Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Character | \(\chi\) | \(=\) | 76.9 |
Dual form | 76.6.i.a.17.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −16.5327 | + | 13.8726i | −1.06057 | + | 0.889926i | −0.994165 | − | 0.107867i | \(-0.965598\pi\) |
−0.0664069 | + | 0.997793i | \(0.521154\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.0893 | + | 6.21998i | 0.305702 | + | 0.111266i | 0.490316 | − | 0.871545i | \(-0.336881\pi\) |
−0.184614 | + | 0.982811i | \(0.559104\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −92.6180 | + | 160.419i | −0.714415 | + | 1.23740i | 0.248770 | + | 0.968563i | \(0.419974\pi\) |
−0.963185 | + | 0.268840i | \(0.913360\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 38.6850 | − | 219.393i | 0.159197 | − | 0.902854i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 107.339 | + | 185.917i | 0.267471 | + | 0.463273i | 0.968208 | − | 0.250147i | \(-0.0804788\pi\) |
−0.700737 | + | 0.713419i | \(0.747146\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −318.074 | − | 266.896i | −0.521999 | − | 0.438009i | 0.343329 | − | 0.939215i | \(-0.388445\pi\) |
−0.865328 | + | 0.501206i | \(0.832890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −368.819 | + | 134.239i | −0.423238 | + | 0.154046i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −270.266 | − | 1532.75i | −0.226813 | − | 1.28632i | −0.859188 | − | 0.511659i | \(-0.829031\pi\) |
0.632375 | − | 0.774662i | \(-0.282080\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −287.327 | − | 1547.11i | −0.182596 | − | 0.983188i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −694.201 | − | 3937.01i | −0.343508 | − | 1.94813i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1754.94 | − | 638.746i | 0.691740 | − | 0.251773i | 0.0278598 | − | 0.999612i | \(-0.491131\pi\) |
0.663880 | + | 0.747839i | \(0.268909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2140.53 | − | 1796.12i | −0.684971 | − | 0.574759i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −218.216 | − | 377.960i | −0.0576071 | − | 0.0997785i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −754.646 | + | 4279.81i | −0.166628 | + | 0.944995i | 0.780742 | + | 0.624854i | \(0.214842\pi\) |
−0.947370 | + | 0.320141i | \(0.896270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2536.15 | + | 4392.74i | −0.473992 | + | 0.820977i | −0.999557 | − | 0.0297760i | \(-0.990521\pi\) |
0.525565 | + | 0.850753i | \(0.323854\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4353.75 | − | 1584.63i | −0.695950 | − | 0.253305i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2580.58 | + | 2165.36i | −0.356079 | + | 0.298786i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 33.9163 | 0.00407290 | 0.00203645 | − | 0.999998i | \(-0.499352\pi\) | ||||
0.00203645 | + | 0.999998i | \(0.499352\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8961.15 | 0.943414 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9726.48 | − | 8161.49i | 0.903642 | − | 0.758245i | −0.0672571 | − | 0.997736i | \(-0.521425\pi\) |
0.970899 | + | 0.239490i | \(0.0769803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4690.09 | − | 1707.05i | −0.386821 | − | 0.140791i | 0.141287 | − | 0.989969i | \(-0.454876\pi\) |
−0.528108 | + | 0.849177i | \(0.677098\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2025.72 | − | 3508.65i | 0.149124 | − | 0.258291i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2242.48 | + | 12717.7i | −0.148076 | + | 0.839779i | 0.816770 | + | 0.576963i | \(0.195762\pi\) |
−0.964846 | + | 0.262816i | \(0.915349\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8752.70 | − | 15160.1i | −0.520777 | − | 0.902013i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 25731.4 | + | 21591.2i | 1.38528 | + | 1.16239i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −24560.0 | + | 8939.11i | −1.20099 | + | 0.437124i | −0.863569 | − | 0.504230i | \(-0.831776\pi\) |
−0.337419 | + | 0.941354i | \(0.609554\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 677.947 | + | 3844.83i | 0.0302196 | + | 0.171384i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 26212.6 | + | 21591.9i | 1.06862 | + | 0.880245i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3322.45 | − | 18842.6i | −0.124259 | − | 0.704710i | −0.981745 | − | 0.190202i | \(-0.939086\pi\) |
0.857486 | − | 0.514508i | \(-0.172025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29662.1 | − | 10796.1i | 1.02065 | − | 0.371487i | 0.223138 | − | 0.974787i | \(-0.428370\pi\) |
0.797514 | + | 0.603300i | \(0.206148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31612.0 | + | 26525.6i | 1.00346 | + | 0.842003i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3775.56 | − | 6539.47i | −0.110840 | − | 0.191981i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5288.86 | + | 29994.6i | −0.143938 | + | 0.816313i | 0.824276 | + | 0.566189i | \(0.191583\pi\) |
−0.968214 | + | 0.250124i | \(0.919529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20152.8 | + | 34905.7i | −0.509581 | + | 0.882620i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −34086.9 | − | 12406.6i | −0.802494 | − | 0.292084i | −0.0919742 | − | 0.995761i | \(-0.529318\pi\) |
−0.710519 | + | 0.703678i | \(0.751540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −62821.4 | + | 52713.4i | −1.37975 | + | 1.15775i | −0.410445 | + | 0.911886i | \(0.634626\pi\) |
−0.969305 | + | 0.245862i | \(0.920929\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 60305.6 | 1.23795 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −39766.1 | −0.764340 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8486.16 | − | 7120.74i | 0.152983 | − | 0.128368i | −0.563084 | − | 0.826400i | \(-0.690385\pi\) |
0.716067 | + | 0.698032i | \(0.245941\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59721.3 | + | 21736.8i | 1.01138 | + | 0.368114i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7468.07 | − | 12935.1i | 0.118991 | − | 0.206098i | −0.800377 | − | 0.599497i | \(-0.795367\pi\) |
0.919368 | + | 0.393399i | \(0.128701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4915.05 | − | 27874.6i | 0.0737872 | − | 0.418468i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −46895.7 | − | 81225.7i | −0.664255 | − | 1.15052i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −73562.7 | − | 61726.4i | −0.984425 | − | 0.826030i | 0.000326264 | − | 1.00000i | \(-0.499896\pi\) |
−0.984751 | + | 0.173969i | \(0.944341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 72274.6 | − | 26305.8i | 0.914918 | − | 0.333003i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −19009.2 | − | 107807.i | −0.227907 | − | 1.29252i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4712.78 | − | 28226.1i | 0.0535758 | − | 0.320879i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11066.5 | − | 62761.3i | −0.119421 | − | 0.677271i | −0.984466 | − | 0.175576i | \(-0.943821\pi\) |
0.865045 | − | 0.501695i | \(-0.167290\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 44941.3 | − | 16357.3i | 0.460848 | − | 0.167735i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −36817.5 | − | 30893.5i | −0.359129 | − | 0.301345i | 0.445314 | − | 0.895374i | \(-0.353092\pi\) |
−0.804444 | + | 0.594029i | \(0.797536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −33680.8 | − | 58336.8i | −0.312816 | − | 0.541813i | 0.666155 | − | 0.745813i | \(-0.267939\pi\) |
−0.978971 | + | 0.204000i | \(0.934606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12624.7 | − | 71598.5i | 0.111751 | − | 0.633769i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −104101. | + | 180308.i | −0.879011 | + | 1.52249i | −0.0265842 | + | 0.999647i | \(0.508463\pi\) |
−0.852427 | + | 0.522846i | \(0.824870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3826.82 | − | 1392.85i | −0.0308512 | − | 0.0112289i | 0.326548 | − | 0.945180i | \(-0.394114\pi\) |
−0.357400 | + | 0.933952i | \(0.616337\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −560.728 | + | 470.506i | −0.00431961 | + | 0.00362458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −172879. | −1.27364 | −0.636819 | − | 0.771013i | \(-0.719750\pi\) | ||||
−0.636819 | + | 0.771013i | \(0.719750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33963.6 | 0.239480 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −70859.9 | + | 59458.5i | −0.478559 | + | 0.401559i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 270914. | + | 98604.7i | 1.75374 | + | 0.638308i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 57482.2 | − | 99562.0i | 0.356919 | − | 0.618202i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −47584.1 | + | 269863.i | −0.283595 | + | 1.60835i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −53823.9 | − | 93225.8i | −0.308106 | − | 0.533656i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −247017. | − | 207272.i | −1.35900 | − | 1.14033i | −0.976291 | − | 0.216462i | \(-0.930548\pi\) |
−0.382704 | − | 0.923871i | \(-0.625007\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 101221. | − | 36841.5i | 0.535546 | − | 0.194923i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 60080.8 | + | 340735.i | 0.305885 | + | 1.73476i | 0.619311 | + | 0.785146i | \(0.287412\pi\) |
−0.313426 | + | 0.949612i | \(0.601477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 274797. | + | 97197.4i | 1.34705 | + | 0.476459i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1378.24 | − | 7816.36i | −0.00650862 | − | 0.0369122i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −94710.1 | + | 34471.7i | −0.431117 | + | 0.156914i | −0.548458 | − | 0.836178i | \(-0.684785\pi\) |
0.117341 | + | 0.993092i | \(0.462563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 226390. | + | 189964.i | 0.993851 | + | 0.833940i | 0.986121 | − | 0.166030i | \(-0.0530950\pi\) |
0.00773009 | + | 0.999970i | \(0.497539\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −139353. | − | 241367.i | −0.590296 | − | 1.02242i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15478.6 | − | 87783.6i | 0.0632983 | − | 0.358983i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −39516.7 | + | 68444.9i | −0.156085 | + | 0.270347i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 355016. | + | 129215.i | 1.35505 | + | 0.493197i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 122658. | − | 102922.i | 0.452615 | − | 0.379789i | −0.387790 | − | 0.921748i | \(-0.626761\pi\) |
0.840405 | + | 0.541958i | \(0.182317\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −315290. | −1.12530 | −0.562649 | − | 0.826696i | \(-0.690218\pi\) | ||||
−0.562649 | + | 0.826696i | \(0.690218\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −346731. | −1.19747 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −70663.7 | + | 59293.9i | −0.236247 | + | 0.198235i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 497814. | + | 181190.i | 1.61183 | + | 0.586657i | 0.981800 | − | 0.189917i | \(-0.0608219\pi\) |
0.630026 | + | 0.776574i | \(0.283044\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 282035. | − | 488498.i | 0.884727 | − | 1.53239i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −60072.0 | + | 340685.i | −0.182645 | + | 1.03583i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 170727. | + | 295707.i | 0.503306 | + | 0.871752i | 0.999993 | + | 0.00382173i | \(0.00121650\pi\) |
−0.496687 | + | 0.867930i | \(0.665450\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −64545.9 | − | 54160.4i | −0.184569 | − | 0.154872i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −95436.5 | + | 34736.0i | −0.264803 | + | 0.0963805i | −0.471010 | − | 0.882128i | \(-0.656110\pi\) |
0.206207 | + | 0.978508i | \(0.433888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −34536.6 | − | 195867.i | −0.0930172 | − | 0.527527i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −350540. | + | 3187.75i | −0.916744 | + | 0.00833670i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 43202.3 | + | 245012.i | 0.109747 | + | 0.622405i | 0.989218 | + | 0.146452i | \(0.0467855\pi\) |
−0.879471 | + | 0.475953i | \(0.842103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 486384. | − | 177029.i | 1.20056 | − | 0.436969i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 316324. | + | 265427.i | 0.758925 | + | 0.636814i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −331263. | − | 573765.i | −0.772753 | − | 1.33845i | −0.936049 | − | 0.351871i | \(-0.885546\pi\) |
0.163295 | − | 0.986577i | \(-0.447788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −122306. | + | 693629.i | −0.277492 | + | 1.57373i | 0.453443 | + | 0.891285i | \(0.350196\pi\) |
−0.730935 | + | 0.682447i | \(0.760916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −340625. | + | 589979.i | −0.751880 | + | 1.30229i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 579.605 | + | 210.959i | 0.00124509 | + | 0.000453177i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 255954. | − | 214771.i | 0.535252 | − | 0.449130i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 80842.8 | 0.164622 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −730125. | −1.44815 | −0.724075 | − | 0.689721i | \(-0.757733\pi\) | ||||
−0.724075 | + | 0.689721i | \(0.757733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 268839. | − | 225583.i | 0.519516 | − | 0.435925i | −0.344947 | − | 0.938622i | \(-0.612103\pi\) |
0.864463 | + | 0.502697i | \(0.167659\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 153139. | + | 55738.2i | 0.288403 | + | 0.104970i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −302321. | + | 523636.i | −0.555013 | + | 0.961311i | 0.442889 | + | 0.896576i | \(0.353953\pi\) |
−0.997903 | + | 0.0647347i | \(0.979380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2245.00 | − | 12732.0i | 0.00401868 | − | 0.0227911i | −0.982732 | − | 0.185032i | \(-0.940761\pi\) |
0.986751 | + | 0.162241i | \(0.0518722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −328664. | − | 569262.i | −0.573801 | − | 0.993853i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −616670. | − | 517448.i | −1.05030 | − | 0.881305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 216983. | − | 78975.3i | 0.360612 | − | 0.131252i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −72246.8 | − | 409732.i | −0.117191 | − | 0.664621i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 256792. | − | 219484.i | 0.406645 | − | 0.347566i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −105477. | − | 598191.i | −0.163100 | − | 0.924983i | −0.951002 | − | 0.309184i | \(-0.899944\pi\) |
0.787903 | − | 0.615800i | \(-0.211167\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 735660. | − | 267758.i | 1.11104 | − | 0.404384i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −69532.4 | − | 58344.6i | −0.102587 | − | 0.0860804i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −469786. | − | 813694.i | −0.677253 | − | 1.17304i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 307336. | − | 1.74299e6i | 0.433015 | − | 2.45575i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −323121. | + | 559661.i | −0.445025 | + | 0.770805i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −439331. | − | 159903.i | −0.591602 | − | 0.215325i | 0.0288320 | − | 0.999584i | \(-0.490821\pi\) |
−0.620434 | + | 0.784259i | \(0.713043\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −476864. | + | 400136.i | −0.627969 | + | 0.526928i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −301861. | −0.388814 | −0.194407 | − | 0.980921i | \(-0.562278\pi\) | ||||
−0.194407 | + | 0.980921i | \(0.562278\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.09881e6 | 1.38463 | 0.692313 | − | 0.721598i | \(-0.256592\pi\) | ||||
0.692313 | + | 0.721598i | \(0.256592\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 657441. | − | 551659.i | 0.810638 | − | 0.680206i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −166874. | − | 60737.2i | −0.201372 | − | 0.0732935i | 0.239365 | − | 0.970930i | \(-0.423061\pi\) |
−0.440737 | + | 0.897636i | \(0.645283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −117426. | + | 203388.i | −0.138706 | + | 0.240246i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −41516.2 | + | 235450.i | −0.0480116 | + | 0.272287i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 116816. | + | 202331.i | 0.132284 | + | 0.229123i | 0.924557 | − | 0.381045i | \(-0.124436\pi\) |
−0.792273 | + | 0.610167i | \(0.791102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 791942. | + | 664518.i | 0.878315 | + | 0.736994i | 0.965832 | − | 0.259169i | \(-0.0834486\pi\) |
−0.0875166 | + | 0.996163i | \(0.527893\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.18924e6 | + | 432848.i | −1.29197 | + | 0.470240i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −55281.5 | − | 313517.i | −0.0588389 | − | 0.333692i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −321525. | + | 568781.i | −0.335330 | + | 0.593202i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 55975.5 | + | 317453.i | 0.0572136 | + | 0.324475i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.16252e6 | + | 423122.i | −1.16470 | + | 0.423917i | −0.850775 | − | 0.525530i | \(-0.823867\pi\) |
−0.313928 | + | 0.949447i | \(0.601645\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 307127. | + | 257710.i | 0.301659 | + | 0.253122i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 305434. | + | 529027.i | 0.294149 | + | 0.509480i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −166782. | + | 945869.i | −0.157513 | + | 0.893301i | 0.798939 | + | 0.601412i | \(0.205395\pi\) |
−0.956452 | + | 0.291889i | \(0.905716\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3141.26 | + | 5440.82i | −0.00290974 | + | 0.00503982i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 909769. | + | 331129.i | 0.826666 | + | 0.300882i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.04243e6 | + | 874704.i | −0.929304 | + | 0.779779i | −0.975692 | − | 0.219145i | \(-0.929673\pi\) |
0.0463880 | + | 0.998923i | \(0.485229\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −475314. | −0.415782 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.07249e6 | 1.77916 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.73934e6 | − | 1.45948e6i | 1.46556 | − | 1.22975i | 0.545413 | − | 0.838167i | \(-0.316373\pi\) |
0.920144 | − | 0.391581i | \(-0.128072\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 881034. | + | 320670.i | 0.728734 | + | 0.265238i | 0.679629 | − | 0.733556i | \(-0.262141\pi\) |
0.0491053 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −829964. | + | 1.43754e6i | −0.673989 | + | 1.16738i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 104166. | − | 590755.i | 0.0830605 | − | 0.471059i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −417874. | − | 723778.i | −0.327224 | − | 0.566769i | 0.654736 | − | 0.755858i | \(-0.272780\pi\) |
−0.981960 | + | 0.189089i | \(0.939447\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 865627. | + | 726348.i | 0.665764 | + | 0.558642i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.47381e6 | + | 536423.i | −1.11346 | + | 0.405268i | −0.832263 | − | 0.554381i | \(-0.812955\pi\) |
−0.281201 | + | 0.959649i | \(0.590733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −359924. | − | 2.04123e6i | −0.267143 | − | 1.51504i | −0.762862 | − | 0.646561i | \(-0.776206\pi\) |
0.495719 | − | 0.868483i | \(-0.334905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 313654. | + | 532032.i | 0.228738 | + | 0.387994i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 408411. | + | 2.31622e6i | 0.292680 | + | 1.65987i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −942056. | + | 342880.i | −0.663486 | + | 0.241489i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.05362e6 | + | 884092.i | 0.729376 | + | 0.612019i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 126571. | + | 219228.i | 0.0861324 | + | 0.149186i | 0.905873 | − | 0.423549i | \(-0.139216\pi\) |
−0.819741 | + | 0.572735i | \(0.805883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 60422.2 | − | 342671.i | 0.0404242 | − | 0.229257i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 46846.1 | − | 81139.8i | 0.0308164 | − | 0.0533756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −728680. | − | 265218.i | −0.471366 | − | 0.171563i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 708231. | − | 594277.i | 0.450567 | − | 0.378070i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.03726e6 | 0.649057 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 574056. | 0.353349 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.45169e6 | + | 1.21811e6i | −0.879078 | + | 0.737634i | −0.965989 | − | 0.258582i | \(-0.916745\pi\) |
0.0869114 | + | 0.996216i | \(0.472300\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.36612e6 | + | 497225.i | 0.813938 | + | 0.296249i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 486478. | − | 842605.i | 0.285209 | − | 0.493996i | −0.687451 | − | 0.726231i | \(-0.741270\pi\) |
0.972660 | + | 0.232235i | \(0.0746038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 578383. | − | 3.28017e6i | 0.333699 | − | 1.89250i | −0.106022 | − | 0.994364i | \(-0.533811\pi\) |
0.439720 | − | 0.898135i | \(-0.355078\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 375237. | + | 649929.i | 0.213073 | + | 0.369054i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 559388. | + | 469382.i | 0.312655 | + | 0.262349i | 0.785588 | − | 0.618750i | \(-0.212360\pi\) |
−0.472933 | + | 0.881098i | \(0.656805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −876692. | + | 319090.i | −0.482359 | + | 0.175564i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −780268. | − | 4.42512e6i | −0.422650 | − | 2.39697i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.29368e6 | + | 858530.i | −1.22328 | + | 0.457878i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 201471. | + | 1.14260e6i | 0.105805 | + | 0.600047i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 82590.0 | − | 30060.3i | 0.0427128 | − | 0.0155462i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.83247e6 | − | 1.53763e6i | −0.933358 | − | 0.783180i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 973238. | + | 1.68570e6i | 0.488258 | + | 0.845687i | 0.999909 | − | 0.0135063i | \(-0.00429933\pi\) |
−0.511651 | + | 0.859193i | \(0.670966\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1312.05 | − | 7441.01i | 0.000648396 | − | 0.00367724i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −276949. | + | 479690.i | −0.134830 | + | 0.233533i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.05743e6 | + | 748842.i | 0.986846 | + | 0.359183i | 0.784498 | − | 0.620131i | \(-0.212921\pi\) |
0.202348 | + | 0.979314i | \(0.435143\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.85815e6 | − | 2.39828e6i | 1.35079 | − | 1.13344i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.08891e6 | −0.507115 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 129370. | 0.0593744 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −561510. | + | 471163.i | −0.253986 | + | 0.213120i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.28044e6 | − | 830011.i | −1.01670 | − | 0.370050i | −0.220700 | − | 0.975342i | \(-0.570834\pi\) |
−0.796004 | + | 0.605292i | \(0.793056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.65873e6 | + | 2.87300e6i | −0.728973 | + | 1.26262i | 0.228345 | + | 0.973580i | \(0.426669\pi\) |
−0.957318 | + | 0.289037i | \(0.906665\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31467.4 | + | 178460.i | −0.0136330 | + | 0.0773168i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.26131e6 | + | 2.18466e6i | 0.538749 | + | 0.933141i | 0.998972 | + | 0.0453374i | \(0.0144363\pi\) |
−0.460222 | + | 0.887804i | \(0.652230\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −505351. | − | 424040.i | −0.212825 | − | 0.178581i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.84684e6 | + | 2.12808e6i | −2.42801 | + | 0.883724i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −573983. | − | 3.25522e6i | −0.235051 | − | 1.33304i | −0.842505 | − | 0.538688i | \(-0.818920\pi\) |
0.607454 | − | 0.794355i | \(-0.292191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.31099e6 | + | 889051.i | −0.933317 | + | 0.359053i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 430847. | + | 2.44345e6i | 0.171615 | + | 0.973279i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.40145e6 | + | 510085.i | −0.550611 | + | 0.200406i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20776.9 | + | 17433.9i | 0.00805222 | + | 0.00675661i | 0.646805 | − | 0.762656i | \(-0.276105\pi\) |
−0.638753 | + | 0.769412i | \(0.720549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.41431e6 | − | 2.44965e6i | −0.540727 | − | 0.936567i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 840695. | − | 4.76782e6i | 0.317106 | − | 1.79839i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.45951e6 | − | 4.26000e6i | 0.915329 | − | 1.58540i | 0.108910 | − | 0.994052i | \(-0.465264\pi\) |
0.806419 | − | 0.591345i | \(-0.201403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.18314e6 | + | 794597.i | 0.801683 | + | 0.291789i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.38230e6 | − | 1.15989e6i | 0.500897 | − | 0.420302i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.21025e6 | −0.432791 | −0.216396 | − | 0.976306i | \(-0.569430\pi\) | ||||
−0.216396 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.95926e6 | 2.45612 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.18047e6 | − | 3.50783e6i | 1.45622 | − | 1.22192i | 0.528349 | − | 0.849027i | \(-0.322811\pi\) |
0.927875 | − | 0.372891i | \(-0.121633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −679574. | − | 247345.i | −0.233660 | − | 0.0850454i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −555953. | + | 962938.i | −0.188695 | + | 0.326829i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 149883. | − | 850029.i | 0.0502202 | − | 0.284813i | −0.949347 | − | 0.314229i | \(-0.898254\pi\) |
0.999567 | + | 0.0294167i | \(0.00936497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.45334e6 | − | 2.51726e6i | −0.480756 | − | 0.832694i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.72017e6 | − | 4.79979e6i | −1.86822 | − | 1.56762i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 189313. | − | 68904.3i | 0.0610503 | − | 0.0222205i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 335321. | + | 1.90170e6i | 0.106779 | + | 0.605572i | 0.990495 | + | 0.137549i | \(0.0439225\pi\) |
−0.883716 | + | 0.468023i | \(0.844966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.89152e6 | + | 2.20521e6i | −1.85266 | + | 0.693455i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 427729. | + | 2.42577e6i | 0.132834 | + | 0.753337i | 0.976344 | + | 0.216224i | \(0.0693740\pi\) |
−0.843510 | + | 0.537113i | \(0.819515\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.97909e6 | − | 720329.i | 0.607019 | − | 0.220937i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 885390. | + | 742930.i | 0.268224 | + | 0.225066i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3640.54 | + | 6305.61i | 0.00108938 | + | 0.00188687i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 162994. | − | 924382.i | 0.0481795 | − | 0.273239i | −0.951196 | − | 0.308589i | \(-0.900143\pi\) |
0.999375 | + | 0.0353494i | \(0.0112544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.08760e6 | − | 1.88378e6i | 0.317589 | − | 0.550080i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.33043e6 | + | 1.21218e6i | 0.960783 | + | 0.349696i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 208080. | − | 174600.i | 0.0593075 | − | 0.0497649i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.37813e6 | −1.79620 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 715148. | 0.199003 | 0.0995017 | − | 0.995037i | \(-0.468275\pi\) | ||||
0.0995017 | + | 0.995037i | \(0.468275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 418023. | − | 350763.i | 0.114946 | − | 0.0964515i | −0.583503 | − | 0.812111i | \(-0.698318\pi\) |
0.698449 | + | 0.715660i | \(0.253874\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.70344e6 | + | 983970.i | 0.734624 | + | 0.267381i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.17450e6 | + | 3.76634e6i | −0.583964 | + | 1.01146i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.01534e6 | + | 5.75829e6i | −0.269490 | + | 1.52835i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 961881. | + | 1.66603e6i | 0.252335 | + | 0.437058i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.61843e6 | + | 4.71442e6i | 1.45687 | + | 1.22246i | 0.927366 | + | 0.374154i | \(0.122067\pi\) |
0.529506 | + | 0.848306i | \(0.322377\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −677794. | + | 246697.i | −0.173731 | + | 0.0632330i | −0.427421 | − | 0.904053i | \(-0.640578\pi\) |
0.253690 | + | 0.967286i | \(0.418356\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −296190. | − | 1.67978e6i | −0.0750494 | − | 0.425626i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.49245e6 | − | 2.53155e6i | −0.373849 | − | 0.634137i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 561812. | + | 3.18620e6i | 0.139133 | + | 0.789062i | 0.971892 | + | 0.235427i | \(0.0756488\pi\) |
−0.832759 | + | 0.553635i | \(0.813240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.66463e6 | + | 1.33382e6i | −0.897292 | + | 0.326587i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.79583e6 | + | 4.86328e6i | 1.40316 | + | 1.17739i | 0.959678 | + | 0.281103i | \(0.0907002\pi\) |
0.443478 | + | 0.896285i | \(0.353744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −873195. | − | 1.51242e6i | −0.209031 | − | 0.362053i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −600068. | + | 3.40315e6i | −0.142047 | + | 0.805588i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −425393. | + | 736803.i | −0.0995806 | + | 0.172479i | −0.911511 | − | 0.411275i | \(-0.865083\pi\) |
0.811931 | + | 0.583754i | \(0.198417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.56139e6 | + | 932269.i | 0.592972 | + | 0.215824i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.21259e6 | − | 4.37388e6i | 1.19346 | − | 1.00143i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.39874e6 | 0.316744 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.57687e6 | 0.801147 | 0.400574 | − | 0.916265i | \(-0.368811\pi\) | ||||
0.400574 | + | 0.916265i | \(0.368811\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −520343. | + | 436620.i | −0.115281 | + | 0.0967324i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.94449e6 | + | 1.43568e6i | 0.864448 | + | 0.314633i | 0.735917 | − | 0.677072i | \(-0.236752\pi\) |
0.128531 | + | 0.991705i | \(0.458974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.12019e6 | + | 5.40434e6i | −0.676440 | + | 1.17163i | 0.299606 | + | 0.954063i | \(0.403145\pi\) |
−0.976046 | + | 0.217565i | \(0.930189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 345702. | − | 1.96057e6i | 0.0741429 | − | 0.420485i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.52384e6 | + | 4.37142e6i | 0.535512 | + | 0.927534i | 0.999138 | + | 0.0415034i | \(0.0132147\pi\) |
−0.463626 | + | 0.886031i | \(0.653452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.32187e6 | − | 3.62648e6i | −0.907276 | − | 0.761295i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.07438e7 | + | 3.91041e6i | −2.23154 | + | 0.812214i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −186060. | − | 1.05520e6i | −0.0382385 | − | 0.216861i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.16376e6 | + | 3.82771e6i | −0.440023 | + | 0.778404i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.01108e6 | + | 5.73411e6i | 0.203465 | + | 1.15391i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.88321e6 | − | 2.86925e6i | 1.56987 | − | 0.571387i | 0.596901 | − | 0.802315i | \(-0.296399\pi\) |
0.972971 | + | 0.230928i | \(0.0741763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10787.9 | − | 9052.12i | −0.00212605 | − | 0.00178397i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.73303e6 | − | 6.46580e6i | −0.728105 | − | 1.26111i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 201256. | − | 1.14138e6i | 0.0388503 | − | 0.220331i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.80494e6 | + | 3.12624e6i | −0.344858 | + | 0.597311i | −0.985328 | − | 0.170672i | \(-0.945406\pi\) |
0.640470 | + | 0.767983i | \(0.278739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.92479e6 | − | 2.52042e6i | −1.30959 | − | 0.476651i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.13684e6 | + | 953919.i | −0.212811 | + | 0.178570i | −0.742962 | − | 0.669334i | \(-0.766580\pi\) |
0.530151 | + | 0.847903i | \(0.322135\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.76384e6 | 1.25336 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 869756. | 0.159545 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.14732e6 | − | 4.31911e6i | 0.934739 | − | 0.784339i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.14449e6 | + | 1.14450e6i | 0.565326 | + | 0.205762i | 0.608843 | − | 0.793291i | \(-0.291634\pi\) |
−0.0435166 | + | 0.999053i | \(0.513856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.09594e6 | − | 1.89823e6i | 0.195071 | − | 0.337874i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.17470e6 | − | 6.66206e6i | 0.207017 | − | 1.17405i | −0.687216 | − | 0.726453i | \(-0.741167\pi\) |
0.894233 | − | 0.447601i | \(-0.147722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −437026. | − | 756952.i | −0.0762569 | − | 0.132081i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.28816e6 | + | 2.75909e6i | 0.568111 | + | 0.476702i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 695885. | − | 253281.i | 0.119054 | − | 0.0433320i | −0.281806 | − | 0.959471i | \(-0.590934\pi\) |
0.400860 | + | 0.916139i | \(0.368711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.63784e6 | − | 1.49600e7i | −0.446886 | − | 2.53442i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −522046. | + | 446201.i | −0.0875822 | + | 0.0748578i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −212726. | − | 1.20643e6i | −0.0353429 | − | 0.200439i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.60514e6 | + | 948195.i | −0.428653 | + | 0.156017i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.11320e6 | − | 3.45139e6i | −0.670289 | − | 0.562439i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.40631e6 | − | 7.63196e6i | −0.711183 | − | 1.23180i | −0.964414 | − | 0.264399i | \(-0.914827\pi\) |
0.253231 | − | 0.967406i | \(-0.418507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.50040e6 | − | 8.50919e6i | 0.239857 | − | 1.36030i | −0.592282 | − | 0.805731i | \(-0.701773\pi\) |
0.832139 | − | 0.554567i | \(-0.187116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.58539e6 | + | 9.67417e6i | −0.884413 | + | 1.53185i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.41841e6 | + | 2.70008e6i | 1.16355 | + | 0.423497i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.25871e6 | + | 1.89528e6i | −0.350930 | + | 0.294465i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.26247e6 | −0.656031 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.27201e6 | −0.803819 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.90052e6 | + | 2.43382e6i | −0.438118 | + | 0.367625i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.34363e7 | + | 4.89040e6i | 2.01068 | + | 0.731828i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.87901e6 | − | 3.25455e6i | 0.278585 | − | 0.482524i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −783205. | + | 4.44178e6i | −0.115049 | + | 0.652475i | 0.871677 | + | 0.490081i | \(0.163033\pi\) |
−0.986726 | + | 0.162394i | \(0.948078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.60038e6 | − | 1.31642e7i | −1.10621 | − | 1.91600i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −56734.0 | − | 47605.5i | −0.00818187 | − | 0.00686540i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.26270e6 | + | 2.27944e6i | −0.894939 | + | 0.325731i | −0.748223 | − | 0.663448i | \(-0.769093\pi\) |
−0.146716 | + | 0.989179i | \(0.546870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.22112e6 | − | 6.92532e6i | −0.172913 | − | 0.980639i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.83816e6 | − | 62185.0i | 0.959534 | − | 0.00872582i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 356331. | + | 2.02085e6i | 0.0495496 | + | 0.281010i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12509.0 | + | 4552.89i | −0.00172381 | + | 0.000627415i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.16086e6 | + | 5.16958e6i | 0.841402 | + | 0.706020i | 0.957879 | − | 0.287174i | \(-0.0927157\pi\) |
−0.116477 | + | 0.993193i | \(0.537160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.03619e6 | + | 1.79474e6i | 0.140252 | + | 0.242924i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.25218e6 | + | 7.10148e6i | −0.167981 | + | 0.952669i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.97212e6 | + | 6.87992e6i | −0.528143 | + | 0.914771i | 0.471318 | + | 0.881963i | \(0.343778\pi\) |
−0.999462 | + | 0.0328080i | \(0.989555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.95437e6 | − | 1.07530e6i | −0.389354 | − | 0.141713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.01826e6 | + | 7.56722e6i | −1.17805 | + | 0.988504i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.10265e7 | −1.42777 | −0.713883 | − | 0.700265i | \(-0.753065\pi\) | ||||
−0.713883 | + | 0.700265i | \(0.753065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.93966e6 | −0.248963 | −0.124482 | − | 0.992222i | \(-0.539727\pi\) | ||||
−0.124482 | + | 0.992222i | \(0.539727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.20709e7 | − | 1.01287e7i | 1.53587 | − | 1.28875i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.90378e6 | − | 1.78483e6i | −0.618530 | − | 0.225127i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.83163e6 | − | 8.36863e6i | 0.604163 | − | 1.04644i | −0.388020 | − | 0.921651i | \(-0.626841\pi\) |
0.992183 | − | 0.124790i | \(-0.0398258\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.31522e6 | + | 7.45897e6i | −0.163043 | + | 0.924661i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.38336e6 | + | 2.39604e6i | 0.170017 | + | 0.294479i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.29818e6 | − | 3.60660e6i | −0.523737 | − | 0.439467i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.58077e6 | + | 575355.i | −0.190977 | + | 0.0695098i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −968493. | − | 5.49260e6i | −0.116012 | − | 0.657934i | −0.986244 | − | 0.165294i | \(-0.947143\pi\) |
0.870233 | − | 0.492641i | \(-0.163968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.52475e6 | + | 2.66155e6i | 0.893724 | + | 0.316115i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.26599e6 | − | 1.28511e7i | −0.266864 | − | 1.51346i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.93353e6 | + | 2.88757e6i | −0.926467 | + | 0.337206i | −0.760808 | − | 0.648977i | \(-0.775197\pi\) |
−0.165659 | + | 0.986183i | \(0.552975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.01640e6 | + | 3.37016e6i | 0.465099 | + | 0.390264i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 139510. | + | 241639.i | 0.0160203 | + | 0.0277479i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.33109e6 | − | 1.32202e7i | 0.265455 | − | 1.50547i | −0.502281 | − | 0.864704i | \(-0.667506\pi\) |
0.767736 | − | 0.640766i | \(-0.221383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.15660e6 | + | 1.06636e7i | −0.695273 | + | 1.20425i | 0.274816 | + | 0.961497i | \(0.411383\pi\) |
−0.970089 | + | 0.242751i | \(0.921950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.37603e6 | + | 2.32068e6i | 0.714096 | + | 0.259910i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.60160e6 | − | 1.34390e6i | 0.177896 | − | 0.149272i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.00810e7 | −1.11053 | −0.555266 | − | 0.831673i | \(-0.687384\pi\) | ||||
−0.555266 | + | 0.831673i | \(0.687384\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.73735e7 | 1.89821 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.10758e6 | − | 3.44667e6i | 0.445127 | − | 0.373506i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.53346e6 | + | 922102.i | 0.272309 | + | 0.0991124i | 0.474565 | − | 0.880220i | \(-0.342605\pi\) |
−0.202256 | + | 0.979333i | \(0.564827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.49172e6 | + | 4.31578e6i | −0.265651 | + | 0.460121i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.33623e6 | − | 7.57813e6i | 0.141308 | − | 0.801400i | −0.828949 | − | 0.559324i | \(-0.811061\pi\) |
0.970257 | − | 0.242076i | \(-0.0778282\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.28561e6 | − | 1.43511e7i | −0.869156 | − | 1.50542i | −0.862860 | − | 0.505443i | \(-0.831329\pi\) |
−0.00629600 | − | 0.999980i | \(-0.502004\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −624376. | − | 523914.i | −0.0649706 | − | 0.0545168i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.67153e7 | − | 6.08388e6i | 1.72542 | − | 0.628002i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.17636e6 | + | 6.67149e6i | 0.120460 | + | 0.683160i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.20065e6 | + | 7.19102e6i | −0.121969 | + | 0.730503i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9166.41 | − | 51985.3i | −0.000923788 | − | 0.00523906i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.16546e6 | − | 2.97198e6i | 0.816408 | − | 0.297148i | 0.100140 | − | 0.994973i | \(-0.468071\pi\) |
0.716268 | + | 0.697825i | \(0.245849\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.00423e7 | + | 8.42647e6i | 0.996146 | + | 0.835865i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.93211e6 | − | 5.07857e6i | −0.288567 | − | 0.499813i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.26217e6 | + | 7.15810e6i | −0.123245 | + | 0.698955i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.04058e6 | + | 6.99849e6i | −0.391464 | + | 0.678035i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.46130e6 | − | 1.62378e6i | −0.428861 | − | 0.156092i | 0.118566 | − | 0.992946i | \(-0.462170\pi\) |
−0.547427 | + | 0.836854i | \(0.684392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.01365e7 | + | 8.50555e6i | −0.966856 | + | 0.811288i | −0.982055 | − | 0.188596i | \(-0.939606\pi\) |
0.0151991 | + | 0.999884i | \(0.495162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.95895e6 | 0.185406 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.09494e7 | −1.02833 | −0.514163 | − | 0.857693i | \(-0.671897\pi\) | ||||
−0.514163 | + | 0.857693i | \(0.671897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.14652e6 | − | 2.64024e6i | 0.293237 | − | 0.246055i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.90549e7 | + | 6.93540e6i | 1.76219 | + | 0.641385i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.84673e6 | + | 8.39478e6i | −0.444801 | + | 0.770418i | −0.998038 | − | 0.0626059i | \(-0.980059\pi\) |
0.553238 | + | 0.833024i | \(0.313392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.09263e6 | + | 6.19662e6i | −0.0995108 | + | 0.564354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.13473e6 | + | 1.58218e7i | 0.825624 | + | 1.43002i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.53873e6 | − | 3.80845e6i | −0.407119 | − | 0.341613i | 0.416119 | − | 0.909310i | \(-0.363390\pi\) |
−0.823238 | + | 0.567697i | \(0.807835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.42106e6 | + | 3.06502e6i | −0.749658 | + | 0.272853i | −0.688462 | − | 0.725272i | \(-0.741714\pi\) |
−0.0611963 | + | 0.998126i | \(0.519492\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.42189e6 | − | 1.37352e7i | −0.213979 | − | 1.21353i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.09152e6 | + | 3.37027e6i | 0.358782 | + | 0.295536i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.40935e6 | + | 7.99284e6i | 0.122661 | + | 0.695643i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.48159e6 | − | 3.45102e6i | 0.819060 | − | 0.298114i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.19109e6 | + | 4.35584e6i | 0.445094 | + | 0.373478i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.16540e6 | − | 5.48263e6i | −0.269396 | − | 0.466607i | 0.699310 | − | 0.714818i | \(-0.253491\pi\) |
−0.968706 | + | 0.248211i | \(0.920157\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −211765. | + | 1.20098e6i | −0.0178894 | + | 0.101456i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.00287e7 | + | 1.73702e7i | −0.840955 | + | 1.45658i | 0.0481324 | + | 0.998841i | \(0.484673\pi\) |
−0.889088 | + | 0.457737i | \(0.848660\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.10931e7 | + | 4.03755e6i | 0.923374 | + | 0.336081i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.99057e6 | − | 4.18759e6i | 0.412366 | − | 0.346016i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.18639e6 | 0.343391 | 0.171695 | − | 0.985150i | \(-0.445076\pi\) | ||||
0.171695 | + | 0.985150i | \(0.445076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.83294e6 | −0.149252 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.81662e7 | + | 1.52433e7i | −1.46849 | + | 1.23221i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.01977e7 | + | 3.71167e6i | 0.818380 | + | 0.297866i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.52964e6 | − | 9.57762e6i | 0.440557 | − | 0.763067i | −0.557174 | − | 0.830396i | \(-0.688114\pi\) |
0.997731 | + | 0.0673289i | \(0.0214477\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.53835e6 | + | 8.72443e6i | −0.121681 | + | 0.690087i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.68727e6 | + | 4.65449e6i | 0.211033 | + | 0.365519i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.51383e7 | − | 1.27025e7i | −1.18031 | − | 0.990394i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.60146e6 | − | 1.31082e6i | 0.278795 | − | 0.101473i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.34964e6 | + | 1.89967e7i | 0.257456 | + | 1.46010i | 0.789689 | + | 0.613507i | \(0.210242\pi\) |
−0.532234 | + | 0.846597i | \(0.678647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9745.06 | − | 52472.2i | −0.000743697 | − | 0.00400443i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −880147. | − | 4.99156e6i | −0.0666934 | − | 0.378237i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.36588e6 | − | 3.04493e6i | 0.629453 | − | 0.229102i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.27087e7 | − | 1.06639e7i | −0.949478 | − | 0.796707i | 0.0297315 | − | 0.999558i | \(-0.490535\pi\) |
−0.979210 | + | 0.202851i | \(0.934979\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.23396e6 | − | 2.13727e6i | −0.0915431 | − | 0.158557i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.64495e6 | + | 9.32895e6i | −0.121179 | + | 0.687241i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 810531. | − | 1.40388e6i | 0.0592931 | − | 0.102699i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.73814e6 | − | 1.72454e6i | −0.344199 | − | 0.125278i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.94784e6 | − | 7.50813e6i | 0.645500 | − | 0.541639i | −0.260202 | − | 0.965554i | \(-0.583789\pi\) |
0.905702 | + | 0.423916i | \(0.139345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.24778e7 | 0.893922 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.23115e7 | −1.58739 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.30241e6 | − | 7.80565e6i | 0.657280 | − | 0.551523i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.81999e6 | − | 662421.i | −0.127712 | − | 0.0464834i | 0.277373 | − | 0.960762i | \(-0.410536\pi\) |
−0.405086 | + | 0.914279i | \(0.632758\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.93481e6 | − | 1.02794e7i | 0.413607 | − | 0.716388i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.34892e6 | + | 7.65011e6i | −0.0933669 | + | 0.529510i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.19699e6 | − | 7.26941e6i | −0.288522 | − | 0.499734i | 0.684935 | − | 0.728604i | \(-0.259830\pi\) |
−0.973457 | + | 0.228870i | \(0.926497\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.26324e6 | + | 4.41638e6i | 0.359364 | + | 0.301542i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.14421e6 | + | 2.23631e6i | −0.416675 | + | 0.151657i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00935e6 | + | 1.13956e7i | 0.135346 | + | 0.767584i | 0.974618 | + | 0.223873i | \(0.0718702\pi\) |
−0.839272 | + | 0.543711i | \(0.817019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.57478e6 | − | 1.38639e7i | −0.172264 | − | 0.927553i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.55970e6 | + | 1.45168e7i | 0.170105 | + | 0.964712i | 0.943644 | + | 0.330963i | \(0.107374\pi\) |
−0.773539 | + | 0.633749i | \(0.781515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.73630e6 | − | 995933.i | 0.180623 | − | 0.0657415i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.54897e6 | − | 2.13884e6i | −0.167133 | − | 0.140241i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.92832e7 | − | 3.33995e7i | −1.25596 | − | 2.17538i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.70521e6 | + | 9.67074e6i | −0.110326 | + | 0.625691i | 0.878632 | + | 0.477499i | \(0.158457\pi\) |
−0.988959 | + | 0.148192i | \(0.952655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.33497e7 | − | 2.31224e7i | 0.857997 | − | 1.48609i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.38807e6 | − | 1.96110e6i | −0.344006 | − | 0.125208i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.32786e7 | − | 1.11421e7i | 0.842195 | − | 0.706685i | −0.115861 | − | 0.993265i | \(-0.536963\pi\) |
0.958056 | + | 0.286580i | \(0.0925184\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.65274e6 | −0.545192 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.96741e6 | −0.623908 | −0.311954 | − | 0.950097i | \(-0.600984\pi\) | ||||
−0.311954 | + | 0.950097i | \(0.600984\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 577872. | − | 484892.i | 0.0359352 | − | 0.0301532i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.92537e6 | − | 2.15666e6i | −0.366068 | − | 0.133238i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.97222e6 | + | 6.88008e6i | −0.243806 | + | 0.422285i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.52845e6 | − | 2.00108e7i | 0.215163 | − | 1.22025i | −0.665459 | − | 0.746434i | \(-0.731764\pi\) |
0.880623 | − | 0.473818i | \(-0.157125\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.03643e7 | − | 1.79514e7i | −0.627918 | − | 1.08759i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.32321e6 | − | 3.62761e6i | −0.260230 | − | 0.218359i | 0.503332 | − | 0.864093i | \(-0.332107\pi\) |
−0.763563 | + | 0.645734i | \(0.776552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.33186e7 | − | 4.84758e6i | 0.796535 | − | 0.289915i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23544.7 | − | 133529.i | −0.00139908 | − | 0.00793455i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.54214e7 | − | 1.27029e7i | −0.910499 | − | 0.749997i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.35226e6 | − | 7.66904e6i | −0.0793290 | − | 0.449897i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.78228e6 | − | 648695.i | 0.103889 | − | 0.0378126i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.38028e6 | + | 6.19279e6i | 0.427463 | + | 0.358684i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.04324e7 | + | 1.80695e7i | 0.600410 | + | 1.03994i | 0.992759 | + | 0.120125i | \(0.0383294\pi\) |
−0.392348 | + | 0.919817i | \(0.628337\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.09980e6 | − | 2.89224e7i | 0.291649 | − | 1.65402i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.60117e7 | − | 2.77331e7i | 0.909906 | − | 1.57600i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.23162e7 | − | 4.48273e6i | −0.695495 | − | 0.253139i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.85821e6 | − | 6.59382e6i | 0.440967 | − | 0.370015i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.50950e6 | −0.195704 | −0.0978520 | − | 0.995201i | \(-0.531197\pi\) | ||||
−0.0978520 | + | 0.995201i | \(0.531197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00992e7 | 1.11381 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.63881e7 | + | 1.37513e7i | −0.902502 | + | 0.757289i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.65435e7 | − | 6.02134e6i | −0.905395 | − | 0.329537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.14564e6 | + | 5.44842e6i | −0.171088 | + | 0.296333i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.50921e6 | + | 4.82581e7i | −0.459944 | + | 2.60847i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.36926e6 | + | 9.29983e6i | 0.288432 | + | 0.499579i | 0.973436 | − | 0.228961i | \(-0.0735328\pi\) |
−0.685004 | + | 0.728540i | \(0.740199\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.20532e6 | − | 4.36778e6i | −0.277904 | − | 0.233189i | 0.493173 | − | 0.869932i | \(-0.335837\pi\) |
−0.771077 | + | 0.636742i | \(0.780282\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.90144e7 | + | 6.92066e6i | −1.00892 | + | 0.367216i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.07830e6 | + | 6.11533e6i | 0.0568650 | + | 0.322497i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.29341e6 | + | 7.74656e6i | −0.0677923 | + | 0.406026i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.97538e6 | − | 1.68742e7i | −0.155000 | − | 0.879050i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.22864e7 | + | 1.17513e7i | −1.67171 | + | 0.608454i | −0.992138 | − | 0.125151i | \(-0.960059\pi\) |
−0.679576 | + | 0.733605i | \(0.737836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.52514e7 | + | 1.27975e7i | 0.784894 | + | 0.658604i | 0.944476 | − | 0.328581i | \(-0.106570\pi\) |
−0.159582 | + | 0.987185i | \(0.551015\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.47315e6 | + | 1.12118e7i | 0.331116 | + | 0.573510i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 102834. | − | 583203.i | 0.00522847 | − | 0.0296521i | −0.982082 | − | 0.188455i | \(-0.939652\pi\) |
0.987310 | + | 0.158802i | \(0.0507633\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.40762e6 | − | 2.43806e6i | 0.0711374 | − | 0.123214i | −0.828263 | − | 0.560340i | \(-0.810670\pi\) |
0.899400 | + | 0.437126i | \(0.144004\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.69492e7 | + | 6.16902e6i | 0.851428 | + | 0.309894i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.08712e7 | + | 1.75130e7i | −1.04216 | + | 0.874475i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.84700e6 | −0.0916748 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.21371e6 | 0.109221 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.48642e7 | + | 1.24725e7i | −0.729013 | + | 0.611715i | −0.929862 | − | 0.367908i | \(-0.880074\pi\) |
0.200849 | + | 0.979622i | \(0.435630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.52688e6 | + | 555738.i | 0.0744413 | + | 0.0270944i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.69245e7 | − | 2.93141e7i | 0.820250 | − | 1.42072i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 628083. | − | 3.56204e6i | 0.0302605 | − | 0.171616i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.06478e7 | + | 1.84425e7i | 0.509976 | + | 0.883305i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.42676e7 | + | 2.87539e7i | 1.63160 | + | 1.36908i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59521.1 | − | 21663.9i | 0.00281739 | − | 0.00102545i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.78417e6 | + | 2.14611e7i | 0.178073 | + | 1.00990i | 0.934537 | + | 0.355866i | \(0.115814\pi\) |
−0.756464 | + | 0.654035i | \(0.773075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.01031e6 | − | 2.12588e6i | −0.281178 | − | 0.0994542i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −100216. | − | 568351.i | −0.00466104 | − | 0.0264341i | 0.982389 | − | 0.186850i | \(-0.0598277\pi\) |
−0.987050 | + | 0.160415i | \(0.948717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.53782e6 | − | 2.01560e6i | 0.256069 | − | 0.0932013i | −0.210796 | − | 0.977530i | \(-0.567606\pi\) |
0.466865 | + | 0.884329i | \(0.345383\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.88840e7 | − | 3.26275e7i | −1.78757 | − | 1.49995i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.07495e6 | + | 1.05221e7i | 0.277661 | + | 0.480924i | 0.970803 | − | 0.239878i | \(-0.0771073\pi\) |
−0.693142 | + | 0.720801i | \(0.743774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −785678. | + | 4.45580e6i | −0.0357030 | + | 0.202482i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.08181e7 | − | 1.87375e7i | 0.488768 | − | 0.846571i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.23476e6 | + | 813386.i | 0.100388 | + | 0.0365382i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.68769e6 | − | 8.12894e6i | 0.432688 | − | 0.363069i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.41975e7 | −0.630488 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.99403e7 | 0.880463 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.25529e6 | − | 7.76611e6i | 0.406342 | − | 0.340961i | −0.416597 | − | 0.909091i | \(-0.636777\pi\) |
0.822939 | + | 0.568130i | \(0.192333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.13382e6 | − | 1.86856e6i | −0.224114 | − | 0.0815708i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.47705e7 | + | 2.55833e7i | −0.641146 | + | 1.11050i | 0.344032 | + | 0.938958i | \(0.388207\pi\) |
−0.985177 | + | 0.171539i | \(0.945126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.44168e6 | − | 3.08613e7i | 0.234872 | − | 1.33203i | −0.608011 | − | 0.793929i | \(-0.708032\pi\) |
0.842883 | − | 0.538097i | \(-0.180857\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.75479e6 | + | 6.50349e6i | 0.161149 | + | 0.279118i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.64474e6 | − | 4.73650e6i | −0.240899 | − | 0.202138i | 0.514343 | − | 0.857585i | \(-0.328036\pi\) |
−0.755241 | + | 0.655447i | \(0.772480\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.61287e7 | − | 2.04292e7i | 2.38194 | − | 0.866954i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.36920e6 | + | 1.34364e7i | 0.0999786 | + | 0.567007i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.03200e7 | − | 184787.i | 0.852699 | − | 0.00775428i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.09224e6 | − | 1.18657e7i | −0.0873079 | − | 0.495148i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.57263e7 | − | 5.72390e6i | 0.652597 | − | 0.237526i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.68862e7 | − | 1.41692e7i | −0.696840 | − | 0.584718i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.03392e7 | + | 3.52285e7i | 0.834682 | + | 1.44571i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.46482e6 | + | 1.96500e7i | −0.141404 | + | 0.801942i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.40447e6 | + | 1.10929e7i | −0.259933 | + | 0.450218i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.61833e7 | − | 5.89023e6i | −0.653203 | − | 0.237747i | −0.00590416 | − | 0.999983i | \(-0.501879\pi\) |
−0.647299 | + | 0.762236i | \(0.724102\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.20212e6 | + | 6.88240e6i | −0.329243 | + | 0.276268i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.31231e7 | 1.72153 | 0.860764 | − | 0.509004i | \(-0.169986\pi\) | ||||
0.860764 | + | 0.509004i | \(0.169986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.20646e6 | 0.127306 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.49068e6 | + | 7.96363e6i | −0.374753 | + | 0.314455i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.02250e7 | − | 2.19201e7i | −2.36512 | − | 0.860834i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.77789e7 | + | 3.07940e7i | −0.694411 | + | 1.20275i | 0.275968 | + | 0.961167i | \(0.411002\pi\) |
−0.970379 | + | 0.241588i | \(0.922332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.10197e6 | − | 4.02773e7i | 0.275886 | − | 1.56463i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.53088e6 | + | 1.30439e7i | 0.290966 | + | 0.503967i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −72599.0 | − | 60917.8i | −0.00278982 | − | 0.00234094i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.41016e7 | + | 5.13258e6i | −0.538977 | + | 0.196172i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.75211e6 | − | 1.56080e7i | −0.104623 | − | 0.593346i | −0.991370 | − | 0.131091i | \(-0.958152\pi\) |
0.886747 | − | 0.462254i | \(-0.152959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.09395e7 | + | 1.78973e7i | −0.791756 | + | 0.676726i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.64631e6 | + | 2.06792e7i | 0.137135 | + | 0.777732i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.70994e6 | − | 2.07825e6i | 0.213601 | − | 0.0777443i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 816887. | + | 685449.i | 0.0303957 | + | 0.0255051i | 0.657859 | − | 0.753141i | \(-0.271462\pi\) |
−0.627463 | + | 0.778646i | \(0.715907\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.59422e7 | + | 6.22537e7i | 1.33027 | + | 2.30410i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.83721e6 | + | 2.74332e7i | −0.178083 | + | 1.00996i | 0.756443 | + | 0.654060i | \(0.226936\pi\) |
−0.934525 | + | 0.355896i | \(0.884176\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.18563e7 | − | 2.05357e7i | 0.434179 | − | 0.752021i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.38154e6 | + | 502841.i | 0.0503251 | + | 0.0183169i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.07632e7 | + | 9.03137e6i | −0.390001 | + | 0.327249i | −0.816613 | − | 0.577185i | \(-0.804151\pi\) |
0.426613 | + | 0.904434i | \(0.359707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.40508e7 | 1.22733 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.57597e7 | −0.565064 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.01258e6 | + | 5.04516e6i | −0.214451 | + | 0.179946i | −0.743685 | − | 0.668530i | \(-0.766924\pi\) |
0.529234 | + | 0.848476i | \(0.322479\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.24773e7 | − | 4.54136e6i | −0.442703 | − | 0.161131i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.00675e7 | − | 1.74374e7i | 0.355337 | − | 0.615462i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.24195e6 | − | 1.83860e7i | 0.113831 | − | 0.645567i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.45047e6 | + | 2.51228e6i | 0.0506640 | + | 0.0877526i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.55312e7 | + | 2.98142e7i | 1.23465 | + | 1.03600i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.99738e6 | − | 2.18287e6i | 0.207321 | − | 0.0754586i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −955958. | − | 5.42151e6i | −0.0328755 | − | 0.186446i | 0.963948 | − | 0.266092i | \(-0.0857324\pi\) |
−0.996823 | + | 0.0796453i | \(0.974621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.60106e7 | − | 4.60130e7i | 0.889901 | − | 1.57424i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.29383e6 | + | 1.30090e7i | 0.0780752 | + | 0.442787i | 0.998637 | + | 0.0521900i | \(0.0166201\pi\) |
−0.920562 | + | 0.390597i | \(0.872269\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.14417e7 | + | 1.87233e7i | −1.74194 | + | 0.634015i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.91816e7 | − | 1.60953e7i | −0.646211 | − | 0.542235i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.17762e7 | + | 3.77175e7i | 0.729871 | + | 1.26417i | 0.956938 | + | 0.290294i | \(0.0937531\pi\) |
−0.227067 | + | 0.973879i | \(0.572914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.57982e6 | − | 2.03022e7i | 0.119373 | − | 0.676996i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −453622. | + | 785697.i | −0.0150495 | + | 0.0260665i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.18118e7 | − | 1.15786e7i | −1.05004 | − | 0.382183i | −0.241361 | − | 0.970435i | \(-0.577594\pi\) |
−0.808677 | + | 0.588253i | \(0.799816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.42346e6 | + | 7.06812e6i | −0.276630 | + | 0.232120i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.16266e7 | 1.68687 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.32121e6 | −0.303027 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.36635e6 | − | 1.14651e6i | 0.0441956 | − | 0.0370845i | −0.620422 | − | 0.784268i | \(-0.713039\pi\) |
0.664618 | + | 0.747183i | \(0.268594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.94752e7 | − | 1.43678e7i | −1.27043 | − | 0.462399i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 117558. | − | 203617.i | 0.00376440 | − | 0.00652014i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.61966e6 | − | 3.75420e7i | 0.210910 | − | 1.19613i | −0.676953 | − | 0.736026i | \(-0.736700\pi\) |
0.887864 | − | 0.460107i | \(-0.152189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7401.06 | − | 12819.0i | −0.000234628 | − | 0.000406388i |
(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.i.a.9.1 | ✓ | 48 | |
19.17 | even | 9 | inner | 76.6.i.a.17.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.i.a.9.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
76.6.i.a.17.1 | yes | 48 | 19.17 | even | 9 | inner |