Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(1343,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1343");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.n (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.3317760000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 100) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1343.2 | ||
Root | \(-0.178197 + 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1343 |
Dual form | 1600.2.n.v.1407.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.58114 | + | 1.58114i | −0.912871 | + | 0.912871i | −0.996497 | − | 0.0836263i | \(-0.973350\pi\) |
0.0836263 | + | 0.996497i | \(0.473350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.00000i | − | 0.666667i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.87298i | 1.16775i | 0.811844 | + | 0.583874i | \(0.198464\pi\) | ||||
−0.811844 | + | 0.583874i | \(0.801536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | − | 2.44949i | −0.679366 | − | 0.679366i | 0.280491 | − | 0.959857i | \(-0.409503\pi\) |
−0.959857 | + | 0.280491i | \(0.909503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.22474 | + | 1.22474i | −0.297044 | + | 0.297044i | −0.839855 | − | 0.542811i | \(-0.817360\pi\) |
0.542811 | + | 0.839855i | \(0.317360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.87298 | 0.888523 | 0.444262 | − | 0.895897i | \(-0.353466\pi\) | ||||
0.444262 | + | 0.895897i | \(0.353466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.16228 | + | 3.16228i | −0.659380 | + | 0.659380i | −0.955233 | − | 0.295853i | \(-0.904396\pi\) |
0.295853 | + | 0.955233i | \(0.404396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.58114 | − | 1.58114i | −0.304290 | − | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.74597i | 1.39122i | 0.718421 | + | 0.695608i | \(0.244865\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.12372 | − | 6.12372i | −1.06600 | − | 1.06600i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.89898 | + | 4.89898i | −0.805387 | + | 0.805387i | −0.983932 | − | 0.178545i | \(-0.942861\pi\) |
0.178545 | + | 0.983932i | \(0.442861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.74597 | 1.24035 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.16228 | − | 3.16228i | −0.461266 | − | 0.461266i | 0.437805 | − | 0.899070i | \(-0.355756\pi\) |
−0.899070 | + | 0.437805i | \(0.855756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.87298i | − | 0.542326i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | − | 2.44949i | −0.336463 | − | 0.336463i | 0.518571 | − | 0.855034i | \(-0.326464\pi\) |
−0.855034 | + | 0.518571i | \(0.826464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.12372 | + | 6.12372i | −0.811107 | + | 0.811107i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.74597 | −1.00844 | −0.504219 | − | 0.863576i | \(-0.668220\pi\) | ||||
−0.504219 | + | 0.863576i | \(0.668220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.74342 | + | 4.74342i | 0.579501 | + | 0.579501i | 0.934766 | − | 0.355265i | \(-0.115609\pi\) |
−0.355265 | + | 0.934766i | \(0.615609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 10.0000i | − | 1.20386i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.74597i | − | 0.919277i | −0.888106 | − | 0.459639i | \(-0.847979\pi\) | ||
0.888106 | − | 0.459639i | \(-0.152021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.67423 | − | 3.67423i | −0.430037 | − | 0.430037i | 0.458604 | − | 0.888641i | \(-0.348350\pi\) |
−0.888641 | + | 0.458604i | \(0.848350\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4919 | −1.74298 | −0.871489 | − | 0.490414i | \(-0.836845\pi\) | ||||
−0.871489 | + | 0.490414i | \(0.836845\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.58114 | − | 1.58114i | 0.173553 | − | 0.173553i | −0.614986 | − | 0.788538i | \(-0.710838\pi\) |
0.788538 | + | 0.614986i | \(0.210838\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.48683 | + | 9.48683i | 1.01710 | + | 1.01710i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.00000i | − | 0.953998i | −0.878904 | − | 0.476999i | \(-0.841725\pi\) | ||
0.878904 | − | 0.476999i | \(-0.158275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.2474 | − | 12.2474i | −1.27000 | − | 1.27000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89898 | − | 4.89898i | 0.497416 | − | 0.497416i | −0.413217 | − | 0.910633i | \(-0.635595\pi\) |
0.910633 | + | 0.413217i | \(0.135595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.74597 | 0.778499 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.48683 | − | 9.48683i | 0.934765 | − | 0.934765i | −0.0632333 | − | 0.997999i | \(-0.520141\pi\) |
0.997999 | + | 0.0632333i | \(0.0201412\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.90569 | − | 7.90569i | −0.764272 | − | 0.764272i | 0.212819 | − | 0.977092i | \(-0.431735\pi\) |
−0.977092 | + | 0.212819i | \(0.931735\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 15.4919i | − | 1.47043i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.67423 | − | 3.67423i | −0.345643 | − | 0.345643i | 0.512841 | − | 0.858484i | \(-0.328593\pi\) |
−0.858484 | + | 0.512841i | \(0.828593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.89898 | + | 4.89898i | −0.452911 | + | 0.452911i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | −0.363636 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.74342 | − | 4.74342i | 0.427699 | − | 0.427699i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.48683 | − | 9.48683i | −0.841820 | − | 0.841820i | 0.147275 | − | 0.989096i | \(-0.452950\pi\) |
−0.989096 | + | 0.147275i | \(0.952950\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.74597i | − | 0.676768i | −0.941008 | − | 0.338384i | \(-0.890120\pi\) | ||
0.941008 | − | 0.338384i | \(-0.109880\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4722 | + | 13.4722i | −1.15101 | + | 1.15101i | −0.164656 | + | 0.986351i | \(0.552651\pi\) |
−0.986351 | + | 0.164656i | \(0.947349\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6190 | −0.985506 | −0.492753 | − | 0.870169i | \(-0.664009\pi\) | ||||
−0.492753 | + | 0.870169i | \(0.664009\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0000 | 0.842152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.48683 | − | 9.48683i | 0.793329 | − | 0.793329i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.0680 | + | 11.0680i | 0.912871 | + | 0.912871i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.44949 | + | 2.44949i | 0.198030 | + | 0.198030i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.34847 | − | 7.34847i | 0.586472 | − | 0.586472i | −0.350202 | − | 0.936674i | \(-0.613887\pi\) |
0.936674 | + | 0.350202i | \(0.113887\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.74597 | 0.614295 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.74342 | − | 4.74342i | 0.371533 | − | 0.371533i | −0.496502 | − | 0.868035i | \(-0.665383\pi\) |
0.868035 | + | 0.496502i | \(0.165383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.16228 | + | 3.16228i | 0.244704 | + | 0.244704i | 0.818793 | − | 0.574089i | \(-0.194644\pi\) |
−0.574089 | + | 0.818793i | \(0.694644\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.00000i | − | 0.0769231i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.74597i | − | 0.592349i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.79796 | + | 9.79796i | 0.744925 | + | 0.744925i | 0.973521 | − | 0.228596i | \(-0.0734136\pi\) |
−0.228596 | + | 0.973521i | \(0.573414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.2474 | − | 12.2474i | 0.920575 | − | 0.920575i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.87298 | −0.289480 | −0.144740 | − | 0.989470i | \(-0.546235\pi\) | ||||
−0.144740 | + | 0.989470i | \(0.546235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.6491 | + | 12.6491i | −0.935049 | + | 0.935049i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.74342 | − | 4.74342i | −0.346873 | − | 0.346873i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.2379i | 1.68144i | 0.541474 | + | 0.840718i | \(0.317867\pi\) | ||||
−0.541474 | + | 0.840718i | \(0.682133\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.67423 | − | 3.67423i | −0.264477 | − | 0.264477i | 0.562393 | − | 0.826870i | \(-0.309881\pi\) |
−0.826870 | + | 0.562393i | \(0.809881\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.1464 | + | 17.1464i | −1.22163 | + | 1.22163i | −0.254581 | + | 0.967051i | \(0.581938\pi\) |
−0.967051 | + | 0.254581i | \(0.918062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0000 | −1.05802 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.32456 | + | 6.32456i | 0.439587 | + | 0.439587i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0000i | 1.03757i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.87298i | 0.266627i | 0.991074 | + | 0.133314i | \(0.0425617\pi\) | ||||
−0.991074 | + | 0.133314i | \(0.957438\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.2474 | + | 12.2474i | 0.839181 | + | 0.839181i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.6190 | 0.785136 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.9737 | + | 18.9737i | −1.27057 | + | 1.27057i | −0.324782 | + | 0.945789i | \(0.605291\pi\) |
−0.945789 | + | 0.324782i | \(0.894709\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.32456 | − | 6.32456i | −0.419775 | − | 0.419775i | 0.465351 | − | 0.885126i | \(-0.345928\pi\) |
−0.885126 | + | 0.465351i | \(0.845928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000i | 0.264327i | 0.991228 | + | 0.132164i | \(0.0421925\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.6969 | + | 14.6969i | 0.962828 | + | 0.962828i | 0.999333 | − | 0.0365050i | \(-0.0116225\pi\) |
−0.0365050 | + | 0.999333i | \(0.511622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.4949 | − | 24.4949i | 1.59111 | − | 1.59111i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.74597 | −0.501045 | −0.250522 | − | 0.968111i | \(-0.580602\pi\) | ||||
−0.250522 | + | 0.968111i | \(0.580602\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0000 | 1.09507 | 0.547533 | − | 0.836784i | \(-0.315567\pi\) | ||||
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.6491 | + | 12.6491i | −0.811441 | + | 0.811441i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.48683 | − | 9.48683i | −0.603633 | − | 0.603633i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.00000i | 0.316862i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.3649i | 1.22230i | 0.791514 | + | 0.611151i | \(0.209293\pi\) | ||||
−0.791514 | + | 0.611151i | \(0.790707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.2474 | − | 12.2474i | −0.769991 | − | 0.769991i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.89898 | − | 4.89898i | 0.305590 | − | 0.305590i | −0.537606 | − | 0.843196i | \(-0.680671\pi\) |
0.843196 | + | 0.537606i | \(0.180671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.0000 | −0.742781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.16228 | − | 3.16228i | 0.194994 | − | 0.194994i | −0.602856 | − | 0.797850i | \(-0.705971\pi\) |
0.797850 | + | 0.602856i | \(0.205971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.2302 | + | 14.2302i | 0.870877 | + | 0.870877i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.0000i | 1.46331i | 0.681677 | + | 0.731653i | \(0.261251\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.74597i | − | 0.470534i | −0.971931 | − | 0.235267i | \(-0.924404\pi\) | ||
0.971931 | − | 0.235267i | \(-0.0755965\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.34847 | − | 7.34847i | 0.441527 | − | 0.441527i | −0.450998 | − | 0.892525i | \(-0.648932\pi\) |
0.892525 | + | 0.450998i | \(0.148932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.4919 | 0.927478 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.2302 | + | 14.2302i | −0.845901 | + | 0.845901i | −0.989619 | − | 0.143718i | \(-0.954094\pi\) |
0.143718 | + | 0.989619i | \(0.454094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0000i | 0.823529i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.4919i | 0.908153i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.79796 | + | 9.79796i | 0.572403 | + | 0.572403i | 0.932799 | − | 0.360396i | \(-0.117359\pi\) |
−0.360396 | + | 0.932799i | \(0.617359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.12372 | − | 6.12372i | 0.355335 | − | 0.355335i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.4919 | 0.895922 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.9737 | − | 18.9737i | 1.09001 | − | 1.09001i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.7171 | − | 23.7171i | −1.35361 | − | 1.35361i | −0.881591 | − | 0.472015i | \(-0.843527\pi\) |
−0.472015 | − | 0.881591i | \(-0.656473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.0000i | 1.70664i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4919i | 0.878467i | 0.898373 | + | 0.439233i | \(0.144750\pi\) | ||||
−0.898373 | + | 0.439233i | \(0.855250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6969 | + | 14.6969i | 0.830720 | + | 0.830720i | 0.987615 | − | 0.156895i | \(-0.0501485\pi\) |
−0.156895 | + | 0.987615i | \(0.550148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.89898 | + | 4.89898i | −0.275154 | + | 0.275154i | −0.831171 | − | 0.556017i | \(-0.812329\pi\) |
0.556017 | + | 0.831171i | \(0.312329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.2379 | 1.30107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.0000 | 1.39536 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.74342 | + | 4.74342i | −0.263931 | + | 0.263931i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.32456 | − | 6.32456i | −0.349749 | − | 0.349749i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6190i | 0.638635i | 0.947648 | + | 0.319318i | \(0.103454\pi\) | ||||
−0.947648 | + | 0.319318i | \(0.896546\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.79796 | + | 9.79796i | 0.536925 | + | 0.536925i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0227 | − | 11.0227i | 0.600445 | − | 0.600445i | −0.339986 | − | 0.940431i | \(-0.610422\pi\) |
0.940431 | + | 0.339986i | \(0.110422\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.6190 | 0.631055 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.0000 | −1.62459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0680 | + | 11.0680i | 0.594160 | + | 0.594160i | 0.938752 | − | 0.344593i | \(-0.111983\pi\) |
−0.344593 | + | 0.938752i | \(0.611983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.0000i | − | 0.856460i | −0.903670 | − | 0.428230i | \(-0.859137\pi\) | ||
0.903670 | − | 0.428230i | \(-0.140863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.74597i | 0.413449i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.6969 | + | 14.6969i | 0.782239 | + | 0.782239i | 0.980208 | − | 0.197969i | \(-0.0634346\pi\) |
−0.197969 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.9839 | −1.63527 | −0.817633 | − | 0.575740i | \(-0.804714\pi\) | ||||
−0.817633 | + | 0.575740i | \(0.804714\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.00000 | −0.210526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.32456 | − | 6.32456i | 0.331953 | − | 0.331953i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.9737 | + | 18.9737i | 0.990417 | + | 0.990417i | 0.999955 | − | 0.00953722i | \(-0.00303584\pi\) |
−0.00953722 | + | 0.999955i | \(0.503036\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000i | 0.312348i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0454 | + | 22.0454i | 1.14147 | + | 1.14147i | 0.988182 | + | 0.153286i | \(0.0489856\pi\) |
0.153286 | + | 0.988182i | \(0.451014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.6969 | + | 14.6969i | −0.756931 | + | 0.756931i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.87298 | −0.198942 | −0.0994709 | − | 0.995040i | \(-0.531715\pi\) | ||||
−0.0994709 | + | 0.995040i | \(0.531715\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.0000 | 1.53695 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.2982 | + | 25.2982i | −1.29268 | + | 1.29268i | −0.359555 | + | 0.933124i | \(0.617071\pi\) |
−0.933124 | + | 0.359555i | \(0.882929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.00000i | − | 0.304212i | −0.988364 | − | 0.152106i | \(-0.951394\pi\) | ||
0.988364 | − | 0.152106i | \(-0.0486055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.74597i | − | 0.391730i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2474 | + | 12.2474i | 0.617802 | + | 0.617802i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5959 | − | 19.5959i | 0.983491 | − | 0.983491i | −0.0163750 | − | 0.999866i | \(-0.505213\pi\) |
0.999866 | + | 0.0163750i | \(0.00521255\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.0000 | −1.64794 | −0.823971 | − | 0.566632i | \(-0.808246\pi\) | ||||
−0.823971 | + | 0.566632i | \(0.808246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.9737 | − | 18.9737i | 0.945146 | − | 0.945146i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.9737 | − | 18.9737i | −0.940490 | − | 0.940490i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.0000i | 1.53285i | 0.642333 | + | 0.766426i | \(0.277967\pi\) | ||||
−0.642333 | + | 0.766426i | \(0.722033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 42.6028i | − | 2.10144i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.3712 | − | 18.3712i | 0.899640 | − | 0.899640i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.8569 | −1.70287 | −0.851434 | − | 0.524461i | \(-0.824267\pi\) | ||||
−0.851434 | + | 0.524461i | \(0.824267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.32456 | + | 6.32456i | −0.307510 | + | 0.307510i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.0000i | 1.44841i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 30.9839i | − | 1.49244i | −0.665699 | − | 0.746220i | \(-0.731867\pi\) | ||
0.665699 | − | 0.746220i | \(-0.268133\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.9217 | − | 15.9217i | −0.765147 | − | 0.765147i | 0.212101 | − | 0.977248i | \(-0.431970\pi\) |
−0.977248 | + | 0.212101i | \(0.931970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.2474 | + | 12.2474i | −0.585875 | + | 0.585875i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.74597 | −0.369695 | −0.184847 | − | 0.982767i | \(-0.559179\pi\) | ||||
−0.184847 | + | 0.982767i | \(0.559179\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.0000 | −0.666667 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.90569 | − | 7.90569i | 0.375611 | − | 0.375611i | −0.493905 | − | 0.869516i | \(-0.664431\pi\) |
0.869516 | + | 0.493905i | \(0.164431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.48683 | + | 9.48683i | 0.448712 | + | 0.448712i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.00000i | − | 0.424736i | −0.977190 | − | 0.212368i | \(-0.931882\pi\) | ||
0.977190 | − | 0.212368i | \(-0.0681176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11.6190i | − | 0.547115i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.22474 | + | 1.22474i | −0.0572911 | + | 0.0572911i | −0.735172 | − | 0.677881i | \(-0.762899\pi\) |
0.677881 | + | 0.735172i | \(0.262899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.87298 | 0.180775 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.9737 | − | 18.9737i | 0.881781 | − | 0.881781i | −0.111935 | − | 0.993716i | \(-0.535705\pi\) |
0.993716 | + | 0.111935i | \(0.0357047\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6491 | + | 12.6491i | 0.585331 | + | 0.585331i | 0.936363 | − | 0.351032i | \(-0.114169\pi\) |
−0.351032 | + | 0.936363i | \(0.614169\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.2379i | 1.07075i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.89898 | + | 4.89898i | −0.224309 | + | 0.224309i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.2379 | 1.06177 | 0.530883 | − | 0.847445i | \(-0.321860\pi\) | ||||
0.530883 | + | 0.847445i | \(0.321860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | 1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.48683 | + | 9.48683i | 0.429889 | + | 0.429889i | 0.888591 | − | 0.458701i | \(-0.151685\pi\) |
−0.458701 | + | 0.888591i | \(0.651685\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.0000i | 0.678323i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.2379i | − | 1.04871i | −0.851499 | − | 0.524356i | \(-0.824306\pi\) | ||
0.851499 | − | 0.524356i | \(-0.175694\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.34847 | + | 7.34847i | 0.330958 | + | 0.330958i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.7298 | −1.73379 | −0.866893 | − | 0.498495i | \(-0.833886\pi\) | ||||
−0.866893 | + | 0.498495i | \(0.833886\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0000 | −0.446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.2982 | − | 25.2982i | 1.12799 | − | 1.12799i | 0.137489 | − | 0.990503i | \(-0.456097\pi\) |
0.990503 | − | 0.137489i | \(-0.0439030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.58114 | + | 1.58114i | 0.0702208 | + | 0.0702208i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 6.00000i | − | 0.265945i | −0.991120 | − | 0.132973i | \(-0.957548\pi\) | ||
0.991120 | − | 0.132973i | \(-0.0424523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.12372 | − | 6.12372i | −0.270369 | − | 0.270369i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2474 | − | 12.2474i | 0.538642 | − | 0.538642i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.9839 | −1.36004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.74342 | + | 4.74342i | −0.207415 | + | 0.207415i | −0.803168 | − | 0.595753i | \(-0.796854\pi\) |
0.595753 | + | 0.803168i | \(0.296854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.48683 | − | 9.48683i | −0.413253 | − | 0.413253i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.00000i | 0.130435i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.4919i | 0.672293i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.34847 | + | 7.34847i | 0.318298 | + | 0.318298i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.12372 | − | 6.12372i | 0.264258 | − | 0.264258i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.1109 | 1.16775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.16228 | − | 3.16228i | 0.135706 | − | 0.135706i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.74342 | − | 4.74342i | −0.202814 | − | 0.202814i | 0.598391 | − | 0.801204i | \(-0.295807\pi\) |
−0.801204 | + | 0.598391i | \(0.795807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 16.0000i | − | 0.682863i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.2379i | − | 0.989968i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.34847 | − | 7.34847i | 0.311365 | − | 0.311365i | −0.534073 | − | 0.845438i | \(-0.679339\pi\) |
0.845438 | + | 0.534073i | \(0.179339\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.0000 | 0.633300 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.6491 | − | 12.6491i | 0.533096 | − | 0.533096i | −0.388396 | − | 0.921493i | \(-0.626971\pi\) |
0.921493 | + | 0.388396i | \(0.126971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 39.0000i | − | 1.63497i | −0.575953 | − | 0.817483i | \(-0.695369\pi\) | ||
0.575953 | − | 0.817483i | \(-0.304631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.74597i | 0.324159i | 0.986778 | + | 0.162079i | \(0.0518200\pi\) | ||||
−0.986778 | + | 0.162079i | \(0.948180\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.7423 | − | 36.7423i | −1.53493 | − | 1.53493i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.22474 | + | 1.22474i | −0.0509868 | + | 0.0509868i | −0.732140 | − | 0.681154i | \(-0.761479\pi\) |
0.681154 | + | 0.732140i | \(0.261479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.6190 | 0.482867 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.48683 | − | 9.48683i | 0.392904 | − | 0.392904i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.58114 | − | 1.58114i | −0.0652606 | − | 0.0652606i | 0.673723 | − | 0.738984i | \(-0.264694\pi\) |
−0.738984 | + | 0.673723i | \(0.764694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.0000i | 1.23613i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 54.2218i | − | 2.23039i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.8207 | + | 20.8207i | 0.855002 | + | 0.855002i | 0.990744 | − | 0.135742i | \(-0.0433418\pi\) |
−0.135742 | + | 0.990744i | \(0.543342\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | 0.693444 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.48683 | − | 9.48683i | 0.386334 | − | 0.386334i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.4919i | 0.626737i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.9444 | − | 26.9444i | −1.08827 | − | 1.08827i | −0.995706 | − | 0.0925671i | \(-0.970493\pi\) |
−0.0925671 | − | 0.995706i | \(-0.529507\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.5959 | + | 19.5959i | −0.788902 | + | 0.788902i | −0.981314 | − | 0.192412i | \(-0.938369\pi\) |
0.192412 | + | 0.981314i | \(0.438369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2379 | 0.934010 | 0.467005 | − | 0.884255i | \(-0.345333\pi\) | ||||
0.467005 | + | 0.884255i | \(0.345333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.0000 | 0.401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −23.7171 | − | 23.7171i | −0.947169 | − | 0.947169i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12.0000i | − | 0.478471i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.74597i | 0.308362i | 0.988043 | + | 0.154181i | \(0.0492739\pi\) | ||||
−0.988043 | + | 0.154181i | \(0.950726\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.12372 | − | 6.12372i | −0.243396 | − | 0.243396i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.1464 | + | 17.1464i | −0.679366 | + | 0.679366i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.4919 | −0.612851 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.6491 | + | 12.6491i | 0.497288 | + | 0.497288i | 0.910593 | − | 0.413305i | \(-0.135626\pi\) |
−0.413305 | + | 0.910593i | \(0.635626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.0000i | − | 1.17760i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.2929 | + | 34.2929i | 1.34198 | + | 1.34198i | 0.894084 | + | 0.447899i | \(0.147828\pi\) |
0.447899 | + | 0.894084i | \(0.352172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.34847 | + | 7.34847i | −0.286691 | + | 0.286691i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.6190 | 0.452610 | 0.226305 | − | 0.974056i | \(-0.427335\pi\) | ||||
0.226305 | + | 0.974056i | \(0.427335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00000 | −0.0777910 | −0.0388955 | − | 0.999243i | \(-0.512384\pi\) | ||||
−0.0388955 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.48683 | + | 9.48683i | −0.368438 | + | 0.368438i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.9737 | + | 18.9737i | 0.734663 | + | 0.734663i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 60.0000i | − | 2.31973i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.9839i | 1.19612i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.79796 | − | 9.79796i | −0.377684 | − | 0.377684i | 0.492582 | − | 0.870266i | \(-0.336053\pi\) |
−0.870266 | + | 0.492582i | \(0.836053\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.3939 | + | 29.3939i | −1.12970 | + | 1.12970i | −0.139473 | + | 0.990226i | \(0.544541\pi\) |
−0.990226 | + | 0.139473i | \(0.955459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0000 | 0.766402 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.0416 | + | 30.0416i | −1.14951 | + | 1.14951i | −0.162863 | + | 0.986649i | \(0.552073\pi\) |
−0.986649 | + | 0.162863i | \(0.947927\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.32456 | − | 6.32456i | −0.241297 | − | 0.241297i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000i | 0.457164i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.87298i | − | 0.147335i | −0.997283 | − | 0.0736676i | \(-0.976530\pi\) | ||
0.997283 | − | 0.0736676i | \(-0.0234704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.67423 | − | 3.67423i | 0.139172 | − | 0.139172i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −46.4758 | −1.75788 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9737 | + | 18.9737i | −0.715605 | + | 0.715605i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000i | 0.150223i | 0.997175 | + | 0.0751116i | \(0.0239313\pi\) | ||||
−0.997175 | + | 0.0751116i | \(0.976069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.9839i | 1.16199i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.4949 | − | 24.4949i | −0.917341 | − | 0.917341i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.2474 | − | 12.2474i | 0.457389 | − | 0.457389i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.4919 | 0.577752 | 0.288876 | − | 0.957367i | \(-0.406719\pi\) | ||||
0.288876 | + | 0.957367i | \(0.406719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.8794 | + | 26.8794i | −0.999654 | + | 0.999654i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.48683 | − | 9.48683i | −0.351847 | − | 0.351847i | 0.508949 | − | 0.860796i | \(-0.330034\pi\) |
−0.860796 | + | 0.508949i | \(0.830034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 7.00000i | − | 0.259259i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.9444 | − | 26.9444i | −0.995214 | − | 0.995214i | 0.00477495 | − | 0.999989i | \(-0.498480\pi\) |
−0.999989 | + | 0.00477495i | \(0.998480\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.3712 | + | 18.3712i | −0.676711 | + | 0.676711i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.74597 | 0.284940 | 0.142470 | − | 0.989799i | \(-0.454496\pi\) | ||||
0.142470 | + | 0.989799i | \(0.454496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.0000 | 1.10208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.8114 | + | 15.8114i | −0.580064 | + | 0.580064i | −0.934921 | − | 0.354857i | \(-0.884530\pi\) |
0.354857 | + | 0.934921i | \(0.384530\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.16228 | − | 3.16228i | −0.115702 | − | 0.115702i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.7298i | 1.41327i | 0.707577 | + | 0.706636i | \(0.249788\pi\) | ||||
−0.707577 | + | 0.706636i | \(0.750212\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.6186 | − | 30.6186i | −1.11580 | − | 1.11580i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.89898 | + | 4.89898i | −0.178056 | + | 0.178056i | −0.790508 | − | 0.612452i | \(-0.790183\pi\) |
0.612452 | + | 0.790508i | \(0.290183\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 38.7298 | 1.40580 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.0000 | −1.19625 | −0.598125 | − | 0.801403i | \(-0.704087\pi\) | ||||
−0.598125 | + | 0.801403i | \(0.704087\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.9737 | + | 18.9737i | 0.685099 | + | 0.685099i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 19.0000i | − | 0.685158i | −0.939489 | − | 0.342579i | \(-0.888700\pi\) | ||
0.939489 | − | 0.342579i | \(-0.111300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4919i | 0.557928i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.9444 | − | 26.9444i | −0.969122 | − | 0.969122i | 0.0304151 | − | 0.999537i | \(-0.490317\pi\) |
−0.999537 | + | 0.0304151i | \(0.990317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.6190 | −0.416292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0000 | 1.07348 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.48683 | + | 9.48683i | −0.339032 | + | 0.339032i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.9473 | + | 37.9473i | 1.35268 | + | 1.35268i | 0.882655 | + | 0.470021i | \(0.155754\pi\) |
0.470021 | + | 0.882655i | \(0.344246\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0000i | 0.356009i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.5959 | − | 19.5959i | −0.695871 | − | 0.695871i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.1464 | + | 17.1464i | −0.607358 | + | 0.607358i | −0.942255 | − | 0.334897i | \(-0.891298\pi\) |
0.334897 | + | 0.942255i | \(0.391298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.74597 | 0.274033 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.2302 | − | 14.2302i | 0.502175 | − | 0.502175i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.9473 | − | 37.9473i | −1.33581 | − | 1.33581i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.2379i | 0.815993i | 0.912983 | + | 0.407997i | \(0.133772\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2474 | + | 12.2474i | 0.429537 | + | 0.429537i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0000 | 0.628204 | 0.314102 | − | 0.949389i | \(-0.398297\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.9737 | + | 18.9737i | −0.661380 | + | 0.661380i | −0.955705 | − | 0.294325i | \(-0.904905\pi\) |
0.294325 | + | 0.955705i | \(0.404905\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.0416 | − | 30.0416i | −1.04465 | − | 1.04465i | −0.998955 | − | 0.0456946i | \(-0.985450\pi\) |
−0.0456946 | − | 0.998955i | \(-0.514550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 46.0000i | − | 1.59765i | −0.601566 | − | 0.798823i | \(-0.705456\pi\) | ||
0.601566 | − | 0.798823i | \(-0.294544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.2379i | 0.806114i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.57321 | + | 8.57321i | 0.297044 | + | 0.297044i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2474 | − | 12.2474i | 0.423334 | − | 0.423334i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.9839 | 1.06968 | 0.534841 | − | 0.844953i | \(-0.320372\pi\) | ||||
0.534841 | + | 0.844953i | \(0.320372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.4605 | − | 28.4605i | 0.980232 | − | 0.980232i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 45.0000i | − | 1.54440i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 30.9839i | − | 1.06211i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.44949 | − | 2.44949i | −0.0838689 | − | 0.0838689i | 0.663928 | − | 0.747797i | \(-0.268888\pi\) |
−0.747797 | + | 0.663928i | \(0.768888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.22474 | + | 1.22474i | −0.0418365 | + | 0.0418365i | −0.727716 | − | 0.685879i | \(-0.759418\pi\) |
0.685879 | + | 0.727716i | \(0.259418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.3488 | 1.71788 | 0.858939 | − | 0.512078i | \(-0.171124\pi\) | ||||
0.858939 | + | 0.512078i | \(0.171124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.16228 | − | 3.16228i | 0.107645 | − | 0.107645i | −0.651233 | − | 0.758878i | \(-0.725748\pi\) |
0.758878 | + | 0.651233i | \(0.225748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.1359 | − | 22.1359i | −0.751776 | − | 0.751776i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 60.0000i | − | 2.03536i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 23.2379i | − | 0.787386i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.79796 | − | 9.79796i | −0.331611 | − | 0.331611i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.89898 | + | 4.89898i | −0.165427 | + | 0.165427i | −0.784966 | − | 0.619539i | \(-0.787320\pi\) |
0.619539 | + | 0.784966i | \(0.287320\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.9839 | −1.04506 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.2302 | + | 14.2302i | −0.478886 | + | 0.478886i | −0.904775 | − | 0.425889i | \(-0.859961\pi\) |
0.425889 | + | 0.904775i | \(0.359961\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.2982 | + | 25.2982i | 0.849431 | + | 0.849431i | 0.990062 | − | 0.140631i | \(-0.0449131\pi\) |
−0.140631 | + | 0.990062i | \(0.544913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.6028i | 1.42725i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.2474 | − | 12.2474i | −0.409845 | − | 0.409845i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.4949 | + | 24.4949i | −0.817861 | + | 0.817861i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.4758 | 1.55005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | 0.199889 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.0000i | 0.796030i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.4919i | 0.513271i | 0.966508 | + | 0.256635i | \(0.0826139\pi\) | ||||
−0.966508 | + | 0.256635i | \(0.917386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.12372 | + | 6.12372i | 0.202666 | + | 0.202666i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.2379 | −0.766548 | −0.383274 | − | 0.923635i | \(-0.625203\pi\) | ||||
−0.383274 | + | 0.923635i | \(0.625203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.0000 | 2.47133 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.9737 | + | 18.9737i | −0.624526 | + | 0.624526i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.9737 | − | 18.9737i | −0.623177 | − | 0.623177i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000i | 0.196854i | 0.995144 | + | 0.0984268i | \(0.0313810\pi\) | ||||
−0.995144 | + | 0.0984268i | \(0.968619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 27.1109i | − | 0.888523i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.4949 | − | 24.4949i | −0.801927 | − | 0.801927i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.5176 | − | 35.5176i | 1.16031 | − | 1.16031i | 0.175902 | − | 0.984408i | \(-0.443716\pi\) |
0.984408 | − | 0.175902i | \(-0.0562841\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.4758 | −1.51668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0000 | −1.36916 | −0.684580 | − | 0.728937i | \(-0.740015\pi\) | ||||
−0.684580 | + | 0.728937i | \(0.740015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.48683 | − | 9.48683i | 0.308934 | − | 0.308934i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.6491 | − | 12.6491i | −0.411041 | − | 0.411041i | 0.471060 | − | 0.882101i | \(-0.343871\pi\) |
−0.882101 | + | 0.471060i | \(0.843871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000i | 0.584305i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 15.4919i | − | 0.502360i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.67423 | − | 3.67423i | −0.119020 | − | 0.119020i | 0.645088 | − | 0.764108i | \(-0.276821\pi\) |
−0.764108 | + | 0.645088i | \(0.776821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.7423 | + | 36.7423i | −1.18771 | + | 1.18771i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.8114 | + | 15.8114i | −0.509515 | + | 0.509515i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.9737 | + | 18.9737i | 0.610152 | + | 0.610152i | 0.942986 | − | 0.332834i | \(-0.108005\pi\) |
−0.332834 | + | 0.942986i | \(0.608005\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 15.0000i | − | 0.481869i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.1109i | 0.870030i | 0.900423 | + | 0.435015i | \(0.143257\pi\) | ||||
−0.900423 | + | 0.435015i | \(0.856743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.7196 | + | 25.7196i | −0.822844 | + | 0.822844i | −0.986515 | − | 0.163671i | \(-0.947667\pi\) |
0.163671 | + | 0.986515i | \(0.447667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.8569 | 1.11403 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.00000 | 0.255420 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.32456 | − | 6.32456i | 0.201722 | − | 0.201722i | −0.599015 | − | 0.800737i | \(-0.704441\pi\) |
0.800737 | + | 0.599015i | \(0.204441\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.4919i | − | 0.492117i | −0.969255 | − | 0.246059i | \(-0.920864\pi\) | ||
0.969255 | − | 0.246059i | \(-0.0791356\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.3712 | − | 18.3712i | −0.582992 | − | 0.582992i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5959 | − | 19.5959i | 0.620609 | − | 0.620609i | −0.325078 | − | 0.945687i | \(-0.605391\pi\) |
0.945687 | + | 0.325078i | \(0.105391\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.4919 | 0.490143 |
(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 | 1600.2.n.v.1343.2 | 8 | ||
4.3 | odd | 2 | inner | 1600.2.n.v.1343.3 | 8 | ||
5.2 | odd | 4 | inner | 1600.2.n.v.1407.4 | 8 | ||
5.3 | odd | 4 | inner | 1600.2.n.v.1407.2 | 8 | ||
5.4 | even | 2 | inner | 1600.2.n.v.1343.4 | 8 | ||
8.3 | odd | 2 | 100.2.e.d.43.3 | yes | 8 | ||
8.5 | even | 2 | 100.2.e.d.43.1 | yes | 8 | ||
20.3 | even | 4 | inner | 1600.2.n.v.1407.3 | 8 | ||
20.7 | even | 4 | inner | 1600.2.n.v.1407.1 | 8 | ||
20.19 | odd | 2 | inner | 1600.2.n.v.1343.1 | 8 | ||
24.5 | odd | 2 | 900.2.k.j.343.4 | 8 | |||
24.11 | even | 2 | 900.2.k.j.343.2 | 8 | |||
40.3 | even | 4 | 100.2.e.d.7.4 | yes | 8 | ||
40.13 | odd | 4 | 100.2.e.d.7.2 | yes | 8 | ||
40.19 | odd | 2 | 100.2.e.d.43.2 | yes | 8 | ||
40.27 | even | 4 | 100.2.e.d.7.1 | ✓ | 8 | ||
40.29 | even | 2 | 100.2.e.d.43.4 | yes | 8 | ||
40.37 | odd | 4 | 100.2.e.d.7.3 | yes | 8 | ||
120.29 | odd | 2 | 900.2.k.j.343.1 | 8 | |||
120.53 | even | 4 | 900.2.k.j.307.3 | 8 | |||
120.59 | even | 2 | 900.2.k.j.343.3 | 8 | |||
120.77 | even | 4 | 900.2.k.j.307.2 | 8 | |||
120.83 | odd | 4 | 900.2.k.j.307.1 | 8 | |||
120.107 | odd | 4 | 900.2.k.j.307.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.2.e.d.7.1 | ✓ | 8 | 40.27 | even | 4 | ||
100.2.e.d.7.2 | yes | 8 | 40.13 | odd | 4 | ||
100.2.e.d.7.3 | yes | 8 | 40.37 | odd | 4 | ||
100.2.e.d.7.4 | yes | 8 | 40.3 | even | 4 | ||
100.2.e.d.43.1 | yes | 8 | 8.5 | even | 2 | ||
100.2.e.d.43.2 | yes | 8 | 40.19 | odd | 2 | ||
100.2.e.d.43.3 | yes | 8 | 8.3 | odd | 2 | ||
100.2.e.d.43.4 | yes | 8 | 40.29 | even | 2 | ||
900.2.k.j.307.1 | 8 | 120.83 | odd | 4 | |||
900.2.k.j.307.2 | 8 | 120.77 | even | 4 | |||
900.2.k.j.307.3 | 8 | 120.53 | even | 4 | |||
900.2.k.j.307.4 | 8 | 120.107 | odd | 4 | |||
900.2.k.j.343.1 | 8 | 120.29 | odd | 2 | |||
900.2.k.j.343.2 | 8 | 24.11 | even | 2 | |||
900.2.k.j.343.3 | 8 | 120.59 | even | 2 | |||
900.2.k.j.343.4 | 8 | 24.5 | odd | 2 | |||
1600.2.n.v.1343.1 | 8 | 20.19 | odd | 2 | inner | ||
1600.2.n.v.1343.2 | 8 | 1.1 | even | 1 | trivial | ||
1600.2.n.v.1343.3 | 8 | 4.3 | odd | 2 | inner | ||
1600.2.n.v.1343.4 | 8 | 5.4 | even | 2 | inner | ||
1600.2.n.v.1407.1 | 8 | 20.7 | even | 4 | inner | ||
1600.2.n.v.1407.2 | 8 | 5.3 | odd | 4 | inner | ||
1600.2.n.v.1407.3 | 8 | 20.3 | even | 4 | inner | ||
1600.2.n.v.1407.4 | 8 | 5.2 | odd | 4 | inner |