Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), 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: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + 25296 x^{8} - 6656 x^{7} - 110848 x^{6} - 227328 x^{5} + 1077248 x^{4} + \cdots + 16777216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.5 | ||
Root | \(1.85226 - 2.13755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.5.c.a.31.6 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.34902 | − | 2.18726i | −0.837254 | − | 0.546814i | ||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | 6.43181 | + | 14.6503i | 0.401988 | + | 0.915645i | ||||
\(5\) | −11.1803 | −0.447214 | ||||||||
\(6\) | 11.3653 | − | 17.4020i | 0.315703 | − | 0.483389i | ||||
\(7\) | − | 1.39605i | − | 0.0284908i | −0.999899 | − | 0.0142454i | \(-0.995465\pi\) | ||
0.999899 | − | 0.0142454i | \(-0.00453461\pi\) | |||||||
\(8\) | 10.5038 | − | 63.1322i | 0.164122 | − | 0.986440i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 37.4431 | + | 24.4543i | 0.374431 | + | 0.244543i | ||||
\(11\) | − | 164.588i | − | 1.36023i | −0.733105 | − | 0.680116i | \(-0.761930\pi\) | ||
0.733105 | − | 0.680116i | \(-0.238070\pi\) | |||||||
\(12\) | −76.1253 | + | 33.4207i | −0.528648 | + | 0.232088i | ||||
\(13\) | −158.663 | −0.938832 | −0.469416 | − | 0.882977i | \(-0.655536\pi\) | ||||
−0.469416 | + | 0.882977i | \(0.655536\pi\) | |||||||
\(14\) | −3.05352 | + | 4.67540i | −0.0155792 | + | 0.0238541i | ||||
\(15\) | − | 58.0948i | − | 0.258199i | ||||||
\(16\) | −173.264 | + | 188.456i | −0.676811 | + | 0.736157i | ||||
\(17\) | −548.214 | −1.89694 | −0.948468 | − | 0.316873i | \(-0.897367\pi\) | ||||
−0.948468 | + | 0.316873i | \(0.897367\pi\) | |||||||
\(18\) | 90.4234 | + | 59.0560i | 0.279085 | + | 0.182271i | ||||
\(19\) | − | 25.6686i | − | 0.0711042i | −0.999368 | − | 0.0355521i | \(-0.988681\pi\) | ||
0.999368 | − | 0.0355521i | \(-0.0113190\pi\) | |||||||
\(20\) | −71.9098 | − | 163.796i | −0.179774 | − | 0.409489i | ||||
\(21\) | 7.25409 | 0.0164492 | ||||||||
\(22\) | −359.996 | + | 551.208i | −0.743794 | + | 1.13886i | ||||
\(23\) | − | 730.150i | − | 1.38025i | −0.723692 | − | 0.690123i | \(-0.757556\pi\) | ||
0.723692 | − | 0.690123i | \(-0.242444\pi\) | |||||||
\(24\) | 328.044 | + | 54.5793i | 0.569521 | + | 0.0947558i | ||||
\(25\) | 125.000 | 0.200000 | ||||||||
\(26\) | 531.364 | + | 347.036i | 0.786041 | + | 0.513367i | ||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | 20.4526 | − | 8.97913i | 0.0260875 | − | 0.0114530i | ||||
\(29\) | 773.909 | 0.920225 | 0.460112 | − | 0.887861i | \(-0.347809\pi\) | ||||
0.460112 | + | 0.887861i | \(0.347809\pi\) | |||||||
\(30\) | −127.068 | + | 194.560i | −0.141187 | + | 0.216178i | ||||
\(31\) | − | 194.974i | − | 0.202887i | −0.994841 | − | 0.101443i | \(-0.967654\pi\) | ||
0.994841 | − | 0.101443i | \(-0.0323461\pi\) | |||||||
\(32\) | 992.465 | − | 252.170i | 0.969204 | − | 0.246260i | ||||
\(33\) | 855.224 | 0.785330 | ||||||||
\(34\) | 1835.98 | + | 1199.09i | 1.58822 | + | 1.03727i | ||||
\(35\) | 15.6083i | 0.0127415i | ||||||||
\(36\) | −173.659 | − | 395.559i | −0.133996 | − | 0.305215i | ||||
\(37\) | −1373.19 | −1.00306 | −0.501529 | − | 0.865141i | \(-0.667229\pi\) | ||||
−0.501529 | + | 0.865141i | \(0.667229\pi\) | |||||||
\(38\) | −56.1439 | + | 85.9646i | −0.0388808 | + | 0.0595323i | ||||
\(39\) | − | 824.435i | − | 0.542035i | ||||||
\(40\) | −117.436 | + | 705.839i | −0.0733975 | + | 0.441149i | ||||
\(41\) | −647.851 | −0.385396 | −0.192698 | − | 0.981258i | \(-0.561724\pi\) | ||||
−0.192698 | + | 0.981258i | \(0.561724\pi\) | |||||||
\(42\) | −24.2941 | − | 15.8666i | −0.0137721 | − | 0.00899465i | ||||
\(43\) | 1502.44i | 0.812568i | 0.913747 | + | 0.406284i | \(0.133176\pi\) | ||||
−0.913747 | + | 0.406284i | \(0.866824\pi\) | |||||||
\(44\) | 2411.27 | − | 1058.60i | 1.24549 | − | 0.546797i | ||||
\(45\) | 301.869 | 0.149071 | ||||||||
\(46\) | −1597.03 | + | 2445.28i | −0.754738 | + | 1.15562i | ||||
\(47\) | 647.613i | 0.293170i | 0.989198 | + | 0.146585i | \(0.0468282\pi\) | ||||
−0.989198 | + | 0.146585i | \(0.953172\pi\) | |||||||
\(48\) | −979.247 | − | 900.305i | −0.425020 | − | 0.390757i | ||||
\(49\) | 2399.05 | 0.999188 | ||||||||
\(50\) | −418.627 | − | 273.407i | −0.167451 | − | 0.109363i | ||||
\(51\) | − | 2848.61i | − | 1.09520i | ||||||
\(52\) | −1020.49 | − | 2324.46i | −0.377399 | − | 0.859637i | ||||
\(53\) | −4407.11 | −1.56892 | −0.784462 | − | 0.620177i | \(-0.787061\pi\) | ||||
−0.784462 | + | 0.620177i | \(0.787061\pi\) | |||||||
\(54\) | −306.864 | + | 469.854i | −0.105234 | + | 0.161130i | ||||
\(55\) | 1840.15i | 0.608314i | ||||||||
\(56\) | −88.1357 | − | 14.6638i | −0.0281045 | − | 0.00467597i | ||||
\(57\) | 133.378 | 0.0410520 | ||||||||
\(58\) | −2591.83 | − | 1692.74i | −0.770462 | − | 0.503192i | ||||
\(59\) | 5978.96i | 1.71760i | 0.512311 | + | 0.858800i | \(0.328789\pi\) | ||||
−0.512311 | + | 0.858800i | \(0.671211\pi\) | |||||||
\(60\) | 851.107 | − | 373.654i | 0.236419 | − | 0.103793i | ||||
\(61\) | −560.288 | −0.150575 | −0.0752873 | − | 0.997162i | \(-0.523987\pi\) | ||||
−0.0752873 | + | 0.997162i | \(0.523987\pi\) | |||||||
\(62\) | −426.459 | + | 652.971i | −0.110941 | + | 0.169868i | ||||
\(63\) | 37.6934i | 0.00949694i | ||||||||
\(64\) | −3875.34 | − | 1326.26i | −0.946128 | − | 0.323793i | ||||
\(65\) | 1773.90 | 0.419859 | ||||||||
\(66\) | −2864.16 | − | 1870.60i | −0.657521 | − | 0.429430i | ||||
\(67\) | − | 2986.47i | − | 0.665286i | −0.943053 | − | 0.332643i | \(-0.892060\pi\) | ||
0.943053 | − | 0.332643i | \(-0.107940\pi\) | |||||||
\(68\) | −3526.01 | − | 8031.52i | −0.762545 | − | 1.73692i | ||||
\(69\) | 3793.97 | 0.796885 | ||||||||
\(70\) | 34.1394 | − | 52.2725i | 0.00696723 | − | 0.0106679i | ||||
\(71\) | − | 2673.19i | − | 0.530290i | −0.964209 | − | 0.265145i | \(-0.914580\pi\) | ||
0.964209 | − | 0.265145i | \(-0.0854198\pi\) | |||||||
\(72\) | −283.603 | + | 1704.57i | −0.0547073 | + | 0.328813i | ||||
\(73\) | 2649.09 | 0.497108 | 0.248554 | − | 0.968618i | \(-0.420045\pi\) | ||||
0.248554 | + | 0.968618i | \(0.420045\pi\) | |||||||
\(74\) | 4598.82 | + | 3003.51i | 0.839815 | + | 0.548487i | ||||
\(75\) | 649.519i | 0.115470i | ||||||||
\(76\) | 376.053 | − | 165.096i | 0.0651062 | − | 0.0285830i | ||||
\(77\) | −229.773 | −0.0387541 | ||||||||
\(78\) | −1803.25 | + | 2761.05i | −0.296393 | + | 0.453821i | ||||
\(79\) | − | 3158.78i | − | 0.506134i | −0.967449 | − | 0.253067i | \(-0.918561\pi\) | ||
0.967449 | − | 0.253067i | \(-0.0814393\pi\) | |||||||
\(80\) | 1937.15 | − | 2107.00i | 0.302679 | − | 0.329219i | ||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 2169.66 | + | 1417.02i | 0.322675 | + | 0.210740i | ||||
\(83\) | 13095.0i | 1.90085i | 0.310952 | + | 0.950426i | \(0.399352\pi\) | ||||
−0.310952 | + | 0.950426i | \(0.600648\pi\) | |||||||
\(84\) | 46.6569 | + | 106.275i | 0.00661238 | + | 0.0150616i | ||||
\(85\) | 6129.22 | 0.848336 | ||||||||
\(86\) | 3286.22 | − | 5031.69i | 0.444324 | − | 0.680325i | ||||
\(87\) | 4021.35i | 0.531292i | ||||||||
\(88\) | −10390.8 | − | 1728.80i | −1.34179 | − | 0.223244i | ||||
\(89\) | −7112.37 | −0.897913 | −0.448956 | − | 0.893554i | \(-0.648204\pi\) | ||||
−0.448956 | + | 0.893554i | \(0.648204\pi\) | |||||||
\(90\) | −1010.96 | − | 660.266i | −0.124810 | − | 0.0815143i | ||||
\(91\) | 221.501i | 0.0267481i | ||||||||
\(92\) | 10696.9 | − | 4696.19i | 1.26382 | − | 0.554842i | ||||
\(93\) | 1013.12 | 0.117137 | ||||||||
\(94\) | 1416.50 | − | 2168.87i | 0.160310 | − | 0.245458i | ||||
\(95\) | 286.984i | 0.0317988i | ||||||||
\(96\) | 1310.31 | + | 5157.00i | 0.142178 | + | 0.559570i | ||||
\(97\) | 5310.91 | 0.564450 | 0.282225 | − | 0.959348i | \(-0.408927\pi\) | ||||
0.282225 | + | 0.959348i | \(0.408927\pi\) | |||||||
\(98\) | −8034.46 | − | 5247.34i | −0.836574 | − | 0.546371i | ||||
\(99\) | 4443.88i | 0.453410i | ||||||||
\(100\) | 803.976 | + | 1831.29i | 0.0803976 | + | 0.183129i | ||||
\(101\) | −17042.8 | −1.67070 | −0.835348 | − | 0.549721i | \(-0.814734\pi\) | ||||
−0.835348 | + | 0.549721i | \(0.814734\pi\) | |||||||
\(102\) | −6230.64 | + | 9540.03i | −0.598869 | + | 0.916957i | ||||
\(103\) | − | 3359.31i | − | 0.316647i | −0.987387 | − | 0.158323i | \(-0.949391\pi\) | ||
0.987387 | − | 0.158323i | \(-0.0506089\pi\) | |||||||
\(104\) | −1666.56 | + | 10016.7i | −0.154083 | + | 0.926102i | ||||
\(105\) | −81.1032 | −0.00735630 | ||||||||
\(106\) | 14759.5 | + | 9639.48i | 1.31359 | + | 0.857910i | ||||
\(107\) | − | 6655.05i | − | 0.581278i | −0.956833 | − | 0.290639i | \(-0.906132\pi\) | ||
0.956833 | − | 0.290639i | \(-0.0938678\pi\) | |||||||
\(108\) | 2055.38 | − | 902.358i | 0.176216 | − | 0.0773626i | ||||
\(109\) | 10400.1 | 0.875355 | 0.437677 | − | 0.899132i | \(-0.355801\pi\) | ||||
0.437677 | + | 0.899132i | \(0.355801\pi\) | |||||||
\(110\) | 4024.88 | − | 6162.69i | 0.332635 | − | 0.509313i | ||||
\(111\) | − | 7135.29i | − | 0.579116i | ||||||
\(112\) | 263.094 | + | 241.885i | 0.0209737 | + | 0.0192829i | ||||
\(113\) | 11224.7 | 0.879056 | 0.439528 | − | 0.898229i | \(-0.355146\pi\) | ||||
0.439528 | + | 0.898229i | \(0.355146\pi\) | |||||||
\(114\) | −446.685 | − | 291.732i | −0.0343710 | − | 0.0224478i | ||||
\(115\) | 8163.33i | 0.617265i | ||||||||
\(116\) | 4977.63 | + | 11338.0i | 0.369919 | + | 0.842599i | ||||
\(117\) | 4283.89 | 0.312944 | ||||||||
\(118\) | 13077.5 | − | 20023.6i | 0.939208 | − | 1.43807i | ||||
\(119\) | 765.335i | 0.0540453i | ||||||||
\(120\) | −3667.65 | − | 610.216i | −0.254698 | − | 0.0423761i | ||||
\(121\) | −12448.2 | −0.850229 | ||||||||
\(122\) | 1876.41 | + | 1225.50i | 0.126069 | + | 0.0823364i | ||||
\(123\) | − | 3366.33i | − | 0.222509i | ||||||
\(124\) | 2856.43 | − | 1254.04i | 0.185772 | − | 0.0815580i | ||||
\(125\) | −1397.54 | −0.0894427 | ||||||||
\(126\) | 82.4451 | − | 126.236i | 0.00519307 | − | 0.00795135i | ||||
\(127\) | − | 25607.7i | − | 1.58768i | −0.608128 | − | 0.793839i | \(-0.708079\pi\) | ||
0.608128 | − | 0.793839i | \(-0.291921\pi\) | |||||||
\(128\) | 10077.7 | + | 12918.0i | 0.615095 | + | 0.788453i | ||||
\(129\) | −7806.89 | −0.469136 | ||||||||
\(130\) | −5940.83 | − | 3879.98i | −0.351528 | − | 0.229585i | ||||
\(131\) | − | 16564.8i | − | 0.965256i | −0.875825 | − | 0.482628i | \(-0.839682\pi\) | ||
0.875825 | − | 0.482628i | \(-0.160318\pi\) | |||||||
\(132\) | 5500.64 | + | 12529.3i | 0.315693 | + | 0.719083i | ||||
\(133\) | −35.8347 | −0.00202582 | ||||||||
\(134\) | −6532.18 | + | 10001.7i | −0.363788 | + | 0.557013i | ||||
\(135\) | 1568.56i | 0.0860663i | ||||||||
\(136\) | −5758.33 | + | 34610.0i | −0.311329 | + | 1.87121i | ||||
\(137\) | −5619.61 | −0.299409 | −0.149705 | − | 0.988731i | \(-0.547832\pi\) | ||||
−0.149705 | + | 0.988731i | \(0.547832\pi\) | |||||||
\(138\) | −12706.1 | − | 8298.39i | −0.667195 | − | 0.435748i | ||||
\(139\) | − | 33597.0i | − | 1.73888i | −0.494036 | − | 0.869442i | \(-0.664479\pi\) | ||
0.494036 | − | 0.869442i | \(-0.335521\pi\) | |||||||
\(140\) | −228.667 | + | 100.390i | −0.0116667 | + | 0.00512193i | ||||
\(141\) | −3365.10 | −0.169262 | ||||||||
\(142\) | −5846.96 | + | 8952.55i | −0.289970 | + | 0.443987i | ||||
\(143\) | 26114.0i | 1.27703i | ||||||||
\(144\) | 4678.12 | − | 5088.31i | 0.225604 | − | 0.245386i | ||||
\(145\) | −8652.57 | −0.411537 | ||||||||
\(146\) | −8871.84 | − | 5794.24i | −0.416206 | − | 0.271826i | ||||
\(147\) | 12465.8i | 0.576882i | ||||||||
\(148\) | −8832.08 | − | 20117.6i | −0.403217 | − | 0.918445i | ||||
\(149\) | −19602.3 | −0.882946 | −0.441473 | − | 0.897275i | \(-0.645544\pi\) | ||||
−0.441473 | + | 0.897275i | \(0.645544\pi\) | |||||||
\(150\) | 1420.67 | − | 2175.25i | 0.0631407 | − | 0.0966777i | ||||
\(151\) | − | 9340.31i | − | 0.409645i | −0.978799 | − | 0.204822i | \(-0.934338\pi\) | ||
0.978799 | − | 0.204822i | \(-0.0656617\pi\) | |||||||
\(152\) | −1620.52 | − | 269.618i | −0.0701400 | − | 0.0116698i | ||||
\(153\) | 14801.8 | 0.632312 | ||||||||
\(154\) | 769.514 | + | 502.573i | 0.0324470 | + | 0.0211913i | ||||
\(155\) | 2179.88i | 0.0907337i | ||||||||
\(156\) | 12078.2 | − | 5302.61i | 0.496312 | − | 0.217892i | ||||
\(157\) | −34913.2 | −1.41642 | −0.708208 | − | 0.706004i | \(-0.750496\pi\) | ||||
−0.708208 | + | 0.706004i | \(0.750496\pi\) | |||||||
\(158\) | −6909.07 | + | 10578.8i | −0.276761 | + | 0.423763i | ||||
\(159\) | − | 22900.0i | − | 0.905818i | ||||||
\(160\) | −11096.1 | + | 2819.35i | −0.433441 | + | 0.110131i | ||||
\(161\) | −1019.33 | −0.0393244 | ||||||||
\(162\) | −2441.43 | − | 1594.51i | −0.0930282 | − | 0.0607572i | ||||
\(163\) | 49700.0i | 1.87060i | 0.353853 | + | 0.935301i | \(0.384871\pi\) | ||||
−0.353853 | + | 0.935301i | \(0.615129\pi\) | |||||||
\(164\) | −4166.85 | − | 9491.23i | −0.154925 | − | 0.352886i | ||||
\(165\) | −9561.70 | −0.351210 | ||||||||
\(166\) | 28642.1 | − | 43855.2i | 1.03941 | − | 1.59149i | ||||
\(167\) | − | 51638.7i | − | 1.85158i | −0.378038 | − | 0.925790i | \(-0.623401\pi\) | ||
0.378038 | − | 0.925790i | \(-0.376599\pi\) | |||||||
\(168\) | 76.1955 | − | 457.967i | 0.00269967 | − | 0.0162261i | ||||
\(169\) | −3387.16 | −0.118594 | ||||||||
\(170\) | −20526.9 | − | 13406.2i | −0.710272 | − | 0.463882i | ||||
\(171\) | 693.053i | 0.0237014i | ||||||||
\(172\) | −22011.2 | + | 9663.39i | −0.744023 | + | 0.326642i | ||||
\(173\) | 48824.2 | 1.63133 | 0.815667 | − | 0.578522i | \(-0.196370\pi\) | ||||
0.815667 | + | 0.578522i | \(0.196370\pi\) | |||||||
\(174\) | 8795.73 | − | 13467.6i | 0.290518 | − | 0.444826i | ||||
\(175\) | − | 174.506i | − | 0.00569817i | ||||||
\(176\) | 31017.6 | + | 28517.1i | 1.00134 | + | 0.920620i | ||||
\(177\) | −31067.6 | −0.991657 | ||||||||
\(178\) | 23819.4 | + | 15556.6i | 0.751781 | + | 0.490992i | ||||
\(179\) | 51061.1i | 1.59362i | 0.604233 | + | 0.796808i | \(0.293480\pi\) | ||||
−0.604233 | + | 0.796808i | \(0.706520\pi\) | |||||||
\(180\) | 1941.56 | + | 4422.48i | 0.0599248 | + | 0.136496i | ||||
\(181\) | 16788.0 | 0.512438 | 0.256219 | − | 0.966619i | \(-0.417523\pi\) | ||||
0.256219 | + | 0.966619i | \(0.417523\pi\) | |||||||
\(182\) | 484.480 | − | 741.811i | 0.0146263 | − | 0.0223950i | ||||
\(183\) | − | 2911.34i | − | 0.0869343i | ||||||
\(184\) | −46096.0 | − | 7669.35i | −1.36153 | − | 0.226529i | ||||
\(185\) | 15352.7 | 0.448581 | ||||||||
\(186\) | −3392.94 | − | 2215.94i | −0.0980732 | − | 0.0640520i | ||||
\(187\) | 90229.5i | 2.58027i | ||||||||
\(188\) | −9487.74 | + | 4165.32i | −0.268440 | + | 0.117851i | ||||
\(189\) | −195.861 | −0.00548306 | ||||||||
\(190\) | 627.708 | − | 961.113i | 0.0173880 | − | 0.0266236i | ||||
\(191\) | − | 34310.5i | − | 0.940504i | −0.882532 | − | 0.470252i | \(-0.844163\pi\) | ||
0.882532 | − | 0.470252i | \(-0.155837\pi\) | |||||||
\(192\) | 6891.42 | − | 20136.9i | 0.186942 | − | 0.546247i | ||||
\(193\) | 33325.8 | 0.894675 | 0.447338 | − | 0.894365i | \(-0.352372\pi\) | ||||
0.447338 | + | 0.894365i | \(0.352372\pi\) | |||||||
\(194\) | −17786.3 | − | 11616.3i | −0.472588 | − | 0.308650i | ||||
\(195\) | 9217.47i | 0.242405i | ||||||||
\(196\) | 15430.2 | + | 35146.9i | 0.401662 | + | 0.914902i | ||||
\(197\) | 53779.0 | 1.38573 | 0.692867 | − | 0.721065i | \(-0.256347\pi\) | ||||
0.692867 | + | 0.721065i | \(0.256347\pi\) | |||||||
\(198\) | 9719.90 | − | 14882.6i | 0.247931 | − | 0.379620i | ||||
\(199\) | − | 7992.31i | − | 0.201821i | −0.994896 | − | 0.100910i | \(-0.967824\pi\) | ||
0.994896 | − | 0.100910i | \(-0.0321755\pi\) | |||||||
\(200\) | 1312.97 | − | 7891.52i | 0.0328244 | − | 0.197288i | ||||
\(201\) | 15518.2 | 0.384103 | ||||||||
\(202\) | 57076.5 | + | 37276.9i | 1.39880 | + | 0.913561i | ||||
\(203\) | − | 1080.42i | − | 0.0262180i | ||||||
\(204\) | 41733.0 | − | 18321.7i | 1.00281 | − | 0.440256i | ||||
\(205\) | 7243.20 | 0.172354 | ||||||||
\(206\) | −7347.67 | + | 11250.4i | −0.173147 | + | 0.265114i | ||||
\(207\) | 19714.1i | 0.460082i | ||||||||
\(208\) | 27490.5 | − | 29900.9i | 0.635412 | − | 0.691128i | ||||
\(209\) | −4224.75 | −0.0967182 | ||||||||
\(210\) | 271.616 | + | 177.394i | 0.00615909 | + | 0.00402253i | ||||
\(211\) | 23096.8i | 0.518785i | 0.965772 | + | 0.259393i | \(0.0835224\pi\) | ||||
−0.965772 | + | 0.259393i | \(0.916478\pi\) | |||||||
\(212\) | −28345.7 | − | 64565.5i | −0.630688 | − | 1.43658i | ||||
\(213\) | 13890.3 | 0.306163 | ||||||||
\(214\) | −14556.3 | + | 22287.9i | −0.317851 | + | 0.486677i | ||||
\(215\) | − | 16797.8i | − | 0.363391i | ||||||
\(216\) | −8857.20 | − | 1473.64i | −0.189840 | − | 0.0315853i | ||||
\(217\) | −272.194 | −0.00578041 | ||||||||
\(218\) | −34830.1 | − | 22747.7i | −0.732894 | − | 0.478657i | ||||
\(219\) | 13765.1i | 0.287006i | ||||||||
\(220\) | −26958.8 | + | 11835.5i | −0.557000 | + | 0.244535i | ||||
\(221\) | 86981.2 | 1.78090 | ||||||||
\(222\) | −15606.7 | + | 23896.2i | −0.316669 | + | 0.484867i | ||||
\(223\) | 46059.3i | 0.926206i | 0.886305 | + | 0.463103i | \(0.153264\pi\) | ||||
−0.886305 | + | 0.463103i | \(0.846736\pi\) | |||||||
\(224\) | −352.042 | − | 1385.53i | −0.00701615 | − | 0.0276134i | ||||
\(225\) | −3375.00 | −0.0666667 | ||||||||
\(226\) | −37591.6 | − | 24551.2i | −0.735993 | − | 0.480681i | ||||
\(227\) | − | 49636.5i | − | 0.963274i | −0.876371 | − | 0.481637i | \(-0.840042\pi\) | ||
0.876371 | − | 0.481637i | \(-0.159958\pi\) | |||||||
\(228\) | 857.862 | + | 1954.03i | 0.0165024 | + | 0.0375891i | ||||
\(229\) | −8900.38 | −0.169722 | −0.0848609 | − | 0.996393i | \(-0.527045\pi\) | ||||
−0.0848609 | + | 0.996393i | \(0.527045\pi\) | |||||||
\(230\) | 17855.3 | − | 27339.1i | 0.337529 | − | 0.516807i | ||||
\(231\) | − | 1193.94i | − | 0.0223747i | ||||||
\(232\) | 8128.98 | − | 48858.5i | 0.151029 | − | 0.907747i | ||||
\(233\) | −13357.8 | −0.246050 | −0.123025 | − | 0.992404i | \(-0.539260\pi\) | ||||
−0.123025 | + | 0.992404i | \(0.539260\pi\) | |||||||
\(234\) | −14346.8 | − | 9369.98i | −0.262014 | − | 0.171122i | ||||
\(235\) | − | 7240.54i | − | 0.131110i | ||||||
\(236\) | −87593.7 | + | 38455.5i | −1.57271 | + | 0.690454i | ||||
\(237\) | 16413.5 | 0.292217 | ||||||||
\(238\) | 1673.99 | − | 2563.12i | 0.0295527 | − | 0.0452496i | ||||
\(239\) | − | 40201.8i | − | 0.703801i | −0.936037 | − | 0.351900i | \(-0.885536\pi\) | ||
0.936037 | − | 0.351900i | \(-0.114464\pi\) | |||||||
\(240\) | 10948.3 | + | 10065.7i | 0.190075 | + | 0.174752i | ||||
\(241\) | −91284.7 | −1.57168 | −0.785840 | − | 0.618430i | \(-0.787769\pi\) | ||||
−0.785840 | + | 0.618430i | \(0.787769\pi\) | |||||||
\(242\) | 41689.2 | + | 27227.4i | 0.711858 | + | 0.464918i | ||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | −3603.67 | − | 8208.40i | −0.0605292 | − | 0.137873i | ||||
\(245\) | −26822.2 | −0.446851 | ||||||||
\(246\) | −7363.04 | + | 11273.9i | −0.121671 | + | 0.186296i | ||||
\(247\) | 4072.65i | 0.0667549i | ||||||||
\(248\) | −12309.1 | − | 2047.97i | −0.200136 | − | 0.0332981i | ||||
\(249\) | −68043.4 | −1.09746 | ||||||||
\(250\) | 4680.39 | + | 3056.79i | 0.0748863 | + | 0.0489086i | ||||
\(251\) | 85298.2i | 1.35392i | 0.736021 | + | 0.676959i | \(0.236703\pi\) | ||||
−0.736021 | + | 0.676959i | \(0.763297\pi\) | |||||||
\(252\) | −552.220 | + | 242.437i | −0.00869583 | + | 0.00381766i | ||||
\(253\) | −120174. | −1.87745 | ||||||||
\(254\) | −56010.6 | + | 85760.5i | −0.868166 | + | 1.32929i | ||||
\(255\) | 31848.4i | 0.489787i | ||||||||
\(256\) | −5495.39 | − | 65305.2i | −0.0838529 | − | 0.996478i | ||||
\(257\) | 23409.7 | 0.354429 | 0.177214 | − | 0.984172i | \(-0.443291\pi\) | ||||
0.177214 | + | 0.984172i | \(0.443291\pi\) | |||||||
\(258\) | 26145.4 | + | 17075.7i | 0.392786 | + | 0.256530i | ||||
\(259\) | 1917.04i | 0.0285780i | ||||||||
\(260\) | 11409.4 | + | 25988.2i | 0.168778 | + | 0.384441i | ||||
\(261\) | −20895.5 | −0.306742 | ||||||||
\(262\) | −36231.4 | + | 55475.6i | −0.527816 | + | 0.808164i | ||||
\(263\) | − | 88925.7i | − | 1.28563i | −0.766021 | − | 0.642815i | \(-0.777766\pi\) | ||
0.766021 | − | 0.642815i | \(-0.222234\pi\) | |||||||
\(264\) | 8983.10 | − | 53992.2i | 0.128890 | − | 0.774681i | ||||
\(265\) | 49272.9 | 0.701644 | ||||||||
\(266\) | 120.011 | + | 78.3797i | 0.00169612 | + | 0.00110775i | ||||
\(267\) | − | 36956.9i | − | 0.518410i | ||||||
\(268\) | 43752.7 | − | 19208.4i | 0.609166 | − | 0.267437i | ||||
\(269\) | −78384.1 | −1.08324 | −0.541619 | − | 0.840624i | \(-0.682188\pi\) | ||||
−0.541619 | + | 0.840624i | \(0.682188\pi\) | |||||||
\(270\) | 3430.84 | − | 5253.13i | 0.0470623 | − | 0.0720593i | ||||
\(271\) | − | 79821.4i | − | 1.08688i | −0.839449 | − | 0.543439i | \(-0.817122\pi\) | ||
0.839449 | − | 0.543439i | \(-0.182878\pi\) | |||||||
\(272\) | 94985.7 | − | 103314.i | 1.28387 | − | 1.39644i | ||||
\(273\) | −1150.95 | −0.0154430 | ||||||||
\(274\) | 18820.2 | + | 12291.5i | 0.250682 | + | 0.163721i | ||||
\(275\) | − | 20573.5i | − | 0.272046i | ||||||
\(276\) | 24402.1 | + | 55582.9i | 0.320338 | + | 0.729664i | ||||
\(277\) | −13987.6 | −0.182299 | −0.0911494 | − | 0.995837i | \(-0.529054\pi\) | ||||
−0.0911494 | + | 0.995837i | \(0.529054\pi\) | |||||||
\(278\) | −73485.2 | + | 112517.i | −0.950847 | + | 1.45589i | ||||
\(279\) | 5264.30i | 0.0676289i | ||||||||
\(280\) | 985.387 | + | 163.947i | 0.0125687 | + | 0.00209116i | ||||
\(281\) | −14451.9 | −0.183026 | −0.0915132 | − | 0.995804i | \(-0.529170\pi\) | ||||
−0.0915132 | + | 0.995804i | \(0.529170\pi\) | |||||||
\(282\) | 11269.8 | + | 7360.33i | 0.141715 | + | 0.0925549i | ||||
\(283\) | − | 117174.i | − | 1.46305i | −0.681817 | − | 0.731523i | \(-0.738810\pi\) | ||
0.681817 | − | 0.731523i | \(-0.261190\pi\) | |||||||
\(284\) | 39163.1 | − | 17193.4i | 0.485557 | − | 0.213170i | ||||
\(285\) | −1491.21 | −0.0183590 | ||||||||
\(286\) | 57118.0 | − | 87456.1i | 0.698298 | − | 1.06920i | ||||
\(287\) | 904.433i | 0.0109803i | ||||||||
\(288\) | −26796.5 | + | 6808.59i | −0.323068 | + | 0.0820866i | ||||
\(289\) | 217018. | 2.59837 | ||||||||
\(290\) | 28977.6 | + | 18925.4i | 0.344561 | + | 0.225034i | ||||
\(291\) | 27596.3i | 0.325885i | ||||||||
\(292\) | 17038.4 | + | 38810.0i | 0.199832 | + | 0.455175i | ||||
\(293\) | −29064.0 | −0.338548 | −0.169274 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169274 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(294\) | 27266.0 | − | 41748.3i | 0.315447 | − | 0.482996i | ||||
\(295\) | − | 66846.8i | − | 0.768134i | ||||||
\(296\) | −14423.7 | + | 86692.3i | −0.164624 | + | 0.989457i | ||||
\(297\) | −23091.1 | −0.261777 | ||||||||
\(298\) | 65648.3 | + | 42875.2i | 0.739250 | + | 0.482808i | ||||
\(299\) | 115848.i | 1.29582i | ||||||||
\(300\) | −9515.66 | + | 4177.58i | −0.105730 | + | 0.0464176i | ||||
\(301\) | 2097.48 | 0.0231507 | ||||||||
\(302\) | −20429.7 | + | 31280.8i | −0.224000 | + | 0.342977i | ||||
\(303\) | − | 88556.8i | − | 0.964577i | ||||||
\(304\) | 4837.41 | + | 4447.44i | 0.0523438 | + | 0.0481241i | ||||
\(305\) | 6264.21 | 0.0673390 | ||||||||
\(306\) | −49571.4 | − | 32375.3i | −0.529406 | − | 0.345757i | ||||
\(307\) | 35059.6i | 0.371989i | 0.982551 | + | 0.185995i | \(0.0595507\pi\) | ||||
−0.982551 | + | 0.185995i | \(0.940449\pi\) | |||||||
\(308\) | −1477.86 | − | 3366.25i | −0.0155787 | − | 0.0354850i | ||||
\(309\) | 17455.5 | 0.182816 | ||||||||
\(310\) | 4767.95 | − | 7300.44i | 0.0496145 | − | 0.0759671i | ||||
\(311\) | 52153.5i | 0.539216i | 0.962970 | + | 0.269608i | \(0.0868942\pi\) | ||||
−0.962970 | + | 0.269608i | \(0.913106\pi\) | |||||||
\(312\) | −52048.4 | − | 8659.70i | −0.534685 | − | 0.0889598i | ||||
\(313\) | −120087. | −1.22577 | −0.612885 | − | 0.790172i | \(-0.709991\pi\) | ||||
−0.612885 | + | 0.790172i | \(0.709991\pi\) | |||||||
\(314\) | 116925. | + | 76364.2i | 1.18590 | + | 0.774516i | ||||
\(315\) | − | 421.425i | − | 0.00424716i | ||||||
\(316\) | 46277.2 | − | 20316.7i | 0.463439 | − | 0.203460i | ||||
\(317\) | 16118.8 | 0.160404 | 0.0802018 | − | 0.996779i | \(-0.474444\pi\) | ||||
0.0802018 | + | 0.996779i | \(0.474444\pi\) | |||||||
\(318\) | −50088.2 | + | 76692.4i | −0.495314 | + | 0.758400i | ||||
\(319\) | − | 127376.i | − | 1.25172i | ||||||
\(320\) | 43327.6 | + | 14828.0i | 0.423121 | + | 0.144805i | ||||
\(321\) | 34580.6 | 0.335601 | ||||||||
\(322\) | 3413.74 | + | 2229.53i | 0.0329245 | + | 0.0215031i | ||||
\(323\) | 14071.9i | 0.134880i | ||||||||
\(324\) | 4688.79 | + | 10680.1i | 0.0446653 | + | 0.101738i | ||||
\(325\) | −19832.8 | −0.187766 | ||||||||
\(326\) | 108707. | − | 166446.i | 1.02287 | − | 1.56617i | ||||
\(327\) | 54040.4i | 0.505386i | ||||||||
\(328\) | −6804.90 | + | 40900.3i | −0.0632520 | + | 0.380170i | ||||
\(329\) | 904.101 | 0.00835267 | ||||||||
\(330\) | 32022.3 | + | 20913.9i | 0.294052 | + | 0.192047i | ||||
\(331\) | − | 7678.94i | − | 0.0700882i | −0.999386 | − | 0.0350441i | \(-0.988843\pi\) | ||
0.999386 | − | 0.0350441i | \(-0.0111572\pi\) | |||||||
\(332\) | −191845. | + | 84224.3i | −1.74050 | + | 0.764119i | ||||
\(333\) | 37076.1 | 0.334353 | ||||||||
\(334\) | −112947. | + | 172939.i | −1.01247 | + | 1.55024i | ||||
\(335\) | 33389.7i | 0.297525i | ||||||||
\(336\) | −1256.87 | + | 1367.08i | −0.0111330 | + | 0.0121092i | ||||
\(337\) | 68133.9 | 0.599934 | 0.299967 | − | 0.953950i | \(-0.403024\pi\) | ||||
0.299967 | + | 0.953950i | \(0.403024\pi\) | |||||||
\(338\) | 11343.7 | + | 7408.59i | 0.0992932 | + | 0.0648489i | ||||
\(339\) | 58325.1i | 0.507523i | ||||||||
\(340\) | 39422.0 | + | 89795.1i | 0.341021 | + | 0.776774i | ||||
\(341\) | −32090.4 | −0.275973 | ||||||||
\(342\) | 1515.88 | − | 2321.04i | 0.0129603 | − | 0.0198441i | ||||
\(343\) | − | 6701.12i | − | 0.0569585i | ||||||
\(344\) | 94852.1 | + | 15781.3i | 0.801549 | + | 0.133360i | ||||
\(345\) | −42417.9 | −0.356378 | ||||||||
\(346\) | −163513. | − | 106791.i | −1.36584 | − | 0.892037i | ||||
\(347\) | − | 33524.6i | − | 0.278423i | −0.990263 | − | 0.139212i | \(-0.955543\pi\) | ||
0.990263 | − | 0.139212i | \(-0.0444568\pi\) | |||||||
\(348\) | −58914.0 | + | 25864.5i | −0.486475 | + | 0.213573i | ||||
\(349\) | 178271. | 1.46362 | 0.731811 | − | 0.681508i | \(-0.238676\pi\) | ||||
0.731811 | + | 0.681508i | \(0.238676\pi\) | |||||||
\(350\) | −381.690 | + | 584.424i | −0.00311584 | + | 0.00477081i | ||||
\(351\) | 22259.8i | 0.180678i | ||||||||
\(352\) | −41504.1 | − | 163348.i | −0.334970 | − | 1.31834i | ||||
\(353\) | −80952.7 | −0.649654 | −0.324827 | − | 0.945773i | \(-0.605306\pi\) | ||||
−0.324827 | + | 0.945773i | \(0.605306\pi\) | |||||||
\(354\) | 104046. | + | 67952.9i | 0.830268 | + | 0.542252i | ||||
\(355\) | 29887.2i | 0.237153i | ||||||||
\(356\) | −45745.4 | − | 104198.i | −0.360950 | − | 0.822169i | ||||
\(357\) | −3976.80 | −0.0312031 | ||||||||
\(358\) | 111684. | − | 171004.i | 0.871412 | − | 1.33426i | ||||
\(359\) | 95946.6i | 0.744459i | 0.928141 | + | 0.372229i | \(0.121407\pi\) | ||||
−0.928141 | + | 0.372229i | \(0.878593\pi\) | |||||||
\(360\) | 3170.77 | − | 19057.7i | 0.0244658 | − | 0.147050i | ||||
\(361\) | 129662. | 0.994944 | ||||||||
\(362\) | −56223.2 | − | 36719.7i | −0.429041 | − | 0.280209i | ||||
\(363\) | − | 64682.8i | − | 0.490880i | ||||||
\(364\) | −3245.06 | + | 1424.65i | −0.0244918 | + | 0.0107524i | ||||
\(365\) | −29617.7 | −0.222314 | ||||||||
\(366\) | −6367.86 | + | 9750.14i | −0.0475369 | + | 0.0727861i | ||||
\(367\) | 36711.3i | 0.272564i | 0.990670 | + | 0.136282i | \(0.0435153\pi\) | ||||
−0.990670 | + | 0.136282i | \(0.956485\pi\) | |||||||
\(368\) | 137601. | + | 126509.i | 1.01608 | + | 0.934166i | ||||
\(369\) | 17492.0 | 0.128465 | ||||||||
\(370\) | −51416.4 | − | 33580.3i | −0.375577 | − | 0.245291i | ||||
\(371\) | 6152.54i | 0.0446999i | ||||||||
\(372\) | 6516.16 | + | 14842.5i | 0.0470876 | + | 0.107256i | ||||
\(373\) | −234487. | −1.68539 | −0.842696 | − | 0.538390i | \(-0.819033\pi\) | ||||
−0.842696 | + | 0.538390i | \(0.819033\pi\) | |||||||
\(374\) | 197355. | − | 302180.i | 1.41093 | − | 2.16034i | ||||
\(375\) | − | 7261.84i | − | 0.0516398i | ||||||
\(376\) | 40885.2 | + | 6802.40i | 0.289195 | + | 0.0481157i | ||||
\(377\) | −122790. | −0.863937 | ||||||||
\(378\) | 655.940 | + | 428.397i | 0.00459072 | + | 0.00299822i | ||||
\(379\) | − | 25997.1i | − | 0.180987i | −0.995897 | − | 0.0904933i | \(-0.971156\pi\) | ||
0.995897 | − | 0.0904933i | \(-0.0288444\pi\) | |||||||
\(380\) | −4204.40 | + | 1845.83i | −0.0291164 | + | 0.0127827i | ||||
\(381\) | 133061. | 0.916647 | ||||||||
\(382\) | −75046.0 | + | 114906.i | −0.514281 | + | 0.787441i | ||||
\(383\) | − | 135973.i | − | 0.926948i | −0.886110 | − | 0.463474i | \(-0.846603\pi\) | ||
0.886110 | − | 0.463474i | \(-0.153397\pi\) | |||||||
\(384\) | −67124.0 | + | 52365.3i | −0.455214 | + | 0.355125i | ||||
\(385\) | 2568.94 | 0.0173314 | ||||||||
\(386\) | −111609. | − | 72892.0i | −0.749070 | − | 0.489221i | ||||
\(387\) | − | 40565.8i | − | 0.270856i | ||||||
\(388\) | 34158.8 | + | 77806.6i | 0.226902 | + | 0.516836i | ||||
\(389\) | 104895. | 0.693196 | 0.346598 | − | 0.938014i | \(-0.387337\pi\) | ||||
0.346598 | + | 0.938014i | \(0.387337\pi\) | |||||||
\(390\) | 20161.0 | − | 30869.4i | 0.132551 | − | 0.202955i | ||||
\(391\) | 400279.i | 2.61824i | ||||||||
\(392\) | 25199.1 | − | 151457.i | 0.163989 | − | 0.985639i | ||||
\(393\) | 86073.0 | 0.557291 | ||||||||
\(394\) | −180107. | − | 117628.i | −1.16021 | − | 0.757740i | ||||
\(395\) | 35316.3i | 0.226350i | ||||||||
\(396\) | −65104.2 | + | 28582.2i | −0.415163 | + | 0.182266i | ||||
\(397\) | 4591.59 | 0.0291328 | 0.0145664 | − | 0.999894i | \(-0.495363\pi\) | ||||
0.0145664 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(398\) | −17481.2 | + | 26766.4i | −0.110359 | + | 0.168975i | ||||
\(399\) | − | 186.203i | − | 0.00116961i | ||||||
\(400\) | −21658.0 | + | 23557.0i | −0.135362 | + | 0.147231i | ||||
\(401\) | −108079. | −0.672128 | −0.336064 | − | 0.941839i | \(-0.609096\pi\) | ||||
−0.336064 | + | 0.941839i | \(0.609096\pi\) | |||||||
\(402\) | −51970.5 | − | 33942.2i | −0.321592 | − | 0.210033i | ||||
\(403\) | 30935.1i | 0.190477i | ||||||||
\(404\) | −109616. | − | 249682.i | −0.671600 | − | 1.52976i | ||||
\(405\) | −8150.47 | −0.0496904 | ||||||||
\(406\) | −2363.15 | + | 3618.33i | −0.0143364 | + | 0.0219511i | ||||
\(407\) | 226010.i | 1.36439i | ||||||||
\(408\) | −179839. | − | 29921.2i | −1.08035 | − | 0.179746i | ||||
\(409\) | 94485.1 | 0.564829 | 0.282414 | − | 0.959293i | \(-0.408865\pi\) | ||||
0.282414 | + | 0.959293i | \(0.408865\pi\) | |||||||
\(410\) | −24257.6 | − | 15842.7i | −0.144304 | − | 0.0942459i | ||||
\(411\) | − | 29200.4i | − | 0.172864i | ||||||
\(412\) | 49214.9 | − | 21606.4i | 0.289936 | − | 0.127288i | ||||
\(413\) | 8346.94 | 0.0489358 | ||||||||
\(414\) | 43119.7 | − | 66022.7i | 0.251579 | − | 0.385205i | ||||
\(415\) | − | 146406.i | − | 0.850086i | ||||||
\(416\) | −157467. | + | 40010.0i | −0.909920 | + | 0.231197i | ||||
\(417\) | 174575. | 1.00394 | ||||||||
\(418\) | 14148.7 | + | 9240.61i | 0.0809777 | + | 0.0528869i | ||||
\(419\) | 33591.5i | 0.191338i | 0.995413 | + | 0.0956691i | \(0.0304991\pi\) | ||||
−0.995413 | + | 0.0956691i | \(0.969501\pi\) | |||||||
\(420\) | −521.640 | − | 1188.19i | −0.00295714 | − | 0.00673576i | ||||
\(421\) | −187912. | −1.06021 | −0.530104 | − | 0.847933i | \(-0.677847\pi\) | ||||
−0.530104 | + | 0.847933i | \(0.677847\pi\) | |||||||
\(422\) | 50518.7 | − | 77351.7i | 0.283679 | − | 0.434355i | ||||
\(423\) | − | 17485.6i | − | 0.0977234i | ||||||
\(424\) | −46291.3 | + | 278230.i | −0.257495 | + | 1.54765i | ||||
\(425\) | −68526.8 | −0.379387 | ||||||||
\(426\) | −46518.8 | − | 30381.7i | −0.256336 | − | 0.167414i | ||||
\(427\) | 782.191i | 0.00429000i | ||||||||
\(428\) | 97498.6 | − | 42804.0i | 0.532244 | − | 0.233667i | ||||
\(429\) | −135692. | −0.737293 | ||||||||
\(430\) | −36741.0 | + | 56256.0i | −0.198708 | + | 0.304251i | ||||
\(431\) | 59456.6i | 0.320070i | 0.987111 | + | 0.160035i | \(0.0511608\pi\) | ||||
−0.987111 | + | 0.160035i | \(0.948839\pi\) | |||||||
\(432\) | 26439.7 | + | 24308.2i | 0.141673 | + | 0.130252i | ||||
\(433\) | 199941. | 1.06641 | 0.533206 | − | 0.845985i | \(-0.320987\pi\) | ||||
0.533206 | + | 0.845985i | \(0.320987\pi\) | |||||||
\(434\) | 911.581 | + | 595.358i | 0.00483967 | + | 0.00316081i | ||||
\(435\) | − | 44960.0i | − | 0.237601i | ||||||
\(436\) | 66891.4 | + | 152365.i | 0.351882 | + | 0.801514i | ||||
\(437\) | −18741.9 | −0.0981413 | ||||||||
\(438\) | 30107.8 | − | 46099.4i | 0.156939 | − | 0.240297i | ||||
\(439\) | − | 12289.2i | − | 0.0637670i | −0.999492 | − | 0.0318835i | \(-0.989849\pi\) | ||
0.999492 | − | 0.0318835i | \(-0.0101505\pi\) | |||||||
\(440\) | 116173. | + | 19328.6i | 0.600065 | + | 0.0998376i | ||||
\(441\) | −64774.4 | −0.333063 | ||||||||
\(442\) | −291301. | − | 190250.i | −1.49107 | − | 0.973824i | ||||
\(443\) | − | 294620.i | − | 1.50125i | −0.660726 | − | 0.750627i | \(-0.729751\pi\) | ||
0.660726 | − | 0.750627i | \(-0.270249\pi\) | |||||||
\(444\) | 104534. | − | 45892.8i | 0.530265 | − | 0.232798i | ||||
\(445\) | 79518.7 | 0.401559 | ||||||||
\(446\) | 100744. | − | 154253.i | 0.506463 | − | 0.775469i | ||||
\(447\) | − | 101856.i | − | 0.509769i | ||||||
\(448\) | −1851.52 | + | 5410.17i | −0.00922512 | + | 0.0269560i | ||||
\(449\) | −301030. | −1.49320 | −0.746599 | − | 0.665274i | \(-0.768315\pi\) | ||||
−0.746599 | + | 0.665274i | \(0.768315\pi\) | |||||||
\(450\) | 11302.9 | + | 7381.99i | 0.0558169 | + | 0.0364543i | ||||
\(451\) | 106629.i | 0.524228i | ||||||||
\(452\) | 72194.9 | + | 164445.i | 0.353370 | + | 0.804903i | ||||
\(453\) | 48533.7 | 0.236508 | ||||||||
\(454\) | −108568. | + | 166234.i | −0.526732 | + | 0.806505i | ||||
\(455\) | − | 2476.46i | − | 0.0119621i | ||||||
\(456\) | 1400.98 | − | 8420.44i | 0.00673753 | − | 0.0404954i | ||||
\(457\) | −65670.5 | −0.314440 | −0.157220 | − | 0.987564i | \(-0.550253\pi\) | ||||
−0.157220 | + | 0.987564i | \(0.550253\pi\) | |||||||
\(458\) | 29807.5 | + | 19467.4i | 0.142100 | + | 0.0928063i | ||||
\(459\) | 76912.4i | 0.365065i | ||||||||
\(460\) | −119595. | + | 52504.9i | −0.565195 | + | 0.248133i | ||||
\(461\) | 330337. | 1.55437 | 0.777187 | − | 0.629270i | \(-0.216646\pi\) | ||||
0.777187 | + | 0.629270i | \(0.216646\pi\) | |||||||
\(462\) | −2611.45 | + | 3998.51i | −0.0122348 | + | 0.0187333i | ||||
\(463\) | 212356.i | 0.990609i | 0.868719 | + | 0.495304i | \(0.164943\pi\) | ||||
−0.868719 | + | 0.495304i | \(0.835057\pi\) | |||||||
\(464\) | −134090. | + | 145848.i | −0.622818 | + | 0.677429i | ||||
\(465\) | −11327.0 | −0.0523851 | ||||||||
\(466\) | 44735.6 | + | 29217.0i | 0.206007 | + | 0.134544i | ||||
\(467\) | 275863.i | 1.26491i | 0.774596 | + | 0.632456i | \(0.217953\pi\) | ||||
−0.774596 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(468\) | 27553.2 | + | 62760.4i | 0.125800 | + | 0.286546i | ||||
\(469\) | −4169.26 | −0.0189546 | ||||||||
\(470\) | −15836.9 | + | 24248.7i | −0.0716927 | + | 0.109772i | ||||
\(471\) | − | 181414.i | − | 0.817768i | ||||||
\(472\) | 377465. | + | 62801.8i | 1.69431 | + | 0.281896i | ||||
\(473\) | 247283. | 1.10528 | ||||||||
\(474\) | −54969.1 | − | 35900.6i | −0.244660 | − | 0.159788i | ||||
\(475\) | − | 3208.58i | − | 0.0142208i | ||||||
\(476\) | −11212.4 | + | 4922.49i | −0.0494863 | + | 0.0217256i | ||||
\(477\) | 118992. | 0.522974 | ||||||||
\(478\) | −87931.7 | + | 134636.i | −0.384848 | + | 0.589260i | ||||
\(479\) | − | 129251.i | − | 0.563329i | −0.959513 | − | 0.281664i | \(-0.909114\pi\) | ||
0.959513 | − | 0.281664i | \(-0.0908865\pi\) | |||||||
\(480\) | −14649.8 | − | 57657.0i | −0.0635840 | − | 0.250247i | ||||
\(481\) | 217874. | 0.941704 | ||||||||
\(482\) | 305714. | + | 199663.i | 1.31589 | + | 0.859417i | ||||
\(483\) | − | 5296.58i | − | 0.0227039i | ||||||
\(484\) | −80064.5 | − | 182370.i | −0.341782 | − | 0.778508i | ||||
\(485\) | −59377.8 | −0.252430 | ||||||||
\(486\) | 8285.32 | − | 12686.1i | 0.0350782 | − | 0.0537099i | ||||
\(487\) | − | 296541.i | − | 1.25034i | −0.780490 | − | 0.625168i | \(-0.785031\pi\) | ||
0.780490 | − | 0.625168i | \(-0.214969\pi\) | |||||||
\(488\) | −5885.16 | + | 35372.2i | −0.0247126 | + | 0.148533i | ||||
\(489\) | −258249. | −1.07999 | ||||||||
\(490\) | 89828.0 | + | 58667.1i | 0.374127 | + | 0.244344i | ||||
\(491\) | − | 340038.i | − | 1.41047i | −0.708972 | − | 0.705236i | \(-0.750841\pi\) | ||
0.708972 | − | 0.705236i | \(-0.249159\pi\) | |||||||
\(492\) | 49317.9 | − | 21651.6i | 0.203739 | − | 0.0894458i | ||||
\(493\) | −424268. | −1.74561 | ||||||||
\(494\) | 8907.94 | − | 13639.4i | 0.0365026 | − | 0.0558908i | ||||
\(495\) | − | 49684.0i | − | 0.202771i | ||||||
\(496\) | 36744.1 | + | 33781.9i | 0.149356 | + | 0.137316i | ||||
\(497\) | −3731.91 | −0.0151084 | ||||||||
\(498\) | 227878. | + | 148828.i | 0.918850 | + | 0.600105i | ||||
\(499\) | − | 146808.i | − | 0.589587i | −0.955561 | − | 0.294794i | \(-0.904749\pi\) | ||
0.955561 | − | 0.294794i | \(-0.0952509\pi\) | |||||||
\(500\) | −8988.72 | − | 20474.4i | −0.0359549 | − | 0.0818978i | ||||
\(501\) | 268323. | 1.06901 | ||||||||
\(502\) | 186569. | − | 285665.i | 0.740342 | − | 1.13357i | ||||
\(503\) | 410402.i | 1.62208i | 0.584989 | + | 0.811041i | \(0.301099\pi\) | ||||
−0.584989 | + | 0.811041i | \(0.698901\pi\) | |||||||
\(504\) | 2379.66 | + | 395.924i | 0.00936817 | + | 0.00155866i | ||||
\(505\) | 190544. | 0.747158 | ||||||||
\(506\) | 402464. | + | 262851.i | 1.57191 | + | 1.02662i | ||||
\(507\) | − | 17600.2i | − | 0.0684702i | ||||||
\(508\) | 375161. | − | 164704.i | 1.45375 | − | 0.638228i | ||||
\(509\) | −170171. | −0.656825 | −0.328413 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328413 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(510\) | 69660.6 | − | 106661.i | 0.267822 | − | 0.410076i | ||||
\(511\) | − | 3698.26i | − | 0.0141630i | ||||||
\(512\) | −124435. | + | 230728.i | −0.474682 | + | 0.880157i | ||||
\(513\) | −3601.21 | −0.0136840 | ||||||||
\(514\) | −78399.3 | − | 51202.9i | −0.296747 | − | 0.193807i | ||||
\(515\) | 37558.2i | 0.141609i | ||||||||
\(516\) | −50212.4 | − | 114373.i | −0.188587 | − | 0.429562i | ||||
\(517\) | 106589. | 0.398779 | ||||||||
\(518\) | 4193.06 | − | 6420.19i | 0.0156268 | − | 0.0239270i | ||||
\(519\) | 253698.i | 0.941851i | ||||||||
\(520\) | 18632.7 | − | 111990.i | 0.0689080 | − | 0.414165i | ||||
\(521\) | 64423.8 | 0.237340 | 0.118670 | − | 0.992934i | \(-0.462137\pi\) | ||||
0.118670 | + | 0.992934i | \(0.462137\pi\) | |||||||
\(522\) | 69979.5 | + | 45703.9i | 0.256821 | + | 0.167731i | ||||
\(523\) | − | 108085.i | − | 0.395150i | −0.980288 | − | 0.197575i | \(-0.936693\pi\) | ||
0.980288 | − | 0.197575i | \(-0.0633066\pi\) | |||||||
\(524\) | 242679. | − | 106541.i | 0.883832 | − | 0.388021i | ||||
\(525\) | 906.762 | 0.00328984 | ||||||||
\(526\) | −194504. | + | 297814.i | −0.703001 | + | 1.07640i | ||||
\(527\) | 106888.i | 0.384863i | ||||||||
\(528\) | −148179. | + | 161172.i | −0.531520 | + | 0.578126i | ||||
\(529\) | −253278. | −0.905079 | ||||||||
\(530\) | −165016. | − | 107773.i | −0.587454 | − | 0.383669i | ||||
\(531\) | − | 161432.i | − | 0.572533i | ||||||
\(532\) | −230.482 | − | 524.990i | −0.000814354 | − | 0.00185493i | ||||
\(533\) | 102790. | 0.361823 | ||||||||
\(534\) | −80834.4 | + | 123769.i | −0.283474 | + | 0.434041i | ||||
\(535\) | 74405.7i | 0.259955i | ||||||||
\(536\) | −188542. | − | 31369.3i | −0.656265 | − | 0.109188i | ||||
\(537\) | −265321. | −0.920075 | ||||||||
\(538\) | 262510. | + | 171446.i | 0.906945 | + | 0.592330i | ||||
\(539\) | − | 394855.i | − | 1.35913i | ||||||
\(540\) | −22979.9 | + | 10088.7i | −0.0788062 | + | 0.0345976i | ||||
\(541\) | −343195. | −1.17259 | −0.586295 | − | 0.810098i | \(-0.699414\pi\) | ||||
−0.586295 | + | 0.810098i | \(0.699414\pi\) | |||||||
\(542\) | −174590. | + | 267323.i | −0.594321 | + | 0.909993i | ||||
\(543\) | 87233.0i | 0.295856i | ||||||||
\(544\) | −544084. | + | 138243.i | −1.83852 | + | 0.467139i | ||||
\(545\) | −116277. | −0.391471 | ||||||||
\(546\) | 3854.56 | + | 2517.43i | 0.0129297 | + | 0.00844447i | ||||
\(547\) | − | 310047.i | − | 1.03622i | −0.855313 | − | 0.518111i | \(-0.826635\pi\) | ||
0.855313 | − | 0.518111i | \(-0.173365\pi\) | |||||||
\(548\) | −36144.3 | − | 82329.1i | −0.120359 | − | 0.274153i | ||||
\(549\) | 15127.8 | 0.0501916 | ||||||||
\(550\) | −44999.5 | + | 68901.0i | −0.148759 | + | 0.227772i | ||||
\(551\) | − | 19865.2i | − | 0.0654318i | ||||||
\(552\) | 39851.1 | − | 239522.i | 0.130786 | − | 0.786080i | ||||
\(553\) | −4409.82 | −0.0144202 | ||||||||
\(554\) | 46844.7 | + | 30594.5i | 0.152630 | + | 0.0996836i | ||||
\(555\) | 79775.0i | 0.258989i | ||||||||
\(556\) | 492206. | − | 216089.i | 1.59220 | − | 0.699010i | ||||
\(557\) | 1815.28 | 0.00585104 | 0.00292552 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292552 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(558\) | 11514.4 | − | 17630.2i | 0.0369805 | − | 0.0566226i | ||||
\(559\) | − | 238381.i | − | 0.762865i | ||||||
\(560\) | −2941.48 | − | 2704.36i | −0.00937973 | − | 0.00862358i | ||||
\(561\) | −468846. | −1.48972 | ||||||||
\(562\) | 48399.8 | + | 31610.1i | 0.153240 | + | 0.100081i | ||||
\(563\) | − | 240858.i | − | 0.759878i | −0.925012 | − | 0.379939i | \(-0.875945\pi\) | ||
0.925012 | − | 0.379939i | \(-0.124055\pi\) | |||||||
\(564\) | −21643.7 | − | 49299.7i | −0.0680413 | − | 0.154984i | ||||
\(565\) | −125496. | −0.393126 | ||||||||
\(566\) | −256289. | + | 392417.i | −0.800014 | + | 1.22494i | ||||
\(567\) | − | 1017.72i | − | 0.00316565i | ||||||
\(568\) | −168764. | − | 28078.6i | −0.523099 | − | 0.0870321i | ||||
\(569\) | −240114. | −0.741639 | −0.370820 | − | 0.928705i | \(-0.620923\pi\) | ||||
−0.370820 | + | 0.928705i | \(0.620923\pi\) | |||||||
\(570\) | 4994.09 | + | 3261.66i | 0.0153712 | + | 0.0100390i | ||||
\(571\) | − | 301943.i | − | 0.926090i | −0.886335 | − | 0.463045i | \(-0.846757\pi\) | ||
0.886335 | − | 0.463045i | \(-0.153243\pi\) | |||||||
\(572\) | −382578. | + | 167960.i | −1.16931 | + | 0.513350i | ||||
\(573\) | 178283. | 0.543000 | ||||||||
\(574\) | 1978.23 | − | 3028.96i | 0.00600417 | − | 0.00919327i | ||||
\(575\) | − | 91268.8i | − | 0.276049i | ||||||
\(576\) | 104634. | + | 35808.9i | 0.315376 | + | 0.107931i | ||||
\(577\) | −67660.1 | −0.203227 | −0.101613 | − | 0.994824i | \(-0.532400\pi\) | ||||
−0.101613 | + | 0.994824i | \(0.532400\pi\) | |||||||
\(578\) | −726797. | − | 474675.i | −2.17549 | − | 1.42082i | ||||
\(579\) | 173166.i | 0.516541i | ||||||||
\(580\) | −55651.6 | − | 126763.i | −0.165433 | − | 0.376822i | ||||
\(581\) | 18281.2 | 0.0541568 | ||||||||
\(582\) | 60360.2 | − | 92420.5i | 0.178199 | − | 0.272849i | ||||
\(583\) | 725357.i | 2.13410i | ||||||||
\(584\) | 27825.5 | − | 167243.i | 0.0815863 | − | 0.490367i | ||||
\(585\) | −47895.4 | −0.139953 | ||||||||
\(586\) | 97335.7 | + | 63570.4i | 0.283450 | + | 0.185123i | ||||
\(587\) | − | 204755.i | − | 0.594235i | −0.954841 | − | 0.297117i | \(-0.903975\pi\) | ||
0.954841 | − | 0.297117i | \(-0.0960253\pi\) | |||||||
\(588\) | −182628. | + | 80177.9i | −0.528219 | + | 0.231899i | ||||
\(589\) | −5004.72 | −0.0144261 | ||||||||
\(590\) | −146211. | + | 223871.i | −0.420027 | + | 0.643123i | ||||
\(591\) | 279444.i | 0.800054i | ||||||||
\(592\) | 237923. | − | 258785.i | 0.678881 | − | 0.738408i | ||||
\(593\) | 361586. | 1.02826 | 0.514129 | − | 0.857713i | \(-0.328115\pi\) | ||||
0.514129 | + | 0.857713i | \(0.328115\pi\) | |||||||
\(594\) | 77332.3 | + | 50506.1i | 0.219174 | + | 0.143143i | ||||
\(595\) | − | 8556.71i | − | 0.0241698i | ||||||
\(596\) | −126078. | − | 287180.i | −0.354934 | − | 0.808465i | ||||
\(597\) | 41529.2 | 0.116521 | ||||||||
\(598\) | 253388. | − | 387975.i | 0.708573 | − | 1.08493i | ||||
\(599\) | − | 314411.i | − | 0.876284i | −0.898906 | − | 0.438142i | \(-0.855637\pi\) | ||
0.898906 | − | 0.438142i | \(-0.144363\pi\) | |||||||
\(600\) | 41005.5 | + | 6822.42i | 0.113904 | + | 0.0189512i | ||||
\(601\) | 4980.63 | 0.0137891 | 0.00689454 | − | 0.999976i | \(-0.497805\pi\) | ||||
0.00689454 | + | 0.999976i | \(0.497805\pi\) | |||||||
\(602\) | −7024.49 | − | 4587.73i | −0.0193830 | − | 0.0126592i | ||||
\(603\) | 80634.7i | 0.221762i | ||||||||
\(604\) | 136838. | − | 60075.1i | 0.375089 | − | 0.164672i | ||||
\(605\) | 139175. | 0.380234 | ||||||||
\(606\) | −193697. | + | 296578.i | −0.527445 | + | 0.807596i | ||||
\(607\) | 224016.i | 0.607998i | 0.952672 | + | 0.303999i | \(0.0983219\pi\) | ||||
−0.952672 | + | 0.303999i | \(0.901678\pi\) | |||||||
\(608\) | −6472.85 | − | 25475.2i | −0.0175101 | − | 0.0689145i | ||||
\(609\) | 5614.01 | 0.0151370 | ||||||||
\(610\) | −20979.0 | − | 13701.5i | −0.0563799 | − | 0.0368220i | ||||
\(611\) | − | 102752.i | − | 0.275238i | ||||||
\(612\) | 95202.3 | + | 216851.i | 0.254182 | + | 0.578973i | ||||
\(613\) | 606099. | 1.61296 | 0.806478 | − | 0.591264i | \(-0.201371\pi\) | ||||
0.806478 | + | 0.591264i | \(0.201371\pi\) | |||||||
\(614\) | 76684.4 | − | 117415.i | 0.203409 | − | 0.311449i | ||||
\(615\) | 37636.8i | 0.0995089i | ||||||||
\(616\) | −2413.49 | + | 14506.1i | −0.00636040 | + | 0.0382286i | ||||
\(617\) | 223682. | 0.587571 | 0.293786 | − | 0.955871i | \(-0.405085\pi\) | ||||
0.293786 | + | 0.955871i | \(0.405085\pi\) | |||||||
\(618\) | −58458.6 | − | 38179.6i | −0.153064 | − | 0.0999665i | ||||
\(619\) | 218632.i | 0.570602i | 0.958438 | + | 0.285301i | \(0.0920936\pi\) | ||||
−0.958438 | + | 0.285301i | \(0.907906\pi\) | |||||||
\(620\) | −31935.9 | + | 14020.6i | −0.0830799 | + | 0.0364739i | ||||
\(621\) | −102437. | −0.265628 | ||||||||
\(622\) | 114073. | − | 174663.i | 0.294851 | − | 0.451461i | ||||
\(623\) | 9929.23i | 0.0255823i | ||||||||
\(624\) | 155370. | + | 142845.i | 0.399023 | + | 0.366855i | ||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 402175. | + | 262662.i | 1.02628 | + | 0.670269i | ||||
\(627\) | − | 21952.4i | − | 0.0558403i | ||||||
\(628\) | −224555. | − | 511490.i | −0.569382 | − | 1.29693i | ||||
\(629\) | 752801. | 1.90274 | ||||||||
\(630\) | −921.764 | + | 1411.36i | −0.00232241 | + | 0.00355595i | ||||
\(631\) | 57752.6i | 0.145048i | 0.997367 | + | 0.0725242i | \(0.0231054\pi\) | ||||
−0.997367 | + | 0.0725242i | \(0.976895\pi\) | |||||||
\(632\) | −199421. | − | 33179.2i | −0.499271 | − | 0.0830677i | ||||
\(633\) | −120015. | −0.299521 | ||||||||
\(634\) | −53982.1 | − | 35255.9i | −0.134298 | − | 0.0877110i | ||||
\(635\) | 286302.i | 0.710031i | ||||||||
\(636\) | 335492. | − | 147288.i | 0.829408 | − | 0.364128i | ||||
\(637\) | −380640. | −0.938070 | ||||||||
\(638\) | −278604. | + | 426585.i | −0.684458 | + | 1.04801i | ||||
\(639\) | 72176.1i | 0.176763i | ||||||||
\(640\) | −112672. | − | 144428.i | −0.275079 | − | 0.352607i | ||||
\(641\) | −239533. | −0.582974 | −0.291487 | − | 0.956575i | \(-0.594150\pi\) | ||||
−0.291487 | + | 0.956575i | \(0.594150\pi\) | |||||||
\(642\) | −115811. | − | 75636.8i | −0.280983 | − | 0.183511i | ||||
\(643\) | 131015.i | 0.316884i | 0.987368 | + | 0.158442i | \(0.0506471\pi\) | ||||
−0.987368 | + | 0.158442i | \(0.949353\pi\) | |||||||
\(644\) | −6556.11 | − | 14933.5i | −0.0158079 | − | 0.0360071i | ||||
\(645\) | 87283.7 | 0.209804 | ||||||||
\(646\) | 30778.9 | − | 47127.0i | 0.0737544 | − | 0.112929i | ||||
\(647\) | 227917.i | 0.544464i | 0.962232 | + | 0.272232i | \(0.0877618\pi\) | ||||
−0.962232 | + | 0.272232i | \(0.912238\pi\) | |||||||
\(648\) | 7657.27 | − | 46023.3i | 0.0182358 | − | 0.109604i | ||||
\(649\) | 984066. | 2.33633 | ||||||||
\(650\) | 66420.5 | + | 43379.5i | 0.157208 | + | 0.102673i | ||||
\(651\) | − | 1414.36i | − | 0.00333732i | ||||||
\(652\) | −728121. | + | 319661.i | −1.71281 | + | 0.751960i | ||||
\(653\) | 334292. | 0.783970 | 0.391985 | − | 0.919972i | \(-0.371789\pi\) | ||||
0.391985 | + | 0.919972i | \(0.371789\pi\) | |||||||
\(654\) | 118200. | − | 180982.i | 0.276352 | − | 0.423137i | ||||
\(655\) | 185200.i | 0.431676i | ||||||||
\(656\) | 112249. | − | 122092.i | 0.260841 | − | 0.283712i | ||||
\(657\) | −71525.4 | −0.165703 | ||||||||
\(658\) | −3027.85 | − | 1977.50i | −0.00699330 | − | 0.00456736i | ||||
\(659\) | 820031.i | 1.88825i | 0.329588 | + | 0.944125i | \(0.393090\pi\) | ||||
−0.329588 | + | 0.944125i | \(0.606910\pi\) | |||||||
\(660\) | −61499.0 | − | 140082.i | −0.141182 | − | 0.321584i | ||||
\(661\) | −368205. | −0.842727 | −0.421363 | − | 0.906892i | \(-0.638448\pi\) | ||||
−0.421363 | + | 0.906892i | \(0.638448\pi\) | |||||||
\(662\) | −16795.8 | + | 25716.9i | −0.0383253 | + | 0.0586816i | ||||
\(663\) | 451967.i | 1.02821i | ||||||||
\(664\) | 826713. | + | 137547.i | 1.87508 | + | 0.311971i | ||||
\(665\) | 400.644 | 0.000905973 | ||||||||
\(666\) | −124168. | − | 81094.9i | −0.279938 | − | 0.182829i | ||||
\(667\) | − | 565070.i | − | 1.27014i | ||||||
\(668\) | 756524. | − | 332130.i | 1.69539 | − | 0.744313i | ||||
\(669\) | −239331. | −0.534745 | ||||||||
\(670\) | 73032.0 | − | 111823.i | 0.162691 | − | 0.249104i | ||||
\(671\) | 92216.7i | 0.204816i | ||||||||
\(672\) | 7199.43 | − | 1829.26i | 0.0159426 | − | 0.00405077i | ||||
\(673\) | −272051. | −0.600649 | −0.300325 | − | 0.953837i | \(-0.597095\pi\) | ||||
−0.300325 | + | 0.953837i | \(0.597095\pi\) | |||||||
\(674\) | −228181. | − | 149026.i | −0.502297 | − | 0.328053i | ||||
\(675\) | − | 17537.0i | − | 0.0384900i | ||||||
\(676\) | −21785.6 | − | 49623.0i | −0.0476733 | − | 0.108590i | ||||
\(677\) | −348582. | −0.760549 | −0.380275 | − | 0.924874i | \(-0.624171\pi\) | ||||
−0.380275 | + | 0.924874i | \(0.624171\pi\) | |||||||
\(678\) | 127572. | − | 195332.i | 0.277521 | − | 0.424926i | ||||
\(679\) | − | 7414.30i | − | 0.0160817i | ||||||
\(680\) | 64380.1 | − | 386951.i | 0.139230 | − | 0.836832i | ||||
\(681\) | 257919. | 0.556147 | ||||||||
\(682\) | 107471. | + | 70190.0i | 0.231059 | + | 0.150906i | ||||
\(683\) | − | 146496.i | − | 0.314040i | −0.987595 | − | 0.157020i | \(-0.949811\pi\) | ||
0.987595 | − | 0.157020i | \(-0.0501887\pi\) | |||||||
\(684\) | −10153.4 | + | 4457.58i | −0.0217021 | + | 0.00952768i | ||||
\(685\) | 62829.2 | 0.133900 | ||||||||
\(686\) | −14657.1 | + | 22442.1i | −0.0311458 | + | 0.0476888i | ||||
\(687\) | − | 46247.7i | − | 0.0979889i | ||||||
\(688\) | −283143. | − | 260318.i | −0.598177 | − | 0.549955i | ||||
\(689\) | 699243. | 1.47296 | ||||||||
\(690\) | 142058. | + | 92778.9i | 0.298379 | + | 0.194873i | ||||
\(691\) | − | 79772.8i | − | 0.167070i | −0.996505 | − | 0.0835350i | \(-0.973379\pi\) | ||
0.996505 | − | 0.0835350i | \(-0.0266211\pi\) | |||||||
\(692\) | 314028. | + | 715290.i | 0.655776 | + | 1.49372i | ||||
\(693\) | 6203.88 | 0.0129180 | ||||||||
\(694\) | −73327.0 | + | 112275.i | −0.152246 | + | 0.233111i | ||||
\(695\) | 375626.i | 0.777652i | ||||||||
\(696\) | 253876. | + | 42239.4i | 0.524088 | + | 0.0871966i | ||||
\(697\) | 355161. | 0.731072 | ||||||||
\(698\) | −597031. | − | 389924.i | −1.22542 | − | 0.800329i | ||||
\(699\) | − | 69409.3i | − | 0.142057i | ||||||
\(700\) | 2556.57 | − | 1122.39i | 0.00521750 | − | 0.00229059i | ||||
\(701\) | −1418.50 | −0.00288665 | −0.00144332 | − | 0.999999i | \(-0.500459\pi\) | ||||
−0.00144332 | + | 0.999999i | \(0.500459\pi\) | |||||||
\(702\) | 48687.8 | − | 74548.3i | 0.0987975 | − | 0.151274i | ||||
\(703\) | 35247.8i | 0.0713217i | ||||||||
\(704\) | −218286. | + | 637835.i | −0.440433 | + | 1.28695i | ||||
\(705\) | 37622.9 | 0.0756963 | ||||||||
\(706\) | 271112. | + | 177064.i | 0.543925 | + | 0.355240i | ||||
\(707\) | 23792.6i | 0.0475995i | ||||||||
\(708\) | −199821. | − | 455150.i | −0.398634 | − | 0.908005i | ||||
\(709\) | −794794. | −1.58111 | −0.790555 | − | 0.612391i | \(-0.790208\pi\) | ||||
−0.790555 | + | 0.612391i | \(0.790208\pi\) | |||||||
\(710\) | 65370.9 | − | 100093.i | 0.129679 | − | 0.198557i | ||||
\(711\) | 85287.1i | 0.168711i | ||||||||
\(712\) | −74706.9 | + | 449019.i | −0.147367 | + | 0.885737i | ||||
\(713\) | −142360. | −0.280034 | ||||||||
\(714\) | 13318.4 | + | 8698.28i | 0.0261249 | + | 0.0170623i | ||||
\(715\) | − | 291963.i | − | 0.571105i | ||||||
\(716\) | −748061. | + | 328415.i | −1.45919 | + | 0.640615i | ||||
\(717\) | 208895. | 0.406339 | ||||||||
\(718\) | 209860. | − | 321327.i | 0.407081 | − | 0.623301i | ||||
\(719\) | − | 713193.i | − | 1.37959i | −0.724006 | − | 0.689794i | \(-0.757701\pi\) | ||
0.724006 | − | 0.689794i | \(-0.242299\pi\) | |||||||
\(720\) | −52303.0 | + | 56889.1i | −0.100893 | + | 0.109740i | ||||
\(721\) | −4689.76 | −0.00902153 | ||||||||
\(722\) | −434240. | − | 283604.i | −0.833021 | − | 0.544050i | ||||
\(723\) | − | 474329.i | − | 0.907410i | ||||||
\(724\) | 107977. | + | 245949.i | 0.205994 | + | 0.469212i | ||||
\(725\) | 96738.6 | 0.184045 | ||||||||
\(726\) | −141478. | + | 216624.i | −0.268420 | + | 0.410991i | ||||
\(727\) | 886306.i | 1.67693i | 0.544955 | + | 0.838465i | \(0.316547\pi\) | ||||
−0.544955 | + | 0.838465i | \(0.683453\pi\) | |||||||
\(728\) | 13983.8 | + | 2326.60i | 0.0263854 | + | 0.00438995i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 99190.2 | + | 64781.6i | 0.186133 | + | 0.121564i | ||||
\(731\) | − | 823658.i | − | 1.54139i | ||||||
\(732\) | 42652.1 | − | 18725.2i | 0.0796010 | − | 0.0349466i | ||||
\(733\) | −267035. | −0.497005 | −0.248502 | − | 0.968631i | \(-0.579938\pi\) | ||||
−0.248502 | + | 0.968631i | \(0.579938\pi\) | |||||||
\(734\) | 80297.2 | − | 122947.i | 0.149042 | − | 0.228205i | ||||
\(735\) | − | 139372.i | − | 0.257989i | ||||||
\(736\) | −184122. | − | 724648.i | −0.339899 | − | 1.33774i | ||||
\(737\) | −491537. | −0.904943 | ||||||||
\(738\) | −58580.9 | − | 38259.5i | −0.107558 | − | 0.0702468i | ||||
\(739\) | 706999.i | 1.29458i | 0.762242 | + | 0.647292i | \(0.224099\pi\) | ||||
−0.762242 | + | 0.647292i | \(0.775901\pi\) | |||||||
\(740\) | 98745.6 | + | 224922.i | 0.180324 | + | 0.410741i | ||||
\(741\) | −21162.1 | −0.0385410 | ||||||||
\(742\) | 13457.2 | − | 20605.0i | 0.0244426 | − | 0.0374252i | ||||
\(743\) | 990710.i | 1.79461i | 0.441416 | + | 0.897303i | \(0.354476\pi\) | ||||
−0.441416 | + | 0.897303i | \(0.645524\pi\) | |||||||
\(744\) | 10641.6 | − | 63960.2i | 0.0192247 | − | 0.115548i | ||||
\(745\) | 219160. | 0.394865 | ||||||||
\(746\) | 785300. | + | 512883.i | 1.41110 | + | 0.921596i | ||||
\(747\) | − | 353564.i | − | 0.633617i | ||||||
\(748\) | −1.32189e6 | + | 580339.i | −2.36261 | + | 1.03724i | ||||
\(749\) | −9290.78 | −0.0165611 | ||||||||
\(750\) | −15883.5 | + | 24320.0i | −0.0282374 | + | 0.0432356i | ||||
\(751\) | − | 629696.i | − | 1.11648i | −0.829679 | − | 0.558240i | \(-0.811477\pi\) | ||
0.829679 | − | 0.558240i | \(-0.188523\pi\) | |||||||
\(752\) | −122047. | − | 112208.i | −0.215819 | − | 0.198421i | ||||
\(753\) | −443222. | −0.781685 | ||||||||
\(754\) | 411227. | + | 268574.i | 0.723334 | + | 0.472413i | ||||
\(755\) | 104428.i | 0.183199i | ||||||||
\(756\) | −1259.74 | − | 2869.42i | −0.00220413 | − | 0.00502054i | ||||
\(757\) | −14822.4 | −0.0258658 | −0.0129329 | − | 0.999916i | \(-0.504117\pi\) | ||||
−0.0129329 | + | 0.999916i | \(0.504117\pi\) | |||||||
\(758\) | −56862.4 | + | 87064.7i | −0.0989661 | + | 0.151532i | ||||
\(759\) | − | 624442.i | − | 1.08395i | ||||||
\(760\) | 18117.9 | + | 3014.42i | 0.0313676 | + | 0.00521887i | ||||
\(761\) | −458988. | −0.792559 | −0.396280 | − | 0.918130i | \(-0.629699\pi\) | ||||
−0.396280 | + | 0.918130i | \(0.629699\pi\) | |||||||
\(762\) | −445625. | − | 291039.i | −0.767466 | − | 0.501236i | ||||
\(763\) | − | 14519.1i | − | 0.0249396i | ||||||
\(764\) | 502660. | − | 220679.i | 0.861168 | − | 0.378071i | ||||
\(765\) | −165489. | −0.282779 | ||||||||
\(766\) | −297408. | + | 455376.i | −0.506869 | + | 0.776091i | ||||
\(767\) | − | 948638.i | − | 1.61254i | ||||||
\(768\) | 339336. | − | 28554.9i | 0.575317 | − | 0.0484125i | ||||
\(769\) | 179362. | 0.303304 | 0.151652 | − | 0.988434i | \(-0.451541\pi\) | ||||
0.151652 | + | 0.988434i | \(0.451541\pi\) | |||||||
\(770\) | −8603.43 | − | 5618.94i | −0.0145108 | − | 0.00947704i | ||||
\(771\) | 121640.i | 0.204629i | ||||||||
\(772\) | 214345. | + | 488233.i | 0.359649 | + | 0.819205i | ||||
\(773\) | −129744. | −0.217134 | −0.108567 | − | 0.994089i | \(-0.534626\pi\) | ||||
−0.108567 | + | 0.994089i | \(0.534626\pi\) | |||||||
\(774\) | −88727.9 | + | 135856.i | −0.148108 | + | 0.226775i | ||||
\(775\) | − | 24371.8i | − | 0.0405773i | ||||||
\(776\) | 55784.8 | − | 335289.i | 0.0926386 | − | 0.556796i | ||||
\(777\) | −9961.23 | −0.0164995 | ||||||||
\(778\) | −351295. | − | 229433.i | −0.580381 | − | 0.379050i | ||||
\(779\) | 16629.4i | 0.0274033i | ||||||||
\(780\) | −135039. | + | 59285.0i | −0.221957 | + | 0.0974441i | ||||
\(781\) | −439975. | −0.721317 | ||||||||
\(782\) | 875513. | − | 1.34054e6i | 1.43169 | − | 2.19213i | ||||
\(783\) | − | 108576.i | − | 0.177097i | ||||||
\(784\) | −415668. | + | 452116.i | −0.676262 | + | 0.735559i | ||||
\(785\) | 390342. | 0.633440 | ||||||||
\(786\) | −288260. | − | 188264.i | −0.466594 | − | 0.304735i | ||||
\(787\) | 293979.i | 0.474643i | 0.971431 | + | 0.237322i | \(0.0762695\pi\) | ||||
−0.971431 | + | 0.237322i | \(0.923730\pi\) | |||||||
\(788\) | 345896. | + | 787879.i | 0.557049 | + | 1.26884i | ||||
\(789\) | 462072. | 0.742259 | ||||||||
\(790\) | 77245.8 | − | 118275.i | 0.123771 | − | 0.189512i | ||||
\(791\) | − | 15670.2i | − | 0.0250450i | ||||||
\(792\) | 280552. | + | 46677.6i | 0.447262 | + | 0.0744146i | ||||
\(793\) | 88896.9 | 0.141364 | ||||||||
\(794\) | −15377.3 | − | 10043.0i | −0.0243915 | − | 0.0159302i | ||||
\(795\) | 256030.i | 0.405094i | ||||||||
\(796\) | 117090. | − | 51405.0i | 0.184796 | − | 0.0811295i | ||||
\(797\) | 281322. | 0.442881 | 0.221441 | − | 0.975174i | \(-0.428924\pi\) | ||||
0.221441 | + | 0.975174i | \(0.428924\pi\) | |||||||
\(798\) | −407.273 | + | 623.595i | −0.000639558 | + | 0.000979258i | ||||
\(799\) | − | 355031.i | − | 0.556125i | ||||||
\(800\) | 124058. | − | 31521.2i | 0.193841 | − | 0.0492519i | ||||
\(801\) | 192034. | 0.299304 | ||||||||
\(802\) | 361958. | + | 236396.i | 0.562742 | + | 0.367529i | ||||
\(803\) | − | 436008.i | − | 0.676182i | ||||||
\(804\) | 99809.8 | + | 227346.i | 0.154405 | + | 0.351702i | ||||
\(805\) | 11396.4 | 0.0175864 | ||||||||
\(806\) | 67663.1 | − | 103602.i | 0.104155 | − | 0.159477i | ||||
\(807\) | − | 407296.i | − | 0.625407i | ||||||
\(808\) | −179014. | + | 1.07595e6i | −0.274198 | + | 1.64804i | ||||
\(809\) | −1.00560e6 | −1.53648 | −0.768239 | − | 0.640163i | \(-0.778867\pi\) | ||||
−0.768239 | + | 0.640163i | \(0.778867\pi\) | |||||||
\(810\) | 27296.0 | + | 17827.2i | 0.0416035 | + | 0.0271714i | ||||
\(811\) | − | 669583.i | − | 1.01804i | −0.860756 | − | 0.509018i | \(-0.830009\pi\) | ||
0.860756 | − | 0.509018i | \(-0.169991\pi\) | |||||||
\(812\) | 15828.4 | − | 6949.03i | 0.0240064 | − | 0.0105393i | ||||
\(813\) | 414764. | 0.627509 | ||||||||
\(814\) | 494342. | − | 756911.i | 0.746069 | − | 1.14234i | ||||
\(815\) | − | 555663.i | − | 0.836559i | ||||||
\(816\) | 536837. | + | 493560.i | 0.806236 | + | 0.741241i | ||||
\(817\) | 38565.5 | 0.0577770 | ||||||||
\(818\) | −316432. | − | 206663.i | −0.472905 | − | 0.308856i | ||||
\(819\) | − | 5980.53i | − | 0.00891604i | ||||||
\(820\) | 46586.9 | + | 106115.i | 0.0692844 | + | 0.157816i | ||||
\(821\) | −706530. | −1.04820 | −0.524100 | − | 0.851657i | \(-0.675598\pi\) | ||||
−0.524100 | + | 0.851657i | \(0.675598\pi\) | |||||||
\(822\) | −63868.7 | + | 97792.5i | −0.0945246 | + | 0.144731i | ||||
\(823\) | − | 925866.i | − | 1.36694i | −0.729980 | − | 0.683468i | \(-0.760471\pi\) | ||
0.729980 | − | 0.683468i | \(-0.239529\pi\) | |||||||
\(824\) | −212080. | − | 35285.5i | −0.312353 | − | 0.0519687i | ||||
\(825\) | 106903. | 0.157066 | ||||||||
\(826\) | −27954.0 | − | 18256.9i | −0.0409717 | − | 0.0267588i | ||||
\(827\) | − | 639584.i | − | 0.935162i | −0.883950 | − | 0.467581i | \(-0.845126\pi\) | ||
0.883950 | − | 0.467581i | \(-0.154874\pi\) | |||||||
\(828\) | −288817. | + | 126797.i | −0.421272 | + | 0.184947i | ||||
\(829\) | −458584. | −0.667283 | −0.333642 | − | 0.942700i | \(-0.608278\pi\) | ||||
−0.333642 | + | 0.942700i | \(0.608278\pi\) | |||||||
\(830\) | −320228. | + | 490316.i | −0.464840 | + | 0.711738i | ||||
\(831\) | − | 72681.7i | − | 0.105250i | ||||||
\(832\) | 614872. | + | 210427.i | 0.888256 | + | 0.303987i | ||||
\(833\) | −1.31519e6 | −1.89540 | ||||||||
\(834\) | −584654. | − | 381840.i | −0.840557 | − | 0.548971i | ||||
\(835\) | 577338.i | 0.828052i | ||||||||
\(836\) | −27172.8 | − | 61893.9i | −0.0388795 | − | 0.0885595i | ||||
\(837\) | −27354.1 | −0.0390456 | ||||||||
\(838\) | 73473.3 | − | 112499.i | 0.104626 | − | 0.160199i | ||||
\(839\) | 734005.i | 1.04274i | 0.853331 | + | 0.521369i | \(0.174579\pi\) | ||||
−0.853331 | + | 0.521369i | \(0.825421\pi\) | |||||||
\(840\) | −851.892 | + | 5120.22i | −0.00120733 | + | 0.00725655i | ||||
\(841\) | −108346. | −0.153186 | ||||||||
\(842\) | 629321. | + | 411013.i | 0.887663 | + | 0.579737i | ||||
\(843\) | − | 75094.5i | − | 0.105670i | ||||||
\(844\) | −338376. | + | 148554.i | −0.475023 | + | 0.208545i | ||||
\(845\) | 37869.6 | 0.0530368 | ||||||||
\(846\) | −38245.4 | + | 58559.4i | −0.0534366 | + | 0.0818193i | ||||
\(847\) | 17378.3i | 0.0242237i | ||||||||
\(848\) | 763591. | − | 830546.i | 1.06186 | − | 1.15497i | ||||
\(849\) | 608853. | 0.844690 | ||||||||
\(850\) | 229497. | + | 149886.i | 0.317643 | + | 0.207454i | ||||
\(851\) | 1.00263e6i | 1.38447i | ||||||||
\(852\) | 89339.8 | + | 203497.i | 0.123074 | + | 0.280336i | ||||
\(853\) | −144945. | −0.199208 | −0.0996039 | − | 0.995027i | \(-0.531758\pi\) | ||||
−0.0996039 | + | 0.995027i | \(0.531758\pi\) | |||||||
\(854\) | 1710.85 | − | 2619.57i | 0.00234583 | − | 0.00359182i | ||||
\(855\) | − | 7748.56i | − | 0.0105996i | ||||||
\(856\) | −420148. | − | 69903.3i | −0.573396 | − | 0.0954004i | ||||
\(857\) | 749831. | 1.02094 | 0.510472 | − | 0.859894i | \(-0.329471\pi\) | ||||
0.510472 | + | 0.859894i | \(0.329471\pi\) | |||||||
\(858\) | 454435. | + | 296794.i | 0.617302 | + | 0.403163i | ||||
\(859\) | 991769.i | 1.34408i | 0.740516 | + | 0.672038i | \(0.234581\pi\) | ||||
−0.740516 | + | 0.672038i | \(0.765419\pi\) | |||||||
\(860\) | 246093. | − | 108040.i | 0.332737 | − | 0.146079i | ||||
\(861\) | −4699.57 | −0.00633946 | ||||||||
\(862\) | 130047. | − | 199121.i | 0.175019 | − | 0.267980i | ||||
\(863\) | 254191.i | 0.341301i | 0.985332 | + | 0.170651i | \(0.0545870\pi\) | ||||
−0.985332 | + | 0.170651i | \(0.945413\pi\) | |||||||
\(864\) | −35378.5 | − | 139239.i | −0.0473927 | − | 0.186523i | ||||
\(865\) | −545871. | −0.729554 | ||||||||
\(866\) | −669604. | − | 437322.i | −0.892858 | − | 0.583130i | ||||
\(867\) | 1.12766e6i | 1.50017i | ||||||||
\(868\) | −1750.70 | − | 3987.73i | −0.00232366 | − | 0.00529280i | ||||
\(869\) | −519898. | −0.688460 | ||||||||
\(870\) | −98339.2 | + | 150572.i | −0.129924 | + | 0.198932i | ||||
\(871\) | 473841.i | 0.624592i | ||||||||
\(872\) | 109240. | − | 656580.i | 0.143665 | − | 0.863485i | ||||
\(873\) | −143395. | −0.188150 | ||||||||
\(874\) | 62767.1 | + | 40993.5i | 0.0821692 | + | 0.0536651i | ||||
\(875\) | 1951.04i | 0.00254830i | ||||||||
\(876\) | −201663. | + | 88534.3i | −0.262795 | + | 0.115373i | ||||
\(877\) | −378981. | −0.492740 | −0.246370 | − | 0.969176i | \(-0.579238\pi\) | ||||
−0.246370 | + | 0.969176i | \(0.579238\pi\) | |||||||
\(878\) | −26879.7 | + | 41156.8i | −0.0348687 | + | 0.0533891i | ||||
\(879\) | − | 151021.i | − | 0.195461i | ||||||
\(880\) | −346787. | − | 318831.i | −0.447814 | − | 0.411714i | ||||
\(881\) | 1.18545e6 | 1.52733 | 0.763665 | − | 0.645613i | \(-0.223398\pi\) | ||||
0.763665 | + | 0.645613i | \(0.223398\pi\) | |||||||
\(882\) | 216930. | + | 141678.i | 0.278858 | + | 0.182124i | ||||
\(883\) | − | 161617.i | − | 0.207284i | −0.994615 | − | 0.103642i | \(-0.966950\pi\) | ||
0.994615 | − | 0.103642i | \(-0.0330496\pi\) | |||||||
\(884\) | 559446. | + | 1.27430e6i | 0.715902 | + | 1.63068i | ||||
\(885\) | 347346. | 0.443482 | ||||||||
\(886\) | −644409. | + | 986686.i | −0.820908 | + | 1.25693i | ||||
\(887\) | 185284.i | 0.235499i | 0.993043 | + | 0.117750i | \(0.0375680\pi\) | ||||
−0.993043 | + | 0.117750i | \(0.962432\pi\) | |||||||
\(888\) | −450466. | − | 74947.6i | −0.571263 | − | 0.0950456i | ||||
\(889\) | −35749.6 | −0.0452343 | ||||||||
\(890\) | −266309. | − | 173928.i | −0.336207 | − | 0.219578i | ||||
\(891\) | − | 119985.i | − | 0.151137i | ||||||
\(892\) | −674783. | + | 296244.i | −0.848076 | + | 0.372324i | ||||
\(893\) | 16623.3 | 0.0208456 | ||||||||
\(894\) | −222786. | + | 341119.i | −0.278749 | + | 0.426806i | ||||
\(895\) | − | 570880.i | − | 0.712687i | ||||||
\(896\) | 18034.2 | − | 14069.0i | 0.0224637 | − | 0.0175246i | ||||
\(897\) | −601962. | −0.748142 | ||||||||
\(898\) | 1.00816e6 | + | 658431.i | 1.25019 | + | 0.816502i | ||||
\(899\) | − | 150892.i | − | 0.186701i | ||||||
\(900\) | −21707.4 | − | 49444.8i | −0.0267992 | − | 0.0610430i | ||||
\(901\) | 2.41604e6 | 2.97615 | ||||||||
\(902\) | 233224. | − | 357101.i | 0.286656 | − | 0.438912i | ||||
\(903\) | 10898.8i | 0.0133661i | ||||||||
\(904\) | 117902. | − | 708638.i | 0.144272 | − | 0.867136i | ||||
\(905\) | −187695. | −0.229169 | ||||||||
\(906\) | −162540. | − | 106156.i | −0.198018 | − | 0.129326i | ||||
\(907\) | − | 81044.4i | − | 0.0985163i | −0.998786 | − | 0.0492582i | \(-0.984314\pi\) | ||
0.998786 | − | 0.0492582i | \(-0.0156857\pi\) | |||||||
\(908\) | 727191. | − | 319253.i | 0.882017 | − | 0.387225i | ||||
\(909\) | 460155. | 0.556899 | ||||||||
\(910\) | −5416.65 | + | 8293.70i | −0.00654106 | + | 0.0100153i | ||||
\(911\) | 990859.i | 1.19392i | 0.802271 | + | 0.596960i | \(0.203625\pi\) | ||||
−0.802271 | + | 0.596960i | \(0.796375\pi\) | |||||||
\(912\) | −23109.6 | + | 25135.9i | −0.0277845 | + | 0.0302207i | ||||
\(913\) | 2.15527e6 | 2.58560 | ||||||||
\(914\) | 219932. | + | 143638.i | 0.263266 | + | 0.171940i | ||||
\(915\) | 32549.8i | 0.0388782i | ||||||||
\(916\) | −57245.5 | − | 130393.i | −0.0682261 | − | 0.155405i | ||||
\(917\) | −23125.2 | −0.0275009 | ||||||||
\(918\) | 168227. | − | 257581.i | 0.199623 | − | 0.305652i | ||||
\(919\) | − | 1.33459e6i | − | 1.58021i | −0.612969 | − | 0.790107i | \(-0.710025\pi\) | ||
0.612969 | − | 0.790107i | \(-0.289975\pi\) | |||||||
\(920\) | 515368. | + | 85745.9i | 0.608895 | + | 0.101307i | ||||
\(921\) | −182175. | −0.214768 | ||||||||
\(922\) | −1.10630e6 | − | 722532.i | −1.30141 | − | 0.849954i | ||||
\(923\) | 424135.i | 0.497853i | ||||||||
\(924\) | 17491.6 | − | 7679.17i | 0.0204873 | − | 0.00899436i | ||||
\(925\) | −171648. | −0.200612 | ||||||||
\(926\) | 464477. | − | 711183.i | 0.541679 | − | 0.829391i | ||||
\(927\) | 90701.3i | 0.105549i | ||||||||
\(928\) | 768077. | − | 195157.i | 0.891885 | − | 0.226614i | ||||
\(929\) | −264841. | −0.306870 | −0.153435 | − | 0.988159i | \(-0.549034\pi\) | ||||
−0.153435 | + | 0.988159i | \(0.549034\pi\) | |||||||
\(930\) | 37934.2 | + | 24775.0i | 0.0438596 | + | 0.0286449i | ||||
\(931\) | − | 61580.3i | − | 0.0710465i | ||||||
\(932\) | −85915.0 | − | 195696.i | −0.0989093 | − | 0.225295i | ||||
\(933\) | −270998. | −0.311317 | ||||||||
\(934\) | 603384. | − | 923871.i | 0.691672 | − | 1.05905i | ||||
\(935\) | − | 1.00880e6i | − | 1.15393i | ||||||
\(936\) | 44997.1 | − | 270451.i | 0.0513610 | − | 0.308701i | ||||
\(937\) | 1.27942e6 | 1.45724 | 0.728622 | − | 0.684916i | \(-0.240161\pi\) | ||||
0.728622 | + | 0.684916i | \(0.240161\pi\) | |||||||
\(938\) | 13962.9 | + | 9119.25i | 0.0158698 | + | 0.0103646i | ||||
\(939\) | − | 623993.i | − | 0.707698i | ||||||
\(940\) | 106076. | − | 46569.7i | 0.120050 | − | 0.0527045i | ||||
\(941\) | −117710. | −0.132934 | −0.0664668 | − | 0.997789i | \(-0.521173\pi\) | ||||
−0.0664668 | + | 0.997789i | \(0.521173\pi\) | |||||||
\(942\) | −396800. | + | 607560.i | −0.447167 | + | 0.684679i | ||||
\(943\) | 473029.i | 0.531942i | ||||||||
\(944\) | −1.12677e6 | − | 1.03594e6i | −1.26442 | − | 1.16249i | ||||
\(945\) | 2189.79 | 0.00245210 | ||||||||
\(946\) | −828155. | − | 540872.i | −0.925400 | − | 0.604383i | ||||
\(947\) | 1.42125e6i | 1.58479i | 0.610011 | + | 0.792393i | \(0.291165\pi\) | ||||
−0.610011 | + | 0.792393i | \(0.708835\pi\) | |||||||
\(948\) | 105569. | + | 240463.i | 0.117468 | + | 0.267567i | ||||
\(949\) | −420312. | −0.466701 | ||||||||
\(950\) | −7017.98 | + | 10745.6i | −0.00777616 | + | 0.0119065i | ||||
\(951\) | 83755.7i | 0.0926090i | ||||||||
\(952\) | 48317.3 | + | 8038.93i | 0.0533124 | + | 0.00887001i | ||||
\(953\) | −544751. | −0.599808 | −0.299904 | − | 0.953969i | \(-0.596955\pi\) | ||||
−0.299904 | + | 0.953969i | \(0.596955\pi\) | |||||||
\(954\) | −398506. | − | 260266.i | −0.437862 | − | 0.285970i | ||||
\(955\) | 383603.i | 0.420606i | ||||||||
\(956\) | 588969. | − | 258570.i | 0.644431 | − | 0.282919i | ||||
\(957\) | 661866. | 0.722680 | ||||||||
\(958\) | −282705. | + | 432863.i | −0.308036 | + | 0.471649i | ||||
\(959\) | 7845.27i | 0.00853042i | ||||||||
\(960\) | −77048.5 | + | 225137.i | −0.0836029 | + | 0.244289i | ||||
\(961\) | 885506. | 0.958837 | ||||||||
\(962\) | −729662. | − | 476546.i | −0.788445 | − | 0.514937i | ||||
\(963\) | 179686.i | 0.193759i | ||||||||
\(964\) | −587126. | − | 1.33735e6i | −0.631796 | − | 1.43910i | ||||
\(965\) | −372593. | −0.400111 | ||||||||
\(966\) | −11585.0 | + | 17738.3i | −0.0124148 | + | 0.0190090i | ||||
\(967\) | 369389.i | 0.395031i | 0.980300 | + | 0.197516i | \(0.0632873\pi\) | ||||
−0.980300 | + | 0.197516i | \(0.936713\pi\) | |||||||
\(968\) | −130753. | + | 785882.i | −0.139541 | + | 0.838700i | ||||
\(969\) | −73119.8 | −0.0778731 | ||||||||
\(970\) | 198857. | + | 129875.i | 0.211348 | + | 0.138032i | ||||
\(971\) | 750410.i | 0.795903i | 0.917406 | + | 0.397952i | \(0.130279\pi\) | ||||
−0.917406 | + | 0.397952i | \(0.869721\pi\) | |||||||
\(972\) | −55495.3 | + | 24363.7i | −0.0587386 | + | 0.0257875i | ||||
\(973\) | −46903.1 | −0.0495422 | ||||||||
\(974\) | −648611. | + | 993120.i | −0.683702 | + | 1.04685i | ||||
\(975\) | − | 103054.i | − | 0.108407i | ||||||
\(976\) | 97077.6 | − | 105590.i | 0.101911 | − | 0.110847i | ||||
\(977\) | −1.18852e6 | −1.24513 | −0.622566 | − | 0.782567i | \(-0.713910\pi\) | ||||
−0.622566 | + | 0.782567i | \(0.713910\pi\) | |||||||
\(978\) | 864880. | + | 564857.i | 0.904228 | + | 0.590556i | ||||
\(979\) | 1.17061e6i | 1.22137i | ||||||||
\(980\) | −172515. | − | 392954.i | −0.179629 | − | 0.409156i | ||||
\(981\) | −280802. | −0.291785 | ||||||||
\(982\) | −743751. | + | 1.13879e6i | −0.771267 | + | 1.18092i | ||||
\(983\) | − | 144516.i | − | 0.149558i | −0.997200 | − | 0.0747789i | \(-0.976175\pi\) | ||
0.997200 | − | 0.0747789i | \(-0.0238251\pi\) | |||||||
\(984\) | −212524. | − | 35359.3i | −0.219491 | − | 0.0365185i | ||||
\(985\) | −601267. | −0.619719 | ||||||||
\(986\) | 1.42088e6 | + | 927984.i | 1.46152 | + | 0.954523i | ||||
\(987\) | 4697.85i | 0.00482241i | ||||||||
\(988\) | −59665.6 | + | 26194.5i | −0.0611238 | + | 0.0268347i | ||||
\(989\) | 1.09700e6 | 1.12154 | ||||||||
\(990\) | −108672. | + | 166393.i | −0.110878 | + | 0.169771i | ||||
\(991\) | − | 382181.i | − | 0.389154i | −0.980887 | − | 0.194577i | \(-0.937667\pi\) | ||
0.980887 | − | 0.194577i | \(-0.0623334\pi\) | |||||||
\(992\) | −49166.6 | − | 193505.i | −0.0499628 | − | 0.196639i | ||||
\(993\) | 39900.9 | 0.0404655 | ||||||||
\(994\) | 12498.2 | + | 8162.65i | 0.0126496 | + | 0.00826149i | ||||
\(995\) | 89356.7i | 0.0902570i | ||||||||
\(996\) | −437642. | − | 996858.i | −0.441164 | − | 1.00488i | ||||
\(997\) | −1.03299e6 | −1.03921 | −0.519607 | − | 0.854406i | \(-0.673921\pi\) | ||||
−0.519607 | + | 0.854406i | \(0.673921\pi\) | |||||||
\(998\) | −321106. | + | 491662.i | −0.322395 | + | 0.493634i | ||||
\(999\) | 192653.i | 0.193039i |
(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 | 60.5.c.a.31.5 | ✓ | 16 | |
3.2 | odd | 2 | 180.5.c.c.91.12 | 16 | |||
4.3 | odd | 2 | inner | 60.5.c.a.31.6 | yes | 16 | |
5.2 | odd | 4 | 300.5.f.b.199.23 | 32 | |||
5.3 | odd | 4 | 300.5.f.b.199.10 | 32 | |||
5.4 | even | 2 | 300.5.c.d.151.12 | 16 | |||
8.3 | odd | 2 | 960.5.e.f.511.15 | 16 | |||
8.5 | even | 2 | 960.5.e.f.511.6 | 16 | |||
12.11 | even | 2 | 180.5.c.c.91.11 | 16 | |||
20.3 | even | 4 | 300.5.f.b.199.24 | 32 | |||
20.7 | even | 4 | 300.5.f.b.199.9 | 32 | |||
20.19 | odd | 2 | 300.5.c.d.151.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.c.a.31.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
60.5.c.a.31.6 | yes | 16 | 4.3 | odd | 2 | inner | |
180.5.c.c.91.11 | 16 | 12.11 | even | 2 | |||
180.5.c.c.91.12 | 16 | 3.2 | odd | 2 | |||
300.5.c.d.151.11 | 16 | 20.19 | odd | 2 | |||
300.5.c.d.151.12 | 16 | 5.4 | even | 2 | |||
300.5.f.b.199.9 | 32 | 20.7 | even | 4 | |||
300.5.f.b.199.10 | 32 | 5.3 | odd | 4 | |||
300.5.f.b.199.23 | 32 | 5.2 | odd | 4 | |||
300.5.f.b.199.24 | 32 | 20.3 | even | 4 | |||
960.5.e.f.511.6 | 16 | 8.5 | even | 2 | |||
960.5.e.f.511.15 | 16 | 8.3 | odd | 2 |