Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.11 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.30 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.471887 | + | 2.18571i | −0.211034 | + | 0.977479i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.05400i | − | 0.398373i | −0.979962 | − | 0.199187i | \(-0.936170\pi\) | ||
0.979962 | − | 0.199187i | \(-0.0638300\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.95761 | −1.79629 | −0.898144 | − | 0.439701i | \(-0.855084\pi\) | ||||
−0.898144 | + | 0.439701i | \(0.855084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.75627i | 1.59650i | 0.602324 | + | 0.798252i | \(0.294241\pi\) | ||||
−0.602324 | + | 0.798252i | \(0.705759\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.18571 | + | 0.471887i | 0.564348 | + | 0.121841i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.60912i | − | 1.11788i | −0.829210 | − | 0.558938i | \(-0.811209\pi\) | ||
0.829210 | − | 0.558938i | \(-0.188791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.92917 | 1.13083 | 0.565415 | − | 0.824807i | \(-0.308716\pi\) | ||||
0.565415 | + | 0.824807i | \(0.308716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.05400 | −0.230001 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.41155i | 1.12839i | 0.825643 | + | 0.564193i | \(0.190813\pi\) | ||||
−0.825643 | + | 0.564193i | \(0.809187\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.55464 | − | 2.06282i | −0.910929 | − | 0.412563i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.23932 | −0.415831 | −0.207916 | − | 0.978147i | \(-0.566668\pi\) | ||||
−0.207916 | + | 0.978147i | \(0.566668\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.73316 | −0.670495 | −0.335248 | − | 0.942130i | \(-0.608820\pi\) | ||||
−0.335248 | + | 0.942130i | \(0.608820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.95761i | 1.03709i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.30373 | + | 0.497368i | 0.389401 | + | 0.0840705i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.8869i | − | 1.78979i | −0.446274 | − | 0.894896i | \(-0.647249\pi\) | ||
0.446274 | − | 0.894896i | \(-0.352751\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.75627 | 0.921742 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0866 | 1.88761 | 0.943805 | − | 0.330502i | \(-0.107218\pi\) | ||||
0.943805 | + | 0.330502i | \(0.107218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.81718i | 1.03961i | 0.854285 | + | 0.519805i | \(0.173995\pi\) | ||||
−0.854285 | + | 0.519805i | \(0.826005\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.471887 | − | 2.18571i | 0.0703448 | − | 0.325826i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.17727i | − | 1.19278i | −0.802696 | − | 0.596388i | \(-0.796602\pi\) | ||
0.802696 | − | 0.596388i | \(-0.203398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.88909 | 0.841299 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60912 | −0.645406 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.55304i | − | 0.213327i | −0.994295 | − | 0.106663i | \(-0.965983\pi\) | ||
0.994295 | − | 0.106663i | \(-0.0340167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.81132 | − | 13.0216i | 0.379079 | − | 1.75583i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.92917i | − | 0.652885i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.2977 | −1.86140 | −0.930699 | − | 0.365787i | \(-0.880800\pi\) | ||||
−0.930699 | + | 0.365787i | \(0.880800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.79653 | 0.358059 | 0.179030 | − | 0.983844i | \(-0.442704\pi\) | ||||
0.179030 | + | 0.983844i | \(0.442704\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.05400i | 0.132791i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.5815 | − | 2.71631i | −1.56055 | − | 0.336917i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.41155 | 0.651474 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.7028 | −1.74490 | −0.872451 | − | 0.488701i | \(-0.837471\pi\) | ||||
−0.872451 | + | 0.488701i | \(0.837471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.57857i | − | 0.887005i | −0.896273 | − | 0.443502i | \(-0.853736\pi\) | ||
0.896273 | − | 0.443502i | \(-0.146264\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.06282 | + | 4.55464i | −0.238194 | + | 0.525925i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.27931i | 0.715593i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8213 | 1.33000 | 0.665002 | − | 0.746842i | \(-0.268431\pi\) | ||||
0.665002 | + | 0.746842i | \(0.268431\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.4407i | − | 1.91436i | −0.289488 | − | 0.957182i | \(-0.593485\pi\) | ||
0.289488 | − | 0.957182i | \(-0.406515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.0742 | + | 2.17498i | 1.09270 | + | 0.235910i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.23932i | 0.240080i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.38538 | 0.146850 | 0.0734250 | − | 0.997301i | \(-0.476607\pi\) | ||||
0.0734250 | + | 0.997301i | \(0.476607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.06709 | 0.636004 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.73316i | 0.387111i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.32601 | + | 10.7737i | −0.238644 | + | 1.10536i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.06742i | − | 0.209915i | −0.994477 | − | 0.104957i | \(-0.966529\pi\) | ||
0.994477 | − | 0.104957i | \(-0.0334706\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.95761 | 0.598763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.77954 | 0.475582 | 0.237791 | − | 0.971316i | \(-0.423577\pi\) | ||||
0.237791 | + | 0.971316i | \(0.423577\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.44398i | − | 0.536411i | −0.963362 | − | 0.268206i | \(-0.913569\pi\) | ||
0.963362 | − | 0.268206i | \(-0.0864306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.497368 | − | 2.30373i | 0.0485381 | − | 0.224821i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.33646i | − | 0.322548i | −0.986910 | − | 0.161274i | \(-0.948440\pi\) | ||
0.986910 | − | 0.161274i | \(-0.0515603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.41914 | −0.614842 | −0.307421 | − | 0.951574i | \(-0.599466\pi\) | ||||
−0.307421 | + | 0.951574i | \(0.599466\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8869 | −1.03334 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.8095i | − | 1.20501i | −0.798114 | − | 0.602507i | \(-0.794169\pi\) | ||
0.798114 | − | 0.602507i | \(-0.205831\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.8281 | − | 2.55364i | −1.10297 | − | 0.238128i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.75627i | − | 0.532168i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.85799 | −0.445332 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.4932 | 2.22665 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 12.0866i | − | 1.08981i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.65800 | − | 8.98171i | 0.595509 | − | 0.803348i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.82063i | − | 0.693969i | −0.937871 | − | 0.346984i | \(-0.887206\pi\) | ||
0.937871 | − | 0.346984i | \(-0.112794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.81718 | 0.600219 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.0662 | −0.966860 | −0.483430 | − | 0.875383i | \(-0.660609\pi\) | ||||
−0.483430 | + | 0.875383i | \(0.660609\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.19533i | − | 0.450492i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.18571 | − | 0.471887i | −0.188116 | − | 0.0406136i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.15865i | − | 0.269861i | −0.990855 | − | 0.134931i | \(-0.956919\pi\) | ||
0.990855 | − | 0.134931i | \(-0.0430812\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.8408 | −1.08915 | −0.544573 | − | 0.838714i | \(-0.683308\pi\) | ||||
−0.544573 | + | 0.838714i | \(0.683308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.17727 | −0.688650 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 34.2937i | − | 2.86778i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.05671 | − | 4.89450i | 0.0877547 | − | 0.406466i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.88909i | − | 0.485724i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5610 | 1.35673 | 0.678365 | − | 0.734725i | \(-0.262689\pi\) | ||||
0.678365 | + | 0.734725i | \(0.262689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.96949 | −0.404411 | −0.202206 | − | 0.979343i | \(-0.564811\pi\) | ||||
−0.202206 | + | 0.979343i | \(0.564811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.60912i | 0.372625i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.76163 | − | 8.15960i | 0.141498 | − | 0.655395i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.21604i | 0.735520i | 0.929921 | + | 0.367760i | \(0.119875\pi\) | ||||
−0.929921 | + | 0.367760i | \(0.880125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.55304 | −0.123164 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.70376 | 0.449519 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.88270i | 0.147465i | 0.997278 | + | 0.0737324i | \(0.0234911\pi\) | ||||
−0.997278 | + | 0.0737324i | \(0.976509\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.0216 | − | 2.81132i | −1.01373 | − | 0.218861i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.39200i | − | 0.494628i | −0.968935 | − | 0.247314i | \(-0.920452\pi\) | ||
0.968935 | − | 0.247314i | \(-0.0795479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.1347 | −1.54882 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.92917 | −0.376943 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0950i | 1.07162i | 0.844339 | + | 0.535810i | \(0.179994\pi\) | ||||
−0.844339 | + | 0.535810i | \(0.820006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.17420 | + | 4.80058i | −0.164354 | + | 0.362890i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.2977i | 1.07468i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.33808 | −0.473730 | −0.236865 | − | 0.971543i | \(-0.576120\pi\) | ||||
−0.236865 | + | 0.971543i | \(0.576120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5417 | 0.783558 | 0.391779 | − | 0.920059i | \(-0.371860\pi\) | ||||
0.391779 | + | 0.920059i | \(0.371860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.79653i | − | 0.206726i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.7956 | + | 5.13738i | 1.74948 | + | 0.377708i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.4593i | 2.00803i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.05400 | 0.0766670 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3720 | 1.25699 | 0.628496 | − | 0.777813i | \(-0.283671\pi\) | ||||
0.628496 | + | 0.777813i | \(0.283671\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58895i | 0.114375i | 0.998363 | + | 0.0571875i | \(0.0182133\pi\) | ||||
−0.998363 | + | 0.0571875i | \(0.981787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.71631 | + | 12.5815i | −0.194519 | + | 0.900983i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.54762i | − | 0.252757i | −0.991982 | − | 0.126379i | \(-0.959665\pi\) | ||
0.991982 | − | 0.126379i | \(-0.0403354\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2568 | 1.15241 | 0.576206 | − | 0.817305i | \(-0.304533\pi\) | ||||
0.576206 | + | 0.817305i | \(0.304533\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.36024i | 0.165656i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.70352 | + | 26.4178i | −0.398351 | + | 1.84510i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.41155i | − | 0.376129i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.3661 | −2.03130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.6131 | −1.48791 | −0.743955 | − | 0.668230i | \(-0.767052\pi\) | ||||
−0.743955 | + | 0.668230i | \(0.767052\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.7028i | 1.00742i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.9004 | − | 3.21694i | −1.01620 | − | 0.219393i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.93474i | 0.267107i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.57857 | −0.512112 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.5313 | 1.78469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.2068i | − | 1.08529i | −0.839963 | − | 0.542644i | \(-0.817423\pi\) | ||
0.839963 | − | 0.542644i | \(-0.182577\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.55464 | + | 2.06282i | 0.303643 | + | 0.137521i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 27.5854i | − | 1.83091i | −0.402424 | − | 0.915453i | \(-0.631832\pi\) | ||
0.402424 | − | 0.915453i | \(-0.368168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.79803 | 0.515309 | 0.257654 | − | 0.966237i | \(-0.417050\pi\) | ||||
0.257654 | + | 0.966237i | \(0.417050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.27931 | 0.413148 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.283397i | − | 0.0185660i | −0.999957 | − | 0.00928299i | \(-0.997045\pi\) | ||
0.999957 | − | 0.00928299i | \(-0.00295491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.8731 | + | 3.85875i | 1.16591 | + | 0.251717i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 11.8213i | − | 0.767878i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.65421 | −0.171687 | −0.0858433 | − | 0.996309i | \(-0.527358\pi\) | ||||
−0.0858433 | + | 0.996309i | \(0.527358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.03842 | 0.582216 | 0.291108 | − | 0.956690i | \(-0.405976\pi\) | ||||
0.291108 | + | 0.956690i | \(0.405976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.77899 | + | 12.8718i | −0.177543 | + | 0.822351i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.3737i | 1.80537i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.4407 | −1.10526 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.51967 | −0.411518 | −0.205759 | − | 0.978603i | \(-0.565966\pi\) | ||||
−0.205759 | + | 0.978603i | \(0.565966\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 32.2399i | − | 2.02691i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.17498 | − | 10.0742i | 0.136203 | − | 0.630870i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 20.0865i | − | 1.25296i | −0.779438 | − | 0.626479i | \(-0.784495\pi\) | ||
0.779438 | − | 0.626479i | \(-0.215505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4747 | −0.713006 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23932 | 0.138610 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.5886i | 1.51620i | 0.652139 | + | 0.758099i | \(0.273872\pi\) | ||||
−0.652139 | + | 0.758099i | \(0.726128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.39450 | + | 0.732861i | 0.208522 | + | 0.0450193i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.38538i | − | 0.0847839i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.4202 | −1.91572 | −0.957861 | − | 0.287233i | \(-0.907265\pi\) | ||||
−0.957861 | + | 0.287233i | \(0.907265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.7654 | 1.62588 | 0.812942 | − | 0.582344i | \(-0.197864\pi\) | ||||
0.812942 | + | 0.582344i | \(0.197864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.06709i | − | 0.367197i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.1348 | + | 12.2895i | 1.63629 | + | 0.741083i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 14.2357i | − | 0.855342i | −0.903935 | − | 0.427671i | \(-0.859334\pi\) | ||
0.903935 | − | 0.427671i | \(-0.140666\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.73316 | 0.223498 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.1025 | −1.37818 | −0.689090 | − | 0.724676i | \(-0.741989\pi\) | ||||
−0.689090 | + | 0.724676i | \(0.741989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.425677i | − | 0.0253039i | −0.999920 | − | 0.0126519i | \(-0.995973\pi\) | ||
0.999920 | − | 0.0126519i | \(-0.00402734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.7737 | + | 2.32601i | 0.638181 | + | 0.137781i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 12.7392i | − | 0.751974i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.24396 | −0.249645 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.06742 | −0.121194 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.67159i | − | 0.506600i | −0.967388 | − | 0.253300i | \(-0.918484\pi\) | ||
0.967388 | − | 0.253300i | \(-0.0815160\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.74689 | − | 31.2505i | 0.392819 | − | 1.81948i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.95761i | − | 0.345696i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.1504 | −1.80147 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.18528 | 0.414153 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.77954i | − | 0.274577i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.31965 | + | 6.11240i | −0.0755628 | + | 0.349995i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6728i | 1.46522i | 0.680646 | + | 0.732612i | \(0.261699\pi\) | ||||
−0.680646 | + | 0.732612i | \(0.738301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.44398 | −0.309697 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.83109 | −0.330651 | −0.165325 | − | 0.986239i | \(-0.552867\pi\) | ||||
−0.165325 | + | 0.986239i | \(0.552867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.0059i | − | 1.80908i | −0.426389 | − | 0.904540i | \(-0.640214\pi\) | ||
0.426389 | − | 0.904540i | \(-0.359786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.30373 | − | 0.497368i | −0.129800 | − | 0.0280235i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 27.5282i | − | 1.54614i | −0.634323 | − | 0.773068i | \(-0.718721\pi\) | ||
0.634323 | − | 0.773068i | \(-0.281279\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3410 | 0.746953 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.33646 | −0.186223 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 22.7191i | − | 1.26413i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.8741 | − | 26.2178i | 0.658659 | − | 1.45430i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.41914i | 0.354979i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.61881 | −0.475170 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.60882 | −0.363254 | −0.181627 | − | 0.983368i | \(-0.558136\pi\) | ||||
−0.181627 | + | 0.983368i | \(0.558136\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.8869i | 0.596598i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.18571 | + | 0.471887i | 0.119418 | + | 0.0257820i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8040i | 0.588530i | 0.955724 | + | 0.294265i | \(0.0950749\pi\) | ||||
−0.955724 | + | 0.294265i | \(0.904925\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.8095 | −0.695715 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.2407 | 1.20440 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.5851i | − | 0.733524i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.55364 | + | 11.8281i | −0.137483 | + | 0.636802i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.1980i | 1.24533i | 0.782488 | + | 0.622666i | \(0.213951\pi\) | ||||
−0.782488 | + | 0.622666i | \(0.786049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.29425 | −0.0692795 | −0.0346398 | − | 0.999400i | \(-0.511028\pi\) | ||||
−0.0346398 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.75627 | −0.307247 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6477i | 0.726393i | 0.931713 | + | 0.363197i | \(0.118315\pi\) | ||||
−0.931713 | + | 0.363197i | \(0.881685\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.93807 | − | 32.1361i | 0.368235 | − | 1.70560i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.85799i | 0.257112i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.2243 | 1.27851 | 0.639255 | − | 0.768995i | \(-0.279243\pi\) | ||||
0.639255 | + | 0.768995i | \(0.279243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.29673 | 0.278775 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 24.4932i | − | 1.28556i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.5645 | + | 3.57623i | 0.867028 | + | 0.187189i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 21.1096i | − | 1.10191i | −0.834535 | − | 0.550955i | \(-0.814264\pi\) | ||
0.834535 | − | 0.550955i | \(-0.185736\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0866 | −0.629203 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.63690 | −0.0849837 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.16636i | 0.0603921i | 0.999544 | + | 0.0301960i | \(0.00961316\pi\) | ||||
−0.999544 | + | 0.0301960i | \(0.990387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.98171 | − | 6.65800i | −0.463813 | − | 0.343817i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.8901i | − | 0.663876i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.3326 | −1.19851 | −0.599257 | − | 0.800556i | \(-0.704537\pi\) | ||||
−0.599257 | + | 0.800556i | \(0.704537\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.82063 | −0.400663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.1343i | − | 1.07991i | −0.841693 | − | 0.539956i | \(-0.818441\pi\) | ||
0.841693 | − | 0.539956i | \(-0.181559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.7247 | − | 2.96313i | −0.699477 | − | 0.151015i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 6.81718i | − | 0.346536i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.4327 | 0.934574 | 0.467287 | − | 0.884106i | \(-0.345232\pi\) | ||||
0.467287 | + | 0.884106i | \(0.345232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9425 | 1.26139 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.0662i | 0.558217i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.57834 | + | 25.8380i | −0.280677 | + | 1.30005i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.41387i | 0.271714i | 0.990728 | + | 0.135857i | \(0.0433788\pi\) | ||||
−0.990728 | + | 0.135857i | \(0.956621\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.19533 | −0.260092 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.7402 | −1.68491 | −0.842453 | − | 0.538770i | \(-0.818889\pi\) | ||||
−0.842453 | + | 0.538770i | \(0.818889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 21.4891i | − | 1.07045i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.471887 | + | 2.18571i | −0.0234483 | + | 0.108609i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 64.8599i | 3.21498i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.47591 | −0.369660 | −0.184830 | − | 0.982771i | \(-0.559173\pi\) | ||||
−0.184830 | + | 0.982771i | \(0.559173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.15865 | −0.155805 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0697i | 0.741531i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.1202 | + | 8.23003i | 1.87125 | + | 0.403997i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.8408i | 0.628819i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5414 | −0.514983 | −0.257491 | − | 0.966281i | \(-0.582896\pi\) | ||||
−0.257491 | + | 0.966281i | \(0.582896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7034 | −0.765338 | −0.382669 | − | 0.923886i | \(-0.624995\pi\) | ||||
−0.382669 | + | 0.923886i | \(0.624995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.17727i | 0.397592i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.50776 | + | 20.9929i | −0.461194 | + | 1.01830i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.94754i | − | 0.142641i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −34.2937 | −1.65571 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.8294 | 0.521633 | 0.260816 | − | 0.965388i | \(-0.416008\pi\) | ||||
0.260816 | + | 0.965388i | \(0.416008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.8147i | − | 1.52892i | −0.644673 | − | 0.764459i | \(-0.723006\pi\) | ||
0.644673 | − | 0.764459i | \(-0.276994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.89450 | − | 1.05671i | −0.234673 | − | 0.0506652i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.6745i | 1.27601i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.0051 | 0.477517 | 0.238758 | − | 0.971079i | \(-0.423260\pi\) | ||||
0.238758 | + | 0.971079i | \(0.423260\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.88909 | −0.280433 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.2793i | 1.43861i | 0.694693 | + | 0.719306i | \(0.255540\pi\) | ||||
−0.694693 | + | 0.719306i | \(0.744460\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.653743 | + | 3.02804i | −0.0309904 | + | 0.143543i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 16.5610i | − | 0.783309i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.9478 | −1.36613 | −0.683066 | − | 0.730357i | \(-0.739354\pi\) | ||||
−0.683066 | + | 0.730357i | \(0.739354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −72.0073 | −3.39069 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.96949i | 0.233487i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.86299 | + | 13.2609i | −0.134219 | + | 0.621681i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.2130i | 0.618079i | 0.951049 | + | 0.309039i | \(0.100007\pi\) | ||||
−0.951049 | + | 0.309039i | \(0.899993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.60912 | 0.215135 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4553 | −0.580100 | −0.290050 | − | 0.957011i | \(-0.593672\pi\) | ||||
−0.290050 | + | 0.957011i | \(0.593672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.23535i | 0.336255i | 0.985765 | + | 0.168128i | \(0.0537721\pi\) | ||||
−0.985765 | + | 0.168128i | \(0.946228\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.15960 | − | 1.76163i | −0.378392 | − | 0.0816937i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.0723i | − | 0.558641i | −0.960198 | − | 0.279321i | \(-0.909891\pi\) | ||
0.960198 | − | 0.279321i | \(-0.0901092\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.05400 | −0.0486690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.21604 | 0.424653 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 40.6141i | − | 1.86744i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.4506 | − | 10.1680i | −1.03011 | − | 0.466539i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.55304i | 0.0711090i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.3952 | −0.977570 | −0.488785 | − | 0.872404i | \(-0.662560\pi\) | ||||
−0.488785 | + | 0.872404i | \(0.662560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 62.6679 | 2.85741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 5.70376i | − | 0.259530i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.51878 | + | 0.975589i | 0.205187 | + | 0.0442992i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 38.9047i | − | 1.76294i | −0.472240 | − | 0.881470i | \(-0.656554\pi\) | ||
0.472240 | − | 0.881470i | \(-0.343446\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.88270 | 0.0851388 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.6008 | 1.01996 | 0.509979 | − | 0.860187i | \(-0.329653\pi\) | ||||
0.509979 | + | 0.860187i | \(0.329653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3213i | 0.464848i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.81132 | + | 13.0216i | −0.126360 | + | 0.585278i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.4967i | 0.695123i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.3659 | 1.00124 | 0.500618 | − | 0.865668i | \(-0.333106\pi\) | ||||
0.500618 | + | 0.865668i | \(0.333106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.39200 | −0.285573 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.1497i | 0.853842i | 0.904289 | + | 0.426921i | \(0.140402\pi\) | ||||
−0.904289 | + | 0.426921i | \(0.859598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.25540 | + | 10.4467i | −0.100364 | + | 0.464871i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.1347i | 0.894213i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.5130 | −1.21949 | −0.609745 | − | 0.792598i | \(-0.708728\pi\) | ||||
−0.609745 | + | 0.792598i | \(0.708728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.98779 | −0.353359 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.92917i | 0.217628i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.8990 | + | 2.56894i | 0.524330 | + | 0.113201i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.7170i | 2.14257i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0950 | 0.618700 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.1764 | −0.752513 | −0.376257 | − | 0.926515i | \(-0.622789\pi\) | ||||
−0.376257 | + | 0.926515i | \(0.622789\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0736i | 0.484216i | 0.970249 | + | 0.242108i | \(0.0778389\pi\) | ||||
−0.970249 | + | 0.242108i | \(0.922161\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.80058 | + | 2.17420i | 0.209515 | + | 0.0948899i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.2066i | 0.749530i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.28487 | −0.273255 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.2977 | 0.620466 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 69.5738i | 3.01358i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.29253 | + | 1.57443i | 0.315284 | + | 0.0680687i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.33808i | 0.273508i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −35.0849 | −1.51122 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.8480 | 1.75619 | 0.878097 | − | 0.478483i | \(-0.158813\pi\) | ||||
0.878097 | + | 0.478483i | \(0.158813\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 10.5417i | − | 0.452387i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.02911 | − | 14.0304i | 0.129753 | − | 0.600995i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.246608i | − | 0.0105442i | −0.999986 | − | 0.00527210i | \(-0.998322\pi\) | ||
0.999986 | − | 0.00527210i | \(-0.00167817\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.79653 | −0.119353 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.0380 | −0.470234 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 12.4596i | − | 0.529838i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.13738 | − | 23.7956i | 0.218070 | − | 1.01007i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 34.2129i | − | 1.44965i | −0.688935 | − | 0.724823i | \(-0.741922\pi\) | ||
0.688935 | − | 0.724823i | \(-0.258078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.2415 | −1.65974 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.4593 | 1.15933 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.6249i | 0.995670i | 0.867272 | + | 0.497835i | \(0.165871\pi\) | ||||
−0.867272 | + | 0.497835i | \(0.834129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.9978 | + | 6.04463i | 1.17788 | + | 0.254299i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.05400i | − | 0.0442637i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.1495 | 1.26393 | 0.631966 | − | 0.774996i | \(-0.282248\pi\) | ||||
0.631966 | + | 0.774996i | \(0.282248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.5928 | −0.903630 | −0.451815 | − | 0.892112i | \(-0.649223\pi\) | ||||
−0.451815 | + | 0.892112i | \(0.649223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 17.3720i | − | 0.725725i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1630 | − | 24.6477i | 0.465531 | − | 1.02788i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11.7363i | − | 0.488587i | −0.969701 | − | 0.244293i | \(-0.921444\pi\) | ||
0.969701 | − | 0.244293i | \(-0.0785560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.58895 | 0.0660344 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.3824 | −0.762631 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.25243i | 0.383197i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.5815 | + | 2.71631i | 0.520183 | + | 0.112306i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 20.3837i | − | 0.841324i | −0.907218 | − | 0.420662i | \(-0.861798\pi\) | ||
0.907218 | − | 0.420662i | \(-0.138202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.4014 | −0.758216 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.54762 | −0.145930 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.43935i | 0.387627i | 0.981038 | + | 0.193814i | \(0.0620857\pi\) | ||||
−0.981038 | + | 0.193814i | \(0.937914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.29243 | − | 10.6182i | 0.0939803 | − | 0.435302i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 16.2568i | − | 0.665345i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.8634 | −0.811597 | −0.405799 | − | 0.913962i | \(-0.633007\pi\) | ||||
−0.405799 | + | 0.913962i | \(0.633007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.7313 | 0.437738 | 0.218869 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218869 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.5580 | + | 53.5349i | −0.469900 | + | 2.17650i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0936i | 0.450277i | 0.974327 | + | 0.225138i | \(0.0722834\pi\) | ||||
−0.974327 | + | 0.225138i | \(0.927717\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.36024 | 0.0956416 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 47.0706 | 1.90427 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.3529i | 1.91257i | 0.292443 | + | 0.956283i | \(0.405532\pi\) | ||||
−0.292443 | + | 0.956283i | \(0.594468\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.4178 | + | 5.70352i | 1.06527 | + | 0.229988i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.2495i | 0.412628i | 0.978486 | + | 0.206314i | \(0.0661469\pi\) | ||||
−0.978486 | + | 0.206314i | \(0.933853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.3560 | 0.697598 | 0.348799 | − | 0.937197i | \(-0.386590\pi\) | ||||
0.348799 | + | 0.937197i | \(0.386590\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.41155 | −0.217158 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.46019i | − | 0.0585011i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.4896 | + | 18.7908i | 0.659583 | + | 0.751632i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.3661i | 1.17277i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.1789 | −2.00077 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3285 | 0.849074 | 0.424537 | − | 0.905411i | \(-0.360437\pi\) | ||||
0.424537 | + | 0.905411i | \(0.360437\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.6131i | 0.859045i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.0936 | + | 3.69046i | 0.678340 | + | 0.146451i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.8992i | 1.34314i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.7028 | 0.581634 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.63011 | 0.0643855 | 0.0321928 | − | 0.999482i | \(-0.489751\pi\) | ||||
0.0321928 | + | 0.999482i | \(0.489751\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4.46775i | − | 0.176191i | −0.996112 | − | 0.0880955i | \(-0.971922\pi\) | ||
0.996112 | − | 0.0880955i | \(-0.0280781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.21694 | + | 14.9004i | −0.126667 | + | 0.586701i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.0164i | − | 0.944184i | −0.881549 | − | 0.472092i | \(-0.843499\pi\) | ||
0.881549 | − | 0.472092i | \(-0.156501\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 85.1800 | 3.34361 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.93474 | 0.154215 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 7.55753i | − | 0.295749i | −0.989006 | − | 0.147875i | \(-0.952757\pi\) | ||
0.989006 | − | 0.147875i | \(-0.0472432\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.22201 | − | 24.1875i | 0.204041 | − | 0.945085i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.57857i | 0.295668i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.1442 | 1.09634 | 0.548172 | − | 0.836366i | \(-0.315324\pi\) | ||||
0.548172 | + | 0.836366i | \(0.315324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5584 | −0.410675 | −0.205338 | − | 0.978691i | \(-0.565829\pi\) | ||||
−0.205338 | + | 0.978691i | \(0.565829\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 26.5313i | − | 1.03039i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3555 | + | 2.45161i | 0.440347 | + | 0.0950694i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 12.1182i | − | 0.469218i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.2068 | −0.626591 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.6607 | −0.643178 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.5266i | 1.29235i | 0.763188 | + | 0.646177i | \(0.223633\pi\) | ||||
−0.763188 | + | 0.646177i | \(0.776367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.06282 | − | 4.55464i | 0.0793978 | − | 0.175308i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.27727i | 0.125956i | 0.998015 | + | 0.0629778i | \(0.0200597\pi\) | ||||
−0.998015 | + | 0.0629778i | \(0.979940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.17905 | −0.0836244 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.5854 | −1.05707 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7957i | 1.21663i | 0.793697 | + | 0.608314i | \(0.208154\pi\) | ||||
−0.793697 | + | 0.608314i | \(0.791846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.90388 | + | 1.49053i | 0.263784 | + | 0.0569500i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.79803i | − | 0.297514i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.93974 | 0.340577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4097 | 0.510130 | 0.255065 | − | 0.966924i | \(-0.417903\pi\) | ||||
0.255065 | + | 0.966924i | \(0.417903\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 6.27931i | − | 0.238531i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.05943 | − | 28.0663i | 0.229847 | − | 1.06462i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 55.7086i | − | 2.11011i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.283397 | −0.0107191 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.29925 | 0.0868415 | 0.0434207 | − | 0.999057i | \(-0.486174\pi\) | ||||
0.0434207 | + | 0.999057i | \(0.486174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 53.6633i | − | 2.02395i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.85875 | − | 17.8731i | 0.145329 | − | 0.673141i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5.03762i | − | 0.189459i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.4751 | 1.14452 | 0.572258 | − | 0.820074i | \(-0.306068\pi\) | ||||
0.572258 | + | 0.820074i | \(0.306068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.8213 | −0.443335 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20.2022i | − | 0.756578i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 74.9560 | + | 16.1827i | 2.80319 | + | 0.605200i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.65421i | 0.0991233i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.2577 | −0.531723 | −0.265861 | − | 0.964011i | \(-0.585656\pi\) | ||||
−0.265861 | + | 0.964011i | \(0.585656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.73794 | −0.213692 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 9.03842i | − | 0.336143i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.1993 | + | 4.61931i | 0.378793 | + | 0.171557i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.4092i | − | 0.608584i | −0.952579 | − | 0.304292i | \(-0.901580\pi\) | ||
0.952579 | − | 0.304292i | \(-0.0984199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.4212 | 1.16215 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.72078i | 0.100494i | 0.998737 | + | 0.0502472i | \(0.0160009\pi\) | ||||
−0.998737 | + | 0.0502472i | \(0.983999\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.8718 | + | 2.77899i | 0.474785 | + | 0.102504i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.95761i | 0.219452i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0392 | −0.737153 | −0.368577 | − | 0.929597i | \(-0.620155\pi\) | ||||
−0.368577 | + | 0.929597i | \(0.620155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.3737 | 1.04233 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.34914i | 0.0861817i | 0.999071 | + | 0.0430909i | \(0.0137205\pi\) | ||||
−0.999071 | + | 0.0430909i | \(0.986280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.81493 | + | 36.1975i | −0.286317 | + | 1.32617i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.4407i | 0.638121i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.51662 | −0.128494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.0028 | −1.38674 | −0.693371 | − | 0.720581i | \(-0.743875\pi\) | ||||
−0.693371 | + | 0.720581i | \(0.743875\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.51967i | 0.237590i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.34504 | − | 10.8619i | 0.0853447 | − | 0.395304i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.99948i | 0.363437i | 0.983351 | + | 0.181719i | \(0.0581660\pi\) | ||||
−0.983351 | + | 0.181719i | \(0.941834\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.2399 | −1.17024 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.8632 | 0.575042 | 0.287521 | − | 0.957774i | \(-0.407169\pi\) | ||||
0.287521 | + | 0.957774i | \(0.407169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.76575i | 0.244937i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.0742 | − | 2.17498i | −0.364233 | − | 0.0786367i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 82.3013i | − | 2.97173i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.0656 | 1.26450 | 0.632248 | − | 0.774766i | \(-0.282132\pi\) | ||||
0.632248 | + | 0.774766i | \(0.282132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0865 | −0.723396 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.5430i | 0.630980i | 0.948929 | + | 0.315490i | \(0.102169\pi\) | ||||
−0.948929 | + | 0.315490i | \(0.897831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.0032 | + | 7.70082i | 0.610774 | + | 0.276622i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4747i | 0.411654i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.5769 | 2.13457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 87.5937 | 3.13435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.23932i | − | 0.0800268i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.1436 | − | 4.34893i | −0.718955 | − | 0.155220i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19.5528i | − | 0.696981i | −0.937312 | − | 0.348491i | \(-0.886694\pi\) | ||
0.937312 | − | 0.348491i | \(-0.113306\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.5886 | 0.875378 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.5011 | −0.480045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0976i | 0.571643i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.732861 | − | 3.39450i | 0.0259919 | − | 0.120390i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.89801i | 0.315184i | 0.987504 | + | 0.157592i | \(0.0503730\pi\) | ||||
−0.987504 | + | 0.157592i | \(0.949627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.6900 | −1.33338 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.38538 | −0.0489500 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 45.1502i | 1.59332i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.69153 | + | 12.4667i | −0.0948640 | + | 0.439395i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.4202i | 1.10604i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.1130 | 1.05872 | 0.529358 | − | 0.848399i | \(-0.322433\pi\) | ||||
0.529358 | + | 0.848399i | \(0.322433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.13516 | −0.145205 | −0.0726026 | − | 0.997361i | \(-0.523130\pi\) | ||||
−0.0726026 | + | 0.997361i | \(0.523130\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 26.7654i | − | 0.938705i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.11504 | − | 0.888424i | −0.144144 | − | 0.0311201i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.6030i | 1.17562i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.06709 | −0.212001 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.81459 | 0.237831 | 0.118915 | − | 0.992904i | \(-0.462058\pi\) | ||||
0.118915 | + | 0.992904i | \(0.462058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7.85021i | − | 0.273641i | −0.990596 | − | 0.136821i | \(-0.956312\pi\) | ||
0.990596 | − | 0.136821i | \(-0.0436884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.2895 | − | 27.1348i | 0.427864 | − | 0.944713i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.7621i | 1.34789i | 0.738781 | + | 0.673946i | \(0.235402\pi\) | ||||
−0.738781 | + | 0.673946i | \(0.764598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.95665 | 0.276346 | 0.138173 | − | 0.990408i | \(-0.455877\pi\) | ||||
0.138173 | + | 0.990408i | \(0.455877\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2357 | −0.493832 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 27.1435i | − | 0.940467i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.9710 | + | 3.01630i | 0.483488 | + | 0.104383i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.73316i | − | 0.129037i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.479751 | 0.0165628 | 0.00828142 | − | 0.999966i | \(-0.497364\pi\) | ||||
0.00828142 | + | 0.999966i | \(0.497364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.9854 | −0.827084 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.1025i | 0.795692i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.50131 | − | 44.0086i | 0.326855 | − | 1.51394i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25.8157i | − | 0.887039i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.425677 | −0.0146092 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.9149 | 2.01958 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.1671i | 0.348114i | 0.984736 | + | 0.174057i | \(0.0556877\pi\) | ||||
−0.984736 | + | 0.174057i | \(0.944312\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.32601 | − | 10.7737i | 0.0795480 | − | 0.368454i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.1488i | 0.551632i | 0.961210 | + | 0.275816i | \(0.0889481\pi\) | ||||
−0.961210 | + | 0.275816i | \(0.911052\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.1353 | −1.13056 | −0.565281 | − | 0.824898i | \(-0.691232\pi\) | ||||
−0.565281 | + | 0.824898i | \(0.691232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.7392 | −0.434152 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1515i | 1.26465i | 0.774702 | + | 0.632326i | \(0.217900\pi\) | ||||
−0.774702 | + | 0.632326i | \(0.782100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.8075 | − | 6.65123i | −1.04749 | − | 0.226149i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.24396i | 0.144133i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −70.4269 | −2.38907 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.75627 | 0.195044 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.06742i | 0.0699716i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.46669 | − | 7.01751i | −0.320033 | − | 0.237235i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.4414i | 0.386349i | 0.981164 | + | 0.193174i | \(0.0618783\pi\) | ||||
−0.981164 | + | 0.193174i | \(0.938122\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.67159 | −0.292486 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0790 | −0.440641 | −0.220321 | − | 0.975427i | \(-0.570710\pi\) | ||||
−0.220321 | + | 0.975427i | \(0.570710\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.10061i | 0.171649i | 0.996310 | + | 0.0858247i | \(0.0273525\pi\) | ||||
−0.996310 | + | 0.0858247i | \(0.972648\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.2505 | − | 6.74689i | −1.05048 | − | 0.226794i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.71010i | 0.191726i | 0.995395 | + | 0.0958632i | \(0.0305611\pi\) | ||||
−0.995395 | + | 0.0958632i | \(0.969439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.24292 | −0.276459 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.95761 | −0.199588 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 40.3071i | − | 1.34883i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.99086 | − | 13.8532i | 0.0999734 | − | 0.463061i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.1504i | 1.04008i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.35974 | 0.278813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.15816 | −0.238473 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 7.18528i | − | 0.239111i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.97449 | + | 23.0411i | −0.165358 | + | 0.765911i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 43.7074i | − | 1.45128i | −0.688074 | − | 0.725640i | \(-0.741544\pi\) | ||
0.688074 | − | 0.725640i | \(-0.258456\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.77954 | −0.158527 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.63409 | 0.120403 | 0.0602014 | − | 0.998186i | \(-0.480826\pi\) | ||||
0.0602014 | + | 0.998186i | \(0.480826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 103.905i | 3.43875i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.11240 | + | 1.31965i | 0.202070 | + | 0.0436262i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.6638i | 0.385171i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.09079 | −0.134943 | −0.0674714 | − | 0.997721i | \(-0.521493\pi\) | ||||
−0.0674714 | + | 0.997721i | \(0.521493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.6728 | 0.845948 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 84.6334i | − | 2.78574i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.4576 | + | 49.5859i | −0.738403 | + | 1.63037i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.44398i | 0.178804i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.3348 | 0.503119 | 0.251559 | − | 0.967842i | \(-0.419057\pi\) | ||||
0.251559 | + | 0.967842i | \(0.419057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.0283 | 0.951365 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.83109i | 0.190901i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −60.0181 | − | 12.9577i | −1.96280 | − | 0.423763i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3325i | 0.696903i | 0.937327 | + | 0.348451i | \(0.113292\pi\) | ||||
−0.937327 | + | 0.348451i | \(0.886708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.0059 | −1.04447 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.1809 | 0.690477 | 0.345239 | − | 0.938515i | \(-0.387798\pi\) | ||||
0.345239 | + | 0.938515i | \(0.387798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 65.4073i | 2.12995i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.497368 | + | 2.30373i | −0.0161794 | + | 0.0749403i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 8.23161i | − | 0.267491i | −0.991016 | − | 0.133746i | \(-0.957299\pi\) | ||
0.991016 | − | 0.133746i | \(-0.0427005\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.6243 | 1.41611 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.5282 | −0.892662 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.8858i | 1.45399i | 0.686641 | + | 0.726996i | \(0.259084\pi\) | ||||
−0.686641 | + | 0.726996i | \(0.740916\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.19762 | + | 37.9701i | −0.265269 | + | 1.22868i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 13.3410i | − | 0.431254i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.32920 | −0.107506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.0635 | −0.550436 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.33646i | 0.107516i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.47298 | − | 0.749804i | −0.111799 | − | 0.0241371i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47.6937i | − | 1.53373i | −0.641810 | − | 0.766863i | \(-0.721816\pi\) | ||
0.641810 | − | 0.766863i | \(-0.278184\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.7191 | −0.729844 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0702 | −0.387350 | −0.193675 | − | 0.981066i | \(-0.562041\pi\) | ||||
−0.193675 | + | 0.981066i | \(0.562041\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.5342i | 0.433887i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.2178 | − | 11.8741i | −0.839641 | − | 0.380277i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.5820i | 0.658477i | 0.944247 | + | 0.329238i | \(0.106792\pi\) | ||||
−0.944247 | + | 0.329238i | \(0.893208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.25356 | −0.263785 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.41914 | 0.204947 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.3186i | 0.839434i | 0.907655 | + | 0.419717i | \(0.137871\pi\) | ||||
−0.907655 | + | 0.419717i | \(0.862129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.75406 | + | 1.67408i | 0.247065 | + | 0.0533405i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.61881i | 0.274340i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.8915 | −1.17308 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.1491 | −1.14832 | −0.574158 | − | 0.818745i | \(-0.694670\pi\) | ||||
−0.574158 | + | 0.818745i | \(0.694670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.60882i | 0.209725i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.67136 | + | 35.5326i | −0.243199 | + | 1.12646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.32045i | 0.231841i | 0.993258 | + | 0.115920i | \(0.0369818\pi\) | ||||
−0.993258 | + | 0.115920i | \(0.963018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.8869 | 0.344446 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4020.2.g.c.1609.11 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.30 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.11 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.30 | yes | 38 | 5.4 | even | 2 | inner |