Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, 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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.03203 | −1.75054 | −0.875271 | − | 0.483634i | \(-0.839317\pi\) | ||||
−0.875271 | + | 0.483634i | \(0.839317\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.166109 | 0.0742861 | 0.0371431 | − | 0.999310i | \(-0.488174\pi\) | ||||
0.0371431 | + | 0.999310i | \(0.488174\pi\) | |||||||
\(6\) | −3.03203 | −1.23782 | ||||||||
\(7\) | −3.81414 | −1.44161 | −0.720804 | − | 0.693139i | \(-0.756227\pi\) | ||||
−0.720804 | + | 0.693139i | \(0.756227\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.19318 | 2.06439 | ||||||||
\(10\) | 0.166109 | 0.0525282 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −3.03203 | −0.875271 | ||||||||
\(13\) | −0.0506337 | −0.0140433 | −0.00702163 | − | 0.999975i | \(-0.502235\pi\) | ||||
−0.00702163 | + | 0.999975i | \(0.502235\pi\) | |||||||
\(14\) | −3.81414 | −1.01937 | ||||||||
\(15\) | −0.503646 | −0.130041 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.87105 | −1.66648 | −0.833238 | − | 0.552915i | \(-0.813515\pi\) | ||||
−0.833238 | + | 0.552915i | \(0.813515\pi\) | |||||||
\(18\) | 6.19318 | 1.45975 | ||||||||
\(19\) | 6.14963 | 1.41082 | 0.705411 | − | 0.708798i | \(-0.250762\pi\) | ||||
0.705411 | + | 0.708798i | \(0.250762\pi\) | |||||||
\(20\) | 0.166109 | 0.0371431 | ||||||||
\(21\) | 11.5646 | 2.52359 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 0.511723 | 0.106702 | 0.0533508 | − | 0.998576i | \(-0.483010\pi\) | ||||
0.0533508 | + | 0.998576i | \(0.483010\pi\) | |||||||
\(24\) | −3.03203 | −0.618910 | ||||||||
\(25\) | −4.97241 | −0.994482 | ||||||||
\(26\) | −0.0506337 | −0.00993008 | ||||||||
\(27\) | −9.68181 | −1.86327 | ||||||||
\(28\) | −3.81414 | −0.720804 | ||||||||
\(29\) | −2.35600 | −0.437498 | −0.218749 | − | 0.975781i | \(-0.570198\pi\) | ||||
−0.218749 | + | 0.975781i | \(0.570198\pi\) | |||||||
\(30\) | −0.503646 | −0.0919528 | ||||||||
\(31\) | 8.10625 | 1.45593 | 0.727963 | − | 0.685617i | \(-0.240467\pi\) | ||||
0.727963 | + | 0.685617i | \(0.240467\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.03203 | 0.527808 | ||||||||
\(34\) | −6.87105 | −1.17838 | ||||||||
\(35\) | −0.633562 | −0.107091 | ||||||||
\(36\) | 6.19318 | 1.03220 | ||||||||
\(37\) | −6.88083 | −1.13120 | −0.565601 | − | 0.824679i | \(-0.691356\pi\) | ||||
−0.565601 | + | 0.824679i | \(0.691356\pi\) | |||||||
\(38\) | 6.14963 | 0.997602 | ||||||||
\(39\) | 0.153523 | 0.0245833 | ||||||||
\(40\) | 0.166109 | 0.0262641 | ||||||||
\(41\) | −11.6490 | −1.81927 | −0.909635 | − | 0.415409i | \(-0.863638\pi\) | ||||
−0.909635 | + | 0.415409i | \(0.863638\pi\) | |||||||
\(42\) | 11.5646 | 1.78445 | ||||||||
\(43\) | −3.00175 | −0.457763 | −0.228882 | − | 0.973454i | \(-0.573507\pi\) | ||||
−0.228882 | + | 0.973454i | \(0.573507\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.02874 | 0.153356 | ||||||||
\(46\) | 0.511723 | 0.0754495 | ||||||||
\(47\) | 0.127523 | 0.0186012 | 0.00930058 | − | 0.999957i | \(-0.497039\pi\) | ||||
0.00930058 | + | 0.999957i | \(0.497039\pi\) | |||||||
\(48\) | −3.03203 | −0.437635 | ||||||||
\(49\) | 7.54764 | 1.07823 | ||||||||
\(50\) | −4.97241 | −0.703205 | ||||||||
\(51\) | 20.8332 | 2.91723 | ||||||||
\(52\) | −0.0506337 | −0.00702163 | ||||||||
\(53\) | −13.4512 | −1.84766 | −0.923832 | − | 0.382798i | \(-0.874961\pi\) | ||||
−0.923832 | + | 0.382798i | \(0.874961\pi\) | |||||||
\(54\) | −9.68181 | −1.31753 | ||||||||
\(55\) | −0.166109 | −0.0223981 | ||||||||
\(56\) | −3.81414 | −0.509686 | ||||||||
\(57\) | −18.6458 | −2.46970 | ||||||||
\(58\) | −2.35600 | −0.309358 | ||||||||
\(59\) | −5.81311 | −0.756802 | −0.378401 | − | 0.925642i | \(-0.623526\pi\) | ||||
−0.378401 | + | 0.925642i | \(0.623526\pi\) | |||||||
\(60\) | −0.503646 | −0.0650204 | ||||||||
\(61\) | 8.08229 | 1.03483 | 0.517416 | − | 0.855734i | \(-0.326894\pi\) | ||||
0.517416 | + | 0.855734i | \(0.326894\pi\) | |||||||
\(62\) | 8.10625 | 1.02949 | ||||||||
\(63\) | −23.6216 | −2.97605 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.00841070 | −0.00104322 | ||||||||
\(66\) | 3.03203 | 0.373217 | ||||||||
\(67\) | 10.7866 | 1.31780 | 0.658899 | − | 0.752231i | \(-0.271022\pi\) | ||||
0.658899 | + | 0.752231i | \(0.271022\pi\) | |||||||
\(68\) | −6.87105 | −0.833238 | ||||||||
\(69\) | −1.55156 | −0.186786 | ||||||||
\(70\) | −0.633562 | −0.0757251 | ||||||||
\(71\) | 6.76163 | 0.802458 | 0.401229 | − | 0.915978i | \(-0.368583\pi\) | ||||
0.401229 | + | 0.915978i | \(0.368583\pi\) | |||||||
\(72\) | 6.19318 | 0.729874 | ||||||||
\(73\) | 16.3022 | 1.90802 | 0.954012 | − | 0.299768i | \(-0.0969092\pi\) | ||||
0.954012 | + | 0.299768i | \(0.0969092\pi\) | |||||||
\(74\) | −6.88083 | −0.799880 | ||||||||
\(75\) | 15.0765 | 1.74088 | ||||||||
\(76\) | 6.14963 | 0.705411 | ||||||||
\(77\) | 3.81414 | 0.434661 | ||||||||
\(78\) | 0.153523 | 0.0173830 | ||||||||
\(79\) | 12.7809 | 1.43797 | 0.718983 | − | 0.695028i | \(-0.244608\pi\) | ||||
0.718983 | + | 0.695028i | \(0.244608\pi\) | |||||||
\(80\) | 0.166109 | 0.0185715 | ||||||||
\(81\) | 10.7760 | 1.19733 | ||||||||
\(82\) | −11.6490 | −1.28642 | ||||||||
\(83\) | −3.92290 | −0.430594 | −0.215297 | − | 0.976549i | \(-0.569072\pi\) | ||||
−0.215297 | + | 0.976549i | \(0.569072\pi\) | |||||||
\(84\) | 11.5646 | 1.26180 | ||||||||
\(85\) | −1.14134 | −0.123796 | ||||||||
\(86\) | −3.00175 | −0.323688 | ||||||||
\(87\) | 7.14345 | 0.765858 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 6.40229 | 0.678641 | 0.339321 | − | 0.940671i | \(-0.389803\pi\) | ||||
0.339321 | + | 0.940671i | \(0.389803\pi\) | |||||||
\(90\) | 1.02874 | 0.108439 | ||||||||
\(91\) | 0.193124 | 0.0202449 | ||||||||
\(92\) | 0.511723 | 0.0533508 | ||||||||
\(93\) | −24.5784 | −2.54866 | ||||||||
\(94\) | 0.127523 | 0.0131530 | ||||||||
\(95\) | 1.02151 | 0.104804 | ||||||||
\(96\) | −3.03203 | −0.309455 | ||||||||
\(97\) | 2.08250 | 0.211446 | 0.105723 | − | 0.994396i | \(-0.466284\pi\) | ||||
0.105723 | + | 0.994396i | \(0.466284\pi\) | |||||||
\(98\) | 7.54764 | 0.762427 | ||||||||
\(99\) | −6.19318 | −0.622438 | ||||||||
\(100\) | −4.97241 | −0.497241 | ||||||||
\(101\) | 14.9644 | 1.48901 | 0.744507 | − | 0.667615i | \(-0.232685\pi\) | ||||
0.744507 | + | 0.667615i | \(0.232685\pi\) | |||||||
\(102\) | 20.8332 | 2.06280 | ||||||||
\(103\) | −10.0999 | −0.995177 | −0.497588 | − | 0.867413i | \(-0.665781\pi\) | ||||
−0.497588 | + | 0.867413i | \(0.665781\pi\) | |||||||
\(104\) | −0.0506337 | −0.00496504 | ||||||||
\(105\) | 1.92098 | 0.187468 | ||||||||
\(106\) | −13.4512 | −1.30650 | ||||||||
\(107\) | −13.8018 | −1.33427 | −0.667137 | − | 0.744935i | \(-0.732480\pi\) | ||||
−0.667137 | + | 0.744935i | \(0.732480\pi\) | |||||||
\(108\) | −9.68181 | −0.931633 | ||||||||
\(109\) | −3.10489 | −0.297395 | −0.148697 | − | 0.988883i | \(-0.547508\pi\) | ||||
−0.148697 | + | 0.988883i | \(0.547508\pi\) | |||||||
\(110\) | −0.166109 | −0.0158379 | ||||||||
\(111\) | 20.8628 | 1.98021 | ||||||||
\(112\) | −3.81414 | −0.360402 | ||||||||
\(113\) | −6.10115 | −0.573948 | −0.286974 | − | 0.957938i | \(-0.592649\pi\) | ||||
−0.286974 | + | 0.957938i | \(0.592649\pi\) | |||||||
\(114\) | −18.6458 | −1.74634 | ||||||||
\(115\) | 0.0850017 | 0.00792645 | ||||||||
\(116\) | −2.35600 | −0.218749 | ||||||||
\(117\) | −0.313584 | −0.0289908 | ||||||||
\(118\) | −5.81311 | −0.535140 | ||||||||
\(119\) | 26.2071 | 2.40240 | ||||||||
\(120\) | −0.503646 | −0.0459764 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.08229 | 0.731736 | ||||||||
\(123\) | 35.3201 | 3.18471 | ||||||||
\(124\) | 8.10625 | 0.727963 | ||||||||
\(125\) | −1.65650 | −0.148162 | ||||||||
\(126\) | −23.6216 | −2.10438 | ||||||||
\(127\) | 9.89255 | 0.877822 | 0.438911 | − | 0.898531i | \(-0.355364\pi\) | ||||
0.438911 | + | 0.898531i | \(0.355364\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.10140 | 0.801333 | ||||||||
\(130\) | −0.00841070 | −0.000737667 0 | ||||||||
\(131\) | −10.7411 | −0.938457 | −0.469228 | − | 0.883077i | \(-0.655468\pi\) | ||||
−0.469228 | + | 0.883077i | \(0.655468\pi\) | |||||||
\(132\) | 3.03203 | 0.263904 | ||||||||
\(133\) | −23.4555 | −2.03385 | ||||||||
\(134\) | 10.7866 | 0.931824 | ||||||||
\(135\) | −1.60823 | −0.138415 | ||||||||
\(136\) | −6.87105 | −0.589188 | ||||||||
\(137\) | 18.3506 | 1.56780 | 0.783899 | − | 0.620889i | \(-0.213228\pi\) | ||||
0.783899 | + | 0.620889i | \(0.213228\pi\) | |||||||
\(138\) | −1.55156 | −0.132077 | ||||||||
\(139\) | 6.12724 | 0.519705 | 0.259853 | − | 0.965648i | \(-0.416326\pi\) | ||||
0.259853 | + | 0.965648i | \(0.416326\pi\) | |||||||
\(140\) | −0.633562 | −0.0535457 | ||||||||
\(141\) | −0.386654 | −0.0325621 | ||||||||
\(142\) | 6.76163 | 0.567423 | ||||||||
\(143\) | 0.0506337 | 0.00423420 | ||||||||
\(144\) | 6.19318 | 0.516099 | ||||||||
\(145\) | −0.391352 | −0.0325000 | ||||||||
\(146\) | 16.3022 | 1.34918 | ||||||||
\(147\) | −22.8847 | −1.88749 | ||||||||
\(148\) | −6.88083 | −0.565601 | ||||||||
\(149\) | 3.56325 | 0.291913 | 0.145956 | − | 0.989291i | \(-0.453374\pi\) | ||||
0.145956 | + | 0.989291i | \(0.453374\pi\) | |||||||
\(150\) | 15.0765 | 1.23099 | ||||||||
\(151\) | 4.62966 | 0.376756 | 0.188378 | − | 0.982097i | \(-0.439677\pi\) | ||||
0.188378 | + | 0.982097i | \(0.439677\pi\) | |||||||
\(152\) | 6.14963 | 0.498801 | ||||||||
\(153\) | −42.5537 | −3.44026 | ||||||||
\(154\) | 3.81414 | 0.307352 | ||||||||
\(155\) | 1.34652 | 0.108155 | ||||||||
\(156\) | 0.153523 | 0.0122916 | ||||||||
\(157\) | 21.9187 | 1.74930 | 0.874652 | − | 0.484751i | \(-0.161090\pi\) | ||||
0.874652 | + | 0.484751i | \(0.161090\pi\) | |||||||
\(158\) | 12.7809 | 1.01680 | ||||||||
\(159\) | 40.7844 | 3.23441 | ||||||||
\(160\) | 0.166109 | 0.0131321 | ||||||||
\(161\) | −1.95178 | −0.153822 | ||||||||
\(162\) | 10.7760 | 0.846640 | ||||||||
\(163\) | 6.65441 | 0.521214 | 0.260607 | − | 0.965445i | \(-0.416077\pi\) | ||||
0.260607 | + | 0.965445i | \(0.416077\pi\) | |||||||
\(164\) | −11.6490 | −0.909635 | ||||||||
\(165\) | 0.503646 | 0.0392088 | ||||||||
\(166\) | −3.92290 | −0.304476 | ||||||||
\(167\) | −7.40584 | −0.573081 | −0.286540 | − | 0.958068i | \(-0.592505\pi\) | ||||
−0.286540 | + | 0.958068i | \(0.592505\pi\) | |||||||
\(168\) | 11.5646 | 0.892225 | ||||||||
\(169\) | −12.9974 | −0.999803 | ||||||||
\(170\) | −1.14134 | −0.0875370 | ||||||||
\(171\) | 38.0858 | 2.91249 | ||||||||
\(172\) | −3.00175 | −0.228882 | ||||||||
\(173\) | −5.35677 | −0.407268 | −0.203634 | − | 0.979047i | \(-0.565275\pi\) | ||||
−0.203634 | + | 0.979047i | \(0.565275\pi\) | |||||||
\(174\) | 7.14345 | 0.541543 | ||||||||
\(175\) | 18.9654 | 1.43365 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 17.6255 | 1.32481 | ||||||||
\(178\) | 6.40229 | 0.479872 | ||||||||
\(179\) | 25.5696 | 1.91116 | 0.955579 | − | 0.294735i | \(-0.0952314\pi\) | ||||
0.955579 | + | 0.294735i | \(0.0952314\pi\) | |||||||
\(180\) | 1.02874 | 0.0766779 | ||||||||
\(181\) | −12.6905 | −0.943275 | −0.471637 | − | 0.881793i | \(-0.656337\pi\) | ||||
−0.471637 | + | 0.881793i | \(0.656337\pi\) | |||||||
\(182\) | 0.193124 | 0.0143153 | ||||||||
\(183\) | −24.5057 | −1.81151 | ||||||||
\(184\) | 0.511723 | 0.0377247 | ||||||||
\(185\) | −1.14297 | −0.0840325 | ||||||||
\(186\) | −24.5784 | −1.80217 | ||||||||
\(187\) | 6.87105 | 0.502461 | ||||||||
\(188\) | 0.127523 | 0.00930058 | ||||||||
\(189\) | 36.9278 | 2.68610 | ||||||||
\(190\) | 1.02151 | 0.0741080 | ||||||||
\(191\) | 1.69359 | 0.122544 | 0.0612720 | − | 0.998121i | \(-0.480484\pi\) | ||||
0.0612720 | + | 0.998121i | \(0.480484\pi\) | |||||||
\(192\) | −3.03203 | −0.218818 | ||||||||
\(193\) | −15.7527 | −1.13391 | −0.566953 | − | 0.823750i | \(-0.691878\pi\) | ||||
−0.566953 | + | 0.823750i | \(0.691878\pi\) | |||||||
\(194\) | 2.08250 | 0.149515 | ||||||||
\(195\) | 0.0255015 | 0.00182620 | ||||||||
\(196\) | 7.54764 | 0.539117 | ||||||||
\(197\) | −1.00000 | −0.0712470 | ||||||||
\(198\) | −6.19318 | −0.440130 | ||||||||
\(199\) | −12.3738 | −0.877157 | −0.438579 | − | 0.898693i | \(-0.644518\pi\) | ||||
−0.438579 | + | 0.898693i | \(0.644518\pi\) | |||||||
\(200\) | −4.97241 | −0.351602 | ||||||||
\(201\) | −32.7054 | −2.30686 | ||||||||
\(202\) | 14.9644 | 1.05289 | ||||||||
\(203\) | 8.98610 | 0.630701 | ||||||||
\(204\) | 20.8332 | 1.45862 | ||||||||
\(205\) | −1.93500 | −0.135146 | ||||||||
\(206\) | −10.0999 | −0.703696 | ||||||||
\(207\) | 3.16920 | 0.220274 | ||||||||
\(208\) | −0.0506337 | −0.00351081 | ||||||||
\(209\) | −6.14963 | −0.425379 | ||||||||
\(210\) | 1.92098 | 0.132560 | ||||||||
\(211\) | 16.7813 | 1.15527 | 0.577636 | − | 0.816294i | \(-0.303975\pi\) | ||||
0.577636 | + | 0.816294i | \(0.303975\pi\) | |||||||
\(212\) | −13.4512 | −0.923832 | ||||||||
\(213\) | −20.5014 | −1.40474 | ||||||||
\(214\) | −13.8018 | −0.943474 | ||||||||
\(215\) | −0.498618 | −0.0340055 | ||||||||
\(216\) | −9.68181 | −0.658764 | ||||||||
\(217\) | −30.9183 | −2.09887 | ||||||||
\(218\) | −3.10489 | −0.210290 | ||||||||
\(219\) | −49.4286 | −3.34008 | ||||||||
\(220\) | −0.166109 | −0.0111991 | ||||||||
\(221\) | 0.347907 | 0.0234027 | ||||||||
\(222\) | 20.8628 | 1.40022 | ||||||||
\(223\) | 12.1229 | 0.811809 | 0.405905 | − | 0.913915i | \(-0.366957\pi\) | ||||
0.405905 | + | 0.913915i | \(0.366957\pi\) | |||||||
\(224\) | −3.81414 | −0.254843 | ||||||||
\(225\) | −30.7950 | −2.05300 | ||||||||
\(226\) | −6.10115 | −0.405842 | ||||||||
\(227\) | 29.0275 | 1.92662 | 0.963310 | − | 0.268390i | \(-0.0864917\pi\) | ||||
0.963310 | + | 0.268390i | \(0.0864917\pi\) | |||||||
\(228\) | −18.6458 | −1.23485 | ||||||||
\(229\) | 14.6144 | 0.965750 | 0.482875 | − | 0.875689i | \(-0.339593\pi\) | ||||
0.482875 | + | 0.875689i | \(0.339593\pi\) | |||||||
\(230\) | 0.0850017 | 0.00560485 | ||||||||
\(231\) | −11.5646 | −0.760892 | ||||||||
\(232\) | −2.35600 | −0.154679 | ||||||||
\(233\) | 21.4191 | 1.40321 | 0.701605 | − | 0.712566i | \(-0.252467\pi\) | ||||
0.701605 | + | 0.712566i | \(0.252467\pi\) | |||||||
\(234\) | −0.313584 | −0.0204996 | ||||||||
\(235\) | 0.0211827 | 0.00138181 | ||||||||
\(236\) | −5.81311 | −0.378401 | ||||||||
\(237\) | −38.7521 | −2.51722 | ||||||||
\(238\) | 26.2071 | 1.69876 | ||||||||
\(239\) | −1.92035 | −0.124217 | −0.0621084 | − | 0.998069i | \(-0.519782\pi\) | ||||
−0.0621084 | + | 0.998069i | \(0.519782\pi\) | |||||||
\(240\) | −0.503646 | −0.0325102 | ||||||||
\(241\) | 13.0050 | 0.837726 | 0.418863 | − | 0.908049i | \(-0.362429\pi\) | ||||
0.418863 | + | 0.908049i | \(0.362429\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −3.62756 | −0.232708 | ||||||||
\(244\) | 8.08229 | 0.517416 | ||||||||
\(245\) | 1.25373 | 0.0800979 | ||||||||
\(246\) | 35.3201 | 2.25193 | ||||||||
\(247\) | −0.311378 | −0.0198125 | ||||||||
\(248\) | 8.10625 | 0.514747 | ||||||||
\(249\) | 11.8943 | 0.753773 | ||||||||
\(250\) | −1.65650 | −0.104767 | ||||||||
\(251\) | 25.9958 | 1.64084 | 0.820421 | − | 0.571760i | \(-0.193739\pi\) | ||||
0.820421 | + | 0.571760i | \(0.193739\pi\) | |||||||
\(252\) | −23.6216 | −1.48802 | ||||||||
\(253\) | −0.511723 | −0.0321718 | ||||||||
\(254\) | 9.89255 | 0.620714 | ||||||||
\(255\) | 3.46058 | 0.216710 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.9429 | 1.30638 | 0.653190 | − | 0.757194i | \(-0.273430\pi\) | ||||
0.653190 | + | 0.757194i | \(0.273430\pi\) | |||||||
\(258\) | 9.10140 | 0.566628 | ||||||||
\(259\) | 26.2444 | 1.63075 | ||||||||
\(260\) | −0.00841070 | −0.000521609 0 | ||||||||
\(261\) | −14.5911 | −0.903168 | ||||||||
\(262\) | −10.7411 | −0.663589 | ||||||||
\(263\) | 25.4745 | 1.57083 | 0.785413 | − | 0.618972i | \(-0.212451\pi\) | ||||
0.785413 | + | 0.618972i | \(0.212451\pi\) | |||||||
\(264\) | 3.03203 | 0.186608 | ||||||||
\(265\) | −2.23436 | −0.137256 | ||||||||
\(266\) | −23.4555 | −1.43815 | ||||||||
\(267\) | −19.4119 | −1.18799 | ||||||||
\(268\) | 10.7866 | 0.658899 | ||||||||
\(269\) | −15.3961 | −0.938719 | −0.469360 | − | 0.883007i | \(-0.655515\pi\) | ||||
−0.469360 | + | 0.883007i | \(0.655515\pi\) | |||||||
\(270\) | −1.60823 | −0.0978740 | ||||||||
\(271\) | 2.54931 | 0.154860 | 0.0774299 | − | 0.996998i | \(-0.475329\pi\) | ||||
0.0774299 | + | 0.996998i | \(0.475329\pi\) | |||||||
\(272\) | −6.87105 | −0.416619 | ||||||||
\(273\) | −0.585556 | −0.0354395 | ||||||||
\(274\) | 18.3506 | 1.10860 | ||||||||
\(275\) | 4.97241 | 0.299847 | ||||||||
\(276\) | −1.55156 | −0.0933928 | ||||||||
\(277\) | 11.0873 | 0.666169 | 0.333084 | − | 0.942897i | \(-0.391911\pi\) | ||||
0.333084 | + | 0.942897i | \(0.391911\pi\) | |||||||
\(278\) | 6.12724 | 0.367487 | ||||||||
\(279\) | 50.2035 | 3.00560 | ||||||||
\(280\) | −0.633562 | −0.0378626 | ||||||||
\(281\) | −14.2505 | −0.850112 | −0.425056 | − | 0.905167i | \(-0.639746\pi\) | ||||
−0.425056 | + | 0.905167i | \(0.639746\pi\) | |||||||
\(282\) | −0.386654 | −0.0230249 | ||||||||
\(283\) | 9.22982 | 0.548656 | 0.274328 | − | 0.961636i | \(-0.411545\pi\) | ||||
0.274328 | + | 0.961636i | \(0.411545\pi\) | |||||||
\(284\) | 6.76163 | 0.401229 | ||||||||
\(285\) | −3.09724 | −0.183465 | ||||||||
\(286\) | 0.0506337 | 0.00299403 | ||||||||
\(287\) | 44.4309 | 2.62267 | ||||||||
\(288\) | 6.19318 | 0.364937 | ||||||||
\(289\) | 30.2114 | 1.77714 | ||||||||
\(290\) | −0.391352 | −0.0229810 | ||||||||
\(291\) | −6.31420 | −0.370145 | ||||||||
\(292\) | 16.3022 | 0.954012 | ||||||||
\(293\) | 8.18464 | 0.478152 | 0.239076 | − | 0.971001i | \(-0.423155\pi\) | ||||
0.239076 | + | 0.971001i | \(0.423155\pi\) | |||||||
\(294\) | −22.8847 | −1.33466 | ||||||||
\(295\) | −0.965608 | −0.0562199 | ||||||||
\(296\) | −6.88083 | −0.399940 | ||||||||
\(297\) | 9.68181 | 0.561796 | ||||||||
\(298\) | 3.56325 | 0.206414 | ||||||||
\(299\) | −0.0259104 | −0.00149844 | ||||||||
\(300\) | 15.0765 | 0.870440 | ||||||||
\(301\) | 11.4491 | 0.659915 | ||||||||
\(302\) | 4.62966 | 0.266407 | ||||||||
\(303\) | −45.3725 | −2.60658 | ||||||||
\(304\) | 6.14963 | 0.352706 | ||||||||
\(305\) | 1.34254 | 0.0768736 | ||||||||
\(306\) | −42.5537 | −2.43263 | ||||||||
\(307\) | 20.3784 | 1.16305 | 0.581527 | − | 0.813527i | \(-0.302455\pi\) | ||||
0.581527 | + | 0.813527i | \(0.302455\pi\) | |||||||
\(308\) | 3.81414 | 0.217331 | ||||||||
\(309\) | 30.6233 | 1.74210 | ||||||||
\(310\) | 1.34652 | 0.0764771 | ||||||||
\(311\) | −30.4710 | −1.72785 | −0.863926 | − | 0.503619i | \(-0.832001\pi\) | ||||
−0.863926 | + | 0.503619i | \(0.832001\pi\) | |||||||
\(312\) | 0.153523 | 0.00869151 | ||||||||
\(313\) | 17.8210 | 1.00730 | 0.503652 | − | 0.863907i | \(-0.331990\pi\) | ||||
0.503652 | + | 0.863907i | \(0.331990\pi\) | |||||||
\(314\) | 21.9187 | 1.23694 | ||||||||
\(315\) | −3.92376 | −0.221079 | ||||||||
\(316\) | 12.7809 | 0.718983 | ||||||||
\(317\) | −25.2830 | −1.42004 | −0.710018 | − | 0.704184i | \(-0.751313\pi\) | ||||
−0.710018 | + | 0.704184i | \(0.751313\pi\) | |||||||
\(318\) | 40.7844 | 2.28707 | ||||||||
\(319\) | 2.35600 | 0.131911 | ||||||||
\(320\) | 0.166109 | 0.00928576 | ||||||||
\(321\) | 41.8475 | 2.33570 | ||||||||
\(322\) | −1.95178 | −0.108769 | ||||||||
\(323\) | −42.2545 | −2.35110 | ||||||||
\(324\) | 10.7760 | 0.598665 | ||||||||
\(325\) | 0.251771 | 0.0139658 | ||||||||
\(326\) | 6.65441 | 0.368554 | ||||||||
\(327\) | 9.41412 | 0.520602 | ||||||||
\(328\) | −11.6490 | −0.643209 | ||||||||
\(329\) | −0.486391 | −0.0268156 | ||||||||
\(330\) | 0.503646 | 0.0277248 | ||||||||
\(331\) | −20.1374 | −1.10685 | −0.553427 | − | 0.832898i | \(-0.686680\pi\) | ||||
−0.553427 | + | 0.832898i | \(0.686680\pi\) | |||||||
\(332\) | −3.92290 | −0.215297 | ||||||||
\(333\) | −42.6142 | −2.33524 | ||||||||
\(334\) | −7.40584 | −0.405229 | ||||||||
\(335\) | 1.79176 | 0.0978941 | ||||||||
\(336\) | 11.5646 | 0.630899 | ||||||||
\(337\) | 9.66620 | 0.526551 | 0.263276 | − | 0.964721i | \(-0.415197\pi\) | ||||
0.263276 | + | 0.964721i | \(0.415197\pi\) | |||||||
\(338\) | −12.9974 | −0.706967 | ||||||||
\(339\) | 18.4988 | 1.00472 | ||||||||
\(340\) | −1.14134 | −0.0618980 | ||||||||
\(341\) | −8.10625 | −0.438978 | ||||||||
\(342\) | 38.0858 | 2.05944 | ||||||||
\(343\) | −2.08879 | −0.112784 | ||||||||
\(344\) | −3.00175 | −0.161844 | ||||||||
\(345\) | −0.257727 | −0.0138756 | ||||||||
\(346\) | −5.35677 | −0.287982 | ||||||||
\(347\) | 9.15792 | 0.491623 | 0.245812 | − | 0.969318i | \(-0.420946\pi\) | ||||
0.245812 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(348\) | 7.14345 | 0.382929 | ||||||||
\(349\) | −1.35630 | −0.0726009 | −0.0363005 | − | 0.999341i | \(-0.511557\pi\) | ||||
−0.0363005 | + | 0.999341i | \(0.511557\pi\) | |||||||
\(350\) | 18.9654 | 1.01375 | ||||||||
\(351\) | 0.490226 | 0.0261663 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −5.33642 | −0.284029 | −0.142015 | − | 0.989865i | \(-0.545358\pi\) | ||||
−0.142015 | + | 0.989865i | \(0.545358\pi\) | |||||||
\(354\) | 17.6255 | 0.936785 | ||||||||
\(355\) | 1.12317 | 0.0596115 | ||||||||
\(356\) | 6.40229 | 0.339321 | ||||||||
\(357\) | −79.4607 | −4.20551 | ||||||||
\(358\) | 25.5696 | 1.35139 | ||||||||
\(359\) | 18.9002 | 0.997516 | 0.498758 | − | 0.866741i | \(-0.333790\pi\) | ||||
0.498758 | + | 0.866741i | \(0.333790\pi\) | |||||||
\(360\) | 1.02874 | 0.0542195 | ||||||||
\(361\) | 18.8180 | 0.990420 | ||||||||
\(362\) | −12.6905 | −0.666996 | ||||||||
\(363\) | −3.03203 | −0.159140 | ||||||||
\(364\) | 0.193124 | 0.0101224 | ||||||||
\(365\) | 2.70793 | 0.141740 | ||||||||
\(366\) | −24.5057 | −1.28093 | ||||||||
\(367\) | −19.7230 | −1.02953 | −0.514765 | − | 0.857331i | \(-0.672121\pi\) | ||||
−0.514765 | + | 0.857331i | \(0.672121\pi\) | |||||||
\(368\) | 0.511723 | 0.0266754 | ||||||||
\(369\) | −72.1444 | −3.75569 | ||||||||
\(370\) | −1.14297 | −0.0594200 | ||||||||
\(371\) | 51.3047 | 2.66361 | ||||||||
\(372\) | −24.5784 | −1.27433 | ||||||||
\(373\) | −9.58095 | −0.496083 | −0.248042 | − | 0.968749i | \(-0.579787\pi\) | ||||
−0.248042 | + | 0.968749i | \(0.579787\pi\) | |||||||
\(374\) | 6.87105 | 0.355294 | ||||||||
\(375\) | 5.02257 | 0.259364 | ||||||||
\(376\) | 0.127523 | 0.00657651 | ||||||||
\(377\) | 0.119293 | 0.00614389 | ||||||||
\(378\) | 36.9278 | 1.89936 | ||||||||
\(379\) | 14.0487 | 0.721633 | 0.360817 | − | 0.932637i | \(-0.382498\pi\) | ||||
0.360817 | + | 0.932637i | \(0.382498\pi\) | |||||||
\(380\) | 1.02151 | 0.0524022 | ||||||||
\(381\) | −29.9945 | −1.53666 | ||||||||
\(382\) | 1.69359 | 0.0866517 | ||||||||
\(383\) | −6.02899 | −0.308067 | −0.154034 | − | 0.988066i | \(-0.549226\pi\) | ||||
−0.154034 | + | 0.988066i | \(0.549226\pi\) | |||||||
\(384\) | −3.03203 | −0.154727 | ||||||||
\(385\) | 0.633562 | 0.0322893 | ||||||||
\(386\) | −15.7527 | −0.801793 | ||||||||
\(387\) | −18.5904 | −0.945004 | ||||||||
\(388\) | 2.08250 | 0.105723 | ||||||||
\(389\) | −32.8783 | −1.66700 | −0.833499 | − | 0.552522i | \(-0.813666\pi\) | ||||
−0.833499 | + | 0.552522i | \(0.813666\pi\) | |||||||
\(390\) | 0.0255015 | 0.00129132 | ||||||||
\(391\) | −3.51608 | −0.177816 | ||||||||
\(392\) | 7.54764 | 0.381214 | ||||||||
\(393\) | 32.5674 | 1.64281 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | 2.12302 | 0.106821 | ||||||||
\(396\) | −6.19318 | −0.311219 | ||||||||
\(397\) | 18.7499 | 0.941031 | 0.470515 | − | 0.882392i | \(-0.344068\pi\) | ||||
0.470515 | + | 0.882392i | \(0.344068\pi\) | |||||||
\(398\) | −12.3738 | −0.620244 | ||||||||
\(399\) | 71.1178 | 3.56034 | ||||||||
\(400\) | −4.97241 | −0.248620 | ||||||||
\(401\) | −3.76413 | −0.187972 | −0.0939858 | − | 0.995574i | \(-0.529961\pi\) | ||||
−0.0939858 | + | 0.995574i | \(0.529961\pi\) | |||||||
\(402\) | −32.7054 | −1.63120 | ||||||||
\(403\) | −0.410449 | −0.0204459 | ||||||||
\(404\) | 14.9644 | 0.744507 | ||||||||
\(405\) | 1.78998 | 0.0889449 | ||||||||
\(406\) | 8.98610 | 0.445973 | ||||||||
\(407\) | 6.88083 | 0.341070 | ||||||||
\(408\) | 20.8332 | 1.03140 | ||||||||
\(409\) | −9.61873 | −0.475616 | −0.237808 | − | 0.971312i | \(-0.576429\pi\) | ||||
−0.237808 | + | 0.971312i | \(0.576429\pi\) | |||||||
\(410\) | −1.93500 | −0.0955629 | ||||||||
\(411\) | −55.6395 | −2.74449 | ||||||||
\(412\) | −10.0999 | −0.497588 | ||||||||
\(413\) | 22.1720 | 1.09101 | ||||||||
\(414\) | 3.16920 | 0.155757 | ||||||||
\(415\) | −0.651628 | −0.0319872 | ||||||||
\(416\) | −0.0506337 | −0.00248252 | ||||||||
\(417\) | −18.5779 | −0.909766 | ||||||||
\(418\) | −6.14963 | −0.300788 | ||||||||
\(419\) | −29.9972 | −1.46546 | −0.732730 | − | 0.680519i | \(-0.761754\pi\) | ||||
−0.732730 | + | 0.680519i | \(0.761754\pi\) | |||||||
\(420\) | 1.92098 | 0.0937340 | ||||||||
\(421\) | 0.643680 | 0.0313710 | 0.0156855 | − | 0.999877i | \(-0.495007\pi\) | ||||
0.0156855 | + | 0.999877i | \(0.495007\pi\) | |||||||
\(422\) | 16.7813 | 0.816901 | ||||||||
\(423\) | 0.789774 | 0.0384001 | ||||||||
\(424\) | −13.4512 | −0.653248 | ||||||||
\(425\) | 34.1657 | 1.65728 | ||||||||
\(426\) | −20.5014 | −0.993298 | ||||||||
\(427\) | −30.8270 | −1.49182 | ||||||||
\(428\) | −13.8018 | −0.667137 | ||||||||
\(429\) | −0.153523 | −0.00741214 | ||||||||
\(430\) | −0.498618 | −0.0240455 | ||||||||
\(431\) | −32.5274 | −1.56679 | −0.783396 | − | 0.621523i | \(-0.786514\pi\) | ||||
−0.783396 | + | 0.621523i | \(0.786514\pi\) | |||||||
\(432\) | −9.68181 | −0.465816 | ||||||||
\(433\) | 27.5766 | 1.32525 | 0.662624 | − | 0.748953i | \(-0.269443\pi\) | ||||
0.662624 | + | 0.748953i | \(0.269443\pi\) | |||||||
\(434\) | −30.9183 | −1.48413 | ||||||||
\(435\) | 1.18659 | 0.0568926 | ||||||||
\(436\) | −3.10489 | −0.148697 | ||||||||
\(437\) | 3.14691 | 0.150537 | ||||||||
\(438\) | −49.4286 | −2.36179 | ||||||||
\(439\) | −6.52532 | −0.311437 | −0.155718 | − | 0.987801i | \(-0.549769\pi\) | ||||
−0.155718 | + | 0.987801i | \(0.549769\pi\) | |||||||
\(440\) | −0.166109 | −0.00791893 | ||||||||
\(441\) | 46.7439 | 2.22590 | ||||||||
\(442\) | 0.347907 | 0.0165482 | ||||||||
\(443\) | −40.7089 | −1.93414 | −0.967068 | − | 0.254517i | \(-0.918084\pi\) | ||||
−0.967068 | + | 0.254517i | \(0.918084\pi\) | |||||||
\(444\) | 20.8628 | 0.990107 | ||||||||
\(445\) | 1.06348 | 0.0504136 | ||||||||
\(446\) | 12.1229 | 0.574036 | ||||||||
\(447\) | −10.8039 | −0.511006 | ||||||||
\(448\) | −3.81414 | −0.180201 | ||||||||
\(449\) | 8.56754 | 0.404327 | 0.202164 | − | 0.979352i | \(-0.435203\pi\) | ||||
0.202164 | + | 0.979352i | \(0.435203\pi\) | |||||||
\(450\) | −30.7950 | −1.45169 | ||||||||
\(451\) | 11.6490 | 0.548530 | ||||||||
\(452\) | −6.10115 | −0.286974 | ||||||||
\(453\) | −14.0373 | −0.659528 | ||||||||
\(454\) | 29.0275 | 1.36233 | ||||||||
\(455\) | 0.0320795 | 0.00150391 | ||||||||
\(456\) | −18.6458 | −0.873172 | ||||||||
\(457\) | −19.1190 | −0.894350 | −0.447175 | − | 0.894446i | \(-0.647570\pi\) | ||||
−0.447175 | + | 0.894446i | \(0.647570\pi\) | |||||||
\(458\) | 14.6144 | 0.682888 | ||||||||
\(459\) | 66.5243 | 3.10509 | ||||||||
\(460\) | 0.0850017 | 0.00396323 | ||||||||
\(461\) | 32.9517 | 1.53471 | 0.767356 | − | 0.641221i | \(-0.221572\pi\) | ||||
0.767356 | + | 0.641221i | \(0.221572\pi\) | |||||||
\(462\) | −11.5646 | −0.538032 | ||||||||
\(463\) | −23.3372 | −1.08457 | −0.542285 | − | 0.840195i | \(-0.682441\pi\) | ||||
−0.542285 | + | 0.840195i | \(0.682441\pi\) | |||||||
\(464\) | −2.35600 | −0.109374 | ||||||||
\(465\) | −4.08268 | −0.189330 | ||||||||
\(466\) | 21.4191 | 0.992220 | ||||||||
\(467\) | 35.7040 | 1.65218 | 0.826091 | − | 0.563536i | \(-0.190559\pi\) | ||||
0.826091 | + | 0.563536i | \(0.190559\pi\) | |||||||
\(468\) | −0.313584 | −0.0144954 | ||||||||
\(469\) | −41.1417 | −1.89975 | ||||||||
\(470\) | 0.0211827 | 0.000977086 0 | ||||||||
\(471\) | −66.4581 | −3.06223 | ||||||||
\(472\) | −5.81311 | −0.267570 | ||||||||
\(473\) | 3.00175 | 0.138021 | ||||||||
\(474\) | −38.7521 | −1.77994 | ||||||||
\(475\) | −30.5785 | −1.40304 | ||||||||
\(476\) | 26.2071 | 1.20120 | ||||||||
\(477\) | −83.3057 | −3.81431 | ||||||||
\(478\) | −1.92035 | −0.0878346 | ||||||||
\(479\) | 15.6255 | 0.713945 | 0.356973 | − | 0.934115i | \(-0.383809\pi\) | ||||
0.356973 | + | 0.934115i | \(0.383809\pi\) | |||||||
\(480\) | −0.503646 | −0.0229882 | ||||||||
\(481\) | 0.348401 | 0.0158857 | ||||||||
\(482\) | 13.0050 | 0.592362 | ||||||||
\(483\) | 5.91786 | 0.269272 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.345922 | 0.0157075 | ||||||||
\(486\) | −3.62756 | −0.164550 | ||||||||
\(487\) | −39.5206 | −1.79085 | −0.895425 | − | 0.445213i | \(-0.853128\pi\) | ||||
−0.895425 | + | 0.445213i | \(0.853128\pi\) | |||||||
\(488\) | 8.08229 | 0.365868 | ||||||||
\(489\) | −20.1763 | −0.912406 | ||||||||
\(490\) | 1.25373 | 0.0566377 | ||||||||
\(491\) | 32.0955 | 1.44845 | 0.724224 | − | 0.689565i | \(-0.242198\pi\) | ||||
0.724224 | + | 0.689565i | \(0.242198\pi\) | |||||||
\(492\) | 35.3201 | 1.59235 | ||||||||
\(493\) | 16.1882 | 0.729080 | ||||||||
\(494\) | −0.311378 | −0.0140096 | ||||||||
\(495\) | −1.02874 | −0.0462385 | ||||||||
\(496\) | 8.10625 | 0.363981 | ||||||||
\(497\) | −25.7898 | −1.15683 | ||||||||
\(498\) | 11.8943 | 0.532998 | ||||||||
\(499\) | −43.8293 | −1.96207 | −0.981034 | − | 0.193836i | \(-0.937907\pi\) | ||||
−0.981034 | + | 0.193836i | \(0.937907\pi\) | |||||||
\(500\) | −1.65650 | −0.0740811 | ||||||||
\(501\) | 22.4547 | 1.00320 | ||||||||
\(502\) | 25.9958 | 1.16025 | ||||||||
\(503\) | 30.0284 | 1.33890 | 0.669450 | − | 0.742857i | \(-0.266530\pi\) | ||||
0.669450 | + | 0.742857i | \(0.266530\pi\) | |||||||
\(504\) | −23.6216 | −1.05219 | ||||||||
\(505\) | 2.48572 | 0.110613 | ||||||||
\(506\) | −0.511723 | −0.0227489 | ||||||||
\(507\) | 39.4086 | 1.75020 | ||||||||
\(508\) | 9.89255 | 0.438911 | ||||||||
\(509\) | −13.7211 | −0.608176 | −0.304088 | − | 0.952644i | \(-0.598352\pi\) | ||||
−0.304088 | + | 0.952644i | \(0.598352\pi\) | |||||||
\(510\) | 3.46058 | 0.153237 | ||||||||
\(511\) | −62.1787 | −2.75062 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −59.5396 | −2.62874 | ||||||||
\(514\) | 20.9429 | 0.923751 | ||||||||
\(515\) | −1.67769 | −0.0739278 | ||||||||
\(516\) | 9.10140 | 0.400667 | ||||||||
\(517\) | −0.127523 | −0.00560846 | ||||||||
\(518\) | 26.2444 | 1.15311 | ||||||||
\(519\) | 16.2419 | 0.712939 | ||||||||
\(520\) | −0.00841070 | −0.000368833 0 | ||||||||
\(521\) | −19.4234 | −0.850954 | −0.425477 | − | 0.904969i | \(-0.639894\pi\) | ||||
−0.425477 | + | 0.904969i | \(0.639894\pi\) | |||||||
\(522\) | −14.5911 | −0.638636 | ||||||||
\(523\) | −26.4242 | −1.15545 | −0.577725 | − | 0.816231i | \(-0.696059\pi\) | ||||
−0.577725 | + | 0.816231i | \(0.696059\pi\) | |||||||
\(524\) | −10.7411 | −0.469228 | ||||||||
\(525\) | −57.5037 | −2.50967 | ||||||||
\(526\) | 25.4745 | 1.11074 | ||||||||
\(527\) | −55.6985 | −2.42626 | ||||||||
\(528\) | 3.03203 | 0.131952 | ||||||||
\(529\) | −22.7381 | −0.988615 | ||||||||
\(530\) | −2.23436 | −0.0970545 | ||||||||
\(531\) | −36.0016 | −1.56234 | ||||||||
\(532\) | −23.4555 | −1.01693 | ||||||||
\(533\) | 0.589832 | 0.0255485 | ||||||||
\(534\) | −19.4119 | −0.840035 | ||||||||
\(535\) | −2.29261 | −0.0991180 | ||||||||
\(536\) | 10.7866 | 0.465912 | ||||||||
\(537\) | −77.5275 | −3.34556 | ||||||||
\(538\) | −15.3961 | −0.663775 | ||||||||
\(539\) | −7.54764 | −0.325100 | ||||||||
\(540\) | −1.60823 | −0.0692074 | ||||||||
\(541\) | −38.7122 | −1.66437 | −0.832183 | − | 0.554501i | \(-0.812909\pi\) | ||||
−0.832183 | + | 0.554501i | \(0.812909\pi\) | |||||||
\(542\) | 2.54931 | 0.109502 | ||||||||
\(543\) | 38.4778 | 1.65124 | ||||||||
\(544\) | −6.87105 | −0.294594 | ||||||||
\(545\) | −0.515750 | −0.0220923 | ||||||||
\(546\) | −0.585556 | −0.0250595 | ||||||||
\(547\) | −2.28442 | −0.0976748 | −0.0488374 | − | 0.998807i | \(-0.515552\pi\) | ||||
−0.0488374 | + | 0.998807i | \(0.515552\pi\) | |||||||
\(548\) | 18.3506 | 0.783899 | ||||||||
\(549\) | 50.0551 | 2.13630 | ||||||||
\(550\) | 4.97241 | 0.212024 | ||||||||
\(551\) | −14.4885 | −0.617232 | ||||||||
\(552\) | −1.55156 | −0.0660387 | ||||||||
\(553\) | −48.7482 | −2.07298 | ||||||||
\(554\) | 11.0873 | 0.471052 | ||||||||
\(555\) | 3.46550 | 0.147102 | ||||||||
\(556\) | 6.12724 | 0.259853 | ||||||||
\(557\) | 13.6862 | 0.579904 | 0.289952 | − | 0.957041i | \(-0.406361\pi\) | ||||
0.289952 | + | 0.957041i | \(0.406361\pi\) | |||||||
\(558\) | 50.2035 | 2.12528 | ||||||||
\(559\) | 0.151990 | 0.00642848 | ||||||||
\(560\) | −0.633562 | −0.0267729 | ||||||||
\(561\) | −20.8332 | −0.879579 | ||||||||
\(562\) | −14.2505 | −0.601120 | ||||||||
\(563\) | 42.1715 | 1.77732 | 0.888659 | − | 0.458569i | \(-0.151638\pi\) | ||||
0.888659 | + | 0.458569i | \(0.151638\pi\) | |||||||
\(564\) | −0.386654 | −0.0162811 | ||||||||
\(565\) | −1.01345 | −0.0426363 | ||||||||
\(566\) | 9.22982 | 0.387958 | ||||||||
\(567\) | −41.1010 | −1.72608 | ||||||||
\(568\) | 6.76163 | 0.283712 | ||||||||
\(569\) | −27.1028 | −1.13621 | −0.568104 | − | 0.822957i | \(-0.692323\pi\) | ||||
−0.568104 | + | 0.822957i | \(0.692323\pi\) | |||||||
\(570\) | −3.09724 | −0.129729 | ||||||||
\(571\) | 3.74835 | 0.156863 | 0.0784317 | − | 0.996919i | \(-0.475009\pi\) | ||||
0.0784317 | + | 0.996919i | \(0.475009\pi\) | |||||||
\(572\) | 0.0506337 | 0.00211710 | ||||||||
\(573\) | −5.13501 | −0.214518 | ||||||||
\(574\) | 44.4309 | 1.85451 | ||||||||
\(575\) | −2.54450 | −0.106113 | ||||||||
\(576\) | 6.19318 | 0.258049 | ||||||||
\(577\) | 9.27951 | 0.386311 | 0.193155 | − | 0.981168i | \(-0.438128\pi\) | ||||
0.193155 | + | 0.981168i | \(0.438128\pi\) | |||||||
\(578\) | 30.2114 | 1.25663 | ||||||||
\(579\) | 47.7627 | 1.98495 | ||||||||
\(580\) | −0.391352 | −0.0162500 | ||||||||
\(581\) | 14.9625 | 0.620748 | ||||||||
\(582\) | −6.31420 | −0.261732 | ||||||||
\(583\) | 13.4512 | 0.557092 | ||||||||
\(584\) | 16.3022 | 0.674588 | ||||||||
\(585\) | −0.0520890 | −0.00215361 | ||||||||
\(586\) | 8.18464 | 0.338105 | ||||||||
\(587\) | 1.99899 | 0.0825071 | 0.0412535 | − | 0.999149i | \(-0.486865\pi\) | ||||
0.0412535 | + | 0.999149i | \(0.486865\pi\) | |||||||
\(588\) | −22.8847 | −0.943747 | ||||||||
\(589\) | 49.8504 | 2.05405 | ||||||||
\(590\) | −0.965608 | −0.0397535 | ||||||||
\(591\) | 3.03203 | 0.124721 | ||||||||
\(592\) | −6.88083 | −0.282800 | ||||||||
\(593\) | 5.13124 | 0.210715 | 0.105357 | − | 0.994434i | \(-0.466401\pi\) | ||||
0.105357 | + | 0.994434i | \(0.466401\pi\) | |||||||
\(594\) | 9.68181 | 0.397250 | ||||||||
\(595\) | 4.35324 | 0.178465 | ||||||||
\(596\) | 3.56325 | 0.145956 | ||||||||
\(597\) | 37.5178 | 1.53550 | ||||||||
\(598\) | −0.0259104 | −0.00105956 | ||||||||
\(599\) | −5.97253 | −0.244031 | −0.122016 | − | 0.992528i | \(-0.538936\pi\) | ||||
−0.122016 | + | 0.992528i | \(0.538936\pi\) | |||||||
\(600\) | 15.0765 | 0.615494 | ||||||||
\(601\) | −20.2190 | −0.824750 | −0.412375 | − | 0.911014i | \(-0.635301\pi\) | ||||
−0.412375 | + | 0.911014i | \(0.635301\pi\) | |||||||
\(602\) | 11.4491 | 0.466631 | ||||||||
\(603\) | 66.8036 | 2.72045 | ||||||||
\(604\) | 4.62966 | 0.188378 | ||||||||
\(605\) | 0.166109 | 0.00675328 | ||||||||
\(606\) | −45.3725 | −1.84313 | ||||||||
\(607\) | 5.55943 | 0.225650 | 0.112825 | − | 0.993615i | \(-0.464010\pi\) | ||||
0.112825 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(608\) | 6.14963 | 0.249401 | ||||||||
\(609\) | −27.2461 | −1.10407 | ||||||||
\(610\) | 1.34254 | 0.0543578 | ||||||||
\(611\) | −0.00645696 | −0.000261221 0 | ||||||||
\(612\) | −42.5537 | −1.72013 | ||||||||
\(613\) | −3.79740 | −0.153376 | −0.0766878 | − | 0.997055i | \(-0.524434\pi\) | ||||
−0.0766878 | + | 0.997055i | \(0.524434\pi\) | |||||||
\(614\) | 20.3784 | 0.822404 | ||||||||
\(615\) | 5.86698 | 0.236579 | ||||||||
\(616\) | 3.81414 | 0.153676 | ||||||||
\(617\) | −3.92954 | −0.158197 | −0.0790986 | − | 0.996867i | \(-0.525204\pi\) | ||||
−0.0790986 | + | 0.996867i | \(0.525204\pi\) | |||||||
\(618\) | 30.6233 | 1.23185 | ||||||||
\(619\) | 17.6742 | 0.710388 | 0.355194 | − | 0.934793i | \(-0.384415\pi\) | ||||
0.355194 | + | 0.934793i | \(0.384415\pi\) | |||||||
\(620\) | 1.34652 | 0.0540775 | ||||||||
\(621\) | −4.95441 | −0.198814 | ||||||||
\(622\) | −30.4710 | −1.22178 | ||||||||
\(623\) | −24.4192 | −0.978335 | ||||||||
\(624\) | 0.153523 | 0.00614582 | ||||||||
\(625\) | 24.5869 | 0.983475 | ||||||||
\(626\) | 17.8210 | 0.712271 | ||||||||
\(627\) | 18.6458 | 0.744643 | ||||||||
\(628\) | 21.9187 | 0.874652 | ||||||||
\(629\) | 47.2785 | 1.88512 | ||||||||
\(630\) | −3.92376 | −0.156326 | ||||||||
\(631\) | 0.316869 | 0.0126144 | 0.00630718 | − | 0.999980i | \(-0.497992\pi\) | ||||
0.00630718 | + | 0.999980i | \(0.497992\pi\) | |||||||
\(632\) | 12.7809 | 0.508398 | ||||||||
\(633\) | −50.8813 | −2.02235 | ||||||||
\(634\) | −25.2830 | −1.00412 | ||||||||
\(635\) | 1.64324 | 0.0652100 | ||||||||
\(636\) | 40.7844 | 1.61721 | ||||||||
\(637\) | −0.382165 | −0.0151419 | ||||||||
\(638\) | 2.35600 | 0.0932749 | ||||||||
\(639\) | 41.8760 | 1.65659 | ||||||||
\(640\) | 0.166109 | 0.00656603 | ||||||||
\(641\) | −0.517942 | −0.0204575 | −0.0102287 | − | 0.999948i | \(-0.503256\pi\) | ||||
−0.0102287 | + | 0.999948i | \(0.503256\pi\) | |||||||
\(642\) | 41.8475 | 1.65159 | ||||||||
\(643\) | −19.5342 | −0.770352 | −0.385176 | − | 0.922843i | \(-0.625859\pi\) | ||||
−0.385176 | + | 0.922843i | \(0.625859\pi\) | |||||||
\(644\) | −1.95178 | −0.0769110 | ||||||||
\(645\) | 1.51182 | 0.0595279 | ||||||||
\(646\) | −42.2545 | −1.66248 | ||||||||
\(647\) | 27.5050 | 1.08133 | 0.540666 | − | 0.841237i | \(-0.318172\pi\) | ||||
0.540666 | + | 0.841237i | \(0.318172\pi\) | |||||||
\(648\) | 10.7760 | 0.423320 | ||||||||
\(649\) | 5.81311 | 0.228184 | ||||||||
\(650\) | 0.251771 | 0.00987528 | ||||||||
\(651\) | 93.7452 | 3.67417 | ||||||||
\(652\) | 6.65441 | 0.260607 | ||||||||
\(653\) | −10.5515 | −0.412912 | −0.206456 | − | 0.978456i | \(-0.566193\pi\) | ||||
−0.206456 | + | 0.978456i | \(0.566193\pi\) | |||||||
\(654\) | 9.41412 | 0.368121 | ||||||||
\(655\) | −1.78420 | −0.0697143 | ||||||||
\(656\) | −11.6490 | −0.454817 | ||||||||
\(657\) | 100.962 | 3.93891 | ||||||||
\(658\) | −0.486391 | −0.0189615 | ||||||||
\(659\) | 11.6989 | 0.455724 | 0.227862 | − | 0.973693i | \(-0.426827\pi\) | ||||
0.227862 | + | 0.973693i | \(0.426827\pi\) | |||||||
\(660\) | 0.503646 | 0.0196044 | ||||||||
\(661\) | 38.8021 | 1.50923 | 0.754614 | − | 0.656169i | \(-0.227824\pi\) | ||||
0.754614 | + | 0.656169i | \(0.227824\pi\) | |||||||
\(662\) | −20.1374 | −0.782664 | ||||||||
\(663\) | −1.05486 | −0.0409674 | ||||||||
\(664\) | −3.92290 | −0.152238 | ||||||||
\(665\) | −3.89617 | −0.151087 | ||||||||
\(666\) | −42.6142 | −1.65127 | ||||||||
\(667\) | −1.20562 | −0.0466818 | ||||||||
\(668\) | −7.40584 | −0.286540 | ||||||||
\(669\) | −36.7569 | −1.42111 | ||||||||
\(670\) | 1.79176 | 0.0692216 | ||||||||
\(671\) | −8.08229 | −0.312013 | ||||||||
\(672\) | 11.5646 | 0.446113 | ||||||||
\(673\) | 13.2547 | 0.510930 | 0.255465 | − | 0.966818i | \(-0.417771\pi\) | ||||
0.255465 | + | 0.966818i | \(0.417771\pi\) | |||||||
\(674\) | 9.66620 | 0.372328 | ||||||||
\(675\) | 48.1419 | 1.85298 | ||||||||
\(676\) | −12.9974 | −0.499901 | ||||||||
\(677\) | 37.2988 | 1.43351 | 0.716755 | − | 0.697325i | \(-0.245626\pi\) | ||||
0.716755 | + | 0.697325i | \(0.245626\pi\) | |||||||
\(678\) | 18.4988 | 0.710444 | ||||||||
\(679\) | −7.94295 | −0.304823 | ||||||||
\(680\) | −1.14134 | −0.0437685 | ||||||||
\(681\) | −88.0120 | −3.37263 | ||||||||
\(682\) | −8.10625 | −0.310404 | ||||||||
\(683\) | −37.2642 | −1.42588 | −0.712938 | − | 0.701227i | \(-0.752636\pi\) | ||||
−0.712938 | + | 0.701227i | \(0.752636\pi\) | |||||||
\(684\) | 38.0858 | 1.45625 | ||||||||
\(685\) | 3.04820 | 0.116466 | ||||||||
\(686\) | −2.08879 | −0.0797503 | ||||||||
\(687\) | −44.3114 | −1.69058 | ||||||||
\(688\) | −3.00175 | −0.114441 | ||||||||
\(689\) | 0.681083 | 0.0259472 | ||||||||
\(690\) | −0.257727 | −0.00981152 | ||||||||
\(691\) | 35.3757 | 1.34576 | 0.672878 | − | 0.739753i | \(-0.265058\pi\) | ||||
0.672878 | + | 0.739753i | \(0.265058\pi\) | |||||||
\(692\) | −5.35677 | −0.203634 | ||||||||
\(693\) | 23.6216 | 0.897312 | ||||||||
\(694\) | 9.15792 | 0.347630 | ||||||||
\(695\) | 1.01779 | 0.0386069 | ||||||||
\(696\) | 7.14345 | 0.270772 | ||||||||
\(697\) | 80.0409 | 3.03177 | ||||||||
\(698\) | −1.35630 | −0.0513366 | ||||||||
\(699\) | −64.9432 | −2.45638 | ||||||||
\(700\) | 18.9654 | 0.716826 | ||||||||
\(701\) | −18.8161 | −0.710674 | −0.355337 | − | 0.934738i | \(-0.615634\pi\) | ||||
−0.355337 | + | 0.934738i | \(0.615634\pi\) | |||||||
\(702\) | 0.490226 | 0.0185024 | ||||||||
\(703\) | −42.3146 | −1.59592 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −0.0642266 | −0.00241891 | ||||||||
\(706\) | −5.33642 | −0.200839 | ||||||||
\(707\) | −57.0763 | −2.14657 | ||||||||
\(708\) | 17.6255 | 0.662407 | ||||||||
\(709\) | 19.3600 | 0.727079 | 0.363540 | − | 0.931579i | \(-0.381568\pi\) | ||||
0.363540 | + | 0.931579i | \(0.381568\pi\) | |||||||
\(710\) | 1.12317 | 0.0421517 | ||||||||
\(711\) | 79.1546 | 2.96853 | ||||||||
\(712\) | 6.40229 | 0.239936 | ||||||||
\(713\) | 4.14816 | 0.155350 | ||||||||
\(714\) | −79.4607 | −2.97374 | ||||||||
\(715\) | 0.00841070 | 0.000314542 0 | ||||||||
\(716\) | 25.5696 | 0.955579 | ||||||||
\(717\) | 5.82254 | 0.217447 | ||||||||
\(718\) | 18.9002 | 0.705351 | ||||||||
\(719\) | 13.3509 | 0.497903 | 0.248952 | − | 0.968516i | \(-0.419914\pi\) | ||||
0.248952 | + | 0.968516i | \(0.419914\pi\) | |||||||
\(720\) | 1.02874 | 0.0383390 | ||||||||
\(721\) | 38.5226 | 1.43466 | ||||||||
\(722\) | 18.8180 | 0.700332 | ||||||||
\(723\) | −39.4315 | −1.46647 | ||||||||
\(724\) | −12.6905 | −0.471637 | ||||||||
\(725\) | 11.7150 | 0.435084 | ||||||||
\(726\) | −3.03203 | −0.112529 | ||||||||
\(727\) | −27.2684 | −1.01133 | −0.505665 | − | 0.862730i | \(-0.668753\pi\) | ||||
−0.505665 | + | 0.862730i | \(0.668753\pi\) | |||||||
\(728\) | 0.193124 | 0.00715764 | ||||||||
\(729\) | −21.3290 | −0.789964 | ||||||||
\(730\) | 2.70793 | 0.100225 | ||||||||
\(731\) | 20.6252 | 0.762851 | ||||||||
\(732\) | −24.5057 | −0.905757 | ||||||||
\(733\) | −31.8139 | −1.17507 | −0.587537 | − | 0.809198i | \(-0.699902\pi\) | ||||
−0.587537 | + | 0.809198i | \(0.699902\pi\) | |||||||
\(734\) | −19.7230 | −0.727988 | ||||||||
\(735\) | −3.80134 | −0.140215 | ||||||||
\(736\) | 0.511723 | 0.0188624 | ||||||||
\(737\) | −10.7866 | −0.397331 | ||||||||
\(738\) | −72.1444 | −2.65567 | ||||||||
\(739\) | 19.4469 | 0.715366 | 0.357683 | − | 0.933843i | \(-0.383567\pi\) | ||||
0.357683 | + | 0.933843i | \(0.383567\pi\) | |||||||
\(740\) | −1.14297 | −0.0420163 | ||||||||
\(741\) | 0.944107 | 0.0346827 | ||||||||
\(742\) | 51.3047 | 1.88346 | ||||||||
\(743\) | 12.8043 | 0.469745 | 0.234872 | − | 0.972026i | \(-0.424533\pi\) | ||||
0.234872 | + | 0.972026i | \(0.424533\pi\) | |||||||
\(744\) | −24.5784 | −0.901086 | ||||||||
\(745\) | 0.591887 | 0.0216851 | ||||||||
\(746\) | −9.58095 | −0.350784 | ||||||||
\(747\) | −24.2952 | −0.888916 | ||||||||
\(748\) | 6.87105 | 0.251231 | ||||||||
\(749\) | 52.6421 | 1.92350 | ||||||||
\(750\) | 5.02257 | 0.183398 | ||||||||
\(751\) | 30.6629 | 1.11890 | 0.559452 | − | 0.828863i | \(-0.311012\pi\) | ||||
0.559452 | + | 0.828863i | \(0.311012\pi\) | |||||||
\(752\) | 0.127523 | 0.00465029 | ||||||||
\(753\) | −78.8200 | −2.87236 | ||||||||
\(754\) | 0.119293 | 0.00434439 | ||||||||
\(755\) | 0.769027 | 0.0279878 | ||||||||
\(756\) | 36.9278 | 1.34305 | ||||||||
\(757\) | −20.9154 | −0.760182 | −0.380091 | − | 0.924949i | \(-0.624107\pi\) | ||||
−0.380091 | + | 0.924949i | \(0.624107\pi\) | |||||||
\(758\) | 14.0487 | 0.510272 | ||||||||
\(759\) | 1.55156 | 0.0563180 | ||||||||
\(760\) | 1.02151 | 0.0370540 | ||||||||
\(761\) | 1.90068 | 0.0688997 | 0.0344499 | − | 0.999406i | \(-0.489032\pi\) | ||||
0.0344499 | + | 0.999406i | \(0.489032\pi\) | |||||||
\(762\) | −29.9945 | −1.08658 | ||||||||
\(763\) | 11.8425 | 0.428727 | ||||||||
\(764\) | 1.69359 | 0.0612720 | ||||||||
\(765\) | −7.06854 | −0.255564 | ||||||||
\(766\) | −6.02899 | −0.217836 | ||||||||
\(767\) | 0.294339 | 0.0106280 | ||||||||
\(768\) | −3.03203 | −0.109409 | ||||||||
\(769\) | −17.2441 | −0.621840 | −0.310920 | − | 0.950436i | \(-0.600637\pi\) | ||||
−0.310920 | + | 0.950436i | \(0.600637\pi\) | |||||||
\(770\) | 0.633562 | 0.0228320 | ||||||||
\(771\) | −63.4993 | −2.28687 | ||||||||
\(772\) | −15.7527 | −0.566953 | ||||||||
\(773\) | 46.3368 | 1.66662 | 0.833309 | − | 0.552807i | \(-0.186443\pi\) | ||||
0.833309 | + | 0.552807i | \(0.186443\pi\) | |||||||
\(774\) | −18.5904 | −0.668219 | ||||||||
\(775\) | −40.3076 | −1.44789 | ||||||||
\(776\) | 2.08250 | 0.0747575 | ||||||||
\(777\) | −79.5738 | −2.85469 | ||||||||
\(778\) | −32.8783 | −1.17875 | ||||||||
\(779\) | −71.6371 | −2.56667 | ||||||||
\(780\) | 0.0255015 | 0.000913098 0 | ||||||||
\(781\) | −6.76163 | −0.241950 | ||||||||
\(782\) | −3.51608 | −0.125735 | ||||||||
\(783\) | 22.8103 | 0.815175 | ||||||||
\(784\) | 7.54764 | 0.269559 | ||||||||
\(785\) | 3.64089 | 0.129949 | ||||||||
\(786\) | 32.5674 | 1.16164 | ||||||||
\(787\) | 6.64678 | 0.236932 | 0.118466 | − | 0.992958i | \(-0.462202\pi\) | ||||
0.118466 | + | 0.992958i | \(0.462202\pi\) | |||||||
\(788\) | −1.00000 | −0.0356235 | ||||||||
\(789\) | −77.2394 | −2.74980 | ||||||||
\(790\) | 2.12302 | 0.0755338 | ||||||||
\(791\) | 23.2706 | 0.827408 | ||||||||
\(792\) | −6.19318 | −0.220065 | ||||||||
\(793\) | −0.409236 | −0.0145324 | ||||||||
\(794\) | 18.7499 | 0.665409 | ||||||||
\(795\) | 6.77464 | 0.240272 | ||||||||
\(796\) | −12.3738 | −0.438579 | ||||||||
\(797\) | −20.9608 | −0.742470 | −0.371235 | − | 0.928539i | \(-0.621066\pi\) | ||||
−0.371235 | + | 0.928539i | \(0.621066\pi\) | |||||||
\(798\) | 71.1178 | 2.51754 | ||||||||
\(799\) | −0.876219 | −0.0309984 | ||||||||
\(800\) | −4.97241 | −0.175801 | ||||||||
\(801\) | 39.6505 | 1.40098 | ||||||||
\(802\) | −3.76413 | −0.132916 | ||||||||
\(803\) | −16.3022 | −0.575291 | ||||||||
\(804\) | −32.7054 | −1.15343 | ||||||||
\(805\) | −0.324208 | −0.0114268 | ||||||||
\(806\) | −0.410449 | −0.0144575 | ||||||||
\(807\) | 46.6815 | 1.64327 | ||||||||
\(808\) | 14.9644 | 0.526446 | ||||||||
\(809\) | −15.1008 | −0.530917 | −0.265458 | − | 0.964122i | \(-0.585523\pi\) | ||||
−0.265458 | + | 0.964122i | \(0.585523\pi\) | |||||||
\(810\) | 1.78998 | 0.0628936 | ||||||||
\(811\) | 44.6558 | 1.56808 | 0.784038 | − | 0.620713i | \(-0.213157\pi\) | ||||
0.784038 | + | 0.620713i | \(0.213157\pi\) | |||||||
\(812\) | 8.98610 | 0.315350 | ||||||||
\(813\) | −7.72959 | −0.271088 | ||||||||
\(814\) | 6.88083 | 0.241173 | ||||||||
\(815\) | 1.10536 | 0.0387189 | ||||||||
\(816\) | 20.8332 | 0.729308 | ||||||||
\(817\) | −18.4597 | −0.645823 | ||||||||
\(818\) | −9.61873 | −0.336311 | ||||||||
\(819\) | 1.19605 | 0.0417934 | ||||||||
\(820\) | −1.93500 | −0.0675732 | ||||||||
\(821\) | 7.56295 | 0.263949 | 0.131974 | − | 0.991253i | \(-0.457868\pi\) | ||||
0.131974 | + | 0.991253i | \(0.457868\pi\) | |||||||
\(822\) | −55.6395 | −1.94065 | ||||||||
\(823\) | −38.3827 | −1.33794 | −0.668968 | − | 0.743291i | \(-0.733264\pi\) | ||||
−0.668968 | + | 0.743291i | \(0.733264\pi\) | |||||||
\(824\) | −10.0999 | −0.351848 | ||||||||
\(825\) | −15.0765 | −0.524895 | ||||||||
\(826\) | 22.1720 | 0.771462 | ||||||||
\(827\) | −15.6983 | −0.545882 | −0.272941 | − | 0.962031i | \(-0.587996\pi\) | ||||
−0.272941 | + | 0.962031i | \(0.587996\pi\) | |||||||
\(828\) | 3.16920 | 0.110137 | ||||||||
\(829\) | 39.2791 | 1.36422 | 0.682110 | − | 0.731250i | \(-0.261063\pi\) | ||||
0.682110 | + | 0.731250i | \(0.261063\pi\) | |||||||
\(830\) | −0.651628 | −0.0226183 | ||||||||
\(831\) | −33.6168 | −1.16616 | ||||||||
\(832\) | −0.0506337 | −0.00175541 | ||||||||
\(833\) | −51.8603 | −1.79685 | ||||||||
\(834\) | −18.5779 | −0.643302 | ||||||||
\(835\) | −1.23017 | −0.0425719 | ||||||||
\(836\) | −6.14963 | −0.212689 | ||||||||
\(837\) | −78.4832 | −2.71278 | ||||||||
\(838\) | −29.9972 | −1.03624 | ||||||||
\(839\) | 22.9830 | 0.793461 | 0.396730 | − | 0.917935i | \(-0.370145\pi\) | ||||
0.396730 | + | 0.917935i | \(0.370145\pi\) | |||||||
\(840\) | 1.92098 | 0.0662800 | ||||||||
\(841\) | −23.4493 | −0.808596 | ||||||||
\(842\) | 0.643680 | 0.0221827 | ||||||||
\(843\) | 43.2078 | 1.48816 | ||||||||
\(844\) | 16.7813 | 0.577636 | ||||||||
\(845\) | −2.15899 | −0.0742715 | ||||||||
\(846\) | 0.789774 | 0.0271530 | ||||||||
\(847\) | −3.81414 | −0.131055 | ||||||||
\(848\) | −13.4512 | −0.461916 | ||||||||
\(849\) | −27.9851 | −0.960445 | ||||||||
\(850\) | 34.1657 | 1.17187 | ||||||||
\(851\) | −3.52108 | −0.120701 | ||||||||
\(852\) | −20.5014 | −0.702368 | ||||||||
\(853\) | 30.7087 | 1.05145 | 0.525723 | − | 0.850656i | \(-0.323795\pi\) | ||||
0.525723 | + | 0.850656i | \(0.323795\pi\) | |||||||
\(854\) | −30.8270 | −1.05488 | ||||||||
\(855\) | 6.32638 | 0.216358 | ||||||||
\(856\) | −13.8018 | −0.471737 | ||||||||
\(857\) | −28.8363 | −0.985029 | −0.492515 | − | 0.870304i | \(-0.663922\pi\) | ||||
−0.492515 | + | 0.870304i | \(0.663922\pi\) | |||||||
\(858\) | −0.153523 | −0.00524117 | ||||||||
\(859\) | 31.3542 | 1.06979 | 0.534895 | − | 0.844918i | \(-0.320351\pi\) | ||||
0.534895 | + | 0.844918i | \(0.320351\pi\) | |||||||
\(860\) | −0.498618 | −0.0170027 | ||||||||
\(861\) | −134.716 | −4.59110 | ||||||||
\(862\) | −32.5274 | −1.10789 | ||||||||
\(863\) | 9.48537 | 0.322886 | 0.161443 | − | 0.986882i | \(-0.448385\pi\) | ||||
0.161443 | + | 0.986882i | \(0.448385\pi\) | |||||||
\(864\) | −9.68181 | −0.329382 | ||||||||
\(865\) | −0.889807 | −0.0302543 | ||||||||
\(866\) | 27.5766 | 0.937091 | ||||||||
\(867\) | −91.6017 | −3.11096 | ||||||||
\(868\) | −30.9183 | −1.04944 | ||||||||
\(869\) | −12.7809 | −0.433563 | ||||||||
\(870\) | 1.18659 | 0.0402292 | ||||||||
\(871\) | −0.546167 | −0.0185062 | ||||||||
\(872\) | −3.10489 | −0.105145 | ||||||||
\(873\) | 12.8973 | 0.436508 | ||||||||
\(874\) | 3.14691 | 0.106446 | ||||||||
\(875\) | 6.31814 | 0.213592 | ||||||||
\(876\) | −49.4286 | −1.67004 | ||||||||
\(877\) | −43.3408 | −1.46352 | −0.731758 | − | 0.681564i | \(-0.761300\pi\) | ||||
−0.731758 | + | 0.681564i | \(0.761300\pi\) | |||||||
\(878\) | −6.52532 | −0.220219 | ||||||||
\(879\) | −24.8161 | −0.837025 | ||||||||
\(880\) | −0.166109 | −0.00559953 | ||||||||
\(881\) | −26.2998 | −0.886062 | −0.443031 | − | 0.896506i | \(-0.646097\pi\) | ||||
−0.443031 | + | 0.896506i | \(0.646097\pi\) | |||||||
\(882\) | 46.7439 | 1.57395 | ||||||||
\(883\) | 1.37722 | 0.0463473 | 0.0231736 | − | 0.999731i | \(-0.492623\pi\) | ||||
0.0231736 | + | 0.999731i | \(0.492623\pi\) | |||||||
\(884\) | 0.347907 | 0.0117014 | ||||||||
\(885\) | 2.92775 | 0.0984152 | ||||||||
\(886\) | −40.7089 | −1.36764 | ||||||||
\(887\) | −0.276896 | −0.00929726 | −0.00464863 | − | 0.999989i | \(-0.501480\pi\) | ||||
−0.00464863 | + | 0.999989i | \(0.501480\pi\) | |||||||
\(888\) | 20.8628 | 0.700111 | ||||||||
\(889\) | −37.7315 | −1.26548 | ||||||||
\(890\) | 1.06348 | 0.0356478 | ||||||||
\(891\) | −10.7760 | −0.361008 | ||||||||
\(892\) | 12.1229 | 0.405905 | ||||||||
\(893\) | 0.784221 | 0.0262429 | ||||||||
\(894\) | −10.8039 | −0.361335 | ||||||||
\(895\) | 4.24733 | 0.141972 | ||||||||
\(896\) | −3.81414 | −0.127421 | ||||||||
\(897\) | 0.0785611 | 0.00262308 | ||||||||
\(898\) | 8.56754 | 0.285903 | ||||||||
\(899\) | −19.0983 | −0.636964 | ||||||||
\(900\) | −30.7950 | −1.02650 | ||||||||
\(901\) | 92.4239 | 3.07909 | ||||||||
\(902\) | 11.6490 | 0.387869 | ||||||||
\(903\) | −34.7140 | −1.15521 | ||||||||
\(904\) | −6.10115 | −0.202921 | ||||||||
\(905\) | −2.10800 | −0.0700722 | ||||||||
\(906\) | −14.0373 | −0.466356 | ||||||||
\(907\) | −9.51101 | −0.315808 | −0.157904 | − | 0.987454i | \(-0.550474\pi\) | ||||
−0.157904 | + | 0.987454i | \(0.550474\pi\) | |||||||
\(908\) | 29.0275 | 0.963310 | ||||||||
\(909\) | 92.6773 | 3.07391 | ||||||||
\(910\) | 0.0320795 | 0.00106343 | ||||||||
\(911\) | −22.3222 | −0.739567 | −0.369783 | − | 0.929118i | \(-0.620568\pi\) | ||||
−0.369783 | + | 0.929118i | \(0.620568\pi\) | |||||||
\(912\) | −18.6458 | −0.617426 | ||||||||
\(913\) | 3.92290 | 0.129829 | ||||||||
\(914\) | −19.1190 | −0.632401 | ||||||||
\(915\) | −4.07062 | −0.134570 | ||||||||
\(916\) | 14.6144 | 0.482875 | ||||||||
\(917\) | 40.9681 | 1.35289 | ||||||||
\(918\) | 66.5243 | 2.19563 | ||||||||
\(919\) | −31.2461 | −1.03072 | −0.515358 | − | 0.856975i | \(-0.672341\pi\) | ||||
−0.515358 | + | 0.856975i | \(0.672341\pi\) | |||||||
\(920\) | 0.0850017 | 0.00280242 | ||||||||
\(921\) | −61.7877 | −2.03597 | ||||||||
\(922\) | 32.9517 | 1.08521 | ||||||||
\(923\) | −0.342366 | −0.0112691 | ||||||||
\(924\) | −11.5646 | −0.380446 | ||||||||
\(925\) | 34.2143 | 1.12496 | ||||||||
\(926\) | −23.3372 | −0.766906 | ||||||||
\(927\) | −62.5508 | −2.05444 | ||||||||
\(928\) | −2.35600 | −0.0773394 | ||||||||
\(929\) | −32.8420 | −1.07751 | −0.538755 | − | 0.842463i | \(-0.681105\pi\) | ||||
−0.538755 | + | 0.842463i | \(0.681105\pi\) | |||||||
\(930\) | −4.08268 | −0.133876 | ||||||||
\(931\) | 46.4152 | 1.52120 | ||||||||
\(932\) | 21.4191 | 0.701605 | ||||||||
\(933\) | 92.3888 | 3.02467 | ||||||||
\(934\) | 35.7040 | 1.16827 | ||||||||
\(935\) | 1.14134 | 0.0373259 | ||||||||
\(936\) | −0.313584 | −0.0102498 | ||||||||
\(937\) | −21.2236 | −0.693345 | −0.346672 | − | 0.937986i | \(-0.612688\pi\) | ||||
−0.346672 | + | 0.937986i | \(0.612688\pi\) | |||||||
\(938\) | −41.1417 | −1.34333 | ||||||||
\(939\) | −54.0338 | −1.76333 | ||||||||
\(940\) | 0.0211827 | 0.000690904 0 | ||||||||
\(941\) | 50.3176 | 1.64031 | 0.820154 | − | 0.572143i | \(-0.193888\pi\) | ||||
0.820154 | + | 0.572143i | \(0.193888\pi\) | |||||||
\(942\) | −66.4581 | −2.16532 | ||||||||
\(943\) | −5.96107 | −0.194119 | ||||||||
\(944\) | −5.81311 | −0.189201 | ||||||||
\(945\) | 6.13403 | 0.199540 | ||||||||
\(946\) | 3.00175 | 0.0975955 | ||||||||
\(947\) | 38.2254 | 1.24216 | 0.621079 | − | 0.783748i | \(-0.286695\pi\) | ||||
0.621079 | + | 0.783748i | \(0.286695\pi\) | |||||||
\(948\) | −38.7521 | −1.25861 | ||||||||
\(949\) | −0.825438 | −0.0267949 | ||||||||
\(950\) | −30.5785 | −0.992097 | ||||||||
\(951\) | 76.6588 | 2.48583 | ||||||||
\(952\) | 26.2071 | 0.849378 | ||||||||
\(953\) | 46.5777 | 1.50880 | 0.754401 | − | 0.656414i | \(-0.227928\pi\) | ||||
0.754401 | + | 0.656414i | \(0.227928\pi\) | |||||||
\(954\) | −83.3057 | −2.69712 | ||||||||
\(955\) | 0.281320 | 0.00910331 | ||||||||
\(956\) | −1.92035 | −0.0621084 | ||||||||
\(957\) | −7.14345 | −0.230915 | ||||||||
\(958\) | 15.6255 | 0.504836 | ||||||||
\(959\) | −69.9917 | −2.26015 | ||||||||
\(960\) | −0.503646 | −0.0162551 | ||||||||
\(961\) | 34.7113 | 1.11972 | ||||||||
\(962\) | 0.348401 | 0.0112329 | ||||||||
\(963\) | −85.4773 | −2.75447 | ||||||||
\(964\) | 13.0050 | 0.418863 | ||||||||
\(965\) | −2.61667 | −0.0842335 | ||||||||
\(966\) | 5.91786 | 0.190404 | ||||||||
\(967\) | −4.65602 | −0.149727 | −0.0748637 | − | 0.997194i | \(-0.523852\pi\) | ||||
−0.0748637 | + | 0.997194i | \(0.523852\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 128.117 | 4.11570 | ||||||||
\(970\) | 0.345922 | 0.0111069 | ||||||||
\(971\) | −34.2132 | −1.09795 | −0.548977 | − | 0.835837i | \(-0.684983\pi\) | ||||
−0.548977 | + | 0.835837i | \(0.684983\pi\) | |||||||
\(972\) | −3.62756 | −0.116354 | ||||||||
\(973\) | −23.3701 | −0.749212 | ||||||||
\(974\) | −39.5206 | −1.26632 | ||||||||
\(975\) | −0.763377 | −0.0244476 | ||||||||
\(976\) | 8.08229 | 0.258708 | ||||||||
\(977\) | −39.2707 | −1.25638 | −0.628190 | − | 0.778060i | \(-0.716204\pi\) | ||||
−0.628190 | + | 0.778060i | \(0.716204\pi\) | |||||||
\(978\) | −20.1763 | −0.645168 | ||||||||
\(979\) | −6.40229 | −0.204618 | ||||||||
\(980\) | 1.25373 | 0.0400489 | ||||||||
\(981\) | −19.2292 | −0.613940 | ||||||||
\(982\) | 32.0955 | 1.02421 | ||||||||
\(983\) | −11.9472 | −0.381057 | −0.190529 | − | 0.981682i | \(-0.561020\pi\) | ||||
−0.190529 | + | 0.981682i | \(0.561020\pi\) | |||||||
\(984\) | 35.3201 | 1.12596 | ||||||||
\(985\) | −0.166109 | −0.00529267 | ||||||||
\(986\) | 16.1882 | 0.515537 | ||||||||
\(987\) | 1.47475 | 0.0469418 | ||||||||
\(988\) | −0.311378 | −0.00990627 | ||||||||
\(989\) | −1.53607 | −0.0488441 | ||||||||
\(990\) | −1.02874 | −0.0326956 | ||||||||
\(991\) | 43.8508 | 1.39297 | 0.696483 | − | 0.717573i | \(-0.254747\pi\) | ||||
0.696483 | + | 0.717573i | \(0.254747\pi\) | |||||||
\(992\) | 8.10625 | 0.257374 | ||||||||
\(993\) | 61.0572 | 1.93759 | ||||||||
\(994\) | −25.7898 | −0.818002 | ||||||||
\(995\) | −2.05540 | −0.0651606 | ||||||||
\(996\) | 11.8943 | 0.376886 | ||||||||
\(997\) | −0.622649 | −0.0197195 | −0.00985974 | − | 0.999951i | \(-0.503139\pi\) | ||||
−0.00985974 | + | 0.999951i | \(0.503139\pi\) | |||||||
\(998\) | −43.8293 | −1.38739 | ||||||||
\(999\) | 66.6189 | 2.10773 |
(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 | 4334.2.a.f.1.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.f.1.1 | ✓ | 24 | 1.1 | even | 1 | trivial |