Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3456,2,Mod(1153,3456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3456.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3456.i (of order \(3\), degree \(2\), 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: | \(27.5962989386\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.1 | ||
Root | \(-0.433633 - 1.67689i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3456.2305 |
Dual form | 3456.2.i.k.1153.1 |
$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(2431\) | \(2945\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22043 | + | 3.84590i | −0.993006 | + | 1.71994i | −0.394260 | + | 0.918999i | \(0.628999\pi\) |
−0.598746 | + | 0.800939i | \(0.704334\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.45488 | − | 2.51992i | −0.549892 | − | 0.952441i | −0.998281 | − | 0.0586028i | \(-0.981335\pi\) |
0.448389 | − | 0.893838i | \(-0.351998\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.08263 | + | 1.87517i | 0.326425 | + | 0.565385i | 0.981800 | − | 0.189919i | \(-0.0608225\pi\) |
−0.655374 | + | 0.755304i | \(0.727489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.96377 | − | 3.40135i | 0.544652 | − | 0.943366i | −0.453976 | − | 0.891014i | \(-0.649995\pi\) |
0.998629 | − | 0.0523518i | \(-0.0166717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.79720 | −0.435885 | −0.217943 | − | 0.975962i | \(-0.569935\pi\) | ||||
−0.217943 | + | 0.975962i | \(0.569935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.76882 | 0.405795 | 0.202898 | − | 0.979200i | \(-0.434964\pi\) | ||||
0.202898 | + | 0.979200i | \(0.434964\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.44197 | + | 5.96166i | −0.717700 | + | 1.24309i | 0.244209 | + | 0.969723i | \(0.421472\pi\) |
−0.961909 | + | 0.273370i | \(0.911862\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.36062 | − | 12.7490i | −1.47212 | − | 2.54979i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.87353 | − | 4.97710i | −0.533601 | − | 0.924224i | −0.999230 | − | 0.0392435i | \(-0.987505\pi\) |
0.465629 | − | 0.884980i | \(-0.345828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.27671 | + | 5.67542i | −0.588514 | + | 1.01934i | 0.405913 | + | 0.913912i | \(0.366953\pi\) |
−0.994427 | + | 0.105425i | \(0.966380\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.9218 | 2.18419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51332 | 0.413187 | 0.206593 | − | 0.978427i | \(-0.433762\pi\) | ||||
0.206593 | + | 0.978427i | \(0.433762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.68420 | − | 6.38122i | 0.575376 | − | 0.996580i | −0.420625 | − | 0.907235i | \(-0.638189\pi\) |
0.996001 | − | 0.0893453i | \(-0.0284775\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53640 | + | 4.39317i | 0.386797 | + | 0.669953i | 0.992017 | − | 0.126106i | \(-0.0402479\pi\) |
−0.605219 | + | 0.796059i | \(0.706915\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.98598 | − | 8.63597i | −0.727280 | − | 1.25969i | −0.958029 | − | 0.286673i | \(-0.907451\pi\) |
0.230748 | − | 0.973013i | \(-0.425883\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.733339 | + | 1.27018i | −0.104763 | + | 0.181454i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.30620 | −0.454141 | −0.227070 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227070 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.61562 | −1.29657 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.30090 | − | 3.98528i | 0.299552 | − | 0.518839i | −0.676482 | − | 0.736459i | \(-0.736496\pi\) |
0.976033 | + | 0.217621i | \(0.0698296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.87353 | − | 3.24505i | −0.239881 | − | 0.415485i | 0.720799 | − | 0.693144i | \(-0.243775\pi\) |
−0.960680 | + | 0.277658i | \(0.910442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.72084 | + | 15.1049i | 1.08169 | + | 1.87354i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.36045 | − | 4.08841i | 0.288374 | − | 0.499479i | −0.685047 | − | 0.728498i | \(-0.740219\pi\) |
0.973422 | + | 0.229019i | \(0.0735519\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.907539 | 0.107705 | 0.0538525 | − | 0.998549i | \(-0.482850\pi\) | ||||
0.0538525 | + | 0.998549i | \(0.482850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.87740 | −0.219733 | −0.109866 | − | 0.993946i | \(-0.535042\pi\) | ||||
−0.109866 | + | 0.993946i | \(0.535042\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.15019 | − | 5.45629i | 0.358998 | − | 0.621802i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.23661 | − | 2.14187i | −0.139129 | − | 0.240979i | 0.788038 | − | 0.615627i | \(-0.211097\pi\) |
−0.927167 | + | 0.374648i | \(0.877764\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.09251 | + | 1.89227i | 0.119918 | + | 0.207704i | 0.919735 | − | 0.392540i | \(-0.128403\pi\) |
−0.799817 | + | 0.600244i | \(0.795070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.99056 | − | 6.91185i | 0.432837 | − | 0.749696i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.30620 | 0.562456 | 0.281228 | − | 0.959641i | \(-0.409258\pi\) | ||||
0.281228 | + | 0.959641i | \(0.409258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.4282 | −1.19800 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.92754 | + | 6.80271i | −0.402958 | + | 0.697943i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.45302 | + | 7.71286i | 0.452136 | + | 0.783123i | 0.998519 | − | 0.0544132i | \(-0.0173288\pi\) |
−0.546382 | + | 0.837536i | \(0.683995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.689326 | + | 1.19395i | 0.0685905 | + | 0.118802i | 0.898281 | − | 0.439421i | \(-0.144816\pi\) |
−0.829691 | + | 0.558224i | \(0.811483\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.54512 | + | 4.40828i | −0.250778 | + | 0.434361i | −0.963740 | − | 0.266842i | \(-0.914020\pi\) |
0.712962 | + | 0.701203i | \(0.247353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.2062 | 1.66338 | 0.831692 | − | 0.555238i | \(-0.187373\pi\) | ||||
0.831692 | + | 0.555238i | \(0.187373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.59351 | 0.631544 | 0.315772 | − | 0.948835i | \(-0.397737\pi\) | ||||
0.315772 | + | 0.948835i | \(0.397737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.90072 | − | 15.4165i | 0.837309 | − | 1.45026i | −0.0548276 | − | 0.998496i | \(-0.517461\pi\) |
0.892137 | − | 0.451766i | \(-0.149206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.2853 | − | 26.4749i | −1.42536 | − | 2.46880i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.61471 | + | 4.52881i | 0.239690 | + | 0.415155i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.15582 | − | 5.46604i | 0.286893 | − | 0.496913i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 43.1706 | 3.86130 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2258 | 1.61728 | 0.808639 | − | 0.588305i | \(-0.200205\pi\) | ||||
0.808639 | + | 0.588305i | \(0.200205\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.33057 | + | 7.50076i | −0.378363 | + | 0.655345i | −0.990824 | − | 0.135156i | \(-0.956846\pi\) |
0.612461 | + | 0.790501i | \(0.290180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.57342 | − | 4.45729i | −0.223144 | − | 0.386496i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.774446 | + | 1.34138i | 0.0661654 | + | 0.114602i | 0.897210 | − | 0.441603i | \(-0.145590\pi\) |
−0.831045 | + | 0.556205i | \(0.812257\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.78618 | − | 16.9502i | 0.830053 | − | 1.43769i | −0.0679426 | − | 0.997689i | \(-0.521643\pi\) |
0.897996 | − | 0.440005i | \(-0.145023\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.50416 | 0.711154 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.5219 | 2.11948 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.945984 | − | 1.63849i | 0.0774980 | − | 0.134230i | −0.824672 | − | 0.565612i | \(-0.808640\pi\) |
0.902170 | + | 0.431381i | \(0.141974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.27927 | + | 7.41191i | 0.348242 | + | 0.603173i | 0.985937 | − | 0.167116i | \(-0.0534454\pi\) |
−0.637695 | + | 0.770289i | \(0.720112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.5514 | − | 25.2038i | −1.16880 | − | 2.02441i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.22265 | − | 3.84974i | 0.177387 | − | 0.307242i | −0.763598 | − | 0.645692i | \(-0.776569\pi\) |
0.940985 | + | 0.338449i | \(0.109902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.0306 | 1.57863 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.8817 | 1.47893 | 0.739465 | − | 0.673195i | \(-0.235078\pi\) | ||||
0.739465 | + | 0.673195i | \(0.235078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.31394 | − | 7.47197i | 0.333823 | − | 0.578198i | −0.649435 | − | 0.760417i | \(-0.724995\pi\) |
0.983258 | + | 0.182219i | \(0.0583279\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.21280 | − | 2.10063i | −0.0932924 | − | 0.161587i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.91423 | + | 6.77965i | 0.297594 | + | 0.515447i | 0.975585 | − | 0.219623i | \(-0.0704826\pi\) |
−0.677991 | + | 0.735070i | \(0.737149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.4176 | + | 37.0964i | −1.61902 | + | 2.80422i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.6390 | −1.01943 | −0.509714 | − | 0.860344i | \(-0.670249\pi\) | ||||
−0.509714 | + | 0.860344i | \(0.670249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.504672 | −0.0375120 | −0.0187560 | − | 0.999824i | \(-0.505971\pi\) | ||||
−0.0187560 | + | 0.999824i | \(0.505971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.58064 | + | 9.66596i | −0.410297 | + | 0.710655i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.94571 | − | 3.37006i | −0.142284 | − | 0.246443i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0083 | − | 17.3349i | −0.724175 | − | 1.25431i | −0.959313 | − | 0.282345i | \(-0.908888\pi\) |
0.235138 | − | 0.971962i | \(-0.424446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.08462 | + | 1.87862i | −0.0780726 | + | 0.135226i | −0.902418 | − | 0.430861i | \(-0.858210\pi\) |
0.824346 | + | 0.566087i | \(0.191543\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.67460 | 0.404298 | 0.202149 | − | 0.979355i | \(-0.435207\pi\) | ||||
0.202149 | + | 0.979355i | \(0.435207\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5032 | 0.815439 | 0.407719 | − | 0.913107i | \(-0.366324\pi\) | ||||
0.407719 | + | 0.913107i | \(0.366324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.36126 | + | 14.4821i | −0.586846 | + | 1.01645i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.3610 | + | 28.3381i | 1.14270 | + | 1.97922i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.91498 | + | 3.31684i | 0.132462 | + | 0.229431i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3177 | + | 17.8707i | −0.710297 | + | 1.23027i | 0.254449 | + | 0.967086i | \(0.418106\pi\) |
−0.964746 | + | 0.263184i | \(0.915227\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.5276 | −1.53637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.0688 | 1.29448 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.52929 | + | 6.11292i | −0.237406 | + | 0.411199i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.54291 | − | 4.40444i | −0.170286 | − | 0.294943i | 0.768234 | − | 0.640169i | \(-0.221136\pi\) |
−0.938520 | + | 0.345226i | \(0.887802\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.14484 | + | 15.8393i | 0.606964 | + | 1.05129i | 0.991738 | + | 0.128282i | \(0.0409462\pi\) |
−0.384773 | + | 0.923011i | \(0.625720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.62341 | − | 16.6682i | 0.635933 | − | 1.10147i | −0.350384 | − | 0.936606i | \(-0.613949\pi\) |
0.986317 | − | 0.164862i | \(-0.0527178\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.4263 | −1.07612 | −0.538061 | − | 0.842906i | \(-0.680843\pi\) | ||||
−0.538061 | + | 0.842906i | \(0.680843\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 44.2841 | 2.88878 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.08563 | + | 15.7368i | −0.587700 | + | 1.01793i | 0.406833 | + | 0.913503i | \(0.366633\pi\) |
−0.994533 | + | 0.104424i | \(0.966700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4344 | − | 19.8050i | −0.736556 | − | 1.27575i | −0.954037 | − | 0.299688i | \(-0.903117\pi\) |
0.217481 | − | 0.976065i | \(-0.430216\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.25666 | − | 5.64070i | −0.208060 | − | 0.360371i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.47356 | − | 6.01639i | 0.221017 | − | 0.382813i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.139530 | −0.00880707 | −0.00440353 | − | 0.999990i | \(-0.501402\pi\) | ||||
−0.00440353 | + | 0.999990i | \(0.501402\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.9055 | −0.937102 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.17682 | − | 12.4306i | 0.447678 | − | 0.775400i | −0.550557 | − | 0.834798i | \(-0.685585\pi\) |
0.998234 | + | 0.0593974i | \(0.0189179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.65657 | − | 6.33336i | −0.227208 | − | 0.393536i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.968751 | − | 1.67793i | −0.0597357 | − | 0.103465i | 0.834611 | − | 0.550840i | \(-0.185692\pi\) |
−0.894347 | + | 0.447374i | \(0.852359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.34118 | − | 12.7153i | 0.450965 | − | 0.781094i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.91415 | −0.604477 | −0.302238 | − | 0.953232i | \(-0.597734\pi\) | ||||
−0.302238 | + | 0.953232i | \(0.597734\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.56777 | 0.277472 | 0.138736 | − | 0.990329i | \(-0.455696\pi\) | ||||
0.138736 | + | 0.990329i | \(0.455696\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.9377 | − | 27.6048i | 0.961077 | − | 1.66463i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.4728 | − | 25.0676i | −0.869585 | − | 1.50616i | −0.862422 | − | 0.506190i | \(-0.831053\pi\) |
−0.00716263 | − | 0.999974i | \(-0.502280\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1351 | − | 19.2865i | −0.664262 | − | 1.15054i | −0.979485 | − | 0.201518i | \(-0.935412\pi\) |
0.315223 | − | 0.949018i | \(-0.397921\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.79946 | + | 11.7770i | −0.404186 | + | 0.700071i | −0.994226 | − | 0.107303i | \(-0.965779\pi\) |
0.590040 | + | 0.807374i | \(0.299112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.4403 | −1.26558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7701 | −0.810004 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.21821 | − | 12.5023i | 0.421693 | − | 0.730393i | −0.574413 | − | 0.818566i | \(-0.694770\pi\) |
0.996105 | + | 0.0881730i | \(0.0281028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2180 | + | 17.6980i | 0.594913 | + | 1.03042i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.5185 | + | 23.4147i | 0.781794 | + | 1.35411i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.38030 | − | 12.7831i | 0.425394 | − | 0.736804i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.6401 | 0.952812 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5451 | 0.944280 | 0.472140 | − | 0.881524i | \(-0.343482\pi\) | ||||
0.472140 | + | 0.881524i | \(0.343482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.19366 | + | 8.99568i | −0.294505 | + | 0.510098i | −0.974870 | − | 0.222776i | \(-0.928488\pi\) |
0.680364 | + | 0.732874i | \(0.261822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.76501 | − | 11.7173i | −0.382381 | − | 0.662303i | 0.609021 | − | 0.793154i | \(-0.291562\pi\) |
−0.991402 | + | 0.130851i | \(0.958229\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9869 | + | 20.7619i | 0.673251 | + | 1.16611i | 0.976977 | + | 0.213346i | \(0.0684360\pi\) |
−0.303726 | + | 0.952760i | \(0.598231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.22194 | − | 10.7767i | 0.348362 | − | 0.603380i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.17893 | −0.176880 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −57.8183 | −3.20718 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.5080 | + | 25.1286i | −0.799851 | + | 1.38538i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.29103 | + | 2.23612i | 0.0709612 | + | 0.122908i | 0.899323 | − | 0.437285i | \(-0.144060\pi\) |
−0.828362 | + | 0.560194i | \(0.810727\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.4824 | + | 18.1561i | 0.572715 | + | 0.991972i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.79736 | + | 3.11313i | −0.0979087 | + | 0.169583i | −0.910819 | − | 0.412806i | \(-0.864549\pi\) |
0.812910 | + | 0.582389i | \(0.197882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.1899 | −0.768424 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1006 | −0.869351 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.85180 | − | 10.1356i | 0.314141 | − | 0.544108i | −0.665114 | − | 0.746742i | \(-0.731617\pi\) |
0.979255 | + | 0.202634i | \(0.0649502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.34856 | + | 16.1922i | 0.500417 | + | 0.866747i | 1.00000 | 0.000481224i | \(0.000153178\pi\) | |
−0.499583 | + | 0.866266i | \(0.666513\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.3410 | − | 24.8394i | −0.763295 | − | 1.32207i | −0.941143 | − | 0.338008i | \(-0.890247\pi\) |
0.177848 | − | 0.984058i | \(-0.443086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.01513 | + | 3.49030i | −0.106952 | + | 0.185246i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.8202 | −0.834958 | −0.417479 | − | 0.908687i | \(-0.637086\pi\) | ||||
−0.417479 | + | 0.908687i | \(0.637086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8713 | −0.835330 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.16863 | − | 7.22028i | 0.218196 | − | 0.377927i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1383 | − | 22.7563i | −0.685815 | − | 1.18787i | −0.973180 | − | 0.230046i | \(-0.926112\pi\) |
0.287364 | − | 0.957821i | \(-0.407221\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.81011 | + | 8.33136i | 0.249729 | + | 0.432543i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.8735 | − | 18.8335i | 0.563010 | − | 0.975162i | −0.434222 | − | 0.900806i | \(-0.642977\pi\) |
0.997232 | − | 0.0743558i | \(-0.0236901\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.5718 | −1.16251 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.8861 | −1.68925 | −0.844623 | − | 0.535362i | \(-0.820175\pi\) | ||||
−0.844623 | + | 0.535362i | \(0.820175\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.81269 | − | 10.0679i | 0.297015 | − | 0.514444i | −0.678437 | − | 0.734659i | \(-0.737342\pi\) |
0.975452 | + | 0.220214i | \(0.0706757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.9896 | + | 24.2306i | 0.712974 | + | 1.23491i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.61687 | + | 6.26460i | 0.183383 | + | 0.317628i | 0.943030 | − | 0.332707i | \(-0.107962\pi\) |
−0.759648 | + | 0.650335i | \(0.774629\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.18591 | − | 10.7143i | 0.312835 | − | 0.541846i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9832 | 0.552625 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.8911 | 1.50019 | 0.750095 | − | 0.661330i | \(-0.230008\pi\) | ||||
0.750095 | + | 0.661330i | \(0.230008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.03226 | + | 5.25202i | −0.151424 | + | 0.262273i | −0.931751 | − | 0.363098i | \(-0.881719\pi\) |
0.780327 | + | 0.625371i | \(0.215052\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.8694 | + | 22.2905i | 0.641071 | + | 1.11037i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.72099 | + | 4.71290i | 0.134875 | + | 0.233610i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4396 | + | 25.0101i | −0.713993 | + | 1.23667i | 0.249354 | + | 0.968412i | \(0.419782\pi\) |
−0.963347 | + | 0.268259i | \(0.913552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.3901 | −0.658884 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.70332 | −0.476317 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.63281 | − | 9.75631i | 0.275181 | − | 0.476627i | −0.695000 | − | 0.719010i | \(-0.744596\pi\) |
0.970181 | + | 0.242383i | \(0.0779290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.03050 | − | 10.4451i | −0.293909 | − | 0.509065i | 0.680822 | − | 0.732449i | \(-0.261623\pi\) |
−0.974730 | + | 0.223384i | \(0.928289\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.2285 | + | 22.9125i | 0.641677 | + | 1.11142i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.45151 | + | 9.44229i | −0.263817 | + | 0.456944i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.5079 | −1.22867 | −0.614336 | − | 0.789045i | \(-0.710576\pi\) | ||||
−0.614336 | + | 0.789045i | \(0.710576\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.4513 | 1.41534 | 0.707670 | − | 0.706543i | \(-0.249746\pi\) | ||||
0.707670 | + | 0.706543i | \(0.249746\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.08823 | + | 10.5451i | −0.291239 | + | 0.504441i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.8086 | − | 30.8454i | −0.849959 | − | 1.47217i | −0.881244 | − | 0.472662i | \(-0.843293\pi\) |
0.0312845 | − | 0.999511i | \(-0.490040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.60886 | − | 11.4469i | −0.313996 | − | 0.543857i | 0.665227 | − | 0.746641i | \(-0.268335\pi\) |
−0.979224 | + | 0.202783i | \(0.935001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7820 | + | 20.4071i | −0.558522 | + | 0.967389i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.83739 | 0.275483 | 0.137742 | − | 0.990468i | \(-0.456016\pi\) | ||||
0.137742 | + | 0.990468i | \(0.456016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.9545 | 0.751269 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.3755 | − | 43.9517i | 1.18962 | − | 2.06049i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5037 | − | 23.3891i | −0.631677 | − | 1.09410i | −0.987209 | − | 0.159433i | \(-0.949034\pi\) |
0.355532 | − | 0.934664i | \(-0.384300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.78550 | − | 3.09258i | −0.0831591 | − | 0.144036i | 0.821446 | − | 0.570286i | \(-0.193168\pi\) |
−0.904605 | + | 0.426250i | \(0.859834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8396 | − | 34.3631i | 0.922023 | − | 1.59699i | 0.125742 | − | 0.992063i | \(-0.459869\pi\) |
0.796281 | − | 0.604927i | \(-0.206798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.8522 | −0.872376 | −0.436188 | − | 0.899855i | \(-0.643672\pi\) | ||||
−0.436188 | + | 0.899855i | \(0.643672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.7366 | −0.634299 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.49197 | + | 9.51237i | −0.252521 | + | 0.437379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.0196 | − | 22.5506i | −0.597381 | − | 1.03469i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0879 | + | 19.2049i | 0.506621 | + | 0.877492i | 0.999971 | + | 0.00766167i | \(0.00243881\pi\) |
−0.493350 | + | 0.869831i | \(0.664228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.93558 | − | 8.54867i | 0.225043 | − | 0.389786i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −39.5505 | −1.79590 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.9432 | 0.813086 | 0.406543 | − | 0.913632i | \(-0.366734\pi\) | ||||
0.406543 | + | 0.913632i | \(0.366734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.71919 | − | 2.97773i | 0.0775861 | − | 0.134383i | −0.824622 | − | 0.565684i | \(-0.808612\pi\) |
0.902208 | + | 0.431301i | \(0.141945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.16431 | + | 8.94485i | 0.232589 | + | 0.402856i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.32036 | − | 2.28693i | −0.0592262 | − | 0.102583i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.41124 | + | 9.37254i | −0.242240 | + | 0.419572i | −0.961352 | − | 0.275322i | \(-0.911216\pi\) |
0.719112 | + | 0.694894i | \(0.244549\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.71510 | 0.433175 | 0.216587 | − | 0.976263i | \(-0.430507\pi\) | ||||
0.216587 | + | 0.976263i | \(0.430507\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.12240 | −0.272443 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.5991 | − | 30.4825i | 0.780066 | − | 1.35111i | −0.151837 | − | 0.988406i | \(-0.548519\pi\) |
0.931903 | − | 0.362708i | \(-0.118148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.73138 | + | 4.73090i | 0.120829 | + | 0.209283i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3025 | − | 19.5766i | −0.498049 | − | 0.862646i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7960 | − | 18.6991i | 0.474806 | − | 0.822387i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.57440 | 0.331840 | 0.165920 | − | 0.986139i | \(-0.446941\pi\) | ||||
0.165920 | + | 0.986139i | \(0.446941\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0630 | −0.440025 | −0.220013 | − | 0.975497i | \(-0.570610\pi\) | ||||
−0.220013 | + | 0.975497i | \(0.570610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.88890 | − | 10.1999i | 0.256525 | − | 0.444314i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.1943 | − | 21.1211i | −0.530187 | − | 0.918310i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.4699 | − | 25.0625i | −0.626759 | − | 1.08558i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.2051 | + | 66.1732i | −1.65175 | + | 2.86092i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.17574 | −0.136789 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.2133 | −1.12700 | −0.563498 | − | 0.826117i | \(-0.690545\pi\) | ||||
−0.563498 | + | 0.826117i | \(0.690545\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.6404 | + | 25.3580i | −0.627127 | + | 1.08622i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.57620 | − | 16.5865i | −0.409449 | − | 0.709186i | 0.585379 | − | 0.810760i | \(-0.300946\pi\) |
−0.994828 | + | 0.101574i | \(0.967612\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.08276 | − | 8.80359i | −0.216533 | − | 0.375046i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.59823 | + | 6.23232i | −0.153012 | + | 0.265025i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.5019 | −0.953435 | −0.476717 | − | 0.879057i | \(-0.658173\pi\) | ||||
−0.476717 | + | 0.879057i | \(0.658173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.9236 | 0.842680 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.7085 | − | 22.0118i | 0.535599 | − | 0.927685i | −0.463535 | − | 0.886079i | \(-0.653419\pi\) |
0.999134 | − | 0.0416066i | \(-0.0132476\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.5268 | + | 68.4625i | 1.66291 | + | 2.88024i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.14798 | − | 15.8448i | −0.383503 | − | 0.664247i | 0.608057 | − | 0.793893i | \(-0.291949\pi\) |
−0.991560 | + | 0.129646i | \(0.958616\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.27484 | + | 2.20808i | −0.0533503 | + | 0.0924054i | −0.891467 | − | 0.453085i | \(-0.850323\pi\) |
0.838117 | + | 0.545491i | \(0.183657\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 101.340 | 4.22617 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.22842 | 0.0927702 | 0.0463851 | − | 0.998924i | \(-0.485230\pi\) | ||||
0.0463851 | + | 0.998924i | \(0.485230\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.17892 | − | 5.50606i | 0.131884 | − | 0.228430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.57939 | − | 6.19968i | −0.148243 | − | 0.256765i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.2694 | + | 26.4473i | 0.630234 | + | 1.09160i | 0.987504 | + | 0.157596i | \(0.0503743\pi\) |
−0.357270 | + | 0.934001i | \(0.616292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.79591 | + | 10.0388i | −0.238816 | + | 0.413642i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.96281 | 0.244863 | 0.122432 | − | 0.992477i | \(-0.460931\pi\) | ||||
0.122432 | + | 0.992477i | \(0.460931\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.2231 | −0.952055 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.29265 | + | 7.43508i | −0.175393 | + | 0.303789i | −0.940297 | − | 0.340355i | \(-0.889453\pi\) |
0.764904 | + | 0.644144i | \(0.222786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.44648 | + | 2.50538i | 0.0590033 | + | 0.102197i | 0.894018 | − | 0.448031i | \(-0.147874\pi\) |
−0.835015 | + | 0.550227i | \(0.814541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.0146 | + | 24.2739i | 0.569773 | + | 0.986876i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.96773 | + | 17.2646i | −0.404577 | + | 0.700749i | −0.994272 | − | 0.106877i | \(-0.965915\pi\) |
0.589695 | + | 0.807626i | \(0.299248\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.1653 | −1.58446 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.4941 | 1.43359 | 0.716797 | − | 0.697282i | \(-0.245607\pi\) | ||||
0.716797 | + | 0.697282i | \(0.245607\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.6891 | − | 27.1743i | 0.631618 | − | 1.09399i | −0.355603 | − | 0.934637i | \(-0.615724\pi\) |
0.987221 | − | 0.159357i | \(-0.0509422\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.7289 | − | 28.9752i | −0.672389 | − | 1.16461i | −0.977225 | − | 0.212207i | \(-0.931935\pi\) |
0.304835 | − | 0.952405i | \(-0.401399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.71987 | − | 13.3712i | −0.309290 | − | 0.535706i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −59.0543 | + | 102.285i | −2.36217 | + | 4.09140i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.51694 | −0.180102 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.12216 | 0.323338 | 0.161669 | − | 0.986845i | \(-0.448312\pi\) | ||||
0.161669 | + | 0.986845i | \(0.448312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.4691 | + | 70.0945i | −1.60597 | + | 2.78162i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.88022 | + | 4.98869i | 0.114119 | + | 0.197659i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.4782 | + | 18.1488i | 0.413865 | + | 0.716836i | 0.995309 | − | 0.0967511i | \(-0.0308451\pi\) |
−0.581443 | + | 0.813587i | \(0.697512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.3547 | + | 28.3272i | −0.644967 | + | 1.11712i | 0.339342 | + | 0.940663i | \(0.389796\pi\) |
−0.984309 | + | 0.176453i | \(0.943538\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.7820 | 0.738395 | 0.369198 | − | 0.929351i | \(-0.379633\pi\) | ||||
0.369198 | + | 0.929351i | \(0.379633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.96410 | 0.391125 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.85977 | + | 8.41736i | −0.190177 | + | 0.329397i | −0.945309 | − | 0.326176i | \(-0.894240\pi\) |
0.755132 | + | 0.655573i | \(0.227573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.2314 | − | 33.3098i | −0.751435 | − | 1.30152i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.1773 | + | 28.0198i | 0.630177 | + | 1.09150i | 0.987515 | + | 0.157523i | \(0.0503510\pi\) |
−0.357338 | + | 0.933975i | \(0.616316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0319 | + | 22.5719i | −0.506883 | + | 0.877946i | 0.493086 | + | 0.869981i | \(0.335869\pi\) |
−0.999968 | + | 0.00796563i | \(0.997464\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.8564 | 0.886333 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.5624 | 1.53186 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.05668 | − | 7.02637i | 0.156606 | − | 0.271250i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.6951 | + | 28.9167i | 0.643549 | + | 1.11466i | 0.984635 | + | 0.174627i | \(0.0558719\pi\) |
−0.341086 | + | 0.940032i | \(0.610795\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.6991 | + | 21.9955i | 0.488065 | + | 0.845354i | 0.999906 | − | 0.0137265i | \(-0.00436941\pi\) |
−0.511840 | + | 0.859081i | \(0.671036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.9572 | − | 22.4425i | 0.497252 | − | 0.861266i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.2800 | −1.42648 | −0.713241 | − | 0.700919i | \(-0.752773\pi\) | ||||
−0.713241 | + | 0.700919i | \(0.752773\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.87841 | −0.262811 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.49261 | + | 11.2455i | −0.247349 | + | 0.428421i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.41730 | + | 11.1151i | 0.244126 | + | 0.422838i | 0.961885 | − | 0.273453i | \(-0.0881657\pi\) |
−0.717760 | + | 0.696291i | \(0.754832\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.4591 | + | 75.2733i | 1.64850 | + | 2.85528i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.62125 | + | 11.4683i | −0.250798 | + | 0.434395i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.89156 | 0.260290 | 0.130145 | − | 0.991495i | \(-0.458456\pi\) | ||||
0.130145 | + | 0.991495i | \(0.458456\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.44561 | 0.167669 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.00577 | − | 3.47410i | 0.0754347 | − | 0.130657i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1178 | + | 17.5246i | 0.379983 | + | 0.658150i | 0.991059 | − | 0.133422i | \(-0.0425964\pi\) |
−0.611076 | + | 0.791572i | \(0.709263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.5566 | − | 39.0693i | −0.844753 | − | 1.46316i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.8829 | + | 32.7061i | −0.706180 | + | 1.22314i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.1706 | 1.64729 | 0.823643 | − | 0.567108i | \(-0.191938\pi\) | ||||
0.823643 | + | 0.567108i | \(0.191938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.8114 | 0.551604 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −42.3019 | + | 73.2690i | −1.57105 | + | 2.72114i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.29193 | − | 12.6300i | −0.270443 | − | 0.468421i | 0.698532 | − | 0.715578i | \(-0.253837\pi\) |
−0.968975 | + | 0.247158i | \(0.920503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.55842 | − | 7.89542i | −0.168599 | − | 0.292023i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4444 | − | 28.4826i | 0.607388 | − | 1.05203i | −0.384281 | − | 0.923216i | \(-0.625551\pi\) |
0.991669 | − | 0.128811i | \(-0.0411161\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.2220 | 0.376531 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.3966 | −1.30208 | −0.651042 | − | 0.759041i | \(-0.725668\pi\) | ||||
−0.651042 | + | 0.759041i | \(0.725668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.8177 | − | 32.5932i | 0.690353 | − | 1.19573i | −0.281369 | − | 0.959600i | \(-0.590788\pi\) |
0.971722 | − | 0.236127i | \(-0.0758782\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.20098 | + | 7.27631i | 0.153912 | + | 0.266584i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.0329 | − | 43.3582i | −0.914682 | − | 1.58427i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.38950 | + | 14.5310i | −0.306137 | + | 0.530245i | −0.977514 | − | 0.210871i | \(-0.932370\pi\) |
0.671377 | + | 0.741116i | \(0.265703\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.0073 | −1.38323 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4825 | 0.708103 | 0.354051 | − | 0.935226i | \(-0.384804\pi\) | ||||
0.354051 | + | 0.935226i | \(0.384804\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.49573 | − | 16.4471i | 0.344220 | − | 0.596206i | −0.640992 | − | 0.767548i | \(-0.721477\pi\) |
0.985212 | + | 0.171341i | \(0.0548101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.59276 | − | 16.6151i | −0.347281 | − | 0.601508i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.03688 | − | 15.6523i | −0.326303 | − | 0.565173i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.2098 | − | 36.7365i | 0.764846 | − | 1.32475i | −0.175482 | − | 0.984483i | \(-0.556148\pi\) |
0.940328 | − | 0.340270i | \(-0.110518\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.55333 | −0.0918368 | −0.0459184 | − | 0.998945i | \(-0.514621\pi\) | ||||
−0.0459184 | + | 0.998945i | \(0.514621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 96.4744 | 3.46546 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.51670 | − | 11.2872i | 0.233485 | − | 0.404408i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.982529 | + | 1.70179i | 0.0351577 | + | 0.0608949i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.87046 | + | 17.0961i | 0.352292 | + | 0.610188i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.70128 | − | 11.6069i | 0.238875 | − | 0.413743i | −0.721517 | − | 0.692397i | \(-0.756555\pi\) |
0.960392 | + | 0.278654i | \(0.0898882\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51.7978 | −1.84172 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7167 | −0.522606 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0873 | − | 27.8640i | 0.569840 | − | 0.986992i | −0.426741 | − | 0.904374i | \(-0.640338\pi\) |
0.996581 | − | 0.0826182i | \(-0.0263282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.96082 | + | 15.5206i | 0.317011 | + | 0.549079i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.03253 | − | 3.52044i | −0.0717264 | − | 0.124234i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −44.4765 | + | 77.0355i | −1.56759 | + | 2.71515i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.7417 | −1.22145 | −0.610727 | − | 0.791841i | \(-0.709123\pi\) | ||||
−0.610727 | + | 0.791841i | \(0.709123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.7570 | −1.43117 | −0.715587 | − | 0.698524i | \(-0.753841\pi\) | ||||
−0.715587 | + | 0.698524i | \(0.753841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.9255 | + | 72.6172i | −1.46859 | + | 2.54367i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.48644 | + | 7.77074i | 0.156961 | + | 0.271864i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.25420 | − | 14.2967i | −0.288073 | − | 0.498958i | 0.685276 | − | 0.728283i | \(-0.259681\pi\) |
−0.973350 | + | 0.229325i | \(0.926348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.28675 | − | 3.96078i | 0.0797113 | − | 0.138064i | −0.823414 | − | 0.567441i | \(-0.807934\pi\) |
0.903125 | + | 0.429377i | \(0.141267\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.2992 | 1.64475 | 0.822377 | − | 0.568943i | \(-0.192648\pi\) | ||||
0.822377 | + | 0.568943i | \(0.192648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.10329 | 0.0730501 | 0.0365251 | − | 0.999333i | \(-0.488371\pi\) | ||||
0.0365251 | + | 0.999333i | \(0.488371\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.31796 | − | 2.28277i | 0.0456646 | − | 0.0790934i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.1576 | + | 33.1820i | 0.662977 | + | 1.14831i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.60255 | + | 7.97185i | 0.158898 | + | 0.275219i | 0.934471 | − | 0.356038i | \(-0.115873\pi\) |
−0.775574 | + | 0.631257i | \(0.782539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.01432 | + | 3.48891i | −0.0694595 | + | 0.120307i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.7718 | 0.370560 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3653 | −0.631041 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.65075 | + | 14.9835i | −0.296544 | + | 0.513629i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.43348 | − | 12.8752i | −0.254518 | − | 0.440837i | 0.710247 | − | 0.703953i | \(-0.248583\pi\) |
−0.964764 | + | 0.263115i | \(0.915250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.9611 | + | 39.7698i | 0.784337 | + | 1.35851i | 0.929394 | + | 0.369088i | \(0.120330\pi\) |
−0.145058 | + | 0.989423i | \(0.546337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.6542 | + | 25.3818i | −0.499994 | + | 0.866015i | −1.00000 | 6.84699e-6i | \(-0.999998\pi\) | |
0.500006 | + | 0.866022i | \(0.333331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.5606 | −0.802012 | −0.401006 | − | 0.916075i | \(-0.631339\pi\) | ||||
−0.401006 | + | 0.916075i | \(0.631339\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.7651 | −1.18205 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.67758 | − | 4.63771i | 0.0908307 | − | 0.157323i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.27076 | − | 16.0574i | −0.314128 | − | 0.544085i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −62.8080 | − | 108.787i | −2.12330 | − | 3.67766i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.29438 | + | 16.0983i | −0.313849 | + | 0.543602i | −0.979192 | − | 0.202935i | \(-0.934952\pi\) |
0.665343 | + | 0.746538i | \(0.268285\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.6693 | −0.831129 | −0.415564 | − | 0.909564i | \(-0.636416\pi\) | ||||
−0.415564 | + | 0.909564i | \(0.636416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.42122 | −0.148786 | −0.0743930 | − | 0.997229i | \(-0.523702\pi\) | ||||
−0.0743930 | + | 0.997229i | \(0.523702\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.1558 | − | 38.3750i | 0.743919 | − | 1.28851i | −0.206779 | − | 0.978388i | \(-0.566298\pi\) |
0.950698 | − | 0.310118i | \(-0.100369\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.5163 | − | 45.9276i | −0.889328 | − | 1.54036i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.81931 | − | 15.2755i | −0.295127 | − | 0.511175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.2845 | − | 52.4543i | 1.01230 | − | 1.75335i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.6628 | 1.25613 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.94190 | 0.197953 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.12059 | − | 1.94092i | 0.0372497 | − | 0.0645183i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.2939 | + | 40.3462i | 0.773461 | + | 1.33967i | 0.935656 | + | 0.352914i | \(0.114809\pi\) |
−0.162195 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.29458 | − | 7.43844i | −0.142286 | − | 0.246446i | 0.786071 | − | 0.618136i | \(-0.212112\pi\) |
−0.928357 | + | 0.371690i | \(0.878779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.36556 | + | 4.09727i | −0.0782886 | + | 0.135600i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.2018 | 0.832236 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.7394 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.78220 | − | 3.08686i | 0.0586618 | − | 0.101605i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.4996 | − | 32.0422i | −0.608262 | − | 1.05354i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.5014 | − | 35.5094i | −0.672628 | − | 1.16503i | −0.977156 | − | 0.212523i | \(-0.931832\pi\) |
0.304528 | − | 0.952503i | \(-0.401501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.29715 | + | 2.24672i | −0.0425123 | + | 0.0736334i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.2812 | 0.565156 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.1921 | −0.332962 | −0.166481 | − | 0.986045i | \(-0.553240\pi\) | ||||
−0.166481 | + | 0.986045i | \(0.553240\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7130 | + | 35.8761i | −0.675226 | + | 1.16953i | 0.301177 | + | 0.953568i | \(0.402621\pi\) |
−0.976403 | + | 0.215958i | \(0.930713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3618 | + | 43.9279i | 0.825894 | + | 1.43049i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.04880 | + | 1.81658i | 0.0340815 | + | 0.0590309i | 0.882563 | − | 0.470194i | \(-0.155816\pi\) |
−0.848482 | + | 0.529225i | \(0.822483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.68678 | + | 6.38569i | −0.119678 | + | 0.207288i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.7663 | −1.02901 | −0.514506 | − | 0.857487i | \(-0.672025\pi\) | ||||
−0.514506 | + | 0.857487i | \(0.672025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 88.8908 | 2.87644 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.25345 | − | 3.90309i | 0.0727677 | − | 0.126037i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.97362 | − | 10.3466i | −0.192697 | − | 0.333762i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.81664 | − | 8.34267i | −0.155053 | − | 0.268560i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.76817 | − | 3.06256i | 0.0568605 | − | 0.0984853i | −0.836194 | − | 0.548434i | \(-0.815224\pi\) |
0.893055 | + | 0.449948i | \(0.148558\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.4727 | 0.689093 | 0.344546 | − | 0.938769i | \(-0.388033\pi\) | ||||
0.344546 | + | 0.938769i | \(0.388033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −56.9508 | −1.82576 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.6237 | + | 40.9174i | −0.755788 | + | 1.30906i | 0.189193 | + | 0.981940i | \(0.439413\pi\) |
−0.944982 | + | 0.327124i | \(0.893921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.74465 | + | 9.95003i | 0.183600 | + | 0.318004i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.4576 | − | 37.1656i | −0.684390 | − | 1.18540i | −0.973628 | − | 0.228141i | \(-0.926735\pi\) |
0.289238 | − | 0.957257i | \(-0.406598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.6001 | + | 21.8239i | −0.401471 | + | 0.695368i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.9208 | −1.11042 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.5080 | 0.365563 | 0.182782 | − | 0.983154i | \(-0.441490\pi\) | ||||
0.182782 | + | 0.983154i | \(0.441490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.5420 | + | 44.2401i | −0.809736 | + | 1.40250i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.46934 | − | 14.6693i | −0.268227 | − | 0.464582i | 0.700177 | − | 0.713969i | \(-0.253104\pi\) |
−0.968404 | + | 0.249387i | \(0.919771\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3456.2.i.k.2305.1 | 12 | ||
3.2 | odd | 2 | 1152.2.i.i.769.2 | yes | 12 | ||
4.3 | odd | 2 | 3456.2.i.l.2305.1 | 12 | |||
8.3 | odd | 2 | 3456.2.i.j.2305.6 | 12 | |||
8.5 | even | 2 | 3456.2.i.i.2305.6 | 12 | |||
9.2 | odd | 6 | 1152.2.i.i.385.2 | ✓ | 12 | ||
9.7 | even | 3 | inner | 3456.2.i.k.1153.1 | 12 | ||
12.11 | even | 2 | 1152.2.i.k.769.5 | yes | 12 | ||
24.5 | odd | 2 | 1152.2.i.l.769.5 | yes | 12 | ||
24.11 | even | 2 | 1152.2.i.j.769.2 | yes | 12 | ||
36.7 | odd | 6 | 3456.2.i.l.1153.1 | 12 | |||
36.11 | even | 6 | 1152.2.i.k.385.5 | yes | 12 | ||
72.11 | even | 6 | 1152.2.i.j.385.2 | yes | 12 | ||
72.29 | odd | 6 | 1152.2.i.l.385.5 | yes | 12 | ||
72.43 | odd | 6 | 3456.2.i.j.1153.6 | 12 | |||
72.61 | even | 6 | 3456.2.i.i.1153.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.i.385.2 | ✓ | 12 | 9.2 | odd | 6 | ||
1152.2.i.i.769.2 | yes | 12 | 3.2 | odd | 2 | ||
1152.2.i.j.385.2 | yes | 12 | 72.11 | even | 6 | ||
1152.2.i.j.769.2 | yes | 12 | 24.11 | even | 2 | ||
1152.2.i.k.385.5 | yes | 12 | 36.11 | even | 6 | ||
1152.2.i.k.769.5 | yes | 12 | 12.11 | even | 2 | ||
1152.2.i.l.385.5 | yes | 12 | 72.29 | odd | 6 | ||
1152.2.i.l.769.5 | yes | 12 | 24.5 | odd | 2 | ||
3456.2.i.i.1153.6 | 12 | 72.61 | even | 6 | |||
3456.2.i.i.2305.6 | 12 | 8.5 | even | 2 | |||
3456.2.i.j.1153.6 | 12 | 72.43 | odd | 6 | |||
3456.2.i.j.2305.6 | 12 | 8.3 | odd | 2 | |||
3456.2.i.k.1153.1 | 12 | 9.7 | even | 3 | inner | ||
3456.2.i.k.2305.1 | 12 | 1.1 | even | 1 | trivial | ||
3456.2.i.l.1153.1 | 12 | 36.7 | odd | 6 | |||
3456.2.i.l.2305.1 | 12 | 4.3 | odd | 2 |