Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(137,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{14} + 146x^{12} - 798x^{10} + 3934x^{8} - 19950x^{6} + 91250x^{4} - 281250x^{2} + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 137.4 | ||
Root | \(2.23266 + 0.123447i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.137 |
Dual form | 460.2.i.b.413.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.237125 | − | 0.237125i | 0.136904 | − | 0.136904i | −0.635334 | − | 0.772238i | \(-0.719137\pi\) |
0.772238 | + | 0.635334i | \(0.219137\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23266 | − | 0.123447i | 0.998475 | − | 0.0552073i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.69421 | + | 1.69421i | −0.640350 | + | 0.640350i | −0.950641 | − | 0.310292i | \(-0.899573\pi\) |
0.310292 | + | 0.950641i | \(0.399573\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.88754i | 0.962514i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.55617i | 1.67525i | 0.546248 | + | 0.837624i | \(0.316056\pi\) | ||||
−0.546248 | + | 0.837624i | \(0.683944\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65542 | − | 2.65542i | 0.736480 | − | 0.736480i | −0.235415 | − | 0.971895i | \(-0.575645\pi\) |
0.971895 | + | 0.235415i | \(0.0756450\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.500147 | − | 0.558692i | 0.129137 | − | 0.144254i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.435244 | + | 0.435244i | −0.105562 | + | 0.105562i | −0.757915 | − | 0.652353i | \(-0.773782\pi\) |
0.652353 | + | 0.757915i | \(0.273782\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.92086 | −0.440676 | −0.220338 | − | 0.975424i | \(-0.570716\pi\) | ||||
−0.220338 | + | 0.975424i | \(0.570716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.803478i | 0.175333i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.76463 | − | 0.546205i | 0.993493 | − | 0.113892i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.96952 | − | 0.551231i | 0.993904 | − | 0.110246i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.39608 | + | 1.39608i | 0.268677 | + | 0.268677i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.41329i | − | 1.37661i | −0.725420 | − | 0.688307i | \(-0.758354\pi\) | ||
0.725420 | − | 0.688307i | \(-0.241646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.525750 | −0.0944275 | −0.0472137 | − | 0.998885i | \(-0.515034\pi\) | ||||
−0.0472137 | + | 0.998885i | \(0.515034\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.31751 | + | 1.31751i | 0.229348 | + | 0.229348i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.57344 | + | 3.99173i | −0.604021 | + | 0.674725i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.94110 | − | 1.94110i | 0.319115 | − | 0.319115i | −0.529312 | − | 0.848427i | \(-0.677550\pi\) |
0.848427 | + | 0.529312i | \(0.177550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.25933i | − | 0.201654i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.78508 | −1.05965 | −0.529826 | − | 0.848106i | \(-0.677743\pi\) | ||||
−0.529826 | + | 0.848106i | \(0.677743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.88256 | − | 1.88256i | −0.287087 | − | 0.287087i | 0.548840 | − | 0.835927i | \(-0.315070\pi\) |
−0.835927 | + | 0.548840i | \(0.815070\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.356459 | + | 6.44690i | 0.0531378 | + | 0.961047i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.54296 | + | 7.54296i | 1.10025 | + | 1.10025i | 0.994380 | + | 0.105874i | \(0.0337640\pi\) |
0.105874 | + | 0.994380i | \(0.466236\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.25933i | 0.179904i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.206415i | 0.0289038i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.467258 | + | 0.467258i | 0.0641828 | + | 0.0641828i | 0.738470 | − | 0.674287i | \(-0.235549\pi\) |
−0.674287 | + | 0.738470i | \(0.735549\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.685894 | + | 12.4050i | 0.0924859 | + | 1.67269i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.455484 | + | 0.455484i | −0.0603304 | + | 0.0603304i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.72412i | − | 1.00560i | −0.864404 | − | 0.502798i | \(-0.832304\pi\) | ||
0.864404 | − | 0.502798i | \(-0.167696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.714153i | − | 0.0914379i | −0.998954 | − | 0.0457189i | \(-0.985442\pi\) | ||
0.998954 | − | 0.0457189i | \(-0.0145579\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.89209 | − | 4.89209i | −0.616346 | − | 0.616346i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.60083 | − | 6.25644i | 0.694697 | − | 0.776016i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.97934 | − | 4.97934i | 0.608324 | − | 0.608324i | −0.334184 | − | 0.942508i | \(-0.608461\pi\) |
0.942508 | + | 0.334184i | \(0.108461\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00029 | − | 1.25933i | 0.120421 | − | 0.151606i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.93904 | −0.586157 | −0.293078 | − | 0.956088i | \(-0.594680\pi\) | ||||
−0.293078 | + | 0.956088i | \(0.594680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.547956 | − | 0.547956i | 0.0641334 | − | 0.0641334i | −0.674313 | − | 0.738446i | \(-0.735560\pi\) |
0.738446 | + | 0.674313i | \(0.235560\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.04769 | − | 1.30911i | 0.120977 | − | 0.151163i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.41329 | − | 9.41329i | −1.07274 | − | 1.07274i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.07438 | −1.02095 | −0.510474 | − | 0.859893i | \(-0.670530\pi\) | ||||
−0.510474 | + | 0.859893i | \(0.670530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.00054 | −0.888949 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.7036 | − | 10.7036i | −1.17488 | − | 1.17488i | −0.981033 | − | 0.193842i | \(-0.937905\pi\) |
−0.193842 | − | 0.981033i | \(-0.562095\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.918022 | + | 1.02548i | −0.0995735 | + | 0.111229i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.75788 | − | 1.75788i | −0.188464 | − | 0.188464i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0332 | 1.38152 | 0.690758 | − | 0.723086i | \(-0.257277\pi\) | ||||
0.690758 | + | 0.723086i | \(0.257277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.99764i | 0.943209i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.124668 | + | 0.124668i | −0.0129275 | + | 0.0129275i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.28862 | + | 0.237125i | −0.440004 | + | 0.0243285i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.99177 | − | 3.99177i | 0.405302 | − | 0.405302i | −0.474794 | − | 0.880097i | \(-0.657478\pi\) |
0.880097 | + | 0.474794i | \(0.157478\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.0437 | −1.61245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.20492 | 0.219398 | 0.109699 | − | 0.993965i | \(-0.465011\pi\) | ||||
0.109699 | + | 0.993965i | \(0.465011\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.08268 | − | 2.08268i | −0.205212 | − | 0.205212i | 0.597016 | − | 0.802229i | \(-0.296353\pi\) |
−0.802229 | + | 0.597016i | \(0.796353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0991871 | + | 1.79389i | 0.00967967 | + | 0.175066i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.68603 | − | 2.68603i | 0.259669 | − | 0.259669i | −0.565251 | − | 0.824919i | \(-0.691221\pi\) |
0.824919 | + | 0.565251i | \(0.191221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.99735 | −0.766007 | −0.383004 | − | 0.923747i | \(-0.625110\pi\) | ||||
−0.383004 | + | 0.923747i | \(0.625110\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.920567i | − | 0.0873764i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9629 | − | 12.9629i | −1.21944 | − | 1.21944i | −0.967827 | − | 0.251618i | \(-0.919037\pi\) |
−0.251618 | − | 0.967827i | \(-0.580963\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.5704 | − | 1.80767i | 0.985690 | − | 0.168566i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.66763 | + | 7.66763i | 0.708872 | + | 0.708872i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.47479i | − | 0.135194i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.8710 | −1.80645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.60891 | + | 1.60891i | −0.145071 | + | 0.145071i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0272 | − | 1.84418i | 0.986302 | − | 0.164949i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.75288 | − | 3.75288i | −0.333014 | − | 0.333014i | 0.520716 | − | 0.853730i | \(-0.325665\pi\) |
−0.853730 | + | 0.520716i | \(0.825665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.892802 | −0.0786069 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.77562 | 0.504619 | 0.252309 | − | 0.967647i | \(-0.418810\pi\) | ||||
0.252309 | + | 0.967647i | \(0.418810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.25433 | − | 3.25433i | 0.282187 | − | 0.282187i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.28932 | + | 2.94464i | 0.283100 | + | 0.253434i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7484 | − | 10.7484i | 0.918294 | − | 0.918294i | −0.0786117 | − | 0.996905i | \(-0.525049\pi\) |
0.996905 | + | 0.0786117i | \(0.0250487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9390i | 0.927838i | 0.885878 | + | 0.463919i | \(0.153557\pi\) | ||||
−0.885878 | + | 0.463919i | \(0.846443\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.57725 | 0.301259 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.7539 | + | 14.7539i | 1.23379 | + | 1.23379i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.915151 | − | 16.5513i | −0.0759992 | − | 1.37451i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.298619 | + | 0.298619i | 0.0246297 | + | 0.0246297i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.5132 | 1.10704 | 0.553521 | − | 0.832835i | \(-0.313284\pi\) | ||||
0.553521 | + | 0.832835i | \(0.313284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2333 | −1.48381 | −0.741904 | − | 0.670507i | \(-0.766077\pi\) | ||||
−0.741904 | + | 0.670507i | \(0.766077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.25679 | − | 1.25679i | −0.101605 | − | 0.101605i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.17382 | + | 0.0649024i | −0.0942834 | + | 0.00521309i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6686 | + | 13.6686i | −1.09087 | + | 1.09087i | −0.0954344 | + | 0.995436i | \(0.530424\pi\) |
−0.995436 | + | 0.0954344i | \(0.969576\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.221597 | 0.0175738 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.14687 | + | 8.99764i | −0.563253 | + | 0.709114i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0122 | + | 10.0122i | −0.784217 | + | 0.784217i | −0.980539 | − | 0.196322i | \(-0.937100\pi\) |
0.196322 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.10418 | + | 2.77890i | 0.241660 | + | 0.216337i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.66763 | + | 7.66763i | 0.593339 | + | 0.593339i | 0.938532 | − | 0.345193i | \(-0.112187\pi\) |
−0.345193 | + | 0.938532i | \(0.612187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.10246i | − | 0.0848048i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.54657i | − | 0.424157i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.2449 | − | 16.2449i | 1.23508 | − | 1.23508i | 0.273085 | − | 0.961990i | \(-0.411956\pi\) |
0.961990 | − | 0.273085i | \(-0.0880441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.48549 | + | 9.35329i | −0.565850 | + | 0.707042i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.83158 | − | 1.83158i | −0.137670 | − | 0.137670i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.7851i | − | 1.10509i | −0.833483 | − | 0.552544i | \(-0.813657\pi\) | ||
0.833483 | − | 0.552544i | \(-0.186343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.2349i | 1.80136i | 0.434480 | + | 0.900681i | \(0.356932\pi\) | ||||
−0.434480 | + | 0.900681i | \(0.643068\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.169344 | − | 0.169344i | −0.0125182 | − | 0.0125182i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.09419 | − | 4.57344i | 0.301011 | − | 0.336246i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.41829 | − | 2.41829i | −0.176843 | − | 0.176843i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.73051 | −0.344094 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.3062i | − | 1.32459i | −0.749243 | − | 0.662295i | \(-0.769582\pi\) | ||
0.749243 | − | 0.662295i | \(-0.230418\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6339 | − | 15.6339i | 1.12535 | − | 1.12535i | 0.134427 | − | 0.990923i | \(-0.457080\pi\) |
0.990923 | − | 0.134427i | \(-0.0429195\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.155461 | − | 2.81166i | −0.0111328 | − | 0.201347i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.2621 | + | 14.2621i | 1.01613 | + | 1.01613i | 0.999868 | + | 0.0162638i | \(0.00517716\pi\) |
0.0162638 | + | 0.999868i | \(0.494823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.5102 | −1.45393 | −0.726966 | − | 0.686674i | \(-0.759070\pi\) | ||||
−0.726966 | + | 0.686674i | \(0.759070\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.36146i | − | 0.166564i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.5596 | + | 12.5596i | 0.881514 | + | 0.881514i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.1488 | + | 0.837600i | −1.05804 | + | 0.0585005i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.57719 | + | 13.7581i | 0.109622 | + | 0.956252i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.6726i | − | 0.738241i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1978 | 1.04626 | 0.523131 | − | 0.852252i | \(-0.324764\pi\) | ||||
0.523131 | + | 0.852252i | \(0.324764\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.17117 | + | 1.17117i | −0.0802473 | + | 0.0802473i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.43550 | − | 3.97071i | −0.302499 | − | 0.270800i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.890729 | − | 0.890729i | 0.0604666 | − | 0.0604666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 0.259868i | − | 0.0175603i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.31151i | 0.155489i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3103 | − | 11.3103i | 0.757393 | − | 0.757393i | −0.218454 | − | 0.975847i | \(-0.570101\pi\) |
0.975847 | + | 0.218454i | \(0.0701013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.59170 | + | 14.3497i | 0.106114 | + | 0.956647i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.68026 | − | 1.68026i | 0.111523 | − | 0.111523i | −0.649143 | − | 0.760666i | \(-0.724873\pi\) |
0.760666 | + | 0.649143i | \(0.224873\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.8881 | 1.24816 | 0.624080 | − | 0.781360i | \(-0.285474\pi\) | ||||
0.624080 | + | 0.781360i | \(0.285474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.46426 | −0.293726 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.07371 | + | 5.07371i | −0.332390 | + | 0.332390i | −0.853493 | − | 0.521104i | \(-0.825520\pi\) |
0.521104 | + | 0.853493i | \(0.325520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.7720 | + | 15.9097i | 1.15932 | + | 1.03783i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.15176 | + | 2.15176i | −0.139772 | + | 0.139772i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.9325i | − | 1.22464i | −0.790610 | − | 0.612321i | \(-0.790236\pi\) | ||
0.790610 | − | 0.612321i | \(-0.209764\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.89044i | 0.637100i | 0.947906 | + | 0.318550i | \(0.103196\pi\) | ||||
−0.947906 | + | 0.318550i | \(0.896804\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.08538 | + | 6.08538i | −0.390377 | + | 0.390377i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.155461 | + | 2.81166i | 0.00993204 | + | 0.179630i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.10068 | + | 5.10068i | −0.324549 | + | 0.324549i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.07619 | −0.321691 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.62272i | 0.228664i | 0.993443 | + | 0.114332i | \(0.0364728\pi\) | ||||
−0.993443 | + | 0.114332i | \(0.963527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.03481 | + | 26.4731i | 0.190797 | + | 1.66435i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0254813 | + | 0.460853i | 0.00159570 | + | 0.0288598i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.86034 | − | 5.86034i | −0.365558 | − | 0.365558i | 0.500296 | − | 0.865854i | \(-0.333224\pi\) |
−0.865854 | + | 0.500296i | \(0.833224\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.57725i | 0.408690i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.4062 | 1.32501 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9661 | + | 15.9661i | 0.984513 | + | 0.984513i | 0.999882 | − | 0.0153685i | \(-0.00489214\pi\) |
−0.0153685 | + | 0.999882i | \(0.504892\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.10091 | + | 0.985546i | 0.0676283 | + | 0.0605416i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.09050 | − | 3.09050i | 0.189135 | − | 0.189135i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.5442i | 1.67940i | 0.543053 | + | 0.839699i | \(0.317268\pi\) | ||||
−0.543053 | + | 0.839699i | \(0.682732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.2233 | 1.41072 | 0.705359 | − | 0.708851i | \(-0.250786\pi\) | ||||
0.705359 | + | 0.708851i | \(0.250786\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.13357 | + | 2.13357i | 0.129129 | + | 0.129129i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.06273 | + | 27.6115i | 0.184690 | + | 1.66504i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.22558 | − | 9.22558i | −0.554311 | − | 0.554311i | 0.373371 | − | 0.927682i | \(-0.378202\pi\) |
−0.927682 | + | 0.373371i | \(0.878202\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.51813i | − | 0.0908878i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.47913i | 0.267203i | 0.991035 | + | 0.133601i | \(0.0426542\pi\) | ||||
−0.991035 | + | 0.133601i | \(0.957346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0277 | − | 13.0277i | −0.774417 | − | 0.774417i | 0.204458 | − | 0.978875i | \(-0.434457\pi\) |
−0.978875 | + | 0.204458i | \(0.934457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.960712 | + | 1.07317i | −0.0569077 | + | 0.0635690i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4953 | − | 11.4953i | 0.678548 | − | 0.678548i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6211i | 0.977713i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.89310i | − | 0.110975i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5250 | − | 17.5250i | −1.02382 | − | 1.02382i | −0.999709 | − | 0.0241147i | \(-0.992323\pi\) |
−0.0241147 | − | 0.999709i | \(-0.507677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.953522 | − | 17.2453i | −0.0555162 | − | 1.00406i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.75688 | + | 7.75688i | −0.450100 | + | 0.450100i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.2017 | − | 14.1025i | 0.647809 | − | 0.815566i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.37888 | 0.367672 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.522843 | − | 0.522843i | 0.0300365 | − | 0.0300365i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0881602 | − | 1.59446i | −0.00504804 | − | 0.0912984i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4598 | + | 10.4598i | 0.596972 | + | 0.596972i | 0.939506 | − | 0.342534i | \(-0.111285\pi\) |
−0.342534 | + | 0.939506i | \(0.611285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.987711 | −0.0561889 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5158 | 0.596294 | 0.298147 | − | 0.954520i | \(-0.403631\pi\) | ||||
0.298147 | + | 0.954520i | \(0.403631\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2497 | − | 21.2497i | −1.20110 | − | 1.20110i | −0.973832 | − | 0.227271i | \(-0.927020\pi\) |
−0.227271 | − | 0.973832i | \(-0.572980\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.5263 | − | 10.3185i | −0.649433 | − | 0.581379i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.9785 | − | 12.9785i | −0.728943 | − | 0.728943i | 0.241466 | − | 0.970409i | \(-0.422372\pi\) |
−0.970409 | + | 0.241466i | \(0.922372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 41.1895 | 2.30617 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.27385i | − | 0.0710995i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.836044 | − | 0.836044i | 0.0465187 | − | 0.0465187i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7324 | − | 14.6599i | 0.650796 | − | 0.813184i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.89637 | + | 1.89637i | −0.104870 | + | 0.104870i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.5587 | −1.40909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.06804 | −0.223600 | −0.111800 | − | 0.993731i | \(-0.535662\pi\) | ||||
−0.111800 | + | 0.993731i | \(0.535662\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.60501 | + | 5.60501i | 0.307153 | + | 0.307153i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.5025 | − | 11.7319i | 0.573812 | − | 0.640980i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.26903 | + | 9.26903i | −0.504916 | + | 0.504916i | −0.912962 | − | 0.408046i | \(-0.866210\pi\) |
0.408046 | + | 0.912962i | \(0.366210\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.14765 | −0.333894 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.92115i | − | 0.158189i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.9930 | − | 13.9930i | −0.755551 | − | 0.755551i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.07785 | − | 2.93514i | 0.111868 | − | 0.158023i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.6211 | − | 16.6211i | −0.892269 | − | 0.892269i | 0.102468 | − | 0.994736i | \(-0.467326\pi\) |
−0.994736 | + | 0.102468i | \(0.967326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1918i | 1.02731i | 0.857995 | + | 0.513657i | \(0.171710\pi\) | ||||
−0.857995 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.41437 | 0.395750 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.1662 | + | 23.1662i | −1.23301 | + | 1.23301i | −0.270209 | + | 0.962802i | \(0.587093\pi\) |
−0.962802 | + | 0.270209i | \(0.912907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.0272 | + | 0.609712i | −0.585263 | + | 0.0323601i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.349709 | − | 0.349709i | −0.0185086 | − | 0.0185086i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3170 | −1.17785 | −0.588923 | − | 0.808189i | \(-0.700448\pi\) | ||||
−0.588923 | + | 0.808189i | \(0.700448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3103 | −0.805805 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.71191 | + | 4.71191i | −0.247311 | + | 0.247311i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.15575 | − | 1.29104i | 0.0604950 | − | 0.0675762i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2742 | − | 11.2742i | 0.588506 | − | 0.588506i | −0.348721 | − | 0.937227i | \(-0.613384\pi\) |
0.937227 | + | 0.348721i | \(0.113384\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 19.5922i | − | 1.01993i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.58326 | −0.0821989 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.0730 | + | 24.0730i | 1.24645 | + | 1.24645i | 0.957275 | + | 0.289180i | \(0.0933826\pi\) |
0.289180 | + | 0.957275i | \(0.406617\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.17752 | − | 3.05213i | 0.112447 | − | 0.157611i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.6854 | − | 19.6854i | −1.01385 | − | 1.01385i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.7558 | 1.37435 | 0.687176 | − | 0.726491i | \(-0.258850\pi\) | ||||
0.687176 | + | 0.726491i | \(0.258850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.77980 | −0.0911821 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.73641 | + | 3.73641i | 0.190921 | + | 0.190921i | 0.796094 | − | 0.605173i | \(-0.206896\pi\) |
−0.605173 | + | 0.796094i | \(0.706896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.1787 | − | 19.8546i | −1.13033 | − | 1.01188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.43596 | − | 5.43596i | 0.276325 | − | 0.276325i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.31180 | 0.167915 | 0.0839575 | − | 0.996469i | \(-0.473244\pi\) | ||||
0.0839575 | + | 0.996469i | \(0.473244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.83604 | + | 2.31151i | −0.0928527 | + | 0.116898i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.36955 | − | 1.36955i | 0.0690844 | − | 0.0690844i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.2600 | + | 1.12021i | −1.01939 | + | 0.0563638i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.65488 | + | 8.65488i | 0.434376 | + | 0.434376i | 0.890114 | − | 0.455738i | \(-0.150625\pi\) |
−0.455738 | + | 0.890114i | \(0.650625\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1.54337i | − | 0.0772651i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.7142i | − | 1.13430i | −0.823616 | − | 0.567148i | \(-0.808047\pi\) | ||
0.823616 | − | 0.567148i | \(-0.191953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.39608 | + | 1.39608i | −0.0695439 | + | 0.0695439i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.8625 | + | 0.987645i | −0.887593 | + | 0.0490765i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7851 | + | 10.7851i | 0.534597 | + | 0.534597i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.1114i | 1.48891i | 0.667671 | + | 0.744457i | \(0.267291\pi\) | ||||
−0.667671 | + | 0.744457i | \(0.732709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.09741i | − | 0.251437i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.0863 | + | 13.0863i | 0.643933 | + | 0.643933i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.2189 | − | 22.5762i | −1.23795 | − | 1.10822i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.59392 | + | 2.59392i | 0.127025 | + | 0.127025i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.68672 | 0.424374 | 0.212187 | − | 0.977229i | \(-0.431941\pi\) | ||||
0.212187 | + | 0.977229i | \(0.431941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.8878i | − | 0.871798i | −0.899996 | − | 0.435899i | \(-0.856431\pi\) | ||
0.899996 | − | 0.435899i | \(-0.143569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.7806 | + | 21.7806i | −1.05901 | + | 1.05901i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.92304 | + | 2.40288i | −0.0932809 | + | 0.116557i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.20992 | + | 1.20992i | 0.0585522 | + | 0.0585522i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.99706 | 0.337821 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.4013i | − | 1.56071i | −0.625335 | − | 0.780357i | \(-0.715037\pi\) | ||
0.625335 | − | 0.780357i | \(-0.284963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.5838 | − | 11.5838i | −0.556684 | − | 0.556684i | 0.371678 | − | 0.928362i | \(-0.378783\pi\) |
−0.928362 | + | 0.371678i | \(0.878783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.14174 | − | 3.70773i | −0.198581 | − | 0.177772i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.15218 | + | 1.04918i | −0.437808 | + | 0.0501893i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 9.72122i | − | 0.463968i | −0.972720 | − | 0.231984i | \(-0.925478\pi\) | ||
0.972720 | − | 0.231984i | \(-0.0745218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.63637 | −0.173161 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.9657 | − | 13.9657i | 0.663531 | − | 0.663531i | −0.292680 | − | 0.956211i | \(-0.594547\pi\) |
0.956211 | + | 0.292680i | \(0.0945470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.0987 | − | 1.60891i | 1.37941 | − | 0.0762698i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.20431 | − | 3.20431i | 0.151559 | − | 0.151559i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.4406i | 1.67255i | 0.548313 | + | 0.836273i | \(0.315270\pi\) | ||||
−0.548313 | + | 0.836273i | \(0.684730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 37.6990i | − | 1.77518i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.32358 | + | 4.32358i | −0.203139 | + | 0.203139i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.11073 | + | 20.0887i | 0.0520720 | + | 0.941771i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.87672 | + | 3.87672i | −0.181345 | + | 0.181345i | −0.791942 | − | 0.610597i | \(-0.790930\pi\) |
0.610597 | + | 0.791942i | \(0.290930\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.21528 | −0.0567242 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.32738 | −0.108397 | −0.0541983 | − | 0.998530i | \(-0.517260\pi\) | ||||
−0.0541983 | + | 0.998530i | \(0.517260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.77509 | + | 4.77509i | −0.221917 | + | 0.221917i | −0.809305 | − | 0.587388i | \(-0.800156\pi\) |
0.587388 | + | 0.809305i | \(0.300156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.262952 | + | 0.293732i | −0.0121941 | + | 0.0136215i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.6067 | + | 13.6067i | −0.629644 | + | 0.629644i | −0.947978 | − | 0.318335i | \(-0.896876\pi\) |
0.318335 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.8721i | 0.779080i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.48232i | 0.298689i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.4598 | − | 10.4598i | 0.480942 | − | 0.480942i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.54576 | + | 1.05884i | −0.437989 | + | 0.0485828i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.34923 | + | 1.34923i | −0.0617769 | + | 0.0617769i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.31151 | 0.105616 | 0.0528078 | − | 0.998605i | \(-0.483183\pi\) | ||||
0.0528078 | + | 0.998605i | \(0.483183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 10.3089i | − | 0.470043i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.438863 | + | 3.82827i | 0.0199690 | + | 0.174192i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.41948 | − | 9.40502i | 0.382309 | − | 0.427060i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.0687 | − | 22.0687i | −1.00003 | − | 1.00003i | −1.00000 | 2.86468e-5i | \(-0.999991\pi\) | |
−2.86468e−5 | − | 1.00000i | \(-0.500009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.74829i | 0.214725i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.01945 | 0.0911366 | 0.0455683 | − | 0.998961i | \(-0.485490\pi\) | ||||
0.0455683 | + | 0.998961i | \(0.485490\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.22659 | + | 3.22659i | 0.145318 | + | 0.145318i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −35.8200 | + | 1.98055i | −1.60999 | + | 0.0890190i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.36776 | − | 8.36776i | 0.375345 | − | 0.375345i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 11.8266i | − | 0.529431i | −0.964327 | − | 0.264715i | \(-0.914722\pi\) | ||
0.964327 | − | 0.264715i | \(-0.0852780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.63637 | 0.162461 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6409 | + | 17.6409i | 0.786569 | + | 0.786569i | 0.980930 | − | 0.194361i | \(-0.0622634\pi\) |
−0.194361 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.92284 | − | 0.272192i | 0.219064 | − | 0.0121124i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.261421 | − | 0.261421i | −0.0116101 | − | 0.0116101i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.36888i | 0.149323i | 0.997209 | + | 0.0746615i | \(0.0237876\pi\) | ||||
−0.997209 | + | 0.0746615i | \(0.976212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.85670i | 0.0821356i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.68168 | − | 2.68168i | −0.118399 | − | 0.118399i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.90701 | − | 4.39281i | −0.216229 | − | 0.193570i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.9099 | + | 41.9099i | −1.84320 | + | 1.84320i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.70414i | − | 0.338174i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 38.1023i | − | 1.66929i | −0.550787 | − | 0.834646i | \(-0.685673\pi\) | ||
0.550787 | − | 0.834646i | \(-0.314327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2246 | − | 10.2246i | −0.447090 | − | 0.447090i | 0.447296 | − | 0.894386i | \(-0.352387\pi\) |
−0.894386 | + | 0.447296i | \(0.852387\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.442902 | + | 3.99290i | 0.0193298 | + | 0.174264i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.228830 | − | 0.228830i | 0.00996797 | − | 0.00996797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4033 | − | 5.20492i | 0.974057 | − | 0.226301i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.3037 | 0.967900 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0172 | + | 18.0172i | −0.780412 | + | 0.780412i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.66541 | − | 6.32858i | 0.244937 | − | 0.273608i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50591 | − | 3.50591i | −0.151291 | − | 0.151291i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.99706 | −0.301385 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6046 | 0.627900 | 0.313950 | − | 0.949440i | \(-0.398348\pi\) | ||||
0.313950 | + | 0.949440i | \(0.398348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.74669 | + | 5.74669i | 0.246614 | + | 0.246614i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.8553 | + | 0.987251i | −0.764839 | + | 0.0422892i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.136753 | − | 0.136753i | −0.00584714 | − | 0.00584714i | 0.704177 | − | 0.710024i | \(-0.251316\pi\) |
−0.710024 | + | 0.704177i | \(0.751316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.06215 | 0.0880103 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.2399i | 0.606640i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.3739 | − | 15.3739i | 0.653764 | − | 0.653764i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.113642 | − | 2.05531i | −0.00482382 | − | 0.0872431i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2348 | − | 27.2348i | 1.15398 | − | 1.15398i | 0.168227 | − | 0.985748i | \(-0.446196\pi\) |
0.985748 | − | 0.168227i | \(-0.0538042\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.99794 | −0.422868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14687 | −0.0484211 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.7093 | + | 11.7093i | 0.493487 | + | 0.493487i | 0.909403 | − | 0.415916i | \(-0.136539\pi\) |
−0.415916 | + | 0.909403i | \(0.636539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.5419 | − | 27.3414i | −1.28491 | − | 1.15026i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.5546 | − | 13.5546i | 0.569238 | − | 0.569238i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.0392 | −1.17546 | −0.587732 | − | 0.809055i | \(-0.699979\pi\) | ||||
−0.587732 | + | 0.809055i | \(0.699979\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.76557i | − | 0.241281i | −0.992696 | − | 0.120641i | \(-0.961505\pi\) | ||
0.992696 | − | 0.120641i | \(-0.0384949\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.34086 | − | 4.34086i | −0.181342 | − | 0.181342i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.3768 | − | 5.34079i | 0.974881 | − | 0.222726i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.9662 | − | 12.9662i | −0.539792 | − | 0.539792i | 0.383676 | − | 0.923468i | \(-0.374658\pi\) |
−0.923468 | + | 0.383676i | \(0.874658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 7.41437i | − | 0.308131i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.2683 | 1.50466 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.59616 | + | 2.59616i | −0.107522 | + | 0.107522i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.0657 | + | 16.1726i | 0.746926 | + | 0.668656i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.6919 | + | 22.6919i | 0.936596 | + | 0.936596i | 0.998106 | − | 0.0615105i | \(-0.0195918\pi\) |
−0.0615105 | + | 0.998106i | \(0.519592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.00989 | 0.0416119 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.76380 | 0.278225 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.5163 | + | 12.5163i | −0.513983 | + | 0.513983i | −0.915744 | − | 0.401762i | \(-0.868398\pi\) |
0.401762 | + | 0.915744i | \(0.368398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.182058 | − | 3.29270i | −0.00746367 | − | 0.134987i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.86349 | + | 4.86349i | −0.199049 | + | 0.199049i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.5607i | 0.840088i | 0.907504 | + | 0.420044i | \(0.137985\pi\) | ||||
−0.907504 | + | 0.420044i | \(0.862015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.89045 | −0.199486 | −0.0997428 | − | 0.995013i | \(-0.531802\pi\) | ||||
−0.0997428 | + | 0.995013i | \(0.531802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3781 | + | 14.3781i | 0.585520 | + | 0.585520i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −44.3651 | + | 2.45302i | −1.80370 | + | 0.0997295i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.79663 | − | 1.79663i | −0.0729229 | − | 0.0729229i | 0.669705 | − | 0.742628i | \(-0.266421\pi\) |
−0.742628 | + | 0.669705i | \(0.766421\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.95641 | 0.241366 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.0594 | 1.62063 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.4325 | − | 14.4325i | −0.582922 | − | 0.582922i | 0.352783 | − | 0.935705i | \(-0.385235\pi\) |
−0.935705 | + | 0.352783i | \(0.885235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.39354 | + | 3.79077i | −0.136841 | + | 0.152859i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3571 | + | 11.3571i | −0.457218 | + | 0.457218i | −0.897741 | − | 0.440523i | \(-0.854793\pi\) |
0.440523 | + | 0.897741i | \(0.354793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4230 | −0.418934 | −0.209467 | − | 0.977816i | \(-0.567173\pi\) | ||||
−0.209467 | + | 0.977816i | \(0.567173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.41437 | + | 5.88927i | 0.297528 | + | 0.236328i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.0809 | + | 22.0809i | −0.884653 | + | 0.884653i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3923 | − | 5.47871i | 0.975692 | − | 0.219148i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.53075 | − | 2.53075i | −0.101068 | − | 0.101068i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.68971i | 0.0673730i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.8170i | 1.62490i | 0.583031 | + | 0.812450i | \(0.301867\pi\) | ||||
−0.583031 | + | 0.812450i | \(0.698133\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.60379 | − | 3.60379i | 0.143238 | − | 0.143238i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.84218 | − | 7.91562i | −0.350891 | − | 0.314122i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.34405 | + | 3.34405i | 0.132496 | + | 0.132496i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 14.2617i | − | 0.564184i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.1898i | 1.66640i | 0.552974 | + | 0.833198i | \(0.313493\pi\) | ||||
−0.552974 | + | 0.833198i | \(0.686507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.0360 | + | 21.0360i | 0.829580 | + | 0.829580i | 0.987459 | − | 0.157879i | \(-0.0504655\pi\) |
−0.157879 | + | 0.987459i | \(0.550465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.99332 | + | 0.110214i | −0.0784870 | + | 0.00433967i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.2306 | + | 22.2306i | 0.873974 | + | 0.873974i | 0.992903 | − | 0.118929i | \(-0.0379460\pi\) |
−0.118929 | + | 0.992903i | \(0.537946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.9165 | 1.68462 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 0.422428i | − | 0.0165563i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7442 | + | 11.7442i | −0.459588 | + | 0.459588i | −0.898520 | − | 0.438932i | \(-0.855357\pi\) |
0.438932 | + | 0.898520i | \(0.355357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.8950 | − | 0.712985i | 0.503849 | − | 0.0278586i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.58225 | + | 1.58225i | 0.0617293 | + | 0.0617293i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.4036 | −0.911675 | −0.455838 | − | 0.890063i | \(-0.650660\pi\) | ||||
−0.455838 | + | 0.890063i | \(0.650660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3907i | 0.870899i | 0.900213 | + | 0.435449i | \(0.143411\pi\) | ||||
−0.900213 | + | 0.435449i | \(0.856589\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.548117 | + | 0.548117i | 0.0212871 | + | 0.0212871i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.86408 | − | 7.66755i | 0.266177 | − | 0.297335i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.04918 | − | 35.3216i | −0.156785 | − | 1.36766i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 5.36391i | − | 0.207381i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.96795 | 0.153181 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5824 | + | 11.5824i | −0.446468 | + | 0.446468i | −0.894178 | − | 0.447711i | \(-0.852239\pi\) |
0.447711 | + | 0.894178i | \(0.352239\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.70744 | + | 6.16831i | 0.296659 | + | 0.237418i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.64702 | + | 6.64702i | −0.255466 | + | 0.255466i | −0.823207 | − | 0.567741i | \(-0.807817\pi\) |
0.567741 | + | 0.823207i | \(0.307817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.5257i | 0.519071i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 0.796862i | − | 0.0305358i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1341 | − | 12.1341i | 0.464299 | − | 0.464299i | −0.435762 | − | 0.900062i | \(-0.643521\pi\) |
0.900062 | + | 0.435762i | \(0.143521\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.6705 | − | 25.3242i | 0.866197 | − | 0.967590i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.47884 | − | 4.47884i | 0.170878 | − | 0.170878i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.48153 | 0.0945387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.2848 | −0.847755 | −0.423877 | − | 0.905720i | \(-0.639331\pi\) | ||||
−0.423877 | + | 0.905720i | \(0.639331\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27.1813 | − | 27.1813i | 1.03253 | − | 1.03253i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.35040 | + | 24.4231i | 0.0512234 | + | 0.926422i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.95317 | − | 2.95317i | 0.111859 | − | 0.111859i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.40621i | 0.0910111i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.20372i | − | 0.0454640i | −0.999742 | − | 0.0227320i | \(-0.992764\pi\) | ||
0.999742 | − | 0.0227320i | \(-0.00723645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.72858 | + | 3.72858i | −0.140626 | + | 0.140626i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.98677 | − | 0.441602i | 0.300799 | − | 0.0166317i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.73560 | + | 3.73560i | −0.140492 | + | 0.140492i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.5049 | 1.37097 | 0.685486 | − | 0.728086i | \(-0.259590\pi\) | ||||
0.685486 | + | 0.728086i | \(0.259590\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 26.2027i | − | 0.982677i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.50500 | + | 0.287167i | −0.0938130 | + | 0.0107545i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.7618 | + | 31.1192i | 1.30002 | + | 1.16379i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.48937 | − | 4.48937i | −0.167659 | − | 0.167659i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5502i | 0.430749i | 0.976532 | + | 0.215374i | \(0.0690972\pi\) | ||||
−0.976532 | + | 0.215374i | \(0.930903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.05698 | 0.262816 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.34527 | + | 2.34527i | 0.0872216 | + | 0.0872216i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.08644 | − | 36.8405i | −0.151767 | − | 1.36822i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.9819 | + | 27.9819i | −1.03779 | + | 1.03779i | −0.0385340 | + | 0.999257i | \(0.512269\pi\) |
−0.999257 | + | 0.0385340i | \(0.987731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 21.1156i | − | 0.782060i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.63874 | 0.0606111 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.8100 | + | 32.8100i | 1.21186 | + | 1.21186i | 0.970413 | + | 0.241451i | \(0.0776232\pi\) |
0.241451 | + | 0.970413i | \(0.422377\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.703578 | + | 0.629850i | 0.0259519 | + | 0.0232324i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.6661 | + | 27.6661i | 1.01909 | + | 1.01909i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.30428i | 0.158336i | 0.996861 | + | 0.0791678i | \(0.0252263\pi\) | ||||
−0.996861 | + | 0.0791678i | \(0.974774\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.41900i | 0.0888642i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.8349 | − | 33.8349i | −1.24128 | − | 1.24128i | −0.959469 | − | 0.281813i | \(-0.909064\pi\) |
−0.281813 | − | 0.959469i | \(-0.590936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.1703 | − | 1.66816i | 1.10535 | − | 0.0611168i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.9072 | − | 30.9072i | 1.13083 | − | 1.13083i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.10139i | 0.332557i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.2961i | 0.850088i | 0.905173 | + | 0.425044i | \(0.139741\pi\) | ||||
−0.905173 | + | 0.425044i | \(0.860259\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.859039 | + | 0.859039i | 0.0313051 | + | 0.0313051i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.7088 | + | 2.25086i | −1.48154 | + | 0.0819170i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.0154 | + | 11.0154i | −0.400360 | + | 0.400360i | −0.878360 | − | 0.478000i | \(-0.841362\pi\) |
0.478000 | + | 0.878360i | \(0.341362\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.99706 | + | 5.55780i | 0.253977 | + | 0.201735i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.31975 | 0.0840909 | 0.0420455 | − | 0.999116i | \(-0.486613\pi\) | ||||
0.0420455 | + | 0.999116i | \(0.486613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5492 | − | 13.5492i | 0.490512 | − | 0.490512i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.96112 | − | 2.65083i | −0.107060 | − | 0.0958409i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.5108 | − | 20.5108i | −0.740601 | − | 0.740601i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.2220 | 0.548920 | 0.274460 | − | 0.961598i | \(-0.411501\pi\) | ||||
0.274460 | + | 0.961598i | \(0.411501\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.77927 | −0.100093 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.882262 | − | 0.882262i | −0.0317328 | − | 0.0317328i | 0.691062 | − | 0.722795i | \(-0.257143\pi\) |
−0.722795 | + | 0.691062i | \(0.757143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.61273 | + | 0.289810i | −0.0938519 | + | 0.0104103i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.55963 | + | 1.55963i | 0.0559514 | + | 0.0559514i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.0332 | 0.466963 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 27.4422i | − | 0.981957i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.3496 | − | 10.3496i | 0.369864 | − | 0.369864i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.8299 | + | 32.2046i | −1.02898 | + | 1.14943i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.5674 | + | 35.5674i | −1.26784 | + | 1.26784i | −0.320641 | + | 0.947201i | \(0.603898\pi\) |
−0.947201 | + | 0.320641i | \(0.896102\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.57194 | 0.269568 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.9236 | 1.56174 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.89637 | − | 1.89637i | −0.0673421 | − | 0.0673421i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.494751 | − | 0.0273556i | 0.0175470 | − | 0.000970202i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.37158 | − | 7.37158i | 0.261115 | − | 0.261115i | −0.564392 | − | 0.825507i | \(-0.690889\pi\) |
0.825507 | + | 0.564392i | \(0.190889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.56606 | −0.232290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.6339i | 1.32973i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.04454 | + | 3.04454i | 0.107439 | + | 0.107439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.8458 | + | 20.9709i | −0.523245 | + | 0.739128i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.53141 | + | 6.53141i | 0.229917 | + | 0.229917i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.8450i | − | 0.978978i | −0.872009 | − | 0.489489i | \(-0.837183\pi\) | ||
0.872009 | − | 0.489489i | \(-0.162817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.9498 | −1.75398 | −0.876988 | − | 0.480513i | \(-0.840451\pi\) | ||||
−0.876988 | + | 0.480513i | \(0.840451\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.50684 | − | 5.50684i | 0.193133 | − | 0.193133i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.1179 | + | 23.5898i | −0.739726 | + | 0.826315i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.61613 | + | 3.61613i | 0.126512 | + | 0.126512i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.9811 | −0.907852 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.0759 | −1.29396 | −0.646979 | − | 0.762508i | \(-0.723968\pi\) | ||||
−0.646979 | + | 0.762508i | \(0.723968\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.660413 | − | 0.660413i | 0.0230205 | − | 0.0230205i | −0.695503 | − | 0.718523i | \(-0.744818\pi\) |
0.718523 | + | 0.695503i | \(0.244818\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.27363 | + | 5.82113i | 0.253235 | + | 0.202666i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.0527 | + | 27.0527i | −0.940716 | + | 0.940716i | −0.998338 | − | 0.0576226i | \(-0.981648\pi\) |
0.0576226 | + | 0.998338i | \(0.481648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.3353i | 1.29671i | 0.761339 | + | 0.648353i | \(0.224542\pi\) | ||||
−0.761339 | + | 0.648353i | \(0.775458\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.37523 | −0.151775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.548117 | − | 0.548117i | −0.0189911 | − | 0.0189911i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0657 | + | 16.1726i | 0.625191 | + | 0.559677i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.733991 | − | 0.733991i | −0.0253704 | − | 0.0253704i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0287 | −0.622420 | −0.311210 | − | 0.950341i | \(-0.600734\pi\) | ||||
−0.311210 | + | 0.950341i | \(0.600734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9569 | −0.895066 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.06211 | + | 1.06211i | 0.0365812 | + | 0.0365812i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.136096 | − | 2.46142i | −0.00468184 | − | 0.0846755i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.6656 | − | 33.6656i | 1.15676 | − | 1.15676i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.17840 | −0.212042 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.18838 | − | 10.3089i | 0.280694 | − | 0.353383i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.9885 | + | 33.9885i | −1.16374 | + | 1.16374i | −0.180093 | + | 0.983650i | \(0.557640\pi\) |
−0.983650 | + | 0.180093i | \(0.942360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.684709 | − | 12.3836i | −0.0234166 | − | 0.423510i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.41108 | + | 5.41108i | 0.184839 | + | 0.184839i | 0.793461 | − | 0.608622i | \(-0.208277\pi\) |
−0.608622 | + | 0.793461i | \(0.708277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 34.2433i | − | 1.16837i | −0.811622 | − | 0.584184i | \(-0.801415\pi\) | ||
0.811622 | − | 0.584184i | \(-0.198585\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 5.45166i | − | 0.185792i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.9583 | − | 25.9583i | 0.883632 | − | 0.883632i | −0.110269 | − | 0.993902i | \(-0.535171\pi\) |
0.993902 | + | 0.110269i | \(0.0351714\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.2639 | − | 38.2746i | 1.16501 | − | 1.30138i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.94129 | + | 3.94129i | 0.133853 | + | 0.133853i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 50.4188i | − | 1.71034i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 26.4445i | − | 0.896036i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.5264 | + | 11.5264i | 0.390109 | + | 0.390109i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.5579 | + | 21.8068i | −0.525953 | + | 0.737203i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.3502 | − | 24.3502i | −0.822249 | − | 0.822249i | 0.164181 | − | 0.986430i | \(-0.447502\pi\) |
−0.986430 | + | 0.164181i | \(0.947502\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.31125 | −0.280332 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.218997i | 0.00737820i | 0.999993 | + | 0.00368910i | \(0.00117428\pi\) | ||||
−0.999993 | + | 0.00368910i | \(0.998826\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.5113 | + | 14.5113i | −0.488344 | + | 0.488344i | −0.907783 | − | 0.419439i | \(-0.862227\pi\) |
0.419439 | + | 0.907783i | \(0.362227\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.31540 | − | 3.86320i | −0.145061 | − | 0.129860i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.6798 | − | 12.6798i | −0.425747 | − | 0.425747i | 0.461430 | − | 0.887177i | \(-0.347337\pi\) |
−0.887177 | + | 0.461430i | \(0.847337\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.7163 | 0.426491 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 44.4523i | − | 1.48921i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.4890 | − | 14.4890i | −0.484855 | − | 0.484855i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.82518 | − | 33.0100i | −0.0610090 | − | 1.10340i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.687853 | − | 6.00024i | −0.0229667 | − | 0.200342i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.89754i | 0.129990i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.406743 | −0.0135506 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.51259 | − | 1.51259i | 0.0503359 | − | 0.0503359i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.99173 | + | 54.1081i | 0.0994484 | + | 1.79862i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.1326 | − | 26.1326i | 0.867719 | − | 0.867719i | −0.124501 | − | 0.992219i | \(-0.539733\pi\) |
0.992219 | + | 0.124501i | \(0.0397330\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.36682i | 0.211174i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.8223i | 0.822400i | 0.911545 | + | 0.411200i | \(0.134890\pi\) | ||||
−0.911545 | + | 0.411200i | \(0.865110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.4711 | − | 59.4711i | 1.96821 | − | 1.96821i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.398991 | − | 0.357181i | −0.0131902 | − | 0.0118080i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.78510 | + | 9.78510i | −0.323132 | + | 0.323132i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.3089 | −0.340058 | −0.170029 | − | 0.985439i | \(-0.554386\pi\) | ||||
−0.170029 | + | 0.985439i | \(0.554386\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.96056 | 0.163456 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.1152 | + | 13.1152i | −0.431692 | + | 0.431692i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.57635 | − | 10.7163i | 0.281989 | − | 0.352351i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.01383 | − | 6.01383i | 0.197520 | − | 0.197520i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 27.6117i | − | 0.905909i | −0.891534 | − | 0.452955i | \(-0.850370\pi\) | ||
0.891534 | − | 0.452955i | \(-0.149630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.41900i | − | 0.0792795i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.49355 | − | 2.49355i | 0.0816351 | − | 0.0816351i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.69775 | − | 5.10068i | −0.186336 | − | 0.166810i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.72139 | − | 5.72139i | 0.186910 | − | 0.186910i | −0.607449 | − | 0.794359i | \(-0.707807\pi\) |
0.794359 | + | 0.607449i | \(0.207807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0777 | −0.328872 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.31871i | − | 0.140786i | −0.997519 | − | 0.0703930i | \(-0.977575\pi\) | ||
0.997519 | − | 0.0703930i | \(-0.0224253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.3284 | + | 3.70604i | −1.05276 | + | 0.120685i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.5616 | + | 0.583969i | −0.343569 | + | 0.0189965i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.4515 | + | 41.4515i | 1.34699 | + | 1.34699i | 0.888908 | + | 0.458086i | \(0.151465\pi\) |
0.458086 | + | 0.888908i | \(0.348535\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.91010i | − | 0.0944659i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.15504 | −0.199591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.8044 | − | 27.8044i | −0.900672 | − | 0.900672i | 0.0948219 | − | 0.995494i | \(-0.469772\pi\) |
−0.995494 | + | 0.0948219i | \(0.969772\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.25985 | − | 40.8715i | −0.0731271 | − | 1.32257i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.76706 | − | 9.76706i | 0.315724 | − | 0.315724i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.4198i | 1.17606i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7236 | −0.991083 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.75604 | + | 7.75604i | 0.249935 | + | 0.249935i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.9751 | − | 36.8350i | 1.06151 | − | 1.18576i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.4321 | + | 17.4321i | 0.560577 | + | 0.560577i | 0.929471 | − | 0.368894i | \(-0.120264\pi\) |
−0.368894 | + | 0.929471i | \(0.620264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.396494i | − | 0.0127372i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.0252i | 0.963555i | 0.876294 | + | 0.481777i | \(0.160009\pi\) | ||||
−0.876294 | + | 0.481777i | \(0.839991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.5330 | − | 18.5330i | −0.594141 | − | 0.594141i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.694183 | − | 6.25827i | −0.0222316 | − | 0.200425i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.18647 | + | 1.18647i | −0.0379585 | + | 0.0379585i | −0.725831 | − | 0.687873i | \(-0.758545\pi\) |
0.687873 | + | 0.725831i | \(0.258545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.4146i | 2.31438i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 23.0927i | − | 0.737293i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.7320 | − | 12.7320i | −0.406088 | − | 0.406088i | 0.474284 | − | 0.880372i | \(-0.342707\pi\) |
−0.880372 | + | 0.474284i | \(0.842707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.6030 | + | 30.0817i | 1.07068 | + | 0.958484i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.06060 | + | 6.06060i | −0.192911 | + | 0.192911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.99794 | − | 7.94141i | −0.317916 | − | 0.252522i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.95248 | −0.125555 | −0.0627774 | − | 0.998028i | \(-0.519996\pi\) | ||||
−0.0627774 | + | 0.998028i | \(0.519996\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.964635 | + | 0.964635i | −0.0306118 | + | 0.0306118i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.7923 | + | 2.53193i | −1.45171 | + | 0.0802676i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.3544 | − | 27.3544i | −0.866323 | − | 0.866323i | 0.125740 | − | 0.992063i | \(-0.459870\pi\) |
−0.992063 | + | 0.125740i | \(0.959870\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.41988 | 0.171477 |
(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 | 460.2.i.b.137.4 | yes | 16 | |
5.2 | odd | 4 | 2300.2.i.d.1793.5 | 16 | |||
5.3 | odd | 4 | inner | 460.2.i.b.413.3 | yes | 16 | |
5.4 | even | 2 | 2300.2.i.d.1057.6 | 16 | |||
23.22 | odd | 2 | inner | 460.2.i.b.137.3 | ✓ | 16 | |
115.22 | even | 4 | 2300.2.i.d.1793.6 | 16 | |||
115.68 | even | 4 | inner | 460.2.i.b.413.4 | yes | 16 | |
115.114 | odd | 2 | 2300.2.i.d.1057.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.i.b.137.3 | ✓ | 16 | 23.22 | odd | 2 | inner | |
460.2.i.b.137.4 | yes | 16 | 1.1 | even | 1 | trivial | |
460.2.i.b.413.3 | yes | 16 | 5.3 | odd | 4 | inner | |
460.2.i.b.413.4 | yes | 16 | 115.68 | even | 4 | inner | |
2300.2.i.d.1057.5 | 16 | 115.114 | odd | 2 | |||
2300.2.i.d.1057.6 | 16 | 5.4 | even | 2 | |||
2300.2.i.d.1793.5 | 16 | 5.2 | odd | 4 | |||
2300.2.i.d.1793.6 | 16 | 115.22 | even | 4 |