Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(229,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("380.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.c (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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.14077504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.6 | ||
Root | \(0.608430i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.229 |
Dual form | 380.2.c.b.229.1 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.28715i | 1.89784i | 0.315521 | + | 0.948919i | \(0.397821\pi\) | ||||
−0.315521 | + | 0.948919i | \(0.602179\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58777 | + | 1.57448i | 0.710073 | + | 0.704128i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93210i | 0.730263i | 0.930956 | + | 0.365132i | \(0.118976\pi\) | ||||
−0.930956 | + | 0.365132i | \(0.881024\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.80536 | −2.60179 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.62981 | 1.69745 | 0.848726 | − | 0.528832i | \(-0.177370\pi\) | ||||
0.848726 | + | 0.528832i | \(0.177370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.07029i | − | 0.574195i | −0.957901 | − | 0.287098i | \(-0.907310\pi\) | ||
0.957901 | − | 0.287098i | \(-0.0926904\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.17554 | + | 5.21925i | −1.33632 | + | 1.34760i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.42535i | − | 0.830768i | −0.909646 | − | 0.415384i | \(-0.863647\pi\) | ||
0.909646 | − | 0.415384i | \(-0.136353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.35109 | −1.38592 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.35744i | − | 1.11710i | −0.829470 | − | 0.558552i | \(-0.811357\pi\) | ||
0.829470 | − | 0.558552i | \(-0.188643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0420411 | + | 4.99982i | 0.00840822 | + | 0.999965i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 15.7959i | − | 3.03993i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.09146 | −0.202679 | −0.101340 | − | 0.994852i | \(-0.532313\pi\) | ||||
−0.101340 | + | 0.994852i | \(0.532313\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.09146 | 0.555243 | 0.277622 | − | 0.960691i | \(-0.410454\pi\) | ||||
0.277622 | + | 0.960691i | \(0.410454\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.5060i | 3.22149i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.04204 | + | 3.06773i | −0.514199 | + | 0.518541i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.28715i | − | 0.540404i | −0.962804 | − | 0.270202i | \(-0.912909\pi\) | ||
0.962804 | − | 0.270202i | \(-0.0870905\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.80536 | 1.08973 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6107 | −1.81329 | −0.906645 | − | 0.421895i | \(-0.861365\pi\) | ||||
−0.906645 | + | 0.421895i | \(0.861365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.501623i | − | 0.0764968i | −0.999268 | − | 0.0382484i | \(-0.987822\pi\) | ||
0.999268 | − | 0.0382484i | \(-0.0121778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.3931 | − | 12.2894i | −1.84746 | − | 1.83199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.6470i | 1.84475i | 0.386294 | + | 0.922376i | \(0.373755\pi\) | ||||
−0.386294 | + | 0.922376i | \(0.626245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.26701 | 0.466715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.2596 | 1.57666 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.01076i | 0.413560i | 0.978388 | + | 0.206780i | \(0.0662984\pi\) | ||||
−0.978388 | + | 0.206780i | \(0.933702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.93886 | + | 8.86401i | 1.20532 | + | 1.19522i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.28715i | − | 0.435394i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.35109 | 0.306086 | 0.153043 | − | 0.988220i | \(-0.451093\pi\) | ||||
0.153043 | + | 0.988220i | \(0.451093\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.62981 | 0.976897 | 0.488449 | − | 0.872593i | \(-0.337563\pi\) | ||||
0.488449 | + | 0.872593i | \(0.337563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 15.0807i | − | 1.89999i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.25963 | − | 3.28715i | 0.404307 | − | 0.407721i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.2324i | − | 1.49442i | −0.664585 | − | 0.747212i | \(-0.731392\pi\) | ||
0.664585 | − | 0.747212i | \(-0.268608\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.6107 | 2.12008 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3511 | 1.70316 | 0.851580 | − | 0.524224i | \(-0.175645\pi\) | ||||
0.851580 | + | 0.524224i | \(0.175645\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.87256i | − | 0.336208i | −0.985769 | − | 0.168104i | \(-0.946236\pi\) | ||
0.985769 | − | 0.168104i | \(-0.0537645\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.4352 | + | 0.138195i | −1.89777 | + | 0.0159574i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8773i | 1.23959i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28.5075 | 3.16750 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.35744i | 0.588056i | 0.955797 | + | 0.294028i | \(0.0949958\pi\) | ||||
−0.955797 | + | 0.294028i | \(0.905004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.39313 | − | 5.43867i | 0.584967 | − | 0.589906i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.58780i | − | 0.384653i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.35109 | −0.885214 | −0.442607 | − | 0.896716i | \(-0.645946\pi\) | ||||
−0.442607 | + | 0.896716i | \(0.645946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.1621i | 1.05376i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.58777 | − | 1.57448i | −0.162902 | − | 0.161538i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.01076i | − | 0.305696i | −0.988250 | − | 0.152848i | \(-0.951155\pi\) | ||
0.988250 | − | 0.152848i | \(-0.0488445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −43.9427 | −4.41641 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.80536 | −0.478151 | −0.239075 | − | 0.971001i | \(-0.576844\pi\) | ||||
−0.239075 | + | 0.971001i | \(0.576844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.22762i | − | 0.416560i | −0.978069 | − | 0.208280i | \(-0.933214\pi\) | ||
0.978069 | − | 0.208280i | \(-0.0667865\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.0841 | − | 9.99965i | −0.984106 | − | 0.975866i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.92098i | 0.862424i | 0.902251 | + | 0.431212i | \(0.141914\pi\) | ||||
−0.902251 | + | 0.431212i | \(0.858086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.25963 | −0.503781 | −0.251890 | − | 0.967756i | \(-0.581052\pi\) | ||||
−0.251890 | + | 0.967756i | \(0.581052\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8054 | 1.02560 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.5088i | − | 1.17673i | −0.808596 | − | 0.588364i | \(-0.799772\pi\) | ||
0.808596 | − | 0.588364i | \(-0.200228\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.43517 | − | 8.50640i | 0.786584 | − | 0.793226i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.1594i | 1.49393i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.61810 | 0.606680 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.6948 | 1.88135 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 38.1662i | − | 3.44133i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.80536 | + | 8.00477i | −0.698132 | + | 0.715969i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2952i | 1.09102i | 0.838104 | + | 0.545510i | \(0.183664\pi\) | ||||
−0.838104 | + | 0.545510i | \(0.816336\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.64891 | 0.145179 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7863 | −0.942400 | −0.471200 | − | 0.882026i | \(-0.656179\pi\) | ||||
−0.471200 | + | 0.882026i | \(0.656179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.93210i | − | 0.167534i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 24.8703 | − | 25.0803i | 2.14050 | − | 2.15857i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4.85582i | − | 0.414861i | −0.978250 | − | 0.207430i | \(-0.933490\pi\) | ||
0.978250 | − | 0.207430i | \(-0.0665100\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2405 | 0.953409 | 0.476705 | − | 0.879064i | \(-0.341831\pi\) | ||||
0.476705 | + | 0.879064i | \(0.341831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −41.5725 | −3.50104 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.6554i | − | 0.974669i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.73299 | − | 1.71848i | −0.143917 | − | 0.142712i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7391i | 0.885750i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.62981 | −0.297366 | −0.148683 | − | 0.988885i | \(-0.547503\pi\) | ||||
−0.148683 | + | 0.988885i | \(0.547503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3511 | −0.842360 | −0.421180 | − | 0.906977i | \(-0.638384\pi\) | ||||
−0.421180 | + | 0.906977i | \(0.638384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 26.7360i | 2.16148i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.90854 | + | 4.86744i | 0.394263 | + | 0.390962i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.12708i | 0.568803i | 0.958705 | + | 0.284402i | \(0.0917949\pi\) | ||||
−0.958705 | + | 0.284402i | \(0.908205\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.89682 | −0.784869 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3511 | 0.815780 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.21686i | − | 0.0953118i | −0.998864 | − | 0.0476559i | \(-0.984825\pi\) | ||
0.998864 | − | 0.0476559i | \(-0.0151751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −29.1373 | + | 29.3834i | −2.26834 | + | 2.28749i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8830i | 1.22906i | 0.788893 | + | 0.614531i | \(0.210655\pi\) | ||||
−0.788893 | + | 0.614531i | \(0.789345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.71390 | 0.670300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.80536 | 0.596891 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7884i | 1.04831i | 0.851622 | + | 0.524157i | \(0.175620\pi\) | ||||
−0.851622 | + | 0.524157i | \(0.824380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.66014 | + | 0.0812274i | −0.730238 | + | 0.00614021i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.72838i | 0.580901i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3511 | −0.773677 | −0.386838 | − | 0.922148i | \(-0.626433\pi\) | ||||
−0.386838 | + | 0.922148i | \(0.626433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.0803i | 1.85399i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.17554 | − | 5.21925i | 0.380514 | − | 0.383727i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 19.2841i | − | 1.41019i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 30.5193 | 2.21995 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.43517 | −0.610348 | −0.305174 | − | 0.952297i | \(-0.598715\pi\) | ||||
−0.305174 | + | 0.952297i | \(0.598715\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 23.2864i | − | 1.67619i | −0.545521 | − | 0.838097i | \(-0.683668\pi\) | ||
0.545521 | − | 0.838097i | \(-0.316332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.8054 | + | 10.7149i | 0.773788 | + | 0.767309i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.28116i | − | 0.590008i | −0.955496 | − | 0.295004i | \(-0.904679\pi\) | ||
0.955496 | − | 0.295004i | \(-0.0953211\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7863 | 1.33172 | 0.665861 | − | 0.746076i | \(-0.268064\pi\) | ||||
0.665861 | + | 0.746076i | \(0.268064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40.2097 | 2.83617 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.10881i | − | 0.148009i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.4352 | − | 18.2808i | −1.28757 | − | 1.27679i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.8167i | 2.90646i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.62981 | −0.389422 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.7789 | −1.49932 | −0.749660 | − | 0.661823i | \(-0.769783\pi\) | ||||
−0.749660 | + | 0.661823i | \(0.769783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 47.1742i | 3.23232i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.789795 | − | 0.796464i | 0.0538635 | − | 0.0543184i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.97300i | 0.405474i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.44255 | 0.638068 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.09146 | −0.477023 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.5548i | − | 0.974662i | −0.873217 | − | 0.487331i | \(-0.837970\pi\) | ||
0.873217 | − | 0.487331i | \(-0.162030\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.328146 | − | 39.0254i | −0.0218764 | − | 2.60169i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.07029i | 0.137410i | 0.997637 | + | 0.0687050i | \(0.0218867\pi\) | ||||
−0.997637 | + | 0.0687050i | \(0.978113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4616 | 1.02173 | 0.510867 | − | 0.859660i | \(-0.329324\pi\) | ||||
0.510867 | + | 0.859660i | \(0.329324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −35.7554 | −2.35254 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 28.8934i | − | 1.89287i | −0.322897 | − | 0.946434i | \(-0.604657\pi\) | ||
0.322897 | − | 0.946434i | \(-0.395343\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.9124 | + | 20.0805i | −1.29894 | + | 1.30991i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.1486i | − | 0.854093i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.6181 | −1.72178 | −0.860891 | − | 0.508790i | \(-0.830093\pi\) | ||||
−0.860891 | + | 0.508790i | \(0.830093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6107 | −1.26324 | −0.631619 | − | 0.775279i | \(-0.717609\pi\) | ||||
−0.631619 | + | 0.775279i | \(0.717609\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 46.3208i | 2.97148i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.18726 | + | 5.14383i | 0.331402 | + | 0.328627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.07029i | 0.131729i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.6107 | −1.11603 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2522 | 0.899594 | 0.449797 | − | 0.893131i | \(-0.351496\pi\) | ||||
0.449797 | + | 0.893131i | \(0.351496\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 30.1614i | − | 1.89623i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.8777 | + | 17.7280i | 1.11955 | + | 1.11017i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.2919i | 0.704371i | 0.935930 | + | 0.352185i | \(0.114561\pi\) | ||||
−0.935930 | + | 0.352185i | \(0.885439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.35109 | 0.394637 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.51925 | 0.527329 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3571i | 0.946959i | 0.880805 | + | 0.473479i | \(0.157002\pi\) | ||||
−0.880805 | + | 0.473479i | \(0.842998\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.74037 | + | 4.78040i | −0.291199 | + | 0.293658i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 27.4513i | − | 1.67999i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4426 | −0.697665 | −0.348832 | − | 0.937185i | \(-0.613422\pi\) | ||||
−0.348832 | + | 0.937185i | \(0.613422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4161 | 0.754223 | 0.377111 | − | 0.926168i | \(-0.376917\pi\) | ||||
0.377111 | + | 0.926168i | \(0.376917\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.1486i | 0.795790i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.236683 | + | 28.1481i | 0.0142725 | + | 1.69739i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 16.0212i | − | 0.962619i | −0.876551 | − | 0.481309i | \(-0.840161\pi\) | ||
0.876551 | − | 0.481309i | \(-0.159839\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.1300 | −1.44462 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.8851 | −1.48452 | −0.742260 | − | 0.670112i | \(-0.766246\pi\) | ||||
−0.742260 | + | 0.670112i | \(0.766246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 16.2348i | − | 0.965057i | −0.875880 | − | 0.482529i | \(-0.839718\pi\) | ||
0.875880 | − | 0.482529i | \(-0.160282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.17554 | − | 5.21925i | 0.306573 | − | 0.309161i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 22.4330i | − | 1.32418i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.26701 | 0.309824 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.89682 | 0.580162 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 23.2864i | − | 1.36041i | −0.733023 | − | 0.680204i | \(-0.761891\pi\) | ||
0.733023 | − | 0.680204i | \(-0.238109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.73299 | + | 3.70174i | 0.217343 | + | 0.215523i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 88.9282i | − | 5.16013i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.0915 | −0.641436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.969184 | 0.0558628 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 15.7959i | − | 0.907453i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.1144 | + | 12.0130i | 0.693669 | + | 0.687861i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.964728i | 0.0550599i | 0.999621 | + | 0.0275300i | \(0.00876417\pi\) | ||||
−0.999621 | + | 0.0275300i | \(0.991236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8968 | 0.790562 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.1638 | 1.02998 | 0.514988 | − | 0.857197i | \(-0.327796\pi\) | ||||
0.514988 | + | 0.857197i | \(0.327796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.30116i | − | 0.412686i | −0.978480 | − | 0.206343i | \(-0.933844\pi\) | ||
0.978480 | − | 0.206343i | \(-0.0661562\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.7442 | − | 23.9447i | 1.33784 | − | 1.34913i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7.64135i | − | 0.429181i | −0.976704 | − | 0.214590i | \(-0.931158\pi\) | ||
0.976704 | − | 0.214590i | \(-0.0688416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.14473 | −0.344039 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.3246 | −1.63674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.42535i | 0.190591i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.3511 | − | 0.0870373i | 0.574175 | − | 0.00482796i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 17.2892i | − | 0.956094i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.4352 | −1.34715 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3129 | 1.22643 | 0.613214 | − | 0.789917i | \(-0.289876\pi\) | ||||
0.613214 | + | 0.789917i | \(0.289876\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.6574i | 1.40602i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.2596 | − | 19.4223i | 1.05227 | − | 1.06115i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.790654i | 0.0430696i | 0.999768 | + | 0.0215348i | \(0.00685528\pi\) | ||||
−0.999768 | + | 0.0215348i | \(0.993145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 41.1183 | 2.23324 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.4044 | 0.942499 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8368i | 1.07109i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 27.9618 | + | 27.7277i | 1.50541 | + | 1.49281i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.95361i | − | 0.426972i | −0.976946 | − | 0.213486i | \(-0.931518\pi\) | ||
0.976946 | − | 0.213486i | \(-0.0684818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.8777 | −0.849915 | −0.424957 | − | 0.905213i | \(-0.639711\pi\) | ||||
−0.424957 | + | 0.905213i | \(0.639711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.7022 | −1.74551 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.45524i | − | 0.450027i | −0.974356 | − | 0.225013i | \(-0.927757\pi\) | ||
0.974356 | − | 0.225013i | \(-0.0722426\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.7863 | + | 22.5955i | 1.20937 | + | 1.19924i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.7547i | 1.15138i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2787 | −0.806380 | −0.403190 | − | 0.915116i | \(-0.632099\pi\) | ||||
−0.403190 | + | 0.915116i | \(0.632099\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 68.0269i | 3.57049i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.52279 | − | 4.56098i | 0.236734 | − | 0.238732i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.6331i | 1.33804i | 0.743245 | + | 0.669019i | \(0.233286\pi\) | ||||
−0.743245 | + | 0.669019i | \(0.766714\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 90.6258 | 4.71779 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.81708 | −0.302008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.30390i | − | 0.0675132i | −0.999430 | − | 0.0337566i | \(-0.989253\pi\) | ||
0.999430 | − | 0.0337566i | \(-0.0107471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.3129 | − | 25.6574i | −1.35879 | − | 1.32494i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.25964i | 0.116378i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.87034 | −0.250173 | −0.125086 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125086 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.4161 | −2.07058 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.6876i | 1.05709i | 0.848906 | + | 0.528544i | \(0.177262\pi\) | ||||
−0.848906 | + | 0.528544i | \(0.822738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.1261 | + | 17.2707i | −0.872828 | + | 0.880198i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.91535i | 0.199028i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.252246 | −0.0127894 | −0.00639470 | − | 0.999980i | \(-0.502036\pi\) | ||||
−0.00639470 | + | 0.999980i | \(0.502036\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.3511 | −0.928054 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 35.4561i | − | 1.78852i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.35109 | − | 6.29791i | −0.319558 | − | 0.316882i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.1665i | − | 1.41364i | −0.707395 | − | 0.706819i | \(-0.750130\pi\) | ||
0.707395 | − | 0.706819i | \(-0.249870\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.35109 | 0.317952 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.25963 | 0.262653 | 0.131327 | − | 0.991339i | \(-0.458076\pi\) | ||||
0.131327 | + | 0.991339i | \(0.458076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.40023i | − | 0.318818i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 45.2635 | + | 44.8845i | 2.24916 | + | 2.23033i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.5060i | − | 0.917310i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.0533 | 1.23880 | 0.619402 | − | 0.785074i | \(-0.287375\pi\) | ||||
0.619402 | + | 0.785074i | \(0.287375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9618 | 0.787338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.54253i | 0.223523i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.43517 | + | 8.50640i | −0.414066 | + | 0.417563i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.9493i | 1.80942i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7022 | −0.620542 | −0.310271 | − | 0.950648i | \(-0.600420\pi\) | ||||
−0.310271 | + | 0.950648i | \(0.600420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9618 | 0.680457 | 0.340228 | − | 0.940343i | \(-0.389496\pi\) | ||||
0.340228 | + | 0.940343i | \(0.389496\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 98.7142i | − | 4.79965i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.1261 | − | 0.144005i | 0.830739 | − | 0.00698528i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.7415i | 0.713393i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38.3129 | 1.84976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.1300 | 1.74032 | 0.870160 | − | 0.492770i | \(-0.164016\pi\) | ||||
0.870160 | + | 0.492770i | \(0.164016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.50726i | 0.264662i | 0.991206 | + | 0.132331i | \(0.0422462\pi\) | ||||
−0.991206 | + | 0.132331i | \(0.957754\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.64891 | − | 5.69661i | 0.270845 | − | 0.273132i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.35744i | 0.256281i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.4811 | 1.64569 | 0.822846 | − | 0.568265i | \(-0.192385\pi\) | ||||
0.822846 | + | 0.568265i | \(0.192385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.5002 | −1.21429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 28.9562i | − | 1.37575i | −0.725830 | − | 0.687874i | \(-0.758544\pi\) | ||
0.725830 | − | 0.687874i | \(-0.241456\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.2596 | − | 13.1486i | −0.628567 | − | 0.623303i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 11.9317i | − | 0.564352i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.5725 | 0.734913 | 0.367456 | − | 0.930041i | \(-0.380229\pi\) | ||||
0.367456 | + | 0.930041i | \(0.380229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −65.3662 | −3.07797 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 34.0256i | − | 1.59866i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.35109 | + | 6.29791i | 0.297744 | + | 0.295251i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 0.715236i | − | 0.0334573i | −0.999860 | − | 0.0167287i | \(-0.994675\pi\) | ||
0.999860 | − | 0.0167287i | \(-0.00532515\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −54.1065 | −2.52548 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.7863 | −1.34071 | −0.670355 | − | 0.742041i | \(-0.733858\pi\) | ||||
−0.670355 | + | 0.742041i | \(0.733858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1055i | 1.02733i | 0.857991 | + | 0.513664i | \(0.171712\pi\) | ||||
−0.857991 | + | 0.513664i | \(0.828288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.0000 | + | 16.1351i | −0.741982 | + | 0.748247i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 37.6645i | − | 1.74291i | −0.490478 | − | 0.871454i | \(-0.663178\pi\) | ||
0.490478 | − | 0.871454i | \(-0.336822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.6342 | 1.09132 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.4278 | −1.07950 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.82405i | − | 0.129850i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0420411 | − | 4.99982i | −0.00192898 | − | 0.229408i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 23.5001i | − | 1.07599i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.32461 | 0.243288 | 0.121644 | − | 0.992574i | \(-0.461183\pi\) | ||||
0.121644 | + | 0.992574i | \(0.461183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.80536 | −0.310298 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 34.0256i | 1.54822i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.74037 | − | 4.78040i | 0.215249 | − | 0.217067i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9425i | 0.677109i | 0.940947 | + | 0.338555i | \(0.109938\pi\) | ||||
−0.940947 | + | 0.338555i | \(0.890062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.81708 | 0.262521 | 0.131260 | − | 0.991348i | \(-0.458098\pi\) | ||||
0.131260 | + | 0.991348i | \(0.458098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.73864i | 0.168380i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −69.7710 | − | 69.1868i | −3.13597 | − | 3.10972i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.7277i | 1.24376i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.4235 | −0.779981 | −0.389990 | − | 0.920819i | \(-0.627522\pi\) | ||||
−0.389990 | + | 0.920819i | \(0.627522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −52.2097 | −2.33256 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.490004i | 0.0218482i | 0.999940 | + | 0.0109241i | \(0.00347731\pi\) | ||||
−0.999940 | + | 0.0109241i | \(0.996523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.62981 | − | 7.56593i | −0.339522 | − | 0.336679i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.6439i | 1.27212i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.4811 | −0.730510 | −0.365255 | − | 0.930908i | \(-0.619018\pi\) | ||||
−0.365255 | + | 0.930908i | \(0.619018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.55007 | 0.245521 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.7959i | 0.697407i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.65629 | − | 6.71250i | 0.293311 | − | 0.295788i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 71.2001i | 3.13138i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −45.3246 | −1.98953 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0533 | 0.747117 | 0.373559 | − | 0.927607i | \(-0.378137\pi\) | ||||
0.373559 | + | 0.927607i | \(0.378137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.2777i | 1.49886i | 0.662084 | + | 0.749430i | \(0.269672\pi\) | ||||
−0.662084 | + | 0.749430i | \(0.730328\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.267007 | − | 31.7543i | −0.0116531 | − | 1.38587i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10.5893i | − | 0.461278i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.70218 | −0.247921 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.3511 | −0.796369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0376i | 1.04118i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.0459 | + | 14.1645i | −0.607257 | + | 0.612384i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 34.0256i | − | 1.46831i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.3926 | 0.792227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.9427 | 1.28734 | 0.643669 | − | 0.765304i | \(-0.277411\pi\) | ||||
0.643669 | + | 0.765304i | \(0.277411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 6.57430i | − | 0.282130i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.35109 | − | 8.28116i | −0.357721 | − | 0.354726i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 29.1339i | − | 1.24568i | −0.782351 | − | 0.622838i | \(-0.785980\pi\) | ||
0.782351 | − | 0.622838i | \(-0.214020\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −59.5534 | −2.54168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.09146 | 0.0464979 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.72838i | − | 0.328644i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.1564 | + | 17.0128i | 0.728251 | + | 0.722153i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.4542i | 1.62936i | 0.579914 | + | 0.814678i | \(0.303086\pi\) | ||||
−0.579914 | + | 0.814678i | \(0.696914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.03851 | −0.0439241 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 63.3896 | 2.67631 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 8.58181i | − | 0.361680i | −0.983512 | − | 0.180840i | \(-0.942118\pi\) | ||
0.983512 | − | 0.180840i | \(-0.0578817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.6948 | − | 19.8611i | 0.828566 | − | 0.835563i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 55.0793i | 2.31311i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.221120 | 0.00926985 | 0.00463492 | − | 0.999989i | \(-0.498525\pi\) | ||||
0.00463492 | + | 0.999989i | \(0.498525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.23315 | 0.0934544 | 0.0467272 | − | 0.998908i | \(-0.485121\pi\) | ||||
0.0467272 | + | 0.998908i | \(0.485121\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 27.7277i | − | 1.15834i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.7863 | − | 0.225233i | 1.11706 | − | 0.00939285i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.6225i | 0.692002i | 0.938234 | + | 0.346001i | \(0.112461\pi\) | ||||
−0.938234 | + | 0.346001i | \(0.887539\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 76.5460 | 3.18114 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3511 | −0.429436 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9500i | 0.701998i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.4426 | + | 25.6574i | −1.05192 | + | 1.06080i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.2213i | − | 0.793347i | −0.917960 | − | 0.396674i | \(-0.870165\pi\) | ||
0.917960 | − | 0.396674i | \(-0.129835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.09146 | −0.127381 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.2214 | 1.11974 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0230i | 0.534792i | 0.963587 | + | 0.267396i | \(0.0861632\pi\) | ||||
−0.963587 | + | 0.267396i | \(0.913837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5080 | + | 10.4200i | 0.430787 | + | 0.427180i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 61.7533i | 2.52739i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.0915 | −1.10693 | −0.553464 | − | 0.832873i | \(-0.686694\pi\) | ||||
−0.553464 | + | 0.832873i | \(0.686694\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.42779 | −0.221404 | −0.110702 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110702 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 95.4782i | 3.88817i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.8586 | + | 32.5835i | 1.33589 | + | 1.32471i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.0663i | − | 0.855056i | −0.904002 | − | 0.427528i | \(-0.859384\pi\) | ||
0.904002 | − | 0.427528i | \(-0.140616\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.93197 | 0.280898 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.1829 | 1.05925 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 30.2753i | − | 1.22281i | −0.791318 | − | 0.611405i | \(-0.790605\pi\) | ||
0.791318 | − | 0.611405i | \(-0.209395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 60.0918 | − | 60.5992i | 2.42313 | − | 2.44359i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.3049i | 1.82391i | 0.410295 | + | 0.911953i | \(0.365426\pi\) | ||||
−0.410295 | + | 0.911953i | \(0.634574\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.2331 | −0.732852 | −0.366426 | − | 0.930447i | \(-0.619419\pi\) | ||||
−0.366426 | + | 0.930447i | \(0.619419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −84.6258 | −3.39592 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 16.1351i | − | 0.646439i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9965 | + | 0.420396i | −0.999859 | + | 0.0168158i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 18.5060i | − | 0.739060i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.2596 | −0.448951 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.4087 | −0.454173 | −0.227086 | − | 0.973875i | \(-0.572920\pi\) | ||||
−0.227086 | + | 0.973875i | \(0.572920\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 71.5905i | − | 2.84547i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.3585 | + | 19.5219i | −0.768217 | + | 0.774704i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.76365i | − | 0.267986i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −112.015 | −4.43126 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.92330 | 0.194459 | 0.0972293 | − | 0.995262i | \(-0.469002\pi\) | ||||
0.0972293 | + | 0.995262i | \(0.469002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.4136i | 0.962779i | 0.876507 | + | 0.481390i | \(0.159868\pi\) | ||||
−0.876507 | + | 0.481390i | \(0.840132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.61810 | + | 2.59617i | 0.103087 | + | 0.102224i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0424i | 0.434123i | 0.976158 | + | 0.217061i | \(0.0696472\pi\) | ||||
−0.976158 | + | 0.217061i | \(0.930353\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.2362 | 0.519566 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.6342 | −0.769523 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.1665i | 1.10224i | 0.834426 | + | 0.551121i | \(0.185800\pi\) | ||||
−0.834426 | + | 0.551121i | \(0.814200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.1261 | − | 16.9827i | −0.669173 | − | 0.663570i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.4214i | 0.874742i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.74037 | −0.184659 | −0.0923294 | − | 0.995729i | \(-0.529431\pi\) | ||||
−0.0923294 | + | 0.995729i | \(0.529431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4426 | −0.756228 | −0.378114 | − | 0.925759i | \(-0.623427\pi\) | ||||
−0.378114 | + | 0.925759i | \(0.623427\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 23.3107i | − | 0.905313i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.04204 | − | 3.06773i | 0.117965 | − | 0.118961i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.84744i | 0.226414i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.8439 | 1.84975 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.9544 | 1.65824 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5088i | 0.482178i | 0.970503 | + | 0.241089i | \(0.0775046\pi\) | ||||
−0.970503 | + | 0.241089i | \(0.922495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 78.9769 | − | 0.664078i | 3.03982 | − | 0.0255604i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.7265i | 1.56525i | 0.622497 | + | 0.782623i | \(0.286118\pi\) | ||||
−0.622497 | + | 0.782623i | \(0.713882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.81708 | 0.223239 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.80536 | −0.260782 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.8312i | 0.567500i | 0.958898 | + | 0.283750i | \(0.0915786\pi\) | ||||
−0.958898 | + | 0.283750i | \(0.908421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.64538 | − | 7.70993i | 0.292115 | − | 0.294581i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.8248i | 1.93909i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.23315 | 0.237464 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0958 | 0.498188 | 0.249094 | − | 0.968479i | \(-0.419867\pi\) | ||||
0.249094 | + | 0.968479i | \(0.419867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 84.9015i | − | 3.22514i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.8474 | + | 17.6980i | 0.676990 | + | 0.671322i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.7707i | 1.50642i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 94.9769 | 3.59236 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.0797 | −0.531785 | −0.265892 | − | 0.964003i | \(-0.585667\pi\) | ||||
−0.265892 | + | 0.964003i | \(0.585667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.28715i | 0.123977i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −66.0077 | − | 65.4550i | −2.48599 | − | 2.46518i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 9.28441i | − | 0.349176i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.38928 | −0.315066 | −0.157533 | − | 0.987514i | \(-0.550354\pi\) | ||||
−0.157533 | + | 0.987514i | \(0.550354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.2214 | 1.17090 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.5623i | − | 0.620264i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.3511 | − | 18.5060i | 0.686292 | − | 0.692087i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 87.4977i | − | 3.26766i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.70652 | −0.250111 | −0.125055 | − | 0.992150i | \(-0.539911\pi\) | ||||
−0.125055 | + | 0.992150i | \(0.539911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.16816 | 0.304198 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 64.4634i | − | 2.39742i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0458862 | − | 5.45712i | −0.00170417 | − | 0.202672i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.5009i | 0.760337i | 0.924917 | + | 0.380168i | \(0.124134\pi\) | ||||
−0.924917 | + | 0.380168i | \(0.875866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −66.7407 | −2.47188 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.71823 | −0.0635512 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.4323i | 1.56727i | 0.621220 | + | 0.783636i | \(0.286637\pi\) | ||||
−0.621220 | + | 0.783636i | \(0.713363\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.9085 | + | 17.0513i | −0.623681 | + | 0.628947i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 68.8661i | − | 2.53671i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.4352 | −1.63457 | −0.817287 | − | 0.576231i | \(-0.804523\pi\) | ||||
−0.817287 | + | 0.576231i | \(0.804523\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.80536 | −0.250001 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.4350i | 1.33667i | 0.743859 | + | 0.668336i | \(0.232993\pi\) | ||||
−0.743859 | + | 0.668336i | \(0.767007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.76332 | − | 5.71506i | −0.211152 | − | 0.209384i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 41.8167i | − | 1.52999i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.2362 | −0.629797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.6107 | −1.08051 | −0.540255 | − | 0.841501i | \(-0.681672\pi\) | ||||
−0.540255 | + | 0.841501i | \(0.681672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.8493i | 1.70728i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.4352 | − | 16.2976i | −0.598137 | − | 0.593129i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 44.0252i | − | 1.60012i | −0.599917 | − | 0.800062i | \(-0.704800\pi\) | ||
0.599917 | − | 0.800062i | \(-0.295200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 99.1450 | 3.59874 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.9809 | 0.941807 | 0.470903 | − | 0.882185i | \(-0.343928\pi\) | ||||
0.470903 | + | 0.882185i | \(0.343928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 10.1621i | − | 0.367893i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −42.0953 | + | 42.4508i | −1.52196 | + | 1.53481i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.86744i | − | 0.175753i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.68308 | −0.0967543 | −0.0483772 | − | 0.998829i | \(-0.515405\pi\) | ||||
−0.0483772 | + | 0.998829i | \(0.515405\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.1183 | −1.33678 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39.5328i | − | 1.42190i | −0.703244 | − | 0.710949i | \(-0.748266\pi\) | ||
0.703244 | − | 0.710949i | \(-0.251734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.129968 | + | 15.4568i | 0.00466860 | + | 0.555223i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.8770i | 0.748958i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.6107 | 0.415997 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.7940 | 2.89103 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.2407i | 0.616131i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.2214 | + | 11.3162i | −0.400510 | + | 0.403892i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.15783i | − | 0.326442i | −0.986590 | − | 0.163221i | \(-0.947812\pi\) | ||
0.986590 | − | 0.163221i | \(-0.0521883\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −50.4811 | −1.79717 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.1682 | 0.859321 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15.7959i | − | 0.560930i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.7139 | − | 15.5823i | −0.557314 | − | 0.552648i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.5581i | 0.551095i | 0.961287 | + | 0.275547i | \(0.0888591\pi\) | ||||
−0.961287 | + | 0.275547i | \(0.911141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.3203 | 1.53256 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 65.1832 | 2.30314 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 16.1720i | − | 0.570698i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.4352 | + | 16.2976i | 0.579264 | + | 0.574413i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 37.6134i | − | 1.32405i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.6184 | 1.46323 | 0.731613 | − | 0.681721i | \(-0.238768\pi\) | ||||
0.731613 | + | 0.681721i | \(0.238768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.1685 | −1.72654 | −0.863269 | − | 0.504744i | \(-0.831587\pi\) | ||||
−0.863269 | + | 0.504744i | \(0.831587\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.8135i | 1.43139i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.91592 | − | 1.93210i | 0.0671117 | − | 0.0676784i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.501623i | 0.0175496i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −31.2214 | −1.09097 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.9012 | −0.485154 | −0.242577 | − | 0.970132i | \(-0.577993\pi\) | ||||
−0.242577 | + | 0.970132i | \(0.577993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.0704i | − | 0.664754i | −0.943147 | − | 0.332377i | \(-0.892149\pi\) | ||
0.943147 | − | 0.332377i | \(-0.107851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −92.5269 | + | 0.778014i | −3.22137 | + | 0.0270870i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 46.7712i | − | 1.62639i | −0.581988 | − | 0.813197i | \(-0.697725\pi\) | ||
0.581988 | − | 0.813197i | \(-0.302275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.37452 | −0.0824706 | −0.0412353 | − | 0.999149i | \(-0.513129\pi\) | ||||
−0.0412353 | + | 0.999149i | \(0.513129\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.6640 | 1.82689 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 11.1906i | − | 0.387732i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.0074 | + | 25.2185i | −0.865416 | + | 0.872724i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 48.8325i | − | 1.68790i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.57252 | 0.0542894 | 0.0271447 | − | 0.999632i | \(-0.491359\pi\) | ||||
0.0271447 | + | 0.999632i | \(0.491359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8087 | −0.958921 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 81.8011i | − | 2.81738i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.8357 | + | 13.7198i | 0.475962 | + | 0.471977i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.9843i | 1.37388i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 53.3662 | 1.83152 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.6107 | −0.603688 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.88094i | − | 0.0644021i | −0.999481 | − | 0.0322010i | \(-0.989748\pi\) | ||
0.999481 | − | 0.0322010i | \(-0.0102517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.3931 | + | 12.2894i | 0.423836 | + | 0.420287i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.0371i | 0.581975i | 0.956727 | + | 0.290987i | \(0.0939837\pi\) | ||||
−0.956727 | + | 0.290987i | \(0.906016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.8395 | −1.70050 | −0.850251 | − | 0.526377i | \(-0.823550\pi\) | ||||
−0.850251 | + | 0.526377i | \(0.823550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 73.7407 | 2.51308 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.1696i | − | 0.414258i | −0.978314 | − | 0.207129i | \(-0.933588\pi\) | ||
0.978314 | − | 0.207129i | \(-0.0664121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.7096 | + | 21.8929i | −0.738147 | + | 0.744380i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3134i | 0.587995i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.5193 | −0.763913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.3246 | −0.858092 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.5001i | 0.795356i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.4660 | − | 15.0807i | −0.522846 | − | 0.509821i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 42.2287i | − | 1.42596i | −0.701184 | − | 0.712981i | \(-0.747345\pi\) | ||
0.701184 | − | 0.712981i | \(-0.252655\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 76.5460 | 2.58183 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.6683 | −0.426807 | −0.213403 | − | 0.976964i | \(-0.568455\pi\) | ||||
−0.213403 | + | 0.976964i | \(0.568455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.5414i | 0.388400i | 0.980962 | + | 0.194200i | \(0.0622110\pi\) | ||||
−0.980962 | + | 0.194200i | \(0.937789\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.1682 | + | 12.2709i | −0.409028 | + | 0.412482i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.36171i | 0.213605i | 0.994280 | + | 0.106803i | \(0.0340613\pi\) | ||||
−0.994280 | + | 0.106803i | \(0.965939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.7554 | −0.796732 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 160.492 | 5.37669 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 12.6470i | − | 0.423215i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4352 | − | 16.2976i | −0.549367 | − | 0.544767i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 36.4593i | − | 1.21734i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.37421 | −0.112536 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3129 | 0.343572 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.18585i | 0.106019i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.17554 | − | 3.14896i | −0.105559 | − | 0.104675i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.9538i | 0.828576i | 0.910146 | + | 0.414288i | \(0.135969\pi\) | ||||
−0.910146 | + | 0.414288i | \(0.864031\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.5075 | 1.24405 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.6640 | −0.949680 | −0.474840 | − | 0.880072i | \(-0.657494\pi\) | ||||
−0.474840 | + | 0.880072i | \(0.657494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.1614i | 0.998196i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.4884 | + | 39.8219i | −1.30545 | + | 1.31647i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 20.8401i | − | 0.688200i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0385 | 0.825944 | 0.412972 | − | 0.910744i | \(-0.364491\pi\) | ||||
0.412972 | + | 0.910744i | \(0.364491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.17121 | −0.104495 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 29.7109i | − | 0.977947i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.4352 | − | 0.138195i | 0.540385 | − | 0.00454383i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.9981i | 1.08380i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.2744 | −0.894844 | −0.447422 | − | 0.894323i | \(-0.647658\pi\) | ||||
−0.447422 | + | 0.894323i | \(0.647658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.26701 | −0.107072 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 59.7072i | 1.95473i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.3623 | − | 30.6187i | 0.992954 | − | 1.00134i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.7193i | − | 0.938219i | −0.883140 | − | 0.469109i | \(-0.844575\pi\) | ||
0.883140 | − | 0.469109i | \(-0.155425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.81708 | 0.254829 | 0.127415 | − | 0.991850i | \(-0.459332\pi\) | ||||
0.127415 | + | 0.991850i | \(0.459332\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 62.2037i | 2.02563i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48.4576 | + | 48.0519i | 1.57633 | + | 1.56313i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40.4886i | − | 1.31570i | −0.753148 | − | 0.657851i | \(-0.771466\pi\) | ||
0.753148 | − | 0.657851i | \(-0.228534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.94704 | −0.193049 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.1183 | 0.814515 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.57857i | 0.245494i | 0.992438 | + | 0.122747i | \(0.0391703\pi\) | ||||
−0.992438 | + | 0.122747i | \(0.960830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.3931 | − | 13.2810i | −0.433392 | − | 0.429763i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 20.1986i | − | 0.652930i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.38190 | 0.302958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.4429 | −0.691705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 69.6315i | − | 2.24384i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.6640 | − | 36.9736i | 1.18026 | − | 1.19022i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.5195i | − | 0.499075i | −0.968365 | − | 0.249537i | \(-0.919721\pi\) | ||
0.968365 | − | 0.249537i | \(-0.0802786\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.2596 | −0.361711 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.81708 | 0.0583127 | 0.0291564 | − | 0.999575i | \(-0.490718\pi\) | ||||
0.0291564 | + | 0.999575i | \(0.490718\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.7178i | 0.696240i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.286105 | + | 34.0256i | 0.00916268 | + | 1.08969i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 21.0178i | − | 0.672420i | −0.941787 | − | 0.336210i | \(-0.890855\pi\) | ||
0.941787 | − | 0.336210i | \(-0.109145\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47.0151 | −1.50261 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.0533 | 1.31073 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.2339i | 0.613467i | 0.951795 | + | 0.306733i | \(0.0992360\pi\) | ||||
−0.951795 | + | 0.306733i | \(0.900764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0385 | − | 13.1486i | 0.415441 | − | 0.418949i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 80.3221i | − | 2.55668i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.68742 | −0.0854549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.1682 | 1.14892 | 0.574460 | − | 0.818533i | \(-0.305212\pi\) | ||||
0.574460 | + | 0.818533i | \(0.305212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 73.3458i | 2.32756i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.8283 | + | 29.5785i | 0.945621 | + | 0.937703i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.6955i | 1.13049i | 0.824923 | + | 0.565245i | \(0.191218\pi\) | ||||
−0.824923 | + | 0.565245i | \(0.808782\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51.9236 | −1.64279 |
(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 | 380.2.c.b.229.6 | yes | 6 | |
3.2 | odd | 2 | 3420.2.f.c.1369.1 | 6 | |||
4.3 | odd | 2 | 1520.2.d.i.609.1 | 6 | |||
5.2 | odd | 4 | 1900.2.a.k.1.6 | 6 | |||
5.3 | odd | 4 | 1900.2.a.k.1.1 | 6 | |||
5.4 | even | 2 | inner | 380.2.c.b.229.1 | ✓ | 6 | |
15.14 | odd | 2 | 3420.2.f.c.1369.2 | 6 | |||
20.3 | even | 4 | 7600.2.a.cj.1.6 | 6 | |||
20.7 | even | 4 | 7600.2.a.cj.1.1 | 6 | |||
20.19 | odd | 2 | 1520.2.d.i.609.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.b.229.1 | ✓ | 6 | 5.4 | even | 2 | inner | |
380.2.c.b.229.6 | yes | 6 | 1.1 | even | 1 | trivial | |
1520.2.d.i.609.1 | 6 | 4.3 | odd | 2 | |||
1520.2.d.i.609.6 | 6 | 20.19 | odd | 2 | |||
1900.2.a.k.1.1 | 6 | 5.3 | odd | 4 | |||
1900.2.a.k.1.6 | 6 | 5.2 | odd | 4 | |||
3420.2.f.c.1369.1 | 6 | 3.2 | odd | 2 | |||
3420.2.f.c.1369.2 | 6 | 15.14 | odd | 2 | |||
7600.2.a.cj.1.1 | 6 | 20.7 | even | 4 | |||
7600.2.a.cj.1.6 | 6 | 20.3 | even | 4 |