Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(3849,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("4004.3849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.e (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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3849.2 | ||
Character | \(\chi\) | \(=\) | 4004.3849 |
Dual form | 4004.2.e.a.3849.47 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.15005i | − | 1.81868i | −0.416049 | − | 0.909342i | \(-0.636586\pi\) | ||
0.416049 | − | 0.909342i | \(-0.363414\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.09918i | − | 0.938781i | −0.882991 | − | 0.469391i | \(-0.844474\pi\) | ||
0.882991 | − | 0.469391i | \(-0.155526\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.59876 | − | 2.10807i | 0.604274 | − | 0.796777i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.92283 | −2.30761 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.48288 | − | 2.96666i | 0.447104 | − | 0.894482i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.61253 | −1.70735 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.21366 | 1.26450 | 0.632249 | − | 0.774765i | \(-0.282132\pi\) | ||||
0.632249 | + | 0.774765i | \(0.282132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50650 | −0.804445 | −0.402223 | − | 0.915542i | \(-0.631762\pi\) | ||||
−0.402223 | + | 0.915542i | \(0.631762\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.64054 | − | 5.03617i | −1.44909 | − | 1.09898i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.97298 | −0.828423 | −0.414211 | − | 0.910181i | \(-0.635943\pi\) | ||||
−0.414211 | + | 0.910181i | \(0.635943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.593447 | 0.118689 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.3571i | 2.37813i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.171004i | − | 0.0317546i | −0.999874 | − | 0.0158773i | \(-0.994946\pi\) | ||
0.999874 | − | 0.0158773i | \(-0.00505412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.22992i | 1.11893i | 0.828855 | + | 0.559463i | \(0.188993\pi\) | ||||
−0.828855 | + | 0.559463i | \(0.811007\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.34514 | − | 4.67114i | −1.62678 | − | 0.813141i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.42522 | − | 3.35608i | −0.747999 | − | 0.567281i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.42308 | −1.54914 | −0.774572 | − | 0.632485i | \(-0.782035\pi\) | ||||
−0.774572 | + | 0.632485i | \(0.782035\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.15005i | − | 0.504412i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.25145 | −0.820139 | −0.410069 | − | 0.912054i | \(-0.634496\pi\) | ||||
−0.410069 | + | 0.912054i | \(0.634496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.92487i | − | 0.446039i | −0.974814 | − | 0.223019i | \(-0.928409\pi\) | ||
0.974814 | − | 0.223019i | \(-0.0715913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.5323i | 2.16634i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.40782i | − | 1.37227i | −0.727474 | − | 0.686135i | \(-0.759306\pi\) | ||
0.727474 | − | 0.686135i | \(-0.240694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.88794 | − | 6.74060i | −0.269706 | − | 0.962943i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 16.4233i | − | 2.29972i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.09027 | 0.699202 | 0.349601 | − | 0.936899i | \(-0.386317\pi\) | ||||
0.349601 | + | 0.936899i | \(0.386317\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.22755 | − | 3.11282i | −0.839723 | − | 0.419733i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0456i | 1.46303i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.32514i | 1.21403i | 0.794690 | + | 0.607015i | \(0.207633\pi\) | ||||
−0.794690 | + | 0.607015i | \(0.792367\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.809574 | −0.103655 | −0.0518277 | − | 0.998656i | \(-0.516505\pi\) | ||||
−0.0518277 | + | 0.998656i | \(0.516505\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.0679 | + | 14.5938i | −1.39443 | + | 1.83865i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.09918i | − | 0.260371i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.09175 | 0.499887 | 0.249943 | − | 0.968260i | \(-0.419588\pi\) | ||||
0.249943 | + | 0.968260i | \(0.419588\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.5151i | 1.50664i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2221 | 1.21314 | 0.606572 | − | 0.795028i | \(-0.292544\pi\) | ||||
0.606572 | + | 0.795028i | \(0.292544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.7302 | −1.84108 | −0.920541 | − | 0.390646i | \(-0.872252\pi\) | ||||
−0.920541 | + | 0.390646i | \(0.872252\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.86939i | − | 0.215859i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.88318 | − | 7.86898i | −0.442529 | − | 0.896754i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.13543i | 0.240255i | 0.992758 | + | 0.120127i | \(0.0383303\pi\) | ||||
−0.992758 | + | 0.120127i | \(0.961670\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 18.1571 | 2.01746 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.96801 | −0.545310 | −0.272655 | − | 0.962112i | \(-0.587902\pi\) | ||||
−0.272655 | + | 0.962112i | \(0.587902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 10.9444i | − | 1.18709i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.538671 | −0.0577516 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0316i | 1.59335i | 0.604409 | + | 0.796674i | \(0.293409\pi\) | ||||
−0.604409 | + | 0.796674i | \(0.706591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.59876 | − | 2.10807i | 0.167595 | − | 0.220986i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.6246 | 2.03497 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.36076i | 0.755198i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.01911i | − | 0.103475i | −0.998661 | − | 0.0517375i | \(-0.983524\pi\) | ||
0.998661 | − | 0.0517375i | \(-0.0164759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.2657 | + | 20.5377i | −1.03174 | + | 2.06412i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.73927 | −0.272568 | −0.136284 | − | 0.990670i | \(-0.543516\pi\) | ||||
−0.136284 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.74842i | − | 0.369343i | −0.982800 | − | 0.184671i | \(-0.940878\pi\) | ||
0.982800 | − | 0.184671i | \(-0.0591220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.5718 | + | 13.9397i | −1.03170 | + | 1.36037i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.64985i | − | 0.932886i | −0.884551 | − | 0.466443i | \(-0.845535\pi\) | ||
0.884551 | − | 0.466443i | \(-0.154465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.7531i | − | 1.79622i | −0.439773 | − | 0.898109i | \(-0.644941\pi\) | ||
0.439773 | − | 0.898109i | \(-0.355059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 29.6832i | 2.81740i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.32274 | −0.688866 | −0.344433 | − | 0.938811i | \(-0.611929\pi\) | ||||
−0.344433 | + | 0.938811i | \(0.611929\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.33999i | 0.777708i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.92283 | −0.640016 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.33538 | − | 10.9908i | 0.764103 | − | 1.00752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.60216 | − | 8.79838i | −0.600196 | − | 0.799853i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.5423i | 1.49157i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.7416i | − | 1.05020i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.980063i | − | 0.0869665i | −0.999054 | − | 0.0434833i | \(-0.986154\pi\) | ||
0.999054 | − | 0.0434833i | \(-0.0138455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.21350 | −0.811203 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.170313 | 0.0148803 | 0.00744015 | − | 0.999972i | \(-0.497632\pi\) | ||||
0.00744015 | + | 0.999972i | \(0.497632\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.60604 | + | 7.39195i | −0.486105 | + | 0.640963i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 25.9398 | 2.23255 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.41851 | −0.121191 | −0.0605957 | − | 0.998162i | \(-0.519300\pi\) | ||||
−0.0605957 | + | 0.998162i | \(0.519300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.8153 | 1.25662 | 0.628308 | − | 0.777965i | \(-0.283748\pi\) | ||||
0.628308 | + | 0.777965i | \(0.283748\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.6351 | −2.49573 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.48288 | − | 2.96666i | 0.124004 | − | 0.248085i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.358968 | −0.0298106 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21.2332 | + | 5.94713i | −1.75129 | + | 0.490511i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.96887i | 0.243220i | 0.992578 | + | 0.121610i | \(0.0388057\pi\) | ||||
−0.992578 | + | 0.121610i | \(0.961194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.33304i | − | 0.271239i | −0.990761 | − | 0.135619i | \(-0.956698\pi\) | ||
0.990761 | − | 0.135619i | \(-0.0433024\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −36.0933 | −2.91797 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.0777 | 1.05043 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.968226i | 0.0772728i | 0.999253 | + | 0.0386364i | \(0.0123014\pi\) | ||||
−0.999253 | + | 0.0386364i | \(0.987699\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 16.0346i | − | 1.27163i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.35183 | + | 8.37532i | −0.500594 | + | 0.660068i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.0798 | 1.72943 | 0.864713 | − | 0.502267i | \(-0.167501\pi\) | ||||
0.864713 | + | 0.502267i | \(0.167501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.80555 | + | 19.6171i | −0.763361 | + | 1.52719i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.4339 | 1.58122 | 0.790611 | − | 0.612319i | \(-0.209763\pi\) | ||||
0.790611 | + | 0.612319i | \(0.209763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.2749 | 1.85635 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.29731 | 0.0986326 | 0.0493163 | − | 0.998783i | \(-0.484296\pi\) | ||||
0.0493163 | + | 0.998783i | \(0.484296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.948779 | − | 1.25103i | 0.0717209 | − | 0.0945690i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.3747 | 2.20794 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.47010 | 0.184624 | 0.0923118 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923118 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.20994i | − | 0.461581i | −0.973003 | − | 0.230791i | \(-0.925869\pi\) | ||
0.973003 | − | 0.230791i | \(-0.0741312\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.55020i | 0.188516i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.7807i | 1.45431i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.73121 | − | 15.4672i | 0.565362 | − | 1.13107i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 26.0498 | + | 19.7561i | 1.89484 | + | 1.43704i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.53840 | 0.256029 | 0.128015 | − | 0.991772i | \(-0.459140\pi\) | ||||
0.128015 | + | 0.991772i | \(0.459140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 15.5634i | − | 1.12028i | −0.828398 | − | 0.560140i | \(-0.810747\pi\) | ||
0.828398 | − | 0.560140i | \(-0.189253\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.61253 | −0.473533 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.40788i | 0.456542i | 0.973598 | + | 0.228271i | \(0.0733073\pi\) | ||||
−0.973598 | + | 0.228271i | \(0.926693\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.0981i | 1.77916i | 0.456779 | + | 0.889580i | \(0.349003\pi\) | ||||
−0.456779 | + | 0.889580i | \(0.650997\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 12.8892i | − | 0.909136i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.360489 | − | 0.273394i | −0.0253013 | − | 0.0191885i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0237i | 0.769931i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 27.5043 | 1.91168 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.19970 | + | 10.4026i | −0.359671 | + | 0.719562i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.10761i | − | 0.489308i | −0.969610 | − | 0.244654i | \(-0.921326\pi\) | ||
0.969610 | − | 0.244654i | \(-0.0786743\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 32.2003i | − | 2.20633i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.13983 | −0.418733 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.1331 | + | 9.96013i | 0.891534 | + | 0.676138i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 49.5510i | 3.34835i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.21366 | 0.350709 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.3680i | − | 1.02911i | −0.857456 | − | 0.514557i | \(-0.827956\pi\) | ||
0.857456 | − | 0.514557i | \(-0.172044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.10834 | −0.273889 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.822579 | 0.0545965 | 0.0272982 | − | 0.999627i | \(-0.491310\pi\) | ||||
0.0272982 | + | 0.999627i | \(0.491310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.8070i | 1.24280i | 0.783492 | + | 0.621402i | \(0.213436\pi\) | ||||
−0.783492 | + | 0.621402i | \(0.786564\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.7877 | + | 12.2322i | −1.63091 | + | 0.804821i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 8.47862i | − | 0.555453i | −0.960660 | − | 0.277727i | \(-0.910419\pi\) | ||
0.960660 | − | 0.277727i | \(-0.0895809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.7487 | −1.28826 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.72672 | 0.436948 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.3037i | 1.83081i | 0.402533 | + | 0.915406i | \(0.368130\pi\) | ||||
−0.402533 | + | 0.915406i | \(0.631870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.6198 | 1.45707 | 0.728534 | − | 0.685010i | \(-0.240202\pi\) | ||||
0.728534 | + | 0.685010i | \(0.240202\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 20.1245i | − | 1.29099i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.1497 | + | 3.96313i | −0.903993 | + | 0.253195i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.50650 | −0.223113 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.6495i | 0.991746i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.9923i | − | 0.883187i | −0.897215 | − | 0.441593i | \(-0.854413\pi\) | ||
0.897215 | − | 0.441593i | \(-0.145587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.89143 | + | 11.7865i | −0.370391 | + | 0.741009i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −34.4755 | −2.15894 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4.25485i | − | 0.265410i | −0.991156 | − | 0.132705i | \(-0.957634\pi\) | ||
0.991156 | − | 0.132705i | \(-0.0423663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0652 | + | 19.8645i | −0.936108 | + | 1.23432i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.18383i | 0.0732773i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.3345i | − | 0.822239i | −0.911581 | − | 0.411120i | \(-0.865138\pi\) | ||
0.911581 | − | 0.411120i | \(-0.134862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.6854i | − | 0.656398i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 47.3504 | 2.89780 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 13.7799i | − | 0.840175i | −0.907484 | − | 0.420087i | \(-0.861999\pi\) | ||
0.907484 | − | 0.420087i | \(-0.138001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.7217 | −1.25876 | −0.629378 | − | 0.777099i | \(-0.716690\pi\) | ||||
−0.629378 | + | 0.777099i | \(0.716690\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.64054 | − | 5.03617i | −0.401904 | − | 0.304803i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.880009 | − | 1.76056i | 0.0530665 | − | 0.106166i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.06853i | − | 0.304538i | −0.988339 | − | 0.152269i | \(-0.951342\pi\) | ||
0.988339 | − | 0.152269i | \(-0.0486580\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 43.1287i | − | 2.58205i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.9168i | − | 1.06883i | −0.845223 | − | 0.534415i | \(-0.820532\pi\) | ||
0.845223 | − | 0.534415i | \(-0.179468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.1327 | 1.91009 | 0.955044 | − | 0.296463i | \(-0.0958072\pi\) | ||||
0.955044 | + | 0.296463i | \(0.0958072\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.1868 | 1.37347 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.39580 | + | 11.0704i | −0.495588 | + | 0.653467i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.1823 | 0.598957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.21025 | −0.188188 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.94308 | 0.171937 | 0.0859684 | − | 0.996298i | \(-0.472602\pi\) | ||||
0.0859684 | + | 0.996298i | \(0.472602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.5751 | 1.13971 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 36.6594 | + | 18.3241i | 2.12720 | + | 1.06327i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.97298 | −0.229763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.16584 | − | 4.67616i | −0.355393 | − | 0.269529i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.62885i | 0.495715i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.69944i | 0.0973098i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.84490 | 0.162367 | 0.0811836 | − | 0.996699i | \(-0.474130\pi\) | ||||
0.0811836 | + | 0.996699i | \(0.474130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.8077 | −0.671717 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.7804i | 0.838117i | 0.907959 | + | 0.419059i | \(0.137640\pi\) | ||||
−0.907959 | + | 0.419059i | \(0.862360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0006i | 1.52616i | 0.646302 | + | 0.763082i | \(0.276315\pi\) | ||||
−0.646302 | + | 0.763082i | \(0.723685\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 30.6351 | + | 23.2336i | 1.72609 | + | 1.30906i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.4706 | −0.644255 | −0.322128 | − | 0.946696i | \(-0.604398\pi\) | ||||
−0.322128 | + | 0.946696i | \(0.604398\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.507311 | − | 0.253577i | −0.0284039 | − | 0.0141976i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.3975 | −1.69663 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.2817 | −1.01722 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.593447 | 0.0329185 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −59.0732 | −3.26675 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.8324 | − | 15.0408i | −1.09339 | − | 0.829227i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.33578 | 0.293281 | 0.146641 | − | 0.989190i | \(-0.453154\pi\) | ||||
0.146641 | + | 0.989190i | \(0.453154\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 65.2344 | 3.57482 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 8.58932i | − | 0.469284i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 34.7485i | − | 1.89287i | −0.322895 | − | 0.946435i | \(-0.604656\pi\) | ||
0.322895 | − | 0.946435i | \(-0.395344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.0670i | 1.25283i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.4821 | + | 9.23819i | 1.00086 | + | 0.500276i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2280 | − | 6.79666i | −0.930227 | − | 0.366985i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26.2714 | 1.41440 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.01536i | 0.0545073i | 0.999629 | + | 0.0272536i | \(0.00867618\pi\) | ||||
−0.999629 | + | 0.0272536i | \(0.991324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6009 | 1.26333 | 0.631664 | − | 0.775242i | \(-0.282372\pi\) | ||||
0.631664 | + | 0.775242i | \(0.282372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.3571i | 0.659575i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0321i | 0.533954i | 0.963703 | + | 0.266977i | \(0.0860248\pi\) | ||||
−0.963703 | + | 0.266977i | \(0.913975\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 21.4581i | − | 1.13888i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −34.6215 | − | 26.2569i | −1.83237 | − | 1.38966i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.34466i | 0.176525i | 0.996097 | + | 0.0882623i | \(0.0281314\pi\) | ||||
−0.996097 | + | 0.0882623i | \(0.971869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.70449 | −0.352868 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.7154 | + | 20.7972i | −1.45468 | + | 1.09157i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.0205i | 1.72837i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.3321i | − | 1.42673i | −0.700795 | − | 0.713363i | \(-0.747171\pi\) | ||
0.700795 | − | 0.713363i | \(-0.252829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 36.3549 | 1.89256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.13810 | − | 10.7307i | 0.422509 | − | 0.557108i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.16687i | − | 0.422865i | −0.977393 | − | 0.211432i | \(-0.932187\pi\) | ||
0.977393 | − | 0.211432i | \(-0.0678128\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −36.9868 | −1.90999 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.171004i | − | 0.00880715i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.7077 | −1.57735 | −0.788674 | − | 0.614812i | \(-0.789232\pi\) | ||||
−0.788674 | + | 0.614812i | \(0.789232\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.08725 | −0.158165 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8.09161i | − | 0.413462i | −0.978398 | − | 0.206731i | \(-0.933718\pi\) | ||
0.978398 | − | 0.206731i | \(-0.0662825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.5184 | + | 8.15149i | −0.841856 | + | 0.415438i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.2484i | 1.02928i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.9260 | 1.61871 | 0.809355 | − | 0.587320i | \(-0.199817\pi\) | ||||
0.809355 | + | 0.587320i | \(0.199817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.7138 | −1.04754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.536495i | − | 0.0270626i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.48265 | 0.225547 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.6682i | 1.23806i | 0.785367 | + | 0.619031i | \(0.212474\pi\) | ||||
−0.785367 | + | 0.619031i | \(0.787526\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.2850 | + | 17.6593i | 1.16571 | + | 0.884072i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.0823 | −0.853051 | −0.426525 | − | 0.904476i | \(-0.640263\pi\) | ||||
−0.426525 | + | 0.904476i | \(0.640263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.22992i | 0.310334i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 38.1151i | − | 1.89395i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.9733 | + | 27.9551i | −0.692629 | + | 1.38568i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.8408 | −1.12941 | −0.564704 | − | 0.825294i | \(-0.691009\pi\) | ||||
−0.564704 | + | 0.825294i | \(0.691009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.46838i | 0.220409i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.6581 | + | 14.9087i | 0.967311 | + | 0.733607i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4287i | 0.511927i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 46.6689i | − | 2.28539i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.8074i | 1.21192i | 0.795494 | + | 0.605961i | \(0.207211\pi\) | ||||
−0.795494 | + | 0.605961i | \(0.792789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.3438 | 0.747809 | 0.373905 | − | 0.927467i | \(-0.378019\pi\) | ||||
0.373905 | + | 0.927467i | \(0.378019\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 65.1288i | 3.16667i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.09403 | 0.150083 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.29431 | + | 1.70664i | −0.0626362 | + | 0.0825902i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.34514 | − | 4.67114i | −0.451188 | − | 0.225525i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.2364i | 1.21560i | 0.794092 | + | 0.607798i | \(0.207947\pi\) | ||||
−0.794092 | + | 0.607798i | \(0.792053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.20917i | − | 0.298394i | −0.988808 | − | 0.149197i | \(-0.952331\pi\) | ||
0.988808 | − | 0.149197i | \(-0.0476688\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.13077i | 0.0542161i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.9312 | 0.666421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3128 | −0.730840 | −0.365420 | − | 0.930843i | \(-0.619075\pi\) | ||||
−0.365420 | + | 0.930843i | \(0.619075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0699 | + | 46.6640i | 0.622378 | + | 2.22210i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.8346 | 1.22744 | 0.613720 | − | 0.789523i | \(-0.289672\pi\) | ||||
0.613720 | + | 0.789523i | \(0.289672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.5540 | 1.49581 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.35211 | 0.442340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.2423 | −1.56880 | −0.784400 | − | 0.620255i | \(-0.787029\pi\) | ||||
−0.784400 | + | 0.620255i | \(0.787029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.78725 | + | 15.5793i | −0.366687 | + | 0.733599i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.4992 | −0.493297 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.42522 | − | 3.35608i | −0.207458 | − | 0.157335i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.5152i | − | 1.24033i | −0.784472 | − | 0.620164i | \(-0.787066\pi\) | ||
0.784472 | − | 0.620164i | \(-0.212934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 64.4259i | 3.00715i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6582 | 1.38132 | 0.690659 | − | 0.723180i | \(-0.257320\pi\) | ||||
0.690659 | + | 0.723180i | \(0.257320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9657 | 1.02083 | 0.510417 | − | 0.859927i | \(-0.329491\pi\) | ||||
0.510417 | + | 0.859927i | \(0.329491\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 41.1955i | − | 1.91040i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 16.2309i | − | 0.751076i | −0.926807 | − | 0.375538i | \(-0.877458\pi\) | ||
0.926807 | − | 0.375538i | \(-0.122542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.54172 | − | 8.62571i | 0.302069 | − | 0.398298i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.04996 | 0.140535 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.67710 | − | 4.33722i | −0.398974 | − | 0.199426i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.08092 | −0.0954792 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.2391 | −1.61349 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.0931 | −1.69483 | −0.847414 | − | 0.530933i | \(-0.821842\pi\) | ||||
−0.847414 | + | 0.530933i | \(0.821842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.42308 | −0.429655 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.3827 | + | 20.0086i | 1.20046 | + | 0.910423i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.13930 | −0.0971404 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.9088 | 1.85376 | 0.926878 | − | 0.375363i | \(-0.122482\pi\) | ||||
0.926878 | + | 0.375363i | \(0.122482\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 69.5526i | − | 3.14528i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0987i | 0.907040i | 0.891246 | + | 0.453520i | \(0.149832\pi\) | ||||
−0.891246 | + | 0.453520i | \(0.850168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.891556i | − | 0.0401537i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 43.1123 | + | 21.5496i | 1.93775 | + | 0.968580i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.3427 | − | 21.5490i | 0.733071 | − | 0.966605i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.8768 | 0.665977 | 0.332988 | − | 0.942931i | \(-0.391943\pi\) | ||||
0.332988 | + | 0.942931i | \(0.391943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 64.3678i | − | 2.87574i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.6090 | −0.829733 | −0.414867 | − | 0.909882i | \(-0.636172\pi\) | ||||
−0.414867 | + | 0.909882i | \(0.636172\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.75022i | 0.255882i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.15005i | − | 0.139899i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.0342i | 0.932324i | 0.884699 | + | 0.466162i | \(0.154364\pi\) | ||||
−0.884699 | + | 0.466162i | \(0.845636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.1488 | + | 33.1604i | −1.11252 | + | 1.46693i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 43.3302i | − | 1.91308i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.86860 | −0.346732 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.9098 | − | 13.9506i | −1.22747 | − | 0.613548i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.08659i | − | 0.179381i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.5632i | 1.60186i | 0.598757 | + | 0.800931i | \(0.295662\pi\) | ||||
−0.598757 | + | 0.800931i | \(0.704338\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.35590 | −0.146743 | −0.0733716 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733716 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.94081 | − | 2.98870i | −0.171991 | − | 0.130438i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.4807i | 1.41488i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.21546 | −0.313716 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 64.5564i | − | 2.80151i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.25145 | −0.227466 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.2568 | −0.875776 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 7.78093i | − | 0.335772i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.7967 | − | 4.39458i | −0.981922 | − | 0.189288i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 36.4575i | − | 1.56743i | −0.621119 | − | 0.783716i | \(-0.713322\pi\) | ||
0.621119 | − | 0.783716i | \(-0.286678\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.5616 | −0.839470 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −39.3660 | −1.68626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 23.6889i | − | 1.01286i | −0.862280 | − | 0.506432i | \(-0.830964\pi\) | ||
0.862280 | − | 0.506432i | \(-0.169036\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.60455 | 0.239196 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.599624i | 0.0255448i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.50164 | + | 3.41404i | 0.191429 | + | 0.145180i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 62.3104 | 2.64493 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 30.9965i | − | 1.31336i | −0.754167 | − | 0.656682i | \(-0.771959\pi\) | ||
0.754167 | − | 0.656682i | \(-0.228041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.92487i | − | 0.123709i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.7224 | − | 24.3537i | −2.05706 | − | 1.02822i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.3122 | −1.65681 | −0.828407 | − | 0.560127i | \(-0.810752\pi\) | ||||
−0.828407 | + | 0.560127i | \(0.810752\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3717i | 0.646694i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.0289 | − | 38.2766i | 1.21910 | − | 1.60747i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 31.5812i | − | 1.32395i | −0.749525 | − | 0.661975i | \(-0.769718\pi\) | ||
0.749525 | − | 0.661975i | \(-0.230282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 44.9066i | − | 1.87928i | −0.342158 | − | 0.939642i | \(-0.611158\pi\) | ||
0.342158 | − | 0.939642i | \(-0.388842\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 11.1461i | − | 0.465636i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.35775 | −0.0983250 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 42.3288i | − | 1.76217i | −0.472956 | − | 0.881086i | \(-0.656813\pi\) | ||
0.472956 | − | 0.881086i | \(-0.343187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.0256 | −2.03743 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.94264 | + | 10.4729i | −0.329516 | + | 0.434490i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.54823 | − | 15.1011i | 0.312616 | − | 0.625423i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.5323i | 0.600835i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.266548i | 0.0110016i | 0.999985 | + | 0.00550080i | \(0.00175097\pi\) | ||||
−0.999985 | + | 0.00550080i | \(0.998249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21.8452i | − | 0.900115i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.1851 | 0.830306 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.7939 | −1.79840 | −0.899200 | − | 0.437537i | \(-0.855851\pi\) | ||||
−0.899200 | + | 0.437537i | \(0.855851\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.0716 | − | 17.4975i | −0.945844 | − | 0.717326i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 79.0605 | 3.23573 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.7211 | 0.519771 | 0.259885 | − | 0.965640i | \(-0.416315\pi\) | ||||
0.259885 | + | 0.965640i | \(0.416315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.82401 | −0.359939 | −0.179969 | − | 0.983672i | \(-0.557600\pi\) | ||||
−0.179969 | + | 0.983672i | \(0.557600\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.3265 | −1.15354 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.4694 | + | 13.8591i | −0.750887 | + | 0.563453i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8452 | 1.04902 | 0.524512 | − | 0.851403i | \(-0.324248\pi\) | ||||
0.524512 | + | 0.851403i | \(0.324248\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.861205 | + | 1.13556i | −0.0348978 | + | 0.0460151i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 9.40782i | − | 0.380599i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.2470i | 0.696598i | 0.937383 | + | 0.348299i | \(0.113241\pi\) | ||||
−0.937383 | + | 0.348299i | \(0.886759\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.7253 | 1.40026 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.9135 | −1.76789 | −0.883944 | − | 0.467592i | \(-0.845122\pi\) | ||||
−0.883944 | + | 0.467592i | \(0.845122\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.60316i | 0.265403i | 0.991156 | + | 0.132702i | \(0.0423652\pi\) | ||||
−0.991156 | + | 0.132702i | \(0.957635\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 49.0946i | − | 1.97010i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.6877 | + | 24.0319i | 1.26954 | + | 0.962818i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.6806 | −0.867223 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.7687 | + | 16.3793i | 1.30866 | + | 0.654127i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.1288 | −1.95889 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.9819 | −1.35280 | −0.676399 | − | 0.736535i | \(-0.736460\pi\) | ||||
−0.676399 | + | 0.736535i | \(0.736460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.3893 | −0.889896 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.05733 | −0.0816425 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.88794 | − | 6.74060i | −0.0748031 | − | 0.267072i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −70.7662 | −2.79947 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.8625 | 1.61397 | 0.806985 | − | 0.590571i | \(-0.201098\pi\) | ||||
0.806985 | + | 0.590571i | \(0.201098\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.31720i | 0.288562i | 0.989537 | + | 0.144281i | \(0.0460870\pi\) | ||||
−0.989537 | + | 0.144281i | \(0.953913\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.3408i | 0.761543i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 15.9627i | − | 0.627558i | −0.949496 | − | 0.313779i | \(-0.898405\pi\) | ||
0.949496 | − | 0.313779i | \(-0.101595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.6645 | + | 13.8280i | 1.08593 | + | 0.542798i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 31.3749 | − | 41.3700i | 1.22968 | − | 1.62142i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.94892 | 0.311065 | 0.155533 | − | 0.987831i | \(-0.450291\pi\) | ||||
0.155533 | + | 0.987831i | \(0.450291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 0.357517i | − | 0.0139694i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 108.898 | 4.24850 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.0044i | 0.545533i | 0.962080 | + | 0.272767i | \(0.0879387\pi\) | ||||
−0.962080 | + | 0.272767i | \(0.912061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22.4701i | − | 0.873985i | −0.899465 | − | 0.436992i | \(-0.856044\pi\) | ||
0.899465 | − | 0.436992i | \(-0.143956\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 16.4233i | − | 0.637829i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.5170 | + | 11.7681i | 0.601724 | + | 0.456346i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.679394i | 0.0263062i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −48.4099 | −1.87163 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.20050 | + | 2.40173i | −0.0463447 | + | 0.0927179i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.4111i | 0.401317i | 0.979661 | + | 0.200659i | \(0.0643082\pi\) | ||||
−0.979661 | + | 0.200659i | \(0.935692\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.33331i | 0.282259i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.5256 | 0.942596 | 0.471298 | − | 0.881974i | \(-0.343786\pi\) | ||||
0.471298 | + | 0.881974i | \(0.343786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.14836 | − | 1.62931i | −0.0824465 | − | 0.0625272i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2.59117i | − | 0.0992938i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.82239 | −0.184524 | −0.0922618 | − | 0.995735i | \(-0.529410\pi\) | ||||
−0.0922618 | + | 0.995735i | \(0.529410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.97770i | 0.113772i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 59.2431 | 2.26027 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.09027 | 0.193924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0222i | 0.761681i | 0.924641 | + | 0.380841i | \(0.124365\pi\) | ||||
−0.924641 | + | 0.380841i | \(0.875635\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26.8826 | + | 54.4757i | 1.02119 | + | 2.06936i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 31.0999i | − | 1.17969i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.3793 | −1.03706 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.7081 | −1.01019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.3123i | − | 0.465031i | −0.972593 | − | 0.232515i | \(-0.925304\pi\) | ||
0.972593 | − | 0.232515i | \(-0.0746956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.0420 | 1.24620 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 62.2094i | 2.34294i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.37943 | + | 5.77459i | −0.164706 | + | 0.217176i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.34658 | 0.163239 | 0.0816196 | − | 0.996664i | \(-0.473991\pi\) | ||||
0.0816196 | + | 0.996664i | \(0.473991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 14.7832i | − | 0.554415i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 24.7513i | − | 0.926944i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.22755 | − | 3.11282i | −0.232897 | − | 0.116413i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 89.1580 | 3.32967 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.17369i | 0.0810649i | 0.999178 | + | 0.0405324i | \(0.0129054\pi\) | ||||
−0.999178 | + | 0.0405324i | \(0.987095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.90194 | − | 5.99281i | −0.294284 | − | 0.223184i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 71.2535i | − | 2.64995i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 0.101482i | − | 0.00376894i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.8320i | − | 0.624264i | −0.950039 | − | 0.312132i | \(-0.898957\pi\) | ||
0.950039 | − | 0.312132i | \(-0.101043\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.92194 | −0.330442 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 15.2493i | − | 0.564015i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4963 | 0.757050 | 0.378525 | − | 0.925591i | \(-0.376431\pi\) | ||||
0.378525 | + | 0.925591i | \(0.376431\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.4841 | + | 44.5724i | 0.460482 | + | 1.64408i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.06756 | − | 12.1388i | 0.223501 | − | 0.447140i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 38.9407i | − | 1.43246i | −0.697865 | − | 0.716229i | \(-0.745867\pi\) | ||
0.697865 | − | 0.716229i | \(-0.254133\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.0456i | 0.405772i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.9933i | − | 0.880229i | −0.897942 | − | 0.440114i | \(-0.854938\pi\) | ||
0.897942 | − | 0.440114i | \(-0.145062\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.23220 | 0.228330 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.3927 | 1.25836 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.3426 | − | 15.4278i | −0.743302 | − | 0.563719i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.2183 | −1.90547 | −0.952736 | − | 0.303800i | \(-0.901745\pi\) | ||||
−0.952736 | + | 0.303800i | \(0.901745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −44.0765 | −1.60624 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.99664 | −0.254634 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.0949 | −0.694015 | −0.347007 | − | 0.937862i | \(-0.612802\pi\) | ||||
−0.347007 | + | 0.937862i | \(0.612802\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.1280 | + | 18.5583i | 1.34766 | + | 0.673624i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.6602 | 1.54643 | 0.773216 | − | 0.634143i | \(-0.218647\pi\) | ||||
0.773216 | + | 0.634143i | \(0.218647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.5328 | − | 29.9816i | −1.43118 | − | 1.08541i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 75.7663i | 2.73934i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.32514i | 0.336711i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.2796 | −1.34434 | −0.672168 | − | 0.740399i | \(-0.734637\pi\) | ||||
−0.672168 | + | 0.740399i | \(0.734637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.4030 | −0.482698 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.9272i | 0.788666i | 0.918968 | + | 0.394333i | \(0.129024\pi\) | ||||
−0.918968 | + | 0.394333i | \(0.870976\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.69713i | 0.132805i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 62.5744 | + | 47.4563i | 2.24484 | + | 1.70248i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.4142 | 0.659757 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.1582 | − | 30.3256i | 0.542402 | − | 1.08514i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.11312 | 0.0755167 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.03248 | 0.0725423 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.4270 | 1.90447 | 0.952234 | − | 0.305370i | \(-0.0987803\pi\) | ||||
0.952234 | + | 0.305370i | \(0.0987803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42.0043 | −1.49539 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.7073 | + | 15.4369i | −0.416263 | + | 0.548872i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.809574 | −0.0287488 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.6595 | −1.19378 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 39.6786i | − | 1.40549i | −0.711443 | − | 0.702744i | \(-0.751958\pi\) | ||
0.711443 | − | 0.702744i | \(-0.248042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49.0492i | − | 1.73523i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 104.061i | − | 3.67683i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.3260 | + | 46.6662i | −0.823155 | + | 1.64682i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.5813 | + | 13.3336i | 0.619660 | + | 0.469948i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.4074 | −1.52801 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15.9594i | − | 0.561102i | −0.959839 | − | 0.280551i | \(-0.909483\pi\) | ||
0.959839 | − | 0.280551i | \(-0.0905172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.05004 | 0.317790 | 0.158895 | − | 0.987295i | \(-0.449207\pi\) | ||||
0.158895 | + | 0.987295i | \(0.449207\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.2746i | 2.28928i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 46.3495i | − | 1.62355i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2560i | 0.358814i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.0679 | + | 14.5938i | −0.386745 | + | 0.509950i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1865i | 0.425312i | 0.977127 | + | 0.212656i | \(0.0682114\pi\) | ||||
−0.977127 | + | 0.212656i | \(0.931789\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8973 | 0.379856 | 0.189928 | − | 0.981798i | \(-0.439174\pi\) | ||||
0.189928 | + | 0.981798i | \(0.439174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.54585 | − | 2.77207i | −0.193082 | − | 0.0965112i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.1714i | 0.423240i | 0.977352 | + | 0.211620i | \(0.0678740\pi\) | ||||
−0.977352 | + | 0.211620i | \(0.932126\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 14.7778i | − | 0.513254i | −0.966510 | − | 0.256627i | \(-0.917389\pi\) | ||
0.966510 | − | 0.256627i | \(-0.0826113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9661 | −0.553859 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.84311 | − | 35.1432i | −0.341043 | − | 1.21764i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 42.8944i | − | 1.48442i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −76.9840 | −2.66095 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.4709i | 0.810305i | 0.914249 | + | 0.405152i | \(0.132782\pi\) | ||||
−0.914249 | + | 0.405152i | \(0.867218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9708 | 0.998992 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −56.4390 | −1.94386 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 2.09918i | − | 0.0722140i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.1029 | − | 0.148648i | −0.999987 | − | 0.00510761i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 101.220i | − | 3.47385i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.4377 | 1.28335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2140 | 0.726353 | 0.363176 | − | 0.931720i | \(-0.381692\pi\) | ||||
0.363176 | + | 0.931720i | \(0.381692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 50.9573i | − | 1.74270i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7861 | −0.368448 | −0.184224 | − | 0.982884i | \(-0.558977\pi\) | ||||
−0.184224 | + | 0.982884i | \(0.558977\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.2000i | 0.723335i | 0.932307 | + | 0.361668i | \(0.117792\pi\) | ||||
−0.932307 | + | 0.361668i | \(0.882208\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.8725 | + | 26.4472i | 1.18845 | + | 0.901319i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.88285 | −0.200255 | −0.100127 | − | 0.994975i | \(-0.531925\pi\) | ||||
−0.100127 | + | 0.994975i | \(0.531925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 2.72328i | − | 0.0925944i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 32.0747i | − | 1.08931i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.33510 | + | 3.16658i | 0.214904 | + | 0.107419i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.09175 | 0.138644 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.05513i | 0.238780i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.7523 | − | 18.7721i | −0.836779 | − | 0.634611i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.29664i | 0.212622i | 0.994333 | + | 0.106311i | \(0.0339040\pi\) | ||||
−0.994333 | + | 0.106311i | \(0.966096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 9.27087i | − | 0.312699i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 0.791613i | − | 0.0266701i | −0.999911 | − | 0.0133351i | \(-0.995755\pi\) | ||
0.999911 | − | 0.0133351i | \(-0.00424481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.3874 | −1.39280 | −0.696399 | − | 0.717655i | \(-0.745216\pi\) | ||||
−0.696399 | + | 0.717655i | \(0.745216\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 61.6628i | − | 2.07277i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.6428 | −0.726693 | −0.363346 | − | 0.931654i | \(-0.618366\pi\) | ||||
−0.363346 | + | 0.931654i | \(0.618366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.06604 | − | 1.56688i | −0.0692929 | − | 0.0525516i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.9248 | − | 53.8661i | 0.902014 | − | 1.80458i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.9885i | 1.10392i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.18517i | − | 0.173321i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.5151i | 0.417867i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.06534 | 0.0355311 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.5389 | 0.884140 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.7302 | + | 19.4227i | −0.490189 | + | 0.646348i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.0358 | −0.433324 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.5319 | −1.17982 | −0.589908 | − | 0.807470i | \(-0.700836\pi\) | ||||
−0.589908 | + | 0.807470i | \(0.700836\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.9635 | 0.628981 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.2433 | 1.83029 | 0.915145 | − | 0.403124i | \(-0.132076\pi\) | ||||
0.915145 | + | 0.403124i | \(0.132076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.36694 | + | 14.7384i | −0.243810 | + | 0.487770i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.35333 | 0.176976 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.272289 | − | 0.359032i | 0.00899178 | − | 0.0118563i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.7368i | 1.01391i | 0.861972 | + | 0.506956i | \(0.169229\pi\) | ||||
−0.861972 | + | 0.506956i | \(0.830771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 8.96159i | − | 0.295295i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.2221 | 0.336466 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.59210 | −0.183867 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.9497i | 0.852299i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.25320i | 0.106734i | 0.998575 | + | 0.0533670i | \(0.0169953\pi\) | ||||
−0.998575 | + | 0.0533670i | \(0.983005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.62007 | + | 23.6359i | 0.216964 | + | 0.774635i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 46.5589 | 1.52427 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.4684 | − | 16.2292i | −1.06183 | − | 0.530752i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.2251 | −1.24876 | −0.624380 | − | 0.781121i | \(-0.714648\pi\) | ||||
−0.624380 | + | 0.781121i | \(0.714648\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 85.0533 | 2.77561 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.4166 | −1.57833 | −0.789167 | − | 0.614178i | \(-0.789488\pi\) | ||||
−0.789167 | + | 0.614178i | \(0.789488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.8639 | 0.679422 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.4715 | − | 54.6831i | 1.34907 | − | 1.77884i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.1470 | 1.20711 | 0.603557 | − | 0.797320i | \(-0.293750\pi\) | ||||
0.603557 | + | 0.797320i | \(0.293750\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.7302 | −0.510624 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.1331i | 1.17170i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 29.0590i | − | 0.941312i | −0.882317 | − | 0.470656i | \(-0.844017\pi\) | ||
0.882317 | − | 0.470656i | \(-0.155983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7.42773i | − | 0.240356i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.798782 | + | 1.59806i | −0.0258210 | + | 0.0516578i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.26785 | + | 2.99032i | −0.0732327 | + | 0.0965624i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.81187 | −0.251996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 66.8043i | 2.15274i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.6704 | −1.05170 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 19.5929i | − | 0.630064i | −0.949081 | − | 0.315032i | \(-0.897985\pi\) | ||
0.949081 | − | 0.315032i | \(-0.102015\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 57.5883i | 1.85000i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 36.0517i | − | 1.15696i | −0.815698 | − | 0.578478i | \(-0.803647\pi\) | ||
0.815698 | − | 0.578478i | \(-0.196353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.6860 | − | 31.2317i | 0.759340 | − | 1.00124i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.86939i | − | 0.0598684i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.7501 | −0.503889 | −0.251945 | − | 0.967742i | \(-0.581070\pi\) | ||||
−0.251945 | + | 0.967742i | \(0.581070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.5937 | + | 22.2900i | 1.42522 | + | 0.712392i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 129.824i | 4.14497i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.6199i | 0.498196i | 0.968478 | + | 0.249098i | \(0.0801342\pi\) | ||||
−0.968478 | + | 0.249098i | \(0.919866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.4513 | 0.428593 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47.3794 | + | 62.4730i | −1.50810 | + | 1.98854i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.6204i | 0.369508i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.64602 | −0.147586 | −0.0737928 | − | 0.997274i | \(-0.523510\pi\) | ||||
−0.0737928 | + | 0.997274i | \(0.523510\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 16.8080i | − | 0.533386i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.6855 | 1.67024 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.8642 | −0.692446 | −0.346223 | − | 0.938152i | \(-0.612536\pi\) | ||||
−0.346223 | + | 0.938152i | \(0.612536\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 116.442i | − | 3.68407i |
(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 | 4004.2.e.a.3849.2 | ✓ | 48 | |
7.6 | odd | 2 | 4004.2.e.b.3849.47 | yes | 48 | ||
11.10 | odd | 2 | 4004.2.e.b.3849.2 | yes | 48 | ||
77.76 | even | 2 | inner | 4004.2.e.a.3849.47 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.e.a.3849.2 | ✓ | 48 | 1.1 | even | 1 | trivial | |
4004.2.e.a.3849.47 | yes | 48 | 77.76 | even | 2 | inner | |
4004.2.e.b.3849.2 | yes | 48 | 11.10 | odd | 2 | ||
4004.2.e.b.3849.47 | yes | 48 | 7.6 | odd | 2 |