Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71128 | −1.91716 | −0.958581 | − | 0.284821i | \(-0.908066\pi\) | ||||
−0.958581 | + | 0.284821i | \(0.908066\pi\) | |||||||
\(3\) | −2.26408 | −1.30717 | −0.653585 | − | 0.756853i | \(-0.726736\pi\) | ||||
−0.653585 | + | 0.756853i | \(0.726736\pi\) | |||||||
\(4\) | 5.35102 | 2.67551 | ||||||||
\(5\) | 1.45359 | 0.650064 | 0.325032 | − | 0.945703i | \(-0.394625\pi\) | ||||
0.325032 | + | 0.945703i | \(0.394625\pi\) | |||||||
\(6\) | 6.13856 | 2.50606 | ||||||||
\(7\) | 1.50475 | 0.568742 | 0.284371 | − | 0.958714i | \(-0.408215\pi\) | ||||
0.284371 | + | 0.958714i | \(0.408215\pi\) | |||||||
\(8\) | −9.08554 | −3.21222 | ||||||||
\(9\) | 2.12608 | 0.708692 | ||||||||
\(10\) | −3.94108 | −1.24628 | ||||||||
\(11\) | −4.35926 | −1.31437 | −0.657183 | − | 0.753731i | \(-0.728252\pi\) | ||||
−0.657183 | + | 0.753731i | \(0.728252\pi\) | |||||||
\(12\) | −12.1152 | −3.49734 | ||||||||
\(13\) | 7.06108 | 1.95839 | 0.979195 | − | 0.202919i | \(-0.0650429\pi\) | ||||
0.979195 | + | 0.202919i | \(0.0650429\pi\) | |||||||
\(14\) | −4.07979 | −1.09037 | ||||||||
\(15\) | −3.29105 | −0.849744 | ||||||||
\(16\) | 13.9314 | 3.48284 | ||||||||
\(17\) | −0.709135 | −0.171990 | −0.0859952 | − | 0.996296i | \(-0.527407\pi\) | ||||
−0.0859952 | + | 0.996296i | \(0.527407\pi\) | |||||||
\(18\) | −5.76438 | −1.35868 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 7.77818 | 1.73925 | ||||||||
\(21\) | −3.40688 | −0.743442 | ||||||||
\(22\) | 11.8192 | 2.51985 | ||||||||
\(23\) | −7.80251 | −1.62694 | −0.813468 | − | 0.581610i | \(-0.802423\pi\) | ||||
−0.813468 | + | 0.581610i | \(0.802423\pi\) | |||||||
\(24\) | 20.5704 | 4.19892 | ||||||||
\(25\) | −2.88708 | −0.577416 | ||||||||
\(26\) | −19.1445 | −3.75455 | ||||||||
\(27\) | 1.97864 | 0.380789 | ||||||||
\(28\) | 8.05195 | 1.52167 | ||||||||
\(29\) | 3.97331 | 0.737825 | 0.368913 | − | 0.929464i | \(-0.379730\pi\) | ||||
0.368913 | + | 0.929464i | \(0.379730\pi\) | |||||||
\(30\) | 8.92293 | 1.62910 | ||||||||
\(31\) | 2.68767 | 0.482719 | 0.241360 | − | 0.970436i | \(-0.422407\pi\) | ||||
0.241360 | + | 0.970436i | \(0.422407\pi\) | |||||||
\(32\) | −19.6007 | −3.46494 | ||||||||
\(33\) | 9.86973 | 1.71810 | ||||||||
\(34\) | 1.92266 | 0.329733 | ||||||||
\(35\) | 2.18729 | 0.369719 | ||||||||
\(36\) | 11.3767 | 1.89611 | ||||||||
\(37\) | 6.42758 | 1.05669 | 0.528344 | − | 0.849031i | \(-0.322813\pi\) | ||||
0.528344 | + | 0.849031i | \(0.322813\pi\) | |||||||
\(38\) | 2.71128 | 0.439827 | ||||||||
\(39\) | −15.9869 | −2.55995 | ||||||||
\(40\) | −13.2066 | −2.08815 | ||||||||
\(41\) | 8.51698 | 1.33013 | 0.665065 | − | 0.746786i | \(-0.268404\pi\) | ||||
0.665065 | + | 0.746786i | \(0.268404\pi\) | |||||||
\(42\) | 9.23699 | 1.42530 | ||||||||
\(43\) | −1.51167 | −0.230527 | −0.115263 | − | 0.993335i | \(-0.536771\pi\) | ||||
−0.115263 | + | 0.993335i | \(0.536771\pi\) | |||||||
\(44\) | −23.3265 | −3.51660 | ||||||||
\(45\) | 3.09044 | 0.460696 | ||||||||
\(46\) | 21.1548 | 3.11910 | ||||||||
\(47\) | 1.38691 | 0.202302 | 0.101151 | − | 0.994871i | \(-0.467748\pi\) | ||||
0.101151 | + | 0.994871i | \(0.467748\pi\) | |||||||
\(48\) | −31.5418 | −4.55266 | ||||||||
\(49\) | −4.73573 | −0.676532 | ||||||||
\(50\) | 7.82768 | 1.10700 | ||||||||
\(51\) | 1.60554 | 0.224821 | ||||||||
\(52\) | 37.7840 | 5.23969 | ||||||||
\(53\) | −2.17715 | −0.299054 | −0.149527 | − | 0.988758i | \(-0.547775\pi\) | ||||
−0.149527 | + | 0.988758i | \(0.547775\pi\) | |||||||
\(54\) | −5.36463 | −0.730033 | ||||||||
\(55\) | −6.33657 | −0.854423 | ||||||||
\(56\) | −13.6715 | −1.82693 | ||||||||
\(57\) | 2.26408 | 0.299885 | ||||||||
\(58\) | −10.7727 | −1.41453 | ||||||||
\(59\) | −11.6081 | −1.51124 | −0.755622 | − | 0.655008i | \(-0.772665\pi\) | ||||
−0.755622 | + | 0.655008i | \(0.772665\pi\) | |||||||
\(60\) | −17.6104 | −2.27350 | ||||||||
\(61\) | −6.48946 | −0.830890 | −0.415445 | − | 0.909618i | \(-0.636374\pi\) | ||||
−0.415445 | + | 0.909618i | \(0.636374\pi\) | |||||||
\(62\) | −7.28701 | −0.925451 | ||||||||
\(63\) | 3.19921 | 0.403063 | ||||||||
\(64\) | 25.2802 | 3.16002 | ||||||||
\(65\) | 10.2639 | 1.27308 | ||||||||
\(66\) | −26.7596 | −3.29387 | ||||||||
\(67\) | −16.0232 | −1.95754 | −0.978772 | − | 0.204954i | \(-0.934296\pi\) | ||||
−0.978772 | + | 0.204954i | \(0.934296\pi\) | |||||||
\(68\) | −3.79459 | −0.460162 | ||||||||
\(69\) | 17.6655 | 2.12668 | ||||||||
\(70\) | −5.93034 | −0.708811 | ||||||||
\(71\) | −14.1590 | −1.68037 | −0.840183 | − | 0.542303i | \(-0.817553\pi\) | ||||
−0.840183 | + | 0.542303i | \(0.817553\pi\) | |||||||
\(72\) | −19.3165 | −2.27648 | ||||||||
\(73\) | 10.8240 | 1.26686 | 0.633429 | − | 0.773800i | \(-0.281647\pi\) | ||||
0.633429 | + | 0.773800i | \(0.281647\pi\) | |||||||
\(74\) | −17.4269 | −2.02584 | ||||||||
\(75\) | 6.53660 | 0.754781 | ||||||||
\(76\) | −5.35102 | −0.613804 | ||||||||
\(77\) | −6.55960 | −0.747535 | ||||||||
\(78\) | 43.3448 | 4.90784 | ||||||||
\(79\) | 12.7647 | 1.43614 | 0.718070 | − | 0.695971i | \(-0.245026\pi\) | ||||
0.718070 | + | 0.695971i | \(0.245026\pi\) | |||||||
\(80\) | 20.2505 | 2.26407 | ||||||||
\(81\) | −10.8580 | −1.20645 | ||||||||
\(82\) | −23.0919 | −2.55007 | ||||||||
\(83\) | 0.498380 | 0.0547044 | 0.0273522 | − | 0.999626i | \(-0.491292\pi\) | ||||
0.0273522 | + | 0.999626i | \(0.491292\pi\) | |||||||
\(84\) | −18.2303 | −1.98909 | ||||||||
\(85\) | −1.03079 | −0.111805 | ||||||||
\(86\) | 4.09854 | 0.441957 | ||||||||
\(87\) | −8.99591 | −0.964463 | ||||||||
\(88\) | 39.6062 | 4.22204 | ||||||||
\(89\) | −5.26848 | −0.558458 | −0.279229 | − | 0.960225i | \(-0.590079\pi\) | ||||
−0.279229 | + | 0.960225i | \(0.590079\pi\) | |||||||
\(90\) | −8.37904 | −0.883228 | ||||||||
\(91\) | 10.6252 | 1.11382 | ||||||||
\(92\) | −41.7514 | −4.35288 | ||||||||
\(93\) | −6.08511 | −0.630996 | ||||||||
\(94\) | −3.76030 | −0.387845 | ||||||||
\(95\) | −1.45359 | −0.149135 | ||||||||
\(96\) | 44.3776 | 4.52927 | ||||||||
\(97\) | −0.267800 | −0.0271909 | −0.0135955 | − | 0.999908i | \(-0.504328\pi\) | ||||
−0.0135955 | + | 0.999908i | \(0.504328\pi\) | |||||||
\(98\) | 12.8399 | 1.29702 | ||||||||
\(99\) | −9.26812 | −0.931481 | ||||||||
\(100\) | −15.4488 | −1.54488 | ||||||||
\(101\) | −4.31887 | −0.429744 | −0.214872 | − | 0.976642i | \(-0.568933\pi\) | ||||
−0.214872 | + | 0.976642i | \(0.568933\pi\) | |||||||
\(102\) | −4.35306 | −0.431018 | ||||||||
\(103\) | −8.64107 | −0.851430 | −0.425715 | − | 0.904857i | \(-0.639977\pi\) | ||||
−0.425715 | + | 0.904857i | \(0.639977\pi\) | |||||||
\(104\) | −64.1537 | −6.29079 | ||||||||
\(105\) | −4.95220 | −0.483285 | ||||||||
\(106\) | 5.90285 | 0.573336 | ||||||||
\(107\) | 12.4337 | 1.20202 | 0.601008 | − | 0.799243i | \(-0.294766\pi\) | ||||
0.601008 | + | 0.799243i | \(0.294766\pi\) | |||||||
\(108\) | 10.5877 | 1.01880 | ||||||||
\(109\) | −11.7454 | −1.12501 | −0.562504 | − | 0.826794i | \(-0.690162\pi\) | ||||
−0.562504 | + | 0.826794i | \(0.690162\pi\) | |||||||
\(110\) | 17.1802 | 1.63807 | ||||||||
\(111\) | −14.5526 | −1.38127 | ||||||||
\(112\) | 20.9632 | 1.98084 | ||||||||
\(113\) | 13.9902 | 1.31609 | 0.658045 | − | 0.752978i | \(-0.271383\pi\) | ||||
0.658045 | + | 0.752978i | \(0.271383\pi\) | |||||||
\(114\) | −6.13856 | −0.574929 | ||||||||
\(115\) | −11.3416 | −1.05761 | ||||||||
\(116\) | 21.2613 | 1.97406 | ||||||||
\(117\) | 15.0124 | 1.38790 | ||||||||
\(118\) | 31.4727 | 2.89730 | ||||||||
\(119\) | −1.06707 | −0.0978182 | ||||||||
\(120\) | 29.9009 | 2.72957 | ||||||||
\(121\) | 8.00315 | 0.727559 | ||||||||
\(122\) | 17.5947 | 1.59295 | ||||||||
\(123\) | −19.2832 | −1.73870 | ||||||||
\(124\) | 14.3818 | 1.29152 | ||||||||
\(125\) | −11.4646 | −1.02542 | ||||||||
\(126\) | −8.67395 | −0.772737 | ||||||||
\(127\) | −8.47754 | −0.752260 | −0.376130 | − | 0.926567i | \(-0.622745\pi\) | ||||
−0.376130 | + | 0.926567i | \(0.622745\pi\) | |||||||
\(128\) | −29.3401 | −2.59332 | ||||||||
\(129\) | 3.42254 | 0.301338 | ||||||||
\(130\) | −27.8283 | −2.44070 | ||||||||
\(131\) | −1.71162 | −0.149545 | −0.0747723 | − | 0.997201i | \(-0.523823\pi\) | ||||
−0.0747723 | + | 0.997201i | \(0.523823\pi\) | |||||||
\(132\) | 52.8131 | 4.59679 | ||||||||
\(133\) | −1.50475 | −0.130478 | ||||||||
\(134\) | 43.4433 | 3.75293 | ||||||||
\(135\) | 2.87612 | 0.247537 | ||||||||
\(136\) | 6.44287 | 0.552471 | ||||||||
\(137\) | 13.1571 | 1.12409 | 0.562045 | − | 0.827107i | \(-0.310015\pi\) | ||||
0.562045 | + | 0.827107i | \(0.310015\pi\) | |||||||
\(138\) | −47.8962 | −4.07719 | ||||||||
\(139\) | 5.33660 | 0.452645 | 0.226322 | − | 0.974052i | \(-0.427330\pi\) | ||||
0.226322 | + | 0.974052i | \(0.427330\pi\) | |||||||
\(140\) | 11.7042 | 0.989186 | ||||||||
\(141\) | −3.14008 | −0.264443 | ||||||||
\(142\) | 38.3890 | 3.22153 | ||||||||
\(143\) | −30.7811 | −2.57404 | ||||||||
\(144\) | 29.6191 | 2.46826 | ||||||||
\(145\) | 5.77556 | 0.479634 | ||||||||
\(146\) | −29.3470 | −2.42877 | ||||||||
\(147\) | 10.7221 | 0.884343 | ||||||||
\(148\) | 34.3941 | 2.82718 | ||||||||
\(149\) | −11.8692 | −0.972365 | −0.486182 | − | 0.873857i | \(-0.661611\pi\) | ||||
−0.486182 | + | 0.873857i | \(0.661611\pi\) | |||||||
\(150\) | −17.7225 | −1.44704 | ||||||||
\(151\) | −9.59642 | −0.780946 | −0.390473 | − | 0.920614i | \(-0.627688\pi\) | ||||
−0.390473 | + | 0.920614i | \(0.627688\pi\) | |||||||
\(152\) | 9.08554 | 0.736934 | ||||||||
\(153\) | −1.50768 | −0.121888 | ||||||||
\(154\) | 17.7849 | 1.43315 | ||||||||
\(155\) | 3.90676 | 0.313799 | ||||||||
\(156\) | −85.5461 | −6.84917 | ||||||||
\(157\) | −17.4949 | −1.39625 | −0.698124 | − | 0.715977i | \(-0.745982\pi\) | ||||
−0.698124 | + | 0.715977i | \(0.745982\pi\) | |||||||
\(158\) | −34.6086 | −2.75331 | ||||||||
\(159\) | 4.92925 | 0.390915 | ||||||||
\(160\) | −28.4913 | −2.25244 | ||||||||
\(161\) | −11.7408 | −0.925307 | ||||||||
\(162\) | 29.4391 | 2.31295 | ||||||||
\(163\) | 24.0810 | 1.88617 | 0.943085 | − | 0.332553i | \(-0.107910\pi\) | ||||
0.943085 | + | 0.332553i | \(0.107910\pi\) | |||||||
\(164\) | 45.5745 | 3.55877 | ||||||||
\(165\) | 14.3465 | 1.11688 | ||||||||
\(166\) | −1.35125 | −0.104877 | ||||||||
\(167\) | 23.7955 | 1.84135 | 0.920675 | − | 0.390331i | \(-0.127639\pi\) | ||||
0.920675 | + | 0.390331i | \(0.127639\pi\) | |||||||
\(168\) | 30.9533 | 2.38810 | ||||||||
\(169\) | 36.8588 | 2.83530 | ||||||||
\(170\) | 2.79476 | 0.214348 | ||||||||
\(171\) | −2.12608 | −0.162585 | ||||||||
\(172\) | −8.08895 | −0.616777 | ||||||||
\(173\) | 21.0239 | 1.59842 | 0.799210 | − | 0.601052i | \(-0.205252\pi\) | ||||
0.799210 | + | 0.601052i | \(0.205252\pi\) | |||||||
\(174\) | 24.3904 | 1.84903 | ||||||||
\(175\) | −4.34434 | −0.328401 | ||||||||
\(176\) | −60.7304 | −4.57773 | ||||||||
\(177\) | 26.2817 | 1.97545 | ||||||||
\(178\) | 14.2843 | 1.07065 | ||||||||
\(179\) | −5.09477 | −0.380801 | −0.190401 | − | 0.981706i | \(-0.560979\pi\) | ||||
−0.190401 | + | 0.981706i | \(0.560979\pi\) | |||||||
\(180\) | 16.5370 | 1.23260 | ||||||||
\(181\) | −6.76836 | −0.503088 | −0.251544 | − | 0.967846i | \(-0.580938\pi\) | ||||
−0.251544 | + | 0.967846i | \(0.580938\pi\) | |||||||
\(182\) | −28.8077 | −2.13537 | ||||||||
\(183\) | 14.6927 | 1.08611 | ||||||||
\(184\) | 70.8900 | 5.22608 | ||||||||
\(185\) | 9.34305 | 0.686915 | ||||||||
\(186\) | 16.4984 | 1.20972 | ||||||||
\(187\) | 3.09130 | 0.226058 | ||||||||
\(188\) | 7.42139 | 0.541260 | ||||||||
\(189\) | 2.97735 | 0.216570 | ||||||||
\(190\) | 3.94108 | 0.285916 | ||||||||
\(191\) | 12.1476 | 0.878966 | 0.439483 | − | 0.898251i | \(-0.355162\pi\) | ||||
0.439483 | + | 0.898251i | \(0.355162\pi\) | |||||||
\(192\) | −57.2364 | −4.13068 | ||||||||
\(193\) | −17.7457 | −1.27736 | −0.638680 | − | 0.769472i | \(-0.720519\pi\) | ||||
−0.638680 | + | 0.769472i | \(0.720519\pi\) | |||||||
\(194\) | 0.726079 | 0.0521294 | ||||||||
\(195\) | −23.2383 | −1.66413 | ||||||||
\(196\) | −25.3410 | −1.81007 | ||||||||
\(197\) | −4.76180 | −0.339264 | −0.169632 | − | 0.985507i | \(-0.554258\pi\) | ||||
−0.169632 | + | 0.985507i | \(0.554258\pi\) | |||||||
\(198\) | 25.1284 | 1.78580 | ||||||||
\(199\) | −4.96847 | −0.352206 | −0.176103 | − | 0.984372i | \(-0.556349\pi\) | ||||
−0.176103 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(200\) | 26.2307 | 1.85479 | ||||||||
\(201\) | 36.2778 | 2.55884 | ||||||||
\(202\) | 11.7096 | 0.823888 | ||||||||
\(203\) | 5.97884 | 0.419632 | ||||||||
\(204\) | 8.59128 | 0.601510 | ||||||||
\(205\) | 12.3802 | 0.864669 | ||||||||
\(206\) | 23.4283 | 1.63233 | ||||||||
\(207\) | −16.5887 | −1.15300 | ||||||||
\(208\) | 98.3704 | 6.82076 | ||||||||
\(209\) | 4.35926 | 0.301536 | ||||||||
\(210\) | 13.4268 | 0.926536 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −11.6500 | −0.800123 | ||||||||
\(213\) | 32.0572 | 2.19652 | ||||||||
\(214\) | −33.7113 | −2.30446 | ||||||||
\(215\) | −2.19734 | −0.149857 | ||||||||
\(216\) | −17.9770 | −1.22318 | ||||||||
\(217\) | 4.04427 | 0.274543 | ||||||||
\(218\) | 31.8451 | 2.15682 | ||||||||
\(219\) | −24.5066 | −1.65600 | ||||||||
\(220\) | −33.9071 | −2.28602 | ||||||||
\(221\) | −5.00726 | −0.336825 | ||||||||
\(222\) | 39.4561 | 2.64812 | ||||||||
\(223\) | −12.3402 | −0.826363 | −0.413181 | − | 0.910649i | \(-0.635582\pi\) | ||||
−0.413181 | + | 0.910649i | \(0.635582\pi\) | |||||||
\(224\) | −29.4941 | −1.97066 | ||||||||
\(225\) | −6.13816 | −0.409211 | ||||||||
\(226\) | −37.9314 | −2.52316 | ||||||||
\(227\) | 24.6639 | 1.63700 | 0.818501 | − | 0.574505i | \(-0.194805\pi\) | ||||
0.818501 | + | 0.574505i | \(0.194805\pi\) | |||||||
\(228\) | 12.1152 | 0.802346 | ||||||||
\(229\) | 2.03910 | 0.134747 | 0.0673737 | − | 0.997728i | \(-0.478538\pi\) | ||||
0.0673737 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(230\) | 30.7503 | 2.02762 | ||||||||
\(231\) | 14.8515 | 0.977156 | ||||||||
\(232\) | −36.0996 | −2.37006 | ||||||||
\(233\) | 13.3634 | 0.875466 | 0.437733 | − | 0.899105i | \(-0.355781\pi\) | ||||
0.437733 | + | 0.899105i | \(0.355781\pi\) | |||||||
\(234\) | −40.7028 | −2.66082 | ||||||||
\(235\) | 2.01600 | 0.131509 | ||||||||
\(236\) | −62.1151 | −4.04335 | ||||||||
\(237\) | −28.9003 | −1.87728 | ||||||||
\(238\) | 2.89312 | 0.187533 | ||||||||
\(239\) | −8.40798 | −0.543867 | −0.271933 | − | 0.962316i | \(-0.587663\pi\) | ||||
−0.271933 | + | 0.962316i | \(0.587663\pi\) | |||||||
\(240\) | −45.8487 | −2.95952 | ||||||||
\(241\) | −7.83928 | −0.504972 | −0.252486 | − | 0.967601i | \(-0.581248\pi\) | ||||
−0.252486 | + | 0.967601i | \(0.581248\pi\) | |||||||
\(242\) | −21.6987 | −1.39485 | ||||||||
\(243\) | 18.6476 | 1.19624 | ||||||||
\(244\) | −34.7252 | −2.22305 | ||||||||
\(245\) | −6.88380 | −0.439790 | ||||||||
\(246\) | 52.2820 | 3.33338 | ||||||||
\(247\) | −7.06108 | −0.449286 | ||||||||
\(248\) | −24.4189 | −1.55060 | ||||||||
\(249\) | −1.12838 | −0.0715079 | ||||||||
\(250\) | 31.0836 | 1.96590 | ||||||||
\(251\) | −7.90833 | −0.499170 | −0.249585 | − | 0.968353i | \(-0.580294\pi\) | ||||
−0.249585 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(252\) | 17.1191 | 1.07840 | ||||||||
\(253\) | 34.0132 | 2.13839 | ||||||||
\(254\) | 22.9850 | 1.44220 | ||||||||
\(255\) | 2.33379 | 0.146148 | ||||||||
\(256\) | 28.9888 | 1.81180 | ||||||||
\(257\) | −22.6093 | −1.41033 | −0.705165 | − | 0.709043i | \(-0.749127\pi\) | ||||
−0.705165 | + | 0.709043i | \(0.749127\pi\) | |||||||
\(258\) | −9.27945 | −0.577713 | ||||||||
\(259\) | 9.67190 | 0.600983 | ||||||||
\(260\) | 54.9223 | 3.40614 | ||||||||
\(261\) | 8.44756 | 0.522891 | ||||||||
\(262\) | 4.64067 | 0.286701 | ||||||||
\(263\) | 20.2133 | 1.24641 | 0.623203 | − | 0.782060i | \(-0.285831\pi\) | ||||
0.623203 | + | 0.782060i | \(0.285831\pi\) | |||||||
\(264\) | −89.6718 | −5.51892 | ||||||||
\(265\) | −3.16468 | −0.194405 | ||||||||
\(266\) | 4.07979 | 0.250148 | ||||||||
\(267\) | 11.9283 | 0.729999 | ||||||||
\(268\) | −85.7403 | −5.23743 | ||||||||
\(269\) | 4.33686 | 0.264423 | 0.132212 | − | 0.991222i | \(-0.457792\pi\) | ||||
0.132212 | + | 0.991222i | \(0.457792\pi\) | |||||||
\(270\) | −7.79796 | −0.474569 | ||||||||
\(271\) | 6.51188 | 0.395568 | 0.197784 | − | 0.980246i | \(-0.436625\pi\) | ||||
0.197784 | + | 0.980246i | \(0.436625\pi\) | |||||||
\(272\) | −9.87921 | −0.599015 | ||||||||
\(273\) | −24.0563 | −1.45595 | ||||||||
\(274\) | −35.6726 | −2.15506 | ||||||||
\(275\) | 12.5855 | 0.758937 | ||||||||
\(276\) | 94.5286 | 5.68996 | ||||||||
\(277\) | 4.80453 | 0.288676 | 0.144338 | − | 0.989528i | \(-0.453895\pi\) | ||||
0.144338 | + | 0.989528i | \(0.453895\pi\) | |||||||
\(278\) | −14.4690 | −0.867793 | ||||||||
\(279\) | 5.71419 | 0.342100 | ||||||||
\(280\) | −19.8727 | −1.18762 | ||||||||
\(281\) | −7.11822 | −0.424637 | −0.212319 | − | 0.977200i | \(-0.568101\pi\) | ||||
−0.212319 | + | 0.977200i | \(0.568101\pi\) | |||||||
\(282\) | 8.51363 | 0.506979 | ||||||||
\(283\) | −27.6936 | −1.64621 | −0.823107 | − | 0.567886i | \(-0.807761\pi\) | ||||
−0.823107 | + | 0.567886i | \(0.807761\pi\) | |||||||
\(284\) | −75.7652 | −4.49584 | ||||||||
\(285\) | 3.29105 | 0.194945 | ||||||||
\(286\) | 83.4560 | 4.93486 | ||||||||
\(287\) | 12.8159 | 0.756500 | ||||||||
\(288\) | −41.6726 | −2.45558 | ||||||||
\(289\) | −16.4971 | −0.970419 | ||||||||
\(290\) | −15.6591 | −0.919536 | ||||||||
\(291\) | 0.606321 | 0.0355432 | ||||||||
\(292\) | 57.9197 | 3.38949 | ||||||||
\(293\) | 17.5570 | 1.02569 | 0.512844 | − | 0.858482i | \(-0.328592\pi\) | ||||
0.512844 | + | 0.858482i | \(0.328592\pi\) | |||||||
\(294\) | −29.0705 | −1.69543 | ||||||||
\(295\) | −16.8734 | −0.982406 | ||||||||
\(296\) | −58.3980 | −3.39431 | ||||||||
\(297\) | −8.62539 | −0.500496 | ||||||||
\(298\) | 32.1807 | 1.86418 | ||||||||
\(299\) | −55.0942 | −3.18618 | ||||||||
\(300\) | 34.9774 | 2.01942 | ||||||||
\(301\) | −2.27468 | −0.131110 | ||||||||
\(302\) | 26.0186 | 1.49720 | ||||||||
\(303\) | 9.77828 | 0.561748 | ||||||||
\(304\) | −13.9314 | −0.799018 | ||||||||
\(305\) | −9.43300 | −0.540132 | ||||||||
\(306\) | 4.08772 | 0.233680 | ||||||||
\(307\) | −26.2545 | −1.49843 | −0.749213 | − | 0.662330i | \(-0.769568\pi\) | ||||
−0.749213 | + | 0.662330i | \(0.769568\pi\) | |||||||
\(308\) | −35.1005 | −2.00004 | ||||||||
\(309\) | 19.5641 | 1.11296 | ||||||||
\(310\) | −10.5923 | −0.601603 | ||||||||
\(311\) | −13.8060 | −0.782866 | −0.391433 | − | 0.920207i | \(-0.628020\pi\) | ||||
−0.391433 | + | 0.920207i | \(0.628020\pi\) | |||||||
\(312\) | 145.249 | 8.22312 | ||||||||
\(313\) | −21.2182 | −1.19932 | −0.599662 | − | 0.800254i | \(-0.704698\pi\) | ||||
−0.599662 | + | 0.800254i | \(0.704698\pi\) | |||||||
\(314\) | 47.4336 | 2.67683 | ||||||||
\(315\) | 4.65034 | 0.262017 | ||||||||
\(316\) | 68.3041 | 3.84240 | ||||||||
\(317\) | −24.0316 | −1.34975 | −0.674876 | − | 0.737931i | \(-0.735803\pi\) | ||||
−0.674876 | + | 0.737931i | \(0.735803\pi\) | |||||||
\(318\) | −13.3646 | −0.749447 | ||||||||
\(319\) | −17.3207 | −0.969773 | ||||||||
\(320\) | 36.7469 | 2.05422 | ||||||||
\(321\) | −28.1511 | −1.57124 | ||||||||
\(322\) | 31.8326 | 1.77396 | ||||||||
\(323\) | 0.709135 | 0.0394573 | ||||||||
\(324\) | −58.1015 | −3.22786 | ||||||||
\(325\) | −20.3859 | −1.13081 | ||||||||
\(326\) | −65.2902 | −3.61609 | ||||||||
\(327\) | 26.5927 | 1.47058 | ||||||||
\(328\) | −77.3813 | −4.27267 | ||||||||
\(329\) | 2.08695 | 0.115058 | ||||||||
\(330\) | −38.8974 | −2.14123 | ||||||||
\(331\) | 16.0964 | 0.884739 | 0.442369 | − | 0.896833i | \(-0.354138\pi\) | ||||
0.442369 | + | 0.896833i | \(0.354138\pi\) | |||||||
\(332\) | 2.66684 | 0.146362 | ||||||||
\(333\) | 13.6655 | 0.748866 | ||||||||
\(334\) | −64.5161 | −3.53016 | ||||||||
\(335\) | −23.2911 | −1.27253 | ||||||||
\(336\) | −47.4625 | −2.58929 | ||||||||
\(337\) | 19.4821 | 1.06126 | 0.530628 | − | 0.847605i | \(-0.321956\pi\) | ||||
0.530628 | + | 0.847605i | \(0.321956\pi\) | |||||||
\(338\) | −99.9345 | −5.43572 | ||||||||
\(339\) | −31.6751 | −1.72035 | ||||||||
\(340\) | −5.51577 | −0.299135 | ||||||||
\(341\) | −11.7162 | −0.634470 | ||||||||
\(342\) | 5.76438 | 0.311702 | ||||||||
\(343\) | −17.6593 | −0.953515 | ||||||||
\(344\) | 13.7343 | 0.740504 | ||||||||
\(345\) | 25.6784 | 1.38248 | ||||||||
\(346\) | −57.0017 | −3.06443 | ||||||||
\(347\) | 33.0214 | 1.77268 | 0.886341 | − | 0.463033i | \(-0.153239\pi\) | ||||
0.886341 | + | 0.463033i | \(0.153239\pi\) | |||||||
\(348\) | −48.1373 | −2.58043 | ||||||||
\(349\) | 2.17408 | 0.116376 | 0.0581880 | − | 0.998306i | \(-0.481468\pi\) | ||||
0.0581880 | + | 0.998306i | \(0.481468\pi\) | |||||||
\(350\) | 11.7787 | 0.629598 | ||||||||
\(351\) | 13.9713 | 0.745733 | ||||||||
\(352\) | 85.4445 | 4.55421 | ||||||||
\(353\) | −29.5040 | −1.57034 | −0.785171 | − | 0.619280i | \(-0.787425\pi\) | ||||
−0.785171 | + | 0.619280i | \(0.787425\pi\) | |||||||
\(354\) | −71.2569 | −3.78726 | ||||||||
\(355\) | −20.5814 | −1.09235 | ||||||||
\(356\) | −28.1917 | −1.49416 | ||||||||
\(357\) | 2.41594 | 0.127865 | ||||||||
\(358\) | 13.8133 | 0.730057 | ||||||||
\(359\) | −32.4505 | −1.71267 | −0.856335 | − | 0.516421i | \(-0.827264\pi\) | ||||
−0.856335 | + | 0.516421i | \(0.827264\pi\) | |||||||
\(360\) | −28.0783 | −1.47986 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 18.3509 | 0.964502 | ||||||||
\(363\) | −18.1198 | −0.951043 | ||||||||
\(364\) | 56.8554 | 2.98003 | ||||||||
\(365\) | 15.7337 | 0.823540 | ||||||||
\(366\) | −39.8359 | −2.08226 | ||||||||
\(367\) | 9.23124 | 0.481867 | 0.240933 | − | 0.970542i | \(-0.422546\pi\) | ||||
0.240933 | + | 0.970542i | \(0.422546\pi\) | |||||||
\(368\) | −108.700 | −5.66636 | ||||||||
\(369\) | 18.1078 | 0.942652 | ||||||||
\(370\) | −25.3316 | −1.31693 | ||||||||
\(371\) | −3.27607 | −0.170085 | ||||||||
\(372\) | −32.5615 | −1.68824 | ||||||||
\(373\) | −32.4703 | −1.68125 | −0.840625 | − | 0.541618i | \(-0.817812\pi\) | ||||
−0.840625 | + | 0.541618i | \(0.817812\pi\) | |||||||
\(374\) | −8.38138 | −0.433391 | ||||||||
\(375\) | 25.9567 | 1.34040 | ||||||||
\(376\) | −12.6008 | −0.649838 | ||||||||
\(377\) | 28.0559 | 1.44495 | ||||||||
\(378\) | −8.07242 | −0.415201 | ||||||||
\(379\) | 0.401230 | 0.0206098 | 0.0103049 | − | 0.999947i | \(-0.496720\pi\) | ||||
0.0103049 | + | 0.999947i | \(0.496720\pi\) | |||||||
\(380\) | −7.77818 | −0.399012 | ||||||||
\(381\) | 19.1939 | 0.983332 | ||||||||
\(382\) | −32.9354 | −1.68512 | ||||||||
\(383\) | 32.7239 | 1.67211 | 0.836057 | − | 0.548642i | \(-0.184855\pi\) | ||||
0.836057 | + | 0.548642i | \(0.184855\pi\) | |||||||
\(384\) | 66.4285 | 3.38991 | ||||||||
\(385\) | −9.53495 | −0.485946 | ||||||||
\(386\) | 48.1134 | 2.44891 | ||||||||
\(387\) | −3.21392 | −0.163373 | ||||||||
\(388\) | −1.43300 | −0.0727496 | ||||||||
\(389\) | −26.9795 | −1.36791 | −0.683956 | − | 0.729523i | \(-0.739742\pi\) | ||||
−0.683956 | + | 0.729523i | \(0.739742\pi\) | |||||||
\(390\) | 63.0055 | 3.19041 | ||||||||
\(391\) | 5.53303 | 0.279817 | ||||||||
\(392\) | 43.0266 | 2.17317 | ||||||||
\(393\) | 3.87525 | 0.195480 | ||||||||
\(394\) | 12.9106 | 0.650425 | ||||||||
\(395\) | 18.5546 | 0.933583 | ||||||||
\(396\) | −49.5939 | −2.49219 | ||||||||
\(397\) | 0.310191 | 0.0155680 | 0.00778401 | − | 0.999970i | \(-0.497522\pi\) | ||||
0.00778401 | + | 0.999970i | \(0.497522\pi\) | |||||||
\(398\) | 13.4709 | 0.675235 | ||||||||
\(399\) | 3.40688 | 0.170557 | ||||||||
\(400\) | −40.2210 | −2.01105 | ||||||||
\(401\) | −10.6504 | −0.531855 | −0.265927 | − | 0.963993i | \(-0.585678\pi\) | ||||
−0.265927 | + | 0.963993i | \(0.585678\pi\) | |||||||
\(402\) | −98.3592 | −4.90571 | ||||||||
\(403\) | 18.9778 | 0.945353 | ||||||||
\(404\) | −23.1103 | −1.14978 | ||||||||
\(405\) | −15.7831 | −0.784268 | ||||||||
\(406\) | −16.2103 | −0.804503 | ||||||||
\(407\) | −28.0195 | −1.38887 | ||||||||
\(408\) | −14.5872 | −0.722174 | ||||||||
\(409\) | 14.2881 | 0.706499 | 0.353250 | − | 0.935529i | \(-0.385077\pi\) | ||||
0.353250 | + | 0.935529i | \(0.385077\pi\) | |||||||
\(410\) | −33.5661 | −1.65771 | ||||||||
\(411\) | −29.7888 | −1.46938 | ||||||||
\(412\) | −46.2385 | −2.27801 | ||||||||
\(413\) | −17.4673 | −0.859508 | ||||||||
\(414\) | 44.9767 | 2.21048 | ||||||||
\(415\) | 0.724440 | 0.0355614 | ||||||||
\(416\) | −138.402 | −6.78572 | ||||||||
\(417\) | −12.0825 | −0.591683 | ||||||||
\(418\) | −11.8192 | −0.578094 | ||||||||
\(419\) | 16.7250 | 0.817071 | 0.408536 | − | 0.912742i | \(-0.366040\pi\) | ||||
0.408536 | + | 0.912742i | \(0.366040\pi\) | |||||||
\(420\) | −26.4993 | −1.29303 | ||||||||
\(421\) | 3.45173 | 0.168227 | 0.0841135 | − | 0.996456i | \(-0.473194\pi\) | ||||
0.0841135 | + | 0.996456i | \(0.473194\pi\) | |||||||
\(422\) | 2.71128 | 0.131983 | ||||||||
\(423\) | 2.94868 | 0.143370 | ||||||||
\(424\) | 19.7806 | 0.960629 | ||||||||
\(425\) | 2.04733 | 0.0993101 | ||||||||
\(426\) | −86.9159 | −4.21109 | ||||||||
\(427\) | −9.76502 | −0.472562 | ||||||||
\(428\) | 66.5332 | 3.21600 | ||||||||
\(429\) | 69.6910 | 3.36471 | ||||||||
\(430\) | 5.95760 | 0.287301 | ||||||||
\(431\) | 14.3548 | 0.691448 | 0.345724 | − | 0.938336i | \(-0.387633\pi\) | ||||
0.345724 | + | 0.938336i | \(0.387633\pi\) | |||||||
\(432\) | 27.5651 | 1.32623 | ||||||||
\(433\) | 5.06697 | 0.243503 | 0.121751 | − | 0.992561i | \(-0.461149\pi\) | ||||
0.121751 | + | 0.992561i | \(0.461149\pi\) | |||||||
\(434\) | −10.9651 | −0.526343 | ||||||||
\(435\) | −13.0763 | −0.626963 | ||||||||
\(436\) | −62.8500 | −3.00997 | ||||||||
\(437\) | 7.80251 | 0.373245 | ||||||||
\(438\) | 66.4440 | 3.17482 | ||||||||
\(439\) | −17.8019 | −0.849640 | −0.424820 | − | 0.905278i | \(-0.639663\pi\) | ||||
−0.424820 | + | 0.905278i | \(0.639663\pi\) | |||||||
\(440\) | 57.5711 | 2.74459 | ||||||||
\(441\) | −10.0685 | −0.479453 | ||||||||
\(442\) | 13.5761 | 0.645747 | ||||||||
\(443\) | −13.2201 | −0.628107 | −0.314054 | − | 0.949405i | \(-0.601687\pi\) | ||||
−0.314054 | + | 0.949405i | \(0.601687\pi\) | |||||||
\(444\) | −77.8711 | −3.69560 | ||||||||
\(445\) | −7.65820 | −0.363033 | ||||||||
\(446\) | 33.4578 | 1.58427 | ||||||||
\(447\) | 26.8729 | 1.27105 | ||||||||
\(448\) | 38.0403 | 1.79724 | ||||||||
\(449\) | 3.07099 | 0.144929 | 0.0724644 | − | 0.997371i | \(-0.476914\pi\) | ||||
0.0724644 | + | 0.997371i | \(0.476914\pi\) | |||||||
\(450\) | 16.6422 | 0.784523 | ||||||||
\(451\) | −37.1277 | −1.74828 | ||||||||
\(452\) | 74.8620 | 3.52121 | ||||||||
\(453\) | 21.7271 | 1.02083 | ||||||||
\(454\) | −66.8707 | −3.13840 | ||||||||
\(455\) | 15.4446 | 0.724054 | ||||||||
\(456\) | −20.5704 | −0.963298 | ||||||||
\(457\) | 6.56637 | 0.307162 | 0.153581 | − | 0.988136i | \(-0.450919\pi\) | ||||
0.153581 | + | 0.988136i | \(0.450919\pi\) | |||||||
\(458\) | −5.52856 | −0.258332 | ||||||||
\(459\) | −1.40312 | −0.0654920 | ||||||||
\(460\) | −60.6893 | −2.82965 | ||||||||
\(461\) | −41.6930 | −1.94184 | −0.970918 | − | 0.239414i | \(-0.923045\pi\) | ||||
−0.970918 | + | 0.239414i | \(0.923045\pi\) | |||||||
\(462\) | −40.2665 | −1.87337 | ||||||||
\(463\) | −12.2976 | −0.571517 | −0.285759 | − | 0.958302i | \(-0.592246\pi\) | ||||
−0.285759 | + | 0.958302i | \(0.592246\pi\) | |||||||
\(464\) | 55.3536 | 2.56973 | ||||||||
\(465\) | −8.84524 | −0.410188 | ||||||||
\(466\) | −36.2319 | −1.67841 | ||||||||
\(467\) | −20.4001 | −0.944002 | −0.472001 | − | 0.881598i | \(-0.656468\pi\) | ||||
−0.472001 | + | 0.881598i | \(0.656468\pi\) | |||||||
\(468\) | 80.3316 | 3.71333 | ||||||||
\(469\) | −24.1109 | −1.11334 | ||||||||
\(470\) | −5.46592 | −0.252124 | ||||||||
\(471\) | 39.6100 | 1.82513 | ||||||||
\(472\) | 105.466 | 4.85445 | ||||||||
\(473\) | 6.58975 | 0.302997 | ||||||||
\(474\) | 78.3567 | 3.59904 | ||||||||
\(475\) | 2.88708 | 0.132468 | ||||||||
\(476\) | −5.70991 | −0.261713 | ||||||||
\(477\) | −4.62879 | −0.211938 | ||||||||
\(478\) | 22.7963 | 1.04268 | ||||||||
\(479\) | −21.1909 | −0.968236 | −0.484118 | − | 0.875003i | \(-0.660859\pi\) | ||||
−0.484118 | + | 0.875003i | \(0.660859\pi\) | |||||||
\(480\) | 64.5068 | 2.94432 | ||||||||
\(481\) | 45.3856 | 2.06941 | ||||||||
\(482\) | 21.2544 | 0.968114 | ||||||||
\(483\) | 26.5822 | 1.20953 | ||||||||
\(484\) | 42.8250 | 1.94659 | ||||||||
\(485\) | −0.389270 | −0.0176759 | ||||||||
\(486\) | −50.5587 | −2.29339 | ||||||||
\(487\) | 20.8164 | 0.943281 | 0.471641 | − | 0.881791i | \(-0.343662\pi\) | ||||
0.471641 | + | 0.881791i | \(0.343662\pi\) | |||||||
\(488\) | 58.9602 | 2.66900 | ||||||||
\(489\) | −54.5214 | −2.46554 | ||||||||
\(490\) | 18.6639 | 0.843148 | ||||||||
\(491\) | −39.9901 | −1.80473 | −0.902363 | − | 0.430976i | \(-0.858169\pi\) | ||||
−0.902363 | + | 0.430976i | \(0.858169\pi\) | |||||||
\(492\) | −103.185 | −4.65192 | ||||||||
\(493\) | −2.81761 | −0.126899 | ||||||||
\(494\) | 19.1445 | 0.861353 | ||||||||
\(495\) | −13.4720 | −0.605523 | ||||||||
\(496\) | 37.4429 | 1.68123 | ||||||||
\(497\) | −21.3058 | −0.955695 | ||||||||
\(498\) | 3.05934 | 0.137092 | ||||||||
\(499\) | 27.0802 | 1.21228 | 0.606138 | − | 0.795360i | \(-0.292718\pi\) | ||||
0.606138 | + | 0.795360i | \(0.292718\pi\) | |||||||
\(500\) | −61.3471 | −2.74353 | ||||||||
\(501\) | −53.8750 | −2.40696 | ||||||||
\(502\) | 21.4417 | 0.956989 | ||||||||
\(503\) | −28.8056 | −1.28438 | −0.642189 | − | 0.766546i | \(-0.721974\pi\) | ||||
−0.642189 | + | 0.766546i | \(0.721974\pi\) | |||||||
\(504\) | −29.0666 | −1.29473 | ||||||||
\(505\) | −6.27786 | −0.279361 | ||||||||
\(506\) | −92.2191 | −4.09964 | ||||||||
\(507\) | −83.4515 | −3.70621 | ||||||||
\(508\) | −45.3635 | −2.01268 | ||||||||
\(509\) | 20.8954 | 0.926174 | 0.463087 | − | 0.886313i | \(-0.346742\pi\) | ||||
0.463087 | + | 0.886313i | \(0.346742\pi\) | |||||||
\(510\) | −6.32756 | −0.280189 | ||||||||
\(511\) | 16.2875 | 0.720516 | ||||||||
\(512\) | −19.9165 | −0.880194 | ||||||||
\(513\) | −1.97864 | −0.0873589 | ||||||||
\(514\) | 61.3001 | 2.70383 | ||||||||
\(515\) | −12.5606 | −0.553484 | ||||||||
\(516\) | 18.3141 | 0.806232 | ||||||||
\(517\) | −6.04591 | −0.265899 | ||||||||
\(518\) | −26.2232 | −1.15218 | ||||||||
\(519\) | −47.5999 | −2.08941 | ||||||||
\(520\) | −93.2530 | −4.08942 | ||||||||
\(521\) | 23.4500 | 1.02736 | 0.513682 | − | 0.857981i | \(-0.328281\pi\) | ||||
0.513682 | + | 0.857981i | \(0.328281\pi\) | |||||||
\(522\) | −22.9037 | −1.00247 | ||||||||
\(523\) | 14.1613 | 0.619233 | 0.309616 | − | 0.950862i | \(-0.399799\pi\) | ||||
0.309616 | + | 0.950862i | \(0.399799\pi\) | |||||||
\(524\) | −9.15889 | −0.400108 | ||||||||
\(525\) | 9.83595 | 0.429276 | ||||||||
\(526\) | −54.8039 | −2.38956 | ||||||||
\(527\) | −1.90592 | −0.0830231 | ||||||||
\(528\) | 137.499 | 5.98387 | ||||||||
\(529\) | 37.8792 | 1.64692 | ||||||||
\(530\) | 8.58031 | 0.372705 | ||||||||
\(531\) | −24.6797 | −1.07101 | ||||||||
\(532\) | −8.05195 | −0.349096 | ||||||||
\(533\) | 60.1391 | 2.60491 | ||||||||
\(534\) | −32.3409 | −1.39953 | ||||||||
\(535\) | 18.0735 | 0.781388 | ||||||||
\(536\) | 145.579 | 6.28806 | ||||||||
\(537\) | 11.5350 | 0.497772 | ||||||||
\(538\) | −11.7584 | −0.506942 | ||||||||
\(539\) | 20.6443 | 0.889211 | ||||||||
\(540\) | 15.3902 | 0.662288 | ||||||||
\(541\) | 33.4921 | 1.43994 | 0.719970 | − | 0.694005i | \(-0.244156\pi\) | ||||
0.719970 | + | 0.694005i | \(0.244156\pi\) | |||||||
\(542\) | −17.6555 | −0.758369 | ||||||||
\(543\) | 15.3241 | 0.657622 | ||||||||
\(544\) | 13.8995 | 0.595937 | ||||||||
\(545\) | −17.0730 | −0.731328 | ||||||||
\(546\) | 65.2232 | 2.79129 | ||||||||
\(547\) | −18.5063 | −0.791274 | −0.395637 | − | 0.918407i | \(-0.629476\pi\) | ||||
−0.395637 | + | 0.918407i | \(0.629476\pi\) | |||||||
\(548\) | 70.4040 | 3.00751 | ||||||||
\(549\) | −13.7971 | −0.588846 | ||||||||
\(550\) | −34.1229 | −1.45500 | ||||||||
\(551\) | −3.97331 | −0.169269 | ||||||||
\(552\) | −160.501 | −6.83137 | ||||||||
\(553\) | 19.2077 | 0.816793 | ||||||||
\(554\) | −13.0264 | −0.553439 | ||||||||
\(555\) | −21.1535 | −0.897914 | ||||||||
\(556\) | 28.5563 | 1.21105 | ||||||||
\(557\) | 14.9705 | 0.634321 | 0.317160 | − | 0.948372i | \(-0.397271\pi\) | ||||
0.317160 | + | 0.948372i | \(0.397271\pi\) | |||||||
\(558\) | −15.4927 | −0.655860 | ||||||||
\(559\) | −10.6740 | −0.451462 | ||||||||
\(560\) | 30.4719 | 1.28767 | ||||||||
\(561\) | −6.99897 | −0.295497 | ||||||||
\(562\) | 19.2995 | 0.814098 | ||||||||
\(563\) | −17.4195 | −0.734146 | −0.367073 | − | 0.930192i | \(-0.619640\pi\) | ||||
−0.367073 | + | 0.930192i | \(0.619640\pi\) | |||||||
\(564\) | −16.8026 | −0.707519 | ||||||||
\(565\) | 20.3360 | 0.855544 | ||||||||
\(566\) | 75.0850 | 3.15606 | ||||||||
\(567\) | −16.3386 | −0.686158 | ||||||||
\(568\) | 128.642 | 5.39771 | ||||||||
\(569\) | −0.149079 | −0.00624971 | −0.00312485 | − | 0.999995i | \(-0.500995\pi\) | ||||
−0.00312485 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(570\) | −8.92293 | −0.373741 | ||||||||
\(571\) | −11.0557 | −0.462666 | −0.231333 | − | 0.972875i | \(-0.574309\pi\) | ||||
−0.231333 | + | 0.972875i | \(0.574309\pi\) | |||||||
\(572\) | −164.710 | −6.88688 | ||||||||
\(573\) | −27.5031 | −1.14896 | ||||||||
\(574\) | −34.7475 | −1.45033 | ||||||||
\(575\) | 22.5265 | 0.939420 | ||||||||
\(576\) | 53.7476 | 2.23948 | ||||||||
\(577\) | 3.70955 | 0.154431 | 0.0772153 | − | 0.997014i | \(-0.475397\pi\) | ||||
0.0772153 | + | 0.997014i | \(0.475397\pi\) | |||||||
\(578\) | 44.7283 | 1.86045 | ||||||||
\(579\) | 40.1777 | 1.66973 | ||||||||
\(580\) | 30.9051 | 1.28326 | ||||||||
\(581\) | 0.749938 | 0.0311127 | ||||||||
\(582\) | −1.64390 | −0.0681420 | ||||||||
\(583\) | 9.49076 | 0.393067 | ||||||||
\(584\) | −98.3423 | −4.06943 | ||||||||
\(585\) | 21.8218 | 0.902222 | ||||||||
\(586\) | −47.6017 | −1.96641 | ||||||||
\(587\) | 26.3091 | 1.08589 | 0.542946 | − | 0.839768i | \(-0.317309\pi\) | ||||
0.542946 | + | 0.839768i | \(0.317309\pi\) | |||||||
\(588\) | 57.3741 | 2.36607 | ||||||||
\(589\) | −2.68767 | −0.110743 | ||||||||
\(590\) | 45.7484 | 1.88343 | ||||||||
\(591\) | 10.7811 | 0.443476 | ||||||||
\(592\) | 89.5449 | 3.68027 | ||||||||
\(593\) | −9.74307 | −0.400100 | −0.200050 | − | 0.979786i | \(-0.564110\pi\) | ||||
−0.200050 | + | 0.979786i | \(0.564110\pi\) | |||||||
\(594\) | 23.3858 | 0.959531 | ||||||||
\(595\) | −1.55108 | −0.0635881 | ||||||||
\(596\) | −63.5124 | −2.60157 | ||||||||
\(597\) | 11.2490 | 0.460393 | ||||||||
\(598\) | 149.375 | 6.10842 | ||||||||
\(599\) | 5.99507 | 0.244952 | 0.122476 | − | 0.992471i | \(-0.460917\pi\) | ||||
0.122476 | + | 0.992471i | \(0.460917\pi\) | |||||||
\(600\) | −59.3885 | −2.42452 | ||||||||
\(601\) | −24.3333 | −0.992576 | −0.496288 | − | 0.868158i | \(-0.665304\pi\) | ||||
−0.496288 | + | 0.868158i | \(0.665304\pi\) | |||||||
\(602\) | 6.16729 | 0.251360 | ||||||||
\(603\) | −34.0665 | −1.38730 | ||||||||
\(604\) | −51.3506 | −2.08943 | ||||||||
\(605\) | 11.6333 | 0.472960 | ||||||||
\(606\) | −26.5116 | −1.07696 | ||||||||
\(607\) | −19.6697 | −0.798369 | −0.399185 | − | 0.916871i | \(-0.630707\pi\) | ||||
−0.399185 | + | 0.916871i | \(0.630707\pi\) | |||||||
\(608\) | 19.6007 | 0.794913 | ||||||||
\(609\) | −13.5366 | −0.548531 | ||||||||
\(610\) | 25.5755 | 1.03552 | ||||||||
\(611\) | 9.79309 | 0.396186 | ||||||||
\(612\) | −8.06760 | −0.326113 | ||||||||
\(613\) | 13.1453 | 0.530933 | 0.265466 | − | 0.964120i | \(-0.414474\pi\) | ||||
0.265466 | + | 0.964120i | \(0.414474\pi\) | |||||||
\(614\) | 71.1833 | 2.87272 | ||||||||
\(615\) | −28.0298 | −1.13027 | ||||||||
\(616\) | 59.5975 | 2.40125 | ||||||||
\(617\) | −34.7390 | −1.39854 | −0.699270 | − | 0.714858i | \(-0.746491\pi\) | ||||
−0.699270 | + | 0.714858i | \(0.746491\pi\) | |||||||
\(618\) | −53.0437 | −2.13373 | ||||||||
\(619\) | −19.5832 | −0.787114 | −0.393557 | − | 0.919300i | \(-0.628756\pi\) | ||||
−0.393557 | + | 0.919300i | \(0.628756\pi\) | |||||||
\(620\) | 20.9052 | 0.839571 | ||||||||
\(621\) | −15.4383 | −0.619519 | ||||||||
\(622\) | 37.4319 | 1.50088 | ||||||||
\(623\) | −7.92775 | −0.317618 | ||||||||
\(624\) | −222.719 | −8.91589 | ||||||||
\(625\) | −2.22935 | −0.0891738 | ||||||||
\(626\) | 57.5284 | 2.29930 | ||||||||
\(627\) | −9.86973 | −0.394159 | ||||||||
\(628\) | −93.6157 | −3.73567 | ||||||||
\(629\) | −4.55802 | −0.181740 | ||||||||
\(630\) | −12.6084 | −0.502329 | ||||||||
\(631\) | −18.4425 | −0.734185 | −0.367093 | − | 0.930184i | \(-0.619647\pi\) | ||||
−0.367093 | + | 0.930184i | \(0.619647\pi\) | |||||||
\(632\) | −115.974 | −4.61320 | ||||||||
\(633\) | 2.26408 | 0.0899893 | ||||||||
\(634\) | 65.1564 | 2.58769 | ||||||||
\(635\) | −12.3229 | −0.489018 | ||||||||
\(636\) | 26.3765 | 1.04590 | ||||||||
\(637\) | −33.4393 | −1.32491 | ||||||||
\(638\) | 46.9612 | 1.85921 | ||||||||
\(639\) | −30.1032 | −1.19086 | ||||||||
\(640\) | −42.6484 | −1.68583 | ||||||||
\(641\) | −45.8161 | −1.80963 | −0.904815 | − | 0.425806i | \(-0.859991\pi\) | ||||
−0.904815 | + | 0.425806i | \(0.859991\pi\) | |||||||
\(642\) | 76.3253 | 3.01232 | ||||||||
\(643\) | −17.8859 | −0.705350 | −0.352675 | − | 0.935746i | \(-0.614728\pi\) | ||||
−0.352675 | + | 0.935746i | \(0.614728\pi\) | |||||||
\(644\) | −62.8254 | −2.47567 | ||||||||
\(645\) | 4.97496 | 0.195889 | ||||||||
\(646\) | −1.92266 | −0.0756461 | ||||||||
\(647\) | −25.6846 | −1.00977 | −0.504883 | − | 0.863188i | \(-0.668464\pi\) | ||||
−0.504883 | + | 0.863188i | \(0.668464\pi\) | |||||||
\(648\) | 98.6510 | 3.87538 | ||||||||
\(649\) | 50.6027 | 1.98633 | ||||||||
\(650\) | 55.2718 | 2.16794 | ||||||||
\(651\) | −9.15656 | −0.358874 | ||||||||
\(652\) | 128.858 | 5.04646 | ||||||||
\(653\) | −10.0009 | −0.391364 | −0.195682 | − | 0.980667i | \(-0.562692\pi\) | ||||
−0.195682 | + | 0.980667i | \(0.562692\pi\) | |||||||
\(654\) | −72.1000 | −2.81933 | ||||||||
\(655\) | −2.48799 | −0.0972137 | ||||||||
\(656\) | 118.653 | 4.63263 | ||||||||
\(657\) | 23.0128 | 0.897813 | ||||||||
\(658\) | −5.65831 | −0.220584 | ||||||||
\(659\) | 10.0611 | 0.391924 | 0.195962 | − | 0.980611i | \(-0.437217\pi\) | ||||
0.195962 | + | 0.980611i | \(0.437217\pi\) | |||||||
\(660\) | 76.7685 | 2.98821 | ||||||||
\(661\) | −28.5893 | −1.11200 | −0.555998 | − | 0.831184i | \(-0.687664\pi\) | ||||
−0.555998 | + | 0.831184i | \(0.687664\pi\) | |||||||
\(662\) | −43.6418 | −1.69619 | ||||||||
\(663\) | 11.3369 | 0.440287 | ||||||||
\(664\) | −4.52805 | −0.175723 | ||||||||
\(665\) | −2.18729 | −0.0848193 | ||||||||
\(666\) | −37.0510 | −1.43570 | ||||||||
\(667\) | −31.0018 | −1.20039 | ||||||||
\(668\) | 127.330 | 4.92655 | ||||||||
\(669\) | 27.9393 | 1.08020 | ||||||||
\(670\) | 63.1486 | 2.43964 | ||||||||
\(671\) | 28.2892 | 1.09209 | ||||||||
\(672\) | 66.7772 | 2.57599 | ||||||||
\(673\) | 3.28233 | 0.126525 | 0.0632623 | − | 0.997997i | \(-0.479850\pi\) | ||||
0.0632623 | + | 0.997997i | \(0.479850\pi\) | |||||||
\(674\) | −52.8213 | −2.03460 | ||||||||
\(675\) | −5.71248 | −0.219874 | ||||||||
\(676\) | 197.232 | 7.58586 | ||||||||
\(677\) | −4.54472 | −0.174668 | −0.0873339 | − | 0.996179i | \(-0.527835\pi\) | ||||
−0.0873339 | + | 0.996179i | \(0.527835\pi\) | |||||||
\(678\) | 85.8799 | 3.29820 | ||||||||
\(679\) | −0.402971 | −0.0154646 | ||||||||
\(680\) | 9.36528 | 0.359142 | ||||||||
\(681\) | −55.8412 | −2.13984 | ||||||||
\(682\) | 31.7660 | 1.21638 | ||||||||
\(683\) | 10.4658 | 0.400462 | 0.200231 | − | 0.979749i | \(-0.435831\pi\) | ||||
0.200231 | + | 0.979749i | \(0.435831\pi\) | |||||||
\(684\) | −11.3767 | −0.434998 | ||||||||
\(685\) | 19.1250 | 0.730730 | ||||||||
\(686\) | 47.8793 | 1.82804 | ||||||||
\(687\) | −4.61669 | −0.176138 | ||||||||
\(688\) | −21.0596 | −0.802888 | ||||||||
\(689\) | −15.3730 | −0.585665 | ||||||||
\(690\) | −69.6213 | −2.65044 | ||||||||
\(691\) | −16.3778 | −0.623039 | −0.311520 | − | 0.950240i | \(-0.600838\pi\) | ||||
−0.311520 | + | 0.950240i | \(0.600838\pi\) | |||||||
\(692\) | 112.499 | 4.27659 | ||||||||
\(693\) | −13.9462 | −0.529773 | ||||||||
\(694\) | −89.5301 | −3.39852 | ||||||||
\(695\) | 7.75722 | 0.294248 | ||||||||
\(696\) | 81.7326 | 3.09807 | ||||||||
\(697\) | −6.03969 | −0.228769 | ||||||||
\(698\) | −5.89454 | −0.223112 | ||||||||
\(699\) | −30.2559 | −1.14438 | ||||||||
\(700\) | −23.2466 | −0.878640 | ||||||||
\(701\) | −0.822538 | −0.0310668 | −0.0155334 | − | 0.999879i | \(-0.504945\pi\) | ||||
−0.0155334 | + | 0.999879i | \(0.504945\pi\) | |||||||
\(702\) | −37.8801 | −1.42969 | ||||||||
\(703\) | −6.42758 | −0.242421 | ||||||||
\(704\) | −110.203 | −4.15342 | ||||||||
\(705\) | −4.56439 | −0.171905 | ||||||||
\(706\) | 79.9936 | 3.01060 | ||||||||
\(707\) | −6.49882 | −0.244413 | ||||||||
\(708\) | 140.634 | 5.28534 | ||||||||
\(709\) | 3.36901 | 0.126526 | 0.0632629 | − | 0.997997i | \(-0.479849\pi\) | ||||
0.0632629 | + | 0.997997i | \(0.479849\pi\) | |||||||
\(710\) | 55.8018 | 2.09420 | ||||||||
\(711\) | 27.1387 | 1.01778 | ||||||||
\(712\) | 47.8670 | 1.79389 | ||||||||
\(713\) | −20.9706 | −0.785354 | ||||||||
\(714\) | −6.55027 | −0.245138 | ||||||||
\(715\) | −44.7430 | −1.67329 | ||||||||
\(716\) | −27.2622 | −1.01884 | ||||||||
\(717\) | 19.0364 | 0.710926 | ||||||||
\(718\) | 87.9821 | 3.28346 | ||||||||
\(719\) | −22.9940 | −0.857532 | −0.428766 | − | 0.903416i | \(-0.641052\pi\) | ||||
−0.428766 | + | 0.903416i | \(0.641052\pi\) | |||||||
\(720\) | 43.0540 | 1.60453 | ||||||||
\(721\) | −13.0027 | −0.484244 | ||||||||
\(722\) | −2.71128 | −0.100903 | ||||||||
\(723\) | 17.7488 | 0.660084 | ||||||||
\(724\) | −36.2176 | −1.34602 | ||||||||
\(725\) | −11.4713 | −0.426032 | ||||||||
\(726\) | 49.1278 | 1.82330 | ||||||||
\(727\) | −24.4920 | −0.908359 | −0.454179 | − | 0.890910i | \(-0.650067\pi\) | ||||
−0.454179 | + | 0.890910i | \(0.650067\pi\) | |||||||
\(728\) | −96.5353 | −3.57783 | ||||||||
\(729\) | −9.64561 | −0.357245 | ||||||||
\(730\) | −42.6584 | −1.57886 | ||||||||
\(731\) | 1.07198 | 0.0396484 | ||||||||
\(732\) | 78.6208 | 2.90591 | ||||||||
\(733\) | −21.6747 | −0.800572 | −0.400286 | − | 0.916390i | \(-0.631089\pi\) | ||||
−0.400286 | + | 0.916390i | \(0.631089\pi\) | |||||||
\(734\) | −25.0284 | −0.923817 | ||||||||
\(735\) | 15.5855 | 0.574880 | ||||||||
\(736\) | 152.935 | 5.63724 | ||||||||
\(737\) | 69.8492 | 2.57293 | ||||||||
\(738\) | −49.0951 | −1.80722 | ||||||||
\(739\) | 33.2883 | 1.22453 | 0.612265 | − | 0.790653i | \(-0.290259\pi\) | ||||
0.612265 | + | 0.790653i | \(0.290259\pi\) | |||||||
\(740\) | 49.9948 | 1.83785 | ||||||||
\(741\) | 15.9869 | 0.587293 | ||||||||
\(742\) | 8.88232 | 0.326080 | ||||||||
\(743\) | 7.48209 | 0.274491 | 0.137246 | − | 0.990537i | \(-0.456175\pi\) | ||||
0.137246 | + | 0.990537i | \(0.456175\pi\) | |||||||
\(744\) | 55.2864 | 2.02690 | ||||||||
\(745\) | −17.2530 | −0.632099 | ||||||||
\(746\) | 88.0360 | 3.22323 | ||||||||
\(747\) | 1.05960 | 0.0387686 | ||||||||
\(748\) | 16.5416 | 0.604821 | ||||||||
\(749\) | 18.7097 | 0.683637 | ||||||||
\(750\) | −70.3759 | −2.56976 | ||||||||
\(751\) | −4.46045 | −0.162764 | −0.0813821 | − | 0.996683i | \(-0.525933\pi\) | ||||
−0.0813821 | + | 0.996683i | \(0.525933\pi\) | |||||||
\(752\) | 19.3216 | 0.704585 | ||||||||
\(753\) | 17.9051 | 0.652499 | ||||||||
\(754\) | −76.0672 | −2.77020 | ||||||||
\(755\) | −13.9492 | −0.507665 | ||||||||
\(756\) | 15.9319 | 0.579436 | ||||||||
\(757\) | −16.4011 | −0.596109 | −0.298055 | − | 0.954549i | \(-0.596338\pi\) | ||||
−0.298055 | + | 0.954549i | \(0.596338\pi\) | |||||||
\(758\) | −1.08785 | −0.0395123 | ||||||||
\(759\) | −77.0087 | −2.79524 | ||||||||
\(760\) | 13.2066 | 0.479055 | ||||||||
\(761\) | −7.09688 | −0.257262 | −0.128631 | − | 0.991693i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991693i | \(0.541058\pi\) | |||||||
\(762\) | −52.0399 | −1.88521 | ||||||||
\(763\) | −17.6739 | −0.639840 | ||||||||
\(764\) | 65.0018 | 2.35168 | ||||||||
\(765\) | −2.19154 | −0.0792352 | ||||||||
\(766\) | −88.7236 | −3.20571 | ||||||||
\(767\) | −81.9656 | −2.95961 | ||||||||
\(768\) | −65.6332 | −2.36833 | ||||||||
\(769\) | 18.9785 | 0.684380 | 0.342190 | − | 0.939631i | \(-0.388831\pi\) | ||||
0.342190 | + | 0.939631i | \(0.388831\pi\) | |||||||
\(770\) | 25.8519 | 0.931637 | ||||||||
\(771\) | 51.1894 | 1.84354 | ||||||||
\(772\) | −94.9573 | −3.41759 | ||||||||
\(773\) | −28.9221 | −1.04026 | −0.520128 | − | 0.854088i | \(-0.674116\pi\) | ||||
−0.520128 | + | 0.854088i | \(0.674116\pi\) | |||||||
\(774\) | 8.71382 | 0.313212 | ||||||||
\(775\) | −7.75952 | −0.278730 | ||||||||
\(776\) | 2.43310 | 0.0873433 | ||||||||
\(777\) | −21.8980 | −0.785586 | ||||||||
\(778\) | 73.1488 | 2.62251 | ||||||||
\(779\) | −8.51698 | −0.305153 | ||||||||
\(780\) | −124.349 | −4.45240 | ||||||||
\(781\) | 61.7228 | 2.20862 | ||||||||
\(782\) | −15.0016 | −0.536455 | ||||||||
\(783\) | 7.86173 | 0.280955 | ||||||||
\(784\) | −65.9751 | −2.35625 | ||||||||
\(785\) | −25.4304 | −0.907651 | ||||||||
\(786\) | −10.5069 | −0.374767 | ||||||||
\(787\) | −6.78211 | −0.241756 | −0.120878 | − | 0.992667i | \(-0.538571\pi\) | ||||
−0.120878 | + | 0.992667i | \(0.538571\pi\) | |||||||
\(788\) | −25.4805 | −0.907705 | ||||||||
\(789\) | −45.7646 | −1.62926 | ||||||||
\(790\) | −50.3066 | −1.78983 | ||||||||
\(791\) | 21.0518 | 0.748516 | ||||||||
\(792\) | 84.2058 | 2.99212 | ||||||||
\(793\) | −45.8226 | −1.62721 | ||||||||
\(794\) | −0.841012 | −0.0298464 | ||||||||
\(795\) | 7.16510 | 0.254120 | ||||||||
\(796\) | −26.5864 | −0.942329 | ||||||||
\(797\) | −40.9308 | −1.44984 | −0.724921 | − | 0.688832i | \(-0.758124\pi\) | ||||
−0.724921 | + | 0.688832i | \(0.758124\pi\) | |||||||
\(798\) | −9.23699 | −0.326986 | ||||||||
\(799\) | −0.983507 | −0.0347940 | ||||||||
\(800\) | 56.5888 | 2.00072 | ||||||||
\(801\) | −11.2012 | −0.395775 | ||||||||
\(802\) | 28.8761 | 1.01965 | ||||||||
\(803\) | −47.1848 | −1.66512 | ||||||||
\(804\) | 194.123 | 6.84620 | ||||||||
\(805\) | −17.0663 | −0.601509 | ||||||||
\(806\) | −51.4541 | −1.81240 | ||||||||
\(807\) | −9.81902 | −0.345646 | ||||||||
\(808\) | 39.2392 | 1.38043 | ||||||||
\(809\) | −34.2982 | −1.20586 | −0.602931 | − | 0.797793i | \(-0.706001\pi\) | ||||
−0.602931 | + | 0.797793i | \(0.706001\pi\) | |||||||
\(810\) | 42.7923 | 1.50357 | ||||||||
\(811\) | −21.2646 | −0.746700 | −0.373350 | − | 0.927691i | \(-0.621791\pi\) | ||||
−0.373350 | + | 0.927691i | \(0.621791\pi\) | |||||||
\(812\) | 31.9929 | 1.12273 | ||||||||
\(813\) | −14.7434 | −0.517075 | ||||||||
\(814\) | 75.9686 | 2.66270 | ||||||||
\(815\) | 35.0038 | 1.22613 | ||||||||
\(816\) | 22.3674 | 0.783014 | ||||||||
\(817\) | 1.51167 | 0.0528865 | ||||||||
\(818\) | −38.7389 | −1.35447 | ||||||||
\(819\) | 22.5899 | 0.789355 | ||||||||
\(820\) | 66.2466 | 2.31343 | ||||||||
\(821\) | −38.5790 | −1.34642 | −0.673209 | − | 0.739453i | \(-0.735084\pi\) | ||||
−0.673209 | + | 0.739453i | \(0.735084\pi\) | |||||||
\(822\) | 80.7658 | 2.81703 | ||||||||
\(823\) | 8.69930 | 0.303238 | 0.151619 | − | 0.988439i | \(-0.451551\pi\) | ||||
0.151619 | + | 0.988439i | \(0.451551\pi\) | |||||||
\(824\) | 78.5088 | 2.73498 | ||||||||
\(825\) | −28.4947 | −0.992059 | ||||||||
\(826\) | 47.3586 | 1.64782 | ||||||||
\(827\) | −16.3438 | −0.568329 | −0.284164 | − | 0.958776i | \(-0.591716\pi\) | ||||
−0.284164 | + | 0.958776i | \(0.591716\pi\) | |||||||
\(828\) | −88.7666 | −3.08485 | ||||||||
\(829\) | 36.1909 | 1.25696 | 0.628481 | − | 0.777825i | \(-0.283677\pi\) | ||||
0.628481 | + | 0.777825i | \(0.283677\pi\) | |||||||
\(830\) | −1.96416 | −0.0681769 | ||||||||
\(831\) | −10.8779 | −0.377349 | ||||||||
\(832\) | 178.505 | 6.18855 | ||||||||
\(833\) | 3.35827 | 0.116357 | ||||||||
\(834\) | 32.7590 | 1.13435 | ||||||||
\(835\) | 34.5888 | 1.19700 | ||||||||
\(836\) | 23.3265 | 0.806763 | ||||||||
\(837\) | 5.31791 | 0.183814 | ||||||||
\(838\) | −45.3462 | −1.56646 | ||||||||
\(839\) | −31.6141 | −1.09144 | −0.545721 | − | 0.837967i | \(-0.683744\pi\) | ||||
−0.545721 | + | 0.837967i | \(0.683744\pi\) | |||||||
\(840\) | 44.9934 | 1.55242 | ||||||||
\(841\) | −13.2128 | −0.455614 | ||||||||
\(842\) | −9.35859 | −0.322518 | ||||||||
\(843\) | 16.1162 | 0.555073 | ||||||||
\(844\) | −5.35102 | −0.184190 | ||||||||
\(845\) | 53.5776 | 1.84312 | ||||||||
\(846\) | −7.99468 | −0.274863 | ||||||||
\(847\) | 12.0427 | 0.413793 | ||||||||
\(848\) | −30.3306 | −1.04156 | ||||||||
\(849\) | 62.7007 | 2.15188 | ||||||||
\(850\) | −5.55088 | −0.190394 | ||||||||
\(851\) | −50.1513 | −1.71916 | ||||||||
\(852\) | 171.539 | 5.87682 | ||||||||
\(853\) | 3.85716 | 0.132067 | 0.0660333 | − | 0.997817i | \(-0.478966\pi\) | ||||
0.0660333 | + | 0.997817i | \(0.478966\pi\) | |||||||
\(854\) | 26.4757 | 0.905978 | ||||||||
\(855\) | −3.09044 | −0.105691 | ||||||||
\(856\) | −112.967 | −3.86114 | ||||||||
\(857\) | −15.2961 | −0.522503 | −0.261252 | − | 0.965271i | \(-0.584135\pi\) | ||||
−0.261252 | + | 0.965271i | \(0.584135\pi\) | |||||||
\(858\) | −188.951 | −6.45070 | ||||||||
\(859\) | 42.7149 | 1.45741 | 0.728707 | − | 0.684826i | \(-0.240122\pi\) | ||||
0.728707 | + | 0.684826i | \(0.240122\pi\) | |||||||
\(860\) | −11.7580 | −0.400945 | ||||||||
\(861\) | −29.0163 | −0.988874 | ||||||||
\(862\) | −38.9199 | −1.32562 | ||||||||
\(863\) | 1.53527 | 0.0522612 | 0.0261306 | − | 0.999659i | \(-0.491681\pi\) | ||||
0.0261306 | + | 0.999659i | \(0.491681\pi\) | |||||||
\(864\) | −38.7826 | −1.31941 | ||||||||
\(865\) | 30.5601 | 1.03908 | ||||||||
\(866\) | −13.7379 | −0.466834 | ||||||||
\(867\) | 37.3509 | 1.26850 | ||||||||
\(868\) | 21.6410 | 0.734542 | ||||||||
\(869\) | −55.6446 | −1.88761 | ||||||||
\(870\) | 35.4536 | 1.20199 | ||||||||
\(871\) | −113.141 | −3.83364 | ||||||||
\(872\) | 106.714 | 3.61378 | ||||||||
\(873\) | −0.569363 | −0.0192700 | ||||||||
\(874\) | −21.1548 | −0.715571 | ||||||||
\(875\) | −17.2513 | −0.583201 | ||||||||
\(876\) | −131.135 | −4.43064 | ||||||||
\(877\) | 46.6919 | 1.57667 | 0.788337 | − | 0.615243i | \(-0.210942\pi\) | ||||
0.788337 | + | 0.615243i | \(0.210942\pi\) | |||||||
\(878\) | 48.2660 | 1.62890 | ||||||||
\(879\) | −39.7504 | −1.34075 | ||||||||
\(880\) | −88.2770 | −2.97582 | ||||||||
\(881\) | 25.8481 | 0.870846 | 0.435423 | − | 0.900226i | \(-0.356599\pi\) | ||||
0.435423 | + | 0.900226i | \(0.356599\pi\) | |||||||
\(882\) | 27.2985 | 0.919190 | ||||||||
\(883\) | −17.9733 | −0.604851 | −0.302425 | − | 0.953173i | \(-0.597796\pi\) | ||||
−0.302425 | + | 0.953173i | \(0.597796\pi\) | |||||||
\(884\) | −26.7939 | −0.901177 | ||||||||
\(885\) | 38.2027 | 1.28417 | ||||||||
\(886\) | 35.8434 | 1.20418 | ||||||||
\(887\) | −10.1577 | −0.341063 | −0.170532 | − | 0.985352i | \(-0.554548\pi\) | ||||
−0.170532 | + | 0.985352i | \(0.554548\pi\) | |||||||
\(888\) | 132.218 | 4.43694 | ||||||||
\(889\) | −12.7566 | −0.427842 | ||||||||
\(890\) | 20.7635 | 0.695994 | ||||||||
\(891\) | 47.3330 | 1.58571 | ||||||||
\(892\) | −66.0328 | −2.21094 | ||||||||
\(893\) | −1.38691 | −0.0464112 | ||||||||
\(894\) | −72.8599 | −2.43680 | ||||||||
\(895\) | −7.40570 | −0.247545 | ||||||||
\(896\) | −44.1495 | −1.47493 | ||||||||
\(897\) | 124.738 | 4.16487 | ||||||||
\(898\) | −8.32629 | −0.277852 | ||||||||
\(899\) | 10.6789 | 0.356163 | ||||||||
\(900\) | −32.8454 | −1.09485 | ||||||||
\(901\) | 1.54389 | 0.0514345 | ||||||||
\(902\) | 100.664 | 3.35173 | ||||||||
\(903\) | 5.15007 | 0.171384 | ||||||||
\(904\) | −127.109 | −4.22758 | ||||||||
\(905\) | −9.83841 | −0.327040 | ||||||||
\(906\) | −58.9082 | −1.95709 | ||||||||
\(907\) | 31.0284 | 1.03028 | 0.515141 | − | 0.857105i | \(-0.327740\pi\) | ||||
0.515141 | + | 0.857105i | \(0.327740\pi\) | |||||||
\(908\) | 131.977 | 4.37981 | ||||||||
\(909\) | −9.18225 | −0.304556 | ||||||||
\(910\) | −41.8746 | −1.38813 | ||||||||
\(911\) | −20.1216 | −0.666659 | −0.333330 | − | 0.942810i | \(-0.608172\pi\) | ||||
−0.333330 | + | 0.942810i | \(0.608172\pi\) | |||||||
\(912\) | 31.5418 | 1.04445 | ||||||||
\(913\) | −2.17257 | −0.0719016 | ||||||||
\(914\) | −17.8032 | −0.588879 | ||||||||
\(915\) | 21.3571 | 0.706044 | ||||||||
\(916\) | 10.9112 | 0.360518 | ||||||||
\(917\) | −2.57556 | −0.0850524 | ||||||||
\(918\) | 3.80424 | 0.125559 | ||||||||
\(919\) | 55.1391 | 1.81887 | 0.909436 | − | 0.415845i | \(-0.136514\pi\) | ||||
0.909436 | + | 0.415845i | \(0.136514\pi\) | |||||||
\(920\) | 103.045 | 3.39729 | ||||||||
\(921\) | 59.4425 | 1.95870 | ||||||||
\(922\) | 113.041 | 3.72281 | ||||||||
\(923\) | −99.9780 | −3.29081 | ||||||||
\(924\) | 79.4705 | 2.61439 | ||||||||
\(925\) | −18.5569 | −0.610149 | ||||||||
\(926\) | 33.3422 | 1.09569 | ||||||||
\(927\) | −18.3716 | −0.603402 | ||||||||
\(928\) | −77.8796 | −2.55652 | ||||||||
\(929\) | −45.0748 | −1.47886 | −0.739428 | − | 0.673235i | \(-0.764904\pi\) | ||||
−0.739428 | + | 0.673235i | \(0.764904\pi\) | |||||||
\(930\) | 23.9819 | 0.786397 | ||||||||
\(931\) | 4.73573 | 0.155207 | ||||||||
\(932\) | 71.5079 | 2.34232 | ||||||||
\(933\) | 31.2579 | 1.02334 | ||||||||
\(934\) | 55.3102 | 1.80980 | ||||||||
\(935\) | 4.49348 | 0.146953 | ||||||||
\(936\) | −136.396 | −4.45823 | ||||||||
\(937\) | 28.8874 | 0.943712 | 0.471856 | − | 0.881676i | \(-0.343584\pi\) | ||||
0.471856 | + | 0.881676i | \(0.343584\pi\) | |||||||
\(938\) | 65.3713 | 2.13445 | ||||||||
\(939\) | 48.0398 | 1.56772 | ||||||||
\(940\) | 10.7876 | 0.351854 | ||||||||
\(941\) | −14.9077 | −0.485977 | −0.242988 | − | 0.970029i | \(-0.578128\pi\) | ||||
−0.242988 | + | 0.970029i | \(0.578128\pi\) | |||||||
\(942\) | −107.394 | −3.49907 | ||||||||
\(943\) | −66.4538 | −2.16404 | ||||||||
\(944\) | −161.716 | −5.26342 | ||||||||
\(945\) | 4.32784 | 0.140785 | ||||||||
\(946\) | −17.8666 | −0.580894 | ||||||||
\(947\) | −7.54647 | −0.245227 | −0.122614 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122614 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(948\) | −154.646 | −5.02267 | ||||||||
\(949\) | 76.4295 | 2.48101 | ||||||||
\(950\) | −7.82768 | −0.253963 | ||||||||
\(951\) | 54.4097 | 1.76435 | ||||||||
\(952\) | 9.69491 | 0.314214 | ||||||||
\(953\) | 12.7006 | 0.411412 | 0.205706 | − | 0.978614i | \(-0.434051\pi\) | ||||
0.205706 | + | 0.978614i | \(0.434051\pi\) | |||||||
\(954\) | 12.5499 | 0.406319 | ||||||||
\(955\) | 17.6575 | 0.571385 | ||||||||
\(956\) | −44.9912 | −1.45512 | ||||||||
\(957\) | 39.2155 | 1.26766 | ||||||||
\(958\) | 57.4543 | 1.85627 | ||||||||
\(959\) | 19.7982 | 0.639317 | ||||||||
\(960\) | −83.1982 | −2.68521 | ||||||||
\(961\) | −23.7764 | −0.766982 | ||||||||
\(962\) | −123.053 | −3.96739 | ||||||||
\(963\) | 26.4351 | 0.851859 | ||||||||
\(964\) | −41.9481 | −1.35106 | ||||||||
\(965\) | −25.7949 | −0.830366 | ||||||||
\(966\) | −72.0718 | −2.31887 | ||||||||
\(967\) | −48.9087 | −1.57280 | −0.786399 | − | 0.617719i | \(-0.788057\pi\) | ||||
−0.786399 | + | 0.617719i | \(0.788057\pi\) | |||||||
\(968\) | −72.7129 | −2.33708 | ||||||||
\(969\) | −1.60554 | −0.0515774 | ||||||||
\(970\) | 1.05542 | 0.0338875 | ||||||||
\(971\) | 22.4904 | 0.721750 | 0.360875 | − | 0.932614i | \(-0.382478\pi\) | ||||
0.360875 | + | 0.932614i | \(0.382478\pi\) | |||||||
\(972\) | 99.7835 | 3.20056 | ||||||||
\(973\) | 8.03025 | 0.257438 | ||||||||
\(974\) | −56.4390 | −1.80842 | ||||||||
\(975\) | 46.1554 | 1.47816 | ||||||||
\(976\) | −90.4070 | −2.89386 | ||||||||
\(977\) | 23.2560 | 0.744025 | 0.372013 | − | 0.928228i | \(-0.378668\pi\) | ||||
0.372013 | + | 0.928228i | \(0.378668\pi\) | |||||||
\(978\) | 147.823 | 4.72684 | ||||||||
\(979\) | 22.9667 | 0.734018 | ||||||||
\(980\) | −36.8353 | −1.17666 | ||||||||
\(981\) | −24.9717 | −0.797285 | ||||||||
\(982\) | 108.424 | 3.45995 | ||||||||
\(983\) | 27.6562 | 0.882094 | 0.441047 | − | 0.897484i | \(-0.354607\pi\) | ||||
0.441047 | + | 0.897484i | \(0.354607\pi\) | |||||||
\(984\) | 175.198 | 5.58510 | ||||||||
\(985\) | −6.92170 | −0.220544 | ||||||||
\(986\) | 7.63933 | 0.243286 | ||||||||
\(987\) | −4.72504 | −0.150400 | ||||||||
\(988\) | −37.7840 | −1.20207 | ||||||||
\(989\) | 11.7948 | 0.375053 | ||||||||
\(990\) | 36.5264 | 1.16089 | ||||||||
\(991\) | 17.2869 | 0.549137 | 0.274568 | − | 0.961568i | \(-0.411465\pi\) | ||||
0.274568 | + | 0.961568i | \(0.411465\pi\) | |||||||
\(992\) | −52.6801 | −1.67260 | ||||||||
\(993\) | −36.4436 | −1.15650 | ||||||||
\(994\) | 57.7659 | 1.83222 | ||||||||
\(995\) | −7.22211 | −0.228956 | ||||||||
\(996\) | −6.03796 | −0.191320 | ||||||||
\(997\) | −32.5777 | −1.03175 | −0.515873 | − | 0.856665i | \(-0.672532\pi\) | ||||
−0.515873 | + | 0.856665i | \(0.672532\pi\) | |||||||
\(998\) | −73.4218 | −2.32413 | ||||||||
\(999\) | 12.7178 | 0.402375 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4009.2.a.d.1.3 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.d.1.3 | ✓ | 75 | 1.1 | even | 1 | trivial |