Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [816,2,Mod(47,816)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(816, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("816.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 816 = 2^{4} \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 816.bf (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: | \(6.51579280494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(-0.535233 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 816.191 |
Dual form | 816.2.bf.c.47.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/816\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(511\) | \(545\) | \(613\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.618034 | − | 1.61803i | −0.356822 | − | 0.934172i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73205 | − | 1.73205i | −0.774597 | − | 0.774597i | 0.204310 | − | 0.978906i | \(-0.434505\pi\) |
−0.978906 | + | 0.204310i | \(0.934505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 1.73205i | 0.654654 | − | 0.654654i | −0.299456 | − | 0.954110i | \(-0.596805\pi\) |
0.954110 | + | 0.299456i | \(0.0968053\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | + | 2.00000i | −0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.00000i | −0.301511 | − | 0.301511i | 0.540094 | − | 0.841605i | \(-0.318389\pi\) |
−0.841605 | + | 0.540094i | \(0.818389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.73205 | + | 3.87298i | −0.447214 | + | 1.00000i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.23607 | − | 3.46410i | −0.542326 | − | 0.840168i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00803 | −0.231259 | −0.115629 | − | 0.993292i | \(-0.536889\pi\) | ||||
−0.115629 | + | 0.993292i | \(0.536889\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.87298 | − | 1.73205i | −0.845154 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.87298 | + | 1.87298i | 0.390544 | + | 0.390544i | 0.874881 | − | 0.484337i | \(-0.160939\pi\) |
−0.484337 | + | 0.874881i | \(0.660939\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.61803 | + | 2.38197i | 0.888741 | + | 0.458410i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.74009 | − | 2.74009i | −0.508821 | − | 0.508821i | 0.405343 | − | 0.914164i | \(-0.367152\pi\) |
−0.914164 | + | 0.405343i | \(0.867152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.20419 | + | 6.20419i | 1.11430 | + | 1.11430i | 0.992562 | + | 0.121743i | \(0.0388484\pi\) |
0.121743 | + | 0.992562i | \(0.461152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | + | 2.23607i | −0.174078 | + | 0.389249i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | −1.01419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.87298 | + | 3.87298i | −0.636715 | + | 0.636715i | −0.949744 | − | 0.313029i | \(-0.898656\pi\) |
0.313029 | + | 0.949744i | \(0.398656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.23607 | + | 3.23607i | 0.197929 | + | 0.518186i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.70820 | + | 6.70820i | −1.04765 | + | 1.04765i | −0.0488388 | + | 0.998807i | \(0.515552\pi\) |
−0.998807 | + | 0.0488388i | \(0.984448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00803 | 0.153724 | 0.0768619 | − | 0.997042i | \(-0.475510\pi\) | ||||
0.0768619 | + | 0.997042i | \(0.475510\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.33708 | + | 0.408882i | 1.09375 | + | 0.0609525i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.22307 | + | 5.75897i | −0.591348 | + | 0.806417i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4003 | −1.56596 | −0.782979 | − | 0.622049i | \(-0.786301\pi\) | ||||
−0.782979 | + | 0.622049i | \(0.786301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46410i | 0.467099i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.622999 | + | 1.63103i | 0.0825183 | + | 0.216036i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.7460i | − | 1.52919i | −0.644508 | − | 0.764597i | \(-0.722938\pi\) | ||
0.644508 | − | 0.764597i | \(-0.277062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.127017 | + | 0.127017i | 0.0162628 | + | 0.0162628i | 0.715191 | − | 0.698929i | \(-0.246339\pi\) |
−0.698929 | + | 0.715191i | \(0.746339\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.408882 | + | 7.33708i | −0.0515143 | + | 0.924386i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.46410 | + | 3.46410i | 0.429669 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.46410i | − | 0.423207i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) | ||
0.977356 | − | 0.211604i | \(-0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.87298 | − | 4.18812i | 0.225481 | − | 0.504190i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.87298 | + | 5.87298i | −0.696995 | + | 0.696995i | −0.963761 | − | 0.266766i | \(-0.914045\pi\) |
0.266766 | + | 0.963761i | \(0.414045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.7460 | − | 10.7460i | 1.25772 | − | 1.25772i | 0.305542 | − | 0.952179i | \(-0.401163\pi\) |
0.952179 | − | 0.305542i | \(-0.0988375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.61803 | − | 0.618034i | 0.186834 | − | 0.0713644i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | −0.394771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.20419 | + | 6.20419i | −0.698026 | + | 0.698026i | −0.963984 | − | 0.265959i | \(-0.914311\pi\) |
0.265959 | + | 0.963984i | \(0.414311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.74597i | − | 0.411173i | −0.978639 | − | 0.205587i | \(-0.934090\pi\) | ||
0.978639 | − | 0.205587i | \(-0.0659102\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.12702 | + | 9.87298i | −0.230707 | + | 1.07088i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.74009 | + | 6.12702i | −0.293768 | + | 0.656885i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.01607i | − | 0.213703i | −0.994275 | − | 0.106851i | \(-0.965923\pi\) | ||
0.994275 | − | 0.106851i | \(-0.0340769\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.46410 | + | 3.46410i | −0.363137 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.20419 | − | 13.8730i | 0.643344 | − | 1.43856i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.74597 | + | 1.74597i | 0.179132 | + | 0.179132i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | + | 3.00000i | −0.304604 | + | 0.304604i | −0.842812 | − | 0.538208i | \(-0.819101\pi\) |
0.538208 | + | 0.842812i | \(0.319101\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.23607 | + | 0.236068i | 0.425741 | + | 0.0237257i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.93624i | 0.789685i | 0.918749 | + | 0.394843i | \(0.129201\pi\) | ||||
−0.918749 | + | 0.394843i | \(0.870799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.3366i | − | 1.90529i | −0.304085 | − | 0.952645i | \(-0.598351\pi\) | ||
0.304085 | − | 0.952645i | \(-0.401649\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.70820 | + | 9.70820i | 0.361884 | + | 0.947424i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.7460 | − | 10.7460i | 1.03885 | − | 1.03885i | 0.0396377 | − | 0.999214i | \(-0.487380\pi\) |
0.999214 | − | 0.0396377i | \(-0.0126204\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.127017 | + | 0.127017i | 0.0121660 | + | 0.0121660i | 0.713164 | − | 0.700998i | \(-0.247262\pi\) |
−0.700998 | + | 0.713164i | \(0.747262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.66025 | + | 3.87298i | 0.821995 | + | 0.367607i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1723 | − | 10.1723i | 0.956930 | − | 0.956930i | −0.0421800 | − | 0.999110i | \(-0.513430\pi\) |
0.999110 | + | 0.0421800i | \(0.0134303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.48820i | − | 0.605028i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.47214 | − | 4.00000i | 0.413449 | − | 0.369800i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.87298 | − | 2.12702i | −0.905055 | − | 0.194983i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.0000 | + | 6.70820i | 1.35250 | + | 0.604858i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | + | 6.92820i | −0.619677 | + | 0.619677i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.622999 | − | 1.63103i | −0.0548520 | − | 0.143605i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.00000 | − | 5.00000i | 0.436852 | − | 0.436852i | −0.454099 | − | 0.890951i | \(-0.650039\pi\) |
0.890951 | + | 0.454099i | \(0.150039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.74597 | + | 1.74597i | −0.151395 | + | 0.151395i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.87298 | − | 12.1244i | −0.333333 | − | 1.04350i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.94427i | 0.764161i | 0.924129 | + | 0.382080i | \(0.124792\pi\) | ||||
−0.924129 | + | 0.382080i | \(0.875208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.15624 | − | 8.15624i | −0.691803 | − | 0.691803i | 0.270825 | − | 0.962628i | \(-0.412703\pi\) |
−0.962628 | + | 0.270825i | \(0.912703\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.47214 | + | 6.47214i | 0.208191 | + | 0.545052i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | + | 2.00000i | 0.167248 | + | 0.167248i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.49193i | 0.788262i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.61803 | − | 0.618034i | 0.133453 | − | 0.0509746i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.95231i | − | 0.815325i | −0.913133 | − | 0.407662i | \(-0.866344\pi\) | ||
0.913133 | − | 0.407662i | \(-0.133656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.01607 | −0.164065 | −0.0820327 | − | 0.996630i | \(-0.526141\pi\) | ||||
−0.0820327 | + | 0.996630i | \(0.526141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.9282 | + | 3.27383i | 0.964338 | + | 0.264674i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 21.4919i | − | 1.72627i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.04580 | + | 18.4461i | 0.558768 | + | 1.46287i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.48820 | 0.511342 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6284 | + | 12.6284i | −0.989130 | + | 0.989130i | −0.999942 | − | 0.0108111i | \(-0.996559\pi\) |
0.0108111 | + | 0.999942i | \(0.496559\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.60503 | − | 2.14093i | 0.436351 | − | 0.166671i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.6190 | − | 17.6190i | 1.36340 | − | 1.36340i | 0.493846 | − | 0.869550i | \(-0.335591\pi\) |
0.869550 | − | 0.493846i | \(-0.164409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.25403 | − | 2.01607i | 0.172370 | − | 0.154173i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1324 | + | 13.1324i | 0.998437 | + | 0.998437i | 0.999999 | − | 0.00156166i | \(-0.000497091\pi\) |
−0.00156166 | + | 0.999999i | \(0.500497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | + | 1.73205i | 0.130931 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.0054 | + | 7.25941i | −1.42853 | + | 0.545650i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 11.7460i | − | 0.877935i | −0.898503 | − | 0.438967i | \(-0.855344\pi\) | ||
0.898503 | − | 0.438967i | \(-0.144656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.12702 | − | 2.12702i | −0.158100 | − | 0.158100i | 0.623624 | − | 0.781724i | \(-0.285660\pi\) |
−0.781724 | + | 0.623624i | \(0.785660\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.127017 | − | 0.284018i | 0.00938934 | − | 0.0209952i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4164 | 0.986394 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.22803 | + | 5.70017i | −0.0898027 | + | 0.416838i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.1244 | − | 3.87298i | 0.881917 | − | 0.281718i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4919 | − | 18.4919i | −1.33108 | − | 1.33108i | −0.904406 | − | 0.426672i | \(-0.859686\pi\) |
−0.426672 | − | 0.904406i | \(-0.640314\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.46410 | − | 7.74597i | 0.248069 | − | 0.554700i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.724016 | + | 0.724016i | −0.0515840 | + | 0.0515840i | −0.732428 | − | 0.680844i | \(-0.761613\pi\) |
0.680844 | + | 0.732428i | \(0.261613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.73205 | − | 1.73205i | −0.122782 | − | 0.122782i | 0.643046 | − | 0.765828i | \(-0.277670\pi\) |
−0.765828 | + | 0.643046i | \(0.777670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.60503 | + | 2.14093i | −0.395349 | + | 0.151010i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.49193 | −0.666203 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.2379 | 1.62301 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.93408 | − | 0.442151i | −0.551457 | − | 0.0307316i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00803 | + | 1.00803i | 0.0697272 | + | 0.0697272i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.15624 | − | 8.15624i | 0.561499 | − | 0.561499i | −0.368234 | − | 0.929733i | \(-0.620038\pi\) |
0.929733 | + | 0.368234i | \(0.120038\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.1324 | + | 5.87298i | 0.899817 | + | 0.402410i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.74597 | − | 1.74597i | −0.119074 | − | 0.119074i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.4919 | 1.45897 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.0287 | − | 10.7460i | −1.62371 | − | 0.726145i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.47214 | + | 6.92820i | 0.300828 | + | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.8007 | 1.52685 | 0.763423 | − | 0.645899i | \(-0.223517\pi\) | ||||
0.763423 | + | 0.645899i | \(0.223517\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | − | 2.23607i | −0.133333 | − | 0.149071i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7460 | + | 12.7460i | 0.845980 | + | 0.845980i | 0.989629 | − | 0.143649i | \(-0.0458837\pi\) |
−0.143649 | + | 0.989629i | \(0.545884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.2379i | − | 1.66777i | −0.551940 | − | 0.833884i | \(-0.686112\pi\) | ||
0.551940 | − | 0.833884i | \(-0.313888\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.14093 | + | 5.60503i | 0.140863 | + | 0.368784i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.6364 | − | 13.6364i | −0.893351 | − | 0.893351i | 0.101486 | − | 0.994837i | \(-0.467640\pi\) |
−0.994837 | + | 0.101486i | \(0.967640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.92820 | + | 6.92820i | 0.451946 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8730 | + | 6.20419i | 0.901147 | + | 0.403005i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | − | 1.00000i | 0.0644157 | − | 0.0644157i | −0.674165 | − | 0.738581i | \(-0.735496\pi\) |
0.738581 | + | 0.674165i | \(0.235496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.0902 | + | 3.90983i | −0.968035 | + | 0.250816i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.73205 | − | 1.73205i | 0.110657 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.01607 | 0.128279 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.06110 | + | 2.31513i | −0.384107 | + | 0.146716i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.74597 | 0.110204 | 0.0551022 | − | 0.998481i | \(-0.482452\pi\) | ||||
0.0551022 | + | 0.998481i | \(0.482452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.74597i | − | 0.235507i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.2894 | − | 2.66025i | 1.08270 | − | 0.166592i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.47214 | −0.278964 | −0.139482 | − | 0.990225i | \(-0.544544\pi\) | ||||
−0.139482 | + | 0.990225i | \(0.544544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.4164i | 0.833655i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.6072 | + | 0.646846i | 0.718467 | + | 0.0400388i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2540i | 1.00227i | 0.865370 | + | 0.501133i | \(0.167083\pi\) | ||||
−0.865370 | + | 0.501133i | \(0.832917\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.7460 | + | 19.7460i | 1.21299 | + | 1.21299i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.26207 | + | 1.24600i | −0.199635 | + | 0.0762539i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.18812 | + | 4.18812i | 0.255354 | + | 0.255354i | 0.823161 | − | 0.567807i | \(-0.192208\pi\) |
−0.567807 | + | 0.823161i | \(0.692208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.46410i | 0.210429i | 0.994450 | + | 0.105215i | \(0.0335529\pi\) | ||||
−0.994450 | + | 0.105215i | \(0.966447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.74597 | + | 3.46410i | 0.468807 | + | 0.209657i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | − | 1.00000i | 0.0603023 | − | 0.0603023i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.1270 | − | 12.1270i | 0.728642 | − | 0.728642i | −0.241707 | − | 0.970349i | \(-0.577707\pi\) |
0.970349 | + | 0.241707i | \(0.0777074\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.2814 | − | 1.46461i | −1.57342 | − | 0.0876839i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.2407 | 1.38642 | 0.693211 | − | 0.720734i | \(-0.256195\pi\) | ||||
0.693211 | + | 0.720734i | \(0.256195\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1803 | − | 11.1803i | 0.664602 | − | 0.664602i | −0.291859 | − | 0.956461i | \(-0.594274\pi\) |
0.956461 | + | 0.291859i | \(0.0942738\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.74597 | − | 3.90410i | 0.103422 | − | 0.231259i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.2379i | 1.37169i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | + | 15.4919i | −0.411765 | + | 0.911290i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.70820 | + | 3.00000i | 0.393242 | + | 0.175863i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.93624i | 0.463640i | 0.972759 | + | 0.231820i | \(0.0744680\pi\) | ||||
−0.972759 | + | 0.231820i | \(0.925532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.3446 | + | 20.3446i | −1.18451 | + | 1.18451i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.23607 | − | 7.00000i | −0.129750 | − | 0.406181i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.74597 | − | 3.74597i | −0.216635 | − | 0.216635i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.74597 | − | 1.74597i | 0.100636 | − | 0.100636i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.8411 | − | 4.90486i | 0.737702 | − | 0.281777i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.439999i | − | 0.0251942i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.3205i | − | 0.988534i | −0.869310 | − | 0.494267i | \(-0.835437\pi\) | ||
0.869310 | − | 0.494267i | \(-0.164563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.2872 | + | 11.9507i | −1.77987 | + | 0.679849i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1270 | − | 10.1270i | 0.574250 | − | 0.574250i | −0.359063 | − | 0.933313i | \(-0.616904\pi\) |
0.933313 | + | 0.359063i | \(0.116904\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.7460 | − | 16.7460i | −0.946538 | − | 0.946538i | 0.0521037 | − | 0.998642i | \(-0.483407\pi\) |
−0.998642 | + | 0.0521037i | \(0.983407\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.4164 | − | 12.0000i | 0.755929 | − | 0.676123i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.6045 | + | 17.6045i | −0.988769 | + | 0.988769i | −0.999938 | − | 0.0111689i | \(-0.996445\pi\) |
0.0111689 | + | 0.999938i | \(0.496445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.48017i | 0.306831i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0287 | − | 10.7460i | −1.34115 | − | 0.599781i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.25403 | + | 3.49193i | 0.125418 | + | 0.194296i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.00000i | − | 0.110940i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.127017 | − | 0.284018i | 0.00702404 | − | 0.0157062i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.92820 | + | 6.92820i | −0.381964 | + | 0.381964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8805 | −0.927837 | −0.463918 | − | 0.885878i | \(-0.653557\pi\) | ||||
−0.463918 | + | 0.885878i | \(0.653557\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.914287 | − | 16.4062i | 0.0501026 | − | 0.899055i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | + | 6.00000i | −0.327815 | + | 0.327815i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.4919 | + | 18.4919i | −1.00732 | + | 1.00732i | −0.00734679 | + | 0.999973i | \(0.502339\pi\) |
−0.999973 | + | 0.00734679i | \(0.997661\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.7460 | − | 10.1723i | −1.23539 | − | 0.552484i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.4084i | − | 0.671951i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8564 | + | 13.8564i | 0.748176 | + | 0.748176i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.4981 | + | 4.00993i | −0.565201 | + | 0.215887i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0000 | + | 15.0000i | 0.805242 | + | 0.805242i | 0.983910 | − | 0.178667i | \(-0.0571786\pi\) |
−0.178667 | + | 0.983910i | \(0.557179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.2379i | 1.77918i | 0.456756 | + | 0.889592i | \(0.349011\pi\) | ||||
−0.456756 | + | 0.889592i | \(0.650989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.23607 | − | 4.76393i | −0.492985 | − | 0.254280i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 20.7846i | − | 1.10625i | −0.833097 | − | 0.553127i | \(-0.813435\pi\) | ||
0.833097 | − | 0.553127i | \(-0.186565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3446 | 1.07978 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.66025 | + | 17.2894i | 0.140796 | + | 0.915052i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.7460i | − | 1.46438i | −0.681103 | − | 0.732188i | \(-0.738499\pi\) | ||
0.681103 | − | 0.732188i | \(-0.261501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9839 | −0.946519 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.5623 | + | 5.56231i | −0.764323 | + | 0.291945i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −37.2251 | −1.94845 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.74009 | − | 2.74009i | 0.143031 | − | 0.143031i | −0.631965 | − | 0.774997i | \(-0.717752\pi\) |
0.774997 | + | 0.631965i | \(0.217752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.58359 | − | 28.4164i | 0.0824385 | − | 1.47930i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.7460 | + | 19.7460i | −1.02516 | + | 1.02516i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0000 | −0.932005 | −0.466002 | − | 0.884783i | \(-0.654306\pi\) | ||||
−0.466002 | + | 0.884783i | \(0.654306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.4919 | + | 6.92820i | 0.800000 | + | 0.357771i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.48017 | + | 5.48017i | 0.282243 | + | 0.282243i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1884 | − | 12.1884i | −0.626075 | − | 0.626075i | 0.321003 | − | 0.947078i | \(-0.395980\pi\) |
−0.947078 | + | 0.321003i | \(0.895980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.2379i | 1.18740i | 0.804686 | + | 0.593701i | \(0.202334\pi\) | ||||
−0.804686 | + | 0.593701i | \(0.797666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 6.00000i | 0.305788 | + | 0.305788i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.25403 | + | 2.01607i | −0.114579 | + | 0.102483i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.4325 | −0.782458 | −0.391229 | − | 0.920293i | \(-0.627950\pi\) | ||||
−0.391229 | + | 0.920293i | \(0.627950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.30009 | − | 10.6763i | 0.116320 | − | 0.539925i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.1803 | − | 5.00000i | −0.563974 | − | 0.252217i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.4919 | 1.08138 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.3649 | − | 15.3649i | −0.771143 | − | 0.771143i | 0.207163 | − | 0.978306i | \(-0.433577\pi\) |
−0.978306 | + | 0.207163i | \(0.933577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.90410 | + | 1.74597i | 0.195449 | + | 0.0874077i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0844 | − | 15.0844i | 0.753281 | − | 0.753281i | −0.221809 | − | 0.975090i | \(-0.571196\pi\) |
0.975090 | + | 0.221809i | \(0.0711962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.4084 | − | 12.4084i | −0.618105 | − | 0.618105i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.2240 | + | 13.7599i | −0.855867 | + | 0.683734i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.74597 | 0.383953 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.49193 | 0.0737714 | 0.0368857 | − | 0.999319i | \(-0.488256\pi\) | ||||
0.0368857 | + | 0.999319i | \(0.488256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.4721 | − | 5.52786i | 0.713858 | − | 0.272669i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.3446 | − | 20.3446i | −1.00109 | − | 1.00109i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.48820 | + | 6.48820i | −0.318493 | + | 0.318493i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.15624 | + | 18.2379i | −0.399413 | + | 0.893114i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.2379 | + | 20.2379i | 0.988686 | + | 0.988686i | 0.999937 | − | 0.0112506i | \(-0.00358125\pi\) |
−0.0112506 | + | 0.999937i | \(0.503581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.9839 | 1.41259 | 0.706294 | − | 0.707919i | \(-0.250366\pi\) | ||||
0.706294 | + | 0.707919i | \(0.250366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.94427 | − | 8.00000i | 0.434885 | − | 0.388973i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | − | 2.23607i | 0.168034 | − | 0.108465i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.439999 | 0.0212930 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.00000 | − | 4.47214i | 0.0965609 | − | 0.215917i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1270 | + | 12.1270i | 0.584138 | + | 0.584138i | 0.936038 | − | 0.351900i | \(-0.114464\pi\) |
−0.351900 | + | 0.936038i | \(0.614464\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0000i | 1.53782i | 0.639356 | + | 0.768911i | \(0.279201\pi\) | ||||
−0.639356 | + | 0.768911i | \(0.720799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.3583 | − | 5.86634i | 0.736373 | − | 0.281269i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.88803 | − | 1.88803i | −0.0903168 | − | 0.0903168i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.284018 | + | 0.284018i | 0.0135554 | + | 0.0135554i | 0.713852 | − | 0.700297i | \(-0.246949\pi\) |
−0.700297 | + | 0.713852i | \(0.746949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | − | 2.23607i | −0.0952381 | − | 0.106479i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.2379 | −1.38913 | −0.694567 | − | 0.719428i | \(-0.744404\pi\) | ||||
−0.694567 | + | 0.719428i | \(0.744404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.49193 | + | 3.49193i | −0.165534 | + | 0.165534i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.1032 | + | 6.15086i | −0.761654 | + | 0.290926i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1005 | − | 17.1005i | 0.807023 | − | 0.807023i | −0.177159 | − | 0.984182i | \(-0.556691\pi\) |
0.984182 | + | 0.177159i | \(0.0566908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.4164 | 0.631754 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.24600 | + | 3.26207i | 0.0585421 | + | 0.153265i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | 0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.49193i | − | 0.163346i | −0.996659 | − | 0.0816729i | \(-0.973974\pi\) | ||
0.996659 | − | 0.0816729i | \(-0.0260263\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.07487 | − | 21.3236i | −0.0968464 | − | 0.995299i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4003 | −0.530967 | −0.265483 | − | 0.964115i | \(-0.585532\pi\) | ||||
−0.265483 | + | 0.964115i | \(0.585532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 19.3366i | − | 0.898647i | −0.893369 | − | 0.449323i | \(-0.851665\pi\) | ||
0.893369 | − | 0.449323i | \(-0.148335\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −34.7747 | + | 13.2827i | −1.61264 | + | 0.615973i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.2379i | 0.890224i | 0.895475 | + | 0.445112i | \(0.146836\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | − | 6.00000i | −0.277054 | − | 0.277054i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.23607 | + | 3.23607i | 0.0569550 | + | 0.149110i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00803 | − | 1.00803i | −0.0463495 | − | 0.0463495i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.00803i | − | 0.0462518i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.4919 | − | 22.8007i | 1.16720 | − | 1.04397i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6190 | + | 19.6190i | −0.896413 | + | 0.896413i | −0.995117 | − | 0.0987041i | \(-0.968530\pi\) |
0.0987041 | + | 0.995117i | \(0.468530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.74597 | − | 7.74597i | 0.353186 | − | 0.353186i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00993 | − | 10.4981i | −0.182458 | − | 0.477682i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3923 | 0.471890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.74812 | − | 3.74812i | 0.169844 | − | 0.169844i | −0.617067 | − | 0.786911i | \(-0.711679\pi\) |
0.786911 | + | 0.617067i | \(0.211679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.2379 | + | 12.6284i | 1.27696 | + | 0.571075i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.25403i | 0.191982i | 0.995382 | + | 0.0959909i | \(0.0306020\pi\) | ||||
−0.995382 | + | 0.0959909i | \(0.969398\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.36492 | + | 15.6190i | −0.151548 | + | 0.703442i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.92820 | − | 7.74597i | −0.311400 | − | 0.348155i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.3446i | 0.912581i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.5887 | + | 23.5887i | −1.05598 | + | 1.05598i | −0.0576383 | + | 0.998338i | \(0.518357\pi\) |
−0.998338 | + | 0.0576383i | \(0.981643\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.3972 | − | 17.6190i | −1.76014 | − | 0.787157i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.87298 | + | 5.87298i | 0.261863 | + | 0.261863i | 0.825811 | − | 0.563947i | \(-0.190718\pi\) |
−0.563947 | + | 0.825811i | \(0.690718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.7460 | − | 13.7460i | 0.611687 | − | 0.611687i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.56231 | + | 14.5623i | 0.247031 | + | 0.646735i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 39.6812i | − | 1.75884i | −0.476049 | − | 0.879419i | \(-0.657931\pi\) | ||
0.476049 | − | 0.879419i | \(-0.342069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 37.2251i | − | 1.64674i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.65514 | − | 2.40110i | −0.205529 | − | 0.106011i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −33.4919 | + | 33.4919i | −1.47583 | + | 1.47583i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000 | + | 4.00000i | 0.175920 | + | 0.175920i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1324 | − | 29.3649i | 0.576448 | − | 1.28898i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0764 | − | 14.0764i | 0.616699 | − | 0.616699i | −0.327985 | − | 0.944683i | \(-0.606369\pi\) |
0.944683 | + | 0.327985i | \(0.106369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.46410i | − | 0.151475i | −0.997128 | − | 0.0757373i | \(-0.975869\pi\) | ||
0.997128 | − | 0.0757373i | \(-0.0241310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.73205 | − | 3.87298i | 0.0755929 | − | 0.169031i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.61895 | − | 35.3649i | 0.331887 | − | 1.54052i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 15.9839i | − | 0.694951i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.4919 | + | 26.2648i | 1.01946 | + | 1.13979i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4164 | − | 13.4164i | 0.581129 | − | 0.581129i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −37.2251 | −1.60938 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.0054 | + | 7.25941i | −0.820142 | + | 0.313267i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | − | 1.00000i | 0.0430730 | − | 0.0430730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.6190 | + | 17.6190i | −0.757498 | + | 0.757498i | −0.975866 | − | 0.218369i | \(-0.929927\pi\) |
0.218369 | + | 0.975866i | \(0.429927\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.12702 | + | 4.75615i | −0.0912790 | + | 0.204106i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 0.439999i | − | 0.0188475i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.5250 | + | 31.5250i | 1.34791 | + | 1.34791i | 0.887929 | + | 0.459981i | \(0.152144\pi\) |
0.459981 | + | 0.887929i | \(0.347856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.538051 | − | 0.0299846i | −0.0229635 | − | 0.00127971i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.76210 | + | 2.76210i | 0.117669 | + | 0.117669i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.4919i | 0.913930i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.29180 | − | 21.7082i | −0.351967 | − | 0.921462i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.8409i | 1.17965i | 0.807529 | + | 0.589827i | \(0.200804\pi\) | ||||
−0.807529 | + | 0.589827i | \(0.799196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.01607 | −0.0852706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.98203 | − | 1.53590i | 0.421442 | − | 0.0648457i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.2379i | 1.14794i | 0.818876 | + | 0.573970i | \(0.194598\pi\) | ||||
−0.818876 | + | 0.573970i | \(0.805402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.2379 | −1.48247 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.7599 | − | 17.2240i | −0.577861 | − | 0.723339i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.45607 | 0.102964 | 0.0514818 | − | 0.998674i | \(-0.483606\pi\) | ||||
0.0514818 | + | 0.998674i | \(0.483606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.5485 | + | 18.5485i | −0.776232 | + | 0.776232i | −0.979188 | − | 0.202956i | \(-0.934945\pi\) |
0.202956 | + | 0.979188i | \(0.434945\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.3607 | + | 32.3607i | 0.516375 | + | 1.35189i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.87298 | + | 1.87298i | −0.0781088 | + | 0.0781088i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.4919 | 1.39429 | 0.697144 | − | 0.716931i | \(-0.254454\pi\) | ||||
0.697144 | + | 0.716931i | \(0.254454\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.4919 | + | 41.3492i | −0.768499 | + | 1.71841i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.48820 | − | 6.48820i | −0.269176 | − | 0.269176i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.4003 | + | 11.4003i | 0.472154 | + | 0.472154i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.6742 | − | 0.817763i | −0.606702 | − | 0.0338104i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.74597i | − | 0.154613i | −0.997007 | − | 0.0773063i | \(-0.975368\pi\) | ||
0.997007 | − | 0.0773063i | \(-0.0246319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.25403 | − | 6.25403i | −0.257693 | − | 0.257693i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.61895 | + | 0.724016i | 0.0665947 | + | 0.0297821i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.45607 | 0.100859 | 0.0504293 | − | 0.998728i | \(-0.483941\pi\) | ||||
0.0504293 | + | 0.998728i | \(0.483941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.4164 | + | 20.7846i | 0.550019 | + | 0.852086i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.73205 | + | 3.87298i | −0.0708881 | + | 0.158511i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.49193 | −0.142677 | −0.0713383 | − | 0.997452i | \(-0.522727\pi\) | ||||
−0.0713383 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.7460 | − | 28.7460i | −1.17257 | − | 1.17257i | −0.981594 | − | 0.190978i | \(-0.938834\pi\) |
−0.190978 | − | 0.981594i | \(-0.561166\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.92820 | + | 7.74597i | 0.282138 | + | 0.315440i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.5885 | + | 15.5885i | −0.633761 | + | 0.633761i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.74009 | − | 2.74009i | −0.111217 | − | 0.111217i | 0.649309 | − | 0.760525i | \(-0.275058\pi\) |
−0.760525 | + | 0.649309i | \(0.775058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.86634 | + | 15.3583i | 0.237716 | + | 0.622349i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.9839 | 1.17065 | 0.585324 | − | 0.810800i | \(-0.300967\pi\) | ||||
0.585324 | + | 0.810800i | \(0.300967\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.3618 | − | 37.5997i | −0.579124 | − | 1.51617i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.67607 | − | 2.67607i | −0.107734 | − | 0.107734i | 0.651185 | − | 0.758919i | \(-0.274272\pi\) |
−0.758919 | + | 0.651185i | \(0.774272\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.25214 | − | 4.25214i | 0.170908 | − | 0.170908i | −0.616470 | − | 0.787378i | \(-0.711438\pi\) |
0.787378 | + | 0.616470i | \(0.211438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.18812 | + | 13.1109i | 0.168063 | + | 0.526122i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.49193 | − | 3.49193i | −0.139901 | − | 0.139901i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.0000 | 1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.00803 | − | 2.25403i | 0.0402570 | − | 0.0900174i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.0767 | + | 4.75615i | 0.880254 | + | 0.189640i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.89607 | −0.115291 | −0.0576453 | − | 0.998337i | \(-0.518359\pi\) | ||||
−0.0576453 | + | 0.998337i | \(0.518359\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.2379 | − | 8.15624i | −0.724891 | − | 0.324181i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.00000i | − | 0.0792429i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.38642 | − | 24.8784i | 0.0548461 | − | 0.984173i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.9569 | + | 30.9569i | 1.22272 | + | 1.22272i | 0.966660 | + | 0.256065i | \(0.0824261\pi\) |
0.256065 | + | 0.966660i | \(0.417574\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.5089 | + | 29.5089i | 1.16372 | + | 1.16372i | 0.983655 | + | 0.180061i | \(0.0576296\pi\) |
0.180061 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.74597 | + | 3.90410i | −0.0687474 | + | 0.153724i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.4919 | 0.923563 | 0.461782 | − | 0.886994i | \(-0.347210\pi\) | ||||
0.461782 | + | 0.886994i | \(0.347210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.7460 | + | 11.7460i | −0.461070 | + | 0.461070i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2827 | − | 34.7747i | −0.520592 | − | 1.36293i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.1726 | − | 18.1726i | 0.711147 | − | 0.711147i | −0.255628 | − | 0.966775i | \(-0.582282\pi\) |
0.966775 | + | 0.255628i | \(0.0822822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.3205 | −0.676768 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.53678 | + | 45.5206i | −0.0989692 | + | 1.77593i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.7460 | −0.691285 | −0.345642 | − | 0.938366i | \(-0.612339\pi\) | ||||
−0.345642 | + | 0.938366i | \(0.612339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.25403i | − | 0.0876717i | −0.999039 | − | 0.0438359i | \(-0.986042\pi\) | ||
0.999039 | − | 0.0438359i | \(-0.0139579\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.44614 | − | 11.5179i | 0.328021 | − | 0.447319i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.04821 | 0.234539 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.2643i | − | 0.397434i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0916 | − | 36.8923i | −0.544813 | − | 1.42634i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 0.254033i | − | 0.00980685i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.00000 | − | 3.00000i | −0.115642 | − | 0.115642i | 0.646918 | − | 0.762560i | \(-0.276058\pi\) |
−0.762560 | + | 0.646918i | \(0.776058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.38197 | + | 4.61803i | −0.0916819 | + | 0.177748i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.9968 | + | 27.9968i | 1.07601 | + | 1.07601i | 0.996863 | + | 0.0791423i | \(0.0252181\pi\) |
0.0791423 | + | 0.996863i | \(0.474782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3923i | 0.398820i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.7460 | − | 28.5008i | 0.488427 | − | 1.09215i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.7460 | − | 14.7460i | 0.564239 | − | 0.564239i | −0.366270 | − | 0.930509i | \(-0.619365\pi\) |
0.930509 | + | 0.366270i | \(0.119365\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4919 | − | 15.4919i | 0.591916 | − | 0.591916i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.8358 | + | 15.5979i | −1.55798 | + | 0.595096i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.8007 | 0.868637 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.9408 | − | 28.9408i | 1.10096 | − | 1.10096i | 0.106667 | − | 0.994295i | \(-0.465982\pi\) |
0.994295 | − | 0.106667i | \(-0.0340178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.74597 | − | 6.92820i | 0.294245 | − | 0.263181i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.2540i | 1.07174i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.2379 | + | 8.23790i | 1.44836 | + | 0.312033i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.6364 | + | 30.4919i | −0.515776 | + | 1.15331i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.6651i | 1.42259i | 0.702893 | + | 0.711296i | \(0.251891\pi\) | ||||
−0.702893 | + | 0.711296i | \(0.748109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.90410 | − | 3.90410i | 0.147246 | − | 0.147246i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.92820 | − | 15.4919i | 0.260931 | − | 0.583460i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7460 | + | 13.7460i | 0.516970 | + | 0.516970i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.61895 | − | 7.61895i | 0.286136 | − | 0.286136i | −0.549414 | − | 0.835550i | \(-0.685149\pi\) |
0.835550 | + | 0.549414i | \(0.185149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.46461 | − | 26.2814i | 0.0549272 | − | 0.985628i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.2407i | 0.870370i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6.92820i | − | 0.259100i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.41641 | + | 19.4164i | 0.276971 | + | 0.725119i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8730 | − | 11.8730i | 0.442788 | − | 0.442788i | −0.450160 | − | 0.892948i | \(-0.648633\pi\) |
0.892948 | + | 0.450160i | \(0.148633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.4919 | − | 33.4919i | −1.24730 | − | 1.24730i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.23607 | − | 1.00000i | −0.0831603 | − | 0.0371904i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.74009 | − | 2.74009i | 0.101764 | − | 0.101764i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 46.1694i | − | 1.71233i | −0.516704 | − | 0.856164i | \(-0.672841\pi\) | ||
0.516704 | − | 0.856164i | \(-0.327159\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.6525 | + | 22.0000i | 0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.25403 | − | 3.49193i | −0.0833684 | − | 0.129154i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.7460i | − | 0.803206i | −0.915814 | − | 0.401603i | \(-0.868453\pi\) | ||
0.915814 | − | 0.401603i | \(-0.131547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.87298 | − | 1.73205i | −0.142857 | − | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.46410 | + | 3.46410i | −0.127602 | + | 0.127602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.02410 | 0.111243 | 0.0556217 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556217 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.24600 | − | 3.26207i | −0.0457729 | − | 0.119835i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.6190 | − | 37.6190i | 1.38011 | − | 1.38011i | 0.535692 | − | 0.844414i | \(-0.320051\pi\) |
0.844414 | − | 0.535692i | \(-0.179949\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.2379 | + | 17.2379i | −0.631548 | + | 0.631548i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.49193 | + | 8.37624i | 0.274116 | + | 0.306470i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 37.2251i | − | 1.36018i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9727 | + | 24.9727i | 0.911268 | + | 0.911268i | 0.996372 | − | 0.0851043i | \(-0.0271223\pi\) |
−0.0851043 | + | 0.996372i | \(0.527122\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.07907 | − | 2.82503i | −0.0393234 | − | 0.102950i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.49193 | + | 3.49193i | 0.127084 | + | 0.127084i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.25403i | − | 0.0819242i | −0.999161 | − | 0.0409621i | \(-0.986958\pi\) | ||
0.999161 | − | 0.0409621i | \(-0.0130423\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.06110 | + | 2.31513i | −0.220004 | + | 0.0840341i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 22.8007i | − | 0.826524i | −0.910612 | − | 0.413262i | \(-0.864389\pi\) | ||
0.910612 | − | 0.413262i | \(-0.135611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.439999 | 0.0159290 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.9898 | − | 26.3307i | −0.541958 | − | 0.951988i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.4919i | 0.848245i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4919 | 0.630775 | 0.315388 | − | 0.948963i | \(-0.397865\pi\) | ||||
0.315388 | + | 0.948963i | \(0.397865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.76393 | + | 7.23607i | 0.0995406 | + | 0.260601i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.3125 | 0.586719 | 0.293359 | − | 0.956002i | \(-0.405227\pi\) | ||||
0.293359 | + | 0.956002i | \(0.405227\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.20419 | + | 6.20419i | −0.222861 | + | 0.222861i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.7082 | − | 8.29180i | 0.778777 | − | 0.297467i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.76210 | − | 6.76210i | 0.242277 | − | 0.242277i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7460 | 0.420304 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.12702 | − | 19.1806i | −0.218962 | − | 0.685459i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.46410 | + | 3.46410i | 0.123639 | + | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.26821 | − | 6.26821i | −0.223437 | − | 0.223437i | 0.586507 | − | 0.809944i | \(-0.300503\pi\) |
−0.809944 | + | 0.586507i | \(0.800503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.2996 | − | 10.0455i | 0.936290 | − | 0.357631i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 35.2379i | − | 1.25292i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.254033 | − | 0.254033i | −0.00902099 | − | 0.00902099i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.7460 | − | 44.1533i | 0.700317 | − | 1.56596i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.2246 | −0.751814 | −0.375907 | − | 0.926657i | \(-0.622669\pi\) | ||||
−0.375907 | + | 0.926657i | \(0.622669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.94427 | + | 13.8564i | 0.316426 | + | 0.490204i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.03214 | + | 4.50807i | 0.142469 | + | 0.159285i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.4919 | −0.758434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.2379 | − | 11.2379i | −0.396084 | − | 0.396084i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.18812 | − | 9.36492i | 0.147429 | − | 0.329661i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.25214 | − | 4.25214i | 0.149497 | − | 0.149497i | −0.628396 | − | 0.777893i | \(-0.716288\pi\) |
0.777893 | + | 0.628396i | \(0.216288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.9569 | − | 30.9569i | −1.08704 | − | 1.08704i | −0.995831 | − | 0.0912129i | \(-0.970926\pi\) |
−0.0912129 | − | 0.995831i | \(-0.529074\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.60503 | − | 2.14093i | 0.196577 | − | 0.0750858i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.7460 | 1.53235 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01613 | −0.0355500 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.817763 | − | 14.6742i | 0.0285750 | − | 0.512757i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6763 | − | 10.6763i | −0.372606 | − | 0.372606i | 0.495819 | − | 0.868426i | \(-0.334868\pi\) |
−0.868426 | + | 0.495819i | \(0.834868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1565 | + | 16.1565i | −0.563180 | + | 0.563180i | −0.930209 | − | 0.367029i | \(-0.880375\pi\) |
0.367029 | + | 0.930209i | \(0.380375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.23607 | − | 1.00000i | −0.0778499 | − | 0.0348155i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.00000 | + | 3.00000i | 0.104320 | + | 0.104320i | 0.757340 | − | 0.653020i | \(-0.226498\pi\) |
−0.653020 | + | 0.757340i | \(0.726498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0000 | −0.903017 | −0.451509 | − | 0.892267i | \(-0.649114\pi\) | ||||
−0.451509 | + | 0.892267i | \(0.649114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.1168 | − | 12.1270i | −0.940673 | − | 0.420682i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | − | 2.23607i | 0.120024 | − | 0.0774752i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −61.0338 | −2.11216 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.8730 | + | 43.4293i | 0.479520 | + | 1.50114i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.1109 | − | 29.1109i | −1.00502 | − | 1.00502i | −0.999987 | − | 0.00503197i | \(-0.998398\pi\) |
−0.00503197 | − | 0.999987i | \(-0.501602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 13.9839i | − | 0.482202i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.3635 | − | 37.6042i | −0.494706 | − | 1.29516i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.5885 | + | 15.5885i | 0.536259 | + | 0.536259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.5885 | − | 15.5885i | −0.535626 | − | 0.535626i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.0000 | − | 11.1803i | −0.857998 | − | 0.383708i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.5081 | −0.497330 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.1270 | − | 20.1270i | 0.689136 | − | 0.689136i | −0.272905 | − | 0.962041i | \(-0.587984\pi\) |
0.962041 | + | 0.272905i | \(0.0879845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.39603 | − | 0.412167i | −0.252939 | − | 0.0140958i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.5089 | + | 29.5089i | −1.00800 | + | 1.00800i | −0.00803651 | + | 0.999968i | \(0.502558\pi\) |
−0.999968 | + | 0.00803651i | \(0.997442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.7530 | 1.11752 | 0.558759 | − | 0.829330i | \(-0.311278\pi\) | ||||
0.558759 | + | 0.829330i | \(0.311278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.5997 | − | 14.3618i | 1.28139 | − | 0.489449i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.00000 | −0.272323 | −0.136162 | − | 0.990687i | \(-0.543477\pi\) | ||||
−0.136162 | + | 0.990687i | \(0.543477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 45.4919i | − | 1.54677i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.3927 | + | 1.75170i | 0.998229 | + | 0.0594907i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.4084 | 0.420925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.92820i | 0.234753i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.708204 | − | 12.7082i | 0.0239691 | − | 0.430108i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0000i | 0.811348i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.1270 | + | 12.1270i | 0.409500 | + | 0.409500i | 0.881564 | − | 0.472064i | \(-0.156491\pi\) |
−0.472064 | + | 0.881564i | \(0.656491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.8411 | − | 4.90486i | 0.433120 | − | 0.165437i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2044 | + | 14.2044i | 0.478560 | + | 0.478560i | 0.904671 | − | 0.426111i | \(-0.140117\pi\) |
−0.426111 | + | 0.904671i | \(0.640117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.49624i | − | 0.252269i | −0.992013 | − | 0.126134i | \(-0.959743\pi\) | ||
0.992013 | − | 0.126134i | \(-0.0402570\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 45.4919 | + | 20.3446i | 1.52919 | + | 0.683877i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.6190 | − | 29.6190i | 0.994507 | − | 0.994507i | −0.00547798 | − | 0.999985i | \(-0.501744\pi\) |
0.999985 | + | 0.00547798i | \(0.00174371\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.94427 | + | 7.94427i | −0.333146 | + | 0.266143i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.03214 | 0.134930 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.3446 | + | 20.3446i | −0.680045 | + | 0.680045i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.74597 | + | 8.37624i | −0.125074 | + | 0.279674i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 34.0000i | − | 1.13396i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.4919 | + | 39.4919i | 0.849259 | + | 1.31567i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.90410 | − | 1.74597i | −0.129920 | − | 0.0581021i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.36820i | 0.244927i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.9810 | − | 33.9810i | 1.12832 | − | 1.12832i | 0.137871 | − | 0.990450i | \(-0.455974\pi\) |
0.990450 | − | 0.137871i | \(-0.0440259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.8725 | − | 17.7460i | −0.526457 | − | 0.588597i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.3649 | − | 19.3649i | −0.641588 | − | 0.641588i | 0.309357 | − | 0.950946i | \(-0.399886\pi\) |
−0.950946 | + | 0.309357i | \(0.899886\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.74597 | + | 3.74597i | −0.123973 | + | 0.123973i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.711933 | + | 0.271934i | −0.0235358 | + | 0.00898986i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 17.3205i | − | 0.571974i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 46.1694i | − | 1.52299i | −0.648172 | − | 0.761494i | \(-0.724466\pi\) | ||
0.648172 | − | 0.761494i | \(-0.275534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.0252 | + | 10.7047i | −0.923461 | + | 0.352731i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.7460 | − | 11.7460i | 0.386623 | − | 0.386623i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.87298 | − | 3.87298i | −0.127343 | − | 0.127343i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.6732 | + | 43.2379i | 1.27019 | + | 1.42012i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0287 | − | 24.0287i | 0.788356 | − | 0.788356i | −0.192868 | − | 0.981225i | \(-0.561779\pi\) |
0.981225 | + | 0.192868i | \(0.0617790\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.00803i | − | 0.0330370i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.6447 | − | 10.1270i | −0.741354 | − | 0.331544i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | − | 7.74597i | 0.392442 | − | 0.253320i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9839i | 0.881525i | 0.897624 | + | 0.440762i | \(0.145292\pi\) | ||||
−0.897624 | + | 0.440762i | \(0.854708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.7460 | + | 37.4451i | −0.546484 | + | 1.22198i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.5885 | + | 15.5885i | −0.508169 | + | 0.508169i | −0.913964 | − | 0.405795i | \(-0.866995\pi\) |
0.405795 | + | 0.913964i | \(0.366995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.1287 | −0.818303 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −27.7082 | − | 14.2918i | −0.901348 | − | 0.464912i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.0000 | + | 23.0000i | −0.747400 | + | 0.747400i | −0.973990 | − | 0.226591i | \(-0.927242\pi\) |
0.226591 | + | 0.973990i | \(0.427242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.4919 | + | 21.4919i | −0.697658 | + | 0.697658i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.3649 | + | 17.6045i | 1.27649 | + | 0.570866i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.6174i | − | 1.54248i | −0.636545 | − | 0.771240i | \(-0.719637\pi\) | ||
0.636545 | − | 0.771240i | \(-0.280363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.6410 | + | 34.6410i | 1.12096 | + | 1.12096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.86710 | − | 3.38693i | 0.286633 | − | 0.109484i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.4919 | + | 15.4919i | 0.500261 | + | 0.500261i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.9839i | 1.48335i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.53678 | + | 45.5206i | −0.0817465 | + | 1.46688i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 64.0579i | 2.06210i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.8167 | −0.798053 | −0.399026 | − | 0.916939i | \(-0.630652\pi\) | ||||
−0.399026 | + | 0.916939i | \(0.630652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.25700 | − | 5.80524i | 0.136754 | − | 0.186491i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.2379i | 1.13084i | 0.824804 | + | 0.565419i | \(0.191286\pi\) | ||||
−0.824804 | + | 0.565419i | \(0.808714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.2540 | −0.905783 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.23607 | + | 1.23607i | −0.103637 | + | 0.0395859i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5203 | 0.336576 | 0.168288 | − | 0.985738i | \(-0.446176\pi\) | ||||
0.168288 | + | 0.985738i | \(0.446176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.01607 | + | 2.01607i | −0.0644338 | + | 0.0644338i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.538051 | − | 0.0299846i | −0.0171787 | − | 0.000957333i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.38105 | + | 6.38105i | −0.203524 | + | 0.203524i | −0.801508 | − | 0.597984i | \(-0.795969\pi\) |
0.597984 | + | 0.801508i | \(0.295969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.50807 | 0.0799136 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.4919 | + | 6.92820i | 0.493114 | + | 0.220527i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.88803 | + | 1.88803i | 0.0600359 | + | 0.0600359i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.0209 | + | 31.0209i | 0.985412 | + | 0.985412i | 0.999895 | − | 0.0144827i | \(-0.00461014\pi\) |
−0.0144827 | + | 0.999895i | \(0.504610\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.4327 | + | 27.3132i | 0.331073 | + | 0.866759i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.00000i | 0.190213i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.38105 | + | 6.38105i | 0.202090 | + | 0.202090i | 0.800895 | − | 0.598805i | \(-0.204358\pi\) |
−0.598805 | + | 0.800895i | \(0.704358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.1109 | + | 8.66025i | −0.857750 | + | 0.273998i |
(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 | 816.2.bf.c.191.1 | yes | 8 | |
3.2 | odd | 2 | 816.2.bf.a.191.2 | yes | 8 | ||
4.3 | odd | 2 | 816.2.bf.a.191.3 | yes | 8 | ||
12.11 | even | 2 | inner | 816.2.bf.c.191.4 | yes | 8 | |
17.13 | even | 4 | inner | 816.2.bf.c.47.4 | yes | 8 | |
51.47 | odd | 4 | 816.2.bf.a.47.3 | yes | 8 | ||
68.47 | odd | 4 | 816.2.bf.a.47.2 | ✓ | 8 | ||
204.47 | even | 4 | inner | 816.2.bf.c.47.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
816.2.bf.a.47.2 | ✓ | 8 | 68.47 | odd | 4 | ||
816.2.bf.a.47.3 | yes | 8 | 51.47 | odd | 4 | ||
816.2.bf.a.191.2 | yes | 8 | 3.2 | odd | 2 | ||
816.2.bf.a.191.3 | yes | 8 | 4.3 | odd | 2 | ||
816.2.bf.c.47.1 | yes | 8 | 204.47 | even | 4 | inner | |
816.2.bf.c.47.4 | yes | 8 | 17.13 | even | 4 | inner | |
816.2.bf.c.191.1 | yes | 8 | 1.1 | even | 1 | trivial | |
816.2.bf.c.191.4 | yes | 8 | 12.11 | even | 2 | inner |