
\(54\) | 3.94413 | + | 3.38287i | 0.536729 | + | 0.460350i | ||||
\(55\) | 2.45611 | + | 4.25411i | 0.331182 | + | 0.573624i | ||||
\(56\) | −1.96058 | −0.261993 | ||||||||
\(57\) | 0.518398 | + | 7.53202i | 0.0686635 | + | 0.997640i | ||||
\(58\) | 5.03345 | 0.660925 | ||||||||
\(59\) | 4.25879 | + | 7.37643i | 0.554447 | + | 0.960330i | 0.997946 | + | 0.0640552i | \(0.0204034\pi\) |
−0.443500 | + | 0.896274i | \(0.646263\pi\) | |||||||
\(60\) | −1.58791 | − | 0.691758i | −0.204999 | − | 0.0893056i | ||||
\(61\) | 3.91378 | − | 6.77887i | 0.501108 | − | 0.867945i | −0.498891 | − | 0.866665i | \(-0.666259\pi\) |
0.999999 | − | 0.00128020i | \(-0.000407502\pi\) | |||||||
\(62\) | −0.202293 | + | 0.116794i | −0.0256912 | + | 0.0148328i | ||||
\(63\) | 4.00534 | + | 4.30720i | 0.504625 | + | 0.542656i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00475 | −0.248658 | ||||||||
\(66\) | 0.957276 | + | 8.45419i | 0.117833 | + | 1.04064i | ||||
\(67\) | −13.7456 | − | 7.93605i | −1.67930 | − | 0.969542i | −0.962110 | − | 0.272661i | \(-0.912096\pi\) |
−0.717186 | − | 0.696882i | \(-0.754570\pi\) | |||||||
\(68\) | − | 3.92055i | − | 0.475437i | ||||||
\(69\) | −9.50907 | + | 7.02611i | −1.14476 | + | 0.845844i | ||||
\(70\) | −1.69791 | − | 0.980288i | −0.202939 | − | 0.117167i | ||||
\(71\) | −2.26439 | − | 3.92204i | −0.268734 | − | 0.465461i | 0.699801 | − | 0.714338i | \(-0.253272\pi\) |
−0.968535 | + | 0.248877i | \(0.919939\pi\) | |||||||
\(72\) | −2.04294 | − | 2.19691i | −0.240763 | − | 0.258908i | ||||
\(73\) | 1.13889 | + | 1.97262i | 0.133297 | + | 0.230877i | 0.924946 | − | 0.380099i | \(-0.124110\pi\) |
−0.791649 | + | 0.610977i | \(0.790777\pi\) | |||||||
\(74\) | −6.23045 | + | 3.59715i | −0.724275 | + | 0.418160i | ||||
\(75\) | −1.02929 | − | 1.39304i | −0.118853 | − | 0.160854i | ||||
\(76\) | 0.191874 | − | 4.35467i | 0.0220095 | − | 0.499515i | ||||
\(77\) | 9.63077i | 1.09753i | ||||||||
\(78\) | −3.18336 | − | 1.38680i | −0.360445 | − | 0.157024i | ||||
\(79\) | 10.7900 | − | 6.22958i | 1.21396 | − | 0.700883i | 0.250344 | − | 0.968157i | \(-0.419456\pi\) |
0.963621 | + | 0.267274i | \(0.0861229\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −0.652788 | + | 8.97629i | −0.0725320 | + | 0.997366i | ||||
\(82\) | 5.88249 | − | 10.1888i | 0.649612 | − | 1.12516i | ||||
\(83\) | − | 13.7111i | − | 1.50499i | −0.658599 | − | 0.752494i | \(-0.728851\pi\) | ||
0.658599 | − | 0.752494i | \(-0.271149\pi\) | |||||||
\(84\) | −2.01801 | − | 2.73115i | −0.220183 | − | 0.297993i | ||||
\(85\) | 1.96028 | − | 3.39530i | 0.212622 | − | 0.368272i | ||||
\(86\) | −2.94487 | + | 5.10067i | −0.317554 | + | 0.550019i | ||||
\(87\) | 5.18091 | + | 7.01179i | 0.555451 | + | 0.751743i | ||||
\(88\) | − | 4.91222i | − | 0.523644i | ||||||
\(89\) | 5.48139 | − | 9.49404i | 0.581026 | − | 1.00637i | −0.414332 | − | 0.910126i | \(-0.635985\pi\) |
0.995358 | − | 0.0962408i | \(-0.0306819\pi\) | |||||||
\(90\) | −0.670786 | − | 2.92405i | −0.0707070 | − | 0.308222i | ||||
\(91\) | −3.40387 | − | 1.96523i | −0.356823 | − | 0.206012i | ||||
\(92\) | 5.91161 | − | 3.41307i | 0.616328 | − | 0.355837i | ||||
\(93\) | −0.370917 | − | 0.161586i | −0.0384623 | − | 0.0167557i | ||||
\(94\) | − | 1.85817i | − | 0.191655i | ||||||
\(95\) | 2.34350 | − | 3.67532i | 0.240439 | − | 0.377080i | ||||
\(96\) | 1.02929 | + | 1.39304i | 0.105052 | + | 0.142176i | ||||
\(97\) | −13.3158 | + | 7.68789i | −1.35202 | + | 0.780587i | −0.988532 | − | 0.151013i | \(-0.951746\pi\) |
−0.363484 | + | 0.931600i | \(0.618413\pi\) | |||||||
\(98\) | 1.57807 | + | 2.73330i | 0.159409 | + | 0.276105i | ||||
\(99\) | −10.7917 | + | 10.0354i | −1.08460 | + | 1.00859i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 9.94449 | + | 5.74146i | 0.989514 | + | 0.571296i | 0.905129 | − | 0.425137i | \(-0.139774\pi\) |
0.0843851 | + | 0.996433i | \(0.473107\pi\) | |||||||
\(102\) | 5.46148 | − | 4.03541i | 0.540767 | − | 0.399565i | ||||
\(103\) | − | 1.76334i | − | 0.173747i | −0.996219 | − | 0.0868736i | \(-0.972312\pi\) | ||
0.996219 | − | 0.0868736i | \(-0.0276876\pi\) | |||||||
\(104\) | 1.73616 | + | 1.00237i | 0.170245 | + | 0.0982907i | ||||
\(105\) | −0.382070 | − | 3.37425i | −0.0372862 | − | 0.329293i | ||||
\(106\) | −10.5809 | −1.02771 | ||||||||
\(107\) | 3.01131 | 0.291115 | 0.145557 | − | 0.989350i | \(-0.453502\pi\) | ||||
0.145557 | + | 0.989350i | \(0.453502\pi\) | |||||||
\(108\) | 0.957584 | − | 5.10716i | 0.0921436 | − | 0.491436i | ||||
\(109\) | 9.05950 | − | 5.23051i | 0.867743 | − | 0.500992i | 0.00114554 | − | 0.999999i | \(-0.499635\pi\) |
0.866598 | + | 0.499008i | \(0.166302\pi\) | |||||||
\(110\) | 2.45611 | − | 4.25411i | 0.234181 | − | 0.405613i | ||||
\(111\) | −11.4239 | − | 4.97672i | −1.08431 | − | 0.472369i | ||||
\(112\) | 0.980288 | + | 1.69791i | 0.0926285 | + | 0.160437i | ||||
\(113\) | −12.1589 | −1.14382 | −0.571909 | − | 0.820317i | \(-0.693797\pi\) | ||||
−0.571909 | + | 0.820317i | \(0.693797\pi\) | |||||||
\(114\) | 6.26372 | − | 4.21495i | 0.586651 | − | 0.394767i | ||||
\(115\) | 6.82614 | 0.636541 | ||||||||
\(116\) | −2.51673 | − | 4.35910i | −0.233672 | − | 0.404732i | ||||
\(117\) | −1.34475 | − | 5.86197i | −0.124323 | − | 0.541939i | ||||
\(118\) | 4.25879 | − | 7.37643i | 0.392053 | − | 0.679056i | ||||
\(119\) | 6.65674 | − | 3.84327i | 0.610222 | − | 0.352312i | ||||
\(120\) | 0.194877 | + | 1.72105i | 0.0177897 | + | 0.157110i | ||||
\(121\) | −13.1299 | −1.19363 | ||||||||
\(122\) | −7.82756 | −0.708674 | ||||||||
\(123\) | 20.2481 | − | 2.29272i | 1.82571 | − | 0.206727i | ||||
\(124\) | 0.202293 | + | 0.116794i | 0.0181664 | + | 0.0104884i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 1.72747 | − | 5.62232i | 0.153896 | − | 0.500876i | ||||
\(127\) | 11.2081 | + | 6.47100i | 0.994557 | + | 0.574208i | 0.906633 | − | 0.421919i | \(-0.138643\pi\) |
0.0879240 | + | 0.996127i | \(0.471977\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −10.1366 | + | 1.14777i | −0.892475 | + | 0.101056i | ||||
\(130\) | 1.00237 | + | 1.73616i | 0.0879139 | + | 0.152271i | ||||
\(131\) | −7.74381 | + | 4.47089i | −0.676580 | + | 0.390624i | −0.798565 | − | 0.601908i | \(-0.794407\pi\) |
0.121985 | + | 0.992532i | \(0.461074\pi\) | |||||||
\(132\) | 6.84290 | − | 5.05612i | 0.595598 | − | 0.440079i | ||||
\(133\) | 7.58193 | − | 3.94305i | 0.657436 | − | 0.341906i | ||||
\(134\) | 15.8721i | 1.37114i | ||||||||
\(135\) | 3.38287 | − | 3.94413i | 0.291151 | − | 0.339457i | ||||
\(136\) | −3.39530 | + | 1.96028i | −0.291145 | + | 0.168092i | ||||
\(137\) | −3.55144 | − | 2.05042i | −0.303420 | − | 0.175180i | 0.340558 | − | 0.940223i | \(-0.389384\pi\) |
−0.643978 | + | 0.765044i | \(0.722717\pi\) | |||||||
\(138\) | 10.8393 | + | 4.72204i | 0.922704 | + | 0.401967i | ||||
\(139\) | 6.74169 | − | 11.6770i | 0.571823 | − | 0.990426i | −0.424556 | − | 0.905402i | \(-0.639570\pi\) |
0.996379 | − | 0.0850246i | \(-0.0270969\pi\) | |||||||
\(140\) | 1.96058i | 0.165699i | ||||||||
\(141\) | 2.58850 | − | 1.91260i | 0.217991 | − | 0.161070i | ||||
\(142\) | −2.26439 | + | 3.92204i | −0.190024 | + | 0.329131i | ||||
\(143\) | 4.92387 | − | 8.52840i | 0.411755 | − | 0.713181i | ||||
\(144\) | −0.881106 | + | 2.86769i | −0.0734255 | + | 0.238974i | ||||
\(145\) | − | 5.03345i | − | 0.418006i | ||||||
\(146\) | 1.13889 | − | 1.97262i | 0.0942553 | − | 0.163255i | ||||
\(147\) | −2.18329 | + | 5.01169i | −0.180075 | + | 0.413357i | ||||
\(148\) | 6.23045 | + | 3.59715i | 0.512140 | + | 0.295684i | ||||
\(149\) | −3.99172 | + | 2.30462i | −0.327014 | + | 0.188802i | −0.654515 | − | 0.756049i | \(-0.727127\pi\) |
0.327500 | + | 0.944851i | \(0.393794\pi\) | |||||||
\(150\) | −0.691758 | + | 1.58791i | −0.0564818 | + | 0.129653i | ||||
\(151\) | − | 17.3564i | − | 1.41245i | −0.707990 | − | 0.706223i | \(-0.750398\pi\) | ||
0.707990 | − | 0.706223i | \(-0.249602\pi\) | |||||||
\(152\) | −3.86720 | + | 2.01117i | −0.313671 | + | 0.163127i | ||||
\(153\) | 11.2429 | + | 3.45442i | 0.908938 | + | 0.279274i | ||||
\(154\) | 8.34049 | − | 4.81539i | 0.672096 | − | 0.388035i | ||||
\(155\) | 0.116794 | + | 0.202293i | 0.00938111 | + | 0.0162486i | ||||
\(156\) | 0.390678 | + | 3.45027i | 0.0312793 | + | 0.276243i | ||||
\(157\) | 0.833700 | + | 1.44401i | 0.0665365 | + | 0.115245i | 0.897375 | − | 0.441270i | \(-0.145472\pi\) |
−0.830838 | + | 0.556514i | \(0.812138\pi\) | |||||||
\(158\) | −10.7900 | − | 6.22958i | −0.858403 | − | 0.495599i | ||||
\(159\) | −10.8908 | − | 14.7396i | −0.863700 | − | 1.16892i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 11.5902 | + | 6.69158i | 0.913432 | + | 0.527370i | ||||
\(162\) | 8.10009 | − | 3.92282i | 0.636403 | − | 0.308206i | ||||
\(163\) | 8.55940 | 0.670424 | 0.335212 | − | 0.942143i | \(-0.391192\pi\) | ||||
0.335212 | + | 0.942143i | \(0.391192\pi\) | |||||||
\(164\) | −11.7650 | −0.918690 | ||||||||
\(165\) | 8.45419 | − | 0.957276i | 0.658158 | − | 0.0745238i | ||||
\(166\) | −11.8742 | + | 6.85554i | −0.921613 | + | 0.532093i | ||||
\(167\) | 4.84533 | − | 8.39236i | 0.374943 | − | 0.649420i | −0.615376 | − | 0.788234i | \(-0.710996\pi\) |
0.990318 | + | 0.138814i | \(0.0443290\pi\) | |||||||
\(168\) | −1.35624 | + | 3.11322i | −0.104637 | + | 0.240190i | ||||
\(169\) | −4.49050 | − | 7.77777i | −0.345423 | − | 0.598290i | ||||
\(170\) | −3.92055 | −0.300693 | ||||||||
\(171\) | 12.3188 | + | 4.38716i | 0.942042 | + | 0.335495i | ||||
\(172\) | 5.88974 | 0.449089 | ||||||||
\(173\) | −5.22274 | − | 9.04605i | −0.397078 | − | 0.687759i | 0.596286 | − | 0.802772i | \(-0.296642\pi\) |
−0.993364 | + | 0.115013i | \(0.963309\pi\) | |||||||
\(174\) | 3.48193 | − | 7.99269i | 0.263965 | − | 0.605924i | ||||
\(175\) | −0.980288 | + | 1.69791i | −0.0741028 | + | 0.128350i | ||||
\(176\) | −4.25411 | + | 2.45611i | −0.320665 | + | 0.185136i | ||||
\(177\) | 14.6592 | − | 1.65987i | 1.10185 | − | 0.124764i | ||||
\(178\) | −10.9628 | −0.821695 | ||||||||
\(179\) | −1.34670 | −0.100657 | −0.0503285 | − | 0.998733i | \(-0.516027\pi\) | ||||
−0.0503285 | + | 0.998733i | \(0.516027\pi\) | |||||||
\(180\) | −2.19691 | + | 2.04294i | −0.163748 | + | 0.152272i | ||||
\(181\) | 12.6588 | + | 7.30854i | 0.940919 | + | 0.543240i | 0.890248 | − | 0.455476i | \(-0.150531\pi\) |
0.0506704 | + | 0.998715i | \(0.483864\pi\) | |||||||
\(182\) | 3.93045i | 0.291345i | ||||||||
\(183\) | −8.05687 | − | 10.9041i | −0.595581 | − | 0.806053i | ||||
\(184\) | −5.91161 | − | 3.41307i | −0.435810 | − | 0.251615i | ||||
\(185\) | 3.59715 | + | 6.23045i | 0.264468 | + | 0.458072i | ||||
\(186\) | 0.0455208 | + | 0.402017i | 0.00333774 | + | 0.0294773i | ||||
\(187\) | 9.62931 | + | 16.6785i | 0.704165 | + | 1.21965i | ||||
\(188\) | −1.60922 | + | 0.929084i | −0.117364 | + | 0.0677604i | ||||
\(189\) | 9.61019 | − | 3.38059i | 0.699038 | − | 0.245902i | ||||
\(190\) | −4.35467 | − | 0.191874i | −0.315921 | − | 0.0139200i | ||||
\(191\) | − | 6.09365i | − | 0.440921i | −0.975396 | − | 0.220461i | \(-0.929244\pi\) | ||
0.975396 | − | 0.220461i | \(-0.0707560\pi\) | |||||||
\(192\) | 0.691758 | − | 1.58791i | 0.0499234 | − | 0.114598i | ||||
\(193\) | 2.59888 | − | 1.50046i | 0.187071 | − | 0.108006i | −0.403540 | − | 0.914962i | \(-0.632220\pi\) |
0.590611 | + | 0.806957i | \(0.298887\pi\) | |||||||
\(194\) | 13.3158 | + | 7.68789i | 0.956020 | + | 0.551958i | ||||
\(195\) | −1.38680 | + | 3.18336i | −0.0993108 | + | 0.227965i | ||||
\(196\) | 1.57807 | − | 2.73330i | 0.112719 | − | 0.195236i | ||||
\(197\) | 2.48104i | 0.176767i | 0.996087 | + | 0.0883833i | \(0.0281700\pi\) | ||||
−0.996087 | + | 0.0883833i | \(0.971830\pi\) | |||||||
\(198\) | 14.0867 | + | 4.32818i | 1.00110 | + | 0.307591i | ||||
\(199\) | −11.8062 | + | 20.4489i | −0.836918 | + | 1.44958i | 0.0555409 | + | 0.998456i | \(0.482312\pi\) |
−0.892459 | + | 0.451128i | \(0.851022\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −22.1104 | + | 16.3371i | −1.55955 | + | 1.15233i | ||||
\(202\) | − | 11.4829i | − | 0.807935i | ||||||
\(203\) | 4.93423 | − | 8.54634i | 0.346315 | − | 0.599836i | ||||
\(204\) | −6.22550 | − | 2.71208i | −0.435872 | − | 0.189883i | ||||
\(205\) | −10.1888 | − | 5.88249i | −0.711614 | − | 0.410851i | ||||
\(206\) | −1.52710 | + | 0.881671i | −0.106398 | + | 0.0614289i | ||||
\(207\) | 4.57888 | + | 19.9599i | 0.318254 | + | 1.38731i | ||||
\(208\) | − | 2.00475i | − | 0.139004i | ||||||
\(209\) | 9.87930 | + | 18.9965i | 0.683366 | + | 1.31402i | ||||
\(210\) | −2.73115 | + | 2.01801i | −0.188468 | + | 0.139256i | ||||
\(211\) | 2.52326 | − | 1.45680i | 0.173708 | − | 0.100290i | −0.410625 | − | 0.911804i | \(-0.634689\pi\) |
0.584333 | + | 0.811514i | \(0.301356\pi\) | |||||||
\(212\) | 5.29044 | + | 9.16331i | 0.363349 | + | 0.629339i | ||||
\(213\) | −7.79428 | + | 0.882554i | −0.534055 | + | 0.0604716i | ||||
\(214\) | −1.50566 | − | 2.60787i | −0.102925 | − | 0.178271i | ||||
\(215\) | 5.10067 | + | 2.94487i | 0.347863 | + | 0.200839i | ||||
\(216\) | −4.90172 | + | 1.72429i | −0.333520 | + | 0.117323i | ||||
\(217\) | 0.457966i | 0.0310888i | ||||||||
\(218\) | −9.05950 | − | 5.23051i | −0.613587 | − | 0.354255i | ||||
\(219\) | 3.92018 | − | 0.443886i | 0.264901 | − | 0.0299950i | ||||
\(220\) | −4.91222 | −0.331182 | ||||||||
\(221\) | −7.85971 | −0.528702 | ||||||||
\(222\) | 1.40200 | + | 12.3818i | 0.0940961 | + | 0.831010i | ||||
\(223\) | 3.39391 | − | 1.95947i | 0.227273 | − | 0.131216i | −0.382040 | − | 0.924146i | \(-0.624778\pi\) |
0.609313 | + | 0.792930i | \(0.291445\pi\) | |||||||
\(224\) | 0.980288 | − | 1.69791i | 0.0654982 | − | 0.113446i | ||||
\(225\) | −2.92405 | + | 0.670786i | −0.194936 | + | 0.0447190i | ||||
\(226\) | 6.07947 | + | 10.5300i | 0.404400 | + | 0.700442i | ||||
\(227\) | −0.316084 | −0.0209793 | −0.0104896 | − | 0.999945i | \(-0.503339\pi\) | ||||
−0.0104896 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(228\) | −6.78212 | − | 3.31706i | −0.449157 | − | 0.219678i | ||||
\(229\) | 6.13340 | 0.405306 | 0.202653 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202653 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(230\) | −3.41307 | − | 5.91161i | −0.225051 | − | 0.389800i | ||||
\(231\) | 15.2928 | + | 6.66217i | 1.00619 | + | 0.438339i | ||||
\(232\) | −2.51673 | + | 4.35910i | −0.165231 | + | 0.286189i | ||||
\(233\) | −9.37631 | + | 5.41341i | −0.614262 | + | 0.354644i | −0.774632 | − | 0.632413i | \(-0.782065\pi\) |
0.160369 | + | 0.987057i | \(0.448731\pi\) | |||||||
\(234\) | −4.40424 | + | 4.09558i | −0.287914 | + | 0.267736i | ||||
\(235\) | −1.85817 | −0.121214 | ||||||||
\(236\) | −8.51757 | −0.554447 | ||||||||
\(237\) | −2.42800 | − | 21.4429i | −0.157715 | − | 1.39287i | ||||
\(238\) | −6.65674 | − | 3.84327i | −0.431492 | − | 0.249122i | ||||
\(239\) | 3.18686i | 0.206141i | 0.994674 | + | 0.103070i | \(0.0328667\pi\) | ||||
−0.994674 | + | 0.103070i | \(0.967133\pi\) | |||||||
\(240\) | 1.39304 | − | 1.02929i | 0.0899202 | − | 0.0664407i | ||||
\(241\) | −16.5317 | − | 9.54461i | −1.06490 | − | 0.614822i | −0.138119 | − | 0.990416i | \(-0.544106\pi\) |
−0.926785 | + | 0.375593i | \(0.877439\pi\) | |||||||
\(242\) | 6.56495 | + | 11.3708i | 0.422011 | + | 0.730944i | ||||
\(243\) | 13.8020 | + | 7.24600i | 0.885399 | + | 0.464831i | ||||
\(244\) | 3.91378 | + | 6.77887i | 0.250554 | + | 0.433973i | ||||
\(245\) | 2.73330 | − | 1.57807i | 0.174624 | − | 0.100819i | ||||
\(246\) | −12.1096 | − | 16.3890i | −0.772081 | − | 1.04493i | ||||
\(247\) | −8.73001 | − | 0.384659i | −0.555477 | − | 0.0244753i | ||||
\(248\) | − | 0.233588i | − | 0.0148328i | ||||||
\(249\) | −21.7720 | − | 9.48476i | −1.37975 | − | 0.601072i | ||||
\(250\) | 0.866025 | − | 0.500000i | 0.0547723 | − | 0.0316228i | ||||
\(251\) | 10.0866 | + | 5.82352i | 0.636663 | + | 0.367578i | 0.783328 | − | 0.621609i | \(-0.213521\pi\) |
−0.146665 | + | 0.989186i | \(0.546854\pi\) | |||||||
\(252\) | −5.73281 | + | 1.31513i | −0.361133 | + | 0.0828451i | ||||
\(253\) | −16.7657 | + | 29.0391i | −1.05405 | + | 1.82567i | ||||
\(254\) | − | 12.9420i | − | 0.812053i | ||||||
\(255\) | −4.03541 | − | 5.46148i | −0.252707 | − | 0.342011i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.7735 | − | 20.3923i | 0.734410 | − | 1.27204i | −0.220571 | − | 0.975371i | \(-0.570792\pi\) |
0.954982 | − | 0.296665i | \(-0.0958746\pi\) | |||||||
\(258\) | 6.06228 | + | 8.20463i | 0.377421 | + | 0.510798i | ||||
\(259\) | 14.1050i | 0.876440i | ||||||||
\(260\) | 1.00237 | − | 1.73616i | 0.0621645 | − | 0.107672i | ||||
\(261\) | 14.7181 | − | 3.37637i | 0.911025 | − | 0.208992i | ||||
\(262\) | 7.74381 | + | 4.47089i | 0.478414 | + | 0.276213i | ||||
\(263\) | 3.46036 | − | 1.99784i | 0.213375 | − | 0.123192i | −0.389504 | − | 0.921025i | \(-0.627354\pi\) |
0.602879 | + | 0.797833i | \(0.294020\pi\) | |||||||
\(264\) | −7.80018 | − | 3.39807i | −0.480068 | − | 0.209137i | ||||
\(265\) | 10.5809i | 0.649979i | ||||||||
\(266\) | −7.20574 | − | 4.59462i | −0.441812 | − | 0.281714i | ||||
\(267\) | −11.2839 | − | 15.2716i | −0.690565 | − | 0.934604i | ||||
\(268\) | 13.7456 | − | 7.93605i | 0.839648 | − | 0.484771i | ||||
\(269\) | −1.12373 | − | 1.94636i | −0.0685152 | − | 0.118672i | 0.829733 | − | 0.558161i | \(-0.188493\pi\) |
−0.898248 | + | 0.439489i | \(0.855160\pi\) | |||||||
\(270\) | −5.10716 | − | 0.957584i | −0.310812 | − | 0.0582767i | ||||
\(271\) | 2.70149 | + | 4.67912i | 0.164104 | + | 0.284236i | 0.936337 | − | 0.351103i | \(-0.114193\pi\) |
−0.772233 | + | 0.635340i | \(0.780860\pi\) | |||||||
\(272\) | 3.39530 | + | 1.96028i | 0.205870 | + | 0.118859i | ||||
\(273\) | −5.47527 | + | 4.04559i | −0.331378 | + | 0.244851i | ||||
\(274\) | 4.10085i | 0.247741i | ||||||||
\(275\) | −4.25411 | − | 2.45611i | −0.256532 | − | 0.148109i | ||||
\(276\) | −1.33025 | − | 11.7481i | −0.0800719 | − | 0.707155i | ||||
\(277\) | −20.1531 | −1.21088 | −0.605441 | − | 0.795890i | \(-0.707003\pi\) | ||||
−0.605441 | + | 0.795890i | \(0.707003\pi\) | |||||||
\(278\) | −13.4834 | −0.808680 | ||||||||
\(279\) | −0.513170 | + | 0.477206i | −0.0307227 | + | 0.0285696i | ||||
\(280\) | 1.69791 | − | 0.980288i | 0.101469 | − | 0.0585834i | ||||
\(281\) | −9.35418 | + | 16.2019i | −0.558023 | + | 0.966525i | 0.439638 | + | 0.898175i | \(0.355107\pi\) |
−0.997661 | + | 0.0683499i | \(0.978227\pi\) | |||||||
\(282\) | −2.95061 | − | 1.28540i | −0.175706 | − | 0.0765447i | ||||
\(283\) | 10.5801 | + | 18.3252i | 0.628919 | + | 1.08932i | 0.987769 | + | 0.155924i | \(0.0498355\pi\) |
−0.358850 | + | 0.933395i | \(0.616831\pi\) | |||||||
\(284\) | 4.52879 | 0.268734 | ||||||||
\(285\) | −4.21495 | − | 6.26372i | −0.249672 | − | 0.371031i | ||||
\(286\) | −9.84775 | −0.582310 | ||||||||
\(287\) | −11.5331 | − | 19.9758i | −0.680775 | − | 1.17914i | ||||
\(288\) | 2.92405 | − | 0.670786i | 0.172301 | − | 0.0395264i | ||||
\(289\) | −0.814625 | + | 1.41097i | −0.0479191 | + | 0.0829984i | ||||
\(290\) | −4.35910 | + | 2.51673i | −0.255975 | + | 0.147787i | ||||
\(291\) | 2.99638 | + | 26.4625i | 0.175651 | + | 1.55126i | ||||
\(292\) | −2.27778 | −0.133297 | ||||||||
\(293\) | −12.3120 | −0.719275 | −0.359638 | − | 0.933092i | \(-0.617100\pi\) | ||||
−0.359638 | + | 0.933092i | \(0.617100\pi\) | |||||||
\(294\) | 5.43189 | − | 0.615059i | 0.316794 | − | 0.0358709i | ||||
\(295\) | −7.37643 | − | 4.25879i | −0.429472 | − | 0.247956i | ||||
\(296\) | − | 7.19430i | − | 0.418160i | ||||||
\(297\) | 8.47007 | + | 24.0783i | 0.491483 | + | 1.39717i | ||||
\(298\) | 3.99172 | + | 2.30462i | 0.231234 | + | 0.133503i | ||||
\(299\) | −6.84234 | − | 11.8513i | −0.395702 | − | 0.685377i | ||||
\(300\) | 1.72105 | − | 0.194877i | 0.0993650 | − | 0.0112512i | ||||
\(301\) | 5.77364 | + | 10.0002i | 0.332787 | + | 0.576405i | ||||
\(302\) | −15.0311 | + | 8.67821i | −0.864943 | + | 0.499375i | ||||
\(303\) | 15.9961 | − | 11.8193i | 0.918953 | − | 0.679001i | ||||
\(304\) | 3.67532 | + | 2.34350i | 0.210794 | + | 0.134409i | ||||
\(305\) | 7.82756i | 0.448205i | ||||||||
\(306\) | −2.62985 | − | 11.4639i | −0.150339 | − | 0.655347i | ||||
\(307\) | −13.1520 | + | 7.59331i | −0.750624 | + | 0.433373i | −0.825919 | − | 0.563788i | \(-0.809343\pi\) |
0.0752952 | + | 0.997161i | \(0.476010\pi\) | |||||||
\(308\) | −8.34049 | − | 4.81539i | −0.475244 | − | 0.274382i | ||||
\(309\) | −2.80004 | − | 1.21981i | −0.159288 | − | 0.0693924i | ||||
\(310\) | 0.116794 | − | 0.202293i | 0.00663344 | − | 0.0114895i | ||||
\(311\) | − | 31.8839i | − | 1.80797i | −0.427563 | − | 0.903986i | \(-0.640628\pi\) | ||
0.427563 | − | 0.903986i | \(-0.359372\pi\) | |||||||
\(312\) | 2.79269 | − | 2.06347i | 0.158105 | − | 0.116821i | ||||
\(313\) | −7.47579 | + | 12.9485i | −0.422557 | + | 0.731890i | −0.996189 | − | 0.0872234i | \(-0.972201\pi\) |
0.573632 | + | 0.819113i | \(0.305534\pi\) | |||||||
\(314\) | 0.833700 | − | 1.44401i | 0.0470484 | − | 0.0814902i | ||||
\(315\) | −5.62232 | − | 1.72747i | −0.316782 | − | 0.0973321i | ||||
\(316\) | 12.4592i | 0.700883i | ||||||||
\(317\) | −12.7583 | + | 22.0980i | −0.716577 | + | 1.24115i | 0.245771 | + | 0.969328i | \(0.420959\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(318\) | −7.31942 | + | 16.8015i | −0.410452 | + | 0.942183i | ||||
\(319\) | 21.4128 | + | 12.3627i | 1.19889 | + | 0.692179i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | 2.08310 | − | 4.78171i | 0.116267 | − | 0.266889i | ||||
\(322\) | − | 13.3832i | − | 0.745814i | ||||||
\(323\) | 9.18784 | − | 14.4093i | 0.511225 | − | 0.801755i | ||||
\(324\) | −7.44731 | − | 5.05348i | −0.413739 | − | 0.280749i | ||||
\(325\) | 1.73616 | − | 1.00237i | 0.0963049 | − | 0.0556016i | ||||
\(326\) | −4.27970 | − | 7.41266i | −0.237031 | − | 0.410549i | ||||
\(327\) | −2.03861 | − | 18.0040i | −0.112735 | − | 0.995621i | ||||
\(328\) | 5.88249 | + | 10.1888i | 0.324806 | + | 0.562580i | ||||
\(329\) | −3.15500 | − | 1.82154i | −0.173941 | − | 0.100425i | ||||
\(330\) | −5.05612 | − | 6.84290i | −0.278330 | − | 0.376689i | ||||
\(331\) | 23.6270i | 1.29866i | 0.760508 | + | 0.649329i | \(0.224950\pi\) | ||||
−0.760508 | + | 0.649329i | \(0.775050\pi\) | |||||||
\(332\) | 11.8742 | + | 6.85554i | 0.651679 | + | 0.376247i | ||||
\(333\) | −15.8052 | + | 14.6975i | −0.866120 | + | 0.805420i | ||||
\(334\) | −9.69066 | −0.530249 | ||||||||
\(335\) | 15.8721 | 0.867185 | ||||||||
\(336\) | 3.37425 | − | 0.382070i | 0.184081 | − | 0.0208436i | ||||
\(337\) | −1.65491 | + | 0.955464i | −0.0901489 | + | 0.0520475i | −0.544397 | − | 0.838828i | \(-0.683241\pi\) |
0.454248 | + | 0.890875i | \(0.349908\pi\) | |||||||
\(338\) | −4.49050 | + | 7.77777i | −0.244251 | + | 0.423055i | ||||
\(339\) | −8.41105 | + | 19.3074i | −0.456826 | + | 1.04863i | ||||
\(340\) | 1.96028 | + | 3.39530i | 0.106311 | + | 0.184136i | ||||
\(341\) | −1.14743 | −0.0621370 | ||||||||
\(342\) | −2.36000 | − | 12.8620i | −0.127614 | − | 0.695496i | ||||
\(343\) | 19.9119 | 1.07514 | ||||||||
\(344\) | −2.94487 | − | 5.10067i | −0.158777 | − | 0.275010i | ||||
\(345\) | 4.72204 | − | 10.8393i | 0.254226 | − | 0.583569i | ||||
\(346\) | −5.22274 | + | 9.04605i | −0.280776 | + | 0.486319i | ||||
\(347\) | 13.6960 | − | 7.90736i | 0.735237 | − | 0.424489i | −0.0850978 | − | 0.996373i | \(-0.527120\pi\) |
0.820335 | + | 0.571883i | \(0.193787\pi\) | |||||||
\(348\) | −8.66284 | + | 0.980902i | −0.464377 | + | 0.0525819i | ||||
\(349\) | −29.7786 | −1.59401 | −0.797006 | − | 0.603972i | \(-0.793584\pi\) | ||||
−0.797006 | + | 0.603972i | \(0.793584\pi\) | |||||||
\(350\) | 1.96058 | 0.104797 | ||||||||
\(351\) | −10.2385 | − | 1.91971i | −0.546493 | − | 0.102467i | ||||
\(352\) | 4.25411 | + | 2.45611i | 0.226745 | + | 0.130911i | ||||
\(353\) | 2.45671i | 0.130758i | 0.997861 | + | 0.0653788i | \(0.0208256\pi\) | ||||
−0.997861 | + | 0.0653788i | \(0.979174\pi\) | |||||||
\(354\) | −8.76709 | − | 11.8653i | −0.465965 | − | 0.630633i | ||||
\(355\) | 3.92204 | + | 2.26439i | 0.208160 | + | 0.120182i | ||||
\(356\) | 5.48139 | + | 9.49404i | 0.290513 | + | 0.503183i | ||||
\(357\) | −1.49793 | − | 13.2289i | −0.0792787 | − | 0.700150i | ||||
\(358\) | 0.673349 | + | 1.16628i | 0.0355876 | + | 0.0616396i | ||||
\(359\) | 3.05773 | − | 1.76538i | 0.161381 | − | 0.0931733i | −0.417135 | − | 0.908845i | \(-0.636966\pi\) |
0.578515 | + | 0.815671i | \(0.303632\pi\) | |||||||
\(360\) | 2.86769 | + | 0.881106i | 0.151141 | + | 0.0464384i | ||||
\(361\) | 10.9104 | − | 15.5552i | 0.574232 | − | 0.818693i | ||||
\(362\) | − | 14.6171i | − | 0.768257i | ||||||
\(363\) | −9.08271 | + | 20.8491i | −0.476719 | + | 1.09430i | ||||
\(364\) | 3.40387 | − | 1.96523i | 0.178411 | − | 0.103006i | ||||
\(365\) | −1.97262 | − | 1.13889i | −0.103251 | − | 0.0596123i | ||||
\(366\) | −5.41478 | + | 12.4295i | −0.283035 | + | 0.649700i | ||||
\(367\) | −1.33512 | + | 2.31249i | −0.0696925 | + | 0.120711i | −0.898766 | − | 0.438429i | \(-0.855535\pi\) |
0.829073 | + | 0.559140i | \(0.188868\pi\) | |||||||
\(368\) | 6.82614i | 0.355837i | ||||||||
\(369\) | 10.3662 | − | 33.7383i | 0.539642 | − | 1.75635i | ||||
\(370\) | 3.59715 | − | 6.23045i | 0.187007 | − | 0.323906i | ||||
\(371\) | −10.3723 | + | 17.9654i | −0.538503 | + | 0.932715i | ||||
\(372\) | 0.325396 | − | 0.240431i | 0.0168710 | − | 0.0124657i | ||||
\(373\) | 4.16443i | 0.215626i | 0.994171 | + | 0.107813i | \(0.0343848\pi\) | ||||
−0.994171 | + | 0.107813i | \(0.965615\pi\) | |||||||
\(374\) | 9.62931 | − | 16.6785i | 0.497920 | − | 0.862422i | ||||
\(375\) | 1.58791 | + | 0.691758i | 0.0819995 | + | 0.0357223i | ||||
\(376\) | 1.60922 | + | 0.929084i | 0.0829892 | + | 0.0479138i | ||||
\(377\) | −8.73888 | + | 5.04540i | −0.450075 | + | 0.259851i | ||||
\(378\) | −7.73277 | − | 6.63237i | −0.397731 | − | 0.341132i | ||||
\(379\) | 10.8219i | 0.555884i | 0.960598 | + | 0.277942i | \(0.0896523\pi\) | ||||
−0.960598 | + | 0.277942i | \(0.910348\pi\) | |||||||
\(380\) | 2.01117 | + | 3.86720i | 0.103171 | + | 0.198383i | ||||
\(381\) | 18.0287 | − | 13.3211i | 0.923637 | − | 0.682462i | ||||
\(382\) | −5.27726 | + | 3.04683i | −0.270008 | + | 0.155889i | ||||
\(383\) | 8.28137 | + | 14.3437i | 0.423158 | + | 0.732931i | 0.996246 | − | 0.0865623i | \(-0.0275882\pi\) |
−0.573088 | + | 0.819494i | \(0.694255\pi\) | |||||||
\(384\) | −1.72105 | + | 0.194877i | −0.0878271 | + | 0.00994475i | ||||
\(385\) | −4.81539 | − | 8.34049i | −0.245415 | − | 0.425071i | ||||
\(386\) | −2.59888 | − | 1.50046i | −0.132279 | − | 0.0763715i | ||||
\(387\) | −5.18949 | + | 16.8900i | −0.263797 | + | 0.858565i | ||||
\(388\) | − | 15.3758i | − | 0.780587i | ||||||
\(389\) | 32.4626 | + | 18.7423i | 1.64592 | + | 0.950273i | 0.978670 | + | 0.205440i | \(0.0658625\pi\) |
0.667251 | + | 0.744833i | \(0.267471\pi\) | |||||||
\(390\) | 3.45027 | − | 0.390678i | 0.174711 | − | 0.0197827i | ||||
\(391\) | 26.7623 | 1.35343 | ||||||||
\(392\) | −3.15615 | −0.159409 | ||||||||
\(393\) | 1.74254 | + | 15.3893i | 0.0878997 | + | 0.776286i | ||||
\(394\) | 2.14864 | − | 1.24052i | 0.108247 | − | 0.0624965i | ||||
\(395\) | −6.22958 | + | 10.7900i | −0.313444 | + | 0.542902i | ||||
\(396\) | −3.29505 | − | 14.3636i | −0.165582 | − | 0.721796i | ||||
\(397\) | −2.65169 | − | 4.59286i | −0.133085 | − | 0.230509i | 0.791780 | − | 0.610807i | \(-0.209155\pi\) |
−0.924864 | + | 0.380298i | \(0.875822\pi\) | |||||||
\(398\) | 23.6124 | 1.18358 | ||||||||
\(399\) | −1.01636 | − | 14.7671i | −0.0508815 | − | 0.739279i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −3.00036 | − | 5.19678i | −0.149831 | − | 0.259515i | 0.781334 | − | 0.624113i | \(-0.214540\pi\) |
−0.931165 | + | 0.364598i | \(0.881206\pi\) | |||||||
\(402\) | 25.2035 | + | 10.9797i | 1.25704 | + | 0.547615i | ||||
\(403\) | 0.234142 | − | 0.405546i | 0.0116634 | − | 0.0202017i | ||||
\(404\) | −9.94449 | + | 5.74146i | −0.494757 | + | 0.285648i | ||||
\(405\) | −3.92282 | − | 8.10009i | −0.194926 | − | 0.402497i | ||||
\(406\) | −9.86847 | −0.489764 | ||||||||
\(407\) | −35.3400 | −1.75174 | ||||||||
\(408\) | 0.764024 | + | 6.74748i | 0.0378248 | + | 0.334050i | ||||
\(409\) | −23.6531 | − | 13.6561i | −1.16957 | − | 0.675253i | −0.215993 | − | 0.976395i | \(-0.569299\pi\) |
−0.953579 | + | 0.301143i | \(0.902632\pi\) | |||||||
\(410\) | 11.7650i | 0.581030i | ||||||||
\(411\) | −5.71263 | + | 4.22098i | −0.281783 | + | 0.208206i | ||||
\(412\) | 1.52710 | + | 0.881671i | 0.0752348 | + | 0.0434368i | ||||
\(413\) | −8.34967 | − | 14.4620i | −0.410860 | − | 0.711631i | ||||
\(414\) | 14.9964 | − | 13.9454i | 0.737032 | − | 0.685379i | ||||
\(415\) | 6.85554 | + | 11.8742i | 0.336525 | + | 0.582879i | ||||
\(416\) | −1.73616 | + | 1.00237i | −0.0851223 | + | 0.0491454i | ||||
\(417\) | −13.8784 | − | 18.7829i | −0.679627 | − | 0.919801i | ||||
\(418\) | 11.5118 | − | 18.0540i | 0.563061 | − | 0.883049i | ||||
\(419\) | 5.21876i | 0.254953i | 0.991842 | + | 0.127477i | \(0.0406878\pi\) | ||||
−0.991842 | + | 0.127477i | \(0.959312\pi\) | |||||||
\(420\) | 3.11322 | + | 1.35624i | 0.151910 | + | 0.0661780i | ||||
\(421\) | 0.601100 | − | 0.347045i | 0.0292958 | − | 0.0169139i | −0.485281 | − | 0.874358i | \(-0.661283\pi\) |
0.514576 | + | 0.857445i | \(0.327949\pi\) | |||||||
\(422\) | −2.52326 | − | 1.45680i | −0.122830 | − | 0.0709160i | ||||
\(423\) | −1.24643 | − | 5.43337i | −0.0606036 | − | 0.264179i | ||||
\(424\) | 5.29044 | − | 9.16331i | 0.256927 | − | 0.445010i | ||||
\(425\) | 3.92055i | 0.190175i | ||||||||
\(426\) | 4.66145 | + | 6.30877i | 0.225848 | + | 0.305661i | ||||
\(427\) | −7.67326 | + | 13.2905i | −0.371335 | + | 0.643171i | ||||
\(428\) | −1.50566 | + | 2.60787i | −0.0727787 | + | 0.126056i | ||||
\(429\) | −10.1362 | − | 13.7183i | −0.489382 | − | 0.662325i | ||||
\(430\) | − | 5.88974i | − | 0.284029i | ||||||
\(431\) | 8.30269 | − | 14.3807i | 0.399926 | − | 0.692693i | −0.593790 | − | 0.804620i | \(-0.702369\pi\) |
0.993716 | + | 0.111927i | \(0.0357024\pi\) | |||||||
\(432\) | 3.94413 | + | 3.38287i | 0.189762 | + | 0.162758i | ||||
\(433\) | 18.0716 | + | 10.4336i | 0.868465 | + | 0.501409i | 0.866838 | − | 0.498590i | \(-0.166149\pi\) |
0.00162720 | + | 0.999999i | \(0.499482\pi\) | |||||||
\(434\) | 0.396610 | − | 0.228983i | 0.0190379 | − | 0.0109915i | ||||
\(435\) | −7.99269 | − | 3.48193i | −0.383220 | − | 0.166946i | ||||
\(436\) | 10.4610i | 0.500992i | ||||||||
\(437\) | 29.7256 | + | 1.30976i | 1.42197 | + | 0.0626543i | ||||
\(438\) | −2.34451 | − | 3.17304i | −0.112025 | − | 0.151613i | ||||
\(439\) | −9.46913 | + | 5.46701i | −0.451937 | + | 0.260926i | −0.708648 | − | 0.705562i | \(-0.750695\pi\) |
0.256711 | + | 0.966488i | \(0.417361\pi\) | |||||||
\(440\) | 2.45611 | + | 4.25411i | 0.117090 | + | 0.202807i | ||||
\(441\) | 6.44782 | + | 6.93375i | 0.307039 | + | 0.330179i | ||||
\(442\) | 3.92986 | + | 6.80671i | 0.186924 | + | 0.323762i | ||||
\(443\) | 32.8931 | + | 18.9908i | 1.56280 | + | 0.902281i | 0.996972 | + | 0.0777559i | \(0.0247755\pi\) |
0.565825 | + | 0.824525i | \(0.308558\pi\) | |||||||
\(444\) | 10.0219 | − | 7.40505i | 0.475620 | − | 0.351428i | ||||
\(445\) | 10.9628i | 0.519685i | ||||||||
\(446\) | −3.39391 | − | 1.95947i | −0.160706 | − | 0.0927838i | ||||
\(447\) | 0.898233 | + | 7.93275i | 0.0424849 | + | 0.375206i | ||||
\(448\) | −1.96058 | −0.0926285 | ||||||||
\(449\) | 37.0794 | 1.74989 | 0.874944 | − | 0.484225i | \(-0.160898\pi\) | ||||
0.874944 | + | 0.484225i | \(0.160898\pi\) | |||||||
\(450\) | 2.04294 | + | 2.19691i | 0.0963051 | + | 0.103563i | ||||
\(451\) | 50.0494 | − | 28.8961i | 2.35674 | − | 1.36066i | ||||
\(452\) | 6.07947 | − | 10.5300i | 0.285954 | − | 0.495287i | ||||
\(453\) | −27.5605 | − | 12.0065i | −1.29491 | − | 0.564112i | ||||
\(454\) | 0.158042 | + | 0.273737i | 0.00741729 | + | 0.0128471i | ||||
\(455\) | 3.93045 | 0.184263 | ||||||||
\(456\) | 0.518398 | + | 7.53202i | 0.0242762 | + | 0.352719i | ||||
\(457\) | 24.8264 | 1.16133 | 0.580665 | − | 0.814142i | \(-0.302793\pi\) | ||||
0.580665 | + | 0.814142i | \(0.302793\pi\) | |||||||
\(458\) | −3.06670 | − | 5.31168i | −0.143297 | − | 0.248198i | ||||
\(459\) | 13.2627 | − | 15.4632i | 0.619051 | − | 0.721760i | ||||
\(460\) | −3.41307 | + | 5.91161i | −0.159135 | + | 0.275630i | ||||
\(461\) | 4.14251 | − | 2.39168i | 0.192936 | − | 0.111392i | −0.400420 | − | 0.916332i | \(-0.631136\pi\) |
0.593356 | + | 0.804940i | \(0.297803\pi\) | |||||||
\(462\) | −1.87681 | − | 16.5751i | −0.0873172 | − | 0.771142i | ||||
\(463\) | −19.1590 | −0.890394 | −0.445197 | − | 0.895433i | \(-0.646866\pi\) | ||||
−0.445197 | + | 0.895433i | \(0.646866\pi\) | |||||||
\(464\) | 5.03345 | 0.233672 | ||||||||
\(465\) | 0.402017 | − | 0.0455208i | 0.0186431 | − | 0.00211097i | ||||
\(466\) | 9.37631 | + | 5.41341i | 0.434349 | + | 0.250772i | ||||
\(467\) | − | 18.5479i | − | 0.858296i | −0.903234 | − | 0.429148i | \(-0.858814\pi\) | ||
0.903234 | − | 0.429148i | \(-0.141186\pi\) | |||||||
\(468\) | 5.74899 | + | 1.76639i | 0.265747 | + | 0.0816515i | ||||
\(469\) | 26.9493 | + | 15.5592i | 1.24441 | + | 0.718458i | ||||
\(470\) | 0.929084 | + | 1.60922i | 0.0428554 | + | 0.0742278i | ||||
\(471\) | 2.86968 | − | 0.324937i | 0.132228 | − | 0.0149723i | ||||
\(472\) | 4.25879 | + | 7.37643i | 0.196026 | + | 0.339528i | ||||
\(473\) | −25.0556 | + | 14.4659i | −1.15206 | + | 0.665141i | ||||
\(474\) | −17.3561 | + | 12.8242i | −0.797191 | + | 0.589033i | ||||
\(475\) | −0.191874 | + | 4.35467i | −0.00880380 | + | 0.199806i | ||||
\(476\) | 7.68654i | 0.352312i | ||||||||
\(477\) | −30.9390 | + | 7.09750i | −1.41660 | + | 0.324972i | ||||
\(478\) | 2.75990 | − | 1.59343i | 0.126235 | − | 0.0728817i | ||||
\(479\) | −22.9732 | − | 13.2636i | −1.04967 | − | 0.606028i | −0.127114 | − | 0.991888i | \(-0.540571\pi\) |
−0.922557 | + | 0.385860i | \(0.873905\pi\) | |||||||
\(480\) | −1.58791 | − | 0.691758i | −0.0724780 | − | 0.0315743i | ||||
\(481\) | 7.21137 | − | 12.4905i | 0.328810 | − | 0.569516i | ||||
\(482\) | 19.0892i | 0.869490i | ||||||||
\(483\) | 18.6432 | − | 13.7752i | 0.848297 | − | 0.626794i | ||||
\(484\) | 6.56495 | − | 11.3708i | 0.298407 | − | 0.516855i | ||||
\(485\) | 7.68789 | − | 13.3158i | 0.349089 | − | 0.604640i | ||||
\(486\) | −0.625786 | − | 15.5759i | −0.0283862 | − | 0.706537i | ||||
\(487\) | − | 11.3164i | − | 0.512796i | −0.966571 | − | 0.256398i | \(-0.917464\pi\) | ||
0.966571 | − | 0.256398i | \(-0.0825357\pi\) | |||||||
\(488\) | 3.91378 | − | 6.77887i | 0.177169 | − | 0.306865i | ||||
\(489\) | 5.92104 | − | 13.5916i | 0.267759 | − | 0.614633i | ||||
\(490\) | −2.73330 | − | 1.57807i | −0.123478 | − | 0.0712900i | ||||
\(491\) | −6.02160 | + | 3.47657i | −0.271751 | + | 0.156896i | −0.629683 | − | 0.776852i | \(-0.716815\pi\) |
0.357932 | + | 0.933748i | \(0.383482\pi\) | |||||||
\(492\) | −8.13852 | + | 18.6818i | −0.366913 | + | 0.842239i | ||||
\(493\) | − | 19.7339i | − | 0.888772i | ||||||
\(494\) | 4.03188 | + | 7.75274i | 0.181403 | + | 0.348812i | ||||
\(495\) | 4.32818 | − | 14.0867i | 0.194537 | − | 0.633151i | ||||
\(496\) | −0.202293 | + | 0.116794i | −0.00908322 | + | 0.00524420i | ||||
\(497\) | 4.43951 | + | 7.68946i | 0.199139 | + | 0.344920i | ||||
\(498\) | 2.67197 | + | 23.5975i | 0.119734 | + | 1.05743i | ||||
\(499\) | −17.0361 | − | 29.5074i | −0.762642 | − | 1.32093i | −0.941484 | − | 0.337057i | \(-0.890569\pi\) |
0.178843 | − | 0.983878i | \(-0.442765\pi\) | |||||||
\(500\) | −0.866025 | − | 0.500000i | −0.0387298 | − | 0.0223607i | ||||
\(501\) | −9.97454 | − | 13.4995i | −0.445630 | − | 0.603111i | ||||
\(502\) | − | 11.6470i | − | 0.519833i | ||||||
\(503\) | 3.97574 | + | 2.29540i | 0.177270 | + | 0.102347i | 0.586009 | − | 0.810304i | \(-0.300698\pi\) |
−0.408740 | + | 0.912651i | \(0.634032\pi\) | |||||||
\(504\) | 4.00534 | + | 4.30720i | 0.178412 | + | 0.191858i | ||||
\(505\) | −11.4829 | −0.510983 | ||||||||
\(506\) | 33.5315 | 1.49066 | ||||||||
\(507\) | −15.4568 | + | 1.75019i | −0.686459 | + | 0.0777284i | ||||
\(508\) | −11.2081 | + | 6.47100i | −0.497279 | + | 0.287104i | ||||
\(509\) | −10.1206 | + | 17.5295i | −0.448590 | + | 0.776980i | −0.998294 | − | 0.0583790i | \(-0.981407\pi\) |
0.549705 | + | 0.835359i | \(0.314740\pi\) | |||||||
\(510\) | −2.71208 | + | 6.22550i | −0.120093 | + | 0.275670i | ||||
\(511\) | −2.23288 | − | 3.86746i | −0.0987769 | − | 0.171087i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.4881 | − | 16.5263i | 0.683815 | − | 0.729655i | ||||
\(514\) | −23.5470 | −1.03861 | ||||||||
\(515\) | 0.881671 | + | 1.52710i | 0.0388511 | + | 0.0672920i | ||||
\(516\) | 4.07428 | − | 9.35241i | 0.179360 | − | 0.411717i | ||||
\(517\) | 4.56386 | − | 7.90484i | 0.200718 | − | 0.347655i | ||||
\(518\) | 12.2153 | − | 7.05248i | 0.536708 | − | 0.309868i | ||||
\(519\) | −17.9772 | + | 2.03558i | −0.789113 | + | 0.0893520i | ||||
\(520\) | −2.00475 | −0.0879139 | ||||||||
\(521\) | −19.3708 | −0.848650 | −0.424325 | − | 0.905510i | \(-0.639489\pi\) | ||||
−0.424325 | + | 0.905510i | \(0.639489\pi\) | |||||||
\(522\) | −10.2830 | − | 11.0580i | −0.450077 | − | 0.483997i | ||||
\(523\) | −35.0535 | − | 20.2382i | −1.53278 | − | 0.884954i | −0.999232 | − | 0.0391867i | \(-0.987523\pi\) |
−0.533553 | − | 0.845767i | \(-0.679143\pi\) | |||||||
\(524\) | − | 8.94178i | − | 0.390624i | ||||||
\(525\) | 2.01801 | + | 2.73115i | 0.0880731 | + | 0.119197i | ||||
\(526\) | −3.46036 | − | 1.99784i | −0.150879 | − | 0.0871099i | ||||
\(527\) | 0.457897 | + | 0.793100i | 0.0199463 | + | 0.0345480i | ||||
\(528\) | 0.957276 | + | 8.45419i | 0.0416601 | + | 0.367921i | ||||
\(529\) | 11.7981 | + | 20.4349i | 0.512960 | + | 0.888473i | ||||
\(530\) | 9.16331 | − | 5.29044i | 0.398029 | − | 0.229802i | ||||
\(531\) | 7.50488 | − | 24.4258i | 0.325684 | − | 1.05999i | ||||
\(532\) | −0.376184 | + | 8.53767i | −0.0163096 | + | 0.370155i | ||||
\(533\) | 23.5858i | 1.02161i | ||||||||
\(534\) | −7.58359 | + | 17.4079i | −0.328174 | + | 0.753315i | ||||
\(535\) | −2.60787 | + | 1.50566i | −0.112748 | + | 0.0650952i | ||||
\(536\) | −13.7456 | − | 7.93605i | −0.593721 | − | 0.342785i | ||||
\(537\) | −0.931590 | + | 2.13844i | −0.0402011 | + | 0.0922806i | ||||
\(538\) | −1.12373 | + | 1.94636i | −0.0484476 | + | 0.0839137i | ||||
\(539\) | 15.5037i | 0.667791i | ||||||||
\(540\) | 1.72429 | + | 4.90172i | 0.0742014 | + | 0.210936i | ||||
\(541\) | 14.7204 | − | 25.4965i | 0.632879 | − | 1.09618i | −0.354082 | − | 0.935215i | \(-0.615206\pi\) |
0.986960 | − | 0.160964i | \(-0.0514602\pi\) | |||||||
\(542\) | 2.70149 | − | 4.67912i | 0.116039 | − | 0.200985i | ||||
\(543\) | 20.3621 | − | 15.0453i | 0.873823 | − | 0.645655i | ||||
\(544\) | − | 3.92055i | − | 0.168092i | ||||||
\(545\) | −5.23051 | + | 9.05950i | −0.224050 | + | 0.388067i | ||||
\(546\) | 6.24122 | + | 2.71892i | 0.267100 | + | 0.116359i | ||||
\(547\) | 10.3833 | + | 5.99478i | 0.443956 | + | 0.256318i | 0.705274 | − | 0.708935i | \(-0.250824\pi\) |
−0.261318 | + | 0.965253i | \(0.584157\pi\) | |||||||
\(548\) | 3.55144 | − | 2.05042i | 0.151710 | − | 0.0875898i | ||||
\(549\) | −22.8882 | + | 5.25062i | −0.976843 | + | 0.224091i | ||||
\(550\) | 4.91222i | 0.209458i | ||||||||
\(551\) | 0.965790 | − | 21.9191i | 0.0411441 | − | 0.933783i | ||||
\(552\) | −9.50907 | + | 7.02611i | −0.404733 | + | 0.299051i | ||||
\(553\) | −21.1545 | + | 12.2136i | −0.899582 | + | 0.519374i | ||||
\(554\) | 10.0766 | + | 17.4531i | 0.428112 | + | 0.741511i | ||||
\(555\) | 12.3818 | − | 1.40200i | 0.525577 | − | 0.0595116i | ||||
\(556\) | 6.74169 | + | 11.6770i | 0.285911 | + | 0.495213i | ||||
\(557\) | −24.0375 | − | 13.8780i | −1.01850 | − | 0.588031i | −0.104831 | − | 0.994490i | \(-0.533430\pi\) |
−0.913669 | + | 0.406459i | \(0.866763\pi\) | |||||||
\(558\) | 0.669857 | + | 0.205815i | 0.0283573 | + | 0.00871286i | ||||
\(559\) | − | 11.8074i | − | 0.499401i | ||||||
\(560\) | −1.69791 | − | 0.980288i | −0.0717497 | − | 0.0414247i | ||||
\(561\) | 33.1451 | − | 3.75305i | 1.39939 | − | 0.158454i | ||||
\(562\) | 18.7084 | 0.789164 | ||||||||
\(563\) | −17.1980 | −0.724809 | −0.362404 | − | 0.932021i | \(-0.618044\pi\) | ||||
−0.362404 | + | 0.932021i | \(0.618044\pi\) | |||||||
\(564\) | 0.362113 | + | 3.19801i | 0.0152477 | + | 0.134660i | ||||
\(565\) | 10.5300 | − | 6.07947i | 0.442998 | − | 0.255765i | ||||
\(566\) | 10.5801 | − | 18.3252i | 0.444713 | − | 0.770265i | ||||
\(567\) | 1.27984 | − | 17.5987i | 0.0537483 | − | 0.739076i | ||||
\(568\) | −2.26439 | − | 3.92204i | −0.0950118 | − | 0.164565i | ||||
\(569\) | 26.3732 | 1.10562 | 0.552812 | − | 0.833306i | \(-0.313555\pi\) | ||||
0.552812 | + | 0.833306i | \(0.313555\pi\) | |||||||
\(570\) | −3.31706 | + | 6.78212i | −0.138936 | + | 0.284072i | ||||
\(571\) | 6.53285 | 0.273391 | 0.136696 | − | 0.990613i | \(-0.456352\pi\) | ||||
0.136696 | + | 0.990613i | \(0.456352\pi\) | |||||||
\(572\) | 4.92387 | + | 8.52840i | 0.205878 | + | 0.356590i | ||||
\(573\) | −9.67619 | − | 4.21534i | −0.404229 | − | 0.176098i | ||||
\(574\) | −11.5331 | + | 19.9758i | −0.481380 | + | 0.833775i | ||||
\(575\) | −5.91161 | + | 3.41307i | −0.246531 | + | 0.142335i | ||||
\(576\) | −2.04294 | − | 2.19691i | −0.0851225 | − | 0.0915377i | ||||
\(577\) | 6.44640 | 0.268367 | 0.134184 | − | 0.990956i | \(-0.457159\pi\) | ||||
0.134184 | + | 0.990956i | \(0.457159\pi\) | |||||||
\(578\) | 1.62925 | 0.0677679 | ||||||||
\(579\) | −0.584810 | − | 5.16475i | −0.0243039 | − | 0.214640i | ||||
\(580\) | 4.35910 | + | 2.51673i | 0.181002 | + | 0.104501i | ||||
\(581\) | 26.8816i | 1.11524i | ||||||||
\(582\) | 21.4190 | − | 15.8262i | 0.887847 | − | 0.656017i | ||||
\(583\) | −45.0122 | − | 25.9878i | −1.86421 | − | 1.07630i | ||||
\(584\) | 1.13889 | + | 1.97262i | 0.0471276 | + | 0.0816275i | ||||
\(585\) | 4.09558 | + | 4.40424i | 0.169331 | + | 0.182093i | ||||
\(586\) | 6.15600 | + | 10.6625i | 0.254302 | + | 0.440464i | ||||
\(587\) | 29.3043 | − | 16.9188i | 1.20952 | − | 0.698315i | 0.246863 | − | 0.969050i | \(-0.420600\pi\) |
0.962654 | + | 0.270736i | \(0.0872670\pi\) | |||||||
\(588\) | −3.24860 | − | 4.39663i | −0.133970 | − | 0.181314i | ||||
\(589\) | 0.469784 | + | 0.903329i | 0.0193571 | + | 0.0372210i | ||||
\(590\) | 8.51757i | 0.350663i | ||||||||
\(591\) | 3.93968 | + | 1.71628i | 0.162057 | + | 0.0705983i | ||||
\(592\) | −6.23045 | + | 3.59715i | −0.256070 | + | 0.147842i | ||||
\(593\) | −25.1953 | − | 14.5465i | −1.03465 | − | 0.597354i | −0.116335 | − | 0.993210i | \(-0.537114\pi\) |
−0.918312 | + | 0.395856i | \(0.870448\pi\) | |||||||
\(594\) | 16.6174 | − | 19.3744i | 0.681820 | − | 0.794943i | ||||
\(595\) | −3.84327 | + | 6.65674i | −0.157559 | + | 0.272900i | ||||
\(596\) | − | 4.60924i | − | 0.188802i | ||||||
\(597\) | 24.3041 | + | 32.8929i | 0.994700 | + | 1.34622i | ||||
\(598\) | −6.84234 | + | 11.8513i | −0.279804 | + | 0.484635i | ||||
\(599\) | −13.7688 | + | 23.8483i | −0.562580 | + | 0.974416i | 0.434691 | + | 0.900580i | \(0.356858\pi\) |
−0.997270 | + | 0.0738365i | \(0.976476\pi\) | |||||||
\(600\) | −1.02929 | − | 1.39304i | −0.0420208 | − | 0.0568705i | ||||
\(601\) | − | 14.9379i | − | 0.609330i | −0.952460 | − | 0.304665i | \(-0.901455\pi\) | ||
0.952460 | − | 0.304665i | \(-0.0985445\pi\) | |||||||
\(602\) | 5.77364 | − | 10.0002i | 0.235316 | − | 0.407580i | ||||
\(603\) | 10.6468 | + | 46.4107i | 0.433570 | + | 1.88999i | ||||
\(604\) | 15.0311 | + | 8.67821i | 0.611607 | + | 0.353111i | ||||
\(605\) | 11.3708 | − | 6.56495i | 0.462290 | − | 0.266903i | ||||
\(606\) | −18.2339 | − | 7.94340i | −0.740701 | − | 0.322679i | ||||
\(607\) | − | 42.6299i | − | 1.73030i | −0.501517 | − | 0.865148i | \(-0.667225\pi\) | ||
0.501517 | − | 0.865148i | \(-0.332775\pi\) | |||||||
\(608\) | 0.191874 | − | 4.35467i | 0.00778153 | − | 0.176605i | ||||
\(609\) | −10.1576 | − | 13.7471i | −0.411605 | − | 0.557062i | ||||
\(610\) | 6.77887 | − | 3.91378i | 0.274468 | − | 0.158464i | ||||
\(611\) | 1.86258 | + | 3.22608i | 0.0753518 | + | 0.130513i | ||||
\(612\) | −8.61309 | + | 8.00946i | −0.348163 | + | 0.323763i | ||||
\(613\) | 8.76635 | + | 15.1838i | 0.354069 | + | 0.613266i | 0.986958 | − | 0.160976i | \(-0.0514643\pi\) |
−0.632889 | + | 0.774243i | \(0.718131\pi\) | |||||||
\(614\) | 13.1520 | + | 7.59331i | 0.530771 | + | 0.306441i | ||||
\(615\) | −16.3890 | + | 12.1096i | −0.660870 | + | 0.488307i | ||||
\(616\) | 9.63077i | 0.388035i | ||||||||
\(617\) | −38.2258 | − | 22.0697i | −1.53891 | − | 0.888491i | −0.998903 | − | 0.0468313i | \(-0.985088\pi\) |
−0.540008 | − | 0.841660i | \(-0.681579\pi\) | |||||||
\(618\) | 0.343634 | + | 3.03481i | 0.0138230 | + | 0.122078i | ||||
\(619\) | −42.3600 | −1.70259 | −0.851296 | − | 0.524685i | \(-0.824183\pi\) | ||||
−0.851296 | + | 0.524685i | \(0.824183\pi\) | |||||||
\(620\) | −0.233588 | −0.00938111 | ||||||||
\(621\) | 34.8622 | + | 6.53660i | 1.39897 | + | 0.262305i | ||||
\(622\) | −27.6123 | + | 15.9420i | −1.10715 | + | 0.639214i | ||||
\(623\) | −10.7467 | + | 18.6138i | −0.430556 | + | 0.745746i | ||||
\(624\) | −3.18336 | − | 1.38680i | −0.127437 | − | 0.0555164i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 14.9516 | 0.597585 | ||||||||
\(627\) | 36.9989 | − | 2.54648i | 1.47759 | − | 0.101697i | ||||
\(628\) | −1.66740 | −0.0665365 | ||||||||
\(629\) | 14.1028 | + | 24.4268i | 0.562316 | + | 0.973961i | ||||
\(630\) | 1.31513 | + | 5.73281i | 0.0523959 | + | 0.228401i | ||||
\(631\) | −17.6187 | + | 30.5165i | −0.701391 | + | 1.21484i | 0.266588 | + | 0.963811i | \(0.414104\pi\) |
−0.967978 | + | 0.251033i | \(0.919230\pi\) | |||||||
\(632\) | 10.7900 | − | 6.22958i | 0.429201 | − | 0.247800i | ||||
\(633\) | −0.567793 | − | 5.01447i | −0.0225678 | − | 0.199307i | ||||
\(634\) | 25.5166 | 1.01339 | ||||||||
\(635\) | −12.9420 | −0.513587 | ||||||||
\(636\) | 18.2103 | − | 2.06197i | 0.722084 | − | 0.0817623i | ||||
\(637\) | −5.47957 | − | 3.16363i | −0.217109 | − | 0.125348i | ||||
\(638\) | − | 24.7254i | − | 0.978889i | ||||||
\(639\) | −3.99034 | + | 12.9872i | −0.157855 | + | 0.513764i | ||||
\(640\) | 0.866025 | + | 0.500000i | 0.0342327 | + | 0.0197642i | ||||
\(641\) | −12.1088 | − | 20.9730i | −0.478267 | − | 0.828383i | 0.521422 | − | 0.853299i | \(-0.325402\pi\) |
−0.999690 | + | 0.0249155i | \(0.992068\pi\) | |||||||
\(642\) | −5.18263 | + | 0.586834i | −0.204542 | + | 0.0231605i | ||||
\(643\) | −8.96485 | − | 15.5276i | −0.353539 | − | 0.612348i | 0.633328 | − | 0.773884i | \(-0.281689\pi\) |
−0.986867 | + | 0.161536i | \(0.948355\pi\) | |||||||
\(644\) | −11.5902 | + | 6.69158i | −0.456716 | + | 0.263685i | ||||
\(645\) | 8.20463 | − | 6.06228i | 0.323057 | − | 0.238702i | ||||
\(646\) | −17.0727 | − | 0.752254i | −0.671718 | − | 0.0295970i | ||||
\(647\) | − | 16.2268i | − | 0.637940i | −0.947765 | − | 0.318970i | \(-0.896663\pi\) | ||
0.947765 | − | 0.318970i | \(-0.103337\pi\) | |||||||
\(648\) | −0.652788 | + | 8.97629i | −0.0256439 | + | 0.352622i | ||||
\(649\) | 36.2346 | − | 20.9201i | 1.42233 | − | 0.821185i | ||||
\(650\) | −1.73616 | − | 1.00237i | −0.0680978 | − | 0.0393163i | ||||
\(651\) | 0.727211 | + | 0.316802i | 0.0285016 | + | 0.0124164i | ||||
\(652\) | −4.27970 | + | 7.41266i | −0.167606 | + | 0.290302i | ||||
\(653\) | 13.0356i | 0.510121i | 0.966925 | + | 0.255060i | \(0.0820953\pi\) | ||||
−0.966925 | + | 0.255060i | \(0.917905\pi\) | |||||||
\(654\) | −14.5726 | + | 10.7675i | −0.569833 | + | 0.421041i | ||||
\(655\) | 4.47089 | − | 7.74381i | 0.174692 | − | 0.302576i | ||||
\(656\) | 5.88249 | − | 10.1888i | 0.229672 | − | 0.397804i | ||||
\(657\) | 2.00697 | − | 6.53197i | 0.0782992 | − | 0.254837i | ||||
\(658\) | 3.64308i | 0.142022i | ||||||||
\(659\) | −16.7755 | + | 29.0560i | −0.653480 | + | 1.13186i | 0.328792 | + | 0.944402i | \(0.393358\pi\) |
−0.982272 | + | 0.187459i | \(0.939975\pi\) | |||||||
\(660\) | −3.39807 | + | 7.80018i | −0.132270 | + | 0.303622i | ||||
\(661\) | 13.8780 | + | 8.01246i | 0.539791 | + | 0.311649i | 0.744994 | − | 0.667071i | \(-0.232452\pi\) |
−0.205203 | + | 0.978719i | \(0.565785\pi\) | |||||||
\(662\) | 20.4616 | − | 11.8135i | 0.795262 | − | 0.459145i | ||||
\(663\) | −5.43702 | + | 12.4805i | −0.211156 | + | 0.484704i | ||||
\(664\) | − | 13.7111i | − | 0.532093i | ||||||
\(665\) | −4.59462 | + | 7.20574i | −0.178172 | + | 0.279427i | ||||
\(666\) | 20.6310 | + | 6.33894i | 0.799436 | + | 0.245629i | ||||
\(667\) | 29.7558 | − | 17.1795i | 1.15215 | − | 0.665194i | ||||
\(668\) | 4.84533 | + | 8.39236i | 0.187471 | + | 0.324710i | ||||
\(669\) | −0.763711 | − | 6.74472i | −0.0295268 | − | 0.260766i | ||||
\(670\) | −7.93605 | − | 13.7456i | −0.306596 | − | 0.531040i | ||||
\(671\) | −33.2993 | − | 19.2253i | −1.28550 | − | 0.742186i | ||||
\(672\) | −2.01801 | − | 2.73115i | −0.0778464 | − | 0.105357i | ||||
\(673\) | 31.9714i | 1.23241i | 0.787586 | + | 0.616204i | \(0.211330\pi\) | ||||
−0.787586 | + | 0.616204i | \(0.788670\pi\) | |||||||
\(674\) | 1.65491 | + | 0.955464i | 0.0637449 | + | 0.0368031i | ||||
\(675\) | −0.957584 | + | 5.10716i | −0.0368574 | + | 0.196574i | ||||
\(676\) | 8.98100 | 0.345423 | ||||||||
\(677\) | 25.2864 | 0.971835 | 0.485918 | − | 0.874005i | \(-0.338486\pi\) | ||||
0.485918 | + | 0.874005i | \(0.338486\pi\) | |||||||
\(678\) | 20.9262 | − | 2.36949i | 0.803665 | − | 0.0909998i | ||||
\(679\) | 26.1067 | − | 15.0727i | 1.00188 | − | 0.578437i | ||||
\(680\) | 1.96028 | − | 3.39530i | 0.0751732 | − | 0.130204i | ||||
\(681\) | −0.218654 | + | 0.501915i | −0.00837884 | + | 0.0192334i | ||||
\(682\) | 0.573717 | + | 0.993707i | 0.0219688 | + | 0.0380510i | ||||
\(683\) | −8.39063 | −0.321059 | −0.160529 | − | 0.987031i | \(-0.551320\pi\) | ||||
−0.160529 | + | 0.987031i | \(0.551320\pi\) | |||||||
\(684\) | −9.95880 | + | 8.47481i | −0.380784 | + | 0.324042i | ||||
\(685\) | 4.10085 | 0.156685 | ||||||||
\(686\) | −9.95594 | − | 17.2442i | −0.380120 | − | 0.658387i | ||||
\(687\) | 4.24283 | − | 9.73931i | 0.161874 | − | 0.371578i | ||||
\(688\) | −2.94487 | + | 5.10067i | −0.112272 | + | 0.194461i | ||||
\(689\) | 18.3701 | − | 10.6060i | 0.699846 | − | 0.404056i | ||||
\(690\) | −11.7481 | + | 1.33025i | −0.447244 | + | 0.0506419i | ||||
\(691\) | −10.0647 | −0.382881 | −0.191440 | − | 0.981504i | \(-0.561316\pi\) | ||||
−0.191440 | + | 0.981504i | \(0.561316\pi\) | |||||||
\(692\) | 10.4455 | 0.397078 | ||||||||
\(693\) | 21.1579 | − | 19.6751i | 0.803722 | − | 0.747395i | ||||
\(694\) | −13.6960 | − | 7.90736i | −0.519891 | − | 0.300159i | ||||
\(695\) | 13.4834i | 0.511454i | ||||||||
\(696\) | 5.18091 | + | 7.01179i | 0.196382 | + | 0.265781i | ||||
\(697\) | −39.9456 | − | 23.0626i | −1.51305 | − | 0.873558i | ||||
\(698\) | 14.8893 | + | 25.7890i | 0.563568 | + | 0.976129i | ||||
\(699\) | 2.10989 | + | 18.6335i | 0.0798035 | + | 0.704785i | ||||
\(700\) | −0.980288 | − | 1.69791i | −0.0370514 | − | 0.0641749i | ||||
\(701\) | 29.1351 | − | 16.8212i | 1.10042 | − | 0.635327i | 0.164087 | − | 0.986446i | \(-0.447532\pi\) |
0.936331 | + | 0.351119i | \(0.114199\pi\) | |||||||
\(702\) | 3.45675 | + | 9.82670i | 0.130467 | + | 0.370885i | ||||
\(703\) | 14.4690 | + | 27.8218i | 0.545707 | + | 1.04932i | ||||
\(704\) | − | 4.91222i | − | 0.185136i | ||||||
\(705\) | −1.28540 | + | 2.95061i | −0.0484111 | + | 0.111126i | ||||
\(706\) | 2.12758 | − | 1.22836i | 0.0800724 | − | 0.0462298i | ||||
\(707\) | −19.4969 | − | 11.2566i | −0.733257 | − | 0.423346i | ||||
\(708\) | −5.89210 | + | 13.5252i | −0.221439 | + | 0.508307i | ||||
\(709\) | 22.1508 | − | 38.3664i | 0.831892 | − | 1.44088i | −0.0646434 | − | 0.997908i | \(-0.520591\pi\) |
0.896536 | − | 0.442971i | \(-0.146076\pi\) | |||||||
\(710\) | − | 4.52879i | − | 0.169962i | ||||||
\(711\) | −35.7290 | − | 10.9778i | −1.33994 | − | 0.411701i | ||||
\(712\) | 5.48139 | − | 9.49404i | 0.205424 | − | 0.355804i | ||||
\(713\) | −0.797251 | + | 1.38088i | −0.0298573 | + | 0.0517143i | ||||
\(714\) | −10.7076 | + | 7.91172i | −0.400723 | + | 0.296089i | ||||
\(715\) | 9.84775i | 0.368285i | ||||||||
\(716\) | 0.673349 | − | 1.16628i | 0.0251642 | − | 0.0435858i | ||||
\(717\) | 5.06045 | + | 2.20454i | 0.188986 | + | 0.0823299i | ||||
\(718\) | −3.05773 | − | 1.76538i | −0.114113 | − | 0.0658834i | ||||
\(719\) | −12.8018 | + | 7.39114i | −0.477428 | + | 0.275643i | −0.719344 | − | 0.694654i | \(-0.755557\pi\) |
0.241916 | + | 0.970297i | \(0.422224\pi\) | |||||||
\(720\) | −0.670786 | − | 2.92405i | −0.0249987 | − | 0.108973i | ||||
\(721\) | 3.45717i | 0.128752i | ||||||||
\(722\) | −18.9264 | − | 1.67110i | −0.704367 | − | 0.0621919i | ||||
\(723\) | −26.5920 | + | 19.6484i | −0.988967 | + | 0.730733i | ||||
\(724\) | −12.6588 | + | 7.30854i | −0.470459 | + | 0.271620i | ||||
\(725\) | 2.51673 | + | 4.35910i | 0.0934689 | + | 0.161893i | ||||
\(726\) | 22.5972 | − | 2.55871i | 0.838662 | − | 0.0949625i | ||||
\(727\) | 2.63804 | + | 4.56923i | 0.0978397 | + | 0.169463i | 0.910790 | − | 0.412869i | \(-0.135473\pi\) |
−0.812951 | + | 0.582333i | \(0.802140\pi\) | |||||||
\(728\) | −3.40387 | − | 1.96523i | −0.126156 | − | 0.0728362i | ||||
\(729\) | 21.0537 | − | 16.9039i | 0.779766 | − | 0.626071i | ||||
\(730\) | 2.27778i | 0.0843045i | ||||||||
\(731\) | 19.9975 | + | 11.5455i | 0.739632 | + | 0.427027i | ||||
\(732\) | 13.4716 | − | 1.52541i | 0.497926 | − | 0.0563807i | ||||
\(733\) | −12.3735 | −0.457025 | −0.228513 | − | 0.973541i | \(-0.573386\pi\) | ||||
−0.228513 | + | 0.973541i | \(0.573386\pi\) | |||||||
\(734\) | 2.67023 | 0.0985601 | ||||||||
\(735\) | −0.615059 | − | 5.43189i | −0.0226868 | − | 0.200358i | ||||
\(736\) | 5.91161 | − | 3.41307i | 0.217905 | − | 0.125807i | ||||
\(737\) | −38.9836 | + | 67.5216i | −1.43598 | + | 2.48719i | ||||
\(738\) | −34.4013 | + | 7.89177i | −1.26633 | + | 0.290500i | ||||
\(739\) | 23.4208 | + | 40.5660i | 0.861548 | + | 1.49224i | 0.870435 | + | 0.492284i | \(0.163838\pi\) |
−0.00888687 | + | 0.999961i | \(0.502829\pi\) | |||||||
\(740\) | −7.19430 | −0.264468 | ||||||||
\(741\) | −6.64987 | + | 13.5964i | −0.244289 | + | 0.499477i | ||||
\(742\) | 20.7446 | 0.761559 | ||||||||
\(743\) | 3.70160 | + | 6.41135i | 0.135798 | + | 0.235210i | 0.925902 | − | 0.377763i | \(-0.123307\pi\) |
−0.790104 | + | 0.612973i | \(0.789973\pi\) | |||||||
\(744\) | −0.370917 | − | 0.161586i | −0.0135985 | − | 0.00592404i | ||||
\(745\) | 2.30462 | − | 3.99172i | 0.0844347 | − | 0.146245i | ||||
\(746\) | 3.60651 | − | 2.08222i | 0.132044 | − | 0.0762354i | ||||
\(747\) | −30.1220 | + | 28.0109i | −1.10211 | + | 1.02487i | ||||
\(748\) | −19.2586 | −0.704165 | ||||||||
\(749\) | −5.90391 | −0.215724 | ||||||||
\(750\) | −0.194877 | − | 1.72105i | −0.00711588 | − | 0.0628440i | ||||
\(751\) | −36.7844 | − | 21.2375i | −1.34228 | − | 0.774966i | −0.355139 | − | 0.934814i | \(-0.615566\pi\) |
−0.987142 | + | 0.159848i | \(0.948900\pi\) | |||||||
\(752\) | − | 1.85817i | − | 0.0677604i | ||||||
\(753\) | 16.2248 | − | 11.9882i | 0.591264 | − | 0.436876i | ||||
\(754\) | 8.73888 | + | 5.04540i | 0.318251 | + | 0.183743i | ||||
\(755\) | 8.67821 | + | 15.0311i | 0.315833 | + | 0.547038i | ||||
\(756\) | −1.87742 | + | 10.0130i | −0.0682809 | + | 0.364168i | ||||
\(757\) | 24.8985 | + | 43.1254i | 0.904950 | + | 1.56742i | 0.820984 | + | 0.570951i | \(0.193425\pi\) |
0.0839656 | + | 0.996469i | \(0.473241\pi\) | |||||||
\(758\) | 9.37204 | − | 5.41095i | 0.340408 | − | 0.196535i | ||||
\(759\) | 34.5138 | + | 46.7106i | 1.25277 | + | 1.69549i | ||||
\(760\) | 2.34350 | − | 3.67532i | 0.0850079 | − | 0.133318i | ||||
\(761\) | − | 32.0785i | − | 1.16284i | −0.813602 | − | 0.581422i | \(-0.802497\pi\) | ||
0.813602 | − | 0.581422i | \(-0.197503\pi\) | |||||||
\(762\) | −20.5508 | − | 8.95273i | −0.744476 | − | 0.324323i | ||||
\(763\) | −17.7618 | + | 10.2548i | −0.643022 | + | 0.371249i | ||||
\(764\) | 5.27726 | + | 3.04683i | 0.190924 | + | 0.110230i | ||||
\(765\) | −11.4639 | + | 2.62985i | −0.414478 | + | 0.0950825i | ||||
\(766\) | 8.28137 | − | 14.3437i | 0.299218 | − | 0.518261i | ||||
\(767\) | 17.0756i | 0.616563i | ||||||||
\(768\) | 1.02929 | + | 1.39304i | 0.0371415 | + | 0.0502669i | ||||
\(769\) | −20.0557 | + | 34.7374i | −0.723225 | + | 1.25266i | 0.236475 | + | 0.971638i | \(0.424008\pi\) |
−0.959700 | + | 0.281026i | \(0.909325\pi\) | |||||||
\(770\) | −4.81539 | + | 8.34049i | −0.173534 | + | 0.300571i | ||||
\(771\) | −24.2368 | − | 32.8018i | −0.872867 | − | 1.18133i | ||||
\(772\) | 3.00092i | 0.108006i | ||||||||
\(773\) | −4.07839 | + | 7.06397i | −0.146689 | + | 0.254074i | −0.930002 | − | 0.367555i | \(-0.880195\pi\) |
0.783313 | + | 0.621628i | \(0.213528\pi\) | |||||||
\(774\) | 17.2219 | − | 3.95076i | 0.619028 | − | 0.142007i | ||||
\(775\) | −0.202293 | − | 0.116794i | −0.00726657 | − | 0.00419536i | ||||
\(776\) | −13.3158 | + | 7.68789i | −0.478010 | + | 0.275979i | ||||
\(777\) | 22.3975 | + | 9.75723i | 0.803505 | + | 0.350039i | ||||
\(778\) | − | 37.4846i | − | 1.34389i | ||||||
\(779\) | −43.2400 | − | 27.5713i | −1.54924 | − | 0.987843i | ||||
\(780\) | −2.06347 | − | 2.79269i | −0.0738842 | − | 0.0999942i | ||||
\(781\) | −19.2659 | + | 11.1232i | −0.689389 | + | 0.398019i | ||||
\(782\) | −13.3811 | − | 23.1768i | −0.478508 | − | 0.828800i | ||||
\(783\) | 4.81996 | − | 25.7066i | 0.172251 | − | 0.918680i | ||||
\(784\) | 1.57807 | + | 2.73330i | 0.0563597 | + | 0.0976179i | ||||
\(785\) | −1.44401 | − | 0.833700i | −0.0515389 | − | 0.0297560i | ||||
\(786\) | 12.4562 | − | 9.20373i | 0.444299 | − | 0.328286i | ||||
\(787\) | − | 41.0793i | − | 1.46432i | −0.681134 | − | 0.732159i | \(-0.738513\pi\) | ||
0.681134 | − | 0.732159i | \(-0.261487\pi\) | |||||||
\(788\) | −2.14864 | − | 1.24052i | −0.0765422 | − | 0.0441917i | ||||
\(789\) | −0.778664 | − | 6.87677i | −0.0277212 | − | 0.244820i | ||||
\(790\) | 12.4592 | 0.443277 | ||||||||
\(791\) | 23.8385 | 0.847600 | ||||||||
\(792\) | −10.7917 | + | 10.0354i | −0.383466 | + | 0.356591i | ||||
\(793\) | 13.5899 | − | 7.84613i | 0.482592 | − | 0.278624i | ||||
\(794\) | −2.65169 | + | 4.59286i | −0.0941050 | + | 0.162995i | ||||
\(795\) | 16.8015 | + | 7.31942i | 0.595889 | + | 0.259593i | ||||
\(796\) | −11.8062 | − | 20.4489i | −0.418459 | − | 0.724792i | ||||
\(797\) | 39.4937 | 1.39894 | 0.699469 | − | 0.714663i | \(-0.253420\pi\) | ||||
0.699469 | + | 0.714663i | \(0.253420\pi\) | |||||||
\(798\) | −12.2805 | + | 8.26373i | −0.434725 | + | 0.292533i | ||||
\(799\) | −7.28505 | −0.257727 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −32.0557 | + | 7.35367i | −1.13263 | + | 0.259829i | ||||
\(802\) | −3.00036 | + | 5.19678i | −0.105946 | + | 0.183505i | ||||
\(803\) | 9.68993 | − | 5.59448i | 0.341950 | − | 0.197425i | ||||
\(804\) | −3.09310 | − | 27.3167i | −0.109085 | − | 0.963386i | ||||
\(805\) | −13.3832 | −0.471694 | ||||||||
\(806\) | −0.468284 | −0.0164946 | ||||||||
\(807\) | −3.86801 | + | 0.437978i | −0.136160 | + | 0.0154176i | ||||
\(808\) | 9.94449 | + | 5.74146i | 0.349846 | + | 0.201984i | ||||
\(809\) | − | 16.4184i | − | 0.577240i | −0.957444 | − | 0.288620i | \(-0.906804\pi\) | ||
0.957444 | − | 0.288620i | \(-0.0931964\pi\) | |||||||
\(810\) | −5.05348 | + | 7.44731i | −0.177561 | + | 0.261672i | ||||
\(811\) | −42.7046 | − | 24.6555i | −1.49956 | − | 0.865773i | −0.499563 | − | 0.866277i | \(-0.666506\pi\) |
−1.00000 | 0.000504396i | \(0.999839\pi\) | ||||||||
\(812\) | 4.93423 | + | 8.54634i | 0.173158 | + | 0.299918i | ||||
\(813\) | 9.29881 | − | 1.05291i | 0.326124 | − | 0.0369273i | ||||
\(814\) | 17.6700 | + | 30.6053i | 0.619333 | + | 1.07272i | ||||
\(815\) | −7.41266 | + | 4.27970i | −0.259654 | + | 0.149911i | ||||
\(816\) | 5.46148 | − | 4.03541i | 0.191190 | − | 0.141267i | ||||
\(817\) | 21.6467 | + | 13.8026i | 0.757322 | + | 0.482893i | ||||
\(818\) | 27.3123i | 0.954951i | ||||||||
\(819\) | 2.63649 | + | 11.4928i | 0.0921265 | + | 0.401592i | ||||
\(820\) | 10.1888 | − | 5.88249i | 0.355807 | − | 0.205425i | ||||
\(821\) | −27.3273 | − | 15.7774i | −0.953730 | − | 0.550636i | −0.0594922 | − | 0.998229i | \(-0.518948\pi\) |
−0.894238 | + | 0.447593i | \(0.852281\pi\) | |||||||
\(822\) | 6.51179 | + | 2.83680i | 0.227125 | + | 0.0989446i | ||||
\(823\) | −1.24210 | + | 2.15138i | −0.0432968 | + | 0.0749923i | −0.886862 | − | 0.462035i | \(-0.847119\pi\) |
0.843565 | + | 0.537027i | \(0.180453\pi\) | |||||||
\(824\) | − | 1.76334i | − | 0.0614289i | ||||||
\(825\) | −6.84290 | + | 5.05612i | −0.238239 | + | 0.176031i | ||||
\(826\) | −8.34967 | + | 14.4620i | −0.290522 | + | 0.503199i | ||||
\(827\) | 16.2300 | − | 28.1113i | 0.564374 | − | 0.977524i | −0.432734 | − | 0.901522i | \(-0.642451\pi\) |
0.997108 | − | 0.0760023i | \(-0.0242156\pi\) | |||||||
\(828\) | −19.5753 | − | 6.01455i | −0.680287 | − | 0.209020i | ||||
\(829\) | − | 30.4181i | − | 1.05647i | −0.849100 | − | 0.528233i | \(-0.822855\pi\) | ||
0.849100 | − | 0.528233i | \(-0.177145\pi\) | |||||||
\(830\) | 6.85554 | − | 11.8742i | 0.237959 | − | 0.412158i | ||||
\(831\) | −13.9411 | + | 32.0014i | −0.483611 | + | 1.11012i | ||||
\(832\) | 1.73616 | + | 1.00237i | 0.0601905 | + | 0.0347510i | ||||
\(833\) | 10.7161 | − | 6.18692i | 0.371289 | − | 0.214364i | ||||
\(834\) | −9.32725 | + | 21.4105i | −0.322976 | + | 0.741383i | ||||
\(835\) | 9.69066i | 0.335359i | ||||||||
\(836\) | −21.3911 | − | 0.942528i | −0.739827 | − | 0.0325980i | ||||
\(837\) | 0.402772 | + | 1.14498i | 0.0139218 | + | 0.0395763i | ||||
\(838\) | 4.51958 | − | 2.60938i | 0.156126 | − | 0.0901396i | ||||
\(839\) | −3.12520 | − | 5.41300i | −0.107894 | − | 0.186878i | 0.807023 | − | 0.590520i | \(-0.201077\pi\) |
−0.914917 | + | 0.403642i | \(0.867744\pi\) | |||||||
\(840\) | −0.382070 | − | 3.37425i | −0.0131827 | − | 0.116423i | ||||
\(841\) | 1.83217 | + | 3.17341i | 0.0631783 | + | 0.109428i | ||||
\(842\) | −0.601100 | − | 0.347045i | −0.0207153 | − | 0.0119600i | ||||
\(843\) | 19.2564 | + | 26.0614i | 0.663226 | + | 0.897604i | ||||
\(844\) | 2.91361i | 0.100290i | ||||||||
\(845\) | 7.77777 | + | 4.49050i | 0.267563 | + | 0.154478i | ||||
\(846\) | −4.08222 | + | 3.79613i | −0.140350 | + | 0.130514i | ||||
\(847\) | 25.7421 | 0.884510 | ||||||||
\(848\) | −10.5809 | −0.363349 | ||||||||
\(849\) | 36.4177 | − | 4.12361i | 1.24985 | − | 0.141522i | ||||
\(850\) | 3.39530 | − | 1.96028i | 0.116458 | − | 0.0672370i | ||||
\(851\) | −24.5546 | + | 42.5299i | −0.841722 | + | 1.45791i | ||||
\(852\) | 3.13283 | − | 7.19132i | 0.107329 | − | 0.246371i | ||||
\(853\) | 24.9526 | + | 43.2191i | 0.854360 | + | 1.47979i | 0.877238 | + | 0.480056i | \(0.159384\pi\) |
−0.0228782 | + | 0.999738i | \(0.507283\pi\) | |||||||
\(854\) | 15.3465 | 0.525147 | ||||||||
\(855\) | −12.8620 | + | 2.36000i | −0.439870 | + | 0.0807104i | ||||
\(856\) | 3.01131 | 0.102925 | ||||||||
\(857\) | −14.9335 | − | 25.8655i | −0.510118 | − | 0.883550i | −0.999931 | − | 0.0117228i | \(-0.996268\pi\) |
0.489813 | − | 0.871827i | \(-0.337065\pi\) | |||||||
\(858\) | −6.81226 | + | 15.6374i | −0.232567 | + | 0.533851i | ||||
\(859\) | −12.1997 | + | 21.1305i | −0.416249 | + | 0.720964i | −0.995559 | − | 0.0941433i | \(-0.969989\pi\) |
0.579310 | + | 0.815107i | \(0.303322\pi\) | |||||||
\(860\) | −5.10067 | + | 2.94487i | −0.173931 | + | 0.100419i | ||||
\(861\) | −39.6980 | + | 4.49504i | −1.35290 | + | 0.153191i | ||||
\(862\) | −16.6054 | −0.565581 | ||||||||
\(863\) | −23.3653 | −0.795363 | −0.397682 | − | 0.917523i | \(-0.630185\pi\) | ||||
−0.397682 | + | 0.917523i | \(0.630185\pi\) | |||||||
\(864\) | 0.957584 | − | 5.10716i | 0.0325777 | − | 0.173749i | ||||
\(865\) | 9.04605 | + | 5.22274i | 0.307575 | + | 0.177579i | ||||
\(866\) | − | 20.8673i | − | 0.709099i | ||||||
\(867\) | 1.67698 | + | 2.26961i | 0.0569532 | + | 0.0770799i | ||||
\(868\) | −0.396610 | − | 0.228983i | −0.0134618 | − | 0.00777219i | ||||
\(869\) | −30.6011 | − | 53.0026i | −1.03807 | − | 1.79799i | ||||
\(870\) | 0.980902 | + | 8.66284i | 0.0332557 | + | 0.293698i | ||||
\(871\) | −15.9098 | − | 27.5565i | −0.539081 | − | 0.933716i | ||||
\(872\) | 9.05950 | − | 5.23051i | 0.306794 | − | 0.177127i | ||||
\(873\) | 44.0930 | + | 13.5477i | 1.49232 | + | 0.458520i | ||||
\(874\) | −13.7285 | − | 26.3980i | −0.464374 | − | 0.892926i | ||||
\(875\) | − | 1.96058i | − | 0.0662795i | ||||||
\(876\) | −1.57567 | + | 3.61692i | −0.0532371 | + | 0.122204i | ||||
\(877\) | 36.6106 | − | 21.1372i | 1.23625 | − | 0.713751i | 0.267927 | − | 0.963439i | \(-0.413661\pi\) |
0.968326 | + | 0.249688i | \(0.0803281\pi\) | |||||||
\(878\) | 9.46913 | + | 5.46701i | 0.319568 | + | 0.184503i | ||||
\(879\) | −8.51694 | + | 19.5504i | −0.287269 | + | 0.659419i | ||||
\(880\) | 2.45611 | − | 4.25411i | 0.0827954 | − | 0.143406i | ||||
\(881\) | − | 17.5330i | − | 0.590703i | −0.955389 | − | 0.295351i | \(-0.904563\pi\) | ||
0.955389 | − | 0.295351i | \(-0.0954367\pi\) | |||||||
\(882\) | 2.78090 | − | 9.05085i | 0.0936377 | − | 0.304758i | ||||
\(883\) | 3.21281 | − | 5.56474i | 0.108120 | − | 0.187268i | −0.806889 | − | 0.590703i | \(-0.798850\pi\) |
0.915008 | + | 0.403435i | \(0.132184\pi\) | |||||||
\(884\) | 3.92986 | − | 6.80671i | 0.132175 | − | 0.228934i | ||||
\(885\) | −11.8653 | + | 8.76709i | −0.398847 | + | 0.294702i | ||||
\(886\) | − | 37.9817i | − | 1.27602i | ||||||
\(887\) | 5.78172 | − | 10.0142i | 0.194131 | − | 0.336245i | −0.752484 | − | 0.658610i | \(-0.771145\pi\) |
0.946615 | + | 0.322365i | \(0.104478\pi\) | |||||||
\(888\) | −11.4239 | − | 4.97672i | −0.383362 | − | 0.167008i | ||||
\(889\) | −21.9743 | − | 12.6869i | −0.736995 | − | 0.425504i | ||||
\(890\) | 9.49404 | − | 5.48139i | 0.318241 | − | 0.183737i | ||||
\(891\) | 44.0935 | + | 3.20664i | 1.47719 | + | 0.107426i | ||||
\(892\) | 3.91895i | 0.131216i | ||||||||
\(893\) | −8.09172 | − | 0.356535i | −0.270779 | − | 0.0119310i | ||||
\(894\) | 6.42084 | − | 4.74427i | 0.214745 | − | 0.158672i | ||||
\(895\) | 1.16628 | − | 0.673349i | 0.0389843 | − | 0.0225076i | ||||
\(896\) | 0.980288 | + | 1.69791i | 0.0327491 | + | 0.0567231i | ||||
\(897\) | −23.5520 | + | 2.66682i | −0.786380 | + | 0.0890426i | ||||
\(898\) | −18.5397 | − | 32.1117i | −0.618678 | − | 1.07158i | ||||
\(899\) | 1.01823 | + | 0.587876i | 0.0339599 | + | 0.0196068i | ||||
\(900\) | 0.881106 | − | 2.86769i | 0.0293702 | − | 0.0955897i | ||||
\(901\) | 41.4829i | 1.38200i | ||||||||
\(902\) | −50.0494 | − | 28.8961i | −1.66646 | − | 0.962133i | ||||
\(903\) | 19.8735 | − | 2.25030i | 0.661348 | − | 0.0748851i | ||||
\(904\) | −12.1589 | −0.404400 | ||||||||
\(905\) | −14.6171 | −0.485888 | ||||||||
\(906\) | 3.38236 | + | 29.8713i | 0.112371 | + | 0.992408i | ||||
\(907\) | −33.9003 | + | 19.5724i | −1.12564 | + | 0.649890i | −0.942835 | − | 0.333259i | \(-0.891852\pi\) |
−0.182807 | + | 0.983149i | \(0.558518\pi\) | |||||||
\(908\) | 0.158042 | − | 0.273737i | 0.00524481 | − | 0.00908428i | ||||
\(909\) | −7.70257 | − | 33.5766i | −0.255478 | − | 1.11366i | ||||
\(910\) | −1.96523 | − | 3.40387i | −0.0651466 | − | 0.112837i | ||||
\(911\) | −27.0371 | −0.895778 | −0.447889 | − | 0.894089i | \(-0.647824\pi\) | ||||
−0.447889 | + | 0.894089i | \(0.647824\pi\) | |||||||
\(912\) | 6.26372 | − | 4.21495i | 0.207412 | − | 0.139571i | ||||
\(913\) | −67.3519 | −2.22902 | ||||||||
\(914\) | −12.4132 | − | 21.5003i | −0.410592 | − | 0.711167i | ||||
\(915\) | 12.4295 | + | 5.41478i | 0.410906 | + | 0.179007i | ||||
\(916\) | −3.06670 | + | 5.31168i | −0.101327 | + | 0.175503i | ||||
\(917\) | 15.1823 | − | 8.76552i | 0.501364 | − | 0.289463i | ||||
\(918\) | −20.0229 | − | 3.75426i | −0.660854 | − | 0.123909i | ||||
\(919\) | 36.3996 | 1.20071 | 0.600356 | − | 0.799733i | \(-0.295025\pi\) | ||||
0.600356 | + | 0.799733i | \(0.295025\pi\) | |||||||
\(920\) | 6.82614 | 0.225051 | ||||||||
\(921\) | 2.95952 | + | 26.1370i | 0.0975193 | + | 0.861243i | ||||
\(922\) | −4.14251 | − | 2.39168i | −0.136426 | − | 0.0787658i | ||||
\(923\) | − | 9.07906i | − | 0.298841i | ||||||
\(924\) | −13.4160 | + | 9.91290i | −0.441355 | + | 0.326111i | ||||
\(925\) | −6.23045 | − | 3.59715i | −0.204856 | − | 0.118274i | ||||
\(926\) | 9.57949 | + | 16.5922i | 0.314802 | + | 0.545253i | ||||
\(927\) | −3.87390 | + | 3.60240i | −0.127235 | + | 0.118318i | ||||
\(928\) | −2.51673 | − | 4.35910i | −0.0826156 | − | 0.143094i | ||||
\(929\) | −10.5812 | + | 6.10909i | −0.347160 | + | 0.200433i | −0.663434 | − | 0.748235i | \(-0.730901\pi\) |
0.316274 | + | 0.948668i | \(0.397568\pi\) | |||||||
\(930\) | −0.240431 | − | 0.325396i | −0.00788403 | − | 0.0106702i | ||||
\(931\) | 12.2054 | − | 6.34754i | 0.400017 | − | 0.208032i | ||||
\(932\) | − | 10.8268i | − | 0.354644i | ||||||
\(933\) | −50.6289 | − | 22.0560i | −1.65752 | − | 0.722080i | ||||
\(934\) | −16.0630 | + | 9.27397i | −0.525597 | + | 0.303454i | ||||
\(935\) | −16.6785 | − | 9.62931i | −0.545444 | − | 0.314912i | ||||
\(936\) | −1.34475 | − | 5.86197i | −0.0439547 | − | 0.191604i | ||||
\(937\) | 15.9162 | − | 27.5678i | 0.519961 | − | 0.900599i | −0.479770 | − | 0.877395i | \(-0.659280\pi\) |
0.999731 | − | 0.0232047i | \(-0.00738695\pi\) | |||||||
\(938\) | − | 31.1184i | − | 1.01605i | ||||||
\(939\) | 15.3896 | + | 20.8281i | 0.502220 | + | 0.679700i | ||||
\(940\) | 0.929084 | − | 1.60922i | 0.0303034 | − | 0.0524870i | ||||
\(941\) | −6.16530 | + | 10.6786i | −0.200983 | + | 0.348113i | −0.948845 | − | 0.315741i | \(-0.897747\pi\) |
0.747862 | + | 0.663854i | \(0.231080\pi\) | |||||||
\(942\) | −1.71625 | − | 2.32275i | −0.0559183 | − | 0.0756793i | ||||
\(943\) | − | 80.3093i | − | 2.61523i | ||||||
\(944\) | 4.25879 | − | 7.37643i | 0.138612 | − | 0.240082i | ||||
\(945\) | −6.63237 | + | 7.73277i | −0.215751 | + | 0.251547i | ||||
\(946\) | 25.0556 | + | 14.4659i | 0.814628 | + | 0.470326i | ||||
\(947\) | −39.3773 | + | 22.7345i | −1.27959 | + | 0.738773i | −0.976773 | − | 0.214276i | \(-0.931261\pi\) |
−0.302818 | + | 0.953048i | \(0.597928\pi\) | |||||||
\(948\) | 19.7841 | + | 8.61873i | 0.642557 | + | 0.279923i | ||||
\(949\) | 4.56637i | 0.148231i | ||||||||
\(950\) | 3.86720 | − | 2.01117i | 0.125468 | − | 0.0652509i | ||||
\(951\) | 26.2641 | + | 35.5456i | 0.851672 | + | 1.15264i | ||||
\(952\) | 6.65674 | − | 3.84327i | 0.215746 | − | 0.124561i | ||||
\(953\) | −19.6623 | − | 34.0560i | −0.636923 | − | 1.10318i | −0.986104 | − | 0.166128i | \(-0.946874\pi\) |
0.349181 | − | 0.937055i | \(-0.386460\pi\) | |||||||
\(954\) | 21.6161 | + | 23.2452i | 0.699848 | + | 0.752591i | ||||
\(955\) | 3.04683 | + | 5.27726i | 0.0985930 | + | 0.170768i | ||||
\(956\) | −2.75990 | − | 1.59343i | −0.0892615 | − | 0.0515352i | ||||
\(957\) | 34.4434 | − | 25.4497i | 1.11340 | − | 0.822673i | ||||
\(958\) | 26.5271i | 0.857053i | ||||||||
\(959\) | 6.96286 | + | 4.02001i | 0.224843 | + | 0.129813i | ||||
\(960\) | 0.194877 | + | 1.72105i | 0.00628961 | + | 0.0555467i | ||||
\(961\) | 30.9454 | 0.998240 | ||||||||
\(962\) | −14.4227 | −0.465008 | ||||||||
\(963\) | −6.15193 | − | 6.61557i | −0.198243 | − | 0.213184i | ||||
\(964\) | 16.5317 | − | 9.54461i | 0.532452 | − | 0.307411i | ||||
\(965\) | −1.50046 | + | 2.59888i | −0.0483016 | + | 0.0836608i | ||||
\(966\) | −21.2513 | − | 9.25791i | −0.683749 | − | 0.297868i | ||||
\(967\) | 28.8842 | + | 50.0289i | 0.928854 | + | 1.60882i | 0.785243 | + | 0.619188i | \(0.212538\pi\) |
0.143611 | + | 0.989634i | \(0.454129\pi\) | |||||||
\(968\) | −13.1299 | −0.422011 | ||||||||
\(969\) | −16.5250 | − | 24.5572i | −0.530858 | − | 0.788893i | ||||
\(970\) | −15.3758 | −0.493686 | ||||||||
\(971\) | −0.428825 | − | 0.742746i | −0.0137616 | − | 0.0238358i | 0.859063 | − | 0.511871i | \(-0.171047\pi\) |
−0.872824 | + | 0.488035i | \(0.837714\pi\) | |||||||
\(972\) | −13.1762 | + | 8.32989i | −0.422628 | + | 0.267181i | ||||
\(973\) | −13.2176 | + | 22.8935i | −0.423737 | + | 0.733933i | ||||
\(974\) | −9.80030 | + | 5.65821i | −0.314022 | + | 0.181301i | ||||
\(975\) | −0.390678 | − | 3.45027i | −0.0125117 | − | 0.110497i | ||||
\(976\) | −7.82756 | −0.250554 | ||||||||
\(977\) | −3.12960 | −0.100125 | −0.0500625 | − | 0.998746i | \(-0.515942\pi\) | ||||
−0.0500625 | + | 0.998746i | \(0.515942\pi\) | |||||||
\(978\) | −14.7312 | + | 1.66803i | −0.471051 | + | 0.0533376i | ||||
\(979\) | −46.6368 | − | 26.9258i | −1.49052 | − | 0.860552i | ||||
\(980\) | 3.15615i | 0.100819i | ||||||||
\(981\) | −29.9990 | − | 9.21726i | −0.957793 | − | 0.294284i | ||||
\(982\) | 6.02160 | + | 3.47657i | 0.192157 | + | 0.110942i | ||||
\(983\) | −16.5230 | − | 28.6187i | −0.527003 | − | 0.912796i | −0.999505 | − | 0.0314664i | \(-0.989982\pi\) |
0.472502 | − | 0.881330i | \(-0.343351\pi\) | |||||||
\(984\) | 20.2481 | − | 2.29272i | 0.645487 | − | 0.0730891i | ||||
\(985\) | −1.24052 | − | 2.14864i | −0.0395262 | − | 0.0684614i | ||||
\(986\) | −17.0901 | + | 9.86697i | −0.544259 | + | 0.314228i | ||||
\(987\) | −5.07494 | + | 3.74980i | −0.161537 | + | 0.119357i | ||||
\(988\) | 4.69813 | − | 7.36808i | 0.149467 | − | 0.234410i | ||||
\(989\) | 40.2042i | 1.27842i | ||||||||
\(990\) | −14.3636 | + | 3.29505i | −0.456504 | + | 0.104723i | ||||
\(991\) | 3.55980 | − | 2.05525i | 0.113081 | − | 0.0652873i | −0.442393 | − | 0.896821i | \(-0.645870\pi\) |
0.555474 | + | 0.831534i | \(0.312537\pi\) | |||||||
\(992\) | 0.202293 | + | 0.116794i | 0.00642280 | + | 0.00370821i | ||||
\(993\) | 37.5177 | + | 16.3442i | 1.19059 | + | 0.518667i | ||||
\(994\) | 4.43951 | − | 7.68946i | 0.140813 | − | 0.243895i | ||||
\(995\) | − | 23.6124i | − | 0.748562i | ||||||
\(996\) | 19.1001 | − | 14.1127i | 0.605208 | − | 0.447179i | ||||
\(997\) | −2.97096 | + | 5.14586i | −0.0940914 | + | 0.162971i | −0.909229 | − | 0.416296i | \(-0.863328\pi\) |
0.815138 | + | 0.579267i | \(0.196661\pi\) | |||||||
\(998\) | −17.0361 | + | 29.5074i | −0.539269 | + | 0.934042i | ||||
\(999\) | 12.4050 | + | 35.2644i | 0.392478 | + | 1.11572i |
(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 | 570.2.s.a.221.8 | ✓ | 24 | |
3.2 | odd | 2 | 570.2.s.b.221.12 | yes | 24 | ||
19.8 | odd | 6 | 570.2.s.b.521.12 | yes | 24 | ||
57.8 | even | 6 | inner | 570.2.s.a.521.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.8 | ✓ | 24 | 1.1 | even | 1 | trivial | |
570.2.s.a.521.8 | yes | 24 | 57.8 | even | 6 | inner | |
570.2.s.b.221.12 | yes | 24 | 3.2 | odd | 2 | ||
570.2.s.b.521.12 | yes | 24 | 19.8 | odd | 6 |