Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66371 | −1.88353 | −0.941764 | − | 0.336274i | \(-0.890833\pi\) | ||||
−0.941764 | + | 0.336274i | \(0.890833\pi\) | |||||||
\(3\) | −2.14217 | −1.23678 | −0.618391 | − | 0.785870i | \(-0.712215\pi\) | ||||
−0.618391 | + | 0.785870i | \(0.712215\pi\) | |||||||
\(4\) | 5.09536 | 2.54768 | ||||||||
\(5\) | −3.47946 | −1.55606 | −0.778031 | − | 0.628226i | \(-0.783781\pi\) | ||||
−0.778031 | + | 0.628226i | \(0.783781\pi\) | |||||||
\(6\) | 5.70612 | 2.32952 | ||||||||
\(7\) | −4.33919 | −1.64006 | −0.820030 | − | 0.572320i | \(-0.806043\pi\) | ||||
−0.820030 | + | 0.572320i | \(0.806043\pi\) | |||||||
\(8\) | −8.24515 | −2.91510 | ||||||||
\(9\) | 1.58889 | 0.529631 | ||||||||
\(10\) | 9.26828 | 2.93089 | ||||||||
\(11\) | 0.107375 | 0.0323747 | 0.0161873 | − | 0.999869i | \(-0.494847\pi\) | ||||
0.0161873 | + | 0.999869i | \(0.494847\pi\) | |||||||
\(12\) | −10.9151 | −3.15093 | ||||||||
\(13\) | −4.16356 | −1.15476 | −0.577382 | − | 0.816474i | \(-0.695926\pi\) | ||||
−0.577382 | + | 0.816474i | \(0.695926\pi\) | |||||||
\(14\) | 11.5584 | 3.08910 | ||||||||
\(15\) | 7.45359 | 1.92451 | ||||||||
\(16\) | 11.7720 | 2.94299 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −4.23236 | −0.997576 | ||||||||
\(19\) | 4.46125 | 1.02348 | 0.511740 | − | 0.859140i | \(-0.329001\pi\) | ||||
0.511740 | + | 0.859140i | \(0.329001\pi\) | |||||||
\(20\) | −17.7291 | −3.96435 | ||||||||
\(21\) | 9.29529 | 2.02840 | ||||||||
\(22\) | −0.286015 | −0.0609786 | ||||||||
\(23\) | 4.06668 | 0.847962 | 0.423981 | − | 0.905671i | \(-0.360632\pi\) | ||||
0.423981 | + | 0.905671i | \(0.360632\pi\) | |||||||
\(24\) | 17.6625 | 3.60534 | ||||||||
\(25\) | 7.10664 | 1.42133 | ||||||||
\(26\) | 11.0905 | 2.17503 | ||||||||
\(27\) | 3.02283 | 0.581744 | ||||||||
\(28\) | −22.1097 | −4.17835 | ||||||||
\(29\) | 7.04676 | 1.30855 | 0.654276 | − | 0.756256i | \(-0.272974\pi\) | ||||
0.654276 | + | 0.756256i | \(0.272974\pi\) | |||||||
\(30\) | −19.8542 | −3.62487 | ||||||||
\(31\) | 5.21206 | 0.936114 | 0.468057 | − | 0.883698i | \(-0.344954\pi\) | ||||
0.468057 | + | 0.883698i | \(0.344954\pi\) | |||||||
\(32\) | −14.8669 | −2.62811 | ||||||||
\(33\) | −0.230015 | −0.0400404 | ||||||||
\(34\) | −2.66371 | −0.456823 | ||||||||
\(35\) | 15.0980 | 2.55203 | ||||||||
\(36\) | 8.09599 | 1.34933 | ||||||||
\(37\) | −1.68423 | −0.276885 | −0.138443 | − | 0.990370i | \(-0.544210\pi\) | ||||
−0.138443 | + | 0.990370i | \(0.544210\pi\) | |||||||
\(38\) | −11.8835 | −1.92775 | ||||||||
\(39\) | 8.91906 | 1.42819 | ||||||||
\(40\) | 28.6887 | 4.53607 | ||||||||
\(41\) | −0.249757 | −0.0390056 | −0.0195028 | − | 0.999810i | \(-0.506208\pi\) | ||||
−0.0195028 | + | 0.999810i | \(0.506208\pi\) | |||||||
\(42\) | −24.7600 | −3.82055 | ||||||||
\(43\) | −10.7881 | −1.64517 | −0.822584 | − | 0.568644i | \(-0.807468\pi\) | ||||
−0.822584 | + | 0.568644i | \(0.807468\pi\) | |||||||
\(44\) | 0.547113 | 0.0824803 | ||||||||
\(45\) | −5.52849 | −0.824139 | ||||||||
\(46\) | −10.8325 | −1.59716 | ||||||||
\(47\) | 13.0494 | 1.90345 | 0.951723 | − | 0.306957i | \(-0.0993109\pi\) | ||||
0.951723 | + | 0.306957i | \(0.0993109\pi\) | |||||||
\(48\) | −25.2176 | −3.63984 | ||||||||
\(49\) | 11.8286 | 1.68980 | ||||||||
\(50\) | −18.9300 | −2.67711 | ||||||||
\(51\) | −2.14217 | −0.299964 | ||||||||
\(52\) | −21.2149 | −2.94197 | ||||||||
\(53\) | −3.53670 | −0.485803 | −0.242902 | − | 0.970051i | \(-0.578099\pi\) | ||||
−0.242902 | + | 0.970051i | \(0.578099\pi\) | |||||||
\(54\) | −8.05195 | −1.09573 | ||||||||
\(55\) | −0.373606 | −0.0503770 | ||||||||
\(56\) | 35.7773 | 4.78094 | ||||||||
\(57\) | −9.55675 | −1.26582 | ||||||||
\(58\) | −18.7705 | −2.46469 | ||||||||
\(59\) | −9.90992 | −1.29016 | −0.645081 | − | 0.764114i | \(-0.723176\pi\) | ||||
−0.645081 | + | 0.764114i | \(0.723176\pi\) | |||||||
\(60\) | 37.9787 | 4.90304 | ||||||||
\(61\) | −11.5256 | −1.47570 | −0.737851 | − | 0.674964i | \(-0.764159\pi\) | ||||
−0.737851 | + | 0.674964i | \(0.764159\pi\) | |||||||
\(62\) | −13.8834 | −1.76320 | ||||||||
\(63\) | −6.89452 | −0.868627 | ||||||||
\(64\) | 16.0571 | 2.00713 | ||||||||
\(65\) | 14.4869 | 1.79688 | ||||||||
\(66\) | 0.612693 | 0.0754173 | ||||||||
\(67\) | −6.10444 | −0.745776 | −0.372888 | − | 0.927876i | \(-0.621632\pi\) | ||||
−0.372888 | + | 0.927876i | \(0.621632\pi\) | |||||||
\(68\) | 5.09536 | 0.617903 | ||||||||
\(69\) | −8.71152 | −1.04874 | ||||||||
\(70\) | −40.2168 | −4.80683 | ||||||||
\(71\) | 6.93075 | 0.822529 | 0.411264 | − | 0.911516i | \(-0.365087\pi\) | ||||
0.411264 | + | 0.911516i | \(0.365087\pi\) | |||||||
\(72\) | −13.1007 | −1.54393 | ||||||||
\(73\) | 5.78929 | 0.677585 | 0.338792 | − | 0.940861i | \(-0.389982\pi\) | ||||
0.338792 | + | 0.940861i | \(0.389982\pi\) | |||||||
\(74\) | 4.48629 | 0.521521 | ||||||||
\(75\) | −15.2236 | −1.75787 | ||||||||
\(76\) | 22.7317 | 2.60750 | ||||||||
\(77\) | −0.465919 | −0.0530964 | ||||||||
\(78\) | −23.7578 | −2.69004 | ||||||||
\(79\) | −12.8255 | −1.44298 | −0.721491 | − | 0.692423i | \(-0.756543\pi\) | ||||
−0.721491 | + | 0.692423i | \(0.756543\pi\) | |||||||
\(80\) | −40.9601 | −4.57948 | ||||||||
\(81\) | −11.2421 | −1.24912 | ||||||||
\(82\) | 0.665282 | 0.0734681 | ||||||||
\(83\) | −6.26444 | −0.687612 | −0.343806 | − | 0.939041i | \(-0.611716\pi\) | ||||
−0.343806 | + | 0.939041i | \(0.611716\pi\) | |||||||
\(84\) | 47.3628 | 5.16771 | ||||||||
\(85\) | −3.47946 | −0.377400 | ||||||||
\(86\) | 28.7363 | 3.09872 | ||||||||
\(87\) | −15.0954 | −1.61839 | ||||||||
\(88\) | −0.885320 | −0.0943754 | ||||||||
\(89\) | 15.7359 | 1.66800 | 0.833999 | − | 0.551766i | \(-0.186046\pi\) | ||||
0.833999 | + | 0.551766i | \(0.186046\pi\) | |||||||
\(90\) | 14.7263 | 1.55229 | ||||||||
\(91\) | 18.0665 | 1.89388 | ||||||||
\(92\) | 20.7212 | 2.16034 | ||||||||
\(93\) | −11.1651 | −1.15777 | ||||||||
\(94\) | −34.7598 | −3.58520 | ||||||||
\(95\) | −15.5227 | −1.59260 | ||||||||
\(96\) | 31.8473 | 3.25040 | ||||||||
\(97\) | 4.41738 | 0.448517 | 0.224259 | − | 0.974530i | \(-0.428004\pi\) | ||||
0.224259 | + | 0.974530i | \(0.428004\pi\) | |||||||
\(98\) | −31.5079 | −3.18278 | ||||||||
\(99\) | 0.170607 | 0.0171466 | ||||||||
\(100\) | 36.2109 | 3.62109 | ||||||||
\(101\) | −9.87180 | −0.982281 | −0.491140 | − | 0.871080i | \(-0.663420\pi\) | ||||
−0.491140 | + | 0.871080i | \(0.663420\pi\) | |||||||
\(102\) | 5.70612 | 0.564990 | ||||||||
\(103\) | −5.00059 | −0.492722 | −0.246361 | − | 0.969178i | \(-0.579235\pi\) | ||||
−0.246361 | + | 0.969178i | \(0.579235\pi\) | |||||||
\(104\) | 34.3292 | 3.36625 | ||||||||
\(105\) | −32.3426 | −3.15631 | ||||||||
\(106\) | 9.42076 | 0.915025 | ||||||||
\(107\) | −14.7928 | −1.43008 | −0.715039 | − | 0.699084i | \(-0.753591\pi\) | ||||
−0.715039 | + | 0.699084i | \(0.753591\pi\) | |||||||
\(108\) | 15.4024 | 1.48210 | ||||||||
\(109\) | 3.83758 | 0.367573 | 0.183787 | − | 0.982966i | \(-0.441164\pi\) | ||||
0.183787 | + | 0.982966i | \(0.441164\pi\) | |||||||
\(110\) | 0.995178 | 0.0948865 | ||||||||
\(111\) | 3.60790 | 0.342447 | ||||||||
\(112\) | −51.0809 | −4.82669 | ||||||||
\(113\) | 15.1635 | 1.42646 | 0.713232 | − | 0.700929i | \(-0.247231\pi\) | ||||
0.713232 | + | 0.700929i | \(0.247231\pi\) | |||||||
\(114\) | 25.4564 | 2.38421 | ||||||||
\(115\) | −14.1499 | −1.31948 | ||||||||
\(116\) | 35.9058 | 3.33377 | ||||||||
\(117\) | −6.61546 | −0.611600 | ||||||||
\(118\) | 26.3972 | 2.43006 | ||||||||
\(119\) | −4.33919 | −0.397773 | ||||||||
\(120\) | −61.4560 | −5.61014 | ||||||||
\(121\) | −10.9885 | −0.998952 | ||||||||
\(122\) | 30.7009 | 2.77953 | ||||||||
\(123\) | 0.535023 | 0.0482414 | ||||||||
\(124\) | 26.5573 | 2.38492 | ||||||||
\(125\) | −7.32996 | −0.655612 | ||||||||
\(126\) | 18.3650 | 1.63608 | ||||||||
\(127\) | −8.74930 | −0.776375 | −0.388187 | − | 0.921580i | \(-0.626899\pi\) | ||||
−0.388187 | + | 0.921580i | \(0.626899\pi\) | |||||||
\(128\) | −13.0377 | −1.15238 | ||||||||
\(129\) | 23.1099 | 2.03471 | ||||||||
\(130\) | −38.5891 | −3.38448 | ||||||||
\(131\) | −19.0364 | −1.66322 | −0.831608 | − | 0.555362i | \(-0.812580\pi\) | ||||
−0.831608 | + | 0.555362i | \(0.812580\pi\) | |||||||
\(132\) | −1.17201 | −0.102010 | ||||||||
\(133\) | −19.3582 | −1.67857 | ||||||||
\(134\) | 16.2605 | 1.40469 | ||||||||
\(135\) | −10.5178 | −0.905229 | ||||||||
\(136\) | −8.24515 | −0.707016 | ||||||||
\(137\) | −9.89062 | −0.845012 | −0.422506 | − | 0.906360i | \(-0.638850\pi\) | ||||
−0.422506 | + | 0.906360i | \(0.638850\pi\) | |||||||
\(138\) | 23.2050 | 1.97534 | ||||||||
\(139\) | 10.2455 | 0.869008 | 0.434504 | − | 0.900670i | \(-0.356924\pi\) | ||||
0.434504 | + | 0.900670i | \(0.356924\pi\) | |||||||
\(140\) | 76.9300 | 6.50177 | ||||||||
\(141\) | −27.9540 | −2.35415 | ||||||||
\(142\) | −18.4615 | −1.54926 | ||||||||
\(143\) | −0.447061 | −0.0373851 | ||||||||
\(144\) | 18.7044 | 1.55870 | ||||||||
\(145\) | −24.5189 | −2.03619 | ||||||||
\(146\) | −15.4210 | −1.27625 | ||||||||
\(147\) | −25.3388 | −2.08991 | ||||||||
\(148\) | −8.58174 | −0.705415 | ||||||||
\(149\) | 16.6339 | 1.36270 | 0.681350 | − | 0.731957i | \(-0.261393\pi\) | ||||
0.681350 | + | 0.731957i | \(0.261393\pi\) | |||||||
\(150\) | 40.5514 | 3.31100 | ||||||||
\(151\) | −15.7251 | −1.27969 | −0.639845 | − | 0.768504i | \(-0.721002\pi\) | ||||
−0.639845 | + | 0.768504i | \(0.721002\pi\) | |||||||
\(152\) | −36.7836 | −2.98355 | ||||||||
\(153\) | 1.58889 | 0.128454 | ||||||||
\(154\) | 1.24107 | 0.100009 | ||||||||
\(155\) | −18.1352 | −1.45665 | ||||||||
\(156\) | 45.4458 | 3.63858 | ||||||||
\(157\) | 11.3060 | 0.902319 | 0.451159 | − | 0.892443i | \(-0.351011\pi\) | ||||
0.451159 | + | 0.892443i | \(0.351011\pi\) | |||||||
\(158\) | 34.1635 | 2.71790 | ||||||||
\(159\) | 7.57622 | 0.600833 | ||||||||
\(160\) | 51.7286 | 4.08951 | ||||||||
\(161\) | −17.6461 | −1.39071 | ||||||||
\(162\) | 29.9457 | 2.35276 | ||||||||
\(163\) | 17.5592 | 1.37534 | 0.687670 | − | 0.726024i | \(-0.258634\pi\) | ||||
0.687670 | + | 0.726024i | \(0.258634\pi\) | |||||||
\(164\) | −1.27260 | −0.0993737 | ||||||||
\(165\) | 0.800327 | 0.0623054 | ||||||||
\(166\) | 16.6867 | 1.29514 | ||||||||
\(167\) | 7.46380 | 0.577566 | 0.288783 | − | 0.957395i | \(-0.406749\pi\) | ||||
0.288783 | + | 0.957395i | \(0.406749\pi\) | |||||||
\(168\) | −76.6410 | −5.91298 | ||||||||
\(169\) | 4.33526 | 0.333481 | ||||||||
\(170\) | 9.26828 | 0.710844 | ||||||||
\(171\) | 7.08845 | 0.542067 | ||||||||
\(172\) | −54.9692 | −4.19136 | ||||||||
\(173\) | 7.43932 | 0.565601 | 0.282800 | − | 0.959179i | \(-0.408737\pi\) | ||||
0.282800 | + | 0.959179i | \(0.408737\pi\) | |||||||
\(174\) | 40.2097 | 3.04829 | ||||||||
\(175\) | −30.8371 | −2.33106 | ||||||||
\(176\) | 1.26401 | 0.0952785 | ||||||||
\(177\) | 21.2287 | 1.59565 | ||||||||
\(178\) | −41.9158 | −3.14172 | ||||||||
\(179\) | 18.2448 | 1.36368 | 0.681842 | − | 0.731500i | \(-0.261179\pi\) | ||||
0.681842 | + | 0.731500i | \(0.261179\pi\) | |||||||
\(180\) | −28.1697 | −2.09964 | ||||||||
\(181\) | 3.46671 | 0.257679 | 0.128839 | − | 0.991665i | \(-0.458875\pi\) | ||||
0.128839 | + | 0.991665i | \(0.458875\pi\) | |||||||
\(182\) | −48.1239 | −3.56718 | ||||||||
\(183\) | 24.6898 | 1.82512 | ||||||||
\(184\) | −33.5304 | −2.47189 | ||||||||
\(185\) | 5.86020 | 0.430850 | ||||||||
\(186\) | 29.7407 | 2.18069 | ||||||||
\(187\) | 0.107375 | 0.00785201 | ||||||||
\(188\) | 66.4913 | 4.84937 | ||||||||
\(189\) | −13.1166 | −0.954095 | ||||||||
\(190\) | 41.3481 | 2.99971 | ||||||||
\(191\) | 22.4947 | 1.62766 | 0.813830 | − | 0.581103i | \(-0.197379\pi\) | ||||
0.813830 | + | 0.581103i | \(0.197379\pi\) | |||||||
\(192\) | −34.3970 | −2.48239 | ||||||||
\(193\) | 21.7503 | 1.56562 | 0.782810 | − | 0.622261i | \(-0.213786\pi\) | ||||
0.782810 | + | 0.622261i | \(0.213786\pi\) | |||||||
\(194\) | −11.7666 | −0.844796 | ||||||||
\(195\) | −31.0335 | −2.22236 | ||||||||
\(196\) | 60.2709 | 4.30506 | ||||||||
\(197\) | 14.0463 | 1.00076 | 0.500380 | − | 0.865806i | \(-0.333194\pi\) | ||||
0.500380 | + | 0.865806i | \(0.333194\pi\) | |||||||
\(198\) | −0.454448 | −0.0322962 | ||||||||
\(199\) | −5.37630 | −0.381116 | −0.190558 | − | 0.981676i | \(-0.561030\pi\) | ||||
−0.190558 | + | 0.981676i | \(0.561030\pi\) | |||||||
\(200\) | −58.5953 | −4.14331 | ||||||||
\(201\) | 13.0767 | 0.922363 | ||||||||
\(202\) | 26.2956 | 1.85015 | ||||||||
\(203\) | −30.5773 | −2.14610 | ||||||||
\(204\) | −10.9151 | −0.764212 | ||||||||
\(205\) | 0.869021 | 0.0606951 | ||||||||
\(206\) | 13.3201 | 0.928057 | ||||||||
\(207\) | 6.46153 | 0.449107 | ||||||||
\(208\) | −49.0134 | −3.39846 | ||||||||
\(209\) | 0.479025 | 0.0331349 | ||||||||
\(210\) | 86.1513 | 5.94500 | ||||||||
\(211\) | −16.7705 | −1.15453 | −0.577264 | − | 0.816558i | \(-0.695880\pi\) | ||||
−0.577264 | + | 0.816558i | \(0.695880\pi\) | |||||||
\(212\) | −18.0208 | −1.23767 | ||||||||
\(213\) | −14.8468 | −1.01729 | ||||||||
\(214\) | 39.4039 | 2.69359 | ||||||||
\(215\) | 37.5367 | 2.55998 | ||||||||
\(216\) | −24.9237 | −1.69584 | ||||||||
\(217\) | −22.6161 | −1.53528 | ||||||||
\(218\) | −10.2222 | −0.692335 | ||||||||
\(219\) | −12.4016 | −0.838025 | ||||||||
\(220\) | −1.90366 | −0.128344 | ||||||||
\(221\) | −4.16356 | −0.280072 | ||||||||
\(222\) | −9.61041 | −0.645008 | ||||||||
\(223\) | 13.8527 | 0.927645 | 0.463822 | − | 0.885928i | \(-0.346478\pi\) | ||||
0.463822 | + | 0.885928i | \(0.346478\pi\) | |||||||
\(224\) | 64.5101 | 4.31026 | ||||||||
\(225\) | 11.2917 | 0.752780 | ||||||||
\(226\) | −40.3912 | −2.68678 | ||||||||
\(227\) | 3.05127 | 0.202520 | 0.101260 | − | 0.994860i | \(-0.467713\pi\) | ||||
0.101260 | + | 0.994860i | \(0.467713\pi\) | |||||||
\(228\) | −48.6951 | −3.22491 | ||||||||
\(229\) | −9.75011 | −0.644305 | −0.322153 | − | 0.946688i | \(-0.604406\pi\) | ||||
−0.322153 | + | 0.946688i | \(0.604406\pi\) | |||||||
\(230\) | 37.6911 | 2.48528 | ||||||||
\(231\) | 0.998078 | 0.0656687 | ||||||||
\(232\) | −58.1016 | −3.81456 | ||||||||
\(233\) | −13.1687 | −0.862709 | −0.431355 | − | 0.902182i | \(-0.641964\pi\) | ||||
−0.431355 | + | 0.902182i | \(0.641964\pi\) | |||||||
\(234\) | 17.6217 | 1.15197 | ||||||||
\(235\) | −45.4048 | −2.96188 | ||||||||
\(236\) | −50.4946 | −3.28692 | ||||||||
\(237\) | 27.4744 | 1.78466 | ||||||||
\(238\) | 11.5584 | 0.749217 | ||||||||
\(239\) | 14.5922 | 0.943888 | 0.471944 | − | 0.881629i | \(-0.343552\pi\) | ||||
0.471944 | + | 0.881629i | \(0.343552\pi\) | |||||||
\(240\) | 87.7435 | 5.66382 | ||||||||
\(241\) | −12.7327 | −0.820185 | −0.410093 | − | 0.912044i | \(-0.634504\pi\) | ||||
−0.410093 | + | 0.912044i | \(0.634504\pi\) | |||||||
\(242\) | 29.2701 | 1.88155 | ||||||||
\(243\) | 15.0140 | 0.963149 | ||||||||
\(244\) | −58.7271 | −3.75962 | ||||||||
\(245\) | −41.1571 | −2.62943 | ||||||||
\(246\) | −1.42515 | −0.0908641 | ||||||||
\(247\) | −18.5747 | −1.18188 | ||||||||
\(248\) | −42.9742 | −2.72887 | ||||||||
\(249\) | 13.4195 | 0.850426 | ||||||||
\(250\) | 19.5249 | 1.23486 | ||||||||
\(251\) | 9.20328 | 0.580906 | 0.290453 | − | 0.956889i | \(-0.406194\pi\) | ||||
0.290453 | + | 0.956889i | \(0.406194\pi\) | |||||||
\(252\) | −35.1300 | −2.21298 | ||||||||
\(253\) | 0.436659 | 0.0274525 | ||||||||
\(254\) | 23.3056 | 1.46232 | ||||||||
\(255\) | 7.45359 | 0.466762 | ||||||||
\(256\) | 2.61448 | 0.163405 | ||||||||
\(257\) | −25.1389 | −1.56812 | −0.784060 | − | 0.620686i | \(-0.786854\pi\) | ||||
−0.784060 | + | 0.620686i | \(0.786854\pi\) | |||||||
\(258\) | −61.5581 | −3.83244 | ||||||||
\(259\) | 7.30818 | 0.454108 | ||||||||
\(260\) | 73.8162 | 4.57789 | ||||||||
\(261\) | 11.1966 | 0.693050 | ||||||||
\(262\) | 50.7074 | 3.13272 | ||||||||
\(263\) | −23.4570 | −1.44642 | −0.723209 | − | 0.690629i | \(-0.757334\pi\) | ||||
−0.723209 | + | 0.690629i | \(0.757334\pi\) | |||||||
\(264\) | 1.89651 | 0.116722 | ||||||||
\(265\) | 12.3058 | 0.755940 | ||||||||
\(266\) | 51.5647 | 3.16163 | ||||||||
\(267\) | −33.7089 | −2.06295 | ||||||||
\(268\) | −31.1043 | −1.90000 | ||||||||
\(269\) | −24.9789 | −1.52299 | −0.761496 | − | 0.648169i | \(-0.775535\pi\) | ||||
−0.761496 | + | 0.648169i | \(0.775535\pi\) | |||||||
\(270\) | 28.0164 | 1.70503 | ||||||||
\(271\) | −17.9907 | −1.09286 | −0.546430 | − | 0.837505i | \(-0.684014\pi\) | ||||
−0.546430 | + | 0.837505i | \(0.684014\pi\) | |||||||
\(272\) | 11.7720 | 0.713781 | ||||||||
\(273\) | −38.7015 | −2.34232 | ||||||||
\(274\) | 26.3457 | 1.59160 | ||||||||
\(275\) | 0.763073 | 0.0460150 | ||||||||
\(276\) | −44.3884 | −2.67186 | ||||||||
\(277\) | 20.1356 | 1.20983 | 0.604916 | − | 0.796290i | \(-0.293207\pi\) | ||||
0.604916 | + | 0.796290i | \(0.293207\pi\) | |||||||
\(278\) | −27.2909 | −1.63680 | ||||||||
\(279\) | 8.28142 | 0.495795 | ||||||||
\(280\) | −124.486 | −7.43944 | ||||||||
\(281\) | −13.9460 | −0.831950 | −0.415975 | − | 0.909376i | \(-0.636560\pi\) | ||||
−0.415975 | + | 0.909376i | \(0.636560\pi\) | |||||||
\(282\) | 74.4613 | 4.43411 | ||||||||
\(283\) | −3.74443 | −0.222583 | −0.111292 | − | 0.993788i | \(-0.535499\pi\) | ||||
−0.111292 | + | 0.993788i | \(0.535499\pi\) | |||||||
\(284\) | 35.3147 | 2.09554 | ||||||||
\(285\) | 33.2523 | 1.96970 | ||||||||
\(286\) | 1.19084 | 0.0704160 | ||||||||
\(287\) | 1.08375 | 0.0639715 | ||||||||
\(288\) | −23.6219 | −1.39193 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 65.3114 | 3.83522 | ||||||||
\(291\) | −9.46279 | −0.554719 | ||||||||
\(292\) | 29.4985 | 1.72627 | ||||||||
\(293\) | −25.4953 | −1.48945 | −0.744725 | − | 0.667371i | \(-0.767419\pi\) | ||||
−0.744725 | + | 0.667371i | \(0.767419\pi\) | |||||||
\(294\) | 67.4954 | 3.93641 | ||||||||
\(295\) | 34.4812 | 2.00757 | ||||||||
\(296\) | 13.8867 | 0.807148 | ||||||||
\(297\) | 0.324575 | 0.0188338 | ||||||||
\(298\) | −44.3079 | −2.56669 | ||||||||
\(299\) | −16.9319 | −0.979196 | ||||||||
\(300\) | −77.5699 | −4.47850 | ||||||||
\(301\) | 46.8116 | 2.69817 | ||||||||
\(302\) | 41.8871 | 2.41033 | ||||||||
\(303\) | 21.1471 | 1.21487 | ||||||||
\(304\) | 52.5177 | 3.01210 | ||||||||
\(305\) | 40.1029 | 2.29628 | ||||||||
\(306\) | −4.23236 | −0.241948 | ||||||||
\(307\) | −5.63105 | −0.321381 | −0.160691 | − | 0.987005i | \(-0.551372\pi\) | ||||
−0.160691 | + | 0.987005i | \(0.551372\pi\) | |||||||
\(308\) | −2.37403 | −0.135273 | ||||||||
\(309\) | 10.7121 | 0.609390 | ||||||||
\(310\) | 48.3068 | 2.74364 | ||||||||
\(311\) | 26.7825 | 1.51869 | 0.759347 | − | 0.650686i | \(-0.225518\pi\) | ||||
0.759347 | + | 0.650686i | \(0.225518\pi\) | |||||||
\(312\) | −73.5390 | −4.16332 | ||||||||
\(313\) | 1.36924 | 0.0773938 | 0.0386969 | − | 0.999251i | \(-0.487679\pi\) | ||||
0.0386969 | + | 0.999251i | \(0.487679\pi\) | |||||||
\(314\) | −30.1160 | −1.69954 | ||||||||
\(315\) | 23.9892 | 1.35164 | ||||||||
\(316\) | −65.3506 | −3.67626 | ||||||||
\(317\) | 12.2841 | 0.689944 | 0.344972 | − | 0.938613i | \(-0.387888\pi\) | ||||
0.344972 | + | 0.938613i | \(0.387888\pi\) | |||||||
\(318\) | −20.1809 | −1.13169 | ||||||||
\(319\) | 0.756644 | 0.0423639 | ||||||||
\(320\) | −55.8699 | −3.12322 | ||||||||
\(321\) | 31.6888 | 1.76870 | ||||||||
\(322\) | 47.0042 | 2.61944 | ||||||||
\(323\) | 4.46125 | 0.248230 | ||||||||
\(324\) | −57.2825 | −3.18236 | ||||||||
\(325\) | −29.5889 | −1.64130 | ||||||||
\(326\) | −46.7725 | −2.59049 | ||||||||
\(327\) | −8.22074 | −0.454608 | ||||||||
\(328\) | 2.05929 | 0.113705 | ||||||||
\(329\) | −56.6237 | −3.12177 | ||||||||
\(330\) | −2.13184 | −0.117354 | ||||||||
\(331\) | −7.37182 | −0.405192 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(332\) | −31.9196 | −1.75181 | ||||||||
\(333\) | −2.67606 | −0.146647 | ||||||||
\(334\) | −19.8814 | −1.08786 | ||||||||
\(335\) | 21.2402 | 1.16047 | ||||||||
\(336\) | 109.424 | 5.96956 | ||||||||
\(337\) | −23.4917 | −1.27967 | −0.639837 | − | 0.768510i | \(-0.720998\pi\) | ||||
−0.639837 | + | 0.768510i | \(0.720998\pi\) | |||||||
\(338\) | −11.5479 | −0.628122 | ||||||||
\(339\) | −32.4828 | −1.76422 | ||||||||
\(340\) | −17.7291 | −0.961495 | ||||||||
\(341\) | 0.559644 | 0.0303064 | ||||||||
\(342\) | −18.8816 | −1.02100 | ||||||||
\(343\) | −20.9522 | −1.13131 | ||||||||
\(344\) | 88.9493 | 4.79583 | ||||||||
\(345\) | 30.3114 | 1.63191 | ||||||||
\(346\) | −19.8162 | −1.06533 | ||||||||
\(347\) | −22.0907 | −1.18589 | −0.592944 | − | 0.805243i | \(-0.702035\pi\) | ||||
−0.592944 | + | 0.805243i | \(0.702035\pi\) | |||||||
\(348\) | −76.9163 | −4.12315 | ||||||||
\(349\) | 6.77381 | 0.362593 | 0.181297 | − | 0.983428i | \(-0.441971\pi\) | ||||
0.181297 | + | 0.983428i | \(0.441971\pi\) | |||||||
\(350\) | 82.1411 | 4.39062 | ||||||||
\(351\) | −12.5857 | −0.671777 | ||||||||
\(352\) | −1.59632 | −0.0850843 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | −56.5472 | −3.00545 | ||||||||
\(355\) | −24.1153 | −1.27991 | ||||||||
\(356\) | 80.1799 | 4.24953 | ||||||||
\(357\) | 9.29529 | 0.491959 | ||||||||
\(358\) | −48.5990 | −2.56854 | ||||||||
\(359\) | −2.23522 | −0.117970 | −0.0589851 | − | 0.998259i | \(-0.518786\pi\) | ||||
−0.0589851 | + | 0.998259i | \(0.518786\pi\) | |||||||
\(360\) | 45.5832 | 2.40245 | ||||||||
\(361\) | 0.902737 | 0.0475125 | ||||||||
\(362\) | −9.23432 | −0.485345 | ||||||||
\(363\) | 23.5392 | 1.23549 | ||||||||
\(364\) | 92.0553 | 4.82501 | ||||||||
\(365\) | −20.1436 | −1.05436 | ||||||||
\(366\) | −65.7665 | −3.43767 | ||||||||
\(367\) | 14.5305 | 0.758484 | 0.379242 | − | 0.925297i | \(-0.376185\pi\) | ||||
0.379242 | + | 0.925297i | \(0.376185\pi\) | |||||||
\(368\) | 47.8729 | 2.49555 | ||||||||
\(369\) | −0.396838 | −0.0206586 | ||||||||
\(370\) | −15.6099 | −0.811519 | ||||||||
\(371\) | 15.3464 | 0.796747 | ||||||||
\(372\) | −56.8903 | −2.94963 | ||||||||
\(373\) | 0.722633 | 0.0374165 | 0.0187083 | − | 0.999825i | \(-0.494045\pi\) | ||||
0.0187083 | + | 0.999825i | \(0.494045\pi\) | |||||||
\(374\) | −0.286015 | −0.0147895 | ||||||||
\(375\) | 15.7020 | 0.810849 | ||||||||
\(376\) | −107.594 | −5.54874 | ||||||||
\(377\) | −29.3396 | −1.51107 | ||||||||
\(378\) | 34.9389 | 1.79707 | ||||||||
\(379\) | 0.337308 | 0.0173263 | 0.00866317 | − | 0.999962i | \(-0.497242\pi\) | ||||
0.00866317 | + | 0.999962i | \(0.497242\pi\) | |||||||
\(380\) | −79.0939 | −4.05743 | ||||||||
\(381\) | 18.7425 | 0.960207 | ||||||||
\(382\) | −59.9194 | −3.06574 | ||||||||
\(383\) | 2.84622 | 0.145435 | 0.0727175 | − | 0.997353i | \(-0.476833\pi\) | ||||
0.0727175 | + | 0.997353i | \(0.476833\pi\) | |||||||
\(384\) | 27.9289 | 1.42524 | ||||||||
\(385\) | 1.62115 | 0.0826213 | ||||||||
\(386\) | −57.9365 | −2.94889 | ||||||||
\(387\) | −17.1411 | −0.871332 | ||||||||
\(388\) | 22.5082 | 1.14268 | ||||||||
\(389\) | 6.95745 | 0.352757 | 0.176378 | − | 0.984322i | \(-0.443562\pi\) | ||||
0.176378 | + | 0.984322i | \(0.443562\pi\) | |||||||
\(390\) | 82.6643 | 4.18587 | ||||||||
\(391\) | 4.06668 | 0.205661 | ||||||||
\(392\) | −97.5284 | −4.92593 | ||||||||
\(393\) | 40.7792 | 2.05704 | ||||||||
\(394\) | −37.4154 | −1.88496 | ||||||||
\(395\) | 44.6258 | 2.24537 | ||||||||
\(396\) | 0.869304 | 0.0436842 | ||||||||
\(397\) | −33.2791 | −1.67023 | −0.835116 | − | 0.550074i | \(-0.814599\pi\) | ||||
−0.835116 | + | 0.550074i | \(0.814599\pi\) | |||||||
\(398\) | 14.3209 | 0.717843 | ||||||||
\(399\) | 41.4686 | 2.07603 | ||||||||
\(400\) | 83.6592 | 4.18296 | ||||||||
\(401\) | −24.1828 | −1.20763 | −0.603815 | − | 0.797125i | \(-0.706353\pi\) | ||||
−0.603815 | + | 0.797125i | \(0.706353\pi\) | |||||||
\(402\) | −34.8327 | −1.73730 | ||||||||
\(403\) | −21.7008 | −1.08099 | ||||||||
\(404\) | −50.3004 | −2.50254 | ||||||||
\(405\) | 39.1164 | 1.94371 | ||||||||
\(406\) | 81.4490 | 4.04225 | ||||||||
\(407\) | −0.180843 | −0.00896407 | ||||||||
\(408\) | 17.6625 | 0.874425 | ||||||||
\(409\) | −0.0721842 | −0.00356928 | −0.00178464 | − | 0.999998i | \(-0.500568\pi\) | ||||
−0.00178464 | + | 0.999998i | \(0.500568\pi\) | |||||||
\(410\) | −2.31482 | −0.114321 | ||||||||
\(411\) | 21.1874 | 1.04510 | ||||||||
\(412\) | −25.4798 | −1.25530 | ||||||||
\(413\) | 43.0010 | 2.11594 | ||||||||
\(414\) | −17.2116 | −0.845906 | ||||||||
\(415\) | 21.7969 | 1.06997 | ||||||||
\(416\) | 61.8991 | 3.03485 | ||||||||
\(417\) | −21.9475 | −1.07477 | ||||||||
\(418\) | −1.27598 | −0.0624104 | ||||||||
\(419\) | −19.1459 | −0.935341 | −0.467670 | − | 0.883903i | \(-0.654907\pi\) | ||||
−0.467670 | + | 0.883903i | \(0.654907\pi\) | |||||||
\(420\) | −164.797 | −8.04127 | ||||||||
\(421\) | −34.4401 | −1.67851 | −0.839254 | − | 0.543739i | \(-0.817008\pi\) | ||||
−0.839254 | + | 0.543739i | \(0.817008\pi\) | |||||||
\(422\) | 44.6717 | 2.17459 | ||||||||
\(423\) | 20.7341 | 1.00812 | ||||||||
\(424\) | 29.1606 | 1.41617 | ||||||||
\(425\) | 7.10664 | 0.344723 | ||||||||
\(426\) | 39.5477 | 1.91609 | ||||||||
\(427\) | 50.0118 | 2.42024 | ||||||||
\(428\) | −75.3749 | −3.64338 | ||||||||
\(429\) | 0.957681 | 0.0462373 | ||||||||
\(430\) | −99.9869 | −4.82180 | ||||||||
\(431\) | −13.6659 | −0.658262 | −0.329131 | − | 0.944284i | \(-0.606756\pi\) | ||||
−0.329131 | + | 0.944284i | \(0.606756\pi\) | |||||||
\(432\) | 35.5847 | 1.71207 | ||||||||
\(433\) | 10.9637 | 0.526879 | 0.263440 | − | 0.964676i | \(-0.415143\pi\) | ||||
0.263440 | + | 0.964676i | \(0.415143\pi\) | |||||||
\(434\) | 60.2429 | 2.89175 | ||||||||
\(435\) | 52.5237 | 2.51832 | ||||||||
\(436\) | 19.5538 | 0.936459 | ||||||||
\(437\) | 18.1425 | 0.867872 | ||||||||
\(438\) | 33.0344 | 1.57844 | ||||||||
\(439\) | 3.63913 | 0.173686 | 0.0868431 | − | 0.996222i | \(-0.472322\pi\) | ||||
0.0868431 | + | 0.996222i | \(0.472322\pi\) | |||||||
\(440\) | 3.08043 | 0.146854 | ||||||||
\(441\) | 18.7944 | 0.894970 | ||||||||
\(442\) | 11.0905 | 0.527523 | ||||||||
\(443\) | 5.89216 | 0.279945 | 0.139973 | − | 0.990155i | \(-0.455299\pi\) | ||||
0.139973 | + | 0.990155i | \(0.455299\pi\) | |||||||
\(444\) | 18.3836 | 0.872445 | ||||||||
\(445\) | −54.7523 | −2.59551 | ||||||||
\(446\) | −36.8996 | −1.74725 | ||||||||
\(447\) | −35.6326 | −1.68536 | ||||||||
\(448\) | −69.6747 | −3.29182 | ||||||||
\(449\) | 33.7957 | 1.59492 | 0.797460 | − | 0.603372i | \(-0.206177\pi\) | ||||
0.797460 | + | 0.603372i | \(0.206177\pi\) | |||||||
\(450\) | −30.0778 | −1.41788 | ||||||||
\(451\) | −0.0268176 | −0.00126279 | ||||||||
\(452\) | 77.2635 | 3.63417 | ||||||||
\(453\) | 33.6859 | 1.58270 | ||||||||
\(454\) | −8.12771 | −0.381452 | ||||||||
\(455\) | −62.8617 | −2.94700 | ||||||||
\(456\) | 78.7968 | 3.69000 | ||||||||
\(457\) | −35.9823 | −1.68318 | −0.841590 | − | 0.540116i | \(-0.818380\pi\) | ||||
−0.841590 | + | 0.540116i | \(0.818380\pi\) | |||||||
\(458\) | 25.9715 | 1.21357 | ||||||||
\(459\) | 3.02283 | 0.141094 | ||||||||
\(460\) | −72.0986 | −3.36161 | ||||||||
\(461\) | 19.1568 | 0.892221 | 0.446110 | − | 0.894978i | \(-0.352809\pi\) | ||||
0.446110 | + | 0.894978i | \(0.352809\pi\) | |||||||
\(462\) | −2.65859 | −0.123689 | ||||||||
\(463\) | −11.0864 | −0.515230 | −0.257615 | − | 0.966248i | \(-0.582937\pi\) | ||||
−0.257615 | + | 0.966248i | \(0.582937\pi\) | |||||||
\(464\) | 82.9543 | 3.85106 | ||||||||
\(465\) | 38.8486 | 1.80156 | ||||||||
\(466\) | 35.0776 | 1.62494 | ||||||||
\(467\) | 15.3154 | 0.708714 | 0.354357 | − | 0.935110i | \(-0.384700\pi\) | ||||
0.354357 | + | 0.935110i | \(0.384700\pi\) | |||||||
\(468\) | −33.7082 | −1.55816 | ||||||||
\(469\) | 26.4883 | 1.22312 | ||||||||
\(470\) | 120.945 | 5.57879 | ||||||||
\(471\) | −24.2194 | −1.11597 | ||||||||
\(472\) | 81.7087 | 3.76095 | ||||||||
\(473\) | −1.15837 | −0.0532618 | ||||||||
\(474\) | −73.1840 | −3.36145 | ||||||||
\(475\) | 31.7045 | 1.45470 | ||||||||
\(476\) | −22.1097 | −1.01340 | ||||||||
\(477\) | −5.61945 | −0.257297 | ||||||||
\(478\) | −38.8693 | −1.77784 | ||||||||
\(479\) | 20.0057 | 0.914083 | 0.457041 | − | 0.889445i | \(-0.348909\pi\) | ||||
0.457041 | + | 0.889445i | \(0.348909\pi\) | |||||||
\(480\) | −110.811 | −5.05783 | ||||||||
\(481\) | 7.01239 | 0.319737 | ||||||||
\(482\) | 33.9162 | 1.54484 | ||||||||
\(483\) | 37.8010 | 1.72000 | ||||||||
\(484\) | −55.9902 | −2.54501 | ||||||||
\(485\) | −15.3701 | −0.697921 | ||||||||
\(486\) | −39.9930 | −1.81412 | ||||||||
\(487\) | 32.0094 | 1.45049 | 0.725243 | − | 0.688493i | \(-0.241728\pi\) | ||||
0.725243 | + | 0.688493i | \(0.241728\pi\) | |||||||
\(488\) | 95.0303 | 4.30182 | ||||||||
\(489\) | −37.6147 | −1.70100 | ||||||||
\(490\) | 109.631 | 4.95261 | ||||||||
\(491\) | 26.4712 | 1.19463 | 0.597315 | − | 0.802007i | \(-0.296234\pi\) | ||||
0.597315 | + | 0.802007i | \(0.296234\pi\) | |||||||
\(492\) | 2.72614 | 0.122904 | ||||||||
\(493\) | 7.04676 | 0.317370 | ||||||||
\(494\) | 49.4776 | 2.22610 | ||||||||
\(495\) | −0.593620 | −0.0266812 | ||||||||
\(496\) | 61.3563 | 2.75498 | ||||||||
\(497\) | −30.0739 | −1.34900 | ||||||||
\(498\) | −35.7457 | −1.60180 | ||||||||
\(499\) | −14.2651 | −0.638595 | −0.319298 | − | 0.947654i | \(-0.603447\pi\) | ||||
−0.319298 | + | 0.947654i | \(0.603447\pi\) | |||||||
\(500\) | −37.3488 | −1.67029 | ||||||||
\(501\) | −15.9887 | −0.714324 | ||||||||
\(502\) | −24.5149 | −1.09415 | ||||||||
\(503\) | 14.3195 | 0.638477 | 0.319238 | − | 0.947674i | \(-0.396573\pi\) | ||||
0.319238 | + | 0.947674i | \(0.396573\pi\) | |||||||
\(504\) | 56.8463 | 2.53214 | ||||||||
\(505\) | 34.3485 | 1.52849 | ||||||||
\(506\) | −1.16313 | −0.0517075 | ||||||||
\(507\) | −9.28686 | −0.412444 | ||||||||
\(508\) | −44.5808 | −1.97795 | ||||||||
\(509\) | −27.3140 | −1.21067 | −0.605337 | − | 0.795970i | \(-0.706961\pi\) | ||||
−0.605337 | + | 0.795970i | \(0.706961\pi\) | |||||||
\(510\) | −19.8542 | −0.879160 | ||||||||
\(511\) | −25.1208 | −1.11128 | ||||||||
\(512\) | 19.1111 | 0.844600 | ||||||||
\(513\) | 13.4856 | 0.595404 | ||||||||
\(514\) | 66.9627 | 2.95360 | ||||||||
\(515\) | 17.3993 | 0.766706 | ||||||||
\(516\) | 117.753 | 5.18380 | ||||||||
\(517\) | 1.40117 | 0.0616235 | ||||||||
\(518\) | −19.4669 | −0.855326 | ||||||||
\(519\) | −15.9363 | −0.699525 | ||||||||
\(520\) | −119.447 | −5.23810 | ||||||||
\(521\) | −11.2984 | −0.494993 | −0.247497 | − | 0.968889i | \(-0.579608\pi\) | ||||
−0.247497 | + | 0.968889i | \(0.579608\pi\) | |||||||
\(522\) | −29.8244 | −1.30538 | ||||||||
\(523\) | 27.5978 | 1.20677 | 0.603385 | − | 0.797450i | \(-0.293818\pi\) | ||||
0.603385 | + | 0.797450i | \(0.293818\pi\) | |||||||
\(524\) | −96.9972 | −4.23734 | ||||||||
\(525\) | 66.0582 | 2.88302 | ||||||||
\(526\) | 62.4826 | 2.72437 | ||||||||
\(527\) | 5.21206 | 0.227041 | ||||||||
\(528\) | −2.70773 | −0.117839 | ||||||||
\(529\) | −6.46210 | −0.280961 | ||||||||
\(530\) | −32.7791 | −1.42383 | ||||||||
\(531\) | −15.7458 | −0.683310 | ||||||||
\(532\) | −98.6371 | −4.27646 | ||||||||
\(533\) | 1.03988 | 0.0450422 | ||||||||
\(534\) | 89.7908 | 3.88563 | ||||||||
\(535\) | 51.4711 | 2.22529 | ||||||||
\(536\) | 50.3320 | 2.17401 | ||||||||
\(537\) | −39.0836 | −1.68658 | ||||||||
\(538\) | 66.5367 | 2.86860 | ||||||||
\(539\) | 1.27009 | 0.0547067 | ||||||||
\(540\) | −53.5920 | −2.30623 | ||||||||
\(541\) | −7.26006 | −0.312134 | −0.156067 | − | 0.987746i | \(-0.549882\pi\) | ||||
−0.156067 | + | 0.987746i | \(0.549882\pi\) | |||||||
\(542\) | 47.9222 | 2.05843 | ||||||||
\(543\) | −7.42629 | −0.318692 | ||||||||
\(544\) | −14.8669 | −0.637411 | ||||||||
\(545\) | −13.3527 | −0.571967 | ||||||||
\(546\) | 103.090 | 4.41183 | ||||||||
\(547\) | 42.6554 | 1.82381 | 0.911906 | − | 0.410399i | \(-0.134611\pi\) | ||||
0.911906 | + | 0.410399i | \(0.134611\pi\) | |||||||
\(548\) | −50.3962 | −2.15282 | ||||||||
\(549\) | −18.3130 | −0.781578 | ||||||||
\(550\) | −2.03261 | −0.0866706 | ||||||||
\(551\) | 31.4374 | 1.33928 | ||||||||
\(552\) | 71.8278 | 3.05719 | ||||||||
\(553\) | 55.6524 | 2.36658 | ||||||||
\(554\) | −53.6354 | −2.27875 | ||||||||
\(555\) | −12.5535 | −0.532868 | ||||||||
\(556\) | 52.2043 | 2.21395 | ||||||||
\(557\) | 24.4792 | 1.03722 | 0.518609 | − | 0.855012i | \(-0.326450\pi\) | ||||
0.518609 | + | 0.855012i | \(0.326450\pi\) | |||||||
\(558\) | −22.0593 | −0.933845 | ||||||||
\(559\) | 44.9169 | 1.89978 | ||||||||
\(560\) | 177.734 | 7.51062 | ||||||||
\(561\) | −0.230015 | −0.00971123 | ||||||||
\(562\) | 37.1482 | 1.56700 | ||||||||
\(563\) | −38.9746 | −1.64258 | −0.821291 | − | 0.570510i | \(-0.806746\pi\) | ||||
−0.821291 | + | 0.570510i | \(0.806746\pi\) | |||||||
\(564\) | −142.436 | −5.99762 | ||||||||
\(565\) | −52.7608 | −2.21966 | ||||||||
\(566\) | 9.97408 | 0.419242 | ||||||||
\(567\) | 48.7816 | 2.04864 | ||||||||
\(568\) | −57.1450 | −2.39775 | ||||||||
\(569\) | −40.7485 | −1.70826 | −0.854132 | − | 0.520056i | \(-0.825911\pi\) | ||||
−0.854132 | + | 0.520056i | \(0.825911\pi\) | |||||||
\(570\) | −88.5746 | −3.70998 | ||||||||
\(571\) | 13.4416 | 0.562515 | 0.281257 | − | 0.959632i | \(-0.409249\pi\) | ||||
0.281257 | + | 0.959632i | \(0.409249\pi\) | |||||||
\(572\) | −2.27794 | −0.0952454 | ||||||||
\(573\) | −48.1875 | −2.01306 | ||||||||
\(574\) | −2.88679 | −0.120492 | ||||||||
\(575\) | 28.9004 | 1.20523 | ||||||||
\(576\) | 25.5130 | 1.06304 | ||||||||
\(577\) | −19.6633 | −0.818593 | −0.409297 | − | 0.912401i | \(-0.634226\pi\) | ||||
−0.409297 | + | 0.912401i | \(0.634226\pi\) | |||||||
\(578\) | −2.66371 | −0.110796 | ||||||||
\(579\) | −46.5928 | −1.93633 | ||||||||
\(580\) | −124.933 | −5.18755 | ||||||||
\(581\) | 27.1826 | 1.12772 | ||||||||
\(582\) | 25.2061 | 1.04483 | ||||||||
\(583\) | −0.379752 | −0.0157277 | ||||||||
\(584\) | −47.7335 | −1.97523 | ||||||||
\(585\) | 23.0182 | 0.951686 | ||||||||
\(586\) | 67.9121 | 2.80542 | ||||||||
\(587\) | −13.2802 | −0.548133 | −0.274067 | − | 0.961711i | \(-0.588369\pi\) | ||||
−0.274067 | + | 0.961711i | \(0.588369\pi\) | |||||||
\(588\) | −129.111 | −5.32443 | ||||||||
\(589\) | 23.2523 | 0.958095 | ||||||||
\(590\) | −91.8479 | −3.78132 | ||||||||
\(591\) | −30.0897 | −1.23772 | ||||||||
\(592\) | −19.8267 | −0.814871 | ||||||||
\(593\) | −2.22802 | −0.0914937 | −0.0457469 | − | 0.998953i | \(-0.514567\pi\) | ||||
−0.0457469 | + | 0.998953i | \(0.514567\pi\) | |||||||
\(594\) | −0.864575 | −0.0354739 | ||||||||
\(595\) | 15.0980 | 0.618959 | ||||||||
\(596\) | 84.7556 | 3.47173 | ||||||||
\(597\) | 11.5170 | 0.471358 | ||||||||
\(598\) | 45.1017 | 1.84434 | ||||||||
\(599\) | −18.8120 | −0.768636 | −0.384318 | − | 0.923201i | \(-0.625563\pi\) | ||||
−0.384318 | + | 0.923201i | \(0.625563\pi\) | |||||||
\(600\) | 125.521 | 5.12438 | ||||||||
\(601\) | 20.2967 | 0.827918 | 0.413959 | − | 0.910296i | \(-0.364146\pi\) | ||||
0.413959 | + | 0.910296i | \(0.364146\pi\) | |||||||
\(602\) | −124.693 | −5.08209 | ||||||||
\(603\) | −9.69931 | −0.394986 | ||||||||
\(604\) | −80.1251 | −3.26024 | ||||||||
\(605\) | 38.2339 | 1.55443 | ||||||||
\(606\) | −56.3297 | −2.28824 | ||||||||
\(607\) | 42.2314 | 1.71412 | 0.857059 | − | 0.515218i | \(-0.172289\pi\) | ||||
0.857059 | + | 0.515218i | \(0.172289\pi\) | |||||||
\(608\) | −66.3247 | −2.68982 | ||||||||
\(609\) | 65.5017 | 2.65426 | ||||||||
\(610\) | −106.822 | −4.32511 | ||||||||
\(611\) | −54.3319 | −2.19803 | ||||||||
\(612\) | 8.09599 | 0.327261 | ||||||||
\(613\) | 7.24682 | 0.292696 | 0.146348 | − | 0.989233i | \(-0.453248\pi\) | ||||
0.146348 | + | 0.989233i | \(0.453248\pi\) | |||||||
\(614\) | 14.9995 | 0.605330 | ||||||||
\(615\) | −1.86159 | −0.0750666 | ||||||||
\(616\) | 3.84157 | 0.154781 | ||||||||
\(617\) | −6.94633 | −0.279649 | −0.139824 | − | 0.990176i | \(-0.544654\pi\) | ||||
−0.139824 | + | 0.990176i | \(0.544654\pi\) | |||||||
\(618\) | −28.5340 | −1.14780 | ||||||||
\(619\) | −9.04042 | −0.363365 | −0.181683 | − | 0.983357i | \(-0.558154\pi\) | ||||
−0.181683 | + | 0.983357i | \(0.558154\pi\) | |||||||
\(620\) | −92.4052 | −3.71108 | ||||||||
\(621\) | 12.2929 | 0.493296 | ||||||||
\(622\) | −71.3408 | −2.86050 | ||||||||
\(623\) | −68.2809 | −2.73562 | ||||||||
\(624\) | 104.995 | 4.20316 | ||||||||
\(625\) | −10.0289 | −0.401156 | ||||||||
\(626\) | −3.64725 | −0.145773 | ||||||||
\(627\) | −1.02615 | −0.0409806 | ||||||||
\(628\) | 57.6083 | 2.29882 | ||||||||
\(629\) | −1.68423 | −0.0671545 | ||||||||
\(630\) | −63.9003 | −2.54585 | ||||||||
\(631\) | −6.02879 | −0.240002 | −0.120001 | − | 0.992774i | \(-0.538290\pi\) | ||||
−0.120001 | + | 0.992774i | \(0.538290\pi\) | |||||||
\(632\) | 105.748 | 4.20644 | ||||||||
\(633\) | 35.9252 | 1.42790 | ||||||||
\(634\) | −32.7213 | −1.29953 | ||||||||
\(635\) | 30.4428 | 1.20809 | ||||||||
\(636\) | 38.6036 | 1.53073 | ||||||||
\(637\) | −49.2491 | −1.95132 | ||||||||
\(638\) | −2.01548 | −0.0797937 | ||||||||
\(639\) | 11.0122 | 0.435637 | ||||||||
\(640\) | 45.3641 | 1.79317 | ||||||||
\(641\) | −7.05661 | −0.278719 | −0.139360 | − | 0.990242i | \(-0.544504\pi\) | ||||
−0.139360 | + | 0.990242i | \(0.544504\pi\) | |||||||
\(642\) | −84.4098 | −3.33139 | ||||||||
\(643\) | −14.4408 | −0.569489 | −0.284745 | − | 0.958603i | \(-0.591909\pi\) | ||||
−0.284745 | + | 0.958603i | \(0.591909\pi\) | |||||||
\(644\) | −89.9133 | −3.54308 | ||||||||
\(645\) | −80.4100 | −3.16614 | ||||||||
\(646\) | −11.8835 | −0.467549 | ||||||||
\(647\) | 41.8281 | 1.64443 | 0.822216 | − | 0.569175i | \(-0.192737\pi\) | ||||
0.822216 | + | 0.569175i | \(0.192737\pi\) | |||||||
\(648\) | 92.6927 | 3.64132 | ||||||||
\(649\) | −1.06407 | −0.0417686 | ||||||||
\(650\) | 78.8164 | 3.09143 | ||||||||
\(651\) | 48.4476 | 1.89881 | ||||||||
\(652\) | 89.4702 | 3.50392 | ||||||||
\(653\) | 1.12686 | 0.0440975 | 0.0220488 | − | 0.999757i | \(-0.492981\pi\) | ||||
0.0220488 | + | 0.999757i | \(0.492981\pi\) | |||||||
\(654\) | 21.8977 | 0.856268 | ||||||||
\(655\) | 66.2363 | 2.58807 | ||||||||
\(656\) | −2.94014 | −0.114793 | ||||||||
\(657\) | 9.19856 | 0.358870 | ||||||||
\(658\) | 150.829 | 5.87994 | ||||||||
\(659\) | 3.31591 | 0.129170 | 0.0645848 | − | 0.997912i | \(-0.479428\pi\) | ||||
0.0645848 | + | 0.997912i | \(0.479428\pi\) | |||||||
\(660\) | 4.07796 | 0.158734 | ||||||||
\(661\) | 36.8442 | 1.43307 | 0.716537 | − | 0.697549i | \(-0.245726\pi\) | ||||
0.716537 | + | 0.697549i | \(0.245726\pi\) | |||||||
\(662\) | 19.6364 | 0.763190 | ||||||||
\(663\) | 8.91906 | 0.346388 | ||||||||
\(664\) | 51.6512 | 2.00446 | ||||||||
\(665\) | 67.3561 | 2.61196 | ||||||||
\(666\) | 7.12825 | 0.276214 | ||||||||
\(667\) | 28.6569 | 1.10960 | ||||||||
\(668\) | 38.0307 | 1.47145 | ||||||||
\(669\) | −29.6748 | −1.14730 | ||||||||
\(670\) | −56.5776 | −2.18578 | ||||||||
\(671\) | −1.23756 | −0.0477754 | ||||||||
\(672\) | −138.192 | −5.33086 | ||||||||
\(673\) | 41.1993 | 1.58812 | 0.794058 | − | 0.607842i | \(-0.207965\pi\) | ||||
0.794058 | + | 0.607842i | \(0.207965\pi\) | |||||||
\(674\) | 62.5751 | 2.41030 | ||||||||
\(675\) | 21.4822 | 0.826849 | ||||||||
\(676\) | 22.0897 | 0.849604 | ||||||||
\(677\) | −45.0236 | −1.73040 | −0.865198 | − | 0.501431i | \(-0.832807\pi\) | ||||
−0.865198 | + | 0.501431i | \(0.832807\pi\) | |||||||
\(678\) | 86.5249 | 3.32297 | ||||||||
\(679\) | −19.1679 | −0.735596 | ||||||||
\(680\) | 28.6887 | 1.10016 | ||||||||
\(681\) | −6.53635 | −0.250473 | ||||||||
\(682\) | −1.49073 | −0.0570830 | ||||||||
\(683\) | 19.0097 | 0.727386 | 0.363693 | − | 0.931519i | \(-0.381516\pi\) | ||||
0.363693 | + | 0.931519i | \(0.381516\pi\) | |||||||
\(684\) | 36.1182 | 1.38101 | ||||||||
\(685\) | 34.4140 | 1.31489 | ||||||||
\(686\) | 55.8105 | 2.13086 | ||||||||
\(687\) | 20.8864 | 0.796866 | ||||||||
\(688\) | −126.997 | −4.84172 | ||||||||
\(689\) | 14.7253 | 0.560989 | ||||||||
\(690\) | −80.7408 | −3.07375 | ||||||||
\(691\) | 23.3578 | 0.888572 | 0.444286 | − | 0.895885i | \(-0.353457\pi\) | ||||
0.444286 | + | 0.895885i | \(0.353457\pi\) | |||||||
\(692\) | 37.9060 | 1.44097 | ||||||||
\(693\) | −0.740296 | −0.0281215 | ||||||||
\(694\) | 58.8431 | 2.23366 | ||||||||
\(695\) | −35.6486 | −1.35223 | ||||||||
\(696\) | 124.464 | 4.71778 | ||||||||
\(697\) | −0.249757 | −0.00946024 | ||||||||
\(698\) | −18.0435 | −0.682955 | ||||||||
\(699\) | 28.2096 | 1.06698 | ||||||||
\(700\) | −157.126 | −5.93880 | ||||||||
\(701\) | −19.7073 | −0.744334 | −0.372167 | − | 0.928166i | \(-0.621385\pi\) | ||||
−0.372167 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(702\) | 33.5248 | 1.26531 | ||||||||
\(703\) | −7.51375 | −0.283387 | ||||||||
\(704\) | 1.72412 | 0.0649803 | ||||||||
\(705\) | 97.2647 | 3.66320 | ||||||||
\(706\) | 2.66371 | 0.100250 | ||||||||
\(707\) | 42.8356 | 1.61100 | ||||||||
\(708\) | 108.168 | 4.06520 | ||||||||
\(709\) | −21.2053 | −0.796380 | −0.398190 | − | 0.917303i | \(-0.630362\pi\) | ||||
−0.398190 | + | 0.917303i | \(0.630362\pi\) | |||||||
\(710\) | 64.2361 | 2.41074 | ||||||||
\(711\) | −20.3784 | −0.764249 | ||||||||
\(712\) | −129.745 | −4.86238 | ||||||||
\(713\) | 21.1958 | 0.793789 | ||||||||
\(714\) | −24.7600 | −0.926619 | ||||||||
\(715\) | 1.55553 | 0.0581736 | ||||||||
\(716\) | 92.9640 | 3.47423 | ||||||||
\(717\) | −31.2589 | −1.16738 | ||||||||
\(718\) | 5.95398 | 0.222200 | ||||||||
\(719\) | 42.8397 | 1.59765 | 0.798826 | − | 0.601563i | \(-0.205455\pi\) | ||||
0.798826 | + | 0.601563i | \(0.205455\pi\) | |||||||
\(720\) | −65.0813 | −2.42544 | ||||||||
\(721\) | 21.6985 | 0.808094 | ||||||||
\(722\) | −2.40463 | −0.0894911 | ||||||||
\(723\) | 27.2756 | 1.01439 | ||||||||
\(724\) | 17.6641 | 0.656483 | ||||||||
\(725\) | 50.0788 | 1.85988 | ||||||||
\(726\) | −62.7016 | −2.32707 | ||||||||
\(727\) | 2.25209 | 0.0835253 | 0.0417627 | − | 0.999128i | \(-0.486703\pi\) | ||||
0.0417627 | + | 0.999128i | \(0.486703\pi\) | |||||||
\(728\) | −148.961 | −5.52086 | ||||||||
\(729\) | 1.56375 | 0.0579166 | ||||||||
\(730\) | 53.6567 | 1.98592 | ||||||||
\(731\) | −10.7881 | −0.399012 | ||||||||
\(732\) | 125.803 | 4.64983 | ||||||||
\(733\) | −23.3510 | −0.862488 | −0.431244 | − | 0.902235i | \(-0.641925\pi\) | ||||
−0.431244 | + | 0.902235i | \(0.641925\pi\) | |||||||
\(734\) | −38.7050 | −1.42863 | ||||||||
\(735\) | 88.1655 | 3.25203 | ||||||||
\(736\) | −60.4588 | −2.22854 | ||||||||
\(737\) | −0.655462 | −0.0241443 | ||||||||
\(738\) | 1.05706 | 0.0389110 | ||||||||
\(739\) | −29.1945 | −1.07394 | −0.536969 | − | 0.843602i | \(-0.680431\pi\) | ||||
−0.536969 | + | 0.843602i | \(0.680431\pi\) | |||||||
\(740\) | 29.8598 | 1.09767 | ||||||||
\(741\) | 39.7901 | 1.46173 | ||||||||
\(742\) | −40.8785 | −1.50070 | ||||||||
\(743\) | 12.4480 | 0.456674 | 0.228337 | − | 0.973582i | \(-0.426671\pi\) | ||||
0.228337 | + | 0.973582i | \(0.426671\pi\) | |||||||
\(744\) | 92.0581 | 3.37501 | ||||||||
\(745\) | −57.8769 | −2.12045 | ||||||||
\(746\) | −1.92489 | −0.0704751 | ||||||||
\(747\) | −9.95353 | −0.364181 | ||||||||
\(748\) | 0.547113 | 0.0200044 | ||||||||
\(749\) | 64.1890 | 2.34541 | ||||||||
\(750\) | −41.8257 | −1.52726 | ||||||||
\(751\) | −9.62616 | −0.351264 | −0.175632 | − | 0.984456i | \(-0.556197\pi\) | ||||
−0.175632 | + | 0.984456i | \(0.556197\pi\) | |||||||
\(752\) | 153.617 | 5.60183 | ||||||||
\(753\) | −19.7150 | −0.718455 | ||||||||
\(754\) | 78.1524 | 2.84614 | ||||||||
\(755\) | 54.7149 | 1.99128 | ||||||||
\(756\) | −66.8340 | −2.43073 | ||||||||
\(757\) | −51.8366 | −1.88403 | −0.942017 | − | 0.335564i | \(-0.891073\pi\) | ||||
−0.942017 | + | 0.335564i | \(0.891073\pi\) | |||||||
\(758\) | −0.898491 | −0.0326347 | ||||||||
\(759\) | −0.935397 | −0.0339528 | ||||||||
\(760\) | 127.987 | 4.64258 | ||||||||
\(761\) | 7.61783 | 0.276146 | 0.138073 | − | 0.990422i | \(-0.455909\pi\) | ||||
0.138073 | + | 0.990422i | \(0.455909\pi\) | |||||||
\(762\) | −49.9246 | −1.80858 | ||||||||
\(763\) | −16.6520 | −0.602842 | ||||||||
\(764\) | 114.619 | 4.14676 | ||||||||
\(765\) | −5.52849 | −0.199883 | ||||||||
\(766\) | −7.58151 | −0.273931 | ||||||||
\(767\) | 41.2606 | 1.48983 | ||||||||
\(768\) | −5.60067 | −0.202097 | ||||||||
\(769\) | −21.9534 | −0.791660 | −0.395830 | − | 0.918324i | \(-0.629543\pi\) | ||||
−0.395830 | + | 0.918324i | \(0.629543\pi\) | |||||||
\(770\) | −4.31827 | −0.155620 | ||||||||
\(771\) | 53.8517 | 1.93942 | ||||||||
\(772\) | 110.826 | 3.98870 | ||||||||
\(773\) | −32.4934 | −1.16871 | −0.584354 | − | 0.811499i | \(-0.698652\pi\) | ||||
−0.584354 | + | 0.811499i | \(0.698652\pi\) | |||||||
\(774\) | 45.6590 | 1.64118 | ||||||||
\(775\) | 37.0402 | 1.33052 | ||||||||
\(776\) | −36.4220 | −1.30747 | ||||||||
\(777\) | −15.6554 | −0.561633 | ||||||||
\(778\) | −18.5326 | −0.664427 | ||||||||
\(779\) | −1.11423 | −0.0399214 | ||||||||
\(780\) | −158.127 | −5.66185 | ||||||||
\(781\) | 0.744187 | 0.0266291 | ||||||||
\(782\) | −10.8325 | −0.387368 | ||||||||
\(783\) | 21.3012 | 0.761242 | ||||||||
\(784\) | 139.246 | 4.97306 | ||||||||
\(785\) | −39.3388 | −1.40406 | ||||||||
\(786\) | −108.624 | −3.87449 | ||||||||
\(787\) | 43.1998 | 1.53991 | 0.769953 | − | 0.638101i | \(-0.220280\pi\) | ||||
0.769953 | + | 0.638101i | \(0.220280\pi\) | |||||||
\(788\) | 71.5712 | 2.54962 | ||||||||
\(789\) | 50.2488 | 1.78890 | ||||||||
\(790\) | −118.870 | −4.22922 | ||||||||
\(791\) | −65.7974 | −2.33949 | ||||||||
\(792\) | −1.40668 | −0.0499842 | ||||||||
\(793\) | 47.9876 | 1.70409 | ||||||||
\(794\) | 88.6460 | 3.14593 | ||||||||
\(795\) | −26.3612 | −0.934934 | ||||||||
\(796\) | −27.3942 | −0.970962 | ||||||||
\(797\) | −22.1213 | −0.783578 | −0.391789 | − | 0.920055i | \(-0.628144\pi\) | ||||
−0.391789 | + | 0.920055i | \(0.628144\pi\) | |||||||
\(798\) | −110.460 | −3.91025 | ||||||||
\(799\) | 13.0494 | 0.461654 | ||||||||
\(800\) | −105.653 | −3.73541 | ||||||||
\(801\) | 25.0026 | 0.883424 | ||||||||
\(802\) | 64.4159 | 2.27460 | ||||||||
\(803\) | 0.621623 | 0.0219366 | ||||||||
\(804\) | 66.6308 | 2.34989 | ||||||||
\(805\) | 61.3989 | 2.16403 | ||||||||
\(806\) | 57.8046 | 2.03608 | ||||||||
\(807\) | 53.5091 | 1.88361 | ||||||||
\(808\) | 81.3945 | 2.86345 | ||||||||
\(809\) | −11.6081 | −0.408120 | −0.204060 | − | 0.978958i | \(-0.565414\pi\) | ||||
−0.204060 | + | 0.978958i | \(0.565414\pi\) | |||||||
\(810\) | −104.195 | −3.66103 | ||||||||
\(811\) | 15.7909 | 0.554492 | 0.277246 | − | 0.960799i | \(-0.410578\pi\) | ||||
0.277246 | + | 0.960799i | \(0.410578\pi\) | |||||||
\(812\) | −155.802 | −5.46758 | ||||||||
\(813\) | 38.5392 | 1.35163 | ||||||||
\(814\) | 0.481714 | 0.0168841 | ||||||||
\(815\) | −61.0964 | −2.14011 | ||||||||
\(816\) | −25.2176 | −0.882792 | ||||||||
\(817\) | −48.1283 | −1.68380 | ||||||||
\(818\) | 0.192278 | 0.00672284 | ||||||||
\(819\) | 28.7058 | 1.00306 | ||||||||
\(820\) | 4.42797 | 0.154632 | ||||||||
\(821\) | −39.5939 | −1.38184 | −0.690918 | − | 0.722933i | \(-0.742793\pi\) | ||||
−0.690918 | + | 0.722933i | \(0.742793\pi\) | |||||||
\(822\) | −56.4371 | −1.96847 | ||||||||
\(823\) | −46.4395 | −1.61878 | −0.809389 | − | 0.587273i | \(-0.800201\pi\) | ||||
−0.809389 | + | 0.587273i | \(0.800201\pi\) | |||||||
\(824\) | 41.2306 | 1.43633 | ||||||||
\(825\) | −1.63463 | −0.0569106 | ||||||||
\(826\) | −114.542 | −3.98544 | ||||||||
\(827\) | 1.38325 | 0.0481004 | 0.0240502 | − | 0.999711i | \(-0.492344\pi\) | ||||
0.0240502 | + | 0.999711i | \(0.492344\pi\) | |||||||
\(828\) | 32.9238 | 1.14418 | ||||||||
\(829\) | −40.4611 | −1.40527 | −0.702637 | − | 0.711549i | \(-0.747994\pi\) | ||||
−0.702637 | + | 0.711549i | \(0.747994\pi\) | |||||||
\(830\) | −58.0606 | −2.01531 | ||||||||
\(831\) | −43.1339 | −1.49630 | ||||||||
\(832\) | −66.8546 | −2.31777 | ||||||||
\(833\) | 11.8286 | 0.409836 | ||||||||
\(834\) | 58.4618 | 2.02437 | ||||||||
\(835\) | −25.9700 | −0.898728 | ||||||||
\(836\) | 2.44080 | 0.0844170 | ||||||||
\(837\) | 15.7552 | 0.544579 | ||||||||
\(838\) | 50.9993 | 1.76174 | ||||||||
\(839\) | −4.68742 | −0.161828 | −0.0809138 | − | 0.996721i | \(-0.525784\pi\) | ||||
−0.0809138 | + | 0.996721i | \(0.525784\pi\) | |||||||
\(840\) | 266.669 | 9.20097 | ||||||||
\(841\) | 20.6569 | 0.712306 | ||||||||
\(842\) | 91.7385 | 3.16152 | ||||||||
\(843\) | 29.8748 | 1.02894 | ||||||||
\(844\) | −85.4516 | −2.94137 | ||||||||
\(845\) | −15.0844 | −0.518918 | ||||||||
\(846\) | −55.2296 | −1.89883 | ||||||||
\(847\) | 47.6811 | 1.63834 | ||||||||
\(848\) | −41.6340 | −1.42972 | ||||||||
\(849\) | 8.02121 | 0.275287 | ||||||||
\(850\) | −18.9300 | −0.649295 | ||||||||
\(851\) | −6.84921 | −0.234788 | ||||||||
\(852\) | −75.6500 | −2.59173 | ||||||||
\(853\) | −39.5992 | −1.35585 | −0.677926 | − | 0.735130i | \(-0.737121\pi\) | ||||
−0.677926 | + | 0.735130i | \(0.737121\pi\) | |||||||
\(854\) | −133.217 | −4.55859 | ||||||||
\(855\) | −24.6640 | −0.843490 | ||||||||
\(856\) | 121.969 | 4.16882 | ||||||||
\(857\) | −36.1159 | −1.23370 | −0.616848 | − | 0.787082i | \(-0.711591\pi\) | ||||
−0.616848 | + | 0.787082i | \(0.711591\pi\) | |||||||
\(858\) | −2.55099 | −0.0870892 | ||||||||
\(859\) | −9.45099 | −0.322464 | −0.161232 | − | 0.986917i | \(-0.551547\pi\) | ||||
−0.161232 | + | 0.986917i | \(0.551547\pi\) | |||||||
\(860\) | 191.263 | 6.52201 | ||||||||
\(861\) | −2.32157 | −0.0791188 | ||||||||
\(862\) | 36.4019 | 1.23986 | ||||||||
\(863\) | 22.5235 | 0.766707 | 0.383354 | − | 0.923602i | \(-0.374769\pi\) | ||||
0.383354 | + | 0.923602i | \(0.374769\pi\) | |||||||
\(864\) | −44.9400 | −1.52889 | ||||||||
\(865\) | −25.8848 | −0.880109 | ||||||||
\(866\) | −29.2040 | −0.992392 | ||||||||
\(867\) | −2.14217 | −0.0727519 | ||||||||
\(868\) | −115.237 | −3.91141 | ||||||||
\(869\) | −1.37713 | −0.0467161 | ||||||||
\(870\) | −139.908 | −4.74333 | ||||||||
\(871\) | 25.4162 | 0.861196 | ||||||||
\(872\) | −31.6414 | −1.07151 | ||||||||
\(873\) | 7.01876 | 0.237549 | ||||||||
\(874\) | −48.3263 | −1.63466 | ||||||||
\(875\) | 31.8061 | 1.07524 | ||||||||
\(876\) | −63.1908 | −2.13502 | ||||||||
\(877\) | −13.5387 | −0.457169 | −0.228585 | − | 0.973524i | \(-0.573410\pi\) | ||||
−0.228585 | + | 0.973524i | \(0.573410\pi\) | |||||||
\(878\) | −9.69359 | −0.327143 | ||||||||
\(879\) | 54.6152 | 1.84213 | ||||||||
\(880\) | −4.39808 | −0.148259 | ||||||||
\(881\) | 30.3322 | 1.02192 | 0.510960 | − | 0.859605i | \(-0.329290\pi\) | ||||
0.510960 | + | 0.859605i | \(0.329290\pi\) | |||||||
\(882\) | −50.0628 | −1.68570 | ||||||||
\(883\) | −25.9146 | −0.872097 | −0.436048 | − | 0.899923i | \(-0.643622\pi\) | ||||
−0.436048 | + | 0.899923i | \(0.643622\pi\) | |||||||
\(884\) | −21.2149 | −0.713533 | ||||||||
\(885\) | −73.8645 | −2.48293 | ||||||||
\(886\) | −15.6950 | −0.527285 | ||||||||
\(887\) | 30.4774 | 1.02333 | 0.511666 | − | 0.859185i | \(-0.329029\pi\) | ||||
0.511666 | + | 0.859185i | \(0.329029\pi\) | |||||||
\(888\) | −29.7477 | −0.998267 | ||||||||
\(889\) | 37.9649 | 1.27330 | ||||||||
\(890\) | 145.844 | 4.88871 | ||||||||
\(891\) | −1.20712 | −0.0404399 | ||||||||
\(892\) | 70.5845 | 2.36334 | ||||||||
\(893\) | 58.2165 | 1.94814 | ||||||||
\(894\) | 94.9150 | 3.17443 | ||||||||
\(895\) | −63.4822 | −2.12198 | ||||||||
\(896\) | 56.5730 | 1.88997 | ||||||||
\(897\) | 36.2710 | 1.21105 | ||||||||
\(898\) | −90.0221 | −3.00408 | ||||||||
\(899\) | 36.7282 | 1.22495 | ||||||||
\(900\) | 57.5352 | 1.91784 | ||||||||
\(901\) | −3.53670 | −0.117825 | ||||||||
\(902\) | 0.0714344 | 0.00237851 | ||||||||
\(903\) | −100.278 | −3.33705 | ||||||||
\(904\) | −125.025 | −4.15828 | ||||||||
\(905\) | −12.0623 | −0.400964 | ||||||||
\(906\) | −89.7294 | −2.98106 | ||||||||
\(907\) | −13.8322 | −0.459292 | −0.229646 | − | 0.973274i | \(-0.573757\pi\) | ||||
−0.229646 | + | 0.973274i | \(0.573757\pi\) | |||||||
\(908\) | 15.5473 | 0.515956 | ||||||||
\(909\) | −15.6852 | −0.520247 | ||||||||
\(910\) | 167.445 | 5.55076 | ||||||||
\(911\) | −18.5334 | −0.614038 | −0.307019 | − | 0.951703i | \(-0.599332\pi\) | ||||
−0.307019 | + | 0.951703i | \(0.599332\pi\) | |||||||
\(912\) | −112.502 | −3.72531 | ||||||||
\(913\) | −0.672642 | −0.0222612 | ||||||||
\(914\) | 95.8465 | 3.17032 | ||||||||
\(915\) | −85.9071 | −2.84000 | ||||||||
\(916\) | −49.6803 | −1.64148 | ||||||||
\(917\) | 82.6025 | 2.72778 | ||||||||
\(918\) | −8.05195 | −0.265754 | ||||||||
\(919\) | 52.3403 | 1.72655 | 0.863274 | − | 0.504736i | \(-0.168410\pi\) | ||||
0.863274 | + | 0.504736i | \(0.168410\pi\) | |||||||
\(920\) | 116.668 | 3.84642 | ||||||||
\(921\) | 12.0627 | 0.397479 | ||||||||
\(922\) | −51.0282 | −1.68052 | ||||||||
\(923\) | −28.8566 | −0.949827 | ||||||||
\(924\) | 5.08557 | 0.167303 | ||||||||
\(925\) | −11.9692 | −0.393545 | ||||||||
\(926\) | 29.5311 | 0.970451 | ||||||||
\(927\) | −7.94540 | −0.260961 | ||||||||
\(928\) | −104.763 | −3.43902 | ||||||||
\(929\) | −21.2353 | −0.696706 | −0.348353 | − | 0.937363i | \(-0.613259\pi\) | ||||
−0.348353 | + | 0.937363i | \(0.613259\pi\) | |||||||
\(930\) | −103.481 | −3.39329 | ||||||||
\(931\) | 52.7703 | 1.72948 | ||||||||
\(932\) | −67.0992 | −2.19791 | ||||||||
\(933\) | −57.3726 | −1.87830 | ||||||||
\(934\) | −40.7959 | −1.33488 | ||||||||
\(935\) | −0.373606 | −0.0122182 | ||||||||
\(936\) | 54.5454 | 1.78287 | ||||||||
\(937\) | −18.3183 | −0.598433 | −0.299217 | − | 0.954185i | \(-0.596725\pi\) | ||||
−0.299217 | + | 0.954185i | \(0.596725\pi\) | |||||||
\(938\) | −70.5573 | −2.30378 | ||||||||
\(939\) | −2.93314 | −0.0957193 | ||||||||
\(940\) | −231.354 | −7.54592 | ||||||||
\(941\) | 29.0984 | 0.948582 | 0.474291 | − | 0.880368i | \(-0.342705\pi\) | ||||
0.474291 | + | 0.880368i | \(0.342705\pi\) | |||||||
\(942\) | 64.5136 | 2.10197 | ||||||||
\(943\) | −1.01568 | −0.0330752 | ||||||||
\(944\) | −116.659 | −3.79694 | ||||||||
\(945\) | 45.6388 | 1.48463 | ||||||||
\(946\) | 3.08556 | 0.100320 | ||||||||
\(947\) | −48.6699 | −1.58156 | −0.790780 | − | 0.612100i | \(-0.790325\pi\) | ||||
−0.790780 | + | 0.612100i | \(0.790325\pi\) | |||||||
\(948\) | 139.992 | 4.54673 | ||||||||
\(949\) | −24.1041 | −0.782451 | ||||||||
\(950\) | −84.4516 | −2.73997 | ||||||||
\(951\) | −26.3147 | −0.853311 | ||||||||
\(952\) | 35.7773 | 1.15955 | ||||||||
\(953\) | 0.235312 | 0.00762251 | 0.00381126 | − | 0.999993i | \(-0.498787\pi\) | ||||
0.00381126 | + | 0.999993i | \(0.498787\pi\) | |||||||
\(954\) | 14.9686 | 0.484626 | ||||||||
\(955\) | −78.2694 | −2.53274 | ||||||||
\(956\) | 74.3523 | 2.40472 | ||||||||
\(957\) | −1.62086 | −0.0523950 | ||||||||
\(958\) | −53.2894 | −1.72170 | ||||||||
\(959\) | 42.9173 | 1.38587 | ||||||||
\(960\) | 119.683 | 3.86275 | ||||||||
\(961\) | −3.83440 | −0.123690 | ||||||||
\(962\) | −18.6790 | −0.602234 | ||||||||
\(963\) | −23.5043 | −0.757414 | ||||||||
\(964\) | −64.8777 | −2.08957 | ||||||||
\(965\) | −75.6793 | −2.43620 | ||||||||
\(966\) | −100.691 | −3.23968 | ||||||||
\(967\) | −42.0355 | −1.35177 | −0.675885 | − | 0.737007i | \(-0.736239\pi\) | ||||
−0.675885 | + | 0.737007i | \(0.736239\pi\) | |||||||
\(968\) | 90.6016 | 2.91204 | ||||||||
\(969\) | −9.55675 | −0.307007 | ||||||||
\(970\) | 40.9415 | 1.31455 | ||||||||
\(971\) | 25.6222 | 0.822255 | 0.411128 | − | 0.911578i | \(-0.365135\pi\) | ||||
0.411128 | + | 0.911578i | \(0.365135\pi\) | |||||||
\(972\) | 76.5017 | 2.45379 | ||||||||
\(973\) | −44.4570 | −1.42523 | ||||||||
\(974\) | −85.2639 | −2.73203 | ||||||||
\(975\) | 63.3845 | 2.02993 | ||||||||
\(976\) | −135.679 | −4.34298 | ||||||||
\(977\) | 1.66752 | 0.0533485 | 0.0266743 | − | 0.999644i | \(-0.491508\pi\) | ||||
0.0266743 | + | 0.999644i | \(0.491508\pi\) | |||||||
\(978\) | 100.195 | 3.20387 | ||||||||
\(979\) | 1.68963 | 0.0540009 | ||||||||
\(980\) | −209.710 | −6.69895 | ||||||||
\(981\) | 6.09750 | 0.194678 | ||||||||
\(982\) | −70.5117 | −2.25012 | ||||||||
\(983\) | −8.40787 | −0.268169 | −0.134085 | − | 0.990970i | \(-0.542809\pi\) | ||||
−0.134085 | + | 0.990970i | \(0.542809\pi\) | |||||||
\(984\) | −4.41134 | −0.140628 | ||||||||
\(985\) | −48.8737 | −1.55724 | ||||||||
\(986\) | −18.7705 | −0.597776 | ||||||||
\(987\) | 121.298 | 3.86095 | ||||||||
\(988\) | −94.6447 | −3.01105 | ||||||||
\(989\) | −43.8717 | −1.39504 | ||||||||
\(990\) | 1.58123 | 0.0502549 | ||||||||
\(991\) | −25.5265 | −0.810877 | −0.405438 | − | 0.914122i | \(-0.632881\pi\) | ||||
−0.405438 | + | 0.914122i | \(0.632881\pi\) | |||||||
\(992\) | −77.4870 | −2.46021 | ||||||||
\(993\) | 15.7917 | 0.501134 | ||||||||
\(994\) | 80.1081 | 2.54087 | ||||||||
\(995\) | 18.7066 | 0.593040 | ||||||||
\(996\) | 68.3772 | 2.16661 | ||||||||
\(997\) | −18.6529 | −0.590744 | −0.295372 | − | 0.955382i | \(-0.595444\pi\) | ||||
−0.295372 | + | 0.955382i | \(0.595444\pi\) | |||||||
\(998\) | 37.9982 | 1.20281 | ||||||||
\(999\) | −5.09113 | −0.161076 |
(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 | 6001.2.a.d.1.4 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.d.1.4 | ✓ | 121 | 1.1 | even | 1 | trivial |