Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(19,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (of order \(12\), degree \(4\), not 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 227.7 | ||
Character | \(\chi\) | \(=\) | 784.227 |
Dual form | 784.2.w.e.411.7 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40658 | − | 0.146726i | 0.994603 | − | 0.103751i | ||||
\(3\) | −1.76215 | + | 0.472168i | −1.01738 | + | 0.272606i | −0.728710 | − | 0.684822i | \(-0.759880\pi\) |
−0.288670 | + | 0.957429i | \(0.593213\pi\) | |||||||
\(4\) | 1.95694 | − | 0.412764i | 0.978471 | − | 0.206382i | ||||
\(5\) | 0.219363 | − | 0.818676i | 0.0981023 | − | 0.366123i | −0.899369 | − | 0.437190i | \(-0.855974\pi\) |
0.997472 | + | 0.0710670i | \(0.0226404\pi\) | |||||||
\(6\) | −2.40933 | + | 0.922696i | −0.983606 | + | 0.376689i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.69204 | − | 0.867721i | 0.951779 | − | 0.306786i | ||||
\(9\) | 0.284168 | − | 0.164064i | 0.0947226 | − | 0.0546881i | ||||
\(10\) | 0.188432 | − | 1.18372i | 0.0595873 | − | 0.374325i | ||||
\(11\) | 2.73205 | − | 0.732051i | 0.823744 | − | 0.220722i | 0.177762 | − | 0.984074i | \(-0.443114\pi\) |
0.645983 | + | 0.763352i | \(0.276448\pi\) | |||||||
\(12\) | −3.25354 | + | 1.65136i | −0.939216 | + | 0.476706i | ||||
\(13\) | −1.00197 | + | 1.00197i | −0.277897 | + | 0.277897i | −0.832269 | − | 0.554372i | \(-0.812959\pi\) |
0.554372 | + | 0.832269i | \(0.312959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.54621i | 0.399229i | ||||||||
\(16\) | 3.65925 | − | 1.61551i | 0.914813 | − | 0.403878i | ||||
\(17\) | 5.61300 | + | 3.24067i | 1.36135 | + | 0.785977i | 0.989804 | − | 0.142436i | \(-0.0454935\pi\) |
0.371549 | + | 0.928413i | \(0.378827\pi\) | |||||||
\(18\) | 0.375633 | − | 0.272465i | 0.0885375 | − | 0.0642205i | ||||
\(19\) | 1.43897 | − | 5.37031i | 0.330123 | − | 1.23203i | −0.578938 | − | 0.815371i | \(-0.696533\pi\) |
0.909061 | − | 0.416663i | \(-0.136800\pi\) | |||||||
\(20\) | 0.0913619 | − | 1.69265i | 0.0204292 | − | 0.378487i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.73544 | − | 1.43055i | 0.796399 | − | 0.304995i | ||||
\(23\) | −2.20366 | − | 3.81684i | −0.459494 | − | 0.795867i | 0.539440 | − | 0.842024i | \(-0.318636\pi\) |
−0.998934 | + | 0.0461569i | \(0.985303\pi\) | |||||||
\(24\) | −4.33407 | + | 2.80015i | −0.884689 | + | 0.571578i | ||||
\(25\) | 3.70802 | + | 2.14082i | 0.741604 | + | 0.428165i | ||||
\(26\) | −1.26234 | + | 1.55637i | −0.247565 | + | 0.305230i | ||||
\(27\) | 3.44668 | − | 3.44668i | 0.663313 | − | 0.663313i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.241319 | + | 0.241319i | 0.0448119 | + | 0.0448119i | 0.729158 | − | 0.684346i | \(-0.239912\pi\) |
−0.684346 | + | 0.729158i | \(0.739912\pi\) | |||||||
\(30\) | 0.226869 | + | 2.17487i | 0.0414204 | + | 0.397075i | ||||
\(31\) | 1.69265 | − | 2.93175i | 0.304008 | − | 0.526558i | −0.673032 | − | 0.739614i | \(-0.735008\pi\) |
0.977040 | + | 0.213056i | \(0.0683416\pi\) | |||||||
\(32\) | 4.91000 | − | 2.80926i | 0.867973 | − | 0.496611i | ||||
\(33\) | −4.46864 | + | 2.57997i | −0.777891 | + | 0.449116i | ||||
\(34\) | 8.37063 | + | 3.73469i | 1.43555 | + | 0.640494i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.488380 | − | 0.438359i | 0.0813967 | − | 0.0730598i | ||||
\(37\) | −3.73668 | − | 1.00124i | −0.614307 | − | 0.164603i | −0.0617685 | − | 0.998091i | \(-0.519674\pi\) |
−0.552538 | + | 0.833488i | \(0.686341\pi\) | |||||||
\(38\) | 1.23607 | − | 7.76492i | 0.200516 | − | 1.25964i | ||||
\(39\) | 1.29253 | − | 2.23873i | 0.206971 | − | 0.358484i | ||||
\(40\) | −0.119847 | − | 2.39425i | −0.0189495 | − | 0.378564i | ||||
\(41\) | −4.88941 | −0.763597 | −0.381799 | − | 0.924246i | \(-0.624695\pi\) | ||||
−0.381799 | + | 0.924246i | \(0.624695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.40731 | + | 4.40731i | 0.672109 | + | 0.672109i | 0.958202 | − | 0.286093i | \(-0.0923566\pi\) |
−0.286093 | + | 0.958202i | \(0.592357\pi\) | |||||||
\(44\) | 5.04430 | − | 2.56027i | 0.760457 | − | 0.385976i | ||||
\(45\) | −0.0719794 | − | 0.268631i | −0.0107301 | − | 0.0400451i | ||||
\(46\) | −3.65965 | − | 5.04537i | −0.539586 | − | 0.743899i | ||||
\(47\) | 4.72731 | + | 8.18793i | 0.689548 | + | 1.19433i | 0.971984 | + | 0.235047i | \(0.0755243\pi\) |
−0.282436 | + | 0.959286i | \(0.591142\pi\) | |||||||
\(48\) | −5.68537 | + | 4.57456i | −0.820613 | + | 0.660281i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.52974 | + | 2.46718i | 0.782024 | + | 0.348912i | ||||
\(51\) | −11.4211 | − | 3.06028i | −1.59928 | − | 0.428525i | ||||
\(52\) | −1.54723 | + | 2.37438i | −0.214562 | + | 0.329268i | ||||
\(53\) | 1.17790 | + | 4.39598i | 0.161797 | + | 0.603834i | 0.998427 | + | 0.0560660i | \(0.0178557\pi\) |
−0.836630 | + | 0.547768i | \(0.815478\pi\) | |||||||
\(54\) | 4.34232 | − | 5.35375i | 0.590914 | − | 0.728553i | ||||
\(55\) | − | 2.39725i | − | 0.323245i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.1428i | 1.34344i | ||||||||
\(58\) | 0.374843 | + | 0.304028i | 0.0492193 | + | 0.0399208i | ||||
\(59\) | −0.494636 | − | 1.84601i | −0.0643961 | − | 0.240329i | 0.926224 | − | 0.376973i | \(-0.123035\pi\) |
−0.990620 | + | 0.136644i | \(0.956368\pi\) | |||||||
\(60\) | 0.638219 | + | 3.02584i | 0.0823938 | + | 0.390635i | ||||
\(61\) | 13.4463 | + | 3.60291i | 1.72162 | + | 0.461306i | 0.978224 | − | 0.207550i | \(-0.0665488\pi\) |
0.743392 | + | 0.668855i | \(0.233216\pi\) | |||||||
\(62\) | 1.95068 | − | 4.37210i | 0.247737 | − | 0.555257i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.49412 | − | 4.67187i | 0.811765 | − | 0.583984i | ||||
\(65\) | 0.600494 | + | 1.04009i | 0.0744822 | + | 0.129007i | ||||
\(66\) | −5.90696 | + | 4.28461i | −0.727097 | + | 0.527399i | ||||
\(67\) | −3.18889 | − | 11.9011i | −0.389585 | − | 1.45395i | −0.830812 | − | 0.556554i | \(-0.812123\pi\) |
0.441227 | − | 0.897396i | \(-0.354543\pi\) | |||||||
\(68\) | 12.3220 | + | 4.02496i | 1.49426 | + | 0.488098i | ||||
\(69\) | 5.68537 | + | 5.68537i | 0.684438 | + | 0.684438i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2855 | −1.45802 | −0.729011 | − | 0.684502i | \(-0.760020\pi\) | ||||
−0.729011 | + | 0.684502i | \(0.760020\pi\) | |||||||
\(72\) | 0.622628 | − | 0.688246i | 0.0733774 | − | 0.0811105i | ||||
\(73\) | −0.402661 | + | 0.697429i | −0.0471279 | + | 0.0816278i | −0.888627 | − | 0.458631i | \(-0.848340\pi\) |
0.841499 | + | 0.540258i | \(0.181673\pi\) | |||||||
\(74\) | −5.40286 | − | 0.860059i | −0.628069 | − | 0.0999798i | ||||
\(75\) | −7.54493 | − | 2.02166i | −0.871213 | − | 0.233441i | ||||
\(76\) | 0.599312 | − | 11.1034i | 0.0687458 | − | 1.27364i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.48957 | − | 3.33860i | 0.168661 | − | 0.378022i | ||||
\(79\) | −9.32549 | + | 5.38407i | −1.04920 | + | 0.605756i | −0.922425 | − | 0.386176i | \(-0.873796\pi\) |
−0.126774 | + | 0.991932i | \(0.540462\pi\) | |||||||
\(80\) | −0.519874 | − | 3.35012i | −0.0581236 | − | 0.374555i | ||||
\(81\) | −4.93836 | + | 8.55349i | −0.548707 | + | 0.950388i | ||||
\(82\) | −6.87735 | + | 0.717403i | −0.759476 | + | 0.0792239i | ||||
\(83\) | −5.76738 | − | 5.76738i | −0.633052 | − | 0.633052i | 0.315780 | − | 0.948832i | \(-0.397734\pi\) |
−0.948832 | + | 0.315780i | \(0.897734\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.88434 | − | 3.88434i | 0.421316 | − | 0.421316i | ||||
\(86\) | 6.84591 | + | 5.55258i | 0.738214 | + | 0.598750i | ||||
\(87\) | −0.539185 | − | 0.311299i | −0.0578067 | − | 0.0333747i | ||||
\(88\) | 6.71957 | − | 4.34136i | 0.716308 | − | 0.462791i | ||||
\(89\) | −6.66406 | − | 11.5425i | −0.706389 | − | 1.22350i | −0.966188 | − | 0.257839i | \(-0.916990\pi\) |
0.259799 | − | 0.965663i | \(-0.416344\pi\) | |||||||
\(90\) | −0.140660 | − | 0.367290i | −0.0148269 | − | 0.0387158i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.88789 | − | 6.55976i | −0.613855 | − | 0.683902i | ||||
\(93\) | −1.59843 | + | 5.96541i | −0.165749 | + | 0.618584i | ||||
\(94\) | 7.85072 | + | 10.8234i | 0.809740 | + | 1.11635i | ||||
\(95\) | −4.08089 | − | 2.35610i | −0.418690 | − | 0.241731i | ||||
\(96\) | −7.32573 | + | 7.26868i | −0.747679 | + | 0.741857i | ||||
\(97\) | 10.8360i | 1.10022i | 0.835091 | + | 0.550112i | \(0.185415\pi\) | ||||
−0.835091 | + | 0.550112i | \(0.814585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.656257 | − | 0.656257i | 0.0659564 | − | 0.0659564i | ||||
\(100\) | 8.14003 | + | 2.65894i | 0.814003 | + | 0.265894i | ||||
\(101\) | −7.48495 | + | 2.00559i | −0.744780 | + | 0.199563i | −0.611202 | − | 0.791475i | \(-0.709314\pi\) |
−0.133579 | + | 0.991038i | \(0.542647\pi\) | |||||||
\(102\) | −16.5137 | − | 2.62876i | −1.63510 | − | 0.260286i | ||||
\(103\) | −10.0056 | + | 5.77673i | −0.985881 | + | 0.569199i | −0.904040 | − | 0.427447i | \(-0.859413\pi\) |
−0.0818403 | + | 0.996645i | \(0.526080\pi\) | |||||||
\(104\) | −1.82791 | + | 3.56678i | −0.179242 | + | 0.349752i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.30182 | + | 6.01047i | 0.223572 | + | 0.583789i | ||||
\(107\) | 1.77929 | − | 6.64039i | 0.172010 | − | 0.641951i | −0.825031 | − | 0.565087i | \(-0.808843\pi\) |
0.997042 | − | 0.0768639i | \(-0.0244907\pi\) | |||||||
\(108\) | 5.32229 | − | 8.16761i | 0.512137 | − | 0.785929i | ||||
\(109\) | −13.7684 | + | 3.68924i | −1.31878 | + | 0.353365i | −0.848519 | − | 0.529165i | \(-0.822505\pi\) |
−0.470257 | + | 0.882530i | \(0.655839\pi\) | |||||||
\(110\) | −0.351739 | − | 3.37193i | −0.0335370 | − | 0.321500i | ||||
\(111\) | 7.05736 | 0.669855 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.05034 | −0.286952 | −0.143476 | − | 0.989654i | \(-0.545828\pi\) | ||||
−0.143476 | + | 0.989654i | \(0.545828\pi\) | |||||||
\(114\) | 1.48821 | + | 14.2666i | 0.139383 | + | 1.33619i | ||||
\(115\) | −3.60816 | + | 0.966803i | −0.336463 | + | 0.0901549i | ||||
\(116\) | 0.571856 | + | 0.372640i | 0.0530955 | + | 0.0345988i | ||||
\(117\) | −0.120340 | + | 0.449116i | −0.0111255 | + | 0.0415208i | ||||
\(118\) | −0.966602 | − | 2.52398i | −0.0889829 | − | 0.232351i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.34168 | + | 4.16245i | 0.122478 | + | 0.379978i | ||||
\(121\) | −2.59808 | + | 1.50000i | −0.236189 | + | 0.136364i | ||||
\(122\) | 19.4419 | + | 3.09488i | 1.76019 | + | 0.280197i | ||||
\(123\) | 8.61589 | − | 2.30862i | 0.776869 | − | 0.208161i | ||||
\(124\) | 2.10229 | − | 6.43593i | 0.188791 | − | 0.577964i | ||||
\(125\) | 5.56261 | − | 5.56261i | 0.497535 | − | 0.497535i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.01709i | 0.800137i | 0.916485 | + | 0.400069i | \(0.131014\pi\) | ||||
−0.916485 | + | 0.400069i | \(0.868986\pi\) | |||||||
\(128\) | 8.44903 | − | 7.52422i | 0.746796 | − | 0.665054i | ||||
\(129\) | −9.84735 | − | 5.68537i | −0.867011 | − | 0.500569i | ||||
\(130\) | 0.997252 | + | 1.37486i | 0.0874648 | + | 0.120583i | ||||
\(131\) | 0.177400 | − | 0.662065i | 0.0154995 | − | 0.0578449i | −0.957743 | − | 0.287625i | \(-0.907134\pi\) |
0.973242 | + | 0.229781i | \(0.0738009\pi\) | |||||||
\(132\) | −7.67996 | + | 6.89335i | −0.668455 | + | 0.599989i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.23163 | − | 16.2720i | −0.538331 | − | 1.40568i | ||||
\(135\) | −2.06564 | − | 3.57779i | −0.177782 | − | 0.307927i | ||||
\(136\) | 17.9224 | + | 3.85348i | 1.53683 | + | 0.330433i | ||||
\(137\) | 14.8494 | + | 8.57331i | 1.26867 | + | 0.732467i | 0.974736 | − | 0.223359i | \(-0.0717022\pi\) |
0.293934 | + | 0.955826i | \(0.405036\pi\) | |||||||
\(138\) | 8.83113 | + | 7.16275i | 0.751756 | + | 0.609734i | ||||
\(139\) | −7.13391 | + | 7.13391i | −0.605090 | + | 0.605090i | −0.941659 | − | 0.336568i | \(-0.890734\pi\) |
0.336568 | + | 0.941659i | \(0.390734\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1963 | − | 12.1963i | −1.02712 | − | 1.02712i | ||||
\(142\) | −17.2806 | + | 1.80260i | −1.45015 | + | 0.151271i | ||||
\(143\) | −2.00395 | + | 3.47094i | −0.167578 | + | 0.290254i | ||||
\(144\) | 0.774794 | − | 1.05943i | 0.0645661 | − | 0.0882858i | ||||
\(145\) | 0.250499 | − | 0.144626i | 0.0208028 | − | 0.0120105i | ||||
\(146\) | −0.464044 | + | 1.04007i | −0.0384046 | + | 0.0860769i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.72575 | − | 0.417003i | −0.635053 | − | 0.0342775i | ||||
\(149\) | 12.0908 | + | 3.23973i | 0.990519 | + | 0.265409i | 0.717468 | − | 0.696591i | \(-0.245301\pi\) |
0.273050 | + | 0.962000i | \(0.411967\pi\) | |||||||
\(150\) | −10.9092 | − | 1.73659i | −0.890731 | − | 0.141792i | ||||
\(151\) | −3.36965 | + | 5.83640i | −0.274218 | + | 0.474960i | −0.969938 | − | 0.243354i | \(-0.921752\pi\) |
0.695719 | + | 0.718314i | \(0.255086\pi\) | |||||||
\(152\) | −0.786169 | − | 15.7057i | −0.0637667 | − | 1.27390i | ||||
\(153\) | 2.12671 | 0.171935 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.02885 | − | 2.02885i | −0.162961 | − | 0.162961i | ||||
\(156\) | 1.60534 | − | 4.91458i | 0.128530 | − | 0.393481i | ||||
\(157\) | −1.86163 | − | 6.94769i | −0.148574 | − | 0.554486i | −0.999570 | − | 0.0293140i | \(-0.990668\pi\) |
0.850996 | − | 0.525172i | \(-0.175999\pi\) | |||||||
\(158\) | −12.3271 | + | 8.94143i | −0.980689 | + | 0.711342i | ||||
\(159\) | −4.15128 | − | 7.19023i | −0.329218 | − | 0.570222i | ||||
\(160\) | −1.22279 | − | 4.63594i | −0.0966704 | − | 0.366504i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.69119 | + | 12.7558i | −0.447142 | + | 1.00219i | ||||
\(163\) | −8.61264 | − | 2.30775i | −0.674594 | − | 0.180757i | −0.0947706 | − | 0.995499i | \(-0.530212\pi\) |
−0.579823 | + | 0.814742i | \(0.696878\pi\) | |||||||
\(164\) | −9.56829 | + | 2.01817i | −0.747158 | + | 0.157593i | ||||
\(165\) | 1.13190 | + | 4.22432i | 0.0881186 | + | 0.328863i | ||||
\(166\) | −8.95851 | − | 7.26606i | −0.695315 | − | 0.563956i | ||||
\(167\) | 16.3480i | 1.26504i | 0.774543 | + | 0.632522i | \(0.217980\pi\) | ||||
−0.774543 | + | 0.632522i | \(0.782020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9921i | 0.845546i | ||||||||
\(170\) | 4.89371 | − | 6.03358i | 0.375331 | − | 0.462754i | ||||
\(171\) | −0.472168 | − | 1.76215i | −0.0361076 | − | 0.134755i | ||||
\(172\) | 10.4440 | + | 6.80568i | 0.796351 | + | 0.518928i | ||||
\(173\) | −15.6337 | − | 4.18902i | −1.18860 | − | 0.318486i | −0.390270 | − | 0.920700i | \(-0.627618\pi\) |
−0.798334 | + | 0.602215i | \(0.794285\pi\) | |||||||
\(174\) | −0.804083 | − | 0.358754i | −0.0609574 | − | 0.0271971i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.81463 | − | 7.09242i | 0.664427 | − | 0.534611i | ||||
\(177\) | 1.74325 | + | 3.01939i | 0.131031 | + | 0.226952i | ||||
\(178\) | −11.0671 | − | 15.2577i | −0.829516 | − | 1.14361i | ||||
\(179\) | −3.23694 | − | 12.0804i | −0.241940 | − | 0.902932i | −0.974897 | − | 0.222657i | \(-0.928527\pi\) |
0.732957 | − | 0.680275i | \(-0.238140\pi\) | |||||||
\(180\) | −0.251741 | − | 0.495985i | −0.0187637 | − | 0.0369685i | ||||
\(181\) | −17.5233 | − | 17.5233i | −1.30250 | − | 1.30250i | −0.926703 | − | 0.375794i | \(-0.877370\pi\) |
−0.375794 | − | 0.926703i | \(-0.622630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.3956 | −1.87729 | ||||||||
\(184\) | −9.24428 | − | 8.36293i | −0.681497 | − | 0.616523i | ||||
\(185\) | −1.63938 | + | 2.83949i | −0.120530 | + | 0.208764i | ||||
\(186\) | −1.37304 | + | 8.62536i | −0.100676 | + | 0.632442i | ||||
\(187\) | 17.7073 | + | 4.74467i | 1.29489 | + | 0.346964i | ||||
\(188\) | 12.6308 | + | 14.0721i | 0.921192 | + | 1.02631i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.08580 | − | 2.71528i | −0.441510 | − | 0.196987i | ||||
\(191\) | 3.90555 | − | 2.25487i | 0.282595 | − | 0.163157i | −0.352002 | − | 0.935999i | \(-0.614499\pi\) |
0.634598 | + | 0.772843i | \(0.281166\pi\) | |||||||
\(192\) | −9.23774 | + | 11.2989i | −0.666676 | + | 0.815426i | ||||
\(193\) | −6.96133 | + | 12.0574i | −0.501087 | + | 0.867909i | 0.498912 | + | 0.866653i | \(0.333733\pi\) |
−0.999999 | + | 0.00125604i | \(0.999600\pi\) | |||||||
\(194\) | 1.58992 | + | 15.2417i | 0.114149 | + | 1.09429i | ||||
\(195\) | −1.54926 | − | 1.54926i | −0.110945 | − | 0.110945i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1598 | − | 10.1598i | 0.723859 | − | 0.723859i | −0.245530 | − | 0.969389i | \(-0.578962\pi\) |
0.969389 | + | 0.245530i | \(0.0789620\pi\) | |||||||
\(198\) | 0.826790 | − | 1.01937i | 0.0587574 | − | 0.0724434i | ||||
\(199\) | 8.58508 | + | 4.95660i | 0.608580 | + | 0.351364i | 0.772410 | − | 0.635125i | \(-0.219051\pi\) |
−0.163829 | + | 0.986489i | \(0.552385\pi\) | |||||||
\(200\) | 11.8398 | + | 2.54566i | 0.837197 | + | 0.180005i | ||||
\(201\) | 11.2386 | + | 19.4659i | 0.792711 | + | 1.37302i | ||||
\(202\) | −10.2339 | + | 3.91926i | −0.720056 | + | 0.275758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −23.6136 | − | 1.27456i | −1.65329 | − | 0.0892374i | ||||
\(205\) | −1.07256 | + | 4.00284i | −0.0749107 | + | 0.279570i | ||||
\(206\) | −13.2261 | + | 9.59353i | −0.921505 | + | 0.668413i | ||||
\(207\) | −1.25242 | − | 0.723083i | −0.0870490 | − | 0.0502577i | ||||
\(208\) | −2.04777 | + | 5.28517i | −0.141987 | + | 0.366461i | ||||
\(209\) | − | 15.7254i | − | 1.08775i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.53445 | − | 6.53445i | 0.449850 | − | 0.449850i | −0.445454 | − | 0.895305i | \(-0.646958\pi\) |
0.895305 | + | 0.445454i | \(0.146958\pi\) | |||||||
\(212\) | 4.11958 | + | 8.11649i | 0.282934 | + | 0.557443i | ||||
\(213\) | 21.6490 | − | 5.80082i | 1.48336 | − | 0.397466i | ||||
\(214\) | 1.52840 | − | 9.60132i | 0.104479 | − | 0.656333i | ||||
\(215\) | 4.57496 | − | 2.64136i | 0.312010 | − | 0.180139i | ||||
\(216\) | 6.28783 | − | 12.2693i | 0.427833 | − | 0.834822i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.8251 | + | 7.20940i | −1.27500 | + | 0.488282i | ||||
\(219\) | 0.380247 | − | 1.41910i | 0.0256947 | − | 0.0958939i | ||||
\(220\) | −0.989498 | − | 4.69128i | −0.0667119 | − | 0.316286i | ||||
\(221\) | −8.87114 | + | 2.37701i | −0.596737 | + | 0.159895i | ||||
\(222\) | 9.92676 | − | 1.03550i | 0.666240 | − | 0.0694981i | ||||
\(223\) | 2.27448 | 0.152311 | 0.0761553 | − | 0.997096i | \(-0.475736\pi\) | ||||
0.0761553 | + | 0.997096i | \(0.475736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.40493 | 0.0936622 | ||||||||
\(226\) | −4.29055 | + | 0.447564i | −0.285403 | + | 0.0297715i | ||||
\(227\) | 12.1693 | − | 3.26076i | 0.807706 | − | 0.216424i | 0.168742 | − | 0.985660i | \(-0.446030\pi\) |
0.638965 | + | 0.769236i | \(0.279363\pi\) | |||||||
\(228\) | 4.18656 | + | 19.8488i | 0.277262 | + | 1.31452i | ||||
\(229\) | −2.21048 | + | 8.24963i | −0.146073 | + | 0.545151i | 0.853633 | + | 0.520876i | \(0.174395\pi\) |
−0.999705 | + | 0.0242754i | \(0.992272\pi\) | |||||||
\(230\) | −4.93331 | + | 1.88930i | −0.325293 | + | 0.124577i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.859038 | + | 0.440243i | 0.0563986 | + | 0.0289034i | ||||
\(233\) | 22.6834 | − | 13.0963i | 1.48604 | − | 0.857966i | 0.486166 | − | 0.873866i | \(-0.338395\pi\) |
0.999874 | + | 0.0159008i | \(0.00506160\pi\) | |||||||
\(234\) | −0.103372 | + | 0.649376i | −0.00675761 | + | 0.0424510i | ||||
\(235\) | 7.74026 | − | 2.07400i | 0.504919 | − | 0.135293i | ||||
\(236\) | −1.72994 | − | 3.40836i | −0.112609 | − | 0.221865i | ||||
\(237\) | 13.8908 | − | 13.8908i | 0.902302 | − | 0.902302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.6122i | − | 1.33329i | −0.745375 | − | 0.666645i | \(-0.767730\pi\) | ||
0.745375 | − | 0.666645i | \(-0.232270\pi\) | |||||||
\(240\) | 2.49792 | + | 5.65797i | 0.161240 | + | 0.365220i | ||||
\(241\) | −0.615233 | − | 0.355205i | −0.0396306 | − | 0.0228808i | 0.480054 | − | 0.877239i | \(-0.340617\pi\) |
−0.519684 | + | 0.854358i | \(0.673950\pi\) | |||||||
\(242\) | −3.43432 | + | 2.49108i | −0.220766 | + | 0.160133i | ||||
\(243\) | 0.878753 | − | 3.27955i | 0.0563720 | − | 0.210383i | ||||
\(244\) | 27.8007 | + | 1.50057i | 1.77976 | + | 0.0960639i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.7802 | − | 4.51144i | 0.751079 | − | 0.287639i | ||||
\(247\) | 3.93910 | + | 6.82272i | 0.250639 | + | 0.434119i | ||||
\(248\) | 2.01273 | − | 9.36112i | 0.127808 | − | 0.594432i | ||||
\(249\) | 12.8862 | + | 7.43984i | 0.816628 | + | 0.471480i | ||||
\(250\) | 7.00808 | − | 8.64044i | 0.443230 | − | 0.546469i | ||||
\(251\) | −4.98077 | + | 4.98077i | −0.314383 | + | 0.314383i | −0.846605 | − | 0.532222i | \(-0.821357\pi\) |
0.532222 | + | 0.846605i | \(0.321357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.81463 | − | 8.81463i | −0.554171 | − | 0.554171i | ||||
\(254\) | 1.32304 | + | 12.6833i | 0.0830150 | + | 0.795819i | ||||
\(255\) | −5.01075 | + | 8.67887i | −0.313785 | + | 0.543492i | ||||
\(256\) | 10.7802 | − | 11.8231i | 0.673765 | − | 0.738945i | ||||
\(257\) | 5.37871 | − | 3.10540i | 0.335515 | − | 0.193710i | −0.322772 | − | 0.946477i | \(-0.604615\pi\) |
0.658287 | + | 0.752767i | \(0.271281\pi\) | |||||||
\(258\) | −14.6853 | − | 6.55208i | −0.914267 | − | 0.407914i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.60444 | + | 1.78753i | 0.0995034 | + | 0.110858i | ||||
\(261\) | 0.108167 | + | 0.0289833i | 0.00669538 | + | 0.00179402i | ||||
\(262\) | 0.152385 | − | 0.957277i | 0.00941438 | − | 0.0591408i | ||||
\(263\) | −0.391699 | + | 0.678442i | −0.0241532 | + | 0.0418345i | −0.877849 | − | 0.478937i | \(-0.841022\pi\) |
0.853696 | + | 0.520771i | \(0.174356\pi\) | |||||||
\(264\) | −9.79106 | + | 10.8229i | −0.602598 | + | 0.666104i | ||||
\(265\) | 3.85727 | 0.236950 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.1931 | + | 17.1931i | 1.05220 | + | 1.05220i | ||||
\(268\) | −11.1528 | − | 21.9735i | −0.681266 | − | 1.34224i | ||||
\(269\) | 4.52188 | + | 16.8759i | 0.275704 | + | 1.02894i | 0.955368 | + | 0.295417i | \(0.0954587\pi\) |
−0.679664 | + | 0.733523i | \(0.737875\pi\) | |||||||
\(270\) | −3.43044 | − | 4.72936i | −0.208770 | − | 0.287820i | ||||
\(271\) | −3.21738 | − | 5.57267i | −0.195442 | − | 0.338516i | 0.751603 | − | 0.659615i | \(-0.229281\pi\) |
−0.947045 | + | 0.321100i | \(0.895947\pi\) | |||||||
\(272\) | 25.7747 | + | 2.79055i | 1.56282 | + | 0.169202i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.1448 | + | 9.88026i | 1.33782 | + | 0.596888i | ||||
\(275\) | 11.6977 | + | 3.13439i | 0.705397 | + | 0.189011i | ||||
\(276\) | 13.4727 | + | 8.77923i | 0.810959 | + | 0.528448i | ||||
\(277\) | −1.91415 | − | 7.14372i | −0.115010 | − | 0.429224i | 0.884277 | − | 0.466962i | \(-0.154652\pi\) |
−0.999288 | + | 0.0377377i | \(0.987985\pi\) | |||||||
\(278\) | −8.98770 | + | 11.0812i | −0.539046 | + | 0.664604i | ||||
\(279\) | − | 1.11081i | − | 0.0665026i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8611i | 0.886539i | 0.896388 | + | 0.443270i | \(0.146182\pi\) | ||||
−0.896388 | + | 0.443270i | \(0.853818\pi\) | |||||||
\(282\) | −18.9446 | − | 15.3656i | −1.12814 | − | 0.915008i | ||||
\(283\) | 3.03340 | + | 11.3208i | 0.180317 | + | 0.672951i | 0.995585 | + | 0.0938672i | \(0.0299229\pi\) |
−0.815268 | + | 0.579084i | \(0.803410\pi\) | |||||||
\(284\) | −24.0420 | + | 5.07102i | −1.42663 | + | 0.300909i | ||||
\(285\) | 8.30362 | + | 2.22495i | 0.491864 | + | 0.131795i | ||||
\(286\) | −2.30944 | + | 5.17618i | −0.136560 | + | 0.306074i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.934365 | − | 1.60386i | 0.0550580 | − | 0.0945081i | ||||
\(289\) | 12.5039 | + | 21.6573i | 0.735521 | + | 1.27396i | ||||
\(290\) | 0.331127 | − | 0.240182i | 0.0194444 | − | 0.0141040i | ||||
\(291\) | −5.11639 | − | 19.0946i | −0.299928 | − | 1.11935i | ||||
\(292\) | −0.500110 | + | 1.53103i | −0.0292667 | + | 0.0895969i | ||||
\(293\) | 8.11929 | + | 8.11929i | 0.474334 | + | 0.474334i | 0.903314 | − | 0.428980i | \(-0.141127\pi\) |
−0.428980 | + | 0.903314i | \(0.641127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.61978 | −0.0943075 | ||||||||
\(296\) | −10.9281 | + | 0.547019i | −0.635182 | + | 0.0317948i | ||||
\(297\) | 6.89335 | − | 11.9396i | 0.399993 | − | 0.692808i | ||||
\(298\) | 17.4821 | + | 2.78290i | 1.01271 | + | 0.161209i | ||||
\(299\) | 6.03238 | + | 1.61637i | 0.348861 | + | 0.0934771i | ||||
\(300\) | −15.5995 | − | 0.841993i | −0.900635 | − | 0.0486125i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.88333 | + | 8.70379i | −0.223461 | + | 0.500847i | ||||
\(303\) | 12.2427 | − | 7.06830i | 0.703322 | − | 0.406063i | ||||
\(304\) | −3.41024 | − | 21.9760i | −0.195591 | − | 1.26041i | ||||
\(305\) | 5.89924 | − | 10.2178i | 0.337789 | − | 0.585068i | ||||
\(306\) | 2.99139 | − | 0.312044i | 0.171007 | − | 0.0178384i | ||||
\(307\) | 14.2527 | + | 14.2527i | 0.813442 | + | 0.813442i | 0.985148 | − | 0.171706i | \(-0.0549279\pi\) |
−0.171706 | + | 0.985148i | \(0.554928\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.9038 | − | 14.9038i | 0.847848 | − | 0.847848i | ||||
\(310\) | −3.15142 | − | 2.55605i | −0.178989 | − | 0.145174i | ||||
\(311\) | −11.0134 | − | 6.35857i | −0.624511 | − | 0.360561i | 0.154112 | − | 0.988053i | \(-0.450748\pi\) |
−0.778623 | + | 0.627492i | \(0.784082\pi\) | |||||||
\(312\) | 1.53695 | − | 7.14830i | 0.0870126 | − | 0.404693i | ||||
\(313\) | −12.3991 | − | 21.4760i | −0.700841 | − | 1.21389i | −0.968172 | − | 0.250288i | \(-0.919475\pi\) |
0.267330 | − | 0.963605i | \(-0.413859\pi\) | |||||||
\(314\) | −3.63794 | − | 9.49934i | −0.205301 | − | 0.536079i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0271 | + | 14.3856i | −0.901595 | + | 0.809250i | ||||
\(317\) | −0.526409 | + | 1.96459i | −0.0295661 | + | 0.110342i | −0.979132 | − | 0.203225i | \(-0.934858\pi\) |
0.949566 | + | 0.313568i | \(0.101524\pi\) | |||||||
\(318\) | −6.89410 | − | 9.50454i | −0.386602 | − | 0.532988i | ||||
\(319\) | 0.835955 | + | 0.482639i | 0.0468045 | + | 0.0270226i | ||||
\(320\) | −2.40017 | − | 6.34142i | −0.134174 | − | 0.354496i | ||||
\(321\) | 12.5415i | 0.699999i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4803 | − | 25.4803i | 1.41776 | − | 1.41776i | ||||
\(324\) | −6.13351 | + | 18.7771i | −0.340751 | + | 1.04317i | ||||
\(325\) | −5.86038 | + | 1.57028i | −0.325075 | + | 0.0871037i | ||||
\(326\) | −12.4530 | − | 1.98234i | −0.689707 | − | 0.109792i | ||||
\(327\) | 22.5201 | − | 13.0020i | 1.24537 | − | 0.719013i | ||||
\(328\) | −13.1625 | + | 4.24264i | −0.726776 | + | 0.234261i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.21193 | + | 5.77577i | 0.121763 | + | 0.317946i | ||||
\(331\) | 0.379375 | − | 1.41585i | 0.0208524 | − | 0.0778221i | −0.954716 | − | 0.297520i | \(-0.903841\pi\) |
0.975568 | + | 0.219698i | \(0.0705072\pi\) | |||||||
\(332\) | −13.6670 | − | 8.90586i | −0.750074 | − | 0.488773i | ||||
\(333\) | −1.22611 | + | 0.328536i | −0.0671906 | + | 0.0180037i | ||||
\(334\) | 2.39867 | + | 22.9947i | 0.131249 | + | 1.25822i | ||||
\(335\) | −10.4427 | −0.570543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9109 | 0.921195 | 0.460598 | − | 0.887609i | \(-0.347635\pi\) | ||||
0.460598 | + | 0.887609i | \(0.347635\pi\) | |||||||
\(338\) | 1.61283 | + | 15.4613i | 0.0877262 | + | 0.840983i | ||||
\(339\) | 5.37516 | − | 1.44027i | 0.291939 | − | 0.0782247i | ||||
\(340\) | 5.99812 | − | 9.20476i | 0.325294 | − | 0.499198i | ||||
\(341\) | 2.47821 | − | 9.24879i | 0.134202 | − | 0.500850i | ||||
\(342\) | −0.922696 | − | 2.40933i | −0.0498937 | − | 0.130282i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 15.6890 | + | 8.04033i | 0.845892 | + | 0.433506i | ||||
\(345\) | 5.90164 | − | 3.40731i | 0.317734 | − | 0.183444i | ||||
\(346\) | −22.6046 | − | 3.59834i | −1.21523 | − | 0.193448i | ||||
\(347\) | 1.80586 | − | 0.483878i | 0.0969436 | − | 0.0259760i | −0.210021 | − | 0.977697i | \(-0.567353\pi\) |
0.306965 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(348\) | −1.18365 | − | 0.386638i | −0.0634502 | − | 0.0207259i | ||||
\(349\) | −17.2528 | + | 17.2528i | −0.923520 | + | 0.923520i | −0.997276 | − | 0.0737567i | \(-0.976501\pi\) |
0.0737567 | + | 0.997276i | \(0.476501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.90695i | 0.368666i | ||||||||
\(352\) | 11.3578 | − | 11.2694i | 0.605375 | − | 0.600661i | ||||
\(353\) | −2.58900 | − | 1.49476i | −0.137798 | − | 0.0795579i | 0.429516 | − | 0.903059i | \(-0.358684\pi\) |
−0.567314 | + | 0.823501i | \(0.692018\pi\) | |||||||
\(354\) | 2.89504 | + | 3.99124i | 0.153870 | + | 0.212132i | ||||
\(355\) | −2.69499 | + | 10.0578i | −0.143035 | + | 0.533815i | ||||
\(356\) | −17.8055 | − | 19.8373i | −0.943690 | − | 1.05138i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.32552 | − | 16.5171i | −0.334314 | − | 0.872958i | ||||
\(359\) | 4.81343 | + | 8.33711i | 0.254043 | + | 0.440016i | 0.964635 | − | 0.263588i | \(-0.0849061\pi\) |
−0.710592 | + | 0.703604i | \(0.751573\pi\) | |||||||
\(360\) | −0.426868 | − | 0.660706i | −0.0224979 | − | 0.0348223i | ||||
\(361\) | −10.3151 | − | 5.95545i | −0.542902 | − | 0.313445i | ||||
\(362\) | −27.2191 | − | 22.0768i | −1.43060 | − | 1.16033i | ||||
\(363\) | 3.86996 | − | 3.86996i | 0.203120 | − | 0.203120i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.482639 | + | 0.482639i | 0.0252625 | + | 0.0252625i | ||||
\(366\) | −35.7209 | + | 3.72619i | −1.86716 | + | 0.194771i | ||||
\(367\) | 3.69078 | − | 6.39263i | 0.192657 | − | 0.333692i | −0.753473 | − | 0.657479i | \(-0.771623\pi\) |
0.946130 | + | 0.323787i | \(0.104956\pi\) | |||||||
\(368\) | −14.2299 | − | 10.4068i | −0.741784 | − | 0.542490i | ||||
\(369\) | −1.38941 | + | 0.802178i | −0.0723299 | + | 0.0417597i | ||||
\(370\) | −1.88930 | + | 4.23452i | −0.0982199 | + | 0.220142i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.665723 | + | 12.3337i | −0.0345161 | + | 0.639474i | ||||
\(373\) | −3.36236 | − | 0.900941i | −0.174096 | − | 0.0466490i | 0.170718 | − | 0.985320i | \(-0.445391\pi\) |
−0.344814 | + | 0.938671i | \(0.612058\pi\) | |||||||
\(374\) | 25.6030 | + | 4.07563i | 1.32390 | + | 0.210746i | ||||
\(375\) | −7.17568 | + | 12.4286i | −0.370551 | + | 0.641813i | ||||
\(376\) | 19.8309 | + | 17.9402i | 1.02270 | + | 0.925197i | ||||
\(377\) | −0.483591 | −0.0249062 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.4803 | + | 11.4803i | 0.589706 | + | 0.589706i | 0.937552 | − | 0.347846i | \(-0.113087\pi\) |
−0.347846 | + | 0.937552i | \(0.613087\pi\) | |||||||
\(380\) | −8.95858 | − | 2.92631i | −0.459565 | − | 0.150117i | ||||
\(381\) | −4.25758 | − | 15.8895i | −0.218122 | − | 0.814044i | ||||
\(382\) | 5.16262 | − | 3.74470i | 0.264143 | − | 0.191596i | ||||
\(383\) | −0.0820044 | − | 0.142036i | −0.00419023 | − | 0.00725769i | 0.863923 | − | 0.503624i | \(-0.168000\pi\) |
−0.868113 | + | 0.496367i | \(0.834667\pi\) | |||||||
\(384\) | −11.3358 | + | 17.2482i | −0.578477 | + | 0.880193i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.02255 | + | 17.9811i | −0.408337 | + | 0.915213i | ||||
\(387\) | 1.97550 | + | 0.529333i | 0.100420 | + | 0.0269075i | ||||
\(388\) | 4.47269 | + | 21.2054i | 0.227067 | + | 1.07654i | ||||
\(389\) | −5.69172 | − | 21.2418i | −0.288582 | − | 1.07700i | −0.946182 | − | 0.323634i | \(-0.895095\pi\) |
0.657601 | − | 0.753367i | \(-0.271571\pi\) | |||||||
\(390\) | −2.40648 | − | 1.95184i | −0.121857 | − | 0.0988354i | ||||
\(391\) | − | 28.5653i | − | 1.44461i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.25042i | 0.0630755i | ||||||||
\(394\) | 12.7999 | − | 15.7814i | 0.644852 | − | 0.795054i | ||||
\(395\) | 2.36214 | + | 8.81562i | 0.118852 | + | 0.443562i | ||||
\(396\) | 1.01338 | − | 1.55514i | 0.0509242 | − | 0.0781486i | ||||
\(397\) | −24.9738 | − | 6.69170i | −1.25340 | − | 0.335847i | −0.429749 | − | 0.902948i | \(-0.641398\pi\) |
−0.823648 | + | 0.567102i | \(0.808065\pi\) | |||||||
\(398\) | 12.8029 | + | 5.71221i | 0.641750 | + | 0.286327i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.0271 | + | 1.84347i | 0.851355 | + | 0.0921736i | ||||
\(401\) | −7.86891 | − | 13.6294i | −0.392955 | − | 0.680617i | 0.599883 | − | 0.800088i | \(-0.295214\pi\) |
−0.992838 | + | 0.119470i | \(0.961880\pi\) | |||||||
\(402\) | 18.6642 | + | 25.7313i | 0.930885 | + | 1.28336i | ||||
\(403\) | 1.24155 | + | 4.63352i | 0.0618459 | + | 0.230812i | ||||
\(404\) | −13.8198 | + | 7.01434i | −0.687560 | + | 0.348976i | ||||
\(405\) | 5.91924 | + | 5.91924i | 0.294129 | + | 0.294129i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9418 | −0.542363 | ||||||||
\(408\) | −33.4015 | + | 1.67195i | −1.65362 | + | 0.0827741i | ||||
\(409\) | −13.9126 | + | 24.0974i | −0.687935 | + | 1.19154i | 0.284570 | + | 0.958655i | \(0.408149\pi\) |
−0.972505 | + | 0.232883i | \(0.925184\pi\) | |||||||
\(410\) | −0.921319 | + | 5.78769i | −0.0455007 | + | 0.285834i | ||||
\(411\) | −30.2150 | − | 8.09608i | −1.49039 | − | 0.399350i | ||||
\(412\) | −17.1960 | + | 15.4347i | −0.847184 | + | 0.760413i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.86772 | − | 0.833313i | −0.0917935 | − | 0.0409551i | ||||
\(415\) | −5.98676 | + | 3.45646i | −0.293879 | + | 0.169671i | ||||
\(416\) | −2.10489 | + | 7.73448i | −0.103201 | + | 0.379214i | ||||
\(417\) | 9.20265 | − | 15.9395i | 0.450656 | − | 0.780558i | ||||
\(418\) | −2.30732 | − | 22.1190i | −0.112855 | − | 1.08188i | ||||
\(419\) | 0.380613 | + | 0.380613i | 0.0185942 | + | 0.0185942i | 0.716343 | − | 0.697749i | \(-0.245815\pi\) |
−0.697749 | + | 0.716343i | \(0.745815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.48089 | − | 5.48089i | 0.267122 | − | 0.267122i | −0.560817 | − | 0.827940i | \(-0.689513\pi\) |
0.827940 | + | 0.560817i | \(0.189513\pi\) | |||||||
\(422\) | 8.23247 | − | 10.1500i | 0.400750 | − | 0.494095i | ||||
\(423\) | 2.68670 | + | 1.55116i | 0.130632 | + | 0.0754202i | ||||
\(424\) | 6.98543 | + | 10.8120i | 0.339242 | + | 0.525080i | ||||
\(425\) | 13.8754 | + | 24.0329i | 0.673056 | + | 1.16577i | ||||
\(426\) | 29.5999 | − | 11.3358i | 1.43412 | − | 0.549221i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.741049 | − | 13.7293i | 0.0358200 | − | 0.663630i | ||||
\(429\) | 1.89240 | − | 7.06252i | 0.0913658 | − | 0.340982i | ||||
\(430\) | 6.04750 | − | 4.38655i | 0.291636 | − | 0.211538i | ||||
\(431\) | −16.0085 | − | 9.24251i | −0.771102 | − | 0.445196i | 0.0621655 | − | 0.998066i | \(-0.480199\pi\) |
−0.833268 | + | 0.552870i | \(0.813533\pi\) | |||||||
\(432\) | 7.04411 | − | 18.1804i | 0.338910 | − | 0.874705i | ||||
\(433\) | − | 30.9347i | − | 1.48663i | −0.668944 | − | 0.743313i | \(-0.733254\pi\) | ||
0.668944 | − | 0.743313i | \(-0.266746\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.373130 | + | 0.373130i | −0.0178902 | + | 0.0178902i | ||||
\(436\) | −25.4212 | + | 12.9027i | −1.21746 | + | 0.617929i | ||||
\(437\) | −23.6686 | + | 6.34200i | −1.13222 | + | 0.303379i | ||||
\(438\) | 0.326629 | − | 2.05187i | 0.0156069 | − | 0.0980422i | ||||
\(439\) | −17.3479 | + | 10.0158i | −0.827971 | + | 0.478029i | −0.853157 | − | 0.521654i | \(-0.825315\pi\) |
0.0251865 | + | 0.999683i | \(0.491982\pi\) | |||||||
\(440\) | −2.08014 | − | 6.45348i | −0.0991669 | − | 0.307658i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.1292 | + | 4.64509i | −0.576927 | + | 0.220944i | ||||
\(443\) | −0.156181 | + | 0.582875i | −0.00742038 | + | 0.0276932i | −0.969537 | − | 0.244946i | \(-0.921230\pi\) |
0.962116 | + | 0.272639i | \(0.0878965\pi\) | |||||||
\(444\) | 13.8109 | − | 2.91303i | 0.655434 | − | 0.138246i | ||||
\(445\) | −10.9114 | + | 2.92370i | −0.517250 | + | 0.138597i | ||||
\(446\) | 3.19924 | − | 0.333726i | 0.151489 | − | 0.0158024i | ||||
\(447\) | −22.8356 | −1.08009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1266 | 0.619483 | 0.309741 | − | 0.950821i | \(-0.399758\pi\) | ||||
0.309741 | + | 0.950821i | \(0.399758\pi\) | |||||||
\(450\) | 1.97615 | − | 0.206140i | 0.0931567 | − | 0.00971753i | ||||
\(451\) | −13.3581 | + | 3.57930i | −0.629009 | + | 0.168542i | ||||
\(452\) | −5.96933 | + | 1.25907i | −0.280774 | + | 0.0592216i | ||||
\(453\) | 3.18208 | − | 11.8757i | 0.149507 | − | 0.557968i | ||||
\(454\) | 16.6387 | − | 6.37208i | 0.780893 | − | 0.299057i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.80108 | + | 27.3047i | 0.412148 | + | 1.27866i | ||||
\(457\) | −13.5488 | + | 7.82243i | −0.633788 | + | 0.365918i | −0.782218 | − | 0.623005i | \(-0.785912\pi\) |
0.148429 | + | 0.988923i | \(0.452578\pi\) | |||||||
\(458\) | −1.89879 | + | 11.9281i | −0.0887246 | + | 0.557364i | ||||
\(459\) | 30.5157 | − | 8.17667i | 1.42435 | − | 0.381654i | ||||
\(460\) | −6.66190 | + | 3.38130i | −0.310613 | + | 0.157654i | ||||
\(461\) | −28.3593 | + | 28.3593i | −1.32082 | + | 1.32082i | −0.407712 | + | 0.913111i | \(0.633673\pi\) |
−0.913111 | + | 0.407712i | \(0.866327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1195i | 0.609716i | 0.952398 | + | 0.304858i | \(0.0986089\pi\) | ||||
−0.952398 | + | 0.304858i | \(0.901391\pi\) | |||||||
\(464\) | 1.27290 | + | 0.493194i | 0.0590930 | + | 0.0228960i | ||||
\(465\) | 4.53310 | + | 2.61719i | 0.210217 | + | 0.121369i | ||||
\(466\) | 29.9845 | − | 21.7492i | 1.38901 | − | 1.00751i | ||||
\(467\) | −10.4125 | + | 38.8600i | −0.481833 | + | 1.79823i | 0.112083 | + | 0.993699i | \(0.464248\pi\) |
−0.593916 | + | 0.804527i | \(0.702419\pi\) | |||||||
\(468\) | −0.0501202 | + | 0.928567i | −0.00231680 | + | 0.0429230i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.5830 | − | 4.05294i | 0.488157 | − | 0.186948i | ||||
\(471\) | 6.56095 | + | 11.3639i | 0.302312 | + | 0.523621i | ||||
\(472\) | −2.93339 | − | 4.54031i | −0.135020 | − | 0.208985i | ||||
\(473\) | 15.2674 | + | 8.81463i | 0.701995 | + | 0.405297i | ||||
\(474\) | 17.5004 | − | 21.5766i | 0.803818 | − | 0.991047i | ||||
\(475\) | 16.8326 | − | 16.8326i | 0.772334 | − | 0.772334i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.05594 | + | 1.05594i | 0.0483484 | + | 0.0483484i | ||||
\(478\) | −3.02434 | − | 28.9927i | −0.138330 | − | 1.32609i | ||||
\(479\) | 16.7806 | − | 29.0649i | 0.766725 | − | 1.32801i | −0.172604 | − | 0.984991i | \(-0.555218\pi\) |
0.939330 | − | 0.343016i | \(-0.111449\pi\) | |||||||
\(480\) | 4.34370 | + | 7.59188i | 0.198262 | + | 0.346520i | ||||
\(481\) | 4.74727 | − | 2.74084i | 0.216457 | − | 0.124971i | ||||
\(482\) | −0.917493 | − | 0.409354i | −0.0417906 | − | 0.0186456i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.46514 | + | 4.00781i | −0.202961 | + | 0.182173i | ||||
\(485\) | 8.87114 | + | 2.37701i | 0.402818 | + | 0.107935i | ||||
\(486\) | 0.754843 | − | 4.74189i | 0.0342404 | − | 0.215097i | ||||
\(487\) | −8.71339 | + | 15.0920i | −0.394841 | + | 0.683886i | −0.993081 | − | 0.117432i | \(-0.962534\pi\) |
0.598239 | + | 0.801317i | \(0.295867\pi\) | |||||||
\(488\) | 39.3241 | − | 1.96842i | 1.78012 | − | 0.0891061i | ||||
\(489\) | 16.2664 | 0.735594 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.00947 | − | 4.00947i | −0.180945 | − | 0.180945i | 0.610823 | − | 0.791767i | \(-0.290839\pi\) |
−0.791767 | + | 0.610823i | \(0.790839\pi\) | |||||||
\(492\) | 15.9079 | − | 8.07417i | 0.717183 | − | 0.364012i | ||||
\(493\) | 0.572490 | + | 2.13656i | 0.0257837 | + | 0.0962259i | ||||
\(494\) | 6.54173 | + | 9.01874i | 0.294326 | + | 0.405772i | ||||
\(495\) | −0.393303 | − | 0.681221i | −0.0176777 | − | 0.0306186i | ||||
\(496\) | 1.45754 | − | 13.4625i | 0.0654457 | − | 0.604484i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 19.2171 | + | 8.57400i | 0.861138 | + | 0.384210i | ||||
\(499\) | 22.1732 | + | 5.94130i | 0.992611 | + | 0.265969i | 0.718347 | − | 0.695685i | \(-0.244899\pi\) |
0.274264 | + | 0.961654i | \(0.411566\pi\) | |||||||
\(500\) | 8.58966 | − | 13.1817i | 0.384141 | − | 0.589506i | ||||
\(501\) | −7.71898 | − | 28.8076i | −0.344859 | − | 1.28703i | ||||
\(502\) | −6.27505 | + | 7.73667i | −0.280069 | + | 0.345304i | ||||
\(503\) | − | 1.85332i | − | 0.0826356i | −0.999146 | − | 0.0413178i | \(-0.986844\pi\) | ||
0.999146 | − | 0.0413178i | \(-0.0131556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.56770i | 0.292259i | ||||||||
\(506\) | −13.6918 | − | 11.1052i | −0.608676 | − | 0.493684i | ||||
\(507\) | −5.19012 | − | 19.3698i | −0.230501 | − | 0.860242i | ||||
\(508\) | 3.72193 | + | 17.6459i | 0.165134 | + | 0.782912i | ||||
\(509\) | 10.4370 | + | 2.79659i | 0.462613 | + | 0.123957i | 0.482595 | − | 0.875844i | \(-0.339694\pi\) |
−0.0199820 | + | 0.999800i | \(0.506361\pi\) | |||||||
\(510\) | −5.77461 | + | 12.9427i | −0.255704 | + | 0.573114i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 13.4285 | − | 18.2119i | 0.593463 | − | 0.804861i | ||||
\(513\) | −13.5501 | − | 23.4694i | −0.598250 | − | 1.03620i | ||||
\(514\) | 7.10995 | − | 5.15719i | 0.313607 | − | 0.227474i | ||||
\(515\) | 2.53441 | + | 9.45854i | 0.111679 | + | 0.416793i | ||||
\(516\) | −21.6174 | − | 7.06132i | −0.951654 | − | 0.310857i | ||||
\(517\) | 18.9092 | + | 18.9092i | 0.831627 | + | 0.831627i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.5268 | 1.29608 | ||||||||
\(520\) | 2.51906 | + | 2.27889i | 0.110468 | + | 0.0999360i | ||||
\(521\) | 16.9527 | − | 29.3630i | 0.742713 | − | 1.28642i | −0.208543 | − | 0.978013i | \(-0.566872\pi\) |
0.951256 | − | 0.308403i | \(-0.0997945\pi\) | |||||||
\(522\) | 0.156398 | + | 0.0248964i | 0.00684537 | + | 0.00108969i | ||||
\(523\) | 1.65274 | + | 0.442850i | 0.0722691 | + | 0.0193645i | 0.294772 | − | 0.955567i | \(-0.404756\pi\) |
−0.222503 | + | 0.974932i | \(0.571423\pi\) | |||||||
\(524\) | 0.0738846 | − | 1.36885i | 0.00322766 | − | 0.0597984i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.451411 | + | 1.01176i | −0.0196825 | + | 0.0441147i | ||||
\(527\) | 19.0017 | − | 10.9706i | 0.827725 | − | 0.477887i | ||||
\(528\) | −12.1839 | + | 16.6599i | −0.530237 | + | 0.725030i | ||||
\(529\) | 1.78780 | − | 3.09656i | 0.0777304 | − | 0.134633i | ||||
\(530\) | 5.42556 | − | 0.565961i | 0.235671 | − | 0.0245838i | ||||
\(531\) | −0.443423 | − | 0.443423i | −0.0192429 | − | 0.0192429i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.89905 | − | 4.89905i | 0.212202 | − | 0.212202i | ||||
\(534\) | 26.7062 | + | 21.6608i | 1.15569 | + | 0.937355i | ||||
\(535\) | −5.04602 | − | 2.91332i | −0.218158 | − | 0.125954i | ||||
\(536\) | −18.9114 | − | 29.2711i | −0.816849 | − | 1.26432i | ||||
\(537\) | 11.4080 | + | 19.7592i | 0.492290 | + | 0.852671i | ||||
\(538\) | 8.83652 | + | 23.0738i | 0.380969 | + | 0.994783i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.51911 | − | 6.14890i | −0.237505 | − | 0.264607i | ||||
\(541\) | −0.878346 | + | 3.27803i | −0.0377631 | + | 0.140934i | −0.982234 | − | 0.187663i | \(-0.939909\pi\) |
0.944470 | + | 0.328596i | \(0.106576\pi\) | |||||||
\(542\) | −5.34317 | − | 7.36634i | −0.229509 | − | 0.316411i | ||||
\(543\) | 39.1527 | + | 22.6048i | 1.68020 | + | 0.970066i | ||||
\(544\) | 36.6637 | + | 0.143317i | 1.57194 | + | 0.00614468i | ||||
\(545\) | 12.0812i | 0.517500i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2048 | − | 14.2048i | 0.607355 | − | 0.607355i | −0.334899 | − | 0.942254i | \(-0.608702\pi\) |
0.942254 | + | 0.334899i | \(0.108702\pi\) | |||||||
\(548\) | 32.5982 | + | 10.6482i | 1.39253 | + | 0.454867i | ||||
\(549\) | 4.41210 | − | 1.18222i | 0.188304 | − | 0.0504559i | ||||
\(550\) | 16.9136 | + | 2.69241i | 0.721200 | + | 0.114805i | ||||
\(551\) | 1.64321 | − | 0.948709i | 0.0700032 | − | 0.0404164i | ||||
\(552\) | 20.2385 | + | 10.3719i | 0.861410 | + | 0.441458i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.74058 | − | 9.76736i | −0.158922 | − | 0.414975i | ||||
\(555\) | 1.54813 | − | 5.77769i | 0.0657144 | − | 0.245249i | ||||
\(556\) | −11.0160 | + | 16.9053i | −0.467184 | + | 0.716944i | ||||
\(557\) | 30.0337 | − | 8.04752i | 1.27257 | − | 0.340984i | 0.441555 | − | 0.897234i | \(-0.354427\pi\) |
0.831015 | + | 0.556250i | \(0.187760\pi\) | |||||||
\(558\) | −0.162985 | − | 1.56245i | −0.00689970 | − | 0.0661437i | ||||
\(559\) | −8.83201 | −0.373554 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.4433 | −1.41198 | ||||||||
\(562\) | 2.18051 | + | 20.9034i | 0.0919793 | + | 0.881755i | ||||
\(563\) | −26.3524 | + | 7.06109i | −1.11062 | + | 0.297590i | −0.767082 | − | 0.641549i | \(-0.778292\pi\) |
−0.343538 | + | 0.939139i | \(0.611625\pi\) | |||||||
\(564\) | −28.9017 | − | 18.8333i | −1.21698 | − | 0.793025i | ||||
\(565\) | −0.669132 | + | 2.49724i | −0.0281506 | + | 0.105060i | ||||
\(566\) | 5.92777 | + | 15.4785i | 0.249163 | + | 0.650611i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −33.0730 | + | 10.6604i | −1.38771 | + | 0.447300i | ||||
\(569\) | 7.94537 | − | 4.58726i | 0.333087 | − | 0.192308i | −0.324124 | − | 0.946015i | \(-0.605069\pi\) |
0.657211 | + | 0.753707i | \(0.271736\pi\) | |||||||
\(570\) | 12.0062 | + | 1.91122i | 0.502884 | + | 0.0800520i | ||||
\(571\) | −40.6239 | + | 10.8851i | −1.70006 | + | 0.455529i | −0.972954 | − | 0.230999i | \(-0.925801\pi\) |
−0.727103 | + | 0.686528i | \(0.759134\pi\) | |||||||
\(572\) | −2.48893 | + | 7.61958i | −0.104067 | + | 0.318591i | ||||
\(573\) | −5.81750 | + | 5.81750i | −0.243029 | + | 0.243029i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 18.8706i | − | 0.786957i | ||||||
\(576\) | 1.07893 | − | 2.39305i | 0.0449555 | − | 0.0997104i | ||||
\(577\) | 22.0711 | + | 12.7427i | 0.918830 | + | 0.530487i | 0.883262 | − | 0.468880i | \(-0.155342\pi\) |
0.0355687 | + | 0.999367i | \(0.488676\pi\) | |||||||
\(578\) | 20.7654 | + | 28.6281i | 0.863726 | + | 1.19077i | ||||
\(579\) | 6.57383 | − | 24.5339i | 0.273199 | − | 1.01959i | ||||
\(580\) | 0.430516 | − | 0.386421i | 0.0178762 | − | 0.0160453i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.99830 | − | 26.1074i | −0.414443 | − | 1.08219i | ||||
\(583\) | 6.43616 | + | 11.1478i | 0.266559 | + | 0.461693i | ||||
\(584\) | −0.478804 | + | 2.22690i | −0.0198130 | + | 0.0921498i | ||||
\(585\) | 0.341282 | + | 0.197039i | 0.0141103 | + | 0.00814658i | ||||
\(586\) | 12.6118 | + | 10.2291i | 0.520987 | + | 0.422562i | ||||
\(587\) | 18.3219 | − | 18.3219i | 0.756227 | − | 0.756227i | −0.219406 | − | 0.975634i | \(-0.570412\pi\) |
0.975634 | + | 0.219406i | \(0.0704121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.3087 | − | 13.3087i | −0.548377 | − | 0.548377i | ||||
\(590\) | −2.27836 | + | 0.237664i | −0.0937985 | + | 0.00978449i | ||||
\(591\) | −13.1061 | + | 22.7004i | −0.539111 | + | 0.933768i | ||||
\(592\) | −15.2910 | + | 2.37286i | −0.628455 | + | 0.0975239i | ||||
\(593\) | 13.4221 | − | 7.74927i | 0.551181 | − | 0.318225i | −0.198417 | − | 0.980118i | \(-0.563580\pi\) |
0.749598 | + | 0.661893i | \(0.230247\pi\) | |||||||
\(594\) | 7.94421 | − | 17.8055i | 0.325955 | − | 0.730569i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.9983 | + | 1.34930i | 1.02397 | + | 0.0552696i | ||||
\(597\) | −17.4686 | − | 4.68069i | −0.714942 | − | 0.191568i | ||||
\(598\) | 8.72219 | + | 1.38845i | 0.356677 | + | 0.0567780i | ||||
\(599\) | −6.73751 | + | 11.6697i | −0.275287 | + | 0.476811i | −0.970208 | − | 0.242275i | \(-0.922106\pi\) |
0.694920 | + | 0.719087i | \(0.255440\pi\) | |||||||
\(600\) | −22.0655 | + | 1.10451i | −0.900818 | + | 0.0450916i | ||||
\(601\) | −0.365448 | −0.0149069 | −0.00745346 | − | 0.999972i | \(-0.502373\pi\) | ||||
−0.00745346 | + | 0.999972i | \(0.502373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.85872 | − | 2.85872i | −0.116416 | − | 0.116416i | ||||
\(604\) | −4.18515 | + | 12.8124i | −0.170292 | + | 0.521328i | ||||
\(605\) | 0.658090 | + | 2.45603i | 0.0267552 | + | 0.0998517i | ||||
\(606\) | 16.1832 | − | 11.7385i | 0.657397 | − | 0.476842i | ||||
\(607\) | 3.15743 | + | 5.46882i | 0.128156 | + | 0.221973i | 0.922962 | − | 0.384891i | \(-0.125761\pi\) |
−0.794806 | + | 0.606863i | \(0.792428\pi\) | |||||||
\(608\) | −8.02124 | − | 30.4107i | −0.325304 | − | 1.23332i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.79854 | − | 15.2377i | 0.275265 | − | 0.616957i | ||||
\(611\) | −12.9407 | − | 3.46745i | −0.523525 | − | 0.140278i | ||||
\(612\) | 4.16185 | − | 0.877830i | 0.168233 | − | 0.0354842i | ||||
\(613\) | 2.57122 | + | 9.59594i | 0.103851 | + | 0.387576i | 0.998212 | − | 0.0597686i | \(-0.0190363\pi\) |
−0.894361 | + | 0.447345i | \(0.852370\pi\) | |||||||
\(614\) | 22.1388 | + | 17.9563i | 0.893448 | + | 0.724657i | ||||
\(615\) | − | 7.56005i | − | 0.304850i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.7832i | 1.36006i | 0.733184 | + | 0.680031i | \(0.238034\pi\) | ||||
−0.733184 | + | 0.680031i | \(0.761966\pi\) | |||||||
\(618\) | 18.7767 | − | 23.1502i | 0.755308 | − | 0.931238i | ||||
\(619\) | −6.97174 | − | 26.0189i | −0.280218 | − | 1.04579i | −0.952263 | − | 0.305278i | \(-0.901251\pi\) |
0.672045 | − | 0.740510i | \(-0.265416\pi\) | |||||||
\(620\) | −4.80777 | − | 3.13290i | −0.193085 | − | 0.125820i | ||||
\(621\) | −20.7507 | − | 5.56014i | −0.832698 | − | 0.223121i | ||||
\(622\) | −16.4242 | − | 7.32790i | −0.658549 | − | 0.293822i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.11300 | − | 10.2802i | 0.0445558 | − | 0.411536i | ||||
\(625\) | 7.37039 | + | 12.7659i | 0.294816 | + | 0.510635i | ||||
\(626\) | −20.5915 | − | 28.3884i | −0.823001 | − | 1.13463i | ||||
\(627\) | 7.42501 | + | 27.7105i | 0.296526 | + | 1.10665i | ||||
\(628\) | −6.51085 | − | 12.8278i | −0.259811 | − | 0.511886i | ||||
\(629\) | −17.7293 | − | 17.7293i | −0.706914 | − | 0.706914i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.5097 | −1.29419 | −0.647096 | − | 0.762408i | \(-0.724017\pi\) | ||||
−0.647096 | + | 0.762408i | \(0.724017\pi\) | |||||||
\(632\) | −20.4327 | + | 22.5860i | −0.812769 | + | 0.898424i | ||||
\(633\) | −8.42935 | + | 14.6001i | −0.335037 | + | 0.580301i | ||||
\(634\) | −0.452182 | + | 2.84059i | −0.0179584 | + | 0.112814i | ||||
\(635\) | 7.38207 | + | 1.97802i | 0.292949 | + | 0.0784953i | ||||
\(636\) | −11.0917 | − | 12.3574i | −0.439814 | − | 0.490001i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.24665 | + | 0.556214i | 0.0493555 | + | 0.0220207i | ||||
\(639\) | −3.49115 | + | 2.01561i | −0.138108 | + | 0.0797365i | ||||
\(640\) | −4.30649 | − | 8.56755i | −0.170229 | − | 0.338662i | ||||
\(641\) | 7.79534 | − | 13.5019i | 0.307897 | − | 0.533294i | −0.670005 | − | 0.742357i | \(-0.733708\pi\) |
0.977902 | + | 0.209063i | \(0.0670414\pi\) | |||||||
\(642\) | 1.84017 | + | 17.6407i | 0.0726255 | + | 0.696221i | ||||
\(643\) | 12.1182 | + | 12.1182i | 0.477896 | + | 0.477896i | 0.904458 | − | 0.426562i | \(-0.140275\pi\) |
−0.426562 | + | 0.904458i | \(0.640275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.81463 | + | 6.81463i | −0.268326 | + | 0.268326i | ||||
\(646\) | 32.1016 | − | 39.5788i | 1.26302 | − | 1.55721i | ||||
\(647\) | −20.9126 | − | 12.0739i | −0.822161 | − | 0.474675i | 0.0290002 | − | 0.999579i | \(-0.490768\pi\) |
−0.851161 | + | 0.524905i | \(0.824101\pi\) | |||||||
\(648\) | −5.87220 | + | 27.3114i | −0.230682 | + | 1.07289i | ||||
\(649\) | −2.70274 | − | 4.68128i | −0.106092 | − | 0.183756i | ||||
\(650\) | −8.01270 | + | 3.06860i | −0.314284 | + | 0.120361i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.8070 | − | 0.961147i | −0.697376 | − | 0.0376414i | ||||
\(653\) | 2.82286 | − | 10.5351i | 0.110467 | − | 0.412269i | −0.888441 | − | 0.458991i | \(-0.848211\pi\) |
0.998908 | + | 0.0467223i | \(0.0148776\pi\) | |||||||
\(654\) | 29.7687 | − | 21.5927i | 1.16405 | − | 0.844340i | ||||
\(655\) | −0.503101 | − | 0.290466i | −0.0196578 | − | 0.0113494i | ||||
\(656\) | −17.8916 | + | 7.89890i | −0.698549 | + | 0.308400i | ||||
\(657\) | 0.264249i | 0.0103093i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7175 | + | 20.7175i | −0.807041 | + | 0.807041i | −0.984185 | − | 0.177144i | \(-0.943314\pi\) |
0.177144 | + | 0.984185i | \(0.443314\pi\) | |||||||
\(660\) | 3.95872 | + | 7.79955i | 0.154093 | + | 0.303597i | ||||
\(661\) | 0.332247 | − | 0.0890254i | 0.0129229 | − | 0.00346269i | −0.252352 | − | 0.967636i | \(-0.581204\pi\) |
0.265275 | + | 0.964173i | \(0.414537\pi\) | |||||||
\(662\) | 0.325881 | − | 2.04717i | 0.0126657 | − | 0.0795655i | ||||
\(663\) | 14.5100 | − | 8.37733i | 0.563520 | − | 0.325348i | ||||
\(664\) | −20.5305 | − | 10.5215i | −0.796736 | − | 0.408314i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.67642 | + | 0.642015i | −0.0649601 | + | 0.0248776i | ||||
\(667\) | 0.389294 | − | 1.45286i | 0.0150735 | − | 0.0562551i | ||||
\(668\) | 6.74785 | + | 31.9920i | 0.261082 | + | 1.23781i | ||||
\(669\) | −4.00799 | + | 1.07394i | −0.154958 | + | 0.0415208i | ||||
\(670\) | −14.6884 | + | 1.53221i | −0.567464 | + | 0.0591944i | ||||
\(671\) | 39.3734 | 1.51999 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4244 | −0.594567 | −0.297284 | − | 0.954789i | \(-0.596081\pi\) | ||||
−0.297284 | + | 0.954789i | \(0.596081\pi\) | |||||||
\(674\) | 23.7866 | − | 2.48127i | 0.916224 | − | 0.0955749i | ||||
\(675\) | 20.1591 | − | 5.40161i | 0.775923 | − | 0.207908i | ||||
\(676\) | 4.53714 | + | 21.5109i | 0.174506 | + | 0.827343i | ||||
\(677\) | −4.90205 | + | 18.2947i | −0.188401 | + | 0.703122i | 0.805476 | + | 0.592629i | \(0.201910\pi\) |
−0.993877 | + | 0.110494i | \(0.964757\pi\) | |||||||
\(678\) | 7.34928 | − | 2.81453i | 0.282247 | − | 0.108092i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.08627 | − | 13.8273i | 0.271746 | − | 0.530253i | ||||
\(681\) | −19.9046 | + | 11.4919i | −0.762746 | + | 0.440371i | ||||
\(682\) | 2.12876 | − | 13.3728i | 0.0815145 | − | 0.512071i | ||||
\(683\) | −8.51213 | + | 2.28082i | −0.325708 | + | 0.0872731i | −0.417968 | − | 0.908462i | \(-0.637258\pi\) |
0.0922601 | + | 0.995735i | \(0.470591\pi\) | |||||||
\(684\) | −1.65136 | − | 3.25354i | −0.0631413 | − | 0.124402i | ||||
\(685\) | 10.2762 | − | 10.2762i | 0.392632 | − | 0.392632i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 15.5808i | − | 0.594446i | ||||||
\(688\) | 23.2475 | + | 9.00740i | 0.886304 | + | 0.343404i | ||||
\(689\) | −5.58487 | − | 3.22443i | −0.212767 | − | 0.122841i | ||||
\(690\) | 7.80119 | − | 5.65859i | 0.296986 | − | 0.215419i | ||||
\(691\) | 2.51074 | − | 9.37022i | 0.0955131 | − | 0.356460i | −0.901584 | − | 0.432605i | \(-0.857595\pi\) |
0.997097 | + | 0.0761450i | \(0.0242612\pi\) | |||||||
\(692\) | −32.3232 | − | 1.74467i | −1.22875 | − | 0.0663225i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.46909 | − | 0.945581i | 0.0937254 | − | 0.0358938i | ||||
\(695\) | 4.27544 | + | 7.40528i | 0.162177 | + | 0.280898i | ||||
\(696\) | −1.72163 | − | 0.370165i | −0.0652581 | − | 0.0140311i | ||||
\(697\) | −27.4443 | − | 15.8449i | −1.03953 | − | 0.600170i | ||||
\(698\) | −21.7360 | + | 26.7989i | −0.822720 | + | 1.01435i | ||||
\(699\) | −33.7880 | + | 33.7880i | −1.27798 | + | 1.27798i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.666263 | + | 0.666263i | 0.0251644 | + | 0.0251644i | 0.719577 | − | 0.694413i | \(-0.244336\pi\) |
−0.694413 | + | 0.719577i | \(0.744336\pi\) | |||||||
\(702\) | 1.01343 | + | 9.71519i | 0.0382494 | + | 0.366676i | ||||
\(703\) | −10.7540 | + | 18.6264i | −0.405593 | + | 0.702508i | ||||
\(704\) | 14.3222 | − | 17.5178i | 0.539789 | − | 0.660228i | ||||
\(705\) | −12.6603 | + | 7.30940i | −0.476813 | + | 0.275288i | ||||
\(706\) | −3.86095 | − | 1.72263i | −0.145309 | − | 0.0648319i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.65773 | + | 5.18923i | 0.175048 | + | 0.195023i | ||||
\(709\) | −39.6900 | − | 10.6349i | −1.49059 | − | 0.399403i | −0.580654 | − | 0.814150i | \(-0.697203\pi\) |
−0.909937 | + | 0.414747i | \(0.863870\pi\) | |||||||
\(710\) | −2.31498 | + | 14.5426i | −0.0868796 | + | 0.545774i | ||||
\(711\) | −1.76667 | + | 3.05996i | −0.0662553 | + | 0.114757i | ||||
\(712\) | −27.9555 | − | 25.2903i | −1.04768 | − | 0.947793i | ||||
\(713\) | −14.9200 | −0.558760 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.40198 | + | 2.40198i | 0.0898289 | + | 0.0898289i | ||||
\(716\) | −11.3209 | − | 22.3046i | −0.423080 | − | 0.833561i | ||||
\(717\) | 9.73240 | + | 36.3218i | 0.363463 | + | 1.35646i | ||||
\(718\) | 7.99376 | + | 11.0206i | 0.298324 | + | 0.411284i | ||||
\(719\) | −15.6434 | − | 27.0951i | −0.583399 | − | 1.01048i | −0.995073 | − | 0.0991455i | \(-0.968389\pi\) |
0.411674 | − | 0.911331i | \(-0.364944\pi\) | |||||||
\(720\) | −0.697367 | − | 0.866705i | −0.0259893 | − | 0.0323002i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.3829 | − | 6.86333i | −0.572493 | − | 0.255427i | ||||
\(723\) | 1.25185 | + | 0.335432i | 0.0465568 | + | 0.0124749i | ||||
\(724\) | −41.5251 | − | 27.0591i | −1.54327 | − | 1.00564i | ||||
\(725\) | 0.378194 | + | 1.41144i | 0.0140458 | + | 0.0524195i | ||||
\(726\) | 4.87559 | − | 6.01124i | 0.180950 | − | 0.223098i | ||||
\(727\) | 22.8730i | 0.848313i | 0.905589 | + | 0.424157i | \(0.139429\pi\) | ||||
−0.905589 | + | 0.424157i | \(0.860571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 23.4362i | − | 0.868006i | ||||||
\(730\) | 0.749686 | + | 0.608055i | 0.0277471 | + | 0.0225051i | ||||
\(731\) | 10.4556 | + | 39.0209i | 0.386715 | + | 1.44324i | ||||
\(732\) | −49.6977 | + | 10.4824i | −1.83688 | + | 0.387440i | ||||
\(733\) | 18.1526 | + | 4.86396i | 0.670480 | + | 0.179655i | 0.577971 | − | 0.816057i | \(-0.303845\pi\) |
0.0925090 | + | 0.995712i | \(0.470511\pi\) | |||||||
\(734\) | 4.25342 | − | 9.53328i | 0.156997 | − | 0.351880i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.5424 | − | 12.5501i | −0.794065 | − | 0.462602i | ||||
\(737\) | −17.4244 | − | 30.1800i | −0.641836 | − | 1.11169i | ||||
\(738\) | −1.83662 | + | 1.33219i | −0.0676070 | + | 0.0490386i | ||||
\(739\) | 7.07321 | + | 26.3976i | 0.260192 | + | 0.971050i | 0.965128 | + | 0.261779i | \(0.0843092\pi\) |
−0.704936 | + | 0.709271i | \(0.749024\pi\) | |||||||
\(740\) | −2.03614 | + | 6.23341i | −0.0748499 | + | 0.229145i | ||||
\(741\) | −10.1628 | − | 10.1628i | −0.373338 | − | 0.373338i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.76335 | 0.0646911 | 0.0323455 | − | 0.999477i | \(-0.489702\pi\) | ||||
0.0323455 | + | 0.999477i | \(0.489702\pi\) | |||||||
\(744\) | 0.873286 | + | 17.4461i | 0.0320162 | + | 0.639605i | ||||
\(745\) | 5.30457 | − | 9.18779i | 0.194344 | − | 0.336614i | ||||
\(746\) | −4.86162 | − | 0.773902i | −0.177997 | − | 0.0283346i | ||||
\(747\) | −2.58512 | − | 0.692682i | −0.0945847 | − | 0.0253439i | ||||
\(748\) | 36.6107 | + | 1.97609i | 1.33862 | + | 0.0722530i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.26958 | + | 18.5348i | −0.301962 | + | 0.676794i | ||||
\(751\) | −38.6945 | + | 22.3403i | −1.41198 | + | 0.815208i | −0.995575 | − | 0.0939709i | \(-0.970044\pi\) |
−0.416406 | + | 0.909179i | \(0.636711\pi\) | |||||||
\(752\) | 30.5261 | + | 22.3247i | 1.11317 | + | 0.814098i | ||||
\(753\) | 6.42513 | − | 11.1286i | 0.234145 | − | 0.405550i | ||||
\(754\) | −0.680210 | + | 0.0709553i | −0.0247718 | + | 0.00258404i | ||||
\(755\) | 4.03894 | + | 4.03894i | 0.146992 | + | 0.146992i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.5033 | + | 36.5033i | −1.32674 | + | 1.32674i | −0.418535 | + | 0.908201i | \(0.637456\pi\) |
−0.908201 | + | 0.418535i | \(0.862544\pi\) | |||||||
\(758\) | 17.8325 | + | 14.4636i | 0.647706 | + | 0.525341i | ||||
\(759\) | 19.6947 | + | 11.3707i | 0.714873 | + | 0.412732i | ||||
\(760\) | −13.0303 | − | 2.80164i | −0.472660 | − | 0.101626i | ||||
\(761\) | −20.6645 | − | 35.7919i | −0.749087 | − | 1.29746i | −0.948261 | − | 0.317493i | \(-0.897159\pi\) |
0.199173 | − | 0.979964i | \(-0.436174\pi\) | |||||||
\(762\) | −8.32003 | − | 21.7252i | −0.301403 | − | 0.787020i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.71220 | − | 6.02472i | 0.242839 | − | 0.217967i | ||||
\(765\) | 0.466523 | − | 1.74109i | 0.0168672 | − | 0.0629492i | ||||
\(766\) | −0.136186 | − | 0.187753i | −0.00492061 | − | 0.00678378i | ||||
\(767\) | 2.34526 | + | 1.35404i | 0.0846824 | + | 0.0488914i | ||||
\(768\) | −13.4140 | + | 25.9243i | −0.484034 | + | 0.935461i | ||||
\(769\) | 11.7612i | 0.424120i | 0.977257 | + | 0.212060i | \(0.0680171\pi\) | ||||
−0.977257 | + | 0.212060i | \(0.931983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.01185 | + | 8.01185i | −0.288540 | + | 0.288540i | ||||
\(772\) | −8.64607 | + | 26.4690i | −0.311179 | + | 0.952639i | ||||
\(773\) | 31.1792 | − | 8.35443i | 1.12144 | − | 0.300488i | 0.349972 | − | 0.936760i | \(-0.386191\pi\) |
0.771465 | + | 0.636272i | \(0.219524\pi\) | |||||||
\(774\) | 2.85637 | + | 0.454694i | 0.102670 | + | 0.0163436i | ||||
\(775\) | 12.5527 | − | 7.24732i | 0.450907 | − | 0.260331i | ||||
\(776\) | 9.40259 | + | 29.1708i | 0.337533 | + | 1.04717i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.1226 | − | 29.0432i | −0.398764 | − | 1.04125i | ||||
\(779\) | −7.03572 | + | 26.2577i | −0.252081 | + | 0.940778i | ||||
\(780\) | −3.67129 | − | 2.39233i | −0.131453 | − | 0.0856593i | ||||
\(781\) | −33.5646 | + | 8.99362i | −1.20104 | + | 0.321817i | ||||
\(782\) | −4.19127 | − | 40.1794i | −0.149879 | − | 1.43681i | ||||
\(783\) | 1.66350 | 0.0594486 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.09628 | −0.217585 | ||||||||
\(786\) | 0.183469 | + | 1.75882i | 0.00654414 | + | 0.0627351i | ||||
\(787\) | 38.5848 | − | 10.3388i | 1.37540 | − | 0.368537i | 0.505952 | − | 0.862562i | \(-0.331141\pi\) |
0.869448 | + | 0.494024i | \(0.164475\pi\) | |||||||
\(788\) | 15.6886 | − | 24.0759i | 0.558884 | − | 0.857667i | ||||
\(789\) | 0.369895 | − | 1.38047i | 0.0131686 | − | 0.0491459i | ||||
\(790\) | 4.61602 | + | 12.0533i | 0.164231 | + | 0.428837i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.19722 | − | 2.33612i | 0.0425414 | − | 0.0830103i | ||||
\(793\) | −17.0828 | + | 9.86276i | −0.606628 | + | 0.350237i | ||||
\(794\) | −36.1095 | − | 5.74812i | −1.28148 | − | 0.203993i | ||||
\(795\) | −6.79710 | + | 1.82128i | −0.241068 | + | 0.0645941i | ||||
\(796\) | 18.8464 | + | 6.15617i | 0.667994 | + | 0.218200i | ||||
\(797\) | 34.7459 | − | 34.7459i | 1.23076 | − | 1.23076i | 0.267092 | − | 0.963671i | \(-0.413937\pi\) |
0.963671 | − | 0.267092i | \(-0.0860628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.2785i | 2.16788i | ||||||||
\(800\) | 24.2205 | + | 0.0946771i | 0.856323 | + | 0.00334734i | ||||
\(801\) | −3.78742 | − | 2.18667i | −0.133822 | − | 0.0772622i | ||||
\(802\) | −13.0680 | − | 18.0162i | −0.461449 | − | 0.636175i | ||||
\(803\) | −0.589536 | + | 2.20018i | −0.0208043 | + | 0.0776426i | ||||
\(804\) | 30.0281 | + | 33.4547i | 1.05901 | + | 1.17986i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.42620 | + | 6.33526i | 0.0854591 | + | 0.223150i | ||||
\(807\) | −15.9365 | − | 27.6028i | −0.560991 | − | 0.971665i | ||||
\(808\) | −18.4095 | + | 11.8940i | −0.647643 | + | 0.418428i | ||||
\(809\) | −0.273987 | − | 0.158186i | −0.00963285 | − | 0.00556153i | 0.495176 | − | 0.868793i | \(-0.335104\pi\) |
−0.504809 | + | 0.863231i | \(0.668437\pi\) | |||||||
\(810\) | 9.19439 | + | 7.45738i | 0.323058 | + | 0.262026i | ||||
\(811\) | −16.0273 | + | 16.0273i | −0.562795 | + | 0.562795i | −0.930100 | − | 0.367305i | \(-0.880280\pi\) |
0.367305 | + | 0.930100i | \(0.380280\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.30076 | + | 8.30076i | 0.291120 | + | 0.291120i | ||||
\(814\) | −15.3905 | + | 1.60544i | −0.539436 | + | 0.0562707i | ||||
\(815\) | −3.77860 | + | 6.54472i | −0.132358 | + | 0.229252i | ||||
\(816\) | −46.7366 | + | 7.25261i | −1.63611 | + | 0.253892i | ||||
\(817\) | 30.0106 | − | 17.3267i | 1.04994 | − | 0.606183i | ||||
\(818\) | −16.0335 | + | 35.9362i | −0.560599 | + | 1.25648i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.446706 | + | 8.27604i | −0.0155996 | + | 0.289012i | ||||
\(821\) | −28.5933 | − | 7.66156i | −0.997914 | − | 0.267390i | −0.277342 | − | 0.960771i | \(-0.589454\pi\) |
−0.720571 | + | 0.693381i | \(0.756120\pi\) | |||||||
\(822\) | −43.6877 | − | 6.95447i | −1.52378 | − | 0.242565i | ||||
\(823\) | −21.9691 | + | 38.0517i | −0.765796 | + | 1.32640i | 0.174029 | + | 0.984741i | \(0.444321\pi\) |
−0.939825 | + | 0.341657i | \(0.889012\pi\) | |||||||
\(824\) | −21.9228 | + | 24.2332i | −0.763718 | + | 0.844205i | ||||
\(825\) | −22.0931 | −0.769182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.6799 | − | 31.6799i | −1.10162 | − | 1.10162i | −0.994216 | − | 0.107401i | \(-0.965747\pi\) |
−0.107401 | − | 0.994216i | \(-0.534253\pi\) | |||||||
\(828\) | −2.74937 | − | 0.898080i | −0.0955472 | − | 0.0312104i | ||||
\(829\) | −3.21597 | − | 12.0022i | −0.111695 | − | 0.416853i | 0.887323 | − | 0.461148i | \(-0.152562\pi\) |
−0.999018 | + | 0.0442955i | \(0.985896\pi\) | |||||||
\(830\) | −7.91372 | + | 5.74020i | −0.274689 | + | 0.199245i | ||||
\(831\) | 6.74606 | + | 11.6845i | 0.234018 | + | 0.405332i | ||||
\(832\) | −1.82585 | + | 11.1880i | −0.0632998 | + | 0.387875i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.6055 | − | 23.7704i | 0.367240 | − | 0.823102i | ||||
\(835\) | 13.3837 | + | 3.58615i | 0.463161 | + | 0.124104i | ||||
\(836\) | −6.49087 | − | 30.7736i | −0.224491 | − | 1.06433i | ||||
\(837\) | −4.27079 | − | 15.9388i | −0.147620 | − | 0.550926i | ||||
\(838\) | 0.591209 | + | 0.479518i | 0.0204230 | + | 0.0165647i | ||||
\(839\) | − | 15.1931i | − | 0.524523i | −0.964997 | − | 0.262261i | \(-0.915532\pi\) | ||
0.964997 | − | 0.262261i | \(-0.0844682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.8835i | − | 0.995984i | ||||||
\(842\) | 6.90513 | − | 8.51350i | 0.237966 | − | 0.293395i | ||||
\(843\) | −7.01693 | − | 26.1876i | −0.241676 | − | 0.901947i | ||||
\(844\) | 10.0904 | − | 15.4847i | 0.347325 | − | 0.533007i | ||||
\(845\) | 8.99896 | + | 2.41127i | 0.309574 | + | 0.0829501i | ||||
\(846\) | 4.00665 | + | 1.78763i | 0.137752 | + | 0.0614600i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.4120 | + | 14.1831i | 0.391889 | + | 0.487049i | ||||
\(849\) | −10.6906 | − | 18.5167i | −0.366901 | − | 0.635491i | ||||
\(850\) | 23.0431 | + | 31.7684i | 0.790373 | + | 1.08965i | ||||
\(851\) | 4.41278 | + | 16.4687i | 0.151268 | + | 0.564541i | ||||
\(852\) | 39.9714 | − | 20.2878i | 1.36940 | − | 0.695048i | ||||
\(853\) | −1.19631 | − | 1.19631i | −0.0409610 | − | 0.0409610i | 0.686330 | − | 0.727291i | \(-0.259221\pi\) |
−0.727291 | + | 0.686330i | \(0.759221\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.54621 | −0.0528792 | ||||||||
\(856\) | −0.972097 | − | 19.4201i | −0.0332256 | − | 0.663765i | ||||
\(857\) | 9.71265 | − | 16.8228i | 0.331778 | − | 0.574656i | −0.651083 | − | 0.759007i | \(-0.725685\pi\) |
0.982860 | + | 0.184351i | \(0.0590183\pi\) | |||||||
\(858\) | 1.62556 | − | 10.2117i | 0.0554955 | − | 0.348621i | ||||
\(859\) | 5.99481 | + | 1.60630i | 0.204540 | + | 0.0548064i | 0.359634 | − | 0.933093i | \(-0.382901\pi\) |
−0.155094 | + | 0.987900i | \(0.549568\pi\) | |||||||
\(860\) | 7.86268 | − | 7.05736i | 0.268115 | − | 0.240654i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.8734 | − | 10.6515i | −0.813130 | − | 0.362791i | ||||
\(863\) | 21.9244 | − | 12.6580i | 0.746315 | − | 0.430885i | −0.0780460 | − | 0.996950i | \(-0.524868\pi\) |
0.824361 | + | 0.566065i | \(0.191535\pi\) | |||||||
\(864\) | 7.24058 | − | 26.6058i | 0.246330 | − | 0.905147i | ||||
\(865\) | −6.85890 | + | 11.8800i | −0.233210 | + | 0.403931i | ||||
\(866\) | −4.53892 | − | 43.5121i | −0.154239 | − | 1.47860i | ||||
\(867\) | −32.2596 | − | 32.2596i | −1.09559 | − | 1.09559i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.5363 | + | 21.5363i | −0.730569 | + | 0.730569i | ||||
\(870\) | −0.470090 | + | 0.579586i | −0.0159375 | + | 0.0196498i | ||||
\(871\) | 15.1197 | + | 8.72939i | 0.512313 | + | 0.295784i | ||||
\(872\) | −33.8639 | + | 21.8787i | −1.14678 | + | 0.740906i | ||||
\(873\) | 1.77779 | + | 3.07923i | 0.0601692 | + | 0.104216i | ||||
\(874\) | −32.3613 | + | 12.3933i | −1.09464 | + | 0.419211i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.158368 | − | 2.93405i | 0.00535075 | − | 0.0991324i | ||||
\(877\) | −5.33968 | + | 19.9280i | −0.180308 | + | 0.672920i | 0.815278 | + | 0.579070i | \(0.196584\pi\) |
−0.995586 | + | 0.0938501i | \(0.970083\pi\) | |||||||
\(878\) | −22.9317 | + | 16.6335i | −0.773907 | + | 0.561352i | ||||
\(879\) | −18.1411 | − | 10.4738i | −0.611884 | − | 0.353272i | ||||
\(880\) | −3.87278 | − | 8.77214i | −0.130551 | − | 0.295709i | ||||
\(881\) | 12.5228i | 0.421904i | 0.977496 | + | 0.210952i | \(0.0676563\pi\) | ||||
−0.977496 | + | 0.210952i | \(0.932344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.9459 | + | 26.9459i | −0.906802 | + | 0.906802i | −0.996013 | − | 0.0892111i | \(-0.971565\pi\) |
0.0892111 | + | 0.996013i | \(0.471565\pi\) | |||||||
\(884\) | −16.3792 | + | 8.31337i | −0.550891 | + | 0.279609i | ||||
\(885\) | 2.85431 | − | 0.764810i | 0.0959466 | − | 0.0257088i | ||||
\(886\) | −0.134158 | + | 0.842777i | −0.00450714 | + | 0.0283137i | ||||
\(887\) | −16.6823 | + | 9.63153i | −0.560137 | + | 0.323395i | −0.753200 | − | 0.657791i | \(-0.771491\pi\) |
0.193064 | + | 0.981186i | \(0.438158\pi\) | |||||||
\(888\) | 18.9987 | − | 6.12382i | 0.637554 | − | 0.205502i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.9188 | + | 5.71341i | −0.500079 | + | 0.191514i | ||||
\(891\) | −7.23026 | + | 26.9837i | −0.242223 | + | 0.903988i | ||||
\(892\) | 4.45103 | − | 0.938824i | 0.149032 | − | 0.0314342i | ||||
\(893\) | 50.7742 | − | 13.6049i | 1.69909 | − | 0.455271i | ||||
\(894\) | −32.1201 | + | 3.35057i | −1.07426 | + | 0.112060i | ||||
\(895\) | −10.6000 | −0.354319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.3932 | −0.380407 | ||||||||
\(898\) | 18.4636 | − | 1.92601i | 0.616139 | − | 0.0642719i | ||||
\(899\) | 1.11596 | − | 0.299020i | 0.0372192 | − | 0.00997286i | ||||
\(900\) | 2.74937 | − | 0.579906i | 0.0916457 | − | 0.0193302i | ||||
\(901\) | −7.63436 | + | 28.4918i | −0.254337 | + | 0.949200i | ||||
\(902\) | −18.2641 | + | 6.99455i | −0.608128 | + | 0.232893i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.21162 | + | 2.64684i | −0.273114 | + | 0.0880326i | ||||
\(905\) | −18.1899 | + | 10.5019i | −0.604652 | + | 0.349096i | ||||
\(906\) | 2.73338 | − | 17.1710i | 0.0908106 | − | 0.570469i | ||||
\(907\) | −4.38593 | + | 1.17521i | −0.145632 | + | 0.0390221i | −0.330899 | − | 0.943666i | \(-0.607352\pi\) |
0.185266 | + | 0.982688i | \(0.440685\pi\) | |||||||
\(908\) | 22.4687 | − | 11.4042i | 0.745652 | − | 0.378461i | ||||
\(909\) | −1.79794 | + | 1.79794i | −0.0596338 | + | 0.0596338i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.2409i | − | 1.49890i | −0.662063 | − | 0.749448i | \(-0.730319\pi\) | ||
0.662063 | − | 0.749448i | \(-0.269681\pi\) | |||||||
\(912\) | 16.3857 | + | 37.1149i | 0.542586 | + | 1.22900i | ||||
\(913\) | −19.9788 | − | 11.5348i | −0.661201 | − | 0.381745i | ||||
\(914\) | −17.9098 | + | 12.9909i | −0.592404 | + | 0.429699i | ||||
\(915\) | −5.57086 | + | 20.7907i | −0.184167 | + | 0.687320i | ||||
\(916\) | −0.920636 | + | 17.0565i | −0.0304187 | + | 0.563562i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 41.7231 | − | 15.9786i | 1.37707 | − | 0.527372i | ||||
\(919\) | 1.45702 | + | 2.52363i | 0.0480626 | + | 0.0832469i | 0.889056 | − | 0.457799i | \(-0.151362\pi\) |
−0.840993 | + | 0.541046i | \(0.818029\pi\) | |||||||
\(920\) | −8.87438 | + | 5.73354i | −0.292580 | + | 0.189029i | ||||
\(921\) | −31.8450 | − | 18.3857i | −1.04933 | − | 0.605830i | ||||
\(922\) | −35.7286 | + | 44.0507i | −1.17666 | + | 1.45073i | ||||
\(923\) | 12.3097 | − | 12.3097i | 0.405180 | − | 0.405180i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.7122 | − | 11.7122i | −0.385095 | − | 0.385095i | ||||
\(926\) | 1.92497 | + | 18.4537i | 0.0632586 | + | 0.606425i | ||||
\(927\) | −1.89551 | + | 3.28312i | −0.0622568 | + | 0.107832i | ||||
\(928\) | 1.86281 | + | 0.506950i | 0.0611496 | + | 0.0166414i | ||||
\(929\) | −24.5497 | + | 14.1738i | −0.805451 | + | 0.465027i | −0.845374 | − | 0.534176i | \(-0.820622\pi\) |
0.0399228 | + | 0.999203i | \(0.487289\pi\) | |||||||
\(930\) | 6.76018 | + | 3.01616i | 0.221675 | + | 0.0989038i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 38.9845 | − | 34.9916i | 1.27698 | − | 1.14619i | ||||
\(933\) | 22.4096 | + | 6.00462i | 0.733656 | + | 0.196582i | ||||
\(934\) | −8.94426 | + | 56.1875i | −0.292665 | + | 1.83851i | ||||
\(935\) | 7.76869 | − | 13.4558i | 0.254063 | − | 0.440050i | ||||
\(936\) | 0.0657469 | + | 1.31346i | 0.00214900 | + | 0.0429318i | ||||
\(937\) | 14.1147 | 0.461108 | 0.230554 | − | 0.973060i | \(-0.425946\pi\) | ||||
0.230554 | + | 0.973060i | \(0.425946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.9895 | + | 31.9895i | 1.04394 | + | 1.04394i | ||||
\(940\) | 14.2912 | − | 7.25359i | 0.466127 | − | 0.236586i | ||||
\(941\) | −7.37453 | − | 27.5221i | −0.240403 | − | 0.897195i | −0.975639 | − | 0.219384i | \(-0.929595\pi\) |
0.735236 | − | 0.677811i | \(-0.237071\pi\) | |||||||
\(942\) | 10.8959 | + | 15.0216i | 0.355007 | + | 0.489430i | ||||
\(943\) | 10.7746 | + | 18.6621i | 0.350868 | + | 0.607722i | ||||
\(944\) | −4.79224 | − | 5.95591i | −0.155974 | − | 0.193848i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.7681 | + | 10.1584i | 0.740256 | + | 0.330277i | ||||
\(947\) | −27.8939 | − | 7.47414i | −0.906429 | − | 0.242877i | −0.224654 | − | 0.974439i | \(-0.572125\pi\) |
−0.681775 | + | 0.731562i | \(0.738792\pi\) | |||||||
\(948\) | 21.4498 | − | 32.9170i | 0.696658 | − | 1.06910i | ||||
\(949\) | −0.295350 | − | 1.10226i | −0.00958745 | − | 0.0357809i | ||||
\(950\) | 21.2067 | − | 26.1463i | 0.688036 | − | 0.848296i | ||||
\(951\) | − | 3.71046i | − | 0.120320i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.38196i | − | 0.239125i | −0.992827 | − | 0.119563i | \(-0.961851\pi\) | ||
0.992827 | − | 0.119563i | \(-0.0381492\pi\) | |||||||
\(954\) | 1.64021 | + | 1.33034i | 0.0531036 | + | 0.0430713i | ||||
\(955\) | −0.989271 | − | 3.69201i | −0.0320121 | − | 0.119471i | ||||
\(956\) | −8.50796 | − | 40.3368i | −0.275167 | − | 1.30459i | ||||
\(957\) | −1.70097 | − | 0.455773i | −0.0549845 | − | 0.0147330i | ||||
\(958\) | 19.3387 | − | 43.3442i | 0.624806 | − | 1.40039i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7.22369 | + | 10.0413i | 0.233144 | + | 0.324081i | ||||
\(961\) | 9.76989 | + | 16.9220i | 0.315158 | + | 0.545869i | ||||
\(962\) | 6.27527 | − | 4.55176i | 0.202323 | − | 0.146755i | ||||
\(963\) | −0.583835 | − | 2.17890i | −0.0188138 | − | 0.0702142i | ||||
\(964\) | −1.35059 | − | 0.441170i | −0.0434996 | − | 0.0142091i | ||||
\(965\) | 8.34402 | + | 8.34402i | 0.268603 | + | 0.268603i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4068 | 1.52450 | 0.762250 | − | 0.647283i | \(-0.224095\pi\) | ||||
0.762250 | + | 0.647283i | \(0.224095\pi\) | |||||||
\(968\) | −5.69254 | + | 6.29246i | −0.182965 | + | 0.202247i | ||||
\(969\) | −32.8693 | + | 56.9313i | −1.05591 | + | 1.82890i | ||||
\(970\) | 12.8267 | + | 2.04184i | 0.411842 | + | 0.0655594i | ||||
\(971\) | 19.5789 | + | 5.24615i | 0.628317 | + | 0.168357i | 0.558906 | − | 0.829231i | \(-0.311221\pi\) |
0.0694112 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(972\) | 0.365989 | − | 6.78061i | 0.0117391 | − | 0.217488i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.0417 | + | 22.5067i | −0.321757 | + | 0.721160i | ||||
\(975\) | 9.58546 | − | 5.53417i | 0.306980 | − | 0.177235i | ||||
\(976\) | 55.0238 | − | 8.53861i | 1.76127 | − | 0.273314i | ||||
\(977\) | 3.29726 | − | 5.71103i | 0.105489 | − | 0.182712i | −0.808449 | − | 0.588566i | \(-0.799693\pi\) |
0.913938 | + | 0.405854i | \(0.133026\pi\) | |||||||
\(978\) | 22.8801 | − | 2.38671i | 0.731624 | − | 0.0763185i | ||||
\(979\) | −26.6562 | − | 26.6562i | −0.851937 | − | 0.851937i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.30727 | + | 3.30727i | −0.105593 | + | 0.105593i | ||||
\(982\) | −6.22793 | − | 5.05135i | −0.198741 | − | 0.161195i | ||||
\(983\) | 32.5034 | + | 18.7658i | 1.03670 | + | 0.598537i | 0.918896 | − | 0.394500i | \(-0.129082\pi\) |
0.117801 | + | 0.993037i | \(0.462416\pi\) | |||||||
\(984\) | 21.1911 | − | 13.6911i | 0.675546 | − | 0.436456i | ||||
\(985\) | −6.08892 | − | 10.5463i | −0.194009 | − | 0.336034i | ||||
\(986\) | 1.11874 | + | 2.92125i | 0.0356280 | + | 0.0930315i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.5248 | + | 11.7258i | 0.334837 | + | 0.373046i | ||||
\(989\) | 7.10983 | − | 26.5342i | 0.226079 | − | 0.843739i | ||||
\(990\) | −0.653166 | − | 0.900485i | −0.0207590 | − | 0.0286193i | ||||
\(991\) | 10.2256 | + | 5.90372i | 0.324825 | + | 0.187538i | 0.653541 | − | 0.756891i | \(-0.273283\pi\) |
−0.328716 | + | 0.944429i | \(0.606616\pi\) | |||||||
\(992\) | 0.0748566 | − | 19.1500i | 0.00237670 | − | 0.608012i | ||||
\(993\) | 2.67407i | 0.0848591i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.94110 | − | 5.94110i | 0.188346 | − | 0.188346i | ||||
\(996\) | 28.2884 | + | 9.24039i | 0.896352 | + | 0.292793i | ||||
\(997\) | −23.2067 | + | 6.21823i | −0.734965 | + | 0.196933i | −0.606839 | − | 0.794825i | \(-0.707563\pi\) |
−0.128126 | + | 0.991758i | \(0.540896\pi\) | |||||||
\(998\) | 32.0602 | + | 5.10354i | 1.01485 | + | 0.161550i | ||||
\(999\) | −16.3301 | + | 9.42818i | −0.516661 | + | 0.298294i |
(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 | 784.2.w.e.227.7 | 32 | ||
7.2 | even | 3 | inner | 784.2.w.e.19.4 | 32 | ||
7.3 | odd | 6 | 112.2.j.d.83.3 | yes | 16 | ||
7.4 | even | 3 | 112.2.j.d.83.4 | yes | 16 | ||
7.5 | odd | 6 | inner | 784.2.w.e.19.3 | 32 | ||
7.6 | odd | 2 | inner | 784.2.w.e.227.8 | 32 | ||
16.11 | odd | 4 | inner | 784.2.w.e.619.3 | 32 | ||
28.3 | even | 6 | 448.2.j.d.111.6 | 16 | |||
28.11 | odd | 6 | 448.2.j.d.111.3 | 16 | |||
56.3 | even | 6 | 896.2.j.g.223.3 | 16 | |||
56.11 | odd | 6 | 896.2.j.g.223.6 | 16 | |||
56.45 | odd | 6 | 896.2.j.h.223.6 | 16 | |||
56.53 | even | 6 | 896.2.j.h.223.3 | 16 | |||
112.3 | even | 12 | 896.2.j.h.671.3 | 16 | |||
112.11 | odd | 12 | 112.2.j.d.27.3 | ✓ | 16 | ||
112.27 | even | 4 | inner | 784.2.w.e.619.4 | 32 | ||
112.45 | odd | 12 | 896.2.j.g.671.6 | 16 | |||
112.53 | even | 12 | 448.2.j.d.335.6 | 16 | |||
112.59 | even | 12 | 112.2.j.d.27.4 | yes | 16 | ||
112.67 | odd | 12 | 896.2.j.h.671.6 | 16 | |||
112.75 | even | 12 | inner | 784.2.w.e.411.7 | 32 | ||
112.101 | odd | 12 | 448.2.j.d.335.3 | 16 | |||
112.107 | odd | 12 | inner | 784.2.w.e.411.8 | 32 | ||
112.109 | even | 12 | 896.2.j.g.671.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.3 | ✓ | 16 | 112.11 | odd | 12 | ||
112.2.j.d.27.4 | yes | 16 | 112.59 | even | 12 | ||
112.2.j.d.83.3 | yes | 16 | 7.3 | odd | 6 | ||
112.2.j.d.83.4 | yes | 16 | 7.4 | even | 3 | ||
448.2.j.d.111.3 | 16 | 28.11 | odd | 6 | |||
448.2.j.d.111.6 | 16 | 28.3 | even | 6 | |||
448.2.j.d.335.3 | 16 | 112.101 | odd | 12 | |||
448.2.j.d.335.6 | 16 | 112.53 | even | 12 | |||
784.2.w.e.19.3 | 32 | 7.5 | odd | 6 | inner | ||
784.2.w.e.19.4 | 32 | 7.2 | even | 3 | inner | ||
784.2.w.e.227.7 | 32 | 1.1 | even | 1 | trivial | ||
784.2.w.e.227.8 | 32 | 7.6 | odd | 2 | inner | ||
784.2.w.e.411.7 | 32 | 112.75 | even | 12 | inner | ||
784.2.w.e.411.8 | 32 | 112.107 | odd | 12 | inner | ||
784.2.w.e.619.3 | 32 | 16.11 | odd | 4 | inner | ||
784.2.w.e.619.4 | 32 | 112.27 | even | 4 | inner | ||
896.2.j.g.223.3 | 16 | 56.3 | even | 6 | |||
896.2.j.g.223.6 | 16 | 56.11 | odd | 6 | |||
896.2.j.g.671.3 | 16 | 112.109 | even | 12 | |||
896.2.j.g.671.6 | 16 | 112.45 | odd | 12 | |||
896.2.j.h.223.3 | 16 | 56.53 | even | 6 | |||
896.2.j.h.223.6 | 16 | 56.45 | odd | 6 | |||
896.2.j.h.671.3 | 16 | 112.3 | even | 12 | |||
896.2.j.h.671.6 | 16 | 112.67 | odd | 12 |