Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99373 | −1.40978 | −0.704888 | − | 0.709318i | \(-0.749003\pi\) | ||||
−0.704888 | + | 0.709318i | \(0.749003\pi\) | |||||||
\(3\) | −2.36120 | −1.36324 | −0.681620 | − | 0.731706i | \(-0.738724\pi\) | ||||
−0.681620 | + | 0.731706i | \(0.738724\pi\) | |||||||
\(4\) | 1.97494 | 0.987470 | ||||||||
\(5\) | −0.776635 | −0.347322 | −0.173661 | − | 0.984806i | \(-0.555560\pi\) | ||||
−0.173661 | + | 0.984806i | \(0.555560\pi\) | |||||||
\(6\) | 4.70759 | 1.92186 | ||||||||
\(7\) | −0.440394 | −0.166453 | −0.0832266 | − | 0.996531i | \(-0.526523\pi\) | ||||
−0.0832266 | + | 0.996531i | \(0.526523\pi\) | |||||||
\(8\) | 0.0499623 | 0.0176644 | ||||||||
\(9\) | 2.57527 | 0.858424 | ||||||||
\(10\) | 1.54840 | 0.489646 | ||||||||
\(11\) | −2.15629 | −0.650145 | −0.325073 | − | 0.945689i | \(-0.605389\pi\) | ||||
−0.325073 | + | 0.945689i | \(0.605389\pi\) | |||||||
\(12\) | −4.66323 | −1.34616 | ||||||||
\(13\) | 0.754850 | 0.209358 | 0.104679 | − | 0.994506i | \(-0.466619\pi\) | ||||
0.104679 | + | 0.994506i | \(0.466619\pi\) | |||||||
\(14\) | 0.878024 | 0.234662 | ||||||||
\(15\) | 1.83379 | 0.473483 | ||||||||
\(16\) | −4.04949 | −1.01237 | ||||||||
\(17\) | −6.90916 | −1.67572 | −0.837859 | − | 0.545887i | \(-0.816193\pi\) | ||||
−0.837859 | + | 0.545887i | \(0.816193\pi\) | |||||||
\(18\) | −5.13438 | −1.21019 | ||||||||
\(19\) | 4.91582 | 1.12777 | 0.563884 | − | 0.825854i | \(-0.309307\pi\) | ||||
0.563884 | + | 0.825854i | \(0.309307\pi\) | |||||||
\(20\) | −1.53381 | −0.342970 | ||||||||
\(21\) | 1.03986 | 0.226916 | ||||||||
\(22\) | 4.29904 | 0.916559 | ||||||||
\(23\) | 1.37766 | 0.287262 | 0.143631 | − | 0.989631i | \(-0.454122\pi\) | ||||
0.143631 | + | 0.989631i | \(0.454122\pi\) | |||||||
\(24\) | −0.117971 | −0.0240808 | ||||||||
\(25\) | −4.39684 | −0.879368 | ||||||||
\(26\) | −1.50496 | −0.295148 | ||||||||
\(27\) | 1.00287 | 0.193002 | ||||||||
\(28\) | −0.869751 | −0.164368 | ||||||||
\(29\) | −1.02580 | −0.190485 | −0.0952427 | − | 0.995454i | \(-0.530363\pi\) | ||||
−0.0952427 | + | 0.995454i | \(0.530363\pi\) | |||||||
\(30\) | −3.65608 | −0.667505 | ||||||||
\(31\) | −9.65359 | −1.73384 | −0.866918 | − | 0.498452i | \(-0.833902\pi\) | ||||
−0.866918 | + | 0.498452i | \(0.833902\pi\) | |||||||
\(32\) | 7.97365 | 1.40956 | ||||||||
\(33\) | 5.09143 | 0.886304 | ||||||||
\(34\) | 13.7750 | 2.36239 | ||||||||
\(35\) | 0.342025 | 0.0578128 | ||||||||
\(36\) | 5.08601 | 0.847668 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −9.80080 | −1.58990 | ||||||||
\(39\) | −1.78235 | −0.285405 | ||||||||
\(40\) | −0.0388025 | −0.00613521 | ||||||||
\(41\) | 10.7474 | 1.67846 | 0.839232 | − | 0.543773i | \(-0.183005\pi\) | ||||
0.839232 | + | 0.543773i | \(0.183005\pi\) | |||||||
\(42\) | −2.07319 | −0.319900 | ||||||||
\(43\) | −2.65371 | −0.404688 | −0.202344 | − | 0.979315i | \(-0.564856\pi\) | ||||
−0.202344 | + | 0.979315i | \(0.564856\pi\) | |||||||
\(44\) | −4.25854 | −0.641999 | ||||||||
\(45\) | −2.00005 | −0.298149 | ||||||||
\(46\) | −2.74668 | −0.404976 | ||||||||
\(47\) | 2.72977 | 0.398178 | 0.199089 | − | 0.979981i | \(-0.436202\pi\) | ||||
0.199089 | + | 0.979981i | \(0.436202\pi\) | |||||||
\(48\) | 9.56167 | 1.38011 | ||||||||
\(49\) | −6.80605 | −0.972293 | ||||||||
\(50\) | 8.76609 | 1.23971 | ||||||||
\(51\) | 16.3139 | 2.28441 | ||||||||
\(52\) | 1.49078 | 0.206734 | ||||||||
\(53\) | 12.7984 | 1.75800 | 0.879001 | − | 0.476820i | \(-0.158211\pi\) | ||||
0.879001 | + | 0.476820i | \(0.158211\pi\) | |||||||
\(54\) | −1.99944 | −0.272090 | ||||||||
\(55\) | 1.67465 | 0.225809 | ||||||||
\(56\) | −0.0220031 | −0.00294029 | ||||||||
\(57\) | −11.6072 | −1.53742 | ||||||||
\(58\) | 2.04515 | 0.268542 | ||||||||
\(59\) | −10.5962 | −1.37951 | −0.689754 | − | 0.724044i | \(-0.742281\pi\) | ||||
−0.689754 | + | 0.724044i | \(0.742281\pi\) | |||||||
\(60\) | 3.62163 | 0.467550 | ||||||||
\(61\) | 0.725629 | 0.0929072 | 0.0464536 | − | 0.998920i | \(-0.485208\pi\) | ||||
0.0464536 | + | 0.998920i | \(0.485208\pi\) | |||||||
\(62\) | 19.2466 | 2.44432 | ||||||||
\(63\) | −1.13413 | −0.142887 | ||||||||
\(64\) | −7.79828 | −0.974785 | ||||||||
\(65\) | −0.586243 | −0.0727145 | ||||||||
\(66\) | −10.1509 | −1.24949 | ||||||||
\(67\) | −6.18534 | −0.755659 | −0.377830 | − | 0.925875i | \(-0.623329\pi\) | ||||
−0.377830 | + | 0.925875i | \(0.623329\pi\) | |||||||
\(68\) | −13.6452 | −1.65472 | ||||||||
\(69\) | −3.25294 | −0.391607 | ||||||||
\(70\) | −0.681904 | −0.0815031 | ||||||||
\(71\) | −3.51520 | −0.417178 | −0.208589 | − | 0.978003i | \(-0.566887\pi\) | ||||
−0.208589 | + | 0.978003i | \(0.566887\pi\) | |||||||
\(72\) | 0.128667 | 0.0151635 | ||||||||
\(73\) | −16.2009 | −1.89617 | −0.948085 | − | 0.318018i | \(-0.896983\pi\) | ||||
−0.948085 | + | 0.318018i | \(0.896983\pi\) | |||||||
\(74\) | −1.99373 | −0.231766 | ||||||||
\(75\) | 10.3818 | 1.19879 | ||||||||
\(76\) | 9.70846 | 1.11364 | ||||||||
\(77\) | 0.949615 | 0.108219 | ||||||||
\(78\) | 3.55352 | 0.402357 | ||||||||
\(79\) | −1.40676 | −0.158273 | −0.0791363 | − | 0.996864i | \(-0.525216\pi\) | ||||
−0.0791363 | + | 0.996864i | \(0.525216\pi\) | |||||||
\(80\) | 3.14498 | 0.351619 | ||||||||
\(81\) | −10.0938 | −1.12153 | ||||||||
\(82\) | −21.4274 | −2.36626 | ||||||||
\(83\) | 13.0553 | 1.43300 | 0.716502 | − | 0.697585i | \(-0.245742\pi\) | ||||
0.716502 | + | 0.697585i | \(0.245742\pi\) | |||||||
\(84\) | 2.05366 | 0.224072 | ||||||||
\(85\) | 5.36590 | 0.582013 | ||||||||
\(86\) | 5.29078 | 0.570519 | ||||||||
\(87\) | 2.42211 | 0.259677 | ||||||||
\(88\) | −0.107733 | −0.0114844 | ||||||||
\(89\) | −7.37894 | −0.782166 | −0.391083 | − | 0.920355i | \(-0.627899\pi\) | ||||
−0.391083 | + | 0.920355i | \(0.627899\pi\) | |||||||
\(90\) | 3.98754 | 0.420324 | ||||||||
\(91\) | −0.332431 | −0.0348482 | ||||||||
\(92\) | 2.72080 | 0.283663 | ||||||||
\(93\) | 22.7941 | 2.36363 | ||||||||
\(94\) | −5.44241 | −0.561342 | ||||||||
\(95\) | −3.81780 | −0.391698 | ||||||||
\(96\) | −18.8274 | −1.92156 | ||||||||
\(97\) | −3.31898 | −0.336991 | −0.168496 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168496 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(98\) | 13.5694 | 1.37072 | ||||||||
\(99\) | −5.55303 | −0.558100 | ||||||||
\(100\) | −8.68349 | −0.868349 | ||||||||
\(101\) | −0.0925698 | −0.00921104 | −0.00460552 | − | 0.999989i | \(-0.501466\pi\) | ||||
−0.00460552 | + | 0.999989i | \(0.501466\pi\) | |||||||
\(102\) | −32.5255 | −3.22050 | ||||||||
\(103\) | 2.72054 | 0.268063 | 0.134031 | − | 0.990977i | \(-0.457208\pi\) | ||||
0.134031 | + | 0.990977i | \(0.457208\pi\) | |||||||
\(104\) | 0.0377141 | 0.00369817 | ||||||||
\(105\) | −0.807590 | −0.0788127 | ||||||||
\(106\) | −25.5166 | −2.47839 | ||||||||
\(107\) | −8.24268 | −0.796850 | −0.398425 | − | 0.917201i | \(-0.630443\pi\) | ||||
−0.398425 | + | 0.917201i | \(0.630443\pi\) | |||||||
\(108\) | 1.98061 | 0.190584 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −3.33879 | −0.318341 | ||||||||
\(111\) | −2.36120 | −0.224115 | ||||||||
\(112\) | 1.78337 | 0.168513 | ||||||||
\(113\) | −5.96935 | −0.561549 | −0.280774 | − | 0.959774i | \(-0.590591\pi\) | ||||
−0.280774 | + | 0.959774i | \(0.590591\pi\) | |||||||
\(114\) | 23.1417 | 2.16742 | ||||||||
\(115\) | −1.06994 | −0.0997724 | ||||||||
\(116\) | −2.02588 | −0.188099 | ||||||||
\(117\) | 1.94394 | 0.179718 | ||||||||
\(118\) | 21.1259 | 1.94480 | ||||||||
\(119\) | 3.04275 | 0.278929 | ||||||||
\(120\) | 0.0916205 | 0.00836377 | ||||||||
\(121\) | −6.35042 | −0.577311 | ||||||||
\(122\) | −1.44670 | −0.130978 | ||||||||
\(123\) | −25.3768 | −2.28815 | ||||||||
\(124\) | −19.0653 | −1.71211 | ||||||||
\(125\) | 7.29791 | 0.652745 | ||||||||
\(126\) | 2.26115 | 0.201439 | ||||||||
\(127\) | −15.6542 | −1.38908 | −0.694541 | − | 0.719453i | \(-0.744393\pi\) | ||||
−0.694541 | + | 0.719453i | \(0.744393\pi\) | |||||||
\(128\) | −0.399667 | −0.0353259 | ||||||||
\(129\) | 6.26595 | 0.551686 | ||||||||
\(130\) | 1.16881 | 0.102511 | ||||||||
\(131\) | −6.45718 | −0.564166 | −0.282083 | − | 0.959390i | \(-0.591025\pi\) | ||||
−0.282083 | + | 0.959390i | \(0.591025\pi\) | |||||||
\(132\) | 10.0553 | 0.875199 | ||||||||
\(133\) | −2.16490 | −0.187720 | ||||||||
\(134\) | 12.3319 | 1.06531 | ||||||||
\(135\) | −0.778863 | −0.0670338 | ||||||||
\(136\) | −0.345198 | −0.0296005 | ||||||||
\(137\) | 12.1342 | 1.03670 | 0.518349 | − | 0.855169i | \(-0.326547\pi\) | ||||
0.518349 | + | 0.855169i | \(0.326547\pi\) | |||||||
\(138\) | 6.48546 | 0.552079 | ||||||||
\(139\) | 7.42721 | 0.629967 | 0.314984 | − | 0.949097i | \(-0.398001\pi\) | ||||
0.314984 | + | 0.949097i | \(0.398001\pi\) | |||||||
\(140\) | 0.675479 | 0.0570884 | ||||||||
\(141\) | −6.44554 | −0.542812 | ||||||||
\(142\) | 7.00834 | 0.588127 | ||||||||
\(143\) | −1.62767 | −0.136113 | ||||||||
\(144\) | −10.4285 | −0.869045 | ||||||||
\(145\) | 0.796669 | 0.0661597 | ||||||||
\(146\) | 32.3001 | 2.67318 | ||||||||
\(147\) | 16.0705 | 1.32547 | ||||||||
\(148\) | 1.97494 | 0.162339 | ||||||||
\(149\) | −3.40709 | −0.279120 | −0.139560 | − | 0.990214i | \(-0.544569\pi\) | ||||
−0.139560 | + | 0.990214i | \(0.544569\pi\) | |||||||
\(150\) | −20.6985 | −1.69003 | ||||||||
\(151\) | −5.51750 | −0.449008 | −0.224504 | − | 0.974473i | \(-0.572076\pi\) | ||||
−0.224504 | + | 0.974473i | \(0.572076\pi\) | |||||||
\(152\) | 0.245606 | 0.0199213 | ||||||||
\(153\) | −17.7930 | −1.43848 | ||||||||
\(154\) | −1.89327 | −0.152564 | ||||||||
\(155\) | 7.49731 | 0.602199 | ||||||||
\(156\) | −3.52004 | −0.281829 | ||||||||
\(157\) | 0.423026 | 0.0337612 | 0.0168806 | − | 0.999858i | \(-0.494626\pi\) | ||||
0.0168806 | + | 0.999858i | \(0.494626\pi\) | |||||||
\(158\) | 2.80469 | 0.223129 | ||||||||
\(159\) | −30.2197 | −2.39658 | ||||||||
\(160\) | −6.19261 | −0.489569 | ||||||||
\(161\) | −0.606713 | −0.0478157 | ||||||||
\(162\) | 20.1242 | 1.58111 | ||||||||
\(163\) | 6.31014 | 0.494248 | 0.247124 | − | 0.968984i | \(-0.420514\pi\) | ||||
0.247124 | + | 0.968984i | \(0.420514\pi\) | |||||||
\(164\) | 21.2255 | 1.65743 | ||||||||
\(165\) | −3.95418 | −0.307833 | ||||||||
\(166\) | −26.0287 | −2.02022 | ||||||||
\(167\) | −7.87108 | −0.609082 | −0.304541 | − | 0.952499i | \(-0.598503\pi\) | ||||
−0.304541 | + | 0.952499i | \(0.598503\pi\) | |||||||
\(168\) | 0.0519538 | 0.00400832 | ||||||||
\(169\) | −12.4302 | −0.956169 | ||||||||
\(170\) | −10.6981 | −0.820508 | ||||||||
\(171\) | 12.6596 | 0.968103 | ||||||||
\(172\) | −5.24093 | −0.399617 | ||||||||
\(173\) | −17.9454 | −1.36437 | −0.682183 | − | 0.731181i | \(-0.738969\pi\) | ||||
−0.682183 | + | 0.731181i | \(0.738969\pi\) | |||||||
\(174\) | −4.82902 | −0.366087 | ||||||||
\(175\) | 1.93634 | 0.146374 | ||||||||
\(176\) | 8.73187 | 0.658189 | ||||||||
\(177\) | 25.0198 | 1.88060 | ||||||||
\(178\) | 14.7116 | 1.10268 | ||||||||
\(179\) | −26.5291 | −1.98288 | −0.991440 | − | 0.130565i | \(-0.958321\pi\) | ||||
−0.991440 | + | 0.130565i | \(0.958321\pi\) | |||||||
\(180\) | −3.94997 | −0.294413 | ||||||||
\(181\) | −17.8134 | −1.32406 | −0.662029 | − | 0.749478i | \(-0.730304\pi\) | ||||
−0.662029 | + | 0.749478i | \(0.730304\pi\) | |||||||
\(182\) | 0.662776 | 0.0491282 | ||||||||
\(183\) | −1.71336 | −0.126655 | ||||||||
\(184\) | 0.0688312 | 0.00507430 | ||||||||
\(185\) | −0.776635 | −0.0570993 | ||||||||
\(186\) | −45.4451 | −3.33220 | ||||||||
\(187\) | 14.8981 | 1.08946 | ||||||||
\(188\) | 5.39114 | 0.393189 | ||||||||
\(189\) | −0.441657 | −0.0321258 | ||||||||
\(190\) | 7.61164 | 0.552207 | ||||||||
\(191\) | −16.3367 | −1.18208 | −0.591042 | − | 0.806640i | \(-0.701283\pi\) | ||||
−0.591042 | + | 0.806640i | \(0.701283\pi\) | |||||||
\(192\) | 18.4133 | 1.32887 | ||||||||
\(193\) | 4.74151 | 0.341301 | 0.170651 | − | 0.985332i | \(-0.445413\pi\) | ||||
0.170651 | + | 0.985332i | \(0.445413\pi\) | |||||||
\(194\) | 6.61713 | 0.475082 | ||||||||
\(195\) | 1.38424 | 0.0991273 | ||||||||
\(196\) | −13.4415 | −0.960111 | ||||||||
\(197\) | 11.0774 | 0.789231 | 0.394616 | − | 0.918846i | \(-0.370878\pi\) | ||||
0.394616 | + | 0.918846i | \(0.370878\pi\) | |||||||
\(198\) | 11.0712 | 0.786797 | ||||||||
\(199\) | −23.0269 | −1.63233 | −0.816167 | − | 0.577817i | \(-0.803905\pi\) | ||||
−0.816167 | + | 0.577817i | \(0.803905\pi\) | |||||||
\(200\) | −0.219676 | −0.0155335 | ||||||||
\(201\) | 14.6048 | 1.03015 | ||||||||
\(202\) | 0.184559 | 0.0129855 | ||||||||
\(203\) | 0.451754 | 0.0317069 | ||||||||
\(204\) | 32.2190 | 2.25578 | ||||||||
\(205\) | −8.34682 | −0.582967 | ||||||||
\(206\) | −5.42401 | −0.377909 | ||||||||
\(207\) | 3.54785 | 0.246593 | ||||||||
\(208\) | −3.05676 | −0.211948 | ||||||||
\(209\) | −10.5999 | −0.733212 | ||||||||
\(210\) | 1.61011 | 0.111108 | ||||||||
\(211\) | 28.2282 | 1.94331 | 0.971656 | − | 0.236398i | \(-0.0759669\pi\) | ||||
0.971656 | + | 0.236398i | \(0.0759669\pi\) | |||||||
\(212\) | 25.2762 | 1.73597 | ||||||||
\(213\) | 8.30010 | 0.568713 | ||||||||
\(214\) | 16.4336 | 1.12338 | ||||||||
\(215\) | 2.06097 | 0.140557 | ||||||||
\(216\) | 0.0501057 | 0.00340926 | ||||||||
\(217\) | 4.25138 | 0.288602 | ||||||||
\(218\) | 1.99373 | 0.135032 | ||||||||
\(219\) | 38.2535 | 2.58493 | ||||||||
\(220\) | 3.30733 | 0.222980 | ||||||||
\(221\) | −5.21538 | −0.350824 | ||||||||
\(222\) | 4.70759 | 0.315953 | ||||||||
\(223\) | 21.9472 | 1.46969 | 0.734846 | − | 0.678234i | \(-0.237254\pi\) | ||||
0.734846 | + | 0.678234i | \(0.237254\pi\) | |||||||
\(224\) | −3.51155 | −0.234625 | ||||||||
\(225\) | −11.3231 | −0.754870 | ||||||||
\(226\) | 11.9012 | 0.791658 | ||||||||
\(227\) | 8.10310 | 0.537822 | 0.268911 | − | 0.963165i | \(-0.413336\pi\) | ||||
0.268911 | + | 0.963165i | \(0.413336\pi\) | |||||||
\(228\) | −22.9236 | −1.51815 | ||||||||
\(229\) | −17.0447 | −1.12634 | −0.563171 | − | 0.826340i | \(-0.690419\pi\) | ||||
−0.563171 | + | 0.826340i | \(0.690419\pi\) | |||||||
\(230\) | 2.13317 | 0.140657 | ||||||||
\(231\) | −2.24223 | −0.147528 | ||||||||
\(232\) | −0.0512512 | −0.00336480 | ||||||||
\(233\) | 23.3146 | 1.52739 | 0.763696 | − | 0.645576i | \(-0.223383\pi\) | ||||
0.763696 | + | 0.645576i | \(0.223383\pi\) | |||||||
\(234\) | −3.87569 | −0.253362 | ||||||||
\(235\) | −2.12004 | −0.138296 | ||||||||
\(236\) | −20.9269 | −1.36222 | ||||||||
\(237\) | 3.32164 | 0.215764 | ||||||||
\(238\) | −6.06641 | −0.393227 | ||||||||
\(239\) | 11.9388 | 0.772259 | 0.386129 | − | 0.922445i | \(-0.373812\pi\) | ||||
0.386129 | + | 0.922445i | \(0.373812\pi\) | |||||||
\(240\) | −7.42592 | −0.479341 | ||||||||
\(241\) | 9.37800 | 0.604090 | 0.302045 | − | 0.953294i | \(-0.402331\pi\) | ||||
0.302045 | + | 0.953294i | \(0.402331\pi\) | |||||||
\(242\) | 12.6610 | 0.813880 | ||||||||
\(243\) | 20.8249 | 1.33592 | ||||||||
\(244\) | 1.43307 | 0.0917431 | ||||||||
\(245\) | 5.28582 | 0.337699 | ||||||||
\(246\) | 50.5944 | 3.22578 | ||||||||
\(247\) | 3.71071 | 0.236107 | ||||||||
\(248\) | −0.482316 | −0.0306271 | ||||||||
\(249\) | −30.8262 | −1.95353 | ||||||||
\(250\) | −14.5500 | −0.920225 | ||||||||
\(251\) | 16.8239 | 1.06191 | 0.530957 | − | 0.847399i | \(-0.321833\pi\) | ||||
0.530957 | + | 0.847399i | \(0.321833\pi\) | |||||||
\(252\) | −2.23985 | −0.141097 | ||||||||
\(253\) | −2.97063 | −0.186762 | ||||||||
\(254\) | 31.2101 | 1.95830 | ||||||||
\(255\) | −12.6700 | −0.793424 | ||||||||
\(256\) | 16.3934 | 1.02459 | ||||||||
\(257\) | 4.10579 | 0.256112 | 0.128056 | − | 0.991767i | \(-0.459126\pi\) | ||||
0.128056 | + | 0.991767i | \(0.459126\pi\) | |||||||
\(258\) | −12.4926 | −0.777755 | ||||||||
\(259\) | −0.440394 | −0.0273647 | ||||||||
\(260\) | −1.15779 | −0.0718033 | ||||||||
\(261\) | −2.64170 | −0.163517 | ||||||||
\(262\) | 12.8738 | 0.795348 | ||||||||
\(263\) | 18.6388 | 1.14932 | 0.574658 | − | 0.818393i | \(-0.305135\pi\) | ||||
0.574658 | + | 0.818393i | \(0.305135\pi\) | |||||||
\(264\) | 0.254380 | 0.0156560 | ||||||||
\(265\) | −9.93972 | −0.610592 | ||||||||
\(266\) | 4.31621 | 0.264644 | ||||||||
\(267\) | 17.4232 | 1.06628 | ||||||||
\(268\) | −12.2157 | −0.746191 | ||||||||
\(269\) | −14.0626 | −0.857409 | −0.428704 | − | 0.903445i | \(-0.641030\pi\) | ||||
−0.428704 | + | 0.903445i | \(0.641030\pi\) | |||||||
\(270\) | 1.55284 | 0.0945027 | ||||||||
\(271\) | 20.0510 | 1.21801 | 0.609004 | − | 0.793167i | \(-0.291569\pi\) | ||||
0.609004 | + | 0.793167i | \(0.291569\pi\) | |||||||
\(272\) | 27.9786 | 1.69645 | ||||||||
\(273\) | 0.784937 | 0.0475065 | ||||||||
\(274\) | −24.1923 | −1.46151 | ||||||||
\(275\) | 9.48085 | 0.571717 | ||||||||
\(276\) | −6.42435 | −0.386701 | ||||||||
\(277\) | −25.2267 | −1.51572 | −0.757862 | − | 0.652415i | \(-0.773756\pi\) | ||||
−0.757862 | + | 0.652415i | \(0.773756\pi\) | |||||||
\(278\) | −14.8078 | −0.888113 | ||||||||
\(279\) | −24.8606 | −1.48837 | ||||||||
\(280\) | 0.0170884 | 0.00102123 | ||||||||
\(281\) | 15.1429 | 0.903349 | 0.451674 | − | 0.892183i | \(-0.350827\pi\) | ||||
0.451674 | + | 0.892183i | \(0.350827\pi\) | |||||||
\(282\) | 12.8506 | 0.765244 | ||||||||
\(283\) | 10.0446 | 0.597088 | 0.298544 | − | 0.954396i | \(-0.403499\pi\) | ||||
0.298544 | + | 0.954396i | \(0.403499\pi\) | |||||||
\(284\) | −6.94231 | −0.411950 | ||||||||
\(285\) | 9.01460 | 0.533979 | ||||||||
\(286\) | 3.24513 | 0.191889 | ||||||||
\(287\) | −4.73310 | −0.279386 | ||||||||
\(288\) | 20.5343 | 1.21000 | ||||||||
\(289\) | 30.7365 | 1.80803 | ||||||||
\(290\) | −1.58834 | −0.0932704 | ||||||||
\(291\) | 7.83677 | 0.459400 | ||||||||
\(292\) | −31.9958 | −1.87241 | ||||||||
\(293\) | −9.43432 | −0.551159 | −0.275579 | − | 0.961278i | \(-0.588870\pi\) | ||||
−0.275579 | + | 0.961278i | \(0.588870\pi\) | |||||||
\(294\) | −32.0401 | −1.86862 | ||||||||
\(295\) | 8.22938 | 0.479133 | ||||||||
\(296\) | 0.0499623 | 0.00290400 | ||||||||
\(297\) | −2.16247 | −0.125479 | ||||||||
\(298\) | 6.79281 | 0.393497 | ||||||||
\(299\) | 1.03993 | 0.0601405 | ||||||||
\(300\) | 20.5035 | 1.18377 | ||||||||
\(301\) | 1.16868 | 0.0673615 | ||||||||
\(302\) | 11.0004 | 0.633001 | ||||||||
\(303\) | 0.218576 | 0.0125569 | ||||||||
\(304\) | −19.9066 | −1.14172 | ||||||||
\(305\) | −0.563549 | −0.0322687 | ||||||||
\(306\) | 35.4743 | 2.02793 | ||||||||
\(307\) | −26.1496 | −1.49243 | −0.746217 | − | 0.665702i | \(-0.768132\pi\) | ||||
−0.746217 | + | 0.665702i | \(0.768132\pi\) | |||||||
\(308\) | 1.87543 | 0.106863 | ||||||||
\(309\) | −6.42375 | −0.365434 | ||||||||
\(310\) | −14.9476 | −0.848965 | ||||||||
\(311\) | 10.0184 | 0.568091 | 0.284046 | − | 0.958811i | \(-0.408323\pi\) | ||||
0.284046 | + | 0.958811i | \(0.408323\pi\) | |||||||
\(312\) | −0.0890505 | −0.00504149 | ||||||||
\(313\) | −6.92225 | −0.391269 | −0.195634 | − | 0.980677i | \(-0.562677\pi\) | ||||
−0.195634 | + | 0.980677i | \(0.562677\pi\) | |||||||
\(314\) | −0.843398 | −0.0475957 | ||||||||
\(315\) | 0.880808 | 0.0496279 | ||||||||
\(316\) | −2.77826 | −0.156289 | ||||||||
\(317\) | −13.7542 | −0.772511 | −0.386255 | − | 0.922392i | \(-0.626232\pi\) | ||||
−0.386255 | + | 0.922392i | \(0.626232\pi\) | |||||||
\(318\) | 60.2498 | 3.37864 | ||||||||
\(319\) | 2.21191 | 0.123843 | ||||||||
\(320\) | 6.05642 | 0.338564 | ||||||||
\(321\) | 19.4626 | 1.08630 | ||||||||
\(322\) | 1.20962 | 0.0674095 | ||||||||
\(323\) | −33.9642 | −1.88982 | ||||||||
\(324\) | −19.9346 | −1.10748 | ||||||||
\(325\) | −3.31895 | −0.184102 | ||||||||
\(326\) | −12.5807 | −0.696779 | ||||||||
\(327\) | 2.36120 | 0.130575 | ||||||||
\(328\) | 0.536966 | 0.0296490 | ||||||||
\(329\) | −1.20217 | −0.0662780 | ||||||||
\(330\) | 7.88355 | 0.433975 | ||||||||
\(331\) | 32.3758 | 1.77954 | 0.889768 | − | 0.456414i | \(-0.150866\pi\) | ||||
0.889768 | + | 0.456414i | \(0.150866\pi\) | |||||||
\(332\) | 25.7834 | 1.41505 | ||||||||
\(333\) | 2.57527 | 0.141124 | ||||||||
\(334\) | 15.6928 | 0.858670 | ||||||||
\(335\) | 4.80375 | 0.262457 | ||||||||
\(336\) | −4.21090 | −0.229723 | ||||||||
\(337\) | 3.48271 | 0.189715 | 0.0948576 | − | 0.995491i | \(-0.469760\pi\) | ||||
0.0948576 | + | 0.995491i | \(0.469760\pi\) | |||||||
\(338\) | 24.7824 | 1.34799 | ||||||||
\(339\) | 14.0948 | 0.765526 | ||||||||
\(340\) | 10.5973 | 0.574721 | ||||||||
\(341\) | 20.8159 | 1.12724 | ||||||||
\(342\) | −25.2397 | −1.36481 | ||||||||
\(343\) | 6.08010 | 0.328295 | ||||||||
\(344\) | −0.132586 | −0.00714855 | ||||||||
\(345\) | 2.52634 | 0.136014 | ||||||||
\(346\) | 35.7783 | 1.92345 | ||||||||
\(347\) | 22.6438 | 1.21559 | 0.607793 | − | 0.794096i | \(-0.292055\pi\) | ||||
0.607793 | + | 0.794096i | \(0.292055\pi\) | |||||||
\(348\) | 4.78352 | 0.256424 | ||||||||
\(349\) | 21.1651 | 1.13294 | 0.566471 | − | 0.824082i | \(-0.308308\pi\) | ||||
0.566471 | + | 0.824082i | \(0.308308\pi\) | |||||||
\(350\) | −3.86053 | −0.206354 | ||||||||
\(351\) | 0.757015 | 0.0404065 | ||||||||
\(352\) | −17.1935 | −0.916415 | ||||||||
\(353\) | 9.18330 | 0.488777 | 0.244389 | − | 0.969677i | \(-0.421413\pi\) | ||||
0.244389 | + | 0.969677i | \(0.421413\pi\) | |||||||
\(354\) | −49.8825 | −2.65123 | ||||||||
\(355\) | 2.73003 | 0.144895 | ||||||||
\(356\) | −14.5730 | −0.772366 | ||||||||
\(357\) | −7.18455 | −0.380247 | ||||||||
\(358\) | 52.8918 | 2.79542 | ||||||||
\(359\) | −18.5426 | −0.978641 | −0.489320 | − | 0.872104i | \(-0.662755\pi\) | ||||
−0.489320 | + | 0.872104i | \(0.662755\pi\) | |||||||
\(360\) | −0.0999270 | −0.00526661 | ||||||||
\(361\) | 5.16532 | 0.271859 | ||||||||
\(362\) | 35.5150 | 1.86663 | ||||||||
\(363\) | 14.9946 | 0.787014 | ||||||||
\(364\) | −0.656532 | −0.0344116 | ||||||||
\(365\) | 12.5822 | 0.658581 | ||||||||
\(366\) | 3.41596 | 0.178555 | ||||||||
\(367\) | 6.60638 | 0.344850 | 0.172425 | − | 0.985023i | \(-0.444840\pi\) | ||||
0.172425 | + | 0.985023i | \(0.444840\pi\) | |||||||
\(368\) | −5.57883 | −0.290816 | ||||||||
\(369\) | 27.6775 | 1.44083 | ||||||||
\(370\) | 1.54840 | 0.0804973 | ||||||||
\(371\) | −5.63636 | −0.292625 | ||||||||
\(372\) | 45.0169 | 2.33402 | ||||||||
\(373\) | −21.1469 | −1.09494 | −0.547471 | − | 0.836824i | \(-0.684409\pi\) | ||||
−0.547471 | + | 0.836824i | \(0.684409\pi\) | |||||||
\(374\) | −29.7028 | −1.53589 | ||||||||
\(375\) | −17.2318 | −0.889848 | ||||||||
\(376\) | 0.136386 | 0.00703356 | ||||||||
\(377\) | −0.774322 | −0.0398796 | ||||||||
\(378\) | 0.880543 | 0.0452902 | ||||||||
\(379\) | −36.6965 | −1.88497 | −0.942486 | − | 0.334247i | \(-0.891518\pi\) | ||||
−0.942486 | + | 0.334247i | \(0.891518\pi\) | |||||||
\(380\) | −7.53993 | −0.386790 | ||||||||
\(381\) | 36.9626 | 1.89365 | ||||||||
\(382\) | 32.5710 | 1.66648 | ||||||||
\(383\) | 17.2626 | 0.882076 | 0.441038 | − | 0.897488i | \(-0.354610\pi\) | ||||
0.441038 | + | 0.897488i | \(0.354610\pi\) | |||||||
\(384\) | 0.943695 | 0.0481577 | ||||||||
\(385\) | −0.737505 | −0.0375867 | ||||||||
\(386\) | −9.45327 | −0.481159 | ||||||||
\(387\) | −6.83404 | −0.347394 | ||||||||
\(388\) | −6.55478 | −0.332769 | ||||||||
\(389\) | 24.7114 | 1.25292 | 0.626459 | − | 0.779455i | \(-0.284504\pi\) | ||||
0.626459 | + | 0.779455i | \(0.284504\pi\) | |||||||
\(390\) | −2.75979 | −0.139747 | ||||||||
\(391\) | −9.51848 | −0.481370 | ||||||||
\(392\) | −0.340046 | −0.0171749 | ||||||||
\(393\) | 15.2467 | 0.769094 | ||||||||
\(394\) | −22.0853 | −1.11264 | ||||||||
\(395\) | 1.09254 | 0.0549715 | ||||||||
\(396\) | −10.9669 | −0.551107 | ||||||||
\(397\) | −8.98396 | −0.450892 | −0.225446 | − | 0.974256i | \(-0.572384\pi\) | ||||
−0.225446 | + | 0.974256i | \(0.572384\pi\) | |||||||
\(398\) | 45.9093 | 2.30123 | ||||||||
\(399\) | 5.11176 | 0.255908 | ||||||||
\(400\) | 17.8050 | 0.890248 | ||||||||
\(401\) | −30.9343 | −1.54478 | −0.772392 | − | 0.635147i | \(-0.780940\pi\) | ||||
−0.772392 | + | 0.635147i | \(0.780940\pi\) | |||||||
\(402\) | −29.1180 | −1.45227 | ||||||||
\(403\) | −7.28701 | −0.362992 | ||||||||
\(404\) | −0.182820 | −0.00909563 | ||||||||
\(405\) | 7.83919 | 0.389532 | ||||||||
\(406\) | −0.900673 | −0.0446997 | ||||||||
\(407\) | −2.15629 | −0.106883 | ||||||||
\(408\) | 0.815082 | 0.0403526 | ||||||||
\(409\) | 7.61058 | 0.376319 | 0.188160 | − | 0.982138i | \(-0.439748\pi\) | ||||
0.188160 | + | 0.982138i | \(0.439748\pi\) | |||||||
\(410\) | 16.6413 | 0.821854 | ||||||||
\(411\) | −28.6514 | −1.41327 | ||||||||
\(412\) | 5.37291 | 0.264704 | ||||||||
\(413\) | 4.66650 | 0.229624 | ||||||||
\(414\) | −7.07344 | −0.347641 | ||||||||
\(415\) | −10.1392 | −0.497714 | ||||||||
\(416\) | 6.01891 | 0.295101 | ||||||||
\(417\) | −17.5371 | −0.858797 | ||||||||
\(418\) | 21.1333 | 1.03367 | ||||||||
\(419\) | 20.5172 | 1.00233 | 0.501165 | − | 0.865352i | \(-0.332905\pi\) | ||||
0.501165 | + | 0.865352i | \(0.332905\pi\) | |||||||
\(420\) | −1.59494 | −0.0778252 | ||||||||
\(421\) | −24.1604 | −1.17750 | −0.588752 | − | 0.808313i | \(-0.700381\pi\) | ||||
−0.588752 | + | 0.808313i | \(0.700381\pi\) | |||||||
\(422\) | −56.2794 | −2.73964 | ||||||||
\(423\) | 7.02990 | 0.341806 | ||||||||
\(424\) | 0.639440 | 0.0310540 | ||||||||
\(425\) | 30.3785 | 1.47357 | ||||||||
\(426\) | −16.5481 | −0.801759 | ||||||||
\(427\) | −0.319562 | −0.0154647 | ||||||||
\(428\) | −16.2788 | −0.786866 | ||||||||
\(429\) | 3.84326 | 0.185555 | ||||||||
\(430\) | −4.10900 | −0.198154 | ||||||||
\(431\) | 19.8449 | 0.955894 | 0.477947 | − | 0.878389i | \(-0.341381\pi\) | ||||
0.477947 | + | 0.878389i | \(0.341381\pi\) | |||||||
\(432\) | −4.06111 | −0.195390 | ||||||||
\(433\) | 24.9681 | 1.19989 | 0.599945 | − | 0.800041i | \(-0.295189\pi\) | ||||
0.599945 | + | 0.800041i | \(0.295189\pi\) | |||||||
\(434\) | −8.47608 | −0.406865 | ||||||||
\(435\) | −1.88110 | −0.0901916 | ||||||||
\(436\) | −1.97494 | −0.0945825 | ||||||||
\(437\) | 6.77234 | 0.323965 | ||||||||
\(438\) | −76.2670 | −3.64418 | ||||||||
\(439\) | 20.1791 | 0.963097 | 0.481548 | − | 0.876419i | \(-0.340075\pi\) | ||||
0.481548 | + | 0.876419i | \(0.340075\pi\) | |||||||
\(440\) | 0.0836693 | 0.00398878 | ||||||||
\(441\) | −17.5274 | −0.834640 | ||||||||
\(442\) | 10.3980 | 0.494584 | ||||||||
\(443\) | 17.1936 | 0.816893 | 0.408446 | − | 0.912782i | \(-0.366071\pi\) | ||||
0.408446 | + | 0.912782i | \(0.366071\pi\) | |||||||
\(444\) | −4.66323 | −0.221307 | ||||||||
\(445\) | 5.73074 | 0.271663 | ||||||||
\(446\) | −43.7567 | −2.07194 | ||||||||
\(447\) | 8.04484 | 0.380508 | ||||||||
\(448\) | 3.43431 | 0.162256 | ||||||||
\(449\) | −9.74972 | −0.460118 | −0.230059 | − | 0.973177i | \(-0.573892\pi\) | ||||
−0.230059 | + | 0.973177i | \(0.573892\pi\) | |||||||
\(450\) | 22.5751 | 1.06420 | ||||||||
\(451\) | −23.1745 | −1.09125 | ||||||||
\(452\) | −11.7891 | −0.554513 | ||||||||
\(453\) | 13.0279 | 0.612106 | ||||||||
\(454\) | −16.1554 | −0.758208 | ||||||||
\(455\) | 0.258178 | 0.0121036 | ||||||||
\(456\) | −0.579925 | −0.0271575 | ||||||||
\(457\) | 16.3041 | 0.762672 | 0.381336 | − | 0.924436i | \(-0.375464\pi\) | ||||
0.381336 | + | 0.924436i | \(0.375464\pi\) | |||||||
\(458\) | 33.9824 | 1.58789 | ||||||||
\(459\) | −6.92898 | −0.323417 | ||||||||
\(460\) | −2.11307 | −0.0985223 | ||||||||
\(461\) | −17.8277 | −0.830319 | −0.415160 | − | 0.909749i | \(-0.636274\pi\) | ||||
−0.415160 | + | 0.909749i | \(0.636274\pi\) | |||||||
\(462\) | 4.47040 | 0.207982 | ||||||||
\(463\) | 26.6964 | 1.24069 | 0.620344 | − | 0.784330i | \(-0.286993\pi\) | ||||
0.620344 | + | 0.784330i | \(0.286993\pi\) | |||||||
\(464\) | 4.15395 | 0.192842 | ||||||||
\(465\) | −17.7027 | −0.820941 | ||||||||
\(466\) | −46.4829 | −2.15328 | ||||||||
\(467\) | −20.3136 | −0.940003 | −0.470002 | − | 0.882666i | \(-0.655747\pi\) | ||||
−0.470002 | + | 0.882666i | \(0.655747\pi\) | |||||||
\(468\) | 3.83917 | 0.177466 | ||||||||
\(469\) | 2.72398 | 0.125782 | ||||||||
\(470\) | 4.22677 | 0.194966 | ||||||||
\(471\) | −0.998850 | −0.0460246 | ||||||||
\(472\) | −0.529411 | −0.0243681 | ||||||||
\(473\) | 5.72217 | 0.263106 | ||||||||
\(474\) | −6.62243 | −0.304178 | ||||||||
\(475\) | −21.6141 | −0.991722 | ||||||||
\(476\) | 6.00925 | 0.275434 | ||||||||
\(477\) | 32.9595 | 1.50911 | ||||||||
\(478\) | −23.8027 | −1.08871 | ||||||||
\(479\) | 21.1669 | 0.967142 | 0.483571 | − | 0.875305i | \(-0.339339\pi\) | ||||
0.483571 | + | 0.875305i | \(0.339339\pi\) | |||||||
\(480\) | 14.6220 | 0.667400 | ||||||||
\(481\) | 0.754850 | 0.0344182 | ||||||||
\(482\) | −18.6972 | −0.851632 | ||||||||
\(483\) | 1.43257 | 0.0651843 | ||||||||
\(484\) | −12.5417 | −0.570078 | ||||||||
\(485\) | 2.57763 | 0.117044 | ||||||||
\(486\) | −41.5191 | −1.88334 | ||||||||
\(487\) | 22.1990 | 1.00593 | 0.502967 | − | 0.864306i | \(-0.332242\pi\) | ||||
0.502967 | + | 0.864306i | \(0.332242\pi\) | |||||||
\(488\) | 0.0362541 | 0.00164115 | ||||||||
\(489\) | −14.8995 | −0.673779 | ||||||||
\(490\) | −10.5385 | −0.476080 | ||||||||
\(491\) | 12.0377 | 0.543252 | 0.271626 | − | 0.962403i | \(-0.412439\pi\) | ||||
0.271626 | + | 0.962403i | \(0.412439\pi\) | |||||||
\(492\) | −50.1177 | −2.25948 | ||||||||
\(493\) | 7.08739 | 0.319200 | ||||||||
\(494\) | −7.39813 | −0.332858 | ||||||||
\(495\) | 4.31267 | 0.193840 | ||||||||
\(496\) | 39.0921 | 1.75529 | ||||||||
\(497\) | 1.54807 | 0.0694405 | ||||||||
\(498\) | 61.4589 | 2.75404 | ||||||||
\(499\) | 8.63006 | 0.386334 | 0.193167 | − | 0.981166i | \(-0.438124\pi\) | ||||
0.193167 | + | 0.981166i | \(0.438124\pi\) | |||||||
\(500\) | 14.4129 | 0.644566 | ||||||||
\(501\) | 18.5852 | 0.830325 | ||||||||
\(502\) | −33.5422 | −1.49706 | ||||||||
\(503\) | 11.8352 | 0.527704 | 0.263852 | − | 0.964563i | \(-0.415007\pi\) | ||||
0.263852 | + | 0.964563i | \(0.415007\pi\) | |||||||
\(504\) | −0.0566640 | −0.00252401 | ||||||||
\(505\) | 0.0718930 | 0.00319919 | ||||||||
\(506\) | 5.92263 | 0.263293 | ||||||||
\(507\) | 29.3502 | 1.30349 | ||||||||
\(508\) | −30.9160 | −1.37168 | ||||||||
\(509\) | 20.6534 | 0.915446 | 0.457723 | − | 0.889095i | \(-0.348665\pi\) | ||||
0.457723 | + | 0.889095i | \(0.348665\pi\) | |||||||
\(510\) | 25.2604 | 1.11855 | ||||||||
\(511\) | 7.13477 | 0.315623 | ||||||||
\(512\) | −31.8846 | −1.40911 | ||||||||
\(513\) | 4.92992 | 0.217661 | ||||||||
\(514\) | −8.18582 | −0.361061 | ||||||||
\(515\) | −2.11287 | −0.0931041 | ||||||||
\(516\) | 12.3749 | 0.544774 | ||||||||
\(517\) | −5.88617 | −0.258874 | ||||||||
\(518\) | 0.878024 | 0.0385782 | ||||||||
\(519\) | 42.3728 | 1.85996 | ||||||||
\(520\) | −0.0292901 | −0.00128445 | ||||||||
\(521\) | −21.0988 | −0.924355 | −0.462178 | − | 0.886787i | \(-0.652932\pi\) | ||||
−0.462178 | + | 0.886787i | \(0.652932\pi\) | |||||||
\(522\) | 5.26683 | 0.230523 | ||||||||
\(523\) | 38.8319 | 1.69800 | 0.849000 | − | 0.528393i | \(-0.177205\pi\) | ||||
0.849000 | + | 0.528393i | \(0.177205\pi\) | |||||||
\(524\) | −12.7525 | −0.557097 | ||||||||
\(525\) | −4.57209 | −0.199542 | ||||||||
\(526\) | −37.1606 | −1.62028 | ||||||||
\(527\) | 66.6982 | 2.90542 | ||||||||
\(528\) | −20.6177 | −0.897270 | ||||||||
\(529\) | −21.1020 | −0.917480 | ||||||||
\(530\) | 19.8171 | 0.860799 | ||||||||
\(531\) | −27.2881 | −1.18420 | ||||||||
\(532\) | −4.27554 | −0.185368 | ||||||||
\(533\) | 8.11269 | 0.351399 | ||||||||
\(534\) | −34.7370 | −1.50322 | ||||||||
\(535\) | 6.40156 | 0.276763 | ||||||||
\(536\) | −0.309034 | −0.0133482 | ||||||||
\(537\) | 62.6406 | 2.70314 | ||||||||
\(538\) | 28.0369 | 1.20876 | ||||||||
\(539\) | 14.6758 | 0.632132 | ||||||||
\(540\) | −1.53821 | −0.0661939 | ||||||||
\(541\) | −16.5642 | −0.712152 | −0.356076 | − | 0.934457i | \(-0.615886\pi\) | ||||
−0.356076 | + | 0.934457i | \(0.615886\pi\) | |||||||
\(542\) | −39.9761 | −1.71712 | ||||||||
\(543\) | 42.0610 | 1.80501 | ||||||||
\(544\) | −55.0912 | −2.36202 | ||||||||
\(545\) | 0.776635 | 0.0332674 | ||||||||
\(546\) | −1.56495 | −0.0669736 | ||||||||
\(547\) | −23.1140 | −0.988285 | −0.494142 | − | 0.869381i | \(-0.664518\pi\) | ||||
−0.494142 | + | 0.869381i | \(0.664518\pi\) | |||||||
\(548\) | 23.9644 | 1.02371 | ||||||||
\(549\) | 1.86869 | 0.0797538 | ||||||||
\(550\) | −18.9022 | −0.805993 | ||||||||
\(551\) | −5.04263 | −0.214823 | ||||||||
\(552\) | −0.162524 | −0.00691749 | ||||||||
\(553\) | 0.619527 | 0.0263450 | ||||||||
\(554\) | 50.2950 | 2.13683 | ||||||||
\(555\) | 1.83379 | 0.0778401 | ||||||||
\(556\) | 14.6683 | 0.622074 | ||||||||
\(557\) | 8.07281 | 0.342056 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(558\) | 49.5652 | 2.09826 | ||||||||
\(559\) | −2.00316 | −0.0847244 | ||||||||
\(560\) | −1.38503 | −0.0585281 | ||||||||
\(561\) | −35.1775 | −1.48520 | ||||||||
\(562\) | −30.1907 | −1.27352 | ||||||||
\(563\) | 7.07105 | 0.298009 | 0.149005 | − | 0.988836i | \(-0.452393\pi\) | ||||
0.149005 | + | 0.988836i | \(0.452393\pi\) | |||||||
\(564\) | −12.7296 | −0.536011 | ||||||||
\(565\) | 4.63600 | 0.195038 | ||||||||
\(566\) | −20.0261 | −0.841761 | ||||||||
\(567\) | 4.44524 | 0.186683 | ||||||||
\(568\) | −0.175628 | −0.00736917 | ||||||||
\(569\) | −22.3535 | −0.937109 | −0.468555 | − | 0.883435i | \(-0.655225\pi\) | ||||
−0.468555 | + | 0.883435i | \(0.655225\pi\) | |||||||
\(570\) | −17.9726 | −0.752790 | ||||||||
\(571\) | 10.9032 | 0.456285 | 0.228142 | − | 0.973628i | \(-0.426735\pi\) | ||||
0.228142 | + | 0.973628i | \(0.426735\pi\) | |||||||
\(572\) | −3.21456 | −0.134407 | ||||||||
\(573\) | 38.5743 | 1.61147 | ||||||||
\(574\) | 9.43649 | 0.393872 | ||||||||
\(575\) | −6.05735 | −0.252609 | ||||||||
\(576\) | −20.0827 | −0.836779 | ||||||||
\(577\) | 17.6921 | 0.736532 | 0.368266 | − | 0.929720i | \(-0.379952\pi\) | ||||
0.368266 | + | 0.929720i | \(0.379952\pi\) | |||||||
\(578\) | −61.2801 | −2.54892 | ||||||||
\(579\) | −11.1957 | −0.465276 | ||||||||
\(580\) | 1.57337 | 0.0653308 | ||||||||
\(581\) | −5.74947 | −0.238528 | ||||||||
\(582\) | −15.6244 | −0.647651 | ||||||||
\(583\) | −27.5971 | −1.14296 | ||||||||
\(584\) | −0.809434 | −0.0334946 | ||||||||
\(585\) | −1.50973 | −0.0624198 | ||||||||
\(586\) | 18.8094 | 0.777011 | ||||||||
\(587\) | 40.8074 | 1.68430 | 0.842151 | − | 0.539243i | \(-0.181289\pi\) | ||||
0.842151 | + | 0.539243i | \(0.181289\pi\) | |||||||
\(588\) | 31.7382 | 1.30886 | ||||||||
\(589\) | −47.4553 | −1.95536 | ||||||||
\(590\) | −16.4071 | −0.675471 | ||||||||
\(591\) | −26.1559 | −1.07591 | ||||||||
\(592\) | −4.04949 | −0.166433 | ||||||||
\(593\) | −32.7953 | −1.34674 | −0.673371 | − | 0.739305i | \(-0.735154\pi\) | ||||
−0.673371 | + | 0.739305i | \(0.735154\pi\) | |||||||
\(594\) | 4.31138 | 0.176898 | ||||||||
\(595\) | −2.36311 | −0.0968779 | ||||||||
\(596\) | −6.72881 | −0.275623 | ||||||||
\(597\) | 54.3711 | 2.22526 | ||||||||
\(598\) | −2.07333 | −0.0847847 | ||||||||
\(599\) | 43.8619 | 1.79215 | 0.896075 | − | 0.443902i | \(-0.146406\pi\) | ||||
0.896075 | + | 0.443902i | \(0.146406\pi\) | |||||||
\(600\) | 0.518700 | 0.0211758 | ||||||||
\(601\) | −7.04820 | −0.287502 | −0.143751 | − | 0.989614i | \(-0.545916\pi\) | ||||
−0.143751 | + | 0.989614i | \(0.545916\pi\) | |||||||
\(602\) | −2.33002 | −0.0949647 | ||||||||
\(603\) | −15.9289 | −0.648676 | ||||||||
\(604\) | −10.8967 | −0.443382 | ||||||||
\(605\) | 4.93196 | 0.200513 | ||||||||
\(606\) | −0.435780 | −0.0177024 | ||||||||
\(607\) | 6.75581 | 0.274210 | 0.137105 | − | 0.990557i | \(-0.456220\pi\) | ||||
0.137105 | + | 0.990557i | \(0.456220\pi\) | |||||||
\(608\) | 39.1971 | 1.58965 | ||||||||
\(609\) | −1.06668 | −0.0432241 | ||||||||
\(610\) | 1.12356 | 0.0454916 | ||||||||
\(611\) | 2.06057 | 0.0833616 | ||||||||
\(612\) | −35.1400 | −1.42045 | ||||||||
\(613\) | 44.1438 | 1.78295 | 0.891476 | − | 0.453068i | \(-0.149671\pi\) | ||||
0.891476 | + | 0.453068i | \(0.149671\pi\) | |||||||
\(614\) | 52.1351 | 2.10400 | ||||||||
\(615\) | 19.7085 | 0.794724 | ||||||||
\(616\) | 0.0474450 | 0.00191161 | ||||||||
\(617\) | 34.8816 | 1.40428 | 0.702140 | − | 0.712039i | \(-0.252228\pi\) | ||||
0.702140 | + | 0.712039i | \(0.252228\pi\) | |||||||
\(618\) | 12.8072 | 0.515181 | ||||||||
\(619\) | −13.0627 | −0.525035 | −0.262517 | − | 0.964927i | \(-0.584553\pi\) | ||||
−0.262517 | + | 0.964927i | \(0.584553\pi\) | |||||||
\(620\) | 14.8067 | 0.594653 | ||||||||
\(621\) | 1.38161 | 0.0554422 | ||||||||
\(622\) | −19.9739 | −0.800882 | ||||||||
\(623\) | 3.24964 | 0.130194 | ||||||||
\(624\) | 7.21762 | 0.288936 | ||||||||
\(625\) | 16.3164 | 0.652655 | ||||||||
\(626\) | 13.8011 | 0.551601 | ||||||||
\(627\) | 25.0286 | 0.999545 | ||||||||
\(628\) | 0.835452 | 0.0333382 | ||||||||
\(629\) | −6.90916 | −0.275486 | ||||||||
\(630\) | −1.75609 | −0.0699643 | ||||||||
\(631\) | 1.60229 | 0.0637860 | 0.0318930 | − | 0.999491i | \(-0.489846\pi\) | ||||
0.0318930 | + | 0.999491i | \(0.489846\pi\) | |||||||
\(632\) | −0.0702849 | −0.00279578 | ||||||||
\(633\) | −66.6526 | −2.64920 | ||||||||
\(634\) | 27.4220 | 1.08907 | ||||||||
\(635\) | 12.1576 | 0.482459 | ||||||||
\(636\) | −59.6821 | −2.36655 | ||||||||
\(637\) | −5.13755 | −0.203557 | ||||||||
\(638\) | −4.40994 | −0.174591 | ||||||||
\(639\) | −9.05260 | −0.358115 | ||||||||
\(640\) | 0.310396 | 0.0122695 | ||||||||
\(641\) | 4.22897 | 0.167034 | 0.0835171 | − | 0.996506i | \(-0.473385\pi\) | ||||
0.0835171 | + | 0.996506i | \(0.473385\pi\) | |||||||
\(642\) | −38.8031 | −1.53144 | ||||||||
\(643\) | −28.7384 | −1.13333 | −0.566666 | − | 0.823948i | \(-0.691767\pi\) | ||||
−0.566666 | + | 0.823948i | \(0.691767\pi\) | |||||||
\(644\) | −1.19822 | −0.0472166 | ||||||||
\(645\) | −4.86636 | −0.191613 | ||||||||
\(646\) | 67.7153 | 2.66422 | ||||||||
\(647\) | 8.66230 | 0.340550 | 0.170275 | − | 0.985397i | \(-0.445534\pi\) | ||||
0.170275 | + | 0.985397i | \(0.445534\pi\) | |||||||
\(648\) | −0.504309 | −0.0198111 | ||||||||
\(649\) | 22.8485 | 0.896880 | ||||||||
\(650\) | 6.61708 | 0.259543 | ||||||||
\(651\) | −10.0384 | −0.393434 | ||||||||
\(652\) | 12.4621 | 0.488055 | ||||||||
\(653\) | −5.37806 | −0.210460 | −0.105230 | − | 0.994448i | \(-0.533558\pi\) | ||||
−0.105230 | + | 0.994448i | \(0.533558\pi\) | |||||||
\(654\) | −4.70759 | −0.184081 | ||||||||
\(655\) | 5.01487 | 0.195947 | ||||||||
\(656\) | −43.5216 | −1.69923 | ||||||||
\(657\) | −41.7217 | −1.62772 | ||||||||
\(658\) | 2.39681 | 0.0934372 | ||||||||
\(659\) | −4.04480 | −0.157563 | −0.0787815 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787815 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(660\) | −7.80927 | −0.303975 | ||||||||
\(661\) | −5.41315 | −0.210547 | −0.105274 | − | 0.994443i | \(-0.533572\pi\) | ||||
−0.105274 | + | 0.994443i | \(0.533572\pi\) | |||||||
\(662\) | −64.5485 | −2.50875 | ||||||||
\(663\) | 12.3146 | 0.478258 | ||||||||
\(664\) | 0.652273 | 0.0253131 | ||||||||
\(665\) | 1.68134 | 0.0651994 | ||||||||
\(666\) | −5.13438 | −0.198953 | ||||||||
\(667\) | −1.41320 | −0.0547193 | ||||||||
\(668\) | −15.5449 | −0.601451 | ||||||||
\(669\) | −51.8217 | −2.00354 | ||||||||
\(670\) | −9.57736 | −0.370006 | ||||||||
\(671\) | −1.56466 | −0.0604032 | ||||||||
\(672\) | 8.29147 | 0.319850 | ||||||||
\(673\) | 11.1253 | 0.428847 | 0.214424 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214424 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(674\) | −6.94356 | −0.267456 | ||||||||
\(675\) | −4.40945 | −0.169720 | ||||||||
\(676\) | −24.5489 | −0.944189 | ||||||||
\(677\) | −0.999958 | −0.0384315 | −0.0192158 | − | 0.999815i | \(-0.506117\pi\) | ||||
−0.0192158 | + | 0.999815i | \(0.506117\pi\) | |||||||
\(678\) | −28.1012 | −1.07922 | ||||||||
\(679\) | 1.46166 | 0.0560932 | ||||||||
\(680\) | 0.268093 | 0.0102809 | ||||||||
\(681\) | −19.1330 | −0.733180 | ||||||||
\(682\) | −41.5012 | −1.58916 | ||||||||
\(683\) | −20.4639 | −0.783029 | −0.391515 | − | 0.920172i | \(-0.628049\pi\) | ||||
−0.391515 | + | 0.920172i | \(0.628049\pi\) | |||||||
\(684\) | 25.0019 | 0.955972 | ||||||||
\(685\) | −9.42387 | −0.360068 | ||||||||
\(686\) | −12.1220 | −0.462822 | ||||||||
\(687\) | 40.2459 | 1.53548 | ||||||||
\(688\) | 10.7462 | 0.409695 | ||||||||
\(689\) | 9.66091 | 0.368051 | ||||||||
\(690\) | −5.03683 | −0.191749 | ||||||||
\(691\) | 9.06320 | 0.344780 | 0.172390 | − | 0.985029i | \(-0.444851\pi\) | ||||
0.172390 | + | 0.985029i | \(0.444851\pi\) | |||||||
\(692\) | −35.4412 | −1.34727 | ||||||||
\(693\) | 2.44552 | 0.0928976 | ||||||||
\(694\) | −45.1456 | −1.71370 | ||||||||
\(695\) | −5.76823 | −0.218801 | ||||||||
\(696\) | 0.121014 | 0.00458703 | ||||||||
\(697\) | −74.2556 | −2.81263 | ||||||||
\(698\) | −42.1974 | −1.59719 | ||||||||
\(699\) | −55.0505 | −2.08220 | ||||||||
\(700\) | 3.82416 | 0.144540 | ||||||||
\(701\) | −6.20654 | −0.234418 | −0.117209 | − | 0.993107i | \(-0.537395\pi\) | ||||
−0.117209 | + | 0.993107i | \(0.537395\pi\) | |||||||
\(702\) | −1.50928 | −0.0569641 | ||||||||
\(703\) | 4.91582 | 0.185404 | ||||||||
\(704\) | 16.8153 | 0.633752 | ||||||||
\(705\) | 5.00583 | 0.188531 | ||||||||
\(706\) | −18.3090 | −0.689067 | ||||||||
\(707\) | 0.0407672 | 0.00153321 | ||||||||
\(708\) | 49.4125 | 1.85704 | ||||||||
\(709\) | −37.1234 | −1.39420 | −0.697099 | − | 0.716975i | \(-0.745526\pi\) | ||||
−0.697099 | + | 0.716975i | \(0.745526\pi\) | |||||||
\(710\) | −5.44292 | −0.204269 | ||||||||
\(711\) | −3.62278 | −0.135865 | ||||||||
\(712\) | −0.368669 | −0.0138165 | ||||||||
\(713\) | −13.2994 | −0.498065 | ||||||||
\(714\) | 14.3240 | 0.536063 | ||||||||
\(715\) | 1.26411 | 0.0472749 | ||||||||
\(716\) | −52.3934 | −1.95803 | ||||||||
\(717\) | −28.1900 | −1.05277 | ||||||||
\(718\) | 36.9688 | 1.37967 | ||||||||
\(719\) | −31.2727 | −1.16628 | −0.583138 | − | 0.812373i | \(-0.698175\pi\) | ||||
−0.583138 | + | 0.812373i | \(0.698175\pi\) | |||||||
\(720\) | 8.09917 | 0.301838 | ||||||||
\(721\) | −1.19811 | −0.0446199 | ||||||||
\(722\) | −10.2982 | −0.383261 | ||||||||
\(723\) | −22.1434 | −0.823520 | ||||||||
\(724\) | −35.1803 | −1.30747 | ||||||||
\(725\) | 4.51026 | 0.167507 | ||||||||
\(726\) | −29.8952 | −1.10951 | ||||||||
\(727\) | −12.3318 | −0.457363 | −0.228681 | − | 0.973501i | \(-0.573441\pi\) | ||||
−0.228681 | + | 0.973501i | \(0.573441\pi\) | |||||||
\(728\) | −0.0166090 | −0.000615572 0 | ||||||||
\(729\) | −18.8903 | −0.699642 | ||||||||
\(730\) | −25.0854 | −0.928452 | ||||||||
\(731\) | 18.3349 | 0.678142 | ||||||||
\(732\) | −3.38377 | −0.125068 | ||||||||
\(733\) | 24.8155 | 0.916582 | 0.458291 | − | 0.888802i | \(-0.348462\pi\) | ||||
0.458291 | + | 0.888802i | \(0.348462\pi\) | |||||||
\(734\) | −13.1713 | −0.486161 | ||||||||
\(735\) | −12.4809 | −0.460364 | ||||||||
\(736\) | 10.9850 | 0.404912 | ||||||||
\(737\) | 13.3374 | 0.491288 | ||||||||
\(738\) | −55.1814 | −2.03125 | ||||||||
\(739\) | −28.7903 | −1.05907 | −0.529534 | − | 0.848288i | \(-0.677633\pi\) | ||||
−0.529534 | + | 0.848288i | \(0.677633\pi\) | |||||||
\(740\) | −1.53381 | −0.0563839 | ||||||||
\(741\) | −8.76173 | −0.321870 | ||||||||
\(742\) | 11.2373 | 0.412536 | ||||||||
\(743\) | 30.3143 | 1.11213 | 0.556063 | − | 0.831140i | \(-0.312311\pi\) | ||||
0.556063 | + | 0.831140i | \(0.312311\pi\) | |||||||
\(744\) | 1.13884 | 0.0417521 | ||||||||
\(745\) | 2.64607 | 0.0969444 | ||||||||
\(746\) | 42.1610 | 1.54362 | ||||||||
\(747\) | 33.6209 | 1.23013 | ||||||||
\(748\) | 29.4229 | 1.07581 | ||||||||
\(749\) | 3.63003 | 0.132638 | ||||||||
\(750\) | 34.3556 | 1.25449 | ||||||||
\(751\) | −34.1201 | −1.24506 | −0.622531 | − | 0.782595i | \(-0.713896\pi\) | ||||
−0.622531 | + | 0.782595i | \(0.713896\pi\) | |||||||
\(752\) | −11.0542 | −0.403105 | ||||||||
\(753\) | −39.7246 | −1.44764 | ||||||||
\(754\) | 1.54378 | 0.0562213 | ||||||||
\(755\) | 4.28509 | 0.155950 | ||||||||
\(756\) | −0.872246 | −0.0317233 | ||||||||
\(757\) | −20.7545 | −0.754334 | −0.377167 | − | 0.926145i | \(-0.623102\pi\) | ||||
−0.377167 | + | 0.926145i | \(0.623102\pi\) | |||||||
\(758\) | 73.1627 | 2.65739 | ||||||||
\(759\) | 7.01426 | 0.254602 | ||||||||
\(760\) | −0.190746 | −0.00691909 | ||||||||
\(761\) | 38.9968 | 1.41363 | 0.706816 | − | 0.707398i | \(-0.250131\pi\) | ||||
0.706816 | + | 0.707398i | \(0.250131\pi\) | |||||||
\(762\) | −73.6934 | −2.66963 | ||||||||
\(763\) | 0.440394 | 0.0159433 | ||||||||
\(764\) | −32.2641 | −1.16727 | ||||||||
\(765\) | 13.8186 | 0.499614 | ||||||||
\(766\) | −34.4168 | −1.24353 | ||||||||
\(767\) | −7.99854 | −0.288811 | ||||||||
\(768\) | −38.7081 | −1.39676 | ||||||||
\(769\) | 21.5805 | 0.778212 | 0.389106 | − | 0.921193i | \(-0.372784\pi\) | ||||
0.389106 | + | 0.921193i | \(0.372784\pi\) | |||||||
\(770\) | 1.47038 | 0.0529889 | ||||||||
\(771\) | −9.69460 | −0.349142 | ||||||||
\(772\) | 9.36420 | 0.337025 | ||||||||
\(773\) | −47.9276 | −1.72384 | −0.861918 | − | 0.507047i | \(-0.830737\pi\) | ||||
−0.861918 | + | 0.507047i | \(0.830737\pi\) | |||||||
\(774\) | 13.6252 | 0.489747 | ||||||||
\(775\) | 42.4453 | 1.52468 | ||||||||
\(776\) | −0.165824 | −0.00595273 | ||||||||
\(777\) | 1.03986 | 0.0373047 | ||||||||
\(778\) | −49.2677 | −1.76633 | ||||||||
\(779\) | 52.8324 | 1.89292 | ||||||||
\(780\) | 2.73379 | 0.0978852 | ||||||||
\(781\) | 7.57978 | 0.271226 | ||||||||
\(782\) | 18.9772 | 0.678625 | ||||||||
\(783\) | −1.02874 | −0.0367641 | ||||||||
\(784\) | 27.5611 | 0.984323 | ||||||||
\(785\) | −0.328537 | −0.0117260 | ||||||||
\(786\) | −30.3977 | −1.08425 | ||||||||
\(787\) | 30.9063 | 1.10169 | 0.550846 | − | 0.834607i | \(-0.314305\pi\) | ||||
0.550846 | + | 0.834607i | \(0.314305\pi\) | |||||||
\(788\) | 21.8772 | 0.779342 | ||||||||
\(789\) | −44.0099 | −1.56679 | ||||||||
\(790\) | −2.17822 | −0.0774975 | ||||||||
\(791\) | 2.62886 | 0.0934716 | ||||||||
\(792\) | −0.277442 | −0.00985848 | ||||||||
\(793\) | 0.547741 | 0.0194508 | ||||||||
\(794\) | 17.9115 | 0.635657 | ||||||||
\(795\) | 23.4697 | 0.832384 | ||||||||
\(796\) | −45.4767 | −1.61188 | ||||||||
\(797\) | −9.94990 | −0.352444 | −0.176222 | − | 0.984350i | \(-0.556388\pi\) | ||||
−0.176222 | + | 0.984350i | \(0.556388\pi\) | |||||||
\(798\) | −10.1914 | −0.360773 | ||||||||
\(799\) | −18.8604 | −0.667234 | ||||||||
\(800\) | −35.0588 | −1.23952 | ||||||||
\(801\) | −19.0028 | −0.671430 | ||||||||
\(802\) | 61.6744 | 2.17780 | ||||||||
\(803\) | 34.9338 | 1.23279 | ||||||||
\(804\) | 28.8437 | 1.01724 | ||||||||
\(805\) | 0.471195 | 0.0166074 | ||||||||
\(806\) | 14.5283 | 0.511737 | ||||||||
\(807\) | 33.2045 | 1.16885 | ||||||||
\(808\) | −0.00462501 | −0.000162707 0 | ||||||||
\(809\) | 0.137829 | 0.00484582 | 0.00242291 | − | 0.999997i | \(-0.499229\pi\) | ||||
0.00242291 | + | 0.999997i | \(0.499229\pi\) | |||||||
\(810\) | −15.6292 | −0.549154 | ||||||||
\(811\) | 38.8734 | 1.36503 | 0.682514 | − | 0.730872i | \(-0.260887\pi\) | ||||
0.682514 | + | 0.730872i | \(0.260887\pi\) | |||||||
\(812\) | 0.892187 | 0.0313096 | ||||||||
\(813\) | −47.3443 | −1.66044 | ||||||||
\(814\) | 4.29904 | 0.150681 | ||||||||
\(815\) | −4.90067 | −0.171663 | ||||||||
\(816\) | −66.0631 | −2.31267 | ||||||||
\(817\) | −13.0452 | −0.456393 | ||||||||
\(818\) | −15.1734 | −0.530526 | ||||||||
\(819\) | −0.856101 | −0.0299146 | ||||||||
\(820\) | −16.4845 | −0.575663 | ||||||||
\(821\) | 17.2529 | 0.602130 | 0.301065 | − | 0.953604i | \(-0.402658\pi\) | ||||
0.301065 | + | 0.953604i | \(0.402658\pi\) | |||||||
\(822\) | 57.1230 | 1.99239 | ||||||||
\(823\) | −7.84996 | −0.273632 | −0.136816 | − | 0.990596i | \(-0.543687\pi\) | ||||
−0.136816 | + | 0.990596i | \(0.543687\pi\) | |||||||
\(824\) | 0.135925 | 0.00473516 | ||||||||
\(825\) | −22.3862 | −0.779387 | ||||||||
\(826\) | −9.30372 | −0.323718 | ||||||||
\(827\) | 29.7916 | 1.03595 | 0.517977 | − | 0.855394i | \(-0.326685\pi\) | ||||
0.517977 | + | 0.855394i | \(0.326685\pi\) | |||||||
\(828\) | 7.00680 | 0.243503 | ||||||||
\(829\) | −16.8482 | −0.585162 | −0.292581 | − | 0.956241i | \(-0.594514\pi\) | ||||
−0.292581 | + | 0.956241i | \(0.594514\pi\) | |||||||
\(830\) | 20.2148 | 0.701665 | ||||||||
\(831\) | 59.5652 | 2.06629 | ||||||||
\(832\) | −5.88653 | −0.204079 | ||||||||
\(833\) | 47.0241 | 1.62929 | ||||||||
\(834\) | 34.9642 | 1.21071 | ||||||||
\(835\) | 6.11295 | 0.211547 | ||||||||
\(836\) | −20.9342 | −0.724025 | ||||||||
\(837\) | −9.68128 | −0.334634 | ||||||||
\(838\) | −40.9056 | −1.41306 | ||||||||
\(839\) | 43.7370 | 1.50997 | 0.754985 | − | 0.655742i | \(-0.227644\pi\) | ||||
0.754985 | + | 0.655742i | \(0.227644\pi\) | |||||||
\(840\) | −0.0403491 | −0.00139218 | ||||||||
\(841\) | −27.9477 | −0.963715 | ||||||||
\(842\) | 48.1692 | 1.66002 | ||||||||
\(843\) | −35.7554 | −1.23148 | ||||||||
\(844\) | 55.7491 | 1.91896 | ||||||||
\(845\) | 9.65373 | 0.332098 | ||||||||
\(846\) | −14.0157 | −0.481870 | ||||||||
\(847\) | 2.79669 | 0.0960953 | ||||||||
\(848\) | −51.8272 | −1.77975 | ||||||||
\(849\) | −23.7173 | −0.813974 | ||||||||
\(850\) | −60.5663 | −2.07741 | ||||||||
\(851\) | 1.37766 | 0.0472256 | ||||||||
\(852\) | 16.3922 | 0.561587 | ||||||||
\(853\) | 10.2227 | 0.350020 | 0.175010 | − | 0.984567i | \(-0.444004\pi\) | ||||
0.175010 | + | 0.984567i | \(0.444004\pi\) | |||||||
\(854\) | 0.637119 | 0.0218018 | ||||||||
\(855\) | −9.83187 | −0.336243 | ||||||||
\(856\) | −0.411824 | −0.0140758 | ||||||||
\(857\) | 45.0054 | 1.53736 | 0.768678 | − | 0.639636i | \(-0.220915\pi\) | ||||
0.768678 | + | 0.639636i | \(0.220915\pi\) | |||||||
\(858\) | −7.66241 | −0.261590 | ||||||||
\(859\) | −0.634499 | −0.0216488 | −0.0108244 | − | 0.999941i | \(-0.503446\pi\) | ||||
−0.0108244 | + | 0.999941i | \(0.503446\pi\) | |||||||
\(860\) | 4.07029 | 0.138796 | ||||||||
\(861\) | 11.1758 | 0.380870 | ||||||||
\(862\) | −39.5652 | −1.34760 | ||||||||
\(863\) | −33.5175 | −1.14095 | −0.570475 | − | 0.821315i | \(-0.693241\pi\) | ||||
−0.570475 | + | 0.821315i | \(0.693241\pi\) | |||||||
\(864\) | 7.99652 | 0.272047 | ||||||||
\(865\) | 13.9371 | 0.473874 | ||||||||
\(866\) | −49.7795 | −1.69158 | ||||||||
\(867\) | −72.5751 | −2.46478 | ||||||||
\(868\) | 8.39622 | 0.284986 | ||||||||
\(869\) | 3.03337 | 0.102900 | ||||||||
\(870\) | 3.75039 | 0.127150 | ||||||||
\(871\) | −4.66900 | −0.158203 | ||||||||
\(872\) | −0.0499623 | −0.00169194 | ||||||||
\(873\) | −8.54727 | −0.289281 | ||||||||
\(874\) | −13.5022 | −0.456718 | ||||||||
\(875\) | −3.21396 | −0.108652 | ||||||||
\(876\) | 75.5485 | 2.55255 | ||||||||
\(877\) | 17.7856 | 0.600577 | 0.300289 | − | 0.953848i | \(-0.402917\pi\) | ||||
0.300289 | + | 0.953848i | \(0.402917\pi\) | |||||||
\(878\) | −40.2316 | −1.35775 | ||||||||
\(879\) | 22.2763 | 0.751362 | ||||||||
\(880\) | −6.78147 | −0.228603 | ||||||||
\(881\) | −50.0743 | −1.68705 | −0.843524 | − | 0.537092i | \(-0.819523\pi\) | ||||
−0.843524 | + | 0.537092i | \(0.819523\pi\) | |||||||
\(882\) | 34.9449 | 1.17666 | ||||||||
\(883\) | −50.1864 | −1.68891 | −0.844454 | − | 0.535628i | \(-0.820075\pi\) | ||||
−0.844454 | + | 0.535628i | \(0.820075\pi\) | |||||||
\(884\) | −10.3001 | −0.346429 | ||||||||
\(885\) | −19.4312 | −0.653173 | ||||||||
\(886\) | −34.2793 | −1.15164 | ||||||||
\(887\) | 17.0592 | 0.572791 | 0.286396 | − | 0.958111i | \(-0.407543\pi\) | ||||
0.286396 | + | 0.958111i | \(0.407543\pi\) | |||||||
\(888\) | −0.117971 | −0.00395885 | ||||||||
\(889\) | 6.89400 | 0.231217 | ||||||||
\(890\) | −11.4255 | −0.382985 | ||||||||
\(891\) | 21.7651 | 0.729159 | ||||||||
\(892\) | 43.3444 | 1.45128 | ||||||||
\(893\) | 13.4191 | 0.449052 | ||||||||
\(894\) | −16.0392 | −0.536431 | ||||||||
\(895\) | 20.6034 | 0.688697 | ||||||||
\(896\) | 0.176011 | 0.00588012 | ||||||||
\(897\) | −2.45548 | −0.0819860 | ||||||||
\(898\) | 19.4383 | 0.648663 | ||||||||
\(899\) | 9.90261 | 0.330270 | ||||||||
\(900\) | −22.3624 | −0.745412 | ||||||||
\(901\) | −88.4265 | −2.94592 | ||||||||
\(902\) | 46.2036 | 1.53841 | ||||||||
\(903\) | −2.75949 | −0.0918300 | ||||||||
\(904\) | −0.298243 | −0.00991940 | ||||||||
\(905\) | 13.8345 | 0.459874 | ||||||||
\(906\) | −25.9741 | −0.862933 | ||||||||
\(907\) | 5.68431 | 0.188744 | 0.0943722 | − | 0.995537i | \(-0.469916\pi\) | ||||
0.0943722 | + | 0.995537i | \(0.469916\pi\) | |||||||
\(908\) | 16.0031 | 0.531083 | ||||||||
\(909\) | −0.238392 | −0.00790698 | ||||||||
\(910\) | −0.514735 | −0.0170633 | ||||||||
\(911\) | 50.0548 | 1.65839 | 0.829194 | − | 0.558961i | \(-0.188800\pi\) | ||||
0.829194 | + | 0.558961i | \(0.188800\pi\) | |||||||
\(912\) | 47.0035 | 1.55644 | ||||||||
\(913\) | −28.1510 | −0.931661 | ||||||||
\(914\) | −32.5058 | −1.07520 | ||||||||
\(915\) | 1.33065 | 0.0439900 | ||||||||
\(916\) | −33.6622 | −1.11223 | ||||||||
\(917\) | 2.84370 | 0.0939073 | ||||||||
\(918\) | 13.8145 | 0.455946 | ||||||||
\(919\) | 16.8978 | 0.557406 | 0.278703 | − | 0.960377i | \(-0.410095\pi\) | ||||
0.278703 | + | 0.960377i | \(0.410095\pi\) | |||||||
\(920\) | −0.0534567 | −0.00176242 | ||||||||
\(921\) | 61.7444 | 2.03455 | ||||||||
\(922\) | 35.5436 | 1.17056 | ||||||||
\(923\) | −2.65345 | −0.0873393 | ||||||||
\(924\) | −4.42828 | −0.145680 | ||||||||
\(925\) | −4.39684 | −0.144567 | ||||||||
\(926\) | −53.2253 | −1.74909 | ||||||||
\(927\) | 7.00613 | 0.230112 | ||||||||
\(928\) | −8.17933 | −0.268500 | ||||||||
\(929\) | −8.12188 | −0.266470 | −0.133235 | − | 0.991084i | \(-0.542537\pi\) | ||||
−0.133235 | + | 0.991084i | \(0.542537\pi\) | |||||||
\(930\) | 35.2942 | 1.15734 | ||||||||
\(931\) | −33.4574 | −1.09652 | ||||||||
\(932\) | 46.0450 | 1.50825 | ||||||||
\(933\) | −23.6555 | −0.774445 | ||||||||
\(934\) | 40.4998 | 1.32519 | ||||||||
\(935\) | −11.5704 | −0.378393 | ||||||||
\(936\) | 0.0971240 | 0.00317460 | ||||||||
\(937\) | −38.9561 | −1.27264 | −0.636321 | − | 0.771424i | \(-0.719545\pi\) | ||||
−0.636321 | + | 0.771424i | \(0.719545\pi\) | |||||||
\(938\) | −5.43088 | −0.177324 | ||||||||
\(939\) | 16.3448 | 0.533393 | ||||||||
\(940\) | −4.18694 | −0.136563 | ||||||||
\(941\) | −29.7168 | −0.968739 | −0.484370 | − | 0.874863i | \(-0.660951\pi\) | ||||
−0.484370 | + | 0.874863i | \(0.660951\pi\) | |||||||
\(942\) | 1.99143 | 0.0648844 | ||||||||
\(943\) | 14.8063 | 0.482160 | ||||||||
\(944\) | 42.9092 | 1.39658 | ||||||||
\(945\) | 0.343006 | 0.0111580 | ||||||||
\(946\) | −11.4084 | −0.370920 | ||||||||
\(947\) | −15.1829 | −0.493379 | −0.246689 | − | 0.969095i | \(-0.579343\pi\) | ||||
−0.246689 | + | 0.969095i | \(0.579343\pi\) | |||||||
\(948\) | 6.56003 | 0.213060 | ||||||||
\(949\) | −12.2292 | −0.396978 | ||||||||
\(950\) | 43.0925 | 1.39811 | ||||||||
\(951\) | 32.4764 | 1.05312 | ||||||||
\(952\) | 0.152023 | 0.00492709 | ||||||||
\(953\) | 2.41286 | 0.0781601 | 0.0390801 | − | 0.999236i | \(-0.487557\pi\) | ||||
0.0390801 | + | 0.999236i | \(0.487557\pi\) | |||||||
\(954\) | −65.7122 | −2.12751 | ||||||||
\(955\) | 12.6877 | 0.410564 | ||||||||
\(956\) | 23.5785 | 0.762582 | ||||||||
\(957\) | −5.22277 | −0.168828 | ||||||||
\(958\) | −42.2011 | −1.36345 | ||||||||
\(959\) | −5.34384 | −0.172562 | ||||||||
\(960\) | −14.3004 | −0.461544 | ||||||||
\(961\) | 62.1917 | 2.00618 | ||||||||
\(962\) | −1.50496 | −0.0485220 | ||||||||
\(963\) | −21.2271 | −0.684035 | ||||||||
\(964\) | 18.5210 | 0.596521 | ||||||||
\(965\) | −3.68242 | −0.118541 | ||||||||
\(966\) | −2.85616 | −0.0918953 | ||||||||
\(967\) | −45.6819 | −1.46903 | −0.734516 | − | 0.678592i | \(-0.762591\pi\) | ||||
−0.734516 | + | 0.678592i | \(0.762591\pi\) | |||||||
\(968\) | −0.317282 | −0.0101978 | ||||||||
\(969\) | 80.1964 | 2.57628 | ||||||||
\(970\) | −5.13909 | −0.165006 | ||||||||
\(971\) | −22.4763 | −0.721297 | −0.360649 | − | 0.932702i | \(-0.617445\pi\) | ||||
−0.360649 | + | 0.932702i | \(0.617445\pi\) | |||||||
\(972\) | 41.1279 | 1.31918 | ||||||||
\(973\) | −3.27090 | −0.104860 | ||||||||
\(974\) | −44.2588 | −1.41814 | ||||||||
\(975\) | 7.83671 | 0.250976 | ||||||||
\(976\) | −2.93843 | −0.0940568 | ||||||||
\(977\) | −28.9202 | −0.925240 | −0.462620 | − | 0.886557i | \(-0.653091\pi\) | ||||
−0.462620 | + | 0.886557i | \(0.653091\pi\) | |||||||
\(978\) | 29.7055 | 0.949878 | ||||||||
\(979\) | 15.9111 | 0.508521 | ||||||||
\(980\) | 10.4392 | 0.333467 | ||||||||
\(981\) | −2.57527 | −0.0822221 | ||||||||
\(982\) | −23.9998 | −0.765864 | ||||||||
\(983\) | 55.8722 | 1.78205 | 0.891023 | − | 0.453959i | \(-0.149989\pi\) | ||||
0.891023 | + | 0.453959i | \(0.149989\pi\) | |||||||
\(984\) | −1.26789 | −0.0404187 | ||||||||
\(985\) | −8.60309 | −0.274117 | ||||||||
\(986\) | −14.1303 | −0.450000 | ||||||||
\(987\) | 2.83858 | 0.0903529 | ||||||||
\(988\) | 7.32843 | 0.233148 | ||||||||
\(989\) | −3.65592 | −0.116251 | ||||||||
\(990\) | −8.59829 | −0.273272 | ||||||||
\(991\) | 39.8801 | 1.26683 | 0.633416 | − | 0.773812i | \(-0.281652\pi\) | ||||
0.633416 | + | 0.773812i | \(0.281652\pi\) | |||||||
\(992\) | −76.9743 | −2.44394 | ||||||||
\(993\) | −76.4458 | −2.42593 | ||||||||
\(994\) | −3.08643 | −0.0978956 | ||||||||
\(995\) | 17.8835 | 0.566945 | ||||||||
\(996\) | −60.8799 | −1.92905 | ||||||||
\(997\) | −4.82631 | −0.152851 | −0.0764254 | − | 0.997075i | \(-0.524351\pi\) | ||||
−0.0764254 | + | 0.997075i | \(0.524351\pi\) | |||||||
\(998\) | −17.2060 | −0.544645 | ||||||||
\(999\) | 1.00287 | 0.0317294 |
(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 | 4033.2.a.f.1.14 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.14 | ✓ | 85 | 1.1 | even | 1 | trivial |