Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.956879 | −0.552454 | −0.276227 | − | 0.961092i | \(-0.589084\pi\) | ||||
−0.276227 | + | 0.961092i | \(0.589084\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.0953014 | −0.0426201 | −0.0213100 | − | 0.999773i | \(-0.506784\pi\) | ||||
−0.0213100 | + | 0.999773i | \(0.506784\pi\) | |||||||
\(6\) | 0.956879 | 0.390644 | ||||||||
\(7\) | −4.20577 | −1.58963 | −0.794817 | − | 0.606850i | \(-0.792433\pi\) | ||||
−0.794817 | + | 0.606850i | \(0.792433\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.08438 | −0.694794 | ||||||||
\(10\) | 0.0953014 | 0.0301369 | ||||||||
\(11\) | −0.121483 | −0.0366286 | −0.0183143 | − | 0.999832i | \(-0.505830\pi\) | ||||
−0.0183143 | + | 0.999832i | \(0.505830\pi\) | |||||||
\(12\) | −0.956879 | −0.276227 | ||||||||
\(13\) | −1.63495 | −0.453454 | −0.226727 | − | 0.973958i | \(-0.572802\pi\) | ||||
−0.226727 | + | 0.973958i | \(0.572802\pi\) | |||||||
\(14\) | 4.20577 | 1.12404 | ||||||||
\(15\) | 0.0911919 | 0.0235457 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.22305 | 0.781703 | 0.390852 | − | 0.920454i | \(-0.372181\pi\) | ||||
0.390852 | + | 0.920454i | \(0.372181\pi\) | |||||||
\(18\) | 2.08438 | 0.491294 | ||||||||
\(19\) | −1.33888 | −0.307159 | −0.153580 | − | 0.988136i | \(-0.549080\pi\) | ||||
−0.153580 | + | 0.988136i | \(0.549080\pi\) | |||||||
\(20\) | −0.0953014 | −0.0213100 | ||||||||
\(21\) | 4.02442 | 0.878200 | ||||||||
\(22\) | 0.121483 | 0.0259003 | ||||||||
\(23\) | 7.51615 | 1.56723 | 0.783613 | − | 0.621249i | \(-0.213374\pi\) | ||||
0.783613 | + | 0.621249i | \(0.213374\pi\) | |||||||
\(24\) | 0.956879 | 0.195322 | ||||||||
\(25\) | −4.99092 | −0.998184 | ||||||||
\(26\) | 1.63495 | 0.320640 | ||||||||
\(27\) | 4.86514 | 0.936297 | ||||||||
\(28\) | −4.20577 | −0.794817 | ||||||||
\(29\) | 9.09309 | 1.68854 | 0.844272 | − | 0.535914i | \(-0.180033\pi\) | ||||
0.844272 | + | 0.535914i | \(0.180033\pi\) | |||||||
\(30\) | −0.0911919 | −0.0166493 | ||||||||
\(31\) | 1.34519 | 0.241604 | 0.120802 | − | 0.992677i | \(-0.461453\pi\) | ||||
0.120802 | + | 0.992677i | \(0.461453\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.116245 | 0.0202356 | ||||||||
\(34\) | −3.22305 | −0.552748 | ||||||||
\(35\) | 0.400816 | 0.0677503 | ||||||||
\(36\) | −2.08438 | −0.347397 | ||||||||
\(37\) | −0.847194 | −0.139278 | −0.0696389 | − | 0.997572i | \(-0.522185\pi\) | ||||
−0.0696389 | + | 0.997572i | \(0.522185\pi\) | |||||||
\(38\) | 1.33888 | 0.217194 | ||||||||
\(39\) | 1.56445 | 0.250513 | ||||||||
\(40\) | 0.0953014 | 0.0150685 | ||||||||
\(41\) | −2.51290 | −0.392449 | −0.196225 | − | 0.980559i | \(-0.562868\pi\) | ||||
−0.196225 | + | 0.980559i | \(0.562868\pi\) | |||||||
\(42\) | −4.02442 | −0.620981 | ||||||||
\(43\) | 6.69337 | 1.02073 | 0.510365 | − | 0.859958i | \(-0.329510\pi\) | ||||
0.510365 | + | 0.859958i | \(0.329510\pi\) | |||||||
\(44\) | −0.121483 | −0.0183143 | ||||||||
\(45\) | 0.198645 | 0.0296122 | ||||||||
\(46\) | −7.51615 | −1.10820 | ||||||||
\(47\) | 11.4944 | 1.67664 | 0.838319 | − | 0.545181i | \(-0.183539\pi\) | ||||
0.838319 | + | 0.545181i | \(0.183539\pi\) | |||||||
\(48\) | −0.956879 | −0.138114 | ||||||||
\(49\) | 10.6885 | 1.52693 | ||||||||
\(50\) | 4.99092 | 0.705822 | ||||||||
\(51\) | −3.08407 | −0.431856 | ||||||||
\(52\) | −1.63495 | −0.226727 | ||||||||
\(53\) | 6.97986 | 0.958757 | 0.479379 | − | 0.877608i | \(-0.340862\pi\) | ||||
0.479379 | + | 0.877608i | \(0.340862\pi\) | |||||||
\(54\) | −4.86514 | −0.662062 | ||||||||
\(55\) | 0.0115775 | 0.00156111 | ||||||||
\(56\) | 4.20577 | 0.562020 | ||||||||
\(57\) | 1.28114 | 0.169692 | ||||||||
\(58\) | −9.09309 | −1.19398 | ||||||||
\(59\) | −3.92557 | −0.511066 | −0.255533 | − | 0.966800i | \(-0.582251\pi\) | ||||
−0.255533 | + | 0.966800i | \(0.582251\pi\) | |||||||
\(60\) | 0.0911919 | 0.0117728 | ||||||||
\(61\) | −10.4678 | −1.34026 | −0.670130 | − | 0.742243i | \(-0.733762\pi\) | ||||
−0.670130 | + | 0.742243i | \(0.733762\pi\) | |||||||
\(62\) | −1.34519 | −0.170840 | ||||||||
\(63\) | 8.76644 | 1.10447 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.155813 | 0.0193262 | ||||||||
\(66\) | −0.116245 | −0.0143087 | ||||||||
\(67\) | −14.1662 | −1.73068 | −0.865339 | − | 0.501187i | \(-0.832897\pi\) | ||||
−0.865339 | + | 0.501187i | \(0.832897\pi\) | |||||||
\(68\) | 3.22305 | 0.390852 | ||||||||
\(69\) | −7.19205 | −0.865821 | ||||||||
\(70\) | −0.400816 | −0.0479067 | ||||||||
\(71\) | 5.68177 | 0.674302 | 0.337151 | − | 0.941451i | \(-0.390537\pi\) | ||||
0.337151 | + | 0.941451i | \(0.390537\pi\) | |||||||
\(72\) | 2.08438 | 0.245647 | ||||||||
\(73\) | 0.786531 | 0.0920565 | 0.0460283 | − | 0.998940i | \(-0.485344\pi\) | ||||
0.0460283 | + | 0.998940i | \(0.485344\pi\) | |||||||
\(74\) | 0.847194 | 0.0984843 | ||||||||
\(75\) | 4.77571 | 0.551451 | ||||||||
\(76\) | −1.33888 | −0.153580 | ||||||||
\(77\) | 0.510931 | 0.0582260 | ||||||||
\(78\) | −1.56445 | −0.177139 | ||||||||
\(79\) | −1.19208 | −0.134119 | −0.0670595 | − | 0.997749i | \(-0.521362\pi\) | ||||
−0.0670595 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(80\) | −0.0953014 | −0.0106550 | ||||||||
\(81\) | 1.59779 | 0.177533 | ||||||||
\(82\) | 2.51290 | 0.277504 | ||||||||
\(83\) | −11.7356 | −1.28815 | −0.644075 | − | 0.764963i | \(-0.722757\pi\) | ||||
−0.644075 | + | 0.764963i | \(0.722757\pi\) | |||||||
\(84\) | 4.02442 | 0.439100 | ||||||||
\(85\) | −0.307161 | −0.0333163 | ||||||||
\(86\) | −6.69337 | −0.721765 | ||||||||
\(87\) | −8.70099 | −0.932844 | ||||||||
\(88\) | 0.121483 | 0.0129502 | ||||||||
\(89\) | −5.77411 | −0.612055 | −0.306027 | − | 0.952023i | \(-0.599000\pi\) | ||||
−0.306027 | + | 0.952023i | \(0.599000\pi\) | |||||||
\(90\) | −0.198645 | −0.0209390 | ||||||||
\(91\) | 6.87624 | 0.720825 | ||||||||
\(92\) | 7.51615 | 0.783613 | ||||||||
\(93\) | −1.28719 | −0.133475 | ||||||||
\(94\) | −11.4944 | −1.18556 | ||||||||
\(95\) | 0.127597 | 0.0130912 | ||||||||
\(96\) | 0.956879 | 0.0976611 | ||||||||
\(97\) | 4.53164 | 0.460119 | 0.230059 | − | 0.973177i | \(-0.426108\pi\) | ||||
0.230059 | + | 0.973177i | \(0.426108\pi\) | |||||||
\(98\) | −10.6885 | −1.07971 | ||||||||
\(99\) | 0.253217 | 0.0254493 | ||||||||
\(100\) | −4.99092 | −0.499092 | ||||||||
\(101\) | −18.8485 | −1.87549 | −0.937746 | − | 0.347322i | \(-0.887091\pi\) | ||||
−0.937746 | + | 0.347322i | \(0.887091\pi\) | |||||||
\(102\) | 3.08407 | 0.305368 | ||||||||
\(103\) | −16.0310 | −1.57958 | −0.789792 | − | 0.613374i | \(-0.789812\pi\) | ||||
−0.789792 | + | 0.613374i | \(0.789812\pi\) | |||||||
\(104\) | 1.63495 | 0.160320 | ||||||||
\(105\) | −0.383533 | −0.0374290 | ||||||||
\(106\) | −6.97986 | −0.677944 | ||||||||
\(107\) | −7.85447 | −0.759321 | −0.379660 | − | 0.925126i | \(-0.623959\pi\) | ||||
−0.379660 | + | 0.925126i | \(0.623959\pi\) | |||||||
\(108\) | 4.86514 | 0.468148 | ||||||||
\(109\) | 12.9103 | 1.23659 | 0.618293 | − | 0.785947i | \(-0.287824\pi\) | ||||
0.618293 | + | 0.785947i | \(0.287824\pi\) | |||||||
\(110\) | −0.0115775 | −0.00110387 | ||||||||
\(111\) | 0.810662 | 0.0769446 | ||||||||
\(112\) | −4.20577 | −0.397408 | ||||||||
\(113\) | −5.40353 | −0.508321 | −0.254160 | − | 0.967162i | \(-0.581799\pi\) | ||||
−0.254160 | + | 0.967162i | \(0.581799\pi\) | |||||||
\(114\) | −1.28114 | −0.119990 | ||||||||
\(115\) | −0.716300 | −0.0667953 | ||||||||
\(116\) | 9.09309 | 0.844272 | ||||||||
\(117\) | 3.40786 | 0.315057 | ||||||||
\(118\) | 3.92557 | 0.361378 | ||||||||
\(119\) | −13.5554 | −1.24262 | ||||||||
\(120\) | −0.0911919 | −0.00832465 | ||||||||
\(121\) | −10.9852 | −0.998658 | ||||||||
\(122\) | 10.4678 | 0.947708 | ||||||||
\(123\) | 2.40454 | 0.216810 | ||||||||
\(124\) | 1.34519 | 0.120802 | ||||||||
\(125\) | 0.952148 | 0.0851627 | ||||||||
\(126\) | −8.76644 | −0.780977 | ||||||||
\(127\) | −11.4199 | −1.01335 | −0.506675 | − | 0.862137i | \(-0.669126\pi\) | ||||
−0.506675 | + | 0.862137i | \(0.669126\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.40475 | −0.563907 | ||||||||
\(130\) | −0.155813 | −0.0136657 | ||||||||
\(131\) | 2.73835 | 0.239251 | 0.119625 | − | 0.992819i | \(-0.461831\pi\) | ||||
0.119625 | + | 0.992819i | \(0.461831\pi\) | |||||||
\(132\) | 0.116245 | 0.0101178 | ||||||||
\(133\) | 5.63101 | 0.488271 | ||||||||
\(134\) | 14.1662 | 1.22377 | ||||||||
\(135\) | −0.463655 | −0.0399050 | ||||||||
\(136\) | −3.22305 | −0.276374 | ||||||||
\(137\) | −12.1095 | −1.03458 | −0.517292 | − | 0.855809i | \(-0.673060\pi\) | ||||
−0.517292 | + | 0.855809i | \(0.673060\pi\) | |||||||
\(138\) | 7.19205 | 0.612228 | ||||||||
\(139\) | 16.1577 | 1.37048 | 0.685241 | − | 0.728316i | \(-0.259697\pi\) | ||||
0.685241 | + | 0.728316i | \(0.259697\pi\) | |||||||
\(140\) | 0.400816 | 0.0338752 | ||||||||
\(141\) | −10.9988 | −0.926266 | ||||||||
\(142\) | −5.68177 | −0.476803 | ||||||||
\(143\) | 0.198619 | 0.0166094 | ||||||||
\(144\) | −2.08438 | −0.173699 | ||||||||
\(145\) | −0.866584 | −0.0719659 | ||||||||
\(146\) | −0.786531 | −0.0650938 | ||||||||
\(147\) | −10.2276 | −0.843562 | ||||||||
\(148\) | −0.847194 | −0.0696389 | ||||||||
\(149\) | −4.96833 | −0.407021 | −0.203511 | − | 0.979073i | \(-0.565235\pi\) | ||||
−0.203511 | + | 0.979073i | \(0.565235\pi\) | |||||||
\(150\) | −4.77571 | −0.389935 | ||||||||
\(151\) | 14.1500 | 1.15151 | 0.575754 | − | 0.817623i | \(-0.304709\pi\) | ||||
0.575754 | + | 0.817623i | \(0.304709\pi\) | |||||||
\(152\) | 1.33888 | 0.108597 | ||||||||
\(153\) | −6.71806 | −0.543123 | ||||||||
\(154\) | −0.510931 | −0.0411720 | ||||||||
\(155\) | −0.128199 | −0.0102972 | ||||||||
\(156\) | 1.56445 | 0.125256 | ||||||||
\(157\) | −3.45379 | −0.275642 | −0.137821 | − | 0.990457i | \(-0.544010\pi\) | ||||
−0.137821 | + | 0.990457i | \(0.544010\pi\) | |||||||
\(158\) | 1.19208 | 0.0948365 | ||||||||
\(159\) | −6.67888 | −0.529670 | ||||||||
\(160\) | 0.0953014 | 0.00753424 | ||||||||
\(161\) | −31.6113 | −2.49132 | ||||||||
\(162\) | −1.59779 | −0.125535 | ||||||||
\(163\) | 7.63173 | 0.597764 | 0.298882 | − | 0.954290i | \(-0.403386\pi\) | ||||
0.298882 | + | 0.954290i | \(0.403386\pi\) | |||||||
\(164\) | −2.51290 | −0.196225 | ||||||||
\(165\) | −0.0110783 | −0.000862444 0 | ||||||||
\(166\) | 11.7356 | 0.910859 | ||||||||
\(167\) | 13.2615 | 1.02621 | 0.513103 | − | 0.858327i | \(-0.328496\pi\) | ||||
0.513103 | + | 0.858327i | \(0.328496\pi\) | |||||||
\(168\) | −4.02442 | −0.310491 | ||||||||
\(169\) | −10.3269 | −0.794380 | ||||||||
\(170\) | 0.307161 | 0.0235582 | ||||||||
\(171\) | 2.79073 | 0.213412 | ||||||||
\(172\) | 6.69337 | 0.510365 | ||||||||
\(173\) | 23.1657 | 1.76126 | 0.880628 | − | 0.473809i | \(-0.157121\pi\) | ||||
0.880628 | + | 0.473809i | \(0.157121\pi\) | |||||||
\(174\) | 8.70099 | 0.659620 | ||||||||
\(175\) | 20.9907 | 1.58675 | ||||||||
\(176\) | −0.121483 | −0.00915714 | ||||||||
\(177\) | 3.75630 | 0.282341 | ||||||||
\(178\) | 5.77411 | 0.432788 | ||||||||
\(179\) | 0.199393 | 0.0149033 | 0.00745165 | − | 0.999972i | \(-0.497628\pi\) | ||||
0.00745165 | + | 0.999972i | \(0.497628\pi\) | |||||||
\(180\) | 0.198645 | 0.0148061 | ||||||||
\(181\) | −23.4780 | −1.74511 | −0.872554 | − | 0.488518i | \(-0.837538\pi\) | ||||
−0.872554 | + | 0.488518i | \(0.837538\pi\) | |||||||
\(182\) | −6.87624 | −0.509701 | ||||||||
\(183\) | 10.0164 | 0.740433 | ||||||||
\(184\) | −7.51615 | −0.554098 | ||||||||
\(185\) | 0.0807387 | 0.00593603 | ||||||||
\(186\) | 1.28719 | 0.0943812 | ||||||||
\(187\) | −0.391546 | −0.0286327 | ||||||||
\(188\) | 11.4944 | 0.838319 | ||||||||
\(189\) | −20.4617 | −1.48837 | ||||||||
\(190\) | −0.127597 | −0.00925684 | ||||||||
\(191\) | 19.7628 | 1.42999 | 0.714994 | − | 0.699130i | \(-0.246429\pi\) | ||||
0.714994 | + | 0.699130i | \(0.246429\pi\) | |||||||
\(192\) | −0.956879 | −0.0690568 | ||||||||
\(193\) | 9.71439 | 0.699257 | 0.349628 | − | 0.936888i | \(-0.386308\pi\) | ||||
0.349628 | + | 0.936888i | \(0.386308\pi\) | |||||||
\(194\) | −4.53164 | −0.325353 | ||||||||
\(195\) | −0.149094 | −0.0106769 | ||||||||
\(196\) | 10.6885 | 0.763467 | ||||||||
\(197\) | −1.91169 | −0.136202 | −0.0681011 | − | 0.997678i | \(-0.521694\pi\) | ||||
−0.0681011 | + | 0.997678i | \(0.521694\pi\) | |||||||
\(198\) | −0.253217 | −0.0179954 | ||||||||
\(199\) | 10.3431 | 0.733205 | 0.366602 | − | 0.930378i | \(-0.380521\pi\) | ||||
0.366602 | + | 0.930378i | \(0.380521\pi\) | |||||||
\(200\) | 4.99092 | 0.352911 | ||||||||
\(201\) | 13.5554 | 0.956121 | ||||||||
\(202\) | 18.8485 | 1.32617 | ||||||||
\(203\) | −38.2435 | −2.68417 | ||||||||
\(204\) | −3.08407 | −0.215928 | ||||||||
\(205\) | 0.239483 | 0.0167262 | ||||||||
\(206\) | 16.0310 | 1.11693 | ||||||||
\(207\) | −15.6665 | −1.08890 | ||||||||
\(208\) | −1.63495 | −0.113363 | ||||||||
\(209\) | 0.162651 | 0.0112508 | ||||||||
\(210\) | 0.383533 | 0.0264663 | ||||||||
\(211\) | 26.4053 | 1.81782 | 0.908909 | − | 0.416995i | \(-0.136917\pi\) | ||||
0.908909 | + | 0.416995i | \(0.136917\pi\) | |||||||
\(212\) | 6.97986 | 0.479379 | ||||||||
\(213\) | −5.43676 | −0.372521 | ||||||||
\(214\) | 7.85447 | 0.536921 | ||||||||
\(215\) | −0.637888 | −0.0435036 | ||||||||
\(216\) | −4.86514 | −0.331031 | ||||||||
\(217\) | −5.65758 | −0.384062 | ||||||||
\(218\) | −12.9103 | −0.874399 | ||||||||
\(219\) | −0.752615 | −0.0508570 | ||||||||
\(220\) | 0.0115775 | 0.000780556 0 | ||||||||
\(221\) | −5.26952 | −0.354466 | ||||||||
\(222\) | −0.810662 | −0.0544081 | ||||||||
\(223\) | −2.87973 | −0.192841 | −0.0964204 | − | 0.995341i | \(-0.530739\pi\) | ||||
−0.0964204 | + | 0.995341i | \(0.530739\pi\) | |||||||
\(224\) | 4.20577 | 0.281010 | ||||||||
\(225\) | 10.4030 | 0.693532 | ||||||||
\(226\) | 5.40353 | 0.359437 | ||||||||
\(227\) | −17.7575 | −1.17861 | −0.589305 | − | 0.807911i | \(-0.700598\pi\) | ||||
−0.589305 | + | 0.807911i | \(0.700598\pi\) | |||||||
\(228\) | 1.28114 | 0.0848458 | ||||||||
\(229\) | −7.68778 | −0.508023 | −0.254011 | − | 0.967201i | \(-0.581750\pi\) | ||||
−0.254011 | + | 0.967201i | \(0.581750\pi\) | |||||||
\(230\) | 0.716300 | 0.0472314 | ||||||||
\(231\) | −0.488899 | −0.0321672 | ||||||||
\(232\) | −9.09309 | −0.596991 | ||||||||
\(233\) | −8.84240 | −0.579285 | −0.289643 | − | 0.957135i | \(-0.593536\pi\) | ||||
−0.289643 | + | 0.957135i | \(0.593536\pi\) | |||||||
\(234\) | −3.40786 | −0.222779 | ||||||||
\(235\) | −1.09544 | −0.0714584 | ||||||||
\(236\) | −3.92557 | −0.255533 | ||||||||
\(237\) | 1.14067 | 0.0740947 | ||||||||
\(238\) | 13.5554 | 0.878666 | ||||||||
\(239\) | −20.4693 | −1.32405 | −0.662025 | − | 0.749481i | \(-0.730303\pi\) | ||||
−0.662025 | + | 0.749481i | \(0.730303\pi\) | |||||||
\(240\) | 0.0911919 | 0.00588641 | ||||||||
\(241\) | −30.2979 | −1.95166 | −0.975828 | − | 0.218538i | \(-0.929871\pi\) | ||||
−0.975828 | + | 0.218538i | \(0.929871\pi\) | |||||||
\(242\) | 10.9852 | 0.706158 | ||||||||
\(243\) | −16.1243 | −1.03438 | ||||||||
\(244\) | −10.4678 | −0.670130 | ||||||||
\(245\) | −1.01863 | −0.0650781 | ||||||||
\(246\) | −2.40454 | −0.153308 | ||||||||
\(247\) | 2.18900 | 0.139283 | ||||||||
\(248\) | −1.34519 | −0.0854199 | ||||||||
\(249\) | 11.2296 | 0.711644 | ||||||||
\(250\) | −0.952148 | −0.0602192 | ||||||||
\(251\) | 12.1789 | 0.768727 | 0.384363 | − | 0.923182i | \(-0.374421\pi\) | ||||
0.384363 | + | 0.923182i | \(0.374421\pi\) | |||||||
\(252\) | 8.76644 | 0.552234 | ||||||||
\(253\) | −0.913087 | −0.0574053 | ||||||||
\(254\) | 11.4199 | 0.716547 | ||||||||
\(255\) | 0.293916 | 0.0184057 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.0370 | 0.750845 | 0.375423 | − | 0.926854i | \(-0.377498\pi\) | ||||
0.375423 | + | 0.926854i | \(0.377498\pi\) | |||||||
\(258\) | 6.40475 | 0.398742 | ||||||||
\(259\) | 3.56311 | 0.221401 | ||||||||
\(260\) | 0.155813 | 0.00966312 | ||||||||
\(261\) | −18.9535 | −1.17319 | ||||||||
\(262\) | −2.73835 | −0.169176 | ||||||||
\(263\) | 0.138602 | 0.00854655 | 0.00427328 | − | 0.999991i | \(-0.498640\pi\) | ||||
0.00427328 | + | 0.999991i | \(0.498640\pi\) | |||||||
\(264\) | −0.116245 | −0.00715437 | ||||||||
\(265\) | −0.665190 | −0.0408623 | ||||||||
\(266\) | −5.63101 | −0.345260 | ||||||||
\(267\) | 5.52513 | 0.338132 | ||||||||
\(268\) | −14.1662 | −0.865339 | ||||||||
\(269\) | −19.3871 | −1.18205 | −0.591027 | − | 0.806652i | \(-0.701277\pi\) | ||||
−0.591027 | + | 0.806652i | \(0.701277\pi\) | |||||||
\(270\) | 0.463655 | 0.0282171 | ||||||||
\(271\) | −8.81160 | −0.535267 | −0.267633 | − | 0.963521i | \(-0.586242\pi\) | ||||
−0.267633 | + | 0.963521i | \(0.586242\pi\) | |||||||
\(272\) | 3.22305 | 0.195426 | ||||||||
\(273\) | −6.57973 | −0.398223 | ||||||||
\(274\) | 12.1095 | 0.731561 | ||||||||
\(275\) | 0.606313 | 0.0365620 | ||||||||
\(276\) | −7.19205 | −0.432911 | ||||||||
\(277\) | 25.6127 | 1.53892 | 0.769458 | − | 0.638698i | \(-0.220527\pi\) | ||||
0.769458 | + | 0.638698i | \(0.220527\pi\) | |||||||
\(278\) | −16.1577 | −0.969077 | ||||||||
\(279\) | −2.80390 | −0.167865 | ||||||||
\(280\) | −0.400816 | −0.0239534 | ||||||||
\(281\) | −13.4325 | −0.801316 | −0.400658 | − | 0.916228i | \(-0.631219\pi\) | ||||
−0.400658 | + | 0.916228i | \(0.631219\pi\) | |||||||
\(282\) | 10.9988 | 0.654969 | ||||||||
\(283\) | 9.19969 | 0.546865 | 0.273432 | − | 0.961891i | \(-0.411841\pi\) | ||||
0.273432 | + | 0.961891i | \(0.411841\pi\) | |||||||
\(284\) | 5.68177 | 0.337151 | ||||||||
\(285\) | −0.122095 | −0.00723227 | ||||||||
\(286\) | −0.198619 | −0.0117446 | ||||||||
\(287\) | 10.5687 | 0.623850 | ||||||||
\(288\) | 2.08438 | 0.122823 | ||||||||
\(289\) | −6.61198 | −0.388940 | ||||||||
\(290\) | 0.866584 | 0.0508876 | ||||||||
\(291\) | −4.33624 | −0.254195 | ||||||||
\(292\) | 0.786531 | 0.0460283 | ||||||||
\(293\) | −6.94996 | −0.406021 | −0.203010 | − | 0.979177i | \(-0.565073\pi\) | ||||
−0.203010 | + | 0.979177i | \(0.565073\pi\) | |||||||
\(294\) | 10.2276 | 0.596488 | ||||||||
\(295\) | 0.374112 | 0.0217817 | ||||||||
\(296\) | 0.847194 | 0.0492421 | ||||||||
\(297\) | −0.591033 | −0.0342952 | ||||||||
\(298\) | 4.96833 | 0.287808 | ||||||||
\(299\) | −12.2885 | −0.710665 | ||||||||
\(300\) | 4.77571 | 0.275725 | ||||||||
\(301\) | −28.1508 | −1.62259 | ||||||||
\(302\) | −14.1500 | −0.814239 | ||||||||
\(303\) | 18.0357 | 1.03612 | ||||||||
\(304\) | −1.33888 | −0.0767898 | ||||||||
\(305\) | 0.997593 | 0.0571220 | ||||||||
\(306\) | 6.71806 | 0.384046 | ||||||||
\(307\) | 26.4614 | 1.51023 | 0.755116 | − | 0.655591i | \(-0.227581\pi\) | ||||
0.755116 | + | 0.655591i | \(0.227581\pi\) | |||||||
\(308\) | 0.510931 | 0.0291130 | ||||||||
\(309\) | 15.3398 | 0.872649 | ||||||||
\(310\) | 0.128199 | 0.00728121 | ||||||||
\(311\) | −5.51240 | −0.312580 | −0.156290 | − | 0.987711i | \(-0.549953\pi\) | ||||
−0.156290 | + | 0.987711i | \(0.549953\pi\) | |||||||
\(312\) | −1.56445 | −0.0885696 | ||||||||
\(313\) | 6.03203 | 0.340950 | 0.170475 | − | 0.985362i | \(-0.445470\pi\) | ||||
0.170475 | + | 0.985362i | \(0.445470\pi\) | |||||||
\(314\) | 3.45379 | 0.194908 | ||||||||
\(315\) | −0.835454 | −0.0470725 | ||||||||
\(316\) | −1.19208 | −0.0670595 | ||||||||
\(317\) | 26.5260 | 1.48985 | 0.744923 | − | 0.667150i | \(-0.232486\pi\) | ||||
0.744923 | + | 0.667150i | \(0.232486\pi\) | |||||||
\(318\) | 6.67888 | 0.374533 | ||||||||
\(319\) | −1.10466 | −0.0618490 | ||||||||
\(320\) | −0.0953014 | −0.00532751 | ||||||||
\(321\) | 7.51578 | 0.419490 | ||||||||
\(322\) | 31.6113 | 1.76163 | ||||||||
\(323\) | −4.31526 | −0.240107 | ||||||||
\(324\) | 1.59779 | 0.0887664 | ||||||||
\(325\) | 8.15991 | 0.452630 | ||||||||
\(326\) | −7.63173 | −0.422683 | ||||||||
\(327\) | −12.3536 | −0.683158 | ||||||||
\(328\) | 2.51290 | 0.138752 | ||||||||
\(329\) | −48.3430 | −2.66524 | ||||||||
\(330\) | 0.0110783 | 0.000609840 0 | ||||||||
\(331\) | −31.7469 | −1.74497 | −0.872483 | − | 0.488645i | \(-0.837491\pi\) | ||||
−0.872483 | + | 0.488645i | \(0.837491\pi\) | |||||||
\(332\) | −11.7356 | −0.644075 | ||||||||
\(333\) | 1.76588 | 0.0967694 | ||||||||
\(334\) | −13.2615 | −0.725638 | ||||||||
\(335\) | 1.35006 | 0.0737616 | ||||||||
\(336\) | 4.02442 | 0.219550 | ||||||||
\(337\) | 31.0606 | 1.69198 | 0.845989 | − | 0.533200i | \(-0.179011\pi\) | ||||
0.845989 | + | 0.533200i | \(0.179011\pi\) | |||||||
\(338\) | 10.3269 | 0.561711 | ||||||||
\(339\) | 5.17052 | 0.280824 | ||||||||
\(340\) | −0.307161 | −0.0166581 | ||||||||
\(341\) | −0.163419 | −0.00884961 | ||||||||
\(342\) | −2.79073 | −0.150905 | ||||||||
\(343\) | −15.5132 | −0.837633 | ||||||||
\(344\) | −6.69337 | −0.360882 | ||||||||
\(345\) | 0.685413 | 0.0369014 | ||||||||
\(346\) | −23.1657 | −1.24540 | ||||||||
\(347\) | 6.01579 | 0.322945 | 0.161472 | − | 0.986877i | \(-0.448376\pi\) | ||||
0.161472 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(348\) | −8.70099 | −0.466422 | ||||||||
\(349\) | 18.7258 | 1.00237 | 0.501184 | − | 0.865341i | \(-0.332898\pi\) | ||||
0.501184 | + | 0.865341i | \(0.332898\pi\) | |||||||
\(350\) | −20.9907 | −1.12200 | ||||||||
\(351\) | −7.95427 | −0.424567 | ||||||||
\(352\) | 0.121483 | 0.00647508 | ||||||||
\(353\) | 17.2725 | 0.919324 | 0.459662 | − | 0.888094i | \(-0.347971\pi\) | ||||
0.459662 | + | 0.888094i | \(0.347971\pi\) | |||||||
\(354\) | −3.75630 | −0.199645 | ||||||||
\(355\) | −0.541480 | −0.0287388 | ||||||||
\(356\) | −5.77411 | −0.306027 | ||||||||
\(357\) | 12.9709 | 0.686492 | ||||||||
\(358\) | −0.199393 | −0.0105382 | ||||||||
\(359\) | 1.11572 | 0.0588852 | 0.0294426 | − | 0.999566i | \(-0.490627\pi\) | ||||
0.0294426 | + | 0.999566i | \(0.490627\pi\) | |||||||
\(360\) | −0.198645 | −0.0104695 | ||||||||
\(361\) | −17.2074 | −0.905653 | ||||||||
\(362\) | 23.4780 | 1.23398 | ||||||||
\(363\) | 10.5116 | 0.551713 | ||||||||
\(364\) | 6.87624 | 0.360413 | ||||||||
\(365\) | −0.0749575 | −0.00392346 | ||||||||
\(366\) | −10.0164 | −0.523565 | ||||||||
\(367\) | −9.30017 | −0.485465 | −0.242733 | − | 0.970093i | \(-0.578044\pi\) | ||||
−0.242733 | + | 0.970093i | \(0.578044\pi\) | |||||||
\(368\) | 7.51615 | 0.391807 | ||||||||
\(369\) | 5.23785 | 0.272671 | ||||||||
\(370\) | −0.0807387 | −0.00419741 | ||||||||
\(371\) | −29.3557 | −1.52407 | ||||||||
\(372\) | −1.28719 | −0.0667376 | ||||||||
\(373\) | −34.6933 | −1.79635 | −0.898176 | − | 0.439635i | \(-0.855108\pi\) | ||||
−0.898176 | + | 0.439635i | \(0.855108\pi\) | |||||||
\(374\) | 0.391546 | 0.0202464 | ||||||||
\(375\) | −0.911091 | −0.0470485 | ||||||||
\(376\) | −11.4944 | −0.592781 | ||||||||
\(377\) | −14.8668 | −0.765677 | ||||||||
\(378\) | 20.4617 | 1.05244 | ||||||||
\(379\) | 23.6958 | 1.21717 | 0.608587 | − | 0.793487i | \(-0.291737\pi\) | ||||
0.608587 | + | 0.793487i | \(0.291737\pi\) | |||||||
\(380\) | 0.127597 | 0.00654558 | ||||||||
\(381\) | 10.9274 | 0.559830 | ||||||||
\(382\) | −19.7628 | −1.01115 | ||||||||
\(383\) | 1.12378 | 0.0574225 | 0.0287112 | − | 0.999588i | \(-0.490860\pi\) | ||||
0.0287112 | + | 0.999588i | \(0.490860\pi\) | |||||||
\(384\) | 0.956879 | 0.0488305 | ||||||||
\(385\) | −0.0486924 | −0.00248160 | ||||||||
\(386\) | −9.71439 | −0.494449 | ||||||||
\(387\) | −13.9515 | −0.709197 | ||||||||
\(388\) | 4.53164 | 0.230059 | ||||||||
\(389\) | −28.5254 | −1.44629 | −0.723147 | − | 0.690694i | \(-0.757305\pi\) | ||||
−0.723147 | + | 0.690694i | \(0.757305\pi\) | |||||||
\(390\) | 0.149094 | 0.00754969 | ||||||||
\(391\) | 24.2249 | 1.22511 | ||||||||
\(392\) | −10.6885 | −0.539853 | ||||||||
\(393\) | −2.62027 | −0.132175 | ||||||||
\(394\) | 1.91169 | 0.0963095 | ||||||||
\(395\) | 0.113607 | 0.00571616 | ||||||||
\(396\) | 0.253217 | 0.0127247 | ||||||||
\(397\) | −14.8873 | −0.747171 | −0.373586 | − | 0.927596i | \(-0.621872\pi\) | ||||
−0.373586 | + | 0.927596i | \(0.621872\pi\) | |||||||
\(398\) | −10.3431 | −0.518454 | ||||||||
\(399\) | −5.38820 | −0.269747 | ||||||||
\(400\) | −4.99092 | −0.249546 | ||||||||
\(401\) | 2.77313 | 0.138484 | 0.0692419 | − | 0.997600i | \(-0.477942\pi\) | ||||
0.0692419 | + | 0.997600i | \(0.477942\pi\) | |||||||
\(402\) | −13.5554 | −0.676080 | ||||||||
\(403\) | −2.19933 | −0.109556 | ||||||||
\(404\) | −18.8485 | −0.937746 | ||||||||
\(405\) | −0.152272 | −0.00756646 | ||||||||
\(406\) | 38.2435 | 1.89799 | ||||||||
\(407\) | 0.102920 | 0.00510155 | ||||||||
\(408\) | 3.08407 | 0.152684 | ||||||||
\(409\) | −37.2648 | −1.84263 | −0.921314 | − | 0.388820i | \(-0.872883\pi\) | ||||
−0.921314 | + | 0.388820i | \(0.872883\pi\) | |||||||
\(410\) | −0.239483 | −0.0118272 | ||||||||
\(411\) | 11.5873 | 0.571560 | ||||||||
\(412\) | −16.0310 | −0.789792 | ||||||||
\(413\) | 16.5101 | 0.812407 | ||||||||
\(414\) | 15.6665 | 0.769968 | ||||||||
\(415\) | 1.11842 | 0.0549010 | ||||||||
\(416\) | 1.63495 | 0.0801601 | ||||||||
\(417\) | −15.4610 | −0.757129 | ||||||||
\(418\) | −0.162651 | −0.00795552 | ||||||||
\(419\) | −29.5915 | −1.44564 | −0.722821 | − | 0.691036i | \(-0.757155\pi\) | ||||
−0.722821 | + | 0.691036i | \(0.757155\pi\) | |||||||
\(420\) | −0.383533 | −0.0187145 | ||||||||
\(421\) | −24.0854 | −1.17385 | −0.586925 | − | 0.809641i | \(-0.699662\pi\) | ||||
−0.586925 | + | 0.809641i | \(0.699662\pi\) | |||||||
\(422\) | −26.4053 | −1.28539 | ||||||||
\(423\) | −23.9588 | −1.16492 | ||||||||
\(424\) | −6.97986 | −0.338972 | ||||||||
\(425\) | −16.0860 | −0.780283 | ||||||||
\(426\) | 5.43676 | 0.263412 | ||||||||
\(427\) | 44.0251 | 2.13052 | ||||||||
\(428\) | −7.85447 | −0.379660 | ||||||||
\(429\) | −0.190055 | −0.00917592 | ||||||||
\(430\) | 0.637888 | 0.0307617 | ||||||||
\(431\) | 34.2509 | 1.64981 | 0.824904 | − | 0.565274i | \(-0.191229\pi\) | ||||
0.824904 | + | 0.565274i | \(0.191229\pi\) | |||||||
\(432\) | 4.86514 | 0.234074 | ||||||||
\(433\) | −40.1135 | −1.92773 | −0.963865 | − | 0.266390i | \(-0.914169\pi\) | ||||
−0.963865 | + | 0.266390i | \(0.914169\pi\) | |||||||
\(434\) | 5.65758 | 0.271573 | ||||||||
\(435\) | 0.829217 | 0.0397579 | ||||||||
\(436\) | 12.9103 | 0.618293 | ||||||||
\(437\) | −10.0632 | −0.481388 | ||||||||
\(438\) | 0.752615 | 0.0359613 | ||||||||
\(439\) | −30.1300 | −1.43803 | −0.719014 | − | 0.694995i | \(-0.755406\pi\) | ||||
−0.719014 | + | 0.694995i | \(0.755406\pi\) | |||||||
\(440\) | −0.0115775 | −0.000551937 0 | ||||||||
\(441\) | −22.2790 | −1.06090 | ||||||||
\(442\) | 5.26952 | 0.250646 | ||||||||
\(443\) | 11.0205 | 0.523599 | 0.261800 | − | 0.965122i | \(-0.415684\pi\) | ||||
0.261800 | + | 0.965122i | \(0.415684\pi\) | |||||||
\(444\) | 0.810662 | 0.0384723 | ||||||||
\(445\) | 0.550281 | 0.0260858 | ||||||||
\(446\) | 2.87973 | 0.136359 | ||||||||
\(447\) | 4.75409 | 0.224861 | ||||||||
\(448\) | −4.20577 | −0.198704 | ||||||||
\(449\) | −6.50049 | −0.306777 | −0.153389 | − | 0.988166i | \(-0.549019\pi\) | ||||
−0.153389 | + | 0.988166i | \(0.549019\pi\) | |||||||
\(450\) | −10.4030 | −0.490401 | ||||||||
\(451\) | 0.305275 | 0.0143749 | ||||||||
\(452\) | −5.40353 | −0.254160 | ||||||||
\(453\) | −13.5398 | −0.636156 | ||||||||
\(454\) | 17.7575 | 0.833403 | ||||||||
\(455\) | −0.655315 | −0.0307216 | ||||||||
\(456\) | −1.28114 | −0.0599950 | ||||||||
\(457\) | 8.73969 | 0.408826 | 0.204413 | − | 0.978885i | \(-0.434472\pi\) | ||||
0.204413 | + | 0.978885i | \(0.434472\pi\) | |||||||
\(458\) | 7.68778 | 0.359226 | ||||||||
\(459\) | 15.6806 | 0.731906 | ||||||||
\(460\) | −0.716300 | −0.0333977 | ||||||||
\(461\) | −25.5346 | −1.18927 | −0.594633 | − | 0.803997i | \(-0.702703\pi\) | ||||
−0.594633 | + | 0.803997i | \(0.702703\pi\) | |||||||
\(462\) | 0.488899 | 0.0227457 | ||||||||
\(463\) | −14.6280 | −0.679820 | −0.339910 | − | 0.940458i | \(-0.610397\pi\) | ||||
−0.339910 | + | 0.940458i | \(0.610397\pi\) | |||||||
\(464\) | 9.09309 | 0.422136 | ||||||||
\(465\) | 0.122671 | 0.00568873 | ||||||||
\(466\) | 8.84240 | 0.409616 | ||||||||
\(467\) | 1.24904 | 0.0577987 | 0.0288993 | − | 0.999582i | \(-0.490800\pi\) | ||||
0.0288993 | + | 0.999582i | \(0.490800\pi\) | |||||||
\(468\) | 3.40786 | 0.157529 | ||||||||
\(469\) | 59.5799 | 2.75114 | ||||||||
\(470\) | 1.09544 | 0.0505287 | ||||||||
\(471\) | 3.30486 | 0.152280 | ||||||||
\(472\) | 3.92557 | 0.180689 | ||||||||
\(473\) | −0.813132 | −0.0373879 | ||||||||
\(474\) | −1.14067 | −0.0523928 | ||||||||
\(475\) | 6.68222 | 0.306601 | ||||||||
\(476\) | −13.5554 | −0.621311 | ||||||||
\(477\) | −14.5487 | −0.666139 | ||||||||
\(478\) | 20.4693 | 0.936245 | ||||||||
\(479\) | 11.4826 | 0.524655 | 0.262327 | − | 0.964979i | \(-0.415510\pi\) | ||||
0.262327 | + | 0.964979i | \(0.415510\pi\) | |||||||
\(480\) | −0.0911919 | −0.00416232 | ||||||||
\(481\) | 1.38512 | 0.0631560 | ||||||||
\(482\) | 30.2979 | 1.38003 | ||||||||
\(483\) | 30.2482 | 1.37634 | ||||||||
\(484\) | −10.9852 | −0.499329 | ||||||||
\(485\) | −0.431872 | −0.0196103 | ||||||||
\(486\) | 16.1243 | 0.731414 | ||||||||
\(487\) | −21.9886 | −0.996400 | −0.498200 | − | 0.867062i | \(-0.666005\pi\) | ||||
−0.498200 | + | 0.867062i | \(0.666005\pi\) | |||||||
\(488\) | 10.4678 | 0.473854 | ||||||||
\(489\) | −7.30265 | −0.330237 | ||||||||
\(490\) | 1.01863 | 0.0460171 | ||||||||
\(491\) | −23.7027 | −1.06969 | −0.534845 | − | 0.844950i | \(-0.679630\pi\) | ||||
−0.534845 | + | 0.844950i | \(0.679630\pi\) | |||||||
\(492\) | 2.40454 | 0.108405 | ||||||||
\(493\) | 29.3074 | 1.31994 | ||||||||
\(494\) | −2.18900 | −0.0984876 | ||||||||
\(495\) | −0.0241320 | −0.00108465 | ||||||||
\(496\) | 1.34519 | 0.0604010 | ||||||||
\(497\) | −23.8962 | −1.07189 | ||||||||
\(498\) | −11.2296 | −0.503208 | ||||||||
\(499\) | −14.8704 | −0.665692 | −0.332846 | − | 0.942981i | \(-0.608009\pi\) | ||||
−0.332846 | + | 0.942981i | \(0.608009\pi\) | |||||||
\(500\) | 0.952148 | 0.0425814 | ||||||||
\(501\) | −12.6897 | −0.566933 | ||||||||
\(502\) | −12.1789 | −0.543572 | ||||||||
\(503\) | −24.9490 | −1.11242 | −0.556210 | − | 0.831042i | \(-0.687745\pi\) | ||||
−0.556210 | + | 0.831042i | \(0.687745\pi\) | |||||||
\(504\) | −8.76644 | −0.390488 | ||||||||
\(505\) | 1.79628 | 0.0799336 | ||||||||
\(506\) | 0.913087 | 0.0405917 | ||||||||
\(507\) | 9.88163 | 0.438859 | ||||||||
\(508\) | −11.4199 | −0.506675 | ||||||||
\(509\) | −10.6418 | −0.471689 | −0.235845 | − | 0.971791i | \(-0.575786\pi\) | ||||
−0.235845 | + | 0.971791i | \(0.575786\pi\) | |||||||
\(510\) | −0.293916 | −0.0130148 | ||||||||
\(511\) | −3.30797 | −0.146336 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.51382 | −0.287592 | ||||||||
\(514\) | −12.0370 | −0.530928 | ||||||||
\(515\) | 1.52778 | 0.0673220 | ||||||||
\(516\) | −6.40475 | −0.281953 | ||||||||
\(517\) | −1.39638 | −0.0614128 | ||||||||
\(518\) | −3.56311 | −0.156554 | ||||||||
\(519\) | −22.1668 | −0.973013 | ||||||||
\(520\) | −0.155813 | −0.00683286 | ||||||||
\(521\) | −28.6167 | −1.25372 | −0.626861 | − | 0.779131i | \(-0.715661\pi\) | ||||
−0.626861 | + | 0.779131i | \(0.715661\pi\) | |||||||
\(522\) | 18.9535 | 0.829571 | ||||||||
\(523\) | 32.4165 | 1.41747 | 0.708737 | − | 0.705473i | \(-0.249265\pi\) | ||||
0.708737 | + | 0.705473i | \(0.249265\pi\) | |||||||
\(524\) | 2.73835 | 0.119625 | ||||||||
\(525\) | −20.0855 | −0.876605 | ||||||||
\(526\) | −0.138602 | −0.00604333 | ||||||||
\(527\) | 4.33562 | 0.188863 | ||||||||
\(528\) | 0.116245 | 0.00505890 | ||||||||
\(529\) | 33.4926 | 1.45620 | ||||||||
\(530\) | 0.665190 | 0.0288940 | ||||||||
\(531\) | 8.18239 | 0.355085 | ||||||||
\(532\) | 5.63101 | 0.244135 | ||||||||
\(533\) | 4.10847 | 0.177958 | ||||||||
\(534\) | −5.52513 | −0.239096 | ||||||||
\(535\) | 0.748542 | 0.0323623 | ||||||||
\(536\) | 14.1662 | 0.611887 | ||||||||
\(537\) | −0.190795 | −0.00823340 | ||||||||
\(538\) | 19.3871 | 0.835838 | ||||||||
\(539\) | −1.29848 | −0.0559294 | ||||||||
\(540\) | −0.463655 | −0.0199525 | ||||||||
\(541\) | 41.3176 | 1.77638 | 0.888190 | − | 0.459476i | \(-0.151963\pi\) | ||||
0.888190 | + | 0.459476i | \(0.151963\pi\) | |||||||
\(542\) | 8.81160 | 0.378491 | ||||||||
\(543\) | 22.4656 | 0.964092 | ||||||||
\(544\) | −3.22305 | −0.138187 | ||||||||
\(545\) | −1.23037 | −0.0527034 | ||||||||
\(546\) | 6.57973 | 0.281586 | ||||||||
\(547\) | 1.57191 | 0.0672100 | 0.0336050 | − | 0.999435i | \(-0.489301\pi\) | ||||
0.0336050 | + | 0.999435i | \(0.489301\pi\) | |||||||
\(548\) | −12.1095 | −0.517292 | ||||||||
\(549\) | 21.8188 | 0.931205 | ||||||||
\(550\) | −0.606313 | −0.0258533 | ||||||||
\(551\) | −12.1745 | −0.518652 | ||||||||
\(552\) | 7.19205 | 0.306114 | ||||||||
\(553\) | 5.01360 | 0.213200 | ||||||||
\(554\) | −25.6127 | −1.08818 | ||||||||
\(555\) | −0.0772572 | −0.00327939 | ||||||||
\(556\) | 16.1577 | 0.685241 | ||||||||
\(557\) | −11.5447 | −0.489165 | −0.244583 | − | 0.969628i | \(-0.578651\pi\) | ||||
−0.244583 | + | 0.969628i | \(0.578651\pi\) | |||||||
\(558\) | 2.80390 | 0.118699 | ||||||||
\(559\) | −10.9433 | −0.462854 | ||||||||
\(560\) | 0.400816 | 0.0169376 | ||||||||
\(561\) | 0.374662 | 0.0158183 | ||||||||
\(562\) | 13.4325 | 0.566616 | ||||||||
\(563\) | 13.1451 | 0.553999 | 0.276999 | − | 0.960870i | \(-0.410660\pi\) | ||||
0.276999 | + | 0.960870i | \(0.410660\pi\) | |||||||
\(564\) | −10.9988 | −0.463133 | ||||||||
\(565\) | 0.514964 | 0.0216647 | ||||||||
\(566\) | −9.19969 | −0.386692 | ||||||||
\(567\) | −6.71997 | −0.282212 | ||||||||
\(568\) | −5.68177 | −0.238402 | ||||||||
\(569\) | −9.75665 | −0.409020 | −0.204510 | − | 0.978864i | \(-0.565560\pi\) | ||||
−0.204510 | + | 0.978864i | \(0.565560\pi\) | |||||||
\(570\) | 0.122095 | 0.00511399 | ||||||||
\(571\) | −15.2353 | −0.637578 | −0.318789 | − | 0.947826i | \(-0.603276\pi\) | ||||
−0.318789 | + | 0.947826i | \(0.603276\pi\) | |||||||
\(572\) | 0.198619 | 0.00830468 | ||||||||
\(573\) | −18.9107 | −0.790004 | ||||||||
\(574\) | −10.5687 | −0.441129 | ||||||||
\(575\) | −37.5125 | −1.56438 | ||||||||
\(576\) | −2.08438 | −0.0868493 | ||||||||
\(577\) | 37.1399 | 1.54616 | 0.773078 | − | 0.634311i | \(-0.218716\pi\) | ||||
0.773078 | + | 0.634311i | \(0.218716\pi\) | |||||||
\(578\) | 6.61198 | 0.275022 | ||||||||
\(579\) | −9.29549 | −0.386308 | ||||||||
\(580\) | −0.866584 | −0.0359830 | ||||||||
\(581\) | 49.3573 | 2.04769 | ||||||||
\(582\) | 4.33624 | 0.179743 | ||||||||
\(583\) | −0.847936 | −0.0351179 | ||||||||
\(584\) | −0.786531 | −0.0325469 | ||||||||
\(585\) | −0.324774 | −0.0134278 | ||||||||
\(586\) | 6.94996 | 0.287100 | ||||||||
\(587\) | −9.51896 | −0.392890 | −0.196445 | − | 0.980515i | \(-0.562940\pi\) | ||||
−0.196445 | + | 0.980515i | \(0.562940\pi\) | |||||||
\(588\) | −10.2276 | −0.421781 | ||||||||
\(589\) | −1.80105 | −0.0742109 | ||||||||
\(590\) | −0.374112 | −0.0154020 | ||||||||
\(591\) | 1.82926 | 0.0752455 | ||||||||
\(592\) | −0.847194 | −0.0348194 | ||||||||
\(593\) | 39.9184 | 1.63925 | 0.819625 | − | 0.572900i | \(-0.194182\pi\) | ||||
0.819625 | + | 0.572900i | \(0.194182\pi\) | |||||||
\(594\) | 0.591033 | 0.0242504 | ||||||||
\(595\) | 1.29185 | 0.0529606 | ||||||||
\(596\) | −4.96833 | −0.203511 | ||||||||
\(597\) | −9.89712 | −0.405062 | ||||||||
\(598\) | 12.2885 | 0.502516 | ||||||||
\(599\) | −33.5087 | −1.36913 | −0.684564 | − | 0.728952i | \(-0.740008\pi\) | ||||
−0.684564 | + | 0.728952i | \(0.740008\pi\) | |||||||
\(600\) | −4.77571 | −0.194967 | ||||||||
\(601\) | −6.98904 | −0.285089 | −0.142545 | − | 0.989788i | \(-0.545528\pi\) | ||||
−0.142545 | + | 0.989788i | \(0.545528\pi\) | |||||||
\(602\) | 28.1508 | 1.14734 | ||||||||
\(603\) | 29.5278 | 1.20246 | ||||||||
\(604\) | 14.1500 | 0.575754 | ||||||||
\(605\) | 1.04691 | 0.0425629 | ||||||||
\(606\) | −18.0357 | −0.732650 | ||||||||
\(607\) | 34.3477 | 1.39413 | 0.697066 | − | 0.717007i | \(-0.254489\pi\) | ||||
0.697066 | + | 0.717007i | \(0.254489\pi\) | |||||||
\(608\) | 1.33888 | 0.0542986 | ||||||||
\(609\) | 36.5944 | 1.48288 | ||||||||
\(610\) | −0.997593 | −0.0403914 | ||||||||
\(611\) | −18.7929 | −0.760278 | ||||||||
\(612\) | −6.71806 | −0.271561 | ||||||||
\(613\) | −38.4326 | −1.55228 | −0.776139 | − | 0.630561i | \(-0.782825\pi\) | ||||
−0.776139 | + | 0.630561i | \(0.782825\pi\) | |||||||
\(614\) | −26.4614 | −1.06790 | ||||||||
\(615\) | −0.229156 | −0.00924047 | ||||||||
\(616\) | −0.510931 | −0.0205860 | ||||||||
\(617\) | −26.4663 | −1.06549 | −0.532747 | − | 0.846275i | \(-0.678840\pi\) | ||||
−0.532747 | + | 0.846275i | \(0.678840\pi\) | |||||||
\(618\) | −15.3398 | −0.617056 | ||||||||
\(619\) | −0.365349 | −0.0146846 | −0.00734231 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734231 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(620\) | −0.128199 | −0.00514859 | ||||||||
\(621\) | 36.5671 | 1.46739 | ||||||||
\(622\) | 5.51240 | 0.221027 | ||||||||
\(623\) | 24.2846 | 0.972943 | ||||||||
\(624\) | 1.56445 | 0.0626282 | ||||||||
\(625\) | 24.8638 | 0.994554 | ||||||||
\(626\) | −6.03203 | −0.241088 | ||||||||
\(627\) | −0.155637 | −0.00621556 | ||||||||
\(628\) | −3.45379 | −0.137821 | ||||||||
\(629\) | −2.73054 | −0.108874 | ||||||||
\(630\) | 0.835454 | 0.0332853 | ||||||||
\(631\) | −15.5463 | −0.618890 | −0.309445 | − | 0.950917i | \(-0.600143\pi\) | ||||
−0.309445 | + | 0.950917i | \(0.600143\pi\) | |||||||
\(632\) | 1.19208 | 0.0474182 | ||||||||
\(633\) | −25.2667 | −1.00426 | ||||||||
\(634\) | −26.5260 | −1.05348 | ||||||||
\(635\) | 1.08833 | 0.0431891 | ||||||||
\(636\) | −6.67888 | −0.264835 | ||||||||
\(637\) | −17.4752 | −0.692394 | ||||||||
\(638\) | 1.10466 | 0.0437338 | ||||||||
\(639\) | −11.8430 | −0.468501 | ||||||||
\(640\) | 0.0953014 | 0.00376712 | ||||||||
\(641\) | −23.9183 | −0.944717 | −0.472359 | − | 0.881406i | \(-0.656597\pi\) | ||||
−0.472359 | + | 0.881406i | \(0.656597\pi\) | |||||||
\(642\) | −7.51578 | −0.296624 | ||||||||
\(643\) | −6.78173 | −0.267445 | −0.133723 | − | 0.991019i | \(-0.542693\pi\) | ||||
−0.133723 | + | 0.991019i | \(0.542693\pi\) | |||||||
\(644\) | −31.6113 | −1.24566 | ||||||||
\(645\) | 0.610381 | 0.0240337 | ||||||||
\(646\) | 4.31526 | 0.169782 | ||||||||
\(647\) | 8.83427 | 0.347311 | 0.173655 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173655 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(648\) | −1.59779 | −0.0627673 | ||||||||
\(649\) | 0.476891 | 0.0187196 | ||||||||
\(650\) | −8.15991 | −0.320058 | ||||||||
\(651\) | 5.41363 | 0.212177 | ||||||||
\(652\) | 7.63173 | 0.298882 | ||||||||
\(653\) | 16.4307 | 0.642984 | 0.321492 | − | 0.946912i | \(-0.395816\pi\) | ||||
0.321492 | + | 0.946912i | \(0.395816\pi\) | |||||||
\(654\) | 12.3536 | 0.483066 | ||||||||
\(655\) | −0.260969 | −0.0101969 | ||||||||
\(656\) | −2.51290 | −0.0981123 | ||||||||
\(657\) | −1.63943 | −0.0639603 | ||||||||
\(658\) | 48.3430 | 1.88461 | ||||||||
\(659\) | 34.4579 | 1.34229 | 0.671145 | − | 0.741326i | \(-0.265803\pi\) | ||||
0.671145 | + | 0.741326i | \(0.265803\pi\) | |||||||
\(660\) | −0.0110783 | −0.000431222 0 | ||||||||
\(661\) | −5.72848 | −0.222812 | −0.111406 | − | 0.993775i | \(-0.535535\pi\) | ||||
−0.111406 | + | 0.993775i | \(0.535535\pi\) | |||||||
\(662\) | 31.7469 | 1.23388 | ||||||||
\(663\) | 5.04230 | 0.195827 | ||||||||
\(664\) | 11.7356 | 0.455430 | ||||||||
\(665\) | −0.536643 | −0.0208101 | ||||||||
\(666\) | −1.76588 | −0.0684263 | ||||||||
\(667\) | 68.3451 | 2.64633 | ||||||||
\(668\) | 13.2615 | 0.513103 | ||||||||
\(669\) | 2.75555 | 0.106536 | ||||||||
\(670\) | −1.35006 | −0.0521574 | ||||||||
\(671\) | 1.27166 | 0.0490918 | ||||||||
\(672\) | −4.02442 | −0.155245 | ||||||||
\(673\) | 23.4230 | 0.902891 | 0.451445 | − | 0.892299i | \(-0.350909\pi\) | ||||
0.451445 | + | 0.892299i | \(0.350909\pi\) | |||||||
\(674\) | −31.0606 | −1.19641 | ||||||||
\(675\) | −24.2815 | −0.934596 | ||||||||
\(676\) | −10.3269 | −0.397190 | ||||||||
\(677\) | 34.8354 | 1.33883 | 0.669416 | − | 0.742887i | \(-0.266544\pi\) | ||||
0.669416 | + | 0.742887i | \(0.266544\pi\) | |||||||
\(678\) | −5.17052 | −0.198573 | ||||||||
\(679\) | −19.0591 | −0.731420 | ||||||||
\(680\) | 0.307161 | 0.0117791 | ||||||||
\(681\) | 16.9918 | 0.651128 | ||||||||
\(682\) | 0.163419 | 0.00625762 | ||||||||
\(683\) | 4.47021 | 0.171048 | 0.0855239 | − | 0.996336i | \(-0.472744\pi\) | ||||
0.0855239 | + | 0.996336i | \(0.472744\pi\) | |||||||
\(684\) | 2.79073 | 0.106706 | ||||||||
\(685\) | 1.15405 | 0.0440940 | ||||||||
\(686\) | 15.5132 | 0.592296 | ||||||||
\(687\) | 7.35628 | 0.280660 | ||||||||
\(688\) | 6.69337 | 0.255182 | ||||||||
\(689\) | −11.4117 | −0.434752 | ||||||||
\(690\) | −0.685413 | −0.0260932 | ||||||||
\(691\) | 25.7956 | 0.981311 | 0.490656 | − | 0.871354i | \(-0.336757\pi\) | ||||
0.490656 | + | 0.871354i | \(0.336757\pi\) | |||||||
\(692\) | 23.1657 | 0.880628 | ||||||||
\(693\) | −1.06498 | −0.0404551 | ||||||||
\(694\) | −6.01579 | −0.228356 | ||||||||
\(695\) | −1.53986 | −0.0584101 | ||||||||
\(696\) | 8.70099 | 0.329810 | ||||||||
\(697\) | −8.09919 | −0.306779 | ||||||||
\(698\) | −18.7258 | −0.708781 | ||||||||
\(699\) | 8.46111 | 0.320029 | ||||||||
\(700\) | 20.9907 | 0.793373 | ||||||||
\(701\) | −26.4901 | −1.00052 | −0.500259 | − | 0.865876i | \(-0.666762\pi\) | ||||
−0.500259 | + | 0.865876i | \(0.666762\pi\) | |||||||
\(702\) | 7.95427 | 0.300214 | ||||||||
\(703\) | 1.13429 | 0.0427805 | ||||||||
\(704\) | −0.121483 | −0.00457857 | ||||||||
\(705\) | 1.04820 | 0.0394775 | ||||||||
\(706\) | −17.2725 | −0.650060 | ||||||||
\(707\) | 79.2724 | 2.98134 | ||||||||
\(708\) | 3.75630 | 0.141170 | ||||||||
\(709\) | −34.3646 | −1.29059 | −0.645295 | − | 0.763933i | \(-0.723266\pi\) | ||||
−0.645295 | + | 0.763933i | \(0.723266\pi\) | |||||||
\(710\) | 0.541480 | 0.0203214 | ||||||||
\(711\) | 2.48474 | 0.0931851 | ||||||||
\(712\) | 5.77411 | 0.216394 | ||||||||
\(713\) | 10.1107 | 0.378648 | ||||||||
\(714\) | −12.9709 | −0.485423 | ||||||||
\(715\) | −0.0189287 | −0.000707893 0 | ||||||||
\(716\) | 0.199393 | 0.00745165 | ||||||||
\(717\) | 19.5867 | 0.731478 | ||||||||
\(718\) | −1.11572 | −0.0416381 | ||||||||
\(719\) | 6.24457 | 0.232883 | 0.116442 | − | 0.993198i | \(-0.462851\pi\) | ||||
0.116442 | + | 0.993198i | \(0.462851\pi\) | |||||||
\(720\) | 0.198645 | 0.00740304 | ||||||||
\(721\) | 67.4229 | 2.51096 | ||||||||
\(722\) | 17.2074 | 0.640393 | ||||||||
\(723\) | 28.9914 | 1.07820 | ||||||||
\(724\) | −23.4780 | −0.872554 | ||||||||
\(725\) | −45.3829 | −1.68548 | ||||||||
\(726\) | −10.5116 | −0.390120 | ||||||||
\(727\) | 36.3330 | 1.34752 | 0.673758 | − | 0.738952i | \(-0.264679\pi\) | ||||
0.673758 | + | 0.738952i | \(0.264679\pi\) | |||||||
\(728\) | −6.87624 | −0.254850 | ||||||||
\(729\) | 10.6356 | 0.393913 | ||||||||
\(730\) | 0.0749575 | 0.00277430 | ||||||||
\(731\) | 21.5730 | 0.797908 | ||||||||
\(732\) | 10.0164 | 0.370217 | ||||||||
\(733\) | −30.4147 | −1.12339 | −0.561696 | − | 0.827344i | \(-0.689851\pi\) | ||||
−0.561696 | + | 0.827344i | \(0.689851\pi\) | |||||||
\(734\) | 9.30017 | 0.343276 | ||||||||
\(735\) | 0.974709 | 0.0359527 | ||||||||
\(736\) | −7.51615 | −0.277049 | ||||||||
\(737\) | 1.72096 | 0.0633923 | ||||||||
\(738\) | −5.23785 | −0.192808 | ||||||||
\(739\) | 3.06910 | 0.112899 | 0.0564493 | − | 0.998405i | \(-0.482022\pi\) | ||||
0.0564493 | + | 0.998405i | \(0.482022\pi\) | |||||||
\(740\) | 0.0807387 | 0.00296801 | ||||||||
\(741\) | −2.09461 | −0.0769473 | ||||||||
\(742\) | 29.3557 | 1.07768 | ||||||||
\(743\) | −16.1309 | −0.591787 | −0.295893 | − | 0.955221i | \(-0.595617\pi\) | ||||
−0.295893 | + | 0.955221i | \(0.595617\pi\) | |||||||
\(744\) | 1.28719 | 0.0471906 | ||||||||
\(745\) | 0.473489 | 0.0173473 | ||||||||
\(746\) | 34.6933 | 1.27021 | ||||||||
\(747\) | 24.4615 | 0.894999 | ||||||||
\(748\) | −0.391546 | −0.0143163 | ||||||||
\(749\) | 33.0341 | 1.20704 | ||||||||
\(750\) | 0.911091 | 0.0332683 | ||||||||
\(751\) | −34.5642 | −1.26127 | −0.630634 | − | 0.776081i | \(-0.717205\pi\) | ||||
−0.630634 | + | 0.776081i | \(0.717205\pi\) | |||||||
\(752\) | 11.4944 | 0.419159 | ||||||||
\(753\) | −11.6538 | −0.424686 | ||||||||
\(754\) | 14.8668 | 0.541415 | ||||||||
\(755\) | −1.34851 | −0.0490774 | ||||||||
\(756\) | −20.4617 | −0.744184 | ||||||||
\(757\) | 30.4546 | 1.10689 | 0.553446 | − | 0.832885i | \(-0.313312\pi\) | ||||
0.553446 | + | 0.832885i | \(0.313312\pi\) | |||||||
\(758\) | −23.6958 | −0.860672 | ||||||||
\(759\) | 0.873714 | 0.0317138 | ||||||||
\(760\) | −0.127597 | −0.00462842 | ||||||||
\(761\) | −32.9139 | −1.19313 | −0.596564 | − | 0.802565i | \(-0.703468\pi\) | ||||
−0.596564 | + | 0.802565i | \(0.703468\pi\) | |||||||
\(762\) | −10.9274 | −0.395859 | ||||||||
\(763\) | −54.2980 | −1.96572 | ||||||||
\(764\) | 19.7628 | 0.714994 | ||||||||
\(765\) | 0.640240 | 0.0231479 | ||||||||
\(766\) | −1.12378 | −0.0406038 | ||||||||
\(767\) | 6.41812 | 0.231745 | ||||||||
\(768\) | −0.956879 | −0.0345284 | ||||||||
\(769\) | −31.4149 | −1.13285 | −0.566426 | − | 0.824113i | \(-0.691674\pi\) | ||||
−0.566426 | + | 0.824113i | \(0.691674\pi\) | |||||||
\(770\) | 0.0486924 | 0.00175475 | ||||||||
\(771\) | −11.5179 | −0.414808 | ||||||||
\(772\) | 9.71439 | 0.349628 | ||||||||
\(773\) | −53.2187 | −1.91414 | −0.957072 | − | 0.289850i | \(-0.906395\pi\) | ||||
−0.957072 | + | 0.289850i | \(0.906395\pi\) | |||||||
\(774\) | 13.9515 | 0.501478 | ||||||||
\(775\) | −6.71375 | −0.241165 | ||||||||
\(776\) | −4.53164 | −0.162676 | ||||||||
\(777\) | −3.40946 | −0.122314 | ||||||||
\(778\) | 28.5254 | 1.02268 | ||||||||
\(779\) | 3.36446 | 0.120544 | ||||||||
\(780\) | −0.149094 | −0.00533843 | ||||||||
\(781\) | −0.690239 | −0.0246987 | ||||||||
\(782\) | −24.2249 | −0.866281 | ||||||||
\(783\) | 44.2392 | 1.58098 | ||||||||
\(784\) | 10.6885 | 0.381734 | ||||||||
\(785\) | 0.329151 | 0.0117479 | ||||||||
\(786\) | 2.62027 | 0.0934620 | ||||||||
\(787\) | −28.9785 | −1.03297 | −0.516486 | − | 0.856296i | \(-0.672760\pi\) | ||||
−0.516486 | + | 0.856296i | \(0.672760\pi\) | |||||||
\(788\) | −1.91169 | −0.0681011 | ||||||||
\(789\) | −0.132625 | −0.00472158 | ||||||||
\(790\) | −0.113607 | −0.00404194 | ||||||||
\(791\) | 22.7260 | 0.808044 | ||||||||
\(792\) | −0.253217 | −0.00899769 | ||||||||
\(793\) | 17.1143 | 0.607746 | ||||||||
\(794\) | 14.8873 | 0.528330 | ||||||||
\(795\) | 0.636507 | 0.0225746 | ||||||||
\(796\) | 10.3431 | 0.366602 | ||||||||
\(797\) | 4.76493 | 0.168782 | 0.0843912 | − | 0.996433i | \(-0.473105\pi\) | ||||
0.0843912 | + | 0.996433i | \(0.473105\pi\) | |||||||
\(798\) | 5.38820 | 0.190740 | ||||||||
\(799\) | 37.0471 | 1.31063 | ||||||||
\(800\) | 4.99092 | 0.176456 | ||||||||
\(801\) | 12.0355 | 0.425252 | ||||||||
\(802\) | −2.77313 | −0.0979228 | ||||||||
\(803\) | −0.0955503 | −0.00337190 | ||||||||
\(804\) | 13.5554 | 0.478060 | ||||||||
\(805\) | 3.01260 | 0.106180 | ||||||||
\(806\) | 2.19933 | 0.0774680 | ||||||||
\(807\) | 18.5511 | 0.653031 | ||||||||
\(808\) | 18.8485 | 0.663086 | ||||||||
\(809\) | 40.1670 | 1.41220 | 0.706098 | − | 0.708114i | \(-0.250454\pi\) | ||||
0.706098 | + | 0.708114i | \(0.250454\pi\) | |||||||
\(810\) | 0.152272 | 0.00535030 | ||||||||
\(811\) | −31.8495 | −1.11839 | −0.559193 | − | 0.829038i | \(-0.688889\pi\) | ||||
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(812\) | −38.2435 | −1.34208 | ||||||||
\(813\) | 8.43164 | 0.295711 | ||||||||
\(814\) | −0.102920 | −0.00360734 | ||||||||
\(815\) | −0.727315 | −0.0254767 | ||||||||
\(816\) | −3.08407 | −0.107964 | ||||||||
\(817\) | −8.96160 | −0.313527 | ||||||||
\(818\) | 37.2648 | 1.30293 | ||||||||
\(819\) | −14.3327 | −0.500825 | ||||||||
\(820\) | 0.239483 | 0.00836311 | ||||||||
\(821\) | −23.3451 | −0.814750 | −0.407375 | − | 0.913261i | \(-0.633556\pi\) | ||||
−0.407375 | + | 0.913261i | \(0.633556\pi\) | |||||||
\(822\) | −11.5873 | −0.404154 | ||||||||
\(823\) | −42.1552 | −1.46944 | −0.734718 | − | 0.678372i | \(-0.762686\pi\) | ||||
−0.734718 | + | 0.678372i | \(0.762686\pi\) | |||||||
\(824\) | 16.0310 | 0.558467 | ||||||||
\(825\) | −0.580168 | −0.0201989 | ||||||||
\(826\) | −16.5101 | −0.574459 | ||||||||
\(827\) | 37.8380 | 1.31576 | 0.657878 | − | 0.753125i | \(-0.271454\pi\) | ||||
0.657878 | + | 0.753125i | \(0.271454\pi\) | |||||||
\(828\) | −15.6665 | −0.544450 | ||||||||
\(829\) | −21.8002 | −0.757154 | −0.378577 | − | 0.925570i | \(-0.623586\pi\) | ||||
−0.378577 | + | 0.925570i | \(0.623586\pi\) | |||||||
\(830\) | −1.11842 | −0.0388209 | ||||||||
\(831\) | −24.5082 | −0.850181 | ||||||||
\(832\) | −1.63495 | −0.0566817 | ||||||||
\(833\) | 34.4497 | 1.19361 | ||||||||
\(834\) | 15.4610 | 0.535371 | ||||||||
\(835\) | −1.26384 | −0.0437370 | ||||||||
\(836\) | 0.162651 | 0.00562540 | ||||||||
\(837\) | 6.54456 | 0.226213 | ||||||||
\(838\) | 29.5915 | 1.02222 | ||||||||
\(839\) | −2.66289 | −0.0919330 | −0.0459665 | − | 0.998943i | \(-0.514637\pi\) | ||||
−0.0459665 | + | 0.998943i | \(0.514637\pi\) | |||||||
\(840\) | 0.383533 | 0.0132331 | ||||||||
\(841\) | 53.6843 | 1.85118 | ||||||||
\(842\) | 24.0854 | 0.830037 | ||||||||
\(843\) | 12.8533 | 0.442691 | ||||||||
\(844\) | 26.4053 | 0.908909 | ||||||||
\(845\) | 0.984171 | 0.0338565 | ||||||||
\(846\) | 23.9588 | 0.823721 | ||||||||
\(847\) | 46.2015 | 1.58750 | ||||||||
\(848\) | 6.97986 | 0.239689 | ||||||||
\(849\) | −8.80299 | −0.302118 | ||||||||
\(850\) | 16.0860 | 0.551744 | ||||||||
\(851\) | −6.36764 | −0.218280 | ||||||||
\(852\) | −5.43676 | −0.186260 | ||||||||
\(853\) | −53.5322 | −1.83291 | −0.916454 | − | 0.400139i | \(-0.868962\pi\) | ||||
−0.916454 | + | 0.400139i | \(0.868962\pi\) | |||||||
\(854\) | −44.0251 | −1.50651 | ||||||||
\(855\) | −0.265960 | −0.00909566 | ||||||||
\(856\) | 7.85447 | 0.268460 | ||||||||
\(857\) | 36.5661 | 1.24907 | 0.624537 | − | 0.780995i | \(-0.285288\pi\) | ||||
0.624537 | + | 0.780995i | \(0.285288\pi\) | |||||||
\(858\) | 0.190055 | 0.00648835 | ||||||||
\(859\) | 8.17959 | 0.279084 | 0.139542 | − | 0.990216i | \(-0.455437\pi\) | ||||
0.139542 | + | 0.990216i | \(0.455437\pi\) | |||||||
\(860\) | −0.637888 | −0.0217518 | ||||||||
\(861\) | −10.1130 | −0.344649 | ||||||||
\(862\) | −34.2509 | −1.16659 | ||||||||
\(863\) | −8.52967 | −0.290353 | −0.145177 | − | 0.989406i | \(-0.546375\pi\) | ||||
−0.145177 | + | 0.989406i | \(0.546375\pi\) | |||||||
\(864\) | −4.86514 | −0.165515 | ||||||||
\(865\) | −2.20772 | −0.0750648 | ||||||||
\(866\) | 40.1135 | 1.36311 | ||||||||
\(867\) | 6.32686 | 0.214872 | ||||||||
\(868\) | −5.65758 | −0.192031 | ||||||||
\(869\) | 0.144817 | 0.00491259 | ||||||||
\(870\) | −0.829217 | −0.0281131 | ||||||||
\(871\) | 23.1611 | 0.784783 | ||||||||
\(872\) | −12.9103 | −0.437199 | ||||||||
\(873\) | −9.44568 | −0.319688 | ||||||||
\(874\) | 10.0632 | 0.340393 | ||||||||
\(875\) | −4.00452 | −0.135378 | ||||||||
\(876\) | −0.752615 | −0.0254285 | ||||||||
\(877\) | −20.2942 | −0.685287 | −0.342643 | − | 0.939466i | \(-0.611322\pi\) | ||||
−0.342643 | + | 0.939466i | \(0.611322\pi\) | |||||||
\(878\) | 30.1300 | 1.01684 | ||||||||
\(879\) | 6.65027 | 0.224308 | ||||||||
\(880\) | 0.0115775 | 0.000390278 0 | ||||||||
\(881\) | 10.6036 | 0.357243 | 0.178621 | − | 0.983918i | \(-0.442836\pi\) | ||||
0.178621 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(882\) | 22.2790 | 0.750173 | ||||||||
\(883\) | 32.7047 | 1.10060 | 0.550301 | − | 0.834966i | \(-0.314513\pi\) | ||||
0.550301 | + | 0.834966i | \(0.314513\pi\) | |||||||
\(884\) | −5.26952 | −0.177233 | ||||||||
\(885\) | −0.357980 | −0.0120334 | ||||||||
\(886\) | −11.0205 | −0.370241 | ||||||||
\(887\) | −12.5042 | −0.419850 | −0.209925 | − | 0.977717i | \(-0.567322\pi\) | ||||
−0.209925 | + | 0.977717i | \(0.567322\pi\) | |||||||
\(888\) | −0.810662 | −0.0272040 | ||||||||
\(889\) | 48.0294 | 1.61086 | ||||||||
\(890\) | −0.550281 | −0.0184455 | ||||||||
\(891\) | −0.194105 | −0.00650277 | ||||||||
\(892\) | −2.87973 | −0.0964204 | ||||||||
\(893\) | −15.3896 | −0.514995 | ||||||||
\(894\) | −4.75409 | −0.159001 | ||||||||
\(895\) | −0.0190024 | −0.000635180 0 | ||||||||
\(896\) | 4.20577 | 0.140505 | ||||||||
\(897\) | 11.7587 | 0.392610 | ||||||||
\(898\) | 6.50049 | 0.216924 | ||||||||
\(899\) | 12.2320 | 0.407959 | ||||||||
\(900\) | 10.4030 | 0.346766 | ||||||||
\(901\) | 22.4964 | 0.749464 | ||||||||
\(902\) | −0.305275 | −0.0101646 | ||||||||
\(903\) | 26.9369 | 0.896405 | ||||||||
\(904\) | 5.40353 | 0.179719 | ||||||||
\(905\) | 2.23749 | 0.0743766 | ||||||||
\(906\) | 13.5398 | 0.449830 | ||||||||
\(907\) | −26.3180 | −0.873876 | −0.436938 | − | 0.899492i | \(-0.643937\pi\) | ||||
−0.436938 | + | 0.899492i | \(0.643937\pi\) | |||||||
\(908\) | −17.7575 | −0.589305 | ||||||||
\(909\) | 39.2874 | 1.30308 | ||||||||
\(910\) | 0.655315 | 0.0217235 | ||||||||
\(911\) | −9.48305 | −0.314187 | −0.157094 | − | 0.987584i | \(-0.550212\pi\) | ||||
−0.157094 | + | 0.987584i | \(0.550212\pi\) | |||||||
\(912\) | 1.28114 | 0.0424229 | ||||||||
\(913\) | 1.42568 | 0.0471831 | ||||||||
\(914\) | −8.73969 | −0.289083 | ||||||||
\(915\) | −0.954576 | −0.0315573 | ||||||||
\(916\) | −7.68778 | −0.254011 | ||||||||
\(917\) | −11.5169 | −0.380321 | ||||||||
\(918\) | −15.6806 | −0.517536 | ||||||||
\(919\) | 33.0466 | 1.09011 | 0.545054 | − | 0.838401i | \(-0.316509\pi\) | ||||
0.545054 | + | 0.838401i | \(0.316509\pi\) | |||||||
\(920\) | 0.716300 | 0.0236157 | ||||||||
\(921\) | −25.3204 | −0.834334 | ||||||||
\(922\) | 25.5346 | 0.840938 | ||||||||
\(923\) | −9.28941 | −0.305765 | ||||||||
\(924\) | −0.488899 | −0.0160836 | ||||||||
\(925\) | 4.22827 | 0.139025 | ||||||||
\(926\) | 14.6280 | 0.480705 | ||||||||
\(927\) | 33.4148 | 1.09749 | ||||||||
\(928\) | −9.09309 | −0.298495 | ||||||||
\(929\) | 41.3770 | 1.35754 | 0.678768 | − | 0.734353i | \(-0.262514\pi\) | ||||
0.678768 | + | 0.734353i | \(0.262514\pi\) | |||||||
\(930\) | −0.122671 | −0.00402254 | ||||||||
\(931\) | −14.3106 | −0.469012 | ||||||||
\(932\) | −8.84240 | −0.289643 | ||||||||
\(933\) | 5.27470 | 0.172686 | ||||||||
\(934\) | −1.24904 | −0.0408698 | ||||||||
\(935\) | 0.0373149 | 0.00122033 | ||||||||
\(936\) | −3.40786 | −0.111389 | ||||||||
\(937\) | 9.40734 | 0.307324 | 0.153662 | − | 0.988123i | \(-0.450893\pi\) | ||||
0.153662 | + | 0.988123i | \(0.450893\pi\) | |||||||
\(938\) | −59.5799 | −1.94535 | ||||||||
\(939\) | −5.77192 | −0.188360 | ||||||||
\(940\) | −1.09544 | −0.0357292 | ||||||||
\(941\) | −30.9469 | −1.00884 | −0.504420 | − | 0.863459i | \(-0.668293\pi\) | ||||
−0.504420 | + | 0.863459i | \(0.668293\pi\) | |||||||
\(942\) | −3.30486 | −0.107678 | ||||||||
\(943\) | −18.8874 | −0.615057 | ||||||||
\(944\) | −3.92557 | −0.127766 | ||||||||
\(945\) | 1.95003 | 0.0634344 | ||||||||
\(946\) | 0.813132 | 0.0264372 | ||||||||
\(947\) | −3.65377 | −0.118732 | −0.0593658 | − | 0.998236i | \(-0.518908\pi\) | ||||
−0.0593658 | + | 0.998236i | \(0.518908\pi\) | |||||||
\(948\) | 1.14067 | 0.0370473 | ||||||||
\(949\) | −1.28594 | −0.0417434 | ||||||||
\(950\) | −6.68222 | −0.216800 | ||||||||
\(951\) | −25.3821 | −0.823072 | ||||||||
\(952\) | 13.5554 | 0.439333 | ||||||||
\(953\) | 28.6327 | 0.927504 | 0.463752 | − | 0.885965i | \(-0.346503\pi\) | ||||
0.463752 | + | 0.885965i | \(0.346503\pi\) | |||||||
\(954\) | 14.5487 | 0.471031 | ||||||||
\(955\) | −1.88343 | −0.0609462 | ||||||||
\(956\) | −20.4693 | −0.662025 | ||||||||
\(957\) | 1.05702 | 0.0341687 | ||||||||
\(958\) | −11.4826 | −0.370987 | ||||||||
\(959\) | 50.9298 | 1.64461 | ||||||||
\(960\) | 0.0911919 | 0.00294321 | ||||||||
\(961\) | −29.1905 | −0.941627 | ||||||||
\(962\) | −1.38512 | −0.0446581 | ||||||||
\(963\) | 16.3717 | 0.527571 | ||||||||
\(964\) | −30.2979 | −0.975828 | ||||||||
\(965\) | −0.925795 | −0.0298024 | ||||||||
\(966\) | −30.2482 | −0.973218 | ||||||||
\(967\) | 2.85719 | 0.0918811 | 0.0459406 | − | 0.998944i | \(-0.485372\pi\) | ||||
0.0459406 | + | 0.998944i | \(0.485372\pi\) | |||||||
\(968\) | 10.9852 | 0.353079 | ||||||||
\(969\) | 4.12918 | 0.132648 | ||||||||
\(970\) | 0.431872 | 0.0138666 | ||||||||
\(971\) | 37.8413 | 1.21439 | 0.607193 | − | 0.794555i | \(-0.292296\pi\) | ||||
0.607193 | + | 0.794555i | \(0.292296\pi\) | |||||||
\(972\) | −16.1243 | −0.517188 | ||||||||
\(973\) | −67.9558 | −2.17856 | ||||||||
\(974\) | 21.9886 | 0.704561 | ||||||||
\(975\) | −7.80804 | −0.250058 | ||||||||
\(976\) | −10.4678 | −0.335065 | ||||||||
\(977\) | −53.8163 | −1.72174 | −0.860868 | − | 0.508828i | \(-0.830079\pi\) | ||||
−0.860868 | + | 0.508828i | \(0.830079\pi\) | |||||||
\(978\) | 7.30265 | 0.233513 | ||||||||
\(979\) | 0.701458 | 0.0224187 | ||||||||
\(980\) | −1.01863 | −0.0325390 | ||||||||
\(981\) | −26.9101 | −0.859173 | ||||||||
\(982\) | 23.7027 | 0.756384 | ||||||||
\(983\) | 42.2353 | 1.34710 | 0.673548 | − | 0.739143i | \(-0.264769\pi\) | ||||
0.673548 | + | 0.739143i | \(0.264769\pi\) | |||||||
\(984\) | −2.40454 | −0.0766540 | ||||||||
\(985\) | 0.182187 | 0.00580495 | ||||||||
\(986\) | −29.3074 | −0.933339 | ||||||||
\(987\) | 46.2585 | 1.47242 | ||||||||
\(988\) | 2.18900 | 0.0696413 | ||||||||
\(989\) | 50.3084 | 1.59971 | ||||||||
\(990\) | 0.0241320 | 0.000766965 0 | ||||||||
\(991\) | 59.5820 | 1.89269 | 0.946343 | − | 0.323165i | \(-0.104747\pi\) | ||||
0.946343 | + | 0.323165i | \(0.104747\pi\) | |||||||
\(992\) | −1.34519 | −0.0427100 | ||||||||
\(993\) | 30.3779 | 0.964014 | ||||||||
\(994\) | 23.8962 | 0.757942 | ||||||||
\(995\) | −0.985715 | −0.0312493 | ||||||||
\(996\) | 11.2296 | 0.355822 | ||||||||
\(997\) | −29.0071 | −0.918665 | −0.459333 | − | 0.888264i | \(-0.651911\pi\) | ||||
−0.459333 | + | 0.888264i | \(0.651911\pi\) | |||||||
\(998\) | 14.8704 | 0.470715 | ||||||||
\(999\) | −4.12172 | −0.130405 |
(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 | 4006.2.a.g.1.14 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.14 | ✓ | 40 | 1.1 | even | 1 | trivial |