Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(25,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 103.5 | ||
Character | \(\chi\) | \(=\) | 117.103 |
Dual form | 117.4.t.a.25.5 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.99826 | + | 2.30840i | −1.41360 | + | 0.816141i | −0.995725 | − | 0.0923644i | \(-0.970558\pi\) |
−0.417873 | + | 0.908506i | \(0.637224\pi\) | |||||||
\(3\) | 3.49652 | − | 3.84374i | 0.672906 | − | 0.739728i | ||||
\(4\) | 6.65738 | − | 11.5309i | 0.832173 | − | 1.44137i | ||||
\(5\) | −5.26914 | − | 3.04214i | −0.471286 | − | 0.272097i | 0.245492 | − | 0.969399i | \(-0.421051\pi\) |
−0.716778 | + | 0.697302i | \(0.754384\pi\) | |||||||
\(6\) | −5.10714 | + | 23.4396i | −0.347497 | + | 1.59486i | ||||
\(7\) | 14.5470 | − | 8.39873i | 0.785465 | − | 0.453489i | −0.0528984 | − | 0.998600i | \(-0.516846\pi\) |
0.838364 | + | 0.545111i | \(0.183513\pi\) | |||||||
\(8\) | 24.5372i | 1.08440i | ||||||||
\(9\) | −2.54865 | − | 26.8794i | −0.0943944 | − | 0.995535i | ||||
\(10\) | 28.0898 | 0.888278 | ||||||||
\(11\) | −31.9191 | + | 18.4285i | −0.874908 | + | 0.505128i | −0.868976 | − | 0.494854i | \(-0.835221\pi\) |
−0.00593166 | + | 0.999982i | \(0.501888\pi\) | |||||||
\(12\) | −21.0442 | − | 65.9074i | −0.506244 | − | 1.58549i | ||||
\(13\) | −32.8133 | + | 33.4707i | −0.700060 | + | 0.714084i | ||||
\(14\) | −38.7752 | + | 67.1606i | −0.740221 | + | 1.28210i | ||||
\(15\) | −30.1168 | + | 9.61628i | −0.518409 | + | 0.165527i | ||||
\(16\) | −3.38244 | − | 5.85856i | −0.0528507 | − | 0.0915401i | ||||
\(17\) | −83.7613 | −1.19501 | −0.597503 | − | 0.801867i | \(-0.703840\pi\) | ||||
−0.597503 | + | 0.801867i | \(0.703840\pi\) | |||||||
\(18\) | 72.2386 | + | 101.588i | 0.945933 | + | 1.33025i | ||||
\(19\) | − | 113.228i | − | 1.36717i | −0.729870 | − | 0.683586i | \(-0.760420\pi\) | ||
0.729870 | − | 0.683586i | \(-0.239580\pi\) | |||||||
\(20\) | −70.1573 | + | 40.5054i | −0.784383 | + | 0.452864i | ||||
\(21\) | 18.5815 | − | 85.2813i | 0.193086 | − | 0.886186i | ||||
\(22\) | 85.0807 | − | 147.364i | 0.824512 | − | 1.42810i | ||||
\(23\) | 49.5385 | − | 85.8033i | 0.449109 | − | 0.777879i | −0.549220 | − | 0.835678i | \(-0.685075\pi\) |
0.998328 | + | 0.0577990i | \(0.0184083\pi\) | |||||||
\(24\) | 94.3145 | + | 85.7948i | 0.802161 | + | 0.729700i | ||||
\(25\) | −43.9908 | − | 76.1943i | −0.351926 | − | 0.609554i | ||||
\(26\) | 53.9327 | − | 209.571i | 0.406811 | − | 1.58078i | ||||
\(27\) | −112.229 | − | 84.1883i | −0.799943 | − | 0.600075i | ||||
\(28\) | − | 223.654i | − | 1.50952i | ||||||
\(29\) | 55.2727 | + | 95.7351i | 0.353927 | + | 0.613019i | 0.986934 | − | 0.161127i | \(-0.0515129\pi\) |
−0.633007 | + | 0.774146i | \(0.718180\pi\) | |||||||
\(30\) | 98.2168 | − | 107.970i | 0.597728 | − | 0.657084i | ||||
\(31\) | −67.0340 | − | 38.7021i | −0.388376 | − | 0.224229i | 0.293080 | − | 0.956088i | \(-0.405320\pi\) |
−0.681456 | + | 0.731859i | \(0.738653\pi\) | |||||||
\(32\) | −142.951 | − | 82.5327i | −0.789699 | − | 0.455933i | ||||
\(33\) | −40.7716 | + | 187.125i | −0.215073 | + | 0.987097i | ||||
\(34\) | 334.899 | − | 193.354i | 1.68926 | − | 0.975293i | ||||
\(35\) | −102.200 | −0.493572 | ||||||||
\(36\) | −326.912 | − | 149.558i | −1.51348 | − | 0.692400i | ||||
\(37\) | 142.423i | 0.632814i | 0.948623 | + | 0.316407i | \(0.102477\pi\) | ||||
−0.948623 | + | 0.316407i | \(0.897523\pi\) | |||||||
\(38\) | 261.375 | + | 452.714i | 1.11580 | + | 1.93263i | ||||
\(39\) | 13.9198 | + | 243.157i | 0.0571528 | + | 0.998365i | ||||
\(40\) | 74.6455 | − | 129.290i | 0.295062 | − | 0.511063i | ||||
\(41\) | −286.330 | − | 165.313i | −1.09066 | − | 0.629695i | −0.156910 | − | 0.987613i | \(-0.550153\pi\) |
−0.933753 | + | 0.357918i | \(0.883487\pi\) | |||||||
\(42\) | 122.569 | + | 383.870i | 0.450306 | + | 1.41030i | ||||
\(43\) | −144.446 | − | 250.188i | −0.512276 | − | 0.887287i | −0.999899 | − | 0.0142332i | \(-0.995469\pi\) |
0.487623 | − | 0.873054i | \(-0.337864\pi\) | |||||||
\(44\) | 490.743i | 1.68142i | ||||||||
\(45\) | −68.3418 | + | 149.385i | −0.226395 | + | 0.494866i | ||||
\(46\) | 457.418i | 1.46614i | ||||||||
\(47\) | 131.767 | − | 76.0756i | 0.408939 | − | 0.236101i | −0.281394 | − | 0.959592i | \(-0.590797\pi\) |
0.690334 | + | 0.723491i | \(0.257464\pi\) | |||||||
\(48\) | −34.3456 | − | 7.48338i | −0.103278 | − | 0.0225028i | ||||
\(49\) | −30.4228 | + | 52.6938i | −0.0886962 | + | 0.153626i | ||||
\(50\) | 351.773 | + | 203.096i | 0.994965 | + | 0.574443i | ||||
\(51\) | −292.873 | + | 321.956i | −0.804127 | + | 0.883979i | ||||
\(52\) | 167.497 | + | 601.195i | 0.446685 | + | 1.60328i | ||||
\(53\) | −44.1481 | −0.114419 | −0.0572094 | − | 0.998362i | \(-0.518220\pi\) | ||||
−0.0572094 | + | 0.998362i | \(0.518220\pi\) | |||||||
\(54\) | 643.060 | + | 77.5376i | 1.62054 | + | 0.195399i | ||||
\(55\) | 224.248 | 0.549776 | ||||||||
\(56\) | 206.081 | + | 356.943i | 0.491763 | + | 0.851759i | ||||
\(57\) | −435.218 | − | 395.904i | −1.01133 | − | 0.919978i | ||||
\(58\) | −441.989 | − | 255.182i | −1.00062 | − | 0.577708i | ||||
\(59\) | 363.234 | + | 209.713i | 0.801508 | + | 0.462751i | 0.843998 | − | 0.536346i | \(-0.180196\pi\) |
−0.0424900 | + | 0.999097i | \(0.513529\pi\) | |||||||
\(60\) | −89.6148 | + | 411.294i | −0.192820 | + | 0.884964i | ||||
\(61\) | −89.3170 | − | 154.702i | −0.187473 | − | 0.324713i | 0.756934 | − | 0.653491i | \(-0.226696\pi\) |
−0.944407 | + | 0.328778i | \(0.893363\pi\) | |||||||
\(62\) | 357.359 | 0.732011 | ||||||||
\(63\) | −262.828 | − | 369.610i | −0.525607 | − | 0.739151i | ||||
\(64\) | 816.191 | 1.59412 | ||||||||
\(65\) | 274.720 | − | 76.5388i | 0.524229 | − | 0.146053i | ||||
\(66\) | −268.942 | − | 842.290i | −0.501583 | − | 1.57089i | ||||
\(67\) | −112.659 | − | 65.0437i | −0.205425 | − | 0.118602i | 0.393758 | − | 0.919214i | \(-0.371175\pi\) |
−0.599183 | + | 0.800612i | \(0.704508\pi\) | |||||||
\(68\) | −557.631 | + | 965.845i | −0.994451 | + | 1.72244i | ||||
\(69\) | −156.593 | − | 490.426i | −0.273211 | − | 0.855658i | ||||
\(70\) | 408.623 | − | 235.919i | 0.697712 | − | 0.402824i | ||||
\(71\) | − | 280.259i | − | 0.468459i | −0.972181 | − | 0.234229i | \(-0.924743\pi\) | ||
0.972181 | − | 0.234229i | \(-0.0752567\pi\) | |||||||
\(72\) | 659.546 | − | 62.5366i | 1.07956 | − | 0.102361i | ||||
\(73\) | 1119.00i | 1.79410i | 0.441933 | + | 0.897048i | \(0.354293\pi\) | ||||
−0.441933 | + | 0.897048i | \(0.645707\pi\) | |||||||
\(74\) | −328.768 | − | 569.443i | −0.516466 | − | 0.894545i | ||||
\(75\) | −446.686 | − | 97.3260i | −0.687718 | − | 0.149843i | ||||
\(76\) | −1305.62 | − | 753.801i | −1.97059 | − | 1.13772i | ||||
\(77\) | −309.552 | + | 536.160i | −0.458140 | + | 0.793521i | ||||
\(78\) | −616.957 | − | 940.071i | −0.895598 | − | 1.36464i | ||||
\(79\) | 177.268 | + | 307.038i | 0.252459 | + | 0.437272i | 0.964202 | − | 0.265168i | \(-0.0854274\pi\) |
−0.711743 | + | 0.702440i | \(0.752094\pi\) | |||||||
\(80\) | 41.1594i | 0.0575221i | ||||||||
\(81\) | −716.009 | + | 137.013i | −0.982179 | + | 0.187946i | ||||
\(82\) | 1526.43 | 2.05568 | ||||||||
\(83\) | 1137.80 | − | 656.909i | 1.50470 | − | 0.868737i | 0.504712 | − | 0.863288i | \(-0.331599\pi\) |
0.999985 | − | 0.00544908i | \(-0.00173451\pi\) | |||||||
\(84\) | −859.668 | − | 782.012i | −1.11664 | − | 1.01577i | ||||
\(85\) | 441.350 | + | 254.813i | 0.563189 | + | 0.325158i | ||||
\(86\) | 1155.07 | + | 666.878i | 1.44830 | + | 0.836179i | ||||
\(87\) | 561.243 | + | 122.286i | 0.691627 | + | 0.150695i | ||||
\(88\) | −452.184 | − | 783.206i | −0.547761 | − | 0.948750i | ||||
\(89\) | − | 589.884i | − | 0.702558i | −0.936271 | − | 0.351279i | \(-0.885747\pi\) | ||
0.936271 | − | 0.351279i | \(-0.114253\pi\) | |||||||
\(90\) | −71.5911 | − | 755.039i | −0.0838485 | − | 0.884312i | ||||
\(91\) | −196.225 | + | 762.489i | −0.226044 | + | 0.878357i | ||||
\(92\) | −659.594 | − | 1142.45i | −0.747472 | − | 1.29466i | ||||
\(93\) | −383.147 | + | 122.338i | −0.427209 | + | 0.136408i | ||||
\(94\) | −351.225 | + | 608.340i | −0.385384 | + | 0.667505i | ||||
\(95\) | −344.455 | + | 596.613i | −0.372003 | + | 0.644329i | ||||
\(96\) | −817.065 | + | 260.888i | −0.868659 | + | 0.277362i | ||||
\(97\) | 916.447 | − | 529.111i | 0.959290 | − | 0.553846i | 0.0633355 | − | 0.997992i | \(-0.479826\pi\) |
0.895954 | + | 0.444146i | \(0.146493\pi\) | |||||||
\(98\) | − | 280.911i | − | 0.289554i | ||||||
\(99\) | 576.699 | + | 811.001i | 0.585459 | + | 0.823320i | ||||
\(100\) | −1171.45 | −1.17145 | ||||||||
\(101\) | −804.800 | − | 1393.95i | −0.792877 | − | 1.37330i | −0.924178 | − | 0.381961i | \(-0.875249\pi\) |
0.131301 | − | 0.991343i | \(-0.458084\pi\) | |||||||
\(102\) | 427.780 | − | 1963.33i | 0.415260 | − | 1.90587i | ||||
\(103\) | 799.137 | − | 1384.15i | 0.764478 | − | 1.32412i | −0.176044 | − | 0.984382i | \(-0.556330\pi\) |
0.940522 | − | 0.339733i | \(-0.110337\pi\) | |||||||
\(104\) | −821.275 | − | 805.147i | −0.774353 | − | 0.759145i | ||||
\(105\) | −357.346 | + | 392.831i | −0.332127 | + | 0.365109i | ||||
\(106\) | 176.515 | − | 101.911i | 0.161742 | − | 0.0933820i | ||||
\(107\) | 1427.69 | 1.28991 | 0.644954 | − | 0.764221i | \(-0.276877\pi\) | ||||
0.644954 | + | 0.764221i | \(0.276877\pi\) | |||||||
\(108\) | −1717.92 | + | 733.630i | −1.53062 | + | 0.653644i | ||||
\(109\) | 1551.79i | 1.36362i | 0.731530 | + | 0.681809i | \(0.238807\pi\) | ||||
−0.731530 | + | 0.681809i | \(0.761193\pi\) | |||||||
\(110\) | −896.603 | + | 517.654i | −0.777162 | + | 0.448694i | ||||
\(111\) | 547.435 | + | 497.984i | 0.468110 | + | 0.425825i | ||||
\(112\) | −98.4090 | − | 56.8164i | −0.0830248 | − | 0.0479344i | ||||
\(113\) | 842.191 | − | 1458.72i | 0.701121 | − | 1.21438i | −0.266953 | − | 0.963710i | \(-0.586017\pi\) |
0.968073 | − | 0.250667i | \(-0.0806499\pi\) | |||||||
\(114\) | 2654.02 | + | 578.270i | 2.18045 | + | 0.475087i | ||||
\(115\) | −522.051 | + | 301.406i | −0.423317 | + | 0.244402i | ||||
\(116\) | 1471.89 | 1.17811 | ||||||||
\(117\) | 983.302 | + | 796.699i | 0.776977 | + | 0.629529i | ||||
\(118\) | −1936.40 | −1.51068 | ||||||||
\(119\) | −1218.48 | + | 703.488i | −0.938636 | + | 0.541921i | ||||
\(120\) | −235.956 | − | 738.982i | −0.179498 | − | 0.562163i | ||||
\(121\) | 13.7212 | − | 23.7658i | 0.0103089 | − | 0.0178556i | ||||
\(122\) | 714.225 | + | 412.358i | 0.530024 | + | 0.306009i | ||||
\(123\) | −1636.58 | + | 522.557i | −1.19972 | + | 0.383068i | ||||
\(124\) | −892.542 | + | 515.310i | −0.646393 | + | 0.373195i | ||||
\(125\) | 1295.84i | 0.927227i | ||||||||
\(126\) | 1904.06 | + | 871.086i | 1.34625 | + | 0.615893i | ||||
\(127\) | −695.897 | −0.486227 | −0.243114 | − | 0.969998i | \(-0.578169\pi\) | ||||
−0.243114 | + | 0.969998i | \(0.578169\pi\) | |||||||
\(128\) | −2119.74 | + | 1223.83i | −1.46375 | + | 0.845097i | ||||
\(129\) | −1466.72 | − | 319.576i | −1.00106 | − | 0.218117i | ||||
\(130\) | −921.721 | + | 940.185i | −0.621848 | + | 0.634305i | ||||
\(131\) | −683.828 | + | 1184.42i | −0.456079 | + | 0.789951i | −0.998750 | − | 0.0499940i | \(-0.984080\pi\) |
0.542671 | + | 0.839945i | \(0.317413\pi\) | |||||||
\(132\) | 1886.29 | + | 1715.89i | 1.24379 | + | 1.13144i | ||||
\(133\) | −950.970 | − | 1647.13i | −0.619997 | − | 1.07387i | ||||
\(134\) | 600.586 | 0.387185 | ||||||||
\(135\) | 335.237 | + | 785.015i | 0.213723 | + | 0.500469i | ||||
\(136\) | − | 2055.27i | − | 1.29586i | ||||||
\(137\) | 1342.88 | − | 775.310i | 0.837443 | − | 0.483498i | −0.0189511 | − | 0.999820i | \(-0.506033\pi\) |
0.856394 | + | 0.516322i | \(0.172699\pi\) | |||||||
\(138\) | 1758.20 | + | 1599.37i | 1.08455 | + | 0.986578i | ||||
\(139\) | −1057.46 | + | 1831.58i | −0.645272 | + | 1.11764i | 0.338967 | + | 0.940798i | \(0.389922\pi\) |
−0.984239 | + | 0.176845i | \(0.943411\pi\) | |||||||
\(140\) | −680.387 | + | 1178.46i | −0.410737 | + | 0.711417i | ||||
\(141\) | 168.311 | − | 772.477i | 0.100527 | − | 0.461378i | ||||
\(142\) | 646.948 | + | 1120.55i | 0.382329 | + | 0.662212i | ||||
\(143\) | 430.559 | − | 1673.06i | 0.251784 | − | 0.978378i | ||||
\(144\) | −148.854 | + | 105.850i | −0.0861425 | + | 0.0612556i | ||||
\(145\) | − | 672.588i | − | 0.385210i | ||||||
\(146\) | −2583.09 | − | 4474.05i | −1.46424 | − | 2.53613i | ||||
\(147\) | 96.1672 | + | 301.182i | 0.0539574 | + | 0.168987i | ||||
\(148\) | 1642.26 | + | 948.162i | 0.912117 | + | 0.526611i | ||||
\(149\) | −890.870 | − | 514.344i | −0.489818 | − | 0.282797i | 0.234681 | − | 0.972072i | \(-0.424595\pi\) |
−0.724499 | + | 0.689276i | \(0.757929\pi\) | |||||||
\(150\) | 2010.63 | − | 641.993i | 1.09445 | − | 0.349457i | ||||
\(151\) | 1646.56 | − | 950.642i | 0.887385 | − | 0.512332i | 0.0142988 | − | 0.999898i | \(-0.495448\pi\) |
0.873086 | + | 0.487566i | \(0.162115\pi\) | |||||||
\(152\) | 2778.29 | 1.48256 | ||||||||
\(153\) | 213.478 | + | 2251.46i | 0.112802 | + | 1.18967i | ||||
\(154\) | − | 2858.28i | − | 1.49563i | ||||||
\(155\) | 235.474 | + | 407.853i | 0.122024 | + | 0.211352i | ||||
\(156\) | 2896.49 | + | 1458.28i | 1.48657 | + | 0.748435i | ||||
\(157\) | 1560.73 | − | 2703.27i | 0.793376 | − | 1.37417i | −0.130490 | − | 0.991450i | \(-0.541655\pi\) |
0.923866 | − | 0.382717i | \(-0.125012\pi\) | |||||||
\(158\) | −1417.53 | − | 818.412i | −0.713751 | − | 0.412084i | ||||
\(159\) | −154.365 | + | 169.694i | −0.0769932 | + | 0.0846388i | ||||
\(160\) | 502.151 | + | 869.752i | 0.248116 | + | 0.429749i | ||||
\(161\) | − | 1664.24i | − | 0.814663i | ||||||
\(162\) | 2546.51 | − | 2200.64i | 1.23502 | − | 1.06728i | ||||
\(163\) | 492.893i | 0.236849i | 0.992963 | + | 0.118424i | \(0.0377843\pi\) | ||||
−0.992963 | + | 0.118424i | \(0.962216\pi\) | |||||||
\(164\) | −3812.41 | + | 2201.10i | −1.81524 | + | 1.04803i | ||||
\(165\) | 784.090 | − | 861.952i | 0.369947 | − | 0.406684i | ||||
\(166\) | −3032.81 | + | 5252.99i | −1.41802 | + | 2.45609i | ||||
\(167\) | −534.594 | − | 308.648i | −0.247713 | − | 0.143017i | 0.371003 | − | 0.928631i | \(-0.379014\pi\) |
−0.618717 | + | 0.785614i | \(0.712347\pi\) | |||||||
\(168\) | 2092.56 | + | 455.937i | 0.960980 | + | 0.209383i | ||||
\(169\) | −43.5696 | − | 2196.57i | −0.0198314 | − | 0.999803i | ||||
\(170\) | −2352.84 | −1.06150 | ||||||||
\(171\) | −3043.50 | + | 288.578i | −1.36107 | + | 0.129053i | ||||
\(172\) | −3846.54 | −1.70521 | ||||||||
\(173\) | 1887.52 | + | 3269.28i | 0.829512 | + | 1.43676i | 0.898422 | + | 0.439133i | \(0.144714\pi\) |
−0.0689104 | + | 0.997623i | \(0.521952\pi\) | |||||||
\(174\) | −2526.28 | + | 806.638i | −1.10067 | + | 0.351443i | ||||
\(175\) | −1279.87 | − | 738.933i | −0.552852 | − | 0.319189i | ||||
\(176\) | 215.929 | + | 124.667i | 0.0924789 | + | 0.0533927i | ||||
\(177\) | 2076.14 | − | 662.908i | 0.881650 | − | 0.281510i | ||||
\(178\) | 1361.69 | + | 2358.51i | 0.573386 | + | 0.993134i | ||||
\(179\) | −1230.15 | −0.513665 | −0.256832 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256832 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(180\) | 1267.57 | + | 1782.56i | 0.524883 | + | 0.738133i | ||||
\(181\) | 3967.59 | 1.62933 | 0.814664 | − | 0.579933i | \(-0.196921\pi\) | ||||
0.814664 | + | 0.579933i | \(0.196921\pi\) | |||||||
\(182\) | −975.565 | − | 3501.59i | −0.397328 | − | 1.42613i | ||||
\(183\) | −906.932 | − | 197.607i | −0.366351 | − | 0.0798224i | ||||
\(184\) | 2105.37 | + | 1215.54i | 0.843532 | + | 0.487014i | ||||
\(185\) | 433.269 | − | 750.444i | 0.172187 | − | 0.298237i | ||||
\(186\) | 1249.51 | − | 1373.60i | 0.492575 | − | 0.541489i | ||||
\(187\) | 2673.59 | − | 1543.60i | 1.04552 | − | 0.603631i | ||||
\(188\) | − | 2025.86i | − | 0.785908i | ||||||
\(189\) | −2339.67 | − | 282.108i | −0.900455 | − | 0.108573i | ||||
\(190\) | − | 3180.55i | − | 1.21443i | ||||||
\(191\) | 99.8592 | + | 172.961i | 0.0378301 | + | 0.0655237i | 0.884321 | − | 0.466880i | \(-0.154622\pi\) |
−0.846490 | + | 0.532404i | \(0.821289\pi\) | |||||||
\(192\) | 2853.83 | − | 3137.23i | 1.07270 | − | 1.17922i | ||||
\(193\) | −1858.54 | − | 1073.03i | −0.693163 | − | 0.400198i | 0.111633 | − | 0.993750i | \(-0.464392\pi\) |
−0.804796 | + | 0.593552i | \(0.797725\pi\) | |||||||
\(194\) | −2442.80 | + | 4231.05i | −0.904034 | + | 1.56583i | ||||
\(195\) | 666.371 | − | 1323.57i | 0.244717 | − | 0.486067i | ||||
\(196\) | 405.072 | + | 701.606i | 0.147621 | + | 0.255687i | ||||
\(197\) | − | 787.804i | − | 0.284917i | −0.989801 | − | 0.142459i | \(-0.954499\pi\) | ||
0.989801 | − | 0.142459i | \(-0.0455008\pi\) | |||||||
\(198\) | −4177.90 | − | 1911.34i | −1.49955 | − | 0.686026i | ||||
\(199\) | −103.934 | −0.0370236 | −0.0185118 | − | 0.999829i | \(-0.505893\pi\) | ||||
−0.0185118 | + | 0.999829i | \(0.505893\pi\) | |||||||
\(200\) | 1869.59 | − | 1079.41i | 0.661001 | − | 0.381629i | ||||
\(201\) | −643.925 | + | 205.605i | −0.225965 | + | 0.0721505i | ||||
\(202\) | 6435.60 | + | 3715.59i | 2.24162 | + | 1.29420i | ||||
\(203\) | 1608.11 | + | 928.440i | 0.555994 | + | 0.321003i | ||||
\(204\) | 1762.69 | + | 5520.49i | 0.604964 | + | 1.89466i | ||||
\(205\) | 1005.81 | + | 1742.11i | 0.342676 | + | 0.593532i | ||||
\(206\) | 7378.89i | 2.49569i | ||||||||
\(207\) | −2432.60 | − | 1112.89i | −0.816799 | − | 0.373676i | ||||
\(208\) | 307.079 | + | 79.0264i | 0.102366 | + | 0.0263437i | ||||
\(209\) | 2086.62 | + | 3614.14i | 0.690597 | + | 1.19615i | ||||
\(210\) | 521.951 | − | 2395.54i | 0.171514 | − | 0.787180i | ||||
\(211\) | −208.462 | + | 361.067i | −0.0680148 | + | 0.117805i | −0.898027 | − | 0.439940i | \(-0.855000\pi\) |
0.830013 | + | 0.557745i | \(0.188333\pi\) | |||||||
\(212\) | −293.911 | + | 509.068i | −0.0952163 | + | 0.164919i | ||||
\(213\) | −1077.24 | − | 979.931i | −0.346532 | − | 0.315229i | ||||
\(214\) | −5708.28 | + | 3295.68i | −1.82341 | + | 1.05275i | ||||
\(215\) | 1757.70i | 0.557555i | ||||||||
\(216\) | 2065.74 | − | 2753.78i | 0.650722 | − | 0.867459i | ||||
\(217\) | −1300.19 | −0.406742 | ||||||||
\(218\) | −3582.14 | − | 6204.45i | −1.11291 | − | 1.92761i | ||||
\(219\) | 4301.14 | + | 3912.61i | 1.32714 | + | 1.20726i | ||||
\(220\) | 1492.91 | − | 2585.79i | 0.457508 | − | 0.792428i | ||||
\(221\) | 2748.49 | − | 2803.55i | 0.836576 | − | 0.853334i | ||||
\(222\) | −3338.33 | − | 727.372i | −1.00925 | − | 0.219901i | ||||
\(223\) | −3498.23 | + | 2019.70i | −1.05049 | + | 0.606499i | −0.922786 | − | 0.385313i | \(-0.874093\pi\) |
−0.127702 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(224\) | −2772.68 | −0.827041 | ||||||||
\(225\) | −1935.94 | + | 1376.64i | −0.573613 | + | 0.407894i | ||||
\(226\) | 7776.44i | 2.28885i | ||||||||
\(227\) | 462.536 | − | 267.045i | 0.135240 | − | 0.0780811i | −0.430853 | − | 0.902422i | \(-0.641787\pi\) |
0.566094 | + | 0.824341i | \(0.308454\pi\) | |||||||
\(228\) | −7462.55 | + | 2382.79i | −2.16763 | + | 0.692122i | ||||
\(229\) | −4866.54 | − | 2809.70i | −1.40432 | − | 0.810786i | −0.409490 | − | 0.912314i | \(-0.634293\pi\) |
−0.994833 | + | 0.101528i | \(0.967627\pi\) | |||||||
\(230\) | 1391.53 | − | 2410.20i | 0.398934 | − | 0.690973i | ||||
\(231\) | 978.503 | + | 3064.54i | 0.278705 | + | 0.872864i | ||||
\(232\) | −2349.07 | + | 1356.23i | −0.664758 | + | 0.383798i | ||||
\(233\) | 6763.20 | 1.90160 | 0.950798 | − | 0.309811i | \(-0.100266\pi\) | ||||
0.950798 | + | 0.309811i | \(0.100266\pi\) | |||||||
\(234\) | −5770.59 | − | 915.559i | −1.61212 | − | 0.255778i | ||||
\(235\) | −925.729 | −0.256970 | ||||||||
\(236\) | 4836.37 | − | 2792.28i | 1.33399 | − | 0.770178i | ||||
\(237\) | 1800.00 | + | 392.192i | 0.493343 | + | 0.107492i | ||||
\(238\) | 3247.86 | − | 5625.46i | 0.884569 | − | 1.53212i | ||||
\(239\) | −3061.66 | − | 1767.65i | −0.828629 | − | 0.478409i | 0.0247538 | − | 0.999694i | \(-0.492120\pi\) |
−0.853383 | + | 0.521284i | \(0.825453\pi\) | |||||||
\(240\) | 158.206 | + | 143.915i | 0.0425507 | + | 0.0387070i | ||||
\(241\) | −4471.44 | + | 2581.59i | −1.19515 | + | 0.690020i | −0.959470 | − | 0.281811i | \(-0.909065\pi\) |
−0.235679 | + | 0.971831i | \(0.575732\pi\) | |||||||
\(242\) | 126.696i | 0.0336542i | ||||||||
\(243\) | −1976.90 | + | 3231.22i | −0.521886 | + | 0.853015i | ||||
\(244\) | −2378.47 | −0.624041 | ||||||||
\(245\) | 320.604 | − | 185.101i | 0.0836025 | − | 0.0482679i | ||||
\(246\) | 5337.19 | − | 5867.19i | 1.38328 | − | 1.52064i | ||||
\(247\) | 3789.81 | + | 3715.38i | 0.976275 | + | 0.957102i | ||||
\(248\) | 949.640 | − | 1644.83i | 0.243154 | − | 0.421155i | ||||
\(249\) | 1453.36 | − | 6670.31i | 0.369891 | − | 1.69764i | ||||
\(250\) | −2991.31 | − | 5181.10i | −0.756748 | − | 1.31073i | ||||
\(251\) | −1455.60 | −0.366043 | −0.183022 | − | 0.983109i | \(-0.558588\pi\) | ||||
−0.183022 | + | 0.983109i | \(0.558588\pi\) | |||||||
\(252\) | −6011.70 | + | 570.016i | −1.50278 | + | 0.142491i | ||||
\(253\) | 3651.69i | 0.907430i | ||||||||
\(254\) | 2782.38 | − | 1606.41i | 0.687330 | − | 0.396830i | ||||
\(255\) | 2522.63 | − | 805.472i | 0.619502 | − | 0.197806i | ||||
\(256\) | 2385.41 | − | 4131.65i | 0.582375 | − | 1.00870i | ||||
\(257\) | 2071.66 | − | 3588.22i | 0.502827 | − | 0.870922i | −0.497168 | − | 0.867655i | \(-0.665627\pi\) |
0.999995 | − | 0.00326752i | \(-0.00104009\pi\) | |||||||
\(258\) | 6602.03 | − | 2108.02i | 1.59312 | − | 0.508681i | ||||
\(259\) | 1196.17 | + | 2071.83i | 0.286974 | + | 0.497054i | ||||
\(260\) | 946.355 | − | 3677.33i | 0.225733 | − | 0.877147i | ||||
\(261\) | 2432.43 | − | 1729.69i | 0.576873 | − | 0.410212i | ||||
\(262\) | − | 6314.18i | − | 1.48890i | ||||||
\(263\) | 867.009 | + | 1501.70i | 0.203278 | + | 0.352088i | 0.949583 | − | 0.313517i | \(-0.101507\pi\) |
−0.746305 | + | 0.665604i | \(0.768174\pi\) | |||||||
\(264\) | −4591.51 | − | 1000.42i | −1.07041 | − | 0.233226i | ||||
\(265\) | 232.622 | + | 134.304i | 0.0539240 | + | 0.0311330i | ||||
\(266\) | 7604.45 | + | 4390.43i | 1.75285 | + | 1.01201i | ||||
\(267\) | −2267.36 | − | 2062.54i | −0.519701 | − | 0.472755i | ||||
\(268\) | −1500.03 | + | 866.041i | −0.341898 | + | 0.197395i | ||||
\(269\) | 856.529 | 0.194139 | 0.0970697 | − | 0.995278i | \(-0.469053\pi\) | ||||
0.0970697 | + | 0.995278i | \(0.469053\pi\) | |||||||
\(270\) | −3152.49 | − | 2364.83i | −0.710572 | − | 0.533034i | ||||
\(271\) | − | 8151.31i | − | 1.82715i | −0.406674 | − | 0.913573i | \(-0.633311\pi\) | ||
0.406674 | − | 0.913573i | \(-0.366689\pi\) | |||||||
\(272\) | 283.318 | + | 490.721i | 0.0631569 | + | 0.109391i | ||||
\(273\) | 2244.70 | + | 3420.30i | 0.497639 | + | 0.758263i | ||||
\(274\) | −3579.45 | + | 6199.78i | −0.789205 | + | 1.36694i | ||||
\(275\) | 2808.30 | + | 1621.37i | 0.615806 | + | 0.355536i | ||||
\(276\) | −6697.57 | − | 1459.30i | −1.46067 | − | 0.318259i | ||||
\(277\) | −3515.11 | − | 6088.36i | −0.762465 | − | 1.32063i | −0.941577 | − | 0.336799i | \(-0.890656\pi\) |
0.179112 | − | 0.983829i | \(-0.442678\pi\) | |||||||
\(278\) | − | 9764.16i | − | 2.10653i | ||||||
\(279\) | −869.445 | + | 1900.48i | −0.186567 | + | 0.407808i | ||||
\(280\) | − | 2507.71i | − | 0.535229i | ||||||
\(281\) | −5216.72 | + | 3011.88i | −1.10749 | + | 0.639408i | −0.938177 | − | 0.346155i | \(-0.887487\pi\) |
−0.169309 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(282\) | 1110.23 | + | 3477.09i | 0.234444 | + | 0.734247i | ||||
\(283\) | 2308.32 | − | 3998.13i | 0.484860 | − | 0.839803i | −0.514988 | − | 0.857197i | \(-0.672204\pi\) |
0.999849 | + | 0.0173946i | \(0.00553714\pi\) | |||||||
\(284\) | −3231.64 | − | 1865.79i | −0.675220 | − | 0.389839i | ||||
\(285\) | 1088.83 | + | 3410.07i | 0.226304 | + | 0.708754i | ||||
\(286\) | 2140.59 | + | 7683.21i | 0.442573 | + | 1.58852i | ||||
\(287\) | −5553.66 | −1.14224 | ||||||||
\(288\) | −1854.10 | + | 4052.78i | −0.379354 | + | 0.829210i | ||||
\(289\) | 2102.95 | 0.428039 | ||||||||
\(290\) | 1552.60 | + | 2689.18i | 0.314386 | + | 0.544532i | ||||
\(291\) | 1170.61 | − | 5372.63i | 0.235817 | − | 1.08230i | ||||
\(292\) | 12903.1 | + | 7449.61i | 2.58595 | + | 1.49300i | ||||
\(293\) | 1424.23 | + | 822.280i | 0.283974 | + | 0.163953i | 0.635221 | − | 0.772330i | \(-0.280909\pi\) |
−0.351247 | + | 0.936283i | \(0.614242\pi\) | |||||||
\(294\) | −1079.75 | − | 982.213i | −0.214191 | − | 0.194843i | ||||
\(295\) | −1275.95 | − | 2210.01i | −0.251826 | − | 0.436176i | ||||
\(296\) | −3494.65 | −0.686224 | ||||||||
\(297\) | 5133.72 | + | 619.003i | 1.00299 | + | 0.120937i | ||||
\(298\) | 4749.24 | 0.923208 | ||||||||
\(299\) | 1246.37 | + | 4473.58i | 0.241068 | + | 0.865263i | ||||
\(300\) | −4096.02 | + | 4502.76i | −0.788279 | + | 0.866557i | ||||
\(301\) | −4202.53 | − | 2426.33i | −0.804749 | − | 0.464622i | ||||
\(302\) | −4388.92 | + | 7601.82i | −0.836271 | + | 1.44846i | ||||
\(303\) | −8172.00 | − | 1780.55i | −1.54940 | − | 0.337591i | ||||
\(304\) | −663.353 | + | 382.987i | −0.125151 | + | 0.0722559i | ||||
\(305\) | 1086.86i | 0.204044i | ||||||||
\(306\) | −6050.79 | − | 8509.12i | −1.13040 | − | 1.58965i | ||||
\(307\) | − | 3577.98i | − | 0.665166i | −0.943074 | − | 0.332583i | \(-0.892080\pi\) | ||
0.943074 | − | 0.332583i | \(-0.107920\pi\) | |||||||
\(308\) | 4121.62 | + | 7138.85i | 0.762503 | + | 1.32069i | ||||
\(309\) | −2526.09 | − | 7911.37i | −0.465063 | − | 1.45651i | ||||
\(310\) | −1882.97 | − | 1087.14i | −0.344986 | − | 0.199178i | ||||
\(311\) | −4464.93 | + | 7733.49i | −0.814093 | + | 1.41005i | 0.0958835 | + | 0.995393i | \(0.469432\pi\) |
−0.909977 | + | 0.414659i | \(0.863901\pi\) | |||||||
\(312\) | −5966.38 | + | 341.553i | −1.08263 | + | 0.0619765i | ||||
\(313\) | 41.1457 | + | 71.2664i | 0.00743032 | + | 0.0128697i | 0.869717 | − | 0.493551i | \(-0.164302\pi\) |
−0.862286 | + | 0.506421i | \(0.830968\pi\) | |||||||
\(314\) | 14411.1i | 2.59003i | ||||||||
\(315\) | 260.473 | + | 2747.09i | 0.0465904 | + | 0.491368i | ||||
\(316\) | 4720.58 | 0.840358 | ||||||||
\(317\) | 6845.34 | − | 3952.16i | 1.21285 | − | 0.700238i | 0.249469 | − | 0.968383i | \(-0.419744\pi\) |
0.963379 | + | 0.268145i | \(0.0864106\pi\) | |||||||
\(318\) | 225.470 | − | 1034.81i | 0.0397602 | − | 0.182483i | ||||
\(319\) | −3528.51 | − | 2037.19i | −0.619306 | − | 0.357557i | ||||
\(320\) | −4300.62 | − | 2482.97i | −0.751288 | − | 0.433756i | ||||
\(321\) | 4991.96 | − | 5487.67i | 0.867987 | − | 0.954181i | ||||
\(322\) | 3841.73 | + | 6654.07i | 0.664880 | + | 1.15161i | ||||
\(323\) | 9484.11i | 1.63378i | ||||||||
\(324\) | −3186.86 | + | 9168.39i | −0.546444 | + | 1.57208i | ||||
\(325\) | 3993.76 | + | 1027.79i | 0.681643 | + | 0.175420i | ||||
\(326\) | −1137.79 | − | 1970.71i | −0.193302 | − | 0.334809i | ||||
\(327\) | 5964.67 | + | 5425.87i | 1.00871 | + | 0.917588i | ||||
\(328\) | 4056.30 | − | 7025.72i | 0.682841 | − | 1.18271i | ||||
\(329\) | 1277.88 | − | 2213.35i | 0.214139 | − | 0.370899i | ||||
\(330\) | −1145.27 | + | 5256.30i | −0.191045 | + | 0.876817i | ||||
\(331\) | 539.405 | − | 311.426i | 0.0895722 | − | 0.0517145i | −0.454545 | − | 0.890724i | \(-0.650198\pi\) |
0.544117 | + | 0.839009i | \(0.316865\pi\) | |||||||
\(332\) | − | 17493.2i | − | 2.89176i | ||||||
\(333\) | 3828.24 | − | 362.985i | 0.629989 | − | 0.0597341i | ||||
\(334\) | 2849.93 | 0.466889 | ||||||||
\(335\) | 395.744 | + | 685.448i | 0.0645426 | + | 0.111791i | ||||
\(336\) | −562.477 | + | 179.598i | −0.0913263 | + | 0.0291604i | ||||
\(337\) | −1988.61 | + | 3444.38i | −0.321444 | + | 0.556758i | −0.980786 | − | 0.195085i | \(-0.937502\pi\) |
0.659342 | + | 0.751843i | \(0.270835\pi\) | |||||||
\(338\) | 5244.75 | + | 8681.87i | 0.844014 | + | 1.39713i | ||||
\(339\) | −2662.19 | − | 8337.60i | −0.426520 | − | 1.33580i | ||||
\(340\) | 5876.47 | − | 3392.78i | 0.937342 | − | 0.541175i | ||||
\(341\) | 2852.89 | 0.453058 | ||||||||
\(342\) | 11502.6 | − | 8179.42i | 1.81868 | − | 1.29325i | ||||
\(343\) | 6783.58i | 1.06787i | ||||||||
\(344\) | 6138.91 | − | 3544.30i | 0.962175 | − | 0.555512i | ||||
\(345\) | −666.836 | + | 3060.50i | −0.104062 | + | 0.477599i | ||||
\(346\) | −15093.6 | − | 8714.29i | −2.34519 | − | 1.35400i | ||||
\(347\) | −2042.53 | + | 3537.77i | −0.315991 | + | 0.547312i | −0.979648 | − | 0.200725i | \(-0.935670\pi\) |
0.663657 | + | 0.748037i | \(0.269004\pi\) | |||||||
\(348\) | 5146.48 | − | 5657.54i | 0.792760 | − | 0.871483i | ||||
\(349\) | 9032.94 | − | 5215.17i | 1.38545 | − | 0.799890i | 0.392652 | − | 0.919687i | \(-0.371558\pi\) |
0.992798 | + | 0.119797i | \(0.0382243\pi\) | |||||||
\(350\) | 6823.00 | 1.04201 | ||||||||
\(351\) | 6500.44 | − | 993.879i | 0.988513 | − | 0.151138i | ||||
\(352\) | 6083.82 | 0.921218 | ||||||||
\(353\) | −8812.51 | + | 5087.91i | −1.32873 | + | 0.767144i | −0.985104 | − | 0.171961i | \(-0.944990\pi\) |
−0.343629 | + | 0.939105i | \(0.611656\pi\) | |||||||
\(354\) | −6770.68 | + | 7443.03i | −1.01655 | + | 1.11749i | ||||
\(355\) | −852.585 | + | 1476.72i | −0.127466 | + | 0.220778i | ||||
\(356\) | −6801.91 | − | 3927.09i | −1.01264 | − | 0.584649i | ||||
\(357\) | −1556.41 | + | 7143.27i | −0.230739 | + | 1.05900i | ||||
\(358\) | 4918.47 | − | 2839.68i | 0.726115 | − | 0.419223i | ||||
\(359\) | 1153.00i | 0.169507i | 0.996402 | + | 0.0847536i | \(0.0270103\pi\) | ||||
−0.996402 | + | 0.0847536i | \(0.972990\pi\) | |||||||
\(360\) | −3665.48 | − | 1676.91i | −0.536633 | − | 0.245503i | ||||
\(361\) | −5961.55 | −0.869157 | ||||||||
\(362\) | −15863.4 | + | 9158.76i | −2.30321 | + | 1.32976i | ||||
\(363\) | −43.3731 | − | 135.838i | −0.00627134 | − | 0.0196409i | ||||
\(364\) | 7485.85 | + | 7338.84i | 1.07793 | + | 1.05676i | ||||
\(365\) | 3404.15 | − | 5896.16i | 0.488168 | − | 0.845532i | ||||
\(366\) | 4082.30 | − | 1303.47i | 0.583020 | − | 0.186158i | ||||
\(367\) | 701.025 | + | 1214.21i | 0.0997091 | + | 0.172701i | 0.911564 | − | 0.411158i | \(-0.134875\pi\) |
−0.811855 | + | 0.583859i | \(0.801542\pi\) | |||||||
\(368\) | −670.245 | −0.0949428 | ||||||||
\(369\) | −3713.75 | + | 8117.70i | −0.523930 | + | 1.14523i | ||||
\(370\) | 4000.63i | 0.562115i | ||||||||
\(371\) | −642.223 | + | 370.787i | −0.0898721 | + | 0.0518877i | ||||
\(372\) | −1140.08 | + | 5232.49i | −0.158899 | + | 0.729280i | ||||
\(373\) | 5040.94 | − | 8731.16i | 0.699758 | − | 1.21202i | −0.268792 | − | 0.963198i | \(-0.586624\pi\) |
0.968550 | − | 0.248818i | \(-0.0800423\pi\) | |||||||
\(374\) | −7126.47 | + | 12343.4i | −0.985296 | + | 1.70658i | ||||
\(375\) | 4980.86 | + | 4530.93i | 0.685895 | + | 0.623937i | ||||
\(376\) | 1866.68 | + | 3233.18i | 0.256028 | + | 0.443454i | ||||
\(377\) | −5018.00 | − | 1291.37i | −0.685517 | − | 0.176417i | ||||
\(378\) | 10005.8 | − | 4272.95i | 1.36149 | − | 0.581420i | ||||
\(379\) | 10065.2i | 1.36416i | 0.731278 | + | 0.682079i | \(0.238924\pi\) | ||||
−0.731278 | + | 0.682079i | \(0.761076\pi\) | |||||||
\(380\) | 4586.33 | + | 7943.76i | 0.619142 | + | 1.07239i | ||||
\(381\) | −2433.22 | + | 2674.85i | −0.327185 | + | 0.359676i | ||||
\(382\) | −798.526 | − | 461.029i | −0.106953 | − | 0.0617495i | ||||
\(383\) | −9040.30 | − | 5219.42i | −1.20610 | − | 0.696344i | −0.244198 | − | 0.969725i | \(-0.578525\pi\) |
−0.961906 | + | 0.273381i | \(0.911858\pi\) | |||||||
\(384\) | −2707.63 | + | 12426.9i | −0.359825 | + | 1.65145i | ||||
\(385\) | 3262.15 | − | 1883.40i | 0.431830 | − | 0.249317i | ||||
\(386\) | 9907.89 | 1.30647 | ||||||||
\(387\) | −6356.78 | + | 4520.28i | −0.834970 | + | 0.593743i | ||||
\(388\) | − | 14090.0i | − | 1.84358i | ||||||
\(389\) | −3944.23 | − | 6831.61i | −0.514088 | − | 0.890427i | −0.999866 | − | 0.0163451i | \(-0.994797\pi\) |
0.485778 | − | 0.874082i | \(-0.338536\pi\) | |||||||
\(390\) | 391.006 | + | 6830.23i | 0.0507676 | + | 0.886827i | ||||
\(391\) | −4149.41 | + | 7186.99i | −0.536687 | + | 0.929570i | ||||
\(392\) | −1292.96 | − | 746.489i | −0.166592 | − | 0.0961821i | ||||
\(393\) | 2161.60 | + | 6769.82i | 0.277451 | + | 0.868937i | ||||
\(394\) | 1818.56 | + | 3149.84i | 0.232533 | + | 0.402759i | ||||
\(395\) | − | 2157.10i | − | 0.274773i | ||||||
\(396\) | 13190.9 | − | 1250.73i | 1.67391 | − | 0.158716i | ||||
\(397\) | − | 8028.38i | − | 1.01494i | −0.861668 | − | 0.507472i | \(-0.830580\pi\) | ||
0.861668 | − | 0.507472i | \(-0.169420\pi\) | |||||||
\(398\) | 415.555 | − | 239.921i | 0.0523364 | − | 0.0302165i | ||||
\(399\) | −9656.22 | − | 2103.94i | −1.21157 | − | 0.263982i | ||||
\(400\) | −297.593 | + | 515.446i | −0.0371991 | + | 0.0644307i | ||||
\(401\) | 8879.20 | + | 5126.41i | 1.10575 | + | 0.638406i | 0.937726 | − | 0.347377i | \(-0.112928\pi\) |
0.168025 | + | 0.985783i | \(0.446261\pi\) | |||||||
\(402\) | 2099.96 | − | 2308.50i | 0.260539 | − | 0.286411i | ||||
\(403\) | 3495.00 | − | 973.727i | 0.432005 | − | 0.120359i | ||||
\(404\) | −21431.4 | −2.63924 | ||||||||
\(405\) | 4189.56 | + | 1456.26i | 0.514027 | + | 0.178672i | ||||
\(406\) | −8572.83 | −1.04794 | ||||||||
\(407\) | −2624.64 | − | 4546.01i | −0.319652 | − | 0.553654i | ||||
\(408\) | −7899.90 | − | 7186.28i | −0.958587 | − | 0.871995i | ||||
\(409\) | −3883.30 | − | 2242.02i | −0.469478 | − | 0.271053i | 0.246543 | − | 0.969132i | \(-0.420705\pi\) |
−0.716021 | + | 0.698078i | \(0.754039\pi\) | |||||||
\(410\) | −8042.95 | − | 4643.60i | −0.968812 | − | 0.559344i | ||||
\(411\) | 1715.31 | − | 7872.56i | 0.205864 | − | 0.944829i | ||||
\(412\) | −10640.3 | − | 18429.6i | −1.27236 | − | 2.20379i | ||||
\(413\) | 7045.29 | 0.839409 | ||||||||
\(414\) | 12295.1 | − | 1165.80i | 1.45960 | − | 0.138396i | ||||
\(415\) | −7993.64 | −0.945523 | ||||||||
\(416\) | 7453.11 | − | 2076.48i | 0.878411 | − | 0.244731i | ||||
\(417\) | 3342.67 | + | 10468.8i | 0.392544 | + | 1.22939i | ||||
\(418\) | −16685.7 | − | 9633.50i | −1.95245 | − | 1.12725i | ||||
\(419\) | 2509.82 | − | 4347.14i | 0.292632 | − | 0.506854i | −0.681799 | − | 0.731540i | \(-0.738802\pi\) |
0.974431 | + | 0.224685i | \(0.0721355\pi\) | |||||||
\(420\) | 2150.72 | + | 6735.76i | 0.249868 | + | 0.782551i | ||||
\(421\) | 4093.63 | − | 2363.46i | 0.473898 | − | 0.273605i | −0.243972 | − | 0.969782i | \(-0.578450\pi\) |
0.717870 | + | 0.696177i | \(0.245117\pi\) | |||||||
\(422\) | − | 1924.85i | − | 0.222039i | ||||||
\(423\) | −2380.70 | − | 3347.93i | −0.273649 | − | 0.384827i | ||||
\(424\) | − | 1083.27i | − | 0.124076i | ||||||
\(425\) | 3684.73 | + | 6382.13i | 0.420554 | + | 0.728421i | ||||
\(426\) | 6569.15 | + | 1431.32i | 0.747128 | + | 0.162788i | ||||
\(427\) | −2598.59 | − | 1500.30i | −0.294508 | − | 0.170034i | ||||
\(428\) | 9504.69 | − | 16462.6i | 1.07343 | − | 1.85923i | ||||
\(429\) | −4925.33 | − | 7504.84i | −0.554306 | − | 0.844608i | ||||
\(430\) | −4057.47 | − | 7027.75i | −0.455043 | − | 0.788158i | ||||
\(431\) | 7360.23i | 0.822575i | 0.911506 | + | 0.411288i | \(0.134921\pi\) | ||||
−0.911506 | + | 0.411288i | \(0.865079\pi\) | |||||||
\(432\) | −113.614 | + | 942.263i | −0.0126534 | + | 0.104941i | ||||
\(433\) | −12358.4 | −1.37161 | −0.685806 | − | 0.727784i | \(-0.740550\pi\) | ||||
−0.685806 | + | 0.727784i | \(0.740550\pi\) | |||||||
\(434\) | 5198.51 | − | 3001.36i | 0.574969 | − | 0.331959i | ||||
\(435\) | −2585.25 | − | 2351.72i | −0.284950 | − | 0.259210i | ||||
\(436\) | 17893.6 | + | 10330.9i | 1.96547 | + | 1.13477i | ||||
\(437\) | −9715.32 | − | 5609.14i | −1.06349 | − | 0.614008i | ||||
\(438\) | −26228.9 | − | 5714.88i | −2.86134 | − | 0.623442i | ||||
\(439\) | −2751.91 | − | 4766.46i | −0.299184 | − | 0.518202i | 0.676766 | − | 0.736199i | \(-0.263381\pi\) |
−0.975949 | + | 0.217997i | \(0.930048\pi\) | |||||||
\(440\) | 5502.42i | 0.596177i | ||||||||
\(441\) | 1493.92 | + | 683.449i | 0.161313 | + | 0.0737987i | ||||
\(442\) | −4517.47 | + | 17553.9i | −0.486141 | + | 1.88904i | ||||
\(443\) | 2200.33 | + | 3811.09i | 0.235984 | + | 0.408736i | 0.959558 | − | 0.281510i | \(-0.0908354\pi\) |
−0.723574 | + | 0.690247i | \(0.757502\pi\) | |||||||
\(444\) | 9386.70 | − | 2997.17i | 1.00332 | − | 0.320359i | ||||
\(445\) | −1794.51 | + | 3108.18i | −0.191164 | + | 0.331106i | ||||
\(446\) | 9324.55 | − | 16150.6i | 0.989978 | − | 1.71469i | ||||
\(447\) | −5091.95 | + | 1625.85i | −0.538794 | + | 0.172036i | ||||
\(448\) | 11873.2 | − | 6854.97i | 1.25213 | − | 0.722917i | ||||
\(449\) | − | 8308.93i | − | 0.873324i | −0.899626 | − | 0.436662i | \(-0.856161\pi\) | ||
0.899626 | − | 0.436662i | \(-0.143839\pi\) | |||||||
\(450\) | 4562.57 | − | 9973.09i | 0.477959 | − | 1.04475i | ||||
\(451\) | 12185.9 | 1.27231 | ||||||||
\(452\) | −11213.6 | − | 19422.5i | −1.16691 | − | 2.02114i | ||||
\(453\) | 2103.22 | − | 9652.89i | 0.218141 | − | 1.00117i | ||||
\(454\) | −1232.89 | + | 2135.43i | −0.127450 | + | 0.220751i | ||||
\(455\) | 3353.53 | − | 3420.71i | 0.345530 | − | 0.352452i | ||||
\(456\) | 9714.36 | − | 10679.0i | 0.997624 | − | 1.09669i | ||||
\(457\) | 3427.67 | − | 1978.97i | 0.350853 | − | 0.202565i | −0.314208 | − | 0.949354i | \(-0.601739\pi\) |
0.665061 | + | 0.746789i | \(0.268406\pi\) | |||||||
\(458\) | 25943.6 | 2.64686 | ||||||||
\(459\) | 9400.44 | + | 7051.72i | 0.955937 | + | 0.717094i | ||||
\(460\) | 8026.30i | 0.813540i | ||||||||
\(461\) | −8621.23 | + | 4977.47i | −0.870999 | + | 0.502872i | −0.867680 | − | 0.497123i | \(-0.834390\pi\) |
−0.00331904 | + | 0.999994i | \(0.501056\pi\) | |||||||
\(462\) | −10986.5 | − | 9994.03i | −1.10636 | − | 1.00642i | ||||
\(463\) | −9886.61 | − | 5708.04i | −0.992375 | − | 0.572948i | −0.0863916 | − | 0.996261i | \(-0.527534\pi\) |
−0.905983 | + | 0.423313i | \(0.860867\pi\) | |||||||
\(464\) | 373.913 | − | 647.637i | 0.0374105 | − | 0.0647970i | ||||
\(465\) | 2391.02 | + | 520.968i | 0.238454 | + | 0.0519555i | ||||
\(466\) | −27041.0 | + | 15612.1i | −2.68809 | + | 1.55197i | ||||
\(467\) | −8518.66 | −0.844104 | −0.422052 | − | 0.906572i | \(-0.638690\pi\) | ||||
−0.422052 | + | 0.906572i | \(0.638690\pi\) | |||||||
\(468\) | 15732.9 | − | 6034.45i | 1.55396 | − | 0.596031i | ||||
\(469\) | −2185.14 | −0.215139 | ||||||||
\(470\) | 3701.31 | − | 2136.95i | 0.363252 | − | 0.209724i | ||||
\(471\) | −4933.52 | − | 15451.1i | −0.482642 | − | 1.51157i | ||||
\(472\) | −5145.76 | + | 8912.73i | −0.501807 | + | 0.869156i | ||||
\(473\) | 9221.20 | + | 5323.86i | 0.896388 | + | 0.517530i | ||||
\(474\) | −8102.19 | + | 2587.02i | −0.785118 | + | 0.250687i | ||||
\(475\) | −8627.32 | + | 4980.98i | −0.833365 | + | 0.481144i | ||||
\(476\) | 18733.6i | 1.80389i | ||||||||
\(477\) | 112.518 | + | 1186.67i | 0.0108005 | + | 0.113908i | ||||
\(478\) | 16321.8 | 1.56180 | ||||||||
\(479\) | 13731.3 | − | 7927.75i | 1.30981 | − | 0.756218i | 0.327744 | − | 0.944767i | \(-0.393712\pi\) |
0.982064 | + | 0.188549i | \(0.0603783\pi\) | |||||||
\(480\) | 5098.88 | + | 1110.97i | 0.484856 | + | 0.105643i | ||||
\(481\) | −4766.98 | − | 4673.36i | −0.451883 | − | 0.443008i | ||||
\(482\) | 11918.7 | − | 20643.7i | 1.12631 | − | 1.95082i | ||||
\(483\) | −6396.91 | − | 5819.06i | −0.602629 | − | 0.548192i | ||||
\(484\) | −182.694 | − | 316.436i | −0.0171576 | − | 0.0297179i | ||||
\(485\) | −6438.52 | −0.602800 | ||||||||
\(486\) | 445.233 | − | 17482.7i | 0.0415559 | − | 1.63175i | ||||
\(487\) | − | 1724.02i | − | 0.160416i | −0.996778 | − | 0.0802080i | \(-0.974442\pi\) | ||
0.996778 | − | 0.0802080i | \(-0.0255585\pi\) | |||||||
\(488\) | 3795.94 | − | 2191.59i | 0.352119 | − | 0.203296i | ||||
\(489\) | 1894.55 | + | 1723.41i | 0.175203 | + | 0.159377i | ||||
\(490\) | −854.571 | + | 1480.16i | −0.0787869 | + | 0.136463i | ||||
\(491\) | −6541.71 | + | 11330.6i | −0.601269 | + | 1.04143i | 0.391360 | + | 0.920238i | \(0.372005\pi\) |
−0.992629 | + | 0.121191i | \(0.961329\pi\) | |||||||
\(492\) | −4869.75 | + | 22350.1i | −0.446230 | + | 2.04801i | ||||
\(493\) | −4629.71 | − | 8018.89i | −0.422944 | − | 0.732561i | ||||
\(494\) | −23729.2 | − | 6106.68i | −2.16119 | − | 0.556180i | ||||
\(495\) | −571.531 | − | 6027.67i | −0.0518957 | − | 0.547321i | ||||
\(496\) | 523.631i | 0.0474027i | ||||||||
\(497\) | −2353.82 | − | 4076.93i | −0.212441 | − | 0.367958i | ||||
\(498\) | 9586.81 | + | 30024.5i | 0.862641 | + | 2.70167i | ||||
\(499\) | 17969.9 | + | 10375.0i | 1.61211 | + | 0.930755i | 0.988879 | + | 0.148720i | \(0.0475154\pi\) |
0.623235 | + | 0.782034i | \(0.285818\pi\) | |||||||
\(500\) | 14942.2 | + | 8626.89i | 1.33647 | + | 0.771613i | ||||
\(501\) | −3055.58 | + | 975.644i | −0.272482 | + | 0.0870031i | ||||
\(502\) | 5819.88 | − | 3360.11i | 0.517438 | − | 0.298743i | ||||
\(503\) | −7430.52 | −0.658669 | −0.329335 | − | 0.944213i | \(-0.606824\pi\) | ||||
−0.329335 | + | 0.944213i | \(0.606824\pi\) | |||||||
\(504\) | 9069.19 | − | 6449.06i | 0.801536 | − | 0.569969i | ||||
\(505\) | 9793.25i | 0.862958i | ||||||||
\(506\) | −8429.54 | − | 14600.4i | −0.740591 | − | 1.28274i | ||||
\(507\) | −8595.37 | − | 7512.88i | −0.752927 | − | 0.658104i | ||||
\(508\) | −4632.85 | + | 8024.34i | −0.404625 | + | 0.700832i | ||||
\(509\) | −10220.6 | − | 5900.84i | −0.890016 | − | 0.513851i | −0.0160686 | − | 0.999871i | \(-0.505115\pi\) |
−0.873948 | + | 0.486020i | \(0.838448\pi\) | |||||||
\(510\) | −8226.76 | + | 9043.70i | −0.714288 | + | 0.785219i | ||||
\(511\) | 9398.17 | + | 16278.1i | 0.813602 | + | 1.40920i | ||||
\(512\) | 2444.58i | 0.211008i | ||||||||
\(513\) | −9532.46 | + | 12707.4i | −0.820406 | + | 1.09366i | ||||
\(514\) | 19128.8i | 1.64151i | ||||||||
\(515\) | −8421.52 | + | 4862.17i | −0.720576 | + | 0.416025i | ||||
\(516\) | −13449.5 | + | 14785.1i | −1.14744 | + | 1.26139i | ||||
\(517\) | −2803.92 | + | 4856.53i | −0.238523 | + | 0.413134i | ||||
\(518\) | −9565.18 | − | 5522.46i | −0.811332 | − | 0.468423i | ||||
\(519\) | 19166.0 | + | 4175.98i | 1.62099 | + | 0.353189i | ||||
\(520\) | 1878.05 | + | 6740.86i | 0.158380 | + | 0.568474i | ||||
\(521\) | −20689.7 | −1.73980 | −0.869898 | − | 0.493232i | \(-0.835815\pi\) | ||||
−0.869898 | + | 0.493232i | \(0.835815\pi\) | |||||||
\(522\) | −5732.69 | + | 12530.8i | −0.480676 | + | 1.05068i | ||||
\(523\) | 8466.52 | 0.707868 | 0.353934 | − | 0.935270i | \(-0.384844\pi\) | ||||
0.353934 | + | 0.935270i | \(0.384844\pi\) | |||||||
\(524\) | 9105.01 | + | 15770.3i | 0.759073 | + | 1.31475i | ||||
\(525\) | −7315.36 | + | 2335.79i | −0.608131 | + | 0.194176i | ||||
\(526\) | −6933.06 | − | 4002.80i | −0.574706 | − | 0.331807i | ||||
\(527\) | 5614.86 | + | 3241.74i | 0.464112 | + | 0.267955i | ||||
\(528\) | 1234.19 | − | 394.075i | 0.101726 | − | 0.0324809i | ||||
\(529\) | 1175.37 | + | 2035.79i | 0.0966028 | + | 0.167321i | ||||
\(530\) | −1240.11 | −0.101636 | ||||||||
\(531\) | 4711.21 | − | 10298.0i | 0.385027 | − | 0.841611i | ||||
\(532\) | −25323.9 | −2.06378 | ||||||||
\(533\) | 14928.5 | − | 4159.19i | 1.21318 | − | 0.338001i | ||||
\(534\) | 13826.7 | + | 3012.62i | 1.12048 | + | 0.244136i | ||||
\(535\) | −7522.70 | − | 4343.23i | −0.607915 | − | 0.350980i | ||||
\(536\) | 1595.99 | − | 2764.33i | 0.128612 | − | 0.222763i | ||||
\(537\) | −4301.26 | + | 4728.39i | −0.345648 | + | 0.379972i | ||||
\(538\) | −3424.63 | + | 1977.21i | −0.274435 | + | 0.158445i | ||||
\(539\) | − | 2242.59i | − | 0.179212i | ||||||
\(540\) | 11283.8 | + | 1360.55i | 0.899214 | + | 0.108424i | ||||
\(541\) | 11971.3i | 0.951360i | 0.879619 | + | 0.475680i | \(0.157798\pi\) | ||||
−0.879619 | + | 0.475680i | \(0.842202\pi\) | |||||||
\(542\) | 18816.4 | + | 32591.0i | 1.49121 | + | 2.58285i | ||||
\(543\) | 13872.8 | − | 15250.4i | 1.09638 | − | 1.20526i | ||||
\(544\) | 11973.7 | + | 6913.04i | 0.943695 | + | 0.544842i | ||||
\(545\) | 4720.76 | − | 8176.59i | 0.371037 | − | 0.642654i | ||||
\(546\) | −16870.3 | − | 8493.58i | −1.32231 | − | 0.665736i | ||||
\(547\) | 6861.31 | + | 11884.1i | 0.536322 | + | 0.928937i | 0.999098 | + | 0.0424621i | \(0.0135202\pi\) |
−0.462776 | + | 0.886475i | \(0.653146\pi\) | |||||||
\(548\) | − | 20646.2i | − | 1.60942i | ||||||
\(549\) | −3930.66 | + | 2795.07i | −0.305567 | + | 0.217287i | ||||
\(550\) | −14971.1 | −1.16067 | ||||||||
\(551\) | 10839.9 | − | 6258.41i | 0.838102 | − | 0.483878i | ||||
\(552\) | 12033.7 | − | 3842.34i | 0.927875 | − | 0.296270i | ||||
\(553\) | 5157.46 | + | 2977.66i | 0.396596 | + | 0.228975i | ||||
\(554\) | 28108.7 | + | 16228.6i | 2.15564 | + | 1.24456i | ||||
\(555\) | −1369.58 | − | 4289.32i | −0.104748 | − | 0.328057i | ||||
\(556\) | 14079.9 | + | 24387.0i | 1.07396 | + | 1.86015i | ||||
\(557\) | 1006.65i | 0.0765762i | 0.999267 | + | 0.0382881i | \(0.0121905\pi\) | ||||
−0.999267 | + | 0.0382881i | \(0.987810\pi\) | |||||||
\(558\) | −910.783 | − | 9605.62i | −0.0690977 | − | 0.728742i | ||||
\(559\) | 13113.7 | + | 3374.80i | 0.992221 | + | 0.255347i | ||||
\(560\) | 345.687 | + | 598.747i | 0.0260856 | + | 0.0451816i | ||||
\(561\) | 3415.08 | − | 15673.8i | 0.257014 | − | 1.17959i | ||||
\(562\) | 13905.2 | − | 24084.5i | 1.04369 | − | 1.80773i | ||||
\(563\) | −684.968 | + | 1186.40i | −0.0512752 | + | 0.0888113i | −0.890524 | − | 0.454937i | \(-0.849662\pi\) |
0.839249 | + | 0.543748i | \(0.182995\pi\) | |||||||
\(564\) | −7786.86 | − | 7083.46i | −0.581358 | − | 0.528843i | ||||
\(565\) | −8875.24 | + | 5124.12i | −0.660857 | + | 0.381546i | ||||
\(566\) | 21314.1i | 1.58286i | ||||||||
\(567\) | −9265.06 | + | 8006.69i | −0.686237 | + | 0.593032i | ||||
\(568\) | 6876.75 | 0.507997 | ||||||||
\(569\) | 2213.92 | + | 3834.62i | 0.163115 | + | 0.282523i | 0.935984 | − | 0.352042i | \(-0.114513\pi\) |
−0.772870 | + | 0.634565i | \(0.781179\pi\) | |||||||
\(570\) | −12225.2 | − | 11120.9i | −0.898347 | − | 0.817197i | ||||
\(571\) | −11718.1 | + | 20296.4i | −0.858825 | + | 1.48753i | 0.0142248 | + | 0.999899i | \(0.495472\pi\) |
−0.873050 | + | 0.487630i | \(0.837861\pi\) | |||||||
\(572\) | −16425.5 | − | 16102.9i | −1.20067 | − | 1.17709i | ||||
\(573\) | 1013.98 | + | 220.930i | 0.0739259 | + | 0.0161073i | ||||
\(574\) | 22205.0 | − | 12820.0i | 1.61466 | − | 0.932227i | ||||
\(575\) | −8716.96 | −0.632213 | ||||||||
\(576\) | −2080.18 | − | 21938.8i | −0.150476 | − | 1.58701i | ||||
\(577\) | 1518.76i | 0.109578i | 0.998498 | + | 0.0547892i | \(0.0174487\pi\) | ||||
−0.998498 | + | 0.0547892i | \(0.982551\pi\) | |||||||
\(578\) | −8408.15 | + | 4854.45i | −0.605074 | + | 0.349340i | ||||
\(579\) | −10622.9 | + | 3391.87i | −0.762471 | + | 0.243456i | ||||
\(580\) | −7755.56 | − | 4477.68i | −0.555228 | − | 0.320561i | ||||
\(581\) | 11034.4 | − | 19112.2i | 0.787925 | − | 1.36473i | ||||
\(582\) | 7721.74 | + | 24183.4i | 0.549960 | + | 1.72240i | ||||
\(583\) | 1409.17 | − | 813.584i | 0.100106 | − | 0.0577962i | ||||
\(584\) | −27457.1 | −1.94552 | ||||||||
\(585\) | −2757.49 | − | 7189.26i | −0.194885 | − | 0.508101i | ||||
\(586\) | −7592.59 | −0.535234 | ||||||||
\(587\) | 7992.71 | − | 4614.59i | 0.562001 | − | 0.324471i | −0.191947 | − | 0.981405i | \(-0.561480\pi\) |
0.753948 | + | 0.656934i | \(0.228147\pi\) | |||||||
\(588\) | 4113.13 | + | 896.189i | 0.288474 | + | 0.0628541i | ||||
\(589\) | −4382.16 | + | 7590.12i | −0.306560 | + | 0.530977i | ||||
\(590\) | 10203.2 | + | 5890.80i | 0.711963 | + | 0.411052i | ||||
\(591\) | −3028.11 | − | 2754.58i | −0.210761 | − | 0.191723i | ||||
\(592\) | 834.392 | − | 481.737i | 0.0579279 | − | 0.0334447i | ||||
\(593\) | − | 4330.70i | − | 0.299900i | −0.988694 | − | 0.149950i | \(-0.952089\pi\) | ||
0.988694 | − | 0.149950i | \(-0.0479112\pi\) | |||||||
\(594\) | −21954.8 | + | 9375.72i | −1.51653 | + | 0.647627i | ||||
\(595\) | 8560.43 | 0.589821 | ||||||||
\(596\) | −11861.7 | + | 6848.37i | −0.815227 | + | 0.470671i | ||||
\(597\) | −363.408 | + | 399.495i | −0.0249134 | + | 0.0273874i | ||||
\(598\) | −15310.1 | − | 15009.4i | −1.04695 | − | 1.02639i | ||||
\(599\) | 9302.14 | − | 16111.8i | 0.634516 | − | 1.09901i | −0.352102 | − | 0.935962i | \(-0.614533\pi\) |
0.986618 | − | 0.163052i | \(-0.0521338\pi\) | |||||||
\(600\) | 2388.11 | − | 10960.4i | 0.162490 | − | 0.745761i | ||||
\(601\) | −6417.47 | − | 11115.4i | −0.435564 | − | 0.754419i | 0.561777 | − | 0.827288i | \(-0.310118\pi\) |
−0.997341 | + | 0.0728693i | \(0.976784\pi\) | |||||||
\(602\) | 22403.7 | 1.51679 | ||||||||
\(603\) | −1461.21 | + | 3193.98i | −0.0986817 | + | 0.215703i | ||||
\(604\) | − | 25315.1i | − | 1.70540i | ||||||
\(605\) | −144.598 | + | 83.4835i | −0.00971691 | + | 0.00561006i | ||||
\(606\) | 36784.0 | − | 11745.1i | 2.46575 | − | 0.787313i | ||||
\(607\) | 8165.78 | − | 14143.5i | 0.546027 | − | 0.945747i | −0.452514 | − | 0.891757i | \(-0.649473\pi\) |
0.998541 | − | 0.0539899i | \(-0.0171939\pi\) | |||||||
\(608\) | −9345.00 | + | 16186.0i | −0.623338 | + | 1.07965i | ||||
\(609\) | 9191.46 | − | 2934.82i | 0.611587 | − | 0.195279i | ||||
\(610\) | −2508.90 | − | 4345.54i | −0.166528 | − | 0.288436i | ||||
\(611\) | −1777.41 | + | 6906.61i | −0.117686 | + | 0.457302i | ||||
\(612\) | 27382.6 | + | 12527.2i | 1.80862 | + | 0.827422i | ||||
\(613\) | 15050.8i | 0.991676i | 0.868415 | + | 0.495838i | \(0.165139\pi\) | ||||
−0.868415 | + | 0.495838i | \(0.834861\pi\) | |||||||
\(614\) | 8259.39 | + | 14305.7i | 0.542869 | + | 0.940278i | ||||
\(615\) | 10213.0 | + | 2225.26i | 0.669641 | + | 0.145905i | ||||
\(616\) | −13155.9 | − | 7595.54i | −0.860495 | − | 0.496807i | ||||
\(617\) | −24235.8 | − | 13992.5i | −1.58135 | − | 0.912996i | −0.994662 | − | 0.103186i | \(-0.967096\pi\) |
−0.586693 | − | 0.809809i | \(-0.699570\pi\) | |||||||
\(618\) | 28362.5 | + | 25800.5i | 1.84613 | + | 1.67936i | ||||
\(619\) | 24665.6 | − | 14240.7i | 1.60160 | − | 0.924686i | 0.610437 | − | 0.792065i | \(-0.290994\pi\) |
0.991167 | − | 0.132621i | \(-0.0423394\pi\) | |||||||
\(620\) | 6270.57 | 0.406181 | ||||||||
\(621\) | −12783.3 | + | 5459.05i | −0.826048 | + | 0.352760i | ||||
\(622\) | − | 41227.3i | − | 2.65766i | ||||||
\(623\) | −4954.28 | − | 8581.06i | −0.318602 | − | 0.551835i | ||||
\(624\) | 1377.47 | − | 904.014i | 0.0883699 | − | 0.0579961i | ||||
\(625\) | −1556.73 | + | 2696.34i | −0.0996308 | + | 0.172566i | ||||
\(626\) | −329.022 | − | 189.961i | −0.0210070 | − | 0.0121284i | ||||
\(627\) | 21187.7 | + | 4616.48i | 1.34953 | + | 0.294042i | ||||
\(628\) | −20780.8 | − | 35993.4i | −1.32045 | − | 2.28709i | ||||
\(629\) | − | 11929.5i | − | 0.756217i | ||||||
\(630\) | −7382.80 | − | 10382.3i | −0.466886 | − | 0.656572i | ||||
\(631\) | 3179.61i | 0.200599i | 0.994957 | + | 0.100300i | \(0.0319802\pi\) | ||||
−0.994957 | + | 0.100300i | \(0.968020\pi\) | |||||||
\(632\) | −7533.85 | + | 4349.67i | −0.474178 | + | 0.273767i | ||||
\(633\) | 658.954 | + | 2063.75i | 0.0413761 | + | 0.129584i | ||||
\(634\) | −18246.3 | + | 31603.5i | −1.14299 | + | 1.97971i | ||||
\(635\) | 3666.78 | + | 2117.01i | 0.229152 | + | 0.132301i | ||||
\(636\) | 929.059 | + | 2909.68i | 0.0579239 | + | 0.181409i | ||||
\(637\) | −765.423 | − | 2747.33i | −0.0476094 | − | 0.170884i | ||||
\(638\) | 18810.5 | 1.16727 | ||||||||
\(639\) | −7533.19 | + | 714.281i | −0.466367 | + | 0.0442199i | ||||
\(640\) | 14892.3 | 0.919794 | ||||||||
\(641\) | −1193.36 | − | 2066.97i | −0.0735336 | − | 0.127364i | 0.826914 | − | 0.562328i | \(-0.190094\pi\) |
−0.900448 | + | 0.434964i | \(0.856761\pi\) | |||||||
\(642\) | −7291.42 | + | 33464.6i | −0.448239 | + | 2.05723i | ||||
\(643\) | 11868.9 | + | 6852.50i | 0.727936 | + | 0.420274i | 0.817667 | − | 0.575692i | \(-0.195267\pi\) |
−0.0897307 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(644\) | −19190.3 | − | 11079.5i | −1.17423 | − | 0.677940i | ||||
\(645\) | 6756.15 | + | 6145.85i | 0.412439 | + | 0.375182i | ||||
\(646\) | −21893.1 | − | 37919.9i | −1.33339 | − | 2.30950i | ||||
\(647\) | −3826.80 | −0.232530 | −0.116265 | − | 0.993218i | \(-0.537092\pi\) | ||||
−0.116265 | + | 0.993218i | \(0.537092\pi\) | |||||||
\(648\) | −3361.90 | − | 17568.8i | −0.203808 | − | 1.06508i | ||||
\(649\) | −15458.8 | −0.934994 | ||||||||
\(650\) | −18340.6 | + | 5109.81i | −1.10674 | + | 0.308343i | ||||
\(651\) | −4546.16 | + | 4997.60i | −0.273699 | + | 0.300878i | ||||
\(652\) | 5683.51 | + | 3281.37i | 0.341385 | + | 0.197099i | ||||
\(653\) | −3585.39 | + | 6210.08i | −0.214866 | + | 0.372158i | −0.953231 | − | 0.302243i | \(-0.902265\pi\) |
0.738365 | + | 0.674401i | \(0.235598\pi\) | |||||||
\(654\) | −36373.3 | − | 7925.20i | −2.17479 | − | 0.473853i | ||||
\(655\) | 7206.36 | − | 4160.60i | 0.429887 | − | 0.248195i | ||||
\(656\) | 2236.64i | 0.133119i | ||||||||
\(657\) | 30078.1 | − | 2851.94i | 1.78609 | − | 0.169353i | ||||
\(658\) | 11799.4i | 0.699069i | ||||||||
\(659\) | 1118.12 | + | 1936.65i | 0.0660940 | + | 0.114478i | 0.897179 | − | 0.441668i | \(-0.145613\pi\) |
−0.831085 | + | 0.556146i | \(0.812280\pi\) | |||||||
\(660\) | −4719.12 | − | 14779.6i | −0.278321 | − | 0.871661i | ||||
\(661\) | 5050.07 | + | 2915.66i | 0.297164 | + | 0.171567i | 0.641168 | − | 0.767401i | \(-0.278450\pi\) |
−0.344004 | + | 0.938968i | \(0.611784\pi\) | |||||||
\(662\) | −1437.79 | + | 2490.32i | −0.0844127 | + | 0.146207i | ||||
\(663\) | −1165.94 | − | 20367.1i | −0.0682979 | − | 1.19305i | ||||
\(664\) | 16118.7 | + | 27918.4i | 0.942059 | + | 1.63169i | ||||
\(665\) | 11571.9i | 0.674797i | ||||||||
\(666\) | −14468.4 | + | 10288.4i | −0.841800 | + | 0.598600i | ||||
\(667\) | 10952.5 | 0.635806 | ||||||||
\(668\) | −7117.99 | + | 4109.58i | −0.412281 | + | 0.238030i | ||||
\(669\) | −4468.43 | + | 20508.2i | −0.258235 | + | 1.18519i | ||||
\(670\) | −3164.57 | − | 1827.07i | −0.182475 | − | 0.105352i | ||||
\(671\) | 5701.85 | + | 3291.96i | 0.328044 | + | 0.189396i | ||||
\(672\) | −9694.73 | + | 10657.4i | −0.556521 | + | 0.611785i | ||||
\(673\) | 4765.20 | + | 8253.58i | 0.272935 | + | 0.472737i | 0.969612 | − | 0.244648i | \(-0.0786723\pi\) |
−0.696677 | + | 0.717385i | \(0.745339\pi\) | |||||||
\(674\) | − | 18362.0i | − | 1.04938i | ||||||
\(675\) | −1477.62 | + | 12254.7i | −0.0842574 | + | 0.698791i | ||||
\(676\) | −25618.5 | − | 14121.0i | −1.45759 | − | 0.803425i | ||||
\(677\) | 8421.77 | + | 14586.9i | 0.478102 | + | 0.828096i | 0.999685 | − | 0.0251041i | \(-0.00799174\pi\) |
−0.521583 | + | 0.853200i | \(0.674658\pi\) | |||||||
\(678\) | 29890.6 | + | 27190.5i | 1.69313 | + | 1.54018i | ||||
\(679\) | 8887.72 | − | 15394.0i | 0.502326 | − | 0.870054i | ||||
\(680\) | −6252.40 | + | 10829.5i | −0.352601 | + | 0.610723i | ||||
\(681\) | 590.816 | − | 2711.60i | 0.0332454 | − | 0.152582i | ||||
\(682\) | −11406.6 | + | 6585.60i | −0.640442 | + | 0.369759i | ||||
\(683\) | 5336.56i | 0.298972i | 0.988764 | + | 0.149486i | \(0.0477619\pi\) | ||||
−0.988764 | + | 0.149486i | \(0.952238\pi\) | |||||||
\(684\) | −16934.2 | + | 37015.6i | −0.946630 | + | 2.06919i | ||||
\(685\) | −9434.40 | −0.526234 | ||||||||
\(686\) | −15659.2 | − | 27122.5i | −0.871531 | − | 1.50954i | ||||
\(687\) | −27815.7 | + | 8881.53i | −1.54474 | + | 0.493234i | ||||
\(688\) | −977.163 | + | 1692.50i | −0.0541482 | + | 0.0937875i | ||||
\(689\) | 1448.64 | − | 1477.66i | 0.0801001 | − | 0.0817047i | ||||
\(690\) | −4398.66 | − | 13776.0i | −0.242687 | − | 0.760062i | ||||
\(691\) | −14214.5 | + | 8206.72i | −0.782552 | + | 0.451807i | −0.837334 | − | 0.546692i | \(-0.815887\pi\) |
0.0547818 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(692\) | 50263.8 | 2.76119 | ||||||||
\(693\) | 15200.6 | + | 6954.11i | 0.833224 | + | 0.381190i | ||||
\(694\) | − | 18859.9i | − | 1.03157i | ||||||
\(695\) | 11143.8 | − | 6433.89i | 0.608215 | − | 0.351153i | ||||
\(696\) | −3000.56 | + | 13771.3i | −0.163414 | + | 0.750000i | ||||
\(697\) | 23983.3 | + | 13846.8i | 1.30335 | + | 0.752489i | ||||
\(698\) | −24077.4 | + | 41703.2i | −1.30565 | + | 2.26145i | ||||
\(699\) | 23647.7 | − | 25996.0i | 1.27960 | − | 1.40666i | ||||
\(700\) | −17041.2 | + | 9838.73i | −0.920137 | + | 0.531241i | ||||
\(701\) | 11737.6 | 0.632415 | 0.316208 | − | 0.948690i | \(-0.397590\pi\) | ||||
0.316208 | + | 0.948690i | \(0.397590\pi\) | |||||||
\(702\) | −23696.2 | + | 18979.4i | −1.27401 | + | 1.02041i | ||||
\(703\) | 16126.2 | 0.865166 | ||||||||
\(704\) | −26052.1 | + | 15041.2i | −1.39471 | + | 0.805237i | ||||
\(705\) | −3236.83 | + | 3558.26i | −0.172917 | + | 0.190088i | ||||
\(706\) | 23489.8 | − | 40685.5i | 1.25220 | − | 2.16887i | ||||
\(707\) | −23414.9 | − | 13518.6i | −1.24556 | − | 0.719122i | ||||
\(708\) | 6177.69 | − | 28353.0i | 0.327926 | − | 1.50504i | ||||
\(709\) | −10319.3 | + | 5957.88i | −0.546617 | + | 0.315589i | −0.747756 | − | 0.663973i | \(-0.768869\pi\) |
0.201140 | + | 0.979563i | \(0.435536\pi\) | |||||||
\(710\) | − | 7872.42i | − | 0.416122i | ||||||
\(711\) | 7801.22 | − | 5547.41i | 0.411489 | − | 0.292608i | ||||
\(712\) | 14474.1 | 0.761854 | ||||||||
\(713\) | −6641.54 | + | 3834.49i | −0.348846 | + | 0.201407i | ||||
\(714\) | −10266.6 | − | 32153.5i | −0.538119 | − | 1.68531i | ||||
\(715\) | −7358.34 | + | 7505.74i | −0.384876 | + | 0.392586i | ||||
\(716\) | −8189.60 | + | 14184.8i | −0.427458 | + | 0.740379i | ||||
\(717\) | −17499.6 | + | 5587.59i | −0.911482 | + | 0.291035i | ||||
\(718\) | −2661.58 | − | 4610.00i | −0.138342 | − | 0.239615i | ||||
\(719\) | −19863.9 | −1.03032 | −0.515158 | − | 0.857095i | \(-0.672267\pi\) | ||||
−0.515158 | + | 0.857095i | \(0.672267\pi\) | |||||||
\(720\) | 1106.34 | − | 104.901i | 0.0572652 | − | 0.00542976i | ||||
\(721\) | − | 26846.9i | − | 1.38673i | ||||||
\(722\) | 23835.8 | − | 13761.6i | 1.22864 | − | 0.709355i | ||||
\(723\) | −5711.55 | + | 26213.6i | −0.293797 | + | 1.34840i | ||||
\(724\) | 26413.7 | − | 45749.9i | 1.35588 | − | 2.34846i | ||||
\(725\) | 4862.98 | − | 8422.92i | 0.249112 | − | 0.431475i | ||||
\(726\) | 486.985 | + | 442.995i | 0.0248949 | + | 0.0226461i | ||||
\(727\) | 2749.95 | + | 4763.06i | 0.140289 | + | 0.242988i | 0.927605 | − | 0.373562i | \(-0.121864\pi\) |
−0.787316 | + | 0.616549i | \(0.788530\pi\) | |||||||
\(728\) | −18709.3 | − | 4814.82i | −0.952491 | − | 0.245122i | ||||
\(729\) | 5507.67 | + | 18896.7i | 0.279819 | + | 0.960053i | ||||
\(730\) | 31432.5i | 1.59366i | ||||||||
\(731\) | 12099.0 | + | 20956.1i | 0.612172 | + | 1.06031i | ||||
\(732\) | −8316.38 | + | 9142.22i | −0.419921 | + | 0.461620i | ||||
\(733\) | 28326.0 | + | 16354.0i | 1.42735 | + | 0.824079i | 0.996911 | − | 0.0785419i | \(-0.0250265\pi\) |
0.430436 | + | 0.902621i | \(0.358360\pi\) | |||||||
\(734\) | −5605.76 | − | 3236.49i | −0.281897 | − | 0.162753i | ||||
\(735\) | 409.520 | − | 1879.52i | 0.0205515 | − | 0.0943229i | ||||
\(736\) | −14163.1 | + | 8177.09i | −0.709321 | + | 0.409527i | ||||
\(737\) | 4794.64 | 0.239637 | ||||||||
\(738\) | −3890.33 | − | 41029.5i | −0.194045 | − | 2.04650i | ||||
\(739\) | − | 25027.3i | − | 1.24580i | −0.782303 | − | 0.622899i | \(-0.785955\pi\) | ||
0.782303 | − | 0.622899i | \(-0.214045\pi\) | |||||||
\(740\) | −5768.88 | − | 9991.99i | −0.286579 | − | 0.496369i | ||||
\(741\) | 27532.1 | − | 1576.11i | 1.36494 | − | 0.0781376i | ||||
\(742\) | 1711.85 | − | 2965.01i | 0.0846953 | − | 0.146697i | ||||
\(743\) | 19280.9 | + | 11131.8i | 0.952013 | + | 0.549645i | 0.893706 | − | 0.448654i | \(-0.148096\pi\) |
0.0583076 | + | 0.998299i | \(0.481430\pi\) | |||||||
\(744\) | −3001.84 | − | 9401.34i | −0.147920 | − | 0.463266i | ||||
\(745\) | 3129.41 | + | 5420.30i | 0.153896 | + | 0.266556i | ||||
\(746\) | 46545.9i | 2.28441i | ||||||||
\(747\) | −20557.2 | − | 28909.2i | −1.00689 | − | 1.41597i | ||||
\(748\) | − | 41105.3i | − | 2.00930i | ||||||
\(749\) | 20768.7 | − | 11990.8i | 1.01318 | − | 0.584959i | ||||
\(750\) | −30374.0 | − | 6618.02i | −1.47880 | − | 0.322208i | ||||
\(751\) | 7317.01 | − | 12673.4i | 0.355528 | − | 0.615792i | −0.631680 | − | 0.775229i | \(-0.717634\pi\) |
0.987208 | + | 0.159437i | \(0.0509678\pi\) | |||||||
\(752\) | −891.387 | − | 514.643i | −0.0432255 | − | 0.0249562i | ||||
\(753\) | −5089.55 | + | 5594.96i | −0.246313 | + | 0.270772i | ||||
\(754\) | 23044.3 | − | 6420.27i | 1.11303 | − | 0.310096i | ||||
\(755\) | −11567.9 | −0.557616 | ||||||||
\(756\) | −18829.1 | + | 25100.5i | −0.905828 | + | 1.20753i | ||||
\(757\) | −9064.08 | −0.435191 | −0.217596 | − | 0.976039i | \(-0.569821\pi\) | ||||
−0.217596 | + | 0.976039i | \(0.569821\pi\) | |||||||
\(758\) | −23234.5 | − | 40243.4i | −1.11335 | − | 1.92837i | ||||
\(759\) | 14036.1 | + | 12768.2i | 0.671251 | + | 0.610615i | ||||
\(760\) | −14639.2 | − | 8451.95i | −0.698710 | − | 0.403400i | ||||
\(761\) | 31657.8 | + | 18277.7i | 1.50801 | + | 0.870650i | 0.999957 | + | 0.00932486i | \(0.00296824\pi\) |
0.508054 | + | 0.861325i | \(0.330365\pi\) | |||||||
\(762\) | 3554.04 | − | 16311.6i | 0.168962 | − | 0.775467i | ||||
\(763\) | 13033.1 | + | 22573.9i | 0.618386 | + | 1.07108i | ||||
\(764\) | 2659.20 | 0.125925 | ||||||||
\(765\) | 5724.40 | − | 12512.7i | 0.270544 | − | 0.591368i | ||||
\(766\) | 48193.9 | 2.27326 | ||||||||
\(767\) | −18938.1 | + | 5276.28i | −0.891547 | + | 0.248391i | ||||
\(768\) | −7540.34 | − | 23615.3i | −0.354282 | − | 1.10956i | ||||
\(769\) | −15900.8 | − | 9180.33i | −0.745640 | − | 0.430496i | 0.0784763 | − | 0.996916i | \(-0.474995\pi\) |
−0.824116 | + | 0.566420i | \(0.808328\pi\) | |||||||
\(770\) | −8695.27 | + | 15060.7i | −0.406956 | + | 0.704868i | ||||
\(771\) | −6548.57 | − | 20509.2i | −0.305890 | − | 0.958004i | ||||
\(772\) | −24746.0 | + | 14287.1i | −1.15366 | + | 0.666068i | ||||
\(773\) | 11167.9i | 0.519638i | 0.965657 | + | 0.259819i | \(0.0836630\pi\) | ||||
−0.965657 | + | 0.259819i | \(0.916337\pi\) | |||||||
\(774\) | 14981.5 | − | 32747.2i | 0.695733 | − | 1.52077i | ||||
\(775\) | 6810.15i | 0.315649i | ||||||||
\(776\) | 12982.9 | + | 22487.0i | 0.600591 | + | 1.04025i | ||||
\(777\) | 12146.0 | + | 2646.42i | 0.560791 | + | 0.122188i | ||||
\(778\) | 31540.1 | + | 18209.7i | 1.45343 | + | 0.839138i | ||||
\(779\) | −18718.0 | + | 32420.5i | −0.860900 | + | 1.49112i | ||||
\(780\) | −10825.7 | − | 16495.4i | −0.496953 | − | 0.757218i | ||||
\(781\) | 5164.75 | + | 8945.61i | 0.236632 | + | 0.409858i | ||||
\(782\) | − | 38313.9i | − | 1.75205i | ||||||
\(783\) | 1856.57 | − | 15397.6i | 0.0847364 | − | 0.702763i | ||||
\(784\) | 411.613 | 0.0187506 | ||||||||
\(785\) | −16447.4 | + | 9495.92i | −0.747814 | + | 0.431750i | ||||
\(786\) | −24270.1 | − | 22077.7i | −1.10138 | − | 1.00189i | ||||
\(787\) | 4797.95 | + | 2770.10i | 0.217317 | + | 0.125468i | 0.604707 | − | 0.796448i | \(-0.293290\pi\) |
−0.387390 | + | 0.921916i | \(0.626623\pi\) | |||||||
\(788\) | −9084.11 | − | 5244.71i | −0.410670 | − | 0.237101i | ||||
\(789\) | 8803.68 | + | 1918.19i | 0.397236 | + | 0.0865517i | ||||
\(790\) | 4979.44 | + | 8624.65i | 0.224254 | + | 0.388419i | ||||
\(791\) | − | 28293.3i | − | 1.27180i | ||||||
\(792\) | −19899.7 | + | 14150.6i | −0.892808 | + | 0.634872i | ||||
\(793\) | 8108.75 | + | 2086.78i | 0.363115 | + | 0.0934472i | ||||
\(794\) | 18532.7 | + | 32099.6i | 0.828338 | + | 1.43472i | ||||
\(795\) | 1329.60 | − | 424.540i | 0.0593158 | − | 0.0189395i | ||||
\(796\) | −691.929 | + | 1198.46i | −0.0308100 | + | 0.0533645i | ||||
\(797\) | −1136.20 | + | 1967.96i | −0.0504972 | + | 0.0874637i | −0.890169 | − | 0.455630i | \(-0.849414\pi\) |
0.839672 | + | 0.543094i | \(0.182747\pi\) | |||||||
\(798\) | 43464.8 | − | 13878.3i | 1.92812 | − | 0.615646i | ||||
\(799\) | −11037.0 | + | 6372.19i | −0.488685 | + | 0.282142i | ||||
\(800\) | 14522.7i | 0.641819i | ||||||||
\(801\) | −15855.8 | + | 1503.41i | −0.699421 | + | 0.0663175i | ||||
\(802\) | −47335.1 | −2.08412 | ||||||||
\(803\) | −20621.5 | − | 35717.5i | −0.906249 | − | 1.56967i | ||||
\(804\) | −1916.05 | + | 8793.85i | −0.0840469 | + | 0.385740i | ||||
\(805\) | −5062.85 | + | 8769.12i | −0.221667 | + | 0.383939i | ||||
\(806\) | −11726.1 | + | 11961.0i | −0.512452 | + | 0.522717i | ||||
\(807\) | 2994.87 | − | 3292.27i | 0.130638 | − | 0.143610i | ||||
\(808\) | 34203.7 | − | 19747.5i | 1.48921 | − | 0.859796i | ||||
\(809\) | −1784.01 | −0.0775307 | −0.0387653 | − | 0.999248i | \(-0.512342\pi\) | ||||
−0.0387653 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(810\) | −20112.6 | + | 3848.66i | −0.872449 | + | 0.166948i | ||||
\(811\) | − | 37105.9i | − | 1.60662i | −0.595563 | − | 0.803308i | \(-0.703071\pi\) | ||
0.595563 | − | 0.803308i | \(-0.296929\pi\) | |||||||
\(812\) | 21411.5 | − | 12362.0i | 0.925367 | − | 0.534261i | ||||
\(813\) | −31331.5 | − | 28501.2i | −1.35159 | − | 1.22950i | ||||
\(814\) | 20988.0 | + | 12117.4i | 0.903720 | + | 0.521763i | ||||
\(815\) | 1499.45 | − | 2597.12i | 0.0644458 | − | 0.111623i | ||||
\(816\) | 2876.83 | + | 626.817i | 0.123418 | + | 0.0268909i | ||||
\(817\) | −28328.3 | + | 16355.3i | −1.21307 | + | 0.700368i | ||||
\(818\) | 20701.9 | 0.884871 | ||||||||
\(819\) | 20995.4 | + | 3331.11i | 0.895773 | + | 0.142123i | ||||
\(820\) | 26784.2 | 1.14066 | ||||||||
\(821\) | 11015.5 | − | 6359.79i | 0.468262 | − | 0.270351i | −0.247250 | − | 0.968952i | \(-0.579527\pi\) |
0.715512 | + | 0.698601i | \(0.246194\pi\) | |||||||
\(822\) | 11314.7 | + | 35436.1i | 0.480105 | + | 1.50362i | ||||
\(823\) | −2072.32 | + | 3589.36i | −0.0877721 | + | 0.152026i | −0.906569 | − | 0.422057i | \(-0.861308\pi\) |
0.818797 | + | 0.574083i | \(0.194641\pi\) | |||||||
\(824\) | 33963.0 | + | 19608.6i | 1.43587 | + | 0.829000i | ||||
\(825\) | 16051.4 | − | 5125.20i | 0.677380 | − | 0.216287i | ||||
\(826\) | −28168.9 | + | 16263.3i | −1.18659 | + | 0.685076i | ||||
\(827\) | − | 7970.36i | − | 0.335135i | −0.985861 | − | 0.167568i | \(-0.946409\pi\) | ||
0.985861 | − | 0.167568i | \(-0.0535912\pi\) | |||||||
\(828\) | −29027.4 | + | 20641.2i | −1.21832 | + | 0.866343i | ||||
\(829\) | −14160.5 | −0.593264 | −0.296632 | − | 0.954992i | \(-0.595863\pi\) | ||||
−0.296632 | + | 0.954992i | \(0.595863\pi\) | |||||||
\(830\) | 31960.6 | − | 18452.5i | 1.33659 | − | 0.771680i | ||||
\(831\) | −35692.7 | − | 7776.90i | −1.48997 | − | 0.324642i | ||||
\(832\) | −26782.0 | + | 27318.5i | −1.11598 | + | 1.13834i | ||||
\(833\) | 2548.25 | − | 4413.70i | 0.105992 | − | 0.183584i | ||||
\(834\) | −37530.9 | − | 34140.6i | −1.55826 | − | 1.41750i | ||||
\(835\) | 1877.90 | + | 3252.62i | 0.0778292 | + | 0.134804i | ||||
\(836\) | 55565.8 | 2.29878 | ||||||||
\(837\) | 4264.89 | + | 9986.98i | 0.176125 | + | 0.412426i | ||||
\(838\) | 23174.7i | 0.955317i | ||||||||
\(839\) | −27508.5 | + | 15882.1i | −1.13194 | + | 0.653527i | −0.944423 | − | 0.328734i | \(-0.893378\pi\) |
−0.187520 | + | 0.982261i | \(0.560045\pi\) | |||||||
\(840\) | −9638.97 | − | 8768.26i | −0.395924 | − | 0.360159i | ||||
\(841\) | 6084.37 | − | 10538.4i | 0.249472 | − | 0.432098i | ||||
\(842\) | −10911.6 | + | 18899.4i | −0.446601 | + | 0.773536i | ||||
\(843\) | −6663.53 | + | 30582.8i | −0.272247 | + | 1.24950i | ||||
\(844\) | 2775.62 | + | 4807.52i | 0.113200 | + | 0.196068i | ||||
\(845\) | −6452.69 | + | 11706.6i | −0.262697 | + | 0.476589i | ||||
\(846\) | 17247.0 | + | 7890.29i | 0.700902 | + | 0.320655i | ||||
\(847\) | − | 460.962i | − | 0.0186999i | ||||||
\(848\) | 149.328 | + | 258.644i | 0.00604712 | + | 0.0104739i | ||||
\(849\) | −7296.66 | − | 22852.1i | −0.294960 | − | 0.923773i | ||||
\(850\) | −29465.0 | − | 17011.6i | −1.18899 | − | 0.686463i | ||||
\(851\) | 12220.3 | + | 7055.41i | 0.492253 | + | 0.284202i | ||||
\(852\) | −18471.1 | + | 5897.81i | −0.742735 | + | 0.237154i | ||||
\(853\) | −4457.61 | + | 2573.60i | −0.178928 | + | 0.103304i | −0.586789 | − | 0.809740i | \(-0.699608\pi\) |
0.407861 | + | 0.913044i | \(0.366275\pi\) | |||||||
\(854\) | 13853.1 | 0.555087 | ||||||||
\(855\) | 16914.5 | + | 7738.19i | 0.676567 | + | 0.309521i | ||||
\(856\) | 35031.5i | 1.39878i | ||||||||
\(857\) | 3778.91 | + | 6545.26i | 0.150624 | + | 0.260889i | 0.931457 | − | 0.363851i | \(-0.118538\pi\) |
−0.780833 | + | 0.624740i | \(0.785205\pi\) | |||||||
\(858\) | 37016.9 | + | 18636.7i | 1.47289 | + | 0.741544i | ||||
\(859\) | 8624.80 | − | 14938.6i | 0.342578 | − | 0.593363i | −0.642333 | − | 0.766426i | \(-0.722033\pi\) |
0.984911 | + | 0.173063i | \(0.0553666\pi\) | |||||||
\(860\) | 20267.9 | + | 11701.7i | 0.803640 | + | 0.463982i | ||||
\(861\) | −19418.5 | + | 21346.8i | −0.768619 | + | 0.844945i | ||||
\(862\) | −16990.3 | − | 29428.1i | −0.671338 | − | 1.16279i | ||||
\(863\) | − | 12719.5i | − | 0.501712i | −0.968024 | − | 0.250856i | \(-0.919288\pi\) | ||
0.968024 | − | 0.250856i | \(-0.0807121\pi\) | |||||||
\(864\) | 9094.93 | + | 21297.3i | 0.358120 | + | 0.838599i | ||||
\(865\) | − | 22968.4i | − | 0.902831i | ||||||
\(866\) | 49412.2 | − | 28528.2i | 1.93891 | − | 1.11943i | ||||
\(867\) | 7353.03 | − | 8083.20i | 0.288030 | − | 0.316632i | ||||
\(868\) | −8655.89 | + | 14992.4i | −0.338479 | + | 0.586263i | ||||
\(869\) | −11316.5 | − | 6533.59i | −0.441757 | − | 0.255048i | ||||
\(870\) | 15765.2 | + | 3435.00i | 0.614357 | + | 0.133859i | ||||
\(871\) | 5873.77 | − | 1636.47i | 0.228502 | − | 0.0636620i | ||||
\(872\) | −38076.5 | −1.47871 | ||||||||
\(873\) | −16557.9 | − | 23285.1i | −0.641925 | − | 0.902727i | ||||
\(874\) | 51792.5 | 2.00447 | ||||||||
\(875\) | 10883.4 | + | 18850.6i | 0.420487 | + | 0.728304i | ||||
\(876\) | 73750.4 | − | 23548.4i | 2.84451 | − | 0.908250i | ||||
\(877\) | 27579.5 | + | 15923.0i | 1.06191 | + | 0.613092i | 0.925959 | − | 0.377624i | \(-0.123259\pi\) |
0.135948 | + | 0.990716i | \(0.456592\pi\) | |||||||
\(878\) | 22005.7 | + | 12705.0i | 0.845851 | + | 0.488353i | ||||
\(879\) | 8140.49 | − | 2599.25i | 0.312368 | − | 0.0997389i | ||||
\(880\) | −758.508 | − | 1313.77i | −0.0290560 | − | 0.0503265i | ||||
\(881\) | 31597.5 | 1.20834 | 0.604169 | − | 0.796856i | \(-0.293505\pi\) | ||||
0.604169 | + | 0.796856i | \(0.293505\pi\) | |||||||
\(882\) | −7550.74 | + | 715.944i | −0.288261 | + | 0.0273323i | ||||
\(883\) | −146.917 | −0.00559927 | −0.00279964 | − | 0.999996i | \(-0.500891\pi\) | ||||
−0.00279964 | + | 0.999996i | \(0.500891\pi\) | |||||||
\(884\) | −14029.7 | − | 50356.9i | −0.533791 | − | 1.91593i | ||||
\(885\) | −12956.1 | − | 2822.94i | −0.492107 | − | 0.107223i | ||||
\(886\) | −17595.0 | − | 10158.5i | −0.667173 | − | 0.385192i | ||||
\(887\) | 8876.07 | − | 15373.8i | 0.335997 | − | 0.581964i | −0.647679 | − | 0.761913i | \(-0.724260\pi\) |
0.983676 | + | 0.179950i | \(0.0575934\pi\) | |||||||
\(888\) | −12219.1 | + | 13432.5i | −0.461764 | + | 0.507619i | ||||
\(889\) | −10123.2 | + | 5844.65i | −0.381915 | + | 0.220499i | ||||
\(890\) | − | 16569.8i | − | 0.624067i | ||||||
\(891\) | 20329.4 | − | 17568.3i | 0.764380 | − | 0.660562i | ||||
\(892\) | 53783.8i | 2.01885i | ||||||||
\(893\) | −8613.87 | − | 14919.7i | −0.322791 | − | 0.559090i | ||||
\(894\) | 16605.8 | − | 18254.8i | 0.621232 | − | 0.682923i | ||||
\(895\) | 6481.85 | + | 3742.29i | 0.242083 | + | 0.139767i | ||||
\(896\) | −20557.3 | + | 35606.2i | −0.766484 | + | 1.32759i | ||||
\(897\) | 21553.2 | + | 10851.3i | 0.802275 | + | 0.403917i | ||||
\(898\) | 19180.3 | + | 33221.2i | 0.712756 | + | 1.23453i | ||||
\(899\) | − | 8556.68i | − | 0.317443i | ||||||
\(900\) | 2985.63 | + | 31488.0i | 0.110579 | + | 1.16622i | ||||
\(901\) | 3697.90 | 0.136731 | ||||||||
\(902\) | −48722.2 | + | 28129.8i | −1.79853 | + | 1.03838i | ||||
\(903\) | −24020.4 | + | 7669.69i | −0.885215 | + | 0.282648i | ||||
\(904\) | 35792.8 | + | 20665.0i | 1.31687 | + | 0.760295i | ||||
\(905\) | −20905.8 | − | 12069.9i | −0.767879 | − | 0.443335i | ||||
\(906\) | 13873.5 | + | 43449.8i | 0.508737 | + | 1.59329i | ||||
\(907\) | −5992.34 | − | 10379.0i | −0.219374 | − | 0.379967i | 0.735243 | − | 0.677804i | \(-0.237068\pi\) |
−0.954617 | + | 0.297837i | \(0.903735\pi\) | |||||||
\(908\) | − | 7111.29i | − | 0.259908i | ||||||
\(909\) | −35417.6 | + | 25185.3i | −1.29233 | + | 0.918969i | ||||
\(910\) | −5511.94 | + | 21418.2i | −0.200790 | + | 0.780226i | ||||
\(911\) | −5250.68 | − | 9094.45i | −0.190958 | − | 0.330749i | 0.754610 | − | 0.656174i | \(-0.227826\pi\) |
−0.945568 | + | 0.325424i | \(0.894493\pi\) | |||||||
\(912\) | −847.327 | + | 3888.88i | −0.0307651 | + | 0.141199i | ||||
\(913\) | −24211.7 | + | 41936.0i | −0.877647 | + | 1.52013i | ||||
\(914\) | −9136.48 | + | 15824.8i | −0.330643 | + | 0.572691i | ||||
\(915\) | 4177.60 | + | 3800.23i | 0.150937 | + | 0.137302i | ||||
\(916\) | −64796.8 | + | 37410.5i | −2.33728 | + | 1.34943i | ||||
\(917\) | 22973.1i | 0.827306i | ||||||||
\(918\) | −53863.6 | − | 6494.65i | −1.93656 | − | 0.233503i | ||||
\(919\) | −21347.4 | −0.766251 | −0.383126 | − | 0.923696i | \(-0.625152\pi\) | ||||
−0.383126 | + | 0.923696i | \(0.625152\pi\) | |||||||
\(920\) | −7395.65 | − | 12809.6i | −0.265030 | − | 0.459045i | ||||
\(921\) | −13752.8 | − | 12510.5i | −0.492042 | − | 0.447594i | ||||
\(922\) | 22979.9 | − | 39802.4i | 0.820829 | − | 1.42172i | ||||
\(923\) | 9380.44 | + | 9196.22i | 0.334519 | + | 0.327949i | ||||
\(924\) | 41851.2 | + | 9118.74i | 1.49005 | + | 0.324659i | ||||
\(925\) | 10851.8 | − | 6265.29i | 0.385735 | − | 0.222704i | ||||
\(926\) | 52705.6 | 1.87043 | ||||||||
\(927\) | −39241.8 | − | 17952.6i | −1.39037 | − | 0.636076i | ||||
\(928\) | − | 18247.2i | − | 0.645467i | ||||||
\(929\) | 4263.91 | − | 2461.77i | 0.150586 | − | 0.0869409i | −0.422814 | − | 0.906217i | \(-0.638958\pi\) |
0.573400 | + | 0.819276i | \(0.305624\pi\) | |||||||
\(930\) | −10762.5 | + | 3436.47i | −0.379481 | + | 0.121168i | ||||
\(931\) | 5966.41 | + | 3444.71i | 0.210033 | + | 0.121263i | ||||
\(932\) | 45025.2 | − | 77986.0i | 1.58246 | − | 2.74090i | ||||
\(933\) | 14113.8 | + | 44202.4i | 0.495246 | + | 1.55104i | ||||
\(934\) | 34059.8 | − | 19664.4i | 1.19322 | − | 0.688908i | ||||
\(935\) | −18783.3 | −0.656985 | ||||||||
\(936\) | −19548.7 | + | 24127.5i | −0.682661 | + | 0.842554i | ||||
\(937\) | −40906.0 | −1.42619 | −0.713095 | − | 0.701067i | \(-0.752707\pi\) | ||||
−0.713095 | + | 0.701067i | \(0.752707\pi\) | |||||||
\(938\) | 8736.74 | − | 5044.16i | 0.304120 | − | 0.175584i | ||||
\(939\) | 417.796 | + | 91.0314i | 0.0145200 | + | 0.00316368i | ||||
\(940\) | −6162.93 | + | 10674.5i | −0.213843 | + | 0.370388i | ||||
\(941\) | −18282.0 | − | 10555.1i | −0.633345 | − | 0.365662i | 0.148701 | − | 0.988882i | \(-0.452491\pi\) |
−0.782046 | + | 0.623220i | \(0.785824\pi\) | |||||||
\(942\) | 55392.7 | + | 50388.9i | 1.91591 | + | 1.74284i | ||||
\(943\) | −28368.7 | + | 16378.7i | −0.979652 | + | 0.565603i | ||||
\(944\) | − | 2837.37i | − | 0.0978268i | ||||||
\(945\) | 11469.8 | + | 8604.07i | 0.394829 | + | 0.296180i | ||||
\(946\) | −49158.3 | −1.68951 | ||||||||
\(947\) | −6809.34 | + | 3931.37i | −0.233658 | + | 0.134902i | −0.612258 | − | 0.790658i | \(-0.709739\pi\) |
0.378601 | + | 0.925560i | \(0.376405\pi\) | |||||||
\(948\) | 16505.6 | − | 18144.7i | 0.565482 | − | 0.621636i | ||||
\(949\) | −37453.7 | − | 36718.1i | −1.28114 | − | 1.25598i | ||||
\(950\) | 22996.2 | − | 39830.5i | 0.785362 | − | 1.36029i | ||||
\(951\) | 8743.83 | − | 40130.5i | 0.298147 | − | 1.36837i | ||||
\(952\) | −17261.6 | − | 29898.0i | −0.587660 | − | 1.01786i | ||||
\(953\) | −15625.1 | −0.531109 | −0.265555 | − | 0.964096i | \(-0.585555\pi\) | ||||
−0.265555 | + | 0.964096i | \(0.585555\pi\) | |||||||
\(954\) | −3189.19 | − | 4484.90i | −0.108233 | − | 0.152205i | ||||
\(955\) | − | 1215.14i | − | 0.0411739i | ||||||
\(956\) | −40765.3 | + | 23535.9i | −1.37913 | + | 0.796239i | ||||
\(957\) | −20167.9 | + | 6439.60i | −0.681230 | + | 0.217516i | ||||
\(958\) | −36600.8 | + | 63394.4i | −1.23436 | + | 2.13798i | ||||
\(959\) | 13023.2 | − | 22556.9i | 0.438522 | − | 0.759542i | ||||
\(960\) | −24581.1 | + | 7848.72i | −0.826408 | + | 0.263871i | ||||
\(961\) | −11899.8 | − | 20611.0i | −0.399443 | − | 0.691855i | ||||
\(962\) | 29847.6 | + | 7681.24i | 1.00034 | + | 0.257436i | ||||
\(963\) | −3638.68 | − | 38375.6i | −0.121760 | − | 1.28415i | ||||
\(964\) | 68746.5i | 2.29686i | ||||||||
\(965\) | 6528.59 | + | 11307.9i | 0.217785 | + | 0.377215i | ||||
\(966\) | 39009.2 | + | 8499.51i | 1.29928 | + | 0.283093i | ||||
\(967\) | −21792.7 | − | 12582.0i | −0.724721 | − | 0.418418i | 0.0917667 | − | 0.995781i | \(-0.470749\pi\) |
−0.816488 | + | 0.577363i | \(0.804082\pi\) | |||||||
\(968\) | 583.146 | + | 336.679i | 0.0193626 | + | 0.0111790i | ||||
\(969\) | 36454.4 | + | 33161.4i | 1.20855 | + | 1.09938i | ||||
\(970\) | 25742.9 | − | 14862.6i | 0.852117 | − | 0.491970i | ||||
\(971\) | 40422.2 | 1.33595 | 0.667977 | − | 0.744182i | \(-0.267161\pi\) | ||||
0.667977 | + | 0.744182i | \(0.267161\pi\) | |||||||
\(972\) | 24097.9 | + | 44307.0i | 0.795208 | + | 1.46208i | ||||
\(973\) | 35525.3i | 1.17049i | ||||||||
\(974\) | 3979.71 | + | 6893.06i | 0.130922 | + | 0.226764i | ||||
\(975\) | 17914.8 | − | 11757.3i | 0.588444 | − | 0.386189i | ||||
\(976\) | −604.220 | + | 1046.54i | −0.0198162 | + | 0.0343226i | ||||
\(977\) | −3071.49 | − | 1773.33i | −0.100579 | − | 0.0580694i | 0.448867 | − | 0.893599i | \(-0.351828\pi\) |
−0.549446 | + | 0.835529i | \(0.685161\pi\) | |||||||
\(978\) | −11553.2 | − | 2517.27i | −0.377741 | − | 0.0823041i | ||||
\(979\) | 10870.7 | + | 18828.6i | 0.354882 | + | 0.614673i | ||||
\(980\) | − | 4929.14i | − | 0.160669i | ||||||
\(981\) | 41711.2 | − | 3954.97i | 1.35753 | − | 0.128718i | ||||
\(982\) | − | 60403.4i | − | 1.96288i | ||||||
\(983\) | −14082.4 | + | 8130.46i | −0.456925 | + | 0.263806i | −0.710751 | − | 0.703444i | \(-0.751645\pi\) |
0.253825 | + | 0.967250i | \(0.418311\pi\) | |||||||
\(984\) | −12822.1 | − | 40157.0i | −0.415399 | − | 1.30097i | ||||
\(985\) | −2396.61 | + | 4151.05i | −0.0775252 | + | 0.134278i | ||||
\(986\) | 37021.6 | + | 21374.4i | 1.19575 | + | 0.690365i | ||||
\(987\) | −4039.40 | − | 12650.8i | −0.130269 | − | 0.407984i | ||||
\(988\) | 68072.0 | − | 18965.3i | 2.19196 | − | 0.610695i | ||||
\(989\) | −28622.6 | −0.920270 | ||||||||
\(990\) | 16199.4 | + | 22780.9i | 0.520051 | + | 0.731337i | ||||
\(991\) | −3887.78 | −0.124621 | −0.0623105 | − | 0.998057i | \(-0.519847\pi\) | ||||
−0.0623105 | + | 0.998057i | \(0.519847\pi\) | |||||||
\(992\) | 6388.38 | + | 11065.0i | 0.204467 | + | 0.354147i | ||||
\(993\) | 689.004 | − | 3162.24i | 0.0220190 | − | 0.101058i | ||||
\(994\) | 18822.3 | + | 10867.1i | 0.600612 | + | 0.346763i | ||||
\(995\) | 547.643 | + | 316.182i | 0.0174487 | + | 0.0100740i | ||||
\(996\) | −67239.3 | − | 61165.4i | −2.13911 | − | 1.94588i | ||||
\(997\) | −20596.6 | − | 35674.3i | −0.654263 | − | 1.13322i | −0.982078 | − | 0.188475i | \(-0.939646\pi\) |
0.327815 | − | 0.944742i | \(-0.393688\pi\) | |||||||
\(998\) | −95798.0 | −3.03851 | ||||||||
\(999\) | 11990.3 | − | 15983.9i | 0.379736 | − | 0.506216i |
(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 | 117.4.t.a.103.5 | yes | 80 | |
3.2 | odd | 2 | 351.4.t.a.64.36 | 80 | |||
9.2 | odd | 6 | 351.4.t.a.181.5 | 80 | |||
9.7 | even | 3 | inner | 117.4.t.a.25.36 | yes | 80 | |
13.12 | even | 2 | inner | 117.4.t.a.103.36 | yes | 80 | |
39.38 | odd | 2 | 351.4.t.a.64.5 | 80 | |||
117.25 | even | 6 | inner | 117.4.t.a.25.5 | ✓ | 80 | |
117.38 | odd | 6 | 351.4.t.a.181.36 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.t.a.25.5 | ✓ | 80 | 117.25 | even | 6 | inner | |
117.4.t.a.25.36 | yes | 80 | 9.7 | even | 3 | inner | |
117.4.t.a.103.5 | yes | 80 | 1.1 | even | 1 | trivial | |
117.4.t.a.103.36 | yes | 80 | 13.12 | even | 2 | inner | |
351.4.t.a.64.5 | 80 | 39.38 | odd | 2 | |||
351.4.t.a.64.36 | 80 | 3.2 | odd | 2 | |||
351.4.t.a.181.5 | 80 | 9.2 | odd | 6 | |||
351.4.t.a.181.36 | 80 | 117.38 | odd | 6 |