Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(100,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.j (of order \(3\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.1 | ||
Root | \(-1.27528 - 2.20885i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.100 |
Dual form | 273.2.j.b.172.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27528 | − | 2.20885i | −0.901760 | − | 1.56189i | −0.825208 | − | 0.564829i | \(-0.808942\pi\) |
−0.0765522 | − | 0.997066i | \(-0.524391\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −2.25269 | + | 3.90177i | −1.12634 | + | 1.95088i | ||||
\(5\) | −1.39351 | + | 2.41363i | −0.623196 | + | 1.07941i | 0.365691 | + | 0.930736i | \(0.380833\pi\) |
−0.988887 | + | 0.148671i | \(0.952501\pi\) | |||||||
\(6\) | 1.27528 | + | 2.20885i | 0.520632 | + | 0.901760i | ||||
\(7\) | 2.06947 | − | 1.64842i | 0.782186 | − | 0.623044i | ||||
\(8\) | 6.39011 | 2.25924 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.10846 | 2.24789 | ||||||||
\(11\) | −2.76747 | −0.834422 | −0.417211 | − | 0.908810i | \(-0.636992\pi\) | ||||
−0.417211 | + | 0.908810i | \(0.636992\pi\) | |||||||
\(12\) | 2.25269 | − | 3.90177i | 0.650294 | − | 1.12634i | ||||
\(13\) | 2.99297 | − | 2.01050i | 0.830101 | − | 0.557613i | ||||
\(14\) | −6.28028 | − | 2.46895i | −1.67847 | − | 0.659856i | ||||
\(15\) | 1.39351 | − | 2.41363i | 0.359802 | − | 0.623196i | ||||
\(16\) | −3.64382 | − | 6.31127i | −0.910954 | − | 1.57782i | ||||
\(17\) | 2.94340 | − | 5.09812i | 0.713880 | − | 1.23648i | −0.249510 | − | 0.968372i | \(-0.580270\pi\) |
0.963390 | − | 0.268104i | \(-0.0863971\pi\) | |||||||
\(18\) | −1.27528 | − | 2.20885i | −0.300587 | − | 0.520632i | ||||
\(19\) | 3.40075 | 0.780185 | 0.390093 | − | 0.920776i | \(-0.372443\pi\) | ||||
0.390093 | + | 0.920776i | \(0.372443\pi\) | |||||||
\(20\) | −6.27828 | − | 10.8743i | −1.40386 | − | 2.43157i | ||||
\(21\) | −2.06947 | + | 1.64842i | −0.451596 | + | 0.359715i | ||||
\(22\) | 3.52930 | + | 6.11292i | 0.752449 | + | 1.30328i | ||||
\(23\) | 3.67246 | + | 6.36089i | 0.765761 | + | 1.32634i | 0.939843 | + | 0.341605i | \(0.110971\pi\) |
−0.174083 | + | 0.984731i | \(0.555696\pi\) | |||||||
\(24\) | −6.39011 | −1.30438 | ||||||||
\(25\) | −1.38373 | − | 2.39670i | −0.276747 | − | 0.479339i | ||||
\(26\) | −8.25778 | − | 4.04708i | −1.61948 | − | 0.793697i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.76989 | + | 11.7880i | 0.334477 | + | 2.22772i | ||||
\(29\) | 1.56328 | − | 2.70768i | 0.290294 | − | 0.502803i | −0.683585 | − | 0.729871i | \(-0.739580\pi\) |
0.973879 | + | 0.227067i | \(0.0729137\pi\) | |||||||
\(30\) | −7.10846 | −1.29782 | ||||||||
\(31\) | 1.93352 | + | 3.34896i | 0.347271 | + | 0.601491i | 0.985764 | − | 0.168137i | \(-0.0537751\pi\) |
−0.638493 | + | 0.769628i | \(0.720442\pi\) | |||||||
\(32\) | −2.90367 | + | 5.02931i | −0.513302 | + | 0.889065i | ||||
\(33\) | 2.76747 | 0.481754 | ||||||||
\(34\) | −15.0147 | −2.57499 | ||||||||
\(35\) | 1.09485 | + | 7.29202i | 0.185063 | + | 1.23258i | ||||
\(36\) | −2.25269 | + | 3.90177i | −0.375448 | + | 0.650294i | ||||
\(37\) | −2.92173 | − | 5.06059i | −0.480330 | − | 0.831956i | 0.519415 | − | 0.854522i | \(-0.326150\pi\) |
−0.999745 | + | 0.0225659i | \(0.992816\pi\) | |||||||
\(38\) | −4.33691 | − | 7.51175i | −0.703540 | − | 1.21857i | ||||
\(39\) | −2.99297 | + | 2.01050i | −0.479259 | + | 0.321938i | ||||
\(40\) | −8.90467 | + | 15.4233i | −1.40795 | + | 2.43865i | ||||
\(41\) | 3.24124 | − | 5.61400i | 0.506197 | − | 0.876759i | −0.493777 | − | 0.869588i | \(-0.664384\pi\) |
0.999974 | − | 0.00717054i | \(-0.00228247\pi\) | |||||||
\(42\) | 6.28028 | + | 2.46895i | 0.969068 | + | 0.380968i | ||||
\(43\) | 2.99197 | + | 5.18224i | 0.456271 | + | 0.790284i | 0.998760 | − | 0.0497783i | \(-0.0158515\pi\) |
−0.542489 | + | 0.840063i | \(0.682518\pi\) | |||||||
\(44\) | 6.23423 | − | 10.7980i | 0.939846 | − | 1.62786i | ||||
\(45\) | −1.39351 | + | 2.41363i | −0.207732 | + | 0.359802i | ||||
\(46\) | 9.36684 | − | 16.2238i | 1.38106 | − | 2.39207i | ||||
\(47\) | 3.95673 | − | 6.85325i | 0.577148 | − | 0.999650i | −0.418656 | − | 0.908145i | \(-0.637499\pi\) |
0.995805 | − | 0.0915053i | \(-0.0291678\pi\) | |||||||
\(48\) | 3.64382 | + | 6.31127i | 0.525940 | + | 0.910954i | ||||
\(49\) | 1.56542 | − | 6.82272i | 0.223631 | − | 0.974674i | ||||
\(50\) | −3.52930 | + | 6.11292i | −0.499118 | + | 0.864498i | ||||
\(51\) | −2.94340 | + | 5.09812i | −0.412159 | + | 0.713880i | ||||
\(52\) | 1.10228 | + | 16.2069i | 0.152859 | + | 2.24749i | ||||
\(53\) | 6.34471 | + | 10.9894i | 0.871513 | + | 1.50951i | 0.860431 | + | 0.509567i | \(0.170194\pi\) |
0.0110819 | + | 0.999939i | \(0.496472\pi\) | |||||||
\(54\) | 1.27528 | + | 2.20885i | 0.173544 | + | 0.300587i | ||||
\(55\) | 3.85649 | − | 6.67963i | 0.520009 | − | 0.900682i | ||||
\(56\) | 13.2241 | − | 10.5336i | 1.76715 | − | 1.40761i | ||||
\(57\) | −3.40075 | −0.450440 | ||||||||
\(58\) | −7.97449 | −1.04710 | ||||||||
\(59\) | −1.36824 | + | 2.36987i | −0.178130 | + | 0.308530i | −0.941240 | − | 0.337738i | \(-0.890338\pi\) |
0.763110 | + | 0.646269i | \(0.223671\pi\) | |||||||
\(60\) | 6.27828 | + | 10.8743i | 0.810522 | + | 1.40386i | ||||
\(61\) | 9.55263 | 1.22309 | 0.611544 | − | 0.791210i | \(-0.290549\pi\) | ||||
0.611544 | + | 0.791210i | \(0.290549\pi\) | |||||||
\(62\) | 4.93157 | − | 8.54173i | 0.626310 | − | 1.08480i | ||||
\(63\) | 2.06947 | − | 1.64842i | 0.260729 | − | 0.207681i | ||||
\(64\) | 0.236742 | 0.0295928 | ||||||||
\(65\) | 0.681870 | + | 10.0256i | 0.0845756 | + | 1.24352i | ||||
\(66\) | −3.52930 | − | 6.11292i | −0.434427 | − | 0.752449i | ||||
\(67\) | −8.68066 | −1.06051 | −0.530255 | − | 0.847838i | \(-0.677904\pi\) | ||||
−0.530255 | + | 0.847838i | \(0.677904\pi\) | |||||||
\(68\) | 13.2611 | + | 22.9689i | 1.60815 | + | 2.78539i | ||||
\(69\) | −3.67246 | − | 6.36089i | −0.442112 | − | 0.765761i | ||||
\(70\) | 14.7108 | − | 11.7177i | 1.75827 | − | 1.40054i | ||||
\(71\) | −1.57062 | − | 2.72039i | −0.186398 | − | 0.322851i | 0.757649 | − | 0.652663i | \(-0.226348\pi\) |
−0.944047 | + | 0.329812i | \(0.893015\pi\) | |||||||
\(72\) | 6.39011 | 0.753082 | ||||||||
\(73\) | −4.80291 | − | 8.31889i | −0.562138 | − | 0.973652i | −0.997310 | − | 0.0733045i | \(-0.976646\pi\) |
0.435171 | − | 0.900348i | \(-0.356688\pi\) | |||||||
\(74\) | −7.45207 | + | 12.9074i | −0.866285 | + | 1.50045i | ||||
\(75\) | 1.38373 | + | 2.39670i | 0.159780 | + | 0.276747i | ||||
\(76\) | −7.66082 | + | 13.2689i | −0.878756 | + | 1.52205i | ||||
\(77\) | −5.72719 | + | 4.56195i | −0.652674 | + | 0.519882i | ||||
\(78\) | 8.25778 | + | 4.04708i | 0.935010 | + | 0.458241i | ||||
\(79\) | −1.88112 | + | 3.25819i | −0.211642 | + | 0.366575i | −0.952229 | − | 0.305386i | \(-0.901215\pi\) |
0.740586 | + | 0.671961i | \(0.234548\pi\) | |||||||
\(80\) | 20.3108 | 2.27081 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.5340 | −1.82587 | ||||||||
\(83\) | 4.82088 | 0.529161 | 0.264580 | − | 0.964364i | \(-0.414767\pi\) | ||||
0.264580 | + | 0.964364i | \(0.414767\pi\) | |||||||
\(84\) | −1.76989 | − | 11.7880i | −0.193110 | − | 1.28617i | ||||
\(85\) | 8.20331 | + | 14.2086i | 0.889774 | + | 1.54113i | ||||
\(86\) | 7.63120 | − | 13.2176i | 0.822894 | − | 1.42529i | ||||
\(87\) | −1.56328 | + | 2.70768i | −0.167601 | + | 0.290294i | ||||
\(88\) | −17.6844 | −1.88516 | ||||||||
\(89\) | −0.877787 | − | 1.52037i | −0.0930453 | − | 0.161159i | 0.815746 | − | 0.578411i | \(-0.196327\pi\) |
−0.908791 | + | 0.417251i | \(0.862993\pi\) | |||||||
\(90\) | 7.10846 | 0.749298 | ||||||||
\(91\) | 2.87972 | − | 9.09435i | 0.301876 | − | 0.953347i | ||||
\(92\) | −33.0916 | −3.45004 | ||||||||
\(93\) | −1.93352 | − | 3.34896i | −0.200497 | − | 0.347271i | ||||
\(94\) | −20.1838 | −2.08180 | ||||||||
\(95\) | −4.73897 | + | 8.20814i | −0.486208 | + | 0.842137i | ||||
\(96\) | 2.90367 | − | 5.02931i | 0.296355 | − | 0.513302i | ||||
\(97\) | 8.48637 | + | 14.6988i | 0.861660 | + | 1.49244i | 0.870325 | + | 0.492477i | \(0.163908\pi\) |
−0.00866511 | + | 0.999962i | \(0.502758\pi\) | |||||||
\(98\) | −17.0667 | + | 5.24311i | −1.72400 | + | 0.529634i | ||||
\(99\) | −2.76747 | −0.278141 | ||||||||
\(100\) | 12.4685 | 1.24685 | ||||||||
\(101\) | −1.84273 | −0.183358 | −0.0916791 | − | 0.995789i | \(-0.529223\pi\) | ||||
−0.0916791 | + | 0.995789i | \(0.529223\pi\) | |||||||
\(102\) | 15.0147 | 1.48667 | ||||||||
\(103\) | −2.38506 | + | 4.13105i | −0.235007 | + | 0.407045i | −0.959275 | − | 0.282474i | \(-0.908845\pi\) |
0.724267 | + | 0.689519i | \(0.242178\pi\) | |||||||
\(104\) | 19.1254 | − | 12.8473i | 1.87540 | − | 1.25978i | ||||
\(105\) | −1.09485 | − | 7.29202i | −0.106846 | − | 0.711628i | ||||
\(106\) | 16.1826 | − | 28.0291i | 1.57179 | − | 2.72242i | ||||
\(107\) | 6.03771 | + | 10.4576i | 0.583688 | + | 1.01098i | 0.995038 | + | 0.0994995i | \(0.0317242\pi\) |
−0.411350 | + | 0.911478i | \(0.634942\pi\) | |||||||
\(108\) | 2.25269 | − | 3.90177i | 0.216765 | − | 0.375448i | ||||
\(109\) | 3.40885 | + | 5.90430i | 0.326508 | + | 0.565529i | 0.981816 | − | 0.189832i | \(-0.0607945\pi\) |
−0.655308 | + | 0.755362i | \(0.727461\pi\) | |||||||
\(110\) | −19.6724 | −1.87569 | ||||||||
\(111\) | 2.92173 | + | 5.06059i | 0.277319 | + | 0.480330i | ||||
\(112\) | −17.9444 | − | 7.05446i | −1.69559 | − | 0.666583i | ||||
\(113\) | −2.72463 | − | 4.71920i | −0.256312 | − | 0.443945i | 0.708939 | − | 0.705270i | \(-0.249174\pi\) |
−0.965251 | + | 0.261325i | \(0.915841\pi\) | |||||||
\(114\) | 4.33691 | + | 7.51175i | 0.406189 | + | 0.703540i | ||||
\(115\) | −20.4704 | −1.90888 | ||||||||
\(116\) | 7.04316 | + | 12.1991i | 0.653941 | + | 1.13266i | ||||
\(117\) | 2.99297 | − | 2.01050i | 0.276700 | − | 0.185871i | ||||
\(118\) | 6.97958 | 0.642522 | ||||||||
\(119\) | −2.31257 | − | 15.4024i | −0.211993 | − | 1.41193i | ||||
\(120\) | 8.90467 | − | 15.4233i | 0.812882 | − | 1.40795i | ||||
\(121\) | −3.34113 | −0.303739 | ||||||||
\(122\) | −12.1823 | − | 21.1003i | −1.10293 | − | 1.91034i | ||||
\(123\) | −3.24124 | + | 5.61400i | −0.292253 | + | 0.506197i | ||||
\(124\) | −17.4225 | −1.56458 | ||||||||
\(125\) | −6.22211 | −0.556523 | ||||||||
\(126\) | −6.28028 | − | 2.46895i | −0.559491 | − | 0.219952i | ||||
\(127\) | −0.886520 | + | 1.53550i | −0.0786660 | + | 0.136253i | −0.902675 | − | 0.430324i | \(-0.858399\pi\) |
0.824009 | + | 0.566577i | \(0.191733\pi\) | |||||||
\(128\) | 5.50543 | + | 9.53569i | 0.486616 | + | 0.842844i | ||||
\(129\) | −2.99197 | − | 5.18224i | −0.263428 | − | 0.456271i | ||||
\(130\) | 21.2754 | − | 14.2916i | 1.86598 | − | 1.25345i | ||||
\(131\) | −3.50734 | + | 6.07490i | −0.306438 | + | 0.530766i | −0.977580 | − | 0.210562i | \(-0.932471\pi\) |
0.671143 | + | 0.741328i | \(0.265804\pi\) | |||||||
\(132\) | −6.23423 | + | 10.7980i | −0.542620 | + | 0.939846i | ||||
\(133\) | 7.03775 | − | 5.60586i | 0.610250 | − | 0.486090i | ||||
\(134\) | 11.0703 | + | 19.1743i | 0.956326 | + | 1.65641i | ||||
\(135\) | 1.39351 | − | 2.41363i | 0.119934 | − | 0.207732i | ||||
\(136\) | 18.8087 | − | 32.5776i | 1.61283 | − | 2.79350i | ||||
\(137\) | 9.82872 | − | 17.0239i | 0.839725 | − | 1.45445i | −0.0504003 | − | 0.998729i | \(-0.516050\pi\) |
0.890125 | − | 0.455717i | \(-0.150617\pi\) | |||||||
\(138\) | −9.36684 | + | 16.2238i | −0.797358 | + | 1.38106i | ||||
\(139\) | −9.17342 | − | 15.8888i | −0.778079 | − | 1.34767i | −0.933048 | − | 0.359753i | \(-0.882861\pi\) |
0.154968 | − | 0.987919i | \(-0.450472\pi\) | |||||||
\(140\) | −30.9181 | − | 12.1548i | −2.61306 | − | 1.02727i | ||||
\(141\) | −3.95673 | + | 6.85325i | −0.333217 | + | 0.577148i | ||||
\(142\) | −4.00596 | + | 6.93852i | −0.336173 | + | 0.582268i | ||||
\(143\) | −8.28295 | + | 5.56400i | −0.692655 | + | 0.465285i | ||||
\(144\) | −3.64382 | − | 6.31127i | −0.303651 | − | 0.525940i | ||||
\(145\) | 4.35689 | + | 7.54635i | 0.361820 | + | 0.626690i | ||||
\(146\) | −12.2501 | + | 21.2178i | −1.01383 | + | 1.75600i | ||||
\(147\) | −1.56542 | + | 6.82272i | −0.129114 | + | 0.562728i | ||||
\(148\) | 26.3270 | 2.16407 | ||||||||
\(149\) | −8.80290 | −0.721162 | −0.360581 | − | 0.932728i | \(-0.617422\pi\) | ||||
−0.360581 | + | 0.932728i | \(0.617422\pi\) | |||||||
\(150\) | 3.52930 | − | 6.11292i | 0.288166 | − | 0.499118i | ||||
\(151\) | −4.83567 | − | 8.37562i | −0.393521 | − | 0.681598i | 0.599390 | − | 0.800457i | \(-0.295410\pi\) |
−0.992911 | + | 0.118859i | \(0.962076\pi\) | |||||||
\(152\) | 21.7311 | 1.76263 | ||||||||
\(153\) | 2.94340 | − | 5.09812i | 0.237960 | − | 0.412159i | ||||
\(154\) | 17.3805 | + | 6.83275i | 1.40056 | + | 0.550599i | ||||
\(155\) | −10.7775 | −0.865672 | ||||||||
\(156\) | −1.10228 | − | 16.2069i | −0.0882532 | − | 1.29759i | ||||
\(157\) | −5.76601 | − | 9.98702i | −0.460177 | − | 0.797051i | 0.538792 | − | 0.842439i | \(-0.318881\pi\) |
−0.998969 | + | 0.0453882i | \(0.985548\pi\) | |||||||
\(158\) | 9.59583 | 0.763403 | ||||||||
\(159\) | −6.34471 | − | 10.9894i | −0.503168 | − | 0.871513i | ||||
\(160\) | −8.09259 | − | 14.0168i | −0.639775 | − | 1.10812i | ||||
\(161\) | 18.0855 | + | 7.10991i | 1.42533 | + | 0.560339i | ||||
\(162\) | −1.27528 | − | 2.20885i | −0.100196 | − | 0.173544i | ||||
\(163\) | −12.1704 | −0.953261 | −0.476631 | − | 0.879104i | \(-0.658142\pi\) | ||||
−0.476631 | + | 0.879104i | \(0.658142\pi\) | |||||||
\(164\) | 14.6030 | + | 25.2931i | 1.14030 | + | 1.97506i | ||||
\(165\) | −3.85649 | + | 6.67963i | −0.300227 | + | 0.520009i | ||||
\(166\) | −6.14798 | − | 10.6486i | −0.477176 | − | 0.826493i | ||||
\(167\) | 4.54697 | − | 7.87559i | 0.351855 | − | 0.609431i | −0.634719 | − | 0.772743i | \(-0.718884\pi\) |
0.986575 | + | 0.163311i | \(0.0522175\pi\) | |||||||
\(168\) | −13.2241 | + | 10.5336i | −1.02026 | + | 0.812684i | ||||
\(169\) | 4.91577 | − | 12.0348i | 0.378136 | − | 0.925750i | ||||
\(170\) | 20.9231 | − | 36.2398i | 1.60473 | − | 2.77947i | ||||
\(171\) | 3.40075 | 0.260062 | ||||||||
\(172\) | −26.9599 | −2.05567 | ||||||||
\(173\) | −1.34730 | −0.102433 | −0.0512165 | − | 0.998688i | \(-0.516310\pi\) | ||||
−0.0512165 | + | 0.998688i | \(0.516310\pi\) | |||||||
\(174\) | 7.97449 | 0.604544 | ||||||||
\(175\) | −6.81436 | − | 2.67892i | −0.515117 | − | 0.202507i | ||||
\(176\) | 10.0841 | + | 17.4662i | 0.760121 | + | 1.31657i | ||||
\(177\) | 1.36824 | − | 2.36987i | 0.102843 | − | 0.178130i | ||||
\(178\) | −2.23885 | + | 3.87781i | −0.167809 | + | 0.290654i | ||||
\(179\) | −5.95993 | −0.445466 | −0.222733 | − | 0.974880i | \(-0.571498\pi\) | ||||
−0.222733 | + | 0.974880i | \(0.571498\pi\) | |||||||
\(180\) | −6.27828 | − | 10.8743i | −0.467955 | − | 0.810522i | ||||
\(181\) | 10.4495 | 0.776707 | 0.388354 | − | 0.921510i | \(-0.373044\pi\) | ||||
0.388354 | + | 0.921510i | \(0.373044\pi\) | |||||||
\(182\) | −23.7605 | + | 5.23699i | −1.76125 | + | 0.388192i | ||||
\(183\) | −9.55263 | −0.706151 | ||||||||
\(184\) | 23.4674 | + | 40.6468i | 1.73004 | + | 2.99652i | ||||
\(185\) | 16.2858 | 1.19736 | ||||||||
\(186\) | −4.93157 | + | 8.54173i | −0.361600 | + | 0.626310i | ||||
\(187\) | −8.14577 | + | 14.1089i | −0.595677 | + | 1.03174i | ||||
\(188\) | 17.8265 | + | 30.8765i | 1.30013 | + | 2.25190i | ||||
\(189\) | −2.06947 | + | 1.64842i | −0.150532 | + | 0.119905i | ||||
\(190\) | 24.1741 | 1.75377 | ||||||||
\(191\) | −0.658114 | −0.0476194 | −0.0238097 | − | 0.999717i | \(-0.507580\pi\) | ||||
−0.0238097 | + | 0.999717i | \(0.507580\pi\) | |||||||
\(192\) | −0.236742 | −0.0170854 | ||||||||
\(193\) | 8.78557 | 0.632399 | 0.316200 | − | 0.948693i | \(-0.397593\pi\) | ||||
0.316200 | + | 0.948693i | \(0.397593\pi\) | |||||||
\(194\) | 21.6450 | − | 37.4903i | 1.55402 | − | 2.69165i | ||||
\(195\) | −0.681870 | − | 10.0256i | −0.0488297 | − | 0.717946i | ||||
\(196\) | 23.0943 | + | 21.4773i | 1.64959 | + | 1.53410i | ||||
\(197\) | −9.29781 | + | 16.1043i | −0.662442 | + | 1.14738i | 0.317530 | + | 0.948248i | \(0.397146\pi\) |
−0.979972 | + | 0.199135i | \(0.936187\pi\) | |||||||
\(198\) | 3.52930 | + | 6.11292i | 0.250816 | + | 0.434427i | ||||
\(199\) | −7.61283 | + | 13.1858i | −0.539659 | + | 0.934717i | 0.459263 | + | 0.888300i | \(0.348113\pi\) |
−0.998922 | + | 0.0464164i | \(0.985220\pi\) | |||||||
\(200\) | −8.84221 | − | 15.3151i | −0.625238 | − | 1.08294i | ||||
\(201\) | 8.68066 | 0.612286 | ||||||||
\(202\) | 2.35000 | + | 4.07031i | 0.165345 | + | 0.286386i | ||||
\(203\) | −1.22823 | − | 8.18041i | −0.0862051 | − | 0.574152i | ||||
\(204\) | −13.2611 | − | 22.9689i | −0.928464 | − | 1.60815i | ||||
\(205\) | 9.03340 | + | 15.6463i | 0.630920 | + | 1.09279i | ||||
\(206\) | 12.1665 | 0.847681 | ||||||||
\(207\) | 3.67246 | + | 6.36089i | 0.255254 | + | 0.442112i | ||||
\(208\) | −23.5947 | − | 11.5636i | −1.63600 | − | 0.801789i | ||||
\(209\) | −9.41145 | −0.651004 | ||||||||
\(210\) | −14.7108 | + | 11.7177i | −1.01514 | + | 0.808601i | ||||
\(211\) | −10.5945 | + | 18.3503i | −0.729357 | + | 1.26328i | 0.227798 | + | 0.973708i | \(0.426847\pi\) |
−0.957155 | + | 0.289575i | \(0.906486\pi\) | |||||||
\(212\) | −57.1706 | −3.92649 | ||||||||
\(213\) | 1.57062 | + | 2.72039i | 0.107617 | + | 0.186398i | ||||
\(214\) | 15.3996 | − | 26.6728i | 1.05269 | − | 1.82332i | ||||
\(215\) | −16.6773 | −1.13738 | ||||||||
\(216\) | −6.39011 | −0.434792 | ||||||||
\(217\) | 9.52186 | + | 3.74332i | 0.646386 | + | 0.254113i | ||||
\(218\) | 8.69448 | − | 15.0593i | 0.588865 | − | 1.01994i | ||||
\(219\) | 4.80291 | + | 8.31889i | 0.324551 | + | 0.562138i | ||||
\(220\) | 17.3749 | + | 30.0942i | 1.17142 | + | 2.02895i | ||||
\(221\) | −1.44026 | − | 21.1763i | −0.0968825 | − | 1.42447i | ||||
\(222\) | 7.45207 | − | 12.9074i | 0.500150 | − | 0.866285i | ||||
\(223\) | −0.453274 | + | 0.785093i | −0.0303534 | + | 0.0525737i | −0.880803 | − | 0.473483i | \(-0.842997\pi\) |
0.850450 | + | 0.526056i | \(0.176330\pi\) | |||||||
\(224\) | 2.28135 | + | 15.1945i | 0.152429 | + | 1.01522i | ||||
\(225\) | −1.38373 | − | 2.39670i | −0.0922489 | − | 0.159780i | ||||
\(226\) | −6.94935 | + | 12.0366i | −0.462264 | + | 0.800664i | ||||
\(227\) | −0.964045 | + | 1.66977i | −0.0639859 | + | 0.110827i | −0.896244 | − | 0.443562i | \(-0.853715\pi\) |
0.832258 | + | 0.554389i | \(0.187048\pi\) | |||||||
\(228\) | 7.66082 | − | 13.2689i | 0.507350 | − | 0.878756i | ||||
\(229\) | 5.05578 | − | 8.75686i | 0.334095 | − | 0.578670i | −0.649216 | − | 0.760604i | \(-0.724903\pi\) |
0.983311 | + | 0.181935i | \(0.0582360\pi\) | |||||||
\(230\) | 26.1055 | + | 45.2161i | 1.72135 | + | 2.98146i | ||||
\(231\) | 5.72719 | − | 4.56195i | 0.376821 | − | 0.300154i | ||||
\(232\) | 9.98953 | − | 17.3024i | 0.655845 | − | 1.13596i | ||||
\(233\) | 13.1134 | − | 22.7130i | 0.859085 | − | 1.48798i | −0.0137178 | − | 0.999906i | \(-0.504367\pi\) |
0.872803 | − | 0.488073i | \(-0.162300\pi\) | |||||||
\(234\) | −8.25778 | − | 4.04708i | −0.539828 | − | 0.264566i | ||||
\(235\) | 11.0275 | + | 19.1001i | 0.719353 | + | 1.24596i | ||||
\(236\) | −6.16444 | − | 10.6771i | −0.401271 | − | 0.695022i | ||||
\(237\) | 1.88112 | − | 3.25819i | 0.122192 | − | 0.211642i | ||||
\(238\) | −31.0724 | + | 24.7505i | −2.01413 | + | 1.60434i | ||||
\(239\) | 28.0556 | 1.81476 | 0.907382 | − | 0.420306i | \(-0.138077\pi\) | ||||
0.907382 | + | 0.420306i | \(0.138077\pi\) | |||||||
\(240\) | −20.3108 | −1.31105 | ||||||||
\(241\) | 2.22625 | − | 3.85597i | 0.143405 | − | 0.248385i | −0.785372 | − | 0.619025i | \(-0.787528\pi\) |
0.928777 | + | 0.370640i | \(0.120861\pi\) | |||||||
\(242\) | 4.26088 | + | 7.38007i | 0.273900 | + | 0.474409i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −21.5191 | + | 37.2721i | −1.37762 | + | 2.38610i | ||||
\(245\) | 14.2861 | + | 13.2859i | 0.912704 | + | 0.848802i | ||||
\(246\) | 16.5340 | 1.05417 | ||||||||
\(247\) | 10.1783 | − | 6.83721i | 0.647632 | − | 0.435041i | ||||
\(248\) | 12.3554 | + | 21.4002i | 0.784570 | + | 1.35892i | ||||
\(249\) | −4.82088 | −0.305511 | ||||||||
\(250\) | 7.93494 | + | 13.7437i | 0.501850 | + | 0.869229i | ||||
\(251\) | 1.55413 | + | 2.69183i | 0.0980956 | + | 0.169907i | 0.910896 | − | 0.412635i | \(-0.135392\pi\) |
−0.812801 | + | 0.582542i | \(0.802058\pi\) | |||||||
\(252\) | 1.76989 | + | 11.7880i | 0.111492 | + | 0.742572i | ||||
\(253\) | −10.1634 | − | 17.6035i | −0.638968 | − | 1.10672i | ||||
\(254\) | 4.52225 | 0.283751 | ||||||||
\(255\) | −8.20331 | − | 14.2086i | −0.513711 | − | 0.889774i | ||||
\(256\) | 14.2787 | − | 24.7314i | 0.892419 | − | 1.54571i | ||||
\(257\) | 12.9927 | + | 22.5040i | 0.810461 | + | 1.40376i | 0.912542 | + | 0.408984i | \(0.134117\pi\) |
−0.102081 | + | 0.994776i | \(0.532550\pi\) | |||||||
\(258\) | −7.63120 | + | 13.2176i | −0.475098 | + | 0.822894i | ||||
\(259\) | −14.3884 | − | 5.65650i | −0.894053 | − | 0.351478i | ||||
\(260\) | −40.6535 | − | 19.9240i | −2.52122 | − | 1.23563i | ||||
\(261\) | 1.56328 | − | 2.70768i | 0.0967646 | − | 0.167601i | ||||
\(262\) | 17.8914 | 1.10533 | ||||||||
\(263\) | 12.7806 | 0.788083 | 0.394042 | − | 0.919093i | \(-0.371077\pi\) | ||||
0.394042 | + | 0.919093i | \(0.371077\pi\) | |||||||
\(264\) | 17.6844 | 1.08840 | ||||||||
\(265\) | −35.3656 | −2.17249 | ||||||||
\(266\) | −21.3576 | − | 8.39629i | −1.30952 | − | 0.514810i | ||||
\(267\) | 0.877787 | + | 1.52037i | 0.0537197 | + | 0.0930453i | ||||
\(268\) | 19.5548 | − | 33.8699i | 1.19450 | − | 2.06893i | ||||
\(269\) | −0.978744 | + | 1.69523i | −0.0596751 | + | 0.103360i | −0.894320 | − | 0.447429i | \(-0.852340\pi\) |
0.834644 | + | 0.550789i | \(0.185673\pi\) | |||||||
\(270\) | −7.10846 | −0.432607 | ||||||||
\(271\) | −13.4609 | − | 23.3150i | −0.817692 | − | 1.41628i | −0.907379 | − | 0.420314i | \(-0.861920\pi\) |
0.0896863 | − | 0.995970i | \(-0.471414\pi\) | |||||||
\(272\) | −42.9009 | −2.60125 | ||||||||
\(273\) | −2.87972 | + | 9.09435i | −0.174288 | + | 0.550415i | ||||
\(274\) | −50.1376 | −3.02892 | ||||||||
\(275\) | 3.82943 | + | 6.63277i | 0.230924 | + | 0.399971i | ||||
\(276\) | 33.0916 | 1.99188 | ||||||||
\(277\) | 11.5778 | − | 20.0533i | 0.695643 | − | 1.20489i | −0.274321 | − | 0.961638i | \(-0.588453\pi\) |
0.969964 | − | 0.243250i | \(-0.0782136\pi\) | |||||||
\(278\) | −23.3974 | + | 40.5254i | −1.40328 | + | 2.43055i | ||||
\(279\) | 1.93352 | + | 3.34896i | 0.115757 | + | 0.200497i | ||||
\(280\) | 6.99620 | + | 46.5968i | 0.418103 | + | 2.78469i | ||||
\(281\) | −26.9347 | −1.60679 | −0.803396 | − | 0.595446i | \(-0.796976\pi\) | ||||
−0.803396 | + | 0.595446i | \(0.796976\pi\) | |||||||
\(282\) | 20.1838 | 1.20193 | ||||||||
\(283\) | 15.2443 | 0.906181 | 0.453091 | − | 0.891464i | \(-0.350321\pi\) | ||||
0.453091 | + | 0.891464i | \(0.350321\pi\) | |||||||
\(284\) | 14.1524 | 0.839792 | ||||||||
\(285\) | 4.73897 | − | 8.20814i | 0.280712 | − | 0.486208i | ||||
\(286\) | 22.8531 | + | 11.2002i | 1.35133 | + | 0.662279i | ||||
\(287\) | −2.54657 | − | 16.9609i | −0.150319 | − | 1.00117i | ||||
\(288\) | −2.90367 | + | 5.02931i | −0.171101 | + | 0.296355i | ||||
\(289\) | −8.82723 | − | 15.2892i | −0.519249 | − | 0.899365i | ||||
\(290\) | 11.1125 | − | 19.2474i | 0.652549 | − | 1.13025i | ||||
\(291\) | −8.48637 | − | 14.6988i | −0.497480 | − | 0.861660i | ||||
\(292\) | 43.2778 | 2.53264 | ||||||||
\(293\) | −2.04388 | − | 3.54010i | −0.119405 | − | 0.206815i | 0.800127 | − | 0.599830i | \(-0.204765\pi\) |
−0.919532 | + | 0.393015i | \(0.871432\pi\) | |||||||
\(294\) | 17.0667 | − | 5.24311i | 0.995352 | − | 0.305784i | ||||
\(295\) | −3.81332 | − | 6.60486i | −0.222020 | − | 0.384550i | ||||
\(296\) | −18.6702 | − | 32.3377i | −1.08518 | − | 1.87959i | ||||
\(297\) | 2.76747 | 0.160585 | ||||||||
\(298\) | 11.2262 | + | 19.4443i | 0.650315 | + | 1.12638i | ||||
\(299\) | 23.7801 | + | 11.6545i | 1.37524 | + | 0.673995i | ||||
\(300\) | −12.4685 | −0.719867 | ||||||||
\(301\) | 14.7343 | + | 5.79247i | 0.849271 | + | 0.333873i | ||||
\(302\) | −12.3337 | + | 21.3625i | −0.709723 | + | 1.22928i | ||||
\(303\) | 1.84273 | 0.105862 | ||||||||
\(304\) | −12.3917 | − | 21.4631i | −0.710713 | − | 1.23099i | ||||
\(305\) | −13.3117 | + | 23.0565i | −0.762224 | + | 1.32021i | ||||
\(306\) | −15.0147 | −0.858331 | ||||||||
\(307\) | 1.04296 | 0.0595250 | 0.0297625 | − | 0.999557i | \(-0.490525\pi\) | ||||
0.0297625 | + | 0.999557i | \(0.490525\pi\) | |||||||
\(308\) | −4.89810 | − | 32.6228i | −0.279095 | − | 1.85886i | ||||
\(309\) | 2.38506 | − | 4.13105i | 0.135682 | − | 0.235007i | ||||
\(310\) | 13.7444 | + | 23.8060i | 0.780628 | + | 1.35209i | ||||
\(311\) | −3.88724 | − | 6.73290i | −0.220425 | − | 0.381788i | 0.734512 | − | 0.678596i | \(-0.237411\pi\) |
−0.954937 | + | 0.296808i | \(0.904078\pi\) | |||||||
\(312\) | −19.1254 | + | 12.8473i | −1.08276 | + | 0.727337i | ||||
\(313\) | −12.1950 | + | 21.1224i | −0.689304 | + | 1.19391i | 0.282759 | + | 0.959191i | \(0.408750\pi\) |
−0.972063 | + | 0.234719i | \(0.924583\pi\) | |||||||
\(314\) | −14.7066 | + | 25.4725i | −0.829939 | + | 1.43750i | ||||
\(315\) | 1.09485 | + | 7.29202i | 0.0616877 | + | 0.410859i | ||||
\(316\) | −8.47514 | − | 14.6794i | −0.476764 | − | 0.825779i | ||||
\(317\) | −5.38045 | + | 9.31922i | −0.302196 | + | 0.523419i | −0.976633 | − | 0.214913i | \(-0.931053\pi\) |
0.674437 | + | 0.738333i | \(0.264386\pi\) | |||||||
\(318\) | −16.1826 | + | 28.0291i | −0.907474 | + | 1.57179i | ||||
\(319\) | −4.32632 | + | 7.49341i | −0.242228 | + | 0.419550i | ||||
\(320\) | −0.329903 | + | 0.571408i | −0.0184421 | + | 0.0319427i | ||||
\(321\) | −6.03771 | − | 10.4576i | −0.336992 | − | 0.583688i | ||||
\(322\) | −7.35932 | − | 49.0153i | −0.410119 | − | 2.73151i | ||||
\(323\) | 10.0098 | − | 17.3374i | 0.556958 | − | 0.964680i | ||||
\(324\) | −2.25269 | + | 3.90177i | −0.125149 | + | 0.216765i | ||||
\(325\) | −8.96004 | − | 4.39125i | −0.497013 | − | 0.243583i | ||||
\(326\) | 15.5207 | + | 26.8827i | 0.859613 | + | 1.48889i | ||||
\(327\) | −3.40885 | − | 5.90430i | −0.188510 | − | 0.326508i | ||||
\(328\) | 20.7119 | − | 35.8741i | 1.14362 | − | 1.98081i | ||||
\(329\) | −3.10871 | − | 20.7050i | −0.171389 | − | 1.14150i | ||||
\(330\) | 19.6724 | 1.08293 | ||||||||
\(331\) | −22.9691 | −1.26250 | −0.631248 | − | 0.775581i | \(-0.717457\pi\) | ||||
−0.631248 | + | 0.775581i | \(0.717457\pi\) | |||||||
\(332\) | −10.8599 | + | 18.8100i | −0.596017 | + | 1.03233i | ||||
\(333\) | −2.92173 | − | 5.06059i | −0.160110 | − | 0.277319i | ||||
\(334\) | −23.1947 | −1.26916 | ||||||||
\(335\) | 12.0966 | − | 20.9519i | 0.660906 | − | 1.14472i | ||||
\(336\) | 17.9444 | + | 7.05446i | 0.978948 | + | 0.384852i | ||||
\(337\) | 6.99034 | 0.380788 | 0.190394 | − | 0.981708i | \(-0.439023\pi\) | ||||
0.190394 | + | 0.981708i | \(0.439023\pi\) | |||||||
\(338\) | −32.8520 | + | 4.48950i | −1.78691 | + | 0.244196i | ||||
\(339\) | 2.72463 | + | 4.71920i | 0.147982 | + | 0.256312i | ||||
\(340\) | −73.9179 | −4.00876 | ||||||||
\(341\) | −5.35096 | − | 9.26813i | −0.289771 | − | 0.501898i | ||||
\(342\) | −4.33691 | − | 7.51175i | −0.234513 | − | 0.406189i | ||||
\(343\) | −8.00712 | − | 16.6999i | −0.432344 | − | 0.901709i | ||||
\(344\) | 19.1190 | + | 33.1151i | 1.03083 | + | 1.78545i | ||||
\(345\) | 20.4704 | 1.10209 | ||||||||
\(346\) | 1.71818 | + | 2.97598i | 0.0923701 | + | 0.159990i | ||||
\(347\) | 1.07692 | − | 1.86528i | 0.0578120 | − | 0.100133i | −0.835671 | − | 0.549230i | \(-0.814921\pi\) |
0.893483 | + | 0.449097i | \(0.148254\pi\) | |||||||
\(348\) | −7.04316 | − | 12.1991i | −0.377553 | − | 0.653941i | ||||
\(349\) | −0.756384 | + | 1.31010i | −0.0404883 | + | 0.0701278i | −0.885559 | − | 0.464526i | \(-0.846225\pi\) |
0.845071 | + | 0.534654i | \(0.179558\pi\) | |||||||
\(350\) | 2.77289 | + | 18.4683i | 0.148217 | + | 0.987171i | ||||
\(351\) | −2.99297 | + | 2.01050i | −0.159753 | + | 0.107313i | ||||
\(352\) | 8.03582 | − | 13.9184i | 0.428311 | − | 0.741856i | ||||
\(353\) | −32.3938 | −1.72415 | −0.862073 | − | 0.506784i | \(-0.830834\pi\) | ||||
−0.862073 | + | 0.506784i | \(0.830834\pi\) | |||||||
\(354\) | −6.97958 | −0.370960 | ||||||||
\(355\) | 8.75467 | 0.464650 | ||||||||
\(356\) | 7.90952 | 0.419204 | ||||||||
\(357\) | 2.31257 | + | 15.4024i | 0.122394 | + | 0.815180i | ||||
\(358\) | 7.60058 | + | 13.1646i | 0.401703 | + | 0.695771i | ||||
\(359\) | −7.93156 | + | 13.7379i | −0.418612 | + | 0.725057i | −0.995800 | − | 0.0915543i | \(-0.970816\pi\) |
0.577188 | + | 0.816611i | \(0.304150\pi\) | |||||||
\(360\) | −8.90467 | + | 15.4233i | −0.469317 | + | 0.812882i | ||||
\(361\) | −7.43492 | −0.391311 | ||||||||
\(362\) | −13.3261 | − | 23.0815i | −0.700404 | − | 1.21314i | ||||
\(363\) | 3.34113 | 0.175364 | ||||||||
\(364\) | 28.9969 | + | 31.7227i | 1.51985 | + | 1.66272i | ||||
\(365\) | 26.7716 | 1.40129 | ||||||||
\(366\) | 12.1823 | + | 21.1003i | 0.636779 | + | 1.10293i | ||||
\(367\) | 12.5937 | 0.657388 | 0.328694 | − | 0.944436i | \(-0.393391\pi\) | ||||
0.328694 | + | 0.944436i | \(0.393391\pi\) | |||||||
\(368\) | 26.7635 | − | 46.3558i | 1.39515 | − | 2.41646i | ||||
\(369\) | 3.24124 | − | 5.61400i | 0.168732 | − | 0.292253i | ||||
\(370\) | −20.7690 | − | 35.9730i | −1.07973 | − | 1.87015i | ||||
\(371\) | 31.2453 | + | 12.2834i | 1.62217 | + | 0.637723i | ||||
\(372\) | 17.4225 | 0.903313 | ||||||||
\(373\) | −11.7036 | −0.605987 | −0.302994 | − | 0.952993i | \(-0.597986\pi\) | ||||
−0.302994 | + | 0.952993i | \(0.597986\pi\) | |||||||
\(374\) | 41.5526 | 2.14863 | ||||||||
\(375\) | 6.22211 | 0.321308 | ||||||||
\(376\) | 25.2839 | − | 43.7930i | 1.30392 | − | 2.25845i | ||||
\(377\) | −0.764942 | − | 11.2470i | −0.0393965 | − | 0.579249i | ||||
\(378\) | 6.28028 | + | 2.46895i | 0.323023 | + | 0.126989i | ||||
\(379\) | −16.4778 | + | 28.5403i | −0.846406 | + | 1.46602i | 0.0379888 | + | 0.999278i | \(0.487905\pi\) |
−0.884395 | + | 0.466740i | \(0.845428\pi\) | |||||||
\(380\) | −21.3508 | − | 36.9807i | −1.09527 | − | 1.89707i | ||||
\(381\) | 0.886520 | − | 1.53550i | 0.0454178 | − | 0.0786660i | ||||
\(382\) | 0.839280 | + | 1.45368i | 0.0429413 | + | 0.0743765i | ||||
\(383\) | 12.6361 | 0.645672 | 0.322836 | − | 0.946455i | \(-0.395364\pi\) | ||||
0.322836 | + | 0.946455i | \(0.395364\pi\) | |||||||
\(384\) | −5.50543 | − | 9.53569i | −0.280948 | − | 0.486616i | ||||
\(385\) | −3.02996 | − | 20.1804i | −0.154421 | − | 1.02849i | ||||
\(386\) | −11.2041 | − | 19.4060i | −0.570272 | − | 0.987741i | ||||
\(387\) | 2.99197 | + | 5.18224i | 0.152090 | + | 0.263428i | ||||
\(388\) | −76.4685 | −3.88210 | ||||||||
\(389\) | −0.0593906 | − | 0.102868i | −0.00301122 | − | 0.00521559i | 0.864516 | − | 0.502606i | \(-0.167625\pi\) |
−0.867527 | + | 0.497390i | \(0.834292\pi\) | |||||||
\(390\) | −21.2754 | + | 14.2916i | −1.07732 | + | 0.723682i | ||||
\(391\) | 43.2381 | 2.18664 | ||||||||
\(392\) | 10.0032 | − | 43.5979i | 0.505238 | − | 2.20203i | ||||
\(393\) | 3.50734 | − | 6.07490i | 0.176922 | − | 0.306438i | ||||
\(394\) | 47.4293 | 2.38945 | ||||||||
\(395\) | −5.24271 | − | 9.08064i | −0.263789 | − | 0.456897i | ||||
\(396\) | 6.23423 | − | 10.7980i | 0.313282 | − | 0.542620i | ||||
\(397\) | 6.98302 | 0.350468 | 0.175234 | − | 0.984527i | \(-0.443932\pi\) | ||||
0.175234 | + | 0.984527i | \(0.443932\pi\) | |||||||
\(398\) | 38.8340 | 1.94657 | ||||||||
\(399\) | −7.03775 | + | 5.60586i | −0.352328 | + | 0.280644i | ||||
\(400\) | −10.0841 | + | 17.4662i | −0.504207 | + | 0.873312i | ||||
\(401\) | 9.57584 | + | 16.5858i | 0.478194 | + | 0.828257i | 0.999687 | − | 0.0249985i | \(-0.00795810\pi\) |
−0.521493 | + | 0.853256i | \(0.674625\pi\) | |||||||
\(402\) | −11.0703 | − | 19.1743i | −0.552135 | − | 0.956326i | ||||
\(403\) | 12.5201 | + | 6.13599i | 0.623669 | + | 0.305656i | ||||
\(404\) | 4.15109 | − | 7.18989i | 0.206524 | − | 0.357711i | ||||
\(405\) | −1.39351 | + | 2.41363i | −0.0692440 | + | 0.119934i | ||||
\(406\) | −16.5030 | + | 13.1453i | −0.819028 | + | 0.652391i | ||||
\(407\) | 8.08580 | + | 14.0050i | 0.400798 | + | 0.694203i | ||||
\(408\) | −18.8087 | + | 32.5776i | −0.931167 | + | 1.61283i | ||||
\(409\) | −5.84506 | + | 10.1239i | −0.289019 | + | 0.500596i | −0.973576 | − | 0.228363i | \(-0.926663\pi\) |
0.684557 | + | 0.728960i | \(0.259996\pi\) | |||||||
\(410\) | 23.0403 | − | 39.9069i | 1.13788 | − | 1.97086i | ||||
\(411\) | −9.82872 | + | 17.0239i | −0.484815 | + | 0.839725i | ||||
\(412\) | −10.7456 | − | 18.6119i | −0.529398 | − | 0.916944i | ||||
\(413\) | 1.07500 | + | 7.15981i | 0.0528972 | + | 0.352311i | ||||
\(414\) | 9.36684 | − | 16.2238i | 0.460355 | − | 0.797358i | ||||
\(415\) | −6.71794 | + | 11.6358i | −0.329771 | + | 0.571180i | ||||
\(416\) | 1.42082 | + | 20.8904i | 0.0696616 | + | 1.02424i | ||||
\(417\) | 9.17342 | + | 15.8888i | 0.449224 | + | 0.778079i | ||||
\(418\) | 12.0023 | + | 20.7885i | 0.587049 | + | 1.01680i | ||||
\(419\) | 7.89905 | − | 13.6816i | 0.385894 | − | 0.668388i | −0.605999 | − | 0.795465i | \(-0.707226\pi\) |
0.991893 | + | 0.127078i | \(0.0405598\pi\) | |||||||
\(420\) | 30.9181 | + | 12.1548i | 1.50865 | + | 0.593093i | ||||
\(421\) | 8.58170 | 0.418247 | 0.209123 | − | 0.977889i | \(-0.432939\pi\) | ||||
0.209123 | + | 0.977889i | \(0.432939\pi\) | |||||||
\(422\) | 54.0440 | 2.63082 | ||||||||
\(423\) | 3.95673 | − | 6.85325i | 0.192383 | − | 0.333217i | ||||
\(424\) | 40.5434 | + | 70.2232i | 1.96896 | + | 3.41034i | ||||
\(425\) | −16.2915 | −0.790255 | ||||||||
\(426\) | 4.00596 | − | 6.93852i | 0.194089 | − | 0.336173i | ||||
\(427\) | 19.7689 | − | 15.7468i | 0.956684 | − | 0.762039i | ||||
\(428\) | −54.4043 | −2.62973 | ||||||||
\(429\) | 8.28295 | − | 5.56400i | 0.399905 | − | 0.268632i | ||||
\(430\) | 21.2683 | + | 36.8378i | 1.02565 | + | 1.77648i | ||||
\(431\) | −19.4446 | −0.936615 | −0.468308 | − | 0.883565i | \(-0.655136\pi\) | ||||
−0.468308 | + | 0.883565i | \(0.655136\pi\) | |||||||
\(432\) | 3.64382 | + | 6.31127i | 0.175313 | + | 0.303651i | ||||
\(433\) | 2.35409 | + | 4.07740i | 0.113130 | + | 0.195948i | 0.917031 | − | 0.398816i | \(-0.130579\pi\) |
−0.803900 | + | 0.594764i | \(0.797246\pi\) | |||||||
\(434\) | −3.87463 | − | 25.8062i | −0.185988 | − | 1.23874i | ||||
\(435\) | −4.35689 | − | 7.54635i | −0.208897 | − | 0.361820i | ||||
\(436\) | −30.7163 | −1.47104 | ||||||||
\(437\) | 12.4891 | + | 21.6318i | 0.597435 | + | 1.03479i | ||||
\(438\) | 12.2501 | − | 21.2178i | 0.585334 | − | 1.01383i | ||||
\(439\) | 10.3311 | + | 17.8941i | 0.493078 | + | 0.854037i | 0.999968 | − | 0.00797405i | \(-0.00253825\pi\) |
−0.506890 | + | 0.862011i | \(0.669205\pi\) | |||||||
\(440\) | 24.6434 | − | 42.6836i | 1.17483 | − | 2.03486i | ||||
\(441\) | 1.56542 | − | 6.82272i | 0.0745437 | − | 0.324891i | ||||
\(442\) | −44.9385 | + | 30.1870i | −2.13751 | + | 1.43585i | ||||
\(443\) | 6.14100 | − | 10.6365i | 0.291768 | − | 0.505357i | −0.682460 | − | 0.730923i | \(-0.739090\pi\) |
0.974228 | + | 0.225566i | \(0.0724232\pi\) | |||||||
\(444\) | −26.3270 | −1.24942 | ||||||||
\(445\) | 4.89282 | 0.231942 | ||||||||
\(446\) | 2.31221 | 0.109486 | ||||||||
\(447\) | 8.80290 | 0.416363 | ||||||||
\(448\) | 0.489931 | − | 0.390251i | 0.0231471 | − | 0.0184376i | ||||
\(449\) | 13.7884 | + | 23.8822i | 0.650714 | + | 1.12707i | 0.982950 | + | 0.183874i | \(0.0588638\pi\) |
−0.332235 | + | 0.943196i | \(0.607803\pi\) | |||||||
\(450\) | −3.52930 | + | 6.11292i | −0.166373 | + | 0.288166i | ||||
\(451\) | −8.97003 | + | 15.5365i | −0.422382 | + | 0.731587i | ||||
\(452\) | 24.5510 | 1.15478 | ||||||||
\(453\) | 4.83567 | + | 8.37562i | 0.227199 | + | 0.393521i | ||||
\(454\) | 4.91771 | 0.230800 | ||||||||
\(455\) | 17.9375 | + | 19.6236i | 0.840922 | + | 0.919970i | ||||
\(456\) | −21.7311 | −1.01765 | ||||||||
\(457\) | −6.93931 | − | 12.0192i | −0.324607 | − | 0.562236i | 0.656826 | − | 0.754042i | \(-0.271899\pi\) |
−0.981433 | + | 0.191806i | \(0.938565\pi\) | |||||||
\(458\) | −25.7901 | −1.20509 | ||||||||
\(459\) | −2.94340 | + | 5.09812i | −0.137386 | + | 0.237960i | ||||
\(460\) | 46.1134 | − | 79.8708i | 2.15005 | − | 3.72399i | ||||
\(461\) | −12.2050 | − | 21.1396i | −0.568441 | − | 0.984569i | −0.996720 | − | 0.0809228i | \(-0.974213\pi\) |
0.428279 | − | 0.903647i | \(-0.359120\pi\) | |||||||
\(462\) | −17.3805 | − | 6.83275i | −0.808612 | − | 0.317888i | ||||
\(463\) | −11.6449 | −0.541185 | −0.270593 | − | 0.962694i | \(-0.587220\pi\) | ||||
−0.270593 | + | 0.962694i | \(0.587220\pi\) | |||||||
\(464\) | −22.7852 | −1.05778 | ||||||||
\(465\) | 10.7775 | 0.499796 | ||||||||
\(466\) | −66.8929 | −3.09875 | ||||||||
\(467\) | 2.09483 | − | 3.62835i | 0.0969370 | − | 0.167900i | −0.813478 | − | 0.581595i | \(-0.802429\pi\) |
0.910415 | + | 0.413695i | \(0.135762\pi\) | |||||||
\(468\) | 1.10228 | + | 16.2069i | 0.0509530 | + | 0.749165i | ||||
\(469\) | −17.9644 | + | 14.3094i | −0.829517 | + | 0.660745i | ||||
\(470\) | 28.1263 | − | 48.7161i | 1.29737 | − | 2.24711i | ||||
\(471\) | 5.76601 | + | 9.98702i | 0.265684 | + | 0.460177i | ||||
\(472\) | −8.74322 | + | 15.1437i | −0.402439 | + | 0.697045i | ||||
\(473\) | −8.28017 | − | 14.3417i | −0.380723 | − | 0.659431i | ||||
\(474\) | −9.59583 | −0.440751 | ||||||||
\(475\) | −4.70573 | − | 8.15056i | −0.215914 | − | 0.373973i | ||||
\(476\) | 65.3060 | + | 25.6736i | 2.99329 | + | 1.17675i | ||||
\(477\) | 6.34471 | + | 10.9894i | 0.290504 | + | 0.503168i | ||||
\(478\) | −35.7788 | − | 61.9706i | −1.63648 | − | 2.83447i | ||||
\(479\) | −15.0085 | −0.685754 | −0.342877 | − | 0.939380i | \(-0.611401\pi\) | ||||
−0.342877 | + | 0.939380i | \(0.611401\pi\) | |||||||
\(480\) | 8.09259 | + | 14.0168i | 0.369375 | + | 0.639775i | ||||
\(481\) | −18.9190 | − | 9.27206i | −0.862632 | − | 0.422769i | ||||
\(482\) | −11.3564 | −0.517268 | ||||||||
\(483\) | −18.0855 | − | 7.10991i | −0.822917 | − | 0.323512i | ||||
\(484\) | 7.52652 | − | 13.0363i | 0.342115 | − | 0.592560i | ||||
\(485\) | −47.3033 | −2.14793 | ||||||||
\(486\) | 1.27528 | + | 2.20885i | 0.0578479 | + | 0.100196i | ||||
\(487\) | −3.30409 | + | 5.72285i | −0.149722 | + | 0.259327i | −0.931125 | − | 0.364701i | \(-0.881171\pi\) |
0.781402 | + | 0.624027i | \(0.214505\pi\) | |||||||
\(488\) | 61.0423 | 2.76326 | ||||||||
\(489\) | 12.1704 | 0.550366 | ||||||||
\(490\) | 11.1277 | − | 48.4990i | 0.502699 | − | 2.19096i | ||||
\(491\) | −16.4555 | + | 28.5018i | −0.742628 | + | 1.28627i | 0.208666 | + | 0.977987i | \(0.433088\pi\) |
−0.951295 | + | 0.308283i | \(0.900246\pi\) | |||||||
\(492\) | −14.6030 | − | 25.2931i | −0.658354 | − | 1.14030i | ||||
\(493\) | −9.20272 | − | 15.9396i | −0.414470 | − | 0.717883i | ||||
\(494\) | −28.0826 | − | 13.7631i | −1.26350 | − | 0.619231i | ||||
\(495\) | 3.85649 | − | 6.67963i | 0.173336 | − | 0.300227i | ||||
\(496\) | 14.0908 | − | 24.4060i | 0.632696 | − | 1.09586i | ||||
\(497\) | −7.73469 | − | 3.04073i | −0.346948 | − | 0.136395i | ||||
\(498\) | 6.14798 | + | 10.6486i | 0.275498 | + | 0.477176i | ||||
\(499\) | −17.9199 | + | 31.0381i | −0.802204 | + | 1.38946i | 0.115959 | + | 0.993254i | \(0.463006\pi\) |
−0.918163 | + | 0.396203i | \(0.870328\pi\) | |||||||
\(500\) | 14.0165 | − | 24.2772i | 0.626835 | − | 1.08571i | ||||
\(501\) | −4.54697 | + | 7.87559i | −0.203144 | + | 0.351855i | ||||
\(502\) | 3.96390 | − | 6.86567i | 0.176917 | − | 0.306430i | ||||
\(503\) | −9.67700 | − | 16.7610i | −0.431476 | − | 0.747338i | 0.565525 | − | 0.824731i | \(-0.308674\pi\) |
−0.997001 | + | 0.0773931i | \(0.975340\pi\) | |||||||
\(504\) | 13.2241 | − | 10.5336i | 0.589050 | − | 0.469203i | ||||
\(505\) | 2.56786 | − | 4.44766i | 0.114268 | − | 0.197918i | ||||
\(506\) | −25.9224 | + | 44.8989i | −1.15239 | + | 1.99600i | ||||
\(507\) | −4.91577 | + | 12.0348i | −0.218317 | + | 0.534482i | ||||
\(508\) | −3.99410 | − | 6.91799i | −0.177210 | − | 0.306936i | ||||
\(509\) | −5.24874 | − | 9.09108i | −0.232646 | − | 0.402955i | 0.725940 | − | 0.687758i | \(-0.241405\pi\) |
−0.958586 | + | 0.284803i | \(0.908072\pi\) | |||||||
\(510\) | −20.9231 | + | 36.2398i | −0.926489 | + | 1.60473i | ||||
\(511\) | −23.6525 | − | 9.29847i | −1.04633 | − | 0.411340i | ||||
\(512\) | −50.8157 | −2.24576 | ||||||||
\(513\) | −3.40075 | −0.150147 | ||||||||
\(514\) | 33.1386 | − | 57.3978i | 1.46168 | − | 2.53171i | ||||
\(515\) | −6.64721 | − | 11.5133i | −0.292911 | − | 0.507337i | ||||
\(516\) | 26.9599 | 1.18684 | ||||||||
\(517\) | −10.9501 | + | 18.9662i | −0.481585 | + | 0.834130i | ||||
\(518\) | 5.85492 | + | 38.9955i | 0.257250 | + | 1.71337i | ||||
\(519\) | 1.34730 | 0.0591398 | ||||||||
\(520\) | 4.35722 | + | 64.0645i | 0.191077 | + | 2.80941i | ||||
\(521\) | 10.7923 | + | 18.6928i | 0.472818 | + | 0.818945i | 0.999516 | − | 0.0311074i | \(-0.00990340\pi\) |
−0.526698 | + | 0.850053i | \(0.676570\pi\) | |||||||
\(522\) | −7.97449 | −0.349034 | ||||||||
\(523\) | −1.73189 | − | 2.99973i | −0.0757304 | − | 0.131169i | 0.825673 | − | 0.564149i | \(-0.190796\pi\) |
−0.901404 | + | 0.432980i | \(0.857462\pi\) | |||||||
\(524\) | −15.8019 | − | 27.3697i | −0.690308 | − | 1.19565i | ||||
\(525\) | 6.81436 | + | 2.67892i | 0.297403 | + | 0.116918i | ||||
\(526\) | −16.2988 | − | 28.2304i | −0.710662 | − | 1.23090i | ||||
\(527\) | 22.7645 | 0.991639 | ||||||||
\(528\) | −10.0841 | − | 17.4662i | −0.438856 | − | 0.760121i | ||||
\(529\) | −15.4739 | + | 26.8016i | −0.672779 | + | 1.16529i | ||||
\(530\) | 45.1012 | + | 78.1175i | 1.95907 | + | 3.39321i | ||||
\(531\) | −1.36824 | + | 2.36987i | −0.0593767 | + | 0.102843i | ||||
\(532\) | 6.01893 | + | 40.0879i | 0.260954 | + | 1.73803i | ||||
\(533\) | −1.58600 | − | 23.3191i | −0.0686973 | − | 1.01006i | ||||
\(534\) | 2.23885 | − | 3.87781i | 0.0968846 | − | 0.167809i | ||||
\(535\) | −33.6544 | −1.45501 | ||||||||
\(536\) | −55.4703 | −2.39595 | ||||||||
\(537\) | 5.95993 | 0.257190 | ||||||||
\(538\) | 4.99270 | 0.215250 | ||||||||
\(539\) | −4.33224 | + | 18.8816i | −0.186603 | + | 0.813290i | ||||
\(540\) | 6.27828 | + | 10.8743i | 0.270174 | + | 0.467955i | ||||
\(541\) | 4.46427 | − | 7.73234i | 0.191934 | − | 0.332439i | −0.753957 | − | 0.656924i | \(-0.771857\pi\) |
0.945891 | + | 0.324484i | \(0.105191\pi\) | |||||||
\(542\) | −34.3329 | + | 59.4663i | −1.47472 | + | 2.55430i | ||||
\(543\) | −10.4495 | −0.448432 | ||||||||
\(544\) | 17.0934 | + | 29.6066i | 0.732872 | + | 1.26937i | ||||
\(545\) | −19.0010 | −0.813915 | ||||||||
\(546\) | 23.7605 | − | 5.23699i | 1.01686 | − | 0.224123i | ||||
\(547\) | −3.62704 | −0.155081 | −0.0775405 | − | 0.996989i | \(-0.524707\pi\) | ||||
−0.0775405 | + | 0.996989i | \(0.524707\pi\) | |||||||
\(548\) | 44.2821 | + | 76.6988i | 1.89164 | + | 3.27641i | ||||
\(549\) | 9.55263 | 0.407696 | ||||||||
\(550\) | 9.76721 | − | 16.9173i | 0.416475 | − | 0.721357i | ||||
\(551\) | 5.31632 | − | 9.20813i | 0.226483 | − | 0.392280i | ||||
\(552\) | −23.4674 | − | 40.6468i | −0.998839 | − | 1.73004i | ||||
\(553\) | 1.47795 | + | 9.84361i | 0.0628490 | + | 0.418593i | ||||
\(554\) | −59.0598 | −2.50921 | ||||||||
\(555\) | −16.2858 | −0.691296 | ||||||||
\(556\) | 82.6593 | 3.50554 | ||||||||
\(557\) | −20.0447 | −0.849320 | −0.424660 | − | 0.905353i | \(-0.639606\pi\) | ||||
−0.424660 | + | 0.905353i | \(0.639606\pi\) | |||||||
\(558\) | 4.93157 | − | 8.54173i | 0.208770 | − | 0.361600i | ||||
\(559\) | 19.3738 | + | 9.49495i | 0.819424 | + | 0.401593i | ||||
\(560\) | 42.0325 | − | 33.4807i | 1.77620 | − | 1.41482i | ||||
\(561\) | 8.14577 | − | 14.1089i | 0.343914 | − | 0.595677i | ||||
\(562\) | 34.3494 | + | 59.4948i | 1.44894 | + | 2.50964i | ||||
\(563\) | 3.77715 | − | 6.54221i | 0.159188 | − | 0.275721i | −0.775388 | − | 0.631485i | \(-0.782446\pi\) |
0.934576 | + | 0.355763i | \(0.115779\pi\) | |||||||
\(564\) | −17.8265 | − | 30.8765i | −0.750632 | − | 1.30013i | ||||
\(565\) | 15.1872 | 0.638930 | ||||||||
\(566\) | −19.4408 | − | 33.6725i | −0.817158 | − | 1.41536i | ||||
\(567\) | 2.06947 | − | 1.64842i | 0.0869096 | − | 0.0692272i | ||||
\(568\) | −10.0364 | − | 17.3836i | −0.421119 | − | 0.729399i | ||||
\(569\) | −14.0828 | − | 24.3921i | −0.590381 | − | 1.02257i | −0.994181 | − | 0.107723i | \(-0.965644\pi\) |
0.403800 | − | 0.914847i | \(-0.367689\pi\) | |||||||
\(570\) | −24.1741 | −1.01254 | ||||||||
\(571\) | 9.03604 | + | 15.6509i | 0.378146 | + | 0.654969i | 0.990793 | − | 0.135389i | \(-0.0432283\pi\) |
−0.612646 | + | 0.790357i | \(0.709895\pi\) | |||||||
\(572\) | −3.05053 | − | 44.8521i | −0.127549 | − | 1.87536i | ||||
\(573\) | 0.658114 | 0.0274931 | ||||||||
\(574\) | −34.2166 | + | 27.2550i | −1.42817 | + | 1.13760i | ||||
\(575\) | 10.1634 | − | 17.6035i | 0.423843 | − | 0.734118i | ||||
\(576\) | 0.236742 | 0.00986427 | ||||||||
\(577\) | 21.5383 | + | 37.3054i | 0.896651 | + | 1.55305i | 0.831747 | + | 0.555154i | \(0.187341\pi\) |
0.0649040 | + | 0.997892i | \(0.479326\pi\) | |||||||
\(578\) | −22.5144 | + | 38.9961i | −0.936476 | + | 1.62202i | ||||
\(579\) | −8.78557 | −0.365116 | ||||||||
\(580\) | −39.2588 | −1.63013 | ||||||||
\(581\) | 9.97668 | − | 7.94684i | 0.413902 | − | 0.329691i | ||||
\(582\) | −21.6450 | + | 37.4903i | −0.897215 | + | 1.55402i | ||||
\(583\) | −17.5588 | − | 30.4127i | −0.727210 | − | 1.25956i | ||||
\(584\) | −30.6911 | − | 53.1586i | −1.27001 | − | 2.19972i | ||||
\(585\) | 0.681870 | + | 10.0256i | 0.0281919 | + | 0.414506i | ||||
\(586\) | −5.21304 | + | 9.02925i | −0.215349 | + | 0.372995i | ||||
\(587\) | 2.26101 | − | 3.91619i | 0.0933220 | − | 0.161638i | −0.815585 | − | 0.578637i | \(-0.803585\pi\) |
0.908907 | + | 0.416999i | \(0.136918\pi\) | |||||||
\(588\) | −23.0943 | − | 21.4773i | −0.952391 | − | 0.885710i | ||||
\(589\) | 6.57542 | + | 11.3890i | 0.270936 | + | 0.469274i | ||||
\(590\) | −9.72610 | + | 16.8461i | −0.400417 | + | 0.693543i | ||||
\(591\) | 9.29781 | − | 16.1043i | 0.382461 | − | 0.662442i | ||||
\(592\) | −21.2925 | + | 36.8797i | −0.875117 | + | 1.51575i | ||||
\(593\) | 1.43449 | − | 2.48460i | 0.0589073 | − | 0.102030i | −0.835068 | − | 0.550147i | \(-0.814572\pi\) |
0.893975 | + | 0.448117i | \(0.147905\pi\) | |||||||
\(594\) | −3.52930 | − | 6.11292i | −0.144809 | − | 0.250816i | ||||
\(595\) | 40.3982 | + | 15.8817i | 1.65616 | + | 0.651085i | ||||
\(596\) | 19.8302 | − | 34.3469i | 0.812276 | − | 1.40690i | ||||
\(597\) | 7.61283 | − | 13.1858i | 0.311572 | − | 0.539659i | ||||
\(598\) | −4.58337 | − | 67.3895i | −0.187428 | − | 2.75576i | ||||
\(599\) | −2.94653 | − | 5.10354i | −0.120392 | − | 0.208525i | 0.799530 | − | 0.600626i | \(-0.205082\pi\) |
−0.919922 | + | 0.392101i | \(0.871748\pi\) | |||||||
\(600\) | 8.84221 | + | 15.3151i | 0.360982 | + | 0.625238i | ||||
\(601\) | −9.46284 | + | 16.3901i | −0.385997 | + | 0.668567i | −0.991907 | − | 0.126967i | \(-0.959476\pi\) |
0.605910 | + | 0.795533i | \(0.292809\pi\) | |||||||
\(602\) | −5.99567 | − | 39.9329i | −0.244365 | − | 1.62754i | ||||
\(603\) | −8.68066 | −0.353504 | ||||||||
\(604\) | 43.5730 | 1.77296 | ||||||||
\(605\) | 4.65590 | − | 8.06425i | 0.189289 | − | 0.327858i | ||||
\(606\) | −2.35000 | − | 4.07031i | −0.0954621 | − | 0.165345i | ||||
\(607\) | 43.8783 | 1.78096 | 0.890482 | − | 0.455019i | \(-0.150367\pi\) | ||||
0.890482 | + | 0.455019i | \(0.150367\pi\) | |||||||
\(608\) | −9.87466 | + | 17.1034i | −0.400470 | + | 0.693635i | ||||
\(609\) | 1.22823 | + | 8.18041i | 0.0497705 | + | 0.331487i | ||||
\(610\) | 67.9045 | 2.74937 | ||||||||
\(611\) | −1.93610 | − | 28.4666i | −0.0783263 | − | 1.15164i | ||||
\(612\) | 13.2611 | + | 22.9689i | 0.536049 | + | 0.928464i | ||||
\(613\) | 30.5826 | 1.23522 | 0.617610 | − | 0.786484i | \(-0.288101\pi\) | ||||
0.617610 | + | 0.786484i | \(0.288101\pi\) | |||||||
\(614\) | −1.33007 | − | 2.30375i | −0.0536773 | − | 0.0929718i | ||||
\(615\) | −9.03340 | − | 15.6463i | −0.364262 | − | 0.630920i | ||||
\(616\) | −36.5974 | + | 29.1513i | −1.47455 | + | 1.17454i | ||||
\(617\) | 22.1042 | + | 38.2856i | 0.889881 | + | 1.54132i | 0.840015 | + | 0.542563i | \(0.182546\pi\) |
0.0498659 | + | 0.998756i | \(0.484121\pi\) | |||||||
\(618\) | −12.1665 | −0.489409 | ||||||||
\(619\) | 0.184678 | + | 0.319871i | 0.00742283 | + | 0.0128567i | 0.869713 | − | 0.493558i | \(-0.164304\pi\) |
−0.862290 | + | 0.506415i | \(0.830971\pi\) | |||||||
\(620\) | 24.2784 | − | 42.0514i | 0.975043 | − | 1.68882i | ||||
\(621\) | −3.67246 | − | 6.36089i | −0.147371 | − | 0.255254i | ||||
\(622\) | −9.91466 | + | 17.1727i | −0.397542 | + | 0.688562i | ||||
\(623\) | −4.32277 | − | 1.69940i | −0.173188 | − | 0.0680851i | ||||
\(624\) | 23.5947 | + | 11.5636i | 0.944543 | + | 0.462913i | ||||
\(625\) | 15.5892 | − | 27.0013i | 0.623569 | − | 1.08005i | ||||
\(626\) | 62.2084 | 2.48635 | ||||||||
\(627\) | 9.41145 | 0.375857 | ||||||||
\(628\) | 51.9560 | 2.07327 | ||||||||
\(629\) | −34.3993 | −1.37159 | ||||||||
\(630\) | 14.7108 | − | 11.7177i | 0.586091 | − | 0.466846i | ||||
\(631\) | 6.70906 | + | 11.6204i | 0.267083 | + | 0.462602i | 0.968107 | − | 0.250536i | \(-0.0806067\pi\) |
−0.701024 | + | 0.713138i | \(0.747273\pi\) | |||||||
\(632\) | −12.0206 | + | 20.8202i | −0.478152 | + | 0.828184i | ||||
\(633\) | 10.5945 | − | 18.3503i | 0.421095 | − | 0.729357i | ||||
\(634\) | 27.4464 | 1.09003 | ||||||||
\(635\) | −2.47075 | − | 4.27946i | −0.0980486 | − | 0.169825i | ||||
\(636\) | 57.1706 | 2.26696 | ||||||||
\(637\) | −9.03183 | − | 23.5675i | −0.357854 | − | 0.933777i | ||||
\(638\) | 22.0691 | 0.873725 | ||||||||
\(639\) | −1.57062 | − | 2.72039i | −0.0621327 | − | 0.107617i | ||||
\(640\) | −30.6875 | −1.21303 | ||||||||
\(641\) | −21.5169 | + | 37.2683i | −0.849865 | + | 1.47201i | 0.0314626 | + | 0.999505i | \(0.489984\pi\) |
−0.881328 | + | 0.472505i | \(0.843350\pi\) | |||||||
\(642\) | −15.3996 | + | 26.6728i | −0.607773 | + | 1.05269i | ||||
\(643\) | 14.6688 | + | 25.4071i | 0.578482 | + | 1.00196i | 0.995654 | + | 0.0931324i | \(0.0296880\pi\) |
−0.417172 | + | 0.908828i | \(0.636979\pi\) | |||||||
\(644\) | −68.4821 | + | 54.5489i | −2.69857 | + | 2.14953i | ||||
\(645\) | 16.6773 | 0.656669 | ||||||||
\(646\) | −51.0611 | −2.00897 | ||||||||
\(647\) | −18.0070 | −0.707930 | −0.353965 | − | 0.935259i | \(-0.615167\pi\) | ||||
−0.353965 | + | 0.935259i | \(0.615167\pi\) | |||||||
\(648\) | 6.39011 | 0.251027 | ||||||||
\(649\) | 3.78656 | − | 6.55852i | 0.148636 | − | 0.257445i | ||||
\(650\) | 1.72695 | + | 25.3915i | 0.0677366 | + | 0.995936i | ||||
\(651\) | −9.52186 | − | 3.74332i | −0.373191 | − | 0.146712i | ||||
\(652\) | 27.4161 | − | 47.4862i | 1.07370 | − | 1.85970i | ||||
\(653\) | −17.3270 | − | 30.0113i | −0.678059 | − | 1.17443i | −0.975565 | − | 0.219713i | \(-0.929488\pi\) |
0.297505 | − | 0.954720i | \(-0.403845\pi\) | |||||||
\(654\) | −8.69448 | + | 15.0593i | −0.339981 | + | 0.588865i | ||||
\(655\) | −9.77502 | − | 16.9308i | −0.381942 | − | 0.661543i | ||||
\(656\) | −47.2420 | −1.84449 | ||||||||
\(657\) | −4.80291 | − | 8.31889i | −0.187379 | − | 0.324551i | ||||
\(658\) | −41.7697 | + | 33.2713i | −1.62835 | + | 1.29705i | ||||
\(659\) | −2.68796 | − | 4.65569i | −0.104708 | − | 0.181360i | 0.808911 | − | 0.587931i | \(-0.200058\pi\) |
−0.913619 | + | 0.406572i | \(0.866724\pi\) | |||||||
\(660\) | −17.3749 | − | 30.0942i | −0.676318 | − | 1.17142i | ||||
\(661\) | 40.4711 | 1.57414 | 0.787072 | − | 0.616861i | \(-0.211596\pi\) | ||||
0.787072 | + | 0.616861i | \(0.211596\pi\) | |||||||
\(662\) | 29.2921 | + | 50.7353i | 1.13847 | + | 1.97188i | ||||
\(663\) | 1.44026 | + | 21.1763i | 0.0559351 | + | 0.822417i | ||||
\(664\) | 30.8060 | 1.19550 | ||||||||
\(665\) | 3.72330 | + | 24.7983i | 0.144384 | + | 0.961638i | ||||
\(666\) | −7.45207 | + | 12.9074i | −0.288762 | + | 0.500150i | ||||
\(667\) | 22.9643 | 0.889182 | ||||||||
\(668\) | 20.4858 | + | 35.4825i | 0.792620 | + | 1.37286i | ||||
\(669\) | 0.453274 | − | 0.785093i | 0.0175246 | − | 0.0303534i | ||||
\(670\) | −61.7061 | −2.38392 | ||||||||
\(671\) | −26.4366 | −1.02057 | ||||||||
\(672\) | −2.28135 | − | 15.1945i | −0.0880051 | − | 0.586140i | ||||
\(673\) | 13.1634 | − | 22.7996i | 0.507411 | − | 0.878861i | −0.492553 | − | 0.870283i | \(-0.663936\pi\) |
0.999963 | − | 0.00857837i | \(-0.00273061\pi\) | |||||||
\(674\) | −8.91465 | − | 15.4406i | −0.343380 | − | 0.594751i | ||||
\(675\) | 1.38373 | + | 2.39670i | 0.0532599 | + | 0.0922489i | ||||
\(676\) | 35.8831 | + | 46.2907i | 1.38012 | + | 1.78041i | ||||
\(677\) | −1.90262 | + | 3.29544i | −0.0731236 | + | 0.126654i | −0.900269 | − | 0.435335i | \(-0.856630\pi\) |
0.827145 | + | 0.561988i | \(0.189963\pi\) | |||||||
\(678\) | 6.94935 | − | 12.0366i | 0.266888 | − | 0.462264i | ||||
\(679\) | 41.7921 | + | 16.4297i | 1.60384 | + | 0.630513i | ||||
\(680\) | 52.4201 | + | 90.7942i | 2.01022 | + | 3.48180i | ||||
\(681\) | 0.964045 | − | 1.66977i | 0.0369423 | − | 0.0639859i | ||||
\(682\) | −13.6480 | + | 23.6390i | −0.522607 | + | 0.905182i | ||||
\(683\) | −5.19765 | + | 9.00259i | −0.198882 | + | 0.344474i | −0.948166 | − | 0.317774i | \(-0.897065\pi\) |
0.749284 | + | 0.662249i | \(0.230398\pi\) | |||||||
\(684\) | −7.66082 | + | 13.2689i | −0.292919 | + | 0.507350i | ||||
\(685\) | 27.3928 | + | 47.4458i | 1.04663 | + | 1.81281i | ||||
\(686\) | −26.6762 | + | 38.9836i | −1.01850 | + | 1.48840i | ||||
\(687\) | −5.05578 | + | 8.75686i | −0.192890 | + | 0.334095i | ||||
\(688\) | 21.8044 | − | 37.7663i | 0.831284 | − | 1.43983i | ||||
\(689\) | 41.0837 | + | 20.1348i | 1.56516 | + | 0.767075i | ||||
\(690\) | −26.1055 | − | 45.2161i | −0.993821 | − | 1.72135i | ||||
\(691\) | 4.09958 | + | 7.10067i | 0.155955 | + | 0.270122i | 0.933406 | − | 0.358821i | \(-0.116821\pi\) |
−0.777451 | + | 0.628943i | \(0.783488\pi\) | |||||||
\(692\) | 3.03504 | − | 5.25684i | 0.115375 | − | 0.199835i | ||||
\(693\) | −5.72719 | + | 4.56195i | −0.217558 | + | 0.173294i | ||||
\(694\) | −5.49350 | −0.208530 | ||||||||
\(695\) | 51.1329 | 1.93958 | ||||||||
\(696\) | −9.98953 | + | 17.3024i | −0.378652 | + | 0.655845i | ||||
\(697\) | −19.0806 | − | 33.0485i | −0.722728 | − | 1.25180i | ||||
\(698\) | 3.85841 | 0.146043 | ||||||||
\(699\) | −13.1134 | + | 22.7130i | −0.495993 | + | 0.859085i | ||||
\(700\) | 25.8031 | − | 20.5533i | 0.975266 | − | 0.776841i | ||||
\(701\) | 4.64503 | 0.175440 | 0.0877201 | − | 0.996145i | \(-0.472042\pi\) | ||||
0.0877201 | + | 0.996145i | \(0.472042\pi\) | |||||||
\(702\) | 8.25778 | + | 4.04708i | 0.311670 | + | 0.152747i | ||||
\(703\) | −9.93608 | − | 17.2098i | −0.374746 | − | 0.649080i | ||||
\(704\) | −0.655177 | −0.0246929 | ||||||||
\(705\) | −11.0275 | − | 19.1001i | −0.415319 | − | 0.719353i | ||||
\(706\) | 41.3112 | + | 71.5531i | 1.55477 | + | 2.69293i | ||||
\(707\) | −3.81347 | + | 3.03759i | −0.143420 | + | 0.114240i | ||||
\(708\) | 6.16444 | + | 10.6771i | 0.231674 | + | 0.401271i | ||||
\(709\) | −44.3975 | −1.66738 | −0.833691 | − | 0.552231i | \(-0.813777\pi\) | ||||
−0.833691 | + | 0.552231i | \(0.813777\pi\) | |||||||
\(710\) | −11.1647 | − | 19.3378i | −0.419003 | − | 0.725734i | ||||
\(711\) | −1.88112 | + | 3.25819i | −0.0705475 | + | 0.122192i | ||||
\(712\) | −5.60916 | − | 9.71534i | −0.210212 | − | 0.364098i | ||||
\(713\) | −14.2016 | + | 24.5978i | −0.531853 | + | 0.921196i | ||||
\(714\) | 31.0724 | − | 24.7505i | 1.16286 | − | 0.926264i | ||||
\(715\) | −1.88705 | − | 27.7454i | −0.0705718 | − | 1.03762i | ||||
\(716\) | 13.4258 | − | 23.2542i | 0.501747 | − | 0.869052i | ||||
\(717\) | −28.0556 | −1.04775 | ||||||||
\(718\) | 40.4599 | 1.50995 | ||||||||
\(719\) | −44.9378 | −1.67590 | −0.837949 | − | 0.545748i | \(-0.816246\pi\) | ||||
−0.837949 | + | 0.545748i | \(0.816246\pi\) | |||||||
\(720\) | 20.3108 | 0.756937 | ||||||||
\(721\) | 1.87389 | + | 12.4807i | 0.0697874 | + | 0.464805i | ||||
\(722\) | 9.48161 | + | 16.4226i | 0.352869 | + | 0.611187i | ||||
\(723\) | −2.22625 | + | 3.85597i | −0.0827950 | + | 0.143405i | ||||
\(724\) | −23.5395 | + | 40.7716i | −0.874839 | + | 1.51527i | ||||
\(725\) | −8.65265 | −0.321351 | ||||||||
\(726\) | −4.26088 | − | 7.38007i | −0.158136 | − | 0.273900i | ||||
\(727\) | −49.7876 | −1.84652 | −0.923260 | − | 0.384177i | \(-0.874485\pi\) | ||||
−0.923260 | + | 0.384177i | \(0.874485\pi\) | |||||||
\(728\) | 18.4017 | − | 58.1139i | 0.682012 | − | 2.15384i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −34.1413 | − | 59.1345i | −1.26363 | − | 2.18867i | ||||
\(731\) | 35.2263 | 1.30289 | ||||||||
\(732\) | 21.5191 | − | 37.2721i | 0.795368 | − | 1.37762i | ||||
\(733\) | 9.96819 | − | 17.2654i | 0.368184 | − | 0.637713i | −0.621098 | − | 0.783733i | \(-0.713313\pi\) |
0.989282 | + | 0.146020i | \(0.0466465\pi\) | |||||||
\(734\) | −16.0606 | − | 27.8177i | −0.592807 | − | 1.02677i | ||||
\(735\) | −14.2861 | − | 13.2859i | −0.526950 | − | 0.490056i | ||||
\(736\) | −42.6545 | −1.57227 | ||||||||
\(737\) | 24.0234 | 0.884914 | ||||||||
\(738\) | −16.5340 | −0.608624 | ||||||||
\(739\) | 48.0471 | 1.76744 | 0.883721 | − | 0.468014i | \(-0.155030\pi\) | ||||
0.883721 | + | 0.468014i | \(0.155030\pi\) | |||||||
\(740\) | −36.6869 | + | 63.5436i | −1.34864 | + | 2.33591i | ||||
\(741\) | −10.1783 | + | 6.83721i | −0.373911 | + | 0.251171i | ||||
\(742\) | −12.7143 | − | 84.6810i | −0.466757 | − | 3.10874i | ||||
\(743\) | −0.250266 | + | 0.433473i | −0.00918137 | + | 0.0159026i | −0.870580 | − | 0.492028i | \(-0.836256\pi\) |
0.861398 | + | 0.507930i | \(0.169589\pi\) | |||||||
\(744\) | −12.3554 | − | 21.4002i | −0.452972 | − | 0.784570i | ||||
\(745\) | 12.2669 | − | 21.2469i | 0.449425 | − | 0.778427i | ||||
\(746\) | 14.9253 | + | 25.8514i | 0.546455 | + | 0.946488i | ||||
\(747\) | 4.82088 | 0.176387 | ||||||||
\(748\) | −36.6997 | − | 63.5657i | −1.34187 | − | 2.32419i | ||||
\(749\) | 29.7334 | + | 11.6891i | 1.08644 | + | 0.427109i | ||||
\(750\) | −7.93494 | − | 13.7437i | −0.289743 | − | 0.501850i | ||||
\(751\) | −21.9025 | − | 37.9363i | −0.799235 | − | 1.38432i | −0.920115 | − | 0.391648i | \(-0.871905\pi\) |
0.120880 | − | 0.992667i | \(-0.461428\pi\) | |||||||
\(752\) | −57.6704 | −2.10302 | ||||||||
\(753\) | −1.55413 | − | 2.69183i | −0.0566355 | − | 0.0980956i | ||||
\(754\) | −23.8674 | + | 16.0327i | −0.869200 | + | 0.583877i | ||||
\(755\) | 26.9542 | 0.980963 | ||||||||
\(756\) | −1.76989 | − | 11.7880i | −0.0643701 | − | 0.428724i | ||||
\(757\) | 1.91271 | − | 3.31291i | 0.0695186 | − | 0.120410i | −0.829171 | − | 0.558995i | \(-0.811187\pi\) |
0.898689 | + | 0.438585i | \(0.144520\pi\) | |||||||
\(758\) | 84.0552 | 3.05302 | ||||||||
\(759\) | 10.1634 | + | 17.6035i | 0.368908 | + | 0.638968i | ||||
\(760\) | −30.2825 | + | 52.4509i | −1.09846 | + | 1.90259i | ||||
\(761\) | −5.73144 | −0.207765 | −0.103882 | − | 0.994590i | \(-0.533127\pi\) | ||||
−0.103882 | + | 0.994590i | \(0.533127\pi\) | |||||||
\(762\) | −4.52225 | −0.163824 | ||||||||
\(763\) | 16.7873 | + | 6.59956i | 0.607740 | + | 0.238920i | ||||
\(764\) | 1.48252 | − | 2.56781i | 0.0536358 | − | 0.0928999i | ||||
\(765\) | 8.20331 | + | 14.2086i | 0.296591 | + | 0.513711i | ||||
\(766\) | −16.1145 | − | 27.9112i | −0.582242 | − | 1.00847i | ||||
\(767\) | 0.669507 | + | 9.84380i | 0.0241745 | + | 0.355439i | ||||
\(768\) | −14.2787 | + | 24.7314i | −0.515238 | + | 0.892419i | ||||
\(769\) | 8.50053 | − | 14.7234i | 0.306537 | − | 0.530938i | −0.671065 | − | 0.741398i | \(-0.734163\pi\) |
0.977602 | + | 0.210461i | \(0.0674964\pi\) | |||||||
\(770\) | −40.7115 | + | 32.4284i | −1.46714 | + | 1.16864i | ||||
\(771\) | −12.9927 | − | 22.5040i | −0.467920 | − | 0.810461i | ||||
\(772\) | −19.7911 | + | 34.2792i | −0.712298 | + | 1.23374i | ||||
\(773\) | 6.09320 | − | 10.5537i | 0.219157 | − | 0.379591i | −0.735393 | − | 0.677640i | \(-0.763003\pi\) |
0.954550 | + | 0.298049i | \(0.0963360\pi\) | |||||||
\(774\) | 7.63120 | − | 13.2176i | 0.274298 | − | 0.475098i | ||||
\(775\) | 5.35096 | − | 9.26813i | 0.192212 | − | 0.332921i | ||||
\(776\) | 54.2288 | + | 93.9271i | 1.94670 | + | 3.37179i | ||||
\(777\) | 14.3884 | + | 5.65650i | 0.516182 | + | 0.202926i | ||||
\(778\) | −0.151480 | + | 0.262370i | −0.00543080 | + | 0.00940643i | ||||
\(779\) | 11.0226 | − | 19.0918i | 0.394927 | − | 0.684034i | ||||
\(780\) | 40.6535 | + | 19.9240i | 1.45563 | + | 0.713393i | ||||
\(781\) | 4.34663 | + | 7.52858i | 0.155535 | + | 0.269394i | ||||
\(782\) | −55.1407 | − | 95.5066i | −1.97183 | − | 3.41531i | ||||
\(783\) | −1.56328 | + | 2.70768i | −0.0558671 | + | 0.0967646i | ||||
\(784\) | −48.7641 | + | 14.9809i | −1.74158 | + | 0.535034i | ||||
\(785\) | 32.1399 | 1.14712 | ||||||||
\(786\) | −17.8914 | −0.638165 | ||||||||
\(787\) | 2.31021 | − | 4.00140i | 0.0823501 | − | 0.142635i | −0.821909 | − | 0.569619i | \(-0.807091\pi\) |
0.904259 | + | 0.426984i | \(0.140424\pi\) | |||||||
\(788\) | −41.8901 | − | 72.5558i | −1.49227 | − | 2.58469i | ||||
\(789\) | −12.7806 | −0.455000 | ||||||||
\(790\) | −13.3719 | + | 23.1608i | −0.475750 | + | 0.824023i | ||||
\(791\) | −13.4178 | − | 5.27491i | −0.477081 | − | 0.187554i | ||||
\(792\) | −17.6844 | −0.628388 | ||||||||
\(793\) | 28.5908 | − | 19.2056i | 1.01529 | − | 0.682010i | ||||
\(794\) | −8.90531 | − | 15.4245i | −0.316038 | − | 0.547393i | ||||
\(795\) | 35.3656 | 1.25429 | ||||||||
\(796\) | −34.2986 | − | 59.4069i | −1.21568 | − | 2.10562i | ||||
\(797\) | −9.12087 | − | 15.7978i | −0.323078 | − | 0.559587i | 0.658044 | − | 0.752980i | \(-0.271384\pi\) |
−0.981121 | + | 0.193393i | \(0.938051\pi\) | |||||||
\(798\) | 21.3576 | + | 8.39629i | 0.756052 | + | 0.297226i | ||||
\(799\) | −23.2925 | − | 40.3438i | −0.824029 | − | 1.42726i | ||||
\(800\) | 16.0716 | 0.568218 | ||||||||
\(801\) | −0.877787 | − | 1.52037i | −0.0310151 | − | 0.0537197i | ||||
\(802\) | 24.4238 | − | 42.3032i | 0.862433 | − | 1.49378i | ||||
\(803\) | 13.2919 | + | 23.0222i | 0.469061 | + | 0.812437i | ||||
\(804\) | −19.5548 | + | 33.8699i | −0.689644 | + | 1.19450i | ||||
\(805\) | −42.3629 | + | 33.7439i | −1.49310 | + | 1.18931i | ||||
\(806\) | −2.41311 | − | 35.4801i | −0.0849982 | − | 1.24973i | ||||
\(807\) | 0.978744 | − | 1.69523i | 0.0344534 | − | 0.0596751i | ||||
\(808\) | −11.7752 | −0.414251 | ||||||||
\(809\) | −34.5921 | −1.21619 | −0.608096 | − | 0.793863i | \(-0.708067\pi\) | ||||
−0.608096 | + | 0.793863i | \(0.708067\pi\) | |||||||
\(810\) | 7.10846 | 0.249766 | ||||||||
\(811\) | −11.9774 | −0.420582 | −0.210291 | − | 0.977639i | \(-0.567441\pi\) | ||||
−0.210291 | + | 0.977639i | \(0.567441\pi\) | |||||||
\(812\) | 34.6849 | + | 13.6356i | 1.21720 | + | 0.478516i | ||||
\(813\) | 13.4609 | + | 23.3150i | 0.472095 | + | 0.817692i | ||||
\(814\) | 20.6233 | − | 35.7207i | 0.722848 | − | 1.25201i | ||||
\(815\) | 16.9596 | − | 29.3749i | 0.594069 | − | 1.02896i | ||||
\(816\) | 42.9009 | 1.50183 | ||||||||
\(817\) | 10.1749 | + | 17.6235i | 0.355976 | + | 0.616568i | ||||
\(818\) | 29.8164 | 1.04250 | ||||||||
\(819\) | 2.87972 | − | 9.09435i | 0.100625 | − | 0.317782i | ||||
\(820\) | −81.3976 | −2.84253 | ||||||||
\(821\) | −10.5936 | − | 18.3486i | −0.369719 | − | 0.640372i | 0.619803 | − | 0.784758i | \(-0.287213\pi\) |
−0.989521 | + | 0.144386i | \(0.953879\pi\) | |||||||
\(822\) | 50.1376 | 1.74875 | ||||||||
\(823\) | −9.96806 | + | 17.2652i | −0.347465 | + | 0.601827i | −0.985798 | − | 0.167933i | \(-0.946291\pi\) |
0.638334 | + | 0.769760i | \(0.279624\pi\) | |||||||
\(824\) | −15.2408 | + | 26.3979i | −0.530939 | + | 0.919614i | ||||
\(825\) | −3.82943 | − | 6.63277i | −0.133324 | − | 0.230924i | ||||
\(826\) | 14.4440 | − | 11.5053i | 0.502572 | − | 0.400320i | ||||
\(827\) | −15.0299 | −0.522639 | −0.261320 | − | 0.965252i | \(-0.584158\pi\) | ||||
−0.261320 | + | 0.965252i | \(0.584158\pi\) | |||||||
\(828\) | −33.0916 | −1.15001 | ||||||||
\(829\) | 16.0717 | 0.558195 | 0.279097 | − | 0.960263i | \(-0.409965\pi\) | ||||
0.279097 | + | 0.960263i | \(0.409965\pi\) | |||||||
\(830\) | 34.2691 | 1.18950 | ||||||||
\(831\) | −11.5778 | + | 20.0533i | −0.401629 | + | 0.695643i | ||||
\(832\) | 0.708563 | − | 0.475971i | 0.0245650 | − | 0.0165013i | ||||
\(833\) | −30.1754 | − | 28.0627i | −1.04552 | − | 0.972315i | ||||
\(834\) | 23.3974 | − | 40.5254i | 0.810185 | − | 1.40328i | ||||
\(835\) | 12.6725 | + | 21.9494i | 0.438550 | + | 0.759591i | ||||
\(836\) | 21.2011 | − | 36.7213i | 0.733254 | − | 1.27003i | ||||
\(837\) | −1.93352 | − | 3.34896i | −0.0668323 | − | 0.115757i | ||||
\(838\) | −40.2940 | −1.39193 | ||||||||
\(839\) | 2.50930 | + | 4.34624i | 0.0866307 | + | 0.150049i | 0.906085 | − | 0.423096i | \(-0.139057\pi\) |
−0.819454 | + | 0.573145i | \(0.805723\pi\) | |||||||
\(840\) | −6.99620 | − | 46.5968i | −0.241392 | − | 1.60774i | ||||
\(841\) | 9.61231 | + | 16.6490i | 0.331459 | + | 0.574104i | ||||
\(842\) | −10.9441 | − | 18.9557i | −0.377158 | − | 0.653257i | ||||
\(843\) | 26.9347 | 0.927681 | ||||||||
\(844\) | −47.7323 | − | 82.6747i | −1.64301 | − | 2.84578i | ||||
\(845\) | 22.1972 | + | 28.6354i | 0.763609 | + | 0.985086i | ||||
\(846\) | −20.1838 | −0.693932 | ||||||||
\(847\) | −6.91437 | + | 5.50759i | −0.237581 | + | 0.189243i | ||||
\(848\) | 46.2379 | − | 80.0864i | 1.58782 | − | 2.75018i | ||||
\(849\) | −15.2443 | −0.523184 | ||||||||
\(850\) | 20.7763 | + | 35.9856i | 0.712621 | + | 1.23430i | ||||
\(851\) | 21.4599 | − | 37.1696i | 0.735636 | − | 1.27416i | ||||
\(852\) | −14.1524 | −0.484854 | ||||||||
\(853\) | −4.22423 | −0.144635 | −0.0723175 | − | 0.997382i | \(-0.523039\pi\) | ||||
−0.0723175 | + | 0.997382i | \(0.523039\pi\) | |||||||
\(854\) | −59.9931 | − | 23.5850i | −2.05292 | − | 0.807063i | ||||
\(855\) | −4.73897 | + | 8.20814i | −0.162069 | + | 0.280712i | ||||
\(856\) | 38.5817 | + | 66.8254i | 1.31869 | + | 2.28404i | ||||
\(857\) | 4.48428 | + | 7.76700i | 0.153180 | + | 0.265316i | 0.932395 | − | 0.361441i | \(-0.117715\pi\) |
−0.779215 | + | 0.626757i | \(0.784382\pi\) | |||||||
\(858\) | −22.8531 | − | 11.2002i | −0.780193 | − | 0.382367i | ||||
\(859\) | 18.3400 | − | 31.7658i | 0.625753 | − | 1.08384i | −0.362642 | − | 0.931928i | \(-0.618125\pi\) |
0.988395 | − | 0.151907i | \(-0.0485414\pi\) | |||||||
\(860\) | 37.5688 | − | 65.0711i | 1.28109 | − | 2.21890i | ||||
\(861\) | 2.54657 | + | 16.9609i | 0.0867869 | + | 0.578027i | ||||
\(862\) | 24.7974 | + | 42.9503i | 0.844602 | + | 1.46289i | ||||
\(863\) | −10.4237 | + | 18.0544i | −0.354828 | + | 0.614580i | −0.987088 | − | 0.160176i | \(-0.948794\pi\) |
0.632261 | + | 0.774756i | \(0.282127\pi\) | |||||||
\(864\) | 2.90367 | − | 5.02931i | 0.0987850 | − | 0.171101i | ||||
\(865\) | 1.87747 | − | 3.25187i | 0.0638359 | − | 0.110567i | ||||
\(866\) | 6.00426 | − | 10.3997i | 0.204033 | − | 0.353395i | ||||
\(867\) | 8.82723 | + | 15.2892i | 0.299788 | + | 0.519249i | ||||
\(868\) | −36.0553 | + | 28.7196i | −1.22380 | + | 0.974806i | ||||
\(869\) | 5.20593 | − | 9.01694i | 0.176599 | − | 0.305879i | ||||
\(870\) | −11.1125 | + | 19.2474i | −0.376750 | + | 0.652549i | ||||
\(871\) | −25.9810 | + | 17.4525i | −0.880331 | + | 0.591354i | ||||
\(872\) | 21.7829 | + | 37.7291i | 0.737663 | + | 1.27767i | ||||
\(873\) | 8.48637 | + | 14.6988i | 0.287220 | + | 0.497480i | ||||
\(874\) | 31.8543 | − | 55.1732i | 1.07749 | − | 1.86626i | ||||
\(875\) | −12.8765 | + | 10.2567i | −0.435304 | + | 0.346738i | ||||
\(876\) | −43.2778 | −1.46222 | ||||||||
\(877\) | −27.6200 | −0.932662 | −0.466331 | − | 0.884610i | \(-0.654425\pi\) | ||||
−0.466331 | + | 0.884610i | \(0.654425\pi\) | |||||||
\(878\) | 26.3502 | − | 45.6399i | 0.889277 | − | 1.54027i | ||||
\(879\) | 2.04388 | + | 3.54010i | 0.0689383 | + | 0.119405i | ||||
\(880\) | −56.2093 | −1.89482 | ||||||||
\(881\) | −12.7092 | + | 22.0130i | −0.428183 | + | 0.741635i | −0.996712 | − | 0.0810283i | \(-0.974180\pi\) |
0.568528 | + | 0.822664i | \(0.307513\pi\) | |||||||
\(882\) | −17.0667 | + | 5.24311i | −0.574666 | + | 0.176545i | ||||
\(883\) | 32.7921 | 1.10354 | 0.551771 | − | 0.833995i | \(-0.313952\pi\) | ||||
0.551771 | + | 0.833995i | \(0.313952\pi\) | |||||||
\(884\) | 85.8692 | + | 42.0839i | 2.88810 | + | 1.41543i | ||||
\(885\) | 3.81332 | + | 6.60486i | 0.128183 | + | 0.222020i | ||||
\(886\) | −31.3260 | −1.05242 | ||||||||
\(887\) | 3.96660 | + | 6.87036i | 0.133185 | + | 0.230684i | 0.924903 | − | 0.380204i | \(-0.124146\pi\) |
−0.791717 | + | 0.610888i | \(0.790813\pi\) | |||||||
\(888\) | 18.6702 | + | 32.3377i | 0.626531 | + | 1.08518i | ||||
\(889\) | 0.696519 | + | 4.63903i | 0.0233605 | + | 0.155588i | ||||
\(890\) | −6.23972 | − | 10.8075i | −0.209156 | − | 0.362269i | ||||
\(891\) | −2.76747 | −0.0927136 | ||||||||
\(892\) | −2.04217 | − | 3.53713i | −0.0683768 | − | 0.118432i | ||||
\(893\) | 13.4558 | − | 23.3062i | 0.450282 | − | 0.779912i | ||||
\(894\) | −11.2262 | − | 19.4443i | −0.375460 | − | 0.650315i | ||||
\(895\) | 8.30521 | − | 14.3850i | 0.277613 | − | 0.480839i | ||||
\(896\) | 27.1122 | + | 10.6586i | 0.905754 | + | 0.356078i | ||||
\(897\) | −23.7801 | − | 11.6545i | −0.793996 | − | 0.389131i | ||||
\(898\) | 35.1682 | − | 60.9130i | 1.17358 | − | 2.03269i | ||||
\(899\) | 12.0905 | 0.403242 | ||||||||
\(900\) | 12.4685 | 0.415615 | ||||||||
\(901\) | 74.7001 | 2.48862 | ||||||||
\(902\) | 45.7572 | 1.52355 | ||||||||
\(903\) | −14.7343 | − | 5.79247i | −0.490327 | − | 0.192761i | ||||
\(904\) | −17.4107 | − | 30.1562i | −0.579071 | − | 1.00298i | ||||
\(905\) | −14.5615 | + | 25.2213i | −0.484041 | + | 0.838384i | ||||
\(906\) | 12.3337 | − | 21.3625i | 0.409759 | − | 0.709723i | ||||
\(907\) | −46.2372 | −1.53528 | −0.767640 | − | 0.640881i | \(-0.778569\pi\) | ||||
−0.767640 | + | 0.640881i | \(0.778569\pi\) | |||||||
\(908\) | −4.34338 | − | 7.52295i | −0.144140 | − | 0.249658i | ||||
\(909\) | −1.84273 | −0.0611194 | ||||||||
\(910\) | 20.4704 | − | 64.6469i | 0.678586 | − | 2.14302i | ||||
\(911\) | −21.5838 | −0.715102 | −0.357551 | − | 0.933894i | \(-0.616388\pi\) | ||||
−0.357551 | + | 0.933894i | \(0.616388\pi\) | |||||||
\(912\) | 12.3917 | + | 21.4631i | 0.410330 | + | 0.710713i | ||||
\(913\) | −13.3416 | −0.441544 | ||||||||
\(914\) | −17.6991 | + | 30.6558i | −0.585436 | + | 1.01400i | ||||
\(915\) | 13.3117 | − | 23.0565i | 0.440070 | − | 0.762224i | ||||
\(916\) | 22.7781 | + | 39.4529i | 0.752611 | + | 1.30356i | ||||
\(917\) | 2.75564 | + | 18.3534i | 0.0909993 | + | 0.606082i | ||||
\(918\) | 15.0147 | 0.495558 | ||||||||
\(919\) | −8.80978 | −0.290608 | −0.145304 | − | 0.989387i | \(-0.546416\pi\) | ||||
−0.145304 | + | 0.989387i | \(0.546416\pi\) | |||||||
\(920\) | −130.808 | −4.31262 | ||||||||
\(921\) | −1.04296 | −0.0343668 | ||||||||
\(922\) | −31.1295 | + | 53.9179i | −1.02520 | + | 1.77569i | ||||
\(923\) | −10.1702 | − | 4.98432i | −0.334755 | − | 0.164061i | ||||
\(924\) | 4.89810 | + | 32.6228i | 0.161136 | + | 1.07321i | ||||
\(925\) | −8.08580 | + | 14.0050i | −0.265859 | + | 0.460482i | ||||
\(926\) | 14.8505 | + | 25.7219i | 0.488019 | + | 0.845274i | ||||
\(927\) | −2.38506 | + | 4.13105i | −0.0783358 | + | 0.135682i | ||||
\(928\) | 9.07851 | + | 15.7244i | 0.298017 | + | 0.516180i | ||||
\(929\) | −52.4694 | −1.72147 | −0.860733 | − | 0.509057i | \(-0.829994\pi\) | ||||
−0.860733 | + | 0.509057i | \(0.829994\pi\) | |||||||
\(930\) | −13.7444 | − | 23.8060i | −0.450696 | − | 0.780628i | ||||
\(931\) | 5.32359 | − | 23.2023i | 0.174474 | − | 0.760426i | ||||
\(932\) | 59.0806 | + | 102.331i | 1.93525 | + | 3.35195i | ||||
\(933\) | 3.88724 | + | 6.73290i | 0.127263 | + | 0.220425i | ||||
\(934\) | −10.6860 | −0.349656 | ||||||||
\(935\) | −22.7024 | − | 39.3217i | −0.742448 | − | 1.28596i | ||||
\(936\) | 19.1254 | − | 12.8473i | 0.625134 | − | 0.419928i | ||||
\(937\) | −19.3131 | −0.630932 | −0.315466 | − | 0.948937i | \(-0.602161\pi\) | ||||
−0.315466 | + | 0.948937i | \(0.602161\pi\) | |||||||
\(938\) | 54.5169 | + | 21.4321i | 1.78004 | + | 0.699784i | ||||
\(939\) | 12.1950 | − | 21.1224i | 0.397970 | − | 0.689304i | ||||
\(940\) | −99.3657 | −3.24095 | ||||||||
\(941\) | −8.45918 | − | 14.6517i | −0.275761 | − | 0.477633i | 0.694566 | − | 0.719429i | \(-0.255597\pi\) |
−0.970327 | + | 0.241797i | \(0.922263\pi\) | |||||||
\(942\) | 14.7066 | − | 25.4725i | 0.479166 | − | 0.829939i | ||||
\(943\) | 47.6133 | 1.55050 | ||||||||
\(944\) | 19.9425 | 0.649073 | ||||||||
\(945\) | −1.09485 | − | 7.29202i | −0.0356154 | − | 0.237209i | ||||
\(946\) | −21.1191 | + | 36.5793i | −0.686641 | + | 1.18930i | ||||
\(947\) | 22.3511 | + | 38.7132i | 0.726313 | + | 1.25801i | 0.958431 | + | 0.285323i | \(0.0921008\pi\) |
−0.232119 | + | 0.972687i | \(0.574566\pi\) | |||||||
\(948\) | 8.47514 | + | 14.6794i | 0.275260 | + | 0.476764i | ||||
\(949\) | −31.1001 | − | 15.2419i | −1.00955 | − | 0.494774i | ||||
\(950\) | −12.0023 | + | 20.7885i | −0.389405 | + | 0.674468i | ||||
\(951\) | 5.38045 | − | 9.31922i | 0.174473 | − | 0.302196i | ||||
\(952\) | −14.7775 | − | 98.4229i | −0.478943 | − | 3.18990i | ||||
\(953\) | −24.8774 | − | 43.0888i | −0.805857 | − | 1.39578i | −0.915711 | − | 0.401837i | \(-0.868372\pi\) |
0.109855 | − | 0.993948i | \(-0.464962\pi\) | |||||||
\(954\) | 16.1826 | − | 28.0291i | 0.523931 | − | 0.907474i | ||||
\(955\) | 0.917087 | − | 1.58844i | 0.0296762 | − | 0.0514008i | ||||
\(956\) | −63.2004 | + | 109.466i | −2.04405 | + | 3.54039i | ||||
\(957\) | 4.32632 | − | 7.49341i | 0.139850 | − | 0.242228i | ||||
\(958\) | 19.1400 | + | 33.1515i | 0.618386 | + | 1.07108i | ||||
\(959\) | −7.72221 | − | 51.4322i | −0.249363 | − | 1.66083i | ||||
\(960\) | 0.329903 | − | 0.571408i | 0.0106476 | − | 0.0184421i | ||||
\(961\) | 8.02298 | − | 13.8962i | 0.258806 | − | 0.448265i | ||||
\(962\) | 3.64644 | + | 53.6137i | 0.117566 | + | 1.72858i | ||||
\(963\) | 6.03771 | + | 10.4576i | 0.194563 | + | 0.336992i | ||||
\(964\) | 10.0301 | + | 17.3726i | 0.323047 | + | 0.559533i | ||||
\(965\) | −12.2428 | + | 21.2051i | −0.394109 | + | 0.682616i | ||||
\(966\) | 7.35932 | + | 49.0153i | 0.236782 | + | 1.57704i | ||||
\(967\) | 1.92897 | 0.0620315 | 0.0310158 | − | 0.999519i | \(-0.490126\pi\) | ||||
0.0310158 | + | 0.999519i | \(0.490126\pi\) | |||||||
\(968\) | −21.3502 | −0.686221 | ||||||||
\(969\) | −10.0098 | + | 17.3374i | −0.321560 | + | 0.556958i | ||||
\(970\) | 60.3251 | + | 104.486i | 1.93692 | + | 3.35485i | ||||
\(971\) | −36.1232 | −1.15925 | −0.579624 | − | 0.814884i | \(-0.696801\pi\) | ||||
−0.579624 | + | 0.814884i | \(0.696801\pi\) | |||||||
\(972\) | 2.25269 | − | 3.90177i | 0.0722549 | − | 0.125149i | ||||
\(973\) | −45.1756 | − | 17.7598i | −1.44826 | − | 0.569353i | ||||
\(974\) | 16.8546 | 0.540055 | ||||||||
\(975\) | 8.96004 | + | 4.39125i | 0.286951 | + | 0.140632i | ||||
\(976\) | −34.8080 | − | 60.2893i | −1.11418 | − | 1.92981i | ||||
\(977\) | 32.9682 | 1.05475 | 0.527373 | − | 0.849634i | \(-0.323177\pi\) | ||||
0.527373 | + | 0.849634i | \(0.323177\pi\) | |||||||
\(978\) | −15.5207 | − | 26.8827i | −0.496298 | − | 0.859613i | ||||
\(979\) | 2.42925 | + | 4.20758i | 0.0776391 | + | 0.134475i | ||||
\(980\) | −84.0203 | + | 25.8121i | −2.68393 | + | 0.824537i | ||||
\(981\) | 3.40885 | + | 5.90430i | 0.108836 | + | 0.188510i | ||||
\(982\) | 83.9418 | 2.67869 | ||||||||
\(983\) | 7.52903 | + | 13.0407i | 0.240139 | + | 0.415933i | 0.960754 | − | 0.277403i | \(-0.0894737\pi\) |
−0.720615 | + | 0.693336i | \(0.756140\pi\) | |||||||
\(984\) | −20.7119 | + | 35.8741i | −0.660271 | + | 1.14362i | ||||
\(985\) | −25.9132 | − | 44.8829i | −0.825662 | − | 1.43009i | ||||
\(986\) | −23.4721 | + | 40.6549i | −0.747504 | + | 1.29472i | ||||
\(987\) | 3.10871 | + | 20.7050i | 0.0989514 | + | 0.659046i | ||||
\(988\) | 3.74858 | + | 55.1156i | 0.119258 | + | 1.75346i | ||||
\(989\) | −21.9758 | + | 38.0631i | −0.698789 | + | 1.21034i | ||||
\(990\) | −19.6724 | −0.625231 | ||||||||
\(991\) | 36.1351 | 1.14787 | 0.573935 | − | 0.818901i | \(-0.305416\pi\) | ||||
0.573935 | + | 0.818901i | \(0.305416\pi\) | |||||||
\(992\) | −22.4573 | −0.713019 | ||||||||
\(993\) | 22.9691 | 0.728902 | ||||||||
\(994\) | 3.14739 | + | 20.9626i | 0.0998292 | + | 0.664892i | ||||
\(995\) | −21.2171 | − | 36.7491i | −0.672627 | − | 1.16502i | ||||
\(996\) | 10.8599 | − | 18.8100i | 0.344110 | − | 0.596017i | ||||
\(997\) | −1.90762 | + | 3.30409i | −0.0604149 | + | 0.104642i | −0.894651 | − | 0.446766i | \(-0.852576\pi\) |
0.834236 | + | 0.551408i | \(0.185909\pi\) | |||||||
\(998\) | 91.4115 | 2.89358 | ||||||||
\(999\) | 2.92173 | + | 5.06059i | 0.0924396 | + | 0.160110i |
(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 | 273.2.j.b.100.1 | ✓ | 16 | |
3.2 | odd | 2 | 819.2.n.e.100.8 | 16 | |||
7.4 | even | 3 | 273.2.l.b.256.8 | yes | 16 | ||
13.3 | even | 3 | 273.2.l.b.16.8 | yes | 16 | ||
21.11 | odd | 6 | 819.2.s.e.802.1 | 16 | |||
39.29 | odd | 6 | 819.2.s.e.289.1 | 16 | |||
91.81 | even | 3 | inner | 273.2.j.b.172.1 | yes | 16 | |
273.263 | odd | 6 | 819.2.n.e.172.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.j.b.100.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
273.2.j.b.172.1 | yes | 16 | 91.81 | even | 3 | inner | |
273.2.l.b.16.8 | yes | 16 | 13.3 | even | 3 | ||
273.2.l.b.256.8 | yes | 16 | 7.4 | even | 3 | ||
819.2.n.e.100.8 | 16 | 3.2 | odd | 2 | |||
819.2.n.e.172.8 | 16 | 273.263 | odd | 6 | |||
819.2.s.e.289.1 | 16 | 39.29 | odd | 6 | |||
819.2.s.e.802.1 | 16 | 21.11 | odd | 6 |