Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,3,Mod(115,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.115");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.70573159530\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 115.9 | ||
Character | \(\chi\) | \(=\) | 136.115 |
Dual form | 136.3.j.b.123.9 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54442 | + | 1.27074i | −0.772209 | + | 0.635369i | ||||
\(3\) | −4.05827 | − | 4.05827i | −1.35276 | − | 1.35276i | −0.882564 | − | 0.470192i | \(-0.844185\pi\) |
−0.470192 | − | 0.882564i | \(-0.655815\pi\) | |||||||
\(4\) | 0.770451 | − | 3.92510i | 0.192613 | − | 0.981275i | ||||
\(5\) | 3.34858 | − | 3.34858i | 0.669715 | − | 0.669715i | −0.287935 | − | 0.957650i | \(-0.592969\pi\) |
0.957650 | + | 0.287935i | \(0.0929687\pi\) | |||||||
\(6\) | 11.4247 | + | 1.11067i | 1.90411 | + | 0.185111i | ||||
\(7\) | −7.12993 | − | 7.12993i | −1.01856 | − | 1.01856i | −0.999824 | − | 0.0187370i | \(-0.994035\pi\) |
−0.0187370 | − | 0.999824i | \(-0.505965\pi\) | |||||||
\(8\) | 3.79787 | + | 7.04103i | 0.474734 | + | 0.880129i | ||||
\(9\) | 23.9391i | 2.65990i | ||||||||
\(10\) | −0.916437 | + | 9.42676i | −0.0916437 | + | 0.942676i | ||||
\(11\) | 1.68469 | − | 1.68469i | 0.153153 | − | 0.153153i | −0.626371 | − | 0.779525i | \(-0.715461\pi\) |
0.779525 | + | 0.626371i | \(0.215461\pi\) | |||||||
\(12\) | −19.0558 | + | 12.8024i | −1.58798 | + | 1.06687i | ||||
\(13\) | − | 4.79400i | − | 0.368769i | −0.982854 | − | 0.184385i | \(-0.940971\pi\) | ||
0.982854 | − | 0.184385i | \(-0.0590292\pi\) | |||||||
\(14\) | 20.0719 | + | 1.95132i | 1.43370 | + | 0.139380i | ||||
\(15\) | −27.1788 | −1.81192 | ||||||||
\(16\) | −14.8128 | − | 6.04819i | −0.925801 | − | 0.378012i | ||||
\(17\) | −16.8443 | − | 2.29531i | −0.990843 | − | 0.135018i | ||||
\(18\) | −30.4203 | − | 36.9719i | −1.69002 | − | 2.05400i | ||||
\(19\) | 11.3212i | 0.595853i | 0.954589 | + | 0.297926i | \(0.0962950\pi\) | ||||
−0.954589 | + | 0.297926i | \(0.903705\pi\) | |||||||
\(20\) | −10.5636 | − | 15.7234i | −0.528179 | − | 0.786170i | ||||
\(21\) | 57.8703i | 2.75573i | ||||||||
\(22\) | −0.461065 | + | 4.74266i | −0.0209575 | + | 0.215575i | ||||
\(23\) | 6.50691 | + | 6.50691i | 0.282909 | + | 0.282909i | 0.834268 | − | 0.551359i | \(-0.185891\pi\) |
−0.551359 | + | 0.834268i | \(0.685891\pi\) | |||||||
\(24\) | 13.1616 | − | 43.9872i | 0.548400 | − | 1.83280i | ||||
\(25\) | 2.57409i | 0.102963i | ||||||||
\(26\) | 6.09191 | + | 7.40393i | 0.234304 | + | 0.284767i | ||||
\(27\) | 60.6268 | − | 60.6268i | 2.24544 | − | 2.24544i | ||||
\(28\) | −33.4789 | + | 22.4924i | −1.19568 | + | 0.803301i | ||||
\(29\) | 3.53343 | − | 3.53343i | 0.121842 | − | 0.121842i | −0.643556 | − | 0.765399i | \(-0.722542\pi\) |
0.765399 | + | 0.643556i | \(0.222542\pi\) | |||||||
\(30\) | 41.9755 | − | 34.5372i | 1.39918 | − | 1.15124i | ||||
\(31\) | −37.3287 | + | 37.3287i | −1.20415 | + | 1.20415i | −0.231259 | + | 0.972892i | \(0.574285\pi\) |
−0.972892 | + | 0.231259i | \(0.925715\pi\) | |||||||
\(32\) | 30.5628 | − | 9.48226i | 0.955089 | − | 0.296321i | ||||
\(33\) | −13.6738 | −0.414358 | ||||||||
\(34\) | 28.9314 | − | 17.8598i | 0.850924 | − | 0.525289i | ||||
\(35\) | −47.7502 | −1.36429 | ||||||||
\(36\) | 93.9633 | + | 18.4439i | 2.61009 | + | 0.512330i | ||||
\(37\) | 22.7670 | − | 22.7670i | 0.615326 | − | 0.615326i | −0.329003 | − | 0.944329i | \(-0.606713\pi\) |
0.944329 | + | 0.329003i | \(0.106713\pi\) | |||||||
\(38\) | −14.3863 | − | 17.4847i | −0.378586 | − | 0.460123i | ||||
\(39\) | −19.4553 | + | 19.4553i | −0.498855 | + | 0.498855i | ||||
\(40\) | 36.2949 | + | 10.8600i | 0.907372 | + | 0.271499i | ||||
\(41\) | 21.5376 | − | 21.5376i | 0.525309 | − | 0.525309i | −0.393861 | − | 0.919170i | \(-0.628861\pi\) |
0.919170 | + | 0.393861i | \(0.128861\pi\) | |||||||
\(42\) | −73.5380 | − | 89.3760i | −1.75091 | − | 2.12800i | ||||
\(43\) | 39.2822i | 0.913539i | 0.889585 | + | 0.456769i | \(0.150994\pi\) | ||||
−0.889585 | + | 0.456769i | \(0.849006\pi\) | |||||||
\(44\) | −5.31460 | − | 7.91054i | −0.120786 | − | 0.179785i | ||||
\(45\) | 80.1618 | + | 80.1618i | 1.78137 | + | 1.78137i | ||||
\(46\) | −18.3180 | − | 1.78081i | −0.398217 | − | 0.0387133i | ||||
\(47\) | − | 53.6139i | − | 1.14072i | −0.821395 | − | 0.570360i | \(-0.806804\pi\) | ||
0.821395 | − | 0.570360i | \(-0.193196\pi\) | |||||||
\(48\) | 35.5692 | + | 84.6595i | 0.741024 | + | 1.76374i | ||||
\(49\) | 52.6718i | 1.07493i | ||||||||
\(50\) | −3.27099 | − | 3.97546i | −0.0654198 | − | 0.0795093i | ||||
\(51\) | 59.0438 | + | 77.6738i | 1.15772 | + | 1.52302i | ||||
\(52\) | −18.8169 | − | 3.69354i | −0.361864 | − | 0.0710296i | ||||
\(53\) | −90.9429 | −1.71590 | −0.857952 | − | 0.513730i | \(-0.828263\pi\) | ||||
−0.857952 | + | 0.513730i | \(0.828263\pi\) | |||||||
\(54\) | −16.5923 | + | 170.674i | −0.307265 | + | 3.16063i | ||||
\(55\) | − | 11.2826i | − | 0.205138i | ||||||
\(56\) | 23.1235 | − | 77.2807i | 0.412920 | − | 1.38001i | ||||
\(57\) | 45.9445 | − | 45.9445i | 0.806044 | − | 0.806044i | ||||
\(58\) | −0.967028 | + | 9.94715i | −0.0166729 | + | 0.171503i | ||||
\(59\) | − | 93.8058i | − | 1.58993i | −0.606656 | − | 0.794964i | \(-0.707489\pi\) | ||
0.606656 | − | 0.794964i | \(-0.292511\pi\) | |||||||
\(60\) | −20.9400 | + | 106.680i | −0.348999 | + | 1.77799i | ||||
\(61\) | −45.9156 | − | 45.9156i | −0.752714 | − | 0.752714i | 0.222271 | − | 0.974985i | \(-0.428653\pi\) |
−0.974985 | + | 0.222271i | \(0.928653\pi\) | |||||||
\(62\) | 10.2161 | − | 105.086i | 0.164776 | − | 1.69494i | ||||
\(63\) | 170.684 | − | 170.684i | 2.70927 | − | 2.70927i | ||||
\(64\) | −35.1523 | + | 53.4819i | −0.549255 | + | 0.835655i | ||||
\(65\) | −16.0531 | − | 16.0531i | −0.246970 | − | 0.246970i | ||||
\(66\) | 21.1181 | − | 17.3758i | 0.319971 | − | 0.263270i | ||||
\(67\) | −18.2300 | −0.272089 | −0.136044 | − | 0.990703i | \(-0.543439\pi\) | ||||
−0.136044 | + | 0.990703i | \(0.543439\pi\) | |||||||
\(68\) | −21.9870 | + | 64.3473i | −0.323339 | + | 0.946283i | ||||
\(69\) | − | 52.8136i | − | 0.765414i | ||||||
\(70\) | 73.7463 | − | 60.6780i | 1.05352 | − | 0.866829i | ||||
\(71\) | −11.0862 | + | 11.0862i | −0.156144 | + | 0.156144i | −0.780855 | − | 0.624712i | \(-0.785216\pi\) |
0.624712 | + | 0.780855i | \(0.285216\pi\) | |||||||
\(72\) | −168.556 | + | 90.9176i | −2.34105 | + | 1.26274i | ||||
\(73\) | −16.7784 | − | 16.7784i | −0.229842 | − | 0.229842i | 0.582785 | − | 0.812626i | \(-0.301963\pi\) |
−0.812626 | + | 0.582785i | \(0.801963\pi\) | |||||||
\(74\) | −6.23088 | + | 64.0928i | −0.0842011 | + | 0.866118i | ||||
\(75\) | 10.4463 | − | 10.4463i | 0.139284 | − | 0.139284i | ||||
\(76\) | 44.4369 | + | 8.72243i | 0.584696 | + | 0.114769i | ||||
\(77\) | −24.0234 | −0.311992 | ||||||||
\(78\) | 5.32453 | − | 54.7698i | 0.0682632 | − | 0.702176i | ||||
\(79\) | −21.5651 | − | 21.5651i | −0.272977 | − | 0.272977i | 0.557321 | − | 0.830297i | \(-0.311829\pi\) |
−0.830297 | + | 0.557321i | \(0.811829\pi\) | |||||||
\(80\) | −69.8546 | + | 29.3490i | −0.873183 | + | 0.366862i | ||||
\(81\) | −276.628 | −3.41516 | ||||||||
\(82\) | −5.89442 | + | 60.6318i | −0.0718832 | + | 0.739413i | ||||
\(83\) | − | 31.5476i | − | 0.380092i | −0.981775 | − | 0.190046i | \(-0.939136\pi\) | ||
0.981775 | − | 0.190046i | \(-0.0608637\pi\) | |||||||
\(84\) | 227.147 | + | 44.5863i | 2.70413 | + | 0.530789i | ||||
\(85\) | −64.0905 | + | 48.7185i | −0.754006 | + | 0.573159i | ||||
\(86\) | −49.9173 | − | 60.6681i | −0.580434 | − | 0.705443i | ||||
\(87\) | −28.6792 | −0.329646 | ||||||||
\(88\) | 18.2602 | + | 5.46371i | 0.207502 | + | 0.0620876i | ||||
\(89\) | 88.4664 | 0.994005 | 0.497002 | − | 0.867749i | \(-0.334434\pi\) | ||||
0.497002 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(90\) | −225.668 | − | 21.9387i | −2.50742 | − | 0.243763i | ||||
\(91\) | −34.1809 | + | 34.1809i | −0.375614 | + | 0.375614i | ||||
\(92\) | 30.5535 | − | 20.5270i | 0.332104 | − | 0.223120i | ||||
\(93\) | 302.980 | 3.25785 | ||||||||
\(94\) | 68.1292 | + | 82.8022i | 0.724779 | + | 0.880875i | ||||
\(95\) | 37.9099 | + | 37.9099i | 0.399052 | + | 0.399052i | ||||
\(96\) | −162.514 | − | 85.5506i | −1.69285 | − | 0.891152i | ||||
\(97\) | −29.8391 | − | 29.8391i | −0.307620 | − | 0.307620i | 0.536366 | − | 0.843986i | \(-0.319797\pi\) |
−0.843986 | + | 0.536366i | \(0.819797\pi\) | |||||||
\(98\) | −66.9320 | − | 81.3472i | −0.682980 | − | 0.830074i | ||||
\(99\) | 40.3299 | + | 40.3299i | 0.407372 | + | 0.407372i | ||||
\(100\) | 10.1035 | + | 1.98321i | 0.101035 | + | 0.0198321i | ||||
\(101\) | − | 49.1217i | − | 0.486353i | −0.969982 | − | 0.243177i | \(-0.921811\pi\) | ||
0.969982 | − | 0.243177i | \(-0.0781895\pi\) | |||||||
\(102\) | −189.891 | − | 44.9315i | −1.86168 | − | 0.440505i | ||||
\(103\) | 155.870i | 1.51330i | 0.653820 | + | 0.756650i | \(0.273166\pi\) | ||||
−0.653820 | + | 0.756650i | \(0.726834\pi\) | |||||||
\(104\) | 33.7547 | − | 18.2070i | 0.324564 | − | 0.175067i | ||||
\(105\) | 193.783 | + | 193.783i | 1.84555 | + | 1.84555i | ||||
\(106\) | 140.454 | − | 115.565i | 1.32504 | − | 1.09023i | ||||
\(107\) | −62.5365 | − | 62.5365i | −0.584454 | − | 0.584454i | 0.351670 | − | 0.936124i | \(-0.385614\pi\) |
−0.936124 | + | 0.351670i | \(0.885614\pi\) | |||||||
\(108\) | −191.256 | − | 284.676i | −1.77089 | − | 2.63589i | ||||
\(109\) | −109.883 | − | 109.883i | −1.00810 | − | 1.00810i | −0.999967 | − | 0.00813505i | \(-0.997411\pi\) |
−0.00813505 | − | 0.999967i | \(-0.502589\pi\) | |||||||
\(110\) | 14.3372 | + | 17.4251i | 0.130339 | + | 0.158410i | ||||
\(111\) | −184.790 | −1.66477 | ||||||||
\(112\) | 62.4911 | + | 148.737i | 0.557956 | + | 1.32801i | ||||
\(113\) | −78.4235 | + | 78.4235i | −0.694014 | + | 0.694014i | −0.963113 | − | 0.269099i | \(-0.913274\pi\) |
0.269099 | + | 0.963113i | \(0.413274\pi\) | |||||||
\(114\) | −12.5741 | + | 129.341i | −0.110299 | + | 1.13457i | ||||
\(115\) | 43.5778 | 0.378937 | ||||||||
\(116\) | −11.1467 | − | 16.5914i | −0.0960924 | − | 0.143029i | ||||
\(117\) | 114.764 | 0.980888 | ||||||||
\(118\) | 119.203 | + | 144.875i | 1.01019 | + | 1.22776i | ||||
\(119\) | 103.734 | + | 136.464i | 0.871710 | + | 1.14676i | ||||
\(120\) | −103.222 | − | 191.367i | −0.860181 | − | 1.59473i | ||||
\(121\) | 115.324i | 0.953088i | ||||||||
\(122\) | 129.259 | + | 12.5662i | 1.05950 | + | 0.103001i | ||||
\(123\) | −174.811 | −1.42123 | ||||||||
\(124\) | 117.759 | + | 175.279i | 0.949669 | + | 1.41354i | ||||
\(125\) | 92.3339 | + | 92.3339i | 0.738671 | + | 0.738671i | ||||
\(126\) | −46.7127 | + | 480.502i | −0.370736 | + | 3.81351i | ||||
\(127\) | −187.466 | −1.47611 | −0.738057 | − | 0.674739i | \(-0.764256\pi\) | ||||
−0.738057 | + | 0.674739i | \(0.764256\pi\) | |||||||
\(128\) | −13.6717 | − | 127.268i | −0.106810 | − | 0.994279i | ||||
\(129\) | 159.418 | − | 159.418i | 1.23579 | − | 1.23579i | ||||
\(130\) | 45.1919 | + | 4.39340i | 0.347630 | + | 0.0337954i | ||||
\(131\) | 33.8003 | + | 33.8003i | 0.258018 | + | 0.258018i | 0.824248 | − | 0.566230i | \(-0.191598\pi\) |
−0.566230 | + | 0.824248i | \(0.691598\pi\) | |||||||
\(132\) | −10.5350 | + | 53.6711i | −0.0798107 | + | 0.406599i | ||||
\(133\) | 80.7194 | − | 80.7194i | 0.606913 | − | 0.606913i | ||||
\(134\) | 28.1547 | − | 23.1655i | 0.210109 | − | 0.172877i | ||||
\(135\) | − | 406.027i | − | 3.00760i | ||||||
\(136\) | −47.8113 | − | 127.319i | −0.351554 | − | 0.936168i | ||||
\(137\) | 41.8673 | 0.305601 | 0.152800 | − | 0.988257i | \(-0.451171\pi\) | ||||
0.152800 | + | 0.988257i | \(0.451171\pi\) | |||||||
\(138\) | 67.1122 | + | 81.5662i | 0.486320 | + | 0.591059i | ||||
\(139\) | −19.5026 | − | 19.5026i | −0.140306 | − | 0.140306i | 0.633465 | − | 0.773771i | \(-0.281632\pi\) |
−0.773771 | + | 0.633465i | \(0.781632\pi\) | |||||||
\(140\) | −36.7892 | + | 187.424i | −0.262780 | + | 1.33875i | ||||
\(141\) | −217.580 | + | 217.580i | −1.54312 | + | 1.54312i | ||||
\(142\) | 3.03407 | − | 31.2093i | 0.0213667 | − | 0.219784i | ||||
\(143\) | −8.07639 | − | 8.07639i | −0.0564782 | − | 0.0564782i | ||||
\(144\) | 144.788 | − | 354.605i | 1.00547 | − | 2.46253i | ||||
\(145\) | − | 23.6639i | − | 0.163199i | ||||||
\(146\) | 47.2339 | + | 4.59192i | 0.323520 | + | 0.0314515i | ||||
\(147\) | 213.756 | − | 213.756i | 1.45412 | − | 1.45412i | ||||
\(148\) | −71.8220 | − | 106.904i | −0.485284 | − | 0.722323i | ||||
\(149\) | 3.45014i | 0.0231553i | 0.999933 | + | 0.0115776i | \(0.00368536\pi\) | ||||
−0.999933 | + | 0.0115776i | \(0.996315\pi\) | |||||||
\(150\) | −2.85895 | + | 29.4080i | −0.0190597 | + | 0.196054i | ||||
\(151\) | −55.4358 | −0.367125 | −0.183562 | − | 0.983008i | \(-0.558763\pi\) | ||||
−0.183562 | + | 0.983008i | \(0.558763\pi\) | |||||||
\(152\) | −79.7130 | + | 42.9965i | −0.524428 | + | 0.282872i | ||||
\(153\) | 54.9476 | − | 403.238i | 0.359134 | − | 2.63554i | ||||
\(154\) | 37.1022 | − | 30.5275i | 0.240923 | − | 0.198230i | ||||
\(155\) | 249.996i | 1.61288i | ||||||||
\(156\) | 61.3747 | + | 91.3535i | 0.393428 | + | 0.585599i | ||||
\(157\) | − | 249.307i | − | 1.58794i | −0.607957 | − | 0.793970i | \(-0.708011\pi\) | ||
0.607957 | − | 0.793970i | \(-0.291989\pi\) | |||||||
\(158\) | 60.7092 | + | 5.90194i | 0.384236 | + | 0.0373541i | ||||
\(159\) | 369.071 | + | 369.071i | 2.32120 | + | 2.32120i | ||||
\(160\) | 70.5899 | − | 134.094i | 0.441187 | − | 0.838088i | ||||
\(161\) | − | 92.7876i | − | 0.576321i | ||||||
\(162\) | 427.229 | − | 351.521i | 2.63721 | − | 2.16988i | ||||
\(163\) | 23.7173 | − | 23.7173i | 0.145505 | − | 0.145505i | −0.630602 | − | 0.776107i | \(-0.717192\pi\) |
0.776107 | + | 0.630602i | \(0.217192\pi\) | |||||||
\(164\) | −67.9437 | − | 101.131i | −0.414291 | − | 0.616653i | ||||
\(165\) | −45.7878 | + | 45.7878i | −0.277502 | + | 0.277502i | ||||
\(166\) | 40.0888 | + | 48.7227i | 0.241499 | + | 0.293510i | ||||
\(167\) | 68.6999 | − | 68.6999i | 0.411377 | − | 0.411377i | −0.470841 | − | 0.882218i | \(-0.656050\pi\) |
0.882218 | + | 0.470841i | \(0.156050\pi\) | |||||||
\(168\) | −407.467 | + | 219.784i | −2.42540 | + | 1.30824i | ||||
\(169\) | 146.018 | 0.864009 | ||||||||
\(170\) | 37.0741 | − | 156.684i | 0.218083 | − | 0.921670i | ||||
\(171\) | −271.019 | −1.58491 | ||||||||
\(172\) | 154.186 | + | 30.2650i | 0.896433 | + | 0.175959i | ||||
\(173\) | 66.2063 | − | 66.2063i | 0.382695 | − | 0.382695i | −0.489377 | − | 0.872072i | \(-0.662776\pi\) |
0.872072 | + | 0.489377i | \(0.162776\pi\) | |||||||
\(174\) | 44.2926 | − | 36.4437i | 0.254555 | − | 0.209447i | ||||
\(175\) | 18.3531 | − | 18.3531i | 0.104875 | − | 0.104875i | ||||
\(176\) | −35.1443 | + | 14.7656i | −0.199683 | + | 0.0838957i | ||||
\(177\) | −380.689 | + | 380.689i | −2.15079 | + | 2.15079i | ||||
\(178\) | −136.629 | + | 112.418i | −0.767579 | + | 0.631560i | ||||
\(179\) | 67.3735i | 0.376388i | 0.982132 | + | 0.188194i | \(0.0602634\pi\) | ||||
−0.982132 | + | 0.188194i | \(0.939737\pi\) | |||||||
\(180\) | 376.404 | − | 252.882i | 2.09113 | − | 1.40490i | ||||
\(181\) | 19.0832 | + | 19.0832i | 0.105432 | + | 0.105432i | 0.757855 | − | 0.652423i | \(-0.226247\pi\) |
−0.652423 | + | 0.757855i | \(0.726247\pi\) | |||||||
\(182\) | 9.35461 | − | 96.2244i | 0.0513990 | − | 0.528706i | ||||
\(183\) | 372.675i | 2.03648i | ||||||||
\(184\) | −21.1029 | + | 70.5278i | −0.114690 | + | 0.383303i | ||||
\(185\) | − | 152.474i | − | 0.824186i | ||||||
\(186\) | −467.927 | + | 385.008i | −2.51574 | + | 2.06993i | ||||
\(187\) | −32.2443 | + | 24.5106i | −0.172430 | + | 0.131073i | ||||
\(188\) | −210.440 | − | 41.3069i | −1.11936 | − | 0.219717i | ||||
\(189\) | −864.529 | −4.57423 | ||||||||
\(190\) | −106.722 | − | 10.3752i | −0.561696 | − | 0.0546062i | ||||
\(191\) | − | 138.978i | − | 0.727632i | −0.931471 | − | 0.363816i | \(-0.881474\pi\) | ||
0.931471 | − | 0.363816i | \(-0.118526\pi\) | |||||||
\(192\) | 359.701 | − | 74.3865i | 1.87344 | − | 0.387430i | ||||
\(193\) | 82.3703 | − | 82.3703i | 0.426789 | − | 0.426789i | −0.460744 | − | 0.887533i | \(-0.652417\pi\) |
0.887533 | + | 0.460744i | \(0.152417\pi\) | |||||||
\(194\) | 84.0017 | + | 8.16636i | 0.432999 | + | 0.0420946i | ||||
\(195\) | 130.295i | 0.668181i | ||||||||
\(196\) | 206.742 | + | 40.5810i | 1.05481 | + | 0.207046i | ||||
\(197\) | −13.2544 | − | 13.2544i | −0.0672814 | − | 0.0672814i | 0.672665 | − | 0.739947i | \(-0.265149\pi\) |
−0.739947 | + | 0.672665i | \(0.765149\pi\) | |||||||
\(198\) | −113.535 | − | 11.0375i | −0.573408 | − | 0.0557448i | ||||
\(199\) | −45.2576 | + | 45.2576i | −0.227425 | + | 0.227425i | −0.811616 | − | 0.584191i | \(-0.801412\pi\) |
0.584191 | + | 0.811616i | \(0.301412\pi\) | |||||||
\(200\) | −18.1242 | + | 9.77605i | −0.0906211 | + | 0.0488803i | ||||
\(201\) | 73.9820 | + | 73.9820i | 0.368070 | + | 0.368070i | ||||
\(202\) | 62.4208 | + | 75.8644i | 0.309014 | + | 0.375566i | ||||
\(203\) | −50.3862 | −0.248208 | ||||||||
\(204\) | 350.368 | − | 171.909i | 1.71749 | − | 0.842692i | ||||
\(205\) | − | 144.241i | − | 0.703614i | ||||||
\(206\) | −198.070 | − | 240.728i | −0.961504 | − | 1.16858i | ||||
\(207\) | −155.769 | + | 155.769i | −0.752509 | + | 0.752509i | ||||
\(208\) | −28.9950 | + | 71.0126i | −0.139399 | + | 0.341407i | ||||
\(209\) | 19.0727 | + | 19.0727i | 0.0912569 | + | 0.0912569i | ||||
\(210\) | −545.530 | − | 53.0345i | −2.59776 | − | 0.252545i | ||||
\(211\) | 164.401 | − | 164.401i | 0.779153 | − | 0.779153i | −0.200534 | − | 0.979687i | \(-0.564268\pi\) |
0.979687 | + | 0.200534i | \(0.0642676\pi\) | |||||||
\(212\) | −70.0670 | + | 356.960i | −0.330505 | + | 1.68377i | ||||
\(213\) | 89.9815 | 0.422448 | ||||||||
\(214\) | 176.050 | + | 17.1150i | 0.822664 | + | 0.0799766i | ||||
\(215\) | 131.539 | + | 131.539i | 0.611811 | + | 0.611811i | ||||
\(216\) | 657.128 | + | 196.622i | 3.04226 | + | 0.910288i | ||||
\(217\) | 532.302 | 2.45300 | ||||||||
\(218\) | 309.338 | + | 30.0728i | 1.41898 | + | 0.137949i | ||||
\(219\) | 136.183i | 0.621839i | ||||||||
\(220\) | −44.2854 | − | 8.69270i | −0.201297 | − | 0.0395123i | ||||
\(221\) | −11.0037 | + | 80.7517i | −0.0497905 | + | 0.365392i | ||||
\(222\) | 285.392 | − | 234.819i | 1.28555 | − | 1.05774i | ||||
\(223\) | 64.6604 | 0.289957 | 0.144978 | − | 0.989435i | \(-0.453689\pi\) | ||||
0.144978 | + | 0.989435i | \(0.453689\pi\) | |||||||
\(224\) | −285.519 | − | 150.303i | −1.27464 | − | 0.670996i | ||||
\(225\) | −61.6212 | −0.273872 | ||||||||
\(226\) | 21.4629 | − | 220.774i | 0.0949687 | − | 0.976878i | ||||
\(227\) | −260.063 | + | 260.063i | −1.14565 | + | 1.14565i | −0.158253 | + | 0.987399i | \(0.550586\pi\) |
−0.987399 | + | 0.158253i | \(0.949414\pi\) | |||||||
\(228\) | −144.939 | − | 215.735i | −0.635696 | − | 0.946205i | ||||
\(229\) | −244.419 | −1.06733 | −0.533667 | − | 0.845695i | \(-0.679186\pi\) | ||||
−0.533667 | + | 0.845695i | \(0.679186\pi\) | |||||||
\(230\) | −67.3023 | + | 55.3759i | −0.292619 | + | 0.240765i | ||||
\(231\) | 97.4934 | + | 97.4934i | 0.422049 | + | 0.422049i | ||||
\(232\) | 38.2985 | + | 11.4595i | 0.165080 | + | 0.0493943i | ||||
\(233\) | −152.332 | − | 152.332i | −0.653786 | − | 0.653786i | 0.300116 | − | 0.953903i | \(-0.402974\pi\) |
−0.953903 | + | 0.300116i | \(0.902974\pi\) | |||||||
\(234\) | −177.243 | + | 145.835i | −0.757450 | + | 0.623226i | ||||
\(235\) | −179.530 | − | 179.530i | −0.763958 | − | 0.763958i | ||||
\(236\) | −368.197 | − | 72.2728i | −1.56016 | − | 0.306241i | ||||
\(237\) | 175.034i | 0.738541i | ||||||||
\(238\) | −333.618 | − | 78.9397i | −1.40176 | − | 0.331680i | ||||
\(239\) | 126.163i | 0.527878i | 0.964539 | + | 0.263939i | \(0.0850217\pi\) | ||||
−0.964539 | + | 0.263939i | \(0.914978\pi\) | |||||||
\(240\) | 402.595 | + | 164.383i | 1.67748 | + | 0.684929i | ||||
\(241\) | −138.655 | − | 138.655i | −0.575331 | − | 0.575331i | 0.358283 | − | 0.933613i | \(-0.383362\pi\) |
−0.933613 | + | 0.358283i | \(0.883362\pi\) | |||||||
\(242\) | −146.546 | − | 178.108i | −0.605562 | − | 0.735983i | ||||
\(243\) | 576.988 | + | 576.988i | 2.37444 | + | 2.37444i | ||||
\(244\) | −215.599 | + | 144.847i | −0.883602 | + | 0.593637i | ||||
\(245\) | 176.375 | + | 176.375i | 0.719900 | + | 0.719900i | ||||
\(246\) | 269.981 | − | 222.139i | 1.09749 | − | 0.903004i | ||||
\(247\) | 54.2738 | 0.219732 | ||||||||
\(248\) | −404.602 | − | 121.063i | −1.63146 | − | 0.488157i | ||||
\(249\) | −128.029 | + | 128.029i | −0.514172 | + | 0.514172i | ||||
\(250\) | −259.934 | − | 25.2699i | −1.03974 | − | 0.101080i | ||||
\(251\) | 345.825 | 1.37779 | 0.688895 | − | 0.724861i | \(-0.258096\pi\) | ||||
0.688895 | + | 0.724861i | \(0.258096\pi\) | |||||||
\(252\) | −538.448 | − | 801.455i | −2.13670 | − | 3.18038i | ||||
\(253\) | 21.9242 | 0.0866570 | ||||||||
\(254\) | 289.526 | − | 238.221i | 1.13987 | − | 0.937876i | ||||
\(255\) | 457.809 | + | 62.3838i | 1.79533 | + | 0.244642i | ||||
\(256\) | 182.839 | + | 179.181i | 0.714214 | + | 0.699928i | ||||
\(257\) | − | 447.501i | − | 1.74125i | −0.491948 | − | 0.870624i | \(-0.663715\pi\) | ||
0.491948 | − | 0.870624i | \(-0.336285\pi\) | |||||||
\(258\) | −43.6294 | + | 448.785i | −0.169106 | + | 1.73948i | ||||
\(259\) | −324.655 | −1.25349 | ||||||||
\(260\) | −75.3780 | + | 50.6418i | −0.289915 | + | 0.194776i | ||||
\(261\) | 84.5870 | + | 84.5870i | 0.324088 | + | 0.324088i | ||||
\(262\) | −95.1532 | − | 9.25047i | −0.363180 | − | 0.0353071i | ||||
\(263\) | 361.979 | 1.37635 | 0.688173 | − | 0.725547i | \(-0.258413\pi\) | ||||
0.688173 | + | 0.725547i | \(0.258413\pi\) | |||||||
\(264\) | −51.9315 | − | 96.2779i | −0.196710 | − | 0.364689i | ||||
\(265\) | −304.529 | + | 304.529i | −1.14917 | + | 1.14917i | ||||
\(266\) | −22.0913 | + | 227.238i | −0.0830499 | + | 0.854277i | ||||
\(267\) | −359.020 | − | 359.020i | −1.34465 | − | 1.34465i | ||||
\(268\) | −14.0453 | + | 71.5544i | −0.0524078 | + | 0.266994i | ||||
\(269\) | 76.8627 | − | 76.8627i | 0.285735 | − | 0.285735i | −0.549656 | − | 0.835391i | \(-0.685241\pi\) |
0.835391 | + | 0.549656i | \(0.185241\pi\) | |||||||
\(270\) | 515.953 | + | 627.075i | 1.91094 | + | 2.32250i | ||||
\(271\) | − | 351.524i | − | 1.29713i | −0.761157 | − | 0.648567i | \(-0.775368\pi\) | ||
0.761157 | − | 0.648567i | \(-0.224632\pi\) | |||||||
\(272\) | 235.629 | + | 135.878i | 0.866285 | + | 0.499551i | ||||
\(273\) | 277.430 | 1.01623 | ||||||||
\(274\) | −64.6606 | + | 53.2024i | −0.235988 | + | 0.194169i | ||||
\(275\) | 4.33653 | + | 4.33653i | 0.0157692 | + | 0.0157692i | ||||
\(276\) | −207.299 | − | 40.6903i | −0.751082 | − | 0.147429i | ||||
\(277\) | −143.565 | + | 143.565i | −0.518286 | + | 0.518286i | −0.917053 | − | 0.398766i | \(-0.869438\pi\) |
0.398766 | + | 0.917053i | \(0.369438\pi\) | |||||||
\(278\) | 54.9027 | + | 5.33745i | 0.197492 | + | 0.0191995i | ||||
\(279\) | −893.614 | − | 893.614i | −3.20292 | − | 3.20292i | ||||
\(280\) | −181.349 | − | 336.211i | −0.647676 | − | 1.20075i | ||||
\(281\) | 101.471i | 0.361107i | 0.983565 | + | 0.180553i | \(0.0577888\pi\) | ||||
−0.983565 | + | 0.180553i | \(0.942211\pi\) | |||||||
\(282\) | 59.5471 | − | 612.520i | 0.211160 | − | 2.17206i | ||||
\(283\) | −148.615 | + | 148.615i | −0.525142 | + | 0.525142i | −0.919120 | − | 0.393978i | \(-0.871099\pi\) |
0.393978 | + | 0.919120i | \(0.371099\pi\) | |||||||
\(284\) | 34.9730 | + | 52.0558i | 0.123144 | + | 0.183295i | ||||
\(285\) | − | 307.697i | − | 1.07964i | ||||||
\(286\) | 22.7363 | + | 2.21034i | 0.0794975 | + | 0.00772848i | ||||
\(287\) | −307.124 | −1.07012 | ||||||||
\(288\) | 226.997 | + | 731.646i | 0.788183 | + | 2.54044i | ||||
\(289\) | 278.463 | + | 77.3259i | 0.963540 | + | 0.267564i | ||||
\(290\) | 30.0706 | + | 36.5469i | 0.103692 | + | 0.126024i | ||||
\(291\) | 242.190i | 0.832269i | ||||||||
\(292\) | −78.7840 | + | 52.9301i | −0.269808 | + | 0.181267i | ||||
\(293\) | 82.6788i | 0.282180i | 0.989997 | + | 0.141090i | \(0.0450607\pi\) | ||||
−0.989997 | + | 0.141090i | \(0.954939\pi\) | |||||||
\(294\) | −58.5008 | + | 601.757i | −0.198982 | + | 2.04679i | ||||
\(295\) | −314.116 | − | 314.116i | −1.06480 | − | 1.06480i | ||||
\(296\) | 246.770 | + | 73.8372i | 0.833682 | + | 0.249450i | ||||
\(297\) | − | 204.274i | − | 0.687792i | ||||||
\(298\) | −4.38422 | − | 5.32845i | −0.0147121 | − | 0.0178807i | ||||
\(299\) | 31.1941 | − | 31.1941i | 0.104328 | − | 0.104328i | ||||
\(300\) | −32.9545 | − | 49.0513i | −0.109848 | − | 0.163504i | ||||
\(301\) | 280.079 | − | 280.079i | 0.930495 | − | 0.930495i | ||||
\(302\) | 85.6161 | − | 70.4444i | 0.283497 | − | 0.233260i | ||||
\(303\) | −199.349 | + | 199.349i | −0.657917 | + | 0.657917i | ||||
\(304\) | 68.4728 | − | 167.699i | 0.225240 | − | 0.551641i | ||||
\(305\) | −307.503 | −1.00821 | ||||||||
\(306\) | 427.548 | + | 692.591i | 1.39721 | + | 2.26337i | ||||
\(307\) | −217.880 | −0.709707 | −0.354853 | − | 0.934922i | \(-0.615469\pi\) | ||||
−0.354853 | + | 0.934922i | \(0.615469\pi\) | |||||||
\(308\) | −18.5089 | + | 94.2943i | −0.0600937 | + | 0.306150i | ||||
\(309\) | 632.562 | − | 632.562i | 2.04713 | − | 2.04713i | ||||
\(310\) | −317.679 | − | 386.098i | −1.02477 | − | 1.24548i | ||||
\(311\) | 361.855 | − | 361.855i | 1.16352 | − | 1.16352i | 0.179823 | − | 0.983699i | \(-0.442448\pi\) |
0.983699 | − | 0.179823i | \(-0.0575524\pi\) | |||||||
\(312\) | −210.874 | − | 63.0967i | −0.675880 | − | 0.202233i | ||||
\(313\) | −189.814 | + | 189.814i | −0.606435 | + | 0.606435i | −0.942013 | − | 0.335577i | \(-0.891069\pi\) |
0.335577 | + | 0.942013i | \(0.391069\pi\) | |||||||
\(314\) | 316.803 | + | 385.033i | 1.00893 | + | 1.22622i | ||||
\(315\) | − | 1143.10i | − | 3.62888i | ||||||
\(316\) | −101.260 | + | 68.0305i | −0.320444 | + | 0.215286i | ||||
\(317\) | 125.146 | + | 125.146i | 0.394784 | + | 0.394784i | 0.876389 | − | 0.481605i | \(-0.159946\pi\) |
−0.481605 | + | 0.876389i | \(0.659946\pi\) | |||||||
\(318\) | −1038.99 | − | 101.007i | −3.26727 | − | 0.317633i | ||||
\(319\) | − | 11.9054i | − | 0.0373211i | ||||||
\(320\) | 61.3781 | + | 296.798i | 0.191806 | + | 0.927495i | ||||
\(321\) | 507.580i | 1.58125i | ||||||||
\(322\) | 117.909 | + | 143.303i | 0.366176 | + | 0.445040i | ||||
\(323\) | 25.9857 | − | 190.698i | 0.0804509 | − | 0.590397i | ||||
\(324\) | −213.128 | + | 1085.79i | −0.657803 | + | 3.35121i | ||||
\(325\) | 12.3402 | 0.0379697 | ||||||||
\(326\) | −6.49095 | + | 66.7679i | −0.0199109 | + | 0.204809i | ||||
\(327\) | 891.870i | 2.72743i | ||||||||
\(328\) | 233.445 | + | 69.8500i | 0.711721 | + | 0.212957i | ||||
\(329\) | −382.263 | + | 382.263i | −1.16189 | + | 1.16189i | ||||
\(330\) | 12.5312 | − | 128.900i | 0.0379734 | − | 0.390606i | ||||
\(331\) | − | 387.195i | − | 1.16977i | −0.811115 | − | 0.584886i | \(-0.801139\pi\) | ||
0.811115 | − | 0.584886i | \(-0.198861\pi\) | |||||||
\(332\) | −123.828 | − | 24.3059i | −0.372975 | − | 0.0732105i | ||||
\(333\) | 545.022 | + | 545.022i | 1.63670 | + | 1.63670i | ||||
\(334\) | −18.8018 | + | 193.401i | −0.0562927 | + | 0.579045i | ||||
\(335\) | −61.0444 | + | 61.0444i | −0.182222 | + | 0.182222i | ||||
\(336\) | 350.011 | − | 857.222i | 1.04170 | − | 2.55126i | ||||
\(337\) | −146.626 | − | 146.626i | −0.435091 | − | 0.435091i | 0.455265 | − | 0.890356i | \(-0.349544\pi\) |
−0.890356 | + | 0.455265i | \(0.849544\pi\) | |||||||
\(338\) | −225.512 | + | 185.550i | −0.667196 | + | 0.548965i | ||||
\(339\) | 636.527 | 1.87766 | ||||||||
\(340\) | 141.846 | + | 289.097i | 0.417195 | + | 0.850285i | ||||
\(341\) | 125.774i | 0.368840i | ||||||||
\(342\) | 418.567 | − | 344.394i | 1.22388 | − | 1.00700i | ||||
\(343\) | 26.1797 | − | 26.1797i | 0.0763256 | − | 0.0763256i | ||||
\(344\) | −276.587 | + | 149.189i | −0.804032 | + | 0.433688i | ||||
\(345\) | −176.850 | − | 176.850i | −0.512609 | − | 0.512609i | ||||
\(346\) | −18.1193 | + | 186.381i | −0.0523680 | + | 0.538673i | ||||
\(347\) | 209.388 | − | 209.388i | 0.603422 | − | 0.603422i | −0.337797 | − | 0.941219i | \(-0.609682\pi\) |
0.941219 | + | 0.337797i | \(0.109682\pi\) | |||||||
\(348\) | −22.0959 | + | 112.569i | −0.0634940 | + | 0.323473i | ||||
\(349\) | 449.548 | 1.28810 | 0.644051 | − | 0.764982i | \(-0.277252\pi\) | ||||
0.644051 | + | 0.764982i | \(0.277252\pi\) | |||||||
\(350\) | −5.02286 | + | 51.6667i | −0.0143510 | + | 0.147619i | ||||
\(351\) | −290.645 | − | 290.645i | −0.828047 | − | 0.828047i | ||||
\(352\) | 35.5142 | − | 67.4635i | 0.100893 | − | 0.191658i | ||||
\(353\) | 290.121 | 0.821872 | 0.410936 | − | 0.911664i | \(-0.365202\pi\) | ||||
0.410936 | + | 0.911664i | \(0.365202\pi\) | |||||||
\(354\) | 104.187 | − | 1071.70i | 0.294313 | − | 3.02740i | ||||
\(355\) | 74.2459i | 0.209143i | ||||||||
\(356\) | 68.1590 | − | 347.240i | 0.191458 | − | 0.975392i | ||||
\(357\) | 132.830 | − | 974.787i | 0.372073 | − | 2.73050i | ||||
\(358\) | −85.6141 | − | 104.053i | −0.239145 | − | 0.290650i | ||||
\(359\) | 17.2774 | 0.0481265 | 0.0240632 | − | 0.999710i | \(-0.492340\pi\) | ||||
0.0240632 | + | 0.999710i | \(0.492340\pi\) | |||||||
\(360\) | −259.978 | + | 868.866i | −0.722160 | + | 2.41352i | ||||
\(361\) | 232.830 | 0.644959 | ||||||||
\(362\) | −53.7223 | − | 5.22270i | −0.148404 | − | 0.0144273i | ||||
\(363\) | 468.014 | − | 468.014i | 1.28930 | − | 1.28930i | ||||
\(364\) | 107.829 | + | 160.498i | 0.296232 | + | 0.440929i | ||||
\(365\) | −112.368 | −0.307857 | ||||||||
\(366\) | −473.573 | − | 575.566i | −1.29391 | − | 1.57259i | ||||
\(367\) | 436.568 | + | 436.568i | 1.18956 | + | 1.18956i | 0.977190 | + | 0.212368i | \(0.0681174\pi\) |
0.212368 | + | 0.977190i | \(0.431883\pi\) | |||||||
\(368\) | −57.0306 | − | 135.741i | −0.154974 | − | 0.368861i | ||||
\(369\) | 515.591 | + | 515.591i | 1.39727 | + | 1.39727i | ||||
\(370\) | 193.755 | + | 235.484i | 0.523662 | + | 0.636443i | ||||
\(371\) | 648.416 | + | 648.416i | 1.74775 | + | 1.74775i | ||||
\(372\) | 233.431 | − | 1189.23i | 0.627503 | − | 3.19684i | ||||
\(373\) | 54.1812i | 0.145258i | 0.997359 | + | 0.0726289i | \(0.0231389\pi\) | ||||
−0.997359 | + | 0.0726289i | \(0.976861\pi\) | |||||||
\(374\) | 18.6522 | − | 78.8286i | 0.0498722 | − | 0.210772i | ||||
\(375\) | − | 749.431i | − | 1.99848i | ||||||
\(376\) | 377.497 | − | 203.619i | 1.00398 | − | 0.541539i | ||||
\(377\) | −16.9392 | − | 16.9392i | −0.0449317 | − | 0.0449317i | ||||
\(378\) | 1335.19 | − | 1098.59i | 3.53226 | − | 2.90632i | ||||
\(379\) | −34.3158 | − | 34.3158i | −0.0905429 | − | 0.0905429i | 0.660385 | − | 0.750928i | \(-0.270393\pi\) |
−0.750928 | + | 0.660385i | \(0.770393\pi\) | |||||||
\(380\) | 178.008 | − | 119.592i | 0.468442 | − | 0.314717i | ||||
\(381\) | 760.789 | + | 760.789i | 1.99682 | + | 1.99682i | ||||
\(382\) | 176.604 | + | 214.639i | 0.462314 | + | 0.561883i | ||||
\(383\) | 72.3226 | 0.188832 | 0.0944159 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944159 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(384\) | −461.003 | + | 571.970i | −1.20053 | + | 1.48951i | ||||
\(385\) | −80.4442 | + | 80.4442i | −0.208946 | + | 0.208946i | ||||
\(386\) | −22.5431 | + | 231.885i | −0.0584017 | + | 0.600739i | ||||
\(387\) | −940.379 | −2.42992 | ||||||||
\(388\) | −140.111 | + | 94.1319i | −0.361111 | + | 0.242608i | ||||
\(389\) | −501.908 | −1.29025 | −0.645126 | − | 0.764076i | \(-0.723195\pi\) | ||||
−0.645126 | + | 0.764076i | \(0.723195\pi\) | |||||||
\(390\) | −165.571 | − | 201.230i | −0.424541 | − | 0.515975i | ||||
\(391\) | −94.6692 | − | 124.540i | −0.242121 | − | 0.318516i | ||||
\(392\) | −370.864 | + | 200.041i | −0.946081 | + | 0.510308i | ||||
\(393\) | − | 274.342i | − | 0.698070i | ||||||
\(394\) | 37.3133 | + | 3.62747i | 0.0947038 | + | 0.00920678i | ||||
\(395\) | −144.425 | −0.365633 | ||||||||
\(396\) | 189.371 | − | 127.227i | 0.478209 | − | 0.321279i | ||||
\(397\) | −160.196 | − | 160.196i | −0.403517 | − | 0.403517i | 0.475953 | − | 0.879471i | \(-0.342103\pi\) |
−0.879471 | + | 0.475953i | \(0.842103\pi\) | |||||||
\(398\) | 12.3861 | − | 127.407i | 0.0311208 | − | 0.320118i | ||||
\(399\) | −655.162 | −1.64201 | ||||||||
\(400\) | 15.5686 | − | 38.1294i | 0.0389214 | − | 0.0953236i | ||||
\(401\) | 305.319 | − | 305.319i | 0.761393 | − | 0.761393i | −0.215181 | − | 0.976574i | \(-0.569034\pi\) |
0.976574 | + | 0.215181i | \(0.0690342\pi\) | |||||||
\(402\) | −208.271 | − | 20.2474i | −0.518087 | − | 0.0503666i | ||||
\(403\) | 178.954 | + | 178.954i | 0.444054 | + | 0.444054i | ||||
\(404\) | −192.807 | − | 37.8459i | −0.477246 | − | 0.0936779i | ||||
\(405\) | −926.309 | + | 926.309i | −2.28718 | + | 2.28718i | ||||
\(406\) | 77.8173 | − | 64.0276i | 0.191668 | − | 0.157704i | ||||
\(407\) | − | 76.7107i | − | 0.188478i | ||||||
\(408\) | −322.663 | + | 710.725i | −0.790840 | + | 1.74197i | ||||
\(409\) | −562.929 | −1.37636 | −0.688178 | − | 0.725542i | \(-0.741589\pi\) | ||||
−0.688178 | + | 0.725542i | \(0.741589\pi\) | |||||||
\(410\) | 183.292 | + | 222.768i | 0.447054 | + | 0.543337i | ||||
\(411\) | −169.909 | − | 169.909i | −0.413404 | − | 0.413404i | ||||
\(412\) | 611.805 | + | 120.090i | 1.48496 | + | 0.291481i | ||||
\(413\) | −668.829 | + | 668.829i | −1.61944 | + | 1.61944i | ||||
\(414\) | 42.6309 | − | 438.515i | 0.102973 | − | 1.05922i | ||||
\(415\) | −105.640 | − | 105.640i | −0.254553 | − | 0.254553i | ||||
\(416\) | −45.4579 | − | 146.518i | −0.109274 | − | 0.352207i | ||||
\(417\) | 158.293i | 0.379600i | ||||||||
\(418\) | −53.6926 | − | 5.21981i | −0.128451 | − | 0.0124876i | ||||
\(419\) | 329.191 | − | 329.191i | 0.785660 | − | 0.785660i | −0.195120 | − | 0.980779i | \(-0.562510\pi\) |
0.980779 | + | 0.195120i | \(0.0625095\pi\) | |||||||
\(420\) | 909.919 | − | 611.318i | 2.16647 | − | 1.45552i | ||||
\(421\) | 505.234i | 1.20008i | 0.799969 | + | 0.600041i | \(0.204849\pi\) | ||||
−0.799969 | + | 0.600041i | \(0.795151\pi\) | |||||||
\(422\) | −44.9933 | + | 462.815i | −0.106619 | + | 1.09672i | ||||
\(423\) | 1283.47 | 3.03420 | ||||||||
\(424\) | −345.390 | − | 640.332i | −0.814598 | − | 1.51022i | ||||
\(425\) | 5.90832 | − | 43.3588i | 0.0139019 | − | 0.102021i | ||||
\(426\) | −138.969 | + | 114.343i | −0.326218 | + | 0.268410i | ||||
\(427\) | 654.750i | 1.53337i | ||||||||
\(428\) | −293.643 | + | 197.281i | −0.686083 | + | 0.460936i | ||||
\(429\) | 65.5523i | 0.152803i | ||||||||
\(430\) | −370.304 | − | 35.9996i | −0.861171 | − | 0.0837201i | ||||
\(431\) | −81.7921 | − | 81.7921i | −0.189773 | − | 0.189773i | 0.605825 | − | 0.795598i | \(-0.292843\pi\) |
−0.795598 | + | 0.605825i | \(0.792843\pi\) | |||||||
\(432\) | −1264.74 | + | 531.370i | −2.92763 | + | 1.23002i | ||||
\(433\) | 320.041i | 0.739126i | 0.929206 | + | 0.369563i | \(0.120493\pi\) | ||||
−0.929206 | + | 0.369563i | \(0.879507\pi\) | |||||||
\(434\) | −822.096 | + | 676.416i | −1.89423 | + | 1.55856i | ||||
\(435\) | −96.0344 | + | 96.0344i | −0.220769 | + | 0.220769i | ||||
\(436\) | −515.962 | + | 346.643i | −1.18340 | + | 0.795052i | ||||
\(437\) | −73.6661 | + | 73.6661i | −0.168572 | + | 0.168572i | ||||
\(438\) | −173.053 | − | 210.323i | −0.395097 | − | 0.480190i | ||||
\(439\) | −236.803 | + | 236.803i | −0.539415 | + | 0.539415i | −0.923357 | − | 0.383942i | \(-0.874566\pi\) |
0.383942 | + | 0.923357i | \(0.374566\pi\) | |||||||
\(440\) | 79.4412 | − | 42.8499i | 0.180548 | − | 0.0973862i | ||||
\(441\) | −1260.91 | −2.85922 | ||||||||
\(442\) | −85.6199 | − | 138.697i | −0.193710 | − | 0.313794i | ||||
\(443\) | 547.137 | 1.23507 | 0.617536 | − | 0.786542i | \(-0.288131\pi\) | ||||
0.617536 | + | 0.786542i | \(0.288131\pi\) | |||||||
\(444\) | −142.371 | + | 725.317i | −0.320656 | + | 1.63360i | ||||
\(445\) | 296.236 | − | 296.236i | 0.665700 | − | 0.665700i | ||||
\(446\) | −99.8627 | + | 82.1664i | −0.223907 | + | 0.184230i | ||||
\(447\) | 14.0016 | − | 14.0016i | 0.0313234 | − | 0.0313234i | ||||
\(448\) | 631.956 | − | 130.689i | 1.41062 | − | 0.291716i | ||||
\(449\) | −77.5113 | + | 77.5113i | −0.172631 | + | 0.172631i | −0.788134 | − | 0.615503i | \(-0.788953\pi\) |
0.615503 | + | 0.788134i | \(0.288953\pi\) | |||||||
\(450\) | 95.1689 | − | 78.3044i | 0.211486 | − | 0.174010i | ||||
\(451\) | − | 72.5684i | − | 0.160906i | ||||||
\(452\) | 247.399 | + | 368.242i | 0.547342 | + | 0.814694i | ||||
\(453\) | 224.974 | + | 224.974i | 0.496630 | + | 0.496630i | ||||
\(454\) | 71.1740 | − | 732.118i | 0.156771 | − | 1.61259i | ||||
\(455\) | 228.914i | 0.503109i | ||||||||
\(456\) | 497.988 | + | 149.005i | 1.09208 | + | 0.326766i | ||||
\(457\) | − | 156.295i | − | 0.342001i | −0.985271 | − | 0.171001i | \(-0.945300\pi\) | ||
0.985271 | − | 0.171001i | \(-0.0547000\pi\) | |||||||
\(458\) | 377.486 | − | 310.593i | 0.824204 | − | 0.678150i | ||||
\(459\) | −1160.37 | + | 882.060i | −2.52805 | + | 1.92170i | ||||
\(460\) | 33.5745 | − | 171.047i | 0.0729881 | − | 0.371841i | ||||
\(461\) | −323.645 | −0.702050 | −0.351025 | − | 0.936366i | \(-0.614167\pi\) | ||||
−0.351025 | + | 0.936366i | \(0.614167\pi\) | |||||||
\(462\) | −274.459 | − | 26.6820i | −0.594067 | − | 0.0577532i | ||||
\(463\) | − | 107.360i | − | 0.231879i | −0.993256 | − | 0.115940i | \(-0.963012\pi\) | ||
0.993256 | − | 0.115940i | \(-0.0369879\pi\) | |||||||
\(464\) | −73.7108 | + | 30.9691i | −0.158860 | + | 0.0667438i | ||||
\(465\) | 1014.55 | − | 1014.55i | 2.18183 | − | 2.18183i | ||||
\(466\) | 428.839 | + | 41.6902i | 0.920255 | + | 0.0894640i | ||||
\(467\) | 322.960i | 0.691563i | 0.938315 | + | 0.345782i | \(0.112386\pi\) | ||||
−0.938315 | + | 0.345782i | \(0.887614\pi\) | |||||||
\(468\) | 88.4199 | − | 450.460i | 0.188931 | − | 0.962520i | ||||
\(469\) | 129.978 | + | 129.978i | 0.277139 | + | 0.277139i | ||||
\(470\) | 505.405 | + | 49.1338i | 1.07533 | + | 0.104540i | ||||
\(471\) | −1011.75 | + | 1011.75i | −2.14810 | + | 2.14810i | ||||
\(472\) | 660.490 | − | 356.263i | 1.39934 | − | 0.754794i | ||||
\(473\) | 66.1782 | + | 66.1782i | 0.139912 | + | 0.139912i | ||||
\(474\) | −222.423 | − | 270.326i | −0.469246 | − | 0.570308i | ||||
\(475\) | −29.1418 | −0.0613511 | ||||||||
\(476\) | 615.558 | − | 302.025i | 1.29319 | − | 0.634507i | ||||
\(477\) | − | 2177.09i | − | 4.56413i | ||||||
\(478\) | −160.320 | − | 194.848i | −0.335397 | − | 0.407632i | ||||
\(479\) | 292.651 | − | 292.651i | 0.610962 | − | 0.610962i | −0.332234 | − | 0.943197i | \(-0.607803\pi\) |
0.943197 | + | 0.332234i | \(0.107803\pi\) | |||||||
\(480\) | −830.662 | + | 257.717i | −1.73055 | + | 0.536910i | ||||
\(481\) | −109.145 | − | 109.145i | −0.226913 | − | 0.226913i | ||||
\(482\) | 390.334 | + | 37.9470i | 0.809822 | + | 0.0787282i | ||||
\(483\) | −376.557 | + | 376.557i | −0.779621 | + | 0.779621i | ||||
\(484\) | 452.657 | + | 88.8512i | 0.935241 | + | 0.183577i | ||||
\(485\) | −199.837 | −0.412035 | ||||||||
\(486\) | −1624.31 | − | 157.910i | −3.34220 | − | 0.324918i | ||||
\(487\) | −399.978 | − | 399.978i | −0.821309 | − | 0.821309i | 0.164986 | − | 0.986296i | \(-0.447242\pi\) |
−0.986296 | + | 0.164986i | \(0.947242\pi\) | |||||||
\(488\) | 148.912 | − | 497.675i | 0.305147 | − | 1.01983i | ||||
\(489\) | −192.502 | −0.393665 | ||||||||
\(490\) | −496.524 | − | 48.2704i | −1.01332 | − | 0.0985110i | ||||
\(491\) | − | 279.523i | − | 0.569293i | −0.958633 | − | 0.284647i | \(-0.908124\pi\) | ||
0.958633 | − | 0.284647i | \(-0.0918762\pi\) | |||||||
\(492\) | −134.683 | + | 686.151i | −0.273747 | + | 1.39462i | ||||
\(493\) | −67.6285 | + | 51.4079i | −0.137178 | + | 0.104276i | ||||
\(494\) | −83.8215 | + | 68.9678i | −0.169679 | + | 0.139611i | ||||
\(495\) | 270.095 | 0.545647 | ||||||||
\(496\) | 778.714 | − | 327.172i | 1.56999 | − | 0.659620i | ||||
\(497\) | 158.088 | 0.318084 | ||||||||
\(498\) | 35.0389 | − | 360.421i | 0.0703592 | − | 0.723736i | ||||
\(499\) | 158.690 | − | 158.690i | 0.318016 | − | 0.318016i | −0.529989 | − | 0.848005i | \(-0.677804\pi\) |
0.848005 | + | 0.529989i | \(0.177804\pi\) | |||||||
\(500\) | 433.559 | − | 291.281i | 0.867117 | − | 0.582562i | ||||
\(501\) | −557.605 | −1.11298 | ||||||||
\(502\) | −534.099 | + | 439.453i | −1.06394 | + | 0.875405i | ||||
\(503\) | −196.532 | − | 196.532i | −0.390719 | − | 0.390719i | 0.484224 | − | 0.874944i | \(-0.339102\pi\) |
−0.874944 | + | 0.484224i | \(0.839102\pi\) | |||||||
\(504\) | 1850.03 | + | 553.555i | 3.67069 | + | 1.09832i | ||||
\(505\) | −164.488 | − | 164.488i | −0.325718 | − | 0.325718i | ||||
\(506\) | −33.8602 | + | 27.8599i | −0.0669173 | + | 0.0550592i | ||||
\(507\) | −592.578 | − | 592.578i | −1.16879 | − | 1.16879i | ||||
\(508\) | −144.434 | + | 735.824i | −0.284318 | + | 1.44847i | ||||
\(509\) | 239.733i | 0.470989i | 0.971876 | + | 0.235494i | \(0.0756710\pi\) | ||||
−0.971876 | + | 0.235494i | \(0.924329\pi\) | |||||||
\(510\) | −786.322 | + | 485.409i | −1.54181 | + | 0.951782i | ||||
\(511\) | 239.258i | 0.468215i | ||||||||
\(512\) | −510.072 | − | 44.3910i | −0.996234 | − | 0.0867012i | ||||
\(513\) | 686.368 | + | 686.368i | 1.33795 | + | 1.33795i | ||||
\(514\) | 568.656 | + | 691.128i | 1.10634 | + | 1.34461i | ||||
\(515\) | 521.942 | + | 521.942i | 1.01348 | + | 1.01348i | ||||
\(516\) | −502.906 | − | 748.553i | −0.974625 | − | 1.45068i | ||||
\(517\) | −90.3226 | − | 90.3226i | −0.174705 | − | 0.174705i | ||||
\(518\) | 501.403 | − | 412.551i | 0.967959 | − | 0.796431i | ||||
\(519\) | −537.366 | −1.03539 | ||||||||
\(520\) | 52.0626 | − | 173.998i | 0.100120 | − | 0.334611i | ||||
\(521\) | −395.435 | + | 395.435i | −0.758993 | + | 0.758993i | −0.976139 | − | 0.217146i | \(-0.930325\pi\) |
0.217146 | + | 0.976139i | \(0.430325\pi\) | |||||||
\(522\) | −238.126 | − | 23.1497i | −0.456179 | − | 0.0443482i | ||||
\(523\) | −233.873 | −0.447176 | −0.223588 | − | 0.974684i | \(-0.571777\pi\) | ||||
−0.223588 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(524\) | 158.711 | − | 106.628i | 0.302884 | − | 0.203489i | ||||
\(525\) | −148.963 | −0.283739 | ||||||||
\(526\) | −559.047 | + | 459.980i | −1.06283 | + | 0.874487i | ||||
\(527\) | 714.458 | − | 543.096i | 1.35571 | − | 1.03054i | ||||
\(528\) | 202.548 | + | 82.7020i | 0.383613 | + | 0.156632i | ||||
\(529\) | − | 444.320i | − | 0.839925i | ||||||
\(530\) | 83.3434 | − | 857.297i | 0.157252 | − | 1.61754i | ||||
\(531\) | 2245.62 | 4.22905 | ||||||||
\(532\) | −254.641 | − | 379.022i | −0.478649 | − | 0.712447i | ||||
\(533\) | −103.251 | − | 103.251i | −0.193718 | − | 0.193718i | ||||
\(534\) | 1010.70 | + | 98.2566i | 1.89269 | + | 0.184001i | ||||
\(535\) | −418.817 | −0.782835 | ||||||||
\(536\) | −69.2351 | − | 128.358i | −0.129170 | − | 0.239473i | ||||
\(537\) | 273.420 | − | 273.420i | 0.509162 | − | 0.509162i | ||||
\(538\) | −21.0358 | + | 216.380i | −0.0390999 | + | 0.402194i | ||||
\(539\) | 88.7355 | + | 88.7355i | 0.164630 | + | 0.164630i | ||||
\(540\) | −1593.69 | − | 312.824i | −2.95129 | − | 0.579303i | ||||
\(541\) | −178.648 | + | 178.648i | −0.330218 | + | 0.330218i | −0.852669 | − | 0.522451i | \(-0.825018\pi\) |
0.522451 | + | 0.852669i | \(0.325018\pi\) | |||||||
\(542\) | 446.694 | + | 542.899i | 0.824159 | + | 1.00166i | ||||
\(543\) | − | 154.890i | − | 0.285248i | ||||||
\(544\) | −536.575 | + | 89.5713i | −0.986352 | + | 0.164653i | ||||
\(545\) | −735.904 | −1.35028 | ||||||||
\(546\) | −428.468 | + | 352.541i | −0.784740 | + | 0.645680i | ||||
\(547\) | −517.372 | − | 517.372i | −0.945836 | − | 0.945836i | 0.0527705 | − | 0.998607i | \(-0.483195\pi\) |
−0.998607 | + | 0.0527705i | \(0.983195\pi\) | |||||||
\(548\) | 32.2567 | − | 164.333i | 0.0588626 | − | 0.299879i | ||||
\(549\) | 1099.18 | − | 1099.18i | 2.00214 | − | 2.00214i | ||||
\(550\) | −12.2080 | − | 1.18682i | −0.0221964 | − | 0.00215786i | ||||
\(551\) | 40.0027 | + | 40.0027i | 0.0726001 | + | 0.0726001i | ||||
\(552\) | 371.862 | − | 200.579i | 0.673663 | − | 0.363368i | ||||
\(553\) | 307.516i | 0.556087i | ||||||||
\(554\) | 39.2909 | − | 404.159i | 0.0709222 | − | 0.729528i | ||||
\(555\) | −618.782 | + | 618.782i | −1.11492 | + | 1.11492i | ||||
\(556\) | −91.5752 | + | 61.5237i | −0.164704 | + | 0.110654i | ||||
\(557\) | 678.176i | 1.21755i | 0.793343 | + | 0.608775i | \(0.208339\pi\) | ||||
−0.793343 | + | 0.608775i | \(0.791661\pi\) | |||||||
\(558\) | 2515.66 | + | 244.564i | 4.50836 | + | 0.438287i | ||||
\(559\) | 188.319 | 0.336885 | ||||||||
\(560\) | 707.315 | + | 288.803i | 1.26306 | + | 0.515719i | ||||
\(561\) | 230.327 | + | 31.3856i | 0.410564 | + | 0.0559459i | ||||
\(562\) | −128.943 | − | 156.714i | −0.229436 | − | 0.278850i | ||||
\(563\) | − | 995.695i | − | 1.76855i | −0.466965 | − | 0.884276i | \(-0.654653\pi\) | ||
0.466965 | − | 0.884276i | \(-0.345347\pi\) | |||||||
\(564\) | 686.387 | + | 1021.66i | 1.21700 | + | 1.81145i | ||||
\(565\) | 525.214i | 0.929583i | ||||||||
\(566\) | 40.6729 | − | 418.374i | 0.0718603 | − | 0.739178i | ||||
\(567\) | 1972.34 | + | 1972.34i | 3.47855 | + | 3.47855i | ||||
\(568\) | −120.162 | − | 35.9543i | −0.211553 | − | 0.0632998i | ||||
\(569\) | 303.840i | 0.533989i | 0.963698 | + | 0.266995i | \(0.0860306\pi\) | ||||
−0.963698 | + | 0.266995i | \(0.913969\pi\) | |||||||
\(570\) | 391.002 | + | 475.213i | 0.685969 | + | 0.833707i | ||||
\(571\) | 127.417 | − | 127.417i | 0.223148 | − | 0.223148i | −0.586675 | − | 0.809823i | \(-0.699563\pi\) |
0.809823 | + | 0.586675i | \(0.199563\pi\) | |||||||
\(572\) | −37.9231 | + | 25.4782i | −0.0662991 | + | 0.0445422i | ||||
\(573\) | −564.008 | + | 564.008i | −0.984308 | + | 0.984308i | ||||
\(574\) | 474.327 | − | 390.274i | 0.826354 | − | 0.679920i | ||||
\(575\) | −16.7493 | + | 16.7493i | −0.0291293 | + | 0.0291293i | ||||
\(576\) | −1280.31 | − | 841.514i | −2.22276 | − | 1.46096i | ||||
\(577\) | 737.054 | 1.27739 | 0.638695 | − | 0.769460i | \(-0.279474\pi\) | ||||
0.638695 | + | 0.769460i | \(0.279474\pi\) | |||||||
\(578\) | −528.324 | + | 234.430i | −0.914056 | + | 0.405589i | ||||
\(579\) | −668.561 | −1.15468 | ||||||||
\(580\) | −92.8831 | − | 18.2319i | −0.160143 | − | 0.0314343i | ||||
\(581\) | −224.932 | + | 224.932i | −0.387147 | + | 0.387147i | ||||
\(582\) | −307.760 | − | 374.043i | −0.528798 | − | 0.642685i | ||||
\(583\) | −153.210 | + | 153.210i | −0.262796 | + | 0.262796i | ||||
\(584\) | 54.4151 | − | 181.860i | 0.0931766 | − | 0.311404i | ||||
\(585\) | 384.295 | − | 384.295i | 0.656915 | − | 0.656915i | ||||
\(586\) | −105.063 | − | 127.691i | −0.179288 | − | 0.217902i | ||||
\(587\) | 1045.64i | 1.78133i | 0.454658 | + | 0.890666i | \(0.349762\pi\) | ||||
−0.454658 | + | 0.890666i | \(0.650238\pi\) | |||||||
\(588\) | −674.326 | − | 1003.70i | −1.14681 | − | 1.70698i | ||||
\(589\) | −422.606 | − | 422.606i | −0.717497 | − | 0.717497i | ||||
\(590\) | 884.285 | + | 85.9671i | 1.49879 | + | 0.145707i | ||||
\(591\) | 107.580i | 0.182031i | ||||||||
\(592\) | −474.943 | + | 199.544i | −0.802269 | + | 0.337068i | ||||
\(593\) | − | 405.674i | − | 0.684105i | −0.939681 | − | 0.342053i | \(-0.888878\pi\) | ||
0.939681 | − | 0.342053i | \(-0.111122\pi\) | |||||||
\(594\) | 259.579 | + | 315.485i | 0.437002 | + | 0.531119i | ||||
\(595\) | 804.321 | + | 109.601i | 1.35180 | + | 0.184204i | ||||
\(596\) | 13.5421 | + | 2.65816i | 0.0227217 | + | 0.00446000i | ||||
\(597\) | 367.335 | 0.615301 | ||||||||
\(598\) | −8.53720 | + | 87.8163i | −0.0142762 | + | 0.146850i | ||||
\(599\) | − | 765.475i | − | 1.27792i | −0.769239 | − | 0.638961i | \(-0.779365\pi\) | ||
0.769239 | − | 0.638961i | \(-0.220635\pi\) | |||||||
\(600\) | 113.227 | + | 33.8791i | 0.188711 | + | 0.0564652i | ||||
\(601\) | −2.71317 | + | 2.71317i | −0.00451443 | + | 0.00451443i | −0.709360 | − | 0.704846i | \(-0.751016\pi\) |
0.704846 | + | 0.709360i | \(0.251016\pi\) | |||||||
\(602\) | −76.6520 | + | 788.466i | −0.127329 | + | 1.30974i | ||||
\(603\) | − | 436.408i | − | 0.723728i | ||||||
\(604\) | −42.7106 | + | 217.591i | −0.0707129 | + | 0.360250i | ||||
\(605\) | 386.170 | + | 386.170i | 0.638297 | + | 0.638297i | ||||
\(606\) | 54.5578 | − | 561.198i | 0.0900293 | − | 0.926070i | ||||
\(607\) | −658.383 | + | 658.383i | −1.08465 | + | 1.08465i | −0.0885817 | + | 0.996069i | \(0.528233\pi\) |
−0.996069 | + | 0.0885817i | \(0.971767\pi\) | |||||||
\(608\) | 107.351 | + | 346.008i | 0.176564 | + | 0.569092i | ||||
\(609\) | 204.481 | + | 204.481i | 0.335765 | + | 0.335765i | ||||
\(610\) | 474.914 | − | 390.756i | 0.778547 | − | 0.640584i | ||||
\(611\) | −257.025 | −0.420663 | ||||||||
\(612\) | −1540.41 | − | 526.350i | −2.51702 | − | 0.860048i | ||||
\(613\) | 544.685i | 0.888556i | 0.895889 | + | 0.444278i | \(0.146540\pi\) | ||||
−0.895889 | + | 0.444278i | \(0.853460\pi\) | |||||||
\(614\) | 336.498 | − | 276.868i | 0.548042 | − | 0.450925i | ||||
\(615\) | −585.368 | + | 585.368i | −0.951818 | + | 0.951818i | ||||
\(616\) | −91.2379 | − | 169.150i | −0.148113 | − | 0.274594i | ||||
\(617\) | 563.768 | + | 563.768i | 0.913724 | + | 0.913724i | 0.996563 | − | 0.0828385i | \(-0.0263986\pi\) |
−0.0828385 | + | 0.996563i | \(0.526399\pi\) | |||||||
\(618\) | −173.119 | + | 1780.76i | −0.280129 | + | 2.88149i | ||||
\(619\) | 451.241 | − | 451.241i | 0.728984 | − | 0.728984i | −0.241433 | − | 0.970417i | \(-0.577617\pi\) |
0.970417 | + | 0.241433i | \(0.0776175\pi\) | |||||||
\(620\) | 981.259 | + | 192.610i | 1.58268 | + | 0.310661i | ||||
\(621\) | 788.986 | 1.27051 | ||||||||
\(622\) | −99.0325 | + | 1018.68i | −0.159216 | + | 1.63775i | ||||
\(623\) | −630.759 | − | 630.759i | −1.01245 | − | 1.01245i | ||||
\(624\) | 405.858 | − | 170.518i | 0.650413 | − | 0.273267i | ||||
\(625\) | 554.022 | 0.886435 | ||||||||
\(626\) | 51.9483 | − | 534.356i | 0.0829845 | − | 0.853605i | ||||
\(627\) | − | 154.804i | − | 0.246897i | ||||||
\(628\) | −978.553 | − | 192.079i | −1.55821 | − | 0.305858i | ||||
\(629\) | −435.753 | + | 331.238i | −0.692771 | + | 0.526611i | ||||
\(630\) | 1452.58 | + | 1765.42i | 2.30568 | + | 2.80225i | ||||
\(631\) | 674.106 | 1.06831 | 0.534157 | − | 0.845385i | \(-0.320629\pi\) | ||||
0.534157 | + | 0.845385i | \(0.320629\pi\) | |||||||
\(632\) | 69.9392 | − | 233.743i | 0.110663 | − | 0.369846i | ||||
\(633\) | −1334.37 | −2.10801 | ||||||||
\(634\) | −352.307 | − | 34.2500i | −0.555689 | − | 0.0540222i | ||||
\(635\) | −627.745 | + | 627.745i | −0.988575 | + | 0.988575i | ||||
\(636\) | 1732.99 | − | 1164.29i | 2.72483 | − | 1.83064i | ||||
\(637\) | 252.508 | 0.396403 | ||||||||
\(638\) | 15.1287 | + | 18.3870i | 0.0237127 | + | 0.0288197i | ||||
\(639\) | −265.393 | − | 265.393i | −0.415326 | − | 0.415326i | ||||
\(640\) | −471.946 | − | 380.385i | −0.737416 | − | 0.594352i | ||||
\(641\) | −256.865 | − | 256.865i | −0.400726 | − | 0.400726i | 0.477763 | − | 0.878489i | \(-0.341448\pi\) |
−0.878489 | + | 0.477763i | \(0.841448\pi\) | |||||||
\(642\) | −645.001 | − | 783.915i | −1.00467 | − | 1.22105i | ||||
\(643\) | 51.7980 | + | 51.7980i | 0.0805568 | + | 0.0805568i | 0.746237 | − | 0.665680i | \(-0.231859\pi\) |
−0.665680 | + | 0.746237i | \(0.731859\pi\) | |||||||
\(644\) | −364.201 | − | 71.4883i | −0.565529 | − | 0.111007i | ||||
\(645\) | − | 1067.64i | − | 1.65526i | ||||||
\(646\) | 202.195 | + | 327.539i | 0.312995 | + | 0.507026i | ||||
\(647\) | − | 436.057i | − | 0.673967i | −0.941510 | − | 0.336984i | \(-0.890593\pi\) | ||
0.941510 | − | 0.336984i | \(-0.109407\pi\) | |||||||
\(648\) | −1050.60 | − | 1947.74i | −1.62129 | − | 3.00578i | ||||
\(649\) | −158.033 | − | 158.033i | −0.243503 | − | 0.243503i | ||||
\(650\) | −19.0584 | + | 15.6811i | −0.0293206 | + | 0.0241248i | ||||
\(651\) | −2160.22 | − | 2160.22i | −3.31832 | − | 3.31832i | ||||
\(652\) | −74.8197 | − | 111.366i | −0.114754 | − | 0.170806i | ||||
\(653\) | −627.724 | − | 627.724i | −0.961292 | − | 0.961292i | 0.0379863 | − | 0.999278i | \(-0.487906\pi\) |
−0.999278 | + | 0.0379863i | \(0.987906\pi\) | |||||||
\(654\) | −1133.33 | − | 1377.42i | −1.73293 | − | 2.10615i | ||||
\(655\) | 226.366 | 0.345597 | ||||||||
\(656\) | −449.297 | + | 188.769i | −0.684904 | + | 0.287758i | ||||
\(657\) | 401.660 | − | 401.660i | 0.611355 | − | 0.611355i | ||||
\(658\) | 104.618 | − | 1076.13i | 0.158993 | − | 1.63546i | ||||
\(659\) | −286.443 | −0.434663 | −0.217331 | − | 0.976098i | \(-0.569735\pi\) | ||||
−0.217331 | + | 0.976098i | \(0.569735\pi\) | |||||||
\(660\) | 144.445 | + | 214.999i | 0.218855 | + | 0.325756i | ||||
\(661\) | 866.938 | 1.31156 | 0.655778 | − | 0.754954i | \(-0.272341\pi\) | ||||
0.655778 | + | 0.754954i | \(0.272341\pi\) | |||||||
\(662\) | 492.023 | + | 597.991i | 0.743237 | + | 0.903309i | ||||
\(663\) | 372.368 | − | 283.056i | 0.561641 | − | 0.426932i | ||||
\(664\) | 222.128 | − | 119.814i | 0.334530 | − | 0.180443i | ||||
\(665\) | − | 540.590i | − | 0.812917i | ||||||
\(666\) | −1534.32 | − | 149.161i | −2.30379 | − | 0.223966i | ||||
\(667\) | 45.9834 | 0.0689406 | ||||||||
\(668\) | −216.724 | − | 322.584i | −0.324437 | − | 0.482910i | ||||
\(669\) | −262.409 | − | 262.409i | −0.392241 | − | 0.392241i | ||||
\(670\) | 16.7066 | − | 171.849i | 0.0249352 | − | 0.256492i | ||||
\(671\) | −154.707 | −0.230562 | ||||||||
\(672\) | 548.742 | + | 1768.68i | 0.816580 | + | 2.63197i | ||||
\(673\) | −599.909 | + | 599.909i | −0.891395 | + | 0.891395i | −0.994654 | − | 0.103259i | \(-0.967073\pi\) |
0.103259 | + | 0.994654i | \(0.467073\pi\) | |||||||
\(674\) | 412.774 | + | 40.1285i | 0.612424 | + | 0.0595378i | ||||
\(675\) | 156.059 | + | 156.059i | 0.231198 | + | 0.231198i | ||||
\(676\) | 112.499 | − | 573.134i | 0.166419 | − | 0.847831i | ||||
\(677\) | 652.310 | − | 652.310i | 0.963530 | − | 0.963530i | −0.0358279 | − | 0.999358i | \(-0.511407\pi\) |
0.999358 | + | 0.0358279i | \(0.0114068\pi\) | |||||||
\(678\) | −983.064 | + | 808.859i | −1.44995 | + | 1.19301i | ||||
\(679\) | 425.502i | 0.626659i | ||||||||
\(680\) | −586.436 | − | 266.237i | −0.862406 | − | 0.391525i | ||||
\(681\) | 2110.81 | 3.09957 | ||||||||
\(682\) | −159.826 | − | 194.248i | −0.234349 | − | 0.284821i | ||||
\(683\) | 20.9689 | + | 20.9689i | 0.0307012 | + | 0.0307012i | 0.722291 | − | 0.691590i | \(-0.243089\pi\) |
−0.691590 | + | 0.722291i | \(0.743089\pi\) | |||||||
\(684\) | −208.807 | + | 1063.78i | −0.305273 | + | 1.55523i | ||||
\(685\) | 140.196 | − | 140.196i | 0.204666 | − | 0.204666i | ||||
\(686\) | −7.16485 | + | 73.6998i | −0.0104444 | + | 0.107434i | ||||
\(687\) | 991.919 | + | 991.919i | 1.44384 | + | 1.44384i | ||||
\(688\) | 237.586 | − | 581.879i | 0.345329 | − | 0.845755i | ||||
\(689\) | 435.980i | 0.632772i | ||||||||
\(690\) | 497.861 | + | 48.4003i | 0.721537 | + | 0.0701454i | ||||
\(691\) | 841.024 | − | 841.024i | 1.21711 | − | 1.21711i | 0.248473 | − | 0.968639i | \(-0.420071\pi\) |
0.968639 | − | 0.248473i | \(-0.0799286\pi\) | |||||||
\(692\) | −208.858 | − | 310.875i | −0.301817 | − | 0.449241i | ||||
\(693\) | − | 575.098i | − | 0.829868i | ||||||
\(694\) | −57.3051 | + | 589.458i | −0.0825722 | + | 0.849364i | ||||
\(695\) | −130.612 | −0.187930 | ||||||||
\(696\) | −108.920 | − | 201.931i | −0.156494 | − | 0.290131i | ||||
\(697\) | −412.223 | + | 313.352i | −0.591425 | + | 0.449572i | ||||
\(698\) | −694.290 | + | 571.258i | −0.994684 | + | 0.818420i | ||||
\(699\) | 1236.41i | 1.76883i | ||||||||
\(700\) | −57.8974 | − | 86.1777i | −0.0827106 | − | 0.123111i | ||||
\(701\) | − | 276.797i | − | 0.394861i | −0.980317 | − | 0.197430i | \(-0.936740\pi\) | ||
0.980317 | − | 0.197430i | \(-0.0632597\pi\) | |||||||
\(702\) | 818.210 | + | 79.5435i | 1.16554 | + | 0.113310i | ||||
\(703\) | 257.750 | + | 257.750i | 0.366644 | + | 0.366644i | ||||
\(704\) | 30.8797 | + | 149.321i | 0.0438632 | + | 0.212104i | ||||
\(705\) | 1457.16i | 2.06690i | ||||||||
\(706\) | −448.068 | + | 368.667i | −0.634657 | + | 0.522192i | ||||
\(707\) | −350.234 | + | 350.234i | −0.495381 | + | 0.495381i | ||||
\(708\) | 1200.94 | + | 1787.54i | 1.69624 | + | 2.52478i | ||||
\(709\) | 215.669 | − | 215.669i | 0.304188 | − | 0.304188i | −0.538462 | − | 0.842650i | \(-0.680995\pi\) |
0.842650 | + | 0.538462i | \(0.180995\pi\) | |||||||
\(710\) | −94.3471 | − | 114.667i | −0.132883 | − | 0.161502i | ||||
\(711\) | 516.250 | − | 516.250i | 0.726090 | − | 0.726090i | ||||
\(712\) | 335.984 | + | 622.895i | 0.471888 | + | 0.874853i | ||||
\(713\) | −485.789 | −0.681331 | ||||||||
\(714\) | 1033.55 | + | 1674.27i | 1.44755 | + | 2.34492i | ||||
\(715\) | −54.0888 | −0.0756487 | ||||||||
\(716\) | 264.448 | + | 51.9080i | 0.369340 | + | 0.0724972i | ||||
\(717\) | 512.002 | − | 512.002i | 0.714090 | − | 0.714090i | ||||
\(718\) | −26.6835 | + | 21.9550i | −0.0371637 | + | 0.0305781i | ||||
\(719\) | −561.510 | + | 561.510i | −0.780960 | + | 0.780960i | −0.979993 | − | 0.199033i | \(-0.936220\pi\) |
0.199033 | + | 0.979993i | \(0.436220\pi\) | |||||||
\(720\) | −702.587 | − | 1672.26i | −0.975816 | − | 2.32258i | ||||
\(721\) | 1111.34 | − | 1111.34i | 1.54139 | − | 1.54139i | ||||
\(722\) | −359.587 | + | 295.866i | −0.498043 | + | 0.409787i | ||||
\(723\) | 1125.40i | 1.55656i | ||||||||
\(724\) | 89.6063 | − | 60.2009i | 0.123766 | − | 0.0831504i | ||||
\(725\) | 9.09535 | + | 9.09535i | 0.0125453 | + | 0.0125453i | ||||
\(726\) | −128.086 | + | 1317.53i | −0.176427 | + | 1.81478i | ||||
\(727\) | − | 607.980i | − | 0.836287i | −0.908381 | − | 0.418143i | \(-0.862681\pi\) | ||
0.908381 | − | 0.418143i | \(-0.137319\pi\) | |||||||
\(728\) | −370.483 | − | 110.854i | −0.508906 | − | 0.152272i | ||||
\(729\) | − | 2193.50i | − | 3.00891i | ||||||
\(730\) | 173.543 | − | 142.790i | 0.237730 | − | 0.195603i | ||||
\(731\) | 90.1647 | − | 661.682i | 0.123344 | − | 0.905174i | ||||
\(732\) | 1462.79 | + | 287.128i | 1.99834 | + | 0.392252i | ||||
\(733\) | −187.812 | −0.256224 | −0.128112 | − | 0.991760i | \(-0.540892\pi\) | ||||
−0.128112 | + | 0.991760i | \(0.540892\pi\) | |||||||
\(734\) | −1229.01 | − | 119.480i | −1.67439 | − | 0.162779i | ||||
\(735\) | − | 1431.56i | − | 1.94770i | ||||||
\(736\) | 260.570 | + | 137.169i | 0.354035 | + | 0.186371i | ||||
\(737\) | −30.7118 | + | 30.7118i | −0.0416713 | + | 0.0416713i | ||||
\(738\) | −1451.47 | − | 141.107i | −1.96676 | − | 0.191202i | ||||
\(739\) | 462.811i | 0.626266i | 0.949709 | + | 0.313133i | \(0.101379\pi\) | ||||
−0.949709 | + | 0.313133i | \(0.898621\pi\) | |||||||
\(740\) | −598.477 | − | 117.474i | −0.808753 | − | 0.158749i | ||||
\(741\) | −220.258 | − | 220.258i | −0.297244 | − | 0.297244i | ||||
\(742\) | −1825.39 | − | 177.458i | −2.46010 | − | 0.239162i | ||||
\(743\) | 380.548 | − | 380.548i | 0.512177 | − | 0.512177i | −0.403016 | − | 0.915193i | \(-0.632038\pi\) |
0.915193 | + | 0.403016i | \(0.132038\pi\) | |||||||
\(744\) | 1150.68 | + | 2133.29i | 1.54661 | + | 2.86733i | ||||
\(745\) | 11.5530 | + | 11.5530i | 0.0155074 | + | 0.0155074i | ||||
\(746\) | −68.8500 | − | 83.6783i | −0.0922923 | − | 0.112169i | ||||
\(747\) | 755.221 | 1.01101 | ||||||||
\(748\) | 71.3637 | + | 145.446i | 0.0954061 | + | 0.194447i | ||||
\(749\) | 891.762i | 1.19060i | ||||||||
\(750\) | 952.331 | + | 1157.44i | 1.26977 | + | 1.54325i | ||||
\(751\) | 531.659 | − | 531.659i | 0.707935 | − | 0.707935i | −0.258166 | − | 0.966101i | \(-0.583118\pi\) |
0.966101 | + | 0.258166i | \(0.0831181\pi\) | |||||||
\(752\) | −324.267 | + | 794.172i | −0.431206 | + | 1.05608i | ||||
\(753\) | −1403.45 | − | 1403.45i | −1.86381 | − | 1.86381i | ||||
\(754\) | 47.6866 | + | 4.63593i | 0.0632448 | + | 0.00614845i | ||||
\(755\) | −185.631 | + | 185.631i | −0.245869 | + | 0.245869i | ||||
\(756\) | −666.077 | + | 3393.36i | −0.881055 | + | 4.48858i | ||||
\(757\) | −386.655 | −0.510773 | −0.255386 | − | 0.966839i | \(-0.582203\pi\) | ||||
−0.255386 | + | 0.966839i | \(0.582203\pi\) | |||||||
\(758\) | 96.6042 | + | 9.39153i | 0.127446 | + | 0.0123899i | ||||
\(759\) | −88.9744 | − | 88.9744i | −0.117226 | − | 0.117226i | ||||
\(760\) | −122.948 | + | 410.902i | −0.161774 | + | 0.540661i | ||||
\(761\) | −1437.86 | −1.88943 | −0.944717 | − | 0.327886i | \(-0.893664\pi\) | ||||
−0.944717 | + | 0.327886i | \(0.893664\pi\) | |||||||
\(762\) | −2141.74 | − | 208.212i | −2.81068 | − | 0.273245i | ||||
\(763\) | 1566.92i | 2.05363i | ||||||||
\(764\) | −545.501 | − | 107.075i | −0.714007 | − | 0.140151i | ||||
\(765\) | −1166.28 | − | 1534.27i | −1.52454 | − | 2.00558i | ||||
\(766\) | −111.696 | + | 91.9031i | −0.145818 | + | 0.119978i | ||||
\(767\) | −449.705 | −0.586316 | ||||||||
\(768\) | −14.8419 | − | 1469.17i | −0.0193254 | − | 1.91299i | ||||
\(769\) | −1151.55 | −1.49746 | −0.748731 | − | 0.662874i | \(-0.769336\pi\) | ||||
−0.748731 | + | 0.662874i | \(0.769336\pi\) | |||||||
\(770\) | 22.0159 | − | 226.463i | 0.0285921 | − | 0.294108i | ||||
\(771\) | −1816.08 | + | 1816.08i | −2.35548 | + | 2.35548i | ||||
\(772\) | −259.849 | − | 386.774i | −0.336592 | − | 0.501002i | ||||
\(773\) | −100.104 | −0.129501 | −0.0647504 | − | 0.997901i | \(-0.520625\pi\) | ||||
−0.0647504 | + | 0.997901i | \(0.520625\pi\) | |||||||
\(774\) | 1452.34 | − | 1194.97i | 1.87640 | − | 1.54389i | ||||
\(775\) | −96.0873 | − | 96.0873i | −0.123984 | − | 0.123984i | ||||
\(776\) | 96.7730 | − | 323.423i | 0.124707 | − | 0.416783i | ||||
\(777\) | 1317.54 | + | 1317.54i | 1.69567 | + | 1.69567i | ||||
\(778\) | 775.155 | − | 637.793i | 0.996343 | − | 0.819786i | ||||
\(779\) | 243.832 | + | 243.832i | 0.313007 | + | 0.313007i | ||||
\(780\) | 511.422 | + | 100.386i | 0.655669 | + | 0.128700i | ||||
\(781\) | 37.3535i | 0.0478278i | ||||||||
\(782\) | 304.466 | + | 72.0419i | 0.389343 | + | 0.0921252i | ||||
\(783\) | − | 428.441i | − | 0.547178i | ||||||
\(784\) | 318.569 | − | 780.217i | 0.406338 | − | 0.995175i | ||||
\(785\) | −834.822 | − | 834.822i | −1.06347 | − | 1.06347i | ||||
\(786\) | 348.616 | + | 423.698i | 0.443532 | + | 0.539056i | ||||
\(787\) | 523.093 | + | 523.093i | 0.664667 | + | 0.664667i | 0.956477 | − | 0.291809i | \(-0.0942573\pi\) |
−0.291809 | + | 0.956477i | \(0.594257\pi\) | |||||||
\(788\) | −62.2369 | + | 41.8131i | −0.0789808 | + | 0.0530623i | ||||
\(789\) | −1469.01 | − | 1469.01i | −1.86186 | − | 1.86186i | ||||
\(790\) | 223.053 | − | 183.526i | 0.282345 | − | 0.232312i | ||||
\(791\) | 1118.31 | 1.41379 | ||||||||
\(792\) | −130.796 | + | 437.132i | −0.165147 | + | 0.551934i | ||||
\(793\) | −220.119 | + | 220.119i | −0.277578 | + | 0.277578i | ||||
\(794\) | 450.978 | + | 43.8425i | 0.567982 | + | 0.0552173i | ||||
\(795\) | 2471.72 | 3.10908 | ||||||||
\(796\) | 142.772 | + | 212.509i | 0.179361 | + | 0.266971i | ||||
\(797\) | −502.732 | −0.630780 | −0.315390 | − | 0.948962i | \(-0.602135\pi\) | ||||
−0.315390 | + | 0.948962i | \(0.602135\pi\) | |||||||
\(798\) | 1011.84 | − | 832.539i | 1.26797 | − | 1.04328i | ||||
\(799\) | −123.060 | + | 903.090i | −0.154018 | + | 1.13028i | ||||
\(800\) | 24.4082 | + | 78.6714i | 0.0305102 | + | 0.0983392i | ||||
\(801\) | 2117.80i | 2.64395i | ||||||||
\(802\) | −83.5595 | + | 859.519i | −0.104189 | + | 1.07172i | ||||
\(803\) | −56.5328 | −0.0704020 | ||||||||
\(804\) | 347.386 | − | 233.387i | 0.432073 | − | 0.290283i | ||||
\(805\) | −310.706 | − | 310.706i | −0.385971 | − | 0.385971i | ||||
\(806\) | −503.782 | − | 48.9760i | −0.625040 | − | 0.0607643i | ||||
\(807\) | −623.859 | −0.773059 | ||||||||
\(808\) | 345.867 | − | 186.558i | 0.428054 | − | 0.230889i | ||||
\(809\) | 818.125 | − | 818.125i | 1.01128 | − | 1.01128i | 0.0113442 | − | 0.999936i | \(-0.496389\pi\) |
0.999936 | − | 0.0113442i | \(-0.00361106\pi\) | |||||||
\(810\) | 253.512 | − | 2607.70i | 0.312978 | − | 3.21939i | ||||
\(811\) | −222.437 | − | 222.437i | −0.274275 | − | 0.274275i | 0.556543 | − | 0.830819i | \(-0.312127\pi\) |
−0.830819 | + | 0.556543i | \(0.812127\pi\) | |||||||
\(812\) | −38.8201 | + | 197.771i | −0.0478080 | + | 0.243560i | ||||
\(813\) | −1426.58 | + | 1426.58i | −1.75471 | + | 1.75471i | ||||
\(814\) | 97.4792 | + | 118.473i | 0.119753 | + | 0.145545i | ||||
\(815\) | − | 158.838i | − | 0.194894i | ||||||
\(816\) | −404.819 | − | 1507.68i | −0.496102 | − | 1.84764i | ||||
\(817\) | −444.721 | −0.544335 | ||||||||
\(818\) | 869.398 | − | 715.336i | 1.06283 | − | 0.874493i | ||||
\(819\) | −818.258 | − | 818.258i | −0.999094 | − | 0.999094i | ||||
\(820\) | −566.160 | − | 111.131i | −0.690439 | − | 0.135525i | ||||
\(821\) | 745.434 | − | 745.434i | 0.907959 | − | 0.907959i | −0.0881483 | − | 0.996107i | \(-0.528095\pi\) |
0.996107 | + | 0.0881483i | \(0.0280949\pi\) | |||||||
\(822\) | 478.320 | + | 46.5006i | 0.581898 | + | 0.0565701i | ||||
\(823\) | 833.870 | + | 833.870i | 1.01321 | + | 1.01321i | 0.999912 | + | 0.0132956i | \(0.00423225\pi\) |
0.0132956 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(824\) | −1097.49 | + | 591.975i | −1.33190 | + | 0.718416i | ||||
\(825\) | − | 35.1976i | − | 0.0426638i | ||||||
\(826\) | 183.045 | − | 1882.86i | 0.221604 | − | 2.27949i | ||||
\(827\) | −277.526 | + | 277.526i | −0.335582 | + | 0.335582i | −0.854702 | − | 0.519120i | \(-0.826260\pi\) |
0.519120 | + | 0.854702i | \(0.326260\pi\) | |||||||
\(828\) | 491.398 | + | 731.423i | 0.593476 | + | 0.883361i | ||||
\(829\) | 1201.51i | 1.44934i | 0.689095 | + | 0.724671i | \(0.258008\pi\) | ||||
−0.689095 | + | 0.724671i | \(0.741992\pi\) | |||||||
\(830\) | 297.392 | + | 28.9114i | 0.358303 | + | 0.0348330i | ||||
\(831\) | 1165.25 | 1.40223 | ||||||||
\(832\) | 256.392 | + | 168.520i | 0.308164 | + | 0.202548i | ||||
\(833\) | 120.898 | − | 887.221i | 0.145136 | − | 1.06509i | ||||
\(834\) | −201.149 | − | 244.471i | −0.241186 | − | 0.293130i | ||||
\(835\) | − | 460.094i | − | 0.551010i | ||||||
\(836\) | 89.5568 | − | 60.1676i | 0.107125 | − | 0.0719709i | ||||
\(837\) | 4526.24i | 5.40769i | ||||||||
\(838\) | −90.0930 | + | 926.725i | −0.107510 | + | 1.10588i | ||||
\(839\) | −652.995 | − | 652.995i | −0.778302 | − | 0.778302i | 0.201240 | − | 0.979542i | \(-0.435503\pi\) |
−0.979542 | + | 0.201240i | \(0.935503\pi\) | |||||||
\(840\) | −628.470 | + | 2100.40i | −0.748178 | + | 2.50047i | ||||
\(841\) | 816.030i | 0.970309i | ||||||||
\(842\) | −642.020 | − | 780.293i | −0.762494 | − | 0.926713i | ||||
\(843\) | 411.796 | − | 411.796i | 0.488489 | − | 0.488489i | ||||
\(844\) | −518.628 | − | 771.955i | −0.614489 | − | 0.914638i | ||||
\(845\) | 488.951 | − | 488.951i | 0.578640 | − | 0.578640i | ||||
\(846\) | −1982.21 | + | 1630.95i | −2.34304 | + | 1.92784i | ||||
\(847\) | 822.250 | − | 822.250i | 0.970779 | − | 0.970779i | ||||
\(848\) | 1347.12 | + | 550.040i | 1.58858 | + | 0.648632i | ||||
\(849\) | 1206.24 | 1.42078 | ||||||||
\(850\) | 45.9727 | + | 74.4720i | 0.0540855 | + | 0.0876141i | ||||
\(851\) | 296.286 | 0.348162 | ||||||||
\(852\) | 69.3263 | − | 353.186i | 0.0813689 | − | 0.414538i | ||||
\(853\) | 771.856 | − | 771.856i | 0.904872 | − | 0.904872i | −0.0909806 | − | 0.995853i | \(-0.529000\pi\) |
0.995853 | + | 0.0909806i | \(0.0290001\pi\) | |||||||
\(854\) | −832.015 | − | 1011.21i | −0.974256 | − | 1.18408i | ||||
\(855\) | −907.528 | + | 907.528i | −1.06144 | + | 1.06144i | ||||
\(856\) | 202.816 | − | 677.828i | 0.236935 | − | 0.791855i | ||||
\(857\) | 129.612 | − | 129.612i | 0.151240 | − | 0.151240i | −0.627432 | − | 0.778671i | \(-0.715894\pi\) |
0.778671 | + | 0.627432i | \(0.215894\pi\) | |||||||
\(858\) | −83.2998 | − | 101.240i | −0.0970860 | − | 0.117995i | ||||
\(859\) | − | 1317.39i | − | 1.53363i | −0.641869 | − | 0.766815i | \(-0.721841\pi\) | ||
0.641869 | − | 0.766815i | \(-0.278159\pi\) | |||||||
\(860\) | 617.649 | − | 414.960i | 0.718197 | − | 0.482512i | ||||
\(861\) | 1246.39 | + | 1246.39i | 1.44761 | + | 1.44761i | ||||
\(862\) | 230.257 | + | 22.3848i | 0.267120 | + | 0.0259685i | ||||
\(863\) | 1683.02i | 1.95019i | 0.221779 | + | 0.975097i | \(0.428814\pi\) | ||||
−0.221779 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(864\) | 1278.05 | − | 2427.80i | 1.47922 | − | 2.80996i | ||||
\(865\) | − | 443.393i | − | 0.512594i | ||||||
\(866\) | −406.689 | − | 494.278i | −0.469617 | − | 0.570759i | ||||
\(867\) | −816.269 | − | 1443.89i | −0.941487 | − | 1.66538i | ||||
\(868\) | 410.113 | − | 2089.34i | 0.472480 | − | 2.40707i | ||||
\(869\) | −72.6611 | −0.0836146 | ||||||||
\(870\) | 26.2827 | − | 270.352i | 0.0302100 | − | 0.310749i | ||||
\(871\) | 87.3944i | 0.100338i | ||||||||
\(872\) | 356.368 | − | 1191.01i | 0.408679 | − | 1.36584i | ||||
\(873\) | 714.321 | − | 714.321i | 0.818237 | − | 0.818237i | ||||
\(874\) | 20.1609 | − | 207.381i | 0.0230674 | − | 0.237279i | ||||
\(875\) | − | 1316.67i | − | 1.50476i | ||||||
\(876\) | 534.531 | + | 104.922i | 0.610195 | + | 0.119774i | ||||
\(877\) | −742.665 | − | 742.665i | −0.846824 | − | 0.846824i | 0.142911 | − | 0.989736i | \(-0.454354\pi\) |
−0.989736 | + | 0.142911i | \(0.954354\pi\) | |||||||
\(878\) | 64.8083 | − | 666.638i | 0.0738135 | − | 0.759269i | ||||
\(879\) | 335.533 | − | 335.533i | 0.381721 | − | 0.381721i | ||||
\(880\) | −68.2394 | + | 167.127i | −0.0775448 | + | 0.189917i | ||||
\(881\) | −653.470 | − | 653.470i | −0.741737 | − | 0.741737i | 0.231175 | − | 0.972912i | \(-0.425743\pi\) |
−0.972912 | + | 0.231175i | \(0.925743\pi\) | |||||||
\(882\) | 1947.38 | − | 1602.29i | 2.20791 | − | 1.81666i | ||||
\(883\) | −1133.04 | −1.28317 | −0.641583 | − | 0.767054i | \(-0.721722\pi\) | ||||
−0.641583 | + | 0.767054i | \(0.721722\pi\) | |||||||
\(884\) | 308.481 | + | 105.406i | 0.348960 | + | 0.119237i | ||||
\(885\) | 2549.53i | 2.88083i | ||||||||
\(886\) | −845.008 | + | 695.268i | −0.953734 | + | 0.784727i | ||||
\(887\) | 80.3118 | − | 80.3118i | 0.0905431 | − | 0.0905431i | −0.660385 | − | 0.750928i | \(-0.729607\pi\) |
0.750928 | + | 0.660385i | \(0.229607\pi\) | |||||||
\(888\) | −701.807 | − | 1301.11i | −0.790324 | − | 1.46521i | ||||
\(889\) | 1336.62 | + | 1336.62i | 1.50351 | + | 1.50351i | ||||
\(890\) | −81.0739 | + | 833.952i | −0.0910943 | + | 0.937024i | ||||
\(891\) | −466.031 | + | 466.031i | −0.523043 | + | 0.523043i | ||||
\(892\) | 49.8177 | − | 253.799i | 0.0558494 | − | 0.284527i | ||||
\(893\) | 606.974 | 0.679702 | ||||||||
\(894\) | −3.83195 | + | 39.4166i | −0.00428630 | + | 0.0440902i | ||||
\(895\) | 225.605 | + | 225.605i | 0.252073 | + | 0.252073i | ||||
\(896\) | −809.932 | + | 1004.89i | −0.903942 | + | 1.12153i | ||||
\(897\) | −253.188 | −0.282261 | ||||||||
\(898\) | 21.2133 | − | 218.206i | 0.0236228 | − | 0.242991i | ||||
\(899\) | 263.796i | 0.293433i | ||||||||
\(900\) | −47.4761 | + | 241.869i | −0.0527513 | + | 0.268744i | ||||
\(901\) | 1531.87 | + | 208.742i | 1.70019 | + | 0.231678i | ||||
\(902\) | 92.2154 | + | 112.076i | 0.102234 | + | 0.124253i | ||||
\(903\) | −2273.27 | −2.51747 | ||||||||
\(904\) | −850.025 | − | 254.340i | −0.940294 | − | 0.281350i | ||||
\(905\) | 127.803 | 0.141219 | ||||||||
\(906\) | −633.335 | − | 61.5707i | −0.699046 | − | 0.0679588i | ||||
\(907\) | 970.143 | − | 970.143i | 1.06962 | − | 1.06962i | 0.0722295 | − | 0.997388i | \(-0.476989\pi\) |
0.997388 | − | 0.0722295i | \(-0.0230114\pi\) | |||||||
\(908\) | 820.407 | + | 1221.14i | 0.903532 | + | 1.34487i | ||||
\(909\) | 1175.93 | 1.29365 | ||||||||
\(910\) | −290.890 | − | 353.539i | −0.319660 | − | 0.388505i | ||||
\(911\) | 258.283 | + | 258.283i | 0.283516 | + | 0.283516i | 0.834509 | − | 0.550994i | \(-0.185751\pi\) |
−0.550994 | + | 0.834509i | \(0.685751\pi\) | |||||||
\(912\) | −958.448 | + | 402.686i | −1.05093 | + | 0.441541i | ||||
\(913\) | −53.1479 | − | 53.1479i | −0.0582124 | − | 0.0582124i | ||||
\(914\) | 198.610 | + | 241.384i | 0.217297 | + | 0.264097i | ||||
\(915\) | 1247.93 | + | 1247.93i | 1.36386 | + | 1.36386i | ||||
\(916\) | −188.313 | + | 959.370i | −0.205582 | + | 1.04735i | ||||
\(917\) | − | 481.988i | − | 0.525614i | ||||||
\(918\) | 671.235 | − | 2836.80i | 0.731193 | − | 3.09020i | ||||
\(919\) | 1752.37i | 1.90683i | 0.301669 | + | 0.953413i | \(0.402456\pi\) | ||||
−0.301669 | + | 0.953413i | \(0.597544\pi\) | |||||||
\(920\) | 165.503 | + | 306.832i | 0.179894 | + | 0.333514i | ||||
\(921\) | 884.215 | + | 884.215i | 0.960060 | + | 0.960060i | ||||
\(922\) | 499.843 | − | 411.268i | 0.542129 | − | 0.446060i | ||||
\(923\) | 53.1472 | + | 53.1472i | 0.0575809 | + | 0.0575809i | ||||
\(924\) | 457.785 | − | 307.557i | 0.495439 | − | 0.332854i | ||||
\(925\) | 58.6043 | + | 58.6043i | 0.0633560 | + | 0.0633560i | ||||
\(926\) | 136.427 | + | 165.809i | 0.147329 | + | 0.179059i | ||||
\(927\) | −3731.38 | −4.02523 | ||||||||
\(928\) | 74.4867 | − | 141.496i | 0.0802658 | − | 0.152475i | ||||
\(929\) | 874.077 | − | 874.077i | 0.940880 | − | 0.940880i | −0.0574676 | − | 0.998347i | \(-0.518303\pi\) |
0.998347 | + | 0.0574676i | \(0.0183026\pi\) | |||||||
\(930\) | −277.662 | + | 2856.12i | −0.298561 | + | 3.07109i | ||||
\(931\) | −596.308 | −0.640503 | ||||||||
\(932\) | −715.283 | + | 480.554i | −0.767472 | + | 0.515616i | ||||
\(933\) | −2937.01 | −3.14792 | ||||||||
\(934\) | −410.398 | − | 498.785i | −0.439398 | − | 0.534031i | ||||
\(935\) | −25.8971 | + | 190.048i | −0.0276974 | + | 0.203260i | ||||
\(936\) | 435.859 | + | 808.056i | 0.465661 | + | 0.863308i | ||||
\(937\) | 617.566i | 0.659089i | 0.944140 | + | 0.329545i | \(0.106895\pi\) | ||||
−0.944140 | + | 0.329545i | \(0.893105\pi\) | |||||||
\(938\) | −365.909 | − | 35.5724i | −0.390095 | − | 0.0379237i | ||||
\(939\) | 1540.63 | 1.64072 | ||||||||
\(940\) | −842.993 | + | 566.354i | −0.896801 | + | 0.602505i | ||||
\(941\) | −810.618 | − | 810.618i | −0.861443 | − | 0.861443i | 0.130063 | − | 0.991506i | \(-0.458482\pi\) |
−0.991506 | + | 0.130063i | \(0.958482\pi\) | |||||||
\(942\) | 276.896 | − | 2848.24i | 0.293945 | − | 3.02361i | ||||
\(943\) | 280.287 | 0.297229 | ||||||||
\(944\) | −567.356 | + | 1389.53i | −0.601012 | + | 1.47196i | ||||
\(945\) | −2894.94 | + | 2894.94i | −3.06343 | + | 3.06343i | ||||
\(946\) | −186.302 | − | 18.1116i | −0.196936 | − | 0.0191455i | ||||
\(947\) | −1016.09 | − | 1016.09i | −1.07296 | − | 1.07296i | −0.997120 | − | 0.0758381i | \(-0.975837\pi\) |
−0.0758381 | − | 0.997120i | \(-0.524163\pi\) | |||||||
\(948\) | 687.027 | + | 134.855i | 0.724712 | + | 0.142252i | ||||
\(949\) | −80.4358 | + | 80.4358i | −0.0847584 | + | 0.0847584i | ||||
\(950\) | 45.0070 | − | 37.0315i | 0.0473758 | − | 0.0389806i | ||||
\(951\) | − | 1015.76i | − | 1.06809i | ||||||
\(952\) | −566.883 | + | 1248.67i | −0.595465 | + | 1.31162i | ||||
\(953\) | 1007.10 | 1.05677 | 0.528384 | − | 0.849006i | \(-0.322798\pi\) | ||||
0.528384 | + | 0.849006i | \(0.322798\pi\) | |||||||
\(954\) | 2766.51 | + | 3362.33i | 2.89990 | + | 3.52446i | ||||
\(955\) | −465.377 | − | 465.377i | −0.487306 | − | 0.487306i | ||||
\(956\) | 495.201 | + | 97.2022i | 0.517993 | + | 0.101676i | ||||
\(957\) | −48.3155 | + | 48.3155i | −0.0504864 | + | 0.0504864i | ||||
\(958\) | −80.0927 | + | 823.858i | −0.0836040 | + | 0.859977i | ||||
\(959\) | −298.511 | − | 298.511i | −0.311273 | − | 0.311273i | ||||
\(960\) | 955.399 | − | 1453.58i | 0.995207 | − | 1.51414i | ||||
\(961\) | − | 1825.86i | − | 1.89996i | ||||||
\(962\) | 307.261 | + | 29.8708i | 0.319398 | + | 0.0310507i | ||||
\(963\) | 1497.07 | − | 1497.07i | 1.55459 | − | 1.55459i | ||||
\(964\) | −651.060 | + | 437.407i | −0.675373 | + | 0.453741i | ||||
\(965\) | − | 551.646i | − | 0.571654i | ||||||
\(966\) | 103.056 | − | 1060.07i | 0.106683 | − | 1.09738i | ||||
\(967\) | −1356.69 | −1.40299 | −0.701496 | − | 0.712674i | \(-0.747484\pi\) | ||||
−0.701496 | + | 0.712674i | \(0.747484\pi\) | |||||||
\(968\) | −811.998 | + | 437.985i | −0.838841 | + | 0.452464i | ||||
\(969\) | −879.361 | + | 668.447i | −0.907493 | + | 0.689832i | ||||
\(970\) | 308.632 | − | 253.940i | 0.318177 | − | 0.261794i | ||||
\(971\) | − | 274.508i | − | 0.282707i | −0.989959 | − | 0.141353i | \(-0.954855\pi\) | ||
0.989959 | − | 0.141353i | \(-0.0451454\pi\) | |||||||
\(972\) | 2709.28 | − | 1820.20i | 2.78732 | − | 1.87263i | ||||
\(973\) | 278.104i | 0.285821i | ||||||||
\(974\) | 1126.00 | + | 109.466i | 1.15606 | + | 0.112388i | ||||
\(975\) | −50.0797 | − | 50.0797i | −0.0513638 | − | 0.0513638i | ||||
\(976\) | 402.432 | + | 957.845i | 0.412328 | + | 0.981398i | ||||
\(977\) | 1035.39i | 1.05976i | 0.848072 | + | 0.529882i | \(0.177764\pi\) | ||||
−0.848072 | + | 0.529882i | \(0.822236\pi\) | |||||||
\(978\) | 297.304 | − | 244.620i | 0.303992 | − | 0.250123i | ||||
\(979\) | 149.038 | − | 149.038i | 0.152235 | − | 0.152235i | ||||
\(980\) | 828.180 | − | 556.403i | 0.845082 | − | 0.567758i | ||||
\(981\) | 2630.50 | − | 2630.50i | 2.68145 | − | 2.68145i | ||||
\(982\) | 355.200 | + | 431.700i | 0.361711 | + | 0.439613i | ||||
\(983\) | 92.8187 | − | 92.8187i | 0.0944239 | − | 0.0944239i | −0.658317 | − | 0.752741i | \(-0.728731\pi\) |
0.752741 | + | 0.658317i | \(0.228731\pi\) | |||||||
\(984\) | −663.911 | − | 1230.85i | −0.674706 | − | 1.25086i | ||||
\(985\) | −88.7670 | −0.0901187 | ||||||||
\(986\) | 39.1207 | − | 165.333i | 0.0396762 | − | 0.167681i | ||||
\(987\) | 3102.65 | 3.14352 | ||||||||
\(988\) | 41.8153 | − | 213.030i | 0.0423232 | − | 0.215618i | ||||
\(989\) | −255.606 | + | 255.606i | −0.258448 | + | 0.258448i | ||||
\(990\) | −417.140 | + | 343.220i | −0.421353 | + | 0.346687i | ||||
\(991\) | −85.6124 | + | 85.6124i | −0.0863899 | + | 0.0863899i | −0.748981 | − | 0.662591i | \(-0.769457\pi\) |
0.662591 | + | 0.748981i | \(0.269457\pi\) | |||||||
\(992\) | −786.910 | + | 1494.83i | −0.793256 | + | 1.50689i | ||||
\(993\) | −1571.34 | + | 1571.34i | −1.58242 | + | 1.58242i | ||||
\(994\) | −244.153 | + | 200.888i | −0.245627 | + | 0.202100i | ||||
\(995\) | 303.097i | 0.304620i | ||||||||
\(996\) | 403.886 | + | 601.165i | 0.405508 | + | 0.603580i | ||||
\(997\) | 1012.05 | + | 1012.05i | 1.01510 | + | 1.01510i | 0.999884 | + | 0.0152111i | \(0.00484204\pi\) |
0.0152111 | + | 0.999884i | \(0.495158\pi\) | |||||||
\(998\) | −43.4302 | + | 446.737i | −0.0435172 | + | 0.447632i | ||||
\(999\) | − | 2760.58i | − | 2.76335i |
(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 | 136.3.j.b.115.9 | ✓ | 64 | |
4.3 | odd | 2 | 544.3.n.b.47.31 | 64 | |||
8.3 | odd | 2 | inner | 136.3.j.b.115.24 | yes | 64 | |
8.5 | even | 2 | 544.3.n.b.47.32 | 64 | |||
17.4 | even | 4 | inner | 136.3.j.b.123.24 | yes | 64 | |
68.55 | odd | 4 | 544.3.n.b.463.32 | 64 | |||
136.21 | even | 4 | 544.3.n.b.463.31 | 64 | |||
136.123 | odd | 4 | inner | 136.3.j.b.123.9 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.3.j.b.115.9 | ✓ | 64 | 1.1 | even | 1 | trivial | |
136.3.j.b.115.24 | yes | 64 | 8.3 | odd | 2 | inner | |
136.3.j.b.123.9 | yes | 64 | 136.123 | odd | 4 | inner | |
136.3.j.b.123.24 | yes | 64 | 17.4 | even | 4 | inner | |
544.3.n.b.47.31 | 64 | 4.3 | odd | 2 | |||
544.3.n.b.47.32 | 64 | 8.5 | even | 2 | |||
544.3.n.b.463.31 | 64 | 136.21 | even | 4 | |||
544.3.n.b.463.32 | 64 | 68.55 | odd | 4 |