Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (of order \(2\), degree \(1\), 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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.14 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.6.d.a.75.13 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.73141 | + | 4.25166i | −0.659626 | + | 0.751594i | ||||
\(3\) | 29.4761 | 1.89090 | 0.945448 | − | 0.325774i | \(-0.105625\pi\) | ||||
0.945448 | + | 0.325774i | \(0.105625\pi\) | |||||||
\(4\) | −4.15316 | − | 31.7293i | −0.129786 | − | 0.991542i | ||||
\(5\) | −71.3638 | −1.27659 | −0.638297 | − | 0.769790i | \(-0.720361\pi\) | ||||
−0.638297 | + | 0.769790i | \(0.720361\pi\) | |||||||
\(6\) | −109.988 | + | 125.322i | −1.24728 | + | 1.42119i | ||||
\(7\) | − | 160.370i | − | 1.23702i | −0.785776 | − | 0.618511i | \(-0.787736\pi\) | ||
0.785776 | − | 0.618511i | \(-0.212264\pi\) | |||||||
\(8\) | 150.399 | + | 100.737i | 0.830847 | + | 0.556501i | ||||
\(9\) | 625.843 | 2.57549 | ||||||||
\(10\) | 266.288 | − | 303.414i | 0.842076 | − | 0.959481i | ||||
\(11\) | 139.176i | 0.346803i | 0.984851 | + | 0.173401i | \(0.0554757\pi\) | ||||
−0.984851 | + | 0.173401i | \(0.944524\pi\) | |||||||
\(12\) | −122.419 | − | 935.259i | −0.245412 | − | 1.87490i | ||||
\(13\) | − | 946.762i | − | 1.55375i | −0.629652 | − | 0.776877i | \(-0.716802\pi\) | ||
0.629652 | − | 0.776877i | \(-0.283198\pi\) | |||||||
\(14\) | 681.838 | + | 598.406i | 0.929738 | + | 0.815973i | ||||
\(15\) | −2103.53 | −2.41391 | ||||||||
\(16\) | −989.503 | + | 263.554i | −0.966311 | + | 0.257377i | ||||
\(17\) | 880.453 | 0.738897 | 0.369449 | − | 0.929251i | \(-0.379547\pi\) | ||||
0.369449 | + | 0.929251i | \(0.379547\pi\) | |||||||
\(18\) | −2335.28 | + | 2660.87i | −1.69886 | + | 1.93572i | ||||
\(19\) | 862.513 | − | 1316.12i | 0.548128 | − | 0.836395i | ||||
\(20\) | 296.385 | + | 2264.33i | 0.165684 | + | 1.26580i | ||||
\(21\) | − | 4727.09i | − | 2.33908i | ||||||
\(22\) | −591.728 | − | 519.322i | −0.260655 | − | 0.228760i | ||||
\(23\) | − | 1491.83i | − | 0.588030i | −0.955801 | − | 0.294015i | \(-0.905008\pi\) | ||
0.955801 | − | 0.294015i | \(-0.0949915\pi\) | |||||||
\(24\) | 4433.19 | + | 2969.35i | 1.57105 | + | 1.05228i | ||||
\(25\) | 1967.79 | 0.629694 | ||||||||
\(26\) | 4025.31 | + | 3532.76i | 1.16779 | + | 1.02490i | ||||
\(27\) | 11284.7 | 2.97908 | ||||||||
\(28\) | −5088.43 | + | 666.041i | −1.22656 | + | 0.160548i | ||||
\(29\) | 2448.22i | 0.540575i | 0.962780 | + | 0.270288i | \(0.0871188\pi\) | ||||
−0.962780 | + | 0.270288i | \(0.912881\pi\) | |||||||
\(30\) | 7849.13 | − | 8943.49i | 1.59228 | − | 1.81428i | ||||
\(31\) | −196.845 | −0.0367893 | −0.0183946 | − | 0.999831i | \(-0.505856\pi\) | ||||
−0.0183946 | + | 0.999831i | \(0.505856\pi\) | |||||||
\(32\) | 2571.70 | − | 5190.45i | 0.443961 | − | 0.896046i | ||||
\(33\) | 4102.37i | 0.655767i | ||||||||
\(34\) | −3285.33 | + | 3743.38i | −0.487396 | + | 0.555350i | ||||
\(35\) | 11444.6i | 1.57918i | ||||||||
\(36\) | −2599.23 | − | 19857.6i | −0.334262 | − | 2.55370i | ||||
\(37\) | 4503.97i | 0.540868i | 0.962738 | + | 0.270434i | \(0.0871672\pi\) | ||||
−0.962738 | + | 0.270434i | \(0.912833\pi\) | |||||||
\(38\) | 2377.30 | + | 8578.09i | 0.267070 | + | 0.963677i | ||||
\(39\) | − | 27906.9i | − | 2.93799i | ||||||
\(40\) | −10733.1 | − | 7189.01i | −1.06066 | − | 0.710426i | ||||
\(41\) | − | 15914.6i | − | 1.47855i | −0.673405 | − | 0.739274i | \(-0.735169\pi\) | ||
0.673405 | − | 0.739274i | \(-0.264831\pi\) | |||||||
\(42\) | 20097.9 | + | 17638.7i | 1.75804 | + | 1.54292i | ||||
\(43\) | 12075.4i | 0.995935i | 0.867196 | + | 0.497968i | \(0.165920\pi\) | ||||
−0.867196 | + | 0.497968i | \(0.834080\pi\) | |||||||
\(44\) | 4415.96 | − | 578.019i | 0.343869 | − | 0.0450102i | ||||
\(45\) | −44662.6 | −3.28785 | ||||||||
\(46\) | 6342.74 | + | 5566.62i | 0.441960 | + | 0.387880i | ||||
\(47\) | 23620.8i | 1.55973i | 0.625946 | + | 0.779866i | \(0.284713\pi\) | ||||
−0.625946 | + | 0.779866i | \(0.715287\pi\) | |||||||
\(48\) | −29166.7 | + | 7768.55i | −1.82719 | + | 0.486673i | ||||
\(49\) | −8911.49 | −0.530225 | ||||||||
\(50\) | −7342.65 | + | 8366.39i | −0.415363 | + | 0.473274i | ||||
\(51\) | 25952.4 | 1.39718 | ||||||||
\(52\) | −30040.1 | + | 3932.05i | −1.54061 | + | 0.201656i | ||||
\(53\) | − | 3991.90i | − | 0.195205i | −0.995226 | − | 0.0976023i | \(-0.968883\pi\) | ||
0.995226 | − | 0.0976023i | \(-0.0311173\pi\) | |||||||
\(54\) | −42108.0 | + | 47978.8i | −1.96508 | + | 2.23906i | ||||
\(55\) | − | 9932.12i | − | 0.442726i | ||||||
\(56\) | 16155.2 | − | 24119.5i | 0.688404 | − | 1.02778i | ||||
\(57\) | 25423.6 | − | 38794.1i | 1.03645 | − | 1.58154i | ||||
\(58\) | −10409.0 | − | 9135.33i | −0.406293 | − | 0.356578i | ||||
\(59\) | −28997.9 | −1.08452 | −0.542260 | − | 0.840211i | \(-0.682431\pi\) | ||||
−0.542260 | + | 0.840211i | \(0.682431\pi\) | |||||||
\(60\) | 8736.29 | + | 66743.6i | 0.313292 | + | 2.39349i | ||||
\(61\) | 11336.7 | 0.390088 | 0.195044 | − | 0.980795i | \(-0.437515\pi\) | ||||
0.195044 | + | 0.980795i | \(0.437515\pi\) | |||||||
\(62\) | 734.511 | − | 836.919i | 0.0242672 | − | 0.0276506i | ||||
\(63\) | − | 100366.i | − | 3.18593i | ||||||
\(64\) | 12472.0 | + | 30301.7i | 0.380614 | + | 0.924734i | ||||
\(65\) | 67564.6i | 1.98352i | ||||||||
\(66\) | −17441.9 | − | 15307.6i | −0.492871 | − | 0.432561i | ||||
\(67\) | 27482.9 | 0.747955 | 0.373977 | − | 0.927438i | \(-0.377994\pi\) | ||||
0.373977 | + | 0.927438i | \(0.377994\pi\) | |||||||
\(68\) | −3656.66 | − | 27936.2i | −0.0958986 | − | 0.732647i | ||||
\(69\) | − | 43973.4i | − | 1.11190i | ||||||
\(70\) | −48658.5 | − | 42704.5i | −1.18690 | − | 1.04167i | ||||
\(71\) | −6688.31 | −0.157460 | −0.0787301 | − | 0.996896i | \(-0.525087\pi\) | ||||
−0.0787301 | + | 0.996896i | \(0.525087\pi\) | |||||||
\(72\) | 94126.4 | + | 63045.8i | 2.13983 | + | 1.43326i | ||||
\(73\) | −81370.8 | −1.78715 | −0.893576 | − | 0.448912i | \(-0.851812\pi\) | ||||
−0.893576 | + | 0.448912i | \(0.851812\pi\) | |||||||
\(74\) | −19149.3 | − | 16806.2i | −0.406513 | − | 0.356771i | ||||
\(75\) | 58003.0 | 1.19069 | ||||||||
\(76\) | −45341.8 | − | 21900.9i | −0.900460 | − | 0.434939i | ||||
\(77\) | 22319.6 | 0.429003 | ||||||||
\(78\) | 118651. | + | 104132.i | 2.20817 | + | 1.93797i | ||||
\(79\) | −12559.2 | −0.226409 | −0.113204 | − | 0.993572i | \(-0.536112\pi\) | ||||
−0.113204 | + | 0.993572i | \(0.536112\pi\) | |||||||
\(80\) | 70614.7 | − | 18808.2i | 1.23359 | − | 0.328566i | ||||
\(81\) | 180551. | 3.05764 | ||||||||
\(82\) | 67663.3 | + | 59383.8i | 1.11127 | + | 0.975289i | ||||
\(83\) | 18195.6i | 0.289915i | 0.989438 | + | 0.144958i | \(0.0463046\pi\) | ||||
−0.989438 | + | 0.144958i | \(0.953695\pi\) | |||||||
\(84\) | −149987. | + | 19632.3i | −2.31930 | + | 0.303580i | ||||
\(85\) | −62832.5 | −0.943272 | ||||||||
\(86\) | −51340.5 | − | 45058.3i | −0.748539 | − | 0.656945i | ||||
\(87\) | 72164.2i | 1.02217i | ||||||||
\(88\) | −14020.2 | + | 20932.0i | −0.192996 | + | 0.288140i | ||||
\(89\) | 11664.2i | 0.156092i | 0.996950 | + | 0.0780460i | \(0.0248681\pi\) | ||||
−0.996950 | + | 0.0780460i | \(0.975132\pi\) | |||||||
\(90\) | 166654. | − | 189890.i | 2.16875 | − | 2.47113i | ||||
\(91\) | −151832. | −1.92203 | ||||||||
\(92\) | −47334.7 | + | 6195.80i | −0.583056 | + | 0.0763182i | ||||
\(93\) | −5802.25 | −0.0695647 | ||||||||
\(94\) | −100428. | − | 88138.9i | −1.17229 | − | 1.02884i | ||||
\(95\) | −61552.2 | + | 93923.3i | −0.699737 | + | 1.06774i | ||||
\(96\) | 75803.8 | − | 152995.i | 0.839485 | − | 1.69433i | ||||
\(97\) | − | 31104.8i | − | 0.335659i | −0.985816 | − | 0.167830i | \(-0.946324\pi\) | ||
0.985816 | − | 0.167830i | \(-0.0536758\pi\) | |||||||
\(98\) | 33252.4 | − | 37888.6i | 0.349750 | − | 0.398514i | ||||
\(99\) | 87102.2i | 0.893185i | ||||||||
\(100\) | −8172.56 | − | 62436.8i | −0.0817256 | − | 0.624368i | ||||
\(101\) | −28919.3 | −0.282088 | −0.141044 | − | 0.990003i | \(-0.545046\pi\) | ||||
−0.141044 | + | 0.990003i | \(0.545046\pi\) | |||||||
\(102\) | −96838.9 | + | 110341.i | −0.921615 | + | 1.05011i | ||||
\(103\) | 59622.1 | 0.553750 | 0.276875 | − | 0.960906i | \(-0.410701\pi\) | ||||
0.276875 | + | 0.960906i | \(0.410701\pi\) | |||||||
\(104\) | 95374.4 | − | 142392.i | 0.864666 | − | 1.29093i | ||||
\(105\) | 337343.i | 2.98606i | ||||||||
\(106\) | 16972.2 | + | 14895.4i | 0.146715 | + | 0.128762i | ||||
\(107\) | 27385.8 | 0.231242 | 0.115621 | − | 0.993293i | \(-0.463114\pi\) | ||||
0.115621 | + | 0.993293i | \(0.463114\pi\) | |||||||
\(108\) | −46867.3 | − | 358057.i | −0.386643 | − | 2.95388i | ||||
\(109\) | − | 37981.6i | − | 0.306202i | −0.988211 | − | 0.153101i | \(-0.951074\pi\) | ||
0.988211 | − | 0.153101i | \(-0.0489259\pi\) | |||||||
\(110\) | 42228.0 | + | 37060.8i | 0.332750 | + | 0.292034i | ||||
\(111\) | 132760.i | 1.02273i | ||||||||
\(112\) | 42266.1 | + | 158686.i | 0.318381 | + | 1.19535i | ||||
\(113\) | 122780.i | 0.904549i | 0.891879 | + | 0.452274i | \(0.149387\pi\) | ||||
−0.891879 | + | 0.452274i | \(0.850613\pi\) | |||||||
\(114\) | 70073.6 | + | 252849.i | 0.505001 | + | 1.82221i | ||||
\(115\) | 106463.i | 0.750676i | ||||||||
\(116\) | 77680.6 | − | 10167.9i | 0.536003 | − | 0.0701592i | ||||
\(117\) | − | 592525.i | − | 4.00167i | ||||||
\(118\) | 108203. | − | 123289.i | 0.715377 | − | 0.815118i | ||||
\(119\) | − | 141198.i | − | 0.914032i | ||||||
\(120\) | −316370. | − | 211904.i | −2.00559 | − | 1.34334i | ||||
\(121\) | 141681. | 0.879728 | ||||||||
\(122\) | −42301.9 | + | 48199.8i | −0.257312 | + | 0.293188i | ||||
\(123\) | − | 469100.i | − | 2.79578i | ||||||
\(124\) | 817.530 | + | 6245.78i | 0.00477474 | + | 0.0364781i | ||||
\(125\) | 82582.6 | 0.472730 | ||||||||
\(126\) | 426723. | + | 374508.i | 2.39453 | + | 2.10153i | ||||
\(127\) | 334765. | 1.84175 | 0.920876 | − | 0.389855i | \(-0.127475\pi\) | ||||
0.920876 | + | 0.389855i | \(0.127475\pi\) | |||||||
\(128\) | −175370. | − | 60041.6i | −0.946087 | − | 0.323912i | ||||
\(129\) | 355937.i | 1.88321i | ||||||||
\(130\) | −287261. | − | 252111.i | −1.49080 | − | 1.30838i | ||||
\(131\) | 138971.i | 0.707533i | 0.935334 | + | 0.353767i | \(0.115099\pi\) | ||||
−0.935334 | + | 0.353767i | \(0.884901\pi\) | |||||||
\(132\) | 130165. | − | 17037.8i | 0.650221 | − | 0.0851095i | ||||
\(133\) | −211066. | − | 138321.i | −1.03464 | − | 0.678046i | ||||
\(134\) | −102550. | + | 116848.i | −0.493371 | + | 0.562158i | ||||
\(135\) | −805322. | −3.80308 | ||||||||
\(136\) | 132420. | + | 88694.5i | 0.613910 | + | 0.411197i | ||||
\(137\) | 97083.5 | 0.441920 | 0.220960 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220960 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(138\) | 186960. | + | 164083.i | 0.835699 | + | 0.733441i | ||||
\(139\) | 268260.i | 1.17766i | 0.808258 | + | 0.588828i | \(0.200411\pi\) | ||||
−0.808258 | + | 0.588828i | \(0.799589\pi\) | |||||||
\(140\) | 363130. | − | 47531.3i | 1.56582 | − | 0.204955i | ||||
\(141\) | 696250.i | 2.94929i | ||||||||
\(142\) | 24956.8 | − | 28436.4i | 0.103865 | − | 0.118346i | ||||
\(143\) | 131766. | 0.538846 | ||||||||
\(144\) | −619273. | + | 164943.i | −2.48872 | + | 0.662871i | ||||
\(145\) | − | 174715.i | − | 0.690096i | ||||||
\(146\) | 303628. | − | 345961.i | 1.17885 | − | 1.34321i | ||||
\(147\) | −262676. | −1.00260 | ||||||||
\(148\) | 142908. | − | 18705.7i | 0.536294 | − | 0.0701972i | ||||
\(149\) | 411244. | 1.51752 | 0.758760 | − | 0.651370i | \(-0.225806\pi\) | ||||
0.758760 | + | 0.651370i | \(0.225806\pi\) | |||||||
\(150\) | −216433. | + | 246609.i | −0.785408 | + | 0.894912i | ||||
\(151\) | −118745. | −0.423813 | −0.211907 | − | 0.977290i | \(-0.567967\pi\) | ||||
−0.211907 | + | 0.977290i | \(0.567967\pi\) | |||||||
\(152\) | 262304. | − | 111056.i | 0.920864 | − | 0.389883i | ||||
\(153\) | 551025. | 1.90302 | ||||||||
\(154\) | −83283.6 | + | 94895.3i | −0.282981 | + | 0.322436i | ||||
\(155\) | 14047.6 | 0.0469650 | ||||||||
\(156\) | −885468. | + | 115902.i | −2.91314 | + | 0.381310i | ||||
\(157\) | −529209. | −1.71348 | −0.856738 | − | 0.515752i | \(-0.827513\pi\) | ||||
−0.856738 | + | 0.515752i | \(0.827513\pi\) | |||||||
\(158\) | 46863.5 | − | 53397.3i | 0.149345 | − | 0.170168i | ||||
\(159\) | − | 117666.i | − | 0.369111i | ||||||
\(160\) | −183526. | + | 370411.i | −0.566759 | + | 1.14389i | ||||
\(161\) | −239244. | −0.727406 | ||||||||
\(162\) | −673709. | + | 767639.i | −2.01690 | + | 2.29810i | ||||
\(163\) | 180326.i | 0.531607i | 0.964027 | + | 0.265803i | \(0.0856372\pi\) | ||||
−0.964027 | + | 0.265803i | \(0.914363\pi\) | |||||||
\(164\) | −504959. | + | 66095.8i | −1.46604 | + | 0.191895i | ||||
\(165\) | − | 292761.i | − | 0.837149i | ||||||
\(166\) | −77361.4 | − | 67895.2i | −0.217898 | − | 0.191236i | ||||
\(167\) | 208590. | 0.578766 | 0.289383 | − | 0.957213i | \(-0.406550\pi\) | ||||
0.289383 | + | 0.957213i | \(0.406550\pi\) | |||||||
\(168\) | 476194. | − | 710951.i | 1.30170 | − | 1.94342i | ||||
\(169\) | −525066. | −1.41415 | ||||||||
\(170\) | 234454. | − | 267142.i | 0.622207 | − | 0.708957i | ||||
\(171\) | 539798. | − | 823684.i | 1.41169 | − | 2.15412i | ||||
\(172\) | 383145. | − | 50151.1i | 0.987511 | − | 0.129259i | ||||
\(173\) | − | 82101.3i | − | 0.208562i | −0.994548 | − | 0.104281i | \(-0.966746\pi\) | ||
0.994548 | − | 0.104281i | \(-0.0332541\pi\) | |||||||
\(174\) | −306817. | − | 269274.i | −0.768258 | − | 0.674251i | ||||
\(175\) | − | 315575.i | − | 0.778946i | ||||||
\(176\) | −36680.4 | − | 137715.i | −0.0892590 | − | 0.335119i | ||||
\(177\) | −854748. | −2.05071 | ||||||||
\(178\) | −49592.2 | − | 43524.0i | −0.117318 | − | 0.102962i | ||||
\(179\) | 537272. | 1.25332 | 0.626660 | − | 0.779293i | \(-0.284422\pi\) | ||||
0.626660 | + | 0.779293i | \(0.284422\pi\) | |||||||
\(180\) | 185491. | + | 1.41711e6i | 0.426718 | + | 3.26004i | ||||
\(181\) | 466070.i | 1.05744i | 0.848797 | + | 0.528719i | \(0.177327\pi\) | ||||
−0.848797 | + | 0.528719i | \(0.822673\pi\) | |||||||
\(182\) | 566548. | − | 645538.i | 1.26782 | − | 1.44459i | ||||
\(183\) | 334163. | 0.737615 | ||||||||
\(184\) | 150283. | − | 224370.i | 0.327239 | − | 0.488563i | ||||
\(185\) | − | 321421.i | − | 0.690470i | ||||||
\(186\) | 21650.6 | − | 24669.2i | 0.0458867 | − | 0.0522844i | ||||
\(187\) | 122538.i | 0.256251i | ||||||||
\(188\) | 749473. | − | 98101.0i | 1.54654 | − | 0.202432i | ||||
\(189\) | − | 1.80973e6i | − | 3.68519i | ||||||
\(190\) | −169653. | − | 612165.i | −0.340940 | − | 1.23023i | ||||
\(191\) | 271824.i | 0.539143i | 0.962980 | + | 0.269572i | \(0.0868821\pi\) | ||||
−0.962980 | + | 0.269572i | \(0.913118\pi\) | |||||||
\(192\) | 367625. | + | 893177.i | 0.719701 | + | 1.74858i | ||||
\(193\) | 311959.i | 0.602842i | 0.953491 | + | 0.301421i | \(0.0974610\pi\) | ||||
−0.953491 | + | 0.301421i | \(0.902539\pi\) | |||||||
\(194\) | 132247. | + | 116065.i | 0.252279 | + | 0.221410i | ||||
\(195\) | 1.99154e6i | 3.75062i | ||||||||
\(196\) | 37010.8 | + | 282756.i | 0.0688159 | + | 0.525741i | ||||
\(197\) | −359897. | −0.660713 | −0.330357 | − | 0.943856i | \(-0.607169\pi\) | ||||
−0.330357 | + | 0.943856i | \(0.607169\pi\) | |||||||
\(198\) | −370329. | − | 325014.i | −0.671312 | − | 0.589168i | ||||
\(199\) | − | 204639.i | − | 0.366316i | −0.983083 | − | 0.183158i | \(-0.941368\pi\) | ||
0.983083 | − | 0.183158i | \(-0.0586321\pi\) | |||||||
\(200\) | 295955. | + | 198231.i | 0.523180 | + | 0.350425i | ||||
\(201\) | 810089. | 1.41430 | ||||||||
\(202\) | 107910. | − | 122955.i | 0.186072 | − | 0.212015i | ||||
\(203\) | 392621. | 0.668704 | ||||||||
\(204\) | −107784. | − | 823451.i | −0.181334 | − | 1.38536i | ||||
\(205\) | 1.13573e6i | 1.88751i | ||||||||
\(206\) | −222474. | + | 253493.i | −0.365268 | + | 0.416195i | ||||
\(207\) | − | 933651.i | − | 1.51446i | ||||||
\(208\) | 249523. | + | 936824.i | 0.399901 | + | 1.50141i | ||||
\(209\) | 183172. | + | 120041.i | 0.290064 | + | 0.190092i | ||||
\(210\) | −1.43427e6 | − | 1.25876e6i | −2.24430 | − | 1.96968i | ||||
\(211\) | 657870. | 1.01727 | 0.508633 | − | 0.860984i | \(-0.330151\pi\) | ||||
0.508633 | + | 0.860984i | \(0.330151\pi\) | |||||||
\(212\) | −126660. | + | 16579.0i | −0.193554 | + | 0.0253349i | ||||
\(213\) | −197146. | −0.297741 | ||||||||
\(214\) | −102188. | + | 116435.i | −0.152533 | + | 0.173800i | ||||
\(215\) | − | 861748.i | − | 1.27141i | ||||||
\(216\) | 1.69722e6 | + | 1.13680e6i | 2.47516 | + | 1.65786i | ||||
\(217\) | 31568.1i | 0.0455092i | ||||||||
\(218\) | 161485. | + | 141725.i | 0.230139 | + | 0.201979i | ||||
\(219\) | −2.39850e6 | −3.37932 | ||||||||
\(220\) | −315140. | + | 41249.7i | −0.438982 | + | 0.0574598i | ||||
\(221\) | − | 833580.i | − | 1.14806i | ||||||
\(222\) | −564449. | − | 495381.i | −0.768674 | − | 0.674617i | ||||
\(223\) | 779985. | 1.05033 | 0.525163 | − | 0.851001i | \(-0.324004\pi\) | ||||
0.525163 | + | 0.851001i | \(0.324004\pi\) | |||||||
\(224\) | −832392. | − | 412423.i | −1.10843 | − | 0.549190i | ||||
\(225\) | 1.23153e6 | 1.62177 | ||||||||
\(226\) | −522019. | − | 458143.i | −0.679853 | − | 0.596664i | ||||
\(227\) | −670276. | −0.863354 | −0.431677 | − | 0.902028i | \(-0.642078\pi\) | ||||
−0.431677 | + | 0.902028i | \(0.642078\pi\) | |||||||
\(228\) | −1.33650e6 | − | 645555.i | −1.70268 | − | 0.822424i | ||||
\(229\) | −109449. | −0.137919 | −0.0689593 | − | 0.997619i | \(-0.521968\pi\) | ||||
−0.0689593 | + | 0.997619i | \(0.521968\pi\) | |||||||
\(230\) | −452642. | − | 397256.i | −0.564203 | − | 0.495166i | ||||
\(231\) | 657896. | 0.811199 | ||||||||
\(232\) | −246628. | + | 368212.i | −0.300831 | + | 0.449136i | ||||
\(233\) | 816310. | 0.985066 | 0.492533 | − | 0.870294i | \(-0.336071\pi\) | ||||
0.492533 | + | 0.870294i | \(0.336071\pi\) | |||||||
\(234\) | 2.51921e6 | + | 2.21095e6i | 3.00763 | + | 2.63961i | ||||
\(235\) | − | 1.68567e6i | − | 1.99115i | ||||||
\(236\) | 120433. | + | 920086.i | 0.140756 | + | 1.07535i | ||||
\(237\) | −370196. | −0.428116 | ||||||||
\(238\) | 600326. | + | 526868.i | 0.686981 | + | 0.602920i | ||||
\(239\) | 1.50386e6i | 1.70299i | 0.524360 | + | 0.851497i | \(0.324305\pi\) | ||||
−0.524360 | + | 0.851497i | \(0.675695\pi\) | |||||||
\(240\) | 2.08145e6 | − | 554394.i | 2.33259 | − | 0.621284i | ||||
\(241\) | − | 1.61223e6i | − | 1.78806i | −0.448003 | − | 0.894032i | \(-0.647865\pi\) | ||
0.448003 | − | 0.894032i | \(-0.352135\pi\) | |||||||
\(242\) | −528670. | + | 602379.i | −0.580292 | + | 0.661198i | ||||
\(243\) | 2.57975e6 | 2.80260 | ||||||||
\(244\) | −47083.2 | − | 359706.i | −0.0506280 | − | 0.386789i | ||||
\(245\) | 635958. | 0.676883 | ||||||||
\(246\) | 1.99445e6 | + | 1.75041e6i | 2.10129 | + | 1.84417i | ||||
\(247\) | −1.24605e6 | − | 816595.i | −1.29955 | − | 0.851656i | ||||
\(248\) | −29605.4 | − | 19829.7i | −0.0305663 | − | 0.0204733i | ||||
\(249\) | 536336.i | 0.548199i | ||||||||
\(250\) | −308149. | + | 351113.i | −0.311825 | + | 0.355301i | ||||
\(251\) | − | 982801.i | − | 0.984649i | −0.870412 | − | 0.492325i | \(-0.836147\pi\) | ||
0.870412 | − | 0.492325i | \(-0.163853\pi\) | |||||||
\(252\) | −3.18456e6 | + | 416837.i | −3.15899 | + | 0.413490i | ||||
\(253\) | 207627. | 0.203930 | ||||||||
\(254\) | −1.24915e6 | + | 1.42331e6i | −1.21487 | + | 1.38425i | ||||
\(255\) | −1.85206e6 | −1.78363 | ||||||||
\(256\) | 909655. | − | 521575.i | 0.867514 | − | 0.497412i | ||||
\(257\) | − | 1.66201e6i | − | 1.56964i | −0.619723 | − | 0.784820i | \(-0.712755\pi\) | ||
0.619723 | − | 0.784820i | \(-0.287245\pi\) | |||||||
\(258\) | −1.51332e6 | − | 1.32815e6i | −1.41541 | − | 1.24221i | ||||
\(259\) | 722302. | 0.669066 | ||||||||
\(260\) | 2.14378e6 | − | 280606.i | 1.96674 | − | 0.257433i | ||||
\(261\) | 1.53220e6i | 1.39224i | ||||||||
\(262\) | −590858. | − | 518559.i | −0.531777 | − | 0.466708i | ||||
\(263\) | 1.62129e6i | 1.44534i | 0.691193 | + | 0.722671i | \(0.257086\pi\) | ||||
−0.691193 | + | 0.722671i | \(0.742914\pi\) | |||||||
\(264\) | −413262. | + | 616994.i | −0.364935 | + | 0.544842i | ||||
\(265\) | 284877.i | 0.249197i | ||||||||
\(266\) | 1.37567e6 | − | 381247.i | 1.19209 | − | 0.330371i | ||||
\(267\) | 343816.i | 0.295153i | ||||||||
\(268\) | −114141. | − | 872014.i | −0.0970742 | − | 0.741629i | ||||
\(269\) | 1.48663e6i | 1.25262i | 0.779572 | + | 0.626312i | \(0.215437\pi\) | ||||
−0.779572 | + | 0.626312i | \(0.784563\pi\) | |||||||
\(270\) | 3.00499e6 | − | 3.42395e6i | 2.50861 | − | 2.85837i | ||||
\(271\) | − | 635235.i | − | 0.525426i | −0.964874 | − | 0.262713i | \(-0.915383\pi\) | ||
0.964874 | − | 0.262713i | \(-0.0846172\pi\) | |||||||
\(272\) | −871211. | + | 232047.i | −0.714004 | + | 0.190175i | ||||
\(273\) | −4.47543e6 | −3.63436 | ||||||||
\(274\) | −362258. | + | 412766.i | −0.291502 | + | 0.332145i | ||||
\(275\) | 273870.i | 0.218380i | ||||||||
\(276\) | −1.39525e6 | + | 182628.i | −1.10250 | + | 0.144310i | ||||
\(277\) | 1.86068e6 | 1.45704 | 0.728521 | − | 0.685023i | \(-0.240208\pi\) | ||||
0.728521 | + | 0.685023i | \(0.240208\pi\) | |||||||
\(278\) | −1.14055e6 | − | 1.00099e6i | −0.885119 | − | 0.776813i | ||||
\(279\) | −123194. | −0.0947503 | ||||||||
\(280\) | −1.15290e6 | + | 1.72126e6i | −0.878813 | + | 1.31205i | ||||
\(281\) | − | 1.62510e6i | − | 1.22776i | −0.789397 | − | 0.613882i | \(-0.789607\pi\) | ||
0.789397 | − | 0.613882i | \(-0.210393\pi\) | |||||||
\(282\) | −2.96022e6 | − | 2.59800e6i | −2.21667 | − | 1.94543i | ||||
\(283\) | 1.93793e6i | 1.43837i | 0.694817 | + | 0.719187i | \(0.255485\pi\) | ||||
−0.694817 | + | 0.719187i | \(0.744515\pi\) | |||||||
\(284\) | 27777.6 | + | 212216.i | 0.0204362 | + | 0.156128i | ||||
\(285\) | −1.81432e6 | + | 2.76850e6i | −1.32313 | + | 2.01898i | ||||
\(286\) | −491675. | + | 560226.i | −0.355437 | + | 0.404993i | ||||
\(287\) | −2.55222e6 | −1.82900 | ||||||||
\(288\) | 1.60948e6 | − | 3.24841e6i | 1.14342 | − | 2.30775i | ||||
\(289\) | −644659. | −0.454031 | ||||||||
\(290\) | 742827. | + | 651932.i | 0.518672 | + | 0.455205i | ||||
\(291\) | − | 916851.i | − | 0.634697i | ||||||
\(292\) | 337946. | + | 2.58184e6i | 0.231948 | + | 1.77204i | ||||
\(293\) | 485189.i | 0.330173i | 0.986279 | + | 0.165087i | \(0.0527904\pi\) | ||||
−0.986279 | + | 0.165087i | \(0.947210\pi\) | |||||||
\(294\) | 980154. | − | 1.11681e6i | 0.661342 | − | 0.753548i | ||||
\(295\) | 2.06940e6 | 1.38449 | ||||||||
\(296\) | −453719. | + | 677395.i | −0.300994 | + | 0.449379i | ||||
\(297\) | 1.57056e6i | 1.03315i | ||||||||
\(298\) | −1.53452e6 | + | 1.74847e6i | −1.00100 | + | 1.14056i | ||||
\(299\) | −1.41241e6 | −0.913654 | ||||||||
\(300\) | −240896. | − | 1.84040e6i | −0.154535 | − | 1.18062i | ||||
\(301\) | 1.93653e6 | 1.23199 | ||||||||
\(302\) | 443088. | − | 504865.i | 0.279558 | − | 0.318535i | ||||
\(303\) | −852429. | −0.533398 | ||||||||
\(304\) | −506590. | + | 1.52962e6i | −0.314393 | + | 0.949293i | ||||
\(305\) | −809031. | −0.497984 | ||||||||
\(306\) | −2.05610e6 | + | 2.34277e6i | −1.25528 | + | 1.43030i | ||||
\(307\) | 22512.8 | 0.0136327 | 0.00681637 | − | 0.999977i | \(-0.497830\pi\) | ||||
0.00681637 | + | 0.999977i | \(0.497830\pi\) | |||||||
\(308\) | −92696.9 | − | 708187.i | −0.0556786 | − | 0.425374i | ||||
\(309\) | 1.75743e6 | 1.04708 | ||||||||
\(310\) | −52417.5 | + | 59725.8i | −0.0309793 | + | 0.0352986i | ||||
\(311\) | − | 316398.i | − | 0.185495i | −0.995690 | − | 0.0927476i | \(-0.970435\pi\) | ||
0.995690 | − | 0.0927476i | \(-0.0295650\pi\) | |||||||
\(312\) | 2.81127e6 | − | 4.19718e6i | 1.63499 | − | 2.44102i | ||||
\(313\) | −2.11326e6 | −1.21925 | −0.609624 | − | 0.792691i | \(-0.708680\pi\) | ||||
−0.609624 | + | 0.792691i | \(0.708680\pi\) | |||||||
\(314\) | 1.97470e6 | − | 2.25001e6i | 1.13025 | − | 1.28784i | ||||
\(315\) | 7.16253e6i | 4.06715i | ||||||||
\(316\) | 52160.3 | + | 398495.i | 0.0293848 | + | 0.224494i | ||||
\(317\) | 2.30604e6i | 1.28890i | 0.764648 | + | 0.644448i | \(0.222913\pi\) | ||||
−0.764648 | + | 0.644448i | \(0.777087\pi\) | |||||||
\(318\) | 500275. | + | 439059.i | 0.277422 | + | 0.243476i | ||||
\(319\) | −340734. | −0.187473 | ||||||||
\(320\) | −890046. | − | 2.16244e6i | −0.485890 | − | 1.18051i | ||||
\(321\) | 807228. | 0.437254 | ||||||||
\(322\) | 892719. | − | 1.01718e6i | 0.479816 | − | 0.546714i | ||||
\(323\) | 759402. | − | 1.15878e6i | 0.405010 | − | 0.618010i | ||||
\(324\) | −749855. | − | 5.72875e6i | −0.396840 | − | 3.03178i | ||||
\(325\) | − | 1.86303e6i | − | 0.978391i | ||||||
\(326\) | −766686. | − | 672872.i | −0.399552 | − | 0.350662i | ||||
\(327\) | − | 1.11955e6i | − | 0.578995i | ||||||
\(328\) | 1.60319e6 | − | 2.39354e6i | 0.822813 | − | 1.22845i | ||||
\(329\) | 3.78807e6 | 1.92942 | ||||||||
\(330\) | 1.24472e6 | + | 1.09241e6i | 0.629196 | + | 0.552206i | ||||
\(331\) | 71095.5 | 0.0356675 | 0.0178337 | − | 0.999841i | \(-0.494323\pi\) | ||||
0.0178337 | + | 0.999841i | \(0.494323\pi\) | |||||||
\(332\) | 577334. | − | 75569.1i | 0.287463 | − | 0.0376270i | ||||
\(333\) | 2.81878e6i | 1.39300i | ||||||||
\(334\) | −778337. | + | 886855.i | −0.381770 | + | 0.434997i | ||||
\(335\) | −1.96128e6 | −0.954835 | ||||||||
\(336\) | 1.24584e6 | + | 4.67746e6i | 0.602025 | + | 2.26028i | ||||
\(337\) | 143735.i | 0.0689427i | 0.999406 | + | 0.0344713i | \(0.0109747\pi\) | ||||
−0.999406 | + | 0.0344713i | \(0.989025\pi\) | |||||||
\(338\) | 1.95923e6 | − | 2.23240e6i | 0.932813 | − | 1.06287i | ||||
\(339\) | 3.61908e6i | 1.71041i | ||||||||
\(340\) | 260953. | + | 1.99363e6i | 0.122424 | + | 0.935294i | ||||
\(341\) | − | 27396.1i | − | 0.0127586i | ||||||
\(342\) | 1.48782e6 | + | 5.36854e6i | 0.687834 | + | 2.48194i | ||||
\(343\) | − | 1.26620e6i | − | 0.581122i | ||||||
\(344\) | −1.21645e6 | + | 1.81614e6i | −0.554239 | + | 0.827470i | ||||
\(345\) | 3.13811e6i | 1.41945i | ||||||||
\(346\) | 349066. | + | 306354.i | 0.156754 | + | 0.137573i | ||||
\(347\) | 915553.i | 0.408187i | 0.978951 | + | 0.204094i | \(0.0654247\pi\) | ||||
−0.978951 | + | 0.204094i | \(0.934575\pi\) | |||||||
\(348\) | 2.28972e6 | − | 299709.i | 1.01353 | − | 0.132664i | ||||
\(349\) | −666577. | −0.292946 | −0.146473 | − | 0.989215i | \(-0.546792\pi\) | ||||
−0.146473 | + | 0.989215i | \(0.546792\pi\) | |||||||
\(350\) | 1.34172e6 | + | 1.17754e6i | 0.585451 | + | 0.513813i | ||||
\(351\) | − | 1.06840e7i | − | 4.62876i | ||||||
\(352\) | 722386. | + | 357918.i | 0.310751 | + | 0.153967i | ||||
\(353\) | −1.79638e6 | −0.767293 | −0.383647 | − | 0.923480i | \(-0.625332\pi\) | ||||
−0.383647 | + | 0.923480i | \(0.625332\pi\) | |||||||
\(354\) | 3.18941e6 | − | 3.63409e6i | 1.35270 | − | 1.54130i | ||||
\(355\) | 477304. | 0.201013 | ||||||||
\(356\) | 370098. | − | 48443.3i | 0.154772 | − | 0.0202586i | ||||
\(357\) | − | 4.16198e6i | − | 1.72834i | ||||||
\(358\) | −2.00478e6 | + | 2.28430e6i | −0.826723 | + | 0.941987i | ||||
\(359\) | 87104.2i | 0.0356700i | 0.999841 | + | 0.0178350i | \(0.00567736\pi\) | ||||
−0.999841 | + | 0.0178350i | \(0.994323\pi\) | |||||||
\(360\) | −6.71722e6 | − | 4.49919e6i | −2.73170 | − | 1.82969i | ||||
\(361\) | −988242. | − | 2.27034e6i | −0.399112 | − | 0.916902i | ||||
\(362\) | −1.98157e6 | − | 1.73910e6i | −0.794764 | − | 0.697514i | ||||
\(363\) | 4.17621e6 | 1.66347 | ||||||||
\(364\) | 630583. | + | 4.81753e6i | 0.249453 | + | 1.90577i | ||||
\(365\) | 5.80693e6 | 2.28147 | ||||||||
\(366\) | −1.24690e6 | + | 1.42074e6i | −0.486551 | + | 0.554387i | ||||
\(367\) | − | 2.34683e6i | − | 0.909530i | −0.890612 | − | 0.454765i | \(-0.849723\pi\) | ||
0.890612 | − | 0.454765i | \(-0.150277\pi\) | |||||||
\(368\) | 393177. | + | 1.47617e6i | 0.151345 | + | 0.568220i | ||||
\(369\) | − | 9.96003e6i | − | 3.80798i | ||||||
\(370\) | 1.36657e6 | + | 1.19935e6i | 0.518953 | + | 0.455452i | ||||
\(371\) | −640180. | −0.241472 | ||||||||
\(372\) | 24097.6 | + | 184101.i | 0.00902853 | + | 0.0689763i | ||||
\(373\) | − | 3.26142e6i | − | 1.21377i | −0.794791 | − | 0.606883i | \(-0.792420\pi\) | ||
0.794791 | − | 0.606883i | \(-0.207580\pi\) | |||||||
\(374\) | −520989. | − | 457239.i | −0.192597 | − | 0.169030i | ||||
\(375\) | 2.43422e6 | 0.893883 | ||||||||
\(376\) | −2.37950e6 | + | 3.55256e6i | −0.867992 | + | 1.29590i | ||||
\(377\) | 2.31789e6 | 0.839922 | ||||||||
\(378\) | 7.69436e6 | + | 6.75285e6i | 2.76976 | + | 2.43085i | ||||
\(379\) | 2.17009e6 | 0.776032 | 0.388016 | − | 0.921653i | \(-0.373160\pi\) | ||||
0.388016 | + | 0.921653i | \(0.373160\pi\) | |||||||
\(380\) | 3.23576e6 | + | 1.56293e6i | 1.14952 | + | 0.555241i | ||||
\(381\) | 9.86759e6 | 3.48256 | ||||||||
\(382\) | −1.15570e6 | − | 1.01429e6i | −0.405216 | − | 0.355633i | ||||
\(383\) | −4.92352e6 | −1.71506 | −0.857530 | − | 0.514435i | \(-0.828002\pi\) | ||||
−0.857530 | + | 0.514435i | \(0.828002\pi\) | |||||||
\(384\) | −5.16924e6 | − | 1.76979e6i | −1.78895 | − | 0.612484i | ||||
\(385\) | −1.59281e6 | −0.547662 | ||||||||
\(386\) | −1.32634e6 | − | 1.16405e6i | −0.453093 | − | 0.397651i | ||||
\(387\) | 7.55732e6i | 2.56502i | ||||||||
\(388\) | −986936. | + | 129183.i | −0.332820 | + | 0.0435639i | ||||
\(389\) | −2.24015e6 | −0.750590 | −0.375295 | − | 0.926905i | \(-0.622459\pi\) | ||||
−0.375295 | + | 0.926905i | \(0.622459\pi\) | |||||||
\(390\) | −8.46736e6 | − | 7.43126e6i | −2.81894 | − | 2.47401i | ||||
\(391\) | − | 1.31349e6i | − | 0.434494i | ||||||
\(392\) | −1.34028e6 | − | 897721.i | −0.440536 | − | 0.295071i | ||||
\(393\) | 4.09634e6i | 1.33787i | ||||||||
\(394\) | 1.34292e6 | − | 1.53016e6i | 0.435824 | − | 0.496588i | ||||
\(395\) | 896271. | 0.289033 | ||||||||
\(396\) | 2.76370e6 | − | 361749.i | 0.885630 | − | 0.115923i | ||||
\(397\) | −4.56336e6 | −1.45314 | −0.726571 | − | 0.687091i | \(-0.758887\pi\) | ||||
−0.726571 | + | 0.687091i | \(0.758887\pi\) | |||||||
\(398\) | 870056. | + | 763593.i | 0.275321 | + | 0.241632i | ||||
\(399\) | −6.22141e6 | − | 4.07717e6i | −1.95639 | − | 1.28211i | ||||
\(400\) | −1.94714e6 | + | 518620.i | −0.608481 | + | 0.162069i | ||||
\(401\) | − | 1.38466e6i | − | 0.430014i | −0.976612 | − | 0.215007i | \(-0.931023\pi\) | ||
0.976612 | − | 0.215007i | \(-0.0689775\pi\) | |||||||
\(402\) | −3.02278e6 | + | 3.44422e6i | −0.932912 | + | 1.06298i | ||||
\(403\) | 186366.i | 0.0571615i | ||||||||
\(404\) | 120106. | + | 917590.i | 0.0366111 | + | 0.279702i | ||||
\(405\) | −1.28848e7 | −3.90337 | ||||||||
\(406\) | −1.46503e6 | + | 1.66929e6i | −0.441095 | + | 0.502594i | ||||
\(407\) | −626844. | −0.187574 | ||||||||
\(408\) | 3.90322e6 | + | 2.61437e6i | 1.16084 | + | 0.777530i | ||||
\(409\) | 42755.9i | 0.0126383i | 0.999980 | + | 0.00631913i | \(0.00201146\pi\) | ||||
−0.999980 | + | 0.00631913i | \(0.997989\pi\) | |||||||
\(410\) | −4.82871e6 | − | 4.23786e6i | −1.41864 | − | 1.24505i | ||||
\(411\) | 2.86165e6 | 0.835625 | ||||||||
\(412\) | −247620. | − | 1.89177e6i | −0.0718691 | − | 0.549067i | ||||
\(413\) | 4.65040e6i | 1.34157i | ||||||||
\(414\) | 3.96956e6 | + | 3.48383e6i | 1.13826 | + | 0.998979i | ||||
\(415\) | − | 1.29851e6i | − | 0.370104i | ||||||
\(416\) | −4.91412e6 | − | 2.43479e6i | −1.39224 | − | 0.689807i | ||||
\(417\) | 7.90726e6i | 2.22683i | ||||||||
\(418\) | −1.19386e6 | + | 330862.i | −0.334206 | + | 0.0926204i | ||||
\(419\) | − | 3.54141e6i | − | 0.985464i | −0.870181 | − | 0.492732i | \(-0.835998\pi\) | ||
0.870181 | − | 0.492732i | \(-0.164002\pi\) | |||||||
\(420\) | 1.07037e7 | − | 1.40104e6i | 2.96080 | − | 0.387549i | ||||
\(421\) | − | 2.44805e6i | − | 0.673156i | −0.941656 | − | 0.336578i | \(-0.890730\pi\) | ||
0.941656 | − | 0.336578i | \(-0.109270\pi\) | |||||||
\(422\) | −2.45478e6 | + | 2.79704e6i | −0.671015 | + | 0.764570i | ||||
\(423\) | 1.47829e7i | 4.01707i | ||||||||
\(424\) | 402134. | − | 600379.i | 0.108631 | − | 0.162185i | ||||
\(425\) | 1.73255e6 | 0.465279 | ||||||||
\(426\) | 735632. | − | 838196.i | 0.196398 | − | 0.223780i | ||||
\(427\) | − | 1.81807e6i | − | 0.482548i | ||||||
\(428\) | −113738. | − | 868934.i | −0.0300120 | − | 0.229286i | ||||
\(429\) | 3.88397e6 | 1.01890 | ||||||||
\(430\) | 3.66386e6 | + | 3.21553e6i | 0.955580 | + | 0.838653i | ||||
\(431\) | 635887. | 0.164887 | 0.0824436 | − | 0.996596i | \(-0.473728\pi\) | ||||
0.0824436 | + | 0.996596i | \(0.473728\pi\) | |||||||
\(432\) | −1.11663e7 | + | 2.97414e6i | −2.87872 | + | 0.766746i | ||||
\(433\) | − | 6.62132e6i | − | 1.69717i | −0.529060 | − | 0.848584i | \(-0.677455\pi\) | ||
0.529060 | − | 0.848584i | \(-0.322545\pi\) | |||||||
\(434\) | −134217. | − | 117793.i | −0.0342044 | − | 0.0300190i | ||||
\(435\) | − | 5.14991e6i | − | 1.30490i | ||||||
\(436\) | −1.20513e6 | + | 157744.i | −0.303612 | + | 0.0397407i | ||||
\(437\) | −1.96342e6 | − | 1.28672e6i | −0.491825 | − | 0.322315i | ||||
\(438\) | 8.94978e6 | − | 1.01976e7i | 2.22909 | − | 2.53987i | ||||
\(439\) | −884092. | −0.218946 | −0.109473 | − | 0.993990i | \(-0.534916\pi\) | ||||
−0.109473 | + | 0.993990i | \(0.534916\pi\) | |||||||
\(440\) | 1.00054e6 | − | 1.49379e6i | 0.246378 | − | 0.367838i | ||||
\(441\) | −5.57720e6 | −1.36559 | ||||||||
\(442\) | 3.54409e6 | + | 3.11043e6i | 0.862878 | + | 0.757294i | ||||
\(443\) | 2.74688e6i | 0.665013i | 0.943101 | + | 0.332507i | \(0.107894\pi\) | ||||
−0.943101 | + | 0.332507i | \(0.892106\pi\) | |||||||
\(444\) | 4.21238e6 | − | 551372.i | 1.01408 | − | 0.132736i | ||||
\(445\) | − | 832403.i | − | 0.199266i | ||||||
\(446\) | −2.91045e6 | + | 3.31623e6i | −0.692823 | + | 0.789419i | ||||
\(447\) | 1.21219e7 | 2.86947 | ||||||||
\(448\) | 4.85948e6 | − | 2.00013e6i | 1.14392 | − | 0.470828i | ||||
\(449\) | 8.05140e6i | 1.88476i | 0.334546 | + | 0.942379i | \(0.391417\pi\) | ||||
−0.334546 | + | 0.942379i | \(0.608583\pi\) | |||||||
\(450\) | −4.59535e6 | + | 5.23605e6i | −1.06976 | + | 1.21891i | ||||
\(451\) | 2.21493e6 | 0.512764 | ||||||||
\(452\) | 3.89573e6 | − | 509925.i | 0.896898 | − | 0.117398i | ||||
\(453\) | −3.50016e6 | −0.801387 | ||||||||
\(454\) | 2.50108e6 | − | 2.84978e6i | 0.569491 | − | 0.648892i | ||||
\(455\) | 1.08353e7 | 2.45365 | ||||||||
\(456\) | 7.73171e6 | − | 3.27351e6i | 1.74126 | − | 0.737228i | ||||
\(457\) | −1.14844e6 | −0.257228 | −0.128614 | − | 0.991695i | \(-0.541053\pi\) | ||||
−0.128614 | + | 0.991695i | \(0.541053\pi\) | |||||||
\(458\) | 408399. | − | 465339.i | 0.0909748 | − | 0.103659i | ||||
\(459\) | 9.93568e6 | 2.20123 | ||||||||
\(460\) | 3.37799e6 | − | 442156.i | 0.744327 | − | 0.0974274i | ||||
\(461\) | −5.96110e6 | −1.30639 | −0.653197 | − | 0.757188i | \(-0.726573\pi\) | ||||
−0.653197 | + | 0.757188i | \(0.726573\pi\) | |||||||
\(462\) | −2.45488e6 | + | 2.79715e6i | −0.535088 | + | 0.609692i | ||||
\(463\) | − | 6.44235e6i | − | 1.39666i | −0.715775 | − | 0.698331i | \(-0.753926\pi\) | ||
0.715775 | − | 0.698331i | \(-0.246074\pi\) | |||||||
\(464\) | −645239. | − | 2.42252e6i | −0.139132 | − | 0.522364i | ||||
\(465\) | 414070. | 0.0888059 | ||||||||
\(466\) | −3.04599e6 | + | 3.47067e6i | −0.649775 | + | 0.740369i | ||||
\(467\) | − | 4.90280e6i | − | 1.04028i | −0.854080 | − | 0.520142i | \(-0.825879\pi\) | ||
0.854080 | − | 0.520142i | \(-0.174121\pi\) | |||||||
\(468\) | −1.88004e7 | + | 2.46085e6i | −3.96783 | + | 0.519362i | ||||
\(469\) | − | 4.40743e6i | − | 0.925237i | ||||||
\(470\) | 7.16690e6 | + | 6.28993e6i | 1.49653 | + | 1.31341i | ||||
\(471\) | −1.55990e7 | −3.24000 | ||||||||
\(472\) | −4.36127e6 | − | 2.92118e6i | −0.901069 | − | 0.603536i | ||||
\(473\) | −1.68061e6 | −0.345393 | ||||||||
\(474\) | 1.38135e6 | − | 1.57395e6i | 0.282396 | − | 0.321769i | ||||
\(475\) | 1.69725e6 | − | 2.58985e6i | 0.345153 | − | 0.526673i | ||||
\(476\) | −4.48012e6 | + | 586418.i | −0.906301 | + | 0.118629i | ||||
\(477\) | − | 2.49830e6i | − | 0.502747i | ||||||
\(478\) | −6.39390e6 | − | 5.61152e6i | −1.27996 | − | 1.12334i | ||||
\(479\) | − | 3.35404e6i | − | 0.667928i | −0.942586 | − | 0.333964i | \(-0.891614\pi\) | ||
0.942586 | − | 0.333964i | \(-0.108386\pi\) | |||||||
\(480\) | −5.40965e6 | + | 1.09183e7i | −1.07168 | + | 2.16297i | ||||
\(481\) | 4.26419e6 | 0.840377 | ||||||||
\(482\) | 6.85463e6 | + | 6.01587e6i | 1.34390 | + | 1.17945i | ||||
\(483\) | −7.05200e6 | −1.37545 | ||||||||
\(484\) | −588424. | − | 4.49545e6i | −0.114177 | − | 0.872287i | ||||
\(485\) | 2.21976e6i | 0.428501i | ||||||||
\(486\) | −9.62609e6 | + | 1.09682e7i | −1.84867 | + | 2.10642i | ||||
\(487\) | 95452.1 | 0.0182374 | 0.00911871 | − | 0.999958i | \(-0.497097\pi\) | ||||
0.00911871 | + | 0.999958i | \(0.497097\pi\) | |||||||
\(488\) | 1.70503e6 | + | 1.14203e6i | 0.324103 | + | 0.217084i | ||||
\(489\) | 5.31533e6i | 1.00521i | ||||||||
\(490\) | −2.37302e6 | + | 2.70388e6i | −0.446490 | + | 0.508741i | ||||
\(491\) | 6.06237e6i | 1.13485i | 0.823425 | + | 0.567425i | \(0.192060\pi\) | ||||
−0.823425 | + | 0.567425i | \(0.807940\pi\) | |||||||
\(492\) | −1.48842e7 | + | 1.94825e6i | −2.77213 | + | 0.362854i | ||||
\(493\) | 2.15555e6i | 0.399430i | ||||||||
\(494\) | 8.12141e6 | − | 2.25074e6i | 1.49732 | − | 0.414961i | ||||
\(495\) | − | 6.21595e6i | − | 1.14024i | ||||||
\(496\) | 194779. | − | 51879.4i | 0.0355499 | − | 0.00946871i | ||||
\(497\) | 1.07260e6i | 0.194782i | ||||||||
\(498\) | −2.28032e6 | − | 2.00129e6i | −0.412023 | − | 0.361607i | ||||
\(499\) | − | 550506.i | − | 0.0989717i | −0.998775 | − | 0.0494858i | \(-0.984242\pi\) | ||
0.998775 | − | 0.0494858i | \(-0.0157583\pi\) | |||||||
\(500\) | −342978. | − | 2.62029e6i | −0.0613539 | − | 0.468732i | ||||
\(501\) | 6.14844e6 | 1.09439 | ||||||||
\(502\) | 4.17853e6 | + | 3.66724e6i | 0.740056 | + | 0.649501i | ||||
\(503\) | 6.21652e6i | 1.09554i | 0.836630 | + | 0.547769i | \(0.184523\pi\) | ||||
−0.836630 | + | 0.547769i | \(0.815477\pi\) | |||||||
\(504\) | 1.01106e7 | − | 1.50950e7i | 1.77297 | − | 2.64702i | ||||
\(505\) | 2.06379e6 | 0.360112 | ||||||||
\(506\) | −774740. | + | 882757.i | −0.134518 | + | 0.153273i | ||||
\(507\) | −1.54769e7 | −2.67402 | ||||||||
\(508\) | −1.39033e6 | − | 1.06219e7i | −0.239034 | − | 1.82617i | ||||
\(509\) | 3.85254e6i | 0.659102i | 0.944138 | + | 0.329551i | \(0.106897\pi\) | ||||
−0.944138 | + | 0.329551i | \(0.893103\pi\) | |||||||
\(510\) | 6.91079e6 | − | 7.87432e6i | 1.17653 | − | 1.34056i | ||||
\(511\) | 1.30494e7i | 2.21075i | ||||||||
\(512\) | −1.17674e6 | + | 5.81375e6i | −0.198383 | + | 0.980125i | ||||
\(513\) | 9.73323e6 | − | 1.48521e7i | 1.63292 | − | 2.49169i | ||||
\(514\) | 7.06628e6 | + | 6.20163e6i | 1.17973 | + | 1.03538i | ||||
\(515\) | −4.25486e6 | −0.706915 | ||||||||
\(516\) | 1.12936e7 | − | 1.47826e6i | 1.86728 | − | 0.244415i | ||||
\(517\) | −3.28745e6 | −0.540919 | ||||||||
\(518\) | −2.69520e6 | + | 3.07098e6i | −0.441334 | + | 0.502866i | ||||
\(519\) | − | 2.42003e6i | − | 0.394369i | ||||||
\(520\) | −6.80628e6 | + | 1.01617e7i | −1.10383 | + | 1.64800i | ||||
\(521\) | 1.76576e6i | 0.284995i | 0.989795 | + | 0.142498i | \(0.0455134\pi\) | ||||
−0.989795 | + | 0.142498i | \(0.954487\pi\) | |||||||
\(522\) | −6.51441e6 | − | 5.71728e6i | −1.04640 | − | 0.918361i | ||||
\(523\) | 5.46493e6 | 0.873636 | 0.436818 | − | 0.899550i | \(-0.356105\pi\) | ||||
0.436818 | + | 0.899550i | \(0.356105\pi\) | |||||||
\(524\) | 4.40947e6 | − | 577170.i | 0.701549 | − | 0.0918280i | ||||
\(525\) | − | 9.30193e6i | − | 1.47291i | ||||||
\(526\) | −6.89315e6 | − | 6.04968e6i | −1.08631 | − | 0.953385i | ||||
\(527\) | −173313. | −0.0271835 | ||||||||
\(528\) | −1.08120e6 | − | 4.05930e6i | −0.168779 | − | 0.633675i | ||||
\(529\) | 4.21079e6 | 0.654221 | ||||||||
\(530\) | −1.21120e6 | − | 1.06299e6i | −0.187295 | − | 0.164377i | ||||
\(531\) | −1.81482e7 | −2.79316 | ||||||||
\(532\) | −3.51225e6 | + | 7.27145e6i | −0.538029 | + | 1.11389i | ||||
\(533\) | −1.50673e7 | −2.29730 | ||||||||
\(534\) | −1.46179e6 | − | 1.28292e6i | −0.221836 | − | 0.194691i | ||||
\(535\) | −1.95436e6 | −0.295202 | ||||||||
\(536\) | 4.13341e6 | + | 2.76855e6i | 0.621436 | + | 0.416237i | ||||
\(537\) | 1.58367e7 | 2.36990 | ||||||||
\(538\) | −6.32062e6 | − | 5.54721e6i | −0.941465 | − | 0.826264i | ||||
\(539\) | − | 1.24026e6i | − | 0.183883i | ||||||
\(540\) | 3.34463e6 | + | 2.55523e7i | 0.493587 | + | 3.77091i | ||||
\(541\) | 1.11044e7 | 1.63118 | 0.815588 | − | 0.578633i | \(-0.196414\pi\) | ||||
0.815588 | + | 0.578633i | \(0.196414\pi\) | |||||||
\(542\) | 2.70080e6 | + | 2.37032e6i | 0.394907 | + | 0.346585i | ||||
\(543\) | 1.37380e7i | 1.99950i | ||||||||
\(544\) | 2.26426e6 | − | 4.56995e6i | 0.328042 | − | 0.662086i | ||||
\(545\) | 2.71051e6i | 0.390895i | ||||||||
\(546\) | 1.66996e7 | − | 1.90280e7i | 2.39732 | − | 2.73156i | ||||
\(547\) | 7.93792e6 | 1.13433 | 0.567164 | − | 0.823605i | \(-0.308041\pi\) | ||||
0.567164 | + | 0.823605i | \(0.308041\pi\) | |||||||
\(548\) | −403203. | − | 3.08040e6i | −0.0573552 | − | 0.438183i | ||||
\(549\) | 7.09500e6 | 1.00467 | ||||||||
\(550\) | −1.16440e6 | − | 1.02192e6i | −0.164133 | − | 0.144049i | ||||
\(551\) | 3.22216e6 | + | 2.11163e6i | 0.452134 | + | 0.296304i | ||||
\(552\) | 4.42976e6 | − | 6.61357e6i | 0.618775 | − | 0.923821i | ||||
\(553\) | 2.01411e6i | 0.280073i | ||||||||
\(554\) | −6.94296e6 | + | 7.91097e6i | −0.961104 | + | 1.09510i | ||||
\(555\) | − | 9.47424e6i | − | 1.30561i | ||||||
\(556\) | 8.51171e6 | − | 1.11413e6i | 1.16770 | − | 0.152844i | ||||
\(557\) | −2.38399e6 | −0.325586 | −0.162793 | − | 0.986660i | \(-0.552050\pi\) | ||||
−0.162793 | + | 0.986660i | \(0.552050\pi\) | |||||||
\(558\) | 459689. | − | 523780.i | 0.0624998 | − | 0.0712137i | ||||
\(559\) | 1.14325e7 | 1.54744 | ||||||||
\(560\) | −3.01627e6 | − | 1.13245e7i | −0.406444 | − | 1.52598i | ||||
\(561\) | 3.61194e6i | 0.484544i | ||||||||
\(562\) | 6.90938e6 | + | 6.06393e6i | 0.922780 | + | 0.809866i | ||||
\(563\) | −2.57932e6 | −0.342952 | −0.171476 | − | 0.985188i | \(-0.554854\pi\) | ||||
−0.171476 | + | 0.985188i | \(0.554854\pi\) | |||||||
\(564\) | 2.20916e7 | − | 2.89164e6i | 2.92435 | − | 0.382777i | ||||
\(565\) | − | 8.76206e6i | − | 1.15474i | ||||||
\(566\) | −8.23941e6 | − | 7.23121e6i | −1.08107 | − | 0.948789i | ||||
\(567\) | − | 2.89549e7i | − | 3.78237i | ||||||
\(568\) | −1.00592e6 | − | 673763.i | −0.130825 | − | 0.0876267i | ||||
\(569\) | − | 1.16131e7i | − | 1.50373i | −0.659319 | − | 0.751863i | \(-0.729155\pi\) | ||
0.659319 | − | 0.751863i | \(-0.270845\pi\) | |||||||
\(570\) | −5.00072e6 | − | 1.80443e7i | −0.644681 | − | 2.32623i | ||||
\(571\) | 2.53748e6i | 0.325696i | 0.986651 | + | 0.162848i | \(0.0520680\pi\) | ||||
−0.986651 | + | 0.162848i | \(0.947932\pi\) | |||||||
\(572\) | −547247. | − | 4.18086e6i | −0.0699348 | − | 0.534289i | ||||
\(573\) | 8.01232e6i | 1.01946i | ||||||||
\(574\) | 9.52337e6 | − | 1.08512e7i | 1.20646 | − | 1.37466i | ||||
\(575\) | − | 2.93561e6i | − | 0.370279i | ||||||
\(576\) | 7.80549e6 | + | 1.89641e7i | 0.980266 | + | 2.38164i | ||||
\(577\) | −7.21334e6 | −0.901980 | −0.450990 | − | 0.892529i | \(-0.648929\pi\) | ||||
−0.450990 | + | 0.892529i | \(0.648929\pi\) | |||||||
\(578\) | 2.40549e6 | − | 2.74087e6i | 0.299491 | − | 0.341247i | ||||
\(579\) | 9.19534e6i | 1.13991i | ||||||||
\(580\) | −5.54358e6 | + | 725618.i | −0.684259 | + | 0.0895649i | ||||
\(581\) | 2.91802e6 | 0.358632 | ||||||||
\(582\) | 3.89813e6 | + | 3.42115e6i | 0.477034 | + | 0.418663i | ||||
\(583\) | 555576. | 0.0676974 | ||||||||
\(584\) | −1.22381e7 | − | 8.19708e6i | −1.48485 | − | 0.994551i | ||||
\(585\) | 4.22848e7i | 5.10852i | ||||||||
\(586\) | −2.06286e6 | − | 1.81044e6i | −0.248156 | − | 0.217791i | ||||
\(587\) | 9.05469e6i | 1.08462i | 0.840178 | + | 0.542311i | \(0.182450\pi\) | ||||
−0.840178 | + | 0.542311i | \(0.817550\pi\) | |||||||
\(588\) | 1.09094e6 | + | 8.33455e6i | 0.130124 | + | 0.994120i | ||||
\(589\) | −169782. | + | 259072.i | −0.0201652 | + | 0.0307704i | ||||
\(590\) | −7.72180e6 | + | 8.79839e6i | −0.913247 | + | 1.04058i | ||||
\(591\) | −1.06084e7 | −1.24934 | ||||||||
\(592\) | −1.18704e6 | − | 4.45669e6i | −0.139207 | − | 0.522647i | ||||
\(593\) | 2.39031e6 | 0.279137 | 0.139569 | − | 0.990212i | \(-0.455428\pi\) | ||||
0.139569 | + | 0.990212i | \(0.455428\pi\) | |||||||
\(594\) | −6.67749e6 | − | 5.86041e6i | −0.776511 | − | 0.681494i | ||||
\(595\) | 1.00764e7i | 1.16685i | ||||||||
\(596\) | −1.70796e6 | − | 1.30485e7i | −0.196953 | − | 1.50468i | ||||
\(597\) | − | 6.03198e6i | − | 0.692666i | ||||||
\(598\) | 5.27027e6 | − | 6.00507e6i | 0.602670 | − | 0.686697i | ||||
\(599\) | −8.79435e6 | −1.00147 | −0.500734 | − | 0.865601i | \(-0.666936\pi\) | ||||
−0.500734 | + | 0.865601i | \(0.666936\pi\) | |||||||
\(600\) | 8.72362e6 | + | 5.84307e6i | 0.989278 | + | 0.662618i | ||||
\(601\) | 1.71848e7i | 1.94070i | 0.241707 | + | 0.970349i | \(0.422293\pi\) | ||||
−0.241707 | + | 0.970349i | \(0.577707\pi\) | |||||||
\(602\) | −7.22600e6 | + | 8.23347e6i | −0.812656 | + | 0.925959i | ||||
\(603\) | 1.72000e7 | 1.92635 | ||||||||
\(604\) | 493169. | + | 3.76772e6i | 0.0550051 | + | 0.420229i | ||||
\(605\) | −1.01109e7 | −1.12306 | ||||||||
\(606\) | 3.18076e6 | − | 3.62423e6i | 0.351844 | − | 0.400899i | ||||
\(607\) | −1.13083e7 | −1.24573 | −0.622865 | − | 0.782329i | \(-0.714032\pi\) | ||||
−0.622865 | + | 0.782329i | \(0.714032\pi\) | |||||||
\(608\) | −4.61313e6 | − | 7.86150e6i | −0.506101 | − | 0.862474i | ||||
\(609\) | 1.15730e7 | 1.26445 | ||||||||
\(610\) | 3.01883e6 | − | 3.43972e6i | 0.328484 | − | 0.374282i | ||||
\(611\) | 2.23633e7 | 2.42344 | ||||||||
\(612\) | −2.28850e6 | − | 1.74837e7i | −0.246986 | − | 1.88692i | ||||
\(613\) | −1.08511e7 | −1.16634 | −0.583169 | − | 0.812351i | \(-0.698187\pi\) | ||||
−0.583169 | + | 0.812351i | \(0.698187\pi\) | |||||||
\(614\) | −84004.4 | + | 95716.6i | −0.00899251 | + | 0.0102463i | ||||
\(615\) | 3.34768e7i | 3.56908i | ||||||||
\(616\) | 3.35686e6 | + | 2.24842e6i | 0.356436 | + | 0.238740i | ||||
\(617\) | −7.66136e6 | −0.810202 | −0.405101 | − | 0.914272i | \(-0.632764\pi\) | ||||
−0.405101 | + | 0.914272i | \(0.632764\pi\) | |||||||
\(618\) | −6.55769e6 | + | 7.47198e6i | −0.690684 | + | 0.786982i | ||||
\(619\) | 7.55698e6i | 0.792723i | 0.918095 | + | 0.396362i | \(0.129727\pi\) | ||||
−0.918095 | + | 0.396362i | \(0.870273\pi\) | |||||||
\(620\) | −58342.1 | − | 445723.i | −0.00609541 | − | 0.0465678i | ||||
\(621\) | − | 1.68349e7i | − | 1.75179i | ||||||
\(622\) | 1.34521e6 | + | 1.18061e6i | 0.139417 | + | 0.122357i | ||||
\(623\) | 1.87059e6 | 0.193089 | ||||||||
\(624\) | 7.35497e6 | + | 2.76139e7i | 0.756170 | + | 2.83901i | ||||
\(625\) | −1.20428e7 | −1.23318 | ||||||||
\(626\) | 7.88544e6 | − | 8.98485e6i | 0.804248 | − | 0.916379i | ||||
\(627\) | 5.39921e6 | + | 3.53835e6i | 0.548480 | + | 0.359444i | ||||
\(628\) | 2.19789e6 | + | 1.67915e7i | 0.222386 | + | 1.69898i | ||||
\(629\) | 3.96554e6i | 0.399646i | ||||||||
\(630\) | −3.04526e7 | − | 2.67263e7i | −3.05684 | − | 2.68280i | ||||
\(631\) | − | 1.23444e7i | − | 1.23424i | −0.786871 | − | 0.617118i | \(-0.788300\pi\) | ||
0.786871 | − | 0.617118i | \(-0.211700\pi\) | |||||||
\(632\) | −1.88889e6 | − | 1.26518e6i | −0.188111 | − | 0.125997i | ||||
\(633\) | 1.93915e7 | 1.92354 | ||||||||
\(634\) | −9.80448e6 | − | 8.60477e6i | −0.968727 | − | 0.850190i | ||||
\(635\) | −2.38901e7 | −2.35117 | ||||||||
\(636\) | −3.73346e6 | + | 488685.i | −0.365989 | + | 0.0479056i | ||||
\(637\) | 8.43707e6i | 0.823840i | ||||||||
\(638\) | 1.27142e6 | − | 1.44868e6i | 0.123662 | − | 0.140903i | ||||
\(639\) | −4.18584e6 | −0.405537 | ||||||||
\(640\) | 1.25151e7 | + | 4.28479e6i | 1.20777 | + | 0.413504i | ||||
\(641\) | − | 1.28061e7i | − | 1.23104i | −0.788120 | − | 0.615522i | \(-0.788945\pi\) | ||
0.788120 | − | 0.615522i | \(-0.211055\pi\) | |||||||
\(642\) | −3.01210e6 | + | 3.43206e6i | −0.288424 | + | 0.328637i | ||||
\(643\) | − | 1.13002e7i | − | 1.07785i | −0.842354 | − | 0.538925i | \(-0.818831\pi\) | ||
0.842354 | − | 0.538925i | \(-0.181169\pi\) | |||||||
\(644\) | 993620. | + | 7.59107e6i | 0.0944073 | + | 0.721254i | ||||
\(645\) | − | 2.54010e7i | − | 2.40410i | ||||||
\(646\) | 2.09310e6 | + | 7.55261e6i | 0.197337 | + | 0.712058i | ||||
\(647\) | − | 3.65875e6i | − | 0.343615i | −0.985131 | − | 0.171807i | \(-0.945039\pi\) | ||
0.985131 | − | 0.171807i | \(-0.0549607\pi\) | |||||||
\(648\) | 2.71547e7 | + | 1.81882e7i | 2.54043 | + | 1.70158i | ||||
\(649\) | − | 4.03581e6i | − | 0.376114i | ||||||
\(650\) | 7.92098e6 | + | 6.95174e6i | 0.735352 | + | 0.645372i | ||||
\(651\) | 930505.i | 0.0860531i | ||||||||
\(652\) | 5.72164e6 | − | 748924.i | 0.527110 | − | 0.0689952i | ||||
\(653\) | −5.13543e6 | −0.471296 | −0.235648 | − | 0.971838i | \(-0.575721\pi\) | ||||
−0.235648 | + | 0.971838i | \(0.575721\pi\) | |||||||
\(654\) | 4.75995e6 | + | 4.17751e6i | 0.435169 | + | 0.381920i | ||||
\(655\) | − | 9.91752e6i | − | 0.903233i | ||||||
\(656\) | 4.19435e6 | + | 1.57475e7i | 0.380544 | + | 1.42874i | ||||
\(657\) | −5.09254e7 | −4.60278 | ||||||||
\(658\) | −1.41348e7 | + | 1.61056e7i | −1.27270 | + | 1.45014i | ||||
\(659\) | −1.11813e7 | −1.00295 | −0.501474 | − | 0.865173i | \(-0.667209\pi\) | ||||
−0.501474 | + | 0.865173i | \(0.667209\pi\) | |||||||
\(660\) | −9.28910e6 | + | 1.21588e6i | −0.830069 | + | 0.108650i | ||||
\(661\) | 7.67629e6i | 0.683357i | 0.939817 | + | 0.341679i | \(0.110995\pi\) | ||||
−0.939817 | + | 0.341679i | \(0.889005\pi\) | |||||||
\(662\) | −265286. | + | 302274.i | −0.0235272 | + | 0.0268074i | ||||
\(663\) | − | 2.45707e7i | − | 2.17087i | ||||||
\(664\) | −1.83298e6 | + | 2.73661e6i | −0.161338 | + | 0.240875i | ||||
\(665\) | 1.50625e7 | + | 9.87112e6i | 1.32082 | + | 0.865590i | ||||
\(666\) | −1.19845e7 | − | 1.05180e7i | −1.04697 | − | 0.918858i | ||||
\(667\) | 3.65233e6 | 0.317875 | ||||||||
\(668\) | −866309. | − | 6.61844e6i | −0.0751159 | − | 0.573871i | ||||
\(669\) | 2.29910e7 | 1.98606 | ||||||||
\(670\) | 7.31835e6 | − | 8.33870e6i | 0.629834 | − | 0.717648i | ||||
\(671\) | 1.57780e6i | 0.135283i | ||||||||
\(672\) | −2.45357e7 | − | 1.21566e7i | −2.09592 | − | 1.03846i | ||||
\(673\) | 5.33165e6i | 0.453758i | 0.973923 | + | 0.226879i | \(0.0728521\pi\) | ||||
−0.973923 | + | 0.226879i | \(0.927148\pi\) | |||||||
\(674\) | −611112. | − | 536335.i | −0.0518169 | − | 0.0454764i | ||||
\(675\) | 2.22060e7 | 1.87591 | ||||||||
\(676\) | 2.18068e6 | + | 1.66600e7i | 0.183538 | + | 1.40219i | ||||
\(677\) | 1.23712e7i | 1.03739i | 0.854960 | + | 0.518695i | \(0.173582\pi\) | ||||
−0.854960 | + | 0.518695i | \(0.826418\pi\) | |||||||
\(678\) | −1.53871e7 | − | 1.35043e7i | −1.28553 | − | 1.12823i | ||||
\(679\) | −4.98828e6 | −0.415218 | ||||||||
\(680\) | −9.44997e6 | − | 6.32958e6i | −0.783715 | − | 0.524932i | ||||
\(681\) | −1.97572e7 | −1.63251 | ||||||||
\(682\) | 116479. | + | 102226.i | 0.00958929 | + | 0.00841592i | ||||
\(683\) | −1.13115e7 | −0.927827 | −0.463914 | − | 0.885880i | \(-0.653555\pi\) | ||||
−0.463914 | + | 0.885880i | \(0.653555\pi\) | |||||||
\(684\) | −2.83768e7 | − | 1.37065e7i | −2.31912 | − | 1.12018i | ||||
\(685\) | −6.92825e6 | −0.564153 | ||||||||
\(686\) | 5.38345e6 | + | 4.72472e6i | 0.436768 | + | 0.383323i | ||||
\(687\) | −3.22613e6 | −0.260790 | ||||||||
\(688\) | −3.18252e6 | − | 1.19487e7i | −0.256331 | − | 0.962383i | ||||
\(689\) | −3.77938e6 | −0.303300 | ||||||||
\(690\) | −1.33422e7 | − | 1.17096e7i | −1.06685 | − | 0.936306i | ||||
\(691\) | 1.04535e7i | 0.832852i | 0.909170 | + | 0.416426i | \(0.136718\pi\) | ||||
−0.909170 | + | 0.416426i | \(0.863282\pi\) | |||||||
\(692\) | −2.60502e6 | + | 340980.i | −0.206798 | + | 0.0270684i | ||||
\(693\) | 1.39686e7 | 1.10489 | ||||||||
\(694\) | −3.89262e6 | − | 3.41630e6i | −0.306791 | − | 0.269251i | ||||
\(695\) | − | 1.91440e7i | − | 1.50339i | ||||||
\(696\) | −7.26964e6 | + | 1.08535e7i | −0.568839 | + | 0.849268i | ||||
\(697\) | − | 1.40120e7i | − | 1.09249i | ||||||
\(698\) | 2.48727e6 | − | 2.83406e6i | 0.193235 | − | 0.220176i | ||||
\(699\) | 2.40617e7 | 1.86266 | ||||||||
\(700\) | −1.00130e7 | + | 1.31063e6i | −0.772358 | + | 0.101096i | ||||
\(701\) | 2.19766e7 | 1.68914 | 0.844571 | − | 0.535443i | \(-0.179855\pi\) | ||||
0.844571 | + | 0.535443i | \(0.179855\pi\) | |||||||
\(702\) | 4.54245e7 | + | 3.98662e7i | 3.47895 | + | 3.05325i | ||||
\(703\) | 5.92777e6 | + | 3.88474e6i | 0.452379 | + | 0.296465i | ||||
\(704\) | −4.21726e6 | + | 1.73580e6i | −0.320700 | + | 0.131998i | ||||
\(705\) | − | 4.96871e7i | − | 3.76505i | ||||||
\(706\) | 6.70303e6 | − | 7.63759e6i | 0.506127 | − | 0.576693i | ||||
\(707\) | 4.63778e6i | 0.348949i | ||||||||
\(708\) | 3.54990e6 | + | 2.71206e7i | 0.266154 | + | 2.03337i | ||||
\(709\) | 9.24351e6 | 0.690591 | 0.345296 | − | 0.938494i | \(-0.387779\pi\) | ||||
0.345296 | + | 0.938494i | \(0.387779\pi\) | |||||||
\(710\) | −1.78102e6 | + | 2.02933e6i | −0.132593 | + | 0.151080i | ||||
\(711\) | −7.86008e6 | −0.583113 | ||||||||
\(712\) | −1.17502e6 | + | 1.75429e6i | −0.0868653 | + | 0.129689i | ||||
\(713\) | 293660.i | 0.0216332i | ||||||||
\(714\) | 1.76953e7 | + | 1.55300e7i | 1.29901 | + | 1.14006i | ||||
\(715\) | −9.40336e6 | −0.687888 | ||||||||
\(716\) | −2.23138e6 | − | 1.70473e7i | −0.162664 | − | 1.24272i | ||||
\(717\) | 4.43280e7i | 3.22018i | ||||||||
\(718\) | −370337. | − | 325021.i | −0.0268093 | − | 0.0235289i | ||||
\(719\) | 1.52985e7i | 1.10364i | 0.833965 | + | 0.551818i | \(0.186066\pi\) | ||||
−0.833965 | + | 0.551818i | \(0.813934\pi\) | |||||||
\(720\) | 4.41937e7 | − | 1.17710e7i | 3.17709 | − | 0.846217i | ||||
\(721\) | − | 9.56158e6i | − | 0.685002i | ||||||
\(722\) | 1.33402e7 | + | 4.26991e6i | 0.952403 | + | 0.304842i | ||||
\(723\) | − | 4.75222e7i | − | 3.38104i | ||||||
\(724\) | 1.47881e7 | − | 1.93566e6i | 1.04849 | − | 0.137241i | ||||
\(725\) | 4.81760e6i | 0.340397i | ||||||||
\(726\) | −1.55832e7 | + | 1.77558e7i | −1.09727 | + | 1.25026i | ||||
\(727\) | − | 1.87082e7i | − | 1.31279i | −0.754416 | − | 0.656397i | \(-0.772080\pi\) | ||
0.754416 | − | 0.656397i | \(-0.227920\pi\) | |||||||
\(728\) | −2.28355e7 | − | 1.52952e7i | −1.59691 | − | 1.06961i | ||||
\(729\) | 3.21672e7 | 2.24178 | ||||||||
\(730\) | −2.16680e7 | + | 2.46891e7i | −1.50492 | + | 1.71474i | ||||
\(731\) | 1.06318e7i | 0.735893i | ||||||||
\(732\) | −1.38783e6 | − | 1.06028e7i | −0.0957323 | − | 0.731377i | ||||
\(733\) | 2.40850e7 | 1.65572 | 0.827861 | − | 0.560933i | \(-0.189558\pi\) | ||||
0.827861 | + | 0.560933i | \(0.189558\pi\) | |||||||
\(734\) | 9.97792e6 | + | 8.75699e6i | 0.683597 | + | 0.599950i | ||||
\(735\) | 1.87456e7 | 1.27991 | ||||||||
\(736\) | −7.74327e6 | − | 3.83653e6i | −0.526902 | − | 0.261063i | ||||
\(737\) | 3.82495e6i | 0.259393i | ||||||||
\(738\) | 4.23466e7 | + | 3.71649e7i | 2.86205 | + | 2.51184i | ||||
\(739\) | 1.82988e7i | 1.23257i | 0.787523 | + | 0.616285i | \(0.211363\pi\) | ||||
−0.787523 | + | 0.616285i | \(0.788637\pi\) | |||||||
\(740\) | −1.01985e7 | + | 1.33491e6i | −0.684630 | + | 0.0896134i | ||||
\(741\) | −3.67288e7 | − | 2.40701e7i | −2.45732 | − | 1.61039i | ||||
\(742\) | 2.38878e6 | − | 2.72183e6i | 0.159282 | − | 0.181489i | ||||
\(743\) | 2.43858e7 | 1.62056 | 0.810280 | − | 0.586044i | \(-0.199315\pi\) | ||||
0.810280 | + | 0.586044i | \(0.199315\pi\) | |||||||
\(744\) | −872654. | − | 584503.i | −0.0577976 | − | 0.0387128i | ||||
\(745\) | −2.93480e7 | −1.93726 | ||||||||
\(746\) | 1.38664e7 | + | 1.21697e7i | 0.912259 | + | 0.800632i | ||||
\(747\) | 1.13876e7i | 0.746672i | ||||||||
\(748\) | 3.88804e6 | − | 508919.i | 0.254084 | − | 0.0332579i | ||||
\(749\) | − | 4.39186e6i | − | 0.286051i | ||||||
\(750\) | −9.08306e6 | + | 1.03494e7i | −0.589629 | + | 0.671837i | ||||
\(751\) | −5.98976e6 | −0.387534 | −0.193767 | − | 0.981048i | \(-0.562071\pi\) | ||||
−0.193767 | + | 0.981048i | \(0.562071\pi\) | |||||||
\(752\) | −6.22536e6 | − | 2.33729e7i | −0.401439 | − | 1.50719i | ||||
\(753\) | − | 2.89692e7i | − | 1.86187i | ||||||
\(754\) | −8.64899e6 | + | 9.85486e6i | −0.554034 | + | 0.631280i | ||||
\(755\) | 8.47413e6 | 0.541038 | ||||||||
\(756\) | −5.74216e7 | + | 7.51610e6i | −3.65402 | + | 0.478287i | ||||
\(757\) | 5.30536e6 | 0.336493 | 0.168246 | − | 0.985745i | \(-0.446190\pi\) | ||||
0.168246 | + | 0.985745i | \(0.446190\pi\) | |||||||
\(758\) | −8.09750e6 | + | 9.22648e6i | −0.511891 | + | 0.583261i | ||||
\(759\) | 6.12003e6 | 0.385611 | ||||||||
\(760\) | −1.87190e7 | + | 7.92540e6i | −1.17557 | + | 0.497722i | ||||
\(761\) | −2.72385e7 | −1.70499 | −0.852493 | − | 0.522738i | \(-0.824910\pi\) | ||||
−0.852493 | + | 0.522738i | \(0.824910\pi\) | |||||||
\(762\) | −3.68200e7 | + | 4.19536e7i | −2.29719 | + | 2.61747i | ||||
\(763\) | −6.09111e6 | −0.378778 | ||||||||
\(764\) | 8.62479e6 | − | 1.12893e6i | 0.534583 | − | 0.0699733i | ||||
\(765\) | −3.93233e7 | −2.42938 | ||||||||
\(766\) | 1.83717e7 | − | 2.09331e7i | 1.13130 | − | 1.28903i | ||||
\(767\) | 2.74542e7i | 1.68508i | ||||||||
\(768\) | 2.68131e7 | − | 1.53740e7i | 1.64038 | − | 0.940555i | ||||
\(769\) | 769942. | 0.0469507 | 0.0234754 | − | 0.999724i | \(-0.492527\pi\) | ||||
0.0234754 | + | 0.999724i | \(0.492527\pi\) | |||||||
\(770\) | 5.94344e6 | − | 6.77209e6i | 0.361253 | − | 0.411620i | ||||
\(771\) | − | 4.89896e7i | − | 2.96803i | ||||||
\(772\) | 9.89825e6 | − | 1.29561e6i | 0.597744 | − | 0.0782406i | ||||
\(773\) | − | 6.87781e6i | − | 0.414001i | −0.978341 | − | 0.207001i | \(-0.933630\pi\) | ||
0.978341 | − | 0.207001i | \(-0.0663702\pi\) | |||||||
\(774\) | −3.21311e7 | − | 2.81994e7i | −1.92785 | − | 1.69195i | ||||
\(775\) | −387352. | −0.0231660 | ||||||||
\(776\) | 3.13342e6 | − | 4.67815e6i | 0.186795 | − | 0.278882i | ||||
\(777\) | 2.12907e7 | 1.26513 | ||||||||
\(778\) | 8.35892e6 | − | 9.52435e6i | 0.495109 | − | 0.564139i | ||||
\(779\) | −2.09455e7 | − | 1.37265e7i | −1.23665 | − | 0.810433i | ||||
\(780\) | 6.31903e7 | − | 8.27119e6i | 3.71890 | − | 0.486779i | ||||
\(781\) | − | 930852.i | − | 0.0546076i | ||||||
\(782\) | 5.58449e6 | + | 4.90115e6i | 0.326563 | + | 0.286603i | ||||
\(783\) | 2.76276e7i | 1.61042i | ||||||||
\(784\) | 8.81795e6 | − | 2.34866e6i | 0.512362 | − | 0.136468i | ||||
\(785\) | 3.77664e7 | 2.18741 | ||||||||
\(786\) | −1.74162e7 | − | 1.52851e7i | −1.00554 | − | 0.882495i | ||||
\(787\) | 1.53865e7 | 0.885527 | 0.442764 | − | 0.896638i | \(-0.353998\pi\) | ||||
0.442764 | + | 0.896638i | \(0.353998\pi\) | |||||||
\(788\) | 1.49471e6 | + | 1.14193e7i | 0.0857515 | + | 0.655125i | ||||
\(789\) | 4.77893e7i | 2.73299i | ||||||||
\(790\) | −3.34436e6 | + | 3.81064e6i | −0.190653 | + | 0.217235i | ||||
\(791\) | 1.96902e7 | 1.11895 | ||||||||
\(792\) | −8.77445e6 | + | 1.31001e7i | −0.497058 | + | 0.742100i | ||||
\(793\) | − | 1.07332e7i | − | 0.606101i | ||||||
\(794\) | 1.70277e7 | − | 1.94018e7i | 0.958531 | − | 1.09217i | ||||
\(795\) | 8.39708e6i | 0.471206i | ||||||||
\(796\) | −6.49307e6 | + | 849899.i | −0.363218 | + | 0.0475428i | ||||
\(797\) | − | 3.13699e6i | − | 0.174931i | −0.996168 | − | 0.0874657i | \(-0.972123\pi\) | ||
0.996168 | − | 0.0874657i | \(-0.0278768\pi\) | |||||||
\(798\) | 4.05494e7 | − | 1.12377e7i | 2.25412 | − | 0.624698i | ||||
\(799\) | 2.07970e7i | 1.15248i | ||||||||
\(800\) | 5.06058e6 | − | 1.02137e7i | 0.279560 | − | 0.564235i | ||||
\(801\) | 7.29997e6i | 0.402013i | ||||||||
\(802\) | 5.88710e6 | + | 5.16674e6i | 0.323196 | + | 0.283649i | ||||
\(803\) | − | 1.13249e7i | − | 0.619789i | ||||||
\(804\) | −3.36443e6 | − | 2.57036e7i | −0.183557 | − | 1.40234i | ||||
\(805\) | 1.70734e7 | 0.928603 | ||||||||
\(806\) | −792363. | − | 695407.i | −0.0429622 | − | 0.0377052i | ||||
\(807\) | 4.38200e7i | 2.36858i | ||||||||
\(808\) | −4.34944e6 | − | 2.91325e6i | −0.234372 | − | 0.156982i | ||||
\(809\) | −3.28391e7 | −1.76409 | −0.882044 | − | 0.471166i | \(-0.843833\pi\) | ||||
−0.882044 | + | 0.471166i | \(0.843833\pi\) | |||||||
\(810\) | 4.80784e7 | − | 5.47817e7i | 2.57477 | − | 2.93375i | ||||
\(811\) | 3.10053e7 | 1.65533 | 0.827663 | − | 0.561226i | \(-0.189670\pi\) | ||||
0.827663 | + | 0.561226i | \(0.189670\pi\) | |||||||
\(812\) | −1.63062e6 | − | 1.24576e7i | −0.0867886 | − | 0.663048i | ||||
\(813\) | − | 1.87243e7i | − | 0.993525i | ||||||
\(814\) | 2.33901e6 | − | 2.66513e6i | 0.123729 | − | 0.140980i | ||||
\(815\) | − | 1.28688e7i | − | 0.678646i | ||||||
\(816\) | −2.56799e7 | + | 6.83985e6i | −1.35011 | + | 0.359601i | ||||
\(817\) | 1.58927e7 | + | 1.04152e7i | 0.832995 | + | 0.545899i | ||||
\(818\) | −181783. | − | 159540.i | −0.00949884 | − | 0.00833653i | ||||
\(819\) | −9.50231e7 | −4.95016 | ||||||||
\(820\) | 3.60358e7 | − | 4.71685e6i | 1.87154 | − | 0.244972i | ||||
\(821\) | 1.03865e7 | 0.537790 | 0.268895 | − | 0.963170i | \(-0.413342\pi\) | ||||
0.268895 | + | 0.963170i | \(0.413342\pi\) | |||||||
\(822\) | −1.06780e7 | + | 1.21667e7i | −0.551200 | + | 0.628051i | ||||
\(823\) | 1.23234e7i | 0.634206i | 0.948391 | + | 0.317103i | \(0.102710\pi\) | ||||
−0.948391 | + | 0.317103i | \(0.897290\pi\) | |||||||
\(824\) | 8.96712e6 | + | 6.00617e6i | 0.460082 | + | 0.308162i | ||||
\(825\) | 8.07262e6i | 0.412933i | ||||||||
\(826\) | −1.97719e7 | − | 1.73525e7i | −1.00832 | − | 0.884938i | ||||
\(827\) | 3.36646e6 | 0.171163 | 0.0855815 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855815 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(828\) | −2.96241e7 | + | 3.87760e6i | −1.50165 | + | 0.196556i | ||||
\(829\) | 1.27772e7i | 0.645727i | 0.946446 | + | 0.322863i | \(0.104645\pi\) | ||||
−0.946446 | + | 0.322863i | \(0.895355\pi\) | |||||||
\(830\) | 5.52080e6 | + | 4.84526e6i | 0.278168 | + | 0.244130i | ||||
\(831\) | 5.48457e7 | 2.75512 | ||||||||
\(832\) | 2.86885e7 | − | 1.18080e7i | 1.43681 | − | 0.591381i | ||||
\(833\) | −7.84615e6 | −0.391782 | ||||||||
\(834\) | −3.36190e7 | − | 2.95052e7i | −1.67367 | − | 1.46887i | ||||
\(835\) | −1.48858e7 | −0.738850 | ||||||||
\(836\) | 3.04808e6 | − | 6.31048e6i | 0.150838 | − | 0.312282i | ||||
\(837\) | −2.22135e6 | −0.109598 | ||||||||
\(838\) | 1.50568e7 | + | 1.32144e7i | 0.740668 | + | 0.650038i | ||||
\(839\) | 7.74948e6 | 0.380074 | 0.190037 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190037 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(840\) | −3.39830e7 | + | 5.07362e7i | −1.66174 | + | 2.48096i | ||||
\(841\) | 1.45173e7 | 0.707778 | ||||||||
\(842\) | 1.04083e7 | + | 9.13469e6i | 0.505940 | + | 0.444031i | ||||
\(843\) | − | 4.79018e7i | − | 2.32157i | ||||||
\(844\) | −2.73224e6 | − | 2.08738e7i | −0.132027 | − | 1.00866i | ||||
\(845\) | 3.74707e7 | 1.80530 | ||||||||
\(846\) | −6.28519e7 | − | 5.51611e7i | −3.01920 | − | 2.64976i | ||||
\(847\) | − | 2.27214e7i | − | 1.08824i | ||||||
\(848\) | 1.05208e6 | + | 3.94999e6i | 0.0502411 | + | 0.188628i | ||||
\(849\) | 5.71227e7i | 2.71981i | ||||||||
\(850\) | −6.46486e6 | + | 7.36621e6i | −0.306910 | + | 0.349701i | ||||
\(851\) | 6.71916e6 | 0.318047 | ||||||||
\(852\) | 818777. | + | 6.25530e6i | 0.0386426 | + | 0.295223i | ||||
\(853\) | −1.92772e7 | −0.907132 | −0.453566 | − | 0.891223i | \(-0.649848\pi\) | ||||
−0.453566 | + | 0.891223i | \(0.649848\pi\) | |||||||
\(854\) | 7.72979e6 | + | 6.78395e6i | 0.362680 | + | 0.318301i | ||||
\(855\) | −3.85220e7 | + | 5.87813e7i | −1.80216 | + | 2.74994i | ||||
\(856\) | 4.11881e6 | + | 2.75877e6i | 0.192126 | + | 0.128686i | ||||
\(857\) | − | 4.08300e7i | − | 1.89901i | −0.313751 | − | 0.949505i | \(-0.601586\pi\) | ||
0.313751 | − | 0.949505i | \(-0.398414\pi\) | |||||||
\(858\) | −1.44927e7 | + | 1.65133e7i | −0.672094 | + | 0.765800i | ||||
\(859\) | 1.02334e7i | 0.473190i | 0.971608 | + | 0.236595i | \(0.0760314\pi\) | ||||
−0.971608 | + | 0.236595i | \(0.923969\pi\) | |||||||
\(860\) | −2.73427e7 | + | 3.57898e6i | −1.26065 | + | 0.165011i | ||||
\(861\) | −7.52296e7 | −3.45844 | ||||||||
\(862\) | −2.37276e6 | + | 2.70357e6i | −0.108764 | + | 0.123928i | ||||
\(863\) | 1.05026e7 | 0.480033 | 0.240017 | − | 0.970769i | \(-0.422847\pi\) | ||||
0.240017 | + | 0.970769i | \(0.422847\pi\) | |||||||
\(864\) | 2.90209e7 | − | 5.85729e7i | 1.32260 | − | 2.66939i | ||||
\(865\) | 5.85906e6i | 0.266249i | ||||||||
\(866\) | 2.81516e7 | + | 2.47069e7i | 1.27558 | + | 1.11950i | ||||
\(867\) | −1.90021e7 | −0.858526 | ||||||||
\(868\) | 1.00163e6 | − | 131107.i | 0.0451243 | − | 0.00590646i | ||||
\(869\) | − | 1.74794e6i | − | 0.0785192i | ||||||
\(870\) | 2.18957e7 | + | 1.92164e7i | 0.980754 | + | 0.860746i | ||||
\(871\) | − | 2.60198e7i | − | 1.16214i | ||||||
\(872\) | 3.82617e6 | − | 5.71241e6i | 0.170401 | − | 0.254407i | ||||
\(873\) | − | 1.94667e7i | − | 0.864486i | ||||||
\(874\) | 1.27970e7 | − | 3.54652e6i | 0.566671 | − | 0.157045i | ||||
\(875\) | − | 1.32438e7i | − | 0.584778i | ||||||
\(876\) | 9.96134e6 | + | 7.61028e7i | 0.438589 | + | 3.35074i | ||||
\(877\) | 3.28786e7i | 1.44349i | 0.692159 | + | 0.721745i | \(0.256660\pi\) | ||||
−0.692159 | + | 0.721745i | \(0.743340\pi\) | |||||||
\(878\) | 3.29891e6 | − | 3.75886e6i | 0.144422 | − | 0.164558i | ||||
\(879\) | 1.43015e7i | 0.624323i | ||||||||
\(880\) | 2.61765e6 | + | 9.82786e6i | 0.113948 | + | 0.427811i | ||||
\(881\) | 1.66312e7 | 0.721912 | 0.360956 | − | 0.932583i | \(-0.382450\pi\) | ||||
0.360956 | + | 0.932583i | \(0.382450\pi\) | |||||||
\(882\) | 2.08108e7 | − | 2.37123e7i | 0.900777 | − | 1.02637i | ||||
\(883\) | − | 2.75935e7i | − | 1.19098i | −0.803363 | − | 0.595490i | \(-0.796958\pi\) | ||
0.803363 | − | 0.595490i | \(-0.203042\pi\) | |||||||
\(884\) | −2.64489e7 | + | 3.46199e6i | −1.13835 | + | 0.149003i | ||||
\(885\) | 6.09981e7 | 2.61793 | ||||||||
\(886\) | −1.16788e7 | − | 1.02497e7i | −0.499820 | − | 0.438660i | ||||
\(887\) | −1.96131e7 | −0.837024 | −0.418512 | − | 0.908211i | \(-0.637448\pi\) | ||||
−0.418512 | + | 0.908211i | \(0.637448\pi\) | |||||||
\(888\) | −1.33739e7 | + | 1.99670e7i | −0.569147 | + | 0.849728i | ||||
\(889\) | − | 5.36863e7i | − | 2.27829i | ||||||
\(890\) | 3.53909e6 | + | 3.10604e6i | 0.149767 | + | 0.131441i | ||||
\(891\) | 2.51283e7i | 1.06040i | ||||||||
\(892\) | −3.23940e6 | − | 2.47484e7i | −0.136318 | − | 1.04144i | ||||
\(893\) | 3.10878e7 | + | 2.03733e7i | 1.30455 | + | 0.854932i | ||||
\(894\) | −4.52318e7 | + | 5.15382e7i | −1.89278 | + | 2.15668i | ||||
\(895\) | −3.83418e7 | −1.59998 | ||||||||
\(896\) | −9.62886e6 | + | 2.81241e7i | −0.400686 | + | 1.17033i | ||||
\(897\) | −4.16323e7 | −1.72762 | ||||||||
\(898\) | −3.42318e7 | − | 3.00431e7i | −1.41657 | − | 1.24324i | ||||
\(899\) | − | 481922.i | − | 0.0198874i | ||||||
\(900\) | −5.11474e6 | − | 3.90757e7i | −0.210483 | − | 1.60805i | ||||
\(901\) | − | 3.51468e6i | − | 0.144236i | ||||||
\(902\) | −8.26479e6 | + | 9.41710e6i | −0.338233 | + | 0.385390i | ||||
\(903\) | 5.70815e7 | 2.32957 | ||||||||
\(904\) | −1.23685e7 | + | 1.84661e7i | −0.503382 | + | 0.751542i | ||||
\(905\) | − | 3.32605e7i | − | 1.34992i | ||||||
\(906\) | 1.30605e7 | − | 1.48815e7i | 0.528616 | − | 0.602317i | ||||
\(907\) | −2.31574e7 | −0.934699 | −0.467349 | − | 0.884073i | \(-0.654791\pi\) | ||||
−0.467349 | + | 0.884073i | \(0.654791\pi\) | |||||||
\(908\) | 2.78376e6 | + | 2.12674e7i | 0.112051 | + | 0.856052i | ||||
\(909\) | −1.80989e7 | −0.726513 | ||||||||
\(910\) | −4.04310e7 | + | 4.60681e7i | −1.61849 | + | 1.84415i | ||||
\(911\) | −2.94135e7 | −1.17423 | −0.587113 | − | 0.809505i | \(-0.699735\pi\) | ||||
−0.587113 | + | 0.809505i | \(0.699735\pi\) | |||||||
\(912\) | −1.49323e7 | + | 4.50874e7i | −0.594484 | + | 1.79501i | ||||
\(913\) | −2.53239e6 | −0.100543 | ||||||||
\(914\) | 4.28530e6 | − | 4.88277e6i | 0.169674 | − | 0.193331i | ||||
\(915\) | −2.38471e7 | −0.941636 | ||||||||
\(916\) | 454559. | + | 3.47274e6i | 0.0178999 | + | 0.136752i | ||||
\(917\) | 2.22868e7 | 0.875235 | ||||||||
\(918\) | −3.70741e7 | + | 4.22431e7i | −1.45199 | + | 1.65443i | ||||
\(919\) | − | 1.88396e7i | − | 0.735840i | −0.929857 | − | 0.367920i | \(-0.880070\pi\) | ||
0.929857 | − | 0.367920i | \(-0.119930\pi\) | |||||||
\(920\) | −1.07248e7 | + | 1.60119e7i | −0.417752 | + | 0.623697i | ||||
\(921\) | 663590. | 0.0257781 | ||||||||
\(922\) | 2.22433e7 | − | 2.53446e7i | 0.861732 | − | 0.981877i | ||||
\(923\) | 6.33224e6i | 0.244655i | ||||||||
\(924\) | −2.73235e6 | − | 2.08746e7i | −0.105282 | − | 0.804338i | ||||
\(925\) | 8.86290e6i | 0.340582i | ||||||||
\(926\) | 2.73906e7 | + | 2.40390e7i | 1.04972 | + | 0.921276i | ||||
\(927\) | 3.73141e7 | 1.42618 | ||||||||
\(928\) | 1.27074e7 | + | 6.29610e6i | 0.484380 | + | 0.239995i | ||||
\(929\) | −7.98203e6 | −0.303441 | −0.151720 | − | 0.988423i | \(-0.548481\pi\) | ||||
−0.151720 | + | 0.988423i | \(0.548481\pi\) | |||||||
\(930\) | −1.54507e6 | + | 1.76049e6i | −0.0585787 | + | 0.0667460i | ||||
\(931\) | −7.68628e6 | + | 1.17286e7i | −0.290631 | + | 0.443478i | ||||
\(932\) | −3.39026e6 | − | 2.59010e7i | −0.127848 | − | 0.976734i | ||||
\(933\) | − | 9.32619e6i | − | 0.350752i | ||||||
\(934\) | 2.08450e7 | + | 1.82944e7i | 0.781871 | + | 0.686199i | ||||
\(935\) | − | 8.74477e6i | − | 0.327129i | ||||||
\(936\) | 5.96894e7 | − | 8.91153e7i | 2.22693 | − | 3.32478i | ||||
\(937\) | 4.28282e6 | 0.159361 | 0.0796803 | − | 0.996820i | \(-0.474610\pi\) | ||||
0.0796803 | + | 0.996820i | \(0.474610\pi\) | |||||||
\(938\) | 1.87389e7 | + | 1.64459e7i | 0.695402 | + | 0.610311i | ||||
\(939\) | −6.22907e7 | −2.30547 | ||||||||
\(940\) | −5.34852e7 | + | 7.00086e6i | −1.97431 | + | 0.258423i | ||||
\(941\) | − | 3.79556e6i | − | 0.139734i | −0.997556 | − | 0.0698670i | \(-0.977743\pi\) | ||
0.997556 | − | 0.0698670i | \(-0.0222575\pi\) | |||||||
\(942\) | 5.82064e7 | − | 6.63217e7i | 2.13719 | − | 2.43517i | ||||
\(943\) | −2.37418e7 | −0.869430 | ||||||||
\(944\) | 2.86935e7 | − | 7.64252e6i | 1.04798 | − | 0.279130i | ||||
\(945\) | 1.29149e8i | 4.70449i | ||||||||
\(946\) | 6.27103e6 | − | 7.14536e6i | 0.227830 | − | 0.259595i | ||||
\(947\) | − | 3.59356e7i | − | 1.30212i | −0.759028 | − | 0.651058i | \(-0.774325\pi\) | ||
0.759028 | − | 0.651058i | \(-0.225675\pi\) | |||||||
\(948\) | 1.53748e6 | + | 1.17461e7i | 0.0555635 | + | 0.424495i | ||||
\(949\) | 7.70388e7i | 2.77680i | ||||||||
\(950\) | 4.67803e6 | + | 1.68799e7i | 0.168172 | + | 0.606822i | ||||
\(951\) | 6.79731e7i | 2.43717i | ||||||||
\(952\) | 1.42239e7 | − | 2.12361e7i | 0.508660 | − | 0.759421i | ||||
\(953\) | 3.01485e7i | 1.07531i | 0.843165 | + | 0.537655i | \(0.180690\pi\) | ||||
−0.843165 | + | 0.537655i | \(0.819310\pi\) | |||||||
\(954\) | 1.06219e7 | + | 9.32219e6i | 0.377861 | + | 0.331625i | ||||
\(955\) | − | 1.93984e7i | − | 0.688267i | ||||||
\(956\) | 4.77165e7 | − | 6.24577e6i | 1.68859 | − | 0.221025i | ||||
\(957\) | −1.00435e7 | −0.354492 | ||||||||
\(958\) | 1.42602e7 | + | 1.25153e7i | 0.502011 | + | 0.440583i | ||||
\(959\) | − | 1.55693e7i | − | 0.546665i | ||||||
\(960\) | −2.62351e7 | − | 6.37405e7i | −0.918767 | − | 2.23222i | ||||
\(961\) | −2.85904e7 | −0.998647 | ||||||||
\(962\) | −1.59114e7 | + | 1.81299e7i | −0.554335 | + | 0.631622i | ||||
\(963\) | 1.71392e7 | 0.595560 | ||||||||
\(964\) | −5.11548e7 | + | 6.69583e6i | −1.77294 | + | 0.232066i | ||||
\(965\) | − | 2.22626e7i | − | 0.769586i | ||||||
\(966\) | 2.63139e7 | − | 2.99827e7i | 0.907283 | − | 1.03378i | ||||
\(967\) | 4.55793e7i | 1.56748i | 0.621090 | + | 0.783739i | \(0.286690\pi\) | ||||
−0.621090 | + | 0.783739i | \(0.713310\pi\) | |||||||
\(968\) | 2.13087e7 | + | 1.42726e7i | 0.730919 | + | 0.489569i | ||||
\(969\) | 2.23842e7 | − | 3.41564e7i | 0.765831 | − | 1.16859i | ||||
\(970\) | −9.43766e6 | − | 8.28284e6i | −0.322059 | − | 0.282650i | ||||
\(971\) | 4.49562e7 | 1.53018 | 0.765088 | − | 0.643926i | \(-0.222696\pi\) | ||||
0.765088 | + | 0.643926i | \(0.222696\pi\) | |||||||
\(972\) | −1.07141e7 | − | 8.18537e7i | −0.363739 | − | 2.77890i | ||||
\(973\) | 4.30208e7 | 1.45679 | ||||||||
\(974\) | −356171. | + | 405830.i | −0.0120299 | + | 0.0137071i | ||||
\(975\) | − | 5.49151e7i | − | 1.85003i | ||||||
\(976\) | −1.12177e7 | + | 2.98784e6i | −0.376946 | + | 0.100400i | ||||
\(977\) | − | 4.29574e7i | − | 1.43980i | −0.694079 | − | 0.719898i | \(-0.744188\pi\) | ||
0.694079 | − | 0.719898i | \(-0.255812\pi\) | |||||||
\(978\) | −2.25989e7 | − | 1.98337e7i | −0.755512 | − | 0.663065i | ||||
\(979\) | −1.62338e6 | −0.0541331 | ||||||||
\(980\) | −2.64124e6 | − | 2.01785e7i | −0.0878500 | − | 0.671158i | ||||
\(981\) | − | 2.37705e7i | − | 0.788618i | ||||||
\(982\) | −2.57751e7 | − | 2.26212e7i | −0.852946 | − | 0.748577i | ||||
\(983\) | 1.76275e7 | 0.581845 | 0.290922 | − | 0.956747i | \(-0.406038\pi\) | ||||
0.290922 | + | 0.956747i | \(0.406038\pi\) | |||||||
\(984\) | 4.72559e7 | − | 7.05524e7i | 1.55585 | − | 2.32287i | ||||
\(985\) | 2.56837e7 | 0.843463 | ||||||||
\(986\) | −9.16464e6 | − | 8.04323e6i | −0.300209 | − | 0.263474i | ||||
\(987\) | 1.11658e8 | 3.64834 | ||||||||
\(988\) | −2.07350e7 | + | 4.29279e7i | −0.675789 | + | 1.39909i | ||||
\(989\) | 1.80145e7 | 0.585640 | ||||||||
\(990\) | 2.64281e7 | + | 2.31943e7i | 0.856994 | + | 0.752129i | ||||
\(991\) | 3.92067e6 | 0.126816 | 0.0634082 | − | 0.997988i | \(-0.479803\pi\) | ||||
0.0634082 | + | 0.997988i | \(0.479803\pi\) | |||||||
\(992\) | −506227. | + | 1.02172e6i | −0.0163330 | + | 0.0329649i | ||||
\(993\) | 2.09562e6 | 0.0674434 | ||||||||
\(994\) | −4.56034e6 | − | 4.00233e6i | −0.146397 | − | 0.128483i | ||||
\(995\) | 1.46038e7i | 0.467638i | ||||||||
\(996\) | 1.70176e7 | − | 2.22749e6i | 0.543562 | − | 0.0711487i | ||||
\(997\) | −2.42573e7 | −0.772868 | −0.386434 | − | 0.922317i | \(-0.626293\pi\) | ||||
−0.386434 | + | 0.922317i | \(0.626293\pi\) | |||||||
\(998\) | 2.34056e6 | + | 2.05416e6i | 0.0743865 | + | 0.0652843i | ||||
\(999\) | 5.08262e7i | 1.61129i |
(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 | 76.6.d.a.75.14 | yes | 48 | |
4.3 | odd | 2 | inner | 76.6.d.a.75.36 | yes | 48 | |
19.18 | odd | 2 | inner | 76.6.d.a.75.35 | yes | 48 | |
76.75 | even | 2 | inner | 76.6.d.a.75.13 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.d.a.75.13 | ✓ | 48 | 76.75 | even | 2 | inner | |
76.6.d.a.75.14 | yes | 48 | 1.1 | even | 1 | trivial | |
76.6.d.a.75.35 | yes | 48 | 19.18 | odd | 2 | inner | |
76.6.d.a.75.36 | yes | 48 | 4.3 | odd | 2 | inner |