Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7595,2,Mod(1,7595)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7595, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7595.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7595 = 5 \cdot 7^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7595.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: | \(60.6463803352\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 1085) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 7595.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26981 | 1.60500 | 0.802500 | − | 0.596653i | \(-0.203503\pi\) | ||||
0.802500 | + | 0.596653i | \(0.203503\pi\) | |||||||
\(3\) | −3.30996 | −1.91101 | −0.955504 | − | 0.294979i | \(-0.904687\pi\) | ||||
−0.955504 | + | 0.294979i | \(0.904687\pi\) | |||||||
\(4\) | 3.15205 | 1.57602 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −7.51299 | −3.06717 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.61493 | 0.924516 | ||||||||
\(9\) | 7.95585 | 2.65195 | ||||||||
\(10\) | 2.26981 | 0.717778 | ||||||||
\(11\) | 4.85520 | 1.46390 | 0.731949 | − | 0.681359i | \(-0.238611\pi\) | ||||
0.731949 | + | 0.681359i | \(0.238611\pi\) | |||||||
\(12\) | −10.4332 | −3.01179 | ||||||||
\(13\) | −6.52160 | −1.80877 | −0.904383 | − | 0.426721i | \(-0.859669\pi\) | ||||
−0.904383 | + | 0.426721i | \(0.859669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30996 | −0.854629 | ||||||||
\(16\) | −0.368699 | −0.0921748 | ||||||||
\(17\) | 0.221263 | 0.0536641 | 0.0268321 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268321 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(18\) | 18.0583 | 4.25638 | ||||||||
\(19\) | 2.71231 | 0.622247 | 0.311123 | − | 0.950370i | \(-0.399295\pi\) | ||||
0.311123 | + | 0.950370i | \(0.399295\pi\) | |||||||
\(20\) | 3.15205 | 0.704819 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.0204 | 2.34956 | ||||||||
\(23\) | −6.33498 | −1.32093 | −0.660467 | − | 0.750855i | \(-0.729642\pi\) | ||||
−0.660467 | + | 0.750855i | \(0.729642\pi\) | |||||||
\(24\) | −8.65531 | −1.76676 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −14.8028 | −2.90307 | ||||||||
\(27\) | −16.4037 | −3.15689 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.63217 | −0.488781 | −0.244391 | − | 0.969677i | \(-0.578588\pi\) | ||||
−0.244391 | + | 0.969677i | \(0.578588\pi\) | |||||||
\(30\) | −7.51299 | −1.37168 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −6.06673 | −1.07246 | ||||||||
\(33\) | −16.0705 | −2.79752 | ||||||||
\(34\) | 0.502225 | 0.0861309 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25.0772 | 4.17953 | ||||||||
\(37\) | −0.742795 | −0.122115 | −0.0610574 | − | 0.998134i | \(-0.519447\pi\) | ||||
−0.0610574 | + | 0.998134i | \(0.519447\pi\) | |||||||
\(38\) | 6.15643 | 0.998706 | ||||||||
\(39\) | 21.5863 | 3.45657 | ||||||||
\(40\) | 2.61493 | 0.413456 | ||||||||
\(41\) | 9.28495 | 1.45007 | 0.725033 | − | 0.688715i | \(-0.241825\pi\) | ||||
0.725033 | + | 0.688715i | \(0.241825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.26124 | −1.25983 | −0.629914 | − | 0.776665i | \(-0.716910\pi\) | ||||
−0.629914 | + | 0.776665i | \(0.716910\pi\) | |||||||
\(44\) | 15.3038 | 2.30714 | ||||||||
\(45\) | 7.95585 | 1.18599 | ||||||||
\(46\) | −14.3792 | −2.12010 | ||||||||
\(47\) | 5.97344 | 0.871315 | 0.435658 | − | 0.900112i | \(-0.356516\pi\) | ||||
0.435658 | + | 0.900112i | \(0.356516\pi\) | |||||||
\(48\) | 1.22038 | 0.176147 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.26981 | 0.321000 | ||||||||
\(51\) | −0.732372 | −0.102553 | ||||||||
\(52\) | −20.5564 | −2.85066 | ||||||||
\(53\) | −4.45885 | −0.612471 | −0.306235 | − | 0.951956i | \(-0.599069\pi\) | ||||
−0.306235 | + | 0.951956i | \(0.599069\pi\) | |||||||
\(54\) | −37.2333 | −5.06681 | ||||||||
\(55\) | 4.85520 | 0.654676 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.97765 | −1.18912 | ||||||||
\(58\) | −5.97452 | −0.784493 | ||||||||
\(59\) | −4.95499 | −0.645085 | −0.322543 | − | 0.946555i | \(-0.604538\pi\) | ||||
−0.322543 | + | 0.946555i | \(0.604538\pi\) | |||||||
\(60\) | −10.4332 | −1.34691 | ||||||||
\(61\) | −14.2834 | −1.82880 | −0.914401 | − | 0.404809i | \(-0.867338\pi\) | ||||
−0.914401 | + | 0.404809i | \(0.867338\pi\) | |||||||
\(62\) | −2.26981 | −0.288266 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0329 | −1.62912 | ||||||||
\(65\) | −6.52160 | −0.808905 | ||||||||
\(66\) | −36.4771 | −4.49002 | ||||||||
\(67\) | −6.21873 | −0.759739 | −0.379870 | − | 0.925040i | \(-0.624031\pi\) | ||||
−0.379870 | + | 0.925040i | \(0.624031\pi\) | |||||||
\(68\) | 0.697431 | 0.0845759 | ||||||||
\(69\) | 20.9685 | 2.52431 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00532 | −0.237988 | −0.118994 | − | 0.992895i | \(-0.537967\pi\) | ||||
−0.118994 | + | 0.992895i | \(0.537967\pi\) | |||||||
\(72\) | 20.8040 | 2.45177 | ||||||||
\(73\) | 3.28275 | 0.384216 | 0.192108 | − | 0.981374i | \(-0.438468\pi\) | ||||
0.192108 | + | 0.981374i | \(0.438468\pi\) | |||||||
\(74\) | −1.68600 | −0.195994 | ||||||||
\(75\) | −3.30996 | −0.382202 | ||||||||
\(76\) | 8.54933 | 0.980675 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 48.9967 | 5.54779 | ||||||||
\(79\) | 4.84953 | 0.545615 | 0.272807 | − | 0.962069i | \(-0.412048\pi\) | ||||
0.272807 | + | 0.962069i | \(0.412048\pi\) | |||||||
\(80\) | −0.368699 | −0.0412218 | ||||||||
\(81\) | 30.4280 | 3.38089 | ||||||||
\(82\) | 21.0751 | 2.32735 | ||||||||
\(83\) | 5.94885 | 0.652971 | 0.326486 | − | 0.945202i | \(-0.394136\pi\) | ||||
0.326486 | + | 0.945202i | \(0.394136\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.221263 | 0.0239993 | ||||||||
\(86\) | −18.7515 | −2.02202 | ||||||||
\(87\) | 8.71237 | 0.934064 | ||||||||
\(88\) | 12.6960 | 1.35340 | ||||||||
\(89\) | 3.33533 | 0.353545 | 0.176772 | − | 0.984252i | \(-0.443434\pi\) | ||||
0.176772 | + | 0.984252i | \(0.443434\pi\) | |||||||
\(90\) | 18.0583 | 1.90351 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −19.9681 | −2.08182 | ||||||||
\(93\) | 3.30996 | 0.343227 | ||||||||
\(94\) | 13.5586 | 1.39846 | ||||||||
\(95\) | 2.71231 | 0.278277 | ||||||||
\(96\) | 20.0807 | 2.04947 | ||||||||
\(97\) | 7.08455 | 0.719327 | 0.359663 | − | 0.933082i | \(-0.382892\pi\) | ||||
0.359663 | + | 0.933082i | \(0.382892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 38.6273 | 3.88219 | ||||||||
\(100\) | 3.15205 | 0.315205 | ||||||||
\(101\) | −8.88272 | −0.883863 | −0.441932 | − | 0.897049i | \(-0.645707\pi\) | ||||
−0.441932 | + | 0.897049i | \(0.645707\pi\) | |||||||
\(102\) | −1.66235 | −0.164597 | ||||||||
\(103\) | 1.05449 | 0.103902 | 0.0519509 | − | 0.998650i | \(-0.483456\pi\) | ||||
0.0519509 | + | 0.998650i | \(0.483456\pi\) | |||||||
\(104\) | −17.0535 | −1.67223 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1208 | −0.983015 | ||||||||
\(107\) | 8.87370 | 0.857853 | 0.428927 | − | 0.903339i | \(-0.358892\pi\) | ||||
0.428927 | + | 0.903339i | \(0.358892\pi\) | |||||||
\(108\) | −51.7051 | −4.97533 | ||||||||
\(109\) | 1.81005 | 0.173371 | 0.0866855 | − | 0.996236i | \(-0.472372\pi\) | ||||
0.0866855 | + | 0.996236i | \(0.472372\pi\) | |||||||
\(110\) | 11.0204 | 1.05075 | ||||||||
\(111\) | 2.45862 | 0.233362 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.2479 | −1.15219 | −0.576094 | − | 0.817383i | \(-0.695424\pi\) | ||||
−0.576094 | + | 0.817383i | \(0.695424\pi\) | |||||||
\(114\) | −20.3776 | −1.90853 | ||||||||
\(115\) | −6.33498 | −0.590740 | ||||||||
\(116\) | −8.29671 | −0.770330 | ||||||||
\(117\) | −51.8849 | −4.79676 | ||||||||
\(118\) | −11.2469 | −1.03536 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −8.65531 | −0.790118 | ||||||||
\(121\) | 12.5730 | 1.14300 | ||||||||
\(122\) | −32.4206 | −2.93523 | ||||||||
\(123\) | −30.7328 | −2.77109 | ||||||||
\(124\) | −3.15205 | −0.283062 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.57855 | 0.140073 | 0.0700366 | − | 0.997544i | \(-0.477688\pi\) | ||||
0.0700366 | + | 0.997544i | \(0.477688\pi\) | |||||||
\(128\) | −17.4489 | −1.54228 | ||||||||
\(129\) | 27.3444 | 2.40754 | ||||||||
\(130\) | −14.8028 | −1.29829 | ||||||||
\(131\) | −10.5229 | −0.919390 | −0.459695 | − | 0.888077i | \(-0.652041\pi\) | ||||
−0.459695 | + | 0.888077i | \(0.652041\pi\) | |||||||
\(132\) | −50.6551 | −4.40896 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.1154 | −1.21938 | ||||||||
\(135\) | −16.4037 | −1.41180 | ||||||||
\(136\) | 0.578586 | 0.0496134 | ||||||||
\(137\) | 8.93351 | 0.763242 | 0.381621 | − | 0.924319i | \(-0.375366\pi\) | ||||
0.381621 | + | 0.924319i | \(0.375366\pi\) | |||||||
\(138\) | 47.5946 | 4.05152 | ||||||||
\(139\) | 0.362168 | 0.0307187 | 0.0153594 | − | 0.999882i | \(-0.495111\pi\) | ||||
0.0153594 | + | 0.999882i | \(0.495111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.7718 | −1.66509 | ||||||||
\(142\) | −4.55170 | −0.381970 | ||||||||
\(143\) | −31.6637 | −2.64785 | ||||||||
\(144\) | −2.93331 | −0.244443 | ||||||||
\(145\) | −2.63217 | −0.218590 | ||||||||
\(146\) | 7.45122 | 0.616667 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.34132 | −0.192456 | ||||||||
\(149\) | −14.4149 | −1.18092 | −0.590458 | − | 0.807068i | \(-0.701053\pi\) | ||||
−0.590458 | + | 0.807068i | \(0.701053\pi\) | |||||||
\(150\) | −7.51299 | −0.613433 | ||||||||
\(151\) | 13.5523 | 1.10287 | 0.551436 | − | 0.834217i | \(-0.314080\pi\) | ||||
0.551436 | + | 0.834217i | \(0.314080\pi\) | |||||||
\(152\) | 7.09249 | 0.575277 | ||||||||
\(153\) | 1.76033 | 0.142315 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 68.0409 | 5.44763 | ||||||||
\(157\) | −20.0346 | −1.59894 | −0.799469 | − | 0.600708i | \(-0.794886\pi\) | ||||
−0.799469 | + | 0.600708i | \(0.794886\pi\) | |||||||
\(158\) | 11.0075 | 0.875711 | ||||||||
\(159\) | 14.7586 | 1.17044 | ||||||||
\(160\) | −6.06673 | −0.479617 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 69.0658 | 5.42633 | ||||||||
\(163\) | −1.17177 | −0.0917803 | −0.0458901 | − | 0.998946i | \(-0.514612\pi\) | ||||
−0.0458901 | + | 0.998946i | \(0.514612\pi\) | |||||||
\(164\) | 29.2666 | 2.28534 | ||||||||
\(165\) | −16.0705 | −1.25109 | ||||||||
\(166\) | 13.5028 | 1.04802 | ||||||||
\(167\) | −16.1871 | −1.25259 | −0.626297 | − | 0.779584i | \(-0.715430\pi\) | ||||
−0.626297 | + | 0.779584i | \(0.715430\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.5313 | 2.27164 | ||||||||
\(170\) | 0.502225 | 0.0385189 | ||||||||
\(171\) | 21.5787 | 1.65017 | ||||||||
\(172\) | −26.0398 | −1.98552 | ||||||||
\(173\) | −7.19520 | −0.547041 | −0.273521 | − | 0.961866i | \(-0.588188\pi\) | ||||
−0.273521 | + | 0.961866i | \(0.588188\pi\) | |||||||
\(174\) | 19.7754 | 1.49917 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.79011 | −0.134935 | ||||||||
\(177\) | 16.4008 | 1.23276 | ||||||||
\(178\) | 7.57058 | 0.567439 | ||||||||
\(179\) | 19.4195 | 1.45148 | 0.725740 | − | 0.687969i | \(-0.241497\pi\) | ||||
0.725740 | + | 0.687969i | \(0.241497\pi\) | |||||||
\(180\) | 25.0772 | 1.86914 | ||||||||
\(181\) | −18.1665 | −1.35030 | −0.675152 | − | 0.737679i | \(-0.735922\pi\) | ||||
−0.675152 | + | 0.737679i | \(0.735922\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 47.2775 | 3.49486 | ||||||||
\(184\) | −16.5655 | −1.22123 | ||||||||
\(185\) | −0.742795 | −0.0546114 | ||||||||
\(186\) | 7.51299 | 0.550879 | ||||||||
\(187\) | 1.07428 | 0.0785589 | ||||||||
\(188\) | 18.8285 | 1.37321 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.15643 | 0.446635 | ||||||||
\(191\) | −26.7503 | −1.93558 | −0.967790 | − | 0.251757i | \(-0.918991\pi\) | ||||
−0.967790 | + | 0.251757i | \(0.918991\pi\) | |||||||
\(192\) | 43.1385 | 3.11326 | ||||||||
\(193\) | −12.5988 | −0.906884 | −0.453442 | − | 0.891286i | \(-0.649804\pi\) | ||||
−0.453442 | + | 0.891286i | \(0.649804\pi\) | |||||||
\(194\) | 16.0806 | 1.15452 | ||||||||
\(195\) | 21.5863 | 1.54582 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.5580 | −1.25096 | −0.625478 | − | 0.780242i | \(-0.715096\pi\) | ||||
−0.625478 | + | 0.780242i | \(0.715096\pi\) | |||||||
\(198\) | 87.6766 | 6.23091 | ||||||||
\(199\) | −20.2841 | −1.43790 | −0.718949 | − | 0.695063i | \(-0.755377\pi\) | ||||
−0.718949 | + | 0.695063i | \(0.755377\pi\) | |||||||
\(200\) | 2.61493 | 0.184903 | ||||||||
\(201\) | 20.5838 | 1.45187 | ||||||||
\(202\) | −20.1621 | −1.41860 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.30847 | −0.161625 | ||||||||
\(205\) | 9.28495 | 0.648489 | ||||||||
\(206\) | 2.39349 | 0.166762 | ||||||||
\(207\) | −50.4001 | −3.50305 | ||||||||
\(208\) | 2.40451 | 0.166723 | ||||||||
\(209\) | 13.1688 | 0.910906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3326 | −0.711327 | −0.355664 | − | 0.934614i | \(-0.615745\pi\) | ||||
−0.355664 | + | 0.934614i | \(0.615745\pi\) | |||||||
\(212\) | −14.0545 | −0.965268 | ||||||||
\(213\) | 6.63754 | 0.454797 | ||||||||
\(214\) | 20.1416 | 1.37685 | ||||||||
\(215\) | −8.26124 | −0.563412 | ||||||||
\(216\) | −42.8944 | −2.91860 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.10846 | 0.278260 | ||||||||
\(219\) | −10.8658 | −0.734240 | ||||||||
\(220\) | 15.3038 | 1.03178 | ||||||||
\(221\) | −1.44299 | −0.0970659 | ||||||||
\(222\) | 5.58061 | 0.374546 | ||||||||
\(223\) | 29.2750 | 1.96040 | 0.980199 | − | 0.198013i | \(-0.0634489\pi\) | ||||
0.980199 | + | 0.198013i | \(0.0634489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.95585 | 0.530390 | ||||||||
\(226\) | −27.8005 | −1.84926 | ||||||||
\(227\) | 3.12495 | 0.207410 | 0.103705 | − | 0.994608i | \(-0.466930\pi\) | ||||
0.103705 | + | 0.994608i | \(0.466930\pi\) | |||||||
\(228\) | −28.2980 | −1.87408 | ||||||||
\(229\) | −6.02790 | −0.398335 | −0.199167 | − | 0.979965i | \(-0.563824\pi\) | ||||
−0.199167 | + | 0.979965i | \(0.563824\pi\) | |||||||
\(230\) | −14.3792 | −0.948137 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.88292 | −0.451886 | ||||||||
\(233\) | −6.82987 | −0.447440 | −0.223720 | − | 0.974653i | \(-0.571820\pi\) | ||||
−0.223720 | + | 0.974653i | \(0.571820\pi\) | |||||||
\(234\) | −117.769 | −7.69880 | ||||||||
\(235\) | 5.97344 | 0.389664 | ||||||||
\(236\) | −15.6184 | −1.01667 | ||||||||
\(237\) | −16.0518 | −1.04267 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.19383 | −0.206591 | −0.103296 | − | 0.994651i | \(-0.532939\pi\) | ||||
−0.103296 | + | 0.994651i | \(0.532939\pi\) | |||||||
\(240\) | 1.22038 | 0.0787752 | ||||||||
\(241\) | 12.5996 | 0.811614 | 0.405807 | − | 0.913959i | \(-0.366991\pi\) | ||||
0.405807 | + | 0.913959i | \(0.366991\pi\) | |||||||
\(242\) | 28.5383 | 1.83451 | ||||||||
\(243\) | −51.5045 | −3.30402 | ||||||||
\(244\) | −45.0219 | −2.88223 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −69.7577 | −4.44759 | ||||||||
\(247\) | −17.6886 | −1.12550 | ||||||||
\(248\) | −2.61493 | −0.166048 | ||||||||
\(249\) | −19.6905 | −1.24783 | ||||||||
\(250\) | 2.26981 | 0.143556 | ||||||||
\(251\) | 9.93678 | 0.627204 | 0.313602 | − | 0.949555i | \(-0.398464\pi\) | ||||
0.313602 | + | 0.949555i | \(0.398464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.7576 | −1.93371 | ||||||||
\(254\) | 3.58300 | 0.224817 | ||||||||
\(255\) | −0.732372 | −0.0458629 | ||||||||
\(256\) | −13.5397 | −0.846234 | ||||||||
\(257\) | −6.22505 | −0.388308 | −0.194154 | − | 0.980971i | \(-0.562196\pi\) | ||||
−0.194154 | + | 0.980971i | \(0.562196\pi\) | |||||||
\(258\) | 62.0666 | 3.86410 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −20.5564 | −1.27485 | ||||||||
\(261\) | −20.9411 | −1.29622 | ||||||||
\(262\) | −23.8850 | −1.47562 | ||||||||
\(263\) | −4.73589 | −0.292028 | −0.146014 | − | 0.989283i | \(-0.546644\pi\) | ||||
−0.146014 | + | 0.989283i | \(0.546644\pi\) | |||||||
\(264\) | −42.0233 | −2.58635 | ||||||||
\(265\) | −4.45885 | −0.273905 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.0398 | −0.675627 | ||||||||
\(268\) | −19.6017 | −1.19737 | ||||||||
\(269\) | 9.32217 | 0.568383 | 0.284191 | − | 0.958768i | \(-0.408275\pi\) | ||||
0.284191 | + | 0.958768i | \(0.408275\pi\) | |||||||
\(270\) | −37.2333 | −2.26594 | ||||||||
\(271\) | −26.4572 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(272\) | −0.0815794 | −0.00494648 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.2774 | 1.22500 | ||||||||
\(275\) | 4.85520 | 0.292780 | ||||||||
\(276\) | 66.0938 | 3.97838 | ||||||||
\(277\) | 4.34480 | 0.261054 | 0.130527 | − | 0.991445i | \(-0.458333\pi\) | ||||
0.130527 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(278\) | 0.822054 | 0.0493035 | ||||||||
\(279\) | −7.95585 | −0.476304 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.7466 | −1.77453 | −0.887267 | − | 0.461256i | \(-0.847399\pi\) | ||||
−0.887267 | + | 0.461256i | \(0.847399\pi\) | |||||||
\(282\) | −44.8784 | −2.67247 | ||||||||
\(283\) | 28.5915 | 1.69959 | 0.849794 | − | 0.527116i | \(-0.176726\pi\) | ||||
0.849794 | + | 0.527116i | \(0.176726\pi\) | |||||||
\(284\) | −6.32087 | −0.375074 | ||||||||
\(285\) | −8.97765 | −0.531790 | ||||||||
\(286\) | −71.8707 | −4.24980 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −48.2660 | −2.84410 | ||||||||
\(289\) | −16.9510 | −0.997120 | ||||||||
\(290\) | −5.97452 | −0.350836 | ||||||||
\(291\) | −23.4496 | −1.37464 | ||||||||
\(292\) | 10.3474 | 0.605534 | ||||||||
\(293\) | 5.06369 | 0.295824 | 0.147912 | − | 0.989001i | \(-0.452745\pi\) | ||||
0.147912 | + | 0.989001i | \(0.452745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.95499 | −0.288491 | ||||||||
\(296\) | −1.94235 | −0.112897 | ||||||||
\(297\) | −79.6432 | −4.62137 | ||||||||
\(298\) | −32.7192 | −1.89537 | ||||||||
\(299\) | 41.3142 | 2.38926 | ||||||||
\(300\) | −10.4332 | −0.602358 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 30.7612 | 1.77011 | ||||||||
\(303\) | 29.4015 | 1.68907 | ||||||||
\(304\) | −1.00003 | −0.0573554 | ||||||||
\(305\) | −14.2834 | −0.817865 | ||||||||
\(306\) | 3.99563 | 0.228415 | ||||||||
\(307\) | 13.7978 | 0.787482 | 0.393741 | − | 0.919221i | \(-0.371181\pi\) | ||||
0.393741 | + | 0.919221i | \(0.371181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.49032 | −0.198557 | ||||||||
\(310\) | −2.26981 | −0.128917 | ||||||||
\(311\) | −15.0651 | −0.854261 | −0.427130 | − | 0.904190i | \(-0.640475\pi\) | ||||
−0.427130 | + | 0.904190i | \(0.640475\pi\) | |||||||
\(312\) | 56.4465 | 3.19565 | ||||||||
\(313\) | −11.7420 | −0.663696 | −0.331848 | − | 0.943333i | \(-0.607672\pi\) | ||||
−0.331848 | + | 0.943333i | \(0.607672\pi\) | |||||||
\(314\) | −45.4748 | −2.56629 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.2859 | 0.859901 | ||||||||
\(317\) | 12.7836 | 0.718001 | 0.359000 | − | 0.933337i | \(-0.383118\pi\) | ||||
0.359000 | + | 0.933337i | \(0.383118\pi\) | |||||||
\(318\) | 33.4993 | 1.87855 | ||||||||
\(319\) | −12.7797 | −0.715526 | ||||||||
\(320\) | −13.0329 | −0.728564 | ||||||||
\(321\) | −29.3716 | −1.63936 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.600134 | 0.0333923 | ||||||||
\(324\) | 95.9105 | 5.32836 | ||||||||
\(325\) | −6.52160 | −0.361753 | ||||||||
\(326\) | −2.65970 | −0.147307 | ||||||||
\(327\) | −5.99118 | −0.331313 | ||||||||
\(328\) | 24.2795 | 1.34061 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −36.4771 | −2.00800 | ||||||||
\(331\) | −2.31971 | −0.127503 | −0.0637514 | − | 0.997966i | \(-0.520306\pi\) | ||||
−0.0637514 | + | 0.997966i | \(0.520306\pi\) | |||||||
\(332\) | 18.7510 | 1.02910 | ||||||||
\(333\) | −5.90956 | −0.323842 | ||||||||
\(334\) | −36.7417 | −2.01041 | ||||||||
\(335\) | −6.21873 | −0.339766 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4313 | 0.949543 | 0.474772 | − | 0.880109i | \(-0.342531\pi\) | ||||
0.474772 | + | 0.880109i | \(0.342531\pi\) | |||||||
\(338\) | 67.0305 | 3.64598 | ||||||||
\(339\) | 40.5402 | 2.20184 | ||||||||
\(340\) | 0.697431 | 0.0378235 | ||||||||
\(341\) | −4.85520 | −0.262924 | ||||||||
\(342\) | 48.9797 | 2.64852 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −21.6025 | −1.16473 | ||||||||
\(345\) | 20.9685 | 1.12891 | ||||||||
\(346\) | −16.3318 | −0.878001 | ||||||||
\(347\) | −23.0300 | −1.23631 | −0.618157 | − | 0.786055i | \(-0.712120\pi\) | ||||
−0.618157 | + | 0.786055i | \(0.712120\pi\) | |||||||
\(348\) | 27.4618 | 1.47211 | ||||||||
\(349\) | −5.45256 | −0.291869 | −0.145934 | − | 0.989294i | \(-0.546619\pi\) | ||||
−0.145934 | + | 0.989294i | \(0.546619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 106.978 | 5.71008 | ||||||||
\(352\) | −29.4552 | −1.56997 | ||||||||
\(353\) | −5.47366 | −0.291334 | −0.145667 | − | 0.989334i | \(-0.546533\pi\) | ||||
−0.145667 | + | 0.989334i | \(0.546533\pi\) | |||||||
\(354\) | 37.2268 | 1.97858 | ||||||||
\(355\) | −2.00532 | −0.106431 | ||||||||
\(356\) | 10.5131 | 0.557195 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 44.0786 | 2.32963 | ||||||||
\(359\) | 10.9587 | 0.578377 | 0.289188 | − | 0.957272i | \(-0.406615\pi\) | ||||
0.289188 | + | 0.957272i | \(0.406615\pi\) | |||||||
\(360\) | 20.8040 | 1.09647 | ||||||||
\(361\) | −11.6434 | −0.612809 | ||||||||
\(362\) | −41.2345 | −2.16724 | ||||||||
\(363\) | −41.6162 | −2.18428 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.28275 | 0.171827 | ||||||||
\(366\) | 107.311 | 5.60924 | ||||||||
\(367\) | −27.0586 | −1.41245 | −0.706223 | − | 0.707989i | \(-0.749603\pi\) | ||||
−0.706223 | + | 0.707989i | \(0.749603\pi\) | |||||||
\(368\) | 2.33570 | 0.121757 | ||||||||
\(369\) | 73.8696 | 3.84550 | ||||||||
\(370\) | −1.68600 | −0.0876512 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.4332 | 0.540934 | ||||||||
\(373\) | −8.72757 | −0.451896 | −0.225948 | − | 0.974139i | \(-0.572548\pi\) | ||||
−0.225948 | + | 0.974139i | \(0.572548\pi\) | |||||||
\(374\) | 2.43841 | 0.126087 | ||||||||
\(375\) | −3.30996 | −0.170926 | ||||||||
\(376\) | 15.6201 | 0.805545 | ||||||||
\(377\) | 17.1659 | 0.884091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.2865 | −0.836583 | −0.418292 | − | 0.908313i | \(-0.637371\pi\) | ||||
−0.418292 | + | 0.908313i | \(0.637371\pi\) | |||||||
\(380\) | 8.54933 | 0.438571 | ||||||||
\(381\) | −5.22493 | −0.267681 | ||||||||
\(382\) | −60.7181 | −3.10661 | ||||||||
\(383\) | 17.7948 | 0.909273 | 0.454636 | − | 0.890677i | \(-0.349769\pi\) | ||||
0.454636 | + | 0.890677i | \(0.349769\pi\) | |||||||
\(384\) | 57.7551 | 2.94730 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.5970 | −1.45555 | ||||||||
\(387\) | −65.7252 | −3.34100 | ||||||||
\(388\) | 22.3308 | 1.13368 | ||||||||
\(389\) | −26.7480 | −1.35618 | −0.678089 | − | 0.734980i | \(-0.737191\pi\) | ||||
−0.678089 | + | 0.734980i | \(0.737191\pi\) | |||||||
\(390\) | 48.9967 | 2.48105 | ||||||||
\(391\) | −1.40170 | −0.0708868 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 34.8304 | 1.75696 | ||||||||
\(394\) | −39.8534 | −2.00778 | ||||||||
\(395\) | 4.84953 | 0.244006 | ||||||||
\(396\) | 121.755 | 6.11842 | ||||||||
\(397\) | −17.0250 | −0.854460 | −0.427230 | − | 0.904143i | \(-0.640511\pi\) | ||||
−0.427230 | + | 0.904143i | \(0.640511\pi\) | |||||||
\(398\) | −46.0410 | −2.30783 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.368699 | −0.0184350 | ||||||||
\(401\) | 7.88405 | 0.393711 | 0.196855 | − | 0.980433i | \(-0.436927\pi\) | ||||
0.196855 | + | 0.980433i | \(0.436927\pi\) | |||||||
\(402\) | 46.7213 | 2.33025 | ||||||||
\(403\) | 6.52160 | 0.324864 | ||||||||
\(404\) | −27.9987 | −1.39299 | ||||||||
\(405\) | 30.4280 | 1.51198 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.60642 | −0.178764 | ||||||||
\(408\) | −1.91510 | −0.0948115 | ||||||||
\(409\) | −18.6570 | −0.922529 | −0.461264 | − | 0.887263i | \(-0.652604\pi\) | ||||
−0.461264 | + | 0.887263i | \(0.652604\pi\) | |||||||
\(410\) | 21.0751 | 1.04082 | ||||||||
\(411\) | −29.5696 | −1.45856 | ||||||||
\(412\) | 3.32380 | 0.163752 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −114.399 | −5.62239 | ||||||||
\(415\) | 5.94885 | 0.292018 | ||||||||
\(416\) | 39.5648 | 1.93982 | ||||||||
\(417\) | −1.19876 | −0.0587037 | ||||||||
\(418\) | 29.8907 | 1.46200 | ||||||||
\(419\) | −12.1866 | −0.595354 | −0.297677 | − | 0.954667i | \(-0.596212\pi\) | ||||
−0.297677 | + | 0.954667i | \(0.596212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.8586 | 1.94259 | 0.971295 | − | 0.237878i | \(-0.0764518\pi\) | ||||
0.971295 | + | 0.237878i | \(0.0764518\pi\) | |||||||
\(422\) | −23.4531 | −1.14168 | ||||||||
\(423\) | 47.5238 | 2.31068 | ||||||||
\(424\) | −11.6596 | −0.566239 | ||||||||
\(425\) | 0.221263 | 0.0107328 | ||||||||
\(426\) | 15.0660 | 0.729948 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 27.9703 | 1.35200 | ||||||||
\(429\) | 104.806 | 5.06007 | ||||||||
\(430\) | −18.7515 | −0.904276 | ||||||||
\(431\) | 13.5975 | 0.654969 | 0.327484 | − | 0.944857i | \(-0.393799\pi\) | ||||
0.327484 | + | 0.944857i | \(0.393799\pi\) | |||||||
\(432\) | 6.04802 | 0.290985 | ||||||||
\(433\) | −8.05133 | −0.386922 | −0.193461 | − | 0.981108i | \(-0.561971\pi\) | ||||
−0.193461 | + | 0.981108i | \(0.561971\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.71237 | 0.417726 | ||||||||
\(436\) | 5.70535 | 0.273237 | ||||||||
\(437\) | −17.1824 | −0.821947 | ||||||||
\(438\) | −24.6632 | −1.17846 | ||||||||
\(439\) | −3.48742 | −0.166445 | −0.0832227 | − | 0.996531i | \(-0.526521\pi\) | ||||
−0.0832227 | + | 0.996531i | \(0.526521\pi\) | |||||||
\(440\) | 12.6960 | 0.605258 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.27531 | −0.155791 | ||||||||
\(443\) | −25.2297 | −1.19870 | −0.599351 | − | 0.800487i | \(-0.704574\pi\) | ||||
−0.599351 | + | 0.800487i | \(0.704574\pi\) | |||||||
\(444\) | 7.74969 | 0.367784 | ||||||||
\(445\) | 3.33533 | 0.158110 | ||||||||
\(446\) | 66.4487 | 3.14644 | ||||||||
\(447\) | 47.7128 | 2.25674 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.3510 | 0.630074 | 0.315037 | − | 0.949079i | \(-0.397983\pi\) | ||||
0.315037 | + | 0.949079i | \(0.397983\pi\) | |||||||
\(450\) | 18.0583 | 0.851276 | ||||||||
\(451\) | 45.0803 | 2.12275 | ||||||||
\(452\) | −38.6061 | −1.81588 | ||||||||
\(453\) | −44.8576 | −2.10760 | ||||||||
\(454\) | 7.09305 | 0.332893 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −23.4759 | −1.09936 | ||||||||
\(457\) | −13.7798 | −0.644590 | −0.322295 | − | 0.946639i | \(-0.604454\pi\) | ||||
−0.322295 | + | 0.946639i | \(0.604454\pi\) | |||||||
\(458\) | −13.6822 | −0.639327 | ||||||||
\(459\) | −3.62953 | −0.169412 | ||||||||
\(460\) | −19.9681 | −0.931019 | ||||||||
\(461\) | −12.7671 | −0.594625 | −0.297313 | − | 0.954780i | \(-0.596090\pi\) | ||||
−0.297313 | + | 0.954780i | \(0.596090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.4272 | 1.50702 | 0.753510 | − | 0.657437i | \(-0.228359\pi\) | ||||
0.753510 | + | 0.657437i | \(0.228359\pi\) | |||||||
\(464\) | 0.970477 | 0.0450533 | ||||||||
\(465\) | 3.30996 | 0.153496 | ||||||||
\(466\) | −15.5025 | −0.718141 | ||||||||
\(467\) | 12.7508 | 0.590037 | 0.295018 | − | 0.955492i | \(-0.404674\pi\) | ||||
0.295018 | + | 0.955492i | \(0.404674\pi\) | |||||||
\(468\) | −163.544 | −7.55980 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.5586 | 0.625410 | ||||||||
\(471\) | 66.3139 | 3.05558 | ||||||||
\(472\) | −12.9569 | −0.596392 | ||||||||
\(473\) | −40.1100 | −1.84426 | ||||||||
\(474\) | −36.4345 | −1.67349 | ||||||||
\(475\) | 2.71231 | 0.124449 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.4740 | −1.62424 | ||||||||
\(478\) | −7.24938 | −0.331579 | ||||||||
\(479\) | −4.12861 | −0.188641 | −0.0943205 | − | 0.995542i | \(-0.530068\pi\) | ||||
−0.0943205 | + | 0.995542i | \(0.530068\pi\) | |||||||
\(480\) | 20.0807 | 0.916552 | ||||||||
\(481\) | 4.84421 | 0.220877 | ||||||||
\(482\) | 28.5988 | 1.30264 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.6307 | 1.80139 | ||||||||
\(485\) | 7.08455 | 0.321693 | ||||||||
\(486\) | −116.906 | −5.30294 | ||||||||
\(487\) | −13.9539 | −0.632310 | −0.316155 | − | 0.948708i | \(-0.602392\pi\) | ||||
−0.316155 | + | 0.948708i | \(0.602392\pi\) | |||||||
\(488\) | −37.3501 | −1.69076 | ||||||||
\(489\) | 3.87852 | 0.175393 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00929 | 0.361454 | 0.180727 | − | 0.983533i | \(-0.442155\pi\) | ||||
0.180727 | + | 0.983533i | \(0.442155\pi\) | |||||||
\(492\) | −96.8713 | −4.36729 | ||||||||
\(493\) | −0.582401 | −0.0262300 | ||||||||
\(494\) | −40.1498 | −1.80643 | ||||||||
\(495\) | 38.6273 | 1.73617 | ||||||||
\(496\) | 0.368699 | 0.0165551 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −44.6937 | −2.00277 | ||||||||
\(499\) | −8.50410 | −0.380696 | −0.190348 | − | 0.981717i | \(-0.560962\pi\) | ||||
−0.190348 | + | 0.981717i | \(0.560962\pi\) | |||||||
\(500\) | 3.15205 | 0.140964 | ||||||||
\(501\) | 53.5787 | 2.39372 | ||||||||
\(502\) | 22.5546 | 1.00666 | ||||||||
\(503\) | 33.2571 | 1.48286 | 0.741430 | − | 0.671030i | \(-0.234148\pi\) | ||||
0.741430 | + | 0.671030i | \(0.234148\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.88272 | −0.395276 | ||||||||
\(506\) | −69.8140 | −3.10361 | ||||||||
\(507\) | −97.7475 | −4.34112 | ||||||||
\(508\) | 4.97565 | 0.220759 | ||||||||
\(509\) | −33.9903 | −1.50659 | −0.753297 | − | 0.657680i | \(-0.771538\pi\) | ||||
−0.753297 | + | 0.657680i | \(0.771538\pi\) | |||||||
\(510\) | −1.66235 | −0.0736099 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.16504 | 0.184070 | ||||||||
\(513\) | −44.4919 | −1.96436 | ||||||||
\(514\) | −14.1297 | −0.623234 | ||||||||
\(515\) | 1.05449 | 0.0464663 | ||||||||
\(516\) | 86.1908 | 3.79434 | ||||||||
\(517\) | 29.0022 | 1.27552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.8159 | 1.04540 | ||||||||
\(520\) | −17.0535 | −0.747846 | ||||||||
\(521\) | −36.5661 | −1.60199 | −0.800995 | − | 0.598671i | \(-0.795696\pi\) | ||||
−0.800995 | + | 0.598671i | \(0.795696\pi\) | |||||||
\(522\) | −47.5324 | −2.08044 | ||||||||
\(523\) | −18.1021 | −0.791551 | −0.395776 | − | 0.918347i | \(-0.629524\pi\) | ||||
−0.395776 | + | 0.918347i | \(0.629524\pi\) | |||||||
\(524\) | −33.1687 | −1.44898 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.7496 | −0.468704 | ||||||||
\(527\) | −0.221263 | −0.00963836 | ||||||||
\(528\) | 5.92519 | 0.257861 | ||||||||
\(529\) | 17.1319 | 0.744867 | ||||||||
\(530\) | −10.1208 | −0.439618 | ||||||||
\(531\) | −39.4212 | −1.71073 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.5527 | −2.62283 | ||||||||
\(534\) | −25.0583 | −1.08438 | ||||||||
\(535\) | 8.87370 | 0.383644 | ||||||||
\(536\) | −16.2615 | −0.702391 | ||||||||
\(537\) | −64.2778 | −2.77379 | ||||||||
\(538\) | 21.1596 | 0.912254 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −51.7051 | −2.22504 | ||||||||
\(541\) | 3.88174 | 0.166889 | 0.0834446 | − | 0.996512i | \(-0.473408\pi\) | ||||
0.0834446 | + | 0.996512i | \(0.473408\pi\) | |||||||
\(542\) | −60.0528 | −2.57949 | ||||||||
\(543\) | 60.1304 | 2.58044 | ||||||||
\(544\) | −1.34234 | −0.0575525 | ||||||||
\(545\) | 1.81005 | 0.0775338 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0385 | 0.557485 | 0.278742 | − | 0.960366i | \(-0.410082\pi\) | ||||
0.278742 | + | 0.960366i | \(0.410082\pi\) | |||||||
\(548\) | 28.1588 | 1.20289 | ||||||||
\(549\) | −113.637 | −4.84989 | ||||||||
\(550\) | 11.0204 | 0.469911 | ||||||||
\(551\) | −7.13925 | −0.304142 | ||||||||
\(552\) | 54.8312 | 2.33377 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.86187 | 0.418991 | ||||||||
\(555\) | 2.45862 | 0.104363 | ||||||||
\(556\) | 1.14157 | 0.0484134 | ||||||||
\(557\) | 19.8954 | 0.842995 | 0.421498 | − | 0.906830i | \(-0.361505\pi\) | ||||
0.421498 | + | 0.906830i | \(0.361505\pi\) | |||||||
\(558\) | −18.0583 | −0.764468 | ||||||||
\(559\) | 53.8765 | 2.27873 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.55581 | −0.150127 | ||||||||
\(562\) | −67.5192 | −2.84813 | ||||||||
\(563\) | 10.6555 | 0.449076 | 0.224538 | − | 0.974465i | \(-0.427913\pi\) | ||||
0.224538 | + | 0.974465i | \(0.427913\pi\) | |||||||
\(564\) | −62.3218 | −2.62422 | ||||||||
\(565\) | −12.2479 | −0.515275 | ||||||||
\(566\) | 64.8973 | 2.72784 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.24377 | −0.220024 | ||||||||
\(569\) | 20.1534 | 0.844874 | 0.422437 | − | 0.906392i | \(-0.361175\pi\) | ||||
0.422437 | + | 0.906392i | \(0.361175\pi\) | |||||||
\(570\) | −20.3776 | −0.853522 | ||||||||
\(571\) | 9.74096 | 0.407646 | 0.203823 | − | 0.979008i | \(-0.434663\pi\) | ||||
0.203823 | + | 0.979008i | \(0.434663\pi\) | |||||||
\(572\) | −99.8054 | −4.17308 | ||||||||
\(573\) | 88.5423 | 3.69891 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.33498 | −0.264187 | ||||||||
\(576\) | −103.688 | −4.32034 | ||||||||
\(577\) | 8.95924 | 0.372978 | 0.186489 | − | 0.982457i | \(-0.440289\pi\) | ||||
0.186489 | + | 0.982457i | \(0.440289\pi\) | |||||||
\(578\) | −38.4757 | −1.60038 | ||||||||
\(579\) | 41.7017 | 1.73306 | ||||||||
\(580\) | −8.29671 | −0.344502 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −53.2261 | −2.20629 | ||||||||
\(583\) | −21.6486 | −0.896595 | ||||||||
\(584\) | 8.58414 | 0.355214 | ||||||||
\(585\) | −51.8849 | −2.14518 | ||||||||
\(586\) | 11.4936 | 0.474797 | ||||||||
\(587\) | −15.9725 | −0.659255 | −0.329627 | − | 0.944111i | \(-0.606923\pi\) | ||||
−0.329627 | + | 0.944111i | \(0.606923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.71231 | −0.111759 | ||||||||
\(590\) | −11.2469 | −0.463028 | ||||||||
\(591\) | 58.1163 | 2.39059 | ||||||||
\(592\) | 0.273868 | 0.0112559 | ||||||||
\(593\) | 29.2134 | 1.19965 | 0.599826 | − | 0.800131i | \(-0.295237\pi\) | ||||
0.599826 | + | 0.800131i | \(0.295237\pi\) | |||||||
\(594\) | −180.775 | −7.41729 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −45.4365 | −1.86115 | ||||||||
\(597\) | 67.1395 | 2.74784 | ||||||||
\(598\) | 93.7755 | 3.83476 | ||||||||
\(599\) | 15.9622 | 0.652199 | 0.326100 | − | 0.945335i | \(-0.394266\pi\) | ||||
0.326100 | + | 0.945335i | \(0.394266\pi\) | |||||||
\(600\) | −8.65531 | −0.353352 | ||||||||
\(601\) | 10.6357 | 0.433839 | 0.216920 | − | 0.976189i | \(-0.430399\pi\) | ||||
0.216920 | + | 0.976189i | \(0.430399\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −49.4753 | −2.01479 | ||||||||
\(604\) | 42.7175 | 1.73815 | ||||||||
\(605\) | 12.5730 | 0.511165 | ||||||||
\(606\) | 66.7358 | 2.71096 | ||||||||
\(607\) | 46.1383 | 1.87269 | 0.936347 | − | 0.351076i | \(-0.114184\pi\) | ||||
0.936347 | + | 0.351076i | \(0.114184\pi\) | |||||||
\(608\) | −16.4549 | −0.667333 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.4206 | −1.31267 | ||||||||
\(611\) | −38.9564 | −1.57601 | ||||||||
\(612\) | 5.54866 | 0.224291 | ||||||||
\(613\) | 30.6510 | 1.23798 | 0.618992 | − | 0.785398i | \(-0.287542\pi\) | ||||
0.618992 | + | 0.785398i | \(0.287542\pi\) | |||||||
\(614\) | 31.3184 | 1.26391 | ||||||||
\(615\) | −30.7328 | −1.23927 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.2647 | −0.815827 | −0.407913 | − | 0.913021i | \(-0.633743\pi\) | ||||
−0.407913 | + | 0.913021i | \(0.633743\pi\) | |||||||
\(618\) | −7.92236 | −0.318684 | ||||||||
\(619\) | 44.7318 | 1.79792 | 0.898962 | − | 0.438027i | \(-0.144322\pi\) | ||||
0.898962 | + | 0.438027i | \(0.144322\pi\) | |||||||
\(620\) | −3.15205 | −0.126589 | ||||||||
\(621\) | 103.917 | 4.17004 | ||||||||
\(622\) | −34.1948 | −1.37109 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.95883 | −0.318608 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −26.6521 | −1.06523 | ||||||||
\(627\) | −43.5883 | −1.74075 | ||||||||
\(628\) | −63.1501 | −2.51996 | ||||||||
\(629\) | −0.164353 | −0.00655318 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.0465 | −0.559180 | −0.279590 | − | 0.960119i | \(-0.590199\pi\) | ||||
−0.279590 | + | 0.960119i | \(0.590199\pi\) | |||||||
\(632\) | 12.6812 | 0.504430 | ||||||||
\(633\) | 34.2006 | 1.35935 | ||||||||
\(634\) | 29.0164 | 1.15239 | ||||||||
\(635\) | 1.57855 | 0.0626427 | ||||||||
\(636\) | 46.5199 | 1.84463 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29.0075 | −1.14842 | ||||||||
\(639\) | −15.9540 | −0.631132 | ||||||||
\(640\) | −17.4489 | −0.689727 | ||||||||
\(641\) | 11.6087 | 0.458515 | 0.229257 | − | 0.973366i | \(-0.426370\pi\) | ||||
0.229257 | + | 0.973366i | \(0.426370\pi\) | |||||||
\(642\) | −66.6681 | −2.63118 | ||||||||
\(643\) | −0.937030 | −0.0369529 | −0.0184764 | − | 0.999829i | \(-0.505882\pi\) | ||||
−0.0184764 | + | 0.999829i | \(0.505882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.3444 | 1.07668 | ||||||||
\(646\) | 1.36219 | 0.0535947 | ||||||||
\(647\) | 31.4041 | 1.23462 | 0.617312 | − | 0.786718i | \(-0.288222\pi\) | ||||
0.617312 | + | 0.786718i | \(0.288222\pi\) | |||||||
\(648\) | 79.5670 | 3.12569 | ||||||||
\(649\) | −24.0575 | −0.944339 | ||||||||
\(650\) | −14.8028 | −0.580614 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.69348 | −0.144648 | ||||||||
\(653\) | −20.8217 | −0.814814 | −0.407407 | − | 0.913247i | \(-0.633567\pi\) | ||||
−0.407407 | + | 0.913247i | \(0.633567\pi\) | |||||||
\(654\) | −13.5989 | −0.531757 | ||||||||
\(655\) | −10.5229 | −0.411164 | ||||||||
\(656\) | −3.42335 | −0.133659 | ||||||||
\(657\) | 26.1170 | 1.01892 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.7895 | −1.04357 | −0.521786 | − | 0.853077i | \(-0.674734\pi\) | ||||
−0.521786 | + | 0.853077i | \(0.674734\pi\) | |||||||
\(660\) | −50.6551 | −1.97175 | ||||||||
\(661\) | 45.5474 | 1.77159 | 0.885794 | − | 0.464078i | \(-0.153614\pi\) | ||||
0.885794 | + | 0.464078i | \(0.153614\pi\) | |||||||
\(662\) | −5.26530 | −0.204642 | ||||||||
\(663\) | 4.77624 | 0.185494 | ||||||||
\(664\) | 15.5558 | 0.603682 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.4136 | −0.519766 | ||||||||
\(667\) | 16.6747 | 0.645648 | ||||||||
\(668\) | −51.0225 | −1.97412 | ||||||||
\(669\) | −96.8991 | −3.74634 | ||||||||
\(670\) | −14.1154 | −0.545324 | ||||||||
\(671\) | −69.3488 | −2.67718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7733 | 0.877847 | 0.438923 | − | 0.898525i | \(-0.355360\pi\) | ||||
0.438923 | + | 0.898525i | \(0.355360\pi\) | |||||||
\(674\) | 39.5658 | 1.52402 | ||||||||
\(675\) | −16.4037 | −0.631378 | ||||||||
\(676\) | 93.0840 | 3.58015 | ||||||||
\(677\) | 21.1995 | 0.814762 | 0.407381 | − | 0.913258i | \(-0.366442\pi\) | ||||
0.407381 | + | 0.913258i | \(0.366442\pi\) | |||||||
\(678\) | 92.0186 | 3.53395 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.578586 | 0.0221878 | ||||||||
\(681\) | −10.3435 | −0.396362 | ||||||||
\(682\) | −11.0204 | −0.421993 | ||||||||
\(683\) | 33.3840 | 1.27740 | 0.638701 | − | 0.769455i | \(-0.279472\pi\) | ||||
0.638701 | + | 0.769455i | \(0.279472\pi\) | |||||||
\(684\) | 68.0172 | 2.60070 | ||||||||
\(685\) | 8.93351 | 0.341332 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.9521 | 0.761221 | ||||||||
\(688\) | 3.04591 | 0.116124 | ||||||||
\(689\) | 29.0789 | 1.10782 | ||||||||
\(690\) | 47.5946 | 1.81190 | ||||||||
\(691\) | 12.0197 | 0.457251 | 0.228626 | − | 0.973514i | \(-0.426577\pi\) | ||||
0.228626 | + | 0.973514i | \(0.426577\pi\) | |||||||
\(692\) | −22.6796 | −0.862149 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −52.2737 | −1.98428 | ||||||||
\(695\) | 0.362168 | 0.0137378 | ||||||||
\(696\) | 22.7822 | 0.863558 | ||||||||
\(697\) | 2.05441 | 0.0778165 | ||||||||
\(698\) | −12.3763 | −0.468449 | ||||||||
\(699\) | 22.6066 | 0.855061 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.66738 | −0.289593 | −0.144796 | − | 0.989461i | \(-0.546253\pi\) | ||||
−0.144796 | + | 0.989461i | \(0.546253\pi\) | |||||||
\(702\) | 242.821 | 9.16467 | ||||||||
\(703\) | −2.01469 | −0.0759855 | ||||||||
\(704\) | −63.2776 | −2.38486 | ||||||||
\(705\) | −19.7718 | −0.744651 | ||||||||
\(706\) | −12.4242 | −0.467590 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 51.6962 | 1.94286 | ||||||||
\(709\) | −26.8786 | −1.00945 | −0.504724 | − | 0.863281i | \(-0.668406\pi\) | ||||
−0.504724 | + | 0.863281i | \(0.668406\pi\) | |||||||
\(710\) | −4.55170 | −0.170822 | ||||||||
\(711\) | 38.5821 | 1.44694 | ||||||||
\(712\) | 8.72166 | 0.326858 | ||||||||
\(713\) | 6.33498 | 0.237247 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.6637 | −1.18416 | ||||||||
\(716\) | 61.2111 | 2.28757 | ||||||||
\(717\) | 10.5714 | 0.394798 | ||||||||
\(718\) | 24.8741 | 0.928295 | ||||||||
\(719\) | −12.3107 | −0.459111 | −0.229555 | − | 0.973296i | \(-0.573727\pi\) | ||||
−0.229555 | + | 0.973296i | \(0.573727\pi\) | |||||||
\(720\) | −2.93331 | −0.109318 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −26.4283 | −0.983558 | ||||||||
\(723\) | −41.7043 | −1.55100 | ||||||||
\(724\) | −57.2616 | −2.12811 | ||||||||
\(725\) | −2.63217 | −0.0977562 | ||||||||
\(726\) | −94.4609 | −3.50577 | ||||||||
\(727\) | 44.7359 | 1.65916 | 0.829582 | − | 0.558386i | \(-0.188579\pi\) | ||||
0.829582 | + | 0.558386i | \(0.188579\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 79.1940 | 2.93311 | ||||||||
\(730\) | 7.45122 | 0.275782 | ||||||||
\(731\) | −1.82791 | −0.0676075 | ||||||||
\(732\) | 149.021 | 5.50797 | ||||||||
\(733\) | −12.1879 | −0.450170 | −0.225085 | − | 0.974339i | \(-0.572266\pi\) | ||||
−0.225085 | + | 0.974339i | \(0.572266\pi\) | |||||||
\(734\) | −61.4179 | −2.26698 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.4326 | 1.41664 | ||||||||
\(737\) | −30.1932 | −1.11218 | ||||||||
\(738\) | 167.670 | 6.17203 | ||||||||
\(739\) | 24.7887 | 0.911869 | 0.455934 | − | 0.890013i | \(-0.349305\pi\) | ||||
0.455934 | + | 0.890013i | \(0.349305\pi\) | |||||||
\(740\) | −2.34132 | −0.0860688 | ||||||||
\(741\) | 58.5486 | 2.15084 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.77641 | −0.101857 | −0.0509284 | − | 0.998702i | \(-0.516218\pi\) | ||||
−0.0509284 | + | 0.998702i | \(0.516218\pi\) | |||||||
\(744\) | 8.65531 | 0.317319 | ||||||||
\(745\) | −14.4149 | −0.528122 | ||||||||
\(746\) | −19.8099 | −0.725293 | ||||||||
\(747\) | 47.3282 | 1.73165 | ||||||||
\(748\) | 3.38617 | 0.123811 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.51299 | −0.274336 | ||||||||
\(751\) | −32.9375 | −1.20191 | −0.600953 | − | 0.799284i | \(-0.705212\pi\) | ||||
−0.600953 | + | 0.799284i | \(0.705212\pi\) | |||||||
\(752\) | −2.20240 | −0.0803133 | ||||||||
\(753\) | −32.8904 | −1.19859 | ||||||||
\(754\) | 38.9635 | 1.41897 | ||||||||
\(755\) | 13.5523 | 0.493219 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.3710 | 1.35827 | 0.679137 | − | 0.734012i | \(-0.262354\pi\) | ||||
0.679137 | + | 0.734012i | \(0.262354\pi\) | |||||||
\(758\) | −36.9674 | −1.34272 | ||||||||
\(759\) | 101.807 | 3.69534 | ||||||||
\(760\) | 7.09249 | 0.257272 | ||||||||
\(761\) | −33.3562 | −1.20916 | −0.604581 | − | 0.796543i | \(-0.706660\pi\) | ||||
−0.604581 | + | 0.796543i | \(0.706660\pi\) | |||||||
\(762\) | −11.8596 | −0.429628 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −84.3180 | −3.05052 | ||||||||
\(765\) | 1.76033 | 0.0636450 | ||||||||
\(766\) | 40.3909 | 1.45938 | ||||||||
\(767\) | 32.3145 | 1.16681 | ||||||||
\(768\) | 44.8161 | 1.61716 | ||||||||
\(769\) | 19.0794 | 0.688022 | 0.344011 | − | 0.938966i | \(-0.388214\pi\) | ||||
0.344011 | + | 0.938966i | \(0.388214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.6047 | 0.742059 | ||||||||
\(772\) | −39.7121 | −1.42927 | ||||||||
\(773\) | 17.7851 | 0.639686 | 0.319843 | − | 0.947471i | \(-0.396370\pi\) | ||||
0.319843 | + | 0.947471i | \(0.396370\pi\) | |||||||
\(774\) | −149.184 | −5.36230 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 18.5256 | 0.665029 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −60.7129 | −2.17666 | ||||||||
\(779\) | 25.1837 | 0.902298 | ||||||||
\(780\) | 68.0409 | 2.43625 | ||||||||
\(781\) | −9.73624 | −0.348390 | ||||||||
\(782\) | −3.18159 | −0.113773 | ||||||||
\(783\) | 43.1772 | 1.54303 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0346 | −0.715067 | ||||||||
\(786\) | 79.0584 | 2.81992 | ||||||||
\(787\) | 52.5927 | 1.87473 | 0.937363 | − | 0.348353i | \(-0.113259\pi\) | ||||
0.937363 | + | 0.348353i | \(0.113259\pi\) | |||||||
\(788\) | −55.3436 | −1.97154 | ||||||||
\(789\) | 15.6756 | 0.558067 | ||||||||
\(790\) | 11.0075 | 0.391630 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 101.008 | 3.58915 | ||||||||
\(793\) | 93.1507 | 3.30788 | ||||||||
\(794\) | −38.6435 | −1.37141 | ||||||||
\(795\) | 14.7586 | 0.523435 | ||||||||
\(796\) | −63.9363 | −2.26616 | ||||||||
\(797\) | −47.0498 | −1.66659 | −0.833295 | − | 0.552828i | \(-0.813548\pi\) | ||||
−0.833295 | + | 0.552828i | \(0.813548\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.32170 | 0.0467584 | ||||||||
\(800\) | −6.06673 | −0.214491 | ||||||||
\(801\) | 26.5354 | 0.937583 | ||||||||
\(802\) | 17.8953 | 0.631905 | ||||||||
\(803\) | 15.9384 | 0.562454 | ||||||||
\(804\) | 64.8810 | 2.28818 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.8028 | 0.521407 | ||||||||
\(807\) | −30.8560 | −1.08618 | ||||||||
\(808\) | −23.2277 | −0.817146 | ||||||||
\(809\) | 33.8768 | 1.19104 | 0.595522 | − | 0.803339i | \(-0.296945\pi\) | ||||
0.595522 | + | 0.803339i | \(0.296945\pi\) | |||||||
\(810\) | 69.0658 | 2.42673 | ||||||||
\(811\) | 20.0237 | 0.703127 | 0.351564 | − | 0.936164i | \(-0.385650\pi\) | ||||
0.351564 | + | 0.936164i | \(0.385650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 87.5722 | 3.07129 | ||||||||
\(814\) | −8.18589 | −0.286915 | ||||||||
\(815\) | −1.17177 | −0.0410454 | ||||||||
\(816\) | 0.270025 | 0.00945276 | ||||||||
\(817\) | −22.4070 | −0.783923 | ||||||||
\(818\) | −42.3479 | −1.48066 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29.2666 | 1.02203 | ||||||||
\(821\) | −19.2432 | −0.671594 | −0.335797 | − | 0.941934i | \(-0.609006\pi\) | ||||
−0.335797 | + | 0.941934i | \(0.609006\pi\) | |||||||
\(822\) | −67.1174 | −2.34099 | ||||||||
\(823\) | 25.7054 | 0.896035 | 0.448017 | − | 0.894025i | \(-0.352130\pi\) | ||||
0.448017 | + | 0.894025i | \(0.352130\pi\) | |||||||
\(824\) | 2.75741 | 0.0960589 | ||||||||
\(825\) | −16.0705 | −0.559504 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.9408 | 1.00637 | 0.503186 | − | 0.864178i | \(-0.332161\pi\) | ||||
0.503186 | + | 0.864178i | \(0.332161\pi\) | |||||||
\(828\) | −158.864 | −5.52089 | ||||||||
\(829\) | −44.9817 | −1.56228 | −0.781140 | − | 0.624356i | \(-0.785361\pi\) | ||||
−0.781140 | + | 0.624356i | \(0.785361\pi\) | |||||||
\(830\) | 13.5028 | 0.468688 | ||||||||
\(831\) | −14.3811 | −0.498875 | ||||||||
\(832\) | 84.9957 | 2.94669 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.72097 | −0.0942194 | ||||||||
\(835\) | −16.1871 | −0.560177 | ||||||||
\(836\) | 41.5087 | 1.43561 | ||||||||
\(837\) | 16.4037 | 0.566994 | ||||||||
\(838\) | −27.6613 | −0.955542 | ||||||||
\(839\) | 24.4461 | 0.843971 | 0.421986 | − | 0.906602i | \(-0.361333\pi\) | ||||
0.421986 | + | 0.906602i | \(0.361333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0717 | −0.761093 | ||||||||
\(842\) | 90.4716 | 3.11786 | ||||||||
\(843\) | 98.4601 | 3.39115 | ||||||||
\(844\) | −32.5689 | −1.12107 | ||||||||
\(845\) | 29.5313 | 1.01591 | ||||||||
\(846\) | 107.870 | 3.70865 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.64397 | 0.0564543 | ||||||||
\(849\) | −94.6367 | −3.24792 | ||||||||
\(850\) | 0.502225 | 0.0172262 | ||||||||
\(851\) | 4.70559 | 0.161305 | ||||||||
\(852\) | 20.9218 | 0.716770 | ||||||||
\(853\) | 1.57093 | 0.0537877 | 0.0268939 | − | 0.999638i | \(-0.491438\pi\) | ||||
0.0268939 | + | 0.999638i | \(0.491438\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.5787 | 0.737977 | ||||||||
\(856\) | 23.2041 | 0.793100 | ||||||||
\(857\) | −0.0229703 | −0.000784650 0 | −0.000392325 | − | 1.00000i | \(-0.500125\pi\) | ||||
−0.000392325 | 1.00000i | \(0.500125\pi\) | ||||||||
\(858\) | 237.889 | 8.12140 | ||||||||
\(859\) | −36.1735 | −1.23422 | −0.617111 | − | 0.786876i | \(-0.711697\pi\) | ||||
−0.617111 | + | 0.786876i | \(0.711697\pi\) | |||||||
\(860\) | −26.0398 | −0.887950 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.8638 | 1.05122 | ||||||||
\(863\) | −14.1974 | −0.483286 | −0.241643 | − | 0.970365i | \(-0.577686\pi\) | ||||
−0.241643 | + | 0.970365i | \(0.577686\pi\) | |||||||
\(864\) | 99.5167 | 3.38563 | ||||||||
\(865\) | −7.19520 | −0.244644 | ||||||||
\(866\) | −18.2750 | −0.621010 | ||||||||
\(867\) | 56.1073 | 1.90550 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.5454 | 0.798725 | ||||||||
\(870\) | 19.7754 | 0.670450 | ||||||||
\(871\) | 40.5561 | 1.37419 | ||||||||
\(872\) | 4.73314 | 0.160284 | ||||||||
\(873\) | 56.3636 | 1.90762 | ||||||||
\(874\) | −39.0009 | −1.31922 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −34.2494 | −1.15718 | ||||||||
\(877\) | −2.21747 | −0.0748787 | −0.0374393 | − | 0.999299i | \(-0.511920\pi\) | ||||
−0.0374393 | + | 0.999299i | \(0.511920\pi\) | |||||||
\(878\) | −7.91578 | −0.267145 | ||||||||
\(879\) | −16.7606 | −0.565322 | ||||||||
\(880\) | −1.79011 | −0.0603446 | ||||||||
\(881\) | −34.8836 | −1.17526 | −0.587629 | − | 0.809131i | \(-0.699938\pi\) | ||||
−0.587629 | + | 0.809131i | \(0.699938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.0834 | −0.608556 | −0.304278 | − | 0.952583i | \(-0.598415\pi\) | ||||
−0.304278 | + | 0.952583i | \(0.598415\pi\) | |||||||
\(884\) | −4.54837 | −0.152978 | ||||||||
\(885\) | 16.4008 | 0.551308 | ||||||||
\(886\) | −57.2668 | −1.92391 | ||||||||
\(887\) | −45.2723 | −1.52009 | −0.760047 | − | 0.649868i | \(-0.774824\pi\) | ||||
−0.760047 | + | 0.649868i | \(0.774824\pi\) | |||||||
\(888\) | 6.42912 | 0.215747 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.57058 | 0.253766 | ||||||||
\(891\) | 147.734 | 4.94928 | ||||||||
\(892\) | 92.2761 | 3.08963 | ||||||||
\(893\) | 16.2018 | 0.542173 | ||||||||
\(894\) | 108.299 | 3.62207 | ||||||||
\(895\) | 19.4195 | 0.649122 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −136.748 | −4.56590 | ||||||||
\(898\) | 30.3043 | 1.01127 | ||||||||
\(899\) | 2.63217 | 0.0877877 | ||||||||
\(900\) | 25.0772 | 0.835907 | ||||||||
\(901\) | −0.986579 | −0.0328677 | ||||||||
\(902\) | 102.324 | 3.40701 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.0275 | −1.06522 | ||||||||
\(905\) | −18.1665 | −0.603874 | ||||||||
\(906\) | −101.818 | −3.38269 | ||||||||
\(907\) | 35.5609 | 1.18078 | 0.590390 | − | 0.807118i | \(-0.298974\pi\) | ||||
0.590390 | + | 0.807118i | \(0.298974\pi\) | |||||||
\(908\) | 9.84998 | 0.326883 | ||||||||
\(909\) | −70.6696 | −2.34396 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.54849 | −0.0844352 | −0.0422176 | − | 0.999108i | \(-0.513442\pi\) | ||||
−0.0422176 | + | 0.999108i | \(0.513442\pi\) | |||||||
\(912\) | 3.31005 | 0.109607 | ||||||||
\(913\) | 28.8829 | 0.955884 | ||||||||
\(914\) | −31.2775 | −1.03457 | ||||||||
\(915\) | 47.2775 | 1.56295 | ||||||||
\(916\) | −19.0002 | −0.627785 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.23834 | −0.271906 | ||||||||
\(919\) | −45.0193 | −1.48505 | −0.742525 | − | 0.669818i | \(-0.766372\pi\) | ||||
−0.742525 | + | 0.669818i | \(0.766372\pi\) | |||||||
\(920\) | −16.5655 | −0.546148 | ||||||||
\(921\) | −45.6702 | −1.50488 | ||||||||
\(922\) | −28.9790 | −0.954373 | ||||||||
\(923\) | 13.0779 | 0.430465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.742795 | −0.0244229 | ||||||||
\(926\) | 73.6036 | 2.41877 | ||||||||
\(927\) | 8.38935 | 0.275542 | ||||||||
\(928\) | 15.9686 | 0.524197 | ||||||||
\(929\) | 25.9964 | 0.852913 | 0.426456 | − | 0.904508i | \(-0.359762\pi\) | ||||
0.426456 | + | 0.904508i | \(0.359762\pi\) | |||||||
\(930\) | 7.51299 | 0.246361 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.5281 | −0.705176 | ||||||||
\(933\) | 49.8648 | 1.63250 | ||||||||
\(934\) | 28.9419 | 0.947009 | ||||||||
\(935\) | 1.07428 | 0.0351326 | ||||||||
\(936\) | −135.675 | −4.43468 | ||||||||
\(937\) | −0.921896 | −0.0301170 | −0.0150585 | − | 0.999887i | \(-0.504793\pi\) | ||||
−0.0150585 | + | 0.999887i | \(0.504793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.8655 | 1.26833 | ||||||||
\(940\) | 18.8285 | 0.614119 | ||||||||
\(941\) | 18.4720 | 0.602170 | 0.301085 | − | 0.953597i | \(-0.402651\pi\) | ||||
0.301085 | + | 0.953597i | \(0.402651\pi\) | |||||||
\(942\) | 150.520 | 4.90421 | ||||||||
\(943\) | −58.8199 | −1.91544 | ||||||||
\(944\) | 1.82690 | 0.0594606 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −91.0421 | −2.96004 | ||||||||
\(947\) | 53.8622 | 1.75029 | 0.875143 | − | 0.483864i | \(-0.160767\pi\) | ||||
0.875143 | + | 0.483864i | \(0.160767\pi\) | |||||||
\(948\) | −50.5959 | −1.64328 | ||||||||
\(949\) | −21.4088 | −0.694958 | ||||||||
\(950\) | 6.15643 | 0.199741 | ||||||||
\(951\) | −42.3134 | −1.37210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.5163 | −1.37724 | −0.688620 | − | 0.725123i | \(-0.741783\pi\) | ||||
−0.688620 | + | 0.725123i | \(0.741783\pi\) | |||||||
\(954\) | −80.5192 | −2.60691 | ||||||||
\(955\) | −26.7503 | −0.865618 | ||||||||
\(956\) | −10.0671 | −0.325593 | ||||||||
\(957\) | 42.3003 | 1.36738 | ||||||||
\(958\) | −9.37117 | −0.302769 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 43.1385 | 1.39229 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 10.9954 | 0.354508 | ||||||||
\(963\) | 70.5979 | 2.27498 | ||||||||
\(964\) | 39.7146 | 1.27912 | ||||||||
\(965\) | −12.5988 | −0.405571 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0210 | 0.901096 | 0.450548 | − | 0.892752i | \(-0.351229\pi\) | ||||
0.450548 | + | 0.892752i | \(0.351229\pi\) | |||||||
\(968\) | 32.8775 | 1.05672 | ||||||||
\(969\) | −1.98642 | −0.0638130 | ||||||||
\(970\) | 16.0806 | 0.516317 | ||||||||
\(971\) | 49.7618 | 1.59693 | 0.798466 | − | 0.602040i | \(-0.205645\pi\) | ||||
0.798466 | + | 0.602040i | \(0.205645\pi\) | |||||||
\(972\) | −162.345 | −5.20721 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.6727 | −1.01486 | ||||||||
\(975\) | 21.5863 | 0.691313 | ||||||||
\(976\) | 5.26628 | 0.168569 | ||||||||
\(977\) | 44.8962 | 1.43636 | 0.718179 | − | 0.695859i | \(-0.244976\pi\) | ||||
0.718179 | + | 0.695859i | \(0.244976\pi\) | |||||||
\(978\) | 8.80351 | 0.281505 | ||||||||
\(979\) | 16.1937 | 0.517554 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4005 | 0.459771 | ||||||||
\(982\) | 18.1796 | 0.580134 | ||||||||
\(983\) | −46.2226 | −1.47427 | −0.737136 | − | 0.675745i | \(-0.763822\pi\) | ||||
−0.737136 | + | 0.675745i | \(0.763822\pi\) | |||||||
\(984\) | −80.3641 | −2.56191 | ||||||||
\(985\) | −17.5580 | −0.559445 | ||||||||
\(986\) | −1.32194 | −0.0420992 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −55.7553 | −1.77381 | ||||||||
\(989\) | 52.3348 | 1.66415 | ||||||||
\(990\) | 87.6766 | 2.78655 | ||||||||
\(991\) | 49.0442 | 1.55794 | 0.778971 | − | 0.627060i | \(-0.215742\pi\) | ||||
0.778971 | + | 0.627060i | \(0.215742\pi\) | |||||||
\(992\) | 6.06673 | 0.192619 | ||||||||
\(993\) | 7.67815 | 0.243659 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.2841 | −0.643048 | ||||||||
\(996\) | −62.0653 | −1.96661 | ||||||||
\(997\) | −25.3966 | −0.804319 | −0.402160 | − | 0.915570i | \(-0.631740\pi\) | ||||
−0.402160 | + | 0.915570i | \(0.631740\pi\) | |||||||
\(998\) | −19.3027 | −0.611016 | ||||||||
\(999\) | 12.1846 | 0.385503 |
(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 | 7595.2.a.bf.1.20 | 21 | ||
7.3 | odd | 6 | 1085.2.j.d.156.2 | ✓ | 42 | ||
7.5 | odd | 6 | 1085.2.j.d.466.2 | yes | 42 | ||
7.6 | odd | 2 | 7595.2.a.bg.1.20 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1085.2.j.d.156.2 | ✓ | 42 | 7.3 | odd | 6 | ||
1085.2.j.d.466.2 | yes | 42 | 7.5 | odd | 6 | ||
7595.2.a.bf.1.20 | 21 | 1.1 | even | 1 | trivial | ||
7595.2.a.bg.1.20 | 21 | 7.6 | odd | 2 |