Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,7,Mod(145,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.145");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bh (of order \(6\), degree \(2\), not 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: | \(77.2981720963\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 82x^{6} - 165x^{5} + 5606x^{4} - 7807x^{3} + 102447x^{2} + 132594x + 1162084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 241.4 | ||
Root | \(3.42459 - 5.93157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.241 |
Dual form | 336.7.bh.e.145.4 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 13.5000 | + | 7.79423i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 201.438 | − | 116.300i | 1.61150 | − | 0.930402i | 0.622482 | − | 0.782634i | \(-0.286124\pi\) |
0.989022 | − | 0.147768i | \(-0.0472088\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −184.358 | + | 289.242i | −0.537486 | + | 0.843272i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 121.500 | + | 210.444i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 460.090 | − | 796.899i | 0.345672 | − | 0.598722i | −0.639803 | − | 0.768539i | \(-0.720984\pi\) |
0.985476 | + | 0.169817i | \(0.0543175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 536.864i | 0.244362i | 0.992508 | + | 0.122181i | \(0.0389889\pi\) | ||||
−0.992508 | + | 0.122181i | \(0.961011\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3625.88 | 1.07434 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2610.93 | + | 1507.42i | 0.531433 | + | 0.306823i | 0.741600 | − | 0.670843i | \(-0.234067\pi\) |
−0.210167 | + | 0.977666i | \(0.567401\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7374.63 | + | 4257.75i | −1.07518 | + | 0.620753i | −0.929591 | − | 0.368592i | \(-0.879840\pi\) |
−0.145585 | + | 0.989346i | \(0.546506\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4743.25 | + | 2467.85i | −0.512175 | + | 0.266477i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10535.7 | + | 18248.4i | 0.865924 | + | 1.49982i | 0.866127 | + | 0.499825i | \(0.166602\pi\) |
−0.000202610 | 1.00000i | \(0.500064\pi\) | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19239.0 | − | 33322.9i | 1.23130 | − | 2.13267i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3788.00i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3910.02 | −0.160319 | −0.0801594 | − | 0.996782i | \(-0.525543\pi\) | ||||
−0.0801594 | + | 0.996782i | \(0.525543\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19930.8 | + | 11507.1i | 0.669021 | + | 0.386260i | 0.795706 | − | 0.605683i | \(-0.207100\pi\) |
−0.126684 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12422.4 | − | 7172.09i | 0.345672 | − | 0.199574i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3497.70 | + | 79705.3i | −0.0815790 | + | 1.85902i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 22097.3 | + | 38273.6i | 0.436249 | + | 0.755605i | 0.997397 | − | 0.0721108i | \(-0.0229735\pi\) |
−0.561148 | + | 0.827715i | \(0.689640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4184.44 | + | 7247.66i | −0.0705413 | + | 0.122181i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 56637.1i | 0.821768i | 0.911688 | + | 0.410884i | \(0.134780\pi\) | ||||
−0.911688 | + | 0.410884i | \(0.865220\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 120736. | 1.51856 | 0.759280 | − | 0.650764i | \(-0.225551\pi\) | ||||
0.759280 | + | 0.650764i | \(0.225551\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 48949.4 | + | 28261.0i | 0.537168 | + | 0.310134i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −131321. | + | 75818.3i | −1.26486 | + | 0.730265i | −0.974010 | − | 0.226505i | \(-0.927270\pi\) |
−0.290845 | + | 0.956770i | \(0.593937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49673.4 | − | 106648.i | −0.422217 | − | 0.906495i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 23498.4 | + | 40700.4i | 0.177144 | + | 0.306823i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 115683. | − | 200370.i | 0.777041 | − | 1.34587i | −0.156600 | − | 0.987662i | \(-0.550053\pi\) |
0.933640 | − | 0.358212i | \(-0.116613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 214034.i | − | 1.28646i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −132743. | −0.716784 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7463.43 | + | 4309.02i | 0.0363398 | + | 0.0209808i | 0.518060 | − | 0.855344i | \(-0.326654\pi\) |
−0.481720 | + | 0.876325i | \(0.659988\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68573.4 | − | 39590.9i | 0.302111 | − | 0.174424i | −0.341280 | − | 0.939962i | \(-0.610860\pi\) |
0.643391 | + | 0.765538i | \(0.277527\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −83268.9 | − | 3654.08i | −0.333013 | − | 0.0146136i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 62437.4 | + | 108145.i | 0.227355 | + | 0.393791i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 156755. | − | 271508.i | 0.521192 | − | 0.902730i | −0.478505 | − | 0.878085i | \(-0.658821\pi\) |
0.999696 | − | 0.0246453i | \(-0.00784565\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 328471.i | 0.999883i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 212805. | 0.594576 | 0.297288 | − | 0.954788i | \(-0.403918\pi\) | ||||
0.297288 | + | 0.954788i | \(0.403918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −198776. | − | 114764.i | −0.510971 | − | 0.295009i | 0.222262 | − | 0.974987i | \(-0.428656\pi\) |
−0.733233 | + | 0.679978i | \(0.761989\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 519453. | − | 299906.i | 1.23130 | − | 0.710889i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 145676. | + | 279992.i | 0.319092 | + | 0.613301i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −379148. | − | 656704.i | −0.769003 | − | 1.33195i | −0.938104 | − | 0.346353i | \(-0.887420\pi\) |
0.169101 | − | 0.985599i | \(-0.445914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29524.5 | + | 51137.9i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 161117.i | 0.281779i | 0.990025 | + | 0.140889i | \(0.0449962\pi\) | ||||
−0.990025 | + | 0.140889i | \(0.955004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 701254. | 1.14187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −52785.2 | − | 30475.6i | −0.0801594 | − | 0.0462801i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −486510. | + | 280886.i | −0.690115 | + | 0.398438i | −0.803655 | − | 0.595095i | \(-0.797114\pi\) |
0.113540 | + | 0.993533i | \(0.463781\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −155284. | − | 98975.1i | −0.206064 | − | 0.131341i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 179377. | + | 310691.i | 0.223007 | + | 0.386260i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −990354. | + | 1.71534e6i | −1.15510 | + | 2.00069i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 199575.i | 0.218670i | 0.994005 | + | 0.109335i | \(0.0348722\pi\) | ||||
−0.994005 | + | 0.109335i | \(0.965128\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 223604. | 0.230448 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 958861. | + | 553599.i | 0.930661 | + | 0.537318i | 0.887021 | − | 0.461730i | \(-0.152771\pi\) |
0.0436406 | + | 0.999047i | \(0.486104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.19877e6 | − | 692111.i | 1.09705 | − | 0.633380i | 0.161602 | − | 0.986856i | \(-0.448334\pi\) |
0.935443 | + | 0.353476i | \(0.115001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −668460. | + | 1.04876e6i | −0.577441 | + | 0.905958i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 786950. | + | 1.36304e6i | 0.642386 | + | 1.11264i | 0.984899 | + | 0.173131i | \(0.0553885\pi\) |
−0.342513 | + | 0.939513i | \(0.611278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.05699e6 | + | 1.83076e6i | −0.816191 | + | 1.41368i | 0.0922779 | + | 0.995733i | \(0.470585\pi\) |
−0.908469 | + | 0.417952i | \(0.862748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 688926.i | 0.503736i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.61150e6 | 1.80990 | 0.904951 | − | 0.425516i | \(-0.139907\pi\) | ||||
0.904951 | + | 0.425516i | \(0.139907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.24458e6 | + | 2.45061e6i | 2.79088 | + | 1.61132i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −112980. | + | 65229.0i | −0.0705413 | + | 0.0407271i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −917356. | + | 477287.i | −0.544373 | + | 0.283230i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 462415. | + | 800926.i | 0.261021 | + | 0.452102i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −441443. | + | 764601.i | −0.237224 | + | 0.410884i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.31562e6i | − | 2.72160i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.99941e6 | −1.46428 | −0.732141 | − | 0.681154i | \(-0.761479\pi\) | ||||
−0.732141 | + | 0.681154i | \(0.761479\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.62994e6 | + | 941046.i | 0.759280 | + | 0.438371i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 36359.2 | − | 20992.0i | 0.0161734 | − | 0.00933769i | −0.491892 | − | 0.870656i | \(-0.663694\pi\) |
0.508065 | + | 0.861319i | \(0.330361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 128051. | − | 2.91801e6i | 0.0544286 | − | 1.24031i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 440545. | + | 763046.i | 0.179056 | + | 0.310134i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.40463e6 | − | 2.43290e6i | 0.546263 | − | 0.946155i | −0.452264 | − | 0.891884i | \(-0.649383\pi\) |
0.998526 | − | 0.0542704i | \(-0.0172833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 224325.i | 0.0835281i | 0.999128 | + | 0.0417640i | \(0.0132978\pi\) | ||||
−0.999128 | + | 0.0417640i | \(0.986702\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.36378e6 | −0.843237 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 427827. | + | 247006.i | 0.146305 | + | 0.0844693i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −787626. | + | 454736.i | −0.258354 | + | 0.149161i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 160650. | − | 1.82692e6i | 0.0505743 | − | 0.575131i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.03342e6 | + | 3.52199e6i | 0.614707 | + | 1.06470i | 0.990436 | + | 0.137974i | \(0.0440591\pi\) |
−0.375729 | + | 0.926730i | \(0.622608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −562185. | + | 973733.i | −0.163286 | + | 0.282819i | −0.936045 | − | 0.351880i | \(-0.885543\pi\) |
0.772759 | + | 0.634699i | \(0.218876\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 732607.i | 0.204549i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.35310e6 | 1.43751 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.12354e6 | + | 2.95807e6i | 1.32395 | + | 0.764382i | 0.984356 | − | 0.176191i | \(-0.0563778\pi\) |
0.339592 | + | 0.940573i | \(0.389711\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.12345e6 | − | 1.80333e6i | 0.777041 | − | 0.448625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.22054e6 | − | 316858.i | −1.73018 | − | 0.0759255i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.01094e6 | − | 3.48305e6i | −0.464340 | − | 0.804260i | 0.534832 | − | 0.844959i | \(-0.320375\pi\) |
−0.999171 | + | 0.0406983i | \(0.987042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.66823e6 | − | 2.88946e6i | 0.371368 | − | 0.643229i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.97767e6i | − | 1.28346i | −0.766930 | − | 0.641730i | \(-0.778217\pi\) | ||
0.766930 | − | 0.641730i | \(-0.221783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.53859e6 | 0.940287 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.79204e6 | − | 1.03463e6i | −0.358392 | − | 0.206918i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.81172e6 | − | 1.04600e6i | 0.349907 | − | 0.202019i | −0.314737 | − | 0.949179i | \(-0.601916\pi\) |
0.664644 | + | 0.747160i | \(0.268583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.09154e6 | + | 1.17081e7i | 1.13661 | + | 2.18460i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 67170.9 | + | 116343.i | 0.0121133 | + | 0.0209808i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.05976e6 | + | 3.56761e6i | −0.359135 | + | 0.622040i | −0.987817 | − | 0.155623i | \(-0.950262\pi\) |
0.628682 | + | 0.777663i | \(0.283595\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 651520.i | 0.109873i | 0.998490 | + | 0.0549366i | \(0.0174957\pi\) | ||||
−0.998490 | + | 0.0549366i | \(0.982504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.23432e6 | 0.201407 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.90247e6 | + | 5.13984e6i | 1.40603 | + | 0.811773i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.40253e6 | − | 1.38710e6i | 0.367403 | − | 0.212120i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.09565e6 | − | 698347.i | −0.162288 | − | 0.103439i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.48252e6 | − | 6.03189e6i | −0.499796 | − | 0.865673i | 0.500204 | − | 0.865908i | \(-0.333258\pi\) |
−1.00000 | 0.000235235i | \(0.999925\pi\) | ||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.65162e6 | + | 1.15209e7i | −0.925242 | + | 1.60257i | −0.134070 | + | 0.990972i | \(0.542805\pi\) |
−0.791172 | + | 0.611594i | \(0.790529\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.94661e6i | 0.262527i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.32260e6 | −0.696186 | −0.348093 | − | 0.937460i | \(-0.613171\pi\) | ||||
−0.348093 | + | 0.937460i | \(0.613171\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.54482e6 | + | 2.62395e6i | 0.576710 | + | 0.332963i | 0.759825 | − | 0.650128i | \(-0.225285\pi\) |
−0.183115 | + | 0.983091i | \(0.558618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.23239e6 | − | 2.44357e6i | 0.521192 | − | 0.300910i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 720842. | − | 1.13094e6i | 0.0861692 | − | 0.135192i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.58691e6 | + | 1.14089e7i | 0.764575 | + | 1.32428i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.56017e6 | + | 4.43435e6i | −0.288641 | + | 0.499942i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.83579e6i | 0.858309i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −522144. | −0.0555831 | −0.0277916 | − | 0.999614i | \(-0.508847\pi\) | ||||
−0.0277916 | + | 0.999614i | \(0.508847\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.87287e6 | + | 1.65865e6i | 0.297288 | + | 0.171639i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.43209e7 | − | 1.40417e7i | 2.44717 | − | 1.41287i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.00273e6 | + | 3.64342e6i | −0.685312 | + | 0.356558i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.78899e6 | − | 3.09862e6i | −0.170324 | − | 0.295009i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −809280. | + | 1.40171e6i | −0.0749760 | + | 0.129862i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.02146e6i | − | 0.0921096i | −0.998939 | − | 0.0460548i | \(-0.985335\pi\) | ||
0.998939 | − | 0.0460548i | \(-0.0146649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.35016e6 | 0.820864 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.65010e6 | − | 5.57149e6i | −0.825001 | − | 0.476314i | 0.0271371 | − | 0.999632i | \(-0.491361\pi\) |
−0.852138 | + | 0.523317i | \(0.824694\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.09488e6 | − | 2.36418e6i | 0.340984 | − | 0.196867i | −0.319723 | − | 0.947511i | \(-0.603590\pi\) |
0.660707 | + | 0.750644i | \(0.270256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −215699. | + | 4.91533e6i | −0.0174989 | + | 0.398764i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 480558. | + | 832352.i | 0.0379908 | + | 0.0658020i | 0.884396 | − | 0.466738i | \(-0.154571\pi\) |
−0.846405 | + | 0.532540i | \(0.821238\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.76354e7 | + | 3.05454e7i | −1.35888 | + | 2.35365i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.18207e7i | − | 0.887968i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.35988e7 | −0.996108 | −0.498054 | − | 0.867146i | \(-0.665952\pi\) | ||||
−0.498054 | + | 0.867146i | \(0.665952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.11183e7 | − | 6.41918e6i | −0.794308 | − | 0.458594i | 0.0471692 | − | 0.998887i | \(-0.484980\pi\) |
−0.841477 | + | 0.540293i | \(0.818313\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −797162. | + | 460241.i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.24093e7 | − | 1.57060e7i | −1.52381 | − | 1.06799i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.28583e6 | − | 3.95918e6i | −0.151689 | − | 0.262733i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.25579e6 | + | 2.17509e6i | −0.0813425 | + | 0.140889i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.03894e7i | 0.657007i | 0.944503 | + | 0.328504i | \(0.106544\pi\) | ||||
−0.944503 | + | 0.328504i | \(0.893456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.93895e7 | 1.19730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.46693e6 | + | 5.46573e6i | 0.570937 | + | 0.329631i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.65816e7 | + | 9.57337e6i | −0.976846 | + | 0.563982i | −0.901316 | − | 0.433162i | \(-0.857398\pi\) |
−0.0755293 | + | 0.997144i | \(0.524065\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.51442e7 | − | 664571.i | −0.871658 | − | 0.0382509i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −475067. | − | 822840.i | −0.0267198 | − | 0.0462801i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.00250e6 | − | 3.46843e6i | 0.110079 | − | 0.190663i | −0.805723 | − | 0.592293i | \(-0.798223\pi\) |
0.915802 | + | 0.401630i | \(0.131556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.38161e7i | − | 2.89184i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.75717e6 | −0.460077 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.73993e7 | − | 1.58190e7i | −1.40761 | − | 0.812685i | −0.412455 | − | 0.910978i | \(-0.635328\pi\) |
−0.995158 | + | 0.0982929i | \(0.968662\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.16572e7 | − | 1.82773e7i | 1.59061 | − | 0.918341i | 0.597413 | − | 0.801934i | \(-0.296196\pi\) |
0.993202 | − | 0.116407i | \(-0.0371378\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.32490e6 | − | 2.54648e6i | −0.0651170 | − | 0.125156i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.77033e7 | − | 3.06631e7i | −0.851250 | − | 1.47441i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.95609e7 | − | 3.38804e7i | 0.920341 | − | 1.59408i | 0.121452 | − | 0.992597i | \(-0.461245\pi\) |
0.798888 | − | 0.601479i | \(-0.205422\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.59243e6i | 0.257506i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −480023. | −0.0216343 | −0.0108172 | − | 0.999941i | \(-0.503443\pi\) | ||||
−0.0108172 | + | 0.999941i | \(0.503443\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.30947e7 | − | 1.91072e7i | −1.46015 | − | 0.843020i | −0.461136 | − | 0.887329i | \(-0.652558\pi\) |
−0.999018 | + | 0.0443090i | \(0.985891\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.67396e7 | + | 1.54381e7i | −1.15510 | + | 0.666897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.63819e7 | − | 1.04415e7i | −0.692975 | − | 0.441689i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.52415e6 | − | 1.30322e7i | −0.311719 | − | 0.539914i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.55553e6 | + | 2.69426e6i | −0.0631247 | + | 0.109335i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.03603e7i | − | 0.411878i | −0.978565 | − | 0.205939i | \(-0.933975\pi\) | ||
0.978565 | − | 0.205939i | \(-0.0660248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00456e6 | 0.0780823 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.01865e6 | + | 1.74282e6i | 0.115224 | + | 0.0665247i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.79689e6 | + | 5.65624e6i | −0.366501 | + | 0.211599i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.22587e7 | + | 3.49220e7i | −0.816206 | + | 1.28056i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.62975e6 | + | 1.49472e7i | 0.310220 | + | 0.537318i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.20886e6 | − | 1.59502e7i | 0.324569 | − | 0.562169i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.06102e6i | − | 0.278596i | −0.990251 | − | 0.139298i | \(-0.955515\pi\) | ||
0.990251 | − | 0.139298i | \(-0.0444846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.15779e7 | 0.731364 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.21674e7 | + | 1.27983e7i | 0.736942 | + | 0.425474i | 0.820956 | − | 0.570991i | \(-0.193441\pi\) |
−0.0840143 | + | 0.996465i | \(0.526774\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.03923e7 | + | 1.75470e7i | −0.991129 | + | 0.572229i | −0.905612 | − | 0.424108i | \(-0.860588\pi\) |
−0.0855178 | + | 0.996337i | \(0.527254\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.71985e7 | + | 8.94812e6i | −0.550248 | + | 0.286286i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.04219e7 | + | 1.80513e7i | 0.327167 | + | 0.566669i | 0.981948 | − | 0.189149i | \(-0.0605728\pi\) |
−0.654782 | + | 0.755818i | \(0.727239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.79896e6 | + | 3.11589e6i | −0.0554178 | + | 0.0959864i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.45347e7i | 0.741763i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.56729e7 | −0.761845 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.78899e7 | + | 1.03287e7i | 0.521144 | + | 0.300882i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.85388e7 | + | 1.64769e7i | −0.816191 | + | 0.471228i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.28022e6 | − | 5.19613e7i | 0.0640307 | − | 1.45912i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10153e7 | − | 1.90791e7i | −0.303748 | − | 0.526107i | 0.673234 | − | 0.739430i | \(-0.264905\pi\) |
−0.976982 | + | 0.213323i | \(0.931571\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.36964e6 | + | 9.30049e6i | −0.145416 | + | 0.251868i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 7.29227e7i | − | 1.93967i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.41316e7 | −1.41436 | −0.707181 | − | 0.707032i | \(-0.750034\pi\) | ||||
−0.707181 | + | 0.707032i | \(0.750034\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.52553e7 | + | 2.03546e7i | 0.904951 | + | 0.522474i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.83399e7 | − | 1.05886e7i | 0.462524 | − | 0.267039i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.00049e7 | + | 5.29379e6i | 0.991358 | + | 0.131185i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.82012e7 | + | 6.61664e7i | 0.930293 | + | 1.61132i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.14201e6 | − | 7.17416e6i | 0.0991339 | − | 0.171705i | −0.812192 | − | 0.583390i | \(-0.801726\pi\) |
0.911326 | + | 0.411685i | \(0.135059\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.43895e7i | 1.74999i | 0.484133 | + | 0.874994i | \(0.339135\pi\) | ||||
−0.484133 | + | 0.874994i | \(0.660865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.03364e6 | −0.0470276 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.81691e6 | + | 2.20369e6i | 0.0867736 | + | 0.0500988i | 0.542759 | − | 0.839889i | \(-0.317380\pi\) |
−0.455985 | + | 0.889987i | \(0.650713\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.28670e7 | − | 2.47493e7i | 0.958161 | − | 0.553194i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.61044e7 | − | 706707.i | −0.353948 | − | 0.0155323i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.12174e7 | − | 1.94292e7i | −0.242443 | − | 0.419924i | 0.718966 | − | 0.695045i | \(-0.244616\pi\) |
−0.961410 | + | 0.275121i | \(0.911282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.27339e7 | − | 2.20557e7i | 0.270669 | − | 0.468813i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.44167e7i | 0.301401i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.33882e7 | −1.09791 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.41637e7 | − | 3.12714e7i | −1.09575 | − | 0.632630i | −0.160646 | − | 0.987012i | \(-0.551358\pi\) |
−0.935101 | + | 0.354382i | \(0.884691\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.19189e7 | + | 6.88141e6i | −0.237224 | + | 0.136961i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.66282e7 | + | 7.04003e7i | 0.717289 | + | 1.37865i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.97129e6 | + | 8.61053e6i | 0.0957950 | + | 0.165922i | 0.909940 | − | 0.414740i | \(-0.136127\pi\) |
−0.814145 | + | 0.580661i | \(0.802794\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.14312e7 | − | 7.17609e7i | 0.785658 | − | 1.36080i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.09915e6i | − | 0.0391759i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.56872e7 | 0.288157 | 0.144078 | − | 0.989566i | \(-0.453978\pi\) | ||||
0.144078 | + | 0.989566i | \(0.453978\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.04920e7 | − | 2.33781e7i | −0.732141 | − | 0.422702i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.32230e7 | + | 3.07283e7i | −0.947333 | + | 0.546943i | −0.892251 | − | 0.451539i | \(-0.850875\pi\) |
−0.0550816 | + | 0.998482i | \(0.517542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.19078e7 | + | 3.94589e7i | 1.08483 | + | 0.691453i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.46695e7 | + | 2.54082e7i | 0.253093 | + | 0.438371i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.45518e7 | − | 7.71659e7i | 0.756861 | − | 1.31092i | −0.187583 | − | 0.982249i | \(-0.560065\pi\) |
0.944444 | − | 0.328673i | \(-0.106601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.35269e7i | 1.06274i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 654465. | 0.0107822 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.52750e8 | − | 8.81901e7i | −2.47850 | − | 1.43096i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.73411e7 | − | 3.31059e7i | 0.916421 | − | 0.529096i | 0.0339293 | − | 0.999424i | \(-0.489198\pi\) |
0.882491 | + | 0.470329i | \(0.155865\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.44723e7 | − | 3.83950e7i | 0.385262 | − | 0.604444i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.38142e7 | − | 5.85679e7i | −0.524404 | − | 0.908294i | −0.999596 | − | 0.0284121i | \(-0.990955\pi\) |
0.475193 | − | 0.879882i | \(-0.342378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.17773e6 | + | 1.07001e7i | −0.0943873 | + | 0.163484i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.37348e7i | 0.206756i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.06670e7 | 0.603196 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.54171e7 | − | 2.62216e7i | −0.663818 | − | 0.383256i | 0.129912 | − | 0.991526i | \(-0.458530\pi\) |
−0.793730 | + | 0.608270i | \(0.791864\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.79251e7 | − | 2.18961e7i | 0.546263 | − | 0.315385i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.62229e6 | + | 1.36434e6i | −0.0372247 | + | 0.0193675i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.87380e7 | + | 3.24552e7i | 0.262168 | + | 0.454088i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.74844e6 | + | 3.02838e6i | −0.0241125 | + | 0.0417640i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.47286e6i | 0.115183i | 0.998340 | + | 0.0575915i | \(0.0183421\pi\) | ||||
−0.998340 | + | 0.0575915i | \(0.981658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.34469e6 | 0.0984299 | 0.0492149 | − | 0.998788i | \(-0.484328\pi\) | ||||
0.0492149 | + | 0.998788i | \(0.484328\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.19110e7 | − | 1.84238e7i | −0.421618 | − | 0.243422i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00463e8 | − | 5.80026e7i | 1.30870 | − | 0.755580i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19069e6 | + | 2.71332e7i | −0.0152937 | + | 0.348512i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.85044e6 | + | 6.66916e6i | 0.0487684 | + | 0.0844693i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.67489e7 | − | 4.63304e7i | 0.334098 | − | 0.578675i | −0.649213 | − | 0.760607i | \(-0.724902\pi\) |
0.983311 | + | 0.181932i | \(0.0582350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.43895e7i | 1.03950i | 0.854318 | + | 0.519751i | \(0.173975\pi\) | ||||
−0.854318 | + | 0.519751i | \(0.826025\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41773e7 | −0.172236 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.55394e8 | − | 8.97167e7i | −1.86204 | − | 1.07505i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.39114e6 | − | 3.68993e6i | 0.0755414 | − | 0.0436138i | −0.461754 | − | 0.887008i | \(-0.652780\pi\) |
0.537295 | + | 0.843394i | \(0.319446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.64082e7 | − | 2.34112e7i | 0.191313 | − | 0.272966i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.86184e7 | + | 6.68890e7i | 0.444204 | + | 0.769384i | 0.997996 | − | 0.0632707i | \(-0.0201531\pi\) |
−0.553792 | + | 0.832655i | \(0.686820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.53343e7 | + | 1.13162e8i | −0.741415 | + | 1.28417i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.33958e7i | 0.709803i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.13928e7 | 0.125861 | 0.0629305 | − | 0.998018i | \(-0.479955\pi\) | ||||
0.0629305 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.51341e7 | + | 2.60582e7i | 0.492011 | + | 0.284063i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.51790e7 | + | 8.76360e6i | −0.163286 | + | 0.0942731i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.27909e7 | − | 1.87779e6i | −0.454273 | − | 0.0199348i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.68556e7 | − | 1.33118e8i | −0.805243 | − | 1.39472i | −0.916127 | − | 0.400888i | \(-0.868702\pi\) |
0.110884 | − | 0.993833i | \(-0.464632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.71010e6 | + | 9.89019e6i | −0.0590481 | + | 0.102274i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.01923e7i | − | 0.818521i | −0.912418 | − | 0.409261i | \(-0.865787\pi\) | ||
0.912418 | − | 0.409261i | \(-0.134213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.37769e7 | −0.340312 | −0.170156 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170156 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.22668e7 | + | 4.17233e7i | 0.718754 | + | 0.414973i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.47999e8 | + | 8.54475e7i | −1.45315 | + | 0.838975i | −0.998659 | − | 0.0517781i | \(-0.983511\pi\) |
−0.454488 | + | 0.890753i | \(0.650178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.96326e7 | + | 9.53949e7i | 0.481114 | + | 0.924712i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.61118e7 | + | 7.98680e7i | 0.441316 | + | 0.764382i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.55495e7 | − | 9.62146e7i | 0.524925 | − | 0.909196i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.27659e8i | 3.05732i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.62222e7 | 0.518027 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.19520e7 | − | 1.26740e7i | −0.199741 | − | 0.115321i | 0.396794 | − | 0.917908i | \(-0.370123\pi\) |
−0.596535 | + | 0.802587i | \(0.703456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.05477e7 | + | 1.18632e7i | −0.184641 | + | 0.106603i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.50076e7 | − | 6.05561e7i | −0.843174 | − | 0.537424i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.32106e7 | + | 4.02019e7i | 0.203451 | + | 0.352388i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.99675e7 | − | 1.55828e8i | 0.778930 | − | 1.34915i | −0.153628 | − | 0.988129i | \(-0.549096\pi\) |
0.932559 | − | 0.361018i | \(-0.117571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.26949e7i | − | 0.536174i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.07343e8 | 0.906838 | 0.453419 | − | 0.891298i | \(-0.350204\pi\) | ||||
0.453419 | + | 0.891298i | \(0.350204\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.02088e7 | − | 5.89404e6i | −0.0851987 | − | 0.0491895i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.50423e7 | − | 2.60052e7i | 0.371368 | − | 0.214410i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.92323e7 | + | 6.15523e7i | −0.319576 | + | 0.501389i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.37396e7 | − | 2.37977e7i | −0.110579 | − | 0.191529i | 0.805425 | − | 0.592698i | \(-0.201937\pi\) |
−0.916004 | + | 0.401169i | \(0.868604\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.65913e7 | − | 8.06985e7i | 0.370503 | − | 0.641730i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.17139e8i | − | 0.920442i | −0.887805 | − | 0.460221i | \(-0.847770\pi\) | ||
0.887805 | − | 0.460221i | \(-0.152230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.57535e8 | 1.99969 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.12709e7 | + | 3.53748e7i | 0.470144 | + | 0.271437i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.18289e7 | + | 4.72439e7i | −0.620517 | + | 0.358255i | −0.777070 | − | 0.629414i | \(-0.783295\pi\) |
0.156554 | + | 0.987669i | \(0.449962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.98405e7 | − | 3.63370e7i | 0.523413 | − | 0.272324i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.61283e7 | − | 2.79351e7i | −0.119464 | − | 0.206918i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.60985e8 | − | 2.78835e8i | 1.17860 | − | 2.04139i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.39533e8i | 1.00973i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.26110e7 | 0.233272 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.43465e8 | + | 8.28297e7i | 1.01446 | + | 0.585697i | 0.912494 | − | 0.409091i | \(-0.134154\pi\) |
0.101964 | + | 0.994788i | \(0.467488\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.74398e7 | + | 2.16159e7i | −0.261715 | + | 0.151101i | −0.625117 | − | 0.780531i | \(-0.714949\pi\) |
0.363402 | + | 0.931633i | \(0.381615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.01961e6 | + | 2.05538e8i | −0.0623318 | + | 1.42041i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.46920e7 | + | 6.00883e7i | 0.237027 | + | 0.410542i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.47984e8 | + | 2.56316e8i | −0.999649 | + | 1.73144i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.09418e6i | 0.0139872i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.04064e7 | −0.200809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.17043e8 | + | 1.83045e8i | 2.07041 | + | 1.19535i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.56135e7 | + | 3.21085e7i | −0.359135 | + | 0.207347i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.07842e8 | − | 9.48312e6i | −0.688687 | − | 0.0605599i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.35853e7 | + | 4.08510e7i | 0.148953 | + | 0.257995i | 0.930841 | − | 0.365425i | \(-0.119076\pi\) |
−0.781887 | + | 0.623420i | \(0.785743\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.07809e6 | + | 8.79552e6i | −0.0317177 | + | 0.0549366i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.91714e8i | 3.03754i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.08291e8 | −1.27265 | −0.636323 | − | 0.771423i | \(-0.719546\pi\) | ||||
−0.636323 | + | 0.771423i | \(0.719546\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.66633e7 | + | 9.62059e6i | 0.100704 | + | 0.0581413i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.88349e7 | − | 1.66479e7i | 0.172371 | − | 0.0995184i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.59846e8 | + | 1.14028e7i | 1.53653 | + | 0.0674273i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.01222e7 | + | 1.38776e8i | 0.468677 | + | 0.811773i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.52394e6 | − | 6.10364e6i | 0.0203921 | − | 0.0353202i | −0.855649 | − | 0.517556i | \(-0.826842\pi\) |
0.876041 | + | 0.482236i | \(0.160175\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.48189e7i | 0.371079i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.32455e7 | 0.244936 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.60089e8 | − | 9.24276e7i | −0.897092 | − | 0.517936i | −0.0208364 | − | 0.999783i | \(-0.506633\pi\) |
−0.876256 | + | 0.481847i | \(0.839966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.26056e8 | − | 3.03718e8i | 2.91666 | − | 1.68394i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.34819e6 | − | 1.79674e7i | −0.0512836 | − | 0.0985681i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.29070e8 | − | 2.23556e8i | −0.700629 | − | 1.21353i | −0.968246 | − | 0.250000i | \(-0.919569\pi\) |
0.267616 | − | 0.963526i | \(-0.413764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.79110e7 | + | 1.52266e8i | −0.472209 | + | 0.817891i | −0.999494 | − | 0.0317978i | \(-0.989877\pi\) |
0.527285 | + | 0.849689i | \(0.323210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.08574e8i | − | 0.577115i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.10785e8 | 4.26484 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.14796e8 | − | 6.62773e7i | −0.597582 | − | 0.345014i | 0.170508 | − | 0.985356i | \(-0.445459\pi\) |
−0.768090 | + | 0.640342i | \(0.778793\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.79594e8 | + | 1.03688e8i | −0.925242 | + | 0.534189i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.66020e7 | − | 2.97033e7i | −0.237616 | − | 0.151452i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.06450e8 | − | 1.84376e8i | −0.537203 | − | 0.930463i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.51723e7 | + | 2.62792e7i | −0.0757851 | + | 0.131264i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2.64040e8i | − | 1.30543i | −0.757602 | − | 0.652717i | \(-0.773629\pi\) | ||
0.757602 | − | 0.652717i | \(-0.226371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.95977e8 | −0.959088 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.18551e7 | − | 4.14855e7i | −0.348093 | − | 0.200971i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.83488e7 | − | 3.36877e7i | 0.279813 | − | 0.161550i | −0.353526 | − | 0.935425i | \(-0.615017\pi\) |
0.633339 | + | 0.773875i | \(0.281684\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.29282e8 | + | 2.02832e8i | −0.613742 | + | 0.962912i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.09034e7 | + | 7.08467e7i | 0.192237 | + | 0.332963i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.28119e7 | + | 5.68319e7i | −0.152669 | + | 0.264430i | −0.932208 | − | 0.361923i | \(-0.882120\pi\) |
0.779539 | + | 0.626354i | \(0.215454\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.08034e8i | 0.958320i | 0.877728 | + | 0.479160i | \(0.159059\pi\) | ||||
−0.877728 | + | 0.479160i | \(0.840941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.61830e7 | 0.347461 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.86296e8 | + | 1.07558e8i | 0.841273 | + | 0.485709i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.48090e8 | − | 2.00970e8i | 1.55642 | − | 0.898598i | 0.558822 | − | 0.829288i | \(-0.311253\pi\) |
0.997595 | − | 0.0693104i | \(-0.0220799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.85462e7 | − | 9.64932e6i | 0.0821113 | − | 0.0427213i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.07041e7 | − | 7.05016e7i | −0.178449 | − | 0.309083i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.14774e7 | + | 8.91614e7i | −0.223478 | + | 0.387075i | −0.955862 | − | 0.293817i | \(-0.905074\pi\) |
0.732384 | + | 0.680892i | \(0.238408\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.05360e8i | 0.882855i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.54994e8 | −1.51135 | −0.755676 | − | 0.654945i | \(-0.772692\pi\) | ||||
−0.755676 | + | 0.654945i | \(0.772692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.87611e7 | − | 5.12462e7i | −0.374240 | − | 0.216068i | 0.301069 | − | 0.953602i | \(-0.402657\pi\) |
−0.675309 | + | 0.737535i | \(0.735990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.91247e7 | + | 3.99092e7i | −0.288641 | + | 0.166647i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.44759e6 | − | 1.92503e8i | 0.0349356 | − | 0.796110i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.17599e8 | − | 5.50097e8i | −1.30089 | − | 2.25320i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.10739e7 | + | 1.05783e8i | −0.247772 | + | 0.429155i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.33240e8i | 0.535404i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.10491e7 | 0.203189 | 0.101595 | − | 0.994826i | \(-0.467606\pi\) | ||||
0.101595 | + | 0.994826i | \(0.467606\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.04894e6 | − | 4.06971e6i | −0.0277916 | − | 0.0160455i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.04195e8 | + | 3.48832e8i | −2.35969 | + | 1.36237i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.72556e7 | − | 2.66678e7i | 0.221513 | − | 0.103174i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.58558e7 | + | 4.47836e7i | 0.0990959 | + | 0.171639i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.19118e8 | − | 2.06319e8i | 0.452276 | − | 0.783365i | −0.546251 | − | 0.837622i | \(-0.683945\pi\) |
0.998527 | + | 0.0542563i | \(0.0172788\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.38667e8i | − | 0.897758i | −0.893593 | − | 0.448879i | \(-0.851823\pi\) | ||
0.893593 | − | 0.448879i | \(-0.148177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.37775e8 | 1.63144 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.59300e8 | + | 1.49707e8i | 0.957391 | + | 0.552750i | 0.895369 | − | 0.445325i | \(-0.146912\pi\) |
0.0620217 | + | 0.998075i | \(0.480245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.86770e6 | − | 3.96507e6i | 0.0251233 | − | 0.0145050i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.22935e8 | − | 5.39473e6i | −0.445585 | − | 0.0195536i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.90019e8 | + | 3.29122e8i | 0.682429 | + | 1.18200i | 0.974237 | + | 0.225525i | \(0.0724096\pi\) |
−0.291809 | + | 0.956477i | \(0.594257\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.88275e6 | − | 8.45716e6i | 0.0173756 | − | 0.0300954i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.57751e7i | − | 0.196673i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.92456e7 | −0.241956 | −0.120978 | − | 0.992655i | \(-0.538603\pi\) | ||||
−0.120978 | + | 0.992655i | \(0.538603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.39149e8 | − | 2.53543e8i | −1.52057 | − | 0.877904i | −0.999706 | − | 0.0242670i | \(-0.992275\pi\) |
−0.520869 | − | 0.853637i | \(-0.674392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.18506e7 | + | 1.26154e7i | −0.0749760 | + | 0.0432874i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.13571e8 | − | 6.02690e8i | −1.06628 | − | 2.04941i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.11948e7 | − | 7.13514e7i | −0.138824 | − | 0.240450i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.96146e6 | − | 1.37896e7i | 0.0265897 | − | 0.0460548i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.28615e7i | − | 0.241174i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.94455e8 | 1.29405 | 0.647027 | − | 0.762467i | \(-0.276012\pi\) | ||||
0.647027 | + | 0.762467i | \(0.276012\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.26227e8 | + | 7.28773e7i | 0.410432 | + | 0.236963i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.66631e8 | − | 2.11675e8i | 1.18158 | − | 0.682186i | 0.225201 | − | 0.974312i | \(-0.427696\pi\) |
0.956380 | + | 0.292126i | \(0.0943627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.77254e7 | − | 3.67931e7i | −0.184399 | − | 0.117532i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.68509e7 | − | 1.50430e8i | −0.275000 | − | 0.476314i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.89199e7 | + | 1.71334e8i | −0.310471 | + | 0.537752i | −0.978464 | − | 0.206415i | \(-0.933820\pi\) |
0.667993 | + | 0.744168i | \(0.267154\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.53437e8i | − | 2.03298i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.37078e7 | 0.227323 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.07571e8 | + | 6.21063e7i | 0.328881 | + | 0.189879i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.88719e6 | + | 5.70837e6i | −0.0299667 | + | 0.0173013i | −0.514909 | − | 0.857245i | \(-0.672174\pi\) |
0.484942 | + | 0.874546i | \(0.338841\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.12231e7 | + | 6.46757e7i | −0.123863 | + | 0.194331i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.60890e7 | + | 4.51875e7i | 0.0777147 | + | 0.134606i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.53760e7 | + | 1.47875e8i | −0.252137 | + | 0.436715i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.49823e7i | 0.0438680i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.88915e8 | −0.838717 | −0.419359 | − | 0.907821i | \(-0.637745\pi\) | ||||
−0.419359 | + | 0.907821i | \(0.637745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.25919e8 | − | 1.88169e8i | −0.938088 | − | 0.541605i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.76155e8 | + | 2.74908e8i | −1.35888 | + | 0.784549i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.36898e8 | + | 1.75283e8i | −0.953323 | + | 0.496000i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.87067e8 | − | 3.24009e8i | −0.524877 | − | 0.909113i | −0.999580 | − | 0.0289676i | \(-0.990778\pi\) |
0.474703 | − | 0.880146i | \(-0.342555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.21331e7 | − | 1.59579e8i | 0.256334 | − | 0.443984i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.84940e8i | 1.33789i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.14907e8 | 0.314362 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.83584e8 | − | 1.05992e8i | −0.498054 | − | 0.287552i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.32566e7 | − | 1.92007e7i | 0.0894728 | − | 0.0516572i | −0.454596 | − | 0.890698i | \(-0.650216\pi\) |
0.544069 | + | 0.839041i | \(0.316883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.08151e7 | + | 4.74332e8i | −0.0555357 | + | 1.26554i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.00065e8 | − | 1.73318e8i | −0.264769 | − | 0.458594i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.52248e7 | + | 1.30293e8i | −0.197400 | + | 0.341907i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.25563e8i | 0.847290i | 0.905828 | + | 0.423645i | \(0.139250\pi\) | ||||
−0.905828 | + | 0.423645i | \(0.860750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.15234e8 | + | 1.82000e8i | 0.807013 | + | 0.465929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.37433e8 | + | 7.93472e7i | −0.348964 | + | 0.201474i | −0.664229 | − | 0.747529i | \(-0.731240\pi\) |
0.315265 | + | 0.949004i | \(0.397907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.80110e8 | − | 3.86694e8i | −0.453602 | − | 0.973880i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.44243e8 | − | 2.49836e8i | −0.360323 | − | 0.624098i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.17829e8 | + | 2.04087e8i | −0.291958 | + | 0.505686i | −0.974273 | − | 0.225373i | \(-0.927640\pi\) |
0.682315 | + | 0.731059i | \(0.260973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 7.12652e7i | − | 0.175155i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.12156e8 | −0.273436 | −0.136718 | − | 0.990610i | \(-0.543655\pi\) | ||||
−0.136718 | + | 0.990610i | \(0.543655\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.19216e8 | + | 4.72975e8i | 1.98121 | + | 1.14385i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.39062e7 | + | 1.95758e7i | −0.0813425 | + | 0.0469631i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.39329e8 | − | 2.36673e7i | −1.28354 | − | 0.0563253i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.19826e8 | − | 2.07544e8i | −0.282898 | − | 0.489994i | 0.689199 | − | 0.724572i | \(-0.257962\pi\) |
−0.972097 | + | 0.234578i | \(0.924629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.09775e7 | + | 1.40257e8i | −0.189662 | + | 0.328504i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.61529e8i | 0.607686i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.05564e7 | 0.0473871 | 0.0236936 | − | 0.999719i | \(-0.492457\pi\) | ||||
0.0236936 | + | 0.999719i | \(0.492457\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.61758e8 | + | 1.51126e8i | 0.598652 | + | 0.345632i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.34822e8 | + | 2.51044e8i | −0.986637 | + | 0.569635i | −0.904267 | − | 0.426967i | \(-0.859582\pi\) |
−0.0823696 | + | 0.996602i | \(0.526249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.34670e8 | − | 6.43242e8i | −0.753430 | − | 1.44811i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.52023e7 | + | 1.47575e8i | 0.190312 | + | 0.329631i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.31336e6 | + | 4.00685e6i | −0.00512692 | + | 0.00888008i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.32826e8i | − | 0.292081i | −0.989279 | − | 0.146041i | \(-0.953347\pi\) | ||
0.989279 | − | 0.146041i | \(-0.0466530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.98468e8 | −0.651230 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.75312e7 | + | 3.89892e7i | 0.146206 | + | 0.0844122i | 0.571319 | − | 0.820728i | \(-0.306432\pi\) |
−0.425112 | + | 0.905141i | \(0.639765\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.66898e8 | − | 4.42769e8i | 1.64753 | − | 0.951200i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.99266e8 | − | 1.27009e8i | −0.424787 | − | 0.270751i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.41146e8 | − | 4.17678e8i | −0.510115 | − | 0.883546i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.79095e7 | − | 1.69584e8i | 0.205528 | − | 0.355986i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.48111e7i | − | 0.0308534i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.37610e9 | 2.84473 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.28535e8 | + | 7.42095e7i | 0.263691 | + | 0.152242i | 0.626017 | − | 0.779809i | \(-0.284684\pi\) |
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.40675e7 | − | 3.12159e7i | 0.110079 | − | 0.0635542i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.81451e8 | + | 7.55357e8i | −0.972798 | + | 1.52624i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.12549e7 | + | 3.68146e7i | 0.0426226 | + | 0.0738245i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.19455e8 | − | 7.26517e8i | 0.834802 | − | 1.44592i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.50628e7i | − | 0.0692583i | −0.999400 | − | 0.0346292i | \(-0.988975\pi\) | ||
0.999400 | − | 0.0346292i | \(-0.0110250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.57160e8 | −0.896248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.18222e8 | − | 6.82554e7i | −0.230038 | − | 0.132813i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.82910e8 | + | 1.05603e8i | −0.353257 | + | 0.203953i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.49134e9 | + | 7.75923e8i | −2.85884 | + | 1.48741i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.46594e8 | − | 4.27113e8i | −0.469204 | − | 0.812685i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.88273e8 | + | 3.26099e8i | −0.355585 | + | 0.615892i | −0.987218 | − | 0.159376i | \(-0.949052\pi\) |
0.631633 | + | 0.775268i | \(0.282385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.58329e8i | 1.04671i | 0.852114 | + | 0.523356i | \(0.175320\pi\) | ||||
−0.852114 | + | 0.523356i | \(0.824680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.69830e8 | 1.06041 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.10159e8 | − | 4.67745e8i | −1.49657 | − | 0.864046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.90385e8 | + | 5.14064e8i | −1.63272 | + | 0.942652i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.96175e6 | − | 4.47041e7i | 0.00357101 | − | 0.0813758i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.85684e8 | − | 3.21615e8i | −0.335541 | − | 0.581174i | 0.648047 | − | 0.761600i | \(-0.275586\pi\) |
−0.983589 | + | 0.180426i | \(0.942253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.07943e7 | + | 7.06579e7i | −0.0731813 | + | 0.126754i | −0.900294 | − | 0.435282i | \(-0.856649\pi\) |
0.827113 | + | 0.562036i | \(0.189982\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.51936e8i | − | 0.982939i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.21411e8 | 1.62906 | 0.814529 | − | 0.580123i | \(-0.196995\pi\) | ||||
0.814529 | + | 0.580123i | \(0.196995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.35666e7 | − | 2.51532e7i | −0.0764698 | − | 0.0441499i | 0.461278 | − | 0.887256i | \(-0.347391\pi\) |
−0.537747 | + | 0.843106i | \(0.680725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.28143e8 | − | 3.04924e8i | 0.920341 | − | 0.531359i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.10701e7 | − | 3.53330e8i | 0.0537536 | − | 0.611287i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.95205e8 | − | 1.20413e9i | −1.19413 | − | 2.06830i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.35887e7 | + | 7.54978e7i | −0.0743357 | + | 0.128753i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.18275e8i | − | 0.200266i | −0.994974 | − | 0.100133i | \(-0.968073\pi\) | ||
0.994974 | − | 0.100133i | \(-0.0319269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.79535e8 | −0.974298 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.48031e6 | − | 3.74141e6i | −0.0108172 | − | 0.00624529i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.14244e8 | − | 5.27839e8i | 1.51528 | − | 0.874845i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.16912e8 | − | 1.39070e7i | −0.521540 | − | 0.0228867i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.97852e8 | − | 5.15895e8i | −0.486718 | − | 0.843020i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.65621e8 | + | 8.06479e8i | −0.755516 | + | 1.30859i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.72140e8i | 0.921840i | 0.887442 | + | 0.460920i | \(0.152480\pi\) | ||||
−0.887442 | + | 0.460920i | \(0.847520\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.81312e8 | −0.770067 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.38731e8 | + | 1.95567e8i | 0.538162 | + | 0.310708i | 0.744334 | − | 0.667808i | \(-0.232767\pi\) |
−0.206172 | + | 0.978516i | \(0.566101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.62106e8 | − | 3.82267e8i | 1.04460 | − | 0.603097i | 0.123464 | − | 0.992349i | \(-0.460600\pi\) |
0.921131 | + | 0.389252i | \(0.127266\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.39772e8 | − | 2.68644e8i | −0.218983 | − | 0.420889i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.28637e8 | − | 1.08883e9i | −0.978065 | − | 1.69406i | −0.669426 | − | 0.742879i | \(-0.733460\pi\) |
−0.308639 | − | 0.951179i | \(-0.599874\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.43300e8 | − | 4.21407e8i | 0.375918 | − | 0.651109i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.34580e8i | − | 0.359943i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.97770e8 | −1.06329 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.45763e8 | + | 8.41562e7i | 0.220593 | + | 0.127360i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.19993e7 | + | 2.42483e7i | −0.0631247 | + | 0.0364451i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.53750e9 | + | 9.79977e8i | 2.29505 | + | 1.46282i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.91957e8 | − | 6.78889e8i | −0.581084 | − | 1.00647i | −0.995351 | − | 0.0963122i | \(-0.969295\pi\) |
0.414267 | − | 0.910155i | \(-0.364038\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.07504e7 | − | 1.39864e8i | 0.118899 | − | 0.205939i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.67078e7i | − | 0.0536823i | −0.999640 | − | 0.0268412i | \(-0.991455\pi\) | ||
0.999640 | − | 0.0268412i | \(-0.00854483\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.33429e8 | 1.06531 | 0.532655 | − | 0.846332i | \(-0.321194\pi\) | ||||
0.532655 | + | 0.846332i | \(0.321194\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.70615e7 | + | 1.56240e7i | 0.0390412 | + | 0.0225404i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.97098e8 | + | 2.87000e8i | −0.712313 | + | 0.411254i | −0.811917 | − | 0.583773i | \(-0.801576\pi\) |
0.0996037 | + | 0.995027i | \(0.468242\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.52965e8 | − | 8.67556e8i | 0.787031 | − | 1.23479i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.71679e7 | + | 4.70561e7i | 0.0384080 | + | 0.0665247i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.45630e8 | − | 1.11826e9i | 0.906628 | − | 1.57033i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.58203e8i | 1.33656i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.76344e8 | −0.244334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.79298e7 | − | 4.49928e7i | −0.107257 | − | 0.0619247i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.04083e8 | − | 3.48767e8i | 0.825890 | − | 0.476828i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.72682e8 | + | 2.97958e8i | −0.777769 | + | 0.404662i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.57719e7 | + | 1.31241e8i | 0.102226 | + | 0.177061i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.53301e8 | + | 9.58345e8i | −0.741548 | + | 1.28440i | 0.210242 | + | 0.977649i | \(0.432575\pi\) |
−0.951790 | + | 0.306750i | \(0.900759\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.69049e8i | 0.358212i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.63025e8 | 1.00921 | 0.504607 | − | 0.863349i | \(-0.331637\pi\) | ||||
0.504607 | + | 0.863349i | \(0.331637\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.28394e8 | + | 7.41285e7i | 0.168707 | + | 0.0974031i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.48639e8 | − | 1.43552e8i | 0.324569 | − | 0.187390i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −631328. | + | 1.43867e7i | −0.000818743 | + | 0.0186574i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.28030e7 | − | 1.60740e8i | −0.119568 | − | 0.207098i | 0.800028 | − | 0.599962i | \(-0.204818\pi\) |
−0.919597 | + | 0.392864i | \(0.871484\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.28294e7 | − | 1.08824e8i | 0.0804237 | − | 0.139298i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.14247e8i | 0.145292i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.70052e9 | 2.14860 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.91301e8 | + | 1.68183e8i | 0.365682 | + | 0.211127i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.21183e7 | − | 6.99652e6i | 0.0151146 | − | 0.00872639i | −0.492424 | − | 0.870356i | \(-0.663889\pi\) |
0.507538 | + | 0.861629i | \(0.330556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.20404e8 | + | 5.74995e8i | 1.01667 | + | 0.712549i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.99507e8 | + | 3.45555e8i | 0.245647 | + | 0.425474i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.22640e8 | − | 5.58829e8i | 0.394715 | − | 0.683666i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.41893e8i | 0.658711i | 0.944206 | + | 0.329355i | \(0.106831\pi\) | ||||
−0.944206 | + | 0.329355i | \(0.893169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.47061e8 | −0.660753 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.09435e9 | − | 6.31821e8i | −1.31337 | − | 0.758273i | −0.330715 | − | 0.943731i | \(-0.607290\pi\) |
−0.982652 | + | 0.185458i | \(0.940623\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.03353e9 | + | 5.96711e8i | −1.23251 | + | 0.711589i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.01923e8 | − | 1.32493e7i | −0.357768 | − | 0.0156999i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.41001e8 | + | 2.44221e8i | 0.166024 | + | 0.287562i | 0.937019 | − | 0.349280i | \(-0.113574\pi\) |
−0.770994 | + | 0.636842i | \(0.780240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.16125e7 | − | 1.06716e8i | 0.0720892 | − | 0.124862i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.24923e8i | 0.377780i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.16665e8 | 0.481403 | 0.240701 | − | 0.970599i | \(-0.422623\pi\) | ||||
0.240701 | + | 0.970599i | \(0.422623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.40302e9 | − | 8.10035e8i | −1.61085 | − | 0.930023i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.85719e7 | + | 2.80430e7i | −0.0554178 | + | 0.0319955i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.44742e8 | + | 8.54804e8i | 0.504257 | + | 0.969194i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.78927e8 | − | 3.09911e8i | −0.201607 | − | 0.349194i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.91229e8 | + | 3.31218e8i | −0.214129 | + | 0.370881i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.09434e9i | 3.44339i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.24846e8 | 0.359251 | 0.179626 | − | 0.983735i | \(-0.442511\pi\) | ||||
0.179626 | + | 0.983735i | \(0.442511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.46584e8 | − | 2.00100e8i | −0.380923 | − | 0.219926i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.37705e9 | − | 7.95041e8i | 1.50416 | − | 0.868425i | 0.504167 | − | 0.863606i | \(-0.331800\pi\) |
0.999988 | − | 0.00481836i | \(-0.00153374\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.48842e7 | − | 4.13560e7i | −0.0704369 | − | 0.0448952i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.61009e8 | + | 2.78876e8i | 0.173715 | + | 0.300882i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.51811e8 | − | 6.09355e8i | 0.377247 | − | 0.653411i | −0.613413 | − | 0.789762i | \(-0.710204\pi\) |
0.990661 | + | 0.136351i | \(0.0435374\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.16932e8i | 0.550916i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.13698e8 | −0.544128 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.23385e8 | − | 7.12362e7i | −0.129897 | − | 0.0749963i | 0.433643 | − | 0.901085i | \(-0.357228\pi\) |
−0.563541 | + | 0.826088i | \(0.690561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.07217e9 | + | 6.19020e8i | −1.12191 | + | 0.647733i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.35781e8 | − | 6.83705e8i | 0.453228 | − | 0.711078i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.27204e9 | + | 2.20324e9i | 1.31496 | + | 2.27757i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.14982e8 | − | 3.72360e8i | 0.220893 | − | 0.382598i | −0.734186 | − | 0.678948i | \(-0.762436\pi\) |
0.955079 | + | 0.296350i | \(0.0957695\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.43424e8i | − | 0.350738i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.22067e9 | 1.23916 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.64708e8 | − | 3.26034e8i | −0.569821 | − | 0.328986i | 0.187257 | − | 0.982311i | \(-0.440040\pi\) |
−0.757078 | + | 0.653325i | \(0.773374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.44980e8 | + | 8.37044e7i | −0.145416 | + | 0.0839561i |
(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 | 336.7.bh.e.241.4 | 8 | ||
4.3 | odd | 2 | 84.7.m.a.73.4 | yes | 8 | ||
7.5 | odd | 6 | inner | 336.7.bh.e.145.4 | 8 | ||
12.11 | even | 2 | 252.7.z.d.73.1 | 8 | |||
28.3 | even | 6 | 588.7.d.b.97.1 | 8 | |||
28.11 | odd | 6 | 588.7.d.b.97.8 | 8 | |||
28.19 | even | 6 | 84.7.m.a.61.4 | ✓ | 8 | ||
28.23 | odd | 6 | 588.7.m.c.313.1 | 8 | |||
28.27 | even | 2 | 588.7.m.c.325.1 | 8 | |||
84.47 | odd | 6 | 252.7.z.d.145.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.7.m.a.61.4 | ✓ | 8 | 28.19 | even | 6 | ||
84.7.m.a.73.4 | yes | 8 | 4.3 | odd | 2 | ||
252.7.z.d.73.1 | 8 | 12.11 | even | 2 | |||
252.7.z.d.145.1 | 8 | 84.47 | odd | 6 | |||
336.7.bh.e.145.4 | 8 | 7.5 | odd | 6 | inner | ||
336.7.bh.e.241.4 | 8 | 1.1 | even | 1 | trivial | ||
588.7.d.b.97.1 | 8 | 28.3 | even | 6 | |||
588.7.d.b.97.8 | 8 | 28.11 | odd | 6 | |||
588.7.m.c.313.1 | 8 | 28.23 | odd | 6 | |||
588.7.m.c.325.1 | 8 | 28.27 | even | 2 |