Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1980,2,Mod(1297,1980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1980, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("1980.1297");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1980.y (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: | \(15.8103796002\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 660) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1297.1 | ||
Character | \(\chi\) | \(=\) | 1980.1297 |
Dual form | 1980.2.y.c.1693.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1980\mathbb{Z}\right)^\times\).
\(n\) | \(397\) | \(541\) | \(991\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.05777 | − | 0.874978i | −0.920262 | − | 0.391302i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.32148 | + | 2.32148i | −0.877438 | + | 0.877438i | −0.993269 | − | 0.115831i | \(-0.963047\pi\) |
0.115831 | + | 0.993269i | \(0.463047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.23741 | + | 2.44827i | −0.674603 | + | 0.738181i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.15629 | + | 3.15629i | 0.875396 | + | 0.875396i | 0.993054 | − | 0.117658i | \(-0.0375386\pi\) |
−0.117658 | + | 0.993054i | \(0.537539\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.61362 | − | 4.61362i | 1.11897 | − | 1.11897i | 0.127075 | − | 0.991893i | \(-0.459441\pi\) |
0.991893 | − | 0.127075i | \(-0.0405589\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.600117 | −0.137676 | −0.0688382 | − | 0.997628i | \(-0.521929\pi\) | ||||
−0.0688382 | + | 0.997628i | \(0.521929\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.436835 | − | 0.436835i | 0.0910865 | − | 0.0910865i | −0.660095 | − | 0.751182i | \(-0.729484\pi\) |
0.751182 | + | 0.660095i | \(0.229484\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.46883 | + | 3.60100i | 0.693766 | + | 0.720201i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.40139 | −0.260231 | −0.130116 | − | 0.991499i | \(-0.541535\pi\) | ||||
−0.130116 | + | 0.991499i | \(0.541535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.67097 | −1.37775 | −0.688874 | − | 0.724881i | \(-0.741895\pi\) | ||||
−0.688874 | + | 0.724881i | \(0.741895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.80832 | − | 2.74583i | 1.15082 | − | 0.464130i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.84287 | + | 3.84287i | 0.631764 | + | 0.631764i | 0.948510 | − | 0.316746i | \(-0.102590\pi\) |
−0.316746 | + | 0.948510i | \(0.602590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.19555i | − | 1.43610i | −0.695990 | − | 0.718051i | \(-0.745034\pi\) | ||
0.695990 | − | 0.718051i | \(-0.254966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.66683 | − | 8.66683i | −1.32168 | − | 1.32168i | −0.912417 | − | 0.409262i | \(-0.865786\pi\) |
−0.409262 | − | 0.912417i | \(-0.634214\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.22477 | − | 8.22477i | −1.19971 | − | 1.19971i | −0.974255 | − | 0.225451i | \(-0.927614\pi\) |
−0.225451 | − | 0.974255i | \(-0.572386\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.77856i | − | 0.539794i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.72320 | + | 3.72320i | −0.511421 | + | 0.511421i | −0.914962 | − | 0.403541i | \(-0.867779\pi\) |
0.403541 | + | 0.914962i | \(0.367779\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.74624 | − | 3.08029i | 0.909663 | − | 0.415346i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.10736i | − | 0.925300i | −0.886541 | − | 0.462650i | \(-0.846899\pi\) | ||
0.886541 | − | 0.462650i | \(-0.153101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.28178i | − | 0.292152i | −0.989273 | − | 0.146076i | \(-0.953336\pi\) | ||
0.989273 | − | 0.146076i | \(-0.0466645\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.73323 | − | 9.25659i | −0.463050 | − | 1.14814i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71070 | − | 1.71070i | −0.208995 | − | 0.208995i | 0.594845 | − | 0.803840i | \(-0.297213\pi\) |
−0.803840 | + | 0.594845i | \(0.797213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.25804 | 0.267981 | 0.133990 | − | 0.990983i | \(-0.457221\pi\) | ||||
0.133990 | + | 0.990983i | \(0.457221\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.34887 | − | 1.34887i | −0.157873 | − | 0.157873i | 0.623750 | − | 0.781624i | \(-0.285608\pi\) |
−0.781624 | + | 0.623750i | \(0.785608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.489514 | − | 10.8777i | −0.0557853 | − | 1.23963i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.85526 | 0.658768 | 0.329384 | − | 0.944196i | \(-0.393159\pi\) | ||||
0.329384 | + | 0.944196i | \(0.393159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.7602 | − | 11.7602i | −1.29085 | − | 1.29085i | −0.934259 | − | 0.356595i | \(-0.883938\pi\) |
−0.356595 | − | 0.934259i | \(-0.616062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.5306 | + | 5.45695i | −1.46760 | + | 0.591890i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.41573i | 0.574067i | 0.957921 | + | 0.287033i | \(0.0926690\pi\) | ||||
−0.957921 | + | 0.287033i | \(0.907331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.6545 | −1.53621 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.23490 | + | 0.525089i | 0.126698 | + | 0.0538730i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.3177 | − | 12.3177i | −1.25067 | − | 1.25067i | −0.955420 | − | 0.295252i | \(-0.904596\pi\) |
−0.295252 | − | 0.955420i | \(-0.595404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8178i | 1.37492i | 0.726221 | + | 0.687461i | \(0.241275\pi\) | ||||
−0.726221 | + | 0.687461i | \(0.758725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.60147 | + | 3.60147i | −0.354863 | + | 0.354863i | −0.861915 | − | 0.507052i | \(-0.830735\pi\) |
0.507052 | + | 0.861915i | \(0.330735\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.73323 | + | 3.73323i | −0.360905 | + | 0.360905i | −0.864146 | − | 0.503241i | \(-0.832141\pi\) |
0.503241 | + | 0.864146i | \(0.332141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.6154 | 1.87882 | 0.939409 | − | 0.342798i | \(-0.111374\pi\) | ||||
0.939409 | + | 0.342798i | \(0.111374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0119 | + | 10.0119i | −0.941845 | + | 0.941845i | −0.998400 | − | 0.0565545i | \(-0.981989\pi\) |
0.0565545 | + | 0.998400i | \(0.481989\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.28113 | + | 0.516685i | −0.119466 | + | 0.0481811i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.4209i | 1.96365i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.988033 | − | 10.9555i | −0.0898212 | − | 0.995958i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.98725 | − | 10.4452i | −0.356630 | − | 0.934246i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.26695 | − | 9.26695i | 0.822309 | − | 0.822309i | −0.164130 | − | 0.986439i | \(-0.552482\pi\) |
0.986439 | + | 0.164130i | \(0.0524817\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.79427i | 0.331507i | 0.986167 | + | 0.165753i | \(0.0530056\pi\) | ||||
−0.986167 | + | 0.165753i | \(0.946994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.39316 | − | 1.39316i | 0.120802 | − | 0.120802i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.53010 | + | 1.53010i | 0.130725 | + | 0.130725i | 0.769442 | − | 0.638717i | \(-0.220534\pi\) |
−0.638717 | + | 0.769442i | \(0.720534\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3446 | 1.21669 | 0.608346 | − | 0.793672i | \(-0.291833\pi\) | ||||
0.608346 | + | 0.793672i | \(0.291833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.7893 | + | 0.665543i | −1.23675 | + | 0.0556555i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.88373 | + | 1.22618i | 0.239481 | + | 0.101829i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.50365 | 0.205107 | 0.102554 | − | 0.994727i | \(-0.467299\pi\) | ||||
0.102554 | + | 0.994727i | \(0.467299\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.3472i | − | 1.41170i | −0.708362 | − | 0.705849i | \(-0.750566\pi\) | ||
0.708362 | − | 0.705849i | \(-0.249434\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.7851 | + | 6.71193i | 1.26789 | + | 0.539115i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.57371 | − | 8.57371i | −0.684257 | − | 0.684257i | 0.276700 | − | 0.960956i | \(-0.410759\pi\) |
−0.960956 | + | 0.276700i | \(0.910759\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.02821i | 0.159845i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.32282 | − | 6.32282i | 0.495241 | − | 0.495241i | −0.414712 | − | 0.909953i | \(-0.636118\pi\) |
0.909953 | + | 0.414712i | \(0.136118\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.23430 | − | 4.23430i | 0.327660 | − | 0.327660i | −0.524036 | − | 0.851696i | \(-0.675574\pi\) |
0.851696 | + | 0.524036i | \(0.175574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.92428i | 0.532637i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.22074 | + | 2.22074i | 0.168840 | + | 0.168840i | 0.786469 | − | 0.617629i | \(-0.211907\pi\) |
−0.617629 | + | 0.786469i | \(0.711907\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.4125 | − | 0.306846i | −1.24067 | − | 0.0231954i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.44971i | − | 0.407331i | −0.979041 | − | 0.203665i | \(-0.934715\pi\) | ||
0.979041 | − | 0.203665i | \(-0.0652854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.35615 | 0.695437 | 0.347718 | − | 0.937599i | \(-0.386956\pi\) | ||||
0.347718 | + | 0.937599i | \(0.386956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.54532 | − | 11.2702i | −0.334178 | − | 0.828599i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.972841 | + | 21.6179i | 0.0711412 | + | 1.58086i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.55894 | −0.257516 | −0.128758 | − | 0.991676i | \(-0.541099\pi\) | ||||
−0.128758 | + | 0.991676i | \(0.541099\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.03819 | + | 6.03819i | 0.434638 | + | 0.434638i | 0.890203 | − | 0.455565i | \(-0.150563\pi\) |
−0.455565 | + | 0.890203i | \(0.650563\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.909737 | + | 0.909737i | −0.0648161 | + | 0.0648161i | −0.738772 | − | 0.673956i | \(-0.764594\pi\) |
0.673956 | + | 0.738772i | \(0.264594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 27.5780i | − | 1.95495i | −0.211049 | − | 0.977476i | \(-0.567688\pi\) | ||
0.211049 | − | 0.977476i | \(-0.432312\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.25330 | − | 3.25330i | 0.228337 | − | 0.228337i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.04590 | + | 18.9223i | −0.561950 | + | 1.32159i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.34271 | − | 1.46925i | 0.0928769 | − | 0.101630i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7166i | 0.875447i | 0.899110 | + | 0.437723i | \(0.144215\pi\) | ||||
−0.899110 | + | 0.437723i | \(0.855785\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.2511 | + | 25.4176i | 0.699116 | + | 1.73347i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.8080 | − | 17.8080i | 1.20889 | − | 1.20889i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.1238 | 1.95908 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.3544 | + | 16.3544i | −1.09517 | + | 1.09517i | −0.100207 | + | 0.994967i | \(0.531950\pi\) |
−0.994967 | + | 0.100207i | \(0.968050\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.33341 | − | 7.33341i | 0.486735 | − | 0.486735i | −0.420539 | − | 0.907274i | \(-0.638159\pi\) |
0.907274 | + | 0.420539i | \(0.138159\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.09535i | − | 0.534955i | −0.963564 | − | 0.267478i | \(-0.913810\pi\) | ||
0.963564 | − | 0.267478i | \(-0.0861902\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.2241 | − | 17.2241i | −1.12839 | − | 1.12839i | −0.990439 | − | 0.137950i | \(-0.955949\pi\) |
−0.137950 | − | 0.990439i | \(-0.544051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.72818 | + | 24.1212i | 0.634597 | + | 1.57349i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.86607 | −0.444129 | −0.222064 | − | 0.975032i | \(-0.571280\pi\) | ||||
−0.222064 | + | 0.975032i | \(0.571280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.35034i | 0.409061i | 0.978860 | + | 0.204531i | \(0.0655668\pi\) | ||||
−0.978860 | + | 0.204531i | \(0.934433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.30616 | + | 7.77541i | −0.211223 | + | 0.496752i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.89414 | − | 1.89414i | −0.120521 | − | 0.120521i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.72752 | −0.487757 | −0.243878 | − | 0.969806i | \(-0.578420\pi\) | ||||
−0.243878 | + | 0.969806i | \(0.578420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0921123 | + | 2.04687i | 0.00579105 | + | 0.128686i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.9325 | − | 12.9325i | −0.806708 | − | 0.806708i | 0.177426 | − | 0.984134i | \(-0.443223\pi\) |
−0.984134 | + | 0.177426i | \(0.943223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.8423 | −1.10867 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.80627 | − | 5.80627i | −0.358030 | − | 0.358030i | 0.505056 | − | 0.863086i | \(-0.331472\pi\) |
−0.863086 | + | 0.505056i | \(0.831472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.9192 | − | 4.40377i | 0.670761 | − | 0.270521i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.0590i | − | 1.58884i | −0.607367 | − | 0.794421i | \(-0.707774\pi\) | ||
0.607367 | − | 0.794421i | \(-0.292226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5992i | 0.765349i | 0.923883 | + | 0.382675i | \(0.124997\pi\) | ||||
−0.923883 | + | 0.382675i | \(0.875003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.5774 | + | 0.435713i | −0.999655 | + | 0.0262745i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.96105 | − | 1.96105i | 0.117828 | − | 0.117828i | −0.645734 | − | 0.763562i | \(-0.723449\pi\) |
0.763562 | + | 0.645734i | \(0.223449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.8559i | 1.18450i | 0.805753 | + | 0.592251i | \(0.201761\pi\) | ||||
−0.805753 | + | 0.592251i | \(0.798239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.47159 | − | 7.47159i | −0.444140 | − | 0.444140i | 0.449261 | − | 0.893401i | \(-0.351687\pi\) |
−0.893401 | + | 0.449261i | \(0.851687\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.3473 | + | 21.3473i | 1.26009 | + | 1.26009i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 25.5710i | − | 1.50418i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.89798 | + | 8.89798i | 0.519826 | + | 0.519826i | 0.917519 | − | 0.397693i | \(-0.130189\pi\) |
−0.397693 | + | 0.917519i | \(0.630189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.21878 | + | 14.6253i | −0.362072 | + | 0.851518i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.75756 | 0.159474 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 40.2398 | 2.31938 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.99651 | + | 4.69538i | −0.114320 | + | 0.268857i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.3561 | + | 13.3561i | −0.762275 | + | 0.762275i | −0.976733 | − | 0.214458i | \(-0.931202\pi\) |
0.214458 | + | 0.976733i | \(0.431202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5350 | 0.824202 | 0.412101 | − | 0.911138i | \(-0.364795\pi\) | ||||
0.412101 | + | 0.911138i | \(0.364795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.2330 | + | 14.2330i | −0.804499 | + | 0.804499i | −0.983795 | − | 0.179296i | \(-0.942618\pi\) |
0.179296 | + | 0.983795i | \(0.442618\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7296 | + | 10.7296i | 0.602634 | + | 0.602634i | 0.941011 | − | 0.338376i | \(-0.109878\pi\) |
−0.338376 | + | 0.941011i | \(0.609878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.13547 | − | 3.43097i | 0.175553 | − | 0.192098i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.76871 | + | 2.76871i | −0.154055 | + | 0.154055i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.417188 | + | 22.3144i | −0.0231414 | + | 1.23778i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 38.1873 | 2.10533 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.1262 | 0.996306 | 0.498153 | − | 0.867089i | \(-0.334012\pi\) | ||||
0.498153 | + | 0.867089i | \(0.334012\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.02340 | + | 5.01704i | 0.110550 | + | 0.274110i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2353 | − | 22.2353i | 1.21123 | − | 1.21123i | 0.240612 | − | 0.970621i | \(-0.422652\pi\) |
0.970621 | − | 0.240612i | \(-0.0773481\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1631 | − | 18.7806i | 0.929433 | − | 1.01703i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.47851 | − | 7.47851i | −0.403802 | − | 0.403802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.4387 | − | 12.4387i | 0.667744 | − | 0.667744i | −0.289450 | − | 0.957193i | \(-0.593472\pi\) |
0.957193 | + | 0.289450i | \(0.0934723\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.30138 | −0.497891 | −0.248946 | − | 0.968517i | \(-0.580084\pi\) | ||||
−0.248946 | + | 0.968517i | \(0.580084\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.79023 | − | 5.79023i | 0.308183 | − | 0.308183i | −0.536022 | − | 0.844204i | \(-0.680073\pi\) |
0.844204 | + | 0.536022i | \(0.180073\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.64653 | − | 1.97574i | −0.246612 | − | 0.104861i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.5247 | −1.66381 | −0.831905 | − | 0.554918i | \(-0.812750\pi\) | ||||
−0.831905 | + | 0.554918i | \(0.812750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6399 | −0.981045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.59543 | + | 3.95590i | 0.0835088 | + | 0.207061i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2922 | + | 16.2922i | 0.850447 | + | 0.850447i | 0.990188 | − | 0.139741i | \(-0.0446270\pi\) |
−0.139741 | + | 0.990188i | \(0.544627\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 17.2867i | − | 0.897480i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.46963 | + | 1.46963i | 0.0760943 | + | 0.0760943i | 0.744130 | − | 0.668035i | \(-0.232864\pi\) |
−0.668035 | + | 0.744130i | \(0.732864\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.42318 | − | 4.42318i | −0.227805 | − | 0.227805i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8638i | 1.07170i | 0.844312 | + | 0.535851i | \(0.180009\pi\) | ||||
−0.844312 | + | 0.535851i | \(0.819991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.8995 | + | 18.8995i | −0.965717 | + | 0.965717i | −0.999432 | − | 0.0337146i | \(-0.989266\pi\) |
0.0337146 | + | 0.999432i | \(0.489266\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.51045 | + | 22.8121i | −0.433733 | + | 1.16261i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 28.1471i | − | 1.42711i | −0.700597 | − | 0.713557i | \(-0.747083\pi\) | ||
0.700597 | − | 0.713557i | \(-0.252917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.03079i | − | 0.203846i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0488 | − | 5.12322i | −0.606239 | − | 0.257777i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.04885 | − | 7.04885i | −0.353772 | − | 0.353772i | 0.507739 | − | 0.861511i | \(-0.330481\pi\) |
−0.861511 | + | 0.507739i | \(0.830481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.1684 | −1.30679 | −0.653394 | − | 0.757018i | \(-0.726656\pi\) | ||||
−0.653394 | + | 0.757018i | \(0.726656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.2118 | − | 24.2118i | −1.20607 | − | 1.20607i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.0064 | + | 0.810318i | −0.892546 | + | 0.0401660i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.7193 | −0.826718 | −0.413359 | − | 0.910568i | \(-0.635645\pi\) | ||||
−0.413359 | + | 0.910568i | \(0.635645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.4996 | + | 16.4996i | 0.811893 | + | 0.811893i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.9099 | + | 34.4898i | 0.682811 | + | 1.69304i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.1843i | 0.595241i | 0.954684 | + | 0.297621i | \(0.0961931\pi\) | ||||
−0.954684 | + | 0.297621i | \(0.903807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.6783 | −1.44643 | −0.723215 | − | 0.690622i | \(-0.757337\pi\) | ||||
−0.723215 | + | 0.690622i | \(0.757337\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.6175 | + | 0.609815i | 1.58218 | + | 0.0295804i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.29712 | + | 5.29712i | 0.256346 | + | 0.256346i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.1186i | 1.35443i | 0.735787 | + | 0.677213i | \(0.236812\pi\) | ||||
−0.735787 | + | 0.677213i | \(0.763188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.8525 | − | 12.8525i | 0.617652 | − | 0.617652i | −0.327276 | − | 0.944929i | \(-0.606131\pi\) |
0.944929 | + | 0.327276i | \(0.106131\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.262152 | + | 0.262152i | −0.0125405 | + | 0.0125405i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.9331 | 1.04681 | 0.523405 | − | 0.852084i | \(-0.324661\pi\) | ||||
0.523405 | + | 0.852084i | \(0.324661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.2383 | + | 10.2383i | −0.486438 | + | 0.486438i | −0.907180 | − | 0.420742i | \(-0.861770\pi\) |
0.420742 | + | 0.907180i | \(0.361770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.73865 | − | 11.1443i | 0.224633 | − | 0.528292i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.1824i | − | 0.810887i | −0.914120 | − | 0.405444i | \(-0.867117\pi\) | ||
0.914120 | − | 0.405444i | \(-0.132883\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5132 | + | 20.5742i | 1.06010 | + | 0.968800i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30.1556 | + | 12.8224i | 1.41372 | + | 0.601123i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.2020 | + | 15.2020i | −0.711121 | + | 0.711121i | −0.966770 | − | 0.255649i | \(-0.917711\pi\) |
0.255649 | + | 0.966770i | \(0.417711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.6990i | 1.61609i | 0.589118 | + | 0.808047i | \(0.299475\pi\) | ||||
−0.589118 | + | 0.808047i | \(0.700525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.09179 | + | 9.09179i | −0.422531 | + | 0.422531i | −0.886074 | − | 0.463543i | \(-0.846578\pi\) |
0.463543 | + | 0.886074i | \(0.346578\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.17044 | − | 6.17044i | −0.285534 | − | 0.285534i | 0.549777 | − | 0.835311i | \(-0.314713\pi\) |
−0.835311 | + | 0.549777i | \(0.814713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.94270 | 0.366760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.6099 | − | 1.82751i | 1.86725 | − | 0.0840290i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.08170 | − | 2.16102i | −0.0955151 | − | 0.0991546i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.7249 | −1.49524 | −0.747620 | − | 0.664126i | \(-0.768804\pi\) | ||||
−0.747620 | + | 0.664126i | \(0.768804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.2584i | 1.10609i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.5692 | + | 36.1246i | 0.661556 | + | 1.64034i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.6586 | − | 15.6586i | −0.709561 | − | 0.709561i | 0.256882 | − | 0.966443i | \(-0.417305\pi\) |
−0.966443 | + | 0.256882i | \(0.917305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.91600i | 0.266985i | 0.991050 | + | 0.133493i | \(0.0426193\pi\) | ||||
−0.991050 | + | 0.133493i | \(0.957381\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.46547 | + | 6.46547i | −0.291190 | + | 0.291190i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.24201 | + | 5.24201i | −0.235136 | + | 0.235136i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.66957i | 0.209039i | 0.994523 | + | 0.104519i | \(0.0333304\pi\) | ||||
−0.994523 | + | 0.104519i | \(0.966670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.5379 | + | 17.5379i | 0.781976 | + | 0.781976i | 0.980164 | − | 0.198188i | \(-0.0635057\pi\) |
−0.198188 | + | 0.980164i | \(0.563506\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0903 | − | 28.4338i | 0.538010 | − | 1.26529i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.3977i | 0.859786i | 0.902880 | + | 0.429893i | \(0.141449\pi\) | ||||
−0.902880 | + | 0.429893i | \(0.858551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.26276 | 0.277048 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.5622 | − | 4.25978i | 0.465426 | − | 0.187708i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.5386 | − | 1.73430i | 1.69492 | − | 0.0762742i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.47145 | −0.152087 | −0.0760434 | − | 0.997105i | \(-0.524229\pi\) | ||||
−0.0760434 | + | 0.997105i | \(0.524229\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.636153 | − | 0.636153i | −0.0278170 | − | 0.0278170i | 0.693061 | − | 0.720879i | \(-0.256261\pi\) |
−0.720879 | + | 0.693061i | \(0.756261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.3910 | + | 35.3910i | −1.54166 | + | 1.54166i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6183i | 0.983407i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.0238 | − | 29.0238i | 1.25716 | − | 1.25716i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9486 | − | 4.41563i | 0.473350 | − | 0.190904i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.25093 | + | 8.45417i | 0.398466 | + | 0.364147i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.74032i | 0.289789i | 0.989447 | + | 0.144894i | \(0.0462843\pi\) | ||||
−0.989447 | + | 0.144894i | \(0.953716\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40.3641 | − | 17.1631i | −1.72901 | − | 0.735185i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.2901 | + | 10.2901i | −0.439972 | + | 0.439972i | −0.892003 | − | 0.452030i | \(-0.850700\pi\) |
0.452030 | + | 0.892003i | \(0.350700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.840997 | 0.0358277 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.5929 | + | 13.5929i | −0.578028 | + | 0.578028i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.23038 | + | 1.23038i | −0.0521327 | + | 0.0521327i | −0.732693 | − | 0.680560i | \(-0.761737\pi\) |
0.680560 | + | 0.732693i | \(0.261737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 54.7100i | − | 2.31399i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.38234 | − | 9.38234i | −0.395418 | − | 0.395418i | 0.481195 | − | 0.876614i | \(-0.340203\pi\) |
−0.876614 | + | 0.481195i | \(0.840203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.3625 | − | 11.8420i | 1.23529 | − | 0.498199i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.2820 | 1.05988 | 0.529938 | − | 0.848036i | \(-0.322215\pi\) | ||||
0.529938 | + | 0.848036i | \(0.322215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9231i | 0.917455i | 0.888577 | + | 0.458727i | \(0.151695\pi\) | ||||
−0.888577 | + | 0.458727i | \(0.848305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.08835 | + | 0.0577396i | 0.128793 | + | 0.00240791i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.1377 | − | 29.1377i | −1.21302 | − | 1.21302i | −0.970028 | − | 0.242992i | \(-0.921871\pi\) |
−0.242992 | − | 0.970028i | \(-0.578129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 54.6024 | 2.26529 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.785083 | − | 17.4457i | −0.0325148 | − | 0.722527i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.93109 | + | 7.93109i | 0.327351 | + | 0.327351i | 0.851578 | − | 0.524227i | \(-0.175646\pi\) |
−0.524227 | + | 0.851578i | \(0.675646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.60348 | 0.189683 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.8447 | − | 14.8447i | −0.609599 | − | 0.609599i | 0.333242 | − | 0.942841i | \(-0.391857\pi\) |
−0.942841 | + | 0.333242i | \(0.891857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.7428 | − | 44.0793i | 0.768380 | − | 1.80707i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0318i | 0.695899i | 0.937513 | + | 0.347949i | \(0.113122\pi\) | ||||
−0.937513 | + | 0.347949i | \(0.886878\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.44422i | 0.303656i | 0.988407 | + | 0.151828i | \(0.0485160\pi\) | ||||
−0.988407 | + | 0.151828i | \(0.951484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.55271 | + | 23.4085i | −0.307061 | + | 0.951690i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00814 | + | 4.00814i | −0.162686 | + | 0.162686i | −0.783755 | − | 0.621070i | \(-0.786698\pi\) |
0.621070 | + | 0.783755i | \(0.286698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 51.9194i | − | 2.10044i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.90502 | + | 4.90502i | 0.198112 | + | 0.198112i | 0.799190 | − | 0.601078i | \(-0.205262\pi\) |
−0.601078 | + | 0.799190i | \(0.705262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7436 | + | 11.7436i | 0.472779 | + | 0.472779i | 0.902813 | − | 0.430034i | \(-0.141498\pi\) |
−0.430034 | + | 0.902813i | \(0.641498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.9601i | − | 0.762070i | −0.924561 | − | 0.381035i | \(-0.875568\pi\) | ||
0.924561 | − | 0.381035i | \(-0.124432\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.5725 | − | 12.5725i | −0.503708 | − | 0.503708i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.934469 | + | 24.9825i | −0.0373788 | + | 0.999301i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.4591 | 1.41385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0398 | 0.678345 | 0.339173 | − | 0.940724i | \(-0.389853\pi\) | ||||
0.339173 | + | 0.940724i | \(0.389853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.1776 | + | 10.9609i | −1.07851 | + | 0.434969i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.9262 | − | 11.9262i | 0.472534 | − | 0.472534i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.30146 | −0.367386 | −0.183693 | − | 0.982984i | \(-0.558805\pi\) | ||||
−0.183693 | + | 0.982984i | \(0.558805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.5501 | + | 24.5501i | −0.968163 | + | 0.968163i | −0.999509 | − | 0.0313460i | \(-0.990021\pi\) |
0.0313460 | + | 0.999509i | \(0.490021\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.9876 | + | 17.9876i | 0.707167 | + | 0.707167i | 0.965939 | − | 0.258771i | \(-0.0833176\pi\) |
−0.258771 | + | 0.965939i | \(0.583318\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.4007 | + | 15.9020i | 0.683038 | + | 0.624210i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.7279 | + | 17.7279i | −0.693746 | + | 0.693746i | −0.963054 | − | 0.269308i | \(-0.913205\pi\) |
0.269308 | + | 0.963054i | \(0.413205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.31990 | − | 7.80773i | 0.129719 | − | 0.305073i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.2994 | 1.10239 | 0.551194 | − | 0.834377i | \(-0.314173\pi\) | ||||
0.551194 | + | 0.834377i | \(0.314173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 51.1753 | 1.99049 | 0.995245 | − | 0.0974080i | \(-0.0310552\pi\) | ||||
0.995245 | + | 0.0974080i | \(0.0310552\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.08579 | + | 1.64782i | −0.158440 | + | 0.0638997i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.612176 | + | 0.612176i | −0.0237035 | + | 0.0237035i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.58642 | + | 5.10527i | 0.215661 | + | 0.197087i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.4918 | − | 31.4918i | −1.21392 | − | 1.21392i | −0.969726 | − | 0.244195i | \(-0.921476\pi\) |
−0.244195 | − | 0.969726i | \(-0.578524\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.01767 | + | 9.01767i | −0.346577 | + | 0.346577i | −0.858833 | − | 0.512256i | \(-0.828810\pi\) |
0.512256 | + | 0.858833i | \(0.328810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 57.1906 | 2.19477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.6006 | − | 25.6006i | 0.979581 | − | 0.979581i | −0.0202143 | − | 0.999796i | \(-0.506435\pi\) |
0.999796 | + | 0.0202143i | \(0.00643486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.80979 | − | 4.48739i | −0.0691484 | − | 0.171454i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.5030 | −0.895391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4669 | 0.588390 | 0.294195 | − | 0.955745i | \(-0.404949\pi\) | ||||
0.294195 | + | 0.955745i | \(0.404949\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.5178 | − | 12.5512i | −1.11968 | − | 0.476094i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.4248 | − | 42.4248i | −1.60695 | − | 1.60695i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.7833i | 1.88029i | 0.340775 | + | 0.940145i | \(0.389311\pi\) | ||||
−0.340775 | + | 0.940145i | \(0.610689\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.30617 | − | 2.30617i | −0.0869790 | − | 0.0869790i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.0778 | − | 32.0778i | −1.20641 | − | 1.20641i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.7982i | 1.56976i | 0.619645 | + | 0.784882i | \(0.287277\pi\) | ||||
−0.619645 | + | 0.784882i | \(0.712723\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.35095 | + | 3.35095i | −0.125494 | + | 0.125494i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.0154 | + | 11.5708i | 1.15991 | + | 0.432723i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0.000382835i | 0 | 1.42773e-5i | 1.00000 | 7.13867e-6i | \(2.27231e-6\pi\) | |||
−1.00000 | 7.13867e-6i | \(0.999998\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.7215i | − | 0.622741i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.86117 | − | 5.04640i | −0.180539 | − | 0.187419i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.03870 | + | 4.03870i | 0.149787 | + | 0.149787i | 0.778023 | − | 0.628236i | \(-0.216223\pi\) |
−0.628236 | + | 0.778023i | \(0.716223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −79.9710 | −2.95783 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.45805 | − | 8.45805i | −0.312405 | − | 0.312405i | 0.533436 | − | 0.845841i | \(-0.320901\pi\) |
−0.845841 | + | 0.533436i | \(0.820901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.01576 | − | 0.360722i | 0.295264 | − | 0.0132874i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.8229 | 1.64884 | 0.824418 | − | 0.565982i | \(-0.191503\pi\) | ||||
0.824418 | + | 0.565982i | \(0.191503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.44418 | + | 7.44418i | 0.273100 | + | 0.273100i | 0.830347 | − | 0.557247i | \(-0.188142\pi\) |
−0.557247 | + | 0.830347i | \(0.688142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.15194 | − | 2.19064i | −0.188752 | − | 0.0802589i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 17.3332i | − | 0.633343i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.0581 | −1.24280 | −0.621398 | − | 0.783495i | \(-0.713435\pi\) | ||||
−0.621398 | + | 0.783495i | \(0.713435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.1784 | + | 35.6966i | −0.552400 | + | 1.29913i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.8456 | − | 31.8456i | −1.15745 | − | 1.15745i | −0.985023 | − | 0.172423i | \(-0.944840\pi\) |
−0.172423 | − | 0.985023i | \(-0.555160\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.1288i | − | 0.548418i | −0.961670 | − | 0.274209i | \(-0.911584\pi\) | ||
0.961670 | − | 0.274209i | \(-0.0884161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −45.5369 | + | 45.5369i | −1.64855 | + | 1.64855i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.4329 | − | 22.4329i | 0.810004 | − | 0.810004i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.2742 | −0.911411 | −0.455706 | − | 0.890131i | \(-0.650613\pi\) | ||||
−0.455706 | + | 0.890131i | \(0.650613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.4697 | + | 14.4697i | −0.520438 | + | 0.520438i | −0.917704 | − | 0.397266i | \(-0.869959\pi\) |
0.397266 | + | 0.917704i | \(0.369959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.6093 | − | 27.6232i | −0.955834 | − | 0.992255i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.51840i | 0.197717i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.05216 | + | 5.52830i | −0.180780 | + | 0.197818i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.1409 | + | 25.1445i | 0.361945 | + | 0.897447i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.6583 | − | 28.6583i | 1.02156 | − | 1.02156i | 0.0217962 | − | 0.999762i | \(-0.493062\pi\) |
0.999762 | − | 0.0217962i | \(-0.00693849\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 46.4851i | − | 1.65282i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.20196 | − | 7.20196i | 0.255749 | − | 0.255749i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.21628 | + | 6.21628i | 0.220192 | + | 0.220192i | 0.808579 | − | 0.588387i | \(-0.200237\pi\) |
−0.588387 | + | 0.808579i | \(0.700237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75.8920 | −2.68486 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.32037 | − | 0.284426i | 0.223041 | − | 0.0100372i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.77464 | − | 4.17359i | 0.0625478 | − | 0.147100i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.8786 | 1.29658 | 0.648292 | − | 0.761392i | \(-0.275484\pi\) | ||||
0.648292 | + | 0.761392i | \(0.275484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.94183i | − | 0.173531i | −0.996229 | − | 0.0867656i | \(-0.972347\pi\) | ||
0.996229 | − | 0.0867656i | \(-0.0276531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.5432 | + | 7.47857i | −0.649541 | + | 0.261963i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.20111 | + | 5.20111i | 0.181964 | + | 0.181964i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 22.1356i | − | 0.772537i | −0.922386 | − | 0.386269i | \(-0.873764\pi\) | ||
0.922386 | − | 0.386269i | \(-0.126236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.7373 | − | 10.7373i | 0.374280 | − | 0.374280i | −0.494753 | − | 0.869033i | \(-0.664742\pi\) |
0.869033 | + | 0.494753i | \(0.164742\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.30961 | + | 2.30961i | −0.0803129 | + | 0.0803129i | −0.746122 | − | 0.665809i | \(-0.768086\pi\) |
0.665809 | + | 0.746122i | \(0.268086\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.61750i | − | 0.160372i | −0.996780 | − | 0.0801862i | \(-0.974449\pi\) | ||
0.996780 | − | 0.0801862i | \(-0.0255515\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.4329 | − | 17.4329i | −0.604013 | − | 0.604013i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.4181 | + | 5.00830i | −0.429747 | + | 0.173319i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 27.3332i | − | 0.943647i | −0.881693 | − | 0.471824i | \(-0.843596\pi\) | ||
0.881693 | − | 0.471824i | \(-0.156404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0361 | −0.932280 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.05859 | − | 14.2486i | 0.208422 | − | 0.490166i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7268 | + | 23.1394i | 0.952704 | + | 0.795079i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.35741 | 0.115090 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.8254 | − | 27.8254i | −0.952723 | − | 0.952723i | 0.0462088 | − | 0.998932i | \(-0.485286\pi\) |
−0.998932 | + | 0.0462088i | \(0.985286\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.1653 | − | 21.1653i | 0.722994 | − | 0.722994i | −0.246220 | − | 0.969214i | \(-0.579189\pi\) |
0.969214 | + | 0.246220i | \(0.0791886\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1745i | 0.858944i | 0.903080 | + | 0.429472i | \(0.141300\pi\) | ||||
−0.903080 | + | 0.429472i | \(0.858700\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.6570 | + | 13.6570i | −0.464891 | + | 0.464891i | −0.900255 | − | 0.435364i | \(-0.856620\pi\) |
0.435364 | + | 0.900255i | \(0.356620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.62667 | − | 6.51287i | −0.0893095 | − | 0.221444i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.1006 | + | 14.3352i | −0.444407 | + | 0.486290i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.7989i | − | 0.365906i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.5046 | + | 14.9920i | 1.13266 | + | 0.506822i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.0523 | + | 21.0523i | −0.710885 | + | 0.710885i | −0.966720 | − | 0.255835i | \(-0.917650\pi\) |
0.255835 | + | 0.966720i | \(0.417650\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.1627 | −1.65633 | −0.828167 | − | 0.560481i | \(-0.810616\pi\) | ||||
−0.828167 | + | 0.560481i | \(0.810616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0264 | + | 16.0264i | −0.539331 | + | 0.539331i | −0.923332 | − | 0.384002i | \(-0.874546\pi\) |
0.384002 | + | 0.923332i | \(0.374546\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.8705 | − | 23.8705i | 0.801492 | − | 0.801492i | −0.181837 | − | 0.983329i | \(-0.558204\pi\) |
0.983329 | + | 0.181837i | \(0.0582043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.0261i | 1.44305i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.93582 | + | 4.93582i | 0.165171 | + | 0.165171i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.76838 | + | 11.2142i | −0.159389 | + | 0.374851i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.7500 | 0.358533 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.3549i | 1.14453i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.2528 | − | 8.18642i | −0.639984 | − | 0.272126i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.1178 | − | 21.1178i | −0.701206 | − | 0.701206i | 0.263463 | − | 0.964669i | \(-0.415135\pi\) |
−0.964669 | + | 0.263463i | \(0.915135\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.22816 | −0.0406908 | −0.0203454 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203454 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.1047 | − | 2.47980i | 1.82370 | − | 0.0820693i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.80833 | − | 8.80833i | −0.290877 | − | 0.290877i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8532 | 0.489963 | 0.244982 | − | 0.969528i | \(-0.421218\pi\) | ||||
0.244982 | + | 0.969528i | \(0.421218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.12703 | + | 7.12703i | 0.234589 | + | 0.234589i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.507939 | + | 27.1685i | −0.0167009 | + | 0.893293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 33.9859i | − | 1.11504i | −0.830163 | − | 0.557520i | \(-0.811753\pi\) | ||
0.830163 | − | 0.557520i | \(-0.188247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.26758i | 0.0743169i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.9133 | − | 45.3359i | 0.553125 | − | 1.48264i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8274 | − | 23.8274i | 0.778406 | − | 0.778406i | −0.201153 | − | 0.979560i | \(-0.564469\pi\) |
0.979560 | + | 0.201153i | \(0.0644690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.3719i | − | 0.403313i | −0.979456 | − | 0.201656i | \(-0.935368\pi\) | ||
0.979456 | − | 0.201656i | \(-0.0646324\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.01694 | − | 4.01694i | −0.130810 | − | 0.130810i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.94411 | − | 4.94411i | −0.160662 | − | 0.160662i | 0.622198 | − | 0.782860i | \(-0.286240\pi\) |
−0.782860 | + | 0.622198i | \(0.786240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 8.51485i | − | 0.276404i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.7717 | − | 23.7717i | −0.770041 | − | 0.770041i | 0.208073 | − | 0.978113i | \(-0.433281\pi\) |
−0.978113 | + | 0.208073i | \(0.933281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.32347 | + | 3.11399i | 0.236982 | + | 0.100766i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.10419 | −0.229406 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.8438 | 0.898188 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.14191 | − | 17.7085i | −0.229906 | − | 0.570056i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.66496 | + | 8.66496i | −0.278646 | + | 0.278646i | −0.832568 | − | 0.553922i | \(-0.813130\pi\) |
0.553922 | + | 0.832568i | \(0.313130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4796 | −0.400491 | −0.200245 | − | 0.979746i | \(-0.564174\pi\) | ||||
−0.200245 | + | 0.979746i | \(0.564174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.3007 | + | 33.3007i | −1.06757 | + | 1.06757i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.4364 | − | 37.4364i | −1.19770 | − | 1.19770i | −0.974854 | − | 0.222843i | \(-0.928466\pi\) |
−0.222843 | − | 0.974854i | \(-0.571534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.2592 | − | 12.1172i | −0.423765 | − | 0.387267i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.20828 | + | 7.20828i | −0.229908 | + | 0.229908i | −0.812654 | − | 0.582746i | \(-0.801978\pi\) |
0.582746 | + | 0.812654i | \(0.301978\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.66803 | − | 1.07603i | 0.0850104 | − | 0.0342851i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.57196 | −0.240774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.7072 | 1.29311 | 0.646554 | − | 0.762868i | \(-0.276209\pi\) | ||||
0.646554 | + | 0.762868i | \(0.276209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.1301 | + | 56.7491i | −0.764976 | + | 1.79907i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.59413 | − | 2.59413i | 0.0821571 | − | 0.0821571i | −0.664834 | − | 0.746991i | \(-0.731498\pi\) |
0.746991 | + | 0.664834i | \(0.231498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1980.2.y.c.1297.1 | 24 | ||
3.2 | odd | 2 | 660.2.x.a.637.5 | yes | 24 | ||
5.3 | odd | 4 | inner | 1980.2.y.c.1693.2 | 24 | ||
11.10 | odd | 2 | inner | 1980.2.y.c.1297.2 | 24 | ||
15.2 | even | 4 | 3300.2.x.c.1693.7 | 24 | |||
15.8 | even | 4 | 660.2.x.a.373.6 | yes | 24 | ||
15.14 | odd | 2 | 3300.2.x.c.1957.8 | 24 | |||
33.32 | even | 2 | 660.2.x.a.637.6 | yes | 24 | ||
55.43 | even | 4 | inner | 1980.2.y.c.1693.1 | 24 | ||
165.32 | odd | 4 | 3300.2.x.c.1693.8 | 24 | |||
165.98 | odd | 4 | 660.2.x.a.373.5 | ✓ | 24 | ||
165.164 | even | 2 | 3300.2.x.c.1957.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
660.2.x.a.373.5 | ✓ | 24 | 165.98 | odd | 4 | ||
660.2.x.a.373.6 | yes | 24 | 15.8 | even | 4 | ||
660.2.x.a.637.5 | yes | 24 | 3.2 | odd | 2 | ||
660.2.x.a.637.6 | yes | 24 | 33.32 | even | 2 | ||
1980.2.y.c.1297.1 | 24 | 1.1 | even | 1 | trivial | ||
1980.2.y.c.1297.2 | 24 | 11.10 | odd | 2 | inner | ||
1980.2.y.c.1693.1 | 24 | 55.43 | even | 4 | inner | ||
1980.2.y.c.1693.2 | 24 | 5.3 | odd | 4 | inner | ||
3300.2.x.c.1693.7 | 24 | 15.2 | even | 4 | |||
3300.2.x.c.1693.8 | 24 | 165.32 | odd | 4 | |||
3300.2.x.c.1957.7 | 24 | 165.164 | even | 2 | |||
3300.2.x.c.1957.8 | 24 | 15.14 | odd | 2 |