Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,11,Mod(157,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.157");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(190.607175802\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 63831600 x^{13} + 120528248672 x^{12} - 17600989215600 x^{11} + \cdots + 38\!\cdots\!56 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{12}\cdot 5^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 157.6 | ||
Root | \(-96.0119 - 96.0119i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.157 |
Dual form | 300.11.k.c.193.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 99.2043 | − | 99.2043i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6761.61 | − | 6761.61i | −0.402309 | − | 0.402309i | 0.476737 | − | 0.879046i | \(-0.341819\pi\) |
−0.879046 | + | 0.476737i | \(0.841819\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 19683.0i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23043.7 | −0.143083 | −0.0715415 | − | 0.997438i | \(-0.522792\pi\) | ||||
−0.0715415 | + | 0.997438i | \(0.522792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −417304. | + | 417304.i | −1.12392 | + | 1.12392i | −0.132774 | + | 0.991146i | \(0.542388\pi\) |
−0.991146 | + | 0.132774i | \(0.957612\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.39626e6 | + | 1.39626e6i | 0.983379 | + | 0.983379i | 0.999864 | − | 0.0164852i | \(-0.00524765\pi\) |
−0.0164852 | + | 0.999864i | \(0.505248\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.30952e6i | − | 1.74045i | −0.492656 | − | 0.870224i | \(-0.663974\pi\) | ||
0.492656 | − | 0.870224i | \(-0.336026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34156e6 | −0.328484 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.67251e6 | − | 7.67251e6i | 1.19206 | − | 1.19206i | 0.215573 | − | 0.976488i | \(-0.430838\pi\) |
0.976488 | − | 0.215573i | \(-0.0691619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.95264e6 | − | 1.95264e6i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.32956e6i | 0.162329i | 0.996701 | + | 0.0811647i | \(0.0258640\pi\) | ||||
−0.996701 | + | 0.0811647i | \(0.974136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.16484e7 | −0.406872 | −0.203436 | − | 0.979088i | \(-0.565211\pi\) | ||||
−0.203436 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.28603e6 | + | 2.28603e6i | −0.0584134 | + | 0.0584134i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.35739e7 | − | 8.35739e7i | −1.20521 | − | 1.20521i | −0.972561 | − | 0.232646i | \(-0.925262\pi\) |
−0.232646 | − | 0.972561i | \(-0.574738\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.27967e7i | 0.917677i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.04533e8 | −0.902263 | −0.451132 | − | 0.892457i | \(-0.648980\pi\) | ||||
−0.451132 | + | 0.892457i | \(0.648980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.74002e8 | + | 1.74002e8i | −1.18362 | + | 1.18362i | −0.204819 | + | 0.978800i | \(0.565661\pi\) |
−0.978800 | + | 0.204819i | \(0.934339\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.83813e8 | + | 1.83813e8i | 0.801470 | + | 0.801470i | 0.983325 | − | 0.181855i | \(-0.0582102\pi\) |
−0.181855 | + | 0.983325i | \(0.558210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.91037e8i | − | 0.676295i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.77030e8 | 0.802925 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.56769e8 | − | 4.56769e8i | 1.09224 | − | 1.09224i | 0.0969476 | − | 0.995289i | \(-0.469092\pi\) |
0.995289 | − | 0.0969476i | \(-0.0309079\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.27523e8 | − | 4.27523e8i | −0.710535 | − | 0.710535i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.95847e8i | 1.39294i | 0.717586 | + | 0.696470i | \(0.245247\pi\) | ||||
−0.717586 | + | 0.696470i | \(0.754753\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.16284e8 | −0.256080 | −0.128040 | − | 0.991769i | \(-0.540869\pi\) | ||||
−0.128040 | + | 0.991769i | \(0.540869\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.33089e8 | + | 1.33089e8i | −0.134103 | + | 0.134103i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.33426e8 | + | 2.33426e8i | 0.172892 | + | 0.172892i | 0.788249 | − | 0.615357i | \(-0.210988\pi\) |
−0.615357 | + | 0.788249i | \(0.710988\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.52229e9i | − | 0.973313i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.18236e8 | 0.342659 | 0.171330 | − | 0.985214i | \(-0.445194\pi\) | ||||
0.171330 | + | 0.985214i | \(0.445194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.26897e8 | + | 7.26897e8i | −0.350638 | + | 0.350638i | −0.860347 | − | 0.509709i | \(-0.829753\pi\) |
0.509709 | + | 0.860347i | \(0.329753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.55812e8 | + | 1.55812e8i | 0.0575636 | + | 0.0575636i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.14188e9i | 0.371095i | 0.982635 | + | 0.185547i | \(0.0594058\pi\) | ||||
−0.982635 | + | 0.185547i | \(0.940594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.87420e8 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.89705e9 | + | 4.89705e9i | −1.24321 | + | 1.24321i | −0.284547 | + | 0.958662i | \(0.591843\pi\) |
−0.958662 | + | 0.284547i | \(0.908157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.30307e8 | + | 3.30307e8i | 0.0662707 | + | 0.0662707i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.94942e9i | 1.60267i | 0.598214 | + | 0.801336i | \(0.295877\pi\) | ||||
−0.598214 | + | 0.801336i | \(0.704123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.64329e9 | 0.904326 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.15557e9 | + | 1.15557e9i | −0.166105 | + | 0.166105i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.32848e9 | − | 3.32848e9i | −0.387604 | − | 0.387604i | 0.486228 | − | 0.873832i | \(-0.338372\pi\) |
−0.873832 | + | 0.486228i | \(0.838372\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.53568e8i | 0.0476943i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.14978e9 | −0.204544 | −0.102272 | − | 0.994756i | \(-0.532611\pi\) | ||||
−0.102272 | + | 0.994756i | \(0.532611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.01953e8 | − | 2.01953e8i | 0.0174207 | − | 0.0174207i | −0.698343 | − | 0.715763i | \(-0.746079\pi\) |
0.715763 | + | 0.698343i | \(0.246079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.29781e9 | − | 7.29781e9i | −0.520324 | − | 0.520324i | 0.397345 | − | 0.917669i | \(-0.369931\pi\) |
−0.917669 | + | 0.397345i | \(0.869931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.76191e9i | 0.244498i | 0.992499 | + | 0.122249i | \(0.0390107\pi\) | ||||
−0.992499 | + | 0.122249i | \(0.960989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.65818e10 | −0.984048 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.54184e10 | − | 1.54184e10i | 0.836851 | − | 0.836851i | −0.151592 | − | 0.988443i | \(-0.548440\pi\) |
0.988443 | + | 0.151592i | \(0.0484400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.21379e9 | + | 8.21379e9i | 0.374640 | + | 0.374640i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.88819e10i | − | 0.791244i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.54064e10 | −0.979527 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.03701e10 | + | 1.03701e10i | −0.368347 | + | 0.368347i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.17773e9 | + | 8.17773e9i | 0.247522 | + | 0.247522i | 0.819953 | − | 0.572431i | \(-0.194000\pi\) |
−0.572431 | + | 0.819953i | \(0.694000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.45235e10i | 0.966421i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.21383e10 | 1.61066 | 0.805328 | − | 0.592830i | \(-0.201989\pi\) | ||||
0.805328 | + | 0.592830i | \(0.201989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.91393e10 | + | 2.91393e10i | −0.700198 | + | 0.700198i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.61816e9 | − | 9.61816e9i | −0.199292 | − | 0.199292i | 0.600405 | − | 0.799696i | \(-0.295006\pi\) |
−0.799696 | + | 0.600405i | \(0.795006\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.71930e10i | 1.29494i | 0.762091 | + | 0.647470i | \(0.224173\pi\) | ||||
−0.762091 | + | 0.647470i | \(0.775827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.64701e10 | 0.654398 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.61620e9 | − | 9.61620e9i | 0.160814 | − | 0.160814i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.89517e10 | − | 1.89517e10i | −0.276096 | − | 0.276096i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.29414e10i | 0.176218i | 0.996111 | + | 0.0881092i | \(0.0280824\pi\) | ||||
−0.996111 | + | 0.0881092i | \(0.971918\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.95842e10 | −1.14116 | −0.570580 | − | 0.821242i | \(-0.693282\pi\) | ||||
−0.570580 | + | 0.821242i | \(0.693282\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.74825e10 | − | 2.74825e10i | 0.327793 | − | 0.327793i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.59119e10 | + | 8.59119e10i | 0.900648 | + | 0.900648i | 0.995492 | − | 0.0948442i | \(-0.0302353\pi\) |
−0.0948442 | + | 0.995492i | \(0.530235\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.06269e10i | − | 0.891808i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.03757e11 | −0.959153 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.40970e10 | − | 5.40970e10i | 0.470149 | − | 0.470149i | −0.431814 | − | 0.901963i | \(-0.642126\pi\) |
0.901963 | + | 0.431814i | \(0.142126\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.25444e11 | + | 1.25444e11i | 0.965752 | + | 0.965752i | 0.999433 | − | 0.0336802i | \(-0.0107228\pi\) |
−0.0336802 | + | 0.999433i | \(0.510723\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2.10426e11i | − | 1.52639i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.48243e10 | −0.580150 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.76438e10 | − | 2.76438e10i | 0.178389 | − | 0.178389i | −0.612264 | − | 0.790653i | \(-0.709741\pi\) |
0.790653 | + | 0.612264i | \(0.209741\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.87923e10 | + | 9.87923e10i | 0.568666 | + | 0.568666i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.25934e11i | 1.77364i | 0.462118 | + | 0.886818i | \(0.347089\pi\) | ||||
−0.462118 | + | 0.886818i | \(0.652911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70024e11 | 0.875218 | 0.437609 | − | 0.899165i | \(-0.355825\pi\) | ||||
0.437609 | + | 0.899165i | \(0.355825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.14563e10 | + | 2.14563e10i | −0.104544 | + | 0.104544i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.21749e10 | − | 3.21749e10i | −0.140705 | − | 0.140705i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.64060e10i | 0.109495i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.59693e11 | −0.628231 | −0.314116 | − | 0.949385i | \(-0.601708\pi\) | ||||
−0.314116 | + | 0.949385i | \(0.601708\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.15753e11 | − | 2.15753e11i | 0.805694 | − | 0.805694i | −0.178285 | − | 0.983979i | \(-0.557055\pi\) |
0.983979 | + | 0.178285i | \(0.0570548\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.08670e11 | + | 2.08670e11i | 0.703280 | + | 0.703280i | 0.965113 | − | 0.261833i | \(-0.0843271\pi\) |
−0.261833 | + | 0.965113i | \(0.584327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.54372e11i | 1.13552i | 0.823195 | + | 0.567759i | \(0.192190\pi\) | ||||
−0.823195 | + | 0.567759i | \(0.807810\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.63138e10 | 0.141166 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.25132e10 | − | 2.25132e10i | 0.0653066 | − | 0.0653066i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.51018e11 | − | 1.51018e11i | −0.397354 | − | 0.397354i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.93072e10i | 0.249029i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.67815e11 | −0.401254 | −0.200627 | − | 0.979668i | \(-0.564298\pi\) | ||||
−0.200627 | + | 0.979668i | \(0.564298\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.13317e10 | − | 6.13317e10i | 0.139890 | − | 0.139890i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.87620e10 | + | 7.87620e10i | 0.163688 | + | 0.163688i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.44223e11i | 0.286294i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.16533e12 | −2.21048 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.48541e10 | + | 9.48541e10i | −0.172001 | + | 0.172001i | −0.787858 | − | 0.615857i | \(-0.788810\pi\) |
0.615857 | + | 0.787858i | \(0.288810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.01318e11 | + | 4.01318e11i | 0.665824 | + | 0.665824i | 0.956747 | − | 0.290923i | \(-0.0939623\pi\) |
−0.290923 | + | 0.956747i | \(0.593962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.11888e12i | 1.77667i | 0.459192 | + | 0.888337i | \(0.348139\pi\) | ||||
−0.459192 | + | 0.888337i | \(0.651861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.09145e10 | 0.0470004 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.62313e10 | − | 9.62313e10i | 0.140132 | − | 0.140132i | −0.633561 | − | 0.773693i | \(-0.718407\pi\) |
0.773693 | + | 0.633561i | \(0.218407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.13279e11 | + | 1.13279e11i | 0.151499 | + | 0.151499i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.82748e11i | − | 0.490821i | −0.969419 | − | 0.245411i | \(-0.921077\pi\) | ||
0.969419 | − | 0.245411i | \(-0.0789228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.74618e11 | −0.829798 | −0.414899 | − | 0.909867i | \(-0.636183\pi\) | ||||
−0.414899 | + | 0.909867i | \(0.636183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.84338e10 | + | 3.84338e10i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.79838e12 | + | 1.79838e12i | 1.95613 | + | 1.95613i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.71618e11i | 1.01508i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.64376e12 | 1.64994 | 0.824972 | − | 0.565173i | \(-0.191191\pi\) | ||||
0.824972 | + | 0.565173i | \(0.191191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.76803e11 | + | 1.76803e11i | −0.170564 | + | 0.170564i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.38985e11 | − | 2.38985e11i | −0.213160 | − | 0.213160i | 0.592448 | − | 0.805608i | \(-0.298161\pi\) |
−0.805608 | + | 0.592448i | \(0.798161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.13019e12i | 0.969732i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.55358e10 | 0.0541098 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.46851e10 | − | 5.46851e10i | 0.0434601 | − | 0.0434601i | −0.685043 | − | 0.728503i | \(-0.740217\pi\) |
0.728503 | + | 0.685043i | \(0.240217\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.87821e11 | + | 8.87821e11i | 0.654288 | + | 0.654288i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.13079e12i | 1.51279i | 0.654114 | + | 0.756396i | \(0.273042\pi\) | ||||
−0.654114 | + | 0.756396i | \(0.726958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.01544e12 | −1.37887 | −0.689437 | − | 0.724346i | \(-0.742142\pi\) | ||||
−0.689437 | + | 0.724346i | \(0.742142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.59839e11 | − | 5.59839e11i | 0.369190 | − | 0.369190i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.75468e11 | − | 4.75468e11i | −0.291556 | − | 0.291556i | 0.546139 | − | 0.837695i | \(-0.316097\pi\) |
−0.837695 | + | 0.546139i | \(0.816097\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.29276e11i | 0.135624i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.42181e12 | −1.38232 | −0.691160 | − | 0.722702i | \(-0.742900\pi\) | ||||
−0.691160 | + | 0.722702i | \(0.742900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.89816e11 | + | 6.89816e11i | −0.380015 | + | 0.380015i | −0.871108 | − | 0.491092i | \(-0.836598\pi\) |
0.491092 | + | 0.871108i | \(0.336598\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.06810e11 | + | 7.06810e11i | 0.362989 | + | 0.362989i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.88308e12i | 0.934068i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.60400e11 | −0.316477 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.64991e12 | + | 2.64991e12i | −1.22713 | + | 1.22713i | −0.262092 | + | 0.965043i | \(0.584412\pi\) |
−0.965043 | + | 0.262092i | \(0.915588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.49959e10 | + | 4.49959e10i | 0.0194711 | + | 0.0194711i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.40353e12i | 2.67956i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.35307e12 | 0.952361 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.13268e11 | + | 2.13268e11i | −0.0835049 | + | 0.0835049i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.37107e11 | + | 7.37107e11i | 0.270295 | + | 0.270295i | 0.829219 | − | 0.558924i | \(-0.188786\pi\) |
−0.558924 | + | 0.829219i | \(0.688786\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.00693e10i | − | 0.0142239i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.20794e12 | −1.10261 | −0.551307 | − | 0.834302i | \(-0.685871\pi\) | ||||
−0.551307 | + | 0.834302i | \(0.685871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.09198e12 | − | 4.09198e12i | 1.36211 | − | 1.36211i | 0.490886 | − | 0.871224i | \(-0.336673\pi\) |
0.871224 | − | 0.490886i | \(-0.163327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.60534e12 | + | 3.60534e12i | 1.12629 | + | 1.12629i | 0.990775 | + | 0.135515i | \(0.0432690\pi\) |
0.135515 | + | 0.990775i | \(0.456731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.67253e10i | − | 0.0232266i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.44795e12 | −0.424843 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.01720e12 | − | 6.01720e12i | 1.71152 | − | 1.71152i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.73198e11 | + | 3.73198e11i | 0.0998160 | + | 0.0998160i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.48575e12i | − | 0.644877i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.03877e12 | −0.513130 | −0.256565 | − | 0.966527i | \(-0.582591\pi\) | ||||
−0.256565 | + | 0.966527i | \(0.582591\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.64498e12 | + | 1.64498e12i | −0.401736 | + | 0.401736i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.88007e12 | + | 3.88007e12i | 0.892669 | + | 0.892669i | 0.994774 | − | 0.102105i | \(-0.0325578\pi\) |
−0.102105 | + | 0.994774i | \(0.532558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 3.05915e12i | − | 0.683286i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.68422e11 | 0.0582165 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.20170e12 | + | 3.20170e12i | −0.674389 | + | 0.674389i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.51054e12 | + | 2.51054e12i | 0.499023 | + | 0.499023i | 0.911134 | − | 0.412111i | \(-0.135208\pi\) |
−0.412111 | + | 0.911134i | \(0.635208\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.81109e12i | 1.70178i | 0.525347 | + | 0.850888i | \(0.323936\pi\) | ||||
−0.525347 | + | 0.850888i | \(0.676064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.62969e12 | 0.305892 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.64808e12 | − | 3.64808e12i | 0.665565 | − | 0.665565i | −0.291121 | − | 0.956686i | \(-0.594028\pi\) |
0.956686 | + | 0.291121i | \(0.0940284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.87317e12 | − | 1.87317e12i | −0.323024 | − | 0.323024i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.58712e12i | 0.769251i | 0.923073 | + | 0.384626i | \(0.125669\pi\) | ||||
−0.923073 | + | 0.384626i | \(0.874331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.24409e13 | −2.02916 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.52043e12 | + | 2.52043e12i | −0.399890 | + | 0.399890i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.32116e11 | + | 9.32116e11i | 0.140004 | + | 0.140004i | 0.773635 | − | 0.633631i | \(-0.218436\pi\) |
−0.633631 | + | 0.773635i | \(0.718436\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.05752e12i | 0.300754i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.17698e12 | −0.878834 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.12809e12 | + | 2.12809e12i | −0.294744 | + | 0.294744i | −0.838951 | − | 0.544207i | \(-0.816831\pi\) |
0.544207 | + | 0.838951i | \(0.316831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.38944e12 | − | 1.38944e12i | −0.182445 | − | 0.182445i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.27243e12i | − | 1.18576i | −0.805290 | − | 0.592881i | \(-0.797990\pi\) | ||
0.805290 | − | 0.592881i | \(-0.202010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.62253e12 | 0.202101 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.88851e12 | + | 2.88851e12i | −0.350494 | + | 0.350494i | −0.860293 | − | 0.509799i | \(-0.829720\pi\) |
0.509799 | + | 0.860293i | \(0.329720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.42488e12 | + | 3.42488e12i | 0.394540 | + | 0.394540i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.70831e12i | 0.304054i | 0.988376 | + | 0.152027i | \(0.0485801\pi\) | ||||
−0.988376 | + | 0.152027i | \(0.951420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.14256e13 | 2.34449 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.16439e12 | − | 6.16439e12i | 0.657548 | − | 0.657548i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.45343e12 | + | 5.45343e12i | 0.552990 | + | 0.552990i | 0.927302 | − | 0.374313i | \(-0.122121\pi\) |
−0.374313 | + | 0.927302i | \(0.622121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.78149e12i | 0.571709i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.02574e13 | 0.989268 | 0.494634 | − | 0.869101i | \(-0.335302\pi\) | ||||
0.494634 | + | 0.869101i | \(0.335302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.86092e12 | − | 4.86092e12i | 0.457292 | − | 0.457292i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.92585e12 | + | 1.92585e12i | 0.172445 | + | 0.172445i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.78823e12i | − | 0.680490i | −0.940337 | − | 0.340245i | \(-0.889490\pi\) | ||
0.940337 | − | 0.340245i | \(-0.110510\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.90833e12 | −0.162721 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.73353e12 | − | 6.73353e12i | 0.560393 | − | 0.560393i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.66584e12 | + | 6.66584e12i | 0.528657 | + | 0.528657i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.40827e13i | − | 1.09047i | −0.838282 | − | 0.545236i | \(-0.816440\pi\) | ||
0.838282 | − | 0.545236i | \(-0.183560\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.92635e13 | −1.45655 | −0.728275 | − | 0.685285i | \(-0.759678\pi\) | ||||
−0.728275 | + | 0.685285i | \(0.759678\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.61800e12 | − | 3.61800e12i | 0.267157 | − | 0.267157i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.46243e12 | + | 1.46243e12i | 0.103023 | + | 0.103023i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.90794e12i | − | 0.131304i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.20644e11 | −0.0215594 | −0.0107797 | − | 0.999942i | \(-0.503431\pi\) | ||||
−0.0107797 | + | 0.999942i | \(0.503431\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.98006e12 | + | 3.98006e12i | −0.261487 | + | 0.261487i | −0.825658 | − | 0.564171i | \(-0.809196\pi\) |
0.564171 | + | 0.825658i | \(0.309196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.30649e13 | − | 3.30649e13i | −2.07472 | − | 2.07472i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.06335e12i | 0.555861i | 0.960601 | + | 0.277931i | \(0.0896485\pi\) | ||||
−0.960601 | + | 0.277931i | \(0.910351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.76017e12 | −0.225432 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.72736e13 | + | 1.72736e13i | −1.01243 | + | 1.01243i | −0.0125060 | + | 0.999922i | \(0.503981\pi\) |
−0.999922 | + | 0.0125060i | \(0.996019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.28385e12 | + | 1.28385e12i | 0.0719408 | + | 0.0719408i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.55160e12i | 0.194622i | 0.995254 | + | 0.0973110i | \(0.0310241\pi\) | ||||
−0.995254 | + | 0.0973110i | \(0.968976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.40882e12 | 0.129099 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.88714e12 | + | 8.88714e12i | −0.465877 | + | 0.465877i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.66276e13 | − | 1.66276e13i | −0.834158 | − | 0.834158i | 0.153925 | − | 0.988083i | \(-0.450809\pi\) |
−0.988083 | + | 0.153925i | \(0.950809\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 5.45277e12i | − | 0.267642i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.85896e13 | −0.892824 | −0.446412 | − | 0.894828i | \(-0.647298\pi\) | ||||
−0.446412 | + | 0.894828i | \(0.647298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.19631e12 | − | 2.19631e12i | 0.103226 | − | 0.103226i | −0.653608 | − | 0.756833i | \(-0.726745\pi\) |
0.756833 | + | 0.653608i | \(0.226745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.49772e11 | + | 3.49772e11i | 0.0157471 | + | 0.0157471i | 0.714937 | − | 0.699189i | \(-0.246456\pi\) |
−0.699189 | + | 0.714937i | \(0.746456\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.15667e12i | − | 0.139112i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.70457e13 | 0.735376 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00964e12 | − | 4.00964e12i | 0.169356 | − | 0.169356i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.99058e12 | − | 8.99058e12i | −0.364079 | − | 0.364079i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 9.58522e12i | − | 0.380123i | −0.981772 | − | 0.190062i | \(-0.939131\pi\) | ||
0.981772 | − | 0.190062i | \(-0.0608688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.97513e13 | 2.70911 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.02931e13 | + | 1.02931e13i | −0.391573 | + | 0.391573i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.19310e13 | − | 1.19310e13i | −0.435543 | − | 0.435543i | 0.454966 | − | 0.890509i | \(-0.349652\pi\) |
−0.890509 | + | 0.454966i | \(0.849652\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.07333e13i | − | 0.383875i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.57312e13 | −0.551258 | −0.275629 | − | 0.961264i | \(-0.588886\pi\) | ||||
−0.275629 | + | 0.961264i | \(0.588886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.64893e12 | + | 4.64893e12i | −0.159631 | + | 0.159631i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.18027e12 | − | 4.18027e12i | −0.137855 | − | 0.137855i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.55193e13i | 0.501614i | 0.968037 | + | 0.250807i | \(0.0806960\pi\) | ||||
−0.968037 | + | 0.250807i | \(0.919304\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.48891e13 | 0.788534 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.43107e13 | + | 1.43107e13i | −0.444449 | + | 0.444449i | −0.893504 | − | 0.449055i | \(-0.851761\pi\) |
0.449055 | + | 0.893504i | \(0.351761\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.08752e13 | − | 2.08752e13i | −0.623147 | − | 0.623147i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 4.97571e13i | − | 1.45635i | −0.685391 | − | 0.728176i | \(-0.740369\pi\) | ||
0.685391 | − | 0.728176i | \(-0.259631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.82998e12 | 0.282129 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.41494e12 | + | 8.41494e12i | −0.236845 | + | 0.236845i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.23573e12 | − | 4.23573e12i | −0.114677 | − | 0.114677i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 5.48477e12i | − | 0.145654i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.53166e12 | −0.0920006 | −0.0460003 | − | 0.998941i | \(-0.514648\pi\) | ||||
−0.0460003 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.83515e13 | + | 3.83515e13i | −0.980108 | + | 0.980108i | −0.999806 | − | 0.0196982i | \(-0.993729\pi\) |
0.0196982 | + | 0.999806i | \(0.493729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.62642e13 | − | 1.62642e13i | −0.400110 | − | 0.400110i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.63083e13i | − | 1.84202i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.96013e13 | 0.464314 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.36219e13 | − | 4.36219e13i | 1.01407 | − | 1.01407i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.23341e13 | + | 3.23341e13i | 0.724084 | + | 0.724084i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.40218e12i | 0.0967663i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.71740e12 | −0.166527 | −0.0832635 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832635 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.68671e13 | − | 1.68671e13i | 0.357306 | − | 0.357306i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.14494e13 | − | 3.14494e13i | −0.642209 | − | 0.642209i | 0.308889 | − | 0.951098i | \(-0.400043\pi\) |
−0.951098 | + | 0.308889i | \(0.900043\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.25712e12i | 0.0853600i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.43488e13 | 0.282526 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.72094e12 | − | 7.72094e12i | 0.149295 | − | 0.149295i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.91011e13 | − | 4.91011e13i | −0.915831 | − | 0.915831i | 0.0808916 | − | 0.996723i | \(-0.474223\pi\) |
−0.996723 | + | 0.0808916i | \(0.974223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.45223e14i | − | 2.66059i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.38377e12 | −0.114885 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.65680e13 | − | 1.65680e13i | 0.292906 | − | 0.292906i | −0.545321 | − | 0.838227i | \(-0.683592\pi\) |
0.838227 | + | 0.545321i | \(0.183592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.61959e12 | + | 2.61959e12i | 0.0447010 | + | 0.0447010i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.95051e13i | 1.33301i | 0.745500 | + | 0.666505i | \(0.232211\pi\) | ||||
−0.745500 | + | 0.666505i | \(0.767789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.32905e13 | 0.548453 | 0.274227 | − | 0.961665i | \(-0.411578\pi\) | ||||
0.274227 | + | 0.961665i | \(0.411578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.58423e13 | + | 1.58423e13i | −0.256474 | + | 0.256474i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.02115e12 | − | 6.02115e12i | −0.0941456 | − | 0.0941456i | 0.658465 | − | 0.752611i | \(-0.271206\pi\) |
−0.752611 | + | 0.658465i | \(0.771206\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 4.28073e13i | − | 0.657847i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.62239e13 | 1.00031 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05256e13 | + | 1.05256e13i | −0.156281 | + | 0.156281i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.05755e13 | − | 8.05755e13i | −1.15615 | − | 1.15615i | −0.985297 | − | 0.170849i | \(-0.945349\pi\) |
−0.170849 | − | 0.985297i | \(-0.554651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.01991e13i | 0.708140i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.14019e13 | 0.574225 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.51354e13 | + | 3.51354e13i | −0.479150 | + | 0.479150i | −0.904860 | − | 0.425710i | \(-0.860024\pi\) |
0.425710 | + | 0.904860i | \(0.360024\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.51553e13 | + | 3.51553e13i | 0.463574 | + | 0.463574i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.91676e13i | − | 1.02663i | −0.858201 | − | 0.513315i | \(-0.828417\pi\) | ||
0.858201 | − | 0.513315i | \(-0.171583\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.93707e13 | 1.13979 | 0.569893 | − | 0.821719i | \(-0.306985\pi\) | ||||
0.569893 | + | 0.821719i | \(0.306985\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.59453e12 | − | 4.59453e12i | 0.0576308 | − | 0.0576308i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.37015e13 | + | 6.37015e13i | 0.773047 | + | 0.773047i | 0.978638 | − | 0.205591i | \(-0.0659117\pi\) |
−0.205591 | + | 0.978638i | \(0.565912\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.46682e12i | − | 0.0533226i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.53412e14 | −1.80158 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.44555e13 | + | 4.44555e13i | −0.513598 | + | 0.513598i | −0.915627 | − | 0.402029i | \(-0.868305\pi\) |
0.402029 | + | 0.915627i | \(0.368305\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.17206e14 | − | 1.17206e14i | −1.31076 | − | 1.31076i | −0.920852 | − | 0.389913i | \(-0.872505\pi\) |
−0.389913 | − | 0.920852i | \(-0.627495\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.96629e13i | 0.216369i | 0.994131 | + | 0.108184i | \(0.0345037\pi\) | ||||
−0.994131 | + | 0.108184i | \(0.965496\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.99633e13 | −0.324438 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.05124e13 | − | 6.05124e13i | 0.644770 | − | 0.644770i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.85170e12 | + | 9.85170e12i | 0.101665 | + | 0.101665i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.33381e14i | − | 2.37035i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51432e14 | −1.51381 | −0.756904 | − | 0.653526i | \(-0.773289\pi\) | ||||
−0.756904 | + | 0.653526i | \(0.773289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.66480e13 | + | 1.66480e13i | −0.163811 | + | 0.163811i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.97203e13 | + | 7.97203e13i | 0.760102 | + | 0.760102i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1.21687e13i | − | 0.114220i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.61881e12 | 0.0334407 | 0.0167204 | − | 0.999860i | \(-0.494677\pi\) | ||||
0.0167204 | + | 0.999860i | \(0.494677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.25083e14 | − | 1.25083e14i | 1.13800 | − | 1.13800i | 0.149192 | − | 0.988808i | \(-0.452333\pi\) |
0.988808 | − | 0.149192i | \(-0.0476673\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.94985e13 | − | 6.94985e13i | −0.612991 | − | 0.612991i | 0.330733 | − | 0.943724i | \(-0.392704\pi\) |
−0.943724 | + | 0.330733i | \(0.892704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.29480e13i | − | 0.199306i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.56271e13 | 0.133651 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.21710e14 | − | 1.21710e14i | 1.02508 | − | 1.02508i | 0.0254058 | − | 0.999677i | \(-0.491912\pi\) |
0.999677 | − | 0.0254058i | \(-0.00808779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.43075e13 | + | 1.43075e13i | 0.116879 | + | 0.116879i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.42173e12i | − | 0.0758060i | −0.999281 | − | 0.0379030i | \(-0.987932\pi\) | ||
0.999281 | − | 0.0379030i | \(-0.0120678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.31255e14 | 1.04018 | 0.520092 | − | 0.854110i | \(-0.325898\pi\) | ||||
0.520092 | + | 0.854110i | \(0.325898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.15605e14 | + | 1.15605e14i | −0.902424 | + | 0.902424i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.55461e13 | + | 2.55461e13i | 0.193507 | + | 0.193507i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.88199e13i | 0.140438i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.98398e12 | 0.0366407 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.06296e13 | + | 1.06296e13i | −0.0769913 | + | 0.0769913i | −0.744554 | − | 0.667562i | \(-0.767338\pi\) |
0.667562 | + | 0.744554i | \(0.267338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.56600e13 | + | 8.56600e13i | 0.602330 | + | 0.602330i | 0.940930 | − | 0.338600i | \(-0.109953\pi\) |
−0.338600 | + | 0.940930i | \(0.609953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.50118e13i | 0.311873i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.96249e13 | 0.543643 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.53174e13 | − | 9.53174e13i | 0.641311 | − | 0.641311i | −0.309567 | − | 0.950878i | \(-0.600184\pi\) |
0.950878 | + | 0.309567i | \(0.100184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.10998e14 | + | 1.10998e14i | 0.725324 | + | 0.725324i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.81222e14i | 2.45517i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.68127e14 | 1.70196 | 0.850981 | − | 0.525196i | \(-0.176008\pi\) | ||||
0.850981 | + | 0.525196i | \(0.176008\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.06685e12 | − | 3.06685e12i | 0.0191879 | − | 0.0191879i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.45955e14 | − | 1.45955e14i | −0.887267 | − | 0.887267i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.90931e13i | − | 0.114417i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.37352e14 | −1.40217 | −0.701087 | − | 0.713076i | \(-0.747302\pi\) | ||||
−0.701087 | + | 0.713076i | \(0.747302\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.60163e14 | + | 3.60163e14i | −2.09760 | + | 2.09760i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.45360e13 | + | 1.45360e13i | 0.0822901 | + | 0.0822901i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.42036e14i | 0.792807i | 0.918076 | + | 0.396404i | \(0.129742\pi\) | ||||
−0.918076 | + | 0.396404i | \(0.870258\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.24756e13 | 0.123698 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.93726e13 | + | 8.93726e13i | −0.485017 | + | 0.485017i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.79703e13 | − | 3.79703e13i | −0.200377 | − | 0.200377i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.74318e14i | 1.42761i | 0.700344 | + | 0.713806i | \(0.253030\pi\) | ||||
−0.700344 | + | 0.713806i | \(0.746970\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.73106e12 | −0.0140170 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.69250e13 | + | 6.69250e13i | −0.338764 | + | 0.338764i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.03490e14 | + | 2.03490e14i | 1.00201 | + | 1.00201i | 0.999998 | + | 0.00200942i | \(0.000639618\pi\) |
0.00200942 | + | 0.999998i | \(0.499360\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.62560e12i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.85903e14 | −2.32789 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.09204e14 | − | 1.09204e14i | 0.516080 | − | 0.516080i | −0.400303 | − | 0.916383i | \(-0.631095\pi\) |
0.916383 | + | 0.400303i | \(0.131095\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.37899e12 | − | 5.37899e12i | −0.0247379 | − | 0.0247379i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.20425e14i | − | 1.00009i | −0.866000 | − | 0.500044i | \(-0.833317\pi\) | ||
0.866000 | − | 0.500044i | \(-0.166683\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.56814e14 | 1.59717 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.23312e13 | − | 6.23312e13i | 0.275272 | − | 0.275272i | −0.555946 | − | 0.831218i | \(-0.687644\pi\) |
0.831218 | + | 0.555946i | \(0.187644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.63887e13 | + | 9.63887e13i | 0.414403 | + | 0.414403i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.86898e13i | 0.418662i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.82747e14 | −1.18358 | −0.591790 | − | 0.806092i | \(-0.701579\pi\) | ||||
−0.591790 | + | 0.806092i | \(0.701579\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.63068e14 | − | 1.63068e14i | 0.673587 | − | 0.673587i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.96117e14 | + | 2.96117e14i | 1.19120 | + | 1.19120i | 0.976731 | + | 0.214469i | \(0.0688021\pi\) |
0.214469 | + | 0.976731i | \(0.431198\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.50792e13i | 0.139265i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.19464e14 | −1.25170 | −0.625848 | − | 0.779945i | \(-0.715247\pi\) | ||||
−0.625848 | + | 0.779945i | \(0.715247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.54365e13 | − | 2.54365e13i | 0.0983638 | − | 0.0983638i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.15571e14 | − | 4.15571e14i | −1.56555 | − | 1.56555i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.28750e13i | 0.345356i | 0.984978 | + | 0.172678i | \(0.0552420\pi\) | ||||
−0.984978 | + | 0.172678i | \(0.944758\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.74168e13 | −0.174044 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.34633e13 | − | 9.34633e13i | 0.338644 | − | 0.338644i | −0.517213 | − | 0.855857i | \(-0.673030\pi\) |
0.855857 | + | 0.517213i | \(0.173030\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.12119e14 | + | 1.12119e14i | 0.395891 | + | 0.395891i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.50486e14i | 1.57034i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.42464e13 | −0.0490287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.50144e12 | − | 6.50144e12i | 0.0220902 | − | 0.0220902i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.32899e14 | − | 1.32899e14i | −0.440197 | − | 0.440197i | 0.451881 | − | 0.892078i | \(-0.350753\pi\) |
−0.892078 | + | 0.451881i | \(0.850753\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.08500e13i | − | 0.0354850i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.08507e14 | −0.673345 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.02562e13 | − | 9.02562e13i | 0.287813 | − | 0.287813i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.90337e13 | + | 6.90337e13i | 0.214669 | + | 0.214669i | 0.806248 | − | 0.591578i | \(-0.201495\pi\) |
−0.591578 | + | 0.806248i | \(0.701495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.13301e14i | 1.57630i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.76151e14 | 0.534224 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.67504e13 | − | 1.67504e13i | 0.0501703 | − | 0.0501703i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.11384e14 | + | 2.11384e14i | 0.617595 | + | 0.617595i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.14329e14i | 0.329925i | 0.986300 | + | 0.164962i | \(0.0527503\pi\) | ||||
−0.986300 | + | 0.164962i | \(0.947250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.71081e13 | 0.0772670 | 0.0386335 | − | 0.999253i | \(-0.487700\pi\) | ||||
0.0386335 | + | 0.999253i | \(0.487700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.99941e14 | + | 1.99941e14i | −0.562923 | + | 0.562923i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.49865e14 | + | 7.49865e14i | 2.06003 | + | 2.06003i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.11077e14i | − | 0.301442i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.13873e13 | 0.0573377 | 0.0286688 | − | 0.999589i | \(-0.490873\pi\) | ||||
0.0286688 | + | 0.999589i | \(0.490873\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.60357e13 | + | 5.60357e13i | −0.148411 | + | 0.148411i | −0.777408 | − | 0.628997i | \(-0.783466\pi\) |
0.628997 | + | 0.777408i | \(0.283466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.91606e13 | + | 5.91606e13i | 0.152934 | + | 0.152934i | 0.779427 | − | 0.626493i | \(-0.215510\pi\) |
−0.626493 | + | 0.779427i | \(0.715510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.94836e14i | 1.51923i | 0.650371 | + | 0.759617i | \(0.274613\pi\) | ||||
−0.650371 | + | 0.759617i | \(0.725387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.43370e13 | −0.238055 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.66736e14 | − | 2.66736e14i | 0.665054 | − | 0.665054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.27451e13 | + | 2.27451e13i | 0.0553683 | + | 0.0553683i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.17759e14i | − | 1.00488i | −0.864611 | − | 0.502442i | \(-0.832435\pi\) | ||
0.864611 | − | 0.502442i | \(-0.167565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.09621e14 | 0.973649 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.40254e14 | + | 2.40254e14i | −0.564330 | + | 0.564330i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.71788e14 | + | 1.71788e14i | 0.394073 | + | 0.394073i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.36866e14i | 0.310281i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.28244e15 | −2.87336 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.34595e14 | + | 1.34595e14i | −0.298046 | + | 0.298046i | −0.840248 | − | 0.542202i | \(-0.817591\pi\) |
0.542202 | + | 0.840248i | \(0.317591\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.43571e14 | − | 5.43571e14i | −1.17585 | − | 1.17585i | −0.980792 | − | 0.195058i | \(-0.937510\pi\) |
−0.195058 | − | 0.980792i | \(-0.562490\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.19039e13i | 0.0895960i | 0.998996 | + | 0.0447980i | \(0.0142644\pi\) | ||||
−0.998996 | + | 0.0447980i | \(0.985736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.40237e14 | 0.296379 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.11426e14 | − | 2.11426e14i | 0.441677 | − | 0.441677i | −0.450898 | − | 0.892575i | \(-0.648896\pi\) |
0.892575 | + | 0.450898i | \(0.148896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.86809e14 | + | 1.86809e14i | 0.381332 | + | 0.381332i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.63131e13i | − | 0.0530973i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.94819e14 | −0.388634 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.55146e13 | + | 6.55146e13i | −0.129201 | + | 0.129201i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.38505e13 | − | 3.38505e13i | −0.0652480 | − | 0.0652480i | 0.673730 | − | 0.738978i | \(-0.264691\pi\) |
−0.738978 | + | 0.673730i | \(0.764691\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.25764e14i | 1.00195i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.55559e14 | −0.293100 | −0.146550 | − | 0.989203i | \(-0.546817\pi\) | ||||
−0.146550 | + | 0.989203i | \(0.546817\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.48149e14 | − | 1.48149e14i | 0.275991 | − | 0.275991i | −0.555515 | − | 0.831506i | \(-0.687479\pi\) |
0.831506 | + | 0.555515i | \(0.187479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.14374e14 | + | 2.14374e14i | 0.390439 | + | 0.390439i | 0.874844 | − | 0.484405i | \(-0.160964\pi\) |
−0.484405 | + | 0.874844i | \(0.660964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.10589e14i | − | 0.199161i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.92758e12 | 0.0158981 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.92147e14 | − | 7.92147e14i | 1.39492 | − | 1.39492i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.35258e14 | + | 6.35258e14i | 1.09393 | + | 1.09393i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 3.87841e13i | − | 0.0660474i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.27553e15 | 2.14817 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.33434e14 | − | 2.33434e14i | 0.388800 | − | 0.388800i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.15559e14 | + | 6.15559e14i | 1.00284 | + | 1.00284i | 0.999996 | + | 0.00284780i | \(0.000906484\pi\) |
0.00284780 | + | 0.999996i | \(0.499094\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.23142e13i | 0.0681815i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.91025e13 | 0.0304437 | 0.0152219 | − | 0.999884i | \(-0.495155\pi\) | ||||
0.0152219 | + | 0.999884i | \(0.495155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.12846e14 | − | 1.12846e14i | 0.177882 | − | 0.177882i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.20155e14 | − | 4.20155e14i | −0.647981 | − | 0.647981i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.76368e14i | − | 1.33693i | −0.743743 | − | 0.668465i | \(-0.766952\pi\) | ||
0.743743 | − | 0.668465i | \(-0.233048\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.46248e14 | 0.220695 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.57992e14 | + | 2.57992e14i | −0.385121 | + | 0.385121i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.97504e12 | − | 3.97504e12i | −0.00580689 | − | 0.00580689i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.11580e14i | 1.02836i | 0.857682 | + | 0.514180i | \(0.171904\pi\) | ||||
−0.857682 | + | 0.514180i | \(0.828096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.23277e14 | −1.17706 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.18241e14 | + | 3.18241e14i | −0.450140 | + | 0.450140i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.26629e14 | − | 3.26629e14i | −0.452228 | − | 0.452228i | 0.443865 | − | 0.896093i | \(-0.353607\pi\) |
−0.896093 | + | 0.443865i | \(0.853607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 8.11885e14i | − | 1.11216i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.09565e15 | −1.48499 | −0.742493 | − | 0.669853i | \(-0.766357\pi\) | ||||
−0.742493 | + | 0.669853i | \(0.766357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.02029e14 | + | 8.02029e14i | −1.07555 | + | 1.07555i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.23879e13 | − | 2.23879e13i | −0.0293944 | − | 0.0293944i | 0.692257 | − | 0.721651i | \(-0.256617\pi\) |
−0.721651 | + | 0.692257i | \(0.756617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.06673e14i | − | 0.788177i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.15332e14 | 0.919612 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.97864e14 | − | 9.97864e14i | 1.26942 | − | 1.26942i | 0.323038 | − | 0.946386i | \(-0.395296\pi\) |
0.946386 | − | 0.323038i | \(-0.104704\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.61148e12 | − | 7.61148e12i | −0.00948221 | − | 0.00948221i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.30068e14i | 0.160354i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.83943e14 | −0.834455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.43643e14 | + | 1.43643e14i | −0.173441 | + | 0.173441i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.06388e14 | + | 9.06388e14i | 1.07197 | + | 1.07197i | 0.997201 | + | 0.0747674i | \(0.0238214\pi\) |
0.0747674 | + | 0.997201i | \(0.476179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.19387e15i | − | 1.39745i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.05106e14 | 0.585176 | 0.292588 | − | 0.956239i | \(-0.405484\pi\) | ||||
0.292588 | + | 0.956239i | \(0.405484\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.54333e14 | − | 4.54333e14i | 0.520966 | − | 0.520966i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.85368e14 | − | 5.85368e14i | −0.657592 | − | 0.657592i | 0.297218 | − | 0.954810i | \(-0.403941\pi\) |
−0.954810 | + | 0.297218i | \(0.903941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.06227e14i | − | 0.229315i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.40456e13 | 0.0814994 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.38275e14 | + | 6.38275e14i | −0.695409 | + | 0.695409i | −0.963417 | − | 0.268008i | \(-0.913635\pi\) |
0.268008 | + | 0.963417i | \(0.413635\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.46597e14 | − | 2.46597e14i | −0.263270 | − | 0.263270i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.67006e15i | 2.82189i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.97076e14 | 0.206189 | 0.103094 | − | 0.994672i | \(-0.467126\pi\) | ||||
0.103094 | + | 0.994672i | \(0.467126\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.02254e14 | + | 2.02254e14i | −0.209485 | + | 0.209485i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.98412e14 | − | 9.98412e14i | −1.01352 | − | 1.01352i | −0.999907 | − | 0.0136164i | \(-0.995666\pi\) |
−0.0136164 | − | 0.999907i | \(-0.504334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.26379e14i | 0.328016i |
(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 | 300.11.k.c.157.6 | yes | 16 | |
5.2 | odd | 4 | inner | 300.11.k.c.193.3 | yes | 16 | |
5.3 | odd | 4 | inner | 300.11.k.c.193.6 | yes | 16 | |
5.4 | even | 2 | inner | 300.11.k.c.157.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.11.k.c.157.3 | ✓ | 16 | 5.4 | even | 2 | inner | |
300.11.k.c.157.6 | yes | 16 | 1.1 | even | 1 | trivial | |
300.11.k.c.193.3 | yes | 16 | 5.2 | odd | 4 | inner | |
300.11.k.c.193.6 | yes | 16 | 5.3 | odd | 4 | inner |