Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [500,2,Mod(101,500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("500.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 500 = 2^{2} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 500.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.99252010106\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 13 x^{10} - 24 x^{9} + 93 x^{8} - 6 x^{7} + 342 x^{6} + 786 x^{5} + 1473 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 100) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.3 | ||
Root | \(-1.25005 + 0.908212i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 500.301 |
Dual form | 500.2.g.a.201.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/500\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(377\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.477475 | − | 1.46952i | 0.275670 | − | 0.848426i | −0.713371 | − | 0.700787i | \(-0.752832\pi\) |
0.989041 | − | 0.147640i | \(-0.0471676\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43270 | 0.919474 | 0.459737 | − | 0.888055i | \(-0.347944\pi\) | ||||
0.459737 | + | 0.888055i | \(0.347944\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.495552 | + | 0.360039i | 0.165184 | + | 0.120013i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41187 | − | 1.75233i | 0.727207 | − | 0.528347i | −0.161471 | − | 0.986877i | \(-0.551624\pi\) |
0.888679 | + | 0.458530i | \(0.151624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.27986 | − | 1.65642i | −0.632320 | − | 0.459407i | 0.224883 | − | 0.974386i | \(-0.427800\pi\) |
−0.857203 | + | 0.514978i | \(0.827800\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.89061 | + | 5.81868i | 0.458539 | + | 1.41124i | 0.866929 | + | 0.498431i | \(0.166090\pi\) |
−0.408390 | + | 0.912807i | \(0.633910\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.61119 | − | 4.95872i | −0.369632 | − | 1.13761i | −0.947030 | − | 0.321146i | \(-0.895932\pi\) |
0.577398 | − | 0.816463i | \(-0.304068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.16155 | − | 3.57489i | 0.253472 | − | 0.780106i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.19552 | + | 0.868599i | −0.249284 | + | 0.181115i | −0.705409 | − | 0.708800i | \(-0.749237\pi\) |
0.456125 | + | 0.889915i | \(0.349237\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.51584 | − | 3.28095i | 0.869073 | − | 0.631419i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.72499 | − | 8.38665i | 0.506018 | − | 1.55736i | −0.293035 | − | 0.956102i | \(-0.594665\pi\) |
0.799053 | − | 0.601261i | \(-0.205335\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.06767 | + | 6.36362i | 0.371364 | + | 1.14294i | 0.945899 | + | 0.324461i | \(0.105183\pi\) |
−0.574535 | + | 0.818480i | \(0.694817\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.42347 | − | 4.38098i | −0.247794 | − | 0.762631i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.78784 | − | 2.75203i | −0.622717 | − | 0.452431i | 0.231152 | − | 0.972918i | \(-0.425750\pi\) |
−0.853870 | + | 0.520487i | \(0.825750\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.52271 | + | 2.55940i | −0.564085 | + | 0.409832i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.92980 | − | 2.12862i | −0.457558 | − | 0.332435i | 0.335015 | − | 0.942213i | \(-0.391259\pi\) |
−0.792573 | + | 0.609778i | \(0.791259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.60984 | −0.550495 | −0.275248 | − | 0.961373i | \(-0.588760\pi\) | ||||
−0.275248 | + | 0.961373i | \(0.588760\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.69382 | − | 5.21306i | 0.247070 | − | 0.760403i | −0.748219 | − | 0.663451i | \(-0.769091\pi\) |
0.995289 | − | 0.0969511i | \(-0.0309091\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.08197 | −0.154568 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.45338 | 1.32374 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.366346 | + | 1.12750i | −0.0503215 | + | 0.154874i | −0.973059 | − | 0.230554i | \(-0.925946\pi\) |
0.922738 | + | 0.385428i | \(0.125946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.05623 | −1.06707 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.70876 | + | 4.87420i | 0.873406 | + | 0.634567i | 0.931499 | − | 0.363744i | \(-0.118502\pi\) |
−0.0580925 | + | 0.998311i | \(0.518502\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2455 | + | 8.89689i | −1.56788 | + | 1.13913i | −0.638724 | + | 0.769436i | \(0.720537\pi\) |
−0.929154 | + | 0.369694i | \(0.879463\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.20553 | + | 0.875867i | 0.151882 | + | 0.110349i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.56011 | + | 14.0346i | 0.557107 | + | 1.71460i | 0.690314 | + | 0.723509i | \(0.257472\pi\) |
−0.133208 | + | 0.991088i | \(0.542528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.705588 | + | 2.17158i | 0.0849429 | + | 0.261427i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.80837 | − | 5.56558i | 0.214614 | − | 0.660513i | −0.784567 | − | 0.620044i | \(-0.787115\pi\) |
0.999181 | − | 0.0404693i | \(-0.0128853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.84077 | − | 3.51703i | 0.566570 | − | 0.411637i | −0.267288 | − | 0.963617i | \(-0.586127\pi\) |
0.833858 | + | 0.551980i | \(0.186127\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.86736 | − | 4.26289i | 0.668648 | − | 0.485801i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.75202 | + | 11.5475i | −0.422135 | + | 1.29920i | 0.483576 | + | 0.875302i | \(0.339338\pi\) |
−0.905711 | + | 0.423896i | \(0.860662\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.09736 | − | 6.45500i | −0.233040 | − | 0.717223i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.78995 | + | 11.6643i | 0.416001 | + | 1.28032i | 0.911353 | + | 0.411626i | \(0.135039\pi\) |
−0.495352 | + | 0.868692i | \(0.664961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.0232 | − | 8.00884i | −1.18181 | − | 0.858638i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.12213 | + | 1.54182i | −0.224946 | + | 0.163433i | −0.694550 | − | 0.719444i | \(-0.744397\pi\) |
0.469605 | + | 0.882877i | \(0.344397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.54622 | − | 4.02956i | −0.581402 | − | 0.422413i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.3387 | 1.07208 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.93972 | + | 9.04752i | −0.298483 | + | 0.918636i | 0.683546 | + | 0.729907i | \(0.260437\pi\) |
−0.982029 | + | 0.188729i | \(0.939563\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.82612 | 0.183531 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.44518 | −0.143801 | −0.0719004 | − | 0.997412i | \(-0.522906\pi\) | ||||
−0.0719004 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.71543 | + | 5.27956i | −0.169027 | + | 0.520211i | −0.999310 | − | 0.0371303i | \(-0.988178\pi\) |
0.830284 | + | 0.557341i | \(0.188178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.44078 | −0.719327 | −0.359664 | − | 0.933082i | \(-0.617109\pi\) | ||||
−0.359664 | + | 0.933082i | \(0.617109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.52018 | − | 5.46373i | −0.720302 | − | 0.523330i | 0.166178 | − | 0.986096i | \(-0.446857\pi\) |
−0.886481 | + | 0.462765i | \(0.846857\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.85275 | + | 4.25227i | −0.555519 | + | 0.403608i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.5068 | + | 9.81326i | 1.27061 | + | 0.923154i | 0.999227 | − | 0.0393171i | \(-0.0125182\pi\) |
0.271385 | + | 0.962471i | \(0.412518\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.533414 | − | 1.64168i | −0.0493141 | − | 0.151773i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.59927 | + | 14.1551i | 0.421615 | + | 1.29760i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.652708 | + | 2.00883i | −0.0593371 | + | 0.182621i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.52696 | + | 3.28903i | −0.408182 | + | 0.296562i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.72353 | − | 7.06456i | 0.862824 | − | 0.626878i | −0.0658279 | − | 0.997831i | \(-0.520969\pi\) |
0.928652 | + | 0.370953i | \(0.120969\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.72361 | + | 5.30472i | −0.151755 | + | 0.467055i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.50078 | + | 16.9297i | 0.480605 | + | 1.47915i | 0.838247 | + | 0.545291i | \(0.183581\pi\) |
−0.357641 | + | 0.933859i | \(0.616419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.91953 | − | 12.0631i | −0.339867 | − | 1.04600i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.7004 | − | 9.22736i | −1.08507 | − | 0.788347i | −0.106507 | − | 0.994312i | \(-0.533967\pi\) |
−0.978559 | + | 0.205965i | \(0.933967\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.91371 | − | 3.57002i | 0.416775 | − | 0.302805i | −0.359564 | − | 0.933120i | \(-0.617075\pi\) |
0.776339 | + | 0.630316i | \(0.217075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.85192 | − | 4.97821i | −0.577036 | − | 0.419241i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.40132 | −0.702554 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.516616 | + | 1.58998i | −0.0426097 | + | 0.131139i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.55995 | 0.291642 | 0.145821 | − | 0.989311i | \(-0.453418\pi\) | ||||
0.145821 | + | 0.989311i | \(0.453418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3185 | −0.839704 | −0.419852 | − | 0.907593i | \(-0.637918\pi\) | ||||
−0.419852 | + | 0.907593i | \(0.637918\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.15806 | + | 3.56415i | −0.0936238 | + | 0.288145i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.6148 | −1.56543 | −0.782714 | − | 0.622382i | \(-0.786165\pi\) | ||||
−0.782714 | + | 0.622382i | \(0.786165\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.48195 | + | 1.07670i | 0.117527 | + | 0.0853881i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.90835 | + | 2.11304i | −0.229210 | + | 0.166531i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3545 | − | 8.97608i | −0.967681 | − | 0.703061i | −0.0127589 | − | 0.999919i | \(-0.504061\pi\) |
−0.954922 | + | 0.296857i | \(0.904061\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.349377 | − | 1.07527i | −0.0270356 | − | 0.0832070i | 0.936628 | − | 0.350325i | \(-0.113929\pi\) |
−0.963664 | + | 0.267118i | \(0.913929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.56317 | − | 4.81094i | −0.120244 | − | 0.370072i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.986909 | − | 3.03739i | 0.0754708 | − | 0.232275i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.72385 | + | 1.97899i | −0.207090 | + | 0.150460i | −0.686496 | − | 0.727133i | \(-0.740852\pi\) |
0.479406 | + | 0.877593i | \(0.340852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3660 | − | 7.53133i | 0.779156 | − | 0.566090i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0143068 | − | 0.0440317i | 0.00106934 | − | 0.00329108i | −0.950520 | − | 0.310662i | \(-0.899449\pi\) |
0.951590 | + | 0.307371i | \(0.0994493\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.69146 | + | 11.3611i | 0.274384 | + | 0.844468i | 0.989382 | + | 0.145341i | \(0.0464278\pi\) |
−0.714998 | + | 0.699127i | \(0.753572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.22720 | + | 22.2430i | 0.534250 | + | 1.64425i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7561 | + | 10.7210i | 1.07908 | + | 0.783995i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.9857 | − | 7.98156i | 0.799090 | − | 0.580573i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.00775 | − | 5.09143i | −0.507063 | − | 0.368403i | 0.304645 | − | 0.952466i | \(-0.401462\pi\) |
−0.811708 | + | 0.584063i | \(0.801462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.47620 | 0.250222 | 0.125111 | − | 0.992143i | \(-0.460071\pi\) | ||||
0.125111 | + | 0.992143i | \(0.460071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.910753 | − | 2.80301i | 0.0648885 | − | 0.199706i | −0.913356 | − | 0.407162i | \(-0.866518\pi\) |
0.978244 | + | 0.207456i | \(0.0665184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9228 | −1.12874 | −0.564369 | − | 0.825523i | \(-0.690881\pi\) | ||||
−0.564369 | + | 0.825523i | \(0.690881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.8014 | 1.60829 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.62908 | − | 20.4022i | 0.465270 | − | 1.43195i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.905174 | −0.0629139 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.5753 | − | 9.13648i | −0.869851 | − | 0.631984i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.72209 | − | 7.06351i | 0.669296 | − | 0.486272i | −0.200493 | − | 0.979695i | \(-0.564254\pi\) |
0.869790 | + | 0.493423i | \(0.164254\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.31527 | − | 5.31486i | −0.501234 | − | 0.364168i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.03001 | + | 15.4808i | 0.341459 | + | 1.05090i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.85699 | − | 8.79290i | −0.193057 | − | 0.594169i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.32785 | − | 16.3974i | 0.358390 | − | 1.10301i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.04587 | − | 2.93949i | 0.270931 | − | 0.196843i | −0.444021 | − | 0.896016i | \(-0.646448\pi\) |
0.714952 | + | 0.699173i | \(0.246448\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.1259 | − | 8.08342i | 0.738450 | − | 0.536516i | −0.153775 | − | 0.988106i | \(-0.549143\pi\) |
0.892225 | + | 0.451590i | \(0.149143\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.31025 | − | 7.11022i | 0.152666 | − | 0.469857i | −0.845251 | − | 0.534369i | \(-0.820549\pi\) |
0.997917 | + | 0.0645124i | \(0.0205492\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.46287 | − | 10.6576i | −0.227840 | − | 0.701220i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.16070 | − | 15.8830i | −0.338089 | − | 1.04053i | −0.965181 | − | 0.261585i | \(-0.915755\pi\) |
0.627092 | − | 0.778945i | \(-0.284245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.1778 | + | 11.0273i | 0.985904 | + | 0.716301i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.36778 | − | 6.07955i | 0.541267 | − | 0.393253i | −0.283288 | − | 0.959035i | \(-0.591425\pi\) |
0.824555 | + | 0.565781i | \(0.191425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.22944 | + | 4.52595i | 0.401273 | + | 0.291542i | 0.770059 | − | 0.637972i | \(-0.220227\pi\) |
−0.368786 | + | 0.929514i | \(0.620227\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.25846 | 0.401481 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.54043 | + | 13.9740i | −0.288900 | + | 0.889144i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.9504 | 1.20094 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.0605 | 0.824372 | 0.412186 | − | 0.911100i | \(-0.364765\pi\) | ||||
0.412186 | + | 0.911100i | \(0.364765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.36138 | + | 4.18990i | −0.0855893 | + | 0.263417i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.1683 | 1.38282 | 0.691411 | − | 0.722461i | \(-0.256989\pi\) | ||||
0.691411 | + | 0.722461i | \(0.256989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.21468 | − | 6.69486i | −0.572572 | − | 0.415998i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.36990 | − | 3.17492i | 0.270490 | − | 0.196522i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.09287 | + | 0.794015i | 0.0673891 | + | 0.0489611i | 0.620970 | − | 0.783834i | \(-0.286739\pi\) |
−0.553581 | + | 0.832796i | \(0.686739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.25246 | + | 3.85469i | 0.0766496 | + | 0.235903i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.77819 | + | 14.7057i | 0.291331 | + | 0.896625i | 0.984429 | + | 0.175782i | \(0.0562453\pi\) |
−0.693098 | + | 0.720843i | \(0.743755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.740383 | + | 2.27866i | −0.0449750 | + | 0.138419i | −0.971022 | − | 0.238988i | \(-0.923184\pi\) |
0.926047 | + | 0.377407i | \(0.123184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.56969 | + | 6.22625i | −0.518662 | + | 0.376830i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.35533 | + | 4.61742i | −0.381855 | + | 0.277434i | −0.762110 | − | 0.647448i | \(-0.775836\pi\) |
0.380255 | + | 0.924882i | \(0.375836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.26652 | + | 3.89795i | −0.0758245 | + | 0.233364i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.70559 | − | 8.32694i | −0.161402 | − | 0.496743i | 0.837351 | − | 0.546665i | \(-0.184103\pi\) |
−0.998753 | + | 0.0499216i | \(0.984103\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.25156 | − | 25.3957i | −0.490504 | − | 1.50962i | −0.823847 | − | 0.566812i | \(-0.808177\pi\) |
0.333343 | − | 0.942806i | \(-0.391823\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.12732 | − | 5.17830i | −0.420713 | − | 0.305666i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5294 | + | 12.0093i | −0.972318 | + | 0.706431i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.8918 | + | 8.63993i | 0.697112 | + | 0.506482i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.7472 | −0.803118 | −0.401559 | − | 0.915833i | \(-0.631531\pi\) | ||||
−0.401559 | + | 0.915833i | \(0.631531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.14233 | − | 15.8265i | 0.298388 | − | 0.918344i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.16439 | 0.240833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.78165 | −0.506166 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.690037 | + | 2.12372i | −0.0396416 | + | 0.122004i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.41804 | 0.309224 | 0.154612 | − | 0.987975i | \(-0.450587\pi\) | ||||
0.154612 | + | 0.987975i | \(0.450587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.93933 | + | 5.04172i | 0.394765 | + | 0.286813i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.70149 | − | 7.04854i | 0.550121 | − | 0.399686i | −0.277709 | − | 0.960665i | \(-0.589575\pi\) |
0.827830 | + | 0.560979i | \(0.189575\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.12496 | − | 2.99696i | −0.233156 | − | 0.169398i | 0.465073 | − | 0.885273i | \(-0.346028\pi\) |
−0.698229 | + | 0.715875i | \(0.746028\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.18248 | − | 6.71698i | −0.122580 | − | 0.377263i | 0.870872 | − | 0.491509i | \(-0.163555\pi\) |
−0.993452 | + | 0.114246i | \(0.963555\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.12385 | − | 25.0026i | −0.454848 | − | 1.39988i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.55279 | + | 10.9344i | −0.198297 | + | 0.610296i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.8071 | − | 18.7500i | 1.43595 | − | 1.04328i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.6197 | + | 8.44224i | −0.642573 | + | 0.466857i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.12057 | − | 12.6818i | 0.227174 | − | 0.699170i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.79401 | + | 5.52140i | 0.0986077 | + | 0.303483i | 0.988177 | − | 0.153317i | \(-0.0489955\pi\) |
−0.889569 | + | 0.456800i | \(0.848995\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.886233 | − | 2.72754i | −0.0485652 | − | 0.149468i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.10613 | + | 0.803650i | 0.0602547 | + | 0.0437776i | 0.617505 | − | 0.786567i | \(-0.288144\pi\) |
−0.557250 | + | 0.830345i | \(0.688144\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.8699 | − | 15.1629i | 1.13350 | − | 0.823535i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.1381 | + | 11.7250i | 0.873928 | + | 0.634946i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6610 | −1.06159 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.308138 | − | 0.948350i | 0.0165417 | − | 0.0509101i | −0.942445 | − | 0.334361i | \(-0.891479\pi\) |
0.958987 | + | 0.283451i | \(0.0914794\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5266 | −0.670534 | −0.335267 | − | 0.942123i | \(-0.608827\pi\) | ||||
−0.335267 | + | 0.942123i | \(0.608827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.7301 | −0.839610 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.97697 | + | 18.3952i | −0.318122 | + | 0.979079i | 0.656328 | + | 0.754476i | \(0.272109\pi\) |
−0.974450 | + | 0.224604i | \(0.927891\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.9972 | 1.21714 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.66127 | + | 3.38661i | 0.246013 | + | 0.178739i | 0.703958 | − | 0.710242i | \(-0.251414\pi\) |
−0.457945 | + | 0.888980i | \(0.651414\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.62169 | + | 4.81094i | −0.348510 | + | 0.253207i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.64036 | + | 1.91833i | 0.138583 | + | 0.100686i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.6509 | − | 32.7802i | −0.555975 | − | 1.71111i | −0.693355 | − | 0.720596i | \(-0.743868\pi\) |
0.137380 | − | 0.990518i | \(-0.456132\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.685479 | − | 2.10969i | −0.0356846 | − | 0.109826i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.891209 | + | 2.74286i | −0.0462693 | + | 0.142402i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.6588 | + | 15.0095i | −1.06967 | + | 0.777163i | −0.975854 | − | 0.218426i | \(-0.929908\pi\) |
−0.0938202 | + | 0.995589i | \(0.529908\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.1044 | + | 14.6067i | −1.03543 | + | 0.752283i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.13595 | − | 12.7291i | 0.212449 | − | 0.653852i | −0.786876 | − | 0.617112i | \(-0.788303\pi\) |
0.999325 | − | 0.0367400i | \(-0.0116973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.73875 | − | 17.6621i | −0.294005 | − | 0.904854i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4948 | + | 35.3772i | 0.587354 | + | 1.80769i | 0.589602 | + | 0.807694i | \(0.299284\pi\) |
−0.00224788 | + | 0.999997i | \(0.500716\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.78886 | − | 1.29968i | −0.0909329 | − | 0.0660666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.3114 | + | 21.2960i | −1.48615 | + | 1.07975i | −0.510638 | + | 0.859796i | \(0.670591\pi\) |
−0.975510 | + | 0.219954i | \(0.929409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.31437 | − | 5.31420i | −0.369903 | − | 0.268751i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.5049 | 1.38744 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.838720 | + | 2.58132i | −0.0420942 | + | 0.129552i | −0.969895 | − | 0.243523i | \(-0.921697\pi\) |
0.927801 | + | 0.373076i | \(0.121697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.5984 | −0.981147 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.6883 | −0.583686 | −0.291843 | − | 0.956466i | \(-0.594269\pi\) | ||||
−0.291843 | + | 0.956466i | \(0.594269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.82682 | − | 17.9331i | 0.290254 | − | 0.893311i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.9583 | −0.691885 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.1020 | + | 15.3315i | 1.04343 | + | 0.758094i | 0.970952 | − | 0.239276i | \(-0.0769101\pi\) |
0.0724753 | + | 0.997370i | \(0.476910\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.6239 | + | 14.2576i | −0.967975 | + | 0.703275i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.3204 | + | 11.8575i | 0.803074 | + | 0.583468i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.90003 | − | 8.92537i | −0.142015 | − | 0.437077i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.20300 | − | 6.78014i | −0.107624 | − | 0.331232i | 0.882714 | − | 0.469911i | \(-0.155714\pi\) |
−0.990337 | + | 0.138680i | \(0.955714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.67304 | + | 17.4598i | −0.276487 | + | 0.850940i | 0.712335 | + | 0.701840i | \(0.247638\pi\) |
−0.988822 | + | 0.149100i | \(0.952362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.71628 | − | 1.97350i | 0.132070 | − | 0.0959546i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.7897 | + | 21.6435i | −1.44162 | + | 1.04740i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.01142 | + | 12.3459i | −0.193673 | + | 0.596065i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.48261 | − | 29.1845i | −0.456761 | − | 1.40577i | −0.869055 | − | 0.494716i | \(-0.835272\pi\) |
0.412294 | − | 0.911051i | \(-0.364728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.963040 | − | 2.96393i | −0.0462808 | − | 0.142438i | 0.925246 | − | 0.379368i | \(-0.123859\pi\) |
−0.971527 | + | 0.236931i | \(0.923859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.23335 | + | 4.52880i | 0.298182 | + | 0.216642i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.1537 | + | 8.83019i | −0.580065 | + | 0.421442i | −0.838748 | − | 0.544520i | \(-0.816712\pi\) |
0.258682 | + | 0.965962i | \(0.416712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.536174 | − | 0.389553i | −0.0255321 | − | 0.0185501i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.6976 | −1.22093 | −0.610466 | − | 0.792043i | \(-0.709018\pi\) | ||||
−0.610466 | + | 0.792043i | \(0.709018\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.69979 | − | 5.23141i | 0.0803972 | − | 0.247437i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.0378 | 1.46476 | 0.732382 | − | 0.680894i | \(-0.238408\pi\) | ||||
0.732382 | + | 0.680894i | \(0.238408\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.7964 | −0.508381 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.92681 | + | 15.1632i | −0.231482 | + | 0.712427i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0889 | 0.518716 | 0.259358 | − | 0.965781i | \(-0.416489\pi\) | ||||
0.259358 | + | 0.965781i | \(0.416489\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.6285 | + | 20.0733i | 1.28959 | + | 0.936939i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.1196 | − | 13.8912i | 0.890490 | − | 0.646979i | −0.0455158 | − | 0.998964i | \(-0.514493\pi\) |
0.936006 | + | 0.351985i | \(0.114493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4389 | + | 9.76393i | 0.624558 | + | 0.453768i | 0.854511 | − | 0.519434i | \(-0.173857\pi\) |
−0.229952 | + | 0.973202i | \(0.573857\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.412338 | + | 1.26905i | 0.0190807 | + | 0.0587245i | 0.960144 | − | 0.279507i | \(-0.0901712\pi\) |
−0.941063 | + | 0.338232i | \(0.890171\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0934 | + | 34.1419i | 0.512245 | + | 1.57653i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.36556 | + | 28.8242i | −0.431542 | + | 1.32815i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.70647 | + | 6.32562i | −0.400324 | + | 0.290852i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.587486 | + | 0.426834i | −0.0268992 | + | 0.0195434i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.53880 | + | 4.73594i | −0.0703095 | + | 0.216390i | −0.980037 | − | 0.198816i | \(-0.936291\pi\) |
0.909727 | + | 0.415206i | \(0.136291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.07725 | + | 12.5485i | 0.185907 | + | 0.572162i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.71648 | + | 5.28280i | 0.0781028 | + | 0.240376i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.66836 | − | 4.84485i | −0.302172 | − | 0.219541i | 0.426358 | − | 0.904554i | \(-0.359796\pi\) |
−0.728530 | + | 0.685013i | \(0.759796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.0895 | + | 13.8693i | −0.863257 | + | 0.627193i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.09586 | − | 1.52273i | −0.0945849 | − | 0.0687199i | 0.539488 | − | 0.841994i | \(-0.318618\pi\) |
−0.634073 | + | 0.773274i | \(0.718618\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.9512 | 2.42984 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.39922 | − | 13.5394i | 0.197332 | − | 0.607325i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7285 | −0.480272 | −0.240136 | − | 0.970739i | \(-0.577192\pi\) | ||||
−0.240136 | + | 0.970739i | \(0.577192\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.74695 | −0.0780479 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.41971 | − | 22.8355i | 0.330829 | − | 1.01819i | −0.637912 | − | 0.770109i | \(-0.720202\pi\) |
0.968740 | − | 0.248077i | \(-0.0797984\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.81613 | −0.347126 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0394 | − | 8.02058i | −0.489312 | − | 0.355506i | 0.315608 | − | 0.948890i | \(-0.397792\pi\) |
−0.804920 | + | 0.593384i | \(0.797792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.7761 | − | 8.55587i | 0.520946 | − | 0.378489i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.5452 | − | 17.1066i | −1.03954 | − | 0.755273i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.04970 | − | 15.5414i | −0.222085 | − | 0.683509i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.60759 | + | 4.94766i | 0.0705654 | + | 0.217178i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.739568 | + | 2.27616i | −0.0324011 | + | 0.0997202i | −0.965949 | − | 0.258732i | \(-0.916695\pi\) |
0.933548 | + | 0.358452i | \(0.116695\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.4575 | − | 13.4101i | 0.807089 | − | 0.586385i | −0.105896 | − | 0.994377i | \(-0.533771\pi\) |
0.912985 | + | 0.407992i | \(0.133771\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.1188 | + | 24.0622i | −1.44268 | + | 1.04817i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.43258 | + | 19.7974i | −0.279677 | + | 0.860758i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.56963 | + | 4.83084i | 0.0681163 | + | 0.209640i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.15365 | + | 9.70594i | 0.136600 | + | 0.420411i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.0578742 | − | 0.0420481i | −0.00249746 | − | 0.00181451i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.60958 | + | 1.89597i | −0.112403 | + | 0.0816654i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.85249 | + | 5.70517i | 0.337605 | + | 0.245284i | 0.743651 | − | 0.668568i | \(-0.233093\pi\) |
−0.406046 | + | 0.913853i | \(0.633093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.4580 | 0.792108 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.42533 | − | 25.9305i | 0.360241 | − | 1.10871i | −0.592667 | − | 0.805448i | \(-0.701925\pi\) |
0.952908 | − | 0.303260i | \(-0.0980752\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.27152 | −0.395699 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.9776 | −1.95871 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.12753 | + | 28.0917i | −0.388142 | + | 1.19458i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.20057 | 0.0508700 | 0.0254350 | − | 0.999676i | \(-0.491903\pi\) | ||||
0.0254350 | + | 0.999676i | \(0.491903\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.22993 | + | 5.97939i | 0.348089 | + | 0.252901i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.8003 | − | 16.5654i | 0.962631 | − | 0.699393i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.7727 | + | 10.0065i | 0.580451 | + | 0.421722i | 0.838887 | − | 0.544306i | \(-0.183207\pi\) |
−0.258436 | + | 0.966028i | \(0.583207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.10224 | − | 15.7031i | −0.214274 | − | 0.659468i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.11398 | − | 6.50617i | −0.0886227 | − | 0.272753i | 0.896917 | − | 0.442200i | \(-0.145802\pi\) |
−0.985539 | + | 0.169447i | \(0.945802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.05817 | − | 24.8005i | 0.337224 | − | 1.03787i | −0.628392 | − | 0.777897i | \(-0.716287\pi\) |
0.965616 | − | 0.259972i | \(-0.0837134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.8280 | + | 7.86698i | −0.452345 | + | 0.328648i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7137 | + | 9.96356i | −0.570907 | + | 0.414789i | −0.835435 | − | 0.549590i | \(-0.814784\pi\) |
0.264527 | + | 0.964378i | \(0.414784\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.65980 | − | 5.10834i | 0.0689789 | − | 0.212295i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.21980 | + | 28.3756i | 0.382502 | + | 1.17722i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.09216 | + | 3.36134i | 0.0452328 | + | 0.139212i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.1035 | + | 26.2307i | 1.49015 | + | 1.08266i | 0.974105 | + | 0.226097i | \(0.0725967\pi\) |
0.516046 | + | 0.856561i | \(0.327403\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.2241 | − | 20.5060i | 1.16295 | − | 0.844934i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.68421 | − | 2.67673i | −0.151548 | − | 0.110106i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.7787 | −1.55139 | −0.775694 | − | 0.631110i | \(-0.782600\pi\) | ||||
−0.775694 | + | 0.631110i | \(0.782600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.60275 | + | 23.3989i | −0.311160 | + | 0.957651i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.06719 | 0.329617 | 0.164808 | − | 0.986326i | \(-0.447299\pi\) | ||||
0.164808 | + | 0.986326i | \(0.447299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.5962 | −0.962509 | −0.481255 | − | 0.876581i | \(-0.659819\pi\) | ||||
−0.481255 | + | 0.876581i | \(0.659819\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.79323 | + | 8.59668i | −0.113749 | + | 0.350084i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.5160 | 1.92861 | 0.964307 | − | 0.264788i | \(-0.0853019\pi\) | ||||
0.964307 | + | 0.264788i | \(0.0853019\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26.8162 | − | 19.4831i | −1.08665 | − | 0.789495i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.4967 | + | 9.07937i | −0.505561 | + | 0.367312i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.57226 | + | 3.32194i | 0.184672 | + | 0.134172i | 0.676280 | − | 0.736644i | \(-0.263591\pi\) |
−0.491608 | + | 0.870816i | \(0.663591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.9382 | − | 39.8198i | −0.520874 | − | 1.60308i | −0.772334 | − | 0.635216i | \(-0.780911\pi\) |
0.251461 | − | 0.967868i | \(-0.419089\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.52654 | − | 17.0089i | −0.222130 | − | 0.683647i | −0.998570 | − | 0.0534558i | \(-0.982976\pi\) |
0.776440 | − | 0.630191i | \(-0.217024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.54896 | + | 7.84490i | −0.102286 | + | 0.314805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.16251 | + | 3.75078i | −0.206832 | + | 0.150272i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.4306 | + | 14.1172i | −0.775984 | + | 0.563785i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.85187 | − | 27.2432i | 0.352947 | − | 1.08626i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8982 | − | 36.6189i | −0.473660 | − | 1.45778i | −0.847756 | − | 0.530386i | \(-0.822047\pi\) |
0.374096 | − | 0.927390i | \(-0.377953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.73790 | − | 17.6594i | −0.228061 | − | 0.701900i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.46675 | + | 1.79220i | 0.0977362 | + | 0.0710095i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.89997 | − | 2.10695i | 0.114721 | − | 0.0833497i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.32064 | + | 3.13913i | 0.170655 | + | 0.123988i | 0.669834 | − | 0.742511i | \(-0.266365\pi\) |
−0.499179 | + | 0.866499i | \(0.666365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.3417 | −0.999381 | −0.499690 | − | 0.866204i | \(-0.666553\pi\) | ||||
−0.499690 | + | 0.866204i | \(0.666553\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.96127 | + | 30.6576i | −0.391618 | + | 1.20528i | 0.539946 | + | 0.841700i | \(0.318445\pi\) |
−0.931564 | + | 0.363577i | \(0.881555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.7219 | 0.970419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.1510 | 0.985745 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.1684 | − | 40.5282i | 0.515319 | − | 1.58599i | −0.267382 | − | 0.963591i | \(-0.586158\pi\) |
0.782701 | − | 0.622398i | \(-0.213842\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.66512 | 0.142990 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.7933 | − | 13.6541i | −0.732082 | − | 0.531889i | 0.158139 | − | 0.987417i | \(-0.449450\pi\) |
−0.890221 | + | 0.455528i | \(0.849450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5558 | − | 18.5674i | 0.994004 | − | 0.722186i | 0.0332099 | − | 0.999448i | \(-0.489427\pi\) |
0.960794 | + | 0.277262i | \(0.0894270\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.5524 | − | 15.6587i | −0.837025 | − | 0.608134i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.02685 | + | 12.3934i | 0.155920 | + | 0.479873i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.38784 | − | 7.34901i | −0.0923191 | − | 0.284129i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.9444 | + | 42.9163i | −0.538316 | + | 1.65677i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.06059 | + | 4.40327i | −0.233618 | + | 0.169734i | −0.698435 | − | 0.715673i | \(-0.746120\pi\) |
0.464817 | + | 0.885407i | \(0.346120\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.3719 | − | 15.5276i | 0.821389 | − | 0.596774i | −0.0957209 | − | 0.995408i | \(-0.530516\pi\) |
0.917110 | + | 0.398634i | \(0.130516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.15144 | + | 22.0099i | −0.274447 | + | 0.844662i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.56640 | − | 20.2093i | −0.251625 | − | 0.774422i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.87077 | + | 5.75763i | 0.0715829 | + | 0.220310i | 0.980447 | − | 0.196782i | \(-0.0630493\pi\) |
−0.908864 | + | 0.417092i | \(0.863049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.34551 | − | 6.78991i | −0.356553 | − | 0.259051i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.70282 | − | 1.96371i | 0.102969 | − | 0.0748116i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3719 | + | 22.0665i | 1.15540 | + | 0.839449i | 0.989190 | − | 0.146641i | \(-0.0468462\pi\) |
0.166212 | + | 0.986090i | \(0.446846\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.44239 | 0.168752 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.84670 | − | 21.0720i | 0.259337 | − | 0.798158i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.8045 | −0.976014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9151 | 0.563334 | 0.281667 | − | 0.959512i | \(-0.409113\pi\) | ||||
0.281667 | + | 0.959512i | \(0.409113\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.54362 | + | 23.2169i | −0.284513 | + | 0.875641i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.51569 | −0.132221 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.79990 | − | 2.76079i | −0.142708 | − | 0.103684i | 0.514140 | − | 0.857706i | \(-0.328111\pi\) |
−0.656849 | + | 0.754022i | \(0.728111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.01688 | + | 4.37152i | −0.225651 | + | 0.163945i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.99938 | − | 5.81189i | −0.299579 | − | 0.217657i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.93860 | − | 15.1994i | −0.184435 | − | 0.567633i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.84285 | − | 5.67172i | −0.0687268 | − | 0.211519i | 0.910794 | − | 0.412860i | \(-0.135470\pi\) |
−0.979521 | + | 0.201341i | \(0.935470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.17313 | + | 12.8436i | −0.155416 | + | 0.478320i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.62537 | − | 6.99324i | 0.357971 | − | 0.260081i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.3640 | − | 24.9669i | 1.27449 | − | 0.925972i | 0.275120 | − | 0.961410i | \(-0.411282\pi\) |
0.999372 | + | 0.0354375i | \(0.0112825\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.28034 | − | 28.5619i | 0.343716 | − | 1.05785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.82478 | − | 21.0045i | −0.252424 | − | 0.776880i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.05041 | − | 12.4659i | −0.149605 | − | 0.460438i | 0.847969 | − | 0.530046i | \(-0.177825\pi\) |
−0.997574 | + | 0.0696075i | \(0.977825\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.5916 | + | 25.8588i | 1.31103 | + | 0.952522i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.7715 | − | 28.8957i | 1.46302 | − | 1.06295i | 0.480456 | − | 0.877019i | \(-0.340471\pi\) |
0.982564 | − | 0.185927i | \(-0.0595288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.3671 | + | 13.3445i | 0.674732 | + | 0.490221i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2935 | −0.817869 | −0.408934 | − | 0.912564i | \(-0.634099\pi\) | ||||
−0.408934 | + | 0.912564i | \(0.634099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.32148 | + | 7.14477i | −0.0849384 | + | 0.261414i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.1012 | −0.661403 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0656 | 1.46202 | 0.731008 | − | 0.682369i | \(-0.239050\pi\) | ||||
0.731008 | + | 0.682369i | \(0.239050\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.23607 | − | 19.1927i | 0.227255 | − | 0.699419i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.47793 | −0.308136 | −0.154068 | − | 0.988060i | \(-0.549237\pi\) | ||||
−0.154068 | + | 0.988060i | \(0.549237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.50711 | + | 4.00115i | 0.199895 | + | 0.145233i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.94790 | − | 3.59486i | 0.179361 | − | 0.130313i | −0.494482 | − | 0.869188i | \(-0.664642\pi\) |
0.673843 | + | 0.738874i | \(0.264642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.2943 | − | 13.2916i | −0.662299 | − | 0.481189i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.22134 | − | 22.2250i | −0.260748 | − | 0.802498i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.57999 | + | 14.0958i | 0.165159 | + | 0.508306i | 0.999048 | − | 0.0436258i | \(-0.0138909\pi\) |
−0.833889 | + | 0.551932i | \(0.813891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5848 | − | 32.5768i | 0.381203 | − | 1.17322i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.8625 | − | 11.5248i | 0.570534 | − | 0.414517i | −0.264765 | − | 0.964313i | \(-0.585294\pi\) |
0.835299 | + | 0.549796i | \(0.185294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.2380 | + | 10.3445i | −0.510785 | + | 0.371107i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.83480 | + | 17.9577i | −0.209054 | + | 0.643401i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.39118 | − | 16.5923i | −0.192912 | − | 0.593721i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.2106 | − | 46.8133i | −0.543581 | − | 1.67297i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2403 | + | 8.16654i | 0.400673 | + | 0.291106i | 0.769815 | − | 0.638267i | \(-0.220348\pi\) |
−0.369142 | + | 0.929373i | \(0.620348\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.68864 | − | 1.22687i | 0.0601170 | − | 0.0436776i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.8580 | + | 23.8727i | 1.16829 | + | 0.848816i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.6550 | 1.51472 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.06395 | + | 27.8960i | −0.321062 | + | 0.988126i | 0.652125 | + | 0.758111i | \(0.273878\pi\) |
−0.973187 | + | 0.230015i | \(0.926122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.5355 | 1.18640 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.60674 | −0.0567714 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.51235 | − | 16.9653i | 0.194526 | − | 0.598691i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.8918 | 0.841032 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.2613 | − | 14.7207i | −0.712349 | − | 0.517552i | 0.171582 | − | 0.985170i | \(-0.445112\pi\) |
−0.883931 | + | 0.467618i | \(0.845112\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.89268 | − | 3.55474i | 0.171805 | − | 0.124824i | −0.498560 | − | 0.866855i | \(-0.666138\pi\) |
0.670365 | + | 0.742032i | \(0.266138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.99502 | + | 2.17601i | 0.105040 | + | 0.0763160i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.81612 | + | 17.9002i | 0.203480 | + | 0.626248i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.29764 | − | 3.99371i | −0.0453431 | − | 0.139552i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.36777 | − | 22.6757i | 0.257137 | − | 0.791386i | −0.736264 | − | 0.676694i | \(-0.763412\pi\) |
0.993401 | − | 0.114692i | \(-0.0365881\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.82288 | + | 1.32440i | −0.0635414 | + | 0.0461656i | −0.619103 | − | 0.785310i | \(-0.712503\pi\) |
0.555561 | + | 0.831476i | \(0.312503\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2058 | − | 13.2273i | 0.633079 | − | 0.459959i | −0.224387 | − | 0.974500i | \(-0.572038\pi\) |
0.857465 | + | 0.514542i | \(0.172038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.64584 | − | 14.2984i | 0.161357 | − | 0.496605i | −0.837393 | − | 0.546602i | \(-0.815921\pi\) |
0.998749 | + | 0.0499970i | \(0.0159212\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.75086 | + | 11.5440i | 0.130116 | + | 0.400456i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.04559 | − | 6.29566i | −0.0708753 | − | 0.218132i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.2160 | + | 21.9532i | 1.04442 | + | 0.758813i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.2255 | + | 12.5150i | −0.594689 | + | 0.432067i | −0.843990 | − | 0.536359i | \(-0.819799\pi\) |
0.249301 | + | 0.968426i | \(0.419799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.4489 | − | 28.6613i | −1.36031 | − | 0.988321i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.5284 | −0.465944 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.58784 | + | 4.88688i | −0.0545589 | + | 0.167915i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.2593 | −1.41602 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.91886 | 0.237176 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.6164 | + | 32.6740i | −0.363500 | + | 1.11874i | 0.587416 | + | 0.809285i | \(0.300145\pi\) |
−0.950915 | + | 0.309452i | \(0.899855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0100587 | 0.000343599 | 0.000171800 | − | 1.00000i | \(-0.499945\pi\) | ||||
0.000171800 | 1.00000i | \(0.499945\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0260 | − | 8.73743i | −0.410323 | − | 0.298117i | 0.363410 | − | 0.931629i | \(-0.381613\pi\) |
−0.773733 | + | 0.633512i | \(0.781613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.0127 | + | 8.00122i | −0.375313 | + | 0.272681i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.2578 | + | 17.6243i | 0.825744 | + | 0.599938i | 0.918352 | − | 0.395765i | \(-0.129520\pi\) |
−0.0926084 | + | 0.995703i | \(0.529520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.75552 | + | 30.0244i | 0.331315 | + | 1.01968i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.1857 | + | 34.4259i | 0.379448 | + | 1.16782i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8507 | − | 39.5504i | 0.435429 | − | 1.34011i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.71424 | + | 3.42510i | −0.159553 | + | 0.115922i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.67426 | + | 3.39605i | −0.157839 | + | 0.114676i | −0.663901 | − | 0.747820i | \(-0.731100\pi\) |
0.506063 | + | 0.862497i | \(0.331100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.56393 | + | 20.2017i | −0.221396 | + | 0.681386i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.2887 | + | 40.8983i | 0.447706 | + | 1.37790i | 0.879489 | + | 0.475920i | \(0.157885\pi\) |
−0.431783 | + | 0.901978i | \(0.642115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.1993 | + | 34.4679i | 0.376886 | + | 1.15994i | 0.942197 | + | 0.335058i | \(0.108756\pi\) |
−0.565311 | + | 0.824878i | \(0.691244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.08529 | + | 2.96814i | 0.137171 | + | 0.0996602i | 0.654255 | − | 0.756274i | \(-0.272983\pi\) |
−0.517084 | + | 0.855935i | \(0.672983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.6544 | − | 17.1859i | 0.793344 | − | 0.576398i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.3699 | − | 11.8934i | −0.548411 | − | 0.398444i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.5792 | −0.956366 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.98839 | − | 6.11965i | 0.0663905 | − | 0.204329i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.0039 | 1.96789 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.25316 | −0.241638 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.19302 | + | 12.9048i | −0.139535 | + | 0.429445i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.2922 | −1.20506 | −0.602532 | − | 0.798095i | \(-0.705841\pi\) | ||||
−0.602532 | + | 0.798095i | \(0.705841\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.716161 | − | 0.520322i | −0.0237536 | − | 0.0172580i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.782203 | + | 0.568304i | −0.0259155 | + | 0.0188287i | −0.600668 | − | 0.799499i | \(-0.705098\pi\) |
0.574752 | + | 0.818328i | \(0.305098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.5805 | + | 21.4915i | 0.978971 | + | 0.711264i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.3817 | + | 41.1848i | 0.441904 | + | 1.36004i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.44217 | − | 7.51624i | −0.0805599 | − | 0.247938i | 0.902662 | − | 0.430349i | \(-0.141610\pi\) |
−0.983222 | + | 0.182412i | \(0.941610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.58698 | − | 7.96190i | 0.0852439 | − | 0.262354i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.3418 | + | 9.69335i | −0.439149 | + | 0.319061i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.75094 | + | 1.99867i | −0.0903526 | + | 0.0656450i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.33760 | + | 16.4275i | −0.175121 | + | 0.538967i | −0.999639 | − | 0.0268686i | \(-0.991446\pi\) |
0.824518 | + | 0.565836i | \(0.191446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.74326 | + | 5.36521i | 0.0571331 | + | 0.175838i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.72574 | − | 17.6220i | −0.187452 | − | 0.576919i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.2197 | − | 23.4090i | −1.05257 | − | 0.764738i | −0.0798723 | − | 0.996805i | \(-0.525451\pi\) |
−0.972700 | + | 0.232067i | \(0.925451\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.37365 | + | 4.63073i | −0.207996 | + | 0.151118i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.6179 | − | 29.5106i | −1.32411 | − | 0.962019i | −0.999871 | − | 0.0160420i | \(-0.994893\pi\) |
−0.324234 | − | 0.945977i | \(-0.605107\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.35157 | 0.174271 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.6528 | − | 45.0966i | 0.476151 | − | 1.46544i | −0.368248 | − | 0.929727i | \(-0.620042\pi\) |
0.844399 | − | 0.535714i | \(-0.179958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.8620 | −0.547362 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.9128 | −0.353872 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.2380 | − | 56.1307i | 0.590786 | − | 1.81825i | 0.0161122 | − | 0.999870i | \(-0.494871\pi\) |
0.574674 | − | 0.818382i | \(-0.305129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −40.6207 | −1.31308 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.8962 | − | 22.4474i | −0.997690 | − | 0.724864i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.1409 | + | 8.09437i | −0.359385 | + | 0.261109i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.68729 | − | 2.67897i | −0.118821 | − | 0.0863287i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6390 | − | 48.1319i | −0.502917 | − | 1.54782i | −0.804245 | − | 0.594298i | \(-0.797430\pi\) |
0.301328 | − | 0.953520i | \(-0.402570\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.2312 | − | 46.8767i | −0.489295 | − | 1.50590i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5600 | + | 47.8887i | −0.499343 | + | 1.53682i | 0.310734 | + | 0.950497i | \(0.399425\pi\) |
−0.810077 | + | 0.586324i | \(0.800575\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.9536 | − | 8.68478i | 0.383214 | − | 0.278421i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.16192 | − | 5.92998i | 0.261123 | − | 0.189717i | −0.449519 | − | 0.893271i | \(-0.648405\pi\) |
0.710642 | + | 0.703554i | \(0.248405\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.41654 | + | 7.43735i | −0.0772330 | + | 0.237699i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75948 | − | 5.41512i | −0.0561758 | − | 0.172891i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.47888 | + | 29.1730i | 0.302329 | + | 0.930474i | 0.980660 | + | 0.195718i | \(0.0627036\pi\) |
−0.678331 | + | 0.734757i | \(0.737296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.6687 | − | 12.1105i | −0.530569 | − | 0.385481i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.31565 | − | 3.13550i | 0.137230 | − | 0.0997032i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.3611 | + | 24.9648i | 1.09152 | + | 0.793034i | 0.979655 | − | 0.200690i | \(-0.0643183\pi\) |
0.111863 | + | 0.993724i | \(0.464318\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.97038 | 0.284667 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.13204 | − | 3.48407i | 0.0358522 | − | 0.110342i | −0.931529 | − | 0.363667i | \(-0.881524\pi\) |
0.967381 | + | 0.253326i | \(0.0815245\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.1345 | −0.826860 |
(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 | 500.2.g.a.301.3 | 12 | ||
5.2 | odd | 4 | 500.2.i.b.449.2 | 24 | |||
5.3 | odd | 4 | 500.2.i.b.449.5 | 24 | |||
5.4 | even | 2 | 100.2.g.a.61.1 | yes | 12 | ||
15.14 | odd | 2 | 900.2.n.c.361.1 | 12 | |||
20.19 | odd | 2 | 400.2.u.f.161.3 | 12 | |||
25.3 | odd | 20 | 2500.2.c.c.1249.9 | 12 | |||
25.4 | even | 10 | 2500.2.a.d.1.2 | 6 | |||
25.9 | even | 10 | 100.2.g.a.41.1 | ✓ | 12 | ||
25.12 | odd | 20 | 500.2.i.b.49.5 | 24 | |||
25.13 | odd | 20 | 500.2.i.b.49.2 | 24 | |||
25.16 | even | 5 | inner | 500.2.g.a.201.3 | 12 | ||
25.21 | even | 5 | 2500.2.a.c.1.5 | 6 | |||
25.22 | odd | 20 | 2500.2.c.c.1249.4 | 12 | |||
75.59 | odd | 10 | 900.2.n.c.541.1 | 12 | |||
100.59 | odd | 10 | 400.2.u.f.241.3 | 12 | |||
100.71 | odd | 10 | 10000.2.a.bd.1.2 | 6 | |||
100.79 | odd | 10 | 10000.2.a.bc.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.2.g.a.41.1 | ✓ | 12 | 25.9 | even | 10 | ||
100.2.g.a.61.1 | yes | 12 | 5.4 | even | 2 | ||
400.2.u.f.161.3 | 12 | 20.19 | odd | 2 | |||
400.2.u.f.241.3 | 12 | 100.59 | odd | 10 | |||
500.2.g.a.201.3 | 12 | 25.16 | even | 5 | inner | ||
500.2.g.a.301.3 | 12 | 1.1 | even | 1 | trivial | ||
500.2.i.b.49.2 | 24 | 25.13 | odd | 20 | |||
500.2.i.b.49.5 | 24 | 25.12 | odd | 20 | |||
500.2.i.b.449.2 | 24 | 5.2 | odd | 4 | |||
500.2.i.b.449.5 | 24 | 5.3 | odd | 4 | |||
900.2.n.c.361.1 | 12 | 15.14 | odd | 2 | |||
900.2.n.c.541.1 | 12 | 75.59 | odd | 10 | |||
2500.2.a.c.1.5 | 6 | 25.21 | even | 5 | |||
2500.2.a.d.1.2 | 6 | 25.4 | even | 10 | |||
2500.2.c.c.1249.4 | 12 | 25.22 | odd | 20 | |||
2500.2.c.c.1249.9 | 12 | 25.3 | odd | 20 | |||
10000.2.a.bc.1.5 | 6 | 100.79 | odd | 10 | |||
10000.2.a.bd.1.2 | 6 | 100.71 | odd | 10 |