Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(49,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.ba (of order \(6\), degree \(2\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.665665 + 1.24775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.49 |
Dual form | 1300.2.ba.c.849.2 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0820885 | + | 0.0473938i | −0.0473938 | + | 0.0273628i | −0.523510 | − | 0.852020i | \(-0.675378\pi\) |
0.476116 | + | 0.879383i | \(0.342044\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.413419 | − | 0.716063i | 0.156258 | − | 0.270646i | −0.777259 | − | 0.629181i | \(-0.783390\pi\) |
0.933516 | + | 0.358535i | \(0.116724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.49551 | + | 2.59030i | −0.498503 | + | 0.863432i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | − | 0.866025i | 0.452267 | − | 0.261116i | −0.256520 | − | 0.966539i | \(-0.582576\pi\) |
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.40072 | + | 3.32235i | −0.388490 | + | 0.921453i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.24026 | − | 0.716063i | −0.300807 | − | 0.173671i | 0.341999 | − | 0.939700i | \(-0.388896\pi\) |
−0.642805 | + | 0.766030i | \(0.722230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.926118 | + | 0.534695i | 0.212466 | + | 0.122667i | 0.602457 | − | 0.798151i | \(-0.294189\pi\) |
−0.389991 | + | 0.920819i | \(0.627522\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0783740i | 0.0171026i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.67238 | + | 1.54290i | −0.557231 | + | 0.321717i | −0.752033 | − | 0.659125i | \(-0.770927\pi\) |
0.194803 | + | 0.980842i | \(0.437593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.567874i | − | 0.109287i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.72756 | + | 6.45632i | 0.692190 | + | 1.19891i | 0.971119 | + | 0.238597i | \(0.0766874\pi\) |
−0.278928 | + | 0.960312i | \(0.589979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.84325i | 1.04948i | 0.851263 | + | 0.524740i | \(0.175837\pi\) | ||||
−0.851263 | + | 0.524740i | \(0.824163\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0820885 | + | 0.142181i | −0.0142898 | + | 0.0247506i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.491793 | − | 0.851811i | −0.0808503 | − | 0.140037i | 0.822765 | − | 0.568382i | \(-0.192430\pi\) |
−0.903615 | + | 0.428345i | \(0.859097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0424756 | − | 0.339112i | −0.00680154 | − | 0.0543013i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.69615 | + | 2.13397i | −0.577242 | + | 0.333271i | −0.760037 | − | 0.649880i | \(-0.774819\pi\) |
0.182795 | + | 0.983151i | \(0.441486\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.26268 | − | 4.77046i | −1.26005 | − | 0.727488i | −0.286963 | − | 0.957942i | \(-0.592646\pi\) |
−0.973083 | + | 0.230453i | \(0.925979\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.15817 | + | 5.47011i | 0.451167 | + | 0.781444i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.135748 | 0.0190085 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.334308i | 0.0459207i | 0.999736 | + | 0.0229603i | \(0.00730915\pi\) | ||||
−0.999736 | + | 0.0229603i | \(0.992691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.101365 | −0.0134261 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.98052 | + | 5.76225i | 1.29935 | + | 0.750181i | 0.980292 | − | 0.197553i | \(-0.0632995\pi\) |
0.319060 | + | 0.947734i | \(0.396633\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.35824 | + | 2.35255i | −0.173905 | + | 0.301213i | −0.939782 | − | 0.341775i | \(-0.888972\pi\) |
0.765877 | + | 0.642988i | \(0.222305\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.23654 | + | 2.14176i | 0.155790 | + | 0.269836i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.87752 | + | 11.9122i | 0.840223 | + | 1.45531i | 0.889706 | + | 0.456534i | \(0.150909\pi\) |
−0.0494832 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.146248 | − | 0.253309i | 0.0176062 | − | 0.0304948i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.46704 | + | 4.88845i | 1.00485 | + | 0.580152i | 0.909680 | − | 0.415309i | \(-0.136327\pi\) |
0.0951721 | + | 0.995461i | \(0.469660\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1806 | −1.30859 | −0.654295 | − | 0.756240i | \(-0.727034\pi\) | ||||
−0.654295 | + | 0.756240i | \(0.727034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.43213i | − | 0.163206i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.252387 | 0.0283958 | 0.0141979 | − | 0.999899i | \(-0.495481\pi\) | ||||
0.0141979 | + | 0.999899i | \(0.495481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.45961 | − | 7.72427i | −0.495512 | − | 0.858252i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.67165 | −0.622544 | −0.311272 | − | 0.950321i | \(-0.600755\pi\) | ||||
−0.311272 | + | 0.950321i | \(0.600755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.611979 | − | 0.353326i | −0.0656110 | − | 0.0378806i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.98052 | + | 2.29815i | −0.421934 | + | 0.243604i | −0.695904 | − | 0.718135i | \(-0.744996\pi\) |
0.273971 | + | 0.961738i | \(0.411663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.79992 | + | 2.37653i | 0.188683 | + | 0.249128i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.276934 | − | 0.479664i | −0.0287167 | − | 0.0497388i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.76717 | − | 8.25698i | 0.484033 | − | 0.838370i | −0.515799 | − | 0.856710i | \(-0.672505\pi\) |
0.999832 | + | 0.0183401i | \(0.00583816\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.18059i | 0.520669i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.90072 | − | 5.02419i | −0.288632 | − | 0.499926i | 0.684851 | − | 0.728683i | \(-0.259867\pi\) |
−0.973484 | + | 0.228757i | \(0.926534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0760i | 0.992814i | 0.868090 | + | 0.496407i | \(0.165348\pi\) | ||||
−0.868090 | + | 0.496407i | \(0.834652\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0985 | + | 8.13977i | −1.36295 | + | 0.786902i | −0.990016 | − | 0.140955i | \(-0.954983\pi\) |
−0.372938 | + | 0.927856i | \(0.621649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.12979i | − | 0.299780i | −0.988703 | − | 0.149890i | \(-0.952108\pi\) | ||
0.988703 | − | 0.149890i | \(-0.0478919\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0807411 | + | 0.0466159i | 0.00766361 | + | 0.00442458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.80813 | + | 5.08538i | 0.828599 | + | 0.478392i | 0.853373 | − | 0.521301i | \(-0.174553\pi\) |
−0.0247735 | + | 0.999693i | \(0.507886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.51107 | − | 8.59687i | −0.601949 | − | 0.794781i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.02549 | + | 0.592068i | −0.0940068 | + | 0.0542748i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | + | 6.92820i | −0.363636 | + | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.202274 | − | 0.350349i | 0.0182385 | − | 0.0315899i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.16846 | − | 2.98401i | 0.458627 | − | 0.264788i | −0.252840 | − | 0.967508i | \(-0.581365\pi\) |
0.711467 | + | 0.702720i | \(0.248031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.904361 | 0.0796245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.6267 | 1.45268 | 0.726342 | − | 0.687334i | \(-0.241219\pi\) | ||||
0.726342 | + | 0.687334i | \(0.241219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.765750 | − | 0.442106i | 0.0663990 | − | 0.0383355i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.202274 | + | 0.350349i | −0.0172815 | + | 0.0299324i | −0.874537 | − | 0.484959i | \(-0.838834\pi\) |
0.857255 | + | 0.514892i | \(0.172168\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.65817 | + | 8.06819i | −0.395101 | + | 0.684335i | −0.993114 | − | 0.117152i | \(-0.962624\pi\) |
0.598013 | + | 0.801486i | \(0.295957\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.284363 | + | 0.164177i | −0.0239477 | + | 0.0138262i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.776156 | + | 6.19658i | 0.0649054 | + | 0.518184i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.518498 | − | 0.299355i | −0.0427650 | − | 0.0246904i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.41179 | − | 5.43390i | −0.771044 | − | 0.445162i | 0.0622030 | − | 0.998064i | \(-0.480187\pi\) |
−0.833247 | + | 0.552901i | \(0.813521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.991015i | − | 0.0806477i | −0.999187 | − | 0.0403238i | \(-0.987161\pi\) | ||
0.999187 | − | 0.0403238i | \(-0.0128390\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.70963 | − | 2.14176i | 0.299906 | − | 0.173151i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.5729i | − | 1.40247i | −0.712930 | − | 0.701235i | \(-0.752632\pi\) | ||
0.712930 | − | 0.701235i | \(-0.247368\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0158441 | − | 0.0274428i | −0.00125652 | − | 0.00217636i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.55146i | 0.201083i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.64098 | − | 14.9666i | 0.676814 | − | 1.17228i | −0.299122 | − | 0.954215i | \(-0.596694\pi\) |
0.975935 | − | 0.218061i | \(-0.0699730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.52978 | + | 2.64965i | 0.118378 | + | 0.205036i | 0.919125 | − | 0.393966i | \(-0.128897\pi\) |
−0.800747 | + | 0.599002i | \(0.795564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.07597 | − | 9.30735i | −0.698151 | − | 0.715950i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.77003 | + | 1.59928i | −0.211830 | + | 0.122300i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.96190 | − | 1.71006i | −0.225189 | − | 0.130013i | 0.383161 | − | 0.923681i | \(-0.374835\pi\) |
−0.608351 | + | 0.793668i | \(0.708169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.09238 | −0.0821083 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.19109 | + | 8.99123i | 0.388000 | + | 0.672036i | 0.992180 | − | 0.124811i | \(-0.0398326\pi\) |
−0.604180 | + | 0.796848i | \(0.706499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3492 | −0.769247 | −0.384624 | − | 0.923073i | \(-0.625669\pi\) | ||||
−0.384624 | + | 0.923073i | \(0.625669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.257489i | − | 0.0190342i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.48052 | −0.181393 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.406634 | − | 0.234770i | −0.0295782 | − | 0.0170770i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.75296 | − | 13.4285i | 0.560984 | − | 0.971653i | −0.436427 | − | 0.899740i | \(-0.643756\pi\) |
0.997411 | − | 0.0719134i | \(-0.0229105\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.78514 | + | 4.82401i | 0.200479 | + | 0.347239i | 0.948683 | − | 0.316229i | \(-0.102417\pi\) |
−0.748204 | + | 0.663469i | \(0.769084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4364 | + | 21.5405i | 0.886058 | + | 1.53470i | 0.844497 | + | 0.535561i | \(0.179900\pi\) |
0.0415608 | + | 0.999136i | \(0.486767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.32443 | − | 16.1504i | 0.660991 | − | 1.14487i | −0.319364 | − | 0.947632i | \(-0.603469\pi\) |
0.980356 | − | 0.197239i | \(-0.0631974\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12913 | − | 0.651904i | −0.0796427 | − | 0.0459817i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.16418 | 0.432640 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 9.22968i | − | 0.641507i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.85224 | 0.128122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.82235 | − | 8.35255i | −0.331984 | − | 0.575013i | 0.650917 | − | 0.759149i | \(-0.274385\pi\) |
−0.982901 | + | 0.184136i | \(0.941051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.926728 | −0.0634984 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.18414 | + | 2.41571i | 0.284038 | + | 0.163989i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.917797 | − | 0.529891i | 0.0620190 | − | 0.0358067i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.11626 | − | 3.11756i | 0.276890 | − | 0.209710i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.580573 | − | 1.00558i | −0.0388780 | − | 0.0673387i | 0.845932 | − | 0.533291i | \(-0.179045\pi\) |
−0.884810 | + | 0.465953i | \(0.845712\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.6230 | + | 23.5957i | −0.904191 | + | 1.56610i | −0.0821911 | + | 0.996617i | \(0.526192\pi\) |
−0.822000 | + | 0.569488i | \(0.807142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.3432i | − | 1.60864i | −0.594193 | − | 0.804322i | \(-0.702529\pi\) | ||
0.594193 | − | 0.804322i | \(-0.297471\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0678739 | + | 0.117561i | 0.00446577 | + | 0.00773495i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 23.0238i | − | 1.50834i | −0.656678 | − | 0.754171i | \(-0.728039\pi\) | ||
0.656678 | − | 0.754171i | \(-0.271961\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0207181 | + | 0.0119616i | −0.00134578 | + | 0.000776989i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.7057i | − | 1.53340i | −0.642008 | − | 0.766698i | \(-0.721898\pi\) | ||
0.642008 | − | 0.766698i | \(-0.278102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.37968 | − | 5.41536i | −0.604198 | − | 0.348834i | 0.166493 | − | 0.986043i | \(-0.446756\pi\) |
−0.770691 | + | 0.637209i | \(0.780089\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.20754 | + | 1.27453i | 0.141614 | + | 0.0817609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.07367 | + | 2.32793i | −0.195573 | + | 0.148123i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.465577 | − | 0.268801i | 0.0295047 | − | 0.0170346i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.560405 | + | 0.970649i | −0.0353724 | + | 0.0612668i | −0.883170 | − | 0.469054i | \(-0.844595\pi\) |
0.847797 | + | 0.530321i | \(0.177928\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.67238 | + | 4.62870i | −0.168011 | + | 0.291004i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.4026 | − | 8.31534i | 0.898409 | − | 0.518697i | 0.0217255 | − | 0.999764i | \(-0.493084\pi\) |
0.876684 | + | 0.481067i | \(0.159751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.813267 | −0.0505340 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.2984 | −1.38023 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.2193 | − | 12.2510i | 1.30844 | − | 0.755427i | 0.326603 | − | 0.945162i | \(-0.394096\pi\) |
0.981836 | + | 0.189734i | \(0.0607626\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.217836 | − | 0.377303i | 0.0133314 | − | 0.0230906i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.26643 | + | 5.65763i | −0.199158 | + | 0.344952i | −0.948256 | − | 0.317508i | \(-0.897154\pi\) |
0.749098 | + | 0.662460i | \(0.230487\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.89831 | − | 2.82804i | 0.297551 | − | 0.171791i | −0.343791 | − | 0.939046i | \(-0.611711\pi\) |
0.641342 | + | 0.767255i | \(0.278378\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.260386 | − | 0.109780i | −0.0157593 | − | 0.00664419i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.21784 | − | 1.85782i | −0.193341 | − | 0.111626i | 0.400205 | − | 0.916426i | \(-0.368939\pi\) |
−0.593546 | + | 0.804800i | \(0.702272\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.1357 | − | 8.73863i | −0.906154 | − | 0.523168i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.70447i | 0.578920i | 0.957190 | + | 0.289460i | \(0.0934758\pi\) | ||||
−0.957190 | + | 0.289460i | \(0.906524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9558 | − | 12.0988i | 1.24569 | − | 0.719200i | 0.275444 | − | 0.961317i | \(-0.411175\pi\) |
0.970247 | + | 0.242117i | \(0.0778419\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.52890i | 0.208305i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.47451 | − | 12.9462i | −0.439677 | − | 0.761543i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.903737i | 0.0529780i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.81414 | − | 3.14218i | 0.105983 | − | 0.183568i | −0.808156 | − | 0.588968i | \(-0.799534\pi\) |
0.914139 | + | 0.405400i | \(0.132868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.491793 | − | 0.851811i | −0.0285367 | − | 0.0494271i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.38279 | − | 11.0398i | −0.0799689 | − | 0.638446i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.83190 | + | 3.94440i | −0.393784 | + | 0.227351i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.476231 | + | 0.274952i | 0.0273588 | + | 0.0157956i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.40129 | −0.536560 | −0.268280 | − | 0.963341i | \(-0.586455\pi\) | ||||
−0.268280 | + | 0.963341i | \(0.586455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.477538 | − | 0.827121i | −0.0271662 | − | 0.0470532i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.5370 | 1.44807 | 0.724034 | − | 0.689764i | \(-0.242286\pi\) | ||||
0.724034 | + | 0.689764i | \(0.242286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.25656i | 0.297118i | 0.988904 | + | 0.148559i | \(0.0474635\pi\) | ||||
−0.988904 | + | 0.148559i | \(0.952536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.1536 | −0.794947 | −0.397474 | − | 0.917614i | \(-0.630113\pi\) | ||||
−0.397474 | + | 0.917614i | \(0.630113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.1827 | + | 6.45632i | 0.626110 | + | 0.361485i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.771550 | − | 1.33636i | 0.0430637 | − | 0.0745885i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.765750 | − | 1.32632i | −0.0426075 | − | 0.0737983i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.148333 | + | 0.256920i | 0.00820282 | + | 0.0142077i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.43213 | − | 2.48052i | 0.0789557 | − | 0.136755i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0945 | − | 9.29214i | −0.884632 | − | 0.510742i | −0.0124490 | − | 0.999923i | \(-0.503963\pi\) |
−0.872183 | + | 0.489180i | \(0.837296\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.94192 | 0.161216 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.4060i | − | 1.22053i | −0.792196 | − | 0.610267i | \(-0.791062\pi\) | ||
0.792196 | − | 0.610267i | \(-0.208938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.964061 | −0.0523606 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.06040 | + | 8.76488i | 0.274036 | + | 0.474645i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0105 | 0.594509 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4699 | + | 10.0862i | 0.937831 | + | 0.541457i | 0.889280 | − | 0.457364i | \(-0.151206\pi\) |
0.0485514 | + | 0.998821i | \(0.484540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.7634 | + | 14.2972i | −1.32556 | + | 0.765310i | −0.984609 | − | 0.174773i | \(-0.944081\pi\) |
−0.340947 | + | 0.940083i | \(0.610748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.88667 | + | 0.795432i | 0.100703 | + | 0.0424570i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.57817 | + | 9.66167i | 0.296896 | + | 0.514239i | 0.975424 | − | 0.220336i | \(-0.0707153\pi\) |
−0.678528 | + | 0.734574i | \(0.737382\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0561207 | − | 0.0972040i | 0.00297022 | − | 0.00514458i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.0490i | − | 0.583145i | −0.956549 | − | 0.291572i | \(-0.905822\pi\) | ||
0.956549 | − | 0.291572i | \(-0.0941784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.92820 | − | 15.4641i | −0.469905 | − | 0.813900i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.758301i | − | 0.0398005i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.1355 | + | 12.2026i | −1.10326 | + | 0.636970i | −0.937076 | − | 0.349124i | \(-0.886479\pi\) |
−0.166188 | + | 0.986094i | \(0.553146\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 12.7655i | − | 0.664545i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.239385 | + | 0.138209i | 0.0124283 | + | 0.00717546i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.59974 | + | 2.65566i | 0.238165 | + | 0.137505i | 0.614333 | − | 0.789047i | \(-0.289425\pi\) |
−0.376168 | + | 0.926552i | \(0.622758\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.6714 | + | 3.34074i | −1.37365 | + | 0.172057i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0469 | + | 16.7703i | −1.49204 | + | 0.861430i | −0.999958 | − | 0.00911888i | \(-0.997097\pi\) |
−0.492082 | + | 0.870549i | \(0.663764\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.282847 | + | 0.489906i | −0.0144907 | + | 0.0250986i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9014 | + | 20.6138i | −0.608131 | + | 1.05331i | 0.383417 | + | 0.923575i | \(0.374747\pi\) |
−0.991548 | + | 0.129739i | \(0.958586\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.7138 | − | 14.2685i | 1.25627 | − | 0.725310i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.2787 | 1.33238 | 0.666191 | − | 0.745781i | \(-0.267923\pi\) | ||||
0.666191 | + | 0.745781i | \(0.267923\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.41926 | 0.223492 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.36486 | + | 0.788003i | −0.0688482 | + | 0.0397495i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6460 | − | 28.8317i | 0.835439 | − | 1.44702i | −0.0582340 | − | 0.998303i | \(-0.518547\pi\) |
0.893673 | − | 0.448719i | \(-0.148120\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0419062 | + | 0.0725836i | −0.00209793 | + | 0.00363373i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2709 | − | 7.08460i | 0.612779 | − | 0.353788i | −0.161273 | − | 0.986910i | \(-0.551560\pi\) |
0.774052 | + | 0.633122i | \(0.218227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.4133 | − | 8.18476i | −0.967046 | − | 0.407712i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.47538 | − | 0.851811i | −0.0731319 | − | 0.0422227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.93213 | − | 3.42491i | −0.293325 | − | 0.169351i | 0.346116 | − | 0.938192i | \(-0.387501\pi\) |
−0.639440 | + | 0.768841i | \(0.720834\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.0383462i | − | 0.00189148i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.25227 | − | 4.76445i | 0.406068 | − | 0.234443i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 0.883073i | − | 0.0432443i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.19109 | − | 14.1874i | −0.400161 | − | 0.693099i | 0.593584 | − | 0.804772i | \(-0.297712\pi\) |
−0.993745 | + | 0.111673i | \(0.964379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.7045i | − | 1.05781i | −0.848681 | − | 0.528906i | \(-0.822603\pi\) | ||
0.848681 | − | 0.528906i | \(-0.177397\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.18059 | + | 8.97305i | −0.251889 | + | 0.436284i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.12305 | + | 1.94518i | 0.0543481 | + | 0.0941337i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.357393 | − | 0.471883i | −0.0172551 | − | 0.0227827i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.0495 | − | 16.1944i | 1.35110 | − | 0.780056i | 0.362693 | − | 0.931909i | \(-0.381857\pi\) |
0.988403 | + | 0.151853i | \(0.0485240\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.9393 | + | 14.3987i | 1.19851 | + | 0.691959i | 0.960223 | − | 0.279236i | \(-0.0900811\pi\) |
0.238286 | + | 0.971195i | \(0.423414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.29992 | −0.157857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.79992 | + | 15.2419i | 0.419997 | + | 0.727457i | 0.995939 | − | 0.0900341i | \(-0.0286976\pi\) |
−0.575941 | + | 0.817491i | \(0.695364\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.8923 | −0.899632 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14.4043i | − | 0.684370i | −0.939633 | − | 0.342185i | \(-0.888833\pi\) | ||
0.939633 | − | 0.342185i | \(-0.111167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.03013 | 0.0487236 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.58821 | + | 1.49430i | 0.122145 | + | 0.0705206i | 0.559828 | − | 0.828609i | \(-0.310867\pi\) |
−0.437683 | + | 0.899130i | \(0.644201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.69615 | + | 6.40192i | −0.174045 | + | 0.301455i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.0469680 | + | 0.0813509i | 0.00220675 | + | 0.00382220i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3102 | + | 23.0540i | 0.622626 | + | 1.07842i | 0.988995 | + | 0.147950i | \(0.0472674\pi\) |
−0.366369 | + | 0.930470i | \(0.619399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.406634 | + | 0.704310i | −0.0189800 | + | 0.0328744i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.26488 | + | 4.19438i | 0.338359 | + | 0.195352i | 0.659546 | − | 0.751664i | \(-0.270748\pi\) |
−0.321187 | + | 0.947016i | \(0.604082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.3014 | 0.989960 | 0.494980 | − | 0.868904i | \(-0.335175\pi\) | ||||
0.494980 | + | 0.868904i | \(0.335175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.12392i | − | 0.0982833i | −0.998792 | − | 0.0491417i | \(-0.984351\pi\) | ||
0.998792 | − | 0.0491417i | \(-0.0156486\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3732 | 0.525165 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.832846 | + | 1.44253i | 0.0383755 | + | 0.0664684i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.5254 | −0.759837 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.865955 | − | 0.499960i | −0.0396494 | − | 0.0228916i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.1617 | − | 14.5271i | 1.14967 | − | 0.663762i | 0.200862 | − | 0.979619i | \(-0.435626\pi\) |
0.948806 | + | 0.315858i | \(0.102292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.51887 | − | 0.440759i | 0.160447 | − | 0.0200969i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.120923 | − | 0.209445i | −0.00550220 | − | 0.00953010i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.1595 | + | 26.2570i | −0.686941 | + | 1.18982i | 0.285881 | + | 0.958265i | \(0.407714\pi\) |
−0.972822 | + | 0.231552i | \(0.925620\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.63811i | 0.0740781i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.0759 | + | 33.0405i | 0.860884 | + | 1.49110i | 0.871076 | + | 0.491148i | \(0.163422\pi\) |
−0.0101919 | + | 0.999948i | \(0.503244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 10.6767i | − | 0.480853i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.00087 | − | 4.04196i | 0.314032 | − | 0.181306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5179i | 0.739444i | 0.929142 | + | 0.369722i | \(0.120547\pi\) | ||||
−0.929142 | + | 0.369722i | \(0.879453\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.251154 | − | 0.145004i | −0.0112207 | − | 0.00647829i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.1859 | − | 5.88081i | −0.454165 | − | 0.262212i | 0.255423 | − | 0.966830i | \(-0.417785\pi\) |
−0.709588 | + | 0.704617i | \(0.751119\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.18614 | + | 0.333882i | 0.0526785 | + | 0.0148282i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.5930 | + | 15.9308i | −1.22304 | + | 0.706122i | −0.965565 | − | 0.260164i | \(-0.916223\pi\) |
−0.257474 | + | 0.966285i | \(0.582890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.62227 | + | 8.00601i | −0.204477 | + | 0.354165i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.303639 | − | 0.525918i | 0.0134060 | − | 0.0232199i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.19615 | − | 3.00000i | 0.228527 | − | 0.131940i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.324184 | 0.0142301 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.5013 | −0.854367 | −0.427183 | − | 0.904165i | \(-0.640494\pi\) | ||||
−0.427183 | + | 0.904165i | \(0.640494\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.5952 | + | 22.2830i | −1.68765 | + | 0.974365i | −0.731340 | + | 0.682014i | \(0.761105\pi\) |
−0.956311 | + | 0.292352i | \(0.905562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.18414 | − | 7.24714i | 0.182264 | − | 0.315690i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.73891 | + | 11.6721i | −0.292996 | + | 0.507484i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.8519 | + | 17.2350i | −1.29546 | + | 0.747935i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.91253 | − | 15.2690i | −0.0828407 | − | 0.661374i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.852257 | − | 0.492051i | −0.0367776 | − | 0.0212336i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.47451 | + | 5.47011i | 0.408096 | + | 0.235614i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.74450i | − | 0.160989i | −0.996755 | − | 0.0804943i | \(-0.974350\pi\) | ||
0.996755 | − | 0.0804943i | \(-0.0256499\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.849547 | − | 0.490486i | 0.0364576 | − | 0.0210488i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 38.3803i | − | 1.64102i | −0.571630 | − | 0.820511i | \(-0.693689\pi\) | ||
0.571630 | − | 0.820511i | \(-0.306311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.06253 | − | 7.03651i | −0.173385 | − | 0.300311i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.97242i | 0.339637i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.104342 | − | 0.180725i | 0.00443706 | − | 0.00768522i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.3231 | + | 23.0763i | 0.564517 | + | 0.977772i | 0.997094 | + | 0.0761755i | \(0.0242709\pi\) |
−0.432577 | + | 0.901597i | \(0.642396\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.4228 | − | 20.7694i | 1.15986 | − | 0.878452i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.203622 | − | 0.117561i | 0.00859691 | − | 0.00496343i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.4570 | − | 8.34675i | −0.609290 | − | 0.351774i | 0.163398 | − | 0.986560i | \(-0.447755\pi\) |
−0.772687 | + | 0.634787i | \(0.781088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.37475 | −0.309710 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.9620 | + | 38.0393i | 0.920694 | + | 1.59469i | 0.798344 | + | 0.602202i | \(0.205710\pi\) |
0.122350 | + | 0.992487i | \(0.460957\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.4641 | −0.479758 | −0.239879 | − | 0.970803i | \(-0.577108\pi\) | ||||
−0.239879 | + | 0.970803i | \(0.577108\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.46977i | 0.0614004i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.9354 | −1.87069 | −0.935343 | − | 0.353743i | \(-0.884909\pi\) | ||||
−0.935343 | + | 0.353743i | \(0.884909\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.457256 | − | 0.263997i | −0.0190029 | − | 0.0109713i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.34477 | + | 4.06126i | −0.0972773 | + | 0.168489i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.289519 | + | 0.501461i | 0.0119906 | + | 0.0207684i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2608 | + | 21.2364i | 0.506059 | + | 0.876520i | 0.999975 | + | 0.00701059i | \(0.00223156\pi\) |
−0.493916 | + | 0.869509i | \(0.664435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.12436 | + | 5.41154i | −0.128737 | + | 0.222979i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.04177 | − | 1.17882i | −0.0839873 | − | 0.0484901i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.7655 | −0.770607 | −0.385303 | − | 0.922790i | \(-0.625903\pi\) | ||||
−0.385303 | + | 0.922790i | \(0.625903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.76768i | 0.0723464i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.9293 | 1.46803 | 0.734015 | − | 0.679133i | \(-0.237644\pi\) | ||||
0.734015 | + | 0.679133i | \(0.237644\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.8863 | + | 34.4441i | 0.811179 | + | 1.40500i | 0.912039 | + | 0.410103i | \(0.134507\pi\) |
−0.100860 | + | 0.994901i | \(0.532160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −41.1415 | −1.67541 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.9783 | + | 16.7306i | 1.17619 | + | 0.679076i | 0.955131 | − | 0.296184i | \(-0.0957141\pi\) |
0.221063 | + | 0.975260i | \(0.429047\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.506008 | + | 0.292144i | −0.0205045 | + | 0.0118383i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.85224 | + | 11.5089i | −0.196300 | + | 0.465602i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.88495 | + | 17.1212i | 0.399249 | + | 0.691520i | 0.993633 | − | 0.112661i | \(-0.0359374\pi\) |
−0.594384 | + | 0.804181i | \(0.702604\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.75436 | + | 16.8950i | −0.392696 | + | 0.680169i | −0.992804 | − | 0.119750i | \(-0.961791\pi\) |
0.600108 | + | 0.799919i | \(0.295124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.4640i | 1.62639i | 0.581994 | + | 0.813193i | \(0.302273\pi\) | ||||
−0.581994 | + | 0.813193i | \(0.697727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.876173 | + | 1.51758i | 0.0351596 | + | 0.0608983i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.80040i | 0.152260i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.152047 | + | 0.0877845i | −0.00607218 | + | 0.00350578i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.40862i | 0.0561653i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.9707 | − | 9.79806i | −0.675594 | − | 0.390054i | 0.122599 | − | 0.992456i | \(-0.460877\pi\) |
−0.798193 | + | 0.602402i | \(0.794211\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.791718 | + | 0.457099i | 0.0314680 | + | 0.0181680i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.5973 | + | 2.83044i | −0.895338 | + | 0.112146i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.3250 | + | 14.6214i | −1.00184 | + | 0.578414i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5238 | − | 26.8881i | 0.613155 | − | 1.06202i | −0.377550 | − | 0.925989i | \(-0.623233\pi\) |
0.990705 | − | 0.136026i | \(-0.0434332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.97329 | − | 5.14990i | 0.117255 | − | 0.203092i | −0.801424 | − | 0.598097i | \(-0.795924\pi\) |
0.918679 | + | 0.395005i | \(0.129257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.8078 | − | 21.2510i | 1.44706 | − | 0.835462i | 0.448757 | − | 0.893654i | \(-0.351867\pi\) |
0.998305 | + | 0.0581916i | \(0.0185334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.9610 | 0.783539 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.457959 | −0.0179488 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.5097 | + | 15.3054i | −1.03740 | + | 0.598945i | −0.919097 | − | 0.394032i | \(-0.871080\pi\) |
−0.118307 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.7207 | − | 28.9610i | 0.652335 | − | 1.12988i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.7191 | + | 22.0302i | −0.495467 | + | 0.858175i | −0.999986 | − | 0.00522582i | \(-0.998337\pi\) |
0.504519 | + | 0.863401i | \(0.331670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.288909 | + | 0.166802i | −0.0112373 | + | 0.00648784i | −0.505608 | − | 0.862763i | \(-0.668732\pi\) |
0.494371 | + | 0.869251i | \(0.335398\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.190145 | + | 0.451001i | −0.00738461 | + | 0.0175154i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.9229 | − | 11.5025i | −0.771419 | − | 0.445379i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.0953167 | + | 0.0550311i | 0.00368516 | + | 0.00212763i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.70510i | 0.181638i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.49928 | + | 4.90706i | −0.327623 | + | 0.189153i | −0.654785 | − | 0.755815i | \(-0.727241\pi\) |
0.327162 | + | 0.944968i | \(0.393908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.2414i | 0.893241i | 0.894724 | + | 0.446620i | \(0.147373\pi\) | ||||
−0.894724 | + | 0.446620i | \(0.852627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.94168 | − | 6.82719i | −0.151268 | − | 0.262004i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2.58258i | − | 0.0989648i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.63355 | + | 4.56144i | −0.100770 | + | 0.174539i | −0.912002 | − | 0.410186i | \(-0.865464\pi\) |
0.811232 | + | 0.584724i | \(0.198797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.15372 | + | 1.99830i | 0.0440171 | + | 0.0762398i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.11069 | − | 0.468271i | −0.0423138 | − | 0.0178397i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.1334 | − | 9.89199i | 0.651787 | − | 0.376309i | −0.137354 | − | 0.990522i | \(-0.543860\pi\) |
0.789140 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.70963 | + | 2.14176i | 0.140917 | + | 0.0813586i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.11224 | 0.231518 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.09119 | + | 1.88999i | 0.0412725 | + | 0.0714861i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1256 | 0.684595 | 0.342298 | − | 0.939592i | \(-0.388795\pi\) | ||||
0.342298 | + | 0.939592i | \(0.388795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.05184i | − | 0.0396708i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.79685 | −0.180404 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.3514 | + | 12.9046i | 0.839424 | + | 0.484642i | 0.857068 | − | 0.515203i | \(-0.172283\pi\) |
−0.0176445 | + | 0.999844i | \(0.505617\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.377447 | + | 0.653758i | −0.0141554 | + | 0.0245178i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.01556 | − | 15.6154i | −0.337635 | − | 0.584802i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.12350 | + | 1.94597i | 0.0419580 | + | 0.0726734i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.51338 | − | 7.81741i | 0.168321 | − | 0.291540i | −0.769509 | − | 0.638636i | \(-0.779499\pi\) |
0.937830 | + | 0.347096i | \(0.112832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.21503 | + | 4.16560i | 0.268702 | + | 0.155135i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.02662 | 0.0381803 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.8934i | − | 0.923245i | −0.887076 | − | 0.461623i | \(-0.847267\pi\) | ||
0.887076 | − | 0.461623i | \(-0.152733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.5160 | 0.982075 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.83190 | + | 11.8332i | 0.252687 | + | 0.437667i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2793 | 0.490484 | 0.245242 | − | 0.969462i | \(-0.421133\pi\) | ||||
0.245242 | + | 0.969462i | \(0.421133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.6326 | + | 11.9122i | 0.760010 | + | 0.438792i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.9656 | + | 9.79508i | −0.624089 | + | 0.360318i | −0.778459 | − | 0.627695i | \(-0.783998\pi\) |
0.154370 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.141984 | − | 0.336769i | 0.00521590 | − | 0.0123715i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.6230 | + | 44.3804i | 0.940017 | + | 1.62816i | 0.765434 | + | 0.643515i | \(0.222525\pi\) |
0.174583 | + | 0.984642i | \(0.444142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.48199 | − | 14.6912i | 0.310340 | − | 0.537524i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.4606i | 0.491838i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5992 | − | 18.3584i | −0.386772 | − | 0.669908i | 0.605242 | − | 0.796042i | \(-0.293077\pi\) |
−0.992013 | + | 0.126134i | \(0.959743\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 0.106239i | − | 0.00387156i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5350 | − | 16.4747i | 1.03712 | − | 0.598783i | 0.118106 | − | 0.993001i | \(-0.462318\pi\) |
0.919017 | + | 0.394218i | \(0.128984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 0.506618i | − | 0.0183891i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.2367 | + | 26.1174i | 1.63983 | + | 0.946756i | 0.980891 | + | 0.194559i | \(0.0623277\pi\) |
0.658939 | + | 0.752197i | \(0.271006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.24113 | − | 1.29392i | −0.0811343 | − | 0.0468429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.1241 | + | 25.0874i | −1.19604 | + | 0.905854i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.2717 | + | 13.4359i | −0.839200 | + | 0.484513i | −0.856992 | − | 0.515329i | \(-0.827670\pi\) |
0.0177920 | + | 0.999842i | \(0.494336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.788191 | + | 1.36519i | −0.0283860 | + | 0.0491660i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.97746 | + | 10.3533i | −0.214994 | + | 0.372381i | −0.953271 | − | 0.302117i | \(-0.902307\pi\) |
0.738276 | + | 0.674498i | \(0.235640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0667598 | − | 0.0385438i | 0.00239500 | − | 0.00138275i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.56410 | −0.163526 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9341 | 0.605949 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.66638 | − | 2.11678i | 0.131026 | − | 0.0756477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.2468 | − | 29.8724i | 0.614783 | − | 1.06484i | −0.375639 | − | 0.926766i | \(-0.622577\pi\) |
0.990422 | − | 0.138070i | \(-0.0440899\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.16124 | + | 2.01133i | −0.0413413 | + | 0.0716051i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.28290 | − | 4.20479i | 0.258950 | − | 0.149505i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.91346 | − | 7.80782i | −0.209993 | − | 0.277264i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.7563 | − | 16.6025i | −1.01860 | − | 0.588089i | −0.104902 | − | 0.994483i | \(-0.533453\pi\) |
−0.913698 | + | 0.406393i | \(0.866786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.29638 | − | 2.48052i | −0.151995 | − | 0.0877543i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.7476i | − | 0.485748i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.7709 | + | 9.68268i | −0.591832 | + | 0.341694i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 0.619235i | − | 0.0217981i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.35139 | − | 7.53682i | −0.152987 | − | 0.264980i | 0.779338 | − | 0.626604i | \(-0.215556\pi\) |
−0.932324 | + | 0.361624i | \(0.882222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.69132i | − | 0.270079i | −0.990840 | − | 0.135039i | \(-0.956884\pi\) | ||
0.990840 | − | 0.135039i | \(-0.0431161\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.268063 | + | 0.464299i | −0.00940139 | + | 0.0162837i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.10148 | − | 8.83602i | −0.178478 | − | 0.309133i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.84770 | + | 1.10822i | −0.309164 | + | 0.0387245i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.532962 | + | 0.307706i | −0.0186005 | + | 0.0107390i | −0.509271 | − | 0.860606i | \(-0.670085\pi\) |
0.490671 | + | 0.871345i | \(0.336752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.3449 | − | 11.1688i | −0.674320 | − | 0.389319i | 0.123391 | − | 0.992358i | \(-0.460623\pi\) |
−0.797712 | + | 0.603039i | \(0.793956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.8701 | −1.17778 | −0.588890 | − | 0.808213i | \(-0.700435\pi\) | ||||
−0.588890 | + | 0.808213i | \(0.700435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2646 | + | 29.9033i | 0.599626 | + | 1.03858i | 0.992876 | + | 0.119151i | \(0.0380173\pi\) |
−0.393250 | + | 0.919432i | \(0.628649\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.352196 | 0.0122176 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 9.04579i | − | 0.313418i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.31823 | 0.114695 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.9386 | + | 14.9757i | 0.895501 | + | 0.517018i | 0.875738 | − | 0.482787i | \(-0.160376\pi\) |
0.0197630 | + | 0.999805i | \(0.493709\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2894 | + | 23.0179i | −0.458255 | + | 0.793720i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.459932 | − | 0.796625i | −0.0158409 | − | 0.0274372i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.30735 | + | 5.72850i | 0.113642 | + | 0.196834i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.14682 | + | 1.98635i | −0.0393587 | + | 0.0681712i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.62852 | + | 1.51758i | 0.0901045 | + | 0.0520219i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.1009 | −1.85238 | −0.926189 | − | 0.377059i | \(-0.876935\pi\) | ||||
−0.926189 | + | 0.377059i | \(0.876935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.4383i | 0.561521i | 0.959778 | + | 0.280761i | \(0.0905867\pi\) | ||||
−0.959778 | + | 0.280761i | \(0.909413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.7187 | −1.11635 | −0.558174 | − | 0.829724i | \(-0.688498\pi\) | ||||
−0.558174 | + | 0.829724i | \(0.688498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.167248 | − | 0.289682i | −0.00569980 | − | 0.00987235i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.7922 | 1.89919 | 0.949594 | − | 0.313482i | \(-0.101496\pi\) | ||||
0.949594 | + | 0.313482i | \(0.101496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.22714 | + | 0.708491i | 0.0416759 | + | 0.0240616i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.378581 | − | 0.218574i | 0.0128425 | − | 0.00741461i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.2100 | + | 6.16382i | −1.66742 | + | 0.208853i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.2587 | + | 24.6968i | 0.482583 | + | 0.835859i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.3461 | + | 33.5084i | −0.653271 | + | 1.13150i | 0.329054 | + | 0.944311i | \(0.393270\pi\) |
−0.982324 | + | 0.187187i | \(0.940063\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.343916i | 0.0116000i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.71058 | − | 4.69485i | −0.0913216 | − | 0.158174i | 0.816746 | − | 0.576998i | \(-0.195776\pi\) |
−0.908067 | + | 0.418824i | \(0.862442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.2583i | 0.715397i | 0.933837 | + | 0.357699i | \(0.116439\pi\) | ||||
−0.933837 | + | 0.357699i | \(0.883561\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.490318 | + | 0.283085i | −0.0164633 | + | 0.00950507i | −0.508209 | − | 0.861234i | \(-0.669692\pi\) |
0.491746 | + | 0.870739i | \(0.336359\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.93459i | − | 0.165501i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.3788 | − | 7.72427i | −0.448208 | − | 0.258773i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.20817 | + | 1.85224i | 0.107357 | + | 0.0619827i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.636727 | + | 0.840701i | 0.0212597 | + | 0.0280702i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −37.7259 | + | 21.7811i | −1.25823 | + | 0.726439i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.239385 | − | 0.414628i | 0.00797508 | − | 0.0138132i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.373880 | − | 0.647579i | 0.0124420 | − | 0.0215501i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0876 | − | 18.5258i | 1.06545 | − | 0.615139i | 0.138516 | − | 0.990360i | \(-0.455767\pi\) |
0.926935 | + | 0.375222i | \(0.122433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3522 | 0.575536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.9952 | −0.927522 | −0.463761 | − | 0.885960i | \(-0.653500\pi\) | ||||
−0.463761 | + | 0.885960i | \(0.653500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.50747 | + | 4.91179i | −0.281556 | + | 0.162557i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.87381 | − | 11.9058i | 0.226993 | − | 0.393164i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.4721 | − | 31.9945i | 0.609337 | − | 1.05540i | −0.382013 | − | 0.924157i | \(-0.624769\pi\) |
0.991350 | − | 0.131246i | \(-0.0418977\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.771737 | − | 0.445563i | 0.0254296 | − | 0.0146818i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.1011 | + | 21.2831i | −0.924958 | + | 0.700541i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.0997 | − | 15.0687i | −0.857228 | − | 0.494921i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.5432 | − | 6.66449i | −0.378721 | − | 0.218655i | 0.298541 | − | 0.954397i | \(-0.403500\pi\) |
−0.677262 | + | 0.735742i | \(0.736834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.75462i | 0.221374i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.09629 | + | 1.21029i | −0.0686294 | + | 0.0396232i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13.0922i | − | 0.427702i | −0.976866 | − | 0.213851i | \(-0.931399\pi\) | ||
0.976866 | − | 0.213851i | \(-0.0686007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.249128 | − | 0.431503i | −0.00812999 | − | 0.0140816i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.0399i | 1.40306i | 0.712639 | + | 0.701531i | \(0.247500\pi\) | ||||
−0.712639 | + | 0.701531i | \(0.752500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.58502 | − | 11.4056i | 0.214438 | − | 0.371417i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.2023 | + | 26.3311i | 0.494008 | + | 0.855646i | 0.999976 | − | 0.00690573i | \(-0.00219818\pi\) |
−0.505969 | + | 0.862552i | \(0.668865\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6609 | − | 37.1458i | 0.508374 | − | 1.20580i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.16185 | − | 0.670795i | 0.0376756 | − | 0.0217520i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.5349 | − | 10.7011i | −0.600404 | − | 0.346643i | 0.168796 | − | 0.985651i | \(-0.446012\pi\) |
−0.769201 | + | 0.639008i | \(0.779345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.22396 | −0.0395649 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.167248 | + | 0.289682i | 0.00540072 | + | 0.00935433i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.14359 | −0.101406 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 48.6924i | − | 1.56909i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.8892 | −1.34707 | −0.673533 | − | 0.739157i | \(-0.735224\pi\) | ||||
−0.673533 | + | 0.739157i | \(0.735224\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.125719 | + | 0.0725836i | 0.00403866 | + | 0.00233172i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.4126 | − | 24.9634i | 0.462524 | − | 0.801114i | −0.536562 | − | 0.843861i | \(-0.680277\pi\) |
0.999086 | + | 0.0427462i | \(0.0136107\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.85155 | + | 6.67109i | 0.123475 | + | 0.213865i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.2339 | + | 47.1705i | 0.871289 | + | 1.50912i | 0.860664 | + | 0.509174i | \(0.170049\pi\) |
0.0106254 | + | 0.999944i | \(0.496618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.98052 | + | 6.89445i | −0.127218 | + | 0.220348i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.10709 | + | 4.68063i | 0.258839 | + | 0.149441i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.5991 | 1.80523 | 0.902616 | − | 0.430447i | \(-0.141644\pi\) | ||||
0.902616 | + | 0.430447i | \(0.141644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.271496i | 0.00864180i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.4414 | 0.936182 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.3462 | − | 19.6522i | −0.360425 | − | 0.624274i | 0.627606 | − | 0.778531i | \(-0.284035\pi\) |
−0.988031 | + | 0.154257i | \(0.950702\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.76156 | 0.0559014 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.4631 | + | 23.3614i | 1.28148 | + | 0.739862i | 0.977119 | − | 0.212695i | \(-0.0682240\pi\) |
0.304360 | + | 0.952557i | \(0.401557\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.483721 | + | 0.279277i | −0.0153043 | + | 0.00883592i |
(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.ba.c.49.2 | 8 | ||
5.2 | odd | 4 | 260.2.x.a.101.3 | ✓ | 8 | ||
5.3 | odd | 4 | 1300.2.y.b.101.2 | 8 | |||
5.4 | even | 2 | 1300.2.ba.b.49.3 | 8 | |||
13.4 | even | 6 | 1300.2.ba.b.849.3 | 8 | |||
15.2 | even | 4 | 2340.2.dj.d.361.4 | 8 | |||
20.7 | even | 4 | 1040.2.da.c.881.2 | 8 | |||
65.2 | even | 12 | 3380.2.a.p.1.2 | 4 | |||
65.4 | even | 6 | inner | 1300.2.ba.c.849.2 | 8 | ||
65.17 | odd | 12 | 260.2.x.a.121.3 | yes | 8 | ||
65.37 | even | 12 | 3380.2.a.q.1.2 | 4 | |||
65.42 | odd | 12 | 3380.2.f.i.3041.3 | 8 | |||
65.43 | odd | 12 | 1300.2.y.b.901.2 | 8 | |||
65.62 | odd | 12 | 3380.2.f.i.3041.4 | 8 | |||
195.17 | even | 12 | 2340.2.dj.d.901.2 | 8 | |||
260.147 | even | 12 | 1040.2.da.c.641.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.x.a.101.3 | ✓ | 8 | 5.2 | odd | 4 | ||
260.2.x.a.121.3 | yes | 8 | 65.17 | odd | 12 | ||
1040.2.da.c.641.2 | 8 | 260.147 | even | 12 | |||
1040.2.da.c.881.2 | 8 | 20.7 | even | 4 | |||
1300.2.y.b.101.2 | 8 | 5.3 | odd | 4 | |||
1300.2.y.b.901.2 | 8 | 65.43 | odd | 12 | |||
1300.2.ba.b.49.3 | 8 | 5.4 | even | 2 | |||
1300.2.ba.b.849.3 | 8 | 13.4 | even | 6 | |||
1300.2.ba.c.49.2 | 8 | 1.1 | even | 1 | trivial | ||
1300.2.ba.c.849.2 | 8 | 65.4 | even | 6 | inner | ||
2340.2.dj.d.361.4 | 8 | 15.2 | even | 4 | |||
2340.2.dj.d.901.2 | 8 | 195.17 | even | 12 | |||
3380.2.a.p.1.2 | 4 | 65.2 | even | 12 | |||
3380.2.a.q.1.2 | 4 | 65.37 | even | 12 | |||
3380.2.f.i.3041.3 | 8 | 65.42 | odd | 12 | |||
3380.2.f.i.3041.4 | 8 | 65.62 | odd | 12 |