Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(14,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.14");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.h (of order \(5\), 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: | \(76\) |
Relative dimension: | \(19\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 14.9 | ||
Character | \(\chi\) | \(=\) | 143.14 |
Dual form | 143.4.h.b.92.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.471643 | + | 0.342668i | −0.166751 | + | 0.121152i | −0.668031 | − | 0.744133i | \(-0.732863\pi\) |
0.501280 | + | 0.865285i | \(0.332863\pi\) | |||||||
\(3\) | −1.46721 | − | 4.51561i | −0.282365 | − | 0.869029i | −0.987176 | − | 0.159635i | \(-0.948968\pi\) |
0.704811 | − | 0.709395i | \(-0.251032\pi\) | |||||||
\(4\) | −2.36711 | + | 7.28522i | −0.295889 | + | 0.910652i | ||||
\(5\) | 1.58259 | + | 1.14982i | 0.141551 | + | 0.102843i | 0.656307 | − | 0.754494i | \(-0.272118\pi\) |
−0.514756 | + | 0.857337i | \(0.672118\pi\) | |||||||
\(6\) | 2.23936 | + | 1.62699i | 0.152369 | + | 0.110702i | ||||
\(7\) | −0.116501 | + | 0.358552i | −0.00629044 | + | 0.0193600i | −0.954152 | − | 0.299321i | \(-0.903240\pi\) |
0.947862 | + | 0.318681i | \(0.103240\pi\) | |||||||
\(8\) | −2.82120 | − | 8.68275i | −0.124680 | − | 0.383727i | ||||
\(9\) | 3.60544 | − | 2.61951i | 0.133535 | − | 0.0970188i | ||||
\(10\) | −1.14042 | −0.0360633 | ||||||||
\(11\) | −24.8165 | − | 26.7421i | −0.680223 | − | 0.733005i | ||||
\(12\) | 36.3702 | 0.874932 | ||||||||
\(13\) | 10.5172 | − | 7.64121i | 0.224381 | − | 0.163022i | ||||
\(14\) | −0.0679178 | − | 0.209029i | −0.00129656 | − | 0.00399039i | ||||
\(15\) | 2.87013 | − | 8.83336i | 0.0494044 | − | 0.152051i | ||||
\(16\) | −45.2715 | − | 32.8917i | −0.707367 | − | 0.513932i | ||||
\(17\) | −14.3293 | − | 10.4108i | −0.204433 | − | 0.148529i | 0.480858 | − | 0.876798i | \(-0.340325\pi\) |
−0.685291 | + | 0.728269i | \(0.740325\pi\) | |||||||
\(18\) | −0.802858 | + | 2.47094i | −0.0105131 | + | 0.0323559i | ||||
\(19\) | −29.7701 | − | 91.6229i | −0.359459 | − | 1.10630i | −0.953378 | − | 0.301777i | \(-0.902420\pi\) |
0.593919 | − | 0.804525i | \(-0.297580\pi\) | |||||||
\(20\) | −12.1228 | + | 8.80775i | −0.135537 | + | 0.0984736i | ||||
\(21\) | 1.79001 | 0.0186006 | ||||||||
\(22\) | 20.8682 | + | 4.10891i | 0.202233 | + | 0.0398192i | ||||
\(23\) | −133.927 | −1.21416 | −0.607080 | − | 0.794641i | \(-0.707659\pi\) | ||||
−0.607080 | + | 0.794641i | \(0.707659\pi\) | |||||||
\(24\) | −35.0686 | + | 25.4788i | −0.298265 | + | 0.216702i | ||||
\(25\) | −37.4446 | − | 115.243i | −0.299557 | − | 0.921942i | ||||
\(26\) | −2.34197 | + | 7.20784i | −0.0176653 | + | 0.0543682i | ||||
\(27\) | −120.831 | − | 87.7890i | −0.861258 | − | 0.625741i | ||||
\(28\) | −2.33636 | − | 1.69746i | −0.0157689 | − | 0.0114568i | ||||
\(29\) | −27.1309 | + | 83.5002i | −0.173727 | + | 0.534676i | −0.999573 | − | 0.0292193i | \(-0.990698\pi\) |
0.825846 | + | 0.563895i | \(0.190698\pi\) | |||||||
\(30\) | 1.67324 | + | 5.14970i | 0.0101830 | + | 0.0313401i | ||||
\(31\) | 156.452 | − | 113.669i | 0.906439 | − | 0.658566i | −0.0336730 | − | 0.999433i | \(-0.510720\pi\) |
0.940112 | + | 0.340867i | \(0.110720\pi\) | |||||||
\(32\) | 105.660 | 0.583692 | ||||||||
\(33\) | −84.3461 | + | 151.298i | −0.444932 | + | 0.798108i | ||||
\(34\) | 10.3258 | 0.0520840 | ||||||||
\(35\) | −0.596641 | + | 0.433485i | −0.00288145 | + | 0.00209350i | ||||
\(36\) | 10.5492 | + | 32.4671i | 0.0488389 | + | 0.150311i | ||||
\(37\) | −0.594108 | + | 1.82848i | −0.00263975 | + | 0.00812432i | −0.952368 | − | 0.304952i | \(-0.901360\pi\) |
0.949728 | + | 0.313076i | \(0.101360\pi\) | |||||||
\(38\) | 45.4371 | + | 33.0120i | 0.193970 | + | 0.140928i | ||||
\(39\) | −49.9357 | − | 36.2804i | −0.205028 | − | 0.148962i | ||||
\(40\) | 5.51878 | − | 16.9851i | 0.0218149 | − | 0.0671393i | ||||
\(41\) | −61.9309 | − | 190.604i | −0.235902 | − | 0.726032i | −0.997000 | − | 0.0773956i | \(-0.975340\pi\) |
0.761098 | − | 0.648637i | \(-0.224660\pi\) | |||||||
\(42\) | −0.844245 | + | 0.613380i | −0.00310166 | + | 0.00225349i | ||||
\(43\) | 112.095 | 0.397542 | 0.198771 | − | 0.980046i | \(-0.436305\pi\) | ||||
0.198771 | + | 0.980046i | \(0.436305\pi\) | |||||||
\(44\) | 253.566 | − | 117.492i | 0.868783 | − | 0.402558i | ||||
\(45\) | 8.71788 | 0.0288796 | ||||||||
\(46\) | 63.1656 | − | 45.8925i | 0.202462 | − | 0.147097i | ||||
\(47\) | −20.1458 | − | 62.0023i | −0.0625226 | − | 0.192425i | 0.914916 | − | 0.403644i | \(-0.132257\pi\) |
−0.977439 | + | 0.211219i | \(0.932257\pi\) | |||||||
\(48\) | −82.1031 | + | 252.687i | −0.246887 | + | 0.759839i | ||||
\(49\) | 277.378 | + | 201.527i | 0.808682 | + | 0.587542i | ||||
\(50\) | 57.1505 | + | 41.5223i | 0.161646 | + | 0.117443i | ||||
\(51\) | −25.9872 | + | 79.9804i | −0.0713517 | + | 0.219598i | ||||
\(52\) | 30.7724 | + | 94.7078i | 0.0820648 | + | 0.252569i | ||||
\(53\) | 377.607 | − | 274.348i | 0.978648 | − | 0.711029i | 0.0212418 | − | 0.999774i | \(-0.493238\pi\) |
0.957406 | + | 0.288745i | \(0.0932380\pi\) | |||||||
\(54\) | 87.0717 | 0.219425 | ||||||||
\(55\) | −8.52567 | − | 70.8562i | −0.0209018 | − | 0.173714i | ||||
\(56\) | 3.44189 | 0.00821324 | ||||||||
\(57\) | −370.054 | + | 268.860i | −0.859910 | + | 0.624761i | ||||
\(58\) | −15.8168 | − | 48.6792i | −0.0358078 | − | 0.110205i | ||||
\(59\) | −261.121 | + | 803.646i | −0.576186 | + | 1.77332i | 0.0559173 | + | 0.998435i | \(0.482192\pi\) |
−0.632104 | + | 0.774884i | \(0.717808\pi\) | |||||||
\(60\) | 57.5591 | + | 41.8191i | 0.123847 | + | 0.0899804i | ||||
\(61\) | −60.8324 | − | 44.1973i | −0.127685 | − | 0.0927686i | 0.522110 | − | 0.852878i | \(-0.325145\pi\) |
−0.649795 | + | 0.760110i | \(0.725145\pi\) | |||||||
\(62\) | −34.8386 | + | 107.222i | −0.0713631 | + | 0.219633i | ||||
\(63\) | 0.519193 | + | 1.59791i | 0.00103829 | + | 0.00319552i | ||||
\(64\) | 312.339 | − | 226.927i | 0.610036 | − | 0.443217i | ||||
\(65\) | 25.4304 | 0.0485270 | ||||||||
\(66\) | −12.0638 | − | 100.261i | −0.0224993 | − | 0.186990i | ||||
\(67\) | −459.767 | −0.838351 | −0.419175 | − | 0.907905i | \(-0.637681\pi\) | ||||
−0.419175 | + | 0.907905i | \(0.637681\pi\) | |||||||
\(68\) | 109.764 | − | 79.7484i | 0.195748 | − | 0.142219i | ||||
\(69\) | 196.499 | + | 604.761i | 0.342836 | + | 1.05514i | ||||
\(70\) | 0.132860 | − | 0.408900i | 0.000226854 | − | 0.000698184i | ||||
\(71\) | −160.110 | − | 116.326i | −0.267627 | − | 0.194442i | 0.445876 | − | 0.895095i | \(-0.352892\pi\) |
−0.713503 | + | 0.700653i | \(0.752892\pi\) | |||||||
\(72\) | −32.9162 | − | 23.9150i | −0.0538779 | − | 0.0391446i | ||||
\(73\) | −292.882 | + | 901.397i | −0.469578 | + | 1.44521i | 0.383554 | + | 0.923519i | \(0.374700\pi\) |
−0.853132 | + | 0.521695i | \(0.825300\pi\) | |||||||
\(74\) | −0.346355 | − | 1.06597i | −0.000544094 | − | 0.00167455i | ||||
\(75\) | −465.452 | + | 338.171i | −0.716610 | + | 0.520648i | ||||
\(76\) | 737.962 | 1.11382 | ||||||||
\(77\) | 12.4796 | − | 5.78252i | 0.0184699 | − | 0.00855817i | ||||
\(78\) | 35.9839 | 0.0522356 | ||||||||
\(79\) | 120.266 | − | 87.3781i | 0.171278 | − | 0.124440i | −0.498844 | − | 0.866692i | \(-0.666242\pi\) |
0.670122 | + | 0.742251i | \(0.266242\pi\) | |||||||
\(80\) | −33.8267 | − | 104.108i | −0.0472742 | − | 0.145495i | ||||
\(81\) | −181.953 | + | 559.993i | −0.249592 | + | 0.768166i | ||||
\(82\) | 94.5232 | + | 68.6751i | 0.127297 | + | 0.0924866i | ||||
\(83\) | −31.7830 | − | 23.0917i | −0.0420318 | − | 0.0305379i | 0.566571 | − | 0.824013i | \(-0.308270\pi\) |
−0.608603 | + | 0.793475i | \(0.708270\pi\) | |||||||
\(84\) | −4.23715 | + | 13.0406i | −0.00550371 | + | 0.0169387i | ||||
\(85\) | −10.7068 | − | 32.9521i | −0.0136625 | − | 0.0420489i | ||||
\(86\) | −52.8687 | + | 38.4113i | −0.0662904 | + | 0.0481628i | ||||
\(87\) | 416.861 | 0.513704 | ||||||||
\(88\) | −162.183 | + | 290.920i | −0.196463 | + | 0.352411i | ||||
\(89\) | 480.228 | 0.571956 | 0.285978 | − | 0.958236i | \(-0.407682\pi\) | ||||
0.285978 | + | 0.958236i | \(0.407682\pi\) | |||||||
\(90\) | −4.11172 | + | 2.98734i | −0.00481571 | + | 0.00349882i | ||||
\(91\) | 1.51451 | + | 4.66117i | 0.00174465 | + | 0.00536949i | ||||
\(92\) | 317.020 | − | 975.686i | 0.359256 | − | 1.10568i | ||||
\(93\) | −742.833 | − | 539.699i | −0.828260 | − | 0.601766i | ||||
\(94\) | 30.7478 | + | 22.3396i | 0.0337383 | + | 0.0245123i | ||||
\(95\) | 58.2358 | − | 179.231i | 0.0628933 | − | 0.193566i | ||||
\(96\) | −155.025 | − | 477.117i | −0.164814 | − | 0.507246i | ||||
\(97\) | 880.641 | − | 639.823i | 0.921810 | − | 0.669734i | −0.0221640 | − | 0.999754i | \(-0.507056\pi\) |
0.943974 | + | 0.330020i | \(0.107056\pi\) | |||||||
\(98\) | −199.880 | −0.206030 | ||||||||
\(99\) | −159.526 | − | 31.4103i | −0.161949 | − | 0.0318874i | ||||
\(100\) | 928.204 | 0.928204 | ||||||||
\(101\) | −1460.88 | + | 1061.39i | −1.43924 | + | 1.04567i | −0.451036 | + | 0.892506i | \(0.648946\pi\) |
−0.988201 | + | 0.153162i | \(0.951054\pi\) | |||||||
\(102\) | −15.1501 | − | 46.6272i | −0.0147067 | − | 0.0452625i | ||||
\(103\) | 293.084 | − | 902.019i | 0.280373 | − | 0.862899i | −0.707375 | − | 0.706839i | \(-0.750121\pi\) |
0.987748 | − | 0.156060i | \(-0.0498793\pi\) | |||||||
\(104\) | −96.0178 | − | 69.7610i | −0.0905319 | − | 0.0657753i | ||||
\(105\) | 2.83285 | + | 2.05818i | 0.00263293 | + | 0.00191293i | ||||
\(106\) | −84.0854 | + | 258.788i | −0.0770480 | + | 0.237129i | ||||
\(107\) | −356.333 | − | 1096.68i | −0.321944 | − | 0.990841i | −0.972801 | − | 0.231641i | \(-0.925591\pi\) |
0.650858 | − | 0.759200i | \(-0.274409\pi\) | |||||||
\(108\) | 925.583 | − | 672.475i | 0.824669 | − | 0.599157i | ||||
\(109\) | 1718.34 | 1.50998 | 0.754988 | − | 0.655738i | \(-0.227643\pi\) | ||||
0.754988 | + | 0.655738i | \(0.227643\pi\) | |||||||
\(110\) | 28.3012 | + | 30.4973i | 0.0245311 | + | 0.0264346i | ||||
\(111\) | 9.12837 | 0.00780565 | ||||||||
\(112\) | 17.0675 | − | 12.4003i | 0.0143994 | − | 0.0104618i | ||||
\(113\) | −357.776 | − | 1101.12i | −0.297848 | − | 0.916681i | −0.982250 | − | 0.187576i | \(-0.939937\pi\) |
0.684402 | − | 0.729104i | \(-0.260063\pi\) | |||||||
\(114\) | 82.4035 | − | 253.612i | 0.0676999 | − | 0.208359i | ||||
\(115\) | −211.951 | − | 153.991i | −0.171865 | − | 0.124867i | ||||
\(116\) | −544.096 | − | 395.309i | −0.435500 | − | 0.316409i | ||||
\(117\) | 17.9030 | − | 55.0999i | 0.0141465 | − | 0.0435383i | ||||
\(118\) | −152.229 | − | 468.512i | −0.118761 | − | 0.365508i | ||||
\(119\) | 5.40220 | − | 3.92492i | 0.00416150 | − | 0.00302351i | ||||
\(120\) | −84.7951 | −0.0645058 | ||||||||
\(121\) | −99.2846 | + | 1327.29i | −0.0745940 | + | 0.997214i | ||||
\(122\) | 43.8362 | 0.0325307 | ||||||||
\(123\) | −769.827 | + | 559.312i | −0.564333 | + | 0.410012i | ||||
\(124\) | 457.764 | + | 1408.85i | 0.331520 | + | 1.02031i | ||||
\(125\) | 148.810 | − | 457.991i | 0.106480 | − | 0.327712i | ||||
\(126\) | −0.792427 | − | 0.575732i | −0.000560278 | − | 0.000407066i | ||||
\(127\) | −1597.97 | − | 1161.00i | −1.11651 | − | 0.811195i | −0.132837 | − | 0.991138i | \(-0.542409\pi\) |
−0.983677 | + | 0.179943i | \(0.942409\pi\) | |||||||
\(128\) | −330.756 | + | 1017.96i | −0.228398 | + | 0.702938i | ||||
\(129\) | −164.467 | − | 506.176i | −0.112252 | − | 0.345475i | ||||
\(130\) | −11.9941 | + | 8.71420i | −0.00809191 | + | 0.00587912i | ||||
\(131\) | −1661.77 | −1.10832 | −0.554158 | − | 0.832412i | \(-0.686960\pi\) | ||||
−0.554158 | + | 0.832412i | \(0.686960\pi\) | |||||||
\(132\) | −902.581 | − | 972.618i | −0.595149 | − | 0.641330i | ||||
\(133\) | 36.3198 | 0.0236791 | ||||||||
\(134\) | 216.846 | − | 157.548i | 0.139796 | − | 0.101568i | ||||
\(135\) | −90.2846 | − | 277.867i | −0.0575590 | − | 0.177148i | ||||
\(136\) | −49.9690 | + | 153.789i | −0.0315059 | + | 0.0969652i | ||||
\(137\) | −1648.61 | − | 1197.78i | −1.02810 | − | 0.746960i | −0.0601743 | − | 0.998188i | \(-0.519166\pi\) |
−0.967928 | + | 0.251228i | \(0.919166\pi\) | |||||||
\(138\) | −299.910 | − | 217.897i | −0.185000 | − | 0.134410i | ||||
\(139\) | −381.605 | + | 1174.46i | −0.232859 | + | 0.716665i | 0.764540 | + | 0.644577i | \(0.222966\pi\) |
−0.997398 | + | 0.0720883i | \(0.977034\pi\) | |||||||
\(140\) | −1.74572 | − | 5.37277i | −0.00105386 | − | 0.00324344i | ||||
\(141\) | −250.420 | + | 181.941i | −0.149569 | + | 0.108668i | ||||
\(142\) | 115.376 | 0.0681840 | ||||||||
\(143\) | −465.343 | − | 91.6251i | −0.272125 | − | 0.0535810i | ||||
\(144\) | −249.384 | −0.144319 | ||||||||
\(145\) | −138.947 | + | 100.951i | −0.0795787 | + | 0.0578173i | ||||
\(146\) | −170.745 | − | 525.499i | −0.0967873 | − | 0.297881i | ||||
\(147\) | 503.045 | − | 1548.21i | 0.282248 | − | 0.868669i | ||||
\(148\) | −11.9145 | − | 8.65642i | −0.00661736 | − | 0.00480779i | ||||
\(149\) | 1224.27 | + | 889.488i | 0.673131 | + | 0.489058i | 0.871072 | − | 0.491156i | \(-0.163425\pi\) |
−0.197941 | + | 0.980214i | \(0.563425\pi\) | |||||||
\(150\) | 103.647 | − | 318.991i | 0.0564180 | − | 0.173637i | ||||
\(151\) | 864.650 | + | 2661.12i | 0.465988 | + | 1.43416i | 0.857735 | + | 0.514091i | \(0.171871\pi\) |
−0.391747 | + | 0.920073i | \(0.628129\pi\) | |||||||
\(152\) | −711.551 | + | 516.972i | −0.379700 | + | 0.275868i | ||||
\(153\) | −78.9347 | −0.0417091 | ||||||||
\(154\) | −3.90441 | + | 7.00364i | −0.00204303 | + | 0.00366474i | ||||
\(155\) | 378.297 | 0.196036 | ||||||||
\(156\) | 382.514 | − | 277.913i | 0.196318 | − | 0.142633i | ||||
\(157\) | 386.587 | + | 1189.79i | 0.196516 | + | 0.604814i | 0.999956 | + | 0.00942768i | \(0.00300097\pi\) |
−0.803440 | + | 0.595386i | \(0.796999\pi\) | |||||||
\(158\) | −26.7807 | + | 82.4224i | −0.0134845 | + | 0.0415011i | ||||
\(159\) | −1792.88 | − | 1302.60i | −0.894241 | − | 0.649704i | ||||
\(160\) | 167.215 | + | 121.489i | 0.0826221 | + | 0.0600285i | ||||
\(161\) | 15.6025 | − | 48.0197i | 0.00763759 | − | 0.0235061i | ||||
\(162\) | −106.075 | − | 326.466i | −0.0514448 | − | 0.158331i | ||||
\(163\) | 1738.58 | − | 1263.15i | 0.835437 | − | 0.606981i | −0.0856551 | − | 0.996325i | \(-0.527298\pi\) |
0.921092 | + | 0.389344i | \(0.127298\pi\) | |||||||
\(164\) | 1535.19 | 0.730964 | ||||||||
\(165\) | −307.450 | + | 142.459i | −0.145060 | + | 0.0672149i | ||||
\(166\) | 22.9030 | 0.0107086 | ||||||||
\(167\) | 1236.23 | − | 898.172i | 0.572828 | − | 0.416184i | −0.263304 | − | 0.964713i | \(-0.584812\pi\) |
0.836131 | + | 0.548529i | \(0.184812\pi\) | |||||||
\(168\) | −5.04997 | − | 15.5422i | −0.00231913 | − | 0.00713754i | ||||
\(169\) | 52.2239 | − | 160.729i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | 16.3414 | + | 11.8727i | 0.00737253 | + | 0.00535646i | ||||
\(171\) | −347.341 | − | 252.358i | −0.155332 | − | 0.112856i | ||||
\(172\) | −265.341 | + | 816.635i | −0.117628 | + | 0.362022i | ||||
\(173\) | 319.230 | + | 982.490i | 0.140293 | + | 0.431776i | 0.996376 | − | 0.0850620i | \(-0.0271088\pi\) |
−0.856083 | + | 0.516838i | \(0.827109\pi\) | |||||||
\(174\) | −196.610 | + | 142.845i | −0.0856605 | + | 0.0622360i | ||||
\(175\) | 45.6828 | 0.0197331 | ||||||||
\(176\) | 243.886 | + | 2026.91i | 0.104452 | + | 0.868093i | ||||
\(177\) | 4012.07 | 1.70376 | ||||||||
\(178\) | −226.496 | + | 164.559i | −0.0953742 | + | 0.0692934i | ||||
\(179\) | −636.935 | − | 1960.28i | −0.265959 | − | 0.818539i | −0.991471 | − | 0.130329i | \(-0.958397\pi\) |
0.725511 | − | 0.688210i | \(-0.241603\pi\) | |||||||
\(180\) | −20.6362 | + | 63.5116i | −0.00854517 | + | 0.0262993i | ||||
\(181\) | −354.236 | − | 257.368i | −0.145471 | − | 0.105691i | 0.512670 | − | 0.858586i | \(-0.328657\pi\) |
−0.658140 | + | 0.752895i | \(0.728657\pi\) | |||||||
\(182\) | −2.31154 | − | 1.67943i | −0.000941445 | − | 0.000684000i | ||||
\(183\) | −110.324 | + | 339.542i | −0.0445649 | + | 0.137157i | ||||
\(184\) | 377.834 | + | 1162.85i | 0.151382 | + | 0.465906i | ||||
\(185\) | −3.04264 | + | 2.21061i | −0.00120919 | + | 0.000878525i | ||||
\(186\) | 535.290 | 0.211018 | ||||||||
\(187\) | 77.1944 | + | 641.557i | 0.0301872 | + | 0.250884i | ||||
\(188\) | 499.387 | 0.193732 | ||||||||
\(189\) | 45.5538 | − | 33.0968i | 0.0175320 | − | 0.0127378i | ||||
\(190\) | 33.9504 | + | 104.489i | 0.0129633 | + | 0.0398969i | ||||
\(191\) | 1493.65 | − | 4596.99i | 0.565848 | − | 1.74150i | −0.0995698 | − | 0.995031i | \(-0.531747\pi\) |
0.665418 | − | 0.746471i | \(-0.268253\pi\) | |||||||
\(192\) | −1482.98 | − | 1077.45i | −0.557422 | − | 0.404990i | ||||
\(193\) | 4183.16 | + | 3039.24i | 1.56016 | + | 1.13352i | 0.935880 | + | 0.352319i | \(0.114607\pi\) |
0.624278 | + | 0.781202i | \(0.285393\pi\) | |||||||
\(194\) | −196.101 | + | 603.536i | −0.0725732 | + | 0.223357i | ||||
\(195\) | −37.3117 | − | 114.834i | −0.0137023 | − | 0.0421714i | ||||
\(196\) | −2124.75 | + | 1543.72i | −0.774326 | + | 0.562581i | ||||
\(197\) | −2271.17 | −0.821391 | −0.410695 | − | 0.911773i | \(-0.634714\pi\) | ||||
−0.410695 | + | 0.911773i | \(0.634714\pi\) | |||||||
\(198\) | 86.0024 | − | 39.8499i | 0.0308683 | − | 0.0143031i | ||||
\(199\) | 4426.57 | 1.57684 | 0.788421 | − | 0.615136i | \(-0.210899\pi\) | ||||
0.788421 | + | 0.615136i | \(0.210899\pi\) | |||||||
\(200\) | −894.985 | + | 650.244i | −0.316425 | + | 0.229896i | ||||
\(201\) | 674.575 | + | 2076.13i | 0.236721 | + | 0.728551i | ||||
\(202\) | 325.308 | − | 1001.19i | 0.113310 | − | 0.348732i | ||||
\(203\) | −26.7784 | − | 19.4556i | −0.00925850 | − | 0.00672669i | ||||
\(204\) | −521.160 | − | 378.645i | −0.178865 | − | 0.129953i | ||||
\(205\) | 121.148 | − | 372.856i | 0.0412750 | − | 0.127031i | ||||
\(206\) | 170.863 | + | 525.861i | 0.0577892 | + | 0.177857i | ||||
\(207\) | −482.865 | + | 350.822i | −0.162133 | + | 0.117796i | ||||
\(208\) | −727.463 | −0.242502 | ||||||||
\(209\) | −1711.40 | + | 3069.87i | −0.566413 | + | 1.01602i | ||||
\(210\) | −2.04137 | −0.000670798 | ||||||||
\(211\) | −980.664 | + | 712.494i | −0.319961 | + | 0.232465i | −0.736159 | − | 0.676809i | \(-0.763362\pi\) |
0.416198 | + | 0.909274i | \(0.363362\pi\) | |||||||
\(212\) | 1104.84 | + | 3400.36i | 0.357929 | + | 1.10159i | ||||
\(213\) | −290.370 | + | 893.668i | −0.0934077 | + | 0.287479i | ||||
\(214\) | 543.859 | + | 395.137i | 0.173726 | + | 0.126220i | ||||
\(215\) | 177.400 | + | 128.888i | 0.0562724 | + | 0.0408843i | ||||
\(216\) | −421.361 | + | 1296.82i | −0.132731 | + | 0.408506i | ||||
\(217\) | 22.5295 | + | 69.3386i | 0.00704793 | + | 0.0216913i | ||||
\(218\) | −810.444 | + | 588.822i | −0.251790 | + | 0.182936i | ||||
\(219\) | 4500.08 | 1.38853 | ||||||||
\(220\) | 536.384 | + | 105.613i | 0.164377 | + | 0.0323656i | ||||
\(221\) | −230.256 | −0.0700845 | ||||||||
\(222\) | −4.30533 | + | 3.12801i | −0.00130160 | + | 0.000945667i | ||||
\(223\) | −232.337 | − | 715.059i | −0.0697687 | − | 0.214726i | 0.910093 | − | 0.414405i | \(-0.136010\pi\) |
−0.979861 | + | 0.199679i | \(0.936010\pi\) | |||||||
\(224\) | −12.3094 | + | 37.8844i | −0.00367168 | + | 0.0113003i | ||||
\(225\) | −436.883 | − | 317.414i | −0.129447 | − | 0.0940487i | ||||
\(226\) | 546.063 | + | 396.738i | 0.160724 | + | 0.116773i | ||||
\(227\) | −590.087 | + | 1816.10i | −0.172535 | + | 0.531008i | −0.999512 | − | 0.0312271i | \(-0.990058\pi\) |
0.826977 | + | 0.562235i | \(0.190058\pi\) | |||||||
\(228\) | −1082.75 | − | 3332.35i | −0.314502 | − | 0.967939i | ||||
\(229\) | −332.331 | + | 241.452i | −0.0958997 | + | 0.0696752i | −0.634702 | − | 0.772757i | \(-0.718877\pi\) |
0.538802 | + | 0.842432i | \(0.318877\pi\) | |||||||
\(230\) | 152.733 | 0.0437866 | ||||||||
\(231\) | −44.4218 | − | 47.8687i | −0.0126525 | − | 0.0136343i | ||||
\(232\) | 801.553 | 0.226830 | ||||||||
\(233\) | −3979.91 | + | 2891.57i | −1.11902 | + | 0.813018i | −0.984061 | − | 0.177832i | \(-0.943092\pi\) |
−0.134963 | + | 0.990851i | \(0.543092\pi\) | |||||||
\(234\) | 10.4372 | + | 32.1222i | 0.00291580 | + | 0.00897392i | ||||
\(235\) | 39.4088 | − | 121.288i | 0.0109394 | − | 0.0336679i | ||||
\(236\) | −5236.64 | − | 3804.64i | −1.44439 | − | 1.04941i | ||||
\(237\) | −571.020 | − | 414.870i | −0.156505 | − | 0.113708i | ||||
\(238\) | −1.20296 | + | 3.70232i | −0.000327631 | + | 0.00100834i | ||||
\(239\) | 371.041 | + | 1141.95i | 0.100421 | + | 0.309064i | 0.988629 | − | 0.150378i | \(-0.0480492\pi\) |
−0.888207 | + | 0.459443i | \(0.848049\pi\) | |||||||
\(240\) | −420.480 | + | 305.496i | −0.113091 | + | 0.0821654i | ||||
\(241\) | −1262.14 | −0.337350 | −0.168675 | − | 0.985672i | \(-0.553949\pi\) | ||||
−0.168675 | + | 0.985672i | \(0.553949\pi\) | |||||||
\(242\) | −407.994 | − | 660.029i | −0.108375 | − | 0.175323i | ||||
\(243\) | −1236.93 | −0.326539 | ||||||||
\(244\) | 465.984 | − | 338.557i | 0.122261 | − | 0.0888275i | ||||
\(245\) | 207.256 | + | 637.867i | 0.0540452 | + | 0.166334i | ||||
\(246\) | 171.425 | − | 527.591i | 0.0444294 | − | 0.136740i | ||||
\(247\) | −1013.21 | − | 736.139i | −0.261008 | − | 0.189633i | ||||
\(248\) | −1428.34 | − | 1037.75i | −0.365725 | − | 0.265715i | ||||
\(249\) | −57.6408 | + | 177.400i | −0.0146700 | + | 0.0451497i | ||||
\(250\) | 86.7538 | + | 267.001i | 0.0219472 | + | 0.0675465i | ||||
\(251\) | 892.980 | − | 648.788i | 0.224559 | − | 0.163152i | −0.469817 | − | 0.882764i | \(-0.655680\pi\) |
0.694377 | + | 0.719612i | \(0.255680\pi\) | |||||||
\(252\) | −12.8701 | −0.00321723 | ||||||||
\(253\) | 3323.59 | + | 3581.49i | 0.825899 | + | 0.889985i | ||||
\(254\) | 1151.51 | 0.284457 | ||||||||
\(255\) | −133.090 | + | 96.6954i | −0.0326839 | + | 0.0237463i | ||||
\(256\) | 761.597 | + | 2343.95i | 0.185937 | + | 0.572254i | ||||
\(257\) | 2002.76 | − | 6163.85i | 0.486103 | − | 1.49607i | −0.344274 | − | 0.938869i | \(-0.611875\pi\) |
0.830377 | − | 0.557202i | \(-0.188125\pi\) | |||||||
\(258\) | 251.020 | + | 182.377i | 0.0605730 | + | 0.0440088i | ||||
\(259\) | −0.586390 | − | 0.426037i | −0.000140681 | − | 0.000102211i | ||||
\(260\) | −60.1966 | + | 185.266i | −0.0143586 | + | 0.0441912i | ||||
\(261\) | 120.911 | + | 372.125i | 0.0286750 | + | 0.0882527i | ||||
\(262\) | 783.761 | − | 569.435i | 0.184813 | − | 0.134274i | ||||
\(263\) | 3139.44 | 0.736068 | 0.368034 | − | 0.929812i | \(-0.380031\pi\) | ||||
0.368034 | + | 0.929812i | \(0.380031\pi\) | |||||||
\(264\) | 1551.64 | + | 305.515i | 0.361730 | + | 0.0712240i | ||||
\(265\) | 913.046 | 0.211653 | ||||||||
\(266\) | −17.1300 | + | 12.4456i | −0.00394852 | + | 0.00286877i | ||||
\(267\) | −704.596 | − | 2168.52i | −0.161500 | − | 0.497047i | ||||
\(268\) | 1088.32 | − | 3349.50i | 0.248059 | − | 0.763446i | ||||
\(269\) | −798.887 | − | 580.426i | −0.181074 | − | 0.131558i | 0.493556 | − | 0.869714i | \(-0.335697\pi\) |
−0.674630 | + | 0.738156i | \(0.735697\pi\) | |||||||
\(270\) | 137.798 | + | 100.116i | 0.0310598 | + | 0.0225663i | ||||
\(271\) | 470.445 | − | 1447.88i | 0.105452 | − | 0.324548i | −0.884384 | − | 0.466760i | \(-0.845421\pi\) |
0.989836 | + | 0.142212i | \(0.0454213\pi\) | |||||||
\(272\) | 306.279 | + | 942.629i | 0.0682753 | + | 0.210130i | ||||
\(273\) | 18.8259 | − | 13.6778i | 0.00417362 | − | 0.00303231i | ||||
\(274\) | 1188.00 | 0.261932 | ||||||||
\(275\) | −2152.59 | + | 3861.27i | −0.472023 | + | 0.846703i | ||||
\(276\) | −4870.95 | −1.06231 | ||||||||
\(277\) | 3068.20 | − | 2229.18i | 0.665525 | − | 0.483532i | −0.202999 | − | 0.979179i | \(-0.565069\pi\) |
0.868524 | + | 0.495647i | \(0.165069\pi\) | |||||||
\(278\) | −222.469 | − | 684.690i | −0.0479957 | − | 0.147716i | ||||
\(279\) | 266.322 | − | 819.654i | 0.0571479 | − | 0.175883i | ||||
\(280\) | 5.44708 | + | 3.95754i | 0.00116259 | + | 0.000844672i | ||||
\(281\) | 3983.90 | + | 2894.47i | 0.845763 | + | 0.614483i | 0.923974 | − | 0.382454i | \(-0.124921\pi\) |
−0.0782117 | + | 0.996937i | \(0.524921\pi\) | |||||||
\(282\) | 55.7634 | − | 171.622i | 0.0117754 | − | 0.0362409i | ||||
\(283\) | −2319.76 | − | 7139.48i | −0.487263 | − | 1.49964i | −0.828677 | − | 0.559727i | \(-0.810906\pi\) |
0.341414 | − | 0.939913i | \(-0.389094\pi\) | |||||||
\(284\) | 1226.46 | − | 891.076i | 0.256257 | − | 0.186182i | ||||
\(285\) | −894.783 | −0.185973 | ||||||||
\(286\) | 250.873 | − | 116.244i | 0.0518685 | − | 0.0240337i | ||||
\(287\) | 75.5563 | 0.0155399 | ||||||||
\(288\) | 380.949 | − | 276.776i | 0.0779433 | − | 0.0566291i | ||||
\(289\) | −1421.26 | − | 4374.18i | −0.289285 | − | 0.890328i | ||||
\(290\) | 30.9406 | − | 95.2255i | 0.00626516 | − | 0.0192822i | ||||
\(291\) | −4181.28 | − | 3037.88i | −0.842305 | − | 0.611971i | ||||
\(292\) | −5873.59 | − | 4267.41i | −1.17714 | − | 0.855245i | ||||
\(293\) | 459.482 | − | 1414.14i | 0.0916151 | − | 0.281962i | −0.894742 | − | 0.446584i | \(-0.852640\pi\) |
0.986357 | + | 0.164622i | \(0.0526404\pi\) | |||||||
\(294\) | 293.266 | + | 902.580i | 0.0581756 | + | 0.179046i | ||||
\(295\) | −1337.29 | + | 971.599i | −0.263933 | + | 0.191758i | ||||
\(296\) | 17.5523 | 0.00344665 | ||||||||
\(297\) | 650.939 | + | 5409.90i | 0.127176 | + | 1.05695i | ||||
\(298\) | −882.220 | −0.171495 | ||||||||
\(299\) | −1408.54 | + | 1023.36i | −0.272434 | + | 0.197935i | ||||
\(300\) | −1361.87 | − | 4191.40i | −0.262092 | − | 0.806636i | ||||
\(301\) | −13.0591 | + | 40.1918i | −0.00250071 | + | 0.00769640i | ||||
\(302\) | −1319.69 | − | 958.809i | −0.251455 | − | 0.182693i | ||||
\(303\) | 6936.25 | + | 5039.48i | 1.31511 | + | 0.955480i | ||||
\(304\) | −1665.89 | + | 5127.10i | −0.314295 | + | 0.967300i | ||||
\(305\) | −45.4537 | − | 139.892i | −0.00853335 | − | 0.0262630i | ||||
\(306\) | 37.2290 | − | 27.0484i | 0.00695503 | − | 0.00505312i | ||||
\(307\) | 8015.67 | 1.49016 | 0.745079 | − | 0.666976i | \(-0.232412\pi\) | ||||
0.745079 | + | 0.666976i | \(0.232412\pi\) | |||||||
\(308\) | 12.5864 | + | 104.604i | 0.00232849 | + | 0.0193519i | ||||
\(309\) | −4503.18 | −0.829052 | ||||||||
\(310\) | −178.421 | + | 129.631i | −0.0326892 | + | 0.0237501i | ||||
\(311\) | −519.374 | − | 1598.47i | −0.0946978 | − | 0.291450i | 0.892477 | − | 0.451093i | \(-0.148966\pi\) |
−0.987175 | + | 0.159643i | \(0.948966\pi\) | |||||||
\(312\) | −174.135 | + | 535.933i | −0.0315976 | + | 0.0972475i | ||||
\(313\) | −5282.94 | − | 3838.28i | −0.954024 | − | 0.693139i | −0.00226870 | − | 0.999997i | \(-0.500722\pi\) |
−0.951755 | + | 0.306859i | \(0.900722\pi\) | |||||||
\(314\) | −590.035 | − | 428.686i | −0.106043 | − | 0.0770450i | ||||
\(315\) | −1.01564 | + | 3.12581i | −0.000181666 | + | 0.000559109i | ||||
\(316\) | 351.886 | + | 1082.99i | 0.0626429 | + | 0.192795i | ||||
\(317\) | 2870.41 | − | 2085.48i | 0.508575 | − | 0.369501i | −0.303708 | − | 0.952765i | \(-0.598225\pi\) |
0.812283 | + | 0.583264i | \(0.198225\pi\) | |||||||
\(318\) | 1291.96 | 0.227828 | ||||||||
\(319\) | 2906.27 | − | 1346.64i | 0.510093 | − | 0.236356i | ||||
\(320\) | 755.227 | 0.131933 | ||||||||
\(321\) | −4429.36 | + | 3218.12i | −0.770164 | + | 0.559557i | ||||
\(322\) | 9.09601 | + | 27.9946i | 0.00157423 | + | 0.00484497i | ||||
\(323\) | −527.287 | + | 1622.82i | −0.0908330 | + | 0.279555i | ||||
\(324\) | −3648.97 | − | 2651.13i | −0.625681 | − | 0.454584i | ||||
\(325\) | −1274.41 | − | 925.911i | −0.217512 | − | 0.158032i | ||||
\(326\) | −387.147 | + | 1191.51i | −0.0657732 | + | 0.202429i | ||||
\(327\) | −2521.17 | − | 7759.37i | −0.426364 | − | 1.31221i | ||||
\(328\) | −1480.25 | + | 1075.46i | −0.249186 | + | 0.181044i | ||||
\(329\) | 24.5780 | 0.00411863 | ||||||||
\(330\) | 96.1901 | − | 172.543i | 0.0160457 | − | 0.0287824i | ||||
\(331\) | 9268.55 | 1.53911 | 0.769555 | − | 0.638581i | \(-0.220478\pi\) | ||||
0.769555 | + | 0.638581i | \(0.220478\pi\) | |||||||
\(332\) | 243.462 | − | 176.886i | 0.0402462 | − | 0.0292406i | ||||
\(333\) | 2.64769 | + | 8.14874i | 0.000435713 | + | 0.00134099i | ||||
\(334\) | −275.283 | + | 847.233i | −0.0450982 | + | 0.138798i | ||||
\(335\) | −727.621 | − | 528.648i | −0.118669 | − | 0.0862183i | ||||
\(336\) | −81.0365 | − | 58.8764i | −0.0131574 | − | 0.00955944i | ||||
\(337\) | −1183.95 | + | 3643.81i | −0.191376 | + | 0.588994i | 0.808624 | + | 0.588326i | \(0.200213\pi\) |
−1.00000 | 0.000668085i | \(0.999787\pi\) | ||||||||
\(338\) | 30.4456 | + | 93.7019i | 0.00489947 | + | 0.0150790i | ||||
\(339\) | −4447.31 | + | 3231.16i | −0.712521 | + | 0.517677i | ||||
\(340\) | 265.408 | 0.0423345 | ||||||||
\(341\) | −6922.34 | − | 1363.00i | −1.09931 | − | 0.216453i | ||||
\(342\) | 250.296 | 0.0395744 | ||||||||
\(343\) | −209.188 | + | 151.984i | −0.0329303 | + | 0.0239253i | ||||
\(344\) | −316.241 | − | 973.291i | −0.0495657 | − | 0.152547i | ||||
\(345\) | −384.388 | + | 1183.02i | −0.0599848 | + | 0.184614i | ||||
\(346\) | −487.231 | − | 353.994i | −0.0757043 | − | 0.0550024i | ||||
\(347\) | 1533.13 | + | 1113.89i | 0.237184 | + | 0.172324i | 0.700028 | − | 0.714116i | \(-0.253171\pi\) |
−0.462844 | + | 0.886440i | \(0.653171\pi\) | |||||||
\(348\) | −986.757 | + | 3036.92i | −0.151999 | + | 0.467805i | ||||
\(349\) | −1861.55 | − | 5729.25i | −0.285520 | − | 0.878739i | −0.986242 | − | 0.165305i | \(-0.947139\pi\) |
0.700723 | − | 0.713434i | \(-0.252861\pi\) | |||||||
\(350\) | −21.5460 | + | 15.6541i | −0.00329051 | + | 0.00239070i | ||||
\(351\) | −1941.62 | −0.295260 | ||||||||
\(352\) | −2622.10 | − | 2825.56i | −0.397041 | − | 0.427850i | ||||
\(353\) | −1067.61 | −0.160972 | −0.0804858 | − | 0.996756i | \(-0.525647\pi\) | ||||
−0.0804858 | + | 0.996756i | \(0.525647\pi\) | |||||||
\(354\) | −1892.26 | + | 1374.81i | −0.284104 | + | 0.206413i | ||||
\(355\) | −119.633 | − | 368.193i | −0.0178858 | − | 0.0550470i | ||||
\(356\) | −1136.75 | + | 3498.57i | −0.169235 | + | 0.520853i | ||||
\(357\) | −25.6496 | − | 18.6355i | −0.00380258 | − | 0.00276273i | ||||
\(358\) | 972.133 | + | 706.296i | 0.143516 | + | 0.104271i | ||||
\(359\) | 2897.10 | − | 8916.35i | 0.425914 | − | 1.31083i | −0.476203 | − | 0.879335i | \(-0.657987\pi\) |
0.902117 | − | 0.431492i | \(-0.142013\pi\) | |||||||
\(360\) | −24.5948 | − | 75.6951i | −0.00360073 | − | 0.0110819i | ||||
\(361\) | −1959.45 | + | 1423.63i | −0.285676 | + | 0.207556i | ||||
\(362\) | 255.265 | 0.0370619 | ||||||||
\(363\) | 6139.20 | − | 1499.09i | 0.887671 | − | 0.216754i | ||||
\(364\) | −37.5427 | −0.00540596 | ||||||||
\(365\) | −1499.95 | + | 1089.78i | −0.215099 | + | 0.156278i | ||||
\(366\) | −64.3169 | − | 197.947i | −0.00918551 | − | 0.0282701i | ||||
\(367\) | 2168.39 | − | 6673.63i | 0.308418 | − | 0.949212i | −0.669962 | − | 0.742395i | \(-0.733690\pi\) |
0.978380 | − | 0.206817i | \(-0.0663103\pi\) | |||||||
\(368\) | 6063.07 | + | 4405.08i | 0.858857 | + | 0.623996i | ||||
\(369\) | −722.576 | − | 524.982i | −0.101940 | − | 0.0740637i | ||||
\(370\) | 0.677534 | − | 2.08524i | 9.51981e−5 | − | 0.000292990i | ||||
\(371\) | 54.3764 | + | 167.353i | 0.00760939 | + | 0.0234193i | ||||
\(372\) | 5690.19 | − | 4134.17i | 0.793072 | − | 0.576201i | ||||
\(373\) | 3621.06 | 0.502658 | 0.251329 | − | 0.967902i | \(-0.419132\pi\) | ||||
0.251329 | + | 0.967902i | \(0.419132\pi\) | |||||||
\(374\) | −256.249 | − | 276.133i | −0.0354287 | − | 0.0381778i | ||||
\(375\) | −2286.45 | −0.314857 | ||||||||
\(376\) | −481.515 | + | 349.841i | −0.0660432 | + | 0.0479832i | ||||
\(377\) | 352.701 | + | 1085.50i | 0.0481831 | + | 0.148292i | ||||
\(378\) | −10.1439 | + | 31.2197i | −0.00138028 | + | 0.00424806i | ||||
\(379\) | −292.533 | − | 212.538i | −0.0396475 | − | 0.0288056i | 0.567785 | − | 0.823177i | \(-0.307800\pi\) |
−0.607433 | + | 0.794371i | \(0.707800\pi\) | |||||||
\(380\) | 1167.89 | + | 848.521i | 0.157662 | + | 0.114548i | ||||
\(381\) | −2898.04 | + | 8919.25i | −0.389688 | + | 1.19934i | ||||
\(382\) | 870.774 | + | 2679.97i | 0.116630 | + | 0.358950i | ||||
\(383\) | 4882.21 | − | 3547.13i | 0.651355 | − | 0.473237i | −0.212377 | − | 0.977188i | \(-0.568121\pi\) |
0.863733 | + | 0.503950i | \(0.168121\pi\) | |||||||
\(384\) | 5082.01 | 0.675365 | ||||||||
\(385\) | 26.3988 | + | 5.19789i | 0.00349457 | + | 0.000688075i | ||||
\(386\) | −3014.41 | −0.397486 | ||||||||
\(387\) | 404.151 | − | 293.633i | 0.0530857 | − | 0.0385690i | ||||
\(388\) | 2576.68 | + | 7930.19i | 0.337142 | + | 1.03762i | ||||
\(389\) | −1927.64 | + | 5932.65i | −0.251247 | + | 0.773258i | 0.743299 | + | 0.668959i | \(0.233260\pi\) |
−0.994546 | + | 0.104299i | \(0.966740\pi\) | |||||||
\(390\) | 56.9477 | + | 41.3749i | 0.00739400 | + | 0.00537205i | ||||
\(391\) | 1919.08 | + | 1394.29i | 0.248214 | + | 0.180338i | ||||
\(392\) | 967.269 | − | 2976.95i | 0.124629 | − | 0.383568i | ||||
\(393\) | 2438.16 | + | 7503.89i | 0.312949 | + | 0.963159i | ||||
\(394\) | 1071.18 | − | 778.257i | 0.136968 | − | 0.0995128i | ||||
\(395\) | 290.799 | 0.0370423 | ||||||||
\(396\) | 606.446 | − | 1087.83i | 0.0769572 | − | 0.138044i | ||||
\(397\) | −3469.46 | −0.438607 | −0.219304 | − | 0.975657i | \(-0.570379\pi\) | ||||
−0.219304 | + | 0.975657i | \(0.570379\pi\) | |||||||
\(398\) | −2087.76 | + | 1516.85i | −0.262940 | + | 0.191037i | ||||
\(399\) | −53.2888 | − | 164.006i | −0.00668615 | − | 0.0205779i | ||||
\(400\) | −2095.35 | + | 6448.83i | −0.261919 | + | 0.806103i | ||||
\(401\) | 10108.4 | + | 7344.18i | 1.25883 | + | 0.914591i | 0.998700 | − | 0.0509831i | \(-0.0162355\pi\) |
0.260127 | + | 0.965574i | \(0.416235\pi\) | |||||||
\(402\) | −1029.58 | − | 748.035i | −0.127739 | − | 0.0928075i | ||||
\(403\) | 776.871 | − | 2390.96i | 0.0960266 | − | 0.295539i | ||||
\(404\) | −4274.40 | − | 13155.3i | −0.526385 | − | 1.62005i | ||||
\(405\) | −931.845 | + | 677.025i | −0.114330 | + | 0.0830658i | ||||
\(406\) | 19.2967 | 0.00235881 | ||||||||
\(407\) | 63.6411 | − | 29.4887i | 0.00775079 | − | 0.00359140i | ||||
\(408\) | 767.764 | 0.0931618 | ||||||||
\(409\) | 3349.81 | − | 2433.78i | 0.404982 | − | 0.294237i | −0.366585 | − | 0.930384i | \(-0.619473\pi\) |
0.771567 | + | 0.636148i | \(0.219473\pi\) | |||||||
\(410\) | 70.6274 | + | 217.369i | 0.00850741 | + | 0.0261831i | ||||
\(411\) | −2989.87 | + | 9201.86i | −0.358830 | + | 1.10437i | ||||
\(412\) | 5877.64 | + | 4270.36i | 0.702842 | + | 0.510644i | ||||
\(413\) | −257.728 | − | 187.250i | −0.0307070 | − | 0.0223099i | ||||
\(414\) | 107.524 | − | 330.925i | 0.0127646 | − | 0.0392852i | ||||
\(415\) | −23.7482 | − | 73.0893i | −0.00280904 | − | 0.00864533i | ||||
\(416\) | 1111.25 | − | 807.367i | 0.130969 | − | 0.0951548i | ||||
\(417\) | 5863.30 | 0.688554 | ||||||||
\(418\) | −244.778 | − | 2034.33i | −0.0286423 | − | 0.238044i | ||||
\(419\) | 2880.64 | 0.335867 | 0.167934 | − | 0.985798i | \(-0.446291\pi\) | ||||
0.167934 | + | 0.985798i | \(0.446291\pi\) | |||||||
\(420\) | −21.7000 | + | 15.7660i | −0.00252107 | + | 0.00183167i | ||||
\(421\) | 615.096 | + | 1893.07i | 0.0712065 | + | 0.219151i | 0.980326 | − | 0.197384i | \(-0.0632445\pi\) |
−0.909120 | + | 0.416535i | \(0.863244\pi\) | |||||||
\(422\) | 218.374 | − | 672.085i | 0.0251902 | − | 0.0775275i | ||||
\(423\) | −235.050 | − | 170.774i | −0.0270177 | − | 0.0196295i | ||||
\(424\) | −3447.40 | − | 2504.68i | −0.394859 | − | 0.286882i | ||||
\(425\) | −663.218 | + | 2041.18i | −0.0756960 | + | 0.232968i | ||||
\(426\) | −169.281 | − | 520.992i | −0.0192528 | − | 0.0592539i | ||||
\(427\) | 22.9340 | − | 16.6625i | 0.00259919 | − | 0.00188842i | ||||
\(428\) | 8833.02 | 0.997571 | ||||||||
\(429\) | 269.012 | + | 2235.74i | 0.0302751 | + | 0.251614i | ||||
\(430\) | −127.835 | −0.0143367 | ||||||||
\(431\) | −4011.29 | + | 2914.37i | −0.448299 | + | 0.325708i | −0.788924 | − | 0.614491i | \(-0.789361\pi\) |
0.340625 | + | 0.940199i | \(0.389361\pi\) | |||||||
\(432\) | 2582.68 | + | 7948.68i | 0.287637 | + | 0.885257i | ||||
\(433\) | −291.171 | + | 896.133i | −0.0323159 | + | 0.0994582i | −0.965913 | − | 0.258865i | \(-0.916651\pi\) |
0.933598 | + | 0.358323i | \(0.116651\pi\) | |||||||
\(434\) | −34.3860 | − | 24.9829i | −0.00380318 | − | 0.00276317i | ||||
\(435\) | 659.719 | + | 479.314i | 0.0727152 | + | 0.0528307i | ||||
\(436\) | −4067.51 | + | 12518.5i | −0.446785 | + | 1.37506i | ||||
\(437\) | 3987.01 | + | 12270.8i | 0.436441 | + | 1.34323i | ||||
\(438\) | −2122.43 | + | 1542.03i | −0.231538 | + | 0.168222i | ||||
\(439\) | −11859.6 | −1.28935 | −0.644676 | − | 0.764456i | \(-0.723008\pi\) | ||||
−0.644676 | + | 0.764456i | \(0.723008\pi\) | |||||||
\(440\) | −591.174 | + | 273.925i | −0.0640525 | + | 0.0296793i | ||||
\(441\) | 1527.97 | 0.164990 | ||||||||
\(442\) | 108.598 | − | 78.9014i | 0.0116867 | − | 0.00849085i | ||||
\(443\) | −2057.79 | − | 6333.22i | −0.220696 | − | 0.679233i | −0.998700 | − | 0.0509736i | \(-0.983768\pi\) |
0.778004 | − | 0.628260i | \(-0.216232\pi\) | |||||||
\(444\) | −21.6079 | + | 66.5022i | −0.00230960 | + | 0.00710823i | ||||
\(445\) | 760.003 | + | 552.174i | 0.0809609 | + | 0.0588215i | ||||
\(446\) | 354.608 | + | 257.638i | 0.0376484 | + | 0.0273532i | ||||
\(447\) | 2220.31 | − | 6833.41i | 0.234937 | − | 0.723063i | ||||
\(448\) | 44.9776 | + | 138.427i | 0.00474328 | + | 0.0145983i | ||||
\(449\) | −1189.43 | + | 864.168i | −0.125017 | + | 0.0908299i | −0.648536 | − | 0.761184i | \(-0.724619\pi\) |
0.523520 | + | 0.852013i | \(0.324619\pi\) | |||||||
\(450\) | 314.821 | 0.0329795 | ||||||||
\(451\) | −3560.25 | + | 6386.28i | −0.371720 | + | 0.666781i | ||||
\(452\) | 8868.82 | 0.922907 | ||||||||
\(453\) | 10747.9 | − | 7808.84i | 1.11475 | − | 0.809915i | ||||
\(454\) | −344.010 | − | 1058.75i | −0.0355621 | − | 0.109449i | ||||
\(455\) | −2.96265 | + | 9.11811i | −0.000305256 | + | 0.000939481i | ||||
\(456\) | 3378.44 | + | 2454.58i | 0.346952 | + | 0.252075i | ||||
\(457\) | 494.318 | + | 359.143i | 0.0505978 | + | 0.0367615i | 0.612797 | − | 0.790241i | \(-0.290044\pi\) |
−0.562199 | + | 0.827002i | \(0.690044\pi\) | |||||||
\(458\) | 74.0033 | − | 227.759i | 0.00755010 | − | 0.0232368i | ||||
\(459\) | 817.468 | + | 2515.91i | 0.0831289 | + | 0.255844i | ||||
\(460\) | 1623.57 | − | 1179.59i | 0.164564 | − | 0.119563i | ||||
\(461\) | −14270.6 | −1.44175 | −0.720876 | − | 0.693064i | \(-0.756260\pi\) | ||||
−0.720876 | + | 0.693064i | \(0.756260\pi\) | |||||||
\(462\) | 37.3543 | + | 7.35499i | 0.00376164 | + | 0.000740661i | ||||
\(463\) | −5997.52 | −0.602005 | −0.301003 | − | 0.953623i | \(-0.597321\pi\) | ||||
−0.301003 | + | 0.953623i | \(0.597321\pi\) | |||||||
\(464\) | 3974.72 | − | 2887.80i | 0.397676 | − | 0.288929i | ||||
\(465\) | −555.042 | − | 1708.24i | −0.0553536 | − | 0.170361i | ||||
\(466\) | 886.244 | − | 2727.58i | 0.0880997 | − | 0.271143i | ||||
\(467\) | 489.854 | + | 355.900i | 0.0485391 | + | 0.0352657i | 0.611790 | − | 0.791020i | \(-0.290450\pi\) |
−0.563251 | + | 0.826286i | \(0.690450\pi\) | |||||||
\(468\) | 359.036 | + | 260.855i | 0.0354625 | + | 0.0257650i | ||||
\(469\) | 53.5631 | − | 164.850i | 0.00527359 | − | 0.0162304i | ||||
\(470\) | 22.9747 | + | 70.7087i | 0.00225477 | + | 0.00693947i | ||||
\(471\) | 4805.43 | − | 3491.35i | 0.470112 | − | 0.341556i | ||||
\(472\) | 7714.53 | 0.752309 | ||||||||
\(473\) | −2781.80 | − | 2997.65i | −0.270417 | − | 0.291400i | ||||
\(474\) | 411.480 | 0.0398732 | ||||||||
\(475\) | −9444.14 | + | 6861.57i | −0.912267 | + | 0.662801i | ||||
\(476\) | 15.8063 | + | 48.6469i | 0.00152202 | + | 0.00468430i | ||||
\(477\) | 642.785 | − | 1978.29i | 0.0617004 | − | 0.189894i | ||||
\(478\) | −566.308 | − | 411.447i | −0.0541890 | − | 0.0393706i | ||||
\(479\) | 4159.65 | + | 3022.16i | 0.396783 | + | 0.288280i | 0.768229 | − | 0.640175i | \(-0.221138\pi\) |
−0.371446 | + | 0.928454i | \(0.621138\pi\) | |||||||
\(480\) | 303.257 | − | 933.330i | 0.0288369 | − | 0.0887510i | ||||
\(481\) | 7.72341 | + | 23.7702i | 0.000732136 | + | 0.00225328i | ||||
\(482\) | 595.277 | − | 432.494i | 0.0562534 | − | 0.0408705i | ||||
\(483\) | −239.730 | −0.0225841 | ||||||||
\(484\) | −9434.59 | − | 3865.16i | −0.886044 | − | 0.362994i | ||||
\(485\) | 2129.37 | 0.199360 | ||||||||
\(486\) | 583.388 | − | 423.856i | 0.0544506 | − | 0.0395607i | ||||
\(487\) | −1139.40 | − | 3506.72i | −0.106019 | − | 0.326293i | 0.883949 | − | 0.467583i | \(-0.154875\pi\) |
−0.989968 | + | 0.141290i | \(0.954875\pi\) | |||||||
\(488\) | −212.134 | + | 652.881i | −0.0196780 | + | 0.0605626i | ||||
\(489\) | −8254.77 | − | 5997.44i | −0.763382 | − | 0.554630i | ||||
\(490\) | −316.328 | − | 229.825i | −0.0291637 | − | 0.0211887i | ||||
\(491\) | −3288.67 | + | 10121.5i | −0.302272 | + | 0.930298i | 0.678409 | + | 0.734685i | \(0.262670\pi\) |
−0.980681 | + | 0.195614i | \(0.937330\pi\) | |||||||
\(492\) | −2252.44 | − | 6932.31i | −0.206398 | − | 0.635229i | ||||
\(493\) | 1258.07 | − | 914.044i | 0.114931 | − | 0.0835020i | ||||
\(494\) | 730.124 | 0.0664976 | ||||||||
\(495\) | −216.347 | − | 233.135i | −0.0196446 | − | 0.0211689i | ||||
\(496\) | −10821.6 | −0.979644 | ||||||||
\(497\) | 60.3619 | − | 43.8555i | 0.00544789 | − | 0.00395812i | ||||
\(498\) | −33.6036 | − | 103.421i | −0.00302372 | − | 0.00930605i | ||||
\(499\) | 2302.24 | − | 7085.58i | 0.206538 | − | 0.635660i | −0.793108 | − | 0.609081i | \(-0.791539\pi\) |
0.999647 | − | 0.0265791i | \(-0.00846137\pi\) | |||||||
\(500\) | 2984.32 | + | 2168.23i | 0.266925 | + | 0.193933i | ||||
\(501\) | −5869.60 | − | 4264.51i | −0.523422 | − | 0.380288i | ||||
\(502\) | −198.848 | + | 611.992i | −0.0176794 | + | 0.0544115i | ||||
\(503\) | −5573.34 | − | 17153.0i | −0.494041 | − | 1.52050i | −0.818445 | − | 0.574585i | \(-0.805164\pi\) |
0.324404 | − | 0.945919i | \(-0.394836\pi\) | |||||||
\(504\) | 12.4095 | − | 9.01604i | 0.00109675 | − | 0.000796838i | ||||
\(505\) | −3532.37 | −0.311265 | ||||||||
\(506\) | −2794.81 | − | 550.293i | −0.245543 | − | 0.0483469i | ||||
\(507\) | −802.411 | −0.0702886 | ||||||||
\(508\) | 12240.7 | − | 8893.38i | 1.06908 | − | 0.776732i | ||||
\(509\) | 2207.11 | + | 6792.79i | 0.192197 | + | 0.591523i | 0.999998 | + | 0.00206686i | \(0.000657902\pi\) |
−0.807800 | + | 0.589456i | \(0.799342\pi\) | |||||||
\(510\) | 29.6364 | − | 91.2113i | 0.00257318 | − | 0.00791942i | ||||
\(511\) | −289.077 | − | 210.027i | −0.0250254 | − | 0.0181820i | ||||
\(512\) | −8089.85 | − | 5877.62i | −0.698289 | − | 0.507337i | ||||
\(513\) | −4446.33 | + | 13684.4i | −0.382671 | + | 1.17774i | ||||
\(514\) | 1167.57 | + | 3593.42i | 0.100193 | + | 0.308363i | ||||
\(515\) | 1500.99 | − | 1090.53i | 0.128430 | − | 0.0933098i | ||||
\(516\) | 4076.91 | 0.347822 | ||||||||
\(517\) | −1158.13 | + | 2077.42i | −0.0985191 | + | 0.176721i | ||||
\(518\) | 0.422556 | 3.58418e−5 | ||||||||
\(519\) | 3968.16 | − | 2883.04i | 0.335613 | − | 0.243837i | ||||
\(520\) | −71.7441 | − | 220.806i | −0.00605036 | − | 0.0186211i | ||||
\(521\) | 725.702 | − | 2233.48i | 0.0610241 | − | 0.187813i | −0.915897 | − | 0.401413i | \(-0.868519\pi\) |
0.976921 | + | 0.213600i | \(0.0685191\pi\) | |||||||
\(522\) | −184.542 | − | 134.078i | −0.0154735 | − | 0.0112422i | ||||
\(523\) | −12397.1 | − | 9007.02i | −1.03650 | − | 0.753059i | −0.0668976 | − | 0.997760i | \(-0.521310\pi\) |
−0.969599 | + | 0.244701i | \(0.921310\pi\) | |||||||
\(524\) | 3933.59 | − | 12106.3i | 0.327938 | − | 1.00929i | ||||
\(525\) | −67.0263 | − | 206.286i | −0.00557193 | − | 0.0171487i | ||||
\(526\) | −1480.69 | + | 1075.79i | −0.122740 | + | 0.0891758i | ||||
\(527\) | −3425.24 | −0.283123 | ||||||||
\(528\) | 8794.92 | − | 4075.20i | 0.724904 | − | 0.335891i | ||||
\(529\) | 5769.38 | 0.474183 | ||||||||
\(530\) | −430.631 | + | 312.872i | −0.0352933 | + | 0.0256421i | ||||
\(531\) | 1163.70 | + | 3581.51i | 0.0951043 | + | 0.292701i | ||||
\(532\) | −85.9730 | + | 264.598i | −0.00700639 | + | 0.0215635i | ||||
\(533\) | −2107.79 | − | 1531.40i | −0.171291 | − | 0.124450i | ||||
\(534\) | 1075.40 | + | 781.325i | 0.0871483 | + | 0.0633169i | ||||
\(535\) | 697.052 | − | 2145.31i | 0.0563294 | − | 0.173364i | ||||
\(536\) | 1297.09 | + | 3992.04i | 0.104526 | + | 0.321698i | ||||
\(537\) | −7917.35 | + | 5752.29i | −0.636237 | + | 0.462253i | ||||
\(538\) | 575.683 | 0.0461328 | ||||||||
\(539\) | −1494.28 | − | 12418.9i | −0.119412 | − | 0.992427i | ||||
\(540\) | 2238.04 | 0.178352 | ||||||||
\(541\) | −7948.83 | + | 5775.16i | −0.631695 | + | 0.458953i | −0.856987 | − | 0.515338i | \(-0.827666\pi\) |
0.225292 | + | 0.974291i | \(0.427666\pi\) | |||||||
\(542\) | 274.261 | + | 844.089i | 0.0217353 | + | 0.0668943i | ||||
\(543\) | −642.433 | + | 1977.21i | −0.0507725 | + | 0.156262i | ||||
\(544\) | −1514.03 | − | 1100.01i | −0.119326 | − | 0.0866955i | ||||
\(545\) | 2719.43 | + | 1975.78i | 0.213738 | + | 0.155290i | ||||
\(546\) | −4.19215 | + | 12.9021i | −0.000328585 | + | 0.00101128i | ||||
\(547\) | 854.832 | + | 2630.90i | 0.0668189 | + | 0.205648i | 0.978891 | − | 0.204382i | \(-0.0655184\pi\) |
−0.912072 | + | 0.410029i | \(0.865518\pi\) | |||||||
\(548\) | 12628.5 | − | 9175.18i | 0.984425 | − | 0.715226i | ||||
\(549\) | −335.103 | −0.0260507 | ||||||||
\(550\) | −307.880 | − | 2558.76i | −0.0238692 | − | 0.198375i | ||||
\(551\) | 8458.22 | 0.653961 | ||||||||
\(552\) | 4696.63 | − | 3412.30i | 0.362141 | − | 0.263111i | ||||
\(553\) | 17.3186 | + | 53.3010i | 0.00133175 | + | 0.00409872i | ||||
\(554\) | −683.226 | + | 2102.75i | −0.0523962 | + | 0.161259i | ||||
\(555\) | 14.4464 | + | 10.4960i | 0.00110490 | + | 0.000802754i | ||||
\(556\) | −7652.90 | − | 5560.16i | −0.583732 | − | 0.424106i | ||||
\(557\) | 2725.88 | − | 8389.40i | 0.207360 | − | 0.638187i | −0.792249 | − | 0.610198i | \(-0.791090\pi\) |
0.999608 | − | 0.0279888i | \(-0.00891027\pi\) | |||||||
\(558\) | 155.261 | + | 477.844i | 0.0117791 | + | 0.0362522i | ||||
\(559\) | 1178.93 | − | 856.539i | 0.0892008 | − | 0.0648082i | ||||
\(560\) | 41.2689 | 0.00311416 | ||||||||
\(561\) | 2783.76 | − | 1289.88i | 0.209502 | − | 0.0970743i | ||||
\(562\) | −2870.82 | −0.215477 | ||||||||
\(563\) | −6503.65 | + | 4725.18i | −0.486850 | + | 0.353717i | −0.803971 | − | 0.594668i | \(-0.797284\pi\) |
0.317122 | + | 0.948385i | \(0.397284\pi\) | |||||||
\(564\) | −732.706 | − | 2255.04i | −0.0547030 | − | 0.168359i | ||||
\(565\) | 699.877 | − | 2154.00i | 0.0521133 | − | 0.160388i | ||||
\(566\) | 3540.57 | + | 2572.38i | 0.262935 | + | 0.191034i | ||||
\(567\) | −179.589 | − | 130.479i | −0.0133016 | − | 0.00966420i | ||||
\(568\) | −558.333 | + | 1718.37i | −0.0412449 | + | 0.126939i | ||||
\(569\) | 874.480 | + | 2691.37i | 0.0644290 | + | 0.198292i | 0.978089 | − | 0.208187i | \(-0.0667563\pi\) |
−0.913660 | + | 0.406479i | \(0.866756\pi\) | |||||||
\(570\) | 422.018 | − | 306.614i | 0.0310112 | − | 0.0225309i | ||||
\(571\) | −23770.3 | −1.74213 | −0.871066 | − | 0.491166i | \(-0.836571\pi\) | ||||
−0.871066 | + | 0.491166i | \(0.836571\pi\) | |||||||
\(572\) | 1769.03 | − | 3173.24i | 0.129312 | − | 0.231957i | ||||
\(573\) | −22949.7 | −1.67319 | ||||||||
\(574\) | −35.6356 | + | 25.8908i | −0.00259129 | + | 0.00188268i | ||||
\(575\) | 5014.84 | + | 15434.1i | 0.363710 | + | 1.11938i | ||||
\(576\) | 531.681 | − | 1636.35i | 0.0384607 | − | 0.118370i | ||||
\(577\) | 7940.16 | + | 5768.87i | 0.572883 | + | 0.416224i | 0.836151 | − | 0.548499i | \(-0.184801\pi\) |
−0.263269 | + | 0.964723i | \(0.584801\pi\) | |||||||
\(578\) | 2169.22 | + | 1576.03i | 0.156103 | + | 0.113416i | ||||
\(579\) | 7586.46 | − | 23348.7i | 0.544529 | − | 1.67589i | ||||
\(580\) | −406.546 | − | 1251.22i | −0.0291050 | − | 0.0895760i | ||||
\(581\) | 11.9823 | − | 8.70567i | 0.000855612 | − | 0.000621638i | ||||
\(582\) | 3013.05 | 0.214596 | ||||||||
\(583\) | −16707.5 | − | 3289.68i | −1.18689 | − | 0.233696i | ||||
\(584\) | 8652.88 | 0.613114 | ||||||||
\(585\) | 91.6878 | − | 66.6151i | 0.00648004 | − | 0.00470803i | ||||
\(586\) | 267.870 | + | 824.419i | 0.0188833 | + | 0.0581168i | ||||
\(587\) | −216.665 | + | 666.827i | −0.0152346 | + | 0.0468874i | −0.958385 | − | 0.285479i | \(-0.907847\pi\) |
0.943150 | + | 0.332367i | \(0.107847\pi\) | |||||||
\(588\) | 10088.3 | + | 7329.58i | 0.707542 | + | 0.514059i | ||||
\(589\) | −15072.3 | − | 10950.6i | −1.05440 | − | 0.766067i | ||||
\(590\) | 297.787 | − | 916.495i | 0.0207792 | − | 0.0639517i | ||||
\(591\) | 3332.28 | + | 10255.7i | 0.231932 | + | 0.713813i | ||||
\(592\) | 87.0379 | − | 63.2367i | 0.00604263 | − | 0.00439023i | ||||
\(593\) | −15700.6 | −1.08726 | −0.543631 | − | 0.839324i | \(-0.682951\pi\) | ||||
−0.543631 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(594\) | −2160.81 | − | 2328.48i | −0.149258 | − | 0.160840i | ||||
\(595\) | 13.0624 | 0.000900009 | ||||||||
\(596\) | −9378.11 | + | 6813.59i | −0.644534 | + | 0.468281i | ||||
\(597\) | −6494.71 | − | 19988.7i | −0.445244 | − | 1.37032i | ||||
\(598\) | 313.652 | − | 965.323i | 0.0214485 | − | 0.0660117i | ||||
\(599\) | 19638.4 | + | 14268.1i | 1.33957 | + | 0.973256i | 0.999460 | + | 0.0328707i | \(0.0104650\pi\) |
0.340112 | + | 0.940385i | \(0.389535\pi\) | |||||||
\(600\) | 4249.38 | + | 3087.36i | 0.289134 | + | 0.210068i | ||||
\(601\) | 8163.21 | − | 25123.8i | 0.554051 | − | 1.70519i | −0.144386 | − | 0.989521i | \(-0.546121\pi\) |
0.698437 | − | 0.715671i | \(-0.253879\pi\) | |||||||
\(602\) | −7.61322 | − | 23.4311i | −0.000515435 | − | 0.00158635i | ||||
\(603\) | −1657.66 | + | 1204.36i | −0.111949 | + | 0.0813358i | ||||
\(604\) | −21433.6 | −1.44391 | ||||||||
\(605\) | −1683.27 | + | 1986.40i | −0.113115 | + | 0.133485i | ||||
\(606\) | −4998.30 | −0.335053 | ||||||||
\(607\) | 22379.7 | − | 16259.8i | 1.49648 | − | 1.08726i | 0.524728 | − | 0.851270i | \(-0.324167\pi\) |
0.971756 | − | 0.235989i | \(-0.0758329\pi\) | |||||||
\(608\) | −3145.49 | − | 9680.84i | −0.209814 | − | 0.645740i | ||||
\(609\) | −48.5645 | + | 149.466i | −0.00323142 | + | 0.00994529i | ||||
\(610\) | 69.3745 | + | 50.4036i | 0.00460474 | + | 0.00334554i | ||||
\(611\) | −685.650 | − | 498.154i | −0.0453984 | − | 0.0329839i | ||||
\(612\) | 186.847 | − | 575.056i | 0.0123413 | − | 0.0379825i | ||||
\(613\) | 8192.76 | + | 25214.7i | 0.539808 | + | 1.66136i | 0.733025 | + | 0.680202i | \(0.238108\pi\) |
−0.193217 | + | 0.981156i | \(0.561892\pi\) | |||||||
\(614\) | −3780.53 | + | 2746.72i | −0.248485 | + | 0.180535i | ||||
\(615\) | −1861.42 | −0.122049 | ||||||||
\(616\) | −85.4155 | − | 92.0434i | −0.00558683 | − | 0.00602035i | ||||
\(617\) | 20378.9 | 1.32970 | 0.664848 | − | 0.746979i | \(-0.268496\pi\) | ||||
0.664848 | + | 0.746979i | \(0.268496\pi\) | |||||||
\(618\) | 2123.89 | − | 1543.10i | 0.138245 | − | 0.100441i | ||||
\(619\) | 3472.05 | + | 10685.9i | 0.225450 | + | 0.693864i | 0.998246 | + | 0.0592089i | \(0.0188578\pi\) |
−0.772796 | + | 0.634655i | \(0.781142\pi\) | |||||||
\(620\) | −895.471 | + | 2755.98i | −0.0580048 | + | 0.178521i | ||||
\(621\) | 16182.5 | + | 11757.3i | 1.04570 | + | 0.759749i | ||||
\(622\) | 792.704 | + | 575.933i | 0.0511006 | + | 0.0371267i | ||||
\(623\) | −55.9468 | + | 172.187i | −0.00359785 | + | 0.0110731i | ||||
\(624\) | 1067.34 | + | 3284.94i | 0.0684741 | + | 0.210742i | ||||
\(625\) | −11491.8 | + | 8349.28i | −0.735475 | + | 0.534354i | ||||
\(626\) | 3806.92 | 0.243059 | ||||||||
\(627\) | 16373.3 | + | 3223.88i | 1.04288 | + | 0.205342i | ||||
\(628\) | −9582.99 | −0.608922 | ||||||||
\(629\) | 27.5491 | − | 20.0156i | 0.00174635 | − | 0.00126880i | ||||
\(630\) | −0.592099 | − | 1.82229i | −3.74441e−5 | − | 0.000115241i | ||||
\(631\) | −1908.02 | + | 5872.29i | −0.120376 | + | 0.370479i | −0.993030 | − | 0.117859i | \(-0.962397\pi\) |
0.872654 | + | 0.488338i | \(0.162397\pi\) | |||||||
\(632\) | −1097.97 | − | 797.725i | −0.0691061 | − | 0.0502085i | ||||
\(633\) | 4656.19 | + | 3382.92i | 0.292365 | + | 0.212415i | ||||
\(634\) | −639.182 | + | 1967.20i | −0.0400397 | + | 0.123229i | ||||
\(635\) | −1194.00 | − | 3674.75i | −0.0746180 | − | 0.229651i | ||||
\(636\) | 13733.7 | − | 9978.09i | 0.856250 | − | 0.622102i | ||||
\(637\) | 4457.15 | 0.277235 | ||||||||
\(638\) | −909.268 | + | 1631.02i | −0.0564236 | + | 0.101211i | ||||
\(639\) | −881.984 | −0.0546021 | ||||||||
\(640\) | −1693.92 | + | 1230.71i | −0.104622 | + | 0.0760124i | ||||
\(641\) | −2311.83 | − | 7115.08i | −0.142452 | − | 0.438422i | 0.854223 | − | 0.519908i | \(-0.174034\pi\) |
−0.996675 | + | 0.0814853i | \(0.974034\pi\) | |||||||
\(642\) | 986.327 | − | 3035.60i | 0.0606343 | − | 0.186613i | ||||
\(643\) | −7465.77 | − | 5424.20i | −0.457887 | − | 0.332674i | 0.334815 | − | 0.942284i | \(-0.391326\pi\) |
−0.792702 | + | 0.609610i | \(0.791326\pi\) | |||||||
\(644\) | 312.901 | + | 227.336i | 0.0191460 | + | 0.0139104i | ||||
\(645\) | 321.727 | − | 990.174i | 0.0196403 | − | 0.0604466i | ||||
\(646\) | −307.399 | − | 946.078i | −0.0187221 | − | 0.0576206i | ||||
\(647\) | −16098.2 | + | 11696.0i | −0.978183 | + | 0.710691i | −0.957302 | − | 0.289091i | \(-0.906647\pi\) |
−0.0208809 | + | 0.999782i | \(0.506647\pi\) | |||||||
\(648\) | 5375.60 | 0.325885 | ||||||||
\(649\) | 27971.3 | − | 12960.8i | 1.69179 | − | 0.783904i | ||||
\(650\) | 918.345 | 0.0554161 | ||||||||
\(651\) | 280.051 | − | 203.469i | 0.0168603 | − | 0.0122497i | ||||
\(652\) | 5086.93 | + | 15656.0i | 0.305552 | + | 0.940392i | ||||
\(653\) | 1185.54 | − | 3648.73i | 0.0710474 | − | 0.218661i | −0.909228 | − | 0.416299i | \(-0.863327\pi\) |
0.980275 | + | 0.197638i | \(0.0633269\pi\) | |||||||
\(654\) | 3847.98 | + | 2795.72i | 0.230073 | + | 0.167158i | ||||
\(655\) | −2629.89 | − | 1910.73i | −0.156883 | − | 0.113982i | ||||
\(656\) | −3465.57 | + | 10665.9i | −0.206262 | + | 0.634809i | ||||
\(657\) | 1305.25 | + | 4017.14i | 0.0775077 | + | 0.238544i | ||||
\(658\) | −11.5920 | + | 8.42211i | −0.000686785 | + | 0.000498979i | ||||
\(659\) | −31860.3 | −1.88331 | −0.941655 | − | 0.336581i | \(-0.890729\pi\) | ||||
−0.941655 | + | 0.336581i | \(0.890729\pi\) | |||||||
\(660\) | −310.081 | − | 2577.06i | −0.0182877 | − | 0.151988i | ||||
\(661\) | −32986.5 | −1.94104 | −0.970518 | − | 0.241028i | \(-0.922515\pi\) | ||||
−0.970518 | + | 0.241028i | \(0.922515\pi\) | |||||||
\(662\) | −4371.44 | + | 3176.04i | −0.256648 | + | 0.186466i | ||||
\(663\) | 337.834 | + | 1039.74i | 0.0197894 | + | 0.0609055i | ||||
\(664\) | −110.833 | + | 341.110i | −0.00647767 | + | 0.0199362i | ||||
\(665\) | 57.4792 | + | 41.7611i | 0.00335180 | + | 0.00243523i | ||||
\(666\) | −4.04108 | − | 2.93602i | −0.000235118 | − | 0.000170823i | ||||
\(667\) | 3633.55 | − | 11182.9i | 0.210932 | − | 0.649182i | ||||
\(668\) | 3617.09 | + | 11132.3i | 0.209505 | + | 0.644791i | ||||
\(669\) | −2888.04 | + | 2098.28i | −0.166903 | + | 0.121262i | ||||
\(670\) | 524.328 | 0.0302337 | ||||||||
\(671\) | 327.715 | + | 2723.61i | 0.0188544 | + | 0.156697i | ||||
\(672\) | 189.132 | 0.0108570 | ||||||||
\(673\) | 9751.55 | − | 7084.91i | 0.558536 | − | 0.405800i | −0.272387 | − | 0.962188i | \(-0.587813\pi\) |
0.830923 | + | 0.556388i | \(0.187813\pi\) | |||||||
\(674\) | −690.219 | − | 2124.28i | −0.0394455 | − | 0.121401i | ||||
\(675\) | −5592.56 | + | 17212.1i | −0.318900 | + | 0.981475i | ||||
\(676\) | 1047.32 | + | 760.925i | 0.0595882 | + | 0.0432934i | ||||
\(677\) | 21331.1 | + | 15498.0i | 1.21096 | + | 0.879815i | 0.995318 | − | 0.0966568i | \(-0.0308149\pi\) |
0.215644 | + | 0.976472i | \(0.430815\pi\) | |||||||
\(678\) | 990.324 | − | 3047.90i | 0.0560961 | − | 0.172646i | ||||
\(679\) | 126.815 | + | 390.295i | 0.00716745 | + | 0.0220591i | ||||
\(680\) | −255.909 | + | 185.929i | −0.0144319 | + | 0.0104854i | ||||
\(681\) | 9066.58 | 0.510179 | ||||||||
\(682\) | 3731.93 | − | 1729.22i | 0.209535 | − | 0.0970898i | ||||
\(683\) | −5126.89 | −0.287226 | −0.143613 | − | 0.989634i | \(-0.545872\pi\) | ||||
−0.143613 | + | 0.989634i | \(0.545872\pi\) | |||||||
\(684\) | 2660.68 | − | 1933.10i | 0.148733 | − | 0.108061i | ||||
\(685\) | −1231.83 | − | 3791.19i | −0.0687094 | − | 0.211466i | ||||
\(686\) | 46.5819 | − | 143.364i | 0.00259257 | − | 0.00797912i | ||||
\(687\) | 1577.90 | + | 1146.41i | 0.0876285 | + | 0.0636659i | ||||
\(688\) | −5074.70 | − | 3686.98i | −0.281208 | − | 0.204310i | ||||
\(689\) | 1875.03 | − | 5770.75i | 0.103676 | − | 0.319083i | ||||
\(690\) | −224.091 | − | 689.682i | −0.0123638 | − | 0.0380518i | ||||
\(691\) | −15212.2 | + | 11052.3i | −0.837483 | + | 0.608467i | −0.921666 | − | 0.387983i | \(-0.873172\pi\) |
0.0841833 | + | 0.996450i | \(0.473172\pi\) | |||||||
\(692\) | −7913.30 | −0.434709 | ||||||||
\(693\) | 29.8470 | − | 53.5389i | 0.00163607 | − | 0.00293474i | ||||
\(694\) | −1104.78 | −0.0604280 | ||||||||
\(695\) | −1954.34 | + | 1419.91i | −0.106665 | + | 0.0774967i | ||||
\(696\) | −1176.05 | − | 3619.50i | −0.0640488 | − | 0.197122i | ||||
\(697\) | −1096.92 | + | 3375.97i | −0.0596109 | + | 0.183463i | ||||
\(698\) | 2841.22 | + | 2064.27i | 0.154071 | + | 0.111939i | ||||
\(699\) | 18896.6 | + | 13729.2i | 1.02251 | + | 0.742897i | ||||
\(700\) | −108.136 | + | 332.809i | −0.00583881 | + | 0.0179700i | ||||
\(701\) | 7452.55 | + | 22936.6i | 0.401539 | + | 1.23581i | 0.923750 | + | 0.382995i | \(0.125107\pi\) |
−0.522211 | + | 0.852816i | \(0.674893\pi\) | |||||||
\(702\) | 915.752 | − | 665.333i | 0.0492348 | − | 0.0357712i | ||||
\(703\) | 185.217 | 0.00993684 | ||||||||
\(704\) | −13819.7 | − | 2721.07i | −0.739841 | − | 0.145673i | ||||
\(705\) | −605.510 | −0.0323473 | ||||||||
\(706\) | 503.529 | − | 365.835i | 0.0268421 | − | 0.0195020i | ||||
\(707\) | −210.370 | − | 647.454i | −0.0111907 | − | 0.0344413i | ||||
\(708\) | −9497.02 | + | 29228.8i | −0.504124 | + | 1.55153i | ||||
\(709\) | −1465.57 | − | 1064.80i | −0.0776315 | − | 0.0564026i | 0.548293 | − | 0.836287i | \(-0.315278\pi\) |
−0.625924 | + | 0.779884i | \(0.715278\pi\) | |||||||
\(710\) | 182.592 | + | 132.661i | 0.00965151 | + | 0.00701223i | ||||
\(711\) | 204.723 | − | 630.073i | 0.0107985 | − | 0.0332343i | ||||
\(712\) | −1354.82 | − | 4169.70i | −0.0713117 | − | 0.219475i | ||||
\(713\) | −20953.1 | + | 15223.3i | −1.10056 | + | 0.799604i | ||||
\(714\) | 18.4832 | 0.000968793 | ||||||||
\(715\) | −631.093 | − | 680.063i | −0.0330091 | − | 0.0355705i | ||||
\(716\) | 15788.8 | 0.824099 | ||||||||
\(717\) | 4612.19 | − | 3350.95i | 0.240231 | − | 0.174538i | ||||
\(718\) | 1688.96 | + | 5198.08i | 0.0877874 | + | 0.270182i | ||||
\(719\) | 4753.09 | − | 14628.5i | 0.246537 | − | 0.758764i | −0.748843 | − | 0.662748i | \(-0.769390\pi\) |
0.995380 | − | 0.0960158i | \(-0.0306099\pi\) | |||||||
\(720\) | −394.671 | − | 286.746i | −0.0204285 | − | 0.0148422i | ||||
\(721\) | 289.276 | + | 210.171i | 0.0149420 | + | 0.0108560i | ||||
\(722\) | 436.330 | − | 1342.89i | 0.0224910 | − | 0.0692203i | ||||
\(723\) | 1851.82 | + | 5699.31i | 0.0952557 | + | 0.293167i | ||||
\(724\) | 2713.50 | − | 1971.47i | 0.139291 | − | 0.101200i | ||||
\(725\) | 10638.7 | 0.544981 | ||||||||
\(726\) | −2381.82 | + | 2810.74i | −0.121760 | + | 0.143687i | ||||
\(727\) | 17850.3 | 0.910636 | 0.455318 | − | 0.890329i | \(-0.349526\pi\) | ||||
0.455318 | + | 0.890329i | \(0.349526\pi\) | |||||||
\(728\) | 36.1991 | − | 26.3002i | 0.00184289 | − | 0.00133894i | ||||
\(729\) | 6727.56 | + | 20705.3i | 0.341795 | + | 1.05194i | ||||
\(730\) | 334.009 | − | 1027.97i | 0.0169345 | − | 0.0521191i | ||||
\(731\) | −1606.24 | − | 1167.00i | −0.0812707 | − | 0.0590466i | ||||
\(732\) | −2212.49 | − | 1607.47i | −0.111716 | − | 0.0811662i | ||||
\(733\) | 5042.11 | − | 15518.0i | 0.254072 | − | 0.781953i | −0.739939 | − | 0.672674i | \(-0.765146\pi\) |
0.994011 | − | 0.109279i | \(-0.0348542\pi\) | |||||||
\(734\) | 1264.14 | + | 3890.61i | 0.0635696 | + | 0.195647i | ||||
\(735\) | 2576.27 | − | 1871.77i | 0.129289 | − | 0.0939337i | ||||
\(736\) | −14150.6 | −0.708695 | ||||||||
\(737\) | 11409.8 | + | 12295.2i | 0.570265 | + | 0.614516i | ||||
\(738\) | 520.693 | 0.0259715 | ||||||||
\(739\) | 20559.0 | − | 14937.0i | 1.02338 | − | 0.743527i | 0.0564049 | − | 0.998408i | \(-0.482036\pi\) |
0.966972 | + | 0.254881i | \(0.0820362\pi\) | |||||||
\(740\) | −8.90250 | − | 27.3991i | −0.000442246 | − | 0.00136109i | ||||
\(741\) | −1837.53 | + | 5655.32i | −0.0910974 | + | 0.280369i | ||||
\(742\) | −82.9929 | − | 60.2979i | −0.00410616 | − | 0.00298330i | ||||
\(743\) | 8852.49 | + | 6431.71i | 0.437102 | + | 0.317573i | 0.784482 | − | 0.620151i | \(-0.212929\pi\) |
−0.347381 | + | 0.937724i | \(0.612929\pi\) | |||||||
\(744\) | −2590.40 | + | 7972.43i | −0.127646 | + | 0.392854i | ||||
\(745\) | 914.773 | + | 2815.38i | 0.0449862 | + | 0.138453i | ||||
\(746\) | −1707.85 | + | 1240.82i | −0.0838186 | + | 0.0608978i | ||||
\(747\) | −175.081 | −0.00857546 | ||||||||
\(748\) | −4856.61 | − | 956.257i | −0.237400 | − | 0.0467436i | ||||
\(749\) | 434.729 | 0.0212078 | ||||||||
\(750\) | 1078.39 | − | 783.493i | 0.0525028 | − | 0.0381455i | ||||
\(751\) | −5615.57 | − | 17283.0i | −0.272856 | − | 0.839765i | −0.989779 | − | 0.142612i | \(-0.954450\pi\) |
0.716922 | − | 0.697153i | \(-0.245550\pi\) | |||||||
\(752\) | −1127.33 | + | 3469.56i | −0.0546669 | + | 0.168247i | ||||
\(753\) | −4239.86 | − | 3080.44i | −0.205191 | − | 0.149080i | ||||
\(754\) | −538.317 | − | 391.110i | −0.0260005 | − | 0.0188904i | ||||
\(755\) | −1691.41 | + | 5205.64i | −0.0815323 | + | 0.250931i | ||||
\(756\) | 133.286 | + | 410.213i | 0.00641214 | + | 0.0197345i | ||||
\(757\) | 22063.5 | − | 16030.1i | 1.05933 | − | 0.769648i | 0.0853654 | − | 0.996350i | \(-0.472794\pi\) |
0.973964 | + | 0.226702i | \(0.0727942\pi\) | |||||||
\(758\) | 210.801 | 0.0101011 | ||||||||
\(759\) | 11296.2 | − | 20262.8i | 0.540219 | − | 0.969031i | ||||
\(760\) | −1720.52 | −0.0821180 | ||||||||
\(761\) | 21617.5 | − | 15706.1i | 1.02974 | − | 0.748152i | 0.0614862 | − | 0.998108i | \(-0.480416\pi\) |
0.968257 | + | 0.249955i | \(0.0804160\pi\) | |||||||
\(762\) | −1689.51 | − | 5199.77i | −0.0803207 | − | 0.247202i | ||||
\(763\) | −200.188 | + | 616.115i | −0.00949841 | + | 0.0292331i | ||||
\(764\) | 29954.5 | + | 21763.2i | 1.41847 | + | 1.03058i | ||||
\(765\) | −124.921 | − | 90.7604i | −0.00590396 | − | 0.00428948i | ||||
\(766\) | −1087.17 | + | 3345.96i | −0.0512806 | + | 0.157825i | ||||
\(767\) | 3394.57 | + | 10447.4i | 0.159805 | + | 0.491830i | ||||
\(768\) | 9466.95 | − | 6878.14i | 0.444804 | − | 0.323169i | ||||
\(769\) | 31295.9 | 1.46757 | 0.733783 | − | 0.679384i | \(-0.237753\pi\) | ||||
0.733783 | + | 0.679384i | \(0.237753\pi\) | |||||||
\(770\) | −14.2320 | + | 6.59451i | −0.000666084 | + | 0.000308636i | ||||
\(771\) | −30772.0 | −1.43739 | ||||||||
\(772\) | −32043.6 | + | 23281.0i | −1.49388 | + | 1.08537i | ||||
\(773\) | −11574.5 | − | 35622.7i | −0.538559 | − | 1.65751i | −0.735830 | − | 0.677166i | \(-0.763208\pi\) |
0.197271 | − | 0.980349i | \(-0.436792\pi\) | |||||||
\(774\) | −89.9961 | + | 276.980i | −0.00417939 | + | 0.0128628i | ||||
\(775\) | −18957.8 | − | 13773.7i | −0.878690 | − | 0.638405i | ||||
\(776\) | −8039.88 | − | 5841.32i | −0.371927 | − | 0.270220i | ||||
\(777\) | −1.06346 | + | 3.27299i | −4.91009e−5 | + | 0.000151117i | ||||
\(778\) | −1123.78 | − | 3458.63i | −0.0517858 | − | 0.159380i | ||||
\(779\) | −15620.0 | + | 11348.6i | −0.718414 | + | 0.521958i | ||||
\(780\) | 924.910 | 0.0424578 | ||||||||
\(781\) | 862.538 | + | 7168.49i | 0.0395186 | + | 0.328436i | ||||
\(782\) | −1382.90 | −0.0632383 | ||||||||
\(783\) | 10608.7 | − | 7707.64i | 0.484192 | − | 0.351786i | ||||
\(784\) | −5928.76 | − | 18246.8i | −0.270078 | − | 0.831216i | ||||
\(785\) | −756.236 | + | 2327.45i | −0.0343837 | + | 0.105822i | ||||
\(786\) | −3721.29 | − | 2703.67i | −0.168873 | − | 0.122693i | ||||
\(787\) | 8425.70 | + | 6121.63i | 0.381631 | + | 0.277271i | 0.762018 | − | 0.647556i | \(-0.224209\pi\) |
−0.380386 | + | 0.924828i | \(0.624209\pi\) | |||||||
\(788\) | 5376.10 | − | 16545.9i | 0.243040 | − | 0.748001i | ||||
\(789\) | −4606.21 | − | 14176.5i | −0.207840 | − | 0.639665i | ||||
\(790\) | −137.153 | + | 99.6478i | −0.00617684 | + | 0.00448773i | ||||
\(791\) | 436.491 | 0.0196205 | ||||||||
\(792\) | 177.325 | + | 1473.74i | 0.00795578 | + | 0.0661198i | ||||
\(793\) | −977.508 | −0.0437734 | ||||||||
\(794\) | 1636.35 | − | 1188.87i | 0.0731382 | − | 0.0531380i | ||||
\(795\) | −1339.63 | − | 4122.96i | −0.0597632 | − | 0.183932i | ||||
\(796\) | −10478.2 | + | 32248.6i | −0.466570 | + | 1.43595i | ||||
\(797\) | −15523.1 | − | 11278.2i | −0.689907 | − | 0.501247i | 0.186722 | − | 0.982413i | \(-0.440214\pi\) |
−0.876630 | + | 0.481166i | \(0.840214\pi\) | |||||||
\(798\) | 81.3329 | + | 59.0918i | 0.00360796 | + | 0.00262134i | ||||
\(799\) | −356.821 | + | 1098.18i | −0.0157990 | + | 0.0486244i | ||||
\(800\) | −3956.38 | − | 12176.5i | −0.174849 | − | 0.538130i | ||||
\(801\) | 1731.43 | − | 1257.96i | 0.0763761 | − | 0.0554905i | ||||
\(802\) | −7284.17 | −0.320715 | ||||||||
\(803\) | 31373.6 | − | 14537.2i | 1.37877 | − | 0.638864i | ||||
\(804\) | −16721.8 | −0.733500 | ||||||||
\(805\) | 79.9062 | − | 58.0552i | 0.00349854 | − | 0.00254184i | ||||
\(806\) | 452.902 | + | 1393.89i | 0.0197926 | + | 0.0609152i | ||||
\(807\) | −1448.84 | + | 4459.07i | −0.0631990 | + | 0.194506i | ||||
\(808\) | 13337.2 | + | 9690.06i | 0.580695 | + | 0.421900i | ||||
\(809\) | 30264.8 | + | 21988.6i | 1.31527 | + | 0.955599i | 0.999978 | + | 0.00660398i | \(0.00210213\pi\) |
0.315291 | + | 0.948995i | \(0.397898\pi\) | |||||||
\(810\) | 207.503 | − | 638.628i | 0.00900112 | − | 0.0277026i | ||||
\(811\) | 9145.74 | + | 28147.7i | 0.395993 | + | 1.21874i | 0.928185 | + | 0.372118i | \(0.121368\pi\) |
−0.532192 | + | 0.846623i | \(0.678632\pi\) | |||||||
\(812\) | 205.126 | − | 149.033i | 0.00886516 | − | 0.00644092i | ||||
\(813\) | −7228.31 | −0.311818 | ||||||||
\(814\) | −19.9110 | + | 35.7159i | −0.000857348 | + | 0.00153789i | ||||
\(815\) | 4203.85 | 0.180680 | ||||||||
\(816\) | 3807.17 | − | 2766.07i | 0.163330 | − | 0.118666i | ||||
\(817\) | −3337.07 | − | 10270.4i | −0.142900 | − | 0.439801i | ||||
\(818\) | −745.935 | + | 2295.75i | −0.0318839 | + | 0.0981284i | ||||
\(819\) | 17.6704 | + | 12.8383i | 0.000753913 | + | 0.000547750i | ||||
\(820\) | 2429.57 | + | 1765.18i | 0.103469 | + | 0.0751743i | ||||
\(821\) | 12366.4 | − | 38059.9i | 0.525689 | − | 1.61790i | −0.237262 | − | 0.971446i | \(-0.576250\pi\) |
0.762950 | − | 0.646457i | \(-0.223750\pi\) | |||||||
\(822\) | −1743.04 | − | 5364.53i | −0.0739605 | − | 0.227627i | ||||
\(823\) | −20512.7 | + | 14903.4i | −0.868808 | + | 0.631226i | −0.930267 | − | 0.366884i | \(-0.880425\pi\) |
0.0614588 | + | 0.998110i | \(0.480425\pi\) | |||||||
\(824\) | −8658.85 | −0.366074 | ||||||||
\(825\) | 20594.3 | + | 4054.98i | 0.869092 | + | 0.171123i | ||||
\(826\) | 185.720 | 0.00782329 | ||||||||
\(827\) | −4981.09 | + | 3618.98i | −0.209443 | + | 0.152169i | −0.687562 | − | 0.726126i | \(-0.741319\pi\) |
0.478118 | + | 0.878295i | \(0.341319\pi\) | |||||||
\(828\) | −1412.82 | − | 4348.21i | −0.0592982 | − | 0.182501i | ||||
\(829\) | 5192.54 | − | 15981.0i | 0.217545 | − | 0.669533i | −0.781419 | − | 0.624007i | \(-0.785504\pi\) |
0.998963 | − | 0.0455260i | \(-0.0144964\pi\) | |||||||
\(830\) | 36.2461 | + | 26.3343i | 0.00151581 | + | 0.00110130i | ||||
\(831\) | −14567.8 | − | 10584.1i | −0.608124 | − | 0.441828i | ||||
\(832\) | 1550.94 | − | 4773.29i | 0.0646262 | − | 0.198899i | ||||
\(833\) | −1876.57 | − | 5775.47i | −0.0780542 | − | 0.240226i | ||||
\(834\) | −2765.38 | + | 2009.17i | −0.114817 | + | 0.0834194i | ||||
\(835\) | 2989.17 | 0.123886 | ||||||||
\(836\) | −18313.6 | − | 19734.7i | −0.757643 | − | 0.816434i | ||||
\(837\) | −28883.2 | −1.19277 | ||||||||
\(838\) | −1358.63 | + | 987.104i | −0.0560061 | + | 0.0406908i | ||||
\(839\) | 7804.26 | + | 24019.0i | 0.321136 | + | 0.988354i | 0.973155 | + | 0.230152i | \(0.0739222\pi\) |
−0.652019 | + | 0.758203i | \(0.726078\pi\) | |||||||
\(840\) | 9.87867 | − | 30.4034i | 0.000405770 | − | 0.00124883i | ||||
\(841\) | 13494.9 | + | 9804.62i | 0.553319 | + | 0.402010i | ||||
\(842\) | −938.801 | − | 682.079i | −0.0384242 | − | 0.0279168i | ||||
\(843\) | 7225.08 | − | 22236.5i | 0.295190 | − | 0.908501i | ||||
\(844\) | −2869.33 | − | 8830.90i | −0.117022 | − | 0.360157i | ||||
\(845\) | 267.457 | − | 194.319i | 0.0108885 | − | 0.00791098i | ||||
\(846\) | 169.378 | 0.00688338 | ||||||||
\(847\) | −464.336 | − | 190.229i | −0.0188368 | − | 0.00771705i | ||||
\(848\) | −26118.6 | −1.05768 | ||||||||
\(849\) | −28835.5 | + | 20950.2i | −1.16565 | + | 0.846891i | ||||
\(850\) | −386.645 | − | 1189.97i | −0.0156021 | − | 0.0480184i | ||||
\(851\) | 79.5670 | − | 244.882i | 0.00320508 | − | 0.00986422i | ||||
\(852\) | −5823.22 | − | 4230.82i | −0.234155 | − | 0.170124i | ||||
\(853\) | −26409.4 | − | 19187.6i | −1.06007 | − | 0.770187i | −0.0859702 | − | 0.996298i | \(-0.527399\pi\) |
−0.974102 | + | 0.226110i | \(0.927399\pi\) | |||||||
\(854\) | −5.10694 | + | 15.7175i | −0.000204632 | + | 0.000629793i | ||||
\(855\) | −259.532 | − | 798.757i | −0.0103811 | − | 0.0319496i | ||||
\(856\) | −8516.90 | + | 6187.89i | −0.340072 | + | 0.247077i | ||||
\(857\) | −38051.1 | −1.51669 | −0.758344 | − | 0.651855i | \(-0.773991\pi\) | ||||
−0.758344 | + | 0.651855i | \(0.773991\pi\) | |||||||
\(858\) | −892.995 | − | 962.288i | −0.0355319 | − | 0.0382890i | ||||
\(859\) | 8358.76 | 0.332011 | 0.166005 | − | 0.986125i | \(-0.446913\pi\) | ||||
0.166005 | + | 0.986125i | \(0.446913\pi\) | |||||||
\(860\) | −1358.90 | + | 987.302i | −0.0538817 | + | 0.0391474i | ||||
\(861\) | −110.857 | − | 341.183i | −0.00438792 | − | 0.0135046i | ||||
\(862\) | 893.232 | − | 2749.08i | 0.0352942 | − | 0.108624i | ||||
\(863\) | −12781.6 | − | 9286.40i | −0.504162 | − | 0.366295i | 0.306442 | − | 0.951889i | \(-0.400861\pi\) |
−0.810605 | + | 0.585594i | \(0.800861\pi\) | |||||||
\(864\) | −12767.0 | − | 9275.75i | −0.502710 | − | 0.365240i | ||||
\(865\) | −624.473 | + | 1921.93i | −0.0245465 | + | 0.0755464i | ||||
\(866\) | −169.748 | − | 522.430i | −0.00666081 | − | 0.0204999i | ||||
\(867\) | −17666.8 | + | 12835.7i | −0.692037 | + | 0.502794i | ||||
\(868\) | −558.477 | −0.0218386 | ||||||||
\(869\) | −5321.24 | − | 1047.74i | −0.207723 | − | 0.0409002i | ||||
\(870\) | −475.397 | −0.0185258 | ||||||||
\(871\) | −4835.47 | + | 3513.18i | −0.188110 | + | 0.136670i | ||||
\(872\) | −4847.78 | − | 14919.9i | −0.188264 | − | 0.579418i | ||||
\(873\) | 1499.08 | − | 4613.69i | 0.0581170 | − | 0.178866i | ||||
\(874\) | −6085.25 | − | 4421.19i | −0.235511 | − | 0.171109i | ||||
\(875\) | 146.877 | + | 106.712i | 0.00567469 | + | 0.00412290i | ||||
\(876\) | −10652.2 | + | 32784.0i | −0.410849 | + | 1.26446i | ||||
\(877\) | −9504.02 | − | 29250.4i | −0.365938 | − | 1.12624i | −0.949391 | − | 0.314095i | \(-0.898299\pi\) |
0.583453 | − | 0.812147i | \(-0.301701\pi\) | |||||||
\(878\) | 5593.47 | − | 4063.89i | 0.215001 | − | 0.156207i | ||||
\(879\) | −7059.86 | −0.270902 | ||||||||
\(880\) | −1944.61 | + | 3488.19i | −0.0744917 | + | 0.133621i | ||||
\(881\) | 33588.3 | 1.28447 | 0.642235 | − | 0.766508i | \(-0.278007\pi\) | ||||
0.642235 | + | 0.766508i | \(0.278007\pi\) | |||||||
\(882\) | −720.656 | + | 523.587i | −0.0275122 | + | 0.0199888i | ||||
\(883\) | 6608.40 | + | 20338.6i | 0.251858 | + | 0.775139i | 0.994433 | + | 0.105376i | \(0.0336045\pi\) |
−0.742575 | + | 0.669763i | \(0.766396\pi\) | |||||||
\(884\) | 545.041 | − | 1677.46i | 0.0207372 | − | 0.0638226i | ||||
\(885\) | 6349.45 | + | 4613.15i | 0.241169 | + | 0.175219i | ||||
\(886\) | 3140.73 | + | 2281.88i | 0.119091 | + | 0.0865250i | ||||
\(887\) | 11631.8 | − | 35799.0i | 0.440313 | − | 1.35514i | −0.447231 | − | 0.894419i | \(-0.647590\pi\) |
0.887543 | − | 0.460724i | \(-0.152410\pi\) | |||||||
\(888\) | −25.7529 | − | 79.2594i | −0.000973211 | − | 0.00299524i | ||||
\(889\) | 602.442 | − | 437.700i | 0.0227281 | − | 0.0165129i | ||||
\(890\) | −547.662 | −0.0206266 | ||||||||
\(891\) | 19490.8 | − | 9031.25i | 0.732848 | − | 0.339572i | ||||
\(892\) | 5759.33 | 0.216185 | ||||||||
\(893\) | −5081.09 | + | 3691.63i | −0.190406 | + | 0.138338i | ||||
\(894\) | 1294.40 | + | 3983.76i | 0.0484242 | + | 0.149034i | ||||
\(895\) | 1245.96 | − | 3834.68i | 0.0465340 | − | 0.143217i | ||||
\(896\) | −326.459 | − | 237.186i | −0.0121721 | − | 0.00884357i | ||||
\(897\) | 6687.73 | + | 4858.92i | 0.248937 | + | 0.180863i | ||||
\(898\) | 264.861 | − | 815.157i | 0.00984244 | − | 0.0302919i | ||||
\(899\) | 5246.71 | + | 16147.7i | 0.194647 | + | 0.599062i | ||||
\(900\) | 3346.58 | − | 2431.44i | 0.123948 | − | 0.0900532i | ||||
\(901\) | −8267.03 | −0.305677 | ||||||||
\(902\) | −509.213 | − | 4232.03i | −0.0187971 | − | 0.156221i | ||||
\(903\) | 200.651 | 0.00739451 | ||||||||
\(904\) | −8551.41 | + | 6212.97i | −0.314619 | + | 0.228584i | ||||
\(905\) | −264.684 | − | 814.614i | −0.00972198 | − | 0.0299212i | ||||
\(906\) | −2393.35 | + | 7365.97i | −0.0877634 | + | 0.270108i | ||||
\(907\) | 16718.8 | + | 12146.9i | 0.612059 | + | 0.444687i | 0.850139 | − | 0.526559i | \(-0.176518\pi\) |
−0.238080 | + | 0.971246i | \(0.576518\pi\) | |||||||
\(908\) | −11833.9 | − | 8597.82i | −0.432513 | − | 0.314239i | ||||
\(909\) | −2486.80 | + | 7653.57i | −0.0907390 | + | 0.279266i | ||||
\(910\) | −1.72718 | − | 5.31570i | −6.29179e−5 | − | 0.000193641i | ||||
\(911\) | −35252.2 | + | 25612.2i | −1.28206 | + | 0.931472i | −0.999613 | − | 0.0278107i | \(-0.991146\pi\) |
−0.282448 | + | 0.959283i | \(0.591146\pi\) | |||||||
\(912\) | 25596.2 | 0.929358 | ||||||||
\(913\) | 171.221 | + | 1423.00i | 0.00620655 | + | 0.0515821i | ||||
\(914\) | −356.208 | −0.0128909 | ||||||||
\(915\) | −565.008 | + | 410.502i | −0.0204138 | + | 0.0148315i | ||||
\(916\) | −972.370 | − | 2992.65i | −0.0350742 | − | 0.107947i | ||||
\(917\) | 193.597 | − | 595.830i | 0.00697179 | − | 0.0214570i | ||||
\(918\) | −1247.68 | − | 906.489i | −0.0448578 | − | 0.0325911i | ||||
\(919\) | 24694.5 | + | 17941.6i | 0.886393 | + | 0.644002i | 0.934935 | − | 0.354819i | \(-0.115457\pi\) |
−0.0485418 | + | 0.998821i | \(0.515457\pi\) | |||||||
\(920\) | −739.112 | + | 2274.75i | −0.0264868 | + | 0.0815179i | ||||
\(921\) | −11760.7 | − | 36195.6i | −0.420768 | − | 1.29499i | ||||
\(922\) | 6730.62 | − | 4890.08i | 0.240413 | − | 0.174671i | ||||
\(923\) | −2572.78 | −0.0917488 | ||||||||
\(924\) | 453.885 | − | 210.312i | 0.0161599 | − | 0.00748782i | ||||
\(925\) | 232.965 | 0.00828091 | ||||||||
\(926\) | 2828.69 | − | 2055.16i | 0.100385 | − | 0.0729339i | ||||
\(927\) | −1306.15 | − | 4019.91i | −0.0462778 | − | 0.142428i | ||||
\(928\) | −2866.64 | + | 8822.60i | −0.101403 | + | 0.312086i | ||||
\(929\) | 1519.84 | + | 1104.23i | 0.0536752 | + | 0.0389973i | 0.614299 | − | 0.789073i | \(-0.289439\pi\) |
−0.560624 | + | 0.828070i | \(0.689439\pi\) | |||||||
\(930\) | 847.142 | + | 615.485i | 0.0298698 | + | 0.0217017i | ||||
\(931\) | 10206.9 | − | 31413.6i | 0.359310 | − | 1.10584i | ||||
\(932\) | −11644.9 | − | 35839.2i | −0.409270 | − | 1.25960i | ||||
\(933\) | −6456.03 | + | 4690.58i | −0.226539 | + | 0.164590i | ||||
\(934\) | −352.992 | −0.0123664 | ||||||||
\(935\) | −615.505 | + | 1104.08i | −0.0215285 | + | 0.0386173i | ||||
\(936\) | −528.926 | −0.0184706 | ||||||||
\(937\) | 35213.6 | − | 25584.2i | 1.22772 | − | 0.891994i | 0.231007 | − | 0.972952i | \(-0.425798\pi\) |
0.996718 | + | 0.0809577i | \(0.0257979\pi\) | |||||||
\(938\) | 31.2264 | + | 96.1048i | 0.00108697 | + | 0.00334535i | ||||
\(939\) | −9580.99 | + | 29487.3i | −0.332975 | + | 1.02479i | ||||
\(940\) | 790.324 | + | 574.204i | 0.0274229 | + | 0.0199239i | ||||
\(941\) | 4981.23 | + | 3619.08i | 0.172565 | + | 0.125376i | 0.670715 | − | 0.741715i | \(-0.265987\pi\) |
−0.498150 | + | 0.867091i | \(0.665987\pi\) | |||||||
\(942\) | −1070.07 | + | 3293.34i | −0.0370115 | + | 0.113910i | ||||
\(943\) | 8294.21 | + | 25527.0i | 0.286423 | + | 0.881519i | ||||
\(944\) | 38254.6 | − | 27793.6i | 1.31894 | − | 0.958267i | ||||
\(945\) | 110.148 | 0.00379166 | ||||||||
\(946\) | 2339.22 | + | 460.587i | 0.0803958 | + | 0.0158298i | ||||
\(947\) | −18413.6 | −0.631849 | −0.315924 | − | 0.948784i | \(-0.602315\pi\) | ||||
−0.315924 | + | 0.948784i | \(0.602315\pi\) | |||||||
\(948\) | 4374.09 | − | 3177.96i | 0.149856 | − | 0.108877i | ||||
\(949\) | 3807.46 | + | 11718.2i | 0.130238 | + | 0.400830i | ||||
\(950\) | 2103.02 | − | 6472.42i | 0.0718220 | − | 0.221045i | ||||
\(951\) | −13628.7 | − | 9901.82i | −0.464711 | − | 0.337633i | ||||
\(952\) | −49.3198 | − | 35.8329i | −0.00167906 | − | 0.00121991i | ||||
\(953\) | −5194.98 | + | 15988.5i | −0.176581 | + | 0.543461i | −0.999702 | − | 0.0244049i | \(-0.992231\pi\) |
0.823121 | + | 0.567866i | \(0.192231\pi\) | |||||||
\(954\) | 374.732 | + | 1153.31i | 0.0127174 | + | 0.0391402i | ||||
\(955\) | 7649.54 | − | 5557.71i | 0.259197 | − | 0.188318i | ||||
\(956\) | −9197.63 | −0.311164 | ||||||||
\(957\) | −10345.0 | − | 11147.8i | −0.349433 | − | 0.376547i | ||||
\(958\) | −2997.47 | −0.101089 | ||||||||
\(959\) | 621.531 | − | 451.569i | 0.0209283 | − | 0.0152053i | ||||
\(960\) | −1108.08 | − | 3410.31i | −0.0372532 | − | 0.114653i | ||||
\(961\) | 2350.64 | − | 7234.54i | 0.0789045 | − | 0.242843i | ||||
\(962\) | −11.7880 | − | 8.56448i | −0.000395073 | − | 0.000287037i | ||||
\(963\) | −4157.49 | − | 3020.60i | −0.139121 | − | 0.101077i | ||||
\(964\) | 2987.62 | − | 9194.94i | 0.0998181 | − | 0.307208i | ||||
\(965\) | 3125.64 | + | 9619.73i | 0.104267 | + | 0.320902i | ||||
\(966\) | 113.067 | − | 82.1480i | 0.00376591 | − | 0.00273610i | ||||
\(967\) | 52939.1 | 1.76050 | 0.880252 | − | 0.474507i | \(-0.157374\pi\) | ||||
0.880252 | + | 0.474507i | \(0.157374\pi\) | |||||||
\(968\) | 11804.6 | − | 2882.49i | 0.391958 | − | 0.0957093i | ||||
\(969\) | 8101.68 | 0.268590 | ||||||||
\(970\) | −1004.30 | + | 729.668i | −0.0332435 | + | 0.0241528i | ||||
\(971\) | 14698.2 | + | 45236.5i | 0.485776 | + | 1.49506i | 0.830854 | + | 0.556490i | \(0.187852\pi\) |
−0.345079 | + | 0.938574i | \(0.612148\pi\) | |||||||
\(972\) | 2927.94 | − | 9011.28i | 0.0966192 | − | 0.297363i | ||||
\(973\) | −376.648 | − | 273.650i | −0.0124098 | − | 0.00901627i | ||||
\(974\) | 1739.03 | + | 1263.48i | 0.0572096 | + | 0.0415652i | ||||
\(975\) | −2311.23 | + | 7113.23i | −0.0759164 | + | 0.233647i | ||||
\(976\) | 1300.25 | + | 4001.76i | 0.0426434 | + | 0.131243i | ||||
\(977\) | 38345.6 | − | 27859.7i | 1.25566 | − | 0.912293i | 0.257128 | − | 0.966377i | \(-0.417224\pi\) |
0.998536 | + | 0.0540841i | \(0.0172239\pi\) | |||||||
\(978\) | 5948.44 | 0.194489 | ||||||||
\(979\) | −11917.6 | − | 12842.3i | −0.389057 | − | 0.419247i | ||||
\(980\) | −5137.60 | −0.167464 | ||||||||
\(981\) | 6195.39 | − | 4501.21i | 0.201634 | − | 0.146496i | ||||
\(982\) | −1917.24 | − | 5900.65i | −0.0623030 | − | 0.191749i | ||||
\(983\) | −3657.85 | + | 11257.7i | −0.118685 | + | 0.365274i | −0.992698 | − | 0.120628i | \(-0.961509\pi\) |
0.874013 | + | 0.485903i | \(0.161509\pi\) | |||||||
\(984\) | 7028.20 | + | 5106.28i | 0.227694 | + | 0.165429i | ||||
\(985\) | −3594.32 | − | 2611.43i | −0.116269 | − | 0.0844740i | ||||
\(986\) | −280.147 | + | 862.205i | −0.00904838 | + | 0.0278481i | ||||
\(987\) | −36.0611 | − | 110.985i | −0.00116296 | − | 0.00357921i | ||||
\(988\) | 7761.31 | − | 5638.92i | 0.249919 | − | 0.181577i | ||||
\(989\) | −15012.5 | −0.482679 | ||||||||
\(990\) | 181.926 | + | 35.8210i | 0.00584040 | + | 0.00114997i | ||||
\(991\) | −6982.40 | −0.223818 | −0.111909 | − | 0.993718i | \(-0.535696\pi\) | ||||
−0.111909 | + | 0.993718i | \(0.535696\pi\) | |||||||
\(992\) | 16530.6 | − | 12010.2i | 0.529081 | − | 0.384400i | ||||
\(993\) | −13598.9 | − | 41853.1i | −0.434590 | − | 1.33753i | ||||
\(994\) | −13.4414 | + | 41.3682i | −0.000428907 | + | 0.00132004i | ||||
\(995\) | 7005.44 | + | 5089.75i | 0.223203 | + | 0.162167i | ||||
\(996\) | −1155.96 | − | 839.852i | −0.0367750 | − | 0.0267186i | ||||
\(997\) | −10380.4 | + | 31947.5i | −0.329739 | + | 1.01483i | 0.639516 | + | 0.768778i | \(0.279135\pi\) |
−0.969256 | + | 0.246056i | \(0.920865\pi\) | |||||||
\(998\) | 1342.17 | + | 4130.77i | 0.0425707 | + | 0.131019i | ||||
\(999\) | 232.307 | − | 168.781i | 0.00735723 | − | 0.00534534i |
(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.h.b.14.9 | ✓ | 76 | |
11.2 | odd | 10 | 1573.4.a.r.1.18 | 38 | |||
11.4 | even | 5 | inner | 143.4.h.b.92.9 | yes | 76 | |
11.9 | even | 5 | 1573.4.a.q.1.21 | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.h.b.14.9 | ✓ | 76 | 1.1 | even | 1 | trivial | |
143.4.h.b.92.9 | yes | 76 | 11.4 | even | 5 | inner | |
1573.4.a.q.1.21 | 38 | 11.9 | even | 5 | |||
1573.4.a.r.1.18 | 38 | 11.2 | odd | 10 |