Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
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, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (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: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1007.9 | ||
Root | \(0.235136 + 1.39453i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1007 |
Dual form | 1600.2.j.d.143.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.96561i | 1.71220i | 0.516813 | + | 0.856099i | \(0.327118\pi\) | ||||
−0.516813 | + | 0.856099i | \(0.672882\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.115101 | − | 0.115101i | −0.0435040 | − | 0.0435040i | 0.685020 | − | 0.728524i | \(-0.259793\pi\) |
−0.728524 | + | 0.685020i | \(0.759793\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.79486 | −1.93162 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.95966 | − | 2.95966i | −0.892372 | − | 0.892372i | 0.102374 | − | 0.994746i | \(-0.467356\pi\) |
−0.994746 | + | 0.102374i | \(0.967356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55822 | −0.432172 | −0.216086 | − | 0.976374i | \(-0.569329\pi\) | ||||
−0.216086 | + | 0.976374i | \(0.569329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.299668 | − | 0.299668i | −0.0726801 | − | 0.0726801i | 0.669832 | − | 0.742512i | \(-0.266366\pi\) |
−0.742512 | + | 0.669832i | \(0.766366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.26261 | − | 2.26261i | −0.519079 | − | 0.519079i | 0.398214 | − | 0.917293i | \(-0.369630\pi\) |
−0.917293 | + | 0.398214i | \(0.869630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.341344 | − | 0.341344i | 0.0744874 | − | 0.0744874i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.14573 | − | 4.14573i | 0.864444 | − | 0.864444i | −0.127406 | − | 0.991851i | \(-0.540665\pi\) |
0.991851 | + | 0.127406i | \(0.0406652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 8.28846i | − | 1.59511i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.289656 | + | 0.289656i | −0.0537878 | + | 0.0537878i | −0.733489 | − | 0.679701i | \(-0.762109\pi\) |
0.679701 | + | 0.733489i | \(0.262109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.18508i | − | 0.751663i | −0.926688 | − | 0.375832i | \(-0.877357\pi\) | ||
0.926688 | − | 0.375832i | \(-0.122643\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.77721 | − | 8.77721i | 1.52792 | − | 1.52792i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.63643 | −0.269027 | −0.134514 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134514 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.62107i | − | 0.739964i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.61648i | − | 1.18949i | −0.803913 | − | 0.594747i | \(-0.797252\pi\) | ||
0.803913 | − | 0.594747i | \(-0.202748\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.72651 | −1.02578 | −0.512892 | − | 0.858453i | \(-0.671426\pi\) | ||||
−0.512892 | + | 0.858453i | \(0.671426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.38366 | + | 4.38366i | −0.639423 | + | 0.639423i | −0.950413 | − | 0.310990i | \(-0.899339\pi\) |
0.310990 | + | 0.950413i | \(0.399339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.97350i | − | 0.996215i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.888698 | − | 0.888698i | 0.124443 | − | 0.124443i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4324i | 1.57036i | 0.619265 | + | 0.785182i | \(0.287431\pi\) | ||||
−0.619265 | + | 0.785182i | \(0.712569\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.71003 | − | 6.71003i | 0.888766 | − | 0.888766i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.63497 | − | 1.63497i | 0.212855 | − | 0.212855i | −0.592624 | − | 0.805479i | \(-0.701908\pi\) |
0.805479 | + | 0.592624i | \(0.201908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23034 | − | 1.23034i | −0.157528 | − | 0.157528i | 0.623942 | − | 0.781471i | \(-0.285530\pi\) |
−0.781471 | + | 0.623942i | \(0.785530\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.666993 | + | 0.666993i | 0.0840332 | + | 0.0840332i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.49337 | 0.304614 | 0.152307 | − | 0.988333i | \(-0.451330\pi\) | ||||
0.152307 | + | 0.988333i | \(0.451330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.2946 | + | 12.2946i | 1.48010 | + | 1.48010i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00096 | −0.949540 | −0.474770 | − | 0.880110i | \(-0.657469\pi\) | ||||
−0.474770 | + | 0.880110i | \(0.657469\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.12102 | − | 1.12102i | −0.131205 | − | 0.131205i | 0.638454 | − | 0.769660i | \(-0.279574\pi\) |
−0.769660 | + | 0.638454i | \(0.779574\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.681319i | 0.0776435i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.62218 | 0.407527 | 0.203763 | − | 0.979020i | \(-0.434683\pi\) | ||||
0.203763 | + | 0.979020i | \(0.434683\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.19579 | 0.799532 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.62629i | − | 0.178509i | −0.996009 | − | 0.0892545i | \(-0.971552\pi\) | ||
0.996009 | − | 0.0892545i | \(-0.0284484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.859007 | − | 0.859007i | −0.0920953 | − | 0.0920953i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7149 | 1.66577 | 0.832887 | − | 0.553443i | \(-0.186686\pi\) | ||||
0.832887 | + | 0.553443i | \(0.186686\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.179352 | + | 0.179352i | 0.0188012 | + | 0.0188012i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.4113 | 1.28700 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.69217 | − | 9.69217i | −0.984091 | − | 0.984091i | 0.0157848 | − | 0.999875i | \(-0.494975\pi\) |
−0.999875 | + | 0.0157848i | \(0.994975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.1508 | + | 17.1508i | 1.72372 | + | 1.72372i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.8067 | + | 12.8067i | −1.27432 | + | 1.27432i | −0.330516 | + | 0.943800i | \(0.607223\pi\) |
−0.943800 | + | 0.330516i | \(0.892777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.33738 | + | 4.33738i | −0.427375 | + | 0.427375i | −0.887733 | − | 0.460358i | \(-0.847721\pi\) |
0.460358 | + | 0.887733i | \(0.347721\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.9807i | − | 1.15822i | −0.815251 | − | 0.579108i | \(-0.803401\pi\) | ||
0.815251 | − | 0.579108i | \(-0.196599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.01503 | + | 4.01503i | −0.384570 | + | 0.384570i | −0.872746 | − | 0.488175i | \(-0.837663\pi\) |
0.488175 | + | 0.872746i | \(0.337663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.85301i | − | 0.460628i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.47754 | + | 6.47754i | −0.609356 | + | 0.609356i | −0.942778 | − | 0.333422i | \(-0.891797\pi\) |
0.333422 | + | 0.942778i | \(0.391797\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.02966 | 0.834792 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0689840i | 0.00632375i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.51921i | 0.592655i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.5875 | 2.03665 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2756 | − | 12.2756i | 1.08928 | − | 1.08928i | 0.0936781 | − | 0.995603i | \(-0.470138\pi\) |
0.995603 | − | 0.0936781i | \(-0.0298625\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 19.9482i | − | 1.75634i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.99562 | + | 7.99562i | −0.698581 | + | 0.698581i | −0.964104 | − | 0.265524i | \(-0.914455\pi\) |
0.265524 | + | 0.964104i | \(0.414455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.520857i | 0.0451641i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.08551 | + | 3.08551i | −0.263613 | + | 0.263613i | −0.826520 | − | 0.562907i | \(-0.809683\pi\) |
0.562907 | + | 0.826520i | \(0.309683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2206 | − | 12.2206i | 1.03654 | − | 1.03654i | 0.0372284 | − | 0.999307i | \(-0.488147\pi\) |
0.999307 | − | 0.0372284i | \(-0.0118529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.0002 | − | 13.0002i | −1.09482 | − | 1.09482i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.61180 | + | 4.61180i | 0.385658 | + | 0.385658i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.6807 | 1.70572 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.59172 | − | 2.59172i | −0.212322 | − | 0.212322i | 0.592931 | − | 0.805253i | \(-0.297971\pi\) |
−0.805253 | + | 0.592931i | \(0.797971\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9594 | 1.38014 | 0.690068 | − | 0.723745i | \(-0.257581\pi\) | ||||
0.690068 | + | 0.723745i | \(0.257581\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.73653 | + | 1.73653i | 0.140390 | + | 0.140390i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.55235i | − | 0.682552i | −0.939963 | − | 0.341276i | \(-0.889141\pi\) | ||
0.939963 | − | 0.341276i | \(-0.110859\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −33.9041 | −2.68877 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.954354 | −0.0752136 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.57797i | 0.280248i | 0.990134 | + | 0.140124i | \(0.0447501\pi\) | ||||
−0.990134 | + | 0.140124i | \(0.955250\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.482874 | + | 0.482874i | 0.0373659 | + | 0.0373659i | 0.725543 | − | 0.688177i | \(-0.241589\pi\) |
−0.688177 | + | 0.725543i | \(0.741589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5720 | −0.813227 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.1115 | + | 13.1115i | 1.00266 | + | 1.00266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8189 | −0.898576 | −0.449288 | − | 0.893387i | \(-0.648322\pi\) | ||||
−0.449288 | + | 0.893387i | \(0.648322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.84870 | + | 4.84870i | 0.364451 | + | 0.364451i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.71524 | − | 4.71524i | −0.352433 | − | 0.352433i | 0.508581 | − | 0.861014i | \(-0.330170\pi\) |
−0.861014 | + | 0.508581i | \(0.830170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1843 | − | 13.1843i | 0.979983 | − | 0.979983i | −0.0198205 | − | 0.999804i | \(-0.506309\pi\) |
0.999804 | + | 0.0198205i | \(0.00630948\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.64870 | − | 3.64870i | 0.269720 | − | 0.269720i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.77383i | 0.129715i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.954008 | + | 0.954008i | −0.0693939 | + | 0.0693939i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 13.9872i | − | 1.01208i | −0.862510 | − | 0.506040i | \(-0.831109\pi\) | ||
0.862510 | − | 0.506040i | \(-0.168891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.88875 | + | 3.88875i | −0.279919 | + | 0.279919i | −0.833076 | − | 0.553158i | \(-0.813423\pi\) |
0.553158 | + | 0.833076i | \(0.313423\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3277 | 1.59078 | 0.795391 | − | 0.606097i | \(-0.207266\pi\) | ||||
0.795391 | + | 0.606097i | \(0.207266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.83847i | 0.697431i | 0.937229 | + | 0.348715i | \(0.113382\pi\) | ||||
−0.937229 | + | 0.348715i | \(0.886618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.39437i | 0.521559i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0666793 | 0.00467997 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.0239 | + | 24.0239i | −1.66978 | + | 1.66978i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.3931i | 0.926423i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0531 | + | 11.0531i | −0.760925 | + | 0.760925i | −0.976490 | − | 0.215565i | \(-0.930841\pi\) |
0.215565 | + | 0.976490i | \(0.430841\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 23.7278i | − | 1.62580i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.481706 | + | 0.481706i | −0.0327004 | + | 0.0327004i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.32451 | − | 3.32451i | 0.224650 | − | 0.224650i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.466948 | + | 0.466948i | 0.0314103 | + | 0.0314103i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.93975 | − | 5.93975i | −0.397755 | − | 0.397755i | 0.479686 | − | 0.877440i | \(-0.340751\pi\) |
−0.877440 | + | 0.479686i | \(0.840751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.2105 | −1.54054 | −0.770269 | − | 0.637720i | \(-0.779878\pi\) | ||||
−0.770269 | + | 0.637720i | \(0.779878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.59944 | − | 5.59944i | −0.370021 | − | 0.370021i | 0.497464 | − | 0.867485i | \(-0.334265\pi\) |
−0.867485 | + | 0.497464i | \(0.834265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.02053 | −0.132941 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.01998 | + | 3.01998i | 0.197845 | + | 0.197845i | 0.799076 | − | 0.601230i | \(-0.205323\pi\) |
−0.601230 | + | 0.799076i | \(0.705323\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.7420i | 0.697766i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.00138865 | −8.98241e−5 | −4.49120e−5 | − | 1.00000i | \(-0.500014\pi\) | ||||
−4.49120e−5 | 1.00000i | \(0.500014\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8578 | −0.828245 | −0.414123 | − | 0.910221i | \(-0.635912\pi\) | ||||
−0.414123 | + | 0.910221i | \(0.635912\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3.52546i | − | 0.226158i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52565 | + | 3.52565i | 0.224332 | + | 0.224332i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.82296 | 0.305643 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.14111 | + | 9.14111i | 0.576982 | + | 0.576982i | 0.934071 | − | 0.357089i | \(-0.116231\pi\) |
−0.357089 | + | 0.934071i | \(0.616231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.5399 | −1.54281 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.2733 | − | 21.2733i | −1.32699 | − | 1.32699i | −0.907980 | − | 0.419013i | \(-0.862376\pi\) |
−0.419013 | − | 0.907980i | \(-0.637624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.188354 | + | 0.188354i | 0.0117038 | + | 0.0117038i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.67851 | − | 1.67851i | 0.103897 | − | 0.103897i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.7214 | + | 16.7214i | −1.03108 | + | 1.03108i | −0.0315818 | + | 0.999501i | \(0.510054\pi\) |
−0.999501 | + | 0.0315818i | \(0.989946\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 46.6043i | 2.85213i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.9096 | + | 15.9096i | −0.970026 | + | 0.970026i | −0.999564 | − | 0.0295378i | \(-0.990596\pi\) |
0.0295378 | + | 0.999564i | \(0.490596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3601i | 0.750824i | 0.926858 | + | 0.375412i | \(0.122499\pi\) | ||||
−0.926858 | + | 0.375412i | \(0.877501\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.531889 | + | 0.531889i | −0.0321914 | + | 0.0321914i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.0270 | −1.26339 | −0.631695 | − | 0.775217i | \(-0.717641\pi\) | ||||
−0.631695 | + | 0.775217i | \(0.717641\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.2520i | 1.45193i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.6807i | − | 0.637158i | −0.947896 | − | 0.318579i | \(-0.896794\pi\) | ||
0.947896 | − | 0.318579i | \(-0.103206\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5946 | 0.748673 | 0.374336 | − | 0.927293i | \(-0.377871\pi\) | ||||
0.374336 | + | 0.927293i | \(0.377871\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.876663 | + | 0.876663i | −0.0517478 | + | 0.0517478i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.8204i | − | 0.989435i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.7432 | − | 28.7432i | 1.68496 | − | 1.68496i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.43132i | 0.200460i | 0.994964 | + | 0.100230i | \(0.0319579\pi\) | ||||
−0.994964 | + | 0.100230i | \(0.968042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.5310 | + | 24.5310i | −1.42344 | + | 1.42344i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.45996 | + | 6.45996i | −0.373589 | + | 0.373589i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.774227 | + | 0.774227i | 0.0446257 | + | 0.0446257i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −37.9798 | − | 37.9798i | −2.18188 | − | 2.18188i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.8104 | −0.674053 | −0.337027 | − | 0.941495i | \(-0.609421\pi\) | ||||
−0.337027 | + | 0.941495i | \(0.609421\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8630 | − | 12.8630i | −0.731750 | − | 0.731750i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.6262 | −1.28301 | −0.641506 | − | 0.767118i | \(-0.721690\pi\) | ||||
−0.641506 | + | 0.767118i | \(0.721690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.08945 | + | 7.08945i | 0.400719 | + | 0.400719i | 0.878486 | − | 0.477767i | \(-0.158554\pi\) |
−0.477767 | + | 0.878486i | \(0.658554\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.1265i | 1.41124i | 0.708589 | + | 0.705621i | \(0.249332\pi\) | ||||
−0.708589 | + | 0.705621i | \(0.750668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.71457 | 0.0959974 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.5300 | 1.98309 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.35606i | 0.0754535i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.9070 | − | 11.9070i | −0.658460 | − | 0.658460i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.00913 | 0.0556349 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.80829 | − | 5.80829i | −0.319253 | − | 0.319253i | 0.529227 | − | 0.848480i | \(-0.322482\pi\) |
−0.848480 | + | 0.529227i | \(0.822482\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.48287 | 0.519658 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.41679 | + | 7.41679i | 0.404019 | + | 0.404019i | 0.879647 | − | 0.475628i | \(-0.157779\pi\) |
−0.475628 | + | 0.879647i | \(0.657779\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.2099 | − | 19.2099i | −1.04334 | − | 1.04334i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.3864 | + | 12.3864i | −0.670763 | + | 0.670763i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.60836 | + | 1.60836i | −0.0868434 | + | 0.0868434i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.2493i | − | 0.979673i | −0.871814 | − | 0.489837i | \(-0.837056\pi\) | ||
0.871814 | − | 0.489837i | \(-0.162944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4413 | − | 19.4413i | 1.04067 | − | 1.04067i | 0.0415330 | − | 0.999137i | \(-0.486776\pi\) |
0.999137 | − | 0.0415330i | \(-0.0132242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.9152i | 0.689364i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.13598 | − | 1.13598i | 0.0604622 | − | 0.0604622i | −0.676229 | − | 0.736691i | \(-0.736387\pi\) |
0.736691 | + | 0.676229i | \(0.236387\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.204580 | −0.0108275 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 28.4140i | − | 1.49963i | −0.661645 | − | 0.749817i | \(-0.730141\pi\) | ||
0.661645 | − | 0.749817i | \(-0.269859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 8.76116i | − | 0.461114i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.3334 | −1.01474 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29692 | − | 2.29692i | 0.119898 | − | 0.119898i | −0.644612 | − | 0.764510i | \(-0.722981\pi\) |
0.764510 | + | 0.644612i | \(0.222981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 44.1364i | 2.29765i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.31588 | − | 1.31588i | 0.0683172 | − | 0.0683172i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.0787i | − | 0.936081i | −0.883707 | − | 0.468040i | \(-0.844960\pi\) | ||
0.883707 | − | 0.468040i | \(-0.155040\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.451348 | − | 0.451348i | 0.0232456 | − | 0.0232456i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.79031 | + | 2.79031i | −0.143328 | + | 0.143328i | −0.775130 | − | 0.631802i | \(-0.782316\pi\) |
0.631802 | + | 0.775130i | \(0.282316\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.4046 | + | 36.4046i | 1.86506 | + | 1.86506i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.12206 | + | 8.12206i | 0.415018 | + | 0.415018i | 0.883482 | − | 0.468464i | \(-0.155193\pi\) |
−0.468464 | + | 0.883482i | \(0.655193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 38.9792 | 1.98142 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4341 | + | 14.4341i | 0.731839 | + | 0.731839i | 0.970984 | − | 0.239145i | \(-0.0768670\pi\) |
−0.239145 | + | 0.970984i | \(0.576867\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.48468 | −0.125656 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.7119 | − | 23.7119i | −1.19611 | − | 1.19611i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.1624i | 1.76475i | 0.470549 | + | 0.882374i | \(0.344056\pi\) | ||||
−0.470549 | + | 0.882374i | \(0.655944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.54466 | −0.0773298 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.5164 | −1.17435 | −0.587176 | − | 0.809459i | \(-0.699760\pi\) | ||||
−0.587176 | + | 0.809459i | \(0.699760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.52128i | 0.324848i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.84328 | + | 4.84328i | 0.240072 | + | 0.240072i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.2595 | −1.15011 | −0.575054 | − | 0.818115i | \(-0.695019\pi\) | ||||
−0.575054 | + | 0.818115i | \(0.695019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.15043 | − | 9.15043i | −0.451357 | − | 0.451357i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.376374 | −0.0185201 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.2415 | + | 36.2415i | 1.77475 | + | 1.77475i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.63975 | + | 6.63975i | 0.324373 | + | 0.324373i | 0.850442 | − | 0.526069i | \(-0.176335\pi\) |
−0.526069 | + | 0.850442i | \(0.676335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.28216 | − | 7.28216i | 0.354911 | − | 0.354911i | −0.507022 | − | 0.861933i | \(-0.669254\pi\) |
0.861933 | + | 0.507022i | \(0.169254\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.4027 | − | 25.4027i | 1.23512 | − | 1.23512i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.283225i | 0.0137062i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.6768 | + | 13.6768i | −0.660323 | + | 0.660323i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 11.7250i | − | 0.564771i | −0.959301 | − | 0.282386i | \(-0.908874\pi\) | ||
0.959301 | − | 0.282386i | \(-0.0911258\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.8827 | − | 20.8827i | 1.00356 | − | 1.00356i | 0.00356603 | − | 0.999994i | \(-0.498865\pi\) |
0.999994 | − | 0.00356603i | \(-0.00113511\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.7604 | −0.897430 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.53661i | 0.359703i | 0.983694 | + | 0.179851i | \(0.0575617\pi\) | ||||
−0.983694 | + | 0.179851i | \(0.942438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 40.4105i | 1.92431i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.7280 | −1.22237 | −0.611187 | − | 0.791486i | \(-0.709308\pi\) | ||||
−0.611187 | + | 0.791486i | \(0.709308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.68604 | − | 7.68604i | 0.363537 | − | 0.363537i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.33824i | 0.110348i | 0.998477 | + | 0.0551741i | \(0.0175714\pi\) | ||||
−0.998477 | + | 0.0551741i | \(0.982429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5422 | + | 22.5422i | −1.06147 | + | 1.06147i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 50.2950i | 2.36306i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4561 | − | 10.4561i | 0.489115 | − | 0.489115i | −0.418912 | − | 0.908027i | \(-0.637588\pi\) |
0.908027 | + | 0.418912i | \(0.137588\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.48378 | + | 2.48378i | −0.115933 | + | 0.115933i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.6903 | + | 15.6903i | 0.730769 | + | 0.730769i | 0.970772 | − | 0.240003i | \(-0.0771484\pi\) |
−0.240003 | + | 0.970772i | \(0.577148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.6332 | + | 19.6332i | 0.912434 | + | 0.912434i | 0.996463 | − | 0.0840297i | \(-0.0267791\pi\) |
−0.0840297 | + | 0.996463i | \(0.526779\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.4862 | −1.13309 | −0.566543 | − | 0.824032i | \(-0.691719\pi\) | ||||
−0.566543 | + | 0.824032i | \(0.691719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.286989 | − | 0.286989i | −0.0132519 | − | 0.0132519i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.3630 | 1.16866 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.9082 | + | 19.9082i | 0.915380 | + | 0.915380i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 66.2493i | − | 3.03335i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.0609 | 1.69335 | 0.846677 | − | 0.532108i | \(-0.178600\pi\) | ||||
0.846677 | + | 0.532108i | \(0.178600\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.54991 | 0.116266 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2.83024i | − | 0.128781i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.1912 | + | 20.1912i | 0.914950 | + | 0.914950i | 0.996656 | − | 0.0817061i | \(-0.0260369\pi\) |
−0.0817061 | + | 0.996656i | \(0.526037\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.6109 | −0.479840 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.45822 | + | 7.45822i | 0.336585 | + | 0.336585i | 0.855080 | − | 0.518496i | \(-0.173508\pi\) |
−0.518496 | + | 0.855080i | \(0.673508\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.173601 | 0.00781860 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.920917 | + | 0.920917i | 0.0413088 | + | 0.0413088i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.17420 | + | 8.17420i | 0.365927 | + | 0.365927i | 0.865990 | − | 0.500062i | \(-0.166689\pi\) |
−0.500062 | + | 0.865990i | \(0.666689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.43202 | + | 1.43202i | −0.0639778 | + | 0.0639778i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.2327 | + | 29.2327i | −1.30342 | + | 1.30342i | −0.377348 | + | 0.926072i | \(0.623164\pi\) |
−0.926072 | + | 0.377348i | \(0.876836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 31.3523i | − | 1.39241i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.0340 | − | 20.0340i | 0.887992 | − | 0.887992i | −0.106338 | − | 0.994330i | \(-0.533912\pi\) |
0.994330 | + | 0.106338i | \(0.0339125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.258061i | 0.0114159i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.7536 | + | 18.7536i | −0.827991 | + | 0.827991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.9483 | 1.14121 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 35.0504i | − | 1.53854i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.89264i | 0.258161i | 0.991634 | + | 0.129081i | \(0.0412026\pi\) | ||||
−0.991634 | + | 0.129081i | \(0.958797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.6537 | −1.07803 | −0.539015 | − | 0.842296i | \(-0.681203\pi\) | ||||
−0.539015 | + | 0.842296i | \(0.681203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.25413 | + | 1.25413i | −0.0546309 | + | 0.0546309i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 11.3742i | − | 0.494528i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.47444 | + | 9.47444i | −0.411156 | + | 0.411156i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.8681i | 0.514066i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.9836 | − | 13.9836i | 0.603435 | − | 0.603435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.6392 | + | 20.6392i | −0.888994 | + | 0.888994i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.1762 | − | 27.1762i | −1.16840 | − | 1.16840i | −0.982585 | − | 0.185812i | \(-0.940508\pi\) |
−0.185812 | − | 0.982585i | \(-0.559492\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 39.0996 | + | 39.0996i | 1.67792 | + | 1.67792i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.69225 | 0.157869 | 0.0789347 | − | 0.996880i | \(-0.474848\pi\) | ||||
0.0789347 | + | 0.996880i | \(0.474848\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.12962 | + | 7.12962i | 0.304285 | + | 0.304285i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.31076 | 0.0558402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.416915 | − | 0.416915i | −0.0177290 | − | 0.0177290i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 12.2117i | − | 0.517426i | −0.965954 | − | 0.258713i | \(-0.916702\pi\) | ||
0.965954 | − | 0.258713i | \(-0.0832984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4814 | 0.443315 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.26049 | −0.222098 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.2211i | 0.515057i | 0.966271 | + | 0.257528i | \(0.0829081\pi\) | ||||
−0.966271 | + | 0.257528i | \(0.917092\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.828241 | − | 0.828241i | −0.0347829 | − | 0.0347829i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.9592 | 1.29788 | 0.648938 | − | 0.760841i | \(-0.275213\pi\) | ||||
0.648938 | + | 0.760841i | \(0.275213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.1508 | − | 30.1508i | −1.26177 | − | 1.26177i | −0.950233 | − | 0.311539i | \(-0.899156\pi\) |
−0.311539 | − | 0.950233i | \(-0.600844\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 41.4806 | 1.73288 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.98215 | − | 1.98215i | −0.0825181 | − | 0.0825181i | 0.664643 | − | 0.747161i | \(-0.268584\pi\) |
−0.747161 | + | 0.664643i | \(0.768584\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.5325 | − | 11.5325i | −0.479276 | − | 0.479276i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.187188 | + | 0.187188i | −0.00776586 | + | 0.00776586i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.8361 | − | 33.8361i | 1.40135 | − | 1.40135i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.9680i | 1.11309i | 0.830818 | + | 0.556544i | \(0.187873\pi\) | ||||
−0.830818 | + | 0.556544i | \(0.812127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.46923 | + | 9.46923i | −0.390173 | + | 0.390173i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 66.2153i | 2.72373i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.6701 | + | 16.6701i | −0.684560 | + | 0.684560i | −0.961024 | − | 0.276464i | \(-0.910837\pi\) |
0.276464 | + | 0.961024i | \(0.410837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.1771 | −1.19414 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.8376i | 1.17827i | 0.808033 | + | 0.589137i | \(0.200532\pi\) | ||||
−0.808033 | + | 0.589137i | \(0.799468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.91377i | 0.0780642i | 0.999238 | + | 0.0390321i | \(0.0124275\pi\) | ||||
−0.999238 | + | 0.0390321i | \(0.987573\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.4487 | −0.588397 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.89049 | − | 7.89049i | 0.320265 | − | 0.320265i | −0.528604 | − | 0.848869i | \(-0.677284\pi\) |
0.848869 | + | 0.528604i | \(0.177284\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.197745i | 0.00801303i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.83071 | − | 6.83071i | 0.276341 | − | 0.276341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 40.1035i | − | 1.61976i | −0.586592 | − | 0.809882i | \(-0.699531\pi\) | ||
0.586592 | − | 0.809882i | \(-0.300469\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.5821 | − | 14.5821i | 0.587052 | − | 0.587052i | −0.349780 | − | 0.936832i | \(-0.613744\pi\) |
0.936832 | + | 0.349780i | \(0.113744\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.01752 | + | 4.01752i | −0.161478 | + | 0.161478i | −0.783221 | − | 0.621743i | \(-0.786425\pi\) |
0.621743 | + | 0.783221i | \(0.286425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −34.3617 | − | 34.3617i | −1.37889 | − | 1.37889i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.80880 | − | 1.80880i | −0.0724679 | − | 0.0724679i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −39.7189 | −1.58622 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.490385 | + | 0.490385i | 0.0195529 | + | 0.0195529i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9309 | 1.07210 | 0.536052 | − | 0.844185i | \(-0.319915\pi\) | ||||
0.536052 | + | 0.844185i | \(0.319915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.7791 | − | 32.7791i | −1.30285 | − | 1.30285i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.8662i | 0.430536i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 46.3644 | 1.83415 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.6880 | 0.738131 | 0.369065 | − | 0.929403i | \(-0.379678\pi\) | ||||
0.369065 | + | 0.929403i | \(0.379678\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.6249i | − | 1.16829i | −0.811648 | − | 0.584146i | \(-0.801429\pi\) | ||
0.811648 | − | 0.584146i | \(-0.198571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.04426 | − | 5.04426i | −0.198310 | − | 0.198310i | 0.600965 | − | 0.799275i | \(-0.294783\pi\) |
−0.799275 | + | 0.600965i | \(0.794783\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.67794 | −0.379893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.42855 | − | 1.42855i | −0.0559895 | − | 0.0559895i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.04934 | −0.119330 | −0.0596649 | − | 0.998218i | \(-0.519003\pi\) | ||||
−0.0596649 | + | 0.998218i | \(0.519003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.49615 | + | 6.49615i | 0.253439 | + | 0.253439i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0441 | + | 22.0441i | 0.858718 | + | 0.858718i | 0.991187 | − | 0.132469i | \(-0.0422906\pi\) |
−0.132469 | + | 0.991187i | \(0.542291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.09788 | − | 8.09788i | 0.314971 | − | 0.314971i | −0.531861 | − | 0.846832i | \(-0.678507\pi\) |
0.846832 | + | 0.531861i | \(0.178507\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.38479 | + | 1.38479i | −0.0537807 | + | 0.0537807i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.40167i | 0.0929931i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.6150 | − | 17.6150i | 0.681035 | − | 0.681035i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.28276i | 0.281148i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.1768 | − | 27.1768i | 1.04759 | − | 1.04759i | 0.0487786 | − | 0.998810i | \(-0.484467\pi\) |
0.998810 | − | 0.0487786i | \(-0.0155329\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.6501 | −1.10111 | −0.550557 | − | 0.834798i | \(-0.685585\pi\) | ||||
−0.550557 | + | 0.834798i | \(0.685585\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.23115i | 0.0856238i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 68.8334i | − | 2.63770i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.8472 | 1.18034 | 0.590168 | − | 0.807281i | \(-0.299062\pi\) | ||||
0.590168 | + | 0.807281i | \(0.299062\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.6058 | − | 16.6058i | 0.633549 | − | 0.633549i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 17.8142i | − | 0.678668i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.253186 | + | 0.253186i | −0.00963164 | + | 0.00963164i | −0.711906 | − | 0.702275i | \(-0.752168\pi\) |
0.702275 | + | 0.711906i | \(0.252168\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 3.94815i | − | 0.149978i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.28241 | + | 2.28241i | −0.0864525 | + | 0.0864525i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.95608 | + | 8.95608i | −0.338750 | + | 0.338750i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.5238 | + | 10.5238i | 0.397479 | + | 0.397479i | 0.877343 | − | 0.479864i | \(-0.159314\pi\) |
−0.479864 | + | 0.877343i | \(0.659314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.70261 | + | 3.70261i | 0.139646 | + | 0.139646i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.94813 | 0.110876 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.58968 | − | 1.58968i | −0.0597015 | − | 0.0597015i | 0.676626 | − | 0.736327i | \(-0.263442\pi\) |
−0.736327 | + | 0.676626i | \(0.763442\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.9900 | −0.787186 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.3502 | − | 17.3502i | −0.649771 | − | 0.649771i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.00411819i | − | 0.000153797i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.8919 | −0.853722 | −0.426861 | − | 0.904317i | \(-0.640381\pi\) | ||||
−0.426861 | + | 0.904317i | \(0.640381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.998472 | 0.0371850 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 38.1313i | − | 1.41812i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1893 | + | 20.1893i | 0.748780 | + | 0.748780i | 0.974250 | − | 0.225470i | \(-0.0723919\pi\) |
−0.225470 | + | 0.974250i | \(0.572392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.0425 | 1.18676 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.01572 | + | 2.01572i | 0.0745540 | + | 0.0745540i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3253 | 0.529118 | 0.264559 | − | 0.964370i | \(-0.414774\pi\) | ||||
0.264559 | + | 0.964370i | \(0.414774\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.37954 | − | 7.37954i | −0.271829 | − | 0.271829i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.3401 | − | 32.3401i | −1.18965 | − | 1.18965i | −0.977164 | − | 0.212487i | \(-0.931844\pi\) |
−0.212487 | − | 0.977164i | \(-0.568156\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.4557 | + | 10.4557i | −0.384100 | + | 0.384100i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.06842 | + | 6.06842i | −0.222629 | + | 0.222629i | −0.809605 | − | 0.586976i | \(-0.800318\pi\) |
0.586976 | + | 0.809605i | \(0.300318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.42414i | 0.344811i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.37898 | + | 1.37898i | −0.0503870 | + | 0.0503870i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 49.6431i | − | 1.81150i | −0.423810 | − | 0.905751i | \(-0.639308\pi\) | ||
0.423810 | − | 0.905751i | \(-0.360692\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.1090 | + | 27.1090i | −0.987907 | + | 0.987907i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.18443 | 0.333814 | 0.166907 | − | 0.985973i | \(-0.446622\pi\) | ||||
0.166907 | + | 0.985973i | \(0.446622\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 72.7759i | − | 2.64160i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.75310i | − | 0.172300i | −0.996282 | − | 0.0861499i | \(-0.972544\pi\) | ||
0.996282 | − | 0.0861499i | \(-0.0274564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.924267 | 0.0334607 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.54765 | + | 2.54765i | −0.0919902 | + | 0.0919902i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4153i | 0.700135i | 0.936724 | + | 0.350067i | \(0.113841\pi\) | ||||
−0.936724 | + | 0.350067i | \(0.886159\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 63.0884 | − | 63.0884i | 2.27207 | − | 2.27207i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0890i | 0.938356i | 0.883104 | + | 0.469178i | \(0.155450\pi\) | ||||
−0.883104 | + | 0.469178i | \(0.844550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.558586 | + | 0.558586i | −0.0200392 | + | 0.0200392i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.2331 | + | 17.2331i | −0.617442 | + | 0.617442i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.6802 | + | 23.6802i | 0.847343 | + | 0.847343i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.40080 | + | 2.40080i | 0.0857977 | + | 0.0857977i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.2339 | −0.507384 | −0.253692 | − | 0.967285i | \(-0.581645\pi\) | ||||
−0.253692 | + | 0.967285i | \(0.581645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −49.5891 | − | 49.5891i | −1.76542 | − | 1.76542i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.49114 | 0.0530189 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.91713 | + | 1.91713i | 0.0680794 | + | 0.0680794i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 19.8283i | − | 0.702353i | −0.936309 | − | 0.351176i | \(-0.885782\pi\) | ||
0.936309 | − | 0.351176i | \(-0.114218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.62729 | 0.0929467 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −91.0655 | −3.21764 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.63568i | 0.234168i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.1817 | − | 47.1817i | −1.66088 | − | 1.66088i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.3864 | −0.751907 | −0.375954 | − | 0.926639i | \(-0.622685\pi\) | ||||
−0.375954 | + | 0.926639i | \(0.622685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.90624 | + | 9.90624i | 0.347855 | + | 0.347855i | 0.859310 | − | 0.511455i | \(-0.170893\pi\) |
−0.511455 | + | 0.859310i | \(0.670893\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36.6553 | −1.28556 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.2195 | + | 15.2195i | 0.532463 | + | 0.532463i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.03932 | − | 1.03932i | −0.0363168 | − | 0.0363168i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.6209 | − | 22.6209i | 0.789474 | − | 0.789474i | −0.191934 | − | 0.981408i | \(-0.561476\pi\) |
0.981408 | + | 0.191934i | \(0.0614759\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.89892 | − | 4.89892i | 0.170766 | − | 0.170766i | −0.616550 | − | 0.787316i | \(-0.711470\pi\) |
0.787316 | + | 0.616550i | \(0.211470\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.05434i | 0.0366630i | 0.999832 | + | 0.0183315i | \(0.00583542\pi\) | ||||
−0.999832 | + | 0.0183315i | \(0.994165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.7754 | + | 11.7754i | −0.408978 | + | 0.408978i | −0.881382 | − | 0.472404i | \(-0.843386\pi\) |
0.472404 | + | 0.881382i | \(0.343386\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 62.3580i | − | 2.16317i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.08973 | + | 2.08973i | −0.0724050 | + | 0.0724050i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.6879 | −1.19899 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.1678i | 1.42127i | 0.703560 | + | 0.710636i | \(0.251593\pi\) | ||||
−0.703560 | + | 0.710636i | \(0.748407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8322i | 0.994214i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.6749 | 1.09094 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.750366 | − | 0.750366i | 0.0257829 | − | 0.0257829i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.3508i | 1.28188i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.78419 | + | 6.78419i | −0.232559 | + | 0.232559i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7179i | 0.401212i | 0.979672 | + | 0.200606i | \(0.0642911\pi\) | ||||
−0.979672 | + | 0.200606i | \(0.935709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.2154 | + | 12.2154i | −0.417270 | + | 0.417270i | −0.884262 | − | 0.466992i | \(-0.845338\pi\) |
0.466992 | + | 0.884262i | \(0.345338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.2170 | − | 17.2170i | 0.587436 | − | 0.587436i | −0.349500 | − | 0.936936i | \(-0.613649\pi\) |
0.936936 | + | 0.349500i | \(0.113649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.59984 | − | 2.59984i | −0.0886024 | − | 0.0886024i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.1929 | + | 11.1929i | 0.381011 | + | 0.381011i | 0.871466 | − | 0.490455i | \(-0.163169\pi\) |
−0.490455 | + | 0.871466i | \(0.663169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 49.8828 | 1.69411 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.7204 | − | 10.7204i | −0.363665 | − | 0.363665i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.88522 | −0.131646 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 56.1647 | + | 56.1647i | 1.90089 | + | 1.90089i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 43.1739i | − | 1.45788i | −0.684578 | − | 0.728940i | \(-0.740013\pi\) | ||
0.684578 | − | 0.728940i | \(-0.259987\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.1760 | −0.343227 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.4204 | −1.12596 | −0.562981 | − | 0.826470i | \(-0.690346\pi\) | ||||
−0.562981 | + | 0.826470i | \(0.690346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.00362i | − | 0.0674270i | −0.999432 | − | 0.0337135i | \(-0.989267\pi\) | ||
0.999432 | − | 0.0337135i | \(-0.0107334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.1765 | − | 16.1765i | −0.543154 | − | 0.543154i | 0.381298 | − | 0.924452i | \(-0.375477\pi\) |
−0.924452 | + | 0.381298i | \(0.875477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.82586 | −0.0947762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.2971 | − | 21.2971i | −0.713480 | − | 0.713480i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.8371 | 0.663822 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.1577 | − | 19.1577i | −0.639658 | − | 0.639658i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.21223 | + | 1.21223i | 0.0404303 | + | 0.0404303i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.42593 | − | 3.42593i | 0.114134 | − | 0.114134i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.29606 | + | 2.29606i | −0.0764080 | + | 0.0764080i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 29.7116i | − | 0.986559i | −0.869871 | − | 0.493279i | \(-0.835798\pi\) | ||
0.869871 | − | 0.493279i | \(-0.164202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 74.2131 | − | 74.2131i | 2.46149 | − | 2.46149i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.6931i | 1.48075i | 0.672195 | + | 0.740374i | \(0.265352\pi\) | ||||
−0.672195 | + | 0.740374i | \(0.734648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.81328 | + | 4.81328i | −0.159296 | + | 0.159296i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.84061 | 0.0607821 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.1278i | 1.32369i | 0.749639 | + | 0.661847i | \(0.230227\pi\) | ||||
−0.749639 | + | 0.661847i | \(0.769773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 35.0250i | − | 1.15411i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.4673 | 0.410365 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.1345 | − | 25.1345i | 0.825525 | − | 0.825525i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.7519i | 0.910512i | 0.890361 | + | 0.455256i | \(0.150452\pi\) | ||||
−0.890361 | + | 0.455256i | \(0.849548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7783 | + | 15.7783i | −0.517114 | + | 0.517114i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 67.1004i | − | 2.19677i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.2805 | + | 17.2805i | −0.564531 | + | 0.564531i | −0.930591 | − | 0.366060i | \(-0.880706\pi\) |
0.366060 | + | 0.930591i | \(0.380706\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.0245 | + | 21.0245i | −0.686110 | + | 0.686110i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.81532 | − | 4.81532i | −0.156975 | − | 0.156975i | 0.624250 | − | 0.781225i | \(-0.285405\pi\) |
−0.781225 | + | 0.624250i | \(0.785405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.5759 | − | 31.5759i | −1.02825 | − | 1.02825i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.37347 | 0.109623 | 0.0548115 | − | 0.998497i | \(-0.482544\pi\) | ||||
0.0548115 | + | 0.998497i | \(0.482544\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.74680 | + | 1.74680i | 0.0567034 | + | 0.0567034i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −74.5153 | −2.41632 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.3663 | + | 14.3663i | 0.465369 | + | 0.465369i | 0.900410 | − | 0.435041i | \(-0.143266\pi\) |
−0.435041 | + | 0.900410i | \(0.643266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.08475i | 0.164366i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.710289 | 0.0229364 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.4851 | 0.435003 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 69.4263i | 2.23723i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.8576 | − | 11.8576i | −0.381315 | − | 0.381315i | 0.490260 | − | 0.871576i | \(-0.336902\pi\) |
−0.871576 | + | 0.490260i | \(0.836902\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.02156 | −0.129191 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.6082 | + | 14.6082i | 0.468799 | + | 0.468799i | 0.901525 | − | 0.432726i | \(-0.142448\pi\) |
−0.432726 | + | 0.901525i | \(0.642448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.81319 | −0.0901869 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.9249 | − | 12.9249i | −0.413504 | − | 0.413504i | 0.469454 | − | 0.882957i | \(-0.344451\pi\) |
−0.882957 | + | 0.469454i | \(0.844451\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.5108 | − | 46.5108i | −1.48649 | − | 1.48649i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.2665 | − | 23.2665i | 0.742843 | − | 0.742843i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.133323 | + | 0.133323i | −0.00425235 | + | 0.00425235i | −0.709230 | − | 0.704977i | \(-0.750957\pi\) |
0.704977 | + | 0.709230i | \(0.250957\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.99268i | 0.0952580i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.8863 | + | 27.8863i | −0.886733 | + | 0.886733i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.9032i | 1.52170i | 0.648930 | + | 0.760848i | \(0.275217\pi\) | ||||
−0.648930 | + | 0.760848i | \(0.724783\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2251 | − | 17.2251i | 0.546624 | − | 0.546624i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.9379 | 1.73990 | 0.869951 | − | 0.493138i | \(-0.164150\pi\) | ||||
0.869951 | + | 0.493138i | \(0.164150\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.5635i | 0.429129i |
(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.j.d.1007.9 | 18 | ||
4.3 | odd | 2 | 400.2.j.d.307.9 | 18 | |||
5.2 | odd | 4 | 320.2.s.b.303.9 | 18 | |||
5.3 | odd | 4 | 1600.2.s.d.943.1 | 18 | |||
5.4 | even | 2 | 320.2.j.b.47.1 | 18 | |||
16.5 | even | 4 | 400.2.s.d.107.5 | 18 | |||
16.11 | odd | 4 | 1600.2.s.d.207.1 | 18 | |||
20.3 | even | 4 | 400.2.s.d.243.5 | 18 | |||
20.7 | even | 4 | 80.2.s.b.3.5 | yes | 18 | ||
20.19 | odd | 2 | 80.2.j.b.67.1 | yes | 18 | ||
40.19 | odd | 2 | 640.2.j.d.607.1 | 18 | |||
40.27 | even | 4 | 640.2.s.d.223.9 | 18 | |||
40.29 | even | 2 | 640.2.j.c.607.9 | 18 | |||
40.37 | odd | 4 | 640.2.s.c.223.1 | 18 | |||
60.47 | odd | 4 | 720.2.z.g.163.5 | 18 | |||
60.59 | even | 2 | 720.2.bd.g.307.9 | 18 | |||
80.19 | odd | 4 | 640.2.s.c.287.1 | 18 | |||
80.27 | even | 4 | 320.2.j.b.143.9 | 18 | |||
80.29 | even | 4 | 640.2.s.d.287.9 | 18 | |||
80.37 | odd | 4 | 80.2.j.b.43.1 | ✓ | 18 | ||
80.43 | even | 4 | inner | 1600.2.j.d.143.1 | 18 | ||
80.53 | odd | 4 | 400.2.j.d.43.9 | 18 | |||
80.59 | odd | 4 | 320.2.s.b.207.9 | 18 | |||
80.67 | even | 4 | 640.2.j.c.543.1 | 18 | |||
80.69 | even | 4 | 80.2.s.b.27.5 | yes | 18 | ||
80.77 | odd | 4 | 640.2.j.d.543.9 | 18 | |||
240.149 | odd | 4 | 720.2.z.g.667.5 | 18 | |||
240.197 | even | 4 | 720.2.bd.g.523.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.1 | ✓ | 18 | 80.37 | odd | 4 | ||
80.2.j.b.67.1 | yes | 18 | 20.19 | odd | 2 | ||
80.2.s.b.3.5 | yes | 18 | 20.7 | even | 4 | ||
80.2.s.b.27.5 | yes | 18 | 80.69 | even | 4 | ||
320.2.j.b.47.1 | 18 | 5.4 | even | 2 | |||
320.2.j.b.143.9 | 18 | 80.27 | even | 4 | |||
320.2.s.b.207.9 | 18 | 80.59 | odd | 4 | |||
320.2.s.b.303.9 | 18 | 5.2 | odd | 4 | |||
400.2.j.d.43.9 | 18 | 80.53 | odd | 4 | |||
400.2.j.d.307.9 | 18 | 4.3 | odd | 2 | |||
400.2.s.d.107.5 | 18 | 16.5 | even | 4 | |||
400.2.s.d.243.5 | 18 | 20.3 | even | 4 | |||
640.2.j.c.543.1 | 18 | 80.67 | even | 4 | |||
640.2.j.c.607.9 | 18 | 40.29 | even | 2 | |||
640.2.j.d.543.9 | 18 | 80.77 | odd | 4 | |||
640.2.j.d.607.1 | 18 | 40.19 | odd | 2 | |||
640.2.s.c.223.1 | 18 | 40.37 | odd | 4 | |||
640.2.s.c.287.1 | 18 | 80.19 | odd | 4 | |||
640.2.s.d.223.9 | 18 | 40.27 | even | 4 | |||
640.2.s.d.287.9 | 18 | 80.29 | even | 4 | |||
720.2.z.g.163.5 | 18 | 60.47 | odd | 4 | |||
720.2.z.g.667.5 | 18 | 240.149 | odd | 4 | |||
720.2.bd.g.307.9 | 18 | 60.59 | even | 2 | |||
720.2.bd.g.523.9 | 18 | 240.197 | even | 4 | |||
1600.2.j.d.143.1 | 18 | 80.43 | even | 4 | inner | ||
1600.2.j.d.1007.9 | 18 | 1.1 | even | 1 | trivial | ||
1600.2.s.d.207.1 | 18 | 16.11 | odd | 4 | |||
1600.2.s.d.943.1 | 18 | 5.3 | odd | 4 |