Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(32,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.o (of order \(12\), degree \(4\), 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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.17 | ||
Character | \(\chi\) | \(=\) | 143.32 |
Dual form | 143.4.o.a.76.17 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15192 | + | 0.308657i | −0.407266 | + | 0.109127i | −0.456635 | − | 0.889654i | \(-0.650946\pi\) |
0.0493690 | + | 0.998781i | \(0.484279\pi\) | |||||||
\(3\) | −3.89437 | + | 6.74525i | −0.749472 | + | 1.29812i | 0.198604 | + | 0.980080i | \(0.436359\pi\) |
−0.948076 | + | 0.318044i | \(0.896974\pi\) | |||||||
\(4\) | −5.69654 | + | 3.28890i | −0.712068 | + | 0.411113i | ||||
\(5\) | 12.2876 | − | 12.2876i | 1.09904 | − | 1.09904i | 0.104511 | − | 0.994524i | \(-0.466672\pi\) |
0.994524 | − | 0.104511i | \(-0.0333279\pi\) | |||||||
\(6\) | 2.40405 | − | 8.97204i | 0.163575 | − | 0.610470i | ||||
\(7\) | 32.4067 | + | 8.68335i | 1.74980 | + | 0.468857i | 0.984583 | − | 0.174918i | \(-0.0559662\pi\) |
0.765215 | + | 0.643775i | \(0.222633\pi\) | |||||||
\(8\) | 12.2930 | − | 12.2930i | 0.543278 | − | 0.543278i | ||||
\(9\) | −16.8323 | − | 29.1543i | −0.623417 | − | 1.07979i | ||||
\(10\) | −10.3617 | + | 17.9470i | −0.327666 | + | 0.567534i | ||||
\(11\) | 35.8108 | − | 6.97037i | 0.981579 | − | 0.191059i | ||||
\(12\) | − | 51.2328i | − | 1.23247i | ||||||
\(13\) | −45.6796 | + | 10.5059i | −0.974557 | + | 0.224140i | ||||
\(14\) | −40.0102 | −0.763799 | ||||||||
\(15\) | 35.0304 | + | 130.735i | 0.602987 | + | 2.25038i | ||||
\(16\) | 15.9450 | − | 27.6175i | 0.249140 | − | 0.431523i | ||||
\(17\) | 57.2173 | + | 99.1033i | 0.816308 | + | 1.41389i | 0.908385 | + | 0.418136i | \(0.137316\pi\) |
−0.0920763 | + | 0.995752i | \(0.529350\pi\) | |||||||
\(18\) | 28.3882 | + | 28.3882i | 0.371731 | + | 0.371731i | ||||
\(19\) | 8.10390 | − | 30.2442i | 0.0978506 | − | 0.365184i | −0.899586 | − | 0.436744i | \(-0.856131\pi\) |
0.997436 | + | 0.0715610i | \(0.0227980\pi\) | |||||||
\(20\) | −29.5841 | + | 110.409i | −0.330761 | + | 1.23442i | ||||
\(21\) | −184.775 | + | 184.775i | −1.92006 | + | 1.92006i | ||||
\(22\) | −39.0999 | + | 19.0826i | −0.378914 | + | 0.184928i | ||||
\(23\) | −44.1676 | − | 25.5002i | −0.400416 | − | 0.231180i | 0.286247 | − | 0.958156i | \(-0.407592\pi\) |
−0.686664 | + | 0.726975i | \(0.740925\pi\) | |||||||
\(24\) | 35.0458 | + | 130.793i | 0.298070 | + | 1.11241i | ||||
\(25\) | − | 176.970i | − | 1.41576i | ||||||
\(26\) | 49.3767 | − | 26.2014i | 0.372445 | − | 0.197635i | ||||
\(27\) | 51.9082 | 0.369991 | ||||||||
\(28\) | −213.165 | + | 57.1174i | −1.43873 | + | 0.385506i | ||||
\(29\) | 136.585 | + | 78.8575i | 0.874594 | + | 0.504947i | 0.868872 | − | 0.495036i | \(-0.164845\pi\) |
0.00572198 | + | 0.999984i | \(0.498179\pi\) | |||||||
\(30\) | −80.7047 | − | 139.785i | −0.491153 | − | 0.850702i | ||||
\(31\) | 29.9915 | − | 29.9915i | 0.173763 | − | 0.173763i | −0.614868 | − | 0.788630i | \(-0.710791\pi\) |
0.788630 | + | 0.614868i | \(0.210791\pi\) | |||||||
\(32\) | −45.8394 | + | 171.075i | −0.253229 | + | 0.945064i | ||||
\(33\) | −92.4437 | + | 268.698i | −0.487648 | + | 1.41740i | ||||
\(34\) | −96.4989 | − | 96.4989i | −0.486748 | − | 0.486748i | ||||
\(35\) | 504.898 | − | 291.503i | 2.43838 | − | 1.40780i | ||||
\(36\) | 191.771 | + | 110.719i | 0.887831 | + | 0.512589i | ||||
\(37\) | −75.7423 | + | 20.2951i | −0.336539 | + | 0.0901755i | −0.423131 | − | 0.906068i | \(-0.639069\pi\) |
0.0865918 | + | 0.996244i | \(0.472402\pi\) | |||||||
\(38\) | 37.3403i | 0.159405i | ||||||||
\(39\) | 107.028 | − | 349.034i | 0.439441 | − | 1.43308i | ||||
\(40\) | − | 302.102i | − | 1.19416i | ||||||
\(41\) | 210.469 | − | 56.3950i | 0.801701 | − | 0.214815i | 0.165370 | − | 0.986232i | \(-0.447118\pi\) |
0.636331 | + | 0.771416i | \(0.280451\pi\) | |||||||
\(42\) | 155.815 | − | 269.879i | 0.572446 | − | 0.991505i | ||||
\(43\) | 128.947 | + | 223.342i | 0.457307 | + | 0.792079i | 0.998818 | − | 0.0486148i | \(-0.0154807\pi\) |
−0.541510 | + | 0.840694i | \(0.682147\pi\) | |||||||
\(44\) | −181.073 | + | 157.485i | −0.620404 | + | 0.539586i | ||||
\(45\) | −565.064 | − | 151.408i | −1.87188 | − | 0.501570i | ||||
\(46\) | 58.7485 | + | 15.7416i | 0.188304 | + | 0.0504559i | ||||
\(47\) | 106.213 | + | 106.213i | 0.329635 | + | 0.329635i | 0.852447 | − | 0.522813i | \(-0.175117\pi\) |
−0.522813 | + | 0.852447i | \(0.675117\pi\) | |||||||
\(48\) | 124.191 | + | 215.106i | 0.373447 | + | 0.646829i | ||||
\(49\) | 677.747 | + | 391.297i | 1.97594 | + | 1.14081i | ||||
\(50\) | 54.6229 | + | 203.855i | 0.154497 | + | 0.576590i | ||||
\(51\) | −891.302 | −2.44720 | ||||||||
\(52\) | 225.663 | − | 210.083i | 0.601804 | − | 0.560256i | ||||
\(53\) | −724.401 | −1.87744 | −0.938718 | − | 0.344687i | \(-0.887985\pi\) | ||||
−0.938718 | + | 0.344687i | \(0.887985\pi\) | |||||||
\(54\) | −59.7943 | + | 16.0218i | −0.150685 | + | 0.0403759i | ||||
\(55\) | 354.379 | − | 525.677i | 0.868809 | − | 1.28877i | ||||
\(56\) | 505.119 | − | 291.631i | 1.20535 | − | 0.695907i | ||||
\(57\) | 172.445 | + | 172.445i | 0.400717 | + | 0.400717i | ||||
\(58\) | −181.676 | − | 48.6798i | −0.411296 | − | 0.110206i | ||||
\(59\) | 50.1583 | − | 187.193i | 0.110679 | − | 0.413059i | −0.888249 | − | 0.459363i | \(-0.848078\pi\) |
0.998927 | + | 0.0463042i | \(0.0147444\pi\) | |||||||
\(60\) | −629.528 | − | 629.528i | −1.35453 | − | 1.35453i | ||||
\(61\) | −106.436 | + | 61.4511i | −0.223406 | + | 0.128984i | −0.607527 | − | 0.794299i | \(-0.707838\pi\) |
0.384120 | + | 0.923283i | \(0.374505\pi\) | |||||||
\(62\) | −25.2909 | + | 43.8051i | −0.0518055 | + | 0.0897298i | ||||
\(63\) | −292.321 | − | 1090.96i | −0.584587 | − | 2.18171i | ||||
\(64\) | 43.9057i | 0.0857532i | ||||||||
\(65\) | −432.199 | + | 690.385i | −0.824734 | + | 1.31741i | ||||
\(66\) | 23.5525 | − | 338.053i | 0.0439260 | − | 0.630476i | ||||
\(67\) | 143.932 | + | 537.163i | 0.262450 | + | 0.979477i | 0.963793 | + | 0.266652i | \(0.0859176\pi\) |
−0.701343 | + | 0.712824i | \(0.747416\pi\) | |||||||
\(68\) | −651.882 | − | 376.364i | −1.16253 | − | 0.671189i | ||||
\(69\) | 344.010 | − | 198.614i | 0.600202 | − | 0.346527i | ||||
\(70\) | −491.629 | + | 491.629i | −0.839441 | + | 0.839441i | ||||
\(71\) | −330.104 | − | 88.4511i | −0.551776 | − | 0.147848i | −0.0278508 | − | 0.999612i | \(-0.508866\pi\) |
−0.523926 | + | 0.851764i | \(0.675533\pi\) | |||||||
\(72\) | −565.312 | − | 151.475i | −0.925315 | − | 0.247937i | ||||
\(73\) | −310.252 | + | 310.252i | −0.497428 | + | 0.497428i | −0.910637 | − | 0.413208i | \(-0.864408\pi\) |
0.413208 | + | 0.910637i | \(0.364408\pi\) | |||||||
\(74\) | 80.9851 | − | 46.7568i | 0.127221 | − | 0.0734509i | ||||
\(75\) | 1193.70 | + | 689.185i | 1.83783 | + | 1.06107i | ||||
\(76\) | 53.3059 | + | 198.940i | 0.0804553 | + | 0.300263i | ||||
\(77\) | 1221.04 | + | 85.0710i | 1.80714 | + | 0.125906i | ||||
\(78\) | −15.5563 | + | 435.096i | −0.0225820 | + | 0.631601i | ||||
\(79\) | − | 784.587i | − | 1.11738i | −0.829377 | − | 0.558690i | \(-0.811304\pi\) | ||
0.829377 | − | 0.558690i | \(-0.188696\pi\) | |||||||
\(80\) | −143.427 | − | 535.277i | −0.200446 | − | 0.748073i | ||||
\(81\) | 252.321 | − | 437.033i | 0.346119 | − | 0.599496i | ||||
\(82\) | −225.037 | + | 129.925i | −0.303064 | + | 0.174974i | ||||
\(83\) | 326.241 | + | 326.241i | 0.431441 | + | 0.431441i | 0.889118 | − | 0.457677i | \(-0.151318\pi\) |
−0.457677 | + | 0.889118i | \(0.651318\pi\) | |||||||
\(84\) | 444.873 | − | 1660.29i | 0.577852 | − | 2.15657i | ||||
\(85\) | 1920.80 | + | 514.678i | 2.45106 | + | 0.656760i | ||||
\(86\) | −217.473 | − | 217.473i | −0.272683 | − | 0.272683i | ||||
\(87\) | −1063.83 | + | 614.201i | −1.31097 | + | 0.756888i | ||||
\(88\) | 354.535 | − | 525.908i | 0.429472 | − | 0.637068i | ||||
\(89\) | 285.539 | − | 76.5098i | 0.340079 | − | 0.0911239i | −0.0847377 | − | 0.996403i | \(-0.527005\pi\) |
0.424817 | + | 0.905279i | \(0.360339\pi\) | |||||||
\(90\) | 697.644 | 0.817090 | ||||||||
\(91\) | −1571.55 | − | 56.1887i | −1.81037 | − | 0.0647272i | ||||
\(92\) | 335.470 | 0.380165 | ||||||||
\(93\) | 85.5022 | + | 319.099i | 0.0953352 | + | 0.355796i | ||||
\(94\) | −155.133 | − | 89.5662i | −0.170221 | − | 0.0982771i | ||||
\(95\) | −272.050 | − | 471.205i | −0.293808 | − | 0.508891i | ||||
\(96\) | −975.427 | − | 975.427i | −1.03702 | − | 1.03702i | ||||
\(97\) | 33.1914 | + | 8.89361i | 0.0347431 | + | 0.00930938i | 0.276149 | − | 0.961115i | \(-0.410942\pi\) |
−0.241406 | + | 0.970424i | \(0.577608\pi\) | |||||||
\(98\) | −901.489 | − | 241.553i | −0.929226 | − | 0.248985i | ||||
\(99\) | −805.993 | − | 926.713i | −0.818236 | − | 0.940790i | ||||
\(100\) | 582.035 | + | 1008.11i | 0.582035 | + | 1.00811i | ||||
\(101\) | −365.816 | + | 633.612i | −0.360397 | + | 0.624225i | −0.988026 | − | 0.154287i | \(-0.950692\pi\) |
0.627629 | + | 0.778512i | \(0.284025\pi\) | |||||||
\(102\) | 1026.71 | − | 275.107i | 0.996663 | − | 0.267055i | ||||
\(103\) | − | 953.318i | − | 0.911973i | −0.889987 | − | 0.455987i | \(-0.849286\pi\) | ||
0.889987 | − | 0.455987i | \(-0.150714\pi\) | |||||||
\(104\) | −432.389 | + | 690.687i | −0.407685 | + | 0.651226i | ||||
\(105\) | 4540.88i | 4.22042i | ||||||||
\(106\) | 834.454 | − | 223.591i | 0.764616 | − | 0.204878i | ||||
\(107\) | −20.2988 | − | 11.7195i | −0.0183398 | − | 0.0105885i | 0.490802 | − | 0.871271i | \(-0.336704\pi\) |
−0.509142 | + | 0.860683i | \(0.670037\pi\) | |||||||
\(108\) | −295.698 | + | 170.721i | −0.263459 | + | 0.152108i | ||||
\(109\) | 13.0285 | + | 13.0285i | 0.0114486 | + | 0.0114486i | 0.712808 | − | 0.701359i | \(-0.247423\pi\) |
−0.701359 | + | 0.712808i | \(0.747423\pi\) | |||||||
\(110\) | −245.964 | + | 714.922i | −0.213198 | + | 0.619683i | ||||
\(111\) | 158.073 | − | 589.937i | 0.135168 | − | 0.504454i | ||||
\(112\) | 756.536 | − | 756.536i | 0.638267 | − | 0.638267i | ||||
\(113\) | 106.843 | + | 185.058i | 0.0889464 | + | 0.154060i | 0.907066 | − | 0.420988i | \(-0.138317\pi\) |
−0.818120 | + | 0.575048i | \(0.804983\pi\) | |||||||
\(114\) | −251.870 | − | 145.417i | −0.206928 | − | 0.119470i | ||||
\(115\) | −856.048 | + | 229.377i | −0.694147 | + | 0.185996i | ||||
\(116\) | −1037.42 | −0.830361 | ||||||||
\(117\) | 1075.18 | + | 1154.92i | 0.849580 | + | 0.912584i | ||||
\(118\) | 231.114i | 0.180303i | ||||||||
\(119\) | 993.676 | + | 3708.45i | 0.765463 | + | 2.85675i | ||||
\(120\) | 2037.75 | + | 1176.50i | 1.55017 | + | 0.894992i | ||||
\(121\) | 1233.83 | − | 499.229i | 0.926993 | − | 0.375078i | ||||
\(122\) | 103.639 | − | 103.639i | 0.0769103 | − | 0.0769103i | ||||
\(123\) | −439.246 | + | 1639.29i | −0.321996 | + | 1.20170i | ||||
\(124\) | −72.2089 | + | 269.487i | −0.0522948 | + | 0.195167i | ||||
\(125\) | −638.580 | − | 638.580i | −0.456931 | − | 0.456931i | ||||
\(126\) | 673.462 | + | 1166.47i | 0.476165 | + | 0.824742i | ||||
\(127\) | −40.4032 | + | 69.9805i | −0.0282300 | + | 0.0488958i | −0.879795 | − | 0.475353i | \(-0.842320\pi\) |
0.851565 | + | 0.524249i | \(0.175654\pi\) | |||||||
\(128\) | −380.267 | − | 1419.17i | −0.262587 | − | 0.979988i | ||||
\(129\) | −2008.67 | −1.37096 | ||||||||
\(130\) | 284.768 | − | 928.671i | 0.192122 | − | 0.626537i | ||||
\(131\) | − | 2610.19i | − | 1.74086i | −0.492289 | − | 0.870432i | \(-0.663840\pi\) | ||
0.492289 | − | 0.870432i | \(-0.336160\pi\) | |||||||
\(132\) | −357.112 | − | 1834.69i | −0.235474 | − | 1.20977i | ||||
\(133\) | 525.241 | − | 909.745i | 0.342438 | − | 0.593119i | ||||
\(134\) | −331.598 | − | 574.345i | −0.213774 | − | 0.370268i | ||||
\(135\) | 637.827 | − | 637.827i | 0.406633 | − | 0.406633i | ||||
\(136\) | 1921.65 | + | 514.903i | 1.21162 | + | 0.324651i | ||||
\(137\) | 315.984 | − | 1179.27i | 0.197054 | − | 0.735414i | −0.794672 | − | 0.607039i | \(-0.792357\pi\) |
0.991726 | − | 0.128375i | \(-0.0409762\pi\) | |||||||
\(138\) | −334.969 | + | 334.969i | −0.206627 | + | 0.206627i | ||||
\(139\) | −206.534 | + | 119.243i | −0.126029 | + | 0.0727628i | −0.561689 | − | 0.827348i | \(-0.689848\pi\) |
0.435660 | + | 0.900111i | \(0.356515\pi\) | |||||||
\(140\) | −1917.45 | + | 3321.12i | −1.15753 | + | 2.00490i | ||||
\(141\) | −1130.07 | + | 302.802i | −0.674958 | + | 0.180855i | ||||
\(142\) | 407.555 | 0.240854 | ||||||||
\(143\) | −1562.59 | + | 694.630i | −0.913780 | + | 0.406209i | ||||
\(144\) | −1073.56 | −0.621273 | ||||||||
\(145\) | 2647.27 | − | 709.334i | 1.51616 | − | 0.406255i | ||||
\(146\) | 261.625 | − | 453.148i | 0.148303 | − | 0.256869i | ||||
\(147\) | −5278.80 | + | 3047.72i | −2.96182 | + | 1.71001i | ||||
\(148\) | 364.721 | − | 364.721i | 0.202567 | − | 0.202567i | ||||
\(149\) | −498.770 | + | 1861.43i | −0.274234 | + | 1.02345i | 0.682120 | + | 0.731241i | \(0.261058\pi\) |
−0.956353 | + | 0.292213i | \(0.905608\pi\) | |||||||
\(150\) | −1587.78 | − | 425.444i | −0.864276 | − | 0.231582i | ||||
\(151\) | 1525.17 | − | 1525.17i | 0.821966 | − | 0.821966i | −0.164424 | − | 0.986390i | \(-0.552576\pi\) |
0.986390 | + | 0.164424i | \(0.0525765\pi\) | |||||||
\(152\) | −272.170 | − | 471.412i | −0.145236 | − | 0.251556i | ||||
\(153\) | 1926.19 | − | 3336.27i | 1.01780 | − | 1.76288i | ||||
\(154\) | −1432.80 | + | 278.886i | −0.749728 | + | 0.145930i | ||||
\(155\) | − | 737.047i | − | 0.381942i | ||||||
\(156\) | 538.249 | + | 2340.29i | 0.276246 | + | 1.20111i | ||||
\(157\) | 49.1073 | 0.0249630 | 0.0124815 | − | 0.999922i | \(-0.496027\pi\) | ||||
0.0124815 | + | 0.999922i | \(0.496027\pi\) | |||||||
\(158\) | 242.168 | + | 903.785i | 0.121936 | + | 0.455071i | ||||
\(159\) | 2821.09 | − | 4886.26i | 1.40709 | − | 2.43714i | ||||
\(160\) | 1538.84 | + | 2665.35i | 0.760351 | + | 1.31697i | ||||
\(161\) | −1209.90 | − | 1209.90i | −0.592257 | − | 0.592257i | ||||
\(162\) | −155.761 | + | 581.309i | −0.0755417 | + | 0.281926i | ||||
\(163\) | 901.439 | − | 3364.22i | 0.433167 | − | 1.61660i | −0.312249 | − | 0.950000i | \(-0.601082\pi\) |
0.745416 | − | 0.666600i | \(-0.232251\pi\) | |||||||
\(164\) | −1013.47 | + | 1013.47i | −0.482552 | + | 0.482552i | ||||
\(165\) | 2165.74 | + | 4437.56i | 1.02183 | + | 2.09372i | ||||
\(166\) | −476.502 | − | 275.108i | −0.222793 | − | 0.128630i | ||||
\(167\) | 710.575 | + | 2651.90i | 0.329257 | + | 1.22880i | 0.909963 | + | 0.414690i | \(0.136110\pi\) |
−0.580706 | + | 0.814114i | \(0.697223\pi\) | |||||||
\(168\) | 4542.87i | 2.08625i | ||||||||
\(169\) | 1976.25 | − | 959.815i | 0.899522 | − | 0.436875i | ||||
\(170\) | −2371.48 | −1.06991 | ||||||||
\(171\) | −1018.16 | + | 272.814i | −0.455323 | + | 0.122004i | ||||
\(172\) | −1469.10 | − | 848.187i | −0.651268 | − | 0.376010i | ||||
\(173\) | −899.519 | − | 1558.01i | −0.395313 | − | 0.684702i | 0.597828 | − | 0.801624i | \(-0.296031\pi\) |
−0.993141 | + | 0.116922i | \(0.962697\pi\) | |||||||
\(174\) | 1035.87 | − | 1035.87i | 0.451317 | − | 0.451317i | ||||
\(175\) | 1536.69 | − | 5735.00i | 0.663787 | − | 2.47729i | ||||
\(176\) | 378.498 | − | 1100.15i | 0.162104 | − | 0.471174i | ||||
\(177\) | 1067.33 | + | 1067.33i | 0.453251 | + | 0.453251i | ||||
\(178\) | −305.303 | + | 176.267i | −0.128559 | + | 0.0742234i | ||||
\(179\) | −3362.58 | − | 1941.39i | −1.40408 | − | 0.810648i | −0.409276 | − | 0.912411i | \(-0.634219\pi\) |
−0.994809 | + | 0.101762i | \(0.967552\pi\) | |||||||
\(180\) | 3716.88 | − | 995.935i | 1.53911 | − | 0.412404i | ||||
\(181\) | 2223.00i | 0.912898i | 0.889750 | + | 0.456449i | \(0.150879\pi\) | ||||
−0.889750 | + | 0.456449i | \(0.849121\pi\) | |||||||
\(182\) | 1827.65 | − | 420.345i | 0.744365 | − | 0.171198i | ||||
\(183\) | − | 957.253i | − | 0.386679i | ||||||
\(184\) | −856.424 | + | 229.478i | −0.343133 | + | 0.0919421i | ||||
\(185\) | −681.312 | + | 1180.07i | −0.270763 | + | 0.468975i | ||||
\(186\) | −196.984 | − | 341.186i | −0.0776536 | − | 0.134500i | ||||
\(187\) | 2739.79 | + | 3150.14i | 1.07141 | + | 1.23188i | ||||
\(188\) | −954.375 | − | 255.724i | −0.370239 | − | 0.0992053i | ||||
\(189\) | 1682.18 | + | 450.737i | 0.647409 | + | 0.173473i | ||||
\(190\) | 458.822 | + | 458.822i | 0.175192 | + | 0.175192i | ||||
\(191\) | 1314.47 | + | 2276.74i | 0.497969 | + | 0.862507i | 0.999997 | − | 0.00234388i | \(-0.000746082\pi\) |
−0.502028 | + | 0.864851i | \(0.667413\pi\) | |||||||
\(192\) | −296.155 | − | 170.985i | −0.111318 | − | 0.0642697i | ||||
\(193\) | −673.943 | − | 2515.19i | −0.251355 | − | 0.938069i | −0.970082 | − | 0.242777i | \(-0.921942\pi\) |
0.718727 | − | 0.695292i | \(-0.244725\pi\) | |||||||
\(194\) | −40.9790 | −0.0151656 | ||||||||
\(195\) | −2973.67 | − | 5603.91i | −1.09205 | − | 2.05797i | ||||
\(196\) | −5147.76 | −1.87600 | ||||||||
\(197\) | −1073.76 | + | 287.714i | −0.388337 | + | 0.104055i | −0.447704 | − | 0.894182i | \(-0.647758\pi\) |
0.0593674 | + | 0.998236i | \(0.481092\pi\) | |||||||
\(198\) | 1214.48 | + | 818.727i | 0.435905 | + | 0.293861i | ||||
\(199\) | −308.655 | + | 178.202i | −0.109950 | + | 0.0634794i | −0.553966 | − | 0.832539i | \(-0.686886\pi\) |
0.444017 | + | 0.896018i | \(0.353553\pi\) | |||||||
\(200\) | −2175.48 | − | 2175.48i | −0.769149 | − | 0.769149i | ||||
\(201\) | −4183.83 | − | 1121.05i | −1.46818 | − | 0.393398i | ||||
\(202\) | 225.823 | − | 842.784i | 0.0786578 | − | 0.293555i | ||||
\(203\) | 3741.53 | + | 3741.53i | 1.29361 | + | 1.29361i | ||||
\(204\) | 5077.34 | − | 2931.41i | 1.74257 | − | 1.00608i | ||||
\(205\) | 1893.20 | − | 3279.11i | 0.645008 | − | 1.11719i | ||||
\(206\) | 294.248 | + | 1098.15i | 0.0995206 | + | 0.371416i | ||||
\(207\) | 1716.90i | 0.576487i | ||||||||
\(208\) | −438.211 | + | 1429.07i | −0.146079 | + | 0.476386i | ||||
\(209\) | 79.3941 | − | 1139.56i | 0.0262766 | − | 0.377152i | ||||
\(210\) | −1401.57 | − | 5230.75i | −0.460561 | − | 1.71884i | ||||
\(211\) | −3743.98 | − | 2161.59i | −1.22154 | − | 0.705259i | −0.256298 | − | 0.966598i | \(-0.582503\pi\) |
−0.965247 | + | 0.261339i | \(0.915836\pi\) | |||||||
\(212\) | 4126.58 | − | 2382.48i | 1.33686 | − | 0.771838i | ||||
\(213\) | 1882.17 | − | 1882.17i | 0.605466 | − | 0.605466i | ||||
\(214\) | 27.0000 | + | 7.23463i | 0.00862468 | + | 0.00231098i | ||||
\(215\) | 4328.78 | + | 1159.89i | 1.37312 | + | 0.367926i | ||||
\(216\) | 638.107 | − | 638.107i | 0.201008 | − | 0.201008i | ||||
\(217\) | 1232.35 | − | 711.500i | 0.385519 | − | 0.222580i | ||||
\(218\) | −19.0291 | − | 10.9865i | −0.00591199 | − | 0.00341329i | ||||
\(219\) | −884.491 | − | 3300.96i | −0.272915 | − | 1.01853i | ||||
\(220\) | −289.837 | + | 4160.06i | −0.0888217 | + | 1.27487i | ||||
\(221\) | −3654.84 | − | 3925.88i | −1.11245 | − | 1.19495i | ||||
\(222\) | 728.353i | 0.220198i | ||||||||
\(223\) | −506.903 | − | 1891.79i | −0.152219 | − | 0.568088i | −0.999327 | − | 0.0366682i | \(-0.988326\pi\) |
0.847109 | − | 0.531419i | \(-0.178341\pi\) | |||||||
\(224\) | −2971.01 | + | 5145.93i | −0.886199 | + | 1.53494i | ||||
\(225\) | −5159.43 | + | 2978.80i | −1.52872 | + | 0.882607i | ||||
\(226\) | −180.194 | − | 180.194i | −0.0530369 | − | 0.0530369i | ||||
\(227\) | −32.3987 | + | 120.914i | −0.00947303 | + | 0.0353538i | −0.970501 | − | 0.241099i | \(-0.922492\pi\) |
0.961028 | + | 0.276453i | \(0.0891589\pi\) | |||||||
\(228\) | −1549.49 | − | 415.186i | −0.450078 | − | 0.120598i | ||||
\(229\) | −836.611 | − | 836.611i | −0.241418 | − | 0.241418i | 0.576018 | − | 0.817437i | \(-0.304606\pi\) |
−0.817437 | + | 0.576018i | \(0.804606\pi\) | |||||||
\(230\) | 915.303 | − | 528.450i | 0.262406 | − | 0.151500i | ||||
\(231\) | −5328.99 | + | 7904.90i | −1.51784 | + | 2.25153i | ||||
\(232\) | 2648.43 | − | 709.645i | 0.749474 | − | 0.200821i | ||||
\(233\) | −2243.51 | −0.630804 | −0.315402 | − | 0.948958i | \(-0.602139\pi\) | ||||
−0.315402 | + | 0.948958i | \(0.602139\pi\) | |||||||
\(234\) | −1595.00 | − | 998.515i | −0.445593 | − | 0.278953i | ||||
\(235\) | 2610.21 | 0.724560 | ||||||||
\(236\) | 329.931 | + | 1231.32i | 0.0910029 | + | 0.339628i | ||||
\(237\) | 5292.24 | + | 3055.47i | 1.45050 | + | 0.837445i | ||||
\(238\) | −2289.28 | − | 3965.15i | −0.623495 | − | 1.07993i | ||||
\(239\) | −966.176 | − | 966.176i | −0.261493 | − | 0.261493i | 0.564168 | − | 0.825660i | \(-0.309197\pi\) |
−0.825660 | + | 0.564168i | \(0.809197\pi\) | |||||||
\(240\) | 4169.14 | + | 1117.12i | 1.12132 | + | 0.300457i | ||||
\(241\) | −6404.47 | − | 1716.07i | −1.71182 | − | 0.458680i | −0.735949 | − | 0.677037i | \(-0.763264\pi\) |
−0.975869 | + | 0.218357i | \(0.929930\pi\) | |||||||
\(242\) | −1267.18 | + | 955.903i | −0.336602 | + | 0.253916i | ||||
\(243\) | 2666.03 | + | 4617.69i | 0.703809 | + | 1.21903i | ||||
\(244\) | 404.213 | − | 700.118i | 0.106054 | − | 0.183690i | ||||
\(245\) | 13136.0 | − | 3519.77i | 3.42542 | − | 0.917837i | ||||
\(246\) | − | 2023.91i | − | 0.524552i | ||||||
\(247\) | −52.4392 | + | 1466.68i | −0.0135086 | + | 0.377824i | ||||
\(248\) | − | 737.371i | − | 0.188803i | ||||||
\(249\) | −3471.08 | + | 930.074i | −0.883418 | + | 0.236711i | ||||
\(250\) | 932.697 | + | 538.493i | 0.235956 | + | 0.136229i | ||||
\(251\) | −3005.39 | + | 1735.16i | −0.755770 | + | 0.436344i | −0.827775 | − | 0.561060i | \(-0.810394\pi\) |
0.0720047 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(252\) | 5253.27 | + | 5253.27i | 1.31319 | + | 1.31319i | ||||
\(253\) | −1759.42 | − | 605.317i | −0.437209 | − | 0.150419i | ||||
\(254\) | 24.9415 | − | 93.0829i | 0.00616129 | − | 0.0229943i | ||||
\(255\) | −10952.0 | + | 10952.0i | −2.68956 | + | 2.68956i | ||||
\(256\) | 700.454 | + | 1213.22i | 0.171009 | + | 0.296197i | ||||
\(257\) | −4216.84 | − | 2434.59i | −1.02350 | − | 0.590917i | −0.108383 | − | 0.994109i | \(-0.534567\pi\) |
−0.915115 | + | 0.403192i | \(0.867901\pi\) | |||||||
\(258\) | 2313.83 | − | 619.989i | 0.558344 | − | 0.149608i | ||||
\(259\) | −2630.79 | −0.631155 | ||||||||
\(260\) | 191.435 | − | 5354.27i | 0.0456626 | − | 1.27714i | ||||
\(261\) | − | 5309.40i | − | 1.25917i | ||||||
\(262\) | 805.652 | + | 3006.74i | 0.189975 | + | 0.708995i | ||||
\(263\) | 3216.01 | + | 1856.76i | 0.754020 | + | 0.435334i | 0.827145 | − | 0.561989i | \(-0.189964\pi\) |
−0.0731243 | + | 0.997323i | \(0.523297\pi\) | |||||||
\(264\) | 2166.69 | + | 4439.51i | 0.505116 | + | 1.03497i | ||||
\(265\) | −8901.14 | + | 8901.14i | −2.06337 | + | 2.06337i | ||||
\(266\) | −324.239 | + | 1210.08i | −0.0747382 | + | 0.278927i | ||||
\(267\) | −595.915 | + | 2223.99i | −0.136590 | + | 0.509759i | ||||
\(268\) | −2586.59 | − | 2586.59i | −0.589558 | − | 0.589558i | ||||
\(269\) | −2370.92 | − | 4106.55i | −0.537389 | − | 0.930785i | −0.999044 | − | 0.0437249i | \(-0.986077\pi\) |
0.461655 | − | 0.887060i | \(-0.347256\pi\) | |||||||
\(270\) | −537.858 | + | 931.598i | −0.121233 | + | 0.209982i | ||||
\(271\) | 841.508 | + | 3140.55i | 0.188627 | + | 0.703966i | 0.993825 | + | 0.110960i | \(0.0353925\pi\) |
−0.805198 | + | 0.593006i | \(0.797941\pi\) | |||||||
\(272\) | 3649.31 | 0.813500 | ||||||||
\(273\) | 6499.21 | − | 10381.7i | 1.44084 | − | 2.30157i | ||||
\(274\) | 1455.96i | 0.321013i | ||||||||
\(275\) | −1233.54 | − | 6337.42i | −0.270493 | − | 1.38968i | ||||
\(276\) | −1306.45 | + | 2262.83i | −0.284923 | + | 0.493501i | ||||
\(277\) | 2638.05 | + | 4569.23i | 0.572220 | + | 0.991114i | 0.996338 | + | 0.0855072i | \(0.0272511\pi\) |
−0.424117 | + | 0.905607i | \(0.639416\pi\) | |||||||
\(278\) | 201.107 | − | 201.107i | 0.0433870 | − | 0.0433870i | ||||
\(279\) | −1379.21 | − | 369.558i | −0.295954 | − | 0.0793006i | ||||
\(280\) | 2623.26 | − | 9790.13i | 0.559891 | − | 2.08954i | ||||
\(281\) | 1096.49 | − | 1096.49i | 0.232780 | − | 0.232780i | −0.581072 | − | 0.813852i | \(-0.697367\pi\) |
0.813852 | + | 0.581072i | \(0.197367\pi\) | |||||||
\(282\) | 1208.29 | − | 697.608i | 0.255152 | − | 0.147312i | ||||
\(283\) | 1514.66 | − | 2623.47i | 0.318153 | − | 0.551057i | −0.661950 | − | 0.749548i | \(-0.730271\pi\) |
0.980103 | + | 0.198491i | \(0.0636041\pi\) | |||||||
\(284\) | 2171.36 | − | 581.814i | 0.453685 | − | 0.121564i | ||||
\(285\) | 4237.86 | 0.880804 | ||||||||
\(286\) | 1585.58 | − | 1282.47i | 0.327824 | − | 0.265153i | ||||
\(287\) | 7310.30 | 1.50353 | ||||||||
\(288\) | 5759.15 | − | 1543.16i | 1.17834 | − | 0.315735i | ||||
\(289\) | −4091.15 | + | 7086.07i | −0.832719 | + | 1.44231i | ||||
\(290\) | −2830.51 | + | 1634.20i | −0.573150 | + | 0.330908i | ||||
\(291\) | −189.249 | + | 189.249i | −0.0381237 | + | 0.0381237i | ||||
\(292\) | 746.976 | − | 2787.75i | 0.149704 | − | 0.558702i | ||||
\(293\) | 5133.39 | + | 1375.49i | 1.02353 | + | 0.274255i | 0.731274 | − | 0.682083i | \(-0.238926\pi\) |
0.292261 | + | 0.956339i | \(0.405593\pi\) | |||||||
\(294\) | 5140.07 | − | 5140.07i | 1.01964 | − | 1.01964i | ||||
\(295\) | −1683.83 | − | 2916.48i | −0.332326 | − | 0.575606i | ||||
\(296\) | −681.611 | + | 1180.58i | −0.133844 | + | 0.231825i | ||||
\(297\) | 1858.88 | − | 361.820i | 0.363175 | − | 0.0706899i | ||||
\(298\) | − | 2298.18i | − | 0.446744i | ||||||
\(299\) | 2285.46 | + | 700.815i | 0.442045 | + | 0.135549i | ||||
\(300\) | −9066.65 | −1.74488 | ||||||||
\(301\) | 2239.38 | + | 8357.48i | 0.428823 | + | 1.60039i | ||||
\(302\) | −1286.13 | + | 2227.64i | −0.245061 | + | 0.424458i | ||||
\(303\) | −2849.25 | − | 4935.04i | −0.540215 | − | 0.935679i | ||||
\(304\) | −706.051 | − | 706.051i | −0.133207 | − | 0.133207i | ||||
\(305\) | −552.761 | + | 2062.93i | −0.103774 | + | 0.387289i | ||||
\(306\) | −1189.07 | + | 4437.66i | −0.222139 | + | 0.829032i | ||||
\(307\) | 5400.28 | − | 5400.28i | 1.00394 | − | 1.00394i | 0.00394949 | − | 0.999992i | \(-0.498743\pi\) |
0.999992 | − | 0.00394949i | \(-0.00125717\pi\) | |||||||
\(308\) | −7235.48 | + | 3531.26i | −1.33857 | + | 0.653286i | ||||
\(309\) | 6430.37 | + | 3712.58i | 1.18385 | + | 0.683499i | ||||
\(310\) | 227.495 | + | 849.022i | 0.0416801 | + | 0.155552i | ||||
\(311\) | − | 361.172i | − | 0.0658527i | −0.999458 | − | 0.0329263i | \(-0.989517\pi\) | ||
0.999458 | − | 0.0329263i | \(-0.0104827\pi\) | |||||||
\(312\) | −2974.98 | − | 5606.36i | −0.539823 | − | 1.01730i | ||||
\(313\) | 3887.77 | 0.702076 | 0.351038 | − | 0.936361i | \(-0.385829\pi\) | ||||
0.351038 | + | 0.936361i | \(0.385829\pi\) | |||||||
\(314\) | −56.5679 | + | 15.1573i | −0.0101666 | + | 0.00272413i | ||||
\(315\) | −16997.1 | − | 9813.30i | −3.04025 | − | 1.75529i | ||||
\(316\) | 2580.43 | + | 4469.44i | 0.459369 | + | 0.795650i | ||||
\(317\) | −838.885 | + | 838.885i | −0.148632 | + | 0.148632i | −0.777507 | − | 0.628874i | \(-0.783516\pi\) |
0.628874 | + | 0.777507i | \(0.283516\pi\) | |||||||
\(318\) | −1741.50 | + | 6499.35i | −0.307101 | + | 1.14612i | ||||
\(319\) | 5440.89 | + | 1871.90i | 0.954958 | + | 0.328547i | ||||
\(320\) | 539.494 | + | 539.494i | 0.0942458 | + | 0.0942458i | ||||
\(321\) | 158.102 | − | 91.2804i | 0.0274904 | − | 0.0158716i | ||||
\(322\) | 1767.15 | + | 1020.27i | 0.305837 | + | 0.176575i | ||||
\(323\) | 3460.98 | − | 927.367i | 0.596205 | − | 0.159753i | ||||
\(324\) | 3319.44i | 0.569176i | ||||||||
\(325\) | 1859.23 | + | 8083.90i | 0.317328 | + | 1.37973i | ||||
\(326\) | 4153.56i | 0.705657i | ||||||||
\(327\) | −138.618 | + | 37.1425i | −0.0234422 | + | 0.00628131i | ||||
\(328\) | 1894.03 | − | 3280.55i | 0.318842 | − | 0.552250i | ||||
\(329\) | 2519.74 | + | 4364.32i | 0.422242 | + | 0.731345i | ||||
\(330\) | −3864.45 | − | 4443.26i | −0.644639 | − | 0.741192i | ||||
\(331\) | −6472.83 | − | 1734.39i | −1.07486 | − | 0.288008i | −0.322372 | − | 0.946613i | \(-0.604480\pi\) |
−0.752489 | + | 0.658605i | \(0.771147\pi\) | |||||||
\(332\) | −2931.42 | − | 785.473i | −0.484587 | − | 0.129845i | ||||
\(333\) | 1866.60 | + | 1866.60i | 0.307175 | + | 0.307175i | ||||
\(334\) | −1637.05 | − | 2835.46i | −0.268191 | − | 0.464520i | ||||
\(335\) | 8369.02 | + | 4831.86i | 1.36492 | + | 0.788037i | ||||
\(336\) | 2156.79 | + | 8049.26i | 0.350186 | + | 1.30691i | ||||
\(337\) | 2113.11 | 0.341569 | 0.170784 | − | 0.985308i | \(-0.445370\pi\) | ||||
0.170784 | + | 0.985308i | \(0.445370\pi\) | |||||||
\(338\) | −1980.24 | + | 1715.62i | −0.318670 | + | 0.276086i | ||||
\(339\) | −1664.35 | −0.266652 | ||||||||
\(340\) | −12634.7 | + | 3385.45i | −2.01533 | + | 0.540005i | ||||
\(341\) | 864.969 | − | 1283.07i | 0.137363 | − | 0.203761i | ||||
\(342\) | 1088.63 | − | 628.521i | 0.172124 | − | 0.0993759i | ||||
\(343\) | 10428.7 | + | 10428.7i | 1.64168 | + | 1.64168i | ||||
\(344\) | 4330.68 | + | 1160.40i | 0.678764 | + | 0.181874i | ||||
\(345\) | 1786.56 | − | 6667.54i | 0.278798 | − | 1.04049i | ||||
\(346\) | 1517.07 | + | 1517.07i | 0.235717 | + | 0.235717i | ||||
\(347\) | 169.434 | − | 97.8226i | 0.0262123 | − | 0.0151337i | −0.486837 | − | 0.873493i | \(-0.661849\pi\) |
0.513049 | + | 0.858359i | \(0.328516\pi\) | |||||||
\(348\) | 4040.09 | − | 6997.64i | 0.622332 | − | 1.07791i | ||||
\(349\) | −2774.29 | − | 10353.8i | −0.425515 | − | 1.58804i | −0.762797 | − | 0.646638i | \(-0.776174\pi\) |
0.337282 | − | 0.941404i | \(-0.390492\pi\) | |||||||
\(350\) | 7080.59i | 1.08135i | ||||||||
\(351\) | −2371.15 | + | 545.345i | −0.360577 | + | 0.0829299i | ||||
\(352\) | −449.090 | + | 6445.85i | −0.0680016 | + | 0.976036i | ||||
\(353\) | 2024.58 | + | 7555.84i | 0.305262 | + | 1.13925i | 0.932719 | + | 0.360603i | \(0.117429\pi\) |
−0.627457 | + | 0.778651i | \(0.715904\pi\) | |||||||
\(354\) | −1558.92 | − | 900.043i | −0.234056 | − | 0.135132i | ||||
\(355\) | −5143.03 | + | 2969.33i | −0.768912 | + | 0.443931i | ||||
\(356\) | −1374.95 | + | 1374.95i | −0.204697 | + | 0.204697i | ||||
\(357\) | −28884.2 | − | 7739.49i | −4.28211 | − | 1.14739i | ||||
\(358\) | 4472.66 | + | 1198.45i | 0.660300 | + | 0.176927i | ||||
\(359\) | −2909.86 | + | 2909.86i | −0.427790 | + | 0.427790i | −0.887875 | − | 0.460085i | \(-0.847819\pi\) |
0.460085 | + | 0.887875i | \(0.347819\pi\) | |||||||
\(360\) | −8807.58 | + | 5085.06i | −1.28944 | + | 0.744461i | ||||
\(361\) | 5091.03 | + | 2939.31i | 0.742241 | + | 0.428533i | ||||
\(362\) | −686.145 | − | 2560.73i | −0.0996215 | − | 0.371793i | ||||
\(363\) | −1437.56 | + | 10266.7i | −0.207857 | + | 1.48446i | ||||
\(364\) | 9137.21 | − | 4848.60i | 1.31571 | − | 0.698175i | ||||
\(365\) | 7624.50i | 1.09338i | ||||||||
\(366\) | 295.463 | + | 1102.68i | 0.0421970 | + | 0.157481i | ||||
\(367\) | 5853.11 | − | 10137.9i | 0.832507 | − | 1.44194i | −0.0635379 | − | 0.997979i | \(-0.520238\pi\) |
0.896044 | − | 0.443964i | \(-0.146428\pi\) | |||||||
\(368\) | −1408.50 | + | 813.198i | −0.199519 | + | 0.115193i | ||||
\(369\) | −5186.83 | − | 5186.83i | −0.731749 | − | 0.731749i | ||||
\(370\) | 420.584 | − | 1569.64i | 0.0590949 | − | 0.220545i | ||||
\(371\) | −23475.4 | − | 6290.22i | −3.28513 | − | 0.880249i | ||||
\(372\) | −1536.55 | − | 1536.55i | −0.214157 | − | 0.214157i | ||||
\(373\) | −8305.49 | + | 4795.18i | −1.15293 | + | 0.665643i | −0.949599 | − | 0.313467i | \(-0.898509\pi\) |
−0.203329 | + | 0.979111i | \(0.565176\pi\) | |||||||
\(374\) | −4128.34 | − | 2783.07i | −0.570779 | − | 0.384784i | ||||
\(375\) | 6794.25 | − | 1820.51i | 0.935609 | − | 0.250696i | ||||
\(376\) | 2611.36 | 0.358166 | ||||||||
\(377\) | −7067.63 | − | 2167.22i | −0.965521 | − | 0.296068i | ||||
\(378\) | −2076.86 | −0.282598 | ||||||||
\(379\) | −1219.85 | − | 4552.54i | −0.165328 | − | 0.617014i | −0.997998 | − | 0.0632439i | \(-0.979855\pi\) |
0.832670 | − | 0.553770i | \(-0.186811\pi\) | |||||||
\(380\) | 3099.49 | + | 1789.49i | 0.418423 | + | 0.241577i | ||||
\(381\) | −314.691 | − | 545.060i | −0.0423152 | − | 0.0732920i | ||||
\(382\) | −2216.90 | − | 2216.90i | −0.296929 | − | 0.296929i | ||||
\(383\) | −7233.47 | − | 1938.20i | −0.965047 | − | 0.258583i | −0.258311 | − | 0.966062i | \(-0.583166\pi\) |
−0.706735 | + | 0.707478i | \(0.749833\pi\) | |||||||
\(384\) | 11053.6 | + | 2961.80i | 1.46895 | + | 0.393603i | ||||
\(385\) | 16048.9 | − | 13958.3i | 2.12449 | − | 1.84774i | ||||
\(386\) | 1552.66 | + | 2689.29i | 0.204737 | + | 0.354614i | ||||
\(387\) | 4340.93 | − | 7518.72i | 0.570186 | − | 0.987591i | ||||
\(388\) | −218.327 | + | 58.5004i | −0.0285666 | + | 0.00765441i | ||||
\(389\) | − | 6533.95i | − | 0.851631i | −0.904810 | − | 0.425815i | \(-0.859987\pi\) | ||
0.904810 | − | 0.425815i | \(-0.140013\pi\) | |||||||
\(390\) | 5155.13 | + | 5537.42i | 0.669333 | + | 0.718970i | ||||
\(391\) | − | 5836.20i | − | 0.754858i | ||||||
\(392\) | 13141.7 | − | 3521.32i | 1.69326 | − | 0.453708i | ||||
\(393\) | 17606.4 | + | 10165.0i | 2.25986 | + | 1.30473i | ||||
\(394\) | 1148.09 | − | 662.848i | 0.146801 | − | 0.0847559i | ||||
\(395\) | −9640.68 | − | 9640.68i | −1.22804 | − | 1.22804i | ||||
\(396\) | 7639.25 | + | 2628.23i | 0.969410 | + | 0.333519i | ||||
\(397\) | −1034.02 | + | 3859.03i | −0.130721 | + | 0.487856i | −0.999979 | − | 0.00650216i | \(-0.997930\pi\) |
0.869258 | + | 0.494358i | \(0.164597\pi\) | |||||||
\(398\) | 300.543 | − | 300.543i | 0.0378514 | − | 0.0378514i | ||||
\(399\) | 4090.97 | + | 7085.77i | 0.513295 | + | 0.889053i | ||||
\(400\) | −4887.45 | − | 2821.77i | −0.610932 | − | 0.352722i | ||||
\(401\) | 5500.89 | − | 1473.96i | 0.685041 | − | 0.183556i | 0.100520 | − | 0.994935i | \(-0.467949\pi\) |
0.584521 | + | 0.811379i | \(0.301283\pi\) | |||||||
\(402\) | 5165.47 | 0.640871 | ||||||||
\(403\) | −1054.91 | + | 1685.09i | −0.130394 | + | 0.208289i | ||||
\(404\) | − | 4812.53i | − | 0.592655i | ||||||
\(405\) | −2269.66 | − | 8470.49i | −0.278470 | − | 1.03926i | ||||
\(406\) | −5464.80 | − | 3155.11i | −0.668014 | − | 0.385678i | ||||
\(407\) | −2570.93 | + | 1254.74i | −0.313111 | + | 0.152813i | ||||
\(408\) | −10956.8 | + | 10956.8i | −1.32951 | + | 1.32951i | ||||
\(409\) | 3195.03 | − | 11924.0i | 0.386269 | − | 1.44158i | −0.449887 | − | 0.893085i | \(-0.648536\pi\) |
0.836156 | − | 0.548491i | \(-0.184798\pi\) | |||||||
\(410\) | −1168.70 | + | 4361.64i | −0.140775 | + | 0.525380i | ||||
\(411\) | 6723.90 | + | 6723.90i | 0.806973 | + | 0.806973i | ||||
\(412\) | 3135.37 | + | 5430.62i | 0.374924 | + | 0.649387i | ||||
\(413\) | 3250.93 | − | 5630.77i | 0.387331 | − | 0.670877i | ||||
\(414\) | −529.934 | − | 1977.74i | −0.0629102 | − | 0.234784i | ||||
\(415\) | 8017.44 | 0.948338 | ||||||||
\(416\) | 296.620 | − | 8296.22i | 0.0349591 | − | 0.977777i | ||||
\(417\) | − | 1857.50i | − | 0.218135i | ||||||
\(418\) | 260.276 | + | 1337.19i | 0.0304557 | + | 0.156469i | ||||
\(419\) | 4713.81 | − | 8164.56i | 0.549605 | − | 0.951945i | −0.448696 | − | 0.893684i | \(-0.648111\pi\) |
0.998301 | − | 0.0582601i | \(-0.0185553\pi\) | |||||||
\(420\) | −14934.5 | − | 25867.3i | −1.73507 | − | 3.00523i | ||||
\(421\) | 5496.82 | − | 5496.82i | 0.636338 | − | 0.636338i | −0.313312 | − | 0.949650i | \(-0.601439\pi\) |
0.949650 | + | 0.313312i | \(0.101439\pi\) | |||||||
\(422\) | 4979.96 | + | 1334.38i | 0.574457 | + | 0.153925i | ||||
\(423\) | 1308.77 | − | 4884.39i | 0.150436 | − | 0.561436i | ||||
\(424\) | −8905.04 | + | 8905.04i | −1.01997 | + | 1.01997i | ||||
\(425\) | 17538.3 | − | 10125.7i | 2.00172 | − | 1.15569i | ||||
\(426\) | −1587.17 | + | 2749.06i | −0.180513 | + | 0.312659i | ||||
\(427\) | −3982.85 | + | 1067.20i | −0.451391 | + | 0.120950i | ||||
\(428\) | 154.178 | 0.0174123 | ||||||||
\(429\) | 1399.86 | − | 13245.2i | 0.157543 | − | 1.49064i | ||||
\(430\) | −5344.44 | −0.599376 | ||||||||
\(431\) | 6317.37 | − | 1692.73i | 0.706025 | − | 0.189179i | 0.112098 | − | 0.993697i | \(-0.464243\pi\) |
0.593928 | + | 0.804518i | \(0.297576\pi\) | |||||||
\(432\) | 827.675 | − | 1433.58i | 0.0921795 | − | 0.159660i | ||||
\(433\) | −3295.04 | + | 1902.39i | −0.365703 | + | 0.211139i | −0.671580 | − | 0.740932i | \(-0.734384\pi\) |
0.305877 | + | 0.952071i | \(0.401050\pi\) | |||||||
\(434\) | −1199.97 | + | 1199.97i | −0.132720 | + | 0.132720i | ||||
\(435\) | −5524.82 | + | 20618.9i | −0.608954 | + | 2.27265i | ||||
\(436\) | −117.066 | − | 31.3679i | −0.0128589 | − | 0.00344552i | ||||
\(437\) | −1129.16 | + | 1129.16i | −0.123604 | + | 0.123604i | ||||
\(438\) | 2037.73 | + | 3529.45i | 0.222298 | + | 0.385032i | ||||
\(439\) | −4171.70 | + | 7225.59i | −0.453541 | + | 0.785555i | −0.998603 | − | 0.0528402i | \(-0.983173\pi\) |
0.545062 | + | 0.838395i | \(0.316506\pi\) | |||||||
\(440\) | −2105.76 | − | 10818.5i | −0.228155 | − | 1.17216i | ||||
\(441\) | − | 26345.7i | − | 2.84480i | ||||||
\(442\) | 5421.84 | + | 3394.22i | 0.583463 | + | 0.365264i | ||||
\(443\) | −2814.79 | −0.301884 | −0.150942 | − | 0.988543i | \(-0.548231\pi\) | ||||
−0.150942 | + | 0.988543i | \(0.548231\pi\) | |||||||
\(444\) | 1039.77 | + | 3880.49i | 0.111139 | + | 0.414775i | ||||
\(445\) | 2568.46 | − | 4448.70i | 0.273610 | − | 0.473907i | ||||
\(446\) | 1167.83 | + | 2022.74i | 0.123987 | + | 0.214752i | ||||
\(447\) | −10613.4 | − | 10613.4i | −1.12304 | − | 1.12304i | ||||
\(448\) | −381.248 | + | 1422.84i | −0.0402060 | + | 0.150051i | ||||
\(449\) | −2343.16 | + | 8744.80i | −0.246282 | + | 0.919137i | 0.726453 | + | 0.687217i | \(0.241168\pi\) |
−0.972735 | + | 0.231921i | \(0.925499\pi\) | |||||||
\(450\) | 5023.84 | − | 5023.84i | 0.526280 | − | 0.526280i | ||||
\(451\) | 7143.97 | − | 3486.60i | 0.745890 | − | 0.364030i | ||||
\(452\) | −1217.27 | − | 702.793i | −0.126672 | − | 0.0731340i | ||||
\(453\) | 4348.08 | + | 16227.3i | 0.450973 | + | 1.68305i | ||||
\(454\) | − | 149.283i | − | 0.0154322i | ||||||
\(455\) | −20001.0 | + | 18620.2i | −2.06079 | + | 1.91852i | ||||
\(456\) | 4239.72 | 0.435401 | ||||||||
\(457\) | −12699.2 | + | 3402.74i | −1.29988 | + | 0.348301i | −0.841404 | − | 0.540407i | \(-0.818270\pi\) |
−0.458473 | + | 0.888708i | \(0.651604\pi\) | |||||||
\(458\) | 1221.94 | + | 705.486i | 0.124667 | + | 0.0719764i | ||||
\(459\) | 2970.05 | + | 5144.28i | 0.302026 | + | 0.523125i | ||||
\(460\) | 4122.12 | − | 4122.12i | 0.417815 | − | 0.417815i | ||||
\(461\) | 304.789 | − | 1137.49i | 0.0307927 | − | 0.114920i | −0.948819 | − | 0.315821i | \(-0.897720\pi\) |
0.979612 | + | 0.200901i | \(0.0643869\pi\) | |||||||
\(462\) | 3698.69 | − | 10750.7i | 0.372465 | − | 1.08261i | ||||
\(463\) | −9517.49 | − | 9517.49i | −0.955324 | − | 0.955324i | 0.0437198 | − | 0.999044i | \(-0.486079\pi\) |
−0.999044 | + | 0.0437198i | \(0.986079\pi\) | |||||||
\(464\) | 4355.69 | − | 2514.76i | 0.435793 | − | 0.251605i | ||||
\(465\) | 4971.57 | + | 2870.34i | 0.495809 | + | 0.286255i | ||||
\(466\) | 2584.35 | − | 692.475i | 0.256905 | − | 0.0688375i | ||||
\(467\) | − | 15212.1i | − | 1.50735i | −0.657249 | − | 0.753674i | \(-0.728280\pi\) | ||
0.657249 | − | 0.753674i | \(-0.271720\pi\) | |||||||
\(468\) | −9923.25 | − | 3042.87i | −0.980134 | − | 0.300549i | ||||
\(469\) | 18657.5i | 1.83694i | ||||||||
\(470\) | −3006.77 | + | 805.661i | −0.295089 | + | 0.0790688i | ||||
\(471\) | −191.242 | + | 331.241i | −0.0187091 | + | 0.0324051i | ||||
\(472\) | −1684.57 | − | 2917.75i | −0.164276 | − | 0.284535i | ||||
\(473\) | 6174.47 | + | 7099.27i | 0.600217 | + | 0.690115i | ||||
\(474\) | −7039.35 | − | 1886.19i | −0.682126 | − | 0.182775i | ||||
\(475\) | −5352.30 | − | 1434.14i | −0.517011 | − | 0.138533i | ||||
\(476\) | −17857.2 | − | 17857.2i | −1.71951 | − | 1.71951i | ||||
\(477\) | 12193.3 | + | 21119.4i | 1.17043 | + | 2.02724i | ||||
\(478\) | 1411.18 | + | 814.744i | 0.135033 | + | 0.0779613i | ||||
\(479\) | 5054.35 | + | 18863.1i | 0.482128 | + | 1.79933i | 0.592659 | + | 0.805453i | \(0.298078\pi\) |
−0.110532 | + | 0.993873i | \(0.535255\pi\) | |||||||
\(480\) | −23971.3 | −2.27945 | ||||||||
\(481\) | 3246.66 | − | 1722.82i | 0.307765 | − | 0.163313i | ||||
\(482\) | 7907.14 | 0.747220 | ||||||||
\(483\) | 12872.9 | − | 3449.27i | 1.21270 | − | 0.324943i | ||||
\(484\) | −5386.64 | + | 6901.82i | −0.505883 | + | 0.648180i | ||||
\(485\) | 517.123 | − | 298.561i | 0.0484152 | − | 0.0279525i | ||||
\(486\) | −4496.34 | − | 4496.34i | −0.419667 | − | 0.419667i | ||||
\(487\) | 13990.8 | + | 3748.82i | 1.30181 | + | 0.348820i | 0.842136 | − | 0.539265i | \(-0.181298\pi\) |
0.459678 | + | 0.888086i | \(0.347965\pi\) | |||||||
\(488\) | −553.003 | + | 2063.84i | −0.0512977 | + | 0.191446i | ||||
\(489\) | 19181.9 | + | 19181.9i | 1.77390 | + | 1.77390i | ||||
\(490\) | −14045.2 | + | 8109.02i | −1.29490 | + | 0.747609i | ||||
\(491\) | −5780.40 | + | 10012.0i | −0.531295 | + | 0.920230i | 0.468038 | + | 0.883709i | \(0.344961\pi\) |
−0.999333 | + | 0.0365217i | \(0.988372\pi\) | |||||||
\(492\) | −2889.27 | − | 10782.9i | −0.264753 | − | 0.988072i | ||||
\(493\) | 18048.1i | 1.64877i | ||||||||
\(494\) | −392.295 | − | 1705.69i | −0.0357291 | − | 0.155349i | ||||
\(495\) | −21290.8 | − | 1483.35i | −1.93323 | − | 0.134690i | ||||
\(496\) | −350.077 | − | 1306.51i | −0.0316914 | − | 0.118274i | ||||
\(497\) | −9929.53 | − | 5732.81i | −0.896177 | − | 0.517408i | ||||
\(498\) | 3711.35 | − | 2142.75i | 0.333955 | − | 0.192809i | ||||
\(499\) | 11348.7 | − | 11348.7i | 1.01811 | − | 1.01811i | 0.0182769 | − | 0.999833i | \(-0.494182\pi\) |
0.999833 | − | 0.0182769i | \(-0.00581805\pi\) | |||||||
\(500\) | 5737.93 | + | 1537.47i | 0.513216 | + | 0.137516i | ||||
\(501\) | −20655.0 | − | 5534.48i | −1.84191 | − | 0.493538i | ||||
\(502\) | 2926.41 | − | 2926.41i | 0.260183 | − | 0.260183i | ||||
\(503\) | −3956.37 | + | 2284.21i | −0.350708 | + | 0.202481i | −0.664997 | − | 0.746846i | \(-0.731567\pi\) |
0.314289 | + | 0.949327i | \(0.398234\pi\) | |||||||
\(504\) | −17004.6 | − | 9817.60i | −1.50287 | − | 0.867680i | ||||
\(505\) | 3290.57 | + | 12280.6i | 0.289957 | + | 1.08213i | ||||
\(506\) | 2213.55 | + | 154.221i | 0.194475 | + | 0.0135493i | ||||
\(507\) | −1222.06 | + | 17068.2i | −0.107049 | + | 1.49512i | ||||
\(508\) | − | 531.529i | − | 0.0464228i | ||||||
\(509\) | 862.832 | + | 3220.13i | 0.0751363 | + | 0.280412i | 0.993264 | − | 0.115872i | \(-0.0369662\pi\) |
−0.918128 | + | 0.396284i | \(0.870299\pi\) | |||||||
\(510\) | 9235.41 | − | 15996.2i | 0.801865 | − | 1.38887i | ||||
\(511\) | −12748.3 | + | 7360.22i | −1.10362 | + | 0.637176i | ||||
\(512\) | 7129.93 | + | 7129.93i | 0.615432 | + | 0.615432i | ||||
\(513\) | 420.659 | − | 1569.92i | 0.0362038 | − | 0.135114i | ||||
\(514\) | 5608.92 | + | 1502.91i | 0.481321 | + | 0.128970i | ||||
\(515\) | −11714.0 | − | 11714.0i | −1.00229 | − | 1.00229i | ||||
\(516\) | 11442.5 | − | 6606.31i | 0.976214 | − | 0.563617i | ||||
\(517\) | 4543.94 | + | 3063.24i | 0.386542 | + | 0.260583i | ||||
\(518\) | 3030.47 | − | 812.011i | 0.257048 | − | 0.0688759i | ||||
\(519\) | 14012.2 | 1.18510 | ||||||||
\(520\) | 3173.87 | + | 13799.9i | 0.267660 | + | 1.16378i | ||||
\(521\) | 11760.2 | 0.988916 | 0.494458 | − | 0.869202i | \(-0.335367\pi\) | ||||
0.494458 | + | 0.869202i | \(0.335367\pi\) | |||||||
\(522\) | 1638.78 | + | 6116.02i | 0.137409 | + | 0.512818i | ||||
\(523\) | −14480.8 | − | 8360.50i | −1.21071 | − | 0.699004i | −0.247796 | − | 0.968812i | \(-0.579706\pi\) |
−0.962914 | + | 0.269808i | \(0.913040\pi\) | |||||||
\(524\) | 8584.65 | + | 14869.0i | 0.715691 | + | 1.23961i | ||||
\(525\) | 32699.6 | + | 32699.6i | 2.71833 | + | 2.71833i | ||||
\(526\) | −4277.69 | − | 1146.20i | −0.354594 | − | 0.0950131i | ||||
\(527\) | 4688.30 | + | 1256.23i | 0.387525 | + | 0.103837i | ||||
\(528\) | 5946.75 | + | 6837.44i | 0.490150 | + | 0.563563i | ||||
\(529\) | −4782.98 | − | 8284.37i | −0.393111 | − | 0.680889i | ||||
\(530\) | 7506.03 | − | 13000.8i | 0.615172 | − | 1.06551i | ||||
\(531\) | −6301.77 | + | 1688.55i | −0.515016 | + | 0.137998i | ||||
\(532\) | 6909.87i | 0.563122i | ||||||||
\(533\) | −9021.65 | + | 4787.28i | −0.733154 | + | 0.389043i | ||||
\(534\) | − | 2745.80i | − | 0.222513i | ||||||
\(535\) | −393.428 | + | 105.419i | −0.0317932 | + | 0.00851897i | ||||
\(536\) | 8372.69 | + | 4833.98i | 0.674711 | + | 0.389545i | ||||
\(537\) | 26190.3 | − | 15121.0i | 2.10464 | − | 1.21512i | ||||
\(538\) | 3998.63 | + | 3998.63i | 0.320434 | + | 0.320434i | ||||
\(539\) | 26998.2 | + | 9288.53i | 2.15750 | + | 0.742273i | ||||
\(540\) | −1535.66 | + | 5731.16i | −0.122378 | + | 0.456722i | ||||
\(541\) | −13461.1 | + | 13461.1i | −1.06976 | + | 1.06976i | −0.0723785 | + | 0.997377i | \(0.523059\pi\) |
−0.997377 | + | 0.0723785i | \(0.976941\pi\) | |||||||
\(542\) | −1938.71 | − | 3357.94i | −0.153643 | − | 0.266118i | ||||
\(543\) | −14994.7 | − | 8657.20i | −1.18505 | − | 0.684192i | ||||
\(544\) | −19576.9 | + | 5245.61i | −1.54293 | + | 0.413426i | ||||
\(545\) | 320.177 | 0.0251649 | ||||||||
\(546\) | −4282.22 | + | 13964.9i | −0.335645 | + | 1.09459i | ||||
\(547\) | − | 18210.8i | − | 1.42347i | −0.702448 | − | 0.711735i | \(-0.747910\pi\) | ||
0.702448 | − | 0.711735i | \(-0.252090\pi\) | |||||||
\(548\) | 2078.48 | + | 7757.00i | 0.162023 | + | 0.604676i | ||||
\(549\) | 3583.13 | + | 2068.72i | 0.278551 | + | 0.160821i | ||||
\(550\) | 3377.04 | + | 6919.48i | 0.261813 | + | 0.536450i | ||||
\(551\) | 3491.85 | − | 3491.85i | 0.269978 | − | 0.269978i | ||||
\(552\) | 1787.35 | − | 6670.46i | 0.137816 | − | 0.514337i | ||||
\(553\) | 6812.85 | − | 25425.9i | 0.523891 | − | 1.95519i | ||||
\(554\) | −4449.16 | − | 4449.16i | −0.341203 | − | 0.341203i | ||||
\(555\) | −5306.57 | − | 9191.24i | −0.405858 | − | 0.702967i | ||||
\(556\) | 784.355 | − | 1358.54i | 0.0598274 | − | 0.103624i | ||||
\(557\) | 1380.70 | + | 5152.83i | 0.105031 | + | 0.391979i | 0.998349 | − | 0.0574456i | \(-0.0182956\pi\) |
−0.893318 | + | 0.449425i | \(0.851629\pi\) | |||||||
\(558\) | 1702.81 | 0.129186 | ||||||||
\(559\) | −8236.66 | − | 8847.48i | −0.623209 | − | 0.669425i | ||||
\(560\) | − | 18592.0i | − | 1.40296i | ||||||
\(561\) | −31918.3 | + | 6212.71i | −2.40212 | + | 0.467559i | ||||
\(562\) | −924.634 | + | 1601.51i | −0.0694009 | + | 0.120206i | ||||
\(563\) | −1476.57 | − | 2557.49i | −0.110533 | − | 0.191448i | 0.805452 | − | 0.592660i | \(-0.201922\pi\) |
−0.915985 | + | 0.401212i | \(0.868589\pi\) | |||||||
\(564\) | 5441.61 | − | 5441.61i | 0.406265 | − | 0.406265i | ||||
\(565\) | 3586.75 | + | 961.068i | 0.267072 | + | 0.0715618i | ||||
\(566\) | −935.022 | + | 3489.55i | −0.0694380 | + | 0.259146i | ||||
\(567\) | 11971.8 | − | 11971.8i | 0.886717 | − | 0.886717i | ||||
\(568\) | −5145.28 | + | 2970.63i | −0.380090 | + | 0.219445i | ||||
\(569\) | −7913.05 | + | 13705.8i | −0.583009 | + | 1.00980i | 0.412111 | + | 0.911134i | \(0.364792\pi\) |
−0.995120 | + | 0.0986683i | \(0.968542\pi\) | |||||||
\(570\) | −4881.69 | + | 1308.05i | −0.358722 | + | 0.0961193i | ||||
\(571\) | −22151.5 | −1.62349 | −0.811744 | − | 0.584014i | \(-0.801481\pi\) | ||||
−0.811744 | + | 0.584014i | \(0.801481\pi\) | |||||||
\(572\) | 6616.81 | − | 9096.21i | 0.483676 | − | 0.664915i | ||||
\(573\) | −20476.2 | −1.49285 | ||||||||
\(574\) | −8420.91 | + | 2256.38i | −0.612338 | + | 0.164075i | ||||
\(575\) | −4512.75 | + | 7816.31i | −0.327295 | + | 0.566892i | ||||
\(576\) | 1280.04 | − | 739.031i | 0.0925955 | − | 0.0534600i | ||||
\(577\) | −14453.6 | + | 14453.6i | −1.04283 | + | 1.04283i | −0.0437881 | + | 0.999041i | \(0.513943\pi\) |
−0.999041 | + | 0.0437881i | \(0.986057\pi\) | |||||||
\(578\) | 2525.52 | − | 9425.37i | 0.181744 | − | 0.678277i | ||||
\(579\) | 19590.2 | + | 5249.17i | 1.40611 | + | 0.376767i | ||||
\(580\) | −12747.4 | + | 12747.4i | −0.912596 | + | 0.912596i | ||||
\(581\) | 7739.54 | + | 13405.3i | 0.552651 | + | 0.957219i | ||||
\(582\) | 159.588 | − | 276.414i | 0.0113662 | − | 0.0196868i | ||||
\(583\) | −25941.4 | + | 5049.34i | −1.84285 | + | 0.358700i | ||||
\(584\) | 7627.84i | 0.540483i | ||||||||
\(585\) | 27402.6 | + | 979.743i | 1.93668 | + | 0.0692434i | ||||
\(586\) | −6337.82 | −0.446780 | ||||||||
\(587\) | −563.998 | − | 2104.87i | −0.0396570 | − | 0.148002i | 0.943258 | − | 0.332059i | \(-0.107743\pi\) |
−0.982916 | + | 0.184057i | \(0.941077\pi\) | |||||||
\(588\) | 20047.3 | − | 34722.9i | 1.40601 | − | 2.43529i | ||||
\(589\) | −664.021 | − | 1150.12i | −0.0464525 | − | 0.0804580i | ||||
\(590\) | 2839.83 | + | 2839.83i | 0.198159 | + | 0.198159i | ||||
\(591\) | 2240.93 | − | 8363.26i | 0.155972 | − | 0.582095i | ||||
\(592\) | −647.209 | + | 2415.42i | −0.0449326 | + | 0.167691i | ||||
\(593\) | −2579.51 | + | 2579.51i | −0.178630 | + | 0.178630i | −0.790759 | − | 0.612128i | \(-0.790314\pi\) |
0.612128 | + | 0.790759i | \(0.290314\pi\) | |||||||
\(594\) | −2029.60 | + | 990.544i | −0.140195 | + | 0.0684217i | ||||
\(595\) | 57777.8 | + | 33358.0i | 3.98094 | + | 2.29840i | ||||
\(596\) | −3280.81 | − | 12244.1i | −0.225482 | − | 0.841510i | ||||
\(597\) | − | 2775.94i | − | 0.190304i | ||||||
\(598\) | −2848.99 | − | 101.862i | −0.194822 | − | 0.00696561i | ||||
\(599\) | 21207.6 | 1.44661 | 0.723305 | − | 0.690529i | \(-0.242622\pi\) | ||||
0.723305 | + | 0.690529i | \(0.242622\pi\) | |||||||
\(600\) | 23146.3 | − | 6202.03i | 1.57491 | − | 0.421995i | ||||
\(601\) | 9221.87 | + | 5324.25i | 0.625904 | + | 0.361366i | 0.779164 | − | 0.626820i | \(-0.215644\pi\) |
−0.153260 | + | 0.988186i | \(0.548977\pi\) | |||||||
\(602\) | −5159.19 | − | 8935.98i | −0.349291 | − | 0.604989i | ||||
\(603\) | 13237.9 | − | 13237.9i | 0.894013 | − | 0.894013i | ||||
\(604\) | −3672.07 | + | 13704.4i | −0.247375 | + | 0.923216i | ||||
\(605\) | 9026.44 | − | 21295.1i | 0.606574 | − | 1.43102i | ||||
\(606\) | 4805.35 | + | 4805.35i | 0.322119 | + | 0.322119i | ||||
\(607\) | 10740.3 | − | 6200.91i | 0.718180 | − | 0.414641i | −0.0959025 | − | 0.995391i | \(-0.530574\pi\) |
0.814082 | + | 0.580749i | \(0.197240\pi\) | |||||||
\(608\) | 4802.54 | + | 2772.75i | 0.320343 | + | 0.184950i | ||||
\(609\) | −39808.4 | + | 10666.6i | −2.64880 | + | 0.709744i | ||||
\(610\) | − | 2546.95i | − | 0.169054i | ||||||
\(611\) | −5967.66 | − | 3735.91i | −0.395132 | − | 0.247363i | ||||
\(612\) | 25340.3i | 1.67372i | ||||||||
\(613\) | 3185.06 | − | 853.434i | 0.209858 | − | 0.0562314i | −0.152358 | − | 0.988325i | \(-0.548687\pi\) |
0.362217 | + | 0.932094i | \(0.382020\pi\) | |||||||
\(614\) | −4553.87 | + | 7887.54i | −0.299315 | + | 0.518429i | ||||
\(615\) | 14745.6 | + | 25540.2i | 0.966831 | + | 1.67460i | ||||
\(616\) | 16055.9 | − | 13964.4i | 1.05018 | − | 0.913379i | ||||
\(617\) | −20360.0 | − | 5455.43i | −1.32846 | − | 0.355960i | −0.476320 | − | 0.879272i | \(-0.658030\pi\) |
−0.852141 | + | 0.523311i | \(0.824696\pi\) | |||||||
\(618\) | −8553.21 | − | 2291.82i | −0.556732 | − | 0.149176i | ||||
\(619\) | −18909.2 | − | 18909.2i | −1.22783 | − | 1.22783i | −0.964784 | − | 0.263042i | \(-0.915274\pi\) |
−0.263042 | − | 0.964784i | \(-0.584726\pi\) | |||||||
\(620\) | 2424.08 | + | 4198.62i | 0.157021 | + | 0.271969i | ||||
\(621\) | −2292.66 | − | 1323.67i | −0.148150 | − | 0.0855346i | ||||
\(622\) | 111.478 | + | 416.042i | 0.00718628 | + | 0.0268196i | ||||
\(623\) | 9917.72 | 0.637793 | ||||||||
\(624\) | −7932.89 | − | 8521.18i | −0.508926 | − | 0.546667i | ||||
\(625\) | 6427.98 | 0.411391 | ||||||||
\(626\) | −4478.41 | + | 1199.99i | −0.285932 | + | 0.0766153i | ||||
\(627\) | 7377.39 | + | 4973.38i | 0.469896 | + | 0.316775i | ||||
\(628\) | −279.742 | + | 161.509i | −0.0177754 | + | 0.0102626i | ||||
\(629\) | −6345.08 | − | 6345.08i | −0.402218 | − | 0.402218i | ||||
\(630\) | 22608.3 | + | 6057.89i | 1.42974 | + | 0.383098i | ||||
\(631\) | 1138.23 | − | 4247.95i | 0.0718104 | − | 0.268000i | −0.920681 | − | 0.390316i | \(-0.872366\pi\) |
0.992491 | + | 0.122316i | \(0.0390323\pi\) | |||||||
\(632\) | −9644.91 | − | 9644.91i | −0.607047 | − | 0.607047i | ||||
\(633\) | 29160.9 | − | 16836.0i | 1.83103 | − | 1.05714i | ||||
\(634\) | 707.404 | − | 1225.26i | 0.0443132 | − | 0.0767528i | ||||
\(635\) | 363.433 | + | 1356.35i | 0.0227124 | + | 0.0847639i | ||||
\(636\) | 37113.1i | 2.31388i | ||||||||
\(637\) | −35070.2 | − | 10753.9i | −2.18137 | − | 0.668895i | ||||
\(638\) | −6845.27 | − | 476.918i | −0.424775 | − | 0.0295946i | ||||
\(639\) | 2977.66 | + | 11112.8i | 0.184342 | + | 0.687974i | ||||
\(640\) | −22110.8 | − | 12765.7i | −1.36563 | − | 0.788449i | ||||
\(641\) | −18464.0 | + | 10660.2i | −1.13773 | + | 0.656869i | −0.945868 | − | 0.324553i | \(-0.894786\pi\) |
−0.191863 | + | 0.981422i | \(0.561453\pi\) | |||||||
\(642\) | −153.947 | + | 153.947i | −0.00946389 | + | 0.00946389i | ||||
\(643\) | 10531.1 | + | 2821.80i | 0.645888 | + | 0.173065i | 0.566869 | − | 0.823808i | \(-0.308154\pi\) |
0.0790193 | + | 0.996873i | \(0.474821\pi\) | |||||||
\(644\) | 10871.5 | + | 2913.00i | 0.665212 | + | 0.178243i | ||||
\(645\) | −24681.7 | + | 24681.7i | −1.50673 | + | 1.50673i | ||||
\(646\) | −3700.55 | + | 2136.51i | −0.225381 | + | 0.130124i | ||||
\(647\) | −10586.0 | − | 6111.81i | −0.643241 | − | 0.371375i | 0.142621 | − | 0.989777i | \(-0.454447\pi\) |
−0.785862 | + | 0.618402i | \(0.787780\pi\) | |||||||
\(648\) | −2270.66 | − | 8474.21i | −0.137654 | − | 0.513732i | ||||
\(649\) | 491.402 | − | 7053.16i | 0.0297214 | − | 0.426596i | ||||
\(650\) | −4636.84 | − | 8738.16i | −0.279803 | − | 0.527291i | ||||
\(651\) | 11083.4i | 0.667269i | ||||||||
\(652\) | 5929.49 | + | 22129.2i | 0.356161 | + | 1.32921i | ||||
\(653\) | −4053.54 | + | 7020.93i | −0.242921 | + | 0.420751i | −0.961545 | − | 0.274648i | \(-0.911439\pi\) |
0.718624 | + | 0.695399i | \(0.244772\pi\) | |||||||
\(654\) | 148.213 | − | 85.5707i | 0.00886174 | − | 0.00511633i | ||||
\(655\) | −32072.9 | − | 32072.9i | −1.91327 | − | 1.91327i | ||||
\(656\) | 1798.43 | − | 6711.84i | 0.107038 | − | 0.399472i | ||||
\(657\) | 14267.4 | + | 3822.95i | 0.847223 | + | 0.227013i | ||||
\(658\) | −4249.62 | − | 4249.62i | −0.251774 | − | 0.251774i | ||||
\(659\) | −16003.9 | + | 9239.86i | −0.946015 | + | 0.546182i | −0.891841 | − | 0.452350i | \(-0.850586\pi\) |
−0.0541741 | + | 0.998532i | \(0.517253\pi\) | |||||||
\(660\) | −26931.9 | − | 18155.9i | −1.58837 | − | 1.07078i | ||||
\(661\) | 10415.1 | − | 2790.71i | 0.612858 | − | 0.164215i | 0.0609792 | − | 0.998139i | \(-0.480578\pi\) |
0.551879 | + | 0.833924i | \(0.313911\pi\) | |||||||
\(662\) | 7991.54 | 0.469184 | ||||||||
\(663\) | 40714.3 | − | 9363.98i | 2.38494 | − | 0.548517i | ||||
\(664\) | 8020.95 | 0.468785 | ||||||||
\(665\) | −4724.62 | − | 17632.5i | −0.275508 | − | 1.02821i | ||||
\(666\) | −2726.32 | − | 1574.04i | −0.158623 | − | 0.0915811i | ||||
\(667\) | −4021.76 | − | 6965.89i | −0.233468 | − | 0.404378i | ||||
\(668\) | −12769.7 | − | 12769.7i | −0.739630 | − | 0.739630i | ||||
\(669\) | 14734.7 | + | 3948.14i | 0.851532 | + | 0.228167i | ||||
\(670\) | −11131.9 | − | 2982.77i | −0.641882 | − | 0.171992i | ||||
\(671\) | −3383.24 | + | 2942.51i | −0.194647 | + | 0.169291i | ||||
\(672\) | −23140.4 | − | 40080.3i | −1.32836 | − | 2.30079i | ||||
\(673\) | −12205.9 | + | 21141.2i | −0.699110 | + | 1.21089i | 0.269665 | + | 0.962954i | \(0.413087\pi\) |
−0.968775 | + | 0.247940i | \(0.920246\pi\) | |||||||
\(674\) | −2434.15 | + | 652.227i | −0.139110 | + | 0.0372743i | ||||
\(675\) | − | 9186.18i | − | 0.523816i | ||||||
\(676\) | −8101.06 | + | 11967.3i | −0.460916 | + | 0.680890i | ||||
\(677\) | − | 27057.0i | − | 1.53602i | −0.640439 | − | 0.768009i | \(-0.721247\pi\) | ||
0.640439 | − | 0.768009i | \(-0.278753\pi\) | |||||||
\(678\) | 1917.20 | − | 513.712i | 0.108598 | − | 0.0290988i | ||||
\(679\) | 998.398 | + | 576.425i | 0.0564286 | + | 0.0325791i | ||||
\(680\) | 29939.3 | − | 17285.5i | 1.68841 | − | 0.974805i | ||||
\(681\) | −689.420 | − | 689.420i | −0.0387939 | − | 0.0387939i | ||||
\(682\) | −600.349 | + | 1744.98i | −0.0337075 | + | 0.0979748i | ||||
\(683\) | −6217.96 | + | 23205.7i | −0.348351 | + | 1.30006i | 0.540298 | + | 0.841474i | \(0.318311\pi\) |
−0.888649 | + | 0.458589i | \(0.848355\pi\) | |||||||
\(684\) | 4902.71 | − | 4902.71i | 0.274064 | − | 0.274064i | ||||
\(685\) | −10607.7 | − | 18373.1i | −0.591677 | − | 1.02481i | ||||
\(686\) | −15231.9 | − | 8794.14i | −0.847750 | − | 0.489449i | ||||
\(687\) | 8901.22 | − | 2385.07i | 0.494327 | − | 0.132455i | ||||
\(688\) | 8224.21 | 0.455734 | ||||||||
\(689\) | 33090.3 | − | 7610.52i | 1.82967 | − | 0.420809i | ||||
\(690\) | 8231.93i | 0.454180i | ||||||||
\(691\) | −1275.89 | − | 4761.70i | −0.0702421 | − | 0.262147i | 0.921870 | − | 0.387499i | \(-0.126661\pi\) |
−0.992112 | + | 0.125352i | \(0.959994\pi\) | |||||||
\(692\) | 10248.3 | + | 5916.86i | 0.562980 | + | 0.325036i | ||||
\(693\) | −18072.6 | − | 37030.4i | −0.990652 | − | 2.02983i | ||||
\(694\) | −164.981 | + | 164.981i | −0.00902391 | + | 0.00902391i | ||||
\(695\) | −1072.60 | + | 4003.01i | −0.0585413 | + | 0.218479i | ||||
\(696\) | −5527.24 | + | 20627.9i | −0.301019 | + | 1.12342i | ||||
\(697\) | 17631.4 | + | 17631.4i | 0.958159 | + | 0.958159i | ||||
\(698\) | 6391.55 | + | 11070.5i | 0.346596 | + | 0.600321i | ||||
\(699\) | 8737.06 | − | 15133.0i | 0.472770 | − | 0.818861i | ||||
\(700\) | 10108.0 | + | 37723.7i | 0.545782 | + | 2.03689i | ||||
\(701\) | −27102.5 | −1.46027 | −0.730133 | − | 0.683305i | \(-0.760542\pi\) | ||||
−0.730133 | + | 0.683305i | \(0.760542\pi\) | |||||||
\(702\) | 2563.06 | − | 1360.07i | 0.137801 | − | 0.0731231i | ||||
\(703\) | 2455.23i | 0.131722i | ||||||||
\(704\) | 306.039 | + | 1572.30i | 0.0163839 | + | 0.0841735i | ||||
\(705\) | −10165.1 | + | 17606.5i | −0.543037 | + | 0.940568i | ||||
\(706\) | −4664.33 | − | 8078.85i | −0.248646 | − | 0.430668i | ||||
\(707\) | −17356.8 | + | 17356.8i | −0.923293 | + | 0.923293i | ||||
\(708\) | −9590.43 | − | 2569.75i | −0.509083 | − | 0.136408i | ||||
\(709\) | 3112.16 | − | 11614.7i | 0.164851 | − | 0.615234i | −0.833208 | − | 0.552960i | \(-0.813498\pi\) |
0.998059 | − | 0.0622738i | \(-0.0198352\pi\) | |||||||
\(710\) | 5007.87 | − | 5007.87i | 0.264707 | − | 0.264707i | ||||
\(711\) | −22874.1 | + | 13206.4i | −1.20654 | + | 0.696593i | ||||
\(712\) | 2569.58 | − | 4450.65i | 0.135252 | − | 0.234263i | ||||
\(713\) | −2089.44 | + | 559.865i | −0.109748 | + | 0.0294069i | ||||
\(714\) | 35661.2 | 1.86917 | ||||||||
\(715\) | −10665.2 | + | 27735.8i | −0.557838 | + | 1.45071i | ||||
\(716\) | 25540.1 | 1.33307 | ||||||||
\(717\) | 10279.7 | − | 2754.45i | 0.535431 | − | 0.143468i | ||||
\(718\) | 2453.79 | − | 4250.08i | 0.127541 | − | 0.220908i | ||||
\(719\) | 23787.8 | − | 13733.9i | 1.23384 | − | 0.712360i | 0.266014 | − | 0.963969i | \(-0.414293\pi\) |
0.967829 | + | 0.251609i | \(0.0809598\pi\) | |||||||
\(720\) | −13191.4 | + | 13191.4i | −0.682800 | + | 0.682800i | ||||
\(721\) | 8278.00 | − | 30893.9i | 0.427585 | − | 1.59577i | ||||
\(722\) | −6771.72 | − | 1814.48i | −0.349054 | − | 0.0935288i | ||||
\(723\) | 36516.7 | − | 36516.7i | 1.87838 | − | 1.87838i | ||||
\(724\) | −7311.24 | − | 12663.4i | −0.375304 | − | 0.650045i | ||||
\(725\) | 13955.4 | − | 24171.4i | 0.714882 | − | 1.23821i | ||||
\(726\) | −1512.92 | − | 12270.1i | −0.0773412 | − | 0.627255i | ||||
\(727\) | − | 19509.5i | − | 0.995278i | −0.867384 | − | 0.497639i | \(-0.834200\pi\) | ||
0.867384 | − | 0.497639i | \(-0.165800\pi\) | |||||||
\(728\) | −20009.8 | + | 18628.3i | −1.01870 | + | 0.948367i | ||||
\(729\) | −27904.6 | −1.41770 | ||||||||
\(730\) | −2353.35 | − | 8782.84i | −0.119317 | − | 0.445298i | ||||
\(731\) | −14756.0 | + | 25558.1i | −0.746607 | + | 1.29316i | ||||
\(732\) | 3148.31 | + | 5453.04i | 0.158969 | + | 0.275342i | ||||
\(733\) | 5125.21 | + | 5125.21i | 0.258259 | + | 0.258259i | 0.824346 | − | 0.566087i | \(-0.191543\pi\) |
−0.566087 | + | 0.824346i | \(0.691543\pi\) | |||||||
\(734\) | −3613.21 | + | 13484.7i | −0.181697 | + | 0.678104i | ||||
\(735\) | −27414.6 | + | 102313.i | −1.37579 | + | 5.13451i | ||||
\(736\) | 6387.05 | − | 6387.05i | 0.319877 | − | 0.319877i | ||||
\(737\) | 8898.56 | + | 18233.0i | 0.444753 | + | 0.911290i | ||||
\(738\) | 7575.78 | + | 4373.88i | 0.377870 | + | 0.218163i | ||||
\(739\) | −7764.62 | − | 28978.0i | −0.386504 | − | 1.44245i | −0.835783 | − | 0.549060i | \(-0.814986\pi\) |
0.449279 | − | 0.893392i | \(-0.351681\pi\) | |||||||
\(740\) | − | 8963.08i | − | 0.445256i | ||||||
\(741\) | −9688.91 | − | 6065.51i | −0.480339 | − | 0.300705i | ||||
\(742\) | 28983.4 | 1.43398 | ||||||||
\(743\) | −4201.36 | + | 1125.75i | −0.207447 | + | 0.0555852i | −0.361046 | − | 0.932548i | \(-0.617580\pi\) |
0.153599 | + | 0.988133i | \(0.450914\pi\) | |||||||
\(744\) | 4973.75 | + | 2871.59i | 0.245089 | + | 0.141502i | ||||
\(745\) | 16743.9 | + | 29001.2i | 0.823419 | + | 1.42620i | ||||
\(746\) | 8087.23 | − | 8087.23i | 0.396909 | − | 0.396909i | ||||
\(747\) | 4019.97 | − | 15002.7i | 0.196898 | − | 0.734834i | ||||
\(748\) | −25967.8 | − | 8934.05i | −1.26936 | − | 0.436713i | ||||
\(749\) | −556.053 | − | 556.053i | −0.0271265 | − | 0.0271265i | ||||
\(750\) | −7264.54 | + | 4194.18i | −0.353685 | + | 0.204200i | ||||
\(751\) | 944.877 | + | 545.525i | 0.0459109 | + | 0.0265066i | 0.522780 | − | 0.852468i | \(-0.324895\pi\) |
−0.476869 | + | 0.878974i | \(0.658228\pi\) | |||||||
\(752\) | 4626.92 | − | 1239.78i | 0.224370 | − | 0.0601198i | ||||
\(753\) | − | 27029.4i | − | 1.30811i | ||||||
\(754\) | 8810.29 | + | 315.000i | 0.425533 | + | 0.0152144i | ||||
\(755\) | − | 37481.4i | − | 1.80674i | ||||||
\(756\) | −11065.0 | + | 2964.86i | −0.532316 | + | 0.142634i | ||||
\(757\) | −8144.20 | + | 14106.2i | −0.391025 | + | 0.677275i | −0.992585 | − | 0.121552i | \(-0.961213\pi\) |
0.601560 | + | 0.798828i | \(0.294546\pi\) | |||||||
\(758\) | 2810.35 | + | 4867.66i | 0.134665 | + | 0.233247i | ||||
\(759\) | 10934.9 | − | 9510.41i | 0.522938 | − | 0.454817i | ||||
\(760\) | −9136.82 | − | 2448.20i | −0.436089 | − | 0.116850i | ||||
\(761\) | 10766.3 | + | 2884.82i | 0.512848 | + | 0.137417i | 0.505956 | − | 0.862559i | \(-0.331140\pi\) |
0.00689156 | + | 0.999976i | \(0.497806\pi\) | |||||||
\(762\) | 530.736 | + | 530.736i | 0.0252317 | + | 0.0252317i | ||||
\(763\) | 309.079 | + | 535.340i | 0.0146650 | + | 0.0254005i | ||||
\(764\) | −14975.9 | − | 8646.35i | −0.709175 | − | 0.409443i | ||||
\(765\) | −17326.4 | − | 64662.9i | −0.818871 | − | 3.05607i | ||||
\(766\) | 8930.64 | 0.421249 | ||||||||
\(767\) | −324.567 | + | 9077.87i | −0.0152796 | + | 0.427357i | ||||
\(768\) | −10911.3 | −0.512667 | ||||||||
\(769\) | 22166.8 | − | 5939.59i | 1.03948 | − | 0.278527i | 0.301579 | − | 0.953441i | \(-0.402486\pi\) |
0.737896 | + | 0.674914i | \(0.235819\pi\) | |||||||
\(770\) | −14178.8 | + | 21032.5i | −0.663595 | + | 0.984360i | ||||
\(771\) | 32843.8 | − | 18962.4i | 1.53417 | − | 0.885751i | ||||
\(772\) | 12111.4 | + | 12111.4i | 0.564634 | + | 0.564634i | ||||
\(773\) | 25182.7 | + | 6747.68i | 1.17174 | + | 0.313968i | 0.791647 | − | 0.610979i | \(-0.209224\pi\) |
0.380097 | + | 0.924947i | \(0.375891\pi\) | |||||||
\(774\) | −2679.72 | + | 10000.8i | −0.124445 | + | 0.464435i | ||||
\(775\) | −5307.59 | − | 5307.59i | −0.246005 | − | 0.246005i | ||||
\(776\) | 517.350 | − | 298.692i | 0.0239327 | − | 0.0138176i | ||||
\(777\) | 10245.3 | − | 17745.3i | 0.473033 | − | 0.819318i | ||||
\(778\) | 2016.75 | + | 7526.61i | 0.0929357 | + | 0.346841i | ||||
\(779\) | − | 6822.48i | − | 0.313788i | ||||||
\(780\) | 35370.4 | + | 22142.8i | 1.62367 | + | 1.01646i | ||||
\(781\) | −12437.8 | − | 866.558i | −0.569860 | − | 0.0397028i | ||||
\(782\) | 1801.39 | + | 6722.86i | 0.0823752 | + | 0.307428i | ||||
\(783\) | 7089.90 | + | 4093.35i | 0.323592 | + | 0.186826i | ||||
\(784\) | 21613.3 | − | 12478.4i | 0.984571 | − | 0.568442i | ||||
\(785\) | 603.410 | − | 603.410i | 0.0274352 | − | 0.0274352i | ||||
\(786\) | −23418.7 | − | 6275.02i | −1.06274 | − | 0.284762i | ||||
\(787\) | 39254.0 | + | 10518.1i | 1.77796 | + | 0.476402i | 0.990209 | − | 0.139594i | \(-0.0445796\pi\) |
0.787749 | + | 0.615996i | \(0.211246\pi\) | |||||||
\(788\) | 5170.47 | − | 5170.47i | 0.233744 | − | 0.233744i | ||||
\(789\) | −25048.6 | + | 14461.8i | −1.13023 | + | 0.652541i | ||||
\(790\) | 14081.0 | + | 8129.67i | 0.634151 | + | 0.366127i | ||||
\(791\) | 1855.51 | + | 6924.86i | 0.0834063 | + | 0.311277i | ||||
\(792\) | −21300.1 | − | 1484.00i | −0.955640 | − | 0.0665805i | ||||
\(793\) | 4216.37 | − | 3925.28i | 0.188812 | − | 0.175776i | ||||
\(794\) | − | 4764.46i | − | 0.212953i | ||||||
\(795\) | −25376.1 | − | 94704.7i | −1.13207 | − | 4.22494i | ||||
\(796\) | 1172.18 | − | 2030.27i | 0.0521944 | − | 0.0904033i | ||||
\(797\) | −17065.6 | + | 9852.83i | −0.758463 | + | 0.437899i | −0.828744 | − | 0.559629i | \(-0.810944\pi\) |
0.0702807 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(798\) | −6899.55 | − | 6899.55i | −0.306067 | − | 0.306067i | ||||
\(799\) | −4448.86 | + | 16603.4i | −0.196983 | + | 0.735150i | ||||
\(800\) | 30275.0 | + | 8112.17i | 1.33798 | + | 0.358511i | ||||
\(801\) | −7036.85 | − | 7036.85i | −0.310406 | − | 0.310406i | ||||
\(802\) | −5881.66 | + | 3395.78i | −0.258963 | + | 0.149512i | ||||
\(803\) | −8947.81 | + | 13272.9i | −0.393227 | + | 0.583303i | ||||
\(804\) | 27520.4 | − | 7374.07i | 1.20718 | − | 0.323462i | ||||
\(805\) | −29733.5 | −1.30182 | ||||||||
\(806\) | 695.063 | − | 2266.70i | 0.0303754 | − | 0.0990585i | ||||
\(807\) | 36933.0 | 1.61103 | ||||||||
\(808\) | 3292.01 | + | 12285.9i | 0.143332 | + | 0.534923i | ||||
\(809\) | −23765.1 | − | 13720.8i | −1.03280 | − | 0.596287i | −0.115015 | − | 0.993364i | \(-0.536691\pi\) |
−0.917786 | + | 0.397076i | \(0.870025\pi\) | |||||||
\(810\) | 5228.95 | + | 9056.81i | 0.226823 | + | 0.392869i | ||||
\(811\) | −7822.39 | − | 7822.39i | −0.338695 | − | 0.338695i | 0.517181 | − | 0.855876i | \(-0.326981\pi\) |
−0.855876 | + | 0.517181i | \(0.826981\pi\) | |||||||
\(812\) | −33619.3 | − | 9008.26i | −1.45296 | − | 0.389320i | ||||
\(813\) | −24460.9 | − | 6554.29i | −1.05521 | − | 0.282742i | ||||
\(814\) | 2574.23 | − | 2238.89i | 0.110844 | − | 0.0964044i | ||||
\(815\) | −30261.6 | − | 52414.6i | −1.30064 | − | 2.25277i | ||||
\(816\) | −14211.8 | + | 24615.5i | −0.609696 | + | 1.05602i | ||||
\(817\) | 7799.78 | − | 2089.94i | 0.334002 | − | 0.0894956i | ||||
\(818\) | 14721.7i | 0.629258i | ||||||||
\(819\) | 24814.6 | + | 46763.3i | 1.05872 | + | 1.99517i | ||||
\(820\) | 24906.2i | 1.06068i | ||||||||
\(821\) | −7316.24 | + | 1960.38i | −0.311009 | + | 0.0833347i | −0.410948 | − | 0.911659i | \(-0.634802\pi\) |
0.0999384 | + | 0.994994i | \(0.468135\pi\) | |||||||
\(822\) | −9820.80 | − | 5670.04i | −0.416715 | − | 0.240591i | ||||
\(823\) | −2511.34 | + | 1449.92i | −0.106367 | + | 0.0614108i | −0.552240 | − | 0.833685i | \(-0.686227\pi\) |
0.445873 | + | 0.895096i | \(0.352893\pi\) | |||||||
\(824\) | −11719.1 | − | 11719.1i | −0.495455 | − | 0.495455i | ||||
\(825\) | 47551.4 | + | 16359.7i | 2.00670 | + | 0.690391i | ||||
\(826\) | −2006.84 | + | 7489.64i | −0.0845363 | + | 0.315494i | ||||
\(827\) | −14963.2 | + | 14963.2i | −0.629167 | + | 0.629167i | −0.947858 | − | 0.318692i | \(-0.896757\pi\) |
0.318692 | + | 0.947858i | \(0.396757\pi\) | |||||||
\(828\) | −5646.72 | − | 9780.41i | −0.237001 | − | 0.410498i | ||||
\(829\) | −22331.0 | − | 12892.8i | −0.935571 | − | 0.540152i | −0.0470019 | − | 0.998895i | \(-0.514967\pi\) |
−0.888569 | + | 0.458743i | \(0.848300\pi\) | |||||||
\(830\) | −9235.47 | + | 2474.64i | −0.386226 | + | 0.103489i | ||||
\(831\) | −41094.2 | −1.71545 | ||||||||
\(832\) | −461.271 | − | 2005.59i | −0.0192208 | − | 0.0835714i | ||||
\(833\) | 89556.0i | 3.72501i | ||||||||
\(834\) | 573.331 | + | 2139.70i | 0.0238043 | + | 0.0888390i | ||||
\(835\) | 41316.7 | + | 23854.2i | 1.71236 | + | 0.988633i | ||||
\(836\) | 3295.61 | + | 6752.65i | 0.136341 | + | 0.279360i | ||||
\(837\) | 1556.81 | − | 1556.81i | 0.0642905 | − | 0.0642905i | ||||
\(838\) | −2909.90 | + | 10859.9i | −0.119953 | + | 0.447672i | ||||
\(839\) | −7377.92 | + | 27534.8i | −0.303593 | + | 1.13302i | 0.630557 | + | 0.776143i | \(0.282826\pi\) |
−0.934150 | + | 0.356881i | \(0.883840\pi\) | |||||||
\(840\) | 55820.9 | + | 55820.9i | 2.29286 | + | 2.29286i | ||||
\(841\) | 242.508 | + | 420.037i | 0.00994334 | + | 0.0172224i | ||||
\(842\) | −4635.28 | + | 8028.54i | −0.189718 | + | 0.328601i | ||||
\(843\) | 3125.96 | + | 11666.2i | 0.127715 | + | 0.476639i | ||||
\(844\) | 28437.0 | 1.15976 | ||||||||
\(845\) | 12489.5 | − | 36077.1i | 0.508465 | − | 1.46875i | ||||
\(846\) | 6030.41i | 0.245071i | ||||||||
\(847\) | 44319.3 | − | 5464.61i | 1.79791 | − | 0.221684i | ||||
\(848\) | −11550.5 | + | 20006.1i | −0.467744 | + | 0.810157i | ||||
\(849\) | 11797.3 | + | 20433.6i | 0.476894 | + | 0.826004i | ||||
\(850\) | −17077.4 | + | 17077.4i | −0.689116 | + | 0.689116i | ||||
\(851\) | 3862.88 | + | 1035.06i | 0.155603 | + | 0.0416936i | ||||
\(852\) | −4531.60 | + | 16912.2i | −0.182218 | + | 0.680048i | ||||
\(853\) | 4472.37 | − | 4472.37i | 0.179520 | − | 0.179520i | −0.611626 | − | 0.791147i | \(-0.709484\pi\) |
0.791147 | + | 0.611626i | \(0.209484\pi\) | |||||||
\(854\) | 4258.54 | − | 2458.67i | 0.170637 | − | 0.0985176i | ||||
\(855\) | −9158.45 | + | 15862.9i | −0.366330 | + | 0.634502i | ||||
\(856\) | −393.601 | + | 105.465i | −0.0157161 | + | 0.00421112i | ||||
\(857\) | −13917.4 | −0.554735 | −0.277368 | − | 0.960764i | \(-0.589462\pi\) | ||||
−0.277368 | + | 0.960764i | \(0.589462\pi\) | |||||||
\(858\) | 2475.70 | + | 15689.6i | 0.0985069 | + | 0.624281i | ||||
\(859\) | −45799.0 | −1.81914 | −0.909570 | − | 0.415551i | \(-0.863589\pi\) | ||||
−0.909570 | + | 0.415551i | \(0.863589\pi\) | |||||||
\(860\) | −28473.9 | + | 7629.56i | −1.12901 | + | 0.302518i | ||||
\(861\) | −28469.0 | + | 49309.8i | −1.12686 | + | 1.95177i | ||||
\(862\) | −6754.65 | + | 3899.80i | −0.266896 | + | 0.154092i | ||||
\(863\) | 21600.1 | − | 21600.1i | 0.852001 | − | 0.852001i | −0.138379 | − | 0.990379i | \(-0.544189\pi\) |
0.990379 | + | 0.138379i | \(0.0441891\pi\) | |||||||
\(864\) | −2379.44 | + | 8880.20i | −0.0936924 | + | 0.349665i | ||||
\(865\) | −30197.1 | − | 8091.30i | −1.18697 | − | 0.318049i | ||||
\(866\) | 3208.44 | − | 3208.44i | 0.125898 | − | 0.125898i | ||||
\(867\) | −31864.9 | − | 55191.6i | −1.24820 | − | 2.16194i | ||||
\(868\) | −4680.11 | + | 8106.18i | −0.183011 | + | 0.316984i | ||||
\(869\) | −5468.86 | − | 28096.7i | −0.213485 | − | 1.09680i | ||||
\(870\) | − | 25456.7i | − | 0.992025i | ||||||
\(871\) | −12218.2 | − | 23025.3i | −0.475313 | − | 0.895730i | ||||
\(872\) | 320.317 | 0.0124396 | ||||||||
\(873\) | −299.399 | − | 1117.37i | −0.0116073 | − | 0.0433188i | ||||
\(874\) | 952.183 | − | 1649.23i | 0.0368513 | − | 0.0638284i | ||||
\(875\) | −15149.3 | − | 26239.3i | −0.585301 | − | 1.01377i | ||||
\(876\) | 15895.1 | + | 15895.1i | 0.613065 | + | 0.613065i | ||||
\(877\) | −8620.48 | + | 32172.1i | −0.331919 | + | 1.23874i | 0.575252 | + | 0.817976i | \(0.304904\pi\) |
−0.907171 | + | 0.420762i | \(0.861763\pi\) | |||||||
\(878\) | 2575.25 | − | 9610.95i | 0.0989868 | − | 0.369424i | ||||
\(879\) | −29269.3 | + | 29269.3i | −1.12313 | + | 1.12313i | ||||
\(880\) | −8867.32 | − | 18169.0i | −0.339679 | − | 0.695995i | ||||
\(881\) | 29194.1 | + | 16855.2i | 1.11643 | + | 0.644571i | 0.940487 | − | 0.339830i | \(-0.110369\pi\) |
0.175942 | + | 0.984400i | \(0.443703\pi\) | |||||||
\(882\) | 8131.78 | + | 30348.2i | 0.310444 | + | 1.15859i | ||||
\(883\) | 20495.2i | 0.781107i | 0.920580 | + | 0.390554i | \(0.127716\pi\) | ||||
−0.920580 | + | 0.390554i | \(0.872284\pi\) | |||||||
\(884\) | 33731.8 | + | 10343.5i | 1.28340 | + | 0.393541i | ||||
\(885\) | 26229.8 | 0.996277 | ||||||||
\(886\) | 3242.42 | − | 868.804i | 0.122947 | − | 0.0329436i | ||||
\(887\) | 9942.13 | + | 5740.09i | 0.376352 | + | 0.217287i | 0.676230 | − | 0.736691i | \(-0.263613\pi\) |
−0.299878 | + | 0.953978i | \(0.596946\pi\) | |||||||
\(888\) | −5308.89 | − | 9195.27i | −0.200625 | − | 0.347492i | ||||
\(889\) | −1917.00 | + | 1917.00i | −0.0723219 | + | 0.0723219i | ||||
\(890\) | −1585.54 | + | 5917.33i | −0.0597164 | + | 0.222865i | ||||
\(891\) | 5989.54 | − | 17409.3i | 0.225204 | − | 0.654582i | ||||
\(892\) | 9109.50 | + | 9109.50i | 0.341938 | + | 0.341938i | ||||
\(893\) | 4073.08 | − | 2351.59i | 0.152632 | − | 0.0881222i | ||||
\(894\) | 15501.8 | + | 8949.96i | 0.579930 | + | 0.334823i | ||||
\(895\) | −65173.0 | + | 17463.0i | −2.43407 | + | 0.652207i | ||||
\(896\) | − | 49292.8i | − | 1.83790i | ||||||
\(897\) | −13627.6 | + | 12686.8i | −0.507260 | + | 0.472239i | ||||
\(898\) | − | 10796.6i | − | 0.401210i | ||||||
\(899\) | 6461.46 | − | 1731.34i | 0.239713 | − | 0.0642308i | ||||
\(900\) | 19593.9 | − | 33937.7i | 0.725702 | − | 1.25695i | ||||
\(901\) | −41448.3 | − | 71790.5i | −1.53257 | − | 2.65448i | ||||
\(902\) | −7153.14 | + | 6221.33i | −0.264051 | + | 0.229654i | ||||
\(903\) | −65094.3 | − | 17442.0i | −2.39890 | − | 0.642782i | ||||
\(904\) | 3588.33 | + | 961.489i | 0.132020 | + | 0.0353746i | ||||
\(905\) | 27315.3 | + | 27315.3i | 1.00331 | + | 1.00331i | ||||
\(906\) | −10017.3 | − | 17350.5i | −0.367332 | − | 0.636238i | ||||
\(907\) | 10629.2 | + | 6136.76i | 0.389125 | + | 0.224661i | 0.681781 | − | 0.731557i | \(-0.261206\pi\) |
−0.292656 | + | 0.956218i | \(0.594539\pi\) | |||||||
\(908\) | −213.112 | − | 795.346i | −0.00778897 | − | 0.0290688i | ||||
\(909\) | 24630.0 | 0.898710 | ||||||||
\(910\) | 17292.4 | − | 27622.4i | 0.629931 | − | 1.00624i | ||||
\(911\) | 46216.2 | 1.68080 | 0.840402 | − | 0.541964i | \(-0.182319\pi\) | ||||
0.840402 | + | 0.541964i | \(0.182319\pi\) | |||||||
\(912\) | 7512.12 | − | 2012.87i | 0.272753 | − | 0.0730841i | ||||
\(913\) | 13957.0 | + | 9408.94i | 0.505924 | + | 0.341063i | ||||
\(914\) | 13578.2 | − | 7839.40i | 0.491387 | − | 0.283703i | ||||
\(915\) | −11762.3 | − | 11762.3i | −0.424973 | − | 0.424973i | ||||
\(916\) | 7517.32 | + | 2014.26i | 0.271156 | + | 0.0726561i | ||||
\(917\) | 22665.2 | − | 84587.6i | 0.816216 | − | 3.04616i | ||||
\(918\) | −5009.09 | − | 5009.09i | −0.180092 | − | 0.180092i | ||||
\(919\) | 19805.7 | − | 11434.8i | 0.710913 | − | 0.410446i | −0.100486 | − | 0.994938i | \(-0.532040\pi\) |
0.811399 | + | 0.584493i | \(0.198706\pi\) | |||||||
\(920\) | −7703.65 | + | 13343.1i | −0.276067 | + | 0.478162i | ||||
\(921\) | 15395.5 | + | 57456.9i | 0.550814 | + | 2.05567i | ||||
\(922\) | 1404.37i | 0.0501633i | ||||||||
\(923\) | 16008.3 | + | 572.354i | 0.570876 | + | 0.0204109i | ||||
\(924\) | 4358.43 | − | 62557.1i | 0.155175 | − | 2.22725i | ||||
\(925\) | 3591.61 | + | 13404.1i | 0.127666 | + | 0.476458i | ||||
\(926\) | 13901.1 | + | 8025.78i | 0.493323 | + | 0.284820i | ||||
\(927\) | −27793.4 | + | 16046.5i | −0.984740 | + | 0.568540i | ||||
\(928\) | −19751.5 | + | 19751.5i | −0.698680 | + | 0.698680i | ||||
\(929\) | 6541.13 | + | 1752.69i | 0.231009 | + | 0.0618987i | 0.372467 | − | 0.928046i | \(-0.378512\pi\) |
−0.141457 | + | 0.989944i | \(0.545179\pi\) | |||||||
\(930\) | −6612.82 | − | 1771.90i | −0.233164 | − | 0.0624762i | ||||
\(931\) | 17326.9 | − | 17326.9i | 0.609952 | − | 0.609952i | ||||
\(932\) | 12780.3 | − | 7378.69i | 0.449175 | − | 0.259331i | ||||
\(933\) | 2436.19 | + | 1406.54i | 0.0854849 | + | 0.0493547i | ||||
\(934\) | 4695.32 | + | 17523.2i | 0.164492 | + | 0.613892i | ||||
\(935\) | 72373.0 | + | 5042.31i | 2.53139 | + | 0.176365i | ||||
\(936\) | 27414.6 | + | 980.172i | 0.957344 | + | 0.0342286i | ||||
\(937\) | − | 26407.2i | − | 0.920690i | −0.887740 | − | 0.460345i | \(-0.847726\pi\) | ||
0.887740 | − | 0.460345i | \(-0.152274\pi\) | |||||||
\(938\) | −5758.77 | − | 21492.0i | −0.200459 | − | 0.748123i | ||||
\(939\) | −15140.4 | + | 26224.0i | −0.526187 | + | 0.911382i | ||||
\(940\) | −14869.2 | + | 8584.74i | −0.515936 | + | 0.297876i | ||||
\(941\) | 38502.5 | + | 38502.5i | 1.33384 | + | 1.33384i | 0.901903 | + | 0.431938i | \(0.142170\pi\) |
0.431938 | + | 0.901903i | \(0.357830\pi\) | |||||||
\(942\) | 118.056 | − | 440.592i | 0.00408332 | − | 0.0152391i | ||||
\(943\) | −10734.0 | − | 2876.16i | −0.370675 | − | 0.0993221i | ||||
\(944\) | −4370.03 | − | 4370.03i | −0.150670 | − | 0.150670i | ||||
\(945\) | 26208.3 | − | 15131.4i | 0.902177 | − | 0.520872i | ||||
\(946\) | −9303.75 | − | 6272.02i | −0.319758 | − | 0.215561i | ||||
\(947\) | −1802.86 | + | 483.075i | −0.0618638 | + | 0.0165764i | −0.289618 | − | 0.957142i | \(-0.593528\pi\) |
0.227754 | + | 0.973719i | \(0.426862\pi\) | |||||||
\(948\) | −40196.6 | −1.37714 | ||||||||
\(949\) | 10912.7 | − | 17431.7i | 0.373278 | − | 0.596266i | ||||
\(950\) | 6608.09 | 0.225679 | ||||||||
\(951\) | −2391.56 | − | 8925.42i | −0.0815474 | − | 0.304339i | ||||
\(952\) | 57803.1 | + | 33372.6i | 1.96787 | + | 1.13615i | ||||
\(953\) | 10911.4 | + | 18899.1i | 0.370887 | + | 0.642396i | 0.989702 | − | 0.143141i | \(-0.0457202\pi\) |
−0.618815 | + | 0.785537i | \(0.712387\pi\) | |||||||
\(954\) | −20564.4 | − | 20564.4i | −0.697901 | − | 0.697901i | ||||
\(955\) | 44127.3 | + | 11823.9i | 1.49521 | + | 0.400641i | ||||
\(956\) | 8681.52 | + | 2326.21i | 0.293703 | + | 0.0786976i | ||||
\(957\) | −33815.3 | + | 29410.3i | −1.14221 | + | 0.993417i | ||||
\(958\) | −11644.5 | − | 20168.8i | −0.392709 | − | 0.680192i | ||||
\(959\) | 20480.0 | − | 35472.4i | 0.689608 | − | 1.19444i | ||||
\(960\) | −5740.02 | + | 1538.03i | −0.192977 | + | 0.0517081i | ||||
\(961\) | 27992.0i | 0.939613i | ||||||||
\(962\) | −3208.14 | + | 2986.66i | −0.107520 | + | 0.100097i | ||||
\(963\) | 789.065i | 0.0264042i | ||||||||
\(964\) | 42127.3 | − | 11288.0i | 1.40750 | − | 0.377139i | ||||
\(965\) | −39186.7 | − | 22624.5i | −1.30722 | − | 0.754723i | ||||
\(966\) | −13763.9 | + | 7946.60i | −0.458433 | + | 0.264677i | ||||
\(967\) | 24046.4 | + | 24046.4i | 0.799668 | + | 0.799668i | 0.983043 | − | 0.183375i | \(-0.0587022\pi\) |
−0.183375 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(968\) | 9030.40 | − | 21304.4i | 0.299843 | − | 0.707386i | ||||
\(969\) | −7223.02 | + | 26956.7i | −0.239460 | + | 0.893678i | ||||
\(970\) | −503.534 | + | 503.534i | −0.0166675 | + | 0.0166675i | ||||
\(971\) | 4616.86 | + | 7996.64i | 0.152587 | + | 0.264289i | 0.932178 | − | 0.362001i | \(-0.117906\pi\) |
−0.779591 | + | 0.626289i | \(0.784573\pi\) | |||||||
\(972\) | −30374.3 | − | 17536.6i | −1.00232 | − | 0.578690i | ||||
\(973\) | −7728.52 | + | 2070.85i | −0.254640 | + | 0.0682307i | ||||
\(974\) | −17273.4 | −0.568251 | ||||||||
\(975\) | −61768.4 | − | 18940.7i | −2.02890 | − | 0.622142i | ||||
\(976\) | 3919.34i | 0.128540i | ||||||||
\(977\) | 702.487 | + | 2621.72i | 0.0230036 | + | 0.0858507i | 0.976473 | − | 0.215638i | \(-0.0691831\pi\) |
−0.953470 | + | 0.301489i | \(0.902516\pi\) | |||||||
\(978\) | −28016.8 | − | 16175.5i | −0.916030 | − | 0.528870i | ||||
\(979\) | 9692.06 | − | 4730.19i | 0.316404 | − | 0.154420i | ||||
\(980\) | −63253.5 | + | 63253.5i | −2.06179 | + | 2.06179i | ||||
\(981\) | 160.538 | − | 599.134i | 0.00522484 | − | 0.0194994i | ||||
\(982\) | 3568.32 | − | 13317.2i | 0.115957 | − | 0.432757i | ||||
\(983\) | 17226.3 | + | 17226.3i | 0.558934 | + | 0.558934i | 0.929004 | − | 0.370070i | \(-0.120666\pi\) |
−0.370070 | + | 0.929004i | \(0.620666\pi\) | |||||||
\(984\) | 14752.1 | + | 25551.4i | 0.477926 | + | 0.827793i | ||||
\(985\) | −9658.64 | + | 16729.2i | −0.312436 | + | 0.541156i | ||||
\(986\) | −5570.66 | − | 20790.0i | −0.179925 | − | 0.671489i | ||||
\(987\) | −39251.2 | −1.26584 | ||||||||
\(988\) | −4525.04 | − | 8527.48i | −0.145709 | − | 0.274590i | ||||
\(989\) | − | 13152.7i | − | 0.422882i | ||||||
\(990\) | 24983.2 | − | 4862.84i | 0.802038 | − | 0.156112i | ||||
\(991\) | −1432.54 | + | 2481.24i | −0.0459195 | + | 0.0795349i | −0.888072 | − | 0.459705i | \(-0.847955\pi\) |
0.842152 | + | 0.539240i | \(0.181288\pi\) | |||||||
\(992\) | 3756.01 | + | 6505.59i | 0.120215 | + | 0.208219i | ||||
\(993\) | 36906.5 | − | 36906.5i | 1.17945 | − | 1.17945i | ||||
\(994\) | 13207.5 | + | 3538.95i | 0.421446 | + | 0.112926i | ||||
\(995\) | −1602.95 | + | 5982.29i | −0.0510723 | + | 0.190604i | ||||
\(996\) | 16714.3 | − | 16714.3i | 0.531739 | − | 0.531739i | ||||
\(997\) | −17716.5 | + | 10228.6i | −0.562776 | + | 0.324919i | −0.754259 | − | 0.656577i | \(-0.772004\pi\) |
0.191483 | + | 0.981496i | \(0.438670\pi\) | |||||||
\(998\) | −9569.96 | + | 16575.7i | −0.303539 | + | 0.525745i | ||||
\(999\) | −3931.65 | + | 1053.48i | −0.124516 | + | 0.0333641i |
(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 | 143.4.o.a.32.17 | ✓ | 160 | |
11.10 | odd | 2 | inner | 143.4.o.a.32.24 | yes | 160 | |
13.11 | odd | 12 | inner | 143.4.o.a.76.24 | yes | 160 | |
143.76 | even | 12 | inner | 143.4.o.a.76.17 | yes | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.o.a.32.17 | ✓ | 160 | 1.1 | even | 1 | trivial | |
143.4.o.a.32.24 | yes | 160 | 11.10 | odd | 2 | inner | |
143.4.o.a.76.17 | yes | 160 | 143.76 | even | 12 | inner | |
143.4.o.a.76.24 | yes | 160 | 13.11 | odd | 12 | inner |