Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,4,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (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: | \(33.6310887033\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{481})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 121x^{2} + 120x + 14400 \) |
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 | 391.1 | ||
Root | \(-5.23293 + 9.06370i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.391 |
Dual form | 570.4.i.i.121.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | −3.00000 | − | 5.19615i | −0.204124 | − | 0.353553i | ||||
\(7\) | −9.46586 | −0.511108 | −0.255554 | − | 0.966795i | \(-0.582258\pi\) | ||||
−0.255554 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | −5.00000 | − | 8.66025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −31.3976 | −0.860611 | −0.430306 | − | 0.902683i | \(-0.641594\pi\) | ||||
−0.430306 | + | 0.902683i | \(0.641594\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 32.7329 | + | 56.6951i | 0.698345 | + | 1.20957i | 0.969040 | + | 0.246903i | \(0.0794130\pi\) |
−0.270695 | + | 0.962665i | \(0.587254\pi\) | |||||||
\(14\) | −9.46586 | + | 16.3953i | −0.180704 | + | 0.312989i | ||||
\(15\) | −7.50000 | − | 12.9904i | −0.129099 | − | 0.223607i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −56.3293 | + | 97.5652i | −0.803639 | + | 1.39194i | 0.113568 | + | 0.993530i | \(0.463772\pi\) |
−0.917206 | + | 0.398413i | \(0.869561\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −82.4939 | − | 7.33165i | −0.996074 | − | 0.0885261i | ||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | −14.1988 | + | 24.5930i | −0.147544 | + | 0.255554i | ||||
\(22\) | −31.3976 | + | 54.3822i | −0.304272 | + | 0.527015i | ||||
\(23\) | 25.4659 | + | 44.1082i | 0.230869 | + | 0.399878i | 0.958064 | − | 0.286554i | \(-0.0925096\pi\) |
−0.727195 | + | 0.686431i | \(0.759176\pi\) | |||||||
\(24\) | −12.0000 | + | 20.7846i | −0.102062 | + | 0.176777i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 130.932 | 0.987609 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 18.9317 | + | 32.7907i | 0.127777 | + | 0.221316i | ||||
\(29\) | −60.3012 | − | 104.445i | −0.386126 | − | 0.668790i | 0.605799 | − | 0.795618i | \(-0.292854\pi\) |
−0.991925 | + | 0.126828i | \(0.959520\pi\) | |||||||
\(30\) | −30.0000 | −0.182574 | ||||||||
\(31\) | 209.932 | 1.21629 | 0.608143 | − | 0.793828i | \(-0.291915\pi\) | ||||
0.608143 | + | 0.793828i | \(0.291915\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −47.0964 | + | 81.5733i | −0.248437 | + | 0.430306i | ||||
\(34\) | 112.659 | + | 195.130i | 0.568258 | + | 0.984252i | ||||
\(35\) | −23.6646 | + | 40.9884i | −0.114287 | + | 0.197951i | ||||
\(36\) | −18.0000 | + | 31.1769i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −164.398 | −0.730454 | −0.365227 | − | 0.930919i | \(-0.619009\pi\) | ||||
−0.365227 | + | 0.930919i | \(0.619009\pi\) | |||||||
\(38\) | −95.1927 | + | 135.552i | −0.406376 | + | 0.578669i | ||||
\(39\) | 196.398 | 0.806379 | ||||||||
\(40\) | −20.0000 | + | 34.6410i | −0.0790569 | + | 0.136931i | ||||
\(41\) | −72.6024 | + | 125.751i | −0.276551 | + | 0.479001i | −0.970525 | − | 0.240999i | \(-0.922525\pi\) |
0.693974 | + | 0.720000i | \(0.255858\pi\) | |||||||
\(42\) | 28.3976 | + | 49.1860i | 0.104330 | + | 0.180704i | ||||
\(43\) | −7.66464 | + | 13.2755i | −0.0271825 | + | 0.0470814i | −0.879297 | − | 0.476275i | \(-0.841987\pi\) |
0.852114 | + | 0.523356i | \(0.175320\pi\) | |||||||
\(44\) | 62.7951 | + | 108.764i | 0.215153 | + | 0.372656i | ||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 101.863 | 0.326499 | ||||||||
\(47\) | 261.988 | + | 453.776i | 0.813082 | + | 1.40830i | 0.910697 | + | 0.413075i | \(0.135545\pi\) |
−0.0976150 | + | 0.995224i | \(0.531121\pi\) | |||||||
\(48\) | 24.0000 | + | 41.5692i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −253.398 | −0.738768 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 168.988 | + | 292.696i | 0.463981 | + | 0.803639i | ||||
\(52\) | 130.932 | − | 226.780i | 0.349172 | − | 0.604784i | ||||
\(53\) | −146.590 | − | 253.902i | −0.379919 | − | 0.658040i | 0.611131 | − | 0.791530i | \(-0.290715\pi\) |
−0.991050 | + | 0.133490i | \(0.957382\pi\) | |||||||
\(54\) | −27.0000 | + | 46.7654i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −78.4939 | + | 135.955i | −0.192439 | + | 0.333313i | ||||
\(56\) | 75.7268 | 0.180704 | ||||||||
\(57\) | −142.789 | + | 203.328i | −0.331805 | + | 0.472482i | ||||
\(58\) | −241.205 | −0.546065 | ||||||||
\(59\) | −2.90365 | + | 5.02927i | −0.00640716 | + | 0.0110975i | −0.869211 | − | 0.494441i | \(-0.835373\pi\) |
0.862804 | + | 0.505539i | \(0.168706\pi\) | |||||||
\(60\) | −30.0000 | + | 51.9615i | −0.0645497 | + | 0.111803i | ||||
\(61\) | −356.624 | − | 617.692i | −0.748542 | − | 1.29651i | −0.948521 | − | 0.316713i | \(-0.897421\pi\) |
0.199979 | − | 0.979800i | \(-0.435913\pi\) | |||||||
\(62\) | 209.932 | − | 363.612i | 0.430022 | − | 0.744820i | ||||
\(63\) | 42.5964 | + | 73.7790i | 0.0851847 | + | 0.147544i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 327.329 | 0.624618 | ||||||||
\(66\) | 94.1927 | + | 163.147i | 0.175672 | + | 0.304272i | ||||
\(67\) | 27.7329 | + | 48.0348i | 0.0505689 | + | 0.0875879i | 0.890202 | − | 0.455566i | \(-0.150563\pi\) |
−0.839633 | + | 0.543154i | \(0.817230\pi\) | |||||||
\(68\) | 450.634 | 0.803639 | ||||||||
\(69\) | 152.795 | 0.266585 | ||||||||
\(70\) | 47.3293 | + | 81.9767i | 0.0808133 | + | 0.139973i | ||||
\(71\) | −112.482 | + | 194.824i | −0.188016 | + | 0.325653i | −0.944589 | − | 0.328256i | \(-0.893539\pi\) |
0.756573 | + | 0.653910i | \(0.226872\pi\) | |||||||
\(72\) | 36.0000 | + | 62.3538i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −177.516 | + | 307.467i | −0.284612 | + | 0.492962i | −0.972515 | − | 0.232840i | \(-0.925198\pi\) |
0.687903 | + | 0.725803i | \(0.258531\pi\) | |||||||
\(74\) | −164.398 | + | 284.745i | −0.258254 | + | 0.447310i | ||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 139.590 | + | 300.431i | 0.210686 | + | 0.453444i | ||||
\(77\) | 297.205 | 0.439865 | ||||||||
\(78\) | 196.398 | − | 340.171i | 0.285098 | − | 0.493804i | ||||
\(79\) | −261.649 | + | 453.189i | −0.372630 | + | 0.645414i | −0.989969 | − | 0.141283i | \(-0.954877\pi\) |
0.617339 | + | 0.786697i | \(0.288211\pi\) | |||||||
\(80\) | 40.0000 | + | 69.2820i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 145.205 | + | 251.502i | 0.195551 | + | 0.338705i | ||||
\(83\) | 499.020 | 0.659934 | 0.329967 | − | 0.943992i | \(-0.392962\pi\) | ||||
0.329967 | + | 0.943992i | \(0.392962\pi\) | |||||||
\(84\) | 113.590 | 0.147544 | ||||||||
\(85\) | 281.646 | + | 487.826i | 0.359398 | + | 0.622496i | ||||
\(86\) | 15.3293 | + | 26.5511i | 0.0192209 | + | 0.0332916i | ||||
\(87\) | −361.807 | −0.445860 | ||||||||
\(88\) | 251.181 | 0.304272 | ||||||||
\(89\) | 148.743 | + | 257.630i | 0.177154 | + | 0.306840i | 0.940905 | − | 0.338672i | \(-0.109978\pi\) |
−0.763751 | + | 0.645511i | \(0.776644\pi\) | |||||||
\(90\) | −45.0000 | + | 77.9423i | −0.0527046 | + | 0.0912871i | ||||
\(91\) | −309.845 | − | 536.668i | −0.356930 | − | 0.618220i | ||||
\(92\) | 101.863 | − | 176.433i | 0.115435 | − | 0.199939i | ||||
\(93\) | 314.898 | − | 545.419i | 0.351111 | − | 0.608143i | ||||
\(94\) | 1047.95 | 1.14987 | ||||||||
\(95\) | −237.982 | + | 338.880i | −0.257015 | + | 0.365983i | ||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −182.261 | + | 315.685i | −0.190781 | + | 0.330443i | −0.945509 | − | 0.325595i | \(-0.894436\pi\) |
0.754728 | + | 0.656038i | \(0.227769\pi\) | |||||||
\(98\) | −253.398 | + | 438.897i | −0.261194 | + | 0.452401i | ||||
\(99\) | 141.289 | + | 244.720i | 0.143435 | + | 0.248437i | ||||
\(100\) | −50.0000 | + | 86.6025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 316.948 | + | 548.969i | 0.312252 | + | 0.540837i | 0.978850 | − | 0.204581i | \(-0.0655833\pi\) |
−0.666597 | + | 0.745418i | \(0.732250\pi\) | |||||||
\(102\) | 675.951 | 0.656168 | ||||||||
\(103\) | 1815.42 | 1.73668 | 0.868342 | − | 0.495967i | \(-0.165186\pi\) | ||||
0.868342 | + | 0.495967i | \(0.165186\pi\) | |||||||
\(104\) | −261.863 | − | 453.561i | −0.246902 | − | 0.427647i | ||||
\(105\) | 70.9939 | + | 122.965i | 0.0659838 | + | 0.114287i | ||||
\(106\) | −586.361 | −0.537287 | ||||||||
\(107\) | −1540.20 | −1.39156 | −0.695779 | − | 0.718256i | \(-0.744941\pi\) | ||||
−0.695779 | + | 0.718256i | \(0.744941\pi\) | |||||||
\(108\) | 54.0000 | + | 93.5307i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 362.482 | − | 627.837i | 0.318527 | − | 0.551705i | −0.661654 | − | 0.749809i | \(-0.730145\pi\) |
0.980181 | + | 0.198104i | \(0.0634785\pi\) | |||||||
\(110\) | 156.988 | + | 271.911i | 0.136075 | + | 0.235688i | ||||
\(111\) | −246.596 | + | 427.117i | −0.210864 | + | 0.365227i | ||||
\(112\) | 75.7268 | − | 131.163i | 0.0638885 | − | 0.110658i | ||||
\(113\) | −1283.29 | −1.06834 | −0.534168 | − | 0.845378i | \(-0.679375\pi\) | ||||
−0.534168 | + | 0.845378i | \(0.679375\pi\) | |||||||
\(114\) | 209.385 | + | 450.646i | 0.172024 | + | 0.370236i | ||||
\(115\) | 254.659 | 0.206496 | ||||||||
\(116\) | −241.205 | + | 417.779i | −0.193063 | + | 0.334395i | ||||
\(117\) | 294.596 | − | 510.256i | 0.232782 | − | 0.403189i | ||||
\(118\) | 5.80730 | + | 10.0585i | 0.00453055 | + | 0.00784714i | ||||
\(119\) | 533.205 | − | 923.538i | 0.410746 | − | 0.711433i | ||||
\(120\) | 60.0000 | + | 103.923i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | −345.193 | −0.259348 | ||||||||
\(122\) | −1426.50 | −1.05860 | ||||||||
\(123\) | 217.807 | + | 377.253i | 0.159667 | + | 0.276551i | ||||
\(124\) | −419.863 | − | 727.225i | −0.304071 | − | 0.526667i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 170.385 | 0.120469 | ||||||||
\(127\) | −804.088 | − | 1392.72i | −0.561821 | − | 0.973103i | −0.997338 | − | 0.0729218i | \(-0.976768\pi\) |
0.435517 | − | 0.900181i | \(-0.356566\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 22.9939 | + | 39.8266i | 0.0156938 | + | 0.0271825i | ||||
\(130\) | 327.329 | − | 566.951i | 0.220836 | − | 0.382499i | ||||
\(131\) | −1441.26 | + | 2496.33i | −0.961245 | + | 1.66493i | −0.241865 | + | 0.970310i | \(0.577759\pi\) |
−0.719381 | + | 0.694616i | \(0.755574\pi\) | |||||||
\(132\) | 376.771 | 0.248437 | ||||||||
\(133\) | 780.876 | + | 69.4003i | 0.509102 | + | 0.0452464i | ||||
\(134\) | 110.932 | 0.0715152 | ||||||||
\(135\) | −67.5000 | + | 116.913i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 450.634 | − | 780.521i | 0.284129 | − | 0.492126i | ||||
\(137\) | 143.049 | + | 247.768i | 0.0892078 | + | 0.154512i | 0.907176 | − | 0.420750i | \(-0.138233\pi\) |
−0.817969 | + | 0.575263i | \(0.804900\pi\) | |||||||
\(138\) | 152.795 | − | 264.649i | 0.0942521 | − | 0.163249i | ||||
\(139\) | 919.174 | + | 1592.06i | 0.560887 | + | 0.971486i | 0.997419 | + | 0.0717968i | \(0.0228733\pi\) |
−0.436532 | + | 0.899689i | \(0.643793\pi\) | |||||||
\(140\) | 189.317 | 0.114287 | ||||||||
\(141\) | 1571.93 | 0.938866 | ||||||||
\(142\) | 224.964 | + | 389.648i | 0.132947 | + | 0.230272i | ||||
\(143\) | −1027.73 | − | 1780.09i | −0.601003 | − | 1.04097i | ||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −603.012 | −0.345362 | ||||||||
\(146\) | 355.032 | + | 614.933i | 0.201251 | + | 0.348577i | ||||
\(147\) | −380.096 | + | 658.346i | −0.213264 | + | 0.369384i | ||||
\(148\) | 328.795 | + | 569.490i | 0.182613 | + | 0.316296i | ||||
\(149\) | 200.165 | − | 346.695i | 0.110055 | − | 0.190620i | −0.805738 | − | 0.592273i | \(-0.798231\pi\) |
0.915792 | + | 0.401653i | \(0.131564\pi\) | |||||||
\(150\) | −75.0000 | + | 129.904i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | 534.739 | 0.288188 | 0.144094 | − | 0.989564i | \(-0.453973\pi\) | ||||
0.144094 | + | 0.989564i | \(0.453973\pi\) | |||||||
\(152\) | 659.951 | + | 58.6532i | 0.352165 | + | 0.0312987i | ||||
\(153\) | 1013.93 | 0.535759 | ||||||||
\(154\) | 297.205 | − | 514.774i | 0.155516 | − | 0.269361i | ||||
\(155\) | 524.829 | − | 909.031i | 0.271970 | − | 0.471065i | ||||
\(156\) | −392.795 | − | 680.341i | −0.201595 | − | 0.349172i | ||||
\(157\) | 161.733 | − | 280.130i | 0.0822146 | − | 0.142400i | −0.821986 | − | 0.569507i | \(-0.807134\pi\) |
0.904201 | + | 0.427107i | \(0.140467\pi\) | |||||||
\(158\) | 523.297 | + | 906.378i | 0.263489 | + | 0.456377i | ||||
\(159\) | −879.542 | −0.438693 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | −241.056 | − | 417.521i | −0.117999 | − | 0.204381i | ||||
\(162\) | 81.0000 | + | 140.296i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −1548.45 | −0.744072 | −0.372036 | − | 0.928218i | \(-0.621340\pi\) | ||||
−0.372036 | + | 0.928218i | \(0.621340\pi\) | |||||||
\(164\) | 580.819 | 0.276551 | ||||||||
\(165\) | 235.482 | + | 407.866i | 0.111104 | + | 0.192439i | ||||
\(166\) | 499.020 | − | 864.327i | 0.233322 | − | 0.404125i | ||||
\(167\) | −87.8073 | − | 152.087i | −0.0406870 | − | 0.0704720i | 0.844965 | − | 0.534822i | \(-0.179621\pi\) |
−0.885652 | + | 0.464350i | \(0.846288\pi\) | |||||||
\(168\) | 113.590 | − | 196.744i | 0.0521648 | − | 0.0903520i | ||||
\(169\) | −1044.39 | + | 1808.94i | −0.475371 | + | 0.823366i | ||||
\(170\) | 1126.59 | 0.508266 | ||||||||
\(171\) | 314.078 | + | 675.969i | 0.140457 | + | 0.302296i | ||||
\(172\) | 61.3171 | 0.0271825 | ||||||||
\(173\) | 408.329 | − | 707.247i | 0.179449 | − | 0.310815i | −0.762243 | − | 0.647291i | \(-0.775902\pi\) |
0.941692 | + | 0.336476i | \(0.109235\pi\) | |||||||
\(174\) | −361.807 | + | 626.669i | −0.157635 | + | 0.273032i | ||||
\(175\) | 118.323 | + | 204.942i | 0.0511108 | + | 0.0885265i | ||||
\(176\) | 251.181 | − | 435.057i | 0.107576 | − | 0.186328i | ||||
\(177\) | 8.71094 | + | 15.0878i | 0.00369918 | + | 0.00640716i | ||||
\(178\) | 594.971 | 0.250534 | ||||||||
\(179\) | −2331.87 | −0.973700 | −0.486850 | − | 0.873486i | \(-0.661854\pi\) | ||||
−0.486850 | + | 0.873486i | \(0.661854\pi\) | |||||||
\(180\) | 90.0000 | + | 155.885i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −1142.57 | − | 1978.98i | −0.469206 | − | 0.812688i | 0.530174 | − | 0.847889i | \(-0.322126\pi\) |
−0.999380 | + | 0.0352002i | \(0.988793\pi\) | |||||||
\(182\) | −1239.38 | −0.504775 | ||||||||
\(183\) | −2139.75 | −0.864342 | ||||||||
\(184\) | −203.727 | − | 352.865i | −0.0816247 | − | 0.141378i | ||||
\(185\) | −410.994 | + | 711.862i | −0.163334 | + | 0.282904i | ||||
\(186\) | −629.795 | − | 1090.84i | −0.248273 | − | 0.430022i | ||||
\(187\) | 1768.60 | − | 3063.31i | 0.691620 | − | 1.19792i | ||||
\(188\) | 1047.95 | − | 1815.11i | 0.406541 | − | 0.704150i | ||||
\(189\) | 255.578 | 0.0983628 | ||||||||
\(190\) | 348.976 | + | 751.077i | 0.133249 | + | 0.286783i | ||||
\(191\) | −2159.56 | −0.818118 | −0.409059 | − | 0.912508i | \(-0.634143\pi\) | ||||
−0.409059 | + | 0.912508i | \(0.634143\pi\) | |||||||
\(192\) | 96.0000 | − | 166.277i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 1257.17 | − | 2177.48i | 0.468876 | − | 0.812117i | −0.530491 | − | 0.847691i | \(-0.677992\pi\) |
0.999367 | + | 0.0355735i | \(0.0113258\pi\) | |||||||
\(194\) | 364.522 | + | 631.371i | 0.134903 | + | 0.233659i | ||||
\(195\) | 490.994 | − | 850.426i | 0.180312 | − | 0.312309i | ||||
\(196\) | 506.795 | + | 877.795i | 0.184692 | + | 0.319896i | ||||
\(197\) | −5315.00 | −1.92222 | −0.961112 | − | 0.276159i | \(-0.910938\pi\) | ||||
−0.961112 | + | 0.276159i | \(0.910938\pi\) | |||||||
\(198\) | 565.156 | 0.202848 | ||||||||
\(199\) | 791.395 | + | 1370.74i | 0.281912 | + | 0.488286i | 0.971856 | − | 0.235577i | \(-0.0756980\pi\) |
−0.689944 | + | 0.723863i | \(0.742365\pi\) | |||||||
\(200\) | 100.000 | + | 173.205i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 166.398 | 0.0583919 | ||||||||
\(202\) | 1267.79 | 0.441591 | ||||||||
\(203\) | 570.803 | + | 988.659i | 0.197352 | + | 0.341824i | ||||
\(204\) | 675.951 | − | 1170.78i | 0.231990 | − | 0.401819i | ||||
\(205\) | 363.012 | + | 628.756i | 0.123677 | + | 0.214216i | ||||
\(206\) | 1815.42 | − | 3144.39i | 0.614010 | − | 1.06350i | ||||
\(207\) | 229.193 | − | 396.973i | 0.0769565 | − | 0.133293i | ||||
\(208\) | −1047.45 | −0.349172 | ||||||||
\(209\) | 2590.11 | + | 230.196i | 0.857232 | + | 0.0761865i | ||||
\(210\) | 283.976 | 0.0933152 | ||||||||
\(211\) | −590.332 | + | 1022.48i | −0.192607 | + | 0.333605i | −0.946113 | − | 0.323835i | \(-0.895028\pi\) |
0.753506 | + | 0.657441i | \(0.228361\pi\) | |||||||
\(212\) | −586.361 | + | 1015.61i | −0.189960 | + | 0.329020i | ||||
\(213\) | 337.445 | + | 584.472i | 0.108551 | + | 0.188016i | ||||
\(214\) | −1540.20 | + | 2667.71i | −0.491990 | + | 0.852152i | ||||
\(215\) | 38.3232 | + | 66.3777i | 0.0121564 | + | 0.0210555i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −1987.18 | −0.621653 | ||||||||
\(218\) | −724.964 | − | 1255.67i | −0.225233 | − | 0.390114i | ||||
\(219\) | 532.548 | + | 922.400i | 0.164321 | + | 0.284612i | ||||
\(220\) | 627.951 | 0.192439 | ||||||||
\(221\) | −7375.29 | −2.24487 | ||||||||
\(222\) | 493.193 | + | 854.235i | 0.149103 | + | 0.258254i | ||||
\(223\) | 1930.92 | − | 3344.45i | 0.579837 | − | 1.00431i | −0.415660 | − | 0.909520i | \(-0.636449\pi\) |
0.995498 | − | 0.0947877i | \(-0.0302172\pi\) | |||||||
\(224\) | −151.454 | − | 262.325i | −0.0451760 | − | 0.0782471i | ||||
\(225\) | −112.500 | + | 194.856i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | −1283.29 | + | 2222.73i | −0.377714 | + | 0.654220i | ||||
\(227\) | −5807.25 | −1.69798 | −0.848988 | − | 0.528412i | \(-0.822788\pi\) | ||||
−0.848988 | + | 0.528412i | \(0.822788\pi\) | |||||||
\(228\) | 989.927 | + | 87.9798i | 0.287542 | + | 0.0255553i | ||||
\(229\) | −2586.63 | −0.746416 | −0.373208 | − | 0.927748i | \(-0.621742\pi\) | ||||
−0.373208 | + | 0.927748i | \(0.621742\pi\) | |||||||
\(230\) | 254.659 | − | 441.082i | 0.0730073 | − | 0.126452i | ||||
\(231\) | 445.807 | − | 772.161i | 0.126978 | − | 0.219933i | ||||
\(232\) | 482.410 | + | 835.558i | 0.136516 | + | 0.236453i | ||||
\(233\) | −207.442 | + | 359.299i | −0.0583260 | + | 0.101024i | −0.893714 | − | 0.448637i | \(-0.851910\pi\) |
0.835388 | + | 0.549661i | \(0.185243\pi\) | |||||||
\(234\) | −589.193 | − | 1020.51i | −0.164601 | − | 0.285098i | ||||
\(235\) | 2619.88 | 0.727243 | ||||||||
\(236\) | 23.2292 | 0.00640716 | ||||||||
\(237\) | 784.946 | + | 1359.57i | 0.215138 | + | 0.372630i | ||||
\(238\) | −1066.41 | − | 1847.08i | −0.290441 | − | 0.503059i | ||||
\(239\) | 5546.06 | 1.50102 | 0.750512 | − | 0.660857i | \(-0.229807\pi\) | ||||
0.750512 | + | 0.660857i | \(0.229807\pi\) | |||||||
\(240\) | 240.000 | 0.0645497 | ||||||||
\(241\) | −393.583 | − | 681.706i | −0.105199 | − | 0.182210i | 0.808621 | − | 0.588330i | \(-0.200215\pi\) |
−0.913819 | + | 0.406121i | \(0.866881\pi\) | |||||||
\(242\) | −345.193 | + | 597.891i | −0.0916935 | + | 0.158818i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −1426.50 | + | 2470.77i | −0.374271 | + | 0.648257i | ||||
\(245\) | −633.494 | + | 1097.24i | −0.165194 | + | 0.286124i | ||||
\(246\) | 871.229 | 0.225803 | ||||||||
\(247\) | −2284.60 | − | 4916.99i | −0.588525 | − | 1.26664i | ||||
\(248\) | −1679.45 | −0.430022 | ||||||||
\(249\) | 748.529 | − | 1296.49i | 0.190507 | − | 0.329967i | ||||
\(250\) | −125.000 | + | 216.506i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 626.128 | + | 1084.49i | 0.157454 | + | 0.272718i | 0.933950 | − | 0.357404i | \(-0.116338\pi\) |
−0.776496 | + | 0.630122i | \(0.783005\pi\) | |||||||
\(252\) | 170.385 | − | 295.116i | 0.0425923 | − | 0.0737721i | ||||
\(253\) | −799.566 | − | 1384.89i | −0.198689 | − | 0.344139i | ||||
\(254\) | −3216.35 | −0.794535 | ||||||||
\(255\) | 1689.88 | 0.414997 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −966.293 | − | 1673.67i | −0.234536 | − | 0.406228i | 0.724602 | − | 0.689168i | \(-0.242024\pi\) |
−0.959138 | + | 0.282940i | \(0.908690\pi\) | |||||||
\(258\) | 91.9757 | 0.0221944 | ||||||||
\(259\) | 1556.16 | 0.373341 | ||||||||
\(260\) | −654.659 | − | 1133.90i | −0.156155 | − | 0.270468i | ||||
\(261\) | −542.711 | + | 940.003i | −0.128709 | + | 0.222930i | ||||
\(262\) | 2882.51 | + | 4992.66i | 0.679703 | + | 1.17728i | ||||
\(263\) | −535.153 | + | 926.913i | −0.125471 | + | 0.217323i | −0.921917 | − | 0.387387i | \(-0.873378\pi\) |
0.796446 | + | 0.604710i | \(0.206711\pi\) | |||||||
\(264\) | 376.771 | − | 652.586i | 0.0878358 | − | 0.152136i | ||||
\(265\) | −1465.90 | −0.339810 | ||||||||
\(266\) | 901.080 | − | 1283.12i | 0.207702 | − | 0.295763i | ||||
\(267\) | 892.457 | 0.204560 | ||||||||
\(268\) | 110.932 | − | 192.139i | 0.0252845 | − | 0.0437940i | ||||
\(269\) | −3700.48 | + | 6409.43i | −0.838745 | + | 1.45275i | 0.0521986 | + | 0.998637i | \(0.483377\pi\) |
−0.890944 | + | 0.454113i | \(0.849956\pi\) | |||||||
\(270\) | 135.000 | + | 233.827i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | 1182.60 | − | 2048.32i | 0.265084 | − | 0.459139i | −0.702502 | − | 0.711682i | \(-0.747934\pi\) |
0.967586 | + | 0.252543i | \(0.0812670\pi\) | |||||||
\(272\) | −901.268 | − | 1561.04i | −0.200910 | − | 0.347986i | ||||
\(273\) | −1859.07 | −0.412147 | ||||||||
\(274\) | 572.195 | 0.126159 | ||||||||
\(275\) | 392.470 | + | 679.777i | 0.0860611 | + | 0.149062i | ||||
\(276\) | −305.590 | − | 529.298i | −0.0666463 | − | 0.115435i | ||||
\(277\) | 5235.96 | 1.13573 | 0.567867 | − | 0.823121i | \(-0.307769\pi\) | ||||
0.567867 | + | 0.823121i | \(0.307769\pi\) | |||||||
\(278\) | 3676.70 | 0.793215 | ||||||||
\(279\) | −944.693 | − | 1636.26i | −0.202714 | − | 0.351111i | ||||
\(280\) | 189.317 | − | 327.907i | 0.0404067 | − | 0.0699864i | ||||
\(281\) | −3956.10 | − | 6852.16i | −0.839861 | − | 1.45468i | −0.890010 | − | 0.455941i | \(-0.849303\pi\) |
0.0501488 | − | 0.998742i | \(-0.484030\pi\) | |||||||
\(282\) | 1571.93 | − | 2722.66i | 0.331939 | − | 0.574936i | ||||
\(283\) | 2520.00 | − | 4364.76i | 0.529323 | − | 0.916814i | −0.470092 | − | 0.882617i | \(-0.655779\pi\) |
0.999415 | − | 0.0341967i | \(-0.0108873\pi\) | |||||||
\(284\) | 899.854 | 0.188016 | ||||||||
\(285\) | 523.464 | + | 1126.61i | 0.108798 | + | 0.234158i | ||||
\(286\) | −4110.94 | −0.849947 | ||||||||
\(287\) | 687.244 | − | 1190.34i | 0.141348 | − | 0.244821i | ||||
\(288\) | 144.000 | − | 249.415i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −3889.48 | − | 6736.77i | −0.791670 | − | 1.37121i | ||||
\(290\) | −603.012 | + | 1044.45i | −0.122104 | + | 0.211490i | ||||
\(291\) | 546.783 | + | 947.056i | 0.110148 | + | 0.190781i | ||||
\(292\) | 1420.13 | 0.284612 | ||||||||
\(293\) | −336.152 | −0.0670245 | −0.0335123 | − | 0.999438i | \(-0.510669\pi\) | ||||
−0.0335123 | + | 0.999438i | \(0.510669\pi\) | |||||||
\(294\) | 760.193 | + | 1316.69i | 0.150800 | + | 0.261194i | ||||
\(295\) | 14.5182 | + | 25.1463i | 0.00286537 | + | 0.00496297i | ||||
\(296\) | 1315.18 | 0.258254 | ||||||||
\(297\) | 847.734 | 0.165625 | ||||||||
\(298\) | −400.329 | − | 693.391i | −0.0778203 | − | 0.134789i | ||||
\(299\) | −1667.14 | + | 2887.58i | −0.322453 | + | 0.558505i | ||||
\(300\) | 150.000 | + | 259.808i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | 72.5524 | − | 125.664i | 0.0138932 | − | 0.0240637i | ||||
\(302\) | 534.739 | − | 926.195i | 0.101890 | − | 0.176479i | ||||
\(303\) | 1901.69 | 0.360558 | ||||||||
\(304\) | 761.542 | − | 1084.42i | 0.143676 | − | 0.204591i | ||||
\(305\) | −3566.24 | −0.669517 | ||||||||
\(306\) | 1013.93 | − | 1756.17i | 0.189419 | − | 0.328084i | ||||
\(307\) | 2153.57 | − | 3730.09i | 0.400360 | − | 0.693444i | −0.593409 | − | 0.804901i | \(-0.702218\pi\) |
0.993769 | + | 0.111457i | \(0.0355518\pi\) | |||||||
\(308\) | −594.410 | − | 1029.55i | −0.109966 | − | 0.190467i | ||||
\(309\) | 2723.13 | − | 4716.59i | 0.501337 | − | 0.868342i | ||||
\(310\) | −1049.66 | − | 1818.06i | −0.192312 | − | 0.333093i | ||||
\(311\) | −9483.69 | −1.72917 | −0.864583 | − | 0.502490i | \(-0.832417\pi\) | ||||
−0.864583 | + | 0.502490i | \(0.832417\pi\) | |||||||
\(312\) | −1571.18 | −0.285098 | ||||||||
\(313\) | 2104.86 | + | 3645.72i | 0.380107 | + | 0.658365i | 0.991077 | − | 0.133289i | \(-0.0425538\pi\) |
−0.610970 | + | 0.791654i | \(0.709220\pi\) | |||||||
\(314\) | −323.466 | − | 560.259i | −0.0581345 | − | 0.100692i | ||||
\(315\) | 425.964 | 0.0761915 | ||||||||
\(316\) | 2093.19 | 0.372630 | ||||||||
\(317\) | −4429.65 | − | 7672.37i | −0.784838 | − | 1.35938i | −0.929096 | − | 0.369840i | \(-0.879413\pi\) |
0.144257 | − | 0.989540i | \(-0.453921\pi\) | |||||||
\(318\) | −879.542 | + | 1523.41i | −0.155101 | + | 0.268644i | ||||
\(319\) | 1893.31 | + | 3279.31i | 0.332304 | + | 0.575568i | ||||
\(320\) | 160.000 | − | 277.128i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −2310.30 | + | 4001.56i | −0.401708 | + | 0.695779i | ||||
\(322\) | −964.225 | −0.166876 | ||||||||
\(323\) | 5362.14 | − | 7635.55i | 0.923707 | − | 1.31534i | ||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 818.323 | − | 1417.38i | 0.139669 | − | 0.241914i | ||||
\(326\) | −1548.45 | + | 2681.99i | −0.263069 | + | 0.455649i | ||||
\(327\) | −1087.45 | − | 1883.51i | −0.183902 | − | 0.318527i | ||||
\(328\) | 580.819 | − | 1006.01i | 0.0977756 | − | 0.169352i | ||||
\(329\) | −2479.94 | − | 4295.38i | −0.415573 | − | 0.719793i | ||||
\(330\) | 941.927 | 0.157125 | ||||||||
\(331\) | −11577.5 | −1.92253 | −0.961263 | − | 0.275632i | \(-0.911113\pi\) | ||||
−0.961263 | + | 0.275632i | \(0.911113\pi\) | |||||||
\(332\) | −998.039 | − | 1728.65i | −0.164984 | − | 0.285760i | ||||
\(333\) | 739.789 | + | 1281.35i | 0.121742 | + | 0.210864i | ||||
\(334\) | −351.229 | −0.0575401 | ||||||||
\(335\) | 277.329 | 0.0452302 | ||||||||
\(336\) | −227.181 | − | 393.488i | −0.0368861 | − | 0.0638885i | ||||
\(337\) | −3149.68 | + | 5455.41i | −0.509122 | + | 0.881826i | 0.490822 | + | 0.871260i | \(0.336697\pi\) |
−0.999944 | + | 0.0105658i | \(0.996637\pi\) | |||||||
\(338\) | 2088.78 | + | 3617.87i | 0.336138 | + | 0.582208i | ||||
\(339\) | −1924.94 | + | 3334.09i | −0.308402 | + | 0.534168i | ||||
\(340\) | 1126.59 | − | 1951.30i | 0.179699 | − | 0.311248i | ||||
\(341\) | −6591.35 | −1.04675 | ||||||||
\(342\) | 1484.89 | + | 131.970i | 0.234777 | + | 0.0208658i | ||||
\(343\) | 5645.41 | 0.888699 | ||||||||
\(344\) | 61.3171 | − | 106.204i | 0.00961046 | − | 0.0166458i | ||||
\(345\) | 381.988 | − | 661.622i | 0.0596102 | − | 0.103248i | ||||
\(346\) | −816.659 | − | 1414.49i | −0.126890 | − | 0.219779i | ||||
\(347\) | −2098.99 | + | 3635.56i | −0.324725 | + | 0.562441i | −0.981457 | − | 0.191684i | \(-0.938605\pi\) |
0.656731 | + | 0.754125i | \(0.271939\pi\) | |||||||
\(348\) | 723.615 | + | 1253.34i | 0.111465 | + | 0.193063i | ||||
\(349\) | 3662.09 | 0.561683 | 0.280841 | − | 0.959754i | \(-0.409387\pi\) | ||||
0.280841 | + | 0.959754i | \(0.409387\pi\) | |||||||
\(350\) | 473.293 | 0.0722816 | ||||||||
\(351\) | −883.789 | − | 1530.77i | −0.134396 | − | 0.232782i | ||||
\(352\) | −502.361 | − | 870.115i | −0.0760680 | − | 0.131754i | ||||
\(353\) | 6923.15 | 1.04386 | 0.521930 | − | 0.852989i | \(-0.325212\pi\) | ||||
0.521930 | + | 0.852989i | \(0.325212\pi\) | |||||||
\(354\) | 34.8438 | 0.00523143 | ||||||||
\(355\) | 562.409 | + | 974.121i | 0.0840833 | + | 0.145636i | ||||
\(356\) | 594.971 | − | 1030.52i | 0.0885770 | − | 0.153420i | ||||
\(357\) | −1599.61 | − | 2770.61i | −0.237144 | − | 0.410746i | ||||
\(358\) | −2331.87 | + | 4038.92i | −0.344255 | + | 0.596267i | ||||
\(359\) | 534.689 | − | 926.108i | 0.0786066 | − | 0.136151i | −0.824042 | − | 0.566528i | \(-0.808286\pi\) |
0.902649 | + | 0.430378i | \(0.141620\pi\) | |||||||
\(360\) | 360.000 | 0.0527046 | ||||||||
\(361\) | 6751.49 | + | 1209.63i | 0.984326 | + | 0.176357i | ||||
\(362\) | −4570.26 | −0.663557 | ||||||||
\(363\) | −517.789 | + | 896.837i | −0.0748674 | + | 0.129674i | ||||
\(364\) | −1239.38 | + | 2146.67i | −0.178465 | + | 0.309110i | ||||
\(365\) | 887.580 | + | 1537.33i | 0.127282 | + | 0.220459i | ||||
\(366\) | −2139.75 | + | 3706.15i | −0.305591 | + | 0.529299i | ||||
\(367\) | 5737.85 | + | 9938.25i | 0.816113 | + | 1.41355i | 0.908526 | + | 0.417828i | \(0.137209\pi\) |
−0.0924134 | + | 0.995721i | \(0.529458\pi\) | |||||||
\(368\) | −814.907 | −0.115435 | ||||||||
\(369\) | 1306.84 | 0.184367 | ||||||||
\(370\) | 821.988 | + | 1423.72i | 0.115495 | + | 0.200043i | ||||
\(371\) | 1387.60 | + | 2403.40i | 0.194180 | + | 0.336329i | ||||
\(372\) | −2519.18 | −0.351111 | ||||||||
\(373\) | 7551.41 | 1.04825 | 0.524125 | − | 0.851641i | \(-0.324392\pi\) | ||||
0.524125 | + | 0.851641i | \(0.324392\pi\) | |||||||
\(374\) | −3537.20 | − | 6126.62i | −0.489049 | − | 0.847059i | ||||
\(375\) | −187.500 | + | 324.760i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −2095.90 | − | 3630.21i | −0.287468 | − | 0.497909i | ||||
\(377\) | 3947.67 | − | 6837.57i | 0.539298 | − | 0.934092i | ||||
\(378\) | 255.578 | − | 442.674i | 0.0347765 | − | 0.0602347i | ||||
\(379\) | 5449.18 | 0.738537 | 0.369269 | − | 0.929323i | \(-0.379608\pi\) | ||||
0.369269 | + | 0.929323i | \(0.379608\pi\) | |||||||
\(380\) | 1649.88 | + | 146.633i | 0.222729 | + | 0.0197950i | ||||
\(381\) | −4824.53 | −0.648735 | ||||||||
\(382\) | −2159.56 | + | 3740.47i | −0.289248 | + | 0.500993i | ||||
\(383\) | −1407.45 | + | 2437.77i | −0.187773 | + | 0.325233i | −0.944508 | − | 0.328490i | \(-0.893460\pi\) |
0.756734 | + | 0.653723i | \(0.226794\pi\) | |||||||
\(384\) | −192.000 | − | 332.554i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 743.012 | − | 1286.93i | 0.0983569 | − | 0.170359i | ||||
\(386\) | −2514.34 | − | 4354.96i | −0.331545 | − | 0.574253i | ||||
\(387\) | 137.964 | 0.0181217 | ||||||||
\(388\) | 1458.09 | 0.190781 | ||||||||
\(389\) | −1434.38 | − | 2484.43i | −0.186957 | − | 0.323819i | 0.757277 | − | 0.653093i | \(-0.226529\pi\) |
−0.944234 | + | 0.329275i | \(0.893196\pi\) | |||||||
\(390\) | −981.988 | − | 1700.85i | −0.127500 | − | 0.220836i | ||||
\(391\) | −5737.89 | −0.742143 | ||||||||
\(392\) | 2027.18 | 0.261194 | ||||||||
\(393\) | 4323.77 | + | 7488.99i | 0.554975 | + | 0.961245i | ||||
\(394\) | −5315.00 | + | 9205.85i | −0.679609 | + | 1.17712i | ||||
\(395\) | 1308.24 | + | 2265.94i | 0.166645 | + | 0.288638i | ||||
\(396\) | 565.156 | − | 978.879i | 0.0717176 | − | 0.124219i | ||||
\(397\) | −1404.03 | + | 2431.85i | −0.177497 | + | 0.307433i | −0.941022 | − | 0.338344i | \(-0.890133\pi\) |
0.763526 | + | 0.645777i | \(0.223467\pi\) | |||||||
\(398\) | 3165.58 | 0.398684 | ||||||||
\(399\) | 1351.62 | − | 1924.67i | 0.169588 | − | 0.241489i | ||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 4243.89 | − | 7350.64i | 0.528503 | − | 0.915395i | −0.470944 | − | 0.882163i | \(-0.656087\pi\) |
0.999448 | − | 0.0332317i | \(-0.0105799\pi\) | |||||||
\(402\) | 166.398 | − | 288.209i | 0.0206447 | − | 0.0357576i | ||||
\(403\) | 6871.68 | + | 11902.1i | 0.849386 | + | 1.47118i | ||||
\(404\) | 1267.79 | − | 2195.88i | 0.156126 | − | 0.270418i | ||||
\(405\) | 202.500 | + | 350.740i | 0.0248452 | + | 0.0430331i | ||||
\(406\) | 2283.21 | 0.279098 | ||||||||
\(407\) | 5161.68 | 0.628637 | ||||||||
\(408\) | −1351.90 | − | 2341.56i | −0.164042 | − | 0.284129i | ||||
\(409\) | 979.037 | + | 1695.74i | 0.118363 | + | 0.205010i | 0.919119 | − | 0.393980i | \(-0.128902\pi\) |
−0.800756 | + | 0.598990i | \(0.795569\pi\) | |||||||
\(410\) | 1452.05 | 0.174906 | ||||||||
\(411\) | 858.292 | 0.103008 | ||||||||
\(412\) | −3630.83 | − | 6288.79i | −0.434171 | − | 0.752006i | ||||
\(413\) | 27.4855 | − | 47.6063i | 0.00327475 | − | 0.00567204i | ||||
\(414\) | −458.385 | − | 793.947i | −0.0544165 | − | 0.0942521i | ||||
\(415\) | 1247.55 | − | 2160.82i | 0.147566 | − | 0.255591i | ||||
\(416\) | −1047.45 | + | 1814.24i | −0.123451 | + | 0.213824i | ||||
\(417\) | 5515.05 | 0.647657 | ||||||||
\(418\) | 2988.82 | − | 4256.00i | 0.349732 | − | 0.498009i | ||||
\(419\) | 6227.21 | 0.726060 | 0.363030 | − | 0.931777i | \(-0.381742\pi\) | ||||
0.363030 | + | 0.931777i | \(0.381742\pi\) | |||||||
\(420\) | 283.976 | − | 491.860i | 0.0329919 | − | 0.0571436i | ||||
\(421\) | 4638.03 | − | 8033.31i | 0.536921 | − | 0.929975i | −0.462147 | − | 0.886804i | \(-0.652921\pi\) |
0.999068 | − | 0.0431711i | \(-0.0137461\pi\) | |||||||
\(422\) | 1180.66 | + | 2044.97i | 0.136194 | + | 0.235895i | ||||
\(423\) | 2357.89 | − | 4083.99i | 0.271027 | − | 0.469433i | ||||
\(424\) | 1172.72 | + | 2031.21i | 0.134322 | + | 0.232652i | ||||
\(425\) | 2816.46 | 0.321455 | ||||||||
\(426\) | 1349.78 | 0.153514 | ||||||||
\(427\) | 3375.76 | + | 5846.98i | 0.382586 | + | 0.662659i | ||||
\(428\) | 3080.40 | + | 5335.41i | 0.347890 | + | 0.602563i | ||||
\(429\) | −6166.41 | −0.693979 | ||||||||
\(430\) | 153.293 | 0.0171917 | ||||||||
\(431\) | 3955.74 | + | 6851.54i | 0.442091 | + | 0.765724i | 0.997844 | − | 0.0656230i | \(-0.0209035\pi\) |
−0.555753 | + | 0.831347i | \(0.687570\pi\) | |||||||
\(432\) | 216.000 | − | 374.123i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 1239.72 | + | 2147.26i | 0.137592 | + | 0.238316i | 0.926585 | − | 0.376087i | \(-0.122730\pi\) |
−0.788993 | + | 0.614402i | \(0.789397\pi\) | |||||||
\(434\) | −1987.18 | + | 3441.90i | −0.219788 | + | 0.380683i | ||||
\(435\) | −904.518 | + | 1566.67i | −0.0996973 | + | 0.172681i | ||||
\(436\) | −2899.85 | −0.318527 | ||||||||
\(437\) | −1777.39 | − | 3825.36i | −0.194563 | − | 0.418746i | ||||
\(438\) | 2130.19 | 0.232385 | ||||||||
\(439\) | −6448.71 | + | 11169.5i | −0.701094 | + | 1.21433i | 0.266989 | + | 0.963699i | \(0.413971\pi\) |
−0.968083 | + | 0.250630i | \(0.919362\pi\) | |||||||
\(440\) | 627.951 | − | 1087.64i | 0.0680373 | − | 0.117844i | ||||
\(441\) | 1140.29 | + | 1975.04i | 0.123128 | + | 0.213264i | ||||
\(442\) | −7375.29 | + | 12774.4i | −0.793680 | + | 1.37469i | ||||
\(443\) | 301.508 | + | 522.227i | 0.0323365 | + | 0.0560085i | 0.881741 | − | 0.471734i | \(-0.156372\pi\) |
−0.849404 | + | 0.527743i | \(0.823039\pi\) | |||||||
\(444\) | 1972.77 | 0.210864 | ||||||||
\(445\) | 1487.43 | 0.158451 | ||||||||
\(446\) | −3861.83 | − | 6688.89i | −0.410007 | − | 0.710153i | ||||
\(447\) | −600.494 | − | 1040.09i | −0.0635400 | − | 0.110055i | ||||
\(448\) | −605.815 | −0.0638885 | ||||||||
\(449\) | −11358.0 | −1.19380 | −0.596902 | − | 0.802314i | \(-0.703602\pi\) | ||||
−0.596902 | + | 0.802314i | \(0.703602\pi\) | |||||||
\(450\) | 225.000 | + | 389.711i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | 2279.54 | − | 3948.28i | 0.238003 | − | 0.412233i | ||||
\(452\) | 2566.59 | + | 4445.46i | 0.267084 | + | 0.462603i | ||||
\(453\) | 802.109 | − | 1389.29i | 0.0831928 | − | 0.144094i | ||||
\(454\) | −5807.25 | + | 10058.5i | −0.600325 | + | 1.03979i | ||||
\(455\) | −3098.45 | −0.319248 | ||||||||
\(456\) | 1142.31 | − | 1626.62i | 0.117311 | − | 0.167047i | ||||
\(457\) | −164.122 | −0.0167994 | −0.00839970 | − | 0.999965i | \(-0.502674\pi\) | ||||
−0.00839970 | + | 0.999965i | \(0.502674\pi\) | |||||||
\(458\) | −2586.63 | + | 4480.17i | −0.263898 | + | 0.457085i | ||||
\(459\) | 1520.89 | − | 2634.26i | 0.154660 | − | 0.267880i | ||||
\(460\) | −509.317 | − | 882.163i | −0.0516240 | − | 0.0894154i | ||||
\(461\) | −2552.00 | + | 4420.19i | −0.257827 | + | 0.446570i | −0.965660 | − | 0.259811i | \(-0.916340\pi\) |
0.707832 | + | 0.706380i | \(0.249673\pi\) | |||||||
\(462\) | −891.615 | − | 1544.32i | −0.0897872 | − | 0.155516i | ||||
\(463\) | −6575.52 | −0.660022 | −0.330011 | − | 0.943977i | \(-0.607052\pi\) | ||||
−0.330011 | + | 0.943977i | \(0.607052\pi\) | |||||||
\(464\) | 1929.64 | 0.193063 | ||||||||
\(465\) | −1574.49 | − | 2727.09i | −0.157022 | − | 0.271970i | ||||
\(466\) | 414.883 | + | 718.599i | 0.0412427 | + | 0.0714344i | ||||
\(467\) | −8860.46 | −0.877972 | −0.438986 | − | 0.898494i | \(-0.644662\pi\) | ||||
−0.438986 | + | 0.898494i | \(0.644662\pi\) | |||||||
\(468\) | −2356.77 | −0.232782 | ||||||||
\(469\) | −262.516 | − | 454.691i | −0.0258462 | − | 0.0447669i | ||||
\(470\) | 2619.88 | − | 4537.76i | 0.257119 | − | 0.445343i | ||||
\(471\) | −485.199 | − | 840.389i | −0.0474666 | − | 0.0822146i | ||||
\(472\) | 23.2292 | − | 40.2341i | 0.00226527 | − | 0.00392357i | ||||
\(473\) | 240.651 | − | 416.820i | 0.0233935 | − | 0.0405188i | ||||
\(474\) | 3139.78 | 0.304251 | ||||||||
\(475\) | 872.439 | + | 1877.69i | 0.0842742 | + | 0.181378i | ||||
\(476\) | −4265.64 | −0.410746 | ||||||||
\(477\) | −1319.31 | + | 2285.12i | −0.126640 | + | 0.219347i | ||||
\(478\) | 5546.06 | − | 9606.05i | 0.530692 | − | 0.919185i | ||||
\(479\) | 1343.78 | + | 2327.50i | 0.128182 | + | 0.222017i | 0.922972 | − | 0.384867i | \(-0.125753\pi\) |
−0.794790 | + | 0.606884i | \(0.792419\pi\) | |||||||
\(480\) | 240.000 | − | 415.692i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | −5381.21 | − | 9320.54i | −0.510109 | − | 0.883534i | ||||
\(482\) | −1574.33 | −0.148774 | ||||||||
\(483\) | −1446.34 | −0.136254 | ||||||||
\(484\) | 690.385 | + | 1195.78i | 0.0648371 | + | 0.112301i | ||||
\(485\) | 911.305 | + | 1578.43i | 0.0853201 | + | 0.147779i | ||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 18255.0 | 1.69859 | 0.849294 | − | 0.527920i | \(-0.177028\pi\) | ||||
0.849294 | + | 0.527920i | \(0.177028\pi\) | |||||||
\(488\) | 2853.00 | + | 4941.53i | 0.264650 | + | 0.458387i | ||||
\(489\) | −2322.67 | + | 4022.98i | −0.214795 | + | 0.372036i | ||||
\(490\) | 1266.99 | + | 2194.49i | 0.116810 | + | 0.202320i | ||||
\(491\) | −490.199 | + | 849.050i | −0.0450558 | + | 0.0780389i | −0.887674 | − | 0.460473i | \(-0.847680\pi\) |
0.842618 | + | 0.538512i | \(0.181013\pi\) | |||||||
\(492\) | 871.229 | − | 1509.01i | 0.0798334 | − | 0.138276i | ||||
\(493\) | 13586.9 | 1.24122 | ||||||||
\(494\) | −10801.1 | − | 959.945i | −0.983731 | − | 0.0874291i | ||||
\(495\) | 1412.89 | 0.128292 | ||||||||
\(496\) | −1679.45 | + | 2908.90i | −0.152036 | + | 0.263334i | ||||
\(497\) | 1064.74 | − | 1844.18i | 0.0960965 | − | 0.166444i | ||||
\(498\) | −1497.06 | − | 2592.98i | −0.134708 | − | 0.233322i | ||||
\(499\) | 5501.54 | − | 9528.94i | 0.493552 | − | 0.854858i | −0.506420 | − | 0.862287i | \(-0.669032\pi\) |
0.999972 | + | 0.00742933i | \(0.00236485\pi\) | |||||||
\(500\) | 250.000 | + | 433.013i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −526.844 | −0.0469813 | ||||||||
\(502\) | 2504.51 | 0.222673 | ||||||||
\(503\) | 6754.71 | + | 11699.5i | 0.598763 | + | 1.03709i | 0.993004 | + | 0.118080i | \(0.0376740\pi\) |
−0.394241 | + | 0.919007i | \(0.628993\pi\) | |||||||
\(504\) | −340.771 | − | 590.232i | −0.0301173 | − | 0.0521648i | ||||
\(505\) | 3169.48 | 0.279287 | ||||||||
\(506\) | −3198.26 | −0.280988 | ||||||||
\(507\) | 3133.17 | + | 5426.81i | 0.274455 | + | 0.475371i | ||||
\(508\) | −3216.35 | + | 5570.88i | −0.280910 | + | 0.486551i | ||||
\(509\) | 10523.1 | + | 18226.5i | 0.916360 | + | 1.58718i | 0.804898 | + | 0.593413i | \(0.202220\pi\) |
0.111462 | + | 0.993769i | \(0.464447\pi\) | |||||||
\(510\) | 1689.88 | − | 2926.96i | 0.146724 | − | 0.254133i | ||||
\(511\) | 1680.34 | − | 2910.43i | 0.145467 | − | 0.251957i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2227.34 | + | 197.954i | 0.191695 | + | 0.0170368i | ||||
\(514\) | −3865.17 | −0.331684 | ||||||||
\(515\) | 4538.54 | − | 7860.99i | 0.388334 | − | 0.672615i | ||||
\(516\) | 91.9757 | − | 159.307i | 0.00784691 | − | 0.0135912i | ||||
\(517\) | −8225.78 | − | 14247.5i | −0.699747 | − | 1.21200i | ||||
\(518\) | 1556.16 | − | 2695.35i | 0.131996 | − | 0.228624i | ||||
\(519\) | −1224.99 | − | 2121.74i | −0.103605 | − | 0.179449i | ||||
\(520\) | −2618.63 | −0.220836 | ||||||||
\(521\) | 20773.2 | 1.74681 | 0.873407 | − | 0.486991i | \(-0.161906\pi\) | ||||
0.873407 | + | 0.486991i | \(0.161906\pi\) | |||||||
\(522\) | 1085.42 | + | 1880.01i | 0.0910108 | + | 0.157635i | ||||
\(523\) | 1998.43 | + | 3461.39i | 0.167085 | + | 0.289399i | 0.937394 | − | 0.348272i | \(-0.113231\pi\) |
−0.770309 | + | 0.637671i | \(0.779898\pi\) | |||||||
\(524\) | 11530.1 | 0.961245 | ||||||||
\(525\) | 709.939 | 0.0590177 | ||||||||
\(526\) | 1070.31 | + | 1853.83i | 0.0887217 | + | 0.153670i | ||||
\(527\) | −11825.3 | + | 20482.0i | −0.977454 | + | 1.69300i | ||||
\(528\) | −753.542 | − | 1305.17i | −0.0621093 | − | 0.107576i | ||||
\(529\) | 4786.48 | − | 8290.43i | 0.393399 | − | 0.681386i | ||||
\(530\) | −1465.90 | + | 2539.02i | −0.120141 | + | 0.208090i | ||||
\(531\) | 52.2657 | 0.00427144 | ||||||||
\(532\) | −1321.34 | − | 2843.83i | −0.107683 | − | 0.231759i | ||||
\(533\) | −9505.96 | −0.772512 | ||||||||
\(534\) | 892.457 | − | 1545.78i | 0.0723228 | − | 0.125267i | ||||
\(535\) | −3850.50 | + | 6669.26i | −0.311162 | + | 0.538948i | ||||
\(536\) | −221.863 | − | 384.279i | −0.0178788 | − | 0.0309670i | ||||
\(537\) | −3497.81 | + | 6058.38i | −0.281083 | + | 0.486850i | ||||
\(538\) | 7400.97 | + | 12818.9i | 0.593083 | + | 1.02725i | ||||
\(539\) | 7956.07 | 0.635792 | ||||||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | 9474.21 | + | 16409.8i | 0.752917 | + | 1.30409i | 0.946403 | + | 0.322988i | \(0.104687\pi\) |
−0.193486 | + | 0.981103i | \(0.561979\pi\) | |||||||
\(542\) | −2365.20 | − | 4096.64i | −0.187443 | − | 0.324660i | ||||
\(543\) | −6855.40 | −0.541792 | ||||||||
\(544\) | −3605.07 | −0.284129 | ||||||||
\(545\) | −1812.41 | − | 3139.18i | −0.142450 | − | 0.246730i | ||||
\(546\) | −1859.07 | + | 3220.01i | −0.145716 | + | 0.252387i | ||||
\(547\) | 5452.79 | + | 9444.50i | 0.426224 | + | 0.738241i | 0.996534 | − | 0.0831885i | \(-0.0265103\pi\) |
−0.570310 | + | 0.821429i | \(0.693177\pi\) | |||||||
\(548\) | 572.195 | − | 991.070i | 0.0446039 | − | 0.0772562i | ||||
\(549\) | −3209.62 | + | 5559.22i | −0.249514 | + | 0.432171i | ||||
\(550\) | 1569.88 | 0.121709 | ||||||||
\(551\) | 4208.73 | + | 9058.17i | 0.325405 | + | 0.700346i | ||||
\(552\) | −1222.36 | −0.0942521 | ||||||||
\(553\) | 2476.73 | − | 4289.82i | 0.190454 | − | 0.329877i | ||||
\(554\) | 5235.96 | − | 9068.94i | 0.401542 | − | 0.695492i | ||||
\(555\) | 1232.98 | + | 2135.59i | 0.0943012 | + | 0.163334i | ||||
\(556\) | 3676.70 | − | 6368.23i | 0.280444 | − | 0.485743i | ||||
\(557\) | 315.378 | + | 546.251i | 0.0239910 | + | 0.0415536i | 0.877772 | − | 0.479079i | \(-0.159029\pi\) |
−0.853781 | + | 0.520633i | \(0.825696\pi\) | |||||||
\(558\) | −3778.77 | −0.286681 | ||||||||
\(559\) | −1003.54 | −0.0759310 | ||||||||
\(560\) | −378.634 | − | 655.814i | −0.0285718 | − | 0.0494878i | ||||
\(561\) | −5305.81 | − | 9189.93i | −0.399307 | − | 0.691620i | ||||
\(562\) | −15824.4 | −1.18774 | ||||||||
\(563\) | 14014.8 | 1.04912 | 0.524561 | − | 0.851373i | \(-0.324230\pi\) | ||||
0.524561 | + | 0.851373i | \(0.324230\pi\) | |||||||
\(564\) | −3143.85 | − | 5445.32i | −0.234717 | − | 0.406541i | ||||
\(565\) | −3208.23 | + | 5556.82i | −0.238887 | + | 0.413765i | ||||
\(566\) | −5040.00 | − | 8729.53i | −0.374288 | − | 0.648285i | ||||
\(567\) | 383.367 | − | 664.011i | 0.0283949 | − | 0.0491814i | ||||
\(568\) | 899.854 | − | 1558.59i | 0.0664737 | − | 0.115136i | ||||
\(569\) | 23499.5 | 1.73137 | 0.865685 | − | 0.500589i | \(-0.166883\pi\) | ||||
0.865685 | + | 0.500589i | \(0.166883\pi\) | |||||||
\(570\) | 2474.82 | + | 219.949i | 0.181857 | + | 0.0161626i | ||||
\(571\) | −19021.1 | −1.39406 | −0.697031 | − | 0.717041i | \(-0.745496\pi\) | ||||
−0.697031 | + | 0.717041i | \(0.745496\pi\) | |||||||
\(572\) | −4110.94 | + | 7120.35i | −0.300502 | + | 0.520484i | ||||
\(573\) | −3239.35 | + | 5610.71i | −0.236170 | + | 0.409059i | ||||
\(574\) | −1374.49 | − | 2380.68i | −0.0999478 | − | 0.173115i | ||||
\(575\) | 636.646 | − | 1102.70i | 0.0461739 | − | 0.0799755i | ||||
\(576\) | −288.000 | − | 498.831i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −15685.2 | −1.13169 | −0.565844 | − | 0.824512i | \(-0.691450\pi\) | ||||
−0.565844 | + | 0.824512i | \(0.691450\pi\) | |||||||
\(578\) | −15557.9 | −1.11959 | ||||||||
\(579\) | −3771.51 | − | 6532.45i | −0.270706 | − | 0.468876i | ||||
\(580\) | 1206.02 | + | 2088.90i | 0.0863404 | + | 0.149546i | ||||
\(581\) | −4723.65 | −0.337298 | ||||||||
\(582\) | 2187.13 | 0.155772 | ||||||||
\(583\) | 4602.58 | + | 7971.90i | 0.326963 | + | 0.566316i | ||||
\(584\) | 1420.13 | − | 2459.73i | 0.100625 | − | 0.174288i | ||||
\(585\) | −1472.98 | − | 2551.28i | −0.104103 | − | 0.180312i | ||||
\(586\) | −336.152 | + | 582.232i | −0.0236967 | + | 0.0410440i | ||||
\(587\) | −221.699 | + | 383.993i | −0.0155886 | + | 0.0270002i | −0.873714 | − | 0.486439i | \(-0.838296\pi\) |
0.858126 | + | 0.513439i | \(0.171629\pi\) | |||||||
\(588\) | 3040.77 | 0.213264 | ||||||||
\(589\) | −17318.1 | − | 1539.15i | −1.21151 | − | 0.107673i | ||||
\(590\) | 58.0730 | 0.00405225 | ||||||||
\(591\) | −7972.50 | + | 13808.8i | −0.554898 | + | 0.961112i | ||||
\(592\) | 1315.18 | − | 2277.96i | 0.0913067 | − | 0.158148i | ||||
\(593\) | 10926.6 | + | 18925.4i | 0.756662 | + | 1.31058i | 0.944544 | + | 0.328385i | \(0.106504\pi\) |
−0.187882 | + | 0.982192i | \(0.560162\pi\) | |||||||
\(594\) | 847.734 | − | 1468.32i | 0.0585572 | − | 0.101424i | ||||
\(595\) | −2666.02 | − | 4617.69i | −0.183691 | − | 0.318163i | ||||
\(596\) | −1601.32 | −0.110055 | ||||||||
\(597\) | 4748.37 | 0.325524 | ||||||||
\(598\) | 3334.29 | + | 5775.16i | 0.228009 | + | 0.394923i | ||||
\(599\) | −7466.47 | − | 12932.3i | −0.509302 | − | 0.882137i | −0.999942 | − | 0.0107744i | \(-0.996570\pi\) |
0.490640 | − | 0.871362i | \(-0.336763\pi\) | |||||||
\(600\) | 600.000 | 0.0408248 | ||||||||
\(601\) | −22409.9 | −1.52100 | −0.760499 | − | 0.649339i | \(-0.775046\pi\) | ||||
−0.760499 | + | 0.649339i | \(0.775046\pi\) | |||||||
\(602\) | −145.105 | − | 251.329i | −0.00982397 | − | 0.0170156i | ||||
\(603\) | 249.596 | − | 432.314i | 0.0168563 | − | 0.0291960i | ||||
\(604\) | −1069.48 | − | 1852.39i | −0.0720471 | − | 0.124789i | ||||
\(605\) | −862.982 | + | 1494.73i | −0.0579921 | + | 0.100445i | ||||
\(606\) | 1901.69 | − | 3293.82i | 0.127476 | − | 0.220796i | ||||
\(607\) | 18731.1 | 1.25250 | 0.626252 | − | 0.779620i | \(-0.284588\pi\) | ||||
0.626252 | + | 0.779620i | \(0.284588\pi\) | |||||||
\(608\) | −1116.72 | − | 2403.44i | −0.0744886 | − | 0.160317i | ||||
\(609\) | 3424.82 | 0.227883 | ||||||||
\(610\) | −3566.24 | + | 6176.92i | −0.236710 | + | 0.409993i | ||||
\(611\) | −17151.3 | + | 29706.9i | −1.13562 | + | 1.96696i | ||||
\(612\) | −2027.85 | − | 3512.35i | −0.133940 | − | 0.231990i | ||||
\(613\) | 6866.35 | − | 11892.9i | 0.452413 | − | 0.783603i | −0.546122 | − | 0.837706i | \(-0.683897\pi\) |
0.998535 | + | 0.0541027i | \(0.0172299\pi\) | |||||||
\(614\) | −4307.13 | − | 7460.17i | −0.283097 | − | 0.490339i | ||||
\(615\) | 2178.07 | 0.142810 | ||||||||
\(616\) | −2377.64 | −0.155516 | ||||||||
\(617\) | 1906.74 | + | 3302.57i | 0.124412 | + | 0.215488i | 0.921503 | − | 0.388371i | \(-0.126962\pi\) |
−0.797091 | + | 0.603859i | \(0.793629\pi\) | |||||||
\(618\) | −5446.25 | − | 9433.18i | −0.354499 | − | 0.614010i | ||||
\(619\) | 15487.6 | 1.00565 | 0.502826 | − | 0.864387i | \(-0.332294\pi\) | ||||
0.502826 | + | 0.864387i | \(0.332294\pi\) | |||||||
\(620\) | −4198.63 | −0.271970 | ||||||||
\(621\) | −687.578 | − | 1190.92i | −0.0444309 | − | 0.0769565i | ||||
\(622\) | −9483.69 | + | 16426.2i | −0.611353 | + | 1.05889i | ||||
\(623\) | −1407.98 | − | 2438.69i | −0.0905448 | − | 0.156828i | ||||
\(624\) | −1571.18 | + | 2721.36i | −0.100797 | + | 0.174586i | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 8419.42 | 0.537552 | ||||||||
\(627\) | 4483.23 | − | 6384.01i | 0.285555 | − | 0.406623i | ||||
\(628\) | −1293.86 | −0.0822146 | ||||||||
\(629\) | 9260.40 | − | 16039.5i | 0.587021 | − | 1.01675i | ||||
\(630\) | 425.964 | − | 737.790i | 0.0269378 | − | 0.0466576i | ||||
\(631\) | 10776.7 | + | 18665.7i | 0.679893 | + | 1.17761i | 0.975013 | + | 0.222149i | \(0.0713072\pi\) |
−0.295119 | + | 0.955460i | \(0.595359\pi\) | |||||||
\(632\) | 2093.19 | − | 3625.51i | 0.131745 | − | 0.228188i | ||||
\(633\) | 1770.99 | + | 3067.45i | 0.111202 | + | 0.192607i | ||||
\(634\) | −17718.6 | −1.10993 | ||||||||
\(635\) | −8040.88 | −0.502508 | ||||||||
\(636\) | 1759.08 | + | 3046.82i | 0.109673 | + | 0.189960i | ||||
\(637\) | −8294.44 | − | 14366.4i | −0.515915 | − | 0.893591i | ||||
\(638\) | 7573.25 | 0.469949 | ||||||||
\(639\) | 2024.67 | 0.125344 | ||||||||
\(640\) | −320.000 | − | 554.256i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 3324.85 | − | 5758.81i | 0.204873 | − | 0.354851i | −0.745219 | − | 0.666820i | \(-0.767655\pi\) |
0.950092 | + | 0.311969i | \(0.100988\pi\) | |||||||
\(642\) | 4620.60 | + | 8003.12i | 0.284051 | + | 0.491990i | ||||
\(643\) | 14372.1 | − | 24893.2i | 0.881462 | − | 1.52674i | 0.0317454 | − | 0.999496i | \(-0.489893\pi\) |
0.849716 | − | 0.527240i | \(-0.176773\pi\) | |||||||
\(644\) | −964.225 | + | 1670.09i | −0.0589996 | + | 0.102190i | ||||
\(645\) | 229.939 | 0.0140370 | ||||||||
\(646\) | −7863.02 | − | 16923.0i | −0.478895 | − | 1.03069i | ||||
\(647\) | 5967.56 | 0.362610 | 0.181305 | − | 0.983427i | \(-0.441968\pi\) | ||||
0.181305 | + | 0.983427i | \(0.441968\pi\) | |||||||
\(648\) | 324.000 | − | 561.184i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 91.1675 | − | 157.907i | 0.00551408 | − | 0.00955066i | ||||
\(650\) | −1636.65 | − | 2834.75i | −0.0987609 | − | 0.171059i | ||||
\(651\) | −2980.78 | + | 5162.85i | −0.179456 | + | 0.310827i | ||||
\(652\) | 3096.89 | + | 5363.97i | 0.186018 | + | 0.322192i | ||||
\(653\) | 12877.8 | 0.771744 | 0.385872 | − | 0.922552i | \(-0.373901\pi\) | ||||
0.385872 | + | 0.922552i | \(0.373901\pi\) | |||||||
\(654\) | −4349.78 | −0.260076 | ||||||||
\(655\) | 7206.28 | + | 12481.6i | 0.429882 | + | 0.744578i | ||||
\(656\) | −1161.64 | − | 2012.02i | −0.0691378 | − | 0.119750i | ||||
\(657\) | 3195.29 | 0.189741 | ||||||||
\(658\) | −9919.76 | −0.587709 | ||||||||
\(659\) | −4061.24 | − | 7034.27i | −0.240066 | − | 0.415806i | 0.720667 | − | 0.693281i | \(-0.243836\pi\) |
−0.960733 | + | 0.277475i | \(0.910502\pi\) | |||||||
\(660\) | 941.927 | − | 1631.47i | 0.0555522 | − | 0.0962193i | ||||
\(661\) | −208.269 | − | 360.732i | −0.0122552 | − | 0.0212267i | 0.859833 | − | 0.510576i | \(-0.170568\pi\) |
−0.872088 | + | 0.489349i | \(0.837234\pi\) | |||||||
\(662\) | −11577.5 | + | 20052.8i | −0.679716 | + | 1.17730i | ||||
\(663\) | −11062.9 | + | 19161.6i | −0.648037 | + | 1.12243i | ||||
\(664\) | −3992.16 | −0.233322 | ||||||||
\(665\) | 2252.70 | − | 3207.79i | 0.131362 | − | 0.187057i | ||||
\(666\) | 2959.16 | 0.172170 | ||||||||
\(667\) | 3071.24 | − | 5319.55i | 0.178289 | − | 0.308806i | ||||
\(668\) | −351.229 | + | 608.347i | −0.0203435 | + | 0.0352360i | ||||
\(669\) | −5792.75 | − | 10033.3i | −0.334769 | − | 0.579837i | ||||
\(670\) | 277.329 | − | 480.348i | 0.0159913 | − | 0.0276977i | ||||
\(671\) | 11197.1 | + | 19394.0i | 0.644204 | + | 1.11579i | ||||
\(672\) | −908.722 | −0.0521648 | ||||||||
\(673\) | 22256.9 | 1.27480 | 0.637400 | − | 0.770533i | \(-0.280010\pi\) | ||||
0.637400 | + | 0.770533i | \(0.280010\pi\) | |||||||
\(674\) | 6299.37 | + | 10910.8i | 0.360004 | + | 0.623545i | ||||
\(675\) | 337.500 | + | 584.567i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 8355.11 | 0.475371 | ||||||||
\(677\) | −3857.05 | −0.218964 | −0.109482 | − | 0.993989i | \(-0.534919\pi\) | ||||
−0.109482 | + | 0.993989i | \(0.534919\pi\) | |||||||
\(678\) | 3849.88 | + | 6668.19i | 0.218073 | + | 0.377714i | ||||
\(679\) | 1725.26 | − | 2988.23i | 0.0975100 | − | 0.168892i | ||||
\(680\) | −2253.17 | − | 3902.61i | −0.127066 | − | 0.220086i | ||||
\(681\) | −8710.87 | + | 15087.7i | −0.490164 | + | 0.848988i | ||||
\(682\) | −6591.35 | + | 11416.5i | −0.370082 | + | 0.641000i | ||||
\(683\) | 13692.5 | 0.767100 | 0.383550 | − | 0.923520i | \(-0.374701\pi\) | ||||
0.383550 | + | 0.923520i | \(0.374701\pi\) | |||||||
\(684\) | 1713.47 | − | 2439.94i | 0.0957838 | − | 0.136394i | ||||
\(685\) | 1430.49 | 0.0797899 | ||||||||
\(686\) | 5645.41 | − | 9778.14i | 0.314202 | − | 0.544215i | ||||
\(687\) | −3879.94 | + | 6720.26i | −0.215472 | + | 0.373208i | ||||
\(688\) | −122.634 | − | 212.409i | −0.00679562 | − | 0.0117704i | ||||
\(689\) | 9596.66 | − | 16621.9i | 0.530629 | − | 0.919077i | ||||
\(690\) | −763.976 | − | 1323.24i | −0.0421508 | − | 0.0730073i | ||||
\(691\) | −13079.0 | −0.720042 | −0.360021 | − | 0.932944i | \(-0.617231\pi\) | ||||
−0.360021 | + | 0.932944i | \(0.617231\pi\) | |||||||
\(692\) | −3266.63 | −0.179449 | ||||||||
\(693\) | −1337.42 | − | 2316.48i | −0.0733109 | − | 0.126978i | ||||
\(694\) | 4197.98 | + | 7271.12i | 0.229616 | + | 0.397706i | ||||
\(695\) | 9191.74 | 0.501673 | ||||||||
\(696\) | 2894.46 | 0.157635 | ||||||||
\(697\) | −8179.29 | − | 14166.9i | −0.444494 | − | 0.769887i | ||||
\(698\) | 3662.09 | − | 6342.93i | 0.198585 | − | 0.343959i | ||||
\(699\) | 622.325 | + | 1077.90i | 0.0336745 | + | 0.0583260i | ||||
\(700\) | 473.293 | − | 819.767i | 0.0255554 | − | 0.0442633i | ||||
\(701\) | −11458.1 | + | 19845.9i | −0.617353 | + | 1.06929i | 0.372613 | + | 0.927987i | \(0.378462\pi\) |
−0.989967 | + | 0.141301i | \(0.954872\pi\) | |||||||
\(702\) | −3535.16 | −0.190065 | ||||||||
\(703\) | 13561.8 | + | 1205.30i | 0.727586 | + | 0.0646642i | ||||
\(704\) | −2009.44 | −0.107576 | ||||||||
\(705\) | 3929.82 | − | 6806.64i | 0.209937 | − | 0.363621i | ||||
\(706\) | 6923.15 | − | 11991.3i | 0.369060 | − | 0.639230i | ||||
\(707\) | −3000.18 | − | 5196.47i | −0.159595 | − | 0.276426i | ||||
\(708\) | 34.8438 | − | 60.3512i | 0.00184959 | − | 0.00320358i | ||||
\(709\) | −13994.2 | − | 24238.6i | −0.741271 | − | 1.28392i | −0.951917 | − | 0.306357i | \(-0.900890\pi\) |
0.210645 | − | 0.977563i | \(-0.432443\pi\) | |||||||
\(710\) | 2249.64 | 0.118912 | ||||||||
\(711\) | 4709.68 | 0.248420 | ||||||||
\(712\) | −1189.94 | − | 2061.04i | −0.0626334 | − | 0.108484i | ||||
\(713\) | 5346.09 | + | 9259.70i | 0.280803 | + | 0.486365i | ||||
\(714\) | −6398.46 | −0.335373 | ||||||||
\(715\) | −10277.3 | −0.537554 | ||||||||
\(716\) | 4663.74 | + | 8077.84i | 0.243425 | + | 0.421624i | ||||
\(717\) | 8319.08 | − | 14409.1i | 0.433308 | − | 0.750512i | ||||
\(718\) | −1069.38 | − | 1852.22i | −0.0555833 | − | 0.0962731i | ||||
\(719\) | −1680.24 | + | 2910.26i | −0.0871521 | + | 0.150952i | −0.906306 | − | 0.422622i | \(-0.861110\pi\) |
0.819154 | + | 0.573573i | \(0.194443\pi\) | |||||||
\(720\) | 360.000 | − | 623.538i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | −17184.5 | −0.887633 | ||||||||
\(722\) | 8846.64 | − | 10484.3i | 0.456008 | − | 0.540423i | ||||
\(723\) | −2361.50 | −0.121473 | ||||||||
\(724\) | −4570.26 | + | 7915.93i | −0.234603 | + | 0.406344i | ||||
\(725\) | −1507.53 | + | 2611.12i | −0.0772252 | + | 0.133758i | ||||
\(726\) | 1035.58 | + | 1793.67i | 0.0529393 | + | 0.0916935i | ||||
\(727\) | 9213.39 | − | 15958.1i | 0.470022 | − | 0.814101i | −0.529391 | − | 0.848378i | \(-0.677579\pi\) |
0.999412 | + | 0.0342769i | \(0.0109128\pi\) | |||||||
\(728\) | 2478.76 | + | 4293.34i | 0.126194 | + | 0.218574i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 3550.32 | 0.180004 | ||||||||
\(731\) | −863.487 | − | 1495.60i | −0.0436898 | − | 0.0756729i | ||||
\(732\) | 4279.49 | + | 7412.30i | 0.216086 | + | 0.374271i | ||||
\(733\) | −32470.5 | −1.63619 | −0.818093 | − | 0.575086i | \(-0.804969\pi\) | ||||
−0.818093 | + | 0.575086i | \(0.804969\pi\) | |||||||
\(734\) | 22951.4 | 1.15416 | ||||||||
\(735\) | 1900.48 | + | 3291.73i | 0.0953746 | + | 0.165194i | ||||
\(736\) | −814.907 | + | 1411.46i | −0.0408123 | + | 0.0706891i | ||||
\(737\) | −870.747 | − | 1508.18i | −0.0435202 | − | 0.0753791i | ||||
\(738\) | 1306.84 | − | 2263.52i | 0.0651837 | − | 0.112902i | ||||
\(739\) | −13815.5 | + | 23929.2i | −0.687703 | + | 1.19114i | 0.284876 | + | 0.958564i | \(0.408048\pi\) |
−0.972579 | + | 0.232572i | \(0.925286\pi\) | |||||||
\(740\) | 3287.95 | 0.163334 | ||||||||
\(741\) | −16201.6 | − | 1439.92i | −0.803213 | − | 0.0713855i | ||||
\(742\) | 5550.41 | 0.274612 | ||||||||
\(743\) | −17707.4 | + | 30670.2i | −0.874324 | + | 1.51437i | −0.0168429 | + | 0.999858i | \(0.505362\pi\) |
−0.857481 | + | 0.514515i | \(0.827972\pi\) | |||||||
\(744\) | −2519.18 | + | 4363.35i | −0.124137 | + | 0.215011i | ||||
\(745\) | −1000.82 | − | 1733.48i | −0.0492179 | − | 0.0852479i | ||||
\(746\) | 7551.41 | − | 13079.4i | 0.370612 | − | 0.641919i | ||||
\(747\) | −2245.59 | − | 3889.47i | −0.109989 | − | 0.190507i | ||||
\(748\) | −14148.8 | −0.691620 | ||||||||
\(749\) | 14579.3 | 0.711237 | ||||||||
\(750\) | 375.000 | + | 649.519i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | −15992.8 | − | 27700.3i | −0.777076 | − | 1.34594i | −0.933620 | − | 0.358264i | \(-0.883369\pi\) |
0.156544 | − | 0.987671i | \(-0.449965\pi\) | |||||||
\(752\) | −8383.61 | −0.406541 | ||||||||
\(753\) | 3756.77 | 0.181812 | ||||||||
\(754\) | −7895.34 | − | 13675.1i | −0.381341 | − | 0.660503i | ||||
\(755\) | 1336.85 | − | 2315.49i | 0.0644409 | − | 0.111615i | ||||
\(756\) | −511.156 | − | 885.349i | −0.0245907 | − | 0.0425923i | ||||
\(757\) | 10980.0 | − | 19017.8i | 0.527178 | − | 0.913098i | −0.472321 | − | 0.881427i | \(-0.656584\pi\) |
0.999498 | − | 0.0316716i | \(-0.0100831\pi\) | |||||||
\(758\) | 5449.18 | − | 9438.26i | 0.261112 | − | 0.452260i | ||||
\(759\) | −4797.40 | −0.229426 | ||||||||
\(760\) | 1903.85 | − | 2711.04i | 0.0908685 | − | 0.129394i | ||||
\(761\) | −24827.1 | −1.18263 | −0.591316 | − | 0.806440i | \(-0.701391\pi\) | ||||
−0.591316 | + | 0.806440i | \(0.701391\pi\) | |||||||
\(762\) | −4824.53 | + | 8356.33i | −0.229362 | + | 0.397267i | ||||
\(763\) | −3431.20 | + | 5943.01i | −0.162802 | + | 0.281981i | ||||
\(764\) | 4319.13 | + | 7480.95i | 0.204530 | + | 0.354256i | ||||
\(765\) | 2534.82 | − | 4390.43i | 0.119799 | − | 0.207499i | ||||
\(766\) | 2814.89 | + | 4875.54i | 0.132776 | + | 0.229974i | ||||
\(767\) | −380.180 | −0.0178976 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | −14112.5 | − | 24443.5i | −0.661779 | − | 1.14623i | −0.980148 | − | 0.198268i | \(-0.936468\pi\) |
0.318369 | − | 0.947967i | \(-0.396865\pi\) | |||||||
\(770\) | −1486.02 | − | 2573.87i | −0.0695488 | − | 0.120462i | ||||
\(771\) | −5797.76 | −0.270819 | ||||||||
\(772\) | −10057.4 | −0.468876 | ||||||||
\(773\) | 66.0794 | + | 114.453i | 0.00307466 | + | 0.00532547i | 0.867559 | − | 0.497335i | \(-0.165688\pi\) |
−0.864484 | + | 0.502660i | \(0.832355\pi\) | |||||||
\(774\) | 137.964 | − | 238.960i | 0.00640697 | − | 0.0110972i | ||||
\(775\) | −2624.15 | − | 4545.15i | −0.121629 | − | 0.210667i | ||||
\(776\) | 1458.09 | − | 2525.48i | 0.0674514 | − | 0.116829i | ||||
\(777\) | 2334.25 | − | 4043.03i | 0.107774 | − | 0.186670i | ||||
\(778\) | −5737.54 | −0.264397 | ||||||||
\(779\) | 6911.22 | − | 9841.41i | 0.317869 | − | 0.452638i | ||||
\(780\) | −3927.95 | −0.180312 | ||||||||
\(781\) | 3531.65 | − | 6117.00i | 0.161809 | − | 0.280261i | ||||
\(782\) | −5737.89 | + | 9938.32i | −0.262387 | + | 0.454468i | ||||
\(783\) | 1628.13 | + | 2820.01i | 0.0743100 | + | 0.128709i | ||||
\(784\) | 2027.18 | − | 3511.18i | 0.0923461 | − | 0.159948i | ||||
\(785\) | −808.665 | − | 1400.65i | −0.0367675 | − | 0.0636832i | ||||
\(786\) | 17295.1 | 0.784854 | ||||||||
\(787\) | 20434.1 | 0.925538 | 0.462769 | − | 0.886479i | \(-0.346856\pi\) | ||||
0.462769 | + | 0.886479i | \(0.346856\pi\) | |||||||
\(788\) | 10630.0 | + | 18411.7i | 0.480556 | + | 0.832347i | ||||
\(789\) | 1605.46 | + | 2780.74i | 0.0724409 | + | 0.125471i | ||||
\(790\) | 5232.97 | 0.235672 | ||||||||
\(791\) | 12147.5 | 0.546036 | ||||||||
\(792\) | −1130.31 | − | 1957.76i | −0.0507120 | − | 0.0878358i | ||||
\(793\) | 23346.7 | − | 40437.7i | 1.04548 | − | 1.81083i | ||||
\(794\) | 2808.06 | + | 4863.69i | 0.125509 | + | 0.217388i | ||||
\(795\) | −2198.85 | + | 3808.53i | −0.0980947 | + | 0.169905i | ||||
\(796\) | 3165.58 | − | 5482.95i | 0.140956 | − | 0.244143i | ||||
\(797\) | −41468.4 | −1.84302 | −0.921510 | − | 0.388355i | \(-0.873043\pi\) | ||||
−0.921510 | + | 0.388355i | \(0.873043\pi\) | |||||||
\(798\) | −1982.01 | − | 4265.75i | −0.0879229 | − | 0.189230i | ||||
\(799\) | −59030.3 | −2.61370 | ||||||||
\(800\) | 400.000 | − | 692.820i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 1338.68 | − | 2318.67i | 0.0590513 | − | 0.102280i | ||||
\(802\) | −8487.78 | − | 14701.3i | −0.373708 | − | 0.647282i | ||||
\(803\) | 5573.57 | − | 9653.70i | 0.244940 | − | 0.424249i | ||||
\(804\) | −332.795 | − | 576.418i | −0.0145980 | − | 0.0252845i | ||||
\(805\) | −2410.56 | −0.105542 | ||||||||
\(806\) | 27486.7 | 1.20121 | ||||||||
\(807\) | 11101.5 | + | 19228.3i | 0.484250 | + | 0.838745i | ||||
\(808\) | −2535.58 | − | 4391.76i | −0.110398 | − | 0.191215i | ||||
\(809\) | 19100.8 | 0.830097 | 0.415048 | − | 0.909799i | \(-0.363765\pi\) | ||||
0.415048 | + | 0.909799i | \(0.363765\pi\) | |||||||
\(810\) | 810.000 | 0.0351364 | ||||||||
\(811\) | 17238.3 | + | 29857.6i | 0.746385 | + | 1.29278i | 0.949545 | + | 0.313632i | \(0.101546\pi\) |
−0.203159 | + | 0.979146i | \(0.565121\pi\) | |||||||
\(812\) | 2283.21 | − | 3954.64i | 0.0986761 | − | 0.170912i | ||||
\(813\) | −3547.80 | − | 6144.96i | −0.153046 | − | 0.265084i | ||||
\(814\) | 5161.68 | − | 8940.30i | 0.222257 | − | 0.384960i | ||||
\(815\) | −3871.12 | + | 6704.97i | −0.166379 | + | 0.288178i | ||||
\(816\) | −5407.61 | −0.231990 | ||||||||
\(817\) | 729.618 | − | 1038.96i | 0.0312437 | − | 0.0444902i | ||||
\(818\) | 3916.15 | 0.167390 | ||||||||
\(819\) | −2788.61 | + | 4830.01i | −0.118977 | + | 0.206073i | ||||
\(820\) | 1452.05 | − | 2515.02i | 0.0618387 | − | 0.107108i | ||||
\(821\) | −7308.71 | − | 12659.1i | −0.310689 | − | 0.538129i | 0.667823 | − | 0.744321i | \(-0.267227\pi\) |
−0.978512 | + | 0.206191i | \(0.933893\pi\) | |||||||
\(822\) | 858.292 | − | 1486.61i | 0.0364189 | − | 0.0630794i | ||||
\(823\) | −11259.3 | − | 19501.7i | −0.476882 | − | 0.825984i | 0.522767 | − | 0.852476i | \(-0.324900\pi\) |
−0.999649 | + | 0.0264916i | \(0.991566\pi\) | |||||||
\(824\) | −14523.3 | −0.614010 | ||||||||
\(825\) | 2354.82 | 0.0993748 | ||||||||
\(826\) | −54.9710 | − | 95.2126i | −0.00231560 | − | 0.00401074i | ||||
\(827\) | −12420.1 | − | 21512.3i | −0.522237 | − | 0.904542i | −0.999665 | − | 0.0258708i | \(-0.991764\pi\) |
0.477428 | − | 0.878671i | \(-0.341569\pi\) | |||||||
\(828\) | −1833.54 | −0.0769565 | ||||||||
\(829\) | −24002.3 | −1.00559 | −0.502795 | − | 0.864405i | \(-0.667695\pi\) | ||||
−0.502795 | + | 0.864405i | \(0.667695\pi\) | |||||||
\(830\) | −2495.10 | − | 4321.64i | −0.104345 | − | 0.180730i | ||||
\(831\) | 7853.94 | − | 13603.4i | 0.327858 | − | 0.567867i | ||||
\(832\) | 2094.91 | + | 3628.49i | 0.0872931 | + | 0.151196i | ||||
\(833\) | 14273.7 | − | 24722.8i | 0.593703 | − | 1.02832i | ||||
\(834\) | 5515.05 | − | 9552.34i | 0.228981 | − | 0.396607i | ||||
\(835\) | −878.073 | −0.0363916 | ||||||||
\(836\) | −4382.80 | − | 9432.79i | −0.181318 | − | 0.390239i | ||||
\(837\) | −5668.16 | −0.234074 | ||||||||
\(838\) | 6227.21 | − | 10785.9i | 0.256701 | − | 0.444619i | ||||
\(839\) | 12877.6 | − | 22304.6i | 0.529897 | − | 0.917809i | −0.469495 | − | 0.882935i | \(-0.655564\pi\) |
0.999392 | − | 0.0348735i | \(-0.0111028\pi\) | |||||||
\(840\) | −567.951 | − | 983.721i | −0.0233288 | − | 0.0404067i | ||||
\(841\) | 4922.03 | − | 8525.20i | 0.201813 | − | 0.349551i | ||||
\(842\) | −9276.06 | − | 16066.6i | −0.379661 | − | 0.657591i | ||||
\(843\) | −23736.6 | −0.969788 | ||||||||
\(844\) | 4722.65 | 0.192607 | ||||||||
\(845\) | 5221.95 | + | 9044.68i | 0.212592 | + | 0.368220i | ||||
\(846\) | −4715.78 | − | 8167.97i | −0.191645 | − | 0.331939i | ||||
\(847\) | 3267.54 | 0.132555 | ||||||||
\(848\) | 4690.89 | 0.189960 | ||||||||
\(849\) | −7559.99 | − | 13094.3i | −0.305605 | − | 0.529323i | ||||
\(850\) | 2816.46 | − | 4878.26i | 0.113652 | − | 0.196850i | ||||
\(851\) | −4186.52 | − | 7251.27i | −0.168640 | − | 0.292092i | ||||
\(852\) | 1349.78 | − | 2337.89i | 0.0542755 | − | 0.0940080i | ||||
\(853\) | 10403.0 | − | 18018.6i | 0.417577 | − | 0.723265i | −0.578118 | − | 0.815953i | \(-0.696213\pi\) |
0.995695 | + | 0.0926880i | \(0.0295459\pi\) | |||||||
\(854\) | 13503.0 | 0.541058 | ||||||||
\(855\) | 3712.23 | + | 329.924i | 0.148486 | + | 0.0131967i | ||||
\(856\) | 12321.6 | 0.491990 | ||||||||
\(857\) | 19663.3 | − | 34057.8i | 0.783764 | − | 1.35752i | −0.145971 | − | 0.989289i | \(-0.546630\pi\) |
0.929735 | − | 0.368230i | \(-0.120036\pi\) | |||||||
\(858\) | −6166.41 | + | 10680.5i | −0.245359 | + | 0.424973i | ||||
\(859\) | 14633.3 | + | 25345.6i | 0.581237 | + | 1.00673i | 0.995333 | + | 0.0964984i | \(0.0307643\pi\) |
−0.414096 | + | 0.910233i | \(0.635902\pi\) | |||||||
\(860\) | 153.293 | − | 265.511i | 0.00607819 | − | 0.0105277i | ||||
\(861\) | −2061.73 | − | 3571.03i | −0.0816070 | − | 0.141348i | ||||
\(862\) | 15823.0 | 0.625211 | ||||||||
\(863\) | 8053.05 | 0.317647 | 0.158823 | − | 0.987307i | \(-0.449230\pi\) | ||||
0.158823 | + | 0.987307i | \(0.449230\pi\) | |||||||
\(864\) | −432.000 | − | 748.246i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −2041.65 | − | 3536.24i | −0.0802521 | − | 0.139001i | ||||
\(866\) | 4958.89 | 0.194584 | ||||||||
\(867\) | −23336.9 | −0.914142 | ||||||||
\(868\) | 3974.37 | + | 6883.81i | 0.155413 | + | 0.269184i | ||||
\(869\) | 8215.13 | − | 14229.0i | 0.320690 | − | 0.555451i | ||||
\(870\) | 1809.04 | + | 3133.34i | 0.0704966 | + | 0.122104i | ||||
\(871\) | −1815.56 | + | 3144.64i | −0.0706290 | + | 0.122333i | ||||
\(872\) | −2899.85 | + | 5022.69i | −0.112616 | + | 0.195057i | ||||
\(873\) | 3280.70 | 0.127188 | ||||||||
\(874\) | −8403.11 | − | 746.827i | −0.325217 | − | 0.0289036i | ||||
\(875\) | 1183.23 | 0.0457149 | ||||||||
\(876\) | 2130.19 | − | 3689.60i | 0.0821604 | − | 0.142306i | ||||
\(877\) | −11930.3 | + | 20663.8i | −0.459357 | + | 0.795629i | −0.998927 | − | 0.0463112i | \(-0.985253\pi\) |
0.539570 | + | 0.841941i | \(0.318587\pi\) | |||||||
\(878\) | 12897.4 | + | 22339.0i | 0.495748 | + | 0.858661i | ||||
\(879\) | −504.227 | + | 873.347i | −0.0193483 | + | 0.0335123i | ||||
\(880\) | −1255.90 | − | 2175.29i | −0.0481096 | − | 0.0833283i | ||||
\(881\) | −17274.7 | −0.660612 | −0.330306 | − | 0.943874i | \(-0.607152\pi\) | ||||
−0.330306 | + | 0.943874i | \(0.607152\pi\) | |||||||
\(882\) | 4561.16 | 0.174129 | ||||||||
\(883\) | −19530.1 | − | 33827.1i | −0.744326 | − | 1.28921i | −0.950509 | − | 0.310698i | \(-0.899437\pi\) |
0.206182 | − | 0.978514i | \(-0.433896\pi\) | |||||||
\(884\) | 14750.6 | + | 25548.8i | 0.561217 | + | 0.972056i | ||||
\(885\) | 87.1094 | 0.00330865 | ||||||||
\(886\) | 1206.03 | 0.0457307 | ||||||||
\(887\) | 18713.8 | + | 32413.2i | 0.708395 | + | 1.22698i | 0.965452 | + | 0.260580i | \(0.0839139\pi\) |
−0.257057 | + | 0.966396i | \(0.582753\pi\) | |||||||
\(888\) | 1972.77 | − | 3416.94i | 0.0745516 | − | 0.129127i | ||||
\(889\) | 7611.38 | + | 13183.3i | 0.287151 | + | 0.497361i | ||||
\(890\) | 1487.43 | − | 2576.30i | 0.0560210 | − | 0.0970312i | ||||
\(891\) | 1271.60 | − | 2202.48i | 0.0478117 | − | 0.0828123i | ||||
\(892\) | −15447.3 | −0.579837 | ||||||||
\(893\) | −18285.5 | − | 39354.6i | −0.685219 | − | 1.47475i | ||||
\(894\) | −2401.98 | −0.0898592 | ||||||||
\(895\) | −5829.68 | + | 10097.3i | −0.217726 | + | 0.377112i | ||||
\(896\) | −605.815 | + | 1049.30i | −0.0225880 | + | 0.0391236i | ||||
\(897\) | 5001.43 | + | 8662.73i | 0.186168 | + | 0.322453i | ||||
\(898\) | −11358.0 | + | 19672.7i | −0.422073 | + | 0.731053i | ||||
\(899\) | −12659.1 | − | 21926.3i | −0.469639 | − | 0.813439i | ||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | 33029.3 | 1.22127 | ||||||||
\(902\) | −4559.08 | − | 7896.56i | −0.168294 | − | 0.291493i | ||||
\(903\) | −217.657 | − | 376.993i | −0.00802124 | − | 0.0138932i | ||||
\(904\) | 10266.3 | 0.377714 | ||||||||
\(905\) | −11425.7 | −0.419670 | ||||||||
\(906\) | −1604.22 | − | 2778.59i | −0.0588262 | − | 0.101890i | ||||
\(907\) | 7325.87 | − | 12688.8i | 0.268193 | − | 0.464525i | −0.700202 | − | 0.713945i | \(-0.746907\pi\) |
0.968395 | + | 0.249420i | \(0.0802401\pi\) | |||||||
\(908\) | 11614.5 | + | 20116.9i | 0.424494 | + | 0.735245i | ||||
\(909\) | 2852.53 | − | 4940.72i | 0.104084 | − | 0.180279i | ||||
\(910\) | −3098.45 | + | 5366.68i | −0.112871 | + | 0.195498i | ||||
\(911\) | 47811.0 | 1.73880 | 0.869401 | − | 0.494108i | \(-0.164505\pi\) | ||||
0.869401 | + | 0.494108i | \(0.164505\pi\) | |||||||
\(912\) | −1675.08 | − | 3605.17i | −0.0608197 | − | 0.130898i | ||||
\(913\) | −15668.0 | −0.567947 | ||||||||
\(914\) | −164.122 | + | 284.268i | −0.00593948 | + | 0.0102875i | ||||
\(915\) | −5349.37 | + | 9265.37i | −0.193273 | + | 0.334758i | ||||
\(916\) | 5173.26 | + | 8960.35i | 0.186604 | + | 0.323208i | ||||
\(917\) | 13642.7 | − | 23629.9i | 0.491300 | − | 0.850957i | ||||
\(918\) | −3041.78 | − | 5268.52i | −0.109361 | − | 0.189419i | ||||
\(919\) | −17167.4 | −0.616212 | −0.308106 | − | 0.951352i | \(-0.599695\pi\) | ||||
−0.308106 | + | 0.951352i | \(0.599695\pi\) | |||||||
\(920\) | −2037.27 | −0.0730073 | ||||||||
\(921\) | −6460.70 | − | 11190.3i | −0.231148 | − | 0.400360i | ||||
\(922\) | 5103.99 | + | 8840.37i | 0.182311 | + | 0.315772i | ||||
\(923\) | −14727.4 | −0.525200 | ||||||||
\(924\) | −3566.46 | −0.126978 | ||||||||
\(925\) | 2054.97 | + | 3559.31i | 0.0730454 | + | 0.126518i | ||||
\(926\) | −6575.52 | + | 11389.1i | −0.233353 | + | 0.404179i | ||||
\(927\) | −8169.38 | − | 14149.8i | −0.289447 | − | 0.501337i | ||||
\(928\) | 1929.64 | − | 3342.23i | 0.0682581 | − | 0.118226i | ||||
\(929\) | −7579.34 | + | 13127.8i | −0.267675 | + | 0.463627i | −0.968261 | − | 0.249941i | \(-0.919589\pi\) |
0.700586 | + | 0.713568i | \(0.252922\pi\) | |||||||
\(930\) | −6297.95 | −0.222062 | ||||||||
\(931\) | 20903.8 | + | 1857.82i | 0.735868 | + | 0.0654003i | ||||
\(932\) | 1659.53 | 0.0583260 | ||||||||
\(933\) | −14225.5 | + | 24639.3i | −0.499167 | + | 0.864583i | ||||
\(934\) | −8860.46 | + | 15346.8i | −0.310410 | + | 0.537646i | ||||
\(935\) | −8843.01 | − | 15316.5i | −0.309302 | − | 0.535727i | ||||
\(936\) | −2356.77 | + | 4082.05i | −0.0823007 | + | 0.142549i | ||||
\(937\) | −6382.57 | − | 11054.9i | −0.222529 | − | 0.385431i | 0.733046 | − | 0.680179i | \(-0.238098\pi\) |
−0.955575 | + | 0.294747i | \(0.904764\pi\) | |||||||
\(938\) | −1050.06 | −0.0365520 | ||||||||
\(939\) | 12629.1 | 0.438910 | ||||||||
\(940\) | −5239.76 | − | 9075.53i | −0.181811 | − | 0.314905i | ||||
\(941\) | 4798.87 | + | 8311.88i | 0.166247 | + | 0.287949i | 0.937097 | − | 0.349068i | \(-0.113502\pi\) |
−0.770850 | + | 0.637016i | \(0.780168\pi\) | |||||||
\(942\) | −1940.80 | −0.0671279 | ||||||||
\(943\) | −7395.53 | −0.255389 | ||||||||
\(944\) | −46.4584 | − | 80.4682i | −0.00160179 | − | 0.00277438i | ||||
\(945\) | 638.945 | − | 1106.69i | 0.0219946 | − | 0.0380958i | ||||
\(946\) | −481.302 | − | 833.640i | −0.0165417 | − | 0.0286511i | ||||
\(947\) | −1199.30 | + | 2077.25i | −0.0411531 | + | 0.0712793i | −0.885868 | − | 0.463937i | \(-0.846436\pi\) |
0.844715 | + | 0.535216i | \(0.179770\pi\) | |||||||
\(948\) | 3139.78 | − | 5438.27i | 0.107569 | − | 0.186315i | ||||
\(949\) | −23242.5 | −0.795029 | ||||||||
\(950\) | 4124.70 | + | 366.582i | 0.140866 | + | 0.0125195i | ||||
\(951\) | −26577.9 | −0.906253 | ||||||||
\(952\) | −4265.64 | + | 7388.30i | −0.145221 | + | 0.251530i | ||||
\(953\) | −2719.93 | + | 4711.05i | −0.0924523 | + | 0.160132i | −0.908542 | − | 0.417793i | \(-0.862804\pi\) |
0.816090 | + | 0.577925i | \(0.196137\pi\) | |||||||
\(954\) | 2638.62 | + | 4570.23i | 0.0895478 | + | 0.155101i | ||||
\(955\) | −5398.91 | + | 9351.19i | −0.182937 | + | 0.316856i | ||||
\(956\) | −11092.1 | − | 19212.1i | −0.375256 | − | 0.649962i | ||||
\(957\) | 11359.9 | 0.383712 | ||||||||
\(958\) | 5375.14 | 0.181276 | ||||||||
\(959\) | −1354.08 | − | 2345.33i | −0.0455948 | − | 0.0789726i | ||||
\(960\) | −480.000 | − | 831.384i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | 14280.3 | 0.479350 | ||||||||
\(962\) | −21524.9 | −0.721402 | ||||||||
\(963\) | 6930.90 | + | 12004.7i | 0.231926 | + | 0.401708i | ||||
\(964\) | −1574.33 | + | 2726.82i | −0.0525994 | + | 0.0911049i | ||||
\(965\) | −6285.85 | − | 10887.4i | −0.209688 | − | 0.363190i | ||||
\(966\) | −1446.34 | + | 2505.13i | −0.0481730 | + | 0.0834381i | ||||
\(967\) | 28267.7 | − | 48961.1i | 0.940049 | − | 1.62821i | 0.174676 | − | 0.984626i | \(-0.444112\pi\) |
0.765373 | − | 0.643586i | \(-0.222554\pi\) | |||||||
\(968\) | 2761.54 | 0.0916935 | ||||||||
\(969\) | −11794.5 | − | 25384.6i | −0.391016 | − | 0.841558i | ||||
\(970\) | 3645.22 | 0.120661 | ||||||||
\(971\) | −963.799 | + | 1669.35i | −0.0318535 | + | 0.0551719i | −0.881513 | − | 0.472160i | \(-0.843474\pi\) |
0.849659 | + | 0.527332i | \(0.176808\pi\) | |||||||
\(972\) | 486.000 | − | 841.777i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −8700.77 | − | 15070.2i | −0.286674 | − | 0.496534i | ||||
\(974\) | 18255.0 | − | 31618.6i | 0.600542 | − | 1.04017i | ||||
\(975\) | −2454.97 | − | 4252.13i | −0.0806379 | − | 0.139669i | ||||
\(976\) | 11412.0 | 0.374271 | ||||||||
\(977\) | 53049.3 | 1.73715 | 0.868576 | − | 0.495557i | \(-0.165036\pi\) | ||||
0.868576 | + | 0.495557i | \(0.165036\pi\) | |||||||
\(978\) | 4645.34 | + | 8045.96i | 0.151883 | + | 0.263069i | ||||
\(979\) | −4670.16 | − | 8088.96i | −0.152461 | − | 0.264070i | ||||
\(980\) | 5067.95 | 0.165194 | ||||||||
\(981\) | −6524.67 | −0.212351 | ||||||||
\(982\) | 980.399 | + | 1698.10i | 0.0318592 | + | 0.0551818i | ||||
\(983\) | −25590.8 | + | 44324.5i | −0.830335 | + | 1.43818i | 0.0674386 | + | 0.997723i | \(0.478517\pi\) |
−0.897773 | + | 0.440458i | \(0.854816\pi\) | |||||||
\(984\) | −1742.46 | − | 3018.03i | −0.0564508 | − | 0.0977756i | ||||
\(985\) | −13287.5 | + | 23014.6i | −0.429822 | + | 0.744474i | ||||
\(986\) | 13586.9 | − | 23533.2i | 0.438839 | − | 0.760091i | ||||
\(987\) | −14879.6 | −0.479862 | ||||||||
\(988\) | −12463.7 | + | 17748.1i | −0.401341 | + | 0.571499i | ||||
\(989\) | −780.747 | −0.0251024 | ||||||||
\(990\) | 1412.89 | − | 2447.20i | 0.0453582 | − | 0.0785627i | ||||
\(991\) | 9939.12 | − | 17215.1i | 0.318594 | − | 0.551821i | −0.661601 | − | 0.749856i | \(-0.730123\pi\) |
0.980195 | + | 0.198035i | \(0.0634560\pi\) | |||||||
\(992\) | 3358.91 | + | 5817.80i | 0.107505 | + | 0.186205i | ||||
\(993\) | −17366.2 | + | 30079.2i | −0.554986 | + | 0.961263i | ||||
\(994\) | −2129.47 | − | 3688.35i | −0.0679505 | − | 0.117694i | ||||
\(995\) | 7913.95 | 0.252150 | ||||||||
\(996\) | −5988.24 | −0.190507 | ||||||||
\(997\) | −13568.2 | − | 23500.8i | −0.431003 | − | 0.746519i | 0.565957 | − | 0.824435i | \(-0.308507\pi\) |
−0.996960 | + | 0.0779159i | \(0.975173\pi\) | |||||||
\(998\) | −11003.1 | − | 19057.9i | −0.348994 | − | 0.604476i | ||||
\(999\) | 4438.73 | 0.140576 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 570.4.i.i.391.1 | yes | 4 | |
19.7 | even | 3 | inner | 570.4.i.i.121.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.4.i.i.121.1 | ✓ | 4 | 19.7 | even | 3 | inner | |
570.4.i.i.391.1 | yes | 4 | 1.1 | even | 1 | trivial |