Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8031,2,Mod(1,8031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8031, 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("8031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8031 = 3 \cdot 2677 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8031.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: | \(64.1278578633\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64556 | −1.87069 | −0.935345 | − | 0.353736i | \(-0.884911\pi\) | ||||
−0.935345 | + | 0.353736i | \(0.884911\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.99897 | 2.49948 | ||||||||
\(5\) | −1.40412 | −0.627939 | −0.313970 | − | 0.949433i | \(-0.601659\pi\) | ||||
−0.313970 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(6\) | 2.64556 | 1.08004 | ||||||||
\(7\) | −0.985442 | −0.372462 | −0.186231 | − | 0.982506i | \(-0.559627\pi\) | ||||
−0.186231 | + | 0.982506i | \(0.559627\pi\) | |||||||
\(8\) | −7.93394 | −2.80507 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.71467 | 1.17468 | ||||||||
\(11\) | 2.33194 | 0.703105 | 0.351553 | − | 0.936168i | \(-0.385654\pi\) | ||||
0.351553 | + | 0.936168i | \(0.385654\pi\) | |||||||
\(12\) | −4.99897 | −1.44308 | ||||||||
\(13\) | −2.71275 | −0.752380 | −0.376190 | − | 0.926543i | \(-0.622766\pi\) | ||||
−0.376190 | + | 0.926543i | \(0.622766\pi\) | |||||||
\(14\) | 2.60704 | 0.696761 | ||||||||
\(15\) | 1.40412 | 0.362541 | ||||||||
\(16\) | 10.9918 | 2.74794 | ||||||||
\(17\) | −2.75070 | −0.667143 | −0.333571 | − | 0.942725i | \(-0.608254\pi\) | ||||
−0.333571 | + | 0.942725i | \(0.608254\pi\) | |||||||
\(18\) | −2.64556 | −0.623564 | ||||||||
\(19\) | −2.99847 | −0.687897 | −0.343948 | − | 0.938989i | \(-0.611765\pi\) | ||||
−0.343948 | + | 0.938989i | \(0.611765\pi\) | |||||||
\(20\) | −7.01913 | −1.56953 | ||||||||
\(21\) | 0.985442 | 0.215041 | ||||||||
\(22\) | −6.16927 | −1.31529 | ||||||||
\(23\) | 7.66768 | 1.59882 | 0.799410 | − | 0.600785i | \(-0.205145\pi\) | ||||
0.799410 | + | 0.600785i | \(0.205145\pi\) | |||||||
\(24\) | 7.93394 | 1.61951 | ||||||||
\(25\) | −3.02846 | −0.605692 | ||||||||
\(26\) | 7.17672 | 1.40747 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.92619 | −0.930963 | ||||||||
\(29\) | 5.96396 | 1.10748 | 0.553739 | − | 0.832690i | \(-0.313200\pi\) | ||||
0.553739 | + | 0.832690i | \(0.313200\pi\) | |||||||
\(30\) | −3.71467 | −0.678202 | ||||||||
\(31\) | 7.67624 | 1.37869 | 0.689347 | − | 0.724431i | \(-0.257898\pi\) | ||||
0.689347 | + | 0.724431i | \(0.257898\pi\) | |||||||
\(32\) | −13.2114 | −2.33547 | ||||||||
\(33\) | −2.33194 | −0.405938 | ||||||||
\(34\) | 7.27713 | 1.24802 | ||||||||
\(35\) | 1.38367 | 0.233884 | ||||||||
\(36\) | 4.99897 | 0.833162 | ||||||||
\(37\) | −10.2707 | −1.68849 | −0.844244 | − | 0.535959i | \(-0.819950\pi\) | ||||
−0.844244 | + | 0.535959i | \(0.819950\pi\) | |||||||
\(38\) | 7.93263 | 1.28684 | ||||||||
\(39\) | 2.71275 | 0.434387 | ||||||||
\(40\) | 11.1402 | 1.76142 | ||||||||
\(41\) | 8.86891 | 1.38509 | 0.692546 | − | 0.721374i | \(-0.256489\pi\) | ||||
0.692546 | + | 0.721374i | \(0.256489\pi\) | |||||||
\(42\) | −2.60704 | −0.402275 | ||||||||
\(43\) | 0.458711 | 0.0699527 | 0.0349764 | − | 0.999388i | \(-0.488864\pi\) | ||||
0.0349764 | + | 0.999388i | \(0.488864\pi\) | |||||||
\(44\) | 11.6573 | 1.75740 | ||||||||
\(45\) | −1.40412 | −0.209313 | ||||||||
\(46\) | −20.2853 | −2.99090 | ||||||||
\(47\) | −9.88478 | −1.44184 | −0.720921 | − | 0.693017i | \(-0.756281\pi\) | ||||
−0.720921 | + | 0.693017i | \(0.756281\pi\) | |||||||
\(48\) | −10.9918 | −1.58652 | ||||||||
\(49\) | −6.02890 | −0.861272 | ||||||||
\(50\) | 8.01196 | 1.13306 | ||||||||
\(51\) | 2.75070 | 0.385175 | ||||||||
\(52\) | −13.5609 | −1.88056 | ||||||||
\(53\) | −5.24831 | −0.720911 | −0.360455 | − | 0.932776i | \(-0.617379\pi\) | ||||
−0.360455 | + | 0.932776i | \(0.617379\pi\) | |||||||
\(54\) | 2.64556 | 0.360015 | ||||||||
\(55\) | −3.27431 | −0.441507 | ||||||||
\(56\) | 7.81844 | 1.04478 | ||||||||
\(57\) | 2.99847 | 0.397157 | ||||||||
\(58\) | −15.7780 | −2.07175 | ||||||||
\(59\) | 14.0479 | 1.82889 | 0.914443 | − | 0.404716i | \(-0.132630\pi\) | ||||
0.914443 | + | 0.404716i | \(0.132630\pi\) | |||||||
\(60\) | 7.01913 | 0.906166 | ||||||||
\(61\) | −7.61343 | −0.974800 | −0.487400 | − | 0.873179i | \(-0.662055\pi\) | ||||
−0.487400 | + | 0.873179i | \(0.662055\pi\) | |||||||
\(62\) | −20.3079 | −2.57911 | ||||||||
\(63\) | −0.985442 | −0.124154 | ||||||||
\(64\) | 12.9681 | 1.62101 | ||||||||
\(65\) | 3.80901 | 0.472449 | ||||||||
\(66\) | 6.16927 | 0.759384 | ||||||||
\(67\) | 14.2913 | 1.74596 | 0.872979 | − | 0.487758i | \(-0.162185\pi\) | ||||
0.872979 | + | 0.487758i | \(0.162185\pi\) | |||||||
\(68\) | −13.7507 | −1.66751 | ||||||||
\(69\) | −7.66768 | −0.923080 | ||||||||
\(70\) | −3.66059 | −0.437524 | ||||||||
\(71\) | −1.35018 | −0.160237 | −0.0801186 | − | 0.996785i | \(-0.525530\pi\) | ||||
−0.0801186 | + | 0.996785i | \(0.525530\pi\) | |||||||
\(72\) | −7.93394 | −0.935024 | ||||||||
\(73\) | −6.43090 | −0.752680 | −0.376340 | − | 0.926482i | \(-0.622817\pi\) | ||||
−0.376340 | + | 0.926482i | \(0.622817\pi\) | |||||||
\(74\) | 27.1716 | 3.15864 | ||||||||
\(75\) | 3.02846 | 0.349696 | ||||||||
\(76\) | −14.9893 | −1.71939 | ||||||||
\(77\) | −2.29799 | −0.261880 | ||||||||
\(78\) | −7.17672 | −0.812604 | ||||||||
\(79\) | 6.95662 | 0.782681 | 0.391341 | − | 0.920246i | \(-0.372011\pi\) | ||||
0.391341 | + | 0.920246i | \(0.372011\pi\) | |||||||
\(80\) | −15.4337 | −1.72554 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −23.4632 | −2.59108 | ||||||||
\(83\) | 9.57486 | 1.05098 | 0.525489 | − | 0.850801i | \(-0.323883\pi\) | ||||
0.525489 | + | 0.850801i | \(0.323883\pi\) | |||||||
\(84\) | 4.92619 | 0.537492 | ||||||||
\(85\) | 3.86230 | 0.418925 | ||||||||
\(86\) | −1.21354 | −0.130860 | ||||||||
\(87\) | −5.96396 | −0.639403 | ||||||||
\(88\) | −18.5014 | −1.97226 | ||||||||
\(89\) | −10.3413 | −1.09618 | −0.548088 | − | 0.836421i | \(-0.684644\pi\) | ||||
−0.548088 | + | 0.836421i | \(0.684644\pi\) | |||||||
\(90\) | 3.71467 | 0.391560 | ||||||||
\(91\) | 2.67325 | 0.280233 | ||||||||
\(92\) | 38.3305 | 3.99623 | ||||||||
\(93\) | −7.67624 | −0.795989 | ||||||||
\(94\) | 26.1507 | 2.69724 | ||||||||
\(95\) | 4.21020 | 0.431958 | ||||||||
\(96\) | 13.2114 | 1.34839 | ||||||||
\(97\) | 0.279354 | 0.0283641 | 0.0141820 | − | 0.999899i | \(-0.495486\pi\) | ||||
0.0141820 | + | 0.999899i | \(0.495486\pi\) | |||||||
\(98\) | 15.9498 | 1.61117 | ||||||||
\(99\) | 2.33194 | 0.234368 | ||||||||
\(100\) | −15.1392 | −1.51392 | ||||||||
\(101\) | −8.32117 | −0.827987 | −0.413994 | − | 0.910280i | \(-0.635866\pi\) | ||||
−0.413994 | + | 0.910280i | \(0.635866\pi\) | |||||||
\(102\) | −7.27713 | −0.720543 | ||||||||
\(103\) | −10.8506 | −1.06914 | −0.534570 | − | 0.845124i | \(-0.679526\pi\) | ||||
−0.534570 | + | 0.845124i | \(0.679526\pi\) | |||||||
\(104\) | 21.5228 | 2.11048 | ||||||||
\(105\) | −1.38367 | −0.135033 | ||||||||
\(106\) | 13.8847 | 1.34860 | ||||||||
\(107\) | 6.04572 | 0.584462 | 0.292231 | − | 0.956348i | \(-0.405602\pi\) | ||||
0.292231 | + | 0.956348i | \(0.405602\pi\) | |||||||
\(108\) | −4.99897 | −0.481026 | ||||||||
\(109\) | −13.4335 | −1.28670 | −0.643350 | − | 0.765572i | \(-0.722456\pi\) | ||||
−0.643350 | + | 0.765572i | \(0.722456\pi\) | |||||||
\(110\) | 8.66236 | 0.825924 | ||||||||
\(111\) | 10.2707 | 0.974849 | ||||||||
\(112\) | −10.8317 | −1.02350 | ||||||||
\(113\) | −14.9232 | −1.40386 | −0.701929 | − | 0.712247i | \(-0.747677\pi\) | ||||
−0.701929 | + | 0.712247i | \(0.747677\pi\) | |||||||
\(114\) | −7.93263 | −0.742959 | ||||||||
\(115\) | −10.7663 | −1.00396 | ||||||||
\(116\) | 29.8136 | 2.76813 | ||||||||
\(117\) | −2.71275 | −0.250793 | ||||||||
\(118\) | −37.1646 | −3.42128 | ||||||||
\(119\) | 2.71065 | 0.248485 | ||||||||
\(120\) | −11.1402 | −1.01695 | ||||||||
\(121\) | −5.56207 | −0.505643 | ||||||||
\(122\) | 20.1418 | 1.82355 | ||||||||
\(123\) | −8.86891 | −0.799683 | ||||||||
\(124\) | 38.3733 | 3.44603 | ||||||||
\(125\) | 11.2729 | 1.00828 | ||||||||
\(126\) | 2.60704 | 0.232254 | ||||||||
\(127\) | 5.83385 | 0.517671 | 0.258835 | − | 0.965921i | \(-0.416661\pi\) | ||||
0.258835 | + | 0.965921i | \(0.416661\pi\) | |||||||
\(128\) | −7.88489 | −0.696933 | ||||||||
\(129\) | −0.458711 | −0.0403872 | ||||||||
\(130\) | −10.0769 | −0.883806 | ||||||||
\(131\) | 11.7221 | 1.02417 | 0.512084 | − | 0.858935i | \(-0.328874\pi\) | ||||
0.512084 | + | 0.858935i | \(0.328874\pi\) | |||||||
\(132\) | −11.6573 | −1.01464 | ||||||||
\(133\) | 2.95482 | 0.256215 | ||||||||
\(134\) | −37.8084 | −3.26615 | ||||||||
\(135\) | 1.40412 | 0.120847 | ||||||||
\(136\) | 21.8239 | 1.87138 | ||||||||
\(137\) | −8.09665 | −0.691744 | −0.345872 | − | 0.938282i | \(-0.612417\pi\) | ||||
−0.345872 | + | 0.938282i | \(0.612417\pi\) | |||||||
\(138\) | 20.2853 | 1.72680 | ||||||||
\(139\) | 3.25457 | 0.276049 | 0.138024 | − | 0.990429i | \(-0.455925\pi\) | ||||
0.138024 | + | 0.990429i | \(0.455925\pi\) | |||||||
\(140\) | 6.91694 | 0.584588 | ||||||||
\(141\) | 9.88478 | 0.832448 | ||||||||
\(142\) | 3.57199 | 0.299754 | ||||||||
\(143\) | −6.32595 | −0.529002 | ||||||||
\(144\) | 10.9918 | 0.915980 | ||||||||
\(145\) | −8.37408 | −0.695430 | ||||||||
\(146\) | 17.0133 | 1.40803 | ||||||||
\(147\) | 6.02890 | 0.497256 | ||||||||
\(148\) | −51.3428 | −4.22035 | ||||||||
\(149\) | 6.34177 | 0.519538 | 0.259769 | − | 0.965671i | \(-0.416354\pi\) | ||||
0.259769 | + | 0.965671i | \(0.416354\pi\) | |||||||
\(150\) | −8.01196 | −0.654174 | ||||||||
\(151\) | −7.44976 | −0.606253 | −0.303127 | − | 0.952950i | \(-0.598030\pi\) | ||||
−0.303127 | + | 0.952950i | \(0.598030\pi\) | |||||||
\(152\) | 23.7897 | 1.92960 | ||||||||
\(153\) | −2.75070 | −0.222381 | ||||||||
\(154\) | 6.07945 | 0.489896 | ||||||||
\(155\) | −10.7783 | −0.865736 | ||||||||
\(156\) | 13.5609 | 1.08574 | ||||||||
\(157\) | 22.0200 | 1.75738 | 0.878692 | − | 0.477389i | \(-0.158417\pi\) | ||||
0.878692 | + | 0.477389i | \(0.158417\pi\) | |||||||
\(158\) | −18.4041 | −1.46415 | ||||||||
\(159\) | 5.24831 | 0.416218 | ||||||||
\(160\) | 18.5504 | 1.46654 | ||||||||
\(161\) | −7.55605 | −0.595500 | ||||||||
\(162\) | −2.64556 | −0.207855 | ||||||||
\(163\) | 6.26580 | 0.490775 | 0.245388 | − | 0.969425i | \(-0.421085\pi\) | ||||
0.245388 | + | 0.969425i | \(0.421085\pi\) | |||||||
\(164\) | 44.3354 | 3.46202 | ||||||||
\(165\) | 3.27431 | 0.254904 | ||||||||
\(166\) | −25.3308 | −1.96605 | ||||||||
\(167\) | 16.1336 | 1.24846 | 0.624228 | − | 0.781242i | \(-0.285414\pi\) | ||||
0.624228 | + | 0.781242i | \(0.285414\pi\) | |||||||
\(168\) | −7.81844 | −0.603206 | ||||||||
\(169\) | −5.64101 | −0.433924 | ||||||||
\(170\) | −10.2179 | −0.783679 | ||||||||
\(171\) | −2.99847 | −0.229299 | ||||||||
\(172\) | 2.29308 | 0.174846 | ||||||||
\(173\) | 0.726527 | 0.0552368 | 0.0276184 | − | 0.999619i | \(-0.491208\pi\) | ||||
0.0276184 | + | 0.999619i | \(0.491208\pi\) | |||||||
\(174\) | 15.7780 | 1.19613 | ||||||||
\(175\) | 2.98437 | 0.225597 | ||||||||
\(176\) | 25.6321 | 1.93209 | ||||||||
\(177\) | −14.0479 | −1.05591 | ||||||||
\(178\) | 27.3585 | 2.05060 | ||||||||
\(179\) | −20.8854 | −1.56105 | −0.780524 | − | 0.625126i | \(-0.785047\pi\) | ||||
−0.780524 | + | 0.625126i | \(0.785047\pi\) | |||||||
\(180\) | −7.01913 | −0.523175 | ||||||||
\(181\) | 13.4557 | 1.00016 | 0.500079 | − | 0.865980i | \(-0.333304\pi\) | ||||
0.500079 | + | 0.865980i | \(0.333304\pi\) | |||||||
\(182\) | −7.07224 | −0.524229 | ||||||||
\(183\) | 7.61343 | 0.562801 | ||||||||
\(184\) | −60.8349 | −4.48481 | ||||||||
\(185\) | 14.4212 | 1.06027 | ||||||||
\(186\) | 20.3079 | 1.48905 | ||||||||
\(187\) | −6.41445 | −0.469071 | ||||||||
\(188\) | −49.4137 | −3.60386 | ||||||||
\(189\) | 0.985442 | 0.0716803 | ||||||||
\(190\) | −11.1383 | −0.808059 | ||||||||
\(191\) | 5.37858 | 0.389180 | 0.194590 | − | 0.980885i | \(-0.437662\pi\) | ||||
0.194590 | + | 0.980885i | \(0.437662\pi\) | |||||||
\(192\) | −12.9681 | −0.935889 | ||||||||
\(193\) | 0.0783143 | 0.00563719 | 0.00281859 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281859 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(194\) | −0.739046 | −0.0530604 | ||||||||
\(195\) | −3.80901 | −0.272769 | ||||||||
\(196\) | −30.1383 | −2.15274 | ||||||||
\(197\) | −12.4020 | −0.883603 | −0.441801 | − | 0.897113i | \(-0.645660\pi\) | ||||
−0.441801 | + | 0.897113i | \(0.645660\pi\) | |||||||
\(198\) | −6.16927 | −0.438431 | ||||||||
\(199\) | −17.8105 | −1.26255 | −0.631275 | − | 0.775559i | \(-0.717468\pi\) | ||||
−0.631275 | + | 0.775559i | \(0.717468\pi\) | |||||||
\(200\) | 24.0276 | 1.69901 | ||||||||
\(201\) | −14.2913 | −1.00803 | ||||||||
\(202\) | 22.0141 | 1.54891 | ||||||||
\(203\) | −5.87713 | −0.412494 | ||||||||
\(204\) | 13.7507 | 0.962739 | ||||||||
\(205\) | −12.4530 | −0.869754 | ||||||||
\(206\) | 28.7058 | 2.00003 | ||||||||
\(207\) | 7.66768 | 0.532940 | ||||||||
\(208\) | −29.8178 | −2.06749 | ||||||||
\(209\) | −6.99225 | −0.483664 | ||||||||
\(210\) | 3.66059 | 0.252604 | ||||||||
\(211\) | 0.860963 | 0.0592712 | 0.0296356 | − | 0.999561i | \(-0.490565\pi\) | ||||
0.0296356 | + | 0.999561i | \(0.490565\pi\) | |||||||
\(212\) | −26.2361 | −1.80191 | ||||||||
\(213\) | 1.35018 | 0.0925130 | ||||||||
\(214\) | −15.9943 | −1.09335 | ||||||||
\(215\) | −0.644083 | −0.0439261 | ||||||||
\(216\) | 7.93394 | 0.539836 | ||||||||
\(217\) | −7.56449 | −0.513511 | ||||||||
\(218\) | 35.5392 | 2.40702 | ||||||||
\(219\) | 6.43090 | 0.434560 | ||||||||
\(220\) | −16.3682 | −1.10354 | ||||||||
\(221\) | 7.46195 | 0.501945 | ||||||||
\(222\) | −27.1716 | −1.82364 | ||||||||
\(223\) | −6.15709 | −0.412309 | −0.206155 | − | 0.978519i | \(-0.566095\pi\) | ||||
−0.206155 | + | 0.978519i | \(0.566095\pi\) | |||||||
\(224\) | 13.0191 | 0.869875 | ||||||||
\(225\) | −3.02846 | −0.201897 | ||||||||
\(226\) | 39.4802 | 2.62618 | ||||||||
\(227\) | −28.0897 | −1.86438 | −0.932189 | − | 0.361971i | \(-0.882104\pi\) | ||||
−0.932189 | + | 0.361971i | \(0.882104\pi\) | |||||||
\(228\) | 14.9893 | 0.992689 | ||||||||
\(229\) | 1.04031 | 0.0687455 | 0.0343727 | − | 0.999409i | \(-0.489057\pi\) | ||||
0.0343727 | + | 0.999409i | \(0.489057\pi\) | |||||||
\(230\) | 28.4829 | 1.87810 | ||||||||
\(231\) | 2.29799 | 0.151196 | ||||||||
\(232\) | −47.3177 | −3.10656 | ||||||||
\(233\) | 5.12414 | 0.335693 | 0.167847 | − | 0.985813i | \(-0.446319\pi\) | ||||
0.167847 | + | 0.985813i | \(0.446319\pi\) | |||||||
\(234\) | 7.17672 | 0.469157 | ||||||||
\(235\) | 13.8794 | 0.905390 | ||||||||
\(236\) | 70.2252 | 4.57127 | ||||||||
\(237\) | −6.95662 | −0.451881 | ||||||||
\(238\) | −7.17119 | −0.464839 | ||||||||
\(239\) | 6.04150 | 0.390792 | 0.195396 | − | 0.980724i | \(-0.437401\pi\) | ||||
0.195396 | + | 0.980724i | \(0.437401\pi\) | |||||||
\(240\) | 15.4337 | 0.996241 | ||||||||
\(241\) | 3.28202 | 0.211413 | 0.105707 | − | 0.994397i | \(-0.466290\pi\) | ||||
0.105707 | + | 0.994397i | \(0.466290\pi\) | |||||||
\(242\) | 14.7148 | 0.945902 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −38.0593 | −2.43650 | ||||||||
\(245\) | 8.46528 | 0.540827 | ||||||||
\(246\) | 23.4632 | 1.49596 | ||||||||
\(247\) | 8.13409 | 0.517560 | ||||||||
\(248\) | −60.9029 | −3.86734 | ||||||||
\(249\) | −9.57486 | −0.606782 | ||||||||
\(250\) | −29.8231 | −1.88618 | ||||||||
\(251\) | 24.9522 | 1.57497 | 0.787484 | − | 0.616335i | \(-0.211383\pi\) | ||||
0.787484 | + | 0.616335i | \(0.211383\pi\) | |||||||
\(252\) | −4.92619 | −0.310321 | ||||||||
\(253\) | 17.8805 | 1.12414 | ||||||||
\(254\) | −15.4338 | −0.968402 | ||||||||
\(255\) | −3.86230 | −0.241867 | ||||||||
\(256\) | −5.07620 | −0.317262 | ||||||||
\(257\) | 9.84196 | 0.613925 | 0.306962 | − | 0.951722i | \(-0.400687\pi\) | ||||
0.306962 | + | 0.951722i | \(0.400687\pi\) | |||||||
\(258\) | 1.21354 | 0.0755520 | ||||||||
\(259\) | 10.1211 | 0.628898 | ||||||||
\(260\) | 19.0411 | 1.18088 | ||||||||
\(261\) | 5.96396 | 0.369160 | ||||||||
\(262\) | −31.0116 | −1.91590 | ||||||||
\(263\) | −29.9080 | −1.84421 | −0.922104 | − | 0.386942i | \(-0.873531\pi\) | ||||
−0.922104 | + | 0.386942i | \(0.873531\pi\) | |||||||
\(264\) | 18.5014 | 1.13869 | ||||||||
\(265\) | 7.36923 | 0.452688 | ||||||||
\(266\) | −7.81714 | −0.479300 | ||||||||
\(267\) | 10.3413 | 0.632877 | ||||||||
\(268\) | 71.4417 | 4.36400 | ||||||||
\(269\) | 12.0051 | 0.731963 | 0.365981 | − | 0.930622i | \(-0.380733\pi\) | ||||
0.365981 | + | 0.930622i | \(0.380733\pi\) | |||||||
\(270\) | −3.71467 | −0.226067 | ||||||||
\(271\) | −11.2519 | −0.683506 | −0.341753 | − | 0.939790i | \(-0.611021\pi\) | ||||
−0.341753 | + | 0.939790i | \(0.611021\pi\) | |||||||
\(272\) | −30.2350 | −1.83327 | ||||||||
\(273\) | −2.67325 | −0.161793 | ||||||||
\(274\) | 21.4201 | 1.29404 | ||||||||
\(275\) | −7.06218 | −0.425865 | ||||||||
\(276\) | −38.3305 | −2.30722 | ||||||||
\(277\) | 14.5854 | 0.876355 | 0.438177 | − | 0.898889i | \(-0.355624\pi\) | ||||
0.438177 | + | 0.898889i | \(0.355624\pi\) | |||||||
\(278\) | −8.61014 | −0.516402 | ||||||||
\(279\) | 7.67624 | 0.459565 | ||||||||
\(280\) | −10.9780 | −0.656060 | ||||||||
\(281\) | 26.4126 | 1.57564 | 0.787822 | − | 0.615903i | \(-0.211209\pi\) | ||||
0.787822 | + | 0.615903i | \(0.211209\pi\) | |||||||
\(282\) | −26.1507 | −1.55725 | ||||||||
\(283\) | 11.5981 | 0.689438 | 0.344719 | − | 0.938706i | \(-0.387974\pi\) | ||||
0.344719 | + | 0.938706i | \(0.387974\pi\) | |||||||
\(284\) | −6.74952 | −0.400511 | ||||||||
\(285\) | −4.21020 | −0.249391 | ||||||||
\(286\) | 16.7357 | 0.989600 | ||||||||
\(287\) | −8.73980 | −0.515894 | ||||||||
\(288\) | −13.2114 | −0.778491 | ||||||||
\(289\) | −9.43365 | −0.554921 | ||||||||
\(290\) | 22.1541 | 1.30093 | ||||||||
\(291\) | −0.279354 | −0.0163760 | ||||||||
\(292\) | −32.1479 | −1.88131 | ||||||||
\(293\) | −16.3897 | −0.957499 | −0.478749 | − | 0.877952i | \(-0.658910\pi\) | ||||
−0.478749 | + | 0.877952i | \(0.658910\pi\) | |||||||
\(294\) | −15.9498 | −0.930212 | ||||||||
\(295\) | −19.7249 | −1.14843 | ||||||||
\(296\) | 81.4869 | 4.73633 | ||||||||
\(297\) | −2.33194 | −0.135313 | ||||||||
\(298\) | −16.7775 | −0.971896 | ||||||||
\(299\) | −20.8004 | −1.20292 | ||||||||
\(300\) | 15.1392 | 0.874061 | ||||||||
\(301\) | −0.452032 | −0.0260547 | ||||||||
\(302\) | 19.7088 | 1.13411 | ||||||||
\(303\) | 8.32117 | 0.478039 | ||||||||
\(304\) | −32.9585 | −1.89030 | ||||||||
\(305\) | 10.6901 | 0.612116 | ||||||||
\(306\) | 7.27713 | 0.416006 | ||||||||
\(307\) | −3.05538 | −0.174380 | −0.0871898 | − | 0.996192i | \(-0.527789\pi\) | ||||
−0.0871898 | + | 0.996192i | \(0.527789\pi\) | |||||||
\(308\) | −11.4876 | −0.654565 | ||||||||
\(309\) | 10.8506 | 0.617268 | ||||||||
\(310\) | 28.5147 | 1.61953 | ||||||||
\(311\) | 9.26605 | 0.525430 | 0.262715 | − | 0.964874i | \(-0.415382\pi\) | ||||
0.262715 | + | 0.964874i | \(0.415382\pi\) | |||||||
\(312\) | −21.5228 | −1.21849 | ||||||||
\(313\) | 2.32324 | 0.131317 | 0.0656586 | − | 0.997842i | \(-0.479085\pi\) | ||||
0.0656586 | + | 0.997842i | \(0.479085\pi\) | |||||||
\(314\) | −58.2550 | −3.28752 | ||||||||
\(315\) | 1.38367 | 0.0779612 | ||||||||
\(316\) | 34.7760 | 1.95630 | ||||||||
\(317\) | −25.0313 | −1.40590 | −0.702948 | − | 0.711241i | \(-0.748133\pi\) | ||||
−0.702948 | + | 0.711241i | \(0.748133\pi\) | |||||||
\(318\) | −13.8847 | −0.778615 | ||||||||
\(319\) | 13.9076 | 0.778674 | ||||||||
\(320\) | −18.2087 | −1.01789 | ||||||||
\(321\) | −6.04572 | −0.337439 | ||||||||
\(322\) | 19.9899 | 1.11400 | ||||||||
\(323\) | 8.24790 | 0.458925 | ||||||||
\(324\) | 4.99897 | 0.277721 | ||||||||
\(325\) | 8.21544 | 0.455711 | ||||||||
\(326\) | −16.5765 | −0.918089 | ||||||||
\(327\) | 13.4335 | 0.742877 | ||||||||
\(328\) | −70.3655 | −3.88528 | ||||||||
\(329\) | 9.74087 | 0.537032 | ||||||||
\(330\) | −8.66236 | −0.476847 | ||||||||
\(331\) | −13.9106 | −0.764594 | −0.382297 | − | 0.924039i | \(-0.624867\pi\) | ||||
−0.382297 | + | 0.924039i | \(0.624867\pi\) | |||||||
\(332\) | 47.8644 | 2.62690 | ||||||||
\(333\) | −10.2707 | −0.562829 | ||||||||
\(334\) | −42.6824 | −2.33548 | ||||||||
\(335\) | −20.0666 | −1.09636 | ||||||||
\(336\) | 10.8317 | 0.590920 | ||||||||
\(337\) | 26.4623 | 1.44149 | 0.720746 | − | 0.693199i | \(-0.243799\pi\) | ||||
0.720746 | + | 0.693199i | \(0.243799\pi\) | |||||||
\(338\) | 14.9236 | 0.811738 | ||||||||
\(339\) | 14.9232 | 0.810517 | ||||||||
\(340\) | 19.3075 | 1.04710 | ||||||||
\(341\) | 17.9005 | 0.969367 | ||||||||
\(342\) | 7.93263 | 0.428948 | ||||||||
\(343\) | 12.8392 | 0.693253 | ||||||||
\(344\) | −3.63938 | −0.196222 | ||||||||
\(345\) | 10.7663 | 0.579638 | ||||||||
\(346\) | −1.92207 | −0.103331 | ||||||||
\(347\) | −34.7535 | −1.86566 | −0.932832 | − | 0.360312i | \(-0.882670\pi\) | ||||
−0.932832 | + | 0.360312i | \(0.882670\pi\) | |||||||
\(348\) | −29.8136 | −1.59818 | ||||||||
\(349\) | 7.79611 | 0.417316 | 0.208658 | − | 0.977989i | \(-0.433090\pi\) | ||||
0.208658 | + | 0.977989i | \(0.433090\pi\) | |||||||
\(350\) | −7.89532 | −0.422023 | ||||||||
\(351\) | 2.71275 | 0.144796 | ||||||||
\(352\) | −30.8082 | −1.64208 | ||||||||
\(353\) | 16.9282 | 0.900998 | 0.450499 | − | 0.892777i | \(-0.351246\pi\) | ||||
0.450499 | + | 0.892777i | \(0.351246\pi\) | |||||||
\(354\) | 37.1646 | 1.97528 | ||||||||
\(355\) | 1.89581 | 0.100619 | ||||||||
\(356\) | −51.6958 | −2.73987 | ||||||||
\(357\) | −2.71065 | −0.143463 | ||||||||
\(358\) | 55.2535 | 2.92024 | ||||||||
\(359\) | 22.9438 | 1.21093 | 0.605463 | − | 0.795874i | \(-0.292988\pi\) | ||||
0.605463 | + | 0.795874i | \(0.292988\pi\) | |||||||
\(360\) | 11.1402 | 0.587139 | ||||||||
\(361\) | −10.0092 | −0.526798 | ||||||||
\(362\) | −35.5979 | −1.87099 | ||||||||
\(363\) | 5.56207 | 0.291933 | ||||||||
\(364\) | 13.3635 | 0.700438 | ||||||||
\(365\) | 9.02972 | 0.472637 | ||||||||
\(366\) | −20.1418 | −1.05283 | ||||||||
\(367\) | 23.5888 | 1.23133 | 0.615664 | − | 0.788009i | \(-0.288888\pi\) | ||||
0.615664 | + | 0.788009i | \(0.288888\pi\) | |||||||
\(368\) | 84.2812 | 4.39346 | ||||||||
\(369\) | 8.86891 | 0.461697 | ||||||||
\(370\) | −38.1521 | −1.98343 | ||||||||
\(371\) | 5.17190 | 0.268512 | ||||||||
\(372\) | −38.3733 | −1.98956 | ||||||||
\(373\) | 10.1278 | 0.524396 | 0.262198 | − | 0.965014i | \(-0.415553\pi\) | ||||
0.262198 | + | 0.965014i | \(0.415553\pi\) | |||||||
\(374\) | 16.9698 | 0.877488 | ||||||||
\(375\) | −11.2729 | −0.582129 | ||||||||
\(376\) | 78.4253 | 4.04447 | ||||||||
\(377\) | −16.1787 | −0.833245 | ||||||||
\(378\) | −2.60704 | −0.134092 | ||||||||
\(379\) | 5.57389 | 0.286311 | 0.143156 | − | 0.989700i | \(-0.454275\pi\) | ||||
0.143156 | + | 0.989700i | \(0.454275\pi\) | |||||||
\(380\) | 21.0467 | 1.07967 | ||||||||
\(381\) | −5.83385 | −0.298877 | ||||||||
\(382\) | −14.2293 | −0.728036 | ||||||||
\(383\) | 9.26151 | 0.473241 | 0.236621 | − | 0.971602i | \(-0.423960\pi\) | ||||
0.236621 | + | 0.971602i | \(0.423960\pi\) | |||||||
\(384\) | 7.88489 | 0.402374 | ||||||||
\(385\) | 3.22664 | 0.164445 | ||||||||
\(386\) | −0.207185 | −0.0105454 | ||||||||
\(387\) | 0.458711 | 0.0233176 | ||||||||
\(388\) | 1.39648 | 0.0708955 | ||||||||
\(389\) | −34.1362 | −1.73077 | −0.865387 | − | 0.501105i | \(-0.832927\pi\) | ||||
−0.865387 | + | 0.501105i | \(0.832927\pi\) | |||||||
\(390\) | 10.0769 | 0.510266 | ||||||||
\(391\) | −21.0915 | −1.06664 | ||||||||
\(392\) | 47.8330 | 2.41593 | ||||||||
\(393\) | −11.7221 | −0.591304 | ||||||||
\(394\) | 32.8101 | 1.65295 | ||||||||
\(395\) | −9.76790 | −0.491477 | ||||||||
\(396\) | 11.6573 | 0.585800 | ||||||||
\(397\) | −5.60042 | −0.281077 | −0.140538 | − | 0.990075i | \(-0.544883\pi\) | ||||
−0.140538 | + | 0.990075i | \(0.544883\pi\) | |||||||
\(398\) | 47.1186 | 2.36184 | ||||||||
\(399\) | −2.95482 | −0.147926 | ||||||||
\(400\) | −33.2881 | −1.66440 | ||||||||
\(401\) | 1.60184 | 0.0799919 | 0.0399960 | − | 0.999200i | \(-0.487265\pi\) | ||||
0.0399960 | + | 0.999200i | \(0.487265\pi\) | |||||||
\(402\) | 37.8084 | 1.88571 | ||||||||
\(403\) | −20.8237 | −1.03730 | ||||||||
\(404\) | −41.5973 | −2.06954 | ||||||||
\(405\) | −1.40412 | −0.0697711 | ||||||||
\(406\) | 15.5483 | 0.771648 | ||||||||
\(407\) | −23.9506 | −1.18718 | ||||||||
\(408\) | −21.8239 | −1.08044 | ||||||||
\(409\) | −23.1867 | −1.14651 | −0.573255 | − | 0.819377i | \(-0.694320\pi\) | ||||
−0.573255 | + | 0.819377i | \(0.694320\pi\) | |||||||
\(410\) | 32.9451 | 1.62704 | ||||||||
\(411\) | 8.09665 | 0.399378 | ||||||||
\(412\) | −54.2418 | −2.67230 | ||||||||
\(413\) | −13.8434 | −0.681190 | ||||||||
\(414\) | −20.2853 | −0.996967 | ||||||||
\(415\) | −13.4442 | −0.659950 | ||||||||
\(416\) | 35.8392 | 1.75716 | ||||||||
\(417\) | −3.25457 | −0.159377 | ||||||||
\(418\) | 18.4984 | 0.904786 | ||||||||
\(419\) | −39.3742 | −1.92356 | −0.961779 | − | 0.273827i | \(-0.911710\pi\) | ||||
−0.961779 | + | 0.273827i | \(0.911710\pi\) | |||||||
\(420\) | −6.91694 | −0.337512 | ||||||||
\(421\) | −35.4382 | −1.72715 | −0.863576 | − | 0.504219i | \(-0.831781\pi\) | ||||
−0.863576 | + | 0.504219i | \(0.831781\pi\) | |||||||
\(422\) | −2.27773 | −0.110878 | ||||||||
\(423\) | −9.88478 | −0.480614 | ||||||||
\(424\) | 41.6398 | 2.02221 | ||||||||
\(425\) | 8.33038 | 0.404083 | ||||||||
\(426\) | −3.57199 | −0.173063 | ||||||||
\(427\) | 7.50259 | 0.363076 | ||||||||
\(428\) | 30.2224 | 1.46085 | ||||||||
\(429\) | 6.32595 | 0.305420 | ||||||||
\(430\) | 1.70396 | 0.0821721 | ||||||||
\(431\) | −24.7313 | −1.19126 | −0.595632 | − | 0.803257i | \(-0.703099\pi\) | ||||
−0.595632 | + | 0.803257i | \(0.703099\pi\) | |||||||
\(432\) | −10.9918 | −0.528841 | ||||||||
\(433\) | 11.2160 | 0.539006 | 0.269503 | − | 0.963000i | \(-0.413141\pi\) | ||||
0.269503 | + | 0.963000i | \(0.413141\pi\) | |||||||
\(434\) | 20.0123 | 0.960620 | ||||||||
\(435\) | 8.37408 | 0.401506 | ||||||||
\(436\) | −67.1539 | −3.21609 | ||||||||
\(437\) | −22.9913 | −1.09982 | ||||||||
\(438\) | −17.0133 | −0.812927 | ||||||||
\(439\) | −23.0691 | −1.10103 | −0.550513 | − | 0.834827i | \(-0.685568\pi\) | ||||
−0.550513 | + | 0.834827i | \(0.685568\pi\) | |||||||
\(440\) | 25.9782 | 1.23846 | ||||||||
\(441\) | −6.02890 | −0.287091 | ||||||||
\(442\) | −19.7410 | −0.938984 | ||||||||
\(443\) | −9.55290 | −0.453872 | −0.226936 | − | 0.973910i | \(-0.572871\pi\) | ||||
−0.226936 | + | 0.973910i | \(0.572871\pi\) | |||||||
\(444\) | 51.3428 | 2.43662 | ||||||||
\(445\) | 14.5204 | 0.688332 | ||||||||
\(446\) | 16.2889 | 0.771303 | ||||||||
\(447\) | −6.34177 | −0.299956 | ||||||||
\(448\) | −12.7793 | −0.603764 | ||||||||
\(449\) | 6.33551 | 0.298991 | 0.149496 | − | 0.988762i | \(-0.452235\pi\) | ||||
0.149496 | + | 0.988762i | \(0.452235\pi\) | |||||||
\(450\) | 8.01196 | 0.377688 | ||||||||
\(451\) | 20.6817 | 0.973865 | ||||||||
\(452\) | −74.6006 | −3.50892 | ||||||||
\(453\) | 7.44976 | 0.350020 | ||||||||
\(454\) | 74.3129 | 3.48768 | ||||||||
\(455\) | −3.75355 | −0.175969 | ||||||||
\(456\) | −23.7897 | −1.11406 | ||||||||
\(457\) | −1.78517 | −0.0835070 | −0.0417535 | − | 0.999128i | \(-0.513294\pi\) | ||||
−0.0417535 | + | 0.999128i | \(0.513294\pi\) | |||||||
\(458\) | −2.75219 | −0.128602 | ||||||||
\(459\) | 2.75070 | 0.128392 | ||||||||
\(460\) | −53.8204 | −2.50939 | ||||||||
\(461\) | 10.4892 | 0.488532 | 0.244266 | − | 0.969708i | \(-0.421453\pi\) | ||||
0.244266 | + | 0.969708i | \(0.421453\pi\) | |||||||
\(462\) | −6.07945 | −0.282842 | ||||||||
\(463\) | −13.2197 | −0.614372 | −0.307186 | − | 0.951649i | \(-0.599387\pi\) | ||||
−0.307186 | + | 0.951649i | \(0.599387\pi\) | |||||||
\(464\) | 65.5543 | 3.04328 | ||||||||
\(465\) | 10.7783 | 0.499833 | ||||||||
\(466\) | −13.5562 | −0.627979 | ||||||||
\(467\) | 20.9613 | 0.969974 | 0.484987 | − | 0.874521i | \(-0.338824\pi\) | ||||
0.484987 | + | 0.874521i | \(0.338824\pi\) | |||||||
\(468\) | −13.5609 | −0.626854 | ||||||||
\(469\) | −14.0832 | −0.650303 | ||||||||
\(470\) | −36.7186 | −1.69370 | ||||||||
\(471\) | −22.0200 | −1.01463 | ||||||||
\(472\) | −111.456 | −5.13016 | ||||||||
\(473\) | 1.06968 | 0.0491841 | ||||||||
\(474\) | 18.4041 | 0.845330 | ||||||||
\(475\) | 9.08076 | 0.416654 | ||||||||
\(476\) | 13.5505 | 0.621085 | ||||||||
\(477\) | −5.24831 | −0.240304 | ||||||||
\(478\) | −15.9831 | −0.731051 | ||||||||
\(479\) | −9.23570 | −0.421990 | −0.210995 | − | 0.977487i | \(-0.567670\pi\) | ||||
−0.210995 | + | 0.977487i | \(0.567670\pi\) | |||||||
\(480\) | −18.5504 | −0.846705 | ||||||||
\(481\) | 27.8617 | 1.27038 | ||||||||
\(482\) | −8.68277 | −0.395489 | ||||||||
\(483\) | 7.55605 | 0.343812 | ||||||||
\(484\) | −27.8046 | −1.26385 | ||||||||
\(485\) | −0.392245 | −0.0178109 | ||||||||
\(486\) | 2.64556 | 0.120005 | ||||||||
\(487\) | 9.66202 | 0.437828 | 0.218914 | − | 0.975744i | \(-0.429749\pi\) | ||||
0.218914 | + | 0.975744i | \(0.429749\pi\) | |||||||
\(488\) | 60.4046 | 2.73439 | ||||||||
\(489\) | −6.26580 | −0.283349 | ||||||||
\(490\) | −22.3954 | −1.01172 | ||||||||
\(491\) | 32.3129 | 1.45826 | 0.729130 | − | 0.684375i | \(-0.239925\pi\) | ||||
0.729130 | + | 0.684375i | \(0.239925\pi\) | |||||||
\(492\) | −44.3354 | −1.99880 | ||||||||
\(493\) | −16.4050 | −0.738846 | ||||||||
\(494\) | −21.5192 | −0.968195 | ||||||||
\(495\) | −3.27431 | −0.147169 | ||||||||
\(496\) | 84.3754 | 3.78857 | ||||||||
\(497\) | 1.33053 | 0.0596823 | ||||||||
\(498\) | 25.3308 | 1.13510 | ||||||||
\(499\) | −32.2772 | −1.44493 | −0.722463 | − | 0.691409i | \(-0.756990\pi\) | ||||
−0.722463 | + | 0.691409i | \(0.756990\pi\) | |||||||
\(500\) | 56.3528 | 2.52017 | ||||||||
\(501\) | −16.1336 | −0.720797 | ||||||||
\(502\) | −66.0124 | −2.94628 | ||||||||
\(503\) | 38.8639 | 1.73286 | 0.866428 | − | 0.499301i | \(-0.166410\pi\) | ||||
0.866428 | + | 0.499301i | \(0.166410\pi\) | |||||||
\(504\) | 7.81844 | 0.348261 | ||||||||
\(505\) | 11.6839 | 0.519926 | ||||||||
\(506\) | −47.3039 | −2.10292 | ||||||||
\(507\) | 5.64101 | 0.250526 | ||||||||
\(508\) | 29.1632 | 1.29391 | ||||||||
\(509\) | −19.4160 | −0.860599 | −0.430299 | − | 0.902686i | \(-0.641592\pi\) | ||||
−0.430299 | + | 0.902686i | \(0.641592\pi\) | |||||||
\(510\) | 10.2179 | 0.452458 | ||||||||
\(511\) | 6.33727 | 0.280344 | ||||||||
\(512\) | 29.1992 | 1.29043 | ||||||||
\(513\) | 2.99847 | 0.132386 | ||||||||
\(514\) | −26.0375 | −1.14846 | ||||||||
\(515\) | 15.2355 | 0.671355 | ||||||||
\(516\) | −2.29308 | −0.100947 | ||||||||
\(517\) | −23.0507 | −1.01377 | ||||||||
\(518\) | −26.7761 | −1.17647 | ||||||||
\(519\) | −0.726527 | −0.0318910 | ||||||||
\(520\) | −30.2204 | −1.32525 | ||||||||
\(521\) | −19.9389 | −0.873540 | −0.436770 | − | 0.899573i | \(-0.643878\pi\) | ||||
−0.436770 | + | 0.899573i | \(0.643878\pi\) | |||||||
\(522\) | −15.7780 | −0.690583 | ||||||||
\(523\) | −13.8287 | −0.604685 | −0.302343 | − | 0.953199i | \(-0.597769\pi\) | ||||
−0.302343 | + | 0.953199i | \(0.597769\pi\) | |||||||
\(524\) | 58.5986 | 2.55989 | ||||||||
\(525\) | −2.98437 | −0.130249 | ||||||||
\(526\) | 79.1234 | 3.44994 | ||||||||
\(527\) | −21.1150 | −0.919786 | ||||||||
\(528\) | −25.6321 | −1.11549 | ||||||||
\(529\) | 35.7932 | 1.55623 | ||||||||
\(530\) | −19.4957 | −0.846840 | ||||||||
\(531\) | 14.0479 | 0.609628 | ||||||||
\(532\) | 14.7711 | 0.640406 | ||||||||
\(533\) | −24.0591 | −1.04212 | ||||||||
\(534\) | −27.3585 | −1.18392 | ||||||||
\(535\) | −8.48889 | −0.367007 | ||||||||
\(536\) | −113.386 | −4.89754 | ||||||||
\(537\) | 20.8854 | 0.901271 | ||||||||
\(538\) | −31.7601 | −1.36928 | ||||||||
\(539\) | −14.0590 | −0.605565 | ||||||||
\(540\) | 7.01913 | 0.302055 | ||||||||
\(541\) | −20.5690 | −0.884331 | −0.442165 | − | 0.896934i | \(-0.645790\pi\) | ||||
−0.442165 | + | 0.896934i | \(0.645790\pi\) | |||||||
\(542\) | 29.7676 | 1.27863 | ||||||||
\(543\) | −13.4557 | −0.577441 | ||||||||
\(544\) | 36.3407 | 1.55809 | ||||||||
\(545\) | 18.8623 | 0.807970 | ||||||||
\(546\) | 7.07224 | 0.302664 | ||||||||
\(547\) | −30.4875 | −1.30355 | −0.651775 | − | 0.758413i | \(-0.725975\pi\) | ||||
−0.651775 | + | 0.758413i | \(0.725975\pi\) | |||||||
\(548\) | −40.4749 | −1.72900 | ||||||||
\(549\) | −7.61343 | −0.324933 | ||||||||
\(550\) | 18.6834 | 0.796662 | ||||||||
\(551\) | −17.8828 | −0.761831 | ||||||||
\(552\) | 60.8349 | 2.58931 | ||||||||
\(553\) | −6.85535 | −0.291519 | ||||||||
\(554\) | −38.5866 | −1.63939 | ||||||||
\(555\) | −14.4212 | −0.612146 | ||||||||
\(556\) | 16.2695 | 0.689980 | ||||||||
\(557\) | 6.96523 | 0.295126 | 0.147563 | − | 0.989053i | \(-0.452857\pi\) | ||||
0.147563 | + | 0.989053i | \(0.452857\pi\) | |||||||
\(558\) | −20.3079 | −0.859704 | ||||||||
\(559\) | −1.24436 | −0.0526310 | ||||||||
\(560\) | 15.2090 | 0.642698 | ||||||||
\(561\) | 6.41445 | 0.270818 | ||||||||
\(562\) | −69.8760 | −2.94754 | ||||||||
\(563\) | 3.25826 | 0.137319 | 0.0686597 | − | 0.997640i | \(-0.478128\pi\) | ||||
0.0686597 | + | 0.997640i | \(0.478128\pi\) | |||||||
\(564\) | 49.4137 | 2.08069 | ||||||||
\(565\) | 20.9539 | 0.881537 | ||||||||
\(566\) | −30.6836 | −1.28973 | ||||||||
\(567\) | −0.985442 | −0.0413847 | ||||||||
\(568\) | 10.7123 | 0.449477 | ||||||||
\(569\) | 12.6387 | 0.529843 | 0.264922 | − | 0.964270i | \(-0.414654\pi\) | ||||
0.264922 | + | 0.964270i | \(0.414654\pi\) | |||||||
\(570\) | 11.1383 | 0.466533 | ||||||||
\(571\) | 24.7001 | 1.03367 | 0.516834 | − | 0.856086i | \(-0.327111\pi\) | ||||
0.516834 | + | 0.856086i | \(0.327111\pi\) | |||||||
\(572\) | −31.6232 | −1.32223 | ||||||||
\(573\) | −5.37858 | −0.224693 | ||||||||
\(574\) | 23.1216 | 0.965078 | ||||||||
\(575\) | −23.2212 | −0.968393 | ||||||||
\(576\) | 12.9681 | 0.540336 | ||||||||
\(577\) | 22.8234 | 0.950149 | 0.475074 | − | 0.879946i | \(-0.342421\pi\) | ||||
0.475074 | + | 0.879946i | \(0.342421\pi\) | |||||||
\(578\) | 24.9573 | 1.03809 | ||||||||
\(579\) | −0.0783143 | −0.00325463 | ||||||||
\(580\) | −41.8618 | −1.73822 | ||||||||
\(581\) | −9.43546 | −0.391449 | ||||||||
\(582\) | 0.739046 | 0.0306344 | ||||||||
\(583\) | −12.2387 | −0.506876 | ||||||||
\(584\) | 51.0224 | 2.11132 | ||||||||
\(585\) | 3.80901 | 0.157483 | ||||||||
\(586\) | 43.3600 | 1.79118 | ||||||||
\(587\) | 13.7674 | 0.568241 | 0.284120 | − | 0.958789i | \(-0.408298\pi\) | ||||
0.284120 | + | 0.958789i | \(0.408298\pi\) | |||||||
\(588\) | 30.1383 | 1.24288 | ||||||||
\(589\) | −23.0170 | −0.948399 | ||||||||
\(590\) | 52.1834 | 2.14836 | ||||||||
\(591\) | 12.4020 | 0.510148 | ||||||||
\(592\) | −112.893 | −4.63986 | ||||||||
\(593\) | −9.62996 | −0.395455 | −0.197727 | − | 0.980257i | \(-0.563356\pi\) | ||||
−0.197727 | + | 0.980257i | \(0.563356\pi\) | |||||||
\(594\) | 6.16927 | 0.253128 | ||||||||
\(595\) | −3.80607 | −0.156034 | ||||||||
\(596\) | 31.7023 | 1.29858 | ||||||||
\(597\) | 17.8105 | 0.728933 | ||||||||
\(598\) | 55.0288 | 2.25029 | ||||||||
\(599\) | 31.7589 | 1.29763 | 0.648816 | − | 0.760945i | \(-0.275264\pi\) | ||||
0.648816 | + | 0.760945i | \(0.275264\pi\) | |||||||
\(600\) | −24.0276 | −0.980924 | ||||||||
\(601\) | 41.5128 | 1.69334 | 0.846671 | − | 0.532117i | \(-0.178603\pi\) | ||||
0.846671 | + | 0.532117i | \(0.178603\pi\) | |||||||
\(602\) | 1.19588 | 0.0487403 | ||||||||
\(603\) | 14.2913 | 0.581986 | ||||||||
\(604\) | −37.2411 | −1.51532 | ||||||||
\(605\) | 7.80979 | 0.317513 | ||||||||
\(606\) | −22.0141 | −0.894263 | ||||||||
\(607\) | 14.5205 | 0.589370 | 0.294685 | − | 0.955594i | \(-0.404785\pi\) | ||||
0.294685 | + | 0.955594i | \(0.404785\pi\) | |||||||
\(608\) | 39.6141 | 1.60656 | ||||||||
\(609\) | 5.87713 | 0.238153 | ||||||||
\(610\) | −28.2814 | −1.14508 | ||||||||
\(611\) | 26.8149 | 1.08481 | ||||||||
\(612\) | −13.7507 | −0.555838 | ||||||||
\(613\) | −33.9679 | −1.37195 | −0.685976 | − | 0.727624i | \(-0.740625\pi\) | ||||
−0.685976 | + | 0.727624i | \(0.740625\pi\) | |||||||
\(614\) | 8.08317 | 0.326210 | ||||||||
\(615\) | 12.4530 | 0.502153 | ||||||||
\(616\) | 18.2321 | 0.734592 | ||||||||
\(617\) | 38.2551 | 1.54009 | 0.770045 | − | 0.637989i | \(-0.220234\pi\) | ||||
0.770045 | + | 0.637989i | \(0.220234\pi\) | |||||||
\(618\) | −28.7058 | −1.15472 | ||||||||
\(619\) | 32.5598 | 1.30869 | 0.654345 | − | 0.756196i | \(-0.272944\pi\) | ||||
0.654345 | + | 0.756196i | \(0.272944\pi\) | |||||||
\(620\) | −53.8806 | −2.16390 | ||||||||
\(621\) | −7.66768 | −0.307693 | ||||||||
\(622\) | −24.5139 | −0.982916 | ||||||||
\(623\) | 10.1907 | 0.408283 | ||||||||
\(624\) | 29.8178 | 1.19367 | ||||||||
\(625\) | −0.686128 | −0.0274451 | ||||||||
\(626\) | −6.14626 | −0.245654 | ||||||||
\(627\) | 6.99225 | 0.279243 | ||||||||
\(628\) | 110.077 | 4.39255 | ||||||||
\(629\) | 28.2515 | 1.12646 | ||||||||
\(630\) | −3.66059 | −0.145841 | ||||||||
\(631\) | 28.3573 | 1.12889 | 0.564444 | − | 0.825472i | \(-0.309091\pi\) | ||||
0.564444 | + | 0.825472i | \(0.309091\pi\) | |||||||
\(632\) | −55.1935 | −2.19548 | ||||||||
\(633\) | −0.860963 | −0.0342202 | ||||||||
\(634\) | 66.2216 | 2.63000 | ||||||||
\(635\) | −8.19140 | −0.325066 | ||||||||
\(636\) | 26.2361 | 1.04033 | ||||||||
\(637\) | 16.3549 | 0.648004 | ||||||||
\(638\) | −36.7932 | −1.45666 | ||||||||
\(639\) | −1.35018 | −0.0534124 | ||||||||
\(640\) | 11.0713 | 0.437632 | ||||||||
\(641\) | 4.34915 | 0.171781 | 0.0858905 | − | 0.996305i | \(-0.472626\pi\) | ||||
0.0858905 | + | 0.996305i | \(0.472626\pi\) | |||||||
\(642\) | 15.9943 | 0.631245 | ||||||||
\(643\) | 15.4463 | 0.609141 | 0.304571 | − | 0.952490i | \(-0.401487\pi\) | ||||
0.304571 | + | 0.952490i | \(0.401487\pi\) | |||||||
\(644\) | −37.7724 | −1.48844 | ||||||||
\(645\) | 0.644083 | 0.0253607 | ||||||||
\(646\) | −21.8203 | −0.858507 | ||||||||
\(647\) | 28.1720 | 1.10756 | 0.553778 | − | 0.832664i | \(-0.313185\pi\) | ||||
0.553778 | + | 0.832664i | \(0.313185\pi\) | |||||||
\(648\) | −7.93394 | −0.311675 | ||||||||
\(649\) | 32.7589 | 1.28590 | ||||||||
\(650\) | −21.7344 | −0.852494 | ||||||||
\(651\) | 7.56449 | 0.296476 | ||||||||
\(652\) | 31.3225 | 1.22669 | ||||||||
\(653\) | −1.66654 | −0.0652166 | −0.0326083 | − | 0.999468i | \(-0.510381\pi\) | ||||
−0.0326083 | + | 0.999468i | \(0.510381\pi\) | |||||||
\(654\) | −35.5392 | −1.38969 | ||||||||
\(655\) | −16.4592 | −0.643115 | ||||||||
\(656\) | 97.4850 | 3.80615 | ||||||||
\(657\) | −6.43090 | −0.250893 | ||||||||
\(658\) | −25.7700 | −1.00462 | ||||||||
\(659\) | 34.2933 | 1.33588 | 0.667940 | − | 0.744215i | \(-0.267176\pi\) | ||||
0.667940 | + | 0.744215i | \(0.267176\pi\) | |||||||
\(660\) | 16.3682 | 0.637130 | ||||||||
\(661\) | −15.2152 | −0.591801 | −0.295901 | − | 0.955219i | \(-0.595620\pi\) | ||||
−0.295901 | + | 0.955219i | \(0.595620\pi\) | |||||||
\(662\) | 36.8012 | 1.43032 | ||||||||
\(663\) | −7.46195 | −0.289798 | ||||||||
\(664\) | −75.9664 | −2.94807 | ||||||||
\(665\) | −4.14891 | −0.160888 | ||||||||
\(666\) | 27.1716 | 1.05288 | ||||||||
\(667\) | 45.7297 | 1.77066 | ||||||||
\(668\) | 80.6514 | 3.12050 | ||||||||
\(669\) | 6.15709 | 0.238047 | ||||||||
\(670\) | 53.0873 | 2.05094 | ||||||||
\(671\) | −17.7540 | −0.685387 | ||||||||
\(672\) | −13.0191 | −0.502222 | ||||||||
\(673\) | 6.58049 | 0.253659 | 0.126830 | − | 0.991925i | \(-0.459520\pi\) | ||||
0.126830 | + | 0.991925i | \(0.459520\pi\) | |||||||
\(674\) | −70.0075 | −2.69659 | ||||||||
\(675\) | 3.02846 | 0.116565 | ||||||||
\(676\) | −28.1993 | −1.08459 | ||||||||
\(677\) | 35.6621 | 1.37061 | 0.685304 | − | 0.728257i | \(-0.259669\pi\) | ||||
0.685304 | + | 0.728257i | \(0.259669\pi\) | |||||||
\(678\) | −39.4802 | −1.51623 | ||||||||
\(679\) | −0.275287 | −0.0105645 | ||||||||
\(680\) | −30.6433 | −1.17512 | ||||||||
\(681\) | 28.0897 | 1.07640 | ||||||||
\(682\) | −47.3568 | −1.81339 | ||||||||
\(683\) | −49.1335 | −1.88004 | −0.940020 | − | 0.341119i | \(-0.889194\pi\) | ||||
−0.940020 | + | 0.341119i | \(0.889194\pi\) | |||||||
\(684\) | −14.9893 | −0.573129 | ||||||||
\(685\) | 11.3686 | 0.434373 | ||||||||
\(686\) | −33.9669 | −1.29686 | ||||||||
\(687\) | −1.04031 | −0.0396902 | ||||||||
\(688\) | 5.04204 | 0.192226 | ||||||||
\(689\) | 14.2373 | 0.542399 | ||||||||
\(690\) | −28.4829 | −1.08432 | ||||||||
\(691\) | 21.5540 | 0.819951 | 0.409976 | − | 0.912097i | \(-0.365537\pi\) | ||||
0.409976 | + | 0.912097i | \(0.365537\pi\) | |||||||
\(692\) | 3.63188 | 0.138064 | ||||||||
\(693\) | −2.29799 | −0.0872933 | ||||||||
\(694\) | 91.9422 | 3.49008 | ||||||||
\(695\) | −4.56979 | −0.173342 | ||||||||
\(696\) | 47.3177 | 1.79357 | ||||||||
\(697\) | −24.3957 | −0.924054 | ||||||||
\(698\) | −20.6251 | −0.780670 | ||||||||
\(699\) | −5.12414 | −0.193813 | ||||||||
\(700\) | 14.9188 | 0.563877 | ||||||||
\(701\) | 37.4040 | 1.41273 | 0.706366 | − | 0.707847i | \(-0.250333\pi\) | ||||
0.706366 | + | 0.707847i | \(0.250333\pi\) | |||||||
\(702\) | −7.17672 | −0.270868 | ||||||||
\(703\) | 30.7963 | 1.16151 | ||||||||
\(704\) | 30.2407 | 1.13974 | ||||||||
\(705\) | −13.8794 | −0.522727 | ||||||||
\(706\) | −44.7845 | −1.68549 | ||||||||
\(707\) | 8.20003 | 0.308394 | ||||||||
\(708\) | −70.2252 | −2.63922 | ||||||||
\(709\) | −17.9676 | −0.674787 | −0.337393 | − | 0.941364i | \(-0.609545\pi\) | ||||
−0.337393 | + | 0.941364i | \(0.609545\pi\) | |||||||
\(710\) | −5.01548 | −0.188228 | ||||||||
\(711\) | 6.95662 | 0.260894 | ||||||||
\(712\) | 82.0472 | 3.07485 | ||||||||
\(713\) | 58.8589 | 2.20428 | ||||||||
\(714\) | 7.17119 | 0.268375 | ||||||||
\(715\) | 8.88236 | 0.332181 | ||||||||
\(716\) | −104.405 | −3.90181 | ||||||||
\(717\) | −6.04150 | −0.225624 | ||||||||
\(718\) | −60.6990 | −2.26527 | ||||||||
\(719\) | 4.56041 | 0.170075 | 0.0850373 | − | 0.996378i | \(-0.472899\pi\) | ||||
0.0850373 | + | 0.996378i | \(0.472899\pi\) | |||||||
\(720\) | −15.4337 | −0.575180 | ||||||||
\(721\) | 10.6926 | 0.398214 | ||||||||
\(722\) | 26.4798 | 0.985476 | ||||||||
\(723\) | −3.28202 | −0.122060 | ||||||||
\(724\) | 67.2649 | 2.49988 | ||||||||
\(725\) | −18.0616 | −0.670791 | ||||||||
\(726\) | −14.7148 | −0.546117 | ||||||||
\(727\) | 46.3194 | 1.71789 | 0.858946 | − | 0.512066i | \(-0.171120\pi\) | ||||
0.858946 | + | 0.512066i | \(0.171120\pi\) | |||||||
\(728\) | −21.2094 | −0.786074 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −23.8886 | −0.884158 | ||||||||
\(731\) | −1.26177 | −0.0466684 | ||||||||
\(732\) | 38.0593 | 1.40671 | ||||||||
\(733\) | 6.07642 | 0.224438 | 0.112219 | − | 0.993684i | \(-0.464204\pi\) | ||||
0.112219 | + | 0.993684i | \(0.464204\pi\) | |||||||
\(734\) | −62.4056 | −2.30343 | ||||||||
\(735\) | −8.46528 | −0.312246 | ||||||||
\(736\) | −101.301 | −3.73400 | ||||||||
\(737\) | 33.3264 | 1.22759 | ||||||||
\(738\) | −23.4632 | −0.863693 | ||||||||
\(739\) | −24.3286 | −0.894944 | −0.447472 | − | 0.894298i | \(-0.647676\pi\) | ||||
−0.447472 | + | 0.894298i | \(0.647676\pi\) | |||||||
\(740\) | 72.0912 | 2.65012 | ||||||||
\(741\) | −8.13409 | −0.298813 | ||||||||
\(742\) | −13.6826 | −0.502303 | ||||||||
\(743\) | −2.52505 | −0.0926349 | −0.0463175 | − | 0.998927i | \(-0.514749\pi\) | ||||
−0.0463175 | + | 0.998927i | \(0.514749\pi\) | |||||||
\(744\) | 60.9029 | 2.23281 | ||||||||
\(745\) | −8.90458 | −0.326239 | ||||||||
\(746\) | −26.7936 | −0.980984 | ||||||||
\(747\) | 9.57486 | 0.350326 | ||||||||
\(748\) | −32.0657 | −1.17244 | ||||||||
\(749\) | −5.95771 | −0.217690 | ||||||||
\(750\) | 29.8231 | 1.08898 | ||||||||
\(751\) | 39.2295 | 1.43150 | 0.715752 | − | 0.698354i | \(-0.246084\pi\) | ||||
0.715752 | + | 0.698354i | \(0.246084\pi\) | |||||||
\(752\) | −108.651 | −3.96210 | ||||||||
\(753\) | −24.9522 | −0.909309 | ||||||||
\(754\) | 42.8016 | 1.55874 | ||||||||
\(755\) | 10.4603 | 0.380690 | ||||||||
\(756\) | 4.92619 | 0.179164 | ||||||||
\(757\) | −45.5952 | −1.65719 | −0.828594 | − | 0.559851i | \(-0.810858\pi\) | ||||
−0.828594 | + | 0.559851i | \(0.810858\pi\) | |||||||
\(758\) | −14.7460 | −0.535600 | ||||||||
\(759\) | −17.8805 | −0.649022 | ||||||||
\(760\) | −33.4035 | −1.21167 | ||||||||
\(761\) | −19.3832 | −0.702640 | −0.351320 | − | 0.936256i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936256i | \(0.614267\pi\) | |||||||
\(762\) | 15.4338 | 0.559107 | ||||||||
\(763\) | 13.2380 | 0.479247 | ||||||||
\(764\) | 26.8874 | 0.972751 | ||||||||
\(765\) | 3.86230 | 0.139642 | ||||||||
\(766\) | −24.5019 | −0.885288 | ||||||||
\(767\) | −38.1085 | −1.37602 | ||||||||
\(768\) | 5.07620 | 0.183171 | ||||||||
\(769\) | 21.9465 | 0.791410 | 0.395705 | − | 0.918378i | \(-0.370500\pi\) | ||||
0.395705 | + | 0.918378i | \(0.370500\pi\) | |||||||
\(770\) | −8.53625 | −0.307625 | ||||||||
\(771\) | −9.84196 | −0.354450 | ||||||||
\(772\) | 0.391491 | 0.0140901 | ||||||||
\(773\) | −25.6914 | −0.924056 | −0.462028 | − | 0.886865i | \(-0.652878\pi\) | ||||
−0.462028 | + | 0.886865i | \(0.652878\pi\) | |||||||
\(774\) | −1.21354 | −0.0436200 | ||||||||
\(775\) | −23.2472 | −0.835064 | ||||||||
\(776\) | −2.21638 | −0.0795632 | ||||||||
\(777\) | −10.1211 | −0.363094 | ||||||||
\(778\) | 90.3092 | 3.23774 | ||||||||
\(779\) | −26.5932 | −0.952800 | ||||||||
\(780\) | −19.0411 | −0.681781 | ||||||||
\(781\) | −3.14854 | −0.112664 | ||||||||
\(782\) | 55.7987 | 1.99536 | ||||||||
\(783\) | −5.96396 | −0.213134 | ||||||||
\(784\) | −66.2683 | −2.36672 | ||||||||
\(785\) | −30.9186 | −1.10353 | ||||||||
\(786\) | 31.0116 | 1.10615 | ||||||||
\(787\) | 53.8180 | 1.91840 | 0.959202 | − | 0.282723i | \(-0.0912377\pi\) | ||||
0.959202 | + | 0.282723i | \(0.0912377\pi\) | |||||||
\(788\) | −61.9970 | −2.20855 | ||||||||
\(789\) | 29.9080 | 1.06475 | ||||||||
\(790\) | 25.8415 | 0.919401 | ||||||||
\(791\) | 14.7059 | 0.522883 | ||||||||
\(792\) | −18.5014 | −0.657420 | ||||||||
\(793\) | 20.6533 | 0.733420 | ||||||||
\(794\) | 14.8162 | 0.525808 | ||||||||
\(795\) | −7.36923 | −0.261360 | ||||||||
\(796\) | −89.0339 | −3.15572 | ||||||||
\(797\) | 32.5335 | 1.15239 | 0.576197 | − | 0.817311i | \(-0.304536\pi\) | ||||
0.576197 | + | 0.817311i | \(0.304536\pi\) | |||||||
\(798\) | 7.81714 | 0.276724 | ||||||||
\(799\) | 27.1900 | 0.961915 | ||||||||
\(800\) | 40.0103 | 1.41458 | ||||||||
\(801\) | −10.3413 | −0.365392 | ||||||||
\(802\) | −4.23775 | −0.149640 | ||||||||
\(803\) | −14.9964 | −0.529213 | ||||||||
\(804\) | −71.4417 | −2.51955 | ||||||||
\(805\) | 10.6096 | 0.373938 | ||||||||
\(806\) | 55.0903 | 1.94047 | ||||||||
\(807\) | −12.0051 | −0.422599 | ||||||||
\(808\) | 66.0197 | 2.32256 | ||||||||
\(809\) | −52.1544 | −1.83365 | −0.916825 | − | 0.399289i | \(-0.869257\pi\) | ||||
−0.916825 | + | 0.399289i | \(0.869257\pi\) | |||||||
\(810\) | 3.71467 | 0.130520 | ||||||||
\(811\) | −6.01280 | −0.211138 | −0.105569 | − | 0.994412i | \(-0.533666\pi\) | ||||
−0.105569 | + | 0.994412i | \(0.533666\pi\) | |||||||
\(812\) | −29.3796 | −1.03102 | ||||||||
\(813\) | 11.2519 | 0.394622 | ||||||||
\(814\) | 63.3625 | 2.22086 | ||||||||
\(815\) | −8.79791 | −0.308177 | ||||||||
\(816\) | 30.2350 | 1.05844 | ||||||||
\(817\) | −1.37543 | −0.0481203 | ||||||||
\(818\) | 61.3418 | 2.14477 | ||||||||
\(819\) | 2.67325 | 0.0934110 | ||||||||
\(820\) | −62.2521 | −2.17394 | ||||||||
\(821\) | 28.9166 | 1.00920 | 0.504599 | − | 0.863354i | \(-0.331640\pi\) | ||||
0.504599 | + | 0.863354i | \(0.331640\pi\) | |||||||
\(822\) | −21.4201 | −0.747113 | ||||||||
\(823\) | 52.7250 | 1.83788 | 0.918939 | − | 0.394400i | \(-0.129048\pi\) | ||||
0.918939 | + | 0.394400i | \(0.129048\pi\) | |||||||
\(824\) | 86.0879 | 2.99902 | ||||||||
\(825\) | 7.06218 | 0.245873 | ||||||||
\(826\) | 36.6235 | 1.27430 | ||||||||
\(827\) | −4.87869 | −0.169649 | −0.0848243 | − | 0.996396i | \(-0.527033\pi\) | ||||
−0.0848243 | + | 0.996396i | \(0.527033\pi\) | |||||||
\(828\) | 38.3305 | 1.33208 | ||||||||
\(829\) | 1.95236 | 0.0678083 | 0.0339042 | − | 0.999425i | \(-0.489206\pi\) | ||||
0.0339042 | + | 0.999425i | \(0.489206\pi\) | |||||||
\(830\) | 35.5674 | 1.23456 | ||||||||
\(831\) | −14.5854 | −0.505964 | ||||||||
\(832\) | −35.1791 | −1.21961 | ||||||||
\(833\) | 16.5837 | 0.574591 | ||||||||
\(834\) | 8.61014 | 0.298145 | ||||||||
\(835\) | −22.6535 | −0.783955 | ||||||||
\(836\) | −34.9540 | −1.20891 | ||||||||
\(837\) | −7.67624 | −0.265330 | ||||||||
\(838\) | 104.167 | 3.59838 | ||||||||
\(839\) | 43.9451 | 1.51715 | 0.758577 | − | 0.651583i | \(-0.225895\pi\) | ||||
0.758577 | + | 0.651583i | \(0.225895\pi\) | |||||||
\(840\) | 10.9780 | 0.378777 | ||||||||
\(841\) | 6.56876 | 0.226509 | ||||||||
\(842\) | 93.7538 | 3.23097 | ||||||||
\(843\) | −26.4126 | −0.909698 | ||||||||
\(844\) | 4.30393 | 0.148147 | ||||||||
\(845\) | 7.92063 | 0.272478 | ||||||||
\(846\) | 26.1507 | 0.899081 | ||||||||
\(847\) | 5.48110 | 0.188333 | ||||||||
\(848\) | −57.6881 | −1.98102 | ||||||||
\(849\) | −11.5981 | −0.398047 | ||||||||
\(850\) | −22.0385 | −0.755914 | ||||||||
\(851\) | −78.7522 | −2.69959 | ||||||||
\(852\) | 6.74952 | 0.231235 | ||||||||
\(853\) | 30.1785 | 1.03329 | 0.516646 | − | 0.856199i | \(-0.327180\pi\) | ||||
0.516646 | + | 0.856199i | \(0.327180\pi\) | |||||||
\(854\) | −19.8485 | −0.679203 | ||||||||
\(855\) | 4.21020 | 0.143986 | ||||||||
\(856\) | −47.9664 | −1.63946 | ||||||||
\(857\) | 45.0534 | 1.53900 | 0.769498 | − | 0.638650i | \(-0.220507\pi\) | ||||
0.769498 | + | 0.638650i | \(0.220507\pi\) | |||||||
\(858\) | −16.7357 | −0.571346 | ||||||||
\(859\) | 36.3472 | 1.24015 | 0.620075 | − | 0.784543i | \(-0.287102\pi\) | ||||
0.620075 | + | 0.784543i | \(0.287102\pi\) | |||||||
\(860\) | −3.21975 | −0.109793 | ||||||||
\(861\) | 8.73980 | 0.297851 | ||||||||
\(862\) | 65.4281 | 2.22849 | ||||||||
\(863\) | 40.1227 | 1.36579 | 0.682896 | − | 0.730516i | \(-0.260720\pi\) | ||||
0.682896 | + | 0.730516i | \(0.260720\pi\) | |||||||
\(864\) | 13.2114 | 0.449462 | ||||||||
\(865\) | −1.02013 | −0.0346854 | ||||||||
\(866\) | −29.6725 | −1.00831 | ||||||||
\(867\) | 9.43365 | 0.320384 | ||||||||
\(868\) | −37.8147 | −1.28351 | ||||||||
\(869\) | 16.2224 | 0.550307 | ||||||||
\(870\) | −22.1541 | −0.751094 | ||||||||
\(871\) | −38.7686 | −1.31362 | ||||||||
\(872\) | 106.581 | 3.60929 | ||||||||
\(873\) | 0.279354 | 0.00945469 | ||||||||
\(874\) | 60.8248 | 2.05743 | ||||||||
\(875\) | −11.1088 | −0.375545 | ||||||||
\(876\) | 32.1479 | 1.08618 | ||||||||
\(877\) | −13.9143 | −0.469853 | −0.234927 | − | 0.972013i | \(-0.575485\pi\) | ||||
−0.234927 | + | 0.972013i | \(0.575485\pi\) | |||||||
\(878\) | 61.0305 | 2.05968 | ||||||||
\(879\) | 16.3897 | 0.552812 | ||||||||
\(880\) | −35.9904 | −1.21324 | ||||||||
\(881\) | 29.0714 | 0.979440 | 0.489720 | − | 0.871880i | \(-0.337099\pi\) | ||||
0.489720 | + | 0.871880i | \(0.337099\pi\) | |||||||
\(882\) | 15.9498 | 0.537058 | ||||||||
\(883\) | −44.1650 | −1.48627 | −0.743136 | − | 0.669141i | \(-0.766662\pi\) | ||||
−0.743136 | + | 0.669141i | \(0.766662\pi\) | |||||||
\(884\) | 37.3020 | 1.25460 | ||||||||
\(885\) | 19.7249 | 0.663046 | ||||||||
\(886\) | 25.2727 | 0.849054 | ||||||||
\(887\) | 54.8069 | 1.84024 | 0.920118 | − | 0.391640i | \(-0.128092\pi\) | ||||
0.920118 | + | 0.391640i | \(0.128092\pi\) | |||||||
\(888\) | −81.4869 | −2.73452 | ||||||||
\(889\) | −5.74892 | −0.192813 | ||||||||
\(890\) | −38.4145 | −1.28766 | ||||||||
\(891\) | 2.33194 | 0.0781228 | ||||||||
\(892\) | −30.7791 | −1.03056 | ||||||||
\(893\) | 29.6392 | 0.991839 | ||||||||
\(894\) | 16.7775 | 0.561124 | ||||||||
\(895\) | 29.3255 | 0.980243 | ||||||||
\(896\) | 7.77010 | 0.259581 | ||||||||
\(897\) | 20.8004 | 0.694507 | ||||||||
\(898\) | −16.7609 | −0.559320 | ||||||||
\(899\) | 45.7808 | 1.52687 | ||||||||
\(900\) | −15.1392 | −0.504639 | ||||||||
\(901\) | 14.4365 | 0.480950 | ||||||||
\(902\) | −54.7147 | −1.82180 | ||||||||
\(903\) | 0.452032 | 0.0150427 | ||||||||
\(904\) | 118.400 | 3.93792 | ||||||||
\(905\) | −18.8934 | −0.628039 | ||||||||
\(906\) | −19.7088 | −0.654780 | ||||||||
\(907\) | −10.4974 | −0.348561 | −0.174281 | − | 0.984696i | \(-0.555760\pi\) | ||||
−0.174281 | + | 0.984696i | \(0.555760\pi\) | |||||||
\(908\) | −140.420 | −4.65999 | ||||||||
\(909\) | −8.32117 | −0.275996 | ||||||||
\(910\) | 9.93024 | 0.329184 | ||||||||
\(911\) | 28.1392 | 0.932294 | 0.466147 | − | 0.884707i | \(-0.345642\pi\) | ||||
0.466147 | + | 0.884707i | \(0.345642\pi\) | |||||||
\(912\) | 32.9585 | 1.09136 | ||||||||
\(913\) | 22.3280 | 0.738947 | ||||||||
\(914\) | 4.72278 | 0.156216 | ||||||||
\(915\) | −10.6901 | −0.353405 | ||||||||
\(916\) | 5.20047 | 0.171828 | ||||||||
\(917\) | −11.5515 | −0.381463 | ||||||||
\(918\) | −7.27713 | −0.240181 | ||||||||
\(919\) | 34.7194 | 1.14529 | 0.572643 | − | 0.819805i | \(-0.305918\pi\) | ||||
0.572643 | + | 0.819805i | \(0.305918\pi\) | |||||||
\(920\) | 85.4192 | 2.81619 | ||||||||
\(921\) | 3.05538 | 0.100678 | ||||||||
\(922\) | −27.7499 | −0.913893 | ||||||||
\(923\) | 3.66270 | 0.120559 | ||||||||
\(924\) | 11.4876 | 0.377913 | ||||||||
\(925\) | 31.1043 | 1.02270 | ||||||||
\(926\) | 34.9735 | 1.14930 | ||||||||
\(927\) | −10.8506 | −0.356380 | ||||||||
\(928\) | −78.7924 | −2.58649 | ||||||||
\(929\) | −30.6217 | −1.00467 | −0.502333 | − | 0.864674i | \(-0.667525\pi\) | ||||
−0.502333 | + | 0.864674i | \(0.667525\pi\) | |||||||
\(930\) | −28.5147 | −0.935033 | ||||||||
\(931\) | 18.0775 | 0.592466 | ||||||||
\(932\) | 25.6154 | 0.839061 | ||||||||
\(933\) | −9.26605 | −0.303357 | ||||||||
\(934\) | −55.4543 | −1.81452 | ||||||||
\(935\) | 9.00663 | 0.294548 | ||||||||
\(936\) | 21.5228 | 0.703494 | ||||||||
\(937\) | −12.9862 | −0.424241 | −0.212121 | − | 0.977243i | \(-0.568037\pi\) | ||||
−0.212121 | + | 0.977243i | \(0.568037\pi\) | |||||||
\(938\) | 37.2580 | 1.21652 | ||||||||
\(939\) | −2.32324 | −0.0758160 | ||||||||
\(940\) | 69.3825 | 2.26301 | ||||||||
\(941\) | −4.93044 | −0.160728 | −0.0803638 | − | 0.996766i | \(-0.525608\pi\) | ||||
−0.0803638 | + | 0.996766i | \(0.525608\pi\) | |||||||
\(942\) | 58.2550 | 1.89805 | ||||||||
\(943\) | 68.0040 | 2.21451 | ||||||||
\(944\) | 154.411 | 5.02567 | ||||||||
\(945\) | −1.38367 | −0.0450109 | ||||||||
\(946\) | −2.82991 | −0.0920083 | ||||||||
\(947\) | 22.6290 | 0.735343 | 0.367672 | − | 0.929956i | \(-0.380155\pi\) | ||||
0.367672 | + | 0.929956i | \(0.380155\pi\) | |||||||
\(948\) | −34.7760 | −1.12947 | ||||||||
\(949\) | 17.4454 | 0.566301 | ||||||||
\(950\) | −24.0237 | −0.779430 | ||||||||
\(951\) | 25.0313 | 0.811694 | ||||||||
\(952\) | −21.5062 | −0.697019 | ||||||||
\(953\) | 29.8943 | 0.968372 | 0.484186 | − | 0.874965i | \(-0.339116\pi\) | ||||
0.484186 | + | 0.874965i | \(0.339116\pi\) | |||||||
\(954\) | 13.8847 | 0.449534 | ||||||||
\(955\) | −7.55215 | −0.244382 | ||||||||
\(956\) | 30.2013 | 0.976779 | ||||||||
\(957\) | −13.9076 | −0.449568 | ||||||||
\(958\) | 24.4336 | 0.789413 | ||||||||
\(959\) | 7.97878 | 0.257648 | ||||||||
\(960\) | 18.2087 | 0.587682 | ||||||||
\(961\) | 27.9247 | 0.900798 | ||||||||
\(962\) | −73.7097 | −2.37650 | ||||||||
\(963\) | 6.04572 | 0.194821 | ||||||||
\(964\) | 16.4067 | 0.528425 | ||||||||
\(965\) | −0.109962 | −0.00353981 | ||||||||
\(966\) | −19.9899 | −0.643166 | ||||||||
\(967\) | −0.0665875 | −0.00214131 | −0.00107065 | − | 0.999999i | \(-0.500341\pi\) | ||||
−0.00107065 | + | 0.999999i | \(0.500341\pi\) | |||||||
\(968\) | 44.1292 | 1.41837 | ||||||||
\(969\) | −8.24790 | −0.264961 | ||||||||
\(970\) | 1.03771 | 0.0333187 | ||||||||
\(971\) | 60.8438 | 1.95257 | 0.976286 | − | 0.216486i | \(-0.0694596\pi\) | ||||
0.976286 | + | 0.216486i | \(0.0694596\pi\) | |||||||
\(972\) | −4.99897 | −0.160342 | ||||||||
\(973\) | −3.20719 | −0.102818 | ||||||||
\(974\) | −25.5614 | −0.819041 | ||||||||
\(975\) | −8.21544 | −0.263105 | ||||||||
\(976\) | −83.6850 | −2.67869 | ||||||||
\(977\) | 8.97093 | 0.287006 | 0.143503 | − | 0.989650i | \(-0.454163\pi\) | ||||
0.143503 | + | 0.989650i | \(0.454163\pi\) | |||||||
\(978\) | 16.5765 | 0.530059 | ||||||||
\(979\) | −24.1152 | −0.770726 | ||||||||
\(980\) | 42.3177 | 1.35179 | ||||||||
\(981\) | −13.4335 | −0.428900 | ||||||||
\(982\) | −85.4856 | −2.72795 | ||||||||
\(983\) | 5.29704 | 0.168949 | 0.0844746 | − | 0.996426i | \(-0.473079\pi\) | ||||
0.0844746 | + | 0.996426i | \(0.473079\pi\) | |||||||
\(984\) | 70.3655 | 2.24317 | ||||||||
\(985\) | 17.4138 | 0.554849 | ||||||||
\(986\) | 43.4005 | 1.38215 | ||||||||
\(987\) | −9.74087 | −0.310055 | ||||||||
\(988\) | 40.6621 | 1.29363 | ||||||||
\(989\) | 3.51724 | 0.111842 | ||||||||
\(990\) | 8.66236 | 0.275308 | ||||||||
\(991\) | −11.4066 | −0.362343 | −0.181172 | − | 0.983451i | \(-0.557989\pi\) | ||||
−0.181172 | + | 0.983451i | \(0.557989\pi\) | |||||||
\(992\) | −101.414 | −3.21990 | ||||||||
\(993\) | 13.9106 | 0.441439 | ||||||||
\(994\) | −3.51998 | −0.111647 | ||||||||
\(995\) | 25.0079 | 0.792805 | ||||||||
\(996\) | −47.8644 | −1.51664 | ||||||||
\(997\) | −37.4798 | −1.18700 | −0.593498 | − | 0.804836i | \(-0.702253\pi\) | ||||
−0.593498 | + | 0.804836i | \(0.702253\pi\) | |||||||
\(998\) | 85.3912 | 2.70301 | ||||||||
\(999\) | 10.2707 | 0.324950 |
(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 | 8031.2.a.c.1.4 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8031.2.a.c.1.4 | ✓ | 121 | 1.1 | even | 1 | trivial |