Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 357.1 | ||
Root | \(-2.44766i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.357 |
Dual form | 1300.2.bs.d.193.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −0.877081 | − | 3.27331i | −0.506383 | − | 1.88985i | −0.453522 | − | 0.891245i | \(-0.649833\pi\) |
−0.0528610 | − | 0.998602i | \(-0.516834\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.27273 | + | 1.31216i | −0.859013 | + | 0.495951i | −0.863682 | − | 0.504038i | \(-0.831847\pi\) |
0.00466893 | + | 0.999989i | \(0.498514\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.34722 | + | 4.24192i | −2.44907 | + | 1.41397i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.71196 | − | 0.458719i | 0.516176 | − | 0.138309i | 0.00867863 | − | 0.999962i | \(-0.497237\pi\) |
0.507497 | + | 0.861653i | \(0.330571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.21746 | + | 3.39379i | −0.337664 | + | 0.941267i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.363048 | − | 0.0972783i | −0.0880520 | − | 0.0235935i | 0.214524 | − | 0.976719i | \(-0.431180\pi\) |
−0.302576 | + | 0.953125i | \(0.597847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.462233 | + | 1.72508i | −0.106044 | + | 0.395760i | −0.998461 | − | 0.0554497i | \(-0.982341\pi\) |
0.892418 | + | 0.451210i | \(0.149007\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.28849 | + | 6.28849i | 1.37226 | + | 1.37226i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.72966 | − | 1.26731i | 0.986203 | − | 0.264252i | 0.270548 | − | 0.962707i | \(-0.412795\pi\) |
0.715655 | + | 0.698454i | \(0.246128\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.1405 | + | 13.1405i | 2.52890 | + | 2.52890i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.28709 | + | 3.62985i | 1.16748 | + | 0.674047i | 0.953086 | − | 0.302699i | \(-0.0978878\pi\) |
0.214398 | + | 0.976746i | \(0.431221\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.98238 | − | 2.98238i | 0.535651 | − | 0.535651i | −0.386597 | − | 0.922249i | \(-0.626350\pi\) |
0.922249 | + | 0.386597i | \(0.126350\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00306 | − | 5.20145i | −0.522765 | − | 0.905456i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.83378 | − | 5.10019i | −1.45226 | − | 0.838465i | −0.453655 | − | 0.891177i | \(-0.649880\pi\) |
−0.998610 | + | 0.0527119i | \(0.983214\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.1767 | + | 1.00852i | 1.94984 | + | 0.161492i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.59861 | + | 5.96611i | 0.249662 | + | 0.931750i | 0.970983 | + | 0.239149i | \(0.0768686\pi\) |
−0.721321 | + | 0.692601i | \(0.756465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.427024 | + | 1.59368i | −0.0651205 | + | 0.243033i | −0.990812 | − | 0.135246i | \(-0.956817\pi\) |
0.925691 | + | 0.378279i | \(0.123484\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.19733i | 0.174649i | 0.996180 | + | 0.0873244i | \(0.0278317\pi\) | ||||
−0.996180 | + | 0.0873244i | \(0.972168\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0564545 | + | 0.0977821i | −0.00806493 | + | 0.0139689i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.27369i | 0.178352i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.13227 | + | 5.13227i | −0.704971 | + | 0.704971i | −0.965473 | − | 0.260502i | \(-0.916112\pi\) |
0.260502 | + | 0.965473i | \(0.416112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.05214 | 0.801625 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.89607 | − | 0.776000i | −0.377036 | − | 0.101027i | 0.0653237 | − | 0.997864i | \(-0.479192\pi\) |
−0.442360 | + | 0.896838i | \(0.645859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.45432 | − | 4.25101i | −0.314244 | − | 0.544286i | 0.665033 | − | 0.746814i | \(-0.268418\pi\) |
−0.979276 | + | 0.202528i | \(0.935084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.1322 | − | 19.2815i | 1.40252 | − | 2.42924i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.98715 | + | 6.90594i | −0.487107 | + | 0.843695i | −0.999890 | − | 0.0148238i | \(-0.995281\pi\) |
0.512783 | + | 0.858518i | \(0.328615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.29659 | − | 14.3701i | −0.998792 | − | 1.72996i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.02481 | + | 1.07844i | 0.477657 | + | 0.127988i | 0.489611 | − | 0.871941i | \(-0.337139\pi\) |
−0.0119546 | + | 0.999929i | \(0.503805\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2043 | 1.31137 | 0.655683 | − | 0.755037i | \(-0.272381\pi\) | ||||
0.655683 | + | 0.755037i | \(0.272381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.28892 | + | 3.28892i | −0.374807 | + | 0.374807i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.72484i | − | 0.306569i | −0.988182 | − | 0.153284i | \(-0.951015\pi\) | ||
0.988182 | − | 0.153284i | \(-0.0489851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 18.7620 | − | 32.4967i | 2.08466 | − | 3.61074i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2434i | 1.23413i | 0.786913 | + | 0.617064i | \(0.211678\pi\) | ||||
−0.786913 | + | 0.617064i | \(0.788322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.36735 | − | 23.7633i | 0.682652 | − | 2.54769i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.91334 | + | 7.14070i | 0.202814 | + | 0.756913i | 0.990105 | + | 0.140330i | \(0.0448165\pi\) |
−0.787291 | + | 0.616582i | \(0.788517\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.68623 | − | 9.31068i | −0.176765 | − | 0.976025i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.3780 | − | 7.14647i | −1.28354 | − | 0.741054i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.838229 | + | 1.45185i | 0.0851092 | + | 0.147413i | 0.905438 | − | 0.424479i | \(-0.139543\pi\) |
−0.820329 | + | 0.571893i | \(0.806209\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.6323 | + | 10.6323i | −1.06859 | + | 1.06859i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2100 | − | 7.04945i | −1.21494 | − | 0.701447i | −0.251110 | − | 0.967959i | \(-0.580796\pi\) |
−0.963832 | + | 0.266512i | \(0.914129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.21560 | + | 8.21560i | 0.809508 | + | 0.809508i | 0.984559 | − | 0.175052i | \(-0.0560093\pi\) |
−0.175052 | + | 0.984559i | \(0.556009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.71070 | − | 2.33402i | 0.842095 | − | 0.225639i | 0.188112 | − | 0.982148i | \(-0.439763\pi\) |
0.653983 | + | 0.756509i | \(0.273097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.48128 | + | 8.48128i | 0.812359 | + | 0.812359i | 0.984987 | − | 0.172628i | \(-0.0552258\pi\) |
−0.172628 | + | 0.984987i | \(0.555226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.94655 | + | 33.3890i | −0.849169 | + | 3.16914i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.71713 | − | 0.728053i | −0.255606 | − | 0.0684895i | 0.128740 | − | 0.991678i | \(-0.458907\pi\) |
−0.384347 | + | 0.923189i | \(0.625573\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.45118 | − | 30.0993i | −0.503962 | − | 2.78268i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.952755 | − | 0.255290i | 0.0873389 | − | 0.0234024i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.80589 | + | 3.92938i | −0.618717 | + | 0.357217i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.1268 | − | 10.4655i | 1.63444 | − | 0.943645i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.71429 | + | 6.39781i | 0.152119 | + | 0.567714i | 0.999335 | + | 0.0364661i | \(0.0116101\pi\) |
−0.847216 | + | 0.531248i | \(0.821723\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.59113 | 0.492271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.68334 | 0.234444 | 0.117222 | − | 0.993106i | \(-0.462601\pi\) | ||||
0.117222 | + | 0.993106i | \(0.462601\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.21305 | − | 4.52717i | −0.105185 | − | 0.392555i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.78743 | − | 1.03197i | 0.152710 | − | 0.0881674i | −0.421698 | − | 0.906737i | \(-0.638566\pi\) |
0.574408 | + | 0.818569i | \(0.305232\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7676 | − | 7.37138i | 1.08293 | − | 0.625233i | 0.151248 | − | 0.988496i | \(-0.451671\pi\) |
0.931687 | + | 0.363263i | \(0.118337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.91924 | − | 1.05016i | 0.330060 | − | 0.0884392i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.527460 | + | 6.36850i | −0.0441084 | + | 0.532561i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.369586 | + | 0.0990304i | 0.0304830 | + | 0.00816789i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.823027 | + | 3.07158i | −0.0674250 | + | 0.251633i | −0.991409 | − | 0.130797i | \(-0.958246\pi\) |
0.923984 | + | 0.382431i | \(0.124913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.20288 | + | 7.20288i | 0.586162 | + | 0.586162i | 0.936590 | − | 0.350428i | \(-0.113964\pi\) |
−0.350428 | + | 0.936590i | \(0.613964\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.08004 | − | 0.825293i | 0.249006 | − | 0.0667210i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0556926 | + | 0.0556926i | 0.00444476 | + | 0.00444476i | 0.709326 | − | 0.704881i | \(-0.249000\pi\) |
−0.704881 | + | 0.709326i | \(0.749000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.3009 | + | 12.2981i | 1.68927 | + | 0.975303i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.08634 | + | 9.08634i | −0.716104 | + | 0.716104i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.92131 | + | 15.4522i | 0.698771 | + | 1.21031i | 0.968893 | + | 0.247481i | \(0.0796027\pi\) |
−0.270122 | + | 0.962826i | \(0.587064\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.20710 | + | 1.27427i | 0.170791 | + | 0.0986060i | 0.582959 | − | 0.812502i | \(-0.301895\pi\) |
−0.412168 | + | 0.911108i | \(0.635228\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0356 | − | 8.26363i | −0.771966 | − | 0.635664i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.92151 | − | 14.6353i | −0.299886 | − | 1.11919i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.65644 | − | 13.6460i | 0.277994 | − | 1.03749i | −0.675815 | − | 0.737071i | \(-0.736208\pi\) |
0.953809 | − | 0.300415i | \(-0.0971252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.1604i | 0.763699i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.85350 | + | 13.6027i | −0.586998 | + | 1.01671i | 0.407625 | + | 0.913149i | \(0.366357\pi\) |
−0.994623 | + | 0.103561i | \(0.966976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.87942i | 0.585673i | 0.956163 | + | 0.292836i | \(0.0945991\pi\) | ||||
−0.956163 | + | 0.292836i | \(0.905401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.7622 | + | 11.7622i | −0.869490 | + | 0.869490i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.666147 | −0.0487135 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −47.1075 | − | 12.6224i | −3.42656 | − | 0.918145i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.41812 | − | 16.3127i | −0.681471 | − | 1.18034i | −0.974532 | − | 0.224249i | \(-0.928007\pi\) |
0.293061 | − | 0.956094i | \(-0.405326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.2328 | + | 21.1878i | −0.880533 | + | 1.52513i | −0.0297844 | + | 0.999556i | \(0.509482\pi\) |
−0.850749 | + | 0.525572i | \(0.823851\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.08076 | + | 12.2642i | −0.504484 | + | 0.873791i | 0.495503 | + | 0.868606i | \(0.334984\pi\) |
−0.999987 | + | 0.00518489i | \(0.998350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.57563 | + | 2.72908i | 0.111694 | + | 0.193459i | 0.916453 | − | 0.400142i | \(-0.131039\pi\) |
−0.804760 | + | 0.593601i | \(0.797706\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.1023 | + | 6.99410i | 1.84112 | + | 0.493326i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.0518 | −1.33718 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −29.3740 | + | 29.3740i | −2.04164 | + | 2.04164i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.16530i | 0.218949i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.323466 | + | 0.560259i | −0.0222683 | + | 0.0385698i | −0.876945 | − | 0.480591i | \(-0.840422\pi\) |
0.854677 | + | 0.519161i | \(0.173755\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 14.1203i | − | 0.967509i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.86479 | + | 10.6915i | −0.194474 | + | 0.725788i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.82709 | − | 36.6752i | −0.664053 | − | 2.47828i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.772139 | − | 1.11367i | 0.0519397 | − | 0.0749137i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.0872 | + | 6.40121i | 0.742456 | + | 0.428657i | 0.822961 | − | 0.568097i | \(-0.192320\pi\) |
−0.0805058 | + | 0.996754i | \(0.525654\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.20690 | + | 9.01862i | 0.345594 | + | 0.598587i | 0.985462 | − | 0.169899i | \(-0.0543441\pi\) |
−0.639867 | + | 0.768485i | \(0.721011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.26361 | − | 4.26361i | 0.281747 | − | 0.281747i | −0.552058 | − | 0.833806i | \(-0.686157\pi\) |
0.833806 | + | 0.552058i | \(0.186157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6503 | + | 7.88100i | 0.898124 | + | 0.518532i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.786053 | − | 0.786053i | −0.0514960 | − | 0.0514960i | 0.680890 | − | 0.732386i | \(-0.261593\pi\) |
−0.732386 | + | 0.680890i | \(0.761593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.91926 | + | 2.38991i | −0.579368 | + | 0.155241i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.7521 | − | 18.7521i | −1.21297 | − | 1.21297i | −0.970045 | − | 0.242925i | \(-0.921893\pi\) |
−0.242925 | − | 0.970045i | \(-0.578107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.89785 | + | 10.8149i | −0.186667 | + | 0.696652i | 0.807600 | + | 0.589730i | \(0.200766\pi\) |
−0.994267 | + | 0.106921i | \(0.965901\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −68.9767 | − | 18.4823i | −4.42486 | − | 1.18564i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.29179 | − | 3.66894i | −0.336709 | − | 0.233449i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 36.8033 | − | 9.86140i | 2.33231 | − | 0.624941i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.6347 | + | 14.2228i | −1.55493 | + | 0.897737i | −0.557198 | + | 0.830380i | \(0.688123\pi\) |
−0.997729 | + | 0.0673574i | \(0.978543\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.51566 | − | 4.33917i | 0.472505 | − | 0.272801i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.88190 | + | 25.6836i | 0.429281 | + | 1.60210i | 0.754393 | + | 0.656423i | \(0.227931\pi\) |
−0.325112 | + | 0.945675i | \(0.605402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.7691 | 1.66335 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −61.5902 | −3.81234 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.86411 | − | 10.6890i | −0.176609 | − | 0.659112i | −0.996272 | − | 0.0862670i | \(-0.972506\pi\) |
0.819663 | − | 0.572845i | \(-0.194160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.6956 | − | 12.5259i | 1.32775 | − | 0.766575i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.97689 | + | 2.29606i | −0.242475 | + | 0.139993i | −0.616314 | − | 0.787501i | \(-0.711375\pi\) |
0.373839 | + | 0.927494i | \(0.378041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.90421 | − | 1.31408i | 0.297909 | − | 0.0798245i | −0.106768 | − | 0.994284i | \(-0.534050\pi\) |
0.404678 | + | 0.914459i | \(0.367384\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28.9978 | + | 13.6858i | −1.75503 | + | 0.828301i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1826 | − | 4.33613i | −0.972321 | − | 0.260533i | −0.262513 | − | 0.964928i | \(-0.584551\pi\) |
−0.709807 | + | 0.704396i | \(0.751218\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.26118 | + | 34.5632i | −0.554452 | + | 2.06924i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.3528 | + | 18.3528i | 1.09483 | + | 1.09483i | 0.995005 | + | 0.0998291i | \(0.0318296\pi\) |
0.0998291 | + | 0.995005i | \(0.468170\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.82286 | + | 1.56023i | −0.346133 | + | 0.0927461i | −0.427697 | − | 0.903922i | \(-0.640675\pi\) |
0.0815641 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4617 | − | 11.4617i | −0.676565 | − | 0.676565i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.6001 | − | 8.42937i | −0.858829 | − | 0.495845i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.01718 | − | 4.01718i | 0.235491 | − | 0.235491i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.86812 | + | 13.6280i | 0.459661 | + | 0.796156i | 0.998943 | − | 0.0459695i | \(-0.0146377\pi\) |
−0.539282 | + | 0.842125i | \(0.681304\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.5239 | + | 16.4683i | 1.65512 | + | 0.955586i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.45722 | + | 17.5944i | −0.0842733 | + | 1.01751i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.12065 | − | 4.18232i | −0.0645932 | − | 0.241065i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.3659 | + | 46.1501i | −0.710401 | + | 2.65125i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.0727i | − | 1.60219i | −0.598536 | − | 0.801096i | \(-0.704251\pi\) | ||
0.598536 | − | 0.801096i | \(-0.295749\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.6865 | − | 34.0980i | 1.11992 | − | 1.93977i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.33583i | − | 0.415977i | −0.978131 | − | 0.207988i | \(-0.933308\pi\) | ||
0.978131 | − | 0.207988i | \(-0.0666916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.41291 | − | 6.41291i | 0.362479 | − | 0.362479i | −0.502246 | − | 0.864725i | \(-0.667493\pi\) |
0.864725 | + | 0.502246i | \(0.167493\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.9597 | −1.79503 | −0.897517 | − | 0.440980i | \(-0.854631\pi\) | ||||
−0.897517 | + | 0.440980i | \(0.854631\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4283 | + | 3.33016i | 0.695853 | + | 0.186453i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.2800 | − | 26.4657i | −0.852845 | − | 1.47717i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.335625 | − | 0.581320i | 0.0186747 | − | 0.0323455i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.3231 | − | 35.2006i | 1.12387 | − | 1.94660i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.57110 | − | 2.72122i | −0.0866173 | − | 0.150026i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.58649 | + | 1.22895i | 0.252096 | + | 0.0675489i | 0.382654 | − | 0.923892i | \(-0.375010\pi\) |
−0.130558 | + | 0.991441i | \(0.541677\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 86.5383 | 4.74227 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.5944 | − | 23.5944i | 1.28527 | − | 1.28527i | 0.347645 | − | 0.937626i | \(-0.386982\pi\) |
0.937626 | − | 0.347645i | \(-0.113018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.53258i | 0.517738i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.73764 | − | 6.47379i | 0.202405 | − | 0.350575i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.6666i | − | 1.00790i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.947430 | − | 3.53586i | 0.0508607 | − | 0.189815i | −0.935822 | − | 0.352474i | \(-0.885340\pi\) |
0.986682 | + | 0.162659i | \(0.0520071\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.937727 | + | 3.49965i | 0.0501954 | + | 0.187332i | 0.986471 | − | 0.163933i | \(-0.0524182\pi\) |
−0.936276 | + | 0.351265i | \(0.885752\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −60.5943 | + | 28.5980i | −3.23428 | + | 1.52645i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.13057 | + | 4.69419i | 0.432747 | + | 0.249846i | 0.700516 | − | 0.713637i | \(-0.252953\pi\) |
−0.267769 | + | 0.963483i | \(0.586287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.67129 | − | 2.89475i | −0.0884539 | − | 0.153207i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.90682 | + | 9.90682i | −0.522862 | + | 0.522862i | −0.918435 | − | 0.395573i | \(-0.870546\pi\) |
0.395573 | + | 0.918435i | \(0.370546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.6922 | + | 7.90522i | 0.720645 | + | 0.416064i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.8314 | + | 18.8314i | 0.988393 | + | 0.988393i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.44176 | − | 1.45811i | 0.284057 | − | 0.0761130i | −0.113977 | − | 0.993483i | \(-0.536359\pi\) |
0.398035 | + | 0.917370i | \(0.369692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −37.0531 | − | 37.0531i | −1.92891 | − | 1.92891i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.92991 | − | 18.3987i | 0.255948 | − | 0.955211i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2192 | − | 2.73824i | −0.529132 | − | 0.141780i | −0.0156446 | − | 0.999878i | \(-0.504980\pi\) |
−0.513487 | + | 0.858097i | \(0.671647\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.9733 | + | 16.9178i | −1.02868 | + | 0.871312i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.5928 | − | 6.85758i | 1.31462 | − | 0.352250i | 0.467657 | − | 0.883910i | \(-0.345098\pi\) |
0.846958 | + | 0.531660i | \(0.178431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.4385 | − | 11.2228i | 0.995863 | − | 0.574962i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.8344 | + | 11.4514i | −1.01349 | + | 0.585139i | −0.912212 | − | 0.409720i | \(-0.865627\pi\) |
−0.101278 | + | 0.994858i | \(0.532293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.62280 | − | 13.5205i | −0.184157 | − | 0.687285i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.00709 | −0.0510614 | −0.0255307 | − | 0.999674i | \(-0.508128\pi\) | ||||
−0.0255307 | + | 0.999674i | \(0.508128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.84037 | −0.0930717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.35350 | − | 8.78339i | −0.118718 | − | 0.443063i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.488978 | − | 0.282311i | 0.0245411 | − | 0.0141688i | −0.487679 | − | 0.873023i | \(-0.662156\pi\) |
0.512220 | + | 0.858854i | \(0.328823\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.7549 | + | 7.94139i | −0.688606 | + | 0.397567i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.79748 | − | 0.749581i | 0.139699 | − | 0.0374323i | −0.188292 | − | 0.982113i | \(-0.560295\pi\) |
0.327991 | + | 0.944681i | \(0.393628\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.49061 | + | 13.7525i | 0.323321 | + | 0.685061i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.4626 | − | 4.67910i | −0.865591 | − | 0.231934i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.82267 | + | 29.1946i | −0.386806 | + | 1.44358i | 0.448493 | + | 0.893786i | \(0.351961\pi\) |
−0.835300 | + | 0.549795i | \(0.814706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.94569 | − | 4.94569i | −0.243953 | − | 0.243953i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.60024 | − | 2.03648i | 0.373983 | − | 0.100208i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.3271 | − | 35.3271i | −1.72997 | − | 1.72997i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.06888 | + | 2.92652i | 0.247631 | + | 0.142970i | 0.618679 | − | 0.785644i | \(-0.287668\pi\) |
−0.371048 | + | 0.928614i | \(0.621002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2231 | + | 10.2231i | −0.498244 | + | 0.498244i | −0.910891 | − | 0.412647i | \(-0.864604\pi\) |
0.412647 | + | 0.910891i | \(0.364604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.07899 | − | 8.79706i | −0.246949 | − | 0.427728i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1560 | + | 6.44095i | 0.539879 | + | 0.311699i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.3087 | − | 3.85915i | 1.02879 | − | 0.186322i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.50264 | − | 35.4643i | −0.457726 | − | 1.70826i | −0.679947 | − | 0.733261i | \(-0.737997\pi\) |
0.222221 | − | 0.974996i | \(-0.428669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.99453 | − | 22.3719i | 0.288079 | − | 1.07513i | −0.658481 | − | 0.752597i | \(-0.728801\pi\) |
0.946560 | − | 0.322528i | \(-0.104533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.74483i | 0.418322i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.34925 | + | 2.33697i | −0.0643962 | + | 0.111537i | −0.896426 | − | 0.443193i | \(-0.853845\pi\) |
0.832030 | + | 0.554731i | \(0.187179\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 0.957902i | − | 0.0456144i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.66186 | − | 9.66186i | 0.459049 | − | 0.459049i | −0.439295 | − | 0.898343i | \(-0.644772\pi\) |
0.898343 | + | 0.439295i | \(0.144772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.7761 | 0.509692 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.88121 | − | 0.504069i | −0.0887799 | − | 0.0237885i | 0.214156 | − | 0.976800i | \(-0.431300\pi\) |
−0.302936 | + | 0.953011i | \(0.597967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.47353 | + | 9.48044i | 0.257739 | + | 0.446416i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.2598 | − | 29.8948i | 0.810934 | − | 1.40458i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.52855 | − | 11.3078i | 0.305393 | − | 0.528956i | −0.671956 | − | 0.740591i | \(-0.734546\pi\) |
0.977349 | + | 0.211635i | \(0.0678789\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.49235 | − | 6.04893i | −0.163009 | − | 0.282340i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.43252 | − | 0.383843i | −0.0667191 | − | 0.0178773i | 0.225305 | − | 0.974288i | \(-0.427662\pi\) |
−0.292024 | + | 0.956411i | \(0.594329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.4825 | −1.27722 | −0.638609 | − | 0.769531i | \(-0.720490\pi\) | ||||
−0.638609 | + | 0.769531i | \(0.720490\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.0831885 | − | 0.0831885i | 0.00384950 | − | 0.00384950i | −0.705179 | − | 0.709029i | \(-0.749134\pi\) |
0.709029 | + | 0.705179i | \(0.249134\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 20.9271i | − | 0.966326i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.133452 | − | 0.231146i | 0.00614916 | − | 0.0106507i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.92419i | 0.134455i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.9372 | − | 59.4786i | 0.729716 | − | 2.72334i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.12267 | + | 22.8501i | 0.279752 | + | 1.04405i | 0.952589 | + | 0.304259i | \(0.0984087\pi\) |
−0.672837 | + | 0.739790i | \(0.734925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.0638 | − | 23.7707i | 1.27960 | − | 1.08385i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.7119 | + | 21.7730i | 1.71595 | + | 0.990704i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.7169 | + | 18.5622i | 0.485628 | + | 0.841133i | 0.999864 | − | 0.0165161i | \(-0.00525746\pi\) |
−0.514235 | + | 0.857649i | \(0.671924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.7550 | − | 42.7550i | 1.93345 | − | 1.93345i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2578 | − | 7.65438i | −0.598315 | − | 0.345437i | 0.170063 | − | 0.985433i | \(-0.445603\pi\) |
−0.768378 | + | 0.639996i | \(0.778936\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.92941 | − | 1.92941i | −0.0868961 | − | 0.0868961i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.5624 | + | 2.83019i | −0.473789 | + | 0.126951i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.64170 | − | 8.64170i | −0.386856 | − | 0.386856i | 0.486709 | − | 0.873564i | \(-0.338197\pi\) |
−0.873564 | + | 0.486709i | \(0.838197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.23528 | − | 8.34216i | 0.0998648 | − | 0.372700i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.5394 | + | 5.77147i | 0.960396 | + | 0.257337i | 0.704768 | − | 0.709438i | \(-0.251051\pi\) |
0.255628 | + | 0.966775i | \(0.417718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.2474 | + | 40.0974i | −0.810397 | + | 1.78079i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.4129 | + | 6.54140i | −1.08208 | + | 0.289943i | −0.755448 | − | 0.655209i | \(-0.772581\pi\) |
−0.326633 | + | 0.945151i | \(0.605914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.4644 | + | 14.7019i | −1.12648 | + | 0.650373i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.7424 | + | 16.5945i | −1.26901 | + | 0.732663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.549239 | + | 2.04979i | 0.0241555 | + | 0.0901495i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −47.8746 | −2.10146 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3421 | 0.847393 | 0.423697 | − | 0.905804i | \(-0.360732\pi\) | ||||
0.423697 | + | 0.905804i | \(0.360732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.06014 | − | 30.0808i | −0.352445 | − | 1.31534i | −0.883669 | − | 0.468112i | \(-0.844934\pi\) |
0.531224 | − | 0.847231i | \(-0.321732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.37287 | + | 0.792625i | −0.0598030 | + | 0.0345273i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.845038 | − | 0.487883i | 0.0367408 | − | 0.0212123i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.5698 | − | 6.58346i | 1.06624 | − | 0.285698i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.1940 | − | 1.83818i | −0.961327 | − | 0.0796202i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.4139 | + | 13.7763i | 2.21867 | + | 0.594492i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0517935 | + | 0.193296i | −0.00223090 | + | 0.00832584i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.9495 | + | 10.9495i | 0.470757 | + | 0.470757i | 0.902159 | − | 0.431403i | \(-0.141981\pi\) |
−0.431403 | + | 0.902159i | \(0.641981\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.7918 | − | 6.91089i | 1.10683 | − | 0.296575i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.2846 | − | 25.2846i | −1.08109 | − | 1.08109i | −0.996408 | − | 0.0846839i | \(-0.973012\pi\) |
−0.0846839 | − | 0.996408i | \(-0.526988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.0649 | + | 20.8221i | 1.53921 | + | 0.888664i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.16789 | + | 9.16789i | −0.390565 | + | 0.390565i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.57544 | + | 6.19284i | 0.152043 | + | 0.263347i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.6667 | + | 8.46780i | 0.621447 | + | 0.358792i | 0.777432 | − | 0.628967i | \(-0.216522\pi\) |
−0.155985 | + | 0.987759i | \(0.549855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.88870 | − | 3.38947i | −0.206770 | − | 0.143359i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.584265 | + | 2.18051i | 0.0246677 | + | 0.0920610i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.67250 | + | 24.9021i | −0.281212 | + | 1.04950i | 0.670351 | + | 0.742044i | \(0.266144\pi\) |
−0.951563 | + | 0.307454i | \(0.900523\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 98.4751i | 4.13557i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.6372 | + | 30.5485i | −0.739390 | + | 1.28066i | 0.213380 | + | 0.976969i | \(0.431553\pi\) |
−0.952770 | + | 0.303692i | \(0.901781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.8260i | 1.45742i | 0.684821 | + | 0.728711i | \(0.259880\pi\) | ||||
−0.684821 | + | 0.728711i | \(0.740120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −45.1359 | + | 45.1359i | −1.88558 | + | 1.88558i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.5561 | 1.14717 | 0.573587 | − | 0.819145i | \(-0.305552\pi\) | ||||
0.573587 | + | 0.819145i | \(0.305552\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 80.0833 | + | 21.4582i | 3.32815 | + | 0.891774i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.7532 | − | 25.5533i | −0.612067 | − | 1.06013i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.43198 | + | 11.1405i | −0.266385 | + | 0.461393i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.693144 | − | 1.20056i | 0.0286091 | − | 0.0495524i | −0.851366 | − | 0.524572i | \(-0.824226\pi\) |
0.879975 | + | 0.475019i | \(0.157559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.76628 | + | 6.52340i | 0.155187 | + | 0.268792i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.3551 | + | 12.4208i | 1.90679 | + | 0.510924i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.7399 | −0.482102 | −0.241051 | − | 0.970512i | \(-0.577492\pi\) | ||||
−0.241051 | + | 0.970512i | \(0.577492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.55116 | − | 7.55116i | 0.309048 | − | 0.309048i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 28.5588i | − | 1.16688i | −0.812155 | − | 0.583441i | \(-0.801706\pi\) | ||
0.812155 | − | 0.583441i | \(-0.198294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.1665 | + | 28.0013i | −0.659447 | + | 1.14220i | 0.321312 | + | 0.946973i | \(0.395876\pi\) |
−0.980759 | + | 0.195222i | \(0.937457\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 67.6526i | − | 2.75503i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.24785 | − | 12.1211i | 0.131826 | − | 0.491982i | −0.868165 | − | 0.496276i | \(-0.834700\pi\) |
0.999991 | + | 0.00429458i | \(0.00136701\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.7100 | + | 62.3626i | 0.677124 | + | 2.52706i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.06349 | − | 1.45771i | −0.164391 | − | 0.0589726i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.8044 | − | 6.23790i | −0.436384 | − | 0.251946i | 0.265679 | − | 0.964062i | \(-0.414404\pi\) |
−0.702063 | + | 0.712115i | \(0.747737\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.2948 | + | 31.6876i | 0.736523 | + | 1.27569i | 0.954052 | + | 0.299641i | \(0.0968668\pi\) |
−0.217530 | + | 0.976054i | \(0.569800\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.93560 | − | 1.93560i | 0.0777985 | − | 0.0777985i | −0.667137 | − | 0.744935i | \(-0.732480\pi\) |
0.744935 | + | 0.667137i | \(0.232480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 78.8034 | + | 45.4971i | 3.16227 | + | 1.82574i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.7183 | − | 13.7183i | −0.549611 | − | 0.549611i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.3610 | − | 2.77623i | 0.413779 | − | 0.110872i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.71095 | + | 2.71095i | 0.108092 | + | 0.108092i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.99996 | − | 18.6601i | 0.199045 | − | 0.742848i | −0.792137 | − | 0.610343i | \(-0.791031\pi\) |
0.991182 | − | 0.132504i | \(-0.0423018\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.11761 | + | 0.567411i | 0.0841674 | + | 0.0225526i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.263120 | − | 0.310641i | −0.0104252 | − | 0.0123080i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.1458 | + | 9.14934i | −1.35079 | + | 0.361942i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.725792 | + | 0.419036i | −0.0286671 | + | 0.0165509i | −0.514265 | − | 0.857631i | \(-0.671935\pi\) |
0.485598 | + | 0.874182i | \(0.338602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9500 | − | 12.6729i | 0.865625 | − | 0.499769i | −0.000267216 | − | 1.00000i | \(-0.500085\pi\) |
0.865892 | + | 0.500231i | \(0.166752\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.72177 | + | 17.6219i | 0.185632 | + | 0.692787i | 0.994494 | + | 0.104790i | \(0.0334169\pi\) |
−0.808863 | + | 0.587998i | \(0.799916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.31393 | −0.208590 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.5093 | 1.47011 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.58401 | − | 28.3039i | −0.296785 | − | 1.10762i | −0.939789 | − | 0.341755i | \(-0.888979\pi\) |
0.643004 | − | 0.765863i | \(-0.277688\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −82.3205 | + | 47.5278i | −3.21163 | + | 1.85423i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.2957 | + | 14.6045i | −0.985380 | + | 0.568909i | −0.903890 | − | 0.427765i | \(-0.859301\pi\) |
−0.0814899 | + | 0.996674i | \(0.525968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.01504 | − | 2.41557i | 0.350645 | − | 0.0939549i | −0.0791977 | − | 0.996859i | \(-0.525236\pi\) |
0.429842 | + | 0.902904i | \(0.358569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.32263 | − | 1.55067i | −0.167877 | − | 0.0602231i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.3360 | + | 9.20029i | 1.32949 | + | 0.356237i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.2288 | − | 41.9063i | 0.434129 | − | 1.62019i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.15172 | − | 6.15172i | −0.237485 | − | 0.237485i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4318 | + | 4.13494i | −0.594852 | + | 0.159390i | −0.543670 | − | 0.839299i | \(-0.682966\pi\) |
−0.0511823 | + | 0.998689i | \(0.516299\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.10291 | + | 5.10291i | 0.196121 | + | 0.196121i | 0.798335 | − | 0.602214i | \(-0.205715\pi\) |
−0.602214 | + | 0.798335i | \(0.705715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.81014 | − | 2.19979i | −0.146220 | − | 0.0844200i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.9539 | − | 24.9539i | 0.956234 | − | 0.956234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5781 | − | 23.5179i | −0.519550 | − | 0.899888i | −0.999742 | − | 0.0227240i | \(-0.992766\pi\) |
0.480191 | − | 0.877164i | \(-0.340567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.6956 | − | 10.2166i | −0.675131 | − | 0.389787i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1695 | − | 23.6662i | −0.425523 | − | 0.901610i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.84688 | + | 29.2849i | 0.298509 | + | 1.11405i | 0.938390 | + | 0.345578i | \(0.112317\pi\) |
−0.639881 | + | 0.768474i | \(0.721016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.2131 | − | 38.1157i | 0.387963 | − | 1.44790i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.32149i | − | 0.0879328i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.88356 | + | 3.26243i | −0.0712429 | + | 0.123396i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.4987i | − | 0.811995i | −0.913874 | − | 0.405998i | \(-0.866924\pi\) | ||
0.913874 | − | 0.405998i | \(-0.133076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.8815 | − | 12.8815i | 0.485835 | − | 0.485835i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.0001 | 1.39153 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.6698 | − | 9.28974i | −1.30205 | − | 0.348883i | −0.459825 | − | 0.888009i | \(-0.652088\pi\) |
−0.842225 | + | 0.539126i | \(0.818755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.5586 | + | 20.0200i | 0.433480 | + | 0.750809i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3260 | − | 17.8852i | 0.386714 | − | 0.669808i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.9342 | + | 77.8284i | −1.67810 | + | 2.90655i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.3572 | − | 21.4033i | −0.460845 | − | 0.798207i | 0.538158 | − | 0.842844i | \(-0.319120\pi\) |
−0.999003 | + | 0.0446370i | \(0.985787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.4521 | − | 7.89167i | −1.09685 | − | 0.293901i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.9423 | 1.41109 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.6487 | + | 18.6487i | −0.691643 | + | 0.691643i | −0.962593 | − | 0.270950i | \(-0.912662\pi\) |
0.270950 | + | 0.962593i | \(0.412662\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 129.421i | 4.79336i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.310060 | − | 0.537040i | 0.0114680 | − | 0.0198631i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.50510i | − | 0.277207i | −0.990348 | − | 0.138604i | \(-0.955739\pi\) | ||
0.990348 | − | 0.138604i | \(-0.0442614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.65796 | + | 13.6517i | −0.134743 | + | 0.502866i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.26789 | − | 30.8562i | −0.304139 | − | 1.13506i | −0.933684 | − | 0.358099i | \(-0.883425\pi\) |
0.629544 | − | 0.776965i | \(-0.283242\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.36826 | + | 20.5396i | −0.270680 | + | 0.754543i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.89526 | + | 1.67158i | 0.106217 | + | 0.0613242i | 0.552167 | − | 0.833733i | \(-0.313801\pi\) |
−0.445951 | + | 0.895058i | \(0.647134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −47.6937 | − | 82.6080i | −1.74502 | − | 3.02247i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.7345 | + | 16.7345i | −0.611464 | + | 0.611464i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.6186 | − | 15.9456i | −1.00782 | − | 0.581864i | −0.0972656 | − | 0.995258i | \(-0.531010\pi\) |
−0.910552 | + | 0.413395i | \(0.864343\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 68.1624 | + | 68.1624i | 2.48397 | + | 2.48397i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.14545 | + | 1.91462i | −0.259706 | + | 0.0695879i | −0.386322 | − | 0.922364i | \(-0.626255\pi\) |
0.126617 | + | 0.991952i | \(0.459588\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.7953 | − | 20.7953i | −0.754821 | − | 0.754821i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.23786 | + | 8.35181i | −0.0811224 | + | 0.302753i | −0.994552 | − | 0.104244i | \(-0.966758\pi\) |
0.913429 | + | 0.406997i | \(0.133424\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.4045 | − | 8.14686i | −1.10072 | − | 0.294936i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.15944 | − | 8.88389i | 0.222405 | − | 0.320779i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.8736 | − | 4.25333i | 0.572418 | − | 0.153379i | 0.0390126 | − | 0.999239i | \(-0.487579\pi\) |
0.533405 | + | 0.845860i | \(0.320912\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 78.0344 | − | 45.0532i | 2.81034 | − | 1.62255i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.5561 | + | 20.5283i | −1.27886 | + | 0.738352i | −0.976639 | − | 0.214885i | \(-0.931062\pi\) |
−0.302223 | + | 0.953237i | \(0.597729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.4787 | − | 87.6236i | −0.842293 | − | 3.14348i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.0309 | −0.395225 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.38502 | 0.264257 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.9175 | + | 130.314i | 1.24785 | + | 4.65704i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.3157 | − | 15.1934i | 0.938053 | − | 0.541585i | 0.0487038 | − | 0.998813i | \(-0.484491\pi\) |
0.889350 | + | 0.457228i | \(0.151158\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.4764 | + | 18.7503i | −1.15619 | + | 0.667527i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.13064 | − | 1.91065i | 0.253536 | − | 0.0679349i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.4151 | − | 3.15399i | 0.618427 | − | 0.112001i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.0048 | + | 7.77181i | 1.02740 | + | 0.275292i | 0.732883 | − | 0.680354i | \(-0.238174\pi\) |
0.294518 | + | 0.955646i | \(0.404841\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.116474 | − | 0.434689i | 0.00412057 | − | 0.0153782i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.3480 | − | 44.3480i | −1.56696 | − | 1.56696i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1813 | − | 5.13963i | 0.676895 | − | 0.181373i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.0038 | + | 11.0038i | 0.387351 | + | 0.387351i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.0361 | − | 16.1867i | −0.985698 | − | 0.569093i | −0.0817125 | − | 0.996656i | \(-0.526039\pi\) |
−0.903986 | + | 0.427563i | \(0.859372\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6643 | − | 34.6643i | 1.21723 | − | 1.21723i | 0.248628 | − | 0.968599i | \(-0.420020\pi\) |
0.968599 | − | 0.248628i | \(-0.0799796\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.60277 | − | 14.9004i | −0.301712 | − | 0.522581i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.55183 | − | 1.47330i | −0.0892772 | − | 0.0515442i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 51.8842 | + | 61.2548i | 1.81298 | + | 2.14041i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.18587 | + | 19.3539i | 0.180988 | + | 0.675457i | 0.995454 | + | 0.0952454i | \(0.0303636\pi\) |
−0.814466 | + | 0.580212i | \(0.802970\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0671 | − | 45.0352i | 0.420634 | − | 1.56983i | −0.352643 | − | 0.935758i | \(-0.614717\pi\) |
0.773276 | − | 0.634069i | \(-0.218617\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.0353i | − | 0.592376i | −0.955130 | − | 0.296188i | \(-0.904285\pi\) | ||
0.955130 | − | 0.296188i | \(-0.0957155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2763 | − | 21.2632i | 0.426373 | − | 0.738500i | −0.570174 | − | 0.821524i | \(-0.693124\pi\) |
0.996548 | + | 0.0830237i | \(0.0264577\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.7740i | 1.96947i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0300078 | − | 0.0300078i | 0.00103971 | − | 0.00103971i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 78.3801 | 2.70921 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.2633 | + | 4.35773i | 0.561470 | + | 0.150446i | 0.528382 | − | 0.849007i | \(-0.322799\pi\) |
0.0330886 | + | 0.999452i | \(0.489466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8517 | + | 20.5277i | 0.408679 | + | 0.707852i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.9774 | − | 76.1711i | 1.51466 | − | 2.62347i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3120 | − | 17.8609i | 0.354324 | − | 0.613707i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.2142 | + | 17.6916i | 0.350552 | + | 0.607174i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48.2443 | − | 12.9270i | −1.65379 | − | 0.443133i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.14403 | 0.244607 | 0.122303 | − | 0.992493i | \(-0.460972\pi\) | ||||
0.122303 | + | 0.992493i | \(0.460972\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.5242 | − | 14.5242i | 0.496138 | − | 0.496138i | −0.414096 | − | 0.910233i | \(-0.635902\pi\) |
0.910233 | + | 0.414096i | \(0.135902\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.3877i | 0.797977i | 0.916956 | + | 0.398989i | \(0.130639\pi\) | ||||
−0.916956 | + | 0.398989i | \(0.869361\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.4650 | + | 47.5707i | −0.936003 | + | 1.62121i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 37.5180i | − | 1.27713i | −0.769569 | − | 0.638564i | \(-0.779529\pi\) | ||
0.769569 | − | 0.638564i | \(-0.220471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.7865 | + | 55.1839i | −0.502175 | + | 1.87414i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.24994 | − | 4.66483i | −0.0424012 | − | 0.158243i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.5831 | − | 21.9393i | −0.629663 | − | 0.743383i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.3173 | − | 7.11139i | −0.416877 | − | 0.240684i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7859 | − | 27.3420i | −0.533052 | − | 0.923273i | −0.999255 | − | 0.0385955i | \(-0.987712\pi\) |
0.466203 | − | 0.884678i | \(-0.345622\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.7077 | − | 37.7077i | 1.27185 | − | 1.27185i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.9389 | + | 9.20231i | 0.536994 | + | 0.310034i | 0.743860 | − | 0.668336i | \(-0.232993\pi\) |
−0.206866 | + | 0.978369i | \(0.566326\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.8290 | − | 25.8290i | −0.869216 | − | 0.869216i | 0.123170 | − | 0.992386i | \(-0.460694\pi\) |
−0.992386 | + | 0.123170i | \(0.960694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.7095 | − | 14.3914i | 1.80339 | − | 0.483216i | 0.808889 | − | 0.587962i | \(-0.200070\pi\) |
0.994499 | + | 0.104746i | \(0.0334029\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.2911 | − | 12.2911i | −0.412230 | − | 0.412230i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.2129 | − | 64.2396i | 0.576655 | − | 2.15211i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.06549 | − | 0.553447i | −0.0691191 | − | 0.0185204i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 58.8699 | − | 10.6617i | 1.96561 | − | 0.355985i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.5761 | − | 7.92489i | 0.986418 | − | 0.264310i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.36252 | − | 1.36400i | 0.0787068 | − | 0.0454414i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.7071 | + | 7.33647i | −0.422867 | + | 0.244143i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.71757 | + | 6.41005i | 0.0570309 | + | 0.212842i | 0.988561 | − | 0.150822i | \(-0.0481921\pi\) |
−0.931530 | + | 0.363665i | \(0.881525\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 119.613 | 3.96731 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.4367 | 1.24033 | 0.620167 | − | 0.784470i | \(-0.287065\pi\) | ||||
0.620167 | + | 0.784470i | \(0.287065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.15757 | + | 19.2483i | 0.170691 | + | 0.637027i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.09851 | + | 3.52097i | −0.201390 | + | 0.116273i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.6405 | − | 15.9583i | 0.911776 | − | 0.526414i | 0.0307739 | − | 0.999526i | \(-0.490203\pi\) |
0.881002 | + | 0.473112i | \(0.156869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −91.8906 | + | 24.6220i | −3.02790 | + | 0.811323i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.56007 | + | 12.3464i | −0.281758 | + | 0.406386i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −95.2118 | − | 25.5119i | −3.12716 | − | 0.837921i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.48551 | + | 31.6684i | −0.278401 | + | 1.03900i | 0.675128 | + | 0.737701i | \(0.264089\pi\) |
−0.953528 | + | 0.301304i | \(0.902578\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.142587 | − | 0.142587i | −0.00467309 | − | 0.00467309i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0124 | + | 6.43411i | −0.786132 | + | 0.210643i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.85825 | − | 4.85825i | −0.158712 | − | 0.158712i | 0.623284 | − | 0.781996i | \(-0.285798\pi\) |
−0.781996 | + | 0.623284i | \(0.785798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.6161 | − | 15.3668i | −0.868584 | − | 0.501477i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.3418 | − | 33.3418i | 1.08691 | − | 1.08691i | 0.0910661 | − | 0.995845i | \(-0.470973\pi\) |
0.995845 | − | 0.0910661i | \(-0.0290275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.1218 | + | 26.1917i | 0.492434 | + | 0.852921i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.9537 | − | 18.4485i | −1.03836 | − | 0.599495i | −0.118988 | − | 0.992896i | \(-0.537965\pi\) |
−0.919367 | + | 0.393401i | \(0.871298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.6409 | + | 38.0250i | −0.442801 | + | 1.23434i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.0312 | + | 104.614i | 0.908975 | + | 3.39234i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.52690 | + | 5.69846i | −0.0494611 | + | 0.184591i | −0.986237 | − | 0.165339i | \(-0.947128\pi\) |
0.936776 | + | 0.349930i | \(0.113795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 43.6026i | − | 1.40947i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.70823 | + | 4.69080i | −0.0874535 | + | 0.151474i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2108i | 0.426156i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −54.0986 | + | 54.0986i | −1.74330 | + | 1.74330i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.23575 | 0.168370 | 0.0841851 | − | 0.996450i | \(-0.473171\pi\) | ||||
0.0841851 | + | 0.996450i | \(0.473171\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.19721 | − | 0.588741i | −0.0705847 | − | 0.0189131i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.3905 | − | 43.9776i | −0.814820 | − | 1.41131i | −0.909457 | − | 0.415797i | \(-0.863503\pi\) |
0.0946379 | − | 0.995512i | \(-0.469831\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.3449 | + | 33.5064i | −0.620170 | + | 1.07417i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.82225 | − | 11.8165i | 0.218263 | − | 0.378043i | −0.736014 | − | 0.676966i | \(-0.763294\pi\) |
0.954277 | + | 0.298924i | \(0.0966275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.55114 | + | 11.3469i | 0.209375 | + | 0.362649i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −98.2907 | − | 26.3369i | −3.13818 | − | 0.840873i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.5627 | 0.847217 | 0.423609 | − | 0.905845i | \(-0.360763\pi\) | ||||
0.423609 | + | 0.905845i | \(0.360763\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.52941 | + | 7.52941i | −0.239664 | + | 0.239664i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.07871i | 0.256888i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.37032 | − | 16.2299i | 0.297658 | − | 0.515559i | −0.677942 | − | 0.735116i | \(-0.737128\pi\) |
0.975600 | + | 0.219557i | \(0.0704611\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 16.0909i | − | 0.510629i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.37101 | + | 8.84872i | −0.0750906 | + | 0.280242i | −0.993254 | − | 0.115960i | \(-0.963005\pi\) |
0.918163 | + | 0.396202i | \(0.129672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.0614 | − | 183.100i | −1.55223 | − | 5.79302i |
(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 | 1300.2.bs.d.357.1 | 20 | ||
5.2 | odd | 4 | 260.2.bf.c.253.1 | yes | 20 | ||
5.3 | odd | 4 | 1300.2.bn.d.1293.5 | 20 | |||
5.4 | even | 2 | 260.2.bk.c.97.5 | yes | 20 | ||
13.11 | odd | 12 | 1300.2.bn.d.557.5 | 20 | |||
65.24 | odd | 12 | 260.2.bf.c.37.1 | ✓ | 20 | ||
65.37 | even | 12 | 260.2.bk.c.193.5 | yes | 20 | ||
65.63 | even | 12 | inner | 1300.2.bs.d.193.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.37.1 | ✓ | 20 | 65.24 | odd | 12 | ||
260.2.bf.c.253.1 | yes | 20 | 5.2 | odd | 4 | ||
260.2.bk.c.97.5 | yes | 20 | 5.4 | even | 2 | ||
260.2.bk.c.193.5 | yes | 20 | 65.37 | even | 12 | ||
1300.2.bn.d.557.5 | 20 | 13.11 | odd | 12 | |||
1300.2.bn.d.1293.5 | 20 | 5.3 | odd | 4 | |||
1300.2.bs.d.193.1 | 20 | 65.63 | even | 12 | inner | ||
1300.2.bs.d.357.1 | 20 | 1.1 | even | 1 | trivial |