Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,3,Mod(28,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 9]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.28");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.l (of order \(12\), degree \(4\), 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: | \(11.0354507066\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 28.8 | ||
Character | \(\chi\) | \(=\) | 405.28 |
Dual form | 405.3.l.o.217.8 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.44665 | + | 0.923527i | 1.72332 | + | 0.461763i | 0.978628 | − | 0.205639i | \(-0.0659274\pi\) |
0.744697 | + | 0.667403i | \(0.232594\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.56239 | + | 4.36615i | 1.89060 | + | 1.09154i | ||||
\(5\) | −4.98625 | + | 0.370516i | −0.997251 | + | 0.0741033i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.99870 | + | 1.60735i | 0.856958 | + | 0.229621i | 0.660440 | − | 0.750879i | \(-0.270370\pi\) |
0.196518 | + | 0.980500i | \(0.437037\pi\) | |||||||
\(8\) | 11.9402 | + | 11.9402i | 1.49252 | + | 1.49252i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −17.5280 | − | 3.32790i | −1.75280 | − | 0.332790i | ||||
\(11\) | 10.3303 | + | 17.8926i | 0.939120 | + | 1.62660i | 0.767117 | + | 0.641507i | \(0.221691\pi\) |
0.172003 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.56860 | + | 1.49210i | −0.428354 | + | 0.114777i | −0.466553 | − | 0.884493i | \(-0.654504\pi\) |
0.0381995 | + | 0.999270i | \(0.487838\pi\) | |||||||
\(14\) | 19.1910 | + | 11.0799i | 1.37079 | + | 0.791424i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.6619 | + | 21.9311i | 0.791369 | + | 1.37069i | ||||
\(17\) | −3.85449 | + | 3.85449i | −0.226735 | + | 0.226735i | −0.811327 | − | 0.584592i | \(-0.801254\pi\) |
0.584592 | + | 0.811327i | \(0.301254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 18.4907i | − | 0.973193i | −0.873627 | − | 0.486597i | \(-0.838238\pi\) | ||
0.873627 | − | 0.486597i | \(-0.161762\pi\) | |||||||
\(20\) | −39.3257 | − | 18.9687i | −1.96629 | − | 0.948436i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 19.0807 | + | 71.2100i | 0.867303 | + | 3.23682i | ||||
\(23\) | 19.3656 | − | 5.18899i | 0.841981 | − | 0.225608i | 0.188047 | − | 0.982160i | \(-0.439784\pi\) |
0.653934 | + | 0.756552i | \(0.273117\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.7254 | − | 3.69498i | 0.989017 | − | 0.147799i | ||||
\(26\) | −20.5710 | −0.791193 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 38.3466 | + | 38.3466i | 1.36952 | + | 1.36952i | ||||
\(29\) | −9.21485 | + | 5.32019i | −0.317753 | + | 0.183455i | −0.650391 | − | 0.759600i | \(-0.725395\pi\) |
0.332637 | + | 0.943055i | \(0.392061\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.5732 | − | 28.7057i | 0.534620 | − | 0.925990i | −0.464561 | − | 0.885541i | \(-0.653788\pi\) |
0.999182 | − | 0.0404488i | \(-0.0128788\pi\) | |||||||
\(32\) | 5.90560 | + | 22.0400i | 0.184550 | + | 0.688750i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.8448 | + | 9.72536i | −0.495436 | + | 0.286040i | ||||
\(35\) | −30.5066 | − | 5.79202i | −0.871617 | − | 0.165486i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −35.8023 | + | 35.8023i | −0.967629 | + | 0.967629i | −0.999492 | − | 0.0318634i | \(-0.989856\pi\) |
0.0318634 | + | 0.999492i | \(0.489856\pi\) | |||||||
\(38\) | 17.0766 | − | 63.7309i | 0.449385 | − | 1.67713i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −63.9607 | − | 55.1126i | −1.59902 | − | 1.37782i | ||||
\(41\) | −6.02916 | + | 10.4428i | −0.147053 | + | 0.254703i | −0.930137 | − | 0.367213i | \(-0.880312\pi\) |
0.783084 | + | 0.621916i | \(0.213645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.0295 | − | 48.6267i | 0.303011 | − | 1.13085i | −0.631633 | − | 0.775268i | \(-0.717615\pi\) |
0.934644 | − | 0.355585i | \(-0.115718\pi\) | |||||||
\(44\) | 180.415i | 4.10034i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 71.5385 | 1.55518 | ||||||||
\(47\) | −0.840958 | − | 0.225334i | −0.0178927 | − | 0.00479434i | 0.249862 | − | 0.968282i | \(-0.419615\pi\) |
−0.267754 | + | 0.963487i | \(0.586282\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.03436 | − | 5.21599i | −0.184375 | − | 0.106449i | ||||
\(50\) | 88.6323 | + | 10.0993i | 1.77265 | + | 0.201986i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −48.6267 | − | 13.0295i | −0.935128 | − | 0.250567i | ||||
\(53\) | −11.6767 | − | 11.6767i | −0.220315 | − | 0.220315i | 0.588316 | − | 0.808631i | \(-0.299791\pi\) |
−0.808631 | + | 0.588316i | \(0.799791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −58.1391 | − | 85.3897i | −1.05707 | − | 1.55254i | ||||
\(56\) | 52.4335 | + | 90.8175i | 0.936313 | + | 1.62174i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −36.6737 | + | 9.82669i | −0.632305 | + | 0.169426i | ||||
\(59\) | −72.8545 | − | 42.0625i | −1.23482 | − | 0.712924i | −0.266790 | − | 0.963755i | \(-0.585963\pi\) |
−0.968031 | + | 0.250830i | \(0.919296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34.8873 | − | 60.4265i | −0.571922 | − | 0.990598i | −0.996369 | − | 0.0851453i | \(-0.972865\pi\) |
0.424446 | − | 0.905453i | \(-0.360469\pi\) | |||||||
\(62\) | 83.6326 | − | 83.6326i | 1.34891 | − | 1.34891i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 19.8770i | − | 0.310578i | ||||||
\(65\) | 27.2136 | − | 9.50325i | 0.418671 | − | 0.146204i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0760 | − | 52.5324i | −0.210090 | − | 0.784066i | −0.987838 | − | 0.155489i | \(-0.950305\pi\) |
0.777748 | − | 0.628577i | \(-0.216362\pi\) | |||||||
\(68\) | −45.9785 | + | 12.3199i | −0.676154 | + | 0.181175i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −99.7965 | − | 48.1368i | −1.42566 | − | 0.687668i | ||||
\(71\) | 107.003 | 1.50709 | 0.753543 | − | 0.657399i | \(-0.228343\pi\) | ||||
0.753543 | + | 0.657399i | \(0.228343\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.17407 | + | 8.17407i | 0.111974 | + | 0.111974i | 0.760874 | − | 0.648900i | \(-0.224771\pi\) |
−0.648900 | + | 0.760874i | \(0.724771\pi\) | |||||||
\(74\) | −156.462 | + | 90.3335i | −2.11435 | + | 1.22072i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 80.7330 | − | 139.834i | 1.06228 | − | 1.83992i | ||||
\(77\) | 33.2088 | + | 123.937i | 0.431284 | + | 1.60957i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.3057 | − | 36.5496i | 0.801338 | − | 0.462653i | −0.0426005 | − | 0.999092i | \(-0.513564\pi\) |
0.843939 | + | 0.536439i | \(0.180231\pi\) | |||||||
\(80\) | −71.2613 | − | 104.662i | −0.890766 | − | 1.30828i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −30.4246 | + | 30.4246i | −0.371032 | + | 0.371032i | ||||
\(83\) | 1.53327 | − | 5.72223i | 0.0184731 | − | 0.0689425i | −0.956074 | − | 0.293125i | \(-0.905305\pi\) |
0.974547 | + | 0.224183i | \(0.0719713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.7913 | − | 20.6476i | 0.209310 | − | 0.242913i | ||||
\(86\) | 89.8161 | − | 155.566i | 1.04437 | − | 1.80891i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −90.2953 | + | 336.987i | −1.02608 | + | 3.82939i | ||||
\(89\) | 6.20731i | 0.0697451i | 0.999392 | + | 0.0348725i | \(0.0111025\pi\) | ||||
−0.999392 | + | 0.0348725i | \(0.988897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35.8027 | −0.393436 | ||||||||
\(92\) | 169.106 | + | 45.3118i | 1.83811 | + | 0.492519i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.69039 | − | 1.55330i | −0.0286211 | − | 0.0165244i | ||||
\(95\) | 6.85110 | + | 92.1992i | 0.0721168 | + | 0.970518i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 75.0582 | + | 20.1118i | 0.773796 | + | 0.207338i | 0.624048 | − | 0.781386i | \(-0.285487\pi\) |
0.149748 | + | 0.988724i | \(0.452154\pi\) | |||||||
\(98\) | −26.3212 | − | 26.3212i | −0.268583 | − | 0.268583i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 203.116 | + | 80.0120i | 2.03116 | + | 0.800120i | ||||
\(101\) | 14.4165 | + | 24.9702i | 0.142738 | + | 0.247230i | 0.928527 | − | 0.371265i | \(-0.121076\pi\) |
−0.785789 | + | 0.618495i | \(0.787743\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 73.5518 | − | 19.7081i | 0.714095 | − | 0.191341i | 0.116560 | − | 0.993184i | \(-0.462813\pi\) |
0.597535 | + | 0.801843i | \(0.296147\pi\) | |||||||
\(104\) | −84.3059 | − | 48.6740i | −0.810634 | − | 0.468020i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.4618 | − | 51.0292i | −0.277941 | − | 0.481408i | ||||
\(107\) | −14.0751 | + | 14.0751i | −0.131543 | + | 0.131543i | −0.769813 | − | 0.638270i | \(-0.779650\pi\) |
0.638270 | + | 0.769813i | \(0.279650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.6923i | − | 0.171489i | −0.996317 | − | 0.0857447i | \(-0.972673\pi\) | ||
0.996317 | − | 0.0857447i | \(-0.0273269\pi\) | |||||||
\(110\) | −121.525 | − | 348.001i | −1.10478 | − | 3.16365i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 40.7042 | + | 151.910i | 0.363430 | + | 1.35634i | ||||
\(113\) | −142.222 | + | 38.1083i | −1.25860 | + | 0.337242i | −0.825654 | − | 0.564176i | \(-0.809194\pi\) |
−0.432949 | + | 0.901418i | \(0.642527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −94.6390 | + | 33.0489i | −0.822948 | + | 0.287381i | ||||
\(116\) | −92.9150 | −0.800991 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −212.258 | − | 212.258i | −1.79880 | − | 1.79880i | ||||
\(119\) | −29.3175 | + | 16.9265i | −0.246365 | + | 0.142239i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −152.931 | + | 264.884i | −1.26389 | + | 2.18913i | ||||
\(122\) | −64.4386 | − | 240.488i | −0.528186 | − | 1.97122i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 250.667 | − | 144.722i | 2.02150 | − | 1.16712i | ||||
\(125\) | −121.918 | + | 27.5853i | −0.975346 | + | 0.220682i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −37.9268 | + | 37.9268i | −0.298637 | + | 0.298637i | −0.840480 | − | 0.541843i | \(-0.817727\pi\) |
0.541843 | + | 0.840480i | \(0.317727\pi\) | |||||||
\(128\) | 41.9794 | − | 156.669i | 0.327964 | − | 1.22398i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 102.572 | − | 7.62190i | 0.789017 | − | 0.0586300i | ||||
\(131\) | −32.7093 | + | 56.6541i | −0.249689 | + | 0.432474i | −0.963440 | − | 0.267926i | \(-0.913662\pi\) |
0.713750 | + | 0.700400i | \(0.246995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 29.7209 | − | 110.920i | 0.223466 | − | 0.833985i | ||||
\(134\) | − | 194.060i | − | 1.44821i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −92.0465 | −0.676813 | ||||||||
\(137\) | 123.460 | + | 33.0810i | 0.901169 | + | 0.241467i | 0.679518 | − | 0.733659i | \(-0.262189\pi\) |
0.221651 | + | 0.975126i | \(0.428856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 214.282 | + | 123.716i | 1.54160 | + | 0.890042i | 0.998738 | + | 0.0502184i | \(0.0159918\pi\) |
0.542860 | + | 0.839823i | \(0.317342\pi\) | |||||||
\(140\) | −205.414 | − | 176.998i | −1.46724 | − | 1.26427i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 368.802 | + | 98.8202i | 2.59720 | + | 0.695917i | ||||
\(143\) | −84.2231 | − | 84.2231i | −0.588972 | − | 0.588972i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 43.9763 | − | 29.9421i | 0.303285 | − | 0.206497i | ||||
\(146\) | 20.6242 | + | 35.7221i | 0.141261 | + | 0.244672i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −427.069 | + | 114.433i | −2.88560 | + | 0.773194i | ||||
\(149\) | 19.8665 | + | 11.4699i | 0.133332 | + | 0.0769795i | 0.565183 | − | 0.824966i | \(-0.308806\pi\) |
−0.431850 | + | 0.901945i | \(0.642139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.24079 | + | 3.88116i | 0.0148397 | + | 0.0257031i | 0.873350 | − | 0.487093i | \(-0.161943\pi\) |
−0.858510 | + | 0.512796i | \(0.828610\pi\) | |||||||
\(152\) | 220.782 | − | 220.782i | 1.45251 | − | 1.45251i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 457.837i | 2.97297i | ||||||||
\(155\) | −72.0024 | + | 149.274i | −0.464532 | + | 0.963061i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −47.8070 | − | 178.418i | −0.304503 | − | 1.13642i | −0.933372 | − | 0.358910i | \(-0.883149\pi\) |
0.628869 | − | 0.777511i | \(-0.283518\pi\) | |||||||
\(158\) | 251.947 | − | 67.5091i | 1.59460 | − | 0.427272i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −37.6130 | − | 107.709i | −0.235081 | − | 0.673181i | ||||
\(161\) | 124.509 | 0.773347 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 33.3255 | + | 33.3255i | 0.204451 | + | 0.204451i | 0.801904 | − | 0.597453i | \(-0.203820\pi\) |
−0.597453 | + | 0.801904i | \(0.703820\pi\) | |||||||
\(164\) | −91.1898 | + | 52.6484i | −0.556035 | + | 0.321027i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.5693 | − | 18.3065i | 0.0636703 | − | 0.110280i | ||||
\(167\) | 12.0582 | + | 45.0018i | 0.0722048 | + | 0.269472i | 0.992585 | − | 0.121553i | \(-0.0387874\pi\) |
−0.920380 | + | 0.391025i | \(0.872121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −117.575 | + | 67.8822i | −0.695712 | + | 0.401670i | ||||
\(170\) | 80.3891 | − | 54.7344i | 0.472877 | − | 0.321967i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 310.845 | − | 310.845i | 1.80724 | − | 1.80724i | ||||
\(173\) | −52.7039 | + | 196.694i | −0.304647 | + | 1.13696i | 0.628602 | + | 0.777727i | \(0.283627\pi\) |
−0.933249 | + | 0.359230i | \(0.883039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 154.260 | + | 17.5773i | 0.881484 | + | 0.100442i | ||||
\(176\) | −261.603 | + | 453.110i | −1.48638 | + | 2.57449i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.73262 | + | 21.3944i | −0.0322057 | + | 0.120193i | ||||
\(179\) | 151.248i | 0.844962i | 0.906372 | + | 0.422481i | \(0.138841\pi\) | ||||
−0.906372 | + | 0.422481i | \(0.861159\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 76.1404 | 0.420665 | 0.210333 | − | 0.977630i | \(-0.432545\pi\) | ||||
0.210333 | + | 0.977630i | \(0.432545\pi\) | |||||||
\(182\) | −123.399 | − | 33.0648i | −0.678019 | − | 0.181675i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 293.185 | + | 169.271i | 1.59340 | + | 0.919949i | ||||
\(185\) | 165.254 | − | 191.784i | 0.893264 | − | 1.03667i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −108.785 | − | 29.1489i | −0.581739 | − | 0.155877i | ||||
\(188\) | −5.37581 | − | 5.37581i | −0.0285947 | − | 0.0285947i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −61.5351 | + | 324.105i | −0.323869 | + | 1.70582i | ||||
\(191\) | 102.184 | + | 176.988i | 0.534994 | + | 0.926637i | 0.999164 | + | 0.0408909i | \(0.0130196\pi\) |
−0.464169 | + | 0.885747i | \(0.653647\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −282.670 | + | 75.7411i | −1.46461 | + | 0.392441i | −0.901079 | − | 0.433654i | \(-0.857224\pi\) |
−0.563530 | + | 0.826095i | \(0.690557\pi\) | |||||||
\(194\) | 240.125 | + | 138.636i | 1.23776 | + | 0.714621i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −45.5476 | − | 78.8907i | −0.232386 | − | 0.402504i | ||||
\(197\) | 52.7467 | − | 52.7467i | 0.267750 | − | 0.267750i | −0.560443 | − | 0.828193i | \(-0.689369\pi\) |
0.828193 | + | 0.560443i | \(0.189369\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 102.233i | − | 0.513734i | −0.966447 | − | 0.256867i | \(-0.917310\pi\) | ||
0.966447 | − | 0.256867i | \(-0.0826902\pi\) | |||||||
\(200\) | 339.344 | + | 251.107i | 1.69672 | + | 1.25554i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.6281 | + | 99.3776i | 0.131822 | + | 0.491968i | ||||
\(203\) | −63.8285 | + | 17.1028i | −0.314426 | + | 0.0842503i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.1937 | − | 54.3044i | 0.127774 | − | 0.264900i | ||||
\(206\) | 271.708 | 1.31897 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −103.232 | − | 103.232i | −0.496310 | − | 0.496310i | ||||
\(209\) | 330.847 | − | 191.015i | 1.58300 | − | 0.913945i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 70.2719 | − | 121.715i | 0.333042 | − | 0.576846i | −0.650064 | − | 0.759879i | \(-0.725258\pi\) |
0.983107 | + | 0.183033i | \(0.0585915\pi\) | |||||||
\(212\) | −37.3216 | − | 139.286i | −0.176045 | − | 0.657009i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −61.5108 | + | 35.5132i | −0.287433 | + | 0.165950i | ||||
\(215\) | −46.9513 | + | 247.292i | −0.218378 | + | 1.15020i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 145.558 | − | 145.558i | 0.670774 | − | 0.670774i | ||||
\(218\) | 17.2629 | − | 64.4259i | 0.0791875 | − | 0.295532i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −66.8467 | − | 899.594i | −0.303848 | − | 4.08906i | ||||
\(221\) | 15.7128 | − | 27.2154i | 0.0710988 | − | 0.123147i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −91.2813 | + | 340.666i | −0.409333 | + | 1.52765i | 0.386589 | + | 0.922252i | \(0.373653\pi\) |
−0.795922 | + | 0.605400i | \(0.793013\pi\) | |||||||
\(224\) | 141.704i | 0.632607i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −525.384 | −2.32471 | ||||||||
\(227\) | −246.041 | − | 65.9265i | −1.08388 | − | 0.290425i | −0.327696 | − | 0.944783i | \(-0.606272\pi\) |
−0.756185 | + | 0.654358i | \(0.772939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −266.828 | − | 154.053i | −1.16519 | − | 0.672720i | −0.212644 | − | 0.977130i | \(-0.568208\pi\) |
−0.952541 | + | 0.304409i | \(0.901541\pi\) | |||||||
\(230\) | −356.709 | + | 26.5062i | −1.55091 | + | 0.115244i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −173.551 | − | 46.5028i | −0.748063 | − | 0.200443i | ||||
\(233\) | −278.738 | − | 278.738i | −1.19630 | − | 1.19630i | −0.975266 | − | 0.221033i | \(-0.929057\pi\) |
−0.221033 | − | 0.975266i | \(-0.570943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.27672 | + | 0.811984i | 0.0181988 | + | 0.00345525i | ||||
\(236\) | −367.303 | − | 636.187i | −1.55637 | − | 2.69571i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −116.679 | + | 31.2641i | −0.490248 | + | 0.131362i | ||||
\(239\) | −340.164 | − | 196.394i | −1.42328 | − | 0.821732i | −0.426703 | − | 0.904392i | \(-0.640325\pi\) |
−0.996578 | + | 0.0826603i | \(0.973658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 62.2167 | + | 107.762i | 0.258160 | + | 0.447147i | 0.965749 | − | 0.259478i | \(-0.0835504\pi\) |
−0.707589 | + | 0.706625i | \(0.750217\pi\) | |||||||
\(242\) | −771.728 | + | 771.728i | −3.18896 | + | 3.18896i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 609.292i | − | 2.49710i | ||||||
\(245\) | 46.9802 | + | 22.6609i | 0.191756 | + | 0.0924934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.5900 | + | 102.967i | 0.111700 | + | 0.416871i | ||||
\(248\) | 540.638 | − | 144.863i | 2.17999 | − | 0.584127i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −445.685 | − | 17.5180i | −1.78274 | − | 0.0700720i | ||||
\(251\) | −11.9714 | −0.0476946 | −0.0238473 | − | 0.999716i | \(-0.507592\pi\) | ||||
−0.0238473 | + | 0.999716i | \(0.507592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 292.897 | + | 292.897i | 1.15770 | + | 1.15770i | ||||
\(254\) | −165.747 | + | 95.6941i | −0.652547 | + | 0.376748i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 249.622 | − | 432.359i | 0.975087 | − | 1.68890i | ||||
\(257\) | 77.7451 | + | 290.149i | 0.302510 | + | 1.12898i | 0.935067 | + | 0.354470i | \(0.115339\pi\) |
−0.632557 | + | 0.774514i | \(0.717995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −272.314 | + | 157.221i | −1.05141 | + | 0.607029i | ||||
\(260\) | 247.292 | + | 46.9513i | 0.951125 | + | 0.180582i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −165.059 | + | 165.059i | −0.629997 | + | 0.629997i | ||||
\(263\) | 0.809272 | − | 3.02025i | 0.00307708 | − | 0.0114838i | −0.964370 | − | 0.264556i | \(-0.914774\pi\) |
0.967447 | + | 0.253073i | \(0.0814411\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 62.5494 | + | 53.8966i | 0.236035 | + | 0.203383i | ||||
\(266\) | 204.875 | − | 354.855i | 0.770208 | − | 1.33404i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 122.916 | − | 458.729i | 0.458642 | − | 1.71167i | ||||
\(269\) | − | 441.324i | − | 1.64061i | −0.571927 | − | 0.820304i | \(-0.693804\pi\) | ||
0.571927 | − | 0.820304i | \(-0.306196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 395.437 | 1.45918 | 0.729589 | − | 0.683886i | \(-0.239711\pi\) | ||||
0.729589 | + | 0.683886i | \(0.239711\pi\) | |||||||
\(272\) | −133.338 | − | 35.7279i | −0.490214 | − | 0.131353i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 394.973 | + | 228.038i | 1.44151 | + | 0.832254i | ||||
\(275\) | 321.535 | + | 404.233i | 1.16922 | + | 1.46994i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −129.970 | − | 34.8254i | −0.469207 | − | 0.125724i | 0.0164656 | − | 0.999864i | \(-0.494759\pi\) |
−0.485673 | + | 0.874141i | \(0.661425\pi\) | |||||||
\(278\) | 624.300 | + | 624.300i | 2.24568 | + | 2.24568i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −295.096 | − | 433.411i | −1.05391 | − | 1.54790i | ||||
\(281\) | −193.582 | − | 335.294i | −0.688904 | − | 1.19322i | −0.972193 | − | 0.234181i | \(-0.924759\pi\) |
0.283289 | − | 0.959034i | \(-0.408574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 53.5130 | − | 14.3388i | 0.189092 | − | 0.0506671i | −0.163030 | − | 0.986621i | \(-0.552127\pi\) |
0.352122 | + | 0.935954i | \(0.385460\pi\) | |||||||
\(284\) | 809.199 | + | 467.191i | 2.84929 | + | 1.64504i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −212.505 | − | 368.070i | −0.743025 | − | 1.28696i | ||||
\(287\) | −52.9524 | + | 52.9524i | −0.184503 | + | 0.184503i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 259.286i | 0.897183i | ||||||||
\(290\) | 179.223 | − | 62.5865i | 0.618012 | − | 0.215816i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.1263 | + | 97.5047i | 0.0894736 | + | 0.333920i | ||||
\(293\) | −424.772 | + | 113.817i | −1.44973 | + | 0.388455i | −0.895931 | − | 0.444194i | \(-0.853490\pi\) |
−0.553802 | + | 0.832649i | \(0.686823\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 378.856 | + | 182.741i | 1.28426 | + | 0.619460i | ||||
\(296\) | −854.970 | −2.88841 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 57.8802 | + | 57.8802i | 0.194229 | + | 0.194229i | ||||
\(299\) | −100.097 | + | 57.7908i | −0.334771 | + | 0.193280i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 156.320 | − | 270.754i | 0.519335 | − | 0.899515i | ||||
\(302\) | 4.13886 | + | 15.4464i | 0.0137048 | + | 0.0511471i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 405.520 | − | 234.127i | 1.33395 | − | 0.770155i | ||||
\(305\) | 196.346 | + | 288.376i | 0.643756 | + | 0.945494i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −352.515 | + | 352.515i | −1.14826 | + | 1.14826i | −0.161361 | + | 0.986895i | \(0.551588\pi\) |
−0.986895 | + | 0.161361i | \(0.948412\pi\) | |||||||
\(308\) | −289.989 | + | 1082.26i | −0.941524 | + | 3.51382i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −386.026 | + | 448.001i | −1.24525 | + | 1.44516i | ||||
\(311\) | 95.5992 | − | 165.583i | 0.307393 | − | 0.532420i | −0.670398 | − | 0.742001i | \(-0.733877\pi\) |
0.977791 | + | 0.209581i | \(0.0672101\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −55.9597 | + | 208.844i | −0.178785 | + | 0.667234i | 0.817091 | + | 0.576509i | \(0.195585\pi\) |
−0.995876 | + | 0.0907257i | \(0.971081\pi\) | |||||||
\(314\) | − | 659.096i | − | 2.09903i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 638.324 | 2.02001 | ||||||||
\(317\) | 131.200 | + | 35.1549i | 0.413879 | + | 0.110899i | 0.459749 | − | 0.888049i | \(-0.347939\pi\) |
−0.0458699 | + | 0.998947i | \(0.514606\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −190.385 | − | 109.919i | −0.596817 | − | 0.344572i | ||||
\(320\) | 7.36476 | + | 99.1118i | 0.0230149 | + | 0.309725i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 429.138 | + | 114.987i | 1.33273 | + | 0.357103i | ||||
\(323\) | 71.2722 | + | 71.2722i | 0.220657 | + | 0.220657i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −132.173 | + | 57.4687i | −0.406685 | + | 0.176827i | ||||
\(326\) | 84.0844 | + | 145.639i | 0.257928 | + | 0.446744i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −196.678 | + | 52.6997i | −0.599628 | + | 0.160670i | ||||
\(329\) | −4.68247 | − | 2.70343i | −0.0142324 | − | 0.00821710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 185.875 | + | 321.945i | 0.561556 | + | 0.972643i | 0.997361 | + | 0.0726021i | \(0.0231303\pi\) |
−0.435805 | + | 0.900041i | \(0.643536\pi\) | |||||||
\(332\) | 36.5792 | − | 36.5792i | 0.110178 | − | 0.110178i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 166.242i | 0.497729i | ||||||||
\(335\) | 89.6507 | + | 256.725i | 0.267614 | + | 0.766342i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 132.543 | + | 494.658i | 0.393303 | + | 1.46783i | 0.824651 | + | 0.565642i | \(0.191371\pi\) |
−0.431348 | + | 0.902186i | \(0.641962\pi\) | |||||||
\(338\) | −467.932 | + | 125.382i | −1.38441 | + | 0.370953i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 224.696 | − | 78.4659i | 0.660869 | − | 0.230782i | ||||
\(341\) | 684.827 | 2.00829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −260.987 | − | 260.987i | −0.760895 | − | 0.760895i | ||||
\(344\) | 736.184 | − | 425.036i | 2.14007 | − | 1.23557i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −363.304 | + | 629.261i | −1.05001 | + | 1.81867i | ||||
\(347\) | −7.61995 | − | 28.4380i | −0.0219595 | − | 0.0819540i | 0.954077 | − | 0.299563i | \(-0.0968409\pi\) |
−0.976036 | + | 0.217609i | \(0.930174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 384.508 | − | 221.996i | 1.10174 | − | 0.636092i | 0.165065 | − | 0.986283i | \(-0.447217\pi\) |
0.936678 | + | 0.350191i | \(0.113883\pi\) | |||||||
\(350\) | 515.446 | + | 203.046i | 1.47270 | + | 0.580131i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −333.347 | + | 333.347i | −0.947009 | + | 0.947009i | ||||
\(353\) | 49.2599 | − | 183.840i | 0.139546 | − | 0.520794i | −0.860391 | − | 0.509634i | \(-0.829781\pi\) |
0.999938 | − | 0.0111603i | \(-0.00355250\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −533.544 | + | 39.6464i | −1.50294 | + | 0.111680i | ||||
\(356\) | −27.1020 | + | 46.9421i | −0.0761293 | + | 0.131860i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −139.682 | + | 521.300i | −0.390173 | + | 1.45614i | ||||
\(359\) | 216.292i | 0.602484i | 0.953548 | + | 0.301242i | \(0.0974011\pi\) | ||||
−0.953548 | + | 0.301242i | \(0.902599\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0951 | 0.0528949 | ||||||||
\(362\) | 262.429 | + | 70.3177i | 0.724943 | + | 0.194248i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −270.754 | − | 156.320i | −0.743830 | − | 0.429450i | ||||
\(365\) | −43.7866 | − | 37.7293i | −0.119963 | − | 0.103368i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −331.717 | − | 88.8833i | −0.903862 | − | 0.242189i | −0.223188 | − | 0.974776i | \(-0.571646\pi\) |
−0.680674 | + | 0.732587i | \(0.738313\pi\) | |||||||
\(368\) | 359.005 | + | 359.005i | 0.975557 | + | 0.975557i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 746.690 | − | 508.398i | 2.01808 | − | 1.37405i | ||||
\(371\) | −51.2766 | − | 88.8136i | −0.138212 | − | 0.239390i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 567.442 | − | 152.046i | 1.52129 | − | 0.407629i | 0.601126 | − | 0.799155i | \(-0.294719\pi\) |
0.920167 | + | 0.391525i | \(0.128052\pi\) | |||||||
\(374\) | −348.025 | − | 200.932i | −0.930547 | − | 0.537252i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.35065 | − | 12.7317i | −0.0195496 | − | 0.0338609i | ||||
\(377\) | 43.3755 | − | 43.3755i | 0.115054 | − | 0.115054i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 87.8194i | − | 0.231713i | −0.993266 | − | 0.115857i | \(-0.963039\pi\) | ||
0.993266 | − | 0.115857i | \(-0.0369613\pi\) | |||||||
\(380\) | −350.745 | + | 727.159i | −0.923012 | + | 1.91358i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 188.739 | + | 704.384i | 0.494082 | + | 1.84394i | ||||
\(383\) | 215.050 | − | 57.6225i | 0.561488 | − | 0.150450i | 0.0330982 | − | 0.999452i | \(-0.489463\pi\) |
0.528390 | + | 0.849002i | \(0.322796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −211.508 | − | 605.677i | −0.549372 | − | 1.57319i | ||||
\(386\) | −1044.21 | −2.70521 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 479.808 | + | 479.808i | 1.23662 | + | 1.23662i | ||||
\(389\) | 438.393 | − | 253.106i | 1.12697 | − | 0.650659i | 0.183802 | − | 0.982963i | \(-0.441160\pi\) |
0.943172 | + | 0.332305i | \(0.107826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.6435 | + | 94.6454i | −0.139753 | + | 0.242060i | ||||
\(392\) | −45.5920 | − | 170.152i | −0.116306 | − | 0.434060i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 230.512 | − | 133.086i | 0.585057 | − | 0.337783i | ||||
\(395\) | −302.116 | + | 205.701i | −0.764851 | + | 0.520763i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −434.470 | + | 434.470i | −1.09438 | + | 1.09438i | −0.0993269 | + | 0.995055i | \(0.531669\pi\) |
−0.995055 | + | 0.0993269i | \(0.968331\pi\) | |||||||
\(398\) | 94.4150 | − | 352.361i | 0.237224 | − | 0.885330i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 394.106 | + | 495.469i | 0.985264 | + | 1.23867i | ||||
\(401\) | 189.456 | − | 328.147i | 0.472459 | − | 0.818323i | −0.527045 | − | 0.849838i | \(-0.676700\pi\) |
0.999503 | + | 0.0315151i | \(0.0100332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −49.4579 | + | 184.579i | −0.122724 | + | 0.458013i | ||||
\(404\) | 251.779i | 0.623216i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −235.790 | −0.580762 | ||||||||
\(407\) | −1010.45 | − | 270.748i | −2.48267 | − | 0.665229i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 118.058 | + | 68.1609i | 0.288651 | + | 0.166652i | 0.637333 | − | 0.770588i | \(-0.280038\pi\) |
−0.348683 | + | 0.937241i | \(0.613371\pi\) | |||||||
\(410\) | 140.432 | − | 162.978i | 0.342517 | − | 0.397507i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 642.276 | + | 172.097i | 1.55892 | + | 0.417712i | ||||
\(413\) | −369.423 | − | 369.423i | −0.894487 | − | 0.894487i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.52507 | + | 29.1006i | −0.0133134 | + | 0.0701219i | ||||
\(416\) | −65.7719 | − | 113.920i | −0.158106 | − | 0.273847i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1316.72 | − | 352.814i | 3.15005 | − | 0.844053i | ||||
\(419\) | −343.171 | − | 198.130i | −0.819024 | − | 0.472864i | 0.0310557 | − | 0.999518i | \(-0.490113\pi\) |
−0.850080 | + | 0.526654i | \(0.823446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 303.293 | + | 525.318i | 0.720410 | + | 1.24779i | 0.960835 | + | 0.277120i | \(0.0893798\pi\) |
−0.240425 | + | 0.970668i | \(0.577287\pi\) | |||||||
\(422\) | 354.609 | − | 354.609i | 0.840307 | − | 0.840307i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 278.843i | − | 0.657650i | ||||||
\(425\) | −81.0617 | + | 109.546i | −0.190734 | + | 0.257756i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −112.152 | − | 418.557i | −0.262651 | − | 0.980226i | ||||
\(428\) | −167.896 | + | 44.9875i | −0.392279 | + | 0.105111i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −390.206 | + | 808.970i | −0.907455 | + | 1.88132i | ||||
\(431\) | 137.454 | 0.318920 | 0.159460 | − | 0.987204i | \(-0.449025\pi\) | ||||
0.159460 | + | 0.987204i | \(0.449025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 101.718 | + | 101.718i | 0.234915 | + | 0.234915i | 0.814740 | − | 0.579826i | \(-0.196879\pi\) |
−0.579826 | + | 0.814740i | \(0.696879\pi\) | |||||||
\(434\) | 636.114 | − | 367.261i | 1.46570 | − | 0.846222i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 81.6135 | − | 141.359i | 0.187187 | − | 0.324217i | ||||
\(437\) | −95.9479 | − | 358.082i | −0.219560 | − | 0.819410i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 708.594 | − | 409.107i | 1.61411 | − | 0.931906i | 0.625704 | − | 0.780060i | \(-0.284812\pi\) |
0.988404 | − | 0.151846i | \(-0.0485217\pi\) | |||||||
\(440\) | 325.376 | − | 1713.76i | 0.739491 | − | 3.89490i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 79.2908 | − | 79.2908i | 0.179391 | − | 0.179391i | ||||
\(443\) | 47.9620 | − | 178.997i | 0.108266 | − | 0.404056i | −0.890429 | − | 0.455123i | \(-0.849595\pi\) |
0.998695 | + | 0.0510668i | \(0.0162621\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.29991 | − | 30.9512i | −0.00516834 | − | 0.0695533i | ||||
\(446\) | −629.229 | + | 1089.86i | −1.41083 | + | 2.44363i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 31.9493 | − | 119.236i | 0.0713154 | − | 0.266153i | ||||
\(449\) | − | 548.270i | − | 1.22109i | −0.791981 | − | 0.610546i | \(-0.790950\pi\) | ||
0.791981 | − | 0.610546i | \(-0.209050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −249.133 | −0.552401 | ||||||||
\(452\) | −1241.93 | − | 332.773i | −2.74762 | − | 0.736224i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −787.132 | − | 454.451i | −1.73377 | − | 1.00099i | ||||
\(455\) | 178.521 | − | 13.2655i | 0.392355 | − | 0.0291549i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −339.368 | − | 90.9333i | −0.742599 | − | 0.198979i | −0.132366 | − | 0.991201i | \(-0.542257\pi\) |
−0.610233 | + | 0.792222i | \(0.708924\pi\) | |||||||
\(458\) | −777.389 | − | 777.389i | −1.69736 | − | 1.69736i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −859.993 | − | 163.279i | −1.86955 | − | 0.354955i | ||||
\(461\) | 74.6957 | + | 129.377i | 0.162030 | + | 0.280644i | 0.935597 | − | 0.353071i | \(-0.114863\pi\) |
−0.773567 | + | 0.633715i | \(0.781529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −480.860 | + | 128.846i | −1.03857 | + | 0.278285i | −0.737522 | − | 0.675323i | \(-0.764004\pi\) |
−0.301052 | + | 0.953608i | \(0.597338\pi\) | |||||||
\(464\) | −233.355 | − | 134.728i | −0.502920 | − | 0.290361i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −703.290 | − | 1218.13i | −1.50920 | − | 2.61402i | ||||
\(467\) | −439.025 | + | 439.025i | −0.940095 | + | 0.940095i | −0.998304 | − | 0.0582090i | \(-0.981461\pi\) |
0.0582090 | + | 0.998304i | \(0.481461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 337.751i | − | 0.720152i | ||||||
\(470\) | 13.9905 | + | 6.74829i | 0.0297670 | + | 0.0143581i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −367.660 | − | 1372.13i | −0.778942 | − | 2.90705i | ||||
\(473\) | 1004.66 | − | 269.197i | 2.12401 | − | 0.569127i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −68.3226 | − | 457.190i | −0.143837 | − | 0.962505i | ||||
\(476\) | −295.614 | −0.621037 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −991.051 | − | 991.051i | −2.07333 | − | 2.07333i | ||||
\(479\) | −253.717 | + | 146.483i | −0.529680 | + | 0.305811i | −0.740886 | − | 0.671631i | \(-0.765594\pi\) |
0.211206 | + | 0.977442i | \(0.432261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 145.948 | − | 252.789i | 0.303426 | − | 0.525549i | ||||
\(482\) | 114.918 | + | 428.878i | 0.238418 | + | 0.889789i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2313.05 | + | 1335.44i | −4.77903 | + | 2.75917i | ||||
\(485\) | −381.711 | − | 72.4721i | −0.787033 | − | 0.149427i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 542.274 | − | 542.274i | 1.11350 | − | 1.11350i | 0.120824 | − | 0.992674i | \(-0.461446\pi\) |
0.992674 | − | 0.120824i | \(-0.0385538\pi\) | |||||||
\(488\) | 304.943 | − | 1138.06i | 0.624883 | − | 2.33209i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 140.996 | + | 121.492i | 0.287748 | + | 0.247942i | ||||
\(491\) | 341.362 | − | 591.256i | 0.695238 | − | 1.20419i | −0.274863 | − | 0.961483i | \(-0.588632\pi\) |
0.970100 | − | 0.242704i | \(-0.0780343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0119 | − | 56.0252i | 0.0304501 | − | 0.113641i | ||||
\(494\) | 380.372i | 0.769983i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 839.395 | 1.69233 | ||||||||
\(497\) | 641.880 | + | 171.991i | 1.29151 | + | 0.346059i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 355.232 | + | 205.093i | 0.711887 | + | 0.411008i | 0.811759 | − | 0.583992i | \(-0.198510\pi\) |
−0.0998723 | + | 0.995000i | \(0.531843\pi\) | |||||||
\(500\) | −1042.43 | − | 323.702i | −2.08487 | − | 0.647405i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −41.2610 | − | 11.0559i | −0.0821933 | − | 0.0220236i | ||||
\(503\) | 543.846 | + | 543.846i | 1.08120 | + | 1.08120i | 0.996397 | + | 0.0848064i | \(0.0270272\pi\) |
0.0848064 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −81.1364 | − | 119.166i | −0.160666 | − | 0.235973i | ||||
\(506\) | 739.016 | + | 1280.01i | 1.46051 | + | 2.52967i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −452.412 | + | 121.223i | −0.890574 | + | 0.238629i | ||||
\(509\) | 101.406 | + | 58.5471i | 0.199227 | + | 0.115024i | 0.596295 | − | 0.802766i | \(-0.296639\pi\) |
−0.397068 | + | 0.917789i | \(0.629972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.8952 | + | 62.1724i | 0.0702451 | + | 0.121668i | ||||
\(512\) | 800.897 | − | 800.897i | 1.56425 | − | 1.56425i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1071.84i | 2.08529i | ||||||||
\(515\) | −359.446 | + | 125.522i | −0.697953 | + | 0.243732i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.65555 | − | 17.3747i | −0.00900493 | − | 0.0336068i | ||||
\(518\) | −1083.77 | + | 290.395i | −2.09222 | + | 0.560608i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 438.405 | + | 211.464i | 0.843087 | + | 0.406662i | ||||
\(521\) | 400.865 | 0.769414 | 0.384707 | − | 0.923039i | \(-0.374302\pi\) | ||||
0.384707 | + | 0.923039i | \(0.374302\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −212.510 | − | 212.510i | −0.406330 | − | 0.406330i | 0.474127 | − | 0.880457i | \(-0.342764\pi\) |
−0.880457 | + | 0.474127i | \(0.842764\pi\) | |||||||
\(524\) | −494.721 | + | 285.627i | −0.944124 | + | 0.545090i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.57856 | − | 9.66234i | 0.0106056 | − | 0.0183695i | ||||
\(527\) | 46.7644 | + | 174.527i | 0.0887371 | + | 0.331171i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −110.028 | + | 63.5246i | −0.207992 | + | 0.120084i | ||||
\(530\) | 165.811 | + | 243.529i | 0.312851 | + | 0.459488i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 709.055 | − | 709.055i | 1.33281 | − | 1.33281i | ||||
\(533\) | 17.9923 | − | 67.1480i | 0.0337566 | − | 0.125981i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 64.9670 | − | 75.3972i | 0.121434 | − | 0.140929i | ||||
\(536\) | 459.176 | − | 795.315i | 0.856671 | − | 1.48380i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 407.574 | − | 1521.09i | 0.757573 | − | 2.82730i | ||||
\(539\) | − | 215.531i | − | 0.399873i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −253.010 | −0.467671 | −0.233836 | − | 0.972276i | \(-0.575128\pi\) | ||||
−0.233836 | + | 0.972276i | \(0.575128\pi\) | |||||||
\(542\) | 1362.93 | + | 365.197i | 2.51464 | + | 0.673795i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −107.716 | − | 62.1900i | −0.198008 | − | 0.114320i | ||||
\(545\) | 6.92582 | + | 93.2047i | 0.0127079 | + | 0.171018i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −750.527 | − | 201.103i | −1.37208 | − | 0.367647i | −0.503841 | − | 0.863797i | \(-0.668080\pi\) |
−0.868237 | + | 0.496149i | \(0.834747\pi\) | |||||||
\(548\) | 789.217 | + | 789.217i | 1.44018 | + | 1.44018i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 734.897 | + | 1690.20i | 1.33618 | + | 3.07308i | ||||
\(551\) | 98.3740 | + | 170.389i | 0.178537 | + | 0.309235i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 438.500 | − | 117.496i | 0.792948 | − | 0.212470i | ||||
\(554\) | −415.800 | − | 240.062i | −0.750541 | − | 0.433325i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1080.32 | + | 1871.17i | 1.94303 | + | 3.36542i | ||||
\(557\) | −488.571 | + | 488.571i | −0.877147 | + | 0.877147i | −0.993239 | − | 0.116091i | \(-0.962963\pi\) |
0.116091 | + | 0.993239i | \(0.462963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 290.224i | 0.519184i | ||||||||
\(560\) | −259.246 | − | 742.380i | −0.462940 | − | 1.32568i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −357.556 | − | 1334.42i | −0.636221 | − | 2.37441i | ||||
\(563\) | −986.935 | + | 264.448i | −1.75299 | + | 0.469713i | −0.985261 | − | 0.171058i | \(-0.945281\pi\) |
−0.767732 | + | 0.640771i | \(0.778615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 695.036 | − | 242.713i | 1.23015 | − | 0.429581i | ||||
\(566\) | 197.683 | 0.349263 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1277.63 | + | 1277.63i | 2.24936 | + | 2.24936i | ||||
\(569\) | 38.8289 | − | 22.4179i | 0.0682406 | − | 0.0393987i | −0.465491 | − | 0.885052i | \(-0.654122\pi\) |
0.533732 | + | 0.845654i | \(0.320789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 58.7139 | − | 101.695i | 0.102826 | − | 0.178101i | −0.810022 | − | 0.586400i | \(-0.800545\pi\) |
0.912848 | + | 0.408299i | \(0.133878\pi\) | |||||||
\(572\) | −269.197 | − | 1004.66i | −0.470625 | − | 1.75640i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −231.411 | + | 133.605i | −0.403156 | + | 0.232762i | ||||
\(575\) | 459.649 | − | 199.855i | 0.799389 | − | 0.347574i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 443.056 | − | 443.056i | 0.767862 | − | 0.767862i | −0.209868 | − | 0.977730i | \(-0.567303\pi\) |
0.977730 | + | 0.209868i | \(0.0673034\pi\) | |||||||
\(578\) | −239.457 | + | 893.667i | −0.414286 | + | 1.54614i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 463.298 | − | 34.4265i | 0.798789 | − | 0.0593561i | ||||
\(581\) | 18.3952 | − | 31.8615i | 0.0316613 | − | 0.0548390i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 88.3030 | − | 329.551i | 0.151463 | − | 0.565268i | ||||
\(584\) | 195.199i | 0.334246i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1569.15 | −2.67773 | ||||||||
\(587\) | 249.752 | + | 66.9210i | 0.425473 | + | 0.114005i | 0.465200 | − | 0.885206i | \(-0.345982\pi\) |
−0.0397276 | + | 0.999211i | \(0.512649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −530.787 | − | 306.450i | −0.901167 | − | 0.520289i | ||||
\(590\) | 1137.02 | + | 979.726i | 1.92715 | + | 1.66055i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1238.51 | − | 331.857i | −2.09207 | − | 0.560569i | ||||
\(593\) | −545.602 | − | 545.602i | −0.920071 | − | 0.920071i | 0.0769628 | − | 0.997034i | \(-0.475478\pi\) |
−0.997034 | + | 0.0769628i | \(0.975478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 139.913 | − | 95.2622i | 0.235148 | − | 0.160104i | ||||
\(596\) | 100.159 | + | 173.480i | 0.168052 | + | 0.291075i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −398.369 | + | 106.743i | −0.666169 | + | 0.178500i | ||||
\(599\) | −101.602 | − | 58.6598i | −0.169619 | − | 0.0979296i | 0.412787 | − | 0.910828i | \(-0.364555\pi\) |
−0.582406 | + | 0.812898i | \(0.697889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −500.357 | − | 866.643i | −0.832540 | − | 1.44200i | −0.896017 | − | 0.444019i | \(-0.853552\pi\) |
0.0634770 | − | 0.997983i | \(-0.479781\pi\) | |||||||
\(602\) | 788.829 | − | 788.829i | 1.31035 | − | 1.31035i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 39.1345i | 0.0647922i | ||||||||
\(605\) | 664.409 | − | 1377.44i | 1.09820 | − | 2.27677i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 117.390 | + | 438.106i | 0.193394 | + | 0.721757i | 0.992677 | + | 0.120801i | \(0.0385464\pi\) |
−0.799283 | + | 0.600955i | \(0.794787\pi\) | |||||||
\(608\) | 407.535 | − | 109.199i | 0.670287 | − | 0.179603i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 410.412 | + | 1175.26i | 0.672807 | + | 1.92666i | ||||
\(611\) | 5.01918 | 0.00821470 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −508.458 | − | 508.458i | −0.829459 | − | 0.829459i | 0.157983 | − | 0.987442i | \(-0.449501\pi\) |
−0.987442 | + | 0.157983i | \(0.949501\pi\) | |||||||
\(614\) | −1540.55 | + | 889.438i | −2.50904 | + | 1.44860i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1083.31 | + | 1876.35i | −1.75862 | + | 3.04602i | ||||
\(617\) | 92.9446 | + | 346.874i | 0.150640 | + | 0.562194i | 0.999439 | + | 0.0334801i | \(0.0106590\pi\) |
−0.848800 | + | 0.528714i | \(0.822674\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 372.454 | − | 215.037i | 0.601703 | − | 0.347393i | −0.168008 | − | 0.985786i | \(-0.553734\pi\) |
0.769711 | + | 0.638392i | \(0.220400\pi\) | |||||||
\(620\) | −1196.26 | + | 814.498i | −1.92946 | + | 1.31371i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 482.417 | − | 482.417i | 0.775590 | − | 0.775590i | ||||
\(623\) | −9.97731 | + | 37.2358i | −0.0160149 | + | 0.0597686i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 597.694 | − | 182.720i | 0.956311 | − | 0.292352i | ||||
\(626\) | −385.747 | + | 668.133i | −0.616209 | + | 1.06731i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 417.465 | − | 1558.00i | 0.664753 | − | 2.48089i | ||||
\(629\) | − | 275.999i | − | 0.438790i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6090 | −0.0675261 | −0.0337631 | − | 0.999430i | \(-0.510749\pi\) | ||||
−0.0337631 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(632\) | 1192.29 | + | 319.473i | 1.88653 | + | 0.505495i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 419.733 | + | 242.333i | 0.662039 | + | 0.382229i | ||||
\(635\) | 175.060 | − | 203.165i | 0.275686 | − | 0.319945i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 58.0915 | + | 15.5656i | 0.0911955 | + | 0.0244358i | ||||
\(638\) | −554.676 | − | 554.676i | −0.869399 | − | 0.869399i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −151.271 | + | 796.746i | −0.236361 | + | 1.24492i | ||||
\(641\) | −429.324 | − | 743.610i | −0.669772 | − | 1.16008i | −0.977968 | − | 0.208756i | \(-0.933059\pi\) |
0.308196 | − | 0.951323i | \(-0.400275\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −973.479 | + | 260.843i | −1.51396 | + | 0.405666i | −0.917750 | − | 0.397159i | \(-0.869996\pi\) |
−0.596215 | + | 0.802825i | \(0.703329\pi\) | |||||||
\(644\) | 941.584 | + | 543.624i | 1.46209 | + | 0.844136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 179.828 | + | 311.472i | 0.278372 | + | 0.482155i | ||||
\(647\) | 509.877 | − | 509.877i | 0.788063 | − | 0.788063i | −0.193113 | − | 0.981176i | \(-0.561859\pi\) |
0.981176 | + | 0.193113i | \(0.0618585\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1738.08i | − | 2.67809i | ||||||
\(650\) | −508.627 | + | 76.0094i | −0.782503 | + | 0.116938i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 106.517 | + | 397.525i | 0.163369 | + | 0.609701i | ||||
\(653\) | −51.1501 | + | 13.7056i | −0.0783309 | + | 0.0209887i | −0.297772 | − | 0.954637i | \(-0.596243\pi\) |
0.219441 | + | 0.975626i | \(0.429577\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 142.105 | − | 294.611i | 0.216955 | − | 0.449788i | ||||
\(656\) | −305.363 | −0.465492 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.6421 | − | 13.6421i | −0.0207327 | − | 0.0207327i | ||||
\(659\) | −718.950 | + | 415.086i | −1.09097 | + | 0.629873i | −0.933835 | − | 0.357704i | \(-0.883560\pi\) |
−0.157137 | + | 0.987577i | \(0.550226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −350.839 | + | 607.670i | −0.530770 | + | 0.919320i | 0.468586 | + | 0.883418i | \(0.344764\pi\) |
−0.999355 | + | 0.0359018i | \(0.988570\pi\) | |||||||
\(662\) | 343.321 | + | 1281.29i | 0.518612 | + | 1.93549i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 86.6318 | − | 50.0169i | 0.130470 | − | 0.0753266i | ||||
\(665\) | −107.098 | + | 564.088i | −0.161050 | + | 0.848252i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −150.844 | + | 150.844i | −0.226153 | + | 0.226153i | ||||
\(668\) | −105.296 | + | 392.969i | −0.157628 | + | 0.588277i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 71.9026 | + | 967.634i | 0.107317 | + | 1.44423i | ||||
\(671\) | 720.793 | − | 1248.45i | 1.07421 | − | 1.86058i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −133.330 | + | 497.594i | −0.198113 | + | 0.739367i | 0.793326 | + | 0.608797i | \(0.208348\pi\) |
−0.991439 | + | 0.130570i | \(0.958319\pi\) | |||||||
\(674\) | 1827.32i | 2.71116i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1185.53 | −1.75375 | ||||||||
\(677\) | −517.705 | − | 138.719i | −0.764704 | − | 0.204902i | −0.144674 | − | 0.989479i | \(-0.546213\pi\) |
−0.620031 | + | 0.784577i | \(0.712880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 417.925 | + | 241.289i | 0.615501 | + | 0.355360i | ||||
\(680\) | 458.967 | − | 34.1048i | 0.674952 | − | 0.0501541i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2360.36 | + | 632.456i | 3.46094 | + | 0.927356i | ||||
\(683\) | 111.371 | + | 111.371i | 0.163061 | + | 0.163061i | 0.783921 | − | 0.620860i | \(-0.213216\pi\) |
−0.620860 | + | 0.783921i | \(0.713216\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −627.861 | − | 119.206i | −0.916585 | − | 0.174024i | ||||
\(686\) | −658.502 | − | 1140.56i | −0.959916 | − | 1.66262i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1231.41 | − | 329.956i | 1.78984 | − | 0.479587i | ||||
\(689\) | 82.4457 | + | 47.6001i | 0.119660 | + | 0.0690857i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −340.544 | − | 589.840i | −0.492828 | − | 0.853603i | 0.507138 | − | 0.861865i | \(-0.330703\pi\) |
−0.999966 | + | 0.00826205i | \(0.997370\pi\) | |||||||
\(692\) | −1257.36 | + | 1257.36i | −1.81700 | + | 1.81700i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 105.053i | − | 0.151373i | ||||||
\(695\) | −1114.30 | − | 537.483i | −1.60331 | − | 0.773357i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.0124 | − | 63.4911i | −0.0244080 | − | 0.0910920i | ||||
\(698\) | 1530.28 | − | 410.039i | 2.19239 | − | 0.587448i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1089.83 | + | 806.447i | 1.55690 | + | 1.15207i | ||||
\(701\) | 722.405 | 1.03053 | 0.515267 | − | 0.857030i | \(-0.327693\pi\) | ||||
0.515267 | + | 0.857030i | \(0.327693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 662.008 | + | 662.008i | 0.941690 | + | 0.941690i | ||||
\(704\) | 355.652 | − | 205.336i | 0.505188 | − | 0.291670i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 339.563 | − | 588.141i | 0.480968 | − | 0.833060i | ||||
\(707\) | 46.3448 | + | 172.961i | 0.0655514 | + | 0.244641i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −505.198 | + | 291.676i | −0.712550 | + | 0.411391i | −0.812005 | − | 0.583651i | \(-0.801624\pi\) |
0.0994544 | + | 0.995042i | \(0.468290\pi\) | |||||||
\(710\) | −1875.55 | − | 356.095i | −2.64163 | − | 0.501543i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −74.1163 | + | 74.1163i | −0.104096 | + | 0.104096i | ||||
\(713\) | 171.997 | − | 641.900i | 0.241230 | − | 0.900281i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 451.164 | + | 388.751i | 0.630998 | + | 0.543708i | ||||
\(716\) | −660.372 | + | 1143.80i | −0.922308 | + | 1.59748i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −199.751 | + | 745.481i | −0.278205 | + | 1.03827i | ||||
\(719\) | 1116.43i | 1.55276i | 0.630266 | + | 0.776379i | \(0.282946\pi\) | ||||
−0.630266 | + | 0.776379i | \(0.717054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 472.893 | 0.655885 | ||||||||
\(722\) | 65.8139 | + | 17.6348i | 0.0911551 | + | 0.0244249i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 575.803 | + | 332.440i | 0.795308 | + | 0.459172i | ||||
\(725\) | −208.183 | + | 165.593i | −0.287149 | + | 0.228404i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 406.633 | + | 108.957i | 0.559329 | + | 0.149872i | 0.527398 | − | 0.849618i | \(-0.323168\pi\) |
0.0319312 | + | 0.999490i | \(0.489834\pi\) | |||||||
\(728\) | −427.490 | − | 427.490i | −0.587212 | − | 0.587212i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −116.073 | − | 170.478i | −0.159004 | − | 0.233531i | ||||
\(731\) | 137.209 | + | 237.653i | 0.187701 | + | 0.325107i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 368.915 | − | 98.8503i | 0.503294 | − | 0.134857i | 0.00176568 | − | 0.999998i | \(-0.499438\pi\) |
0.501528 | + | 0.865141i | \(0.332771\pi\) | |||||||
\(734\) | −1061.23 | − | 612.700i | −1.44581 | − | 0.834740i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 228.731 | + | 396.173i | 0.310775 | + | 0.538279i | ||||
\(737\) | 794.534 | − | 794.534i | 1.07806 | − | 1.07806i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1406.06i | 1.90266i | 0.308177 | + | 0.951329i | \(0.400281\pi\) | ||||
−0.308177 | + | 0.951329i | \(0.599719\pi\) | |||||||
\(740\) | 2087.07 | − | 728.826i | 2.82037 | − | 0.984901i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −94.7106 | − | 353.465i | −0.127642 | − | 0.476367i | ||||
\(743\) | −184.754 | + | 49.5046i | −0.248659 | + | 0.0666280i | −0.380996 | − | 0.924577i | \(-0.624419\pi\) |
0.132337 | + | 0.991205i | \(0.457752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −103.309 | − | 49.8312i | −0.138670 | − | 0.0668875i | ||||
\(746\) | 2096.19 | 2.80991 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −695.408 | − | 695.408i | −0.929689 | − | 0.929689i | ||||
\(749\) | −107.056 | + | 61.8089i | −0.142932 | + | 0.0825218i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 57.5621 | − | 99.7004i | 0.0766472 | − | 0.132757i | −0.825154 | − | 0.564908i | \(-0.808912\pi\) |
0.901801 | + | 0.432151i | \(0.142245\pi\) | |||||||
\(752\) | −5.70632 | − | 21.2963i | −0.00758819 | − | 0.0283195i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 189.559 | − | 109.442i | 0.251404 | − | 0.145148i | ||||
\(755\) | −12.6112 | − | 18.5222i | −0.0167035 | − | 0.0245327i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −737.945 | + | 737.945i | −0.974828 | + | 0.974828i | −0.999691 | − | 0.0248625i | \(-0.992085\pi\) |
0.0248625 | + | 0.999691i | \(0.492085\pi\) | |||||||
\(758\) | 81.1036 | − | 302.683i | 0.106997 | − | 0.399317i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1019.07 | + | 1182.68i | −1.34088 | + | 1.55615i | ||||
\(761\) | −505.692 | + | 875.884i | −0.664509 | + | 1.15096i | 0.314909 | + | 0.949122i | \(0.398026\pi\) |
−0.979418 | + | 0.201842i | \(0.935307\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.0451 | − | 112.130i | 0.0393776 | − | 0.146959i | ||||
\(764\) | 1784.60i | 2.33586i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 794.418 | 1.03710 | ||||||||
\(767\) | 468.459 | + | 125.523i | 0.610768 | + | 0.163655i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 566.011 | + | 326.787i | 0.736035 | + | 0.424950i | 0.820626 | − | 0.571466i | \(-0.193625\pi\) |
−0.0845906 | + | 0.996416i | \(0.526958\pi\) | |||||||
\(770\) | −169.636 | − | 2282.89i | −0.220307 | − | 2.96479i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2468.36 | − | 661.394i | −3.19735 | − | 0.856728i | ||||
\(773\) | −2.30444 | − | 2.30444i | −0.00298116 | − | 0.00298116i | 0.705615 | − | 0.708596i | \(-0.250671\pi\) |
−0.708596 | + | 0.705615i | \(0.750671\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 303.714 | − | 770.998i | 0.391888 | − | 0.994836i | ||||
\(776\) | 656.069 | + | 1136.34i | 0.845450 | + | 1.46436i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1744.74 | − | 467.501i | 2.24259 | − | 0.600901i | ||||
\(779\) | 193.095 | + | 111.483i | 0.247875 | + | 0.143111i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1105.38 | + | 1914.57i | 1.41533 | + | 2.45143i | ||||
\(782\) | −275.745 | + | 275.745i | −0.352615 | + | 0.352615i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 264.177i | − | 0.336961i | ||||||
\(785\) | 304.485 | + | 871.924i | 0.387878 | + | 1.11073i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.4341 | − | 50.1368i | −0.0170700 | − | 0.0637062i | 0.956865 | − | 0.290531i | \(-0.0938321\pi\) |
−0.973935 | + | 0.226825i | \(0.927165\pi\) | |||||||
\(788\) | 629.191 | − | 168.591i | 0.798466 | − | 0.213948i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1231.26 | + | 429.968i | −1.55856 | + | 0.544263i | ||||
\(791\) | −914.402 | −1.15601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 284.436 | + | 284.436i | 0.358683 | + | 0.358683i | ||||
\(794\) | −1898.71 | + | 1096.22i | −2.39132 | + | 1.38063i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 446.365 | − | 773.126i | 0.560759 | − | 0.971264i | ||||
\(797\) | −236.435 | − | 882.386i | −0.296656 | − | 1.10713i | −0.939893 | − | 0.341468i | \(-0.889076\pi\) |
0.643238 | − | 0.765667i | \(-0.277591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.11002 | − | 2.37292i | 0.00514395 | − | 0.00296986i | ||||
\(800\) | 227.456 | + | 523.128i | 0.284320 | + | 0.653910i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 956.041 | − | 956.041i | 1.19207 | − | 1.19207i | ||||
\(803\) | −61.8149 | + | 230.696i | −0.0769800 | + | 0.287293i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −620.832 | + | 46.1326i | −0.771220 | + | 0.0573075i | ||||
\(806\) | −340.928 | + | 590.505i | −0.422988 | + | 0.732636i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −126.012 | + | 470.284i | −0.155956 | + | 0.582035i | ||||
\(809\) | − | 467.239i | − | 0.577552i | −0.957397 | − | 0.288776i | \(-0.906752\pi\) | ||
0.957397 | − | 0.288776i | \(-0.0932483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 984.857 | 1.21437 | 0.607187 | − | 0.794559i | \(-0.292298\pi\) | ||||
0.607187 | + | 0.794559i | \(0.292298\pi\) | |||||||
\(812\) | −557.370 | − | 149.347i | −0.686416 | − | 0.183925i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3232.61 | − | 1866.35i | −3.97127 | − | 2.29281i | ||||
\(815\) | −178.517 | − | 153.822i | −0.219040 | − | 0.188739i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −899.140 | − | 240.924i | −1.10054 | − | 0.294888i | ||||
\(818\) | 343.956 | + | 343.956i | 0.420485 | + | 0.420485i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 435.188 | − | 296.306i | 0.530717 | − | 0.361348i | ||||
\(821\) | 483.078 | + | 836.716i | 0.588402 | + | 1.01914i | 0.994442 | + | 0.105287i | \(0.0335760\pi\) |
−0.406040 | + | 0.913855i | \(0.633091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.7313 | − | 7.96649i | 0.0361256 | − | 0.00967981i | −0.240711 | − | 0.970597i | \(-0.577381\pi\) |
0.276837 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(824\) | 1113.54 | + | 642.902i | 1.35138 | + | 0.780221i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −932.100 | − | 1614.44i | −1.12845 | − | 1.95453i | ||||
\(827\) | −434.978 | + | 434.978i | −0.525971 | + | 0.525971i | −0.919368 | − | 0.393398i | \(-0.871300\pi\) |
0.393398 | + | 0.919368i | \(0.371300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 308.711i | 0.372390i | 0.982513 | + | 0.186195i | \(0.0596156\pi\) | ||||
−0.982513 | + | 0.186195i | \(0.940384\pi\) | |||||||
\(830\) | −45.9182 | + | 95.1969i | −0.0553231 | + | 0.114695i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 29.6585 | + | 110.687i | 0.0356473 | + | 0.133037i | ||||
\(833\) | 54.9279 | − | 14.7179i | 0.0659398 | − | 0.0176685i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −76.7992 | − | 219.923i | −0.0919750 | − | 0.263380i | ||||
\(836\) | 3335.99 | 3.99042 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −999.812 | − | 999.812i | −1.19309 | − | 1.19309i | ||||
\(839\) | 302.565 | − | 174.686i | 0.360625 | − | 0.208207i | −0.308730 | − | 0.951150i | \(-0.599904\pi\) |
0.669355 | + | 0.742943i | \(0.266571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −363.891 | + | 630.278i | −0.432689 | + | 0.749439i | ||||
\(842\) | 560.198 | + | 2090.69i | 0.665318 | + | 2.48300i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1062.85 | − | 613.635i | 1.25930 | − | 0.727056i | ||||
\(845\) | 561.109 | − | 382.041i | 0.664034 | − | 0.452120i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1343.15 | + | 1343.15i | −1.58577 | + | 1.58577i | ||||
\(848\) | 108.233 | − | 403.932i | 0.127633 | − | 0.476334i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −380.560 | + | 302.705i | −0.447718 | + | 0.356123i | ||||
\(851\) | −507.554 | + | 879.109i | −0.596420 | + | 1.03303i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −174.201 | + | 650.129i | −0.204222 | + | 0.762167i | 0.785463 | + | 0.618908i | \(0.212425\pi\) |
−0.989685 | + | 0.143259i | \(0.954242\pi\) | |||||||
\(854\) | − | 1546.19i | − | 1.81053i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −336.118 | −0.392662 | ||||||||
\(857\) | 1503.95 | + | 402.983i | 1.75490 | + | 0.470225i | 0.985662 | − | 0.168732i | \(-0.0539673\pi\) |
0.769242 | + | 0.638957i | \(0.220634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −323.898 | − | 187.002i | −0.377064 | − | 0.217698i | 0.299476 | − | 0.954104i | \(-0.403188\pi\) |
−0.676540 | + | 0.736406i | \(0.736521\pi\) | |||||||
\(860\) | −1434.78 | + | 1665.13i | −1.66835 | + | 1.93619i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 473.757 | + | 126.943i | 0.549602 | + | 0.147265i | ||||
\(863\) | 169.154 | + | 169.154i | 0.196007 | + | 0.196007i | 0.798286 | − | 0.602279i | \(-0.205740\pi\) |
−0.602279 | + | 0.798286i | \(0.705740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 189.917 | − | 1000.29i | 0.219557 | − | 1.15641i | ||||
\(866\) | 256.647 | + | 444.526i | 0.296359 | + | 0.513309i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1736.29 | − | 465.238i | 2.00034 | − | 0.535989i | ||||
\(869\) | 1307.94 | + | 755.138i | 1.50511 | + | 0.868973i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 156.767 | + | 271.529i | 0.179986 | + | 0.311744i | ||||
\(872\) | 223.190 | − | 223.190i | 0.255951 | − | 0.255951i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1322.79i | − | 1.51350i | ||||||
\(875\) | −775.690 | − | 30.4891i | −0.886503 | − | 0.0348447i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −316.907 | − | 1182.71i | −0.361353 | − | 1.34859i | −0.872298 | − | 0.488974i | \(-0.837371\pi\) |
0.510945 | − | 0.859613i | \(-0.329295\pi\) | |||||||
\(878\) | 2820.10 | − | 755.642i | 3.21195 | − | 0.860640i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1136.53 | − | 2356.25i | 1.29152 | − | 2.67755i | ||||
\(881\) | −1252.48 | −1.42165 | −0.710827 | − | 0.703366i | \(-0.751679\pi\) | ||||
−0.710827 | + | 0.703366i | \(0.751679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 997.163 | + | 997.163i | 1.12929 | + | 1.12929i | 0.990293 | + | 0.138998i | \(0.0443880\pi\) |
0.138998 | + | 0.990293i | \(0.455612\pi\) | |||||||
\(884\) | 237.653 | − | 137.209i | 0.268838 | − | 0.155214i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 330.617 | − | 572.645i | 0.373156 | − | 0.646326i | ||||
\(887\) | −176.313 | − | 658.011i | −0.198775 | − | 0.741839i | −0.991257 | − | 0.131943i | \(-0.957878\pi\) |
0.792482 | − | 0.609895i | \(-0.208788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −288.474 | + | 166.550i | −0.324492 | + | 0.187346i | ||||
\(890\) | 20.6573 | − | 108.802i | 0.0232104 | − | 0.122249i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2177.70 | + | 2177.70i | −2.44137 | + | 2.44137i | ||||
\(893\) | −4.16658 | + | 15.5499i | −0.00466582 | + | 0.0174131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.0400 | − | 754.162i | −0.0626145 | − | 0.842639i | ||||
\(896\) | 503.644 | − | 872.337i | 0.562102 | − | 0.973590i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 506.342 | − | 1889.69i | 0.563856 | − | 2.10434i | ||||
\(899\) | 352.691i | 0.392315i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 90.0155 | 0.0999062 | ||||||||
\(902\) | −858.673 | − | 230.081i | −0.951966 | − | 0.255079i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2153.18 | − | 1243.14i | −2.38183 | − | 1.37515i | ||||
\(905\) | −379.655 | + | 28.2113i | −0.419509 | + | 0.0311727i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 85.2651 | + | 22.8467i | 0.0940078 | + | 0.0251893i | 0.305516 | − | 0.952187i | \(-0.401171\pi\) |
−0.211509 | + | 0.977376i | \(0.567838\pi\) | |||||||
\(908\) | −1572.81 | − | 1572.81i | −1.73217 | − | 1.73217i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 627.552 | + | 119.148i | 0.689617 | + | 0.130932i | ||||
\(911\) | 659.617 | + | 1142.49i | 0.724058 | + | 1.25411i | 0.959360 | + | 0.282183i | \(0.0910587\pi\) |
−0.235302 | + | 0.971922i | \(0.575608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 118.225 | − | 31.6783i | 0.129491 | − | 0.0346969i | ||||
\(914\) | −1085.70 | − | 626.830i | −1.18786 | − | 0.685810i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1345.24 | − | 2330.02i | −1.46860 | − | 2.54369i | ||||
\(917\) | −287.276 | + | 287.276i | −0.313278 | + | 0.313278i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 669.478i | − | 0.728486i | −0.931304 | − | 0.364243i | \(-0.881328\pi\) | ||
0.931304 | − | 0.364243i | \(-0.118672\pi\) | |||||||
\(920\) | −1524.61 | − | 735.396i | −1.65719 | − | 0.799344i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 137.967 | + | 514.900i | 0.149639 | + | 0.558460i | ||||
\(923\) | −595.857 | + | 159.659i | −0.645566 | + | 0.172979i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −752.938 | + | 1017.52i | −0.813987 | + | 1.10002i | ||||
\(926\) | −1776.35 | −1.91830 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −171.676 | − | 171.676i | −0.184996 | − | 0.184996i | ||||
\(929\) | −1221.93 | + | 705.481i | −1.31532 | + | 0.759398i | −0.982971 | − | 0.183760i | \(-0.941173\pi\) |
−0.332345 | + | 0.943158i | \(0.607840\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −96.4472 | + | 167.051i | −0.103595 | + | 0.179432i | ||||
\(932\) | −890.913 | − | 3324.93i | −0.955916 | − | 3.56753i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1918.61 | + | 1107.71i | −2.05419 | + | 1.18599i | ||||
\(935\) | 553.231 | + | 105.037i | 0.591691 | + | 0.112339i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −482.685 | + | 482.685i | −0.515139 | + | 0.515139i | −0.916097 | − | 0.400958i | \(-0.868677\pi\) |
0.400958 | + | 0.916097i | \(0.368677\pi\) | |||||||
\(938\) | 311.923 | − | 1164.11i | 0.332540 | − | 1.24106i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28.7970 | + | 24.8133i | 0.0306351 | + | 0.0263972i | ||||
\(941\) | −367.359 | + | 636.284i | −0.390392 | + | 0.676179i | −0.992501 | − | 0.122235i | \(-0.960994\pi\) |
0.602109 | + | 0.798414i | \(0.294327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.5705 | + | 233.516i | −0.0663526 | + | 0.247631i | ||||
\(944\) | − | 2130.37i | − | 2.25674i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3711.31 | 3.92317 | ||||||||
\(947\) | −665.038 | − | 178.196i | −0.702258 | − | 0.188169i | −0.110016 | − | 0.993930i | \(-0.535090\pi\) |
−0.592242 | + | 0.805760i | \(0.701757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.7147 | − | 33.3216i | −0.0608163 | − | 0.0351123i | ||||
\(950\) | 186.743 | − | 1638.87i | 0.196572 | − | 1.72513i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −552.160 | − | 147.951i | −0.580000 | − | 0.155411i | ||||
\(953\) | 47.5647 | + | 47.5647i | 0.0499105 | + | 0.0499105i | 0.731622 | − | 0.681711i | \(-0.238764\pi\) |
−0.681711 | + | 0.731622i | \(0.738764\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −575.092 | − | 844.645i | −0.602190 | − | 0.884445i | ||||
\(956\) | −1714.97 | − | 2970.41i | −1.79390 | − | 3.10713i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1009.75 | + | 270.563i | −1.05402 | + | 0.282424i | ||||
\(959\) | 687.428 | + | 396.887i | 0.716818 | + | 0.413855i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −68.8442 | − | 119.242i | −0.0716381 | − | 0.124081i | ||||
\(962\) | 736.489 | − | 736.489i | 0.765581 | − | 0.765581i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1086.59i | 1.12717i | ||||||||
\(965\) | 1381.40 | − | 482.398i | 1.43150 | − | 0.499894i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −283.016 | − | 1056.23i | −0.292674 | − | 1.09227i | −0.943047 | − | 0.332659i | \(-0.892054\pi\) |
0.650373 | − | 0.759615i | \(-0.274613\pi\) | |||||||
\(968\) | −4988.78 | + | 1336.74i | −5.15370 | + | 1.38093i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1248.69 | − | 602.306i | −1.28731 | − | 0.620934i | ||||
\(971\) | −1595.62 | −1.64327 | −0.821637 | − | 0.570011i | \(-0.806939\pi\) | ||||
−0.821637 | + | 0.570011i | \(0.806939\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1086.56 | + | 1086.56i | 1.11671 | + | 1.11671i | ||||
\(974\) | 2369.83 | − | 1368.22i | 2.43309 | − | 1.40475i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 883.478 | − | 1530.23i | 0.905203 | − | 1.56786i | ||||
\(977\) | −372.395 | − | 1389.80i | −0.381161 | − | 1.42251i | −0.844130 | − | 0.536139i | \(-0.819882\pi\) |
0.462968 | − | 0.886375i | \(-0.346784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −111.065 | + | 64.1235i | −0.113448 | + | 0.0654990i | ||||
\(980\) | 256.342 | + | 376.493i | 0.261574 | + | 0.384176i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1722.60 | − | 1722.60i | 1.75417 | − | 1.75417i | ||||
\(983\) | −98.4066 | + | 367.259i | −0.100108 | + | 0.373610i | −0.997744 | − | 0.0671278i | \(-0.978616\pi\) |
0.897636 | + | 0.440738i | \(0.145283\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −243.465 | + | 282.552i | −0.247173 | + | 0.286855i | ||||
\(986\) | 103.482 | − | 179.235i | 0.104951 | − | 0.181780i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −240.924 | + | 899.140i | −0.243850 | + | 0.910060i | ||||
\(989\) | − | 1009.29i | − | 1.02052i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 563.583 | 0.568701 | 0.284350 | − | 0.958720i | \(-0.408222\pi\) | ||||
0.284350 | + | 0.958720i | \(0.408222\pi\) | |||||||
\(992\) | 730.549 | + | 195.750i | 0.736440 | + | 0.197329i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2053.50 | + | 1185.59i | 2.06589 | + | 1.19274i | ||||
\(995\) | 37.8790 | + | 509.760i | 0.0380694 | + | 0.512321i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1181.22 | + | 316.507i | 1.18477 | + | 0.317459i | 0.796818 | − | 0.604219i | \(-0.206515\pi\) |
0.387956 | + | 0.921678i | \(0.373181\pi\) | |||||||
\(998\) | 1034.95 | + | 1034.95i | 1.03702 | + | 1.03702i | ||||
\(999\) | 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 | 405.3.l.o.28.8 | 32 | ||
3.2 | odd | 2 | inner | 405.3.l.o.28.1 | 32 | ||
5.2 | odd | 4 | inner | 405.3.l.o.352.1 | 32 | ||
9.2 | odd | 6 | inner | 405.3.l.o.298.8 | 32 | ||
9.4 | even | 3 | 135.3.g.a.28.1 | ✓ | 16 | ||
9.5 | odd | 6 | 135.3.g.a.28.8 | yes | 16 | ||
9.7 | even | 3 | inner | 405.3.l.o.298.1 | 32 | ||
15.2 | even | 4 | inner | 405.3.l.o.352.8 | 32 | ||
45.2 | even | 12 | inner | 405.3.l.o.217.1 | 32 | ||
45.4 | even | 6 | 675.3.g.k.568.8 | 16 | |||
45.7 | odd | 12 | inner | 405.3.l.o.217.8 | 32 | ||
45.13 | odd | 12 | 675.3.g.k.82.8 | 16 | |||
45.14 | odd | 6 | 675.3.g.k.568.1 | 16 | |||
45.22 | odd | 12 | 135.3.g.a.82.1 | yes | 16 | ||
45.23 | even | 12 | 675.3.g.k.82.1 | 16 | |||
45.32 | even | 12 | 135.3.g.a.82.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.3.g.a.28.1 | ✓ | 16 | 9.4 | even | 3 | ||
135.3.g.a.28.8 | yes | 16 | 9.5 | odd | 6 | ||
135.3.g.a.82.1 | yes | 16 | 45.22 | odd | 12 | ||
135.3.g.a.82.8 | yes | 16 | 45.32 | even | 12 | ||
405.3.l.o.28.1 | 32 | 3.2 | odd | 2 | inner | ||
405.3.l.o.28.8 | 32 | 1.1 | even | 1 | trivial | ||
405.3.l.o.217.1 | 32 | 45.2 | even | 12 | inner | ||
405.3.l.o.217.8 | 32 | 45.7 | odd | 12 | inner | ||
405.3.l.o.298.1 | 32 | 9.7 | even | 3 | inner | ||
405.3.l.o.298.8 | 32 | 9.2 | odd | 6 | inner | ||
405.3.l.o.352.1 | 32 | 5.2 | odd | 4 | inner | ||
405.3.l.o.352.8 | 32 | 15.2 | even | 4 | inner | ||
675.3.g.k.82.1 | 16 | 45.23 | even | 12 | |||
675.3.g.k.82.8 | 16 | 45.13 | odd | 12 | |||
675.3.g.k.568.1 | 16 | 45.14 | odd | 6 | |||
675.3.g.k.568.8 | 16 | 45.4 | even | 6 |