Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(98\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52650 | −1.78650 | −0.893251 | − | 0.449557i | \(-0.851582\pi\) | ||||
−0.893251 | + | 0.449557i | \(0.851582\pi\) | |||||||
\(3\) | 1.56416 | 0.903067 | 0.451534 | − | 0.892254i | \(-0.350877\pi\) | ||||
0.451534 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(4\) | 4.38319 | 2.19159 | ||||||||
\(5\) | 1.08994 | 0.487434 | 0.243717 | − | 0.969846i | \(-0.421633\pi\) | ||||
0.243717 | + | 0.969846i | \(0.421633\pi\) | |||||||
\(6\) | −3.95184 | −1.61333 | ||||||||
\(7\) | 4.94624 | 1.86950 | 0.934751 | − | 0.355302i | \(-0.115622\pi\) | ||||
0.934751 | + | 0.355302i | \(0.115622\pi\) | |||||||
\(8\) | −6.02111 | −2.12878 | ||||||||
\(9\) | −0.553409 | −0.184470 | ||||||||
\(10\) | −2.75372 | −0.870803 | ||||||||
\(11\) | 1.08607 | 0.327461 | 0.163731 | − | 0.986505i | \(-0.447647\pi\) | ||||
0.163731 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(12\) | 6.85600 | 1.97916 | ||||||||
\(13\) | −7.15585 | −1.98468 | −0.992338 | − | 0.123555i | \(-0.960571\pi\) | ||||
−0.992338 | + | 0.123555i | \(0.960571\pi\) | |||||||
\(14\) | −12.4967 | −3.33987 | ||||||||
\(15\) | 1.70483 | 0.440186 | ||||||||
\(16\) | 6.44594 | 1.61149 | ||||||||
\(17\) | −0.679762 | −0.164867 | −0.0824333 | − | 0.996597i | \(-0.526269\pi\) | ||||
−0.0824333 | + | 0.996597i | \(0.526269\pi\) | |||||||
\(18\) | 1.39818 | 0.329555 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 4.77739 | 1.06826 | ||||||||
\(21\) | 7.73670 | 1.68829 | ||||||||
\(22\) | −2.74394 | −0.585011 | ||||||||
\(23\) | 0.230492 | 0.0480609 | 0.0240305 | − | 0.999711i | \(-0.492350\pi\) | ||||
0.0240305 | + | 0.999711i | \(0.492350\pi\) | |||||||
\(24\) | −9.41797 | −1.92243 | ||||||||
\(25\) | −3.81204 | −0.762408 | ||||||||
\(26\) | 18.0792 | 3.54563 | ||||||||
\(27\) | −5.55809 | −1.06966 | ||||||||
\(28\) | 21.6803 | 4.09719 | ||||||||
\(29\) | −3.96002 | −0.735357 | −0.367679 | − | 0.929953i | \(-0.619847\pi\) | ||||
−0.367679 | + | 0.929953i | \(0.619847\pi\) | |||||||
\(30\) | −4.30726 | −0.786394 | ||||||||
\(31\) | −3.60722 | −0.647875 | −0.323938 | − | 0.946078i | \(-0.605007\pi\) | ||||
−0.323938 | + | 0.946078i | \(0.605007\pi\) | |||||||
\(32\) | −4.24343 | −0.750140 | ||||||||
\(33\) | 1.69878 | 0.295720 | ||||||||
\(34\) | 1.71742 | 0.294535 | ||||||||
\(35\) | 5.39109 | 0.911260 | ||||||||
\(36\) | −2.42569 | −0.404282 | ||||||||
\(37\) | −11.1155 | −1.82737 | −0.913687 | − | 0.406419i | \(-0.866777\pi\) | ||||
−0.913687 | + | 0.406419i | \(0.866777\pi\) | |||||||
\(38\) | −2.52650 | −0.409852 | ||||||||
\(39\) | −11.1929 | −1.79230 | ||||||||
\(40\) | −6.56263 | −1.03764 | ||||||||
\(41\) | −0.857779 | −0.133963 | −0.0669813 | − | 0.997754i | \(-0.521337\pi\) | ||||
−0.0669813 | + | 0.997754i | \(0.521337\pi\) | |||||||
\(42\) | −19.5468 | −3.01613 | ||||||||
\(43\) | −4.76742 | −0.727025 | −0.363512 | − | 0.931589i | \(-0.618423\pi\) | ||||
−0.363512 | + | 0.931589i | \(0.618423\pi\) | |||||||
\(44\) | 4.76043 | 0.717662 | ||||||||
\(45\) | −0.603180 | −0.0899168 | ||||||||
\(46\) | −0.582338 | −0.0858610 | ||||||||
\(47\) | −4.63322 | −0.675825 | −0.337912 | − | 0.941178i | \(-0.609721\pi\) | ||||
−0.337912 | + | 0.941178i | \(0.609721\pi\) | |||||||
\(48\) | 10.0825 | 1.45528 | ||||||||
\(49\) | 17.4653 | 2.49504 | ||||||||
\(50\) | 9.63110 | 1.36204 | ||||||||
\(51\) | −1.06326 | −0.148886 | ||||||||
\(52\) | −31.3654 | −4.34960 | ||||||||
\(53\) | −1.85027 | −0.254154 | −0.127077 | − | 0.991893i | \(-0.540560\pi\) | ||||
−0.127077 | + | 0.991893i | \(0.540560\pi\) | |||||||
\(54\) | 14.0425 | 1.91094 | ||||||||
\(55\) | 1.18374 | 0.159616 | ||||||||
\(56\) | −29.7818 | −3.97977 | ||||||||
\(57\) | 1.56416 | 0.207178 | ||||||||
\(58\) | 10.0050 | 1.31372 | ||||||||
\(59\) | 13.1898 | 1.71716 | 0.858580 | − | 0.512680i | \(-0.171347\pi\) | ||||
0.858580 | + | 0.512680i | \(0.171347\pi\) | |||||||
\(60\) | 7.47260 | 0.964708 | ||||||||
\(61\) | 8.77867 | 1.12399 | 0.561997 | − | 0.827139i | \(-0.310033\pi\) | ||||
0.561997 | + | 0.827139i | \(0.310033\pi\) | |||||||
\(62\) | 9.11362 | 1.15743 | ||||||||
\(63\) | −2.73729 | −0.344866 | ||||||||
\(64\) | −2.17087 | −0.271359 | ||||||||
\(65\) | −7.79942 | −0.967399 | ||||||||
\(66\) | −4.29196 | −0.528304 | ||||||||
\(67\) | 14.4757 | 1.76849 | 0.884247 | − | 0.467020i | \(-0.154672\pi\) | ||||
0.884247 | + | 0.467020i | \(0.154672\pi\) | |||||||
\(68\) | −2.97952 | −0.361320 | ||||||||
\(69\) | 0.360526 | 0.0434023 | ||||||||
\(70\) | −13.6206 | −1.62797 | ||||||||
\(71\) | 10.2052 | 1.21113 | 0.605565 | − | 0.795796i | \(-0.292947\pi\) | ||||
0.605565 | + | 0.795796i | \(0.292947\pi\) | |||||||
\(72\) | 3.33213 | 0.392696 | ||||||||
\(73\) | −7.59914 | −0.889412 | −0.444706 | − | 0.895677i | \(-0.646692\pi\) | ||||
−0.444706 | + | 0.895677i | \(0.646692\pi\) | |||||||
\(74\) | 28.0832 | 3.26461 | ||||||||
\(75\) | −5.96263 | −0.688505 | ||||||||
\(76\) | 4.38319 | 0.502786 | ||||||||
\(77\) | 5.37195 | 0.612190 | ||||||||
\(78\) | 28.2788 | 3.20194 | ||||||||
\(79\) | −11.4880 | −1.29250 | −0.646250 | − | 0.763125i | \(-0.723664\pi\) | ||||
−0.646250 | + | 0.763125i | \(0.723664\pi\) | |||||||
\(80\) | 7.02567 | 0.785493 | ||||||||
\(81\) | −7.03351 | −0.781501 | ||||||||
\(82\) | 2.16717 | 0.239324 | ||||||||
\(83\) | −11.0248 | −1.21012 | −0.605062 | − | 0.796178i | \(-0.706852\pi\) | ||||
−0.605062 | + | 0.796178i | \(0.706852\pi\) | |||||||
\(84\) | 33.9114 | 3.70004 | ||||||||
\(85\) | −0.740898 | −0.0803616 | ||||||||
\(86\) | 12.0449 | 1.29883 | ||||||||
\(87\) | −6.19410 | −0.664077 | ||||||||
\(88\) | −6.53932 | −0.697094 | ||||||||
\(89\) | −5.17570 | −0.548623 | −0.274311 | − | 0.961641i | \(-0.588450\pi\) | ||||
−0.274311 | + | 0.961641i | \(0.588450\pi\) | |||||||
\(90\) | 1.52393 | 0.160637 | ||||||||
\(91\) | −35.3945 | −3.71036 | ||||||||
\(92\) | 1.01029 | 0.105330 | ||||||||
\(93\) | −5.64226 | −0.585075 | ||||||||
\(94\) | 11.7058 | 1.20736 | ||||||||
\(95\) | 1.08994 | 0.111825 | ||||||||
\(96\) | −6.63740 | −0.677426 | ||||||||
\(97\) | −6.09815 | −0.619173 | −0.309586 | − | 0.950871i | \(-0.600191\pi\) | ||||
−0.309586 | + | 0.950871i | \(0.600191\pi\) | |||||||
\(98\) | −44.1260 | −4.45740 | ||||||||
\(99\) | −0.601038 | −0.0604066 | ||||||||
\(100\) | −16.7089 | −1.67089 | ||||||||
\(101\) | 8.32395 | 0.828264 | 0.414132 | − | 0.910217i | \(-0.364085\pi\) | ||||
0.414132 | + | 0.910217i | \(0.364085\pi\) | |||||||
\(102\) | 2.68631 | 0.265985 | ||||||||
\(103\) | −2.78965 | −0.274872 | −0.137436 | − | 0.990511i | \(-0.543886\pi\) | ||||
−0.137436 | + | 0.990511i | \(0.543886\pi\) | |||||||
\(104\) | 43.0861 | 4.22494 | ||||||||
\(105\) | 8.43251 | 0.822929 | ||||||||
\(106\) | 4.67470 | 0.454047 | ||||||||
\(107\) | −6.32819 | −0.611769 | −0.305884 | − | 0.952069i | \(-0.598952\pi\) | ||||
−0.305884 | + | 0.952069i | \(0.598952\pi\) | |||||||
\(108\) | −24.3622 | −2.34425 | ||||||||
\(109\) | −9.97996 | −0.955907 | −0.477954 | − | 0.878385i | \(-0.658621\pi\) | ||||
−0.477954 | + | 0.878385i | \(0.658621\pi\) | |||||||
\(110\) | −2.99072 | −0.285154 | ||||||||
\(111\) | −17.3864 | −1.65024 | ||||||||
\(112\) | 31.8832 | 3.01268 | ||||||||
\(113\) | −10.3965 | −0.978021 | −0.489011 | − | 0.872278i | \(-0.662642\pi\) | ||||
−0.489011 | + | 0.872278i | \(0.662642\pi\) | |||||||
\(114\) | −3.95184 | −0.370124 | ||||||||
\(115\) | 0.251222 | 0.0234266 | ||||||||
\(116\) | −17.3575 | −1.61160 | ||||||||
\(117\) | 3.96011 | 0.366112 | ||||||||
\(118\) | −33.3239 | −3.06771 | ||||||||
\(119\) | −3.36227 | −0.308218 | ||||||||
\(120\) | −10.2650 | −0.937061 | ||||||||
\(121\) | −9.82046 | −0.892769 | ||||||||
\(122\) | −22.1793 | −2.00802 | ||||||||
\(123\) | −1.34170 | −0.120977 | ||||||||
\(124\) | −15.8111 | −1.41988 | ||||||||
\(125\) | −9.60456 | −0.859058 | ||||||||
\(126\) | 6.91576 | 0.616105 | ||||||||
\(127\) | 12.1778 | 1.08060 | 0.540301 | − | 0.841472i | \(-0.318310\pi\) | ||||
0.540301 | + | 0.841472i | \(0.318310\pi\) | |||||||
\(128\) | 13.9716 | 1.23492 | ||||||||
\(129\) | −7.45700 | −0.656552 | ||||||||
\(130\) | 19.7052 | 1.72826 | ||||||||
\(131\) | 10.9871 | 0.959952 | 0.479976 | − | 0.877282i | \(-0.340645\pi\) | ||||
0.479976 | + | 0.877282i | \(0.340645\pi\) | |||||||
\(132\) | 7.44607 | 0.648097 | ||||||||
\(133\) | 4.94624 | 0.428893 | ||||||||
\(134\) | −36.5729 | −3.15942 | ||||||||
\(135\) | −6.05797 | −0.521387 | ||||||||
\(136\) | 4.09292 | 0.350965 | ||||||||
\(137\) | −14.4313 | −1.23295 | −0.616476 | − | 0.787374i | \(-0.711440\pi\) | ||||
−0.616476 | + | 0.787374i | \(0.711440\pi\) | |||||||
\(138\) | −0.910868 | −0.0775383 | ||||||||
\(139\) | 2.31242 | 0.196137 | 0.0980685 | − | 0.995180i | \(-0.468734\pi\) | ||||
0.0980685 | + | 0.995180i | \(0.468734\pi\) | |||||||
\(140\) | 23.6301 | 1.99711 | ||||||||
\(141\) | −7.24709 | −0.610315 | ||||||||
\(142\) | −25.7833 | −2.16369 | ||||||||
\(143\) | −7.77173 | −0.649905 | ||||||||
\(144\) | −3.56724 | −0.297270 | ||||||||
\(145\) | −4.31617 | −0.358438 | ||||||||
\(146\) | 19.1992 | 1.58894 | ||||||||
\(147\) | 27.3185 | 2.25319 | ||||||||
\(148\) | −48.7212 | −4.00486 | ||||||||
\(149\) | −8.39291 | −0.687574 | −0.343787 | − | 0.939048i | \(-0.611710\pi\) | ||||
−0.343787 | + | 0.939048i | \(0.611710\pi\) | |||||||
\(150\) | 15.0646 | 1.23002 | ||||||||
\(151\) | −19.5139 | −1.58802 | −0.794008 | − | 0.607907i | \(-0.792009\pi\) | ||||
−0.794008 | + | 0.607907i | \(0.792009\pi\) | |||||||
\(152\) | −6.02111 | −0.488376 | ||||||||
\(153\) | 0.376186 | 0.0304129 | ||||||||
\(154\) | −13.5722 | −1.09368 | ||||||||
\(155\) | −3.93164 | −0.315797 | ||||||||
\(156\) | −49.0605 | −3.92798 | ||||||||
\(157\) | −1.52650 | −0.121828 | −0.0609138 | − | 0.998143i | \(-0.519401\pi\) | ||||
−0.0609138 | + | 0.998143i | \(0.519401\pi\) | |||||||
\(158\) | 29.0244 | 2.30906 | ||||||||
\(159\) | −2.89412 | −0.229518 | ||||||||
\(160\) | −4.62507 | −0.365644 | ||||||||
\(161\) | 1.14007 | 0.0898501 | ||||||||
\(162\) | 17.7701 | 1.39615 | ||||||||
\(163\) | −0.774360 | −0.0606526 | −0.0303263 | − | 0.999540i | \(-0.509655\pi\) | ||||
−0.0303263 | + | 0.999540i | \(0.509655\pi\) | |||||||
\(164\) | −3.75980 | −0.293591 | ||||||||
\(165\) | 1.85156 | 0.144144 | ||||||||
\(166\) | 27.8540 | 2.16189 | ||||||||
\(167\) | 14.8449 | 1.14873 | 0.574365 | − | 0.818599i | \(-0.305249\pi\) | ||||
0.574365 | + | 0.818599i | \(0.305249\pi\) | |||||||
\(168\) | −46.5835 | −3.59400 | ||||||||
\(169\) | 38.2062 | 2.93894 | ||||||||
\(170\) | 1.87188 | 0.143566 | ||||||||
\(171\) | −0.553409 | −0.0423202 | ||||||||
\(172\) | −20.8965 | −1.59334 | ||||||||
\(173\) | 3.38019 | 0.256991 | 0.128495 | − | 0.991710i | \(-0.458985\pi\) | ||||
0.128495 | + | 0.991710i | \(0.458985\pi\) | |||||||
\(174\) | 15.6494 | 1.18638 | ||||||||
\(175\) | −18.8553 | −1.42532 | ||||||||
\(176\) | 7.00072 | 0.527699 | ||||||||
\(177\) | 20.6309 | 1.55071 | ||||||||
\(178\) | 13.0764 | 0.980116 | ||||||||
\(179\) | −17.4992 | −1.30795 | −0.653977 | − | 0.756514i | \(-0.726901\pi\) | ||||
−0.653977 | + | 0.756514i | \(0.726901\pi\) | |||||||
\(180\) | −2.64385 | −0.197061 | ||||||||
\(181\) | −20.1776 | −1.49979 | −0.749894 | − | 0.661558i | \(-0.769896\pi\) | ||||
−0.749894 | + | 0.661558i | \(0.769896\pi\) | |||||||
\(182\) | 89.4242 | 6.62856 | ||||||||
\(183\) | 13.7312 | 1.01504 | ||||||||
\(184\) | −1.38782 | −0.102311 | ||||||||
\(185\) | −12.1152 | −0.890725 | ||||||||
\(186\) | 14.2552 | 1.04524 | ||||||||
\(187\) | −0.738267 | −0.0539874 | ||||||||
\(188\) | −20.3083 | −1.48113 | ||||||||
\(189\) | −27.4917 | −1.99972 | ||||||||
\(190\) | −2.75372 | −0.199776 | ||||||||
\(191\) | 15.8641 | 1.14788 | 0.573942 | − | 0.818896i | \(-0.305413\pi\) | ||||
0.573942 | + | 0.818896i | \(0.305413\pi\) | |||||||
\(192\) | −3.39559 | −0.245055 | ||||||||
\(193\) | −19.3179 | −1.39053 | −0.695266 | − | 0.718752i | \(-0.744713\pi\) | ||||
−0.695266 | + | 0.718752i | \(0.744713\pi\) | |||||||
\(194\) | 15.4069 | 1.10615 | ||||||||
\(195\) | −12.1995 | −0.873626 | ||||||||
\(196\) | 76.5536 | 5.46811 | ||||||||
\(197\) | 20.9441 | 1.49221 | 0.746103 | − | 0.665831i | \(-0.231923\pi\) | ||||
0.746103 | + | 0.665831i | \(0.231923\pi\) | |||||||
\(198\) | 1.51852 | 0.107917 | ||||||||
\(199\) | −8.92410 | −0.632613 | −0.316306 | − | 0.948657i | \(-0.602443\pi\) | ||||
−0.316306 | + | 0.948657i | \(0.602443\pi\) | |||||||
\(200\) | 22.9527 | 1.62300 | ||||||||
\(201\) | 22.6424 | 1.59707 | ||||||||
\(202\) | −21.0304 | −1.47970 | ||||||||
\(203\) | −19.5872 | −1.37475 | ||||||||
\(204\) | −4.66045 | −0.326297 | ||||||||
\(205\) | −0.934924 | −0.0652979 | ||||||||
\(206\) | 7.04803 | 0.491060 | ||||||||
\(207\) | −0.127556 | −0.00886578 | ||||||||
\(208\) | −46.1262 | −3.19828 | ||||||||
\(209\) | 1.08607 | 0.0751248 | ||||||||
\(210\) | −21.3047 | −1.47017 | ||||||||
\(211\) | 2.97263 | 0.204644 | 0.102322 | − | 0.994751i | \(-0.467373\pi\) | ||||
0.102322 | + | 0.994751i | \(0.467373\pi\) | |||||||
\(212\) | −8.11008 | −0.557003 | ||||||||
\(213\) | 15.9625 | 1.09373 | ||||||||
\(214\) | 15.9881 | 1.09293 | ||||||||
\(215\) | −5.19619 | −0.354377 | ||||||||
\(216\) | 33.4659 | 2.27707 | ||||||||
\(217\) | −17.8422 | −1.21121 | ||||||||
\(218\) | 25.2143 | 1.70773 | ||||||||
\(219\) | −11.8863 | −0.803199 | ||||||||
\(220\) | 5.18857 | 0.349813 | ||||||||
\(221\) | 4.86428 | 0.327207 | ||||||||
\(222\) | 43.9266 | 2.94816 | ||||||||
\(223\) | −28.2585 | −1.89233 | −0.946165 | − | 0.323685i | \(-0.895078\pi\) | ||||
−0.946165 | + | 0.323685i | \(0.895078\pi\) | |||||||
\(224\) | −20.9890 | −1.40239 | ||||||||
\(225\) | 2.10961 | 0.140641 | ||||||||
\(226\) | 26.2667 | 1.74724 | ||||||||
\(227\) | −25.2225 | −1.67408 | −0.837039 | − | 0.547143i | \(-0.815715\pi\) | ||||
−0.837039 | + | 0.547143i | \(0.815715\pi\) | |||||||
\(228\) | 6.85600 | 0.454049 | ||||||||
\(229\) | −14.1035 | −0.931984 | −0.465992 | − | 0.884789i | \(-0.654303\pi\) | ||||
−0.465992 | + | 0.884789i | \(0.654303\pi\) | |||||||
\(230\) | −0.634711 | −0.0418516 | ||||||||
\(231\) | 8.40257 | 0.552849 | ||||||||
\(232\) | 23.8437 | 1.56542 | ||||||||
\(233\) | 14.7493 | 0.966257 | 0.483128 | − | 0.875550i | \(-0.339500\pi\) | ||||
0.483128 | + | 0.875550i | \(0.339500\pi\) | |||||||
\(234\) | −10.0052 | −0.654060 | ||||||||
\(235\) | −5.04992 | −0.329420 | ||||||||
\(236\) | 57.8131 | 3.76332 | ||||||||
\(237\) | −17.9690 | −1.16722 | ||||||||
\(238\) | 8.49476 | 0.550633 | ||||||||
\(239\) | −17.7477 | −1.14800 | −0.574002 | − | 0.818854i | \(-0.694610\pi\) | ||||
−0.574002 | + | 0.818854i | \(0.694610\pi\) | |||||||
\(240\) | 10.9893 | 0.709353 | ||||||||
\(241\) | 6.15271 | 0.396331 | 0.198165 | − | 0.980169i | \(-0.436502\pi\) | ||||
0.198165 | + | 0.980169i | \(0.436502\pi\) | |||||||
\(242\) | 24.8114 | 1.59493 | ||||||||
\(243\) | 5.67275 | 0.363907 | ||||||||
\(244\) | 38.4785 | 2.46334 | ||||||||
\(245\) | 19.0361 | 1.21617 | ||||||||
\(246\) | 3.38980 | 0.216126 | ||||||||
\(247\) | −7.15585 | −0.455316 | ||||||||
\(248\) | 21.7195 | 1.37919 | ||||||||
\(249\) | −17.2445 | −1.09282 | ||||||||
\(250\) | 24.2659 | 1.53471 | ||||||||
\(251\) | −15.0438 | −0.949556 | −0.474778 | − | 0.880106i | \(-0.657472\pi\) | ||||
−0.474778 | + | 0.880106i | \(0.657472\pi\) | |||||||
\(252\) | −11.9981 | −0.755806 | ||||||||
\(253\) | 0.250330 | 0.0157381 | ||||||||
\(254\) | −30.7671 | −1.93050 | ||||||||
\(255\) | −1.15888 | −0.0725720 | ||||||||
\(256\) | −30.9573 | −1.93483 | ||||||||
\(257\) | 17.8353 | 1.11253 | 0.556267 | − | 0.831003i | \(-0.312233\pi\) | ||||
0.556267 | + | 0.831003i | \(0.312233\pi\) | |||||||
\(258\) | 18.8401 | 1.17293 | ||||||||
\(259\) | −54.9798 | −3.41628 | ||||||||
\(260\) | −34.1863 | −2.12014 | ||||||||
\(261\) | 2.19151 | 0.135651 | ||||||||
\(262\) | −27.7590 | −1.71496 | ||||||||
\(263\) | 19.8621 | 1.22475 | 0.612374 | − | 0.790568i | \(-0.290215\pi\) | ||||
0.612374 | + | 0.790568i | \(0.290215\pi\) | |||||||
\(264\) | −10.2285 | −0.629523 | ||||||||
\(265\) | −2.01668 | −0.123884 | ||||||||
\(266\) | −12.4967 | −0.766219 | ||||||||
\(267\) | −8.09561 | −0.495443 | ||||||||
\(268\) | 63.4499 | 3.87582 | ||||||||
\(269\) | 14.7102 | 0.896899 | 0.448450 | − | 0.893808i | \(-0.351976\pi\) | ||||
0.448450 | + | 0.893808i | \(0.351976\pi\) | |||||||
\(270\) | 15.3054 | 0.931459 | ||||||||
\(271\) | 19.6873 | 1.19592 | 0.597959 | − | 0.801527i | \(-0.295978\pi\) | ||||
0.597959 | + | 0.801527i | \(0.295978\pi\) | |||||||
\(272\) | −4.38171 | −0.265680 | ||||||||
\(273\) | −55.3627 | −3.35070 | ||||||||
\(274\) | 36.4607 | 2.20267 | ||||||||
\(275\) | −4.14013 | −0.249659 | ||||||||
\(276\) | 1.58025 | 0.0951201 | ||||||||
\(277\) | −11.8717 | −0.713302 | −0.356651 | − | 0.934238i | \(-0.616082\pi\) | ||||
−0.356651 | + | 0.934238i | \(0.616082\pi\) | |||||||
\(278\) | −5.84233 | −0.350399 | ||||||||
\(279\) | 1.99627 | 0.119513 | ||||||||
\(280\) | −32.4603 | −1.93988 | ||||||||
\(281\) | 29.0110 | 1.73065 | 0.865327 | − | 0.501209i | \(-0.167111\pi\) | ||||
0.865327 | + | 0.501209i | \(0.167111\pi\) | |||||||
\(282\) | 18.3097 | 1.09033 | ||||||||
\(283\) | 8.21889 | 0.488562 | 0.244281 | − | 0.969704i | \(-0.421448\pi\) | ||||
0.244281 | + | 0.969704i | \(0.421448\pi\) | |||||||
\(284\) | 44.7311 | 2.65430 | ||||||||
\(285\) | 1.70483 | 0.100986 | ||||||||
\(286\) | 19.6352 | 1.16106 | ||||||||
\(287\) | −4.24278 | −0.250443 | ||||||||
\(288\) | 2.34835 | 0.138378 | ||||||||
\(289\) | −16.5379 | −0.972819 | ||||||||
\(290\) | 10.9048 | 0.640351 | ||||||||
\(291\) | −9.53847 | −0.559155 | ||||||||
\(292\) | −33.3084 | −1.94923 | ||||||||
\(293\) | 11.3717 | 0.664344 | 0.332172 | − | 0.943219i | \(-0.392218\pi\) | ||||
0.332172 | + | 0.943219i | \(0.392218\pi\) | |||||||
\(294\) | −69.0200 | −4.02533 | ||||||||
\(295\) | 14.3760 | 0.837003 | ||||||||
\(296\) | 66.9275 | 3.89008 | ||||||||
\(297\) | −6.03646 | −0.350271 | ||||||||
\(298\) | 21.2047 | 1.22835 | ||||||||
\(299\) | −1.64937 | −0.0953854 | ||||||||
\(300\) | −26.1353 | −1.50892 | ||||||||
\(301\) | −23.5808 | −1.35918 | ||||||||
\(302\) | 49.3017 | 2.83700 | ||||||||
\(303\) | 13.0200 | 0.747978 | ||||||||
\(304\) | 6.44594 | 0.369700 | ||||||||
\(305\) | 9.56819 | 0.547873 | ||||||||
\(306\) | −0.950433 | −0.0543326 | ||||||||
\(307\) | 20.2354 | 1.15490 | 0.577448 | − | 0.816427i | \(-0.304048\pi\) | ||||
0.577448 | + | 0.816427i | \(0.304048\pi\) | |||||||
\(308\) | 23.5462 | 1.34167 | ||||||||
\(309\) | −4.36345 | −0.248228 | ||||||||
\(310\) | 9.93327 | 0.564172 | ||||||||
\(311\) | 28.2180 | 1.60010 | 0.800049 | − | 0.599935i | \(-0.204807\pi\) | ||||
0.800049 | + | 0.599935i | \(0.204807\pi\) | |||||||
\(312\) | 67.3936 | 3.81541 | ||||||||
\(313\) | −12.7460 | −0.720448 | −0.360224 | − | 0.932866i | \(-0.617300\pi\) | ||||
−0.360224 | + | 0.932866i | \(0.617300\pi\) | |||||||
\(314\) | 3.85669 | 0.217645 | ||||||||
\(315\) | −2.98347 | −0.168100 | ||||||||
\(316\) | −50.3540 | −2.83263 | ||||||||
\(317\) | 1.00000 | 0.0561656 | ||||||||
\(318\) | 7.31198 | 0.410035 | ||||||||
\(319\) | −4.30084 | −0.240801 | ||||||||
\(320\) | −2.36611 | −0.132270 | ||||||||
\(321\) | −9.89829 | −0.552468 | ||||||||
\(322\) | −2.88038 | −0.160517 | ||||||||
\(323\) | −0.679762 | −0.0378230 | ||||||||
\(324\) | −30.8292 | −1.71273 | ||||||||
\(325\) | 27.2784 | 1.51313 | ||||||||
\(326\) | 1.95642 | 0.108356 | ||||||||
\(327\) | −15.6102 | −0.863248 | ||||||||
\(328\) | 5.16478 | 0.285177 | ||||||||
\(329\) | −22.9170 | −1.26346 | ||||||||
\(330\) | −4.67797 | −0.257514 | ||||||||
\(331\) | −22.1309 | −1.21642 | −0.608211 | − | 0.793775i | \(-0.708113\pi\) | ||||
−0.608211 | + | 0.793775i | \(0.708113\pi\) | |||||||
\(332\) | −48.3236 | −2.65210 | ||||||||
\(333\) | 6.15140 | 0.337095 | ||||||||
\(334\) | −37.5055 | −2.05221 | ||||||||
\(335\) | 15.7776 | 0.862025 | ||||||||
\(336\) | 49.8703 | 2.72065 | ||||||||
\(337\) | −0.334438 | −0.0182180 | −0.00910900 | − | 0.999959i | \(-0.502900\pi\) | ||||
−0.00910900 | + | 0.999959i | \(0.502900\pi\) | |||||||
\(338\) | −96.5278 | −5.25042 | ||||||||
\(339\) | −16.2618 | −0.883219 | ||||||||
\(340\) | −3.24749 | −0.176120 | ||||||||
\(341\) | −3.91768 | −0.212154 | ||||||||
\(342\) | 1.39818 | 0.0756052 | ||||||||
\(343\) | 51.7638 | 2.79498 | ||||||||
\(344\) | 28.7052 | 1.54768 | ||||||||
\(345\) | 0.392951 | 0.0211558 | ||||||||
\(346\) | −8.54003 | −0.459115 | ||||||||
\(347\) | −19.4158 | −1.04230 | −0.521148 | − | 0.853466i | \(-0.674496\pi\) | ||||
−0.521148 | + | 0.853466i | \(0.674496\pi\) | |||||||
\(348\) | −27.1499 | −1.45539 | ||||||||
\(349\) | 23.5709 | 1.26172 | 0.630860 | − | 0.775896i | \(-0.282702\pi\) | ||||
0.630860 | + | 0.775896i | \(0.282702\pi\) | |||||||
\(350\) | 47.6377 | 2.54634 | ||||||||
\(351\) | 39.7729 | 2.12292 | ||||||||
\(352\) | −4.60865 | −0.245642 | ||||||||
\(353\) | −20.0642 | −1.06791 | −0.533954 | − | 0.845514i | \(-0.679294\pi\) | ||||
−0.533954 | + | 0.845514i | \(0.679294\pi\) | |||||||
\(354\) | −52.1238 | −2.77035 | ||||||||
\(355\) | 11.1230 | 0.590346 | ||||||||
\(356\) | −22.6860 | −1.20236 | ||||||||
\(357\) | −5.25912 | −0.278342 | ||||||||
\(358\) | 44.2118 | 2.33667 | ||||||||
\(359\) | −9.74718 | −0.514437 | −0.257218 | − | 0.966353i | \(-0.582806\pi\) | ||||
−0.257218 | + | 0.966353i | \(0.582806\pi\) | |||||||
\(360\) | 3.63181 | 0.191413 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 50.9786 | 2.67938 | ||||||||
\(363\) | −15.3608 | −0.806230 | ||||||||
\(364\) | −155.141 | −8.13159 | ||||||||
\(365\) | −8.28258 | −0.433530 | ||||||||
\(366\) | −34.6919 | −1.81338 | ||||||||
\(367\) | −18.9550 | −0.989442 | −0.494721 | − | 0.869052i | \(-0.664730\pi\) | ||||
−0.494721 | + | 0.869052i | \(0.664730\pi\) | |||||||
\(368\) | 1.48574 | 0.0774495 | ||||||||
\(369\) | 0.474702 | 0.0247120 | ||||||||
\(370\) | 30.6089 | 1.59128 | ||||||||
\(371\) | −9.15189 | −0.475142 | ||||||||
\(372\) | −24.7311 | −1.28225 | ||||||||
\(373\) | 20.2175 | 1.04682 | 0.523411 | − | 0.852080i | \(-0.324659\pi\) | ||||
0.523411 | + | 0.852080i | \(0.324659\pi\) | |||||||
\(374\) | 1.86523 | 0.0964487 | ||||||||
\(375\) | −15.0231 | −0.775787 | ||||||||
\(376\) | 27.8971 | 1.43868 | ||||||||
\(377\) | 28.3373 | 1.45945 | ||||||||
\(378\) | 69.4576 | 3.57251 | ||||||||
\(379\) | −16.9758 | −0.871986 | −0.435993 | − | 0.899950i | \(-0.643603\pi\) | ||||
−0.435993 | + | 0.899950i | \(0.643603\pi\) | |||||||
\(380\) | 4.77739 | 0.245075 | ||||||||
\(381\) | 19.0479 | 0.975856 | ||||||||
\(382\) | −40.0806 | −2.05070 | ||||||||
\(383\) | −23.9921 | −1.22594 | −0.612970 | − | 0.790106i | \(-0.710025\pi\) | ||||
−0.612970 | + | 0.790106i | \(0.710025\pi\) | |||||||
\(384\) | 21.8537 | 1.11522 | ||||||||
\(385\) | 5.85508 | 0.298402 | ||||||||
\(386\) | 48.8066 | 2.48419 | ||||||||
\(387\) | 2.63833 | 0.134114 | ||||||||
\(388\) | −26.7293 | −1.35697 | ||||||||
\(389\) | 22.3846 | 1.13494 | 0.567471 | − | 0.823393i | \(-0.307922\pi\) | ||||
0.567471 | + | 0.823393i | \(0.307922\pi\) | |||||||
\(390\) | 30.8221 | 1.56074 | ||||||||
\(391\) | −0.156680 | −0.00792364 | ||||||||
\(392\) | −105.160 | −5.31140 | ||||||||
\(393\) | 17.1856 | 0.866901 | ||||||||
\(394\) | −52.9152 | −2.66583 | ||||||||
\(395\) | −12.5212 | −0.630009 | ||||||||
\(396\) | −2.63446 | −0.132387 | ||||||||
\(397\) | 27.7445 | 1.39246 | 0.696229 | − | 0.717820i | \(-0.254860\pi\) | ||||
0.696229 | + | 0.717820i | \(0.254860\pi\) | |||||||
\(398\) | 22.5467 | 1.13016 | ||||||||
\(399\) | 7.73670 | 0.387320 | ||||||||
\(400\) | −24.5722 | −1.22861 | ||||||||
\(401\) | 35.3887 | 1.76723 | 0.883615 | − | 0.468215i | \(-0.155103\pi\) | ||||
0.883615 | + | 0.468215i | \(0.155103\pi\) | |||||||
\(402\) | −57.2058 | −2.85317 | ||||||||
\(403\) | 25.8127 | 1.28582 | ||||||||
\(404\) | 36.4854 | 1.81522 | ||||||||
\(405\) | −7.66608 | −0.380931 | ||||||||
\(406\) | 49.4870 | 2.45600 | ||||||||
\(407\) | −12.0722 | −0.598394 | ||||||||
\(408\) | 6.40198 | 0.316945 | ||||||||
\(409\) | −25.7216 | −1.27185 | −0.635925 | − | 0.771750i | \(-0.719381\pi\) | ||||
−0.635925 | + | 0.771750i | \(0.719381\pi\) | |||||||
\(410\) | 2.36208 | 0.116655 | ||||||||
\(411\) | −22.5729 | −1.11344 | ||||||||
\(412\) | −12.2275 | −0.602407 | ||||||||
\(413\) | 65.2397 | 3.21024 | ||||||||
\(414\) | 0.322271 | 0.0158387 | ||||||||
\(415\) | −12.0163 | −0.589856 | ||||||||
\(416\) | 30.3653 | 1.48878 | ||||||||
\(417\) | 3.61699 | 0.177125 | ||||||||
\(418\) | −2.74394 | −0.134211 | ||||||||
\(419\) | 22.9381 | 1.12060 | 0.560299 | − | 0.828290i | \(-0.310686\pi\) | ||||
0.560299 | + | 0.828290i | \(0.310686\pi\) | |||||||
\(420\) | 36.9613 | 1.80353 | ||||||||
\(421\) | 28.5656 | 1.39220 | 0.696100 | − | 0.717945i | \(-0.254917\pi\) | ||||
0.696100 | + | 0.717945i | \(0.254917\pi\) | |||||||
\(422\) | −7.51034 | −0.365598 | ||||||||
\(423\) | 2.56406 | 0.124669 | ||||||||
\(424\) | 11.1407 | 0.541039 | ||||||||
\(425\) | 2.59128 | 0.125696 | ||||||||
\(426\) | −40.3291 | −1.95395 | ||||||||
\(427\) | 43.4214 | 2.10131 | ||||||||
\(428\) | −27.7376 | −1.34075 | ||||||||
\(429\) | −12.1562 | −0.586908 | ||||||||
\(430\) | 13.1281 | 0.633095 | ||||||||
\(431\) | −30.5462 | −1.47136 | −0.735680 | − | 0.677329i | \(-0.763137\pi\) | ||||
−0.735680 | + | 0.677329i | \(0.763137\pi\) | |||||||
\(432\) | −35.8271 | −1.72373 | ||||||||
\(433\) | 18.6217 | 0.894903 | 0.447452 | − | 0.894308i | \(-0.352332\pi\) | ||||
0.447452 | + | 0.894308i | \(0.352332\pi\) | |||||||
\(434\) | 45.0782 | 2.16382 | ||||||||
\(435\) | −6.75117 | −0.323694 | ||||||||
\(436\) | −43.7440 | −2.09496 | ||||||||
\(437\) | 0.230492 | 0.0110259 | ||||||||
\(438\) | 30.0306 | 1.43492 | ||||||||
\(439\) | 7.49912 | 0.357913 | 0.178957 | − | 0.983857i | \(-0.442728\pi\) | ||||
0.178957 | + | 0.983857i | \(0.442728\pi\) | |||||||
\(440\) | −7.12745 | −0.339788 | ||||||||
\(441\) | −9.66544 | −0.460259 | ||||||||
\(442\) | −12.2896 | −0.584556 | ||||||||
\(443\) | 3.57056 | 0.169643 | 0.0848213 | − | 0.996396i | \(-0.472968\pi\) | ||||
0.0848213 | + | 0.996396i | \(0.472968\pi\) | |||||||
\(444\) | −76.2077 | −3.61666 | ||||||||
\(445\) | −5.64118 | −0.267418 | ||||||||
\(446\) | 71.3950 | 3.38065 | ||||||||
\(447\) | −13.1278 | −0.620926 | ||||||||
\(448\) | −10.7376 | −0.507306 | ||||||||
\(449\) | 15.5917 | 0.735820 | 0.367910 | − | 0.929861i | \(-0.380073\pi\) | ||||
0.367910 | + | 0.929861i | \(0.380073\pi\) | |||||||
\(450\) | −5.32993 | −0.251256 | ||||||||
\(451\) | −0.931605 | −0.0438676 | ||||||||
\(452\) | −45.5698 | −2.14342 | ||||||||
\(453\) | −30.5228 | −1.43409 | ||||||||
\(454\) | 63.7246 | 2.99074 | ||||||||
\(455\) | −38.5778 | −1.80856 | ||||||||
\(456\) | −9.41797 | −0.441037 | ||||||||
\(457\) | −6.59009 | −0.308271 | −0.154136 | − | 0.988050i | \(-0.549259\pi\) | ||||
−0.154136 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(458\) | 35.6324 | 1.66499 | ||||||||
\(459\) | 3.77818 | 0.176350 | ||||||||
\(460\) | 1.10115 | 0.0513415 | ||||||||
\(461\) | −1.33639 | −0.0622418 | −0.0311209 | − | 0.999516i | \(-0.509908\pi\) | ||||
−0.0311209 | + | 0.999516i | \(0.509908\pi\) | |||||||
\(462\) | −21.2291 | −0.987666 | ||||||||
\(463\) | 17.4498 | 0.810962 | 0.405481 | − | 0.914103i | \(-0.367104\pi\) | ||||
0.405481 | + | 0.914103i | \(0.367104\pi\) | |||||||
\(464\) | −25.5260 | −1.18502 | ||||||||
\(465\) | −6.14970 | −0.285186 | ||||||||
\(466\) | −37.2640 | −1.72622 | ||||||||
\(467\) | −28.5225 | −1.31986 | −0.659932 | − | 0.751325i | \(-0.729415\pi\) | ||||
−0.659932 | + | 0.751325i | \(0.729415\pi\) | |||||||
\(468\) | 17.3579 | 0.802369 | ||||||||
\(469\) | 71.6005 | 3.30620 | ||||||||
\(470\) | 12.7586 | 0.588510 | ||||||||
\(471\) | −2.38768 | −0.110019 | ||||||||
\(472\) | −79.4170 | −3.65546 | ||||||||
\(473\) | −5.17774 | −0.238073 | ||||||||
\(474\) | 45.3987 | 2.08523 | ||||||||
\(475\) | −3.81204 | −0.174908 | ||||||||
\(476\) | −14.7374 | −0.675489 | ||||||||
\(477\) | 1.02396 | 0.0468837 | ||||||||
\(478\) | 44.8395 | 2.05091 | ||||||||
\(479\) | 15.5893 | 0.712291 | 0.356146 | − | 0.934430i | \(-0.384091\pi\) | ||||
0.356146 | + | 0.934430i | \(0.384091\pi\) | |||||||
\(480\) | −7.23434 | −0.330201 | ||||||||
\(481\) | 79.5407 | 3.62674 | ||||||||
\(482\) | −15.5448 | −0.708046 | ||||||||
\(483\) | 1.78325 | 0.0811407 | ||||||||
\(484\) | −43.0449 | −1.95659 | ||||||||
\(485\) | −6.64659 | −0.301806 | ||||||||
\(486\) | −14.3322 | −0.650121 | ||||||||
\(487\) | 16.8684 | 0.764381 | 0.382190 | − | 0.924084i | \(-0.375170\pi\) | ||||
0.382190 | + | 0.924084i | \(0.375170\pi\) | |||||||
\(488\) | −52.8573 | −2.39274 | ||||||||
\(489\) | −1.21122 | −0.0547734 | ||||||||
\(490\) | −48.0945 | −2.17269 | ||||||||
\(491\) | 32.8365 | 1.48189 | 0.740945 | − | 0.671566i | \(-0.234378\pi\) | ||||
0.740945 | + | 0.671566i | \(0.234378\pi\) | |||||||
\(492\) | −5.88093 | −0.265133 | ||||||||
\(493\) | 2.69187 | 0.121236 | ||||||||
\(494\) | 18.0792 | 0.813423 | ||||||||
\(495\) | −0.655094 | −0.0294443 | ||||||||
\(496\) | −23.2519 | −1.04404 | ||||||||
\(497\) | 50.4771 | 2.26421 | ||||||||
\(498\) | 43.5681 | 1.95233 | ||||||||
\(499\) | −28.1262 | −1.25910 | −0.629552 | − | 0.776958i | \(-0.716761\pi\) | ||||
−0.629552 | + | 0.776958i | \(0.716761\pi\) | |||||||
\(500\) | −42.0986 | −1.88271 | ||||||||
\(501\) | 23.2197 | 1.03738 | ||||||||
\(502\) | 38.0081 | 1.69638 | ||||||||
\(503\) | −26.8851 | −1.19875 | −0.599374 | − | 0.800469i | \(-0.704584\pi\) | ||||
−0.599374 | + | 0.800469i | \(0.704584\pi\) | |||||||
\(504\) | 16.4815 | 0.734146 | ||||||||
\(505\) | 9.07258 | 0.403724 | ||||||||
\(506\) | −0.632457 | −0.0281162 | ||||||||
\(507\) | 59.7605 | 2.65406 | ||||||||
\(508\) | 53.3774 | 2.36824 | ||||||||
\(509\) | −34.1150 | −1.51212 | −0.756060 | − | 0.654502i | \(-0.772878\pi\) | ||||
−0.756060 | + | 0.654502i | \(0.772878\pi\) | |||||||
\(510\) | 2.92791 | 0.129650 | ||||||||
\(511\) | −37.5872 | −1.66276 | ||||||||
\(512\) | 50.2705 | 2.22166 | ||||||||
\(513\) | −5.55809 | −0.245396 | ||||||||
\(514\) | −45.0608 | −1.98755 | ||||||||
\(515\) | −3.04054 | −0.133982 | ||||||||
\(516\) | −32.6854 | −1.43890 | ||||||||
\(517\) | −5.03199 | −0.221306 | ||||||||
\(518\) | 138.906 | 6.10320 | ||||||||
\(519\) | 5.28715 | 0.232080 | ||||||||
\(520\) | 46.9612 | 2.05938 | ||||||||
\(521\) | 5.07349 | 0.222274 | 0.111137 | − | 0.993805i | \(-0.464551\pi\) | ||||
0.111137 | + | 0.993805i | \(0.464551\pi\) | |||||||
\(522\) | −5.53684 | −0.242341 | ||||||||
\(523\) | 3.54269 | 0.154911 | 0.0774555 | − | 0.996996i | \(-0.475320\pi\) | ||||
0.0774555 | + | 0.996996i | \(0.475320\pi\) | |||||||
\(524\) | 48.1587 | 2.10382 | ||||||||
\(525\) | −29.4926 | −1.28716 | ||||||||
\(526\) | −50.1814 | −2.18802 | ||||||||
\(527\) | 2.45205 | 0.106813 | ||||||||
\(528\) | 10.9502 | 0.476548 | ||||||||
\(529\) | −22.9469 | −0.997690 | ||||||||
\(530\) | 5.09513 | 0.221318 | ||||||||
\(531\) | −7.29932 | −0.316764 | ||||||||
\(532\) | 21.6803 | 0.939960 | ||||||||
\(533\) | 6.13813 | 0.265872 | ||||||||
\(534\) | 20.4535 | 0.885111 | ||||||||
\(535\) | −6.89732 | −0.298197 | ||||||||
\(536\) | −87.1600 | −3.76474 | ||||||||
\(537\) | −27.3716 | −1.18117 | ||||||||
\(538\) | −37.1654 | −1.60231 | ||||||||
\(539\) | 18.9685 | 0.817030 | ||||||||
\(540\) | −26.5532 | −1.14267 | ||||||||
\(541\) | −20.8311 | −0.895599 | −0.447800 | − | 0.894134i | \(-0.647792\pi\) | ||||
−0.447800 | + | 0.894134i | \(0.647792\pi\) | |||||||
\(542\) | −49.7399 | −2.13651 | ||||||||
\(543\) | −31.5609 | −1.35441 | ||||||||
\(544\) | 2.88452 | 0.123673 | ||||||||
\(545\) | −10.8775 | −0.465942 | ||||||||
\(546\) | 139.874 | 5.98604 | ||||||||
\(547\) | −30.5107 | −1.30454 | −0.652272 | − | 0.757985i | \(-0.726184\pi\) | ||||
−0.652272 | + | 0.757985i | \(0.726184\pi\) | |||||||
\(548\) | −63.2552 | −2.70213 | ||||||||
\(549\) | −4.85819 | −0.207343 | ||||||||
\(550\) | 10.4600 | 0.446017 | ||||||||
\(551\) | −3.96002 | −0.168702 | ||||||||
\(552\) | −2.17077 | −0.0923940 | ||||||||
\(553\) | −56.8224 | −2.41633 | ||||||||
\(554\) | 29.9939 | 1.27432 | ||||||||
\(555\) | −18.9500 | −0.804384 | ||||||||
\(556\) | 10.1358 | 0.429853 | ||||||||
\(557\) | −30.2259 | −1.28071 | −0.640357 | − | 0.768078i | \(-0.721213\pi\) | ||||
−0.640357 | + | 0.768078i | \(0.721213\pi\) | |||||||
\(558\) | −5.04356 | −0.213511 | ||||||||
\(559\) | 34.1149 | 1.44291 | ||||||||
\(560\) | 34.7506 | 1.46848 | ||||||||
\(561\) | −1.15477 | −0.0487543 | ||||||||
\(562\) | −73.2963 | −3.09182 | ||||||||
\(563\) | −20.3338 | −0.856966 | −0.428483 | − | 0.903550i | \(-0.640952\pi\) | ||||
−0.428483 | + | 0.903550i | \(0.640952\pi\) | |||||||
\(564\) | −31.7653 | −1.33756 | ||||||||
\(565\) | −11.3315 | −0.476721 | ||||||||
\(566\) | −20.7650 | −0.872818 | ||||||||
\(567\) | −34.7894 | −1.46102 | ||||||||
\(568\) | −61.4463 | −2.57823 | ||||||||
\(569\) | 1.56010 | 0.0654027 | 0.0327014 | − | 0.999465i | \(-0.489589\pi\) | ||||
0.0327014 | + | 0.999465i | \(0.489589\pi\) | |||||||
\(570\) | −4.30726 | −0.180411 | ||||||||
\(571\) | 1.29713 | 0.0542831 | 0.0271416 | − | 0.999632i | \(-0.491360\pi\) | ||||
0.0271416 | + | 0.999632i | \(0.491360\pi\) | |||||||
\(572\) | −34.0649 | −1.42433 | ||||||||
\(573\) | 24.8139 | 1.03662 | ||||||||
\(574\) | 10.7194 | 0.447418 | ||||||||
\(575\) | −0.878645 | −0.0366420 | ||||||||
\(576\) | 1.20138 | 0.0500574 | ||||||||
\(577\) | 30.6272 | 1.27503 | 0.637513 | − | 0.770440i | \(-0.279963\pi\) | ||||
0.637513 | + | 0.770440i | \(0.279963\pi\) | |||||||
\(578\) | 41.7830 | 1.73794 | ||||||||
\(579\) | −30.2162 | −1.25574 | ||||||||
\(580\) | −18.9186 | −0.785551 | ||||||||
\(581\) | −54.5311 | −2.26233 | ||||||||
\(582\) | 24.0989 | 0.998932 | ||||||||
\(583\) | −2.00952 | −0.0832257 | ||||||||
\(584\) | 45.7552 | 1.89337 | ||||||||
\(585\) | 4.31627 | 0.178456 | ||||||||
\(586\) | −28.7307 | −1.18685 | ||||||||
\(587\) | 13.3473 | 0.550903 | 0.275452 | − | 0.961315i | \(-0.411173\pi\) | ||||
0.275452 | + | 0.961315i | \(0.411173\pi\) | |||||||
\(588\) | 119.742 | 4.93807 | ||||||||
\(589\) | −3.60722 | −0.148633 | ||||||||
\(590\) | −36.3209 | −1.49531 | ||||||||
\(591\) | 32.7599 | 1.34756 | ||||||||
\(592\) | −71.6497 | −2.94479 | ||||||||
\(593\) | −31.1248 | −1.27814 | −0.639071 | − | 0.769148i | \(-0.720681\pi\) | ||||
−0.639071 | + | 0.769148i | \(0.720681\pi\) | |||||||
\(594\) | 15.2511 | 0.625760 | ||||||||
\(595\) | −3.66466 | −0.150236 | ||||||||
\(596\) | −36.7877 | −1.50688 | ||||||||
\(597\) | −13.9587 | −0.571292 | ||||||||
\(598\) | 4.16712 | 0.170406 | ||||||||
\(599\) | −18.5336 | −0.757264 | −0.378632 | − | 0.925547i | \(-0.623605\pi\) | ||||
−0.378632 | + | 0.925547i | \(0.623605\pi\) | |||||||
\(600\) | 35.9017 | 1.46568 | ||||||||
\(601\) | 1.96473 | 0.0801428 | 0.0400714 | − | 0.999197i | \(-0.487241\pi\) | ||||
0.0400714 | + | 0.999197i | \(0.487241\pi\) | |||||||
\(602\) | 59.5768 | 2.42817 | ||||||||
\(603\) | −8.01100 | −0.326233 | ||||||||
\(604\) | −85.5329 | −3.48029 | ||||||||
\(605\) | −10.7037 | −0.435166 | ||||||||
\(606\) | −32.8949 | −1.33627 | ||||||||
\(607\) | −2.33732 | −0.0948689 | −0.0474345 | − | 0.998874i | \(-0.515105\pi\) | ||||
−0.0474345 | + | 0.998874i | \(0.515105\pi\) | |||||||
\(608\) | −4.24343 | −0.172094 | ||||||||
\(609\) | −30.6375 | −1.24149 | ||||||||
\(610\) | −24.1740 | −0.978777 | ||||||||
\(611\) | 33.1546 | 1.34129 | ||||||||
\(612\) | 1.64889 | 0.0666526 | ||||||||
\(613\) | 39.2279 | 1.58440 | 0.792201 | − | 0.610261i | \(-0.208935\pi\) | ||||
0.792201 | + | 0.610261i | \(0.208935\pi\) | |||||||
\(614\) | −51.1247 | −2.06323 | ||||||||
\(615\) | −1.46237 | −0.0589684 | ||||||||
\(616\) | −32.3451 | −1.30322 | ||||||||
\(617\) | 33.8445 | 1.36253 | 0.681263 | − | 0.732038i | \(-0.261431\pi\) | ||||
0.681263 | + | 0.732038i | \(0.261431\pi\) | |||||||
\(618\) | 11.0242 | 0.443460 | ||||||||
\(619\) | −6.80103 | −0.273356 | −0.136678 | − | 0.990615i | \(-0.543643\pi\) | ||||
−0.136678 | + | 0.990615i | \(0.543643\pi\) | |||||||
\(620\) | −17.2331 | −0.692098 | ||||||||
\(621\) | −1.28110 | −0.0514087 | ||||||||
\(622\) | −71.2928 | −2.85858 | ||||||||
\(623\) | −25.6002 | −1.02565 | ||||||||
\(624\) | −72.1487 | −2.88826 | ||||||||
\(625\) | 8.59183 | 0.343673 | ||||||||
\(626\) | 32.2028 | 1.28708 | ||||||||
\(627\) | 1.69878 | 0.0678427 | ||||||||
\(628\) | −6.69091 | −0.266997 | ||||||||
\(629\) | 7.55588 | 0.301273 | ||||||||
\(630\) | 7.53774 | 0.300311 | ||||||||
\(631\) | −28.3081 | −1.12693 | −0.563463 | − | 0.826141i | \(-0.690531\pi\) | ||||
−0.563463 | + | 0.826141i | \(0.690531\pi\) | |||||||
\(632\) | 69.1705 | 2.75145 | ||||||||
\(633\) | 4.64966 | 0.184808 | ||||||||
\(634\) | −2.52650 | −0.100340 | ||||||||
\(635\) | 13.2730 | 0.526722 | ||||||||
\(636\) | −12.6855 | −0.503011 | ||||||||
\(637\) | −124.979 | −4.95185 | ||||||||
\(638\) | 10.8661 | 0.430192 | ||||||||
\(639\) | −5.64762 | −0.223416 | ||||||||
\(640\) | 15.2281 | 0.601944 | ||||||||
\(641\) | 46.3460 | 1.83056 | 0.915278 | − | 0.402822i | \(-0.131971\pi\) | ||||
0.915278 | + | 0.402822i | \(0.131971\pi\) | |||||||
\(642\) | 25.0080 | 0.986986 | ||||||||
\(643\) | −23.8157 | −0.939199 | −0.469600 | − | 0.882879i | \(-0.655602\pi\) | ||||
−0.469600 | + | 0.882879i | \(0.655602\pi\) | |||||||
\(644\) | 4.99714 | 0.196915 | ||||||||
\(645\) | −8.12766 | −0.320026 | ||||||||
\(646\) | 1.71742 | 0.0675709 | ||||||||
\(647\) | −4.30112 | −0.169094 | −0.0845472 | − | 0.996419i | \(-0.526944\pi\) | ||||
−0.0845472 | + | 0.996419i | \(0.526944\pi\) | |||||||
\(648\) | 42.3495 | 1.66365 | ||||||||
\(649\) | 14.3250 | 0.562304 | ||||||||
\(650\) | −68.9187 | −2.70321 | ||||||||
\(651\) | −27.9080 | −1.09380 | ||||||||
\(652\) | −3.39416 | −0.132926 | ||||||||
\(653\) | −1.74204 | −0.0681714 | −0.0340857 | − | 0.999419i | \(-0.510852\pi\) | ||||
−0.0340857 | + | 0.999419i | \(0.510852\pi\) | |||||||
\(654\) | 39.4392 | 1.54220 | ||||||||
\(655\) | 11.9753 | 0.467913 | ||||||||
\(656\) | −5.52919 | −0.215879 | ||||||||
\(657\) | 4.20543 | 0.164069 | ||||||||
\(658\) | 57.8998 | 2.25717 | ||||||||
\(659\) | −1.76466 | −0.0687413 | −0.0343706 | − | 0.999409i | \(-0.510943\pi\) | ||||
−0.0343706 | + | 0.999409i | \(0.510943\pi\) | |||||||
\(660\) | 8.11574 | 0.315905 | ||||||||
\(661\) | −22.2928 | −0.867088 | −0.433544 | − | 0.901132i | \(-0.642737\pi\) | ||||
−0.433544 | + | 0.901132i | \(0.642737\pi\) | |||||||
\(662\) | 55.9135 | 2.17314 | ||||||||
\(663\) | 7.60850 | 0.295490 | ||||||||
\(664\) | 66.3813 | 2.57609 | ||||||||
\(665\) | 5.39109 | 0.209057 | ||||||||
\(666\) | −15.5415 | −0.602221 | ||||||||
\(667\) | −0.912753 | −0.0353420 | ||||||||
\(668\) | 65.0678 | 2.51755 | ||||||||
\(669\) | −44.2008 | −1.70890 | ||||||||
\(670\) | −39.8622 | −1.54001 | ||||||||
\(671\) | 9.53422 | 0.368064 | ||||||||
\(672\) | −32.8302 | −1.26645 | ||||||||
\(673\) | −4.85367 | −0.187095 | −0.0935476 | − | 0.995615i | \(-0.529821\pi\) | ||||
−0.0935476 | + | 0.995615i | \(0.529821\pi\) | |||||||
\(674\) | 0.844956 | 0.0325465 | ||||||||
\(675\) | 21.1877 | 0.815514 | ||||||||
\(676\) | 167.465 | 6.44095 | ||||||||
\(677\) | 3.03074 | 0.116481 | 0.0582404 | − | 0.998303i | \(-0.481451\pi\) | ||||
0.0582404 | + | 0.998303i | \(0.481451\pi\) | |||||||
\(678\) | 41.0853 | 1.57787 | ||||||||
\(679\) | −30.1629 | −1.15755 | ||||||||
\(680\) | 4.46102 | 0.171072 | ||||||||
\(681\) | −39.4520 | −1.51180 | ||||||||
\(682\) | 9.89800 | 0.379014 | ||||||||
\(683\) | −1.60987 | −0.0615999 | −0.0308000 | − | 0.999526i | \(-0.509805\pi\) | ||||
−0.0308000 | + | 0.999526i | \(0.509805\pi\) | |||||||
\(684\) | −2.42569 | −0.0927487 | ||||||||
\(685\) | −15.7292 | −0.600983 | ||||||||
\(686\) | −130.781 | −4.99325 | ||||||||
\(687\) | −22.0601 | −0.841645 | ||||||||
\(688\) | −30.7305 | −1.17159 | ||||||||
\(689\) | 13.2403 | 0.504414 | ||||||||
\(690\) | −0.992789 | −0.0377948 | ||||||||
\(691\) | −48.1106 | −1.83022 | −0.915108 | − | 0.403210i | \(-0.867894\pi\) | ||||
−0.915108 | + | 0.403210i | \(0.867894\pi\) | |||||||
\(692\) | 14.8160 | 0.563219 | ||||||||
\(693\) | −2.97288 | −0.112930 | ||||||||
\(694\) | 49.0540 | 1.86207 | ||||||||
\(695\) | 2.52039 | 0.0956040 | ||||||||
\(696\) | 37.2953 | 1.41368 | ||||||||
\(697\) | 0.583086 | 0.0220859 | ||||||||
\(698\) | −59.5518 | −2.25407 | ||||||||
\(699\) | 23.0702 | 0.872595 | ||||||||
\(700\) | −82.6461 | −3.12373 | ||||||||
\(701\) | −12.5629 | −0.474495 | −0.237247 | − | 0.971449i | \(-0.576245\pi\) | ||||
−0.237247 | + | 0.971449i | \(0.576245\pi\) | |||||||
\(702\) | −100.486 | −3.79260 | ||||||||
\(703\) | −11.1155 | −0.419228 | ||||||||
\(704\) | −2.35771 | −0.0888595 | ||||||||
\(705\) | −7.89887 | −0.297489 | ||||||||
\(706\) | 50.6921 | 1.90782 | ||||||||
\(707\) | 41.1723 | 1.54844 | ||||||||
\(708\) | 90.4289 | 3.39853 | ||||||||
\(709\) | 14.9568 | 0.561713 | 0.280857 | − | 0.959750i | \(-0.409381\pi\) | ||||
0.280857 | + | 0.959750i | \(0.409381\pi\) | |||||||
\(710\) | −28.1021 | −1.05465 | ||||||||
\(711\) | 6.35756 | 0.238427 | ||||||||
\(712\) | 31.1634 | 1.16790 | ||||||||
\(713\) | −0.831435 | −0.0311375 | ||||||||
\(714\) | 13.2871 | 0.497259 | ||||||||
\(715\) | −8.47069 | −0.316786 | ||||||||
\(716\) | −76.7024 | −2.86650 | ||||||||
\(717\) | −27.7602 | −1.03672 | ||||||||
\(718\) | 24.6262 | 0.919042 | ||||||||
\(719\) | −29.6085 | −1.10421 | −0.552105 | − | 0.833775i | \(-0.686175\pi\) | ||||
−0.552105 | + | 0.833775i | \(0.686175\pi\) | |||||||
\(720\) | −3.88806 | −0.144900 | ||||||||
\(721\) | −13.7983 | −0.513874 | ||||||||
\(722\) | −2.52650 | −0.0940265 | ||||||||
\(723\) | 9.62381 | 0.357913 | ||||||||
\(724\) | −88.4421 | −3.28692 | ||||||||
\(725\) | 15.0957 | 0.560642 | ||||||||
\(726\) | 38.8089 | 1.44033 | ||||||||
\(727\) | 48.2384 | 1.78906 | 0.894531 | − | 0.447005i | \(-0.147509\pi\) | ||||
0.894531 | + | 0.447005i | \(0.147509\pi\) | |||||||
\(728\) | 213.114 | 7.89855 | ||||||||
\(729\) | 29.9736 | 1.11013 | ||||||||
\(730\) | 20.9259 | 0.774503 | ||||||||
\(731\) | 3.24071 | 0.119862 | ||||||||
\(732\) | 60.1865 | 2.22456 | ||||||||
\(733\) | −40.9201 | −1.51142 | −0.755709 | − | 0.654908i | \(-0.772707\pi\) | ||||
−0.755709 | + | 0.654908i | \(0.772707\pi\) | |||||||
\(734\) | 47.8897 | 1.76764 | ||||||||
\(735\) | 29.7754 | 1.09828 | ||||||||
\(736\) | −0.978077 | −0.0360524 | ||||||||
\(737\) | 15.7216 | 0.579113 | ||||||||
\(738\) | −1.19933 | −0.0441481 | ||||||||
\(739\) | 24.2818 | 0.893221 | 0.446611 | − | 0.894728i | \(-0.352631\pi\) | ||||
0.446611 | + | 0.894728i | \(0.352631\pi\) | |||||||
\(740\) | −53.1030 | −1.95211 | ||||||||
\(741\) | −11.1929 | −0.411181 | ||||||||
\(742\) | 23.1222 | 0.848843 | ||||||||
\(743\) | 48.3605 | 1.77417 | 0.887087 | − | 0.461602i | \(-0.152725\pi\) | ||||
0.887087 | + | 0.461602i | \(0.152725\pi\) | |||||||
\(744\) | 33.9727 | 1.24550 | ||||||||
\(745\) | −9.14774 | −0.335147 | ||||||||
\(746\) | −51.0794 | −1.87015 | ||||||||
\(747\) | 6.10120 | 0.223231 | ||||||||
\(748\) | −3.23596 | −0.118318 | ||||||||
\(749\) | −31.3007 | −1.14370 | ||||||||
\(750\) | 37.9557 | 1.38595 | ||||||||
\(751\) | 2.37184 | 0.0865497 | 0.0432749 | − | 0.999063i | \(-0.486221\pi\) | ||||
0.0432749 | + | 0.999063i | \(0.486221\pi\) | |||||||
\(752\) | −29.8655 | −1.08908 | ||||||||
\(753\) | −23.5309 | −0.857513 | ||||||||
\(754\) | −71.5941 | −2.60730 | ||||||||
\(755\) | −21.2689 | −0.774054 | ||||||||
\(756\) | −120.501 | −4.38258 | ||||||||
\(757\) | 36.2025 | 1.31580 | 0.657902 | − | 0.753104i | \(-0.271444\pi\) | ||||
0.657902 | + | 0.753104i | \(0.271444\pi\) | |||||||
\(758\) | 42.8892 | 1.55781 | ||||||||
\(759\) | 0.391556 | 0.0142126 | ||||||||
\(760\) | −6.56263 | −0.238051 | ||||||||
\(761\) | 6.61942 | 0.239954 | 0.119977 | − | 0.992777i | \(-0.461718\pi\) | ||||
0.119977 | + | 0.992777i | \(0.461718\pi\) | |||||||
\(762\) | −48.1246 | −1.74337 | ||||||||
\(763\) | −49.3633 | −1.78707 | ||||||||
\(764\) | 69.5352 | 2.51570 | ||||||||
\(765\) | 0.410019 | 0.0148243 | ||||||||
\(766\) | 60.6160 | 2.19014 | ||||||||
\(767\) | −94.3839 | −3.40801 | ||||||||
\(768\) | −48.4222 | −1.74729 | ||||||||
\(769\) | −31.7930 | −1.14649 | −0.573243 | − | 0.819385i | \(-0.694315\pi\) | ||||
−0.573243 | + | 0.819385i | \(0.694315\pi\) | |||||||
\(770\) | −14.7928 | −0.533097 | ||||||||
\(771\) | 27.8972 | 1.00469 | ||||||||
\(772\) | −84.6739 | −3.04748 | ||||||||
\(773\) | 42.4789 | 1.52786 | 0.763929 | − | 0.645300i | \(-0.223268\pi\) | ||||
0.763929 | + | 0.645300i | \(0.223268\pi\) | |||||||
\(774\) | −6.66574 | −0.239595 | ||||||||
\(775\) | 13.7509 | 0.493945 | ||||||||
\(776\) | 36.7176 | 1.31808 | ||||||||
\(777\) | −85.9972 | −3.08513 | ||||||||
\(778\) | −56.5545 | −2.02758 | ||||||||
\(779\) | −0.857779 | −0.0307331 | ||||||||
\(780\) | −53.4728 | −1.91463 | ||||||||
\(781\) | 11.0835 | 0.396598 | ||||||||
\(782\) | 0.395851 | 0.0141556 | ||||||||
\(783\) | 22.0102 | 0.786579 | ||||||||
\(784\) | 112.580 | 4.02072 | ||||||||
\(785\) | −1.66378 | −0.0593830 | ||||||||
\(786\) | −43.4195 | −1.54872 | ||||||||
\(787\) | −19.1658 | −0.683186 | −0.341593 | − | 0.939848i | \(-0.610966\pi\) | ||||
−0.341593 | + | 0.939848i | \(0.610966\pi\) | |||||||
\(788\) | 91.8018 | 3.27031 | ||||||||
\(789\) | 31.0674 | 1.10603 | ||||||||
\(790\) | 31.6347 | 1.12551 | ||||||||
\(791\) | −51.4236 | −1.82841 | ||||||||
\(792\) | 3.61892 | 0.128593 | ||||||||
\(793\) | −62.8188 | −2.23076 | ||||||||
\(794\) | −70.0964 | −2.48763 | ||||||||
\(795\) | −3.15440 | −0.111875 | ||||||||
\(796\) | −39.1160 | −1.38643 | ||||||||
\(797\) | −0.226571 | −0.00802554 | −0.00401277 | − | 0.999992i | \(-0.501277\pi\) | ||||
−0.00401277 | + | 0.999992i | \(0.501277\pi\) | |||||||
\(798\) | −19.5468 | −0.691948 | ||||||||
\(799\) | 3.14949 | 0.111421 | ||||||||
\(800\) | 16.1761 | 0.571912 | ||||||||
\(801\) | 2.86428 | 0.101204 | ||||||||
\(802\) | −89.4095 | −3.15716 | ||||||||
\(803\) | −8.25317 | −0.291248 | ||||||||
\(804\) | 99.2456 | 3.50012 | ||||||||
\(805\) | 1.24260 | 0.0437960 | ||||||||
\(806\) | −65.2157 | −2.29713 | ||||||||
\(807\) | 23.0091 | 0.809960 | ||||||||
\(808\) | −50.1194 | −1.76319 | ||||||||
\(809\) | 21.5192 | 0.756574 | 0.378287 | − | 0.925688i | \(-0.376513\pi\) | ||||
0.378287 | + | 0.925688i | \(0.376513\pi\) | |||||||
\(810\) | 19.3683 | 0.680534 | ||||||||
\(811\) | 28.8811 | 1.01415 | 0.507077 | − | 0.861901i | \(-0.330726\pi\) | ||||
0.507077 | + | 0.861901i | \(0.330726\pi\) | |||||||
\(812\) | −85.8543 | −3.01290 | ||||||||
\(813\) | 30.7941 | 1.07999 | ||||||||
\(814\) | 30.5003 | 1.06903 | ||||||||
\(815\) | −0.844004 | −0.0295642 | ||||||||
\(816\) | −6.85368 | −0.239927 | ||||||||
\(817\) | −4.76742 | −0.166791 | ||||||||
\(818\) | 64.9855 | 2.27217 | ||||||||
\(819\) | 19.5876 | 0.684448 | ||||||||
\(820\) | −4.09795 | −0.143106 | ||||||||
\(821\) | 26.8015 | 0.935380 | 0.467690 | − | 0.883893i | \(-0.345086\pi\) | ||||
0.467690 | + | 0.883893i | \(0.345086\pi\) | |||||||
\(822\) | 57.0303 | 1.98916 | ||||||||
\(823\) | 21.0600 | 0.734106 | 0.367053 | − | 0.930200i | \(-0.380367\pi\) | ||||
0.367053 | + | 0.930200i | \(0.380367\pi\) | |||||||
\(824\) | 16.7968 | 0.585143 | ||||||||
\(825\) | −6.47582 | −0.225459 | ||||||||
\(826\) | −164.828 | −5.73510 | ||||||||
\(827\) | 24.9182 | 0.866489 | 0.433245 | − | 0.901276i | \(-0.357369\pi\) | ||||
0.433245 | + | 0.901276i | \(0.357369\pi\) | |||||||
\(828\) | −0.559103 | −0.0194302 | ||||||||
\(829\) | 23.7210 | 0.823864 | 0.411932 | − | 0.911215i | \(-0.364854\pi\) | ||||
0.411932 | + | 0.911215i | \(0.364854\pi\) | |||||||
\(830\) | 30.3591 | 1.05378 | ||||||||
\(831\) | −18.5692 | −0.644160 | ||||||||
\(832\) | 15.5344 | 0.538559 | ||||||||
\(833\) | −11.8722 | −0.411349 | ||||||||
\(834\) | −9.13832 | −0.316434 | ||||||||
\(835\) | 16.1800 | 0.559930 | ||||||||
\(836\) | 4.76043 | 0.164643 | ||||||||
\(837\) | 20.0493 | 0.693004 | ||||||||
\(838\) | −57.9530 | −2.00195 | ||||||||
\(839\) | −3.94848 | −0.136317 | −0.0681584 | − | 0.997675i | \(-0.521712\pi\) | ||||
−0.0681584 | + | 0.997675i | \(0.521712\pi\) | |||||||
\(840\) | −50.7731 | −1.75184 | ||||||||
\(841\) | −13.3182 | −0.459250 | ||||||||
\(842\) | −72.1708 | −2.48717 | ||||||||
\(843\) | 45.3778 | 1.56290 | ||||||||
\(844\) | 13.0296 | 0.448497 | ||||||||
\(845\) | 41.6423 | 1.43254 | ||||||||
\(846\) | −6.47810 | −0.222722 | ||||||||
\(847\) | −48.5743 | −1.66903 | ||||||||
\(848\) | −11.9267 | −0.409566 | ||||||||
\(849\) | 12.8556 | 0.441205 | ||||||||
\(850\) | −6.54686 | −0.224555 | ||||||||
\(851\) | −2.56203 | −0.0878253 | ||||||||
\(852\) | 69.9665 | 2.39701 | ||||||||
\(853\) | 17.6713 | 0.605053 | 0.302527 | − | 0.953141i | \(-0.402170\pi\) | ||||
0.302527 | + | 0.953141i | \(0.402170\pi\) | |||||||
\(854\) | −109.704 | −3.75399 | ||||||||
\(855\) | −0.603180 | −0.0206283 | ||||||||
\(856\) | 38.1027 | 1.30232 | ||||||||
\(857\) | −18.0772 | −0.617507 | −0.308754 | − | 0.951142i | \(-0.599912\pi\) | ||||
−0.308754 | + | 0.951142i | \(0.599912\pi\) | |||||||
\(858\) | 30.7126 | 1.04851 | ||||||||
\(859\) | 7.23881 | 0.246985 | 0.123493 | − | 0.992345i | \(-0.460590\pi\) | ||||
0.123493 | + | 0.992345i | \(0.460590\pi\) | |||||||
\(860\) | −22.7758 | −0.776650 | ||||||||
\(861\) | −6.63638 | −0.226167 | ||||||||
\(862\) | 77.1749 | 2.62859 | ||||||||
\(863\) | −31.2903 | −1.06514 | −0.532568 | − | 0.846387i | \(-0.678773\pi\) | ||||
−0.532568 | + | 0.846387i | \(0.678773\pi\) | |||||||
\(864\) | 23.5854 | 0.802391 | ||||||||
\(865\) | 3.68419 | 0.125266 | ||||||||
\(866\) | −47.0477 | −1.59875 | ||||||||
\(867\) | −25.8679 | −0.878521 | ||||||||
\(868\) | −78.2055 | −2.65447 | ||||||||
\(869\) | −12.4767 | −0.423244 | ||||||||
\(870\) | 17.0568 | 0.578280 | ||||||||
\(871\) | −103.586 | −3.50989 | ||||||||
\(872\) | 60.0904 | 2.03492 | ||||||||
\(873\) | 3.37477 | 0.114219 | ||||||||
\(874\) | −0.582338 | −0.0196979 | ||||||||
\(875\) | −47.5065 | −1.60601 | ||||||||
\(876\) | −52.0997 | −1.76028 | ||||||||
\(877\) | 38.9893 | 1.31658 | 0.658288 | − | 0.752766i | \(-0.271281\pi\) | ||||
0.658288 | + | 0.752766i | \(0.271281\pi\) | |||||||
\(878\) | −18.9465 | −0.639413 | ||||||||
\(879\) | 17.7872 | 0.599948 | ||||||||
\(880\) | 7.63034 | 0.257219 | ||||||||
\(881\) | 16.8434 | 0.567468 | 0.283734 | − | 0.958903i | \(-0.408427\pi\) | ||||
0.283734 | + | 0.958903i | \(0.408427\pi\) | |||||||
\(882\) | 24.4197 | 0.822254 | ||||||||
\(883\) | 51.2388 | 1.72432 | 0.862161 | − | 0.506634i | \(-0.169111\pi\) | ||||
0.862161 | + | 0.506634i | \(0.169111\pi\) | |||||||
\(884\) | 21.3210 | 0.717104 | ||||||||
\(885\) | 22.4863 | 0.755870 | ||||||||
\(886\) | −9.02101 | −0.303067 | ||||||||
\(887\) | −50.0077 | −1.67909 | −0.839547 | − | 0.543287i | \(-0.817180\pi\) | ||||
−0.839547 | + | 0.543287i | \(0.817180\pi\) | |||||||
\(888\) | 104.685 | 3.51301 | ||||||||
\(889\) | 60.2341 | 2.02019 | ||||||||
\(890\) | 14.2524 | 0.477742 | ||||||||
\(891\) | −7.63886 | −0.255912 | ||||||||
\(892\) | −123.862 | −4.14722 | ||||||||
\(893\) | −4.63322 | −0.155045 | ||||||||
\(894\) | 33.1675 | 1.10929 | ||||||||
\(895\) | −19.0731 | −0.637542 | ||||||||
\(896\) | 69.1067 | 2.30869 | ||||||||
\(897\) | −2.57987 | −0.0861394 | ||||||||
\(898\) | −39.3925 | −1.31454 | ||||||||
\(899\) | 14.2847 | 0.476420 | ||||||||
\(900\) | 9.24683 | 0.308228 | ||||||||
\(901\) | 1.25774 | 0.0419015 | ||||||||
\(902\) | 2.35370 | 0.0783695 | ||||||||
\(903\) | −36.8841 | −1.22743 | ||||||||
\(904\) | 62.5985 | 2.08200 | ||||||||
\(905\) | −21.9923 | −0.731048 | ||||||||
\(906\) | 77.1157 | 2.56200 | ||||||||
\(907\) | 8.58049 | 0.284910 | 0.142455 | − | 0.989801i | \(-0.454500\pi\) | ||||
0.142455 | + | 0.989801i | \(0.454500\pi\) | |||||||
\(908\) | −110.555 | −3.66890 | ||||||||
\(909\) | −4.60655 | −0.152789 | ||||||||
\(910\) | 97.4667 | 3.23099 | ||||||||
\(911\) | 13.8391 | 0.458509 | 0.229254 | − | 0.973367i | \(-0.426371\pi\) | ||||
0.229254 | + | 0.973367i | \(0.426371\pi\) | |||||||
\(912\) | 10.0825 | 0.333864 | ||||||||
\(913\) | −11.9736 | −0.396269 | ||||||||
\(914\) | 16.6498 | 0.550728 | ||||||||
\(915\) | 14.9662 | 0.494766 | ||||||||
\(916\) | −61.8182 | −2.04253 | ||||||||
\(917\) | 54.3451 | 1.79463 | ||||||||
\(918\) | −9.54556 | −0.315051 | ||||||||
\(919\) | 29.9296 | 0.987285 | 0.493642 | − | 0.869665i | \(-0.335665\pi\) | ||||
0.493642 | + | 0.869665i | \(0.335665\pi\) | |||||||
\(920\) | −1.51263 | −0.0498701 | ||||||||
\(921\) | 31.6514 | 1.04295 | ||||||||
\(922\) | 3.37638 | 0.111195 | ||||||||
\(923\) | −73.0265 | −2.40370 | ||||||||
\(924\) | 36.8300 | 1.21162 | ||||||||
\(925\) | 42.3726 | 1.39320 | ||||||||
\(926\) | −44.0869 | −1.44879 | ||||||||
\(927\) | 1.54381 | 0.0507055 | ||||||||
\(928\) | 16.8041 | 0.551620 | ||||||||
\(929\) | 16.1468 | 0.529760 | 0.264880 | − | 0.964281i | \(-0.414668\pi\) | ||||
0.264880 | + | 0.964281i | \(0.414668\pi\) | |||||||
\(930\) | 15.5372 | 0.509485 | ||||||||
\(931\) | 17.4653 | 0.572402 | ||||||||
\(932\) | 64.6488 | 2.11764 | ||||||||
\(933\) | 44.1375 | 1.44500 | ||||||||
\(934\) | 72.0620 | 2.35794 | ||||||||
\(935\) | −0.804664 | −0.0263153 | ||||||||
\(936\) | −23.8442 | −0.779373 | ||||||||
\(937\) | −32.5614 | −1.06373 | −0.531867 | − | 0.846828i | \(-0.678510\pi\) | ||||
−0.531867 | + | 0.846828i | \(0.678510\pi\) | |||||||
\(938\) | −180.898 | −5.90654 | ||||||||
\(939\) | −19.9368 | −0.650613 | ||||||||
\(940\) | −22.1347 | −0.721955 | ||||||||
\(941\) | 30.4932 | 0.994049 | 0.497024 | − | 0.867737i | \(-0.334426\pi\) | ||||
0.497024 | + | 0.867737i | \(0.334426\pi\) | |||||||
\(942\) | 6.03247 | 0.196548 | ||||||||
\(943\) | −0.197711 | −0.00643836 | ||||||||
\(944\) | 85.0204 | 2.76718 | ||||||||
\(945\) | −29.9642 | −0.974734 | ||||||||
\(946\) | 13.0815 | 0.425317 | ||||||||
\(947\) | −4.38751 | −0.142575 | −0.0712874 | − | 0.997456i | \(-0.522711\pi\) | ||||
−0.0712874 | + | 0.997456i | \(0.522711\pi\) | |||||||
\(948\) | −78.7617 | −2.55806 | ||||||||
\(949\) | 54.3783 | 1.76519 | ||||||||
\(950\) | 9.63110 | 0.312474 | ||||||||
\(951\) | 1.56416 | 0.0507213 | ||||||||
\(952\) | 20.2446 | 0.656130 | ||||||||
\(953\) | −55.9899 | −1.81369 | −0.906846 | − | 0.421462i | \(-0.861517\pi\) | ||||
−0.906846 | + | 0.421462i | \(0.861517\pi\) | |||||||
\(954\) | −2.58702 | −0.0837579 | ||||||||
\(955\) | 17.2908 | 0.559518 | ||||||||
\(956\) | −77.7914 | −2.51596 | ||||||||
\(957\) | −6.72720 | −0.217460 | ||||||||
\(958\) | −39.3862 | −1.27251 | ||||||||
\(959\) | −71.3808 | −2.30501 | ||||||||
\(960\) | −3.70097 | −0.119448 | ||||||||
\(961\) | −17.9880 | −0.580257 | ||||||||
\(962\) | −200.959 | −6.47919 | ||||||||
\(963\) | 3.50207 | 0.112853 | ||||||||
\(964\) | 26.9685 | 0.868596 | ||||||||
\(965\) | −21.0553 | −0.677793 | ||||||||
\(966\) | −4.50537 | −0.144958 | ||||||||
\(967\) | −40.7878 | −1.31165 | −0.655824 | − | 0.754913i | \(-0.727679\pi\) | ||||
−0.655824 | + | 0.754913i | \(0.727679\pi\) | |||||||
\(968\) | 59.1301 | 1.90051 | ||||||||
\(969\) | −1.06326 | −0.0341567 | ||||||||
\(970\) | 16.7926 | 0.539178 | ||||||||
\(971\) | −49.7805 | −1.59753 | −0.798766 | − | 0.601642i | \(-0.794513\pi\) | ||||
−0.798766 | + | 0.601642i | \(0.794513\pi\) | |||||||
\(972\) | 24.8647 | 0.797536 | ||||||||
\(973\) | 11.4378 | 0.366679 | ||||||||
\(974\) | −42.6180 | −1.36557 | ||||||||
\(975\) | 42.6677 | 1.36646 | ||||||||
\(976\) | 56.5868 | 1.81130 | ||||||||
\(977\) | −17.1616 | −0.549047 | −0.274524 | − | 0.961580i | \(-0.588520\pi\) | ||||
−0.274524 | + | 0.961580i | \(0.588520\pi\) | |||||||
\(978\) | 3.06015 | 0.0978528 | ||||||||
\(979\) | −5.62115 | −0.179653 | ||||||||
\(980\) | 83.4385 | 2.66535 | ||||||||
\(981\) | 5.52300 | 0.176336 | ||||||||
\(982\) | −82.9613 | −2.64740 | ||||||||
\(983\) | −18.4797 | −0.589412 | −0.294706 | − | 0.955588i | \(-0.595222\pi\) | ||||
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(984\) | 8.07853 | 0.257534 | ||||||||
\(985\) | 22.8277 | 0.727352 | ||||||||
\(986\) | −6.80100 | −0.216588 | ||||||||
\(987\) | −35.8458 | −1.14099 | ||||||||
\(988\) | −31.3654 | −0.997867 | ||||||||
\(989\) | −1.09885 | −0.0349415 | ||||||||
\(990\) | 1.65509 | 0.0526023 | ||||||||
\(991\) | −28.4916 | −0.905065 | −0.452533 | − | 0.891748i | \(-0.649479\pi\) | ||||
−0.452533 | + | 0.891748i | \(0.649479\pi\) | |||||||
\(992\) | 15.3070 | 0.485997 | ||||||||
\(993\) | −34.6162 | −1.09851 | ||||||||
\(994\) | −127.530 | −4.04502 | ||||||||
\(995\) | −9.72670 | −0.308357 | ||||||||
\(996\) | −75.5857 | −2.39502 | ||||||||
\(997\) | −31.4158 | −0.994948 | −0.497474 | − | 0.867479i | \(-0.665739\pi\) | ||||
−0.497474 | + | 0.867479i | \(0.665739\pi\) | |||||||
\(998\) | 71.0609 | 2.24939 | ||||||||
\(999\) | 61.7809 | 1.95466 |
(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 | 6023.2.a.a.1.5 | ✓ | 98 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.a.1.5 | ✓ | 98 | 1.1 | even | 1 | trivial |