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 | 521.12 | ||
Character | \(\chi\) | \(=\) | 570.521 |
Dual form | 570.2.s.b.221.12 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||
\(3\) | 1.72105 | − | 0.194877i | 0.993650 | − | 0.112512i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 0.691758 | − | 1.58791i | 0.282409 | − | 0.648263i | ||||
\(7\) | −1.96058 | −0.741028 | −0.370514 | − | 0.928827i | \(-0.620818\pi\) | ||||
−0.370514 | + | 0.928827i | \(0.620818\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.92405 | − | 0.670786i | 0.974682 | − | 0.223595i | ||||
\(10\) | 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 | −0.239527 | − | 0.970890i | \(-0.576992\pi\) |
0.721051 | + | 0.692881i | \(0.243659\pi\) | |||||||
\(14\) | −0.980288 | + | 1.69791i | −0.261993 | + | 0.453785i | ||||
\(15\) | 1.58791 | + | 0.691758i | 0.409998 | + | 0.178611i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.39530 | + | 1.96028i | 0.823481 | + | 0.475437i | 0.851615 | − | 0.524167i | \(-0.175623\pi\) |
−0.0281343 | + | 0.999604i | \(0.508957\pi\) | |||||||
\(18\) | 0.881106 | − | 2.86769i | 0.207679 | − | 0.675921i | ||||
\(19\) | −3.86720 | − | 2.01117i | −0.887195 | − | 0.461394i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | −3.37425 | + | 0.382070i | −0.736323 | + | 0.0833745i | ||||
\(22\) | −4.25411 | − | 2.45611i | −0.906978 | − | 0.523644i | ||||
\(23\) | 5.91161 | − | 3.41307i | 1.23266 | − | 0.711674i | 0.265073 | − | 0.964228i | \(-0.414604\pi\) |
0.967583 | + | 0.252554i | \(0.0812706\pi\) | |||||||
\(24\) | −1.72105 | + | 0.194877i | −0.351308 | + | 0.0397790i | ||||
\(25\) | 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 | \(-0.0118775\pi\) |
−0.531959 | + | 0.846770i | \(0.678544\pi\) | |||||||
\(30\) | 1.39304 | − | 1.02929i | 0.254333 | − | 0.187923i | ||||
\(31\) | 0.233588i | 0.0419536i | 0.999780 | + | 0.0209768i | \(0.00667761\pi\) | ||||
−0.999780 | + | 0.0209768i | \(0.993322\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.957276 | − | 8.45419i | −0.166640 | − | 1.47169i | ||||
\(34\) | 3.39530 | − | 1.96028i | 0.582289 | − | 0.336185i | ||||
\(35\) | −1.69791 | − | 0.980288i | −0.286999 | − | 0.165699i | ||||
\(36\) | −2.04294 | − | 2.19691i | −0.340490 | − | 0.366151i | ||||
\(37\) | 7.19430i | 1.18274i | 0.806402 | + | 0.591368i | \(0.201412\pi\) | ||||
−0.806402 | + | 0.591368i | \(0.798588\pi\) | |||||||
\(38\) | −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 | −0.117282 | + | 0.993099i | \(0.537418\pi\) |
−0.801407 | + | 0.598119i | \(0.795915\pi\) | |||||||
\(42\) | −1.35624 | + | 3.11322i | −0.209273 | + | 0.480381i | ||||
\(43\) | −2.94487 | + | 5.10067i | −0.449089 | + | 0.777845i | −0.998327 | − | 0.0578212i | \(-0.981585\pi\) |
0.549238 | + | 0.835666i | \(0.314918\pi\) | |||||||
\(44\) | −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 | \(-0.709937\pi\) |
0.378023 | + | 0.925796i | \(0.376604\pi\) | |||||||
\(48\) | −0.691758 | + | 1.58791i | −0.0998467 | + | 0.229196i | ||||
\(49\) | −3.15615 | −0.450878 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 6.22550 | + | 2.71208i | 0.871745 | + | 0.379767i | ||||
\(52\) | −1.73616 | − | 1.00237i | −0.240762 | − | 0.139004i | ||||
\(53\) | −5.29044 | − | 9.16331i | −0.726698 | − | 1.25868i | −0.958271 | − | 0.285861i | \(-0.907721\pi\) |
0.231573 | − | 0.972817i | \(-0.425613\pi\) | |||||||
\(54\) | 0.957584 | − | 5.10716i | 0.130311 | − | 0.694996i | ||||
\(55\) | 2.45611 | − | 4.25411i | 0.331182 | − | 0.573624i | ||||
\(56\) | 1.96058 | 0.261993 | ||||||||
\(57\) | −7.04758 | − | 2.70770i | −0.933474 | − | 0.358644i | ||||
\(58\) | 5.03345 | 0.660925 | ||||||||
\(59\) | −4.25879 | + | 7.37643i | −0.554447 | + | 0.960330i | 0.443500 | + | 0.896274i | \(0.353737\pi\) |
−0.997946 | + | 0.0640552i | \(0.979597\pi\) | |||||||
\(60\) | −0.194877 | − | 1.72105i | −0.0251584 | − | 0.222187i | ||||
\(61\) | 3.91378 | + | 6.77887i | 0.501108 | + | 0.867945i | 0.999999 | + | 0.00128020i | \(0.000407502\pi\) |
−0.498891 | + | 0.866665i | \(0.666259\pi\) | |||||||
\(62\) | 0.202293 | + | 0.116794i | 0.0256912 | + | 0.0148328i | ||||
\(63\) | −5.73281 | + | 1.31513i | −0.722266 | + | 0.165690i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00475 | 0.248658 | ||||||||
\(66\) | −7.80018 | − | 3.39807i | −0.960136 | − | 0.418273i | ||||
\(67\) | −13.7456 | + | 7.93605i | −1.67930 | + | 0.969542i | −0.717186 | + | 0.696882i | \(0.754570\pi\) |
−0.962110 | + | 0.272661i | \(0.912096\pi\) | |||||||
\(68\) | − | 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 | \(-0.746728\pi\) |
0.968535 | + | 0.248877i | \(0.0800614\pi\) | |||||||
\(72\) | −2.92405 | + | 0.670786i | −0.344602 | + | 0.0790528i | ||||
\(73\) | 1.13889 | − | 1.97262i | 0.133297 | − | 0.230877i | −0.791649 | − | 0.610977i | \(-0.790777\pi\) |
0.924946 | + | 0.380099i | \(0.124110\pi\) | |||||||
\(74\) | 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 | ||||||||
\(78\) | −0.390678 | − | 3.45027i | −0.0442355 | − | 0.390666i | ||||
\(79\) | 10.7900 | + | 6.22958i | 1.21396 | + | 0.700883i | 0.963621 | − | 0.267274i | \(-0.0861229\pi\) |
0.250344 | + | 0.968157i | \(0.419456\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | 8.10009 | − | 3.92282i | 0.900010 | − | 0.435868i | ||||
\(82\) | 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 | −0.995358 | − | 0.0962408i | \(-0.969318\pi\) |
0.414332 | − | 0.910126i | \(-0.364015\pi\) | |||||||
\(90\) | 2.19691 | − | 2.04294i | 0.231574 | − | 0.215345i | ||||
\(91\) | −3.40387 | + | 1.96523i | −0.356823 | + | 0.206012i | ||||
\(92\) | −5.91161 | − | 3.41307i | −0.616328 | − | 0.355837i | ||||
\(93\) | 0.0455208 | + | 0.402017i | 0.00472028 | + | 0.0416872i | ||||
\(94\) | 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 | −0.363484 | − | 0.931600i | \(-0.618413\pi\) |
−0.988532 | + | 0.151013i | \(0.951746\pi\) | |||||||
\(98\) | −1.57807 | + | 2.73330i | −0.159409 | + | 0.276105i | ||||
\(99\) | −3.29505 | − | 14.3636i | −0.331165 | − | 1.44359i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −9.94449 | + | 5.74146i | −0.989514 | + | 0.571296i | −0.905129 | − | 0.425137i | \(-0.860226\pi\) |
−0.0843851 | + | 0.996433i | \(0.526893\pi\) | |||||||
\(102\) | 5.46148 | − | 4.03541i | 0.540767 | − | 0.399565i | ||||
\(103\) | 1.76334i | 0.173747i | 0.996219 | + | 0.0868736i | \(0.0276876\pi\) | ||||
−0.996219 | + | 0.0868736i | \(0.972312\pi\) | |||||||
\(104\) | −1.73616 | + | 1.00237i | −0.170245 | + | 0.0982907i | ||||
\(105\) | −3.11322 | − | 1.35624i | −0.303820 | − | 0.132356i | ||||
\(106\) | −10.5809 | −1.02771 | ||||||||
\(107\) | −3.01131 | −0.291115 | −0.145557 | − | 0.989350i | \(-0.546498\pi\) | ||||
−0.145557 | + | 0.989350i | \(0.546498\pi\) | |||||||
\(108\) | −3.94413 | − | 3.38287i | −0.379524 | − | 0.325517i | ||||
\(109\) | 9.05950 | + | 5.23051i | 0.867743 | + | 0.500992i | 0.866598 | − | 0.499008i | \(-0.166302\pi\) |
0.00114554 | + | 0.999999i | \(0.499635\pi\) | |||||||
\(110\) | −2.45611 | − | 4.25411i | −0.234181 | − | 0.405613i | ||||
\(111\) | 1.40200 | + | 12.3818i | 0.133072 | + | 1.17523i | ||||
\(112\) | 0.980288 | − | 1.69791i | 0.0926285 | − | 0.160437i | ||||
\(113\) | 12.1589 | 1.14382 | 0.571909 | − | 0.820317i | \(-0.306203\pi\) | ||||
0.571909 | + | 0.820317i | \(0.306203\pi\) | |||||||
\(114\) | −5.86873 | + | 4.74953i | −0.549657 | + | 0.444834i | ||||
\(115\) | 6.82614 | 0.636541 | ||||||||
\(116\) | 2.51673 | − | 4.35910i | 0.233672 | − | 0.404732i | ||||
\(117\) | 4.40424 | − | 4.09558i | 0.407172 | − | 0.378636i | ||||
\(118\) | 4.25879 | + | 7.37643i | 0.392053 | + | 0.679056i | ||||
\(119\) | −6.65674 | − | 3.84327i | −0.610222 | − | 0.352312i | ||||
\(120\) | −1.58791 | − | 0.691758i | −0.144956 | − | 0.0631486i | ||||
\(121\) | −13.1299 | −1.19363 | ||||||||
\(122\) | 7.82756 | 0.708674 | ||||||||
\(123\) | −8.13852 | + | 18.6818i | −0.733825 | + | 1.68448i | ||||
\(124\) | 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 | 0.0879240 | − | 0.996127i | \(-0.471977\pi\) |
0.906633 | + | 0.421919i | \(0.138643\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −4.07428 | + | 9.35241i | −0.358720 | + | 0.823434i | ||||
\(130\) | 1.00237 | − | 1.73616i | 0.0879139 | − | 0.152271i | ||||
\(131\) | 7.74381 | + | 4.47089i | 0.676580 | + | 0.390624i | 0.798565 | − | 0.601908i | \(-0.205593\pi\) |
−0.121985 | + | 0.992532i | \(0.538926\pi\) | |||||||
\(132\) | −6.84290 | + | 5.05612i | −0.595598 | + | 0.440079i | ||||
\(133\) | 7.58193 | + | 3.94305i | 0.657436 | + | 0.341906i | ||||
\(134\) | 15.8721i | 1.37114i | ||||||||
\(135\) | 5.10716 | + | 0.957584i | 0.439554 | + | 0.0824157i | ||||
\(136\) | −3.39530 | − | 1.96028i | −0.291145 | − | 0.168092i | ||||
\(137\) | 3.55144 | − | 2.05042i | 0.303420 | − | 0.175180i | −0.340558 | − | 0.940223i | \(-0.610616\pi\) |
0.643978 | + | 0.765044i | \(0.277283\pi\) | |||||||
\(138\) | −1.33025 | − | 11.7481i | −0.113239 | − | 1.00007i | ||||
\(139\) | 6.74169 | + | 11.6770i | 0.571823 | + | 0.990426i | 0.996379 | + | 0.0850246i | \(0.0270969\pi\) |
−0.424556 | + | 0.905402i | \(0.639570\pi\) | |||||||
\(140\) | 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 | ||||
\(147\) | −5.43189 | + | 0.615059i | −0.448015 | + | 0.0507292i | ||||
\(148\) | 6.23045 | − | 3.59715i | 0.512140 | − | 0.295684i | ||||
\(149\) | 3.99172 | + | 2.30462i | 0.327014 | + | 0.188802i | 0.654515 | − | 0.756049i | \(-0.272873\pi\) |
−0.327500 | + | 0.944851i | \(0.606206\pi\) | |||||||
\(150\) | 1.72105 | − | 0.194877i | 0.140523 | − | 0.0159116i | ||||
\(151\) | 17.3564i | 1.41245i | 0.707990 | + | 0.706223i | \(0.249602\pi\) | ||||
−0.707990 | + | 0.706223i | \(0.750398\pi\) | |||||||
\(152\) | 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 | ||||
\(156\) | −3.18336 | − | 1.38680i | −0.254873 | − | 0.111033i | ||||
\(157\) | 0.833700 | − | 1.44401i | 0.0665365 | − | 0.115245i | −0.830838 | − | 0.556514i | \(-0.812138\pi\) |
0.897375 | + | 0.441270i | \(0.145472\pi\) | |||||||
\(158\) | 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 | ||||
\(162\) | 0.652788 | − | 8.97629i | 0.0512879 | − | 0.705244i | ||||
\(163\) | 8.55940 | 0.670424 | 0.335212 | − | 0.942143i | \(-0.391192\pi\) | ||||
0.335212 | + | 0.942143i | \(0.391192\pi\) | |||||||
\(164\) | 11.7650 | 0.918690 | ||||||||
\(165\) | 3.39807 | − | 7.80018i | 0.264539 | − | 0.607243i | ||||
\(166\) | −11.8742 | − | 6.85554i | −0.921613 | − | 0.532093i | ||||
\(167\) | −4.84533 | − | 8.39236i | −0.374943 | − | 0.649420i | 0.615376 | − | 0.788234i | \(-0.289004\pi\) |
−0.990318 | + | 0.138814i | \(0.955671\pi\) | |||||||
\(168\) | 3.37425 | − | 0.382070i | 0.260329 | − | 0.0294773i | ||||
\(169\) | −4.49050 | + | 7.77777i | −0.345423 | + | 0.598290i | ||||
\(170\) | 3.92055 | 0.300693 | ||||||||
\(171\) | −12.6569 | − | 3.28669i | −0.967899 | − | 0.251340i | ||||
\(172\) | 5.88974 | 0.449089 | ||||||||
\(173\) | 5.22274 | − | 9.04605i | 0.397078 | − | 0.687759i | −0.596286 | − | 0.802772i | \(-0.703358\pi\) |
0.993364 | + | 0.115013i | \(0.0366910\pi\) | |||||||
\(174\) | 8.66284 | − | 0.980902i | 0.656728 | − | 0.0743620i | ||||
\(175\) | −0.980288 | − | 1.69791i | −0.0741028 | − | 0.128350i | ||||
\(176\) | 4.25411 | + | 2.45611i | 0.320665 | + | 0.185136i | ||||
\(177\) | −5.89210 | + | 13.5252i | −0.442877 | + | 1.01661i | ||||
\(178\) | −10.9628 | −0.821695 | ||||||||
\(179\) | 1.34670 | 0.100657 | 0.0503285 | − | 0.998733i | \(-0.483973\pi\) | ||||
0.0503285 | + | 0.998733i | \(0.483973\pi\) | |||||||
\(180\) | −0.670786 | − | 2.92405i | −0.0499974 | − | 0.217946i | ||||
\(181\) | 12.6588 | − | 7.30854i | 0.940919 | − | 0.543240i | 0.0506704 | − | 0.998715i | \(-0.483864\pi\) |
0.890248 | + | 0.455476i | \(0.150531\pi\) | |||||||
\(182\) | 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 | ||||
\(186\) | 0.370917 | + | 0.161586i | 0.0271970 | + | 0.0118481i | ||||
\(187\) | 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 | \(-0.0707560\pi\) | |||||||
\(192\) | 1.72105 | − | 0.194877i | 0.124206 | − | 0.0140640i | ||||
\(193\) | 2.59888 | + | 1.50046i | 0.187071 | + | 0.108006i | 0.590611 | − | 0.806957i | \(-0.298887\pi\) |
−0.403540 | + | 0.914962i | \(0.632220\pi\) | |||||||
\(194\) | −13.3158 | + | 7.68789i | −0.956020 | + | 0.551958i | ||||
\(195\) | 3.45027 | − | 0.390678i | 0.247079 | − | 0.0279770i | ||||
\(196\) | 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 | −0.892459 | − | 0.451128i | \(-0.851022\pi\) |
0.0555409 | − | 0.998456i | \(-0.482312\pi\) | |||||||
\(200\) | −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 | ||||
\(204\) | −0.764024 | − | 6.74748i | −0.0534924 | − | 0.472418i | ||||
\(205\) | −10.1888 | + | 5.88249i | −0.711614 | + | 0.410851i | ||||
\(206\) | 1.52710 | + | 0.881671i | 0.106398 | + | 0.0614289i | ||||
\(207\) | 14.9964 | − | 13.9454i | 1.04232 | − | 0.969272i | ||||
\(208\) | 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 | 0.584333 | − | 0.811514i | \(-0.301356\pi\) |
−0.410625 | + | 0.911804i | \(0.634689\pi\) | |||||||
\(212\) | −5.29044 | + | 9.16331i | −0.363349 | + | 0.629339i | ||||
\(213\) | 3.13283 | − | 7.19132i | 0.214658 | − | 0.492741i | ||||
\(214\) | −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 | ||||
\(219\) | 1.57567 | − | 3.61692i | 0.106474 | − | 0.244409i | ||||
\(220\) | −4.91222 | −0.331182 | ||||||||
\(221\) | 7.85971 | 0.528702 | ||||||||
\(222\) | 11.4239 | + | 4.97672i | 0.766724 | + | 0.334015i | ||||
\(223\) | 3.39391 | + | 1.95947i | 0.227273 | + | 0.131216i | 0.609313 | − | 0.792930i | \(-0.291445\pi\) |
−0.382040 | + | 0.924146i | \(0.624778\pi\) | |||||||
\(224\) | −0.980288 | − | 1.69791i | −0.0654982 | − | 0.113446i | ||||
\(225\) | 2.04294 | + | 2.19691i | 0.136196 | + | 0.146460i | ||||
\(226\) | 6.07947 | − | 10.5300i | 0.404400 | − | 0.700442i | ||||
\(227\) | 0.316084 | 0.0209793 | 0.0104896 | − | 0.999945i | \(-0.496661\pi\) | ||||
0.0104896 | + | 0.999945i | \(0.496661\pi\) | |||||||
\(228\) | 1.17885 | + | 7.45723i | 0.0780712 | + | 0.493867i | ||||
\(229\) | 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 | ||||
\(231\) | 1.87681 | + | 16.5751i | 0.123485 | + | 1.09056i | ||||
\(232\) | −2.51673 | − | 4.35910i | −0.165231 | − | 0.286189i | ||||
\(233\) | 9.37631 | + | 5.41341i | 0.614262 | + | 0.354644i | 0.774632 | − | 0.632413i | \(-0.217935\pi\) |
−0.160369 | + | 0.987057i | \(0.551269\pi\) | |||||||
\(234\) | −1.34475 | − | 5.86197i | −0.0879093 | − | 0.383209i | ||||
\(235\) | −1.85817 | −0.121214 | ||||||||
\(236\) | 8.51757 | 0.554447 | ||||||||
\(237\) | 19.7841 | + | 8.61873i | 1.28511 | + | 0.559847i | ||||
\(238\) | −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 | −0.926785 | − | 0.375593i | \(-0.877439\pi\) |
−0.138119 | + | 0.990416i | \(0.544106\pi\) | |||||||
\(242\) | −6.56495 | + | 11.3708i | −0.422011 | + | 0.730944i | ||||
\(243\) | 13.1762 | − | 8.32989i | 0.845255 | − | 0.534363i | ||||
\(244\) | 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 | ||||||
\(249\) | −2.67197 | − | 23.5975i | −0.169329 | − | 1.49543i | ||||
\(250\) | 0.866025 | + | 0.500000i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | −10.0866 | + | 5.82352i | −0.636663 | + | 0.367578i | −0.783328 | − | 0.621609i | \(-0.786479\pi\) |
0.146665 | + | 0.989186i | \(0.453146\pi\) | |||||||
\(252\) | 4.00534 | + | 4.30720i | 0.252313 | + | 0.271328i | ||||
\(253\) | −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 | −0.954982 | − | 0.296665i | \(-0.904125\pi\) |
0.220571 | − | 0.975371i | \(-0.429208\pi\) | |||||||
\(258\) | 6.06228 | + | 8.20463i | 0.377421 | + | 0.510798i | ||||
\(259\) | − | 14.1050i | − | 0.876440i | ||||||
\(260\) | −1.00237 | − | 1.73616i | −0.0621645 | − | 0.107672i | ||||
\(261\) | 10.2830 | + | 11.0580i | 0.636505 | + | 0.684474i | ||||
\(262\) | 7.74381 | − | 4.47089i | 0.478414 | − | 0.276213i | ||||
\(263\) | −3.46036 | − | 1.99784i | −0.213375 | − | 0.123192i | 0.389504 | − | 0.921025i | \(-0.372646\pi\) |
−0.602879 | + | 0.797833i | \(0.705980\pi\) | |||||||
\(264\) | 0.957276 | + | 8.45419i | 0.0589163 | + | 0.520319i | ||||
\(265\) | − | 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 | \(-0.811507\pi\) |
0.898248 | + | 0.439489i | \(0.144840\pi\) | |||||||
\(270\) | 3.38287 | − | 3.94413i | 0.205875 | − | 0.240032i | ||||
\(271\) | 2.70149 | − | 4.67912i | 0.164104 | − | 0.284236i | −0.772233 | − | 0.635340i | \(-0.780860\pi\) |
0.936337 | + | 0.351103i | \(0.114193\pi\) | |||||||
\(272\) | −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 | ||||
\(276\) | −10.8393 | − | 4.72204i | −0.652450 | − | 0.284233i | ||||
\(277\) | −20.1531 | −1.21088 | −0.605441 | − | 0.795890i | \(-0.707003\pi\) | ||||
−0.605441 | + | 0.795890i | \(0.707003\pi\) | |||||||
\(278\) | 13.4834 | 0.808680 | ||||||||
\(279\) | 0.156687 | + | 0.683021i | 0.00938062 | + | 0.0408914i | ||||
\(280\) | 1.69791 | + | 0.980288i | 0.101469 | + | 0.0585834i | ||||
\(281\) | 9.35418 | + | 16.2019i | 0.558023 | + | 0.966525i | 0.997661 | + | 0.0683499i | \(0.0217734\pi\) |
−0.439638 | + | 0.898175i | \(0.644893\pi\) | |||||||
\(282\) | 0.362113 | + | 3.19801i | 0.0215635 | + | 0.190438i | ||||
\(283\) | 10.5801 | − | 18.3252i | 0.628919 | − | 1.08932i | −0.358850 | − | 0.933395i | \(-0.616831\pi\) |
0.987769 | − | 0.155924i | \(-0.0498355\pi\) | |||||||
\(284\) | −4.52879 | −0.268734 | ||||||||
\(285\) | −4.74953 | − | 5.86873i | −0.281338 | − | 0.347633i | ||||
\(286\) | −9.84775 | −0.582310 | ||||||||
\(287\) | 11.5331 | − | 19.9758i | 0.680775 | − | 1.17914i | ||||
\(288\) | 2.04294 | + | 2.19691i | 0.120381 | + | 0.129454i | ||||
\(289\) | −0.814625 | − | 1.41097i | −0.0479191 | − | 0.0829984i | ||||
\(290\) | 4.35910 | + | 2.51673i | 0.255975 | + | 0.147787i | ||||
\(291\) | −24.4154 | − | 10.6363i | −1.43126 | − | 0.623512i | ||||
\(292\) | −2.27778 | −0.133297 | ||||||||
\(293\) | 12.3120 | 0.719275 | 0.359638 | − | 0.933092i | \(-0.382900\pi\) | ||||
0.359638 | + | 0.933092i | \(0.382900\pi\) | |||||||
\(294\) | −2.18329 | + | 5.01169i | −0.127332 | + | 0.292287i | ||||
\(295\) | −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 | ||||
\(300\) | 0.691758 | − | 1.58791i | 0.0399387 | − | 0.0916782i | ||||
\(301\) | 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 | ||||||||
\(306\) | 8.61309 | − | 8.00946i | 0.492377 | − | 0.457870i | ||||
\(307\) | −13.1520 | − | 7.59331i | −0.750624 | − | 0.433373i | 0.0752952 | − | 0.997161i | \(-0.476010\pi\) |
−0.825919 | + | 0.563788i | \(0.809343\pi\) | |||||||
\(308\) | 8.34049 | − | 4.81539i | 0.475244 | − | 0.274382i | ||||
\(309\) | 0.343634 | + | 3.03481i | 0.0195487 | + | 0.172644i | ||||
\(310\) | 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 | 0.573632 | − | 0.819113i | \(-0.305534\pi\) |
−0.996189 | + | 0.0872234i | \(0.972201\pi\) | |||||||
\(314\) | −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 | 0.962348 | + | 0.271821i | \(0.0876257\pi\) |
−0.245771 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(318\) | −18.2103 | + | 2.06197i | −1.02118 | + | 0.115629i | ||||
\(319\) | 21.4128 | − | 12.3627i | 1.19889 | − | 0.692179i | ||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | −5.18263 | + | 0.586834i | −0.289266 | + | 0.0327539i | ||||
\(322\) | 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 | ||||
\(327\) | 16.6112 | + | 7.23650i | 0.918601 | + | 0.400179i | ||||
\(328\) | 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 | \(-0.775050\pi\) | ||
0.760508 | − | 0.649329i | \(-0.224950\pi\) | |||||||
\(332\) | −11.8742 | + | 6.85554i | −0.651679 | + | 0.376247i | ||||
\(333\) | 4.82583 | + | 21.0365i | 0.264454 | + | 1.15279i | ||||
\(334\) | −9.69066 | −0.530249 | ||||||||
\(335\) | −15.8721 | −0.867185 | ||||||||
\(336\) | 1.35624 | − | 3.11322i | 0.0739892 | − | 0.169840i | ||||
\(337\) | −1.65491 | − | 0.955464i | −0.0901489 | − | 0.0520475i | 0.454248 | − | 0.890875i | \(-0.349908\pi\) |
−0.544397 | + | 0.838828i | \(0.683241\pi\) | |||||||
\(338\) | 4.49050 | + | 7.77777i | 0.244251 | + | 0.423055i | ||||
\(339\) | 20.9262 | − | 2.36949i | 1.13655 | − | 0.128693i | ||||
\(340\) | 1.96028 | − | 3.39530i | 0.106311 | − | 0.184136i | ||||
\(341\) | 1.14743 | 0.0621370 | ||||||||
\(342\) | −9.17482 | + | 9.31787i | −0.496117 | + | 0.503853i | ||||
\(343\) | 19.9119 | 1.07514 | ||||||||
\(344\) | 2.94487 | − | 5.10067i | 0.158777 | − | 0.275010i | ||||
\(345\) | 11.7481 | − | 1.33025i | 0.632499 | − | 0.0716185i | ||||
\(346\) | −5.22274 | − | 9.04605i | −0.280776 | − | 0.486319i | ||||
\(347\) | −13.6960 | − | 7.90736i | −0.735237 | − | 0.424489i | 0.0850978 | − | 0.996373i | \(-0.472880\pi\) |
−0.820335 | + | 0.571883i | \(0.806213\pi\) | |||||||
\(348\) | 3.48193 | − | 7.99269i | 0.186651 | − | 0.428453i | ||||
\(349\) | −29.7786 | −1.59401 | −0.797006 | − | 0.603972i | \(-0.793584\pi\) | ||||
−0.797006 | + | 0.603972i | \(0.793584\pi\) | |||||||
\(350\) | −1.96058 | −0.104797 | ||||||||
\(351\) | 6.78179 | − | 7.90698i | 0.361985 | − | 0.422044i | ||||
\(352\) | 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 | ||||
\(357\) | −12.2056 | − | 5.31723i | −0.645987 | − | 0.281418i | ||||
\(358\) | 0.673349 | − | 1.16628i | 0.0355876 | − | 0.0616396i | ||||
\(359\) | −3.05773 | − | 1.76538i | −0.161381 | − | 0.0931733i | 0.417135 | − | 0.908845i | \(-0.363034\pi\) |
−0.578515 | + | 0.815671i | \(0.696368\pi\) | |||||||
\(360\) | −2.86769 | − | 0.881106i | −0.151141 | − | 0.0464384i | ||||
\(361\) | 10.9104 | + | 15.5552i | 0.574232 | + | 0.818693i | ||||
\(362\) | − | 14.6171i | − | 0.768257i | ||||||
\(363\) | −22.5972 | + | 2.55871i | −1.18605 | + | 0.134297i | ||||
\(364\) | 3.40387 | + | 1.96523i | 0.178411 | + | 0.103006i | ||||
\(365\) | 1.97262 | − | 1.13889i | 0.103251 | − | 0.0596123i | ||||
\(366\) | 13.4716 | − | 1.52541i | 0.704174 | − | 0.0797343i | ||||
\(367\) | −1.33512 | − | 2.31249i | −0.0696925 | − | 0.120711i | 0.829073 | − | 0.559140i | \(-0.188868\pi\) |
−0.898766 | + | 0.438429i | \(0.855535\pi\) | |||||||
\(368\) | 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 | \(-0.965615\pi\) | ||
0.994171 | − | 0.107813i | \(-0.0343848\pi\) | |||||||
\(374\) | −9.62931 | − | 16.6785i | −0.497920 | − | 0.862422i | ||||
\(375\) | 0.194877 | + | 1.72105i | 0.0100634 | + | 0.0888748i | ||||
\(376\) | 1.60922 | − | 0.929084i | 0.0829892 | − | 0.0479138i | ||||
\(377\) | 8.73888 | + | 5.04540i | 0.450075 | + | 0.259851i | ||||
\(378\) | −1.87742 | + | 10.0130i | −0.0965638 | + | 0.515011i | ||||
\(379\) | − | 10.8219i | − | 0.555884i | −0.960598 | − | 0.277942i | \(-0.910348\pi\) | ||
0.960598 | − | 0.277942i | \(-0.0896523\pi\) | |||||||
\(380\) | −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 | \(-0.972412\pi\) |
0.573088 | + | 0.819494i | \(0.305745\pi\) | |||||||
\(384\) | 0.691758 | − | 1.58791i | 0.0353012 | − | 0.0810329i | ||||
\(385\) | −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 | −0.667251 | + | 0.744833i | \(0.732529\pi\) |
−0.978670 | + | 0.205440i | \(0.934138\pi\) | |||||||
\(390\) | 1.38680 | − | 3.18336i | 0.0702233 | − | 0.161196i | ||||
\(391\) | 26.7623 | 1.35343 | ||||||||
\(392\) | 3.15615 | 0.159409 | ||||||||
\(393\) | 14.1988 | + | 6.18555i | 0.716234 | + | 0.312020i | ||||
\(394\) | 2.14864 | + | 1.24052i | 0.108247 | + | 0.0624965i | ||||
\(395\) | 6.22958 | + | 10.7900i | 0.313444 | + | 0.542902i | ||||
\(396\) | −10.7917 | + | 10.0354i | −0.542302 | + | 0.504296i | ||||
\(397\) | −2.65169 | + | 4.59286i | −0.133085 | + | 0.230509i | −0.924864 | − | 0.380298i | \(-0.875822\pi\) |
0.791780 | + | 0.610807i | \(0.209155\pi\) | |||||||
\(398\) | −23.6124 | −1.18358 | ||||||||
\(399\) | 13.8173 | + | 5.30865i | 0.691730 | + | 0.265765i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 3.00036 | − | 5.19678i | 0.149831 | − | 0.259515i | −0.781334 | − | 0.624113i | \(-0.785460\pi\) |
0.931165 | + | 0.364598i | \(0.118794\pi\) | |||||||
\(402\) | 3.09310 | + | 27.3167i | 0.154270 | + | 1.36243i | ||||
\(403\) | 0.234142 | + | 0.405546i | 0.0116634 | + | 0.0202017i | ||||
\(404\) | 9.94449 | + | 5.74146i | 0.494757 | + | 0.285648i | ||||
\(405\) | 8.97629 | + | 0.652788i | 0.446036 | + | 0.0324373i | ||||
\(406\) | −9.86847 | −0.489764 | ||||||||
\(407\) | 35.3400 | 1.75174 | ||||||||
\(408\) | −6.22550 | − | 2.71208i | −0.308208 | − | 0.134268i | ||||
\(409\) | −23.6531 | + | 13.6561i | −1.16957 | + | 0.675253i | −0.953579 | − | 0.301143i | \(-0.902632\pi\) |
−0.215993 | + | 0.976395i | \(0.569299\pi\) | |||||||
\(410\) | 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 | ||||
\(414\) | −4.57888 | − | 19.9599i | −0.225039 | − | 0.980978i | ||||
\(415\) | 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 | \(0.959312\pi\) | |||||||
\(420\) | 0.382070 | + | 3.37425i | 0.0186431 | + | 0.164647i | ||||
\(421\) | 0.601100 | + | 0.347045i | 0.0292958 | + | 0.0169139i | 0.514576 | − | 0.857445i | \(-0.327949\pi\) |
−0.485281 | + | 0.874358i | \(0.661283\pi\) | |||||||
\(422\) | 2.52326 | − | 1.45680i | 0.122830 | − | 0.0709160i | ||||
\(423\) | −4.08222 | + | 3.79613i | −0.198484 | + | 0.184574i | ||||
\(424\) | 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 | \(-0.297631\pi\) |
−0.993716 | + | 0.111927i | \(0.964298\pi\) | |||||||
\(432\) | −0.957584 | + | 5.10716i | −0.0460718 | + | 0.245718i | ||||
\(433\) | 18.0716 | − | 10.4336i | 0.868465 | − | 0.501409i | 0.00162720 | − | 0.999999i | \(-0.499482\pi\) |
0.866838 | + | 0.498590i | \(0.166149\pi\) | |||||||
\(434\) | −0.396610 | − | 0.228983i | −0.0190379 | − | 0.0109915i | ||||
\(435\) | 0.980902 | + | 8.66284i | 0.0470306 | + | 0.415351i | ||||
\(436\) | − | 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 | 0.256711 | − | 0.966488i | \(-0.417361\pi\) |
−0.708648 | + | 0.705562i | \(0.750695\pi\) | |||||||
\(440\) | −2.45611 | + | 4.25411i | −0.117090 | + | 0.202807i | ||||
\(441\) | −9.22871 | + | 2.11710i | −0.439463 | + | 0.100814i | ||||
\(442\) | 3.92986 | − | 6.80671i | 0.186924 | − | 0.323762i | ||||
\(443\) | −32.8931 | + | 18.9908i | −1.56280 | + | 0.902281i | −0.565825 | + | 0.824525i | \(0.691442\pi\) |
−0.996972 | + | 0.0777559i | \(0.975225\pi\) | |||||||
\(444\) | 10.0219 | − | 7.40505i | 0.475620 | − | 0.351428i | ||||
\(445\) | − | 10.9628i | − | 0.519685i | ||||||
\(446\) | 3.39391 | − | 1.95947i | 0.160706 | − | 0.0927838i | ||||
\(447\) | 7.31908 | + | 3.18848i | 0.346180 | + | 0.150810i | ||||
\(448\) | −1.96058 | −0.0926285 | ||||||||
\(449\) | −37.0794 | −1.74989 | −0.874944 | − | 0.484225i | \(-0.839102\pi\) | ||||
−0.874944 | + | 0.484225i | \(0.839102\pi\) | |||||||
\(450\) | 2.92405 | − | 0.670786i | 0.137841 | − | 0.0316211i | ||||
\(451\) | 50.0494 | + | 28.8961i | 2.35674 | + | 1.36066i | ||||
\(452\) | −6.07947 | − | 10.5300i | −0.285954 | − | 0.495287i | ||||
\(453\) | 3.38236 | + | 29.8713i | 0.158917 | + | 1.40348i | ||||
\(454\) | 0.158042 | − | 0.273737i | 0.00741729 | − | 0.0128471i | ||||
\(455\) | −3.93045 | −0.184263 | ||||||||
\(456\) | 7.04758 | + | 2.70770i | 0.330033 | + | 0.126800i | ||||
\(457\) | 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 | ||||
\(459\) | 20.0229 | + | 3.75426i | 0.934588 | + | 0.175234i | ||||
\(460\) | −3.41307 | − | 5.91161i | −0.159135 | − | 0.275630i | ||||
\(461\) | −4.14251 | − | 2.39168i | −0.192936 | − | 0.111392i | 0.400420 | − | 0.916332i | \(-0.368864\pi\) |
−0.593356 | + | 0.804940i | \(0.702197\pi\) | |||||||
\(462\) | 15.2928 | + | 6.66217i | 0.711487 | + | 0.309952i | ||||
\(463\) | −19.1590 | −0.890394 | −0.445197 | − | 0.895433i | \(-0.646866\pi\) | ||||
−0.445197 | + | 0.895433i | \(0.646866\pi\) | |||||||
\(464\) | −5.03345 | −0.233672 | ||||||||
\(465\) | −0.161586 | + | 0.370917i | −0.00749338 | + | 0.0172009i | ||||
\(466\) | 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 | ||||
\(471\) | 1.15344 | − | 2.64769i | 0.0531476 | − | 0.121999i | ||||
\(472\) | 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 | ||||||||
\(477\) | −21.6161 | − | 23.2452i | −0.989734 | − | 1.06432i | ||||
\(478\) | 2.75990 | + | 1.59343i | 0.126235 | + | 0.0728817i | ||||
\(479\) | 22.9732 | − | 13.2636i | 1.04967 | − | 0.606028i | 0.127114 | − | 0.991888i | \(-0.459429\pi\) |
0.922557 | + | 0.385860i | \(0.126095\pi\) | |||||||
\(480\) | 0.194877 | + | 1.72105i | 0.00889485 | + | 0.0785550i | ||||
\(481\) | 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 | \(0.0825357\pi\) | ||||
−0.966571 | + | 0.256398i | \(0.917464\pi\) | |||||||
\(488\) | −3.91378 | − | 6.77887i | −0.177169 | − | 0.306865i | ||||
\(489\) | 14.7312 | − | 1.66803i | 0.666167 | − | 0.0754308i | ||||
\(490\) | −2.73330 | + | 1.57807i | −0.123478 | + | 0.0712900i | ||||
\(491\) | 6.02160 | + | 3.47657i | 0.271751 | + | 0.156896i | 0.629683 | − | 0.776852i | \(-0.283185\pi\) |
−0.357932 | + | 0.933748i | \(0.616518\pi\) | |||||||
\(492\) | 20.2481 | − | 2.29272i | 0.912857 | − | 0.103364i | ||||
\(493\) | 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 | ||||
\(498\) | −21.7720 | − | 9.48476i | −0.975628 | − | 0.425022i | ||||
\(499\) | −17.0361 | + | 29.5074i | −0.762642 | + | 1.32093i | 0.178843 | + | 0.983878i | \(0.442765\pi\) |
−0.941484 | + | 0.337057i | \(0.890569\pi\) | |||||||
\(500\) | 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 | \(-0.699302\pi\) |
0.408740 | + | 0.912651i | \(0.365968\pi\) | |||||||
\(504\) | 5.73281 | − | 1.31513i | 0.255360 | − | 0.0585803i | ||||
\(505\) | −11.4829 | −0.510983 | ||||||||
\(506\) | −33.5315 | −1.49066 | ||||||||
\(507\) | −6.21268 | + | 14.2610i | −0.275915 | + | 0.633355i | ||||
\(508\) | −11.2081 | − | 6.47100i | −0.497279 | − | 0.287104i | ||||
\(509\) | 10.1206 | + | 17.5295i | 0.448590 | + | 0.776980i | 0.998294 | − | 0.0583790i | \(-0.0185932\pi\) |
−0.549705 | + | 0.835359i | \(0.685260\pi\) | |||||||
\(510\) | 6.74748 | − | 0.764024i | 0.298784 | − | 0.0338316i | ||||
\(511\) | −2.23288 | + | 3.86746i | −0.0987769 | + | 0.171087i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −22.4237 | − | 3.19003i | −0.990032 | − | 0.140843i | ||||
\(514\) | −23.5470 | −1.03861 | ||||||||
\(515\) | −0.881671 | + | 1.52710i | −0.0388511 | + | 0.0672920i | ||||
\(516\) | 10.1366 | − | 1.14777i | 0.446237 | − | 0.0505279i | ||||
\(517\) | 4.56386 | + | 7.90484i | 0.200718 | + | 0.347655i | ||||
\(518\) | −12.2153 | − | 7.05248i | −0.536708 | − | 0.309868i | ||||
\(519\) | 7.22575 | − | 16.5865i | 0.317175 | − | 0.728068i | ||||
\(520\) | −2.00475 | −0.0879139 | ||||||||
\(521\) | 19.3708 | 0.848650 | 0.424325 | − | 0.905510i | \(-0.360511\pi\) | ||||
0.424325 | + | 0.905510i | \(0.360511\pi\) | |||||||
\(522\) | 14.7181 | − | 3.37637i | 0.644192 | − | 0.147780i | ||||
\(523\) | −35.0535 | + | 20.2382i | −1.53278 | + | 0.884954i | −0.533553 | + | 0.845767i | \(0.679143\pi\) |
−0.999232 | + | 0.0391867i | \(0.987523\pi\) | |||||||
\(524\) | − | 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 | ||||
\(528\) | 7.80018 | + | 3.39807i | 0.339459 | + | 0.147882i | ||||
\(529\) | 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 | ||||||||
\(534\) | −18.8675 | + | 2.13639i | −0.816477 | + | 0.0924505i | ||||
\(535\) | −2.60787 | − | 1.50566i | −0.112748 | − | 0.0650952i | ||||
\(536\) | 13.7456 | − | 7.93605i | 0.593721 | − | 0.342785i | ||||
\(537\) | 2.31774 | − | 0.262440i | 0.100018 | − | 0.0113251i | ||||
\(538\) | −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 | 0.986960 | + | 0.160964i | \(0.0514602\pi\) |
−0.354082 | + | 0.935215i | \(0.615206\pi\) | |||||||
\(542\) | −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 | ||||
\(546\) | 0.765953 | + | 6.76452i | 0.0327798 | + | 0.289495i | ||||
\(547\) | 10.3833 | − | 5.99478i | 0.443956 | − | 0.256318i | −0.261318 | − | 0.965253i | \(-0.584157\pi\) |
0.705274 | + | 0.708935i | \(0.250824\pi\) | |||||||
\(548\) | −3.55144 | − | 2.05042i | −0.151710 | − | 0.0875898i | ||||
\(549\) | 15.9912 | + | 17.1964i | 0.682490 | + | 0.733925i | ||||
\(550\) | − | 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 | ||||
\(555\) | −4.97672 | + | 11.4239i | −0.211250 | + | 0.484919i | ||||
\(556\) | 6.74169 | − | 11.6770i | 0.285911 | − | 0.495213i | ||||
\(557\) | 24.0375 | − | 13.8780i | 1.01850 | − | 0.588031i | 0.104831 | − | 0.994490i | \(-0.466570\pi\) |
0.913669 | + | 0.406459i | \(0.133237\pi\) | |||||||
\(558\) | 0.669857 | + | 0.205815i | 0.0283573 | + | 0.00871286i | ||||
\(559\) | 11.8074i | 0.499401i | ||||||||
\(560\) | 1.69791 | − | 0.980288i | 0.0717497 | − | 0.0414247i | ||||
\(561\) | 13.3223 | − | 30.5810i | 0.562469 | − | 1.29113i | ||||
\(562\) | 18.7084 | 0.789164 | ||||||||
\(563\) | 17.1980 | 0.724809 | 0.362404 | − | 0.932021i | \(-0.381956\pi\) | ||||
0.362404 | + | 0.932021i | \(0.381956\pi\) | |||||||
\(564\) | 2.95061 | + | 1.28540i | 0.124243 | + | 0.0541252i | ||||
\(565\) | 10.5300 | + | 6.07947i | 0.442998 | + | 0.255765i | ||||
\(566\) | −10.5801 | − | 18.3252i | −0.444713 | − | 0.770265i | ||||
\(567\) | −15.8808 | + | 7.69098i | −0.666933 | + | 0.322991i | ||||
\(568\) | −2.26439 | + | 3.92204i | −0.0950118 | + | 0.164565i | ||||
\(569\) | −26.3732 | −1.10562 | −0.552812 | − | 0.833306i | \(-0.686445\pi\) | ||||
−0.552812 | + | 0.833306i | \(0.686445\pi\) | |||||||
\(570\) | −7.45723 | + | 1.17885i | −0.312349 | + | 0.0493766i | ||||
\(571\) | 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 | ||||
\(573\) | −1.18751 | − | 10.4875i | −0.0496089 | − | 0.438122i | ||||
\(574\) | −11.5331 | − | 19.9758i | −0.481380 | − | 0.833775i | ||||
\(575\) | 5.91161 | + | 3.41307i | 0.246531 | + | 0.142335i | ||||
\(576\) | 2.92405 | − | 0.670786i | 0.121835 | − | 0.0279494i | ||||
\(577\) | 6.44640 | 0.268367 | 0.134184 | − | 0.990956i | \(-0.457159\pi\) | ||||
0.134184 | + | 0.990956i | \(0.457159\pi\) | |||||||
\(578\) | −1.62925 | −0.0677679 | ||||||||
\(579\) | 4.76521 | + | 2.07591i | 0.198035 | + | 0.0862721i | ||||
\(580\) | 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 | ||||
\(585\) | 5.86197 | − | 1.34475i | 0.242363 | − | 0.0555987i | ||||
\(586\) | 6.15600 | − | 10.6625i | 0.254302 | − | 0.440464i | ||||
\(587\) | −29.3043 | − | 16.9188i | −1.20952 | − | 0.698315i | −0.246863 | − | 0.969050i | \(-0.579400\pi\) |
−0.962654 | + | 0.270736i | \(0.912733\pi\) | |||||||
\(588\) | 3.24860 | + | 4.39663i | 0.133970 | + | 0.181314i | ||||
\(589\) | 0.469784 | − | 0.903329i | 0.0193571 | − | 0.0372210i | ||||
\(590\) | 8.51757i | 0.350663i | ||||||||
\(591\) | 0.483496 | + | 4.27000i | 0.0198884 | + | 0.175644i | ||||
\(592\) | −6.23045 | − | 3.59715i | −0.256070 | − | 0.147842i | ||||
\(593\) | 25.1953 | − | 14.5465i | 1.03465 | − | 0.597354i | 0.116335 | − | 0.993210i | \(-0.462886\pi\) |
0.918312 | + | 0.395856i | \(0.129552\pi\) | |||||||
\(594\) | −25.0875 | − | 4.70386i | −1.02935 | − | 0.193002i | ||||
\(595\) | −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 | 0.997270 | + | 0.0738365i | \(0.0235243\pi\) |
−0.434691 | + | 0.900580i | \(0.643142\pi\) | |||||||
\(600\) | −1.02929 | − | 1.39304i | −0.0420208 | − | 0.0568705i | ||||
\(601\) | 14.9379i | 0.609330i | 0.952460 | + | 0.304665i | \(0.0985445\pi\) | ||||
−0.952460 | + | 0.304665i | \(0.901455\pi\) | |||||||
\(602\) | −5.77364 | − | 10.0002i | −0.235316 | − | 0.407580i | ||||
\(603\) | −34.8695 | + | 32.4257i | −1.42000 | + | 1.32048i | ||||
\(604\) | 15.0311 | − | 8.67821i | 0.611607 | − | 0.353111i | ||||
\(605\) | −11.3708 | − | 6.56495i | −0.462290 | − | 0.266903i | ||||
\(606\) | 2.23775 | + | 19.7627i | 0.0909024 | + | 0.802805i | ||||
\(607\) | 42.6299i | 1.73030i | 0.501517 | + | 0.865148i | \(0.332775\pi\) | ||||
−0.501517 | + | 0.865148i | \(0.667225\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | −2.62985 | − | 11.4639i | −0.106305 | − | 0.463400i | ||||
\(613\) | 8.76635 | − | 15.1838i | 0.354069 | − | 0.613266i | −0.632889 | − | 0.774243i | \(-0.718131\pi\) |
0.986958 | + | 0.160976i | \(0.0514643\pi\) | |||||||
\(614\) | −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 | 0.540008 | − | 0.841660i | \(-0.318421\pi\) |
0.998903 | − | 0.0468313i | \(-0.0149123\pi\) | |||||||
\(618\) | 2.80004 | + | 1.21981i | 0.112634 | + | 0.0490678i | ||||
\(619\) | −42.3600 | −1.70259 | −0.851296 | − | 0.524685i | \(-0.824183\pi\) | ||||
−0.851296 | + | 0.524685i | \(0.824183\pi\) | |||||||
\(620\) | 0.233588 | 0.00938111 | ||||||||
\(621\) | 23.0919 | − | 26.9232i | 0.926648 | − | 1.08039i | ||||
\(622\) | −27.6123 | − | 15.9420i | −1.10715 | − | 0.639214i | ||||
\(623\) | 10.7467 | + | 18.6138i | 0.430556 | + | 0.745746i | ||||
\(624\) | 0.390678 | + | 3.45027i | 0.0156396 | + | 0.138121i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −14.9516 | −0.597585 | ||||||||
\(627\) | −13.3008 | + | 34.6192i | −0.531184 | + | 1.38256i | ||||
\(628\) | −1.66740 | −0.0665365 | ||||||||
\(629\) | −14.1028 | + | 24.4268i | −0.562316 | + | 0.973961i | ||||
\(630\) | −4.30720 | + | 4.00534i | −0.171603 | + | 0.159577i | ||||
\(631\) | −17.6187 | − | 30.5165i | −0.701391 | − | 1.21484i | −0.967978 | − | 0.251033i | \(-0.919230\pi\) |
0.266588 | − | 0.963811i | \(-0.414104\pi\) | |||||||
\(632\) | −10.7900 | − | 6.22958i | −0.429201 | − | 0.247800i | ||||
\(633\) | 4.62655 | + | 2.01551i | 0.183889 | + | 0.0801094i | ||||
\(634\) | 25.5166 | 1.01339 | ||||||||
\(635\) | 12.9420 | 0.513587 | ||||||||
\(636\) | −7.31942 | + | 16.8015i | −0.290234 | + | 0.666224i | ||||
\(637\) | −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 | \(-0.674598\pi\) |
0.999690 | + | 0.0249155i | \(0.00793168\pi\) | |||||||
\(642\) | −2.08310 | + | 4.78171i | −0.0822135 | + | 0.188719i | ||||
\(643\) | −8.96485 | + | 15.5276i | −0.353539 | + | 0.612348i | −0.986867 | − | 0.161536i | \(-0.948355\pi\) |
0.633328 | + | 0.773884i | \(0.281689\pi\) | |||||||
\(644\) | 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 | \(-0.103337\pi\) | |||||||
\(648\) | −8.10009 | + | 3.92282i | −0.318202 | + | 0.154103i | ||||
\(649\) | 36.2346 | + | 20.9201i | 1.42233 | + | 0.821185i | ||||
\(650\) | 1.73616 | − | 1.00237i | 0.0680978 | − | 0.0393163i | ||||
\(651\) | −0.0892469 | − | 0.788184i | −0.00349786 | − | 0.0308914i | ||||
\(652\) | −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 | 0.982272 | + | 0.187459i | \(0.0600252\pi\) |
−0.328792 | + | 0.944402i | \(0.606642\pi\) | |||||||
\(660\) | −8.45419 | + | 0.957276i | −0.329079 | + | 0.0372619i | ||||
\(661\) | 13.8780 | − | 8.01246i | 0.539791 | − | 0.311649i | −0.205203 | − | 0.978719i | \(-0.565785\pi\) |
0.744994 | + | 0.667071i | \(0.232452\pi\) | |||||||
\(662\) | −20.4616 | − | 11.8135i | −0.795262 | − | 0.459145i | ||||
\(663\) | 13.5270 | − | 1.53167i | 0.525345 | − | 0.0594853i | ||||
\(664\) | 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 | ||||
\(669\) | 6.22295 | + | 2.71097i | 0.240593 | + | 0.104812i | ||||
\(670\) | −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 | \(-0.788670\pi\) | ||
0.787586 | − | 0.616204i | \(-0.211330\pi\) | |||||||
\(674\) | −1.65491 | + | 0.955464i | −0.0637449 | + | 0.0368031i | ||||
\(675\) | 3.94413 | + | 3.38287i | 0.151810 | + | 0.130207i | ||||
\(676\) | 8.98100 | 0.345423 | ||||||||
\(677\) | −25.2864 | −0.971835 | −0.485918 | − | 0.874005i | \(-0.661514\pi\) | ||||
−0.485918 | + | 0.874005i | \(0.661514\pi\) | |||||||
\(678\) | 8.41105 | − | 19.3074i | 0.323024 | − | 0.741494i | ||||
\(679\) | 26.1067 | + | 15.0727i | 1.00188 | + | 0.578437i | ||||
\(680\) | −1.96028 | − | 3.39530i | −0.0751732 | − | 0.130204i | ||||
\(681\) | 0.543998 | − | 0.0615974i | 0.0208460 | − | 0.00236042i | ||||
\(682\) | 0.573717 | − | 0.993707i | 0.0219688 | − | 0.0380510i | ||||
\(683\) | 8.39063 | 0.321059 | 0.160529 | − | 0.987031i | \(-0.448680\pi\) | ||||
0.160529 | + | 0.987031i | \(0.448680\pi\) | |||||||
\(684\) | 3.48210 | + | 12.6046i | 0.133141 | + | 0.481947i | ||||
\(685\) | 4.10085 | 0.156685 | ||||||||
\(686\) | 9.95594 | − | 17.2442i | 0.380120 | − | 0.658387i | ||||
\(687\) | 10.5559 | − | 1.19526i | 0.402733 | − | 0.0456018i | ||||
\(688\) | −2.94487 | − | 5.10067i | −0.112272 | − | 0.194461i | ||||
\(689\) | −18.3701 | − | 10.6060i | −0.699846 | − | 0.404056i | ||||
\(690\) | 4.72204 | − | 10.8393i | 0.179765 | − | 0.412646i | ||||
\(691\) | −10.0647 | −0.382881 | −0.191440 | − | 0.981504i | \(-0.561316\pi\) | ||||
−0.191440 | + | 0.981504i | \(0.561316\pi\) | |||||||
\(692\) | −10.4455 | −0.397078 | ||||||||
\(693\) | 6.46018 | + | 28.1608i | 0.245402 | + | 1.06974i | ||||
\(694\) | −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 | ||||
\(699\) | 17.1921 | + | 7.48955i | 0.650264 | + | 0.283281i | ||||
\(700\) | −0.980288 | + | 1.69791i | −0.0370514 | + | 0.0641749i | ||||
\(701\) | −29.1351 | − | 16.8212i | −1.10042 | − | 0.635327i | −0.164087 | − | 0.986446i | \(-0.552468\pi\) |
−0.936331 | + | 0.351119i | \(0.885801\pi\) | |||||||
\(702\) | −3.45675 | − | 9.82670i | −0.130467 | − | 0.370885i | ||||
\(703\) | 14.4690 | − | 27.8218i | 0.545707 | − | 1.04932i | ||||
\(704\) | − | 4.91222i | − | 0.185136i | ||||||
\(705\) | −3.19801 | + | 0.362113i | −0.120444 | + | 0.0136380i | ||||
\(706\) | 2.12758 | + | 1.22836i | 0.0800724 | + | 0.0462298i | ||||
\(707\) | 19.4969 | − | 11.2566i | 0.733257 | − | 0.423346i | ||||
\(708\) | 14.6592 | − | 1.65987i | 0.550926 | − | 0.0623819i | ||||
\(709\) | 22.1508 | + | 38.3664i | 0.831892 | + | 1.44088i | 0.896536 | + | 0.442971i | \(0.146076\pi\) |
−0.0646434 | + | 0.997908i | \(0.520591\pi\) | |||||||
\(710\) | − | 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 | ||||
\(717\) | 0.621044 | + | 5.48475i | 0.0231933 | + | 0.204832i | ||||
\(718\) | −3.05773 | + | 1.76538i | −0.114113 | + | 0.0658834i | ||||
\(719\) | 12.8018 | + | 7.39114i | 0.477428 | + | 0.275643i | 0.719344 | − | 0.694654i | \(-0.244443\pi\) |
−0.241916 | + | 0.970297i | \(0.577776\pi\) | |||||||
\(720\) | −2.19691 | + | 2.04294i | −0.0818738 | + | 0.0761359i | ||||
\(721\) | − | 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 | ||||
\(726\) | −9.08271 | + | 20.8491i | −0.337091 | + | 0.773784i | ||||
\(727\) | 2.63804 | − | 4.56923i | 0.0978397 | − | 0.169463i | −0.812951 | − | 0.582333i | \(-0.802140\pi\) |
0.910790 | + | 0.412869i | \(0.135473\pi\) | |||||||
\(728\) | 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 | ||||
\(732\) | 5.41478 | − | 12.4295i | 0.200136 | − | 0.459407i | ||||
\(733\) | −12.3735 | −0.457025 | −0.228513 | − | 0.973541i | \(-0.573386\pi\) | ||||
−0.228513 | + | 0.973541i | \(0.573386\pi\) | |||||||
\(734\) | −2.67023 | −0.0985601 | ||||||||
\(735\) | −5.01169 | − | 2.18329i | −0.184859 | − | 0.0805319i | ||||
\(736\) | 5.91161 | + | 3.41307i | 0.217905 | + | 0.125807i | ||||
\(737\) | 38.9836 | + | 67.5216i | 1.43598 | + | 2.48719i | ||||
\(738\) | 24.0351 | + | 25.8465i | 0.884746 | + | 0.951424i | ||||
\(739\) | 23.4208 | − | 40.5660i | 0.861548 | − | 1.49224i | −0.00888687 | − | 0.999961i | \(-0.502829\pi\) |
0.870435 | − | 0.492284i | \(-0.163838\pi\) | |||||||
\(740\) | 7.19430 | 0.264468 | ||||||||
\(741\) | −14.9499 | + | 2.36329i | −0.549197 | + | 0.0868177i | ||||
\(742\) | 20.7446 | 0.761559 | ||||||||
\(743\) | −3.70160 | + | 6.41135i | −0.135798 | + | 0.235210i | −0.925902 | − | 0.377763i | \(-0.876693\pi\) |
0.790104 | + | 0.612973i | \(0.210027\pi\) | |||||||
\(744\) | −0.0455208 | − | 0.402017i | −0.00166887 | − | 0.0147386i | ||||
\(745\) | 2.30462 | + | 3.99172i | 0.0844347 | + | 0.146245i | ||||
\(746\) | −3.60651 | − | 2.08222i | −0.132044 | − | 0.0762354i | ||||
\(747\) | −9.19720 | − | 40.0919i | −0.336508 | − | 1.46688i | ||||
\(748\) | −19.2586 | −0.704165 | ||||||||
\(749\) | 5.90391 | 0.215724 | ||||||||
\(750\) | 1.58791 | + | 0.691758i | 0.0579824 | + | 0.0252594i | ||||
\(751\) | −36.7844 | + | 21.2375i | −1.34228 | + | 0.774966i | −0.987142 | − | 0.159848i | \(-0.948900\pi\) |
−0.355139 | + | 0.934814i | \(0.615566\pi\) | |||||||
\(752\) | − | 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 | ||||
\(756\) | 7.73277 | + | 6.63237i | 0.281238 | + | 0.241217i | ||||
\(757\) | 24.8985 | − | 43.1254i | 0.904950 | − | 1.56742i | 0.0839656 | − | 0.996469i | \(-0.473241\pi\) |
0.820984 | − | 0.570951i | \(-0.193425\pi\) | |||||||
\(758\) | −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 | \(-0.197503\pi\) | |||||||
\(762\) | −2.52209 | − | 22.2739i | −0.0913657 | − | 0.806896i | ||||
\(763\) | −17.7618 | − | 10.2548i | −0.643022 | − | 0.371249i | ||||
\(764\) | −5.27726 | + | 3.04683i | −0.190924 | + | 0.110230i | ||||
\(765\) | 8.00946 | + | 8.61309i | 0.289583 | + | 0.311407i | ||||
\(766\) | 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 | −0.959700 | − | 0.281026i | \(-0.909325\pi\) |
0.236475 | − | 0.971638i | \(-0.424008\pi\) | |||||||
\(770\) | 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 | \(-0.119805\pi\) |
−0.783313 | + | 0.621628i | \(0.786472\pi\) | |||||||
\(774\) | 12.0324 | + | 12.9392i | 0.432496 | + | 0.465090i | ||||
\(775\) | −0.202293 | + | 0.116794i | −0.00726657 | + | 0.00419536i | ||||
\(776\) | 13.3158 | + | 7.68789i | 0.478010 | + | 0.275979i | ||||
\(777\) | −2.74873 | − | 24.2754i | −0.0986100 | − | 0.870875i | ||||
\(778\) | 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 | ||||
\(783\) | 19.8526 | + | 17.0275i | 0.709475 | + | 0.608514i | ||||
\(784\) | 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 | \(0.261487\pi\) | ||||
−0.681134 | + | 0.732159i | \(0.738513\pi\) | |||||||
\(788\) | 2.14864 | − | 1.24052i | 0.0765422 | − | 0.0441917i | ||||
\(789\) | −6.34479 | − | 2.76404i | −0.225881 | − | 0.0984026i | ||||
\(790\) | 12.4592 | 0.443277 | ||||||||
\(791\) | −23.8385 | −0.847600 | ||||||||
\(792\) | 3.29505 | + | 14.3636i | 0.117084 | + | 0.510387i | ||||
\(793\) | 13.5899 | + | 7.84613i | 0.482592 | + | 0.278624i | ||||
\(794\) | 2.65169 | + | 4.59286i | 0.0941050 | + | 0.162995i | ||||
\(795\) | −2.06197 | − | 18.2103i | −0.0731304 | − | 0.645851i | ||||
\(796\) | −11.8062 | + | 20.4489i | −0.418459 | + | 0.724792i | ||||
\(797\) | −39.4937 | −1.39894 | −0.699469 | − | 0.714663i | \(-0.746580\pi\) | ||||
−0.699469 | + | 0.714663i | \(0.746580\pi\) | |||||||
\(798\) | 11.5061 | − | 9.31181i | 0.407311 | − | 0.329634i | ||||
\(799\) | −7.28505 | −0.257727 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −22.3963 | − | 24.0842i | −0.791334 | − | 0.850973i | ||||
\(802\) | −3.00036 | − | 5.19678i | −0.105946 | − | 0.183505i | ||||
\(803\) | −9.68993 | − | 5.59448i | −0.341950 | − | 0.197425i | ||||
\(804\) | 25.2035 | + | 10.9797i | 0.888859 | + | 0.387223i | ||||
\(805\) | −13.3832 | −0.471694 | ||||||||
\(806\) | 0.468284 | 0.0164946 | ||||||||
\(807\) | 1.55470 | − | 3.56878i | 0.0547282 | − | 0.125627i | ||||
\(808\) | 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 | −1.00000 | 0.000504396i | \(-0.999839\pi\) | |
−0.499563 | + | 0.866277i | \(0.666506\pi\) | |||||||
\(812\) | −4.93423 | + | 8.54634i | −0.173158 | + | 0.299918i | ||||
\(813\) | 3.73756 | − | 8.57947i | 0.131082 | − | 0.300895i | ||||
\(814\) | 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 | ||||||||
\(819\) | −8.63484 | + | 8.02968i | −0.301726 | + | 0.280580i | ||||
\(820\) | 10.1888 | + | 5.88249i | 0.355807 | + | 0.205425i | ||||
\(821\) | 27.3273 | − | 15.7774i | 0.953730 | − | 0.550636i | 0.0594922 | − | 0.998229i | \(-0.481052\pi\) |
0.894238 | + | 0.447593i | \(0.147719\pi\) | |||||||
\(822\) | −0.799159 | − | 7.05778i | −0.0278739 | − | 0.246168i | ||||
\(823\) | −1.24210 | − | 2.15138i | −0.0432968 | − | 0.0749923i | 0.843565 | − | 0.537027i | \(-0.180453\pi\) |
−0.886862 | + | 0.462035i | \(0.847119\pi\) | |||||||
\(824\) | − | 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 | −0.997108 | − | 0.0760023i | \(-0.975784\pi\) |
0.432734 | − | 0.901522i | \(-0.357549\pi\) | |||||||
\(828\) | −19.5753 | − | 6.01455i | −0.680287 | − | 0.209020i | ||||
\(829\) | 30.4181i | 1.05647i | 0.849100 | + | 0.528233i | \(0.177145\pi\) | ||||
−0.849100 | + | 0.528233i | \(0.822855\pi\) | |||||||
\(830\) | −6.85554 | − | 11.8742i | −0.237959 | − | 0.412158i | ||||
\(831\) | −34.6846 | + | 3.92737i | −1.20319 | + | 0.136239i | ||||
\(832\) | 1.73616 | − | 1.00237i | 0.0601905 | − | 0.0347510i | ||||
\(833\) | −10.7161 | − | 6.18692i | −0.371289 | − | 0.214364i | ||||
\(834\) | 23.2056 | − | 2.62760i | 0.803545 | − | 0.0909862i | ||||
\(835\) | − | 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 | \(-0.798923\pi\) |
0.914917 | + | 0.403642i | \(0.132256\pi\) | |||||||
\(840\) | 3.11322 | + | 1.35624i | 0.107416 | + | 0.0467949i | ||||
\(841\) | 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 | ||||
\(846\) | 1.24643 | + | 5.43337i | 0.0428532 | + | 0.186803i | ||||
\(847\) | 25.7421 | 0.884510 | ||||||||
\(848\) | 10.5809 | 0.363349 | ||||||||
\(849\) | 14.6377 | − | 33.6004i | 0.502364 | − | 1.15316i | ||||
\(850\) | 3.39530 | + | 1.96028i | 0.116458 | + | 0.0672370i | ||||
\(851\) | 24.5546 | + | 42.5299i | 0.841722 | + | 1.45791i | ||||
\(852\) | −7.79428 | + | 0.882554i | −0.267028 | + | 0.0302358i | ||||
\(853\) | 24.9526 | − | 43.2191i | 0.854360 | − | 1.47979i | −0.0228782 | − | 0.999738i | \(-0.507283\pi\) |
0.877238 | − | 0.480056i | \(-0.159384\pi\) | |||||||
\(854\) | −15.3465 | −0.525147 | ||||||||
\(855\) | −9.31787 | − | 9.17482i | −0.318664 | − | 0.313772i | ||||
\(856\) | 3.01131 | 0.102925 | ||||||||
\(857\) | 14.9335 | − | 25.8655i | 0.510118 | − | 0.883550i | −0.489813 | − | 0.871827i | \(-0.662935\pi\) |
0.999931 | − | 0.0117228i | \(-0.00373156\pi\) | |||||||
\(858\) | −16.9485 | + | 1.91909i | −0.578612 | + | 0.0655168i | ||||
\(859\) | −12.1997 | − | 21.1305i | −0.416249 | − | 0.720964i | 0.579310 | − | 0.815107i | \(-0.303322\pi\) |
−0.995559 | + | 0.0941433i | \(0.969989\pi\) | |||||||
\(860\) | 5.10067 | + | 2.94487i | 0.173931 | + | 0.100419i | ||||
\(861\) | 15.9562 | − | 36.6270i | 0.543785 | − | 1.24824i | ||||
\(862\) | −16.6054 | −0.565581 | ||||||||
\(863\) | 23.3653 | 0.795363 | 0.397682 | − | 0.917523i | \(-0.369815\pi\) | ||||
0.397682 | + | 0.917523i | \(0.369815\pi\) | |||||||
\(864\) | 3.94413 | + | 3.38287i | 0.134182 | + | 0.115088i | ||||
\(865\) | 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 | ||||
\(870\) | 7.99269 | + | 3.48193i | 0.270978 | + | 0.118049i | ||||
\(871\) | −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 | ||||||
\(876\) | −3.92018 | + | 0.443886i | −0.132451 | + | 0.0149975i | ||||
\(877\) | 36.6106 | + | 21.1372i | 1.23625 | + | 0.713751i | 0.968326 | − | 0.249688i | \(-0.0803281\pi\) |
0.267927 | + | 0.963439i | \(0.413661\pi\) | |||||||
\(878\) | −9.46913 | + | 5.46701i | −0.319568 | + | 0.184503i | ||||
\(879\) | 21.1896 | − | 2.39932i | 0.714708 | − | 0.0809271i | ||||
\(880\) | 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 | 0.915008 | − | 0.403435i | \(-0.132184\pi\) |
−0.806889 | + | 0.590703i | \(0.798850\pi\) | |||||||
\(884\) | −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 | \(-0.228855\pi\) |
−0.946615 | + | 0.322365i | \(0.895522\pi\) | |||||||
\(888\) | −1.40200 | − | 12.3818i | −0.0470480 | − | 0.415505i | ||||
\(889\) | −21.9743 | + | 12.6869i | −0.736995 | + | 0.425504i | ||||
\(890\) | −9.49404 | − | 5.48139i | −0.318241 | − | 0.183737i | ||||
\(891\) | −19.2697 | − | 39.7894i | −0.645560 | − | 1.33300i | ||||
\(892\) | − | 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 | ||||
\(897\) | 9.46649 | − | 21.7301i | 0.316077 | − | 0.725546i | ||||
\(898\) | −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 | ||||
\(903\) | 7.98793 | − | 18.3361i | 0.265822 | − | 0.610187i | ||||
\(904\) | −12.1589 | −0.404400 | ||||||||
\(905\) | 14.6171 | 0.485888 | ||||||||
\(906\) | 27.5605 | + | 12.0065i | 0.915637 | + | 0.398888i | ||||
\(907\) | −33.9003 | − | 19.5724i | −1.12564 | − | 0.649890i | −0.182807 | − | 0.983149i | \(-0.558518\pi\) |
−0.942835 | + | 0.333259i | \(0.891852\pi\) | |||||||
\(908\) | −0.158042 | − | 0.273737i | −0.00524481 | − | 0.00908428i | ||||
\(909\) | −25.2269 | + | 23.4589i | −0.836723 | + | 0.778083i | ||||
\(910\) | −1.96523 | + | 3.40387i | −0.0651466 | + | 0.112837i | ||||
\(911\) | 27.0371 | 0.895778 | 0.447889 | − | 0.894089i | \(-0.352176\pi\) | ||||
0.447889 | + | 0.894089i | \(0.352176\pi\) | |||||||
\(912\) | 5.86873 | − | 4.74953i | 0.194333 | − | 0.157273i | ||||
\(913\) | −67.3519 | −2.22902 | ||||||||
\(914\) | 12.4132 | − | 21.5003i | 0.410592 | − | 0.711167i | ||||
\(915\) | 1.52541 | + | 13.4716i | 0.0504284 | + | 0.445359i | ||||
\(916\) | −3.06670 | − | 5.31168i | −0.101327 | − | 0.175503i | ||||
\(917\) | −15.1823 | − | 8.76552i | −0.501364 | − | 0.289463i | ||||
\(918\) | 13.2627 | − | 15.4632i | 0.437735 | − | 0.510361i | ||||
\(919\) | 36.3996 | 1.20071 | 0.600356 | − | 0.799733i | \(-0.295025\pi\) | ||||
0.600356 | + | 0.799733i | \(0.295025\pi\) | |||||||
\(920\) | −6.82614 | −0.225051 | ||||||||
\(921\) | −24.1150 | − | 10.5055i | −0.794618 | − | 0.346167i | ||||
\(922\) | −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 | ||||
\(927\) | 1.18282 | + | 5.15609i | 0.0388491 | + | 0.169348i | ||||
\(928\) | −2.51673 | + | 4.35910i | −0.0826156 | + | 0.143094i | ||||
\(929\) | 10.5812 | + | 6.10909i | 0.347160 | + | 0.200433i | 0.663434 | − | 0.748235i | \(-0.269099\pi\) |
−0.316274 | + | 0.948668i | \(0.602432\pi\) | |||||||
\(930\) | 0.240431 | + | 0.325396i | 0.00788403 | + | 0.0106702i | ||||
\(931\) | 12.2054 | + | 6.34754i | 0.400017 | + | 0.208032i | ||||
\(932\) | − | 10.8268i | − | 0.354644i | ||||||
\(933\) | −6.21343 | − | 54.8739i | −0.203418 | − | 1.79649i | ||||
\(934\) | −16.0630 | − | 9.27397i | −0.525597 | − | 0.303454i | ||||
\(935\) | 16.6785 | − | 9.62931i | 0.545444 | − | 0.314912i | ||||
\(936\) | −4.40424 | + | 4.09558i | −0.143957 | + | 0.133868i | ||||
\(937\) | 15.9162 | + | 27.5678i | 0.519961 | + | 0.900599i | 0.999731 | + | 0.0232047i | \(0.00738695\pi\) |
−0.479770 | + | 0.877395i | \(0.659280\pi\) | |||||||
\(938\) | − | 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 | \(-0.102253\pi\) |
−0.747862 | + | 0.663854i | \(0.768920\pi\) | |||||||
\(942\) | −1.71625 | − | 2.32275i | −0.0559183 | − | 0.0756793i | ||||
\(943\) | 80.3093i | 2.61523i | ||||||||
\(944\) | −4.25879 | − | 7.37643i | −0.138612 | − | 0.240082i | ||||
\(945\) | −10.0130 | − | 1.87742i | −0.325722 | − | 0.0610723i | ||||
\(946\) | 25.0556 | − | 14.4659i | 0.814628 | − | 0.470326i | ||||
\(947\) | 39.3773 | + | 22.7345i | 1.27959 | + | 0.738773i | 0.976773 | − | 0.214276i | \(-0.0687391\pi\) |
0.302818 | + | 0.953048i | \(0.402072\pi\) | |||||||
\(948\) | −2.42800 | − | 21.4429i | −0.0788577 | − | 0.696433i | ||||
\(949\) | − | 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 | −0.349181 | − | 0.937055i | \(-0.613540\pi\) |
0.986104 | − | 0.166128i | \(-0.0531265\pi\) | |||||||
\(954\) | −30.9390 | + | 7.09750i | −1.00169 | + | 0.229790i | ||||
\(955\) | 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 | ||||
\(960\) | 1.58791 | + | 0.691758i | 0.0512497 | + | 0.0223264i | ||||
\(961\) | 30.9454 | 0.998240 | ||||||||
\(962\) | 14.4227 | 0.465008 | ||||||||
\(963\) | −8.80522 | + | 2.01995i | −0.283744 | + | 0.0650918i | ||||
\(964\) | 16.5317 | + | 9.54461i | 0.532452 | + | 0.307411i | ||||
\(965\) | 1.50046 | + | 2.59888i | 0.0483016 | + | 0.0836608i | ||||
\(966\) | 2.60806 | + | 23.0331i | 0.0839131 | + | 0.741079i | ||||
\(967\) | 28.8842 | − | 50.0289i | 0.928854 | − | 1.60882i | 0.143611 | − | 0.989634i | \(-0.454129\pi\) |
0.785243 | − | 0.619188i | \(-0.212538\pi\) | |||||||
\(968\) | 13.1299 | 0.422011 | ||||||||
\(969\) | −18.6208 | − | 23.0087i | −0.598186 | − | 0.739145i | ||||
\(970\) | −15.3758 | −0.493686 | ||||||||
\(971\) | 0.428825 | − | 0.742746i | 0.0137616 | − | 0.0238358i | −0.859063 | − | 0.511871i | \(-0.828953\pi\) |
0.872824 | + | 0.488035i | \(0.162286\pi\) | |||||||
\(972\) | −13.8020 | − | 7.24600i | −0.442700 | − | 0.232416i | ||||
\(973\) | −13.2176 | − | 22.8935i | −0.423737 | − | 0.733933i | ||||
\(974\) | 9.80030 | + | 5.65821i | 0.314022 | + | 0.181301i | ||||
\(975\) | 3.18336 | + | 1.38680i | 0.101949 | + | 0.0444131i | ||||
\(976\) | −7.82756 | −0.250554 | ||||||||
\(977\) | 3.12960 | 0.100125 | 0.0500625 | − | 0.998746i | \(-0.484058\pi\) | ||||
0.0500625 | + | 0.998746i | \(0.484058\pi\) | |||||||
\(978\) | 5.92104 | − | 13.5916i | 0.189334 | − | 0.434611i | ||||
\(979\) | −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 | −0.472502 | − | 0.881330i | \(-0.656649\pi\) |
0.999505 | − | 0.0314664i | \(-0.0100177\pi\) | |||||||
\(984\) | 8.13852 | − | 18.6818i | 0.259446 | − | 0.595553i | ||||
\(985\) | −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 | ||||||||
\(990\) | −10.0354 | − | 10.7917i | −0.318945 | − | 0.342982i | ||||
\(991\) | 3.55980 | + | 2.05525i | 0.113081 | + | 0.0652873i | 0.555474 | − | 0.831534i | \(-0.312537\pi\) |
−0.442393 | + | 0.896821i | \(0.645870\pi\) | |||||||
\(992\) | −0.202293 | + | 0.116794i | −0.00642280 | + | 0.00370821i | ||||
\(993\) | −4.60435 | − | 40.6633i | −0.146115 | − | 1.29041i | ||||
\(994\) | 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 | 0.815138 | − | 0.579267i | \(-0.196661\pi\) |
−0.909229 | + | 0.416296i | \(0.863328\pi\) | |||||||
\(998\) | 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.b.521.12 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.a.521.8 | yes | 24 | ||
19.12 | odd | 6 | 570.2.s.a.221.8 | ✓ | 24 | ||
57.50 | even | 6 | inner | 570.2.s.b.221.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.8 | ✓ | 24 | 19.12 | odd | 6 | ||
570.2.s.a.521.8 | yes | 24 | 3.2 | odd | 2 | ||
570.2.s.b.221.12 | yes | 24 | 57.50 | even | 6 | inner | |
570.2.s.b.521.12 | yes | 24 | 1.1 | even | 1 | trivial |