Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(657,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, 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("1400.657");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.x (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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 993.6 | ||
Character | \(\chi\) | \(=\) | 1400.993 |
Dual form | 1400.2.x.b.657.6 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.0703127 | + | 0.0703127i | −0.0405951 | + | 0.0405951i | −0.727113 | − | 0.686518i | \(-0.759138\pi\) |
0.686518 | + | 0.727113i | \(0.259138\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.562657 | − | 2.58523i | 0.212664 | − | 0.977125i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.99011i | 0.996704i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.777018 | 0.234280 | 0.117140 | − | 0.993115i | \(-0.462627\pi\) | ||||
0.117140 | + | 0.993115i | \(0.462627\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.93876 | + | 3.93876i | −1.09241 | + | 1.09241i | −0.0971446 | + | 0.995270i | \(0.530971\pi\) |
−0.995270 | + | 0.0971446i | \(0.969029\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.982018 | + | 0.982018i | 0.238174 | + | 0.238174i | 0.816094 | − | 0.577920i | \(-0.196135\pi\) |
−0.577920 | + | 0.816094i | \(0.696135\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.14872 | 0.263534 | 0.131767 | − | 0.991281i | \(-0.457935\pi\) | ||||
0.131767 | + | 0.991281i | \(0.457935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.142213 | + | 0.221337i | 0.0310333 | + | 0.0482996i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46167 | + | 1.46167i | 0.304780 | + | 0.304780i | 0.842881 | − | 0.538101i | \(-0.180858\pi\) |
−0.538101 | + | 0.842881i | \(0.680858\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.421181 | − | 0.421181i | −0.0810563 | − | 0.0810563i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.69033i | 0.870973i | 0.900195 | + | 0.435486i | \(0.143424\pi\) | ||||
−0.900195 | + | 0.435486i | \(0.856576\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.45186i | 1.15879i | 0.815048 | + | 0.579394i | \(0.196711\pi\) | ||||
−0.815048 | + | 0.579394i | \(0.803289\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0546342 | + | 0.0546342i | −0.00951060 | + | 0.00951060i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.30390 | − | 1.30390i | 0.214359 | − | 0.214359i | −0.591757 | − | 0.806116i | \(-0.701565\pi\) |
0.806116 | + | 0.591757i | \(0.201565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.553890i | − | 0.0886933i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.81800i | − | 1.53331i | −0.642057 | − | 0.766657i | \(-0.721919\pi\) | ||
0.642057 | − | 0.766657i | \(-0.278081\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.13800 | + | 7.13800i | 1.08853 | + | 1.08853i | 0.995680 | + | 0.0928552i | \(0.0295994\pi\) |
0.0928552 | + | 0.995680i | \(0.470401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.34914 | + | 7.34914i | 1.07198 | + | 1.07198i | 0.997200 | + | 0.0747825i | \(0.0238263\pi\) |
0.0747825 | + | 0.997200i | \(0.476174\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.36683 | − | 2.90920i | −0.909548 | − | 0.415600i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.138097 | −0.0193374 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.08092 | + | 2.08092i | 0.285836 | + | 0.285836i | 0.835431 | − | 0.549595i | \(-0.185218\pi\) |
−0.549595 | + | 0.835431i | \(0.685218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0807696 | + | 0.0807696i | −0.0106982 | + | 0.0106982i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.29508 | −1.07993 | −0.539964 | − | 0.841688i | \(-0.681562\pi\) | ||||
−0.539964 | + | 0.841688i | \(0.681562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.88837i | 0.753929i | 0.926228 | + | 0.376965i | \(0.123032\pi\) | ||||
−0.926228 | + | 0.376965i | \(0.876968\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.73013 | + | 1.68241i | 0.973905 | + | 0.211963i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.30957 | − | 6.30957i | 0.770837 | − | 0.770837i | −0.207416 | − | 0.978253i | \(-0.566505\pi\) |
0.978253 | + | 0.207416i | \(0.0665053\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.205548 | −0.0247451 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3373 | 1.46417 | 0.732084 | − | 0.681214i | \(-0.238548\pi\) | ||||
0.732084 | + | 0.681214i | \(0.238548\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.23861 | − | 7.23861i | 0.847216 | − | 0.847216i | −0.142569 | − | 0.989785i | \(-0.545536\pi\) |
0.989785 | + | 0.142569i | \(0.0455364\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.437195 | − | 2.00877i | 0.0498229 | − | 0.228921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.83831i | 0.319335i | 0.987171 | + | 0.159668i | \(0.0510423\pi\) | ||||
−0.987171 | + | 0.159668i | \(0.948958\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.91111 | −0.990123 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4188 | + | 10.4188i | −1.14361 | + | 1.14361i | −0.155823 | + | 0.987785i | \(0.549803\pi\) |
−0.987785 | + | 0.155823i | \(0.950197\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.329790 | − | 0.329790i | −0.0353572 | − | 0.0353572i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.41911 | −0.362425 | −0.181213 | − | 0.983444i | \(-0.558002\pi\) | ||||
−0.181213 | + | 0.983444i | \(0.558002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.96643 | + | 12.3988i | 0.835108 | + | 1.29974i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.453647 | − | 0.453647i | −0.0470411 | − | 0.0470411i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50258 | + | 8.50258i | 0.863306 | + | 0.863306i | 0.991721 | − | 0.128414i | \(-0.0409888\pi\) |
−0.128414 | + | 0.991721i | \(0.540989\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.32337i | 0.233507i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.88126i | 0.485703i | 0.970063 | + | 0.242852i | \(0.0780828\pi\) | ||||
−0.970063 | + | 0.242852i | \(0.921917\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0443 | + | 10.0443i | −0.989697 | + | 0.989697i | −0.999947 | − | 0.0102503i | \(-0.996737\pi\) |
0.0102503 | + | 0.999947i | \(0.496737\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.67065 | + | 5.67065i | −0.548203 | + | 0.548203i | −0.925921 | − | 0.377718i | \(-0.876709\pi\) |
0.377718 | + | 0.925921i | \(0.376709\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9012i | 1.13993i | 0.821669 | + | 0.569965i | \(0.193043\pi\) | ||||
−0.821669 | + | 0.569965i | \(0.806957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.183361i | 0.0174039i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.36519 | + | 1.36519i | 0.128427 | + | 0.128427i | 0.768398 | − | 0.639972i | \(-0.221054\pi\) |
−0.639972 | + | 0.768398i | \(0.721054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.7773 | − | 11.7773i | −1.08881 | − | 1.08881i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.09128 | − | 1.98620i | 0.283377 | − | 0.182075i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3962 | −0.945113 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.690330 | + | 0.690330i | 0.0622450 | + | 0.0622450i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.49331 | − | 9.49331i | 0.842395 | − | 0.842395i | −0.146775 | − | 0.989170i | \(-0.546889\pi\) |
0.989170 | + | 0.146775i | \(0.0468894\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00378 | −0.0883783 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.4938i | − | 1.70318i | −0.524206 | − | 0.851592i | \(-0.675638\pi\) | ||
0.524206 | − | 0.851592i | \(-0.324362\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.646335 | − | 2.96971i | 0.0560444 | − | 0.257506i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.77702 | + | 5.77702i | −0.493564 | + | 0.493564i | −0.909427 | − | 0.415863i | \(-0.863479\pi\) |
0.415863 | + | 0.909427i | \(0.363479\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2115 | 1.29023 | 0.645113 | − | 0.764087i | \(-0.276810\pi\) | ||||
0.645113 | + | 0.764087i | \(0.276810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.03348 | −0.0870344 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.06048 | + | 3.06048i | −0.255931 | + | 0.255931i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.652223 | − | 0.243116i | 0.0537944 | − | 0.0200519i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5328i | 1.35442i | 0.735789 | + | 0.677211i | \(0.236812\pi\) | ||||
−0.735789 | + | 0.677211i | \(0.763188\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4421 | 1.01252 | 0.506262 | − | 0.862380i | \(-0.331027\pi\) | ||||
0.506262 | + | 0.862380i | \(0.331027\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.93634 | + | 2.93634i | −0.237389 | + | 0.237389i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.24218 | − | 6.24218i | −0.498180 | − | 0.498180i | 0.412691 | − | 0.910871i | \(-0.364589\pi\) |
−0.910871 | + | 0.412691i | \(0.864589\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.292630 | −0.0232070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.60118 | − | 2.95634i | 0.362624 | − | 0.232992i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.47383 | − | 9.47383i | −0.742048 | − | 0.742048i | 0.230924 | − | 0.972972i | \(-0.425825\pi\) |
−0.972972 | + | 0.230924i | \(0.925825\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.725303 | − | 0.725303i | −0.0561257 | − | 0.0561257i | 0.678487 | − | 0.734613i | \(-0.262636\pi\) |
−0.734613 | + | 0.678487i | \(0.762636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 18.0276i | − | 1.38674i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.43480i | 0.262666i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.12344 | − | 3.12344i | 0.237471 | − | 0.237471i | −0.578331 | − | 0.815802i | \(-0.696296\pi\) |
0.815802 | + | 0.578331i | \(0.196296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.583250 | − | 0.583250i | 0.0438397 | − | 0.0438397i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.18800i | − | 0.686743i | −0.939200 | − | 0.343372i | \(-0.888431\pi\) | ||
0.939200 | − | 0.343372i | \(-0.111569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.51164i | − | 0.706995i | −0.935435 | − | 0.353497i | \(-0.884992\pi\) | ||
0.935435 | − | 0.353497i | \(-0.115008\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.414028 | − | 0.414028i | −0.0306058 | − | 0.0306058i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.763045 | + | 0.763045i | 0.0557994 | + | 0.0557994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32583 | + | 0.851870i | −0.0964400 | + | 0.0619644i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2171 | −1.53522 | −0.767609 | − | 0.640918i | \(-0.778554\pi\) | ||||
−0.767609 | + | 0.640918i | \(0.778554\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.15371 | − | 5.15371i | −0.370972 | − | 0.370972i | 0.496859 | − | 0.867831i | \(-0.334487\pi\) |
−0.867831 | + | 0.496859i | \(0.834487\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.83269 | + | 3.83269i | −0.273068 | + | 0.273068i | −0.830334 | − | 0.557266i | \(-0.811850\pi\) |
0.557266 | + | 0.830334i | \(0.311850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4648 | 0.954496 | 0.477248 | − | 0.878769i | \(-0.341634\pi\) | ||||
0.477248 | + | 0.878769i | \(0.341634\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.887286i | 0.0625844i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.1256 | + | 2.63905i | 0.851049 | + | 0.185225i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.37057 | + | 4.37057i | −0.303775 | + | 0.303775i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.892576 | 0.0617408 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.11050 | 0.558350 | 0.279175 | − | 0.960240i | \(-0.409939\pi\) | ||||
0.279175 | + | 0.960240i | \(0.409939\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.867469 | + | 0.867469i | −0.0594380 | + | 0.0594380i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.6795 | + | 3.63018i | 1.13228 | + | 0.246433i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.01793i | 0.0687855i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.73586 | −0.520370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.5407 | − | 18.5407i | 1.24157 | − | 1.24157i | 0.282226 | − | 0.959348i | \(-0.408927\pi\) |
0.959348 | − | 0.282226i | \(-0.0910727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.84230 | + | 4.84230i | 0.321395 | + | 0.321395i | 0.849302 | − | 0.527907i | \(-0.177023\pi\) |
−0.527907 | + | 0.849302i | \(0.677023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.14288 | 0.273769 | 0.136884 | − | 0.990587i | \(-0.456291\pi\) | ||||
0.136884 | + | 0.990587i | \(0.456291\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.110502 | + | 0.171982i | 0.00727048 | + | 0.0113156i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.7734 | − | 17.7734i | −1.16437 | − | 1.16437i | −0.983508 | − | 0.180864i | \(-0.942110\pi\) |
−0.180864 | − | 0.983508i | \(-0.557890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.199570 | − | 0.199570i | −0.0129634 | − | 0.0129634i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.8714i | − | 1.60880i | −0.594090 | − | 0.804399i | \(-0.702488\pi\) | ||
0.594090 | − | 0.804399i | \(-0.297512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.11385i | − | 0.329412i | −0.986343 | − | 0.164706i | \(-0.947332\pi\) | ||
0.986343 | − | 0.164706i | \(-0.0526676\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.89011 | − | 1.89011i | 0.121250 | − | 0.121250i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.52453 | + | 4.52453i | −0.287889 | + | 0.287889i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.46514i | − | 0.0928497i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4745i | 1.35546i | 0.735311 | + | 0.677729i | \(0.237036\pi\) | ||||
−0.735311 | + | 0.677729i | \(0.762964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.13575 | + | 1.13575i | 0.0714037 | + | 0.0714037i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.08456 | − | 2.08456i | −0.130031 | − | 0.130031i | 0.639096 | − | 0.769127i | \(-0.279309\pi\) |
−0.769127 | + | 0.639096i | \(0.779309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.63723 | − | 4.10452i | −0.163869 | − | 0.255043i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.0246 | −0.868102 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.37087 | − | 6.37087i | −0.392845 | − | 0.392845i | 0.482855 | − | 0.875700i | \(-0.339600\pi\) |
−0.875700 | + | 0.482855i | \(0.839600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.240407 | − | 0.240407i | 0.0147127 | − | 0.0147127i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.57242 | −0.583641 | −0.291820 | − | 0.956473i | \(-0.594261\pi\) | ||||
−0.291820 | + | 0.956473i | \(0.594261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1076i | 0.735486i | 0.929927 | + | 0.367743i | \(0.119869\pi\) | ||||
−0.929927 | + | 0.367743i | \(0.880131\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.43193 | − | 0.311650i | −0.0866645 | − | 0.0188619i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2663 | + | 16.2663i | −0.977345 | + | 0.977345i | −0.999749 | − | 0.0224036i | \(-0.992868\pi\) |
0.0224036 | + | 0.999749i | \(0.492868\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.2918 | −1.15497 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.910882 | −0.0543387 | −0.0271693 | − | 0.999631i | \(-0.508649\pi\) | ||||
−0.0271693 | + | 0.999631i | \(0.508649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5625 | − | 12.5625i | 0.746766 | − | 0.746766i | −0.227105 | − | 0.973870i | \(-0.572926\pi\) |
0.973870 | + | 0.227105i | \(0.0729259\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.3818 | − | 5.52417i | −1.49824 | − | 0.326081i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.0713i | − | 0.886546i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.19568 | −0.0700920 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.48178 | − | 6.48178i | 0.378670 | − | 0.378670i | −0.491952 | − | 0.870622i | \(-0.663717\pi\) |
0.870622 | + | 0.491952i | \(0.163717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.327265 | − | 0.327265i | −0.0189899 | − | 0.0189899i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.5144 | −0.665892 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.4696 | − | 14.4371i | 1.29513 | − | 0.832142i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.343215 | − | 0.343215i | −0.0197172 | − | 0.0197172i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.48970 | − | 8.48970i | −0.484533 | − | 0.484533i | 0.422043 | − | 0.906576i | \(-0.361313\pi\) |
−0.906576 | + | 0.422043i | \(0.861313\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.41249i | − | 0.0803537i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 25.9749i | − | 1.47290i | −0.676490 | − | 0.736452i | \(-0.736500\pi\) | ||
0.676490 | − | 0.736452i | \(-0.263500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3142 | − | 12.3142i | 0.696037 | − | 0.696037i | −0.267516 | − | 0.963553i | \(-0.586203\pi\) |
0.963553 | + | 0.267516i | \(0.0862029\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.4909 | + | 14.4909i | −0.813888 | + | 0.813888i | −0.985214 | − | 0.171327i | \(-0.945195\pi\) |
0.171327 | + | 0.985214i | \(0.445195\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.64447i | 0.204051i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 0.797438i | − | 0.0445086i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.12806 | + | 1.12806i | 0.0627671 | + | 0.0627671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.836807 | − | 0.836807i | −0.0462755 | − | 0.0462755i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 23.1343 | − | 14.8642i | 1.27543 | − | 0.819489i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.4165 | −1.50695 | −0.753474 | − | 0.657477i | \(-0.771624\pi\) | ||||
−0.753474 | + | 0.657477i | \(0.771624\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.89880 | + | 3.89880i | 0.213653 | + | 0.213653i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1698 | − | 11.1698i | 0.608460 | − | 0.608460i | −0.334084 | − | 0.942543i | \(-0.608427\pi\) |
0.942543 | + | 0.334084i | \(0.108427\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.191981 | −0.0104270 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.01321i | 0.271480i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.1033 | + | 14.8229i | −0.599521 | + | 0.800359i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.4376 | − | 11.4376i | 0.614004 | − | 0.614004i | −0.329983 | − | 0.943987i | \(-0.607043\pi\) |
0.943987 | + | 0.329983i | \(0.107043\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1401 | −0.917487 | −0.458744 | − | 0.888569i | \(-0.651700\pi\) | ||||
−0.458744 | + | 0.888569i | \(0.651700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.31786 | 0.177094 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1570 | + | 11.1570i | −0.593826 | + | 0.593826i | −0.938663 | − | 0.344837i | \(-0.887934\pi\) |
0.344837 | + | 0.938663i | \(0.387934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0777011 | + | 0.357012i | −0.00411238 | + | 0.0188951i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.9982i | 1.10824i | 0.832437 | + | 0.554120i | \(0.186945\pi\) | ||||
−0.832437 | + | 0.554120i | \(0.813055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6804 | −0.930550 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.730988 | − | 0.730988i | 0.0383669 | − | 0.0383669i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.32101 | + | 2.32101i | 0.121156 | + | 0.121156i | 0.765085 | − | 0.643929i | \(-0.222697\pi\) |
−0.643929 | + | 0.765085i | \(0.722697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.3569 | 1.52826 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.55049 | − | 4.20880i | 0.340084 | − | 0.218510i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.8674 | − | 25.8674i | −1.33937 | − | 1.33937i | −0.896674 | − | 0.442691i | \(-0.854024\pi\) |
−0.442691 | − | 0.896674i | \(-0.645976\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.4741 | − | 18.4741i | −0.951463 | − | 0.951463i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.1682i | − | 0.676406i | −0.941073 | − | 0.338203i | \(-0.890181\pi\) | ||
0.941073 | − | 0.338203i | \(-0.109819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.33500i | 0.0683942i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.7289 | − | 13.7289i | 0.701514 | − | 0.701514i | −0.263221 | − | 0.964736i | \(-0.584785\pi\) |
0.964736 | + | 0.263221i | \(0.0847849\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.3434 | + | 21.3434i | −1.08495 | + | 1.08495i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4553i | 0.682209i | 0.940025 | + | 0.341104i | \(0.110801\pi\) | ||||
−0.940025 | + | 0.341104i | \(0.889199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.87078i | 0.145181i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.37066 | + | 1.37066i | 0.0691408 | + | 0.0691408i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.78221 | + | 9.78221i | 0.490955 | + | 0.490955i | 0.908607 | − | 0.417652i | \(-0.137147\pi\) |
−0.417652 | + | 0.908607i | \(0.637147\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.163362 | + | 0.254254i | 0.00817835 | + | 0.0127286i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.6960 | −0.534134 | −0.267067 | − | 0.963678i | \(-0.586055\pi\) | ||||
−0.267067 | + | 0.963678i | \(0.586055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.4123 | − | 25.4123i | −1.26588 | − | 1.26588i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.01315 | − | 1.01315i | 0.0502201 | − | 0.0502201i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.2026 | 1.49342 | 0.746712 | − | 0.665148i | \(-0.231631\pi\) | ||||
0.746712 | + | 0.665148i | \(0.231631\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.812396i | − | 0.0400725i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.66729 | + | 21.4447i | −0.229662 | + | 1.05522i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.06957 | + | 1.06957i | −0.0523768 | + | 0.0523768i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.8749 | 1.45948 | 0.729742 | − | 0.683722i | \(-0.239640\pi\) | ||||
0.729742 | + | 0.683722i | \(0.239640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.1836 | 1.71474 | 0.857372 | − | 0.514697i | \(-0.172096\pi\) | ||||
0.857372 | + | 0.514697i | \(0.172096\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.9748 | + | 21.9748i | −1.06845 | + | 1.06845i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.2228 | + | 3.31314i | 0.736683 | + | 0.160334i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 0.430382i | − | 0.0207790i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.9552 | −1.00937 | −0.504687 | − | 0.863302i | \(-0.668392\pi\) | ||||
−0.504687 | + | 0.863302i | \(0.668392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5824 | − | 12.5824i | 0.604670 | − | 0.604670i | −0.336878 | − | 0.941548i | \(-0.609371\pi\) |
0.941548 | + | 0.336878i | \(0.109371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.67905 | + | 1.67905i | 0.0803200 | + | 0.0803200i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.23208 | 0.345168 | 0.172584 | − | 0.984995i | \(-0.444788\pi\) | ||||
0.172584 | + | 0.984995i | \(0.444788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.69882 | − | 19.0375i | 0.414230 | − | 0.906550i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.46509 | − | 3.46509i | −0.164632 | − | 0.164632i | 0.619983 | − | 0.784615i | \(-0.287139\pi\) |
−0.784615 | + | 0.619983i | \(0.787139\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.16247 | − | 1.16247i | −0.0549829 | − | 0.0549829i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.08724i | 0.287274i | 0.989630 | + | 0.143637i | \(0.0458798\pi\) | ||||
−0.989630 | + | 0.143637i | \(0.954120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.62876i | − | 0.359224i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.874838 | + | 0.874838i | −0.0411035 | + | 0.0411035i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.2746 | − | 19.2746i | 0.901630 | − | 0.901630i | −0.0939472 | − | 0.995577i | \(-0.529948\pi\) |
0.995577 | + | 0.0939472i | \(0.0299485\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 0.827214i | − | 0.0386111i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.3964i | 1.41570i | 0.706363 | + | 0.707850i | \(0.250335\pi\) | ||||
−0.706363 | + | 0.707850i | \(0.749665\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.0768 | − | 12.0768i | −0.561259 | − | 0.561259i | 0.368406 | − | 0.929665i | \(-0.379904\pi\) |
−0.929665 | + | 0.368406i | \(0.879904\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.89096 | + | 4.89096i | 0.226327 | + | 0.226327i | 0.811156 | − | 0.584830i | \(-0.198839\pi\) |
−0.584830 | + | 0.811156i | \(0.698839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7616 | − | 19.8618i | −0.589275 | − | 0.917134i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.877809 | 0.0404473 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.54635 | + | 5.54635i | 0.255022 | + | 0.255022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.22217 | + | 6.22217i | −0.284894 | + | 0.284894i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.8349 | 1.04335 | 0.521676 | − | 0.853144i | \(-0.325307\pi\) | ||||
0.521676 | + | 0.853144i | \(0.325307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.2715i | 0.468339i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.115653 | + | 0.531390i | −0.00526241 | + | 0.0241791i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1182 | − | 11.1182i | 0.503812 | − | 0.503812i | −0.408808 | − | 0.912620i | \(-0.634056\pi\) |
0.912620 | + | 0.408808i | \(0.134056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.33226 | 0.0602470 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.45336 | 0.200977 | 0.100489 | − | 0.994938i | \(-0.467959\pi\) | ||||
0.100489 | + | 0.994938i | \(0.467959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.60599 | + | 4.60599i | −0.207443 | + | 0.207443i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.94167 | − | 31.8948i | 0.311376 | − | 1.43068i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.6446i | 1.23754i | 0.785572 | + | 0.618770i | \(0.212369\pi\) | ||||
−0.785572 | + | 0.618770i | \(0.787631\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.101996 | 0.00455685 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9763 | − | 16.9763i | 0.756936 | − | 0.756936i | −0.218828 | − | 0.975764i | \(-0.570223\pi\) |
0.975764 | + | 0.218828i | \(0.0702232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.26757 | + | 1.26757i | 0.0562948 | + | 0.0562948i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.3762 | −1.43505 | −0.717525 | − | 0.696533i | \(-0.754725\pi\) | ||||
−0.717525 | + | 0.696533i | \(0.754725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6406 | − | 22.7863i | −0.647663 | − | 1.00801i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.483819 | − | 0.483819i | −0.0213611 | − | 0.0213611i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.71041 | + | 5.71041i | 0.251144 | + | 0.251144i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.439236i | 0.0192803i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.38603i | 0.192156i | 0.995374 | + | 0.0960778i | \(0.0306297\pi\) | ||||
−0.995374 | + | 0.0960778i | \(0.969370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.73788 | + | 4.73788i | −0.207173 | + | 0.207173i | −0.803065 | − | 0.595892i | \(-0.796799\pi\) |
0.595892 | + | 0.803065i | \(0.296799\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.33583 | + | 6.33583i | −0.275993 | + | 0.275993i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 18.7270i | − | 0.814218i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 24.8032i | − | 1.07637i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.6707 | + | 38.6707i | 1.67502 | + | 1.67502i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.646033 | + | 0.646033i | 0.0278784 | + | 0.0278784i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.94714 | − | 2.26050i | −0.213089 | − | 0.0973665i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.48796 | 0.321933 | 0.160966 | − | 0.986960i | \(-0.448539\pi\) | ||||
0.160966 | + | 0.986960i | \(0.448539\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.668790 | + | 0.668790i | 0.0287005 | + | 0.0287005i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.12562 | + | 1.12562i | −0.0481278 | + | 0.0481278i | −0.730761 | − | 0.682633i | \(-0.760835\pi\) |
0.682633 | + | 0.730761i | \(0.260835\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.6069 | −0.751444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.38788i | 0.229531i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.33770 | + | 1.59700i | 0.312031 | + | 0.0679113i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.9130 | + | 20.9130i | −0.886113 | + | 0.886113i | −0.994147 | − | 0.108034i | \(-0.965544\pi\) |
0.108034 | + | 0.994147i | \(0.465544\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.2297 | −2.37826 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.107304 | −0.00453036 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.94306 | − | 5.94306i | 0.250470 | − | 0.250470i | −0.570693 | − | 0.821163i | \(-0.693325\pi\) |
0.821163 | + | 0.570693i | \(0.193325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.01390 | + | 23.0373i | −0.210564 | + | 0.967474i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.64150i | 0.278426i | 0.990262 | + | 0.139213i | \(0.0444573\pi\) | ||||
−0.990262 | + | 0.139213i | \(0.955543\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4643 | 1.40044 | 0.700218 | − | 0.713929i | \(-0.253086\pi\) | ||||
0.700218 | + | 0.713929i | \(0.253086\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.49183 | − | 1.49183i | 0.0623223 | − | 0.0623223i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.86048 | + | 7.86048i | 0.327236 | + | 0.327236i | 0.851535 | − | 0.524299i | \(-0.175672\pi\) |
−0.524299 | + | 0.851535i | \(0.675672\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.724743 | 0.0301193 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.0727 | + | 32.7971i | 0.874244 | + | 1.36065i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.61691 | + | 1.61691i | 0.0669655 | + | 0.0669655i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.65881 | − | 7.65881i | −0.316113 | − | 0.316113i | 0.531159 | − | 0.847272i | \(-0.321757\pi\) |
−0.847272 | + | 0.531159i | \(0.821757\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.41137i | 0.305380i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 0.538974i | − | 0.0221704i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.24682 | + | 8.24682i | −0.338656 | + | 0.338656i | −0.855861 | − | 0.517205i | \(-0.826972\pi\) |
0.517205 | + | 0.855861i | \(0.326972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.946748 | + | 0.946748i | −0.0387478 | + | 0.0387478i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.72554i | − | 0.0705038i | −0.999378 | − | 0.0352519i | \(-0.988777\pi\) | ||
0.999378 | − | 0.0352519i | \(-0.0112233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.3868i | 1.60662i | 0.595561 | + | 0.803310i | \(0.296930\pi\) | ||||
−0.595561 | + | 0.803310i | \(0.703070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.8663 | + | 18.8663i | 0.768296 | + | 0.768296i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.0555 | − | 13.0555i | −0.529905 | − | 0.529905i | 0.390639 | − | 0.920544i | \(-0.372254\pi\) |
−0.920544 | + | 0.390639i | \(0.872254\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.03814 | + | 0.667024i | −0.0420676 | + | 0.0270292i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −57.8930 | −2.34210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5565 | + | 19.5565i | 0.789878 | + | 0.789878i | 0.981474 | − | 0.191596i | \(-0.0613664\pi\) |
−0.191596 | + | 0.981474i | \(0.561366\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.82431 | − | 4.82431i | 0.194219 | − | 0.194219i | −0.603297 | − | 0.797517i | \(-0.706147\pi\) |
0.797517 | + | 0.603297i | \(0.206147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.5806 | −1.43011 | −0.715053 | − | 0.699070i | \(-0.753598\pi\) | ||||
−0.715053 | + | 0.699070i | \(0.753598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.23126i | − | 0.0494087i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.92379 | + | 8.83919i | −0.0770749 | + | 0.354135i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0627594 | + | 0.0627594i | −0.00250637 | + | 0.00250637i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.56090 | 0.102110 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.6285 | 1.13968 | 0.569841 | − | 0.821755i | \(-0.307005\pi\) | ||||
0.569841 | + | 0.821755i | \(0.307005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.570271 | + | 0.570271i | −0.0226663 | + | 0.0226663i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.5360 | − | 13.6188i | 1.44761 | − | 0.539596i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.8899i | 1.45934i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.9369 | −0.826956 | −0.413478 | − | 0.910514i | \(-0.635686\pi\) | ||||
−0.413478 | + | 0.910514i | \(0.635686\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.5706 | + | 13.5706i | −0.535174 | + | 0.535174i | −0.922108 | − | 0.386934i | \(-0.873534\pi\) |
0.386934 | + | 0.922108i | \(0.373534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.1526 | − | 12.1526i | −0.477768 | − | 0.477768i | 0.426649 | − | 0.904417i | \(-0.359694\pi\) |
−0.904417 | + | 0.426649i | \(0.859694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.44543 | −0.253005 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.42803 | + | 0.917535i | −0.0559690 | + | 0.0359610i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.3014 | + | 16.3014i | 0.637921 | + | 0.637921i | 0.950042 | − | 0.312121i | \(-0.101039\pi\) |
−0.312121 | + | 0.950042i | \(0.601039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.6443 | + | 21.6443i | 0.844423 | + | 0.844423i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.5415i | 0.956001i | 0.878360 | + | 0.478000i | \(0.158638\pi\) | ||||
−0.878360 | + | 0.478000i | \(0.841362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22.1516i | − | 0.861596i | −0.902448 | − | 0.430798i | \(-0.858232\pi\) | ||
0.902448 | − | 0.430798i | \(-0.141768\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.543929 | − | 0.543929i | 0.0211245 | − | 0.0211245i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.85573 | + | 6.85573i | −0.265455 | + | 0.265455i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.60729i | 0.100804i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.57537i | 0.176630i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.43387 | + | 9.43387i | 0.363649 | + | 0.363649i | 0.865154 | − | 0.501505i | \(-0.167220\pi\) |
−0.501505 | + | 0.865154i | \(0.667220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.4956 | + | 10.4956i | 0.403378 | + | 0.403378i | 0.879422 | − | 0.476044i | \(-0.157930\pi\) |
−0.476044 | + | 0.879422i | \(0.657930\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.7652 | − | 17.1971i | 1.02715 | − | 0.659964i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.680951 | −0.0260941 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.11456 | − | 7.11456i | −0.272231 | − | 0.272231i | 0.557767 | − | 0.829998i | \(-0.311658\pi\) |
−0.829998 | + | 0.557767i | \(0.811658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.291297 | + | 0.291297i | −0.0111137 | + | 0.0111137i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.3924 | −0.624502 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.29829i | 0.239598i | 0.992798 | + | 0.119799i | \(0.0382251\pi\) | ||||
−0.992798 | + | 0.119799i | \(0.961775\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.00645 | + | 1.30726i | 0.228166 | + | 0.0496587i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.64145 | − | 9.64145i | 0.365196 | − | 0.365196i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.49939 | 0.0945356 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.1579 | 1.13905 | 0.569523 | − | 0.821975i | \(-0.307128\pi\) | ||||
0.569523 | + | 0.821975i | \(0.307128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.49781 | − | 1.49781i | 0.0564911 | − | 0.0564911i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.6192 | + | 2.74648i | 0.474593 | + | 0.103292i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.75232i | 0.0658099i | 0.999458 | + | 0.0329049i | \(0.0104759\pi\) | ||||
−0.999458 | + | 0.0329049i | \(0.989524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.48688 | −0.318283 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.43050 | + | 9.43050i | −0.353175 | + | 0.353175i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.74878 | + | 1.74878i | 0.0653093 | + | 0.0653093i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.1398 | −0.825675 | −0.412837 | − | 0.910805i | \(-0.635462\pi\) | ||||
−0.412837 | + | 0.910805i | \(0.635462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.3154 | + | 31.6184i | 0.756585 | + | 1.17753i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.359569 | + | 0.359569i | 0.0133725 | + | 0.0133725i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.3804 | + | 36.3804i | 1.34927 | + | 1.34927i | 0.886450 | + | 0.462825i | \(0.153164\pi\) |
0.462825 | + | 0.886450i | \(0.346836\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 26.4675i | − | 0.980279i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0193i | 0.518522i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.3741 | + | 26.3741i | −0.974149 | + | 0.974149i | −0.999674 | − | 0.0255249i | \(-0.991874\pi\) |
0.0255249 | + | 0.999674i | \(0.491874\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.90265 | − | 4.90265i | 0.180591 | − | 0.180591i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.48932i | 0.238714i | 0.992851 | + | 0.119357i | \(0.0380832\pi\) | ||||
−0.992851 | + | 0.119357i | \(0.961917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.636264i | − | 0.0233737i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.68617 | − | 7.68617i | −0.281978 | − | 0.281978i | 0.551919 | − | 0.833897i | \(-0.313896\pi\) |
−0.833897 | + | 0.551919i | \(0.813896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.1533 | − | 31.1533i | −1.13984 | − | 1.13984i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.4693 | + | 17.8506i | 0.419079 | + | 0.652246i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.05149 | −0.0748599 | −0.0374300 | − | 0.999299i | \(-0.511917\pi\) | ||||
−0.0374300 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.50993 | − | 1.50993i | −0.0550249 | − | 0.0550249i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.22246 | − | 4.22246i | 0.153468 | − | 0.153468i | −0.626197 | − | 0.779665i | \(-0.715389\pi\) |
0.779665 | + | 0.626197i | \(0.215389\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.159715 | −0.00579728 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 46.0616i | − | 1.66973i | −0.550453 | − | 0.834866i | \(-0.685545\pi\) | ||
0.550453 | − | 0.834866i | \(-0.314455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.7674 | + | 6.69631i | 1.11385 | + | 0.242423i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.6723 | − | 32.6723i | 1.17973 | − | 1.17973i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.8809 | 1.61845 | 0.809223 | − | 0.587501i | \(-0.199888\pi\) | ||||
0.809223 | + | 0.587501i | \(0.199888\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.293143 | 0.0105573 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.22724 | + | 4.22724i | −0.152043 | + | 0.152043i | −0.779030 | − | 0.626987i | \(-0.784288\pi\) |
0.626987 | + | 0.779030i | \(0.284288\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.474031 | + | 0.103169i | 0.0170058 | + | 0.00370118i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 11.2781i | − | 0.404081i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.58630 | 0.343025 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.97548 | − | 1.97548i | 0.0705978 | − | 0.0705978i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.71942 | + | 2.71942i | 0.0969367 | + | 0.0969367i | 0.753912 | − | 0.656975i | \(-0.228164\pi\) |
−0.656975 | + | 0.753912i | \(0.728164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.895906 | 0.0318951 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.29748 | − | 2.76121i | 0.152801 | − | 0.0981772i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.1929 | − | 23.1929i | −0.823603 | − | 0.823603i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.8991 | − | 28.8991i | −1.02366 | − | 1.02366i | −0.999713 | − | 0.0239445i | \(-0.992377\pi\) |
−0.0239445 | − | 0.999713i | \(-0.507623\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4340i | 0.510637i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10.2235i | − | 0.361231i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.62453 | − | 5.62453i | 0.198485 | − | 0.198485i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.673063 | − | 0.673063i | 0.0236929 | − | 0.0236929i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.7627i | 1.15187i | 0.817494 | + | 0.575937i | \(0.195363\pi\) | ||||
−0.817494 | + | 0.575937i | \(0.804637\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.6348i | − | 0.865045i | −0.901623 | − | 0.432523i | \(-0.857624\pi\) | ||
0.901623 | − | 0.432523i | \(-0.142376\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.851321 | − | 0.851321i | −0.0298571 | − | 0.0298571i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.19956 | + | 8.19956i | 0.286866 | + | 0.286866i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37.0737 | + | 23.8205i | −1.29546 | + | 0.832356i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.5320 | 1.27498 | 0.637488 | − | 0.770460i | \(-0.279974\pi\) | ||||
0.637488 | + | 0.770460i | \(0.279974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6526 | + | 14.6526i | 0.510758 | + | 0.510758i | 0.914759 | − | 0.404001i | \(-0.132381\pi\) |
−0.404001 | + | 0.914759i | \(0.632381\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.1880 | − | 22.1880i | 0.771552 | − | 0.771552i | −0.206826 | − | 0.978378i | \(-0.566313\pi\) |
0.978378 | + | 0.206826i | \(0.0663134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.4490 | 1.61324 | 0.806620 | − | 0.591070i | \(-0.201294\pi\) | ||||
0.806620 | + | 0.591070i | \(0.201294\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2.28745i | − | 0.0793508i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.39546 | − | 9.10922i | −0.117646 | − | 0.315616i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.71740 | − | 2.71740i | 0.0939271 | − | 0.0939271i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.5166 | 0.708312 | 0.354156 | − | 0.935186i | \(-0.384768\pi\) | ||||
0.354156 | + | 0.935186i | \(0.384768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00080 | 0.241407 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.0640466 | − | 0.0640466i | 0.00220588 | − | 0.00220588i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.84952 | + | 26.8767i | −0.200992 | + | 0.923494i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.76661i | 0.0606300i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.81174 | 0.130665 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5496 | + | 17.5496i | −0.600887 | + | 0.600887i | −0.940548 | − | 0.339661i | \(-0.889688\pi\) |
0.339661 | + | 0.940548i | \(0.389688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.1708 | + | 11.1708i | 0.381588 | + | 0.381588i | 0.871674 | − | 0.490086i | \(-0.163035\pi\) |
−0.490086 | + | 0.871674i | \(0.663035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.5442 | 1.45159 | 0.725795 | − | 0.687911i | \(-0.241472\pi\) | ||||
0.725795 | + | 0.687911i | \(0.241472\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.17308 | − | 1.39624i | 0.0740585 | − | 0.0475839i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.66647 | + | 6.66647i | 0.226929 | + | 0.226929i | 0.811409 | − | 0.584479i | \(-0.198701\pi\) |
−0.584479 | + | 0.811409i | \(0.698701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.05970 | + | 1.05970i | 0.0359894 | + | 0.0359894i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.20542i | 0.0748138i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.7038i | 1.68415i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.4237 | + | 25.4237i | −0.860461 | + | 0.860461i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.1080 | − | 24.1080i | 0.814069 | − | 0.814069i | −0.171172 | − | 0.985241i | \(-0.554755\pi\) |
0.985241 | + | 0.171172i | \(0.0547555\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.911503i | 0.0307442i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41.2812i | − | 1.39080i | −0.718623 | − | 0.695399i | \(-0.755227\pi\) | ||
0.718623 | − | 0.695399i | \(-0.244773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.58783 | + | 7.58783i | 0.255351 | + | 0.255351i | 0.823160 | − | 0.567809i | \(-0.192209\pi\) |
−0.567809 | + | 0.823160i | \(0.692209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.2247 | + | 21.2247i | 0.712657 | + | 0.712657i | 0.967090 | − | 0.254433i | \(-0.0818889\pi\) |
−0.254433 | + | 0.967090i | \(0.581889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2009 | − | 29.8839i | −0.643978 | − | 1.00227i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.92409 | −0.231966 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.44210 | + | 8.44210i | 0.282504 | + | 0.282504i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.809606 | − | 0.809606i | 0.0270319 | − | 0.0270319i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.2613 | −1.00927 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.08699i | 0.136157i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.564786 | + | 2.59501i | −0.0187949 | + | 0.0863567i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.69307 | − | 2.69307i | 0.0894219 | − | 0.0894219i | −0.660981 | − | 0.750403i | \(-0.729860\pi\) |
0.750403 | + | 0.660981i | \(0.229860\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.5955 | −0.484103 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.2220 | −1.36575 | −0.682874 | − | 0.730536i | \(-0.739270\pi\) | ||||
−0.682874 | + | 0.730536i | \(0.739270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.09556 | + | 8.09556i | −0.267924 | + | 0.267924i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −50.3960 | − | 10.9683i | −1.66422 | − | 0.362206i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.87087i | − | 0.160675i | −0.996768 | − | 0.0803376i | \(-0.974400\pi\) | ||
0.996768 | − | 0.0803376i | \(-0.0255998\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.19387 | 0.0393393 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.5936 | + | 48.5936i | −1.59948 | + | 1.59948i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.0337 | − | 30.0337i | −0.986435 | − | 0.986435i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.6087 | −0.708957 | −0.354479 | − | 0.935064i | \(-0.615342\pi\) | ||||
−0.354479 | + | 0.935064i | \(0.615342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.31371 | − | 3.34185i | −0.239697 | − | 0.109525i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.82637 | + | 1.82637i | 0.0597926 | + | 0.0597926i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.78051 | + | 5.78051i | 0.188841 | + | 0.188841i | 0.795195 | − | 0.606354i | \(-0.207369\pi\) |
−0.606354 | + | 0.795195i | \(0.707369\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.73168i | 0.0565113i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5016i | 1.15732i | 0.815569 | + | 0.578660i | \(0.196424\pi\) | ||||
−0.815569 | + | 0.578660i | \(0.803576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.3507 | − | 14.3507i | 0.467323 | − | 0.467323i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.6185 | + | 29.6185i | −0.962472 | + | 0.962472i | −0.999321 | − | 0.0368489i | \(-0.988268\pi\) |
0.0368489 | + | 0.999321i | \(0.488268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.0223i | 1.85102i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2.03778i | − | 0.0660797i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.58171 | + | 2.58171i | 0.0836298 | + | 0.0836298i | 0.747684 | − | 0.664054i | \(-0.231166\pi\) |
−0.664054 | + | 0.747684i | \(0.731166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.256253 | − | 0.256253i | −0.00828347 | − | 0.00828347i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.6844 | + | 18.1854i | 0.377310 | + | 0.587237i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.6264 | −0.342788 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.9559 | − | 16.9559i | −0.546396 | − | 0.546396i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8202 | − | 15.8202i | 0.508744 | − | 0.508744i | −0.405397 | − | 0.914141i | \(-0.632867\pi\) |
0.914141 | + | 0.405397i | \(0.132867\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.158634 | −0.00509607 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5709i | 0.852701i | 0.904558 | + | 0.426351i | \(0.140201\pi\) | ||||
−0.904558 | + | 0.426351i | \(0.859799\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.55889 | − | 39.3254i | 0.274385 | − | 1.26071i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.8575 | + | 40.8575i | −1.30715 | + | 1.30715i | −0.383683 | + | 0.923465i | \(0.625344\pi\) |
−0.923465 | + | 0.383683i | \(0.874656\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.65671 | −0.0849089 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35.5860 | −1.13617 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.75434 | − | 4.75434i | 0.151640 | − | 0.151640i | −0.627210 | − | 0.778850i | \(-0.715803\pi\) |
0.778850 | + | 0.627210i | \(0.215803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.581493 | + | 2.67177i | −0.0185091 | + | 0.0850435i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.8668i | 0.663527i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2402 | 0.865312 | 0.432656 | − | 0.901559i | \(-0.357576\pi\) | ||||
0.432656 | + | 0.901559i | \(0.357576\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.92773 | − | 1.92773i | 0.0611747 | − | 0.0611747i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.58513 | + | 6.58513i | 0.208553 | + | 0.208553i | 0.803652 | − | 0.595099i | \(-0.202887\pi\) |
−0.595099 | + | 0.803652i | \(0.702887\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.09835 | −0.0347504 |
(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 | 1400.2.x.b.993.6 | 24 | ||
5.2 | odd | 4 | inner | 1400.2.x.b.657.7 | 24 | ||
5.3 | odd | 4 | 280.2.x.a.97.6 | ✓ | 24 | ||
5.4 | even | 2 | 280.2.x.a.153.7 | yes | 24 | ||
7.6 | odd | 2 | inner | 1400.2.x.b.993.7 | 24 | ||
20.3 | even | 4 | 560.2.bj.d.97.7 | 24 | |||
20.19 | odd | 2 | 560.2.bj.d.433.6 | 24 | |||
35.13 | even | 4 | 280.2.x.a.97.7 | yes | 24 | ||
35.27 | even | 4 | inner | 1400.2.x.b.657.6 | 24 | ||
35.34 | odd | 2 | 280.2.x.a.153.6 | yes | 24 | ||
140.83 | odd | 4 | 560.2.bj.d.97.6 | 24 | |||
140.139 | even | 2 | 560.2.bj.d.433.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.x.a.97.6 | ✓ | 24 | 5.3 | odd | 4 | ||
280.2.x.a.97.7 | yes | 24 | 35.13 | even | 4 | ||
280.2.x.a.153.6 | yes | 24 | 35.34 | odd | 2 | ||
280.2.x.a.153.7 | yes | 24 | 5.4 | even | 2 | ||
560.2.bj.d.97.6 | 24 | 140.83 | odd | 4 | |||
560.2.bj.d.97.7 | 24 | 20.3 | even | 4 | |||
560.2.bj.d.433.6 | 24 | 20.19 | odd | 2 | |||
560.2.bj.d.433.7 | 24 | 140.139 | even | 2 | |||
1400.2.x.b.657.6 | 24 | 35.27 | even | 4 | inner | ||
1400.2.x.b.657.7 | 24 | 5.2 | odd | 4 | inner | ||
1400.2.x.b.993.6 | 24 | 1.1 | even | 1 | trivial | ||
1400.2.x.b.993.7 | 24 | 7.6 | odd | 2 | inner |