Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 88x^{8} - 197x^{6} + 172x^{4} - 36x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.30327\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30327 | −1.62866 | −0.814328 | − | 0.580405i | \(-0.802894\pi\) | ||||
−0.814328 | + | 0.580405i | \(0.802894\pi\) | |||||||
\(3\) | −1.47336 | −0.850645 | −0.425323 | − | 0.905042i | \(-0.639839\pi\) | ||||
−0.425323 | + | 0.905042i | \(0.639839\pi\) | |||||||
\(4\) | 3.30504 | 1.65252 | ||||||||
\(5\) | −0.847292 | −0.378920 | −0.189460 | − | 0.981888i | \(-0.560674\pi\) | ||||
−0.189460 | + | 0.981888i | \(0.560674\pi\) | |||||||
\(6\) | 3.39354 | 1.38541 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00585 | −1.06273 | ||||||||
\(9\) | −0.829208 | −0.276403 | ||||||||
\(10\) | 1.95154 | 0.617131 | ||||||||
\(11\) | 1.50340 | 0.453293 | 0.226646 | − | 0.973977i | \(-0.427224\pi\) | ||||
0.226646 | + | 0.973977i | \(0.427224\pi\) | |||||||
\(12\) | −4.86951 | −1.40571 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.24837 | 0.322327 | ||||||||
\(16\) | 0.313194 | 0.0782985 | ||||||||
\(17\) | 2.07140 | 0.502389 | 0.251194 | − | 0.967937i | \(-0.419177\pi\) | ||||
0.251194 | + | 0.967937i | \(0.419177\pi\) | |||||||
\(18\) | 1.90989 | 0.450164 | ||||||||
\(19\) | 0.0474272 | 0.0108805 | 0.00544027 | − | 0.999985i | \(-0.498268\pi\) | ||||
0.00544027 | + | 0.999985i | \(0.498268\pi\) | |||||||
\(20\) | −2.80033 | −0.626173 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.46274 | −0.738258 | ||||||||
\(23\) | −7.81870 | −1.63031 | −0.815156 | − | 0.579241i | \(-0.803349\pi\) | ||||
−0.815156 | + | 0.579241i | \(0.803349\pi\) | |||||||
\(24\) | 4.42870 | 0.904004 | ||||||||
\(25\) | −4.28210 | −0.856419 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64180 | 1.08577 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.35971 | 0.252491 | 0.126246 | − | 0.991999i | \(-0.459707\pi\) | ||||
0.126246 | + | 0.991999i | \(0.459707\pi\) | |||||||
\(30\) | −2.87532 | −0.524959 | ||||||||
\(31\) | −7.86105 | −1.41189 | −0.705943 | − | 0.708269i | \(-0.749477\pi\) | ||||
−0.705943 | + | 0.708269i | \(0.749477\pi\) | |||||||
\(32\) | 5.29033 | 0.935206 | ||||||||
\(33\) | −2.21505 | −0.385591 | ||||||||
\(34\) | −4.77099 | −0.818218 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.74056 | −0.456760 | ||||||||
\(37\) | −6.70219 | −1.10183 | −0.550917 | − | 0.834560i | \(-0.685722\pi\) | ||||
−0.550917 | + | 0.834560i | \(0.685722\pi\) | |||||||
\(38\) | −0.109237 | −0.0177206 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.54683 | 0.402689 | ||||||||
\(41\) | −10.0184 | −1.56462 | −0.782309 | − | 0.622891i | \(-0.785958\pi\) | ||||
−0.782309 | + | 0.622891i | \(0.785958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.26566 | 1.41300 | 0.706500 | − | 0.707713i | \(-0.250273\pi\) | ||||
0.706500 | + | 0.707713i | \(0.250273\pi\) | |||||||
\(44\) | 4.96880 | 0.749075 | ||||||||
\(45\) | 0.702581 | 0.104735 | ||||||||
\(46\) | 18.0086 | 2.65522 | ||||||||
\(47\) | −0.360014 | −0.0525134 | −0.0262567 | − | 0.999655i | \(-0.508359\pi\) | ||||
−0.0262567 | + | 0.999655i | \(0.508359\pi\) | |||||||
\(48\) | −0.461448 | −0.0666042 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.86281 | 1.39481 | ||||||||
\(51\) | −3.05192 | −0.427355 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.71181 | 0.372496 | 0.186248 | − | 0.982503i | \(-0.440367\pi\) | ||||
0.186248 | + | 0.982503i | \(0.440367\pi\) | |||||||
\(54\) | −12.9946 | −1.76834 | ||||||||
\(55\) | −1.27382 | −0.171762 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0698773 | −0.00925548 | ||||||||
\(58\) | −3.13177 | −0.411222 | ||||||||
\(59\) | −1.64120 | −0.213666 | −0.106833 | − | 0.994277i | \(-0.534071\pi\) | ||||
−0.106833 | + | 0.994277i | \(0.534071\pi\) | |||||||
\(60\) | 4.12590 | 0.532651 | ||||||||
\(61\) | 4.52194 | 0.578975 | 0.289488 | − | 0.957182i | \(-0.406515\pi\) | ||||
0.289488 | + | 0.957182i | \(0.406515\pi\) | |||||||
\(62\) | 18.1061 | 2.29948 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8114 | −1.60143 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.10186 | 0.627995 | ||||||||
\(67\) | 2.04266 | 0.249551 | 0.124775 | − | 0.992185i | \(-0.460179\pi\) | ||||
0.124775 | + | 0.992185i | \(0.460179\pi\) | |||||||
\(68\) | 6.84606 | 0.830206 | ||||||||
\(69\) | 11.5198 | 1.38682 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2139 | −1.68688 | −0.843442 | − | 0.537220i | \(-0.819474\pi\) | ||||
−0.843442 | + | 0.537220i | \(0.819474\pi\) | |||||||
\(72\) | 2.49247 | 0.293741 | ||||||||
\(73\) | −6.76150 | −0.791373 | −0.395687 | − | 0.918386i | \(-0.629493\pi\) | ||||
−0.395687 | + | 0.918386i | \(0.629493\pi\) | |||||||
\(74\) | 15.4369 | 1.79451 | ||||||||
\(75\) | 6.30907 | 0.728509 | ||||||||
\(76\) | 0.156749 | 0.0179803 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6590 | 1.31175 | 0.655873 | − | 0.754871i | \(-0.272301\pi\) | ||||
0.655873 | + | 0.754871i | \(0.272301\pi\) | |||||||
\(80\) | −0.265367 | −0.0296689 | ||||||||
\(81\) | −5.82479 | −0.647199 | ||||||||
\(82\) | 23.0751 | 2.54822 | ||||||||
\(83\) | −11.5362 | −1.26627 | −0.633133 | − | 0.774043i | \(-0.718232\pi\) | ||||
−0.633133 | + | 0.774043i | \(0.718232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.75508 | −0.190365 | ||||||||
\(86\) | −21.3413 | −2.30129 | ||||||||
\(87\) | −2.00334 | −0.214781 | ||||||||
\(88\) | −4.51900 | −0.481727 | ||||||||
\(89\) | 17.5112 | 1.85619 | 0.928093 | − | 0.372350i | \(-0.121448\pi\) | ||||
0.928093 | + | 0.372350i | \(0.121448\pi\) | |||||||
\(90\) | −1.61823 | −0.170576 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.8411 | −2.69412 | ||||||||
\(93\) | 11.5822 | 1.20101 | ||||||||
\(94\) | 0.829208 | 0.0855262 | ||||||||
\(95\) | −0.0401846 | −0.00412286 | ||||||||
\(96\) | −7.79456 | −0.795529 | ||||||||
\(97\) | −0.426229 | −0.0432770 | −0.0216385 | − | 0.999766i | \(-0.506888\pi\) | ||||
−0.0216385 | + | 0.999766i | \(0.506888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.24663 | −0.125291 | ||||||||
\(100\) | −14.1525 | −1.41525 | ||||||||
\(101\) | 9.66997 | 0.962198 | 0.481099 | − | 0.876666i | \(-0.340238\pi\) | ||||
0.481099 | + | 0.876666i | \(0.340238\pi\) | |||||||
\(102\) | 7.02939 | 0.696013 | ||||||||
\(103\) | −9.97823 | −0.983185 | −0.491592 | − | 0.870825i | \(-0.663585\pi\) | ||||
−0.491592 | + | 0.870825i | \(0.663585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.24603 | −0.606668 | ||||||||
\(107\) | 9.86223 | 0.953417 | 0.476709 | − | 0.879061i | \(-0.341830\pi\) | ||||
0.476709 | + | 0.879061i | \(0.341830\pi\) | |||||||
\(108\) | 18.6464 | 1.79425 | ||||||||
\(109\) | −11.6055 | −1.11161 | −0.555803 | − | 0.831314i | \(-0.687589\pi\) | ||||
−0.555803 | + | 0.831314i | \(0.687589\pi\) | |||||||
\(110\) | 2.93395 | 0.279741 | ||||||||
\(111\) | 9.87475 | 0.937269 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.47758 | −0.327143 | −0.163572 | − | 0.986531i | \(-0.552301\pi\) | ||||
−0.163572 | + | 0.986531i | \(0.552301\pi\) | |||||||
\(114\) | 0.160946 | 0.0150740 | ||||||||
\(115\) | 6.62472 | 0.617758 | ||||||||
\(116\) | 4.49388 | 0.417247 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.78011 | 0.347987 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.75240 | −0.342546 | ||||||||
\(121\) | −8.73978 | −0.794526 | ||||||||
\(122\) | −10.4152 | −0.942951 | ||||||||
\(123\) | 14.7608 | 1.33093 | ||||||||
\(124\) | −25.9811 | −2.33317 | ||||||||
\(125\) | 7.86464 | 0.703435 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6998 | −1.39313 | −0.696567 | − | 0.717491i | \(-0.745290\pi\) | ||||
−0.696567 | + | 0.717491i | \(0.745290\pi\) | |||||||
\(128\) | 18.9275 | 1.67297 | ||||||||
\(129\) | −13.6517 | −1.20196 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.54517 | −0.222373 | −0.111186 | − | 0.993800i | \(-0.535465\pi\) | ||||
−0.111186 | + | 0.993800i | \(0.535465\pi\) | |||||||
\(132\) | −7.32083 | −0.637197 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.70479 | −0.406432 | ||||||||
\(135\) | −4.78025 | −0.411419 | ||||||||
\(136\) | −6.22632 | −0.533902 | ||||||||
\(137\) | 1.86472 | 0.159314 | 0.0796571 | − | 0.996822i | \(-0.474617\pi\) | ||||
0.0796571 | + | 0.996822i | \(0.474617\pi\) | |||||||
\(138\) | −26.5331 | −2.25865 | ||||||||
\(139\) | 15.6092 | 1.32396 | 0.661979 | − | 0.749522i | \(-0.269717\pi\) | ||||
0.661979 | + | 0.749522i | \(0.269717\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.530430 | 0.0446703 | ||||||||
\(142\) | 32.7385 | 2.74735 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.259703 | −0.0216419 | ||||||||
\(145\) | −1.15207 | −0.0956741 | ||||||||
\(146\) | 15.5735 | 1.28887 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −22.1510 | −1.82080 | ||||||||
\(149\) | 6.36363 | 0.521329 | 0.260664 | − | 0.965429i | \(-0.416058\pi\) | ||||
0.260664 | + | 0.965429i | \(0.416058\pi\) | |||||||
\(150\) | −14.5315 | −1.18649 | ||||||||
\(151\) | −0.664094 | −0.0540432 | −0.0270216 | − | 0.999635i | \(-0.508602\pi\) | ||||
−0.0270216 | + | 0.999635i | \(0.508602\pi\) | |||||||
\(152\) | −0.142559 | −0.0115630 | ||||||||
\(153\) | −1.71762 | −0.138861 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.66060 | 0.534992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.5760 | −1.32291 | −0.661453 | − | 0.749986i | \(-0.730060\pi\) | ||||
−0.661453 | + | 0.749986i | \(0.730060\pi\) | |||||||
\(158\) | −26.8539 | −2.13638 | ||||||||
\(159\) | −3.99548 | −0.316862 | ||||||||
\(160\) | −4.48245 | −0.354369 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.4160 | 1.05406 | ||||||||
\(163\) | −9.05127 | −0.708950 | −0.354475 | − | 0.935065i | \(-0.615340\pi\) | ||||
−0.354475 | + | 0.935065i | \(0.615340\pi\) | |||||||
\(164\) | −33.1113 | −2.58556 | ||||||||
\(165\) | 1.87680 | 0.146108 | ||||||||
\(166\) | 26.5710 | 2.06231 | ||||||||
\(167\) | 2.65761 | 0.205652 | 0.102826 | − | 0.994699i | \(-0.467212\pi\) | ||||
0.102826 | + | 0.994699i | \(0.467212\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.04242 | 0.310039 | ||||||||
\(171\) | −0.0393270 | −0.00300741 | ||||||||
\(172\) | 30.6234 | 2.33501 | ||||||||
\(173\) | 19.5870 | 1.48918 | 0.744588 | − | 0.667525i | \(-0.232646\pi\) | ||||
0.744588 | + | 0.667525i | \(0.232646\pi\) | |||||||
\(174\) | 4.61423 | 0.349804 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.470856 | 0.0354921 | ||||||||
\(177\) | 2.41807 | 0.181754 | ||||||||
\(178\) | −40.3330 | −3.02309 | ||||||||
\(179\) | −2.89332 | −0.216257 | −0.108129 | − | 0.994137i | \(-0.534486\pi\) | ||||
−0.108129 | + | 0.994137i | \(0.534486\pi\) | |||||||
\(180\) | 2.32205 | 0.173076 | ||||||||
\(181\) | 1.36804 | 0.101686 | 0.0508429 | − | 0.998707i | \(-0.483809\pi\) | ||||
0.0508429 | + | 0.998707i | \(0.483809\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.66245 | −0.492503 | ||||||||
\(184\) | 23.5018 | 1.73258 | ||||||||
\(185\) | 5.67871 | 0.417507 | ||||||||
\(186\) | −26.6768 | −1.95604 | ||||||||
\(187\) | 3.11415 | 0.227729 | ||||||||
\(188\) | −1.18986 | −0.0867794 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0925559 | 0.00671471 | ||||||||
\(191\) | −1.51325 | −0.109495 | −0.0547475 | − | 0.998500i | \(-0.517435\pi\) | ||||
−0.0547475 | + | 0.998500i | \(0.517435\pi\) | |||||||
\(192\) | 18.8758 | 1.36225 | ||||||||
\(193\) | −6.95394 | −0.500556 | −0.250278 | − | 0.968174i | \(-0.580522\pi\) | ||||
−0.250278 | + | 0.968174i | \(0.580522\pi\) | |||||||
\(194\) | 0.981719 | 0.0704834 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4772 | −1.10271 | −0.551353 | − | 0.834272i | \(-0.685888\pi\) | ||||
−0.551353 | + | 0.834272i | \(0.685888\pi\) | |||||||
\(198\) | 2.87133 | 0.204056 | ||||||||
\(199\) | 6.61529 | 0.468945 | 0.234473 | − | 0.972123i | \(-0.424664\pi\) | ||||
0.234473 | + | 0.972123i | \(0.424664\pi\) | |||||||
\(200\) | 12.8713 | 0.910140 | ||||||||
\(201\) | −3.00958 | −0.212279 | ||||||||
\(202\) | −22.2725 | −1.56709 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.0867 | −0.706211 | ||||||||
\(205\) | 8.48854 | 0.592865 | ||||||||
\(206\) | 22.9825 | 1.60127 | ||||||||
\(207\) | 6.48333 | 0.450622 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0713021 | 0.00493207 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.09428 | −0.557234 | −0.278617 | − | 0.960402i | \(-0.589876\pi\) | ||||
−0.278617 | + | 0.960402i | \(0.589876\pi\) | |||||||
\(212\) | 8.96264 | 0.615557 | ||||||||
\(213\) | 20.9423 | 1.43494 | ||||||||
\(214\) | −22.7153 | −1.55279 | ||||||||
\(215\) | −7.85072 | −0.535415 | ||||||||
\(216\) | −16.9584 | −1.15387 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 26.7306 | 1.81042 | ||||||||
\(219\) | 9.96212 | 0.673178 | ||||||||
\(220\) | −4.21002 | −0.283840 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −22.7442 | −1.52649 | ||||||||
\(223\) | 16.0581 | 1.07533 | 0.537664 | − | 0.843159i | \(-0.319307\pi\) | ||||
0.537664 | + | 0.843159i | \(0.319307\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.55075 | 0.236716 | ||||||||
\(226\) | 8.00979 | 0.532804 | ||||||||
\(227\) | −1.29581 | −0.0860057 | −0.0430029 | − | 0.999075i | \(-0.513692\pi\) | ||||
−0.0430029 | + | 0.999075i | \(0.513692\pi\) | |||||||
\(228\) | −0.230947 | −0.0152948 | ||||||||
\(229\) | 20.8175 | 1.37566 | 0.687831 | − | 0.725871i | \(-0.258563\pi\) | ||||
0.687831 | + | 0.725871i | \(0.258563\pi\) | |||||||
\(230\) | −15.2585 | −1.00612 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.08707 | −0.268330 | ||||||||
\(233\) | −13.3043 | −0.871591 | −0.435796 | − | 0.900046i | \(-0.643533\pi\) | ||||
−0.435796 | + | 0.900046i | \(0.643533\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.305037 | 0.0198984 | ||||||||
\(236\) | −5.42421 | −0.353086 | ||||||||
\(237\) | −17.1780 | −1.11583 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3652 | −0.864525 | −0.432263 | − | 0.901748i | \(-0.642285\pi\) | ||||
−0.432263 | + | 0.901748i | \(0.642285\pi\) | |||||||
\(240\) | 0.390981 | 0.0252377 | ||||||||
\(241\) | 0.834153 | 0.0537325 | 0.0268663 | − | 0.999639i | \(-0.491447\pi\) | ||||
0.0268663 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(242\) | 20.1300 | 1.29401 | ||||||||
\(243\) | −8.34339 | −0.535229 | ||||||||
\(244\) | 14.9452 | 0.956767 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −33.9980 | −2.16763 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 23.6291 | 1.50045 | ||||||||
\(249\) | 16.9970 | 1.07714 | ||||||||
\(250\) | −18.1144 | −1.14565 | ||||||||
\(251\) | 27.2721 | 1.72140 | 0.860699 | − | 0.509114i | \(-0.170027\pi\) | ||||
0.860699 | + | 0.509114i | \(0.170027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.7547 | −0.739009 | ||||||||
\(254\) | 36.1609 | 2.26894 | ||||||||
\(255\) | 2.58587 | 0.161933 | ||||||||
\(256\) | −17.9721 | −1.12326 | ||||||||
\(257\) | 6.55188 | 0.408695 | 0.204348 | − | 0.978898i | \(-0.434493\pi\) | ||||
0.204348 | + | 0.978898i | \(0.434493\pi\) | |||||||
\(258\) | 31.4434 | 1.95758 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.12748 | −0.0697893 | ||||||||
\(262\) | 5.86221 | 0.362168 | ||||||||
\(263\) | −22.5891 | −1.39290 | −0.696450 | − | 0.717605i | \(-0.745238\pi\) | ||||
−0.696450 | + | 0.717605i | \(0.745238\pi\) | |||||||
\(264\) | 6.65811 | 0.409779 | ||||||||
\(265\) | −2.29770 | −0.141146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.8003 | −1.57896 | ||||||||
\(268\) | 6.75107 | 0.412387 | ||||||||
\(269\) | 16.0013 | 0.975617 | 0.487808 | − | 0.872951i | \(-0.337797\pi\) | ||||
0.487808 | + | 0.872951i | \(0.337797\pi\) | |||||||
\(270\) | 11.0102 | 0.670059 | ||||||||
\(271\) | −8.75935 | −0.532093 | −0.266046 | − | 0.963960i | \(-0.585717\pi\) | ||||
−0.266046 | + | 0.963960i | \(0.585717\pi\) | |||||||
\(272\) | 0.648750 | 0.0393363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29496 | −0.259468 | ||||||||
\(275\) | −6.43771 | −0.388209 | ||||||||
\(276\) | 38.0733 | 2.29174 | ||||||||
\(277\) | −19.9183 | −1.19677 | −0.598387 | − | 0.801208i | \(-0.704191\pi\) | ||||
−0.598387 | + | 0.801208i | \(0.704191\pi\) | |||||||
\(278\) | −35.9522 | −2.15627 | ||||||||
\(279\) | 6.51844 | 0.390249 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0234 | −0.836566 | −0.418283 | − | 0.908317i | \(-0.637368\pi\) | ||||
−0.418283 | + | 0.908317i | \(0.637368\pi\) | |||||||
\(282\) | −1.22172 | −0.0727525 | ||||||||
\(283\) | 1.01259 | 0.0601922 | 0.0300961 | − | 0.999547i | \(-0.490419\pi\) | ||||
0.0300961 | + | 0.999547i | \(0.490419\pi\) | |||||||
\(284\) | −46.9776 | −2.78761 | ||||||||
\(285\) | 0.0592065 | 0.00350709 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.38678 | −0.258493 | ||||||||
\(289\) | −12.7093 | −0.747606 | ||||||||
\(290\) | 2.65352 | 0.155820 | ||||||||
\(291\) | 0.627989 | 0.0368134 | ||||||||
\(292\) | −22.3470 | −1.30776 | ||||||||
\(293\) | −0.199235 | −0.0116394 | −0.00581972 | − | 0.999983i | \(-0.501852\pi\) | ||||
−0.00581972 | + | 0.999983i | \(0.501852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.39057 | 0.0809622 | ||||||||
\(296\) | 20.1458 | 1.17095 | ||||||||
\(297\) | 8.48190 | 0.492170 | ||||||||
\(298\) | −14.6571 | −0.849065 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 20.8517 | 1.20387 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.52958 | 0.0880177 | ||||||||
\(303\) | −14.2474 | −0.818489 | ||||||||
\(304\) | 0.0148539 | 0.000851930 0 | ||||||||
\(305\) | −3.83140 | −0.219386 | ||||||||
\(306\) | 3.95614 | 0.226157 | ||||||||
\(307\) | −27.2004 | −1.55241 | −0.776204 | − | 0.630482i | \(-0.782857\pi\) | ||||
−0.776204 | + | 0.630482i | \(0.782857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7015 | 0.836341 | ||||||||
\(310\) | −15.3411 | −0.871318 | ||||||||
\(311\) | 27.1009 | 1.53675 | 0.768376 | − | 0.639999i | \(-0.221065\pi\) | ||||
0.768376 | + | 0.639999i | \(0.221065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0785 | −1.24795 | −0.623975 | − | 0.781445i | \(-0.714483\pi\) | ||||
−0.623975 | + | 0.781445i | \(0.714483\pi\) | |||||||
\(314\) | 38.1789 | 2.15456 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 38.5336 | 2.16768 | ||||||||
\(317\) | 7.06823 | 0.396991 | 0.198496 | − | 0.980102i | \(-0.436394\pi\) | ||||
0.198496 | + | 0.980102i | \(0.436394\pi\) | |||||||
\(318\) | 9.20265 | 0.516059 | ||||||||
\(319\) | 2.04419 | 0.114453 | ||||||||
\(320\) | 10.8550 | 0.606813 | ||||||||
\(321\) | −14.5306 | −0.811020 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0982407 | 0.00546626 | ||||||||
\(324\) | −19.2512 | −1.06951 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.8475 | 1.15464 | ||||||||
\(327\) | 17.0991 | 0.945582 | ||||||||
\(328\) | 30.1139 | 1.66276 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.32276 | −0.237960 | ||||||||
\(331\) | 6.58858 | 0.362141 | 0.181071 | − | 0.983470i | \(-0.442044\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(332\) | −38.1277 | −2.09253 | ||||||||
\(333\) | 5.55751 | 0.304550 | ||||||||
\(334\) | −6.12118 | −0.334936 | ||||||||
\(335\) | −1.73073 | −0.0945599 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.22290 | 0.230036 | 0.115018 | − | 0.993363i | \(-0.463307\pi\) | ||||
0.115018 | + | 0.993363i | \(0.463307\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.12373 | 0.278283 | ||||||||
\(340\) | −5.80061 | −0.314582 | ||||||||
\(341\) | −11.8183 | −0.639998 | ||||||||
\(342\) | 0.0905805 | 0.00489803 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −27.8512 | −1.50163 | ||||||||
\(345\) | −9.76060 | −0.525493 | ||||||||
\(346\) | −45.1142 | −2.42535 | ||||||||
\(347\) | −9.09478 | −0.488233 | −0.244117 | − | 0.969746i | \(-0.578498\pi\) | ||||
−0.244117 | + | 0.969746i | \(0.578498\pi\) | |||||||
\(348\) | −6.62111 | −0.354929 | ||||||||
\(349\) | −9.22053 | −0.493564 | −0.246782 | − | 0.969071i | \(-0.579373\pi\) | ||||
−0.246782 | + | 0.969071i | \(0.579373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.95349 | 0.423922 | ||||||||
\(353\) | −2.15449 | −0.114672 | −0.0573359 | − | 0.998355i | \(-0.518261\pi\) | ||||
−0.0573359 | + | 0.998355i | \(0.518261\pi\) | |||||||
\(354\) | −5.56947 | −0.296014 | ||||||||
\(355\) | 12.0433 | 0.639195 | ||||||||
\(356\) | 57.8752 | 3.06738 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.66410 | 0.352208 | ||||||||
\(359\) | −8.55756 | −0.451651 | −0.225825 | − | 0.974168i | \(-0.572508\pi\) | ||||
−0.225825 | + | 0.974168i | \(0.572508\pi\) | |||||||
\(360\) | −2.11185 | −0.111304 | ||||||||
\(361\) | −18.9978 | −0.999882 | ||||||||
\(362\) | −3.15096 | −0.165611 | ||||||||
\(363\) | 12.8769 | 0.675860 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.72896 | 0.299867 | ||||||||
\(366\) | 15.3454 | 0.802117 | ||||||||
\(367\) | 2.29823 | 0.119967 | 0.0599833 | − | 0.998199i | \(-0.480895\pi\) | ||||
0.0599833 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(368\) | −2.44877 | −0.127651 | ||||||||
\(369\) | 8.30736 | 0.432464 | ||||||||
\(370\) | −13.0796 | −0.679975 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 38.2795 | 1.98470 | ||||||||
\(373\) | 11.7684 | 0.609343 | 0.304672 | − | 0.952457i | \(-0.401453\pi\) | ||||
0.304672 | + | 0.952457i | \(0.401453\pi\) | |||||||
\(374\) | −7.17271 | −0.370892 | ||||||||
\(375\) | −11.5875 | −0.598374 | ||||||||
\(376\) | 1.08215 | 0.0558074 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.99093 | −0.410466 | −0.205233 | − | 0.978713i | \(-0.565795\pi\) | ||||
−0.205233 | + | 0.978713i | \(0.565795\pi\) | |||||||
\(380\) | −0.132812 | −0.00681310 | ||||||||
\(381\) | 23.1315 | 1.18506 | ||||||||
\(382\) | 3.48542 | 0.178329 | ||||||||
\(383\) | −28.2446 | −1.44323 | −0.721616 | − | 0.692294i | \(-0.756600\pi\) | ||||
−0.721616 | + | 0.692294i | \(0.756600\pi\) | |||||||
\(384\) | −27.8870 | −1.42310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0168 | 0.815233 | ||||||||
\(387\) | −7.68316 | −0.390557 | ||||||||
\(388\) | −1.40870 | −0.0715161 | ||||||||
\(389\) | 7.68086 | 0.389435 | 0.194717 | − | 0.980859i | \(-0.437621\pi\) | ||||
0.194717 | + | 0.980859i | \(0.437621\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1957 | −0.819050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.74996 | 0.189160 | ||||||||
\(394\) | 35.6481 | 1.79593 | ||||||||
\(395\) | −9.87862 | −0.497047 | ||||||||
\(396\) | −4.12017 | −0.207046 | ||||||||
\(397\) | −7.45281 | −0.374046 | −0.187023 | − | 0.982356i | \(-0.559884\pi\) | ||||
−0.187023 | + | 0.982356i | \(0.559884\pi\) | |||||||
\(398\) | −15.2368 | −0.763750 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.34113 | −0.0670563 | ||||||||
\(401\) | −18.1982 | −0.908777 | −0.454389 | − | 0.890804i | \(-0.650142\pi\) | ||||
−0.454389 | + | 0.890804i | \(0.650142\pi\) | |||||||
\(402\) | 6.93186 | 0.345730 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 31.9596 | 1.59005 | ||||||||
\(405\) | 4.93530 | 0.245237 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0761 | −0.499453 | ||||||||
\(408\) | 9.17361 | 0.454161 | ||||||||
\(409\) | −29.2825 | −1.44793 | −0.723964 | − | 0.689838i | \(-0.757682\pi\) | ||||
−0.723964 | + | 0.689838i | \(0.757682\pi\) | |||||||
\(410\) | −19.5514 | −0.965573 | ||||||||
\(411\) | −2.74741 | −0.135520 | ||||||||
\(412\) | −32.9784 | −1.62473 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −14.9328 | −0.733909 | ||||||||
\(415\) | 9.77456 | 0.479814 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.9980 | −1.12622 | ||||||||
\(418\) | −0.164228 | −0.00803264 | ||||||||
\(419\) | −20.7393 | −1.01318 | −0.506591 | − | 0.862187i | \(-0.669095\pi\) | ||||
−0.506591 | + | 0.862187i | \(0.669095\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.8696 | 1.21207 | 0.606036 | − | 0.795437i | \(-0.292759\pi\) | ||||
0.606036 | + | 0.795437i | \(0.292759\pi\) | |||||||
\(422\) | 18.6433 | 0.907541 | ||||||||
\(423\) | 0.298526 | 0.0145148 | ||||||||
\(424\) | −8.15130 | −0.395862 | ||||||||
\(425\) | −8.86994 | −0.430255 | ||||||||
\(426\) | −48.2356 | −2.33702 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 32.5950 | 1.57554 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.0823 | 0.872006 | ||||||||
\(431\) | 21.1688 | 1.01966 | 0.509832 | − | 0.860274i | \(-0.329708\pi\) | ||||
0.509832 | + | 0.860274i | \(0.329708\pi\) | |||||||
\(432\) | 1.76698 | 0.0850138 | ||||||||
\(433\) | −23.4296 | −1.12595 | −0.562977 | − | 0.826472i | \(-0.690344\pi\) | ||||
−0.562977 | + | 0.826472i | \(0.690344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.69741 | 0.0813848 | ||||||||
\(436\) | −38.3566 | −1.83695 | ||||||||
\(437\) | −0.370819 | −0.0177387 | ||||||||
\(438\) | −22.9454 | −1.09637 | ||||||||
\(439\) | −12.0384 | −0.574561 | −0.287280 | − | 0.957847i | \(-0.592751\pi\) | ||||
−0.287280 | + | 0.957847i | \(0.592751\pi\) | |||||||
\(440\) | 3.82891 | 0.182536 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.7331 | 0.747503 | 0.373752 | − | 0.927529i | \(-0.378071\pi\) | ||||
0.373752 | + | 0.927529i | \(0.378071\pi\) | |||||||
\(444\) | 32.6364 | 1.54885 | ||||||||
\(445\) | −14.8371 | −0.703346 | ||||||||
\(446\) | −36.9860 | −1.75134 | ||||||||
\(447\) | −9.37592 | −0.443466 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.0012 | 1.22707 | 0.613536 | − | 0.789667i | \(-0.289747\pi\) | ||||
0.613536 | + | 0.789667i | \(0.289747\pi\) | |||||||
\(450\) | −8.17832 | −0.385530 | ||||||||
\(451\) | −15.0617 | −0.709230 | ||||||||
\(452\) | −11.4935 | −0.540610 | ||||||||
\(453\) | 0.978449 | 0.0459716 | ||||||||
\(454\) | 2.98459 | 0.140074 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.210041 | 0.00983605 | ||||||||
\(457\) | −30.7958 | −1.44057 | −0.720284 | − | 0.693679i | \(-0.755989\pi\) | ||||
−0.720284 | + | 0.693679i | \(0.755989\pi\) | |||||||
\(458\) | −47.9483 | −2.24048 | ||||||||
\(459\) | 11.6864 | 0.545476 | ||||||||
\(460\) | 21.8949 | 1.02086 | ||||||||
\(461\) | 34.0958 | 1.58800 | 0.794000 | − | 0.607918i | \(-0.207995\pi\) | ||||
0.794000 | + | 0.607918i | \(0.207995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.69184 | 0.0786263 | 0.0393131 | − | 0.999227i | \(-0.487483\pi\) | ||||
0.0393131 | + | 0.999227i | \(0.487483\pi\) | |||||||
\(464\) | 0.425852 | 0.0197697 | ||||||||
\(465\) | −9.81347 | −0.455089 | ||||||||
\(466\) | 30.6433 | 1.41952 | ||||||||
\(467\) | 28.3524 | 1.31199 | 0.655996 | − | 0.754764i | \(-0.272249\pi\) | ||||
0.655996 | + | 0.754764i | \(0.272249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.702581 | −0.0324076 | ||||||||
\(471\) | 24.4224 | 1.12532 | ||||||||
\(472\) | 4.93318 | 0.227068 | ||||||||
\(473\) | 13.9300 | 0.640503 | ||||||||
\(474\) | 39.5655 | 1.81730 | ||||||||
\(475\) | −0.203088 | −0.00931830 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.24866 | −0.102959 | ||||||||
\(478\) | 30.7837 | 1.40801 | ||||||||
\(479\) | 6.28246 | 0.287053 | 0.143526 | − | 0.989646i | \(-0.454156\pi\) | ||||
0.143526 | + | 0.989646i | \(0.454156\pi\) | |||||||
\(480\) | 6.60426 | 0.301442 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.92128 | −0.0875117 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28.8853 | −1.31297 | ||||||||
\(485\) | 0.361140 | 0.0163985 | ||||||||
\(486\) | 19.2171 | 0.871703 | ||||||||
\(487\) | −13.0176 | −0.589883 | −0.294942 | − | 0.955515i | \(-0.595300\pi\) | ||||
−0.294942 | + | 0.955515i | \(0.595300\pi\) | |||||||
\(488\) | −13.5923 | −0.615293 | ||||||||
\(489\) | 13.3358 | 0.603065 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.3523 | −0.557453 | −0.278726 | − | 0.960371i | \(-0.589912\pi\) | ||||
−0.278726 | + | 0.960371i | \(0.589912\pi\) | |||||||
\(492\) | 48.7849 | 2.19939 | ||||||||
\(493\) | 2.81650 | 0.126849 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.05626 | 0.0474754 | ||||||||
\(496\) | −2.46203 | −0.110549 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −39.1487 | −1.75430 | ||||||||
\(499\) | −9.15340 | −0.409763 | −0.204881 | − | 0.978787i | \(-0.565681\pi\) | ||||
−0.204881 | + | 0.978787i | \(0.565681\pi\) | |||||||
\(500\) | 25.9929 | 1.16244 | ||||||||
\(501\) | −3.91562 | −0.174937 | ||||||||
\(502\) | −62.8149 | −2.80357 | ||||||||
\(503\) | 22.5037 | 1.00339 | 0.501696 | − | 0.865044i | \(-0.332710\pi\) | ||||
0.501696 | + | 0.865044i | \(0.332710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.19329 | −0.364596 | ||||||||
\(506\) | 27.0741 | 1.20359 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −51.8885 | −2.30218 | ||||||||
\(509\) | 38.6606 | 1.71360 | 0.856800 | − | 0.515649i | \(-0.172449\pi\) | ||||
0.856800 | + | 0.515649i | \(0.172449\pi\) | |||||||
\(510\) | −5.95594 | −0.263734 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.53972 | 0.156435 | ||||||||
\(513\) | 0.267575 | 0.0118137 | ||||||||
\(514\) | −15.0907 | −0.665623 | ||||||||
\(515\) | 8.45447 | 0.372549 | ||||||||
\(516\) | −45.1193 | −1.98626 | ||||||||
\(517\) | −0.541245 | −0.0238039 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.8588 | −1.26676 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.2351 | 1.76273 | 0.881366 | − | 0.472434i | \(-0.156625\pi\) | ||||
0.881366 | + | 0.472434i | \(0.156625\pi\) | |||||||
\(522\) | 2.59689 | 0.113663 | ||||||||
\(523\) | −0.732146 | −0.0320145 | −0.0160073 | − | 0.999872i | \(-0.505095\pi\) | ||||
−0.0160073 | + | 0.999872i | \(0.505095\pi\) | |||||||
\(524\) | −8.41189 | −0.367475 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 52.0286 | 2.26856 | ||||||||
\(527\) | −16.2834 | −0.709316 | ||||||||
\(528\) | −0.693741 | −0.0301912 | ||||||||
\(529\) | 38.1321 | 1.65792 | ||||||||
\(530\) | 5.29221 | 0.229879 | ||||||||
\(531\) | 1.36089 | 0.0590577 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 59.4251 | 2.57157 | ||||||||
\(535\) | −8.35618 | −0.361269 | ||||||||
\(536\) | −6.13993 | −0.265204 | ||||||||
\(537\) | 4.26291 | 0.183958 | ||||||||
\(538\) | −36.8553 | −1.58894 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −15.7989 | −0.679877 | ||||||||
\(541\) | −23.6537 | −1.01695 | −0.508476 | − | 0.861076i | \(-0.669791\pi\) | ||||
−0.508476 | + | 0.861076i | \(0.669791\pi\) | |||||||
\(542\) | 20.1751 | 0.866595 | ||||||||
\(543\) | −2.01562 | −0.0864985 | ||||||||
\(544\) | 10.9584 | 0.469837 | ||||||||
\(545\) | 9.83325 | 0.421210 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9472 | −0.553582 | −0.276791 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276791 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(548\) | 6.16298 | 0.263270 | ||||||||
\(549\) | −3.74963 | −0.160030 | ||||||||
\(550\) | 14.8278 | 0.632258 | ||||||||
\(551\) | 0.0644871 | 0.00274724 | ||||||||
\(552\) | −34.6267 | −1.47381 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 45.8771 | 1.94913 | ||||||||
\(555\) | −8.36679 | −0.355150 | ||||||||
\(556\) | 51.5891 | 2.18787 | ||||||||
\(557\) | 6.40680 | 0.271465 | 0.135732 | − | 0.990746i | \(-0.456661\pi\) | ||||
0.135732 | + | 0.990746i | \(0.456661\pi\) | |||||||
\(558\) | −15.0137 | −0.635581 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.58827 | −0.193717 | ||||||||
\(562\) | 32.2996 | 1.36248 | ||||||||
\(563\) | 7.32084 | 0.308537 | 0.154268 | − | 0.988029i | \(-0.450698\pi\) | ||||
0.154268 | + | 0.988029i | \(0.450698\pi\) | |||||||
\(564\) | 1.75309 | 0.0738185 | ||||||||
\(565\) | 2.94652 | 0.123961 | ||||||||
\(566\) | −2.33226 | −0.0980324 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.7249 | 1.79270 | ||||||||
\(569\) | −4.31743 | −0.180996 | −0.0904981 | − | 0.995897i | \(-0.528846\pi\) | ||||
−0.0904981 | + | 0.995897i | \(0.528846\pi\) | |||||||
\(570\) | −0.136368 | −0.00571184 | ||||||||
\(571\) | 34.1695 | 1.42995 | 0.714974 | − | 0.699152i | \(-0.246439\pi\) | ||||
0.714974 | + | 0.699152i | \(0.246439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.22956 | 0.0931413 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.4804 | 1.39623 | ||||||||
\(576\) | 10.6233 | 0.442639 | ||||||||
\(577\) | −6.35656 | −0.264627 | −0.132314 | − | 0.991208i | \(-0.542241\pi\) | ||||
−0.132314 | + | 0.991208i | \(0.542241\pi\) | |||||||
\(578\) | 29.2729 | 1.21759 | ||||||||
\(579\) | 10.2457 | 0.425795 | ||||||||
\(580\) | −3.80763 | −0.158103 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.44643 | −0.0599563 | ||||||||
\(583\) | 4.07695 | 0.168850 | ||||||||
\(584\) | 20.3240 | 0.841014 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.458892 | 0.0189566 | ||||||||
\(587\) | 31.4120 | 1.29651 | 0.648256 | − | 0.761422i | \(-0.275499\pi\) | ||||
0.648256 | + | 0.761422i | \(0.275499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.372827 | −0.0153621 | ||||||||
\(590\) | −3.20286 | −0.131860 | ||||||||
\(591\) | 22.8035 | 0.938011 | ||||||||
\(592\) | −2.09909 | −0.0862719 | ||||||||
\(593\) | 0.473013 | 0.0194243 | 0.00971215 | − | 0.999953i | \(-0.496908\pi\) | ||||
0.00971215 | + | 0.999953i | \(0.496908\pi\) | |||||||
\(594\) | −19.5361 | −0.801575 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.0320 | 0.861505 | ||||||||
\(597\) | −9.74670 | −0.398906 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.62695 | −0.393347 | −0.196673 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196673 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(600\) | −18.9641 | −0.774207 | ||||||||
\(601\) | −41.0799 | −1.67568 | −0.837842 | − | 0.545914i | \(-0.816183\pi\) | ||||
−0.837842 | + | 0.545914i | \(0.816183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.69379 | −0.0689765 | ||||||||
\(604\) | −2.19485 | −0.0893073 | ||||||||
\(605\) | 7.40514 | 0.301062 | ||||||||
\(606\) | 32.8155 | 1.33304 | ||||||||
\(607\) | 19.0858 | 0.774668 | 0.387334 | − | 0.921939i | \(-0.373396\pi\) | ||||
0.387334 | + | 0.921939i | \(0.373396\pi\) | |||||||
\(608\) | 0.250905 | 0.0101755 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.82474 | 0.357303 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.67680 | −0.229471 | ||||||||
\(613\) | 38.0048 | 1.53500 | 0.767500 | − | 0.641049i | \(-0.221501\pi\) | ||||
0.767500 | + | 0.641049i | \(0.221501\pi\) | |||||||
\(614\) | 62.6498 | 2.52834 | ||||||||
\(615\) | −12.5067 | −0.504318 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.31519 | −0.334757 | −0.167378 | − | 0.985893i | \(-0.553530\pi\) | ||||
−0.167378 | + | 0.985893i | \(0.553530\pi\) | |||||||
\(618\) | −33.8616 | −1.36211 | ||||||||
\(619\) | 44.4728 | 1.78751 | 0.893756 | − | 0.448553i | \(-0.148060\pi\) | ||||
0.893756 | + | 0.448553i | \(0.148060\pi\) | |||||||
\(620\) | 22.0135 | 0.884085 | ||||||||
\(621\) | −44.1116 | −1.77014 | ||||||||
\(622\) | −62.4206 | −2.50284 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.7468 | 0.589874 | ||||||||
\(626\) | 50.8526 | 2.03248 | ||||||||
\(627\) | −0.105054 | −0.00419544 | ||||||||
\(628\) | −54.7842 | −2.18613 | ||||||||
\(629\) | −13.8829 | −0.553549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.7524 | −0.467858 | −0.233929 | − | 0.972254i | \(-0.575158\pi\) | ||||
−0.233929 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(632\) | −35.0453 | −1.39403 | ||||||||
\(633\) | 11.9258 | 0.474008 | ||||||||
\(634\) | −16.2800 | −0.646562 | ||||||||
\(635\) | 13.3023 | 0.527887 | ||||||||
\(636\) | −13.2052 | −0.523620 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.70831 | −0.186404 | ||||||||
\(639\) | 11.7863 | 0.466259 | ||||||||
\(640\) | −16.0371 | −0.633921 | ||||||||
\(641\) | 10.4868 | 0.414205 | 0.207102 | − | 0.978319i | \(-0.433597\pi\) | ||||
0.207102 | + | 0.978319i | \(0.433597\pi\) | |||||||
\(642\) | 33.4679 | 1.32087 | ||||||||
\(643\) | −31.2822 | −1.23365 | −0.616825 | − | 0.787101i | \(-0.711581\pi\) | ||||
−0.616825 | + | 0.787101i | \(0.711581\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5669 | 0.455448 | ||||||||
\(646\) | −0.226275 | −0.00890265 | ||||||||
\(647\) | −26.8675 | −1.05627 | −0.528135 | − | 0.849160i | \(-0.677109\pi\) | ||||
−0.528135 | + | 0.849160i | \(0.677109\pi\) | |||||||
\(648\) | 17.5084 | 0.687796 | ||||||||
\(649\) | −2.46738 | −0.0968530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.9148 | −1.17155 | ||||||||
\(653\) | −4.14161 | −0.162074 | −0.0810369 | − | 0.996711i | \(-0.525823\pi\) | ||||
−0.0810369 | + | 0.996711i | \(0.525823\pi\) | |||||||
\(654\) | −39.3838 | −1.54003 | ||||||||
\(655\) | 2.15650 | 0.0842615 | ||||||||
\(656\) | −3.13771 | −0.122507 | ||||||||
\(657\) | 5.60668 | 0.218738 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.4551 | 0.835773 | 0.417887 | − | 0.908499i | \(-0.362771\pi\) | ||||
0.417887 | + | 0.908499i | \(0.362771\pi\) | |||||||
\(660\) | 6.20288 | 0.241447 | ||||||||
\(661\) | −42.3872 | −1.64867 | −0.824335 | − | 0.566102i | \(-0.808451\pi\) | ||||
−0.824335 | + | 0.566102i | \(0.808451\pi\) | |||||||
\(662\) | −15.1753 | −0.589803 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 34.6762 | 1.34570 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.8004 | −0.496006 | ||||||||
\(667\) | −10.6312 | −0.411640 | ||||||||
\(668\) | 8.78349 | 0.339844 | ||||||||
\(669\) | −23.6593 | −0.914722 | ||||||||
\(670\) | 3.98633 | 0.154005 | ||||||||
\(671\) | 6.79830 | 0.262445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.5856 | −1.14044 | −0.570220 | − | 0.821492i | \(-0.693142\pi\) | ||||
−0.570220 | + | 0.821492i | \(0.693142\pi\) | |||||||
\(674\) | −9.72645 | −0.374649 | ||||||||
\(675\) | −24.1588 | −0.929871 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.1659 | 1.23624 | 0.618118 | − | 0.786085i | \(-0.287895\pi\) | ||||
0.618118 | + | 0.786085i | \(0.287895\pi\) | |||||||
\(678\) | −11.8013 | −0.453227 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.27551 | 0.202306 | ||||||||
\(681\) | 1.90919 | 0.0731604 | ||||||||
\(682\) | 27.2207 | 1.04234 | ||||||||
\(683\) | 8.60236 | 0.329160 | 0.164580 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164580 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(684\) | −0.129977 | −0.00496980 | ||||||||
\(685\) | −1.57997 | −0.0603674 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.6717 | −1.17020 | ||||||||
\(688\) | 2.90195 | 0.110636 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 22.4813 | 0.855847 | ||||||||
\(691\) | −20.4420 | −0.777651 | −0.388826 | − | 0.921311i | \(-0.627119\pi\) | ||||
−0.388826 | + | 0.921311i | \(0.627119\pi\) | |||||||
\(692\) | 64.7359 | 2.46089 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.9477 | 0.795164 | ||||||||
\(695\) | −13.2256 | −0.501675 | ||||||||
\(696\) | 6.02174 | 0.228253 | ||||||||
\(697\) | −20.7522 | −0.786046 | ||||||||
\(698\) | 21.2373 | 0.803845 | ||||||||
\(699\) | 19.6020 | 0.741415 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1373 | 0.949422 | 0.474711 | − | 0.880142i | \(-0.342553\pi\) | ||||
0.474711 | + | 0.880142i | \(0.342553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.317866 | −0.0119885 | ||||||||
\(704\) | −19.2607 | −0.725915 | ||||||||
\(705\) | −0.449429 | −0.0169265 | ||||||||
\(706\) | 4.96236 | 0.186761 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.99182 | 0.300351 | ||||||||
\(709\) | 29.4929 | 1.10763 | 0.553814 | − | 0.832640i | \(-0.313172\pi\) | ||||
0.553814 | + | 0.832640i | \(0.313172\pi\) | |||||||
\(710\) | −27.7390 | −1.04103 | ||||||||
\(711\) | −9.66777 | −0.362570 | ||||||||
\(712\) | −52.6360 | −1.97262 | ||||||||
\(713\) | 61.4632 | 2.30182 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.56254 | −0.357369 | ||||||||
\(717\) | 19.6918 | 0.735404 | ||||||||
\(718\) | 19.7104 | 0.735584 | ||||||||
\(719\) | −8.33153 | −0.310713 | −0.155357 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155357 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(720\) | 0.220044 | 0.00820055 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 43.7569 | 1.62846 | ||||||||
\(723\) | −1.22901 | −0.0457073 | ||||||||
\(724\) | 4.52143 | 0.168038 | ||||||||
\(725\) | −5.82240 | −0.216239 | ||||||||
\(726\) | −29.6588 | −1.10074 | ||||||||
\(727\) | −9.66141 | −0.358322 | −0.179161 | − | 0.983820i | \(-0.557338\pi\) | ||||
−0.179161 | + | 0.983820i | \(0.557338\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7672 | 1.10249 | ||||||||
\(730\) | −13.1953 | −0.488381 | ||||||||
\(731\) | 19.1929 | 0.709875 | ||||||||
\(732\) | −22.0197 | −0.813870 | ||||||||
\(733\) | 14.0179 | 0.517762 | 0.258881 | − | 0.965909i | \(-0.416646\pi\) | ||||
0.258881 | + | 0.965909i | \(0.416646\pi\) | |||||||
\(734\) | −5.29344 | −0.195384 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41.3635 | −1.52468 | ||||||||
\(737\) | 3.07094 | 0.113120 | ||||||||
\(738\) | −19.1341 | −0.704335 | ||||||||
\(739\) | 38.8147 | 1.42782 | 0.713910 | − | 0.700237i | \(-0.246923\pi\) | ||||
0.713910 | + | 0.700237i | \(0.246923\pi\) | |||||||
\(740\) | 18.7683 | 0.689938 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.3942 | 1.26180 | 0.630901 | − | 0.775863i | \(-0.282685\pi\) | ||||
0.630901 | + | 0.775863i | \(0.282685\pi\) | |||||||
\(744\) | −34.8142 | −1.27635 | ||||||||
\(745\) | −5.39185 | −0.197542 | ||||||||
\(746\) | −27.1057 | −0.992410 | ||||||||
\(747\) | 9.56594 | 0.349999 | ||||||||
\(748\) | 10.2924 | 0.376327 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 26.6890 | 0.974545 | ||||||||
\(751\) | 48.1470 | 1.75691 | 0.878454 | − | 0.477827i | \(-0.158575\pi\) | ||||
0.878454 | + | 0.477827i | \(0.158575\pi\) | |||||||
\(752\) | −0.112754 | −0.00411172 | ||||||||
\(753\) | −40.1816 | −1.46430 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.562681 | 0.0204781 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.90638 | −0.251016 | −0.125508 | − | 0.992093i | \(-0.540056\pi\) | ||||
−0.125508 | + | 0.992093i | \(0.540056\pi\) | |||||||
\(758\) | 18.4052 | 0.668508 | ||||||||
\(759\) | 17.3188 | 0.628634 | ||||||||
\(760\) | 0.120789 | 0.00438147 | ||||||||
\(761\) | 31.9730 | 1.15902 | 0.579511 | − | 0.814965i | \(-0.303244\pi\) | ||||
0.579511 | + | 0.814965i | \(0.303244\pi\) | |||||||
\(762\) | −53.2781 | −1.93006 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.00135 | −0.180942 | ||||||||
\(765\) | 1.45533 | 0.0526174 | ||||||||
\(766\) | 65.0548 | 2.35053 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 26.4795 | 0.955495 | ||||||||
\(769\) | 14.3950 | 0.519099 | 0.259549 | − | 0.965730i | \(-0.416426\pi\) | ||||
0.259549 | + | 0.965730i | \(0.416426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.65328 | −0.347654 | ||||||||
\(772\) | −22.9830 | −0.827177 | ||||||||
\(773\) | −37.2771 | −1.34076 | −0.670382 | − | 0.742016i | \(-0.733870\pi\) | ||||
−0.670382 | + | 0.742016i | \(0.733870\pi\) | |||||||
\(774\) | 17.6964 | 0.636083 | ||||||||
\(775\) | 33.6618 | 1.20917 | ||||||||
\(776\) | 1.28118 | 0.0459917 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.6911 | −0.634255 | ||||||||
\(779\) | −0.475146 | −0.0170239 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.3693 | −0.764652 | ||||||||
\(782\) | 37.3029 | 1.33395 | ||||||||
\(783\) | 7.67121 | 0.274147 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0447 | 0.501276 | ||||||||
\(786\) | −8.63715 | −0.308077 | ||||||||
\(787\) | 14.3486 | 0.511472 | 0.255736 | − | 0.966747i | \(-0.417682\pi\) | ||||
0.255736 | + | 0.966747i | \(0.417682\pi\) | |||||||
\(788\) | −51.1527 | −1.82224 | ||||||||
\(789\) | 33.2818 | 1.18486 | ||||||||
\(790\) | 22.7531 | 0.809518 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.74719 | 0.133150 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 17.1658 | 0.609192 | ||||||||
\(795\) | 3.38534 | 0.120066 | ||||||||
\(796\) | 21.8638 | 0.774940 | ||||||||
\(797\) | 11.0844 | 0.392629 | 0.196314 | − | 0.980541i | \(-0.437103\pi\) | ||||
0.196314 | + | 0.980541i | \(0.437103\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.745733 | −0.0263821 | ||||||||
\(800\) | −22.6537 | −0.800929 | ||||||||
\(801\) | −14.5204 | −0.513054 | ||||||||
\(802\) | 41.9154 | 1.48008 | ||||||||
\(803\) | −10.1652 | −0.358724 | ||||||||
\(804\) | −9.94676 | −0.350795 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.5757 | −0.829904 | ||||||||
\(808\) | −29.0665 | −1.02255 | ||||||||
\(809\) | −42.5536 | −1.49610 | −0.748052 | − | 0.663640i | \(-0.769011\pi\) | ||||
−0.748052 | + | 0.663640i | \(0.769011\pi\) | |||||||
\(810\) | −11.3673 | −0.399406 | ||||||||
\(811\) | 16.3622 | 0.574554 | 0.287277 | − | 0.957848i | \(-0.407250\pi\) | ||||
0.287277 | + | 0.957848i | \(0.407250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9057 | 0.452622 | ||||||||
\(814\) | 23.2079 | 0.813437 | ||||||||
\(815\) | 7.66906 | 0.268636 | ||||||||
\(816\) | −0.955843 | −0.0334612 | ||||||||
\(817\) | 0.439444 | 0.0153742 | ||||||||
\(818\) | 67.4455 | 2.35818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.0549 | 0.979721 | ||||||||
\(821\) | −3.10550 | −0.108383 | −0.0541913 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541913 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(822\) | 6.32802 | 0.220715 | ||||||||
\(823\) | 49.0164 | 1.70860 | 0.854301 | − | 0.519778i | \(-0.173985\pi\) | ||||
0.854301 | + | 0.519778i | \(0.173985\pi\) | |||||||
\(824\) | 29.9930 | 1.04486 | ||||||||
\(825\) | 9.48507 | 0.330228 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.0887 | 0.455140 | 0.227570 | − | 0.973762i | \(-0.426922\pi\) | ||||
0.227570 | + | 0.973762i | \(0.426922\pi\) | |||||||
\(828\) | 21.4276 | 0.744662 | ||||||||
\(829\) | 49.2565 | 1.71075 | 0.855374 | − | 0.518010i | \(-0.173327\pi\) | ||||
0.855374 | + | 0.518010i | \(0.173327\pi\) | |||||||
\(830\) | −22.5134 | −0.781452 | ||||||||
\(831\) | 29.3468 | 1.01803 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 52.9706 | 1.83422 | ||||||||
\(835\) | −2.25177 | −0.0779257 | ||||||||
\(836\) | 0.235656 | 0.00815034 | ||||||||
\(837\) | −44.3505 | −1.53298 | ||||||||
\(838\) | 47.7682 | 1.65012 | ||||||||
\(839\) | 17.2636 | 0.596007 | 0.298004 | − | 0.954565i | \(-0.403679\pi\) | ||||
0.298004 | + | 0.954565i | \(0.403679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1512 | −0.936248 | ||||||||
\(842\) | −57.2814 | −1.97405 | ||||||||
\(843\) | 20.6615 | 0.711621 | ||||||||
\(844\) | −26.7519 | −0.920839 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.687585 | −0.0236397 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.849323 | 0.0291659 | ||||||||
\(849\) | −1.49191 | −0.0512022 | ||||||||
\(850\) | 20.4298 | 0.700738 | ||||||||
\(851\) | 52.4024 | 1.79633 | ||||||||
\(852\) | 69.2149 | 2.37126 | ||||||||
\(853\) | 52.4163 | 1.79470 | 0.897350 | − | 0.441319i | \(-0.145489\pi\) | ||||
0.897350 | + | 0.441319i | \(0.145489\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0333214 | 0.00113957 | ||||||||
\(856\) | −29.6443 | −1.01322 | ||||||||
\(857\) | 10.1271 | 0.345935 | 0.172967 | − | 0.984928i | \(-0.444664\pi\) | ||||
0.172967 | + | 0.984928i | \(0.444664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.510237 | −0.0174090 | −0.00870452 | − | 0.999962i | \(-0.502771\pi\) | ||||
−0.00870452 | + | 0.999962i | \(0.502771\pi\) | |||||||
\(860\) | −25.9469 | −0.884782 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −48.7573 | −1.66068 | ||||||||
\(863\) | 20.4991 | 0.697797 | 0.348898 | − | 0.937161i | \(-0.386556\pi\) | ||||
0.348898 | + | 0.937161i | \(0.386556\pi\) | |||||||
\(864\) | 29.8470 | 1.01541 | ||||||||
\(865\) | −16.5959 | −0.564279 | ||||||||
\(866\) | 53.9646 | 1.83379 | ||||||||
\(867\) | 18.7254 | 0.635947 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.5282 | 0.594605 | ||||||||
\(870\) | −3.90960 | −0.132548 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 34.8844 | 1.18133 | ||||||||
\(873\) | 0.353433 | 0.0119619 | ||||||||
\(874\) | 0.854095 | 0.0288902 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 32.9252 | 1.11244 | ||||||||
\(877\) | −11.2906 | −0.381256 | −0.190628 | − | 0.981662i | \(-0.561052\pi\) | ||||
−0.190628 | + | 0.981662i | \(0.561052\pi\) | |||||||
\(878\) | 27.7276 | 0.935762 | ||||||||
\(879\) | 0.293545 | 0.00990103 | ||||||||
\(880\) | −0.398953 | −0.0134487 | ||||||||
\(881\) | 22.5268 | 0.758947 | 0.379474 | − | 0.925203i | \(-0.376105\pi\) | ||||
0.379474 | + | 0.925203i | \(0.376105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0268 | 0.943178 | 0.471589 | − | 0.881819i | \(-0.343681\pi\) | ||||
0.471589 | + | 0.881819i | \(0.343681\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.04881 | −0.0688701 | ||||||||
\(886\) | −36.2376 | −1.21743 | ||||||||
\(887\) | −20.6235 | −0.692470 | −0.346235 | − | 0.938148i | \(-0.612540\pi\) | ||||
−0.346235 | + | 0.938148i | \(0.612540\pi\) | |||||||
\(888\) | −29.6820 | −0.996062 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 34.1738 | 1.14551 | ||||||||
\(891\) | −8.75700 | −0.293371 | ||||||||
\(892\) | 53.0725 | 1.77700 | ||||||||
\(893\) | −0.0170744 | −0.000571374 0 | ||||||||
\(894\) | 21.5952 | 0.722253 | ||||||||
\(895\) | 2.45149 | 0.0819443 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −59.8876 | −1.99848 | ||||||||
\(899\) | −10.6887 | −0.356489 | ||||||||
\(900\) | 11.7353 | 0.391178 | ||||||||
\(901\) | 5.61725 | 0.187138 | ||||||||
\(902\) | 34.6912 | 1.15509 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.4531 | 0.347664 | ||||||||
\(905\) | −1.15913 | −0.0385308 | ||||||||
\(906\) | −2.25363 | −0.0748718 | ||||||||
\(907\) | 41.4631 | 1.37676 | 0.688379 | − | 0.725351i | \(-0.258322\pi\) | ||||
0.688379 | + | 0.725351i | \(0.258322\pi\) | |||||||
\(908\) | −4.28269 | −0.142126 | ||||||||
\(909\) | −8.01841 | −0.265954 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.8187 | 1.35239 | 0.676193 | − | 0.736725i | \(-0.263629\pi\) | ||||
0.676193 | + | 0.736725i | \(0.263629\pi\) | |||||||
\(912\) | −0.0218852 | −0.000724690 0 | ||||||||
\(913\) | −17.3436 | −0.573990 | ||||||||
\(914\) | 70.9310 | 2.34619 | ||||||||
\(915\) | 5.64504 | 0.186619 | ||||||||
\(916\) | 68.8027 | 2.27331 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −26.9170 | −0.888393 | ||||||||
\(919\) | −48.7678 | −1.60870 | −0.804350 | − | 0.594155i | \(-0.797486\pi\) | ||||
−0.804350 | + | 0.594155i | \(0.797486\pi\) | |||||||
\(920\) | −19.9129 | −0.656509 | ||||||||
\(921\) | 40.0760 | 1.32055 | ||||||||
\(922\) | −78.5317 | −2.58630 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.6994 | 0.943631 | ||||||||
\(926\) | −3.89675 | −0.128055 | ||||||||
\(927\) | 8.27403 | 0.271755 | ||||||||
\(928\) | 7.19330 | 0.236132 | ||||||||
\(929\) | −29.3829 | −0.964023 | −0.482012 | − | 0.876165i | \(-0.660094\pi\) | ||||
−0.482012 | + | 0.876165i | \(0.660094\pi\) | |||||||
\(930\) | 22.6030 | 0.741183 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −43.9711 | −1.44032 | ||||||||
\(933\) | −39.9294 | −1.30723 | ||||||||
\(934\) | −65.3031 | −2.13678 | ||||||||
\(935\) | −2.63859 | −0.0862912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0196 | −0.686681 | −0.343340 | − | 0.939211i | \(-0.611558\pi\) | ||||
−0.343340 | + | 0.939211i | \(0.611558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.5296 | 1.06156 | ||||||||
\(940\) | 1.00816 | 0.0328825 | ||||||||
\(941\) | −24.1033 | −0.785744 | −0.392872 | − | 0.919593i | \(-0.628518\pi\) | ||||
−0.392872 | + | 0.919593i | \(0.628518\pi\) | |||||||
\(942\) | −56.2513 | −1.83277 | ||||||||
\(943\) | 78.3312 | 2.55081 | ||||||||
\(944\) | −0.514013 | −0.0167297 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.0845 | −1.04316 | ||||||||
\(947\) | −3.34046 | −0.108550 | −0.0542751 | − | 0.998526i | \(-0.517285\pi\) | ||||
−0.0542751 | + | 0.998526i | \(0.517285\pi\) | |||||||
\(948\) | −56.7739 | −1.84393 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.467765 | 0.0151763 | ||||||||
\(951\) | −10.4141 | −0.337699 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.97124 | −0.161034 | −0.0805171 | − | 0.996753i | \(-0.525657\pi\) | ||||
−0.0805171 | + | 0.996753i | \(0.525657\pi\) | |||||||
\(954\) | 5.17925 | 0.167685 | ||||||||
\(955\) | 1.28216 | 0.0414898 | ||||||||
\(956\) | −44.1726 | −1.42864 | ||||||||
\(957\) | −3.01183 | −0.0973585 | ||||||||
\(958\) | −14.4702 | −0.467510 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15.9933 | −0.516183 | ||||||||
\(961\) | 30.7961 | 0.993423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.17783 | −0.263527 | ||||||||
\(964\) | 2.75691 | 0.0887939 | ||||||||
\(965\) | 5.89202 | 0.189671 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4943 | 1.52731 | 0.763657 | − | 0.645623i | \(-0.223402\pi\) | ||||
0.763657 | + | 0.645623i | \(0.223402\pi\) | |||||||
\(968\) | 26.2705 | 0.844364 | ||||||||
\(969\) | −0.144744 | −0.00464985 | ||||||||
\(970\) | −0.831803 | −0.0267076 | ||||||||
\(971\) | 34.4715 | 1.10624 | 0.553121 | − | 0.833101i | \(-0.313437\pi\) | ||||
0.553121 | + | 0.833101i | \(0.313437\pi\) | |||||||
\(972\) | −27.5752 | −0.884476 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.9830 | 0.960717 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.41624 | 0.0453329 | ||||||||
\(977\) | −13.3481 | −0.427044 | −0.213522 | − | 0.976938i | \(-0.568494\pi\) | ||||
−0.213522 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(978\) | −30.7159 | −0.982185 | ||||||||
\(979\) | 26.3264 | 0.841395 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.62337 | 0.307251 | ||||||||
\(982\) | 28.4507 | 0.907898 | ||||||||
\(983\) | 12.5344 | 0.399785 | 0.199893 | − | 0.979818i | \(-0.435941\pi\) | ||||
0.199893 | + | 0.979818i | \(0.435941\pi\) | |||||||
\(984\) | −44.3686 | −1.41442 | ||||||||
\(985\) | 13.1137 | 0.417838 | ||||||||
\(986\) | −6.48715 | −0.206593 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −72.4455 | −2.30363 | ||||||||
\(990\) | −2.43285 | −0.0773211 | ||||||||
\(991\) | −10.4119 | −0.330745 | −0.165373 | − | 0.986231i | \(-0.552883\pi\) | ||||
−0.165373 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(992\) | −41.5875 | −1.32040 | ||||||||
\(993\) | −9.70736 | −0.308054 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.60508 | −0.177693 | ||||||||
\(996\) | 56.1759 | 1.78000 | ||||||||
\(997\) | 5.75270 | 0.182190 | 0.0910949 | − | 0.995842i | \(-0.470963\pi\) | ||||
0.0910949 | + | 0.995842i | \(0.470963\pi\) | |||||||
\(998\) | 21.0827 | 0.667362 | ||||||||
\(999\) | −37.8125 | −1.19633 |
(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 | 8281.2.a.cp.1.2 | 12 | ||
7.2 | even | 3 | 1183.2.e.j.508.11 | 24 | |||
7.4 | even | 3 | 1183.2.e.j.170.11 | 24 | |||
7.6 | odd | 2 | 8281.2.a.co.1.2 | 12 | |||
13.2 | odd | 12 | 637.2.q.g.589.1 | 12 | |||
13.7 | odd | 12 | 637.2.q.g.491.1 | 12 | |||
13.12 | even | 2 | inner | 8281.2.a.cp.1.11 | 12 | ||
91.2 | odd | 12 | 91.2.k.b.4.6 | ✓ | 12 | ||
91.20 | even | 12 | 637.2.q.i.491.1 | 12 | |||
91.25 | even | 6 | 1183.2.e.j.170.2 | 24 | |||
91.33 | even | 12 | 637.2.u.g.361.6 | 12 | |||
91.41 | even | 12 | 637.2.q.i.589.1 | 12 | |||
91.46 | odd | 12 | 91.2.k.b.23.1 | yes | 12 | ||
91.51 | even | 6 | 1183.2.e.j.508.2 | 24 | |||
91.54 | even | 12 | 637.2.k.i.459.6 | 12 | |||
91.59 | even | 12 | 637.2.k.i.569.1 | 12 | |||
91.67 | odd | 12 | 91.2.u.b.30.6 | yes | 12 | ||
91.72 | odd | 12 | 91.2.u.b.88.6 | yes | 12 | ||
91.80 | even | 12 | 637.2.u.g.30.6 | 12 | |||
91.90 | odd | 2 | 8281.2.a.co.1.11 | 12 | |||
273.2 | even | 12 | 819.2.bm.f.550.1 | 12 | |||
273.137 | even | 12 | 819.2.bm.f.478.6 | 12 | |||
273.158 | even | 12 | 819.2.do.e.667.1 | 12 | |||
273.254 | even | 12 | 819.2.do.e.361.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.6 | ✓ | 12 | 91.2 | odd | 12 | ||
91.2.k.b.23.1 | yes | 12 | 91.46 | odd | 12 | ||
91.2.u.b.30.6 | yes | 12 | 91.67 | odd | 12 | ||
91.2.u.b.88.6 | yes | 12 | 91.72 | odd | 12 | ||
637.2.k.i.459.6 | 12 | 91.54 | even | 12 | |||
637.2.k.i.569.1 | 12 | 91.59 | even | 12 | |||
637.2.q.g.491.1 | 12 | 13.7 | odd | 12 | |||
637.2.q.g.589.1 | 12 | 13.2 | odd | 12 | |||
637.2.q.i.491.1 | 12 | 91.20 | even | 12 | |||
637.2.q.i.589.1 | 12 | 91.41 | even | 12 | |||
637.2.u.g.30.6 | 12 | 91.80 | even | 12 | |||
637.2.u.g.361.6 | 12 | 91.33 | even | 12 | |||
819.2.bm.f.478.6 | 12 | 273.137 | even | 12 | |||
819.2.bm.f.550.1 | 12 | 273.2 | even | 12 | |||
819.2.do.e.361.1 | 12 | 273.254 | even | 12 | |||
819.2.do.e.667.1 | 12 | 273.158 | even | 12 | |||
1183.2.e.j.170.2 | 24 | 91.25 | even | 6 | |||
1183.2.e.j.170.11 | 24 | 7.4 | even | 3 | |||
1183.2.e.j.508.2 | 24 | 91.51 | even | 6 | |||
1183.2.e.j.508.11 | 24 | 7.2 | even | 3 | |||
8281.2.a.co.1.2 | 12 | 7.6 | odd | 2 | |||
8281.2.a.co.1.11 | 12 | 91.90 | odd | 2 | |||
8281.2.a.cp.1.2 | 12 | 1.1 | even | 1 | trivial | ||
8281.2.a.cp.1.11 | 12 | 13.12 | even | 2 | inner |