Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(71,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ba (of order \(6\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 575.14 | ||
Character | \(\chi\) | \(=\) | 756.575 |
Dual form | 756.2.ba.a.71.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.498620 | + | 1.32340i | −0.352577 | + | 0.935783i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.50276 | − | 1.31974i | −0.751378 | − | 0.659872i | ||||
\(5\) | −2.06874 | + | 1.19439i | −0.925167 | + | 0.534146i | −0.885280 | − | 0.465059i | \(-0.846033\pi\) |
−0.0398874 | + | 0.999204i | \(0.512700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | 2.49585 | − | 1.33069i | 0.882415 | − | 0.470471i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.549133 | − | 3.33330i | −0.173651 | − | 1.05408i | ||||
\(11\) | 3.21792 | − | 5.57360i | 0.970240 | − | 1.68050i | 0.275416 | − | 0.961325i | \(-0.411184\pi\) |
0.694824 | − | 0.719180i | \(-0.255482\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.15010 | + | 3.72408i | 0.596331 | + | 1.03288i | 0.993358 | + | 0.115068i | \(0.0367086\pi\) |
−0.397027 | + | 0.917807i | \(0.629958\pi\) | |||||||
\(14\) | −1.09352 | + | 0.896785i | −0.292254 | + | 0.239676i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.516556 | + | 3.96651i | 0.129139 | + | 0.991626i | ||||
\(17\) | 1.89547i | 0.459718i | 0.973224 | + | 0.229859i | \(0.0738266\pi\) | ||||
−0.973224 | + | 0.229859i | \(0.926173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.529348i | − | 0.121441i | −0.998155 | − | 0.0607204i | \(-0.980660\pi\) | ||
0.998155 | − | 0.0607204i | \(-0.0193398\pi\) | |||||||
\(20\) | 4.68509 | + | 0.935330i | 1.04762 | + | 0.209146i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.77157 | + | 7.03770i | 1.23050 | + | 1.50044i | ||||
\(23\) | 2.64942 | + | 4.58894i | 0.552443 | + | 0.956859i | 0.998098 | + | 0.0616543i | \(0.0196376\pi\) |
−0.445655 | + | 0.895205i | \(0.647029\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.353115 | − | 0.611613i | 0.0706230 | − | 0.122323i | ||||
\(26\) | −6.00052 | + | 0.988535i | −1.17680 | + | 0.193868i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.641554 | − | 1.89431i | −0.121242 | − | 0.357991i | ||||
\(29\) | 0.301871 | + | 0.174285i | 0.0560561 | + | 0.0323640i | 0.527766 | − | 0.849390i | \(-0.323030\pi\) |
−0.471710 | + | 0.881754i | \(0.656363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.09757 | + | 2.94308i | −0.915550 | + | 0.528593i | −0.882213 | − | 0.470851i | \(-0.843947\pi\) |
−0.0333376 | + | 0.999444i | \(0.510614\pi\) | |||||||
\(32\) | −5.50683 | − | 1.29417i | −0.973478 | − | 0.228779i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.50846 | − | 0.945118i | −0.430197 | − | 0.162086i | ||||
\(35\) | −2.38877 | −0.403776 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.842466 | 0.138501 | 0.0692503 | − | 0.997599i | \(-0.477939\pi\) | ||||
0.0692503 | + | 0.997599i | \(0.477939\pi\) | |||||||
\(38\) | 0.700537 | + | 0.263943i | 0.113642 | + | 0.0428173i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.57389 | + | 5.73386i | −0.565082 | + | 0.906603i | ||||
\(41\) | −4.58530 | + | 2.64733i | −0.716104 | + | 0.413443i | −0.813317 | − | 0.581821i | \(-0.802340\pi\) |
0.0972131 | + | 0.995264i | \(0.469007\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.38095 | + | 4.26140i | 1.12559 | + | 0.649857i | 0.942821 | − | 0.333300i | \(-0.108162\pi\) |
0.182764 | + | 0.983157i | \(0.441496\pi\) | |||||||
\(44\) | −12.1915 | + | 4.12894i | −1.83793 | + | 0.622461i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.39404 | + | 1.21810i | −1.09019 | + | 0.179600i | ||||
\(47\) | 2.04252 | − | 3.53774i | 0.297932 | − | 0.516033i | −0.677731 | − | 0.735310i | \(-0.737037\pi\) |
0.975663 | + | 0.219277i | \(0.0703699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 0.633336 | + | 0.772273i | 0.0895673 | + | 0.109216i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.68376 | − | 8.43397i | 0.233495 | − | 1.16958i | ||||
\(53\) | 12.5979i | 1.73046i | 0.501376 | + | 0.865230i | \(0.332827\pi\) | ||||
−0.501376 | + | 0.865230i | \(0.667173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.3738i | 2.07300i | ||||||||
\(56\) | 2.82681 | + | 0.0955095i | 0.377749 | + | 0.0127630i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.381168 | + | 0.312593i | −0.0500497 | + | 0.0410455i | ||||
\(59\) | 2.66171 | + | 4.61021i | 0.346524 | + | 0.600198i | 0.985630 | − | 0.168921i | \(-0.0540284\pi\) |
−0.639105 | + | 0.769119i | \(0.720695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.49882 | + | 6.06013i | −0.447978 | + | 0.775920i | −0.998254 | − | 0.0590625i | \(-0.981189\pi\) |
0.550277 | + | 0.834982i | \(0.314522\pi\) | |||||||
\(62\) | −1.35312 | − | 8.21358i | −0.171846 | − | 1.04313i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.45851 | − | 6.64242i | 0.557314 | − | 0.830302i | ||||
\(65\) | −8.89599 | − | 5.13610i | −1.10341 | − | 0.637055i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.32818 | − | 5.38563i | 1.13962 | − | 0.657959i | 0.193282 | − | 0.981143i | \(-0.438087\pi\) |
0.946336 | + | 0.323184i | \(0.104753\pi\) | |||||||
\(68\) | 2.50153 | − | 2.84843i | 0.303355 | − | 0.345423i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.19109 | − | 3.16129i | 0.142362 | − | 0.377847i | ||||
\(71\) | 6.12137 | 0.726473 | 0.363236 | − | 0.931697i | \(-0.381672\pi\) | ||||
0.363236 | + | 0.931697i | \(0.381672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.07942 | 0.594501 | 0.297251 | − | 0.954799i | \(-0.403930\pi\) | ||||
0.297251 | + | 0.954799i | \(0.403930\pi\) | |||||||
\(74\) | −0.420070 | + | 1.11492i | −0.0488322 | + | 0.129606i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.698603 | + | 0.795481i | −0.0801353 | + | 0.0912480i | ||||
\(77\) | 5.57360 | − | 3.21792i | 0.635171 | − | 0.366716i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.87851 | + | 1.66191i | 0.323858 | + | 0.186979i | 0.653111 | − | 0.757262i | \(-0.273464\pi\) |
−0.329253 | + | 0.944242i | \(0.606797\pi\) | |||||||
\(80\) | −5.80616 | − | 7.58869i | −0.649148 | − | 0.848441i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.21714 | − | 7.38818i | −0.134411 | − | 0.815888i | ||||
\(83\) | −3.23597 | + | 5.60486i | −0.355193 | + | 0.615213i | −0.987151 | − | 0.159790i | \(-0.948918\pi\) |
0.631958 | + | 0.775003i | \(0.282252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.26392 | − | 3.92122i | −0.245557 | − | 0.425317i | ||||
\(86\) | −9.31981 | + | 7.64311i | −1.00498 | + | 0.824178i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.614684 | − | 18.1929i | 0.0655256 | − | 1.93937i | ||||
\(89\) | − | 14.4170i | − | 1.52820i | −0.645099 | − | 0.764099i | \(-0.723184\pi\) | ||
0.645099 | − | 0.764099i | \(-0.276816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.30020i | 0.450784i | ||||||||
\(92\) | 2.07478 | − | 10.3926i | 0.216310 | − | 1.08350i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.66340 | + | 4.46705i | 0.377851 | + | 0.460741i | ||||
\(95\) | 0.632246 | + | 1.09508i | 0.0648670 | + | 0.112353i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.86625 | + | 6.69654i | −0.392558 | + | 0.679931i | −0.992786 | − | 0.119898i | \(-0.961743\pi\) |
0.600228 | + | 0.799829i | \(0.295077\pi\) | |||||||
\(98\) | −1.39540 | + | 0.229881i | −0.140957 | + | 0.0232215i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.33782 | + | 0.453085i | −0.133782 | + | 0.0453085i | ||||
\(101\) | 14.7999 | + | 8.54473i | 1.47265 | + | 0.850233i | 0.999527 | − | 0.0307657i | \(-0.00979457\pi\) |
0.473119 | + | 0.880998i | \(0.343128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0362 | + | 5.79440i | −0.988896 | + | 0.570939i | −0.904944 | − | 0.425531i | \(-0.860087\pi\) |
−0.0839517 | + | 0.996470i | \(0.526754\pi\) | |||||||
\(104\) | 10.3219 | + | 6.43362i | 1.01215 | + | 0.630868i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.6721 | − | 6.28158i | −1.61933 | − | 0.610121i | ||||
\(107\) | −1.66184 | −0.160656 | −0.0803278 | − | 0.996768i | \(-0.525597\pi\) | ||||
−0.0803278 | + | 0.996768i | \(0.525597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.21513 | −0.786867 | −0.393434 | − | 0.919353i | \(-0.628713\pi\) | ||||
−0.393434 | + | 0.919353i | \(0.628713\pi\) | |||||||
\(110\) | −20.3456 | − | 7.66566i | −1.93988 | − | 0.730892i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.53590 | + | 3.69337i | −0.145129 | + | 0.348991i | ||||
\(113\) | 7.87513 | − | 4.54671i | 0.740830 | − | 0.427718i | −0.0815410 | − | 0.996670i | \(-0.525984\pi\) |
0.822371 | + | 0.568952i | \(0.192651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.9619 | − | 6.32887i | −1.02220 | − | 0.590170i | ||||
\(116\) | −0.223627 | − | 0.660301i | −0.0207632 | − | 0.0613074i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.42831 | + | 1.22375i | −0.683832 | + | 0.112655i | ||||
\(119\) | −0.947734 | + | 1.64152i | −0.0868786 | + | 0.150478i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.2100 | − | 26.3446i | −1.38273 | − | 2.39496i | ||||
\(122\) | −6.27537 | − | 7.65202i | −0.568146 | − | 0.692781i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.5445 | + | 2.30474i | 1.03673 | + | 0.206972i | ||||
\(125\) | − | 10.2568i | − | 0.917399i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.0630i | − | 1.51409i | −0.653360 | − | 0.757047i | \(-0.726641\pi\) | ||
0.653360 | − | 0.757047i | \(-0.273359\pi\) | |||||||
\(128\) | 6.56745 | + | 9.21242i | 0.580486 | + | 0.814270i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.2328 | − | 9.21196i | 0.985183 | − | 0.807942i | ||||
\(131\) | 5.58971 | + | 9.68166i | 0.488375 | + | 0.845890i | 0.999911 | − | 0.0133718i | \(-0.00425652\pi\) |
−0.511536 | + | 0.859262i | \(0.670923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.264674 | − | 0.458429i | 0.0229501 | − | 0.0397508i | ||||
\(134\) | 2.47611 | + | 15.0303i | 0.213903 | + | 1.29842i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.52229 | + | 4.73080i | 0.216284 | + | 0.405663i | ||||
\(137\) | −4.30543 | − | 2.48574i | −0.367838 | − | 0.212371i | 0.304676 | − | 0.952456i | \(-0.401452\pi\) |
−0.672513 | + | 0.740085i | \(0.734785\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.46366 | − | 4.30915i | 0.633060 | − | 0.365497i | −0.148876 | − | 0.988856i | \(-0.547566\pi\) |
0.781936 | + | 0.623359i | \(0.214232\pi\) | |||||||
\(140\) | 3.58974 | + | 3.15256i | 0.303389 | + | 0.266440i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.05223 | + | 8.10100i | −0.256138 | + | 0.679821i | ||||
\(143\) | 27.6754 | 2.31434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.832656 | −0.0691483 | ||||||||
\(146\) | −2.53270 | + | 6.72209i | −0.209608 | + | 0.556324i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.26602 | − | 1.11184i | −0.104066 | − | 0.0913926i | ||||
\(149\) | −2.18247 | + | 1.26005i | −0.178795 | + | 0.103227i | −0.586727 | − | 0.809785i | \(-0.699584\pi\) |
0.407931 | + | 0.913013i | \(0.366250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.331047 | − | 0.191130i | −0.0269402 | − | 0.0155539i | 0.486469 | − | 0.873698i | \(-0.338285\pi\) |
−0.513410 | + | 0.858144i | \(0.671618\pi\) | |||||||
\(152\) | −0.704400 | − | 1.32117i | −0.0571344 | − | 0.107161i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.47948 | + | 8.98061i | 0.119220 | + | 0.723678i | ||||
\(155\) | 7.03035 | − | 12.1769i | 0.564691 | − | 0.978074i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.39885 | + | 7.61904i | 0.351067 | + | 0.608065i | 0.986437 | − | 0.164143i | \(-0.0524857\pi\) |
−0.635370 | + | 0.772208i | \(0.719152\pi\) | |||||||
\(158\) | −3.63465 | + | 2.98075i | −0.289157 | + | 0.237136i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.9379 | − | 3.89998i | 1.02283 | − | 0.308320i | ||||
\(161\) | 5.29885i | 0.417608i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7694i | 0.843521i | 0.906707 | + | 0.421760i | \(0.138588\pi\) | ||||
−0.906707 | + | 0.421760i | \(0.861412\pi\) | |||||||
\(164\) | 10.3844 | + | 2.07313i | 0.810884 | + | 0.161885i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.80393 | − | 7.07716i | −0.450473 | − | 0.549294i | ||||
\(167\) | −3.92462 | − | 6.79765i | −0.303697 | − | 0.526018i | 0.673274 | − | 0.739393i | \(-0.264888\pi\) |
−0.976970 | + | 0.213375i | \(0.931554\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.74587 | + | 4.75598i | −0.211221 | + | 0.365845i | ||||
\(170\) | 6.31817 | − | 1.04086i | 0.484582 | − | 0.0798306i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.46783 | − | 16.1448i | −0.416918 | − | 1.23103i | ||||
\(173\) | 16.5653 | + | 9.56396i | 1.25943 | + | 0.727134i | 0.972964 | − | 0.230955i | \(-0.0741850\pi\) |
0.286469 | + | 0.958089i | \(0.407518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.611613 | − | 0.353115i | 0.0462336 | − | 0.0266930i | ||||
\(176\) | 23.7700 | + | 9.88483i | 1.79173 | + | 0.745097i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.0794 | + | 7.18860i | 1.43006 | + | 0.538808i | ||||
\(179\) | −26.1468 | −1.95431 | −0.977153 | − | 0.212538i | \(-0.931827\pi\) | ||||
−0.977153 | + | 0.212538i | \(0.931827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.9172 | 1.40610 | 0.703052 | − | 0.711139i | \(-0.251820\pi\) | ||||
0.703052 | + | 0.711139i | \(0.251820\pi\) | |||||||
\(182\) | −5.69087 | − | 2.14417i | −0.421836 | − | 0.158936i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.7190 | + | 7.92771i | 0.937659 | + | 0.584439i | ||||
\(185\) | −1.74284 | + | 1.00623i | −0.128136 | + | 0.0739795i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.5646 | + | 6.09947i | 0.772559 | + | 0.446037i | ||||
\(188\) | −7.73832 | + | 2.62077i | −0.564375 | + | 0.191139i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.76448 | + | 0.290682i | −0.128009 | + | 0.0210883i | ||||
\(191\) | 4.70709 | − | 8.15291i | 0.340593 | − | 0.589924i | −0.643950 | − | 0.765068i | \(-0.722706\pi\) |
0.984543 | + | 0.175143i | \(0.0560389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.658744 | − | 1.14098i | −0.0474174 | − | 0.0821294i | 0.841343 | − | 0.540502i | \(-0.181766\pi\) |
−0.888760 | + | 0.458373i | \(0.848432\pi\) | |||||||
\(194\) | −6.93439 | − | 8.45561i | −0.497860 | − | 0.607078i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.391553 | − | 1.96130i | 0.0279680 | − | 0.140093i | ||||
\(197\) | − | 3.56413i | − | 0.253933i | −0.991907 | − | 0.126967i | \(-0.959476\pi\) | ||
0.991907 | − | 0.126967i | \(-0.0405241\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.9739i | − | 1.13236i | −0.824282 | − | 0.566179i | \(-0.808421\pi\) | ||
0.824282 | − | 0.566179i | \(-0.191579\pi\) | |||||||
\(200\) | 0.0674517 | − | 1.99638i | 0.00476955 | − | 0.141165i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.6876 | + | 15.3256i | −1.31485 | + | 1.07830i | ||||
\(203\) | 0.174285 | + | 0.301871i | 0.0122324 | + | 0.0211872i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.32386 | − | 10.9532i | 0.441677 | − | 0.765007i | ||||
\(206\) | −2.66404 | − | 16.1711i | −0.185613 | − | 1.12669i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.6610 | + | 10.4521i | −0.947217 | + | 0.724722i | ||||
\(209\) | −2.95038 | − | 1.70340i | −0.204082 | − | 0.117827i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.39401 | − | 1.95953i | 0.233653 | − | 0.134900i | −0.378603 | − | 0.925559i | \(-0.623595\pi\) |
0.612256 | + | 0.790659i | \(0.290262\pi\) | |||||||
\(212\) | 16.6260 | − | 18.9316i | 1.14188 | − | 1.30023i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.828624 | − | 2.19927i | 0.0566436 | − | 0.150339i | ||||
\(215\) | −20.3590 | −1.38847 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.88617 | −0.399579 | ||||||||
\(218\) | 4.09623 | − | 10.8719i | 0.277432 | − | 0.736337i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.2894 | − | 23.1030i | 1.36791 | − | 1.55761i | ||||
\(221\) | −7.05888 | + | 4.07545i | −0.474832 | + | 0.274144i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.25600 | − | 1.30250i | −0.151073 | − | 0.0872218i | 0.422558 | − | 0.906336i | \(-0.361132\pi\) |
−0.573631 | + | 0.819114i | \(0.694466\pi\) | |||||||
\(224\) | −4.12197 | − | 3.87420i | −0.275410 | − | 0.258856i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.09040 | + | 12.6890i | 0.139052 | + | 0.844060i | ||||
\(227\) | 1.56505 | − | 2.71075i | 0.103876 | − | 0.179919i | −0.809402 | − | 0.587254i | \(-0.800209\pi\) |
0.913278 | + | 0.407336i | \(0.133542\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.33583 | − | 5.77783i | −0.220438 | − | 0.381809i | 0.734503 | − | 0.678605i | \(-0.237415\pi\) |
−0.954941 | + | 0.296796i | \(0.904082\pi\) | |||||||
\(230\) | 13.8414 | − | 11.3513i | 0.912677 | − | 0.748481i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.985345 | + | 0.0332918i | 0.0646910 | + | 0.00218572i | ||||
\(233\) | − | 15.0197i | − | 0.983971i | −0.870603 | − | 0.491985i | \(-0.836271\pi\) | ||
0.870603 | − | 0.491985i | \(-0.163729\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.75821i | 0.636556i | ||||||||
\(236\) | 2.08440 | − | 10.4408i | 0.135683 | − | 0.679637i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.69983 | − | 2.07272i | −0.110183 | − | 0.134355i | ||||
\(239\) | −1.10101 | − | 1.90701i | −0.0712185 | − | 0.123354i | 0.828217 | − | 0.560407i | \(-0.189355\pi\) |
−0.899436 | + | 0.437053i | \(0.856022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.28440 | + | 16.0811i | −0.598061 | + | 1.03587i | 0.395046 | + | 0.918661i | \(0.370729\pi\) |
−0.993107 | + | 0.117211i | \(0.962605\pi\) | |||||||
\(242\) | 42.4483 | − | 6.99300i | 2.72868 | − | 0.449527i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.2557 | − | 4.48936i | 0.848608 | − | 0.287402i | ||||
\(245\) | −2.06874 | − | 1.19439i | −0.132167 | − | 0.0763065i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.97134 | − | 1.13815i | 0.125433 | − | 0.0724188i | ||||
\(248\) | −8.80641 | + | 14.1288i | −0.559208 | + | 0.897179i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.5739 | + | 5.11426i | 0.858486 | + | 0.323454i | ||||
\(251\) | −6.18166 | −0.390183 | −0.195092 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195092 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.1026 | 2.14401 | ||||||||
\(254\) | 22.5811 | + | 8.50794i | 1.41686 | + | 0.533836i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.4663 | + | 4.09785i | −0.966646 | + | 0.256115i | ||||
\(257\) | −6.98685 | + | 4.03386i | −0.435828 | + | 0.251625i | −0.701826 | − | 0.712348i | \(-0.747632\pi\) |
0.265998 | + | 0.963973i | \(0.414298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.729597 | + | 0.421233i | 0.0453350 | + | 0.0261741i | ||||
\(260\) | 6.59017 | + | 19.4587i | 0.408705 | + | 1.20678i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.5998 | + | 2.56993i | −0.963759 | + | 0.158771i | ||||
\(263\) | 0.0757144 | − | 0.131141i | 0.00466875 | − | 0.00808651i | −0.863682 | − | 0.504038i | \(-0.831847\pi\) |
0.868350 | + | 0.495951i | \(0.165181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0468 | − | 26.0618i | −0.924317 | − | 1.60096i | ||||
\(266\) | 0.474711 | + | 0.578850i | 0.0291064 | + | 0.0354916i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.1256 | − | 4.21751i | −1.29045 | − | 0.257626i | ||||
\(269\) | 2.18065i | 0.132957i | 0.997788 | + | 0.0664784i | \(0.0211763\pi\) | ||||
−0.997788 | + | 0.0664784i | \(0.978824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.08448i | 0.187369i | 0.995602 | + | 0.0936844i | \(0.0298645\pi\) | ||||
−0.995602 | + | 0.0936844i | \(0.970136\pi\) | |||||||
\(272\) | −7.51838 | + | 0.979116i | −0.455869 | + | 0.0593676i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.43639 | − | 4.45835i | 0.328425 | − | 0.269339i | ||||
\(275\) | −2.27259 | − | 3.93624i | −0.137042 | − | 0.237364i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.31095 | + | 14.3950i | −0.499357 | + | 0.864911i | −1.00000 | 0.000742657i | \(-0.999764\pi\) | |
0.500643 | + | 0.865654i | \(0.333097\pi\) | |||||||
\(278\) | 1.98118 | + | 12.0260i | 0.118823 | + | 0.721272i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.96201 | + | 3.17872i | −0.356298 | + | 0.189965i | ||||
\(281\) | −8.93878 | − | 5.16081i | −0.533243 | − | 0.307868i | 0.209093 | − | 0.977896i | \(-0.432949\pi\) |
−0.742336 | + | 0.670028i | \(0.766282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.3659 | − | 7.13943i | 0.735074 | − | 0.424395i | −0.0852016 | − | 0.996364i | \(-0.527153\pi\) |
0.820275 | + | 0.571969i | \(0.193820\pi\) | |||||||
\(284\) | −9.19893 | − | 8.07863i | −0.545856 | − | 0.479379i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.7995 | + | 36.6256i | −0.815982 | + | 2.16572i | ||||
\(287\) | −5.29465 | −0.312533 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.4072 | 0.788659 | ||||||||
\(290\) | 0.415179 | − | 1.10193i | 0.0243801 | − | 0.0647078i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.63314 | − | 6.70353i | −0.446696 | − | 0.392295i | ||||
\(293\) | 2.10270 | − | 1.21399i | 0.122841 | − | 0.0709223i | −0.437320 | − | 0.899306i | \(-0.644072\pi\) |
0.560161 | + | 0.828383i | \(0.310739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0127 | − | 6.35821i | −0.641186 | − | 0.370189i | ||||
\(296\) | 2.10267 | − | 1.12106i | 0.122215 | − | 0.0651605i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.579324 | − | 3.51657i | −0.0335593 | − | 0.203709i | ||||
\(299\) | −11.3931 | + | 19.7334i | −0.658877 | + | 1.14121i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.26140 | + | 7.38095i | 0.245623 | + | 0.425431i | ||||
\(302\) | 0.418007 | − | 0.342805i | 0.0240536 | − | 0.0197262i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.09966 | − | 0.273438i | 0.120424 | − | 0.0156827i | ||||
\(305\) | − | 16.7157i | − | 0.957141i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.87237i | − | 0.506373i | −0.967417 | − | 0.253187i | \(-0.918521\pi\) | ||
0.967417 | − | 0.253187i | \(-0.0814787\pi\) | |||||||
\(308\) | −12.6226 | − | 2.51997i | −0.719240 | − | 0.143589i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.6094 | + | 15.3756i | 0.716168 | + | 0.873275i | ||||
\(311\) | −3.03771 | − | 5.26147i | −0.172253 | − | 0.298350i | 0.766954 | − | 0.641702i | \(-0.221771\pi\) |
−0.939207 | + | 0.343351i | \(0.888438\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.3245 | + | 17.8825i | −0.583575 | + | 1.01078i | 0.411477 | + | 0.911420i | \(0.365013\pi\) |
−0.995051 | + | 0.0993607i | \(0.968320\pi\) | |||||||
\(314\) | −12.2764 | + | 2.02242i | −0.692795 | + | 0.114132i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.13241 | − | 6.29634i | −0.119957 | − | 0.354197i | ||||
\(317\) | −21.2581 | − | 12.2734i | −1.19397 | − | 0.689341i | −0.234769 | − | 0.972051i | \(-0.575433\pi\) |
−0.959205 | + | 0.282710i | \(0.908767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.94280 | − | 1.12167i | 0.108776 | − | 0.0628017i | ||||
\(320\) | −1.28988 | + | 19.0666i | −0.0721064 | + | 1.06585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.01248 | − | 2.64211i | −0.390790 | − | 0.147239i | ||||
\(323\) | 1.00336 | 0.0558286 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.03693 | 0.168459 | ||||||||
\(326\) | −14.2521 | − | 5.36981i | −0.789352 | − | 0.297406i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.92144 | + | 12.7090i | −0.437388 | + | 0.701734i | ||||
\(329\) | 3.53774 | − | 2.04252i | 0.195042 | − | 0.112608i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.9866 | − | 15.0034i | −1.42835 | − | 0.824660i | −0.431362 | − | 0.902179i | \(-0.641967\pi\) |
−0.996991 | + | 0.0775195i | \(0.975300\pi\) | |||||||
\(332\) | 12.2598 | − | 4.15210i | 0.672846 | − | 0.227876i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.9529 | − | 1.80439i | 0.599315 | − | 0.0987320i | ||||
\(335\) | −12.8650 | + | 22.2829i | −0.702892 | + | 1.21744i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.27401 | − | 9.13486i | −0.287294 | − | 0.497608i | 0.685869 | − | 0.727725i | \(-0.259422\pi\) |
−0.973163 | + | 0.230117i | \(0.926089\pi\) | |||||||
\(338\) | −4.92491 | − | 6.00530i | −0.267880 | − | 0.326645i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.77289 | + | 8.88044i | −0.0961483 | + | 0.481609i | ||||
\(341\) | 37.8824i | 2.05145i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 24.0924 | + | 0.814008i | 1.29897 | + | 0.0438884i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.9167 | + | 17.1536i | −1.12449 | + | 0.922185i | ||||
\(347\) | 4.55660 | + | 7.89227i | 0.244611 | + | 0.423679i | 0.962022 | − | 0.272971i | \(-0.0880063\pi\) |
−0.717411 | + | 0.696650i | \(0.754673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2978 | − | 19.5684i | 0.604760 | − | 1.04747i | −0.387330 | − | 0.921941i | \(-0.626602\pi\) |
0.992089 | − | 0.125533i | \(-0.0400642\pi\) | |||||||
\(350\) | 0.162349 | + | 0.985476i | 0.00867791 | + | 0.0526759i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.9337 | + | 26.5283i | −1.32897 | + | 1.41396i | ||||
\(353\) | 5.76564 | + | 3.32879i | 0.306874 | + | 0.177174i | 0.645527 | − | 0.763738i | \(-0.276638\pi\) |
−0.338653 | + | 0.940911i | \(0.609971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.6635 | + | 7.31128i | −0.672109 | + | 0.388042i | ||||
\(356\) | −19.0267 | + | 21.6652i | −1.00841 | + | 1.14826i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.0373 | − | 34.6026i | 0.689044 | − | 1.82881i | ||||
\(359\) | −8.03334 | −0.423984 | −0.211992 | − | 0.977271i | \(-0.567995\pi\) | ||||
−0.211992 | + | 0.977271i | \(0.567995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7198 | 0.985252 | ||||||||
\(362\) | −9.43248 | + | 25.0349i | −0.495760 | + | 1.31581i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.67516 | − | 6.46216i | 0.297459 | − | 0.338709i | ||||
\(365\) | −10.5080 | + | 6.06679i | −0.550013 | + | 0.317550i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.9220 | − | 8.61523i | −0.778923 | − | 0.449712i | 0.0571254 | − | 0.998367i | \(-0.481807\pi\) |
−0.836049 | + | 0.548656i | \(0.815140\pi\) | |||||||
\(368\) | −16.8335 | + | 12.8794i | −0.877505 | + | 0.671385i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.462626 | − | 2.80820i | −0.0240508 | − | 0.145991i | ||||
\(371\) | −6.29897 | + | 10.9101i | −0.327026 | + | 0.566426i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.260742 | − | 0.451618i | −0.0135007 | − | 0.0233839i | 0.859196 | − | 0.511646i | \(-0.170964\pi\) |
−0.872697 | + | 0.488262i | \(0.837631\pi\) | |||||||
\(374\) | −13.3397 | + | 10.9398i | −0.689781 | + | 0.565685i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.390160 | − | 11.5476i | 0.0201209 | − | 0.595524i | ||||
\(377\) | 1.49892i | 0.0771985i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.8440i | − | 1.17342i | −0.809797 | − | 0.586710i | \(-0.800423\pi\) | ||
0.809797 | − | 0.586710i | \(-0.199577\pi\) | |||||||
\(380\) | 0.495115 | − | 2.48004i | 0.0253989 | − | 0.127224i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.44249 | + | 10.2945i | 0.431956 | + | 0.526715i | ||||
\(383\) | −12.4781 | − | 21.6128i | −0.637603 | − | 1.10436i | −0.985957 | − | 0.166998i | \(-0.946593\pi\) |
0.348354 | − | 0.937363i | \(-0.386741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.68688 | + | 13.3141i | −0.391760 | + | 0.678548i | ||||
\(386\) | 1.83843 | − | 0.302865i | 0.0935736 | − | 0.0154154i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.6478 | − | 4.96082i | 0.743627 | − | 0.251847i | ||||
\(389\) | 22.0002 | + | 12.7018i | 1.11545 | + | 0.644007i | 0.940236 | − | 0.340523i | \(-0.110604\pi\) |
0.175216 | + | 0.984530i | \(0.443938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.69818 | + | 5.02190i | −0.439886 | + | 0.253968i | ||||
\(392\) | 2.40034 | + | 1.49612i | 0.121235 | + | 0.0755655i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.71675 | + | 1.77714i | 0.237627 | + | 0.0895312i | ||||
\(395\) | −7.93985 | −0.399497 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.32969 | 0.267489 | 0.133745 | − | 0.991016i | \(-0.457300\pi\) | ||||
0.133745 | + | 0.991016i | \(0.457300\pi\) | |||||||
\(398\) | 21.1398 | + | 7.96489i | 1.05964 | + | 0.399244i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.60837 | + | 1.08470i | 0.130418 | + | 0.0542350i | ||||
\(401\) | −20.2109 | + | 11.6688i | −1.00928 | + | 0.582710i | −0.910982 | − | 0.412447i | \(-0.864674\pi\) |
−0.0983016 | + | 0.995157i | \(0.531341\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.9206 | − | 12.6558i | −1.09194 | − | 0.630433i | ||||
\(404\) | −10.9638 | − | 32.3727i | −0.545470 | − | 1.61060i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.486397 | + | 0.0801298i | −0.0241395 | + | 0.00397677i | ||||
\(407\) | 2.71099 | − | 4.69557i | 0.134379 | − | 0.232751i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5599 | + | 26.9506i | 0.769389 | + | 1.33262i | 0.937895 | + | 0.346920i | \(0.112772\pi\) |
−0.168506 | + | 0.985701i | \(0.553894\pi\) | |||||||
\(410\) | 11.3423 | + | 13.8305i | 0.560155 | + | 0.683038i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.7291 | + | 4.53763i | 1.11978 | + | 0.223553i | ||||
\(413\) | 5.32341i | 0.261948i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.4600i | − | 0.758900i | ||||||
\(416\) | −7.02064 | − | 23.2905i | −0.344215 | − | 1.14191i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.72539 | − | 3.05517i | 0.182215 | − | 0.149433i | ||||
\(419\) | −13.4133 | − | 23.2325i | −0.655283 | − | 1.13498i | −0.981823 | − | 0.189800i | \(-0.939216\pi\) |
0.326540 | − | 0.945183i | \(-0.394117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00100 | − | 6.92994i | 0.194997 | − | 0.337744i | −0.751903 | − | 0.659274i | \(-0.770864\pi\) |
0.946899 | + | 0.321530i | \(0.104197\pi\) | |||||||
\(422\) | 0.900918 | + | 5.46868i | 0.0438560 | + | 0.266211i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.7640 | + | 31.4425i | 0.814131 | + | 1.52698i | ||||
\(425\) | 1.15929 | + | 0.669318i | 0.0562339 | + | 0.0324667i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.06013 | + | 3.49882i | −0.293270 | + | 0.169320i | ||||
\(428\) | 2.49733 | + | 2.19320i | 0.120713 | + | 0.106012i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.1514 | − | 26.9430i | 0.489544 | − | 1.29931i | ||||
\(431\) | 23.2635 | 1.12056 | 0.560282 | − | 0.828302i | \(-0.310693\pi\) | ||||
0.560282 | + | 0.828302i | \(0.310693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.4077 | −1.94187 | −0.970936 | − | 0.239340i | \(-0.923069\pi\) | ||||
−0.970936 | + | 0.239340i | \(0.923069\pi\) | |||||||
\(434\) | 2.93496 | − | 7.78973i | 0.140882 | − | 0.373919i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.3453 | + | 10.8419i | 0.591235 | + | 0.519231i | ||||
\(437\) | 2.42914 | − | 1.40247i | 0.116202 | − | 0.0670891i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.54218 | + | 2.62243i | 0.216786 | + | 0.125162i | 0.604461 | − | 0.796634i | \(-0.293388\pi\) |
−0.387675 | + | 0.921796i | \(0.626722\pi\) | |||||||
\(440\) | 20.4578 | + | 38.3706i | 0.975286 | + | 1.82924i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.87374 | − | 11.3738i | −0.0891245 | − | 0.540996i | ||||
\(443\) | −4.84903 | + | 8.39876i | −0.230384 | + | 0.399037i | −0.957921 | − | 0.287031i | \(-0.907332\pi\) |
0.727537 | + | 0.686068i | \(0.240665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2195 | + | 29.8250i | 0.816280 | + | 1.41384i | ||||
\(446\) | 2.84861 | − | 2.33613i | 0.134885 | − | 0.110619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.18239 | − | 3.52325i | 0.339336 | − | 0.166458i | ||||
\(449\) | 38.7800i | 1.83014i | 0.403294 | + | 0.915071i | \(0.367865\pi\) | ||||
−0.403294 | + | 0.915071i | \(0.632135\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.0755i | 1.60455i | ||||||||
\(452\) | −17.8349 | − | 3.56055i | −0.838883 | − | 0.167474i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.80703 | + | 3.42282i | 0.131740 | + | 0.160641i | ||||
\(455\) | −5.13610 | − | 8.89599i | −0.240784 | − | 0.417050i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3244 | − | 19.6145i | 0.529735 | − | 0.917528i | −0.469663 | − | 0.882846i | \(-0.655625\pi\) |
0.999398 | − | 0.0346824i | \(-0.0110420\pi\) | |||||||
\(458\) | 9.30966 | − | 1.53369i | 0.435012 | − | 0.0716645i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.12062 | + | 23.9777i | 0.378626 | + | 1.11796i | ||||
\(461\) | −32.0052 | − | 18.4782i | −1.49063 | − | 0.860617i | −0.490689 | − | 0.871335i | \(-0.663255\pi\) |
−0.999943 | + | 0.0107183i | \(0.996588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.93748 | − | 5.16006i | 0.415360 | − | 0.239808i | −0.277730 | − | 0.960659i | \(-0.589582\pi\) |
0.693090 | + | 0.720851i | \(0.256249\pi\) | |||||||
\(464\) | −0.535370 | + | 1.28740i | −0.0248540 | + | 0.0597661i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.8770 | + | 7.48910i | 0.920783 | + | 0.346926i | ||||
\(467\) | 0.900019 | 0.0416479 | 0.0208239 | − | 0.999783i | \(-0.493371\pi\) | ||||
0.0208239 | + | 0.999783i | \(0.493371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7713 | 0.497370 | ||||||||
\(470\) | −12.9140 | − | 4.86564i | −0.595678 | − | 0.224435i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.7780 | + | 7.96446i | 0.588154 | + | 0.366594i | ||||
\(473\) | 47.5027 | − | 27.4257i | 2.18418 | − | 1.26103i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.323756 | − | 0.186921i | −0.0148549 | − | 0.00857651i | ||||
\(476\) | 3.59060 | − | 1.21605i | 0.164575 | − | 0.0557373i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.07271 | − | 0.506203i | 0.140543 | − | 0.0231532i | ||||
\(479\) | −15.9460 | + | 27.6192i | −0.728590 | + | 1.26195i | 0.228889 | + | 0.973452i | \(0.426491\pi\) |
−0.957479 | + | 0.288502i | \(0.906843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.81139 | + | 3.13741i | 0.0825921 | + | 0.143054i | ||||
\(482\) | −16.6522 | − | 20.3053i | −0.758488 | − | 0.924880i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.9111 | + | 59.6628i | −0.541412 | + | 2.71195i | ||||
\(485\) | − | 18.4712i | − | 0.838733i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.65522i | − | 0.346891i | −0.984843 | − | 0.173446i | \(-0.944510\pi\) | ||
0.984843 | − | 0.173446i | \(-0.0554901\pi\) | |||||||
\(488\) | −0.668341 | + | 19.7810i | −0.0302544 | + | 0.895444i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.61216 | − | 2.14221i | 0.118005 | − | 0.0967754i | ||||
\(491\) | −1.59570 | − | 2.76383i | −0.0720128 | − | 0.124730i | 0.827771 | − | 0.561067i | \(-0.189609\pi\) |
−0.899783 | + | 0.436337i | \(0.856276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.330352 | + | 0.572187i | −0.0148783 | + | 0.0257700i | ||||
\(494\) | 0.523279 | + | 3.17636i | 0.0235434 | + | 0.142911i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.3069 | − | 18.6993i | −0.642400 | − | 0.839622i | ||||
\(497\) | 5.30126 | + | 3.06068i | 0.237794 | + | 0.137290i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.07585 | + | 5.23995i | −0.406291 | + | 0.234572i | −0.689195 | − | 0.724576i | \(-0.742036\pi\) |
0.282904 | + | 0.959148i | \(0.408702\pi\) | |||||||
\(500\) | −13.5364 | + | 15.4135i | −0.605366 | + | 0.689314i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.08230 | − | 8.18079i | 0.137570 | − | 0.365127i | ||||
\(503\) | 12.6421 | 0.563685 | 0.281843 | − | 0.959461i | \(-0.409054\pi\) | ||||
0.281843 | + | 0.959461i | \(0.409054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.8228 | −1.81659 | ||||||||
\(506\) | −17.0042 | + | 45.1312i | −0.755929 | + | 2.00633i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.5188 | + | 25.6415i | −0.999108 | + | 1.13766i | ||||
\(509\) | 23.8125 | − | 13.7481i | 1.05547 | − | 0.609376i | 0.131294 | − | 0.991343i | \(-0.458087\pi\) |
0.924176 | + | 0.381968i | \(0.124753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.39891 | + | 2.53971i | 0.194596 | + | 0.112350i | ||||
\(512\) | 2.28874 | − | 22.5114i | 0.101149 | − | 0.994871i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.85462 | − | 11.2577i | −0.0818036 | − | 0.496558i | ||||
\(515\) | 13.8415 | − | 23.9742i | 0.609929 | − | 1.05643i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1453 | − | 22.7684i | −0.578130 | − | 1.00135i | ||||
\(518\) | −0.921250 | + | 0.755511i | −0.0404774 | + | 0.0331953i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −29.0376 | − | 0.981093i | −1.27338 | − | 0.0430238i | ||||
\(521\) | − | 16.7533i | − | 0.733975i | −0.930226 | − | 0.366988i | \(-0.880389\pi\) | ||
0.930226 | − | 0.366988i | \(-0.119611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 39.1120i | − | 1.71025i | −0.518424 | − | 0.855124i | \(-0.673481\pi\) | ||
0.518424 | − | 0.855124i | \(-0.326519\pi\) | |||||||
\(524\) | 4.37733 | − | 21.9262i | 0.191224 | − | 0.957848i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.135799 | + | 0.165590i | 0.00592112 | + | 0.00722006i | ||||
\(527\) | −5.57852 | − | 9.66228i | −0.243004 | − | 0.420895i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.53889 | + | 4.39749i | −0.110387 | + | 0.191195i | ||||
\(530\) | 41.9927 | − | 6.91794i | 1.82405 | − | 0.300496i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.00275 | + | 0.339605i | −0.0434747 | + | 0.0147238i | ||||
\(533\) | −19.7177 | − | 11.3840i | −0.854069 | − | 0.493097i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.43790 | − | 1.98487i | 0.148633 | − | 0.0858135i | ||||
\(536\) | 16.1151 | − | 25.8546i | 0.696066 | − | 1.11675i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.88587 | − | 1.08732i | −0.124419 | − | 0.0468775i | ||||
\(539\) | 6.43584 | 0.277211 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.1182 | −0.478010 | −0.239005 | − | 0.971018i | \(-0.576821\pi\) | ||||
−0.239005 | + | 0.971018i | \(0.576821\pi\) | |||||||
\(542\) | −4.08199 | − | 1.53798i | −0.175337 | − | 0.0660620i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.45306 | − | 10.4380i | 0.105174 | − | 0.447526i | ||||
\(545\) | 16.9950 | − | 9.81204i | 0.727984 | − | 0.420302i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.1315 | + | 13.9323i | 1.03179 | + | 0.595703i | 0.917496 | − | 0.397745i | \(-0.130207\pi\) |
0.114291 | + | 0.993447i | \(0.463540\pi\) | |||||||
\(548\) | 3.18948 | + | 9.41753i | 0.136248 | + | 0.402297i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.34237 | − | 1.04485i | 0.270440 | − | 0.0445526i | ||||
\(551\) | 0.0922576 | − | 0.159795i | 0.00393031 | − | 0.00680749i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.66191 | + | 2.87851i | 0.0706716 | + | 0.122407i | ||||
\(554\) | −14.9063 | − | 18.1763i | −0.633307 | − | 0.772237i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.9030 | − | 3.37452i | −0.716848 | − | 0.143111i | ||||
\(557\) | 23.5098i | 0.996142i | 0.867136 | + | 0.498071i | \(0.165958\pi\) | ||||
−0.867136 | + | 0.498071i | \(0.834042\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.6497i | 1.55012i | ||||||||
\(560\) | −1.23394 | − | 9.47508i | −0.0521433 | − | 0.400395i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.2868 | − | 9.25627i | 0.476107 | − | 0.390452i | ||||
\(563\) | −16.5569 | − | 28.6774i | −0.697790 | − | 1.20861i | −0.969231 | − | 0.246152i | \(-0.920834\pi\) |
0.271442 | − | 0.962455i | \(-0.412500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.8610 | + | 18.8119i | −0.456928 | + | 0.791422i | ||||
\(566\) | 3.28244 | + | 19.9248i | 0.137971 | + | 0.837501i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.2780 | − | 8.14566i | 0.641051 | − | 0.341784i | ||||
\(569\) | −16.2900 | − | 9.40502i | −0.682911 | − | 0.394279i | 0.118040 | − | 0.993009i | \(-0.462339\pi\) |
−0.800951 | + | 0.598730i | \(0.795672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0636 | − | 10.4290i | 0.755937 | − | 0.436440i | −0.0718982 | − | 0.997412i | \(-0.522906\pi\) |
0.827835 | + | 0.560972i | \(0.189572\pi\) | |||||||
\(572\) | −41.5894 | − | 36.5245i | −1.73894 | − | 1.52716i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.64002 | − | 7.00692i | 0.110192 | − | 0.292463i | ||||
\(575\) | 3.74220 | 0.156061 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.3394 | −1.42957 | −0.714783 | − | 0.699346i | \(-0.753475\pi\) | ||||
−0.714783 | + | 0.699346i | \(0.753475\pi\) | |||||||
\(578\) | −6.68509 | + | 17.7430i | −0.278063 | + | 0.738013i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.25128 | + | 1.09889i | 0.0519565 | + | 0.0456290i | ||||
\(581\) | −5.60486 | + | 3.23597i | −0.232529 | + | 0.134251i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 70.2159 | + | 40.5392i | 2.90805 | + | 1.67896i | ||||
\(584\) | 12.6775 | − | 6.75915i | 0.524597 | − | 0.279696i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.558148 | + | 3.38803i | 0.0230569 | + | 0.139958i | ||||
\(587\) | 18.1996 | − | 31.5226i | 0.751177 | − | 1.30108i | −0.196076 | − | 0.980589i | \(-0.562820\pi\) |
0.947253 | − | 0.320487i | \(-0.103847\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.55791 | + | 2.69839i | 0.0641928 | + | 0.111185i | ||||
\(590\) | 13.9056 | − | 11.4039i | 0.572484 | − | 0.469491i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.435181 | + | 3.34165i | 0.0178858 | + | 0.137341i | ||||
\(593\) | − | 2.74882i | − | 0.112880i | −0.998406 | − | 0.0564402i | \(-0.982025\pi\) | ||
0.998406 | − | 0.0564402i | \(-0.0179750\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 4.52784i | − | 0.185623i | ||||||
\(596\) | 4.94267 | + | 0.986753i | 0.202460 | + | 0.0404190i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.4342 | − | 24.9170i | −0.835619 | − | 1.01893i | ||||
\(599\) | 13.1712 | + | 22.8132i | 0.538162 | + | 0.932124i | 0.999003 | + | 0.0446413i | \(0.0142145\pi\) |
−0.460841 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6251 | − | 18.4032i | 0.433406 | − | 0.750682i | −0.563758 | − | 0.825940i | \(-0.690645\pi\) |
0.997164 | + | 0.0752583i | \(0.0239781\pi\) | |||||||
\(602\) | −11.8927 | + | 1.95923i | −0.484712 | + | 0.0798522i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.245240 | + | 0.724119i | 0.00997869 | + | 0.0294640i | ||||
\(605\) | 62.9312 | + | 36.3333i | 2.55852 | + | 1.47716i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9081 | + | 7.45251i | −0.523924 | + | 0.302488i | −0.738539 | − | 0.674211i | \(-0.764484\pi\) |
0.214614 | + | 0.976699i | \(0.431151\pi\) | |||||||
\(608\) | −0.685066 | + | 2.91503i | −0.0277831 | + | 0.118220i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.1216 | + | 8.33480i | 0.895676 | + | 0.337466i | ||||
\(611\) | 17.5665 | 0.710663 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.497742 | 0.0201036 | 0.0100518 | − | 0.999949i | \(-0.496800\pi\) | ||||
0.0100518 | + | 0.999949i | \(0.496800\pi\) | |||||||
\(614\) | 11.7417 | + | 4.42394i | 0.473855 | + | 0.178536i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.62880 | − | 15.4482i | 0.387955 | − | 0.622426i | ||||
\(617\) | 13.3288 | − | 7.69541i | 0.536599 | − | 0.309806i | −0.207100 | − | 0.978320i | \(-0.566403\pi\) |
0.743700 | + | 0.668514i | \(0.233069\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.09500 | − | 3.51895i | −0.244979 | − | 0.141439i | 0.372484 | − | 0.928039i | \(-0.378506\pi\) |
−0.617463 | + | 0.786600i | \(0.711839\pi\) | |||||||
\(620\) | −26.6353 | + | 9.02070i | −1.06970 | + | 0.362280i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.47767 | − | 1.39662i | 0.339924 | − | 0.0559995i | ||||
\(623\) | 7.20850 | − | 12.4855i | 0.288802 | − | 0.500220i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0162 | + | 24.2768i | 0.560648 | + | 0.971070i | ||||
\(626\) | −18.5177 | − | 22.5800i | −0.740116 | − | 0.902478i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.44476 | − | 17.2549i | 0.137461 | − | 0.688546i | ||||
\(629\) | 1.59687i | 0.0636713i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.297508i | 0.0118436i | 0.999982 | + | 0.00592180i | \(0.00188498\pi\) | ||||
−0.999982 | + | 0.00592180i | \(0.998115\pi\) | |||||||
\(632\) | 9.39582 | + | 0.317456i | 0.373746 | + | 0.0126277i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.8423 | − | 22.0132i | 1.06604 | − | 0.874254i | ||||
\(635\) | 20.3798 | + | 35.2988i | 0.808747 | + | 1.40079i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.15010 | + | 3.72408i | −0.0851901 | + | 0.147554i | ||||
\(638\) | 0.515703 | + | 3.13038i | 0.0204169 | + | 0.123933i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.5895 | − | 11.2140i | −0.971985 | − | 0.443272i | ||||
\(641\) | −8.18111 | − | 4.72337i | −0.323134 | − | 0.186562i | 0.329654 | − | 0.944102i | \(-0.393068\pi\) |
−0.652789 | + | 0.757540i | \(0.726401\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2594 | − | 16.8929i | 1.15388 | − | 0.666193i | 0.204050 | − | 0.978960i | \(-0.434590\pi\) |
0.949830 | + | 0.312768i | \(0.101256\pi\) | |||||||
\(644\) | 6.99312 | − | 7.96288i | 0.275567 | − | 0.313781i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.500296 | + | 1.32785i | −0.0196839 | + | 0.0522434i | ||||
\(647\) | −8.81904 | −0.346712 | −0.173356 | − | 0.984859i | \(-0.555461\pi\) | ||||
−0.173356 | + | 0.984859i | \(0.555461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.2606 | 1.34485 | ||||||||
\(650\) | −1.51427 | + | 4.01906i | −0.0593947 | + | 0.157641i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.2128 | − | 16.1837i | 0.556615 | − | 0.633803i | ||||
\(653\) | −26.1332 | + | 15.0880i | −1.02267 | + | 0.590440i | −0.914877 | − | 0.403733i | \(-0.867712\pi\) |
−0.107795 | + | 0.994173i | \(0.534379\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.1273 | − | 13.3525i | −0.903657 | − | 0.521727i | ||||
\(656\) | −12.8692 | − | 16.8201i | −0.502458 | − | 0.656716i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.939071 | + | 5.70028i | 0.0366088 | + | 0.222220i | ||||
\(659\) | −4.08576 | + | 7.07674i | −0.159158 | + | 0.275671i | −0.934565 | − | 0.355791i | \(-0.884211\pi\) |
0.775407 | + | 0.631462i | \(0.217545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1468 | − | 38.3593i | −0.861409 | − | 1.49200i | −0.870569 | − | 0.492046i | \(-0.836249\pi\) |
0.00916009 | − | 0.999958i | \(-0.497084\pi\) | |||||||
\(662\) | 32.8128 | − | 26.9096i | 1.27531 | − | 1.04587i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.618131 | + | 18.2950i | −0.0239881 | + | 0.709982i | ||||
\(665\) | 1.26449i | 0.0490349i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.84702i | 0.0715170i | ||||||||
\(668\) | −3.07339 | + | 15.3947i | −0.118913 | + | 0.595639i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.0743 | − | 28.1362i | −0.891439 | − | 1.08700i | ||||
\(671\) | 22.5178 | + | 39.0020i | 0.869291 | + | 1.50566i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.17994 | − | 10.7040i | 0.238219 | − | 0.412608i | −0.721984 | − | 0.691910i | \(-0.756770\pi\) |
0.960203 | + | 0.279302i | \(0.0901030\pi\) | |||||||
\(674\) | 14.7188 | − | 2.42479i | 0.566946 | − | 0.0933995i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4030 | − | 3.52325i | 0.400117 | − | 0.135509i | ||||
\(677\) | 2.57177 | + | 1.48481i | 0.0988412 | + | 0.0570660i | 0.548606 | − | 0.836081i | \(-0.315159\pi\) |
−0.449765 | + | 0.893147i | \(0.648492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.69654 | + | 3.86625i | −0.256990 | + | 0.148373i | ||||
\(680\) | −10.8683 | − | 6.77420i | −0.416782 | − | 0.259779i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −50.1335 | − | 18.8889i | −1.91971 | − | 0.723294i | ||||
\(683\) | 13.3131 | 0.509413 | 0.254707 | − | 0.967018i | \(-0.418021\pi\) | ||||
0.254707 | + | 0.967018i | \(0.418021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.8757 | 0.453749 | ||||||||
\(686\) | −1.32340 | − | 0.498620i | −0.0505275 | − | 0.0190374i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.0902 | + | 31.4779i | −0.499058 | + | 1.20008i | ||||
\(689\) | −46.9158 | + | 27.0868i | −1.78735 | + | 1.03193i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.4607 | + | 20.4733i | 1.34899 | + | 0.778840i | 0.988107 | − | 0.153771i | \(-0.0491417\pi\) |
0.360884 | + | 0.932611i | \(0.382475\pi\) | |||||||
\(692\) | −12.2716 | − | 36.2342i | −0.466496 | − | 1.37742i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.7166 | + | 2.09495i | −0.482716 | + | 0.0795233i | ||||
\(695\) | −10.2936 | + | 17.8290i | −0.390457 | + | 0.676292i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.01792 | − | 8.69129i | −0.190067 | − | 0.329206i | ||||
\(698\) | 20.2635 | + | 24.7087i | 0.766984 | + | 0.935239i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.38513 | − | 0.276526i | −0.0523529 | − | 0.0104517i | ||||
\(701\) | 18.8087i | 0.710396i | 0.934791 | + | 0.355198i | \(0.115587\pi\) | ||||
−0.934791 | + | 0.355198i | \(0.884413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.445958i | − | 0.0168196i | ||||||
\(704\) | −22.6751 | − | 46.2247i | −0.854598 | − | 1.74216i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.28018 | + | 5.97043i | −0.273993 | + | 0.224700i | ||||
\(707\) | 8.54473 | + | 14.7999i | 0.321358 | + | 0.556608i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.3884 | − | 33.5818i | 0.728148 | − | 1.26119i | −0.229517 | − | 0.973305i | \(-0.573715\pi\) |
0.957665 | − | 0.287885i | \(-0.0929520\pi\) | |||||||
\(710\) | −3.36145 | − | 20.4044i | −0.126153 | − | 0.765763i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −19.1846 | − | 35.9826i | −0.718973 | − | 1.34851i | ||||
\(713\) | −27.0112 | − | 15.5949i | −1.01158 | − | 0.584035i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −57.2532 | + | 33.0551i | −2.14115 | + | 1.23619i | ||||
\(716\) | 39.2923 | + | 34.5071i | 1.46842 | + | 1.28959i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.00558 | − | 10.6313i | 0.149487 | − | 0.396757i | ||||
\(719\) | 27.9873 | 1.04375 | 0.521875 | − | 0.853022i | \(-0.325233\pi\) | ||||
0.521875 | + | 0.853022i | \(0.325233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5888 | −0.431589 | ||||||||
\(722\) | −9.33406 | + | 24.7737i | −0.347378 | + | 0.921982i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.4279 | − | 24.9658i | −1.05652 | − | 0.927848i | ||||
\(725\) | 0.213190 | − | 0.123085i | 0.00791769 | − | 0.00457128i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9395 | − | 6.89330i | −0.442813 | − | 0.255658i | 0.261977 | − | 0.965074i | \(-0.415626\pi\) |
−0.704790 | + | 0.709416i | \(0.748959\pi\) | |||||||
\(728\) | 5.72225 | + | 10.7326i | 0.212081 | + | 0.397778i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.78928 | − | 16.9313i | −0.103236 | − | 0.626654i | ||||
\(731\) | −8.07734 | + | 13.9904i | −0.298751 | + | 0.517452i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9012 | + | 36.2020i | 0.772005 | + | 1.33715i | 0.936463 | + | 0.350767i | \(0.114079\pi\) |
−0.164458 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(734\) | 18.8418 | − | 15.4520i | 0.695463 | − | 0.570345i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.65105 | − | 28.6993i | −0.318882 | − | 1.05787i | ||||
\(737\) | − | 69.3221i | − | 2.55351i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.3413i | 1.74148i | 0.491746 | + | 0.870739i | \(0.336359\pi\) | ||||
−0.491746 | + | 0.870739i | \(0.663641\pi\) | |||||||
\(740\) | 3.94703 | + | 0.787984i | 0.145096 | + | 0.0289669i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.2976 | − | 13.7760i | −0.414749 | − | 0.505734i | ||||
\(743\) | 1.10160 | + | 1.90802i | 0.0404136 | + | 0.0699984i | 0.885525 | − | 0.464592i | \(-0.153799\pi\) |
−0.845111 | + | 0.534591i | \(0.820466\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00998 | − | 5.21343i | 0.110277 | − | 0.191005i | ||||
\(746\) | 0.727681 | − | 0.119879i | 0.0266423 | − | 0.00438909i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.82628 | − | 23.1086i | −0.286157 | − | 0.844933i | ||||
\(749\) | −1.43919 | − | 0.830918i | −0.0525869 | − | 0.0303611i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.02644 | + | 5.21142i | −0.329379 | + | 0.190167i | −0.655566 | − | 0.755138i | \(-0.727570\pi\) |
0.326186 | + | 0.945306i | \(0.394236\pi\) | |||||||
\(752\) | 15.0876 | + | 6.27421i | 0.550186 | + | 0.228797i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.98367 | − | 0.747393i | −0.0722411 | − | 0.0272185i | ||||
\(755\) | 0.913132 | 0.0332323 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0656 | 0.511224 | 0.255612 | − | 0.966779i | \(-0.417723\pi\) | ||||
0.255612 | + | 0.966779i | \(0.417723\pi\) | |||||||
\(758\) | 30.2317 | + | 11.3905i | 1.09807 | + | 0.413721i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.03521 | + | 1.89183i | 0.110099 | + | 0.0686239i | ||||
\(761\) | 23.2533 | − | 13.4253i | 0.842931 | − | 0.486667i | −0.0153283 | − | 0.999883i | \(-0.504879\pi\) |
0.858260 | + | 0.513216i | \(0.171546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.11451 | − | 4.10757i | −0.257563 | − | 0.148704i | ||||
\(764\) | −17.8334 | + | 6.03970i | −0.645188 | + | 0.218509i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.8241 | − | 5.73697i | 1.25825 | − | 0.207285i | ||||
\(767\) | −11.4459 | + | 19.8248i | −0.413286 | + | 0.715833i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.9397 | + | 32.8045i | 0.682983 | + | 1.18296i | 0.974066 | + | 0.226263i | \(0.0726510\pi\) |
−0.291083 | + | 0.956698i | \(0.594016\pi\) | |||||||
\(770\) | −13.7870 | − | 16.8114i | −0.496848 | − | 0.605842i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.515866 | + | 2.58399i | −0.0185664 | + | 0.0929997i | ||||
\(773\) | − | 26.0697i | − | 0.937662i | −0.883288 | − | 0.468831i | \(-0.844675\pi\) | ||
0.883288 | − | 0.468831i | \(-0.155325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.15698i | 0.149323i | ||||||||
\(776\) | −0.738528 | + | 21.8583i | −0.0265116 | + | 0.784669i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −27.7792 | + | 22.7816i | −0.995934 | + | 0.816759i | ||||
\(779\) | 1.40136 | + | 2.42722i | 0.0502088 | + | 0.0869642i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.6981 | − | 34.1181i | 0.704853 | − | 1.22084i | ||||
\(782\) | −2.30888 | − | 14.0152i | −0.0825653 | − | 0.501181i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.17682 | + | 2.43060i | −0.113458 | + | 0.0868073i | ||||
\(785\) | −18.2001 | − | 10.5079i | −0.649591 | − | 0.375041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.3071 | − | 25.0034i | 1.54373 | − | 0.891275i | 0.545135 | − | 0.838349i | \(-0.316479\pi\) |
0.998598 | − | 0.0529261i | \(-0.0168548\pi\) | |||||||
\(788\) | −4.70373 | + | 5.35601i | −0.167563 | + | 0.190800i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.95896 | − | 10.5076i | 0.140854 | − | 0.373842i | ||||
\(791\) | 9.09342 | 0.323325 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.0912 | −1.06857 | ||||||||
\(794\) | −2.65749 | + | 7.05329i | −0.0943107 | + | 0.250312i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.0814 | + | 24.0048i | −0.747211 | + | 0.850829i | ||||
\(797\) | −7.70027 | + | 4.44575i | −0.272757 | + | 0.157477i | −0.630140 | − | 0.776481i | \(-0.717003\pi\) |
0.357383 | + | 0.933958i | \(0.383669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.70568 | + | 3.87152i | 0.237230 | + | 0.136965i | ||||
\(800\) | −2.73607 | + | 2.91105i | −0.0967348 | + | 0.102921i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.36485 | − | 32.5653i | −0.189440 | − | 1.14992i | ||||
\(803\) | 16.3452 | − | 28.3107i | 0.576809 | − | 0.999063i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.32887 | − | 10.9619i | −0.223063 | − | 0.386357i | ||||
\(806\) | 27.6787 | − | 22.6992i | 0.974942 | − | 0.799544i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 48.3087 | + | 1.63221i | 1.69950 | + | 0.0574208i | ||||
\(809\) | 21.3028i | 0.748967i | 0.927234 | + | 0.374484i | \(0.122180\pi\) | ||||
−0.927234 | + | 0.374484i | \(0.877820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.10606i | − | 0.179298i | −0.995973 | − | 0.0896491i | \(-0.971425\pi\) | ||
0.995973 | − | 0.0896491i | \(-0.0285745\pi\) | |||||||
\(812\) | 0.136484 | − | 0.683651i | 0.00478964 | − | 0.0239914i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.86235 | + | 5.92902i | 0.170425 | + | 0.207812i | ||||
\(815\) | −12.8628 | − | 22.2790i | −0.450563 | − | 0.780398i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.25576 | − | 3.90709i | 0.0789191 | − | 0.136692i | ||||
\(818\) | −43.4248 | + | 7.15386i | −1.51831 | + | 0.250129i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.9587 | + | 8.11419i | −0.836673 | + | 0.283360i | ||||
\(821\) | 38.3644 | + | 22.1497i | 1.33893 | + | 0.773030i | 0.986648 | − | 0.162865i | \(-0.0520734\pi\) |
0.352279 | + | 0.935895i | \(0.385407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7375 | + | 11.9728i | −0.722864 | + | 0.417346i | −0.815806 | − | 0.578326i | \(-0.803706\pi\) |
0.0929417 | + | 0.995672i | \(0.470373\pi\) | |||||||
\(824\) | −17.3382 | + | 27.8170i | −0.604006 | + | 0.969052i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.04498 | − | 2.65436i | −0.245126 | − | 0.0923569i | ||||
\(827\) | 28.7823 | 1.00086 | 0.500429 | − | 0.865777i | \(-0.333176\pi\) | ||||
0.500429 | + | 0.865777i | \(0.333176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0893 | 0.454611 | 0.227306 | − | 0.973823i | \(-0.427008\pi\) | ||||
0.227306 | + | 0.973823i | \(0.427008\pi\) | |||||||
\(830\) | 20.4597 | + | 7.70865i | 0.710166 | + | 0.267571i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 34.3232 | + | 2.32200i | 1.18994 | + | 0.0805010i | ||||
\(833\) | −1.64152 | + | 0.947734i | −0.0568754 | + | 0.0328370i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.2380 | + | 9.37503i | 0.561940 | + | 0.324436i | ||||
\(836\) | 2.18565 | + | 6.45353i | 0.0755922 | + | 0.223200i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.4340 | − | 6.16693i | 1.29314 | − | 0.213033i | ||||
\(839\) | 4.65016 | − | 8.05432i | 0.160541 | − | 0.278066i | −0.774522 | − | 0.632547i | \(-0.782009\pi\) |
0.935063 | + | 0.354482i | \(0.115343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4392 | − | 25.0095i | −0.497905 | − | 0.862397i | ||||
\(842\) | 7.17608 | + | 8.75031i | 0.247304 | + | 0.301556i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.68645 | − | 1.53452i | −0.264578 | − | 0.0528203i | ||||
\(845\) | − | 13.1185i | − | 0.451290i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30.4201i | − | 1.04525i | ||||||
\(848\) | −49.9698 | + | 6.50754i | −1.71597 | + | 0.223470i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.46382 | + | 1.20047i | −0.0502086 | + | 0.0411757i | ||||
\(851\) | 2.23205 | + | 3.86602i | 0.0765137 | + | 0.132526i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.68249 | − | 6.37826i | 0.126086 | − | 0.218387i | −0.796071 | − | 0.605203i | \(-0.793092\pi\) |
0.922157 | + | 0.386816i | \(0.126425\pi\) | |||||||
\(854\) | −1.60862 | − | 9.76453i | −0.0550459 | − | 0.334135i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.14769 | + | 2.21139i | −0.141765 | + | 0.0755839i | ||||
\(857\) | −8.88430 | − | 5.12935i | −0.303482 | − | 0.175215i | 0.340524 | − | 0.940236i | \(-0.389395\pi\) |
−0.644006 | + | 0.765020i | \(0.722729\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.8854 | + | 25.3372i | −1.49735 | + | 0.864495i | −0.999995 | − | 0.00305268i | \(-0.999028\pi\) |
−0.497354 | + | 0.867548i | \(0.665695\pi\) | |||||||
\(860\) | 30.5946 | + | 26.8687i | 1.04327 | + | 0.916214i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.5996 | + | 30.7868i | −0.395085 | + | 1.04860i | ||||
\(863\) | 10.9590 | 0.373049 | 0.186524 | − | 0.982450i | \(-0.440278\pi\) | ||||
0.186524 | + | 0.982450i | \(0.440278\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.6922 | −1.55358 | ||||||||
\(866\) | 20.1481 | − | 53.4754i | 0.684660 | − | 1.81717i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.84548 | + | 7.76823i | 0.300235 | + | 0.263671i | ||||
\(869\) | 18.5257 | − | 10.6958i | 0.628440 | − | 0.362830i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.1130 | + | 23.1593i | 1.35918 | + | 0.784722i | ||||
\(872\) | −20.5037 | + | 10.9318i | −0.694344 | + | 0.370198i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.644801 | + | 3.91402i | 0.0218107 | + | 0.132394i | ||||
\(875\) | 5.12842 | − | 8.88268i | 0.173372 | − | 0.300289i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.1977 | − | 47.1079i | −0.918402 | − | 1.59072i | −0.801842 | − | 0.597536i | \(-0.796147\pi\) |
−0.116560 | − | 0.993184i | \(-0.537187\pi\) | |||||||
\(878\) | −5.73533 | + | 4.70351i | −0.193558 | + | 0.158736i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −60.9801 | + | 7.94141i | −2.05564 | + | 0.267705i | ||||
\(881\) | 15.1656i | 0.510942i | 0.966817 | + | 0.255471i | \(0.0822305\pi\) | ||||
−0.966817 | + | 0.255471i | \(0.917770\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.5171i | 0.555843i | 0.960604 | + | 0.277922i | \(0.0896456\pi\) | ||||
−0.960604 | + | 0.277922i | \(0.910354\pi\) | |||||||
\(884\) | 15.9863 | + | 3.19150i | 0.537678 | + | 0.107342i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.69707 | − | 10.6050i | −0.292184 | − | 0.356281i | ||||
\(887\) | −20.7959 | − | 36.0195i | −0.698257 | − | 1.20942i | −0.969070 | − | 0.246785i | \(-0.920626\pi\) |
0.270813 | − | 0.962632i | \(-0.412707\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.53149 | − | 14.7770i | 0.286137 | − | 0.495604i | ||||
\(890\) | −48.0562 | + | 7.91685i | −1.61085 | + | 0.265373i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.67125 | + | 4.93468i | 0.0559575 | + | 0.165225i | ||||
\(893\) | −1.87270 | − | 1.08120i | −0.0626674 | − | 0.0361810i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54.0909 | − | 31.2294i | 1.80806 | − | 1.04388i | ||||
\(896\) | 1.08137 | + | 11.2619i | 0.0361260 | + | 0.376234i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −51.3213 | − | 19.3365i | −1.71261 | − | 0.645266i | ||||
\(899\) | −2.05174 | −0.0684295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.8790 | −0.795524 | ||||||||
\(902\) | −45.0955 | − | 16.9907i | −1.50151 | − | 0.565730i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.6049 | − | 21.8273i | 0.452491 | − | 0.725964i | ||||
\(905\) | −39.1347 | + | 22.5944i | −1.30088 | + | 0.751064i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.95363 | + | 2.85998i | 0.164482 | + | 0.0949640i | 0.579982 | − | 0.814630i | \(-0.303060\pi\) |
−0.415499 | + | 0.909594i | \(0.636393\pi\) | |||||||
\(908\) | −5.92938 | + | 2.00813i | −0.196774 | + | 0.0666422i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.3339 | − | 2.36138i | 0.475163 | − | 0.0782791i | ||||
\(911\) | −8.80268 | + | 15.2467i | −0.291646 | + | 0.505145i | −0.974199 | − | 0.225691i | \(-0.927536\pi\) |
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.8262 | + | 36.0720i | 0.689246 | + | 1.19381i | ||||
\(914\) | 20.3112 | + | 24.7669i | 0.671834 | + | 0.819216i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.61231 | + | 13.0851i | −0.0863130 | + | 0.432344i | ||||
\(917\) | 11.1794i | 0.369177i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.5323i | − | 0.776259i | −0.921605 | − | 0.388129i | \(-0.873121\pi\) | ||
0.921605 | − | 0.388129i | \(-0.126879\pi\) | |||||||
\(920\) | −35.7811 | − | 1.20893i | −1.17967 | − | 0.0398574i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 40.4124 | − | 33.1420i | 1.33091 | − | 1.09147i | ||||
\(923\) | 13.1616 | + | 22.7965i | 0.433218 | + | 0.750356i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.297487 | − | 0.515263i | 0.00978132 | − | 0.0169417i | ||||
\(926\) | 2.37240 | + | 14.4007i | 0.0779618 | + | 0.473238i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.43680 | − | 1.35043i | −0.0471652 | − | 0.0443301i | ||||
\(929\) | 24.3118 | + | 14.0364i | 0.797645 | + | 0.460521i | 0.842647 | − | 0.538466i | \(-0.180996\pi\) |
−0.0450020 | + | 0.998987i | \(0.514329\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.458429 | − | 0.264674i | 0.0150244 | − | 0.00867434i | ||||
\(932\) | −19.8221 | + | 22.5709i | −0.649294 | + | 0.739335i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.448767 | + | 1.19108i | −0.0146841 | + | 0.0389734i | ||||
\(935\) | −29.1405 | −0.952995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.7222 | −0.611628 | −0.305814 | − | 0.952091i | \(-0.598929\pi\) | ||||
−0.305814 | + | 0.952091i | \(0.598929\pi\) | |||||||
\(938\) | −5.37076 | + | 14.2546i | −0.175361 | + | 0.465430i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.8783 | − | 14.6642i | 0.420045 | − | 0.478294i | ||||
\(941\) | 1.01009 | − | 0.583173i | 0.0329279 | − | 0.0190109i | −0.483446 | − | 0.875374i | \(-0.660615\pi\) |
0.516374 | + | 0.856363i | \(0.327282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.2968 | − | 14.0278i | −0.791213 | − | 0.456807i | ||||
\(944\) | −16.9115 | + | 12.9391i | −0.550422 | + | 0.421132i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.6093 | + | 76.5399i | 0.409963 | + | 2.48853i | ||||
\(947\) | 22.6706 | − | 39.2667i | 0.736696 | − | 1.27600i | −0.217279 | − | 0.976110i | \(-0.569718\pi\) |
0.953975 | − | 0.299886i | \(-0.0969486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.9213 | + | 18.9162i | 0.354519 | + | 0.614046i | ||||
\(950\) | 0.408801 | − | 0.335255i | 0.0132633 | − | 0.0108771i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.181035 | + | 5.35814i | −0.00586739 | + | 0.173658i | ||||
\(953\) | − | 49.1845i | − | 1.59324i | −0.604479 | − | 0.796621i | \(-0.706619\pi\) | ||
0.604479 | − | 0.796621i | \(-0.293381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.4883i | 0.727705i | ||||||||
\(956\) | −0.862208 | + | 4.31882i | −0.0278858 | + | 0.139681i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.6002 | − | 34.8743i | −0.924031 | − | 1.12674i | ||||
\(959\) | −2.48574 | − | 4.30543i | −0.0802688 | − | 0.139030i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.82347 | − | 3.15834i | 0.0588216 | − | 0.101882i | ||||
\(962\) | −5.05524 | + | 0.832807i | −0.162987 | + | 0.0268508i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.1751 | − | 11.9129i | 1.13291 | − | 0.383688i | ||||
\(965\) | 2.72554 | + | 1.57359i | 0.0877381 | + | 0.0506556i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.53707 | − | 4.35153i | 0.242376 | − | 0.139936i | −0.373892 | − | 0.927472i | \(-0.621977\pi\) |
0.616268 | + | 0.787536i | \(0.288644\pi\) | |||||||
\(968\) | −73.0185 | − | 45.5121i | −2.34690 | − | 1.46281i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.4447 | + | 9.21009i | 0.784872 | + | 0.295718i | ||||
\(971\) | −13.3993 | −0.430005 | −0.215002 | − | 0.976614i | \(-0.568976\pi\) | ||||
−0.215002 | + | 0.976614i | \(0.568976\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.61829 | 0.276290 | ||||||||
\(974\) | 10.1309 | + | 3.81704i | 0.324615 | + | 0.122306i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.8449 | − | 10.7477i | −0.827274 | − | 0.344025i | ||||
\(977\) | −17.4473 | + | 10.0732i | −0.558190 | + | 0.322271i | −0.752419 | − | 0.658685i | \(-0.771113\pi\) |
0.194229 | + | 0.980956i | \(0.437780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −80.3546 | − | 46.3928i | −2.56814 | − | 1.48272i | ||||
\(980\) | 1.53253 | + | 4.52507i | 0.0489548 | + | 0.144548i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.45329 | − | 0.733641i | 0.142110 | − | 0.0234114i | ||||
\(983\) | 22.3323 | − | 38.6807i | 0.712291 | − | 1.23372i | −0.251704 | − | 0.967804i | \(-0.580991\pi\) |
0.963995 | − | 0.265920i | \(-0.0856757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.25694 | + | 7.37324i | 0.135637 | + | 0.234931i | ||||
\(986\) | −0.592510 | − | 0.722491i | −0.0188694 | − | 0.0230088i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.46451 | − | 0.891292i | −0.142035 | − | 0.0283558i | ||||
\(989\) | 45.1610i | 1.43604i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.8937i | 1.29903i | 0.760349 | + | 0.649515i | \(0.225028\pi\) | ||||
−0.760349 | + | 0.649515i | \(0.774972\pi\) | |||||||
\(992\) | 31.8803 | − | 9.60993i | 1.01220 | − | 0.305115i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.69381 | + | 5.48955i | −0.212315 | + | 0.174118i | ||||
\(995\) | 19.0790 | + | 33.0457i | 0.604844 | + | 1.04762i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.1863 | + | 50.5521i | −0.924339 | + | 1.60100i | −0.131718 | + | 0.991287i | \(0.542049\pi\) |
−0.792621 | + | 0.609715i | \(0.791284\pi\) | |||||||
\(998\) | −2.40913 | − | 14.6237i | −0.0762596 | − | 0.462905i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.ba.a.575.14 | 72 | ||
3.2 | odd | 2 | 252.2.ba.a.155.23 | yes | 72 | ||
4.3 | odd | 2 | inner | 756.2.ba.a.575.26 | 72 | ||
9.4 | even | 3 | 252.2.ba.a.239.11 | yes | 72 | ||
9.5 | odd | 6 | inner | 756.2.ba.a.71.26 | 72 | ||
12.11 | even | 2 | 252.2.ba.a.155.11 | ✓ | 72 | ||
36.23 | even | 6 | inner | 756.2.ba.a.71.14 | 72 | ||
36.31 | odd | 6 | 252.2.ba.a.239.23 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.ba.a.155.11 | ✓ | 72 | 12.11 | even | 2 | ||
252.2.ba.a.155.23 | yes | 72 | 3.2 | odd | 2 | ||
252.2.ba.a.239.11 | yes | 72 | 9.4 | even | 3 | ||
252.2.ba.a.239.23 | yes | 72 | 36.31 | odd | 6 | ||
756.2.ba.a.71.14 | 72 | 36.23 | even | 6 | inner | ||
756.2.ba.a.71.26 | 72 | 9.5 | odd | 6 | inner | ||
756.2.ba.a.575.14 | 72 | 1.1 | even | 1 | trivial | ||
756.2.ba.a.575.26 | 72 | 4.3 | odd | 2 | inner |