Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.a (trivial) |
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: | yes |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7674048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.82356\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.823556 | 0.582342 | 0.291171 | − | 0.956671i | \(-0.405955\pi\) | ||||
0.291171 | + | 0.956671i | \(0.405955\pi\) | |||||||
\(3\) | −0.960649 | −0.554631 | −0.277315 | − | 0.960779i | \(-0.589445\pi\) | ||||
−0.277315 | + | 0.960779i | \(0.589445\pi\) | |||||||
\(4\) | −1.32176 | −0.660878 | ||||||||
\(5\) | 2.98565 | 1.33522 | 0.667611 | − | 0.744510i | \(-0.267317\pi\) | ||||
0.667611 | + | 0.744510i | \(0.267317\pi\) | |||||||
\(6\) | −0.791148 | −0.322985 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.73565 | −0.967199 | ||||||||
\(9\) | −2.07715 | −0.692385 | ||||||||
\(10\) | 2.45885 | 0.777556 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.26974 | 0.366543 | ||||||||
\(13\) | −2.20144 | −0.610571 | −0.305285 | − | 0.952261i | \(-0.598752\pi\) | ||||
−0.305285 | + | 0.952261i | \(0.598752\pi\) | |||||||
\(14\) | −0.823556 | −0.220105 | ||||||||
\(15\) | −2.86816 | −0.740556 | ||||||||
\(16\) | 0.390549 | 0.0976372 | ||||||||
\(17\) | −4.40669 | −1.06878 | −0.534390 | − | 0.845238i | \(-0.679459\pi\) | ||||
−0.534390 | + | 0.845238i | \(0.679459\pi\) | |||||||
\(18\) | −1.71065 | −0.403205 | ||||||||
\(19\) | 1.72563 | 0.395886 | 0.197943 | − | 0.980214i | \(-0.436574\pi\) | ||||
0.197943 | + | 0.980214i | \(0.436574\pi\) | |||||||
\(20\) | −3.94630 | −0.882419 | ||||||||
\(21\) | 0.960649 | 0.209631 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.39774 | −1.75105 | −0.875525 | − | 0.483173i | \(-0.839484\pi\) | ||||
−0.875525 | + | 0.483173i | \(0.839484\pi\) | |||||||
\(24\) | 2.62800 | 0.536438 | ||||||||
\(25\) | 3.91410 | 0.782819 | ||||||||
\(26\) | −1.81301 | −0.355561 | ||||||||
\(27\) | 4.87736 | 0.938649 | ||||||||
\(28\) | 1.32176 | 0.249788 | ||||||||
\(29\) | −3.29295 | −0.611485 | −0.305743 | − | 0.952114i | \(-0.598905\pi\) | ||||
−0.305743 | + | 0.952114i | \(0.598905\pi\) | |||||||
\(30\) | −2.36209 | −0.431257 | ||||||||
\(31\) | 7.47573 | 1.34268 | 0.671341 | − | 0.741149i | \(-0.265719\pi\) | ||||
0.671341 | + | 0.741149i | \(0.265719\pi\) | |||||||
\(32\) | 5.79294 | 1.02406 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.62916 | −0.622396 | ||||||||
\(35\) | −2.98565 | −0.504667 | ||||||||
\(36\) | 2.74549 | 0.457582 | ||||||||
\(37\) | −8.78071 | −1.44354 | −0.721770 | − | 0.692133i | \(-0.756671\pi\) | ||||
−0.721770 | + | 0.692133i | \(0.756671\pi\) | |||||||
\(38\) | 1.42115 | 0.230541 | ||||||||
\(39\) | 2.11481 | 0.338641 | ||||||||
\(40\) | −8.16769 | −1.29143 | ||||||||
\(41\) | −5.39351 | −0.842325 | −0.421163 | − | 0.906985i | \(-0.638378\pi\) | ||||
−0.421163 | + | 0.906985i | \(0.638378\pi\) | |||||||
\(42\) | 0.791148 | 0.122077 | ||||||||
\(43\) | −9.44629 | −1.44055 | −0.720273 | − | 0.693691i | \(-0.755983\pi\) | ||||
−0.720273 | + | 0.693691i | \(0.755983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.20165 | −0.924487 | ||||||||
\(46\) | −6.91601 | −1.01971 | ||||||||
\(47\) | −5.39667 | −0.787185 | −0.393593 | − | 0.919285i | \(-0.628768\pi\) | ||||
−0.393593 | + | 0.919285i | \(0.628768\pi\) | |||||||
\(48\) | −0.375180 | −0.0541526 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.22348 | 0.455869 | ||||||||
\(51\) | 4.23329 | 0.592779 | ||||||||
\(52\) | 2.90977 | 0.403513 | ||||||||
\(53\) | 9.39774 | 1.29088 | 0.645439 | − | 0.763812i | \(-0.276674\pi\) | ||||
0.645439 | + | 0.763812i | \(0.276674\pi\) | |||||||
\(54\) | 4.01678 | 0.546615 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.73565 | 0.365567 | ||||||||
\(57\) | −1.65772 | −0.219571 | ||||||||
\(58\) | −2.71193 | −0.356094 | ||||||||
\(59\) | 3.47462 | 0.452357 | 0.226178 | − | 0.974086i | \(-0.427377\pi\) | ||||
0.226178 | + | 0.974086i | \(0.427377\pi\) | |||||||
\(60\) | 3.79101 | 0.489417 | ||||||||
\(61\) | −12.9942 | −1.66374 | −0.831870 | − | 0.554970i | \(-0.812730\pi\) | ||||
−0.831870 | + | 0.554970i | \(0.812730\pi\) | |||||||
\(62\) | 6.15668 | 0.781900 | ||||||||
\(63\) | 2.07715 | 0.261697 | ||||||||
\(64\) | 3.98971 | 0.498714 | ||||||||
\(65\) | −6.57274 | −0.815248 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.32138 | 0.527940 | 0.263970 | − | 0.964531i | \(-0.414968\pi\) | ||||
0.263970 | + | 0.964531i | \(0.414968\pi\) | |||||||
\(68\) | 5.82457 | 0.706333 | ||||||||
\(69\) | 8.06728 | 0.971186 | ||||||||
\(70\) | −2.45885 | −0.293889 | ||||||||
\(71\) | 4.40046 | 0.522238 | 0.261119 | − | 0.965307i | \(-0.415908\pi\) | ||||
0.261119 | + | 0.965307i | \(0.415908\pi\) | |||||||
\(72\) | 5.68237 | 0.669674 | ||||||||
\(73\) | −14.7509 | −1.72647 | −0.863233 | − | 0.504805i | \(-0.831564\pi\) | ||||
−0.863233 | + | 0.504805i | \(0.831564\pi\) | |||||||
\(74\) | −7.23140 | −0.840634 | ||||||||
\(75\) | −3.76007 | −0.434176 | ||||||||
\(76\) | −2.28086 | −0.261632 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.74167 | 0.197205 | ||||||||
\(79\) | 7.18768 | 0.808677 | 0.404338 | − | 0.914609i | \(-0.367502\pi\) | ||||
0.404338 | + | 0.914609i | \(0.367502\pi\) | |||||||
\(80\) | 1.16604 | 0.130367 | ||||||||
\(81\) | 1.54603 | 0.171781 | ||||||||
\(82\) | −4.44186 | −0.490521 | ||||||||
\(83\) | −7.63445 | −0.837990 | −0.418995 | − | 0.907989i | \(-0.637617\pi\) | ||||
−0.418995 | + | 0.907989i | \(0.637617\pi\) | |||||||
\(84\) | −1.26974 | −0.138540 | ||||||||
\(85\) | −13.1568 | −1.42706 | ||||||||
\(86\) | −7.77955 | −0.838890 | ||||||||
\(87\) | 3.16337 | 0.339149 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8428 | 1.14934 | 0.574668 | − | 0.818386i | \(-0.305131\pi\) | ||||
0.574668 | + | 0.818386i | \(0.305131\pi\) | |||||||
\(90\) | −5.10741 | −0.538368 | ||||||||
\(91\) | 2.20144 | 0.230774 | ||||||||
\(92\) | 11.0998 | 1.15723 | ||||||||
\(93\) | −7.18156 | −0.744693 | ||||||||
\(94\) | −4.44446 | −0.458411 | ||||||||
\(95\) | 5.15211 | 0.528596 | ||||||||
\(96\) | −5.56498 | −0.567974 | ||||||||
\(97\) | 2.85498 | 0.289879 | 0.144940 | − | 0.989440i | \(-0.453701\pi\) | ||||
0.144940 | + | 0.989440i | \(0.453701\pi\) | |||||||
\(98\) | 0.823556 | 0.0831917 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.17348 | −0.517348 | ||||||||
\(101\) | 14.6011 | 1.45287 | 0.726434 | − | 0.687236i | \(-0.241176\pi\) | ||||
0.726434 | + | 0.687236i | \(0.241176\pi\) | |||||||
\(102\) | 3.48635 | 0.345200 | ||||||||
\(103\) | −0.107767 | −0.0106186 | −0.00530932 | − | 0.999986i | \(-0.501690\pi\) | ||||
−0.00530932 | + | 0.999986i | \(0.501690\pi\) | |||||||
\(104\) | 6.02238 | 0.590543 | ||||||||
\(105\) | 2.86816 | 0.279904 | ||||||||
\(106\) | 7.73956 | 0.751733 | ||||||||
\(107\) | 4.64902 | 0.449438 | 0.224719 | − | 0.974424i | \(-0.427854\pi\) | ||||
0.224719 | + | 0.974424i | \(0.427854\pi\) | |||||||
\(108\) | −6.44668 | −0.620332 | ||||||||
\(109\) | −3.23140 | −0.309512 | −0.154756 | − | 0.987953i | \(-0.549459\pi\) | ||||
−0.154756 | + | 0.987953i | \(0.549459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.43518 | 0.800632 | ||||||||
\(112\) | −0.390549 | −0.0369034 | ||||||||
\(113\) | −11.3194 | −1.06484 | −0.532420 | − | 0.846480i | \(-0.678717\pi\) | ||||
−0.532420 | + | 0.846480i | \(0.678717\pi\) | |||||||
\(114\) | −1.36523 | −0.127865 | ||||||||
\(115\) | −25.0727 | −2.33804 | ||||||||
\(116\) | 4.35247 | 0.404117 | ||||||||
\(117\) | 4.57274 | 0.422750 | ||||||||
\(118\) | 2.86154 | 0.263426 | ||||||||
\(119\) | 4.40669 | 0.403961 | ||||||||
\(120\) | 7.84629 | 0.716265 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −10.7015 | −0.968866 | ||||||||
\(123\) | 5.18127 | 0.467180 | ||||||||
\(124\) | −9.88109 | −0.887348 | ||||||||
\(125\) | −3.24213 | −0.289985 | ||||||||
\(126\) | 1.71065 | 0.152397 | ||||||||
\(127\) | 19.9802 | 1.77295 | 0.886476 | − | 0.462774i | \(-0.153146\pi\) | ||||
0.886476 | + | 0.462774i | \(0.153146\pi\) | |||||||
\(128\) | −8.30013 | −0.733635 | ||||||||
\(129\) | 9.07457 | 0.798971 | ||||||||
\(130\) | −5.41302 | −0.474753 | ||||||||
\(131\) | −8.45523 | −0.738737 | −0.369368 | − | 0.929283i | \(-0.620426\pi\) | ||||
−0.369368 | + | 0.929283i | \(0.620426\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.72563 | −0.149631 | ||||||||
\(134\) | 3.55890 | 0.307442 | ||||||||
\(135\) | 14.5621 | 1.25331 | ||||||||
\(136\) | 12.0552 | 1.03372 | ||||||||
\(137\) | 8.35456 | 0.713779 | 0.356889 | − | 0.934147i | \(-0.383837\pi\) | ||||
0.356889 | + | 0.934147i | \(0.383837\pi\) | |||||||
\(138\) | 6.64385 | 0.565562 | ||||||||
\(139\) | 14.7134 | 1.24797 | 0.623986 | − | 0.781436i | \(-0.285512\pi\) | ||||
0.623986 | + | 0.781436i | \(0.285512\pi\) | |||||||
\(140\) | 3.94630 | 0.333523 | ||||||||
\(141\) | 5.18430 | 0.436597 | ||||||||
\(142\) | 3.62402 | 0.304121 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.811230 | −0.0676025 | ||||||||
\(145\) | −9.83159 | −0.816469 | ||||||||
\(146\) | −12.1482 | −1.00539 | ||||||||
\(147\) | −0.960649 | −0.0792330 | ||||||||
\(148\) | 11.6059 | 0.954003 | ||||||||
\(149\) | −8.84271 | −0.724423 | −0.362212 | − | 0.932096i | \(-0.617978\pi\) | ||||
−0.362212 | + | 0.932096i | \(0.617978\pi\) | |||||||
\(150\) | −3.09663 | −0.252839 | ||||||||
\(151\) | 19.9699 | 1.62513 | 0.812563 | − | 0.582873i | \(-0.198071\pi\) | ||||
0.812563 | + | 0.582873i | \(0.198071\pi\) | |||||||
\(152\) | −4.72071 | −0.382900 | ||||||||
\(153\) | 9.15338 | 0.740007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.3199 | 1.79278 | ||||||||
\(156\) | −2.79527 | −0.223801 | ||||||||
\(157\) | 13.0517 | 1.04164 | 0.520818 | − | 0.853668i | \(-0.325627\pi\) | ||||
0.520818 | + | 0.853668i | \(0.325627\pi\) | |||||||
\(158\) | 5.91945 | 0.470926 | ||||||||
\(159\) | −9.02793 | −0.715961 | ||||||||
\(160\) | 17.2957 | 1.36734 | ||||||||
\(161\) | 8.39774 | 0.661834 | ||||||||
\(162\) | 1.27324 | 0.100035 | ||||||||
\(163\) | 5.96447 | 0.467174 | 0.233587 | − | 0.972336i | \(-0.424954\pi\) | ||||
0.233587 | + | 0.972336i | \(0.424954\pi\) | |||||||
\(164\) | 7.12891 | 0.556674 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.28740 | −0.487997 | ||||||||
\(167\) | −13.2472 | −1.02510 | −0.512548 | − | 0.858659i | \(-0.671298\pi\) | ||||
−0.512548 | + | 0.858659i | \(0.671298\pi\) | |||||||
\(168\) | −2.62800 | −0.202755 | ||||||||
\(169\) | −8.15365 | −0.627204 | ||||||||
\(170\) | −10.8354 | −0.831037 | ||||||||
\(171\) | −3.58439 | −0.274105 | ||||||||
\(172\) | 12.4857 | 0.952025 | ||||||||
\(173\) | 0.517716 | 0.0393612 | 0.0196806 | − | 0.999806i | \(-0.493735\pi\) | ||||
0.0196806 | + | 0.999806i | \(0.493735\pi\) | |||||||
\(174\) | 2.60521 | 0.197500 | ||||||||
\(175\) | −3.91410 | −0.295878 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.33789 | −0.250891 | ||||||||
\(178\) | 8.92967 | 0.669307 | ||||||||
\(179\) | 1.69615 | 0.126776 | 0.0633881 | − | 0.997989i | \(-0.479809\pi\) | ||||
0.0633881 | + | 0.997989i | \(0.479809\pi\) | |||||||
\(180\) | 8.19707 | 0.610973 | ||||||||
\(181\) | −9.88599 | −0.734820 | −0.367410 | − | 0.930059i | \(-0.619755\pi\) | ||||
−0.367410 | + | 0.930059i | \(0.619755\pi\) | |||||||
\(182\) | 1.81301 | 0.134389 | ||||||||
\(183\) | 12.4829 | 0.922762 | ||||||||
\(184\) | 22.9733 | 1.69361 | ||||||||
\(185\) | −26.2161 | −1.92745 | ||||||||
\(186\) | −5.91441 | −0.433666 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.13308 | 0.520233 | ||||||||
\(189\) | −4.87736 | −0.354776 | ||||||||
\(190\) | 4.24305 | 0.307823 | ||||||||
\(191\) | 23.1329 | 1.67384 | 0.836918 | − | 0.547328i | \(-0.184355\pi\) | ||||
0.836918 | + | 0.547328i | \(0.184355\pi\) | |||||||
\(192\) | −3.83271 | −0.276602 | ||||||||
\(193\) | 23.0888 | 1.66197 | 0.830983 | − | 0.556297i | \(-0.187778\pi\) | ||||
0.830983 | + | 0.556297i | \(0.187778\pi\) | |||||||
\(194\) | 2.35124 | 0.168809 | ||||||||
\(195\) | 6.31409 | 0.452162 | ||||||||
\(196\) | −1.32176 | −0.0944111 | ||||||||
\(197\) | −6.68989 | −0.476635 | −0.238318 | − | 0.971187i | \(-0.576596\pi\) | ||||
−0.238318 | + | 0.971187i | \(0.576596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.8233 | −1.12169 | −0.560844 | − | 0.827922i | \(-0.689523\pi\) | ||||
−0.560844 | + | 0.827922i | \(0.689523\pi\) | |||||||
\(200\) | −10.7076 | −0.757142 | ||||||||
\(201\) | −4.15133 | −0.292812 | ||||||||
\(202\) | 12.0249 | 0.846066 | ||||||||
\(203\) | 3.29295 | 0.231120 | ||||||||
\(204\) | −5.59537 | −0.391754 | ||||||||
\(205\) | −16.1031 | −1.12469 | ||||||||
\(206\) | −0.0887525 | −0.00618368 | ||||||||
\(207\) | 17.4434 | 1.21240 | ||||||||
\(208\) | −0.859771 | −0.0596144 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.36209 | 0.163000 | ||||||||
\(211\) | −11.3525 | −0.781538 | −0.390769 | − | 0.920489i | \(-0.627791\pi\) | ||||
−0.390769 | + | 0.920489i | \(0.627791\pi\) | |||||||
\(212\) | −12.4215 | −0.853113 | ||||||||
\(213\) | −4.22730 | −0.289649 | ||||||||
\(214\) | 3.82873 | 0.261727 | ||||||||
\(215\) | −28.2033 | −1.92345 | ||||||||
\(216\) | −13.3428 | −0.907860 | ||||||||
\(217\) | −7.47573 | −0.507486 | ||||||||
\(218\) | −2.66124 | −0.180242 | ||||||||
\(219\) | 14.1705 | 0.957552 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.70109 | 0.652566 | ||||||||
\(222\) | 6.94684 | 0.466241 | ||||||||
\(223\) | −10.6899 | −0.715846 | −0.357923 | − | 0.933751i | \(-0.616515\pi\) | ||||
−0.357923 | + | 0.933751i | \(0.616515\pi\) | |||||||
\(224\) | −5.79294 | −0.387057 | ||||||||
\(225\) | −8.13018 | −0.542012 | ||||||||
\(226\) | −9.32217 | −0.620102 | ||||||||
\(227\) | 3.73783 | 0.248089 | 0.124044 | − | 0.992277i | \(-0.460414\pi\) | ||||
0.124044 | + | 0.992277i | \(0.460414\pi\) | |||||||
\(228\) | 2.19110 | 0.145109 | ||||||||
\(229\) | −23.6585 | −1.56340 | −0.781699 | − | 0.623656i | \(-0.785647\pi\) | ||||
−0.781699 | + | 0.623656i | \(0.785647\pi\) | |||||||
\(230\) | −20.6488 | −1.36154 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00836 | 0.591428 | ||||||||
\(233\) | −3.86675 | −0.253319 | −0.126660 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126660 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(234\) | 3.76590 | 0.246185 | ||||||||
\(235\) | −16.1126 | −1.05107 | ||||||||
\(236\) | −4.59259 | −0.298952 | ||||||||
\(237\) | −6.90483 | −0.448517 | ||||||||
\(238\) | 3.62916 | 0.235243 | ||||||||
\(239\) | 10.0717 | 0.651482 | 0.325741 | − | 0.945459i | \(-0.394386\pi\) | ||||
0.325741 | + | 0.945459i | \(0.394386\pi\) | |||||||
\(240\) | −1.12016 | −0.0723058 | ||||||||
\(241\) | −13.4265 | −0.864878 | −0.432439 | − | 0.901663i | \(-0.642347\pi\) | ||||
−0.432439 | + | 0.901663i | \(0.642347\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1173 | −1.03392 | ||||||||
\(244\) | 17.1752 | 1.09953 | ||||||||
\(245\) | 2.98565 | 0.190746 | ||||||||
\(246\) | 4.26707 | 0.272058 | ||||||||
\(247\) | −3.79887 | −0.241716 | ||||||||
\(248\) | −20.4510 | −1.29864 | ||||||||
\(249\) | 7.33403 | 0.464775 | ||||||||
\(250\) | −2.67007 | −0.168870 | ||||||||
\(251\) | 0.0764471 | 0.00482530 | 0.00241265 | − | 0.999997i | \(-0.499232\pi\) | ||||
0.00241265 | + | 0.999997i | \(0.499232\pi\) | |||||||
\(252\) | −2.74549 | −0.172950 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.4548 | 1.03246 | ||||||||
\(255\) | 12.6391 | 0.791491 | ||||||||
\(256\) | −14.8151 | −0.925941 | ||||||||
\(257\) | 9.51194 | 0.593338 | 0.296669 | − | 0.954980i | \(-0.404124\pi\) | ||||
0.296669 | + | 0.954980i | \(0.404124\pi\) | |||||||
\(258\) | 7.47342 | 0.465275 | ||||||||
\(259\) | 8.78071 | 0.545607 | ||||||||
\(260\) | 8.68755 | 0.538779 | ||||||||
\(261\) | 6.83996 | 0.423383 | ||||||||
\(262\) | −6.96335 | −0.430197 | ||||||||
\(263\) | −14.7919 | −0.912107 | −0.456053 | − | 0.889952i | \(-0.650737\pi\) | ||||
−0.456053 | + | 0.889952i | \(0.650737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.0583 | 1.72361 | ||||||||
\(266\) | −1.42115 | −0.0871363 | ||||||||
\(267\) | −10.4161 | −0.637458 | ||||||||
\(268\) | −5.71181 | −0.348904 | ||||||||
\(269\) | −30.0556 | −1.83252 | −0.916262 | − | 0.400580i | \(-0.868809\pi\) | ||||
−0.916262 | + | 0.400580i | \(0.868809\pi\) | |||||||
\(270\) | 11.9927 | 0.729852 | ||||||||
\(271\) | 10.3918 | 0.631260 | 0.315630 | − | 0.948882i | \(-0.397784\pi\) | ||||
0.315630 | + | 0.948882i | \(0.397784\pi\) | |||||||
\(272\) | −1.72103 | −0.104353 | ||||||||
\(273\) | −2.11481 | −0.127994 | ||||||||
\(274\) | 6.88045 | 0.415663 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.6630 | −0.641835 | ||||||||
\(277\) | −28.1138 | −1.68919 | −0.844597 | − | 0.535403i | \(-0.820160\pi\) | ||||
−0.844597 | + | 0.535403i | \(0.820160\pi\) | |||||||
\(278\) | 12.1173 | 0.726747 | ||||||||
\(279\) | −15.5282 | −0.929652 | ||||||||
\(280\) | 8.16769 | 0.488113 | ||||||||
\(281\) | −9.57010 | −0.570904 | −0.285452 | − | 0.958393i | \(-0.592144\pi\) | ||||
−0.285452 | + | 0.958393i | \(0.592144\pi\) | |||||||
\(282\) | 4.26956 | 0.254249 | ||||||||
\(283\) | 1.65526 | 0.0983947 | 0.0491974 | − | 0.998789i | \(-0.484334\pi\) | ||||
0.0491974 | + | 0.998789i | \(0.484334\pi\) | |||||||
\(284\) | −5.81633 | −0.345136 | ||||||||
\(285\) | −4.94937 | −0.293176 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.39351 | 0.318369 | ||||||||
\(288\) | −12.0328 | −0.709041 | ||||||||
\(289\) | 2.41896 | 0.142292 | ||||||||
\(290\) | −8.09686 | −0.475464 | ||||||||
\(291\) | −2.74263 | −0.160776 | ||||||||
\(292\) | 19.4971 | 1.14098 | ||||||||
\(293\) | −4.68188 | −0.273519 | −0.136759 | − | 0.990604i | \(-0.543669\pi\) | ||||
−0.136759 | + | 0.990604i | \(0.543669\pi\) | |||||||
\(294\) | −0.791148 | −0.0461407 | ||||||||
\(295\) | 10.3740 | 0.603997 | ||||||||
\(296\) | 24.0210 | 1.39619 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.28247 | −0.421862 | ||||||||
\(299\) | 18.4871 | 1.06914 | ||||||||
\(300\) | 4.96990 | 0.286937 | ||||||||
\(301\) | 9.44629 | 0.544475 | ||||||||
\(302\) | 16.4463 | 0.946379 | ||||||||
\(303\) | −14.0266 | −0.805806 | ||||||||
\(304\) | 0.673941 | 0.0386532 | ||||||||
\(305\) | −38.7962 | −2.22146 | ||||||||
\(306\) | 7.53832 | 0.430937 | ||||||||
\(307\) | 16.9829 | 0.969266 | 0.484633 | − | 0.874718i | \(-0.338953\pi\) | ||||
0.484633 | + | 0.874718i | \(0.338953\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.103527 | 0.00588942 | ||||||||
\(310\) | 18.3817 | 1.04401 | ||||||||
\(311\) | −21.9257 | −1.24329 | −0.621645 | − | 0.783299i | \(-0.713535\pi\) | ||||
−0.621645 | + | 0.783299i | \(0.713535\pi\) | |||||||
\(312\) | −5.78540 | −0.327534 | ||||||||
\(313\) | 10.0555 | 0.568368 | 0.284184 | − | 0.958770i | \(-0.408277\pi\) | ||||
0.284184 | + | 0.958770i | \(0.408277\pi\) | |||||||
\(314\) | 10.7488 | 0.606589 | ||||||||
\(315\) | 6.20165 | 0.349423 | ||||||||
\(316\) | −9.50035 | −0.534436 | ||||||||
\(317\) | 23.5602 | 1.32327 | 0.661635 | − | 0.749826i | \(-0.269863\pi\) | ||||
0.661635 | + | 0.749826i | \(0.269863\pi\) | |||||||
\(318\) | −7.43500 | −0.416934 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 11.9119 | 0.665895 | ||||||||
\(321\) | −4.46608 | −0.249272 | ||||||||
\(322\) | 6.91601 | 0.385414 | ||||||||
\(323\) | −7.60431 | −0.423115 | ||||||||
\(324\) | −2.04347 | −0.113526 | ||||||||
\(325\) | −8.61666 | −0.477966 | ||||||||
\(326\) | 4.91208 | 0.272055 | ||||||||
\(327\) | 3.10425 | 0.171665 | ||||||||
\(328\) | 14.7548 | 0.814696 | ||||||||
\(329\) | 5.39667 | 0.297528 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8607 | −1.14661 | −0.573304 | − | 0.819343i | \(-0.694339\pi\) | ||||
−0.573304 | + | 0.819343i | \(0.694339\pi\) | |||||||
\(332\) | 10.0909 | 0.553809 | ||||||||
\(333\) | 18.2389 | 0.999484 | ||||||||
\(334\) | −10.9098 | −0.596956 | ||||||||
\(335\) | 12.9021 | 0.704918 | ||||||||
\(336\) | 0.375180 | 0.0204678 | ||||||||
\(337\) | −13.3544 | −0.727458 | −0.363729 | − | 0.931505i | \(-0.618497\pi\) | ||||
−0.363729 | + | 0.931505i | \(0.618497\pi\) | |||||||
\(338\) | −6.71498 | −0.365247 | ||||||||
\(339\) | 10.8740 | 0.590594 | ||||||||
\(340\) | 17.3901 | 0.943112 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.95195 | −0.159623 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 25.8418 | 1.39329 | ||||||||
\(345\) | 24.0861 | 1.29675 | ||||||||
\(346\) | 0.426368 | 0.0229217 | ||||||||
\(347\) | 1.59256 | 0.0854933 | 0.0427466 | − | 0.999086i | \(-0.486389\pi\) | ||||
0.0427466 | + | 0.999086i | \(0.486389\pi\) | |||||||
\(348\) | −4.18120 | −0.224136 | ||||||||
\(349\) | −6.63475 | −0.355150 | −0.177575 | − | 0.984107i | \(-0.556825\pi\) | ||||
−0.177575 | + | 0.984107i | \(0.556825\pi\) | |||||||
\(350\) | −3.22348 | −0.172302 | ||||||||
\(351\) | −10.7372 | −0.573111 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.4141 | −1.35265 | −0.676327 | − | 0.736601i | \(-0.736430\pi\) | ||||
−0.676327 | + | 0.736601i | \(0.736430\pi\) | |||||||
\(354\) | −2.74894 | −0.146104 | ||||||||
\(355\) | 13.1382 | 0.697304 | ||||||||
\(356\) | −14.3316 | −0.759571 | ||||||||
\(357\) | −4.23329 | −0.224049 | ||||||||
\(358\) | 1.39688 | 0.0738271 | ||||||||
\(359\) | −16.0792 | −0.848629 | −0.424314 | − | 0.905515i | \(-0.639485\pi\) | ||||
−0.424314 | + | 0.905515i | \(0.639485\pi\) | |||||||
\(360\) | 16.9656 | 0.894163 | ||||||||
\(361\) | −16.0222 | −0.843274 | ||||||||
\(362\) | −8.14167 | −0.427916 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.90977 | −0.152513 | ||||||||
\(365\) | −44.0411 | −2.30522 | ||||||||
\(366\) | 10.2804 | 0.537363 | ||||||||
\(367\) | −3.02606 | −0.157959 | −0.0789796 | − | 0.996876i | \(-0.525166\pi\) | ||||
−0.0789796 | + | 0.996876i | \(0.525166\pi\) | |||||||
\(368\) | −3.27973 | −0.170968 | ||||||||
\(369\) | 11.2032 | 0.583213 | ||||||||
\(370\) | −21.5904 | −1.12243 | ||||||||
\(371\) | −9.39774 | −0.487906 | ||||||||
\(372\) | 9.49226 | 0.492151 | ||||||||
\(373\) | −1.73856 | −0.0900192 | −0.0450096 | − | 0.998987i | \(-0.514332\pi\) | ||||
−0.0450096 | + | 0.998987i | \(0.514332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.11455 | 0.160834 | ||||||||
\(376\) | 14.7634 | 0.761365 | ||||||||
\(377\) | 7.24924 | 0.373355 | ||||||||
\(378\) | −4.01678 | −0.206601 | ||||||||
\(379\) | 19.5728 | 1.00538 | 0.502692 | − | 0.864465i | \(-0.332343\pi\) | ||||
0.502692 | + | 0.864465i | \(0.332343\pi\) | |||||||
\(380\) | −6.80983 | −0.349337 | ||||||||
\(381\) | −19.1939 | −0.983334 | ||||||||
\(382\) | 19.0512 | 0.974746 | ||||||||
\(383\) | 4.76472 | 0.243466 | 0.121733 | − | 0.992563i | \(-0.461155\pi\) | ||||
0.121733 | + | 0.992563i | \(0.461155\pi\) | |||||||
\(384\) | 7.97351 | 0.406897 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.0149 | 0.967833 | ||||||||
\(387\) | 19.6214 | 0.997412 | ||||||||
\(388\) | −3.77359 | −0.191575 | ||||||||
\(389\) | −1.42208 | −0.0721024 | −0.0360512 | − | 0.999350i | \(-0.511478\pi\) | ||||
−0.0360512 | + | 0.999350i | \(0.511478\pi\) | |||||||
\(390\) | 5.20001 | 0.263313 | ||||||||
\(391\) | 37.0063 | 1.87149 | ||||||||
\(392\) | −2.73565 | −0.138171 | ||||||||
\(393\) | 8.12251 | 0.409726 | ||||||||
\(394\) | −5.50950 | −0.277565 | ||||||||
\(395\) | 21.4599 | 1.07976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3969 | −0.923314 | −0.461657 | − | 0.887059i | \(-0.652745\pi\) | ||||
−0.461657 | + | 0.887059i | \(0.652745\pi\) | |||||||
\(398\) | −13.0314 | −0.653206 | ||||||||
\(399\) | 1.65772 | 0.0829899 | ||||||||
\(400\) | 1.52865 | 0.0764323 | ||||||||
\(401\) | −1.65268 | −0.0825308 | −0.0412654 | − | 0.999148i | \(-0.513139\pi\) | ||||
−0.0412654 | + | 0.999148i | \(0.513139\pi\) | |||||||
\(402\) | −3.41885 | −0.170517 | ||||||||
\(403\) | −16.4574 | −0.819802 | ||||||||
\(404\) | −19.2991 | −0.960168 | ||||||||
\(405\) | 4.61589 | 0.229366 | ||||||||
\(406\) | 2.71193 | 0.134591 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −11.5808 | −0.573335 | ||||||||
\(409\) | 36.6858 | 1.81400 | 0.906999 | − | 0.421133i | \(-0.138368\pi\) | ||||
0.906999 | + | 0.421133i | \(0.138368\pi\) | |||||||
\(410\) | −13.2618 | −0.654955 | ||||||||
\(411\) | −8.02580 | −0.395884 | ||||||||
\(412\) | 0.142442 | 0.00701762 | ||||||||
\(413\) | −3.47462 | −0.170975 | ||||||||
\(414\) | 14.3656 | 0.706031 | ||||||||
\(415\) | −22.7938 | −1.11890 | ||||||||
\(416\) | −12.7528 | −0.625259 | ||||||||
\(417\) | −14.1344 | −0.692164 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3452 | −0.847366 | −0.423683 | − | 0.905810i | \(-0.639263\pi\) | ||||
−0.423683 | + | 0.905810i | \(0.639263\pi\) | |||||||
\(420\) | −3.79101 | −0.184982 | ||||||||
\(421\) | 5.32683 | 0.259614 | 0.129807 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129807 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(422\) | −9.34941 | −0.455122 | ||||||||
\(423\) | 11.2097 | 0.545035 | ||||||||
\(424\) | −25.7089 | −1.24854 | ||||||||
\(425\) | −17.2482 | −0.836662 | ||||||||
\(426\) | −3.48141 | −0.168675 | ||||||||
\(427\) | 12.9942 | 0.628835 | ||||||||
\(428\) | −6.14487 | −0.297024 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −23.2270 | −1.12011 | ||||||||
\(431\) | 28.2081 | 1.35873 | 0.679367 | − | 0.733798i | \(-0.262254\pi\) | ||||
0.679367 | + | 0.733798i | \(0.262254\pi\) | |||||||
\(432\) | 1.90485 | 0.0916471 | ||||||||
\(433\) | 17.7060 | 0.850895 | 0.425447 | − | 0.904983i | \(-0.360117\pi\) | ||||
0.425447 | + | 0.904983i | \(0.360117\pi\) | |||||||
\(434\) | −6.15668 | −0.295530 | ||||||||
\(435\) | 9.44470 | 0.452839 | ||||||||
\(436\) | 4.27113 | 0.204550 | ||||||||
\(437\) | −14.4914 | −0.693216 | ||||||||
\(438\) | 11.6702 | 0.557623 | ||||||||
\(439\) | 25.1189 | 1.19886 | 0.599430 | − | 0.800427i | \(-0.295394\pi\) | ||||
0.599430 | + | 0.800427i | \(0.295394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.07715 | −0.0989121 | ||||||||
\(442\) | 7.98939 | 0.380017 | ||||||||
\(443\) | −26.9567 | −1.28075 | −0.640376 | − | 0.768061i | \(-0.721222\pi\) | ||||
−0.640376 | + | 0.768061i | \(0.721222\pi\) | |||||||
\(444\) | −11.1492 | −0.529120 | ||||||||
\(445\) | 32.3728 | 1.53462 | ||||||||
\(446\) | −8.80369 | −0.416867 | ||||||||
\(447\) | 8.49474 | 0.401788 | ||||||||
\(448\) | −3.98971 | −0.188496 | ||||||||
\(449\) | −21.0964 | −0.995599 | −0.497799 | − | 0.867292i | \(-0.665858\pi\) | ||||
−0.497799 | + | 0.867292i | \(0.665858\pi\) | |||||||
\(450\) | −6.69566 | −0.315636 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14.9615 | 0.703730 | ||||||||
\(453\) | −19.1841 | −0.901345 | ||||||||
\(454\) | 3.07831 | 0.144472 | ||||||||
\(455\) | 6.57274 | 0.308135 | ||||||||
\(456\) | 4.53495 | 0.212368 | ||||||||
\(457\) | 1.90356 | 0.0890448 | 0.0445224 | − | 0.999008i | \(-0.485823\pi\) | ||||
0.0445224 | + | 0.999008i | \(0.485823\pi\) | |||||||
\(458\) | −19.4841 | −0.910432 | ||||||||
\(459\) | −21.4930 | −1.00321 | ||||||||
\(460\) | 33.1400 | 1.54516 | ||||||||
\(461\) | −25.0440 | −1.16641 | −0.583207 | − | 0.812324i | \(-0.698202\pi\) | ||||
−0.583207 | + | 0.812324i | \(0.698202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1721 | −0.983952 | −0.491976 | − | 0.870609i | \(-0.663725\pi\) | ||||
−0.491976 | + | 0.870609i | \(0.663725\pi\) | |||||||
\(464\) | −1.28606 | −0.0597037 | ||||||||
\(465\) | −21.4416 | −0.994330 | ||||||||
\(466\) | −3.18449 | −0.147519 | ||||||||
\(467\) | 16.6484 | 0.770398 | 0.385199 | − | 0.922834i | \(-0.374133\pi\) | ||||
0.385199 | + | 0.922834i | \(0.374133\pi\) | |||||||
\(468\) | −6.04404 | −0.279386 | ||||||||
\(469\) | −4.32138 | −0.199543 | ||||||||
\(470\) | −13.2696 | −0.612081 | ||||||||
\(471\) | −12.5381 | −0.577724 | ||||||||
\(472\) | −9.50534 | −0.437519 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.68652 | −0.261190 | ||||||||
\(475\) | 6.75427 | 0.309907 | ||||||||
\(476\) | −5.82457 | −0.266969 | ||||||||
\(477\) | −19.5205 | −0.893784 | ||||||||
\(478\) | 8.29459 | 0.379386 | ||||||||
\(479\) | −21.6613 | −0.989730 | −0.494865 | − | 0.868970i | \(-0.664783\pi\) | ||||
−0.494865 | + | 0.868970i | \(0.664783\pi\) | |||||||
\(480\) | −16.6151 | −0.758371 | ||||||||
\(481\) | 19.3302 | 0.881383 | ||||||||
\(482\) | −11.0575 | −0.503655 | ||||||||
\(483\) | −8.06728 | −0.367074 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.52397 | 0.387053 | ||||||||
\(486\) | −13.2735 | −0.602097 | ||||||||
\(487\) | −2.81335 | −0.127485 | −0.0637426 | − | 0.997966i | \(-0.520304\pi\) | ||||
−0.0637426 | + | 0.997966i | \(0.520304\pi\) | |||||||
\(488\) | 35.5477 | 1.60917 | ||||||||
\(489\) | −5.72976 | −0.259109 | ||||||||
\(490\) | 2.45885 | 0.111079 | ||||||||
\(491\) | −3.20580 | −0.144676 | −0.0723379 | − | 0.997380i | \(-0.523046\pi\) | ||||
−0.0723379 | + | 0.997380i | \(0.523046\pi\) | |||||||
\(492\) | −6.84838 | −0.308749 | ||||||||
\(493\) | 14.5110 | 0.653543 | ||||||||
\(494\) | −3.12858 | −0.140762 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.91964 | 0.131096 | ||||||||
\(497\) | −4.40046 | −0.197388 | ||||||||
\(498\) | 6.03998 | 0.270658 | ||||||||
\(499\) | −20.0512 | −0.897616 | −0.448808 | − | 0.893628i | \(-0.648151\pi\) | ||||
−0.448808 | + | 0.893628i | \(0.648151\pi\) | |||||||
\(500\) | 4.28530 | 0.191644 | ||||||||
\(501\) | 12.7259 | 0.568550 | ||||||||
\(502\) | 0.0629585 | 0.00280997 | ||||||||
\(503\) | −35.5089 | −1.58326 | −0.791631 | − | 0.610999i | \(-0.790768\pi\) | ||||
−0.791631 | + | 0.610999i | \(0.790768\pi\) | |||||||
\(504\) | −5.68237 | −0.253113 | ||||||||
\(505\) | 43.5939 | 1.93990 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.83279 | 0.347867 | ||||||||
\(508\) | −26.4089 | −1.17170 | ||||||||
\(509\) | 9.18980 | 0.407331 | 0.203665 | − | 0.979041i | \(-0.434715\pi\) | ||||
0.203665 | + | 0.979041i | \(0.434715\pi\) | |||||||
\(510\) | 10.4090 | 0.460919 | ||||||||
\(511\) | 14.7509 | 0.652543 | ||||||||
\(512\) | 4.39924 | 0.194421 | ||||||||
\(513\) | 8.41650 | 0.371598 | ||||||||
\(514\) | 7.83361 | 0.345526 | ||||||||
\(515\) | −0.321756 | −0.0141782 | ||||||||
\(516\) | −11.9944 | −0.528022 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.23140 | 0.317730 | ||||||||
\(519\) | −0.497343 | −0.0218310 | ||||||||
\(520\) | 17.9807 | 0.788507 | ||||||||
\(521\) | 12.3998 | 0.543246 | 0.271623 | − | 0.962404i | \(-0.412440\pi\) | ||||
0.271623 | + | 0.962404i | \(0.412440\pi\) | |||||||
\(522\) | 5.63309 | 0.246554 | ||||||||
\(523\) | −22.7105 | −0.993062 | −0.496531 | − | 0.868019i | \(-0.665393\pi\) | ||||
−0.496531 | + | 0.868019i | \(0.665393\pi\) | |||||||
\(524\) | 11.1757 | 0.488215 | ||||||||
\(525\) | 3.76007 | 0.164103 | ||||||||
\(526\) | −12.1819 | −0.531158 | ||||||||
\(527\) | −32.9433 | −1.43503 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.5220 | 2.06617 | ||||||||
\(530\) | 23.1076 | 1.00373 | ||||||||
\(531\) | −7.21731 | −0.313205 | ||||||||
\(532\) | 2.28086 | 0.0988877 | ||||||||
\(533\) | 11.8735 | 0.514299 | ||||||||
\(534\) | −8.57828 | −0.371218 | ||||||||
\(535\) | 13.8803 | 0.600100 | ||||||||
\(536\) | −11.8218 | −0.510623 | ||||||||
\(537\) | −1.62941 | −0.0703140 | ||||||||
\(538\) | −24.7525 | −1.06716 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.2475 | −0.828281 | ||||||||
\(541\) | −17.2748 | −0.742703 | −0.371351 | − | 0.928492i | \(-0.621105\pi\) | ||||
−0.371351 | + | 0.928492i | \(0.621105\pi\) | |||||||
\(542\) | 8.55827 | 0.367609 | ||||||||
\(543\) | 9.49697 | 0.407554 | ||||||||
\(544\) | −25.5277 | −1.09449 | ||||||||
\(545\) | −9.64784 | −0.413268 | ||||||||
\(546\) | −1.74167 | −0.0745365 | ||||||||
\(547\) | 13.1740 | 0.563278 | 0.281639 | − | 0.959520i | \(-0.409122\pi\) | ||||
0.281639 | + | 0.959520i | \(0.409122\pi\) | |||||||
\(548\) | −11.0427 | −0.471720 | ||||||||
\(549\) | 26.9910 | 1.15195 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.68240 | −0.242078 | ||||||||
\(552\) | −22.0693 | −0.939330 | ||||||||
\(553\) | −7.18768 | −0.305651 | ||||||||
\(554\) | −23.1533 | −0.983689 | ||||||||
\(555\) | 25.1845 | 1.06902 | ||||||||
\(556\) | −19.4475 | −0.824757 | ||||||||
\(557\) | 12.6216 | 0.534793 | 0.267396 | − | 0.963587i | \(-0.413837\pi\) | ||||
0.267396 | + | 0.963587i | \(0.413837\pi\) | |||||||
\(558\) | −12.7884 | −0.541375 | ||||||||
\(559\) | 20.7955 | 0.879555 | ||||||||
\(560\) | −1.16604 | −0.0492743 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.88151 | −0.332462 | ||||||||
\(563\) | −9.81924 | −0.413832 | −0.206916 | − | 0.978359i | \(-0.566343\pi\) | ||||
−0.206916 | + | 0.978359i | \(0.566343\pi\) | |||||||
\(564\) | −6.85238 | −0.288537 | ||||||||
\(565\) | −33.7958 | −1.42180 | ||||||||
\(566\) | 1.36320 | 0.0572994 | ||||||||
\(567\) | −1.54603 | −0.0649271 | ||||||||
\(568\) | −12.0381 | −0.505108 | ||||||||
\(569\) | −20.3544 | −0.853301 | −0.426650 | − | 0.904417i | \(-0.640307\pi\) | ||||
−0.426650 | + | 0.904417i | \(0.640307\pi\) | |||||||
\(570\) | −4.07608 | −0.170728 | ||||||||
\(571\) | 32.3174 | 1.35244 | 0.676221 | − | 0.736699i | \(-0.263616\pi\) | ||||
0.676221 | + | 0.736699i | \(0.263616\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.2226 | −0.928362 | ||||||||
\(574\) | 4.44186 | 0.185400 | ||||||||
\(575\) | −32.8696 | −1.37076 | ||||||||
\(576\) | −8.28725 | −0.345302 | ||||||||
\(577\) | −11.3181 | −0.471179 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(578\) | 1.99215 | 0.0828623 | ||||||||
\(579\) | −22.1802 | −0.921778 | ||||||||
\(580\) | 12.9950 | 0.539586 | ||||||||
\(581\) | 7.63445 | 0.316730 | ||||||||
\(582\) | −2.25871 | −0.0936266 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 40.3534 | 1.66984 | ||||||||
\(585\) | 13.6526 | 0.564465 | ||||||||
\(586\) | −3.85579 | −0.159281 | ||||||||
\(587\) | −38.2388 | −1.57828 | −0.789142 | − | 0.614211i | \(-0.789474\pi\) | ||||
−0.789142 | + | 0.614211i | \(0.789474\pi\) | |||||||
\(588\) | 1.26974 | 0.0523633 | ||||||||
\(589\) | 12.9003 | 0.531548 | ||||||||
\(590\) | 8.54356 | 0.351733 | ||||||||
\(591\) | 6.42664 | 0.264357 | ||||||||
\(592\) | −3.42930 | −0.140943 | ||||||||
\(593\) | 26.4263 | 1.08520 | 0.542598 | − | 0.839992i | \(-0.317441\pi\) | ||||
0.542598 | + | 0.839992i | \(0.317441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1568 | 0.539378 | ||||||||
\(596\) | 11.6879 | 0.478755 | ||||||||
\(597\) | 15.2007 | 0.622123 | ||||||||
\(598\) | 15.2252 | 0.622605 | ||||||||
\(599\) | −20.2994 | −0.829413 | −0.414706 | − | 0.909955i | \(-0.636116\pi\) | ||||
−0.414706 | + | 0.909955i | \(0.636116\pi\) | |||||||
\(600\) | 10.2862 | 0.419934 | ||||||||
\(601\) | 5.09410 | 0.207793 | 0.103896 | − | 0.994588i | \(-0.466869\pi\) | ||||
0.103896 | + | 0.994588i | \(0.466869\pi\) | |||||||
\(602\) | 7.77955 | 0.317071 | ||||||||
\(603\) | −8.97617 | −0.365538 | ||||||||
\(604\) | −26.3953 | −1.07401 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.5517 | −0.469254 | ||||||||
\(607\) | −30.6407 | −1.24367 | −0.621833 | − | 0.783150i | \(-0.713612\pi\) | ||||
−0.621833 | + | 0.783150i | \(0.713612\pi\) | |||||||
\(608\) | 9.99645 | 0.405410 | ||||||||
\(609\) | −3.16337 | −0.128186 | ||||||||
\(610\) | −31.9508 | −1.29365 | ||||||||
\(611\) | 11.8805 | 0.480632 | ||||||||
\(612\) | −12.0985 | −0.489054 | ||||||||
\(613\) | 24.8391 | 1.00324 | 0.501620 | − | 0.865088i | \(-0.332737\pi\) | ||||
0.501620 | + | 0.865088i | \(0.332737\pi\) | |||||||
\(614\) | 13.9864 | 0.564444 | ||||||||
\(615\) | 15.4695 | 0.623789 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.521714 | 0.0210034 | 0.0105017 | − | 0.999945i | \(-0.496657\pi\) | ||||
0.0105017 | + | 0.999945i | \(0.496657\pi\) | |||||||
\(618\) | 0.0852600 | 0.00342966 | ||||||||
\(619\) | 31.4859 | 1.26552 | 0.632762 | − | 0.774346i | \(-0.281921\pi\) | ||||
0.632762 | + | 0.774346i | \(0.281921\pi\) | |||||||
\(620\) | −29.5015 | −1.18481 | ||||||||
\(621\) | −40.9588 | −1.64362 | ||||||||
\(622\) | −18.0570 | −0.724020 | ||||||||
\(623\) | −10.8428 | −0.434408 | ||||||||
\(624\) | 0.825938 | 0.0330640 | ||||||||
\(625\) | −29.2503 | −1.17001 | ||||||||
\(626\) | 8.28124 | 0.330985 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.2511 | −0.688395 | ||||||||
\(629\) | 38.6939 | 1.54283 | ||||||||
\(630\) | 5.10741 | 0.203484 | ||||||||
\(631\) | −0.114230 | −0.00454742 | −0.00227371 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227371 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(632\) | −19.6630 | −0.782151 | ||||||||
\(633\) | 10.9058 | 0.433465 | ||||||||
\(634\) | 19.4031 | 0.770596 | ||||||||
\(635\) | 59.6537 | 2.36729 | ||||||||
\(636\) | 11.9327 | 0.473163 | ||||||||
\(637\) | −2.20144 | −0.0872244 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.14043 | −0.361590 | ||||||||
\(640\) | −24.7813 | −0.979566 | ||||||||
\(641\) | 13.2141 | 0.521927 | 0.260963 | − | 0.965349i | \(-0.415960\pi\) | ||||
0.260963 | + | 0.965349i | \(0.415960\pi\) | |||||||
\(642\) | −3.67807 | −0.145162 | ||||||||
\(643\) | 2.45599 | 0.0968550 | 0.0484275 | − | 0.998827i | \(-0.484579\pi\) | ||||
0.0484275 | + | 0.998827i | \(0.484579\pi\) | |||||||
\(644\) | −11.0998 | −0.437392 | ||||||||
\(645\) | 27.0935 | 1.06680 | ||||||||
\(646\) | −6.26257 | −0.246398 | ||||||||
\(647\) | −18.6116 | −0.731698 | −0.365849 | − | 0.930674i | \(-0.619221\pi\) | ||||
−0.365849 | + | 0.930674i | \(0.619221\pi\) | |||||||
\(648\) | −4.22939 | −0.166146 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.09630 | −0.278340 | ||||||||
\(651\) | 7.18156 | 0.281467 | ||||||||
\(652\) | −7.88357 | −0.308745 | ||||||||
\(653\) | 19.4481 | 0.761065 | 0.380532 | − | 0.924768i | \(-0.375741\pi\) | ||||
0.380532 | + | 0.924768i | \(0.375741\pi\) | |||||||
\(654\) | 2.55652 | 0.0999678 | ||||||||
\(655\) | −25.2443 | −0.986378 | ||||||||
\(656\) | −2.10643 | −0.0822423 | ||||||||
\(657\) | 30.6400 | 1.19538 | ||||||||
\(658\) | 4.44446 | 0.173263 | ||||||||
\(659\) | −4.71629 | −0.183721 | −0.0918603 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918603 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.9330 | 0.969782 | 0.484891 | − | 0.874575i | \(-0.338859\pi\) | ||||
0.484891 | + | 0.874575i | \(0.338859\pi\) | |||||||
\(662\) | −17.1800 | −0.667718 | ||||||||
\(663\) | −9.31934 | −0.361933 | ||||||||
\(664\) | 20.8852 | 0.810503 | ||||||||
\(665\) | −5.15211 | −0.199790 | ||||||||
\(666\) | 15.0207 | 0.582042 | ||||||||
\(667\) | 27.6533 | 1.07074 | ||||||||
\(668\) | 17.5095 | 0.677463 | ||||||||
\(669\) | 10.2692 | 0.397030 | ||||||||
\(670\) | 10.6256 | 0.410503 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.56498 | 0.214674 | ||||||||
\(673\) | 5.12972 | 0.197736 | 0.0988681 | − | 0.995101i | \(-0.468478\pi\) | ||||
0.0988681 | + | 0.995101i | \(0.468478\pi\) | |||||||
\(674\) | −10.9981 | −0.423629 | ||||||||
\(675\) | 19.0905 | 0.734792 | ||||||||
\(676\) | 10.7771 | 0.414505 | ||||||||
\(677\) | 51.2610 | 1.97012 | 0.985060 | − | 0.172213i | \(-0.0550917\pi\) | ||||
0.985060 | + | 0.172213i | \(0.0550917\pi\) | |||||||
\(678\) | 8.95533 | 0.343927 | ||||||||
\(679\) | −2.85498 | −0.109564 | ||||||||
\(680\) | 35.9925 | 1.38025 | ||||||||
\(681\) | −3.59074 | −0.137598 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.9448 | −0.954485 | −0.477242 | − | 0.878772i | \(-0.658364\pi\) | ||||
−0.477242 | + | 0.878772i | \(0.658364\pi\) | |||||||
\(684\) | 4.73769 | 0.181150 | ||||||||
\(685\) | 24.9438 | 0.953053 | ||||||||
\(686\) | −0.823556 | −0.0314435 | ||||||||
\(687\) | 22.7275 | 0.867109 | ||||||||
\(688\) | −3.68924 | −0.140651 | ||||||||
\(689\) | −20.6886 | −0.788172 | ||||||||
\(690\) | 19.8362 | 0.755152 | ||||||||
\(691\) | 11.7847 | 0.448312 | 0.224156 | − | 0.974553i | \(-0.428038\pi\) | ||||
0.224156 | + | 0.974553i | \(0.428038\pi\) | |||||||
\(692\) | −0.684294 | −0.0260130 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.31156 | 0.0497863 | ||||||||
\(695\) | 43.9290 | 1.66632 | ||||||||
\(696\) | −8.65387 | −0.328024 | ||||||||
\(697\) | 23.7676 | 0.900261 | ||||||||
\(698\) | −5.46409 | −0.206819 | ||||||||
\(699\) | 3.71459 | 0.140499 | ||||||||
\(700\) | 5.17348 | 0.195539 | ||||||||
\(701\) | 31.3172 | 1.18283 | 0.591417 | − | 0.806366i | \(-0.298569\pi\) | ||||
0.591417 | + | 0.806366i | \(0.298569\pi\) | |||||||
\(702\) | −8.84272 | −0.333747 | ||||||||
\(703\) | −15.1522 | −0.571477 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.4785 | 0.582954 | ||||||||
\(706\) | −20.9299 | −0.787708 | ||||||||
\(707\) | −14.6011 | −0.549133 | ||||||||
\(708\) | 4.41187 | 0.165808 | ||||||||
\(709\) | −41.4751 | −1.55763 | −0.778815 | − | 0.627254i | \(-0.784179\pi\) | ||||
−0.778815 | + | 0.627254i | \(0.784179\pi\) | |||||||
\(710\) | 10.8201 | 0.406070 | ||||||||
\(711\) | −14.9299 | −0.559915 | ||||||||
\(712\) | −29.6622 | −1.11164 | ||||||||
\(713\) | −62.7792 | −2.35110 | ||||||||
\(714\) | −3.48635 | −0.130473 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.24190 | −0.0837836 | ||||||||
\(717\) | −9.67534 | −0.361332 | ||||||||
\(718\) | −13.2421 | −0.494192 | ||||||||
\(719\) | −7.89027 | −0.294258 | −0.147129 | − | 0.989117i | \(-0.547003\pi\) | ||||
−0.147129 | + | 0.989117i | \(0.547003\pi\) | |||||||
\(720\) | −2.42205 | −0.0902644 | ||||||||
\(721\) | 0.107767 | 0.00401347 | ||||||||
\(722\) | −13.1952 | −0.491074 | ||||||||
\(723\) | 12.8982 | 0.479688 | ||||||||
\(724\) | 13.0669 | 0.485626 | ||||||||
\(725\) | −12.8889 | −0.478682 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.12729 | 0.190161 | 0.0950803 | − | 0.995470i | \(-0.469689\pi\) | ||||
0.0950803 | + | 0.995470i | \(0.469689\pi\) | |||||||
\(728\) | −6.02238 | −0.223204 | ||||||||
\(729\) | 10.8450 | 0.401665 | ||||||||
\(730\) | −36.2703 | −1.34242 | ||||||||
\(731\) | 41.6269 | 1.53963 | ||||||||
\(732\) | −16.4993 | −0.609833 | ||||||||
\(733\) | 33.7736 | 1.24746 | 0.623728 | − | 0.781642i | \(-0.285617\pi\) | ||||
0.623728 | + | 0.781642i | \(0.285617\pi\) | |||||||
\(734\) | −2.49213 | −0.0919863 | ||||||||
\(735\) | −2.86816 | −0.105794 | ||||||||
\(736\) | −48.6476 | −1.79317 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 9.22643 | 0.339629 | ||||||||
\(739\) | 42.7431 | 1.57233 | 0.786164 | − | 0.618017i | \(-0.212064\pi\) | ||||
0.786164 | + | 0.618017i | \(0.212064\pi\) | |||||||
\(740\) | 34.6513 | 1.27381 | ||||||||
\(741\) | 3.64938 | 0.134063 | ||||||||
\(742\) | −7.73956 | −0.284128 | ||||||||
\(743\) | −22.9565 | −0.842192 | −0.421096 | − | 0.907016i | \(-0.638354\pi\) | ||||
−0.421096 | + | 0.907016i | \(0.638354\pi\) | |||||||
\(744\) | 19.6462 | 0.720266 | ||||||||
\(745\) | −26.4012 | −0.967266 | ||||||||
\(746\) | −1.43180 | −0.0524220 | ||||||||
\(747\) | 15.8579 | 0.580211 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.64902 | −0.169872 | ||||||||
\(750\) | 2.56500 | 0.0936607 | ||||||||
\(751\) | −0.930719 | −0.0339624 | −0.0169812 | − | 0.999856i | \(-0.505406\pi\) | ||||
−0.0169812 | + | 0.999856i | \(0.505406\pi\) | |||||||
\(752\) | −2.10766 | −0.0768586 | ||||||||
\(753\) | −0.0734388 | −0.00267626 | ||||||||
\(754\) | 5.97016 | 0.217420 | ||||||||
\(755\) | 59.6231 | 2.16991 | ||||||||
\(756\) | 6.44668 | 0.234464 | ||||||||
\(757\) | −11.4824 | −0.417334 | −0.208667 | − | 0.977987i | \(-0.566913\pi\) | ||||
−0.208667 | + | 0.977987i | \(0.566913\pi\) | |||||||
\(758\) | 16.1193 | 0.585478 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.0944 | −0.511257 | ||||||||
\(761\) | −38.8640 | −1.40882 | −0.704410 | − | 0.709794i | \(-0.748788\pi\) | ||||
−0.704410 | + | 0.709794i | \(0.748788\pi\) | |||||||
\(762\) | −15.8073 | −0.572637 | ||||||||
\(763\) | 3.23140 | 0.116985 | ||||||||
\(764\) | −30.5760 | −1.10620 | ||||||||
\(765\) | 27.3288 | 0.988074 | ||||||||
\(766\) | 3.92402 | 0.141780 | ||||||||
\(767\) | −7.64917 | −0.276196 | ||||||||
\(768\) | 14.2321 | 0.513555 | ||||||||
\(769\) | 35.6509 | 1.28560 | 0.642802 | − | 0.766032i | \(-0.277772\pi\) | ||||
0.642802 | + | 0.766032i | \(0.277772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.13763 | −0.329084 | ||||||||
\(772\) | −30.5177 | −1.09836 | ||||||||
\(773\) | −1.77045 | −0.0636788 | −0.0318394 | − | 0.999493i | \(-0.510137\pi\) | ||||
−0.0318394 | + | 0.999493i | \(0.510137\pi\) | |||||||
\(774\) | 16.1593 | 0.580835 | ||||||||
\(775\) | 29.2607 | 1.05108 | ||||||||
\(776\) | −7.81023 | −0.280371 | ||||||||
\(777\) | −8.43518 | −0.302610 | ||||||||
\(778\) | −1.17116 | −0.0419883 | ||||||||
\(779\) | −9.30719 | −0.333465 | ||||||||
\(780\) | −8.34569 | −0.298824 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 30.4767 | 1.08985 | ||||||||
\(783\) | −16.0609 | −0.573970 | ||||||||
\(784\) | 0.390549 | 0.0139482 | ||||||||
\(785\) | 38.9677 | 1.39082 | ||||||||
\(786\) | 6.68934 | 0.238601 | ||||||||
\(787\) | −3.35315 | −0.119527 | −0.0597635 | − | 0.998213i | \(-0.519035\pi\) | ||||
−0.0597635 | + | 0.998213i | \(0.519035\pi\) | |||||||
\(788\) | 8.84240 | 0.314998 | ||||||||
\(789\) | 14.2098 | 0.505883 | ||||||||
\(790\) | 17.6734 | 0.628792 | ||||||||
\(791\) | 11.3194 | 0.402472 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.6061 | 1.01583 | ||||||||
\(794\) | −15.1509 | −0.537684 | ||||||||
\(795\) | −26.9542 | −0.955968 | ||||||||
\(796\) | 20.9146 | 0.741298 | ||||||||
\(797\) | 4.92542 | 0.174467 | 0.0872337 | − | 0.996188i | \(-0.472197\pi\) | ||||
0.0872337 | + | 0.996188i | \(0.472197\pi\) | |||||||
\(798\) | 1.36523 | 0.0483285 | ||||||||
\(799\) | 23.7815 | 0.841328 | ||||||||
\(800\) | 22.6741 | 0.801652 | ||||||||
\(801\) | −22.5222 | −0.795783 | ||||||||
\(802\) | −1.36107 | −0.0480612 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.48704 | 0.193513 | ||||||||
\(805\) | 25.0727 | 0.883696 | ||||||||
\(806\) | −13.5536 | −0.477405 | ||||||||
\(807\) | 28.8729 | 1.01637 | ||||||||
\(808\) | −39.9436 | −1.40521 | ||||||||
\(809\) | 6.97322 | 0.245165 | 0.122583 | − | 0.992458i | \(-0.460882\pi\) | ||||
0.122583 | + | 0.992458i | \(0.460882\pi\) | |||||||
\(810\) | 3.80145 | 0.133569 | ||||||||
\(811\) | −5.93377 | −0.208363 | −0.104181 | − | 0.994558i | \(-0.533222\pi\) | ||||
−0.104181 | + | 0.994558i | \(0.533222\pi\) | |||||||
\(812\) | −4.35247 | −0.152742 | ||||||||
\(813\) | −9.98292 | −0.350116 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.8078 | 0.623781 | ||||||||
\(816\) | 1.65331 | 0.0578773 | ||||||||
\(817\) | −16.3008 | −0.570292 | ||||||||
\(818\) | 30.2128 | 1.05637 | ||||||||
\(819\) | −4.57274 | −0.159784 | ||||||||
\(820\) | 21.2844 | 0.743284 | ||||||||
\(821\) | −41.7468 | −1.45697 | −0.728487 | − | 0.685060i | \(-0.759776\pi\) | ||||
−0.728487 | + | 0.685060i | \(0.759776\pi\) | |||||||
\(822\) | −6.60970 | −0.230540 | ||||||||
\(823\) | −23.2004 | −0.808714 | −0.404357 | − | 0.914601i | \(-0.632505\pi\) | ||||
−0.404357 | + | 0.914601i | \(0.632505\pi\) | |||||||
\(824\) | 0.294814 | 0.0102703 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.86154 | −0.0995658 | ||||||||
\(827\) | 13.1779 | 0.458240 | 0.229120 | − | 0.973398i | \(-0.426415\pi\) | ||||
0.229120 | + | 0.973398i | \(0.426415\pi\) | |||||||
\(828\) | −23.0559 | −0.801248 | ||||||||
\(829\) | 4.29090 | 0.149029 | 0.0745146 | − | 0.997220i | \(-0.476259\pi\) | ||||
0.0745146 | + | 0.997220i | \(0.476259\pi\) | |||||||
\(830\) | −18.7720 | −0.651584 | ||||||||
\(831\) | 27.0075 | 0.936879 | ||||||||
\(832\) | −8.78313 | −0.304500 | ||||||||
\(833\) | −4.40669 | −0.152683 | ||||||||
\(834\) | −11.6405 | −0.403076 | ||||||||
\(835\) | −39.5513 | −1.36873 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.4619 | 1.26031 | ||||||||
\(838\) | −14.2847 | −0.493457 | ||||||||
\(839\) | −15.7453 | −0.543588 | −0.271794 | − | 0.962355i | \(-0.587617\pi\) | ||||
−0.271794 | + | 0.962355i | \(0.587617\pi\) | |||||||
\(840\) | −7.84629 | −0.270723 | ||||||||
\(841\) | −18.1565 | −0.626086 | ||||||||
\(842\) | 4.38694 | 0.151184 | ||||||||
\(843\) | 9.19351 | 0.316641 | ||||||||
\(844\) | 15.0052 | 0.516501 | ||||||||
\(845\) | −24.3439 | −0.837456 | ||||||||
\(846\) | 9.23182 | 0.317397 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.67028 | 0.126038 | ||||||||
\(849\) | −1.59012 | −0.0545728 | ||||||||
\(850\) | −14.2049 | −0.487223 | ||||||||
\(851\) | 73.7381 | 2.52771 | ||||||||
\(852\) | 5.58745 | 0.191423 | ||||||||
\(853\) | −6.14015 | −0.210235 | −0.105117 | − | 0.994460i | \(-0.533522\pi\) | ||||
−0.105117 | + | 0.994460i | \(0.533522\pi\) | |||||||
\(854\) | 10.7015 | 0.366197 | ||||||||
\(855\) | −10.7017 | −0.365991 | ||||||||
\(856\) | −12.7181 | −0.434696 | ||||||||
\(857\) | −34.4740 | −1.17761 | −0.588804 | − | 0.808276i | \(-0.700401\pi\) | ||||
−0.588804 | + | 0.808276i | \(0.700401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.21553 | 0.280310 | 0.140155 | − | 0.990130i | \(-0.455240\pi\) | ||||
0.140155 | + | 0.990130i | \(0.455240\pi\) | |||||||
\(860\) | 37.2779 | 1.27116 | ||||||||
\(861\) | −5.18127 | −0.176577 | ||||||||
\(862\) | 23.2309 | 0.791248 | ||||||||
\(863\) | 13.0390 | 0.443852 | 0.221926 | − | 0.975063i | \(-0.428766\pi\) | ||||
0.221926 | + | 0.975063i | \(0.428766\pi\) | |||||||
\(864\) | 28.2543 | 0.961230 | ||||||||
\(865\) | 1.54572 | 0.0525560 | ||||||||
\(866\) | 14.5819 | 0.495512 | ||||||||
\(867\) | −2.32377 | −0.0789193 | ||||||||
\(868\) | 9.88109 | 0.335386 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 7.77824 | 0.263707 | ||||||||
\(871\) | −9.51327 | −0.322345 | ||||||||
\(872\) | 8.84000 | 0.299360 | ||||||||
\(873\) | −5.93023 | −0.200708 | ||||||||
\(874\) | −11.9344 | −0.403689 | ||||||||
\(875\) | 3.24213 | 0.109604 | ||||||||
\(876\) | −18.7299 | −0.632825 | ||||||||
\(877\) | −17.9259 | −0.605316 | −0.302658 | − | 0.953099i | \(-0.597874\pi\) | ||||
−0.302658 | + | 0.953099i | \(0.597874\pi\) | |||||||
\(878\) | 20.6868 | 0.698147 | ||||||||
\(879\) | 4.49765 | 0.151702 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.3276 | −0.583780 | −0.291890 | − | 0.956452i | \(-0.594284\pi\) | ||||
−0.291890 | + | 0.956452i | \(0.594284\pi\) | |||||||
\(882\) | −1.71065 | −0.0576007 | ||||||||
\(883\) | 21.8740 | 0.736120 | 0.368060 | − | 0.929802i | \(-0.380022\pi\) | ||||
0.368060 | + | 0.929802i | \(0.380022\pi\) | |||||||
\(884\) | −12.8225 | −0.431266 | ||||||||
\(885\) | −9.96576 | −0.334995 | ||||||||
\(886\) | −22.2004 | −0.745836 | ||||||||
\(887\) | −25.6098 | −0.859893 | −0.429946 | − | 0.902854i | \(-0.641468\pi\) | ||||
−0.429946 | + | 0.902854i | \(0.641468\pi\) | |||||||
\(888\) | −23.0757 | −0.774370 | ||||||||
\(889\) | −19.9802 | −0.670113 | ||||||||
\(890\) | 26.6608 | 0.893674 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.1294 | 0.473087 | ||||||||
\(893\) | −9.31263 | −0.311635 | ||||||||
\(894\) | 6.99590 | 0.233978 | ||||||||
\(895\) | 5.06411 | 0.169275 | ||||||||
\(896\) | 8.30013 | 0.277288 | ||||||||
\(897\) | −17.7597 | −0.592978 | ||||||||
\(898\) | −17.3740 | −0.579779 | ||||||||
\(899\) | −24.6172 | −0.821030 | ||||||||
\(900\) | 10.7461 | 0.358204 | ||||||||
\(901\) | −41.4130 | −1.37967 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.07457 | −0.301983 | ||||||||
\(904\) | 30.9660 | 1.02991 | ||||||||
\(905\) | −29.5161 | −0.981148 | ||||||||
\(906\) | −15.7991 | −0.524891 | ||||||||
\(907\) | −14.4388 | −0.479431 | −0.239716 | − | 0.970843i | \(-0.577054\pi\) | ||||
−0.239716 | + | 0.970843i | \(0.577054\pi\) | |||||||
\(908\) | −4.94050 | −0.163956 | ||||||||
\(909\) | −30.3288 | −1.00594 | ||||||||
\(910\) | 5.41302 | 0.179440 | ||||||||
\(911\) | 37.1858 | 1.23202 | 0.616010 | − | 0.787739i | \(-0.288748\pi\) | ||||
0.616010 | + | 0.787739i | \(0.288748\pi\) | |||||||
\(912\) | −0.647421 | −0.0214383 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.56769 | 0.0518545 | ||||||||
\(915\) | 37.2695 | 1.23209 | ||||||||
\(916\) | 31.2708 | 1.03321 | ||||||||
\(917\) | 8.45523 | 0.279216 | ||||||||
\(918\) | −17.7007 | −0.584211 | ||||||||
\(919\) | 16.0496 | 0.529426 | 0.264713 | − | 0.964327i | \(-0.414723\pi\) | ||||
0.264713 | + | 0.964327i | \(0.414723\pi\) | |||||||
\(920\) | 68.5901 | 2.26135 | ||||||||
\(921\) | −16.3146 | −0.537585 | ||||||||
\(922\) | −20.6251 | −0.679252 | ||||||||
\(923\) | −9.68736 | −0.318863 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.3685 | −1.13003 | ||||||||
\(926\) | −17.4364 | −0.572997 | ||||||||
\(927\) | 0.223849 | 0.00735218 | ||||||||
\(928\) | −19.0759 | −0.626196 | ||||||||
\(929\) | 33.8914 | 1.11194 | 0.555970 | − | 0.831202i | \(-0.312347\pi\) | ||||
0.555970 | + | 0.831202i | \(0.312347\pi\) | |||||||
\(930\) | −17.6584 | −0.579040 | ||||||||
\(931\) | 1.72563 | 0.0565551 | ||||||||
\(932\) | 5.11090 | 0.167413 | ||||||||
\(933\) | 21.0629 | 0.689567 | ||||||||
\(934\) | 13.7109 | 0.448635 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.5094 | −0.408883 | ||||||||
\(937\) | 9.22624 | 0.301408 | 0.150704 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150704 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(938\) | −3.55890 | −0.116202 | ||||||||
\(939\) | −9.65977 | −0.315235 | ||||||||
\(940\) | 21.2969 | 0.694627 | ||||||||
\(941\) | 53.3626 | 1.73957 | 0.869786 | − | 0.493430i | \(-0.164257\pi\) | ||||
0.869786 | + | 0.493430i | \(0.164257\pi\) | |||||||
\(942\) | −10.3258 | −0.336433 | ||||||||
\(943\) | 45.2933 | 1.47495 | ||||||||
\(944\) | 1.35701 | 0.0441668 | ||||||||
\(945\) | −14.5621 | −0.473705 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.0986 | 1.01057 | 0.505285 | − | 0.862953i | \(-0.331388\pi\) | ||||
0.505285 | + | 0.862953i | \(0.331388\pi\) | |||||||
\(948\) | 9.12650 | 0.296415 | ||||||||
\(949\) | 32.4734 | 1.05413 | ||||||||
\(950\) | 5.56252 | 0.180472 | ||||||||
\(951\) | −22.6330 | −0.733927 | ||||||||
\(952\) | −12.0552 | −0.390711 | ||||||||
\(953\) | −34.9286 | −1.13145 | −0.565724 | − | 0.824595i | \(-0.691403\pi\) | ||||
−0.565724 | + | 0.824595i | \(0.691403\pi\) | |||||||
\(954\) | −16.0763 | −0.520488 | ||||||||
\(955\) | 69.0667 | 2.23494 | ||||||||
\(956\) | −13.3123 | −0.430550 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.8393 | −0.576361 | ||||||||
\(959\) | −8.35456 | −0.269783 | ||||||||
\(960\) | −11.4431 | −0.369326 | ||||||||
\(961\) | 24.8866 | 0.802793 | ||||||||
\(962\) | 15.9195 | 0.513266 | ||||||||
\(963\) | −9.65673 | −0.311184 | ||||||||
\(964\) | 17.7466 | 0.571579 | ||||||||
\(965\) | 68.9350 | 2.21910 | ||||||||
\(966\) | −6.64385 | −0.213763 | ||||||||
\(967\) | 20.8029 | 0.668975 | 0.334488 | − | 0.942400i | \(-0.391437\pi\) | ||||
0.334488 | + | 0.942400i | \(0.391437\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.30507 | 0.234673 | ||||||||
\(970\) | 7.01996 | 0.225397 | ||||||||
\(971\) | −40.0308 | −1.28465 | −0.642325 | − | 0.766433i | \(-0.722030\pi\) | ||||
−0.642325 | + | 0.766433i | \(0.722030\pi\) | |||||||
\(972\) | 21.3031 | 0.683297 | ||||||||
\(973\) | −14.7134 | −0.471689 | ||||||||
\(974\) | −2.31695 | −0.0742400 | ||||||||
\(975\) | 8.27759 | 0.265095 | ||||||||
\(976\) | −5.07488 | −0.162443 | ||||||||
\(977\) | 6.48609 | 0.207509 | 0.103754 | − | 0.994603i | \(-0.466914\pi\) | ||||
0.103754 | + | 0.994603i | \(0.466914\pi\) | |||||||
\(978\) | −4.71878 | −0.150890 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.94630 | −0.126060 | ||||||||
\(981\) | 6.71212 | 0.214302 | ||||||||
\(982\) | −2.64016 | −0.0842508 | ||||||||
\(983\) | 10.9782 | 0.350150 | 0.175075 | − | 0.984555i | \(-0.443983\pi\) | ||||
0.175075 | + | 0.984555i | \(0.443983\pi\) | |||||||
\(984\) | −14.1742 | −0.451856 | ||||||||
\(985\) | −19.9737 | −0.636414 | ||||||||
\(986\) | 11.9506 | 0.380586 | ||||||||
\(987\) | −5.18430 | −0.165018 | ||||||||
\(988\) | 5.02118 | 0.159745 | ||||||||
\(989\) | 79.3275 | 2.52247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.2666 | −1.88267 | −0.941333 | − | 0.337479i | \(-0.890426\pi\) | ||||
−0.941333 | + | 0.337479i | \(0.890426\pi\) | |||||||
\(992\) | 43.3065 | 1.37498 | ||||||||
\(993\) | 20.0398 | 0.635944 | ||||||||
\(994\) | −3.62402 | −0.114947 | ||||||||
\(995\) | −47.2430 | −1.49770 | ||||||||
\(996\) | −9.69379 | −0.307160 | ||||||||
\(997\) | 43.3517 | 1.37296 | 0.686481 | − | 0.727148i | \(-0.259155\pi\) | ||||
0.686481 | + | 0.727148i | \(0.259155\pi\) | |||||||
\(998\) | −16.5133 | −0.522720 | ||||||||
\(999\) | −42.8267 | −1.35498 |
(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 | 847.2.a.m.1.5 | ✓ | 6 | |
3.2 | odd | 2 | 7623.2.a.cs.1.2 | 6 | |||
7.6 | odd | 2 | 5929.2.a.bj.1.5 | 6 | |||
11.2 | odd | 10 | 847.2.f.y.323.5 | 24 | |||
11.3 | even | 5 | 847.2.f.z.372.5 | 24 | |||
11.4 | even | 5 | 847.2.f.z.148.5 | 24 | |||
11.5 | even | 5 | 847.2.f.z.729.2 | 24 | |||
11.6 | odd | 10 | 847.2.f.y.729.5 | 24 | |||
11.7 | odd | 10 | 847.2.f.y.148.2 | 24 | |||
11.8 | odd | 10 | 847.2.f.y.372.2 | 24 | |||
11.9 | even | 5 | 847.2.f.z.323.2 | 24 | |||
11.10 | odd | 2 | 847.2.a.n.1.2 | yes | 6 | ||
33.32 | even | 2 | 7623.2.a.cp.1.5 | 6 | |||
77.76 | even | 2 | 5929.2.a.bm.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
847.2.a.n.1.2 | yes | 6 | 11.10 | odd | 2 | ||
847.2.f.y.148.2 | 24 | 11.7 | odd | 10 | |||
847.2.f.y.323.5 | 24 | 11.2 | odd | 10 | |||
847.2.f.y.372.2 | 24 | 11.8 | odd | 10 | |||
847.2.f.y.729.5 | 24 | 11.6 | odd | 10 | |||
847.2.f.z.148.5 | 24 | 11.4 | even | 5 | |||
847.2.f.z.323.2 | 24 | 11.9 | even | 5 | |||
847.2.f.z.372.5 | 24 | 11.3 | even | 5 | |||
847.2.f.z.729.2 | 24 | 11.5 | even | 5 | |||
5929.2.a.bj.1.5 | 6 | 7.6 | odd | 2 | |||
5929.2.a.bm.1.2 | 6 | 77.76 | even | 2 | |||
7623.2.a.cp.1.5 | 6 | 33.32 | even | 2 | |||
7623.2.a.cs.1.2 | 6 | 3.2 | odd | 2 |