Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1007.5 | ||
Root | \(-1.37691 + 0.322680i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1007 |
Dual form | 1600.2.j.d.143.5 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | − | 0.614566i | − | 0.354820i | −0.984137 | − | 0.177410i | \(-0.943228\pi\) | ||
0.984137 | − | 0.177410i | \(-0.0567718\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.83610 | + | 2.83610i | 1.07194 | + | 1.07194i | 0.997203 | + | 0.0747413i | \(0.0238131\pi\) |
0.0747413 | + | 0.997203i | \(0.476187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.62231 | 0.874103 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.95928 | − | 1.95928i | −0.590745 | − | 0.590745i | 0.347088 | − | 0.937833i | \(-0.387171\pi\) |
−0.937833 | + | 0.347088i | \(0.887171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.05493 | 0.569934 | 0.284967 | − | 0.958537i | \(-0.408017\pi\) | ||||
0.284967 | + | 0.958537i | \(0.408017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.06774 | + | 4.06774i | 0.986571 | + | 0.986571i | 0.999911 | − | 0.0133401i | \(-0.00424641\pi\) |
−0.0133401 | + | 0.999911i | \(0.504246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.683479 | − | 0.683479i | −0.156801 | − | 0.156801i | 0.624347 | − | 0.781147i | \(-0.285365\pi\) |
−0.781147 | + | 0.624347i | \(0.785365\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.74297 | − | 1.74297i | 0.380347 | − | 0.380347i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.95014 | + | 4.95014i | −1.03218 | + | 1.03218i | −0.0327113 | + | 0.999465i | \(0.510414\pi\) |
−0.999465 | + | 0.0327113i | \(0.989586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.45528i | − | 0.664969i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.835439 | + | 0.835439i | −0.155137 | + | 0.155137i | −0.780408 | − | 0.625271i | \(-0.784989\pi\) |
0.625271 | + | 0.780408i | \(0.284989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.35978i | 0.423829i | 0.977288 | + | 0.211915i | \(0.0679698\pi\) | ||||
−0.977288 | + | 0.211915i | \(0.932030\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.20411 | + | 1.20411i | −0.209608 | + | 0.209608i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.54384 | 0.747002 | 0.373501 | − | 0.927630i | \(-0.378157\pi\) | ||||
0.373501 | + | 0.927630i | \(0.378157\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.26289i | − | 0.202224i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.07255i | − | 0.792199i | −0.918208 | − | 0.396100i | \(-0.870364\pi\) | ||
0.918208 | − | 0.396100i | \(-0.129636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.849753 | −0.129586 | −0.0647930 | − | 0.997899i | \(-0.520639\pi\) | ||||
−0.0647930 | + | 0.997899i | \(0.520639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.72646 | − | 2.72646i | 0.397696 | − | 0.397696i | −0.479724 | − | 0.877419i | \(-0.659263\pi\) |
0.877419 | + | 0.479724i | \(0.159263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.08690i | 1.29813i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.49989 | − | 2.49989i | 0.350055 | − | 0.350055i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.17605i | 0.710985i | 0.934679 | + | 0.355492i | \(0.115687\pi\) | ||||
−0.934679 | + | 0.355492i | \(0.884313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.420043 | + | 0.420043i | −0.0556360 | + | 0.0556360i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.16328 | + | 4.16328i | −0.542013 | + | 0.542013i | −0.924119 | − | 0.382105i | \(-0.875199\pi\) |
0.382105 | + | 0.924119i | \(0.375199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.55706 | + | 5.55706i | 0.711509 | + | 0.711509i | 0.966851 | − | 0.255342i | \(-0.0821880\pi\) |
−0.255342 | + | 0.966851i | \(0.582188\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.43712 | + | 7.43712i | 0.936990 | + | 0.936990i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73609 | −0.212097 | −0.106048 | − | 0.994361i | \(-0.533820\pi\) | ||||
−0.106048 | + | 0.994361i | \(0.533820\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.04219 | + | 3.04219i | 0.366237 | + | 0.366237i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.33526 | −0.277144 | −0.138572 | − | 0.990352i | \(-0.544251\pi\) | ||||
−0.138572 | + | 0.990352i | \(0.544251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.39686 | − | 4.39686i | −0.514613 | − | 0.514613i | 0.401323 | − | 0.915936i | \(-0.368550\pi\) |
−0.915936 | + | 0.401323i | \(0.868550\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 11.1134i | − | 1.26649i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0993 | 1.58629 | 0.793146 | − | 0.609032i | \(-0.208442\pi\) | ||||
0.793146 | + | 0.609032i | \(0.208442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.74343 | 0.638159 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.75725i | 0.302648i | 0.988484 | + | 0.151324i | \(0.0483536\pi\) | ||||
−0.988484 | + | 0.151324i | \(0.951646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.513433 | + | 0.513433i | 0.0550458 | + | 0.0550458i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.6448 | −1.23435 | −0.617173 | − | 0.786828i | \(-0.711722\pi\) | ||||
−0.617173 | + | 0.786828i | \(0.711722\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.82797 | + | 5.82797i | 0.610937 | + | 0.610937i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.45024 | 0.150383 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52933 | + | 3.52933i | 0.358349 | + | 0.358349i | 0.863204 | − | 0.504855i | \(-0.168454\pi\) |
−0.504855 | + | 0.863204i | \(0.668454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.13783 | − | 5.13783i | −0.516372 | − | 0.516372i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.39467 | − | 7.39467i | 0.735797 | − | 0.735797i | −0.235964 | − | 0.971762i | \(-0.575825\pi\) |
0.971762 | + | 0.235964i | \(0.0758249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.72605 | − | 3.72605i | 0.367139 | − | 0.367139i | −0.499294 | − | 0.866433i | \(-0.666407\pi\) |
0.866433 | + | 0.499294i | \(0.166407\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4605i | 1.59130i | 0.605758 | + | 0.795649i | \(0.292870\pi\) | ||||
−0.605758 | + | 0.795649i | \(0.707130\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8554 | − | 12.8554i | 1.23133 | − | 1.23133i | 0.267870 | − | 0.963455i | \(-0.413680\pi\) |
0.963455 | − | 0.267870i | \(-0.0863199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.79249i | − | 0.265051i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.863630 | + | 0.863630i | −0.0812435 | + | 0.0812435i | −0.746561 | − | 0.665317i | \(-0.768296\pi\) |
0.665317 | + | 0.746561i | \(0.268296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.38865 | 0.498181 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.0730i | 2.11510i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.32246i | − | 0.302042i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.11742 | −0.281088 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7944 | − | 11.7944i | 1.04659 | − | 1.04659i | 0.0477265 | − | 0.998860i | \(-0.484802\pi\) |
0.998860 | − | 0.0477265i | \(-0.0151976\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.522229i | 0.0459797i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9756 | − | 15.9756i | 1.39579 | − | 1.39579i | 0.584132 | − | 0.811659i | \(-0.301435\pi\) |
0.811659 | − | 0.584132i | \(-0.198565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.87683i | − | 0.336163i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.29423 | − | 1.29423i | 0.110573 | − | 0.110573i | −0.649655 | − | 0.760229i | \(-0.725087\pi\) |
0.760229 | + | 0.649655i | \(0.225087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.61413 | − | 8.61413i | 0.730641 | − | 0.730641i | −0.240106 | − | 0.970747i | \(-0.577182\pi\) |
0.970747 | + | 0.240106i | \(0.0771821\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.67559 | − | 1.67559i | −0.141110 | − | 0.141110i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.02617 | − | 4.02617i | −0.336685 | − | 0.336685i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.58450 | 0.460602 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.0806133 | − | 0.0806133i | −0.00660410 | − | 0.00660410i | 0.703797 | − | 0.710401i | \(-0.251486\pi\) |
−0.710401 | + | 0.703797i | \(0.751486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.25198 | 0.264643 | 0.132321 | − | 0.991207i | \(-0.457757\pi\) | ||||
0.132321 | + | 0.991207i | \(0.457757\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.6669 | + | 10.6669i | 0.862364 | + | 0.862364i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.06652i | 0.723587i | 0.932258 | + | 0.361793i | \(0.117835\pi\) | ||||
−0.932258 | + | 0.361793i | \(0.882165\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.18102 | 0.252271 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.0782 | −2.21287 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.93313i | − | 0.308067i | −0.988066 | − | 0.154033i | \(-0.950774\pi\) | ||
0.988066 | − | 0.154033i | \(-0.0492263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.13216 | + | 8.13216i | 0.629285 | + | 0.629285i | 0.947888 | − | 0.318603i | \(-0.103214\pi\) |
−0.318603 | + | 0.947888i | \(0.603214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.77728 | −0.675175 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.79229 | − | 1.79229i | −0.137060 | − | 0.137060i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.86735 | −0.522115 | −0.261057 | − | 0.965323i | \(-0.584071\pi\) | ||||
−0.261057 | + | 0.965323i | \(0.584071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.55861 | + | 2.55861i | 0.192317 | + | 0.192317i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7117 | − | 15.7117i | −1.17435 | − | 1.17435i | −0.981163 | − | 0.193183i | \(-0.938119\pi\) |
−0.193183 | − | 0.981163i | \(-0.561881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9112 | + | 13.9112i | −1.03401 | + | 1.03401i | −0.0346142 | + | 0.999401i | \(0.511020\pi\) |
−0.999401 | + | 0.0346142i | \(0.988980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.41518 | − | 3.41518i | 0.252458 | − | 0.252458i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 15.9397i | − | 1.16562i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.79951 | − | 9.79951i | 0.712810 | − | 0.712810i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3393i | 0.748123i | 0.927404 | + | 0.374061i | \(0.122035\pi\) | ||||
−0.927404 | + | 0.374061i | \(0.877965\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.2080 | + | 13.2080i | −0.950734 | + | 0.950734i | −0.998842 | − | 0.0481079i | \(-0.984681\pi\) |
0.0481079 | + | 0.998842i | \(0.484681\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.2437 | −1.08607 | −0.543036 | − | 0.839709i | \(-0.682725\pi\) | ||||
−0.543036 | + | 0.839709i | \(0.682725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.98761i | − | 0.353562i | −0.984250 | − | 0.176781i | \(-0.943432\pi\) | ||
0.984250 | − | 0.176781i | \(-0.0565684\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.06694i | 0.0752561i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.73878 | −0.332597 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.9808 | + | 12.9808i | −0.902228 | + | 0.902228i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.67825i | 0.185258i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3803 | + | 10.3803i | −0.714608 | + | 0.714608i | −0.967496 | − | 0.252887i | \(-0.918620\pi\) |
0.252887 | + | 0.967496i | \(0.418620\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.43517i | 0.0983362i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.69257 | + | 6.69257i | −0.454321 | + | 0.454321i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.70216 | + | 2.70216i | −0.182595 | + | 0.182595i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.35890 | + | 8.35890i | 0.562280 | + | 0.562280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.49853 | − | 1.49853i | −0.100349 | − | 0.100349i | 0.655150 | − | 0.755499i | \(-0.272605\pi\) |
−0.755499 | + | 0.655150i | \(0.772605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.6346 | −1.03771 | −0.518853 | − | 0.854864i | \(-0.673641\pi\) | ||||
−0.518853 | + | 0.854864i | \(0.673641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.74097 | − | 9.74097i | −0.643702 | − | 0.643702i | 0.307762 | − | 0.951463i | \(-0.400420\pi\) |
−0.951463 | + | 0.307762i | \(0.900420\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.82992 | −0.449376 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.509123 | − | 0.509123i | −0.0333538 | − | 0.0333538i | 0.690233 | − | 0.723587i | \(-0.257508\pi\) |
−0.723587 | + | 0.690233i | \(0.757508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 8.66493i | − | 0.562848i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.19486 | −0.530081 | −0.265041 | − | 0.964237i | \(-0.585385\pi\) | ||||
−0.265041 | + | 0.964237i | \(0.585385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.66775 | 0.365092 | 0.182546 | − | 0.983197i | \(-0.441566\pi\) | ||||
0.182546 | + | 0.983197i | \(0.441566\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 13.8956i | − | 0.891400i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.40450 | − | 1.40450i | −0.0893661 | − | 0.0893661i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.69451 | 0.107385 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.7484 | − | 14.7484i | −0.930911 | − | 0.930911i | 0.0668521 | − | 0.997763i | \(-0.478704\pi\) |
−0.997763 | + | 0.0668521i | \(0.978704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.3974 | 1.21951 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.61143 | − | 3.61143i | −0.225275 | − | 0.225275i | 0.585440 | − | 0.810715i | \(-0.300922\pi\) |
−0.810715 | + | 0.585440i | \(0.800922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.8868 | + | 12.8868i | 0.800745 | + | 0.800745i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.19078 | + | 2.19078i | −0.135606 | + | 0.135606i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.80041 | + | 6.80041i | −0.419331 | + | 0.419331i | −0.884973 | − | 0.465642i | \(-0.845823\pi\) |
0.465642 | + | 0.884973i | \(0.345823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.15650i | 0.437970i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.20010 | + | 1.20010i | −0.0731711 | + | 0.0731711i | −0.742745 | − | 0.669574i | \(-0.766477\pi\) |
0.669574 | + | 0.742745i | \(0.266477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.79591i | 0.169840i | 0.996388 | + | 0.0849199i | \(0.0270634\pi\) | ||||
−0.996388 | + | 0.0849199i | \(0.972937\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.58167 | − | 3.58167i | 0.216773 | − | 0.216773i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8115 | −0.829852 | −0.414926 | − | 0.909855i | \(-0.636193\pi\) | ||||
−0.414926 | + | 0.909855i | \(0.636193\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.18807i | 0.370470i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.21718i | 0.430541i | 0.976554 | + | 0.215270i | \(0.0690633\pi\) | ||||
−0.976554 | + | 0.215270i | \(0.930937\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.2988 | 1.50386 | 0.751930 | − | 0.659243i | \(-0.229123\pi\) | ||||
0.751930 | + | 0.659243i | \(0.229123\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.3862 | − | 14.3862i | 0.849193 | − | 0.849193i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0930i | 0.946644i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.16901 | − | 2.16901i | 0.127149 | − | 0.127149i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.1276i | − | 0.825344i | −0.910880 | − | 0.412672i | \(-0.864596\pi\) | ||
0.910880 | − | 0.412672i | \(-0.135404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.76985 | + | 6.76985i | −0.392827 | + | 0.392827i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.1722 | + | 10.1722i | −0.588272 | + | 0.588272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.40998 | − | 2.40998i | −0.138909 | − | 0.138909i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.54451 | − | 4.54451i | −0.261076 | − | 0.261076i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.6081 | −1.29031 | −0.645156 | − | 0.764051i | \(-0.723208\pi\) | ||||
−0.645156 | + | 0.764051i | \(0.723208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.28990 | − | 2.28990i | −0.130268 | − | 0.130268i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.7903 | 0.611859 | 0.305929 | − | 0.952054i | \(-0.401033\pi\) | ||||
0.305929 | + | 0.952054i | \(0.401033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6842 | − | 20.6842i | −1.16914 | − | 1.16914i | −0.982412 | − | 0.186727i | \(-0.940212\pi\) |
−0.186727 | − | 0.982412i | \(-0.559788\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.8207i | − | 1.33791i | −0.743305 | − | 0.668953i | \(-0.766743\pi\) | ||
0.743305 | − | 0.668953i | \(-0.233257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.27372 | 0.183293 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.1161 | 0.564624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.56042i | − | 0.309390i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.90050 | − | 7.90050i | −0.436899 | − | 0.436899i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.4650 | 0.852615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7688 | + | 19.7688i | 1.08659 | + | 1.08659i | 0.995877 | + | 0.0907155i | \(0.0289154\pi\) |
0.0907155 | + | 0.995877i | \(0.471085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.9153 | 0.652957 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.26955 | − | 7.26955i | −0.395998 | − | 0.395998i | 0.480821 | − | 0.876819i | \(-0.340339\pi\) |
−0.876819 | + | 0.480821i | \(0.840339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.530758 | + | 0.530758i | 0.0288268 | + | 0.0288268i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.62347 | − | 4.62347i | 0.250375 | − | 0.250375i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.91866 | + | 5.91866i | −0.319578 | + | 0.319578i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 23.4667i | − | 1.25976i | −0.776692 | − | 0.629880i | \(-0.783104\pi\) | ||
0.776692 | − | 0.629880i | \(-0.216896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.2089 | + | 23.2089i | −1.24234 | + | 1.24234i | −0.283315 | + | 0.959027i | \(0.591434\pi\) |
−0.959027 | + | 0.283315i | \(0.908566\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 7.10035i | − | 0.378988i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3220 | − | 13.3220i | 0.709059 | − | 0.709059i | −0.257278 | − | 0.966337i | \(-0.582826\pi\) |
0.966337 | + | 0.257278i | \(0.0828256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.1799 | 0.750479 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.9902i | − | 1.42449i | −0.701932 | − | 0.712244i | \(-0.747679\pi\) | ||
0.701932 | − | 0.712244i | \(-0.252321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.0657i | − | 0.950827i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.04187 | −0.107170 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4758 | + | 19.4758i | −1.01663 | + | 1.01663i | −0.0167684 | + | 0.999859i | \(0.505338\pi\) |
−0.999859 | + | 0.0167684i | \(0.994662\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 13.3018i | − | 0.692464i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.6798 | + | 14.6798i | −0.762136 | + | 0.762136i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.87069i | 0.252195i | 0.992018 | + | 0.126097i | \(0.0402452\pi\) | ||||
−0.992018 | + | 0.126097i | \(0.959755\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.71677 | + | 1.71677i | −0.0884180 | + | 0.0884180i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.54450 | + | 2.54450i | −0.130702 | + | 0.130702i | −0.769432 | − | 0.638729i | \(-0.779460\pi\) |
0.638729 | + | 0.769432i | \(0.279460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.24846 | − | 7.24846i | −0.371350 | − | 0.371350i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.193238 | + | 0.193238i | 0.00987399 | + | 0.00987399i | 0.712027 | − | 0.702153i | \(-0.247778\pi\) |
−0.702153 | + | 0.712027i | \(0.747778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.22831 | −0.113272 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.01528 | + | 2.01528i | 0.102179 | + | 0.102179i | 0.756348 | − | 0.654169i | \(-0.226982\pi\) |
−0.654169 | + | 0.756348i | \(0.726982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.2718 | −2.03663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.81803 | − | 9.81803i | −0.495254 | − | 0.495254i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5509i | 1.08161i | 0.841149 | + | 0.540804i | \(0.181880\pi\) | ||||
−0.841149 | + | 0.540804i | \(0.818120\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.38257 | −0.119277 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3965 | −0.519176 | −0.259588 | − | 0.965719i | \(-0.583587\pi\) | ||||
−0.259588 | + | 0.965719i | \(0.583587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.84917i | 0.241555i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.90264 | − | 8.90264i | −0.441288 | − | 0.441288i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.330732 | −0.0163536 | −0.00817682 | − | 0.999967i | \(-0.502603\pi\) | ||||
−0.00817682 | + | 0.999967i | \(0.502603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.795389 | − | 0.795389i | −0.0392337 | − | 0.0392337i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.6150 | −1.16202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.29395 | − | 5.29395i | −0.259246 | − | 0.259246i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.71354 | + | 6.71354i | 0.327978 | + | 0.327978i | 0.851817 | − | 0.523839i | \(-0.175501\pi\) |
−0.523839 | + | 0.851817i | \(0.675501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.99831 | − | 2.99831i | 0.146129 | − | 0.146129i | −0.630258 | − | 0.776386i | \(-0.717051\pi\) |
0.776386 | + | 0.630258i | \(0.217051\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.14963 | − | 7.14963i | 0.347627 | − | 0.347627i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.5208i | 1.52540i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.47435 | + | 2.47435i | −0.119463 | + | 0.119463i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.9548i | 0.961191i | 0.876942 | + | 0.480596i | \(0.159580\pi\) | ||||
−0.876942 | + | 0.480596i | \(0.840420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.1910 | − | 16.1910i | 0.778092 | − | 0.778092i | −0.201414 | − | 0.979506i | \(-0.564554\pi\) |
0.979506 | + | 0.201414i | \(0.0645537\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.76664 | 0.323692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.3734i | − | 1.40191i | −0.713204 | − | 0.700957i | \(-0.752757\pi\) | ||
0.713204 | − | 0.700957i | \(-0.247243\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.8287i | 1.13470i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.8713 | −0.944115 | −0.472057 | − | 0.881568i | \(-0.656489\pi\) | ||||
−0.472057 | + | 0.881568i | \(0.656489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0495422 | + | 0.0495422i | −0.00234326 | + | 0.00234326i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.7577i | − | 0.790844i | −0.918500 | − | 0.395422i | \(-0.870598\pi\) | ||
0.918500 | − | 0.395422i | \(-0.129402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.93854 | + | 9.93854i | −0.467987 | + | 0.467987i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.99856i | − | 0.0939005i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00267 | − | 5.00267i | 0.234015 | − | 0.234015i | −0.580351 | − | 0.814366i | \(-0.697085\pi\) |
0.814366 | + | 0.580351i | \(0.197085\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.0552 | − | 14.0552i | 0.656039 | − | 0.656039i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.71518 | + | 2.71518i | 0.126459 | + | 0.126459i | 0.767503 | − | 0.641045i | \(-0.221499\pi\) |
−0.641045 | + | 0.767503i | \(0.721499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.18551 | + | 9.18551i | 0.426887 | + | 0.426887i | 0.887566 | − | 0.460680i | \(-0.152394\pi\) |
−0.460680 | + | 0.887566i | \(0.652394\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.06405 | −0.0492385 | −0.0246193 | − | 0.999697i | \(-0.507837\pi\) | ||||
−0.0246193 | + | 0.999697i | \(0.507837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92371 | − | 4.92371i | −0.227356 | − | 0.227356i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.57197 | 0.256743 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.66490 | + | 1.66490i | 0.0765523 | + | 0.0765523i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.5732i | 0.621474i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.8658 | −0.724926 | −0.362463 | − | 0.931998i | \(-0.618064\pi\) | ||||
−0.362463 | + | 0.931998i | \(0.618064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.33725 | 0.425742 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.2559i | 0.785170i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.7947 | − | 13.7947i | −0.625099 | − | 0.625099i | 0.321732 | − | 0.946831i | \(-0.395735\pi\) |
−0.946831 | + | 0.321732i | \(0.895735\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.41717 | −0.109308 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4471 | − | 19.4471i | −0.877637 | − | 0.877637i | 0.115652 | − | 0.993290i | \(-0.463104\pi\) |
−0.993290 | + | 0.115652i | \(0.963104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.79669 | −0.306108 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.62302 | − | 6.62302i | −0.297083 | − | 0.297083i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.0141 | − | 23.0141i | −1.03025 | − | 1.03025i | −0.999528 | − | 0.0307258i | \(-0.990218\pi\) |
−0.0307258 | − | 0.999528i | \(-0.509782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.99775 | − | 4.99775i | 0.223283 | − | 0.223283i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.63364 | − | 6.63364i | 0.295780 | − | 0.295780i | −0.543579 | − | 0.839358i | \(-0.682931\pi\) |
0.839358 | + | 0.543579i | \(0.182931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.39422i | 0.239566i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.04140 | − | 8.04140i | 0.356429 | − | 0.356429i | −0.506066 | − | 0.862495i | \(-0.668901\pi\) |
0.862495 | + | 0.506066i | \(0.168901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 24.9398i | − | 1.10327i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.36161 | + | 2.36161i | −0.104268 | + | 0.104268i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6838 | −0.469873 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.22044i | 0.185257i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.8549i | 1.43940i | 0.694285 | + | 0.719700i | \(0.255721\pi\) | ||||
−0.694285 | + | 0.719700i | \(0.744279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.46341 | −0.107717 | −0.0538587 | − | 0.998549i | \(-0.517152\pi\) | ||||
−0.0538587 | + | 0.998549i | \(0.517152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.59896 | + | 9.59896i | −0.418137 | + | 0.418137i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 26.0078i | − | 1.13078i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9174 | + | 10.9174i | −0.473775 | + | 0.473775i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.4237i | − | 0.451501i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.65586 | + | 9.65586i | −0.416681 | + | 0.416681i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.8038 | − | 17.8038i | 0.766863 | − | 0.766863i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0772 | − | 18.0772i | −0.777198 | − | 0.777198i | 0.202156 | − | 0.979353i | \(-0.435205\pi\) |
−0.979353 | + | 0.202156i | \(0.935205\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.54938 | + | 8.54938i | 0.366889 | + | 0.366889i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.6742 | 1.86738 | 0.933688 | − | 0.358089i | \(-0.116572\pi\) | ||||
0.933688 | + | 0.358089i | \(0.116572\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.5723 | + | 14.5723i | 0.621932 | + | 0.621932i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.14201 | 0.0486513 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.9869 | + | 39.9869i | 1.70042 | + | 1.70042i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.18948i | 0.219885i | 0.993938 | + | 0.109943i | \(0.0350667\pi\) | ||||
−0.993938 | + | 0.109943i | \(0.964933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.74618 | −0.0738555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.79597 | −0.413586 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 11.3756i | − | 0.479423i | −0.970844 | − | 0.239711i | \(-0.922947\pi\) | ||
0.970844 | − | 0.239711i | \(-0.0770528\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.2889 | + | 16.2889i | 0.684071 | + | 0.684071i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.51787 | −0.315165 | −0.157583 | − | 0.987506i | \(-0.550370\pi\) | ||||
−0.157583 | + | 0.987506i | \(0.550370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.76889 | + | 7.76889i | 0.325118 | + | 0.325118i | 0.850726 | − | 0.525609i | \(-0.176162\pi\) |
−0.525609 | + | 0.850726i | \(0.676162\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.35416 | 0.265449 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.84819 | + | 9.84819i | 0.409986 | + | 0.409986i | 0.881733 | − | 0.471748i | \(-0.156377\pi\) |
−0.471748 | + | 0.881733i | \(0.656377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.11720 | + | 8.11720i | 0.337339 | + | 0.337339i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.81984 | + | 7.81984i | −0.324421 | + | 0.324421i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.1413 | − | 10.1413i | 0.420010 | − | 0.420010i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.0447i | − | 1.36390i | −0.731398 | − | 0.681951i | \(-0.761132\pi\) | ||
0.731398 | − | 0.681951i | \(-0.238868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.61286 | − | 1.61286i | 0.0664567 | − | 0.0664567i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.36829i | 0.385360i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.5424 | + | 18.5424i | −0.761445 | + | 0.761445i | −0.976584 | − | 0.215139i | \(-0.930980\pi\) |
0.215139 | + | 0.976584i | \(0.430980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.06521 | −0.125451 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.3117i | 1.15678i | 0.815759 | + | 0.578392i | \(0.196319\pi\) | ||||
−0.815759 | + | 0.578392i | \(0.803681\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.7630i | − | 1.70355i | −0.523909 | − | 0.851774i | \(-0.675527\pi\) | ||
0.523909 | − | 0.851774i | \(-0.324473\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.55255 | −0.185394 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.01973 | − | 4.01973i | 0.163156 | − | 0.163156i | −0.620807 | − | 0.783963i | \(-0.713195\pi\) |
0.783963 | + | 0.620807i | \(0.213195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.91229i | 0.118012i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.60268 | − | 5.60268i | 0.226660 | − | 0.226660i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.5230i | 0.869305i | 0.900598 | + | 0.434652i | \(0.143129\pi\) | ||||
−0.900598 | + | 0.434652i | \(0.856871\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.4655 | − | 26.4655i | 1.06546 | − | 1.06546i | 0.0677580 | − | 0.997702i | \(-0.478415\pi\) |
0.997702 | − | 0.0677580i | \(-0.0215846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.7935 | + | 21.7935i | −0.875955 | + | 0.875955i | −0.993113 | − | 0.117158i | \(-0.962622\pi\) |
0.117158 | + | 0.993113i | \(0.462622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.1041 | + | 17.1041i | 0.686365 | + | 0.686365i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.0258 | − | 33.0258i | −1.32315 | − | 1.32315i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.64596 | 0.0657334 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.4831 | + | 18.4831i | 0.736971 | + | 0.736971i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.7412 | 1.70150 | 0.850751 | − | 0.525570i | \(-0.176148\pi\) | ||||
0.850751 | + | 0.525570i | \(0.176148\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.37937 | + | 6.37937i | 0.253557 | + | 0.253557i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.6729i | 0.739848i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.12376 | −0.242252 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.4930 | 1.79687 | 0.898433 | − | 0.439110i | \(-0.144706\pi\) | ||||
0.898433 | + | 0.439110i | \(0.144706\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3531i | 1.23645i | 0.786002 | + | 0.618224i | \(0.212147\pi\) | ||||
−0.786002 | + | 0.618224i | \(0.787853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0355 | − | 24.0355i | −0.944932 | − | 0.944932i | 0.0536292 | − | 0.998561i | \(-0.482921\pi\) |
−0.998561 | + | 0.0536292i | \(0.982921\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.3141 | 0.640383 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.11303 | + | 4.11303i | 0.161202 | + | 0.161202i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.4153 | −0.603248 | −0.301624 | − | 0.953427i | \(-0.597529\pi\) | ||||
−0.301624 | + | 0.953427i | \(0.597529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.5299 | − | 11.5299i | −0.449825 | − | 0.449825i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.4355 | + | 30.4355i | 1.18560 | + | 1.18560i | 0.978272 | + | 0.207327i | \(0.0664763\pi\) |
0.207327 | + | 0.978272i | \(0.433524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.2208 | + | 11.2208i | −0.436437 | + | 0.436437i | −0.890811 | − | 0.454374i | \(-0.849863\pi\) |
0.454374 | + | 0.890811i | \(0.349863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.13709 | − | 5.13709i | 0.199508 | − | 0.199508i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.27109i | − | 0.320258i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.920946 | + | 0.920946i | −0.0356058 | + | 0.0356058i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.7757i | − | 0.840640i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.2965 | − | 29.2965i | 1.12930 | − | 1.12930i | 0.139006 | − | 0.990291i | \(-0.455609\pi\) |
0.990291 | − | 0.139006i | \(-0.0443908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.74511 | −0.105503 | −0.0527516 | − | 0.998608i | \(-0.516799\pi\) | ||||
−0.0527516 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0191i | 0.768261i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.60850i | 0.368199i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0796 | −1.26576 | −0.632878 | − | 0.774251i | \(-0.718127\pi\) | ||||
−0.632878 | + | 0.774251i | \(0.718127\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.98647 | + | 5.98647i | −0.228398 | + | 0.228398i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.6364i | 0.405214i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.8216 | − | 30.8216i | 1.17251 | − | 1.17251i | 0.190899 | − | 0.981610i | \(-0.438860\pi\) |
0.981610 | − | 0.190899i | \(-0.0611404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 29.1428i | − | 1.10704i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.6338 | − | 20.6338i | 0.781561 | − | 0.781561i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.312890 | + | 0.312890i | −0.0118346 | + | 0.0118346i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.1242 | − | 22.1242i | −0.835619 | − | 0.835619i | 0.152660 | − | 0.988279i | \(-0.451216\pi\) |
−0.988279 | + | 0.152660i | \(0.951216\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.10562 | − | 3.10562i | −0.117131 | − | 0.117131i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41.9440 | 1.57747 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.09244 | − | 7.09244i | −0.266362 | − | 0.266362i | 0.561270 | − | 0.827632i | \(-0.310313\pi\) |
−0.827632 | + | 0.561270i | \(0.810313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.9726 | 1.38658 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.6812 | − | 11.6812i | −0.437466 | − | 0.437466i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.03628i | 0.188083i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.2949 | −1.12981 | −0.564905 | − | 0.825156i | \(-0.691087\pi\) | ||||
−0.564905 | + | 0.825156i | \(0.691087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.1349 | 0.787104 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 3.48320i | − | 0.129542i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9503 | + | 15.9503i | 0.591566 | + | 0.591566i | 0.938054 | − | 0.346489i | \(-0.112626\pi\) |
−0.346489 | + | 0.938054i | \(0.612626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.69055 | 0.321872 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.45657 | − | 3.45657i | −0.127846 | − | 0.127846i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.8535 | −1.32428 | −0.662140 | − | 0.749380i | \(-0.730352\pi\) | ||||
−0.662140 | + | 0.749380i | \(0.730352\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.40147 | + | 3.40147i | 0.125295 | + | 0.125295i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4532 | + | 21.4532i | 0.789168 | + | 0.789168i | 0.981358 | − | 0.192190i | \(-0.0615590\pi\) |
−0.192190 | + | 0.981358i | \(0.561559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.863157 | + | 0.863157i | −0.0317089 | + | 0.0317089i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.0311 | − | 13.0311i | 0.478063 | − | 0.478063i | −0.426449 | − | 0.904512i | \(-0.640235\pi\) |
0.904512 | + | 0.426449i | \(0.140235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.23036i | 0.264545i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.6836 | + | 46.6836i | −1.70578 | + | 1.70578i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 22.4879i | − | 0.820595i | −0.911952 | − | 0.410297i | \(-0.865425\pi\) | ||
0.911952 | − | 0.410297i | \(-0.134575\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.06387 | + | 9.06387i | −0.330306 | + | 0.330306i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.8781 | −0.577100 | −0.288550 | − | 0.957465i | \(-0.593173\pi\) | ||||
−0.288550 | + | 0.957465i | \(0.593173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 11.9210i | − | 0.432705i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.5227i | − | 0.707696i | −0.935303 | − | 0.353848i | \(-0.884873\pi\) | ||
0.935303 | − | 0.353848i | \(-0.115127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 72.9184 | 2.63982 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.55524 | + | 8.55524i | −0.308912 | + | 0.308912i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.03843i | − | 0.289873i | −0.989441 | − | 0.144937i | \(-0.953702\pi\) | ||
0.989441 | − | 0.144937i | \(-0.0462978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.21946 | + | 2.21946i | −0.0799320 | + | 0.0799320i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.5118i | 1.45711i | 0.684988 | + | 0.728554i | \(0.259807\pi\) | ||||
−0.684988 | + | 0.728554i | \(0.740193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.91977 | − | 7.91977i | 0.284120 | − | 0.284120i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.46698 | + | 3.46698i | −0.124217 | + | 0.124217i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.57542 | + | 4.57542i | 0.163721 | + | 0.163721i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.88668 | + | 2.88668i | 0.103161 | + | 0.103161i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8333 | 0.564396 | 0.282198 | − | 0.959356i | \(-0.408937\pi\) | ||||
0.282198 | + | 0.959356i | \(0.408937\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.17930 | + | 4.17930i | 0.148787 | + | 0.148787i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.89868 | −0.174177 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4194 | + | 11.4194i | 0.405513 | + | 0.405513i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.2670i | 0.363674i | 0.983329 | + | 0.181837i | \(0.0582044\pi\) | ||||
−0.983329 | + | 0.181837i | \(0.941796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.1811 | 0.784710 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.5362 | −1.07895 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.2293i | 0.608010i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.737538 | + | 0.737538i | 0.0259626 | + | 0.0259626i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.16442 | −0.322204 | −0.161102 | − | 0.986938i | \(-0.551505\pi\) | ||||
−0.161102 | + | 0.986938i | \(0.551505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1702 | + | 22.1702i | 0.778502 | + | 0.778502i | 0.979576 | − | 0.201074i | \(-0.0644432\pi\) |
−0.201074 | + | 0.979576i | \(0.564443\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.71827 | 0.0602625 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.580788 | + | 0.580788i | 0.0203192 | + | 0.0203192i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.2827 | + | 15.2827i | 0.534022 | + | 0.534022i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3258 | − | 13.3258i | 0.465074 | − | 0.465074i | −0.435240 | − | 0.900314i | \(-0.643337\pi\) |
0.900314 | + | 0.435240i | \(0.143337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.7796 | + | 34.7796i | −1.21234 | + | 1.21234i | −0.242084 | + | 0.970255i | \(0.577831\pi\) |
−0.970255 | + | 0.242084i | \(0.922169\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.5717i | 0.576253i | 0.957592 | + | 0.288127i | \(0.0930324\pi\) | ||||
−0.957592 | + | 0.288127i | \(0.906968\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.9869 | + | 11.9869i | −0.416321 | + | 0.416321i | −0.883933 | − | 0.467613i | \(-0.845114\pi\) |
0.467613 | + | 0.883933i | \(0.345114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.48807i | 0.294448i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.9631 | + | 36.9631i | −1.28070 | + | 1.28070i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.15370 | 0.281833 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.44215i | − | 0.153360i | −0.997056 | − | 0.0766800i | \(-0.975568\pi\) | ||
0.997056 | − | 0.0766800i | \(-0.0244320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6041i | 0.951865i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.43543 | 0.152764 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.42281 | − | 9.42281i | 0.323772 | − | 0.323772i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 15.5478i | − | 0.533599i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.4926 | + | 22.4926i | −0.771038 | + | 0.771038i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6748i | 1.22148i | 0.791830 | + | 0.610742i | \(0.209129\pi\) | ||||
−0.791830 | + | 0.610742i | \(0.790871\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.8568 | − | 13.8568i | 0.473340 | − | 0.473340i | −0.429654 | − | 0.902994i | \(-0.641364\pi\) |
0.902994 | + | 0.429654i | \(0.141364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4217 | − | 19.4217i | 0.662660 | − | 0.662660i | −0.293346 | − | 0.956006i | \(-0.594769\pi\) |
0.956006 | + | 0.293346i | \(0.0947690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.84130 | − | 8.84130i | −0.301311 | − | 0.301311i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.22041 | + | 9.22041i | 0.313866 | + | 0.313866i | 0.846405 | − | 0.532539i | \(-0.178762\pi\) |
−0.532539 | + | 0.846405i | \(0.678762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.89018 | 0.335888 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.6244 | − | 27.6244i | −0.937093 | − | 0.937093i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.56753 | −0.120881 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.25500 | + | 9.25500i | 0.313234 | + | 0.313234i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 10.4267i | − | 0.352084i | −0.984383 | − | 0.176042i | \(-0.943670\pi\) | ||
0.984383 | − | 0.176042i | \(-0.0563295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.68236 | −0.292849 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.7405 | −0.429239 | −0.214619 | − | 0.976698i | \(-0.568851\pi\) | ||||
−0.214619 | + | 0.976698i | \(0.568851\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27.9073i | − | 0.939156i | −0.882891 | − | 0.469578i | \(-0.844406\pi\) | ||
0.882891 | − | 0.469578i | \(-0.155594\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.7449 | + | 41.7449i | 1.40166 | + | 1.40166i | 0.794846 | + | 0.606811i | \(0.207552\pi\) |
0.606811 | + | 0.794846i | \(0.292448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 66.9004 | 2.24377 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.2530 | − | 11.2530i | −0.376989 | − | 0.376989i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.72696 | −0.124718 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.25148 | + | 6.25148i | 0.208731 | + | 0.208731i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.97145 | − | 1.97145i | −0.0657516 | − | 0.0657516i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.0548 | + | 21.0548i | −0.701437 | + | 0.701437i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.48109 | + | 1.48109i | −0.0492877 | + | 0.0492877i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.7614i | 0.888597i | 0.895879 | + | 0.444298i | \(0.146547\pi\) | ||||
−0.895879 | + | 0.444298i | \(0.853453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.3911 | − | 19.3911i | 0.643163 | − | 0.643163i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19.2403i | − | 0.637459i | −0.947846 | − | 0.318729i | \(-0.896744\pi\) | ||
0.947846 | − | 0.318729i | \(-0.103256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.40222 | − | 5.40222i | 0.178787 | − | 0.178787i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 90.6165 | 2.99242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 42.6903i | − | 1.40822i | −0.710090 | − | 0.704111i | \(-0.751346\pi\) | ||
0.710090 | − | 0.704111i | \(-0.248654\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8942i | 0.457828i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.79878 | −0.157954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.77085 | − | 9.77085i | 0.320917 | − | 0.320917i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.58037i | 0.183086i | 0.995801 | + | 0.0915430i | \(0.0291799\pi\) | ||||
−0.995801 | + | 0.0915430i | \(0.970820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.21070 | − | 6.21070i | 0.203548 | − | 0.203548i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 6.63132i | − | 0.217100i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.0680 | + | 41.0680i | −1.34163 | + | 1.34163i | −0.447197 | + | 0.894435i | \(0.647578\pi\) |
−0.894435 | + | 0.447197i | \(0.852422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.7118 | + | 12.7118i | −0.414834 | + | 0.414834i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.5476 | − | 31.5476i | −1.02842 | − | 1.02842i | −0.999584 | − | 0.0288377i | \(-0.990819\pi\) |
−0.0288377 | − | 0.999584i | \(-0.509181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.1098 | + | 25.1098i | 0.817689 | + | 0.817689i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.7892 | −1.13050 | −0.565248 | − | 0.824921i | \(-0.691220\pi\) | ||||
−0.565248 | + | 0.824921i | \(0.691220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.03522 | − | 9.03522i | −0.293296 | − | 0.293296i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.6394 | −0.474715 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.7047 | − | 26.7047i | −0.865050 | − | 0.865050i | 0.126870 | − | 0.991919i | \(-0.459507\pi\) |
−0.991919 | + | 0.126870i | \(0.959507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2.01191i | − | 0.0650360i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.34112 | 0.237057 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.4314 | 0.820369 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.1645i | 1.39096i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8711 | − | 12.8711i | −0.413906 | − | 0.413906i | 0.469191 | − | 0.883097i | \(-0.344546\pi\) |
−0.883097 | + | 0.469191i | \(0.844546\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.41725 | −0.109778 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.9028 | + | 23.9028i | 0.767078 | + | 0.767078i | 0.977591 | − | 0.210513i | \(-0.0675134\pi\) |
−0.210513 | + | 0.977591i | \(0.567513\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.8610 | 1.56641 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.71449 | − | 2.71449i | −0.0868441 | − | 0.0868441i | 0.662350 | − | 0.749194i | \(-0.269559\pi\) |
−0.749194 | + | 0.662350i | \(0.769559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.8154 | + | 22.8154i | 0.729183 | + | 0.729183i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.7109 | − | 33.7109i | 1.07630 | − | 1.07630i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.7542 | + | 13.7542i | −0.438692 | + | 0.438692i | −0.891572 | − | 0.452880i | \(-0.850397\pi\) |
0.452880 | + | 0.891572i | \(0.350397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 9.50428i | − | 0.302525i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.20640 | − | 4.20640i | 0.133756 | − | 0.133756i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 26.5971i | − | 0.844883i | −0.906390 | − | 0.422442i | \(-0.861173\pi\) | ||
0.906390 | − | 0.422442i | \(-0.138827\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.1492 | − | 12.1492i | 0.385545 | − | 0.385545i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.4590 | 0.806295 | 0.403148 | − | 0.915135i | \(-0.367916\pi\) | ||||
0.403148 | + | 0.915135i | \(0.367916\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 15.7002i | − | 0.496733i |
(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 | 1600.2.j.d.1007.5 | 18 | ||
4.3 | odd | 2 | 400.2.j.d.307.3 | 18 | |||
5.2 | odd | 4 | 320.2.s.b.303.5 | 18 | |||
5.3 | odd | 4 | 1600.2.s.d.943.5 | 18 | |||
5.4 | even | 2 | 320.2.j.b.47.5 | 18 | |||
16.5 | even | 4 | 400.2.s.d.107.7 | 18 | |||
16.11 | odd | 4 | 1600.2.s.d.207.5 | 18 | |||
20.3 | even | 4 | 400.2.s.d.243.7 | 18 | |||
20.7 | even | 4 | 80.2.s.b.3.3 | yes | 18 | ||
20.19 | odd | 2 | 80.2.j.b.67.7 | yes | 18 | ||
40.19 | odd | 2 | 640.2.j.d.607.5 | 18 | |||
40.27 | even | 4 | 640.2.s.d.223.5 | 18 | |||
40.29 | even | 2 | 640.2.j.c.607.5 | 18 | |||
40.37 | odd | 4 | 640.2.s.c.223.5 | 18 | |||
60.47 | odd | 4 | 720.2.z.g.163.7 | 18 | |||
60.59 | even | 2 | 720.2.bd.g.307.3 | 18 | |||
80.19 | odd | 4 | 640.2.s.c.287.5 | 18 | |||
80.27 | even | 4 | 320.2.j.b.143.5 | 18 | |||
80.29 | even | 4 | 640.2.s.d.287.5 | 18 | |||
80.37 | odd | 4 | 80.2.j.b.43.7 | ✓ | 18 | ||
80.43 | even | 4 | inner | 1600.2.j.d.143.5 | 18 | ||
80.53 | odd | 4 | 400.2.j.d.43.3 | 18 | |||
80.59 | odd | 4 | 320.2.s.b.207.5 | 18 | |||
80.67 | even | 4 | 640.2.j.c.543.5 | 18 | |||
80.69 | even | 4 | 80.2.s.b.27.3 | yes | 18 | ||
80.77 | odd | 4 | 640.2.j.d.543.5 | 18 | |||
240.149 | odd | 4 | 720.2.z.g.667.7 | 18 | |||
240.197 | even | 4 | 720.2.bd.g.523.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.7 | ✓ | 18 | 80.37 | odd | 4 | ||
80.2.j.b.67.7 | yes | 18 | 20.19 | odd | 2 | ||
80.2.s.b.3.3 | yes | 18 | 20.7 | even | 4 | ||
80.2.s.b.27.3 | yes | 18 | 80.69 | even | 4 | ||
320.2.j.b.47.5 | 18 | 5.4 | even | 2 | |||
320.2.j.b.143.5 | 18 | 80.27 | even | 4 | |||
320.2.s.b.207.5 | 18 | 80.59 | odd | 4 | |||
320.2.s.b.303.5 | 18 | 5.2 | odd | 4 | |||
400.2.j.d.43.3 | 18 | 80.53 | odd | 4 | |||
400.2.j.d.307.3 | 18 | 4.3 | odd | 2 | |||
400.2.s.d.107.7 | 18 | 16.5 | even | 4 | |||
400.2.s.d.243.7 | 18 | 20.3 | even | 4 | |||
640.2.j.c.543.5 | 18 | 80.67 | even | 4 | |||
640.2.j.c.607.5 | 18 | 40.29 | even | 2 | |||
640.2.j.d.543.5 | 18 | 80.77 | odd | 4 | |||
640.2.j.d.607.5 | 18 | 40.19 | odd | 2 | |||
640.2.s.c.223.5 | 18 | 40.37 | odd | 4 | |||
640.2.s.c.287.5 | 18 | 80.19 | odd | 4 | |||
640.2.s.d.223.5 | 18 | 40.27 | even | 4 | |||
640.2.s.d.287.5 | 18 | 80.29 | even | 4 | |||
720.2.z.g.163.7 | 18 | 60.47 | odd | 4 | |||
720.2.z.g.667.7 | 18 | 240.149 | odd | 4 | |||
720.2.bd.g.307.3 | 18 | 60.59 | even | 2 | |||
720.2.bd.g.523.3 | 18 | 240.197 | even | 4 | |||
1600.2.j.d.143.5 | 18 | 80.43 | even | 4 | inner | ||
1600.2.j.d.1007.5 | 18 | 1.1 | even | 1 | trivial | ||
1600.2.s.d.207.5 | 18 | 16.11 | odd | 4 | |||
1600.2.s.d.943.5 | 18 | 5.3 | odd | 4 |