Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(641,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.h (of order \(2\), degree \(1\), not 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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} + \cdots + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{34}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.9 | ||
Root | \(-1.09921 - 2.65372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.641 |
Dual form | 768.3.h.h.641.10 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.888828 | − | 2.86531i | 0.296276 | − | 0.955102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.59176 | 1.71835 | 0.859176 | − | 0.511680i | \(-0.170977\pi\) | ||||
0.859176 | + | 0.511680i | \(0.170977\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.9340 | 1.56199 | 0.780997 | − | 0.624535i | \(-0.214712\pi\) | ||||
0.780997 | + | 0.624535i | \(0.214712\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.41997 | − | 5.09353i | −0.824441 | − | 0.565948i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.75255 | 0.250232 | 0.125116 | − | 0.992142i | \(-0.460070\pi\) | ||||
0.125116 | + | 0.992142i | \(0.460070\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.43326i | − | 0.341020i | −0.985356 | − | 0.170510i | \(-0.945459\pi\) | ||
0.985356 | − | 0.170510i | \(-0.0545415\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.63660 | − | 24.6180i | 0.509107 | − | 1.64120i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 25.4208i | − | 1.49534i | −0.664070 | − | 0.747670i | \(-0.731172\pi\) | ||
0.664070 | − | 0.747670i | \(-0.268828\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.5426i | 0.923294i | 0.887064 | + | 0.461647i | \(0.152741\pi\) | ||||
−0.887064 | + | 0.461647i | \(0.847259\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.71841 | − | 31.3291i | 0.462781 | − | 1.49186i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.5482i | 0.762966i | 0.924376 | + | 0.381483i | \(0.124587\pi\) | ||||
−0.924376 | + | 0.381483i | \(0.875413\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 48.8183 | 1.95273 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −21.1896 | + | 16.7332i | −0.784800 | + | 0.619749i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −19.6224 | −0.676635 | −0.338317 | − | 0.941032i | \(-0.609858\pi\) | ||||
−0.338317 | + | 0.941032i | \(0.609858\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.58322 | −0.0833295 | −0.0416648 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416648 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.44655 | − | 7.88691i | 0.0741377 | − | 0.238997i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 93.9419 | 2.68405 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.73178i | − | 0.208967i | −0.994527 | − | 0.104484i | \(-0.966681\pi\) | ||
0.994527 | − | 0.104484i | \(-0.0333189\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.7026 | − | 3.94040i | −0.325709 | − | 0.101036i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 58.0069i | 1.41480i | 0.706812 | + | 0.707402i | \(0.250133\pi\) | ||||
−0.706812 | + | 0.707402i | \(0.749867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 42.1932i | 0.981238i | 0.871374 | + | 0.490619i | \(0.163229\pi\) | ||||
−0.871374 | + | 0.490619i | \(0.836771\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −63.7506 | − | 43.7624i | −1.41668 | − | 0.972498i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17.4666i | 0.371629i | 0.982585 | + | 0.185815i | \(0.0594924\pi\) | ||||
−0.982585 | + | 0.185815i | \(0.940508\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 70.5514 | 1.43982 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −72.8384 | − | 22.5947i | −1.42820 | − | 0.443034i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −69.0052 | −1.30198 | −0.650992 | − | 0.759085i | \(-0.725647\pi\) | ||||
−0.650992 | + | 0.759085i | \(0.725647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23.6493 | 0.429987 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 50.2649 | + | 15.5923i | 0.881840 | + | 0.273550i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −50.5878 | −0.857420 | −0.428710 | − | 0.903442i | \(-0.641032\pi\) | ||||
−0.428710 | + | 0.903442i | \(0.641032\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 32.5983i | − | 0.534398i | −0.963641 | − | 0.267199i | \(-0.913902\pi\) | ||
0.963641 | − | 0.267199i | \(-0.0860981\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −81.1296 | − | 55.6924i | −1.28777 | − | 0.884007i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 38.0895i | − | 0.585992i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 48.0128i | − | 0.716609i | −0.933605 | − | 0.358305i | \(-0.883355\pi\) | ||
0.933605 | − | 0.358305i | \(-0.116645\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 50.2811 | + | 15.5974i | 0.728711 | + | 0.226049i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 22.1021i | 0.311297i | 0.987813 | + | 0.155648i | \(0.0497466\pi\) | ||||
−0.987813 | + | 0.155648i | \(0.950253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 27.0316 | 0.370295 | 0.185148 | − | 0.982711i | \(-0.440724\pi\) | ||||
0.185148 | + | 0.982711i | \(0.440724\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 43.3911 | − | 139.880i | 0.578548 | − | 1.86506i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30.0963 | 0.390861 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 97.4827 | 1.23396 | 0.616979 | − | 0.786980i | \(-0.288356\pi\) | ||||
0.616979 | + | 0.786980i | \(0.288356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.1119 | + | 75.5877i | 0.359406 | + | 0.933181i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −59.5252 | −0.717170 | −0.358585 | − | 0.933497i | \(-0.616741\pi\) | ||||
−0.358585 | + | 0.933497i | \(0.616741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 218.409i | − | 2.56952i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.4409 | + | 56.2242i | −0.200471 | + | 0.646255i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 110.469i | − | 1.24122i | −0.784119 | − | 0.620611i | \(-0.786885\pi\) | ||
0.784119 | − | 0.620611i | \(-0.213115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 48.4730i | − | 0.532671i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.29603 | + | 7.40171i | −0.0246885 | + | 0.0795882i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 150.722i | 1.58654i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 55.1169 | 0.568215 | 0.284108 | − | 0.958792i | \(-0.408303\pi\) | ||||
0.284108 | + | 0.958792i | \(0.408303\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.4238 | − | 14.0202i | −0.206301 | − | 0.141618i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −20.2294 | −0.200291 | −0.100146 | − | 0.994973i | \(-0.531931\pi\) | ||||
−0.100146 | + | 0.994973i | \(0.531931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −65.3051 | −0.634030 | −0.317015 | − | 0.948421i | \(-0.602680\pi\) | ||||
−0.317015 | + | 0.948421i | \(0.602680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 83.4982 | − | 269.172i | 0.795221 | − | 2.56355i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3305 | −0.0965468 | −0.0482734 | − | 0.998834i | \(-0.515372\pi\) | ||||
−0.0482734 | + | 0.998834i | \(0.515372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 151.542i | − | 1.39029i | −0.718870 | − | 0.695145i | \(-0.755340\pi\) | ||
0.718870 | − | 0.695145i | \(-0.244660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.1539 | − | 6.87222i | −0.199585 | − | 0.0619119i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 106.377i | − | 0.941391i | −0.882296 | − | 0.470696i | \(-0.844003\pi\) | ||
0.882296 | − | 0.470696i | \(-0.155997\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 150.770i | 1.31104i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22.5809 | + | 32.8946i | −0.192999 | + | 0.281151i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 277.950i | − | 2.33571i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −113.423 | −0.937384 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 166.208 | + | 51.5582i | 1.35128 | + | 0.419172i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 204.641 | 1.63713 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −112.285 | −0.884138 | −0.442069 | − | 0.896981i | \(-0.645755\pi\) | ||||
−0.442069 | + | 0.896981i | \(0.645755\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 120.897 | + | 37.5025i | 0.937183 | + | 0.290717i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −137.804 | −1.05194 | −0.525968 | − | 0.850504i | \(-0.676297\pi\) | ||||
−0.525968 | + | 0.850504i | \(0.676297\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 191.810i | 1.44218i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −182.056 | + | 143.768i | −1.34856 | + | 1.06495i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 152.889i | 1.11598i | 0.829847 | + | 0.557990i | \(0.188427\pi\) | ||||
−0.829847 | + | 0.557990i | \(0.811573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 236.450i | 1.70108i | 0.525910 | + | 0.850540i | \(0.323725\pi\) | ||||
−0.525910 | + | 0.850540i | \(0.676275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 50.0471 | + | 15.5248i | 0.354944 | + | 0.110105i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 12.2028i | − | 0.0853340i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −168.591 | −1.16270 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 62.7080 | − | 202.151i | 0.426585 | − | 1.37518i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −185.019 | −1.24174 | −0.620869 | − | 0.783914i | \(-0.713220\pi\) | ||||
−0.620869 | + | 0.783914i | \(0.713220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 283.340 | 1.87643 | 0.938214 | − | 0.346057i | \(-0.112480\pi\) | ||||
0.938214 | + | 0.346057i | \(0.112480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −129.482 | + | 188.621i | −0.846285 | + | 1.23282i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.1944 | −0.143189 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 32.9672i | − | 0.209982i | −0.994473 | − | 0.104991i | \(-0.966519\pi\) | ||
0.994473 | − | 0.104991i | \(-0.0334814\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −61.3337 | + | 197.721i | −0.385747 | + | 1.24353i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 191.872i | 1.19175i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 248.216i | 1.52280i | 0.648283 | + | 0.761399i | \(0.275487\pi\) | ||||
−0.648283 | + | 0.761399i | \(0.724513\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.0201 | − | 67.7624i | 0.127395 | − | 0.410681i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 235.204i | − | 1.40841i | −0.709997 | − | 0.704205i | \(-0.751304\pi\) | ||
0.709997 | − | 0.704205i | \(-0.248696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 149.346 | 0.883706 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 89.3537 | − | 130.165i | 0.522536 | − | 0.761201i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −38.6880 | −0.223630 | −0.111815 | − | 0.993729i | \(-0.535666\pi\) | ||||
−0.111815 | + | 0.993729i | \(0.535666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 533.777 | 3.05016 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −44.9639 | + | 144.950i | −0.254033 | + | 0.818924i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 287.329 | 1.60519 | 0.802595 | − | 0.596524i | \(-0.203452\pi\) | ||||
0.802595 | + | 0.596524i | \(0.203452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 199.173i | 1.10040i | 0.835032 | + | 0.550201i | \(0.185449\pi\) | ||||
−0.835032 | + | 0.550201i | \(0.814551\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −93.4041 | − | 28.9743i | −0.510405 | − | 0.158329i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 66.4296i | − | 0.359079i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 69.9720i | − | 0.374182i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −231.686 | + | 182.960i | −1.22585 | + | 0.968044i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 227.555i | − | 1.19139i | −0.803211 | − | 0.595695i | \(-0.796877\pi\) | ||
0.803211 | − | 0.595695i | \(-0.203123\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.8956 | −0.123811 | −0.0619056 | − | 0.998082i | \(-0.519718\pi\) | ||||
−0.0619056 | + | 0.998082i | \(0.519718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −109.138 | − | 33.8550i | −0.559682 | − | 0.173615i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −78.6009 | −0.398990 | −0.199495 | − | 0.979899i | \(-0.563930\pi\) | ||||
−0.199495 | + | 0.979899i | \(0.563930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 181.811 | 0.913625 | 0.456812 | − | 0.889563i | \(-0.348991\pi\) | ||||
0.456812 | + | 0.889563i | \(0.348991\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −137.571 | − | 42.6751i | −0.684435 | − | 0.212314i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −214.550 | −1.05690 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 498.382i | 2.43113i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 89.3824 | − | 130.207i | 0.431799 | − | 0.629021i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 48.2869i | 0.231038i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.18826i | 0.0103709i | 0.999987 | + | 0.00518544i | \(0.00165058\pi\) | ||||
−0.999987 | + | 0.00518544i | \(0.998349\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 63.3292 | + | 19.6449i | 0.297320 | + | 0.0922297i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 362.514i | 1.68611i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.2448 | −0.130160 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.0264 | − | 77.4537i | 0.109710 | − | 0.353670i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −112.697 | −0.509941 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −317.724 | −1.42477 | −0.712386 | − | 0.701788i | \(-0.752385\pi\) | ||||
−0.712386 | + | 0.701788i | \(0.752385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −362.231 | − | 248.658i | −1.60991 | − | 1.10515i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −241.233 | −1.06270 | −0.531350 | − | 0.847152i | \(-0.678315\pi\) | ||||
−0.531350 | + | 0.847152i | \(0.678315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 58.1799i | − | 0.254061i | −0.991899 | − | 0.127030i | \(-0.959455\pi\) | ||
0.991899 | − | 0.127030i | \(-0.0405446\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.7504 | − | 86.2351i | 0.115803 | − | 0.373312i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 242.432i | 1.04048i | 0.854020 | + | 0.520240i | \(0.174158\pi\) | ||||
−0.854020 | + | 0.520240i | \(0.825842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 150.069i | 0.638590i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 86.6453 | − | 279.318i | 0.365592 | − | 1.17856i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 215.651i | − | 0.902304i | −0.892447 | − | 0.451152i | \(-0.851013\pi\) | ||
0.892447 | − | 0.451152i | \(-0.148987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 123.252 | 0.511417 | 0.255709 | − | 0.966754i | \(-0.417691\pi\) | ||||
0.255709 | + | 0.966754i | \(0.417691\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 242.457 | − | 16.2300i | 0.997767 | − | 0.0667902i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 606.160 | 2.47412 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 77.7708 | 0.314861 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −52.9076 | + | 170.558i | −0.212480 | + | 0.684971i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 194.768 | 0.775967 | 0.387984 | − | 0.921666i | \(-0.373172\pi\) | ||||
0.387984 | + | 0.921666i | \(0.373172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.3024i | 0.190919i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −625.810 | − | 194.128i | −2.45416 | − | 0.761288i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 200.615i | − | 0.780605i | −0.920687 | − | 0.390303i | \(-0.872370\pi\) | ||
0.920687 | − | 0.390303i | \(-0.127630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 84.5389i | − | 0.326405i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 145.598 | + | 99.9473i | 0.557845 | + | 0.382940i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 440.044i | 1.67317i | 0.547837 | + | 0.836585i | \(0.315451\pi\) | ||||
−0.547837 | + | 0.836585i | \(0.684549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −592.876 | −2.23727 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −316.527 | − | 98.1877i | −1.18549 | − | 0.367744i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −64.1922 | −0.238633 | −0.119316 | − | 0.992856i | \(-0.538070\pi\) | ||||
−0.119316 | + | 0.992856i | \(0.538070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 229.609 | 0.847265 | 0.423633 | − | 0.905834i | \(-0.360755\pi\) | ||||
0.423633 | + | 0.905834i | \(0.360755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −138.890 | − | 43.0842i | −0.508755 | − | 0.157818i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 134.375 | 0.488636 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 329.621i | 1.18997i | 0.803738 | + | 0.594983i | \(0.202841\pi\) | ||||
−0.803738 | + | 0.594983i | \(0.797159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.1674 | + | 13.1577i | 0.0687003 | + | 0.0471602i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 222.349i | − | 0.791279i | −0.918406 | − | 0.395640i | \(-0.870523\pi\) | ||
0.918406 | − | 0.395640i | \(-0.129477\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 550.386i | 1.94483i | 0.233261 | + | 0.972414i | \(0.425060\pi\) | ||||
−0.233261 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 431.864 | + | 133.966i | 1.51531 | + | 0.470055i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 634.245i | 2.20991i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −357.217 | −1.23604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 48.9894 | − | 157.927i | 0.168349 | − | 0.542704i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 322.712 | 1.10141 | 0.550703 | − | 0.834701i | \(-0.314360\pi\) | ||||
0.550703 | + | 0.834701i | \(0.314360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −434.638 | −1.47335 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −58.3255 | + | 46.0590i | −0.196382 | + | 0.155081i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 77.7958 | 0.260187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 461.339i | 1.53269i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.9805 | + | 57.9635i | −0.0593415 | + | 0.191299i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 280.077i | − | 0.918284i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 66.6568i | − | 0.217123i | −0.994090 | − | 0.108562i | \(-0.965376\pi\) | ||
0.994090 | − | 0.108562i | \(-0.0346244\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −58.0450 | + | 187.119i | −0.187848 | + | 0.605563i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.7250i | − | 0.0666398i | −0.999445 | − | 0.0333199i | \(-0.989392\pi\) | ||
0.999445 | − | 0.0333199i | \(-0.0106080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 211.296 | 0.675066 | 0.337533 | − | 0.941314i | \(-0.390408\pi\) | ||||
0.337533 | + | 0.941314i | \(0.390408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −697.046 | − | 478.496i | −2.21284 | − | 1.51904i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −238.040 | −0.750915 | −0.375457 | − | 0.926840i | \(-0.622514\pi\) | ||||
−0.375457 | + | 0.926840i | \(0.622514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54.0117 | −0.169316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.18205 | + | 29.6001i | −0.0286045 | + | 0.0922121i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 445.946 | 1.38064 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 216.424i | − | 0.665921i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −434.213 | − | 134.694i | −1.32787 | − | 0.411910i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 190.979i | 0.580483i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 344.811i | − | 1.04173i | −0.853640 | − | 0.520863i | \(-0.825610\pi\) | ||
0.853640 | − | 0.520863i | \(-0.174390\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −39.3821 | + | 57.3696i | −0.118264 | + | 0.172281i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 412.515i | − | 1.23139i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −355.471 | −1.05481 | −0.527405 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527405 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −304.803 | − | 94.5511i | −0.899125 | − | 0.278912i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.11043 | −0.0208517 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 235.642 | 0.687002 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 432.003 | + | 134.009i | 1.25218 | + | 0.388431i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 73.9748 | 0.213184 | 0.106592 | − | 0.994303i | \(-0.466006\pi\) | ||||
0.106592 | + | 0.994303i | \(0.466006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 443.377i | − | 1.27042i | −0.772340 | − | 0.635210i | \(-0.780914\pi\) | ||
0.772340 | − | 0.635210i | \(-0.219086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 74.1827 | + | 93.9390i | 0.211347 | + | 0.267632i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 553.017i | 1.56662i | 0.621630 | + | 0.783311i | \(0.286471\pi\) | ||||
−0.621630 | + | 0.783311i | \(0.713529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 189.896i | 0.534917i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −796.411 | − | 247.050i | −2.23084 | − | 0.692016i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 352.615i | 0.982214i | 0.871099 | + | 0.491107i | \(0.163408\pi\) | ||||
−0.871099 | + | 0.491107i | \(0.836592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 53.2578 | 0.147529 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −100.814 | + | 324.993i | −0.277724 | + | 0.895298i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 232.249 | 0.636298 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 305.686 | 0.832932 | 0.416466 | − | 0.909151i | \(-0.363269\pi\) | ||||
0.416466 | + | 0.909151i | \(0.363269\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 295.460 | − | 430.410i | 0.800705 | − | 1.16642i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −754.499 | −2.03369 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 133.295i | − | 0.357359i | −0.983907 | − | 0.178679i | \(-0.942818\pi\) | ||
0.983907 | − | 0.178679i | \(-0.0571825\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 181.891 | − | 586.361i | 0.485043 | − | 1.56363i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 86.9912i | 0.230746i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 239.300i | − | 0.631399i | −0.948859 | − | 0.315699i | \(-0.897761\pi\) | ||
0.948859 | − | 0.315699i | \(-0.102239\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −99.8025 | + | 321.732i | −0.261949 | + | 0.844442i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 249.576i | − | 0.651634i | −0.945433 | − | 0.325817i | \(-0.894361\pi\) | ||
0.945433 | − | 0.325817i | \(-0.105639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 258.580 | 0.671636 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 214.913 | − | 313.073i | 0.555330 | − | 0.808973i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −499.992 | −1.28533 | −0.642664 | − | 0.766148i | \(-0.722171\pi\) | ||||
−0.642664 | + | 0.766148i | \(0.722171\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 446.090 | 1.14089 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −122.484 | + | 394.850i | −0.311663 | + | 1.00471i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 837.548 | 2.12037 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 302.418i | − | 0.761759i | −0.924625 | − | 0.380880i | \(-0.875621\pi\) | ||
0.924625 | − | 0.380880i | \(-0.124379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 549.594 | + | 170.486i | 1.37743 | + | 0.427283i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 799.221i | 1.99307i | 0.0831706 | + | 0.996535i | \(0.473495\pi\) | ||||
−0.0831706 | + | 0.996535i | \(0.526505\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.4521i | 0.0284170i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 250.122 | + | 649.431i | 0.617586 | + | 1.60353i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 21.2821i | − | 0.0522902i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −108.812 | −0.266044 | −0.133022 | − | 0.991113i | \(-0.542468\pi\) | ||||
−0.133022 | + | 0.991113i | \(0.542468\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 438.075 | + | 135.892i | 1.06588 | + | 0.330638i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −553.125 | −1.33929 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −511.426 | −1.23235 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 677.502 | + | 210.164i | 1.62471 | + | 0.503989i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 183.076 | 0.436936 | 0.218468 | − | 0.975844i | \(-0.429894\pi\) | ||||
0.218468 | + | 0.975844i | \(0.429894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 213.105i | 0.506187i | 0.967442 | + | 0.253093i | \(0.0814480\pi\) | ||||
−0.967442 | + | 0.253093i | \(0.918552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 88.9666 | − | 129.602i | 0.210323 | − | 0.306387i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1241.00i | − | 2.92000i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 356.428i | − | 0.834727i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −34.9647 | − | 10.8462i | −0.0815027 | − | 0.0252824i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 471.854i | 1.09479i | 0.836875 | + | 0.547394i | \(0.184380\pi\) | ||||
−0.836875 | + | 0.547394i | \(0.815620\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 396.992 | 0.916841 | 0.458421 | − | 0.888735i | \(-0.348415\pi\) | ||||
0.458421 | + | 0.888735i | \(0.348415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −149.848 | + | 483.065i | −0.344479 | + | 1.11049i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −307.841 | −0.704442 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 201.084 | 0.458050 | 0.229025 | − | 0.973420i | \(-0.426446\pi\) | ||||
0.229025 | + | 0.973420i | \(0.426446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −523.489 | − | 359.356i | −1.18705 | − | 0.814865i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −189.532 | −0.427838 | −0.213919 | − | 0.976851i | \(-0.568623\pi\) | ||||
−0.213919 | + | 0.976851i | \(0.568623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 949.121i | − | 2.13286i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −164.450 | + | 530.136i | −0.367897 | + | 1.18599i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 49.3773i | − | 0.109972i | −0.998487 | − | 0.0549859i | \(-0.982489\pi\) | ||
0.998487 | − | 0.0549859i | \(-0.0175114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 159.667i | 0.354029i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 251.841 | − | 811.858i | 0.555940 | − | 1.79218i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 416.469i | − | 0.915316i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 438.599 | 0.959734 | 0.479867 | − | 0.877341i | \(-0.340685\pi\) | ||||
0.479867 | + | 0.877341i | \(0.340685\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 425.372 | + | 538.657i | 0.926736 | + | 1.17354i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.0211 | −0.0586142 | −0.0293071 | − | 0.999570i | \(-0.509330\pi\) | ||||
−0.0293071 | + | 0.999570i | \(0.509330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 128.181 | 0.276850 | 0.138425 | − | 0.990373i | \(-0.455796\pi\) | ||||
0.138425 | + | 0.990373i | \(0.455796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.7270 | + | 63.5937i | −0.0424236 | + | 0.136761i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −624.873 | −1.33806 | −0.669029 | − | 0.743236i | \(-0.733290\pi\) | ||||
−0.669029 | + | 0.743236i | \(0.733290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 524.970i | − | 1.11934i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −94.4612 | − | 29.3022i | −0.200554 | − | 0.0622127i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 116.139i | 0.245537i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 856.400i | 1.80295i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 512.016 | + | 351.480i | 1.07341 | + | 0.736855i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 782.010i | − | 1.63259i | −0.577636 | − | 0.816295i | \(-0.696025\pi\) | ||
0.577636 | − | 0.816295i | \(-0.303975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.2770 | −0.0712619 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 549.771 | + | 170.541i | 1.13824 | + | 0.353087i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 473.551 | 0.976393 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −732.325 | −1.50375 | −0.751874 | − | 0.659307i | \(-0.770850\pi\) | ||||
−0.751874 | + | 0.659307i | \(0.770850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 711.215 | + | 220.621i | 1.45443 | + | 0.451169i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −65.5662 | −0.133536 | −0.0667680 | − | 0.997769i | \(-0.521269\pi\) | ||||
−0.0667680 | + | 0.997769i | \(0.521269\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 498.817i | 1.01180i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −175.477 | − | 120.458i | −0.354499 | − | 0.243350i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 241.663i | 0.486243i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 846.549i | 1.69649i | 0.529604 | + | 0.848245i | \(0.322341\pi\) | ||||
−0.529604 | + | 0.848245i | \(0.677659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −673.933 | − | 209.056i | −1.34518 | − | 0.417278i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 186.077i | − | 0.369934i | −0.982745 | − | 0.184967i | \(-0.940782\pi\) | ||
0.982745 | − | 0.184967i | \(-0.0592179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −173.806 | −0.344171 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 132.743 | − | 427.923i | 0.261821 | − | 0.844029i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 996.730 | 1.95821 | 0.979106 | − | 0.203350i | \(-0.0651830\pi\) | ||||
0.979106 | + | 0.203350i | \(0.0651830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 295.562 | 0.578399 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −293.544 | − | 371.720i | −0.572210 | − | 0.724601i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −561.085 | −1.08949 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.0777i | 0.0929936i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34.3870 | + | 110.853i | −0.0662563 | + | 0.213590i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 471.553i | − | 0.905092i | −0.891741 | − | 0.452546i | \(-0.850516\pi\) | ||
0.891741 | − | 0.452546i | \(-0.149484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 364.836i | − | 0.697582i | −0.937200 | − | 0.348791i | \(-0.886592\pi\) | ||
0.937200 | − | 0.348791i | \(-0.113408\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 474.436 | − | 1529.44i | 0.903688 | − | 2.91321i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 65.6674i | 0.124606i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 221.060 | 0.417882 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 375.360 | + | 257.671i | 0.706893 | + | 0.485255i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 257.160 | 0.482476 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −88.7573 | −0.165901 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 255.386 | − | 823.286i | 0.475579 | − | 1.53312i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 194.196 | 0.360290 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 68.1097i | − | 0.125896i | −0.998017 | − | 0.0629480i | \(-0.979950\pi\) | ||
0.998017 | − | 0.0629480i | \(-0.0200502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 570.691 | + | 177.030i | 1.05100 | + | 0.326023i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1302.01i | − | 2.38901i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 459.725i | − | 0.840448i | −0.907420 | − | 0.420224i | \(-0.861951\pi\) | ||
0.907420 | − | 0.420224i | \(-0.138049\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −166.040 | + | 241.878i | −0.302442 | + | 0.440580i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 344.228i | − | 0.624733i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1065.87 | 1.92743 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −190.341 | − | 59.0445i | −0.342957 | − | 0.106386i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −95.1108 | −0.170756 | −0.0853778 | − | 0.996349i | \(-0.527210\pi\) | ||||
−0.0853778 | + | 0.996349i | \(0.527210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 187.053 | 0.334622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −200.491 | − | 62.1931i | −0.357382 | − | 0.110861i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 422.228 | 0.749960 | 0.374980 | − | 0.927033i | \(-0.377650\pi\) | ||||
0.374980 | + | 0.927033i | \(0.377650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 913.967i | − | 1.61764i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 318.308 | + | 826.472i | 0.561390 | + | 1.45762i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 328.583i | 0.577474i | 0.957408 | + | 0.288737i | \(0.0932354\pi\) | ||||
−0.957408 | + | 0.288737i | \(0.906765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 503.834i | − | 0.882371i | −0.897416 | − | 0.441186i | \(-0.854558\pi\) | ||
0.897416 | − | 0.441186i | \(-0.145442\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −652.016 | − | 202.258i | −1.13790 | − | 0.352980i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 856.675i | 1.48987i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1035.33 | 1.79433 | 0.897163 | − | 0.441700i | \(-0.145624\pi\) | ||||
0.897163 | + | 0.441700i | \(0.145624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.2391 | + | 68.4681i | −0.0366823 | + | 0.118252i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −650.845 | −1.12022 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −189.940 | −0.325798 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −194.010 | + | 282.623i | −0.331641 | + | 0.483116i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −501.148 | −0.853745 | −0.426872 | − | 0.904312i | \(-0.640385\pi\) | ||||
−0.426872 | + | 0.904312i | \(0.640385\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 45.3163i | − | 0.0769376i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −69.8627 | + | 225.216i | −0.118211 | + | 0.381076i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 737.286i | − | 1.24332i | −0.783289 | − | 0.621658i | \(-0.786459\pi\) | ||
0.783289 | − | 0.621658i | \(-0.213541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2388.08i | − | 4.01358i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 161.599 | − | 520.945i | 0.270685 | − | 0.872605i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 801.823i | − | 1.33860i | −0.742991 | − | 0.669301i | \(-0.766593\pi\) | ||
0.742991 | − | 0.669301i | \(-0.233407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −252.561 | −0.420234 | −0.210117 | − | 0.977676i | \(-0.567385\pi\) | ||||
−0.210117 | + | 0.977676i | \(0.567385\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −244.555 | + | 356.254i | −0.405564 | + | 0.590802i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −974.507 | −1.61076 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −627.073 | −1.03307 | −0.516535 | − | 0.856266i | \(-0.672778\pi\) | ||||
−0.516535 | + | 0.856266i | \(0.672778\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −190.699 | + | 614.753i | −0.313134 | + | 1.00945i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 77.4339 | 0.126733 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 375.629i | 0.612772i | 0.951907 | + | 0.306386i | \(0.0991198\pi\) | ||||
−0.951907 | + | 0.306386i | \(0.900880\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1428.02 | + | 442.976i | 2.32198 | + | 0.720286i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 161.548i | 0.261829i | 0.991394 | + | 0.130914i | \(0.0417913\pi\) | ||||
−0.991394 | + | 0.130914i | \(0.958209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.45164i | − | 0.0152692i | −0.999971 | − | 0.00763460i | \(-0.997570\pi\) | ||
0.999971 | − | 0.00763460i | \(-0.00243019\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −293.638 | − | 371.840i | −0.472847 | − | 0.598776i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1207.86i | − | 1.93878i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 537.772 | 0.860435 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 138.357 | + | 42.9187i | 0.220665 | + | 0.0684509i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −196.548 | −0.312477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1073.00 | −1.70048 | −0.850239 | − | 0.526398i | \(-0.823542\pi\) | ||||
−0.850239 | + | 0.526398i | \(0.823542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.27002 | + | 1.94498i | 0.00990525 | + | 0.00307264i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −964.730 | −1.51926 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 312.772i | − | 0.491008i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 112.578 | − | 163.997i | 0.176178 | − | 0.256646i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 713.963i | 1.11383i | 0.830570 | + | 0.556914i | \(0.188015\pi\) | ||||
−0.830570 | + | 0.556914i | \(0.811985\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 339.764i | − | 0.528405i | −0.964467 | − | 0.264202i | \(-0.914891\pi\) | ||
0.964467 | − | 0.264202i | \(-0.0851087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1038.71 | + | 322.213i | 1.61041 | + | 0.499555i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 108.874i | 0.168275i | 0.996454 | + | 0.0841375i | \(0.0268135\pi\) | ||||
−0.996454 | + | 0.0841375i | \(0.973187\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −139.246 | −0.214554 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.1047 | + | 80.9299i | −0.0385633 | + | 0.124316i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −970.043 | −1.48552 | −0.742759 | − | 0.669559i | \(-0.766483\pi\) | ||||
−0.742759 | + | 0.669559i | \(0.766483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1183.98 | −1.80760 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −200.573 | − | 137.686i | −0.305287 | − | 0.209568i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 302.641 | 0.459243 | 0.229622 | − | 0.973280i | \(-0.426251\pi\) | ||||
0.229622 | + | 0.973280i | \(0.426251\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 406.011i | 0.614237i | 0.951671 | + | 0.307118i | \(0.0993648\pi\) | ||||
−0.951671 | + | 0.307118i | \(0.900635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −100.168 | + | 322.911i | −0.151083 | + | 0.487046i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1647.98i | 2.47817i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 344.338i | − | 0.516250i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −282.402 | + | 910.377i | −0.422126 | + | 1.36080i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 89.7285i | − | 0.133724i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −143.090 | −0.212615 | −0.106307 | − | 0.994333i | \(-0.533903\pi\) | ||||
−0.106307 | + | 0.994333i | \(0.533903\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1034.44 | + | 816.888i | −1.53251 | + | 1.21020i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 791.131 | 1.16858 | 0.584292 | − | 0.811544i | \(-0.301372\pi\) | ||||
0.584292 | + | 0.811544i | \(0.301372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 602.645 | 0.887548 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −214.415 | + | 691.207i | −0.314853 | + | 1.01499i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −925.330 | −1.35480 | −0.677401 | − | 0.735614i | \(-0.736894\pi\) | ||||
−0.677401 | + | 0.735614i | \(0.736894\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1313.59i | 1.91765i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −166.703 | − | 51.7120i | −0.242654 | − | 0.0752722i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 305.918i | 0.444002i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 666.330i | 0.964299i | 0.876089 | + | 0.482149i | \(0.160144\pi\) | ||||
−0.876089 | + | 0.482149i | \(0.839856\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −223.313 | − | 153.296i | −0.322242 | − | 0.221207i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2031.52i | 2.92305i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1474.58 | 2.11561 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 694.642 | + | 215.480i | 0.993765 | + | 0.308269i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1238.38 | 1.76659 | 0.883294 | − | 0.468820i | \(-0.155321\pi\) | ||||
0.883294 | + | 0.468820i | \(0.155321\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 135.635 | 0.192938 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 429.993 | + | 133.385i | 0.609919 | + | 0.189199i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −221.187 | −0.312854 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 162.142i | − | 0.228692i | −0.993441 | − | 0.114346i | \(-0.963523\pi\) | ||
0.993441 | − | 0.114346i | \(-0.0364772\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −723.318 | − | 496.531i | −1.01733 | − | 0.698356i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 45.3309i | − | 0.0635776i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 104.843i | − | 0.146634i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −617.906 | − | 191.676i | −0.861793 | − | 0.267331i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 534.958i | 0.744031i | 0.928226 | + | 0.372016i | \(0.121333\pi\) | ||||
−0.928226 | + | 0.372016i | \(0.878667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −714.042 | −0.990350 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 109.549 | − | 353.154i | 0.151521 | − | 0.488456i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −957.933 | −1.32129 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −723.175 | −0.994738 | −0.497369 | − | 0.867539i | \(-0.665701\pi\) | ||||
−0.497369 | + | 0.867539i | \(0.665701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 168.999 | − | 709.141i | 0.231823 | − | 0.972758i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1072.59 | 1.46729 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 473.296i | − | 0.645697i | −0.946451 | − | 0.322849i | \(-0.895360\pi\) | ||
0.946451 | − | 0.322849i | \(-0.104640\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 538.772 | − | 1736.84i | 0.733024 | − | 2.36304i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 132.158i | − | 0.179319i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 724.955i | 0.980994i | 0.871443 | + | 0.490497i | \(0.163185\pi\) | ||||
−0.871443 | + | 0.490497i | \(0.836815\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 69.1249 | − | 222.837i | 0.0932859 | − | 0.300725i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 905.636i | 1.21889i | 0.792828 | + | 0.609445i | \(0.208608\pi\) | ||||
−0.792828 | + | 0.609445i | \(0.791392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1589.64 | −2.13374 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 441.675 | + | 303.193i | 0.591265 | + | 0.405881i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −112.953 | −0.150806 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1039.66 | −1.38436 | −0.692181 | − | 0.721724i | \(-0.743350\pi\) | ||||
−0.692181 | + | 0.721724i | \(0.743350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 173.115 | − | 558.070i | 0.229901 | − | 0.741128i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2434.39 | 3.22436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 826.135i | − | 1.09133i | −0.838004 | − | 0.545664i | \(-0.816278\pi\) | ||
0.838004 | − | 0.545664i | \(-0.183722\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 138.401 | + | 42.9325i | 0.182347 | + | 0.0565646i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 159.752i | 0.209924i | 0.994476 | + | 0.104962i | \(0.0334721\pi\) | ||||
−0.994476 | + | 0.104962i | \(0.966528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1656.95i | − | 2.17162i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1112.47 | + | 1620.59i | −1.45422 | + | 2.11842i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 224.269i | 0.292397i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1382.69 | −1.79804 | −0.899020 | − | 0.437908i | \(-0.855720\pi\) | ||||
−0.899020 | + | 0.437908i | \(0.855720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −574.825 | − | 178.313i | −0.745558 | − | 0.231275i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.4297 | −0.0432466 | −0.0216233 | − | 0.999766i | \(-0.506883\pi\) | ||||
−0.0216233 | + | 0.999766i | \(0.506883\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −126.108 | −0.162720 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −242.230 | − | 75.1406i | −0.311750 | − | 0.0967060i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1017.59 | −1.30628 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.8370i | 0.0778964i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 415.791 | − | 328.346i | 0.531023 | − | 0.419343i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 283.246i | − | 0.360823i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 516.814i | 0.656688i | 0.944558 | + | 0.328344i | \(0.106491\pi\) | ||||
−0.944558 | + | 0.328344i | \(0.893509\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1260.86 | + | 391.123i | 1.59805 | + | 0.495720i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1163.12i | − | 1.47045i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −144.517 | −0.182240 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −526.965 | + | 1698.77i | −0.662849 | + | 2.13682i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 593.861 | 0.745120 | 0.372560 | − | 0.928008i | \(-0.378480\pi\) | ||||
0.372560 | + | 0.928008i | \(0.378480\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 444.014 | 0.555713 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −562.676 | + | 819.675i | −0.702467 | + | 1.02331i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 74.4057 | 0.0926597 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1648.51i | 2.04784i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −57.0559 | + | 183.930i | −0.0707012 | + | 0.227919i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 163.348i | − | 0.201913i | −0.994891 | − | 0.100956i | \(-0.967810\pi\) | ||
0.994891 | − | 0.100956i | \(-0.0321903\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 911.243i | 1.12360i | 0.827271 | + | 0.561802i | \(0.189892\pi\) | ||||
−0.827271 | + | 0.561802i | \(0.810108\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 204.083 | − | 657.900i | 0.251024 | − | 0.809225i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2132.61i | 2.61670i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −740.178 | −0.905971 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −246.899 | + | 359.668i | −0.301464 | + | 0.439156i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 803.790 | 0.979038 | 0.489519 | − | 0.871993i | \(-0.337172\pi\) | ||||
0.489519 | + | 0.871993i | \(0.337172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1214.84 | 1.47611 | 0.738056 | − | 0.674740i | \(-0.235744\pi\) | ||||
0.738056 | + | 0.674740i | \(0.235744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 119.436 | − | 385.026i | 0.144771 | − | 0.466698i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.7192 | −0.0661658 | −0.0330829 | − | 0.999453i | \(-0.510533\pi\) | ||||
−0.0330829 | + | 0.999453i | \(0.510533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 656.990i | − | 0.792508i | −0.918141 | − | 0.396254i | \(-0.870310\pi\) | ||
0.918141 | − | 0.396254i | \(-0.129690\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 944.465 | + | 292.976i | 1.13654 | + | 0.352559i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1793.47i | − | 2.15303i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2020.82i | − | 2.42014i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 54.7373 | − | 43.2255i | 0.0653970 | − | 0.0516434i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1104.30i | − | 1.31621i | −0.752927 | − | 0.658104i | \(-0.771359\pi\) | ||
0.752927 | − | 0.658104i | \(-0.228641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −455.961 | −0.542166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −637.099 | − | 197.630i | −0.755753 | − | 0.234437i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1283.15 | 1.51852 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1240.17 | −1.46419 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1577.03 | + | 489.199i | 1.85751 | + | 0.576206i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 135.679 | 0.159435 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 455.418i | − | 0.533901i | −0.963710 | − | 0.266950i | \(-0.913984\pi\) | ||
0.963710 | − | 0.266950i | \(-0.0860160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 767.705 | − | 1118.35i | 0.897901 | − | 1.30801i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 909.199i | − | 1.06091i | −0.847713 | − | 0.530454i | \(-0.822021\pi\) | ||
0.847713 | − | 0.530454i | \(-0.177979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 653.942i | 0.761283i | 0.924723 | + | 0.380641i | \(0.124297\pi\) | ||||
−0.924723 | + | 0.380641i | \(0.875703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1817.31 | + | 563.735i | 2.11069 | + | 0.654744i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1592.91i | − | 1.84578i | −0.385062 | − | 0.922891i | \(-0.625820\pi\) | ||
0.385062 | − | 0.922891i | \(-0.374180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −332.398 | −0.384275 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −317.504 | + | 1023.54i | −0.366210 | + | 1.18055i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 268.326 | 0.308776 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −212.853 | −0.244378 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −408.965 | − | 280.739i | −0.468460 | − | 0.321580i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2237.54 | 2.55719 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 91.9913i | − | 0.104893i | −0.998624 | − | 0.0524466i | \(-0.983298\pi\) | ||
0.998624 | − | 0.0524466i | \(-0.0167019\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 286.835 | − | 924.668i | 0.326320 | − | 1.05195i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 278.420i | − | 0.316027i | −0.987437 | − | 0.158014i | \(-0.949491\pi\) | ||
0.987437 | − | 0.158014i | \(-0.0505090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 487.284i | − | 0.551851i | −0.961179 | − | 0.275925i | \(-0.911016\pi\) | ||
0.961179 | − | 0.275925i | \(-0.0889842\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −386.319 | + | 1245.37i | −0.436518 | + | 1.40720i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 910.822i | − | 1.02686i | −0.858132 | − | 0.513428i | \(-0.828375\pi\) | ||
0.858132 | − | 0.513428i | \(-0.171625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1227.72 | −1.38102 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 80.1320 | + | 208.059i | 0.0899349 | + | 0.233512i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −306.409 | −0.343123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2468.66 | 2.75828 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 69.1471 | − | 222.909i | 0.0770871 | − | 0.248505i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 50.6889 | 0.0563837 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1754.17i | 1.94691i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1321.88 | + | 410.051i | 1.46387 | + | 0.454099i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1711.24i | 1.89088i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 476.332i | − | 0.525173i | −0.964908 | − | 0.262587i | \(-0.915424\pi\) | ||
0.964908 | − | 0.262587i | \(-0.0845756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 150.102 | + | 103.039i | 0.165128 | + | 0.113354i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1146.69i | 1.25871i | 0.777117 | + | 0.629356i | \(0.216681\pi\) | ||||
−0.777117 | + | 0.629356i | \(0.783319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −163.846 | −0.179459 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −802.506 | − | 248.940i | −0.877055 | − | 0.272066i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1506.74 | −1.64312 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1156.90 | −1.25887 | −0.629435 | − | 0.777053i | \(-0.716714\pi\) | ||||
−0.629435 | + | 0.777053i | \(0.716714\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −190.992 | − | 59.2464i | −0.207375 | − | 0.0643284i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 97.9841 | 0.106158 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 377.453i | − | 0.408057i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 484.561 | + | 332.633i | 0.522720 | + | 0.358828i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 721.346i | 0.776476i | 0.921559 | + | 0.388238i | \(0.126916\pi\) | ||||
−0.921559 | + | 0.388238i | \(0.873084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1237.65i | 1.32938i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −59.3834 | − | 18.4209i | −0.0636478 | − | 0.0197438i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 601.183i | − | 0.642976i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −629.504 | −0.671829 | −0.335915 | − | 0.941892i | \(-0.609045\pi\) | ||||
−0.335915 | + | 0.941892i | \(0.609045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 187.805 | − | 605.427i | 0.200006 | − | 0.644757i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1735.34 | 1.84414 | 0.922072 | − | 0.387017i | \(-0.126495\pi\) | ||||
0.922072 | + | 0.387017i | \(0.126495\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1017.92 | −1.07945 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1990.59 | + | 1571.95i | −2.10645 | + | 1.66344i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1363.10 | −1.43939 | −0.719693 | − | 0.694293i | \(-0.755717\pi\) | ||||
−0.719693 | + | 0.694293i | \(0.755717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 119.838i | − | 0.126278i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −211.577 | + | 682.058i | −0.222478 | + | 0.717201i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 83.9917i | − | 0.0881340i | −0.999029 | − | 0.0440670i | \(-0.985968\pi\) | ||
0.999029 | − | 0.0440670i | \(-0.0140315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1955.10i | − | 2.04723i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.0071 | + | 154.760i | −0.0501642 | + | 0.161714i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1671.69i | 1.74315i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −954.327 | −0.993056 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 76.6521 | + | 52.6188i | 0.0795972 | + | 0.0546405i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −205.305 | −0.212751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 450.068 | 0.465427 | 0.232714 | − | 0.972545i | \(-0.425239\pi\) | ||||
0.232714 | + | 0.972545i | \(0.425239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 396.370 | − | 1277.77i | 0.409050 | − | 1.31865i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −129.710 | −0.133584 | −0.0667921 | − | 0.997767i | \(-0.521276\pi\) | ||||
−0.0667921 | + | 0.997767i | \(0.521276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2585.33i | 2.65708i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −620.122 | − | 192.364i | −0.636022 | − | 0.197296i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1234.40i | 1.26346i | 0.775189 | + | 0.631729i | \(0.217655\pi\) | ||||
−0.775189 | + | 0.631729i | \(0.782345\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 304.071i | − | 0.310593i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −771.882 | + | 1124.43i | −0.786831 | + | 1.14621i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 686.635i | 0.698509i | 0.937028 | + | 0.349255i | \(0.113565\pi\) | ||||
−0.937028 | + | 0.349255i | \(0.886435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −675.320 | −0.685604 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 547.213 | + | 169.747i | 0.554420 | + | 0.171983i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −740.417 | −0.748652 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 564.593 | 0.569721 | 0.284860 | − | 0.958569i | \(-0.408053\pi\) | ||||
0.284860 | + | 0.958569i | \(0.408053\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −987.991 | − | 306.478i | −0.994955 | − | 0.308639i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1562.08 | 1.56993 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1411.47i | − | 1.41572i | −0.706354 | − | 0.707858i | \(-0.749662\pi\) | ||
0.706354 | − | 0.707858i | \(-0.250338\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 129.378 | + | 163.833i | 0.129507 | + | 0.163997i |
(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 | 768.3.h.h.641.9 | 16 | ||
3.2 | odd | 2 | inner | 768.3.h.h.641.7 | 16 | ||
4.3 | odd | 2 | 768.3.h.g.641.8 | 16 | |||
8.3 | odd | 2 | 768.3.h.g.641.9 | 16 | |||
8.5 | even | 2 | inner | 768.3.h.h.641.8 | 16 | ||
12.11 | even | 2 | 768.3.h.g.641.10 | 16 | |||
16.3 | odd | 4 | 384.3.e.b.257.1 | yes | 8 | ||
16.5 | even | 4 | 384.3.e.a.257.1 | ✓ | 8 | ||
16.11 | odd | 4 | 384.3.e.d.257.8 | yes | 8 | ||
16.13 | even | 4 | 384.3.e.c.257.8 | yes | 8 | ||
24.5 | odd | 2 | inner | 768.3.h.h.641.10 | 16 | ||
24.11 | even | 2 | 768.3.h.g.641.7 | 16 | |||
48.5 | odd | 4 | 384.3.e.a.257.2 | yes | 8 | ||
48.11 | even | 4 | 384.3.e.d.257.7 | yes | 8 | ||
48.29 | odd | 4 | 384.3.e.c.257.7 | yes | 8 | ||
48.35 | even | 4 | 384.3.e.b.257.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.1 | ✓ | 8 | 16.5 | even | 4 | ||
384.3.e.a.257.2 | yes | 8 | 48.5 | odd | 4 | ||
384.3.e.b.257.1 | yes | 8 | 16.3 | odd | 4 | ||
384.3.e.b.257.2 | yes | 8 | 48.35 | even | 4 | ||
384.3.e.c.257.7 | yes | 8 | 48.29 | odd | 4 | ||
384.3.e.c.257.8 | yes | 8 | 16.13 | even | 4 | ||
384.3.e.d.257.7 | yes | 8 | 48.11 | even | 4 | ||
384.3.e.d.257.8 | yes | 8 | 16.11 | odd | 4 | ||
768.3.h.g.641.7 | 16 | 24.11 | even | 2 | |||
768.3.h.g.641.8 | 16 | 4.3 | odd | 2 | |||
768.3.h.g.641.9 | 16 | 8.3 | odd | 2 | |||
768.3.h.g.641.10 | 16 | 12.11 | even | 2 | |||
768.3.h.h.641.7 | 16 | 3.2 | odd | 2 | inner | ||
768.3.h.h.641.8 | 16 | 8.5 | even | 2 | inner | ||
768.3.h.h.641.9 | 16 | 1.1 | even | 1 | trivial | ||
768.3.h.h.641.10 | 16 | 24.5 | odd | 2 | inner |