Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.54502 | 1.09250 | 0.546248 | − | 0.837623i | \(-0.316056\pi\) | ||||
0.546248 | + | 0.837623i | \(0.316056\pi\) | |||||||
\(3\) | 2.73368 | 1.57829 | 0.789146 | − | 0.614205i | \(-0.210523\pi\) | ||||
0.789146 | + | 0.614205i | \(0.210523\pi\) | |||||||
\(4\) | 0.387096 | 0.193548 | ||||||||
\(5\) | −3.25406 | −1.45526 | −0.727629 | − | 0.685970i | \(-0.759378\pi\) | ||||
−0.727629 | + | 0.685970i | \(0.759378\pi\) | |||||||
\(6\) | 4.22360 | 1.72428 | ||||||||
\(7\) | −3.29481 | −1.24532 | −0.622660 | − | 0.782492i | \(-0.713948\pi\) | ||||
−0.622660 | + | 0.782492i | \(0.713948\pi\) | |||||||
\(8\) | −2.49197 | −0.881046 | ||||||||
\(9\) | 4.47303 | 1.49101 | ||||||||
\(10\) | −5.02759 | −1.58986 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.05820 | 0.305475 | ||||||||
\(13\) | −5.51417 | −1.52936 | −0.764678 | − | 0.644412i | \(-0.777102\pi\) | ||||
−0.764678 | + | 0.644412i | \(0.777102\pi\) | |||||||
\(14\) | −5.09056 | −1.36051 | ||||||||
\(15\) | −8.89556 | −2.29682 | ||||||||
\(16\) | −4.62435 | −1.15609 | ||||||||
\(17\) | 0.673006 | 0.163228 | 0.0816140 | − | 0.996664i | \(-0.473993\pi\) | ||||
0.0816140 | + | 0.996664i | \(0.473993\pi\) | |||||||
\(18\) | 6.91093 | 1.62892 | ||||||||
\(19\) | 3.11070 | 0.713644 | 0.356822 | − | 0.934172i | \(-0.383860\pi\) | ||||
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(20\) | −1.25963 | −0.281662 | ||||||||
\(21\) | −9.00696 | −1.96548 | ||||||||
\(22\) | −1.54502 | −0.329400 | ||||||||
\(23\) | 0.320864 | 0.0669048 | 0.0334524 | − | 0.999440i | \(-0.489350\pi\) | ||||
0.0334524 | + | 0.999440i | \(0.489350\pi\) | |||||||
\(24\) | −6.81227 | −1.39055 | ||||||||
\(25\) | 5.58889 | 1.11778 | ||||||||
\(26\) | −8.51952 | −1.67082 | ||||||||
\(27\) | 4.02679 | 0.774955 | ||||||||
\(28\) | −1.27541 | −0.241029 | ||||||||
\(29\) | −1.44518 | −0.268362 | −0.134181 | − | 0.990957i | \(-0.542840\pi\) | ||||
−0.134181 | + | 0.990957i | \(0.542840\pi\) | |||||||
\(30\) | −13.7438 | −2.50927 | ||||||||
\(31\) | −1.86574 | −0.335096 | −0.167548 | − | 0.985864i | \(-0.553585\pi\) | ||||
−0.167548 | + | 0.985864i | \(0.553585\pi\) | |||||||
\(32\) | −2.16078 | −0.381975 | ||||||||
\(33\) | −2.73368 | −0.475873 | ||||||||
\(34\) | 1.03981 | 0.178326 | ||||||||
\(35\) | 10.7215 | 1.81226 | ||||||||
\(36\) | 1.73149 | 0.288582 | ||||||||
\(37\) | −5.81490 | −0.955963 | −0.477982 | − | 0.878370i | \(-0.658631\pi\) | ||||
−0.477982 | + | 0.878370i | \(0.658631\pi\) | |||||||
\(38\) | 4.80611 | 0.779654 | ||||||||
\(39\) | −15.0740 | −2.41377 | ||||||||
\(40\) | 8.10903 | 1.28215 | ||||||||
\(41\) | −2.70144 | −0.421893 | −0.210947 | − | 0.977498i | \(-0.567655\pi\) | ||||
−0.210947 | + | 0.977498i | \(0.567655\pi\) | |||||||
\(42\) | −13.9160 | −2.14728 | ||||||||
\(43\) | 7.48431 | 1.14135 | 0.570673 | − | 0.821177i | \(-0.306682\pi\) | ||||
0.570673 | + | 0.821177i | \(0.306682\pi\) | |||||||
\(44\) | −0.387096 | −0.0583569 | ||||||||
\(45\) | −14.5555 | −2.16980 | ||||||||
\(46\) | 0.495742 | 0.0730932 | ||||||||
\(47\) | 10.5675 | 1.54142 | 0.770712 | − | 0.637184i | \(-0.219901\pi\) | ||||
0.770712 | + | 0.637184i | \(0.219901\pi\) | |||||||
\(48\) | −12.6415 | −1.82464 | ||||||||
\(49\) | 3.85576 | 0.550824 | ||||||||
\(50\) | 8.63496 | 1.22117 | ||||||||
\(51\) | 1.83979 | 0.257622 | ||||||||
\(52\) | −2.13451 | −0.296004 | ||||||||
\(53\) | −1.04762 | −0.143902 | −0.0719510 | − | 0.997408i | \(-0.522923\pi\) | ||||
−0.0719510 | + | 0.997408i | \(0.522923\pi\) | |||||||
\(54\) | 6.22148 | 0.846636 | ||||||||
\(55\) | 3.25406 | 0.438777 | ||||||||
\(56\) | 8.21058 | 1.09718 | ||||||||
\(57\) | 8.50368 | 1.12634 | ||||||||
\(58\) | −2.23283 | −0.293185 | ||||||||
\(59\) | −5.63765 | −0.733959 | −0.366980 | − | 0.930229i | \(-0.619608\pi\) | ||||
−0.366980 | + | 0.930229i | \(0.619608\pi\) | |||||||
\(60\) | −3.44344 | −0.444546 | ||||||||
\(61\) | 4.55464 | 0.583161 | 0.291581 | − | 0.956546i | \(-0.405819\pi\) | ||||
0.291581 | + | 0.956546i | \(0.405819\pi\) | |||||||
\(62\) | −2.88260 | −0.366091 | ||||||||
\(63\) | −14.7378 | −1.85678 | ||||||||
\(64\) | 5.91025 | 0.738781 | ||||||||
\(65\) | 17.9434 | 2.22561 | ||||||||
\(66\) | −4.22360 | −0.519890 | ||||||||
\(67\) | −15.7868 | −1.92866 | −0.964332 | − | 0.264696i | \(-0.914728\pi\) | ||||
−0.964332 | + | 0.264696i | \(0.914728\pi\) | |||||||
\(68\) | 0.260518 | 0.0315924 | ||||||||
\(69\) | 0.877141 | 0.105595 | ||||||||
\(70\) | 16.5650 | 1.97989 | ||||||||
\(71\) | −7.75176 | −0.919965 | −0.459982 | − | 0.887928i | \(-0.652144\pi\) | ||||
−0.459982 | + | 0.887928i | \(0.652144\pi\) | |||||||
\(72\) | −11.1467 | −1.31365 | ||||||||
\(73\) | 2.58126 | 0.302114 | 0.151057 | − | 0.988525i | \(-0.451732\pi\) | ||||
0.151057 | + | 0.988525i | \(0.451732\pi\) | |||||||
\(74\) | −8.98415 | −1.04439 | ||||||||
\(75\) | 15.2783 | 1.76418 | ||||||||
\(76\) | 1.20414 | 0.138124 | ||||||||
\(77\) | 3.29481 | 0.375478 | ||||||||
\(78\) | −23.2897 | −2.63704 | ||||||||
\(79\) | 16.3556 | 1.84015 | 0.920073 | − | 0.391748i | \(-0.128129\pi\) | ||||
0.920073 | + | 0.391748i | \(0.128129\pi\) | |||||||
\(80\) | 15.0479 | 1.68241 | ||||||||
\(81\) | −2.41112 | −0.267902 | ||||||||
\(82\) | −4.17378 | −0.460917 | ||||||||
\(83\) | 4.48950 | 0.492787 | 0.246393 | − | 0.969170i | \(-0.420754\pi\) | ||||
0.246393 | + | 0.969170i | \(0.420754\pi\) | |||||||
\(84\) | −3.48656 | −0.380415 | ||||||||
\(85\) | −2.19000 | −0.237539 | ||||||||
\(86\) | 11.5634 | 1.24692 | ||||||||
\(87\) | −3.95065 | −0.423554 | ||||||||
\(88\) | 2.49197 | 0.265645 | ||||||||
\(89\) | −10.2834 | −1.09003 | −0.545017 | − | 0.838425i | \(-0.683477\pi\) | ||||
−0.545017 | + | 0.838425i | \(0.683477\pi\) | |||||||
\(90\) | −22.4886 | −2.37050 | ||||||||
\(91\) | 18.1681 | 1.90454 | ||||||||
\(92\) | 0.124205 | 0.0129493 | ||||||||
\(93\) | −5.10033 | −0.528880 | ||||||||
\(94\) | 16.3270 | 1.68400 | ||||||||
\(95\) | −10.1224 | −1.03854 | ||||||||
\(96\) | −5.90688 | −0.602868 | ||||||||
\(97\) | −18.8099 | −1.90985 | −0.954926 | − | 0.296844i | \(-0.904066\pi\) | ||||
−0.954926 | + | 0.296844i | \(0.904066\pi\) | |||||||
\(98\) | 5.95725 | 0.601773 | ||||||||
\(99\) | −4.47303 | −0.449556 | ||||||||
\(100\) | 2.16344 | 0.216344 | ||||||||
\(101\) | −7.92610 | −0.788676 | −0.394338 | − | 0.918965i | \(-0.629026\pi\) | ||||
−0.394338 | + | 0.918965i | \(0.629026\pi\) | |||||||
\(102\) | 2.84251 | 0.281451 | ||||||||
\(103\) | −10.0377 | −0.989049 | −0.494524 | − | 0.869164i | \(-0.664658\pi\) | ||||
−0.494524 | + | 0.869164i | \(0.664658\pi\) | |||||||
\(104\) | 13.7412 | 1.34743 | ||||||||
\(105\) | 29.3092 | 2.86028 | ||||||||
\(106\) | −1.61860 | −0.157212 | ||||||||
\(107\) | 9.78669 | 0.946115 | 0.473057 | − | 0.881032i | \(-0.343150\pi\) | ||||
0.473057 | + | 0.881032i | \(0.343150\pi\) | |||||||
\(108\) | 1.55875 | 0.149991 | ||||||||
\(109\) | −5.84952 | −0.560283 | −0.280141 | − | 0.959959i | \(-0.590381\pi\) | ||||
−0.280141 | + | 0.959959i | \(0.590381\pi\) | |||||||
\(110\) | 5.02759 | 0.479362 | ||||||||
\(111\) | −15.8961 | −1.50879 | ||||||||
\(112\) | 15.2363 | 1.43970 | ||||||||
\(113\) | −4.16421 | −0.391735 | −0.195868 | − | 0.980630i | \(-0.562752\pi\) | ||||
−0.195868 | + | 0.980630i | \(0.562752\pi\) | |||||||
\(114\) | 13.1384 | 1.23052 | ||||||||
\(115\) | −1.04411 | −0.0973637 | ||||||||
\(116\) | −0.559421 | −0.0519410 | ||||||||
\(117\) | −24.6650 | −2.28028 | ||||||||
\(118\) | −8.71029 | −0.801848 | ||||||||
\(119\) | −2.21743 | −0.203271 | ||||||||
\(120\) | 22.1675 | 2.02361 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.03702 | 0.637102 | ||||||||
\(123\) | −7.38487 | −0.665871 | ||||||||
\(124\) | −0.722219 | −0.0648571 | ||||||||
\(125\) | −1.91628 | −0.171397 | ||||||||
\(126\) | −22.7702 | −2.02853 | ||||||||
\(127\) | −16.6543 | −1.47783 | −0.738917 | − | 0.673796i | \(-0.764663\pi\) | ||||
−0.738917 | + | 0.673796i | \(0.764663\pi\) | |||||||
\(128\) | 13.4530 | 1.18909 | ||||||||
\(129\) | 20.4597 | 1.80138 | ||||||||
\(130\) | 27.7230 | 2.43147 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −1.05820 | −0.0921043 | ||||||||
\(133\) | −10.2492 | −0.888716 | ||||||||
\(134\) | −24.3910 | −2.10706 | ||||||||
\(135\) | −13.1034 | −1.12776 | ||||||||
\(136\) | −1.67711 | −0.143811 | ||||||||
\(137\) | 12.0488 | 1.02940 | 0.514699 | − | 0.857371i | \(-0.327904\pi\) | ||||
0.514699 | + | 0.857371i | \(0.327904\pi\) | |||||||
\(138\) | 1.35520 | 0.115362 | ||||||||
\(139\) | 12.0168 | 1.01925 | 0.509626 | − | 0.860396i | \(-0.329784\pi\) | ||||
0.509626 | + | 0.860396i | \(0.329784\pi\) | |||||||
\(140\) | 4.15025 | 0.350760 | ||||||||
\(141\) | 28.8881 | 2.43282 | ||||||||
\(142\) | −11.9766 | −1.00506 | ||||||||
\(143\) | 5.51417 | 0.461118 | ||||||||
\(144\) | −20.6848 | −1.72374 | ||||||||
\(145\) | 4.70268 | 0.390537 | ||||||||
\(146\) | 3.98811 | 0.330058 | ||||||||
\(147\) | 10.5404 | 0.869361 | ||||||||
\(148\) | −2.25092 | −0.185025 | ||||||||
\(149\) | 5.85354 | 0.479541 | 0.239770 | − | 0.970830i | \(-0.422928\pi\) | ||||
0.239770 | + | 0.970830i | \(0.422928\pi\) | |||||||
\(150\) | 23.6053 | 1.92736 | ||||||||
\(151\) | 2.52100 | 0.205156 | 0.102578 | − | 0.994725i | \(-0.467291\pi\) | ||||
0.102578 | + | 0.994725i | \(0.467291\pi\) | |||||||
\(152\) | −7.75179 | −0.628753 | ||||||||
\(153\) | 3.01038 | 0.243374 | ||||||||
\(154\) | 5.09056 | 0.410209 | ||||||||
\(155\) | 6.07121 | 0.487651 | ||||||||
\(156\) | −5.83508 | −0.467181 | ||||||||
\(157\) | 20.3807 | 1.62656 | 0.813279 | − | 0.581874i | \(-0.197680\pi\) | ||||
0.813279 | + | 0.581874i | \(0.197680\pi\) | |||||||
\(158\) | 25.2697 | 2.01035 | ||||||||
\(159\) | −2.86387 | −0.227120 | ||||||||
\(160\) | 7.03129 | 0.555872 | ||||||||
\(161\) | −1.05719 | −0.0833179 | ||||||||
\(162\) | −3.72523 | −0.292682 | ||||||||
\(163\) | 12.1542 | 0.951988 | 0.475994 | − | 0.879449i | \(-0.342088\pi\) | ||||
0.475994 | + | 0.879449i | \(0.342088\pi\) | |||||||
\(164\) | −1.04571 | −0.0816566 | ||||||||
\(165\) | 8.89556 | 0.692519 | ||||||||
\(166\) | 6.93638 | 0.538368 | ||||||||
\(167\) | 5.33778 | 0.413050 | 0.206525 | − | 0.978441i | \(-0.433785\pi\) | ||||
0.206525 | + | 0.978441i | \(0.433785\pi\) | |||||||
\(168\) | 22.4451 | 1.73168 | ||||||||
\(169\) | 17.4061 | 1.33893 | ||||||||
\(170\) | −3.38360 | −0.259510 | ||||||||
\(171\) | 13.9143 | 1.06405 | ||||||||
\(172\) | 2.89715 | 0.220905 | ||||||||
\(173\) | −4.53547 | −0.344825 | −0.172413 | − | 0.985025i | \(-0.555156\pi\) | ||||
−0.172413 | + | 0.985025i | \(0.555156\pi\) | |||||||
\(174\) | −6.10385 | −0.462731 | ||||||||
\(175\) | −18.4143 | −1.39199 | ||||||||
\(176\) | 4.62435 | 0.348573 | ||||||||
\(177\) | −15.4115 | −1.15840 | ||||||||
\(178\) | −15.8880 | −1.19086 | ||||||||
\(179\) | −22.3191 | −1.66820 | −0.834102 | − | 0.551610i | \(-0.814014\pi\) | ||||
−0.834102 | + | 0.551610i | \(0.814014\pi\) | |||||||
\(180\) | −5.63437 | −0.419961 | ||||||||
\(181\) | −1.86197 | −0.138399 | −0.0691995 | − | 0.997603i | \(-0.522045\pi\) | ||||
−0.0691995 | + | 0.997603i | \(0.522045\pi\) | |||||||
\(182\) | 28.0702 | 2.08070 | ||||||||
\(183\) | 12.4509 | 0.920400 | ||||||||
\(184\) | −0.799585 | −0.0589462 | ||||||||
\(185\) | 18.9220 | 1.39117 | ||||||||
\(186\) | −7.88013 | −0.577799 | ||||||||
\(187\) | −0.673006 | −0.0492151 | ||||||||
\(188\) | 4.09062 | 0.298339 | ||||||||
\(189\) | −13.2675 | −0.965068 | ||||||||
\(190\) | −15.6393 | −1.13460 | ||||||||
\(191\) | −16.4987 | −1.19380 | −0.596900 | − | 0.802315i | \(-0.703601\pi\) | ||||
−0.596900 | + | 0.802315i | \(0.703601\pi\) | |||||||
\(192\) | 16.1567 | 1.16601 | ||||||||
\(193\) | −11.3043 | −0.813702 | −0.406851 | − | 0.913495i | \(-0.633373\pi\) | ||||
−0.406851 | + | 0.913495i | \(0.633373\pi\) | |||||||
\(194\) | −29.0617 | −2.08651 | ||||||||
\(195\) | 49.0517 | 3.51266 | ||||||||
\(196\) | 1.49255 | 0.106611 | ||||||||
\(197\) | −15.1553 | −1.07977 | −0.539885 | − | 0.841739i | \(-0.681532\pi\) | ||||
−0.539885 | + | 0.841739i | \(0.681532\pi\) | |||||||
\(198\) | −6.91093 | −0.491138 | ||||||||
\(199\) | −14.9645 | −1.06081 | −0.530403 | − | 0.847745i | \(-0.677959\pi\) | ||||
−0.530403 | + | 0.847745i | \(0.677959\pi\) | |||||||
\(200\) | −13.9274 | −0.984814 | ||||||||
\(201\) | −43.1561 | −3.04400 | ||||||||
\(202\) | −12.2460 | −0.861626 | ||||||||
\(203\) | 4.76158 | 0.334197 | ||||||||
\(204\) | 0.712174 | 0.0498621 | ||||||||
\(205\) | 8.79063 | 0.613964 | ||||||||
\(206\) | −15.5085 | −1.08053 | ||||||||
\(207\) | 1.43523 | 0.0997556 | ||||||||
\(208\) | 25.4995 | 1.76807 | ||||||||
\(209\) | −3.11070 | −0.215172 | ||||||||
\(210\) | 45.2834 | 3.12485 | ||||||||
\(211\) | −3.96743 | −0.273129 | −0.136565 | − | 0.990631i | \(-0.543606\pi\) | ||||
−0.136565 | + | 0.990631i | \(0.543606\pi\) | |||||||
\(212\) | −0.405531 | −0.0278520 | ||||||||
\(213\) | −21.1909 | −1.45197 | ||||||||
\(214\) | 15.1207 | 1.03363 | ||||||||
\(215\) | −24.3544 | −1.66095 | ||||||||
\(216\) | −10.0346 | −0.682771 | ||||||||
\(217\) | 6.14724 | 0.417302 | ||||||||
\(218\) | −9.03765 | −0.612107 | ||||||||
\(219\) | 7.05635 | 0.476824 | ||||||||
\(220\) | 1.25963 | 0.0849244 | ||||||||
\(221\) | −3.71107 | −0.249634 | ||||||||
\(222\) | −24.5598 | −1.64835 | ||||||||
\(223\) | 10.1257 | 0.678070 | 0.339035 | − | 0.940774i | \(-0.389900\pi\) | ||||
0.339035 | + | 0.940774i | \(0.389900\pi\) | |||||||
\(224\) | 7.11935 | 0.475681 | ||||||||
\(225\) | 24.9992 | 1.66662 | ||||||||
\(226\) | −6.43379 | −0.427969 | ||||||||
\(227\) | 0.0578550 | 0.00383997 | 0.00191999 | − | 0.999998i | \(-0.499389\pi\) | ||||
0.00191999 | + | 0.999998i | \(0.499389\pi\) | |||||||
\(228\) | 3.29174 | 0.218001 | ||||||||
\(229\) | −11.2902 | −0.746074 | −0.373037 | − | 0.927816i | \(-0.621684\pi\) | ||||
−0.373037 | + | 0.927816i | \(0.621684\pi\) | |||||||
\(230\) | −1.61317 | −0.106370 | ||||||||
\(231\) | 9.00696 | 0.592615 | ||||||||
\(232\) | 3.60134 | 0.236439 | ||||||||
\(233\) | −13.7996 | −0.904044 | −0.452022 | − | 0.892007i | \(-0.649297\pi\) | ||||
−0.452022 | + | 0.892007i | \(0.649297\pi\) | |||||||
\(234\) | −38.1080 | −2.49120 | ||||||||
\(235\) | −34.3871 | −2.24317 | ||||||||
\(236\) | −2.18231 | −0.142056 | ||||||||
\(237\) | 44.7110 | 2.90429 | ||||||||
\(238\) | −3.42598 | −0.222073 | ||||||||
\(239\) | −8.61019 | −0.556947 | −0.278474 | − | 0.960444i | \(-0.589828\pi\) | ||||
−0.278474 | + | 0.960444i | \(0.589828\pi\) | |||||||
\(240\) | 41.1362 | 2.65533 | ||||||||
\(241\) | 8.68434 | 0.559408 | 0.279704 | − | 0.960086i | \(-0.409764\pi\) | ||||
0.279704 | + | 0.960086i | \(0.409764\pi\) | |||||||
\(242\) | 1.54502 | 0.0993178 | ||||||||
\(243\) | −18.6716 | −1.19778 | ||||||||
\(244\) | 1.76308 | 0.112870 | ||||||||
\(245\) | −12.5469 | −0.801591 | ||||||||
\(246\) | −11.4098 | −0.727462 | ||||||||
\(247\) | −17.1530 | −1.09142 | ||||||||
\(248\) | 4.64936 | 0.295235 | ||||||||
\(249\) | 12.2729 | 0.777762 | ||||||||
\(250\) | −2.96070 | −0.187251 | ||||||||
\(251\) | 7.94755 | 0.501645 | 0.250822 | − | 0.968033i | \(-0.419299\pi\) | ||||
0.250822 | + | 0.968033i | \(0.419299\pi\) | |||||||
\(252\) | −5.70493 | −0.359377 | ||||||||
\(253\) | −0.320864 | −0.0201725 | ||||||||
\(254\) | −25.7313 | −1.61453 | ||||||||
\(255\) | −5.98677 | −0.374906 | ||||||||
\(256\) | 8.96473 | 0.560296 | ||||||||
\(257\) | 15.2272 | 0.949849 | 0.474925 | − | 0.880027i | \(-0.342475\pi\) | ||||
0.474925 | + | 0.880027i | \(0.342475\pi\) | |||||||
\(258\) | 31.6108 | 1.96800 | ||||||||
\(259\) | 19.1590 | 1.19048 | ||||||||
\(260\) | 6.94583 | 0.430762 | ||||||||
\(261\) | −6.46431 | −0.400130 | ||||||||
\(262\) | −1.54502 | −0.0954518 | ||||||||
\(263\) | −17.9040 | −1.10401 | −0.552003 | − | 0.833842i | \(-0.686136\pi\) | ||||
−0.552003 | + | 0.833842i | \(0.686136\pi\) | |||||||
\(264\) | 6.81227 | 0.419266 | ||||||||
\(265\) | 3.40903 | 0.209415 | ||||||||
\(266\) | −15.8352 | −0.970919 | ||||||||
\(267\) | −28.1115 | −1.72039 | ||||||||
\(268\) | −6.11100 | −0.373289 | ||||||||
\(269\) | −25.9932 | −1.58484 | −0.792418 | − | 0.609979i | \(-0.791178\pi\) | ||||
−0.792418 | + | 0.609979i | \(0.791178\pi\) | |||||||
\(270\) | −20.2450 | −1.23207 | ||||||||
\(271\) | 19.0435 | 1.15681 | 0.578404 | − | 0.815751i | \(-0.303676\pi\) | ||||
0.578404 | + | 0.815751i | \(0.303676\pi\) | |||||||
\(272\) | −3.11222 | −0.188706 | ||||||||
\(273\) | 49.6660 | 3.00592 | ||||||||
\(274\) | 18.6157 | 1.12461 | ||||||||
\(275\) | −5.58889 | −0.337023 | ||||||||
\(276\) | 0.339537 | 0.0204378 | ||||||||
\(277\) | 21.0210 | 1.26303 | 0.631516 | − | 0.775363i | \(-0.282433\pi\) | ||||
0.631516 | + | 0.775363i | \(0.282433\pi\) | |||||||
\(278\) | 18.5662 | 1.11353 | ||||||||
\(279\) | −8.34548 | −0.499631 | ||||||||
\(280\) | −26.7177 | −1.59669 | ||||||||
\(281\) | 0.480384 | 0.0286573 | 0.0143287 | − | 0.999897i | \(-0.495439\pi\) | ||||
0.0143287 | + | 0.999897i | \(0.495439\pi\) | |||||||
\(282\) | 44.6328 | 2.65784 | ||||||||
\(283\) | 18.7058 | 1.11194 | 0.555972 | − | 0.831201i | \(-0.312346\pi\) | ||||
0.555972 | + | 0.831201i | \(0.312346\pi\) | |||||||
\(284\) | −3.00067 | −0.178057 | ||||||||
\(285\) | −27.6715 | −1.63912 | ||||||||
\(286\) | 8.51952 | 0.503770 | ||||||||
\(287\) | 8.90072 | 0.525393 | ||||||||
\(288\) | −9.66521 | −0.569528 | ||||||||
\(289\) | −16.5471 | −0.973357 | ||||||||
\(290\) | 7.26575 | 0.426660 | ||||||||
\(291\) | −51.4202 | −3.01431 | ||||||||
\(292\) | 0.999196 | 0.0584735 | ||||||||
\(293\) | −28.9779 | −1.69291 | −0.846453 | − | 0.532463i | \(-0.821266\pi\) | ||||
−0.846453 | + | 0.532463i | \(0.821266\pi\) | |||||||
\(294\) | 16.2852 | 0.949773 | ||||||||
\(295\) | 18.3452 | 1.06810 | ||||||||
\(296\) | 14.4906 | 0.842247 | ||||||||
\(297\) | −4.02679 | −0.233658 | ||||||||
\(298\) | 9.04385 | 0.523896 | ||||||||
\(299\) | −1.76930 | −0.102321 | ||||||||
\(300\) | 5.91415 | 0.341454 | ||||||||
\(301\) | −24.6594 | −1.42134 | ||||||||
\(302\) | 3.89500 | 0.224132 | ||||||||
\(303\) | −21.6674 | −1.24476 | ||||||||
\(304\) | −14.3850 | −0.825035 | ||||||||
\(305\) | −14.8210 | −0.848651 | ||||||||
\(306\) | 4.65110 | 0.265886 | ||||||||
\(307\) | 23.7743 | 1.35687 | 0.678435 | − | 0.734661i | \(-0.262659\pi\) | ||||
0.678435 | + | 0.734661i | \(0.262659\pi\) | |||||||
\(308\) | 1.27541 | 0.0726730 | ||||||||
\(309\) | −27.4400 | −1.56101 | ||||||||
\(310\) | 9.38016 | 0.532757 | ||||||||
\(311\) | 5.85577 | 0.332050 | 0.166025 | − | 0.986122i | \(-0.446907\pi\) | ||||
0.166025 | + | 0.986122i | \(0.446907\pi\) | |||||||
\(312\) | 37.5640 | 2.12664 | ||||||||
\(313\) | −25.9307 | −1.46569 | −0.732845 | − | 0.680395i | \(-0.761808\pi\) | ||||
−0.732845 | + | 0.680395i | \(0.761808\pi\) | |||||||
\(314\) | 31.4887 | 1.77701 | ||||||||
\(315\) | 47.9575 | 2.70210 | ||||||||
\(316\) | 6.33117 | 0.356156 | ||||||||
\(317\) | −4.87657 | −0.273896 | −0.136948 | − | 0.990578i | \(-0.543729\pi\) | ||||
−0.136948 | + | 0.990578i | \(0.543729\pi\) | |||||||
\(318\) | −4.42474 | −0.248127 | ||||||||
\(319\) | 1.44518 | 0.0809143 | ||||||||
\(320\) | −19.2323 | −1.07512 | ||||||||
\(321\) | 26.7537 | 1.49325 | ||||||||
\(322\) | −1.63338 | −0.0910245 | ||||||||
\(323\) | 2.09352 | 0.116487 | ||||||||
\(324\) | −0.933334 | −0.0518519 | ||||||||
\(325\) | −30.8181 | −1.70948 | ||||||||
\(326\) | 18.7785 | 1.04004 | ||||||||
\(327\) | −15.9907 | −0.884290 | ||||||||
\(328\) | 6.73191 | 0.371707 | ||||||||
\(329\) | −34.8178 | −1.91957 | ||||||||
\(330\) | 13.7438 | 0.756574 | ||||||||
\(331\) | 11.1378 | 0.612188 | 0.306094 | − | 0.952001i | \(-0.400978\pi\) | ||||
0.306094 | + | 0.952001i | \(0.400978\pi\) | |||||||
\(332\) | 1.73787 | 0.0953779 | ||||||||
\(333\) | −26.0102 | −1.42535 | ||||||||
\(334\) | 8.24699 | 0.451255 | ||||||||
\(335\) | 51.3711 | 2.80670 | ||||||||
\(336\) | 41.6513 | 2.27227 | ||||||||
\(337\) | 18.2130 | 0.992128 | 0.496064 | − | 0.868286i | \(-0.334778\pi\) | ||||
0.496064 | + | 0.868286i | \(0.334778\pi\) | |||||||
\(338\) | 26.8928 | 1.46278 | ||||||||
\(339\) | −11.3836 | −0.618273 | ||||||||
\(340\) | −0.847741 | −0.0459752 | ||||||||
\(341\) | 1.86574 | 0.101035 | ||||||||
\(342\) | 21.4978 | 1.16247 | ||||||||
\(343\) | 10.3597 | 0.559369 | ||||||||
\(344\) | −18.6507 | −1.00558 | ||||||||
\(345\) | −2.85427 | −0.153668 | ||||||||
\(346\) | −7.00740 | −0.376720 | ||||||||
\(347\) | 24.3068 | 1.30486 | 0.652429 | − | 0.757850i | \(-0.273750\pi\) | ||||
0.652429 | + | 0.757850i | \(0.273750\pi\) | |||||||
\(348\) | −1.52928 | −0.0819781 | ||||||||
\(349\) | −34.2737 | −1.83463 | −0.917314 | − | 0.398165i | \(-0.869647\pi\) | ||||
−0.917314 | + | 0.398165i | \(0.869647\pi\) | |||||||
\(350\) | −28.4505 | −1.52075 | ||||||||
\(351\) | −22.2044 | −1.18518 | ||||||||
\(352\) | 2.16078 | 0.115170 | ||||||||
\(353\) | −13.3932 | −0.712847 | −0.356424 | − | 0.934324i | \(-0.616004\pi\) | ||||
−0.356424 | + | 0.934324i | \(0.616004\pi\) | |||||||
\(354\) | −23.8112 | −1.26555 | ||||||||
\(355\) | 25.2247 | 1.33879 | ||||||||
\(356\) | −3.98065 | −0.210974 | ||||||||
\(357\) | −6.06174 | −0.320822 | ||||||||
\(358\) | −34.4835 | −1.82251 | ||||||||
\(359\) | 5.57906 | 0.294452 | 0.147226 | − | 0.989103i | \(-0.452966\pi\) | ||||
0.147226 | + | 0.989103i | \(0.452966\pi\) | |||||||
\(360\) | 36.2719 | 1.91170 | ||||||||
\(361\) | −9.32353 | −0.490712 | ||||||||
\(362\) | −2.87679 | −0.151200 | ||||||||
\(363\) | 2.73368 | 0.143481 | ||||||||
\(364\) | 7.03281 | 0.368620 | ||||||||
\(365\) | −8.39957 | −0.439654 | ||||||||
\(366\) | 19.2370 | 1.00553 | ||||||||
\(367\) | 26.1407 | 1.36453 | 0.682265 | − | 0.731105i | \(-0.260995\pi\) | ||||
0.682265 | + | 0.731105i | \(0.260995\pi\) | |||||||
\(368\) | −1.48379 | −0.0773477 | ||||||||
\(369\) | −12.0836 | −0.629047 | ||||||||
\(370\) | 29.2349 | 1.51985 | ||||||||
\(371\) | 3.45172 | 0.179204 | ||||||||
\(372\) | −1.97432 | −0.102364 | ||||||||
\(373\) | −24.7201 | −1.27996 | −0.639980 | − | 0.768392i | \(-0.721057\pi\) | ||||
−0.639980 | + | 0.768392i | \(0.721057\pi\) | |||||||
\(374\) | −1.03981 | −0.0537673 | ||||||||
\(375\) | −5.23850 | −0.270515 | ||||||||
\(376\) | −26.3339 | −1.35806 | ||||||||
\(377\) | 7.96895 | 0.410422 | ||||||||
\(378\) | −20.4986 | −1.05433 | ||||||||
\(379\) | 14.5359 | 0.746661 | 0.373330 | − | 0.927699i | \(-0.378216\pi\) | ||||
0.373330 | + | 0.927699i | \(0.378216\pi\) | |||||||
\(380\) | −3.91834 | −0.201007 | ||||||||
\(381\) | −45.5277 | −2.33246 | ||||||||
\(382\) | −25.4908 | −1.30422 | ||||||||
\(383\) | −24.6096 | −1.25749 | −0.628745 | − | 0.777612i | \(-0.716431\pi\) | ||||
−0.628745 | + | 0.777612i | \(0.716431\pi\) | |||||||
\(384\) | 36.7763 | 1.87673 | ||||||||
\(385\) | −10.7215 | −0.546418 | ||||||||
\(386\) | −17.4654 | −0.888966 | ||||||||
\(387\) | 33.4775 | 1.70176 | ||||||||
\(388\) | −7.28122 | −0.369648 | ||||||||
\(389\) | 14.4517 | 0.732733 | 0.366366 | − | 0.930471i | \(-0.380602\pi\) | ||||
0.366366 | + | 0.930471i | \(0.380602\pi\) | |||||||
\(390\) | 75.7860 | 3.83757 | ||||||||
\(391\) | 0.215944 | 0.0109207 | ||||||||
\(392\) | −9.60847 | −0.485301 | ||||||||
\(393\) | −2.73368 | −0.137896 | ||||||||
\(394\) | −23.4153 | −1.17965 | ||||||||
\(395\) | −53.2220 | −2.67789 | ||||||||
\(396\) | −1.73149 | −0.0870106 | ||||||||
\(397\) | 9.96478 | 0.500118 | 0.250059 | − | 0.968231i | \(-0.419550\pi\) | ||||
0.250059 | + | 0.968231i | \(0.419550\pi\) | |||||||
\(398\) | −23.1205 | −1.15893 | ||||||||
\(399\) | −28.0180 | −1.40265 | ||||||||
\(400\) | −25.8450 | −1.29225 | ||||||||
\(401\) | −12.1122 | −0.604856 | −0.302428 | − | 0.953172i | \(-0.597797\pi\) | ||||
−0.302428 | + | 0.953172i | \(0.597797\pi\) | |||||||
\(402\) | −66.6772 | −3.32555 | ||||||||
\(403\) | 10.2880 | 0.512481 | ||||||||
\(404\) | −3.06816 | −0.152647 | ||||||||
\(405\) | 7.84592 | 0.389867 | ||||||||
\(406\) | 7.35674 | 0.365109 | ||||||||
\(407\) | 5.81490 | 0.288234 | ||||||||
\(408\) | −4.58470 | −0.226976 | ||||||||
\(409\) | −10.6917 | −0.528668 | −0.264334 | − | 0.964431i | \(-0.585152\pi\) | ||||
−0.264334 | + | 0.964431i | \(0.585152\pi\) | |||||||
\(410\) | 13.5817 | 0.670753 | ||||||||
\(411\) | 32.9376 | 1.62469 | ||||||||
\(412\) | −3.88557 | −0.191428 | ||||||||
\(413\) | 18.5750 | 0.914015 | ||||||||
\(414\) | 2.21747 | 0.108983 | ||||||||
\(415\) | −14.6091 | −0.717132 | ||||||||
\(416\) | 11.9149 | 0.584176 | ||||||||
\(417\) | 32.8501 | 1.60868 | ||||||||
\(418\) | −4.80611 | −0.235074 | ||||||||
\(419\) | 31.3600 | 1.53203 | 0.766017 | − | 0.642820i | \(-0.222236\pi\) | ||||
0.766017 | + | 0.642820i | \(0.222236\pi\) | |||||||
\(420\) | 11.3455 | 0.553602 | ||||||||
\(421\) | −22.1870 | −1.08133 | −0.540665 | − | 0.841238i | \(-0.681827\pi\) | ||||
−0.540665 | + | 0.841238i | \(0.681827\pi\) | |||||||
\(422\) | −6.12977 | −0.298393 | ||||||||
\(423\) | 47.2686 | 2.29828 | ||||||||
\(424\) | 2.61065 | 0.126784 | ||||||||
\(425\) | 3.76136 | 0.182453 | ||||||||
\(426\) | −32.7404 | −1.58628 | ||||||||
\(427\) | −15.0067 | −0.726223 | ||||||||
\(428\) | 3.78839 | 0.183119 | ||||||||
\(429\) | 15.0740 | 0.727780 | ||||||||
\(430\) | −37.6281 | −1.81459 | ||||||||
\(431\) | −29.2280 | −1.40786 | −0.703931 | − | 0.710269i | \(-0.748573\pi\) | ||||
−0.703931 | + | 0.710269i | \(0.748573\pi\) | |||||||
\(432\) | −18.6213 | −0.895916 | ||||||||
\(433\) | 13.1577 | 0.632317 | 0.316158 | − | 0.948706i | \(-0.397607\pi\) | ||||
0.316158 | + | 0.948706i | \(0.397607\pi\) | |||||||
\(434\) | 9.49763 | 0.455901 | ||||||||
\(435\) | 12.8556 | 0.616381 | ||||||||
\(436\) | −2.26433 | −0.108442 | ||||||||
\(437\) | 0.998112 | 0.0477462 | ||||||||
\(438\) | 10.9022 | 0.520928 | ||||||||
\(439\) | −32.0762 | −1.53091 | −0.765456 | − | 0.643488i | \(-0.777487\pi\) | ||||
−0.765456 | + | 0.643488i | \(0.777487\pi\) | |||||||
\(440\) | −8.10903 | −0.386583 | ||||||||
\(441\) | 17.2469 | 0.821283 | ||||||||
\(442\) | −5.73369 | −0.272724 | ||||||||
\(443\) | 31.8373 | 1.51264 | 0.756318 | − | 0.654204i | \(-0.226996\pi\) | ||||
0.756318 | + | 0.654204i | \(0.226996\pi\) | |||||||
\(444\) | −6.15331 | −0.292023 | ||||||||
\(445\) | 33.4626 | 1.58628 | ||||||||
\(446\) | 15.6445 | 0.740788 | ||||||||
\(447\) | 16.0017 | 0.756856 | ||||||||
\(448\) | −19.4731 | −0.920019 | ||||||||
\(449\) | −17.2091 | −0.812146 | −0.406073 | − | 0.913841i | \(-0.633102\pi\) | ||||
−0.406073 | + | 0.913841i | \(0.633102\pi\) | |||||||
\(450\) | 38.6244 | 1.82077 | ||||||||
\(451\) | 2.70144 | 0.127206 | ||||||||
\(452\) | −1.61195 | −0.0758196 | ||||||||
\(453\) | 6.89162 | 0.323796 | ||||||||
\(454\) | 0.0893873 | 0.00419516 | ||||||||
\(455\) | −59.1202 | −2.77160 | ||||||||
\(456\) | −21.1909 | −0.992357 | ||||||||
\(457\) | 4.79162 | 0.224143 | 0.112071 | − | 0.993700i | \(-0.464251\pi\) | ||||
0.112071 | + | 0.993700i | \(0.464251\pi\) | |||||||
\(458\) | −17.4435 | −0.815083 | ||||||||
\(459\) | 2.71005 | 0.126494 | ||||||||
\(460\) | −0.404171 | −0.0188445 | ||||||||
\(461\) | 33.8620 | 1.57711 | 0.788554 | − | 0.614965i | \(-0.210830\pi\) | ||||
0.788554 | + | 0.614965i | \(0.210830\pi\) | |||||||
\(462\) | 13.9160 | 0.647429 | ||||||||
\(463\) | 5.82989 | 0.270938 | 0.135469 | − | 0.990782i | \(-0.456746\pi\) | ||||
0.135469 | + | 0.990782i | \(0.456746\pi\) | |||||||
\(464\) | 6.68299 | 0.310250 | ||||||||
\(465\) | 16.5968 | 0.769657 | ||||||||
\(466\) | −21.3208 | −0.987665 | ||||||||
\(467\) | 36.3416 | 1.68169 | 0.840844 | − | 0.541277i | \(-0.182059\pi\) | ||||
0.840844 | + | 0.541277i | \(0.182059\pi\) | |||||||
\(468\) | −9.54773 | −0.441344 | ||||||||
\(469\) | 52.0145 | 2.40180 | ||||||||
\(470\) | −53.1289 | −2.45066 | ||||||||
\(471\) | 55.7144 | 2.56719 | ||||||||
\(472\) | 14.0489 | 0.646652 | ||||||||
\(473\) | −7.48431 | −0.344129 | ||||||||
\(474\) | 69.0795 | 3.17292 | ||||||||
\(475\) | 17.3854 | 0.797696 | ||||||||
\(476\) | −0.858357 | −0.0393427 | ||||||||
\(477\) | −4.68604 | −0.214559 | ||||||||
\(478\) | −13.3029 | −0.608463 | ||||||||
\(479\) | −15.9821 | −0.730243 | −0.365121 | − | 0.930960i | \(-0.618972\pi\) | ||||
−0.365121 | + | 0.930960i | \(0.618972\pi\) | |||||||
\(480\) | 19.2213 | 0.877329 | ||||||||
\(481\) | 32.0643 | 1.46201 | ||||||||
\(482\) | 13.4175 | 0.611151 | ||||||||
\(483\) | −2.89001 | −0.131500 | ||||||||
\(484\) | 0.387096 | 0.0175953 | ||||||||
\(485\) | 61.2084 | 2.77933 | ||||||||
\(486\) | −28.8480 | −1.30857 | ||||||||
\(487\) | 30.7826 | 1.39489 | 0.697447 | − | 0.716636i | \(-0.254319\pi\) | ||||
0.697447 | + | 0.716636i | \(0.254319\pi\) | |||||||
\(488\) | −11.3500 | −0.513792 | ||||||||
\(489\) | 33.2256 | 1.50252 | ||||||||
\(490\) | −19.3852 | −0.875735 | ||||||||
\(491\) | −30.3735 | −1.37074 | −0.685369 | − | 0.728196i | \(-0.740359\pi\) | ||||
−0.685369 | + | 0.728196i | \(0.740359\pi\) | |||||||
\(492\) | −2.85865 | −0.128878 | ||||||||
\(493\) | −0.972612 | −0.0438042 | ||||||||
\(494\) | −26.5017 | −1.19237 | ||||||||
\(495\) | 14.5555 | 0.654220 | ||||||||
\(496\) | 8.62781 | 0.387400 | ||||||||
\(497\) | 25.5406 | 1.14565 | ||||||||
\(498\) | 18.9619 | 0.849702 | ||||||||
\(499\) | 0.397630 | 0.0178004 | 0.00890019 | − | 0.999960i | \(-0.497167\pi\) | ||||
0.00890019 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(500\) | −0.741784 | −0.0331736 | ||||||||
\(501\) | 14.5918 | 0.651913 | ||||||||
\(502\) | 12.2791 | 0.548045 | ||||||||
\(503\) | −7.83869 | −0.349510 | −0.174755 | − | 0.984612i | \(-0.555913\pi\) | ||||
−0.174755 | + | 0.984612i | \(0.555913\pi\) | |||||||
\(504\) | 36.7261 | 1.63591 | ||||||||
\(505\) | 25.7920 | 1.14773 | ||||||||
\(506\) | −0.495742 | −0.0220384 | ||||||||
\(507\) | 47.5828 | 2.11323 | ||||||||
\(508\) | −6.44683 | −0.286032 | ||||||||
\(509\) | −21.1021 | −0.935334 | −0.467667 | − | 0.883905i | \(-0.654905\pi\) | ||||
−0.467667 | + | 0.883905i | \(0.654905\pi\) | |||||||
\(510\) | −9.24970 | −0.409584 | ||||||||
\(511\) | −8.50476 | −0.376229 | ||||||||
\(512\) | −13.0553 | −0.576969 | ||||||||
\(513\) | 12.5261 | 0.553042 | ||||||||
\(514\) | 23.5264 | 1.03771 | ||||||||
\(515\) | 32.6634 | 1.43932 | ||||||||
\(516\) | 7.91988 | 0.348653 | ||||||||
\(517\) | −10.5675 | −0.464757 | ||||||||
\(518\) | 29.6010 | 1.30060 | ||||||||
\(519\) | −12.3985 | −0.544235 | ||||||||
\(520\) | −44.7146 | −1.96086 | ||||||||
\(521\) | 44.7251 | 1.95944 | 0.979722 | − | 0.200364i | \(-0.0642125\pi\) | ||||
0.979722 | + | 0.200364i | \(0.0642125\pi\) | |||||||
\(522\) | −9.98750 | −0.437141 | ||||||||
\(523\) | 11.3957 | 0.498299 | 0.249150 | − | 0.968465i | \(-0.419849\pi\) | ||||
0.249150 | + | 0.968465i | \(0.419849\pi\) | |||||||
\(524\) | −0.387096 | −0.0169104 | ||||||||
\(525\) | −50.3389 | −2.19697 | ||||||||
\(526\) | −27.6621 | −1.20612 | ||||||||
\(527\) | −1.25565 | −0.0546971 | ||||||||
\(528\) | 12.6415 | 0.550151 | ||||||||
\(529\) | −22.8970 | −0.995524 | ||||||||
\(530\) | 5.26702 | 0.228785 | ||||||||
\(531\) | −25.2173 | −1.09434 | ||||||||
\(532\) | −3.96741 | −0.172009 | ||||||||
\(533\) | 14.8962 | 0.645225 | ||||||||
\(534\) | −43.4328 | −1.87952 | ||||||||
\(535\) | −31.8464 | −1.37684 | ||||||||
\(536\) | 39.3403 | 1.69924 | ||||||||
\(537\) | −61.0133 | −2.63292 | ||||||||
\(538\) | −40.1601 | −1.73143 | ||||||||
\(539\) | −3.85576 | −0.166080 | ||||||||
\(540\) | −5.07227 | −0.218276 | ||||||||
\(541\) | 37.4149 | 1.60859 | 0.804296 | − | 0.594229i | \(-0.202543\pi\) | ||||
0.804296 | + | 0.594229i | \(0.202543\pi\) | |||||||
\(542\) | 29.4226 | 1.26381 | ||||||||
\(543\) | −5.09003 | −0.218434 | ||||||||
\(544\) | −1.45422 | −0.0623490 | ||||||||
\(545\) | 19.0347 | 0.815356 | ||||||||
\(546\) | 76.7350 | 3.28396 | ||||||||
\(547\) | 12.5850 | 0.538095 | 0.269048 | − | 0.963127i | \(-0.413291\pi\) | ||||
0.269048 | + | 0.963127i | \(0.413291\pi\) | |||||||
\(548\) | 4.66404 | 0.199238 | ||||||||
\(549\) | 20.3730 | 0.869499 | ||||||||
\(550\) | −8.63496 | −0.368196 | ||||||||
\(551\) | −4.49551 | −0.191515 | ||||||||
\(552\) | −2.18581 | −0.0930343 | ||||||||
\(553\) | −53.8885 | −2.29157 | ||||||||
\(554\) | 32.4780 | 1.37986 | ||||||||
\(555\) | 51.7268 | 2.19568 | ||||||||
\(556\) | 4.65165 | 0.197274 | ||||||||
\(557\) | 6.13432 | 0.259920 | 0.129960 | − | 0.991519i | \(-0.458515\pi\) | ||||
0.129960 | + | 0.991519i | \(0.458515\pi\) | |||||||
\(558\) | −12.8940 | −0.545845 | ||||||||
\(559\) | −41.2698 | −1.74553 | ||||||||
\(560\) | −49.5799 | −2.09513 | ||||||||
\(561\) | −1.83979 | −0.0776758 | ||||||||
\(562\) | 0.742205 | 0.0313080 | ||||||||
\(563\) | −15.4142 | −0.649630 | −0.324815 | − | 0.945778i | \(-0.605302\pi\) | ||||
−0.324815 | + | 0.945778i | \(0.605302\pi\) | |||||||
\(564\) | 11.1825 | 0.470867 | ||||||||
\(565\) | 13.5506 | 0.570076 | ||||||||
\(566\) | 28.9009 | 1.21479 | ||||||||
\(567\) | 7.94417 | 0.333624 | ||||||||
\(568\) | 19.3172 | 0.810531 | ||||||||
\(569\) | −13.6152 | −0.570780 | −0.285390 | − | 0.958411i | \(-0.592123\pi\) | ||||
−0.285390 | + | 0.958411i | \(0.592123\pi\) | |||||||
\(570\) | −42.7530 | −1.79073 | ||||||||
\(571\) | −36.9828 | −1.54768 | −0.773842 | − | 0.633379i | \(-0.781667\pi\) | ||||
−0.773842 | + | 0.633379i | \(0.781667\pi\) | |||||||
\(572\) | 2.13451 | 0.0892485 | ||||||||
\(573\) | −45.1021 | −1.88417 | ||||||||
\(574\) | 13.7518 | 0.573989 | ||||||||
\(575\) | 1.79327 | 0.0747847 | ||||||||
\(576\) | 26.4367 | 1.10153 | ||||||||
\(577\) | −33.1889 | −1.38167 | −0.690836 | − | 0.723011i | \(-0.742758\pi\) | ||||
−0.690836 | + | 0.723011i | \(0.742758\pi\) | |||||||
\(578\) | −25.5656 | −1.06339 | ||||||||
\(579\) | −30.9024 | −1.28426 | ||||||||
\(580\) | 1.82039 | 0.0755875 | ||||||||
\(581\) | −14.7921 | −0.613678 | ||||||||
\(582\) | −79.4454 | −3.29312 | ||||||||
\(583\) | 1.04762 | 0.0433881 | ||||||||
\(584\) | −6.43244 | −0.266176 | ||||||||
\(585\) | 80.2614 | 3.31840 | ||||||||
\(586\) | −44.7715 | −1.84949 | ||||||||
\(587\) | −36.7254 | −1.51582 | −0.757910 | − | 0.652359i | \(-0.773779\pi\) | ||||
−0.757910 | + | 0.652359i | \(0.773779\pi\) | |||||||
\(588\) | 4.08016 | 0.168263 | ||||||||
\(589\) | −5.80375 | −0.239139 | ||||||||
\(590\) | 28.3438 | 1.16690 | ||||||||
\(591\) | −41.4298 | −1.70419 | ||||||||
\(592\) | 26.8901 | 1.10518 | ||||||||
\(593\) | −43.7224 | −1.79546 | −0.897731 | − | 0.440544i | \(-0.854786\pi\) | ||||
−0.897731 | + | 0.440544i | \(0.854786\pi\) | |||||||
\(594\) | −6.22148 | −0.255270 | ||||||||
\(595\) | 7.21564 | 0.295812 | ||||||||
\(596\) | 2.26588 | 0.0928141 | ||||||||
\(597\) | −40.9083 | −1.67426 | ||||||||
\(598\) | −2.73361 | −0.111786 | ||||||||
\(599\) | 26.6179 | 1.08758 | 0.543789 | − | 0.839222i | \(-0.316989\pi\) | ||||
0.543789 | + | 0.839222i | \(0.316989\pi\) | |||||||
\(600\) | −38.0730 | −1.55432 | ||||||||
\(601\) | 19.3001 | 0.787267 | 0.393634 | − | 0.919267i | \(-0.371218\pi\) | ||||
0.393634 | + | 0.919267i | \(0.371218\pi\) | |||||||
\(602\) | −38.0993 | −1.55281 | ||||||||
\(603\) | −70.6147 | −2.87565 | ||||||||
\(604\) | 0.975869 | 0.0397075 | ||||||||
\(605\) | −3.25406 | −0.132296 | ||||||||
\(606\) | −33.4767 | −1.35990 | ||||||||
\(607\) | 42.2893 | 1.71647 | 0.858235 | − | 0.513256i | \(-0.171561\pi\) | ||||
0.858235 | + | 0.513256i | \(0.171561\pi\) | |||||||
\(608\) | −6.72153 | −0.272594 | ||||||||
\(609\) | 13.0166 | 0.527461 | ||||||||
\(610\) | −22.8989 | −0.927148 | ||||||||
\(611\) | −58.2709 | −2.35739 | ||||||||
\(612\) | 1.16530 | 0.0471046 | ||||||||
\(613\) | 42.5174 | 1.71726 | 0.858630 | − | 0.512596i | \(-0.171316\pi\) | ||||
0.858630 | + | 0.512596i | \(0.171316\pi\) | |||||||
\(614\) | 36.7318 | 1.48237 | ||||||||
\(615\) | 24.0308 | 0.969015 | ||||||||
\(616\) | −8.21058 | −0.330814 | ||||||||
\(617\) | 41.2254 | 1.65967 | 0.829835 | − | 0.558008i | \(-0.188434\pi\) | ||||
0.829835 | + | 0.558008i | \(0.188434\pi\) | |||||||
\(618\) | −42.3955 | −1.70540 | ||||||||
\(619\) | 28.9911 | 1.16525 | 0.582625 | − | 0.812741i | \(-0.302026\pi\) | ||||
0.582625 | + | 0.812741i | \(0.302026\pi\) | |||||||
\(620\) | 2.35014 | 0.0943839 | ||||||||
\(621\) | 1.29205 | 0.0518482 | ||||||||
\(622\) | 9.04730 | 0.362764 | ||||||||
\(623\) | 33.8817 | 1.35744 | ||||||||
\(624\) | 69.7074 | 2.79053 | ||||||||
\(625\) | −21.7088 | −0.868350 | ||||||||
\(626\) | −40.0635 | −1.60126 | ||||||||
\(627\) | −8.50368 | −0.339604 | ||||||||
\(628\) | 7.88929 | 0.314817 | ||||||||
\(629\) | −3.91346 | −0.156040 | ||||||||
\(630\) | 74.0955 | 2.95203 | ||||||||
\(631\) | −15.7533 | −0.627131 | −0.313565 | − | 0.949567i | \(-0.601523\pi\) | ||||
−0.313565 | + | 0.949567i | \(0.601523\pi\) | |||||||
\(632\) | −40.7577 | −1.62125 | ||||||||
\(633\) | −10.8457 | −0.431078 | ||||||||
\(634\) | −7.53442 | −0.299230 | ||||||||
\(635\) | 54.1942 | 2.15063 | ||||||||
\(636\) | −1.10859 | −0.0439585 | ||||||||
\(637\) | −21.2614 | −0.842406 | ||||||||
\(638\) | 2.23283 | 0.0883985 | ||||||||
\(639\) | −34.6738 | −1.37168 | ||||||||
\(640\) | −43.7769 | −1.73043 | ||||||||
\(641\) | −2.16918 | −0.0856773 | −0.0428387 | − | 0.999082i | \(-0.513640\pi\) | ||||
−0.0428387 | + | 0.999082i | \(0.513640\pi\) | |||||||
\(642\) | 41.3351 | 1.63137 | ||||||||
\(643\) | 32.1923 | 1.26954 | 0.634771 | − | 0.772701i | \(-0.281095\pi\) | ||||
0.634771 | + | 0.772701i | \(0.281095\pi\) | |||||||
\(644\) | −0.409232 | −0.0161260 | ||||||||
\(645\) | −66.5771 | −2.62147 | ||||||||
\(646\) | 3.23454 | 0.127261 | ||||||||
\(647\) | 7.84217 | 0.308308 | 0.154154 | − | 0.988047i | \(-0.450735\pi\) | ||||
0.154154 | + | 0.988047i | \(0.450735\pi\) | |||||||
\(648\) | 6.00844 | 0.236034 | ||||||||
\(649\) | 5.63765 | 0.221297 | ||||||||
\(650\) | −47.6147 | −1.86760 | ||||||||
\(651\) | 16.8046 | 0.658625 | ||||||||
\(652\) | 4.70483 | 0.184255 | ||||||||
\(653\) | 11.1317 | 0.435617 | 0.217808 | − | 0.975992i | \(-0.430109\pi\) | ||||
0.217808 | + | 0.975992i | \(0.430109\pi\) | |||||||
\(654\) | −24.7061 | −0.966084 | ||||||||
\(655\) | 3.25406 | 0.127147 | ||||||||
\(656\) | 12.4924 | 0.487746 | ||||||||
\(657\) | 11.5460 | 0.450454 | ||||||||
\(658\) | −53.7943 | −2.09712 | ||||||||
\(659\) | −12.4652 | −0.485576 | −0.242788 | − | 0.970079i | \(-0.578062\pi\) | ||||
−0.242788 | + | 0.970079i | \(0.578062\pi\) | |||||||
\(660\) | 3.44344 | 0.134036 | ||||||||
\(661\) | 32.4838 | 1.26348 | 0.631738 | − | 0.775182i | \(-0.282342\pi\) | ||||
0.631738 | + | 0.775182i | \(0.282342\pi\) | |||||||
\(662\) | 17.2081 | 0.668813 | ||||||||
\(663\) | −10.1449 | −0.393995 | ||||||||
\(664\) | −11.1877 | −0.434168 | ||||||||
\(665\) | 33.3514 | 1.29331 | ||||||||
\(666\) | −40.1863 | −1.55719 | ||||||||
\(667\) | −0.463705 | −0.0179547 | ||||||||
\(668\) | 2.06623 | 0.0799449 | ||||||||
\(669\) | 27.6806 | 1.07019 | ||||||||
\(670\) | 79.3696 | 3.06631 | ||||||||
\(671\) | −4.55464 | −0.175830 | ||||||||
\(672\) | 19.4620 | 0.750764 | ||||||||
\(673\) | −7.39051 | −0.284883 | −0.142442 | − | 0.989803i | \(-0.545495\pi\) | ||||
−0.142442 | + | 0.989803i | \(0.545495\pi\) | |||||||
\(674\) | 28.1396 | 1.08390 | ||||||||
\(675\) | 22.5053 | 0.866228 | ||||||||
\(676\) | 6.73783 | 0.259147 | ||||||||
\(677\) | 41.6597 | 1.60111 | 0.800557 | − | 0.599257i | \(-0.204537\pi\) | ||||
0.800557 | + | 0.599257i | \(0.204537\pi\) | |||||||
\(678\) | −17.5880 | −0.675461 | ||||||||
\(679\) | 61.9749 | 2.37838 | ||||||||
\(680\) | 5.45743 | 0.209283 | ||||||||
\(681\) | 0.158157 | 0.00606060 | ||||||||
\(682\) | 2.88260 | 0.110381 | ||||||||
\(683\) | −41.3039 | −1.58045 | −0.790224 | − | 0.612817i | \(-0.790036\pi\) | ||||
−0.790224 | + | 0.612817i | \(0.790036\pi\) | |||||||
\(684\) | 5.38615 | 0.205945 | ||||||||
\(685\) | −39.2075 | −1.49804 | ||||||||
\(686\) | 16.0059 | 0.611108 | ||||||||
\(687\) | −30.8637 | −1.17752 | ||||||||
\(688\) | −34.6101 | −1.31950 | ||||||||
\(689\) | 5.77677 | 0.220078 | ||||||||
\(690\) | −4.40991 | −0.167882 | ||||||||
\(691\) | −13.2163 | −0.502772 | −0.251386 | − | 0.967887i | \(-0.580886\pi\) | ||||
−0.251386 | + | 0.967887i | \(0.580886\pi\) | |||||||
\(692\) | −1.75566 | −0.0667402 | ||||||||
\(693\) | 14.7378 | 0.559841 | ||||||||
\(694\) | 37.5546 | 1.42555 | ||||||||
\(695\) | −39.1034 | −1.48328 | ||||||||
\(696\) | 9.84492 | 0.373171 | ||||||||
\(697\) | −1.81808 | −0.0688648 | ||||||||
\(698\) | −52.9536 | −2.00432 | ||||||||
\(699\) | −37.7238 | −1.42685 | ||||||||
\(700\) | −7.12811 | −0.269417 | ||||||||
\(701\) | 42.7837 | 1.61592 | 0.807960 | − | 0.589238i | \(-0.200572\pi\) | ||||
0.807960 | + | 0.589238i | \(0.200572\pi\) | |||||||
\(702\) | −34.3063 | −1.29481 | ||||||||
\(703\) | −18.0884 | −0.682217 | ||||||||
\(704\) | −5.91025 | −0.222751 | ||||||||
\(705\) | −94.0036 | −3.54038 | ||||||||
\(706\) | −20.6928 | −0.778783 | ||||||||
\(707\) | 26.1150 | 0.982155 | ||||||||
\(708\) | −5.96574 | −0.224206 | ||||||||
\(709\) | −7.91729 | −0.297340 | −0.148670 | − | 0.988887i | \(-0.547499\pi\) | ||||
−0.148670 | + | 0.988887i | \(0.547499\pi\) | |||||||
\(710\) | 38.9727 | 1.46262 | ||||||||
\(711\) | 73.1589 | 2.74367 | ||||||||
\(712\) | 25.6259 | 0.960370 | ||||||||
\(713\) | −0.598647 | −0.0224195 | ||||||||
\(714\) | −9.36553 | −0.350496 | ||||||||
\(715\) | −17.9434 | −0.671046 | ||||||||
\(716\) | −8.63962 | −0.322878 | ||||||||
\(717\) | −23.5375 | −0.879026 | ||||||||
\(718\) | 8.61978 | 0.321687 | ||||||||
\(719\) | −47.9553 | −1.78843 | −0.894215 | − | 0.447639i | \(-0.852265\pi\) | ||||
−0.894215 | + | 0.447639i | \(0.852265\pi\) | |||||||
\(720\) | 67.3096 | 2.50848 | ||||||||
\(721\) | 33.0725 | 1.23168 | ||||||||
\(722\) | −14.4051 | −0.536101 | ||||||||
\(723\) | 23.7402 | 0.882909 | ||||||||
\(724\) | −0.720761 | −0.0267869 | ||||||||
\(725\) | −8.07692 | −0.299969 | ||||||||
\(726\) | 4.22360 | 0.156753 | ||||||||
\(727\) | −5.77077 | −0.214026 | −0.107013 | − | 0.994258i | \(-0.534129\pi\) | ||||
−0.107013 | + | 0.994258i | \(0.534129\pi\) | |||||||
\(728\) | −45.2745 | −1.67799 | ||||||||
\(729\) | −43.8089 | −1.62255 | ||||||||
\(730\) | −12.9775 | −0.480320 | ||||||||
\(731\) | 5.03699 | 0.186300 | ||||||||
\(732\) | 4.81971 | 0.178141 | ||||||||
\(733\) | 5.15826 | 0.190525 | 0.0952623 | − | 0.995452i | \(-0.469631\pi\) | ||||
0.0952623 | + | 0.995452i | \(0.469631\pi\) | |||||||
\(734\) | 40.3879 | 1.49074 | ||||||||
\(735\) | −34.2992 | −1.26515 | ||||||||
\(736\) | −0.693315 | −0.0255559 | ||||||||
\(737\) | 15.7868 | 0.581514 | ||||||||
\(738\) | −18.6694 | −0.687231 | ||||||||
\(739\) | −35.4979 | −1.30581 | −0.652906 | − | 0.757439i | \(-0.726450\pi\) | ||||
−0.652906 | + | 0.757439i | \(0.726450\pi\) | |||||||
\(740\) | 7.32463 | 0.269259 | ||||||||
\(741\) | −46.8907 | −1.72257 | ||||||||
\(742\) | 5.33298 | 0.195780 | ||||||||
\(743\) | 22.4474 | 0.823514 | 0.411757 | − | 0.911294i | \(-0.364915\pi\) | ||||
0.411757 | + | 0.911294i | \(0.364915\pi\) | |||||||
\(744\) | 12.7099 | 0.465967 | ||||||||
\(745\) | −19.0478 | −0.697856 | ||||||||
\(746\) | −38.1932 | −1.39835 | ||||||||
\(747\) | 20.0817 | 0.734749 | ||||||||
\(748\) | −0.260518 | −0.00952548 | ||||||||
\(749\) | −32.2453 | −1.17822 | ||||||||
\(750\) | −8.09361 | −0.295537 | ||||||||
\(751\) | 28.4385 | 1.03774 | 0.518868 | − | 0.854854i | \(-0.326354\pi\) | ||||
0.518868 | + | 0.854854i | \(0.326354\pi\) | |||||||
\(752\) | −48.8677 | −1.78202 | ||||||||
\(753\) | 21.7261 | 0.791742 | ||||||||
\(754\) | 12.3122 | 0.448384 | ||||||||
\(755\) | −8.20348 | −0.298555 | ||||||||
\(756\) | −5.13579 | −0.186787 | ||||||||
\(757\) | −2.12328 | −0.0771720 | −0.0385860 | − | 0.999255i | \(-0.512285\pi\) | ||||
−0.0385860 | + | 0.999255i | \(0.512285\pi\) | |||||||
\(758\) | 22.4583 | 0.815724 | ||||||||
\(759\) | −0.877141 | −0.0318382 | ||||||||
\(760\) | 25.2248 | 0.914999 | ||||||||
\(761\) | −1.92689 | −0.0698498 | −0.0349249 | − | 0.999390i | \(-0.511119\pi\) | ||||
−0.0349249 | + | 0.999390i | \(0.511119\pi\) | |||||||
\(762\) | −70.3414 | −2.54820 | ||||||||
\(763\) | 19.2731 | 0.697732 | ||||||||
\(764\) | −6.38656 | −0.231058 | ||||||||
\(765\) | −9.79593 | −0.354173 | ||||||||
\(766\) | −38.0223 | −1.37380 | ||||||||
\(767\) | 31.0870 | 1.12249 | ||||||||
\(768\) | 24.5067 | 0.884311 | ||||||||
\(769\) | −4.44718 | −0.160370 | −0.0801848 | − | 0.996780i | \(-0.525551\pi\) | ||||
−0.0801848 | + | 0.996780i | \(0.525551\pi\) | |||||||
\(770\) | −16.5650 | −0.596960 | ||||||||
\(771\) | 41.6265 | 1.49914 | ||||||||
\(772\) | −4.37585 | −0.157490 | ||||||||
\(773\) | 13.4750 | 0.484663 | 0.242331 | − | 0.970194i | \(-0.422088\pi\) | ||||
0.242331 | + | 0.970194i | \(0.422088\pi\) | |||||||
\(774\) | 51.7235 | 1.85916 | ||||||||
\(775\) | −10.4274 | −0.374563 | ||||||||
\(776\) | 46.8737 | 1.68267 | ||||||||
\(777\) | 52.3746 | 1.87893 | ||||||||
\(778\) | 22.3283 | 0.800508 | ||||||||
\(779\) | −8.40336 | −0.301082 | ||||||||
\(780\) | 18.9877 | 0.679869 | ||||||||
\(781\) | 7.75176 | 0.277380 | ||||||||
\(782\) | 0.333638 | 0.0119309 | ||||||||
\(783\) | −5.81941 | −0.207969 | ||||||||
\(784\) | −17.8304 | −0.636800 | ||||||||
\(785\) | −66.3200 | −2.36706 | ||||||||
\(786\) | −4.22360 | −0.150651 | ||||||||
\(787\) | 6.72808 | 0.239830 | 0.119915 | − | 0.992784i | \(-0.461738\pi\) | ||||
0.119915 | + | 0.992784i | \(0.461738\pi\) | |||||||
\(788\) | −5.86655 | −0.208987 | ||||||||
\(789\) | −48.9438 | −1.74245 | ||||||||
\(790\) | −82.2292 | −2.92558 | ||||||||
\(791\) | 13.7203 | 0.487836 | ||||||||
\(792\) | 11.1467 | 0.396079 | ||||||||
\(793\) | −25.1151 | −0.891862 | ||||||||
\(794\) | 15.3958 | 0.546377 | ||||||||
\(795\) | 9.31920 | 0.330518 | ||||||||
\(796\) | −5.79270 | −0.205317 | ||||||||
\(797\) | −39.5004 | −1.39918 | −0.699588 | − | 0.714547i | \(-0.746633\pi\) | ||||
−0.699588 | + | 0.714547i | \(0.746633\pi\) | |||||||
\(798\) | −43.2884 | −1.53239 | ||||||||
\(799\) | 7.11197 | 0.251604 | ||||||||
\(800\) | −12.0763 | −0.426963 | ||||||||
\(801\) | −45.9977 | −1.62525 | ||||||||
\(802\) | −18.7137 | −0.660803 | ||||||||
\(803\) | −2.58126 | −0.0910907 | ||||||||
\(804\) | −16.7055 | −0.589159 | ||||||||
\(805\) | 3.44014 | 0.121249 | ||||||||
\(806\) | 15.8952 | 0.559884 | ||||||||
\(807\) | −71.0573 | −2.50133 | ||||||||
\(808\) | 19.7516 | 0.694860 | ||||||||
\(809\) | −48.8110 | −1.71610 | −0.858051 | − | 0.513564i | \(-0.828325\pi\) | ||||
−0.858051 | + | 0.513564i | \(0.828325\pi\) | |||||||
\(810\) | 12.1221 | 0.425928 | ||||||||
\(811\) | −32.6211 | −1.14548 | −0.572741 | − | 0.819737i | \(-0.694120\pi\) | ||||
−0.572741 | + | 0.819737i | \(0.694120\pi\) | |||||||
\(812\) | 1.84319 | 0.0646832 | ||||||||
\(813\) | 52.0588 | 1.82578 | ||||||||
\(814\) | 8.98415 | 0.314894 | ||||||||
\(815\) | −39.5504 | −1.38539 | ||||||||
\(816\) | −8.50781 | −0.297833 | ||||||||
\(817\) | 23.2815 | 0.814515 | ||||||||
\(818\) | −16.5189 | −0.577568 | ||||||||
\(819\) | 81.2666 | 2.83968 | ||||||||
\(820\) | 3.40282 | 0.118831 | ||||||||
\(821\) | −46.6063 | −1.62657 | −0.813286 | − | 0.581865i | \(-0.802323\pi\) | ||||
−0.813286 | + | 0.581865i | \(0.802323\pi\) | |||||||
\(822\) | 50.8893 | 1.77497 | ||||||||
\(823\) | −35.0927 | −1.22325 | −0.611627 | − | 0.791147i | \(-0.709485\pi\) | ||||
−0.611627 | + | 0.791147i | \(0.709485\pi\) | |||||||
\(824\) | 25.0138 | 0.871397 | ||||||||
\(825\) | −15.2783 | −0.531921 | ||||||||
\(826\) | 28.6988 | 0.998557 | ||||||||
\(827\) | −53.4331 | −1.85805 | −0.929026 | − | 0.370015i | \(-0.879353\pi\) | ||||
−0.929026 | + | 0.370015i | \(0.879353\pi\) | |||||||
\(828\) | 0.555573 | 0.0193075 | ||||||||
\(829\) | 30.7341 | 1.06744 | 0.533719 | − | 0.845662i | \(-0.320794\pi\) | ||||
0.533719 | + | 0.845662i | \(0.320794\pi\) | |||||||
\(830\) | −22.5714 | −0.783464 | ||||||||
\(831\) | 57.4649 | 1.99343 | ||||||||
\(832\) | −32.5901 | −1.12986 | ||||||||
\(833\) | 2.59495 | 0.0899098 | ||||||||
\(834\) | 50.7542 | 1.75747 | ||||||||
\(835\) | −17.3694 | −0.601094 | ||||||||
\(836\) | −1.20414 | −0.0416461 | ||||||||
\(837\) | −7.51292 | −0.259684 | ||||||||
\(838\) | 48.4519 | 1.67374 | ||||||||
\(839\) | 49.3178 | 1.70264 | 0.851319 | − | 0.524648i | \(-0.175803\pi\) | ||||
0.851319 | + | 0.524648i | \(0.175803\pi\) | |||||||
\(840\) | −73.0377 | −2.52004 | ||||||||
\(841\) | −26.9115 | −0.927982 | ||||||||
\(842\) | −34.2795 | −1.18135 | ||||||||
\(843\) | 1.31322 | 0.0452297 | ||||||||
\(844\) | −1.53578 | −0.0528636 | ||||||||
\(845\) | −56.6405 | −1.94849 | ||||||||
\(846\) | 73.0310 | 2.51086 | ||||||||
\(847\) | −3.29481 | −0.113211 | ||||||||
\(848\) | 4.84457 | 0.166363 | ||||||||
\(849\) | 51.1357 | 1.75497 | ||||||||
\(850\) | 5.81139 | 0.199329 | ||||||||
\(851\) | −1.86579 | −0.0639585 | ||||||||
\(852\) | −8.20289 | −0.281026 | ||||||||
\(853\) | −0.819663 | −0.0280647 | −0.0140324 | − | 0.999902i | \(-0.504467\pi\) | ||||
−0.0140324 | + | 0.999902i | \(0.504467\pi\) | |||||||
\(854\) | −23.1856 | −0.793396 | ||||||||
\(855\) | −45.2778 | −1.54847 | ||||||||
\(856\) | −24.3882 | −0.833571 | ||||||||
\(857\) | 3.01099 | 0.102853 | 0.0514267 | − | 0.998677i | \(-0.483623\pi\) | ||||
0.0514267 | + | 0.998677i | \(0.483623\pi\) | |||||||
\(858\) | 23.2897 | 0.795097 | ||||||||
\(859\) | −4.77571 | −0.162945 | −0.0814726 | − | 0.996676i | \(-0.525962\pi\) | ||||
−0.0814726 | + | 0.996676i | \(0.525962\pi\) | |||||||
\(860\) | −9.42748 | −0.321474 | ||||||||
\(861\) | 24.3317 | 0.829223 | ||||||||
\(862\) | −45.1579 | −1.53808 | ||||||||
\(863\) | 3.01791 | 0.102731 | 0.0513655 | − | 0.998680i | \(-0.483643\pi\) | ||||
0.0513655 | + | 0.998680i | \(0.483643\pi\) | |||||||
\(864\) | −8.70099 | −0.296014 | ||||||||
\(865\) | 14.7587 | 0.501810 | ||||||||
\(866\) | 20.3289 | 0.690804 | ||||||||
\(867\) | −45.2344 | −1.53624 | ||||||||
\(868\) | 2.37957 | 0.0807679 | ||||||||
\(869\) | −16.3556 | −0.554825 | ||||||||
\(870\) | 19.8623 | 0.673394 | ||||||||
\(871\) | 87.0511 | 2.94961 | ||||||||
\(872\) | 14.5769 | 0.493635 | ||||||||
\(873\) | −84.1370 | −2.84761 | ||||||||
\(874\) | 1.54211 | 0.0521625 | ||||||||
\(875\) | 6.31378 | 0.213445 | ||||||||
\(876\) | 2.73148 | 0.0922883 | ||||||||
\(877\) | 34.4673 | 1.16388 | 0.581939 | − | 0.813232i | \(-0.302294\pi\) | ||||
0.581939 | + | 0.813232i | \(0.302294\pi\) | |||||||
\(878\) | −49.5584 | −1.67252 | ||||||||
\(879\) | −79.2164 | −2.67190 | ||||||||
\(880\) | −15.0479 | −0.507264 | ||||||||
\(881\) | −16.4588 | −0.554510 | −0.277255 | − | 0.960796i | \(-0.589425\pi\) | ||||
−0.277255 | + | 0.960796i | \(0.589425\pi\) | |||||||
\(882\) | 26.6469 | 0.897248 | ||||||||
\(883\) | 42.6507 | 1.43531 | 0.717656 | − | 0.696398i | \(-0.245215\pi\) | ||||
0.717656 | + | 0.696398i | \(0.245215\pi\) | |||||||
\(884\) | −1.43654 | −0.0483161 | ||||||||
\(885\) | 50.1500 | 1.68578 | ||||||||
\(886\) | 49.1893 | 1.65255 | ||||||||
\(887\) | −1.57557 | −0.0529024 | −0.0264512 | − | 0.999650i | \(-0.508421\pi\) | ||||
−0.0264512 | + | 0.999650i | \(0.508421\pi\) | |||||||
\(888\) | 39.6126 | 1.32931 | ||||||||
\(889\) | 54.8729 | 1.84038 | ||||||||
\(890\) | 51.7006 | 1.73301 | ||||||||
\(891\) | 2.41112 | 0.0807755 | ||||||||
\(892\) | 3.91963 | 0.131239 | ||||||||
\(893\) | 32.8723 | 1.10003 | ||||||||
\(894\) | 24.7230 | 0.826862 | ||||||||
\(895\) | 72.6275 | 2.42767 | ||||||||
\(896\) | −44.3251 | −1.48080 | ||||||||
\(897\) | −4.83670 | −0.161493 | ||||||||
\(898\) | −26.5884 | −0.887266 | ||||||||
\(899\) | 2.69632 | 0.0899271 | ||||||||
\(900\) | 9.67710 | 0.322570 | ||||||||
\(901\) | −0.705057 | −0.0234889 | ||||||||
\(902\) | 4.17378 | 0.138972 | ||||||||
\(903\) | −67.4109 | −2.24329 | ||||||||
\(904\) | 10.3771 | 0.345137 | ||||||||
\(905\) | 6.05895 | 0.201406 | ||||||||
\(906\) | 10.6477 | 0.353746 | ||||||||
\(907\) | −46.0305 | −1.52842 | −0.764209 | − | 0.644968i | \(-0.776871\pi\) | ||||
−0.764209 | + | 0.644968i | \(0.776871\pi\) | |||||||
\(908\) | 0.0223954 | 0.000743219 0 | ||||||||
\(909\) | −35.4536 | −1.17592 | ||||||||
\(910\) | −91.3420 | −3.02796 | ||||||||
\(911\) | −52.6729 | −1.74513 | −0.872565 | − | 0.488498i | \(-0.837545\pi\) | ||||
−0.872565 | + | 0.488498i | \(0.837545\pi\) | |||||||
\(912\) | −39.3240 | −1.30215 | ||||||||
\(913\) | −4.48950 | −0.148581 | ||||||||
\(914\) | 7.40317 | 0.244875 | ||||||||
\(915\) | −40.5161 | −1.33942 | ||||||||
\(916\) | −4.37037 | −0.144401 | ||||||||
\(917\) | 3.29481 | 0.108804 | ||||||||
\(918\) | 4.18709 | 0.138195 | ||||||||
\(919\) | 14.4730 | 0.477421 | 0.238710 | − | 0.971091i | \(-0.423275\pi\) | ||||
0.238710 | + | 0.971091i | \(0.423275\pi\) | |||||||
\(920\) | 2.60189 | 0.0857819 | ||||||||
\(921\) | 64.9913 | 2.14154 | ||||||||
\(922\) | 52.3175 | 1.72299 | ||||||||
\(923\) | 42.7445 | 1.40695 | ||||||||
\(924\) | 3.48656 | 0.114699 | ||||||||
\(925\) | −32.4988 | −1.06855 | ||||||||
\(926\) | 9.00732 | 0.295999 | ||||||||
\(927\) | −44.8991 | −1.47468 | ||||||||
\(928\) | 3.12270 | 0.102508 | ||||||||
\(929\) | 20.0925 | 0.659213 | 0.329606 | − | 0.944118i | \(-0.393084\pi\) | ||||
0.329606 | + | 0.944118i | \(0.393084\pi\) | |||||||
\(930\) | 25.6424 | 0.840847 | ||||||||
\(931\) | 11.9941 | 0.393092 | ||||||||
\(932\) | −5.34178 | −0.174976 | ||||||||
\(933\) | 16.0078 | 0.524073 | ||||||||
\(934\) | 56.1486 | 1.83724 | ||||||||
\(935\) | 2.19000 | 0.0716207 | ||||||||
\(936\) | 61.4646 | 2.00903 | ||||||||
\(937\) | −6.25372 | −0.204300 | −0.102150 | − | 0.994769i | \(-0.532572\pi\) | ||||
−0.102150 | + | 0.994769i | \(0.532572\pi\) | |||||||
\(938\) | 80.3635 | 2.62396 | ||||||||
\(939\) | −70.8863 | −2.31329 | ||||||||
\(940\) | −13.3111 | −0.434161 | ||||||||
\(941\) | 16.4267 | 0.535494 | 0.267747 | − | 0.963489i | \(-0.413721\pi\) | ||||
0.267747 | + | 0.963489i | \(0.413721\pi\) | |||||||
\(942\) | 86.0801 | 2.80464 | ||||||||
\(943\) | −0.866793 | −0.0282267 | ||||||||
\(944\) | 26.0704 | 0.848521 | ||||||||
\(945\) | 43.1732 | 1.40442 | ||||||||
\(946\) | −11.5634 | −0.375960 | ||||||||
\(947\) | −26.6074 | −0.864623 | −0.432312 | − | 0.901724i | \(-0.642302\pi\) | ||||
−0.432312 | + | 0.901724i | \(0.642302\pi\) | |||||||
\(948\) | 17.3074 | 0.562119 | ||||||||
\(949\) | −14.2335 | −0.462040 | ||||||||
\(950\) | 26.8608 | 0.871479 | ||||||||
\(951\) | −13.3310 | −0.432288 | ||||||||
\(952\) | 5.52577 | 0.179091 | ||||||||
\(953\) | −34.3273 | −1.11197 | −0.555986 | − | 0.831192i | \(-0.687659\pi\) | ||||
−0.555986 | + | 0.831192i | \(0.687659\pi\) | |||||||
\(954\) | −7.24005 | −0.234405 | ||||||||
\(955\) | 53.6876 | 1.73729 | ||||||||
\(956\) | −3.33297 | −0.107796 | ||||||||
\(957\) | 3.95065 | 0.127706 | ||||||||
\(958\) | −24.6928 | −0.797787 | ||||||||
\(959\) | −39.6985 | −1.28193 | ||||||||
\(960\) | −52.5750 | −1.69685 | ||||||||
\(961\) | −27.5190 | −0.887711 | ||||||||
\(962\) | 49.5401 | 1.59724 | ||||||||
\(963\) | 43.7761 | 1.41067 | ||||||||
\(964\) | 3.36167 | 0.108272 | ||||||||
\(965\) | 36.7849 | 1.18415 | ||||||||
\(966\) | −4.46513 | −0.143663 | ||||||||
\(967\) | −41.5468 | −1.33605 | −0.668027 | − | 0.744137i | \(-0.732861\pi\) | ||||
−0.668027 | + | 0.744137i | \(0.732861\pi\) | |||||||
\(968\) | −2.49197 | −0.0800951 | ||||||||
\(969\) | 5.72303 | 0.183850 | ||||||||
\(970\) | 94.5683 | 3.03641 | ||||||||
\(971\) | −12.7640 | −0.409615 | −0.204808 | − | 0.978802i | \(-0.565657\pi\) | ||||
−0.204808 | + | 0.978802i | \(0.565657\pi\) | |||||||
\(972\) | −7.22770 | −0.231828 | ||||||||
\(973\) | −39.5931 | −1.26930 | ||||||||
\(974\) | 47.5599 | 1.52392 | ||||||||
\(975\) | −84.2469 | −2.69806 | ||||||||
\(976\) | −21.0622 | −0.674185 | ||||||||
\(977\) | −5.30707 | −0.169788 | −0.0848941 | − | 0.996390i | \(-0.527055\pi\) | ||||
−0.0848941 | + | 0.996390i | \(0.527055\pi\) | |||||||
\(978\) | 51.3344 | 1.64149 | ||||||||
\(979\) | 10.2834 | 0.328658 | ||||||||
\(980\) | −4.85685 | −0.155146 | ||||||||
\(981\) | −26.1651 | −0.835386 | ||||||||
\(982\) | −46.9278 | −1.49753 | ||||||||
\(983\) | −28.1899 | −0.899120 | −0.449560 | − | 0.893250i | \(-0.648419\pi\) | ||||
−0.449560 | + | 0.893250i | \(0.648419\pi\) | |||||||
\(984\) | 18.4029 | 0.586663 | ||||||||
\(985\) | 49.3162 | 1.57135 | ||||||||
\(986\) | −1.50271 | −0.0478560 | ||||||||
\(987\) | −95.1808 | −3.02964 | ||||||||
\(988\) | −6.63984 | −0.211241 | ||||||||
\(989\) | 2.40145 | 0.0763615 | ||||||||
\(990\) | 22.4886 | 0.714733 | ||||||||
\(991\) | 41.8088 | 1.32810 | 0.664050 | − | 0.747688i | \(-0.268836\pi\) | ||||
0.664050 | + | 0.747688i | \(0.268836\pi\) | |||||||
\(992\) | 4.03144 | 0.127998 | ||||||||
\(993\) | 30.4472 | 0.966212 | ||||||||
\(994\) | 39.4608 | 1.25162 | ||||||||
\(995\) | 48.6954 | 1.54375 | ||||||||
\(996\) | 4.75078 | 0.150534 | ||||||||
\(997\) | −0.0216208 | −0.000684737 0 | −0.000342368 | − | 1.00000i | \(-0.500109\pi\) | ||||
−0.000342368 | 1.00000i | \(0.500109\pi\) | ||||||||
\(998\) | 0.614348 | 0.0194468 | ||||||||
\(999\) | −23.4153 | −0.740829 |
(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 | 1441.2.a.d.1.19 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.d.1.19 | ✓ | 23 | 1.1 | even | 1 | trivial |