Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,4,Mod(5,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.944030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Root | \(1.97476 + 0.316760i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.13 |
Dual form | 16.4.e.a.5.2 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.29152 | − | 1.65800i | −0.810173 | − | 0.586190i | ||||
\(3\) | −5.96513 | − | 5.96513i | −1.14799 | − | 1.14799i | −0.986947 | − | 0.161043i | \(-0.948514\pi\) |
−0.161043 | − | 0.986947i | \(-0.551486\pi\) | |||||||
\(4\) | 2.50210 | + | 7.59865i | 0.312762 | + | 0.949832i | ||||
\(5\) | 8.67959 | − | 8.67959i | 0.776326 | − | 0.776326i | −0.202878 | − | 0.979204i | \(-0.565029\pi\) |
0.979204 | + | 0.202878i | \(0.0650295\pi\) | |||||||
\(6\) | 3.77903 | + | 23.5594i | 0.257130 | + | 1.60301i | ||||
\(7\) | − | 1.63924i | − | 0.0885109i | −0.999020 | − | 0.0442554i | \(-0.985908\pi\) | ||
0.999020 | − | 0.0442554i | \(-0.0140915\pi\) | |||||||
\(8\) | 6.86495 | − | 21.5609i | 0.303391 | − | 0.952866i | ||||
\(9\) | 44.1656i | 1.63576i | ||||||||
\(10\) | −34.2802 | + | 5.49869i | −1.08403 | + | 0.173884i | ||||
\(11\) | 18.2021 | − | 18.2021i | 0.498921 | − | 0.498921i | −0.412181 | − | 0.911102i | \(-0.635233\pi\) |
0.911102 | + | 0.412181i | \(0.135233\pi\) | |||||||
\(12\) | 30.4016 | − | 60.2523i | 0.731350 | − | 1.44945i | ||||
\(13\) | −9.34700 | − | 9.34700i | −0.199415 | − | 0.199415i | 0.600334 | − | 0.799749i | \(-0.295034\pi\) |
−0.799749 | + | 0.600334i | \(0.795034\pi\) | |||||||
\(14\) | −2.71786 | + | 3.75636i | −0.0518842 | + | 0.0717092i | ||||
\(15\) | −103.550 | −1.78243 | ||||||||
\(16\) | −51.4790 | + | 38.0251i | −0.804360 | + | 0.594142i | ||||
\(17\) | 53.6113 | 0.764862 | 0.382431 | − | 0.923984i | \(-0.375087\pi\) | ||||
0.382431 | + | 0.923984i | \(0.375087\pi\) | |||||||
\(18\) | 73.2264 | − | 101.206i | 0.958869 | − | 1.32525i | ||||
\(19\) | 70.9870 | + | 70.9870i | 0.857133 | + | 0.857133i | 0.990999 | − | 0.133866i | \(-0.0427392\pi\) |
−0.133866 | + | 0.990999i | \(0.542739\pi\) | |||||||
\(20\) | 87.6704 | + | 44.2360i | 0.980184 | + | 0.494574i | ||||
\(21\) | −9.77831 | + | 9.77831i | −0.101610 | + | 0.101610i | ||||
\(22\) | −71.8893 | + | 11.5314i | −0.696675 | + | 0.111750i | ||||
\(23\) | 25.1189i | 0.227724i | 0.993497 | + | 0.113862i | \(0.0363222\pi\) | ||||
−0.993497 | + | 0.113862i | \(0.963678\pi\) | |||||||
\(24\) | −169.564 | + | 87.6633i | −1.44217 | + | 0.745592i | ||||
\(25\) | − | 25.6706i | − | 0.205365i | ||||||
\(26\) | 5.92151 | + | 36.9161i | 0.0446656 | + | 0.278456i | ||||
\(27\) | 102.395 | − | 102.395i | 0.729850 | − | 0.729850i | ||||
\(28\) | 12.4560 | − | 4.10155i | 0.0840704 | − | 0.0276828i | ||||
\(29\) | −181.094 | − | 181.094i | −1.15960 | − | 1.15960i | −0.984563 | − | 0.175033i | \(-0.943997\pi\) |
−0.175033 | − | 0.984563i | \(-0.556003\pi\) | |||||||
\(30\) | 237.286 | + | 171.685i | 1.44408 | + | 1.04484i | ||||
\(31\) | 132.684 | 0.768733 | 0.384367 | − | 0.923180i | \(-0.374420\pi\) | ||||
0.384367 | + | 0.923180i | \(0.374420\pi\) | |||||||
\(32\) | 181.011 | − | 1.78308i | 0.999951 | − | 0.00985023i | ||||
\(33\) | −217.155 | −1.14551 | ||||||||
\(34\) | −122.851 | − | 88.8874i | −0.619671 | − | 0.448355i | ||||
\(35\) | −14.2280 | − | 14.2280i | −0.0687133 | − | 0.0687133i | ||||
\(36\) | −335.599 | + | 110.507i | −1.55370 | + | 0.511604i | ||||
\(37\) | 174.872 | − | 174.872i | 0.776994 | − | 0.776994i | −0.202324 | − | 0.979319i | \(-0.564849\pi\) |
0.979319 | + | 0.202324i | \(0.0648495\pi\) | |||||||
\(38\) | −44.9717 | − | 280.364i | −0.191983 | − | 1.19687i | ||||
\(39\) | 111.512i | 0.457853i | ||||||||
\(40\) | −127.555 | − | 246.725i | −0.504205 | − | 0.975265i | ||||
\(41\) | 198.660i | 0.756720i | 0.925658 | + | 0.378360i | \(0.123512\pi\) | ||||
−0.925658 | + | 0.378360i | \(0.876488\pi\) | |||||||
\(42\) | 38.6196 | − | 6.19475i | 0.141884 | − | 0.0227588i | ||||
\(43\) | −285.717 | + | 285.717i | −1.01329 | + | 1.01329i | −0.0133770 | + | 0.999911i | \(0.504258\pi\) |
−0.999911 | + | 0.0133770i | \(0.995742\pi\) | |||||||
\(44\) | 183.854 | + | 92.7678i | 0.629934 | + | 0.317847i | ||||
\(45\) | 383.339 | + | 383.339i | 1.26989 | + | 1.26989i | ||||
\(46\) | 41.6471 | − | 57.5605i | 0.133490 | − | 0.184496i | ||||
\(47\) | 78.3629 | 0.243200 | 0.121600 | − | 0.992579i | \(-0.461197\pi\) | ||||
0.121600 | + | 0.992579i | \(0.461197\pi\) | |||||||
\(48\) | 533.904 | + | 80.2545i | 1.60547 | + | 0.241328i | ||||
\(49\) | 340.313 | 0.992166 | ||||||||
\(50\) | −42.5617 | + | 58.8245i | −0.120383 | + | 0.166381i | ||||
\(51\) | −319.799 | − | 319.799i | −0.878054 | − | 0.878054i | ||||
\(52\) | 47.6375 | − | 94.4117i | 0.127041 | − | 0.251780i | ||||
\(53\) | −525.776 | + | 525.776i | −1.36266 | + | 1.36266i | −0.492143 | + | 0.870515i | \(0.663786\pi\) |
−0.870515 | + | 0.492143i | \(0.836214\pi\) | |||||||
\(54\) | −404.411 | + | 64.8694i | −1.01914 | + | 0.163474i | ||||
\(55\) | − | 315.973i | − | 0.774650i | ||||||
\(56\) | −35.3436 | − | 11.2533i | −0.0843390 | − | 0.0268534i | ||||
\(57\) | − | 846.894i | − | 1.96796i | ||||||
\(58\) | 114.727 | + | 715.232i | 0.259730 | + | 1.61922i | ||||
\(59\) | 46.5301 | − | 46.5301i | 0.102673 | − | 0.102673i | −0.653904 | − | 0.756577i | \(-0.726870\pi\) |
0.756577 | + | 0.653904i | \(0.226870\pi\) | |||||||
\(60\) | −259.091 | − | 786.839i | −0.557476 | − | 1.69301i | ||||
\(61\) | 193.318 | + | 193.318i | 0.405767 | + | 0.405767i | 0.880259 | − | 0.474493i | \(-0.157368\pi\) |
−0.474493 | + | 0.880259i | \(0.657368\pi\) | |||||||
\(62\) | −304.047 | − | 219.990i | −0.622807 | − | 0.450624i | ||||
\(63\) | 72.3982 | 0.144783 | ||||||||
\(64\) | −417.745 | − | 296.029i | −0.815908 | − | 0.578181i | ||||
\(65\) | −162.256 | −0.309622 | ||||||||
\(66\) | 497.615 | + | 360.043i | 0.928063 | + | 0.671488i | ||||
\(67\) | 282.182 | + | 282.182i | 0.514538 | + | 0.514538i | 0.915914 | − | 0.401375i | \(-0.131468\pi\) |
−0.401375 | + | 0.915914i | \(0.631468\pi\) | |||||||
\(68\) | 134.141 | + | 407.374i | 0.239220 | + | 0.726490i | ||||
\(69\) | 149.838 | − | 149.838i | 0.261425 | − | 0.261425i | ||||
\(70\) | 9.01370 | + | 56.1935i | 0.0153906 | + | 0.0959488i | ||||
\(71\) | − | 727.536i | − | 1.21609i | −0.793901 | − | 0.608046i | \(-0.791953\pi\) | ||
0.793901 | − | 0.608046i | \(-0.208047\pi\) | |||||||
\(72\) | 952.250 | + | 303.195i | 1.55866 | + | 0.496275i | ||||
\(73\) | 106.065i | 0.170054i | 0.996379 | + | 0.0850270i | \(0.0270977\pi\) | ||||
−0.996379 | + | 0.0850270i | \(0.972902\pi\) | |||||||
\(74\) | −690.659 | + | 110.785i | −1.08497 | + | 0.174034i | ||||
\(75\) | −153.128 | + | 153.128i | −0.235757 | + | 0.235757i | ||||
\(76\) | −361.789 | + | 717.022i | −0.546054 | + | 1.08221i | ||||
\(77\) | −29.8376 | − | 29.8376i | −0.0441599 | − | 0.0441599i | ||||
\(78\) | 184.887 | − | 255.532i | 0.268389 | − | 0.370940i | ||||
\(79\) | −58.9970 | −0.0840213 | −0.0420107 | − | 0.999117i | \(-0.513376\pi\) | ||||
−0.0420107 | + | 0.999117i | \(0.513376\pi\) | |||||||
\(80\) | −116.775 | + | 776.859i | −0.163198 | + | 1.08569i | ||||
\(81\) | −29.1298 | −0.0399586 | ||||||||
\(82\) | 329.378 | − | 455.233i | 0.443582 | − | 0.613075i | ||||
\(83\) | −410.156 | − | 410.156i | −0.542416 | − | 0.542416i | 0.381821 | − | 0.924236i | \(-0.375297\pi\) |
−0.924236 | + | 0.381821i | \(0.875297\pi\) | |||||||
\(84\) | −98.7682 | − | 49.8357i | −0.128292 | − | 0.0647324i | ||||
\(85\) | 465.324 | − | 465.324i | 0.593783 | − | 0.593783i | ||||
\(86\) | 1128.44 | − | 181.007i | 1.41492 | − | 0.226959i | ||||
\(87\) | 2160.50i | 2.66241i | ||||||||
\(88\) | −267.497 | − | 517.409i | −0.324037 | − | 0.626772i | ||||
\(89\) | 768.959i | 0.915837i | 0.888994 | + | 0.457918i | \(0.151405\pi\) | ||||
−0.888994 | + | 0.457918i | \(0.848595\pi\) | |||||||
\(90\) | −242.853 | − | 1514.00i | −0.284433 | − | 1.77322i | ||||
\(91\) | −15.3220 | + | 15.3220i | −0.0176504 | + | 0.0176504i | ||||
\(92\) | −190.870 | + | 62.8500i | −0.216300 | + | 0.0712235i | ||||
\(93\) | −791.477 | − | 791.477i | −0.882499 | − | 0.882499i | ||||
\(94\) | −179.570 | − | 129.925i | −0.197034 | − | 0.142562i | ||||
\(95\) | 1232.28 | 1.33083 | ||||||||
\(96\) | −1090.39 | − | 1069.12i | −1.15924 | − | 1.13663i | ||||
\(97\) | −809.953 | −0.847817 | −0.423908 | − | 0.905705i | \(-0.639342\pi\) | ||||
−0.423908 | + | 0.905705i | \(0.639342\pi\) | |||||||
\(98\) | −779.833 | − | 564.238i | −0.803826 | − | 0.581598i | ||||
\(99\) | 803.905 | + | 803.905i | 0.816116 | + | 0.816116i | ||||
\(100\) | 195.062 | − | 64.2302i | 0.195062 | − | 0.0642302i | ||||
\(101\) | −303.189 | + | 303.189i | −0.298698 | + | 0.298698i | −0.840504 | − | 0.541806i | \(-0.817741\pi\) |
0.541806 | + | 0.840504i | \(0.317741\pi\) | |||||||
\(102\) | 202.599 | + | 1263.05i | 0.196669 | + | 1.22608i | ||||
\(103\) | − | 962.201i | − | 0.920471i | −0.887797 | − | 0.460235i | \(-0.847765\pi\) | ||
0.887797 | − | 0.460235i | \(-0.152235\pi\) | |||||||
\(104\) | −265.697 | + | 137.363i | −0.250516 | + | 0.129515i | ||||
\(105\) | 169.743i | 0.157764i | ||||||||
\(106\) | 2076.56 | − | 333.089i | 1.90277 | − | 0.305212i | ||||
\(107\) | 728.337 | − | 728.337i | 0.658046 | − | 0.658046i | −0.296871 | − | 0.954918i | \(-0.595943\pi\) |
0.954918 | + | 0.296871i | \(0.0959432\pi\) | |||||||
\(108\) | 1034.27 | + | 521.863i | 0.921504 | + | 0.464965i | ||||
\(109\) | −593.258 | − | 593.258i | −0.521319 | − | 0.521319i | 0.396651 | − | 0.917970i | \(-0.370172\pi\) |
−0.917970 | + | 0.396651i | \(0.870172\pi\) | |||||||
\(110\) | −523.882 | + | 724.057i | −0.454092 | + | 0.627601i | ||||
\(111\) | −2086.27 | −1.78396 | ||||||||
\(112\) | 62.3324 | + | 84.3867i | 0.0525880 | + | 0.0711946i | ||||
\(113\) | 351.938 | 0.292987 | 0.146493 | − | 0.989212i | \(-0.453201\pi\) | ||||
0.146493 | + | 0.989212i | \(0.453201\pi\) | |||||||
\(114\) | −1404.15 | + | 1940.67i | −1.15360 | + | 1.59439i | ||||
\(115\) | 218.022 | + | 218.022i | 0.176788 | + | 0.176788i | ||||
\(116\) | 922.955 | − | 1829.18i | 0.738743 | − | 1.46410i | ||||
\(117\) | 412.816 | − | 412.816i | 0.326195 | − | 0.326195i | ||||
\(118\) | −183.771 | + | 29.4778i | −0.143369 | + | 0.0229970i | ||||
\(119\) | − | 87.8821i | − | 0.0676986i | ||||||
\(120\) | −710.864 | + | 2232.63i | −0.540773 | + | 1.69842i | ||||
\(121\) | 668.370i | 0.502157i | ||||||||
\(122\) | −122.471 | − | 763.510i | −0.0908849 | − | 0.566598i | ||||
\(123\) | 1185.04 | − | 1185.04i | 0.868707 | − | 0.868707i | ||||
\(124\) | 331.988 | + | 1008.22i | 0.240431 | + | 0.730167i | ||||
\(125\) | 862.139 | + | 862.139i | 0.616896 | + | 0.616896i | ||||
\(126\) | −165.902 | − | 120.036i | −0.117299 | − | 0.0848703i | ||||
\(127\) | −2365.81 | −1.65301 | −0.826504 | − | 0.562931i | \(-0.809674\pi\) | ||||
−0.826504 | + | 0.562931i | \(0.809674\pi\) | |||||||
\(128\) | 466.455 | + | 1370.97i | 0.322103 | + | 0.946705i | ||||
\(129\) | 3408.67 | 2.32649 | ||||||||
\(130\) | 371.813 | + | 269.020i | 0.250847 | + | 0.181497i | ||||
\(131\) | 403.454 | + | 403.454i | 0.269083 | + | 0.269083i | 0.828731 | − | 0.559647i | \(-0.189063\pi\) |
−0.559647 | + | 0.828731i | \(0.689063\pi\) | |||||||
\(132\) | −543.343 | − | 1650.09i | −0.358272 | − | 1.08804i | ||||
\(133\) | 116.365 | − | 116.365i | 0.0758656 | − | 0.0758656i | ||||
\(134\) | −178.768 | − | 1114.48i | −0.115248 | − | 0.718483i | ||||
\(135\) | − | 1777.50i | − | 1.13320i | ||||||
\(136\) | 368.039 | − | 1155.91i | 0.232052 | − | 0.728811i | ||||
\(137\) | − | 856.850i | − | 0.534348i | −0.963648 | − | 0.267174i | \(-0.913910\pi\) | ||
0.963648 | − | 0.267174i | \(-0.0860898\pi\) | |||||||
\(138\) | −591.786 | + | 94.9252i | −0.365045 | + | 0.0585549i | ||||
\(139\) | −1689.33 | + | 1689.33i | −1.03084 | + | 1.03084i | −0.0313345 | + | 0.999509i | \(0.509976\pi\) |
−0.999509 | + | 0.0313345i | \(0.990024\pi\) | |||||||
\(140\) | 72.5137 | − | 143.713i | 0.0437752 | − | 0.0867570i | ||||
\(141\) | −467.445 | − | 467.445i | −0.279191 | − | 0.279191i | ||||
\(142\) | −1206.25 | + | 1667.16i | −0.712862 | + | 0.985246i | ||||
\(143\) | −340.269 | −0.198984 | ||||||||
\(144\) | −1679.40 | − | 2273.60i | −0.971876 | − | 1.31574i | ||||
\(145\) | −3143.64 | −1.80045 | ||||||||
\(146\) | 175.855 | − | 243.049i | 0.0996840 | − | 0.137773i | ||||
\(147\) | −2030.01 | − | 2030.01i | −1.13900 | − | 1.13900i | ||||
\(148\) | 1766.34 | + | 891.246i | 0.981028 | + | 0.495000i | ||||
\(149\) | −32.2208 | + | 32.2208i | −0.0177156 | + | 0.0177156i | −0.715909 | − | 0.698193i | \(-0.753988\pi\) |
0.698193 | + | 0.715909i | \(0.253988\pi\) | |||||||
\(150\) | 604.782 | − | 97.0099i | 0.329202 | − | 0.0528055i | ||||
\(151\) | 1077.06i | 0.580460i | 0.956957 | + | 0.290230i | \(0.0937319\pi\) | ||||
−0.956957 | + | 0.290230i | \(0.906268\pi\) | |||||||
\(152\) | 2017.87 | − | 1043.22i | 1.07678 | − | 0.556687i | ||||
\(153\) | 2367.78i | 1.25113i | ||||||||
\(154\) | 18.9027 | + | 117.844i | 0.00989107 | + | 0.0616633i | ||||
\(155\) | 1151.64 | − | 1151.64i | 0.596788 | − | 0.596788i | ||||
\(156\) | −847.343 | + | 279.014i | −0.434883 | + | 0.143199i | ||||
\(157\) | 1905.61 | + | 1905.61i | 0.968691 | + | 0.968691i | 0.999525 | − | 0.0308332i | \(-0.00981607\pi\) |
−0.0308332 | + | 0.999525i | \(0.509816\pi\) | |||||||
\(158\) | 135.193 | + | 97.8169i | 0.0680718 | + | 0.0492525i | ||||
\(159\) | 6272.64 | 3.12863 | ||||||||
\(160\) | 1555.62 | − | 1586.57i | 0.768641 | − | 0.783935i | ||||
\(161\) | 41.1761 | 0.0201561 | ||||||||
\(162\) | 66.7514 | + | 48.2971i | 0.0323734 | + | 0.0234233i | ||||
\(163\) | 709.828 | + | 709.828i | 0.341092 | + | 0.341092i | 0.856778 | − | 0.515686i | \(-0.172463\pi\) |
−0.515686 | + | 0.856778i | \(0.672463\pi\) | |||||||
\(164\) | −1509.55 | + | 497.067i | −0.718757 | + | 0.236673i | ||||
\(165\) | −1884.82 | + | 1884.82i | −0.889291 | + | 0.889291i | ||||
\(166\) | 259.842 | + | 1619.92i | 0.121492 | + | 0.757410i | ||||
\(167\) | 3460.66i | 1.60356i | 0.597623 | + | 0.801778i | \(0.296112\pi\) | ||||
−0.597623 | + | 0.801778i | \(0.703888\pi\) | |||||||
\(168\) | 143.702 | + | 277.957i | 0.0659930 | + | 0.127648i | ||||
\(169\) | − | 2022.27i | − | 0.920467i | ||||||
\(170\) | −1837.80 | + | 294.792i | −0.829136 | + | 0.132997i | ||||
\(171\) | −3135.18 | + | 3135.18i | −1.40207 | + | 1.40207i | ||||
\(172\) | −2885.95 | − | 1456.17i | −1.27937 | − | 0.645535i | ||||
\(173\) | −1303.54 | − | 1303.54i | −0.572871 | − | 0.572871i | 0.360059 | − | 0.932930i | \(-0.382757\pi\) |
−0.932930 | + | 0.360059i | \(0.882757\pi\) | |||||||
\(174\) | 3582.10 | − | 4950.81i | 1.56068 | − | 2.15701i | ||||
\(175\) | −42.0803 | −0.0181770 | ||||||||
\(176\) | −244.889 | + | 1629.16i | −0.104882 | + | 0.697742i | ||||
\(177\) | −555.117 | −0.235735 | ||||||||
\(178\) | 1274.93 | − | 1762.08i | 0.536855 | − | 0.741987i | ||||
\(179\) | −1082.35 | − | 1082.35i | −0.451947 | − | 0.451947i | 0.444054 | − | 0.896000i | \(-0.353540\pi\) |
−0.896000 | + | 0.444054i | \(0.853540\pi\) | |||||||
\(180\) | −1953.71 | + | 3872.01i | −0.809006 | + | 1.60335i | ||||
\(181\) | 2943.93 | − | 2943.93i | 1.20895 | − | 1.20895i | 0.237588 | − | 0.971366i | \(-0.423643\pi\) |
0.971366 | − | 0.237588i | \(-0.0763567\pi\) | |||||||
\(182\) | 60.5145 | − | 9.70681i | 0.0246463 | − | 0.00395339i | ||||
\(183\) | − | 2306.33i | − | 0.931633i | ||||||
\(184\) | 541.587 | + | 172.440i | 0.216991 | + | 0.0690895i | ||||
\(185\) | − | 3035.64i | − | 1.20640i | ||||||
\(186\) | 501.417 | + | 3125.95i | 0.197665 | + | 1.23229i | ||||
\(187\) | 975.837 | − | 975.837i | 0.381606 | − | 0.381606i | ||||
\(188\) | 196.072 | + | 595.453i | 0.0760637 | + | 0.230999i | ||||
\(189\) | −167.851 | − | 167.851i | −0.0645997 | − | 0.0645997i | ||||
\(190\) | −2823.78 | − | 2043.11i | −1.07820 | − | 0.780120i | ||||
\(191\) | −430.650 | −0.163145 | −0.0815726 | − | 0.996667i | \(-0.525994\pi\) | ||||
−0.0815726 | + | 0.996667i | \(0.525994\pi\) | |||||||
\(192\) | 726.053 | + | 4257.76i | 0.272908 | + | 1.60040i | ||||
\(193\) | −2266.98 | −0.845497 | −0.422749 | − | 0.906247i | \(-0.638935\pi\) | ||||
−0.422749 | + | 0.906247i | \(0.638935\pi\) | |||||||
\(194\) | 1856.02 | + | 1342.90i | 0.686879 | + | 0.496982i | ||||
\(195\) | 967.881 | + | 967.881i | 0.355443 | + | 0.355443i | ||||
\(196\) | 851.495 | + | 2585.92i | 0.310312 | + | 0.942390i | ||||
\(197\) | −1039.41 | + | 1039.41i | −0.375913 | + | 0.375913i | −0.869625 | − | 0.493712i | \(-0.835640\pi\) |
0.493712 | + | 0.869625i | \(0.335640\pi\) | |||||||
\(198\) | −509.290 | − | 3175.03i | −0.182796 | − | 1.13959i | ||||
\(199\) | − | 4989.44i | − | 1.77735i | −0.458540 | − | 0.888674i | \(-0.651627\pi\) | ||
0.458540 | − | 0.888674i | \(-0.348373\pi\) | |||||||
\(200\) | −553.481 | − | 176.227i | −0.195685 | − | 0.0623057i | ||||
\(201\) | − | 3366.51i | − | 1.18137i | ||||||
\(202\) | 1197.45 | − | 192.077i | 0.417091 | − | 0.0669033i | ||||
\(203\) | −296.857 | + | 296.857i | −0.102637 | + | 0.102637i | ||||
\(204\) | 1629.87 | − | 3230.21i | 0.559382 | − | 1.10863i | ||||
\(205\) | 1724.29 | + | 1724.29i | 0.587462 | + | 0.587462i | ||||
\(206\) | −1595.33 | + | 2204.90i | −0.539571 | + | 0.745741i | ||||
\(207\) | −1109.39 | −0.372503 | ||||||||
\(208\) | 836.596 | + | 125.754i | 0.278882 | + | 0.0419205i | ||||
\(209\) | 2584.22 | 0.855283 | ||||||||
\(210\) | 281.434 | − | 388.970i | 0.0924800 | − | 0.127817i | ||||
\(211\) | 2651.50 | + | 2651.50i | 0.865103 | + | 0.865103i | 0.991925 | − | 0.126823i | \(-0.0404779\pi\) |
−0.126823 | + | 0.991925i | \(0.540478\pi\) | |||||||
\(212\) | −5310.73 | − | 2679.65i | −1.72048 | − | 0.868108i | ||||
\(213\) | −4339.85 | + | 4339.85i | −1.39606 | + | 1.39606i | ||||
\(214\) | −2876.58 | + | 461.416i | −0.918872 | + | 0.147391i | ||||
\(215\) | 4959.80i | 1.57328i | ||||||||
\(216\) | −1504.79 | − | 2910.67i | −0.474020 | − | 0.916879i | ||||
\(217\) | − | 217.501i | − | 0.0680413i | ||||||
\(218\) | 375.841 | + | 2343.08i | 0.116767 | + | 0.727951i | ||||
\(219\) | 632.691 | − | 632.691i | 0.195220 | − | 0.195220i | ||||
\(220\) | 2400.97 | − | 790.594i | 0.735787 | − | 0.242281i | ||||
\(221\) | −501.105 | − | 501.105i | −0.152525 | − | 0.152525i | ||||
\(222\) | 4780.72 | + | 3459.03i | 1.44532 | + | 1.04574i | ||||
\(223\) | 3690.85 | 1.10833 | 0.554165 | − | 0.832407i | \(-0.313038\pi\) | ||||
0.554165 | + | 0.832407i | \(0.313038\pi\) | |||||||
\(224\) | −2.92291 | − | 296.721i | −0.000871853 | − | 0.0885066i | ||||
\(225\) | 1133.76 | 0.335928 | ||||||||
\(226\) | −806.471 | − | 583.512i | −0.237370 | − | 0.171746i | ||||
\(227\) | −1710.42 | − | 1710.42i | −0.500108 | − | 0.500108i | 0.411363 | − | 0.911471i | \(-0.365053\pi\) |
−0.911471 | + | 0.411363i | \(0.865053\pi\) | |||||||
\(228\) | 6435.25 | − | 2119.01i | 1.86923 | − | 0.615503i | ||||
\(229\) | −91.8012 | + | 91.8012i | −0.0264908 | + | 0.0264908i | −0.720228 | − | 0.693737i | \(-0.755963\pi\) |
0.693737 | + | 0.720228i | \(0.255963\pi\) | |||||||
\(230\) | −138.121 | − | 861.081i | −0.0395976 | − | 0.246861i | ||||
\(231\) | 355.971i | 0.101390i | ||||||||
\(232\) | −5147.74 | + | 2661.35i | −1.45675 | + | 0.753129i | ||||
\(233\) | 4259.71i | 1.19769i | 0.800863 | + | 0.598847i | \(0.204374\pi\) | ||||
−0.800863 | + | 0.598847i | \(0.795626\pi\) | |||||||
\(234\) | −1630.42 | + | 261.527i | −0.455487 | + | 0.0730623i | ||||
\(235\) | 680.158 | − | 680.158i | 0.188803 | − | 0.188803i | ||||
\(236\) | 469.989 | + | 237.144i | 0.129634 | + | 0.0654099i | ||||
\(237\) | 351.925 | + | 351.925i | 0.0964556 | + | 0.0964556i | ||||
\(238\) | −145.708 | + | 201.383i | −0.0396843 | + | 0.0548476i | ||||
\(239\) | −5053.12 | −1.36761 | −0.683806 | − | 0.729664i | \(-0.739676\pi\) | ||||
−0.683806 | + | 0.729664i | \(0.739676\pi\) | |||||||
\(240\) | 5330.64 | − | 3937.49i | 1.43372 | − | 1.05902i | ||||
\(241\) | 48.8379 | 0.0130536 | 0.00652681 | − | 0.999979i | \(-0.497922\pi\) | ||||
0.00652681 | + | 0.999979i | \(0.497922\pi\) | |||||||
\(242\) | 1108.16 | − | 1531.58i | 0.294359 | − | 0.406834i | ||||
\(243\) | −2590.91 | − | 2590.91i | −0.683978 | − | 0.683978i | ||||
\(244\) | −985.254 | + | 1952.65i | −0.258502 | + | 0.512319i | ||||
\(245\) | 2953.78 | − | 2953.78i | 0.770244 | − | 0.770244i | ||||
\(246\) | −4680.31 | + | 750.743i | −1.21303 | + | 0.194576i | ||||
\(247\) | − | 1327.03i | − | 0.341850i | ||||||
\(248\) | 910.868 | − | 2860.79i | 0.233227 | − | 0.732500i | ||||
\(249\) | 4893.28i | 1.24538i | ||||||||
\(250\) | −546.182 | − | 3405.03i | −0.138174 | − | 0.861412i | ||||
\(251\) | −2604.76 | + | 2604.76i | −0.655025 | + | 0.655025i | −0.954199 | − | 0.299174i | \(-0.903289\pi\) |
0.299174 | + | 0.954199i | \(0.403289\pi\) | |||||||
\(252\) | 181.147 | + | 550.129i | 0.0452826 | + | 0.137519i | ||||
\(253\) | 457.216 | + | 457.216i | 0.113616 | + | 0.113616i | ||||
\(254\) | 5421.30 | + | 3922.51i | 1.33922 | + | 0.968977i | ||||
\(255\) | −5551.44 | −1.36331 | ||||||||
\(256\) | 1204.18 | − | 3914.99i | 0.293990 | − | 0.955808i | ||||
\(257\) | 739.054 | 0.179381 | 0.0896905 | − | 0.995970i | \(-0.471412\pi\) | ||||
0.0896905 | + | 0.995970i | \(0.471412\pi\) | |||||||
\(258\) | −7811.03 | − | 5651.57i | −1.88486 | − | 1.36376i | ||||
\(259\) | −286.658 | − | 286.658i | −0.0687724 | − | 0.0687724i | ||||
\(260\) | −405.981 | − | 1232.93i | −0.0968379 | − | 0.294089i | ||||
\(261\) | 7998.12 | − | 7998.12i | 1.89682 | − | 1.89682i | ||||
\(262\) | −255.596 | − | 1593.45i | −0.0602701 | − | 0.375738i | ||||
\(263\) | − | 2448.30i | − | 0.574025i | −0.957927 | − | 0.287012i | \(-0.907338\pi\) | ||
0.957927 | − | 0.287012i | \(-0.0926621\pi\) | |||||||
\(264\) | −1490.76 | + | 4682.07i | −0.347538 | + | 1.09152i | ||||
\(265\) | 9127.03i | 2.11573i | ||||||||
\(266\) | −459.585 | + | 73.7196i | −0.105936 | + | 0.0169926i | ||||
\(267\) | 4586.94 | − | 4586.94i | 1.05137 | − | 1.05137i | ||||
\(268\) | −1438.16 | + | 2850.25i | −0.327797 | + | 0.649653i | ||||
\(269\) | −829.952 | − | 829.952i | −0.188116 | − | 0.188116i | 0.606765 | − | 0.794881i | \(-0.292467\pi\) |
−0.794881 | + | 0.606765i | \(0.792467\pi\) | |||||||
\(270\) | −2947.08 | + | 4073.16i | −0.664273 | + | 0.918091i | ||||
\(271\) | 1404.85 | 0.314902 | 0.157451 | − | 0.987527i | \(-0.449672\pi\) | ||||
0.157451 | + | 0.987527i | \(0.449672\pi\) | |||||||
\(272\) | −2759.86 | + | 2038.58i | −0.615225 | + | 0.454437i | ||||
\(273\) | 182.796 | 0.0405249 | ||||||||
\(274\) | −1420.65 | + | 1963.49i | −0.313229 | + | 0.432914i | ||||
\(275\) | −467.257 | − | 467.257i | −0.102461 | − | 0.102461i | ||||
\(276\) | 1513.47 | + | 763.657i | 0.330074 | + | 0.166546i | ||||
\(277\) | −2245.69 | + | 2245.69i | −0.487112 | + | 0.487112i | −0.907394 | − | 0.420281i | \(-0.861931\pi\) |
0.420281 | + | 0.907394i | \(0.361931\pi\) | |||||||
\(278\) | 6672.04 | − | 1070.23i | 1.43943 | − | 0.230892i | ||||
\(279\) | 5860.07i | 1.25747i | ||||||||
\(280\) | −404.442 | + | 209.094i | −0.0863216 | + | 0.0446276i | ||||
\(281\) | − | 6045.97i | − | 1.28353i | −0.766900 | − | 0.641766i | \(-0.778202\pi\) | ||
0.766900 | − | 0.641766i | \(-0.221798\pi\) | |||||||
\(282\) | 296.136 | + | 1846.18i | 0.0625342 | + | 0.389853i | ||||
\(283\) | 2459.63 | − | 2459.63i | 0.516643 | − | 0.516643i | −0.399911 | − | 0.916554i | \(-0.630959\pi\) |
0.916554 | + | 0.399911i | \(0.130959\pi\) | |||||||
\(284\) | 5528.29 | − | 1820.36i | 1.15508 | − | 0.380347i | ||||
\(285\) | −7350.69 | − | 7350.69i | −1.52778 | − | 1.52778i | ||||
\(286\) | 779.733 | + | 564.165i | 0.161212 | + | 0.116643i | ||||
\(287\) | 325.653 | 0.0669780 | ||||||||
\(288\) | 78.7509 | + | 7994.44i | 0.0161126 | + | 1.63568i | ||||
\(289\) | −2038.82 | −0.414986 | ||||||||
\(290\) | 7203.70 | + | 5212.14i | 1.45868 | + | 1.05541i | ||||
\(291\) | 4831.48 | + | 4831.48i | 0.973286 | + | 0.973286i | ||||
\(292\) | −805.950 | + | 265.384i | −0.161523 | + | 0.0531864i | ||||
\(293\) | −1852.49 | + | 1852.49i | −0.369364 | + | 0.369364i | −0.867245 | − | 0.497881i | \(-0.834112\pi\) |
0.497881 | + | 0.867245i | \(0.334112\pi\) | |||||||
\(294\) | 1286.05 | + | 8017.56i | 0.255116 | + | 1.59045i | ||||
\(295\) | − | 807.725i | − | 0.159415i | ||||||
\(296\) | −2569.91 | − | 4970.89i | −0.504639 | − | 0.976105i | ||||
\(297\) | − | 3727.60i | − | 0.728275i | ||||||
\(298\) | 127.256 | − | 20.4125i | 0.0247375 | − | 0.00396801i | ||||
\(299\) | 234.787 | − | 234.787i | 0.0454116 | − | 0.0454116i | ||||
\(300\) | −1546.71 | − | 780.427i | −0.297665 | − | 0.150193i | ||||
\(301\) | 468.359 | + | 468.359i | 0.0896870 | + | 0.0896870i | ||||
\(302\) | 1785.75 | − | 2468.09i | 0.340260 | − | 0.470274i | ||||
\(303\) | 3617.13 | 0.685804 | ||||||||
\(304\) | −6353.63 | − | 955.055i | −1.19870 | − | 0.180185i | ||||
\(305\) | 3355.83 | 0.630015 | ||||||||
\(306\) | 3925.77 | − | 5425.80i | 0.733402 | − | 1.01364i | ||||
\(307\) | 2107.35 | + | 2107.35i | 0.391768 | + | 0.391768i | 0.875317 | − | 0.483549i | \(-0.160653\pi\) |
−0.483549 | + | 0.875317i | \(0.660653\pi\) | |||||||
\(308\) | 152.069 | − | 301.382i | 0.0281329 | − | 0.0557560i | ||||
\(309\) | −5739.66 | + | 5739.66i | −1.05669 | + | 1.05669i | ||||
\(310\) | −4548.43 | + | 729.588i | −0.833333 | + | 0.133670i | ||||
\(311\) | − | 5294.90i | − | 0.965422i | −0.875780 | − | 0.482711i | \(-0.839652\pi\) | ||
0.875780 | − | 0.482711i | \(-0.160348\pi\) | |||||||
\(312\) | 2404.30 | + | 765.526i | 0.436272 | + | 0.138908i | ||||
\(313\) | − | 4005.87i | − | 0.723403i | −0.932294 | − | 0.361702i | \(-0.882196\pi\) | ||
0.932294 | − | 0.361702i | \(-0.117804\pi\) | |||||||
\(314\) | −1207.24 | − | 7526.25i | −0.216971 | − | 1.35265i | ||||
\(315\) | 628.387 | − | 628.387i | 0.112399 | − | 0.112399i | ||||
\(316\) | −147.616 | − | 448.298i | −0.0262787 | − | 0.0798061i | ||||
\(317\) | 809.240 | + | 809.240i | 0.143380 | + | 0.143380i | 0.775153 | − | 0.631773i | \(-0.217673\pi\) |
−0.631773 | + | 0.775153i | \(0.717673\pi\) | |||||||
\(318\) | −14373.9 | − | 10400.0i | −2.53474 | − | 1.83398i | ||||
\(319\) | −6592.56 | −1.15709 | ||||||||
\(320\) | −6195.27 | + | 1056.45i | −1.08227 | + | 0.184554i | ||||
\(321\) | −8689.25 | −1.51086 | ||||||||
\(322\) | −94.3557 | − | 68.2698i | −0.0163299 | − | 0.0118153i | ||||
\(323\) | 3805.71 | + | 3805.71i | 0.655589 | + | 0.655589i | ||||
\(324\) | −72.8856 | − | 221.347i | −0.0124975 | − | 0.0379539i | ||||
\(325\) | −239.943 | + | 239.943i | −0.0409527 | + | 0.0409527i | ||||
\(326\) | −449.690 | − | 2803.47i | −0.0763989 | − | 0.476289i | ||||
\(327\) | 7077.72i | 1.19694i | ||||||||
\(328\) | 4283.30 | + | 1363.79i | 0.721053 | + | 0.229582i | ||||
\(329\) | − | 128.456i | − | 0.0215259i | ||||||
\(330\) | 7444.12 | − | 1194.07i | 1.24177 | − | 0.199186i | ||||
\(331\) | −4229.66 | + | 4229.66i | −0.702366 | + | 0.702366i | −0.964918 | − | 0.262552i | \(-0.915436\pi\) |
0.262552 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(332\) | 2090.39 | − | 4142.89i | 0.345557 | − | 0.684851i | ||||
\(333\) | 7723.33 | + | 7723.33i | 1.27098 | + | 1.27098i | ||||
\(334\) | 5737.76 | − | 7930.15i | 0.939988 | − | 1.29916i | ||||
\(335\) | 4898.46 | 0.798899 | ||||||||
\(336\) | 131.557 | − | 875.199i | 0.0213601 | − | 0.142101i | ||||
\(337\) | 10002.6 | 1.61684 | 0.808419 | − | 0.588607i | \(-0.200323\pi\) | ||||
0.808419 | + | 0.588607i | \(0.200323\pi\) | |||||||
\(338\) | −3352.91 | + | 4634.06i | −0.539569 | + | 0.745738i | ||||
\(339\) | −2099.36 | − | 2099.36i | −0.336346 | − | 0.336346i | ||||
\(340\) | 4700.12 | + | 2371.55i | 0.749706 | + | 0.378281i | ||||
\(341\) | 2415.12 | − | 2415.12i | 0.383537 | − | 0.383537i | ||||
\(342\) | 12382.5 | − | 1986.20i | 1.95780 | − | 0.314039i | ||||
\(343\) | − | 1120.12i | − | 0.176328i | ||||||
\(344\) | 4198.88 | + | 8121.74i | 0.658106 | + | 1.27295i | ||||
\(345\) | − | 2601.06i | − | 0.405903i | ||||||
\(346\) | 825.821 | + | 5148.37i | 0.128313 | + | 0.799936i | ||||
\(347\) | −6409.49 | + | 6409.49i | −0.991583 | + | 0.991583i | −0.999965 | − | 0.00838198i | \(-0.997332\pi\) |
0.00838198 | + | 0.999965i | \(0.497332\pi\) | |||||||
\(348\) | −16416.9 | + | 5405.77i | −2.52884 | + | 0.832700i | ||||
\(349\) | −5503.23 | − | 5503.23i | −0.844071 | − | 0.844071i | 0.145314 | − | 0.989386i | \(-0.453581\pi\) |
−0.989386 | + | 0.145314i | \(0.953581\pi\) | |||||||
\(350\) | 96.4278 | + | 69.7691i | 0.0147265 | + | 0.0106552i | ||||
\(351\) | −1914.18 | −0.291086 | ||||||||
\(352\) | 3262.31 | − | 3327.22i | 0.493982 | − | 0.503811i | ||||
\(353\) | −1411.35 | −0.212800 | −0.106400 | − | 0.994323i | \(-0.533932\pi\) | ||||
−0.106400 | + | 0.994323i | \(0.533932\pi\) | |||||||
\(354\) | 1272.06 | + | 920.382i | 0.190986 | + | 0.138186i | ||||
\(355\) | −6314.71 | − | 6314.71i | −0.944085 | − | 0.944085i | ||||
\(356\) | −5843.05 | + | 1924.01i | −0.869891 | + | 0.286439i | ||||
\(357\) | −524.228 | + | 524.228i | −0.0777174 | + | 0.0777174i | ||||
\(358\) | 685.689 | + | 4274.75i | 0.101228 | + | 0.631082i | ||||
\(359\) | 2160.73i | 0.317658i | 0.987306 | + | 0.158829i | \(0.0507718\pi\) | ||||
−0.987306 | + | 0.158829i | \(0.949228\pi\) | |||||||
\(360\) | 10896.7 | − | 5633.54i | 1.59530 | − | 0.824760i | ||||
\(361\) | 3219.31i | 0.469355i | ||||||||
\(362\) | −11627.1 | + | 1865.04i | −1.68814 | + | 0.270785i | ||||
\(363\) | 3986.92 | − | 3986.92i | 0.576471 | − | 0.576471i | ||||
\(364\) | −154.764 | − | 78.0896i | −0.0222853 | − | 0.0112445i | ||||
\(365\) | 920.599 | + | 920.599i | 0.132017 | + | 0.132017i | ||||
\(366\) | −3823.89 | + | 5284.99i | −0.546114 | + | 0.754784i | ||||
\(367\) | 10757.7 | 1.53010 | 0.765052 | − | 0.643969i | \(-0.222713\pi\) | ||||
0.765052 | + | 0.643969i | \(0.222713\pi\) | |||||||
\(368\) | −955.150 | − | 1293.10i | −0.135301 | − | 0.183172i | ||||
\(369\) | −8773.95 | −1.23782 | ||||||||
\(370\) | −5033.07 | + | 6956.21i | −0.707181 | + | 0.977395i | ||||
\(371\) | 861.875 | + | 861.875i | 0.120610 | + | 0.120610i | ||||
\(372\) | 4033.81 | − | 7994.51i | 0.562213 | − | 1.11424i | ||||
\(373\) | 1406.99 | − | 1406.99i | 0.195312 | − | 0.195312i | −0.602675 | − | 0.797987i | \(-0.705898\pi\) |
0.797987 | + | 0.602675i | \(0.205898\pi\) | |||||||
\(374\) | −3854.08 | + | 618.212i | −0.532860 | + | 0.0854732i | ||||
\(375\) | − | 10285.5i | − | 1.41638i | ||||||
\(376\) | 537.957 | − | 1689.58i | 0.0737847 | − | 0.231737i | ||||
\(377\) | 3385.37i | 0.462481i | ||||||||
\(378\) | 106.337 | + | 662.928i | 0.0144692 | + | 0.0902046i | ||||
\(379\) | −1146.95 | + | 1146.95i | −0.155449 | + | 0.155449i | −0.780547 | − | 0.625098i | \(-0.785059\pi\) |
0.625098 | + | 0.780547i | \(0.285059\pi\) | |||||||
\(380\) | 3083.27 | + | 9363.64i | 0.416233 | + | 1.26406i | ||||
\(381\) | 14112.4 | + | 14112.4i | 1.89764 | + | 1.89764i | ||||
\(382\) | 986.842 | + | 714.016i | 0.132176 | + | 0.0956342i | ||||
\(383\) | 9042.17 | 1.20635 | 0.603176 | − | 0.797608i | \(-0.293902\pi\) | ||||
0.603176 | + | 0.797608i | \(0.293902\pi\) | |||||||
\(384\) | 5395.58 | − | 10960.5i | 0.717037 | − | 1.45658i | ||||
\(385\) | −517.957 | −0.0685650 | ||||||||
\(386\) | 5194.83 | + | 3758.65i | 0.684999 | + | 0.495622i | ||||
\(387\) | −12618.8 | − | 12618.8i | −1.65750 | − | 1.65750i | ||||
\(388\) | −2026.58 | − | 6154.55i | −0.265165 | − | 0.805283i | ||||
\(389\) | 2575.34 | − | 2575.34i | 0.335668 | − | 0.335668i | −0.519066 | − | 0.854734i | \(-0.673720\pi\) |
0.854734 | + | 0.519066i | \(0.173720\pi\) | |||||||
\(390\) | −613.172 | − | 3822.66i | −0.0796132 | − | 0.496328i | ||||
\(391\) | 1346.66i | 0.174178i | ||||||||
\(392\) | 2336.23 | − | 7337.45i | 0.301014 | − | 0.945401i | ||||
\(393\) | − | 4813.31i | − | 0.617810i | ||||||
\(394\) | 4105.16 | − | 658.486i | 0.524911 | − | 0.0841981i | ||||
\(395\) | −512.070 | + | 512.070i | −0.0652279 | + | 0.0652279i | ||||
\(396\) | −4097.15 | + | 8120.04i | −0.519923 | + | 1.03042i | ||||
\(397\) | −7121.46 | − | 7121.46i | −0.900292 | − | 0.900292i | 0.0951695 | − | 0.995461i | \(-0.469661\pi\) |
−0.995461 | + | 0.0951695i | \(0.969661\pi\) | |||||||
\(398\) | −8272.48 | + | 11433.4i | −1.04186 | + | 1.43996i | ||||
\(399\) | −1388.27 | −0.174186 | ||||||||
\(400\) | 976.126 | + | 1321.50i | 0.122016 | + | 0.165187i | ||||
\(401\) | −3025.14 | −0.376729 | −0.188365 | − | 0.982099i | \(-0.560319\pi\) | ||||
−0.188365 | + | 0.982099i | \(0.560319\pi\) | |||||||
\(402\) | −5581.66 | + | 7714.42i | −0.692508 | + | 0.957115i | ||||
\(403\) | −1240.20 | − | 1240.20i | −0.153297 | − | 0.153297i | ||||
\(404\) | −3062.44 | − | 1545.22i | −0.377134 | − | 0.190291i | ||||
\(405\) | −252.835 | + | 252.835i | −0.0310209 | + | 0.0310209i | ||||
\(406\) | 1172.44 | − | 188.065i | 0.143318 | − | 0.0229889i | ||||
\(407\) | − | 6366.06i | − | 0.775317i | ||||||
\(408\) | −9090.55 | + | 4699.75i | −1.10306 | + | 0.570275i | ||||
\(409\) | − | 9440.21i | − | 1.14129i | −0.821196 | − | 0.570646i | \(-0.806693\pi\) | ||
0.821196 | − | 0.570646i | \(-0.193307\pi\) | |||||||
\(410\) | −1092.37 | − | 6810.11i | −0.131581 | − | 0.820310i | ||||
\(411\) | −5111.22 | + | 5111.22i | −0.613426 | + | 0.613426i | ||||
\(412\) | 7311.43 | − | 2407.52i | 0.874292 | − | 0.287888i | ||||
\(413\) | −76.2743 | − | 76.2743i | −0.00908768 | − | 0.00908768i | ||||
\(414\) | 2542.19 | + | 1839.37i | 0.301792 | + | 0.218358i | ||||
\(415\) | −7119.98 | −0.842183 | ||||||||
\(416\) | −1708.57 | − | 1675.24i | −0.201369 | − | 0.197441i | ||||
\(417\) | 20154.2 | 2.36680 | ||||||||
\(418\) | −5921.78 | − | 4284.63i | −0.692928 | − | 0.501359i | ||||
\(419\) | −3255.69 | − | 3255.69i | −0.379597 | − | 0.379597i | 0.491360 | − | 0.870957i | \(-0.336500\pi\) |
−0.870957 | + | 0.491360i | \(0.836500\pi\) | |||||||
\(420\) | −1289.82 | + | 424.714i | −0.149850 | + | 0.0493427i | ||||
\(421\) | −9438.04 | + | 9438.04i | −1.09259 | + | 1.09259i | −0.0973423 | + | 0.995251i | \(0.531034\pi\) |
−0.995251 | + | 0.0973423i | \(0.968966\pi\) | |||||||
\(422\) | −1679.78 | − | 10472.1i | −0.193768 | − | 1.20800i | ||||
\(423\) | 3460.95i | 0.397818i | ||||||||
\(424\) | 7726.77 | + | 14945.6i | 0.885013 | + | 1.71185i | ||||
\(425\) | − | 1376.23i | − | 0.157076i | ||||||
\(426\) | 17140.3 | − | 2749.38i | 1.94941 | − | 0.312694i | ||||
\(427\) | 316.895 | − | 316.895i | 0.0359148 | − | 0.0359148i | ||||
\(428\) | 7356.75 | + | 3712.01i | 0.830845 | + | 0.419221i | ||||
\(429\) | 2029.75 | + | 2029.75i | 0.228432 | + | 0.228432i | ||||
\(430\) | 8223.34 | − | 11365.5i | 0.922243 | − | 1.27463i | ||||
\(431\) | −10617.7 | −1.18663 | −0.593314 | − | 0.804971i | \(-0.702181\pi\) | ||||
−0.593314 | + | 0.804971i | \(0.702181\pi\) | |||||||
\(432\) | −1377.62 | + | 9164.79i | −0.153427 | + | 1.02070i | ||||
\(433\) | 706.479 | 0.0784093 | 0.0392046 | − | 0.999231i | \(-0.487518\pi\) | ||||
0.0392046 | + | 0.999231i | \(0.487518\pi\) | |||||||
\(434\) | −360.617 | + | 498.408i | −0.0398851 | + | 0.0551252i | ||||
\(435\) | 18752.2 | + | 18752.2i | 2.06690 | + | 2.06690i | ||||
\(436\) | 3023.57 | − | 5992.35i | 0.332117 | − | 0.658214i | ||||
\(437\) | −1783.12 | + | 1783.12i | −0.195190 | + | 0.195190i | ||||
\(438\) | −2498.82 | + | 400.822i | −0.272599 | + | 0.0437261i | ||||
\(439\) | 13611.8i | 1.47985i | 0.672688 | + | 0.739926i | \(0.265140\pi\) | ||||
−0.672688 | + | 0.739926i | \(0.734860\pi\) | |||||||
\(440\) | −6812.66 | − | 2169.14i | −0.738138 | − | 0.235022i | ||||
\(441\) | 15030.1i | 1.62295i | ||||||||
\(442\) | 317.460 | + | 1979.12i | 0.0341630 | + | 0.212980i | ||||
\(443\) | 3126.97 | − | 3126.97i | 0.335366 | − | 0.335366i | −0.519254 | − | 0.854620i | \(-0.673790\pi\) |
0.854620 | + | 0.519254i | \(0.173790\pi\) | |||||||
\(444\) | −5220.05 | − | 15852.8i | −0.557956 | − | 1.69447i | ||||
\(445\) | 6674.25 | + | 6674.25i | 0.710988 | + | 0.710988i | ||||
\(446\) | −8457.64 | − | 6119.42i | −0.897939 | − | 0.649692i | ||||
\(447\) | 384.403 | 0.0406748 | ||||||||
\(448\) | −485.264 | + | 684.786i | −0.0511753 | + | 0.0722167i | ||||
\(449\) | −5231.76 | −0.549893 | −0.274947 | − | 0.961460i | \(-0.588660\pi\) | ||||
−0.274947 | + | 0.961460i | \(0.588660\pi\) | |||||||
\(450\) | −2598.02 | − | 1879.76i | −0.272160 | − | 0.196918i | ||||
\(451\) | 3616.03 | + | 3616.03i | 0.377543 | + | 0.377543i | ||||
\(452\) | 880.582 | + | 2674.25i | 0.0916352 | + | 0.278288i | ||||
\(453\) | 6424.78 | − | 6424.78i | 0.666363 | − | 0.666363i | ||||
\(454\) | 1083.58 | + | 6755.32i | 0.112016 | + | 0.698333i | ||||
\(455\) | 265.978i | 0.0274049i | ||||||||
\(456\) | −18259.8 | − | 5813.88i | −1.87520 | − | 0.597061i | ||||
\(457\) | − | 6833.10i | − | 0.699429i | −0.936856 | − | 0.349715i | \(-0.886279\pi\) | ||
0.936856 | − | 0.349715i | \(-0.113721\pi\) | |||||||
\(458\) | 362.570 | − | 58.1579i | 0.0369908 | − | 0.00593350i | ||||
\(459\) | 5489.54 | − | 5489.54i | 0.558235 | − | 0.558235i | ||||
\(460\) | −1111.16 | + | 2202.19i | −0.112627 | + | 0.223212i | ||||
\(461\) | −5975.90 | − | 5975.90i | −0.603742 | − | 0.603742i | 0.337561 | − | 0.941304i | \(-0.390398\pi\) |
−0.941304 | + | 0.337561i | \(0.890398\pi\) | |||||||
\(462\) | 590.198 | − | 815.713i | 0.0594340 | − | 0.0821437i | ||||
\(463\) | −4273.38 | −0.428943 | −0.214472 | − | 0.976730i | \(-0.568803\pi\) | ||||
−0.214472 | + | 0.976730i | \(0.568803\pi\) | |||||||
\(464\) | 16208.6 | + | 2436.42i | 1.62170 | + | 0.243768i | ||||
\(465\) | −13739.4 | −1.37021 | ||||||||
\(466\) | 7062.59 | − | 9761.20i | 0.702077 | − | 0.970341i | ||||
\(467\) | 12245.6 | + | 12245.6i | 1.21340 | + | 1.21340i | 0.969901 | + | 0.243500i | \(0.0782956\pi\) |
0.243500 | + | 0.969901i | \(0.421704\pi\) | |||||||
\(468\) | 4169.75 | + | 2103.94i | 0.411852 | + | 0.207809i | ||||
\(469\) | 462.566 | − | 462.566i | 0.0455422 | − | 0.0455422i | ||||
\(470\) | −2686.29 | + | 430.894i | −0.263637 | + | 0.0422886i | ||||
\(471\) | − | 22734.5i | − | 2.22410i | ||||||
\(472\) | −683.805 | − | 1322.66i | −0.0666836 | − | 0.128984i | ||||
\(473\) | 10401.3i | 1.01110i | ||||||||
\(474\) | −222.952 | − | 1389.93i | −0.0216044 | − | 0.134687i | ||||
\(475\) | 1822.28 | − | 1822.28i | 0.176025 | − | 0.176025i | ||||
\(476\) | 667.785 | − | 219.889i | 0.0643023 | − | 0.0211736i | ||||
\(477\) | −23221.2 | − | 23221.2i | −2.22898 | − | 2.22898i | ||||
\(478\) | 11579.3 | + | 8378.05i | 1.10800 | + | 0.801681i | ||||
\(479\) | −4067.97 | −0.388038 | −0.194019 | − | 0.980998i | \(-0.562152\pi\) | ||||
−0.194019 | + | 0.980998i | \(0.562152\pi\) | |||||||
\(480\) | −18743.6 | + | 184.638i | −1.78234 | + | 0.0175573i | ||||
\(481\) | −3269.06 | −0.309888 | ||||||||
\(482\) | −111.913 | − | 80.9730i | −0.0105757 | − | 0.00765191i | ||||
\(483\) | −245.621 | − | 245.621i | −0.0231390 | − | 0.0231390i | ||||
\(484\) | −5078.71 | + | 1672.33i | −0.476964 | + | 0.157055i | ||||
\(485\) | −7030.06 | + | 7030.06i | −0.658182 | + | 0.658182i | ||||
\(486\) | 1641.39 | + | 10232.8i | 0.153200 | + | 0.955082i | ||||
\(487\) | 16174.3i | 1.50499i | 0.658600 | + | 0.752493i | \(0.271149\pi\) | ||||
−0.658600 | + | 0.752493i | \(0.728851\pi\) | |||||||
\(488\) | 5495.22 | − | 2840.99i | 0.509747 | − | 0.263536i | ||||
\(489\) | − | 8468.44i | − | 0.783141i | ||||||
\(490\) | −11666.0 | + | 1871.28i | −1.07554 | + | 0.172522i | ||||
\(491\) | 13596.7 | − | 13596.7i | 1.24971 | − | 1.24971i | 0.293866 | − | 0.955847i | \(-0.405058\pi\) |
0.955847 | − | 0.293866i | \(-0.0949420\pi\) | |||||||
\(492\) | 11969.7 | + | 6039.60i | 1.09682 | + | 0.553427i | ||||
\(493\) | −9708.68 | − | 9708.68i | −0.886931 | − | 0.886931i | ||||
\(494\) | −2200.21 | + | 3040.91i | −0.200389 | + | 0.276958i | ||||
\(495\) | 13955.1 | 1.26714 | ||||||||
\(496\) | −6830.44 | + | 5045.32i | −0.618338 | + | 0.456737i | ||||
\(497\) | −1192.61 | −0.107637 | ||||||||
\(498\) | 8113.03 | − | 11213.0i | 0.730028 | − | 1.00897i | ||||
\(499\) | −14646.7 | − | 14646.7i | −1.31398 | − | 1.31398i | −0.918453 | − | 0.395530i | \(-0.870561\pi\) |
−0.395530 | − | 0.918453i | \(-0.629439\pi\) | |||||||
\(500\) | −4393.94 | + | 8708.25i | −0.393006 | + | 0.778889i | ||||
\(501\) | 20643.3 | − | 20643.3i | 1.84087 | − | 1.84087i | ||||
\(502\) | 10287.5 | − | 1650.17i | 0.914652 | − | 0.146714i | ||||
\(503\) | 9828.84i | 0.871265i | 0.900125 | + | 0.435632i | \(0.143475\pi\) | ||||
−0.900125 | + | 0.435632i | \(0.856525\pi\) | |||||||
\(504\) | 497.010 | − | 1560.97i | 0.0439258 | − | 0.137959i | ||||
\(505\) | 5263.12i | 0.463774i | ||||||||
\(506\) | −289.656 | − | 1805.78i | −0.0254482 | − | 0.158650i | ||||
\(507\) | −12063.1 | + | 12063.1i | −1.05669 | + | 1.05669i | ||||
\(508\) | −5919.49 | − | 17977.0i | −0.516998 | − | 1.57008i | ||||
\(509\) | 13456.1 | + | 13456.1i | 1.17177 | + | 1.17177i | 0.981787 | + | 0.189985i | \(0.0608439\pi\) |
0.189985 | + | 0.981787i | \(0.439156\pi\) | |||||||
\(510\) | 12721.2 | + | 9204.27i | 1.10452 | + | 0.799161i | ||||
\(511\) | 173.866 | 0.0150516 | ||||||||
\(512\) | −9250.45 | + | 6974.74i | −0.798469 | + | 0.602037i | ||||
\(513\) | 14537.5 | 1.25116 | ||||||||
\(514\) | −1693.55 | − | 1225.35i | −0.145330 | − | 0.105151i | ||||
\(515\) | −8351.51 | − | 8351.51i | −0.714585 | − | 0.714585i | ||||
\(516\) | 8528.83 | + | 25901.3i | 0.727637 | + | 2.20977i | ||||
\(517\) | 1426.37 | − | 1426.37i | 0.121338 | − | 0.121338i | ||||
\(518\) | 181.604 | + | 1132.16i | 0.0154039 | + | 0.0960313i | ||||
\(519\) | 15551.6i | 1.31530i | ||||||||
\(520\) | −1113.88 | + | 3498.39i | −0.0939364 | + | 0.295028i | ||||
\(521\) | 10607.1i | 0.891950i | 0.895045 | + | 0.445975i | \(0.147143\pi\) | ||||
−0.895045 | + | 0.445975i | \(0.852857\pi\) | |||||||
\(522\) | −31588.7 | + | 5066.97i | −2.64866 | + | 0.424857i | ||||
\(523\) | 3903.15 | − | 3903.15i | 0.326334 | − | 0.326334i | −0.524857 | − | 0.851191i | \(-0.675881\pi\) |
0.851191 | + | 0.524857i | \(0.175881\pi\) | |||||||
\(524\) | −2056.22 | + | 4075.18i | −0.171425 | + | 0.339743i | ||||
\(525\) | 251.015 | + | 251.015i | 0.0208670 | + | 0.0208670i | ||||
\(526\) | −4059.27 | + | 5610.32i | −0.336488 | + | 0.465060i | ||||
\(527\) | 7113.36 | 0.587975 | ||||||||
\(528\) | 11178.9 | − | 8257.35i | 0.921404 | − | 0.680597i | ||||
\(529\) | 11536.0 | 0.948142 | ||||||||
\(530\) | 15132.6 | − | 20914.7i | 1.24022 | − | 1.71411i | ||||
\(531\) | 2055.03 | + | 2055.03i | 0.167949 | + | 0.167949i | ||||
\(532\) | 1175.37 | + | 593.061i | 0.0957874 | + | 0.0483317i | ||||
\(533\) | 1856.88 | − | 1856.88i | 0.150901 | − | 0.150901i | ||||
\(534\) | −18116.2 | + | 2905.92i | −1.46810 | + | 0.235489i | ||||
\(535\) | − | 12643.3i | − | 1.02172i | ||||||
\(536\) | 8021.28 | − | 4146.94i | 0.646392 | − | 0.334180i | ||||
\(537\) | 12912.7i | 1.03766i | ||||||||
\(538\) | 525.791 | + | 3277.91i | 0.0421347 | + | 0.262678i | ||||
\(539\) | 6194.39 | − | 6194.39i | 0.495012 | − | 0.495012i | ||||
\(540\) | 13506.6 | − | 4447.46i | 1.07635 | − | 0.354423i | ||||
\(541\) | 9532.77 | + | 9532.77i | 0.757570 | + | 0.757570i | 0.975880 | − | 0.218309i | \(-0.0700541\pi\) |
−0.218309 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(542\) | −3219.23 | − | 2329.23i | −0.255125 | − | 0.184592i | ||||
\(543\) | −35121.9 | −2.77573 | ||||||||
\(544\) | 9704.22 | − | 95.5934i | 0.764825 | − | 0.00753407i | ||||
\(545\) | −10298.5 | −0.809427 | ||||||||
\(546\) | −418.880 | − | 303.075i | −0.0328322 | − | 0.0237553i | ||||
\(547\) | −1232.88 | − | 1232.88i | −0.0963693 | − | 0.0963693i | 0.657278 | − | 0.753648i | \(-0.271708\pi\) |
−0.753648 | + | 0.657278i | \(0.771708\pi\) | |||||||
\(548\) | 6510.90 | − | 2143.92i | 0.507540 | − | 0.167124i | ||||
\(549\) | −8537.99 | + | 8537.99i | −0.663739 | + | 0.663739i | ||||
\(550\) | 296.017 | + | 1845.44i | 0.0229494 | + | 0.143072i | ||||
\(551\) | − | 25710.6i | − | 1.98786i | ||||||
\(552\) | −2202.01 | − | 4259.27i | −0.169789 | − | 0.328417i | ||||
\(553\) | 96.7105i | 0.00743680i | ||||||||
\(554\) | 8869.36 | − | 1422.69i | 0.680186 | − | 0.109105i | ||||
\(555\) | −18108.0 | + | 18108.0i | −1.38494 | + | 1.38494i | ||||
\(556\) | −17063.5 | − | 8609.78i | −1.30154 | − | 0.656719i | ||||
\(557\) | −2889.57 | − | 2889.57i | −0.219812 | − | 0.219812i | 0.588607 | − | 0.808419i | \(-0.299676\pi\) |
−0.808419 | + | 0.588607i | \(0.799676\pi\) | |||||||
\(558\) | 9715.97 | − | 13428.4i | 0.737114 | − | 1.01877i | ||||
\(559\) | 5341.19 | 0.404129 | ||||||||
\(560\) | 1273.46 | + | 191.422i | 0.0960957 | + | 0.0144448i | ||||
\(561\) | −11642.0 | −0.876159 | ||||||||
\(562\) | −10024.2 | + | 13854.4i | −0.752394 | + | 1.03988i | ||||
\(563\) | 70.0753 | + | 70.0753i | 0.00524569 | + | 0.00524569i | 0.709725 | − | 0.704479i | \(-0.248819\pi\) |
−0.704479 | + | 0.709725i | \(0.748819\pi\) | |||||||
\(564\) | 2382.36 | − | 4721.55i | 0.177864 | − | 0.352505i | ||||
\(565\) | 3054.68 | − | 3054.68i | 0.227453 | − | 0.227453i | ||||
\(566\) | −9714.35 | + | 1558.23i | −0.721422 | + | 0.115719i | ||||
\(567\) | 47.7509i | 0.00353677i | ||||||||
\(568\) | −15686.3 | − | 4994.49i | −1.15877 | − | 0.368951i | ||||
\(569\) | − | 8915.23i | − | 0.656847i | −0.944531 | − | 0.328423i | \(-0.893483\pi\) | ||
0.944531 | − | 0.328423i | \(-0.106517\pi\) | |||||||
\(570\) | 4656.81 | + | 29031.6i | 0.342197 | + | 2.13334i | ||||
\(571\) | 4946.30 | − | 4946.30i | 0.362515 | − | 0.362515i | −0.502223 | − | 0.864738i | \(-0.667484\pi\) |
0.864738 | + | 0.502223i | \(0.167484\pi\) | |||||||
\(572\) | −851.386 | − | 2585.59i | −0.0622347 | − | 0.189002i | ||||
\(573\) | 2568.89 | + | 2568.89i | 0.187289 | + | 0.187289i | ||||
\(574\) | −746.239 | − | 539.931i | −0.0542638 | − | 0.0392618i | ||||
\(575\) | 644.818 | 0.0467665 | ||||||||
\(576\) | 13074.3 | − | 18450.0i | 0.945768 | − | 1.33463i | ||||
\(577\) | 17911.5 | 1.29232 | 0.646159 | − | 0.763203i | \(-0.276374\pi\) | ||||
0.646159 | + | 0.763203i | \(0.276374\pi\) | |||||||
\(578\) | 4672.00 | + | 3380.36i | 0.336210 | + | 0.243261i | ||||
\(579\) | 13522.8 | + | 13522.8i | 0.970622 | + | 0.970622i | ||||
\(580\) | −7865.68 | − | 23887.4i | −0.563112 | − | 1.71012i | ||||
\(581\) | −672.347 | + | 672.347i | −0.0480097 | + | 0.0480097i | ||||
\(582\) | −3060.84 | − | 19082.0i | −0.218000 | − | 1.35906i | ||||
\(583\) | 19140.4i | 1.35972i | ||||||||
\(584\) | 2286.85 | + | 728.129i | 0.162039 | + | 0.0515928i | ||||
\(585\) | − | 7166.15i | − | 0.506468i | ||||||
\(586\) | 7316.44 | − | 1173.59i | 0.515767 | − | 0.0827314i | ||||
\(587\) | 7940.26 | − | 7940.26i | 0.558312 | − | 0.558312i | −0.370514 | − | 0.928827i | \(-0.620819\pi\) |
0.928827 | + | 0.370514i | \(0.120819\pi\) | |||||||
\(588\) | 10346.1 | − | 20504.6i | 0.725620 | − | 1.43809i | ||||
\(589\) | 9418.83 | + | 9418.83i | 0.658907 | + | 0.658907i | ||||
\(590\) | −1339.21 | + | 1850.92i | −0.0934478 | + | 0.129154i | ||||
\(591\) | 12400.4 | 0.863088 | ||||||||
\(592\) | −2352.72 | + | 15651.8i | −0.163338 | + | 1.08663i | ||||
\(593\) | −7006.26 | −0.485181 | −0.242591 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242591 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(594\) | −6180.36 | + | 8541.87i | −0.426908 | + | 0.590029i | ||||
\(595\) | −762.780 | − | 762.780i | −0.0525562 | − | 0.0525562i | ||||
\(596\) | −325.454 | − | 164.215i | −0.0223677 | − | 0.0112861i | ||||
\(597\) | −29762.7 | + | 29762.7i | −2.04038 | + | 2.04038i | ||||
\(598\) | −927.294 | + | 148.742i | −0.0634111 | + | 0.0101714i | ||||
\(599\) | − | 8502.74i | − | 0.579987i | −0.957029 | − | 0.289994i | \(-0.906347\pi\) | ||
0.957029 | − | 0.289994i | \(-0.0936532\pi\) | |||||||
\(600\) | 2250.37 | + | 4352.80i | 0.153118 | + | 0.296171i | ||||
\(601\) | − | 11936.2i | − | 0.810127i | −0.914289 | − | 0.405063i | \(-0.867249\pi\) | ||
0.914289 | − | 0.405063i | \(-0.132751\pi\) | |||||||
\(602\) | −296.715 | − | 1849.79i | −0.0200884 | − | 0.125236i | ||||
\(603\) | −12462.8 | + | 12462.8i | −0.841663 | + | 0.841663i | ||||
\(604\) | −8184.17 | + | 2694.89i | −0.551340 | + | 0.181546i | ||||
\(605\) | 5801.18 | + | 5801.18i | 0.389837 | + | 0.389837i | ||||
\(606\) | −8288.71 | − | 5997.19i | −0.555620 | − | 0.402012i | ||||
\(607\) | −3850.00 | −0.257441 | −0.128721 | − | 0.991681i | \(-0.541087\pi\) | ||||
−0.128721 | + | 0.991681i | \(0.541087\pi\) | |||||||
\(608\) | 12976.0 | + | 12722.8i | 0.865535 | + | 0.848649i | ||||
\(609\) | 3541.58 | 0.235652 | ||||||||
\(610\) | −7689.95 | − | 5563.96i | −0.510421 | − | 0.369309i | ||||
\(611\) | −732.459 | − | 732.459i | −0.0484977 | − | 0.0484977i | ||||
\(612\) | −17991.9 | + | 5924.40i | −1.18837 | + | 0.391307i | ||||
\(613\) | −6320.36 | + | 6320.36i | −0.416439 | + | 0.416439i | −0.883974 | − | 0.467536i | \(-0.845142\pi\) |
0.467536 | + | 0.883974i | \(0.345142\pi\) | |||||||
\(614\) | −1335.05 | − | 8323.01i | −0.0877494 | − | 0.547051i | ||||
\(615\) | − | 20571.2i | − | 1.34880i | ||||||
\(616\) | −848.160 | + | 438.492i | −0.0554762 | + | 0.0286808i | ||||
\(617\) | − | 2585.09i | − | 0.168674i | −0.996437 | − | 0.0843370i | \(-0.973123\pi\) | ||
0.996437 | − | 0.0843370i | \(-0.0268772\pi\) | |||||||
\(618\) | 22668.8 | − | 3636.19i | 1.47553 | − | 0.236681i | ||||
\(619\) | 7325.02 | − | 7325.02i | 0.475634 | − | 0.475634i | −0.428098 | − | 0.903732i | \(-0.640816\pi\) |
0.903732 | + | 0.428098i | \(0.140816\pi\) | |||||||
\(620\) | 11632.4 | + | 5869.41i | 0.753501 | + | 0.380195i | ||||
\(621\) | 2572.06 | + | 2572.06i | 0.166205 | + | 0.166205i | ||||
\(622\) | −8778.92 | + | 12133.3i | −0.565921 | + | 0.782159i | ||||
\(623\) | 1260.51 | 0.0810615 | ||||||||
\(624\) | −4240.26 | − | 5740.54i | −0.272030 | − | 0.368278i | ||||
\(625\) | 18174.8 | 1.16319 | ||||||||
\(626\) | −6641.72 | + | 9179.52i | −0.424052 | + | 0.586082i | ||||
\(627\) | −15415.2 | − | 15415.2i | −0.981857 | − | 0.981857i | ||||
\(628\) | −9712.07 | + | 19248.1i | −0.617124 | + | 1.22306i | ||||
\(629\) | 9375.13 | − | 9375.13i | 0.594294 | − | 0.594294i | ||||
\(630\) | −2481.82 | + | 398.096i | −0.156949 | + | 0.0251754i | ||||
\(631\) | 14411.5i | 0.909210i | 0.890693 | + | 0.454605i | \(0.150220\pi\) | ||||
−0.890693 | + | 0.454605i | \(0.849780\pi\) | |||||||
\(632\) | −405.011 | + | 1272.03i | −0.0254913 | + | 0.0800611i | ||||
\(633\) | − | 31633.1i | − | 1.98626i | ||||||
\(634\) | −512.670 | − | 3196.10i | −0.0321147 | − | 0.200211i | ||||
\(635\) | −20534.3 | + | 20534.3i | −1.28327 | + | 1.28327i | ||||
\(636\) | 15694.7 | + | 47663.6i | 0.978518 | + | 2.97168i | ||||
\(637\) | −3180.91 | − | 3180.91i | −0.197853 | − | 0.197853i | ||||
\(638\) | 15107.0 | + | 10930.4i | 0.937445 | + | 0.678276i | ||||
\(639\) | 32132.1 | 1.98924 | ||||||||
\(640\) | 15948.1 | + | 7850.86i | 0.985008 | + | 0.484895i | ||||
\(641\) | −25724.0 | −1.58508 | −0.792542 | − | 0.609818i | \(-0.791243\pi\) | ||||
−0.792542 | + | 0.609818i | \(0.791243\pi\) | |||||||
\(642\) | 19911.6 | + | 14406.7i | 1.22406 | + | 0.885653i | ||||
\(643\) | −7835.74 | − | 7835.74i | −0.480578 | − | 0.480578i | 0.424738 | − | 0.905316i | \(-0.360366\pi\) |
−0.905316 | + | 0.424738i | \(0.860366\pi\) | |||||||
\(644\) | 103.026 | + | 312.883i | 0.00630406 | + | 0.0191449i | ||||
\(645\) | 29585.9 | − | 29585.9i | 1.80611 | − | 1.80611i | ||||
\(646\) | −2410.99 | − | 15030.7i | −0.146841 | − | 0.915441i | ||||
\(647\) | − | 1247.43i | − | 0.0757981i | −0.999282 | − | 0.0378991i | \(-0.987933\pi\) | ||
0.999282 | − | 0.0378991i | \(-0.0120665\pi\) | |||||||
\(648\) | −199.975 | + | 628.065i | −0.0121231 | + | 0.0380752i | ||||
\(649\) | − | 1693.89i | − | 0.102451i | ||||||
\(650\) | 947.658 | − | 152.009i | 0.0571849 | − | 0.00917272i | ||||
\(651\) | −1297.42 | + | 1297.42i | −0.0781107 | + | 0.0781107i | ||||
\(652\) | −3617.68 | + | 7169.79i | −0.217299 | + | 0.430661i | ||||
\(653\) | 8302.21 | + | 8302.21i | 0.497535 | + | 0.497535i | 0.910670 | − | 0.413135i | \(-0.135566\pi\) |
−0.413135 | + | 0.910670i | \(0.635566\pi\) | |||||||
\(654\) | 11734.8 | − | 16218.7i | 0.701634 | − | 0.969728i | ||||
\(655\) | 7003.63 | 0.417793 | ||||||||
\(656\) | −7554.08 | − | 10226.8i | −0.449599 | − | 0.608675i | ||||
\(657\) | −4684.42 | −0.278168 | ||||||||
\(658\) | −212.980 | + | 294.359i | −0.0126182 | + | 0.0174397i | ||||
\(659\) | 1696.16 | + | 1696.16i | 0.100262 | + | 0.100262i | 0.755459 | − | 0.655196i | \(-0.227414\pi\) |
−0.655196 | + | 0.755459i | \(0.727414\pi\) | |||||||
\(660\) | −19038.1 | − | 9606.09i | −1.12281 | − | 0.566540i | ||||
\(661\) | −8788.30 | + | 8788.30i | −0.517134 | + | 0.517134i | −0.916703 | − | 0.399569i | \(-0.869160\pi\) |
0.399569 | + | 0.916703i | \(0.369160\pi\) | |||||||
\(662\) | 16705.1 | − | 2679.57i | 0.980758 | − | 0.157318i | ||||
\(663\) | 5978.32i | 0.350194i | ||||||||
\(664\) | −11659.0 | + | 6027.64i | −0.681414 | + | 0.352286i | ||||
\(665\) | − | 2020.00i | − | 0.117793i | ||||||
\(666\) | −4892.88 | − | 30503.4i | −0.284678 | − | 1.77475i | ||||
\(667\) | 4548.88 | − | 4548.88i | 0.264068 | − | 0.264068i | ||||
\(668\) | −26296.3 | + | 8658.89i | −1.52311 | + | 0.501531i | ||||
\(669\) | −22016.4 | − | 22016.4i | −1.27235 | − | 1.27235i | ||||
\(670\) | −11224.9 | − | 8121.62i | −0.647247 | − | 0.468307i | ||||
\(671\) | 7037.56 | 0.404891 | ||||||||
\(672\) | −1752.54 | + | 1787.41i | −0.100604 | + | 0.102606i | ||||
\(673\) | −23869.3 | −1.36716 | −0.683578 | − | 0.729878i | \(-0.739577\pi\) | ||||
−0.683578 | + | 0.729878i | \(0.739577\pi\) | |||||||
\(674\) | −22921.1 | − | 16584.2i | −1.30992 | − | 0.947775i | ||||
\(675\) | −2628.54 | − | 2628.54i | −0.149885 | − | 0.149885i | ||||
\(676\) | 15366.5 | − | 5059.90i | 0.874289 | − | 0.287887i | ||||
\(677\) | −5663.30 | + | 5663.30i | −0.321504 | + | 0.321504i | −0.849344 | − | 0.527840i | \(-0.823002\pi\) |
0.527840 | + | 0.849344i | \(0.323002\pi\) | |||||||
\(678\) | 1329.98 | + | 8291.43i | 0.0753359 | + | 0.469662i | ||||
\(679\) | 1327.71i | 0.0750410i | ||||||||
\(680\) | −6838.39 | − | 13227.2i | −0.385647 | − | 0.745943i | ||||
\(681\) | 20405.8i | 1.14824i | ||||||||
\(682\) | −9538.55 | + | 1530.03i | −0.535557 | + | 0.0859058i | ||||
\(683\) | −9152.80 | + | 9152.80i | −0.512770 | + | 0.512770i | −0.915374 | − | 0.402604i | \(-0.868105\pi\) |
0.402604 | + | 0.915374i | \(0.368105\pi\) | |||||||
\(684\) | −31667.7 | − | 15978.6i | −1.77024 | − | 0.893215i | ||||
\(685\) | −7437.11 | − | 7437.11i | −0.414828 | − | 0.414828i | ||||
\(686\) | −1857.15 | + | 2566.77i | −0.103362 | + | 0.142857i | ||||
\(687\) | 1095.21 | 0.0608224 | ||||||||
\(688\) | 3844.01 | − | 25572.8i | 0.213011 | − | 1.41708i | ||||
\(689\) | 9828.85 | 0.543468 | ||||||||
\(690\) | −4312.55 | + | 5960.38i | −0.237936 | + | 0.328852i | ||||
\(691\) | 17057.9 | + | 17057.9i | 0.939091 | + | 0.939091i | 0.998249 | − | 0.0591580i | \(-0.0188416\pi\) |
−0.0591580 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(692\) | 6643.59 | − | 13166.8i | 0.364959 | − | 0.723303i | ||||
\(693\) | 1317.80 | − | 1317.80i | 0.0722351 | − | 0.0722351i | ||||
\(694\) | 25314.3 | − | 4060.54i | 1.38461 | − | 0.222098i | ||||
\(695\) | 29325.4i | 1.60054i | ||||||||
\(696\) | 46582.3 | + | 14831.7i | 2.53692 | + | 0.807750i | ||||
\(697\) | 10650.4i | 0.578787i | ||||||||
\(698\) | 3486.40 | + | 21735.1i | 0.189058 | + | 1.17863i | ||||
\(699\) | 25409.7 | − | 25409.7i | 1.37494 | − | 1.37494i | ||||
\(700\) | −105.289 | − | 319.754i | −0.00568507 | − | 0.0172651i | ||||
\(701\) | −7720.44 | − | 7720.44i | −0.415973 | − | 0.415973i | 0.467840 | − | 0.883813i | \(-0.345032\pi\) |
−0.883813 | + | 0.467840i | \(0.845032\pi\) | |||||||
\(702\) | 4386.37 | + | 3173.70i | 0.235830 | + | 0.170632i | ||||
\(703\) | 24827.3 | 1.33198 | ||||||||
\(704\) | −12992.2 | + | 2215.48i | −0.695540 | + | 0.118607i | ||||
\(705\) | −8114.47 | −0.433487 | ||||||||
\(706\) | 3234.13 | + | 2340.01i | 0.172405 | + | 0.124741i | ||||
\(707\) | 497.001 | + | 497.001i | 0.0264380 | + | 0.0264380i | ||||
\(708\) | −1388.96 | − | 4218.14i | −0.0737290 | − | 0.223909i | ||||
\(709\) | 4577.66 | − | 4577.66i | 0.242479 | − | 0.242479i | −0.575396 | − | 0.817875i | \(-0.695152\pi\) |
0.817875 | + | 0.575396i | \(0.195152\pi\) | |||||||
\(710\) | 4000.50 | + | 24940.0i | 0.211459 | + | 1.31829i | ||||
\(711\) | − | 2605.64i | − | 0.137439i | ||||||
\(712\) | 16579.4 | + | 5278.86i | 0.872670 | + | 0.277856i | ||||
\(713\) | 3332.88i | 0.175059i | ||||||||
\(714\) | 2070.45 | − | 332.109i | 0.108522 | − | 0.0174074i | ||||
\(715\) | −2953.40 | + | 2953.40i | −0.154477 | + | 0.154477i | ||||
\(716\) | 5516.25 | − | 10932.5i | 0.287921 | − | 0.570625i | ||||
\(717\) | 30142.5 | + | 30142.5i | 1.57000 | + | 1.57000i | ||||
\(718\) | 3582.49 | − | 4951.36i | 0.186208 | − | 0.257358i | ||||
\(719\) | −30210.0 | −1.56696 | −0.783479 | − | 0.621418i | \(-0.786557\pi\) | ||||
−0.783479 | + | 0.621418i | \(0.786557\pi\) | |||||||
\(720\) | −34310.5 | − | 5157.42i | −1.77594 | − | 0.266953i | ||||
\(721\) | −1577.28 | −0.0814717 | ||||||||
\(722\) | 5337.60 | − | 7377.10i | 0.275132 | − | 0.380259i | ||||
\(723\) | −291.324 | − | 291.324i | −0.0149854 | − | 0.0149854i | ||||
\(724\) | 29735.9 | + | 15003.9i | 1.52642 | + | 0.770188i | ||||
\(725\) | −4648.78 | + | 4648.78i | −0.238140 | + | 0.238140i | ||||
\(726\) | −15746.4 | + | 2525.79i | −0.804963 | + | 0.129120i | ||||
\(727\) | − | 20721.3i | − | 1.05710i | −0.848903 | − | 0.528549i | \(-0.822736\pi\) | ||
0.848903 | − | 0.528549i | \(-0.177264\pi\) | |||||||
\(728\) | 225.172 | + | 435.541i | 0.0114635 | + | 0.0221734i | ||||
\(729\) | 31696.7i | 1.61036i | ||||||||
\(730\) | −583.218 | − | 3635.92i | −0.0295697 | − | 0.184344i | ||||
\(731\) | −15317.6 | + | 15317.6i | −0.775025 | + | 0.775025i | ||||
\(732\) | 17525.0 | − | 5770.66i | 0.884894 | − | 0.291379i | ||||
\(733\) | −13879.8 | − | 13879.8i | −0.699404 | − | 0.699404i | 0.264878 | − | 0.964282i | \(-0.414668\pi\) |
−0.964282 | + | 0.264878i | \(0.914668\pi\) | |||||||
\(734\) | −24651.5 | − | 17836.2i | −1.23965 | − | 0.896932i | ||||
\(735\) | −35239.3 | −1.76847 | ||||||||
\(736\) | 44.7891 | + | 4546.79i | 0.00224314 | + | 0.227713i | ||||
\(737\) | 10272.6 | 0.513428 | ||||||||
\(738\) | 20105.7 | + | 14547.2i | 1.00284 | + | 0.725595i | ||||
\(739\) | 8793.93 | + | 8793.93i | 0.437740 | + | 0.437740i | 0.891251 | − | 0.453511i | \(-0.149829\pi\) |
−0.453511 | + | 0.891251i | \(0.649829\pi\) | |||||||
\(740\) | 23066.7 | − | 7595.45i | 1.14588 | − | 0.377317i | ||||
\(741\) | −7915.92 | + | 7915.92i | −0.392441 | + | 0.392441i | ||||
\(742\) | −546.015 | − | 3403.98i | −0.0270146 | − | 0.168415i | ||||
\(743\) | − | 7669.27i | − | 0.378678i | −0.981912 | − | 0.189339i | \(-0.939365\pi\) | ||
0.981912 | − | 0.189339i | \(-0.0606346\pi\) | |||||||
\(744\) | −22498.4 | + | 11631.5i | −1.10864 | + | 0.573161i | ||||
\(745\) | 559.327i | 0.0275062i | ||||||||
\(746\) | −5556.94 | + | 891.359i | −0.272727 | + | 0.0437466i | ||||
\(747\) | 18114.8 | − | 18114.8i | 0.887264 | − | 0.887264i | ||||
\(748\) | 9856.68 | + | 4973.41i | 0.481813 | + | 0.243109i | ||||
\(749\) | −1193.92 | − | 1193.92i | −0.0582443 | − | 0.0582443i | ||||
\(750\) | −17053.4 | + | 23569.5i | −0.830269 | + | 1.14751i | ||||
\(751\) | −26531.8 | −1.28916 | −0.644580 | − | 0.764537i | \(-0.722968\pi\) | ||||
−0.644580 | + | 0.764537i | \(0.722968\pi\) | |||||||
\(752\) | −4034.05 | + | 2979.76i | −0.195620 | + | 0.144495i | ||||
\(753\) | 31075.5 | 1.50392 | ||||||||
\(754\) | 5612.93 | − | 7757.63i | 0.271102 | − | 0.374690i | ||||
\(755\) | 9348.40 | + | 9348.40i | 0.450627 | + | 0.450627i | ||||
\(756\) | 855.461 | − | 1695.42i | 0.0411545 | − | 0.0815631i | ||||
\(757\) | −79.4192 | + | 79.4192i | −0.00381313 | + | 0.00381313i | −0.709011 | − | 0.705198i | \(-0.750858\pi\) |
0.705198 | + | 0.709011i | \(0.250858\pi\) | |||||||
\(758\) | 4529.91 | − | 726.619i | 0.217063 | − | 0.0348179i | ||||
\(759\) | − | 5454.71i | − | 0.260861i | ||||||
\(760\) | 8459.51 | − | 26569.0i | 0.403761 | − | 1.26810i | ||||
\(761\) | − | 36991.3i | − | 1.76207i | −0.473055 | − | 0.881033i | \(-0.656849\pi\) | ||
0.473055 | − | 0.881033i | \(-0.343151\pi\) | |||||||
\(762\) | −8940.48 | − | 55737.1i | −0.425039 | − | 2.64979i | ||||
\(763\) | −972.494 | + | 972.494i | −0.0461424 | + | 0.0461424i | ||||
\(764\) | −1077.53 | − | 3272.36i | −0.0510256 | − | 0.154961i | ||||
\(765\) | 20551.3 | + | 20551.3i | 0.971288 | + | 0.971288i | ||||
\(766\) | −20720.3 | − | 14991.9i | −0.977355 | − | 0.707152i | ||||
\(767\) | −869.835 | −0.0409490 | ||||||||
\(768\) | −30536.6 | + | 16170.3i | −1.43476 | + | 0.759761i | ||||
\(769\) | 26637.0 | 1.24910 | 0.624548 | − | 0.780987i | \(-0.285283\pi\) | ||||
0.624548 | + | 0.780987i | \(0.285283\pi\) | |||||||
\(770\) | 1186.91 | + | 858.770i | 0.0555495 | + | 0.0401921i | ||||
\(771\) | −4408.55 | − | 4408.55i | −0.205928 | − | 0.205928i | ||||
\(772\) | −5672.20 | − | 17226.0i | −0.264439 | − | 0.803080i | ||||
\(773\) | 19743.6 | − | 19743.6i | 0.918667 | − | 0.918667i | −0.0782657 | − | 0.996933i | \(-0.524938\pi\) |
0.996933 | + | 0.0782657i | \(0.0249382\pi\) | |||||||
\(774\) | 7994.29 | + | 49838.3i | 0.371252 | + | 2.31447i | ||||
\(775\) | − | 3406.07i | − | 0.157871i | ||||||
\(776\) | −5560.28 | + | 17463.3i | −0.257220 | + | 0.807856i | ||||
\(777\) | 3419.91i | 0.157900i | ||||||||
\(778\) | −10171.3 | + | 1631.53i | −0.468715 | + | 0.0751840i | ||||
\(779\) | −14102.3 | + | 14102.3i | −0.648610 | + | 0.648610i | ||||
\(780\) | −4932.86 | + | 9776.32i | −0.226442 | + | 0.448780i | ||||
\(781\) | −13242.6 | − | 13242.6i | −0.606734 | − | 0.606734i | ||||
\(782\) | 2232.76 | − | 3085.89i | 0.102101 | − | 0.141114i | ||||
\(783\) | −37086.2 | −1.69266 | ||||||||
\(784\) | −17519.0 | + | 12940.4i | −0.798058 | + | 0.589488i | ||||
\(785\) | 33079.9 | 1.50404 | ||||||||
\(786\) | −7980.45 | + | 11029.8i | −0.362154 | + | 0.500533i | ||||
\(787\) | −28878.1 | − | 28878.1i | −1.30800 | − | 1.30800i | −0.922860 | − | 0.385136i | \(-0.874155\pi\) |
−0.385136 | − | 0.922860i | \(-0.625845\pi\) | |||||||
\(788\) | −10498.8 | − | 5297.41i | −0.474625 | − | 0.239483i | ||||
\(789\) | −14604.4 | + | 14604.4i | −0.658975 | + | 0.658975i | ||||
\(790\) | 2022.43 | − | 324.407i | 0.0910819 | − | 0.0146100i | ||||
\(791\) | − | 576.912i | − | 0.0259325i | ||||||
\(792\) | 22851.7 | − | 11814.2i | 1.02525 | − | 0.530047i | ||||
\(793\) | − | 3613.88i | − | 0.161832i | ||||||
\(794\) | 4511.59 | + | 28126.3i | 0.201650 | + | 1.25713i | ||||
\(795\) | 54444.0 | − | 54444.0i | 2.42884 | − | 2.42884i | ||||
\(796\) | 37913.0 | − | 12484.1i | 1.68818 | − | 0.555887i | ||||
\(797\) | −16656.0 | − | 16656.0i | −0.740257 | − | 0.740257i | 0.232371 | − | 0.972627i | \(-0.425352\pi\) |
−0.972627 | + | 0.232371i | \(0.925352\pi\) | |||||||
\(798\) | 3181.23 | + | 2301.74i | 0.141121 | + | 0.102106i | ||||
\(799\) | 4201.14 | 0.186015 | ||||||||
\(800\) | −45.7727 | − | 4646.64i | −0.00202289 | − | 0.205355i | ||||
\(801\) | −33961.5 | −1.49809 | ||||||||
\(802\) | 6932.16 | + | 5015.68i | 0.305216 | + | 0.220835i | ||||
\(803\) | 1930.60 | + | 1930.60i | 0.0848435 | + | 0.0848435i | ||||
\(804\) | 25581.0 | − | 8423.33i | 1.12210 | − | 0.369488i | ||||
\(805\) | 357.391 | − | 357.391i | 0.0156477 | − | 0.0156477i | ||||
\(806\) | 785.690 | + | 4898.18i | 0.0343359 | + | 0.214058i | ||||
\(807\) | 9901.55i | 0.431910i | ||||||||
\(808\) | 4455.66 | + | 8618.42i | 0.193997 | + | 0.375241i | ||||
\(809\) | 34940.4i | 1.51847i | 0.650819 | + | 0.759233i | \(0.274426\pi\) | ||||
−0.650819 | + | 0.759233i | \(0.725574\pi\) | |||||||
\(810\) | 998.574 | − | 160.176i | 0.0433165 | − | 0.00694816i | ||||
\(811\) | −15168.2 | + | 15168.2i | −0.656753 | + | 0.656753i | −0.954610 | − | 0.297857i | \(-0.903728\pi\) |
0.297857 | + | 0.954610i | \(0.403728\pi\) | |||||||
\(812\) | −2998.48 | − | 1512.95i | −0.129589 | − | 0.0653868i | ||||
\(813\) | −8380.10 | − | 8380.10i | −0.361504 | − | 0.361504i | ||||
\(814\) | −10554.9 | + | 14587.9i | −0.454483 | + | 0.628141i | ||||
\(815\) | 12322.0 | 0.529597 | ||||||||
\(816\) | 28623.3 | + | 4302.55i | 1.22796 | + | 0.184583i | ||||
\(817\) | −40564.3 | −1.73705 | ||||||||
\(818\) | −15651.8 | + | 21632.4i | −0.669014 | + | 0.924644i | ||||
\(819\) | −676.707 | − | 676.707i | −0.0288718 | − | 0.0288718i | ||||
\(820\) | −8787.94 | + | 17416.6i | −0.374254 | + | 0.741725i | ||||
\(821\) | 8710.55 | − | 8710.55i | 0.370280 | − | 0.370280i | −0.497299 | − | 0.867579i | \(-0.665675\pi\) |
0.867579 | + | 0.497299i | \(0.165675\pi\) | |||||||
\(822\) | 20186.8 | − | 3238.06i | 0.856566 | − | 0.137397i | ||||
\(823\) | − | 24493.5i | − | 1.03741i | −0.854952 | − | 0.518707i | \(-0.826414\pi\) | ||
0.854952 | − | 0.518707i | \(-0.173586\pi\) | |||||||
\(824\) | −20745.9 | − | 6605.46i | −0.877085 | − | 0.279262i | ||||
\(825\) | 5574.50i | 0.235248i | ||||||||
\(826\) | 48.3213 | + | 301.246i | 0.00203549 | + | 0.0126897i | ||||
\(827\) | 26328.0 | − | 26328.0i | 1.10703 | − | 1.10703i | 0.113492 | − | 0.993539i | \(-0.463796\pi\) |
0.993539 | − | 0.113492i | \(-0.0362037\pi\) | |||||||
\(828\) | −2775.81 | − | 8429.90i | −0.116505 | − | 0.353815i | ||||
\(829\) | 9108.25 | + | 9108.25i | 0.381596 | + | 0.381596i | 0.871677 | − | 0.490081i | \(-0.163033\pi\) |
−0.490081 | + | 0.871677i | \(0.663033\pi\) | |||||||
\(830\) | 16315.6 | + | 11804.9i | 0.682315 | + | 0.493680i | ||||
\(831\) | 26791.6 | 1.11840 | ||||||||
\(832\) | 1137.68 | + | 6671.65i | 0.0474062 | + | 0.278002i | ||||
\(833\) | 18244.6 | 0.758870 | ||||||||
\(834\) | −46183.6 | − | 33415.6i | −1.91752 | − | 1.38739i | ||||
\(835\) | 30037.1 | + | 30037.1i | 1.24488 | + | 1.24488i | ||||
\(836\) | 6465.96 | + | 19636.6i | 0.267500 | + | 0.812375i | ||||
\(837\) | 13586.2 | − | 13586.2i | 0.561060 | − | 0.561060i | ||||
\(838\) | 2062.55 | + | 12858.4i | 0.0850233 | + | 0.530055i | ||||
\(839\) | − | 1394.89i | − | 0.0573982i | −0.999588 | − | 0.0286991i | \(-0.990864\pi\) | ||
0.999588 | − | 0.0286991i | \(-0.00913646\pi\) | |||||||
\(840\) | 3659.82 | + | 1165.28i | 0.150328 | + | 0.0478642i | ||||
\(841\) | 41200.9i | 1.68932i | ||||||||
\(842\) | 37275.6 | − | 5979.18i | 1.52566 | − | 0.244722i | ||||
\(843\) | −36065.0 | + | 36065.0i | −1.47348 | + | 1.47348i | ||||
\(844\) | −13513.5 | + | 26782.1i | −0.551131 | + | 1.09227i | ||||
\(845\) | −17552.4 | − | 17552.4i | −0.714583 | − | 0.714583i | ||||
\(846\) | 5738.24 | − | 7930.82i | 0.233197 | − | 0.322302i | ||||
\(847\) | 1095.62 | 0.0444463 | ||||||||
\(848\) | 7073.75 | − | 47059.1i | 0.286455 | − | 1.90568i | ||||
\(849\) | −29344.1 | −1.18620 | ||||||||
\(850\) | −2281.79 | + | 3153.66i | −0.0920762 | + | 0.127258i | ||||
\(851\) | 4392.60 | + | 4392.60i | 0.176941 | + | 0.176941i | ||||
\(852\) | −43835.7 | − | 22118.3i | −1.76266 | − | 0.889389i | ||||
\(853\) | 15284.7 | − | 15284.7i | 0.613527 | − | 0.613527i | −0.330337 | − | 0.943863i | \(-0.607162\pi\) |
0.943863 | + | 0.330337i | \(0.107162\pi\) | |||||||
\(854\) | −1251.58 | + | 200.759i | −0.0501501 | + | 0.00804430i | ||||
\(855\) | 54424.2i | 2.17692i | ||||||||
\(856\) | −10703.6 | − | 20703.6i | −0.427385 | − | 0.826675i | ||||
\(857\) | 2273.70i | 0.0906277i | 0.998973 | + | 0.0453139i | \(0.0144288\pi\) | ||||
−0.998973 | + | 0.0453139i | \(0.985571\pi\) | |||||||
\(858\) | −1285.89 | − | 8016.53i | −0.0511649 | − | 0.318974i | ||||
\(859\) | −21674.3 | + | 21674.3i | −0.860905 | + | 0.860905i | −0.991443 | − | 0.130538i | \(-0.958329\pi\) |
0.130538 | + | 0.991443i | \(0.458329\pi\) | |||||||
\(860\) | −37687.8 | + | 12409.9i | −1.49435 | + | 0.492063i | ||||
\(861\) | −1942.56 | − | 1942.56i | −0.0768900 | − | 0.0768900i | ||||
\(862\) | 24330.6 | + | 17604.1i | 0.961374 | + | 0.695589i | ||||
\(863\) | 23721.7 | 0.935686 | 0.467843 | − | 0.883812i | \(-0.345031\pi\) | ||||
0.467843 | + | 0.883812i | \(0.345031\pi\) | |||||||
\(864\) | 18352.0 | − | 18717.2i | 0.722626 | − | 0.737004i | ||||
\(865\) | −22628.5 | −0.889469 | ||||||||
\(866\) | −1618.91 | − | 1171.34i | −0.0635251 | − | 0.0459628i | ||||
\(867\) | 12161.9 | + | 12161.9i | 0.476400 | + | 0.476400i | ||||
\(868\) | 1652.72 | − | 544.209i | 0.0646277 | − | 0.0212807i | ||||
\(869\) | −1073.87 | + | 1073.87i | −0.0419200 | + | 0.0419200i | ||||
\(870\) | −11879.9 | − | 74062.2i | −0.462950 | − | 2.88614i | ||||
\(871\) | − | 5275.12i | − | 0.205213i | ||||||
\(872\) | −16863.9 | + | 8718.49i | −0.654911 | + | 0.338584i | ||||
\(873\) | − | 35772.1i | − | 1.38683i | ||||||
\(874\) | 7042.45 | − | 1129.64i | 0.272557 | − | 0.0437193i | ||||
\(875\) | 1413.26 | − | 1413.26i | 0.0546020 | − | 0.0546020i | ||||
\(876\) | 6390.65 | + | 3224.54i | 0.246484 | + | 0.124369i | ||||
\(877\) | 22429.6 | + | 22429.6i | 0.863617 | + | 0.863617i | 0.991756 | − | 0.128139i | \(-0.0409004\pi\) |
−0.128139 | + | 0.991756i | \(0.540900\pi\) | |||||||
\(878\) | 22568.3 | − | 31191.6i | 0.867475 | − | 1.19894i | ||||
\(879\) | 22100.7 | 0.848054 | ||||||||
\(880\) | 12014.9 | + | 16266.0i | 0.460252 | + | 0.623098i | ||||
\(881\) | 24603.0 | 0.940859 | 0.470429 | − | 0.882438i | \(-0.344099\pi\) | ||||
0.470429 | + | 0.882438i | \(0.344099\pi\) | |||||||
\(882\) | 24919.9 | − | 34441.8i | 0.951357 | − | 1.31487i | ||||
\(883\) | −23486.7 | − | 23486.7i | −0.895120 | − | 0.895120i | 0.0998799 | − | 0.995000i | \(-0.468154\pi\) |
−0.995000 | + | 0.0998799i | \(0.968154\pi\) | |||||||
\(884\) | 2553.91 | − | 5061.54i | 0.0971690 | − | 0.192577i | ||||
\(885\) | −4818.19 | + | 4818.19i | −0.183007 | + | 0.183007i | ||||
\(886\) | −12350.0 | + | 1981.00i | −0.468293 | + | 0.0751163i | ||||
\(887\) | 39722.9i | 1.50368i | 0.659345 | + | 0.751841i | \(0.270834\pi\) | ||||
−0.659345 | + | 0.751841i | \(0.729166\pi\) | |||||||
\(888\) | −14322.1 | + | 44981.9i | −0.541238 | + | 1.69988i | ||||
\(889\) | 3878.15i | 0.146309i | ||||||||
\(890\) | −4228.27 | − | 26360.0i | −0.159249 | − | 0.992798i | ||||
\(891\) | −530.222 | + | 530.222i | −0.0199362 | + | 0.0199362i | ||||
\(892\) | 9234.86 | + | 28045.5i | 0.346643 | + | 1.05273i | ||||
\(893\) | 5562.75 | + | 5562.75i | 0.208455 | + | 0.208455i | ||||
\(894\) | −880.865 | − | 637.338i | −0.0329536 | − | 0.0238432i | ||||
\(895\) | −18788.7 | −0.701716 | ||||||||
\(896\) | 2247.36 | − | 764.633i | 0.0837937 | − | 0.0285096i | ||||
\(897\) | −2801.07 | −0.104264 | ||||||||
\(898\) | 11988.7 | + | 8674.24i | 0.445509 | + | 0.322342i | ||||
\(899\) | −24028.2 | − | 24028.2i | −0.891420 | − | 0.891420i | ||||
\(900\) | 2836.77 | + | 8615.02i | 0.105065 | + | 0.319075i | ||||
\(901\) | −28187.5 | + | 28187.5i | −1.04225 | + | 1.04225i | ||||
\(902\) | −2290.82 | − | 14281.5i | −0.0845633 | − | 0.527188i | ||||
\(903\) | − | 5587.65i | − | 0.205920i | ||||||
\(904\) | 2416.03 | − | 7588.10i | 0.0888895 | − | 0.279177i | ||||
\(905\) | − | 51104.2i | − | 1.87708i | ||||||
\(906\) | −25374.7 | + | 4070.22i | −0.930485 | + | 0.149254i | ||||
\(907\) | 4565.44 | − | 4565.44i | 0.167136 | − | 0.167136i | −0.618583 | − | 0.785719i | \(-0.712293\pi\) |
0.785719 | + | 0.618583i | \(0.212293\pi\) | |||||||
\(908\) | 8717.25 | − | 17276.5i | 0.318604 | − | 0.631433i | ||||
\(909\) | −13390.5 | − | 13390.5i | −0.488599 | − | 0.488599i | ||||
\(910\) | 440.990 | − | 609.492i | 0.0160645 | − | 0.0222027i | ||||
\(911\) | −2013.95 | −0.0732438 | −0.0366219 | − | 0.999329i | \(-0.511660\pi\) | ||||
−0.0366219 | + | 0.999329i | \(0.511660\pi\) | |||||||
\(912\) | 32203.2 | + | 43597.3i | 1.16925 | + | 1.58295i | ||||
\(913\) | −14931.4 | −0.541245 | ||||||||
\(914\) | −11329.3 | + | 15658.2i | −0.409999 | + | 0.566659i | ||||
\(915\) | −20018.0 | − | 20018.0i | −0.723251 | − | 0.723251i | ||||
\(916\) | −927.261 | − | 467.870i | −0.0334471 | − | 0.0168765i | ||||
\(917\) | 661.359 | − | 661.359i | 0.0238168 | − | 0.0238168i | ||||
\(918\) | −21681.0 | + | 3477.73i | −0.779499 | + | 0.125035i | ||||
\(919\) | − | 37746.5i | − | 1.35489i | −0.735575 | − | 0.677443i | \(-0.763088\pi\) | ||
0.735575 | − | 0.677443i | \(-0.236912\pi\) | |||||||
\(920\) | 6197.46 | − | 3204.04i | 0.222092 | − | 0.114820i | ||||
\(921\) | − | 25141.2i | − | 0.899492i | ||||||
\(922\) | 3785.85 | + | 23601.9i | 0.135228 | + | 0.843044i | ||||
\(923\) | −6800.28 | + | 6800.28i | −0.242507 | + | 0.242507i | ||||
\(924\) | −2704.90 | + | 890.672i | −0.0963037 | + | 0.0317110i | ||||
\(925\) | −4489.07 | − | 4489.07i | −0.159567 | − | 0.159567i | ||||
\(926\) | 9792.51 | + | 7085.24i | 0.347518 | + | 0.251442i | ||||
\(927\) | 42496.2 | 1.50567 | ||||||||
\(928\) | −33102.8 | − | 32457.0i | −1.17096 | − | 1.14812i | ||||
\(929\) | 45643.5 | 1.61197 | 0.805983 | − | 0.591939i | \(-0.201637\pi\) | ||||
0.805983 | + | 0.591939i | \(0.201637\pi\) | |||||||
\(930\) | 31484.1 | + | 22779.9i | 1.11011 | + | 0.803206i | ||||
\(931\) | 24157.8 | + | 24157.8i | 0.850418 | + | 0.850418i | ||||
\(932\) | −32368.1 | + | 10658.2i | −1.13761 | + | 0.374593i | ||||
\(933\) | −31584.8 | + | 31584.8i | −1.10829 | + | 1.10829i | ||||
\(934\) | −7757.82 | − | 48364.1i | −0.271781 | − | 1.69435i | ||||
\(935\) | − | 16939.7i | − | 0.592501i | ||||||
\(936\) | −6066.73 | − | 11734.6i | −0.211856 | − | 0.409785i | ||||
\(937\) | − | 47317.5i | − | 1.64973i | −0.565331 | − | 0.824864i | \(-0.691252\pi\) | ||
0.565331 | − | 0.824864i | \(-0.308748\pi\) | |||||||
\(938\) | −1826.91 | + | 293.045i | −0.0635935 | + | 0.0102007i | ||||
\(939\) | −23895.6 | + | 23895.6i | −0.830460 | + | 0.830460i | ||||
\(940\) | 6870.11 | + | 3466.46i | 0.238381 | + | 0.120280i | ||||
\(941\) | 15074.7 | + | 15074.7i | 0.522234 | + | 0.522234i | 0.918246 | − | 0.396012i | \(-0.129606\pi\) |
−0.396012 | + | 0.918246i | \(0.629606\pi\) | |||||||
\(942\) | −37693.7 | + | 52096.4i | −1.30374 | + | 1.80190i | ||||
\(943\) | −4990.14 | −0.172324 | ||||||||
\(944\) | −626.013 | + | 4164.64i | −0.0215837 | + | 0.143588i | ||||
\(945\) | −2913.75 | −0.100301 | ||||||||
\(946\) | 17245.2 | − | 23834.7i | 0.592697 | − | 0.819166i | ||||
\(947\) | 14567.7 | + | 14567.7i | 0.499880 | + | 0.499880i | 0.911400 | − | 0.411521i | \(-0.135002\pi\) |
−0.411521 | + | 0.911400i | \(0.635002\pi\) | |||||||
\(948\) | −1793.61 | + | 3554.71i | −0.0614490 | + | 0.121784i | ||||
\(949\) | 991.388 | − | 991.388i | 0.0339113 | − | 0.0339113i | ||||
\(950\) | −7197.11 | + | 1154.45i | −0.245795 | + | 0.0394266i | ||||
\(951\) | − | 9654.45i | − | 0.329198i | ||||||
\(952\) | −1894.82 | − | 603.306i | −0.0645077 | − | 0.0205391i | ||||
\(953\) | 42987.2i | 1.46117i | 0.682824 | + | 0.730583i | \(0.260752\pi\) | ||||
−0.682824 | + | 0.730583i | \(0.739248\pi\) | |||||||
\(954\) | 14711.1 | + | 91712.4i | 0.499255 | + | 3.11247i | ||||
\(955\) | −3737.87 | + | 3737.87i | −0.126654 | + | 0.126654i | ||||
\(956\) | −12643.4 | − | 38396.9i | −0.427737 | − | 1.29900i | ||||
\(957\) | 39325.5 | + | 39325.5i | 1.32833 | + | 1.32833i | ||||
\(958\) | 9321.81 | + | 6744.67i | 0.314378 | + | 0.227464i | ||||
\(959\) | −1404.59 | −0.0472956 | ||||||||
\(960\) | 43257.4 | + | 30653.7i | 1.45430 | + | 1.03057i | ||||
\(961\) | −12186.0 | −0.409049 | ||||||||
\(962\) | 7491.10 | + | 5420.09i | 0.251063 | + | 0.181654i | ||||
\(963\) | 32167.4 | + | 32167.4i | 1.07641 | + | 1.07641i | ||||
\(964\) | 122.197 | + | 371.102i | 0.00408268 | + | 0.0123987i | ||||
\(965\) | −19676.5 | + | 19676.5i | −0.656381 | + | 0.656381i | ||||
\(966\) | 155.606 | + | 970.082i | 0.00518274 | + | 0.0323104i | ||||
\(967\) | − | 44030.7i | − | 1.46425i | −0.681170 | − | 0.732126i | \(-0.738528\pi\) | ||
0.681170 | − | 0.732126i | \(-0.261472\pi\) | |||||||
\(968\) | 14410.7 | + | 4588.33i | 0.478488 | + | 0.152350i | ||||
\(969\) | − | 45403.1i | − | 1.50522i | ||||||
\(970\) | 27765.3 | − | 4453.68i | 0.919062 | − | 0.147422i | ||||
\(971\) | 35699.8 | − | 35699.8i | 1.17988 | − | 1.17988i | 0.200101 | − | 0.979775i | \(-0.435873\pi\) |
0.979775 | − | 0.200101i | \(-0.0641270\pi\) | |||||||
\(972\) | 13204.7 | − | 26170.1i | 0.435742 | − | 0.863586i | ||||
\(973\) | 2769.23 | + | 2769.23i | 0.0912409 | + | 0.0912409i | ||||
\(974\) | 26817.0 | − | 37063.7i | 0.882208 | − | 1.21930i | ||||
\(975\) | 2862.58 | 0.0940267 | ||||||||
\(976\) | −17302.7 | − | 2600.88i | −0.567466 | − | 0.0852994i | ||||
\(977\) | −49515.3 | −1.62143 | −0.810714 | − | 0.585442i | \(-0.800921\pi\) | ||||
−0.810714 | + | 0.585442i | \(0.800921\pi\) | |||||||
\(978\) | −14040.6 | + | 19405.6i | −0.459070 | + | 0.634480i | ||||
\(979\) | 13996.6 | + | 13996.6i | 0.456930 | + | 0.456930i | ||||
\(980\) | 29835.3 | + | 15054.1i | 0.972505 | + | 0.490699i | ||||
\(981\) | 26201.6 | − | 26201.6i | 0.852755 | − | 0.852755i | ||||
\(982\) | −53700.2 | + | 8613.76i | −1.74505 | + | 0.279915i | ||||
\(983\) | 40046.2i | 1.29936i | 0.760206 | + | 0.649682i | \(0.225098\pi\) | ||||
−0.760206 | + | 0.649682i | \(0.774902\pi\) | |||||||
\(984\) | −17415.2 | − | 33685.6i | −0.564204 | − | 1.09132i | ||||
\(985\) | 18043.3i | 0.583662i | ||||||||
\(986\) | 6150.64 | + | 38344.6i | 0.198658 | + | 1.23848i | ||||
\(987\) | −766.257 | + | 766.257i | −0.0247115 | + | 0.0247115i | ||||
\(988\) | 10083.7 | − | 3320.36i | 0.324700 | − | 0.106918i | ||||
\(989\) | −7176.90 | − | 7176.90i | −0.230750 | − | 0.230750i | ||||
\(990\) | −31978.4 | − | 23137.6i | −1.02661 | − | 0.742788i | ||||
\(991\) | 18673.2 | 0.598560 | 0.299280 | − | 0.954165i | \(-0.403254\pi\) | ||||
0.299280 | + | 0.954165i | \(0.403254\pi\) | |||||||
\(992\) | 24017.2 | − | 236.586i | 0.768696 | − | 0.00757220i | ||||
\(993\) | 50460.9 | 1.61262 | ||||||||
\(994\) | 2732.88 | + | 1977.34i | 0.0872050 | + | 0.0630960i | ||||
\(995\) | −43306.3 | − | 43306.3i | −1.37980 | − | 1.37980i | ||||
\(996\) | −37182.3 | + | 12243.4i | −1.18290 | + | 0.389506i | ||||
\(997\) | 21982.1 | − | 21982.1i | 0.698274 | − | 0.698274i | −0.265764 | − | 0.964038i | \(-0.585624\pi\) |
0.964038 | + | 0.265764i | \(0.0856243\pi\) | |||||||
\(998\) | 9279.00 | + | 57847.4i | 0.294310 | + | 1.83480i | ||||
\(999\) | − | 35812.1i | − | 1.13418i |
(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 | 16.4.e.a.13.2 | yes | 10 | |
3.2 | odd | 2 | 144.4.k.a.109.4 | 10 | |||
4.3 | odd | 2 | 64.4.e.a.17.5 | 10 | |||
8.3 | odd | 2 | 128.4.e.a.33.1 | 10 | |||
8.5 | even | 2 | 128.4.e.b.33.5 | 10 | |||
12.11 | even | 2 | 576.4.k.a.145.1 | 10 | |||
16.3 | odd | 4 | 128.4.e.a.97.1 | 10 | |||
16.5 | even | 4 | inner | 16.4.e.a.5.2 | ✓ | 10 | |
16.11 | odd | 4 | 64.4.e.a.49.5 | 10 | |||
16.13 | even | 4 | 128.4.e.b.97.5 | 10 | |||
32.3 | odd | 8 | 1024.4.b.k.513.10 | 10 | |||
32.5 | even | 8 | 1024.4.a.n.1.10 | 10 | |||
32.11 | odd | 8 | 1024.4.a.m.1.10 | 10 | |||
32.13 | even | 8 | 1024.4.b.j.513.10 | 10 | |||
32.19 | odd | 8 | 1024.4.b.k.513.1 | 10 | |||
32.21 | even | 8 | 1024.4.a.n.1.1 | 10 | |||
32.27 | odd | 8 | 1024.4.a.m.1.1 | 10 | |||
32.29 | even | 8 | 1024.4.b.j.513.1 | 10 | |||
48.5 | odd | 4 | 144.4.k.a.37.4 | 10 | |||
48.11 | even | 4 | 576.4.k.a.433.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.2 | ✓ | 10 | 16.5 | even | 4 | inner | |
16.4.e.a.13.2 | yes | 10 | 1.1 | even | 1 | trivial | |
64.4.e.a.17.5 | 10 | 4.3 | odd | 2 | |||
64.4.e.a.49.5 | 10 | 16.11 | odd | 4 | |||
128.4.e.a.33.1 | 10 | 8.3 | odd | 2 | |||
128.4.e.a.97.1 | 10 | 16.3 | odd | 4 | |||
128.4.e.b.33.5 | 10 | 8.5 | even | 2 | |||
128.4.e.b.97.5 | 10 | 16.13 | even | 4 | |||
144.4.k.a.37.4 | 10 | 48.5 | odd | 4 | |||
144.4.k.a.109.4 | 10 | 3.2 | odd | 2 | |||
576.4.k.a.145.1 | 10 | 12.11 | even | 2 | |||
576.4.k.a.433.1 | 10 | 48.11 | even | 4 | |||
1024.4.a.m.1.1 | 10 | 32.27 | odd | 8 | |||
1024.4.a.m.1.10 | 10 | 32.11 | odd | 8 | |||
1024.4.a.n.1.1 | 10 | 32.21 | even | 8 | |||
1024.4.a.n.1.10 | 10 | 32.5 | even | 8 | |||
1024.4.b.j.513.1 | 10 | 32.29 | even | 8 | |||
1024.4.b.j.513.10 | 10 | 32.13 | even | 8 | |||
1024.4.b.k.513.1 | 10 | 32.19 | odd | 8 | |||
1024.4.b.k.513.10 | 10 | 32.3 | odd | 8 |