Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(142\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55403 | −1.80597 | −0.902987 | − | 0.429668i | \(-0.858631\pi\) | ||||
−0.902987 | + | 0.429668i | \(0.858631\pi\) | |||||||
\(3\) | 1.62979 | 0.940961 | 0.470481 | − | 0.882410i | \(-0.344081\pi\) | ||||
0.470481 | + | 0.882410i | \(0.344081\pi\) | |||||||
\(4\) | 4.52309 | 2.26154 | ||||||||
\(5\) | 1.02400 | 0.457947 | 0.228973 | − | 0.973433i | \(-0.426463\pi\) | ||||
0.228973 | + | 0.973433i | \(0.426463\pi\) | |||||||
\(6\) | −4.16254 | −1.69935 | ||||||||
\(7\) | −2.90866 | −1.09937 | −0.549685 | − | 0.835372i | \(-0.685252\pi\) | ||||
−0.549685 | + | 0.835372i | \(0.685252\pi\) | |||||||
\(8\) | −6.44404 | −2.27831 | ||||||||
\(9\) | −0.343777 | −0.114592 | ||||||||
\(10\) | −2.61533 | −0.827040 | ||||||||
\(11\) | 3.97579 | 1.19875 | 0.599373 | − | 0.800470i | \(-0.295417\pi\) | ||||
0.599373 | + | 0.800470i | \(0.295417\pi\) | |||||||
\(12\) | 7.37169 | 2.12802 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 7.42882 | 1.98544 | ||||||||
\(15\) | 1.66891 | 0.430910 | ||||||||
\(16\) | 7.41213 | 1.85303 | ||||||||
\(17\) | 1.98444 | 0.481298 | 0.240649 | − | 0.970612i | \(-0.422640\pi\) | ||||
0.240649 | + | 0.970612i | \(0.422640\pi\) | |||||||
\(18\) | 0.878017 | 0.206951 | ||||||||
\(19\) | −4.42735 | −1.01570 | −0.507851 | − | 0.861445i | \(-0.669560\pi\) | ||||
−0.507851 | + | 0.861445i | \(0.669560\pi\) | |||||||
\(20\) | 4.63164 | 1.03567 | ||||||||
\(21\) | −4.74052 | −1.03447 | ||||||||
\(22\) | −10.1543 | −2.16490 | ||||||||
\(23\) | 0.308540 | 0.0643350 | 0.0321675 | − | 0.999482i | \(-0.489759\pi\) | ||||
0.0321675 | + | 0.999482i | \(0.489759\pi\) | |||||||
\(24\) | −10.5025 | −2.14380 | ||||||||
\(25\) | −3.95142 | −0.790285 | ||||||||
\(26\) | −2.55403 | −0.500887 | ||||||||
\(27\) | −5.44966 | −1.04879 | ||||||||
\(28\) | −13.1561 | −2.48627 | ||||||||
\(29\) | 8.91343 | 1.65518 | 0.827591 | − | 0.561331i | \(-0.189710\pi\) | ||||
0.827591 | + | 0.561331i | \(0.189710\pi\) | |||||||
\(30\) | −4.26245 | −0.778213 | ||||||||
\(31\) | 6.21590 | 1.11641 | 0.558204 | − | 0.829704i | \(-0.311491\pi\) | ||||
0.558204 | + | 0.829704i | \(0.311491\pi\) | |||||||
\(32\) | −6.04274 | −1.06822 | ||||||||
\(33\) | 6.47971 | 1.12797 | ||||||||
\(34\) | −5.06833 | −0.869211 | ||||||||
\(35\) | −2.97847 | −0.503453 | ||||||||
\(36\) | −1.55493 | −0.259155 | ||||||||
\(37\) | 3.18018 | 0.522819 | 0.261409 | − | 0.965228i | \(-0.415813\pi\) | ||||
0.261409 | + | 0.965228i | \(0.415813\pi\) | |||||||
\(38\) | 11.3076 | 1.83433 | ||||||||
\(39\) | 1.62979 | 0.260976 | ||||||||
\(40\) | −6.59870 | −1.04335 | ||||||||
\(41\) | −0.0267494 | −0.00417755 | −0.00208878 | − | 0.999998i | \(-0.500665\pi\) | ||||
−0.00208878 | + | 0.999998i | \(0.500665\pi\) | |||||||
\(42\) | 12.1074 | 1.86822 | ||||||||
\(43\) | −9.51525 | −1.45106 | −0.725531 | − | 0.688190i | \(-0.758406\pi\) | ||||
−0.725531 | + | 0.688190i | \(0.758406\pi\) | |||||||
\(44\) | 17.9828 | 2.71101 | ||||||||
\(45\) | −0.352027 | −0.0524771 | ||||||||
\(46\) | −0.788021 | −0.116187 | ||||||||
\(47\) | −4.23608 | −0.617896 | −0.308948 | − | 0.951079i | \(-0.599977\pi\) | ||||
−0.308948 | + | 0.951079i | \(0.599977\pi\) | |||||||
\(48\) | 12.0802 | 1.74363 | ||||||||
\(49\) | 1.46032 | 0.208616 | ||||||||
\(50\) | 10.0921 | 1.42723 | ||||||||
\(51\) | 3.23423 | 0.452882 | ||||||||
\(52\) | 4.52309 | 0.627239 | ||||||||
\(53\) | −14.1988 | −1.95036 | −0.975180 | − | 0.221415i | \(-0.928932\pi\) | ||||
−0.975180 | + | 0.221415i | \(0.928932\pi\) | |||||||
\(54\) | 13.9186 | 1.89408 | ||||||||
\(55\) | 4.07121 | 0.548962 | ||||||||
\(56\) | 18.7435 | 2.50471 | ||||||||
\(57\) | −7.21565 | −0.955737 | ||||||||
\(58\) | −22.7652 | −2.98922 | ||||||||
\(59\) | −6.82188 | −0.888133 | −0.444067 | − | 0.895994i | \(-0.646465\pi\) | ||||
−0.444067 | + | 0.895994i | \(0.646465\pi\) | |||||||
\(60\) | 7.54861 | 0.974522 | ||||||||
\(61\) | −5.60653 | −0.717842 | −0.358921 | − | 0.933368i | \(-0.616855\pi\) | ||||
−0.358921 | + | 0.933368i | \(0.616855\pi\) | |||||||
\(62\) | −15.8756 | −2.01620 | ||||||||
\(63\) | 0.999930 | 0.125979 | ||||||||
\(64\) | 0.609101 | 0.0761376 | ||||||||
\(65\) | 1.02400 | 0.127012 | ||||||||
\(66\) | −16.5494 | −2.03709 | ||||||||
\(67\) | 2.47014 | 0.301776 | 0.150888 | − | 0.988551i | \(-0.451787\pi\) | ||||
0.150888 | + | 0.988551i | \(0.451787\pi\) | |||||||
\(68\) | 8.97580 | 1.08848 | ||||||||
\(69\) | 0.502856 | 0.0605367 | ||||||||
\(70\) | 7.60711 | 0.909224 | ||||||||
\(71\) | −2.65237 | −0.314779 | −0.157389 | − | 0.987537i | \(-0.550308\pi\) | ||||
−0.157389 | + | 0.987537i | \(0.550308\pi\) | |||||||
\(72\) | 2.21531 | 0.261077 | ||||||||
\(73\) | 2.32901 | 0.272590 | 0.136295 | − | 0.990668i | \(-0.456481\pi\) | ||||
0.136295 | + | 0.990668i | \(0.456481\pi\) | |||||||
\(74\) | −8.12229 | −0.944198 | ||||||||
\(75\) | −6.44000 | −0.743627 | ||||||||
\(76\) | −20.0253 | −2.29706 | ||||||||
\(77\) | −11.5642 | −1.31787 | ||||||||
\(78\) | −4.16254 | −0.471315 | ||||||||
\(79\) | −12.0907 | −1.36031 | −0.680157 | − | 0.733067i | \(-0.738088\pi\) | ||||
−0.680157 | + | 0.733067i | \(0.738088\pi\) | |||||||
\(80\) | 7.59003 | 0.848591 | ||||||||
\(81\) | −7.85049 | −0.872276 | ||||||||
\(82\) | 0.0683188 | 0.00754455 | ||||||||
\(83\) | 10.0470 | 1.10280 | 0.551399 | − | 0.834242i | \(-0.314094\pi\) | ||||
0.551399 | + | 0.834242i | \(0.314094\pi\) | |||||||
\(84\) | −21.4418 | −2.33949 | ||||||||
\(85\) | 2.03207 | 0.220409 | ||||||||
\(86\) | 24.3023 | 2.62058 | ||||||||
\(87\) | 14.5270 | 1.55746 | ||||||||
\(88\) | −25.6202 | −2.73112 | ||||||||
\(89\) | 15.5551 | 1.64884 | 0.824418 | − | 0.565981i | \(-0.191503\pi\) | ||||
0.824418 | + | 0.565981i | \(0.191503\pi\) | |||||||
\(90\) | 0.899090 | 0.0947724 | ||||||||
\(91\) | −2.90866 | −0.304911 | ||||||||
\(92\) | 1.39555 | 0.145496 | ||||||||
\(93\) | 10.1306 | 1.05050 | ||||||||
\(94\) | 10.8191 | 1.11590 | ||||||||
\(95\) | −4.53360 | −0.465138 | ||||||||
\(96\) | −9.84842 | −1.00515 | ||||||||
\(97\) | −2.41387 | −0.245092 | −0.122546 | − | 0.992463i | \(-0.539106\pi\) | ||||
−0.122546 | + | 0.992463i | \(0.539106\pi\) | |||||||
\(98\) | −3.72969 | −0.376756 | ||||||||
\(99\) | −1.36678 | −0.137367 | ||||||||
\(100\) | −17.8726 | −1.78726 | ||||||||
\(101\) | −10.6593 | −1.06064 | −0.530318 | − | 0.847799i | \(-0.677927\pi\) | ||||
−0.530318 | + | 0.847799i | \(0.677927\pi\) | |||||||
\(102\) | −8.26033 | −0.817894 | ||||||||
\(103\) | −6.09693 | −0.600748 | −0.300374 | − | 0.953821i | \(-0.597112\pi\) | ||||
−0.300374 | + | 0.953821i | \(0.597112\pi\) | |||||||
\(104\) | −6.44404 | −0.631891 | ||||||||
\(105\) | −4.85429 | −0.473730 | ||||||||
\(106\) | 36.2643 | 3.52230 | ||||||||
\(107\) | −7.31454 | −0.707123 | −0.353562 | − | 0.935411i | \(-0.615030\pi\) | ||||
−0.353562 | + | 0.935411i | \(0.615030\pi\) | |||||||
\(108\) | −24.6493 | −2.37188 | ||||||||
\(109\) | −6.67058 | −0.638926 | −0.319463 | − | 0.947599i | \(-0.603503\pi\) | ||||
−0.319463 | + | 0.947599i | \(0.603503\pi\) | |||||||
\(110\) | −10.3980 | −0.991411 | ||||||||
\(111\) | 5.18304 | 0.491952 | ||||||||
\(112\) | −21.5594 | −2.03717 | ||||||||
\(113\) | −2.69215 | −0.253256 | −0.126628 | − | 0.991950i | \(-0.540415\pi\) | ||||
−0.126628 | + | 0.991950i | \(0.540415\pi\) | |||||||
\(114\) | 18.4290 | 1.72604 | ||||||||
\(115\) | 0.315945 | 0.0294620 | ||||||||
\(116\) | 40.3162 | 3.74327 | ||||||||
\(117\) | −0.343777 | −0.0317822 | ||||||||
\(118\) | 17.4233 | 1.60395 | ||||||||
\(119\) | −5.77207 | −0.529125 | ||||||||
\(120\) | −10.7545 | −0.981749 | ||||||||
\(121\) | 4.80690 | 0.436991 | ||||||||
\(122\) | 14.3193 | 1.29640 | ||||||||
\(123\) | −0.0435959 | −0.00393091 | ||||||||
\(124\) | 28.1150 | 2.52480 | ||||||||
\(125\) | −9.16626 | −0.819855 | ||||||||
\(126\) | −2.55385 | −0.227515 | ||||||||
\(127\) | 19.6413 | 1.74288 | 0.871441 | − | 0.490501i | \(-0.163186\pi\) | ||||
0.871441 | + | 0.490501i | \(0.163186\pi\) | |||||||
\(128\) | 10.5298 | 0.930713 | ||||||||
\(129\) | −15.5079 | −1.36539 | ||||||||
\(130\) | −2.61533 | −0.229380 | ||||||||
\(131\) | 7.20969 | 0.629914 | 0.314957 | − | 0.949106i | \(-0.398010\pi\) | ||||
0.314957 | + | 0.949106i | \(0.398010\pi\) | |||||||
\(132\) | 29.3083 | 2.55096 | ||||||||
\(133\) | 12.8777 | 1.11663 | ||||||||
\(134\) | −6.30882 | −0.544999 | ||||||||
\(135\) | −5.58046 | −0.480289 | ||||||||
\(136\) | −12.7878 | −1.09655 | ||||||||
\(137\) | 6.56121 | 0.560562 | 0.280281 | − | 0.959918i | \(-0.409572\pi\) | ||||
0.280281 | + | 0.959918i | \(0.409572\pi\) | |||||||
\(138\) | −1.28431 | −0.109328 | ||||||||
\(139\) | 17.1211 | 1.45219 | 0.726096 | − | 0.687594i | \(-0.241333\pi\) | ||||
0.726096 | + | 0.687594i | \(0.241333\pi\) | |||||||
\(140\) | −13.4719 | −1.13858 | ||||||||
\(141\) | −6.90394 | −0.581416 | ||||||||
\(142\) | 6.77425 | 0.568482 | ||||||||
\(143\) | 3.97579 | 0.332472 | ||||||||
\(144\) | −2.54812 | −0.212343 | ||||||||
\(145\) | 9.12736 | 0.757986 | ||||||||
\(146\) | −5.94836 | −0.492290 | ||||||||
\(147\) | 2.38001 | 0.196300 | ||||||||
\(148\) | 14.3842 | 1.18238 | ||||||||
\(149\) | 11.7777 | 0.964864 | 0.482432 | − | 0.875933i | \(-0.339754\pi\) | ||||
0.482432 | + | 0.875933i | \(0.339754\pi\) | |||||||
\(150\) | 16.4480 | 1.34297 | ||||||||
\(151\) | 6.67775 | 0.543428 | 0.271714 | − | 0.962378i | \(-0.412410\pi\) | ||||
0.271714 | + | 0.962378i | \(0.412410\pi\) | |||||||
\(152\) | 28.5300 | 2.31409 | ||||||||
\(153\) | −0.682205 | −0.0551530 | ||||||||
\(154\) | 29.5354 | 2.38003 | ||||||||
\(155\) | 6.36508 | 0.511255 | ||||||||
\(156\) | 7.37169 | 0.590208 | ||||||||
\(157\) | −21.3365 | −1.70284 | −0.851421 | − | 0.524484i | \(-0.824258\pi\) | ||||
−0.851421 | + | 0.524484i | \(0.824258\pi\) | |||||||
\(158\) | 30.8801 | 2.45669 | ||||||||
\(159\) | −23.1411 | −1.83521 | ||||||||
\(160\) | −6.18777 | −0.489186 | ||||||||
\(161\) | −0.897438 | −0.0707280 | ||||||||
\(162\) | 20.0504 | 1.57531 | ||||||||
\(163\) | 3.18815 | 0.249715 | 0.124857 | − | 0.992175i | \(-0.460153\pi\) | ||||
0.124857 | + | 0.992175i | \(0.460153\pi\) | |||||||
\(164\) | −0.120990 | −0.00944771 | ||||||||
\(165\) | 6.63523 | 0.516552 | ||||||||
\(166\) | −25.6603 | −1.99162 | ||||||||
\(167\) | 3.88570 | 0.300685 | 0.150342 | − | 0.988634i | \(-0.451962\pi\) | ||||
0.150342 | + | 0.988634i | \(0.451962\pi\) | |||||||
\(168\) | 30.5481 | 2.35684 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −5.18997 | −0.398053 | ||||||||
\(171\) | 1.52202 | 0.116392 | ||||||||
\(172\) | −43.0383 | −3.28164 | ||||||||
\(173\) | −16.1138 | −1.22511 | −0.612553 | − | 0.790429i | \(-0.709857\pi\) | ||||
−0.612553 | + | 0.790429i | \(0.709857\pi\) | |||||||
\(174\) | −37.1026 | −2.81274 | ||||||||
\(175\) | 11.4934 | 0.868816 | ||||||||
\(176\) | 29.4691 | 2.22132 | ||||||||
\(177\) | −11.1182 | −0.835699 | ||||||||
\(178\) | −39.7282 | −2.97776 | ||||||||
\(179\) | −14.3389 | −1.07174 | −0.535868 | − | 0.844302i | \(-0.680016\pi\) | ||||
−0.535868 | + | 0.844302i | \(0.680016\pi\) | |||||||
\(180\) | −1.59225 | −0.118679 | ||||||||
\(181\) | 15.1000 | 1.12237 | 0.561187 | − | 0.827689i | \(-0.310345\pi\) | ||||
0.561187 | + | 0.827689i | \(0.310345\pi\) | |||||||
\(182\) | 7.42882 | 0.550661 | ||||||||
\(183\) | −9.13748 | −0.675462 | ||||||||
\(184\) | −1.98824 | −0.146575 | ||||||||
\(185\) | 3.25651 | 0.239423 | ||||||||
\(186\) | −25.8739 | −1.89717 | ||||||||
\(187\) | 7.88972 | 0.576954 | ||||||||
\(188\) | −19.1602 | −1.39740 | ||||||||
\(189\) | 15.8512 | 1.15301 | ||||||||
\(190\) | 11.5790 | 0.840027 | ||||||||
\(191\) | 1.14122 | 0.0825754 | 0.0412877 | − | 0.999147i | \(-0.486854\pi\) | ||||
0.0412877 | + | 0.999147i | \(0.486854\pi\) | |||||||
\(192\) | 0.992708 | 0.0716426 | ||||||||
\(193\) | −2.92073 | −0.210239 | −0.105119 | − | 0.994460i | \(-0.533523\pi\) | ||||
−0.105119 | + | 0.994460i | \(0.533523\pi\) | |||||||
\(194\) | 6.16511 | 0.442629 | ||||||||
\(195\) | 1.66891 | 0.119513 | ||||||||
\(196\) | 6.60513 | 0.471795 | ||||||||
\(197\) | −7.08505 | −0.504789 | −0.252394 | − | 0.967624i | \(-0.581218\pi\) | ||||
−0.252394 | + | 0.967624i | \(0.581218\pi\) | |||||||
\(198\) | 3.49081 | 0.248081 | ||||||||
\(199\) | −0.196138 | −0.0139038 | −0.00695191 | − | 0.999976i | \(-0.502213\pi\) | ||||
−0.00695191 | + | 0.999976i | \(0.502213\pi\) | |||||||
\(200\) | 25.4631 | 1.80052 | ||||||||
\(201\) | 4.02582 | 0.283959 | ||||||||
\(202\) | 27.2241 | 1.91548 | ||||||||
\(203\) | −25.9262 | −1.81966 | ||||||||
\(204\) | 14.6287 | 1.02421 | ||||||||
\(205\) | −0.0273914 | −0.00191310 | ||||||||
\(206\) | 15.5718 | 1.08494 | ||||||||
\(207\) | −0.106069 | −0.00737229 | ||||||||
\(208\) | 7.41213 | 0.513939 | ||||||||
\(209\) | −17.6022 | −1.21757 | ||||||||
\(210\) | 12.3980 | 0.855544 | ||||||||
\(211\) | 23.3760 | 1.60927 | 0.804634 | − | 0.593770i | \(-0.202361\pi\) | ||||
0.804634 | + | 0.593770i | \(0.202361\pi\) | |||||||
\(212\) | −64.2225 | −4.41082 | ||||||||
\(213\) | −4.32282 | −0.296195 | ||||||||
\(214\) | 18.6816 | 1.27705 | ||||||||
\(215\) | −9.74361 | −0.664509 | ||||||||
\(216\) | 35.1179 | 2.38947 | ||||||||
\(217\) | −18.0799 | −1.22735 | ||||||||
\(218\) | 17.0369 | 1.15388 | ||||||||
\(219\) | 3.79580 | 0.256496 | ||||||||
\(220\) | 18.4144 | 1.24150 | ||||||||
\(221\) | 1.98444 | 0.133488 | ||||||||
\(222\) | −13.2377 | −0.888453 | ||||||||
\(223\) | −26.1888 | −1.75373 | −0.876866 | − | 0.480735i | \(-0.840370\pi\) | ||||
−0.876866 | + | 0.480735i | \(0.840370\pi\) | |||||||
\(224\) | 17.5763 | 1.17437 | ||||||||
\(225\) | 1.35841 | 0.0905605 | ||||||||
\(226\) | 6.87584 | 0.457374 | ||||||||
\(227\) | −6.63089 | −0.440108 | −0.220054 | − | 0.975488i | \(-0.570623\pi\) | ||||
−0.220054 | + | 0.975488i | \(0.570623\pi\) | |||||||
\(228\) | −32.6370 | −2.16144 | ||||||||
\(229\) | 0.611183 | 0.0403881 | 0.0201941 | − | 0.999796i | \(-0.493572\pi\) | ||||
0.0201941 | + | 0.999796i | \(0.493572\pi\) | |||||||
\(230\) | −0.806933 | −0.0532076 | ||||||||
\(231\) | −18.8473 | −1.24006 | ||||||||
\(232\) | −57.4386 | −3.77103 | ||||||||
\(233\) | −5.30818 | −0.347750 | −0.173875 | − | 0.984768i | \(-0.555629\pi\) | ||||
−0.173875 | + | 0.984768i | \(0.555629\pi\) | |||||||
\(234\) | 0.878017 | 0.0573978 | ||||||||
\(235\) | −4.33775 | −0.282964 | ||||||||
\(236\) | −30.8559 | −2.00855 | ||||||||
\(237\) | −19.7054 | −1.28000 | ||||||||
\(238\) | 14.7421 | 0.955586 | ||||||||
\(239\) | −8.62869 | −0.558144 | −0.279072 | − | 0.960270i | \(-0.590027\pi\) | ||||
−0.279072 | + | 0.960270i | \(0.590027\pi\) | |||||||
\(240\) | 12.3702 | 0.798491 | ||||||||
\(241\) | −18.2713 | −1.17696 | −0.588480 | − | 0.808512i | \(-0.700273\pi\) | ||||
−0.588480 | + | 0.808512i | \(0.700273\pi\) | |||||||
\(242\) | −12.2770 | −0.789195 | ||||||||
\(243\) | 3.55432 | 0.228010 | ||||||||
\(244\) | −25.3588 | −1.62343 | ||||||||
\(245\) | 1.49536 | 0.0955352 | ||||||||
\(246\) | 0.111345 | 0.00709913 | ||||||||
\(247\) | −4.42735 | −0.281705 | ||||||||
\(248\) | −40.0555 | −2.54353 | ||||||||
\(249\) | 16.3745 | 1.03769 | ||||||||
\(250\) | 23.4109 | 1.48064 | ||||||||
\(251\) | −5.12680 | −0.323601 | −0.161801 | − | 0.986823i | \(-0.551730\pi\) | ||||
−0.161801 | + | 0.986823i | \(0.551730\pi\) | |||||||
\(252\) | 4.52277 | 0.284908 | ||||||||
\(253\) | 1.22669 | 0.0771213 | ||||||||
\(254\) | −50.1645 | −3.14760 | ||||||||
\(255\) | 3.31185 | 0.207396 | ||||||||
\(256\) | −28.1117 | −1.75698 | ||||||||
\(257\) | −2.73524 | −0.170620 | −0.0853098 | − | 0.996354i | \(-0.527188\pi\) | ||||
−0.0853098 | + | 0.996354i | \(0.527188\pi\) | |||||||
\(258\) | 39.6076 | 2.46586 | ||||||||
\(259\) | −9.25008 | −0.574772 | ||||||||
\(260\) | 4.63164 | 0.287242 | ||||||||
\(261\) | −3.06423 | −0.189671 | ||||||||
\(262\) | −18.4138 | −1.13761 | ||||||||
\(263\) | 12.1182 | 0.747241 | 0.373621 | − | 0.927582i | \(-0.378116\pi\) | ||||
0.373621 | + | 0.927582i | \(0.378116\pi\) | |||||||
\(264\) | −41.7555 | −2.56988 | ||||||||
\(265\) | −14.5396 | −0.893161 | ||||||||
\(266\) | −32.8900 | −2.01661 | ||||||||
\(267\) | 25.3516 | 1.55149 | ||||||||
\(268\) | 11.1727 | 0.682479 | ||||||||
\(269\) | 6.00156 | 0.365922 | 0.182961 | − | 0.983120i | \(-0.441432\pi\) | ||||
0.182961 | + | 0.983120i | \(0.441432\pi\) | |||||||
\(270\) | 14.2527 | 0.867390 | ||||||||
\(271\) | −4.34502 | −0.263941 | −0.131971 | − | 0.991254i | \(-0.542130\pi\) | ||||
−0.131971 | + | 0.991254i | \(0.542130\pi\) | |||||||
\(272\) | 14.7089 | 0.891861 | ||||||||
\(273\) | −4.74052 | −0.286909 | ||||||||
\(274\) | −16.7575 | −1.01236 | ||||||||
\(275\) | −15.7100 | −0.947350 | ||||||||
\(276\) | 2.27446 | 0.136906 | ||||||||
\(277\) | 0.625737 | 0.0375969 | 0.0187984 | − | 0.999823i | \(-0.494016\pi\) | ||||
0.0187984 | + | 0.999823i | \(0.494016\pi\) | |||||||
\(278\) | −43.7278 | −2.62262 | ||||||||
\(279\) | −2.13688 | −0.127932 | ||||||||
\(280\) | 19.1934 | 1.14702 | ||||||||
\(281\) | −4.69727 | −0.280216 | −0.140108 | − | 0.990136i | \(-0.544745\pi\) | ||||
−0.140108 | + | 0.990136i | \(0.544745\pi\) | |||||||
\(282\) | 17.6329 | 1.05002 | ||||||||
\(283\) | −2.01970 | −0.120059 | −0.0600293 | − | 0.998197i | \(-0.519119\pi\) | ||||
−0.0600293 | + | 0.998197i | \(0.519119\pi\) | |||||||
\(284\) | −11.9969 | −0.711886 | ||||||||
\(285\) | −7.38883 | −0.437677 | ||||||||
\(286\) | −10.1543 | −0.600436 | ||||||||
\(287\) | 0.0778049 | 0.00459268 | ||||||||
\(288\) | 2.07735 | 0.122409 | ||||||||
\(289\) | −13.0620 | −0.768352 | ||||||||
\(290\) | −23.3116 | −1.36890 | ||||||||
\(291\) | −3.93411 | −0.230622 | ||||||||
\(292\) | 10.5343 | 0.616473 | ||||||||
\(293\) | −30.0046 | −1.75289 | −0.876445 | − | 0.481502i | \(-0.840091\pi\) | ||||
−0.876445 | + | 0.481502i | \(0.840091\pi\) | |||||||
\(294\) | −6.07863 | −0.354513 | ||||||||
\(295\) | −6.98561 | −0.406718 | ||||||||
\(296\) | −20.4932 | −1.19115 | ||||||||
\(297\) | −21.6667 | −1.25723 | ||||||||
\(298\) | −30.0805 | −1.74252 | ||||||||
\(299\) | 0.308540 | 0.0178433 | ||||||||
\(300\) | −29.1287 | −1.68174 | ||||||||
\(301\) | 27.6766 | 1.59525 | ||||||||
\(302\) | −17.0552 | −0.981417 | ||||||||
\(303\) | −17.3724 | −0.998017 | ||||||||
\(304\) | −32.8161 | −1.88213 | ||||||||
\(305\) | −5.74109 | −0.328734 | ||||||||
\(306\) | 1.74237 | 0.0996048 | ||||||||
\(307\) | −1.51115 | −0.0862457 | −0.0431228 | − | 0.999070i | \(-0.513731\pi\) | ||||
−0.0431228 | + | 0.999070i | \(0.513731\pi\) | |||||||
\(308\) | −52.3060 | −2.98041 | ||||||||
\(309\) | −9.93673 | −0.565281 | ||||||||
\(310\) | −16.2566 | −0.923314 | ||||||||
\(311\) | −21.5447 | −1.22169 | −0.610845 | − | 0.791750i | \(-0.709170\pi\) | ||||
−0.610845 | + | 0.791750i | \(0.709170\pi\) | |||||||
\(312\) | −10.5025 | −0.594584 | ||||||||
\(313\) | −14.5264 | −0.821083 | −0.410542 | − | 0.911842i | \(-0.634660\pi\) | ||||
−0.410542 | + | 0.911842i | \(0.634660\pi\) | |||||||
\(314\) | 54.4942 | 3.07529 | ||||||||
\(315\) | 1.02393 | 0.0576918 | ||||||||
\(316\) | −54.6874 | −3.07641 | ||||||||
\(317\) | −14.5019 | −0.814508 | −0.407254 | − | 0.913315i | \(-0.633514\pi\) | ||||
−0.407254 | + | 0.913315i | \(0.633514\pi\) | |||||||
\(318\) | 59.1033 | 3.31435 | ||||||||
\(319\) | 35.4379 | 1.98414 | ||||||||
\(320\) | 0.623720 | 0.0348670 | ||||||||
\(321\) | −11.9212 | −0.665376 | ||||||||
\(322\) | 2.29209 | 0.127733 | ||||||||
\(323\) | −8.78581 | −0.488855 | ||||||||
\(324\) | −35.5084 | −1.97269 | ||||||||
\(325\) | −3.95142 | −0.219186 | ||||||||
\(326\) | −8.14263 | −0.450979 | ||||||||
\(327\) | −10.8717 | −0.601205 | ||||||||
\(328\) | 0.172374 | 0.00951777 | ||||||||
\(329\) | 12.3213 | 0.679297 | ||||||||
\(330\) | −16.9466 | −0.932879 | ||||||||
\(331\) | 26.7247 | 1.46892 | 0.734461 | − | 0.678651i | \(-0.237435\pi\) | ||||
0.734461 | + | 0.678651i | \(0.237435\pi\) | |||||||
\(332\) | 45.4433 | 2.49402 | ||||||||
\(333\) | −1.09327 | −0.0599110 | ||||||||
\(334\) | −9.92421 | −0.543029 | ||||||||
\(335\) | 2.52942 | 0.138197 | ||||||||
\(336\) | −35.1373 | −1.91690 | ||||||||
\(337\) | −16.4810 | −0.897776 | −0.448888 | − | 0.893588i | \(-0.648180\pi\) | ||||
−0.448888 | + | 0.893588i | \(0.648180\pi\) | |||||||
\(338\) | −2.55403 | −0.138921 | ||||||||
\(339\) | −4.38765 | −0.238304 | ||||||||
\(340\) | 9.19122 | 0.498464 | ||||||||
\(341\) | 24.7131 | 1.33829 | ||||||||
\(342\) | −3.88728 | −0.210200 | ||||||||
\(343\) | 16.1131 | 0.870024 | ||||||||
\(344\) | 61.3167 | 3.30597 | ||||||||
\(345\) | 0.514924 | 0.0277226 | ||||||||
\(346\) | 41.1551 | 2.21251 | ||||||||
\(347\) | −0.946071 | −0.0507877 | −0.0253939 | − | 0.999678i | \(-0.508084\pi\) | ||||
−0.0253939 | + | 0.999678i | \(0.508084\pi\) | |||||||
\(348\) | 65.7071 | 3.52227 | ||||||||
\(349\) | 25.3789 | 1.35850 | 0.679250 | − | 0.733907i | \(-0.262305\pi\) | ||||
0.679250 | + | 0.733907i | \(0.262305\pi\) | |||||||
\(350\) | −29.3544 | −1.56906 | ||||||||
\(351\) | −5.44966 | −0.290881 | ||||||||
\(352\) | −24.0247 | −1.28052 | ||||||||
\(353\) | −11.7032 | −0.622897 | −0.311449 | − | 0.950263i | \(-0.600814\pi\) | ||||
−0.311449 | + | 0.950263i | \(0.600814\pi\) | |||||||
\(354\) | 28.3964 | 1.50925 | ||||||||
\(355\) | −2.71603 | −0.144152 | ||||||||
\(356\) | 70.3570 | 3.72891 | ||||||||
\(357\) | −9.40728 | −0.497886 | ||||||||
\(358\) | 36.6219 | 1.93553 | ||||||||
\(359\) | −4.76066 | −0.251258 | −0.125629 | − | 0.992077i | \(-0.540095\pi\) | ||||
−0.125629 | + | 0.992077i | \(0.540095\pi\) | |||||||
\(360\) | 2.26848 | 0.119559 | ||||||||
\(361\) | 0.601391 | 0.0316521 | ||||||||
\(362\) | −38.5659 | −2.02698 | ||||||||
\(363\) | 7.83425 | 0.411192 | ||||||||
\(364\) | −13.1561 | −0.689568 | ||||||||
\(365\) | 2.38490 | 0.124832 | ||||||||
\(366\) | 23.3374 | 1.21987 | ||||||||
\(367\) | 10.6744 | 0.557199 | 0.278600 | − | 0.960407i | \(-0.410130\pi\) | ||||
0.278600 | + | 0.960407i | \(0.410130\pi\) | |||||||
\(368\) | 2.28694 | 0.119215 | ||||||||
\(369\) | 0.00919581 | 0.000478715 0 | ||||||||
\(370\) | −8.31723 | −0.432392 | ||||||||
\(371\) | 41.2996 | 2.14417 | ||||||||
\(372\) | 45.8217 | 2.37574 | ||||||||
\(373\) | 17.7186 | 0.917434 | 0.458717 | − | 0.888582i | \(-0.348309\pi\) | ||||
0.458717 | + | 0.888582i | \(0.348309\pi\) | |||||||
\(374\) | −20.1506 | −1.04196 | ||||||||
\(375\) | −14.9391 | −0.771452 | ||||||||
\(376\) | 27.2975 | 1.40776 | ||||||||
\(377\) | 8.91343 | 0.459065 | ||||||||
\(378\) | −40.4846 | −2.08230 | ||||||||
\(379\) | −22.9984 | −1.18135 | −0.590674 | − | 0.806910i | \(-0.701138\pi\) | ||||
−0.590674 | + | 0.806910i | \(0.701138\pi\) | |||||||
\(380\) | −20.5059 | −1.05193 | ||||||||
\(381\) | 32.0112 | 1.63998 | ||||||||
\(382\) | −2.91470 | −0.149129 | ||||||||
\(383\) | −0.696736 | −0.0356015 | −0.0178008 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0178008 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(384\) | 17.1614 | 0.875765 | ||||||||
\(385\) | −11.8418 | −0.603513 | ||||||||
\(386\) | 7.45965 | 0.379686 | ||||||||
\(387\) | 3.27112 | 0.166280 | ||||||||
\(388\) | −10.9182 | −0.554285 | ||||||||
\(389\) | 2.43948 | 0.123686 | 0.0618432 | − | 0.998086i | \(-0.480302\pi\) | ||||
0.0618432 | + | 0.998086i | \(0.480302\pi\) | |||||||
\(390\) | −4.26245 | −0.215837 | ||||||||
\(391\) | 0.612279 | 0.0309643 | ||||||||
\(392\) | −9.41033 | −0.475294 | ||||||||
\(393\) | 11.7503 | 0.592724 | ||||||||
\(394\) | 18.0954 | 0.911636 | ||||||||
\(395\) | −12.3809 | −0.622951 | ||||||||
\(396\) | −6.18208 | −0.310661 | ||||||||
\(397\) | −34.0916 | −1.71101 | −0.855504 | − | 0.517797i | \(-0.826752\pi\) | ||||
−0.855504 | + | 0.517797i | \(0.826752\pi\) | |||||||
\(398\) | 0.500942 | 0.0251100 | ||||||||
\(399\) | 20.9879 | 1.05071 | ||||||||
\(400\) | −29.2885 | −1.46442 | ||||||||
\(401\) | −30.2271 | −1.50947 | −0.754735 | − | 0.656030i | \(-0.772234\pi\) | ||||
−0.754735 | + | 0.656030i | \(0.772234\pi\) | |||||||
\(402\) | −10.2821 | −0.512823 | ||||||||
\(403\) | 6.21590 | 0.309636 | ||||||||
\(404\) | −48.2127 | −2.39867 | ||||||||
\(405\) | −8.03890 | −0.399456 | ||||||||
\(406\) | 66.2163 | 3.28626 | ||||||||
\(407\) | 12.6437 | 0.626727 | ||||||||
\(408\) | −20.8415 | −1.03181 | ||||||||
\(409\) | −9.89835 | −0.489442 | −0.244721 | − | 0.969594i | \(-0.578696\pi\) | ||||
−0.244721 | + | 0.969594i | \(0.578696\pi\) | |||||||
\(410\) | 0.0699585 | 0.00345500 | ||||||||
\(411\) | 10.6934 | 0.527467 | ||||||||
\(412\) | −27.5769 | −1.35862 | ||||||||
\(413\) | 19.8425 | 0.976388 | ||||||||
\(414\) | 0.270903 | 0.0133142 | ||||||||
\(415\) | 10.2881 | 0.505022 | ||||||||
\(416\) | −6.04274 | −0.296270 | ||||||||
\(417\) | 27.9038 | 1.36646 | ||||||||
\(418\) | 44.9566 | 2.19890 | ||||||||
\(419\) | −11.0171 | −0.538221 | −0.269111 | − | 0.963109i | \(-0.586730\pi\) | ||||
−0.269111 | + | 0.963109i | \(0.586730\pi\) | |||||||
\(420\) | −21.9564 | −1.07136 | ||||||||
\(421\) | 34.5975 | 1.68618 | 0.843089 | − | 0.537774i | \(-0.180735\pi\) | ||||
0.843089 | + | 0.537774i | \(0.180735\pi\) | |||||||
\(422\) | −59.7030 | −2.90630 | ||||||||
\(423\) | 1.45627 | 0.0708061 | ||||||||
\(424\) | 91.4979 | 4.44353 | ||||||||
\(425\) | −7.84137 | −0.380362 | ||||||||
\(426\) | 11.0406 | 0.534920 | ||||||||
\(427\) | 16.3075 | 0.789175 | ||||||||
\(428\) | −33.0843 | −1.59919 | ||||||||
\(429\) | 6.47971 | 0.312843 | ||||||||
\(430\) | 24.8855 | 1.20009 | ||||||||
\(431\) | −19.9265 | −0.959825 | −0.479913 | − | 0.877316i | \(-0.659332\pi\) | ||||
−0.479913 | + | 0.877316i | \(0.659332\pi\) | |||||||
\(432\) | −40.3936 | −1.94344 | ||||||||
\(433\) | −4.63653 | −0.222817 | −0.111409 | − | 0.993775i | \(-0.535536\pi\) | ||||
−0.111409 | + | 0.993775i | \(0.535536\pi\) | |||||||
\(434\) | 46.1768 | 2.21656 | ||||||||
\(435\) | 14.8757 | 0.713235 | ||||||||
\(436\) | −30.1716 | −1.44496 | ||||||||
\(437\) | −1.36601 | −0.0653452 | ||||||||
\(438\) | −9.69459 | −0.463226 | ||||||||
\(439\) | 14.5172 | 0.692868 | 0.346434 | − | 0.938074i | \(-0.387392\pi\) | ||||
0.346434 | + | 0.938074i | \(0.387392\pi\) | |||||||
\(440\) | −26.2351 | −1.25071 | ||||||||
\(441\) | −0.502022 | −0.0239058 | ||||||||
\(442\) | −5.06833 | −0.241076 | ||||||||
\(443\) | −9.38896 | −0.446083 | −0.223041 | − | 0.974809i | \(-0.571599\pi\) | ||||
−0.223041 | + | 0.974809i | \(0.571599\pi\) | |||||||
\(444\) | 23.4433 | 1.11257 | ||||||||
\(445\) | 15.9284 | 0.755079 | ||||||||
\(446\) | 66.8871 | 3.16719 | ||||||||
\(447\) | 19.1952 | 0.907899 | ||||||||
\(448\) | −1.77167 | −0.0837035 | ||||||||
\(449\) | −31.0801 | −1.46676 | −0.733379 | − | 0.679820i | \(-0.762058\pi\) | ||||
−0.733379 | + | 0.679820i | \(0.762058\pi\) | |||||||
\(450\) | −3.46942 | −0.163550 | ||||||||
\(451\) | −0.106350 | −0.00500782 | ||||||||
\(452\) | −12.1768 | −0.572750 | ||||||||
\(453\) | 10.8834 | 0.511344 | ||||||||
\(454\) | 16.9355 | 0.794823 | ||||||||
\(455\) | −2.97847 | −0.139633 | ||||||||
\(456\) | 46.4980 | 2.17747 | ||||||||
\(457\) | 14.0870 | 0.658963 | 0.329482 | − | 0.944162i | \(-0.393126\pi\) | ||||
0.329482 | + | 0.944162i | \(0.393126\pi\) | |||||||
\(458\) | −1.56098 | −0.0729399 | ||||||||
\(459\) | −10.8145 | −0.504779 | ||||||||
\(460\) | 1.42905 | 0.0666296 | ||||||||
\(461\) | 37.0414 | 1.72519 | 0.862594 | − | 0.505897i | \(-0.168838\pi\) | ||||
0.862594 | + | 0.505897i | \(0.168838\pi\) | |||||||
\(462\) | 48.1366 | 2.23952 | ||||||||
\(463\) | 22.0189 | 1.02330 | 0.511652 | − | 0.859193i | \(-0.329034\pi\) | ||||
0.511652 | + | 0.859193i | \(0.329034\pi\) | |||||||
\(464\) | 66.0675 | 3.06711 | ||||||||
\(465\) | 10.3738 | 0.481071 | ||||||||
\(466\) | 13.5573 | 0.628028 | ||||||||
\(467\) | 8.09255 | 0.374478 | 0.187239 | − | 0.982314i | \(-0.440046\pi\) | ||||
0.187239 | + | 0.982314i | \(0.440046\pi\) | |||||||
\(468\) | −1.55493 | −0.0718767 | ||||||||
\(469\) | −7.18480 | −0.331763 | ||||||||
\(470\) | 11.0788 | 0.511025 | ||||||||
\(471\) | −34.7741 | −1.60231 | ||||||||
\(472\) | 43.9605 | 2.02345 | ||||||||
\(473\) | −37.8306 | −1.73945 | ||||||||
\(474\) | 50.3282 | 2.31165 | ||||||||
\(475\) | 17.4943 | 0.802694 | ||||||||
\(476\) | −26.1076 | −1.19664 | ||||||||
\(477\) | 4.88123 | 0.223496 | ||||||||
\(478\) | 22.0380 | 1.00799 | ||||||||
\(479\) | 16.1781 | 0.739196 | 0.369598 | − | 0.929192i | \(-0.379495\pi\) | ||||
0.369598 | + | 0.929192i | \(0.379495\pi\) | |||||||
\(480\) | −10.0848 | −0.460305 | ||||||||
\(481\) | 3.18018 | 0.145004 | ||||||||
\(482\) | 46.6656 | 2.12556 | ||||||||
\(483\) | −1.46264 | −0.0665523 | ||||||||
\(484\) | 21.7420 | 0.988274 | ||||||||
\(485\) | −2.47181 | −0.112239 | ||||||||
\(486\) | −9.07785 | −0.411780 | ||||||||
\(487\) | −19.6696 | −0.891316 | −0.445658 | − | 0.895203i | \(-0.647030\pi\) | ||||
−0.445658 | + | 0.895203i | \(0.647030\pi\) | |||||||
\(488\) | 36.1287 | 1.63547 | ||||||||
\(489\) | 5.19602 | 0.234972 | ||||||||
\(490\) | −3.81921 | −0.172534 | ||||||||
\(491\) | −28.7346 | −1.29678 | −0.648388 | − | 0.761310i | \(-0.724557\pi\) | ||||
−0.648388 | + | 0.761310i | \(0.724557\pi\) | |||||||
\(492\) | −0.197188 | −0.00888993 | ||||||||
\(493\) | 17.6882 | 0.796636 | ||||||||
\(494\) | 11.3076 | 0.508752 | ||||||||
\(495\) | −1.39959 | −0.0629067 | ||||||||
\(496\) | 46.0730 | 2.06874 | ||||||||
\(497\) | 7.71486 | 0.346059 | ||||||||
\(498\) | −41.8209 | −1.87404 | ||||||||
\(499\) | 10.9592 | 0.490601 | 0.245301 | − | 0.969447i | \(-0.421113\pi\) | ||||
0.245301 | + | 0.969447i | \(0.421113\pi\) | |||||||
\(500\) | −41.4598 | −1.85414 | ||||||||
\(501\) | 6.33289 | 0.282933 | ||||||||
\(502\) | 13.0940 | 0.584415 | ||||||||
\(503\) | 0.948787 | 0.0423043 | 0.0211522 | − | 0.999776i | \(-0.493267\pi\) | ||||
0.0211522 | + | 0.999776i | \(0.493267\pi\) | |||||||
\(504\) | −6.44359 | −0.287020 | ||||||||
\(505\) | −10.9151 | −0.485715 | ||||||||
\(506\) | −3.13300 | −0.139279 | ||||||||
\(507\) | 1.62979 | 0.0723816 | ||||||||
\(508\) | 88.8392 | 3.94160 | ||||||||
\(509\) | −31.3466 | −1.38941 | −0.694707 | − | 0.719293i | \(-0.744466\pi\) | ||||
−0.694707 | + | 0.719293i | \(0.744466\pi\) | |||||||
\(510\) | −8.45858 | −0.374552 | ||||||||
\(511\) | −6.77429 | −0.299677 | ||||||||
\(512\) | 50.7386 | 2.24235 | ||||||||
\(513\) | 24.1275 | 1.06526 | ||||||||
\(514\) | 6.98590 | 0.308135 | ||||||||
\(515\) | −6.24326 | −0.275111 | ||||||||
\(516\) | −70.1434 | −3.08789 | ||||||||
\(517\) | −16.8418 | −0.740700 | ||||||||
\(518\) | 23.6250 | 1.03802 | ||||||||
\(519\) | −26.2621 | −1.15278 | ||||||||
\(520\) | −6.59870 | −0.289372 | ||||||||
\(521\) | 2.83178 | 0.124063 | 0.0620313 | − | 0.998074i | \(-0.480242\pi\) | ||||
0.0620313 | + | 0.998074i | \(0.480242\pi\) | |||||||
\(522\) | 7.82614 | 0.342541 | ||||||||
\(523\) | −33.6100 | −1.46966 | −0.734831 | − | 0.678250i | \(-0.762739\pi\) | ||||
−0.734831 | + | 0.678250i | \(0.762739\pi\) | |||||||
\(524\) | 32.6101 | 1.42458 | ||||||||
\(525\) | 18.7318 | 0.817522 | ||||||||
\(526\) | −30.9503 | −1.34950 | ||||||||
\(527\) | 12.3351 | 0.537325 | ||||||||
\(528\) | 48.0285 | 2.09017 | ||||||||
\(529\) | −22.9048 | −0.995861 | ||||||||
\(530\) | 37.1346 | 1.61303 | ||||||||
\(531\) | 2.34520 | 0.101773 | ||||||||
\(532\) | 58.2467 | 2.52532 | ||||||||
\(533\) | −0.0267494 | −0.00115864 | ||||||||
\(534\) | −64.7487 | −2.80195 | ||||||||
\(535\) | −7.49009 | −0.323825 | ||||||||
\(536\) | −15.9177 | −0.687540 | ||||||||
\(537\) | −23.3694 | −1.00846 | ||||||||
\(538\) | −15.3282 | −0.660845 | ||||||||
\(539\) | 5.80591 | 0.250078 | ||||||||
\(540\) | −25.2409 | −1.08619 | ||||||||
\(541\) | −35.9301 | −1.54475 | −0.772377 | − | 0.635164i | \(-0.780932\pi\) | ||||
−0.772377 | + | 0.635164i | \(0.780932\pi\) | |||||||
\(542\) | 11.0973 | 0.476671 | ||||||||
\(543\) | 24.6099 | 1.05611 | ||||||||
\(544\) | −11.9915 | −0.514130 | ||||||||
\(545\) | −6.83068 | −0.292594 | ||||||||
\(546\) | 12.1074 | 0.518150 | ||||||||
\(547\) | 0.307514 | 0.0131483 | 0.00657417 | − | 0.999978i | \(-0.497907\pi\) | ||||
0.00657417 | + | 0.999978i | \(0.497907\pi\) | |||||||
\(548\) | 29.6769 | 1.26773 | ||||||||
\(549\) | 1.92739 | 0.0822592 | ||||||||
\(550\) | 40.1239 | 1.71089 | ||||||||
\(551\) | −39.4628 | −1.68117 | ||||||||
\(552\) | −3.24042 | −0.137922 | ||||||||
\(553\) | 35.1678 | 1.49549 | ||||||||
\(554\) | −1.59815 | −0.0678990 | ||||||||
\(555\) | 5.30743 | 0.225288 | ||||||||
\(556\) | 77.4401 | 3.28419 | ||||||||
\(557\) | −26.3182 | −1.11514 | −0.557570 | − | 0.830130i | \(-0.688266\pi\) | ||||
−0.557570 | + | 0.830130i | \(0.688266\pi\) | |||||||
\(558\) | 5.45766 | 0.231041 | ||||||||
\(559\) | −9.51525 | −0.402452 | ||||||||
\(560\) | −22.0768 | −0.932916 | ||||||||
\(561\) | 12.8586 | 0.542891 | ||||||||
\(562\) | 11.9970 | 0.506062 | ||||||||
\(563\) | 6.77145 | 0.285383 | 0.142691 | − | 0.989767i | \(-0.454424\pi\) | ||||
0.142691 | + | 0.989767i | \(0.454424\pi\) | |||||||
\(564\) | −31.2271 | −1.31490 | ||||||||
\(565\) | −2.75676 | −0.115978 | ||||||||
\(566\) | 5.15838 | 0.216823 | ||||||||
\(567\) | 22.8344 | 0.958955 | ||||||||
\(568\) | 17.0920 | 0.717165 | ||||||||
\(569\) | 41.5018 | 1.73984 | 0.869922 | − | 0.493189i | \(-0.164169\pi\) | ||||
0.869922 | + | 0.493189i | \(0.164169\pi\) | |||||||
\(570\) | 18.8713 | 0.790433 | ||||||||
\(571\) | 3.86062 | 0.161562 | 0.0807810 | − | 0.996732i | \(-0.474259\pi\) | ||||
0.0807810 | + | 0.996732i | \(0.474259\pi\) | |||||||
\(572\) | 17.9828 | 0.751900 | ||||||||
\(573\) | 1.85994 | 0.0777003 | ||||||||
\(574\) | −0.198716 | −0.00829426 | ||||||||
\(575\) | −1.21917 | −0.0508430 | ||||||||
\(576\) | −0.209395 | −0.00872478 | ||||||||
\(577\) | 24.5035 | 1.02009 | 0.510047 | − | 0.860147i | \(-0.329628\pi\) | ||||
0.510047 | + | 0.860147i | \(0.329628\pi\) | |||||||
\(578\) | 33.3608 | 1.38762 | ||||||||
\(579\) | −4.76019 | −0.197827 | ||||||||
\(580\) | 41.2838 | 1.71422 | ||||||||
\(581\) | −29.2232 | −1.21238 | ||||||||
\(582\) | 10.0479 | 0.416497 | ||||||||
\(583\) | −56.4516 | −2.33798 | ||||||||
\(584\) | −15.0082 | −0.621045 | ||||||||
\(585\) | −0.352027 | −0.0145545 | ||||||||
\(586\) | 76.6328 | 3.16567 | ||||||||
\(587\) | 18.7607 | 0.774336 | 0.387168 | − | 0.922009i | \(-0.373453\pi\) | ||||
0.387168 | + | 0.922009i | \(0.373453\pi\) | |||||||
\(588\) | 10.7650 | 0.443941 | ||||||||
\(589\) | −27.5199 | −1.13394 | ||||||||
\(590\) | 17.8415 | 0.734522 | ||||||||
\(591\) | −11.5472 | −0.474987 | ||||||||
\(592\) | 23.5719 | 0.968801 | ||||||||
\(593\) | 33.0962 | 1.35910 | 0.679550 | − | 0.733629i | \(-0.262175\pi\) | ||||
0.679550 | + | 0.733629i | \(0.262175\pi\) | |||||||
\(594\) | 55.3375 | 2.27052 | ||||||||
\(595\) | −5.91060 | −0.242311 | ||||||||
\(596\) | 53.2714 | 2.18208 | ||||||||
\(597\) | −0.319664 | −0.0130830 | ||||||||
\(598\) | −0.788021 | −0.0322246 | ||||||||
\(599\) | −29.2262 | −1.19415 | −0.597075 | − | 0.802185i | \(-0.703671\pi\) | ||||
−0.597075 | + | 0.802185i | \(0.703671\pi\) | |||||||
\(600\) | 41.4996 | 1.69422 | ||||||||
\(601\) | −0.652714 | −0.0266248 | −0.0133124 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133124 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(602\) | −70.6870 | −2.88099 | ||||||||
\(603\) | −0.849177 | −0.0345811 | ||||||||
\(604\) | 30.2041 | 1.22899 | ||||||||
\(605\) | 4.92227 | 0.200119 | ||||||||
\(606\) | 44.3696 | 1.80239 | ||||||||
\(607\) | −10.4935 | −0.425918 | −0.212959 | − | 0.977061i | \(-0.568310\pi\) | ||||
−0.212959 | + | 0.977061i | \(0.568310\pi\) | |||||||
\(608\) | 26.7533 | 1.08499 | ||||||||
\(609\) | −42.2543 | −1.71223 | ||||||||
\(610\) | 14.6629 | 0.593685 | ||||||||
\(611\) | −4.23608 | −0.171374 | ||||||||
\(612\) | −3.08567 | −0.124731 | ||||||||
\(613\) | −10.5606 | −0.426539 | −0.213270 | − | 0.976993i | \(-0.568411\pi\) | ||||
−0.213270 | + | 0.976993i | \(0.568411\pi\) | |||||||
\(614\) | 3.85952 | 0.155757 | ||||||||
\(615\) | −0.0446423 | −0.00180015 | ||||||||
\(616\) | 74.5204 | 3.00251 | ||||||||
\(617\) | −18.6433 | −0.750551 | −0.375276 | − | 0.926913i | \(-0.622452\pi\) | ||||
−0.375276 | + | 0.926913i | \(0.622452\pi\) | |||||||
\(618\) | 25.3787 | 1.02088 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 28.7898 | 1.15623 | ||||||||
\(621\) | −1.68144 | −0.0674738 | ||||||||
\(622\) | 55.0260 | 2.20634 | ||||||||
\(623\) | −45.2445 | −1.81268 | ||||||||
\(624\) | 12.0802 | 0.483596 | ||||||||
\(625\) | 10.3709 | 0.414835 | ||||||||
\(626\) | 37.1010 | 1.48286 | ||||||||
\(627\) | −28.6879 | −1.14569 | ||||||||
\(628\) | −96.5070 | −3.85105 | ||||||||
\(629\) | 6.31089 | 0.251632 | ||||||||
\(630\) | −2.61515 | −0.104190 | ||||||||
\(631\) | −25.0624 | −0.997719 | −0.498859 | − | 0.866683i | \(-0.666248\pi\) | ||||
−0.498859 | + | 0.866683i | \(0.666248\pi\) | |||||||
\(632\) | 77.9132 | 3.09922 | ||||||||
\(633\) | 38.0980 | 1.51426 | ||||||||
\(634\) | 37.0383 | 1.47098 | ||||||||
\(635\) | 20.1127 | 0.798147 | ||||||||
\(636\) | −104.669 | −4.15041 | ||||||||
\(637\) | 1.46032 | 0.0578598 | ||||||||
\(638\) | −90.5097 | −3.58331 | ||||||||
\(639\) | 0.911824 | 0.0360712 | ||||||||
\(640\) | 10.7825 | 0.426217 | ||||||||
\(641\) | 6.74162 | 0.266278 | 0.133139 | − | 0.991097i | \(-0.457494\pi\) | ||||
0.133139 | + | 0.991097i | \(0.457494\pi\) | |||||||
\(642\) | 30.4471 | 1.20165 | ||||||||
\(643\) | −19.3974 | −0.764960 | −0.382480 | − | 0.923964i | \(-0.624930\pi\) | ||||
−0.382480 | + | 0.923964i | \(0.624930\pi\) | |||||||
\(644\) | −4.05919 | −0.159954 | ||||||||
\(645\) | −15.8801 | −0.625277 | ||||||||
\(646\) | 22.4392 | 0.882860 | ||||||||
\(647\) | −24.4001 | −0.959267 | −0.479634 | − | 0.877469i | \(-0.659230\pi\) | ||||
−0.479634 | + | 0.877469i | \(0.659230\pi\) | |||||||
\(648\) | 50.5889 | 1.98732 | ||||||||
\(649\) | −27.1224 | −1.06465 | ||||||||
\(650\) | 10.0921 | 0.395843 | ||||||||
\(651\) | −29.4665 | −1.15489 | ||||||||
\(652\) | 14.4203 | 0.564741 | ||||||||
\(653\) | −21.8357 | −0.854499 | −0.427249 | − | 0.904134i | \(-0.640517\pi\) | ||||
−0.427249 | + | 0.904134i | \(0.640517\pi\) | |||||||
\(654\) | 27.7666 | 1.08576 | ||||||||
\(655\) | 7.38273 | 0.288467 | ||||||||
\(656\) | −0.198270 | −0.00774114 | ||||||||
\(657\) | −0.800658 | −0.0312366 | ||||||||
\(658\) | −31.4691 | −1.22679 | ||||||||
\(659\) | −1.10163 | −0.0429135 | −0.0214568 | − | 0.999770i | \(-0.506830\pi\) | ||||
−0.0214568 | + | 0.999770i | \(0.506830\pi\) | |||||||
\(660\) | 30.0117 | 1.16820 | ||||||||
\(661\) | 10.5964 | 0.412152 | 0.206076 | − | 0.978536i | \(-0.433931\pi\) | ||||
0.206076 | + | 0.978536i | \(0.433931\pi\) | |||||||
\(662\) | −68.2557 | −2.65283 | ||||||||
\(663\) | 3.23423 | 0.125607 | ||||||||
\(664\) | −64.7431 | −2.51252 | ||||||||
\(665\) | 13.1867 | 0.511359 | ||||||||
\(666\) | 2.79225 | 0.108198 | ||||||||
\(667\) | 2.75015 | 0.106486 | ||||||||
\(668\) | 17.5754 | 0.680011 | ||||||||
\(669\) | −42.6823 | −1.65019 | ||||||||
\(670\) | −6.46024 | −0.249581 | ||||||||
\(671\) | −22.2904 | −0.860511 | ||||||||
\(672\) | 28.6457 | 1.10503 | ||||||||
\(673\) | −39.9817 | −1.54118 | −0.770591 | − | 0.637330i | \(-0.780039\pi\) | ||||
−0.770591 | + | 0.637330i | \(0.780039\pi\) | |||||||
\(674\) | 42.0930 | 1.62136 | ||||||||
\(675\) | 21.5339 | 0.828841 | ||||||||
\(676\) | 4.52309 | 0.173965 | ||||||||
\(677\) | −32.2859 | −1.24085 | −0.620424 | − | 0.784266i | \(-0.713040\pi\) | ||||
−0.620424 | + | 0.784266i | \(0.713040\pi\) | |||||||
\(678\) | 11.2062 | 0.430371 | ||||||||
\(679\) | 7.02114 | 0.269447 | ||||||||
\(680\) | −13.0947 | −0.502160 | ||||||||
\(681\) | −10.8070 | −0.414124 | ||||||||
\(682\) | −63.1181 | −2.41692 | ||||||||
\(683\) | 35.2089 | 1.34723 | 0.673616 | − | 0.739082i | \(-0.264740\pi\) | ||||
0.673616 | + | 0.739082i | \(0.264740\pi\) | |||||||
\(684\) | 6.88422 | 0.263225 | ||||||||
\(685\) | 6.71868 | 0.256708 | ||||||||
\(686\) | −41.1533 | −1.57124 | ||||||||
\(687\) | 0.996101 | 0.0380036 | ||||||||
\(688\) | −70.5283 | −2.68886 | ||||||||
\(689\) | −14.1988 | −0.540932 | ||||||||
\(690\) | −1.31513 | −0.0500663 | ||||||||
\(691\) | 32.7784 | 1.24695 | 0.623475 | − | 0.781843i | \(-0.285720\pi\) | ||||
0.623475 | + | 0.781843i | \(0.285720\pi\) | |||||||
\(692\) | −72.8839 | −2.77063 | ||||||||
\(693\) | 3.97551 | 0.151017 | ||||||||
\(694\) | 2.41630 | 0.0917213 | ||||||||
\(695\) | 17.5320 | 0.665026 | ||||||||
\(696\) | −93.6129 | −3.54839 | ||||||||
\(697\) | −0.0530826 | −0.00201065 | ||||||||
\(698\) | −64.8185 | −2.45342 | ||||||||
\(699\) | −8.65123 | −0.327220 | ||||||||
\(700\) | 51.9854 | 1.96486 | ||||||||
\(701\) | 18.6055 | 0.702721 | 0.351361 | − | 0.936240i | \(-0.385719\pi\) | ||||
0.351361 | + | 0.936240i | \(0.385719\pi\) | |||||||
\(702\) | 13.9186 | 0.525324 | ||||||||
\(703\) | −14.0798 | −0.531029 | ||||||||
\(704\) | 2.42166 | 0.0912697 | ||||||||
\(705\) | −7.06963 | −0.266258 | ||||||||
\(706\) | 29.8903 | 1.12494 | ||||||||
\(707\) | 31.0042 | 1.16603 | ||||||||
\(708\) | −50.2888 | −1.88997 | ||||||||
\(709\) | 6.90762 | 0.259421 | 0.129711 | − | 0.991552i | \(-0.458595\pi\) | ||||
0.129711 | + | 0.991552i | \(0.458595\pi\) | |||||||
\(710\) | 6.93683 | 0.260335 | ||||||||
\(711\) | 4.15651 | 0.155881 | ||||||||
\(712\) | −100.238 | −3.75657 | ||||||||
\(713\) | 1.91785 | 0.0718241 | ||||||||
\(714\) | 24.0265 | 0.899169 | ||||||||
\(715\) | 4.07121 | 0.152255 | ||||||||
\(716\) | −64.8559 | −2.42378 | ||||||||
\(717\) | −14.0630 | −0.525192 | ||||||||
\(718\) | 12.1589 | 0.453766 | ||||||||
\(719\) | −3.87798 | −0.144624 | −0.0723122 | − | 0.997382i | \(-0.523038\pi\) | ||||
−0.0723122 | + | 0.997382i | \(0.523038\pi\) | |||||||
\(720\) | −2.60927 | −0.0972419 | ||||||||
\(721\) | 17.7339 | 0.660445 | ||||||||
\(722\) | −1.53597 | −0.0571629 | ||||||||
\(723\) | −29.7785 | −1.10747 | ||||||||
\(724\) | 68.2986 | 2.53830 | ||||||||
\(725\) | −35.2207 | −1.30807 | ||||||||
\(726\) | −20.0089 | −0.742601 | ||||||||
\(727\) | 32.5422 | 1.20692 | 0.603462 | − | 0.797392i | \(-0.293788\pi\) | ||||
0.603462 | + | 0.797392i | \(0.293788\pi\) | |||||||
\(728\) | 18.7435 | 0.694682 | ||||||||
\(729\) | 29.3443 | 1.08682 | ||||||||
\(730\) | −6.09112 | −0.225443 | ||||||||
\(731\) | −18.8824 | −0.698393 | ||||||||
\(732\) | −41.3296 | −1.52759 | ||||||||
\(733\) | 11.9408 | 0.441043 | 0.220521 | − | 0.975382i | \(-0.429224\pi\) | ||||
0.220521 | + | 0.975382i | \(0.429224\pi\) | |||||||
\(734\) | −27.2628 | −1.00629 | ||||||||
\(735\) | 2.43713 | 0.0898949 | ||||||||
\(736\) | −1.86443 | −0.0687237 | ||||||||
\(737\) | 9.82076 | 0.361752 | ||||||||
\(738\) | −0.0234864 | −0.000864547 0 | ||||||||
\(739\) | −41.1678 | −1.51438 | −0.757191 | − | 0.653193i | \(-0.773429\pi\) | ||||
−0.757191 | + | 0.653193i | \(0.773429\pi\) | |||||||
\(740\) | 14.7295 | 0.541466 | ||||||||
\(741\) | −7.21565 | −0.265074 | ||||||||
\(742\) | −105.481 | −3.87231 | ||||||||
\(743\) | −9.84809 | −0.361291 | −0.180646 | − | 0.983548i | \(-0.557819\pi\) | ||||
−0.180646 | + | 0.983548i | \(0.557819\pi\) | |||||||
\(744\) | −65.2822 | −2.39336 | ||||||||
\(745\) | 12.0603 | 0.441856 | ||||||||
\(746\) | −45.2539 | −1.65686 | ||||||||
\(747\) | −3.45391 | −0.126372 | ||||||||
\(748\) | 35.6859 | 1.30481 | ||||||||
\(749\) | 21.2755 | 0.777391 | ||||||||
\(750\) | 38.1550 | 1.39322 | ||||||||
\(751\) | −5.66009 | −0.206540 | −0.103270 | − | 0.994653i | \(-0.532931\pi\) | ||||
−0.103270 | + | 0.994653i | \(0.532931\pi\) | |||||||
\(752\) | −31.3984 | −1.14498 | ||||||||
\(753\) | −8.35563 | −0.304496 | ||||||||
\(754\) | −22.7652 | −0.829060 | ||||||||
\(755\) | 6.83802 | 0.248861 | ||||||||
\(756\) | 71.6964 | 2.60757 | ||||||||
\(757\) | 45.5787 | 1.65659 | 0.828293 | − | 0.560295i | \(-0.189312\pi\) | ||||
0.828293 | + | 0.560295i | \(0.189312\pi\) | |||||||
\(758\) | 58.7386 | 2.13348 | ||||||||
\(759\) | 1.99925 | 0.0725681 | ||||||||
\(760\) | 29.2147 | 1.05973 | ||||||||
\(761\) | −18.5609 | −0.672832 | −0.336416 | − | 0.941714i | \(-0.609215\pi\) | ||||
−0.336416 | + | 0.941714i | \(0.609215\pi\) | |||||||
\(762\) | −81.7577 | −2.96177 | ||||||||
\(763\) | 19.4025 | 0.702417 | ||||||||
\(764\) | 5.16181 | 0.186748 | ||||||||
\(765\) | −0.698578 | −0.0252571 | ||||||||
\(766\) | 1.77949 | 0.0642955 | ||||||||
\(767\) | −6.82188 | −0.246324 | ||||||||
\(768\) | −45.8163 | −1.65325 | ||||||||
\(769\) | −18.2706 | −0.658854 | −0.329427 | − | 0.944181i | \(-0.606855\pi\) | ||||
−0.329427 | + | 0.944181i | \(0.606855\pi\) | |||||||
\(770\) | 30.2443 | 1.08993 | ||||||||
\(771\) | −4.45787 | −0.160546 | ||||||||
\(772\) | −13.2107 | −0.475464 | ||||||||
\(773\) | −39.8456 | −1.43315 | −0.716574 | − | 0.697511i | \(-0.754291\pi\) | ||||
−0.716574 | + | 0.697511i | \(0.754291\pi\) | |||||||
\(774\) | −8.35455 | −0.300298 | ||||||||
\(775\) | −24.5616 | −0.882280 | ||||||||
\(776\) | 15.5551 | 0.558396 | ||||||||
\(777\) | −15.0757 | −0.540838 | ||||||||
\(778\) | −6.23050 | −0.223374 | ||||||||
\(779\) | 0.118429 | 0.00424315 | ||||||||
\(780\) | 7.54861 | 0.270284 | ||||||||
\(781\) | −10.5453 | −0.377340 | ||||||||
\(782\) | −1.56378 | −0.0559207 | ||||||||
\(783\) | −48.5752 | −1.73594 | ||||||||
\(784\) | 10.8240 | 0.386573 | ||||||||
\(785\) | −21.8486 | −0.779811 | ||||||||
\(786\) | −30.0107 | −1.07044 | ||||||||
\(787\) | 5.40363 | 0.192619 | 0.0963093 | − | 0.995351i | \(-0.469296\pi\) | ||||
0.0963093 | + | 0.995351i | \(0.469296\pi\) | |||||||
\(788\) | −32.0463 | −1.14160 | ||||||||
\(789\) | 19.7502 | 0.703125 | ||||||||
\(790\) | 31.6213 | 1.12503 | ||||||||
\(791\) | 7.83056 | 0.278422 | ||||||||
\(792\) | 8.80761 | 0.312965 | ||||||||
\(793\) | −5.60653 | −0.199094 | ||||||||
\(794\) | 87.0710 | 3.09003 | ||||||||
\(795\) | −23.6965 | −0.840430 | ||||||||
\(796\) | −0.887147 | −0.0314441 | ||||||||
\(797\) | −19.3230 | −0.684455 | −0.342228 | − | 0.939617i | \(-0.611181\pi\) | ||||
−0.342228 | + | 0.939617i | \(0.611181\pi\) | |||||||
\(798\) | −53.6038 | −1.89755 | ||||||||
\(799\) | −8.40626 | −0.297392 | ||||||||
\(800\) | 23.8774 | 0.844195 | ||||||||
\(801\) | −5.34748 | −0.188944 | ||||||||
\(802\) | 77.2010 | 2.72606 | ||||||||
\(803\) | 9.25964 | 0.326766 | ||||||||
\(804\) | 18.2091 | 0.642186 | ||||||||
\(805\) | −0.918977 | −0.0323897 | ||||||||
\(806\) | −15.8756 | −0.559194 | ||||||||
\(807\) | 9.78131 | 0.344318 | ||||||||
\(808\) | 68.6887 | 2.41646 | ||||||||
\(809\) | 14.8754 | 0.522991 | 0.261495 | − | 0.965205i | \(-0.415784\pi\) | ||||
0.261495 | + | 0.965205i | \(0.415784\pi\) | |||||||
\(810\) | 20.5316 | 0.721408 | ||||||||
\(811\) | 47.0386 | 1.65175 | 0.825875 | − | 0.563853i | \(-0.190682\pi\) | ||||
0.825875 | + | 0.563853i | \(0.190682\pi\) | |||||||
\(812\) | −117.266 | −4.11524 | ||||||||
\(813\) | −7.08148 | −0.248358 | ||||||||
\(814\) | −32.2925 | −1.13185 | ||||||||
\(815\) | 3.26466 | 0.114356 | ||||||||
\(816\) | 23.9725 | 0.839206 | ||||||||
\(817\) | 42.1273 | 1.47385 | ||||||||
\(818\) | 25.2807 | 0.883920 | ||||||||
\(819\) | 0.999930 | 0.0349404 | ||||||||
\(820\) | −0.123894 | −0.00432655 | ||||||||
\(821\) | −28.9893 | −1.01173 | −0.505867 | − | 0.862612i | \(-0.668827\pi\) | ||||
−0.505867 | + | 0.862612i | \(0.668827\pi\) | |||||||
\(822\) | −27.3113 | −0.952592 | ||||||||
\(823\) | −1.09719 | −0.0382455 | −0.0191228 | − | 0.999817i | \(-0.506087\pi\) | ||||
−0.0191228 | + | 0.999817i | \(0.506087\pi\) | |||||||
\(824\) | 39.2889 | 1.36869 | ||||||||
\(825\) | −25.6041 | −0.891420 | ||||||||
\(826\) | −50.6785 | −1.76333 | ||||||||
\(827\) | 15.4497 | 0.537239 | 0.268620 | − | 0.963246i | \(-0.413433\pi\) | ||||
0.268620 | + | 0.963246i | \(0.413433\pi\) | |||||||
\(828\) | −0.479758 | −0.0166727 | ||||||||
\(829\) | 18.4367 | 0.640332 | 0.320166 | − | 0.947361i | \(-0.396261\pi\) | ||||
0.320166 | + | 0.947361i | \(0.396261\pi\) | |||||||
\(830\) | −26.2761 | −0.912058 | ||||||||
\(831\) | 1.01982 | 0.0353772 | ||||||||
\(832\) | 0.609101 | 0.0211168 | ||||||||
\(833\) | 2.89791 | 0.100407 | ||||||||
\(834\) | −71.2673 | −2.46778 | ||||||||
\(835\) | 3.97896 | 0.137698 | ||||||||
\(836\) | −79.6162 | −2.75359 | ||||||||
\(837\) | −33.8745 | −1.17088 | ||||||||
\(838\) | 28.1381 | 0.972013 | ||||||||
\(839\) | −10.7781 | −0.372102 | −0.186051 | − | 0.982540i | \(-0.559569\pi\) | ||||
−0.186051 | + | 0.982540i | \(0.559569\pi\) | |||||||
\(840\) | 31.2813 | 1.07931 | ||||||||
\(841\) | 50.4493 | 1.73963 | ||||||||
\(842\) | −88.3631 | −3.04519 | ||||||||
\(843\) | −7.65558 | −0.263672 | ||||||||
\(844\) | 105.732 | 3.63943 | ||||||||
\(845\) | 1.02400 | 0.0352267 | ||||||||
\(846\) | −3.71935 | −0.127874 | ||||||||
\(847\) | −13.9817 | −0.480415 | ||||||||
\(848\) | −105.244 | −3.61408 | ||||||||
\(849\) | −3.29169 | −0.112971 | ||||||||
\(850\) | 20.0271 | 0.686924 | ||||||||
\(851\) | 0.981213 | 0.0336356 | ||||||||
\(852\) | −19.5525 | −0.669857 | ||||||||
\(853\) | 53.0279 | 1.81564 | 0.907820 | − | 0.419361i | \(-0.137746\pi\) | ||||
0.907820 | + | 0.419361i | \(0.137746\pi\) | |||||||
\(854\) | −41.6499 | −1.42523 | ||||||||
\(855\) | 1.55855 | 0.0533012 | ||||||||
\(856\) | 47.1352 | 1.61105 | ||||||||
\(857\) | −46.8574 | −1.60062 | −0.800309 | − | 0.599587i | \(-0.795331\pi\) | ||||
−0.800309 | + | 0.599587i | \(0.795331\pi\) | |||||||
\(858\) | −16.5494 | −0.564987 | ||||||||
\(859\) | −48.4914 | −1.65450 | −0.827252 | − | 0.561831i | \(-0.810097\pi\) | ||||
−0.827252 | + | 0.561831i | \(0.810097\pi\) | |||||||
\(860\) | −44.0712 | −1.50282 | ||||||||
\(861\) | 0.126806 | 0.00432153 | ||||||||
\(862\) | 50.8929 | 1.73342 | ||||||||
\(863\) | −28.7922 | −0.980098 | −0.490049 | − | 0.871695i | \(-0.663021\pi\) | ||||
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(864\) | 32.9309 | 1.12033 | ||||||||
\(865\) | −16.5005 | −0.561034 | ||||||||
\(866\) | 11.8418 | 0.402402 | ||||||||
\(867\) | −21.2883 | −0.722990 | ||||||||
\(868\) | −81.7771 | −2.77570 | ||||||||
\(869\) | −48.0702 | −1.63067 | ||||||||
\(870\) | −37.9930 | −1.28808 | ||||||||
\(871\) | 2.47014 | 0.0836975 | ||||||||
\(872\) | 42.9855 | 1.45567 | ||||||||
\(873\) | 0.829833 | 0.0280856 | ||||||||
\(874\) | 3.48884 | 0.118012 | ||||||||
\(875\) | 26.6616 | 0.901325 | ||||||||
\(876\) | 17.1687 | 0.580077 | ||||||||
\(877\) | 7.73754 | 0.261278 | 0.130639 | − | 0.991430i | \(-0.458297\pi\) | ||||
0.130639 | + | 0.991430i | \(0.458297\pi\) | |||||||
\(878\) | −37.0774 | −1.25130 | ||||||||
\(879\) | −48.9013 | −1.64940 | ||||||||
\(880\) | 30.1763 | 1.01724 | ||||||||
\(881\) | −5.25275 | −0.176970 | −0.0884849 | − | 0.996078i | \(-0.528203\pi\) | ||||
−0.0884849 | + | 0.996078i | \(0.528203\pi\) | |||||||
\(882\) | 1.28218 | 0.0431733 | ||||||||
\(883\) | −50.0178 | −1.68323 | −0.841616 | − | 0.540077i | \(-0.818395\pi\) | ||||
−0.841616 | + | 0.540077i | \(0.818395\pi\) | |||||||
\(884\) | 8.97580 | 0.301889 | ||||||||
\(885\) | −11.3851 | −0.382706 | ||||||||
\(886\) | 23.9797 | 0.805614 | ||||||||
\(887\) | 17.6175 | 0.591539 | 0.295770 | − | 0.955259i | \(-0.404424\pi\) | ||||
0.295770 | + | 0.955259i | \(0.404424\pi\) | |||||||
\(888\) | −33.3997 | −1.12082 | ||||||||
\(889\) | −57.1298 | −1.91607 | ||||||||
\(890\) | −40.6817 | −1.36365 | ||||||||
\(891\) | −31.2119 | −1.04564 | ||||||||
\(892\) | −118.454 | −3.96614 | ||||||||
\(893\) | 18.7546 | 0.627599 | ||||||||
\(894\) | −49.0251 | −1.63964 | ||||||||
\(895\) | −14.6830 | −0.490798 | ||||||||
\(896\) | −30.6277 | −1.02320 | ||||||||
\(897\) | 0.502856 | 0.0167899 | ||||||||
\(898\) | 79.3795 | 2.64893 | ||||||||
\(899\) | 55.4050 | 1.84786 | ||||||||
\(900\) | 6.14419 | 0.204806 | ||||||||
\(901\) | −28.1767 | −0.938704 | ||||||||
\(902\) | 0.271621 | 0.00904400 | ||||||||
\(903\) | 45.1072 | 1.50107 | ||||||||
\(904\) | 17.3483 | 0.576997 | ||||||||
\(905\) | 15.4624 | 0.513988 | ||||||||
\(906\) | −27.7964 | −0.923475 | ||||||||
\(907\) | 9.67109 | 0.321123 | 0.160562 | − | 0.987026i | \(-0.448669\pi\) | ||||
0.160562 | + | 0.987026i | \(0.448669\pi\) | |||||||
\(908\) | −29.9921 | −0.995322 | ||||||||
\(909\) | 3.66440 | 0.121541 | ||||||||
\(910\) | 7.60711 | 0.252173 | ||||||||
\(911\) | 14.7174 | 0.487608 | 0.243804 | − | 0.969825i | \(-0.421605\pi\) | ||||
0.243804 | + | 0.969825i | \(0.421605\pi\) | |||||||
\(912\) | −53.4834 | −1.77101 | ||||||||
\(913\) | 39.9446 | 1.32197 | ||||||||
\(914\) | −35.9787 | −1.19007 | ||||||||
\(915\) | −9.35678 | −0.309326 | ||||||||
\(916\) | 2.76443 | 0.0913394 | ||||||||
\(917\) | −20.9706 | −0.692509 | ||||||||
\(918\) | 27.6207 | 0.911618 | ||||||||
\(919\) | −13.7418 | −0.453302 | −0.226651 | − | 0.973976i | \(-0.572778\pi\) | ||||
−0.226651 | + | 0.973976i | \(0.572778\pi\) | |||||||
\(920\) | −2.03596 | −0.0671237 | ||||||||
\(921\) | −2.46285 | −0.0811538 | ||||||||
\(922\) | −94.6049 | −3.11565 | ||||||||
\(923\) | −2.65237 | −0.0873039 | ||||||||
\(924\) | −85.2479 | −2.80445 | ||||||||
\(925\) | −12.5663 | −0.413176 | ||||||||
\(926\) | −56.2370 | −1.84806 | ||||||||
\(927\) | 2.09598 | 0.0688411 | ||||||||
\(928\) | −53.8616 | −1.76809 | ||||||||
\(929\) | −25.3935 | −0.833133 | −0.416567 | − | 0.909105i | \(-0.636767\pi\) | ||||
−0.416567 | + | 0.909105i | \(0.636767\pi\) | |||||||
\(930\) | −26.4949 | −0.868803 | ||||||||
\(931\) | −6.46532 | −0.211892 | ||||||||
\(932\) | −24.0094 | −0.786453 | ||||||||
\(933\) | −35.1135 | −1.14956 | ||||||||
\(934\) | −20.6686 | −0.676298 | ||||||||
\(935\) | 8.07908 | 0.264214 | ||||||||
\(936\) | 2.21531 | 0.0724097 | ||||||||
\(937\) | 40.5030 | 1.32317 | 0.661587 | − | 0.749868i | \(-0.269883\pi\) | ||||
0.661587 | + | 0.749868i | \(0.269883\pi\) | |||||||
\(938\) | 18.3502 | 0.599156 | ||||||||
\(939\) | −23.6751 | −0.772607 | ||||||||
\(940\) | −19.6200 | −0.639934 | ||||||||
\(941\) | 18.2501 | 0.594935 | 0.297468 | − | 0.954732i | \(-0.403858\pi\) | ||||
0.297468 | + | 0.954732i | \(0.403858\pi\) | |||||||
\(942\) | 88.8143 | 2.89373 | ||||||||
\(943\) | −0.00825325 | −0.000268763 0 | ||||||||
\(944\) | −50.5647 | −1.64574 | ||||||||
\(945\) | 16.2317 | 0.528016 | ||||||||
\(946\) | 96.6206 | 3.14141 | ||||||||
\(947\) | −32.2871 | −1.04919 | −0.524594 | − | 0.851352i | \(-0.675783\pi\) | ||||
−0.524594 | + | 0.851352i | \(0.675783\pi\) | |||||||
\(948\) | −89.1291 | −2.89478 | ||||||||
\(949\) | 2.32901 | 0.0756028 | ||||||||
\(950\) | −44.6811 | −1.44965 | ||||||||
\(951\) | −23.6351 | −0.766420 | ||||||||
\(952\) | 37.1955 | 1.20551 | ||||||||
\(953\) | 9.14062 | 0.296094 | 0.148047 | − | 0.988980i | \(-0.452701\pi\) | ||||
0.148047 | + | 0.988980i | \(0.452701\pi\) | |||||||
\(954\) | −12.4668 | −0.403628 | ||||||||
\(955\) | 1.16860 | 0.0378152 | ||||||||
\(956\) | −39.0283 | −1.26227 | ||||||||
\(957\) | 57.7565 | 1.86700 | ||||||||
\(958\) | −41.3194 | −1.33497 | ||||||||
\(959\) | −19.0843 | −0.616266 | ||||||||
\(960\) | 1.01653 | 0.0328085 | ||||||||
\(961\) | 7.63736 | 0.246366 | ||||||||
\(962\) | −8.12229 | −0.261873 | ||||||||
\(963\) | 2.51457 | 0.0810308 | ||||||||
\(964\) | −82.6428 | −2.66174 | ||||||||
\(965\) | −2.99083 | −0.0962783 | ||||||||
\(966\) | 3.73562 | 0.120192 | ||||||||
\(967\) | 57.2053 | 1.83960 | 0.919800 | − | 0.392387i | \(-0.128351\pi\) | ||||
0.919800 | + | 0.392387i | \(0.128351\pi\) | |||||||
\(968\) | −30.9759 | −0.995603 | ||||||||
\(969\) | −14.3190 | −0.459994 | ||||||||
\(970\) | 6.31308 | 0.202701 | ||||||||
\(971\) | −5.65710 | −0.181545 | −0.0907725 | − | 0.995872i | \(-0.528934\pi\) | ||||
−0.0907725 | + | 0.995872i | \(0.528934\pi\) | |||||||
\(972\) | 16.0765 | 0.515654 | ||||||||
\(973\) | −49.7994 | −1.59650 | ||||||||
\(974\) | 50.2369 | 1.60969 | ||||||||
\(975\) | −6.44000 | −0.206245 | ||||||||
\(976\) | −41.5563 | −1.33019 | ||||||||
\(977\) | 21.4501 | 0.686248 | 0.343124 | − | 0.939290i | \(-0.388515\pi\) | ||||
0.343124 | + | 0.939290i | \(0.388515\pi\) | |||||||
\(978\) | −13.2708 | −0.424354 | ||||||||
\(979\) | 61.8438 | 1.97653 | ||||||||
\(980\) | 6.76365 | 0.216057 | ||||||||
\(981\) | 2.29319 | 0.0732160 | ||||||||
\(982\) | 73.3892 | 2.34194 | ||||||||
\(983\) | 34.6664 | 1.10569 | 0.552843 | − | 0.833285i | \(-0.313543\pi\) | ||||
0.552843 | + | 0.833285i | \(0.313543\pi\) | |||||||
\(984\) | 0.280934 | 0.00895586 | ||||||||
\(985\) | −7.25509 | −0.231166 | ||||||||
\(986\) | −45.1762 | −1.43870 | ||||||||
\(987\) | 20.0812 | 0.639192 | ||||||||
\(988\) | −20.0253 | −0.637089 | ||||||||
\(989\) | −2.93583 | −0.0933540 | ||||||||
\(990\) | 3.57459 | 0.113608 | ||||||||
\(991\) | 10.4081 | 0.330626 | 0.165313 | − | 0.986241i | \(-0.447137\pi\) | ||||
0.165313 | + | 0.986241i | \(0.447137\pi\) | |||||||
\(992\) | −37.5611 | −1.19256 | ||||||||
\(993\) | 43.5557 | 1.38220 | ||||||||
\(994\) | −19.7040 | −0.624973 | ||||||||
\(995\) | −0.200845 | −0.00636721 | ||||||||
\(996\) | 74.0631 | 2.34678 | ||||||||
\(997\) | −3.70648 | −0.117385 | −0.0586927 | − | 0.998276i | \(-0.518693\pi\) | ||||
−0.0586927 | + | 0.998276i | \(0.518693\pi\) | |||||||
\(998\) | −27.9902 | −0.886013 | ||||||||
\(999\) | −17.3309 | −0.548326 |
(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 | 8047.2.a.b.1.9 | ✓ | 142 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.b.1.9 | ✓ | 142 | 1.1 | even | 1 | trivial |