Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.16 | ||
Character | \(\chi\) | \(=\) | 43.7 |
Dual form | 43.7.d.a.37.6 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.15234i | 1.01904i | 0.860458 | + | 0.509522i | \(0.170178\pi\) | ||||
−0.860458 | + | 0.509522i | \(0.829822\pi\) | |||||||
\(3\) | 41.5767 | − | 24.0043i | 1.53988 | − | 0.889050i | 0.541035 | − | 0.841000i | \(-0.318033\pi\) |
0.998845 | − | 0.0480495i | \(-0.0153005\pi\) | |||||||
\(4\) | −2.46071 | −0.0384487 | ||||||||
\(5\) | −26.4676 | + | 15.2811i | −0.211741 | + | 0.122249i | −0.602120 | − | 0.798405i | \(-0.705677\pi\) |
0.390379 | + | 0.920654i | \(0.372344\pi\) | |||||||
\(6\) | 195.692 | + | 338.948i | 0.905980 | + | 1.56920i | ||||
\(7\) | 6.27128 | + | 3.62073i | 0.0182836 | + | 0.0105561i | 0.509114 | − | 0.860699i | \(-0.329973\pi\) |
−0.490830 | + | 0.871255i | \(0.663307\pi\) | |||||||
\(8\) | 501.689i | 0.979862i | ||||||||
\(9\) | 787.917 | − | 1364.71i | 1.08082 | − | 1.87203i | ||||
\(10\) | −124.577 | − | 215.773i | −0.124577 | − | 0.215773i | ||||
\(11\) | 1439.76 | 1.08172 | 0.540858 | − | 0.841114i | \(-0.318100\pi\) | ||||
0.540858 | + | 0.841114i | \(0.318100\pi\) | |||||||
\(12\) | −102.309 | + | 59.0678i | −0.0592063 | + | 0.0341828i | ||||
\(13\) | 1145.73 | − | 1984.46i | 0.521496 | − | 0.903257i | −0.478192 | − | 0.878255i | \(-0.658708\pi\) |
0.999687 | − | 0.0250014i | \(-0.00795903\pi\) | |||||||
\(14\) | −29.5174 | + | 51.1257i | −0.0107571 | + | 0.0186318i | ||||
\(15\) | −733.625 | + | 1270.68i | −0.217370 | + | 0.376497i | ||||
\(16\) | −4247.43 | −1.03697 | ||||||||
\(17\) | −3899.16 | + | 6753.54i | −0.793641 | + | 1.37463i | 0.130058 | + | 0.991506i | \(0.458484\pi\) |
−0.923699 | + | 0.383120i | \(0.874850\pi\) | |||||||
\(18\) | 11125.6 | + | 6423.37i | 1.90768 | + | 1.10140i | ||||
\(19\) | 5660.64 | − | 3268.17i | 0.825287 | − | 0.476480i | −0.0269492 | − | 0.999637i | \(-0.508579\pi\) |
0.852236 | + | 0.523157i | \(0.175246\pi\) | |||||||
\(20\) | 65.1293 | − | 37.6024i | 0.00814116 | − | 0.00470030i | ||||
\(21\) | 347.653 | 0.0375394 | ||||||||
\(22\) | 11737.5i | 1.10232i | ||||||||
\(23\) | 1004.12 | + | 1739.19i | 0.0825282 | + | 0.142943i | 0.904335 | − | 0.426823i | \(-0.140367\pi\) |
−0.821807 | + | 0.569766i | \(0.807034\pi\) | |||||||
\(24\) | 12042.7 | + | 20858.6i | 0.871146 | + | 1.50887i | ||||
\(25\) | −7345.48 | + | 12722.7i | −0.470110 | + | 0.814255i | ||||
\(26\) | 16178.0 | + | 9340.35i | 0.920458 | + | 0.531426i | ||||
\(27\) | − | 40655.4i | − | 2.06551i | ||||||
\(28\) | −15.4318 | − | 8.90958i | −0.000702981 | − | 0.000405866i | ||||
\(29\) | −33780.2 | − | 19503.0i | −1.38506 | − | 0.799664i | −0.392305 | − | 0.919835i | \(-0.628322\pi\) |
−0.992753 | + | 0.120171i | \(0.961656\pi\) | |||||||
\(30\) | −10359.0 | − | 5980.77i | −0.383666 | − | 0.221510i | ||||
\(31\) | −11411.5 | − | 19765.3i | −0.383052 | − | 0.663465i | 0.608445 | − | 0.793596i | \(-0.291794\pi\) |
−0.991497 | + | 0.130131i | \(0.958460\pi\) | |||||||
\(32\) | − | 2518.39i | − | 0.0768552i | ||||||
\(33\) | 59860.7 | − | 34560.6i | 1.66571 | − | 0.961700i | ||||
\(34\) | −55057.2 | − | 31787.3i | −1.40080 | − | 0.808754i | ||||
\(35\) | −221.315 | −0.00516186 | ||||||||
\(36\) | −1938.84 | + | 3358.17i | −0.0415561 | + | 0.0719772i | ||||
\(37\) | −30246.5 | + | 17462.8i | −0.597132 | + | 0.344754i | −0.767912 | − | 0.640555i | \(-0.778704\pi\) |
0.170781 | + | 0.985309i | \(0.445371\pi\) | |||||||
\(38\) | 26643.3 | + | 46147.5i | 0.485553 | + | 0.841003i | ||||
\(39\) | − | 110010.i | − | 1.85454i | ||||||
\(40\) | −7666.36 | − | 13278.5i | −0.119787 | − | 0.207477i | ||||
\(41\) | −33522.3 | −0.486387 | −0.243193 | − | 0.969978i | \(-0.578195\pi\) | ||||
−0.243193 | + | 0.969978i | \(0.578195\pi\) | |||||||
\(42\) | 2834.19i | 0.0382543i | ||||||||
\(43\) | 39701.1 | + | 68885.3i | 0.499341 | + | 0.866406i | ||||
\(44\) | −3542.85 | −0.0415905 | ||||||||
\(45\) | 48160.9i | 0.528515i | ||||||||
\(46\) | −14178.5 | + | 8185.93i | −0.145665 | + | 0.0840997i | ||||
\(47\) | 10418.8 | 0.100352 | 0.0501759 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501759 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(48\) | −176594. | + | 101957.i | −1.59681 | + | 0.921918i | ||||
\(49\) | −58798.3 | − | 101842.i | −0.499777 | − | 0.865639i | ||||
\(50\) | −103720. | − | 59882.9i | −0.829761 | − | 0.479063i | ||||
\(51\) | 374387.i | 2.82234i | ||||||||
\(52\) | −2819.30 | + | 4883.18i | −0.0200508 | + | 0.0347290i | ||||
\(53\) | −15557.7 | − | 26946.7i | −0.104500 | − | 0.181000i | 0.809034 | − | 0.587762i | \(-0.199991\pi\) |
−0.913534 | + | 0.406762i | \(0.866658\pi\) | |||||||
\(54\) | 331437. | 2.10484 | ||||||||
\(55\) | −38107.1 | + | 22001.2i | −0.229044 | + | 0.132238i | ||||
\(56\) | −1816.48 | + | 3146.24i | −0.0103435 | + | 0.0179154i | ||||
\(57\) | 156901. | − | 271760.i | 0.847228 | − | 1.46744i | ||||
\(58\) | 158995. | − | 275388.i | 0.814892 | − | 1.41143i | ||||
\(59\) | −140030. | −0.681810 | −0.340905 | − | 0.940098i | \(-0.610734\pi\) | ||||
−0.340905 | + | 0.940098i | \(0.610734\pi\) | |||||||
\(60\) | 1805.24 | − | 3126.77i | 0.00835760 | − | 0.0144758i | ||||
\(61\) | −117712. | − | 67961.0i | −0.518598 | − | 0.299413i | 0.217763 | − | 0.976002i | \(-0.430124\pi\) |
−0.736361 | + | 0.676589i | \(0.763457\pi\) | |||||||
\(62\) | 161133. | − | 93030.5i | 0.676100 | − | 0.390346i | ||||
\(63\) | 9882.51 | − | 5705.67i | 0.0395226 | − | 0.0228184i | ||||
\(64\) | −251305. | −0.958652 | ||||||||
\(65\) | 70031.8i | 0.255009i | ||||||||
\(66\) | 281750. | + | 488005.i | 0.980013 | + | 1.69743i | ||||
\(67\) | −115099. | − | 199357.i | −0.382689 | − | 0.662838i | 0.608756 | − | 0.793357i | \(-0.291669\pi\) |
−0.991446 | + | 0.130520i | \(0.958335\pi\) | |||||||
\(68\) | 9594.71 | − | 16618.5i | 0.0305144 | − | 0.0528525i | ||||
\(69\) | 83496.1 | + | 48206.5i | 0.254167 | + | 0.146743i | ||||
\(70\) | − | 1804.23i | − | 0.00526016i | ||||||
\(71\) | 391431. | + | 225993.i | 1.09365 | + | 0.631422i | 0.934547 | − | 0.355840i | \(-0.115805\pi\) |
0.159107 | + | 0.987261i | \(0.449138\pi\) | |||||||
\(72\) | 684662. | + | 395290.i | 1.83434 | + | 1.05905i | ||||
\(73\) | −374956. | − | 216481.i | −0.963854 | − | 0.556481i | −0.0664970 | − | 0.997787i | \(-0.521182\pi\) |
−0.897357 | + | 0.441305i | \(0.854516\pi\) | |||||||
\(74\) | −142363. | − | 246580.i | −0.351319 | − | 0.608503i | ||||
\(75\) | 705293.i | 1.67181i | ||||||||
\(76\) | −13929.2 | + | 8042.04i | −0.0317312 | + | 0.0183200i | ||||
\(77\) | 9029.17 | + | 5212.99i | 0.0197777 | + | 0.0114187i | ||||
\(78\) | 896836. | 1.88986 | ||||||||
\(79\) | 78420.4 | − | 135828.i | 0.159055 | − | 0.275491i | −0.775473 | − | 0.631381i | \(-0.782489\pi\) |
0.934528 | + | 0.355889i | \(0.115822\pi\) | |||||||
\(80\) | 112419. | − | 64905.4i | 0.219569 | − | 0.126768i | ||||
\(81\) | −401515. | − | 695444.i | −0.755521 | − | 1.30860i | ||||
\(82\) | − | 273285.i | − | 0.495649i | ||||||
\(83\) | 372851. | + | 645797.i | 0.652081 | + | 1.12944i | 0.982617 | + | 0.185644i | \(0.0594370\pi\) |
−0.330536 | + | 0.943793i | \(0.607230\pi\) | |||||||
\(84\) | −855.474 | −0.00144334 | ||||||||
\(85\) | − | 238334.i | − | 0.388086i | ||||||
\(86\) | −561577. | + | 323657.i | −0.882905 | + | 0.508850i | ||||
\(87\) | −1.87263e6 | −2.84376 | ||||||||
\(88\) | 722315.i | 1.05993i | ||||||||
\(89\) | 97786.0 | − | 56456.8i | 0.138710 | − | 0.0800841i | −0.429039 | − | 0.903286i | \(-0.641148\pi\) |
0.567749 | + | 0.823202i | \(0.307814\pi\) | |||||||
\(90\) | −392625. | −0.538580 | ||||||||
\(91\) | 14370.3 | − | 8296.72i | 0.0190697 | − | 0.0110099i | ||||
\(92\) | −2470.85 | − | 4279.64i | −0.00317310 | − | 0.00549597i | ||||
\(93\) | −948906. | − | 547851.i | −1.17971 | − | 0.681104i | ||||
\(94\) | 84937.8i | 0.102263i | ||||||||
\(95\) | −99882.5 | + | 173002.i | −0.116498 | + | 0.201781i | ||||
\(96\) | −60452.4 | − | 104707.i | −0.0683281 | − | 0.118348i | ||||
\(97\) | −1.45590e6 | −1.59521 | −0.797604 | − | 0.603182i | \(-0.793899\pi\) | ||||
−0.797604 | + | 0.603182i | \(0.793899\pi\) | |||||||
\(98\) | 830248. | − | 479344.i | 0.882124 | − | 0.509294i | ||||
\(99\) | 1.13442e6 | − | 1.96486e6i | 1.16914 | − | 2.02501i | ||||
\(100\) | 18075.1 | − | 31307.0i | 0.0180751 | − | 0.0313070i | ||||
\(101\) | 935006. | − | 1.61948e6i | 0.907507 | − | 1.57185i | 0.0899919 | − | 0.995942i | \(-0.471316\pi\) |
0.817516 | − | 0.575906i | \(-0.195351\pi\) | |||||||
\(102\) | −3.05213e6 | −2.87609 | ||||||||
\(103\) | 268269. | − | 464656.i | 0.245504 | − | 0.425226i | −0.716769 | − | 0.697311i | \(-0.754380\pi\) |
0.962273 | + | 0.272085i | \(0.0877131\pi\) | |||||||
\(104\) | 995580. | + | 574799.i | 0.885067 | + | 0.510994i | ||||
\(105\) | −9201.55 | + | 5312.51i | −0.00794864 | + | 0.00458915i | ||||
\(106\) | 219679. | − | 126832.i | 0.184447 | − | 0.106490i | ||||
\(107\) | 1.28220e6 | 1.04665 | 0.523327 | − | 0.852132i | \(-0.324690\pi\) | ||||
0.523327 | + | 0.852132i | \(0.324690\pi\) | |||||||
\(108\) | 100041.i | 0.0794161i | ||||||||
\(109\) | 970522. | + | 1.68099e6i | 0.749421 | + | 1.29804i | 0.948101 | + | 0.317971i | \(0.103001\pi\) |
−0.198680 | + | 0.980064i | \(0.563665\pi\) | |||||||
\(110\) | −179361. | − | 310663.i | −0.134757 | − | 0.233405i | ||||
\(111\) | −838367. | + | 1.45210e6i | −0.613007 | + | 1.06176i | ||||
\(112\) | −26636.8 | − | 15378.8i | −0.0189596 | − | 0.0109463i | ||||
\(113\) | 2.83684e6i | 1.96607i | 0.183414 | + | 0.983036i | \(0.441285\pi\) | ||||
−0.183414 | + | 0.983036i | \(0.558715\pi\) | |||||||
\(114\) | 2.21548e6 | + | 1.27911e6i | 1.49539 | + | 0.863362i | ||||
\(115\) | −53153.4 | − | 30688.1i | −0.0349492 | − | 0.0201779i | ||||
\(116\) | 83123.4 | + | 47991.3i | 0.0532536 | + | 0.0307460i | ||||
\(117\) | −1.80547e6 | − | 3.12717e6i | −1.12728 | − | 1.95251i | ||||
\(118\) | − | 1.14157e6i | − | 0.694794i | ||||||
\(119\) | −48905.4 | + | 28235.6i | −0.0290213 | + | 0.0167554i | ||||
\(120\) | −637485. | − | 368052.i | −0.368915 | − | 0.212993i | ||||
\(121\) | 301360. | 0.170110 | ||||||||
\(122\) | 554041. | − | 959628.i | 0.305114 | − | 0.528474i | ||||
\(123\) | −1.39375e6 | + | 804680.i | −0.748977 | + | 0.432422i | ||||
\(124\) | 28080.4 | + | 48636.8i | 0.0147278 | + | 0.0255094i | ||||
\(125\) | − | 926522.i | − | 0.474379i | ||||||
\(126\) | 46514.6 | + | 80565.6i | 0.0232529 | + | 0.0402752i | ||||
\(127\) | 1.83203e6 | 0.894379 | 0.447189 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447189 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(128\) | − | 2.20990e6i | − | 1.05376i | ||||||
\(129\) | 3.30419e6 | + | 1.91103e6i | 1.53920 | + | 0.890221i | ||||
\(130\) | −570923. | −0.259865 | ||||||||
\(131\) | 2.22791e6i | 0.991022i | 0.868602 | + | 0.495511i | \(0.165019\pi\) | ||||
−0.868602 | + | 0.495511i | \(0.834981\pi\) | |||||||
\(132\) | −147300. | + | 85043.8i | −0.0640444 | + | 0.0369761i | ||||
\(133\) | 47332.7 | 0.0201190 | ||||||||
\(134\) | 1.62523e6 | − | 938325.i | 0.675460 | − | 0.389977i | ||||
\(135\) | 621259. | + | 1.07605e6i | 0.252506 | + | 0.437353i | ||||
\(136\) | −3.38818e6 | − | 1.95617e6i | −1.34694 | − | 0.777659i | ||||
\(137\) | 138627.i | 0.0539120i | 0.999637 | + | 0.0269560i | \(0.00858141\pi\) | ||||
−0.999637 | + | 0.0269560i | \(0.991419\pi\) | |||||||
\(138\) | −392996. | + | 680689.i | −0.149538 | + | 0.259007i | ||||
\(139\) | 2.11377e6 | + | 3.66116e6i | 0.787070 | + | 1.36324i | 0.927755 | + | 0.373190i | \(0.121736\pi\) |
−0.140685 | + | 0.990054i | \(0.544930\pi\) | |||||||
\(140\) | 544.592 | 0.000198467 | ||||||||
\(141\) | 433180. | − | 250097.i | 0.154530 | − | 0.0892177i | ||||
\(142\) | −1.84237e6 | + | 3.19108e6i | −0.643446 | + | 1.11448i | ||||
\(143\) | 1.64958e6 | − | 2.85715e6i | 0.564110 | − | 0.977068i | ||||
\(144\) | −3.34662e6 | + | 5.79652e6i | −1.12078 | + | 1.94124i | ||||
\(145\) | 1.19211e6 | 0.391032 | ||||||||
\(146\) | 1.76483e6 | − | 3.05677e6i | 0.567079 | − | 0.982209i | ||||
\(147\) | −4.88928e6 | − | 2.82283e6i | −1.53919 | − | 0.888654i | ||||
\(148\) | 74428.0 | − | 42971.0i | 0.0229589 | − | 0.0132553i | ||||
\(149\) | 4.56847e6 | − | 2.63761e6i | 1.38106 | − | 0.797354i | 0.388773 | − | 0.921334i | \(-0.372899\pi\) |
0.992285 | + | 0.123980i | \(0.0395658\pi\) | |||||||
\(150\) | −5.74979e6 | −1.70364 | ||||||||
\(151\) | − | 2.96589e6i | − | 0.861439i | −0.902486 | − | 0.430720i | \(-0.858260\pi\) | ||
0.902486 | − | 0.430720i | \(-0.141740\pi\) | |||||||
\(152\) | 1.63961e6 | + | 2.83989e6i | 0.466884 | + | 0.808668i | ||||
\(153\) | 6.14443e6 | + | 1.06425e7i | 1.71556 | + | 2.97144i | ||||
\(154\) | −42498.1 | + | 73608.9i | −0.0116361 | + | 0.0201543i | ||||
\(155\) | 604071. | + | 348760.i | 0.162216 | + | 0.0936552i | ||||
\(156\) | 270702.i | 0.0713047i | ||||||||
\(157\) | −3.55451e6 | − | 2.05220e6i | −0.918505 | − | 0.530299i | −0.0353470 | − | 0.999375i | \(-0.511254\pi\) |
−0.883158 | + | 0.469076i | \(0.844587\pi\) | |||||||
\(158\) | 1.10732e6 | + | 639310.i | 0.280738 | + | 0.162084i | ||||
\(159\) | −1.29368e6 | − | 746905.i | −0.321836 | − | 0.185812i | ||||
\(160\) | 38483.8 | + | 66655.9i | 0.00939546 | + | 0.0162734i | ||||
\(161\) | 14542.6i | 0.00348469i | ||||||||
\(162\) | 5.66950e6 | − | 3.27329e6i | 1.33352 | − | 0.769909i | ||||
\(163\) | 4.21898e6 | + | 2.43583e6i | 0.974191 | + | 0.562450i | 0.900511 | − | 0.434832i | \(-0.143192\pi\) |
0.0736800 | + | 0.997282i | \(0.476526\pi\) | |||||||
\(164\) | 82488.7 | 0.0187009 | ||||||||
\(165\) | −1.05625e6 | + | 1.82947e6i | −0.235133 | + | 0.407263i | ||||
\(166\) | −5.26476e6 | + | 3.03961e6i | −1.15094 | + | 0.664498i | ||||
\(167\) | −2.63154e6 | − | 4.55796e6i | −0.565016 | − | 0.978636i | −0.997048 | − | 0.0767779i | \(-0.975537\pi\) |
0.432033 | − | 0.901858i | \(-0.357797\pi\) | |||||||
\(168\) | 174414.i | 0.0367835i | ||||||||
\(169\) | −211971. | − | 367144.i | −0.0439152 | − | 0.0760634i | ||||
\(170\) | 1.94298e6 | 0.395477 | ||||||||
\(171\) | − | 1.03002e7i | − | 2.05995i | ||||||
\(172\) | −97693.1 | − | 169507.i | −0.0191990 | − | 0.0333121i | ||||
\(173\) | 4.07003e6 | 0.786067 | 0.393033 | − | 0.919524i | \(-0.371426\pi\) | ||||
0.393033 | + | 0.919524i | \(0.371426\pi\) | |||||||
\(174\) | − | 1.52663e7i | − | 2.89792i | ||||||
\(175\) | −92131.1 | + | 53191.9i | −0.0171907 | + | 0.00992503i | ||||
\(176\) | −6.11530e6 | −1.12171 | ||||||||
\(177\) | −5.82197e6 | + | 3.36132e6i | −1.04991 | + | 0.606163i | ||||
\(178\) | 460255. | + | 797185.i | 0.0816091 | + | 0.141351i | ||||
\(179\) | −3.22579e6 | − | 1.86241e6i | −0.562441 | − | 0.324726i | 0.191683 | − | 0.981457i | \(-0.438605\pi\) |
−0.754125 | + | 0.656731i | \(0.771939\pi\) | |||||||
\(180\) | − | 118510.i | − | 0.0203207i | ||||||
\(181\) | 2.27580e6 | − | 3.94180e6i | 0.383794 | − | 0.664751i | −0.607807 | − | 0.794085i | \(-0.707951\pi\) |
0.991601 | + | 0.129334i | \(0.0412839\pi\) | |||||||
\(182\) | 67637.7 | + | 117152.i | 0.0112195 | + | 0.0194328i | ||||
\(183\) | −6.52544e6 | −1.06477 | ||||||||
\(184\) | −872532. | + | 503756.i | −0.140064 | + | 0.0808662i | ||||
\(185\) | 533702. | − | 924399.i | 0.0842915 | − | 0.145997i | ||||
\(186\) | 4.46627e6 | − | 7.73581e6i | 0.694075 | − | 1.20217i | ||||
\(187\) | −5.61387e6 | + | 9.72350e6i | −0.858494 | + | 1.48696i | ||||
\(188\) | −25637.7 | −0.00385839 | ||||||||
\(189\) | 147202. | − | 254962.i | 0.0218036 | − | 0.0377650i | ||||
\(190\) | −1.41037e6 | − | 814277.i | −0.205623 | − | 0.118717i | ||||
\(191\) | −1.86630e6 | + | 1.07751e6i | −0.267844 | + | 0.154640i | −0.627907 | − | 0.778288i | \(-0.716088\pi\) |
0.360063 | + | 0.932928i | \(0.382755\pi\) | |||||||
\(192\) | −1.04484e7 | + | 6.03241e6i | −1.47621 | + | 0.852289i | ||||
\(193\) | −1.81325e6 | −0.252224 | −0.126112 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126112 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(194\) | − | 1.18690e7i | − | 1.62559i | ||||||
\(195\) | 1.68107e6 | + | 2.91169e6i | 0.226715 | + | 0.392683i | ||||
\(196\) | 144686. | + | 250603.i | 0.0192158 | + | 0.0332827i | ||||
\(197\) | −3.96974e6 | + | 6.87579e6i | −0.519234 | + | 0.899340i | 0.480516 | + | 0.876986i | \(0.340449\pi\) |
−0.999750 | + | 0.0223541i | \(0.992884\pi\) | |||||||
\(198\) | 1.60183e7 | + | 9.24814e6i | 2.06357 | + | 1.19140i | ||||
\(199\) | 6.67161e6i | 0.846587i | 0.905993 | + | 0.423293i | \(0.139126\pi\) | ||||
−0.905993 | + | 0.423293i | \(0.860874\pi\) | |||||||
\(200\) | −6.38286e6 | − | 3.68515e6i | −0.797858 | − | 0.460643i | ||||
\(201\) | −9.57087e6 | − | 5.52574e6i | −1.17859 | − | 0.680460i | ||||
\(202\) | 1.32025e7 | + | 7.62249e6i | 1.60178 | + | 0.924789i | ||||
\(203\) | −141230. | − | 244618.i | −0.0168826 | − | 0.0292415i | ||||
\(204\) | − | 921259.i | − | 0.108515i | ||||||
\(205\) | 887255. | − | 512257.i | 0.102988 | − | 0.0594602i | ||||
\(206\) | 3.78804e6 | + | 2.18702e6i | 0.433324 | + | 0.250180i | ||||
\(207\) | 3.16465e6 | 0.356792 | ||||||||
\(208\) | −4.86639e6 | + | 8.42884e6i | −0.540775 | + | 0.936651i | ||||
\(209\) | 8.14999e6 | − | 4.70540e6i | 0.892726 | − | 0.515416i | ||||
\(210\) | −43309.4 | − | 75014.2i | −0.00467654 | − | 0.00810001i | ||||
\(211\) | 1.45878e6i | 0.155290i | 0.996981 | + | 0.0776450i | \(0.0247401\pi\) | ||||
−0.996981 | + | 0.0776450i | \(0.975260\pi\) | |||||||
\(212\) | 38283.1 | + | 66308.2i | 0.00401790 | + | 0.00695921i | ||||
\(213\) | 2.16992e7 | 2.24546 | ||||||||
\(214\) | 1.04529e7i | 1.06659i | ||||||||
\(215\) | −2.10344e6 | − | 1.21655e6i | −0.211648 | − | 0.122410i | ||||
\(216\) | 2.03964e7 | 2.02391 | ||||||||
\(217\) | − | 165272.i | − | 0.0161741i | ||||||
\(218\) | −1.37040e7 | + | 7.91203e6i | −1.32275 | + | 0.763692i | ||||
\(219\) | −2.07859e7 | −1.97896 | ||||||||
\(220\) | 93770.8 | − | 54138.6i | 0.00880643 | − | 0.00508439i | ||||
\(221\) | 8.93473e6 | + | 1.54754e7i | 0.827760 | + | 1.43372i | ||||
\(222\) | −1.18380e7 | − | 6.83466e6i | −1.08198 | − | 0.624681i | ||||
\(223\) | − | 1.90784e7i | − | 1.72040i | −0.509960 | − | 0.860198i | \(-0.670340\pi\) | ||
0.509960 | − | 0.860198i | \(-0.329660\pi\) | |||||||
\(224\) | 9118.41 | − | 15793.6i | 0.000811288 | − | 0.00140519i | ||||
\(225\) | 1.15753e7 | + | 2.00489e7i | 1.01621 | + | 1.76013i | ||||
\(226\) | −2.31269e7 | −2.00351 | ||||||||
\(227\) | 1.78714e7 | − | 1.03181e7i | 1.52785 | − | 0.882106i | 0.528400 | − | 0.848996i | \(-0.322792\pi\) |
0.999452 | − | 0.0331099i | \(-0.0105411\pi\) | |||||||
\(228\) | −386088. | + | 668724.i | −0.0325748 | + | 0.0564212i | ||||
\(229\) | −1.00520e7 | + | 1.74106e7i | −0.837042 | + | 1.44980i | 0.0553154 | + | 0.998469i | \(0.482384\pi\) |
−0.892357 | + | 0.451330i | \(0.850950\pi\) | |||||||
\(230\) | 250180. | − | 433324.i | 0.0205622 | − | 0.0356147i | ||||
\(231\) | 500538. | 0.0406070 | ||||||||
\(232\) | 9.78445e6 | − | 1.69472e7i | 0.783560 | − | 1.35717i | ||||
\(233\) | 1.01924e7 | + | 5.88457e6i | 0.805764 | + | 0.465208i | 0.845483 | − | 0.534003i | \(-0.179313\pi\) |
−0.0397189 | + | 0.999211i | \(0.512646\pi\) | |||||||
\(234\) | 2.54938e7 | − | 1.47188e7i | 1.98970 | − | 1.14875i | ||||
\(235\) | −275761. | + | 159211.i | −0.0212486 | + | 0.0122679i | ||||
\(236\) | 344573. | 0.0262147 | ||||||||
\(237\) | − | 7.52972e6i | − | 0.565632i | ||||||
\(238\) | −230186. | − | 398694.i | −0.0170745 | − | 0.0295739i | ||||
\(239\) | −1.23232e7 | − | 2.13444e7i | −0.902671 | − | 1.56347i | −0.824013 | − | 0.566571i | \(-0.808270\pi\) |
−0.0786587 | − | 0.996902i | \(-0.525064\pi\) | |||||||
\(240\) | 3.11602e6 | − | 5.39711e6i | 0.225407 | − | 0.390416i | ||||
\(241\) | −8.92777e6 | − | 5.15445e6i | −0.637811 | − | 0.368240i | 0.145960 | − | 0.989291i | \(-0.453373\pi\) |
−0.783771 | + | 0.621050i | \(0.786706\pi\) | |||||||
\(242\) | 2.45679e6i | 0.173349i | ||||||||
\(243\) | −7.72028e6 | − | 4.45731e6i | −0.538040 | − | 0.310637i | ||||
\(244\) | 289655. | + | 167233.i | 0.0199394 | + | 0.0115120i | ||||
\(245\) | 3.11250e6 | + | 1.79700e6i | 0.211647 | + | 0.122194i | ||||
\(246\) | −6.56003e6 | − | 1.13623e7i | −0.440657 | − | 0.763240i | ||||
\(247\) | − | 1.49777e7i | − | 0.993928i | ||||||
\(248\) | 9.91604e6 | − | 5.72503e6i | 0.650105 | − | 0.375338i | ||||
\(249\) | 3.10039e7 | + | 1.79001e7i | 2.00825 | + | 1.15946i | ||||
\(250\) | 7.55332e6 | 0.483413 | ||||||||
\(251\) | 6.92571e6 | − | 1.19957e7i | 0.437969 | − | 0.758585i | −0.559564 | − | 0.828787i | \(-0.689031\pi\) |
0.997533 | + | 0.0702027i | \(0.0223646\pi\) | |||||||
\(252\) | −24318.0 | + | 14040.0i | −0.00151959 | + | 0.000877336i | ||||
\(253\) | 1.44570e6 | + | 2.50402e6i | 0.0892720 | + | 0.154624i | ||||
\(254\) | 1.49353e7i | 0.911411i | ||||||||
\(255\) | −5.72104e6 | − | 9.90913e6i | −0.345028 | − | 0.597606i | ||||
\(256\) | 1.93236e6 | 0.115178 | ||||||||
\(257\) | 5.45908e6i | 0.321603i | 0.986987 | + | 0.160801i | \(0.0514079\pi\) | ||||
−0.986987 | + | 0.160801i | \(0.948592\pi\) | |||||||
\(258\) | −1.55794e7 | + | 2.69369e7i | −0.907174 | + | 1.56851i | ||||
\(259\) | −252913. | −0.0145570 | ||||||||
\(260\) | − | 172328.i | − | 0.00980474i | ||||||
\(261\) | −5.32320e7 | + | 3.07335e7i | −2.99400 | + | 1.72858i | ||||
\(262\) | −1.81627e7 | −1.00989 | ||||||||
\(263\) | −3.02521e7 | + | 1.74661e7i | −1.66299 | + | 0.960125i | −0.691708 | + | 0.722177i | \(0.743141\pi\) |
−0.971278 | + | 0.237948i | \(0.923525\pi\) | |||||||
\(264\) | 1.73387e7 | + | 3.00315e7i | 0.942333 | + | 1.63217i | ||||
\(265\) | 823551. | + | 475477.i | 0.0442540 | + | 0.0255501i | ||||
\(266\) | 385872.i | 0.0205021i | ||||||||
\(267\) | 2.71042e6 | − | 4.69458e6i | 0.142397 | − | 0.246640i | ||||
\(268\) | 283225. | + | 490561.i | 0.0147139 | + | 0.0254852i | ||||
\(269\) | 1.47720e7 | 0.758896 | 0.379448 | − | 0.925213i | \(-0.376114\pi\) | ||||
0.379448 | + | 0.925213i | \(0.376114\pi\) | |||||||
\(270\) | −8.77235e6 | + | 5.06472e6i | −0.445682 | + | 0.257314i | ||||
\(271\) | 1.14718e7 | − | 1.98697e7i | 0.576398 | − | 0.998350i | −0.419490 | − | 0.907760i | \(-0.637791\pi\) |
0.995888 | − | 0.0905905i | \(-0.0288754\pi\) | |||||||
\(272\) | 1.65614e7 | − | 2.86852e7i | 0.822982 | − | 1.42545i | ||||
\(273\) | 398315. | − | 689901.i | 0.0195767 | − | 0.0339078i | ||||
\(274\) | −1.13013e6 | −0.0549387 | ||||||||
\(275\) | −1.05758e7 | + | 1.83177e7i | −0.508526 | + | 0.880793i | ||||
\(276\) | −205460. | − | 118622.i | −0.00977237 | − | 0.00564208i | ||||
\(277\) | 2.89271e7 | − | 1.67010e7i | 1.36102 | − | 0.785786i | 0.371261 | − | 0.928528i | \(-0.378925\pi\) |
0.989760 | + | 0.142743i | \(0.0455921\pi\) | |||||||
\(278\) | −2.98470e7 | + | 1.72322e7i | −1.38921 | + | 0.802058i | ||||
\(279\) | −3.59653e7 | −1.65604 | ||||||||
\(280\) | − | 111031.i | − | 0.00505791i | ||||||
\(281\) | −5.23585e6 | − | 9.06876e6i | −0.235976 | − | 0.408723i | 0.723580 | − | 0.690241i | \(-0.242495\pi\) |
−0.959556 | + | 0.281518i | \(0.909162\pi\) | |||||||
\(282\) | 2.03888e6 | + | 3.53144e6i | 0.0909166 | + | 0.157472i | ||||
\(283\) | 2.10170e7 | − | 3.64024e7i | 0.927279 | − | 1.60609i | 0.139425 | − | 0.990233i | \(-0.455475\pi\) |
0.787854 | − | 0.615862i | \(-0.211192\pi\) | |||||||
\(284\) | −963200. | − | 556104.i | −0.0420496 | − | 0.0242773i | ||||
\(285\) | 9.59046e6i | 0.414290i | ||||||||
\(286\) | 2.32925e7 | + | 1.34479e7i | 0.995674 | + | 0.574853i | ||||
\(287\) | −210228. | − | 121375.i | −0.00889291 | − | 0.00513432i | ||||
\(288\) | −3.43688e6 | − | 1.98428e6i | −0.143876 | − | 0.0830666i | ||||
\(289\) | −1.83381e7 | − | 3.17625e7i | −0.759731 | − | 1.31589i | ||||
\(290\) | 9.71848e6i | 0.398478i | ||||||||
\(291\) | −6.05317e7 | + | 3.49480e7i | −2.45643 | + | 1.41822i | ||||
\(292\) | 922659. | + | 532697.i | 0.0370589 | + | 0.0213960i | ||||
\(293\) | 5.82606e6 | 0.231618 | 0.115809 | − | 0.993272i | \(-0.463054\pi\) | ||||
0.115809 | + | 0.993272i | \(0.463054\pi\) | |||||||
\(294\) | 2.30127e7 | − | 3.98591e7i | 0.905576 | − | 1.56850i | ||||
\(295\) | 3.70625e6 | − | 2.13980e6i | 0.144367 | − | 0.0833505i | ||||
\(296\) | −8.76092e6 | − | 1.51744e7i | −0.337811 | − | 0.585107i | ||||
\(297\) | − | 5.85342e7i | − | 2.23429i | ||||||
\(298\) | 2.15027e7 | + | 3.72437e7i | 0.812538 | + | 1.40736i | ||||
\(299\) | 4.60178e6 | 0.172152 | ||||||||
\(300\) | − | 1.73553e6i | − | 0.0642787i | ||||||
\(301\) | −438.026 | + | 575746.i | −1.60620e−5 | + | 0.0211121i | ||||
\(302\) | 2.41790e7 | 0.877844 | ||||||||
\(303\) | − | 8.97768e7i | − | 3.22728i | ||||||
\(304\) | −2.40432e7 | + | 1.38813e7i | −0.855798 | + | 0.494095i | ||||
\(305\) | 4.15407e6 | 0.146411 | ||||||||
\(306\) | −8.67610e7 | + | 5.00915e7i | −3.02803 | + | 1.74823i | ||||
\(307\) | 7.18005e6 | + | 1.24362e7i | 0.248149 | + | 0.429806i | 0.963012 | − | 0.269458i | \(-0.0868445\pi\) |
−0.714863 | + | 0.699264i | \(0.753511\pi\) | |||||||
\(308\) | −22218.2 | − | 12827.7i | −0.000760426 | − | 0.000439032i | ||||
\(309\) | − | 2.57585e7i | − | 0.873063i | ||||||
\(310\) | −2.84321e6 | + | 4.92459e6i | −0.0954387 | + | 0.165305i | ||||
\(311\) | 2.17155e7 | + | 3.76124e7i | 0.721920 | + | 1.25040i | 0.960229 | + | 0.279213i | \(0.0900737\pi\) |
−0.238309 | + | 0.971189i | \(0.576593\pi\) | |||||||
\(312\) | 5.51906e7 | 1.81720 | ||||||||
\(313\) | −4.68305e6 | + | 2.70376e6i | −0.152720 | + | 0.0881730i | −0.574413 | − | 0.818566i | \(-0.694769\pi\) |
0.421693 | + | 0.906739i | \(0.361436\pi\) | |||||||
\(314\) | 1.67302e7 | − | 2.89776e7i | 0.540397 | − | 0.935996i | ||||
\(315\) | −174378. | + | 302031.i | −0.00557904 | + | 0.00966318i | ||||
\(316\) | −192970. | + | 334234.i | −0.00611546 | + | 0.0105923i | ||||
\(317\) | −2.19229e7 | −0.688209 | −0.344105 | − | 0.938931i | \(-0.611817\pi\) | ||||
−0.344105 | + | 0.938931i | \(0.611817\pi\) | |||||||
\(318\) | 6.08903e6 | − | 1.05465e7i | 0.189350 | − | 0.327965i | ||||
\(319\) | −4.86355e7 | − | 2.80797e7i | −1.49824 | − | 0.865009i | ||||
\(320\) | 6.65144e6 | − | 3.84021e6i | 0.202986 | − | 0.117194i | ||||
\(321\) | 5.33096e7 | − | 3.07783e7i | 1.61172 | − | 0.930528i | ||||
\(322\) | −118556. | −0.00355105 | ||||||||
\(323\) | 5.09725e7i | 1.51261i | ||||||||
\(324\) | 988014. | + | 1.71129e6i | 0.0290488 | + | 0.0503140i | ||||
\(325\) | 1.68318e7 | + | 2.91535e7i | 0.490321 | + | 0.849261i | ||||
\(326\) | −1.98577e7 | + | 3.43946e7i | −0.573160 | + | 0.992743i | ||||
\(327\) | 8.07023e7 | + | 4.65935e7i | 2.30804 | + | 1.33254i | ||||
\(328\) | − | 1.68178e7i | − | 0.476592i | ||||||
\(329\) | 65339.4 | + | 37723.7i | 0.00183479 | + | 0.00105932i | ||||
\(330\) | −1.49145e7 | − | 8.61089e6i | −0.415018 | − | 0.239611i | ||||
\(331\) | 1.51743e7 | + | 8.76089e6i | 0.418432 | + | 0.241582i | 0.694406 | − | 0.719583i | \(-0.255667\pi\) |
−0.275974 | + | 0.961165i | \(0.589000\pi\) | |||||||
\(332\) | −917481. | − | 1.58912e6i | −0.0250716 | − | 0.0434253i | ||||
\(333\) | 5.50370e7i | 1.49047i | ||||||||
\(334\) | 3.71581e7 | − | 2.14532e7i | 0.997272 | − | 0.575775i | ||||
\(335\) | 6.09279e6 | + | 3.51767e6i | 0.162062 | + | 0.0935666i | ||||
\(336\) | −1.47663e6 | −0.0389273 | ||||||||
\(337\) | 2.83853e7 | − | 4.91647e7i | 0.741658 | − | 1.28459i | −0.210083 | − | 0.977684i | \(-0.567373\pi\) |
0.951740 | − | 0.306905i | \(-0.0992934\pi\) | |||||||
\(338\) | 2.99308e6 | − | 1.72806e6i | 0.0775119 | − | 0.0447515i | ||||
\(339\) | 6.80965e7 | + | 1.17947e8i | 1.74794 | + | 3.02751i | ||||
\(340\) | 586471.i | 0.0149214i | ||||||||
\(341\) | −1.64299e7 | − | 2.84574e7i | −0.414353 | − | 0.717681i | ||||
\(342\) | 8.39708e7 | 2.09918 | ||||||||
\(343\) | − | 1.70352e6i | − | 0.0422148i | ||||||
\(344\) | −3.45590e7 | + | 1.99176e7i | −0.848958 | + | 0.489285i | ||||
\(345\) | −2.94659e6 | −0.0717567 | ||||||||
\(346\) | 3.31803e7i | 0.801036i | ||||||||
\(347\) | −4.80656e7 | + | 2.77507e7i | −1.15039 | + | 0.664179i | −0.948983 | − | 0.315328i | \(-0.897885\pi\) |
−0.201409 | + | 0.979507i | \(0.564552\pi\) | |||||||
\(348\) | 4.60800e6 | 0.109339 | ||||||||
\(349\) | −3.48049e7 | + | 2.00946e7i | −0.818774 | + | 0.472720i | −0.849994 | − | 0.526793i | \(-0.823394\pi\) |
0.0312193 | + | 0.999513i | \(0.490061\pi\) | |||||||
\(350\) | −433639. | − | 751085.i | −0.0101140 | − | 0.0175180i | ||||
\(351\) | −8.06788e7 | − | 4.65800e7i | −1.86569 | − | 1.07715i | ||||
\(352\) | − | 3.62589e6i | − | 0.0831356i | ||||||
\(353\) | −6.92043e6 | + | 1.19865e7i | −0.157329 | + | 0.272502i | −0.933905 | − | 0.357522i | \(-0.883622\pi\) |
0.776576 | + | 0.630024i | \(0.216955\pi\) | |||||||
\(354\) | −2.74026e7 | − | 4.74627e7i | −0.617707 | − | 1.06990i | ||||
\(355\) | −1.38137e7 | −0.308762 | ||||||||
\(356\) | −240624. | + | 138924.i | −0.00533320 | + | 0.00307913i | ||||
\(357\) | −1.35555e6 | + | 2.34789e6i | −0.0297928 | + | 0.0516027i | ||||
\(358\) | 1.51830e7 | − | 2.62978e7i | 0.330909 | − | 0.573152i | ||||
\(359\) | −1.89626e7 | + | 3.28441e7i | −0.409839 | + | 0.709863i | −0.994871 | − | 0.101147i | \(-0.967749\pi\) |
0.585032 | + | 0.811010i | \(0.301082\pi\) | |||||||
\(360\) | −2.41618e7 | −0.517872 | ||||||||
\(361\) | −2.16102e6 | + | 3.74299e6i | −0.0459342 | + | 0.0795605i | ||||
\(362\) | 3.21349e7 | + | 1.85531e7i | 0.677410 | + | 0.391103i | ||||
\(363\) | 1.25296e7 | − | 7.23395e6i | 0.261949 | − | 0.151236i | ||||
\(364\) | −35361.3 | + | 20415.9i | −0.000733203 | + | 0.000423315i | ||||
\(365\) | 1.32322e7 | 0.272117 | ||||||||
\(366\) | − | 5.31976e7i | − | 1.08505i | ||||||
\(367\) | 5.09218e6 | + | 8.81991e6i | 0.103016 | + | 0.178429i | 0.912926 | − | 0.408125i | \(-0.133817\pi\) |
−0.809910 | + | 0.586554i | \(0.800484\pi\) | |||||||
\(368\) | −4.26493e6 | − | 7.38708e6i | −0.0855792 | − | 0.148228i | ||||
\(369\) | −2.64128e7 | + | 4.57482e7i | −0.525696 | + | 0.910532i | ||||
\(370\) | 7.53602e6 | + | 4.35092e6i | 0.148777 | + | 0.0858967i | ||||
\(371\) | − | 225321.i | − | 0.00441245i | ||||||
\(372\) | 2.33499e6 | + | 1.34811e6i | 0.0453582 | + | 0.0261876i | ||||
\(373\) | 3.13825e7 | + | 1.81187e7i | 0.604729 | + | 0.349141i | 0.770900 | − | 0.636956i | \(-0.219807\pi\) |
−0.166170 | + | 0.986097i | \(0.553140\pi\) | |||||||
\(374\) | −7.92693e7 | − | 4.57662e7i | −1.51527 | − | 0.874842i | ||||
\(375\) | −2.22405e7 | − | 3.85218e7i | −0.421747 | − | 0.730487i | ||||
\(376\) | 5.22701e6i | 0.0983308i | ||||||||
\(377\) | −7.74057e7 | + | 4.46902e7i | −1.44460 | + | 0.834042i | ||||
\(378\) | 2.07854e6 | + | 1.20004e6i | 0.0384842 | + | 0.0222188i | ||||
\(379\) | 3.32913e7 | 0.611523 | 0.305762 | − | 0.952108i | \(-0.401089\pi\) | ||||
0.305762 | + | 0.952108i | \(0.401089\pi\) | |||||||
\(380\) | 245782. | − | 425708.i | 0.00447920 | − | 0.00775819i | ||||
\(381\) | 7.61699e7 | − | 4.39767e7i | 1.37724 | − | 0.795147i | ||||
\(382\) | −8.78424e6 | − | 1.52147e7i | −0.157585 | − | 0.272945i | ||||
\(383\) | − | 4.47425e7i | − | 0.796387i | −0.917302 | − | 0.398193i | \(-0.869637\pi\) | ||
0.917302 | − | 0.398193i | \(-0.130363\pi\) | |||||||
\(384\) | −5.30472e7 | − | 9.18805e7i | −0.936847 | − | 1.62267i | ||||
\(385\) | −318641. | −0.00558367 | ||||||||
\(386\) | − | 1.47823e7i | − | 0.257027i | ||||||
\(387\) | 1.25290e8 | + | 95320.2i | 2.16164 | + | 0.00164457i | ||||
\(388\) | 3.58256e6 | 0.0613336 | ||||||||
\(389\) | − | 8.65818e6i | − | 0.147088i | −0.997292 | − | 0.0735441i | \(-0.976569\pi\) | ||
0.997292 | − | 0.0735441i | \(-0.0234310\pi\) | |||||||
\(390\) | −2.37371e7 | + | 1.37046e7i | −0.400161 | + | 0.231033i | ||||
\(391\) | −1.56609e7 | −0.261991 | ||||||||
\(392\) | 5.10929e7 | − | 2.94985e7i | 0.848207 | − | 0.489713i | ||||
\(393\) | 5.34795e7 | + | 9.26292e7i | 0.881068 | + | 1.52605i | ||||
\(394\) | −5.60538e7 | − | 3.23627e7i | −0.916466 | − | 0.529122i | ||||
\(395\) | 4.79339e6i | 0.0777771i | ||||||||
\(396\) | −2.79147e6 | + | 4.83497e6i | −0.0449519 | + | 0.0778589i | ||||
\(397\) | 1.42987e6 | + | 2.47662e6i | 0.0228521 | + | 0.0395810i | 0.877225 | − | 0.480079i | \(-0.159392\pi\) |
−0.854373 | + | 0.519660i | \(0.826059\pi\) | |||||||
\(398\) | −5.43893e7 | −0.862708 | ||||||||
\(399\) | 1.96794e6 | − | 1.13619e6i | 0.0309808 | − | 0.0178868i | ||||
\(400\) | 3.11994e7 | − | 5.40389e7i | 0.487491 | − | 0.844359i | ||||
\(401\) | −1.13615e7 | + | 1.96786e7i | −0.176198 | + | 0.305184i | −0.940575 | − | 0.339585i | \(-0.889713\pi\) |
0.764377 | + | 0.644769i | \(0.223047\pi\) | |||||||
\(402\) | 4.50478e7 | − | 7.80250e7i | 0.693418 | − | 1.20104i | ||||
\(403\) | −5.22978e7 | −0.799039 | ||||||||
\(404\) | −2.30078e6 | + | 3.98507e6i | −0.0348924 | + | 0.0604355i | ||||
\(405\) | 2.12543e7 | + | 1.22712e7i | 0.319950 | + | 0.184723i | ||||
\(406\) | 1.99421e6 | − | 1.15136e6i | 0.0297984 | − | 0.0172041i | ||||
\(407\) | −4.35478e7 | + | 2.51424e7i | −0.645927 | + | 0.372926i | ||||
\(408\) | −1.87826e8 | −2.76551 | ||||||||
\(409\) | 2.29787e7i | 0.335858i | 0.985799 | + | 0.167929i | \(0.0537080\pi\) | ||||
−0.985799 | + | 0.167929i | \(0.946292\pi\) | |||||||
\(410\) | 4.17609e6 | + | 7.23320e6i | 0.0605925 | + | 0.104949i | ||||
\(411\) | 3.32765e6 | + | 5.76366e6i | 0.0479305 | + | 0.0830180i | ||||
\(412\) | −660134. | + | 1.14339e6i | −0.00943932 | + | 0.0163494i | ||||
\(413\) | −878165. | − | 507009.i | −0.0124660 | − | 0.00719723i | ||||
\(414\) | 2.57993e7i | 0.363586i | ||||||||
\(415\) | −1.97370e7 | − | 1.13952e7i | −0.276145 | − | 0.159432i | ||||
\(416\) | −4.99764e6 | − | 2.88539e6i | −0.0694200 | − | 0.0400797i | ||||
\(417\) | 1.75767e8 | + | 1.01479e8i | 2.42399 | + | 1.39949i | ||||
\(418\) | 3.83600e7 | + | 6.64415e7i | 0.525231 | + | 0.909727i | ||||
\(419\) | − | 2.05464e7i | − | 0.279314i | −0.990200 | − | 0.139657i | \(-0.955400\pi\) | ||
0.990200 | − | 0.139657i | \(-0.0446000\pi\) | |||||||
\(420\) | 22642.4 | − | 13072.6i | 0.000305615 | − | 0.000176447i | ||||
\(421\) | −5.70971e7 | − | 3.29650e7i | −0.765187 | − | 0.441781i | 0.0659678 | − | 0.997822i | \(-0.478987\pi\) |
−0.831155 | + | 0.556041i | \(0.812320\pi\) | |||||||
\(422\) | −1.18925e7 | −0.158247 | ||||||||
\(423\) | 8.20916e6 | − | 1.42187e7i | 0.108462 | − | 0.187862i | ||||
\(424\) | 1.35189e7 | − | 7.80513e6i | 0.177355 | − | 0.102396i | ||||
\(425\) | −5.72823e7 | − | 9.92159e7i | −0.746198 | − | 1.29245i | ||||
\(426\) | 1.76900e8i | 2.28822i | ||||||||
\(427\) | −492136. | − | 852405.i | −0.00632123 | − | 0.0109487i | ||||
\(428\) | −3.15512e6 | −0.0402425 | ||||||||
\(429\) | − | 1.58388e8i | − | 2.00609i | ||||||
\(430\) | 9.91777e6 | − | 1.71479e7i | 0.124741 | − | 0.215678i | ||||
\(431\) | −4.62834e7 | −0.578088 | −0.289044 | − | 0.957316i | \(-0.593337\pi\) | ||||
−0.289044 | + | 0.957316i | \(0.593337\pi\) | |||||||
\(432\) | 1.72681e8i | 2.14187i | ||||||||
\(433\) | 1.12810e8 | − | 6.51309e7i | 1.38958 | − | 0.802275i | 0.396314 | − | 0.918115i | \(-0.370289\pi\) |
0.993268 | + | 0.115840i | \(0.0369559\pi\) | |||||||
\(434\) | 1.34735e6 | 0.0164821 | ||||||||
\(435\) | 4.95640e7 | − | 2.86158e7i | 0.602142 | − | 0.347647i | ||||
\(436\) | −2.38818e6 | − | 4.13644e6i | −0.0288142 | − | 0.0499077i | ||||
\(437\) | 1.13679e7 | + | 6.56328e6i | 0.136219 | + | 0.0786460i | ||||
\(438\) | − | 1.69454e8i | − | 2.01664i | ||||||
\(439\) | 1.04839e7 | − | 1.81586e7i | 0.123917 | − | 0.214630i | −0.797392 | − | 0.603461i | \(-0.793788\pi\) |
0.921309 | + | 0.388831i | \(0.127121\pi\) | |||||||
\(440\) | −1.10378e7 | − | 1.91180e7i | −0.129575 | − | 0.224431i | ||||
\(441\) | −1.85313e8 | −2.16067 | ||||||||
\(442\) | −1.26161e8 | + | 7.28390e7i | −1.46103 | + | 0.843523i | ||||
\(443\) | 1.81291e7 | − | 3.14005e7i | 0.208528 | − | 0.361181i | −0.742723 | − | 0.669599i | \(-0.766466\pi\) |
0.951251 | + | 0.308418i | \(0.0997995\pi\) | |||||||
\(444\) | 2.06298e6 | − | 3.57319e6i | 0.0235693 | − | 0.0408232i | ||||
\(445\) | −1.72544e6 | + | 2.98856e6i | −0.0195804 | + | 0.0339142i | ||||
\(446\) | 1.55534e8 | 1.75316 | ||||||||
\(447\) | 1.26628e8 | − | 2.19326e8i | 1.41777 | − | 2.45566i | ||||
\(448\) | −1.57600e6 | − | 909906.i | −0.0175276 | − | 0.0101196i | ||||
\(449\) | −7.64079e7 | + | 4.41141e7i | −0.844110 | + | 0.487347i | −0.858659 | − | 0.512547i | \(-0.828702\pi\) |
0.0145490 | + | 0.999894i | \(0.495369\pi\) | |||||||
\(450\) | −1.63446e8 | + | 9.43655e7i | −1.79364 | + | 1.03556i | ||||
\(451\) | −4.82641e7 | −0.526132 | ||||||||
\(452\) | − | 6.98065e6i | − | 0.0755928i | ||||||
\(453\) | −7.11943e7 | − | 1.23312e8i | −0.765862 | − | 1.32651i | ||||
\(454\) | 8.41164e7 | + | 1.45694e8i | 0.898903 | + | 1.55695i | ||||
\(455\) | −253566. | + | 439189.i | −0.00269189 | + | 0.00466248i | ||||
\(456\) | 1.36339e8 | + | 7.87155e7i | 1.43789 | + | 0.830167i | ||||
\(457\) | 1.20099e8i | 1.25832i | 0.777274 | + | 0.629162i | \(0.216602\pi\) | ||||
−0.777274 | + | 0.629162i | \(0.783398\pi\) | |||||||
\(458\) | −1.41937e8 | − | 8.19476e7i | −1.47741 | − | 0.852982i | ||||
\(459\) | 2.74568e8 | + | 1.58522e8i | 2.83930 | + | 1.63927i | ||||
\(460\) | 130795. | + | 75514.7i | 0.00134375 | + | 0.000775814i | ||||
\(461\) | 4.31499e6 | + | 7.47379e6i | 0.0440430 | + | 0.0762848i | 0.887207 | − | 0.461372i | \(-0.152643\pi\) |
−0.843164 | + | 0.537657i | \(0.819309\pi\) | |||||||
\(462\) | 4.08056e6i | 0.0413803i | ||||||||
\(463\) | −2.90455e7 | + | 1.67694e7i | −0.292642 | + | 0.168957i | −0.639133 | − | 0.769097i | \(-0.720706\pi\) |
0.346491 | + | 0.938053i | \(0.387373\pi\) | |||||||
\(464\) | 1.43479e8 | + | 8.28376e7i | 1.43626 | + | 0.829228i | ||||
\(465\) | 3.34871e7 | 0.333057 | ||||||||
\(466\) | −4.79730e7 | + | 8.30918e7i | −0.474067 | + | 0.821108i | ||||
\(467\) | −1.37508e8 | + | 7.93901e7i | −1.35013 | + | 0.779500i | −0.988268 | − | 0.152731i | \(-0.951193\pi\) |
−0.361865 | + | 0.932230i | \(0.617860\pi\) | |||||||
\(468\) | 4.44276e6 | + | 7.69508e6i | 0.0433426 | + | 0.0750716i | ||||
\(469\) | − | 1.66697e6i | − | 0.0161588i | ||||||
\(470\) | −1.29794e6 | − | 2.24810e6i | −0.0125015 | − | 0.0216532i | ||||
\(471\) | −1.97047e8 | −1.88585 | ||||||||
\(472\) | − | 7.02513e7i | − | 0.668080i | ||||||
\(473\) | 5.71602e7 | + | 9.91786e7i | 0.540145 | + | 0.937205i | ||||
\(474\) | 6.13848e7 | 0.576403 | ||||||||
\(475\) | 9.60252e7i | 0.895992i | ||||||||
\(476\) | 120342. | − | 69479.7i | 0.00111583 | − | 0.000644224i | ||||
\(477\) | −4.90327e7 | −0.451784 | ||||||||
\(478\) | 1.74007e8 | − | 1.00463e8i | 1.59325 | − | 0.919861i | ||||
\(479\) | −9.37100e7 | − | 1.62311e8i | −0.852667 | − | 1.47686i | −0.878792 | − | 0.477204i | \(-0.841650\pi\) |
0.0261252 | − | 0.999659i | \(-0.491683\pi\) | |||||||
\(480\) | 3.20006e6 | + | 1.84756e6i | 0.0289357 | + | 0.0167061i | ||||
\(481\) | 8.00304e7i | 0.719151i | ||||||||
\(482\) | 4.20209e7 | − | 7.27823e7i | 0.375253 | − | 0.649957i | ||||
\(483\) | 349085. | + | 604633.i | 0.00309806 | + | 0.00536600i | ||||
\(484\) | −741561. | −0.00654050 | ||||||||
\(485\) | 3.85343e7 | − | 2.22478e7i | 0.337771 | − | 0.195012i | ||||
\(486\) | 3.63375e7 | − | 6.29384e7i | 0.316553 | − | 0.548286i | ||||
\(487\) | −3.59551e7 | + | 6.22761e7i | −0.311296 | + | 0.539181i | −0.978643 | − | 0.205566i | \(-0.934096\pi\) |
0.667347 | + | 0.744747i | \(0.267430\pi\) | |||||||
\(488\) | 3.40953e7 | − | 5.90548e7i | 0.293383 | − | 0.508154i | ||||
\(489\) | 2.33882e8 | 2.00018 | ||||||||
\(490\) | −1.46498e7 | + | 2.53742e7i | −0.124521 | + | 0.215677i | ||||
\(491\) | 5.41704e7 | + | 3.12753e7i | 0.457633 | + | 0.264215i | 0.711048 | − | 0.703143i | \(-0.248221\pi\) |
−0.253415 | + | 0.967358i | \(0.581554\pi\) | |||||||
\(492\) | 3.42961e6 | − | 1.98009e6i | 0.0287972 | − | 0.0166260i | ||||
\(493\) | 2.63429e8 | − | 1.52091e8i | 2.19848 | − | 1.26929i | ||||
\(494\) | 1.22104e8 | 1.01286 | ||||||||
\(495\) | 6.93404e7i | 0.571703i | ||||||||
\(496\) | 4.84696e7 | + | 8.39517e7i | 0.397213 | + | 0.687994i | ||||
\(497\) | 1.63652e6 | + | 2.83453e6i | 0.0133306 | + | 0.0230894i | ||||
\(498\) | −1.45928e8 | + | 2.52754e8i | −1.18154 | + | 2.04649i | ||||
\(499\) | 828308. | + | 478224.i | 0.00666638 | + | 0.00384884i | 0.503329 | − | 0.864095i | \(-0.332108\pi\) |
−0.496663 | + | 0.867943i | \(0.665442\pi\) | |||||||
\(500\) | 2.27991e6i | 0.0182392i | ||||||||
\(501\) | −2.18822e8 | − | 1.26337e8i | −1.74011 | − | 1.00465i | ||||
\(502\) | 9.77930e7 | + | 5.64608e7i | 0.773030 | + | 0.446309i | ||||
\(503\) | 9.58802e7 | + | 5.53564e7i | 0.753399 | + | 0.434975i | 0.826921 | − | 0.562319i | \(-0.190091\pi\) |
−0.0735220 | + | 0.997294i | \(0.523424\pi\) | |||||||
\(504\) | 2.86247e6 | + | 4.95795e6i | 0.0223589 | + | 0.0387267i | ||||
\(505\) | 5.71516e7i | 0.443767i | ||||||||
\(506\) | −2.04136e7 | + | 1.17858e7i | −0.157568 | + | 0.0909720i | ||||
\(507\) | −1.76261e7 | − | 1.01764e7i | −0.135248 | − | 0.0780857i | ||||
\(508\) | −4.50810e6 | −0.0343877 | ||||||||
\(509\) | −8.23454e7 | + | 1.42626e8i | −0.624433 | + | 1.08155i | 0.364217 | + | 0.931314i | \(0.381337\pi\) |
−0.988650 | + | 0.150236i | \(0.951997\pi\) | |||||||
\(510\) | 8.07827e7 | − | 4.66399e7i | 0.608986 | − | 0.351598i | ||||
\(511\) | −1.56764e6 | − | 2.71522e6i | −0.0117485 | − | 0.0203490i | ||||
\(512\) | − | 1.25680e8i | − | 0.936391i | ||||||
\(513\) | −1.32869e8 | − | 2.30136e8i | −0.984173 | − | 1.70464i | ||||
\(514\) | −4.45043e7 | −0.327727 | ||||||||
\(515\) | 1.63978e7i | 0.120050i | ||||||||
\(516\) | −8.13067e6 | − | 4.70249e6i | −0.0591803 | − | 0.0342278i | ||||
\(517\) | 1.50006e7 | 0.108552 | ||||||||
\(518\) | − | 2.06183e6i | − | 0.0148342i | ||||||
\(519\) | 1.69219e8 | − | 9.76985e7i | 1.21045 | − | 0.698853i | ||||
\(520\) | −3.51342e7 | −0.249873 | ||||||||
\(521\) | −1.06288e7 | + | 6.13652e6i | −0.0751570 | + | 0.0433919i | −0.537108 | − | 0.843514i | \(-0.680483\pi\) |
0.461951 | + | 0.886906i | \(0.347150\pi\) | |||||||
\(522\) | −2.50550e8 | − | 4.33965e8i | −1.76150 | − | 3.05101i | ||||
\(523\) | −1.38606e8 | − | 8.00243e7i | −0.968896 | − | 0.559392i | −0.0699965 | − | 0.997547i | \(-0.522299\pi\) |
−0.898900 | + | 0.438155i | \(0.855632\pi\) | |||||||
\(524\) | − | 5.48225e6i | − | 0.0381035i | ||||||
\(525\) | −2.55368e6 | + | 4.42310e6i | −0.0176477 | + | 0.0305667i | ||||
\(526\) | −1.42389e8 | − | 2.46626e8i | −0.978409 | − | 1.69465i | ||||
\(527\) | 1.77981e8 | 1.21602 | ||||||||
\(528\) | −2.54254e8 | + | 1.46794e8i | −1.72729 | + | 0.997254i | ||||
\(529\) | 7.20014e7 | − | 1.24710e8i | 0.486378 | − | 0.842432i | ||||
\(530\) | −3.87625e6 | + | 6.71387e6i | −0.0260366 | + | 0.0450968i | ||||
\(531\) | −1.10332e8 | + | 1.91100e8i | −0.736914 | + | 1.27637i | ||||
\(532\) | −116472. | −0.000773548 | ||||||||
\(533\) | −3.84073e7 | + | 6.65234e7i | −0.253648 | + | 0.439332i | ||||
\(534\) | 3.82718e7 | + | 2.20963e7i | 0.251336 | + | 0.145109i | ||||
\(535\) | −3.39367e7 | + | 1.95934e7i | −0.221620 | + | 0.127952i | ||||
\(536\) | 1.00015e8 | − | 5.77439e7i | 0.649489 | − | 0.374983i | ||||
\(537\) | −1.78824e8 | −1.15479 | ||||||||
\(538\) | 1.20426e8i | 0.773348i | ||||||||
\(539\) | −8.46557e7 | − | 1.46628e8i | −0.540617 | − | 0.936376i | ||||
\(540\) | −1.52874e6 | − | 2.64786e6i | −0.00970851 | − | 0.0168156i | ||||
\(541\) | −8.77934e7 | + | 1.52063e8i | −0.554460 | + | 0.960352i | 0.443486 | + | 0.896281i | \(0.353742\pi\) |
−0.997945 | + | 0.0640709i | \(0.979592\pi\) | |||||||
\(542\) | 1.61984e8 | + | 9.35218e7i | 1.01736 | + | 0.587374i | ||||
\(543\) | − | 2.18516e8i | − | 1.36485i | ||||||
\(544\) | 1.70081e7 | + | 9.81961e6i | 0.105647 | + | 0.0609954i | ||||
\(545\) | −5.13748e7 | − | 2.96613e7i | −0.317366 | − | 0.183232i | ||||
\(546\) | 5.62431e6 | + | 3.24720e6i | 0.0345535 | + | 0.0199495i | ||||
\(547\) | −4.88812e7 | − | 8.46647e7i | −0.298662 | − | 0.517298i | 0.677168 | − | 0.735828i | \(-0.263207\pi\) |
−0.975830 | + | 0.218531i | \(0.929874\pi\) | |||||||
\(548\) | − | 341121.i | − | 0.00207285i | ||||||
\(549\) | −1.85494e8 | + | 1.07095e8i | −1.12102 | + | 0.647222i | ||||
\(550\) | −1.49333e8 | − | 8.62172e7i | −0.897566 | − | 0.518210i | ||||
\(551\) | −2.54957e8 | −1.52409 | ||||||||
\(552\) | −2.41847e7 | + | 4.18891e7i | −0.143788 | + | 0.249048i | ||||
\(553\) | 983593. | − | 567877.i | 0.00581621 | − | 0.00335799i | ||||
\(554\) | 1.36153e8 | + | 2.35823e8i | 0.800750 | + | 1.38694i | ||||
\(555\) | − | 5.12447e7i | − | 0.299757i | ||||||
\(556\) | −5.20138e6 | − | 9.00906e6i | −0.0302618 | − | 0.0524149i | ||||
\(557\) | 9.67694e7 | 0.559980 | 0.279990 | − | 0.960003i | \(-0.409669\pi\) | ||||
0.279990 | + | 0.960003i | \(0.409669\pi\) | |||||||
\(558\) | − | 2.93201e8i | − | 1.68758i | ||||||
\(559\) | 1.82186e8 | + | 138607.i | 1.04299 | + | 0.000793505i | ||||
\(560\) | 940019. | 0.00535270 | ||||||||
\(561\) | 5.39029e8i | 3.05298i | ||||||||
\(562\) | 7.39317e7 | − | 4.26845e7i | 0.416506 | − | 0.240470i | ||||
\(563\) | 2.46126e8 | 1.37921 | 0.689607 | − | 0.724184i | \(-0.257783\pi\) | ||||
0.689607 | + | 0.724184i | \(0.257783\pi\) | |||||||
\(564\) | −1.06593e6 | + | 615417.i | −0.00594145 | + | 0.00343030i | ||||
\(565\) | −4.33500e7 | − | 7.50844e7i | −0.240350 | − | 0.416298i | ||||
\(566\) | 2.96765e8 | + | 1.71337e8i | 1.63668 | + | 0.944937i | ||||
\(567\) | − | 5.81510e6i | − | 0.0319013i | ||||||
\(568\) | −1.13378e8 | + | 1.96377e8i | −0.618706 | + | 1.07163i | ||||
\(569\) | −8.31886e6 | − | 1.44087e7i | −0.0451572 | − | 0.0782146i | 0.842563 | − | 0.538597i | \(-0.181046\pi\) |
−0.887721 | + | 0.460383i | \(0.847712\pi\) | |||||||
\(570\) | −7.81847e7 | −0.422180 | ||||||||
\(571\) | 4.36399e7 | − | 2.51955e7i | 0.234410 | − | 0.135336i | −0.378195 | − | 0.925726i | \(-0.623455\pi\) |
0.612605 | + | 0.790390i | \(0.290122\pi\) | |||||||
\(572\) | −4.05913e6 | + | 7.03062e6i | −0.0216893 | + | 0.0375669i | ||||
\(573\) | −5.17299e7 | + | 8.95988e7i | −0.274965 | + | 0.476253i | ||||
\(574\) | 989490. | − | 1.71385e6i | 0.00523210 | − | 0.00906226i | ||||
\(575\) | −2.95030e7 | −0.155189 | ||||||||
\(576\) | −1.98007e8 | + | 3.42959e8i | −1.03613 | + | 1.79463i | ||||
\(577\) | −7.75273e7 | − | 4.47604e7i | −0.403578 | − | 0.233006i | 0.284449 | − | 0.958691i | \(-0.408189\pi\) |
−0.688027 | + | 0.725686i | \(0.741523\pi\) | |||||||
\(578\) | 2.58939e8 | − | 1.49498e8i | 1.34095 | − | 0.774199i | ||||
\(579\) | −7.53891e7 | + | 4.35259e7i | −0.388394 | + | 0.224240i | ||||
\(580\) | −2.93344e6 | −0.0150346 | ||||||||
\(581\) | 5.39997e6i | 0.0275336i | ||||||||
\(582\) | −2.84908e8 | − | 4.93475e8i | −1.44523 | − | 2.50321i | ||||
\(583\) | −2.23994e7 | − | 3.87969e7i | −0.113040 | − | 0.195791i | ||||
\(584\) | 1.08606e8 | − | 1.88111e8i | 0.545275 | − | 0.944444i | ||||
\(585\) | 9.55732e7 | + | 5.51792e7i | 0.477385 | + | 0.275618i | ||||
\(586\) | 4.74960e7i | 0.236029i | ||||||||
\(587\) | −1.07719e8 | − | 6.21918e7i | −0.532573 | − | 0.307481i | 0.209490 | − | 0.977811i | \(-0.432819\pi\) |
−0.742064 | + | 0.670329i | \(0.766153\pi\) | |||||||
\(588\) | 1.20311e7 | + | 6.94618e6i | 0.0591799 | + | 0.0341675i | ||||
\(589\) | −1.29193e8 | − | 7.45895e7i | −0.632255 | − | 0.365033i | ||||
\(590\) | 1.74444e7 | + | 3.02146e7i | 0.0849377 | + | 0.147116i | ||||
\(591\) | 3.81164e8i | 1.84650i | ||||||||
\(592\) | 1.28470e8 | − | 7.41721e7i | 0.619208 | − | 0.357500i | ||||
\(593\) | 6.07991e7 | + | 3.51024e7i | 0.291563 | + | 0.168334i | 0.638647 | − | 0.769500i | \(-0.279495\pi\) |
−0.347083 | + | 0.937834i | \(0.612828\pi\) | |||||||
\(594\) | 4.77191e8 | 2.27684 | ||||||||
\(595\) | 862941. | − | 1.49466e6i | 0.00409666 | − | 0.00709563i | ||||
\(596\) | −1.12417e7 | + | 6.49040e6i | −0.0530998 | + | 0.0306572i | ||||
\(597\) | 1.60148e8 | + | 2.77384e8i | 0.752658 | + | 1.30364i | ||||
\(598\) | 3.75153e7i | 0.175431i | ||||||||
\(599\) | −1.14249e8 | − | 1.97884e8i | −0.531582 | − | 0.920728i | −0.999320 | − | 0.0368604i | \(-0.988264\pi\) |
0.467738 | − | 0.883867i | \(-0.345069\pi\) | |||||||
\(600\) | −3.53838e8 | −1.63814 | ||||||||
\(601\) | − | 1.99284e8i | − | 0.918013i | −0.888433 | − | 0.459007i | \(-0.848205\pi\) | ||
0.888433 | − | 0.459007i | \(-0.151795\pi\) | |||||||
\(602\) | −4.69368e6 | − | 3570.94i | −0.0215141 | − | 1.63679e-5i | ||||
\(603\) | −3.62753e8 | −1.65447 | ||||||||
\(604\) | 7.29822e6i | 0.0331212i | ||||||||
\(605\) | −7.97629e6 | + | 4.60511e6i | −0.0360193 | + | 0.0207957i | ||||
\(606\) | 7.31891e8 | 3.28873 | ||||||||
\(607\) | −1.05543e8 | + | 6.09355e7i | −0.471916 | + | 0.272461i | −0.717042 | − | 0.697030i | \(-0.754504\pi\) |
0.245125 | + | 0.969491i | \(0.421171\pi\) | |||||||
\(608\) | −8.23054e6 | − | 1.42557e7i | −0.0366200 | − | 0.0634276i | ||||
\(609\) | −1.17438e7 | − | 6.78027e6i | −0.0519943 | − | 0.0300189i | ||||
\(610\) | 3.38654e7i | 0.149199i | ||||||||
\(611\) | 1.19371e7 | − | 2.06757e7i | 0.0523330 | − | 0.0906434i | ||||
\(612\) | −1.51197e7 | − | 2.61881e7i | −0.0659612 | − | 0.114248i | ||||
\(613\) | 1.12643e8 | 0.489016 | 0.244508 | − | 0.969647i | \(-0.421374\pi\) | ||||
0.244508 | + | 0.969647i | \(0.421374\pi\) | |||||||
\(614\) | −1.01384e8 | + | 5.85342e7i | −0.437991 | + | 0.252874i | ||||
\(615\) | 2.45928e7 | − | 4.25959e7i | 0.105726 | − | 0.183123i | ||||
\(616\) | −2.61530e6 | + | 4.52984e6i | −0.0111887 | + | 0.0193794i | ||||
\(617\) | 2.22221e8 | − | 3.84898e8i | 0.946083 | − | 1.63866i | 0.192514 | − | 0.981294i | \(-0.438336\pi\) |
0.753569 | − | 0.657369i | \(-0.228331\pi\) | |||||||
\(618\) | 2.09992e8 | 0.889689 | ||||||||
\(619\) | 6.31978e7 | − | 1.09462e8i | 0.266459 | − | 0.461520i | −0.701486 | − | 0.712683i | \(-0.747480\pi\) |
0.967945 | + | 0.251163i | \(0.0808131\pi\) | |||||||
\(620\) | −1.48645e6 | − | 858200.i | −0.00623697 | − | 0.00360092i | ||||
\(621\) | 7.07074e7 | − | 4.08229e7i | 0.295250 | − | 0.170463i | ||||
\(622\) | −3.06629e8 | + | 1.77033e8i | −1.27421 | + | 0.735668i | ||||
\(623\) | 817659. | 0.00338149 | ||||||||
\(624\) | 4.67258e8i | 1.92311i | ||||||||
\(625\) | −1.00615e8 | − | 1.74270e8i | −0.412118 | − | 0.713810i | ||||
\(626\) | −2.20420e7 | − | 3.81779e7i | −0.0898521 | − | 0.155628i | ||||
\(627\) | 2.25900e8 | − | 3.91270e8i | 0.916461 | − | 1.58736i | ||||
\(628\) | 8.74665e6 | + | 5.04988e6i | 0.0353153 | + | 0.0203893i | ||||
\(629\) | − | 2.72361e8i | − | 1.09444i | ||||||
\(630\) | −2.46226e6 | − | 1.42159e6i | −0.00984719 | − | 0.00568528i | ||||
\(631\) | 1.35801e8 | + | 7.84050e7i | 0.540525 | + | 0.312072i | 0.745292 | − | 0.666738i | \(-0.232310\pi\) |
−0.204766 | + | 0.978811i | \(0.565643\pi\) | |||||||
\(632\) | 6.81435e7 | + | 3.93427e7i | 0.269944 | + | 0.155852i | ||||
\(633\) | 3.50171e7 | + | 6.06515e7i | 0.138061 | + | 0.239128i | ||||
\(634\) | − | 1.78723e8i | − | 0.701315i | ||||||
\(635\) | −4.84895e7 | + | 2.79954e7i | −0.189377 | + | 0.109337i | ||||
\(636\) | 3.18337e6 | + | 1.83792e6i | 0.0123742 | + | 0.00714423i | ||||
\(637\) | −2.69467e8 | −1.04253 | ||||||||
\(638\) | 2.28916e8 | − | 3.96493e8i | 0.881482 | − | 1.52677i | ||||
\(639\) | 6.16830e8 | − | 3.56127e8i | 2.36409 | − | 1.36491i | ||||
\(640\) | 3.37697e7 | + | 5.84908e7i | 0.128821 | + | 0.223125i | ||||
\(641\) | 8.61043e7i | 0.326927i | 0.986549 | + | 0.163464i | \(0.0522666\pi\) | ||||
−0.986549 | + | 0.163464i | \(0.947733\pi\) | |||||||
\(642\) | 2.50915e8 | + | 4.34598e8i | 0.948248 | + | 1.64241i | ||||
\(643\) | 2.48943e8 | 0.936413 | 0.468207 | − | 0.883619i | \(-0.344900\pi\) | ||||
0.468207 | + | 0.883619i | \(0.344900\pi\) | |||||||
\(644\) | − | 35785.1i | − | 0.000133982i | ||||||
\(645\) | −1.16657e8 | − | 88752.1i | −0.434741 | − | 0.000330750i | ||||
\(646\) | −4.15545e8 | −1.54142 | ||||||||
\(647\) | 4.22748e8i | 1.56088i | 0.625233 | + | 0.780438i | \(0.285004\pi\) | ||||
−0.625233 | + | 0.780438i | \(0.714996\pi\) | |||||||
\(648\) | 3.48897e8 | − | 2.01436e8i | 1.28225 | − | 0.740307i | ||||
\(649\) | −2.01610e8 | −0.737525 | ||||||||
\(650\) | −2.37670e8 | + | 1.37219e8i | −0.865433 | + | 0.499658i | ||||
\(651\) | −3.96724e6 | − | 6.87146e6i | −0.0143796 | − | 0.0249061i | ||||
\(652\) | −1.03817e7 | − | 5.99388e6i | −0.0374564 | − | 0.0216254i | ||||
\(653\) | 1.66746e8i | 0.598848i | 0.954120 | + | 0.299424i | \(0.0967946\pi\) | ||||
−0.954120 | + | 0.299424i | \(0.903205\pi\) | |||||||
\(654\) | −3.79846e8 | + | 6.57913e8i | −1.35792 | + | 2.35199i | ||||
\(655\) | −3.40449e7 | − | 5.89674e7i | −0.121151 | − | 0.209840i | ||||
\(656\) | 1.42383e8 | 0.504368 | ||||||||
\(657\) | −5.90868e8 | + | 3.41138e8i | −2.08350 | + | 1.20291i | ||||
\(658\) | −307537. | + | 532669.i | −0.00107949 | + | 0.00186973i | ||||
\(659\) | −1.38937e8 | + | 2.40646e8i | −0.485468 | + | 0.840856i | −0.999861 | − | 0.0166991i | \(-0.994684\pi\) |
0.514392 | + | 0.857555i | \(0.328018\pi\) | |||||||
\(660\) | 2.59912e6 | − | 4.50181e6i | 0.00904056 | − | 0.0156587i | ||||
\(661\) | 3.23600e7 | 0.112048 | 0.0560240 | − | 0.998429i | \(-0.482158\pi\) | ||||
0.0560240 | + | 0.998429i | \(0.482158\pi\) | |||||||
\(662\) | −7.14218e7 | + | 1.23706e8i | −0.246182 | + | 0.426400i | ||||
\(663\) | 7.42954e8 | + | 4.28945e8i | 2.54930 | + | 1.47184i | ||||
\(664\) | −3.23990e8 | + | 1.87056e8i | −1.10669 | + | 0.638949i | ||||
\(665\) | −1.25278e6 | + | 723295.i | −0.00426002 | + | 0.00245952i | ||||
\(666\) | −4.48681e8 | −1.51885 | ||||||||
\(667\) | − | 7.83334e7i | − | 0.263979i | ||||||
\(668\) | 6.47547e6 | + | 1.12158e7i | 0.0217241 | + | 0.0376272i | ||||
\(669\) | −4.57966e8 | − | 7.93220e8i | −1.52952 | − | 2.64920i | ||||
\(670\) | −2.86773e7 | + | 4.96705e7i | −0.0953484 | + | 0.165148i | ||||
\(671\) | −1.69477e8 | − | 9.78478e7i | −0.560976 | − | 0.323879i | ||||
\(672\) | − | 875526.i | − | 0.00288510i | ||||||
\(673\) | 3.43439e8 | + | 1.98284e8i | 1.12669 | + | 0.650494i | 0.943100 | − | 0.332509i | \(-0.107895\pi\) |
0.183589 | + | 0.983003i | \(0.441229\pi\) | |||||||
\(674\) | 4.00808e8 | + | 2.31407e8i | 1.30905 | + | 0.755781i | ||||
\(675\) | 5.17248e8 | + | 2.98633e8i | 1.68185 | + | 0.971017i | ||||
\(676\) | 521599. | + | 903436.i | 0.00168848 | + | 0.00292454i | ||||
\(677\) | 1.45406e7i | 0.0468617i | 0.999725 | + | 0.0234308i | \(0.00745895\pi\) | ||||
−0.999725 | + | 0.0234308i | \(0.992541\pi\) | |||||||
\(678\) | −9.61541e8 | + | 5.55146e8i | −3.08517 | + | 1.78122i | ||||
\(679\) | −9.13038e6 | − | 5.27143e6i | −0.0291662 | − | 0.0168391i | ||||
\(680\) | 1.19569e8 | 0.380271 | ||||||||
\(681\) | 4.95357e8 | − | 8.57983e8i | 1.56847 | − | 2.71667i | ||||
\(682\) | 2.31994e8 | − | 1.33942e8i | 0.731348 | − | 0.422244i | ||||
\(683\) | 7.78012e7 | + | 1.34756e8i | 0.244188 | + | 0.422946i | 0.961903 | − | 0.273391i | \(-0.0881453\pi\) |
−0.717715 | + | 0.696337i | \(0.754812\pi\) | |||||||
\(684\) | 2.53459e7i | 0.0792025i | ||||||||
\(685\) | −2.11837e6 | − | 3.66913e6i | −0.00659068 | − | 0.0114154i | ||||
\(686\) | 1.38877e7 | 0.0430187 | ||||||||
\(687\) | 9.65169e8i | 2.97669i | ||||||||
\(688\) | −1.68628e8 | − | 2.92586e8i | −0.517802 | − | 0.898437i | ||||
\(689\) | −7.12994e7 | −0.217986 | ||||||||
\(690\) | − | 2.40216e7i | − | 0.0731232i | ||||||
\(691\) | −6.75623e7 | + | 3.90071e7i | −0.204772 | + | 0.118225i | −0.598879 | − | 0.800839i | \(-0.704387\pi\) |
0.394107 | + | 0.919064i | \(0.371054\pi\) | |||||||
\(692\) | −1.00152e7 | −0.0302232 | ||||||||
\(693\) | 1.42285e7 | − | 8.21482e6i | 0.0427522 | − | 0.0246830i | ||||
\(694\) | −2.26233e8 | − | 3.91847e8i | −0.676827 | − | 1.17230i | ||||
\(695\) | −1.11893e8 | − | 6.46014e7i | −0.333310 | − | 0.192437i | ||||
\(696\) | − | 9.39477e8i | − | 2.78650i | ||||||
\(697\) | 1.30709e8 | − | 2.26394e8i | 0.386016 | − | 0.668600i | ||||
\(698\) | −1.63818e8 | − | 2.83742e8i | −0.481722 | − | 0.834366i | ||||
\(699\) | 5.65021e8 | 1.65437 | ||||||||
\(700\) | 226708. | − | 130890.i | 0.000660958 | − | 0.000381604i | ||||
\(701\) | −1.04896e8 | + | 1.81685e8i | −0.304512 | + | 0.527430i | −0.977153 | − | 0.212539i | \(-0.931827\pi\) |
0.672641 | + | 0.739969i | \(0.265160\pi\) | |||||||
\(702\) | 3.79736e8 | − | 6.57722e8i | 1.09767 | − | 1.90121i | ||||
\(703\) | −1.14143e8 | + | 1.97702e8i | −0.328537 | + | 0.569042i | ||||
\(704\) | −3.61820e8 | −1.03699 | ||||||||
\(705\) | −7.64351e6 | + | 1.32389e7i | −0.0218135 | + | 0.0377821i | ||||
\(706\) | −9.77183e7 | − | 5.64177e7i | −0.277691 | − | 0.160325i | ||||
\(707\) | 1.17274e7 | − | 6.77080e6i | 0.0331851 | − | 0.0191594i | ||||
\(708\) | 1.43262e7 | − | 8.27124e6i | 0.0403675 | − | 0.0233062i | ||||
\(709\) | 9.03275e7 | 0.253443 | 0.126722 | − | 0.991938i | \(-0.459554\pi\) | ||||
0.126722 | + | 0.991938i | \(0.459554\pi\) | |||||||
\(710\) | − | 1.12614e8i | − | 0.314642i | ||||||
\(711\) | −1.23577e8 | − | 2.14042e8i | −0.343820 | − | 0.595513i | ||||
\(712\) | 2.83238e7 | + | 4.90582e7i | 0.0784714 | + | 0.135916i | ||||
\(713\) | 2.29170e7 | − | 3.96935e7i | 0.0632251 | − | 0.109509i | ||||
\(714\) | −1.91408e7 | − | 1.10509e7i | −0.0525854 | − | 0.0303602i | ||||
\(715\) | 1.00829e8i | 0.275847i | ||||||||
\(716\) | 7.93775e6 | + | 4.58286e6i | 0.0216251 | + | 0.0124853i | ||||
\(717\) | −1.02472e9 | − | 5.91621e8i | −2.78001 | − | 1.60504i | ||||
\(718\) | −2.67757e8 | − | 1.54589e8i | −0.723381 | − | 0.417644i | ||||
\(719\) | −1.65055e7 | − | 2.85884e7i | −0.0444060 | − | 0.0769135i | 0.842968 | − | 0.537964i | \(-0.180806\pi\) |
−0.887374 | + | 0.461050i | \(0.847473\pi\) | |||||||
\(720\) | − | 2.04560e8i | − | 0.548055i | ||||||
\(721\) | 3.36479e6 | − | 1.94266e6i | 0.00897742 | − | 0.00518312i | ||||
\(722\) | −3.05142e7 | − | 1.76174e7i | −0.0810755 | − | 0.0468090i | ||||
\(723\) | −4.94917e8 | −1.30954 | ||||||||
\(724\) | −5.60009e6 | + | 9.69965e6i | −0.0147564 | + | 0.0255588i | ||||
\(725\) | 4.96263e8 | − | 2.86518e8i | 1.30226 | − | 0.751861i | ||||
\(726\) | 5.89737e7 | + | 1.02145e8i | 0.154116 | + | 0.266937i | ||||
\(727\) | 6.61674e8i | 1.72203i | 0.508579 | + | 0.861015i | \(0.330171\pi\) | ||||
−0.508579 | + | 0.861015i | \(0.669829\pi\) | |||||||
\(728\) | 4.16238e6 | + | 7.20945e6i | 0.0107882 | + | 0.0186856i | ||||
\(729\) | 1.57430e8 | 0.406354 | ||||||||
\(730\) | 1.07874e8i | 0.277299i | ||||||||
\(731\) | −6.20020e8 | − | 471710.i | −1.58728 | − | 0.00120760i | ||||
\(732\) | 1.60572e7 | 0.0409390 | ||||||||
\(733\) | 5.86187e8i | 1.48841i | 0.667949 | + | 0.744207i | \(0.267173\pi\) | ||||
−0.667949 | + | 0.744207i | \(0.732827\pi\) | |||||||
\(734\) | −7.19029e7 | + | 4.15132e7i | −0.181827 | + | 0.104978i | ||||
\(735\) | 1.72544e8 | 0.434547 | ||||||||
\(736\) | 4.37995e6 | − | 2.52877e6i | 0.0109859 | − | 0.00634272i | ||||
\(737\) | −1.65715e8 | − | 2.87027e8i | −0.413961 | − | 0.717002i | ||||
\(738\) | −3.72955e8 | − | 2.15326e8i | −0.927871 | − | 0.535707i | ||||
\(739\) | 4.05488e8i | 1.00472i | 0.864659 | + | 0.502360i | \(0.167535\pi\) | ||||
−0.864659 | + | 0.502360i | \(0.832465\pi\) | |||||||
\(740\) | −1.31329e6 | + | 2.27468e6i | −0.00324090 | + | 0.00561340i | ||||
\(741\) | −3.59530e8 | − | 6.22725e8i | −0.883652 | − | 1.53053i | ||||
\(742\) | 1.83689e6 | 0.00449647 | ||||||||
\(743\) | 2.02789e8 | − | 1.17080e8i | 0.494398 | − | 0.285441i | −0.231999 | − | 0.972716i | \(-0.574527\pi\) |
0.726397 | + | 0.687275i | \(0.241193\pi\) | |||||||
\(744\) | 2.74851e8 | − | 4.76056e8i | 0.667388 | − | 1.15595i | ||||
\(745\) | −8.06110e7 | + | 1.39622e8i | −0.194951 | + | 0.337665i | ||||
\(746\) | −1.47710e8 | + | 2.55841e8i | −0.355789 | + | 0.616245i | ||||
\(747\) | 1.17510e9 | 2.81913 | ||||||||
\(748\) | 1.38141e7 | − | 2.39268e7i | 0.0330079 | − | 0.0571714i | ||||
\(749\) | 8.04102e6 | + | 4.64249e6i | 0.0191366 | + | 0.0110485i | ||||
\(750\) | 3.14043e8 | − | 1.81313e8i | 0.744397 | − | 0.429778i | ||||
\(751\) | 9.99745e7 | − | 5.77203e7i | 0.236031 | − | 0.136273i | −0.377320 | − | 0.926083i | \(-0.623154\pi\) |
0.613351 | + | 0.789810i | \(0.289821\pi\) | |||||||
\(752\) | −4.42532e7 | −0.104062 | ||||||||
\(753\) | − | 6.64989e8i | − | 1.55751i | ||||||
\(754\) | −3.64330e8 | − | 6.31038e8i | −0.849925 | − | 1.47211i | ||||
\(755\) | 4.53221e7 | + | 7.85002e7i | 0.105310 | + | 0.182402i | ||||
\(756\) | −362223. | + | 627388.i | −0.000838321 | + | 0.00145201i | ||||
\(757\) | 3.77559e8 | + | 2.17984e8i | 0.870355 | + | 0.502500i | 0.867466 | − | 0.497496i | \(-0.165747\pi\) |
0.00288910 | + | 0.999996i | \(0.499080\pi\) | |||||||
\(758\) | 2.71402e8i | 0.623169i | ||||||||
\(759\) | 1.20215e8 | + | 6.94060e7i | 0.274936 | + | 0.158735i | ||||
\(760\) | −8.67931e7 | − | 5.01100e7i | −0.197717 | − | 0.114152i | ||||
\(761\) | 6.56397e8 | + | 3.78971e8i | 1.48940 | + | 0.859907i | 0.999927 | − | 0.0121089i | \(-0.00385447\pi\) |
0.489477 | + | 0.872016i | \(0.337188\pi\) | |||||||
\(762\) | 3.58513e8 | + | 6.20963e8i | 0.810289 | + | 1.40346i | ||||
\(763\) | 1.40560e7i | 0.0316437i | ||||||||
\(764\) | 4.59244e6 | − | 2.65145e6i | 0.0102982 | − | 0.00594570i | ||||
\(765\) | −3.25257e8 | − | 1.87787e8i | −0.726511 | − | 0.419451i | ||||
\(766\) | 3.64756e8 | 0.811552 | ||||||||
\(767\) | −1.60435e8 | + | 2.77882e8i | −0.355561 | + | 0.615850i | ||||
\(768\) | 8.03413e7 | − | 4.63851e7i | 0.177360 | − | 0.102399i | ||||
\(769\) | −1.57126e8 | − | 2.72150e8i | −0.345517 | − | 0.598452i | 0.639931 | − | 0.768432i | \(-0.278963\pi\) |
−0.985447 | + | 0.169980i | \(0.945630\pi\) | |||||||
\(770\) | − | 2.59767e6i | − | 0.00569000i | ||||||
\(771\) | 1.31042e8 | + | 2.26971e8i | 0.285921 | + | 0.495230i | ||||
\(772\) | 4.46190e6 | 0.00969767 | ||||||||
\(773\) | − | 3.82989e7i | − | 0.0829177i | −0.999140 | − | 0.0414589i | \(-0.986799\pi\) | ||
0.999140 | − | 0.0414589i | \(-0.0132005\pi\) | |||||||
\(774\) | −777083. | + | 1.02141e9i | −0.00167589 | + | 2.20280i | ||||
\(775\) | 3.35292e8 | 0.720307 | ||||||||
\(776\) | − | 7.30411e8i | − | 1.56308i | ||||||
\(777\) | −1.05153e7 | + | 6.07100e6i | −0.0224160 | + | 0.0129419i | ||||
\(778\) | 7.05844e7 | 0.149889 | ||||||||
\(779\) | −1.89758e8 | + | 1.09557e8i | −0.401409 | + | 0.231753i | ||||
\(780\) | −4.13663e6 | − | 7.16485e6i | −0.00871691 | − | 0.0150981i | ||||
\(781\) | 5.63568e8 | + | 3.25376e8i | 1.18302 | + | 0.683019i | ||||
\(782\) | − | 1.27673e8i | − | 0.266980i | ||||||
\(783\) | −7.92903e8 | + | 1.37335e9i | −1.65171 | + | 2.86085i | ||||
\(784\) | 2.49742e8 | + | 4.32565e8i | 0.518254 | + | 0.897642i | ||||
\(785\) | 1.25439e8 | 0.259314 | ||||||||
\(786\) | −7.55145e8 | + | 4.35983e8i | −1.55512 | + | 0.897846i | ||||
\(787\) | 3.35254e8 | − | 5.80677e8i | 0.687781 | − | 1.19127i | −0.284773 | − | 0.958595i | \(-0.591918\pi\) |
0.972554 | − | 0.232677i | \(-0.0747484\pi\) | |||||||
\(788\) | 9.76840e6 | − | 1.69194e7i | 0.0199639 | − | 0.0345784i | ||||
\(789\) | −8.38523e8 | + | 1.45236e9i | −1.70720 | + | 2.95695i | ||||
\(790\) | −3.90774e7 | −0.0792582 | ||||||||
\(791\) | −1.02714e7 | + | 1.77906e7i | −0.0207540 | + | 0.0359469i | ||||
\(792\) | 9.85752e8 | + | 5.69124e8i | 1.98423 | + | 1.14560i | ||||
\(793\) | −2.69731e8 | + | 1.55729e8i | −0.540893 | + | 0.312285i | ||||
\(794\) | −2.01902e7 | + | 1.16568e7i | −0.0403348 | + | 0.0232873i | ||||
\(795\) | 4.56541e7 | 0.0908612 | ||||||||
\(796\) | − | 1.64169e7i | − | 0.0325501i | ||||||
\(797\) | 2.17294e8 | + | 3.76364e8i | 0.429212 | + | 0.743417i | 0.996803 | − | 0.0798932i | \(-0.0254579\pi\) |
−0.567591 | + | 0.823310i | \(0.692125\pi\) | |||||||
\(798\) | 9.26261e6 | + | 1.60433e7i | 0.0182274 | + | 0.0315708i | ||||
\(799\) | −4.06246e7 | + | 7.03639e7i | −0.0796432 | + | 0.137946i | ||||
\(800\) | 3.20408e7 | + | 1.84988e7i | 0.0625798 | + | 0.0361305i | ||||
\(801\) | − | 1.77933e8i | − | 0.346226i | ||||||
\(802\) | −1.60427e8 | − | 9.26226e7i | −0.310996 | − | 0.179554i | ||||
\(803\) | −5.39848e8 | − | 3.11681e8i | −1.04262 | − | 0.601955i | ||||
\(804\) | 2.35512e7 | + | 1.35973e7i | 0.0453153 | + | 0.0261628i | ||||
\(805\) | −222227. | − | 384908.i | −0.000425999 | − | 0.000737851i | ||||
\(806\) | − | 4.26350e8i | − | 0.814256i | ||||||
\(807\) | 6.14172e8 | − | 3.54592e8i | 1.16861 | − | 0.674697i | ||||
\(808\) | 8.12475e8 | + | 4.69083e8i | 1.54020 | + | 0.889232i | ||||
\(809\) | −4.75382e8 | −0.897835 | −0.448918 | − | 0.893573i | \(-0.648190\pi\) | ||||
−0.448918 | + | 0.893573i | \(0.648190\pi\) | |||||||
\(810\) | −1.00039e8 | + | 1.73272e8i | −0.188241 | + | 0.326042i | ||||
\(811\) | 1.46160e8 | − | 8.43858e7i | 0.274011 | − | 0.158200i | −0.356698 | − | 0.934220i | \(-0.616098\pi\) |
0.630709 | + | 0.776020i | \(0.282764\pi\) | |||||||
\(812\) | 347527. | + | 601934.i | 0.000649113 | + | 0.00112430i | ||||
\(813\) | − | 1.10149e9i | − | 2.04979i | ||||||
\(814\) | −2.04969e8 | − | 3.55017e8i | −0.380028 | − | 0.658227i | ||||
\(815\) | −1.48888e8 | −0.275035 | ||||||||
\(816\) | − | 1.59018e9i | − | 2.92669i | ||||||
\(817\) | 4.49863e8 | + | 2.60185e8i | 0.824924 | + | 0.477107i | ||||
\(818\) | −1.87330e8 | −0.342254 | ||||||||
\(819\) | − | 2.61485e7i | − | 0.0475987i | ||||||
\(820\) | −2.18328e6 | + | 1.26052e6i | −0.00395975 | + | 0.00228616i | ||||
\(821\) | −9.39854e8 | −1.69836 | −0.849182 | − | 0.528101i | \(-0.822904\pi\) | ||||
−0.849182 | + | 0.528101i | \(0.822904\pi\) | |||||||
\(822\) | −4.69873e7 | + | 2.71281e7i | −0.0845990 | + | 0.0488432i | ||||
\(823\) | −1.60149e8 | − | 2.77387e8i | −0.287293 | − | 0.497606i | 0.685870 | − | 0.727725i | \(-0.259422\pi\) |
−0.973163 | + | 0.230118i | \(0.926089\pi\) | |||||||
\(824\) | 2.33113e8 | + | 1.34588e8i | 0.416663 | + | 0.240561i | ||||
\(825\) | 1.01546e9i | 1.80842i | ||||||||
\(826\) | 4.13331e6 | − | 7.15910e6i | 0.00733429 | − | 0.0127034i | ||||
\(827\) | −3.57984e8 | − | 6.20046e8i | −0.632917 | − | 1.09625i | −0.986952 | − | 0.161013i | \(-0.948524\pi\) |
0.354035 | − | 0.935232i | \(-0.384809\pi\) | |||||||
\(828\) | −7.78731e6 | −0.0137182 | ||||||||
\(829\) | 4.53650e8 | − | 2.61915e8i | 0.796264 | − | 0.459723i | −0.0458990 | − | 0.998946i | \(-0.514615\pi\) |
0.842163 | + | 0.539223i | \(0.181282\pi\) | |||||||
\(830\) | 9.28972e7 | − | 1.60903e8i | 0.162468 | − | 0.281403i | ||||
\(831\) | 8.01795e8 | − | 1.38875e9i | 1.39721 | − | 2.42003i | ||||
\(832\) | −2.87926e8 | + | 4.98703e8i | −0.499933 | + | 0.865909i | ||||
\(833\) | 9.17055e8 | 1.58657 | ||||||||
\(834\) | −8.27294e8 | + | 1.43292e9i | −1.42614 | + | 2.47015i | ||||
\(835\) | 1.39301e8 | + | 8.04256e7i | 0.239274 | + | 0.138145i | ||||
\(836\) | −2.00548e7 | + | 1.15786e7i | −0.0343241 | + | 0.0198170i | ||||
\(837\) | −8.03566e8 | + | 4.63939e8i | −1.37039 | + | 0.791197i | ||||
\(838\) | 1.67501e8 | 0.284633 | ||||||||
\(839\) | − | 3.80811e8i | − | 0.644797i | −0.946604 | − | 0.322399i | \(-0.895511\pi\) | ||
0.946604 | − | 0.322399i | \(-0.104489\pi\) | |||||||
\(840\) | −2.66523e6 | − | 4.61632e6i | −0.00449673 | − | 0.00778857i | ||||
\(841\) | 4.63323e8 | + | 8.02498e8i | 0.778925 | + | 1.34914i | ||||
\(842\) | 2.68742e8 | − | 4.65475e8i | 0.450194 | − | 0.779759i | ||||
\(843\) | −4.35379e8 | − | 2.51366e8i | −0.726750 | − | 0.419589i | ||||
\(844\) | − | 3.58965e6i | − | 0.00597069i | ||||||
\(845\) | 1.12207e7 | + | 6.47828e6i | 0.0185973 | + | 0.0107372i | ||||
\(846\) | 1.15916e8 | + | 6.69239e7i | 0.191439 | + | 0.110528i | ||||
\(847\) | 1.88992e6 | + | 1.09114e6i | 0.00311023 | + | 0.00179569i | ||||
\(848\) | 6.60803e7 | + | 1.14454e8i | 0.108364 | + | 0.187692i | ||||
\(849\) | − | 2.01799e9i | − | 3.29759i | ||||||
\(850\) | 8.08842e8 | − | 4.66985e8i | 1.31706 | − | 0.760408i | ||||
\(851\) | −6.07422e7 | − | 3.50695e7i | −0.0985603 | − | 0.0569038i | ||||
\(852\) | −5.33956e7 | −0.0863350 | ||||||||
\(853\) | 2.10288e7 | − | 3.64230e7i | 0.0338819 | − | 0.0586852i | −0.848587 | − | 0.529056i | \(-0.822546\pi\) |
0.882469 | + | 0.470370i | \(0.155880\pi\) | |||||||
\(854\) | 6.94910e6 | − | 4.01207e6i | 0.0111572 | − | 0.00644161i | ||||
\(855\) | 1.57398e8 | + | 2.72622e8i | 0.251827 | + | 0.436177i | ||||
\(856\) | 6.43265e8i | 1.02558i | ||||||||
\(857\) | 3.58463e8 | + | 6.20876e8i | 0.569510 | + | 0.986421i | 0.996614 | + | 0.0822183i | \(0.0262005\pi\) |
−0.427104 | + | 0.904202i | \(0.640466\pi\) | |||||||
\(858\) | 1.29123e9 | 2.04429 | ||||||||
\(859\) | − | 3.82821e8i | − | 0.603972i | −0.953312 | − | 0.301986i | \(-0.902350\pi\) | ||
0.953312 | − | 0.301986i | \(-0.0976495\pi\) | |||||||
\(860\) | 5.17596e6 | + | 2.99359e6i | 0.00813758 | + | 0.00470649i | ||||
\(861\) | −1.16541e7 | −0.0182587 | ||||||||
\(862\) | − | 3.77319e8i | − | 0.589096i | ||||||
\(863\) | −1.69984e8 | + | 9.81404e7i | −0.264470 | + | 0.152692i | −0.626372 | − | 0.779524i | \(-0.715461\pi\) |
0.361902 | + | 0.932216i | \(0.382127\pi\) | |||||||
\(864\) | −1.02386e8 | −0.158745 | ||||||||
\(865\) | −1.07724e8 | + | 6.21945e7i | −0.166443 | + | 0.0960957i | ||||
\(866\) | 5.30970e8 | + | 9.19666e8i | 0.817553 | + | 1.41604i | ||||
\(867\) | −1.52487e9 | − | 8.80387e8i | −2.33979 | − | 1.35088i | ||||
\(868\) | 406687.i | 0.000621871i | ||||||||
\(869\) | 1.12907e8 | − | 1.95560e8i | 0.172052 | − | 0.298004i | ||||
\(870\) | 2.33286e8 | + | 4.04063e8i | 0.354267 | + | 0.613608i | ||||
\(871\) | −5.27487e8 | −0.798283 | ||||||||
\(872\) | −8.43336e8 | + | 4.86901e8i | −1.27190 | + | 0.734329i | ||||
\(873\) | −1.14713e9 | + | 1.98689e9i | −1.72413 | + | 2.98628i | ||||
\(874\) | −5.35061e7 | + | 9.26753e7i | −0.0801436 | + | 0.138813i | ||||
\(875\) | 3.35468e6 | − | 5.81048e6i | 0.00500757 | − | 0.00867337i | ||||
\(876\) | 5.11482e7 | 0.0760883 | ||||||||
\(877\) | 4.89350e8 | − | 8.47579e8i | 0.725472 | − | 1.25655i | −0.233307 | − | 0.972403i | \(-0.574955\pi\) |
0.958779 | − | 0.284152i | \(-0.0917119\pi\) | |||||||
\(878\) | 1.48035e8 | + | 8.54683e7i | 0.218717 | + | 0.126276i | ||||
\(879\) | 2.42229e8 | − | 1.39851e8i | 0.356664 | − | 0.205920i | ||||
\(880\) | 1.61857e8 | − | 9.34485e7i | 0.237512 | − | 0.137127i | ||||
\(881\) | −5.15172e8 | −0.753398 | −0.376699 | − | 0.926336i | \(-0.622941\pi\) | ||||
−0.376699 | + | 0.926336i | \(0.622941\pi\) | |||||||
\(882\) | − | 1.51073e9i | − | 2.20182i | ||||||
\(883\) | 1.09972e7 | + | 1.90478e7i | 0.0159736 | + | 0.0276670i | 0.873902 | − | 0.486103i | \(-0.161582\pi\) |
−0.857928 | + | 0.513770i | \(0.828249\pi\) | |||||||
\(884\) | −2.19858e7 | − | 3.80806e7i | −0.0318263 | − | 0.0551247i | ||||
\(885\) | 1.02729e8 | − | 1.77932e8i | 0.148205 | − | 0.256699i | ||||
\(886\) | 2.55987e8 | + | 1.47794e8i | 0.368059 | + | 0.212499i | ||||
\(887\) | 8.43085e8i | 1.20809i | 0.796949 | + | 0.604047i | \(0.206446\pi\) | ||||
−0.796949 | + | 0.604047i | \(0.793554\pi\) | |||||||
\(888\) | −7.28501e8 | − | 4.20600e8i | −1.04038 | − | 0.600662i | ||||
\(889\) | 1.14892e7 | + | 6.63328e6i | 0.0163525 | + | 0.00944112i | ||||
\(890\) | −2.43637e7 | − | 1.40664e7i | −0.0345600 | − | 0.0199532i | ||||
\(891\) | −5.78087e8 | − | 1.00128e9i | −0.817259 | − | 1.41553i | ||||
\(892\) | 4.69466e7i | 0.0661469i | ||||||||
\(893\) | 5.89772e7 | − | 3.40505e7i | 0.0828190 | − | 0.0478156i | ||||
\(894\) | 1.78802e9 | + | 1.03232e9i | 2.50242 | + | 1.44477i | ||||
\(895\) | 1.13839e8 | 0.158789 | ||||||||
\(896\) | 8.00145e6 | − | 1.38589e7i | 0.0111236 | − | 0.0192666i | ||||
\(897\) | 1.91327e8 | − | 1.10463e8i | 0.265094 | − | 0.153052i | ||||
\(898\) | −3.59633e8 | − | 6.22903e8i | −0.496628 | − | 0.860185i | ||||
\(899\) | 8.90234e8i | 1.22525i | ||||||||
\(900\) | −2.84834e7 | − | 4.93347e7i | −0.0390719 | − | 0.0676745i | ||||
\(901\) | 2.42648e8 | 0.331743 | ||||||||
\(902\) | − | 3.93466e8i | − | 0.536151i | ||||||
\(903\) | 1.38022e7 | + | 2.39482e7i | 0.0187450 | + | 0.0325244i | ||||
\(904\) | −1.42321e9 | −1.92648 | ||||||||
\(905\) | 1.39107e8i | 0.187673i | ||||||||
\(906\) | 1.00528e9 | − | 5.80401e8i | 1.35177 | − | 0.780447i | ||||
\(907\) | −1.05904e8 | −0.141936 | −0.0709679 | − | 0.997479i | \(-0.522609\pi\) | ||||
−0.0709679 | + | 0.997479i | \(0.522609\pi\) | |||||||
\(908\) | −4.39764e7 | + | 2.53898e7i | −0.0587439 | + | 0.0339158i | ||||
\(909\) | −1.47341e9 | − | 2.55203e9i | −1.96170 | − | 3.39777i | ||||
\(910\) | −3.58042e6 | − | 2.06716e6i | −0.00475127 | − | 0.00274315i | ||||
\(911\) | 3.35146e8i | 0.443281i | 0.975129 | + | 0.221640i | \(0.0711411\pi\) | ||||
−0.975129 | + | 0.221640i | \(0.928859\pi\) | |||||||
\(912\) | −6.66425e8 | + | 1.15428e9i | −0.878551 | + | 1.52169i | ||||
\(913\) | 5.36818e8 | + | 9.29796e8i | 0.705366 | + | 1.22173i | ||||
\(914\) | −9.79092e8 | −1.28229 | ||||||||
\(915\) | 1.72713e8 | − | 9.97158e7i | 0.225456 | − | 0.130167i | ||||
\(916\) | 2.47352e7 | − | 4.28426e7i | 0.0321831 | − | 0.0557428i | ||||
\(917\) | −8.06665e6 | + | 1.39718e7i | −0.0104613 | + | 0.0181195i | ||||
\(918\) | −1.29232e9 | + | 2.23837e9i | −1.67049 | + | 2.89337i | ||||
\(919\) | −5.07149e8 | −0.653415 | −0.326708 | − | 0.945125i | \(-0.605939\pi\) | ||||
−0.326708 | + | 0.945125i | \(0.605939\pi\) | |||||||
\(920\) | 1.53959e7 | − | 2.66665e7i | 0.0197716 | − | 0.0342454i | ||||
\(921\) | 5.97046e8 | + | 3.44705e8i | 0.764239 | + | 0.441233i | ||||
\(922\) | −6.09289e7 | + | 3.51773e7i | −0.0777375 | + | 0.0448818i | ||||
\(923\) | 8.96945e8 | − | 5.17851e8i | 1.14067 | − | 0.658567i | ||||
\(924\) | −1.23168e6 | −0.00156129 | ||||||||
\(925\) | − | 5.13091e8i | − | 0.648290i | ||||||
\(926\) | −1.36710e8 | − | 2.36789e8i | −0.172174 | − | 0.298214i | ||||
\(927\) | −4.22748e8 | − | 7.32221e8i | −0.530692 | − | 0.919185i | ||||
\(928\) | −4.91162e7 | + | 8.50718e7i | −0.0614584 | + | 0.106449i | ||||
\(929\) | −2.80832e8 | − | 1.62138e8i | −0.350267 | − | 0.202227i | 0.314536 | − | 0.949246i | \(-0.398151\pi\) |
−0.664803 | + | 0.747019i | \(0.731485\pi\) | |||||||
\(930\) | 2.72998e8i | 0.339399i | ||||||||
\(931\) | −6.65672e8 | − | 3.84326e8i | −0.824919 | − | 0.476267i | ||||
\(932\) | −2.50805e7 | − | 1.44802e7i | −0.0309805 | − | 0.0178866i | ||||
\(933\) | 1.80572e9 | + | 1.04253e9i | 2.22334 | + | 1.28365i | ||||
\(934\) | −6.47216e8 | − | 1.12101e9i | −0.794344 | − | 1.37584i | ||||
\(935\) | − | 3.43144e8i | − | 0.419799i | ||||||
\(936\) | 1.56887e9 | − | 9.05787e8i | 1.91320 | − | 1.10458i | ||||
\(937\) | 1.08101e9 | + | 6.24120e8i | 1.31404 | + | 0.758664i | 0.982763 | − | 0.184868i | \(-0.0591858\pi\) |
0.331281 | + | 0.943532i | \(0.392519\pi\) | |||||||
\(938\) | 1.35897e7 | 0.0164665 | ||||||||
\(939\) | −1.29804e8 | + | 2.24827e8i | −0.156780 | + | 0.271552i | ||||
\(940\) | 678570. | − | 391773.i | 0.000816979 | − | 0.000471683i | ||||
\(941\) | 8.51466e7 | + | 1.47478e8i | 0.102188 | + | 0.176994i | 0.912586 | − | 0.408885i | \(-0.134082\pi\) |
−0.810398 | + | 0.585880i | \(0.800749\pi\) | |||||||
\(942\) | − | 1.60639e9i | − | 1.92176i | ||||||
\(943\) | −3.36604e7 | − | 5.83015e7i | −0.0401406 | − | 0.0695255i | ||||
\(944\) | 5.94766e8 | 0.707017 | ||||||||
\(945\) | 8.99764e6i | 0.0106619i | ||||||||
\(946\) | −8.08538e8 | + | 4.65990e8i | −0.955052 | + | 0.550431i | ||||
\(947\) | −1.25127e9 | −1.47334 | −0.736668 | − | 0.676254i | \(-0.763602\pi\) | ||||
−0.736668 | + | 0.676254i | \(0.763602\pi\) | |||||||
\(948\) | 1.85285e7i | 0.0217478i | ||||||||
\(949\) | −8.59193e8 | + | 4.96055e8i | −1.00529 | + | 0.580405i | ||||
\(950\) | −7.82830e8 | −0.913055 | ||||||||
\(951\) | −9.11483e8 | + | 5.26245e8i | −1.05976 | + | 0.611852i | ||||
\(952\) | −1.41655e7 | − | 2.45353e7i | −0.0164180 | − | 0.0284368i | ||||
\(953\) | −6.29922e8 | − | 3.63686e8i | −0.727794 | − | 0.420192i | 0.0898208 | − | 0.995958i | \(-0.471371\pi\) |
−0.817614 | + | 0.575766i | \(0.804704\pi\) | |||||||
\(954\) | − | 3.99732e8i | − | 0.460387i | ||||||
\(955\) | 3.29311e7 | − | 5.70383e7i | 0.0378091 | − | 0.0654872i | ||||
\(956\) | 3.03239e7 | + | 5.25225e7i | 0.0347065 | + | 0.0601134i | ||||
\(957\) | −2.69614e9 | −3.07615 | ||||||||
\(958\) | 1.32321e9 | − | 7.63956e8i | 1.50499 | − | 0.868905i | ||||
\(959\) | −501930. | + | 869369.i | −0.000569099 | + | 0.000985708i | ||||
\(960\) | 1.84364e8 | − | 3.19327e8i | 0.208383 | − | 0.360929i | ||||
\(961\) | 1.83307e8 | − | 3.17497e8i | 0.206542 | − | 0.357742i | ||||
\(962\) | −6.52436e8 | −0.732846 | ||||||||
\(963\) | 1.01027e9 | − | 1.74983e9i | 1.13124 | − | 1.95937i | ||||
\(964\) | 2.19687e7 | + | 1.26836e7i | 0.0245230 | + | 0.0141584i | ||||
\(965\) | 4.79925e7 | − | 2.77085e7i | 0.0534062 | − | 0.0308341i | ||||
\(966\) | −4.92918e6 | + | 2.84586e6i | −0.00546818 | + | 0.00315706i | ||||
\(967\) | 6.80039e8 | 0.752063 | 0.376032 | − | 0.926607i | \(-0.377288\pi\) | ||||
0.376032 | + | 0.926607i | \(0.377288\pi\) | |||||||
\(968\) | 1.51189e8i | 0.166684i | ||||||||
\(969\) | 1.22356e9 | + | 2.11927e9i | 1.34479 | + | 2.32924i | ||||
\(970\) | 1.81372e8 | + | 3.14145e8i | 0.198726 | + | 0.344203i | ||||
\(971\) | −4.32290e8 | + | 7.48748e8i | −0.472191 | + | 0.817858i | −0.999494 | − | 0.0318192i | \(-0.989870\pi\) |
0.527303 | + | 0.849677i | \(0.323203\pi\) | |||||||
\(972\) | 1.89974e7 | + | 1.09682e7i | 0.0206869 | + | 0.0119436i | ||||
\(973\) | 3.06135e7i | 0.0332334i | ||||||||
\(974\) | −5.07696e8 | − | 2.93118e8i | −0.549448 | − | 0.317224i | ||||
\(975\) | 1.39962e9 | + | 8.08073e8i | 1.51007 | + | 0.871840i | ||||
\(976\) | 4.99973e8 | + | 2.88660e8i | 0.537771 | + | 0.310482i | ||||
\(977\) | 3.45237e8 | + | 5.97968e8i | 0.370198 | + | 0.641201i | 0.989596 | − | 0.143876i | \(-0.0459566\pi\) |
−0.619398 | + | 0.785077i | \(0.712623\pi\) | |||||||
\(978\) | 1.90668e9i | 2.03827i | ||||||||
\(979\) | 1.40789e8 | − | 8.12845e7i | 0.150045 | − | 0.0866282i | ||||
\(980\) | −7.65898e6 | − | 4.42191e6i | −0.00813753 | − | 0.00469821i | ||||
\(981\) | 3.05876e9 | 3.23995 | ||||||||
\(982\) | −2.54967e8 | + | 4.41616e8i | −0.269246 | + | 0.466348i | ||||
\(983\) | −4.16911e8 | + | 2.40704e8i | −0.438918 | + | 0.253409i | −0.703138 | − | 0.711053i | \(-0.748219\pi\) |
0.264221 | + | 0.964462i | \(0.414885\pi\) | |||||||
\(984\) | −4.03699e8 | − | 6.99228e8i | −0.423714 | − | 0.733894i | ||||
\(985\) | − | 2.42648e8i | − | 0.253903i | ||||||
\(986\) | 1.23989e9 | + | 2.14756e9i | 1.29346 | + | 2.24034i | ||||
\(987\) | 3.62213e6 | 0.00376715 | ||||||||
\(988\) | 3.68559e7i | 0.0382152i | ||||||||
\(989\) | −7.99397e7 | + | 1.38217e8i | −0.0826369 | + | 0.142880i | ||||
\(990\) | −5.65287e8 | −0.582590 | ||||||||
\(991\) | 1.23489e9i | 1.26884i | 0.772989 | + | 0.634420i | \(0.218761\pi\) | ||||
−0.772989 | + | 0.634420i | \(0.781239\pi\) | |||||||
\(992\) | −4.97768e7 | + | 2.87386e7i | −0.0509908 | + | 0.0294395i | ||||
\(993\) | 8.41198e8 | 0.859114 | ||||||||
\(994\) | −2.31081e7 | + | 1.33414e7i | −0.0235290 | + | 0.0135845i | ||||
\(995\) | −1.01949e8 | − | 1.76582e8i | −0.103494 | − | 0.179257i | ||||
\(996\) | −7.62917e7 | − | 4.40470e7i | −0.0772146 | − | 0.0445799i | ||||
\(997\) | − | 1.03182e9i | − | 1.04117i | −0.853811 | − | 0.520583i | \(-0.825715\pi\) | ||
0.853811 | − | 0.520583i | \(-0.174285\pi\) | |||||||
\(998\) | −3.89864e6 | + | 6.75265e6i | −0.00392213 | + | 0.00679333i | ||||
\(999\) | 7.09958e8 | + | 1.22968e9i | 0.712093 | + | 1.23338i |
(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 | 43.7.d.a.7.16 | ✓ | 42 | |
43.37 | odd | 6 | inner | 43.7.d.a.37.6 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.16 | ✓ | 42 | 1.1 | even | 1 | trivial | |
43.7.d.a.37.6 | yes | 42 | 43.37 | odd | 6 | inner |