Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(26,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.26");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.15 | ||
Character | \(\chi\) | \(=\) | 105.101 |
Dual form | 105.4.s.a.26.15 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.95258 | − | 2.28202i | 1.39745 | − | 0.806818i | 0.403324 | − | 0.915057i | \(-0.367855\pi\) |
0.994125 | + | 0.108239i | \(0.0345213\pi\) | |||||||
\(3\) | 3.88244 | − | 3.45350i | 0.747177 | − | 0.664626i | ||||
\(4\) | 6.41528 | − | 11.1116i | 0.801909 | − | 1.38895i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 7.46472 | − | 22.5101i | 0.507910 | − | 1.53162i | ||||
\(7\) | −15.3726 | + | 10.3287i | −0.830043 | + | 0.557699i | ||||
\(8\) | − | 22.0469i | − | 0.974343i | ||||||
\(9\) | 3.14674 | − | 26.8160i | 0.116546 | − | 0.993185i | ||||
\(10\) | −19.7629 | − | 11.4101i | −0.624958 | − | 0.360820i | ||||
\(11\) | 38.8392 | + | 22.4238i | 1.06459 | + | 0.614640i | 0.926698 | − | 0.375807i | \(-0.122634\pi\) |
0.137890 | + | 0.990447i | \(0.455968\pi\) | |||||||
\(12\) | −13.4669 | − | 65.2952i | −0.323962 | − | 1.57076i | ||||
\(13\) | 21.9561i | 0.468426i | 0.972185 | + | 0.234213i | \(0.0752513\pi\) | ||||
−0.972185 | + | 0.234213i | \(0.924749\pi\) | |||||||
\(14\) | −37.1911 | + | 75.9059i | −0.709981 | + | 1.44905i | ||||
\(15\) | −24.6602 | − | 8.17773i | −0.424482 | − | 0.140765i | ||||
\(16\) | 1.01069 | + | 1.75057i | 0.0157920 | + | 0.0273526i | ||||
\(17\) | −18.3222 | + | 31.7351i | −0.261400 | + | 0.452758i | −0.966614 | − | 0.256236i | \(-0.917517\pi\) |
0.705214 | + | 0.708994i | \(0.250851\pi\) | |||||||
\(18\) | −48.7571 | − | 113.173i | −0.638453 | − | 1.48196i | ||||
\(19\) | 91.7755 | − | 52.9866i | 1.10814 | − | 0.639788i | 0.169796 | − | 0.985479i | \(-0.445689\pi\) |
0.938348 | + | 0.345692i | \(0.112356\pi\) | |||||||
\(20\) | −64.1528 | −0.717250 | ||||||||
\(21\) | −24.0130 | + | 93.1900i | −0.249527 | + | 0.968368i | ||||
\(22\) | 204.687 | 1.98361 | ||||||||
\(23\) | −21.5307 | + | 12.4308i | −0.195194 | + | 0.112695i | −0.594412 | − | 0.804161i | \(-0.702615\pi\) |
0.399218 | + | 0.916856i | \(0.369282\pi\) | |||||||
\(24\) | −76.1388 | − | 85.5957i | −0.647573 | − | 0.728007i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 50.1044 | + | 86.7834i | 0.377934 | + | 0.654601i | ||||
\(27\) | −80.3919 | − | 114.979i | −0.573016 | − | 0.819544i | ||||
\(28\) | 16.1491 | + | 237.076i | 0.108996 | + | 1.60011i | ||||
\(29\) | − | 31.6068i | − | 0.202387i | −0.994867 | − | 0.101194i | \(-0.967734\pi\) | ||
0.994867 | − | 0.101194i | \(-0.0322662\pi\) | |||||||
\(30\) | −116.133 | + | 23.9520i | −0.706764 | + | 0.145767i | ||||
\(31\) | −262.288 | − | 151.432i | −1.51962 | − | 0.877356i | −0.999733 | − | 0.0231240i | \(-0.992639\pi\) |
−0.519892 | − | 0.854232i | \(-0.674028\pi\) | |||||||
\(32\) | 160.735 | + | 92.8003i | 0.887943 | + | 0.512654i | ||||
\(33\) | 228.232 | − | 47.0718i | 1.20394 | − | 0.248308i | ||||
\(34\) | 167.247i | 0.843608i | ||||||||
\(35\) | 83.1563 | + | 40.7435i | 0.401599 | + | 0.196769i | ||||
\(36\) | −277.781 | − | 206.997i | −1.28602 | − | 0.958321i | ||||
\(37\) | 130.913 | + | 226.748i | 0.581674 | + | 1.00749i | 0.995281 | + | 0.0970336i | \(0.0309354\pi\) |
−0.413607 | + | 0.910456i | \(0.635731\pi\) | |||||||
\(38\) | 241.834 | − | 418.868i | 1.03238 | − | 1.78814i | ||||
\(39\) | 75.8254 | + | 85.2434i | 0.311328 | + | 0.349997i | ||||
\(40\) | −95.4658 | + | 55.1172i | −0.377362 | + | 0.217870i | ||||
\(41\) | −294.707 | −1.12257 | −0.561287 | − | 0.827621i | \(-0.689693\pi\) | ||||
−0.561287 | + | 0.827621i | \(0.689693\pi\) | |||||||
\(42\) | 117.748 | + | 423.140i | 0.432594 | + | 1.55457i | ||||
\(43\) | −302.029 | −1.07114 | −0.535570 | − | 0.844491i | \(-0.679903\pi\) | ||||
−0.535570 | + | 0.844491i | \(0.679903\pi\) | |||||||
\(44\) | 498.329 | − | 287.710i | 1.70741 | − | 0.985772i | ||||
\(45\) | −123.984 | + | 53.4142i | −0.410719 | + | 0.176945i | ||||
\(46\) | −56.7346 | + | 98.2673i | −0.181849 | + | 0.314972i | ||||
\(47\) | 59.6172 | + | 103.260i | 0.185023 | + | 0.320468i | 0.943584 | − | 0.331133i | \(-0.107431\pi\) |
−0.758562 | + | 0.651601i | \(0.774098\pi\) | |||||||
\(48\) | 9.96952 | + | 3.30606i | 0.0299787 | + | 0.00994143i | ||||
\(49\) | 129.634 | − | 317.559i | 0.377943 | − | 0.925829i | ||||
\(50\) | 114.101i | 0.322727i | ||||||||
\(51\) | 38.4618 | + | 186.485i | 0.105603 | + | 0.512023i | ||||
\(52\) | 243.967 | + | 140.855i | 0.650619 | + | 0.375635i | ||||
\(53\) | 560.586 | + | 323.654i | 1.45287 | + | 0.838818i | 0.998644 | − | 0.0520662i | \(-0.0165807\pi\) |
0.454231 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(54\) | −580.140 | − | 271.007i | −1.46198 | − | 0.682952i | ||||
\(55\) | − | 224.238i | − | 0.549751i | ||||||
\(56\) | 227.716 | + | 338.918i | 0.543391 | + | 0.808747i | ||||
\(57\) | 173.324 | − | 522.664i | 0.402761 | − | 1.21454i | ||||
\(58\) | −72.1275 | − | 124.928i | −0.163290 | − | 0.282826i | ||||
\(59\) | 3.12046 | − | 5.40479i | 0.00688557 | − | 0.0119262i | −0.862562 | − | 0.505951i | \(-0.831142\pi\) |
0.869448 | + | 0.494025i | \(0.164475\pi\) | |||||||
\(60\) | −249.069 | + | 221.551i | −0.535912 | + | 0.476702i | ||||
\(61\) | −702.683 | + | 405.694i | −1.47491 | + | 0.851538i | −0.999600 | − | 0.0282811i | \(-0.990997\pi\) |
−0.475308 | + | 0.879820i | \(0.657663\pi\) | |||||||
\(62\) | −1382.29 | −2.83146 | ||||||||
\(63\) | 228.602 | + | 444.734i | 0.457161 | + | 0.889384i | ||||
\(64\) | 830.920 | 1.62289 | ||||||||
\(65\) | 95.0728 | − | 54.8903i | 0.181420 | − | 0.104743i | ||||
\(66\) | 794.686 | − | 706.886i | 1.48211 | − | 1.31836i | ||||
\(67\) | 13.4336 | − | 23.2677i | 0.0244952 | − | 0.0424269i | −0.853518 | − | 0.521063i | \(-0.825536\pi\) |
0.878013 | + | 0.478637i | \(0.158869\pi\) | |||||||
\(68\) | 235.085 | + | 407.178i | 0.419238 | + | 0.726142i | ||||
\(69\) | −40.6622 | + | 122.618i | −0.0709443 | + | 0.213934i | ||||
\(70\) | 421.660 | − | 28.7226i | 0.719971 | − | 0.0490430i | ||||
\(71\) | 639.735i | 1.06933i | 0.845064 | + | 0.534666i | \(0.179563\pi\) | ||||
−0.845064 | + | 0.534666i | \(0.820437\pi\) | |||||||
\(72\) | −591.209 | − | 69.3757i | −0.967703 | − | 0.113556i | ||||
\(73\) | −619.765 | − | 357.821i | −0.993671 | − | 0.573696i | −0.0873014 | − | 0.996182i | \(-0.527824\pi\) |
−0.906370 | + | 0.422486i | \(0.861158\pi\) | |||||||
\(74\) | 1034.89 | + | 597.493i | 1.62572 | + | 0.938610i | ||||
\(75\) | 26.2398 | + | 127.226i | 0.0403989 | + | 0.195877i | ||||
\(76\) | − | 1359.69i | − | 2.05221i | ||||||
\(77\) | −828.671 | + | 56.4473i | −1.22644 | + | 0.0835425i | ||||
\(78\) | 494.234 | + | 163.896i | 0.717448 | + | 0.237918i | ||||
\(79\) | −312.723 | − | 541.652i | −0.445368 | − | 0.771401i | 0.552709 | − | 0.833374i | \(-0.313594\pi\) |
−0.998078 | + | 0.0619733i | \(0.980261\pi\) | |||||||
\(80\) | 5.05345 | − | 8.75283i | 0.00706241 | − | 0.0122324i | ||||
\(81\) | −709.196 | − | 168.766i | −0.972834 | − | 0.231503i | ||||
\(82\) | −1164.85 | + | 672.529i | −1.56874 | + | 0.905712i | ||||
\(83\) | 630.475 | 0.833778 | 0.416889 | − | 0.908957i | \(-0.363120\pi\) | ||||
0.416889 | + | 0.908957i | \(0.363120\pi\) | |||||||
\(84\) | 881.438 | + | 864.662i | 1.14491 | + | 1.12312i | ||||
\(85\) | 183.222 | 0.233803 | ||||||||
\(86\) | −1193.80 | + | 689.239i | −1.49686 | + | 0.864215i | ||||
\(87\) | −109.154 | − | 122.712i | −0.134512 | − | 0.151219i | ||||
\(88\) | 494.376 | − | 856.284i | 0.598871 | − | 1.03727i | ||||
\(89\) | −350.854 | − | 607.698i | −0.417871 | − | 0.723773i | 0.577854 | − | 0.816140i | \(-0.303890\pi\) |
−0.995725 | + | 0.0923667i | \(0.970557\pi\) | |||||||
\(90\) | −368.163 | + | 494.058i | −0.431197 | + | 0.578647i | ||||
\(91\) | −226.779 | − | 337.523i | −0.261241 | − | 0.388813i | ||||
\(92\) | 318.987i | 0.361486i | ||||||||
\(93\) | −1541.29 | + | 317.884i | −1.71854 | + | 0.354442i | ||||
\(94\) | 471.284 | + | 272.096i | 0.517119 | + | 0.298559i | ||||
\(95\) | −458.878 | − | 264.933i | −0.495577 | − | 0.286122i | ||||
\(96\) | 944.530 | − | 194.805i | 1.00417 | − | 0.207106i | ||||
\(97\) | − | 528.346i | − | 0.553046i | −0.961007 | − | 0.276523i | \(-0.910818\pi\) | ||
0.961007 | − | 0.276523i | \(-0.0891822\pi\) | |||||||
\(98\) | −212.288 | − | 1551.01i | −0.218820 | − | 1.59873i | ||||
\(99\) | 723.535 | − | 970.951i | 0.734525 | − | 0.985700i | ||||
\(100\) | 160.382 | + | 277.790i | 0.160382 | + | 0.277790i | ||||
\(101\) | 862.493 | − | 1493.88i | 0.849716 | − | 1.47175i | −0.0317464 | − | 0.999496i | \(-0.510107\pi\) |
0.881462 | − | 0.472255i | \(-0.156560\pi\) | |||||||
\(102\) | 577.588 | + | 649.328i | 0.560684 | + | 0.630324i | ||||
\(103\) | −337.686 | + | 194.963i | −0.323041 | + | 0.186508i | −0.652747 | − | 0.757576i | \(-0.726384\pi\) |
0.329706 | + | 0.944083i | \(0.393050\pi\) | |||||||
\(104\) | 484.064 | 0.456407 | ||||||||
\(105\) | 463.557 | − | 128.995i | 0.430843 | − | 0.119892i | ||||
\(106\) | 2954.35 | 2.70709 | ||||||||
\(107\) | 271.579 | − | 156.796i | 0.245369 | − | 0.141664i | −0.372273 | − | 0.928123i | \(-0.621421\pi\) |
0.617642 | + | 0.786459i | \(0.288088\pi\) | |||||||
\(108\) | −1793.33 | + | 155.661i | −1.59781 | + | 0.138689i | ||||
\(109\) | 395.429 | − | 684.903i | 0.347479 | − | 0.601852i | −0.638322 | − | 0.769770i | \(-0.720371\pi\) |
0.985801 | + | 0.167918i | \(0.0537044\pi\) | |||||||
\(110\) | −511.718 | − | 886.321i | −0.443549 | − | 0.768249i | ||||
\(111\) | 1291.33 | + | 428.228i | 1.10422 | + | 0.366177i | ||||
\(112\) | −33.6181 | − | 16.4716i | −0.0283626 | − | 0.0138966i | ||||
\(113\) | − | 2390.56i | − | 1.99014i | −0.0991983 | − | 0.995068i | \(-0.531628\pi\) | ||
0.0991983 | − | 0.995068i | \(-0.468372\pi\) | |||||||
\(114\) | −507.654 | − | 2461.40i | −0.417071 | − | 2.02221i | ||||
\(115\) | 107.654 | + | 62.1538i | 0.0872935 | + | 0.0503989i | ||||
\(116\) | −351.201 | − | 202.766i | −0.281105 | − | 0.162296i | ||||
\(117\) | 588.776 | + | 69.0901i | 0.465234 | + | 0.0545930i | ||||
\(118\) | − | 28.4838i | − | 0.0222216i | ||||||
\(119\) | −46.1224 | − | 677.097i | −0.0355297 | − | 0.521591i | ||||
\(120\) | −180.293 | + | 543.680i | −0.137154 | + | 0.413591i | ||||
\(121\) | 340.158 | + | 589.170i | 0.255566 | + | 0.442652i | ||||
\(122\) | −1851.61 | + | 3207.08i | −1.37407 | + | 2.37996i | ||||
\(123\) | −1144.18 | + | 1017.77i | −0.838760 | + | 0.746091i | ||||
\(124\) | −3365.30 | + | 1942.96i | −2.43720 | + | 1.40712i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 1918.46 | + | 1236.17i | 1.35643 | + | 0.874023i | ||||
\(127\) | −2416.95 | −1.68874 | −0.844369 | − | 0.535762i | \(-0.820024\pi\) | ||||
−0.844369 | + | 0.535762i | \(0.820024\pi\) | |||||||
\(128\) | 1998.40 | − | 1153.78i | 1.37996 | − | 0.796722i | ||||
\(129\) | −1172.61 | + | 1043.06i | −0.800331 | + | 0.711907i | ||||
\(130\) | 250.522 | − | 433.917i | 0.169017 | − | 0.292747i | ||||
\(131\) | 718.896 | + | 1245.16i | 0.479467 | + | 0.830462i | 0.999723 | − | 0.0235490i | \(-0.00749658\pi\) |
−0.520255 | + | 0.854011i | \(0.674163\pi\) | |||||||
\(132\) | 941.127 | − | 2838.00i | 0.620565 | − | 1.87133i | ||||
\(133\) | −863.544 | + | 1762.47i | −0.562998 | + | 1.14906i | ||||
\(134\) | − | 122.623i | − | 0.0790525i | ||||||
\(135\) | −296.893 | + | 635.554i | −0.189278 | + | 0.405184i | ||||
\(136\) | 699.659 | + | 403.948i | 0.441142 | + | 0.254693i | ||||
\(137\) | 1162.71 | + | 671.288i | 0.725085 | + | 0.418628i | 0.816621 | − | 0.577174i | \(-0.195844\pi\) |
−0.0915363 | + | 0.995802i | \(0.529178\pi\) | |||||||
\(138\) | 119.097 | + | 577.450i | 0.0734650 | + | 0.356201i | ||||
\(139\) | − | 644.525i | − | 0.393294i | −0.980474 | − | 0.196647i | \(-0.936995\pi\) | ||
0.980474 | − | 0.196647i | \(-0.0630053\pi\) | |||||||
\(140\) | 986.195 | − | 662.617i | 0.595348 | − | 0.400010i | ||||
\(141\) | 588.068 | + | 195.013i | 0.351236 | + | 0.116476i | ||||
\(142\) | 1459.89 | + | 2528.61i | 0.862756 | + | 1.49434i | ||||
\(143\) | −492.341 | + | 852.759i | −0.287913 | + | 0.498681i | ||||
\(144\) | 50.1235 | − | 21.5941i | 0.0290067 | − | 0.0124966i | ||||
\(145\) | −136.861 | + | 79.0170i | −0.0783843 | + | 0.0452552i | ||||
\(146\) | −3266.23 | −1.85147 | ||||||||
\(147\) | −593.392 | − | 1680.60i | −0.332940 | − | 0.942948i | ||||
\(148\) | 3359.37 | 1.86580 | ||||||||
\(149\) | −1048.47 | + | 605.332i | −0.576467 | + | 0.332823i | −0.759728 | − | 0.650241i | \(-0.774668\pi\) |
0.183261 | + | 0.983064i | \(0.441335\pi\) | |||||||
\(150\) | 394.048 | + | 442.992i | 0.214493 | + | 0.241134i | ||||
\(151\) | −276.105 | + | 478.227i | −0.148802 | + | 0.257732i | −0.930785 | − | 0.365567i | \(-0.880875\pi\) |
0.781983 | + | 0.623300i | \(0.214208\pi\) | |||||||
\(152\) | −1168.19 | − | 2023.36i | −0.623373 | − | 1.07971i | ||||
\(153\) | 793.352 | + | 591.191i | 0.419207 | + | 0.312386i | ||||
\(154\) | −3146.57 | + | 2114.16i | −1.64648 | + | 1.10626i | ||||
\(155\) | 1514.32i | 0.784731i | ||||||||
\(156\) | 1433.63 | − | 295.680i | 0.735784 | − | 0.151752i | ||||
\(157\) | 1891.12 | + | 1091.84i | 0.961326 | + | 0.555022i | 0.896581 | − | 0.442880i | \(-0.146043\pi\) |
0.0647452 | + | 0.997902i | \(0.479377\pi\) | |||||||
\(158\) | −2472.13 | − | 1427.28i | −1.24476 | − | 0.718662i | ||||
\(159\) | 3294.18 | − | 679.411i | 1.64305 | − | 0.338873i | ||||
\(160\) | − | 928.003i | − | 0.458532i | ||||||
\(161\) | 202.589 | − | 413.479i | 0.0991694 | − | 0.202402i | ||||
\(162\) | −3188.28 | + | 951.343i | −1.54627 | + | 0.461386i | ||||
\(163\) | 1805.11 | + | 3126.55i | 0.867407 | + | 1.50239i | 0.864637 | + | 0.502397i | \(0.167548\pi\) |
0.00277017 | + | 0.999996i | \(0.499118\pi\) | |||||||
\(164\) | −1890.63 | + | 3274.66i | −0.900202 | + | 1.55920i | ||||
\(165\) | −774.407 | − | 870.593i | −0.365379 | − | 0.410761i | ||||
\(166\) | 2492.00 | − | 1438.76i | 1.16516 | − | 0.672707i | ||||
\(167\) | 1747.33 | 0.809657 | 0.404829 | − | 0.914393i | \(-0.367331\pi\) | ||||
0.404829 | + | 0.914393i | \(0.367331\pi\) | |||||||
\(168\) | 2054.55 | + | 529.412i | 0.943523 | + | 0.243125i | ||||
\(169\) | 1714.93 | 0.780577 | ||||||||
\(170\) | 724.202 | − | 418.118i | 0.326728 | − | 0.188637i | ||||
\(171\) | −1132.10 | − | 2627.79i | −0.506278 | − | 1.17516i | ||||
\(172\) | −1937.60 | + | 3356.02i | −0.858958 | + | 1.48776i | ||||
\(173\) | 1752.80 | + | 3035.94i | 0.770306 | + | 1.33421i | 0.937395 | + | 0.348268i | \(0.113230\pi\) |
−0.167089 | + | 0.985942i | \(0.553437\pi\) | |||||||
\(174\) | −711.471 | − | 235.936i | −0.309980 | − | 0.102794i | ||||
\(175\) | −31.4661 | − | 461.936i | −0.0135921 | − | 0.199538i | ||||
\(176\) | 90.6542i | 0.0388257i | ||||||||
\(177\) | −6.55042 | − | 31.7603i | −0.00278169 | − | 0.0134873i | ||||
\(178\) | −2773.56 | − | 1601.32i | −1.16791 | − | 0.674291i | ||||
\(179\) | −1735.08 | − | 1001.75i | −0.724502 | − | 0.418291i | 0.0919057 | − | 0.995768i | \(-0.470704\pi\) |
−0.816407 | + | 0.577477i | \(0.804037\pi\) | |||||||
\(180\) | −201.872 | + | 1720.32i | −0.0835924 | + | 0.712362i | ||||
\(181\) | − | 1090.28i | − | 0.447734i | −0.974620 | − | 0.223867i | \(-0.928132\pi\) | ||
0.974620 | − | 0.223867i | \(-0.0718682\pi\) | |||||||
\(182\) | −1666.60 | − | 816.572i | −0.678772 | − | 0.332573i | ||||
\(183\) | −1327.06 | + | 4001.80i | −0.536062 | + | 1.61651i | ||||
\(184\) | 274.060 | + | 474.685i | 0.109804 | + | 0.190186i | ||||
\(185\) | 654.564 | − | 1133.74i | 0.260133 | − | 0.450563i | ||||
\(186\) | −5366.66 | + | 4773.73i | −2.11560 | + | 1.88186i | ||||
\(187\) | −1423.24 | + | 821.711i | −0.556567 | + | 0.321334i | ||||
\(188\) | 1529.84 | 0.593485 | ||||||||
\(189\) | 2423.42 | + | 937.178i | 0.932687 | + | 0.360686i | ||||
\(190\) | −2418.34 | −0.923392 | ||||||||
\(191\) | −943.845 | + | 544.929i | −0.357561 | + | 0.206438i | −0.668011 | − | 0.744152i | \(-0.732854\pi\) |
0.310449 | + | 0.950590i | \(0.399521\pi\) | |||||||
\(192\) | 3226.00 | − | 2869.58i | 1.21259 | − | 1.07861i | ||||
\(193\) | 2473.45 | − | 4284.14i | 0.922502 | − | 1.59782i | 0.126973 | − | 0.991906i | \(-0.459474\pi\) |
0.795530 | − | 0.605915i | \(-0.207193\pi\) | |||||||
\(194\) | −1205.70 | − | 2088.33i | −0.446207 | − | 0.772854i | ||||
\(195\) | 179.551 | − | 541.442i | 0.0659382 | − | 0.198838i | ||||
\(196\) | −2696.95 | − | 3477.67i | −0.982853 | − | 1.26737i | ||||
\(197\) | − | 3296.31i | − | 1.19215i | −0.802930 | − | 0.596073i | \(-0.796727\pi\) | ||
0.802930 | − | 0.596073i | \(-0.203273\pi\) | |||||||
\(198\) | 644.096 | − | 5488.89i | 0.231181 | − | 1.97009i | ||||
\(199\) | −680.689 | − | 392.996i | −0.242476 | − | 0.139994i | 0.373838 | − | 0.927494i | \(-0.378042\pi\) |
−0.616314 | + | 0.787500i | \(0.711375\pi\) | |||||||
\(200\) | 477.329 | + | 275.586i | 0.168761 | + | 0.0974343i | ||||
\(201\) | −28.1996 | − | 136.728i | −0.00989577 | − | 0.0479805i | ||||
\(202\) | − | 7872.92i | − | 2.74226i | ||||||
\(203\) | 326.458 | + | 485.879i | 0.112871 | + | 0.167990i | ||||
\(204\) | 2318.89 | + | 768.984i | 0.795857 | + | 0.263920i | ||||
\(205\) | 736.768 | + | 1276.12i | 0.251015 | + | 0.434771i | ||||
\(206\) | −889.821 | + | 1541.22i | −0.300955 | + | 0.521270i | ||||
\(207\) | 265.592 | + | 616.484i | 0.0891784 | + | 0.206998i | ||||
\(208\) | −38.4356 | + | 22.1908i | −0.0128127 | + | 0.00739739i | ||||
\(209\) | 4752.65 | 1.57296 | ||||||||
\(210\) | 1537.88 | − | 1567.71i | 0.505350 | − | 0.515155i | ||||
\(211\) | −117.042 | −0.0381872 | −0.0190936 | − | 0.999818i | \(-0.506078\pi\) | ||||
−0.0190936 | + | 0.999818i | \(0.506078\pi\) | |||||||
\(212\) | 7192.62 | − | 4152.66i | 2.33015 | − | 1.34531i | ||||
\(213\) | 2209.32 | + | 2483.73i | 0.710705 | + | 0.798980i | ||||
\(214\) | 715.625 | − | 1239.50i | 0.228594 | − | 0.395936i | ||||
\(215\) | 755.073 | + | 1307.83i | 0.239514 | + | 0.414851i | ||||
\(216\) | −2534.92 | + | 1772.39i | −0.798517 | + | 0.558314i | ||||
\(217\) | 5596.16 | − | 381.199i | 1.75065 | − | 0.119251i | ||||
\(218\) | − | 3609.52i | − | 1.12141i | ||||||
\(219\) | −3641.94 | + | 751.134i | −1.12374 | + | 0.231767i | ||||
\(220\) | −2491.64 | − | 1438.55i | −0.763576 | − | 0.440851i | ||||
\(221\) | −696.779 | − | 402.286i | −0.212083 | − | 0.122446i | ||||
\(222\) | 6081.33 | − | 1254.25i | 1.83852 | − | 0.379188i | ||||
\(223\) | 3582.58i | 1.07582i | 0.843003 | + | 0.537908i | \(0.180785\pi\) | ||||
−0.843003 | + | 0.537908i | \(0.819215\pi\) | |||||||
\(224\) | −3429.43 | + | 233.605i | −1.02294 | + | 0.0696804i | ||||
\(225\) | 541.249 | + | 403.329i | 0.160370 | + | 0.119505i | ||||
\(226\) | −5455.33 | − | 9448.90i | −1.60568 | − | 2.78111i | ||||
\(227\) | −635.352 | + | 1100.46i | −0.185770 | + | 0.321763i | −0.943836 | − | 0.330415i | \(-0.892811\pi\) |
0.758066 | + | 0.652178i | \(0.226145\pi\) | |||||||
\(228\) | −4695.70 | − | 5278.94i | −1.36395 | − | 1.53336i | ||||
\(229\) | 2500.75 | − | 1443.81i | 0.721633 | − | 0.416635i | −0.0937206 | − | 0.995599i | \(-0.529876\pi\) |
0.815353 | + | 0.578964i | \(0.196543\pi\) | |||||||
\(230\) | 567.346 | 0.162651 | ||||||||
\(231\) | −3022.33 | + | 3080.96i | −0.860842 | + | 0.877543i | ||||
\(232\) | −696.831 | −0.197195 | ||||||||
\(233\) | −1421.01 | + | 820.421i | −0.399543 | + | 0.230676i | −0.686287 | − | 0.727331i | \(-0.740760\pi\) |
0.286744 | + | 0.958007i | \(0.407427\pi\) | |||||||
\(234\) | 2484.85 | − | 1070.52i | 0.694187 | − | 0.299068i | ||||
\(235\) | 298.086 | − | 516.300i | 0.0827446 | − | 0.143318i | ||||
\(236\) | −40.0372 | − | 69.3464i | −0.0110432 | − | 0.0191274i | ||||
\(237\) | −3084.72 | − | 1022.95i | −0.845462 | − | 0.280369i | ||||
\(238\) | −1727.45 | − | 2571.03i | −0.470480 | − | 0.700231i | ||||
\(239\) | − | 3084.64i | − | 0.834849i | −0.908712 | − | 0.417424i | \(-0.862933\pi\) | ||
0.908712 | − | 0.417424i | \(-0.137067\pi\) | |||||||
\(240\) | −10.6081 | − | 51.4344i | −0.00285313 | − | 0.0138337i | ||||
\(241\) | 493.799 | + | 285.095i | 0.131985 | + | 0.0762015i | 0.564539 | − | 0.825407i | \(-0.309054\pi\) |
−0.432554 | + | 0.901608i | \(0.642387\pi\) | |||||||
\(242\) | 2689.00 | + | 1552.50i | 0.714280 | + | 0.412390i | ||||
\(243\) | −3336.25 | + | 1793.98i | −0.880742 | + | 0.473597i | ||||
\(244\) | 10410.6i | 2.73143i | ||||||||
\(245\) | −1699.16 | + | 232.565i | −0.443083 | + | 0.0606452i | ||||
\(246\) | −2199.90 | + | 6633.87i | −0.570166 | + | 1.71935i | ||||
\(247\) | 1163.38 | + | 2015.03i | 0.299693 | + | 0.519083i | ||||
\(248\) | −3338.61 | + | 5782.64i | −0.854846 | + | 1.48064i | ||||
\(249\) | 2447.78 | − | 2177.34i | 0.622980 | − | 0.554150i | ||||
\(250\) | 494.073 | − | 285.253i | 0.124992 | − | 0.0721640i | ||||
\(251\) | 3678.99 | 0.925162 | 0.462581 | − | 0.886577i | \(-0.346923\pi\) | ||||
0.462581 | + | 0.886577i | \(0.346923\pi\) | |||||||
\(252\) | 6408.24 | + | 312.960i | 1.60191 | + | 0.0782326i | ||||
\(253\) | −1114.98 | −0.277069 | ||||||||
\(254\) | −9553.20 | + | 5515.54i | −2.35993 | + | 1.36250i | ||||
\(255\) | 711.351 | − | 632.758i | 0.174692 | − | 0.155392i | ||||
\(256\) | 1942.22 | − | 3364.02i | 0.474174 | − | 0.821293i | ||||
\(257\) | 2372.26 | + | 4108.88i | 0.575789 | + | 0.997295i | 0.995955 | + | 0.0898484i | \(0.0286382\pi\) |
−0.420167 | + | 0.907447i | \(0.638028\pi\) | |||||||
\(258\) | −2254.56 | + | 6798.70i | −0.544043 | + | 1.64058i | ||||
\(259\) | −4354.49 | − | 2133.54i | −1.04469 | − | 0.511860i | ||||
\(260\) | − | 1408.55i | − | 0.335978i | ||||||
\(261\) | −847.568 | − | 99.4582i | −0.201008 | − | 0.0235874i | ||||
\(262\) | 5682.99 | + | 3281.08i | 1.34006 | + | 0.773685i | ||||
\(263\) | −714.976 | − | 412.792i | −0.167632 | − | 0.0967826i | 0.413837 | − | 0.910351i | \(-0.364188\pi\) |
−0.581469 | + | 0.813569i | \(0.697522\pi\) | |||||||
\(264\) | −1037.79 | − | 5031.80i | −0.241937 | − | 1.17305i | ||||
\(265\) | − | 3236.54i | − | 0.750261i | ||||||
\(266\) | 608.765 | + | 8936.93i | 0.140323 | + | 2.05999i | ||||
\(267\) | −3460.85 | − | 1147.68i | −0.793261 | − | 0.263059i | ||||
\(268\) | −172.361 | − | 298.537i | −0.0392858 | − | 0.0680450i | ||||
\(269\) | 2053.16 | − | 3556.17i | 0.465365 | − | 0.806036i | −0.533853 | − | 0.845577i | \(-0.679256\pi\) |
0.999218 | + | 0.0395417i | \(0.0125898\pi\) | |||||||
\(270\) | 276.856 | + | 3189.60i | 0.0624034 | + | 0.718936i | ||||
\(271\) | −4293.33 | + | 2478.76i | −0.962367 | + | 0.555623i | −0.896901 | − | 0.442232i | \(-0.854187\pi\) |
−0.0654661 | + | 0.997855i | \(0.520853\pi\) | |||||||
\(272\) | −74.0724 | −0.0165121 | ||||||||
\(273\) | −2046.09 | − | 527.233i | −0.453608 | − | 0.116885i | ||||
\(274\) | 6127.59 | 1.35103 | ||||||||
\(275\) | −970.981 | + | 560.596i | −0.212918 | + | 0.122928i | ||||
\(276\) | 1101.62 | + | 1238.45i | 0.240253 | + | 0.270094i | ||||
\(277\) | −1146.40 | + | 1985.63i | −0.248667 | + | 0.430704i | −0.963156 | − | 0.268943i | \(-0.913326\pi\) |
0.714489 | + | 0.699646i | \(0.246659\pi\) | |||||||
\(278\) | −1470.82 | − | 2547.54i | −0.317316 | − | 0.549608i | ||||
\(279\) | −4886.16 | + | 6557.01i | −1.04848 | + | 1.40702i | ||||
\(280\) | 898.267 | − | 1833.34i | 0.191720 | − | 0.391296i | ||||
\(281\) | − | 4298.26i | − | 0.912501i | −0.889851 | − | 0.456250i | \(-0.849192\pi\) | ||
0.889851 | − | 0.456250i | \(-0.150808\pi\) | |||||||
\(282\) | 2769.41 | − | 571.180i | 0.584809 | − | 0.120614i | ||||
\(283\) | −1454.18 | − | 839.571i | −0.305449 | − | 0.176351i | 0.339439 | − | 0.940628i | \(-0.389763\pi\) |
−0.644888 | + | 0.764277i | \(0.723096\pi\) | |||||||
\(284\) | 7108.47 | + | 4104.07i | 1.48525 | + | 0.857507i | ||||
\(285\) | −2696.51 | + | 556.144i | −0.560448 | + | 0.115590i | ||||
\(286\) | 4494.14i | 0.929174i | ||||||||
\(287\) | 4530.42 | − | 3043.95i | 0.931784 | − | 0.626059i | ||||
\(288\) | 2994.32 | − | 4018.25i | 0.612647 | − | 0.822144i | ||||
\(289\) | 1785.09 | + | 3091.87i | 0.363340 | + | 0.629324i | ||||
\(290\) | −360.637 | + | 624.642i | −0.0730254 | + | 0.126484i | ||||
\(291\) | −1824.64 | − | 2051.28i | −0.367568 | − | 0.413223i | ||||
\(292\) | −7951.92 | + | 4591.04i | −1.59367 | + | 0.920105i | ||||
\(293\) | −3429.39 | −0.683779 | −0.341889 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341889 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(294\) | −6180.60 | − | 5288.57i | −1.22605 | − | 1.04910i | ||||
\(295\) | −31.2046 | −0.00615864 | ||||||||
\(296\) | 4999.08 | − | 2886.22i | 0.981640 | − | 0.566750i | ||||
\(297\) | −544.093 | − | 6268.39i | −0.106301 | − | 1.22468i | ||||
\(298\) | −2762.76 | + | 4785.25i | −0.537056 | + | 0.930208i | ||||
\(299\) | −272.932 | − | 472.731i | −0.0527894 | − | 0.0914340i | ||||
\(300\) | 1582.02 | + | 524.624i | 0.304460 | + | 0.100964i | ||||
\(301\) | 4642.98 | − | 3119.58i | 0.889093 | − | 0.597375i | ||||
\(302\) | 2520.31i | 0.480224i | ||||||||
\(303\) | −1810.53 | − | 8778.53i | −0.343275 | − | 1.66440i | ||||
\(304\) | 185.513 | + | 107.106i | 0.0349997 | + | 0.0202071i | ||||
\(305\) | 3513.42 | + | 2028.47i | 0.659599 | + | 0.380820i | ||||
\(306\) | 4484.90 | + | 526.283i | 0.837859 | + | 0.0983189i | ||||
\(307\) | 726.092i | 0.134985i | 0.997720 | + | 0.0674923i | \(0.0214998\pi\) | ||||
−0.997720 | + | 0.0674923i | \(0.978500\pi\) | |||||||
\(308\) | −4688.93 | + | 9569.97i | −0.867456 | + | 1.77045i | ||||
\(309\) | −637.742 | + | 1923.13i | −0.117411 | + | 0.354055i | ||||
\(310\) | 3455.72 | + | 5985.48i | 0.633135 | + | 1.09662i | ||||
\(311\) | 3360.18 | − | 5820.01i | 0.612664 | − | 1.06116i | −0.378126 | − | 0.925754i | \(-0.623431\pi\) |
0.990790 | − | 0.135411i | \(-0.0432353\pi\) | |||||||
\(312\) | 1879.35 | − | 1671.71i | 0.341017 | − | 0.303340i | ||||
\(313\) | 5210.38 | − | 3008.21i | 0.940920 | − | 0.543241i | 0.0506716 | − | 0.998715i | \(-0.483864\pi\) |
0.890249 | + | 0.455475i | \(0.150531\pi\) | |||||||
\(314\) | 9966.44 | 1.79121 | ||||||||
\(315\) | 1354.25 | − | 2101.71i | 0.242233 | − | 0.375930i | ||||
\(316\) | −8024.82 | −1.42858 | ||||||||
\(317\) | −4471.73 | + | 2581.75i | −0.792295 | + | 0.457431i | −0.840770 | − | 0.541393i | \(-0.817897\pi\) |
0.0484752 | + | 0.998824i | \(0.484564\pi\) | |||||||
\(318\) | 11470.1 | − | 10202.8i | 2.02268 | − | 1.79920i | ||||
\(319\) | 708.746 | − | 1227.58i | 0.124395 | − | 0.215459i | ||||
\(320\) | −2077.30 | − | 3597.99i | −0.362889 | − | 0.628543i | ||||
\(321\) | 512.894 | − | 1546.65i | 0.0891806 | − | 0.268927i | ||||
\(322\) | −142.818 | − | 2096.62i | −0.0247171 | − | 0.362858i | ||||
\(323\) | 3883.34i | 0.668962i | ||||||||
\(324\) | −6424.94 | + | 6797.61i | −1.10167 | + | 1.16557i | ||||
\(325\) | −475.364 | − | 274.452i | −0.0811337 | − | 0.0468426i | ||||
\(326\) | 14269.7 | + | 8238.63i | 2.42431 | + | 1.39968i | ||||
\(327\) | −830.079 | − | 4024.71i | −0.140378 | − | 0.680633i | ||||
\(328\) | 6497.37i | 1.09377i | ||||||||
\(329\) | −1983.02 | − | 971.605i | −0.332302 | − | 0.162816i | ||||
\(330\) | −5047.62 | − | 1673.88i | −0.842007 | − | 0.279224i | ||||
\(331\) | 1601.38 | + | 2773.68i | 0.265921 | + | 0.460589i | 0.967805 | − | 0.251703i | \(-0.0809905\pi\) |
−0.701883 | + | 0.712292i | \(0.747657\pi\) | |||||||
\(332\) | 4044.67 | − | 7005.57i | 0.668615 | − | 1.15807i | ||||
\(333\) | 6492.42 | − | 2797.04i | 1.06842 | − | 0.460292i | ||||
\(334\) | 6906.48 | − | 3987.46i | 1.13145 | − | 0.653246i | ||||
\(335\) | −134.336 | −0.0219091 | ||||||||
\(336\) | −187.405 | + | 52.1498i | −0.0304279 | + | 0.00846727i | ||||
\(337\) | −11770.7 | −1.90264 | −0.951320 | − | 0.308204i | \(-0.900272\pi\) | ||||
−0.951320 | + | 0.308204i | \(0.900272\pi\) | |||||||
\(338\) | 6778.40 | − | 3913.51i | 1.09082 | − | 0.629784i | ||||
\(339\) | −8255.80 | − | 9281.23i | −1.32269 | − | 1.48698i | ||||
\(340\) | 1175.42 | − | 2035.89i | 0.187489 | − | 0.324740i | ||||
\(341\) | −6791.39 | − | 11763.0i | −1.07852 | − | 1.86805i | ||||
\(342\) | −10471.4 | − | 7803.08i | −1.65564 | − | 1.23375i | ||||
\(343\) | 1287.17 | + | 6220.68i | 0.202626 | + | 0.979256i | ||||
\(344\) | 6658.80i | 1.04366i | ||||||||
\(345\) | 632.607 | − | 130.472i | 0.0987200 | − | 0.0203606i | ||||
\(346\) | 13856.2 | + | 7999.87i | 2.15293 | + | 1.24299i | ||||
\(347\) | 810.218 | + | 467.780i | 0.125345 | + | 0.0723681i | 0.561362 | − | 0.827571i | \(-0.310278\pi\) |
−0.436016 | + | 0.899939i | \(0.643611\pi\) | |||||||
\(348\) | −2063.77 | + | 425.644i | −0.317902 | + | 0.0655659i | ||||
\(349\) | 6000.40i | 0.920326i | 0.887834 | + | 0.460163i | \(0.152209\pi\) | ||||
−0.887834 | + | 0.460163i | \(0.847791\pi\) | |||||||
\(350\) | −1178.52 | − | 1754.03i | −0.179985 | − | 0.267877i | ||||
\(351\) | 2524.49 | − | 1765.10i | 0.383896 | − | 0.268415i | ||||
\(352\) | 4161.88 | + | 7208.59i | 0.630196 | + | 1.09153i | ||||
\(353\) | −3391.26 | + | 5873.83i | −0.511327 | + | 0.885644i | 0.488587 | + | 0.872515i | \(0.337513\pi\) |
−0.999914 | + | 0.0131291i | \(0.995821\pi\) | |||||||
\(354\) | −98.3688 | − | 110.587i | −0.0147690 | − | 0.0166035i | ||||
\(355\) | 2770.13 | − | 1599.34i | 0.414150 | − | 0.239110i | ||||
\(356\) | −9003.31 | −1.34038 | ||||||||
\(357\) | −2517.42 | − | 2469.51i | −0.373210 | − | 0.366107i | ||||
\(358\) | −9144.05 | −1.34994 | ||||||||
\(359\) | −394.879 | + | 227.984i | −0.0580528 | + | 0.0335168i | −0.528745 | − | 0.848780i | \(-0.677337\pi\) |
0.470693 | + | 0.882297i | \(0.344004\pi\) | |||||||
\(360\) | 1177.62 | + | 2733.45i | 0.172405 | + | 0.400182i | ||||
\(361\) | 2185.66 | − | 3785.68i | 0.318656 | − | 0.551929i | ||||
\(362\) | −2488.05 | − | 4309.42i | −0.361240 | − | 0.625686i | ||||
\(363\) | 3355.34 | + | 1112.69i | 0.485151 | + | 0.160884i | ||||
\(364\) | −5205.27 | + | 354.572i | −0.749533 | + | 0.0510567i | ||||
\(365\) | 3578.21i | 0.513129i | ||||||||
\(366\) | 3886.87 | + | 18845.8i | 0.555110 | + | 2.69150i | ||||
\(367\) | −4548.06 | − | 2625.82i | −0.646884 | − | 0.373479i | 0.140377 | − | 0.990098i | \(-0.455169\pi\) |
−0.787262 | + | 0.616619i | \(0.788502\pi\) | |||||||
\(368\) | −43.5217 | − | 25.1273i | −0.00616502 | − | 0.00355938i | ||||
\(369\) | −927.365 | + | 7902.86i | −0.130831 | + | 1.11492i | ||||
\(370\) | − | 5974.93i | − | 0.839518i | ||||||
\(371\) | −11960.6 | + | 814.732i | −1.67376 | + | 0.114013i | ||||
\(372\) | −6355.60 | + | 19165.5i | −0.885813 | + | 2.67119i | ||||
\(373\) | 277.993 | + | 481.498i | 0.0385896 | + | 0.0668391i | 0.884675 | − | 0.466208i | \(-0.154380\pi\) |
−0.846086 | + | 0.533047i | \(0.821047\pi\) | |||||||
\(374\) | −3750.33 | + | 6495.76i | −0.518516 | + | 0.898095i | ||||
\(375\) | 485.305 | − | 431.687i | 0.0668295 | − | 0.0594459i | ||||
\(376\) | 2276.56 | − | 1314.37i | 0.312246 | − | 0.180276i | ||||
\(377\) | 693.963 | 0.0948034 | ||||||||
\(378\) | 11717.4 | − | 1826.03i | 1.59439 | − | 0.248468i | ||||
\(379\) | −775.818 | −0.105148 | −0.0525740 | − | 0.998617i | \(-0.516743\pi\) | ||||
−0.0525740 | + | 0.998617i | \(0.516743\pi\) | |||||||
\(380\) | −5887.65 | + | 3399.24i | −0.794816 | + | 0.458887i | ||||
\(381\) | −9383.67 | + | 8346.93i | −1.26179 | + | 1.12238i | ||||
\(382\) | −2487.08 | + | 4307.76i | −0.333116 | + | 0.576974i | ||||
\(383\) | 2985.84 | + | 5171.63i | 0.398354 | + | 0.689969i | 0.993523 | − | 0.113631i | \(-0.0362483\pi\) |
−0.595169 | + | 0.803600i | \(0.702915\pi\) | |||||||
\(384\) | 3774.11 | − | 11380.9i | 0.501554 | − | 1.51245i | ||||
\(385\) | 2316.10 | + | 3447.13i | 0.306596 | + | 0.456317i | ||||
\(386\) | − | 22577.9i | − | 2.97716i | ||||||
\(387\) | −950.406 | + | 8099.22i | −0.124837 | + | 1.06384i | ||||
\(388\) | −5870.77 | − | 3389.49i | −0.768152 | − | 0.443493i | ||||
\(389\) | 677.294 | + | 391.036i | 0.0882781 | + | 0.0509674i | 0.543489 | − | 0.839416i | \(-0.317103\pi\) |
−0.455211 | + | 0.890384i | \(0.650436\pi\) | |||||||
\(390\) | −525.893 | − | 2549.84i | −0.0682811 | − | 0.331067i | ||||
\(391\) | − | 911.038i | − | 0.117834i | ||||||
\(392\) | −7001.19 | − | 2858.03i | −0.902075 | − | 0.368246i | ||||
\(393\) | 7091.24 | + | 2351.58i | 0.910193 | + | 0.301835i | ||||
\(394\) | −7522.27 | − | 13029.0i | −0.961844 | − | 1.66596i | ||||
\(395\) | −1563.62 | + | 2708.26i | −0.199175 | + | 0.344981i | ||||
\(396\) | −6147.13 | − | 14268.5i | −0.780063 | − | 1.81066i | ||||
\(397\) | 2311.52 | − | 1334.56i | 0.292221 | − | 0.168714i | −0.346722 | − | 0.937968i | \(-0.612705\pi\) |
0.638943 | + | 0.769254i | \(0.279372\pi\) | |||||||
\(398\) | −3587.31 | −0.451798 | ||||||||
\(399\) | 2734.01 | + | 9824.93i | 0.343037 | + | 1.23274i | ||||
\(400\) | −50.5345 | −0.00631681 | ||||||||
\(401\) | 12909.6 | − | 7453.36i | 1.60767 | − | 0.928187i | 0.617777 | − | 0.786353i | \(-0.288033\pi\) |
0.989890 | − | 0.141834i | \(-0.0452999\pi\) | |||||||
\(402\) | −423.479 | − | 476.078i | −0.0525403 | − | 0.0590662i | ||||
\(403\) | 3324.87 | − | 5758.84i | 0.410976 | − | 0.711831i | ||||
\(404\) | −11066.3 | − | 19167.3i | −1.36279 | − | 2.36042i | ||||
\(405\) | 1042.21 | + | 3492.82i | 0.127872 | + | 0.428543i | ||||
\(406\) | 2399.14 | + | 1175.49i | 0.293269 | + | 0.143691i | ||||
\(407\) | 11742.3i | 1.43008i | ||||||||
\(408\) | 4111.42 | − | 847.963i | 0.498886 | − | 0.102893i | ||||
\(409\) | −6740.03 | − | 3891.36i | −0.814849 | − | 0.470453i | 0.0337880 | − | 0.999429i | \(-0.489243\pi\) |
−0.848637 | + | 0.528976i | \(0.822576\pi\) | |||||||
\(410\) | 5824.27 | + | 3362.64i | 0.701561 | + | 0.405047i | ||||
\(411\) | 6832.43 | − | 1409.16i | 0.819998 | − | 0.169121i | ||||
\(412\) | 5002.97i | 0.598249i | ||||||||
\(413\) | 7.85510 | + | 115.316i | 0.000935894 | + | 0.0137393i | ||||
\(414\) | 2456.61 | + | 1830.62i | 0.291632 | + | 0.217319i | ||||
\(415\) | −1576.19 | − | 2730.04i | −0.186438 | − | 0.322921i | ||||
\(416\) | −2037.54 | + | 3529.12i | −0.240140 | + | 0.415935i | ||||
\(417\) | −2225.86 | − | 2502.33i | −0.261393 | − | 0.293860i | ||||
\(418\) | 18785.3 | − | 10845.7i | 2.19813 | − | 1.26909i | ||||
\(419\) | −10191.7 | −1.18830 | −0.594149 | − | 0.804355i | \(-0.702511\pi\) | ||||
−0.594149 | + | 0.804355i | \(0.702511\pi\) | |||||||
\(420\) | 1540.50 | − | 5978.39i | 0.178973 | − | 0.694561i | ||||
\(421\) | 11747.0 | 1.35989 | 0.679946 | − | 0.733262i | \(-0.262003\pi\) | ||||
0.679946 | + | 0.733262i | \(0.262003\pi\) | |||||||
\(422\) | −462.618 | + | 267.093i | −0.0533647 | + | 0.0308101i | ||||
\(423\) | 2956.62 | − | 1273.76i | 0.339848 | − | 0.146412i | ||||
\(424\) | 7135.57 | − | 12359.2i | 0.817296 | − | 1.41560i | ||||
\(425\) | −458.056 | − | 793.377i | −0.0522800 | − | 0.0905516i | ||||
\(426\) | 14400.5 | + | 4775.44i | 1.63781 | + | 0.543124i | ||||
\(427\) | 6611.76 | − | 13494.4i | 0.749334 | − | 1.52937i | ||||
\(428\) | − | 4023.56i | − | 0.454407i | ||||||
\(429\) | 1033.52 | + | 5011.09i | 0.116314 | + | 0.563957i | ||||
\(430\) | 5968.98 | + | 3446.19i | 0.669418 | + | 0.386489i | ||||
\(431\) | 4728.20 | + | 2729.83i | 0.528421 | + | 0.305084i | 0.740373 | − | 0.672196i | \(-0.234649\pi\) |
−0.211952 | + | 0.977280i | \(0.567982\pi\) | |||||||
\(432\) | 120.027 | − | 256.939i | 0.0133676 | − | 0.0286157i | ||||
\(433\) | − | 1450.51i | − | 0.160987i | −0.996755 | − | 0.0804934i | \(-0.974350\pi\) | ||
0.996755 | − | 0.0804934i | \(-0.0256496\pi\) | |||||||
\(434\) | 21249.4 | − | 14277.3i | 2.35024 | − | 1.57911i | ||||
\(435\) | −258.472 | + | 779.429i | −0.0284891 | + | 0.0859098i | ||||
\(436\) | −5073.57 | − | 8787.69i | −0.557294 | − | 0.965261i | ||||
\(437\) | −1317.33 | + | 2281.68i | −0.144202 | + | 0.249766i | ||||
\(438\) | −12680.9 | + | 11279.9i | −1.38338 | + | 1.23054i | ||||
\(439\) | −7329.40 | + | 4231.63i | −0.796841 | + | 0.460056i | −0.842365 | − | 0.538907i | \(-0.818837\pi\) |
0.0455245 | + | 0.998963i | \(0.485504\pi\) | |||||||
\(440\) | −4943.76 | −0.535646 | ||||||||
\(441\) | −8107.75 | − | 4475.55i | −0.875472 | − | 0.483268i | ||||
\(442\) | −3672.10 | −0.395168 | ||||||||
\(443\) | −36.6425 | + | 21.1556i | −0.00392988 | + | 0.00226892i | −0.501964 | − | 0.864889i | \(-0.667389\pi\) |
0.498034 | + | 0.867158i | \(0.334056\pi\) | |||||||
\(444\) | 13042.6 | − | 11601.6i | 1.39408 | − | 1.24006i | ||||
\(445\) | −1754.27 | + | 3038.49i | −0.186877 | + | 0.323681i | ||||
\(446\) | 8175.53 | + | 14160.4i | 0.867987 | + | 1.50340i | ||||
\(447\) | −1980.10 | + | 5971.04i | −0.209520 | + | 0.631813i | ||||
\(448\) | −12773.4 | + | 8582.35i | −1.34707 | + | 0.905085i | ||||
\(449\) | − | 944.250i | − | 0.0992470i | −0.998768 | − | 0.0496235i | \(-0.984198\pi\) | ||
0.998768 | − | 0.0496235i | \(-0.0158021\pi\) | |||||||
\(450\) | 3059.74 | + | 359.046i | 0.320528 | + | 0.0376125i | ||||
\(451\) | −11446.2 | − | 6608.46i | −1.19508 | − | 0.689979i | ||||
\(452\) | −26562.9 | − | 15336.1i | −2.76419 | − | 1.59591i | ||||
\(453\) | 579.595 | + | 2810.22i | 0.0601143 | + | 0.291469i | ||||
\(454\) | 5799.55i | 0.599530i | ||||||||
\(455\) | −894.570 | + | 1825.79i | −0.0921716 | + | 0.188119i | ||||
\(456\) | −11523.1 | − | 3821.26i | −1.18337 | − | 0.392427i | ||||
\(457\) | −4436.67 | − | 7684.53i | −0.454133 | − | 0.786581i | 0.544505 | − | 0.838757i | \(-0.316717\pi\) |
−0.998638 | + | 0.0521768i | \(0.983384\pi\) | |||||||
\(458\) | 6589.60 | − | 11413.5i | 0.672297 | − | 1.16445i | ||||
\(459\) | 5121.82 | − | 444.572i | 0.520841 | − | 0.0452088i | ||||
\(460\) | 1381.25 | − | 797.468i | 0.140003 | − | 0.0808307i | ||||
\(461\) | 8958.04 | 0.905027 | 0.452514 | − | 0.891757i | \(-0.350527\pi\) | ||||
0.452514 | + | 0.891757i | \(0.350527\pi\) | |||||||
\(462\) | −4915.16 | + | 19074.8i | −0.494965 | + | 1.92086i | ||||
\(463\) | −5709.17 | −0.573062 | −0.286531 | − | 0.958071i | \(-0.592502\pi\) | ||||
−0.286531 | + | 0.958071i | \(0.592502\pi\) | |||||||
\(464\) | 55.3297 | − | 31.9446i | 0.00553582 | − | 0.00319611i | ||||
\(465\) | 5229.71 | + | 5879.27i | 0.521552 | + | 0.586333i | ||||
\(466\) | −3744.44 | + | 6485.56i | −0.372227 | + | 0.644716i | ||||
\(467\) | 9120.65 | + | 15797.4i | 0.903754 | + | 1.56535i | 0.822581 | + | 0.568648i | \(0.192533\pi\) |
0.0811730 | + | 0.996700i | \(0.474133\pi\) | |||||||
\(468\) | 4544.86 | − | 6099.00i | 0.448902 | − | 0.602406i | ||||
\(469\) | 33.8163 | + | 496.437i | 0.00332940 | + | 0.0488771i | ||||
\(470\) | − | 2720.96i | − | 0.267039i | ||||||
\(471\) | 11112.9 | − | 2291.98i | 1.08716 | − | 0.224223i | ||||
\(472\) | −119.159 | − | 68.7963i | −0.0116202 | − | 0.00670891i | ||||
\(473\) | −11730.6 | − | 6772.66i | −1.14032 | − | 0.658366i | ||||
\(474\) | −14527.0 | + | 2996.14i | −1.40770 | + | 0.290331i | ||||
\(475\) | 2649.33i | 0.255915i | ||||||||
\(476\) | −7819.50 | − | 3831.27i | −0.752954 | − | 0.368920i | ||||
\(477\) | 10443.1 | − | 14014.2i | 1.00243 | − | 1.34521i | ||||
\(478\) | −7039.23 | − | 12192.3i | −0.673571 | − | 1.16666i | ||||
\(479\) | −4771.66 | + | 8264.76i | −0.455162 | + | 0.788364i | −0.998698 | − | 0.0510220i | \(-0.983752\pi\) |
0.543535 | + | 0.839386i | \(0.317085\pi\) | |||||||
\(480\) | −3204.86 | − | 3602.92i | −0.304752 | − | 0.342604i | ||||
\(481\) | −4978.50 | + | 2874.34i | −0.471934 | + | 0.272471i | ||||
\(482\) | 2602.37 | 0.245923 | ||||||||
\(483\) | −641.405 | − | 2304.95i | −0.0604243 | − | 0.217140i | ||||
\(484\) | 8728.82 | 0.819762 | ||||||||
\(485\) | −2287.81 | + | 1320.87i | −0.214194 | + | 0.123665i | ||||
\(486\) | −9092.88 | + | 14704.3i | −0.848686 | + | 1.37243i | ||||
\(487\) | −3629.41 | + | 6286.32i | −0.337709 | + | 0.584929i | −0.984001 | − | 0.178161i | \(-0.942985\pi\) |
0.646293 | + | 0.763090i | \(0.276319\pi\) | |||||||
\(488\) | 8944.29 | + | 15492.0i | 0.829691 | + | 1.43707i | ||||
\(489\) | 17805.8 | + | 5904.69i | 1.64664 | + | 0.546052i | ||||
\(490\) | −6185.34 | + | 4796.76i | −0.570256 | + | 0.442235i | ||||
\(491\) | 4273.37i | 0.392779i | 0.980526 | + | 0.196390i | \(0.0629218\pi\) | ||||
−0.980526 | + | 0.196390i | \(0.937078\pi\) | |||||||
\(492\) | 3968.78 | + | 19243.0i | 0.363671 | + | 1.76329i | ||||
\(493\) | 1003.04 | + | 579.107i | 0.0916325 | + | 0.0529040i | ||||
\(494\) | 9196.72 | + | 5309.73i | 0.837611 | + | 0.483595i | ||||
\(495\) | −6013.18 | − | 705.619i | −0.546005 | − | 0.0640711i | ||||
\(496\) | − | 612.204i | − | 0.0554209i | ||||||
\(497\) | −6607.65 | − | 9834.39i | −0.596366 | − | 0.887591i | ||||
\(498\) | 4706.32 | − | 14192.0i | 0.423484 | − | 1.27703i | ||||
\(499\) | 570.563 | + | 988.245i | 0.0511862 | + | 0.0886571i | 0.890483 | − | 0.455016i | \(-0.150366\pi\) |
−0.839297 | + | 0.543673i | \(0.817033\pi\) | |||||||
\(500\) | 801.909 | − | 1388.95i | 0.0717250 | − | 0.124231i | ||||
\(501\) | 6783.93 | − | 6034.41i | 0.604957 | − | 0.538119i | ||||
\(502\) | 14541.5 | − | 8395.54i | 1.29287 | − | 0.746437i | ||||
\(503\) | −8487.44 | −0.752358 | −0.376179 | − | 0.926547i | \(-0.622762\pi\) | ||||
−0.376179 | + | 0.926547i | \(0.622762\pi\) | |||||||
\(504\) | 9804.99 | − | 5039.96i | 0.866565 | − | 0.445432i | ||||
\(505\) | −8624.93 | −0.760009 | ||||||||
\(506\) | −4407.06 | + | 2544.42i | −0.387189 | + | 0.223544i | ||||
\(507\) | 6658.11 | − | 5922.50i | 0.583229 | − | 0.518792i | ||||
\(508\) | −15505.4 | + | 26856.1i | −1.35421 | + | 2.34557i | ||||
\(509\) | −332.930 | − | 576.652i | −0.0289919 | − | 0.0502154i | 0.851165 | − | 0.524898i | \(-0.175896\pi\) |
−0.880157 | + | 0.474682i | \(0.842563\pi\) | |||||||
\(510\) | 1367.70 | − | 4124.35i | 0.118751 | − | 0.358097i | ||||
\(511\) | 13223.2 | − | 900.740i | 1.14474 | − | 0.0779773i | ||||
\(512\) | 731.690i | 0.0631571i | ||||||||
\(513\) | −13470.4 | − | 6292.55i | −1.15932 | − | 0.541565i | ||||
\(514\) | 18753.1 | + | 10827.1i | 1.60927 | + | 0.929113i | ||||
\(515\) | 1688.43 | + | 974.815i | 0.144468 | + | 0.0834087i | ||||
\(516\) | 4067.39 | + | 19721.1i | 0.347009 | + | 1.68250i | ||||
\(517\) | 5347.39i | 0.454889i | ||||||||
\(518\) | −22080.3 | + | 1504.06i | −1.87288 | + | 0.127577i | ||||
\(519\) | 17289.8 | + | 5733.58i | 1.46230 | + | 0.484925i | ||||
\(520\) | −1210.16 | − | 2096.06i | −0.102056 | − | 0.176766i | ||||
\(521\) | −4394.33 | + | 7611.20i | −0.369518 | + | 0.640024i | −0.989490 | − | 0.144600i | \(-0.953811\pi\) |
0.619972 | + | 0.784624i | \(0.287144\pi\) | |||||||
\(522\) | −3577.05 | + | 1541.05i | −0.299929 | + | 0.129215i | ||||
\(523\) | 9827.76 | − | 5674.06i | 0.821679 | − | 0.474396i | −0.0293162 | − | 0.999570i | \(-0.509333\pi\) |
0.850995 | + | 0.525174i | \(0.176000\pi\) | |||||||
\(524\) | 18447.7 | 1.53796 | ||||||||
\(525\) | −1717.46 | − | 1684.77i | −0.142773 | − | 0.140056i | ||||
\(526\) | −3768.00 | −0.312344 | ||||||||
\(527\) | 9611.42 | − | 5549.16i | 0.794460 | − | 0.458681i | ||||
\(528\) | 313.074 | + | 351.960i | 0.0258045 | + | 0.0290096i | ||||
\(529\) | −5774.45 | + | 10001.6i | −0.474599 | + | 0.822030i | ||||
\(530\) | −7385.87 | − | 12792.7i | −0.605324 | − | 1.04845i | ||||
\(531\) | −135.116 | − | 100.686i | −0.0110424 | − | 0.00822859i | ||||
\(532\) | 14043.9 | + | 20902.1i | 1.14451 | + | 1.70342i | ||||
\(533\) | − | 6470.62i | − | 0.525842i | ||||||
\(534\) | −16298.3 | + | 3361.46i | −1.32078 | + | 0.272406i | ||||
\(535\) | −1357.89 | − | 783.980i | −0.109732 | − | 0.0633540i | ||||
\(536\) | −512.980 | − | 296.169i | −0.0413383 | − | 0.0238667i | ||||
\(537\) | −10195.9 | + | 2102.85i | −0.819338 | + | 0.168985i | ||||
\(538\) | − | 18741.4i | − | 1.50186i | ||||||
\(539\) | 12155.8 | − | 9426.86i | 0.971405 | − | 0.753328i | ||||
\(540\) | 5157.36 | + | 7376.21i | 0.410996 | + | 0.587818i | ||||
\(541\) | −9438.27 | − | 16347.6i | −0.750061 | − | 1.29914i | −0.947793 | − | 0.318887i | \(-0.896691\pi\) |
0.197732 | − | 0.980256i | \(-0.436643\pi\) | |||||||
\(542\) | −11313.2 | + | 19595.0i | −0.896572 | + | 1.55291i | ||||
\(543\) | −3765.28 | − | 4232.95i | −0.297576 | − | 0.334537i | ||||
\(544\) | −5890.05 | + | 3400.62i | −0.464216 | + | 0.268016i | ||||
\(545\) | −3954.29 | −0.310795 | ||||||||
\(546\) | −9290.51 | + | 2585.30i | −0.728199 | + | 0.202638i | ||||
\(547\) | 15999.4 | 1.25061 | 0.625307 | − | 0.780379i | \(-0.284974\pi\) | ||||
0.625307 | + | 0.780379i | \(0.284974\pi\) | |||||||
\(548\) | 14918.2 | − | 8613.00i | 1.16291 | − | 0.671404i | ||||
\(549\) | 8667.94 | + | 20119.8i | 0.673841 | + | 1.56410i | ||||
\(550\) | −2558.59 | + | 4431.61i | −0.198361 | + | 0.343571i | ||||
\(551\) | −1674.74 | − | 2900.73i | −0.129485 | − | 0.224274i | ||||
\(552\) | 2703.34 | + | 896.474i | 0.208446 | + | 0.0691241i | ||||
\(553\) | 10402.0 | + | 5096.58i | 0.799885 | + | 0.391914i | ||||
\(554\) | 10464.5i | 0.802515i | ||||||||
\(555\) | −1374.05 | − | 6662.21i | −0.105091 | − | 0.509541i | ||||
\(556\) | −7161.69 | − | 4134.80i | −0.546265 | − | 0.315386i | ||||
\(557\) | −11300.4 | − | 6524.27i | −0.859627 | − | 0.496306i | 0.00426065 | − | 0.999991i | \(-0.498644\pi\) |
−0.863887 | + | 0.503685i | \(0.831977\pi\) | |||||||
\(558\) | −4349.70 | + | 37067.5i | −0.329995 | + | 2.81217i | ||||
\(559\) | − | 6631.40i | − | 0.501750i | ||||||
\(560\) | 12.7210 | + | 186.750i | 0.000959929 | + | 0.0140922i | ||||
\(561\) | −2687.89 | + | 8105.41i | −0.202287 | + | 0.610001i | ||||
\(562\) | −9808.74 | − | 16989.2i | −0.736222 | − | 1.27517i | ||||
\(563\) | 1062.90 | − | 1840.99i | 0.0795661 | − | 0.137813i | −0.823497 | − | 0.567321i | \(-0.807980\pi\) |
0.903063 | + | 0.429508i | \(0.141313\pi\) | |||||||
\(564\) | 5939.53 | − | 5283.31i | 0.443438 | − | 0.394446i | ||||
\(565\) | −10351.4 | + | 5976.41i | −0.770776 | + | 0.445008i | ||||
\(566\) | −7663.68 | −0.569132 | ||||||||
\(567\) | 12645.3 | − | 4730.73i | 0.936603 | − | 0.350392i | ||||
\(568\) | 14104.2 | 1.04190 | ||||||||
\(569\) | 22953.8 | − | 13252.4i | 1.69116 | − | 0.976394i | 0.737583 | − | 0.675257i | \(-0.235967\pi\) |
0.953581 | − | 0.301137i | \(-0.0973661\pi\) | |||||||
\(570\) | −9389.05 | + | 8351.71i | −0.689937 | + | 0.613710i | ||||
\(571\) | −10310.6 | + | 17858.5i | −0.755667 | + | 1.30885i | 0.189375 | + | 0.981905i | \(0.439354\pi\) |
−0.945042 | + | 0.326949i | \(0.893979\pi\) | |||||||
\(572\) | 6317.00 | + | 10941.4i | 0.461761 | + | 0.799793i | ||||
\(573\) | −1782.51 | + | 5375.22i | −0.129957 | + | 0.391890i | ||||
\(574\) | 10960.5 | − | 22370.0i | 0.797006 | − | 1.62666i | ||||
\(575\) | − | 621.538i | − | 0.0450782i | ||||||
\(576\) | 2614.68 | − | 22281.9i | 0.189141 | − | 1.61183i | ||||
\(577\) | 12030.2 | + | 6945.61i | 0.867976 | + | 0.501126i | 0.866675 | − | 0.498873i | \(-0.166253\pi\) |
0.00130062 | + | 0.999999i | \(0.499586\pi\) | |||||||
\(578\) | 14111.4 | + | 8147.24i | 1.01550 | + | 0.586299i | ||||
\(579\) | −5192.24 | − | 25175.0i | −0.372680 | − | 1.80697i | ||||
\(580\) | 2027.66i | 0.145162i | ||||||||
\(581\) | −9692.04 | + | 6512.01i | −0.692072 | + | 0.464998i | ||||
\(582\) | −11893.1 | − | 3943.96i | −0.847054 | − | 0.280897i | ||||
\(583\) | 14515.1 | + | 25141.0i | 1.03114 | + | 1.78599i | ||||
\(584\) | −7888.84 | + | 13663.9i | −0.558977 | + | 0.968177i | ||||
\(585\) | −1172.77 | − | 2722.20i | −0.0828856 | − | 0.192392i | ||||
\(586\) | −13555.0 | + | 7825.96i | −0.955546 | + | 0.551685i | ||||
\(587\) | −1785.23 | −0.125527 | −0.0627634 | − | 0.998028i | \(-0.519991\pi\) | ||||
−0.0627634 | + | 0.998028i | \(0.519991\pi\) | |||||||
\(588\) | −22480.9 | − | 4187.97i | −1.57669 | − | 0.293723i | ||||
\(589\) | −32095.5 | −2.24529 | ||||||||
\(590\) | −123.339 | + | 71.2096i | −0.00860639 | + | 0.00496890i | ||||
\(591\) | −11383.8 | − | 12797.8i | −0.792330 | − | 0.890743i | ||||
\(592\) | −264.625 | + | 458.343i | −0.0183716 | + | 0.0318206i | ||||
\(593\) | −3382.75 | − | 5859.10i | −0.234255 | − | 0.405741i | 0.724801 | − | 0.688958i | \(-0.241932\pi\) |
−0.959056 | + | 0.283217i | \(0.908598\pi\) | |||||||
\(594\) | −16455.2 | − | 23534.7i | −1.13664 | − | 1.62566i | ||||
\(595\) | −2816.61 | + | 1892.46i | −0.194067 | + | 0.130392i | ||||
\(596\) | 15533.5i | 1.06758i | ||||||||
\(597\) | −3999.95 | + | 824.972i | −0.274216 | + | 0.0565559i | ||||
\(598\) | −2157.57 | − | 1245.67i | −0.147541 | − | 0.0851829i | ||||
\(599\) | −22410.2 | − | 12938.5i | −1.52864 | − | 0.882561i | −0.999419 | − | 0.0340772i | \(-0.989151\pi\) |
−0.529221 | − | 0.848484i | \(-0.677516\pi\) | |||||||
\(600\) | 2804.94 | − | 578.506i | 0.190852 | − | 0.0393624i | ||||
\(601\) | 21917.8i | 1.48760i | 0.668403 | + | 0.743799i | \(0.266978\pi\) | ||||
−0.668403 | + | 0.743799i | \(0.733022\pi\) | |||||||
\(602\) | 11232.8 | − | 22925.8i | 0.760490 | − | 1.55214i | ||||
\(603\) | −581.674 | − | 433.453i | −0.0392829 | − | 0.0292729i | ||||
\(604\) | 3542.58 | + | 6135.92i | 0.238651 | + | 0.413356i | ||||
\(605\) | 1700.79 | − | 2945.85i | 0.114292 | − | 0.197960i | ||||
\(606\) | −27189.1 | − | 30566.2i | −1.82258 | − | 2.04895i | ||||
\(607\) | −10602.4 | + | 6121.27i | −0.708956 | + | 0.409316i | −0.810674 | − | 0.585497i | \(-0.800899\pi\) |
0.101718 | + | 0.994813i | \(0.467566\pi\) | |||||||
\(608\) | 19668.7 | 1.31196 | ||||||||
\(609\) | 2945.44 | + | 758.975i | 0.195985 | + | 0.0505012i | ||||
\(610\) | 18516.1 | 1.22901 | ||||||||
\(611\) | −2267.19 | + | 1308.96i | −0.150116 | + | 0.0866693i | ||||
\(612\) | 11658.6 | − | 5022.75i | 0.770054 | − | 0.331752i | ||||
\(613\) | 9316.91 | − | 16137.4i | 0.613877 | − | 1.06327i | −0.376704 | − | 0.926334i | \(-0.622943\pi\) |
0.990580 | − | 0.136932i | \(-0.0437242\pi\) | |||||||
\(614\) | 1656.96 | + | 2869.94i | 0.108908 | + | 0.188634i | ||||
\(615\) | 7267.53 | + | 2410.04i | 0.476512 | + | 0.158020i | ||||
\(616\) | 1244.49 | + | 18269.6i | 0.0813991 | + | 1.19497i | ||||
\(617\) | − | 11465.5i | − | 0.748112i | −0.927406 | − | 0.374056i | \(-0.877967\pi\) | ||
0.927406 | − | 0.374056i | \(-0.122033\pi\) | |||||||
\(618\) | 1867.90 | + | 9056.68i | 0.121582 | + | 0.589503i | ||||
\(619\) | −5119.14 | − | 2955.53i | −0.332400 | − | 0.191911i | 0.324506 | − | 0.945884i | \(-0.394802\pi\) |
−0.656906 | + | 0.753972i | \(0.728135\pi\) | |||||||
\(620\) | 16826.5 | + | 9714.79i | 1.08995 | + | 0.629283i | ||||
\(621\) | 3160.17 | + | 1476.24i | 0.204208 | + | 0.0953939i | ||||
\(622\) | − | 30672.1i | − | 1.97723i | ||||||
\(623\) | 11670.3 | + | 5718.01i | 0.750499 | + | 0.367717i | ||||
\(624\) | −72.5883 | + | 218.892i | −0.00465682 | + | 0.0140428i | ||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 13729.6 | − | 23780.4i | 0.876592 | − | 1.51830i | ||||
\(627\) | 18451.9 | − | 16413.3i | 1.17528 | − | 1.04543i | ||||
\(628\) | 24264.2 | − | 14008.9i | 1.54179 | − | 0.890155i | ||||
\(629\) | −9594.47 | −0.608198 | ||||||||
\(630\) | 556.626 | − | 11397.6i | 0.0352008 | − | 0.720781i | ||||
\(631\) | −6488.94 | −0.409383 | −0.204691 | − | 0.978827i | \(-0.565619\pi\) | ||||
−0.204691 | + | 0.978827i | \(0.565619\pi\) | |||||||
\(632\) | −11941.7 | + | 6894.57i | −0.751609 | + | 0.433942i | ||||
\(633\) | −454.409 | + | 404.204i | −0.0285326 | + | 0.0253802i | ||||
\(634\) | −11783.3 | + | 20409.2i | −0.738128 | + | 1.27847i | ||||
\(635\) | 6042.38 | + | 10465.7i | 0.377613 | + | 0.654045i | ||||
\(636\) | 13583.7 | − | 40962.2i | 0.846904 | − | 2.55386i | ||||
\(637\) | 6972.37 | + | 2846.27i | 0.433682 | + | 0.177038i | ||||
\(638\) | − | 6469.50i | − | 0.401458i | ||||||
\(639\) | 17155.1 | + | 2013.08i | 1.06204 | + | 0.124626i | ||||
\(640\) | −9992.00 | − | 5768.88i | −0.617138 | − | 0.356305i | ||||
\(641\) | 5980.20 | + | 3452.67i | 0.368493 | + | 0.212749i | 0.672800 | − | 0.739825i | \(-0.265092\pi\) |
−0.304307 | + | 0.952574i | \(0.598425\pi\) | |||||||
\(642\) | −1502.23 | − | 7283.69i | −0.0923493 | − | 0.447764i | ||||
\(643\) | − | 25890.4i | − | 1.58790i | −0.607983 | − | 0.793950i | \(-0.708021\pi\) | ||
0.607983 | − | 0.793950i | \(-0.291979\pi\) | |||||||
\(644\) | −3294.74 | − | 4903.67i | −0.201601 | − | 0.300049i | ||||
\(645\) | 7448.10 | + | 2469.92i | 0.454680 | + | 0.150780i | ||||
\(646\) | 8861.87 | + | 15349.2i | 0.539730 | + | 0.934840i | ||||
\(647\) | −10178.6 | + | 17629.8i | −0.618487 | + | 1.07125i | 0.371275 | + | 0.928523i | \(0.378921\pi\) |
−0.989762 | + | 0.142728i | \(0.954413\pi\) | |||||||
\(648\) | −3720.76 | + | 15635.6i | −0.225563 | + | 0.947874i | ||||
\(649\) | 242.392 | − | 139.945i | 0.0146606 | − | 0.00846430i | ||||
\(650\) | −2505.22 | −0.151174 | ||||||||
\(651\) | 20410.3 | − | 20806.3i | 1.22879 | − | 1.25263i | ||||
\(652\) | 46321.2 | 2.78233 | ||||||||
\(653\) | 15369.4 | − | 8873.52i | 0.921058 | − | 0.531773i | 0.0370853 | − | 0.999312i | \(-0.488193\pi\) |
0.883972 | + | 0.467539i | \(0.154859\pi\) | |||||||
\(654\) | −12465.4 | − | 14013.7i | −0.745317 | − | 0.837891i | ||||
\(655\) | 3594.48 | − | 6225.82i | 0.214424 | − | 0.371394i | ||||
\(656\) | −297.857 | − | 515.904i | −0.0177277 | − | 0.0307053i | ||||
\(657\) | −11545.6 | + | 15493.6i | −0.685595 | + | 0.920038i | ||||
\(658\) | −10055.3 | + | 684.944i | −0.595737 | + | 0.0405804i | ||||
\(659\) | 346.589i | 0.0204874i | 0.999948 | + | 0.0102437i | \(0.00326073\pi\) | ||||
−0.999948 | + | 0.0102437i | \(0.996739\pi\) | |||||||
\(660\) | −14641.7 | + | 3019.79i | −0.863526 | + | 0.178099i | ||||
\(661\) | −2606.71 | − | 1504.98i | −0.153388 | − | 0.0885584i | 0.421342 | − | 0.906902i | \(-0.361559\pi\) |
−0.574729 | + | 0.818344i | \(0.694893\pi\) | |||||||
\(662\) | 12659.2 | + | 7308.79i | 0.743223 | + | 0.429100i | ||||
\(663\) | −4094.50 | + | 844.473i | −0.239845 | + | 0.0494670i | ||||
\(664\) | − | 13900.0i | − | 0.812386i | ||||||
\(665\) | 9790.57 | − | 666.914i | 0.570920 | − | 0.0388899i | ||||
\(666\) | 19278.9 | − | 25871.4i | 1.12168 | − | 1.50525i | ||||
\(667\) | 392.897 | + | 680.517i | 0.0228081 | + | 0.0395048i | ||||
\(668\) | 11209.6 | − | 19415.6i | 0.649272 | − | 1.12457i | ||||
\(669\) | 12372.4 | + | 13909.1i | 0.715015 | + | 0.803825i | ||||
\(670\) | −530.974 | + | 306.558i | −0.0306169 | + | 0.0176767i | ||||
\(671\) | −36388.9 | −2.09356 | ||||||||
\(672\) | −12507.8 | + | 12750.5i | −0.718004 | + | 0.731934i | ||||
\(673\) | −21537.4 | −1.23359 | −0.616795 | − | 0.787124i | \(-0.711569\pi\) | ||||
−0.616795 | + | 0.787124i | \(0.711569\pi\) | |||||||
\(674\) | −46524.6 | + | 26861.0i | −2.65884 | + | 1.53508i | ||||
\(675\) | 3494.26 | − | 303.301i | 0.199251 | − | 0.0172949i | ||||
\(676\) | 11001.7 | − | 19055.6i | 0.625952 | − | 1.08418i | ||||
\(677\) | −3113.61 | − | 5392.93i | −0.176759 | − | 0.306155i | 0.764010 | − | 0.645205i | \(-0.223228\pi\) |
−0.940769 | + | 0.339050i | \(0.889895\pi\) | |||||||
\(678\) | −53811.7 | − | 17844.9i | −3.04812 | − | 1.01081i | ||||
\(679\) | 5457.15 | + | 8122.06i | 0.308433 | + | 0.459052i | ||||
\(680\) | − | 4039.48i | − | 0.227805i | ||||||
\(681\) | 1333.72 | + | 6466.66i | 0.0750490 | + | 0.363881i | ||||
\(682\) | −53687.0 | − | 30996.2i | −3.01434 | − | 1.74033i | ||||
\(683\) | −10377.9 | − | 5991.66i | −0.581402 | − | 0.335673i | 0.180288 | − | 0.983614i | \(-0.442297\pi\) |
−0.761690 | + | 0.647941i | \(0.775630\pi\) | |||||||
\(684\) | −36461.6 | − | 4278.60i | −2.03822 | − | 0.239176i | ||||
\(685\) | − | 6712.88i | − | 0.374432i | ||||||
\(686\) | 19283.4 | + | 21650.4i | 1.07324 | + | 1.20498i | ||||
\(687\) | 4722.82 | − | 14241.8i | 0.262281 | − | 0.790915i | ||||
\(688\) | −305.258 | − | 528.722i | −0.0169155 | − | 0.0292985i | ||||
\(689\) | −7106.20 | + | 12308.3i | −0.392924 | + | 0.680564i | ||||
\(690\) | 2202.69 | − | 1959.33i | 0.121529 | − | 0.108102i | ||||
\(691\) | 21090.2 | − | 12176.5i | 1.16109 | − | 0.670354i | 0.209522 | − | 0.977804i | \(-0.432809\pi\) |
0.951564 | + | 0.307450i | \(0.0994758\pi\) | |||||||
\(692\) | 44978.8 | 2.47086 | ||||||||
\(693\) | −1093.91 | + | 22399.3i | −0.0599630 | + | 1.22782i | ||||
\(694\) | 4269.94 | 0.233551 | ||||||||
\(695\) | −2790.87 | + | 1611.31i | −0.152322 | + | 0.0879432i | ||||
\(696\) | −2705.41 | + | 2406.50i | −0.147339 | + | 0.131061i | ||||
\(697\) | 5399.70 | − | 9352.55i | 0.293441 | − | 0.508254i | ||||
\(698\) | 13693.1 | + | 23717.1i | 0.742536 | + | 1.28611i | ||||
\(699\) | −2683.67 | + | 8092.69i | −0.145216 | + | 0.437902i | ||||
\(700\) | −5334.70 | − | 2613.81i | −0.288047 | − | 0.141132i | ||||
\(701\) | 23347.4i | 1.25794i | 0.777428 | + | 0.628972i | \(0.216524\pi\) | ||||
−0.777428 | + | 0.628972i | \(0.783476\pi\) | |||||||
\(702\) | 5950.27 | − | 12737.6i | 0.319912 | − | 0.684831i | ||||
\(703\) | 24029.2 | + | 13873.3i | 1.28916 | + | 0.744296i | ||||
\(704\) | 32272.3 | + | 18632.4i | 1.72771 | + | 0.997494i | ||||
\(705\) | −625.738 | − | 3033.94i | −0.0334279 | − | 0.162078i | ||||
\(706\) | 30955.7i | 1.65019i | ||||||||
\(707\) | 2171.15 | + | 31873.3i | 0.115494 | + | 1.69550i | ||||
\(708\) | −394.930 | − | 130.965i | −0.0209638 | − | 0.00695195i | ||||
\(709\) | 3202.09 | + | 5546.19i | 0.169615 | + | 0.293782i | 0.938285 | − | 0.345864i | \(-0.112414\pi\) |
−0.768669 | + | 0.639646i | \(0.779081\pi\) | |||||||
\(710\) | 7299.45 | − | 12643.0i | 0.385836 | − | 0.668288i | ||||
\(711\) | −15509.0 | + | 6681.55i | −0.818050 | + | 0.352430i | ||||
\(712\) | −13397.8 | + | 7735.24i | −0.705204 | + | 0.407149i | ||||
\(713\) | 7529.67 | 0.395496 | ||||||||
\(714\) | −15585.8 | − | 4016.12i | −0.816923 | − | 0.210503i | ||||
\(715\) | 4923.41 | 0.257518 | ||||||||
\(716\) | −22262.0 | + | 12853.0i | −1.16197 | + | 0.670863i | ||||
\(717\) | −10652.8 | − | 11975.9i | −0.554862 | − | 0.623779i | ||||
\(718\) | −1040.53 | + | 1802.25i | −0.0540839 | + | 0.0936760i | ||||
\(719\) | −11057.5 | − | 19152.2i | −0.573541 | − | 0.993403i | −0.996198 | − | 0.0871132i | \(-0.972236\pi\) |
0.422657 | − | 0.906290i | \(-0.361098\pi\) | |||||||
\(720\) | −218.814 | − | 163.056i | −0.0113260 | − | 0.00843992i | ||||
\(721\) | 3177.39 | − | 6484.96i | 0.164122 | − | 0.334969i | ||||
\(722\) | − | 19951.0i | − | 1.02839i | ||||||
\(723\) | 2901.72 | − | 598.467i | 0.149262 | − | 0.0307845i | ||||
\(724\) | −12114.7 | − | 6994.45i | −0.621879 | − | 0.359042i | ||||
\(725\) | 684.307 | + | 395.085i | 0.0350545 | + | 0.0202387i | ||||
\(726\) | 15801.4 | − | 3258.98i | 0.807778 | − | 0.166601i | ||||
\(727\) | − | 2412.41i | − | 0.123069i | −0.998105 | − | 0.0615346i | \(-0.980401\pi\) | ||
0.998105 | − | 0.0615346i | \(-0.0195994\pi\) | |||||||
\(728\) | −7441.33 | + | 4999.77i | −0.378838 | + | 0.254538i | ||||
\(729\) | −6757.27 | + | 18486.7i | −0.343305 | + | 0.939224i | ||||
\(730\) | 8165.57 | + | 14143.2i | 0.414002 | + | 0.717072i | ||||
\(731\) | 5533.86 | − | 9584.92i | 0.279996 | − | 0.484967i | ||||
\(732\) | 35952.8 | + | 40418.4i | 1.81538 | + | 2.04086i | ||||
\(733\) | −25158.3 | + | 14525.2i | −1.26773 | + | 0.731923i | −0.974557 | − | 0.224138i | \(-0.928043\pi\) |
−0.293170 | + | 0.956060i | \(0.594710\pi\) | |||||||
\(734\) | −23968.8 | −1.20532 | ||||||||
\(735\) | −5793.72 | + | 6770.96i | −0.290755 | + | 0.339797i | ||||
\(736\) | −4614.32 | −0.231095 | ||||||||
\(737\) | 1043.50 | − | 602.466i | 0.0521545 | − | 0.0301114i | ||||
\(738\) | 14369.0 | + | 33353.0i | 0.716710 | + | 1.66361i | ||||
\(739\) | 17961.7 | − | 31110.6i | 0.894089 | − | 1.54861i | 0.0591619 | − | 0.998248i | \(-0.481157\pi\) |
0.834928 | − | 0.550360i | \(-0.185510\pi\) | |||||||
\(740\) | −8398.42 | − | 14546.5i | −0.417206 | − | 0.722621i | ||||
\(741\) | 11475.7 | + | 3805.53i | 0.568920 | + | 0.188663i | ||||
\(742\) | −45416.1 | + | 30514.7i | −2.24700 | + | 1.50974i | ||||
\(743\) | 707.501i | 0.0349337i | 0.999847 | + | 0.0174668i | \(0.00556015\pi\) | ||||
−0.999847 | + | 0.0174668i | \(0.994440\pi\) | |||||||
\(744\) | 7008.36 | + | 33980.6i | 0.345348 | + | 1.67445i | ||||
\(745\) | 5242.33 | + | 3026.66i | 0.257804 | + | 0.148843i | ||||
\(746\) | 2197.58 | + | 1268.77i | 0.107854 | + | 0.0622695i | ||||
\(747\) | 1983.94 | − | 16906.8i | 0.0971733 | − | 0.828096i | ||||
\(748\) | 21086.0i | 1.03072i | ||||||||
\(749\) | −2555.37 | + | 5215.43i | −0.124661 | + | 0.254429i | ||||
\(750\) | 933.090 | − | 2813.76i | 0.0454288 | − | 0.136992i | ||||
\(751\) | 9718.47 | + | 16832.9i | 0.472213 | + | 0.817897i | 0.999494 | − | 0.0317938i | \(-0.0101220\pi\) |
−0.527281 | + | 0.849691i | \(0.676789\pi\) | |||||||
\(752\) | −120.509 | + | 208.728i | −0.00584376 | + | 0.0101217i | ||||
\(753\) | 14283.5 | − | 12705.4i | 0.691259 | − | 0.614886i | ||||
\(754\) | 2742.94 | − | 1583.64i | 0.132483 | − | 0.0764891i | ||||
\(755\) | 2761.05 | 0.133092 | ||||||||
\(756\) | 25960.4 | − | 20915.8i | 1.24890 | − | 1.00622i | ||||
\(757\) | 10730.3 | 0.515190 | 0.257595 | − | 0.966253i | \(-0.417070\pi\) | ||||
0.257595 | + | 0.966253i | \(0.417070\pi\) | |||||||
\(758\) | −3066.48 | + | 1770.44i | −0.146939 | + | 0.0848352i | ||||
\(759\) | −4328.86 | + | 3850.59i | −0.207019 | + | 0.184147i | ||||
\(760\) | −5840.95 | + | 10116.8i | −0.278781 | + | 0.482862i | ||||
\(761\) | −608.496 | − | 1053.95i | −0.0289855 | − | 0.0502043i | 0.851169 | − | 0.524892i | \(-0.175894\pi\) |
−0.880154 | + | 0.474688i | \(0.842561\pi\) | |||||||
\(762\) | −18041.9 | + | 54405.7i | −0.857726 | + | 2.58650i | ||||
\(763\) | 995.410 | + | 14613.0i | 0.0472297 | + | 0.693352i | ||||
\(764\) | 13983.5i | 0.662179i | ||||||||
\(765\) | 576.553 | − | 4913.30i | 0.0272488 | − | 0.232210i | ||||
\(766\) | 23603.6 | + | 13627.5i | 1.11336 | + | 0.642798i | ||||
\(767\) | 118.668 | + | 68.5131i | 0.00558652 | + | 0.00322538i | ||||
\(768\) | −4077.07 | − | 19768.0i | −0.191561 | − | 0.928799i | ||||
\(769\) | − | 40387.9i | − | 1.89392i | −0.321349 | − | 0.946961i | \(-0.604136\pi\) | ||
0.321349 | − | 0.946961i | \(-0.395864\pi\) | |||||||
\(770\) | 17021.0 | + | 8339.67i | 0.796617 | + | 0.390313i | ||||
\(771\) | 23400.2 | + | 7759.89i | 1.09304 | + | 0.362472i | ||||
\(772\) | −31735.7 | − | 54967.9i | −1.47953 | − | 2.56262i | ||||
\(773\) | 11554.8 | − | 20013.6i | 0.537644 | − | 0.931226i | −0.461387 | − | 0.887199i | \(-0.652648\pi\) |
0.999030 | − | 0.0440271i | \(-0.0140188\pi\) | |||||||
\(774\) | 14726.1 | + | 34181.7i | 0.683873 | + | 1.58738i | ||||
\(775\) | 6557.21 | − | 3785.81i | 0.303925 | − | 0.175471i | ||||
\(776\) | −11648.4 | −0.538857 | ||||||||
\(777\) | −24274.2 | + | 6754.87i | −1.12076 | + | 0.311878i | ||||
\(778\) | 3569.42 | 0.164486 | ||||||||
\(779\) | −27046.9 | + | 15615.5i | −1.24397 | + | 0.718208i | ||||
\(780\) | −4864.41 | − | 5468.60i | −0.223300 | − | 0.251035i | ||||
\(781\) | −14345.3 | + | 24846.8i | −0.657254 | + | 1.13840i | ||||
\(782\) | −2079.01 | − | 3600.96i | −0.0950708 | − | 0.164667i | ||||
\(783\) | −3634.11 | + | 2540.93i | −0.165865 | + | 0.115971i | ||||
\(784\) | 686.929 | − | 94.0206i | 0.0312923 | − | 0.00428301i | ||||
\(785\) | − | 10918.4i | − | 0.496427i | ||||||
\(786\) | 33395.1 | − | 6887.59i | 1.51547 | − | 0.312560i | ||||
\(787\) | −6494.51 | − | 3749.61i | −0.294161 | − | 0.169834i | 0.345656 | − | 0.938361i | \(-0.387656\pi\) |
−0.639817 | + | 0.768528i | \(0.720990\pi\) | |||||||
\(788\) | −36627.3 | − | 21146.8i | −1.65583 | − | 0.955993i | ||||
\(789\) | −4201.43 | + | 866.527i | −0.189575 | + | 0.0390991i | ||||
\(790\) | 14272.8i | 0.642791i | ||||||||
\(791\) | 24691.5 | + | 36749.2i | 1.10990 | + | 1.65190i | ||||
\(792\) | −21406.4 | − | 15951.7i | −0.960410 | − | 0.715680i | ||||
\(793\) | −8907.48 | − | 15428.2i | −0.398882 | − | 0.690885i | ||||
\(794\) | 6090.98 | − | 10549.9i | 0.272243 | − | 0.471538i | ||||
\(795\) | −11177.4 | − | 12565.7i | −0.498643 | − | 0.560578i | ||||
\(796\) | −8733.62 | + | 5042.36i | −0.388888 | + | 0.224525i | ||||
\(797\) | 38280.7 | 1.70134 | 0.850672 | − | 0.525697i | \(-0.176195\pi\) | ||||
0.850672 | + | 0.525697i | \(0.176195\pi\) | |||||||
\(798\) | 33227.1 | + | 32594.8i | 1.47397 | + | 1.44592i | ||||
\(799\) | −4369.28 | −0.193460 | ||||||||
\(800\) | −4018.37 | + | 2320.01i | −0.177589 | + | 0.102531i | ||||
\(801\) | −17400.1 | + | 7496.25i | −0.767542 | + | 0.330670i | ||||
\(802\) | 34017.5 | − | 58920.1i | 1.49776 | − | 2.59419i | ||||
\(803\) | −16047.5 | − | 27795.0i | −0.705234 | − | 1.22150i | ||||
\(804\) | −1700.18 | − | 563.807i | −0.0745779 | − | 0.0247313i | ||||
\(805\) | −2296.89 | + | 156.459i | −0.100565 | + | 0.00685027i | ||||
\(806\) | − | 30349.7i | − | 1.32633i | ||||||
\(807\) | −4309.96 | − | 20897.2i | −0.188002 | − | 0.911544i | ||||
\(808\) | −32935.4 | − | 19015.3i | −1.43399 | − | 0.827915i | ||||
\(809\) | 24427.1 | + | 14103.0i | 1.06157 | + | 0.612899i | 0.925867 | − | 0.377850i | \(-0.123337\pi\) |
0.135706 | + | 0.990749i | \(0.456670\pi\) | |||||||
\(810\) | 12090.1 | + | 11427.3i | 0.524450 | + | 0.495698i | ||||
\(811\) | − | 14044.9i | − | 0.608116i | −0.952654 | − | 0.304058i | \(-0.901658\pi\) | ||
0.952654 | − | 0.304058i | \(-0.0983417\pi\) | |||||||
\(812\) | 7493.20 | − | 510.422i | 0.323842 | − | 0.0220595i | ||||
\(813\) | −8108.25 | + | 24450.6i | −0.349777 | + | 1.05476i | ||||
\(814\) | 26796.2 | + | 46412.3i | 1.15382 | + | 1.99847i | ||||
\(815\) | 9025.57 | − | 15632.7i | 0.387916 | − | 0.671891i | ||||
\(816\) | −287.582 | + | 255.809i | −0.0123375 | + | 0.0109744i | ||||
\(817\) | −27718.9 | + | 16003.5i | −1.18698 | + | 0.685302i | ||||
\(818\) | −35520.7 | −1.51828 | ||||||||
\(819\) | −9764.63 | + | 5019.21i | −0.416610 | + | 0.214146i | ||||
\(820\) | 18906.3 | 0.805165 | ||||||||
\(821\) | −12092.4 | + | 6981.54i | −0.514041 | + | 0.296781i | −0.734493 | − | 0.678616i | \(-0.762580\pi\) |
0.220452 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(822\) | 23790.0 | − | 21161.6i | 1.00946 | − | 0.897926i | ||||
\(823\) | −7562.23 | + | 13098.2i | −0.320295 | + | 0.554767i | −0.980549 | − | 0.196275i | \(-0.937115\pi\) |
0.660254 | + | 0.751043i | \(0.270449\pi\) | |||||||
\(824\) | 4298.33 | + | 7444.92i | 0.181722 | + | 0.314752i | ||||
\(825\) | −1833.76 | + | 5529.76i | −0.0773860 | + | 0.233359i | ||||
\(826\) | 294.202 | + | 437.871i | 0.0123930 | + | 0.0184449i | ||||
\(827\) | − | 1559.49i | − | 0.0655728i | −0.999462 | − | 0.0327864i | \(-0.989562\pi\) | ||
0.999462 | − | 0.0327864i | \(-0.0104381\pi\) | |||||||
\(828\) | 8553.96 | + | 1003.77i | 0.359023 | + | 0.0421297i | ||||
\(829\) | 5790.85 | + | 3343.35i | 0.242611 | + | 0.140072i | 0.616376 | − | 0.787452i | \(-0.288600\pi\) |
−0.373765 | + | 0.927523i | \(0.621933\pi\) | |||||||
\(830\) | −12460.0 | − | 7193.80i | −0.521077 | − | 0.300844i | ||||
\(831\) | 2406.51 | + | 11668.2i | 0.100459 | + | 0.487082i | ||||
\(832\) | 18243.8i | 0.760203i | ||||||||
\(833\) | 7702.58 | + | 9932.35i | 0.320382 | + | 0.413128i | ||||
\(834\) | −14508.3 | − | 4811.19i | −0.602375 | − | 0.199758i | ||||
\(835\) | −4368.34 | − | 7566.18i | −0.181045 | − | 0.313579i | ||||
\(836\) | 30489.6 | − | 52809.5i | 1.26137 | − | 2.18476i | ||||
\(837\) | 3674.36 | + | 42331.5i | 0.151738 | + | 1.74814i | ||||
\(838\) | −40283.5 | + | 23257.7i | −1.66059 | + | 0.958739i | ||||
\(839\) | 28415.9 | 1.16928 | 0.584640 | − | 0.811293i | \(-0.301236\pi\) | ||||
0.584640 | + | 0.811293i | \(0.301236\pi\) | |||||||
\(840\) | −2843.95 | − | 10220.0i | −0.116816 | − | 0.419789i | ||||
\(841\) | 23390.0 | 0.959039 | ||||||||
\(842\) | 46431.1 | − | 26807.0i | 1.90038 | − | 1.09718i | ||||
\(843\) | −14844.0 | − | 16687.8i | −0.606471 | − | 0.681799i | ||||
\(844\) | −750.856 | + | 1300.52i | −0.0306227 | + | 0.0530400i | ||||
\(845\) | −4287.32 | − | 7425.86i | −0.174542 | − | 0.302316i | ||||
\(846\) | 8779.53 | − | 11781.7i | 0.356792 | − | 0.478799i | ||||
\(847\) | −11314.5 | − | 5543.69i | −0.458997 | − | 0.224892i | ||||
\(848\) | 1308.46i | 0.0529865i | ||||||||
\(849\) | −8545.22 | + | 1762.42i | −0.345431 | + | 0.0712437i | ||||
\(850\) | −3621.01 | − | 2090.59i | −0.146117 | − | 0.0843608i | ||||
\(851\) | −5637.30 | − | 3254.69i | −0.227079 | − | 0.131104i | ||||
\(852\) | 41771.6 | − | 8615.22i | 1.67966 | − | 0.346423i | ||||
\(853\) | 2437.87i | 0.0978558i | 0.998802 | + | 0.0489279i | \(0.0155805\pi\) | ||||
−0.998802 | + | 0.0489279i | \(0.984420\pi\) | |||||||
\(854\) | −4661.04 | − | 68426.0i | −0.186765 | − | 2.74179i | ||||
\(855\) | −8548.41 | + | 11471.6i | −0.341929 | + | 0.458854i | ||||
\(856\) | −3456.86 | − | 5987.46i | −0.138029 | − | 0.239074i | ||||
\(857\) | −15603.4 | + | 27025.9i | −0.621940 | + | 1.07723i | 0.367185 | + | 0.930148i | \(0.380322\pi\) |
−0.989124 | + | 0.147083i | \(0.953012\pi\) | |||||||
\(858\) | 15520.5 | + | 17448.2i | 0.617553 | + | 0.694257i | ||||
\(859\) | 2757.08 | − | 1591.80i | 0.109512 | − | 0.0632265i | −0.444244 | − | 0.895906i | \(-0.646528\pi\) |
0.553755 | + | 0.832679i | \(0.313194\pi\) | |||||||
\(860\) | 19376.0 | 0.768275 | ||||||||
\(861\) | 7076.81 | − | 27463.7i | 0.280113 | − | 1.08706i | ||||
\(862\) | 24918.1 | 0.984589 | ||||||||
\(863\) | 13566.8 | − | 7832.80i | 0.535133 | − | 0.308959i | −0.207971 | − | 0.978135i | \(-0.566686\pi\) |
0.743104 | + | 0.669176i | \(0.233353\pi\) | |||||||
\(864\) | −2251.71 | − | 25941.5i | −0.0886630 | − | 1.02147i | ||||
\(865\) | 8764.01 | − | 15179.7i | 0.344492 | − | 0.596677i | ||||
\(866\) | −3310.11 | − | 5733.28i | −0.129887 | − | 0.224971i | ||||
\(867\) | 17608.3 | + | 5839.20i | 0.689744 | + | 0.228731i | ||||
\(868\) | 31665.2 | − | 64627.7i | 1.23823 | − | 2.52720i | ||||
\(869\) | − | 28049.8i | − | 1.09497i | ||||||
\(870\) | 757.045 | + | 3670.60i | 0.0295014 | + | 0.143040i | ||||
\(871\) | 510.868 | + | 294.950i | 0.0198738 | + | 0.0114742i | ||||
\(872\) | −15100.0 | − | 8717.97i | −0.586410 | − | 0.338564i | ||||
\(873\) | −14168.1 | − | 1662.57i | −0.549277 | − | 0.0644552i | ||||
\(874\) | 12024.7i | 0.465380i | ||||||||
\(875\) | −1921.58 | + | 1291.09i | −0.0742413 | + | 0.0498822i | ||||
\(876\) | −15017.7 | + | 45286.4i | −0.579226 | + | 1.74667i | ||||
\(877\) | −5140.43 | − | 8903.49i | −0.197925 | − | 0.342816i | 0.749931 | − | 0.661517i | \(-0.230087\pi\) |
−0.947855 | + | 0.318701i | \(0.896754\pi\) | |||||||
\(878\) | −19313.4 | + | 33451.7i | −0.742363 | + | 1.28581i | ||||
\(879\) | −13314.4 | + | 11843.4i | −0.510904 | + | 0.454457i | ||||
\(880\) | 392.544 | − | 226.635i | 0.0150371 | − | 0.00868168i | ||||
\(881\) | −27228.8 | −1.04127 | −0.520636 | − | 0.853779i | \(-0.674305\pi\) | ||||
−0.520636 | + | 0.853779i | \(0.674305\pi\) | |||||||
\(882\) | −42259.9 | + | 812.105i | −1.61334 | + | 0.0310034i | ||||
\(883\) | −39997.5 | −1.52437 | −0.762187 | − | 0.647357i | \(-0.775874\pi\) | ||||
−0.762187 | + | 0.647357i | \(0.775874\pi\) | |||||||
\(884\) | −8940.06 | + | 5161.55i | −0.340143 | + | 0.196382i | ||||
\(885\) | −121.150 | + | 107.765i | −0.00460159 | + | 0.00409319i | ||||
\(886\) | −96.5550 | + | 167.238i | −0.00366121 | + | 0.00634140i | ||||
\(887\) | 8117.83 | + | 14060.5i | 0.307294 | + | 0.532250i | 0.977770 | − | 0.209682i | \(-0.0672430\pi\) |
−0.670475 | + | 0.741932i | \(0.733910\pi\) | |||||||
\(888\) | 9441.09 | − | 28469.9i | 0.356782 | − | 1.07589i | ||||
\(889\) | 37154.8 | − | 24964.1i | 1.40172 | − | 0.941808i | ||||
\(890\) | 16013.2i | 0.603104i | ||||||||
\(891\) | −23760.3 | − | 22457.6i | −0.893377 | − | 0.844399i | ||||
\(892\) | 39808.1 | + | 22983.2i | 1.49425 | + | 0.862707i | ||||
\(893\) | 10942.8 | + | 6317.83i | 0.410064 | + | 0.236750i | ||||
\(894\) | 5799.56 | + | 28119.6i | 0.216964 | + | 1.05197i | ||||
\(895\) | 10017.5i | 0.374131i | ||||||||
\(896\) | −18803.6 | + | 38377.5i | −0.701097 | + | 1.43092i | ||||
\(897\) | −2692.22 | − | 892.785i | −0.100212 | − | 0.0332321i | ||||
\(898\) | −2154.80 | − | 3732.23i | −0.0800743 | − | 0.138693i | ||||
\(899\) | −4786.29 | + | 8290.09i | −0.177566 | + | 0.307553i | ||||
\(900\) | 7953.89 | − | 3426.67i | 0.294588 | − | 0.126914i | ||||
\(901\) | −20542.4 | + | 11860.1i | −0.759563 | + | 0.438534i | ||||
\(902\) | −60322.7 | −2.22675 | ||||||||
\(903\) | 7252.64 | − | 28146.1i | 0.267279 | − | 1.03726i | ||||
\(904\) | −52704.4 | −1.93908 | ||||||||
\(905\) | −4721.05 | + | 2725.70i | −0.173407 | + | 0.100116i | ||||
\(906\) | 8703.88 | + | 9784.97i | 0.319169 | + | 0.358812i | ||||
\(907\) | −113.354 | + | 196.335i | −0.00414978 | + | 0.00718763i | −0.868093 | − | 0.496402i | \(-0.834654\pi\) |
0.863943 | + | 0.503590i | \(0.167988\pi\) | |||||||
\(908\) | 8151.91 | + | 14119.5i | 0.297941 | + | 0.516050i | ||||
\(909\) | −37345.9 | − | 27829.5i | −1.36269 | − | 1.01545i | ||||
\(910\) | 630.637 | + | 9258.02i | 0.0229730 | + | 0.337253i | ||||
\(911\) | − | 7251.95i | − | 0.263741i | −0.991267 | − | 0.131870i | \(-0.957902\pi\) | ||
0.991267 | − | 0.131870i | \(-0.0420983\pi\) | |||||||
\(912\) | 1090.13 | − | 224.836i | 0.0395811 | − | 0.00816343i | ||||
\(913\) | 24487.2 | + | 14137.7i | 0.887631 | + | 0.512474i | ||||
\(914\) | −35072.6 | − | 20249.2i | −1.26925 | − | 0.732804i | ||||
\(915\) | 20646.0 | − | 4258.14i | 0.745939 | − | 0.153847i | ||||
\(916\) | − | 37049.7i | − | 1.33641i | ||||||
\(917\) | −23912.3 | − | 11716.1i | −0.861126 | − | 0.421920i | ||||
\(918\) | 19229.9 | − | 13445.3i | 0.691374 | − | 0.483401i | ||||
\(919\) | 8177.68 | + | 14164.2i | 0.293533 | + | 0.508414i | 0.974643 | − | 0.223768i | \(-0.0718356\pi\) |
−0.681110 | + | 0.732181i | \(0.738502\pi\) | |||||||
\(920\) | 1370.30 | − | 2373.43i | 0.0491058 | − | 0.0850538i | ||||
\(921\) | 2507.56 | + | 2819.01i | 0.0897142 | + | 0.100857i | ||||
\(922\) | 35407.4 | − | 20442.5i | 1.26473 | − | 0.730192i | ||||
\(923\) | −14046.1 | −0.500902 | ||||||||
\(924\) | 14845.3 | + | 53348.1i | 0.528545 | + | 1.89937i | ||||
\(925\) | −6545.64 | −0.232670 | ||||||||
\(926\) | −22566.0 | + | 13028.5i | −0.800825 | + | 0.462357i | ||||
\(927\) | 4165.52 | + | 9668.88i | 0.147588 | + | 0.342576i | ||||
\(928\) | 2933.12 | − | 5080.31i | 0.103755 | − | 0.179708i | ||||
\(929\) | 17239.9 | + | 29860.3i | 0.608850 | + | 1.05456i | 0.991430 | + | 0.130637i | \(0.0417022\pi\) |
−0.382580 | + | 0.923922i | \(0.624964\pi\) | |||||||
\(930\) | 34087.5 | + | 11304.0i | 1.20191 | + | 0.398572i | ||||
\(931\) | −4929.14 | − | 36013.1i | −0.173519 | − | 1.26776i | ||||
\(932\) | 21052.9i | 0.739925i | ||||||||
\(933\) | −7053.65 | − | 34200.2i | −0.247509 | − | 1.20007i | ||||
\(934\) | 72100.2 | + | 41627.1i | 2.52590 | + | 1.45833i | ||||
\(935\) | 7116.22 | + | 4108.55i | 0.248904 | + | 0.143705i | ||||
\(936\) | 1523.22 | − | 12980.7i | 0.0531923 | − | 0.453297i | ||||
\(937\) | 23700.4i | 0.826315i | 0.910660 | + | 0.413158i | \(0.135574\pi\) | ||||
−0.910660 | + | 0.413158i | \(0.864426\pi\) | |||||||
\(938\) | 1266.54 | + | 1885.04i | 0.0440875 | + | 0.0656170i | ||||
\(939\) | 9840.15 | − | 29673.2i | 0.341982 | − | 1.03126i | ||||
\(940\) | −3824.61 | − | 6624.41i | −0.132707 | − | 0.229856i | ||||
\(941\) | 17640.5 | − | 30554.2i | 0.611120 | − | 1.05849i | −0.379932 | − | 0.925014i | \(-0.624053\pi\) |
0.991052 | − | 0.133476i | \(-0.0426140\pi\) | |||||||
\(942\) | 38694.1 | − | 34419.0i | 1.33835 | − | 1.19048i | ||||
\(943\) | 6345.25 | − | 3663.43i | 0.219120 | − | 0.126509i | ||||
\(944\) | 12.6153 | 0.000434949 | ||||||||
\(945\) | −2000.45 | − | 12836.7i | −0.0688621 | − | 0.441880i | ||||
\(946\) | −61821.5 | −2.12473 | ||||||||
\(947\) | −25823.1 | + | 14909.0i | −0.886100 | + | 0.511590i | −0.872665 | − | 0.488320i | \(-0.837610\pi\) |
−0.0134353 | + | 0.999910i | \(0.504277\pi\) | |||||||
\(948\) | −31155.9 | + | 27713.7i | −1.06740 | + | 0.949471i | ||||
\(949\) | 7856.37 | − | 13607.6i | 0.268734 | − | 0.465461i | ||||
\(950\) | 6045.84 | + | 10471.7i | 0.206477 | + | 0.357628i | ||||
\(951\) | −8445.16 | + | 25466.6i | −0.287963 | + | 0.868361i | ||||
\(952\) | −14927.9 | + | 1016.86i | −0.508209 | + | 0.0346181i | ||||
\(953\) | − | 8553.43i | − | 0.290737i | −0.989378 | − | 0.145369i | \(-0.953563\pi\) | ||
0.989378 | − | 0.145369i | \(-0.0464368\pi\) | |||||||
\(954\) | 9296.55 | − | 79223.8i | 0.315500 | − | 2.68864i | ||||
\(955\) | 4719.23 | + | 2724.65i | 0.159906 | + | 0.0923220i | ||||
\(956\) | −34275.2 | − | 19788.8i | −1.15956 | − | 0.669473i | ||||
\(957\) | −1487.79 | − | 7213.67i | −0.0502543 | − | 0.243662i | ||||
\(958\) | 43556.2i | 1.46893i | ||||||||
\(959\) | −24807.4 | + | 1689.83i | −0.835320 | + | 0.0569003i | ||||
\(960\) | −20490.6 | − | 6795.04i | −0.688888 | − | 0.228447i | ||||
\(961\) | 30967.9 | + | 53638.0i | 1.03951 | + | 1.80048i | ||||
\(962\) | −13118.6 | + | 22722.1i | −0.439669 | + | 0.761529i | ||||
\(963\) | −3350.06 | − | 7776.05i | −0.112102 | − | 0.260207i | ||||
\(964\) | 6335.71 | − | 3657.92i | 0.211680 | − | 0.122213i | ||||
\(965\) | −24734.5 | −0.825111 | ||||||||
\(966\) | −7795.16 | − | 7646.80i | −0.259633 | − | 0.254691i | ||||
\(967\) | 37158.5 | 1.23572 | 0.617858 | − | 0.786290i | \(-0.288001\pi\) | ||||
0.617858 | + | 0.786290i | \(0.288001\pi\) | |||||||
\(968\) | 12989.4 | − | 7499.41i | 0.431295 | − | 0.249009i | ||||
\(969\) | 13411.1 | + | 15076.8i | 0.444609 | + | 0.499832i | ||||
\(970\) | −6028.50 | + | 10441.7i | −0.199550 | + | 0.345631i | ||||
\(971\) | 10770.2 | + | 18654.5i | 0.355955 | + | 0.616532i | 0.987281 | − | 0.158986i | \(-0.0508223\pi\) |
−0.631326 | + | 0.775518i | \(0.717489\pi\) | |||||||
\(972\) | −1468.95 | + | 48579.9i | −0.0484739 | + | 1.60309i | ||||
\(973\) | 6657.13 | + | 9908.02i | 0.219340 | + | 0.326451i | ||||
\(974\) | 33129.6i | 1.08988i | ||||||||
\(975\) | −2793.39 | + | 576.125i | −0.0917540 | + | 0.0189239i | ||||
\(976\) | −1420.39 | − | 820.062i | −0.0465836 | − | 0.0268950i | ||||
\(977\) | −43080.4 | − | 24872.5i | −1.41071 | − | 0.814475i | −0.415256 | − | 0.909704i | \(-0.636308\pi\) |
−0.995455 | + | 0.0952296i | \(0.969641\pi\) | |||||||
\(978\) | 83853.4 | − | 17294.4i | 2.74165 | − | 0.565454i | ||||
\(979\) | − | 31470.0i | − | 1.02736i | ||||||
\(980\) | −8316.40 | + | 20372.3i | −0.271079 | + | 0.664050i | ||||
\(981\) | −17122.1 | − | 12759.0i | −0.557253 | − | 0.415255i | ||||
\(982\) | 9751.95 | + | 16890.9i | 0.316901 | + | 0.548889i | ||||
\(983\) | −8320.88 | + | 14412.2i | −0.269985 | + | 0.467627i | −0.968858 | − | 0.247619i | \(-0.920352\pi\) |
0.698873 | + | 0.715246i | \(0.253685\pi\) | |||||||
\(984\) | 22438.6 | + | 25225.7i | 0.726949 | + | 0.817241i | ||||
\(985\) | −14273.5 | + | 8240.79i | −0.461716 | + | 0.266572i | ||||
\(986\) | 5286.15 | 0.170736 | ||||||||
\(987\) | −11054.4 | + | 3076.14i | −0.356500 | + | 0.0992042i | ||||
\(988\) | 29853.6 | 0.961306 | ||||||||
\(989\) | 6502.91 | − | 3754.46i | 0.209080 | − | 0.120713i | ||||
\(990\) | −25377.8 | + | 10933.2i | −0.814707 | + | 0.350990i | ||||
\(991\) | −9989.26 | + | 17301.9i | −0.320201 | + | 0.554605i | −0.980529 | − | 0.196372i | \(-0.937084\pi\) |
0.660328 | + | 0.750977i | \(0.270417\pi\) | |||||||
\(992\) | −28105.9 | − | 48680.9i | −0.899560 | − | 1.55808i | ||||
\(993\) | 15796.2 | + | 5238.28i | 0.504810 | + | 0.167403i | ||||
\(994\) | −48559.6 | − | 23792.4i | −1.54952 | − | 0.759205i | ||||
\(995\) | 3929.96i | 0.125214i | ||||||||
\(996\) | −8490.51 | − | 41167.0i | −0.270113 | − | 1.30966i | ||||
\(997\) | −999.878 | − | 577.280i | −0.0317617 | − | 0.0183377i | 0.484035 | − | 0.875049i | \(-0.339171\pi\) |
−0.515797 | + | 0.856711i | \(0.672504\pi\) | |||||||
\(998\) | 4510.40 | + | 2604.08i | 0.143060 | + | 0.0825959i | ||||
\(999\) | 15546.9 | − | 33280.9i | 0.492373 | − | 1.05402i |
(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 | 105.4.s.a.101.15 | yes | 32 | |
3.2 | odd | 2 | 105.4.s.b.101.2 | yes | 32 | ||
7.5 | odd | 6 | 105.4.s.b.26.2 | yes | 32 | ||
21.5 | even | 6 | inner | 105.4.s.a.26.15 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.15 | ✓ | 32 | 21.5 | even | 6 | inner | |
105.4.s.a.101.15 | yes | 32 | 1.1 | even | 1 | trivial | |
105.4.s.b.26.2 | yes | 32 | 7.5 | odd | 6 | ||
105.4.s.b.101.2 | yes | 32 | 3.2 | odd | 2 |