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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.9 | ||
Character | \(\chi\) | \(=\) | 2100.1457 |
Dual form | 2100.2.s.b.1793.9 |
$q$-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 | ||||||||
\(3\) | 1.27746 | + | 1.16966i | 0.737540 | + | 0.675303i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.263792 | + | 2.98838i | 0.0879306 | + | 0.996127i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.66926i | 0.804813i | 0.915461 | + | 0.402406i | \(0.131826\pi\) | ||||
−0.915461 | + | 0.402406i | \(0.868174\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.79204 | + | 1.79204i | −0.497023 | + | 0.497023i | −0.910510 | − | 0.413487i | \(-0.864311\pi\) |
0.413487 | + | 0.910510i | \(0.364311\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.27125 | + | 1.27125i | −0.308324 | + | 0.308324i | −0.844259 | − | 0.535935i | \(-0.819959\pi\) |
0.535935 | + | 0.844259i | \(0.319959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.59577i | 1.28376i | 0.766806 | + | 0.641879i | \(0.221845\pi\) | ||||
−0.766806 | + | 0.641879i | \(0.778155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0762239 | − | 1.73037i | −0.0166334 | − | 0.377598i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.30672 | − | 6.30672i | −1.31504 | − | 1.31504i | −0.917647 | − | 0.397395i | \(-0.869914\pi\) |
−0.397395 | − | 0.917647i | \(-0.630086\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.15841 | + | 4.12607i | −0.607835 | + | 0.794063i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.475975 | −0.0883863 | −0.0441932 | − | 0.999023i | \(-0.514072\pi\) | ||||
−0.0441932 | + | 0.999023i | \(0.514072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.444136 | −0.0797691 | −0.0398846 | − | 0.999204i | \(-0.512699\pi\) | ||||
−0.0398846 | + | 0.999204i | \(0.512699\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.12213 | + | 3.40987i | −0.543493 | + | 0.593581i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.01080 | − | 3.01080i | −0.494972 | − | 0.494972i | 0.414897 | − | 0.909869i | \(-0.363818\pi\) |
−0.909869 | + | 0.414897i | \(0.863818\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.38533 | + | 0.193177i | −0.702215 | + | 0.0309330i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.01600i | 0.627193i | 0.949556 | + | 0.313597i | \(0.101534\pi\) | ||||
−0.949556 | + | 0.313597i | \(0.898466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.42331 | − | 6.42331i | 0.979545 | − | 0.979545i | −0.0202500 | − | 0.999795i | \(-0.506446\pi\) |
0.999795 | + | 0.0202500i | \(0.00644620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.964802 | + | 0.964802i | −0.140731 | + | 0.140731i | −0.773962 | − | 0.633232i | \(-0.781728\pi\) |
0.633232 | + | 0.773962i | \(0.281728\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.11091 | + | 0.137037i | −0.435614 | + | 0.0191890i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.484079 | − | 0.484079i | −0.0664933 | − | 0.0664933i | 0.673078 | − | 0.739571i | \(-0.264972\pi\) |
−0.739571 | + | 0.673078i | \(0.764972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.54515 | + | 7.14835i | −0.866926 | + | 0.946823i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.72277 | −1.13561 | −0.567804 | − | 0.823164i | \(-0.692207\pi\) | ||||
−0.567804 | + | 0.823164i | \(0.692207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.10457 | −0.269463 | −0.134731 | − | 0.990882i | \(-0.543017\pi\) | ||||
−0.134731 | + | 0.990882i | \(0.543017\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.92657 | − | 2.29963i | 0.242726 | − | 0.289726i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.71588 | + | 8.71588i | 1.06481 | + | 1.06481i | 0.997749 | + | 0.0670663i | \(0.0213639\pi\) |
0.0670663 | + | 0.997749i | \(0.478636\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.679845 | − | 15.4333i | −0.0818438 | − | 1.85795i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4237i | 1.35575i | 0.735179 | + | 0.677873i | \(0.237098\pi\) | ||||
−0.735179 | + | 0.677873i | \(0.762902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.99671 | + | 8.99671i | −1.05299 | + | 1.05299i | −0.0544701 | + | 0.998515i | \(0.517347\pi\) |
−0.998515 | + | 0.0544701i | \(0.982653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.88745 | − | 1.88745i | 0.215095 | − | 0.215095i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3740i | 1.16717i | 0.812053 | + | 0.583583i | \(0.198350\pi\) | ||||
−0.812053 | + | 0.583583i | \(0.801650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.86083 | + | 1.57662i | −0.984536 | + | 0.175180i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.12377 | − | 6.12377i | −0.672171 | − | 0.672171i | 0.286045 | − | 0.958216i | \(-0.407659\pi\) |
−0.958216 | + | 0.286045i | \(0.907659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.608037 | − | 0.556729i | −0.0651884 | − | 0.0596876i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.60386 | 0.594008 | 0.297004 | − | 0.954876i | \(-0.404013\pi\) | ||||
0.297004 | + | 0.954876i | \(0.404013\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.53433 | 0.265670 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.567364 | − | 0.519488i | −0.0588329 | − | 0.0538684i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6451 | + | 12.6451i | 1.28392 | + | 1.28392i | 0.938420 | + | 0.345495i | \(0.112289\pi\) |
0.345495 | + | 0.938420i | \(0.387711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.97677 | + | 0.704129i | −0.801695 | + | 0.0707676i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4047i | 1.23431i | 0.786841 | + | 0.617156i | \(0.211715\pi\) | ||||
−0.786841 | + | 0.617156i | \(0.788285\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.62130 | − | 8.62130i | 0.849482 | − | 0.849482i | −0.140587 | − | 0.990068i | \(-0.544899\pi\) |
0.990068 | + | 0.140587i | \(0.0448989\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.2775 | + | 11.2775i | −1.09023 | + | 1.09023i | −0.0947294 | + | 0.995503i | \(0.530199\pi\) |
−0.995503 | + | 0.0947294i | \(0.969801\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.3852i | − | 1.28207i | −0.767514 | − | 0.641033i | \(-0.778506\pi\) | ||
0.767514 | − | 0.641033i | \(-0.221494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.324555 | − | 7.36777i | −0.0308054 | − | 0.699318i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.01522 | + | 2.01522i | 0.189576 | + | 0.189576i | 0.795513 | − | 0.605937i | \(-0.207202\pi\) |
−0.605937 | + | 0.795513i | \(0.707202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.82802 | − | 4.88257i | −0.538801 | − | 0.451394i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.79782 | 0.164806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.87504 | 0.352277 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.69735 | + | 5.13026i | −0.423546 | + | 0.462580i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.33400 | − | 8.33400i | −0.739523 | − | 0.739523i | 0.232962 | − | 0.972486i | \(-0.425158\pi\) |
−0.972486 | + | 0.232962i | \(0.925158\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.7186 | − | 0.692413i | 1.38394 | − | 0.0609635i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.60764i | − | 0.140460i | −0.997531 | − | 0.0702299i | \(-0.977627\pi\) | ||
0.997531 | − | 0.0702299i | \(-0.0223733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.95681 | − | 3.95681i | 0.343099 | − | 0.343099i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.3887 | + | 13.3887i | −1.14387 | + | 1.14387i | −0.156137 | + | 0.987735i | \(0.549904\pi\) |
−0.987735 | + | 0.156137i | \(0.950096\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.5750i | − | 1.57551i | −0.615988 | − | 0.787755i | \(-0.711243\pi\) | ||
0.615988 | − | 0.787755i | \(-0.288757\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.36098 | + | 0.104003i | −0.198831 | + | 0.00875861i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.78343 | − | 4.78343i | −0.400010 | − | 0.400010i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.16966 | + | 1.27746i | −0.0964719 | + | 0.105363i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.1846 | −1.73551 | −0.867754 | − | 0.496994i | \(-0.834437\pi\) | ||||
−0.867754 | + | 0.496994i | \(0.834437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.6302 | 1.59748 | 0.798742 | − | 0.601674i | \(-0.205499\pi\) | ||||
0.798742 | + | 0.601674i | \(0.205499\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.13433 | − | 3.46364i | −0.334241 | − | 0.280019i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.67010 | − | 8.67010i | −0.691949 | − | 0.691949i | 0.270712 | − | 0.962661i | \(-0.412741\pi\) |
−0.962661 | + | 0.270712i | \(0.912741\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0521822 | − | 1.18460i | −0.00413832 | − | 0.0939447i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.91905i | 0.702920i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.49057 | − | 5.49057i | 0.430054 | − | 0.430054i | −0.458592 | − | 0.888647i | \(-0.651646\pi\) |
0.888647 | + | 0.458592i | \(0.151646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.27850 | − | 2.27850i | 0.176316 | − | 0.176316i | −0.613432 | − | 0.789748i | \(-0.710211\pi\) |
0.789748 | + | 0.613432i | \(0.210211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.57718i | 0.505937i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.7223 | + | 1.47612i | −1.27879 | + | 0.112882i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.59286 | + | 1.59286i | 0.121103 | + | 0.121103i | 0.765061 | − | 0.643958i | \(-0.222709\pi\) |
−0.643958 | + | 0.765061i | \(0.722709\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.1430 | − | 10.2027i | −0.837557 | − | 0.766880i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.3198 | 1.51877 | 0.759386 | − | 0.650640i | \(-0.225499\pi\) | ||||
0.759386 | + | 0.650640i | \(0.225499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0406 | 0.820642 | 0.410321 | − | 0.911941i | \(-0.365417\pi\) | ||||
0.410321 | + | 0.911941i | \(0.365417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.68850 | − | 2.46163i | −0.198740 | − | 0.181969i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.39331 | − | 3.39331i | −0.248143 | − | 0.248143i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.15090 | − | 0.684244i | 0.374673 | − | 0.0497714i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 17.8623i | − | 1.29247i | −0.763138 | − | 0.646236i | \(-0.776342\pi\) | ||
0.763138 | − | 0.646236i | \(-0.223658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.1871 | − | 10.1871i | 0.733281 | − | 0.733281i | −0.237987 | − | 0.971268i | \(-0.576488\pi\) |
0.971268 | + | 0.237987i | \(0.0764876\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.883558 | − | 0.883558i | 0.0629509 | − | 0.0629509i | −0.674930 | − | 0.737881i | \(-0.735826\pi\) |
0.737881 | + | 0.674930i | \(0.235826\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8123i | 1.05002i | 0.851097 | + | 0.525009i | \(0.175938\pi\) | ||||
−0.851097 | + | 0.525009i | \(0.824062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.939546 | + | 21.3288i | 0.0662704 | + | 1.50442i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.336565 | + | 0.336565i | 0.0236222 | + | 0.0236222i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.1832 | − | 20.5105i | 1.19432 | − | 1.42558i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.9366 | −1.03318 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9856 | 1.03165 | 0.515825 | − | 0.856694i | \(-0.327486\pi\) | ||||
0.515825 | + | 0.856694i | \(0.327486\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.3619 | + | 14.5933i | −0.915540 | + | 0.999917i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.314051 | + | 0.314051i | 0.0213192 | + | 0.0213192i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.0160 | + | 0.969818i | −1.48770 | + | 0.0655342i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.55628i | − | 0.306488i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.47628 | + | 5.47628i | −0.366719 | + | 0.366719i | −0.866279 | − | 0.499560i | \(-0.833495\pi\) |
0.499560 | + | 0.866279i | \(0.333495\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0160 | − | 10.0160i | 0.664784 | − | 0.664784i | −0.291720 | − | 0.956504i | \(-0.594228\pi\) |
0.956504 | + | 0.291720i | \(0.0942275\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7390i | 0.841817i | 0.907103 | + | 0.420908i | \(0.138289\pi\) | ||||
−0.907103 | + | 0.420908i | \(0.861711\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.61882 | − | 0.203462i | 0.303896 | − | 0.0133868i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.64712 | + | 6.64712i | 0.435467 | + | 0.435467i | 0.890483 | − | 0.455016i | \(-0.150366\pi\) |
−0.455016 | + | 0.890483i | \(0.650366\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.1341 | + | 13.2523i | −0.788191 | + | 0.860832i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.9148 | −1.02944 | −0.514720 | − | 0.857358i | \(-0.672104\pi\) | ||||
−0.514720 | + | 0.857358i | \(0.672104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.83380 | 0.246957 | 0.123478 | − | 0.992347i | \(-0.460595\pi\) | ||||
0.123478 | + | 0.992347i | \(0.460595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.1634 | − | 8.35009i | −0.844435 | − | 0.535659i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0278 | − | 10.0278i | −0.638057 | − | 0.638057i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.660123 | − | 14.9856i | −0.0418336 | − | 0.949672i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.9866i | − | 0.882829i | −0.897303 | − | 0.441415i | \(-0.854477\pi\) | ||
0.897303 | − | 0.441415i | \(-0.145523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8343 | − | 16.8343i | 1.05836 | − | 1.05836i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.37271 | − | 6.37271i | 0.397519 | − | 0.397519i | −0.479838 | − | 0.877357i | \(-0.659305\pi\) |
0.877357 | + | 0.479838i | \(0.159305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.25791i | 0.264574i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.125558 | − | 1.42239i | −0.00777186 | − | 0.0880440i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.37801 | + | 2.37801i | 0.146634 | + | 0.146634i | 0.776613 | − | 0.629978i | \(-0.216936\pi\) |
−0.629978 | + | 0.776613i | \(0.716936\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.15868 | + | 6.55461i | 0.438104 | + | 0.401135i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.5152 | 1.55569 | 0.777843 | − | 0.628459i | \(-0.216314\pi\) | ||||
0.777843 | + | 0.628459i | \(0.216314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.39006 | 0.448914 | 0.224457 | − | 0.974484i | \(-0.427939\pi\) | ||||
0.224457 | + | 0.974484i | \(0.427939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.23750 | + | 2.96430i | 0.195942 | + | 0.179408i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.79932 | + | 3.79932i | 0.228279 | + | 0.228279i | 0.811973 | − | 0.583694i | \(-0.198393\pi\) |
−0.583694 | + | 0.811973i | \(0.698393\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.117159 | − | 1.32725i | −0.00701414 | − | 0.0794602i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.5840i | − | 1.76484i | −0.470466 | − | 0.882418i | \(-0.655914\pi\) | ||
0.470466 | − | 0.882418i | \(-0.344086\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.07493 | + | 2.07493i | −0.123342 | + | 0.123342i | −0.766083 | − | 0.642741i | \(-0.777797\pi\) |
0.642741 | + | 0.766083i | \(0.277797\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.83974 | − | 2.83974i | 0.167624 | − | 0.167624i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7678i | 0.809872i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.36310 | + | 30.9440i | 0.0799065 | + | 1.81397i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.4481 | + | 13.4481i | 0.785644 | + | 0.785644i | 0.980777 | − | 0.195133i | \(-0.0625138\pi\) |
−0.195133 | + | 0.980777i | \(0.562514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.0136 | − | 8.43061i | −0.639072 | − | 0.489194i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.6038 | 1.30721 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.08393 | −0.523589 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.5093 | + | 15.8465i | −0.833535 | + | 0.910355i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7929 | + | 11.7929i | 0.673055 | + | 0.673055i | 0.958419 | − | 0.285364i | \(-0.0921147\pi\) |
−0.285364 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.0973 | − | 0.929349i | 1.20018 | − | 0.0528688i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.97298i | 0.395402i | 0.980262 | + | 0.197701i | \(0.0633474\pi\) | ||||
−0.980262 | + | 0.197701i | \(0.936653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3101 | + | 13.3101i | −0.752330 | + | 0.752330i | −0.974914 | − | 0.222584i | \(-0.928551\pi\) |
0.222584 | + | 0.974914i | \(0.428551\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.5663 | + | 15.5663i | −0.874288 | + | 0.874288i | −0.992936 | − | 0.118648i | \(-0.962144\pi\) |
0.118648 | + | 0.992936i | \(0.462144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.27050i | − | 0.0711344i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.5972 | + | 1.21567i | −1.54033 | + | 0.0678523i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.11364 | − | 7.11364i | −0.395814 | − | 0.395814i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.6561 | − | 17.0990i | 0.865783 | − | 0.945574i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.36444 | 0.0752238 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1958 | −0.615379 | −0.307690 | − | 0.951487i | \(-0.599556\pi\) | ||||
−0.307690 | + | 0.951487i | \(0.599556\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.20318 | − | 9.79163i | 0.449532 | − | 0.536578i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.1259 | + | 21.1259i | 1.15080 | + | 1.15080i | 0.986392 | + | 0.164411i | \(0.0525723\pi\) |
0.164411 | + | 0.986392i | \(0.447428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.217235 | + | 4.93148i | 0.0117986 | + | 0.267841i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.18551i | − | 0.0641992i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.85696 | + | 2.85696i | −0.153370 | + | 0.153370i | −0.779621 | − | 0.626251i | \(-0.784588\pi\) |
0.626251 | + | 0.779621i | \(0.284588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.9735i | 1.55091i | 0.631400 | + | 0.775457i | \(0.282481\pi\) | ||||
−0.631400 | + | 0.775457i | \(0.717519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.73410 | − | 13.0541i | −0.0925594 | − | 0.696775i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.9357 | + | 15.9357i | 0.848171 | + | 0.848171i | 0.989905 | − | 0.141733i | \(-0.0452676\pi\) |
−0.141733 | + | 0.989905i | \(0.545268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.29664 | + | 2.10284i | 0.121551 | + | 0.111294i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3154 | −0.597205 | −0.298603 | − | 0.954378i | \(-0.596520\pi\) | ||||
−0.298603 | + | 0.954378i | \(0.596520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3126 | −0.648034 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.95020 | + | 4.53248i | 0.259818 | + | 0.237894i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.6706 | + | 19.6706i | 1.02679 | + | 1.02679i | 0.999631 | + | 0.0271636i | \(0.00864749\pi\) |
0.0271636 | + | 0.999631i | \(0.491353\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0013 | + | 1.05939i | −0.624764 | + | 0.0551495i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.684591i | 0.0355422i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.02204 | + | 2.02204i | −0.104697 | + | 0.104697i | −0.757515 | − | 0.652818i | \(-0.773587\pi\) |
0.652818 | + | 0.757515i | \(0.273587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.852966 | − | 0.852966i | 0.0439300 | − | 0.0439300i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.9963i | − | 1.28397i | −0.766716 | − | 0.641986i | \(-0.778111\pi\) | ||
0.766716 | − | 0.641986i | \(-0.221889\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.898380 | − | 20.3943i | −0.0460254 | − | 1.04483i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.9362 | + | 15.9362i | 0.814300 | + | 0.814300i | 0.985275 | − | 0.170975i | \(-0.0546917\pi\) |
−0.170975 | + | 0.985275i | \(0.554692\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.8897 | + | 17.5009i | 1.06188 | + | 0.889619i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8000 | 0.851792 | 0.425896 | − | 0.904772i | \(-0.359959\pi\) | ||||
0.425896 | + | 0.904772i | \(0.359959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0349 | 0.810919 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.88039 | − | 2.05369i | 0.0948530 | − | 0.103595i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.55276 | + | 2.55276i | 0.128119 | + | 0.128119i | 0.768259 | − | 0.640139i | \(-0.221123\pi\) |
−0.640139 | + | 0.768259i | \(0.721123\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.68277 | − | 0.426532i | 0.484745 | − | 0.0213533i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 19.8000i | − | 0.988764i | −0.869245 | − | 0.494382i | \(-0.835394\pi\) | ||
0.869245 | − | 0.494382i | \(-0.164606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.795909 | − | 0.795909i | 0.0396471 | − | 0.0396471i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.03660 | − | 8.03660i | 0.398360 | − | 0.398360i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5780i | 0.968071i | 0.875048 | + | 0.484036i | \(0.160829\pi\) | ||||
−0.875048 | + | 0.484036i | \(0.839171\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.7637 | + | 1.44326i | −1.61611 | + | 0.0711907i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.16793 | + | 6.16793i | 0.303504 | + | 0.303504i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.7264 | − | 23.7288i | 1.06395 | − | 1.16200i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.3282 | −1.82360 | −0.911800 | − | 0.410635i | \(-0.865307\pi\) | ||||
−0.911800 | + | 0.410635i | \(0.865307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.98929 | −0.291900 | −0.145950 | − | 0.989292i | \(-0.546624\pi\) | ||||
−0.145950 | + | 0.989292i | \(0.546624\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.13770 | − | 2.62869i | −0.152560 | − | 0.127811i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.48816 | + | 1.48816i | 0.0720170 | + | 0.0720170i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.515639 | − | 11.7056i | −0.0248953 | − | 0.565152i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.2463i | − | 1.60142i | −0.599054 | − | 0.800708i | \(-0.704457\pi\) | ||
0.599054 | − | 0.800708i | \(-0.295543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.5209 | − | 10.5209i | 0.505605 | − | 0.505605i | −0.407570 | − | 0.913174i | \(-0.633624\pi\) |
0.913174 | + | 0.407570i | \(0.133624\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 35.2910 | − | 35.2910i | 1.68820 | − | 1.68820i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.4243i | − | 0.736160i | −0.929794 | − | 0.368080i | \(-0.880015\pi\) | ||
0.929794 | − | 0.368080i | \(-0.119985\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.98838 | + | 0.263792i | −0.142304 | + | 0.0125615i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.4400 | − | 24.4400i | −1.16118 | − | 1.16118i | −0.984218 | − | 0.176961i | \(-0.943373\pi\) |
−0.176961 | − | 0.984218i | \(-0.556627\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.0624 | − | 24.7787i | −1.28001 | − | 1.17199i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.04423 | 0.426824 | 0.213412 | − | 0.976962i | \(-0.431542\pi\) | ||||
0.213412 | + | 0.976962i | \(0.431542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.7197 | −0.504773 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.0767 | + | 22.9607i | 1.17821 | + | 1.07879i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.45007 | + | 5.45007i | 0.254944 | + | 0.254944i | 0.822994 | − | 0.568050i | \(-0.192302\pi\) |
−0.568050 | + | 0.822994i | \(0.692302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.23015 | − | 9.26042i | −0.0574185 | − | 0.432239i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.1279i | 1.12375i | 0.827223 | + | 0.561873i | \(0.189919\pi\) | ||||
−0.827223 | + | 0.561873i | \(0.810081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.28613 | + | 6.28613i | −0.292141 | + | 0.292141i | −0.837926 | − | 0.545784i | \(-0.816232\pi\) |
0.545784 | + | 0.837926i | \(0.316232\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.26765 | − | 6.26765i | 0.290032 | − | 0.290032i | −0.547061 | − | 0.837093i | \(-0.684253\pi\) |
0.837093 | + | 0.547061i | \(0.184253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12.3261i | − | 0.569167i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.934610 | − | 21.2167i | −0.0430645 | − | 0.977616i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.1455 | + | 17.1455i | 0.788350 | + | 0.788350i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.31892 | − | 1.57431i | 0.0603890 | − | 0.0720826i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.3706 | 0.930754 | 0.465377 | − | 0.885112i | \(-0.345919\pi\) | ||||
0.465377 | + | 0.885112i | \(0.345919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.7909 | 0.492025 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.4323 | + | 11.3937i | −0.474684 | + | 0.518432i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.973120 | − | 0.973120i | −0.0440963 | − | 0.0440963i | 0.684715 | − | 0.728811i | \(-0.259927\pi\) |
−0.728811 | + | 0.684715i | \(0.759927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4361 | − | 0.591866i | 0.607600 | − | 0.0267651i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.61037i | − | 0.0726748i | −0.999340 | − | 0.0363374i | \(-0.988431\pi\) | ||
0.999340 | − | 0.0363374i | \(-0.0115691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.605085 | − | 0.605085i | 0.0272516 | − | 0.0272516i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.07779 | − | 8.07779i | 0.362338 | − | 0.362338i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 25.2071i | − | 1.12842i | −0.825630 | − | 0.564212i | \(-0.809180\pi\) | ||
0.825630 | − | 0.564212i | \(-0.190820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.57576 | − | 0.245616i | 0.249107 | − | 0.0109733i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.1786 | − | 21.1786i | −0.944306 | − | 0.944306i | 0.0542227 | − | 0.998529i | \(-0.482732\pi\) |
−0.998529 | + | 0.0542227i | \(0.982732\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.69306 | + | 8.40206i | −0.341661 | + | 0.373149i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.4419 | 1.26066 | 0.630332 | − | 0.776326i | \(-0.282919\pi\) | ||||
0.630332 | + | 0.776326i | \(0.282919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7233 | 0.562844 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.0886 | − | 17.6737i | −1.01938 | − | 0.780313i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.57531 | − | 2.57531i | −0.113262 | − | 0.113262i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.171705 | + | 3.89791i | 0.00753702 | + | 0.171099i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3688i | 0.804753i | 0.915474 | + | 0.402377i | \(0.131816\pi\) | ||||
−0.915474 | + | 0.402377i | \(0.868184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.13799 | − | 1.13799i | 0.0497609 | − | 0.0497609i | −0.681788 | − | 0.731549i | \(-0.738798\pi\) |
0.731549 | + | 0.681788i | \(0.238798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.564609 | − | 0.564609i | 0.0245948 | − | 0.0245948i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.5495i | 2.45868i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.30099 | − | 26.0670i | −0.0998547 | − | 1.13121i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.19683 | − | 7.19683i | −0.311729 | − | 0.311729i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.9577 | + | 23.7672i | 1.12016 | + | 1.02563i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.66926 | −0.114973 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.24013 | 0.311277 | 0.155639 | − | 0.987814i | \(-0.450256\pi\) | ||||
0.155639 | + | 0.987814i | \(0.450256\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.1039 | + | 12.9138i | 0.605256 | + | 0.554182i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.3360 | − | 19.3360i | −0.826748 | − | 0.826748i | 0.160317 | − | 0.987066i | \(-0.448748\pi\) |
−0.987066 | + | 0.160317i | \(0.948748\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.555168 | − | 6.28926i | −0.0236940 | − | 0.268419i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.66345i | − | 0.113467i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.33553 | − | 7.33553i | 0.311938 | − | 0.311938i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.47041 | + | 1.47041i | −0.0623034 | + | 0.0623034i | −0.737572 | − | 0.675269i | \(-0.764028\pi\) |
0.675269 | + | 0.737572i | \(0.264028\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.0217i | 0.973712i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.365788 | − | 8.30382i | −0.0154436 | − | 0.350588i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3206 | + | 15.3206i | 0.645685 | + | 0.645685i | 0.951947 | − | 0.306262i | \(-0.0990784\pi\) |
−0.306262 | + | 0.951947i | \(0.599078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.38039 | + | 5.15071i | 0.309947 | + | 0.216310i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.1530 | −0.886779 | −0.443390 | − | 0.896329i | \(-0.646224\pi\) | ||||
−0.443390 | + | 0.896329i | \(0.646224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.8161 | 1.03852 | 0.519260 | − | 0.854616i | \(-0.326208\pi\) | ||||
0.519260 | + | 0.854616i | \(0.326208\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.8928 | − | 22.8183i | 0.872811 | − | 0.953250i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.5100 | − | 17.5100i | −0.728952 | − | 0.728952i | 0.241459 | − | 0.970411i | \(-0.422374\pi\) |
−0.970411 | + | 0.241459i | \(0.922374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.9289 | − | 1.09813i | 1.03601 | − | 0.0456369i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.66031i | 0.359290i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.29213 | − | 1.29213i | 0.0535147 | − | 0.0535147i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.76500 | − | 5.76500i | 0.237947 | − | 0.237947i | −0.578053 | − | 0.816000i | \(-0.696187\pi\) |
0.816000 | + | 0.578053i | \(0.196187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.48528i | − | 0.102404i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.16217 | − | 0.0952449i | 0.0889398 | − | 0.00391785i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9961 | + | 12.9961i | 0.533687 | + | 0.533687i | 0.921667 | − | 0.387981i | \(-0.126827\pi\) |
−0.387981 | + | 0.921667i | \(0.626827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.3254 | + | 18.9221i | −0.709080 | + | 0.774430i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.2770 | 0.419907 | 0.209954 | − | 0.977711i | \(-0.432669\pi\) | ||||
0.209954 | + | 0.977711i | \(0.432669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0122 | 0.734734 | 0.367367 | − | 0.930076i | \(-0.380259\pi\) | ||||
0.367367 | + | 0.930076i | \(0.380259\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.7472 | + | 28.3456i | −0.967061 | + | 1.15432i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7602 | − | 18.7602i | −0.761452 | − | 0.761452i | 0.215133 | − | 0.976585i | \(-0.430981\pi\) |
−0.976585 | + | 0.215133i | \(0.930981\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0362807 | + | 0.823614i | 0.00147017 | + | 0.0333745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.45793i | − | 0.139893i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.21630 | + | 8.21630i | −0.331853 | + | 0.331853i | −0.853290 | − | 0.521437i | \(-0.825396\pi\) |
0.521437 | + | 0.853290i | \(0.325396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.81959 | − | 8.81959i | 0.355063 | − | 0.355063i | −0.506926 | − | 0.861989i | \(-0.669218\pi\) |
0.861989 | + | 0.506926i | \(0.169218\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.40002i | − | 0.297432i | −0.988880 | − | 0.148716i | \(-0.952486\pi\) | ||
0.988880 | − | 0.148716i | \(-0.0475140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 45.9412 | − | 6.10281i | 1.84356 | − | 0.244897i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.96252 | − | 3.96252i | −0.158755 | − | 0.158755i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.0808 | − | 17.4707i | −0.762015 | − | 0.697713i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.65497 | 0.305224 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.48623 | −0.178594 | −0.0892970 | − | 0.996005i | \(-0.528462\pi\) | ||||
−0.0892970 | + | 0.996005i | \(0.528462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.1434 | + | 17.5280i | 0.760883 | + | 0.696676i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.79204 | − | 1.79204i | −0.0710032 | − | 0.0710032i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.1384 | + | 3.01348i | −1.35049 | + | 0.119212i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.11120i | − | 0.0833872i | −0.999130 | − | 0.0416936i | \(-0.986725\pi\) | ||
0.999130 | − | 0.0416936i | \(-0.0132753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3898 | − | 18.3898i | 0.725221 | − | 0.725221i | −0.244442 | − | 0.969664i | \(-0.578605\pi\) |
0.969664 | + | 0.244442i | \(0.0786049\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.2831 | − | 27.2831i | 1.07261 | − | 1.07261i | 0.0754588 | − | 0.997149i | \(-0.475958\pi\) |
0.997149 | − | 0.0754588i | \(-0.0240421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 23.2834i | − | 0.913952i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0338538 | + | 0.768520i | 0.00132683 | + | 0.0301207i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.55556 | + | 2.55556i | 0.100007 | + | 0.100007i | 0.755340 | − | 0.655333i | \(-0.227472\pi\) |
−0.655333 | + | 0.755340i | \(0.727472\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.2589 | − | 24.5123i | −1.14150 | − | 0.956317i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.4933 | −0.954124 | −0.477062 | − | 0.878870i | \(-0.658298\pi\) | ||||
−0.477062 | + | 0.878870i | \(0.658298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.7051 | 1.69993 | 0.849965 | − | 0.526838i | \(-0.176623\pi\) | ||||
0.849965 | + | 0.526838i | \(0.176623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.32929 | − | 5.82045i | 0.206973 | − | 0.226047i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.00184 | + | 3.00184i | 0.116232 | + | 0.116232i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.4011 | + | 0.590327i | −0.518117 | + | 0.0228233i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.61765i | − | 0.216867i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.5974 | + | 14.5974i | −0.562689 | + | 0.562689i | −0.930071 | − | 0.367381i | \(-0.880254\pi\) |
0.367381 | + | 0.930071i | \(0.380254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.68440 | + | 5.68440i | −0.218469 | + | 0.218469i | −0.807853 | − | 0.589384i | \(-0.799371\pi\) |
0.589384 | + | 0.807853i | \(0.299371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.8829i | − | 0.686282i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.5103 | − | 1.07969i | 0.939235 | − | 0.0413739i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.3035 | − | 13.3035i | −0.509045 | − | 0.509045i | 0.405189 | − | 0.914233i | \(-0.367206\pi\) |
−0.914233 | + | 0.405189i | \(0.867206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9003 | + | 16.2735i | −0.568482 | + | 0.620874i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.73498 | 0.0660974 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1289 | −1.22224 | −0.611121 | − | 0.791537i | \(-0.709281\pi\) | ||||
−0.611121 | + | 0.791537i | \(0.709281\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.13832 | + | 5.14253i | 0.233176 | + | 0.195349i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.10535 | − | 5.10535i | −0.193379 | − | 0.193379i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.716539 | + | 16.2663i | 0.0271020 | + | 0.615247i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.5725i | 1.26802i | 0.773327 | + | 0.634008i | \(0.218591\pi\) | ||||
−0.773327 | + | 0.634008i | \(0.781409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.8477 | − | 16.8477i | 0.635424 | − | 0.635424i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.77144 | − | 8.77144i | 0.329884 | − | 0.329884i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 43.1199i | − | 1.61940i | −0.586844 | − | 0.809700i | \(-0.699630\pi\) | ||
0.586844 | − | 0.809700i | \(-0.300370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −31.0014 | + | 2.73657i | −1.16265 | + | 0.102630i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.80104 | + | 2.80104i | 0.104900 | + | 0.104900i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.3304 | − | 18.6149i | −0.759253 | − | 0.695184i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.620453 | 0.0231390 | 0.0115695 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115695 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.1924 | −0.454067 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.89752 | + | 4.48424i | 0.182141 | + | 0.166771i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.8301 | − | 18.8301i | −0.698371 | − | 0.698371i | 0.265688 | − | 0.964059i | \(-0.414401\pi\) |
−0.964059 | + | 0.265688i | \(0.914401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.04895 | − | 26.0636i | −0.261072 | − | 0.965319i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3313i | 0.604035i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.51249 | − | 2.51249i | 0.0928008 | − | 0.0928008i | −0.659182 | − | 0.751983i | \(-0.729097\pi\) |
0.751983 | + | 0.659182i | \(0.229097\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.2650 | + | 23.2650i | −0.856976 | + | 0.856976i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.5679i | 0.793387i | 0.917951 | + | 0.396694i | \(0.129842\pi\) | ||||
−0.917951 | + | 0.396694i | \(0.870158\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.08097 | − | 24.5393i | −0.0397105 | − | 0.901474i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.1908 | + | 22.1908i | 0.814102 | + | 0.814102i | 0.985246 | − | 0.171144i | \(-0.0547463\pi\) |
−0.171144 | + | 0.985246i | \(0.554746\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.6847 | − | 19.9155i | 0.610463 | − | 0.728672i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.9487 | 0.582754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.09442 | −0.331860 | −0.165930 | − | 0.986138i | \(-0.553063\pi\) | ||||
−0.165930 | + | 0.986138i | \(0.553063\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.3596 | − | 17.8673i | 0.596178 | − | 0.651122i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.23834 | + | 3.23834i | 0.117699 | + | 0.117699i | 0.763503 | − | 0.645804i | \(-0.223478\pi\) |
−0.645804 | + | 0.763503i | \(0.723478\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 41.1955 | − | 1.81469i | 1.49530 | − | 0.0658689i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1713i | 1.38371i | 0.722037 | + | 0.691854i | \(0.243206\pi\) | ||||
−0.722037 | + | 0.691854i | \(0.756794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.46473 | + | 9.46473i | −0.342646 | + | 0.342646i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.6316 | − | 15.6316i | 0.564423 | − | 0.564423i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.4661i | 0.738026i | 0.929424 | + | 0.369013i | \(0.120304\pi\) | ||||
−0.929424 | + | 0.369013i | \(0.879696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.5948 | − | 0.686959i | 0.561632 | − | 0.0247402i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.6069 | − | 28.6069i | −1.02892 | − | 1.02892i | −0.999569 | − | 0.0293513i | \(-0.990656\pi\) |
−0.0293513 | − | 0.999569i | \(-0.509344\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.98031 | + | 5.43930i | −0.178668 | + | 0.195134i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.4726 | −0.805164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.4929 | −1.09112 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.50332 | − | 1.96391i | 0.0537243 | − | 0.0701843i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.92169 | + | 8.92169i | 0.318024 | + | 0.318024i | 0.848008 | − | 0.529984i | \(-0.177802\pi\) |
−0.529984 | + | 0.848008i | \(0.677802\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.256342 | + | 5.81926i | 0.00912601 | + | 0.207171i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.84995i | − | 0.101333i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.77148 | − | 3.77148i | 0.133929 | − | 0.133929i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.52194 | + | 8.52194i | −0.301863 | + | 0.301863i | −0.841742 | − | 0.539880i | \(-0.818470\pi\) |
0.539880 | + | 0.841742i | \(0.318470\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.45302i | − | 0.0867815i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.47825 | + | 16.7465i | 0.0522314 | + | 0.591707i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.0146 | − | 24.0146i | −0.847456 | − | 0.847456i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.5945 | + | 29.8440i | 1.14738 | + | 1.05056i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.3222 | 1.59344 | 0.796722 | − | 0.604346i | \(-0.206565\pi\) | ||||
0.796722 | + | 0.604346i | \(0.206565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.6399 | 0.865225 | 0.432612 | − | 0.901580i | \(-0.357592\pi\) | ||||
0.432612 | + | 0.901580i | \(0.357592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.44049 | + | 8.64386i | 0.331092 | + | 0.303153i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.9433 | + | 35.9433i | 1.25750 | + | 1.25750i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.668535 | + | 7.57354i | 0.0233605 | + | 0.264641i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 30.0676i | − | 1.04937i | −0.851297 | − | 0.524684i | \(-0.824184\pi\) | ||
0.851297 | − | 0.524684i | \(-0.175816\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8560 | + | 22.8560i | −0.796711 | + | 0.796711i | −0.982575 | − | 0.185864i | \(-0.940491\pi\) |
0.185864 | + | 0.982575i | \(0.440491\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.5172 | + | 38.5172i | −1.33937 | + | 1.33937i | −0.442706 | + | 0.896667i | \(0.645982\pi\) |
−0.896667 | + | 0.442706i | \(0.854018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31.3544i | − | 1.08898i | −0.838766 | − | 0.544491i | \(-0.816723\pi\) | ||
0.838766 | − | 0.544491i | \(-0.183277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.409555 | + | 9.29738i | 0.0142073 | + | 0.322522i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.27125 | − | 1.27125i | −0.0440463 | − | 0.0440463i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.40276 | − | 1.83254i | 0.0484865 | − | 0.0633417i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.18461 | −0.248040 | −0.124020 | − | 0.992280i | \(-0.539579\pi\) | ||||
−0.124020 | + | 0.992280i | \(0.539579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7734 | −0.992188 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.6033 | − | 37.7923i | 1.19180 | − | 1.30164i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.74007 | − | 2.74007i | −0.0941499 | − | 0.0941499i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.07760 | + | 0.223671i | −0.174263 | + | 0.00767637i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.9765i | 1.30182i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.0919 | + | 20.0919i | −0.687934 | + | 0.687934i | −0.961775 | − | 0.273841i | \(-0.911706\pi\) |
0.273841 | + | 0.961775i | \(0.411706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.4295 | + | 26.4295i | −0.902813 | + | 0.902813i | −0.995679 | − | 0.0928657i | \(-0.970397\pi\) |
0.0928657 | + | 0.995679i | \(0.470397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.40855i | − | 0.321016i | −0.987035 | − | 0.160508i | \(-0.948687\pi\) | ||
0.987035 | − | 0.160508i | \(-0.0513132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.94917 | − | 0.306115i | 0.236827 | − | 0.0104324i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.90611 | − | 3.90611i | −0.132965 | − | 0.132965i | 0.637492 | − | 0.770457i | \(-0.279972\pi\) |
−0.770457 | + | 0.637492i | \(0.779972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.1037 | + | 17.5878i | −0.546910 | + | 0.597313i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.6909 | −0.939350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.2384 | −1.05847 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.4527 | + | 41.1240i | −1.16605 | + | 1.39184i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.9724 | − | 18.9724i | −0.640651 | − | 0.640651i | 0.310065 | − | 0.950715i | \(-0.399649\pi\) |
−0.950715 | + | 0.310065i | \(0.899649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.44966 | + | 32.9090i | 0.0488958 | + | 1.10999i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 55.8433i | − | 1.88141i | −0.339225 | − | 0.940705i | \(-0.610165\pi\) | ||
0.339225 | − | 0.940705i | \(-0.389835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.13111 | − | 6.13111i | 0.206328 | − | 0.206328i | −0.596376 | − | 0.802705i | \(-0.703393\pi\) |
0.802705 | + | 0.596376i | \(0.203393\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.2424 | − | 13.2424i | 0.444638 | − | 0.444638i | −0.448930 | − | 0.893567i | \(-0.648195\pi\) |
0.893567 | + | 0.448930i | \(0.148195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.7861i | 0.395292i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.20841 | − | 23.6519i | −0.140987 | − | 0.792367i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.39881 | − | 5.39881i | −0.180664 | − | 0.180664i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.8754 | + | 26.4388i | 0.964121 | + | 0.882765i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.211397 | 0.00705050 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.23077 | 0.0410030 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.6043 | − | 10.6251i | −0.386168 | − | 0.353581i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.62949 | + | 6.62949i | 0.220129 | + | 0.220129i | 0.808553 | − | 0.588424i | \(-0.200251\pi\) |
−0.588424 | + | 0.808553i | \(0.700251\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.0699 | + | 3.27225i | −1.22953 | + | 0.108534i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4696i | 0.843844i | 0.906632 | + | 0.421922i | \(0.138644\pi\) | ||||
−0.906632 | + | 0.421922i | \(0.861356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.3459 | − | 16.3459i | 0.540971 | − | 0.540971i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.13677 | + | 1.13677i | −0.0375395 | + | 0.0375395i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.2535i | − | 0.734076i | −0.930206 | − | 0.367038i | \(-0.880372\pi\) | ||
0.930206 | − | 0.367038i | \(-0.119628\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.27124 | + | 28.8585i | 0.0418886 | + | 0.950921i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.4718 | − | 20.4718i | −0.673837 | − | 0.673837i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.0379 | + | 23.4895i | 0.920887 | + | 0.771496i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.9864 | 1.04944 | 0.524720 | − | 0.851275i | \(-0.324170\pi\) | ||||
0.524720 | + | 0.851275i | \(0.324170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.59577 | −0.183394 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.15602 | + | 8.90768i | −0.267016 | + | 0.291624i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4191 | + | 23.4191i | 0.765068 | + | 0.765068i | 0.977234 | − | 0.212166i | \(-0.0680517\pi\) |
−0.212166 | + | 0.977234i | \(0.568052\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.5713 | + | 1.43478i | −1.06292 | + | 0.0468224i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.26007i | 0.0410770i | 0.999789 | + | 0.0205385i | \(0.00653807\pi\) | ||||
−0.999789 | + | 0.0205385i | \(0.993462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3278 | − | 25.3278i | 0.824786 | − | 0.824786i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.8361 | + | 18.8361i | −0.612092 | + | 0.612092i | −0.943491 | − | 0.331399i | \(-0.892479\pi\) |
0.331399 | + | 0.943491i | \(0.392479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 32.2450i | − | 1.04672i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.0924 | + | 1.67799i | −1.23523 | + | 0.0544127i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.2821 | − | 27.2821i | −0.883753 | − | 0.883753i | 0.110161 | − | 0.993914i | \(-0.464863\pi\) |
−0.993914 | + | 0.110161i | \(0.964863\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.48605 | − | 1.62301i | 0.0480373 | − | 0.0524645i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.9345 | 0.611425 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8027 | −0.993637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.6762 | − | 30.7264i | −1.18187 | − | 0.990145i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.31919 | − | 4.31919i | −0.138896 | − | 0.138896i | 0.634240 | − | 0.773136i | \(-0.281313\pi\) |
−0.773136 | + | 0.634240i | \(0.781313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.766829 | − | 17.4079i | −0.0246341 | − | 0.559223i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 8.97863i | − | 0.288138i | −0.989568 | − | 0.144069i | \(-0.953981\pi\) | ||
0.989568 | − | 0.144069i | \(-0.0460187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.1345 | + | 13.1345i | −0.421073 | + | 0.421073i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.7172 | − | 13.7172i | 0.438853 | − | 0.438853i | −0.452773 | − | 0.891626i | \(-0.649565\pi\) |
0.891626 | + | 0.452773i | \(0.149565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.9582i | 0.478065i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.9999 | − | 3.53089i | 1.27710 | − | 0.112733i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.1638 | + | 33.1638i | 1.05776 | + | 1.05776i | 0.998226 | + | 0.0595334i | \(0.0189613\pi\) |
0.0595334 | + | 0.998226i | \(0.481039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.74301 | + | 1.59593i | 0.0554806 | + | 0.0507989i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.0200 | −2.57629 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.4841 | 0.809529 | 0.404764 | − | 0.914421i | \(-0.367354\pi\) | ||||
0.404764 | + | 0.914421i | \(0.367354\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.3022 | − | 13.0953i | −0.453867 | − | 0.415568i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.6367 | + | 41.6367i | 1.31865 | + | 1.31865i | 0.914847 | + | 0.403801i | \(0.132311\pi\) |
0.403801 | + | 0.914847i | \(0.367689\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.9321 | − | 2.91345i | 0.693900 | − | 0.0921775i |
(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.b.1457.9 | 24 | ||
3.2 | odd | 2 | inner | 2100.2.s.b.1457.3 | 24 | ||
5.2 | odd | 4 | 420.2.s.a.113.10 | yes | 24 | ||
5.3 | odd | 4 | inner | 2100.2.s.b.1793.3 | 24 | ||
5.4 | even | 2 | 420.2.s.a.197.4 | yes | 24 | ||
15.2 | even | 4 | 420.2.s.a.113.4 | ✓ | 24 | ||
15.8 | even | 4 | inner | 2100.2.s.b.1793.9 | 24 | ||
15.14 | odd | 2 | 420.2.s.a.197.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.s.a.113.4 | ✓ | 24 | 15.2 | even | 4 | ||
420.2.s.a.113.10 | yes | 24 | 5.2 | odd | 4 | ||
420.2.s.a.197.4 | yes | 24 | 5.4 | even | 2 | ||
420.2.s.a.197.10 | yes | 24 | 15.14 | odd | 2 | ||
2100.2.s.b.1457.3 | 24 | 3.2 | odd | 2 | inner | ||
2100.2.s.b.1457.9 | 24 | 1.1 | even | 1 | trivial | ||
2100.2.s.b.1793.3 | 24 | 5.3 | odd | 4 | inner | ||
2100.2.s.b.1793.9 | 24 | 15.8 | even | 4 | inner |