Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52406 | −1.78478 | −0.892391 | − | 0.451263i | \(-0.850974\pi\) | ||||
−0.892391 | + | 0.451263i | \(0.850974\pi\) | |||||||
\(3\) | −2.15147 | −1.24215 | −0.621076 | − | 0.783750i | \(-0.713304\pi\) | ||||
−0.621076 | + | 0.783750i | \(0.713304\pi\) | |||||||
\(4\) | 4.37089 | 2.18545 | ||||||||
\(5\) | −1.88445 | −0.842754 | −0.421377 | − | 0.906886i | \(-0.638453\pi\) | ||||
−0.421377 | + | 0.906886i | \(0.638453\pi\) | |||||||
\(6\) | 5.43045 | 2.21697 | ||||||||
\(7\) | −0.0300064 | −0.0113414 | −0.00567068 | − | 0.999984i | \(-0.501805\pi\) | ||||
−0.00567068 | + | 0.999984i | \(0.501805\pi\) | |||||||
\(8\) | −5.98429 | −2.11576 | ||||||||
\(9\) | 1.62883 | 0.542944 | ||||||||
\(10\) | 4.75648 | 1.50413 | ||||||||
\(11\) | −1.05669 | −0.318603 | −0.159302 | − | 0.987230i | \(-0.550924\pi\) | ||||
−0.159302 | + | 0.987230i | \(0.550924\pi\) | |||||||
\(12\) | −9.40386 | −2.71466 | ||||||||
\(13\) | −2.00226 | −0.555327 | −0.277663 | − | 0.960678i | \(-0.589560\pi\) | ||||
−0.277663 | + | 0.960678i | \(0.589560\pi\) | |||||||
\(14\) | 0.0757381 | 0.0202418 | ||||||||
\(15\) | 4.05435 | 1.04683 | ||||||||
\(16\) | 6.36293 | 1.59073 | ||||||||
\(17\) | −1.58468 | −0.384340 | −0.192170 | − | 0.981362i | \(-0.561553\pi\) | ||||
−0.192170 | + | 0.981362i | \(0.561553\pi\) | |||||||
\(18\) | −4.11127 | −0.969037 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −8.23675 | −1.84179 | ||||||||
\(21\) | 0.0645579 | 0.0140877 | ||||||||
\(22\) | 2.66714 | 0.568637 | ||||||||
\(23\) | 4.43409 | 0.924572 | 0.462286 | − | 0.886731i | \(-0.347029\pi\) | ||||
0.462286 | + | 0.886731i | \(0.347029\pi\) | |||||||
\(24\) | 12.8750 | 2.62810 | ||||||||
\(25\) | −1.44883 | −0.289766 | ||||||||
\(26\) | 5.05383 | 0.991137 | ||||||||
\(27\) | 2.95003 | 0.567733 | ||||||||
\(28\) | −0.131155 | −0.0247859 | ||||||||
\(29\) | −9.99262 | −1.85558 | −0.927791 | − | 0.373100i | \(-0.878295\pi\) | ||||
−0.927791 | + | 0.373100i | \(0.878295\pi\) | |||||||
\(30\) | −10.2334 | −1.86836 | ||||||||
\(31\) | 6.58144 | 1.18206 | 0.591030 | − | 0.806649i | \(-0.298721\pi\) | ||||
0.591030 | + | 0.806649i | \(0.298721\pi\) | |||||||
\(32\) | −4.09186 | −0.723346 | ||||||||
\(33\) | 2.27343 | 0.395754 | ||||||||
\(34\) | 3.99982 | 0.685964 | ||||||||
\(35\) | 0.0565457 | 0.00955797 | ||||||||
\(36\) | 7.11945 | 1.18658 | ||||||||
\(37\) | 9.77672 | 1.60728 | 0.803641 | − | 0.595114i | \(-0.202893\pi\) | ||||
0.803641 | + | 0.595114i | \(0.202893\pi\) | |||||||
\(38\) | 2.52406 | 0.409457 | ||||||||
\(39\) | 4.30780 | 0.689801 | ||||||||
\(40\) | 11.2771 | 1.78307 | ||||||||
\(41\) | 0.483248 | 0.0754707 | 0.0377353 | − | 0.999288i | \(-0.487986\pi\) | ||||
0.0377353 | + | 0.999288i | \(0.487986\pi\) | |||||||
\(42\) | −0.162948 | −0.0251435 | ||||||||
\(43\) | 2.46914 | 0.376540 | 0.188270 | − | 0.982117i | \(-0.439712\pi\) | ||||
0.188270 | + | 0.982117i | \(0.439712\pi\) | |||||||
\(44\) | −4.61867 | −0.696290 | ||||||||
\(45\) | −3.06946 | −0.457568 | ||||||||
\(46\) | −11.1919 | −1.65016 | ||||||||
\(47\) | −11.1906 | −1.63232 | −0.816158 | − | 0.577829i | \(-0.803900\pi\) | ||||
−0.816158 | + | 0.577829i | \(0.803900\pi\) | |||||||
\(48\) | −13.6897 | −1.97593 | ||||||||
\(49\) | −6.99910 | −0.999871 | ||||||||
\(50\) | 3.65694 | 0.517170 | ||||||||
\(51\) | 3.40939 | 0.477409 | ||||||||
\(52\) | −8.75166 | −1.21364 | ||||||||
\(53\) | −1.30835 | −0.179716 | −0.0898580 | − | 0.995955i | \(-0.528641\pi\) | ||||
−0.0898580 | + | 0.995955i | \(0.528641\pi\) | |||||||
\(54\) | −7.44606 | −1.01328 | ||||||||
\(55\) | 1.99128 | 0.268504 | ||||||||
\(56\) | 0.179567 | 0.0239956 | ||||||||
\(57\) | 2.15147 | 0.284969 | ||||||||
\(58\) | 25.2220 | 3.31181 | ||||||||
\(59\) | −4.32698 | −0.563324 | −0.281662 | − | 0.959514i | \(-0.590886\pi\) | ||||
−0.281662 | + | 0.959514i | \(0.590886\pi\) | |||||||
\(60\) | 17.7211 | 2.28779 | ||||||||
\(61\) | −1.78340 | −0.228340 | −0.114170 | − | 0.993461i | \(-0.536421\pi\) | ||||
−0.114170 | + | 0.993461i | \(0.536421\pi\) | |||||||
\(62\) | −16.6120 | −2.10972 | ||||||||
\(63\) | −0.0488754 | −0.00615772 | ||||||||
\(64\) | −2.39774 | −0.299718 | ||||||||
\(65\) | 3.77317 | 0.468004 | ||||||||
\(66\) | −5.73829 | −0.706334 | ||||||||
\(67\) | 9.99586 | 1.22119 | 0.610594 | − | 0.791944i | \(-0.290931\pi\) | ||||
0.610594 | + | 0.791944i | \(0.290931\pi\) | |||||||
\(68\) | −6.92645 | −0.839955 | ||||||||
\(69\) | −9.53982 | −1.14846 | ||||||||
\(70\) | −0.142725 | −0.0170589 | ||||||||
\(71\) | 7.41827 | 0.880386 | 0.440193 | − | 0.897903i | \(-0.354910\pi\) | ||||
0.440193 | + | 0.897903i | \(0.354910\pi\) | |||||||
\(72\) | −9.74740 | −1.14874 | ||||||||
\(73\) | 10.1761 | 1.19102 | 0.595510 | − | 0.803348i | \(-0.296950\pi\) | ||||
0.595510 | + | 0.803348i | \(0.296950\pi\) | |||||||
\(74\) | −24.6771 | −2.86865 | ||||||||
\(75\) | 3.11712 | 0.359934 | ||||||||
\(76\) | −4.37089 | −0.501376 | ||||||||
\(77\) | 0.0317074 | 0.00361339 | ||||||||
\(78\) | −10.8732 | −1.23114 | ||||||||
\(79\) | −8.83374 | −0.993873 | −0.496937 | − | 0.867787i | \(-0.665542\pi\) | ||||
−0.496937 | + | 0.867787i | \(0.665542\pi\) | |||||||
\(80\) | −11.9906 | −1.34060 | ||||||||
\(81\) | −11.2334 | −1.24816 | ||||||||
\(82\) | −1.21975 | −0.134699 | ||||||||
\(83\) | 5.61499 | 0.616325 | 0.308163 | − | 0.951334i | \(-0.400286\pi\) | ||||
0.308163 | + | 0.951334i | \(0.400286\pi\) | |||||||
\(84\) | 0.282176 | 0.0307879 | ||||||||
\(85\) | 2.98625 | 0.323904 | ||||||||
\(86\) | −6.23226 | −0.672042 | ||||||||
\(87\) | 21.4988 | 2.30492 | ||||||||
\(88\) | 6.32352 | 0.674089 | ||||||||
\(89\) | −1.84974 | −0.196072 | −0.0980362 | − | 0.995183i | \(-0.531256\pi\) | ||||
−0.0980362 | + | 0.995183i | \(0.531256\pi\) | |||||||
\(90\) | 7.74751 | 0.816659 | ||||||||
\(91\) | 0.0600806 | 0.00629816 | ||||||||
\(92\) | 19.3809 | 2.02060 | ||||||||
\(93\) | −14.1598 | −1.46830 | ||||||||
\(94\) | 28.2458 | 2.91333 | ||||||||
\(95\) | 1.88445 | 0.193341 | ||||||||
\(96\) | 8.80352 | 0.898506 | ||||||||
\(97\) | 2.99708 | 0.304307 | 0.152154 | − | 0.988357i | \(-0.451379\pi\) | ||||
0.152154 | + | 0.988357i | \(0.451379\pi\) | |||||||
\(98\) | 17.6662 | 1.78455 | ||||||||
\(99\) | −1.72117 | −0.172984 | ||||||||
\(100\) | −6.33269 | −0.633269 | ||||||||
\(101\) | 1.50288 | 0.149542 | 0.0747712 | − | 0.997201i | \(-0.476177\pi\) | ||||
0.0747712 | + | 0.997201i | \(0.476177\pi\) | |||||||
\(102\) | −8.60550 | −0.852072 | ||||||||
\(103\) | 15.1436 | 1.49214 | 0.746070 | − | 0.665868i | \(-0.231938\pi\) | ||||
0.746070 | + | 0.665868i | \(0.231938\pi\) | |||||||
\(104\) | 11.9821 | 1.17494 | ||||||||
\(105\) | −0.121656 | −0.0118725 | ||||||||
\(106\) | 3.30236 | 0.320754 | ||||||||
\(107\) | 14.7355 | 1.42453 | 0.712267 | − | 0.701909i | \(-0.247668\pi\) | ||||
0.712267 | + | 0.701909i | \(0.247668\pi\) | |||||||
\(108\) | 12.8943 | 1.24075 | ||||||||
\(109\) | 0.211487 | 0.0202568 | 0.0101284 | − | 0.999949i | \(-0.496776\pi\) | ||||
0.0101284 | + | 0.999949i | \(0.496776\pi\) | |||||||
\(110\) | −5.02611 | −0.479221 | ||||||||
\(111\) | −21.0343 | −1.99649 | ||||||||
\(112\) | −0.190929 | −0.0180411 | ||||||||
\(113\) | 13.9112 | 1.30866 | 0.654329 | − | 0.756210i | \(-0.272951\pi\) | ||||
0.654329 | + | 0.756210i | \(0.272951\pi\) | |||||||
\(114\) | −5.43045 | −0.508608 | ||||||||
\(115\) | −8.35584 | −0.779186 | ||||||||
\(116\) | −43.6767 | −4.05528 | ||||||||
\(117\) | −3.26134 | −0.301511 | ||||||||
\(118\) | 10.9216 | 1.00541 | ||||||||
\(119\) | 0.0475504 | 0.00435894 | ||||||||
\(120\) | −24.2624 | −2.21484 | ||||||||
\(121\) | −9.88341 | −0.898492 | ||||||||
\(122\) | 4.50140 | 0.407538 | ||||||||
\(123\) | −1.03969 | −0.0937461 | ||||||||
\(124\) | 28.7668 | 2.58333 | ||||||||
\(125\) | 12.1525 | 1.08696 | ||||||||
\(126\) | 0.123365 | 0.0109902 | ||||||||
\(127\) | −21.5251 | −1.91004 | −0.955021 | − | 0.296538i | \(-0.904168\pi\) | ||||
−0.955021 | + | 0.296538i | \(0.904168\pi\) | |||||||
\(128\) | 14.2358 | 1.25828 | ||||||||
\(129\) | −5.31228 | −0.467720 | ||||||||
\(130\) | −9.52371 | −0.835284 | ||||||||
\(131\) | −3.62027 | −0.316304 | −0.158152 | − | 0.987415i | \(-0.550554\pi\) | ||||
−0.158152 | + | 0.987415i | \(0.550554\pi\) | |||||||
\(132\) | 9.93693 | 0.864899 | ||||||||
\(133\) | 0.0300064 | 0.00260189 | ||||||||
\(134\) | −25.2302 | −2.17956 | ||||||||
\(135\) | −5.55920 | −0.478459 | ||||||||
\(136\) | 9.48315 | 0.813174 | ||||||||
\(137\) | −21.7964 | −1.86219 | −0.931096 | − | 0.364774i | \(-0.881146\pi\) | ||||
−0.931096 | + | 0.364774i | \(0.881146\pi\) | |||||||
\(138\) | 24.0791 | 2.04975 | ||||||||
\(139\) | 10.8620 | 0.921306 | 0.460653 | − | 0.887580i | \(-0.347615\pi\) | ||||
0.460653 | + | 0.887580i | \(0.347615\pi\) | |||||||
\(140\) | 0.247155 | 0.0208884 | ||||||||
\(141\) | 24.0763 | 2.02759 | ||||||||
\(142\) | −18.7242 | −1.57130 | ||||||||
\(143\) | 2.11576 | 0.176929 | ||||||||
\(144\) | 10.3641 | 0.863679 | ||||||||
\(145\) | 18.8306 | 1.56380 | ||||||||
\(146\) | −25.6851 | −2.12571 | ||||||||
\(147\) | 15.0584 | 1.24199 | ||||||||
\(148\) | 42.7330 | 3.51263 | ||||||||
\(149\) | 0.201078 | 0.0164729 | 0.00823647 | − | 0.999966i | \(-0.497378\pi\) | ||||
0.00823647 | + | 0.999966i | \(0.497378\pi\) | |||||||
\(150\) | −7.86781 | −0.642404 | ||||||||
\(151\) | 7.69857 | 0.626501 | 0.313250 | − | 0.949671i | \(-0.398582\pi\) | ||||
0.313250 | + | 0.949671i | \(0.398582\pi\) | |||||||
\(152\) | 5.98429 | 0.485390 | ||||||||
\(153\) | −2.58117 | −0.208675 | ||||||||
\(154\) | −0.0800314 | −0.00644911 | ||||||||
\(155\) | −12.4024 | −0.996186 | ||||||||
\(156\) | 18.8290 | 1.50752 | ||||||||
\(157\) | 12.4128 | 0.990650 | 0.495325 | − | 0.868708i | \(-0.335049\pi\) | ||||
0.495325 | + | 0.868708i | \(0.335049\pi\) | |||||||
\(158\) | 22.2969 | 1.77385 | ||||||||
\(159\) | 2.81488 | 0.223235 | ||||||||
\(160\) | 7.71092 | 0.609602 | ||||||||
\(161\) | −0.133051 | −0.0104859 | ||||||||
\(162\) | 28.3538 | 2.22769 | ||||||||
\(163\) | 14.1956 | 1.11189 | 0.555943 | − | 0.831220i | \(-0.312357\pi\) | ||||
0.555943 | + | 0.831220i | \(0.312357\pi\) | |||||||
\(164\) | 2.11223 | 0.164937 | ||||||||
\(165\) | −4.28418 | −0.333523 | ||||||||
\(166\) | −14.1726 | −1.10001 | ||||||||
\(167\) | −5.70430 | −0.441412 | −0.220706 | − | 0.975340i | \(-0.570836\pi\) | ||||
−0.220706 | + | 0.975340i | \(0.570836\pi\) | |||||||
\(168\) | −0.386333 | −0.0298063 | ||||||||
\(169\) | −8.99096 | −0.691612 | ||||||||
\(170\) | −7.53748 | −0.578098 | ||||||||
\(171\) | −1.62883 | −0.124560 | ||||||||
\(172\) | 10.7923 | 0.822908 | ||||||||
\(173\) | −3.06403 | −0.232954 | −0.116477 | − | 0.993193i | \(-0.537160\pi\) | ||||
−0.116477 | + | 0.993193i | \(0.537160\pi\) | |||||||
\(174\) | −54.2644 | −4.11377 | ||||||||
\(175\) | 0.0434742 | 0.00328634 | ||||||||
\(176\) | −6.72362 | −0.506812 | ||||||||
\(177\) | 9.30937 | 0.699735 | ||||||||
\(178\) | 4.66887 | 0.349946 | ||||||||
\(179\) | 11.6233 | 0.868764 | 0.434382 | − | 0.900729i | \(-0.356967\pi\) | ||||
0.434382 | + | 0.900729i | \(0.356967\pi\) | |||||||
\(180\) | −13.4163 | −0.999991 | ||||||||
\(181\) | 25.4037 | 1.88824 | 0.944121 | − | 0.329598i | \(-0.106913\pi\) | ||||
0.944121 | + | 0.329598i | \(0.106913\pi\) | |||||||
\(182\) | −0.151647 | −0.0112408 | ||||||||
\(183\) | 3.83693 | 0.283634 | ||||||||
\(184\) | −26.5349 | −1.95618 | ||||||||
\(185\) | −18.4238 | −1.35454 | ||||||||
\(186\) | 35.7402 | 2.62060 | ||||||||
\(187\) | 1.67451 | 0.122452 | ||||||||
\(188\) | −48.9129 | −3.56734 | ||||||||
\(189\) | −0.0885198 | −0.00643887 | ||||||||
\(190\) | −4.75648 | −0.345071 | ||||||||
\(191\) | 16.1846 | 1.17108 | 0.585538 | − | 0.810645i | \(-0.300883\pi\) | ||||
0.585538 | + | 0.810645i | \(0.300883\pi\) | |||||||
\(192\) | 5.15868 | 0.372296 | ||||||||
\(193\) | 20.9037 | 1.50468 | 0.752340 | − | 0.658775i | \(-0.228925\pi\) | ||||
0.752340 | + | 0.658775i | \(0.228925\pi\) | |||||||
\(194\) | −7.56482 | −0.543123 | ||||||||
\(195\) | −8.11786 | −0.581332 | ||||||||
\(196\) | −30.5923 | −2.18517 | ||||||||
\(197\) | 16.1742 | 1.15237 | 0.576183 | − | 0.817321i | \(-0.304542\pi\) | ||||
0.576183 | + | 0.817321i | \(0.304542\pi\) | |||||||
\(198\) | 4.34433 | 0.308738 | ||||||||
\(199\) | −1.43825 | −0.101955 | −0.0509775 | − | 0.998700i | \(-0.516234\pi\) | ||||
−0.0509775 | + | 0.998700i | \(0.516234\pi\) | |||||||
\(200\) | 8.67023 | 0.613078 | ||||||||
\(201\) | −21.5058 | −1.51690 | ||||||||
\(202\) | −3.79337 | −0.266900 | ||||||||
\(203\) | 0.299842 | 0.0210448 | ||||||||
\(204\) | 14.9021 | 1.04335 | ||||||||
\(205\) | −0.910659 | −0.0636032 | ||||||||
\(206\) | −38.2233 | −2.66314 | ||||||||
\(207\) | 7.22239 | 0.501991 | ||||||||
\(208\) | −12.7402 | −0.883376 | ||||||||
\(209\) | 1.05669 | 0.0730925 | ||||||||
\(210\) | 0.307069 | 0.0211897 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −5.71867 | −0.392760 | ||||||||
\(213\) | −15.9602 | −1.09357 | ||||||||
\(214\) | −37.1933 | −2.54248 | ||||||||
\(215\) | −4.65298 | −0.317330 | ||||||||
\(216\) | −17.6538 | −1.20119 | ||||||||
\(217\) | −0.197485 | −0.0134062 | ||||||||
\(218\) | −0.533806 | −0.0361539 | ||||||||
\(219\) | −21.8935 | −1.47943 | ||||||||
\(220\) | 8.70366 | 0.586801 | ||||||||
\(221\) | 3.17293 | 0.213434 | ||||||||
\(222\) | 53.0920 | 3.56330 | ||||||||
\(223\) | −14.7601 | −0.988406 | −0.494203 | − | 0.869346i | \(-0.664540\pi\) | ||||
−0.494203 | + | 0.869346i | \(0.664540\pi\) | |||||||
\(224\) | 0.122782 | 0.00820372 | ||||||||
\(225\) | −2.35990 | −0.157327 | ||||||||
\(226\) | −35.1128 | −2.33567 | ||||||||
\(227\) | −7.39221 | −0.490638 | −0.245319 | − | 0.969442i | \(-0.578893\pi\) | ||||
−0.245319 | + | 0.969442i | \(0.578893\pi\) | |||||||
\(228\) | 9.40386 | 0.622786 | ||||||||
\(229\) | 17.7818 | 1.17505 | 0.587526 | − | 0.809206i | \(-0.300102\pi\) | ||||
0.587526 | + | 0.809206i | \(0.300102\pi\) | |||||||
\(230\) | 21.0907 | 1.39068 | ||||||||
\(231\) | −0.0682175 | −0.00448838 | ||||||||
\(232\) | 59.7987 | 3.92598 | ||||||||
\(233\) | 28.3451 | 1.85695 | 0.928474 | − | 0.371399i | \(-0.121122\pi\) | ||||
0.928474 | + | 0.371399i | \(0.121122\pi\) | |||||||
\(234\) | 8.23184 | 0.538132 | ||||||||
\(235\) | 21.0882 | 1.37564 | ||||||||
\(236\) | −18.9128 | −1.23112 | ||||||||
\(237\) | 19.0055 | 1.23454 | ||||||||
\(238\) | −0.120020 | −0.00777976 | ||||||||
\(239\) | −15.2381 | −0.985671 | −0.492835 | − | 0.870123i | \(-0.664039\pi\) | ||||
−0.492835 | + | 0.870123i | \(0.664039\pi\) | |||||||
\(240\) | 25.7975 | 1.66522 | ||||||||
\(241\) | 15.5631 | 1.00251 | 0.501254 | − | 0.865300i | \(-0.332872\pi\) | ||||
0.501254 | + | 0.865300i | \(0.332872\pi\) | |||||||
\(242\) | 24.9464 | 1.60361 | ||||||||
\(243\) | 15.3183 | 0.982667 | ||||||||
\(244\) | −7.79503 | −0.499026 | ||||||||
\(245\) | 13.1895 | 0.842645 | ||||||||
\(246\) | 2.62425 | 0.167316 | ||||||||
\(247\) | 2.00226 | 0.127401 | ||||||||
\(248\) | −39.3852 | −2.50096 | ||||||||
\(249\) | −12.0805 | −0.765570 | ||||||||
\(250\) | −30.6738 | −1.93998 | ||||||||
\(251\) | −12.4932 | −0.788566 | −0.394283 | − | 0.918989i | \(-0.629007\pi\) | ||||
−0.394283 | + | 0.918989i | \(0.629007\pi\) | |||||||
\(252\) | −0.213629 | −0.0134574 | ||||||||
\(253\) | −4.68544 | −0.294571 | ||||||||
\(254\) | 54.3307 | 3.40901 | ||||||||
\(255\) | −6.42483 | −0.402339 | ||||||||
\(256\) | −31.1365 | −1.94603 | ||||||||
\(257\) | 15.0878 | 0.941149 | 0.470575 | − | 0.882360i | \(-0.344047\pi\) | ||||
0.470575 | + | 0.882360i | \(0.344047\pi\) | |||||||
\(258\) | 13.4085 | 0.834779 | ||||||||
\(259\) | −0.293364 | −0.0182288 | ||||||||
\(260\) | 16.4921 | 1.02280 | ||||||||
\(261\) | −16.2763 | −1.00748 | ||||||||
\(262\) | 9.13778 | 0.564534 | ||||||||
\(263\) | −24.2515 | −1.49541 | −0.747706 | − | 0.664030i | \(-0.768845\pi\) | ||||
−0.747706 | + | 0.664030i | \(0.768845\pi\) | |||||||
\(264\) | −13.6049 | −0.837322 | ||||||||
\(265\) | 2.46553 | 0.151456 | ||||||||
\(266\) | −0.0757381 | −0.00464380 | ||||||||
\(267\) | 3.97967 | 0.243552 | ||||||||
\(268\) | 43.6909 | 2.66884 | ||||||||
\(269\) | 17.3904 | 1.06031 | 0.530155 | − | 0.847901i | \(-0.322134\pi\) | ||||
0.530155 | + | 0.847901i | \(0.322134\pi\) | |||||||
\(270\) | 14.0318 | 0.853946 | ||||||||
\(271\) | −6.83729 | −0.415336 | −0.207668 | − | 0.978199i | \(-0.566587\pi\) | ||||
−0.207668 | + | 0.978199i | \(0.566587\pi\) | |||||||
\(272\) | −10.0832 | −0.611383 | ||||||||
\(273\) | −0.129262 | −0.00782328 | ||||||||
\(274\) | 55.0155 | 3.32361 | ||||||||
\(275\) | 1.53096 | 0.0923205 | ||||||||
\(276\) | −41.6976 | −2.50990 | ||||||||
\(277\) | −31.0354 | −1.86474 | −0.932369 | − | 0.361509i | \(-0.882262\pi\) | ||||
−0.932369 | + | 0.361509i | \(0.882262\pi\) | |||||||
\(278\) | −27.4165 | −1.64433 | ||||||||
\(279\) | 10.7201 | 0.641793 | ||||||||
\(280\) | −0.338386 | −0.0202224 | ||||||||
\(281\) | −7.98321 | −0.476239 | −0.238119 | − | 0.971236i | \(-0.576531\pi\) | ||||
−0.238119 | + | 0.971236i | \(0.576531\pi\) | |||||||
\(282\) | −60.7700 | −3.61880 | ||||||||
\(283\) | 23.3527 | 1.38817 | 0.694086 | − | 0.719892i | \(-0.255809\pi\) | ||||
0.694086 | + | 0.719892i | \(0.255809\pi\) | |||||||
\(284\) | 32.4245 | 1.92404 | ||||||||
\(285\) | −4.05435 | −0.240159 | ||||||||
\(286\) | −5.34031 | −0.315779 | ||||||||
\(287\) | −0.0145005 | −0.000855940 0 | ||||||||
\(288\) | −6.66495 | −0.392736 | ||||||||
\(289\) | −14.4888 | −0.852283 | ||||||||
\(290\) | −47.5297 | −2.79104 | ||||||||
\(291\) | −6.44814 | −0.377996 | ||||||||
\(292\) | 44.4786 | 2.60291 | ||||||||
\(293\) | −21.7306 | −1.26951 | −0.634756 | − | 0.772712i | \(-0.718899\pi\) | ||||
−0.634756 | + | 0.772712i | \(0.718899\pi\) | |||||||
\(294\) | −38.0083 | −2.21669 | ||||||||
\(295\) | 8.15399 | 0.474744 | ||||||||
\(296\) | −58.5067 | −3.40063 | ||||||||
\(297\) | −3.11726 | −0.180882 | ||||||||
\(298\) | −0.507533 | −0.0294006 | ||||||||
\(299\) | −8.87820 | −0.513439 | ||||||||
\(300\) | 13.6246 | 0.786617 | ||||||||
\(301\) | −0.0740899 | −0.00427047 | ||||||||
\(302\) | −19.4317 | −1.11817 | ||||||||
\(303\) | −3.23341 | −0.185754 | ||||||||
\(304\) | −6.36293 | −0.364939 | ||||||||
\(305\) | 3.36073 | 0.192435 | ||||||||
\(306\) | 6.51504 | 0.372440 | ||||||||
\(307\) | −22.0265 | −1.25712 | −0.628559 | − | 0.777762i | \(-0.716355\pi\) | ||||
−0.628559 | + | 0.777762i | \(0.716355\pi\) | |||||||
\(308\) | 0.138590 | 0.00789687 | ||||||||
\(309\) | −32.5810 | −1.85347 | ||||||||
\(310\) | 31.3045 | 1.77798 | ||||||||
\(311\) | −9.59387 | −0.544018 | −0.272009 | − | 0.962295i | \(-0.587688\pi\) | ||||
−0.272009 | + | 0.962295i | \(0.587688\pi\) | |||||||
\(312\) | −25.7791 | −1.45946 | ||||||||
\(313\) | −14.1696 | −0.800915 | −0.400457 | − | 0.916315i | \(-0.631149\pi\) | ||||
−0.400457 | + | 0.916315i | \(0.631149\pi\) | |||||||
\(314\) | −31.3307 | −1.76809 | ||||||||
\(315\) | 0.0921034 | 0.00518944 | ||||||||
\(316\) | −38.6113 | −2.17206 | ||||||||
\(317\) | −34.5057 | −1.93803 | −0.969017 | − | 0.246996i | \(-0.920557\pi\) | ||||
−0.969017 | + | 0.246996i | \(0.920557\pi\) | |||||||
\(318\) | −7.10494 | −0.398426 | ||||||||
\(319\) | 10.5591 | 0.591194 | ||||||||
\(320\) | 4.51844 | 0.252588 | ||||||||
\(321\) | −31.7030 | −1.76949 | ||||||||
\(322\) | 0.335829 | 0.0187150 | ||||||||
\(323\) | 1.58468 | 0.0881737 | ||||||||
\(324\) | −49.1000 | −2.72778 | ||||||||
\(325\) | 2.90094 | 0.160915 | ||||||||
\(326\) | −35.8306 | −1.98448 | ||||||||
\(327\) | −0.455008 | −0.0251620 | ||||||||
\(328\) | −2.89189 | −0.159678 | ||||||||
\(329\) | 0.335790 | 0.0185127 | ||||||||
\(330\) | 10.8135 | 0.595266 | ||||||||
\(331\) | 18.9592 | 1.04209 | 0.521045 | − | 0.853529i | \(-0.325542\pi\) | ||||
0.521045 | + | 0.853529i | \(0.325542\pi\) | |||||||
\(332\) | 24.5425 | 1.34695 | ||||||||
\(333\) | 15.9246 | 0.872664 | ||||||||
\(334\) | 14.3980 | 0.787824 | ||||||||
\(335\) | −18.8367 | −1.02916 | ||||||||
\(336\) | 0.410778 | 0.0224098 | ||||||||
\(337\) | −13.1717 | −0.717506 | −0.358753 | − | 0.933433i | \(-0.616798\pi\) | ||||
−0.358753 | + | 0.933433i | \(0.616798\pi\) | |||||||
\(338\) | 22.6937 | 1.23438 | ||||||||
\(339\) | −29.9296 | −1.62555 | ||||||||
\(340\) | 13.0526 | 0.707875 | ||||||||
\(341\) | −6.95452 | −0.376608 | ||||||||
\(342\) | 4.11127 | 0.222312 | ||||||||
\(343\) | 0.420063 | 0.0226813 | ||||||||
\(344\) | −14.7760 | −0.796670 | ||||||||
\(345\) | 17.9774 | 0.967868 | ||||||||
\(346\) | 7.73380 | 0.415772 | ||||||||
\(347\) | −29.8639 | −1.60318 | −0.801590 | − | 0.597874i | \(-0.796012\pi\) | ||||
−0.801590 | + | 0.597874i | \(0.796012\pi\) | |||||||
\(348\) | 93.9691 | 5.03727 | ||||||||
\(349\) | −3.38787 | −0.181348 | −0.0906742 | − | 0.995881i | \(-0.528902\pi\) | ||||
−0.0906742 | + | 0.995881i | \(0.528902\pi\) | |||||||
\(350\) | −0.109732 | −0.00586541 | ||||||||
\(351\) | −5.90672 | −0.315278 | ||||||||
\(352\) | 4.32381 | 0.230460 | ||||||||
\(353\) | −12.0195 | −0.639736 | −0.319868 | − | 0.947462i | \(-0.603639\pi\) | ||||
−0.319868 | + | 0.947462i | \(0.603639\pi\) | |||||||
\(354\) | −23.4974 | −1.24887 | ||||||||
\(355\) | −13.9794 | −0.741949 | ||||||||
\(356\) | −8.08503 | −0.428506 | ||||||||
\(357\) | −0.102303 | −0.00541447 | ||||||||
\(358\) | −29.3379 | −1.55055 | ||||||||
\(359\) | −4.40718 | −0.232602 | −0.116301 | − | 0.993214i | \(-0.537104\pi\) | ||||
−0.116301 | + | 0.993214i | \(0.537104\pi\) | |||||||
\(360\) | 18.3685 | 0.968106 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −64.1206 | −3.37010 | ||||||||
\(363\) | 21.2639 | 1.11606 | ||||||||
\(364\) | 0.262606 | 0.0137643 | ||||||||
\(365\) | −19.1764 | −1.00374 | ||||||||
\(366\) | −9.68464 | −0.506224 | ||||||||
\(367\) | 8.79114 | 0.458894 | 0.229447 | − | 0.973321i | \(-0.426308\pi\) | ||||
0.229447 | + | 0.973321i | \(0.426308\pi\) | |||||||
\(368\) | 28.2138 | 1.47075 | ||||||||
\(369\) | 0.787130 | 0.0409763 | ||||||||
\(370\) | 46.5028 | 2.41756 | ||||||||
\(371\) | 0.0392590 | 0.00203822 | ||||||||
\(372\) | −61.8909 | −3.20889 | ||||||||
\(373\) | −22.0627 | −1.14236 | −0.571182 | − | 0.820824i | \(-0.693515\pi\) | ||||
−0.571182 | + | 0.820824i | \(0.693515\pi\) | |||||||
\(374\) | −4.22656 | −0.218550 | ||||||||
\(375\) | −26.1458 | −1.35016 | ||||||||
\(376\) | 66.9677 | 3.45360 | ||||||||
\(377\) | 20.0078 | 1.03045 | ||||||||
\(378\) | 0.223430 | 0.0114920 | ||||||||
\(379\) | 37.6682 | 1.93488 | 0.967442 | − | 0.253094i | \(-0.0814481\pi\) | ||||
0.967442 | + | 0.253094i | \(0.0814481\pi\) | |||||||
\(380\) | 8.23675 | 0.422536 | ||||||||
\(381\) | 46.3106 | 2.37256 | ||||||||
\(382\) | −40.8510 | −2.09012 | ||||||||
\(383\) | −6.76286 | −0.345566 | −0.172783 | − | 0.984960i | \(-0.555276\pi\) | ||||
−0.172783 | + | 0.984960i | \(0.555276\pi\) | |||||||
\(384\) | −30.6279 | −1.56297 | ||||||||
\(385\) | −0.0597511 | −0.00304520 | ||||||||
\(386\) | −52.7622 | −2.68553 | ||||||||
\(387\) | 4.02181 | 0.204440 | ||||||||
\(388\) | 13.0999 | 0.665048 | ||||||||
\(389\) | 8.43093 | 0.427465 | 0.213733 | − | 0.976892i | \(-0.431438\pi\) | ||||
0.213733 | + | 0.976892i | \(0.431438\pi\) | |||||||
\(390\) | 20.4900 | 1.03755 | ||||||||
\(391\) | −7.02660 | −0.355350 | ||||||||
\(392\) | 41.8846 | 2.11549 | ||||||||
\(393\) | 7.78890 | 0.392898 | ||||||||
\(394\) | −40.8247 | −2.05672 | ||||||||
\(395\) | 16.6468 | 0.837590 | ||||||||
\(396\) | −7.52303 | −0.378047 | ||||||||
\(397\) | 32.5114 | 1.63170 | 0.815851 | − | 0.578263i | \(-0.196269\pi\) | ||||
0.815851 | + | 0.578263i | \(0.196269\pi\) | |||||||
\(398\) | 3.63024 | 0.181968 | ||||||||
\(399\) | −0.0645579 | −0.00323194 | ||||||||
\(400\) | −9.21882 | −0.460941 | ||||||||
\(401\) | −18.0249 | −0.900120 | −0.450060 | − | 0.892998i | \(-0.648597\pi\) | ||||
−0.450060 | + | 0.892998i | \(0.648597\pi\) | |||||||
\(402\) | 54.2820 | 2.70734 | ||||||||
\(403\) | −13.1777 | −0.656430 | ||||||||
\(404\) | 6.56894 | 0.326817 | ||||||||
\(405\) | 21.1688 | 1.05189 | ||||||||
\(406\) | −0.756821 | −0.0375604 | ||||||||
\(407\) | −10.3309 | −0.512085 | ||||||||
\(408\) | −20.4027 | −1.01009 | ||||||||
\(409\) | −35.9550 | −1.77786 | −0.888931 | − | 0.458041i | \(-0.848551\pi\) | ||||
−0.888931 | + | 0.458041i | \(0.848551\pi\) | |||||||
\(410\) | 2.29856 | 0.113518 | ||||||||
\(411\) | 46.8943 | 2.31313 | ||||||||
\(412\) | 66.1909 | 3.26099 | ||||||||
\(413\) | 0.129837 | 0.00638886 | ||||||||
\(414\) | −18.2298 | −0.895944 | ||||||||
\(415\) | −10.5812 | −0.519410 | ||||||||
\(416\) | 8.19296 | 0.401693 | ||||||||
\(417\) | −23.3694 | −1.14440 | ||||||||
\(418\) | −2.66714 | −0.130454 | ||||||||
\(419\) | −32.6069 | −1.59295 | −0.796475 | − | 0.604672i | \(-0.793304\pi\) | ||||
−0.796475 | + | 0.604672i | \(0.793304\pi\) | |||||||
\(420\) | −0.531748 | −0.0259466 | ||||||||
\(421\) | 28.4931 | 1.38867 | 0.694334 | − | 0.719653i | \(-0.255699\pi\) | ||||
0.694334 | + | 0.719653i | \(0.255699\pi\) | |||||||
\(422\) | 2.52406 | 0.122869 | ||||||||
\(423\) | −18.2276 | −0.886256 | ||||||||
\(424\) | 7.82956 | 0.380237 | ||||||||
\(425\) | 2.29593 | 0.111369 | ||||||||
\(426\) | 40.2845 | 1.95179 | ||||||||
\(427\) | 0.0535133 | 0.00258969 | ||||||||
\(428\) | 64.4073 | 3.11324 | ||||||||
\(429\) | −4.55200 | −0.219773 | ||||||||
\(430\) | 11.7444 | 0.566366 | ||||||||
\(431\) | −36.2652 | −1.74683 | −0.873417 | − | 0.486973i | \(-0.838101\pi\) | ||||
−0.873417 | + | 0.486973i | \(0.838101\pi\) | |||||||
\(432\) | 18.7708 | 0.903112 | ||||||||
\(433\) | −0.0466208 | −0.00224045 | −0.00112023 | − | 0.999999i | \(-0.500357\pi\) | ||||
−0.00112023 | + | 0.999999i | \(0.500357\pi\) | |||||||
\(434\) | 0.498465 | 0.0239271 | ||||||||
\(435\) | −40.5136 | −1.94248 | ||||||||
\(436\) | 0.924387 | 0.0442701 | ||||||||
\(437\) | −4.43409 | −0.212111 | ||||||||
\(438\) | 55.2607 | 2.64046 | ||||||||
\(439\) | −24.7229 | −1.17996 | −0.589980 | − | 0.807418i | \(-0.700864\pi\) | ||||
−0.589980 | + | 0.807418i | \(0.700864\pi\) | |||||||
\(440\) | −11.9164 | −0.568091 | ||||||||
\(441\) | −11.4004 | −0.542874 | ||||||||
\(442\) | −8.00868 | −0.380934 | ||||||||
\(443\) | −0.893765 | −0.0424640 | −0.0212320 | − | 0.999775i | \(-0.506759\pi\) | ||||
−0.0212320 | + | 0.999775i | \(0.506759\pi\) | |||||||
\(444\) | −91.9389 | −4.36323 | ||||||||
\(445\) | 3.48576 | 0.165241 | ||||||||
\(446\) | 37.2553 | 1.76409 | ||||||||
\(447\) | −0.432613 | −0.0204619 | ||||||||
\(448\) | 0.0719477 | 0.00339921 | ||||||||
\(449\) | −30.2572 | −1.42793 | −0.713963 | − | 0.700184i | \(-0.753101\pi\) | ||||
−0.713963 | + | 0.700184i | \(0.753101\pi\) | |||||||
\(450\) | 5.95655 | 0.280794 | ||||||||
\(451\) | −0.510642 | −0.0240452 | ||||||||
\(452\) | 60.8045 | 2.86000 | ||||||||
\(453\) | −16.5633 | −0.778210 | ||||||||
\(454\) | 18.6584 | 0.875682 | ||||||||
\(455\) | −0.113219 | −0.00530779 | ||||||||
\(456\) | −12.8750 | −0.602928 | ||||||||
\(457\) | 16.9998 | 0.795215 | 0.397608 | − | 0.917556i | \(-0.369841\pi\) | ||||
0.397608 | + | 0.917556i | \(0.369841\pi\) | |||||||
\(458\) | −44.8823 | −2.09721 | ||||||||
\(459\) | −4.67484 | −0.218203 | ||||||||
\(460\) | −36.5225 | −1.70287 | ||||||||
\(461\) | 32.9250 | 1.53347 | 0.766735 | − | 0.641964i | \(-0.221880\pi\) | ||||
0.766735 | + | 0.641964i | \(0.221880\pi\) | |||||||
\(462\) | 0.172185 | 0.00801079 | ||||||||
\(463\) | −39.7687 | −1.84821 | −0.924105 | − | 0.382139i | \(-0.875188\pi\) | ||||
−0.924105 | + | 0.382139i | \(0.875188\pi\) | |||||||
\(464\) | −63.5823 | −2.95173 | ||||||||
\(465\) | 26.6835 | 1.23742 | ||||||||
\(466\) | −71.5447 | −3.31425 | ||||||||
\(467\) | −27.3212 | −1.26428 | −0.632138 | − | 0.774856i | \(-0.717823\pi\) | ||||
−0.632138 | + | 0.774856i | \(0.717823\pi\) | |||||||
\(468\) | −14.2550 | −0.658937 | ||||||||
\(469\) | −0.299940 | −0.0138499 | ||||||||
\(470\) | −53.2279 | −2.45522 | ||||||||
\(471\) | −26.7058 | −1.23054 | ||||||||
\(472\) | 25.8939 | 1.19186 | ||||||||
\(473\) | −2.60910 | −0.119967 | ||||||||
\(474\) | −47.9712 | −2.20339 | ||||||||
\(475\) | 1.44883 | 0.0664770 | ||||||||
\(476\) | 0.207838 | 0.00952623 | ||||||||
\(477\) | −2.13109 | −0.0975758 | ||||||||
\(478\) | 38.4619 | 1.75921 | ||||||||
\(479\) | 23.1598 | 1.05820 | 0.529100 | − | 0.848559i | \(-0.322530\pi\) | ||||
0.529100 | + | 0.848559i | \(0.322530\pi\) | |||||||
\(480\) | −16.5898 | −0.757219 | ||||||||
\(481\) | −19.5755 | −0.892567 | ||||||||
\(482\) | −39.2823 | −1.78926 | ||||||||
\(483\) | 0.286256 | 0.0130251 | ||||||||
\(484\) | −43.1994 | −1.96361 | ||||||||
\(485\) | −5.64786 | −0.256456 | ||||||||
\(486\) | −38.6643 | −1.75385 | ||||||||
\(487\) | −0.518795 | −0.0235088 | −0.0117544 | − | 0.999931i | \(-0.503742\pi\) | ||||
−0.0117544 | + | 0.999931i | \(0.503742\pi\) | |||||||
\(488\) | 10.6724 | 0.483115 | ||||||||
\(489\) | −30.5415 | −1.38113 | ||||||||
\(490\) | −33.2911 | −1.50394 | ||||||||
\(491\) | −10.1054 | −0.456049 | −0.228025 | − | 0.973655i | \(-0.573227\pi\) | ||||
−0.228025 | + | 0.973655i | \(0.573227\pi\) | |||||||
\(492\) | −4.54440 | −0.204877 | ||||||||
\(493\) | 15.8351 | 0.713175 | ||||||||
\(494\) | −5.05383 | −0.227382 | ||||||||
\(495\) | 3.24346 | 0.145783 | ||||||||
\(496\) | 41.8772 | 1.88034 | ||||||||
\(497\) | −0.222596 | −0.00998477 | ||||||||
\(498\) | 30.4919 | 1.36638 | ||||||||
\(499\) | 0.989559 | 0.0442987 | 0.0221494 | − | 0.999755i | \(-0.492949\pi\) | ||||
0.0221494 | + | 0.999755i | \(0.492949\pi\) | |||||||
\(500\) | 53.1174 | 2.37548 | ||||||||
\(501\) | 12.2726 | 0.548301 | ||||||||
\(502\) | 31.5337 | 1.40742 | ||||||||
\(503\) | 18.7123 | 0.834339 | 0.417169 | − | 0.908829i | \(-0.363022\pi\) | ||||
0.417169 | + | 0.908829i | \(0.363022\pi\) | |||||||
\(504\) | 0.292484 | 0.0130283 | ||||||||
\(505\) | −2.83211 | −0.126027 | ||||||||
\(506\) | 11.8264 | 0.525746 | ||||||||
\(507\) | 19.3438 | 0.859088 | ||||||||
\(508\) | −94.0839 | −4.17430 | ||||||||
\(509\) | 28.4241 | 1.25988 | 0.629938 | − | 0.776646i | \(-0.283080\pi\) | ||||
0.629938 | + | 0.776646i | \(0.283080\pi\) | |||||||
\(510\) | 16.2167 | 0.718087 | ||||||||
\(511\) | −0.305348 | −0.0135078 | ||||||||
\(512\) | 50.1190 | 2.21497 | ||||||||
\(513\) | −2.95003 | −0.130247 | ||||||||
\(514\) | −38.0825 | −1.67975 | ||||||||
\(515\) | −28.5374 | −1.25751 | ||||||||
\(516\) | −23.2194 | −1.02218 | ||||||||
\(517\) | 11.8250 | 0.520061 | ||||||||
\(518\) | 0.740470 | 0.0325344 | ||||||||
\(519\) | 6.59217 | 0.289364 | ||||||||
\(520\) | −22.5797 | −0.990186 | ||||||||
\(521\) | −12.7716 | −0.559534 | −0.279767 | − | 0.960068i | \(-0.590257\pi\) | ||||
−0.279767 | + | 0.960068i | \(0.590257\pi\) | |||||||
\(522\) | 41.0824 | 1.79813 | ||||||||
\(523\) | 20.3194 | 0.888505 | 0.444252 | − | 0.895902i | \(-0.353469\pi\) | ||||
0.444252 | + | 0.895902i | \(0.353469\pi\) | |||||||
\(524\) | −15.8238 | −0.691266 | ||||||||
\(525\) | −0.0935336 | −0.00408214 | ||||||||
\(526\) | 61.2123 | 2.66898 | ||||||||
\(527\) | −10.4294 | −0.454314 | ||||||||
\(528\) | 14.4657 | 0.629538 | ||||||||
\(529\) | −3.33884 | −0.145167 | ||||||||
\(530\) | −6.22315 | −0.270317 | ||||||||
\(531\) | −7.04792 | −0.305854 | ||||||||
\(532\) | 0.131155 | 0.00568628 | ||||||||
\(533\) | −0.967588 | −0.0419109 | ||||||||
\(534\) | −10.0449 | −0.434687 | ||||||||
\(535\) | −27.7684 | −1.20053 | ||||||||
\(536\) | −59.8181 | −2.58375 | ||||||||
\(537\) | −25.0071 | −1.07914 | ||||||||
\(538\) | −43.8944 | −1.89242 | ||||||||
\(539\) | 7.39586 | 0.318562 | ||||||||
\(540\) | −24.2987 | −1.04565 | ||||||||
\(541\) | −22.4990 | −0.967307 | −0.483654 | − | 0.875260i | \(-0.660691\pi\) | ||||
−0.483654 | + | 0.875260i | \(0.660691\pi\) | |||||||
\(542\) | 17.2577 | 0.741284 | ||||||||
\(543\) | −54.6554 | −2.34549 | ||||||||
\(544\) | 6.48427 | 0.278011 | ||||||||
\(545\) | −0.398538 | −0.0170715 | ||||||||
\(546\) | 0.326265 | 0.0139628 | ||||||||
\(547\) | 26.8522 | 1.14812 | 0.574059 | − | 0.818814i | \(-0.305368\pi\) | ||||
0.574059 | + | 0.818814i | \(0.305368\pi\) | |||||||
\(548\) | −95.2698 | −4.06972 | ||||||||
\(549\) | −2.90485 | −0.123976 | ||||||||
\(550\) | −3.86424 | −0.164772 | ||||||||
\(551\) | 9.99262 | 0.425700 | ||||||||
\(552\) | 57.0890 | 2.42987 | ||||||||
\(553\) | 0.265069 | 0.0112719 | ||||||||
\(554\) | 78.3354 | 3.32815 | ||||||||
\(555\) | 39.6382 | 1.68255 | ||||||||
\(556\) | 47.4768 | 2.01347 | ||||||||
\(557\) | −28.6371 | −1.21339 | −0.606696 | − | 0.794934i | \(-0.707505\pi\) | ||||
−0.606696 | + | 0.794934i | \(0.707505\pi\) | |||||||
\(558\) | −27.0581 | −1.14546 | ||||||||
\(559\) | −4.94385 | −0.209103 | ||||||||
\(560\) | 0.359796 | 0.0152042 | ||||||||
\(561\) | −3.60265 | −0.152104 | ||||||||
\(562\) | 20.1501 | 0.849982 | ||||||||
\(563\) | −16.5476 | −0.697399 | −0.348699 | − | 0.937235i | \(-0.613377\pi\) | ||||
−0.348699 | + | 0.937235i | \(0.613377\pi\) | |||||||
\(564\) | 105.235 | 4.43118 | ||||||||
\(565\) | −26.2151 | −1.10288 | ||||||||
\(566\) | −58.9436 | −2.47758 | ||||||||
\(567\) | 0.337074 | 0.0141558 | ||||||||
\(568\) | −44.3930 | −1.86269 | ||||||||
\(569\) | 16.7226 | 0.701047 | 0.350523 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350523 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(570\) | 10.2334 | 0.428632 | ||||||||
\(571\) | −34.9884 | −1.46422 | −0.732110 | − | 0.681187i | \(-0.761464\pi\) | ||||
−0.732110 | + | 0.681187i | \(0.761464\pi\) | |||||||
\(572\) | 9.24777 | 0.386669 | ||||||||
\(573\) | −34.8207 | −1.45466 | ||||||||
\(574\) | 0.0366003 | 0.00152767 | ||||||||
\(575\) | −6.42425 | −0.267910 | ||||||||
\(576\) | −3.90552 | −0.162730 | ||||||||
\(577\) | −29.9566 | −1.24711 | −0.623555 | − | 0.781780i | \(-0.714312\pi\) | ||||
−0.623555 | + | 0.781780i | \(0.714312\pi\) | |||||||
\(578\) | 36.5707 | 1.52114 | ||||||||
\(579\) | −44.9737 | −1.86904 | ||||||||
\(580\) | 82.3067 | 3.41760 | ||||||||
\(581\) | −0.168486 | −0.00698996 | ||||||||
\(582\) | 16.2755 | 0.674641 | ||||||||
\(583\) | 1.38252 | 0.0572581 | ||||||||
\(584\) | −60.8966 | −2.51992 | ||||||||
\(585\) | 6.14585 | 0.254100 | ||||||||
\(586\) | 54.8493 | 2.26580 | ||||||||
\(587\) | 18.0669 | 0.745700 | 0.372850 | − | 0.927892i | \(-0.378381\pi\) | ||||
0.372850 | + | 0.927892i | \(0.378381\pi\) | |||||||
\(588\) | 65.8185 | 2.71431 | ||||||||
\(589\) | −6.58144 | −0.271183 | ||||||||
\(590\) | −20.5812 | −0.847314 | ||||||||
\(591\) | −34.7984 | −1.43141 | ||||||||
\(592\) | 62.2086 | 2.55676 | ||||||||
\(593\) | 18.4516 | 0.757715 | 0.378857 | − | 0.925455i | \(-0.376317\pi\) | ||||
0.378857 | + | 0.925455i | \(0.376317\pi\) | |||||||
\(594\) | 7.86815 | 0.322834 | ||||||||
\(595\) | −0.0896066 | −0.00367351 | ||||||||
\(596\) | 0.878890 | 0.0360007 | ||||||||
\(597\) | 3.09436 | 0.126644 | ||||||||
\(598\) | 22.4091 | 0.916378 | ||||||||
\(599\) | 6.68751 | 0.273244 | 0.136622 | − | 0.990623i | \(-0.456375\pi\) | ||||
0.136622 | + | 0.990623i | \(0.456375\pi\) | |||||||
\(600\) | −18.6538 | −0.761536 | ||||||||
\(601\) | −5.64057 | −0.230084 | −0.115042 | − | 0.993361i | \(-0.536700\pi\) | ||||
−0.115042 | + | 0.993361i | \(0.536700\pi\) | |||||||
\(602\) | 0.187008 | 0.00762186 | ||||||||
\(603\) | 16.2816 | 0.663037 | ||||||||
\(604\) | 33.6496 | 1.36918 | ||||||||
\(605\) | 18.6248 | 0.757207 | ||||||||
\(606\) | 8.16133 | 0.331531 | ||||||||
\(607\) | 18.8606 | 0.765527 | 0.382763 | − | 0.923846i | \(-0.374972\pi\) | ||||
0.382763 | + | 0.923846i | \(0.374972\pi\) | |||||||
\(608\) | 4.09186 | 0.165947 | ||||||||
\(609\) | −0.645103 | −0.0261409 | ||||||||
\(610\) | −8.48269 | −0.343454 | ||||||||
\(611\) | 22.4065 | 0.906469 | ||||||||
\(612\) | −11.2820 | −0.456049 | ||||||||
\(613\) | −22.7479 | −0.918777 | −0.459389 | − | 0.888235i | \(-0.651931\pi\) | ||||
−0.459389 | + | 0.888235i | \(0.651931\pi\) | |||||||
\(614\) | 55.5963 | 2.24368 | ||||||||
\(615\) | 1.95926 | 0.0790049 | ||||||||
\(616\) | −0.189746 | −0.00764508 | ||||||||
\(617\) | 6.49220 | 0.261366 | 0.130683 | − | 0.991424i | \(-0.458283\pi\) | ||||
0.130683 | + | 0.991424i | \(0.458283\pi\) | |||||||
\(618\) | 82.2364 | 3.30803 | ||||||||
\(619\) | −38.3622 | −1.54191 | −0.770953 | − | 0.636892i | \(-0.780220\pi\) | ||||
−0.770953 | + | 0.636892i | \(0.780220\pi\) | |||||||
\(620\) | −54.2097 | −2.17711 | ||||||||
\(621\) | 13.0807 | 0.524910 | ||||||||
\(622\) | 24.2155 | 0.970954 | ||||||||
\(623\) | 0.0555041 | 0.00222373 | ||||||||
\(624\) | 27.4103 | 1.09729 | ||||||||
\(625\) | −15.6567 | −0.626269 | ||||||||
\(626\) | 35.7650 | 1.42946 | ||||||||
\(627\) | −2.27343 | −0.0907921 | ||||||||
\(628\) | 54.2551 | 2.16501 | ||||||||
\(629\) | −15.4929 | −0.617743 | ||||||||
\(630\) | −0.232475 | −0.00926202 | ||||||||
\(631\) | 31.3435 | 1.24776 | 0.623882 | − | 0.781519i | \(-0.285555\pi\) | ||||
0.623882 | + | 0.781519i | \(0.285555\pi\) | |||||||
\(632\) | 52.8636 | 2.10280 | ||||||||
\(633\) | 2.15147 | 0.0855133 | ||||||||
\(634\) | 87.0946 | 3.45897 | ||||||||
\(635\) | 40.5630 | 1.60969 | ||||||||
\(636\) | 12.3036 | 0.487868 | ||||||||
\(637\) | 14.0140 | 0.555255 | ||||||||
\(638\) | −26.6517 | −1.05515 | ||||||||
\(639\) | 12.0831 | 0.478001 | ||||||||
\(640\) | −26.8267 | −1.06042 | ||||||||
\(641\) | 3.78248 | 0.149399 | 0.0746995 | − | 0.997206i | \(-0.476200\pi\) | ||||
0.0746995 | + | 0.997206i | \(0.476200\pi\) | |||||||
\(642\) | 80.0204 | 3.15815 | ||||||||
\(643\) | −19.8824 | −0.784086 | −0.392043 | − | 0.919947i | \(-0.628232\pi\) | ||||
−0.392043 | + | 0.919947i | \(0.628232\pi\) | |||||||
\(644\) | −0.581552 | −0.0229164 | ||||||||
\(645\) | 10.0107 | 0.394173 | ||||||||
\(646\) | −3.99982 | −0.157371 | ||||||||
\(647\) | −38.0577 | −1.49620 | −0.748102 | − | 0.663584i | \(-0.769035\pi\) | ||||
−0.748102 | + | 0.663584i | \(0.769035\pi\) | |||||||
\(648\) | 67.2239 | 2.64080 | ||||||||
\(649\) | 4.57226 | 0.179477 | ||||||||
\(650\) | −7.32215 | −0.287198 | ||||||||
\(651\) | 0.424884 | 0.0166525 | ||||||||
\(652\) | 62.0475 | 2.42997 | ||||||||
\(653\) | 9.68491 | 0.379000 | 0.189500 | − | 0.981881i | \(-0.439313\pi\) | ||||
0.189500 | + | 0.981881i | \(0.439313\pi\) | |||||||
\(654\) | 1.14847 | 0.0449087 | ||||||||
\(655\) | 6.82223 | 0.266566 | ||||||||
\(656\) | 3.07487 | 0.120054 | ||||||||
\(657\) | 16.5751 | 0.646657 | ||||||||
\(658\) | −0.847554 | −0.0330411 | ||||||||
\(659\) | −10.9756 | −0.427548 | −0.213774 | − | 0.976883i | \(-0.568576\pi\) | ||||
−0.213774 | + | 0.976883i | \(0.568576\pi\) | |||||||
\(660\) | −18.7257 | −0.728897 | ||||||||
\(661\) | 19.2154 | 0.747394 | 0.373697 | − | 0.927551i | \(-0.378090\pi\) | ||||
0.373697 | + | 0.927551i | \(0.378090\pi\) | |||||||
\(662\) | −47.8542 | −1.85991 | ||||||||
\(663\) | −6.82647 | −0.265118 | ||||||||
\(664\) | −33.6017 | −1.30400 | ||||||||
\(665\) | −0.0565457 | −0.00219275 | ||||||||
\(666\) | −40.1948 | −1.55752 | ||||||||
\(667\) | −44.3082 | −1.71562 | ||||||||
\(668\) | −24.9329 | −0.964682 | ||||||||
\(669\) | 31.7558 | 1.22775 | ||||||||
\(670\) | 47.5451 | 1.83683 | ||||||||
\(671\) | 1.88449 | 0.0727499 | ||||||||
\(672\) | −0.264162 | −0.0101903 | ||||||||
\(673\) | −13.1026 | −0.505066 | −0.252533 | − | 0.967588i | \(-0.581264\pi\) | ||||
−0.252533 | + | 0.967588i | \(0.581264\pi\) | |||||||
\(674\) | 33.2461 | 1.28059 | ||||||||
\(675\) | −4.27410 | −0.164510 | ||||||||
\(676\) | −39.2985 | −1.51148 | ||||||||
\(677\) | 33.3769 | 1.28278 | 0.641389 | − | 0.767216i | \(-0.278359\pi\) | ||||
0.641389 | + | 0.767216i | \(0.278359\pi\) | |||||||
\(678\) | 75.5443 | 2.90126 | ||||||||
\(679\) | −0.0899316 | −0.00345126 | ||||||||
\(680\) | −17.8706 | −0.685305 | ||||||||
\(681\) | 15.9041 | 0.609447 | ||||||||
\(682\) | 17.5536 | 0.672164 | ||||||||
\(683\) | 18.9880 | 0.726554 | 0.363277 | − | 0.931681i | \(-0.381658\pi\) | ||||
0.363277 | + | 0.931681i | \(0.381658\pi\) | |||||||
\(684\) | −7.11945 | −0.272219 | ||||||||
\(685\) | 41.0743 | 1.56937 | ||||||||
\(686\) | −1.06026 | −0.0404811 | ||||||||
\(687\) | −38.2569 | −1.45959 | ||||||||
\(688\) | 15.7109 | 0.598974 | ||||||||
\(689\) | 2.61966 | 0.0998011 | ||||||||
\(690\) | −45.3760 | −1.72743 | ||||||||
\(691\) | −36.1174 | −1.37397 | −0.686986 | − | 0.726671i | \(-0.741067\pi\) | ||||
−0.686986 | + | 0.726671i | \(0.741067\pi\) | |||||||
\(692\) | −13.3925 | −0.509108 | ||||||||
\(693\) | 0.0516460 | 0.00196187 | ||||||||
\(694\) | 75.3785 | 2.86133 | ||||||||
\(695\) | −20.4690 | −0.776434 | ||||||||
\(696\) | −128.655 | −4.87666 | ||||||||
\(697\) | −0.765791 | −0.0290064 | ||||||||
\(698\) | 8.55119 | 0.323667 | ||||||||
\(699\) | −60.9836 | −2.30661 | ||||||||
\(700\) | 0.190021 | 0.00718213 | ||||||||
\(701\) | −48.4828 | −1.83117 | −0.915586 | − | 0.402123i | \(-0.868273\pi\) | ||||
−0.915586 | + | 0.402123i | \(0.868273\pi\) | |||||||
\(702\) | 14.9089 | 0.562702 | ||||||||
\(703\) | −9.77672 | −0.368736 | ||||||||
\(704\) | 2.53366 | 0.0954911 | ||||||||
\(705\) | −45.3706 | −1.70876 | ||||||||
\(706\) | 30.3381 | 1.14179 | ||||||||
\(707\) | −0.0450961 | −0.00169601 | ||||||||
\(708\) | 40.6903 | 1.52923 | ||||||||
\(709\) | 8.53426 | 0.320511 | 0.160255 | − | 0.987076i | \(-0.448768\pi\) | ||||
0.160255 | + | 0.987076i | \(0.448768\pi\) | |||||||
\(710\) | 35.2849 | 1.32422 | ||||||||
\(711\) | −14.3887 | −0.539617 | ||||||||
\(712\) | 11.0694 | 0.414843 | ||||||||
\(713\) | 29.1827 | 1.09290 | ||||||||
\(714\) | 0.258220 | 0.00966365 | ||||||||
\(715\) | −3.98705 | −0.149107 | ||||||||
\(716\) | 50.8041 | 1.89864 | ||||||||
\(717\) | 32.7843 | 1.22435 | ||||||||
\(718\) | 11.1240 | 0.415144 | ||||||||
\(719\) | 40.1253 | 1.49642 | 0.748210 | − | 0.663462i | \(-0.230914\pi\) | ||||
0.748210 | + | 0.663462i | \(0.230914\pi\) | |||||||
\(720\) | −19.5308 | −0.727868 | ||||||||
\(721\) | −0.454404 | −0.0169229 | ||||||||
\(722\) | −2.52406 | −0.0939359 | ||||||||
\(723\) | −33.4836 | −1.24527 | ||||||||
\(724\) | 111.037 | 4.12665 | ||||||||
\(725\) | 14.4776 | 0.537685 | ||||||||
\(726\) | −53.6714 | −1.99193 | ||||||||
\(727\) | −29.4684 | −1.09292 | −0.546461 | − | 0.837484i | \(-0.684025\pi\) | ||||
−0.546461 | + | 0.837484i | \(0.684025\pi\) | |||||||
\(728\) | −0.359540 | −0.0133254 | ||||||||
\(729\) | 0.743392 | 0.0275330 | ||||||||
\(730\) | 48.4023 | 1.79145 | ||||||||
\(731\) | −3.91278 | −0.144719 | ||||||||
\(732\) | 16.7708 | 0.619867 | ||||||||
\(733\) | −12.9069 | −0.476728 | −0.238364 | − | 0.971176i | \(-0.576611\pi\) | ||||
−0.238364 | + | 0.971176i | \(0.576611\pi\) | |||||||
\(734\) | −22.1894 | −0.819025 | ||||||||
\(735\) | −28.3768 | −1.04669 | ||||||||
\(736\) | −18.1437 | −0.668785 | ||||||||
\(737\) | −10.5625 | −0.389074 | ||||||||
\(738\) | −1.98677 | −0.0731338 | ||||||||
\(739\) | 0.644649 | 0.0237138 | 0.0118569 | − | 0.999930i | \(-0.496226\pi\) | ||||
0.0118569 | + | 0.999930i | \(0.496226\pi\) | |||||||
\(740\) | −80.5284 | −2.96028 | ||||||||
\(741\) | −4.30780 | −0.158251 | ||||||||
\(742\) | −0.0990921 | −0.00363778 | ||||||||
\(743\) | −4.80387 | −0.176237 | −0.0881184 | − | 0.996110i | \(-0.528085\pi\) | ||||
−0.0881184 | + | 0.996110i | \(0.528085\pi\) | |||||||
\(744\) | 84.7362 | 3.10658 | ||||||||
\(745\) | −0.378922 | −0.0138826 | ||||||||
\(746\) | 55.6876 | 2.03887 | ||||||||
\(747\) | 9.14587 | 0.334630 | ||||||||
\(748\) | 7.31909 | 0.267612 | ||||||||
\(749\) | −0.442159 | −0.0161561 | ||||||||
\(750\) | 65.9937 | 2.40975 | ||||||||
\(751\) | −15.5330 | −0.566808 | −0.283404 | − | 0.959001i | \(-0.591464\pi\) | ||||
−0.283404 | + | 0.959001i | \(0.591464\pi\) | |||||||
\(752\) | −71.2050 | −2.59658 | ||||||||
\(753\) | 26.8789 | 0.979520 | ||||||||
\(754\) | −50.5010 | −1.83914 | ||||||||
\(755\) | −14.5076 | −0.527986 | ||||||||
\(756\) | −0.386911 | −0.0140718 | ||||||||
\(757\) | −33.3109 | −1.21071 | −0.605353 | − | 0.795957i | \(-0.706968\pi\) | ||||
−0.605353 | + | 0.795957i | \(0.706968\pi\) | |||||||
\(758\) | −95.0768 | −3.45335 | ||||||||
\(759\) | 10.0806 | 0.365903 | ||||||||
\(760\) | −11.2771 | −0.409064 | ||||||||
\(761\) | −9.71815 | −0.352283 | −0.176141 | − | 0.984365i | \(-0.556362\pi\) | ||||
−0.176141 | + | 0.984365i | \(0.556362\pi\) | |||||||
\(762\) | −116.891 | −4.23451 | ||||||||
\(763\) | −0.00634596 | −0.000229739 0 | ||||||||
\(764\) | 70.7412 | 2.55933 | ||||||||
\(765\) | 4.86410 | 0.175862 | ||||||||
\(766\) | 17.0699 | 0.616760 | ||||||||
\(767\) | 8.66373 | 0.312829 | ||||||||
\(768\) | 66.9893 | 2.41727 | ||||||||
\(769\) | −21.1214 | −0.761658 | −0.380829 | − | 0.924646i | \(-0.624361\pi\) | ||||
−0.380829 | + | 0.924646i | \(0.624361\pi\) | |||||||
\(770\) | 0.150816 | 0.00543501 | ||||||||
\(771\) | −32.4609 | −1.16905 | ||||||||
\(772\) | 91.3678 | 3.28840 | ||||||||
\(773\) | −11.3508 | −0.408261 | −0.204130 | − | 0.978944i | \(-0.565437\pi\) | ||||
−0.204130 | + | 0.978944i | \(0.565437\pi\) | |||||||
\(774\) | −10.1513 | −0.364881 | ||||||||
\(775\) | −9.53540 | −0.342522 | ||||||||
\(776\) | −17.9354 | −0.643843 | ||||||||
\(777\) | 0.631165 | 0.0226429 | ||||||||
\(778\) | −21.2802 | −0.762932 | ||||||||
\(779\) | −0.483248 | −0.0173142 | ||||||||
\(780\) | −35.4823 | −1.27047 | ||||||||
\(781\) | −7.83878 | −0.280494 | ||||||||
\(782\) | 17.7356 | 0.634223 | ||||||||
\(783\) | −29.4785 | −1.05348 | ||||||||
\(784\) | −44.5348 | −1.59053 | ||||||||
\(785\) | −23.3914 | −0.834874 | ||||||||
\(786\) | −19.6597 | −0.701238 | ||||||||
\(787\) | −27.6980 | −0.987327 | −0.493664 | − | 0.869653i | \(-0.664343\pi\) | ||||
−0.493664 | + | 0.869653i | \(0.664343\pi\) | |||||||
\(788\) | 70.6958 | 2.51843 | ||||||||
\(789\) | 52.1764 | 1.85753 | ||||||||
\(790\) | −42.0175 | −1.49492 | ||||||||
\(791\) | −0.417426 | −0.0148420 | ||||||||
\(792\) | 10.2999 | 0.365993 | ||||||||
\(793\) | 3.57082 | 0.126804 | ||||||||
\(794\) | −82.0609 | −2.91223 | ||||||||
\(795\) | −5.30452 | −0.188132 | ||||||||
\(796\) | −6.28645 | −0.222817 | ||||||||
\(797\) | 33.9368 | 1.20210 | 0.601052 | − | 0.799210i | \(-0.294748\pi\) | ||||
0.601052 | + | 0.799210i | \(0.294748\pi\) | |||||||
\(798\) | 0.162948 | 0.00576831 | ||||||||
\(799\) | 17.7335 | 0.627365 | ||||||||
\(800\) | 5.92842 | 0.209601 | ||||||||
\(801\) | −3.01292 | −0.106456 | ||||||||
\(802\) | 45.4960 | 1.60652 | ||||||||
\(803\) | −10.7529 | −0.379463 | ||||||||
\(804\) | −93.9996 | −3.31511 | ||||||||
\(805\) | 0.250729 | 0.00883703 | ||||||||
\(806\) | 33.2615 | 1.17158 | ||||||||
\(807\) | −37.4149 | −1.31707 | ||||||||
\(808\) | −8.99367 | −0.316396 | ||||||||
\(809\) | 42.6190 | 1.49840 | 0.749201 | − | 0.662342i | \(-0.230438\pi\) | ||||
0.749201 | + | 0.662342i | \(0.230438\pi\) | |||||||
\(810\) | −53.4315 | −1.87739 | ||||||||
\(811\) | −32.3710 | −1.13670 | −0.568350 | − | 0.822787i | \(-0.692418\pi\) | ||||
−0.568350 | + | 0.822787i | \(0.692418\pi\) | |||||||
\(812\) | 1.31058 | 0.0459923 | ||||||||
\(813\) | 14.7102 | 0.515910 | ||||||||
\(814\) | 26.0759 | 0.913960 | ||||||||
\(815\) | −26.7510 | −0.937046 | ||||||||
\(816\) | 21.6937 | 0.759431 | ||||||||
\(817\) | −2.46914 | −0.0863842 | ||||||||
\(818\) | 90.7528 | 3.17310 | ||||||||
\(819\) | 0.0978612 | 0.00341955 | ||||||||
\(820\) | −3.98039 | −0.139001 | ||||||||
\(821\) | −5.95062 | −0.207678 | −0.103839 | − | 0.994594i | \(-0.533113\pi\) | ||||
−0.103839 | + | 0.994594i | \(0.533113\pi\) | |||||||
\(822\) | −118.364 | −4.12843 | ||||||||
\(823\) | −1.00236 | −0.0349399 | −0.0174700 | − | 0.999847i | \(-0.505561\pi\) | ||||
−0.0174700 | + | 0.999847i | \(0.505561\pi\) | |||||||
\(824\) | −90.6234 | −3.15702 | ||||||||
\(825\) | −3.29382 | −0.114676 | ||||||||
\(826\) | −0.327717 | −0.0114027 | ||||||||
\(827\) | 1.62336 | 0.0564496 | 0.0282248 | − | 0.999602i | \(-0.491015\pi\) | ||||
0.0282248 | + | 0.999602i | \(0.491015\pi\) | |||||||
\(828\) | 31.5683 | 1.09707 | ||||||||
\(829\) | 31.6385 | 1.09885 | 0.549425 | − | 0.835543i | \(-0.314847\pi\) | ||||
0.549425 | + | 0.835543i | \(0.314847\pi\) | |||||||
\(830\) | 26.7076 | 0.927034 | ||||||||
\(831\) | 66.7718 | 2.31629 | ||||||||
\(832\) | 4.80091 | 0.166441 | ||||||||
\(833\) | 11.0913 | 0.384291 | ||||||||
\(834\) | 58.9858 | 2.04251 | ||||||||
\(835\) | 10.7495 | 0.372001 | ||||||||
\(836\) | 4.61867 | 0.159740 | ||||||||
\(837\) | 19.4154 | 0.671096 | ||||||||
\(838\) | 82.3018 | 2.84307 | ||||||||
\(839\) | 30.1852 | 1.04211 | 0.521054 | − | 0.853524i | \(-0.325539\pi\) | ||||
0.521054 | + | 0.853524i | \(0.325539\pi\) | |||||||
\(840\) | 0.728027 | 0.0251193 | ||||||||
\(841\) | 70.8524 | 2.44318 | ||||||||
\(842\) | −71.9184 | −2.47847 | ||||||||
\(843\) | 17.1757 | 0.591561 | ||||||||
\(844\) | −4.37089 | −0.150452 | ||||||||
\(845\) | 16.9430 | 0.582859 | ||||||||
\(846\) | 46.0076 | 1.58177 | ||||||||
\(847\) | 0.296566 | 0.0101901 | ||||||||
\(848\) | −8.32495 | −0.285880 | ||||||||
\(849\) | −50.2426 | −1.72432 | ||||||||
\(850\) | −5.79507 | −0.198769 | ||||||||
\(851\) | 43.3509 | 1.48605 | ||||||||
\(852\) | −69.7603 | −2.38995 | ||||||||
\(853\) | 27.5434 | 0.943068 | 0.471534 | − | 0.881848i | \(-0.343700\pi\) | ||||
0.471534 | + | 0.881848i | \(0.343700\pi\) | |||||||
\(854\) | −0.135071 | −0.00462203 | ||||||||
\(855\) | 3.06946 | 0.104973 | ||||||||
\(856\) | −88.1814 | −3.01398 | ||||||||
\(857\) | 16.4943 | 0.563435 | 0.281718 | − | 0.959497i | \(-0.409096\pi\) | ||||
0.281718 | + | 0.959497i | \(0.409096\pi\) | |||||||
\(858\) | 11.4895 | 0.392246 | ||||||||
\(859\) | −38.1095 | −1.30028 | −0.650139 | − | 0.759815i | \(-0.725289\pi\) | ||||
−0.650139 | + | 0.759815i | \(0.725289\pi\) | |||||||
\(860\) | −20.3377 | −0.693509 | ||||||||
\(861\) | 0.0311975 | 0.00106321 | ||||||||
\(862\) | 91.5357 | 3.11772 | ||||||||
\(863\) | −9.77818 | −0.332853 | −0.166427 | − | 0.986054i | \(-0.553223\pi\) | ||||
−0.166427 | + | 0.986054i | \(0.553223\pi\) | |||||||
\(864\) | −12.0711 | −0.410667 | ||||||||
\(865\) | 5.77402 | 0.196323 | ||||||||
\(866\) | 0.117674 | 0.00399872 | ||||||||
\(867\) | 31.1723 | 1.05867 | ||||||||
\(868\) | −0.863187 | −0.0292985 | ||||||||
\(869\) | 9.33449 | 0.316651 | ||||||||
\(870\) | 102.259 | 3.46690 | ||||||||
\(871\) | −20.0143 | −0.678159 | ||||||||
\(872\) | −1.26560 | −0.0428586 | ||||||||
\(873\) | 4.88174 | 0.165222 | ||||||||
\(874\) | 11.1919 | 0.378573 | ||||||||
\(875\) | −0.364654 | −0.0123275 | ||||||||
\(876\) | −95.6944 | −3.23321 | ||||||||
\(877\) | 28.6121 | 0.966163 | 0.483081 | − | 0.875575i | \(-0.339517\pi\) | ||||
0.483081 | + | 0.875575i | \(0.339517\pi\) | |||||||
\(878\) | 62.4022 | 2.10597 | ||||||||
\(879\) | 46.7527 | 1.57693 | ||||||||
\(880\) | 12.6704 | 0.427118 | ||||||||
\(881\) | −4.09192 | −0.137860 | −0.0689301 | − | 0.997621i | \(-0.521959\pi\) | ||||
−0.0689301 | + | 0.997621i | \(0.521959\pi\) | |||||||
\(882\) | 28.7752 | 0.968912 | ||||||||
\(883\) | 24.5185 | 0.825114 | 0.412557 | − | 0.910932i | \(-0.364636\pi\) | ||||
0.412557 | + | 0.910932i | \(0.364636\pi\) | |||||||
\(884\) | 13.8685 | 0.466450 | ||||||||
\(885\) | −17.5431 | −0.589704 | ||||||||
\(886\) | 2.25592 | 0.0757891 | ||||||||
\(887\) | 31.9688 | 1.07341 | 0.536704 | − | 0.843771i | \(-0.319669\pi\) | ||||
0.536704 | + | 0.843771i | \(0.319669\pi\) | |||||||
\(888\) | 125.876 | 4.22411 | ||||||||
\(889\) | 0.645890 | 0.0216625 | ||||||||
\(890\) | −8.79827 | −0.294919 | ||||||||
\(891\) | 11.8702 | 0.397666 | ||||||||
\(892\) | −64.5146 | −2.16011 | ||||||||
\(893\) | 11.1906 | 0.374479 | ||||||||
\(894\) | 1.09194 | 0.0365201 | ||||||||
\(895\) | −21.9035 | −0.732154 | ||||||||
\(896\) | −0.427165 | −0.0142706 | ||||||||
\(897\) | 19.1012 | 0.637770 | ||||||||
\(898\) | 76.3711 | 2.54854 | ||||||||
\(899\) | −65.7658 | −2.19341 | ||||||||
\(900\) | −10.3149 | −0.343830 | ||||||||
\(901\) | 2.07331 | 0.0690721 | ||||||||
\(902\) | 1.28889 | 0.0429154 | ||||||||
\(903\) | 0.159402 | 0.00530458 | ||||||||
\(904\) | −83.2488 | −2.76881 | ||||||||
\(905\) | −47.8721 | −1.59132 | ||||||||
\(906\) | 41.8067 | 1.38894 | ||||||||
\(907\) | −37.6444 | −1.24996 | −0.624982 | − | 0.780640i | \(-0.714894\pi\) | ||||
−0.624982 | + | 0.780640i | \(0.714894\pi\) | |||||||
\(908\) | −32.3106 | −1.07226 | ||||||||
\(909\) | 2.44794 | 0.0811931 | ||||||||
\(910\) | 0.285772 | 0.00947326 | ||||||||
\(911\) | −48.3751 | −1.60274 | −0.801369 | − | 0.598170i | \(-0.795895\pi\) | ||||
−0.801369 | + | 0.598170i | \(0.795895\pi\) | |||||||
\(912\) | 13.6897 | 0.453310 | ||||||||
\(913\) | −5.93328 | −0.196363 | ||||||||
\(914\) | −42.9085 | −1.41929 | ||||||||
\(915\) | −7.23051 | −0.239033 | ||||||||
\(916\) | 77.7222 | 2.56801 | ||||||||
\(917\) | 0.108631 | 0.00358732 | ||||||||
\(918\) | 11.7996 | 0.389445 | ||||||||
\(919\) | 48.9429 | 1.61448 | 0.807239 | − | 0.590224i | \(-0.200961\pi\) | ||||
0.807239 | + | 0.590224i | \(0.200961\pi\) | |||||||
\(920\) | 50.0038 | 1.64857 | ||||||||
\(921\) | 47.3894 | 1.56153 | ||||||||
\(922\) | −83.1047 | −2.73691 | ||||||||
\(923\) | −14.8533 | −0.488902 | ||||||||
\(924\) | −0.298172 | −0.00980912 | ||||||||
\(925\) | −14.1648 | −0.465737 | ||||||||
\(926\) | 100.379 | 3.29865 | ||||||||
\(927\) | 24.6663 | 0.810148 | ||||||||
\(928\) | 40.8884 | 1.34223 | ||||||||
\(929\) | 42.0953 | 1.38110 | 0.690550 | − | 0.723284i | \(-0.257368\pi\) | ||||
0.690550 | + | 0.723284i | \(0.257368\pi\) | |||||||
\(930\) | −67.3507 | −2.20852 | ||||||||
\(931\) | 6.99910 | 0.229386 | ||||||||
\(932\) | 123.893 | 4.05826 | ||||||||
\(933\) | 20.6409 | 0.675754 | ||||||||
\(934\) | 68.9606 | 2.25646 | ||||||||
\(935\) | −3.15553 | −0.103197 | ||||||||
\(936\) | 19.5168 | 0.637927 | ||||||||
\(937\) | 12.4036 | 0.405207 | 0.202604 | − | 0.979261i | \(-0.435060\pi\) | ||||
0.202604 | + | 0.979261i | \(0.435060\pi\) | |||||||
\(938\) | 0.757067 | 0.0247191 | ||||||||
\(939\) | 30.4856 | 0.994859 | ||||||||
\(940\) | 92.1741 | 3.00639 | ||||||||
\(941\) | −40.4438 | −1.31843 | −0.659215 | − | 0.751955i | \(-0.729111\pi\) | ||||
−0.659215 | + | 0.751955i | \(0.729111\pi\) | |||||||
\(942\) | 67.4071 | 2.19624 | ||||||||
\(943\) | 2.14277 | 0.0697780 | ||||||||
\(944\) | −27.5323 | −0.896098 | ||||||||
\(945\) | 0.166811 | 0.00542638 | ||||||||
\(946\) | 6.58554 | 0.214115 | ||||||||
\(947\) | 55.1836 | 1.79322 | 0.896612 | − | 0.442816i | \(-0.146021\pi\) | ||||
0.896612 | + | 0.442816i | \(0.146021\pi\) | |||||||
\(948\) | 83.0712 | 2.69803 | ||||||||
\(949\) | −20.3751 | −0.661405 | ||||||||
\(950\) | −3.65694 | −0.118647 | ||||||||
\(951\) | 74.2381 | 2.40733 | ||||||||
\(952\) | −0.284555 | −0.00922249 | ||||||||
\(953\) | 30.2971 | 0.981420 | 0.490710 | − | 0.871323i | \(-0.336737\pi\) | ||||
0.490710 | + | 0.871323i | \(0.336737\pi\) | |||||||
\(954\) | 5.37900 | 0.174151 | ||||||||
\(955\) | −30.4991 | −0.986929 | ||||||||
\(956\) | −66.6041 | −2.15413 | ||||||||
\(957\) | −22.7175 | −0.734353 | ||||||||
\(958\) | −58.4569 | −1.88866 | ||||||||
\(959\) | 0.654031 | 0.0211198 | ||||||||
\(960\) | −9.72130 | −0.313754 | ||||||||
\(961\) | 12.3153 | 0.397268 | ||||||||
\(962\) | 49.4099 | 1.59304 | ||||||||
\(963\) | 24.0016 | 0.773442 | ||||||||
\(964\) | 68.0247 | 2.19093 | ||||||||
\(965\) | −39.3920 | −1.26807 | ||||||||
\(966\) | −0.722528 | −0.0232469 | ||||||||
\(967\) | 4.26436 | 0.137133 | 0.0685663 | − | 0.997647i | \(-0.478158\pi\) | ||||
0.0685663 | + | 0.997647i | \(0.478158\pi\) | |||||||
\(968\) | 59.1452 | 1.90100 | ||||||||
\(969\) | −3.40939 | −0.109525 | ||||||||
\(970\) | 14.2556 | 0.457718 | ||||||||
\(971\) | −9.23405 | −0.296335 | −0.148167 | − | 0.988962i | \(-0.547337\pi\) | ||||
−0.148167 | + | 0.988962i | \(0.547337\pi\) | |||||||
\(972\) | 66.9545 | 2.14757 | ||||||||
\(973\) | −0.325931 | −0.0104489 | ||||||||
\(974\) | 1.30947 | 0.0419582 | ||||||||
\(975\) | −6.24129 | −0.199881 | ||||||||
\(976\) | −11.3476 | −0.363228 | ||||||||
\(977\) | 14.2786 | 0.456814 | 0.228407 | − | 0.973566i | \(-0.426648\pi\) | ||||
0.228407 | + | 0.973566i | \(0.426648\pi\) | |||||||
\(978\) | 77.0886 | 2.46502 | ||||||||
\(979\) | 1.95460 | 0.0624692 | ||||||||
\(980\) | 57.6498 | 1.84156 | ||||||||
\(981\) | 0.344477 | 0.0109983 | ||||||||
\(982\) | 25.5066 | 0.813948 | ||||||||
\(983\) | 41.8189 | 1.33381 | 0.666907 | − | 0.745141i | \(-0.267618\pi\) | ||||
0.666907 | + | 0.745141i | \(0.267618\pi\) | |||||||
\(984\) | 6.22183 | 0.198345 | ||||||||
\(985\) | −30.4796 | −0.971160 | ||||||||
\(986\) | −39.9687 | −1.27286 | ||||||||
\(987\) | −0.722442 | −0.0229956 | ||||||||
\(988\) | 8.75166 | 0.278427 | ||||||||
\(989\) | 10.9484 | 0.348138 | ||||||||
\(990\) | −8.18669 | −0.260190 | ||||||||
\(991\) | −55.0997 | −1.75030 | −0.875149 | − | 0.483853i | \(-0.839237\pi\) | ||||
−0.875149 | + | 0.483853i | \(0.839237\pi\) | |||||||
\(992\) | −26.9303 | −0.855039 | ||||||||
\(993\) | −40.7902 | −1.29444 | ||||||||
\(994\) | 0.561845 | 0.0178206 | ||||||||
\(995\) | 2.71032 | 0.0859230 | ||||||||
\(996\) | −52.8026 | −1.67311 | ||||||||
\(997\) | 23.7035 | 0.750697 | 0.375349 | − | 0.926884i | \(-0.377523\pi\) | ||||
0.375349 | + | 0.926884i | \(0.377523\pi\) | |||||||
\(998\) | −2.49771 | −0.0790636 | ||||||||
\(999\) | 28.8416 | 0.912508 |
(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 | 4009.2.a.d.1.7 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.d.1.7 | ✓ | 75 | 1.1 | even | 1 | trivial |