Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(101,1300)]
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, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.y (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3805522628\) |
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: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(0.665665 - 1.24775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.101 |
Dual form | 1300.2.y.b.901.2 |
$q$-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 | ||||||||
\(3\) | −0.0473938 | − | 0.0820885i | −0.0273628 | − | 0.0473938i | 0.852020 | − | 0.523510i | \(-0.175378\pi\) |
−0.879383 | + | 0.476116i | \(0.842044\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.716063 | − | 0.413419i | −0.270646 | − | 0.156258i | 0.358535 | − | 0.933516i | \(-0.383276\pi\) |
−0.629181 | + | 0.777259i | \(0.716610\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −3.32235 | − | 1.40072i | −0.921453 | − | 0.388490i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.716063 | + | 1.24026i | −0.173671 | + | 0.300807i | −0.939700 | − | 0.341999i | \(-0.888896\pi\) |
0.766030 | + | 0.642805i | \(0.222230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.926118 | − | 0.534695i | −0.212466 | − | 0.122667i | 0.389991 | − | 0.920819i | \(-0.372478\pi\) |
−0.602457 | + | 0.798151i | \(0.705811\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0783740i | 0.0171026i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.54290 | − | 2.67238i | −0.321717 | − | 0.557231i | 0.659125 | − | 0.752033i | \(-0.270927\pi\) |
−0.980842 | + | 0.194803i | \(0.937593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.567874 | −0.109287 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.72756 | − | 6.45632i | −0.692190 | − | 1.19891i | −0.971119 | − | 0.238597i | \(-0.923313\pi\) |
0.278928 | − | 0.960312i | \(-0.410021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.84325i | 1.04948i | 0.851263 | + | 0.524740i | \(0.175837\pi\) | ||||
−0.851263 | + | 0.524740i | \(0.824163\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.142181 | − | 0.0820885i | −0.0247506 | − | 0.0142898i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.851811 | + | 0.491793i | −0.140037 | + | 0.0808503i | −0.568382 | − | 0.822765i | \(-0.692430\pi\) |
0.428345 | + | 0.903615i | \(0.359097\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 4.77046 | − | 8.26268i | 0.727488 | − | 1.26005i | −0.230453 | − | 0.973083i | \(-0.574021\pi\) |
0.957942 | − | 0.286963i | \(-0.0926458\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.46410i | − | 0.505291i | −0.967559 | − | 0.252646i | \(-0.918699\pi\) | ||
0.967559 | − | 0.252646i | \(-0.0813007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.15817 | − | 5.47011i | −0.451167 | − | 0.781444i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.135748 | 0.0190085 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.334308 | −0.0459207 | −0.0229603 | − | 0.999736i | \(-0.507309\pi\) | ||||
−0.0229603 | + | 0.999736i | \(0.507309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.101365i | 0.0134261i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.98052 | − | 5.76225i | −1.29935 | − | 0.750181i | −0.319060 | − | 0.947734i | \(-0.603367\pi\) |
−0.980292 | + | 0.197553i | \(0.936701\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −2.14176 | + | 1.23654i | −0.269836 | + | 0.155790i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9122 | − | 6.87752i | 1.45531 | − | 0.840223i | 0.456534 | − | 0.889706i | \(-0.349091\pi\) |
0.998775 | + | 0.0494832i | \(0.0157574\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | − | 11.1806i | − | 1.30859i | −0.756240 | − | 0.654295i | \(-0.772966\pi\) | ||
0.756240 | − | 0.654295i | \(-0.227034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.43213 | −0.163206 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.252387 | −0.0283958 | −0.0141979 | − | 0.999899i | \(-0.504519\pi\) | ||||
−0.0141979 | + | 0.999899i | \(0.504519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.45961 | − | 7.72427i | −0.495512 | − | 0.858252i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.67165i | − | 0.622544i | −0.950321 | − | 0.311272i | \(-0.899245\pi\) | ||
0.950321 | − | 0.311272i | \(-0.100755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.353326 | + | 0.611979i | −0.0378806 | + | 0.0656110i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.98052 | − | 2.29815i | 0.421934 | − | 0.243604i | −0.273971 | − | 0.961738i | \(-0.588337\pi\) |
0.695904 | + | 0.718135i | \(0.255004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.79992 | + | 2.37653i | 0.188683 | + | 0.249128i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.479664 | − | 0.276934i | 0.0497388 | − | 0.0287167i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.25698 | − | 4.76717i | −0.838370 | − | 0.484033i | 0.0183401 | − | 0.999832i | \(-0.494162\pi\) |
−0.856710 | + | 0.515799i | \(0.827495\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −10.0760 | −0.992814 | −0.496407 | − | 0.868090i | \(-0.665348\pi\) | ||||
−0.496407 | + | 0.868090i | \(0.665348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.13977 | + | 14.0985i | 0.786902 | + | 1.36295i | 0.927856 | + | 0.372938i | \(0.121649\pi\) |
−0.140955 | + | 0.990016i | \(0.545017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.12979i | 0.299780i | 0.988703 | + | 0.149890i | \(0.0478919\pi\) | ||||
−0.988703 | + | 0.149890i | \(0.952108\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0807411 | + | 0.0466159i | 0.00766361 | + | 0.00442458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.08538 | + | 8.80813i | −0.478392 | + | 0.828599i | −0.999693 | − | 0.0247735i | \(-0.992114\pi\) |
0.521301 | + | 0.853373i | \(0.325447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.59687 | + | 6.51107i | −0.794781 | + | 0.601949i | ||||
\(118\) | 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 | ||||||||
\(123\) | 0.350349 | + | 0.202274i | 0.0315899 | + | 0.0182385i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.98401 | − | 5.16846i | −0.264788 | − | 0.458627i | 0.702720 | − | 0.711467i | \(-0.251969\pi\) |
−0.967508 | + | 0.252840i | \(0.918635\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 0.442106 | + | 0.765750i | 0.0383355 | + | 0.0663990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.350349 | + | 0.202274i | 0.0299324 | + | 0.0172815i | 0.514892 | − | 0.857255i | \(-0.327832\pi\) |
−0.484959 | + | 0.874537i | \(0.661166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.65817 | − | 8.06819i | 0.395101 | − | 0.684335i | −0.598013 | − | 0.801486i | \(-0.704043\pi\) |
0.993114 | + | 0.117152i | \(0.0373763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.284363 | + | 0.164177i | −0.0239477 | + | 0.0138262i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.19658 | + | 0.776156i | −0.518184 | + | 0.0649054i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.299355 | + | 0.518498i | −0.0246904 | + | 0.0427650i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.41179 | + | 5.43390i | 0.771044 | + | 0.445162i | 0.833247 | − | 0.552901i | \(-0.186479\pi\) |
−0.0622030 | + | 0.998064i | \(0.519813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.991015i | − | 0.0806477i | −0.999187 | − | 0.0403238i | \(-0.987161\pi\) | ||
0.999187 | − | 0.0403238i | \(-0.0128390\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.14176 | + | 3.70963i | 0.173151 | + | 0.299906i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.5729 | −1.40247 | −0.701235 | − | 0.712930i | \(-0.747368\pi\) | ||||
−0.701235 | + | 0.712930i | \(0.747368\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0158441 | + | 0.0274428i | 0.00125652 | + | 0.00217636i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.55146i | 0.201083i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.9666 | + | 8.64098i | 1.17228 | + | 0.676814i | 0.954215 | − | 0.299122i | \(-0.0966936\pi\) |
0.218061 | + | 0.975935i | \(0.430027\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.64965 | − | 1.52978i | 0.205036 | − | 0.118378i | −0.393966 | − | 0.919125i | \(-0.628897\pi\) |
0.599002 | + | 0.800747i | \(0.295564\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | 1.71006 | − | 2.96190i | 0.130013 | − | 0.225189i | −0.793668 | − | 0.608351i | \(-0.791831\pi\) |
0.923681 | + | 0.383161i | \(0.125165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.09238i | 0.0821083i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.19109 | − | 8.99123i | −0.388000 | − | 0.672036i | 0.604180 | − | 0.796848i | \(-0.293501\pi\) |
−0.992180 | + | 0.124811i | \(0.960167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3492 | −0.769247 | −0.384624 | − | 0.923073i | \(-0.625669\pi\) | ||||
−0.384624 | + | 0.923073i | \(0.625669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.257489 | 0.0190342 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.48052i | 0.181393i | ||||||||
\(188\) | 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 | ||||||||
\(193\) | −4.82401 | + | 2.78514i | −0.347239 | + | 0.200479i | −0.663469 | − | 0.748204i | \(-0.730916\pi\) |
0.316229 | + | 0.948683i | \(0.397583\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5405 | − | 12.4364i | 1.53470 | − | 0.886058i | 0.535561 | − | 0.844497i | \(-0.320100\pi\) |
0.999136 | − | 0.0415608i | \(-0.0132330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.32443 | + | 16.1504i | −0.660991 | + | 1.14487i | 0.319364 | + | 0.947632i | \(0.396531\pi\) |
−0.980356 | + | 0.197239i | \(0.936803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12913 | − | 0.651904i | −0.0796427 | − | 0.0459817i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.16418i | 0.432640i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.22968 | −0.641507 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | − | 0.926728i | − | 0.0634984i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.41571 | − | 4.18414i | 0.163989 | − | 0.284038i | ||||
\(218\) | 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 | ||||||||
\(223\) | 1.00558 | − | 0.580573i | 0.0673387 | − | 0.0388780i | −0.465953 | − | 0.884810i | \(-0.654288\pi\) |
0.533291 | + | 0.845932i | \(0.320955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.5957 | + | 13.6230i | 1.56610 | + | 0.904191i | 0.996617 | + | 0.0821911i | \(0.0261918\pi\) |
0.569488 | + | 0.822000i | \(0.307142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.3432i | 1.60864i | 0.594193 | + | 0.804322i | \(0.297471\pi\) | ||||
−0.594193 | + | 0.804322i | \(0.702529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0678739 | + | 0.117561i | 0.00446577 | + | 0.00773495i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.0238 | 1.50834 | 0.754171 | − | 0.656678i | \(-0.228039\pi\) | ||||
0.754171 | + | 0.656678i | \(0.228039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.0119616 | + | 0.0207181i | 0.000776989 | + | 0.00134578i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.7057i | 1.53340i | 0.642008 | + | 0.766698i | \(0.278102\pi\) | ||||
−0.642008 | + | 0.766698i | \(0.721898\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −1.27453 | + | 2.20754i | −0.0817609 | + | 0.141614i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.32793 | + | 3.07367i | 0.148123 | + | 0.195573i | ||||
\(248\) | 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 | ||||||||
\(253\) | −4.62870 | − | 2.67238i | −0.291004 | − | 0.168011i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.31534 | − | 14.4026i | −0.518697 | − | 0.898409i | −0.999764 | − | 0.0217255i | \(-0.993084\pi\) |
0.481067 | − | 0.876684i | \(-0.340249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.813267 | 0.0505340 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.2984 | −1.38023 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.2510 | + | 21.2193i | 0.755427 | + | 1.30844i | 0.945162 | + | 0.326603i | \(0.105904\pi\) |
−0.189734 | + | 0.981836i | \(0.560763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.377303 | − | 0.217836i | −0.0230906 | − | 0.0133314i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.26643 | − | 5.65763i | 0.199158 | − | 0.344952i | −0.749098 | − | 0.662460i | \(-0.769513\pi\) |
0.948256 | + | 0.317508i | \(0.102846\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0.109780 | − | 0.260386i | 0.00664419 | − | 0.0157593i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.85782 | + | 3.21784i | −0.111626 | + | 0.193341i | −0.916426 | − | 0.400205i | \(-0.868939\pi\) |
0.804800 | + | 0.593546i | \(0.202272\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 12.0988 | + | 20.9558i | 0.719200 | + | 1.24569i | 0.961317 | + | 0.275444i | \(0.0888248\pi\) |
−0.242117 | + | 0.970247i | \(0.577842\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.52890 | 0.208305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.47451 | + | 12.9462i | 0.439677 | + | 0.761543i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.903737i | 0.0529780i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.14218 | + | 1.81414i | 0.183568 | + | 0.105983i | 0.588968 | − | 0.808156i | \(-0.299534\pi\) |
−0.405400 | + | 0.914139i | \(0.632868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.851811 | + | 0.491793i | −0.0494271 | + | 0.0285367i | ||||
\(298\) | 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 | ||||||||
\(303\) | −0.274952 | + | 0.476231i | −0.0157956 | + | 0.0273588i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.40129i | 0.536560i | 0.963341 | + | 0.268280i | \(0.0864552\pi\) | ||||
−0.963341 | + | 0.268280i | \(0.913545\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −5.25656 | −0.297118 | −0.148559 | − | 0.988904i | \(-0.547464\pi\) | ||||
−0.148559 | + | 0.988904i | \(0.547464\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.1536i | 0.794947i | 0.917614 | + | 0.397474i | \(0.130113\pi\) | ||||
−0.917614 | + | 0.397474i | \(0.869887\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 1.32632 | − | 0.765750i | 0.0737983 | − | 0.0426075i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.256920 | − | 0.148333i | 0.0142077 | − | 0.00820282i | ||||
\(328\) | 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 | ||||||||
\(333\) | 2.94192i | 0.161216i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.4060 | −1.22053 | −0.610267 | − | 0.792196i | \(-0.708938\pi\) | ||||
−0.610267 | + | 0.792196i | \(0.708938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.964061 | 0.0523606 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.06040 | + | 8.76488i | 0.274036 | + | 0.474645i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0105i | 0.594509i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0862 | − | 17.4699i | 0.541457 | − | 0.937831i | −0.457364 | − | 0.889280i | \(-0.651206\pi\) |
0.998821 | − | 0.0485514i | \(-0.0154605\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.7634 | − | 14.2972i | 1.32556 | − | 0.765310i | 0.340947 | − | 0.940083i | \(-0.389252\pi\) |
0.984609 | + | 0.174773i | \(0.0559192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.88667 | + | 0.795432i | 0.100703 | + | 0.0424570i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.66167 | + | 5.57817i | −0.514239 | + | 0.296896i | −0.734574 | − | 0.678528i | \(-0.762618\pi\) |
0.220336 | + | 0.975424i | \(0.429285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0972040 | − | 0.0561207i | −0.00514458 | − | 0.00297022i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0490i | 0.583145i | 0.956549 | + | 0.291572i | \(0.0941784\pi\) | ||||
−0.956549 | + | 0.291572i | \(0.905822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.92820 | − | 15.4641i | −0.469905 | − | 0.813900i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.758301 | 0.0398005 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2026 | + | 21.1355i | 0.636970 | + | 1.10326i | 0.986094 | + | 0.166188i | \(0.0531457\pi\) |
−0.349124 | + | 0.937076i | \(0.613521\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.7655i | 0.664545i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.239385 | + | 0.138209i | 0.0124283 | + | 0.00717546i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.65566 | + | 4.59974i | −0.137505 | + | 0.238165i | −0.926552 | − | 0.376168i | \(-0.877242\pi\) |
0.789047 | + | 0.614333i | \(0.210575\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.34074 | + | 26.6714i | 0.172057 | + | 1.37365i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0469 | − | 16.7703i | 1.49204 | − | 0.861430i | 0.492082 | − | 0.870549i | \(-0.336236\pi\) |
0.999958 | + | 0.00911888i | \(0.00290267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.282847 | + | 0.489906i | −0.0144907 | + | 0.0250986i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.6138 | − | 11.9014i | −1.05331 | − | 0.608131i | −0.129739 | − | 0.991548i | \(-0.541414\pi\) |
−0.923575 | + | 0.383417i | \(0.874747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.2685 | − | 24.7138i | −0.725310 | − | 1.25627i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.2787 | −1.33238 | −0.666191 | − | 0.745781i | \(-0.732077\pi\) | ||||
−0.666191 | + | 0.745781i | \(0.732077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.41926 | 0.223492 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.788003 | − | 1.36486i | −0.0397495 | − | 0.0688482i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8317 | − | 16.6460i | −1.44702 | − | 0.835439i | −0.448719 | − | 0.893673i | \(-0.648120\pi\) |
−0.998303 | + | 0.0582340i | \(0.981453\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 8.18476 | − | 19.4133i | 0.407712 | − | 0.967046i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.851811 | + | 1.47538i | −0.0422227 | + | 0.0731319i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.93213 | + | 3.42491i | 0.293325 | + | 0.169351i | 0.639440 | − | 0.768841i | \(-0.279166\pi\) |
−0.346116 | + | 0.938192i | \(0.612499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.0383462i | − | 0.00189148i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.76445 | + | 8.25227i | 0.234443 | + | 0.406068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.883073 | −0.0432443 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.19109 | + | 14.1874i | 0.400161 | + | 0.693099i | 0.993745 | − | 0.111673i | \(-0.0356209\pi\) |
−0.593584 | + | 0.804772i | \(0.702288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.7045i | − | 1.05781i | −0.848681 | − | 0.528906i | \(-0.822603\pi\) | ||
0.848681 | − | 0.528906i | \(-0.177397\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.97305 | − | 5.18059i | −0.436284 | − | 0.251889i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.94518 | − | 1.12305i | 0.0941337 | − | 0.0543481i | ||||
\(428\) | 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 | ||||||||
\(433\) | −14.3987 | + | 24.9393i | −0.691959 | + | 1.19851i | 0.279236 | + | 0.960223i | \(0.409919\pi\) |
−0.971195 | + | 0.238286i | \(0.923414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.29992i | 0.157857i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.79992 | − | 15.2419i | −0.419997 | − | 0.727457i | 0.575941 | − | 0.817491i | \(-0.304636\pi\) |
−0.995939 | + | 0.0900341i | \(0.971302\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.8923 | −0.899632 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.4043 | 0.684370 | 0.342185 | − | 0.939633i | \(-0.388833\pi\) | ||||
0.342185 | + | 0.939633i | \(0.388833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.03013i | − | 0.0487236i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.58821 | − | 1.49430i | −0.122145 | − | 0.0705206i | 0.437683 | − | 0.899130i | \(-0.355799\pi\) |
−0.559828 | + | 0.828609i | \(0.689133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.69615 | + | 6.40192i | −0.174045 | + | 0.301455i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.0813509 | + | 0.0469680i | −0.00382220 | + | 0.00220675i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.0540 | − | 13.3102i | 1.07842 | − | 0.622626i | 0.147950 | − | 0.988995i | \(-0.452733\pi\) |
0.930470 | + | 0.366369i | \(0.119399\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 21.3014i | 0.989960i | 0.868904 | + | 0.494980i | \(0.164825\pi\) | ||||
−0.868904 | + | 0.494980i | \(0.835175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.12392 | −0.0982833 | −0.0491417 | − | 0.998792i | \(-0.515649\pi\) | ||||
−0.0491417 | + | 0.998792i | \(0.515649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.3732 | −0.525165 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.832846 | + | 1.44253i | 0.0383755 | + | 0.0664684i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 16.5254i | − | 0.759837i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.499960 | + | 0.865955i | −0.0228916 | + | 0.0396494i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.1617 | + | 14.5271i | −1.14967 | + | 0.663762i | −0.948806 | − | 0.315858i | \(-0.897708\pi\) |
−0.200862 | + | 0.979619i | \(0.564374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.51887 | − | 0.440759i | 0.160447 | − | 0.0200969i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.209445 | − | 0.120923i | 0.00953010 | − | 0.00550220i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2570 | + | 15.1595i | 1.18982 | + | 0.686941i | 0.958265 | − | 0.285881i | \(-0.0922862\pi\) |
0.231552 | + | 0.972822i | \(0.425620\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 10.6767 | 0.480853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.04196 | − | 7.00087i | −0.181306 | − | 0.314032i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.5179i | − | 0.739444i | −0.929142 | − | 0.369722i | \(-0.879453\pi\) | ||
0.929142 | − | 0.369722i | \(-0.120547\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.251154 | − | 0.145004i | −0.0112207 | − | 0.00647829i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.88081 | − | 10.1859i | 0.262212 | − | 0.454165i | −0.704617 | − | 0.709588i | \(-0.748881\pi\) |
0.966830 | + | 0.255423i | \(0.0822146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.333882 | − | 1.18614i | 0.0148282 | − | 0.0526785i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.5930 | − | 15.9308i | 1.22304 | − | 0.706122i | 0.257474 | − | 0.966285i | \(-0.417110\pi\) |
0.965565 | + | 0.260164i | \(0.0837765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.62227 | + | 8.00601i | −0.204477 | + | 0.354165i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.525918 | + | 0.303639i | 0.0232199 | + | 0.0134060i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | − | 5.19615i | −0.131940 | − | 0.228527i | ||||
\(518\) | 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 | ||||||||
\(523\) | −22.2830 | − | 38.5952i | −0.974365 | − | 1.68765i | −0.682014 | − | 0.731340i | \(-0.738895\pi\) |
−0.292352 | − | 0.956311i | \(-0.594438\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.24714 | − | 4.18414i | −0.315690 | − | 0.182264i | ||||
\(528\) | 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 | ||||||||
\(533\) | 15.2690 | − | 1.91253i | 0.661374 | − | 0.0828407i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.492051 | + | 0.852257i | −0.0212336 | + | 0.0367776i | ||||
\(538\) | 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 | ||||||||
\(543\) | 0.490486 | + | 0.849547i | 0.0210488 | + | 0.0364576i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.3803 | −1.64102 | −0.820511 | − | 0.571630i | \(-0.806311\pi\) | ||||
−0.820511 | + | 0.571630i | \(0.806311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.06253 | + | 7.03651i | 0.173385 | + | 0.300311i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.97242i | 0.339637i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.180725 | + | 0.104342i | 0.00768522 | + | 0.00443706i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.0763 | − | 13.3231i | 0.977772 | − | 0.564517i | 0.0761755 | − | 0.997094i | \(-0.475729\pi\) |
0.901597 | + | 0.432577i | \(0.142396\pi\) | |||||||
\(558\) | 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 | ||||||||
\(563\) | 8.34675 | − | 14.4570i | 0.351774 | − | 0.609290i | −0.634787 | − | 0.772687i | \(-0.718912\pi\) |
0.986560 | + | 0.163398i | \(0.0522454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.37475i | 0.309710i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.9620 | − | 38.0393i | −0.920694 | − | 1.59469i | −0.798344 | − | 0.602202i | \(-0.794290\pi\) |
−0.122350 | − | 0.992487i | \(-0.539043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.4641 | −0.479758 | −0.239879 | − | 0.970803i | \(-0.577108\pi\) | ||||
−0.239879 | + | 0.970803i | \(0.577108\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.46977 | −0.0614004 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.9354i | 1.87069i | 0.353743 | + | 0.935343i | \(0.384909\pi\) | ||||
−0.353743 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −0.501461 | + | 0.289519i | −0.0207684 | + | 0.0119906i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.2364 | − | 12.2608i | 0.876520 | − | 0.506059i | 0.00701059 | − | 0.999975i | \(-0.497768\pi\) |
0.869509 | + | 0.493916i | \(0.164435\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | − | 18.7655i | − | 0.770607i | −0.922790 | − | 0.385303i | \(-0.874097\pi\) | ||
0.922790 | − | 0.385303i | \(-0.125903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.76768 | 0.0723464 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.9293 | −1.46803 | −0.734015 | − | 0.679133i | \(-0.762356\pi\) | ||||
−0.734015 | + | 0.679133i | \(0.762356\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | − | 41.1415i | − | 1.67541i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.7306 | − | 28.9783i | 0.679076 | − | 1.17619i | −0.296184 | − | 0.955131i | \(-0.595714\pi\) |
0.975260 | − | 0.221063i | \(-0.0709525\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −17.1212 | + | 9.88495i | −0.691520 | + | 0.399249i | −0.804181 | − | 0.594384i | \(-0.797396\pi\) |
0.112661 | + | 0.993633i | \(0.464063\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.8950 | + | 9.75436i | 0.680169 | + | 0.392696i | 0.799919 | − | 0.600108i | \(-0.204876\pi\) |
−0.119750 | + | 0.992804i | \(0.538209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.4640i | − | 1.62639i | −0.581994 | − | 0.813193i | \(-0.697727\pi\) | ||
0.581994 | − | 0.813193i | \(-0.302273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.876173 | + | 1.51758i | 0.0351596 | + | 0.0608983i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.80040 | −0.152260 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0877845 | + | 0.152047i | 0.00350578 | + | 0.00607218i | ||||
\(628\) | 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 | ||||||||
\(633\) | −0.457099 | + | 0.791718i | −0.0181680 | + | 0.0314680i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.83044 | + | 22.5973i | 0.112146 | + | 0.895338i | ||||
\(638\) | 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 | ||||||||
\(643\) | 5.14990 | + | 2.97329i | 0.203092 | + | 0.117255i | 0.598097 | − | 0.801424i | \(-0.295924\pi\) |
−0.395005 | + | 0.918679i | \(0.629257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.2510 | − | 36.8078i | −0.835462 | − | 1.44706i | −0.893654 | − | 0.448757i | \(-0.851867\pi\) |
0.0581916 | − | 0.998305i | \(-0.481467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.9610 | −0.783539 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.457959 | −0.0179488 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.3054 | − | 26.5097i | −0.598945 | − | 1.03740i | −0.992977 | − | 0.118307i | \(-0.962253\pi\) |
0.394032 | − | 0.919097i | \(-0.371080\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.9610 | − | 16.7207i | −1.12988 | − | 0.652335i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.7191 | − | 22.0302i | 0.495467 | − | 0.858175i | −0.504519 | − | 0.863401i | \(-0.668330\pi\) |
0.999986 | + | 0.00522582i | \(0.00166344\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −0.451001 | − | 0.190145i | −0.0175154 | − | 0.00738461i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.5025 | + | 19.9229i | −0.445379 | + | 0.771419i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.0953167 | − | 0.0550311i | −0.00368516 | − | 0.00212763i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.70510i | 0.181638i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.90706 | − | 8.49928i | −0.189153 | − | 0.327623i | 0.755815 | − | 0.654785i | \(-0.227241\pi\) |
−0.944968 | + | 0.327162i | \(0.893908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.2414 | 0.893241 | 0.446620 | − | 0.894724i | \(-0.352627\pi\) | ||||
0.446620 | + | 0.894724i | \(0.352627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.94168 | + | 6.82719i | 0.151268 | + | 0.262004i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2.58258i | − | 0.0989648i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.56144 | − | 2.63355i | −0.174539 | − | 0.100770i | 0.410186 | − | 0.912002i | \(-0.365464\pi\) |
−0.584724 | + | 0.811232i | \(0.698797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.99830 | − | 1.15372i | 0.0762398 | − | 0.0440171i | ||||
\(688\) | 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 | ||||||||
\(693\) | −2.14176 | + | 3.70963i | −0.0813586 | + | 0.140917i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.11224i | − | 0.231518i | ||||||
\(698\) | 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 | ||||||||
\(703\) | 1.05184 | 0.0396708 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.79685i | 0.180404i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.3514 | − | 12.9046i | −0.839424 | − | 0.484642i | 0.0176445 | − | 0.999844i | \(-0.494383\pi\) |
−0.857068 | + | 0.515203i | \(0.827717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.377447 | + | 0.653758i | −0.0141554 | + | 0.0245178i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.6154 | − | 9.01556i | 0.584802 | − | 0.337635i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.94597 | − | 1.12350i | 0.0726734 | − | 0.0419580i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.51338 | + | 7.81741i | −0.168321 | + | 0.291540i | −0.937830 | − | 0.347096i | \(-0.887168\pi\) |
0.769509 | + | 0.638636i | \(0.220501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.21503 | + | 4.16560i | 0.268702 | + | 0.155135i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.02662i | 0.0381803i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.8934 | −0.923245 | −0.461623 | − | 0.887076i | \(-0.652733\pi\) | ||||
−0.461623 | + | 0.887076i | \(0.652733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5160 | −0.982075 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.83190 | + | 11.8332i | 0.252687 | + | 0.437667i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2793i | 0.490484i | 0.969462 | + | 0.245242i | \(0.0788674\pi\) | ||||
−0.969462 | + | 0.245242i | \(0.921133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.9122 | − | 20.6326i | 0.438792 | − | 0.760010i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9656 | − | 9.79508i | 0.624089 | − | 0.360318i | −0.154370 | − | 0.988013i | \(-0.549335\pi\) |
0.778459 | + | 0.627695i | \(0.216002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.141984 | − | 0.336769i | 0.00521590 | − | 0.0123715i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.3804 | + | 25.6230i | −1.62816 | + | 0.940017i | −0.643515 | + | 0.765434i | \(0.722525\pi\) |
−0.984642 | + | 0.174583i | \(0.944142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.6912 | − | 8.48199i | −0.537524 | − | 0.310340i | ||||
\(748\) | 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 | ||||||||
\(753\) | 0.106239 | 0.00387156 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4747 | − | 28.5350i | −0.598783 | − | 1.03712i | −0.993001 | − | 0.118106i | \(-0.962318\pi\) |
0.394218 | − | 0.919017i | \(-0.371016\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1.29392 | − | 2.24113i | 0.0468429 | − | 0.0811343i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.0874 | + | 33.1241i | 0.905854 | + | 1.19604i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.2717 | − | 13.4359i | 0.839200 | − | 0.484513i | −0.0177920 | − | 0.999842i | \(-0.505664\pi\) |
0.856992 | + | 0.515329i | \(0.172330\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.788191 | + | 1.36519i | −0.0283860 | + | 0.0491660i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.3533 | − | 5.97746i | −0.372381 | − | 0.214994i | 0.302117 | − | 0.953271i | \(-0.402307\pi\) |
−0.674498 | + | 0.738276i | \(0.735640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.0385438 | − | 0.0667598i | −0.00138275 | − | 0.00239500i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.56410 | 0.163526 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9341 | 0.605949 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.11678 | + | 3.66638i | 0.0756477 | + | 0.131026i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.8724 | − | 17.2468i | −1.06484 | − | 0.614783i | −0.138070 | − | 0.990422i | \(-0.544090\pi\) |
−0.926766 | + | 0.375639i | \(0.877423\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 7.80782 | − | 5.91346i | 0.277264 | − | 0.209993i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.6025 | + | 28.7563i | −0.588089 | + | 1.01860i | 0.406393 | + | 0.913698i | \(0.366786\pi\) |
−0.994483 | + | 0.104902i | \(0.966547\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.29638 | + | 2.48052i | 0.151995 | + | 0.0877543i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.7476i | − | 0.485748i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.68268 | − | 16.7709i | −0.341694 | − | 0.591832i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.619235 | −0.0217981 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.35139 | + | 7.53682i | 0.152987 | + | 0.264980i | 0.932324 | − | 0.361624i | \(-0.117778\pi\) |
−0.779338 | + | 0.626604i | \(0.784444\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.69132i | − | 0.270079i | −0.990840 | − | 0.135039i | \(-0.956884\pi\) | ||
0.990840 | − | 0.135039i | \(-0.0431161\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.464299 | − | 0.268063i | −0.0162837 | − | 0.00940139i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.83602 | + | 5.10148i | −0.309133 | + | 0.178478i | ||||
\(818\) | 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 | ||||||||
\(823\) | 11.1688 | − | 19.3449i | 0.389319 | − | 0.674320i | −0.603039 | − | 0.797712i | \(-0.706044\pi\) |
0.992358 | + | 0.123391i | \(0.0393771\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.8701i | 1.17778i | 0.808213 | + | 0.588890i | \(0.200435\pi\) | ||||
−0.808213 | + | 0.588890i | \(0.799565\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.2646 | − | 29.9033i | −0.599626 | − | 1.03858i | −0.992876 | − | 0.119151i | \(-0.961983\pi\) |
0.393250 | − | 0.919432i | \(-0.371351\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.352196 | 0.0122176 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.04579 | 0.313418 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.31823i | − | 0.114695i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.9386 | − | 14.9757i | −0.895501 | − | 0.517018i | −0.0197630 | − | 0.999805i | \(-0.506291\pi\) |
−0.875738 | + | 0.482787i | \(0.839624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2894 | + | 23.0179i | −0.458255 | + | 0.793720i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.796625 | − | 0.459932i | 0.0274372 | − | 0.0158409i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.72850 | − | 3.30735i | 0.196834 | − | 0.113642i | ||||
\(848\) | 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 | ||||||||
\(853\) | − | 54.1009i | − | 1.85238i | −0.377059 | − | 0.926189i | \(-0.623065\pi\) | ||
0.377059 | − | 0.926189i | \(-0.376935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.4383 | 0.561521 | 0.280761 | − | 0.959778i | \(-0.409413\pi\) | ||||
0.280761 | + | 0.959778i | \(0.409413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.7187 | 1.11635 | 0.558174 | − | 0.829724i | \(-0.311502\pi\) | ||||
0.558174 | + | 0.829724i | \(0.311502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.167248 | − | 0.289682i | −0.00569980 | − | 0.00987235i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.7922i | 1.89919i | 0.313482 | + | 0.949594i | \(0.398504\pi\) | ||||
−0.313482 | + | 0.949594i | \(0.601496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.708491 | − | 1.22714i | 0.0240616 | − | 0.0416759i | ||||
\(868\) | 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 | ||||||||
\(873\) | −24.6968 | + | 14.2587i | −0.835859 | + | 0.482583i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5084 | + | 19.3461i | 1.13150 | + | 0.653271i | 0.944311 | − | 0.329054i | \(-0.106730\pi\) |
0.187187 | + | 0.982324i | \(0.440063\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −21.2583 | −0.715397 | −0.357699 | − | 0.933837i | \(-0.616439\pi\) | ||||
−0.357699 | + | 0.933837i | \(0.616439\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.283085 | + | 0.490318i | 0.00950507 | + | 0.0164633i | 0.870739 | − | 0.491746i | \(-0.163641\pi\) |
−0.861234 | + | 0.508209i | \(0.830308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.93459i | 0.165501i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.3788 | − | 7.72427i | −0.448208 | − | 0.258773i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.85224 | + | 3.20817i | −0.0619827 | + | 0.107357i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.840701 | − | 0.636727i | 0.0280702 | − | 0.0212597i | ||||
\(898\) | 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 | ||||||||
\(903\) | 0.647579 | + | 0.373880i | 0.0215501 | + | 0.0124420i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5258 | − | 32.0876i | −0.615139 | − | 1.06545i | −0.990360 | − | 0.138516i | \(-0.955767\pi\) |
0.375222 | − | 0.926935i | \(-0.377567\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −4.91179 | − | 8.50747i | −0.162557 | − | 0.281556i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.9058 | − | 6.87381i | −0.393164 | − | 0.226993i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.4721 | + | 31.9945i | −0.609337 | + | 1.05540i | 0.382013 | + | 0.924157i | \(0.375231\pi\) |
−0.991350 | + | 0.131246i | \(0.958102\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.771737 | − | 0.445563i | 0.0254296 | − | 0.0146818i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.2831 | − | 28.1011i | −0.700541 | − | 0.924958i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.0687 | + | 26.0997i | −0.494921 | + | 0.857228i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.5432 | + | 6.66449i | 0.378721 | + | 0.218655i | 0.677262 | − | 0.735742i | \(-0.263166\pi\) |
−0.298541 | + | 0.954397i | \(0.596500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.75462i | 0.221374i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.21029 | − | 2.09629i | −0.0396232 | − | 0.0686294i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0922 | −0.427702 | −0.213851 | − | 0.976866i | \(-0.568601\pi\) | ||||
−0.213851 | + | 0.976866i | \(0.568601\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 11.4056 | + | 6.58502i | 0.371417 | + | 0.214438i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.3311 | − | 15.2023i | 0.855646 | − | 0.494008i | −0.00690573 | − | 0.999976i | \(-0.502198\pi\) |
0.862552 | + | 0.505969i | \(0.168865\pi\) | |||||||
\(948\) | 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 | ||||||||
\(953\) | 10.7011 | − | 18.5349i | 0.346643 | − | 0.600404i | −0.639008 | − | 0.769201i | \(-0.720655\pi\) |
0.985651 | + | 0.168796i | \(0.0539881\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.22396i | 0.0395649i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.167248 | − | 0.289682i | −0.00540072 | − | 0.00935433i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.14359 | −0.101406 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 48.6924 | 1.56909 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.8892i | 1.34707i | 0.739157 | + | 0.673533i | \(0.235224\pi\) | ||||
−0.739157 | + | 0.673533i | \(0.764776\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −6.67109 | + | 3.85155i | −0.213865 | + | 0.123475i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.1705 | − | 27.2339i | 1.50912 | − | 0.871289i | 0.509174 | − | 0.860664i | \(-0.329951\pi\) |
0.999944 | − | 0.0106254i | \(-0.00338225\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 56.5991i | 1.80523i | 0.430447 | + | 0.902616i | \(0.358356\pi\) | ||||
−0.430447 | + | 0.902616i | \(0.641644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.271496 | 0.00864180 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 1.76156i | 0.0559014i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.3614 | − | 40.4631i | 0.739862 | − | 1.28148i | −0.212695 | − | 0.977119i | \(-0.568224\pi\) |
0.952557 | − | 0.304360i | \(-0.0984427\pi\) | |||||||
\(998\) | 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.y.b.101.2 | 8 | ||
5.2 | odd | 4 | 1300.2.ba.c.49.2 | 8 | |||
5.3 | odd | 4 | 1300.2.ba.b.49.3 | 8 | |||
5.4 | even | 2 | 260.2.x.a.101.3 | ✓ | 8 | ||
13.4 | even | 6 | inner | 1300.2.y.b.901.2 | 8 | ||
15.14 | odd | 2 | 2340.2.dj.d.361.4 | 8 | |||
20.19 | odd | 2 | 1040.2.da.c.881.2 | 8 | |||
65.4 | even | 6 | 260.2.x.a.121.3 | yes | 8 | ||
65.17 | odd | 12 | 1300.2.ba.b.849.3 | 8 | |||
65.24 | odd | 12 | 3380.2.a.q.1.2 | 4 | |||
65.29 | even | 6 | 3380.2.f.i.3041.3 | 8 | |||
65.43 | odd | 12 | 1300.2.ba.c.849.2 | 8 | |||
65.49 | even | 6 | 3380.2.f.i.3041.4 | 8 | |||
65.54 | odd | 12 | 3380.2.a.p.1.2 | 4 | |||
195.134 | odd | 6 | 2340.2.dj.d.901.2 | 8 | |||
260.199 | odd | 6 | 1040.2.da.c.641.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.x.a.101.3 | ✓ | 8 | 5.4 | even | 2 | ||
260.2.x.a.121.3 | yes | 8 | 65.4 | even | 6 | ||
1040.2.da.c.641.2 | 8 | 260.199 | odd | 6 | |||
1040.2.da.c.881.2 | 8 | 20.19 | odd | 2 | |||
1300.2.y.b.101.2 | 8 | 1.1 | even | 1 | trivial | ||
1300.2.y.b.901.2 | 8 | 13.4 | even | 6 | inner | ||
1300.2.ba.b.49.3 | 8 | 5.3 | odd | 4 | |||
1300.2.ba.b.849.3 | 8 | 65.17 | odd | 12 | |||
1300.2.ba.c.49.2 | 8 | 5.2 | odd | 4 | |||
1300.2.ba.c.849.2 | 8 | 65.43 | odd | 12 | |||
2340.2.dj.d.361.4 | 8 | 15.14 | odd | 2 | |||
2340.2.dj.d.901.2 | 8 | 195.134 | odd | 6 | |||
3380.2.a.p.1.2 | 4 | 65.54 | odd | 12 | |||
3380.2.a.q.1.2 | 4 | 65.24 | odd | 12 | |||
3380.2.f.i.3041.3 | 8 | 65.29 | even | 6 | |||
3380.2.f.i.3041.4 | 8 | 65.49 | even | 6 |