Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2300,2,Mod(1057,2300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2300.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2300.i (of order \(4\), 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: | \(18.3655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 74x^{12} + 1357x^{8} + 3177x^{4} + 1296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1793.7 | ||
Root | \(1.58699 + 1.58699i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2300.1793 |
Dual form | 2300.2.i.f.1057.7 |
$q$-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 \(\left(\mathbb{Z}/2300\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1151\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.58699 | + | 1.58699i | 0.916251 | + | 0.916251i | 0.996754 | − | 0.0805030i | \(-0.0256527\pi\) |
−0.0805030 | + | 0.996754i | \(0.525653\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.216666 | + | 0.216666i | 0.0818921 | + | 0.0818921i | 0.746866 | − | 0.664974i | \(-0.231557\pi\) |
−0.664974 | + | 0.746866i | \(0.731557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.03710i | 0.679033i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.54348i | 1.06840i | 0.845359 | + | 0.534199i | \(0.179387\pi\) | ||||
−0.845359 | + | 0.534199i | \(0.820613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.55380 | − | 2.55380i | −0.708298 | − | 0.708298i | 0.257879 | − | 0.966177i | \(-0.416976\pi\) |
−0.966177 | + | 0.257879i | \(0.916976\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.67428 | + | 4.67428i | 1.13368 | + | 1.13368i | 0.989561 | + | 0.144118i | \(0.0460344\pi\) |
0.144118 | + | 0.989561i | \(0.453966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.45652 | 0.563565 | 0.281782 | − | 0.959478i | \(-0.409074\pi\) | ||||
0.281782 | + | 0.959478i | \(0.409074\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.687695i | 0.150067i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.33178 | + | 3.44953i | −0.694724 | + | 0.719277i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.52812 | − | 1.52812i | 0.294086 | − | 0.294086i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.693252i | 0.128734i | 0.997926 | + | 0.0643668i | \(0.0205028\pi\) | ||||
−0.997926 | + | 0.0643668i | \(0.979497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.83747 | −0.330019 | −0.165010 | − | 0.986292i | \(-0.552766\pi\) | ||||
−0.165010 | + | 0.986292i | \(0.552766\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.62348 | + | 5.62348i | −0.978922 | + | 0.978922i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00601 | + | 7.00601i | 1.15178 | + | 1.15178i | 0.986195 | + | 0.165586i | \(0.0529515\pi\) |
0.165586 | + | 0.986195i | \(0.447048\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 8.10574i | − | 1.29796i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.34385 | −0.366048 | −0.183024 | − | 0.983108i | \(-0.558589\pi\) | ||||
−0.183024 | + | 0.983108i | \(0.558589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.16644 | + | 4.16644i | −0.635377 | + | 0.635377i | −0.949411 | − | 0.314035i | \(-0.898319\pi\) |
0.314035 | + | 0.949411i | \(0.398319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.83743 | + | 3.83743i | −0.559746 | + | 0.559746i | −0.929235 | − | 0.369489i | \(-0.879533\pi\) |
0.369489 | + | 0.929235i | \(0.379533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.90611i | − | 0.986587i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.8361i | 2.07747i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.724498 | + | 0.724498i | −0.0995175 | + | 0.0995175i | −0.755113 | − | 0.655595i | \(-0.772418\pi\) |
0.655595 | + | 0.755113i | \(0.272418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.89849 | + | 3.89849i | 0.516367 | + | 0.516367i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.3796i | 1.74187i | 0.491397 | + | 0.870936i | \(0.336487\pi\) | ||||
−0.491397 | + | 0.870936i | \(0.663513\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.37539i | − | 0.944322i | −0.881512 | − | 0.472161i | \(-0.843474\pi\) | ||
0.881512 | − | 0.472161i | \(-0.156526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.441370 | + | 0.441370i | −0.0556074 | + | 0.0556074i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.28102 | + | 5.28102i | 0.645179 | + | 0.645179i | 0.951824 | − | 0.306645i | \(-0.0992063\pi\) |
−0.306645 | + | 0.951824i | \(0.599206\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.7619 | + | 0.186874i | −1.29558 | + | 0.0224969i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.63784 | −0.313054 | −0.156527 | − | 0.987674i | \(-0.550030\pi\) | ||||
−0.156527 | + | 0.987674i | \(0.550030\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.02304 | + | 4.02304i | 0.470862 | + | 0.470862i | 0.902193 | − | 0.431332i | \(-0.141956\pi\) |
−0.431332 | + | 0.902193i | \(0.641956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.767751 | + | 0.767751i | −0.0874934 | + | 0.0874934i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3181 | −1.27339 | −0.636694 | − | 0.771116i | \(-0.719699\pi\) | ||||
−0.636694 | + | 0.771116i | \(0.719699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.9615 | 1.21795 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.40137 | + | 1.40137i | −0.153821 | + | 0.153821i | −0.779822 | − | 0.626001i | \(-0.784690\pi\) |
0.626001 | + | 0.779822i | \(0.284690\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.10019 | + | 1.10019i | −0.117952 | + | 0.117952i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.83609 | −0.300625 | −0.150313 | − | 0.988639i | \(-0.548028\pi\) | ||||
−0.150313 | + | 0.988639i | \(0.548028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.10664i | − | 0.116008i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.91605 | − | 2.91605i | −0.302381 | − | 0.302381i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.72507 | + | 3.72507i | 0.378224 | + | 0.378224i | 0.870461 | − | 0.492237i | \(-0.163821\pi\) |
−0.492237 | + | 0.870461i | \(0.663821\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.21842 | −0.725478 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.469279 | −0.0466950 | −0.0233475 | − | 0.999727i | \(-0.507432\pi\) | ||||
−0.0233475 | + | 0.999727i | \(0.507432\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.74927 | − | 5.74927i | 0.566492 | − | 0.566492i | −0.364652 | − | 0.931144i | \(-0.618812\pi\) |
0.931144 | + | 0.364652i | \(0.118812\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.67419 | − | 2.67419i | −0.258524 | − | 0.258524i | 0.565930 | − | 0.824454i | \(-0.308517\pi\) |
−0.824454 | + | 0.565930i | \(0.808517\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.16115 | −0.494349 | −0.247174 | − | 0.968971i | \(-0.579502\pi\) | ||||
−0.247174 | + | 0.968971i | \(0.579502\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.2370i | 2.11064i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6402 | − | 10.6402i | 1.00095 | − | 1.00095i | 0.000947228 | − | 1.00000i | \(-0.499698\pi\) |
1.00000 | 0.000947228i | \(-0.000301512\pi\) | ||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.20235 | − | 5.20235i | 0.480958 | − | 0.480958i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.02551i | 0.185678i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.55623 | −0.141476 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.71967 | − | 3.71967i | −0.335392 | − | 0.335392i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.57153 | − | 8.57153i | 0.760600 | − | 0.760600i | −0.215831 | − | 0.976431i | \(-0.569246\pi\) |
0.976431 | + | 0.215831i | \(0.0692459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.2242 | −1.16433 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.24996 | −0.371321 | −0.185660 | − | 0.982614i | \(-0.559442\pi\) | ||||
−0.185660 | + | 0.982614i | \(0.559442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.532245 | + | 0.532245i | 0.0461515 | + | 0.0461515i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.99529 | + | 8.99529i | 0.768520 | + | 0.768520i | 0.977846 | − | 0.209326i | \(-0.0671271\pi\) |
−0.209326 | + | 0.977846i | \(0.567127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.36216i | 0.115537i | 0.998330 | + | 0.0577685i | \(0.0183985\pi\) | ||||
−0.998330 | + | 0.0577685i | \(0.981601\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1799 | −1.02574 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.04935 | − | 9.04935i | 0.756744 | − | 0.756744i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9600 | − | 10.9600i | 0.903962 | − | 0.903962i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.7491 | −1.12637 | −0.563187 | − | 0.826330i | \(-0.690425\pi\) | ||||
−0.563187 | + | 0.826330i | \(0.690425\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8118 | 1.04261 | 0.521303 | − | 0.853372i | \(-0.325446\pi\) | ||||
0.521303 | + | 0.853372i | \(0.325446\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.52196 | + | 9.52196i | −0.769805 | + | 0.769805i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.39820 | − | 2.39820i | −0.191397 | − | 0.191397i | 0.604902 | − | 0.796300i | \(-0.293212\pi\) |
−0.796300 | + | 0.604902i | \(0.793212\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.29955 | −0.182366 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.46928 | + | 0.0255131i | −0.115795 | + | 0.00201071i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.75616 | − | 7.75616i | −0.607509 | − | 0.607509i | 0.334785 | − | 0.942294i | \(-0.391336\pi\) |
−0.942294 | + | 0.334785i | \(0.891336\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.85634 | + | 8.85634i | −0.685324 | + | 0.685324i | −0.961195 | − | 0.275870i | \(-0.911034\pi\) |
0.275870 | + | 0.961195i | \(0.411034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.0438262i | 0.00337125i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.00418i | 0.382679i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7717 | + | 13.7717i | 1.04704 | + | 1.04704i | 0.998837 | + | 0.0482052i | \(0.0153501\pi\) |
0.0482052 | + | 0.998837i | \(0.484650\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.2333 | + | 21.2333i | −1.59599 | + | 1.59599i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.7733i | − | 1.40318i | −0.712581 | − | 0.701590i | \(-0.752474\pi\) | ||
0.712581 | − | 0.701590i | \(-0.247526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.3599i | − | 1.81066i | −0.424713 | − | 0.905328i | \(-0.639625\pi\) | ||
0.424713 | − | 0.905328i | \(-0.360375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7047 | − | 11.7047i | 0.865236 | − | 0.865236i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.5632 | + | 16.5632i | −1.21122 | + | 1.21122i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.662182 | 0.0481667 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4793i | 1.19240i | 0.802836 | + | 0.596200i | \(0.203323\pi\) | ||||
−0.802836 | + | 0.596200i | \(0.796677\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.11721 | + | 9.11721i | 0.656271 | + | 0.656271i | 0.954496 | − | 0.298224i | \(-0.0963944\pi\) |
−0.298224 | + | 0.954496i | \(0.596394\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6012 | − | 12.6012i | 0.897799 | − | 0.897799i | −0.0974424 | − | 0.995241i | \(-0.531066\pi\) |
0.995241 | + | 0.0974424i | \(0.0310662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6808 | −1.53691 | −0.768454 | − | 0.639905i | \(-0.778974\pi\) | ||||
−0.768454 | + | 0.639905i | \(0.778974\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.7619i | 1.18229i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.150204 | + | 0.150204i | −0.0105423 | + | 0.0105423i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.02704 | − | 6.78716i | −0.488413 | − | 0.471740i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.70463i | 0.602112i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.31813 | 0.572644 | 0.286322 | − | 0.958134i | \(-0.407567\pi\) | ||||
0.286322 | + | 0.958134i | \(0.407567\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.18623 | − | 4.18623i | −0.286836 | − | 0.286836i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.398117 | − | 0.398117i | −0.0270260 | − | 0.0270260i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.7691i | 0.862855i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 23.8744i | − | 1.60596i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.50787 | − | 1.50787i | −0.100975 | − | 0.100975i | 0.654815 | − | 0.755789i | \(-0.272747\pi\) |
−0.755789 | + | 0.654815i | \(0.772747\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.8704 | + | 16.8704i | 1.11973 | + | 1.11973i | 0.991781 | + | 0.127949i | \(0.0408395\pi\) |
0.127949 | + | 0.991781i | \(0.459161\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.373747 | 0.0246979 | 0.0123489 | − | 0.999924i | \(-0.496069\pi\) | ||||
0.0123489 | + | 0.999924i | \(0.496069\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.43683 | −0.160332 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0094 | − | 14.0094i | −0.917785 | − | 0.917785i | 0.0790826 | − | 0.996868i | \(-0.474801\pi\) |
−0.996868 | + | 0.0790826i | \(0.974801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.9618 | − | 17.9618i | −1.16674 | − | 1.16674i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.3608i | − | 0.799553i | −0.916613 | − | 0.399776i | \(-0.869088\pi\) | ||
0.916613 | − | 0.399776i | \(-0.130912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.9845i | − | 1.09407i | −0.837111 | − | 0.547034i | \(-0.815757\pi\) | ||
0.837111 | − | 0.547034i | \(-0.184243\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.8115 | + | 12.8115i | 0.821859 | + | 0.821859i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.27348 | − | 6.27348i | −0.399172 | − | 0.399172i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.44795 | −0.281877 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3626i | 0.654084i | 0.945010 | + | 0.327042i | \(0.106052\pi\) | ||||
−0.945010 | + | 0.327042i | \(0.893948\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.2233 | − | 11.8061i | −0.768474 | − | 0.742242i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.7324 | − | 16.7324i | 1.04374 | − | 1.04374i | 0.0447420 | − | 0.998999i | \(-0.485753\pi\) |
0.998999 | − | 0.0447420i | \(-0.0142466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.03593i | 0.188643i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41222 | −0.0874144 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.47398 | − | 4.47398i | 0.275878 | − | 0.275878i | −0.555583 | − | 0.831461i | \(-0.687505\pi\) |
0.831461 | + | 0.555583i | \(0.187505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.50086 | − | 4.50086i | −0.275448 | − | 0.275448i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 20.2041i | − | 1.23186i | −0.787799 | − | 0.615932i | \(-0.788780\pi\) | ||
0.787799 | − | 0.615932i | \(-0.211220\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2567 | −0.926778 | −0.463389 | − | 0.886155i | \(-0.653367\pi\) | ||||
−0.463389 | + | 0.886155i | \(0.653367\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.75624 | − | 1.75624i | 0.106292 | − | 0.106292i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.46771 | + | 9.46771i | −0.568859 | + | 0.568859i | −0.931809 | − | 0.362949i | \(-0.881770\pi\) |
0.362949 | + | 0.931809i | \(0.381770\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.74311i | − | 0.224094i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.9386i | − | 0.652540i | −0.945277 | − | 0.326270i | \(-0.894208\pi\) | ||
0.945277 | − | 0.326270i | \(-0.105792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0622 | + | 10.0622i | −0.598138 | + | 0.598138i | −0.939817 | − | 0.341678i | \(-0.889005\pi\) |
0.341678 | + | 0.939817i | \(0.389005\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.507832 | − | 0.507832i | −0.0299764 | − | 0.0299764i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.6977i | 1.57045i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.8233i | 0.693096i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.57268 | − | 6.57268i | 0.383980 | − | 0.383980i | −0.488554 | − | 0.872534i | \(-0.662475\pi\) |
0.872534 | + | 0.488554i | \(0.162475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.41485 | + | 5.41485i | 0.314201 | + | 0.314201i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.3181 | − | 0.300718i | 1.00153 | − | 0.0173910i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.80545 | −0.104065 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.744743 | − | 0.744743i | −0.0427843 | − | 0.0427843i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.6117 | − | 22.6117i | 1.29052 | − | 1.29052i | 0.356048 | − | 0.934468i | \(-0.384124\pi\) |
0.934468 | − | 0.356048i | \(-0.115876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.2481 | 1.03810 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.9244 | 0.959696 | 0.479848 | − | 0.877352i | \(-0.340692\pi\) | ||||
0.479848 | + | 0.877352i | \(0.340692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1800 | + | 10.1800i | −0.575408 | + | 0.575408i | −0.933635 | − | 0.358227i | \(-0.883381\pi\) |
0.358227 | + | 0.933635i | \(0.383381\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.21773 | − | 4.21773i | 0.236892 | − | 0.236892i | −0.578670 | − | 0.815562i | \(-0.696428\pi\) |
0.815562 | + | 0.578670i | \(0.196428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.45652 | −0.137539 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 8.48786i | − | 0.473746i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.4825 | + | 11.4825i | 0.638901 | + | 0.638901i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.19072 | − | 8.19072i | −0.452948 | − | 0.452948i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.66288 | −0.0916775 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3984 | 0.681475 | 0.340738 | − | 0.940158i | \(-0.389323\pi\) | ||||
0.340738 | + | 0.940158i | \(0.389323\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.2719 | + | 14.2719i | −0.782098 | + | 0.782098i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.39919 | + | 4.39919i | 0.239639 | + | 0.239639i | 0.816701 | − | 0.577062i | \(-0.195801\pi\) |
−0.577062 | + | 0.816701i | \(0.695801\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.7719 | 1.83424 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.51103i | − | 0.352592i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.01298 | − | 3.01298i | 0.162686 | − | 0.162686i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.77561 | − | 3.77561i | 0.202686 | − | 0.202686i | −0.598464 | − | 0.801150i | \(-0.704222\pi\) |
0.801150 | + | 0.598464i | \(0.204222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.5053i | 1.25821i | 0.777321 | + | 0.629104i | \(0.216578\pi\) | ||||
−0.777321 | + | 0.629104i | \(0.783422\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.80502 | −0.416601 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.29273 | + | 4.29273i | 0.228479 | + | 0.228479i | 0.812057 | − | 0.583578i | \(-0.198348\pi\) |
−0.583578 | + | 0.812057i | \(0.698348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.21448 | + | 3.21448i | −0.170128 | + | 0.170128i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.9792 | 1.74058 | 0.870288 | − | 0.492543i | \(-0.163933\pi\) | ||||
0.870288 | + | 0.492543i | \(0.163933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9655 | −0.682395 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.46973 | − | 2.46973i | −0.129627 | − | 0.129627i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6991 | + | 11.6991i | 0.610689 | + | 0.610689i | 0.943126 | − | 0.332436i | \(-0.107871\pi\) |
−0.332436 | + | 0.943126i | \(0.607871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.77465i | − | 0.248558i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.313948 | −0.0162994 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.8299 | + | 14.8299i | −0.767861 | + | 0.767861i | −0.977730 | − | 0.209868i | \(-0.932696\pi\) |
0.209868 | + | 0.977730i | \(0.432696\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.77043 | − | 1.77043i | 0.0911817 | − | 0.0911817i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.8505 | 1.58468 | 0.792342 | − | 0.610078i | \(-0.208862\pi\) | ||||
0.792342 | + | 0.610078i | \(0.208862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.2059 | 1.39380 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.76255 | − | 8.76255i | 0.447745 | − | 0.447745i | −0.446859 | − | 0.894604i | \(-0.647457\pi\) |
0.894604 | + | 0.446859i | \(0.147457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.48746 | − | 8.48746i | −0.431442 | − | 0.431442i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.4735 | 1.13945 | 0.569725 | − | 0.821836i | \(-0.307050\pi\) | ||||
0.569725 | + | 0.821836i | \(0.307050\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.6977 | + | 0.550411i | −1.60302 | + | 0.0278355i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.74466 | − | 6.74466i | −0.340223 | − | 0.340223i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.6494 | + | 17.6494i | −0.885796 | + | 0.885796i | −0.994116 | − | 0.108320i | \(-0.965453\pi\) |
0.108320 | + | 0.994116i | \(0.465453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.68934i | 0.0845727i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.7364i | 0.835775i | 0.908499 | + | 0.417887i | \(0.137229\pi\) | ||||
−0.908499 | + | 0.417887i | \(0.862771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.69254 | + | 4.69254i | 0.233752 | + | 0.233752i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.8256 | + | 24.8256i | −1.23056 | + | 1.23056i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 37.4425i | − | 1.85141i | −0.378246 | − | 0.925705i | \(-0.623473\pi\) | ||
0.378246 | − | 0.925705i | \(-0.376527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.5509i | 1.40831i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.89890 | + | 2.89890i | −0.142645 | + | 0.142645i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.16174 | + | 2.16174i | −0.105861 | + | 0.105861i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.5280 | 1.00286 | 0.501428 | − | 0.865199i | \(-0.332808\pi\) | ||||
0.501428 | + | 0.865199i | \(0.332808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16.4596i | − | 0.802191i | −0.916036 | − | 0.401096i | \(-0.868629\pi\) | ||
0.916036 | − | 0.401096i | \(-0.131371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.81722 | − | 7.81722i | −0.380086 | − | 0.380086i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.59800 | − | 1.59800i | 0.0773325 | − | 0.0773325i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.7225 | 1.38674 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 22.7364i | − | 1.09517i | −0.836749 | − | 0.547586i | \(-0.815547\pi\) | ||
0.836749 | − | 0.547586i | \(-0.184453\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0577 | + | 23.0577i | −1.10808 | + | 1.10808i | −0.114680 | + | 0.993403i | \(0.536584\pi\) |
−0.993403 | + | 0.114680i | \(0.963416\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.18459 | + | 8.47385i | −0.391522 | + | 0.405359i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3984i | 0.782651i | 0.920252 | + | 0.391325i | \(0.127983\pi\) | ||||
−0.920252 | + | 0.391325i | \(0.872017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.0684 | 0.669926 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.8220 | − | 14.8220i | −0.704214 | − | 0.704214i | 0.261098 | − | 0.965312i | \(-0.415915\pi\) |
−0.965312 | + | 0.261098i | \(0.915915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.8198 | − | 21.8198i | −1.03204 | − | 1.03204i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4554i | 1.15412i | 0.816701 | + | 0.577061i | \(0.195801\pi\) | ||||
−0.816701 | + | 0.577061i | \(0.804199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.30537i | − | 0.391085i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.3322 | + | 20.3322i | 0.955289 | + | 0.955289i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.8209 | − | 25.8209i | −1.20785 | − | 1.20785i | −0.971722 | − | 0.236127i | \(-0.924122\pi\) |
−0.236127 | − | 0.971722i | \(-0.575878\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.2857 | 0.666799 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.3186 | 1.31893 | 0.659464 | − | 0.751736i | \(-0.270783\pi\) | ||||
0.659464 | + | 0.751736i | \(0.270783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7236 | + | 12.7236i | 0.591315 | + | 0.591315i | 0.937987 | − | 0.346672i | \(-0.112688\pi\) |
−0.346672 | + | 0.937987i | \(0.612688\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.8132 | + | 22.8132i | 1.05567 | + | 1.05567i | 0.998356 | + | 0.0573107i | \(0.0182526\pi\) |
0.0573107 | + | 0.998356i | \(0.481747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.28844i | 0.105670i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.61185i | − | 0.350736i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.7637 | − | 14.7637i | −0.678836 | − | 0.678836i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.47587 | − | 1.47587i | −0.0675757 | − | 0.0675757i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.6963 | −0.488725 | −0.244363 | − | 0.969684i | \(-0.578579\pi\) | ||||
−0.244363 | + | 0.969684i | \(0.578579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 35.7840i | − | 1.63161i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.37223 | − | 2.29125i | −0.107940 | − | 0.104255i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.8814 | − | 22.8814i | 1.03685 | − | 1.03685i | 0.0375586 | − | 0.999294i | \(-0.488042\pi\) |
0.999294 | − | 0.0375586i | \(-0.0119581\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 24.6179i | − | 1.11326i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.17549 | −0.278696 | −0.139348 | − | 0.990243i | \(-0.544501\pi\) | ||||
−0.139348 | + | 0.990243i | \(0.544501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.24045 | + | 3.24045i | −0.145943 | + | 0.145943i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.571530 | − | 0.571530i | −0.0256366 | − | 0.0256366i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 37.0601i | − | 1.65904i | −0.558478 | − | 0.829520i | \(-0.688614\pi\) | ||
0.558478 | − | 0.829520i | \(-0.311386\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.1099 | −1.25586 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.02535 | − | 8.02535i | 0.357832 | − | 0.357832i | −0.505181 | − | 0.863013i | \(-0.668574\pi\) |
0.863013 | + | 0.505181i | \(0.168574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.0695519 | + | 0.0695519i | −0.00308891 | + | 0.00308891i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 28.9970i | − | 1.28527i | −0.766172 | − | 0.642636i | \(-0.777841\pi\) | ||
0.766172 | − | 0.642636i | \(-0.222159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.74331i | 0.0771197i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.75385 | − | 3.75385i | 0.165737 | − | 0.165737i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.5978 | − | 13.5978i | −0.598032 | − | 0.598032i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.7112i | 1.91871i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.69881i | − | 0.118237i | −0.998251 | − | 0.0591185i | \(-0.981171\pi\) | ||
0.998251 | − | 0.0591185i | \(-0.0188290\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.374908 | − | 0.374908i | 0.0163936 | − | 0.0163936i | −0.698862 | − | 0.715256i | \(-0.746310\pi\) |
0.715256 | + | 0.698862i | \(0.246310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.58884 | − | 8.58884i | −0.374136 | − | 0.374136i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.798520 | − | 22.9861i | −0.0347183 | − | 0.999397i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.2555 | −1.18279 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.98573 | + | 5.98573i | 0.259271 | + | 0.259271i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.7931 | − | 29.7931i | 1.28567 | − | 1.28567i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.4717 | 1.05407 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.9462 | 1.07252 | 0.536261 | − | 0.844052i | \(-0.319836\pi\) | ||||
0.536261 | + | 0.844052i | \(0.319836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.6590 | − | 38.6590i | 1.65902 | − | 1.65902i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.2872 | + | 20.2872i | −0.867419 | + | 0.867419i | −0.992186 | − | 0.124767i | \(-0.960182\pi\) |
0.124767 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.0244 | 0.641226 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.70299i | 0.0725497i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.45225 | − | 2.45225i | −0.104280 | − | 0.104280i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.4666 | − | 23.4666i | −0.994313 | − | 0.994313i | 0.00567133 | − | 0.999984i | \(-0.498195\pi\) |
−0.999984 | + | 0.00567133i | \(0.998195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.2806 | 0.900072 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −52.5714 | −2.21956 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3000 | − | 15.3000i | 0.644819 | − | 0.644819i | −0.306917 | − | 0.951736i | \(-0.599298\pi\) |
0.951736 | + | 0.306917i | \(0.0992975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.37499 | + | 2.37499i | 0.0997402 | + | 0.0997402i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.1860 | −1.43315 | −0.716575 | − | 0.697510i | \(-0.754291\pi\) | ||||
−0.716575 | + | 0.697510i | \(0.754291\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 43.8726i | − | 1.83601i | −0.396570 | − | 0.918005i | \(-0.629799\pi\) | ||
0.396570 | − | 0.918005i | \(-0.370201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.1525 | + | 26.1525i | −1.09254 | + | 1.09254i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.3549 | − | 31.3549i | 1.30532 | − | 1.30532i | 0.380567 | − | 0.924753i | \(-0.375729\pi\) |
0.924753 | − | 0.380567i | \(-0.124271\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.9379i | 1.20262i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.607260 | −0.0251934 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.56724 | − | 2.56724i | −0.106324 | − | 0.106324i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.83841 | + | 5.83841i | −0.240977 | + | 0.240977i | −0.817254 | − | 0.576277i | \(-0.804505\pi\) |
0.576277 | + | 0.817254i | \(0.304505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.51378 | −0.185987 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.9961 | 1.64522 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.36096 | − | 9.36096i | −0.384408 | − | 0.384408i | 0.488279 | − | 0.872688i | \(-0.337625\pi\) |
−0.872688 | + | 0.488279i | \(0.837625\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.4072 | − | 34.4072i | −1.40819 | − | 1.40819i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.1304i | 1.06766i | 0.845593 | + | 0.533829i | \(0.179247\pi\) | ||||
−0.845593 | + | 0.533829i | \(0.820753\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2017 | 0.456929 | 0.228464 | − | 0.973552i | \(-0.426630\pi\) | ||||
0.228464 | + | 0.973552i | \(0.426630\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.7580 | + | 10.7580i | −0.438098 | + | 0.438098i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.08024 | + | 4.08024i | −0.165612 | + | 0.165612i | −0.785047 | − | 0.619436i | \(-0.787361\pi\) |
0.619436 | + | 0.785047i | \(0.287361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.476746 | −0.0193187 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.6001 | 0.792934 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.95093 | − | 9.95093i | 0.401914 | − | 0.401914i | −0.476993 | − | 0.878907i | \(-0.658273\pi\) |
0.878907 | + | 0.476993i | \(0.158273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.50185 | − | 6.50185i | −0.261755 | − | 0.261755i | 0.564012 | − | 0.825767i | \(-0.309257\pi\) |
−0.825767 | + | 0.564012i | \(0.809257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.6346 | −0.628408 | −0.314204 | − | 0.949355i | \(-0.601738\pi\) | ||||
−0.314204 | + | 0.949355i | \(0.601738\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.179941 | + | 10.3626i | 0.00722077 | + | 0.415838i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.614485 | − | 0.614485i | −0.0246188 | − | 0.0246188i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.8142 | + | 13.8142i | −0.551686 | + | 0.551686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 65.4961i | 2.61150i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 32.7046i | − | 1.30195i | −0.759099 | − | 0.650975i | \(-0.774360\pi\) | ||
0.759099 | − | 0.650975i | \(-0.225640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.2008 | + | 13.2008i | 0.524685 | + | 0.524685i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.6369 | + | 17.6369i | −0.698798 | + | 0.698798i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5.37354i | − | 0.212574i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.51103i | 0.257170i | 0.991698 | + | 0.128585i | \(0.0410436\pi\) | ||||
−0.991698 | + | 0.128585i | \(0.958956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.4636 | + | 11.4636i | −0.452081 | + | 0.452081i | −0.896045 | − | 0.443964i | \(-0.853572\pi\) |
0.443964 | + | 0.896045i | \(0.353572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.24557 | − | 1.24557i | 0.0489684 | − | 0.0489684i | −0.682199 | − | 0.731167i | \(-0.738976\pi\) |
0.731167 | + | 0.682199i | \(0.238976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.4102 | −1.86101 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.26362i | − | 0.0495251i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.0403 | − | 10.0403i | −0.392906 | − | 0.392906i | 0.482816 | − | 0.875722i | \(-0.339614\pi\) |
−0.875722 | + | 0.482816i | \(0.839614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.19534 | + | 8.19534i | −0.319731 | + | 0.319731i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.0673 | 1.21021 | 0.605104 | − | 0.796146i | \(-0.293131\pi\) | ||||
0.605104 | + | 0.796146i | \(0.293131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 41.9458i | − | 1.63150i | −0.578403 | − | 0.815751i | \(-0.696324\pi\) | ||
0.578403 | − | 0.815751i | \(-0.303676\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.8885 | − | 37.8885i | 1.47147 | − | 1.47147i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.39139 | − | 2.30976i | −0.0925951 | − | 0.0894343i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 4.78597i | − | 0.185036i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.1345 | 1.00891 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3214 | + | 21.3214i | 0.821880 | + | 0.821880i | 0.986377 | − | 0.164498i | \(-0.0526003\pi\) |
−0.164498 | + | 0.986377i | \(0.552600\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3686 | + | 10.3686i | 0.398497 | + | 0.398497i | 0.877703 | − | 0.479206i | \(-0.159075\pi\) |
−0.479206 | + | 0.877703i | \(0.659075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.61419i | 0.0619471i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 53.5465i | 2.05191i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.72053 | − | 8.72053i | −0.333682 | − | 0.333682i | 0.520301 | − | 0.853983i | \(-0.325820\pi\) |
−0.853983 | + | 0.520301i | \(0.825820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.593134 | + | 0.593134i | 0.0226295 | + | 0.0226295i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.70045 | 0.140976 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.59492 | 0.0987153 | 0.0493576 | − | 0.998781i | \(-0.484283\pi\) | ||||
0.0493576 | + | 0.998781i | \(0.484283\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.56399 | − | 1.56399i | −0.0594109 | − | 0.0594109i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.9558 | − | 10.9558i | −0.414980 | − | 0.414980i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 44.4656i | − | 1.68184i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.3881i | 1.52544i | 0.646729 | + | 0.762720i | \(0.276136\pi\) | ||||
−0.646729 | + | 0.762720i | \(0.723864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.2104 | + | 17.2104i | 0.649103 | + | 0.649103i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.101677 | − | 0.101677i | −0.00382395 | − | 0.00382395i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3495 | 1.10224 | 0.551121 | − | 0.834425i | \(-0.314200\pi\) | ||||
0.551121 | + | 0.834425i | \(0.314200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 23.0562i | − | 0.864673i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.12204 | − | 6.33841i | 0.229272 | − | 0.237375i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.6165 | − | 19.6165i | 0.732591 | − | 0.732591i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 40.4568i | − | 1.50879i | −0.656423 | − | 0.754393i | \(-0.727931\pi\) | ||
0.656423 | − | 0.754393i | \(-0.272069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.49134 | 0.0927824 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.9543 | − | 26.9543i | 1.00244 | − | 1.00244i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.42458 | + | 1.42458i | 0.0528349 | + | 0.0528349i | 0.733031 | − | 0.680196i | \(-0.238105\pi\) |
−0.680196 | + | 0.733031i | \(0.738105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.77904i | 0.288112i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.9502 | −1.44063 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.76868 | − | 8.76868i | 0.323879 | − | 0.323879i | −0.526374 | − | 0.850253i | \(-0.676449\pi\) |
0.850253 | + | 0.526374i | \(0.176449\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.7132 | + | 18.7132i | −0.689309 | + | 0.689309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.285415i | 0.0104992i | 0.999986 | + | 0.00524959i | \(0.00167100\pi\) | ||||
−0.999986 | + | 0.00524959i | \(0.998329\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 19.9119i | − | 0.731483i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.8792 | − | 23.8792i | 0.876043 | − | 0.876043i | −0.117079 | − | 0.993123i | \(-0.537353\pi\) |
0.993123 | + | 0.117079i | \(0.0373532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.85474 | − | 2.85474i | −0.104449 | − | 0.104449i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.15881i | − | 0.0423421i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.3191i | 0.850925i | 0.904976 | + | 0.425463i | \(0.139889\pi\) | ||||
−0.904976 | + | 0.425463i | \(0.860111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.4454 | + | 16.4454i | −0.599305 | + | 0.599305i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.6429 | − | 17.6429i | −0.641240 | − | 0.641240i | 0.309620 | − | 0.950860i | \(-0.399798\pi\) |
−0.950860 | + | 0.309620i | \(0.899798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.662182 | − | 38.1345i | −0.0240357 | − | 1.38420i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.5697 | −0.854400 | −0.427200 | − | 0.904157i | \(-0.640500\pi\) | ||||
−0.427200 | + | 0.904157i | \(0.640500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.11825 | − | 1.11825i | −0.0404832 | − | 0.0404832i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.1688 | − | 34.1688i | 1.23376 | − | 1.23376i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.9706 | −1.91017 | −0.955085 | − | 0.296333i | \(-0.904236\pi\) | ||||
−0.955085 | + | 0.296333i | \(0.904236\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.1085 | 1.91266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.4220 | − | 18.4220i | 0.662594 | − | 0.662594i | −0.293397 | − | 0.955991i | \(-0.594786\pi\) |
0.955991 | + | 0.293397i | \(0.0947858\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.81800 | + | 4.81800i | −0.172845 | + | 0.172845i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.75771 | −0.206292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.34712i | − | 0.334466i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.05937 | + | 1.05937i | 0.0378588 | + | 0.0378588i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.0879 | + | 32.0879i | 1.14381 | + | 1.14381i | 0.987747 | + | 0.156063i | \(0.0498804\pi\) |
0.156063 | + | 0.987747i | \(0.450120\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.2004 | 0.505547 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.61074 | 0.163939 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.8353 | + | 18.8353i | −0.668861 | + | 0.668861i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.9128 | − | 29.9128i | −1.05957 | − | 1.05957i | −0.998110 | − | 0.0614563i | \(-0.980426\pi\) |
−0.0614563 | − | 0.998110i | \(-0.519574\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.8744 | −1.26914 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.77740i | − | 0.204135i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.2556 | + | 14.2556i | −0.503068 | + | 0.503068i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.0637 | − | 32.0637i | 1.12870 | − | 1.12870i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8971i | 0.945652i | 0.881156 | + | 0.472826i | \(0.156766\pi\) | ||||
−0.881156 | + | 0.472826i | \(0.843234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.1827 | −0.673597 | −0.336799 | − | 0.941577i | \(-0.609344\pi\) | ||||
−0.336799 | + | 0.941577i | \(0.609344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.2123 | − | 24.2123i | −0.849161 | − | 0.849161i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2350 | + | 10.2350i | −0.358076 | + | 0.358076i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.25435 | 0.0787732 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.1207 | −1.29552 | −0.647760 | − | 0.761844i | \(-0.724294\pi\) | ||||
−0.647760 | + | 0.761844i | \(0.724294\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.1279 | − | 26.1279i | −0.910762 | − | 0.910762i | 0.0855705 | − | 0.996332i | \(-0.472729\pi\) |
−0.996332 | + | 0.0855705i | \(0.972729\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.28023 | − | 4.28023i | −0.148838 | − | 0.148838i | 0.628761 | − | 0.777599i | \(-0.283563\pi\) |
−0.777599 | + | 0.628761i | \(0.783563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.5238i | 0.643358i | 0.946849 | + | 0.321679i | \(0.104247\pi\) | ||||
−0.946849 | + | 0.321679i | \(0.895753\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.0504 | −1.04244 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.2811 | − | 32.2811i | 1.11847 | − | 1.11847i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.80787 | + | 2.80787i | −0.0970541 | + | 0.0970541i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.5518 | −0.882147 | −0.441074 | − | 0.897471i | \(-0.645402\pi\) | ||||
−0.441074 | + | 0.897471i | \(0.645402\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5194 | 0.983428 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.3594 | − | 17.3594i | 0.597890 | − | 0.597890i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.337183 | − | 0.337183i | −0.0115857 | − | 0.0115857i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.9374 | −1.09609 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.5099 | + | 0.824980i | −1.62862 | + | 0.0282799i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.46948 | − | 8.46948i | −0.289989 | − | 0.289989i | 0.547087 | − | 0.837076i | \(-0.315737\pi\) |
−0.837076 | + | 0.547087i | \(0.815737\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.8682 | + | 33.8682i | −1.15692 | + | 1.15692i | −0.171780 | + | 0.985135i | \(0.554952\pi\) |
−0.985135 | + | 0.171780i | \(0.945048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.9189i | 0.986701i | 0.869831 | + | 0.493350i | \(0.164228\pi\) | ||||
−0.869831 | + | 0.493350i | \(0.835772\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 1.61185i | − | 0.0549318i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.2769 | + | 26.2769i | 0.894476 | + | 0.894476i | 0.994941 | − | 0.100464i | \(-0.0320328\pi\) |
−0.100464 | + | 0.994941i | \(0.532033\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −42.3691 | + | 42.3691i | −1.43893 | + | 1.43893i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 40.1055i | − | 1.36049i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 26.9734i | − | 0.913958i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.58834 | + | 7.58834i | −0.256827 | + | 0.256827i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.62273 | + | 5.62273i | −0.189866 | + | 0.189866i | −0.795638 | − | 0.605772i | \(-0.792864\pi\) |
0.605772 | + | 0.795638i | \(0.292864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.8616 | 0.703645 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.77465i | 0.0597895i | 0.999553 | + | 0.0298948i | \(0.00951721\pi\) | ||||
−0.999553 | + | 0.0298948i | \(0.990483\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.1726 | − | 14.1726i | −0.476945 | − | 0.476945i | 0.427208 | − | 0.904153i | \(-0.359497\pi\) |
−0.904153 | + | 0.427208i | \(0.859497\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.1647 | − | 13.1647i | 0.442027 | − | 0.442027i | −0.450666 | − | 0.892693i | \(-0.648813\pi\) |
0.892693 | + | 0.450666i | \(0.148813\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.71432 | 0.124574 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38.8419i | 1.30125i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.42672 | + | 9.42672i | −0.315453 | + | 0.315453i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.9610 | + | 27.0065i | 0.933591 | + | 0.901722i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.27383i | − | 0.0424846i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.77301 | −0.225642 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.86524 | − | 2.86524i | −0.0953493 | − | 0.0953493i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.5641 | + | 24.5641i | 0.815638 | + | 0.815638i | 0.985473 | − | 0.169834i | \(-0.0543233\pi\) |
−0.169834 | + | 0.985473i | \(0.554323\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 0.955968i | − | 0.0317074i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.8519i | 1.85046i | 0.379411 | + | 0.925228i | \(0.376127\pi\) | ||||
−0.379411 | + | 0.925228i | \(0.623873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.96574 | − | 4.96574i | −0.164342 | − | 0.164342i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.920822 | − | 0.920822i | −0.0304082 | − | 0.0304082i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.0592 | −1.61831 | −0.809157 | − | 0.587592i | \(-0.800076\pi\) | ||||
−0.809157 | + | 0.587592i | \(0.800076\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 71.7691 | 2.36487 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.73652 | + | 6.73652i | 0.221735 | + | 0.221735i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.7118 | + | 11.7118i | 0.384667 | + | 0.384667i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.1164i | 0.397526i | 0.980048 | + | 0.198763i | \(0.0636923\pi\) | ||||
−0.980048 | + | 0.198763i | \(0.936308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 16.9650i | − | 0.556006i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.8590 | + | 26.8590i | 0.879323 | + | 0.879323i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.2751 | − | 25.2751i | −0.825700 | − | 0.825700i | 0.161219 | − | 0.986919i | \(-0.448458\pi\) |
−0.986919 | + | 0.161219i | \(0.948458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.3112 | −1.05444 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.2968i | 0.726855i | 0.931623 | + | 0.363427i | \(0.118394\pi\) | ||||
−0.931623 | + | 0.363427i | \(0.881606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.80918 | − | 8.08517i | 0.254302 | − | 0.263289i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.4481 | − | 34.4481i | 1.11941 | − | 1.11941i | 0.127584 | − | 0.991828i | \(-0.459278\pi\) |
0.991828 | − | 0.127584i | \(-0.0407221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 20.5481i | − | 0.667021i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.3870 | 0.434104 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.5954 | + | 18.5954i | −0.602365 | + | 0.602365i | −0.940940 | − | 0.338575i | \(-0.890055\pi\) |
0.338575 | + | 0.940940i | \(0.390055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.89849 | − | 3.89849i | −0.126020 | − | 0.126020i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.89795i | 0.125871i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6237 | −0.891087 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.44760 | − | 5.44760i | 0.175546 | − | 0.175546i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0209 | + | 16.0209i | −0.515197 | + | 0.515197i | −0.916114 | − | 0.400917i | \(-0.868691\pi\) |
0.400917 | + | 0.916114i | \(0.368691\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.4452i | 1.17079i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 29.9293i | − | 0.960476i | −0.877138 | − | 0.480238i | \(-0.840550\pi\) | ||
0.877138 | − | 0.480238i | \(-0.159450\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.295134 | + | 0.295134i | −0.00946156 | + | 0.00946156i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.4894 | + | 37.4894i | 1.19939 | + | 1.19939i | 0.974348 | + | 0.225045i | \(0.0722530\pi\) |
0.225045 | + | 0.974348i | \(0.427747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 10.0496i | − | 0.321188i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 10.5138i | − | 0.335679i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.2157 | + | 25.2157i | −0.804257 | + | 0.804257i | −0.983758 | − | 0.179501i | \(-0.942552\pi\) |
0.179501 | + | 0.983758i | \(0.442552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.63898 | − | 2.63898i | −0.0839996 | − | 0.0839996i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.490612 | − | 28.2539i | −0.0156005 | − | 0.898423i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.0634 | 1.05029 | 0.525147 | − | 0.851012i | \(-0.324010\pi\) | ||||
0.525147 | + | 0.851012i | \(0.324010\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.6761 | + | 19.6761i | 0.624403 | + | 0.624403i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.4366 | − | 35.4366i | 1.12229 | − | 1.12229i | 0.130893 | − | 0.991397i | \(-0.458216\pi\) |
0.991397 | − | 0.130893i | \(-0.0417843\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.4120 | 0.677446 |
(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 | 2300.2.i.f.1793.7 | yes | 16 | |
5.2 | odd | 4 | 2300.2.i.e.1057.7 | yes | 16 | ||
5.3 | odd | 4 | 2300.2.i.e.1057.2 | ✓ | 16 | ||
5.4 | even | 2 | inner | 2300.2.i.f.1793.2 | yes | 16 | |
23.22 | odd | 2 | 2300.2.i.e.1793.7 | yes | 16 | ||
115.22 | even | 4 | inner | 2300.2.i.f.1057.7 | yes | 16 | |
115.68 | even | 4 | inner | 2300.2.i.f.1057.2 | yes | 16 | |
115.114 | odd | 2 | 2300.2.i.e.1793.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2300.2.i.e.1057.2 | ✓ | 16 | 5.3 | odd | 4 | ||
2300.2.i.e.1057.7 | yes | 16 | 5.2 | odd | 4 | ||
2300.2.i.e.1793.2 | yes | 16 | 115.114 | odd | 2 | ||
2300.2.i.e.1793.7 | yes | 16 | 23.22 | odd | 2 | ||
2300.2.i.f.1057.2 | yes | 16 | 115.68 | even | 4 | inner | |
2300.2.i.f.1057.7 | yes | 16 | 115.22 | even | 4 | inner | |
2300.2.i.f.1793.2 | yes | 16 | 5.4 | even | 2 | inner | |
2300.2.i.f.1793.7 | yes | 16 | 1.1 | even | 1 | trivial |