Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1100,2,Mod(593,1100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1100.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1100.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.78354422234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.3 | ||
Root | \(0.323042 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1100.593 |
Dual form | 1100.2.k.d.857.3 |
$q$-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 \(\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(551\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.323042 | + | 0.323042i | 0.186508 | + | 0.186508i | 0.794185 | − | 0.607676i | \(-0.207898\pi\) |
−0.607676 | + | 0.794185i | \(0.707898\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.901703 | + | 0.901703i | 0.340812 | + | 0.340812i | 0.856672 | − | 0.515861i | \(-0.172528\pi\) |
−0.515861 | + | 0.856672i | \(0.672528\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.79129i | − | 0.930429i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79129 | − | 2.79129i | −0.540094 | − | 0.841605i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51691 | − | 2.51691i | 0.698066 | − | 0.698066i | −0.265927 | − | 0.963993i | \(-0.585678\pi\) |
0.963993 | + | 0.265927i | \(0.0856781\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.22202 | − | 5.22202i | −1.26653 | − | 1.26653i | −0.947871 | − | 0.318656i | \(-0.896769\pi\) |
−0.318656 | − | 0.947871i | \(-0.603231\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.582576i | 0.127128i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.83995 | + | 2.83995i | 0.592171 | + | 0.592171i | 0.938218 | − | 0.346046i | \(-0.112476\pi\) |
−0.346046 | + | 0.938218i | \(0.612476\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.87083 | − | 1.87083i | 0.360041 | − | 0.360041i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.37386 | −1.55499 | −0.777494 | − | 0.628891i | \(-0.783509\pi\) | ||||
−0.777494 | + | 0.628891i | \(0.783509\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58258 | 0.823055 | 0.411527 | − | 0.911397i | \(-0.364995\pi\) | ||||
0.411527 | + | 0.911397i | \(0.364995\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.323042 | − | 1.48036i | 0.0562344 | − | 0.257698i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.96640 | − | 4.96640i | 0.816472 | − | 0.816472i | −0.169123 | − | 0.985595i | \(-0.554094\pi\) |
0.985595 | + | 0.169123i | \(0.0540936\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.62614 | 0.260390 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000i | 0.780869i | 0.920631 | + | 0.390434i | \(0.127675\pi\) | ||||
−0.920631 | + | 0.390434i | \(0.872325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.83723 | − | 6.83723i | 1.04267 | − | 1.04267i | 0.0436197 | − | 0.999048i | \(-0.486111\pi\) |
0.999048 | − | 0.0436197i | \(-0.0138890\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.578661 | + | 0.578661i | −0.0844064 | + | 0.0844064i | −0.748049 | − | 0.663643i | \(-0.769009\pi\) |
0.663643 | + | 0.748049i | \(0.269009\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.37386i | − | 0.767695i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.37386i | − | 0.472435i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.09285 | + | 7.09285i | 0.974278 | + | 0.974278i | 0.999677 | − | 0.0253995i | \(-0.00808578\pi\) |
−0.0253995 | + | 0.999677i | \(0.508086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.61521 | − | 1.61521i | −0.213940 | − | 0.213940i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.58258i | − | 1.11736i | −0.829385 | − | 0.558678i | \(-0.811309\pi\) | ||
0.829385 | − | 0.558678i | \(-0.188691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.79129i | − | 0.997572i | −0.866725 | − | 0.498786i | \(-0.833779\pi\) | ||
0.866725 | − | 0.498786i | \(-0.166221\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.51691 | − | 2.51691i | 0.317101 | − | 0.317101i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.19115 | + | 6.19115i | −0.756369 | + | 0.756369i | −0.975660 | − | 0.219291i | \(-0.929626\pi\) |
0.219291 | + | 0.975660i | \(0.429626\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.83485i | 0.220890i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.417424 | −0.0495392 | −0.0247696 | − | 0.999693i | \(-0.507885\pi\) | ||||
−0.0247696 | + | 0.999693i | \(0.507885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.901703 | − | 0.901703i | 0.105536 | − | 0.105536i | −0.652367 | − | 0.757903i | \(-0.726224\pi\) |
0.757903 | + | 0.652367i | \(0.226224\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.901703 | − | 4.13212i | 0.102759 | − | 0.470899i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.20871 | −0.811043 | −0.405522 | − | 0.914085i | \(-0.632910\pi\) | ||||
−0.405522 | + | 0.914085i | \(0.632910\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.16515 | −0.796128 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.22202 | − | 5.22202i | 0.573191 | − | 0.573191i | −0.359828 | − | 0.933019i | \(-0.617164\pi\) |
0.933019 | + | 0.359828i | \(0.117164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.70511 | − | 2.70511i | −0.290018 | − | 0.290018i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.79129i | 0.507875i | 0.967221 | + | 0.253938i | \(0.0817258\pi\) | ||||
−0.967221 | + | 0.253938i | \(0.918274\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.53901 | 0.475818 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.48036 | + | 1.48036i | 0.153507 | + | 0.153507i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.35119 | − | 3.35119i | 0.340262 | − | 0.340262i | −0.516204 | − | 0.856466i | \(-0.672655\pi\) |
0.856466 | + | 0.516204i | \(0.172655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.79129 | + | 5.00000i | −0.783054 | + | 0.502519i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.79129i | 0.775262i | 0.921815 | + | 0.387631i | \(0.126707\pi\) | ||||
−0.921815 | + | 0.387631i | \(0.873293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.60976 | + | 9.60976i | 0.946878 | + | 0.946878i | 0.998658 | − | 0.0517804i | \(-0.0164896\pi\) |
−0.0517804 | + | 0.998658i | \(0.516490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.713507 | − | 0.713507i | −0.0689773 | − | 0.0689773i | 0.671777 | − | 0.740754i | \(-0.265532\pi\) |
−0.740754 | + | 0.671777i | \(0.765532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.62614 | 0.155756 | 0.0778778 | − | 0.996963i | \(-0.475186\pi\) | ||||
0.0778778 | + | 0.996963i | \(0.475186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.20871 | 0.304557 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.4497 | − | 12.4497i | −1.17117 | − | 1.17117i | −0.981931 | − | 0.189240i | \(-0.939398\pi\) |
−0.189240 | − | 0.981931i | \(-0.560602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.02543 | − | 7.02543i | −0.649501 | − | 0.649501i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.41742i | − | 0.863294i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.58258 | + | 10.0000i | −0.416598 | + | 0.909091i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.61521 | + | 1.61521i | −0.145639 | + | 0.145639i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2558 | + | 10.2558i | 0.910059 | + | 0.910059i | 0.996276 | − | 0.0862172i | \(-0.0274779\pi\) |
−0.0862172 | + | 0.996276i | \(0.527478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.41742 | 0.388933 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.37386i | − | 0.294776i | −0.989079 | − | 0.147388i | \(-0.952913\pi\) | ||
0.989079 | − | 0.147388i | \(-0.0470866\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.50851 | − | 4.50851i | −0.390938 | − | 0.390938i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.06470 | − | 4.06470i | 0.347271 | − | 0.347271i | −0.511821 | − | 0.859092i | \(-0.671029\pi\) |
0.859092 | + | 0.511821i | \(0.171029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.7477 | 1.84462 | 0.922309 | − | 0.386453i | \(-0.126300\pi\) | ||||
0.922309 | + | 0.386453i | \(0.126300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.373864 | −0.0314850 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.5339 | − | 2.51691i | −0.964517 | − | 0.210475i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73598 | − | 1.73598i | 0.143181 | − | 0.143181i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.41742 | −0.361889 | −0.180945 | − | 0.983493i | \(-0.557916\pi\) | ||||
−0.180945 | + | 0.983493i | \(0.557916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 20.5826i | − | 1.67499i | −0.546448 | − | 0.837493i | \(-0.684020\pi\) | ||
0.546448 | − | 0.837493i | \(-0.315980\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.5762 | + | 14.5762i | −1.17841 | + | 1.17841i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.79796 | + | 9.79796i | −0.781962 | + | 0.781962i | −0.980162 | − | 0.198199i | \(-0.936491\pi\) |
0.198199 | + | 0.980162i | \(0.436491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.58258i | 0.363422i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.12159i | 0.403638i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6997 | + | 10.6997i | 0.838062 | + | 0.838062i | 0.988604 | − | 0.150541i | \(-0.0481017\pi\) |
−0.150541 | + | 0.988604i | \(0.548102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.1575 | + | 11.1575i | 0.863397 | + | 0.863397i | 0.991731 | − | 0.128334i | \(-0.0409629\pi\) |
−0.128334 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.330303i | 0.0254079i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.9564i | 1.06728i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.713507 | + | 0.713507i | −0.0542469 | + | 0.0542469i | −0.733710 | − | 0.679463i | \(-0.762213\pi\) |
0.679463 | + | 0.733710i | \(0.262213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.77253 | − | 2.77253i | 0.208396 | − | 0.208396i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2087i | 1.06201i | 0.847369 | + | 0.531005i | \(0.178185\pi\) | ||||
−0.847369 | + | 0.531005i | \(0.821815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.37386 | 0.548095 | 0.274047 | − | 0.961716i | \(-0.411637\pi\) | ||||
0.274047 | + | 0.961716i | \(0.411637\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.51691 | − | 2.51691i | 0.186056 | − | 0.186056i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.22202 | + | 23.9303i | −0.381872 | + | 1.74996i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.37386 | 0.245412 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2087 | 0.811034 | 0.405517 | − | 0.914088i | \(-0.367092\pi\) | ||||
0.405517 | + | 0.914088i | \(0.367092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.4440 | + | 10.4440i | −0.751779 | + | 0.751779i | −0.974811 | − | 0.223032i | \(-0.928404\pi\) |
0.223032 | + | 0.974811i | \(0.428404\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.93553 | − | 5.93553i | −0.422889 | − | 0.422889i | 0.463308 | − | 0.886197i | \(-0.346662\pi\) |
−0.886197 | + | 0.463308i | \(0.846662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5390i | 1.10153i | 0.834660 | + | 0.550766i | \(0.185664\pi\) | ||||
−0.834660 | + | 0.550766i | \(0.814336\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.55074 | − | 7.55074i | −0.529958 | − | 0.529958i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.92713 | − | 7.92713i | 0.550974 | − | 0.550974i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.95644 | + | 13.9564i | 0.619530 | + | 0.965387i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.3303i | − | 1.19307i | −0.802588 | − | 0.596534i | \(-0.796544\pi\) | ||
0.802588 | − | 0.596534i | \(-0.203456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.134846 | − | 0.134846i | −0.00923946 | − | 0.00923946i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.13212 | + | 4.13212i | 0.280507 | + | 0.280507i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.582576 | 0.0393668 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.2867 | −1.76824 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8599 | − | 17.8599i | −1.19599 | − | 1.19599i | −0.975357 | − | 0.220633i | \(-0.929188\pi\) |
−0.220633 | − | 0.975357i | \(-0.570812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.41862 | + | 3.41862i | 0.226901 | + | 0.226901i | 0.811397 | − | 0.584495i | \(-0.198708\pi\) |
−0.584495 | + | 0.811397i | \(0.698708\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.3739i | − | 1.74283i | −0.490543 | − | 0.871417i | \(-0.663202\pi\) | ||
0.490543 | − | 0.871417i | \(-0.336798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.62614 | − | 1.04356i | 0.106992 | − | 0.0686613i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5762 | + | 14.5762i | −0.954916 | + | 0.954916i | −0.999027 | − | 0.0441104i | \(-0.985955\pi\) |
0.0441104 | + | 0.999027i | \(0.485955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.32872 | − | 2.32872i | −0.151266 | − | 0.151266i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1216 | 1.30156 | 0.650779 | − | 0.759267i | \(-0.274443\pi\) | ||||
0.650779 | + | 0.759267i | \(0.274443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.62614i | 0.104749i | 0.998628 | + | 0.0523743i | \(0.0166789\pi\) | ||||
−0.998628 | + | 0.0523743i | \(0.983321\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.92713 | − | 7.92713i | −0.508526 | − | 0.508526i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.5846 | + | 12.5846i | −0.800737 | + | 0.800737i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.37386 | 0.213810 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.37386 | 0.149837 | 0.0749185 | − | 0.997190i | \(-0.476130\pi\) | ||||
0.0749185 | + | 0.997190i | \(0.476130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.83995 | − | 13.0143i | 0.178546 | − | 0.818202i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.29217 | + | 1.29217i | −0.0806032 | + | 0.0806032i | −0.746259 | − | 0.665656i | \(-0.768152\pi\) |
0.665656 | + | 0.746259i | \(0.268152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.95644 | 0.556526 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.3739i | 1.44681i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.74733 | + | 5.74733i | −0.354396 | + | 0.354396i | −0.861742 | − | 0.507346i | \(-0.830626\pi\) |
0.507346 | + | 0.861742i | \(0.330626\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.54779 | + | 1.54779i | −0.0947230 | + | 0.0947230i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.79129i | − | 0.414072i | −0.978333 | − | 0.207036i | \(-0.933618\pi\) | ||
0.978333 | − | 0.207036i | \(-0.0663817\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.83485i | 0.232950i | 0.993194 | + | 0.116475i | \(0.0371596\pi\) | ||||
−0.993194 | + | 0.116475i | \(0.962840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.46629 | + | 1.46629i | 0.0887440 | + | 0.0887440i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.12372 | − | 6.12372i | −0.367939 | − | 0.367939i | 0.498786 | − | 0.866725i | \(-0.333779\pi\) |
−0.866725 | + | 0.498786i | \(0.833779\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 12.7913i | − | 0.765794i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5826i | 0.631304i | 0.948875 | + | 0.315652i | \(0.102223\pi\) | ||||
−0.948875 | + | 0.315652i | \(0.897777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.8627 | + | 13.8627i | −0.824049 | + | 0.824049i | −0.986686 | − | 0.162637i | \(-0.948000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.50851 | + | 4.50851i | −0.266129 | + | 0.266129i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.5390i | 2.20818i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.16515 | 0.126923 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.2474 | + | 12.2474i | −0.715504 | + | 0.715504i | −0.967681 | − | 0.252177i | \(-0.918853\pi\) |
0.252177 | + | 0.967681i | \(0.418853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.57321 | − | 1.87083i | −0.497468 | − | 0.108556i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.2958 | 0.826749 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3303 | 0.710707 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.51691 | + | 2.51691i | −0.144593 | + | 0.144593i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5033 | + | 22.5033i | 1.28433 | + | 1.28433i | 0.938178 | + | 0.346153i | \(0.112512\pi\) |
0.346153 | + | 0.938178i | \(0.387488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.20871i | 0.353201i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0000 | −0.737162 | −0.368581 | − | 0.929596i | \(-0.620156\pi\) | ||||
−0.368581 | + | 0.929596i | \(0.620156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.15188 | + | 9.15188i | 0.517295 | + | 0.517295i | 0.916752 | − | 0.399457i | \(-0.130801\pi\) |
−0.399457 | + | 0.916752i | \(0.630801\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.1494 | − | 23.1494i | 1.30020 | − | 1.30020i | 0.371943 | − | 0.928256i | \(-0.378692\pi\) |
0.928256 | − | 0.371943i | \(-0.121308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0000 | + | 23.3739i | 0.839839 | + | 1.30869i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 0.460985i | − | 0.0257297i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.1101 | + | 26.1101i | 1.45281 | + | 1.45281i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.525310 | + | 0.525310i | 0.0290497 | + | 0.0290497i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.04356 | −0.0575334 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00000 | −0.0549650 | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) | ||||
−0.0274825 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.8627 | − | 13.8627i | −0.759669 | − | 0.759669i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.8881 | + | 20.8881i | 1.13785 | + | 1.13785i | 0.988836 | + | 0.149011i | \(0.0476090\pi\) |
0.149011 | + | 0.988836i | \(0.452391\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 8.04356i | − | 0.436866i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.20871 | − | 12.7913i | −0.444527 | − | 0.692687i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1575 | − | 11.1575i | 0.602451 | − | 0.602451i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.70511 | − | 2.70511i | −0.145218 | − | 0.145218i | 0.630760 | − | 0.775978i | \(-0.282743\pi\) |
−0.775978 | + | 0.630760i | \(0.782743\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7477 | −1.16413 | −0.582065 | − | 0.813143i | \(-0.697755\pi\) | ||||
−0.582065 | + | 0.813143i | \(0.697755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9.41742i | − | 0.502665i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.8938 | − | 22.8938i | −1.21851 | − | 1.21851i | −0.968153 | − | 0.250359i | \(-0.919451\pi\) |
−0.250359 | − | 0.968153i | \(-0.580549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.04222 | − | 3.04222i | 0.161012 | − | 0.161012i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.7477 | −1.41169 | −0.705846 | − | 0.708366i | \(-0.749433\pi\) | ||||
−0.705846 | + | 0.708366i | \(0.749433\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.71078 | + | 1.75006i | −0.247252 | + | 0.0918541i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.120774 | − | 0.120774i | 0.00630433 | − | 0.00630433i | −0.703948 | − | 0.710252i | \(-0.748581\pi\) |
0.710252 | + | 0.703948i | \(0.248581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.9564 | 0.726543 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.7913i | 0.664091i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.9948 | − | 17.9948i | 0.931734 | − | 0.931734i | −0.0660799 | − | 0.997814i | \(-0.521049\pi\) |
0.997814 | + | 0.0660799i | \(0.0210492\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.0763 | + | 21.0763i | −1.08548 | + | 1.08548i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.16515i | − | 0.213949i | −0.994262 | − | 0.106975i | \(-0.965884\pi\) | ||
0.994262 | − | 0.106975i | \(-0.0341164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.62614i | 0.339467i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7925 | + | 17.7925i | 0.909155 | + | 0.909155i | 0.996204 | − | 0.0870491i | \(-0.0277437\pi\) |
−0.0870491 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.0847 | − | 19.0847i | −0.970129 | − | 0.970129i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 18.0000i | − | 0.912636i | −0.889817 | − | 0.456318i | \(-0.849168\pi\) | ||
0.889817 | − | 0.456318i | \(-0.150832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 29.6606i | − | 1.50000i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.08990 | − | 1.08990i | 0.0549781 | − | 0.0549781i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.10397 | + | 1.10397i | −0.0554067 | + | 0.0554067i | −0.734267 | − | 0.678861i | \(-0.762474\pi\) |
0.678861 | + | 0.734267i | \(0.262474\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 2.91288i | − | 0.145826i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5339 | − | 11.5339i | 0.574547 | − | 0.574547i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.7589 | − | 4.96640i | −1.12812 | − | 0.246175i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.7477 | 0.580888 | 0.290444 | − | 0.956892i | \(-0.406197\pi\) | ||||
0.290444 | + | 0.956892i | \(0.406197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.62614 | 0.129538 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.73893 | − | 7.73893i | 0.380808 | − | 0.380808i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.02543 | + | 7.02543i | 0.344037 | + | 0.344037i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.5826i | 0.810112i | 0.914292 | + | 0.405056i | \(0.132748\pi\) | ||||
−0.914292 | + | 0.405056i | \(0.867252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9564 | 0.533984 | 0.266992 | − | 0.963699i | \(-0.413970\pi\) | ||||
0.266992 | + | 0.963699i | \(0.413970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.61521 | + | 1.61521i | 0.0785342 | + | 0.0785342i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.02543 | − | 7.02543i | 0.339984 | − | 0.339984i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.91288 | − | 4.53901i | −0.140635 | − | 0.219146i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.9129i | 1.58536i | 0.609640 | + | 0.792679i | \(0.291314\pi\) | ||||
−0.609640 | + | 0.792679i | \(0.708686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8992 | + | 14.8992i | 0.716010 | + | 0.716010i | 0.967786 | − | 0.251775i | \(-0.0810145\pi\) |
−0.251775 | + | 0.967786i | \(0.581014\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.1998 | − | 14.1998i | −0.679267 | − | 0.679267i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.95644 | 0.188831 | 0.0944153 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944153 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.9498 | − | 18.9498i | −0.900334 | − | 0.900334i | 0.0951310 | − | 0.995465i | \(-0.469673\pi\) |
−0.995465 | + | 0.0951310i | \(0.969673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.42701 | − | 1.42701i | −0.0674954 | − | 0.0674954i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 36.9564i | − | 1.74408i | −0.489433 | − | 0.872041i | \(-0.662796\pi\) | ||
0.489433 | − | 0.872041i | \(-0.337204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.9564 | − | 8.95644i | 0.657183 | − | 0.421742i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.64903 | − | 6.64903i | 0.312399 | − | 0.312399i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.901703 | + | 0.901703i | 0.0421799 | + | 0.0421799i | 0.727882 | − | 0.685702i | \(-0.240505\pi\) |
−0.685702 | + | 0.727882i | \(0.740505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.5390 | −0.912003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.5826i | 0.958626i | 0.877644 | + | 0.479313i | \(0.159114\pi\) | ||||
−0.877644 | + | 0.479313i | \(0.840886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.25857 | + | 6.25857i | 0.290860 | + | 0.290860i | 0.837420 | − | 0.546560i | \(-0.184063\pi\) |
−0.546560 | + | 0.837420i | \(0.684063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.8207 | − | 20.8207i | 0.963465 | − | 0.963465i | −0.0358904 | − | 0.999356i | \(-0.511427\pi\) |
0.999356 | + | 0.0358904i | \(0.0114267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.1652 | −0.515559 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.33030 | −0.291685 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.3321 | − | 6.83723i | −1.44065 | − | 0.314376i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.7982 | − | 19.7982i | 0.906497 | − | 0.906497i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.7477 | −1.45059 | −0.725295 | − | 0.688438i | \(-0.758297\pi\) | ||||
−0.725295 | + | 0.688438i | \(0.758297\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 25.0000i | − | 1.13990i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.65449 | + | 1.65449i | −0.0752818 | + | 0.0752818i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.0674228 | + | 0.0674228i | −0.00305522 | + | 0.00305522i | −0.708633 | − | 0.705578i | \(-0.750688\pi\) |
0.705578 | + | 0.708633i | \(0.250688\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.91288i | 0.312611i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.0000i | − | 0.676941i | −0.940977 | − | 0.338470i | \(-0.890091\pi\) | ||
0.940977 | − | 0.338470i | \(-0.109909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.7285 | + | 43.7285i | 1.96943 | + | 1.96943i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.376393 | − | 0.376393i | −0.0168835 | − | 0.0168835i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.1216i | − | 1.52749i | −0.645517 | − | 0.763746i | \(-0.723358\pi\) | ||
0.645517 | − | 0.763746i | \(-0.276642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.20871i | 0.322062i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9049 | − | 16.9049i | 0.753751 | − | 0.753751i | −0.221426 | − | 0.975177i | \(-0.571071\pi\) |
0.975177 | + | 0.221426i | \(0.0710711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.106702 | + | 0.106702i | −0.00473879 | + | 0.00473879i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6261i | 0.825589i | 0.910824 | + | 0.412794i | \(0.135447\pi\) | ||||
−0.910824 | + | 0.412794i | \(0.864553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.62614 | 0.0719360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.35414 | + | 9.35414i | −0.412996 | + | 0.412996i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.65176 | + | 0.578661i | 0.116624 | + | 0.0254495i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.460985 | −0.0202350 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.33030 | −0.364957 | −0.182479 | − | 0.983210i | \(-0.558412\pi\) | ||||
−0.182479 | + | 0.983210i | \(0.558412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.23042 | − | 3.23042i | 0.141256 | − | 0.141256i | −0.632942 | − | 0.774199i | \(-0.718153\pi\) |
0.774199 | + | 0.632942i | \(0.218153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.9303 | − | 23.9303i | −1.04242 | − | 1.04242i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 6.86932i | − | 0.298666i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.9564 | −1.03962 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.5846 | + | 12.5846i | 0.545098 | + | 0.545098i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.59001 | + | 4.59001i | −0.198074 | + | 0.198074i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.0000 | + | 9.62614i | −0.646096 | + | 0.414627i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 37.7913i | − | 1.62477i | −0.583118 | − | 0.812387i | \(-0.698168\pi\) | ||
0.583118 | − | 0.812387i | \(-0.301832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.38207 | + | 2.38207i | 0.102224 | + | 0.102224i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5762 | + | 14.5762i | 0.623232 | + | 0.623232i | 0.946356 | − | 0.323125i | \(-0.104733\pi\) |
−0.323125 | + | 0.946356i | \(0.604733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.7477 | −0.928170 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.8693 | 1.78369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.50012 | − | 6.50012i | −0.276413 | − | 0.276413i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.0118 | − | 27.0118i | −1.14453 | − | 1.14453i | −0.987612 | − | 0.156915i | \(-0.949845\pi\) |
−0.156915 | − | 0.987612i | \(-0.550155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.4174i | − | 1.45570i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.41742 | + | 6.04356i | −0.397604 | + | 0.255159i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.9526 | − | 14.9526i | 0.630175 | − | 0.630175i | −0.317937 | − | 0.948112i | \(-0.602990\pi\) |
0.948112 | + | 0.317937i | \(0.102990\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.46084 | − | 6.46084i | −0.271330 | − | 0.271330i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.7913 | 1.16507 | 0.582536 | − | 0.812805i | \(-0.302061\pi\) | ||||
0.582536 | + | 0.812805i | \(0.302061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7042i | 0.657199i | 0.944469 | + | 0.328599i | \(0.106577\pi\) | ||||
−0.944469 | + | 0.328599i | \(0.893423\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.62088 | + | 3.62088i | 0.151265 | + | 0.151265i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.4132 | + | 11.4132i | −0.475136 | + | 0.475136i | −0.903572 | − | 0.428436i | \(-0.859065\pi\) |
0.428436 | + | 0.903572i | \(0.359065\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.74773 | −0.280426 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.41742 | 0.390701 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.09285 | − | 32.5035i | 0.293756 | − | 1.34616i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.1941 | − | 12.1941i | 0.503304 | − | 0.503304i | −0.409159 | − | 0.912463i | \(-0.634178\pi\) |
0.912463 | + | 0.409159i | \(0.134178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.9129 | −0.944109 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 3.83485i | − | 0.157745i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.4050 | − | 23.4050i | 0.961128 | − | 0.961128i | −0.0381442 | − | 0.999272i | \(-0.512145\pi\) |
0.999272 | + | 0.0381442i | \(0.0121446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.01975 | + | 5.01975i | −0.205445 | + | 0.205445i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 24.7042i | − | 1.00938i | −0.863299 | − | 0.504692i | \(-0.831606\pi\) | ||
0.863299 | − | 0.504692i | \(-0.168394\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26.8693i | − | 1.09602i | −0.836471 | − | 0.548011i | \(-0.815385\pi\) | ||
0.836471 | − | 0.548011i | \(-0.184615\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.2813 | + | 17.2813i | 0.703748 | + | 0.703748i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.8881 | + | 20.8881i | 0.847821 | + | 0.847821i | 0.989861 | − | 0.142040i | \(-0.0453661\pi\) |
−0.142040 | + | 0.989861i | \(0.545366\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.87841i | − | 0.197683i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.91288i | 0.117842i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.3235 | − | 20.3235i | 0.820858 | − | 0.820858i | −0.165373 | − | 0.986231i | \(-0.552883\pi\) |
0.986231 | + | 0.165373i | \(0.0528827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.55641 | + | 9.55641i | −0.384727 | + | 0.384727i | −0.872802 | − | 0.488075i | \(-0.837699\pi\) |
0.488075 | + | 0.872802i | \(0.337699\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.7477i | 0.954502i | 0.878767 | + | 0.477251i | \(0.158367\pi\) | ||||
−0.878767 | + | 0.477251i | \(0.841633\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.6261 | 0.426412 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.32032 | + | 4.32032i | −0.173090 | + | 0.173090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.61521 | + | 7.40182i | −0.0645053 | + | 0.295600i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −51.8693 | −2.06817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.79129 | 0.0713100 | 0.0356550 | − | 0.999364i | \(-0.488648\pi\) | ||||
0.0356550 | + | 0.999364i | \(0.488648\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.59841 | − | 5.59841i | 0.222517 | − | 0.222517i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.5255 | − | 13.5255i | −0.535902 | − | 0.535902i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.16515i | 0.0460927i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8348 | 1.09941 | 0.549705 | − | 0.835359i | \(-0.314740\pi\) | ||||
0.549705 | + | 0.835359i | \(0.314740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.93825 | + | 1.93825i | 0.0764372 | + | 0.0764372i | 0.744292 | − | 0.667855i | \(-0.232787\pi\) |
−0.667855 | + | 0.744292i | \(0.732787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.1187 | − | 34.1187i | 1.34135 | − | 1.34135i | 0.446624 | − | 0.894722i | \(-0.352626\pi\) |
0.894722 | − | 0.446624i | \(-0.147374\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.9564 | + | 15.3739i | −0.940372 | + | 0.603477i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.66970i | 0.104634i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.1773 | + | 16.1773i | 0.633067 | + | 0.633067i | 0.948836 | − | 0.315769i | \(-0.102263\pi\) |
−0.315769 | + | 0.948836i | \(0.602263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.51691 | − | 2.51691i | −0.0981941 | − | 0.0981941i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.12159 | −0.199509 | −0.0997544 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997544 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.91288 | 0.268880 | 0.134440 | − | 0.990922i | \(-0.457076\pi\) | ||||
0.134440 | + | 0.990922i | \(0.457076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.49172 | − | 8.49172i | −0.329791 | − | 0.329791i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.7814 | − | 23.7814i | −0.920819 | − | 0.920819i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 11.5390i | − | 0.446124i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.7477 | + | 13.9564i | −0.839562 | + | 0.538782i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.08990 | + | 1.08990i | −0.0420125 | + | 0.0420125i | −0.727801 | − | 0.685788i | \(-0.759458\pi\) |
0.685788 | + | 0.727801i | \(0.259458\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0847 | + | 19.0847i | 0.733484 | + | 0.733484i | 0.971308 | − | 0.237824i | \(-0.0764343\pi\) |
−0.237824 | + | 0.971308i | \(0.576434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.04356 | 0.231931 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.20871i | 0.0846380i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.16300 | − | 3.16300i | −0.121029 | − | 0.121029i | 0.643998 | − | 0.765027i | \(-0.277274\pi\) |
−0.765027 | + | 0.643998i | \(0.777274\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.51986 | − | 8.51986i | 0.325053 | − | 0.325053i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.7042 | 1.36022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.0345 | 1.59907 | 0.799533 | − | 0.600622i | \(-0.205080\pi\) | ||||
0.799533 | + | 0.600622i | \(0.205080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.5339 | − | 2.51691i | −0.438138 | − | 0.0956096i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.1101 | − | 26.1101i | 0.988991 | − | 0.988991i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.41742 | −0.356200 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 29.0780i | − | 1.09826i | −0.835736 | − | 0.549131i | \(-0.814959\pi\) | ||
0.835736 | − | 0.549131i | \(-0.185041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.8320 | + | 24.8320i | −0.936557 | + | 0.936557i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.02543 | + | 7.02543i | −0.264218 | + | 0.264218i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.58258i | − | 0.134546i | −0.997735 | − | 0.0672732i | \(-0.978570\pi\) | ||
0.997735 | − | 0.0672732i | \(-0.0214299\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.1216i | 0.754619i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0143 | + | 13.0143i | 0.487390 | + | 0.487390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.50012 | + | 6.50012i | 0.242751 | + | 0.242751i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 10.9129i | − | 0.406982i | −0.979077 | − | 0.203491i | \(-0.934771\pi\) | ||
0.979077 | − | 0.203491i | \(-0.0652287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.3303i | 0.645414i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.525310 | + | 0.525310i | −0.0195365 | + | 0.0195365i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.4978 | + | 30.4978i | −1.13110 | + | 1.13110i | −0.141108 | + | 0.989994i | \(0.545067\pi\) |
−0.989994 | + | 0.141108i | \(0.954933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.3739i | 0.606439i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −71.4083 | −2.64113 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.8997 | − | 34.8997i | 1.28905 | − | 1.28905i | 0.353683 | − | 0.935365i | \(-0.384929\pi\) |
0.935365 | − | 0.353683i | \(-0.115071\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.3714 | + | 6.19115i | 1.04507 | + | 0.228054i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5390 | 0.534826 | 0.267413 | − | 0.963582i | \(-0.413831\pi\) | ||||
0.267413 | + | 0.963582i | \(0.413831\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.13068 | −0.298688 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.9864 | + | 19.9864i | −0.733229 | + | 0.733229i | −0.971258 | − | 0.238029i | \(-0.923499\pi\) |
0.238029 | + | 0.971258i | \(0.423499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.5762 | − | 14.5762i | −0.533314 | − | 0.533314i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.28674i | − | 0.0470165i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.7042 | −1.70426 | −0.852130 | − | 0.523331i | \(-0.824689\pi\) | ||||
−0.852130 | + | 0.523331i | \(0.824689\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.766857 | + | 0.766857i | 0.0279458 | + | 0.0279458i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.84291 | + | 8.84291i | −0.321401 | + | 0.321401i | −0.849304 | − | 0.527904i | \(-0.822978\pi\) |
0.527904 | + | 0.849304i | \(0.322978\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.12159 | − | 3.28674i | 0.185902 | − | 0.119301i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.66970i | 0.278026i | 0.990291 | + | 0.139013i | \(0.0443930\pi\) | ||||
−0.990291 | + | 0.139013i | \(0.955607\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.46629 | + | 1.46629i | 0.0530833 | + | 0.0530833i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.6016 | − | 21.6016i | −0.779988 | − | 0.779988i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.7477 | 0.784243 | 0.392122 | − | 0.919913i | \(-0.371741\pi\) | ||||
0.392122 | + | 0.919913i | \(0.371741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.834849 | −0.0300663 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.3571 | + | 15.3571i | 0.552356 | + | 0.552356i | 0.927120 | − | 0.374764i | \(-0.122276\pi\) |
−0.374764 | + | 0.927120i | \(0.622276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.89331 | + | 2.89331i | 0.103797 | + | 0.103797i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 25.0000i | − | 0.895718i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.747727 | + | 1.16515i | 0.0267558 | + | 0.0416924i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.6661 | + | 15.6661i | −0.559859 | + | 0.559859i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.92713 | − | 7.92713i | −0.282572 | − | 0.282572i | 0.551562 | − | 0.834134i | \(-0.314032\pi\) |
−0.834134 | + | 0.551562i | \(0.814032\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.71326 | −0.132195 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 22.4519i | − | 0.798297i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.6100 | − | 19.6100i | −0.696371 | − | 0.696371i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.39614 | + | 2.39614i | −0.0848756 | + | 0.0848756i | −0.748270 | − | 0.663394i | \(-0.769115\pi\) |
0.663394 | + | 0.748270i | \(0.269115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.04356 | 0.213806 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.3739 | 0.472542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.13212 | − | 0.901703i | −0.145819 | − | 0.0318204i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.19387 | − | 2.19387i | 0.0772279 | − | 0.0772279i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.8348 | 1.01378 | 0.506890 | − | 0.862011i | \(-0.330795\pi\) | ||||
0.506890 | + | 0.862011i | \(0.330795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.0000i | 0.877869i | 0.898519 | + | 0.438934i | \(0.144644\pi\) | ||||
−0.898519 | + | 0.438934i | \(0.855356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.23882 | + | 1.23882i | −0.0434472 | + | 0.0434472i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.1862 | + | 34.1862i | −1.19602 | + | 1.19602i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 12.6697i | − | 0.442715i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.49545i | 0.121992i | 0.998138 | + | 0.0609961i | \(0.0194277\pi\) | ||||
−0.998138 | + | 0.0609961i | \(0.980572\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.52827 | + | 9.52827i | 0.332135 | + | 0.332135i | 0.853397 | − | 0.521262i | \(-0.174539\pi\) |
−0.521262 | + | 0.853397i | \(0.674539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.2981 | − | 13.2981i | −0.462419 | − | 0.462419i | 0.437028 | − | 0.899448i | \(-0.356031\pi\) |
−0.899448 | + | 0.437028i | \(0.856031\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 45.4519i | − | 1.57861i | −0.614002 | − | 0.789305i | \(-0.710441\pi\) | ||
0.614002 | − | 0.789305i | \(-0.289559\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 3.95644i | − | 0.137247i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.0624 | + | 28.0624i | −0.972306 | + | 0.972306i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.57321 | − | 8.57321i | 0.296334 | − | 0.296334i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.1996i | 1.76761i | 0.467858 | + | 0.883804i | \(0.345026\pi\) | ||||
−0.467858 | + | 0.883804i | \(0.654974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.1216 | 1.41799 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.41862 | + | 3.41862i | −0.117743 | + | 0.117743i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.1492 | + | 4.88491i | −0.451810 | + | 0.167847i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.95644 | −0.307384 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.2087 | 0.966982 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.3744 | − | 34.3744i | 1.17696 | − | 1.17696i | 0.196439 | − | 0.980516i | \(-0.437062\pi\) |
0.980516 | − | 0.196439i | \(-0.0629379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.0456 | + | 32.0456i | 1.09466 | + | 1.09466i | 0.995024 | + | 0.0996339i | \(0.0317672\pi\) |
0.0996339 | + | 0.995024i | \(0.468233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.3303i | 1.51253i | 0.654265 | + | 0.756265i | \(0.272978\pi\) | ||||
−0.654265 | + | 0.756265i | \(0.727022\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.91288 | −0.0992706 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.3766 | − | 10.3766i | −0.353224 | − | 0.353224i | 0.508084 | − | 0.861308i | \(-0.330354\pi\) |
−0.861308 | + | 0.508084i | \(0.830354\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.1267 | + | 12.1267i | −0.411843 | + | 0.411843i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.9129 | + | 20.1216i | 0.438039 | + | 0.682578i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1652i | 1.05599i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.35414 | − | 9.35414i | −0.316590 | − | 0.316590i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.8711 | + | 11.8711i | 0.400857 | + | 0.400857i | 0.878535 | − | 0.477678i | \(-0.158521\pi\) |
−0.477678 | + | 0.878535i | \(0.658521\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.91288 | −0.266895 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.04356 | −0.237304 | −0.118652 | − | 0.992936i | \(-0.537857\pi\) | ||||
−0.118652 | + | 0.992936i | \(0.537857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.2647 | − | 31.2647i | −1.05214 | − | 1.05214i | −0.998564 | − | 0.0535774i | \(-0.982938\pi\) |
−0.0535774 | − | 0.998564i | \(-0.517062\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.0795 | + | 37.0795i | 1.24501 | + | 1.24501i | 0.957898 | + | 0.287108i | \(0.0926940\pi\) |
0.287108 | + | 0.957898i | \(0.407306\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.4955i | 0.620318i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.8348 | + | 20.0000i | 0.429984 | + | 0.670025i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.89331 | − | 2.89331i | 0.0968208 | − | 0.0968208i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.61815 | + | 4.61815i | 0.154196 | + | 0.154196i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3739 | −1.27984 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 74.0780i | − | 2.46790i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.98320 | + | 3.98320i | 0.132553 | + | 0.132553i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.8263 | − | 22.8263i | 0.757936 | − | 0.757936i | −0.218010 | − | 0.975946i | \(-0.569957\pi\) |
0.975946 | + | 0.218010i | \(0.0699567\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.7477 | 0.721327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.7477 | −1.15124 | −0.575622 | − | 0.817716i | \(-0.695240\pi\) | ||||
−0.575622 | + | 0.817716i | \(0.695240\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.9303 | − | 5.22202i | −0.791978 | − | 0.172824i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.04222 | − | 3.04222i | 0.100463 | − | 0.100463i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.3303 | 1.39635 | 0.698174 | − | 0.715928i | \(-0.253996\pi\) | ||||
0.698174 | + | 0.715928i | \(0.253996\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.5390i | 0.479077i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.05062 | + | 1.05062i | −0.0345816 | + | 0.0345816i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.8236 | − | 26.8236i | 0.881003 | − | 0.881003i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.3303i | 1.09353i | 0.837286 | + | 0.546766i | \(0.184141\pi\) | ||||
−0.837286 | + | 0.546766i | \(0.815859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.8693i | 0.880606i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.19954 | − | 4.19954i | −0.137487 | − | 0.137487i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.03383 | + | 5.03383i | 0.164448 | + | 0.164448i | 0.784534 | − | 0.620086i | \(-0.212902\pi\) |
−0.620086 | + | 0.784534i | \(0.712902\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.91288i | 0.192959i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.5826i | − | 0.670973i | −0.942045 | − | 0.335486i | \(-0.891099\pi\) | ||
0.942045 | − | 0.335486i | \(-0.108901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.1998 | + | 14.1998i | −0.462408 | + | 0.462408i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.6913 | + | 12.6913i | −0.412411 | + | 0.412411i | −0.882578 | − | 0.470167i | \(-0.844194\pi\) |
0.470167 | + | 0.882578i | \(0.344194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.53901i | − | 0.147343i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.9564 | 0.484996 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.41022 | + | 5.41022i | −0.175254 | + | 0.175254i | −0.789283 | − | 0.614029i | \(-0.789548\pi\) |
0.614029 | + | 0.789283i | \(0.289548\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.70511 | + | 12.3964i | −0.0874438 | + | 0.400718i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.33030 | 0.236708 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0000 | −0.322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.99160 | + | 1.99160i | −0.0641785 | + | 0.0641785i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.1269 | + | 22.1269i | 0.711553 | + | 0.711553i | 0.966860 | − | 0.255307i | \(-0.0821765\pi\) |
−0.255307 | + | 0.966860i | \(0.582176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.8693i | 0.541921i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5390 | −0.338213 | −0.169107 | − | 0.985598i | \(-0.554088\pi\) | ||||
−0.169107 | + | 0.985598i | \(0.554088\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.6100 | + | 19.6100i | 0.628667 | + | 0.628667i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.308970 | − | 0.308970i | 0.00988482 | − | 0.00988482i | −0.702147 | − | 0.712032i | \(-0.747775\pi\) |
0.712032 | + | 0.702147i | \(0.247775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.3739 | − | 8.58258i | 0.427431 | − | 0.274300i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.53901i | − | 0.144920i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.915775 | − | 0.915775i | −0.0292087 | − | 0.0292087i | 0.692352 | − | 0.721560i | \(-0.256575\pi\) |
−0.721560 | + | 0.692352i | \(0.756575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.337114 | − | 0.337114i | −0.0107305 | − | 0.0107305i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.8348 | 1.23488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.20871 | 0.292524 | 0.146262 | − | 0.989246i | \(-0.453276\pi\) | ||||
0.146262 | + | 0.989246i | \(0.453276\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.323042 | − | 0.323042i | −0.0102514 | − | 0.0102514i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.8797 | + | 22.8797i | 0.724607 | + | 0.724607i | 0.969540 | − | 0.244933i | \(-0.0787660\pi\) |
−0.244933 | + | 0.969540i | \(0.578766\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 18.5826i | − | 0.587927i |
(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 | 1100.2.k.d.593.3 | yes | 8 | |
5.2 | odd | 4 | 1100.2.k.e.857.3 | yes | 8 | ||
5.3 | odd | 4 | 1100.2.k.e.857.2 | yes | 8 | ||
5.4 | even | 2 | inner | 1100.2.k.d.593.2 | ✓ | 8 | |
11.10 | odd | 2 | 1100.2.k.e.593.3 | yes | 8 | ||
55.32 | even | 4 | inner | 1100.2.k.d.857.3 | yes | 8 | |
55.43 | even | 4 | inner | 1100.2.k.d.857.2 | yes | 8 | |
55.54 | odd | 2 | 1100.2.k.e.593.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1100.2.k.d.593.2 | ✓ | 8 | 5.4 | even | 2 | inner | |
1100.2.k.d.593.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1100.2.k.d.857.2 | yes | 8 | 55.43 | even | 4 | inner | |
1100.2.k.d.857.3 | yes | 8 | 55.32 | even | 4 | inner | |
1100.2.k.e.593.2 | yes | 8 | 55.54 | odd | 2 | ||
1100.2.k.e.593.3 | yes | 8 | 11.10 | odd | 2 | ||
1100.2.k.e.857.2 | yes | 8 | 5.3 | odd | 4 | ||
1100.2.k.e.857.3 | yes | 8 | 5.2 | odd | 4 |