Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,2,Mod(65,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.e (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: | \(2.04417029174\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.65 |
Dual form | 256.2.e.a.193.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.93185 | − | 1.93185i | −1.11536 | − | 1.11536i | −0.992414 | − | 0.122941i | \(-0.960767\pi\) |
−0.122941 | − | 0.992414i | \(-0.539233\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205 | − | 1.73205i | 0.774597 | − | 0.774597i | −0.204310 | − | 0.978906i | \(-0.565495\pi\) |
0.978906 | + | 0.204310i | \(0.0654949\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.03528i | − | 0.391298i | −0.980674 | − | 0.195649i | \(-0.937319\pi\) | ||
0.980674 | − | 0.195649i | \(-0.0626813\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410i | 1.48803i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.896575 | + | 0.896575i | −0.270328 | + | 0.270328i | −0.829232 | − | 0.558904i | \(-0.811222\pi\) |
0.558904 | + | 0.829232i | \(0.311222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.73205 | − | 3.73205i | −1.03508 | − | 1.03508i | −0.999362 | − | 0.0357229i | \(-0.988627\pi\) |
−0.0357229 | − | 0.999362i | \(-0.511373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.69213 | −1.72790 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.896575 | + | 0.896575i | 0.205689 | + | 0.205689i | 0.802432 | − | 0.596744i | \(-0.203539\pi\) |
−0.596744 | + | 0.802432i | \(0.703539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 2.00000i | −0.436436 | + | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.69213i | − | 1.39541i | −0.716387 | − | 0.697703i | \(-0.754206\pi\) | ||
0.716387 | − | 0.697703i | \(-0.245794\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.82843 | − | 2.82843i | 0.544331 | − | 0.544331i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.73205 | + | 1.73205i | 0.321634 | + | 0.321634i | 0.849394 | − | 0.527760i | \(-0.176968\pi\) |
−0.527760 | + | 0.849394i | \(0.676968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.46410 | 0.603023 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.79315 | − | 1.79315i | −0.303098 | − | 0.303098i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.267949 | − | 0.267949i | 0.0440506 | − | 0.0440506i | −0.684738 | − | 0.728789i | \(-0.740084\pi\) |
0.728789 | + | 0.684738i | \(0.240084\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.4195i | 2.30897i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.79555 | + | 5.79555i | −0.883814 | + | 0.883814i | −0.993920 | − | 0.110106i | \(-0.964881\pi\) |
0.110106 | + | 0.993920i | \(0.464881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.73205 | + | 7.73205i | 1.15263 | + | 1.15263i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.79796 | 1.42918 | 0.714590 | − | 0.699544i | \(-0.246613\pi\) | ||||
0.714590 | + | 0.699544i | \(0.246613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.92820 | 0.846886 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.69213 | + | 6.69213i | 0.937086 | + | 0.937086i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.26795 | − | 4.26795i | 0.586248 | − | 0.586248i | −0.350365 | − | 0.936613i | \(-0.613943\pi\) |
0.936613 | + | 0.350365i | \(0.113943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.10583i | 0.418790i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.46410i | − | 0.458831i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.58871 | − | 7.58871i | 0.987965 | − | 0.987965i | −0.0119631 | − | 0.999928i | \(-0.503808\pi\) |
0.999928 | + | 0.0119631i | \(0.00380806\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.267949 | + | 0.267949i | 0.0343074 | + | 0.0343074i | 0.724052 | − | 0.689745i | \(-0.242277\pi\) |
−0.689745 | + | 0.724052i | \(0.742277\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.62158 | 0.582264 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.9282 | −1.60355 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.96713 | + | 2.96713i | 0.362492 | + | 0.362492i | 0.864730 | − | 0.502237i | \(-0.167490\pi\) |
−0.502237 | + | 0.864730i | \(0.667490\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9282 | + | 12.9282i | −1.55637 | + | 1.55637i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.69213i | − | 0.794210i | −0.917773 | − | 0.397105i | \(-0.870015\pi\) | ||
0.917773 | − | 0.397105i | \(-0.129985\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.46410i | − | 1.10769i | −0.832620 | − | 0.553845i | \(-0.813160\pi\) | ||
0.832620 | − | 0.553845i | \(-0.186840\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.93185 | + | 1.93185i | −0.223071 | + | 0.223071i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.928203 | + | 0.928203i | 0.105779 | + | 0.105779i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4548 | −1.73880 | −0.869401 | − | 0.494107i | \(-0.835495\pi\) | ||||
−0.869401 | + | 0.494107i | \(0.835495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.46410 | 0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.79555 | + | 5.79555i | 0.636145 | + | 0.636145i | 0.949602 | − | 0.313457i | \(-0.101487\pi\) |
−0.313457 | + | 0.949602i | \(0.601487\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | + | 6.00000i | −0.650791 | + | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 6.69213i | − | 0.717472i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.46410i | 1.00319i | 0.865102 | + | 0.501596i | \(0.167254\pi\) | ||||
−0.865102 | + | 0.501596i | \(0.832746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.86370 | + | 3.86370i | −0.405026 | + | 0.405026i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.9282 | − | 10.9282i | −1.13320 | − | 1.13320i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.10583 | 0.318651 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.46410 | −0.351726 | −0.175863 | − | 0.984415i | \(-0.556272\pi\) | ||||
−0.175863 | + | 0.984415i | \(0.556272\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00240 | − | 4.00240i | −0.402257 | − | 0.402257i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1962 | − | 11.1962i | 1.11406 | − | 1.11406i | 0.121463 | − | 0.992596i | \(-0.461241\pi\) |
0.992596 | − | 0.121463i | \(-0.0387585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.62158i | 0.455378i | 0.973734 | + | 0.227689i | \(0.0731169\pi\) | ||||
−0.973734 | + | 0.227689i | \(0.926883\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.92820i | 0.676123i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.90138 | − | 8.90138i | 0.860529 | − | 0.860529i | −0.130870 | − | 0.991400i | \(-0.541777\pi\) |
0.991400 | + | 0.130870i | \(0.0417771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.80385 | + | 2.80385i | 0.268560 | + | 0.268560i | 0.828520 | − | 0.559960i | \(-0.189183\pi\) |
−0.559960 | + | 0.828520i | \(0.689183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.03528 | −0.0982641 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.928203 | −0.0873180 | −0.0436590 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436590 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.5911 | − | 11.5911i | −1.08088 | − | 1.08088i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.6603 | − | 16.6603i | 1.54024 | − | 1.54024i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.58630i | 0.328756i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.39230i | 0.853846i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.3843 | + | 13.3843i | −1.20682 | + | 1.20682i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | + | 6.92820i | 0.619677 | + | 0.619677i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65685 | −0.501965 | −0.250982 | − | 0.967992i | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.3923 | 1.97153 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4877 | − | 12.4877i | −1.09105 | − | 1.09105i | −0.995416 | − | 0.0956380i | \(-0.969511\pi\) |
−0.0956380 | − | 0.995416i | \(-0.530489\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.928203 | − | 0.928203i | 0.0804854 | − | 0.0804854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 9.79796i | − | 0.843274i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.138701 | + | 0.138701i | −0.0117644 | + | 0.0117644i | −0.712965 | − | 0.701200i | \(-0.752648\pi\) |
0.701200 | + | 0.712965i | \(0.252648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.9282 | − | 18.9282i | −1.59404 | − | 1.59404i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.69213 | 0.559624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.4524 | − | 11.4524i | −0.944579 | − | 0.944579i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.2679 | + | 10.2679i | −0.841183 | + | 0.841183i | −0.989013 | − | 0.147830i | \(-0.952771\pi\) |
0.147830 | + | 0.989013i | \(0.452771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.62158i | 0.376099i | 0.982160 | + | 0.188049i | \(0.0602165\pi\) | ||||
−0.982160 | + | 0.188049i | \(0.939784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 15.4641i | − | 1.25020i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.79796 | − | 9.79796i | 0.786991 | − | 0.786991i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.19615 | + | 3.19615i | 0.255081 | + | 0.255081i | 0.823050 | − | 0.567969i | \(-0.192271\pi\) |
−0.567969 | + | 0.823050i | \(0.692271\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.4901 | −1.30775 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.92820 | −0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.38186 | + | 9.38186i | 0.734844 | + | 0.734844i | 0.971575 | − | 0.236731i | \(-0.0760761\pi\) |
−0.236731 | + | 0.971575i | \(0.576076\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.00000 | − | 6.00000i | 0.467099 | − | 0.467099i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 23.6627i | − | 1.83107i | −0.402234 | − | 0.915537i | \(-0.631766\pi\) | ||
0.402234 | − | 0.915537i | \(-0.368234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.8564i | 1.14280i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00240 | + | 4.00240i | −0.306071 | + | 0.306071i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.26795 | + | 4.26795i | 0.324486 | + | 0.324486i | 0.850485 | − | 0.525999i | \(-0.176308\pi\) |
−0.525999 | + | 0.850485i | \(0.676308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.03528 | −0.0782595 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −29.3205 | −2.20386 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.79555 | + | 5.79555i | 0.433180 | + | 0.433180i | 0.889709 | − | 0.456529i | \(-0.150907\pi\) |
−0.456529 | + | 0.889709i | \(0.650907\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.12436 | + | 8.12436i | −0.603879 | + | 0.603879i | −0.941340 | − | 0.337461i | \(-0.890432\pi\) |
0.337461 | + | 0.941340i | \(0.390432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.03528i | − | 0.0765298i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 0.928203i | − | 0.0682429i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.10583 | − | 3.10583i | 0.227121 | − | 0.227121i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.92820 | − | 2.92820i | −0.212995 | − | 0.212995i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.39230 | 0.172202 | 0.0861009 | − | 0.996286i | \(-0.472559\pi\) | ||||
0.0861009 | + | 0.996286i | \(0.472559\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.9754 | + | 24.9754i | 1.78852 | + | 1.78852i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.73205 | − | 1.73205i | 0.123404 | − | 0.123404i | −0.642708 | − | 0.766111i | \(-0.722189\pi\) |
0.766111 | + | 0.642708i | \(0.222189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.5606i | 1.31573i | 0.753136 | + | 0.657865i | \(0.228540\pi\) | ||||
−0.753136 | + | 0.657865i | \(0.771460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 11.4641i | − | 0.808615i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.79315 | − | 1.79315i | 0.125855 | − | 0.125855i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | − | 12.0000i | −0.838116 | − | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 29.8744 | 2.07641 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.60770 | −0.111207 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.138701 | + | 0.138701i | 0.00954855 | + | 0.00954855i | 0.711865 | − | 0.702316i | \(-0.247851\pi\) |
−0.702316 | + | 0.711865i | \(0.747851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.9282 | + | 12.9282i | −0.885826 | + | 0.885826i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.0764i | 1.36920i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.85641i | − | 0.397559i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.2832 | + | 18.2832i | −1.23547 | + | 1.23547i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.9282 | + | 12.9282i | 0.869645 | + | 0.869645i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65685 | 0.378811 | 0.189405 | − | 0.981899i | \(-0.439344\pi\) | ||||
0.189405 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.20925 | + | 2.20925i | 0.146633 | + | 0.146633i | 0.776612 | − | 0.629979i | \(-0.216936\pi\) |
−0.629979 | + | 0.776612i | \(0.716936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.19615 | + | 1.19615i | −0.0790440 | + | 0.0790440i | −0.745523 | − | 0.666479i | \(-0.767800\pi\) |
0.666479 | + | 0.745523i | \(0.267800\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3.58630i | − | 0.235961i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.46410i | − | 0.620014i | −0.950734 | − | 0.310007i | \(-0.899669\pi\) | ||
0.950734 | − | 0.310007i | \(-0.100331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9706 | − | 16.9706i | 1.10704 | − | 1.10704i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 29.8564 | + | 29.8564i | 1.93938 | + | 1.93938i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.17260 | 0.463957 | 0.231979 | − | 0.972721i | \(-0.425480\pi\) | ||||
0.231979 | + | 0.972721i | \(0.425480\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3923 | 1.18475 | 0.592376 | − | 0.805661i | \(-0.298190\pi\) | ||||
0.592376 | + | 0.805661i | \(0.298190\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.2456 | − | 13.2456i | −0.849703 | − | 0.849703i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.2679 | − | 10.2679i | 0.655995 | − | 0.655995i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.69213i | − | 0.425810i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 22.3923i | − | 1.41905i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.20925 | + | 2.20925i | −0.139447 | + | 0.139447i | −0.773384 | − | 0.633937i | \(-0.781438\pi\) |
0.633937 | + | 0.773384i | \(0.281438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | + | 6.00000i | 0.377217 | + | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.1822 | 1.45173 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.928203 | −0.0578997 | −0.0289499 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289499 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.277401 | − | 0.277401i | −0.0172369 | − | 0.0172369i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.73205 | + | 7.73205i | −0.478602 | + | 0.478602i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9038i | 0.795682i | 0.917454 | + | 0.397841i | \(0.130240\pi\) | ||||
−0.917454 | + | 0.397841i | \(0.869760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 14.7846i | − | 0.908211i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.2832 | − | 18.2832i | 1.11892 | − | 1.11892i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.19615 | − | 5.19615i | −0.316815 | − | 0.316815i | 0.530728 | − | 0.847543i | \(-0.321919\pi\) |
−0.847543 | + | 0.530728i | \(0.821919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1117 | 1.28244 | 0.641221 | − | 0.767356i | \(-0.278428\pi\) | ||||
0.641221 | + | 0.767356i | \(0.278428\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.9282 | 0.903496 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.896575 | + | 0.896575i | 0.0540655 | + | 0.0540655i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.19615 | − | 7.19615i | 0.432375 | − | 0.432375i | −0.457061 | − | 0.889436i | \(-0.651098\pi\) |
0.889436 | + | 0.457061i | \(0.151098\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.2528i | 1.51184i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.39230i | 0.262023i | 0.991381 | + | 0.131011i | \(0.0418225\pi\) | ||||
−0.991381 | + | 0.131011i | \(0.958178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.62398 | + | 8.62398i | −0.512643 | + | 0.512643i | −0.915335 | − | 0.402693i | \(-0.868074\pi\) |
0.402693 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00000 | − | 6.00000i | −0.355409 | − | 0.355409i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.17260 | −0.423385 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.69213 | + | 6.69213i | 0.392300 | + | 0.392300i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.1244 | + | 12.1244i | −0.708312 | + | 0.708312i | −0.966180 | − | 0.257868i | \(-0.916980\pi\) |
0.257868 | + | 0.966180i | \(0.416980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 26.2880i | − | 1.53055i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.07180i | 0.294295i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.9754 | + | 24.9754i | −1.44436 | + | 1.44436i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | + | 6.00000i | 0.345834 | + | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.2586 | −2.48514 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.928203 | 0.0531488 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8356 | + | 14.8356i | 0.846715 | + | 0.846715i | 0.989722 | − | 0.143007i | \(-0.0456772\pi\) |
−0.143007 | + | 0.989722i | \(0.545677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.92820 | − | 8.92820i | 0.507908 | − | 0.507908i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2784i | 0.582836i | 0.956596 | + | 0.291418i | \(0.0941271\pi\) | ||||
−0.956596 | + | 0.291418i | \(0.905873\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.7846i | 1.62700i | 0.581563 | + | 0.813501i | \(0.302441\pi\) | ||||
−0.581563 | + | 0.813501i | \(0.697559\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.00481 | − | 8.00481i | 0.451020 | − | 0.451020i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.1962 | − | 17.1962i | −0.965832 | − | 0.965832i | 0.0336031 | − | 0.999435i | \(-0.489302\pi\) |
−0.999435 | + | 0.0336031i | \(0.989302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.10583 | −0.173893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −34.3923 | −1.91959 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.10583 | − | 3.10583i | −0.172813 | − | 0.172813i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.73205 | + | 3.73205i | −0.207017 | + | 0.207017i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 10.8332i | − | 0.599079i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 10.1436i | − | 0.559234i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.24453 | − | 3.24453i | 0.178335 | − | 0.178335i | −0.612294 | − | 0.790630i | \(-0.709753\pi\) |
0.790630 | + | 0.612294i | \(0.209753\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.19615 | + | 1.19615i | 0.0655487 | + | 0.0655487i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.2784 | 0.561571 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.7128 | −1.83645 | −0.918227 | − | 0.396055i | \(-0.870379\pi\) | ||||
−0.918227 | + | 0.396055i | \(0.870379\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.79315 | + | 1.79315i | 0.0973906 | + | 0.0973906i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.07180 | + | 5.07180i | −0.274653 | + | 0.274653i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.3843i | − | 0.722682i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 44.7846i | 2.41112i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.58871 | − | 7.58871i | 0.407383 | − | 0.407383i | −0.473442 | − | 0.880825i | \(-0.656989\pi\) |
0.880825 | + | 0.473442i | \(0.156989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.1244 | − | 20.1244i | −1.07723 | − | 1.07723i | −0.996757 | − | 0.0804755i | \(-0.974356\pi\) |
−0.0804755 | − | 0.996757i | \(-0.525644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.1117 | −1.12686 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9282 | 0.688099 | 0.344049 | − | 0.938952i | \(-0.388201\pi\) | ||||
0.344049 | + | 0.938952i | \(0.388201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.5911 | − | 11.5911i | −0.615192 | − | 0.615192i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.92820 | − | 6.92820i | 0.366679 | − | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.2880i | − | 1.38743i | −0.720250 | − | 0.693715i | \(-0.755973\pi\) | ||
0.720250 | − | 0.693715i | \(-0.244027\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.3923i | − | 0.915384i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.1445 | − | 18.1445i | 0.952341 | − | 0.952341i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3923 | − | 16.3923i | −0.858012 | − | 0.858012i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.8295 | −0.669692 | −0.334846 | − | 0.942273i | \(-0.608684\pi\) | ||||
−0.334846 | + | 0.942273i | \(0.608684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.9282 | 1.61006 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.41851 | − | 4.41851i | −0.229397 | − | 0.229397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1244 | − | 10.1244i | 0.524219 | − | 0.524219i | −0.394624 | − | 0.918843i | \(-0.629125\pi\) |
0.918843 | + | 0.394624i | \(0.129125\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 26.7685i | − | 1.38232i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.9282i | − | 0.665836i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.1798 | + | 19.1798i | −0.985201 | + | 0.985201i | −0.999892 | − | 0.0146911i | \(-0.995324\pi\) |
0.0146911 | + | 0.999892i | \(0.495324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9282 | + | 10.9282i | 0.559869 | + | 0.559869i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.5959 | −1.00130 | −0.500652 | − | 0.865648i | \(-0.666906\pi\) | ||||
−0.500652 | + | 0.865648i | \(0.666906\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.21539 | 0.163871 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.8719 | − | 25.8719i | −1.31514 | − | 1.31514i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.73205 | + | 7.73205i | −0.392031 | + | 0.392031i | −0.875411 | − | 0.483380i | \(-0.839409\pi\) |
0.483380 | + | 0.875411i | \(0.339409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.1822i | 1.17238i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 48.2487i | 2.43383i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.7685 | + | 26.7685i | −1.34687 | + | 1.34687i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.5885 | + | 11.5885i | 0.581608 | + | 0.581608i | 0.935345 | − | 0.353737i | \(-0.115089\pi\) |
−0.353737 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.58630 | −0.179540 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.3923 | 1.71747 | 0.858735 | − | 0.512420i | \(-0.171251\pi\) | ||||
0.858735 | + | 0.512420i | \(0.171251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.1117 | − | 21.1117i | −1.05165 | − | 1.05165i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.26795 | − | 4.26795i | 0.212076 | − | 0.212076i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.480473i | 0.0238162i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 30.9282i | − | 1.52930i | −0.644445 | − | 0.764651i | \(-0.722912\pi\) | ||
0.644445 | − | 0.764651i | \(-0.277088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.1822 | − | 23.1822i | 1.14349 | − | 1.14349i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.85641 | − | 7.85641i | −0.386588 | − | 0.386588i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0764 | 0.985511 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.535898 | 0.0262431 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.68973 | − | 2.68973i | −0.131402 | − | 0.131402i | 0.638347 | − | 0.769749i | \(-0.279619\pi\) |
−0.769749 | + | 0.638347i | \(0.779619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.5167 | − | 26.5167i | 1.29234 | − | 1.29234i | 0.359009 | − | 0.933334i | \(-0.383115\pi\) |
0.933334 | − | 0.359009i | \(-0.116885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 43.7391i | 2.12667i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410i | 0.168034i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.277401 | − | 0.277401i | 0.0134244 | − | 0.0134244i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.9282 | − | 12.9282i | −0.624180 | − | 0.624180i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.17260 | 0.345492 | 0.172746 | − | 0.984966i | \(-0.444736\pi\) | ||||
0.172746 | + | 0.984966i | \(0.444736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.6077 | −0.653944 | −0.326972 | − | 0.945034i | \(-0.606028\pi\) | ||||
−0.326972 | + | 0.945034i | \(0.606028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.5911 | − | 11.5911i | −0.555751 | − | 0.555751i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.00000 | − | 6.00000i | 0.287019 | − | 0.287019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 31.9449i | − | 1.52465i | −0.647196 | − | 0.762324i | \(-0.724059\pi\) | ||
0.647196 | − | 0.762324i | \(-0.275941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26.4641i | 1.26020i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.68973 | − | 2.68973i | 0.127793 | − | 0.127793i | −0.640318 | − | 0.768110i | \(-0.721197\pi\) |
0.768110 | + | 0.640318i | \(0.221197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.3923 | + | 16.3923i | 0.777070 | + | 0.777070i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.6723 | 1.87644 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.2487 | 1.14437 | 0.572184 | − | 0.820125i | \(-0.306096\pi\) | ||||
0.572184 | + | 0.820125i | \(0.306096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.21166 | + | 6.21166i | 0.292496 | + | 0.292496i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.92820 | − | 8.92820i | 0.419484 | − | 0.419484i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.3843i | 0.627464i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7846i | 0.972263i | 0.873886 | + | 0.486132i | \(0.161592\pi\) | ||||
−0.873886 | + | 0.486132i | \(0.838408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.79796 | + | 9.79796i | −0.457330 | + | 0.457330i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.124356 | − | 0.124356i | −0.00579182 | − | 0.00579182i | 0.704205 | − | 0.709997i | \(-0.251304\pi\) |
−0.709997 | + | 0.704205i | \(0.751304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4863 | −0.859132 | −0.429566 | − | 0.903036i | \(-0.641333\pi\) | ||||
−0.429566 | + | 0.903036i | \(0.641333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −37.8564 | −1.75555 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.8671 | + | 17.8671i | 0.826793 | + | 0.826793i | 0.987072 | − | 0.160279i | \(-0.0512394\pi\) |
−0.160279 | + | 0.987072i | \(0.551239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.07180 | − | 3.07180i | 0.141842 | − | 0.141842i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 12.3490i | − | 0.569011i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.3923i | − | 0.477839i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.896575 | − | 0.896575i | 0.0411377 | − | 0.0411377i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.0526 | + | 19.0526i | 0.872357 | + | 0.872357i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.62536 | −0.119956 | −0.0599778 | − | 0.998200i | \(-0.519103\pi\) | ||||
−0.0599778 | + | 0.998200i | \(0.519103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.3843 | + | 13.3843i | 0.609005 | + | 0.609005i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.00000 | + | 6.00000i | −0.272446 | + | 0.272446i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.24693i | 0.328390i | 0.986428 | + | 0.164195i | \(0.0525026\pi\) | ||||
−0.986428 | + | 0.164195i | \(0.947497\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.2487i | − | 1.63922i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.7661 | + | 22.7661i | −1.02742 | + | 1.02742i | −0.0278072 | + | 0.999613i | \(0.508852\pi\) |
−0.999613 | + | 0.0278072i | \(0.991148\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | − | 6.00000i | −0.270226 | − | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.8647 | −0.623173 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.92820 | −0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.4524 | + | 11.4524i | 0.512680 | + | 0.512680i | 0.915347 | − | 0.402667i | \(-0.131917\pi\) |
−0.402667 | + | 0.915347i | \(0.631917\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.7128 | + | 45.7128i | −2.04230 | + | 2.04230i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.4997i | 1.44909i | 0.689227 | + | 0.724545i | \(0.257950\pi\) | ||||
−0.689227 | + | 0.724545i | \(0.742050\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 38.7846i | − | 1.72589i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.7004 | − | 28.7004i | 1.27463 | − | 1.27463i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.5885 | − | 21.5885i | −0.956892 | − | 0.956892i | 0.0422169 | − | 0.999108i | \(-0.486558\pi\) |
−0.999108 | + | 0.0422169i | \(0.986558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.79796 | −0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.07180 | 0.223925 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00481 | + | 8.00481i | 0.352734 | + | 0.352734i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.78461 | + | 8.78461i | −0.386347 | + | 0.386347i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 16.4901i | − | 0.723835i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000i | 0.525730i | 0.964833 | + | 0.262865i | \(0.0846673\pi\) | ||||
−0.964833 | + | 0.262865i | \(0.915333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0740 | − | 16.0740i | 0.702866 | − | 0.702866i | −0.262158 | − | 0.965025i | \(-0.584434\pi\) |
0.965025 | + | 0.262158i | \(0.0844343\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.00000 | + | 2.00000i | 0.0872872 | + | 0.0872872i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.5959 | −0.853612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7846 | −0.947157 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33.8768 | + | 33.8768i | 1.47013 | + | 1.47013i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.8564 | + | 25.8564i | −1.11997 | + | 1.11997i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 30.8353i | − | 1.33313i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 22.3923i | − | 0.966299i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.31508 | + | 5.31508i | −0.228937 | + | 0.228937i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1244 | + | 14.1244i | 0.607253 | + | 0.607253i | 0.942227 | − | 0.334974i | \(-0.108728\pi\) |
−0.334974 | + | 0.942227i | \(0.608728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.3901 | 1.34708 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.71281 | 0.416051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.4877 | − | 12.4877i | −0.533935 | − | 0.533935i | 0.387806 | − | 0.921741i | \(-0.373233\pi\) |
−0.921741 | + | 0.387806i | \(0.873233\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.19615 | + | 1.19615i | −0.0510505 | + | 0.0510505i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.10583i | 0.132313i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000i | 0.680389i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.79315 | + | 1.79315i | −0.0761150 | + | 0.0761150i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.803848 | − | 0.803848i | −0.0340601 | − | 0.0340601i | 0.689872 | − | 0.723932i | \(-0.257667\pi\) |
−0.723932 | + | 0.689872i | \(0.757667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.2586 | 1.82964 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.6651 | + | 27.6651i | 1.16594 | + | 1.16594i | 0.983151 | + | 0.182794i | \(0.0585140\pi\) |
0.182794 | + | 0.983151i | \(0.441486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.60770 | + | 1.60770i | −0.0676362 | + | 0.0676362i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.55103i | − | 0.107133i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 12.0000i | − | 0.503066i | −0.967849 | − | 0.251533i | \(-0.919065\pi\) | ||
0.967849 | − | 0.251533i | \(-0.0809347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0034 | − | 14.0034i | 0.586026 | − | 0.586026i | −0.350527 | − | 0.936553i | \(-0.613998\pi\) |
0.936553 | + | 0.350527i | \(0.113998\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.7846 | + | 32.7846i | 1.36960 | + | 1.36960i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.69213 | −0.279081 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.1436 | −0.672067 | −0.336033 | − | 0.941850i | \(-0.609085\pi\) | ||||
−0.336033 | + | 0.941850i | \(0.609085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.62158 | − | 4.62158i | −0.192066 | − | 0.192066i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | − | 6.00000i | 0.248922 | − | 0.248922i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.65308i | 0.316958i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 57.7128i | − | 2.38613i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.6945 | + | 10.6945i | −0.441411 | + | 0.441411i | −0.892486 | − | 0.451075i | \(-0.851041\pi\) |
0.451075 | + | 0.892486i | \(0.351041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.07180 | + | 5.07180i | 0.208980 | + | 0.208980i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.69213 | −0.275277 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.85641 | 0.322624 | 0.161312 | − | 0.986903i | \(-0.448427\pi\) | ||||
0.161312 | + | 0.986903i | \(0.448427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.21166 | + | 6.21166i | 0.254653 | + | 0.254653i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 35.8564 | − | 35.8564i | 1.46751 | − | 1.46751i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.8744i | 1.22063i | 0.792158 | + | 0.610316i | \(0.208958\pi\) | ||||
−0.792158 | + | 0.610316i | \(0.791042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6077i | 0.799815i | 0.916556 | + | 0.399907i | \(0.130958\pi\) | ||||
−0.916556 | + | 0.399907i | \(0.869042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.2456 | + | 13.2456i | −0.539401 | + | 0.539401i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.2679 | + | 16.2679i | 0.661386 | + | 0.661386i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.9096 | 1.25458 | 0.627292 | − | 0.778785i | \(-0.284163\pi\) | ||||
0.627292 | + | 0.778785i | \(0.284163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.92820 | −0.280745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.5665 | − | 36.5665i | −1.47932 | − | 1.47932i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0526 | + | 23.0526i | −0.931084 | + | 0.931084i | −0.997774 | − | 0.0666897i | \(-0.978756\pi\) |
0.0666897 | + | 0.997774i | \(0.478756\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 46.3644i | 1.86959i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3205i | 0.938848i | 0.882973 | + | 0.469424i | \(0.155538\pi\) | ||||
−0.882973 | + | 0.469424i | \(0.844462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.24453 | − | 3.24453i | 0.130409 | − | 0.130409i | −0.638890 | − | 0.769298i | \(-0.720606\pi\) |
0.769298 | + | 0.638890i | \(0.220606\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.9282 | − | 18.9282i | −0.759563 | − | 0.759563i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.79796 | 0.392547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.0000 | 1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.10583 | + | 3.10583i | 0.124035 | + | 0.124035i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.928203 | + | 0.928203i | −0.0370099 | + | 0.0370099i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5312i | 1.41447i | 0.706976 | + | 0.707237i | \(0.250059\pi\) | ||||
−0.706976 | + | 0.707237i | \(0.749941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 0.535898i | − | 0.0213000i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.79796 | + | 9.79796i | −0.388820 | + | 0.388820i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.1244 | − | 22.1244i | −0.876599 | − | 0.876599i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.8744 | 1.18181 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.3923 | 1.35841 | 0.679207 | − | 0.733947i | \(-0.262324\pi\) | ||||
0.679207 | + | 0.733947i | \(0.262324\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2808 | + | 14.2808i | 0.563181 | + | 0.563181i | 0.930210 | − | 0.367028i | \(-0.119625\pi\) |
−0.367028 | + | 0.930210i | \(0.619625\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.7846 | − | 38.7846i | 1.52714 | − | 1.52714i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.69213i | − | 0.263095i | −0.991310 | − | 0.131547i | \(-0.958005\pi\) | ||
0.991310 | − | 0.131547i | \(-0.0419946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6077i | 0.534149i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3137 | + | 11.3137i | −0.443419 | + | 0.443419i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.6603 | + | 32.6603i | 1.27809 | + | 1.27809i | 0.941733 | + | 0.336362i | \(0.109196\pi\) |
0.336362 | + | 0.941733i | \(0.390804\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.2586 | −1.69025 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.2487 | 1.64828 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.8004 | − | 13.8004i | −0.537586 | − | 0.537586i | 0.385233 | − | 0.922819i | \(-0.374121\pi\) |
−0.922819 | + | 0.385233i | \(0.874121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.7321 | − | 21.7321i | 0.845279 | − | 0.845279i | −0.144261 | − | 0.989540i | \(-0.546080\pi\) |
0.989540 | + | 0.144261i | \(0.0460804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 49.9507i | − | 1.93993i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.21539i | − | 0.124687i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.5911 | − | 11.5911i | 0.448810 | − | 0.448810i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.9282 | − | 10.9282i | −0.422509 | − | 0.422509i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.480473 | −0.0185485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.67949 | 0.257475 | 0.128738 | − | 0.991679i | \(-0.458907\pi\) | ||||
0.128738 | + | 0.991679i | \(0.458907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.82843 | − | 2.82843i | −0.108866 | − | 0.108866i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.7321 | + | 31.7321i | −1.21956 | + | 1.21956i | −0.251776 | + | 0.967785i | \(0.581015\pi\) |
−0.967785 | + | 0.251776i | \(0.918985\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.58630i | 0.137630i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 8.53590i | − | 0.327096i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.9730 | − | 20.9730i | 0.802508 | − | 0.802508i | −0.180979 | − | 0.983487i | \(-0.557927\pi\) |
0.983487 | + | 0.180979i | \(0.0579265\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7846 | + | 20.7846i | 0.794139 | + | 0.794139i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.62158 | 0.176324 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31.8564 | −1.21363 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5983 | − | 23.5983i | −0.897722 | − | 0.897722i | 0.0975119 | − | 0.995234i | \(-0.468912\pi\) |
−0.995234 | + | 0.0975119i | \(0.968912\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.14359 | + | 4.14359i | −0.157402 | + | 0.157402i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.480473i | 0.0182254i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000i | 0.909065i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.2832 | + | 18.2832i | −0.691536 | + | 0.691536i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.6603 | − | 26.6603i | −1.00694 | − | 1.00694i | −0.999976 | − | 0.00696818i | \(-0.997782\pi\) |
−0.00696818 | − | 0.999976i | \(-0.502218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.480473 | 0.0181214 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −65.5692 | −2.46948 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.5911 | − | 11.5911i | −0.435929 | − | 0.435929i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.05256 | − | 9.05256i | 0.339976 | − | 0.339976i | −0.516382 | − | 0.856358i | \(-0.672722\pi\) |
0.856358 | + | 0.516382i | \(0.172722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 68.9919i | − | 2.58740i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 37.8564i | − | 1.41773i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.5911 | − | 11.5911i | 0.433483 | − | 0.433483i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.8564 | − | 13.8564i | −0.517477 | − | 0.517477i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.3644 | −1.72910 | −0.864551 | − | 0.502545i | \(-0.832397\pi\) | ||||
−0.864551 | + | 0.502545i | \(0.832397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.78461 | 0.178188 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.5312 | − | 35.5312i | −1.32142 | − | 1.32142i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.73205 | − | 1.73205i | 0.0643268 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 20.6312i | − | 0.765169i | −0.923921 | − | 0.382584i | \(-0.875034\pi\) | ||
0.923921 | − | 0.382584i | \(-0.124966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.7846i | 1.62165i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0764 | − | 20.0764i | 0.742552 | − | 0.742552i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.1962 | − | 25.1962i | −0.930641 | − | 0.930641i | 0.0671048 | − | 0.997746i | \(-0.478624\pi\) |
−0.997746 | + | 0.0671048i | \(0.978624\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −39.6723 | −1.46334 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.32051 | −0.195983 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.6346 | + | 34.6346i | 1.27406 | + | 1.27406i | 0.943941 | + | 0.330115i | \(0.107087\pi\) |
0.330115 | + | 0.943941i | \(0.392913\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.9282 | + | 12.9282i | −0.474929 | + | 0.474929i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2784i | 0.377079i | 0.982066 | + | 0.188540i | \(0.0603754\pi\) | ||||
−0.982066 | + | 0.188540i | \(0.939625\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.5692i | 1.30316i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.8719 | + | 25.8719i | −0.946605 | + | 0.946605i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.21539 | − | 9.21539i | −0.336723 | − | 0.336723i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.4548 | 0.563954 | 0.281977 | − | 0.959421i | \(-0.409010\pi\) | ||||
0.281977 | + | 0.959421i | \(0.409010\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.53590 | 0.311065 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00481 | + | 8.00481i | 0.291325 | + | 0.291325i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.2679 | + | 18.2679i | −0.663960 | + | 0.663960i | −0.956311 | − | 0.292351i | \(-0.905562\pi\) |
0.292351 | + | 0.956311i | \(0.405562\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 23.1822i | − | 0.841461i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6410i | 1.25574i | 0.778320 | + | 0.627868i | \(0.216072\pi\) | ||||
−0.778320 | + | 0.627868i | \(0.783928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.90276 | − | 2.90276i | 0.105087 | − | 0.105087i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.7846 | − | 26.7846i | −0.968400 | − | 0.968400i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −56.6429 | −2.04526 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3923 | 0.663243 | 0.331622 | − | 0.943412i | \(-0.392404\pi\) | ||||
0.331622 | + | 0.943412i | \(0.392404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.79315 | + | 1.79315i | 0.0645788 | + | 0.0645788i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.66025 | + | 2.66025i | −0.0956827 | + | 0.0956827i | −0.753328 | − | 0.657645i | \(-0.771553\pi\) |
0.657645 | + | 0.753328i | \(0.271553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.65685i | − | 0.203200i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.07180i | 0.0384505i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.21166 | − | 6.21166i | 0.222556 | − | 0.222556i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | + | 6.00000i | 0.214697 | + | 0.214697i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.79796 | 0.350150 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0718 | 0.395169 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9682 | + | 12.9682i | 0.462265 | + | 0.462265i | 0.899397 | − | 0.437132i | \(-0.144006\pi\) |
−0.437132 | + | 0.899397i | \(0.644006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.9282 | − | 24.9282i | 0.887468 | − | 0.887468i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.960947i | 0.0341673i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.00000i | − | 0.0710221i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.5617 | + | 28.5617i | −1.01298 | + | 1.01298i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.41154 | + | 2.41154i | 0.0854212 | + | 0.0854212i | 0.748526 | − | 0.663105i | \(-0.230762\pi\) |
−0.663105 | + | 0.748526i | \(0.730762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.9411 | −1.20075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42.2487 | −1.49278 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.48528 | + | 8.48528i | 0.299439 | + | 0.299439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | + | 12.0000i | −0.422944 | + | 0.422944i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0764i | 0.706722i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.9282i | 1.08738i | 0.839287 | + | 0.543689i | \(0.182973\pi\) | ||||
−0.839287 | + | 0.543689i | \(0.817027\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.52193 | + | 3.52193i | −0.123672 | + | 0.123672i | −0.766234 | − | 0.642562i | \(-0.777872\pi\) |
0.642562 | + | 0.766234i | \(0.277872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.7846 | − | 40.7846i | −1.43038 | − | 1.43038i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.4997 | 1.13842 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3923 | −0.363581 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.2480 | − | 17.2480i | −0.602693 | − | 0.602693i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.9808 | − | 31.9808i | 1.11614 | − | 1.11614i | 0.123833 | − | 0.992303i | \(-0.460481\pi\) |
0.992303 | − | 0.123833i | \(-0.0395188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.5606i | 0.646983i | 0.946231 | + | 0.323492i | \(0.104857\pi\) | ||||
−0.946231 | + | 0.323492i | \(0.895143\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.46410i | − | 0.120605i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.48288 | + | 4.48288i | −0.155885 | + | 0.155885i | −0.780740 | − | 0.624856i | \(-0.785158\pi\) |
0.624856 | + | 0.780740i | \(0.285158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.1244 | + | 22.1244i | 0.768411 | + | 0.768411i | 0.977827 | − | 0.209416i | \(-0.0671563\pi\) |
−0.209416 | + | 0.977827i | \(0.567156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.8038 | −0.964503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.5359 | −0.711527 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.9850 | − | 40.9850i | −1.41834 | − | 1.41834i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0000 | − | 16.0000i | 0.553041 | − | 0.553041i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.06678i | − | 0.140401i | −0.997533 | − | 0.0702003i | \(-0.977636\pi\) | ||
0.997533 | − | 0.0702003i | \(-0.0223639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 23.0000i | − | 0.793103i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.48528 | − | 8.48528i | 0.292249 | − | 0.292249i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.7321 | + | 25.7321i | 0.885209 | + | 0.885209i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.72363 | 0.334108 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.3205 | 1.14356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.79315 | − | 1.79315i | −0.0614684 | − | 0.0614684i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.1244 | − | 34.1244i | 1.16840 | − | 1.16840i | 0.185810 | − | 0.982586i | \(-0.440509\pi\) |
0.982586 | − | 0.185810i | \(-0.0594909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.8647i | 0.474164i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.85641i | − | 0.0634136i | −0.999497 | − | 0.0317068i | \(-0.989906\pi\) | ||
0.999497 | − | 0.0317068i | \(-0.0100943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.1846 | − | 27.1846i | 0.927527 | − | 0.927527i | −0.0700183 | − | 0.997546i | \(-0.522306\pi\) |
0.997546 | + | 0.0700183i | \(0.0223058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.8564 | + | 13.8564i | 0.472225 | + | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.5665 | 1.24474 | 0.622369 | − | 0.782724i | \(-0.286170\pi\) | ||||
0.622369 | + | 0.782724i | \(0.286170\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7846 | 0.502692 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.65926 | + | 9.65926i | 0.328046 | + | 0.328046i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.8564 | − | 13.8564i | 0.470046 | − | 0.470046i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 22.1469i | − | 0.750421i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 15.4641i | − | 0.523381i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.17260 | − | 7.17260i | 0.242478 | − | 0.242478i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.12436 | − | 8.12436i | −0.274340 | − | 0.274340i | 0.556505 | − | 0.830845i | \(-0.312142\pi\) |
−0.830845 | + | 0.556505i | \(0.812142\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.8449 | 1.58004 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.14359 | 0.139601 | 0.0698006 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0698006 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.2466 | − | 23.2466i | −0.782310 | − | 0.782310i | 0.197910 | − | 0.980220i | \(-0.436585\pi\) |
−0.980220 | + | 0.197910i | \(0.936585\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −50.7846 | + | 50.7846i | −1.70711 | + | 1.70711i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.2784i | 0.345116i | 0.984999 | + | 0.172558i | \(0.0552032\pi\) | ||||
−0.984999 | + | 0.172558i | \(0.944797\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.85641i | 0.196418i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.20925 | + | 2.20925i | −0.0740128 | + | 0.0740128i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.78461 | + | 8.78461i | 0.293966 | + | 0.293966i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0764 | 0.671080 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 96.4974 | 3.22196 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.79796 | + | 9.79796i | 0.326780 | + | 0.326780i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.7846 | + | 14.7846i | −0.492547 | + | 0.492547i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 23.1822i | − | 0.771456i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.1436i | 0.935525i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.3915 | + | 25.3915i | −0.843110 | + | 0.843110i | −0.989262 | − | 0.146152i | \(-0.953311\pi\) |
0.146152 | + | 0.989262i | \(0.453311\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 49.9808 | + | 49.9808i | 1.65776 | + | 1.65776i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.7391 | 1.44914 | 0.724570 | − | 0.689201i | \(-0.242038\pi\) | ||||
0.724570 | + | 0.689201i | \(0.242038\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3923 | −0.343935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.79315 | − | 1.79315i | −0.0592797 | − | 0.0592797i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.9282 | + | 12.9282i | −0.426927 | + | 0.426927i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.1271i | 1.81848i | 0.416277 | + | 0.909238i | \(0.363335\pi\) | ||||
−0.416277 | + | 0.909238i | \(0.636665\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 57.3205i | − | 1.88877i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.9754 | + | 24.9754i | −0.822074 | + | 0.822074i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.267949 | − | 0.267949i | −0.00881012 | − | 0.00881012i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.6312 | −0.677617 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.46410 | −0.113653 | −0.0568267 | − | 0.998384i | \(-0.518098\pi\) | ||||
−0.0568267 | + | 0.998384i | \(0.518098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.31508 | + | 5.31508i | 0.174195 | + | 0.174195i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.8564 | − | 19.8564i | 0.650070 | − | 0.650070i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 10.7589i | − | 0.351854i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53.1769i | − | 1.73721i | −0.495502 | − | 0.868607i | \(-0.665016\pi\) | ||
0.495502 | − | 0.868607i | \(-0.334984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 55.6076 | − | 55.6076i | 1.81469 | − | 1.81469i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.1962 | − | 29.1962i | −0.951767 | − | 0.951767i | 0.0471218 | − | 0.998889i | \(-0.484995\pi\) |
−0.998889 | + | 0.0471218i | \(0.984995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.3644 | −1.50983 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.1436 | −0.329971 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.0740 | − | 16.0740i | −0.522334 | − | 0.522334i | 0.395941 | − | 0.918276i | \(-0.370418\pi\) |
−0.918276 | + | 0.395941i | \(0.870418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.3205 | + | 35.3205i | −1.14655 | + | 1.14655i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 66.4408i | 2.15449i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 29.5692i | − | 0.957841i | −0.877858 | − | 0.478920i | \(-0.841028\pi\) | ||
0.877858 | − | 0.478920i | \(-0.158972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.3939 | + | 29.3939i | −0.951164 | + | 0.951164i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.00000 | + | 6.00000i | 0.193952 | + | 0.193952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.4233 | 0.401170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 39.7367 | + | 39.7367i | 1.28050 | + | 1.28050i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.14359 | − | 4.14359i | 0.133387 | − | 0.133387i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.24693i | 0.233046i | 0.993188 | + | 0.116523i | \(0.0371748\pi\) | ||||
−0.993188 | + | 0.116523i | \(0.962825\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.0000i | 0.385496i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5983 | − | 23.5983i | 0.757306 | − | 0.757306i | −0.218525 | − | 0.975831i | \(-0.570125\pi\) |
0.975831 | + | 0.218525i | \(0.0701246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.143594 | + | 0.143594i | 0.00460340 | + | 0.00460340i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.4195 | 0.461795 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.4641 | −1.64648 | −0.823241 | − | 0.567692i | \(-0.807837\pi\) | ||||
−0.823241 | + | 0.567692i | \(0.807837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.48528 | − | 8.48528i | −0.271191 | − | 0.271191i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.5167 | + | 12.5167i | −0.399626 | + | 0.399626i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 57.6038i | − | 1.83728i | −0.395100 | − | 0.918638i | \(-0.629290\pi\) | ||
0.395100 | − | 0.918638i | \(-0.370710\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.00000i | − | 0.191176i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.5959 | + | 19.5959i | −0.623745 | + | 0.623745i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.7846 | + | 38.7846i | 1.23328 | + | 1.23328i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.5644 | 0.526186 | 0.263093 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263093 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.5359 | −0.397815 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.1480 | + | 32.1480i | 1.01916 | + | 1.01916i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.80385 | + | 4.80385i | −0.152139 | + | 0.152139i | −0.779073 | − | 0.626933i | \(-0.784310\pi\) |
0.626933 | + | 0.779073i | \(0.284310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.51575i | − | 0.0479562i |
(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 | 256.2.e.a.65.1 | ✓ | 8 | |
3.2 | odd | 2 | 2304.2.k.f.577.1 | 8 | |||
4.3 | odd | 2 | inner | 256.2.e.a.65.4 | yes | 8 | |
8.3 | odd | 2 | 256.2.e.b.65.1 | yes | 8 | ||
8.5 | even | 2 | 256.2.e.b.65.4 | yes | 8 | ||
12.11 | even | 2 | 2304.2.k.f.577.2 | 8 | |||
16.3 | odd | 4 | 256.2.e.b.193.1 | yes | 8 | ||
16.5 | even | 4 | inner | 256.2.e.a.193.1 | yes | 8 | |
16.11 | odd | 4 | inner | 256.2.e.a.193.4 | yes | 8 | |
16.13 | even | 4 | 256.2.e.b.193.4 | yes | 8 | ||
24.5 | odd | 2 | 2304.2.k.k.577.3 | 8 | |||
24.11 | even | 2 | 2304.2.k.k.577.4 | 8 | |||
32.3 | odd | 8 | 1024.2.b.h.513.8 | 8 | |||
32.5 | even | 8 | 1024.2.a.j.1.4 | 4 | |||
32.11 | odd | 8 | 1024.2.a.j.1.3 | 4 | |||
32.13 | even | 8 | 1024.2.b.h.513.7 | 8 | |||
32.19 | odd | 8 | 1024.2.b.h.513.1 | 8 | |||
32.21 | even | 8 | 1024.2.a.g.1.1 | 4 | |||
32.27 | odd | 8 | 1024.2.a.g.1.2 | 4 | |||
32.29 | even | 8 | 1024.2.b.h.513.2 | 8 | |||
48.5 | odd | 4 | 2304.2.k.f.1729.2 | 8 | |||
48.11 | even | 4 | 2304.2.k.f.1729.1 | 8 | |||
48.29 | odd | 4 | 2304.2.k.k.1729.4 | 8 | |||
48.35 | even | 4 | 2304.2.k.k.1729.3 | 8 | |||
96.5 | odd | 8 | 9216.2.a.bb.1.1 | 4 | |||
96.11 | even | 8 | 9216.2.a.bb.1.4 | 4 | |||
96.53 | odd | 8 | 9216.2.a.bk.1.3 | 4 | |||
96.59 | even | 8 | 9216.2.a.bk.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
256.2.e.a.65.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
256.2.e.a.65.4 | yes | 8 | 4.3 | odd | 2 | inner | |
256.2.e.a.193.1 | yes | 8 | 16.5 | even | 4 | inner | |
256.2.e.a.193.4 | yes | 8 | 16.11 | odd | 4 | inner | |
256.2.e.b.65.1 | yes | 8 | 8.3 | odd | 2 | ||
256.2.e.b.65.4 | yes | 8 | 8.5 | even | 2 | ||
256.2.e.b.193.1 | yes | 8 | 16.3 | odd | 4 | ||
256.2.e.b.193.4 | yes | 8 | 16.13 | even | 4 | ||
1024.2.a.g.1.1 | 4 | 32.21 | even | 8 | |||
1024.2.a.g.1.2 | 4 | 32.27 | odd | 8 | |||
1024.2.a.j.1.3 | 4 | 32.11 | odd | 8 | |||
1024.2.a.j.1.4 | 4 | 32.5 | even | 8 | |||
1024.2.b.h.513.1 | 8 | 32.19 | odd | 8 | |||
1024.2.b.h.513.2 | 8 | 32.29 | even | 8 | |||
1024.2.b.h.513.7 | 8 | 32.13 | even | 8 | |||
1024.2.b.h.513.8 | 8 | 32.3 | odd | 8 | |||
2304.2.k.f.577.1 | 8 | 3.2 | odd | 2 | |||
2304.2.k.f.577.2 | 8 | 12.11 | even | 2 | |||
2304.2.k.f.1729.1 | 8 | 48.11 | even | 4 | |||
2304.2.k.f.1729.2 | 8 | 48.5 | odd | 4 | |||
2304.2.k.k.577.3 | 8 | 24.5 | odd | 2 | |||
2304.2.k.k.577.4 | 8 | 24.11 | even | 2 | |||
2304.2.k.k.1729.3 | 8 | 48.35 | even | 4 | |||
2304.2.k.k.1729.4 | 8 | 48.29 | odd | 4 | |||
9216.2.a.bb.1.1 | 4 | 96.5 | odd | 8 | |||
9216.2.a.bb.1.4 | 4 | 96.11 | even | 8 | |||
9216.2.a.bk.1.2 | 4 | 96.59 | even | 8 | |||
9216.2.a.bk.1.3 | 4 | 96.53 | odd | 8 |