Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(827,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.827");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.y (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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 20 x^{14} - 12 x^{13} + 40 x^{12} + 40 x^{11} + 82 x^{10} + 104 x^{9} + 537 x^{8} - 2528 x^{7} + 5494 x^{6} - 7284 x^{5} + 6002 x^{4} - 2984 x^{3} + 1000 x^{2} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 827.7 | ||
Root | \(-1.90660 - 0.789738i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.827 |
Dual form | 1638.2.y.c.1331.7 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.746053 | − | 0.746053i | 0.333645 | − | 0.333645i | −0.520324 | − | 0.853969i | \(-0.674189\pi\) |
0.853969 | + | 0.520324i | \(0.174189\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.05508i | − | 0.333645i | ||||||
\(11\) | 3.35792 | + | 3.35792i | 1.01245 | + | 1.01245i | 0.999922 | + | 0.0125287i | \(0.00398811\pi\) |
0.0125287 | + | 0.999922i | \(0.496012\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.20860 | + | 3.39695i | −0.335206 | + | 0.942145i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.02598 | 0.491372 | 0.245686 | − | 0.969349i | \(-0.420987\pi\) | ||||
0.245686 | + | 0.969349i | \(0.420987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.03497 | + | 5.03497i | 1.15510 | + | 1.15510i | 0.985515 | + | 0.169586i | \(0.0542432\pi\) |
0.169586 | + | 0.985515i | \(0.445757\pi\) | |||||||
\(20\) | −0.746053 | − | 0.746053i | −0.166823 | − | 0.166823i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.74881 | 1.01245 | ||||||||
\(23\) | −2.39154 | −0.498670 | −0.249335 | − | 0.968417i | \(-0.580212\pi\) | ||||
−0.249335 | + | 0.968417i | \(0.580212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.88681i | 0.777362i | ||||||||
\(26\) | 1.54740 | + | 3.25662i | 0.303470 | + | 0.638675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | 8.46166i | 1.57129i | 0.618677 | + | 0.785645i | \(0.287669\pi\) | ||||
−0.618677 | + | 0.785645i | \(0.712331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.55035 | − | 5.55035i | −0.996872 | − | 0.996872i | 0.00312287 | − | 0.999995i | \(-0.499006\pi\) |
−0.999995 | + | 0.00312287i | \(0.999006\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.43258 | − | 1.43258i | 0.245686 | − | 0.245686i | ||||
\(35\) | 1.05508i | 0.178341i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.97346 | − | 6.97346i | 1.14643 | − | 1.14643i | 0.159180 | − | 0.987250i | \(-0.449115\pi\) |
0.987250 | − | 0.159180i | \(-0.0508849\pi\) | |||||||
\(38\) | 7.12053 | 1.15510 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.05508 | −0.166823 | ||||||||
\(41\) | 2.39122 | − | 2.39122i | 0.373446 | − | 0.373446i | −0.495285 | − | 0.868731i | \(-0.664936\pi\) |
0.868731 | + | 0.495285i | \(0.164936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.24408i | − | 1.40971i | −0.709352 | − | 0.704855i | \(-0.751012\pi\) | ||
0.709352 | − | 0.704855i | \(-0.248988\pi\) | |||||||
\(44\) | 3.35792 | − | 3.35792i | 0.506225 | − | 0.506225i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.69107 | + | 1.69107i | −0.249335 | + | 0.249335i | ||||
\(47\) | 3.48199 | + | 3.48199i | 0.507901 | + | 0.507901i | 0.913882 | − | 0.405981i | \(-0.133070\pi\) |
−0.405981 | + | 0.913882i | \(0.633070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 2.74839 | + | 2.74839i | 0.388681 | + | 0.388681i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.39695 | + | 1.20860i | 0.471072 | + | 0.167603i | ||||
\(53\) | 1.35557i | 0.186202i | 0.995657 | + | 0.0931011i | \(0.0296780\pi\) | ||||
−0.995657 | + | 0.0931011i | \(0.970322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.01037 | 0.675598 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.98330 | + | 5.98330i | 0.785645 | + | 0.785645i | ||||
\(59\) | 4.49527 | + | 4.49527i | 0.585235 | + | 0.585235i | 0.936337 | − | 0.351103i | \(-0.114193\pi\) |
−0.351103 | + | 0.936337i | \(0.614193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.56297 | −0.200118 | −0.100059 | − | 0.994982i | \(-0.531903\pi\) | ||||
−0.100059 | + | 0.994982i | \(0.531903\pi\) | |||||||
\(62\) | −7.84938 | −0.996872 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 1.63263 | + | 3.43599i | 0.202502 | + | 0.426182i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.78711 | − | 1.78711i | −0.218331 | − | 0.218331i | 0.589464 | − | 0.807795i | \(-0.299339\pi\) |
−0.807795 | + | 0.589464i | \(0.799339\pi\) | |||||||
\(68\) | − | 2.02598i | − | 0.245686i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.746053 | + | 0.746053i | 0.0891704 | + | 0.0891704i | ||||
\(71\) | 9.95954 | − | 9.95954i | 1.18198 | − | 1.18198i | 0.202749 | − | 0.979231i | \(-0.435013\pi\) |
0.979231 | − | 0.202749i | \(-0.0649875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.90170 | + | 3.90170i | −0.456659 | + | 0.456659i | −0.897557 | − | 0.440898i | \(-0.854660\pi\) |
0.440898 | + | 0.897557i | \(0.354660\pi\) | |||||||
\(74\) | − | 9.86196i | − | 1.14643i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.03497 | − | 5.03497i | 0.577551 | − | 0.577551i | ||||
\(77\) | −4.74881 | −0.541177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2625 | 1.15463 | 0.577313 | − | 0.816523i | \(-0.304101\pi\) | ||||
0.577313 | + | 0.816523i | \(0.304101\pi\) | |||||||
\(80\) | −0.746053 | + | 0.746053i | −0.0834113 | + | 0.0834113i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.38170i | − | 0.373446i | ||||||
\(83\) | −10.2261 | + | 10.2261i | −1.12246 | + | 1.12246i | −0.131088 | + | 0.991371i | \(0.541847\pi\) |
−0.991371 | + | 0.131088i | \(0.958153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.51149 | − | 1.51149i | 0.163944 | − | 0.163944i | ||||
\(86\) | −6.53655 | − | 6.53655i | −0.704855 | − | 0.704855i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.74881i | − | 0.506225i | ||||||
\(89\) | −4.40919 | − | 4.40919i | −0.467373 | − | 0.467373i | 0.433690 | − | 0.901062i | \(-0.357211\pi\) |
−0.901062 | + | 0.433690i | \(0.857211\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.54740 | − | 3.25662i | −0.162211 | − | 0.341386i | ||||
\(92\) | 2.39154i | 0.249335i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.92428 | 0.507901 | ||||||||
\(95\) | 7.51271 | 0.770788 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0928 | − | 11.0928i | −1.12630 | − | 1.12630i | −0.990773 | − | 0.135531i | \(-0.956726\pi\) |
−0.135531 | − | 0.990773i | \(-0.543274\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.88681 | 0.388681 | ||||||||
\(101\) | 4.43684 | 0.441482 | 0.220741 | − | 0.975332i | \(-0.429152\pi\) | ||||
0.220741 | + | 0.975332i | \(0.429152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.93465i | − | 0.978890i | −0.872034 | − | 0.489445i | \(-0.837199\pi\) | ||
0.872034 | − | 0.489445i | \(-0.162801\pi\) | |||||||
\(104\) | 3.25662 | − | 1.54740i | 0.319338 | − | 0.151735i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.958534 | + | 0.958534i | 0.0931011 | + | 0.0931011i | ||||
\(107\) | 12.0250i | 1.16250i | 0.813725 | + | 0.581250i | \(0.197436\pi\) | ||||
−0.813725 | + | 0.581250i | \(0.802564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.47819 | + | 2.47819i | 0.237367 | + | 0.237367i | 0.815759 | − | 0.578392i | \(-0.196320\pi\) |
−0.578392 | + | 0.815759i | \(0.696320\pi\) | |||||||
\(110\) | 3.54287 | − | 3.54287i | 0.337799 | − | 0.337799i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | 19.4049i | 1.82546i | 0.408561 | + | 0.912731i | \(0.366031\pi\) | ||||
−0.408561 | + | 0.912731i | \(0.633969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.78421 | + | 1.78421i | −0.166379 | + | 0.166379i | ||||
\(116\) | 8.46166 | 0.785645 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.35727 | 0.585235 | ||||||||
\(119\) | −1.43258 | + | 1.43258i | −0.131325 | + | 0.131325i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5512i | 1.05011i | ||||||||
\(122\) | −1.10519 | + | 1.10519i | −0.100059 | + | 0.100059i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.55035 | + | 5.55035i | −0.498436 | + | 0.498436i | ||||
\(125\) | 6.63003 | + | 6.63003i | 0.593008 | + | 0.593008i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.6946i | − | 1.30393i | −0.758248 | − | 0.651966i | \(-0.773944\pi\) | ||
0.758248 | − | 0.651966i | \(-0.226056\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.58405 | + | 1.27517i | 0.314342 | + | 0.111840i | ||||
\(131\) | 2.22152i | 0.194095i | 0.995280 | + | 0.0970477i | \(0.0309399\pi\) | ||||
−0.995280 | + | 0.0970477i | \(0.969060\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.12053 | −0.617428 | ||||||||
\(134\) | −2.52736 | −0.218331 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.43258 | − | 1.43258i | −0.122843 | − | 0.122843i | ||||
\(137\) | 0.387266 | + | 0.387266i | 0.0330864 | + | 0.0330864i | 0.723456 | − | 0.690370i | \(-0.242552\pi\) |
−0.690370 | + | 0.723456i | \(0.742552\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.80074 | −0.237556 | −0.118778 | − | 0.992921i | \(-0.537898\pi\) | ||||
−0.118778 | + | 0.992921i | \(0.537898\pi\) | |||||||
\(140\) | 1.05508 | 0.0891704 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 14.0849i | − | 1.18198i | ||||||
\(143\) | −15.4651 | + | 7.34830i | −1.29325 | + | 0.614496i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.31285 | + | 6.31285i | 0.524253 | + | 0.524253i | ||||
\(146\) | 5.51784i | 0.456659i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.97346 | − | 6.97346i | −0.573215 | − | 0.573215i | ||||
\(149\) | 0.866918 | − | 0.866918i | 0.0710207 | − | 0.0710207i | −0.670704 | − | 0.741725i | \(-0.734008\pi\) |
0.741725 | + | 0.670704i | \(0.234008\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7845 | − | 14.7845i | 1.20315 | − | 1.20315i | 0.229945 | − | 0.973204i | \(-0.426145\pi\) |
0.973204 | − | 0.229945i | \(-0.0738546\pi\) | |||||||
\(152\) | − | 7.12053i | − | 0.577551i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.35792 | + | 3.35792i | −0.270589 | + | 0.270589i | ||||
\(155\) | −8.28171 | −0.665203 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2471 | 1.21685 | 0.608424 | − | 0.793612i | \(-0.291802\pi\) | ||||
0.608424 | + | 0.793612i | \(0.291802\pi\) | |||||||
\(158\) | 7.25671 | − | 7.25671i | 0.577313 | − | 0.577313i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.05508i | 0.0834113i | ||||||||
\(161\) | 1.69107 | − | 1.69107i | 0.133275 | − | 0.133275i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2208 | + | 16.2208i | −1.27051 | + | 1.27051i | −0.324693 | + | 0.945819i | \(0.605261\pi\) |
−0.945819 | + | 0.324693i | \(0.894739\pi\) | |||||||
\(164\) | −2.39122 | − | 2.39122i | −0.186723 | − | 0.186723i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.4619i | 1.12246i | ||||||||
\(167\) | −17.0656 | − | 17.0656i | −1.32058 | − | 1.32058i | −0.913308 | − | 0.407269i | \(-0.866481\pi\) |
−0.407269 | − | 0.913308i | \(-0.633519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0786 | − | 8.21112i | −0.775274 | − | 0.631625i | ||||
\(170\) | − | 2.13757i | − | 0.163944i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.24408 | −0.704855 | ||||||||
\(173\) | 8.52210 | 0.647923 | 0.323961 | − | 0.946070i | \(-0.394985\pi\) | ||||
0.323961 | + | 0.946070i | \(0.394985\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.74839 | − | 2.74839i | −0.207759 | − | 0.207759i | ||||
\(176\) | −3.35792 | − | 3.35792i | −0.253113 | − | 0.253113i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.23553 | −0.467373 | ||||||||
\(179\) | −3.46058 | −0.258656 | −0.129328 | − | 0.991602i | \(-0.541282\pi\) | ||||
−0.129328 | + | 0.991602i | \(0.541282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8236i | 1.84513i | 0.385846 | + | 0.922563i | \(0.373910\pi\) | ||||
−0.385846 | + | 0.922563i | \(0.626090\pi\) | |||||||
\(182\) | −3.39695 | − | 1.20860i | −0.251799 | − | 0.0895875i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.69107 | + | 1.69107i | 0.124668 | + | 0.124668i | ||||
\(185\) | − | 10.4051i | − | 0.765001i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.80307 | + | 6.80307i | 0.497490 | + | 0.497490i | ||||
\(188\) | 3.48199 | − | 3.48199i | 0.253951 | − | 0.253951i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.31229 | − | 5.31229i | 0.385394 | − | 0.385394i | ||||
\(191\) | 7.86219i | 0.568888i | 0.958693 | + | 0.284444i | \(0.0918090\pi\) | ||||
−0.958693 | + | 0.284444i | \(0.908191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.85067 | − | 4.85067i | 0.349159 | − | 0.349159i | −0.510637 | − | 0.859796i | \(-0.670591\pi\) |
0.859796 | + | 0.510637i | \(0.170591\pi\) | |||||||
\(194\) | −15.6876 | −1.12630 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 9.34718 | − | 9.34718i | 0.665959 | − | 0.665959i | −0.290819 | − | 0.956778i | \(-0.593928\pi\) |
0.956778 | + | 0.290819i | \(0.0939278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23.0454i | − | 1.63365i | −0.576887 | − | 0.816824i | \(-0.695733\pi\) | ||
0.576887 | − | 0.816824i | \(-0.304267\pi\) | |||||||
\(200\) | 2.74839 | − | 2.74839i | 0.194340 | − | 0.194340i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.13732 | − | 3.13732i | 0.220741 | − | 0.220741i | ||||
\(203\) | −5.98330 | − | 5.98330i | −0.419945 | − | 0.419945i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.56796i | − | 0.249197i | ||||||
\(206\) | −7.02486 | − | 7.02486i | −0.489445 | − | 0.489445i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.20860 | − | 3.39695i | 0.0838014 | − | 0.235536i | ||||
\(209\) | 33.8140i | 2.33897i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.931807 | −0.0641482 | −0.0320741 | − | 0.999485i | \(-0.510211\pi\) | ||||
−0.0320741 | + | 0.999485i | \(0.510211\pi\) | |||||||
\(212\) | 1.35557 | 0.0931011 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.50295 | + | 8.50295i | 0.581250 | + | 0.581250i | ||||
\(215\) | −6.89658 | − | 6.89658i | −0.470343 | − | 0.470343i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.84938 | 0.532851 | ||||||||
\(218\) | 3.50468 | 0.237367 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 5.01037i | − | 0.337799i | ||||||
\(221\) | −2.44860 | + | 6.88216i | −0.164711 | + | 0.462944i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.806330 | − | 0.806330i | −0.0539959 | − | 0.0539959i | 0.679593 | − | 0.733589i | \(-0.262156\pi\) |
−0.733589 | + | 0.679593i | \(0.762156\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.7214 | + | 13.7214i | 0.912731 | + | 0.912731i | ||||
\(227\) | 2.04742 | − | 2.04742i | 0.135892 | − | 0.135892i | −0.635889 | − | 0.771781i | \(-0.719366\pi\) |
0.771781 | + | 0.635889i | \(0.219366\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.3112 | + | 12.3112i | −0.813549 | + | 0.813549i | −0.985164 | − | 0.171615i | \(-0.945101\pi\) |
0.171615 | + | 0.985164i | \(0.445101\pi\) | |||||||
\(230\) | 2.52326i | 0.166379i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.98330 | − | 5.98330i | 0.392823 | − | 0.392823i | ||||
\(233\) | 24.7227 | 1.61964 | 0.809818 | − | 0.586682i | \(-0.199566\pi\) | ||||
0.809818 | + | 0.586682i | \(0.199566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.19550 | 0.338917 | ||||||||
\(236\) | 4.49527 | − | 4.49527i | 0.292617 | − | 0.292617i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.02598i | 0.131325i | ||||||||
\(239\) | −1.69453 | + | 1.69453i | −0.109610 | + | 0.109610i | −0.759785 | − | 0.650175i | \(-0.774696\pi\) |
0.650175 | + | 0.759785i | \(0.274696\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.52253 | − | 4.52253i | 0.291322 | − | 0.291322i | −0.546281 | − | 0.837602i | \(-0.683957\pi\) |
0.837602 | + | 0.546281i | \(0.183957\pi\) | |||||||
\(242\) | 8.16794 | + | 8.16794i | 0.525055 | + | 0.525055i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.56297i | 0.100059i | ||||||||
\(245\) | −0.746053 | − | 0.746053i | −0.0476636 | − | 0.0476636i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.1888 | + | 11.0183i | −1.47547 | + | 0.701077i | ||||
\(248\) | 7.84938i | 0.498436i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.37628 | 0.593008 | ||||||||
\(251\) | −27.3370 | −1.72549 | −0.862747 | − | 0.505636i | \(-0.831258\pi\) | ||||
−0.862747 | + | 0.505636i | \(0.831258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.03059 | − | 8.03059i | −0.504879 | − | 0.504879i | ||||
\(254\) | −10.3906 | − | 10.3906i | −0.651966 | − | 0.651966i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.6049 | −1.72195 | −0.860975 | − | 0.508648i | \(-0.830145\pi\) | ||||
−0.860975 | + | 0.508648i | \(0.830145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.86196i | 0.612792i | ||||||||
\(260\) | 3.43599 | − | 1.63263i | 0.213091 | − | 0.101251i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.57085 | + | 1.57085i | 0.0970477 | + | 0.0970477i | ||||
\(263\) | − | 26.9692i | − | 1.66299i | −0.555529 | − | 0.831497i | \(-0.687484\pi\) | ||
0.555529 | − | 0.831497i | \(-0.312516\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.01133 | + | 1.01133i | 0.0621254 | + | 0.0621254i | ||||
\(266\) | −5.03497 | + | 5.03497i | −0.308714 | + | 0.308714i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.78711 | + | 1.78711i | −0.109165 | + | 0.109165i | ||||
\(269\) | − | 15.1618i | − | 0.924433i | −0.886767 | − | 0.462217i | \(-0.847054\pi\) | ||
0.886767 | − | 0.462217i | \(-0.152946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8111 | + | 17.8111i | −1.08195 | + | 1.08195i | −0.0856179 | + | 0.996328i | \(0.527286\pi\) |
−0.996328 | + | 0.0856179i | \(0.972714\pi\) | |||||||
\(272\) | −2.02598 | −0.122843 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.547677 | 0.0330864 | ||||||||
\(275\) | −13.0516 | + | 13.0516i | −0.787040 | + | 0.787040i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.04741i | − | 0.183101i | −0.995800 | − | 0.0915507i | \(-0.970818\pi\) | ||
0.995800 | − | 0.0915507i | \(-0.0291823\pi\) | |||||||
\(278\) | −1.98042 | + | 1.98042i | −0.118778 | + | 0.118778i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.746053 | − | 0.746053i | 0.0445852 | − | 0.0445852i | ||||
\(281\) | 10.5654 | + | 10.5654i | 0.630278 | + | 0.630278i | 0.948138 | − | 0.317859i | \(-0.102964\pi\) |
−0.317859 | + | 0.948138i | \(0.602964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 21.8771i | − | 1.30046i | −0.759738 | − | 0.650229i | \(-0.774673\pi\) | ||
0.759738 | − | 0.650229i | \(-0.225327\pi\) | |||||||
\(284\) | −9.95954 | − | 9.95954i | −0.590990 | − | 0.590990i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.73942 | + | 16.1315i | −0.339379 | + | 0.953875i | ||||
\(287\) | 3.38170i | 0.199615i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8954 | −0.758553 | ||||||||
\(290\) | 8.92771 | 0.524253 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.90170 | + | 3.90170i | 0.228330 | + | 0.228330i | ||||
\(293\) | 9.78815 | + | 9.78815i | 0.571830 | + | 0.571830i | 0.932640 | − | 0.360809i | \(-0.117500\pi\) |
−0.360809 | + | 0.932640i | \(0.617500\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.70742 | 0.390521 | ||||||||
\(296\) | −9.86196 | −0.573215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 1.22601i | − | 0.0710207i | ||||||
\(299\) | 2.89042 | − | 8.12394i | 0.167157 | − | 0.469820i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.53655 | + | 6.53655i | 0.376761 | + | 0.376761i | ||||
\(302\) | − | 20.9085i | − | 1.20315i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.03497 | − | 5.03497i | −0.288775 | − | 0.288775i | ||||
\(305\) | −1.16606 | + | 1.16606i | −0.0667684 | + | 0.0667684i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3093 | + | 12.3093i | −0.702527 | + | 0.702527i | −0.964952 | − | 0.262425i | \(-0.915478\pi\) |
0.262425 | + | 0.964952i | \(0.415478\pi\) | |||||||
\(308\) | 4.74881i | 0.270589i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.85605 | + | 5.85605i | −0.332601 | + | 0.332601i | ||||
\(311\) | −2.57110 | −0.145794 | −0.0728968 | − | 0.997339i | \(-0.523224\pi\) | ||||
−0.0728968 | + | 0.997339i | \(0.523224\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.14291 | 0.0646013 | 0.0323006 | − | 0.999478i | \(-0.489717\pi\) | ||||
0.0323006 | + | 0.999478i | \(0.489717\pi\) | |||||||
\(314\) | 10.7813 | − | 10.7813i | 0.608424 | − | 0.608424i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 10.2625i | − | 0.577313i | ||||||
\(317\) | 9.45116 | − | 9.45116i | 0.530830 | − | 0.530830i | −0.389989 | − | 0.920819i | \(-0.627521\pi\) |
0.920819 | + | 0.389989i | \(0.127521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.4136 | + | 28.4136i | −1.59085 | + | 1.59085i | ||||
\(320\) | 0.746053 | + | 0.746053i | 0.0417056 | + | 0.0417056i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 2.39154i | − | 0.133275i | ||||||
\(323\) | 10.2008 | + | 10.2008i | 0.567585 | + | 0.567585i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.2033 | − | 4.69760i | −0.732388 | − | 0.260576i | ||||
\(326\) | 22.9397i | 1.27051i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.38170 | −0.186723 | ||||||||
\(329\) | −4.92428 | −0.271485 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.76490 | + | 8.76490i | 0.481763 | + | 0.481763i | 0.905694 | − | 0.423932i | \(-0.139350\pi\) |
−0.423932 | + | 0.905694i | \(0.639350\pi\) | |||||||
\(332\) | 10.2261 | + | 10.2261i | 0.561229 | + | 0.561229i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.1344 | −1.32058 | ||||||||
\(335\) | −2.66656 | −0.145690 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 31.8297i | − | 1.73387i | −0.498418 | − | 0.866937i | \(-0.666086\pi\) | ||
0.498418 | − | 0.866937i | \(-0.333914\pi\) | |||||||
\(338\) | −12.9328 | + | 1.32048i | −0.703449 | + | 0.0718249i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.51149 | − | 1.51149i | −0.0819720 | − | 0.0819720i | ||||
\(341\) | − | 37.2752i | − | 2.01857i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −6.53655 | + | 6.53655i | −0.352427 | + | 0.352427i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.02603 | − | 6.02603i | 0.323961 | − | 0.323961i | ||||
\(347\) | − | 20.0727i | − | 1.07756i | −0.842447 | − | 0.538780i | \(-0.818886\pi\) | ||
0.842447 | − | 0.538780i | \(-0.181114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.88355 | + | 8.88355i | −0.475525 | + | 0.475525i | −0.903697 | − | 0.428172i | \(-0.859158\pi\) |
0.428172 | + | 0.903697i | \(0.359158\pi\) | |||||||
\(350\) | −3.88681 | −0.207759 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.74881 | −0.253113 | ||||||||
\(353\) | −12.9241 | + | 12.9241i | −0.687878 | + | 0.687878i | −0.961763 | − | 0.273884i | \(-0.911691\pi\) |
0.273884 | + | 0.961763i | \(0.411691\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 14.8607i | − | 0.788723i | ||||||
\(356\) | −4.40919 | + | 4.40919i | −0.233686 | + | 0.233686i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.44700 | + | 2.44700i | −0.129328 | + | 0.129328i | ||||
\(359\) | −10.7224 | − | 10.7224i | −0.565907 | − | 0.565907i | 0.365072 | − | 0.930979i | \(-0.381044\pi\) |
−0.930979 | + | 0.365072i | \(0.881044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.7019i | 1.66852i | ||||||||
\(362\) | 17.5530 | + | 17.5530i | 0.922563 | + | 0.922563i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.25662 | + | 1.54740i | −0.170693 | + | 0.0811057i | ||||
\(365\) | 5.82175i | 0.304724i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.5681 | −0.760447 | −0.380224 | − | 0.924895i | \(-0.624153\pi\) | ||||
−0.380224 | + | 0.924895i | \(0.624153\pi\) | |||||||
\(368\) | 2.39154 | 0.124668 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.35754 | − | 7.35754i | −0.382500 | − | 0.382500i | ||||
\(371\) | −0.958534 | − | 0.958534i | −0.0497646 | − | 0.0497646i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.64322 | −0.240417 | −0.120208 | − | 0.992749i | \(-0.538356\pi\) | ||||
−0.120208 | + | 0.992749i | \(0.538356\pi\) | |||||||
\(374\) | 9.62100 | 0.497490 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 4.92428i | − | 0.253951i | ||||||
\(377\) | −28.7438 | − | 10.2268i | −1.48038 | − | 0.526705i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.74493 | − | 6.74493i | −0.346464 | − | 0.346464i | 0.512327 | − | 0.858791i | \(-0.328784\pi\) |
−0.858791 | + | 0.512327i | \(0.828784\pi\) | |||||||
\(380\) | − | 7.51271i | − | 0.385394i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.55941 | + | 5.55941i | 0.284444 | + | 0.284444i | ||||
\(383\) | 1.32694 | − | 1.32694i | 0.0678037 | − | 0.0678037i | −0.672392 | − | 0.740195i | \(-0.734733\pi\) |
0.740195 | + | 0.672392i | \(0.234733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.54287 | + | 3.54287i | −0.180561 | + | 0.180561i | ||||
\(386\) | − | 6.85988i | − | 0.349159i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.0928 | + | 11.0928i | −0.563152 | + | 0.563152i | ||||
\(389\) | 25.9151 | 1.31395 | 0.656974 | − | 0.753913i | \(-0.271836\pi\) | ||||
0.656974 | + | 0.753913i | \(0.271836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.84521 | −0.245033 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 13.2189i | − | 0.665959i | ||||||
\(395\) | 7.65639 | − | 7.65639i | 0.385235 | − | 0.385235i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1031 | + | 21.1031i | −1.05913 | + | 1.05913i | −0.0609954 | + | 0.998138i | \(0.519427\pi\) |
−0.998138 | + | 0.0609954i | \(0.980573\pi\) | |||||||
\(398\) | −16.2956 | − | 16.2956i | −0.816824 | − | 0.816824i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 3.88681i | − | 0.194340i | ||||||
\(401\) | 18.9302 | + | 18.9302i | 0.945332 | + | 0.945332i | 0.998581 | − | 0.0532497i | \(-0.0169579\pi\) |
−0.0532497 | + | 0.998581i | \(0.516958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.5624 | − | 12.1461i | 1.27336 | − | 0.605041i | ||||
\(404\) | − | 4.43684i | − | 0.220741i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.46166 | −0.419945 | ||||||||
\(407\) | 46.8326 | 2.32141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4950 | − | 10.4950i | −0.518945 | − | 0.518945i | 0.398307 | − | 0.917252i | \(-0.369598\pi\) |
−0.917252 | + | 0.398307i | \(0.869598\pi\) | |||||||
\(410\) | −2.52293 | − | 2.52293i | −0.124598 | − | 0.124598i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.93465 | −0.489445 | ||||||||
\(413\) | −6.35727 | −0.312821 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.2584i | 0.749005i | ||||||||
\(416\) | −1.54740 | − | 3.25662i | −0.0758674 | − | 0.159669i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 23.9101 | + | 23.9101i | 1.16948 | + | 1.16948i | ||||
\(419\) | − | 22.9538i | − | 1.12136i | −0.828031 | − | 0.560682i | \(-0.810539\pi\) | ||
0.828031 | − | 0.560682i | \(-0.189461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3182 | + | 20.3182i | 0.990247 | + | 0.990247i | 0.999953 | − | 0.00970630i | \(-0.00308966\pi\) |
−0.00970630 | + | 0.999953i | \(0.503090\pi\) | |||||||
\(422\) | −0.658887 | + | 0.658887i | −0.0320741 | + | 0.0320741i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.958534 | − | 0.958534i | 0.0465505 | − | 0.0465505i | ||||
\(425\) | 7.87460i | 0.381974i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.10519 | − | 1.10519i | 0.0534838 | − | 0.0534838i | ||||
\(428\) | 12.0250 | 0.581250 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.75323 | −0.470343 | ||||||||
\(431\) | −0.553365 | + | 0.553365i | −0.0266547 | + | 0.0266547i | −0.720309 | − | 0.693654i | \(-0.756000\pi\) |
0.693654 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.38424i | − | 0.0665222i | −0.999447 | − | 0.0332611i | \(-0.989411\pi\) | ||
0.999447 | − | 0.0332611i | \(-0.0105893\pi\) | |||||||
\(434\) | 5.55035 | − | 5.55035i | 0.266425 | − | 0.266425i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.47819 | − | 2.47819i | 0.118684 | − | 0.118684i | ||||
\(437\) | −12.0413 | − | 12.0413i | −0.576015 | − | 0.576015i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.3680i | − | 0.685746i | −0.939382 | − | 0.342873i | \(-0.888600\pi\) | ||
0.939382 | − | 0.342873i | \(-0.111400\pi\) | |||||||
\(440\) | −3.54287 | − | 3.54287i | −0.168899 | − | 0.168899i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.13500 | + | 6.59784i | 0.149117 | + | 0.313827i | ||||
\(443\) | − | 7.27225i | − | 0.345515i | −0.984964 | − | 0.172758i | \(-0.944732\pi\) | ||
0.984964 | − | 0.172758i | \(-0.0552677\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.57897 | −0.311873 | ||||||||
\(446\) | −1.14032 | −0.0539959 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | −11.1201 | − | 11.1201i | −0.524789 | − | 0.524789i | 0.394225 | − | 0.919014i | \(-0.371013\pi\) |
−0.919014 | + | 0.394225i | \(0.871013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0591 | 0.756191 | ||||||||
\(452\) | 19.4049 | 0.912731 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.89548i | − | 0.135892i | ||||||
\(455\) | −3.58405 | − | 1.27517i | −0.168023 | − | 0.0597808i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.25037 | + | 7.25037i | 0.339158 | + | 0.339158i | 0.856050 | − | 0.516892i | \(-0.172911\pi\) |
−0.516892 | + | 0.856050i | \(0.672911\pi\) | |||||||
\(458\) | 17.4107i | 0.813549i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.78421 | + | 1.78421i | 0.0831894 | + | 0.0831894i | ||||
\(461\) | 20.4191 | − | 20.4191i | 0.951011 | − | 0.951011i | −0.0478439 | − | 0.998855i | \(-0.515235\pi\) |
0.998855 | + | 0.0478439i | \(0.0152350\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.16963 | − | 5.16963i | 0.240253 | − | 0.240253i | −0.576702 | − | 0.816955i | \(-0.695661\pi\) |
0.816955 | + | 0.576702i | \(0.195661\pi\) | |||||||
\(464\) | − | 8.46166i | − | 0.392823i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.4816 | − | 17.4816i | 0.809818 | − | 0.809818i | ||||
\(467\) | −16.6030 | −0.768293 | −0.384147 | − | 0.923272i | \(-0.625504\pi\) | ||||
−0.384147 | + | 0.923272i | \(0.625504\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.52736 | 0.116703 | ||||||||
\(470\) | 3.67378 | − | 3.67378i | 0.169459 | − | 0.169459i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.35727i | − | 0.292617i | ||||||
\(473\) | 31.0409 | − | 31.0409i | 1.42726 | − | 1.42726i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.5700 | + | 19.5700i | −0.897932 | + | 0.897932i | ||||
\(476\) | 1.43258 | + | 1.43258i | 0.0656624 | + | 0.0656624i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.39642i | 0.109610i | ||||||||
\(479\) | 20.7447 | + | 20.7447i | 0.947851 | + | 0.947851i | 0.998706 | − | 0.0508550i | \(-0.0161946\pi\) |
−0.0508550 | + | 0.998706i | \(0.516195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2604 | + | 32.1166i | 0.695813 | + | 1.46439i | ||||
\(482\) | − | 6.39582i | − | 0.291322i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.5512 | 0.525055 | ||||||||
\(485\) | −16.5516 | −0.751572 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.21573 | − | 5.21573i | −0.236347 | − | 0.236347i | 0.578989 | − | 0.815336i | \(-0.303448\pi\) |
−0.815336 | + | 0.578989i | \(0.803448\pi\) | |||||||
\(488\) | 1.10519 | + | 1.10519i | 0.0500295 | + | 0.0500295i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.05508 | −0.0476636 | ||||||||
\(491\) | −11.0398 | −0.498220 | −0.249110 | − | 0.968475i | \(-0.580138\pi\) | ||||
−0.249110 | + | 0.968475i | \(0.580138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.1431i | 0.772089i | ||||||||
\(494\) | −8.60587 | + | 24.1881i | −0.387197 | + | 1.08827i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.55035 | + | 5.55035i | 0.249218 | + | 0.249218i | ||||
\(497\) | 14.0849i | 0.631795i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.56893 | + | 3.56893i | 0.159767 | + | 0.159767i | 0.782464 | − | 0.622696i | \(-0.213963\pi\) |
−0.622696 | + | 0.782464i | \(0.713963\pi\) | |||||||
\(500\) | 6.63003 | − | 6.63003i | 0.296504 | − | 0.296504i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.3302 | + | 19.3302i | −0.862747 | + | 0.862747i | ||||
\(503\) | 36.7436i | 1.63832i | 0.573566 | + | 0.819159i | \(0.305559\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.31012 | − | 3.31012i | 0.147298 | − | 0.147298i | ||||
\(506\) | −11.3570 | −0.504879 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.6946 | −0.651966 | ||||||||
\(509\) | 8.92586 | − | 8.92586i | 0.395632 | − | 0.395632i | −0.481057 | − | 0.876689i | \(-0.659747\pi\) |
0.876689 | + | 0.481057i | \(0.159747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.51784i | − | 0.244095i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.5196 | + | 19.5196i | −0.860975 | + | 0.860975i | ||||
\(515\) | −7.41178 | − | 7.41178i | −0.326602 | − | 0.326602i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.3845i | 1.02845i | ||||||||
\(518\) | 6.97346 | + | 6.97346i | 0.306396 | + | 0.306396i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.27517 | − | 3.58405i | 0.0559198 | − | 0.157171i | ||||
\(521\) | 11.5826i | 0.507445i | 0.967277 | + | 0.253722i | \(0.0816550\pi\) | ||||
−0.967277 | + | 0.253722i | \(0.918345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.9601 | 1.39752 | 0.698758 | − | 0.715358i | \(-0.253737\pi\) | ||||
0.698758 | + | 0.715358i | \(0.253737\pi\) | |||||||
\(524\) | 2.22152 | 0.0970477 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.0701 | − | 19.0701i | −0.831497 | − | 0.831497i | ||||
\(527\) | −11.2449 | − | 11.2449i | −0.489835 | − | 0.489835i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2805 | −0.751328 | ||||||||
\(530\) | 1.43023 | 0.0621254 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.12053i | 0.308714i | ||||||||
\(533\) | 5.23283 | + | 11.0129i | 0.226659 | + | 0.477022i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.97127 | + | 8.97127i | 0.387862 | + | 0.387862i | ||||
\(536\) | 2.52736i | 0.109165i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.7210 | − | 10.7210i | −0.462217 | − | 0.462217i | ||||
\(539\) | 3.35792 | − | 3.35792i | 0.144636 | − | 0.144636i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.83741 | − | 3.83741i | 0.164983 | − | 0.164983i | −0.619787 | − | 0.784770i | \(-0.712781\pi\) |
0.784770 | + | 0.619787i | \(0.212781\pi\) | |||||||
\(542\) | 25.1887i | 1.08195i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.43258 | + | 1.43258i | −0.0614215 | + | 0.0614215i | ||||
\(545\) | 3.69772 | 0.158393 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7371 | −0.459087 | −0.229544 | − | 0.973298i | \(-0.573723\pi\) | ||||
−0.229544 | + | 0.973298i | \(0.573723\pi\) | |||||||
\(548\) | 0.387266 | − | 0.387266i | 0.0165432 | − | 0.0165432i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.4577i | 0.787040i | ||||||||
\(551\) | −42.6042 | + | 42.6042i | −1.81500 | + | 1.81500i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.25671 | + | 7.25671i | −0.308587 | + | 0.308587i | ||||
\(554\) | −2.15485 | − | 2.15485i | −0.0915507 | − | 0.0915507i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.80074i | 0.118778i | ||||||||
\(557\) | −5.56727 | − | 5.56727i | −0.235893 | − | 0.235893i | 0.579254 | − | 0.815147i | \(-0.303344\pi\) |
−0.815147 | + | 0.579254i | \(0.803344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.4017 | + | 11.1724i | 1.32815 | + | 0.472543i | ||||
\(560\) | − | 1.05508i | − | 0.0445852i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.9417 | 0.630278 | ||||||||
\(563\) | −35.8520 | −1.51098 | −0.755491 | − | 0.655159i | \(-0.772601\pi\) | ||||
−0.755491 | + | 0.655159i | \(0.772601\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.4771 | + | 14.4771i | 0.609056 | + | 0.609056i | ||||
\(566\) | −15.4694 | − | 15.4694i | −0.650229 | − | 0.650229i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.0849 | −0.590990 | ||||||||
\(569\) | 11.7932 | 0.494398 | 0.247199 | − | 0.968965i | \(-0.420490\pi\) | ||||
0.247199 | + | 0.968965i | \(0.420490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 36.8437i | − | 1.54186i | −0.636920 | − | 0.770930i | \(-0.719792\pi\) | ||
0.636920 | − | 0.770930i | \(-0.280208\pi\) | |||||||
\(572\) | 7.34830 | + | 15.4651i | 0.307248 | + | 0.646627i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.39122 | + | 2.39122i | 0.0998077 | + | 0.0998077i | ||||
\(575\) | − | 9.29545i | − | 0.387647i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.65397 | − | 2.65397i | −0.110486 | − | 0.110486i | 0.649702 | − | 0.760189i | \(-0.274893\pi\) |
−0.760189 | + | 0.649702i | \(0.774893\pi\) | |||||||
\(578\) | −9.11843 | + | 9.11843i | −0.379277 | + | 0.379277i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.31285 | − | 6.31285i | 0.262127 | − | 0.262127i | ||||
\(581\) | − | 14.4619i | − | 0.599979i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.55190 | + | 4.55190i | −0.188520 | + | 0.188520i | ||||
\(584\) | 5.51784 | 0.228330 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.8425 | 0.571830 | ||||||||
\(587\) | −8.67198 | + | 8.67198i | −0.357931 | + | 0.357931i | −0.863050 | − | 0.505119i | \(-0.831449\pi\) |
0.505119 | + | 0.863050i | \(0.331449\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 55.8917i | − | 2.30298i | ||||||
\(590\) | 4.74286 | − | 4.74286i | 0.195261 | − | 0.195261i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.97346 | + | 6.97346i | −0.286607 | + | 0.286607i | ||||
\(593\) | 23.0726 | + | 23.0726i | 0.947478 | + | 0.947478i | 0.998688 | − | 0.0512098i | \(-0.0163077\pi\) |
−0.0512098 | + | 0.998688i | \(0.516308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.13757i | 0.0876317i | ||||||||
\(596\) | −0.866918 | − | 0.866918i | −0.0355103 | − | 0.0355103i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.70066 | − | 7.78833i | −0.151331 | − | 0.318488i | ||||
\(599\) | − | 12.1997i | − | 0.498465i | −0.968444 | − | 0.249232i | \(-0.919822\pi\) | ||
0.968444 | − | 0.249232i | \(-0.0801783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.975365 | −0.0397860 | −0.0198930 | − | 0.999802i | \(-0.506333\pi\) | ||||
−0.0198930 | + | 0.999802i | \(0.506333\pi\) | |||||||
\(602\) | 9.24408 | 0.376761 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.7845 | − | 14.7845i | −0.601574 | − | 0.601574i | ||||
\(605\) | 8.61782 | + | 8.61782i | 0.350364 | + | 0.350364i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.1566 | −0.858721 | −0.429360 | − | 0.903133i | \(-0.641261\pi\) | ||||
−0.429360 | + | 0.903133i | \(0.641261\pi\) | |||||||
\(608\) | −7.12053 | −0.288775 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.64906i | 0.0667684i | ||||||||
\(611\) | −16.0365 | + | 7.61983i | −0.648768 | + | 0.308265i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.67466 | − | 3.67466i | −0.148418 | − | 0.148418i | 0.628993 | − | 0.777411i | \(-0.283467\pi\) |
−0.777411 | + | 0.628993i | \(0.783467\pi\) | |||||||
\(614\) | 17.4079i | 0.702527i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.35792 | + | 3.35792i | 0.135294 | + | 0.135294i | ||||
\(617\) | 28.6513 | − | 28.6513i | 1.15346 | − | 1.15346i | 0.167604 | − | 0.985854i | \(-0.446397\pi\) |
0.985854 | − | 0.167604i | \(-0.0536031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.2324 | − | 20.2324i | 0.813211 | − | 0.813211i | −0.171903 | − | 0.985114i | \(-0.554992\pi\) |
0.985114 | + | 0.171903i | \(0.0549916\pi\) | |||||||
\(620\) | 8.28171i | 0.332601i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.81804 | + | 1.81804i | −0.0728968 | + | 0.0728968i | ||||
\(623\) | 6.23553 | 0.249821 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.54134 | −0.381654 | ||||||||
\(626\) | 0.808162 | − | 0.808162i | 0.0323006 | − | 0.0323006i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 15.2471i | − | 0.608424i | ||||||
\(629\) | 14.1281 | − | 14.1281i | 0.563324 | − | 0.563324i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.8814 | − | 15.8814i | 0.632228 | − | 0.632228i | −0.316398 | − | 0.948626i | \(-0.602474\pi\) |
0.948626 | + | 0.316398i | \(0.102474\pi\) | |||||||
\(632\) | −7.25671 | − | 7.25671i | −0.288656 | − | 0.288656i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 13.3660i | − | 0.530830i | ||||||
\(635\) | −10.9629 | − | 10.9629i | −0.435051 | − | 0.435051i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.39695 | + | 1.20860i | 0.134592 | + | 0.0478865i | ||||
\(638\) | 40.1828i | 1.59085i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.05508 | 0.0417056 | ||||||||
\(641\) | 35.2108 | 1.39074 | 0.695371 | − | 0.718651i | \(-0.255240\pi\) | ||||
0.695371 | + | 0.718651i | \(0.255240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.8170 | − | 19.8170i | −0.781505 | − | 0.781505i | 0.198580 | − | 0.980085i | \(-0.436367\pi\) |
−0.980085 | + | 0.198580i | \(0.936367\pi\) | |||||||
\(644\) | −1.69107 | − | 1.69107i | −0.0666376 | − | 0.0666376i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.4260 | 0.567585 | ||||||||
\(647\) | 11.6901 | 0.459585 | 0.229793 | − | 0.973240i | \(-0.426195\pi\) | ||||
0.229793 | + | 0.973240i | \(0.426195\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.1895i | 1.18504i | ||||||||
\(650\) | −12.6579 | + | 6.01444i | −0.496482 | + | 0.235906i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.2208 | + | 16.2208i | 0.635256 | + | 0.635256i | ||||
\(653\) | − | 34.8963i | − | 1.36560i | −0.730606 | − | 0.682800i | \(-0.760762\pi\) | ||
0.730606 | − | 0.682800i | \(-0.239238\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.65737 | + | 1.65737i | 0.0647590 | + | 0.0647590i | ||||
\(656\) | −2.39122 | + | 2.39122i | −0.0933616 | + | 0.0933616i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.48199 | + | 3.48199i | −0.135742 | + | 0.135742i | ||||
\(659\) | 10.9137i | 0.425136i | 0.977146 | + | 0.212568i | \(0.0681828\pi\) | ||||
−0.977146 | + | 0.212568i | \(0.931817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9445 | − | 17.9445i | 0.697959 | − | 0.697959i | −0.266011 | − | 0.963970i | \(-0.585706\pi\) |
0.963970 | + | 0.266011i | \(0.0857056\pi\) | |||||||
\(662\) | 12.3954 | 0.481763 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.4619 | 0.561229 | ||||||||
\(665\) | −5.31229 | + | 5.31229i | −0.206002 | + | 0.206002i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20.2364i | − | 0.783556i | ||||||
\(668\) | −17.0656 | + | 17.0656i | −0.660289 | + | 0.660289i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.88554 | + | 1.88554i | −0.0728449 | + | 0.0728449i | ||||
\(671\) | −5.24833 | − | 5.24833i | −0.202610 | − | 0.202610i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 44.1565i | − | 1.70211i | −0.525078 | − | 0.851054i | \(-0.675964\pi\) | ||
0.525078 | − | 0.851054i | \(-0.324036\pi\) | |||||||
\(674\) | −22.5070 | − | 22.5070i | −0.866937 | − | 0.866937i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.21112 | + | 10.0786i | −0.315812 | + | 0.387637i | ||||
\(677\) | − | 14.9679i | − | 0.575262i | −0.957741 | − | 0.287631i | \(-0.907132\pi\) | ||
0.957741 | − | 0.287631i | \(-0.0928676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.6876 | 0.602035 | ||||||||
\(680\) | −2.13757 | −0.0819720 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −26.3576 | − | 26.3576i | −1.00928 | − | 1.00928i | ||||
\(683\) | 9.38498 | + | 9.38498i | 0.359106 | + | 0.359106i | 0.863483 | − | 0.504377i | \(-0.168278\pi\) |
−0.504377 | + | 0.863483i | \(0.668278\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.577842 | 0.0220782 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.24408i | 0.352427i | ||||||||
\(689\) | −4.60481 | − | 1.63835i | −0.175429 | − | 0.0624160i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2672 | − | 15.2672i | −0.580793 | − | 0.580793i | 0.354328 | − | 0.935121i | \(-0.384710\pi\) |
−0.935121 | + | 0.354328i | \(0.884710\pi\) | |||||||
\(692\) | − | 8.52210i | − | 0.323961i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.1935 | − | 14.1935i | −0.538780 | − | 0.538780i | ||||
\(695\) | −2.08950 | + | 2.08950i | −0.0792594 | + | 0.0792594i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.84457 | − | 4.84457i | 0.183501 | − | 0.183501i | ||||
\(698\) | 12.5632i | 0.475525i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.74839 | + | 2.74839i | −0.103879 | + | 0.103879i | ||||
\(701\) | −1.91734 | −0.0724168 | −0.0362084 | − | 0.999344i | \(-0.511528\pi\) | ||||
−0.0362084 | + | 0.999344i | \(0.511528\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 70.2223 | 2.64848 | ||||||||
\(704\) | −3.35792 | + | 3.35792i | −0.126556 | + | 0.126556i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.2774i | 0.687878i | ||||||||
\(707\) | −3.13732 | + | 3.13732i | −0.117991 | + | 0.117991i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.5754 | + | 35.5754i | −1.33606 | + | 1.33606i | −0.436222 | + | 0.899839i | \(0.643684\pi\) |
−0.899839 | + | 0.436222i | \(0.856316\pi\) | |||||||
\(710\) | −10.5081 | − | 10.5081i | −0.394362 | − | 0.394362i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.23553i | 0.233686i | ||||||||
\(713\) | 13.2739 | + | 13.2739i | 0.497110 | + | 0.497110i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.05554 | + | 17.0200i | −0.226464 | + | 0.636511i | ||||
\(716\) | 3.46058i | 0.129328i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.1638 | −0.565907 | ||||||||
\(719\) | −3.52562 | −0.131484 | −0.0657418 | − | 0.997837i | \(-0.520941\pi\) | ||||
−0.0657418 | + | 0.997837i | \(0.520941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.02486 | + | 7.02486i | 0.261619 | + | 0.261619i | ||||
\(722\) | 22.4166 | + | 22.4166i | 0.834260 | + | 0.834260i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.8236 | 0.922563 | ||||||||
\(725\) | −32.8889 | −1.22146 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 20.5218i | − | 0.761112i | −0.924758 | − | 0.380556i | \(-0.875733\pi\) | ||
0.924758 | − | 0.380556i | \(-0.124267\pi\) | |||||||
\(728\) | −1.20860 | + | 3.39695i | −0.0447937 | + | 0.125899i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.11660 | + | 4.11660i | 0.152362 | + | 0.152362i | ||||
\(731\) | − | 18.7283i | − | 0.692692i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.62778 | + | 7.62778i | 0.281739 | + | 0.281739i | 0.833802 | − | 0.552064i | \(-0.186159\pi\) |
−0.552064 | + | 0.833802i | \(0.686159\pi\) | |||||||
\(734\) | −10.3012 | + | 10.3012i | −0.380224 | + | 0.380224i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.69107 | − | 1.69107i | 0.0623338 | − | 0.0623338i | ||||
\(737\) | − | 12.0020i | − | 0.442098i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.0350 | − | 22.0350i | 0.810572 | − | 0.810572i | −0.174148 | − | 0.984720i | \(-0.555717\pi\) |
0.984720 | + | 0.174148i | \(0.0557170\pi\) | |||||||
\(740\) | −10.4051 | −0.382500 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.35557 | −0.0497646 | ||||||||
\(743\) | 7.44855 | − | 7.44855i | 0.273261 | − | 0.273261i | −0.557151 | − | 0.830411i | \(-0.688105\pi\) |
0.830411 | + | 0.557151i | \(0.188105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.29353i | − | 0.0473914i | ||||||
\(746\) | −3.28325 | + | 3.28325i | −0.120208 | + | 0.120208i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.80307 | − | 6.80307i | 0.248745 | − | 0.248745i | ||||
\(749\) | −8.50295 | − | 8.50295i | −0.310691 | − | 0.310691i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.76517i | 0.356336i | 0.984000 | + | 0.178168i | \(0.0570171\pi\) | ||||
−0.984000 | + | 0.178168i | \(0.942983\pi\) | |||||||
\(752\) | −3.48199 | − | 3.48199i | −0.126975 | − | 0.126975i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −27.5564 | + | 13.0936i | −1.00354 | + | 0.476839i | ||||
\(755\) | − | 22.0601i | − | 0.802849i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.6708 | 0.860329 | 0.430165 | − | 0.902750i | \(-0.358456\pi\) | ||||
0.430165 | + | 0.902750i | \(0.358456\pi\) | |||||||
\(758\) | −9.53877 | −0.346464 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.31229 | − | 5.31229i | −0.192697 | − | 0.192697i | ||||
\(761\) | −20.9560 | − | 20.9560i | −0.759656 | − | 0.759656i | 0.216604 | − | 0.976260i | \(-0.430502\pi\) |
−0.976260 | + | 0.216604i | \(0.930502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.50468 | −0.126878 | ||||||||
\(764\) | 7.86219 | 0.284444 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 1.87658i | − | 0.0678037i | ||||||
\(767\) | −20.7032 | + | 9.83723i | −0.747550 | + | 0.355202i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.9775 | + | 26.9775i | 0.972835 | + | 0.972835i | 0.999641 | − | 0.0268055i | \(-0.00853346\pi\) |
−0.0268055 | + | 0.999641i | \(0.508533\pi\) | |||||||
\(770\) | 5.01037i | 0.180561i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.85067 | − | 4.85067i | −0.174579 | − | 0.174579i | ||||
\(773\) | 22.9037 | − | 22.9037i | 0.823788 | − | 0.823788i | −0.162861 | − | 0.986649i | \(-0.552072\pi\) |
0.986649 | + | 0.162861i | \(0.0520722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.5732 | − | 21.5732i | 0.774931 | − | 0.774931i | ||||
\(776\) | 15.6876i | 0.563152i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.3247 | − | 18.3247i | 0.656974 | − | 0.656974i | ||||
\(779\) | 24.0795 | 0.862737 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 66.8866 | 2.39339 | ||||||||
\(782\) | −3.42608 | + | 3.42608i | −0.122516 | + | 0.122516i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 11.3751 | − | 11.3751i | 0.405995 | − | 0.405995i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.47326 | − | 7.47326i | 0.266393 | − | 0.266393i | −0.561252 | − | 0.827645i | \(-0.689680\pi\) |
0.827645 | + | 0.561252i | \(0.189680\pi\) | |||||||
\(788\) | −9.34718 | − | 9.34718i | −0.332979 | − | 0.332979i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 10.8278i | − | 0.385235i | ||||||
\(791\) | −13.7214 | − | 13.7214i | −0.487875 | − | 0.487875i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.88901 | − | 5.30934i | 0.0670807 | − | 0.188540i | ||||
\(794\) | 29.8443i | 1.05913i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.0454 | −0.816824 | ||||||||
\(797\) | 23.7417 | 0.840973 | 0.420487 | − | 0.907299i | \(-0.361859\pi\) | ||||
0.420487 | + | 0.907299i | \(0.361859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.05445 | + | 7.05445i | 0.249569 | + | 0.249569i | ||||
\(800\) | −2.74839 | − | 2.74839i | −0.0971702 | − | 0.0971702i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.7714 | 0.945332 | ||||||||
\(803\) | −26.2032 | −0.924690 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 2.52326i | − | 0.0889332i | ||||||
\(806\) | 9.48677 | − | 26.6640i | 0.334157 | − | 0.939198i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.13732 | − | 3.13732i | −0.110371 | − | 0.110371i | ||||
\(809\) | 28.8848i | 1.01553i | 0.861494 | + | 0.507767i | \(0.169529\pi\) | ||||
−0.861494 | + | 0.507767i | \(0.830471\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.3037 | + | 19.3037i | 0.677845 | + | 0.677845i | 0.959512 | − | 0.281667i | \(-0.0908873\pi\) |
−0.281667 | + | 0.959512i | \(0.590887\pi\) | |||||||
\(812\) | −5.98330 | + | 5.98330i | −0.209973 | + | 0.209973i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.1156 | − | 33.1156i | 1.16070 | − | 1.16070i | ||||
\(815\) | 24.2032i | 0.847800i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.5437 | − | 46.5437i | 1.62836 | − | 1.62836i | ||||
\(818\) | −14.8422 | −0.518945 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.56796 | −0.124598 | ||||||||
\(821\) | −31.2406 | + | 31.2406i | −1.09030 | + | 1.09030i | −0.0948096 | + | 0.995495i | \(0.530224\pi\) |
−0.995495 | + | 0.0948096i | \(0.969776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6275i | 0.684173i | 0.939668 | + | 0.342086i | \(0.111134\pi\) | ||||
−0.939668 | + | 0.342086i | \(0.888866\pi\) | |||||||
\(824\) | −7.02486 | + | 7.02486i | −0.244723 | + | 0.244723i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.49527 | + | 4.49527i | −0.156411 | + | 0.156411i | ||||
\(827\) | 24.2147 | + | 24.2147i | 0.842026 | + | 0.842026i | 0.989122 | − | 0.147096i | \(-0.0469927\pi\) |
−0.147096 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 29.0909i | − | 1.01037i | −0.863012 | − | 0.505184i | \(-0.831425\pi\) | ||
0.863012 | − | 0.505184i | \(-0.168575\pi\) | |||||||
\(830\) | 10.7893 | + | 10.7893i | 0.374503 | + | 0.374503i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.39695 | − | 1.20860i | −0.117768 | − | 0.0419007i | ||||
\(833\) | − | 2.02598i | − | 0.0701960i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.4637 | −0.881208 | ||||||||
\(836\) | 33.8140 | 1.16948 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.2308 | − | 16.2308i | −0.560682 | − | 0.560682i | ||||
\(839\) | −13.2912 | − | 13.2912i | −0.458863 | − | 0.458863i | 0.439419 | − | 0.898282i | \(-0.355184\pi\) |
−0.898282 | + | 0.439419i | \(0.855184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −42.5997 | −1.46895 | ||||||||
\(842\) | 28.7342 | 0.990247 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.931807i | 0.0320741i | ||||||||
\(845\) | −13.6451 | + | 1.39321i | −0.469405 | + | 0.0479280i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.16794 | − | 8.16794i | −0.280654 | − | 0.280654i | ||||
\(848\) | − | 1.35557i | − | 0.0465505i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.56818 | + | 5.56818i | 0.190987 | + | 0.190987i | ||||
\(851\) | −16.6773 | + | 16.6773i | −0.571690 | + | 0.571690i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3079 | + | 15.3079i | −0.524133 | + | 0.524133i | −0.918817 | − | 0.394684i | \(-0.870854\pi\) |
0.394684 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(854\) | − | 1.56297i | − | 0.0534838i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.50295 | − | 8.50295i | 0.290625 | − | 0.290625i | ||||
\(857\) | 37.8080 | 1.29150 | 0.645749 | − | 0.763550i | \(-0.276545\pi\) | ||||
0.645749 | + | 0.763550i | \(0.276545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6413 | 0.772512 | 0.386256 | − | 0.922392i | \(-0.373768\pi\) | ||||
0.386256 | + | 0.922392i | \(0.373768\pi\) | |||||||
\(860\) | −6.89658 | + | 6.89658i | −0.235171 | + | 0.235171i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.782576i | 0.0266547i | ||||||||
\(863\) | −29.0990 | + | 29.0990i | −0.990543 | + | 0.990543i | −0.999956 | − | 0.00941262i | \(-0.997004\pi\) |
0.00941262 | + | 0.999956i | \(0.497004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.35793 | − | 6.35793i | 0.216176 | − | 0.216176i | ||||
\(866\) | −0.978804 | − | 0.978804i | −0.0332611 | − | 0.0332611i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 7.84938i | − | 0.266425i | ||||||
\(869\) | 34.4607 | + | 34.4607i | 1.16900 | + | 1.16900i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.23064 | − | 3.91083i | 0.278885 | − | 0.132513i | ||||
\(872\) | − | 3.50468i | − | 0.118684i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.0290 | −0.576015 | ||||||||
\(875\) | −9.37628 | −0.316976 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.6423 | − | 19.6423i | −0.663273 | − | 0.663273i | 0.292877 | − | 0.956150i | \(-0.405387\pi\) |
−0.956150 | + | 0.292877i | \(0.905387\pi\) | |||||||
\(878\) | −10.1597 | − | 10.1597i | −0.342873 | − | 0.342873i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.01037 | −0.168899 | ||||||||
\(881\) | −19.3210 | −0.650942 | −0.325471 | − | 0.945552i | \(-0.605523\pi\) | ||||
−0.325471 | + | 0.945552i | \(0.605523\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.1008i | − | 0.508181i | −0.967180 | − | 0.254090i | \(-0.918224\pi\) | ||
0.967180 | − | 0.254090i | \(-0.0817761\pi\) | |||||||
\(884\) | 6.88216 | + | 2.44860i | 0.231472 | + | 0.0823554i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.14226 | − | 5.14226i | −0.172758 | − | 0.172758i | ||||
\(887\) | − | 51.8363i | − | 1.74049i | −0.492617 | − | 0.870246i | \(-0.663960\pi\) | ||
0.492617 | − | 0.870246i | \(-0.336040\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3906 | + | 10.3906i | 0.348491 | + | 0.348491i | ||||
\(890\) | −4.65204 | + | 4.65204i | −0.155937 | + | 0.155937i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.806330 | + | 0.806330i | −0.0269979 | + | 0.0269979i | ||||
\(893\) | 35.0635i | 1.17335i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.58178 | + | 2.58178i | −0.0862993 | + | 0.0862993i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.7262 | −0.524789 | ||||||||
\(899\) | 46.9652 | − | 46.9652i | 1.56638 | − | 1.56638i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.74636i | 0.0914946i | ||||||||
\(902\) | 11.3555 | − | 11.3555i | 0.378096 | − | 0.378096i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.7214 | − | 13.7214i | 0.456365 | − | 0.456365i | ||||
\(905\) | 18.5197 | + | 18.5197i | 0.615617 | + | 0.615617i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 50.0706i | − | 1.66257i | −0.555848 | − | 0.831284i | \(-0.687606\pi\) | ||
0.555848 | − | 0.831284i | \(-0.312394\pi\) | |||||||
\(908\) | −2.04742 | − | 2.04742i | −0.0679459 | − | 0.0679459i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.43599 | + | 1.63263i | −0.113902 | + | 0.0541210i | ||||
\(911\) | 4.50281i | 0.149185i | 0.997214 | + | 0.0745924i | \(0.0237656\pi\) | ||||
−0.997214 | + | 0.0745924i | \(0.976234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −68.6767 | −2.27287 | ||||||||
\(914\) | 10.2536 | 0.339158 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.3112 | + | 12.3112i | 0.406774 | + | 0.406774i | ||||
\(917\) | −1.57085 | − | 1.57085i | −0.0518742 | − | 0.0518742i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.6075 | −0.613806 | −0.306903 | − | 0.951741i | \(-0.599293\pi\) | ||||
−0.306903 | + | 0.951741i | \(0.599293\pi\) | |||||||
\(920\) | 2.52326 | 0.0831894 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 28.8769i | − | 0.951011i | ||||||
\(923\) | 21.7950 | + | 45.8692i | 0.717390 | + | 1.50980i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.1045 | + | 27.1045i | 0.891191 | + | 0.891191i | ||||
\(926\) | − | 7.31096i | − | 0.240253i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.98330 | − | 5.98330i | −0.196411 | − | 0.196411i | ||||
\(929\) | 31.8475 | − | 31.8475i | 1.04488 | − | 1.04488i | 0.0459383 | − | 0.998944i | \(-0.485372\pi\) |
0.998944 | − | 0.0459383i | \(-0.0146278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.03497 | − | 5.03497i | 0.165015 | − | 0.165015i | ||||
\(932\) | − | 24.7227i | − | 0.809818i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.7401 | + | 11.7401i | −0.384147 | + | 0.384147i | ||||
\(935\) | 10.1509 | 0.331970 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3250 | 0.663987 | 0.331994 | − | 0.943282i | \(-0.392279\pi\) | ||||
0.331994 | + | 0.943282i | \(0.392279\pi\) | |||||||
\(938\) | 1.78711 | − | 1.78711i | 0.0583513 | − | 0.0583513i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 5.19550i | − | 0.169459i | ||||||
\(941\) | −32.4919 | + | 32.4919i | −1.05921 | + | 1.05921i | −0.0610727 | + | 0.998133i | \(0.519452\pi\) |
−0.998133 | + | 0.0610727i | \(0.980548\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.71870 | + | 5.71870i | −0.186226 | + | 0.186226i | ||||
\(944\) | −4.49527 | − | 4.49527i | −0.146309 | − | 0.146309i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 43.8984i | − | 1.42726i | ||||||
\(947\) | 14.9562 | + | 14.9562i | 0.486013 | + | 0.486013i | 0.907045 | − | 0.421033i | \(-0.138332\pi\) |
−0.421033 | + | 0.907045i | \(0.638332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.53829 | − | 17.9695i | −0.277165 | − | 0.583314i | ||||
\(950\) | 27.6761i | 0.897932i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.02598 | 0.0656624 | ||||||||
\(953\) | 4.44039 | 0.143838 | 0.0719192 | − | 0.997410i | \(-0.477088\pi\) | ||||
0.0719192 | + | 0.997410i | \(0.477088\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.86561 | + | 5.86561i | 0.189807 | + | 0.189807i | ||||
\(956\) | 1.69453 | + | 1.69453i | 0.0548050 | + | 0.0548050i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.3375 | 0.947851 | ||||||||
\(959\) | −0.547677 | −0.0176854 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6128i | 0.987509i | ||||||||
\(962\) | 33.5006 | + | 11.9192i | 1.08010 | + | 0.384290i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.52253 | − | 4.52253i | −0.145661 | − | 0.145661i | ||||
\(965\) | − | 7.23771i | − | 0.232990i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.2096 | + | 13.2096i | 0.424792 | + | 0.424792i | 0.886850 | − | 0.462058i | \(-0.152889\pi\) |
−0.462058 | + | 0.886850i | \(0.652889\pi\) | |||||||
\(968\) | 8.16794 | − | 8.16794i | 0.262528 | − | 0.262528i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.7038 | + | 11.7038i | −0.375786 | + | 0.375786i | ||||
\(971\) | − | 26.3005i | − | 0.844025i | −0.906590 | − | 0.422012i | \(-0.861324\pi\) | ||
0.906590 | − | 0.422012i | \(-0.138676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.98042 | − | 1.98042i | 0.0634895 | − | 0.0634895i | ||||
\(974\) | −7.37615 | −0.236347 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.56297 | 0.0500295 | ||||||||
\(977\) | −35.2572 | + | 35.2572i | −1.12798 | + | 1.12798i | −0.137470 | + | 0.990506i | \(0.543897\pi\) |
−0.990506 | + | 0.137470i | \(0.956103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 29.6114i | − | 0.946383i | ||||||
\(980\) | −0.746053 | + | 0.746053i | −0.0238318 | + | 0.0238318i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.80634 | + | 7.80634i | −0.249110 | + | 0.249110i | ||||
\(983\) | −20.2759 | − | 20.2759i | −0.646699 | − | 0.646699i | 0.305494 | − | 0.952194i | \(-0.401178\pi\) |
−0.952194 | + | 0.305494i | \(0.901178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 13.9470i | − | 0.444388i | ||||||
\(986\) | 12.1220 | + | 12.1220i | 0.386044 | + | 0.386044i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.0183 | + | 23.1888i | 0.350538 | + | 0.737735i | ||||
\(989\) | 22.1076i | 0.702980i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.24098 | −0.102953 | −0.0514765 | − | 0.998674i | \(-0.516393\pi\) | ||||
−0.0514765 | + | 0.998674i | \(0.516393\pi\) | |||||||
\(992\) | 7.84938 | 0.249218 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.95954 | + | 9.95954i | 0.315897 | + | 0.315897i | ||||
\(995\) | −17.1931 | − | 17.1931i | −0.545059 | − | 0.545059i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.8807 | 0.629629 | 0.314814 | − | 0.949153i | \(-0.398058\pi\) | ||||
0.314814 | + | 0.949153i | \(0.398058\pi\) | |||||||
\(998\) | 5.04723 | 0.159767 | ||||||||
\(999\) | 0 | 0 |
(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 | 1638.2.y.c.827.7 | ✓ | 16 | |
3.2 | odd | 2 | 1638.2.y.d.827.2 | yes | 16 | ||
13.5 | odd | 4 | 1638.2.y.d.1331.2 | yes | 16 | ||
39.5 | even | 4 | inner | 1638.2.y.c.1331.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1638.2.y.c.827.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1638.2.y.c.1331.7 | yes | 16 | 39.5 | even | 4 | inner | |
1638.2.y.d.827.2 | yes | 16 | 3.2 | odd | 2 | ||
1638.2.y.d.1331.2 | yes | 16 | 13.5 | odd | 4 |