Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.6 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.25 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.953985 | − | 2.02235i | −0.426635 | − | 0.904424i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.11769i | 1.93430i | 0.254197 | + | 0.967152i | \(0.418189\pi\) | ||||
−0.254197 | + | 0.967152i | \(0.581811\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.39135 | 1.02253 | 0.511265 | − | 0.859423i | \(-0.329177\pi\) | ||||
0.511265 | + | 0.859423i | \(0.329177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.34341i | 1.48200i | 0.671507 | + | 0.740998i | \(0.265647\pi\) | ||||
−0.671507 | + | 0.740998i | \(0.734353\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.02235 | + | 0.953985i | −0.522169 | + | 0.246318i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.17121i | 0.284060i | 0.989862 | + | 0.142030i | \(0.0453630\pi\) | ||||
−0.989862 | + | 0.142030i | \(0.954637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.64168 | 1.06487 | 0.532437 | − | 0.846469i | \(-0.321276\pi\) | ||||
0.532437 | + | 0.846469i | \(0.321276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.11769 | 1.11677 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.93672i | − | 1.86344i | −0.363184 | − | 0.931718i | \(-0.618310\pi\) | ||
0.363184 | − | 0.931718i | \(-0.381690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.17982 | + | 3.85859i | −0.635965 | + | 0.771718i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.07819 | −1.31439 | −0.657194 | − | 0.753722i | \(-0.728257\pi\) | ||||
−0.657194 | + | 0.753722i | \(0.728257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.13671 | −1.64100 | −0.820501 | − | 0.571646i | \(-0.806305\pi\) | ||||
−0.820501 | + | 0.571646i | \(0.806305\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.39135i | − | 0.590358i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3498 | − | 4.88220i | 1.74943 | − | 0.825243i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.98969i | 0.984699i | 0.870398 | + | 0.492349i | \(0.163862\pi\) | ||||
−0.870398 | + | 0.492349i | \(0.836138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.34341 | 0.855631 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.63052 | 1.03551 | 0.517757 | − | 0.855528i | \(-0.326767\pi\) | ||||
0.517757 | + | 0.855528i | \(0.326767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.21888i | 1.10087i | 0.834878 | + | 0.550434i | \(0.185538\pi\) | ||||
−0.834878 | + | 0.550434i | \(0.814462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.953985 | + | 2.02235i | 0.142212 | + | 0.301475i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.89712i | 0.568453i | 0.958757 | + | 0.284226i | \(0.0917368\pi\) | ||||
−0.958757 | + | 0.284226i | \(0.908263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.1907 | −2.74154 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17121 | 0.164002 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.25245i | − | 0.721480i | −0.932666 | − | 0.360740i | \(-0.882524\pi\) | ||
0.932666 | − | 0.360740i | \(-0.117476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23529 | − | 6.85850i | −0.436247 | − | 0.924800i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.64168i | − | 0.614806i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.4570 | −1.62176 | −0.810880 | − | 0.585212i | \(-0.801011\pi\) | ||||
−0.810880 | + | 0.585212i | \(0.801011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.377182 | −0.0482933 | −0.0241466 | − | 0.999708i | \(-0.507687\pi\) | ||||
−0.0241466 | + | 0.999708i | \(0.507687\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.11769i | − | 0.644768i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.8063 | − | 5.09754i | 1.34035 | − | 0.632272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.93672 | −1.07585 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8496 | −1.28761 | −0.643803 | − | 0.765191i | \(-0.722644\pi\) | ||||
−0.643803 | + | 0.765191i | \(0.722644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.211801i | − | 0.0247894i | −0.999923 | − | 0.0123947i | \(-0.996055\pi\) | ||
0.999923 | − | 0.0123947i | \(-0.00394546\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.85859 | + | 3.17982i | 0.445552 | + | 0.367174i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.3559i | 1.97788i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.440613 | −0.0495729 | −0.0247864 | − | 0.999693i | \(-0.507891\pi\) | ||||
−0.0247864 | + | 0.999693i | \(0.507891\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.58727i | 0.174226i | 0.996198 | + | 0.0871128i | \(0.0277641\pi\) | ||||
−0.996198 | + | 0.0871128i | \(0.972236\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.36860 | − | 1.11732i | 0.256911 | − | 0.121190i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.07819i | 0.758862i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.78310 | 0.825007 | 0.412504 | − | 0.910956i | \(-0.364654\pi\) | ||||
0.412504 | + | 0.910956i | \(0.364654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.3459 | −2.86663 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.13671i | 0.947432i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.42810 | − | 9.38712i | −0.454313 | − | 0.963098i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.8160i | − | 1.50434i | −0.658968 | − | 0.752171i | \(-0.729007\pi\) | ||
0.658968 | − | 0.752171i | \(-0.270993\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.39135 | −0.340843 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4939 | −1.54170 | −0.770848 | − | 0.637019i | \(-0.780167\pi\) | ||||
−0.770848 | + | 0.637019i | \(0.780167\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.78957i | − | 0.176331i | −0.996106 | − | 0.0881657i | \(-0.971899\pi\) | ||
0.996106 | − | 0.0881657i | \(-0.0281005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.88220 | − | 10.3498i | −0.476454 | − | 1.01003i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.98883i | − | 0.385615i | −0.981237 | − | 0.192808i | \(-0.938241\pi\) | ||
0.981237 | − | 0.192808i | \(-0.0617593\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0206283 | −0.00197584 | −0.000987919 | − | 1.00000i | \(-0.500314\pi\) | ||||
−0.000987919 | 1.00000i | \(0.500314\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.98969 | 0.568516 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.317783i | − | 0.0298945i | −0.999888 | − | 0.0149472i | \(-0.995242\pi\) | ||
0.999888 | − | 0.0149472i | \(-0.00475803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.0732 | + | 8.52550i | −1.68534 | + | 0.795007i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.34341i | − | 0.493999i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.99389 | −0.549459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.501230 | 0.0455664 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 6.63052i | − | 0.597854i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8369 | + | 2.74969i | 0.969285 | + | 0.245940i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9048i | 1.85500i | 0.373817 | + | 0.927502i | \(0.378049\pi\) | ||||
−0.373817 | + | 0.927502i | \(0.621951\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.21888 | 0.635587 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.05037 | −0.615993 | −0.307997 | − | 0.951387i | \(-0.599659\pi\) | ||||
−0.307997 | + | 0.951387i | \(0.599659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.7547i | 2.05979i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.02235 | − | 0.953985i | 0.174056 | − | 0.0821060i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4238i | 1.23231i | 0.787625 | + | 0.616155i | \(0.211310\pi\) | ||||
−0.787625 | + | 0.616155i | \(0.788690\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1248 | 1.19805 | 0.599023 | − | 0.800732i | \(-0.295556\pi\) | ||||
0.599023 | + | 0.800732i | \(0.295556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.89712 | 0.328196 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.1214i | 1.51538i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.75249 | + | 14.3146i | 0.560764 | + | 1.18876i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.1907i | 1.58283i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0223 | −1.47644 | −0.738222 | − | 0.674557i | \(-0.764334\pi\) | ||||
−0.738222 | + | 0.674557i | \(0.764334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2180 | 1.07566 | 0.537831 | − | 0.843052i | \(-0.319244\pi\) | ||||
0.537831 | + | 0.843052i | \(0.319244\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.17121i | − | 0.0946867i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.71629 | + | 18.4776i | 0.700109 | + | 1.48416i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1177i | 1.28634i | 0.765725 | + | 0.643168i | \(0.222380\pi\) | ||||
−0.765725 | + | 0.643168i | \(0.777620\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.25245 | −0.416547 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 45.7354 | 3.60445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.80123i | − | 0.376062i | −0.982163 | − | 0.188031i | \(-0.939790\pi\) | ||
0.982163 | − | 0.188031i | \(-0.0602105\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.85850 | + | 3.23529i | −0.533933 | + | 0.251867i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.8545i | − | 0.994709i | −0.867547 | − | 0.497354i | \(-0.834305\pi\) | ||
0.867547 | − | 0.497354i | \(-0.165695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.5521 | −1.19631 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.64168 | −0.354958 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.63200i | − | 0.352165i | −0.984375 | − | 0.176082i | \(-0.943657\pi\) | ||
0.984375 | − | 0.176082i | \(-0.0563425\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.7471 | − | 16.2734i | −1.49274 | − | 1.23015i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.4570i | 0.936324i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.7187 | −1.69808 | −0.849038 | − | 0.528332i | \(-0.822818\pi\) | ||||
−0.849038 | + | 0.528332i | \(0.822818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.3823 | 1.51500 | 0.757502 | − | 0.652833i | \(-0.226420\pi\) | ||||
0.757502 | + | 0.652833i | \(0.226420\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.377182i | 0.0278821i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.1133 | − | 5.71408i | 0.890585 | − | 0.420107i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.97198i | 0.290460i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.11769 | −0.372257 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.4223 | −1.40535 | −0.702676 | − | 0.711510i | \(-0.748012\pi\) | ||||
−0.702676 | + | 0.711510i | \(0.748012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0507i | 1.44328i | 0.692269 | + | 0.721639i | \(0.256611\pi\) | ||||
−0.692269 | + | 0.721639i | \(0.743389\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.09754 | − | 10.8063i | −0.365042 | − | 0.773853i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.6003i | 1.25397i | 0.779032 | + | 0.626985i | \(0.215711\pi\) | ||||
−0.779032 | + | 0.626985i | \(0.784289\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.51874 | 0.178549 | 0.0892745 | − | 0.996007i | \(-0.471545\pi\) | ||||
0.0892745 | + | 0.996007i | \(0.471545\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 36.2240i | − | 2.54243i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.32542 | − | 13.4093i | −0.441787 | − | 0.936543i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.93672i | 0.621145i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.7415 | 1.08887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.9689 | 1.51240 | 0.756200 | − | 0.654340i | \(-0.227054\pi\) | ||||
0.756200 | + | 0.654340i | \(0.227054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.8496i | 0.743400i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.5991 | − | 6.88671i | 0.995652 | − | 0.469669i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 46.7588i | − | 3.17420i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.211801 | −0.0143122 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.25826 | −0.420976 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.79987i | 0.254458i | 0.991873 | + | 0.127229i | \(0.0406083\pi\) | ||||
−0.991873 | + | 0.127229i | \(0.959392\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.17982 | − | 3.85859i | 0.211988 | − | 0.257239i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.5533i | 1.29780i | 0.760874 | + | 0.648900i | \(0.224771\pi\) | ||||
−0.760874 | + | 0.648900i | \(0.775229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.8386 | −1.31097 | −0.655487 | − | 0.755207i | \(-0.727536\pi\) | ||||
−0.655487 | + | 0.755207i | \(0.727536\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.3559 | 1.14193 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.79049i | 0.313835i | 0.987612 | + | 0.156918i | \(0.0501557\pi\) | ||||
−0.987612 | + | 0.156918i | \(0.949844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.88135 | − | 3.71779i | 0.514122 | − | 0.242522i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.440613i | 0.0286209i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2367 | 0.856213 | 0.428107 | − | 0.903728i | \(-0.359181\pi\) | ||||
0.428107 | + | 0.903728i | \(0.359181\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.13638 | 0.330863 | 0.165432 | − | 0.986221i | \(-0.447098\pi\) | ||||
0.165432 | + | 0.986221i | \(0.447098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.3077 | + | 38.8105i | 1.16964 | + | 2.47951i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.8024i | 1.57814i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.58727 | 0.100589 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.95641 | 0.186607 | 0.0933034 | − | 0.995638i | \(-0.470257\pi\) | ||||
0.0933034 | + | 0.995638i | \(0.470257\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 30.3075i | − | 1.90542i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.11732 | − | 2.36860i | −0.0699691 | − | 0.148328i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.23941i | 0.139690i | 0.997558 | + | 0.0698452i | \(0.0222505\pi\) | ||||
−0.997558 | + | 0.0698452i | \(0.977749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.6534 | −1.90471 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.07819 | 0.438129 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.0597i | 1.29860i | 0.760534 | + | 0.649298i | \(0.224937\pi\) | ||||
−0.760534 | + | 0.649298i | \(0.775063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6223 | + | 5.01076i | −0.652524 | + | 0.307809i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 7.78310i | − | 0.476318i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.2211 | 0.928046 | 0.464023 | − | 0.885823i | \(-0.346406\pi\) | ||||
0.464023 | + | 0.885823i | \(0.346406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.3909 | −0.752693 | −0.376346 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376346 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 27.3459i | 1.65505i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.7839 | + | 13.0858i | −0.650293 | + | 0.789104i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 17.4978i | − | 1.05134i | −0.850688 | − | 0.525670i | \(-0.823815\pi\) | ||
0.850688 | − | 0.525670i | \(-0.176185\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.13671 | 0.547000 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.90459 | 0.352238 | 0.176119 | − | 0.984369i | \(-0.443646\pi\) | ||||
0.176119 | + | 0.984369i | \(0.443646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.67030i | 0.455952i | 0.973667 | + | 0.227976i | \(0.0732108\pi\) | ||||
−0.973667 | + | 0.227976i | \(0.926789\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.38712 | + | 4.42810i | −0.556045 | + | 0.262298i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 33.9330i | 2.00300i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6283 | 0.919310 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8160 | −0.868532 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.8099i | − | 0.865201i | −0.901586 | − | 0.432601i | \(-0.857596\pi\) | ||
0.901586 | − | 0.432601i | \(-0.142404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.8838 | + | 25.1924i | 0.691900 | + | 1.46676i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.39135i | 0.196786i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 47.7526 | 2.76160 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.9440 | −2.12942 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.4939i | 0.890099i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.359827 | + | 0.762796i | 0.0206036 | + | 0.0436776i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.3403i | 1.50332i | 0.659550 | + | 0.751661i | \(0.270747\pi\) | ||||
−0.659550 | + | 0.751661i | \(0.729253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.78957 | −0.101805 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.32729 | 0.0752636 | 0.0376318 | − | 0.999292i | \(-0.488019\pi\) | ||||
0.0376318 | + | 0.999292i | \(0.488019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.30479i | − | 0.356368i | −0.983997 | − | 0.178184i | \(-0.942978\pi\) | ||
0.983997 | − | 0.178184i | \(-0.0570222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.3498 | + | 4.88220i | −0.583144 | + | 0.275081i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.17493i | − | 0.515315i | −0.966236 | − | 0.257658i | \(-0.917049\pi\) | ||
0.966236 | − | 0.257658i | \(-0.0829507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.0046 | −1.34400 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.98883 | −0.222635 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.43638i | 0.302489i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.6180 | − | 16.9911i | −1.14368 | − | 0.942497i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0206283i | 0.00114075i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.9442 | −1.09956 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.21379 | 0.396506 | 0.198253 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.98969i | − | 0.328233i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.02235 | + | 0.953985i | −0.110493 | + | 0.0521218i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.48218i | − | 0.189687i | −0.995492 | − | 0.0948433i | \(-0.969765\pi\) | ||
0.995492 | − | 0.0948433i | \(-0.0302350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.317783 | −0.0172596 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.9857 | −1.67797 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 62.3885i | − | 3.36866i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.52550 | + | 18.0732i | 0.458998 | + | 0.973029i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.3361i | 0.715920i | 0.933737 | + | 0.357960i | \(0.116528\pi\) | ||||
−0.933737 | + | 0.357960i | \(0.883472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.8340 | 1.48992 | 0.744960 | − | 0.667109i | \(-0.232469\pi\) | ||||
0.744960 | + | 0.667109i | \(0.232469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.34341 | −0.285210 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.7798i | 1.63824i | 0.573621 | + | 0.819121i | \(0.305538\pi\) | ||||
−0.573621 | + | 0.819121i | \(0.694462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3503 | + | 21.9416i | 0.549338 | + | 1.16454i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.99389i | 0.317230i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.96058 | −0.103475 | −0.0517377 | − | 0.998661i | \(-0.516476\pi\) | ||||
−0.0517377 | + | 0.998661i | \(0.516476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.54520 | 0.133958 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.501230i | − | 0.0263078i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.428336 | + | 0.202055i | −0.0224202 | + | 0.0105760i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7555i | 0.561434i | 0.959791 | + | 0.280717i | \(0.0905723\pi\) | ||||
−0.959791 | + | 0.280717i | \(0.909428\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.63052 | −0.345171 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.8804 | 1.39556 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 33.6408i | − | 1.74186i | −0.491410 | − | 0.870928i | \(-0.663518\pi\) | ||
0.491410 | − | 0.870928i | \(-0.336482\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.74969 | − | 10.8369i | 0.141993 | − | 0.559617i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 37.8217i | − | 1.94792i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1029 | 0.621683 | 0.310842 | − | 0.950462i | \(-0.399389\pi\) | ||||
0.310842 | + | 0.950462i | \(0.399389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.9048 | 1.07099 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.6042i | 0.644047i | 0.946732 | + | 0.322023i | \(0.104363\pi\) | ||||
−0.946732 | + | 0.322023i | \(0.895637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.0997 | − | 16.5572i | 1.78885 | − | 0.843835i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.21888i | − | 0.366956i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.5653 | −0.738489 | −0.369245 | − | 0.929332i | \(-0.620384\pi\) | ||||
−0.369245 | + | 0.929332i | \(0.620384\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4668 | 0.529328 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.05037i | 0.355644i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.420339 | + | 0.891076i | 0.0211495 | + | 0.0448349i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13.0782i | − | 0.656374i | −0.944613 | − | 0.328187i | \(-0.893562\pi\) | ||
0.944613 | − | 0.328187i | \(-0.106438\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.7547 | 1.18922 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.1412 | 0.606302 | 0.303151 | − | 0.952943i | \(-0.401961\pi\) | ||||
0.303151 | + | 0.952943i | \(0.401961\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 48.8212i | − | 2.43196i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.953985 | − | 2.02235i | −0.0474039 | − | 0.100492i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.3131i | 1.00688i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.178641 | −0.00883324 | −0.00441662 | − | 0.999990i | \(-0.501406\pi\) | ||||
−0.00441662 | + | 0.999990i | \(0.501406\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.4238 | 0.711474 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 63.7509i | − | 3.13698i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.21002 | − | 1.51423i | 0.157574 | − | 0.0743308i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 14.1248i | − | 0.691692i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.8431 | −0.920548 | −0.460274 | − | 0.887777i | \(-0.652249\pi\) | ||||
−0.460274 | + | 0.887777i | \(0.652249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.7953 | −1.01350 | −0.506750 | − | 0.862093i | \(-0.669153\pi\) | ||||
−0.506750 | + | 0.862093i | \(0.669153\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.89712i | − | 0.189484i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.51922 | − | 3.72424i | −0.219214 | − | 0.180652i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.93030i | − | 0.0934139i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.1214 | 0.874908 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1277 | −0.536001 | −0.268001 | − | 0.963419i | \(-0.586363\pi\) | ||||
−0.268001 | + | 0.963419i | \(0.586363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.25110i | 0.156238i | 0.996944 | + | 0.0781189i | \(0.0248914\pi\) | ||||
−0.996944 | + | 0.0781189i | \(0.975109\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.3146 | − | 6.75249i | 0.686333 | − | 0.323757i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 41.4814i | − | 1.98432i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.7516 | −1.56315 | −0.781573 | − | 0.623814i | \(-0.785582\pi\) | ||||
−0.781573 | + | 0.623814i | \(0.785582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.1907 | 0.913845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.1112i | 0.622933i | 0.950257 | + | 0.311466i | \(0.100820\pi\) | ||||
−0.950257 | + | 0.311466i | \(0.899180\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.42497 | − | 15.7402i | −0.351977 | − | 0.746156i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0223i | 0.852426i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.3035 | 1.14695 | 0.573475 | − | 0.819223i | \(-0.305595\pi\) | ||||
0.573475 | + | 0.819223i | \(0.305595\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.4864 | 1.05884 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 13.2180i | − | 0.621034i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.0876 | + | 55.3031i | 1.22301 | + | 2.59265i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1710i | 0.475778i | 0.971292 | + | 0.237889i | \(0.0764554\pi\) | ||||
−0.971292 | + | 0.237889i | \(0.923545\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.17121 | −0.0546674 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.7653 | −1.06029 | −0.530143 | − | 0.847908i | \(-0.677862\pi\) | ||||
−0.530143 | + | 0.847908i | \(0.677862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.77872i | − | 0.0826641i | −0.999145 | − | 0.0413320i | \(-0.986840\pi\) | ||
0.999145 | − | 0.0413320i | \(-0.0131601\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.4776 | − | 8.71629i | 0.856880 | − | 0.404208i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.5258i | 0.810999i | 0.914095 | + | 0.405499i | \(0.132902\pi\) | ||||
−0.914095 | + | 0.405499i | \(0.867098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.11769 | 0.236313 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.1177 | 0.742666 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.4817i | 1.12567i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.7597 | + | 17.9103i | −0.677223 | + | 0.821783i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.25245i | 0.240493i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.4371 | −1.34502 | −0.672509 | − | 0.740089i | \(-0.734783\pi\) | ||||
−0.672509 | + | 0.740089i | \(0.734783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0054 | −1.45932 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 45.7354i | − | 2.08103i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.9633 | + | 14.1343i | −1.36056 | + | 0.641805i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.4565i | − | 0.926973i | −0.886104 | − | 0.463486i | \(-0.846598\pi\) | ||
0.886104 | − | 0.463486i | \(-0.153402\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.80123 | −0.217119 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.930273 | 0.0419826 | 0.0209913 | − | 0.999780i | \(-0.493318\pi\) | ||||
0.0209913 | + | 0.999780i | \(0.493318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.29005i | − | 0.373365i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.23529 | + | 6.85850i | 0.145416 | + | 0.308267i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 55.5247i | − | 2.49062i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.87465 | −0.173453 | −0.0867265 | − | 0.996232i | \(-0.527641\pi\) | ||||
−0.0867265 | + | 0.996232i | \(0.527641\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.8545 | −0.574295 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.3661i | 0.506789i | 0.967363 | + | 0.253395i | \(0.0815471\pi\) | ||||
−0.967363 | + | 0.253395i | \(0.918453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.7809 | + | 31.3340i | 0.657742 | + | 1.39435i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.5521i | 0.690692i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.35680 | 0.370409 | 0.185204 | − | 0.982700i | \(-0.440705\pi\) | ||||
0.185204 | + | 0.982700i | \(0.440705\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.08393 | 0.0479503 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.64168i | 0.204935i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.61914 | + | 1.70722i | −0.159478 | + | 0.0752292i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2165i | 0.581260i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.63200 | −0.203322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.1645 | −1.67202 | −0.836009 | − | 0.548715i | \(-0.815117\pi\) | ||||
−0.836009 | + | 0.548715i | \(0.815117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.7355i | 1.65006i | 0.565090 | + | 0.825030i | \(0.308842\pi\) | ||||
−0.565090 | + | 0.825030i | \(0.691158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.2734 | + | 19.7471i | −0.710227 | + | 0.861833i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10.7010i | − | 0.466143i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −56.8650 | −2.47239 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.4570 | 0.540587 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.4296i | 1.53463i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.06683 | + | 3.80529i | −0.348759 | + | 0.164517i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.7187i | 0.980384i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −65.0825 | −2.80330 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.194176 | 0.00834827 | 0.00417413 | − | 0.999991i | \(-0.498671\pi\) | ||||
0.00417413 | + | 0.999991i | \(0.498671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 20.3823i | − | 0.874688i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0196791 | + | 0.0417178i | 0.000842962 | + | 0.00178699i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 35.1151i | − | 1.50141i | −0.660636 | − | 0.750707i | \(-0.729713\pi\) | ||
0.660636 | − | 0.750707i | \(-0.270287\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.377182 | 0.0160978 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.8547 | −1.39966 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.25492i | − | 0.0958890i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.71408 | − | 12.1133i | −0.242549 | − | 0.514179i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19.6198i | − | 0.831316i | −0.909521 | − | 0.415658i | \(-0.863551\pi\) | ||
0.909521 | − | 0.415658i | \(-0.136449\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.5735 | −1.63148 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.97198 | 0.167697 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 10.4057i | − | 0.438550i | −0.975663 | − | 0.219275i | \(-0.929631\pi\) | ||
0.975663 | − | 0.219275i | \(-0.0703692\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.642669 | + | 0.303160i | −0.0270373 | + | 0.0127540i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.11769i | 0.214923i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.264046 | −0.0110694 | −0.00553469 | − | 0.999985i | \(-0.501762\pi\) | ||||
−0.00553469 | + | 0.999985i | \(0.501762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.8468 | 0.872410 | 0.436205 | − | 0.899847i | \(-0.356322\pi\) | ||||
0.436205 | + | 0.899847i | \(0.356322\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.4223i | 0.811380i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.4831 | + | 28.4172i | 1.43805 | + | 1.18508i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 47.1344i | − | 1.96223i | −0.193423 | − | 0.981116i | \(-0.561959\pi\) | ||
0.193423 | − | 0.981116i | \(-0.438041\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.0507 | 0.833277 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.12316 | −0.337005 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17.8129i | − | 0.737734i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.8063 | + | 5.09754i | −0.446784 | + | 0.210757i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 45.7880i | − | 1.88987i | −0.327251 | − | 0.944937i | \(-0.606122\pi\) | ||
0.327251 | − | 0.944937i | \(-0.393878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.4097 | −1.74746 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.6003 | 0.723980 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.4500i | − | 0.716586i | −0.933609 | − | 0.358293i | \(-0.883359\pi\) | ||
0.933609 | − | 0.358293i | \(-0.116641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.71808 | + | 12.1218i | 0.234419 | + | 0.496944i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.51874i | − | 0.103085i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.03107 | −0.287282 | −0.143641 | − | 0.989630i | \(-0.545881\pi\) | ||||
−0.143641 | + | 0.989630i | \(0.545881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.6911 | 0.844009 | 0.422004 | − | 0.906594i | \(-0.361327\pi\) | ||||
0.422004 | + | 0.906594i | \(0.361327\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.478166 | − | 1.01366i | −0.0194402 | − | 0.0412113i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7855i | 0.924834i | 0.886663 | + | 0.462417i | \(0.153018\pi\) | ||||
−0.886663 | + | 0.462417i | \(0.846982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.2240 | −1.46787 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.8239 | −0.842445 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 19.6989i | − | 0.795633i | −0.917465 | − | 0.397816i | \(-0.869768\pi\) | ||
0.917465 | − | 0.397816i | \(-0.130232\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.4093 | + | 6.32542i | −0.540713 | + | 0.255066i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11.7960i | − | 0.474888i | −0.971401 | − | 0.237444i | \(-0.923690\pi\) | ||
0.971401 | − | 0.237444i | \(-0.0763096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.5381 | −1.50879 | −0.754393 | − | 0.656423i | \(-0.772069\pi\) | ||||
−0.754393 | + | 0.656423i | \(0.772069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.93672 | 0.358618 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.8315i | 1.59582i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.77744 | − | 24.5393i | −0.191098 | − | 0.981571i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 15.7415i | − | 0.628657i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.01519 | −0.279714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.0248 | 1.67298 | 0.836491 | − | 0.547981i | \(-0.184603\pi\) | ||||
0.836491 | + | 0.547981i | \(0.184603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 21.9689i | − | 0.873185i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.2770 | − | 19.9429i | 1.67771 | − | 0.791410i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 102.544i | − | 4.06295i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.8496 | 0.429202 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.5510 | 1.00920 | 0.504602 | − | 0.863352i | \(-0.331639\pi\) | ||||
0.504602 | + | 0.863352i | \(0.331639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.0912i | 1.58104i | 0.612434 | + | 0.790521i | \(0.290190\pi\) | ||||
−0.612434 | + | 0.790521i | \(0.709810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.88671 | − | 14.5991i | −0.271164 | − | 0.574840i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 0.192403i | − | 0.00756415i | −0.999993 | − | 0.00378207i | \(-0.998796\pi\) | ||
0.999993 | − | 0.00378207i | \(-0.00120387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42.2459 | −1.65830 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −46.7588 | −1.83262 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.02892i | 0.196797i | 0.995147 | + | 0.0983984i | \(0.0313719\pi\) | ||||
−0.995147 | + | 0.0983984i | \(0.968628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.72595 | + | 14.2583i | 0.262804 | + | 0.557119i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.211801i | 0.00826314i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.1160 | 0.666746 | 0.333373 | − | 0.942795i | \(-0.391813\pi\) | ||||
0.333373 | + | 0.942795i | \(0.391813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.53734 | −0.254273 | −0.127137 | − | 0.991885i | \(-0.540579\pi\) | ||||
−0.127137 | + | 0.991885i | \(0.540579\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.25826i | 0.243051i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 48.0404 | − | 22.6616i | 1.86292 | − | 0.878780i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.2558i | 2.44928i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.79987 | 0.146911 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.27916 | −0.0493813 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9176i | 0.420842i | 0.977611 | + | 0.210421i | \(0.0674835\pi\) | ||||
−0.977611 | + | 0.210421i | \(0.932516\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.85859 | − | 3.17982i | −0.148517 | − | 0.122391i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.8559i | 1.26276i | 0.775475 | + | 0.631378i | \(0.217510\pi\) | ||||
−0.775475 | + | 0.631378i | \(0.782490\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 75.8239 | 2.90986 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.5533 | 0.749285 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.1006i | − | 0.577807i | −0.957358 | − | 0.288904i | \(-0.906709\pi\) | ||
0.957358 | − | 0.288904i | \(-0.0932907\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.1700 | − | 13.7601i | 1.11453 | − | 0.525747i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.8386i | 0.756891i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.0660 | 1.06923 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.7671 | −0.942184 | −0.471092 | − | 0.882084i | \(-0.656140\pi\) | ||||
−0.471092 | + | 0.882084i | \(0.656140\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 17.3559i | − | 0.659295i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.4748 | − | 28.5652i | −0.511129 | − | 1.08354i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.76574i | 0.294148i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.79049 | 0.181193 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2934 | −1.55963 | −0.779816 | − | 0.626009i | \(-0.784687\pi\) | ||||
−0.779816 | + | 0.626009i | \(0.784687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.8022i | 1.04858i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.71779 | − | 7.88135i | −0.140020 | − | 0.296829i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 79.2927i | − | 2.98211i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.88509 | −0.221019 | −0.110510 | − | 0.993875i | \(-0.535248\pi\) | ||||
−0.110510 | + | 0.993875i | \(0.535248\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.440613 | 0.0165243 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 81.6522i | 3.05790i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.6478 | − | 17.2875i | 1.37055 | − | 0.646517i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 13.2367i | − | 0.494335i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.10618 | −0.0785473 | −0.0392736 | − | 0.999228i | \(-0.512504\pi\) | ||||
−0.0392736 | + | 0.999228i | \(0.512504\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.15846 | 0.341079 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.13638i | − | 0.191024i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.5074 | − | 27.3118i | 0.835904 | − | 1.01434i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.89457i | − | 0.366969i | −0.983023 | − | 0.183485i | \(-0.941262\pi\) | ||
0.983023 | − | 0.183485i | \(-0.0587378\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.45483 | −0.312713 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.7159i | − | 1.02371i | −0.859072 | − | 0.511854i | \(-0.828959\pi\) | ||
0.859072 | − | 0.511854i | \(-0.171041\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 38.8105 | − | 18.3077i | 1.43155 | − | 0.675289i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.39135i | − | 0.124922i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6685 | −0.539588 | −0.269794 | − | 0.962918i | \(-0.586956\pi\) | ||||
−0.269794 | + | 0.962918i | \(0.586956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.8024 | 0.911140 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.6629i | 1.60184i | 0.598774 | + | 0.800918i | \(0.295655\pi\) | ||||
−0.598774 | + | 0.800918i | \(0.704345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.1930 | + | 36.4475i | 0.629903 | + | 1.33533i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.58727i | − | 0.0580752i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.4136 | 0.745897 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.3000 | 0.412344 | 0.206172 | − | 0.978516i | \(-0.433899\pi\) | ||||
0.206172 | + | 0.978516i | \(0.433899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 2.95641i | − | 0.107737i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.6097 | − | 26.7314i | −0.458916 | − | 0.972855i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.67590i | 0.242640i | 0.992613 | + | 0.121320i | \(0.0387127\pi\) | ||||
−0.992613 | + | 0.121320i | \(0.961287\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.3075 | −1.10009 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.3971 | 0.739395 | 0.369697 | − | 0.929152i | \(-0.379461\pi\) | ||||
0.369697 | + | 0.929152i | \(0.379461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 0.105569i | − | 0.00382187i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.36860 | + | 1.11732i | −0.0856369 | + | 0.0403967i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 66.5628i | − | 2.40344i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.0845 | 1.48154 | 0.740772 | − | 0.671757i | \(-0.234460\pi\) | ||||
0.740772 | + | 0.671757i | \(0.234460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.23941 | 0.0806503 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 23.6900i | − | 0.852071i | −0.904706 | − | 0.426035i | \(-0.859910\pi\) | ||
0.904706 | − | 0.426035i | \(-0.140090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.0531 | − | 35.2548i | 1.04362 | − | 1.26639i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.6534i | 1.09968i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.7768 | 1.10269 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.7946 | −1.31662 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 7.07819i | − | 0.252954i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.5958 | − | 15.3761i | 1.16339 | − | 0.548796i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.93869i | − | 0.140399i | −0.997533 | − | 0.0701996i | \(-0.977636\pi\) | ||
0.997533 | − | 0.0701996i | \(-0.0223636\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0597 | 0.749745 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.62631 | 0.0578251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.01544i | − | 0.0715704i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.01076 | + | 10.6223i | 0.177713 | + | 0.376735i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.3764i | 0.757190i | 0.925563 | + | 0.378595i | \(0.123593\pi\) | ||||
−0.925563 | + | 0.378595i | \(0.876407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.56434 | −0.161475 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.78310 | −0.275002 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 0.718291i | − | 0.0253479i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −43.6309 | − | 92.4931i | −1.53779 | − | 3.25995i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 15.2211i | − | 0.535808i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.4650 | 0.649195 | 0.324597 | − | 0.945852i | \(-0.394771\pi\) | ||||
0.324597 | + | 0.945852i | \(0.394771\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0745 | 1.30186 | 0.650931 | − | 0.759137i | \(-0.274379\pi\) | ||||
0.650931 | + | 0.759137i | \(0.274379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.3909i | 0.434567i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.70979 | + | 4.58031i | −0.340119 | + | 0.160441i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.5077i | 1.17229i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.3459 | 0.955544 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.6137 | 0.544921 | 0.272461 | − | 0.962167i | \(-0.412163\pi\) | ||||
0.272461 | + | 0.962167i | \(0.412163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.7112i | 1.45396i | 0.686659 | + | 0.726980i | \(0.259077\pi\) | ||||
−0.686659 | + | 0.726980i | \(0.740923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.0858 | + | 10.7839i | 0.455590 | + | 0.375447i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.2269i | 1.85088i | 0.378895 | + | 0.925440i | \(0.376304\pi\) | ||||
−0.378895 | + | 0.925440i | \(0.623696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.1230 | −1.42826 | −0.714131 | − | 0.700012i | \(-0.753178\pi\) | ||||
−0.714131 | + | 0.700012i | \(0.753178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.4978 | −0.606992 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 22.4764i | − | 0.778761i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.9963 | + | 12.2630i | −0.899638 | + | 0.424378i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.13671i | − | 0.315811i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.5947 | −1.12530 | −0.562648 | − | 0.826697i | \(-0.690217\pi\) | ||||
−0.562648 | + | 0.826697i | \(0.690217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1008 | 0.727614 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.90459i | − | 0.203365i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.8364 | + | 31.4518i | 0.510389 | + | 1.08197i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.56514i | 0.0881393i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.67030 | 0.263244 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.5282 | 1.83492 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.4834i | − | 0.769818i | −0.922955 | − | 0.384909i | \(-0.874233\pi\) | ||
0.922955 | − | 0.384909i | \(-0.125767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.42810 | + | 9.38712i | 0.151438 | + | 0.321033i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 40.2909i | − | 1.37631i | −0.725564 | − | 0.688155i | \(-0.758421\pi\) | ||
0.725564 | − | 0.688155i | \(-0.241579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0326 | −1.12706 | −0.563529 | − | 0.826097i | \(-0.690557\pi\) | ||||
−0.563529 | + | 0.826097i | \(0.690557\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.9330 | 1.15643 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.49014i | 0.152846i | 0.997075 | + | 0.0764231i | \(0.0243500\pi\) | ||||
−0.997075 | + | 0.0764231i | \(0.975650\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.36755 | + | 4.41886i | −0.318506 | + | 0.150246i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 15.6283i | − | 0.530764i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.49427 | −0.0506897 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.34341 | 0.181055 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.8160i | 0.501447i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.0720 | + | 55.4601i | −0.475722 | + | 1.87489i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.8347i | 0.973677i | 0.873492 | + | 0.486838i | \(0.161850\pi\) | ||||
−0.873492 | + | 0.486838i | \(0.838150\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.8099 | −0.499524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.1284 | 1.41934 | 0.709671 | − | 0.704534i | \(-0.248844\pi\) | ||||
0.709671 | + | 0.704534i | \(0.248844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.5693i | − | 0.456644i | −0.973586 | − | 0.228322i | \(-0.926676\pi\) | ||
0.973586 | − | 0.228322i | \(-0.0733239\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.1924 | − | 11.8838i | 0.846833 | − | 0.399469i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 27.6078i | − | 0.926979i | −0.886102 | − | 0.463490i | \(-0.846597\pi\) | ||
0.886102 | − | 0.463490i | \(-0.153403\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −106.984 | −3.58814 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.39135 | 0.113614 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.0892i | 0.605331i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.6733 | + | 45.9452i | 0.724459 | + | 1.53578i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 47.7526i | − | 1.59441i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.6714 | 2.15691 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.15173 | 0.204944 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.9440i | 1.22942i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.4444 | − | 41.2202i | −0.646354 | − | 1.37021i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 36.5080i | − | 1.21223i | −0.795378 | − | 0.606113i | \(-0.792728\pi\) | ||
0.795378 | − | 0.606113i | \(-0.207272\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.4939 | 0.513899 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.2630 | 1.06892 | 0.534461 | − | 0.845193i | \(-0.320515\pi\) | ||||
0.534461 | + | 0.845193i | \(0.320515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.38298i | 0.178151i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.762796 | − | 0.359827i | 0.0252173 | − | 0.0118955i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 36.0816i | − | 1.19152i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.4683 | 0.972071 | 0.486035 | − | 0.873939i | \(-0.338443\pi\) | ||||
0.486035 | + | 0.873939i | \(0.338443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.3403 | 0.867943 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 57.9737i | − | 1.90823i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.1118 | − | 19.0462i | −0.759910 | − | 0.626234i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.78957i | 0.0587772i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0597 | 0.362856 | 0.181428 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181428 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −89.0773 | −2.91939 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.32729i | − | 0.0434535i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.03275 | − | 3.78921i | 0.262699 | − | 0.123920i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.2560i | 0.465725i | 0.972510 | + | 0.232862i | \(0.0748092\pi\) | ||||
−0.972510 | + | 0.232862i | \(0.925191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.30479 | −0.205749 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.4682 | 1.51482 | 0.757411 | − | 0.652939i | \(-0.226464\pi\) | ||||
0.757411 | + | 0.652939i | \(0.226464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 59.2551i | − | 1.92961i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.88220 | + | 10.3498i | 0.158818 | + | 0.336678i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.71124i | 0.153095i | 0.997066 | + | 0.0765474i | \(0.0243896\pi\) | ||||
−0.997066 | + | 0.0765474i | \(0.975610\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.13174 | 0.0367379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.17493 | −0.297518 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.9057i | 0.547631i | 0.961782 | + | 0.273815i | \(0.0882857\pi\) | ||||
−0.961782 | + | 0.273815i | \(0.911714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.5286 | + | 39.2788i | 0.599573 | + | 1.27103i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.0046i | 0.775959i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −73.8166 | −2.38366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.4794 | 1.69288 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.98883i | 0.128538i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 40.5495 | − | 19.1280i | 1.30534 | − | 0.615754i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30.9840i | − | 0.996377i | −0.867069 | − | 0.498189i | \(-0.833999\pi\) | ||
0.867069 | − | 0.498189i | \(-0.166001\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.43638 | 0.174642 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.2599 | 1.09945 | 0.549726 | − | 0.835345i | \(-0.314732\pi\) | ||||
0.549726 | + | 0.835345i | \(0.314732\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 72.2861i | 2.31739i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.9911 | + | 20.6180i | −0.544151 | + | 0.660306i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.7151i | 0.918677i | 0.888261 | + | 0.459339i | \(0.151914\pi\) | ||||
−0.888261 | + | 0.459339i | \(0.848086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.3952 | 0.843594 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0206283 | 0.000658612 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.8073i | 1.52482i | 0.647097 | + | 0.762408i | \(0.275983\pi\) | ||||
−0.647097 | + | 0.762408i | \(0.724017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.5940 | − | 16.7904i | 1.13412 | − | 0.534987i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.9442i | 0.634832i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.5131 | 2.05140 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.59683 | 0.177789 | 0.0888947 | − | 0.996041i | \(-0.471667\pi\) | ||||
0.0888947 | + | 0.996041i | \(0.471667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 7.21379i | − | 0.228923i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.40284 | − | 5.09379i | −0.0761753 | − | 0.161484i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 51.8824i | − | 1.64313i | −0.570114 | − | 0.821566i | \(-0.693101\pi\) | ||
0.570114 | − | 0.821566i | \(-0.306899\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.98969 | −0.189505 |
(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 | 4020.2.g.c.1609.6 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.25 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.6 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.25 | yes | 38 | 5.4 | even | 2 | inner |