Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69245 | −1.90385 | −0.951926 | − | 0.306328i | \(-0.900899\pi\) | ||||
−0.951926 | + | 0.306328i | \(0.900899\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.24930 | 2.62465 | ||||||||
\(5\) | 3.40876 | 1.52444 | 0.762222 | − | 0.647316i | \(-0.224109\pi\) | ||||
0.762222 | + | 0.647316i | \(0.224109\pi\) | |||||||
\(6\) | −2.69245 | −1.09919 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.74860 | −3.09310 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.17792 | −2.90231 | ||||||||
\(11\) | 2.47740 | 0.746963 | 0.373482 | − | 0.927638i | \(-0.378164\pi\) | ||||
0.373482 | + | 0.927638i | \(0.378164\pi\) | |||||||
\(12\) | 5.24930 | 1.51534 | ||||||||
\(13\) | −2.61944 | −0.726502 | −0.363251 | − | 0.931691i | \(-0.618333\pi\) | ||||
−0.363251 | + | 0.931691i | \(0.618333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.40876 | 0.880138 | ||||||||
\(16\) | 13.0566 | 3.26414 | ||||||||
\(17\) | −5.06684 | −1.22889 | −0.614445 | − | 0.788960i | \(-0.710620\pi\) | ||||
−0.614445 | + | 0.788960i | \(0.710620\pi\) | |||||||
\(18\) | −2.69245 | −0.634617 | ||||||||
\(19\) | −2.94589 | −0.675833 | −0.337917 | − | 0.941176i | \(-0.609722\pi\) | ||||
−0.337917 | + | 0.941176i | \(0.609722\pi\) | |||||||
\(20\) | 17.8936 | 4.00113 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.67027 | −1.42211 | ||||||||
\(23\) | 2.48116 | 0.517358 | 0.258679 | − | 0.965963i | \(-0.416713\pi\) | ||||
0.258679 | + | 0.965963i | \(0.416713\pi\) | |||||||
\(24\) | −8.74860 | −1.78580 | ||||||||
\(25\) | 6.61964 | 1.32393 | ||||||||
\(26\) | 7.05272 | 1.38315 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.267181 | 0.0496142 | 0.0248071 | − | 0.999692i | \(-0.492103\pi\) | ||||
0.0248071 | + | 0.999692i | \(0.492103\pi\) | |||||||
\(30\) | −9.17792 | −1.67565 | ||||||||
\(31\) | −6.04056 | −1.08492 | −0.542459 | − | 0.840083i | \(-0.682506\pi\) | ||||
−0.542459 | + | 0.840083i | \(0.682506\pi\) | |||||||
\(32\) | −17.6570 | −3.12135 | ||||||||
\(33\) | 2.47740 | 0.431259 | ||||||||
\(34\) | 13.6422 | 2.33962 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.24930 | 0.874884 | ||||||||
\(37\) | 9.78122 | 1.60802 | 0.804012 | − | 0.594614i | \(-0.202695\pi\) | ||||
0.804012 | + | 0.594614i | \(0.202695\pi\) | |||||||
\(38\) | 7.93167 | 1.28669 | ||||||||
\(39\) | −2.61944 | −0.419446 | ||||||||
\(40\) | −29.8219 | −4.71525 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.25634 | 1.10658 | 0.553291 | − | 0.832988i | \(-0.313372\pi\) | ||||
0.553291 | + | 0.832988i | \(0.313372\pi\) | |||||||
\(44\) | 13.0046 | 1.96052 | ||||||||
\(45\) | 3.40876 | 0.508148 | ||||||||
\(46\) | −6.68041 | −0.984973 | ||||||||
\(47\) | −8.30624 | −1.21159 | −0.605795 | − | 0.795621i | \(-0.707145\pi\) | ||||
−0.605795 | + | 0.795621i | \(0.707145\pi\) | |||||||
\(48\) | 13.0566 | 1.88455 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −17.8231 | −2.52056 | ||||||||
\(51\) | −5.06684 | −0.709500 | ||||||||
\(52\) | −13.7502 | −1.90682 | ||||||||
\(53\) | 10.8096 | 1.48481 | 0.742406 | − | 0.669951i | \(-0.233685\pi\) | ||||
0.742406 | + | 0.669951i | \(0.233685\pi\) | |||||||
\(54\) | −2.69245 | −0.366396 | ||||||||
\(55\) | 8.44485 | 1.13870 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.94589 | −0.390192 | ||||||||
\(58\) | −0.719372 | −0.0944581 | ||||||||
\(59\) | −2.98222 | −0.388252 | −0.194126 | − | 0.980977i | \(-0.562187\pi\) | ||||
−0.194126 | + | 0.980977i | \(0.562187\pi\) | |||||||
\(60\) | 17.8936 | 2.31005 | ||||||||
\(61\) | −7.07265 | −0.905560 | −0.452780 | − | 0.891622i | \(-0.649568\pi\) | ||||
−0.452780 | + | 0.891622i | \(0.649568\pi\) | |||||||
\(62\) | 16.2639 | 2.06552 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 21.4276 | 2.67845 | ||||||||
\(65\) | −8.92904 | −1.10751 | ||||||||
\(66\) | −6.67027 | −0.821054 | ||||||||
\(67\) | 14.1114 | 1.72398 | 0.861989 | − | 0.506927i | \(-0.169219\pi\) | ||||
0.861989 | + | 0.506927i | \(0.169219\pi\) | |||||||
\(68\) | −26.5974 | −3.22541 | ||||||||
\(69\) | 2.48116 | 0.298697 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.21376 | 0.974794 | 0.487397 | − | 0.873181i | \(-0.337946\pi\) | ||||
0.487397 | + | 0.873181i | \(0.337946\pi\) | |||||||
\(72\) | −8.74860 | −1.03103 | ||||||||
\(73\) | −6.66722 | −0.780339 | −0.390169 | − | 0.920743i | \(-0.627584\pi\) | ||||
−0.390169 | + | 0.920743i | \(0.627584\pi\) | |||||||
\(74\) | −26.3355 | −3.06144 | ||||||||
\(75\) | 6.61964 | 0.764370 | ||||||||
\(76\) | −15.4639 | −1.77383 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.05272 | 0.798564 | ||||||||
\(79\) | −10.7721 | −1.21196 | −0.605979 | − | 0.795481i | \(-0.707218\pi\) | ||||
−0.605979 | + | 0.795481i | \(0.707218\pi\) | |||||||
\(80\) | 44.5067 | 4.97600 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.69245 | 0.297332 | ||||||||
\(83\) | 14.0497 | 1.54215 | 0.771077 | − | 0.636743i | \(-0.219719\pi\) | ||||
0.771077 | + | 0.636743i | \(0.219719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.2716 | −1.87337 | ||||||||
\(86\) | −19.5374 | −2.10677 | ||||||||
\(87\) | 0.267181 | 0.0286448 | ||||||||
\(88\) | −21.6737 | −2.31043 | ||||||||
\(89\) | 15.6068 | 1.65432 | 0.827161 | − | 0.561966i | \(-0.189955\pi\) | ||||
0.827161 | + | 0.561966i | \(0.189955\pi\) | |||||||
\(90\) | −9.17792 | −0.967438 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.0244 | 1.35788 | ||||||||
\(93\) | −6.04056 | −0.626377 | ||||||||
\(94\) | 22.3642 | 2.30669 | ||||||||
\(95\) | −10.0418 | −1.03027 | ||||||||
\(96\) | −17.6570 | −1.80211 | ||||||||
\(97\) | −7.72850 | −0.784710 | −0.392355 | − | 0.919814i | \(-0.628340\pi\) | ||||
−0.392355 | + | 0.919814i | \(0.628340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.47740 | 0.248988 | ||||||||
\(100\) | 34.7485 | 3.47485 | ||||||||
\(101\) | 9.67726 | 0.962923 | 0.481462 | − | 0.876467i | \(-0.340106\pi\) | ||||
0.481462 | + | 0.876467i | \(0.340106\pi\) | |||||||
\(102\) | 13.6422 | 1.35078 | ||||||||
\(103\) | −4.45587 | −0.439050 | −0.219525 | − | 0.975607i | \(-0.570451\pi\) | ||||
−0.219525 | + | 0.975607i | \(0.570451\pi\) | |||||||
\(104\) | 22.9164 | 2.24714 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.1043 | −2.82686 | ||||||||
\(107\) | 10.3878 | 1.00423 | 0.502115 | − | 0.864801i | \(-0.332555\pi\) | ||||
0.502115 | + | 0.864801i | \(0.332555\pi\) | |||||||
\(108\) | 5.24930 | 0.505114 | ||||||||
\(109\) | −7.88580 | −0.755322 | −0.377661 | − | 0.925944i | \(-0.623272\pi\) | ||||
−0.377661 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(110\) | −22.7373 | −2.16792 | ||||||||
\(111\) | 9.78122 | 0.928393 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.9778 | 1.78528 | 0.892641 | − | 0.450768i | \(-0.148850\pi\) | ||||
0.892641 | + | 0.450768i | \(0.148850\pi\) | |||||||
\(114\) | 7.93167 | 0.742869 | ||||||||
\(115\) | 8.45768 | 0.788683 | ||||||||
\(116\) | 1.40251 | 0.130220 | ||||||||
\(117\) | −2.61944 | −0.242167 | ||||||||
\(118\) | 8.02950 | 0.739175 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −29.8219 | −2.72235 | ||||||||
\(121\) | −4.86251 | −0.442046 | ||||||||
\(122\) | 19.0428 | 1.72405 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −31.7087 | −2.84753 | ||||||||
\(125\) | 5.52095 | 0.493809 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4451 | 1.19306 | 0.596529 | − | 0.802592i | \(-0.296546\pi\) | ||||
0.596529 | + | 0.802592i | \(0.296546\pi\) | |||||||
\(128\) | −22.3787 | −1.97801 | ||||||||
\(129\) | 7.25634 | 0.638885 | ||||||||
\(130\) | 24.0410 | 2.10854 | ||||||||
\(131\) | 1.31500 | 0.114892 | 0.0574460 | − | 0.998349i | \(-0.481704\pi\) | ||||
0.0574460 | + | 0.998349i | \(0.481704\pi\) | |||||||
\(132\) | 13.0046 | 1.13191 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −37.9942 | −3.28220 | ||||||||
\(135\) | 3.40876 | 0.293379 | ||||||||
\(136\) | 44.3278 | 3.80107 | ||||||||
\(137\) | 14.4957 | 1.23845 | 0.619224 | − | 0.785214i | \(-0.287447\pi\) | ||||
0.619224 | + | 0.785214i | \(0.287447\pi\) | |||||||
\(138\) | −6.68041 | −0.568674 | ||||||||
\(139\) | 3.68532 | 0.312585 | 0.156292 | − | 0.987711i | \(-0.450046\pi\) | ||||
0.156292 | + | 0.987711i | \(0.450046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.30624 | −0.699512 | ||||||||
\(142\) | −22.1152 | −1.85586 | ||||||||
\(143\) | −6.48939 | −0.542670 | ||||||||
\(144\) | 13.0566 | 1.08805 | ||||||||
\(145\) | 0.910755 | 0.0756341 | ||||||||
\(146\) | 17.9512 | 1.48565 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 51.3446 | 4.22050 | ||||||||
\(149\) | 15.8559 | 1.29897 | 0.649485 | − | 0.760375i | \(-0.274985\pi\) | ||||
0.649485 | + | 0.760375i | \(0.274985\pi\) | |||||||
\(150\) | −17.8231 | −1.45525 | ||||||||
\(151\) | 11.0469 | 0.898987 | 0.449493 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449493 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(152\) | 25.7724 | 2.09042 | ||||||||
\(153\) | −5.06684 | −0.409630 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.5908 | −1.65389 | ||||||||
\(156\) | −13.7502 | −1.10090 | ||||||||
\(157\) | 8.18928 | 0.653576 | 0.326788 | − | 0.945098i | \(-0.394034\pi\) | ||||
0.326788 | + | 0.945098i | \(0.394034\pi\) | |||||||
\(158\) | 29.0034 | 2.30739 | ||||||||
\(159\) | 10.8096 | 0.857256 | ||||||||
\(160\) | −60.1885 | −4.75832 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.69245 | −0.211539 | ||||||||
\(163\) | −0.540625 | −0.0423450 | −0.0211725 | − | 0.999776i | \(-0.506740\pi\) | ||||
−0.0211725 | + | 0.999776i | \(0.506740\pi\) | |||||||
\(164\) | −5.24930 | −0.409902 | ||||||||
\(165\) | 8.44485 | 0.657430 | ||||||||
\(166\) | −37.8281 | −2.93603 | ||||||||
\(167\) | 22.1797 | 1.71631 | 0.858157 | − | 0.513388i | \(-0.171610\pi\) | ||||
0.858157 | + | 0.513388i | \(0.171610\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.13853 | −0.472194 | ||||||||
\(170\) | 46.5031 | 3.56662 | ||||||||
\(171\) | −2.94589 | −0.225278 | ||||||||
\(172\) | 38.0908 | 2.90439 | ||||||||
\(173\) | 18.9158 | 1.43814 | 0.719070 | − | 0.694937i | \(-0.244568\pi\) | ||||
0.719070 | + | 0.694937i | \(0.244568\pi\) | |||||||
\(174\) | −0.719372 | −0.0545354 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 32.3463 | 2.43820 | ||||||||
\(177\) | −2.98222 | −0.224158 | ||||||||
\(178\) | −42.0207 | −3.14958 | ||||||||
\(179\) | −4.70118 | −0.351383 | −0.175691 | − | 0.984445i | \(-0.556216\pi\) | ||||
−0.175691 | + | 0.984445i | \(0.556216\pi\) | |||||||
\(180\) | 17.8936 | 1.33371 | ||||||||
\(181\) | 20.8428 | 1.54923 | 0.774616 | − | 0.632432i | \(-0.217943\pi\) | ||||
0.774616 | + | 0.632432i | \(0.217943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.07265 | −0.522825 | ||||||||
\(184\) | −21.7067 | −1.60024 | ||||||||
\(185\) | 33.3418 | 2.45134 | ||||||||
\(186\) | 16.2639 | 1.19253 | ||||||||
\(187\) | −12.5526 | −0.917935 | ||||||||
\(188\) | −43.6020 | −3.18000 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27.0371 | 1.96148 | ||||||||
\(191\) | 2.02143 | 0.146266 | 0.0731329 | − | 0.997322i | \(-0.476700\pi\) | ||||
0.0731329 | + | 0.997322i | \(0.476700\pi\) | |||||||
\(192\) | 21.4276 | 1.54640 | ||||||||
\(193\) | 0.759337 | 0.0546583 | 0.0273291 | − | 0.999626i | \(-0.491300\pi\) | ||||
0.0273291 | + | 0.999626i | \(0.491300\pi\) | |||||||
\(194\) | 20.8086 | 1.49397 | ||||||||
\(195\) | −8.92904 | −0.639422 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.2289 | 1.22751 | 0.613755 | − | 0.789496i | \(-0.289658\pi\) | ||||
0.613755 | + | 0.789496i | \(0.289658\pi\) | |||||||
\(198\) | −6.67027 | −0.474036 | ||||||||
\(199\) | 20.8621 | 1.47887 | 0.739436 | − | 0.673227i | \(-0.235092\pi\) | ||||
0.739436 | + | 0.673227i | \(0.235092\pi\) | |||||||
\(200\) | −57.9125 | −4.09503 | ||||||||
\(201\) | 14.1114 | 0.995339 | ||||||||
\(202\) | −26.0556 | −1.83326 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −26.5974 | −1.86219 | ||||||||
\(205\) | −3.40876 | −0.238078 | ||||||||
\(206\) | 11.9972 | 0.835887 | ||||||||
\(207\) | 2.48116 | 0.172453 | ||||||||
\(208\) | −34.2009 | −2.37141 | ||||||||
\(209\) | −7.29813 | −0.504822 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7824 | −0.879978 | −0.439989 | − | 0.898003i | \(-0.645018\pi\) | ||||
−0.439989 | + | 0.898003i | \(0.645018\pi\) | |||||||
\(212\) | 56.7428 | 3.89711 | ||||||||
\(213\) | 8.21376 | 0.562798 | ||||||||
\(214\) | −27.9688 | −1.91190 | ||||||||
\(215\) | 24.7351 | 1.68692 | ||||||||
\(216\) | −8.74860 | −0.595267 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 21.2321 | 1.43802 | ||||||||
\(219\) | −6.66722 | −0.450529 | ||||||||
\(220\) | 44.3296 | 2.98870 | ||||||||
\(221\) | 13.2723 | 0.892791 | ||||||||
\(222\) | −26.3355 | −1.76752 | ||||||||
\(223\) | 7.42145 | 0.496977 | 0.248489 | − | 0.968635i | \(-0.420066\pi\) | ||||
0.248489 | + | 0.968635i | \(0.420066\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.61964 | 0.441309 | ||||||||
\(226\) | −51.0969 | −3.39891 | ||||||||
\(227\) | 12.4666 | 0.827437 | 0.413718 | − | 0.910405i | \(-0.364230\pi\) | ||||
0.413718 | + | 0.910405i | \(0.364230\pi\) | |||||||
\(228\) | −15.4639 | −1.02412 | ||||||||
\(229\) | −14.2997 | −0.944948 | −0.472474 | − | 0.881345i | \(-0.656639\pi\) | ||||
−0.472474 | + | 0.881345i | \(0.656639\pi\) | |||||||
\(230\) | −22.7719 | −1.50154 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.33746 | −0.153462 | ||||||||
\(233\) | −23.7816 | −1.55798 | −0.778991 | − | 0.627035i | \(-0.784268\pi\) | ||||
−0.778991 | + | 0.627035i | \(0.784268\pi\) | |||||||
\(234\) | 7.05272 | 0.461051 | ||||||||
\(235\) | −28.3140 | −1.84700 | ||||||||
\(236\) | −15.6546 | −1.01903 | ||||||||
\(237\) | −10.7721 | −0.699724 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0560 | 0.650472 | 0.325236 | − | 0.945633i | \(-0.394556\pi\) | ||||
0.325236 | + | 0.945633i | \(0.394556\pi\) | |||||||
\(240\) | 44.5067 | 2.87290 | ||||||||
\(241\) | −9.20788 | −0.593132 | −0.296566 | − | 0.955012i | \(-0.595841\pi\) | ||||
−0.296566 | + | 0.955012i | \(0.595841\pi\) | |||||||
\(242\) | 13.0921 | 0.841591 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −37.1265 | −2.37678 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.69245 | 0.171665 | ||||||||
\(247\) | 7.71658 | 0.490994 | ||||||||
\(248\) | 52.8464 | 3.35575 | ||||||||
\(249\) | 14.0497 | 0.890362 | ||||||||
\(250\) | −14.8649 | −0.940138 | ||||||||
\(251\) | −25.0778 | −1.58290 | −0.791450 | − | 0.611234i | \(-0.790673\pi\) | ||||
−0.791450 | + | 0.611234i | \(0.790673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.14682 | 0.386447 | ||||||||
\(254\) | −36.2002 | −2.27140 | ||||||||
\(255\) | −17.2716 | −1.08159 | ||||||||
\(256\) | 17.3983 | 1.08740 | ||||||||
\(257\) | 22.7564 | 1.41950 | 0.709752 | − | 0.704452i | \(-0.248807\pi\) | ||||
0.709752 | + | 0.704452i | \(0.248807\pi\) | |||||||
\(258\) | −19.5374 | −1.21634 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −46.8713 | −2.90683 | ||||||||
\(261\) | 0.267181 | 0.0165381 | ||||||||
\(262\) | −3.54057 | −0.218737 | ||||||||
\(263\) | −5.98638 | −0.369136 | −0.184568 | − | 0.982820i | \(-0.559089\pi\) | ||||
−0.184568 | + | 0.982820i | \(0.559089\pi\) | |||||||
\(264\) | −21.6737 | −1.33393 | ||||||||
\(265\) | 36.8473 | 2.26351 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.6068 | 0.955123 | ||||||||
\(268\) | 74.0749 | 4.52484 | ||||||||
\(269\) | −31.2140 | −1.90315 | −0.951575 | − | 0.307418i | \(-0.900535\pi\) | ||||
−0.951575 | + | 0.307418i | \(0.900535\pi\) | |||||||
\(270\) | −9.17792 | −0.558551 | ||||||||
\(271\) | −6.47522 | −0.393342 | −0.196671 | − | 0.980470i | \(-0.563013\pi\) | ||||
−0.196671 | + | 0.980470i | \(0.563013\pi\) | |||||||
\(272\) | −66.1556 | −4.01127 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −39.0289 | −2.35782 | ||||||||
\(275\) | 16.3995 | 0.988925 | ||||||||
\(276\) | 13.0244 | 0.783975 | ||||||||
\(277\) | 20.3614 | 1.22340 | 0.611699 | − | 0.791091i | \(-0.290486\pi\) | ||||
0.611699 | + | 0.791091i | \(0.290486\pi\) | |||||||
\(278\) | −9.92255 | −0.595115 | ||||||||
\(279\) | −6.04056 | −0.361639 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5325 | 1.10556 | 0.552778 | − | 0.833328i | \(-0.313568\pi\) | ||||
0.552778 | + | 0.833328i | \(0.313568\pi\) | |||||||
\(282\) | 22.3642 | 1.33177 | ||||||||
\(283\) | −5.17781 | −0.307789 | −0.153894 | − | 0.988087i | \(-0.549182\pi\) | ||||
−0.153894 | + | 0.988087i | \(0.549182\pi\) | |||||||
\(284\) | 43.1165 | 2.55849 | ||||||||
\(285\) | −10.0418 | −0.594826 | ||||||||
\(286\) | 17.4724 | 1.03316 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −17.6570 | −1.04045 | ||||||||
\(289\) | 8.67290 | 0.510171 | ||||||||
\(290\) | −2.45216 | −0.143996 | ||||||||
\(291\) | −7.72850 | −0.453053 | ||||||||
\(292\) | −34.9982 | −2.04812 | ||||||||
\(293\) | −5.72975 | −0.334735 | −0.167368 | − | 0.985895i | \(-0.553527\pi\) | ||||
−0.167368 | + | 0.985895i | \(0.553527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1657 | −0.591869 | ||||||||
\(296\) | −85.5720 | −4.97377 | ||||||||
\(297\) | 2.47740 | 0.143753 | ||||||||
\(298\) | −42.6914 | −2.47305 | ||||||||
\(299\) | −6.49926 | −0.375862 | ||||||||
\(300\) | 34.7485 | 2.00620 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −29.7434 | −1.71154 | ||||||||
\(303\) | 9.67726 | 0.555944 | ||||||||
\(304\) | −38.4632 | −2.20602 | ||||||||
\(305\) | −24.1089 | −1.38047 | ||||||||
\(306\) | 13.6422 | 0.779875 | ||||||||
\(307\) | 1.87189 | 0.106835 | 0.0534173 | − | 0.998572i | \(-0.482989\pi\) | ||||
0.0534173 | + | 0.998572i | \(0.482989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.45587 | −0.253486 | ||||||||
\(310\) | 55.4398 | 3.14877 | ||||||||
\(311\) | −14.0836 | −0.798608 | −0.399304 | − | 0.916819i | \(-0.630748\pi\) | ||||
−0.399304 | + | 0.916819i | \(0.630748\pi\) | |||||||
\(312\) | 22.9164 | 1.29739 | ||||||||
\(313\) | 26.4775 | 1.49659 | 0.748297 | − | 0.663363i | \(-0.230872\pi\) | ||||
0.748297 | + | 0.663363i | \(0.230872\pi\) | |||||||
\(314\) | −22.0493 | −1.24431 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −56.5461 | −3.18097 | ||||||||
\(317\) | −2.22286 | −0.124848 | −0.0624242 | − | 0.998050i | \(-0.519883\pi\) | ||||
−0.0624242 | + | 0.998050i | \(0.519883\pi\) | |||||||
\(318\) | −29.1043 | −1.63209 | ||||||||
\(319\) | 0.661913 | 0.0370600 | ||||||||
\(320\) | 73.0414 | 4.08314 | ||||||||
\(321\) | 10.3878 | 0.579792 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.9264 | 0.830525 | ||||||||
\(324\) | 5.24930 | 0.291628 | ||||||||
\(325\) | −17.3397 | −0.961836 | ||||||||
\(326\) | 1.45561 | 0.0806187 | ||||||||
\(327\) | −7.88580 | −0.436086 | ||||||||
\(328\) | 8.74860 | 0.483060 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −22.7373 | −1.25165 | ||||||||
\(331\) | −18.1534 | −0.997800 | −0.498900 | − | 0.866660i | \(-0.666262\pi\) | ||||
−0.498900 | + | 0.866660i | \(0.666262\pi\) | |||||||
\(332\) | 73.7510 | 4.04761 | ||||||||
\(333\) | 9.78122 | 0.536008 | ||||||||
\(334\) | −59.7177 | −3.26761 | ||||||||
\(335\) | 48.1023 | 2.62811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.69887 | −0.419384 | −0.209692 | − | 0.977767i | \(-0.567246\pi\) | ||||
−0.209692 | + | 0.977767i | \(0.567246\pi\) | |||||||
\(338\) | 16.5277 | 0.898988 | ||||||||
\(339\) | 18.9778 | 1.03073 | ||||||||
\(340\) | −90.6641 | −4.91695 | ||||||||
\(341\) | −14.9649 | −0.810393 | ||||||||
\(342\) | 7.93167 | 0.428895 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −63.4828 | −3.42276 | ||||||||
\(345\) | 8.45768 | 0.455346 | ||||||||
\(346\) | −50.9299 | −2.73801 | ||||||||
\(347\) | −28.2126 | −1.51453 | −0.757266 | − | 0.653107i | \(-0.773465\pi\) | ||||
−0.757266 | + | 0.653107i | \(0.773465\pi\) | |||||||
\(348\) | 1.40251 | 0.0751826 | ||||||||
\(349\) | 24.3427 | 1.30303 | 0.651517 | − | 0.758634i | \(-0.274133\pi\) | ||||
0.651517 | + | 0.758634i | \(0.274133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.61944 | −0.139815 | ||||||||
\(352\) | −43.7435 | −2.33153 | ||||||||
\(353\) | −34.9906 | −1.86236 | −0.931180 | − | 0.364559i | \(-0.881220\pi\) | ||||
−0.931180 | + | 0.364559i | \(0.881220\pi\) | |||||||
\(354\) | 8.02950 | 0.426763 | ||||||||
\(355\) | 27.9987 | 1.48602 | ||||||||
\(356\) | 81.9250 | 4.34202 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6577 | 0.668980 | ||||||||
\(359\) | −34.5993 | −1.82608 | −0.913039 | − | 0.407871i | \(-0.866271\pi\) | ||||
−0.913039 | + | 0.407871i | \(0.866271\pi\) | |||||||
\(360\) | −29.8219 | −1.57175 | ||||||||
\(361\) | −10.3217 | −0.543250 | ||||||||
\(362\) | −56.1182 | −2.94951 | ||||||||
\(363\) | −4.86251 | −0.255216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.7269 | −1.18958 | ||||||||
\(366\) | 19.0428 | 0.995381 | ||||||||
\(367\) | −23.3100 | −1.21677 | −0.608387 | − | 0.793640i | \(-0.708183\pi\) | ||||
−0.608387 | + | 0.793640i | \(0.708183\pi\) | |||||||
\(368\) | 32.3955 | 1.68873 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −89.7713 | −4.66699 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −31.7087 | −1.64402 | ||||||||
\(373\) | −19.5468 | −1.01209 | −0.506047 | − | 0.862506i | \(-0.668894\pi\) | ||||
−0.506047 | + | 0.862506i | \(0.668894\pi\) | |||||||
\(374\) | 33.7972 | 1.74761 | ||||||||
\(375\) | 5.52095 | 0.285101 | ||||||||
\(376\) | 72.6679 | 3.74756 | ||||||||
\(377\) | −0.699865 | −0.0360449 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.74324 | 0.192277 | 0.0961386 | − | 0.995368i | \(-0.469351\pi\) | ||||
0.0961386 | + | 0.995368i | \(0.469351\pi\) | |||||||
\(380\) | −52.7126 | −2.70410 | ||||||||
\(381\) | 13.4451 | 0.688812 | ||||||||
\(382\) | −5.44262 | −0.278468 | ||||||||
\(383\) | −4.35761 | −0.222664 | −0.111332 | − | 0.993783i | \(-0.535512\pi\) | ||||
−0.111332 | + | 0.993783i | \(0.535512\pi\) | |||||||
\(384\) | −22.3787 | −1.14201 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.04448 | −0.104061 | ||||||||
\(387\) | 7.25634 | 0.368861 | ||||||||
\(388\) | −40.5692 | −2.05959 | ||||||||
\(389\) | −28.6074 | −1.45045 | −0.725226 | − | 0.688511i | \(-0.758265\pi\) | ||||
−0.725226 | + | 0.688511i | \(0.758265\pi\) | |||||||
\(390\) | 24.0410 | 1.21736 | ||||||||
\(391\) | −12.5717 | −0.635776 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.31500 | 0.0663329 | ||||||||
\(394\) | −46.3881 | −2.33700 | ||||||||
\(395\) | −36.7195 | −1.84756 | ||||||||
\(396\) | 13.0046 | 0.653506 | ||||||||
\(397\) | −11.4747 | −0.575898 | −0.287949 | − | 0.957646i | \(-0.592973\pi\) | ||||
−0.287949 | + | 0.957646i | \(0.592973\pi\) | |||||||
\(398\) | −56.1701 | −2.81555 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 86.4298 | 4.32149 | ||||||||
\(401\) | −16.8298 | −0.840442 | −0.420221 | − | 0.907422i | \(-0.638047\pi\) | ||||
−0.420221 | + | 0.907422i | \(0.638047\pi\) | |||||||
\(402\) | −37.9942 | −1.89498 | ||||||||
\(403\) | 15.8229 | 0.788195 | ||||||||
\(404\) | 50.7989 | 2.52734 | ||||||||
\(405\) | 3.40876 | 0.169383 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2320 | 1.20113 | ||||||||
\(408\) | 44.3278 | 2.19455 | ||||||||
\(409\) | 33.7391 | 1.66829 | 0.834144 | − | 0.551546i | \(-0.185962\pi\) | ||||
0.834144 | + | 0.551546i | \(0.185962\pi\) | |||||||
\(410\) | 9.17792 | 0.453265 | ||||||||
\(411\) | 14.4957 | 0.715019 | ||||||||
\(412\) | −23.3902 | −1.15235 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.68041 | −0.328324 | ||||||||
\(415\) | 47.8920 | 2.35092 | ||||||||
\(416\) | 46.2516 | 2.26767 | ||||||||
\(417\) | 3.68532 | 0.180471 | ||||||||
\(418\) | 19.6499 | 0.961107 | ||||||||
\(419\) | 13.3241 | 0.650923 | 0.325461 | − | 0.945555i | \(-0.394480\pi\) | ||||
0.325461 | + | 0.945555i | \(0.394480\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0597 | −1.22134 | −0.610668 | − | 0.791887i | \(-0.709099\pi\) | ||||
−0.610668 | + | 0.791887i | \(0.709099\pi\) | |||||||
\(422\) | 34.4161 | 1.67535 | ||||||||
\(423\) | −8.30624 | −0.403863 | ||||||||
\(424\) | −94.5687 | −4.59266 | ||||||||
\(425\) | −33.5407 | −1.62696 | ||||||||
\(426\) | −22.1152 | −1.07148 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 54.5289 | 2.63575 | ||||||||
\(429\) | −6.48939 | −0.313311 | ||||||||
\(430\) | −66.5982 | −3.21165 | ||||||||
\(431\) | 6.65870 | 0.320738 | 0.160369 | − | 0.987057i | \(-0.448732\pi\) | ||||
0.160369 | + | 0.987057i | \(0.448732\pi\) | |||||||
\(432\) | 13.0566 | 0.628185 | ||||||||
\(433\) | 30.8114 | 1.48070 | 0.740352 | − | 0.672220i | \(-0.234659\pi\) | ||||
0.740352 | + | 0.672220i | \(0.234659\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.910755 | 0.0436674 | ||||||||
\(436\) | −41.3949 | −1.98246 | ||||||||
\(437\) | −7.30923 | −0.349648 | ||||||||
\(438\) | 17.9512 | 0.857740 | ||||||||
\(439\) | −9.81611 | −0.468497 | −0.234249 | − | 0.972177i | \(-0.575263\pi\) | ||||
−0.234249 | + | 0.972177i | \(0.575263\pi\) | |||||||
\(440\) | −73.8805 | −3.52212 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −35.7350 | −1.69974 | ||||||||
\(443\) | −21.1360 | −1.00420 | −0.502101 | − | 0.864809i | \(-0.667439\pi\) | ||||
−0.502101 | + | 0.864809i | \(0.667439\pi\) | |||||||
\(444\) | 51.3446 | 2.43671 | ||||||||
\(445\) | 53.1999 | 2.52192 | ||||||||
\(446\) | −19.9819 | −0.946171 | ||||||||
\(447\) | 15.8559 | 0.749960 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6148 | 1.39761 | 0.698805 | − | 0.715312i | \(-0.253715\pi\) | ||||
0.698805 | + | 0.715312i | \(0.253715\pi\) | |||||||
\(450\) | −17.8231 | −0.840187 | ||||||||
\(451\) | −2.47740 | −0.116656 | ||||||||
\(452\) | 99.6203 | 4.68574 | ||||||||
\(453\) | 11.0469 | 0.519030 | ||||||||
\(454\) | −33.5657 | −1.57532 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 25.7724 | 1.20690 | ||||||||
\(457\) | −8.41928 | −0.393837 | −0.196919 | − | 0.980420i | \(-0.563094\pi\) | ||||
−0.196919 | + | 0.980420i | \(0.563094\pi\) | |||||||
\(458\) | 38.5012 | 1.79904 | ||||||||
\(459\) | −5.06684 | −0.236500 | ||||||||
\(460\) | 44.3969 | 2.07002 | ||||||||
\(461\) | −16.5792 | −0.772171 | −0.386086 | − | 0.922463i | \(-0.626173\pi\) | ||||
−0.386086 | + | 0.922463i | \(0.626173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.25788 | 0.337302 | 0.168651 | − | 0.985676i | \(-0.446059\pi\) | ||||
0.168651 | + | 0.985676i | \(0.446059\pi\) | |||||||
\(464\) | 3.48847 | 0.161948 | ||||||||
\(465\) | −20.5908 | −0.954876 | ||||||||
\(466\) | 64.0307 | 2.96617 | ||||||||
\(467\) | −33.5488 | −1.55245 | −0.776226 | − | 0.630454i | \(-0.782869\pi\) | ||||
−0.776226 | + | 0.630454i | \(0.782869\pi\) | |||||||
\(468\) | −13.7502 | −0.635605 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 76.2340 | 3.51641 | ||||||||
\(471\) | 8.18928 | 0.377342 | ||||||||
\(472\) | 26.0903 | 1.20090 | ||||||||
\(473\) | 17.9768 | 0.826576 | ||||||||
\(474\) | 29.0034 | 1.33217 | ||||||||
\(475\) | −19.5007 | −0.894754 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8096 | 0.494937 | ||||||||
\(478\) | −27.0754 | −1.23840 | ||||||||
\(479\) | 18.5081 | 0.845656 | 0.422828 | − | 0.906210i | \(-0.361037\pi\) | ||||
0.422828 | + | 0.906210i | \(0.361037\pi\) | |||||||
\(480\) | −60.1885 | −2.74722 | ||||||||
\(481\) | −25.6213 | −1.16823 | ||||||||
\(482\) | 24.7918 | 1.12923 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.5248 | −1.16022 | ||||||||
\(485\) | −26.3446 | −1.19625 | ||||||||
\(486\) | −2.69245 | −0.122132 | ||||||||
\(487\) | −43.5938 | −1.97542 | −0.987711 | − | 0.156290i | \(-0.950046\pi\) | ||||
−0.987711 | + | 0.156290i | \(0.950046\pi\) | |||||||
\(488\) | 61.8757 | 2.80098 | ||||||||
\(489\) | −0.540625 | −0.0244479 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8439 | 1.52735 | 0.763676 | − | 0.645599i | \(-0.223392\pi\) | ||||
0.763676 | + | 0.645599i | \(0.223392\pi\) | |||||||
\(492\) | −5.24930 | −0.236657 | ||||||||
\(493\) | −1.35376 | −0.0609704 | ||||||||
\(494\) | −20.7765 | −0.934781 | ||||||||
\(495\) | 8.44485 | 0.379568 | ||||||||
\(496\) | −78.8691 | −3.54133 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −37.8281 | −1.69512 | ||||||||
\(499\) | 35.4016 | 1.58479 | 0.792396 | − | 0.610008i | \(-0.208834\pi\) | ||||
0.792396 | + | 0.610008i | \(0.208834\pi\) | |||||||
\(500\) | 28.9811 | 1.29608 | ||||||||
\(501\) | 22.1797 | 0.990914 | ||||||||
\(502\) | 67.5209 | 3.01361 | ||||||||
\(503\) | 35.0856 | 1.56439 | 0.782195 | − | 0.623033i | \(-0.214100\pi\) | ||||
0.782195 | + | 0.623033i | \(0.214100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.9874 | 1.46792 | ||||||||
\(506\) | −16.5500 | −0.735738 | ||||||||
\(507\) | −6.13853 | −0.272622 | ||||||||
\(508\) | 70.5773 | 3.13136 | ||||||||
\(509\) | −24.7682 | −1.09783 | −0.548917 | − | 0.835877i | \(-0.684960\pi\) | ||||
−0.548917 | + | 0.835877i | \(0.684960\pi\) | |||||||
\(510\) | 46.5031 | 2.05919 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.08691 | −0.0922294 | ||||||||
\(513\) | −2.94589 | −0.130064 | ||||||||
\(514\) | −61.2705 | −2.70253 | ||||||||
\(515\) | −15.1890 | −0.669307 | ||||||||
\(516\) | 38.0908 | 1.67685 | ||||||||
\(517\) | −20.5778 | −0.905013 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.9158 | 0.830311 | ||||||||
\(520\) | 78.1166 | 3.42564 | ||||||||
\(521\) | −20.6917 | −0.906520 | −0.453260 | − | 0.891378i | \(-0.649739\pi\) | ||||
−0.453260 | + | 0.891378i | \(0.649739\pi\) | |||||||
\(522\) | −0.719372 | −0.0314860 | ||||||||
\(523\) | 3.14418 | 0.137485 | 0.0687426 | − | 0.997634i | \(-0.478101\pi\) | ||||
0.0687426 | + | 0.997634i | \(0.478101\pi\) | |||||||
\(524\) | 6.90283 | 0.301551 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.1180 | 0.702780 | ||||||||
\(527\) | 30.6066 | 1.33324 | ||||||||
\(528\) | 32.3463 | 1.40769 | ||||||||
\(529\) | −16.8438 | −0.732341 | ||||||||
\(530\) | −99.2096 | −4.30939 | ||||||||
\(531\) | −2.98222 | −0.129417 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.61944 | 0.113461 | ||||||||
\(534\) | −42.0207 | −1.81841 | ||||||||
\(535\) | 35.4096 | 1.53089 | ||||||||
\(536\) | −123.455 | −5.33243 | ||||||||
\(537\) | −4.70118 | −0.202871 | ||||||||
\(538\) | 84.0421 | 3.62331 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 17.8936 | 0.770018 | ||||||||
\(541\) | −1.25034 | −0.0537565 | −0.0268782 | − | 0.999639i | \(-0.508557\pi\) | ||||
−0.0268782 | + | 0.999639i | \(0.508557\pi\) | |||||||
\(542\) | 17.4342 | 0.748864 | ||||||||
\(543\) | 20.8428 | 0.894449 | ||||||||
\(544\) | 89.4654 | 3.83580 | ||||||||
\(545\) | −26.8808 | −1.15145 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9208 | −1.19381 | −0.596903 | − | 0.802313i | \(-0.703602\pi\) | ||||
−0.596903 | + | 0.802313i | \(0.703602\pi\) | |||||||
\(548\) | 76.0922 | 3.25050 | ||||||||
\(549\) | −7.07265 | −0.301853 | ||||||||
\(550\) | −44.1548 | −1.88277 | ||||||||
\(551\) | −0.787085 | −0.0335309 | ||||||||
\(552\) | −21.7067 | −0.923898 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −54.8221 | −2.32917 | ||||||||
\(555\) | 33.3418 | 1.41528 | ||||||||
\(556\) | 19.3454 | 0.820426 | ||||||||
\(557\) | −3.83843 | −0.162639 | −0.0813197 | − | 0.996688i | \(-0.525913\pi\) | ||||
−0.0813197 | + | 0.996688i | \(0.525913\pi\) | |||||||
\(558\) | 16.2639 | 0.688507 | ||||||||
\(559\) | −19.0076 | −0.803935 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.5526 | −0.529970 | ||||||||
\(562\) | −49.8979 | −2.10482 | ||||||||
\(563\) | −19.5595 | −0.824335 | −0.412167 | − | 0.911108i | \(-0.635228\pi\) | ||||
−0.412167 | + | 0.911108i | \(0.635228\pi\) | |||||||
\(564\) | −43.6020 | −1.83597 | ||||||||
\(565\) | 64.6908 | 2.72156 | ||||||||
\(566\) | 13.9410 | 0.585984 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −71.8589 | −3.01513 | ||||||||
\(569\) | −4.77753 | −0.200284 | −0.100142 | − | 0.994973i | \(-0.531930\pi\) | ||||
−0.100142 | + | 0.994973i | \(0.531930\pi\) | |||||||
\(570\) | 27.0371 | 1.13246 | ||||||||
\(571\) | 16.0786 | 0.672870 | 0.336435 | − | 0.941707i | \(-0.390779\pi\) | ||||
0.336435 | + | 0.941707i | \(0.390779\pi\) | |||||||
\(572\) | −34.0648 | −1.42432 | ||||||||
\(573\) | 2.02143 | 0.0844466 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.4244 | 0.684944 | ||||||||
\(576\) | 21.4276 | 0.892815 | ||||||||
\(577\) | 2.45923 | 0.102379 | 0.0511896 | − | 0.998689i | \(-0.483699\pi\) | ||||
0.0511896 | + | 0.998689i | \(0.483699\pi\) | |||||||
\(578\) | −23.3514 | −0.971289 | ||||||||
\(579\) | 0.759337 | 0.0315570 | ||||||||
\(580\) | 4.78083 | 0.198513 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.8086 | 0.862545 | ||||||||
\(583\) | 26.7796 | 1.10910 | ||||||||
\(584\) | 58.3288 | 2.41366 | ||||||||
\(585\) | −8.92904 | −0.369171 | ||||||||
\(586\) | 15.4271 | 0.637286 | ||||||||
\(587\) | −16.0272 | −0.661512 | −0.330756 | − | 0.943716i | \(-0.607304\pi\) | ||||
−0.330756 | + | 0.943716i | \(0.607304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.7948 | 0.733223 | ||||||||
\(590\) | 27.3706 | 1.12683 | ||||||||
\(591\) | 17.2289 | 0.708704 | ||||||||
\(592\) | 127.709 | 5.24882 | ||||||||
\(593\) | 15.5184 | 0.637266 | 0.318633 | − | 0.947878i | \(-0.396776\pi\) | ||||
0.318633 | + | 0.947878i | \(0.396776\pi\) | |||||||
\(594\) | −6.67027 | −0.273685 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 83.2327 | 3.40934 | ||||||||
\(597\) | 20.8621 | 0.853827 | ||||||||
\(598\) | 17.4989 | 0.715585 | ||||||||
\(599\) | 21.8286 | 0.891892 | 0.445946 | − | 0.895060i | \(-0.352867\pi\) | ||||
0.445946 | + | 0.895060i | \(0.352867\pi\) | |||||||
\(600\) | −57.9125 | −2.36427 | ||||||||
\(601\) | 2.88582 | 0.117715 | 0.0588575 | − | 0.998266i | \(-0.481254\pi\) | ||||
0.0588575 | + | 0.998266i | \(0.481254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.1114 | 0.574659 | ||||||||
\(604\) | 57.9887 | 2.35953 | ||||||||
\(605\) | −16.5751 | −0.673874 | ||||||||
\(606\) | −26.0556 | −1.05844 | ||||||||
\(607\) | −6.38555 | −0.259182 | −0.129591 | − | 0.991568i | \(-0.541366\pi\) | ||||
−0.129591 | + | 0.991568i | \(0.541366\pi\) | |||||||
\(608\) | 52.0156 | 2.10951 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 64.9122 | 2.62822 | ||||||||
\(611\) | 21.7577 | 0.880223 | ||||||||
\(612\) | −26.5974 | −1.07514 | ||||||||
\(613\) | 17.3087 | 0.699092 | 0.349546 | − | 0.936919i | \(-0.386336\pi\) | ||||
0.349546 | + | 0.936919i | \(0.386336\pi\) | |||||||
\(614\) | −5.03998 | −0.203397 | ||||||||
\(615\) | −3.40876 | −0.137454 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.81470 | 0.113316 | 0.0566579 | − | 0.998394i | \(-0.481956\pi\) | ||||
0.0566579 | + | 0.998394i | \(0.481956\pi\) | |||||||
\(618\) | 11.9972 | 0.482599 | ||||||||
\(619\) | −28.7390 | −1.15512 | −0.577559 | − | 0.816349i | \(-0.695995\pi\) | ||||
−0.577559 | + | 0.816349i | \(0.695995\pi\) | |||||||
\(620\) | −108.087 | −4.34090 | ||||||||
\(621\) | 2.48116 | 0.0995656 | ||||||||
\(622\) | 37.9194 | 1.52043 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −34.2009 | −1.36913 | ||||||||
\(625\) | −14.2786 | −0.571144 | ||||||||
\(626\) | −71.2893 | −2.84929 | ||||||||
\(627\) | −7.29813 | −0.291459 | ||||||||
\(628\) | 42.9880 | 1.71541 | ||||||||
\(629\) | −49.5599 | −1.97608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.108140 | 0.00430497 | 0.00215249 | − | 0.999998i | \(-0.499315\pi\) | ||||
0.00215249 | + | 0.999998i | \(0.499315\pi\) | |||||||
\(632\) | 94.2409 | 3.74870 | ||||||||
\(633\) | −12.7824 | −0.508056 | ||||||||
\(634\) | 5.98496 | 0.237693 | ||||||||
\(635\) | 45.8310 | 1.81875 | ||||||||
\(636\) | 56.7428 | 2.25000 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.78217 | −0.0705567 | ||||||||
\(639\) | 8.21376 | 0.324931 | ||||||||
\(640\) | −76.2834 | −3.01537 | ||||||||
\(641\) | 14.5924 | 0.576366 | 0.288183 | − | 0.957575i | \(-0.406949\pi\) | ||||
0.288183 | + | 0.957575i | \(0.406949\pi\) | |||||||
\(642\) | −27.9688 | −1.10384 | ||||||||
\(643\) | −19.0479 | −0.751178 | −0.375589 | − | 0.926786i | \(-0.622560\pi\) | ||||
−0.375589 | + | 0.926786i | \(0.622560\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.7351 | 0.973945 | ||||||||
\(646\) | −40.1885 | −1.58120 | ||||||||
\(647\) | −2.49785 | −0.0982008 | −0.0491004 | − | 0.998794i | \(-0.515635\pi\) | ||||
−0.0491004 | + | 0.998794i | \(0.515635\pi\) | |||||||
\(648\) | −8.74860 | −0.343677 | ||||||||
\(649\) | −7.38815 | −0.290010 | ||||||||
\(650\) | 46.6865 | 1.83119 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.83791 | −0.111141 | ||||||||
\(653\) | 7.16644 | 0.280444 | 0.140222 | − | 0.990120i | \(-0.455218\pi\) | ||||
0.140222 | + | 0.990120i | \(0.455218\pi\) | |||||||
\(654\) | 21.2321 | 0.830242 | ||||||||
\(655\) | 4.48251 | 0.175146 | ||||||||
\(656\) | −13.0566 | −0.509774 | ||||||||
\(657\) | −6.66722 | −0.260113 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.4135 | 0.951016 | 0.475508 | − | 0.879712i | \(-0.342264\pi\) | ||||
0.475508 | + | 0.879712i | \(0.342264\pi\) | |||||||
\(660\) | 44.3296 | 1.72553 | ||||||||
\(661\) | −22.6127 | −0.879530 | −0.439765 | − | 0.898113i | \(-0.644938\pi\) | ||||
−0.439765 | + | 0.898113i | \(0.644938\pi\) | |||||||
\(662\) | 48.8771 | 1.89966 | ||||||||
\(663\) | 13.2723 | 0.515453 | ||||||||
\(664\) | −122.915 | −4.77003 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.3355 | −1.02048 | ||||||||
\(667\) | 0.662919 | 0.0256683 | ||||||||
\(668\) | 116.428 | 4.50473 | ||||||||
\(669\) | 7.42145 | 0.286930 | ||||||||
\(670\) | −129.513 | −5.00353 | ||||||||
\(671\) | −17.5217 | −0.676419 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8973 | 0.458607 | 0.229303 | − | 0.973355i | \(-0.426355\pi\) | ||||
0.229303 | + | 0.973355i | \(0.426355\pi\) | |||||||
\(674\) | 20.7288 | 0.798445 | ||||||||
\(675\) | 6.61964 | 0.254790 | ||||||||
\(676\) | −32.2230 | −1.23935 | ||||||||
\(677\) | −4.70172 | −0.180702 | −0.0903509 | − | 0.995910i | \(-0.528799\pi\) | ||||
−0.0903509 | + | 0.995910i | \(0.528799\pi\) | |||||||
\(678\) | −51.0969 | −1.96236 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 151.103 | 5.79452 | ||||||||
\(681\) | 12.4666 | 0.477721 | ||||||||
\(682\) | 40.2922 | 1.54287 | ||||||||
\(683\) | −16.7037 | −0.639149 | −0.319575 | − | 0.947561i | \(-0.603540\pi\) | ||||
−0.319575 | + | 0.947561i | \(0.603540\pi\) | |||||||
\(684\) | −15.4639 | −0.591276 | ||||||||
\(685\) | 49.4122 | 1.88794 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.2997 | −0.545566 | ||||||||
\(688\) | 94.7430 | 3.61204 | ||||||||
\(689\) | −28.3151 | −1.07872 | ||||||||
\(690\) | −22.7719 | −0.866912 | ||||||||
\(691\) | −1.53565 | −0.0584187 | −0.0292093 | − | 0.999573i | \(-0.509299\pi\) | ||||
−0.0292093 | + | 0.999573i | \(0.509299\pi\) | |||||||
\(692\) | 99.2947 | 3.77462 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 75.9611 | 2.88344 | ||||||||
\(695\) | 12.5624 | 0.476518 | ||||||||
\(696\) | −2.33746 | −0.0886011 | ||||||||
\(697\) | 5.06684 | 0.191920 | ||||||||
\(698\) | −65.5415 | −2.48078 | ||||||||
\(699\) | −23.7816 | −0.899501 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.6576 | −0.704687 | −0.352343 | − | 0.935871i | \(-0.614615\pi\) | ||||
−0.352343 | + | 0.935871i | \(0.614615\pi\) | |||||||
\(702\) | 7.05272 | 0.266188 | ||||||||
\(703\) | −28.8144 | −1.08676 | ||||||||
\(704\) | 53.0846 | 2.00070 | ||||||||
\(705\) | −28.3140 | −1.06637 | ||||||||
\(706\) | 94.2105 | 3.54566 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −15.6546 | −0.588336 | ||||||||
\(709\) | 17.4961 | 0.657079 | 0.328540 | − | 0.944490i | \(-0.393444\pi\) | ||||
0.328540 | + | 0.944490i | \(0.393444\pi\) | |||||||
\(710\) | −75.3853 | −2.82916 | ||||||||
\(711\) | −10.7721 | −0.403986 | ||||||||
\(712\) | −136.538 | −5.11697 | ||||||||
\(713\) | −14.9876 | −0.561291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.1208 | −0.827270 | ||||||||
\(716\) | −24.6779 | −0.922257 | ||||||||
\(717\) | 10.0560 | 0.375550 | ||||||||
\(718\) | 93.1569 | 3.47658 | ||||||||
\(719\) | 10.4177 | 0.388513 | 0.194257 | − | 0.980951i | \(-0.437771\pi\) | ||||
0.194257 | + | 0.980951i | \(0.437771\pi\) | |||||||
\(720\) | 44.5067 | 1.65867 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 27.7908 | 1.03427 | ||||||||
\(723\) | −9.20788 | −0.342445 | ||||||||
\(724\) | 109.410 | 4.06619 | ||||||||
\(725\) | 1.76864 | 0.0656856 | ||||||||
\(726\) | 13.0921 | 0.485893 | ||||||||
\(727\) | 13.3290 | 0.494346 | 0.247173 | − | 0.968971i | \(-0.420498\pi\) | ||||
0.247173 | + | 0.968971i | \(0.420498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 61.1912 | 2.26479 | ||||||||
\(731\) | −36.7668 | −1.35987 | ||||||||
\(732\) | −37.1265 | −1.37223 | ||||||||
\(733\) | 10.0515 | 0.371262 | 0.185631 | − | 0.982620i | \(-0.440567\pi\) | ||||
0.185631 | + | 0.982620i | \(0.440567\pi\) | |||||||
\(734\) | 62.7612 | 2.31656 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −43.8099 | −1.61486 | ||||||||
\(737\) | 34.9595 | 1.28775 | ||||||||
\(738\) | 2.69245 | 0.0991106 | ||||||||
\(739\) | 22.6282 | 0.832392 | 0.416196 | − | 0.909275i | \(-0.363363\pi\) | ||||
0.416196 | + | 0.909275i | \(0.363363\pi\) | |||||||
\(740\) | 175.021 | 6.43391 | ||||||||
\(741\) | 7.71658 | 0.283476 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.5658 | 1.67165 | 0.835823 | − | 0.548999i | \(-0.184991\pi\) | ||||
0.835823 | + | 0.548999i | \(0.184991\pi\) | |||||||
\(744\) | 52.8464 | 1.93744 | ||||||||
\(745\) | 54.0491 | 1.98021 | ||||||||
\(746\) | 52.6288 | 1.92688 | ||||||||
\(747\) | 14.0497 | 0.514051 | ||||||||
\(748\) | −65.8923 | −2.40926 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.8649 | −0.542789 | ||||||||
\(751\) | −24.9793 | −0.911507 | −0.455753 | − | 0.890106i | \(-0.650630\pi\) | ||||
−0.455753 | + | 0.890106i | \(0.650630\pi\) | |||||||
\(752\) | −108.451 | −3.95480 | ||||||||
\(753\) | −25.0778 | −0.913888 | ||||||||
\(754\) | 1.88435 | 0.0686241 | ||||||||
\(755\) | 37.6563 | 1.37045 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.3070 | −0.919799 | −0.459899 | − | 0.887971i | \(-0.652115\pi\) | ||||
−0.459899 | + | 0.887971i | \(0.652115\pi\) | |||||||
\(758\) | −10.0785 | −0.366067 | ||||||||
\(759\) | 6.14682 | 0.223115 | ||||||||
\(760\) | 87.8518 | 3.18672 | ||||||||
\(761\) | −23.9832 | −0.869391 | −0.434695 | − | 0.900578i | \(-0.643144\pi\) | ||||
−0.434695 | + | 0.900578i | \(0.643144\pi\) | |||||||
\(762\) | −36.2002 | −1.31140 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.6111 | 0.383897 | ||||||||
\(765\) | −17.2716 | −0.624458 | ||||||||
\(766\) | 11.7327 | 0.423919 | ||||||||
\(767\) | 7.81176 | 0.282066 | ||||||||
\(768\) | 17.3983 | 0.627809 | ||||||||
\(769\) | −9.22042 | −0.332497 | −0.166248 | − | 0.986084i | \(-0.553165\pi\) | ||||
−0.166248 | + | 0.986084i | \(0.553165\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.7564 | 0.819551 | ||||||||
\(772\) | 3.98599 | 0.143459 | ||||||||
\(773\) | 12.9567 | 0.466020 | 0.233010 | − | 0.972474i | \(-0.425142\pi\) | ||||
0.233010 | + | 0.972474i | \(0.425142\pi\) | |||||||
\(774\) | −19.5374 | −0.702256 | ||||||||
\(775\) | −39.9863 | −1.43635 | ||||||||
\(776\) | 67.6135 | 2.42718 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 77.0240 | 2.76144 | ||||||||
\(779\) | 2.94589 | 0.105547 | ||||||||
\(780\) | −46.8713 | −1.67826 | ||||||||
\(781\) | 20.3487 | 0.728135 | ||||||||
\(782\) | 33.8486 | 1.21042 | ||||||||
\(783\) | 0.267181 | 0.00954826 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.9153 | 0.996339 | ||||||||
\(786\) | −3.54057 | −0.126288 | ||||||||
\(787\) | −21.9896 | −0.783845 | −0.391923 | − | 0.919998i | \(-0.628190\pi\) | ||||
−0.391923 | + | 0.919998i | \(0.628190\pi\) | |||||||
\(788\) | 90.4399 | 3.22179 | ||||||||
\(789\) | −5.98638 | −0.213121 | ||||||||
\(790\) | 98.8656 | 3.51748 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −21.6737 | −0.770143 | ||||||||
\(793\) | 18.5264 | 0.657891 | ||||||||
\(794\) | 30.8950 | 1.09642 | ||||||||
\(795\) | 36.8473 | 1.30684 | ||||||||
\(796\) | 109.511 | 3.88152 | ||||||||
\(797\) | 54.7322 | 1.93871 | 0.969356 | − | 0.245658i | \(-0.0790041\pi\) | ||||
0.969356 | + | 0.245658i | \(0.0790041\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.0864 | 1.48891 | ||||||||
\(800\) | −116.883 | −4.13244 | ||||||||
\(801\) | 15.6068 | 0.551440 | ||||||||
\(802\) | 45.3136 | 1.60008 | ||||||||
\(803\) | −16.5173 | −0.582884 | ||||||||
\(804\) | 74.0749 | 2.61242 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.6024 | −1.50061 | ||||||||
\(807\) | −31.2140 | −1.09878 | ||||||||
\(808\) | −84.6624 | −2.97841 | ||||||||
\(809\) | 43.6588 | 1.53496 | 0.767482 | − | 0.641071i | \(-0.221510\pi\) | ||||
0.767482 | + | 0.641071i | \(0.221510\pi\) | |||||||
\(810\) | −9.17792 | −0.322479 | ||||||||
\(811\) | −1.40296 | −0.0492645 | −0.0246322 | − | 0.999697i | \(-0.507841\pi\) | ||||
−0.0246322 | + | 0.999697i | \(0.507841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.47522 | −0.227096 | ||||||||
\(814\) | −65.2434 | −2.28678 | ||||||||
\(815\) | −1.84286 | −0.0645526 | ||||||||
\(816\) | −66.1556 | −2.31591 | ||||||||
\(817\) | −21.3764 | −0.747865 | ||||||||
\(818\) | −90.8408 | −3.17617 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.8936 | −0.624872 | ||||||||
\(821\) | −31.7107 | −1.10671 | −0.553355 | − | 0.832946i | \(-0.686653\pi\) | ||||
−0.553355 | + | 0.832946i | \(0.686653\pi\) | |||||||
\(822\) | −39.0289 | −1.36129 | ||||||||
\(823\) | −31.6705 | −1.10396 | −0.551981 | − | 0.833856i | \(-0.686128\pi\) | ||||
−0.551981 | + | 0.833856i | \(0.686128\pi\) | |||||||
\(824\) | 38.9826 | 1.35802 | ||||||||
\(825\) | 16.3995 | 0.570956 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.7291 | −0.407861 | −0.203931 | − | 0.978985i | \(-0.565372\pi\) | ||||
−0.203931 | + | 0.978985i | \(0.565372\pi\) | |||||||
\(828\) | 13.0244 | 0.452628 | ||||||||
\(829\) | −37.7160 | −1.30993 | −0.654965 | − | 0.755659i | \(-0.727317\pi\) | ||||
−0.654965 | + | 0.755659i | \(0.727317\pi\) | |||||||
\(830\) | −128.947 | −4.47581 | ||||||||
\(831\) | 20.3614 | 0.706329 | ||||||||
\(832\) | −56.1283 | −1.94590 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9.92255 | −0.343590 | ||||||||
\(835\) | 75.6051 | 2.61642 | ||||||||
\(836\) | −38.3101 | −1.32498 | ||||||||
\(837\) | −6.04056 | −0.208792 | ||||||||
\(838\) | −35.8744 | −1.23926 | ||||||||
\(839\) | −26.0811 | −0.900420 | −0.450210 | − | 0.892923i | \(-0.648651\pi\) | ||||
−0.450210 | + | 0.892923i | \(0.648651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9286 | −0.997538 | ||||||||
\(842\) | 67.4721 | 2.32524 | ||||||||
\(843\) | 18.5325 | 0.638293 | ||||||||
\(844\) | −67.0988 | −2.30964 | ||||||||
\(845\) | −20.9248 | −0.719833 | ||||||||
\(846\) | 22.3642 | 0.768896 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 141.136 | 4.84664 | ||||||||
\(849\) | −5.17781 | −0.177702 | ||||||||
\(850\) | 90.3066 | 3.09749 | ||||||||
\(851\) | 24.2688 | 0.831924 | ||||||||
\(852\) | 43.1165 | 1.47715 | ||||||||
\(853\) | −48.0414 | −1.64491 | −0.822453 | − | 0.568833i | \(-0.807395\pi\) | ||||
−0.822453 | + | 0.568833i | \(0.807395\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.0418 | −0.343423 | ||||||||
\(856\) | −90.8790 | −3.10618 | ||||||||
\(857\) | −41.5181 | −1.41823 | −0.709116 | − | 0.705092i | \(-0.750906\pi\) | ||||
−0.709116 | + | 0.705092i | \(0.750906\pi\) | |||||||
\(858\) | 17.4724 | 0.596498 | ||||||||
\(859\) | 47.5478 | 1.62231 | 0.811156 | − | 0.584830i | \(-0.198839\pi\) | ||||
0.811156 | + | 0.584830i | \(0.198839\pi\) | |||||||
\(860\) | 129.842 | 4.42758 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.9282 | −0.610638 | ||||||||
\(863\) | 3.80787 | 0.129621 | 0.0648107 | − | 0.997898i | \(-0.479356\pi\) | ||||
0.0648107 | + | 0.997898i | \(0.479356\pi\) | |||||||
\(864\) | −17.6570 | −0.600704 | ||||||||
\(865\) | 64.4794 | 2.19236 | ||||||||
\(866\) | −82.9584 | −2.81904 | ||||||||
\(867\) | 8.67290 | 0.294547 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.6868 | −0.905288 | ||||||||
\(870\) | −2.45216 | −0.0831362 | ||||||||
\(871\) | −36.9639 | −1.25247 | ||||||||
\(872\) | 68.9897 | 2.33628 | ||||||||
\(873\) | −7.72850 | −0.261570 | ||||||||
\(874\) | 19.6797 | 0.665677 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −34.9982 | −1.18248 | ||||||||
\(877\) | −46.2498 | −1.56175 | −0.780873 | − | 0.624690i | \(-0.785226\pi\) | ||||
−0.780873 | + | 0.624690i | \(0.785226\pi\) | |||||||
\(878\) | 26.4294 | 0.891949 | ||||||||
\(879\) | −5.72975 | −0.193260 | ||||||||
\(880\) | 110.261 | 3.71689 | ||||||||
\(881\) | −8.19976 | −0.276257 | −0.138128 | − | 0.990414i | \(-0.544109\pi\) | ||||
−0.138128 | + | 0.990414i | \(0.544109\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.2720 | −1.25430 | −0.627151 | − | 0.778898i | \(-0.715779\pi\) | ||||
−0.627151 | + | 0.778898i | \(0.715779\pi\) | |||||||
\(884\) | 69.6703 | 2.34327 | ||||||||
\(885\) | −10.1657 | −0.341716 | ||||||||
\(886\) | 56.9077 | 1.91185 | ||||||||
\(887\) | −24.8683 | −0.834996 | −0.417498 | − | 0.908678i | \(-0.637093\pi\) | ||||
−0.417498 | + | 0.908678i | \(0.637093\pi\) | |||||||
\(888\) | −85.5720 | −2.87161 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −143.238 | −4.80136 | ||||||||
\(891\) | 2.47740 | 0.0829959 | ||||||||
\(892\) | 38.9574 | 1.30439 | ||||||||
\(893\) | 24.4693 | 0.818832 | ||||||||
\(894\) | −42.6914 | −1.42781 | ||||||||
\(895\) | −16.0252 | −0.535663 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.49926 | −0.217004 | ||||||||
\(898\) | −79.7366 | −2.66084 | ||||||||
\(899\) | −1.61392 | −0.0538273 | ||||||||
\(900\) | 34.7485 | 1.15828 | ||||||||
\(901\) | −54.7705 | −1.82467 | ||||||||
\(902\) | 6.67027 | 0.222096 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −166.029 | −5.52205 | ||||||||
\(905\) | 71.0480 | 2.36172 | ||||||||
\(906\) | −29.7434 | −0.988157 | ||||||||
\(907\) | −10.1610 | −0.337389 | −0.168694 | − | 0.985668i | \(-0.553955\pi\) | ||||
−0.168694 | + | 0.985668i | \(0.553955\pi\) | |||||||
\(908\) | 65.4409 | 2.17173 | ||||||||
\(909\) | 9.67726 | 0.320974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.7737 | −0.555738 | −0.277869 | − | 0.960619i | \(-0.589628\pi\) | ||||
−0.277869 | + | 0.960619i | \(0.589628\pi\) | |||||||
\(912\) | −38.4632 | −1.27364 | ||||||||
\(913\) | 34.8066 | 1.15193 | ||||||||
\(914\) | 22.6685 | 0.749808 | ||||||||
\(915\) | −24.1089 | −0.797017 | ||||||||
\(916\) | −75.0632 | −2.48016 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.6422 | 0.450261 | ||||||||
\(919\) | 2.31695 | 0.0764290 | 0.0382145 | − | 0.999270i | \(-0.487833\pi\) | ||||
0.0382145 | + | 0.999270i | \(0.487833\pi\) | |||||||
\(920\) | −73.9928 | −2.43947 | ||||||||
\(921\) | 1.87189 | 0.0616810 | ||||||||
\(922\) | 44.6388 | 1.47010 | ||||||||
\(923\) | −21.5155 | −0.708190 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 64.7481 | 2.12891 | ||||||||
\(926\) | −19.5415 | −0.642173 | ||||||||
\(927\) | −4.45587 | −0.146350 | ||||||||
\(928\) | −4.71762 | −0.154863 | ||||||||
\(929\) | 48.6233 | 1.59528 | 0.797640 | − | 0.603134i | \(-0.206082\pi\) | ||||
0.797640 | + | 0.603134i | \(0.206082\pi\) | |||||||
\(930\) | 55.4398 | 1.81794 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −124.837 | −4.08916 | ||||||||
\(933\) | −14.0836 | −0.461077 | ||||||||
\(934\) | 90.3285 | 2.95564 | ||||||||
\(935\) | −42.7887 | −1.39934 | ||||||||
\(936\) | 22.9164 | 0.749047 | ||||||||
\(937\) | 9.53054 | 0.311349 | 0.155675 | − | 0.987808i | \(-0.450245\pi\) | ||||
0.155675 | + | 0.987808i | \(0.450245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.4775 | 0.864059 | ||||||||
\(940\) | −148.629 | −4.84773 | ||||||||
\(941\) | 47.8808 | 1.56087 | 0.780434 | − | 0.625238i | \(-0.214998\pi\) | ||||
0.780434 | + | 0.625238i | \(0.214998\pi\) | |||||||
\(942\) | −22.0493 | −0.718403 | ||||||||
\(943\) | −2.48116 | −0.0807977 | ||||||||
\(944\) | −38.9376 | −1.26731 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −48.4018 | −1.57368 | ||||||||
\(947\) | −40.4665 | −1.31498 | −0.657492 | − | 0.753461i | \(-0.728383\pi\) | ||||
−0.657492 | + | 0.753461i | \(0.728383\pi\) | |||||||
\(948\) | −56.5461 | −1.83653 | ||||||||
\(949\) | 17.4644 | 0.566918 | ||||||||
\(950\) | 52.5047 | 1.70348 | ||||||||
\(951\) | −2.22286 | −0.0720813 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.0547 | −1.26511 | −0.632554 | − | 0.774517i | \(-0.717993\pi\) | ||||
−0.632554 | + | 0.774517i | \(0.717993\pi\) | |||||||
\(954\) | −29.1043 | −0.942287 | ||||||||
\(955\) | 6.89058 | 0.222974 | ||||||||
\(956\) | 52.7872 | 1.70726 | ||||||||
\(957\) | 0.661913 | 0.0213966 | ||||||||
\(958\) | −49.8321 | −1.61000 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 73.0414 | 2.35740 | ||||||||
\(961\) | 5.48840 | 0.177045 | ||||||||
\(962\) | 68.9843 | 2.22414 | ||||||||
\(963\) | 10.3878 | 0.334743 | ||||||||
\(964\) | −48.3350 | −1.55676 | ||||||||
\(965\) | 2.58840 | 0.0833234 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.3993 | −0.591681 | −0.295840 | − | 0.955237i | \(-0.595600\pi\) | ||||
−0.295840 | + | 0.955237i | \(0.595600\pi\) | |||||||
\(968\) | 42.5401 | 1.36729 | ||||||||
\(969\) | 14.9264 | 0.479504 | ||||||||
\(970\) | 70.9316 | 2.27748 | ||||||||
\(971\) | 31.1119 | 0.998429 | 0.499215 | − | 0.866478i | \(-0.333622\pi\) | ||||
0.499215 | + | 0.866478i | \(0.333622\pi\) | |||||||
\(972\) | 5.24930 | 0.168371 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 117.374 | 3.76091 | ||||||||
\(975\) | −17.3397 | −0.555316 | ||||||||
\(976\) | −92.3445 | −2.95588 | ||||||||
\(977\) | −13.4478 | −0.430232 | −0.215116 | − | 0.976588i | \(-0.569013\pi\) | ||||
−0.215116 | + | 0.976588i | \(0.569013\pi\) | |||||||
\(978\) | 1.45561 | 0.0465452 | ||||||||
\(979\) | 38.6643 | 1.23572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.88580 | −0.251774 | ||||||||
\(982\) | −91.1230 | −2.90785 | ||||||||
\(983\) | −23.3009 | −0.743184 | −0.371592 | − | 0.928396i | \(-0.621188\pi\) | ||||
−0.371592 | + | 0.928396i | \(0.621188\pi\) | |||||||
\(984\) | 8.74860 | 0.278895 | ||||||||
\(985\) | 58.7293 | 1.87127 | ||||||||
\(986\) | 3.64494 | 0.116079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 40.5067 | 1.28869 | ||||||||
\(989\) | 18.0042 | 0.572499 | ||||||||
\(990\) | −22.7373 | −0.722640 | ||||||||
\(991\) | 23.4475 | 0.744835 | 0.372417 | − | 0.928065i | \(-0.378529\pi\) | ||||
0.372417 | + | 0.928065i | \(0.378529\pi\) | |||||||
\(992\) | 106.658 | 3.38641 | ||||||||
\(993\) | −18.1534 | −0.576080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 71.1137 | 2.25446 | ||||||||
\(996\) | 73.7510 | 2.33689 | ||||||||
\(997\) | 0.865413 | 0.0274079 | 0.0137039 | − | 0.999906i | \(-0.495638\pi\) | ||||
0.0137039 | + | 0.999906i | \(0.495638\pi\) | |||||||
\(998\) | −95.3170 | −3.01721 | ||||||||
\(999\) | 9.78122 | 0.309464 |
(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 | 6027.2.a.bo.1.1 | yes | 24 | |
7.6 | odd | 2 | 6027.2.a.bn.1.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.1 | ✓ | 24 | 7.6 | odd | 2 | ||
6027.2.a.bo.1.1 | yes | 24 | 1.1 | even | 1 | trivial |