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 | 1457.3 | ||
Character | \(\chi\) | \(=\) | 2100.1457 |
Dual form | 2100.2.s.c.1793.3 |
$q$-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 | ||||||||
\(3\) | −1.63431 | + | 0.573626i | −0.943566 | + | 0.331183i | ||||
\(4\) | 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 | \(-0.627847\pi\) | ||
0.390931 | − | 0.920420i | \(-0.372153\pi\) | |||||||
\(12\) | 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 | −0.544648 | − | 0.838665i | \(-0.683337\pi\) |
0.838665 | + | 0.544648i | \(0.183337\pi\) | |||||||
\(18\) | 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 | 0.887348 | − | 0.461100i | \(-0.152545\pi\) |
−0.461100 | + | 0.887348i | \(0.652545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.75186 | + | 4.40764i | −0.529596 | + | 0.848250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.67664 | −1.05413 | −0.527063 | − | 0.849826i | \(-0.676707\pi\) | ||||
−0.527063 | + | 0.849826i | \(0.676707\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.37257 | 0.246520 | 0.123260 | − | 0.992374i | \(-0.460665\pi\) | ||||
0.123260 | + | 0.992374i | \(0.460665\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.50220 | + | 9.97805i | 0.609655 | + | 1.73695i | ||||
\(34\) | 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 | \(0.144010\pi\) | ||||
−0.899391 | + | 0.437144i | \(0.855990\pi\) | |||||||
\(42\) | 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 | −0.603984 | − | 0.796996i | \(-0.706421\pi\) |
0.796996 | + | 0.603984i | \(0.206421\pi\) | |||||||
\(48\) | 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 | \(0.0955751\pi\) |
0.295767 | + | 0.955260i | \(0.404425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.223964 | + | 0.638091i | 0.0296647 | + | 0.0845172i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.21447 | −0.809056 | −0.404528 | − | 0.914526i | \(-0.632564\pi\) | ||||
−0.404528 | + | 0.914526i | \(0.632564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.30077 | −0.806731 | −0.403365 | − | 0.915039i | \(-0.632160\pi\) | ||||
−0.403365 | + | 0.915039i | \(0.632160\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.98177 | − | 0.330181i | −0.375668 | − | 0.0415989i | ||||
\(64\) | 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 | \(-0.878810\pi\) | ||
0.928393 | − | 0.371599i | \(-0.121190\pi\) | |||||||
\(72\) | 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 | 0.481639 | − | 0.876370i | \(-0.340042\pi\) |
−0.876370 | + | 0.481639i | \(0.840042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.27736 | − | 3.25627i | 0.994637 | − | 0.349109i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.7783 | 1.88450 | 0.942248 | − | 0.334917i | \(-0.108708\pi\) | ||||
0.942248 | + | 0.334917i | \(0.108708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.01787 | 0.316359 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.24319 | + | 0.787340i | −0.232608 | + | 0.0816433i | ||||
\(94\) | 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 | \(0.297500\pi\) | ||||
−0.594120 | + | 0.804376i | \(0.702500\pi\) | |||||||
\(102\) | 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 | −0.851025 | − | 0.525125i | \(-0.824019\pi\) |
0.525125 | + | 0.851025i | \(0.324019\pi\) | |||||||
\(108\) | 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 | 0.132695 | − | 0.991157i | \(-0.457637\pi\) |
−0.991157 | + | 0.132695i | \(0.957637\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.996442 | + | 8.99861i | −0.0921211 | + | 0.831921i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.71439 | −0.157158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26.2756 | −2.38869 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.21126 | − | 9.14913i | −0.289550 | − | 0.824949i | ||||
\(124\) | 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 | \(-0.968986\pi\) | ||
0.995257 | − | 0.0972794i | \(-0.0310140\pi\) | |||||||
\(132\) | 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 | −0.978640 | − | 0.205581i | \(-0.934092\pi\) |
0.205581 | + | 0.978640i | \(0.434092\pi\) | |||||||
\(138\) | 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 | ||||||||
\(147\) | −0.573626 | − | 1.63431i | −0.0473119 | − | 0.134795i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.9855 | −1.55535 | −0.777676 | − | 0.628666i | \(-0.783601\pi\) | ||||
−0.777676 | + | 0.628666i | \(0.783601\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.10243 | 0.496609 | 0.248304 | − | 0.968682i | \(-0.420127\pi\) | ||||
0.248304 | + | 0.968682i | \(0.420127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.566060 | − | 5.11194i | 0.0457632 | − | 0.413276i | ||||
\(154\) | 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 | −0.909017 | − | 0.416760i | \(-0.863166\pi\) |
0.416760 | + | 0.909017i | \(0.363166\pi\) | |||||||
\(168\) | 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 | 0.450068 | − | 0.892994i | \(-0.351400\pi\) |
−0.892994 | + | 0.450068i | \(0.851400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.1563 | − | 3.56478i | 0.763398 | − | 0.267946i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1127 | −1.05483 | −0.527417 | − | 0.849607i | \(-0.676839\pi\) | ||||
−0.527417 | + | 0.849607i | \(0.676839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.7170 | −1.76287 | −0.881437 | − | 0.472301i | \(-0.843423\pi\) | ||||
−0.881437 | + | 0.472301i | \(0.843423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.2974 | − | 3.61429i | 0.761204 | − | 0.267176i | ||||
\(184\) | 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 | \(0.449038\pi\) | ||||
−0.159420 | + | 0.987211i | \(0.550962\pi\) | |||||||
\(192\) | 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 | −0.760850 | − | 0.648928i | \(-0.775218\pi\) |
0.648928 | + | 0.760850i | \(0.275218\pi\) | |||||||
\(198\) | 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 | ||||||||
\(207\) | 8.62017 | + | 0.954537i | 0.599143 | + | 0.0663449i | ||||
\(208\) | 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 | ||||||||
\(213\) | 3.59222 | + | 10.2345i | 0.246135 | + | 0.701257i | ||||
\(214\) | 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 | −0.140735 | − | 0.990047i | \(-0.544947\pi\) |
0.990047 | + | 0.140735i | \(0.0449466\pi\) | |||||||
\(228\) | 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 | 0.751985 | − | 0.659180i | \(-0.229096\pi\) |
−0.659180 | + | 0.751985i | \(0.729096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.76399 | + | 10.7239i | 0.244497 | + | 0.696591i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8802 | 1.22126 | 0.610630 | − | 0.791916i | \(-0.290916\pi\) | ||||
0.610630 | + | 0.791916i | \(0.290916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3942 | −1.05604 | −0.528021 | − | 0.849231i | \(-0.677066\pi\) | ||||
−0.528021 | + | 0.849231i | \(0.677066\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.81953 | + | 15.4819i | 0.116723 | + | 0.993164i | ||||
\(244\) | 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 | \(-0.714400\pi\) | ||
0.623770 | − | 0.781608i | \(-0.285600\pi\) | |||||||
\(252\) | 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 | −0.137621 | − | 0.990485i | \(-0.543946\pi\) |
0.990485 | + | 0.137621i | \(0.0439457\pi\) | |||||||
\(258\) | 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 | \(-0.972550\pi\) |
−0.0861303 | − | 0.996284i | \(-0.527450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29.0552 | + | 10.1981i | −1.77815 | + | 0.624113i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.3802 | 1.05969 | 0.529844 | − | 0.848095i | \(-0.322250\pi\) | ||||
0.529844 | + | 0.848095i | \(0.322250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8246 | 1.26500 | 0.632502 | − | 0.774559i | \(-0.282028\pi\) | ||||
0.632502 | + | 0.774559i | \(0.282028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.93212 | + | 1.73113i | −0.298505 | + | 0.104773i | ||||
\(274\) | 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 | \(-0.887068\pi\) | ||
0.937720 | − | 0.347391i | \(-0.112932\pi\) | |||||||
\(282\) | 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 | 0.570832 | − | 0.821067i | \(-0.306621\pi\) |
−0.821067 | + | 0.570832i | \(0.806621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.9103 | + | 16.8012i | 1.56149 | + | 0.974902i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.72452 | −0.504552 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.30369 | 0.248060 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.27425 | − | 26.4231i | −0.532792 | − | 1.51796i | ||||
\(304\) | 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 | \(-0.809704\pi\) | ||
0.826557 | − | 0.562852i | \(-0.190296\pi\) | |||||||
\(312\) | 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 | −0.292529 | − | 0.956257i | \(-0.594497\pi\) |
0.956257 | + | 0.292529i | \(0.0944968\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | 2.16881 | + | 6.17910i | 0.119935 | + | 0.341705i | ||||
\(328\) | 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 | ||||||||
\(333\) | −11.9804 | − | 1.32662i | −0.656521 | − | 0.0726985i | ||||
\(334\) | 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 | −0.926736 | − | 0.375714i | \(-0.877397\pi\) |
0.375714 | + | 0.926736i | \(0.377397\pi\) | |||||||
\(348\) | 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 | \(0.0418001\pi\) |
0.130942 | + | 0.991390i | \(0.458200\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.80184 | − | 0.983421i | 0.148289 | − | 0.0520482i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.701397 | −0.0370183 | −0.0185092 | − | 0.999829i | \(-0.505892\pi\) | ||||
−0.0185092 | + | 0.999829i | \(0.505892\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8476 | 0.991977 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 42.9424 | − | 15.0724i | 2.25389 | − | 0.791094i | ||||
\(364\) | 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 | 0.639224 | − | 0.769021i | \(-0.279256\pi\) |
−0.769021 | + | 0.639224i | \(0.779256\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.42099 | + | 12.8326i | −0.0722332 | + | 0.652319i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.30912 | 0.117077 | 0.0585385 | − | 0.998285i | \(-0.481356\pi\) | ||||
0.0585385 | + | 0.998285i | \(0.481356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.95624 | 0.250648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.27737 | + | 3.63931i | 0.0644346 | + | 0.183579i | ||||
\(394\) | 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 | \(0.0483058\pi\) | ||||
−0.988507 | + | 0.151175i | \(0.951694\pi\) | |||||||
\(402\) | 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 | ||||||||
\(417\) | 6.37615 | + | 18.1661i | 0.312241 | + | 0.889599i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.95119 | −0.0953218 | −0.0476609 | − | 0.998864i | \(-0.515177\pi\) | ||||
−0.0476609 | + | 0.998864i | \(0.515177\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5297 | −0.903084 | −0.451542 | − | 0.892250i | \(-0.649126\pi\) | ||||
−0.451542 | + | 0.892250i | \(0.649126\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.617875 | − | 5.57986i | 0.0300421 | − | 0.271302i | ||||
\(424\) | 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 | \(-0.933394\pi\) | ||
0.978187 | − | 0.207727i | \(-0.0666064\pi\) | |||||||
\(432\) | 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 | 0.313302 | − | 0.949654i | \(-0.398565\pi\) |
−0.949654 | + | 0.313302i | \(0.898565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.0281 | − | 10.8906i | 1.46758 | − | 0.515106i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.96802 | 0.140069 | 0.0700347 | − | 0.997545i | \(-0.477689\pi\) | ||||
0.0700347 | + | 0.997545i | \(0.477689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.1790 | 1.60942 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.97323 | + | 3.50051i | −0.468583 | + | 0.164468i | ||||
\(454\) | 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 | \(0.129850\pi\) | ||||
−0.917941 | + | 0.396716i | \(0.870150\pi\) | |||||||
\(462\) | 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 | −0.555911 | − | 0.831242i | \(-0.687630\pi\) |
0.831242 | + | 0.555911i | \(0.187630\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | 38.4056 | + | 4.25276i | 1.75847 | + | 0.194721i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.9746 | 1.32389 | 0.661943 | − | 0.749555i | \(-0.269732\pi\) | ||||
0.661943 | + | 0.749555i | \(0.269732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1254 | 0.552871 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.65833 | + | 4.72470i | 0.0754565 | + | 0.214981i | ||||
\(484\) | 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 | \(0.312150\pi\) | ||||
−0.556483 | + | 0.830859i | \(0.687850\pi\) | |||||||
\(492\) | 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 | 0.199669 | − | 0.979863i | \(-0.436013\pi\) |
−0.979863 | + | 0.199669i | \(0.936013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.23282 | − | 6.36147i | −0.0991630 | − | 0.282523i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.1171 | 0.980322 | 0.490161 | − | 0.871632i | \(-0.336938\pi\) | ||||
0.490161 | + | 0.871632i | \(0.336938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0437 | 0.709732 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.72090 | + | 1.07442i | 0.0759795 | + | 0.0474370i | ||||
\(514\) | 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 | \(-0.944084\pi\) | ||
0.984610 | − | 0.174763i | \(-0.0559161\pi\) | |||||||
\(522\) | 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 | ||||||||
\(537\) | 23.0645 | − | 8.09542i | 0.995305 | − | 0.349343i | ||||
\(538\) | 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 | ||||||||
\(543\) | 38.7609 | − | 13.6047i | 1.66339 | − | 0.583834i | ||||
\(544\) | 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 | −0.161374 | − | 0.986893i | \(-0.551592\pi\) |
0.986893 | + | 0.161374i | \(0.0515924\pi\) | |||||||
\(558\) | 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 | 0.229821 | − | 0.973233i | \(-0.426186\pi\) |
−0.973233 | + | 0.229821i | \(0.926186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.60211 | + | 4.81746i | −0.319259 | + | 0.202314i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.7356 | 0.450059 | 0.225029 | − | 0.974352i | \(-0.427752\pi\) | ||||
0.225029 | + | 0.974352i | \(0.427752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.68291 | 0.279671 | 0.139836 | − | 0.990175i | \(-0.455343\pi\) | ||||
0.139836 | + | 0.990175i | \(0.455343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.6526 | − | 44.5954i | −0.653895 | − | 1.86300i | ||||
\(574\) | 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 | \(0.521654\pi\) |
−0.997687 | + | 0.0679761i | \(0.978346\pi\) | |||||||
\(588\) | 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 | 0.881352 | − | 0.472461i | \(-0.156634\pi\) |
−0.472461 | + | 0.881352i | \(0.656634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.3786 | − | 32.4186i | −0.465697 | − | 1.32681i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.8800 | 1.46602 | 0.733010 | − | 0.680218i | \(-0.238115\pi\) | ||||
0.733010 | + | 0.680218i | \(0.238115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.4277 | −1.68987 | −0.844936 | − | 0.534867i | \(-0.820362\pi\) | ||||
−0.844936 | + | 0.534867i | \(0.820362\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.1994 | − | 3.56554i | −1.31126 | − | 0.145200i | ||||
\(604\) | 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 | −0.400843 | − | 0.916147i | \(-0.631283\pi\) |
0.916147 | + | 0.400843i | \(0.131283\pi\) | |||||||
\(618\) | 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 | ||||||||
\(627\) | 3.89578 | − | 1.36738i | 0.155583 | − | 0.0546081i | ||||
\(628\) | 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 | ||||||||
\(633\) | −12.1319 | + | 4.25817i | −0.482198 | + | 0.169247i | ||||
\(634\) | 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 | \(-0.790549\pi\) | ||
0.791211 | − | 0.611543i | \(-0.209451\pi\) | |||||||
\(642\) | 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 | −0.893184 | − | 0.449692i | \(-0.851534\pi\) |
0.449692 | + | 0.893184i | \(0.351534\pi\) | |||||||
\(648\) | 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 | 0.0581466 | − | 0.998308i | \(-0.481481\pi\) |
−0.998308 | + | 0.0581466i | \(0.981481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.29733 | + | 47.8387i | −0.206668 | + | 1.86637i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.4805 | −1.26526 | −0.632630 | − | 0.774454i | \(-0.718025\pi\) | ||||
−0.632630 | + | 0.774454i | \(0.718025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.0233 | 1.12888 | 0.564438 | − | 0.825475i | \(-0.309093\pi\) | ||||
0.564438 | + | 0.825475i | \(0.309093\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.96784 | − | 8.45560i | −0.115261 | − | 0.328388i | ||||
\(664\) | 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 | −0.899661 | − | 0.436589i | \(-0.856186\pi\) |
0.436589 | + | 0.899661i | \(0.356186\pi\) | |||||||
\(678\) | 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 | 0.661973 | − | 0.749528i | \(-0.269719\pi\) |
−0.749528 | + | 0.661973i | \(0.769719\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.0460 | − | 34.3199i | −0.459582 | − | 1.30939i | ||||
\(688\) | 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 | ||||||||
\(693\) | −2.01588 | + | 18.2049i | −0.0765769 | + | 0.691545i | ||||
\(694\) | 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 | \(0.0551396\pi\) | ||||
−0.985034 | + | 0.172361i | \(0.944860\pi\) | |||||||
\(702\) | 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 | ||||||||
\(717\) | −30.8560 | + | 10.8302i | −1.15234 | + | 0.404461i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.1296 | −0.937177 | −0.468588 | − | 0.883417i | \(-0.655237\pi\) | ||||
−0.468588 | + | 0.883417i | \(0.655237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.88549 | 0.330913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.7931 | − | 9.40413i | 0.996445 | − | 0.349743i | ||||
\(724\) | 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 | 0.981410 | − | 0.191925i | \(-0.0614731\pi\) |
−0.191925 | + | 0.981410i | \(0.561473\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.1645 | − | 1.67921i | −0.554842 | − | 0.0614393i | ||||
\(748\) | 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 | ||||||||
\(753\) | 14.2064 | + | 40.4752i | 0.517711 | + | 1.47500i | ||||
\(754\) | 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 | \(-0.701370\pi\) | ||
0.591262 | − | 0.806480i | \(-0.298630\pi\) | |||||||
\(762\) | 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 | 0.162991 | − | 0.986628i | \(-0.447886\pi\) |
−0.986628 | + | 0.162991i | \(0.947886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.30475 | − | 6.56642i | −0.0826826 | − | 0.235569i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.18573 | 0.0783118 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.2337 | −1.36811 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.6213 | − | 25.0206i | 0.558261 | − | 0.894162i | ||||
\(784\) | 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 | −0.180246 | − | 0.983622i | \(-0.557689\pi\) |
0.983622 | + | 0.180246i | \(0.0576893\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | −28.4045 | + | 9.96973i | −0.999887 | + | 0.350951i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.31835 | 0.257299 | 0.128650 | − | 0.991690i | \(-0.458936\pi\) | ||||
0.128650 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.32051 | 0.0463693 | 0.0231847 | − | 0.999731i | \(-0.492619\pi\) | ||||
0.0231847 | + | 0.999731i | \(0.492619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.0337 | + | 11.9455i | −1.19361 | + | 0.418948i | ||||
\(814\) | 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 | \(0.0771163\pi\) | ||||
−0.970796 | + | 0.239905i | \(0.922884\pi\) | |||||||
\(822\) | 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 | −0.365803 | − | 0.930692i | \(-0.619206\pi\) |
0.930692 | + | 0.365803i | \(0.119206\pi\) | |||||||
\(828\) | 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 | ||||||||
\(837\) | −3.77711 | + | 6.04977i | −0.130556 | + | 0.209111i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.0750 | −0.658541 | −0.329270 | − | 0.944236i | \(-0.606803\pi\) | ||||
−0.329270 | + | 0.944236i | \(0.606803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.22424 | 0.111181 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.68083 | + | 19.0342i | 0.230100 | + | 0.655572i | ||||
\(844\) | 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 | −0.00141712 | − | 0.999999i | \(-0.500451\pi\) |
0.999999 | + | 0.00141712i | \(0.000451084\pi\) | |||||||
\(858\) | 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 | \(-0.955645\pi\) |
−0.138894 | − | 0.990307i | \(-0.544355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.06567 | − | 22.9797i | −0.273925 | − | 0.780432i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.0619 | −1.35901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.5892 | 1.10424 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −43.4939 | − | 4.81621i | −1.47205 | − | 0.163004i | ||||
\(874\) | 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 | \(0.337184\pi\) | ||||
−0.489486 | + | 0.872011i | \(0.662816\pi\) | |||||||
\(882\) | 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 | \(0.541891\pi\) |
−0.991353 | + | 0.131225i | \(0.958109\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | 14.2585 | − | 5.00461i | 0.476078 | − | 0.167099i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.79156 | −0.259863 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.0816 | 0.735644 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.03354 | + | 2.46871i | −0.234062 | + | 0.0821534i | ||||
\(904\) | 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 | \(-0.814428\pi\) | ||
0.834819 | − | 0.550524i | \(-0.185572\pi\) | |||||||
\(912\) | 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 | ||||||||
\(927\) | −2.93382 | + | 26.4945i | −0.0963592 | + | 0.870194i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.8616 | −0.618830 | −0.309415 | − | 0.950927i | \(-0.600133\pi\) | ||||
−0.309415 | + | 0.950927i | \(0.600133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.390435 | 0.0127960 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.3876 | + | 32.4443i | 0.372814 | + | 1.06218i | ||||
\(934\) | 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 | \(-0.628508\pi\) | ||
0.392842 | − | 0.919606i | \(-0.371492\pi\) | |||||||
\(942\) | 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 | \(-0.361278\pi\) |
0.906530 | − | 0.422142i | \(-0.138722\pi\) | |||||||
\(948\) | 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 | 0.682975 | − | 0.730442i | \(-0.260686\pi\) |
−0.730442 | + | 0.682975i | \(0.760686\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.8807 | − | 56.6418i | −0.642653 | − | 1.83097i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.7964 | 0.413218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1161 | −0.939228 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.57414 | + | 14.2156i | −0.0507259 | + | 0.458093i | ||||
\(964\) | 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 | \(0.0842211\pi\) | ||||
−0.965200 | + | 0.261512i | \(0.915779\pi\) | |||||||
\(972\) | 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 | \(-0.429340\pi\) |
0.975462 | − | 0.220167i | \(-0.0706602\pi\) | |||||||
\(978\) | 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 | 0.748653 | − | 0.662962i | \(-0.230701\pi\) |
−0.662962 | + | 0.748653i | \(0.730701\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.05831 | − | 1.07344i | 0.0973471 | − | 0.0341680i | ||||
\(988\) | 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 | ||||||||
\(993\) | 38.6317 | − | 13.5594i | 1.22594 | − | 0.430294i | ||||
\(994\) | 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.1457.3 | ✓ | 32 | |
3.2 | odd | 2 | inner | 2100.2.s.c.1457.6 | yes | 32 | |
5.2 | odd | 4 | inner | 2100.2.s.c.1793.11 | yes | 32 | |
5.3 | odd | 4 | inner | 2100.2.s.c.1793.6 | yes | 32 | |
5.4 | even | 2 | inner | 2100.2.s.c.1457.14 | yes | 32 | |
15.2 | even | 4 | inner | 2100.2.s.c.1793.14 | yes | 32 | |
15.8 | even | 4 | inner | 2100.2.s.c.1793.3 | yes | 32 | |
15.14 | odd | 2 | inner | 2100.2.s.c.1457.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.s.c.1457.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
2100.2.s.c.1457.6 | yes | 32 | 3.2 | odd | 2 | inner | |
2100.2.s.c.1457.11 | yes | 32 | 15.14 | odd | 2 | inner | |
2100.2.s.c.1457.14 | yes | 32 | 5.4 | even | 2 | inner | |
2100.2.s.c.1793.3 | yes | 32 | 15.8 | even | 4 | inner | |
2100.2.s.c.1793.6 | yes | 32 | 5.3 | odd | 4 | inner | |
2100.2.s.c.1793.11 | yes | 32 | 5.2 | odd | 4 | inner | |
2100.2.s.c.1793.14 | yes | 32 | 15.2 | even | 4 | inner |