Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
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, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
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.m (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: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.2 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.1 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −3.27485 | −1.89074 | −0.945368 | − | 0.326004i | \(-0.894298\pi\) | ||||
−0.945368 | + | 0.326004i | \(0.894298\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.17871i | 0.974351i | 0.873304 | + | 0.487175i | \(0.161973\pi\) | ||||
−0.873304 | + | 0.487175i | \(0.838027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.72466 | 2.57489 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.04907 | − | 1.92437i | 0.845659 | − | 0.533723i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.13497i | − | 1.84224i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.89205 | −1.18650 | −0.593248 | − | 0.805020i | \(-0.702155\pi\) | ||||
−0.593248 | + | 0.805020i | \(0.702155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.89530i | − | 0.664227i | −0.943239 | − | 0.332113i | \(-0.892238\pi\) | ||
0.943239 | − | 0.332113i | \(-0.107762\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.27485i | 0.714631i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.83267 | −0.799167 | −0.399583 | − | 0.916697i | \(-0.630845\pi\) | ||||
−0.399583 | + | 0.916697i | \(0.630845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.253205 | 0.0506410 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.4725 | −2.97769 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.96938 | 0.737095 | 0.368548 | − | 0.929609i | \(-0.379855\pi\) | ||||
0.368548 | + | 0.929609i | \(0.379855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.338018i | 0.0607098i | 0.999539 | + | 0.0303549i | \(0.00966374\pi\) | ||||
−0.999539 | + | 0.0303549i | \(0.990336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.27485i | − | 0.570079i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.17871 | 0.368270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.41513i | − | 1.54784i | −0.633284 | − | 0.773919i | \(-0.718294\pi\) | ||
0.633284 | − | 0.773919i | \(-0.281706\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.98525 | + | 6.30202i | −1.59892 | + | 1.00913i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.25457i | 0.195931i | 0.995190 | + | 0.0979656i | \(0.0312335\pi\) | ||||
−0.995190 | + | 0.0979656i | \(0.968766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.90954 | −1.20619 | −0.603097 | − | 0.797668i | \(-0.706067\pi\) | ||||
−0.603097 | + | 0.797668i | \(0.706067\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.8298i | 2.50884i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2549i | 1.64169i | 0.571150 | + | 0.820845i | \(0.306497\pi\) | ||||
−0.571150 | + | 0.820845i | \(0.693503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.0207 | 2.24335 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.19463 | −0.164094 | −0.0820472 | − | 0.996628i | \(-0.526146\pi\) | ||||
−0.0820472 | + | 0.996628i | \(0.526146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.17871 | −0.293778 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.48167i | 1.25588i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.32058i | 1.21344i | 0.794917 | + | 0.606718i | \(0.207514\pi\) | ||||
−0.794917 | + | 0.606718i | \(0.792486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2280 | 1.56564 | 0.782818 | − | 0.622251i | \(-0.213781\pi\) | ||||
0.782818 | + | 0.622251i | \(0.213781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 7.72466i | − | 0.973215i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.19264 | + | 6.64305i | 0.520034 | + | 0.823968i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.95290i | 0.238585i | 0.992859 | + | 0.119293i | \(0.0380627\pi\) | ||||
−0.992859 | + | 0.119293i | \(0.961937\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.5514 | 1.51101 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.38691i | − | 0.639309i | −0.947534 | − | 0.319654i | \(-0.896433\pi\) | ||
0.947534 | − | 0.319654i | \(-0.103567\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.975589i | 0.114184i | 0.998369 | + | 0.0570920i | \(0.0181828\pi\) | ||||
−0.998369 | + | 0.0570920i | \(0.981817\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.829209 | −0.0957488 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.42795 | 0.610692 | 0.305346 | − | 0.952241i | \(-0.401228\pi\) | ||||
0.305346 | + | 0.952241i | \(0.401228\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 27.4963 | 3.05515 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.61107i | − | 0.506131i | −0.967449 | − | 0.253065i | \(-0.918561\pi\) | ||
0.967449 | − | 0.253065i | \(-0.0814388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 10.6584i | − | 1.15606i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.9991 | −1.39365 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.06453i | 0.218840i | 0.993996 | + | 0.109420i | \(0.0348993\pi\) | ||||
−0.993996 | + | 0.109420i | \(0.965101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.92437 | − | 3.04907i | −0.201728 | − | 0.319629i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.10696i | − | 0.114786i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.30802 | 0.647190 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.930612i | 0.0944894i | 0.998883 | + | 0.0472447i | \(0.0150441\pi\) | ||||
−0.998883 | + | 0.0472447i | \(0.984956\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.72466i | 0.776357i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.0014 | −1.29369 | −0.646844 | − | 0.762622i | \(-0.723912\pi\) | ||||
−0.646844 | + | 0.762622i | \(0.723912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9032 | −1.56699 | −0.783495 | − | 0.621398i | \(-0.786565\pi\) | ||||
−0.783495 | + | 0.621398i | \(0.786565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.13497 | −0.696301 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.07538 | 0.297308 | 0.148654 | − | 0.988889i | \(-0.452506\pi\) | ||||
0.148654 | + | 0.988889i | \(0.452506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.6995i | 1.59952i | 0.600318 | + | 0.799762i | \(0.295041\pi\) | ||||
−0.600318 | + | 0.799762i | \(0.704959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30.8332i | 2.92656i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.43772 | 0.793754 | 0.396877 | − | 0.917872i | \(-0.370094\pi\) | ||||
0.396877 | + | 0.917872i | \(0.370094\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.35029i | − | 0.778668i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.5530 | − | 14.8651i | 2.17748 | − | 1.37428i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.89205i | 0.448454i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.10854i | − | 0.370454i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.4452i | 1.02369i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.18598 | −0.193975 | −0.0969874 | − | 0.995286i | \(-0.530921\pi\) | ||||
−0.0969874 | + | 0.995286i | \(0.530921\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.9026 | 2.28059 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.1555 | −1.58626 | −0.793129 | − | 0.609054i | \(-0.791549\pi\) | ||||
−0.793129 | + | 0.609054i | \(0.791549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89530 | −0.251054 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 33.7103i | − | 2.90132i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5418i | 1.15696i | 0.815698 | + | 0.578478i | \(0.196353\pi\) | ||||
−0.815698 | + | 0.578478i | \(0.803647\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.84495 | 0.241306 | 0.120653 | − | 0.992695i | \(-0.461501\pi\) | ||||
0.120653 | + | 0.992695i | \(0.461501\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 36.8580i | − | 3.10401i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.92437 | + | 3.04907i | 0.160924 | + | 0.254976i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.64814i | 0.718189i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.27485 | 0.270105 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 21.4754i | − | 1.75933i | −0.475594 | − | 0.879665i | \(-0.657767\pi\) | ||
0.475594 | − | 0.879665i | \(-0.342233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.1883i | − | 1.56152i | −0.624832 | − | 0.780759i | \(-0.714833\pi\) | ||
0.624832 | − | 0.780759i | \(-0.285167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −37.7894 | −3.05509 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.736444 | −0.0591526 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.3380 | −1.30391 | −0.651956 | − | 0.758256i | \(-0.726051\pi\) | ||||
−0.651956 | + | 0.758256i | \(0.726051\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.91222 | 0.310259 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.83267i | 0.302057i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.5545i | − | 1.37497i | −0.726197 | − | 0.687486i | \(-0.758714\pi\) | ||
0.726197 | − | 0.687486i | \(-0.241286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.13497 | 0.555456 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6797i | 1.44548i | 0.691122 | + | 0.722738i | \(0.257117\pi\) | ||||
−0.691122 | + | 0.722738i | \(0.742883\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.59363 | − | 11.7350i | 0.430279 | − | 0.902696i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 22.3652i | − | 1.71031i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.72541 | −0.511324 | −0.255662 | − | 0.966766i | \(-0.582293\pi\) | ||||
−0.255662 | + | 0.966766i | \(0.582293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.253205i | − | 0.0191405i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 30.5235i | − | 2.29429i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.51974 | −0.636795 | −0.318398 | − | 0.947957i | \(-0.603145\pi\) | ||||
−0.318398 | + | 0.947957i | \(0.603145\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.7965 | −1.84311 | −0.921554 | − | 0.388250i | \(-0.873080\pi\) | ||||
−0.921554 | + | 0.388250i | \(0.873080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −40.0449 | −2.96021 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.5129 | 1.50814 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.89205i | − | 0.357742i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.4725i | 1.12546i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2007 | 1.17224 | 0.586120 | − | 0.810224i | \(-0.300655\pi\) | ||||
0.586120 | + | 0.810224i | \(0.300655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4161i | 1.25364i | 0.779166 | + | 0.626818i | \(0.215643\pi\) | ||||
−0.779166 | + | 0.626818i | \(0.784357\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.7303 | − | 21.7550i | −0.983247 | − | 1.55791i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.7956i | − | 0.911647i | −0.890070 | − | 0.455824i | \(-0.849345\pi\) | ||
0.890070 | − | 0.455824i | \(-0.150655\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.08910 | 0.218980 | 0.109490 | − | 0.993988i | \(-0.465078\pi\) | ||||
0.109490 | + | 0.993988i | \(0.465078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.39547i | − | 0.451102i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 3.96938i | − | 0.278596i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.73335 | −0.190906 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −29.6060 | −2.05776 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.89530 | 0.200272 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.04110 | −0.209358 | −0.104679 | − | 0.994506i | \(-0.533382\pi\) | ||||
−0.104679 | + | 0.994506i | \(0.533382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.6413i | 1.20876i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 17.2326i | − | 1.17525i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.338018 | 0.0229461 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 3.19491i | − | 0.215892i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.9162 | + | 9.41410i | −1.00337 | + | 0.633261i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.8016i | − | 1.12512i | −0.826756 | − | 0.562561i | \(-0.809816\pi\) | ||
0.826756 | − | 0.562561i | \(-0.190184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.95592 | 0.130395 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 21.4933i | − | 1.42656i | −0.700880 | − | 0.713280i | \(-0.747209\pi\) | ||
0.700880 | − | 0.713280i | \(-0.252791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.4208i | − | 0.754711i | −0.926069 | − | 0.377355i | \(-0.876834\pi\) | ||
0.926069 | − | 0.377355i | \(-0.123166\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.27485 | −0.215469 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.9996 | −0.786118 | −0.393059 | − | 0.919513i | \(-0.628583\pi\) | ||||
−0.393059 | + | 0.919513i | \(0.628583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.5211 | −1.59958 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.7757 | −1.15466 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.58559i | − | 0.490671i | −0.969438 | − | 0.245335i | \(-0.921102\pi\) | ||
0.969438 | − | 0.245335i | \(-0.0788981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.0927i | 1.35870i | 0.733814 | + | 0.679351i | \(0.237739\pi\) | ||||
−0.733814 | + | 0.679351i | \(0.762261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −43.6288 | −2.79879 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2.17871i | − | 0.139193i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.57161 | − | 8.82796i | −0.354513 | − | 0.561709i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.1006i | 0.956960i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.10029 | −0.132569 | −0.0662847 | − | 0.997801i | \(-0.521115\pi\) | ||||
−0.0662847 | + | 0.997801i | \(0.521115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.83267i | − | 0.240958i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 34.9046i | 2.18581i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.6802 | −1.66427 | −0.832133 | − | 0.554576i | \(-0.812881\pi\) | ||||
−0.832133 | + | 0.554576i | \(0.812881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.41513 | −0.585028 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.6621 | 1.89794 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.8812 | 0.917615 | 0.458808 | − | 0.888536i | \(-0.348277\pi\) | ||||
0.458808 | + | 0.888536i | \(0.348277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.60275i | − | 0.159886i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.76102i | − | 0.413768i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.7648 | −1.32702 | −0.663512 | − | 0.748166i | \(-0.730935\pi\) | ||||
−0.663512 | + | 0.748166i | \(0.730935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.6386i | − | 0.949976i | −0.879992 | − | 0.474988i | \(-0.842452\pi\) | ||
0.879992 | − | 0.474988i | \(-0.157548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.30202 | + | 9.98525i | 0.381415 | + | 0.604335i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.253205i | 0.0152688i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6493 | −0.760026 | −0.380013 | − | 0.924981i | \(-0.624080\pi\) | ||||
−0.380013 | + | 0.924981i | \(0.624080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.61107i | 0.156321i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.2607i | 0.850725i | 0.905023 | + | 0.425362i | \(0.139853\pi\) | ||||
−0.905023 | + | 0.425362i | \(0.860147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3957 | −0.915182 | −0.457591 | − | 0.889163i | \(-0.651288\pi\) | ||||
−0.457591 | + | 0.889163i | \(0.651288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −20.6578 | −1.22367 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.25457 | 0.0740550 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.93216 | 0.407774 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3.04762i | − | 0.178655i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.0707i | 0.997283i | 0.866808 | + | 0.498642i | \(0.166168\pi\) | ||||
−0.866808 | + | 0.498642i | \(0.833832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.3069 | −1.18231 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 15.4725i | − | 0.897808i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.6861 | + | 7.37546i | −0.675823 | + | 0.426534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.90954i | 0.455898i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 42.5777 | 2.44602 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.6413i | 1.52548i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.8541i | − | 0.619477i | −0.950822 | − | 0.309739i | \(-0.899758\pi\) | ||
0.950822 | − | 0.309739i | \(-0.100242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.0807 | 2.96277 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.3877 | −1.49631 | −0.748155 | − | 0.663524i | \(-0.769060\pi\) | ||||
−0.748155 | + | 0.663524i | \(0.769060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.6577 | 1.28069 | 0.640344 | − | 0.768088i | \(-0.278792\pi\) | ||||
0.640344 | + | 0.768088i | \(0.278792\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.8298 | 0.948253 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.8773i | − | 1.39725i | −0.715489 | − | 0.698624i | \(-0.753796\pi\) | ||
0.715489 | − | 0.698624i | \(-0.246204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.96938i | 0.222243i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0714 | −0.562131 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.1639i | 0.788103i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.772039 | − | 0.487259i | 0.0428250 | − | 0.0270283i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 54.6884i | − | 3.02428i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.2549 | 0.620501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 12.1567i | − | 0.668191i | −0.942539 | − | 0.334096i | \(-0.891569\pi\) | ||
0.942539 | − | 0.334096i | \(-0.108431\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 72.7287i | − | 3.98551i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.25482 | −0.232466 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.7652 | −1.78483 | −0.892416 | − | 0.451213i | \(-0.850991\pi\) | ||||
−0.892416 | + | 0.451213i | \(0.850991\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.6323 | −1.50078 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.338018 | −0.0183047 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 27.3460i | 1.47226i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.46324 | −0.346965 | −0.173482 | − | 0.984837i | \(-0.555502\pi\) | ||||
−0.173482 | + | 0.984837i | \(0.555502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.6995i | − | 0.626261i | −0.949710 | − | 0.313131i | \(-0.898622\pi\) | ||
0.949710 | − | 0.313131i | \(-0.101378\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −47.1768 | + | 29.7749i | −2.51811 | + | 1.58926i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.2069i | − | 0.596481i | −0.954491 | − | 0.298241i | \(-0.903600\pi\) | ||
0.954491 | − | 0.298241i | \(-0.0963998\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.7365 | 0.622911 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 16.0207i | − | 0.847908i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.81775i | 0.254271i | 0.991885 | + | 0.127136i | \(0.0405783\pi\) | ||||
−0.991885 | + | 0.127136i | \(0.959422\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6173 | 0.558803 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.27485 | 0.171885 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.12553 | −0.111255 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8322 | 1.03523 | 0.517615 | − | 0.855614i | \(-0.326820\pi\) | ||||
0.517615 | + | 0.855614i | \(0.326820\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.69114i | 0.504500i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.19463i | 0.0620219i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0693 | 1.14271 | 0.571354 | − | 0.820704i | \(-0.306419\pi\) | ||||
0.571354 | + | 0.820704i | \(0.306419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 37.4814i | − | 1.93553i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.1029 | − | 7.63854i | 0.623331 | − | 0.393405i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1259i | 0.776966i | 0.921456 | + | 0.388483i | \(0.127001\pi\) | ||||
−0.921456 | + | 0.388483i | \(0.872999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.15877 | 0.366755 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.8829i | 0.658285i | 0.944280 | + | 0.329143i | \(0.106760\pi\) | ||||
−0.944280 | + | 0.329143i | \(0.893240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.17871i | 0.111038i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −61.0985 | −3.10581 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.6105 | −1.24780 | −0.623901 | − | 0.781503i | \(-0.714453\pi\) | ||||
−0.623901 | + | 0.781503i | \(0.714453\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.7496 | 0.948208 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 59.4567 | 2.99919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.8260i | 0.595028i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 27.5294i | − | 1.38166i | −0.723016 | − | 0.690831i | \(-0.757245\pi\) | ||
0.723016 | − | 0.690831i | \(-0.242755\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.48167 | 0.474677 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.88250i | − | 0.193883i | −0.995290 | − | 0.0969414i | \(-0.969094\pi\) | ||
0.995290 | − | 0.0969414i | \(-0.0309059\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.650470 | + | 1.03064i | 0.0324022 | + | 0.0513398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 59.9067i | 2.97679i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.41513 | 0.466691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 11.8113i | − | 0.584033i | −0.956413 | − | 0.292016i | \(-0.905674\pi\) | ||
0.956413 | − | 0.292016i | \(-0.0943262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 44.3475i | − | 2.18750i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.32058 | 0.458636 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.0462 | 0.493149 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.31680 | −0.456246 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.72086 | 0.230629 | 0.115315 | − | 0.993329i | \(-0.463212\pi\) | ||||
0.115315 | + | 0.993329i | \(0.463212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.6560i | − | 0.860501i | −0.902710 | − | 0.430251i | \(-0.858425\pi\) | ||
0.902710 | − | 0.430251i | \(-0.141575\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 86.9400i | 4.22717i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.23869 | −0.0600854 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 12.2280i | − | 0.591755i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.30202 | − | 9.98525i | −0.304264 | − | 0.482092i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.4949i | 1.37255i | 0.727341 | + | 0.686277i | \(0.240756\pi\) | ||||
−0.727341 | + | 0.686277i | \(0.759244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.16389 | −0.103990 | −0.0519949 | − | 0.998647i | \(-0.516558\pi\) | ||||
−0.0519949 | + | 0.998647i | \(0.516558\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 28.3214i | − | 1.35791i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.0967i | 0.530828i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4914 | 0.596181 | 0.298091 | − | 0.954538i | \(-0.403650\pi\) | ||||
0.298091 | + | 0.954538i | \(0.403650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.72466 | −0.367841 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.1958 | −1.43464 | −0.717322 | − | 0.696742i | \(-0.754632\pi\) | ||||
−0.717322 | + | 0.696742i | \(0.754632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.49802 | −0.213226 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 70.3286i | 3.32643i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 25.7787i | − | 1.21657i | −0.793719 | − | 0.608285i | \(-0.791858\pi\) | ||
0.793719 | − | 0.608285i | \(-0.208142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.25457 | −0.0590755 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 62.8387i | 2.95242i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.64305 | − | 4.19264i | 0.311431 | − | 0.196554i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2388i | 1.18062i | 0.807176 | + | 0.590310i | \(0.200995\pi\) | ||||
−0.807176 | + | 0.590310i | \(0.799005\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 75.6925 | 3.53302 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.737940i | − | 0.0343693i | −0.999852 | − | 0.0171847i | \(-0.994530\pi\) | ||
0.999852 | − | 0.0171847i | \(-0.00547031\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0845i | 0.886931i | 0.896291 | + | 0.443466i | \(0.146251\pi\) | ||||
−0.896291 | + | 0.443466i | \(0.853749\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.41174 | 0.111842 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9860 | 0.693470 | 0.346735 | − | 0.937963i | \(-0.387290\pi\) | ||||
0.346735 | + | 0.937963i | \(0.387290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.95290 | 0.0901768 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 53.5045 | 2.46536 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.90954i | − | 0.363681i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.733104i | − | 0.0336371i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.22807 | −0.422524 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 38.5988i | − | 1.76363i | −0.471600 | − | 0.881813i | \(-0.656323\pi\) | ||
0.471600 | − | 0.881813i | \(-0.343677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.1182 | − | 28.7074i | −0.826117 | − | 1.30894i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 12.5514i | − | 0.571109i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.02754 | −0.0920658 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5038i | 0.793173i | 0.917997 | + | 0.396587i | \(0.129805\pi\) | ||||
−0.917997 | + | 0.396587i | \(0.870195\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 57.4883i | 2.59971i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.6205 | 1.20137 | 0.600683 | − | 0.799487i | \(-0.294895\pi\) | ||||
0.600683 | + | 0.799487i | \(0.294895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.4184 | −0.874561 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.8298 | −0.756444 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.38691 | −0.241636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.0002i | 1.34299i | 0.741007 | + | 0.671497i | \(0.234348\pi\) | ||||
−0.741007 | + | 0.671497i | \(0.765652\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 61.1732i | − | 2.73302i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.4859 | −0.556719 | −0.278360 | − | 0.960477i | \(-0.589791\pi\) | ||||
−0.278360 | + | 0.960477i | \(0.589791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 28.3264i | − | 1.26051i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.3183 | + | 38.4305i | −0.813544 | + | 1.70676i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.54412i | 0.0684420i | 0.999414 | + | 0.0342210i | \(0.0108950\pi\) | ||||
−0.999414 | + | 0.0342210i | \(0.989105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.975589 | 0.0431575 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 44.7976i | 1.97786i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 34.6486i | − | 1.52680i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.2549 | −0.494988 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0247 | 0.966779 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3243 | −1.15329 | −0.576644 | − | 0.816996i | \(-0.695638\pi\) | ||||
−0.576644 | + | 0.816996i | \(0.695638\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.84825 | 0.255726 | 0.127863 | − | 0.991792i | \(-0.459188\pi\) | ||||
0.127863 | + | 0.991792i | \(0.459188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.829209i | 0.0361896i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.65360i | − | 0.0720319i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.31065 | −0.361333 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 71.9983i | 3.12446i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.41426 | + | 3.82527i | 0.104573 | + | 0.165691i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.70037i | 0.289682i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.9009 | 1.20401 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.00000i | − | 0.0430730i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.30458i | 0.357042i | 0.983936 | + | 0.178521i | \(0.0571312\pi\) | ||||
−0.983936 | + | 0.178521i | \(0.942869\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 81.2048 | 3.48483 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −36.3835 | −1.55850 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0828 | 0.644894 | 0.322447 | − | 0.946588i | \(-0.395495\pi\) | ||||
0.322447 | + | 0.946588i | \(0.395495\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 94.4572 | 4.03133 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.4925i | − | 0.489598i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.42795i | − | 0.230820i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −67.1767 | −2.85149 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 46.4880i | − | 1.96976i | −0.173240 | − | 0.984880i | \(-0.555424\pi\) | ||
0.173240 | − | 0.984880i | \(-0.444576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.1167 | + | 15.2208i | −1.02003 | + | 0.643773i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0207i | 0.676396i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0508 | −0.802895 | −0.401447 | − | 0.915882i | \(-0.631493\pi\) | ||||
−0.401447 | + | 0.915882i | \(0.631493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.3834i | 0.773394i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 27.4963i | − | 1.15474i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.9533 | −0.878407 | −0.439203 | − | 0.898388i | \(-0.644739\pi\) | ||||
−0.439203 | + | 0.898388i | \(0.644739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.3037 | 0.431196 | 0.215598 | − | 0.976482i | \(-0.430830\pi\) | ||||
0.215598 | + | 0.976482i | \(0.430830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −53.0548 | −2.21640 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.970451 | −0.0404706 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.7471i | − | 0.905343i | −0.891677 | − | 0.452672i | \(-0.850471\pi\) | ||
0.891677 | − | 0.452672i | \(-0.149529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 57.0350i | − | 2.37030i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.61107 | −0.191299 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.19463i | − | 0.0494763i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 32.3867 | + | 51.3152i | 1.33903 | + | 2.12162i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 42.1122i | − | 1.73816i | −0.494675 | − | 0.869078i | \(-0.664713\pi\) | ||
0.494675 | − | 0.869078i | \(-0.335287\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.978661 | 0.0403250 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.9036i | 1.72368i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.68629i | 0.0692476i | 0.999400 | + | 0.0346238i | \(0.0110233\pi\) | ||||
−0.999400 | + | 0.0346238i | \(0.988977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.6584 | −0.436951 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.1163 | −0.414034 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.7342 | −1.86865 | −0.934324 | − | 0.356424i | \(-0.883996\pi\) | ||||
−0.934324 | + | 0.356424i | \(0.883996\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.6835 | 1.33319 | 0.666594 | − | 0.745421i | \(-0.267752\pi\) | ||||
0.666594 | + | 0.745421i | \(0.267752\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.0855i | 0.614330i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.17871i | − | 0.0885773i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.9722 | −0.851234 | −0.425617 | − | 0.904903i | \(-0.639943\pi\) | ||||
−0.425617 | + | 0.904903i | \(0.639943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.9991i | 0.526751i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.6585 | + | 34.3168i | 0.876209 | + | 1.38831i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 32.3811i | − | 1.30786i | −0.756555 | − | 0.653930i | \(-0.773119\pi\) | ||
0.756555 | − | 0.653930i | \(-0.226881\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.95133 | 0.360952 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.51325i | − | 0.342731i | −0.985208 | − | 0.171365i | \(-0.945182\pi\) | ||
0.985208 | − | 0.171365i | \(-0.0548178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 0.843990i | − | 0.0339228i | −0.999856 | − | 0.0169614i | \(-0.994601\pi\) | ||
0.999856 | − | 0.0169614i | \(-0.00539925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59.3012 | 2.37967 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.06453 | 0.0827136 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.6699 | −0.946794 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.48167 | −0.378661 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 46.0593i | 1.83650i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 46.8526i | − | 1.86517i | −0.360948 | − | 0.932586i | \(-0.617547\pi\) | ||
0.360948 | − | 0.932586i | \(-0.382453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.95916 | 0.395841 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 4.76263i | − | 0.188999i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.04907 | + | 1.92437i | −0.120808 | + | 0.0762462i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 41.6120i | − | 1.64615i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.5344 | 0.732064 | 0.366032 | − | 0.930602i | \(-0.380716\pi\) | ||||
0.366032 | + | 0.930602i | \(0.380716\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.4921i | 0.532075i | 0.963963 | + | 0.266037i | \(0.0857145\pi\) | ||||
−0.963963 | + | 0.266037i | \(0.914286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 56.4343i | 2.22210i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.2199 | −0.519729 | −0.259865 | − | 0.965645i | \(-0.583678\pi\) | ||||
−0.259865 | + | 0.965645i | \(0.583678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.32058 | −0.365865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.10696 | −0.0433851 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.18417 | −0.320271 | −0.160136 | − | 0.987095i | \(-0.551193\pi\) | ||||
−0.160136 | + | 0.987095i | \(0.551193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 39.5557i | − | 1.54557i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.53609i | 0.294011i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.9898 | −1.05138 | −0.525688 | − | 0.850678i | \(-0.676192\pi\) | ||||
−0.525688 | + | 0.850678i | \(0.676192\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.73606i | 0.0675249i | 0.999430 | + | 0.0337625i | \(0.0107490\pi\) | ||||
−0.999430 | + | 0.0337625i | \(0.989251\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.8483 | − | 30.8298i | 1.89711 | − | 1.19733i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 6.30802i | − | 0.244615i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.2133 | −0.589062 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55.0229i | 2.12731i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.2280i | 0.472057i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.56865 | −0.0604672 | −0.0302336 | − | 0.999543i | \(-0.509625\pi\) | ||||
−0.0302336 | + | 0.999543i | \(0.509625\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.91773 | −0.150793 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.5238 | 1.40372 | 0.701861 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701861 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.930612 | 0.0357136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 70.3873i | 2.69725i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 31.0436i | − | 1.18785i | −0.804521 | − | 0.593924i | \(-0.797578\pi\) | ||
0.804521 | − | 0.593924i | \(-0.202422\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.5038 | −1.12728 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.4016i | 1.42696i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.64249 | + | 2.29890i | −0.138768 | + | 0.0875810i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.8777i | 1.17464i | 0.809353 | + | 0.587322i | \(0.199818\pi\) | ||||
−0.809353 | + | 0.587322i | \(0.800182\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.72466 | 0.293435 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.19834i | 0.235117i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.13743i | − | 0.232472i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.2968 | 1.48634 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.3763 | 0.882911 | 0.441455 | − | 0.897283i | \(-0.354462\pi\) | ||||
0.441455 | + | 0.897283i | \(0.354462\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.2596 | −1.02812 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 80.3031 | 3.02439 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0014i | 0.488968i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.4087i | 1.55514i | 0.628798 | + | 0.777568i | \(0.283547\pi\) | ||||
−0.628798 | + | 0.777568i | \(0.716453\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.9291 | 1.57246 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.29551i | − | 0.0485172i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.64305 | + | 4.19264i | −0.248436 | + | 0.156796i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.8417i | 0.927730i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.0533 | 1.34456 | 0.672281 | − | 0.740296i | \(-0.265315\pi\) | ||||
0.672281 | + | 0.740296i | \(0.265315\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9032i | 0.592267i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 69.0756i | − | 2.56895i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00507 | 0.0373273 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5955 | 0.615492 | 0.307746 | − | 0.951469i | \(-0.400425\pi\) | ||||
0.307746 | + | 0.951469i | \(0.400425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 60.3889 | 2.23662 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.6939 | 1.43114 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 18.3864i | − | 0.679117i | −0.940585 | − | 0.339559i | \(-0.889722\pi\) | ||
0.940585 | − | 0.339559i | \(-0.110278\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.13497i | 0.263177i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.95290 | −0.0719362 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.0008i | − | 0.588600i | −0.955713 | − | 0.294300i | \(-0.904914\pi\) | ||
0.955713 | − | 0.294300i | \(-0.0950865\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.2462 | + | 28.9103i | 0.670291 | + | 1.06204i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.0070i | 1.39434i | 0.716905 | + | 0.697171i | \(0.245558\pi\) | ||||
−0.716905 | + | 0.697171i | \(0.754442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.7887 | 1.71420 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 35.6189i | − | 1.30323i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.07538i | − | 0.112372i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.0475 | −1.05996 | −0.529980 | − | 0.848010i | \(-0.677800\pi\) | ||||
−0.529980 | + | 0.848010i | \(0.677800\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.87815 | 0.250654 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.8057 | 1.52147 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.7817 | −1.70031 | −0.850154 | − | 0.526534i | \(-0.823491\pi\) | ||||
−0.850154 | + | 0.526534i | \(0.823491\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.5514i | 0.455588i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 22.9367i | − | 0.831454i | −0.909489 | − | 0.415727i | \(-0.863527\pi\) | ||
0.909489 | − | 0.415727i | \(-0.136473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.6995 | 0.604563 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 82.3323i | − | 2.97673i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9362 | + | 28.4191i | 0.647639 | + | 1.02615i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.9721i | 1.04476i | 0.852713 | + | 0.522380i | \(0.174956\pi\) | ||||
−0.852713 | + | 0.522380i | \(0.825044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 87.3738 | 3.14669 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30.7776i | − | 1.10699i | −0.832852 | − | 0.553496i | \(-0.813293\pi\) | ||
0.832852 | − | 0.553496i | \(-0.186707\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0855878i | 0.00307440i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.8332 | 1.10613 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.63236 | 0.130143 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.38691 | 0.192759 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −61.4164 | −2.19484 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 35.5958i | − | 1.27047i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.9562i | − | 0.461838i | −0.972973 | − | 0.230919i | \(-0.925827\pi\) | ||
0.972973 | − | 0.230919i | \(-0.0741732\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.7338 | −1.73497 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.43772i | − | 0.300011i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.2840 | − | 23.5312i | 1.32399 | − | 0.835617i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.52361i | 0.302301i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.58529 | −0.126997 | −0.0634987 | − | 0.997982i | \(-0.520226\pi\) | ||||
−0.0634987 | + | 0.997982i | \(0.520226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 55.0594i | − | 1.94786i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.9478i | 0.563487i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.975589 | −0.0344278 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.35029 | −0.294309 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 71.2765 | 2.50905 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.7325 | 0.728915 | 0.364458 | − | 0.931220i | \(-0.381254\pi\) | ||||
0.364458 | + | 0.931220i | \(0.381254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.4266i | − | 0.717274i | −0.933477 | − | 0.358637i | \(-0.883242\pi\) | ||
0.933477 | − | 0.358637i | \(-0.116758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.2140i | 1.79616i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.2462 | 1.33971 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.9005i | 0.801186i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.8651 | − | 23.5530i | −0.519428 | − | 0.823008i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 14.6461i | − | 0.511151i | −0.966789 | − | 0.255575i | \(-0.917735\pi\) | ||
0.966789 | − | 0.255575i | \(-0.0822649\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.5033 | −0.610125 | −0.305063 | − | 0.952332i | \(-0.598677\pi\) | ||||
−0.305063 | + | 0.952332i | \(0.598677\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.829209i | − | 0.0288694i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.1646i | − | 0.562100i | −0.959693 | − | 0.281050i | \(-0.909317\pi\) | ||
0.959693 | − | 0.281050i | \(-0.0906826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3419 | −0.706502 | −0.353251 | − | 0.935529i | \(-0.614924\pi\) | ||||
−0.353251 | + | 0.935529i | \(0.614924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.4247 | 1.43701 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.89205 | 0.169500 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.6977 | −1.40840 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.22999i | − | 0.180775i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.1571i | 0.592328i | 0.955137 | + | 0.296164i | \(0.0957075\pi\) | ||||
−0.955137 | + | 0.296164i | \(0.904293\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2440 | −0.456690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 46.7018i | − | 1.60850i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.5673 | + | 12.1869i | 0.879542 | + | 0.419242i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.4188 | 1.73037 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0851i | 1.23698i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.6635i | 1.80317i | 0.432607 | + | 0.901583i | \(0.357594\pi\) | ||||
−0.432607 | + | 0.901583i | \(0.642406\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 48.7273 | 1.66644 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.09733 | −0.174121 | −0.0870607 | − | 0.996203i | \(-0.527747\pi\) | ||||
−0.0870607 | + | 0.996203i | \(0.527747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.7716 | −0.879316 | −0.439658 | − | 0.898165i | \(-0.644900\pi\) | ||||
−0.439658 | + | 0.898165i | \(0.644900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.10854 | −0.140019 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.3410i | 1.40726i | 0.710564 | + | 0.703632i | \(0.248440\pi\) | ||||
−0.710564 | + | 0.703632i | \(0.751560\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 14.6528i | − | 0.498209i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.7018 | −0.770993 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.42795i | 0.184131i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.75810 | + | 5.95454i | 0.127339 | + | 0.201762i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.18866i | 0.243299i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.4452 | 0.386919 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8469i | 0.805254i | 0.915364 | + | 0.402627i | \(0.131903\pi\) | ||||
−0.915364 | + | 0.402627i | \(0.868097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 55.9041i | − | 1.88560i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.2863 | −0.683464 | −0.341732 | − | 0.939797i | \(-0.611013\pi\) | ||||
−0.341732 | + | 0.939797i | \(0.611013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.6758 | −0.561184 | −0.280592 | − | 0.959827i | \(-0.590531\pi\) | ||||
−0.280592 | + | 0.959827i | \(0.590531\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 66.5020 | 2.23544 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.53976 | 0.152430 | 0.0762151 | − | 0.997091i | \(-0.475716\pi\) | ||||
0.0762151 | + | 0.997091i | \(0.475716\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.18598i | 0.0733155i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.4963i | 0.921162i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.5862 | 1.09045 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18.5621i | − | 0.620462i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.2701 | − | 24.1535i | 1.27780 | − | 0.806463i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.34172i | 0.0447489i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.84417 | 0.194698 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 25.9026i | − | 0.861983i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 54.0245i | − | 1.79583i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.3756 | −1.07501 | −0.537507 | − | 0.843259i | \(-0.680634\pi\) | ||||
−0.537507 | + | 0.843259i | \(0.680634\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −100.431 | −3.33110 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7428 | −0.819766 | −0.409883 | − | 0.912138i | \(-0.634430\pi\) | ||||
−0.409883 | + | 0.912138i | \(0.634430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.61107 | 0.152604 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 87.2464i | − | 2.88428i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.1555i | 0.599549i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.5762 | −0.414851 | −0.207425 | − | 0.978251i | \(-0.566508\pi\) | ||||
−0.207425 | + | 0.978251i | \(0.566508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.5456i | 1.17127i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.3664 | − | 16.4251i | −0.341214 | − | 0.540637i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.38396i | − | 0.0783841i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −122.847 | −4.03482 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.3919i | 0.865889i | 0.901420 | + | 0.432945i | \(0.142525\pi\) | ||||
−0.901420 | + | 0.432945i | \(0.857475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.89530i | 0.0948895i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 86.4159 | 2.82913 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.6584 | 0.348566 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.76670 | 0.155721 | 0.0778607 | − | 0.996964i | \(-0.475191\pi\) | ||||
0.0778607 | + | 0.996964i | \(0.475191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −74.2005 | −2.42144 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.13885i | 0.0697244i | 0.999392 | + | 0.0348622i | \(0.0110992\pi\) | ||||
−0.999392 | + | 0.0348622i | \(0.988901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.80836i | − | 0.156582i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −33.7103 | −1.09659 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.6002i | 1.51430i | 0.653239 | + | 0.757151i | \(0.273410\pi\) | ||||
−0.653239 | + | 0.757151i | \(0.726590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.87739 | + | 2.97464i | 0.0609427 | + | 0.0965608i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 81.4695i | 2.64183i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.01203 | −0.0975692 | −0.0487846 | − | 0.998809i | \(-0.515535\pi\) | ||||
−0.0487846 | + | 0.998809i | \(0.515535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.2966i | 1.14217i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 12.9991i | − | 0.420202i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.5418 | 0.437288 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8857 | 0.996314 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.7562 | 0.765534 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37.9446 | −1.22148 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.85730i | − | 0.156200i | −0.996946 | − | 0.0781001i | \(-0.975115\pi\) | ||
0.996946 | − | 0.0781001i | \(-0.0248854\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 46.3848i | − | 1.49009i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.0224 | 1.57320 | 0.786602 | − | 0.617461i | \(-0.211838\pi\) | ||||
0.786602 | + | 0.617461i | \(0.211838\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.84495i | − | 0.0912050i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.52831 | + | 1.59570i | −0.0809709 | + | 0.0511034i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.4475i | 1.26204i | 0.775768 | + | 0.631018i | \(0.217363\pi\) | ||||
−0.775768 | + | 0.631018i | \(0.782637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.06453 | −0.0659826 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 128.998i | 4.11859i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 7.05616i | − | 0.225057i | −0.993649 | − | 0.112528i | \(-0.964105\pi\) | ||
0.993649 | − | 0.112528i | \(-0.0358949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.8779 | 0.888264 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36.8580 | −1.17320 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.3146 | 0.963949 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.8740 | 0.377191 | 0.188596 | − | 0.982055i | \(-0.439606\pi\) | ||||
0.188596 | + | 0.982055i | \(0.439606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.8113i | 1.26337i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.73026i | 0.213364i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.4403 | −1.91416 | −0.957081 | − | 0.289821i | \(-0.906404\pi\) | ||||
−0.957081 | + | 0.289821i | \(0.906404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 145.676i | 4.60899i |
(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.m.c.2157.2 | yes | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.1 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.1 | ✓ | 36 | 13.12 | even | 2 | inner | |
4004.2.m.c.2157.2 | yes | 36 | 1.1 | even | 1 | trivial |