Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1457,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 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("2100.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.s (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.6 | ||
Character | \(\chi\) | \(=\) | 2100.1457 |
Dual form | 2100.2.s.c.1793.6 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.573626 | + | 1.63431i | −0.331183 | + | 0.943566i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.34191 | − | 1.87496i | −0.780635 | − | 0.624987i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.10537i | 1.84084i | 0.390931 | + | 0.920420i | \(0.372153\pi\) | ||||
−0.390931 | + | 0.920420i | \(0.627847\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.13396 | + | 2.13396i | −0.591853 | + | 0.591853i | −0.938132 | − | 0.346279i | \(-0.887445\pi\) |
0.346279 | + | 0.938132i | \(0.387445\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.21226 | + | 1.21226i | −0.294016 | + | 0.294016i | −0.838665 | − | 0.544648i | \(-0.816663\pi\) |
0.544648 | + | 0.838665i | \(0.316663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.390435i | − | 0.0895720i | −0.998997 | − | 0.0447860i | \(-0.985739\pi\) | ||
0.998997 | − | 0.0447860i | \(-0.0142606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.56124 | − | 0.750013i | 0.340691 | − | 0.163666i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.04421 | − | 2.04421i | −0.426248 | − | 0.426248i | 0.461100 | − | 0.887348i | \(-0.347455\pi\) |
−0.887348 | + | 0.461100i | \(0.847455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.40764 | − | 2.75186i | 0.848250 | − | 0.529596i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.67664 | 1.05413 | 0.527063 | − | 0.849826i | \(-0.323293\pi\) | ||||
0.527063 | + | 0.849826i | \(0.323293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.37257 | 0.246520 | 0.123260 | − | 0.992374i | \(-0.460665\pi\) | ||||
0.123260 | + | 0.992374i | \(0.460665\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.97805 | − | 3.50220i | −1.73695 | − | 0.609655i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.84106 | − | 2.84106i | −0.467068 | − | 0.467068i | 0.433895 | − | 0.900963i | \(-0.357139\pi\) |
−0.900963 | + | 0.433895i | \(0.857139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.26344 | − | 4.71163i | −0.362441 | − | 0.754464i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.59818i | − | 0.874288i | −0.899391 | − | 0.437144i | \(-0.855990\pi\) | ||
0.899391 | − | 0.437144i | \(-0.144010\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.04317 | + | 3.04317i | −0.464079 | + | 0.464079i | −0.899990 | − | 0.435911i | \(-0.856426\pi\) |
0.435911 | + | 0.899990i | \(0.356426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.32322 | + | 1.32322i | −0.193012 | + | 0.193012i | −0.796996 | − | 0.603984i | \(-0.793579\pi\) |
0.603984 | + | 0.796996i | \(0.293579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.28582 | − | 2.67659i | −0.180051 | − | 0.374797i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.10761 | − | 9.10761i | −1.25103 | − | 1.25103i | −0.955260 | − | 0.295767i | \(-0.904425\pi\) |
−0.295767 | − | 0.955260i | \(-0.595575\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.638091 | + | 0.223964i | 0.0845172 | + | 0.0296647i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.21447 | 0.809056 | 0.404528 | − | 0.914526i | \(-0.367436\pi\) | ||||
0.404528 | + | 0.914526i | \(0.367436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.30077 | −0.806731 | −0.403365 | − | 0.915039i | \(-0.632160\pi\) | ||||
−0.403365 | + | 0.915039i | \(0.632160\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.330181 | + | 2.98177i | 0.0415989 | + | 0.375668i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.63586 | − | 7.63586i | −0.932869 | − | 0.932869i | 0.0650152 | − | 0.997884i | \(-0.479290\pi\) |
−0.997884 | + | 0.0650152i | \(0.979290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.51348 | − | 2.16825i | 0.543359 | − | 0.261027i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.26230i | 0.743199i | 0.928393 | + | 0.371599i | \(0.121190\pi\) | ||||
−0.928393 | + | 0.371599i | \(0.878810\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3446 | + | 11.3446i | −1.32779 | + | 1.32779i | −0.420490 | + | 0.907297i | \(0.638142\pi\) |
−0.907297 | + | 0.420490i | \(0.861858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.31715 | − | 4.31715i | 0.491985 | − | 0.491985i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.56174i | − | 0.738254i | −0.929379 | − | 0.369127i | \(-0.879657\pi\) | ||
0.929379 | − | 0.369127i | \(-0.120343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.96905 | + | 8.78196i | 0.218783 | + | 0.975773i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.59616 | + | 3.59616i | 0.394730 | + | 0.394730i | 0.876370 | − | 0.481639i | \(-0.159958\pi\) |
−0.481639 | + | 0.876370i | \(0.659958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.25627 | + | 9.27736i | −0.349109 | + | 0.994637i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.7783 | −1.88450 | −0.942248 | − | 0.334917i | \(-0.891292\pi\) | ||||
−0.942248 | + | 0.334917i | \(0.891292\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.01787 | 0.316359 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.787340 | + | 2.24319i | −0.0816433 | + | 0.232608i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.3143 | − | 10.3143i | −1.04726 | − | 1.04726i | −0.998827 | − | 0.0484294i | \(-0.984578\pi\) |
−0.0484294 | − | 0.998827i | \(-0.515422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.4473 | − | 14.2982i | 1.15050 | − | 1.43702i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 16.1678i | − | 1.60875i | −0.594120 | − | 0.804376i | \(-0.702500\pi\) | ||
0.594120 | − | 0.804376i | \(-0.297500\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.28299 | + | 6.28299i | −0.619081 | + | 0.619081i | −0.945296 | − | 0.326215i | \(-0.894227\pi\) |
0.326215 | + | 0.945296i | \(0.394227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.37114 | − | 3.37114i | 0.325900 | − | 0.325900i | −0.525125 | − | 0.851025i | \(-0.675981\pi\) |
0.851025 | + | 0.525125i | \(0.175981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.78087i | − | 0.362142i | −0.983470 | − | 0.181071i | \(-0.942044\pi\) | ||
0.983470 | − | 0.181071i | \(-0.0579563\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.27287 | − | 3.01346i | 0.595395 | − | 0.286025i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.12558 | + | 9.12558i | 0.858462 | + | 0.858462i | 0.991157 | − | 0.132695i | \(-0.0423631\pi\) |
−0.132695 | + | 0.991157i | \(0.542363\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.99861 | − | 0.996442i | 0.831921 | − | 0.0921211i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.71439 | 0.157158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26.2756 | −2.38869 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.14913 | + | 3.21126i | 0.824949 | + | 0.289550i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.57696 | − | 9.57696i | −0.849818 | − | 0.849818i | 0.140292 | − | 0.990110i | \(-0.455196\pi\) |
−0.990110 | + | 0.140292i | \(0.955196\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.22782 | − | 6.71910i | −0.284194 | − | 0.591584i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.22683i | 0.194559i | 0.995257 | + | 0.0972794i | \(0.0310140\pi\) | ||||
−0.995257 | + | 0.0972794i | \(0.968986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.276080 | + | 0.276080i | −0.0239391 | + | 0.0239391i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.04843 | − | 9.04843i | 0.773060 | − | 0.773060i | −0.205581 | − | 0.978640i | \(-0.565908\pi\) |
0.978640 | + | 0.205581i | \(0.0659083\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.1155i | − | 0.942805i | −0.881918 | − | 0.471403i | \(-0.843748\pi\) | ||
0.881918 | − | 0.471403i | \(-0.156252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.40352 | − | 2.92159i | −0.118197 | − | 0.246042i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.0286 | − | 13.0286i | −1.08951 | − | 1.08951i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.63431 | − | 0.573626i | −0.134795 | − | 0.0473119i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.9855 | 1.55535 | 0.777676 | − | 0.628666i | \(-0.216399\pi\) | ||||
0.777676 | + | 0.628666i | \(0.216399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.10243 | 0.496609 | 0.248304 | − | 0.968682i | \(-0.420127\pi\) | ||||
0.248304 | + | 0.968682i | \(0.420127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.11194 | − | 0.566060i | 0.413276 | − | 0.0457632i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.73647 | + | 5.73647i | 0.457820 | + | 0.457820i | 0.897939 | − | 0.440119i | \(-0.145064\pi\) |
−0.440119 | + | 0.897939i | \(0.645064\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.1090 | − | 9.66025i | 1.59475 | − | 0.766108i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.89095i | 0.227839i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.48806 | − | 9.48806i | 0.743162 | − | 0.743162i | −0.230023 | − | 0.973185i | \(-0.573880\pi\) |
0.973185 | + | 0.230023i | \(0.0738801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.36137 | − | 6.36137i | 0.492257 | − | 0.492257i | −0.416760 | − | 0.909017i | \(-0.636834\pi\) |
0.909017 | + | 0.416760i | \(0.136834\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.89246i | 0.299420i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.732051 | + | 0.914363i | −0.0559813 | + | 0.0699231i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.82578 | + | 5.82578i | 0.442926 | + | 0.442926i | 0.892994 | − | 0.450068i | \(-0.148600\pi\) |
−0.450068 | + | 0.892994i | \(0.648600\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.56478 | + | 10.1563i | −0.267946 | + | 0.763398i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1127 | 1.05483 | 0.527417 | − | 0.849607i | \(-0.323161\pi\) | ||||
0.527417 | + | 0.849607i | \(0.323161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.7170 | −1.76287 | −0.881437 | − | 0.472301i | \(-0.843423\pi\) | ||||
−0.881437 | + | 0.472301i | \(0.843423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.61429 | − | 10.2974i | 0.267176 | − | 0.761204i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.40130 | − | 7.40130i | −0.541237 | − | 0.541237i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.06253 | − | 1.17081i | −0.368245 | − | 0.0851637i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 27.2871i | − | 1.97442i | −0.159420 | − | 0.987211i | \(-0.550962\pi\) | ||
0.159420 | − | 0.987211i | \(-0.449038\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.7722 | + | 13.7722i | −0.991346 | + | 0.991346i | −0.999963 | − | 0.00861662i | \(-0.997257\pi\) |
0.00861662 | + | 0.999963i | \(0.497257\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.57090 | − | 1.57090i | 0.111922 | − | 0.111922i | −0.648928 | − | 0.760850i | \(-0.724782\pi\) |
0.760850 | + | 0.648928i | \(0.224782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8363i | 1.40616i | 0.711110 | + | 0.703081i | \(0.248193\pi\) | ||||
−0.711110 | + | 0.703081i | \(0.751807\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.8595 | − | 8.09920i | 1.18917 | − | 0.571273i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.01399 | − | 4.01399i | −0.281727 | − | 0.281727i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.954537 | + | 8.62017i | 0.0663449 | + | 0.599143i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.38375 | 0.164888 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.42326 | 0.511038 | 0.255519 | − | 0.966804i | \(-0.417754\pi\) | ||||
0.255519 | + | 0.966804i | \(0.417754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.2345 | − | 3.59222i | −0.701257 | − | 0.246135i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.970551 | − | 0.970551i | −0.0658853 | − | 0.0658853i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0330 | − | 25.0481i | −0.813115 | − | 1.69260i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.17382i | − | 0.348029i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.88512 | − | 7.88512i | 0.528027 | − | 0.528027i | −0.391957 | − | 0.919984i | \(-0.628202\pi\) |
0.919984 | + | 0.391957i | \(0.128202\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.7962 | + | 12.7962i | −0.849312 | + | 0.849312i | −0.990047 | − | 0.140735i | \(-0.955053\pi\) |
0.140735 | + | 0.990047i | \(0.455053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.9997i | 1.38770i | 0.720121 | + | 0.693849i | \(0.244086\pi\) | ||||
−0.720121 | + | 0.693849i | \(0.755914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.57911 | + | 9.53197i | 0.301283 | + | 0.627158i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.41661 | − | 1.41661i | −0.0928055 | − | 0.0928055i | 0.659180 | − | 0.751985i | \(-0.270904\pi\) |
−0.751985 | + | 0.659180i | \(0.770904\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.7239 | + | 3.76399i | 0.696591 | + | 0.244497i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.8802 | −1.22126 | −0.610630 | − | 0.791916i | \(-0.709084\pi\) | ||||
−0.610630 | + | 0.791916i | \(0.709084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3942 | −1.05604 | −0.528021 | − | 0.849231i | \(-0.677066\pi\) | ||||
−0.528021 | + | 0.849231i | \(0.677066\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4819 | − | 1.81953i | −0.993164 | − | 0.116723i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.833172 | + | 0.833172i | 0.0530135 | + | 0.0530135i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.94008 | + | 3.81438i | −0.503182 | + | 0.241726i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.7660i | 1.56322i | 0.623770 | + | 0.781608i | \(0.285600\pi\) | ||||
−0.623770 | + | 0.781608i | \(0.714400\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4807 | − | 12.4807i | 0.784654 | − | 0.784654i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.6724 | + | 13.6724i | −0.852864 | + | 0.852864i | −0.990485 | − | 0.137621i | \(-0.956054\pi\) |
0.137621 | + | 0.990485i | \(0.456054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.01787i | 0.249658i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.2942 | − | 10.6435i | −0.822888 | − | 0.658814i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.5538 | + | 17.5538i | 1.08241 | + | 1.08241i | 0.996284 | + | 0.0861303i | \(0.0274501\pi\) |
0.0861303 | + | 0.996284i | \(0.472550\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.1981 | − | 29.0552i | 0.624113 | − | 1.77815i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.3802 | −1.05969 | −0.529844 | − | 0.848095i | \(-0.677750\pi\) | ||||
−0.529844 | + | 0.848095i | \(0.677750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8246 | 1.26500 | 0.632502 | − | 0.774559i | \(-0.282028\pi\) | ||||
0.632502 | + | 0.774559i | \(0.282028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.73113 | + | 4.93212i | −0.104773 | + | 0.298505i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.19684 | − | 2.19684i | −0.131996 | − | 0.131996i | 0.638022 | − | 0.770018i | \(-0.279753\pi\) |
−0.770018 | + | 0.638022i | \(0.779753\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.21442 | − | 2.57351i | −0.192442 | − | 0.154072i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6467i | 0.694781i | 0.937720 | + | 0.347391i | \(0.112932\pi\) | ||||
−0.937720 | + | 0.347391i | \(0.887068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5339 | + | 16.5339i | −0.982836 | + | 0.982836i | −0.999855 | − | 0.0170192i | \(-0.994582\pi\) |
0.0170192 | + | 0.999855i | \(0.494582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.95851 | + | 3.95851i | −0.233663 | + | 0.233663i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0609i | 0.827109i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.7732 | − | 10.9401i | 1.33499 | − | 0.641322i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.28333 | + | 4.28333i | 0.250235 | + | 0.250235i | 0.821067 | − | 0.570832i | \(-0.193379\pi\) |
−0.570832 | + | 0.821067i | \(0.693379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.8012 | + | 26.9103i | 0.974902 | + | 1.56149i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.72452 | 0.504552 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.30369 | 0.248060 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.4231 | + | 9.27425i | 1.51796 | + | 0.532792i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5609 | − | 11.5609i | −0.659816 | − | 0.659816i | 0.295521 | − | 0.955336i | \(-0.404507\pi\) |
−0.955336 | + | 0.295521i | \(0.904507\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.66423 | − | 13.8724i | −0.379115 | − | 0.789174i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8520i | 1.12570i | 0.826557 | + | 0.562852i | \(0.190296\pi\) | ||||
−0.826557 | + | 0.562852i | \(0.809704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.272468 | + | 0.272468i | −0.0154008 | + | 0.0154008i | −0.714765 | − | 0.699364i | \(-0.753466\pi\) |
0.699364 | + | 0.714765i | \(0.253466\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.8173 | + | 11.8173i | −0.663728 | + | 0.663728i | −0.956257 | − | 0.292529i | \(-0.905503\pi\) |
0.292529 | + | 0.956257i | \(0.405503\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.6580i | 1.94048i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.57570 | + | 7.44324i | 0.199576 | + | 0.415441i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.473309 | + | 0.473309i | 0.0263356 | + | 0.0263356i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.17910 | + | 2.16881i | 0.341705 | + | 0.119935i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.87132 | 0.103169 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.6380 | −1.29926 | −0.649631 | − | 0.760250i | \(-0.725077\pi\) | ||||
−0.649631 | + | 0.760250i | \(0.725077\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.32662 | + | 11.9804i | 0.0726985 | + | 0.656521i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.284624 | − | 0.284624i | −0.0155045 | − | 0.0155045i | 0.699312 | − | 0.714817i | \(-0.253490\pi\) |
−0.714817 | + | 0.699312i | \(0.753490\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.1486 | + | 9.67931i | −1.09432 | + | 0.525708i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.38003i | 0.453804i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.2644 | − | 10.2644i | 0.551021 | − | 0.551021i | −0.375714 | − | 0.926736i | \(-0.622603\pi\) |
0.926736 | + | 0.375714i | \(0.122603\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.36459i | − | 0.501275i | −0.968081 | − | 0.250638i | \(-0.919360\pi\) | ||
0.968081 | − | 0.250638i | \(-0.0806402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.53334 | + | 15.2781i | −0.188596 | + | 0.815482i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.0867 | − | 21.0867i | −1.12233 | − | 1.12233i | −0.991390 | − | 0.130942i | \(-0.958200\pi\) |
−0.130942 | − | 0.991390i | \(-0.541800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.983421 | + | 2.80184i | −0.0520482 | + | 0.148289i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.701397 | 0.0370183 | 0.0185092 | − | 0.999829i | \(-0.494108\pi\) | ||||
0.0185092 | + | 0.999829i | \(0.494108\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8476 | 0.991977 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.0724 | − | 42.9424i | 0.791094 | − | 2.25389i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.57837 | − | 3.57837i | −0.186790 | − | 0.186790i | 0.607517 | − | 0.794307i | \(-0.292166\pi\) |
−0.794307 | + | 0.607517i | \(0.792166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.4964 | + | 13.1104i | −0.546418 | + | 0.682500i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.8801i | 0.668702i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.4288 | − | 25.4288i | 1.31665 | − | 1.31665i | 0.400242 | − | 0.916410i | \(-0.368926\pi\) |
0.916410 | − | 0.400242i | \(-0.131074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.1137 | + | 12.1137i | −0.623887 | + | 0.623887i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1065i | 1.28963i | 0.764337 | + | 0.644817i | \(0.223066\pi\) | ||||
−0.764337 | + | 0.644817i | \(0.776934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.1453 | − | 10.1581i | 1.08331 | − | 0.520414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.54018 | + | 2.54018i | 0.129797 | + | 0.129797i | 0.769021 | − | 0.639224i | \(-0.220744\pi\) |
−0.639224 | + | 0.769021i | \(0.720744\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.8326 | − | 1.42099i | 0.652319 | − | 0.0722332i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.30912 | −0.117077 | −0.0585385 | − | 0.998285i | \(-0.518644\pi\) | ||||
−0.0585385 | + | 0.998285i | \(0.518644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.95624 | 0.250648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.63931 | − | 1.27737i | −0.183579 | − | 0.0644346i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7818 | + | 18.7818i | 0.942630 | + | 0.942630i | 0.998441 | − | 0.0558117i | \(-0.0177747\pi\) |
−0.0558117 | + | 0.998441i | \(0.517775\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.292832 | − | 0.609565i | −0.0146599 | − | 0.0305164i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6.05457i | − | 0.302351i | −0.988507 | − | 0.151175i | \(-0.951694\pi\) | ||
0.988507 | − | 0.151175i | \(-0.0483058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.92900 | + | 2.92900i | −0.145904 | + | 0.145904i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.3458 | − | 17.3458i | 0.859797 | − | 0.859797i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8086i | 0.979471i | 0.871871 | + | 0.489736i | \(0.162907\pi\) | ||||
−0.871871 | + | 0.489736i | \(0.837093\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.59748 | + | 19.9783i | 0.473409 | + | 0.985457i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.39430 | − | 4.39430i | −0.216229 | − | 0.216229i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.1661 | + | 6.37615i | 0.889599 | + | 0.312241i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.95119 | 0.0953218 | 0.0476609 | − | 0.998864i | \(-0.484823\pi\) | ||||
0.0476609 | + | 0.998864i | \(0.484823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5297 | −0.903084 | −0.451542 | − | 0.892250i | \(-0.649126\pi\) | ||||
−0.451542 | + | 0.892250i | \(0.649126\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.57986 | − | 0.617875i | 0.271302 | − | 0.0300421i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.45532 | + | 4.45532i | 0.215608 | + | 0.215608i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.7663 | − | 13.8192i | 1.38885 | − | 0.667195i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.62503i | 0.415453i | 0.978187 | + | 0.207727i | \(0.0666064\pi\) | ||||
−0.978187 | + | 0.207727i | \(0.933394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.79494 | − | 5.79494i | 0.278487 | − | 0.278487i | −0.554018 | − | 0.832505i | \(-0.686906\pi\) |
0.832505 | + | 0.554018i | \(0.186906\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.798133 | + | 0.798133i | −0.0381799 | + | 0.0381799i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7072i | 1.27466i | 0.770590 | + | 0.637331i | \(0.219962\pi\) | ||||
−0.770590 | + | 0.637331i | \(0.780038\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.87496 | − | 2.34191i | 0.0892838 | − | 0.111519i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.3937 | + | 13.3937i | 0.636352 | + | 0.636352i | 0.949654 | − | 0.313302i | \(-0.101435\pi\) |
−0.313302 | + | 0.949654i | \(0.601435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.8906 | + | 31.0281i | −0.515106 | + | 1.46758i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.96802 | −0.140069 | −0.0700347 | − | 0.997545i | \(-0.522311\pi\) | ||||
−0.0700347 | + | 0.997545i | \(0.522311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.1790 | 1.60942 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.50051 | + | 9.97323i | −0.164468 | + | 0.468583i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.54155 | + | 2.54155i | 0.118889 | + | 0.118889i | 0.764048 | − | 0.645159i | \(-0.223209\pi\) |
−0.645159 | + | 0.764048i | \(0.723209\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00723 | + | 8.67917i | −0.0936893 | + | 0.405109i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.0357i | − | 0.793432i | −0.917941 | − | 0.396716i | \(-0.870150\pi\) | ||
0.917941 | − | 0.396716i | \(-0.129850\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7681 | − | 17.7681i | 0.825756 | − | 0.825756i | −0.161171 | − | 0.986927i | \(-0.551527\pi\) |
0.986927 | + | 0.161171i | \(0.0515270\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.94995 | + | 5.94995i | −0.275331 | + | 0.275331i | −0.831242 | − | 0.555911i | \(-0.812370\pi\) |
0.555911 | + | 0.831242i | \(0.312370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7987i | 0.498639i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.6657 | + | 6.08455i | −0.583606 | + | 0.280361i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.5797 | − | 18.5797i | −0.854294 | − | 0.854294i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.25276 | + | 38.4056i | 0.194721 | + | 1.75847i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.9746 | −1.32389 | −0.661943 | − | 0.749555i | \(-0.730268\pi\) | ||||
−0.661943 | + | 0.749555i | \(0.730268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1254 | 0.552871 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.72470 | − | 1.65833i | −0.214981 | − | 0.0754565i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.07521 | − | 8.07521i | −0.365923 | − | 0.365923i | 0.500065 | − | 0.865988i | \(-0.333309\pi\) |
−0.865988 | + | 0.500065i | \(0.833309\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.0638 | + | 20.9490i | 0.455100 | + | 0.947346i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.8212i | − | 1.66172i | −0.556483 | − | 0.830859i | \(-0.687850\pi\) | ||
0.556483 | − | 0.830859i | \(-0.312150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.88156 | + | 6.88156i | −0.309930 | + | 0.309930i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.42812 | − | 4.42812i | 0.198628 | − | 0.198628i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.27186i | − | 0.101703i | −0.998706 | − | 0.0508513i | \(-0.983807\pi\) | ||
0.998706 | − | 0.0508513i | \(-0.0161935\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.74737 | + | 14.0455i | 0.301450 | + | 0.627505i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.4979 | + | 17.4979i | 0.780195 | + | 0.780195i | 0.979863 | − | 0.199669i | \(-0.0639867\pi\) |
−0.199669 | + | 0.979863i | \(0.563987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.36147 | − | 2.23282i | −0.282523 | − | 0.0991630i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.1171 | −0.980322 | −0.490161 | − | 0.871632i | \(-0.663062\pi\) | ||||
−0.490161 | + | 0.871632i | \(0.663062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0437 | 0.709732 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.07442 | − | 1.72090i | −0.0474370 | − | 0.0759795i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.07878 | − | 8.07878i | −0.355304 | − | 0.355304i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.8629 | + | 6.17928i | −0.564619 | + | 0.271240i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.97810i | 0.349527i | 0.984610 | + | 0.174763i | \(0.0559161\pi\) | ||||
−0.984610 | + | 0.174763i | \(0.944084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9549 | + | 13.9549i | −0.610206 | + | 0.610206i | −0.943000 | − | 0.332794i | \(-0.892009\pi\) |
0.332794 | + | 0.943000i | \(0.392009\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.66391 | + | 1.66391i | −0.0724809 | + | 0.0724809i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 14.6424i | − | 0.636625i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.5537 | − | 11.6519i | −0.631577 | − | 0.505649i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.9463 | + | 11.9463i | 0.517450 | + | 0.517450i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.09542 | + | 23.0645i | −0.349343 | + | 0.995305i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.10537 | −0.262977 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.2256 | −1.90141 | −0.950703 | − | 0.310102i | \(-0.899637\pi\) | ||||
−0.950703 | + | 0.310102i | \(0.899637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.6047 | − | 38.7609i | 0.583834 | − | 1.66339i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.87648 | − | 4.87648i | −0.208503 | − | 0.208503i | 0.595128 | − | 0.803631i | \(-0.297101\pi\) |
−0.803631 | + | 0.595128i | \(0.797101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.7558 | + | 11.8137i | 0.629763 | + | 0.504196i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.21636i | − | 0.0944202i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.63985 | + | 4.63985i | −0.197307 | + | 0.197307i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.4830 | + | 19.4830i | −0.825520 | + | 0.825520i | −0.986893 | − | 0.161374i | \(-0.948408\pi\) |
0.161374 | + | 0.986893i | \(0.448408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.9880i | − | 0.549333i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.3416 | − | 7.85040i | 0.689941 | − | 0.331444i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.6394 | + | 17.6394i | 0.743413 | + | 0.743413i | 0.973233 | − | 0.229821i | \(-0.0738139\pi\) |
−0.229821 | + | 0.973233i | \(0.573814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.81746 | − | 7.60211i | 0.202314 | − | 0.319259i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.7356 | −0.450059 | −0.225029 | − | 0.974352i | \(-0.572248\pi\) | ||||
−0.225029 | + | 0.974352i | \(0.572248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.68291 | 0.279671 | 0.139836 | − | 0.990175i | \(-0.455343\pi\) | ||||
0.139836 | + | 0.990175i | \(0.455343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.5954 | + | 15.6526i | 1.86300 | + | 0.653895i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1198 | + | 12.1198i | 0.504555 | + | 0.504555i | 0.912850 | − | 0.408295i | \(-0.133876\pi\) |
−0.408295 | + | 0.912850i | \(0.633876\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.6079 | − | 30.4081i | −0.607084 | − | 1.26372i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.08574i | − | 0.210992i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 55.6054 | − | 55.6054i | 2.30294 | − | 2.30294i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.8190 | − | 25.8190i | 1.06566 | − | 1.06566i | 0.0679761 | − | 0.997687i | \(-0.478346\pi\) |
0.997687 | − | 0.0679761i | \(-0.0216541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.535898i | − | 0.0220813i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.66622 | + | 3.46845i | 0.0685393 | + | 0.142673i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.95714 | − | 9.95714i | −0.408891 | − | 0.408891i | 0.472461 | − | 0.881352i | \(-0.343366\pi\) |
−0.881352 | + | 0.472461i | \(0.843366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.4186 | − | 11.3786i | −1.32681 | − | 0.465697i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.8800 | −1.46602 | −0.733010 | − | 0.680218i | \(-0.761885\pi\) | ||||
−0.733010 | + | 0.680218i | \(0.761885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.4277 | −1.68987 | −0.844936 | − | 0.534867i | \(-0.820362\pi\) | ||||
−0.844936 | + | 0.534867i | \(0.820362\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.56554 | + | 32.1994i | 0.145200 | + | 1.31126i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.53816 | + | 2.53816i | 0.103021 | + | 0.103021i | 0.756739 | − | 0.653718i | \(-0.226792\pi\) |
−0.653718 | + | 0.756739i | \(0.726792\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.86261 | − | 4.25756i | 0.359131 | − | 0.172525i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.64741i | − | 0.228470i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.604060 | − | 0.604060i | 0.0243978 | − | 0.0243978i | −0.694803 | − | 0.719200i | \(-0.744508\pi\) |
0.719200 | + | 0.694803i | \(0.244508\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.7999 | + | 12.7999i | −0.515304 | + | 0.515304i | −0.916147 | − | 0.400843i | \(-0.868717\pi\) |
0.400843 | + | 0.916147i | \(0.368717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1870i | 0.530030i | 0.964244 | + | 0.265015i | \(0.0853769\pi\) | ||||
−0.964244 | + | 0.265015i | \(0.914623\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.6355 | − | 3.38475i | −0.587304 | − | 0.135825i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.5711 | + | 12.5711i | 0.503652 | + | 0.503652i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.36738 | + | 3.89578i | −0.0546081 | + | 0.155583i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.88821 | 0.274651 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.6951 | −0.983097 | −0.491549 | − | 0.870850i | \(-0.663569\pi\) | ||||
−0.491549 | + | 0.870850i | \(0.663569\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.25817 | + | 12.1319i | −0.169247 | + | 0.482198i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.13396 | − | 2.13396i | −0.0845504 | − | 0.0845504i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.7416 | − | 14.6657i | 0.464489 | − | 0.580167i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.9661i | 1.22309i | 0.791211 | + | 0.611543i | \(0.209451\pi\) | ||||
−0.791211 | + | 0.611543i | \(0.790549\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.7147 | + | 25.7147i | −1.01409 | + | 1.01409i | −0.0141913 | + | 0.999899i | \(0.504517\pi\) |
−0.999899 | + | 0.0141913i | \(0.995483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.2808 | − | 11.2808i | 0.443492 | − | 0.443492i | −0.449692 | − | 0.893184i | \(-0.648466\pi\) |
0.893184 | + | 0.449692i | \(0.148466\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.9417i | 1.48934i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.14291 | − | 1.02944i | 0.0839872 | − | 0.0403470i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.0248 | + | 24.0248i | 0.940161 | + | 0.940161i | 0.998308 | − | 0.0581466i | \(-0.0185191\pi\) |
−0.0581466 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 47.8387 | − | 5.29733i | 1.86637 | − | 0.206668i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.4805 | 1.26526 | 0.632630 | − | 0.774454i | \(-0.281975\pi\) | ||||
0.632630 | + | 0.774454i | \(0.281975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.0233 | 1.12888 | 0.564438 | − | 0.825475i | \(-0.309093\pi\) | ||||
0.564438 | + | 0.825475i | \(0.309093\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.45560 | + | 2.96784i | 0.328388 | + | 0.115261i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.6043 | − | 11.6043i | −0.449319 | − | 0.449319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.36358 | + | 17.4098i | 0.323355 | + | 0.673102i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 38.4686i | − | 1.48506i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.6591 | − | 33.6591i | 1.29746 | − | 1.29746i | 0.367403 | − | 0.930062i | \(-0.380247\pi\) |
0.930062 | − | 0.367403i | \(-0.119753\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0488 | − | 12.0488i | 0.463072 | − | 0.463072i | −0.436589 | − | 0.899661i | \(-0.643814\pi\) |
0.899661 | + | 0.436589i | \(0.143814\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.5866i | 0.559782i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.5726 | − | 28.2531i | −0.520104 | − | 1.08266i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.28819 | + | 2.28819i | 0.0875552 | + | 0.0875552i | 0.749528 | − | 0.661973i | \(-0.230281\pi\) |
−0.661973 | + | 0.749528i | \(0.730281\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.3199 | − | 12.0460i | −1.30939 | − | 0.459582i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.8705 | 1.48085 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.1232 | 0.423147 | 0.211574 | − | 0.977362i | \(-0.432141\pi\) | ||||
0.211574 | + | 0.977362i | \(0.432141\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.2049 | + | 2.01588i | −0.691545 | + | 0.0765769i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.78644 | + | 6.78644i | 0.257055 | + | 0.257055i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.12779 | − | 1.50257i | 0.118304 | − | 0.0568325i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.12700i | − | 0.344722i | −0.985034 | − | 0.172361i | \(-0.944860\pi\) | ||
0.985034 | − | 0.172361i | \(-0.0551396\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.10925 | + | 1.10925i | −0.0418362 | + | 0.0418362i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.4323 | + | 11.4323i | −0.429957 | + | 0.429957i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 43.7645i | − | 1.64361i | −0.569769 | − | 0.821805i | \(-0.692967\pi\) | ||
0.569769 | − | 0.821805i | \(-0.307033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.3030 | + | 15.3670i | −0.461399 | + | 0.576307i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.80582 | − | 2.80582i | −0.105079 | − | 0.105079i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.8302 | − | 30.8560i | 0.404461 | − | 1.15234i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.1296 | 0.937177 | 0.468588 | − | 0.883417i | \(-0.344763\pi\) | ||||
0.468588 | + | 0.883417i | \(0.344763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.88549 | 0.330913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.40413 | − | 26.7931i | 0.349743 | − | 0.996445i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.31511 | + | 2.31511i | 0.0858625 | + | 0.0858625i | 0.748734 | − | 0.662871i | \(-0.230662\pi\) |
−0.662871 | + | 0.748734i | \(0.730662\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.8545 | − | 24.2584i | 0.439055 | − | 0.898460i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.37822i | − | 0.272893i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.92735 | − | 4.92735i | 0.181996 | − | 0.181996i | −0.610229 | − | 0.792225i | \(-0.708923\pi\) |
0.792225 | + | 0.610229i | \(0.208923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46.6198 | − | 46.6198i | 1.71726 | − | 1.71726i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3.42357i | − | 0.125938i | −0.998015 | − | 0.0629691i | \(-0.979943\pi\) | ||
0.998015 | − | 0.0629691i | \(-0.0200570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.83959 | + | 0.883728i | −0.0675789 | + | 0.0324646i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5198 | − | 21.5198i | −0.789484 | − | 0.789484i | 0.191925 | − | 0.981410i | \(-0.438527\pi\) |
−0.981410 | + | 0.191925i | \(0.938527\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.67921 | − | 15.1645i | −0.0614393 | − | 0.554842i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.76751 | −0.174201 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.8653 | 0.432969 | 0.216485 | − | 0.976286i | \(-0.430541\pi\) | ||||
0.216485 | + | 0.976286i | \(0.430541\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −40.4752 | − | 14.2064i | −1.47500 | − | 0.517711i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4693 | + | 34.4693i | 1.25281 | + | 1.25281i | 0.954456 | + | 0.298352i | \(0.0964370\pi\) |
0.298352 | + | 0.954456i | \(0.403563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.2380 | + | 27.5565i | 0.480509 | + | 1.00024i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.4955i | 1.61296i | 0.591262 | + | 0.806480i | \(0.298630\pi\) | ||||
−0.591262 | + | 0.806480i | \(0.701370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.67348 | + | 2.67348i | −0.0967865 | + | 0.0967865i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.2614 | + | 13.2614i | −0.478842 | + | 0.478842i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.23513i | − | 0.296966i | −0.988915 | − | 0.148483i | \(-0.952561\pi\) | ||
0.988915 | − | 0.148483i | \(-0.0474391\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.5021 | − | 30.1878i | −0.522279 | − | 1.08719i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.8995 | + | 22.8995i | 0.823637 | + | 0.823637i | 0.986628 | − | 0.162991i | \(-0.0521140\pi\) |
−0.162991 | + | 0.986628i | \(0.552114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.56642 | − | 2.30475i | −0.235569 | − | 0.0826826i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.18573 | −0.0783118 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.2337 | −1.36811 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.0206 | − | 15.6213i | 0.894162 | − | 0.558261i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7721 | − | 19.7721i | −0.704800 | − | 0.704800i | 0.260637 | − | 0.965437i | \(-0.416068\pi\) |
−0.965437 | + | 0.260637i | \(0.916068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.7576 | + | 18.6190i | −1.37981 | + | 0.662852i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 12.9055i | − | 0.458867i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4456 | − | 13.4456i | 0.477466 | − | 0.477466i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.6803 | + | 22.6803i | −0.803376 | + | 0.803376i | −0.983622 | − | 0.180246i | \(-0.942311\pi\) |
0.180246 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.20818i | − | 0.113497i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.6351 | + | 33.3336i | 1.47110 | + | 1.17778i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −69.2631 | − | 69.2631i | −2.44424 | − | 2.44424i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.96973 | − | 28.4045i | 0.350951 | − | 0.999887i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.31835 | −0.257299 | −0.128650 | − | 0.991690i | \(-0.541064\pi\) | ||||
−0.128650 | + | 0.991690i | \(0.541064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.32051 | 0.0463693 | 0.0231847 | − | 0.999731i | \(-0.492619\pi\) | ||||
0.0231847 | + | 0.999731i | \(0.492619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.9455 | + | 34.0337i | −0.418948 | + | 1.19361i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.18816 | + | 1.18816i | 0.0415685 | + | 0.0415685i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.06757 | − | 5.65838i | −0.246961 | − | 0.197720i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 13.7480i | − | 0.479810i | −0.970796 | − | 0.239905i | \(-0.922884\pi\) | ||
0.970796 | − | 0.239905i | \(-0.0771163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.2118 | + | 30.2118i | −1.05312 | + | 1.05312i | −0.0546082 | + | 0.998508i | \(0.517391\pi\) |
−0.998508 | + | 0.0546082i | \(0.982609\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.2448 | + | 16.2448i | −0.564889 | + | 0.564889i | −0.930692 | − | 0.365803i | \(-0.880794\pi\) |
0.365803 | + | 0.930692i | \(0.380794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.9100i | − | 1.45559i | −0.685793 | − | 0.727797i | \(-0.740544\pi\) | ||
0.685793 | − | 0.727797i | \(-0.259456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.85048 | − | 2.33015i | 0.168261 | − | 0.0808319i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.21226 | − | 1.21226i | −0.0420023 | − | 0.0420023i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.04977 | − | 3.77711i | 0.209111 | − | 0.130556i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.0750 | 0.658541 | 0.329270 | − | 0.944236i | \(-0.393197\pi\) | ||||
0.329270 | + | 0.944236i | \(0.393197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.22424 | 0.111181 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.0342 | − | 6.68083i | −0.655572 | − | 0.230100i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.5797 | + | 18.5797i | 0.638405 | + | 0.638405i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.5371 | − | 36.5056i | −0.601872 | − | 1.25287i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.6155i | 0.398173i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.44543 | + | 7.44543i | −0.254927 | + | 0.254927i | −0.822987 | − | 0.568060i | \(-0.807694\pi\) |
0.568060 | + | 0.822987i | \(0.307694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.2330 | + | 29.2330i | −0.998582 | + | 0.998582i | −0.999999 | − | 0.00141712i | \(-0.999549\pi\) |
0.00141712 | + | 0.999999i | \(0.499549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.6587i | − | 0.875465i | −0.899105 | − | 0.437733i | \(-0.855782\pi\) | ||
0.899105 | − | 0.437733i | \(-0.144218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.19871 | − | 8.74011i | −0.143092 | − | 0.297862i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.1724 | + | 33.1724i | 1.12920 | + | 1.12920i | 0.990307 | + | 0.138894i | \(0.0443547\pi\) |
0.138894 | + | 0.990307i | \(0.455645\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.9797 | − | 8.06567i | −0.780432 | − | 0.273925i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.0619 | 1.35901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.5892 | 1.10424 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.81621 | + | 43.4939i | 0.163004 | + | 1.47205i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.05243 | + | 6.05243i | 0.204376 | + | 0.204376i | 0.801872 | − | 0.597496i | \(-0.203838\pi\) |
−0.597496 | + | 0.801872i | \(0.703838\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.45730 | + | 4.54324i | −0.318987 | + | 0.153240i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 51.7654i | − | 1.74402i | −0.489486 | − | 0.872011i | \(-0.662816\pi\) | ||
0.489486 | − | 0.872011i | \(-0.337184\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.1198 | + | 25.1198i | −0.845350 | + | 0.845350i | −0.989549 | − | 0.144199i | \(-0.953939\pi\) |
0.144199 | + | 0.989549i | \(0.453939\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.4332 | − | 33.4332i | 1.12258 | − | 1.12258i | 0.131225 | − | 0.991353i | \(-0.458109\pi\) |
0.991353 | − | 0.131225i | \(-0.0418910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.5439i | 0.454247i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −53.6172 | + | 12.0218i | −1.79624 | + | 0.402745i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.516634 | + | 0.516634i | 0.0172885 | + | 0.0172885i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.00461 | + | 14.2585i | −0.167099 | + | 0.476078i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.79156 | 0.259863 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.0816 | 0.735644 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.46871 | + | 7.03354i | −0.0821534 | + | 0.234062i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.627972 | − | 0.627972i | −0.0208515 | − | 0.0208515i | 0.696604 | − | 0.717456i | \(-0.254693\pi\) |
−0.717456 | + | 0.696604i | \(0.754693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.3139 | + | 37.8634i | −1.00545 | + | 1.25585i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.2327i | 1.10105i | 0.834819 | + | 0.550524i | \(0.185572\pi\) | ||||
−0.834819 | + | 0.550524i | \(0.814428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9559 | + | 21.9559i | −0.726635 | + | 0.726635i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.57460 | − | 1.57460i | 0.0519980 | − | 0.0519980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.4484i | 0.971412i | 0.874122 | + | 0.485706i | \(0.161437\pi\) | ||||
−0.874122 | + | 0.485706i | \(0.838563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.5257 | − | 12.2624i | 0.841100 | − | 0.404060i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.3635 | − | 13.3635i | −0.439864 | − | 0.439864i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.4945 | − | 2.93382i | 0.870194 | − | 0.0963592i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.8616 | 0.618830 | 0.309415 | − | 0.950927i | \(-0.399867\pi\) | ||||
0.309415 | + | 0.950927i | \(0.399867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.390435 | 0.0127960 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.4443 | − | 11.3876i | −1.06218 | − | 0.372814i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.6123 | − | 22.6123i | −0.738711 | − | 0.738711i | 0.233618 | − | 0.972328i | \(-0.424944\pi\) |
−0.972328 | + | 0.233618i | \(0.924944\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.289001 | − | 0.601591i | −0.00943120 | − | 0.0196322i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.4192i | 1.83921i | 0.392842 | + | 0.919606i | \(0.371492\pi\) | ||||
−0.392842 | + | 0.919606i | \(0.628508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.4439 | + | 11.4439i | −0.372663 | + | 0.372663i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.8877 | + | 40.8877i | −1.32867 | + | 1.32867i | −0.422142 | + | 0.906530i | \(0.638722\pi\) |
−0.906530 | + | 0.422142i | \(0.861278\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 48.4178i | − | 1.57171i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.5344 | − | 26.0919i | −0.406456 | − | 0.846086i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.46536 | + | 1.46536i | 0.0474676 | + | 0.0474676i | 0.730442 | − | 0.682975i | \(-0.239314\pi\) |
−0.682975 | + | 0.730442i | \(0.739314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −56.6418 | − | 19.8807i | −1.83097 | − | 0.642653i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.7964 | −0.413218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1161 | −0.939228 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.2156 | + | 1.57414i | −0.458093 | + | 0.0507259i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.869720 | − | 0.869720i | −0.0279683 | − | 0.0279683i | 0.692984 | − | 0.720953i | \(-0.256295\pi\) |
−0.720953 | + | 0.692984i | \(0.756295\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.04503 | + | 0.502029i | −0.0335713 | + | 0.0161275i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 16.2979i | − | 0.523024i | −0.965200 | − | 0.261512i | \(-0.915779\pi\) | ||
0.965200 | − | 0.261512i | \(-0.0842211\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.85985 | + | 7.85985i | −0.251975 | + | 0.251975i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.3718 | + | 37.3718i | −1.19563 | + | 1.19563i | −0.220167 | + | 0.975462i | \(0.570660\pi\) |
−0.975462 | + | 0.220167i | \(0.929340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 108.543i | − | 3.46905i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.08898 | + | 8.85444i | −0.226334 | + | 0.282701i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.68668 | − | 2.68668i | −0.0856917 | − | 0.0856917i | 0.662962 | − | 0.748653i | \(-0.269299\pi\) |
−0.748653 | + | 0.662962i | \(0.769299\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.07344 | + | 3.05831i | −0.0341680 | + | 0.0973471i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.4418 | 0.395625 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.3109 | 0.391070 | 0.195535 | − | 0.980697i | \(-0.437356\pi\) | ||||
0.195535 | + | 0.980697i | \(0.437356\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.5594 | − | 38.6317i | 0.430294 | − | 1.22594i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.1288 | − | 16.1288i | −0.510806 | − | 0.510806i | 0.403968 | − | 0.914773i | \(-0.367631\pi\) |
−0.914773 | + | 0.403968i | \(0.867631\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.3406 | − | 4.70415i | −0.643548 | − | 0.148833i |
(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 | 2100.2.s.c.1457.6 | yes | 32 | |
3.2 | odd | 2 | inner | 2100.2.s.c.1457.3 | ✓ | 32 | |
5.2 | odd | 4 | inner | 2100.2.s.c.1793.14 | yes | 32 | |
5.3 | odd | 4 | inner | 2100.2.s.c.1793.3 | yes | 32 | |
5.4 | even | 2 | inner | 2100.2.s.c.1457.11 | yes | 32 | |
15.2 | even | 4 | inner | 2100.2.s.c.1793.11 | yes | 32 | |
15.8 | even | 4 | inner | 2100.2.s.c.1793.6 | yes | 32 | |
15.14 | odd | 2 | inner | 2100.2.s.c.1457.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.s.c.1457.3 | ✓ | 32 | 3.2 | odd | 2 | inner | |
2100.2.s.c.1457.6 | yes | 32 | 1.1 | even | 1 | trivial | |
2100.2.s.c.1457.11 | yes | 32 | 5.4 | even | 2 | inner | |
2100.2.s.c.1457.14 | yes | 32 | 15.14 | odd | 2 | inner | |
2100.2.s.c.1793.3 | yes | 32 | 5.3 | odd | 4 | inner | |
2100.2.s.c.1793.6 | yes | 32 | 15.8 | even | 4 | inner | |
2100.2.s.c.1793.11 | yes | 32 | 15.2 | even | 4 | inner | |
2100.2.s.c.1793.14 | yes | 32 | 5.2 | odd | 4 | inner |