Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(1\) |
Dimension: | \(83\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25188 | −1.59232 | −0.796160 | − | 0.605086i | \(-0.793139\pi\) | ||||
−0.796160 | + | 0.605086i | \(0.793139\pi\) | |||||||
\(3\) | −3.15195 | −1.81978 | −0.909891 | − | 0.414848i | \(-0.863835\pi\) | ||||
−0.909891 | + | 0.414848i | \(0.863835\pi\) | |||||||
\(4\) | 3.07097 | 1.53549 | ||||||||
\(5\) | 1.48598 | 0.664550 | 0.332275 | − | 0.943183i | \(-0.392184\pi\) | ||||
0.332275 | + | 0.943183i | \(0.392184\pi\) | |||||||
\(6\) | 7.09783 | 2.89768 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.41170 | −0.852665 | ||||||||
\(9\) | 6.93481 | 2.31160 | ||||||||
\(10\) | −3.34625 | −1.05818 | ||||||||
\(11\) | −1.80720 | −0.544892 | −0.272446 | − | 0.962171i | \(-0.587833\pi\) | ||||
−0.272446 | + | 0.962171i | \(0.587833\pi\) | |||||||
\(12\) | −9.67956 | −2.79425 | ||||||||
\(13\) | 0.118205 | 0.0327841 | 0.0163920 | − | 0.999866i | \(-0.494782\pi\) | ||||
0.0163920 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(14\) | −2.25188 | −0.601841 | ||||||||
\(15\) | −4.68374 | −1.20934 | ||||||||
\(16\) | −0.711080 | −0.177770 | ||||||||
\(17\) | 4.60783 | 1.11756 | 0.558781 | − | 0.829315i | \(-0.311269\pi\) | ||||
0.558781 | + | 0.829315i | \(0.311269\pi\) | |||||||
\(18\) | −15.6164 | −3.68081 | ||||||||
\(19\) | 2.60432 | 0.597471 | 0.298735 | − | 0.954336i | \(-0.403435\pi\) | ||||
0.298735 | + | 0.954336i | \(0.403435\pi\) | |||||||
\(20\) | 4.56340 | 1.02041 | ||||||||
\(21\) | −3.15195 | −0.687813 | ||||||||
\(22\) | 4.06961 | 0.867643 | ||||||||
\(23\) | 4.16764 | 0.869013 | 0.434506 | − | 0.900669i | \(-0.356923\pi\) | ||||
0.434506 | + | 0.900669i | \(0.356923\pi\) | |||||||
\(24\) | 7.60156 | 1.55166 | ||||||||
\(25\) | −2.79187 | −0.558373 | ||||||||
\(26\) | −0.266183 | −0.0522028 | ||||||||
\(27\) | −12.4023 | −2.38683 | ||||||||
\(28\) | 3.07097 | 0.580359 | ||||||||
\(29\) | 1.70849 | 0.317258 | 0.158629 | − | 0.987338i | \(-0.449293\pi\) | ||||
0.158629 | + | 0.987338i | \(0.449293\pi\) | |||||||
\(30\) | 10.5472 | 1.92565 | ||||||||
\(31\) | −2.00013 | −0.359235 | −0.179617 | − | 0.983737i | \(-0.557486\pi\) | ||||
−0.179617 | + | 0.983737i | \(0.557486\pi\) | |||||||
\(32\) | 6.42467 | 1.13573 | ||||||||
\(33\) | 5.69622 | 0.991584 | ||||||||
\(34\) | −10.3763 | −1.77952 | ||||||||
\(35\) | 1.48598 | 0.251176 | ||||||||
\(36\) | 21.2966 | 3.54943 | ||||||||
\(37\) | 10.7135 | 1.76129 | 0.880646 | − | 0.473775i | \(-0.157109\pi\) | ||||
0.880646 | + | 0.473775i | \(0.157109\pi\) | |||||||
\(38\) | −5.86461 | −0.951365 | ||||||||
\(39\) | −0.372576 | −0.0596599 | ||||||||
\(40\) | −3.58373 | −0.566638 | ||||||||
\(41\) | −0.734404 | −0.114695 | −0.0573473 | − | 0.998354i | \(-0.518264\pi\) | ||||
−0.0573473 | + | 0.998354i | \(0.518264\pi\) | |||||||
\(42\) | 7.09783 | 1.09522 | ||||||||
\(43\) | −4.62001 | −0.704545 | −0.352272 | − | 0.935897i | \(-0.614591\pi\) | ||||
−0.352272 | + | 0.935897i | \(0.614591\pi\) | |||||||
\(44\) | −5.54987 | −0.836674 | ||||||||
\(45\) | 10.3050 | 1.53618 | ||||||||
\(46\) | −9.38503 | −1.38375 | ||||||||
\(47\) | −9.25577 | −1.35009 | −0.675047 | − | 0.737775i | \(-0.735877\pi\) | ||||
−0.675047 | + | 0.737775i | \(0.735877\pi\) | |||||||
\(48\) | 2.24129 | 0.323502 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.28696 | 0.889110 | ||||||||
\(51\) | −14.5237 | −2.03372 | ||||||||
\(52\) | 0.363003 | 0.0503395 | ||||||||
\(53\) | −6.59285 | −0.905598 | −0.452799 | − | 0.891613i | \(-0.649574\pi\) | ||||
−0.452799 | + | 0.891613i | \(0.649574\pi\) | |||||||
\(54\) | 27.9286 | 3.80060 | ||||||||
\(55\) | −2.68546 | −0.362108 | ||||||||
\(56\) | −2.41170 | −0.322277 | ||||||||
\(57\) | −8.20868 | −1.08727 | ||||||||
\(58\) | −3.84731 | −0.505177 | ||||||||
\(59\) | 3.63595 | 0.473360 | 0.236680 | − | 0.971588i | \(-0.423941\pi\) | ||||
0.236680 | + | 0.971588i | \(0.423941\pi\) | |||||||
\(60\) | −14.3836 | −1.85692 | ||||||||
\(61\) | 6.74094 | 0.863089 | 0.431545 | − | 0.902092i | \(-0.357969\pi\) | ||||
0.431545 | + | 0.902092i | \(0.357969\pi\) | |||||||
\(62\) | 4.50406 | 0.572017 | ||||||||
\(63\) | 6.93481 | 0.873704 | ||||||||
\(64\) | −13.0454 | −1.63068 | ||||||||
\(65\) | 0.175650 | 0.0217867 | ||||||||
\(66\) | −12.8272 | −1.57892 | ||||||||
\(67\) | 3.40992 | 0.416588 | 0.208294 | − | 0.978066i | \(-0.433209\pi\) | ||||
0.208294 | + | 0.978066i | \(0.433209\pi\) | |||||||
\(68\) | 14.1505 | 1.71600 | ||||||||
\(69\) | −13.1362 | −1.58141 | ||||||||
\(70\) | −3.34625 | −0.399953 | ||||||||
\(71\) | −11.0355 | −1.30968 | −0.654839 | − | 0.755769i | \(-0.727263\pi\) | ||||
−0.654839 | + | 0.755769i | \(0.727263\pi\) | |||||||
\(72\) | −16.7247 | −1.97102 | ||||||||
\(73\) | −10.0393 | −1.17501 | −0.587506 | − | 0.809219i | \(-0.699890\pi\) | ||||
−0.587506 | + | 0.809219i | \(0.699890\pi\) | |||||||
\(74\) | −24.1256 | −2.80454 | ||||||||
\(75\) | 8.79984 | 1.01612 | ||||||||
\(76\) | 7.99778 | 0.917408 | ||||||||
\(77\) | −1.80720 | −0.205950 | ||||||||
\(78\) | 0.838997 | 0.0949977 | ||||||||
\(79\) | −12.9837 | −1.46078 | −0.730392 | − | 0.683028i | \(-0.760663\pi\) | ||||
−0.730392 | + | 0.683028i | \(0.760663\pi\) | |||||||
\(80\) | −1.05665 | −0.118137 | ||||||||
\(81\) | 18.2872 | 2.03191 | ||||||||
\(82\) | 1.65379 | 0.182631 | ||||||||
\(83\) | −13.0562 | −1.43311 | −0.716554 | − | 0.697532i | \(-0.754282\pi\) | ||||
−0.716554 | + | 0.697532i | \(0.754282\pi\) | |||||||
\(84\) | −9.67956 | −1.05613 | ||||||||
\(85\) | 6.84714 | 0.742676 | ||||||||
\(86\) | 10.4037 | 1.12186 | ||||||||
\(87\) | −5.38508 | −0.577341 | ||||||||
\(88\) | 4.35843 | 0.464610 | ||||||||
\(89\) | −9.51537 | −1.00863 | −0.504313 | − | 0.863521i | \(-0.668254\pi\) | ||||
−0.504313 | + | 0.863521i | \(0.668254\pi\) | |||||||
\(90\) | −23.2056 | −2.44608 | ||||||||
\(91\) | 0.118205 | 0.0123912 | ||||||||
\(92\) | 12.7987 | 1.33436 | ||||||||
\(93\) | 6.30433 | 0.653728 | ||||||||
\(94\) | 20.8429 | 2.14978 | ||||||||
\(95\) | 3.86996 | 0.397049 | ||||||||
\(96\) | −20.2502 | −2.06678 | ||||||||
\(97\) | 3.63825 | 0.369408 | 0.184704 | − | 0.982794i | \(-0.440867\pi\) | ||||
0.184704 | + | 0.982794i | \(0.440867\pi\) | |||||||
\(98\) | −2.25188 | −0.227474 | ||||||||
\(99\) | −12.5326 | −1.25957 | ||||||||
\(100\) | −8.57374 | −0.857374 | ||||||||
\(101\) | −8.44168 | −0.839979 | −0.419989 | − | 0.907529i | \(-0.637966\pi\) | ||||
−0.419989 | + | 0.907529i | \(0.637966\pi\) | |||||||
\(102\) | 32.7056 | 3.23833 | ||||||||
\(103\) | 3.10717 | 0.306159 | 0.153079 | − | 0.988214i | \(-0.451081\pi\) | ||||
0.153079 | + | 0.988214i | \(0.451081\pi\) | |||||||
\(104\) | −0.285074 | −0.0279538 | ||||||||
\(105\) | −4.68374 | −0.457086 | ||||||||
\(106\) | 14.8463 | 1.44200 | ||||||||
\(107\) | −14.8324 | −1.43390 | −0.716950 | − | 0.697125i | \(-0.754462\pi\) | ||||
−0.716950 | + | 0.697125i | \(0.754462\pi\) | |||||||
\(108\) | −38.0872 | −3.66494 | ||||||||
\(109\) | −0.795075 | −0.0761544 | −0.0380772 | − | 0.999275i | \(-0.512123\pi\) | ||||
−0.0380772 | + | 0.999275i | \(0.512123\pi\) | |||||||
\(110\) | 6.04735 | 0.576592 | ||||||||
\(111\) | −33.7685 | −3.20517 | ||||||||
\(112\) | −0.711080 | −0.0671907 | ||||||||
\(113\) | 9.71076 | 0.913512 | 0.456756 | − | 0.889592i | \(-0.349011\pi\) | ||||
0.456756 | + | 0.889592i | \(0.349011\pi\) | |||||||
\(114\) | 18.4850 | 1.73128 | ||||||||
\(115\) | 6.19302 | 0.577502 | ||||||||
\(116\) | 5.24672 | 0.487146 | ||||||||
\(117\) | 0.819728 | 0.0757838 | ||||||||
\(118\) | −8.18773 | −0.753742 | ||||||||
\(119\) | 4.60783 | 0.422399 | ||||||||
\(120\) | 11.2958 | 1.03116 | ||||||||
\(121\) | −7.73402 | −0.703093 | ||||||||
\(122\) | −15.1798 | −1.37432 | ||||||||
\(123\) | 2.31481 | 0.208719 | ||||||||
\(124\) | −6.14235 | −0.551600 | ||||||||
\(125\) | −11.5785 | −1.03562 | ||||||||
\(126\) | −15.6164 | −1.39122 | ||||||||
\(127\) | −11.0562 | −0.981078 | −0.490539 | − | 0.871419i | \(-0.663200\pi\) | ||||
−0.490539 | + | 0.871419i | \(0.663200\pi\) | |||||||
\(128\) | 16.5274 | 1.46083 | ||||||||
\(129\) | 14.5621 | 1.28212 | ||||||||
\(130\) | −0.395542 | −0.0346914 | ||||||||
\(131\) | 19.7556 | 1.72605 | 0.863027 | − | 0.505157i | \(-0.168565\pi\) | ||||
0.863027 | + | 0.505157i | \(0.168565\pi\) | |||||||
\(132\) | 17.4929 | 1.52256 | ||||||||
\(133\) | 2.60432 | 0.225823 | ||||||||
\(134\) | −7.67873 | −0.663341 | ||||||||
\(135\) | −18.4296 | −1.58617 | ||||||||
\(136\) | −11.1127 | −0.952906 | ||||||||
\(137\) | 3.67314 | 0.313817 | 0.156909 | − | 0.987613i | \(-0.449847\pi\) | ||||
0.156909 | + | 0.987613i | \(0.449847\pi\) | |||||||
\(138\) | 29.5812 | 2.51812 | ||||||||
\(139\) | −19.6361 | −1.66551 | −0.832757 | − | 0.553638i | \(-0.813239\pi\) | ||||
−0.832757 | + | 0.553638i | \(0.813239\pi\) | |||||||
\(140\) | 4.56340 | 0.385677 | ||||||||
\(141\) | 29.1738 | 2.45687 | ||||||||
\(142\) | 24.8507 | 2.08543 | ||||||||
\(143\) | −0.213620 | −0.0178638 | ||||||||
\(144\) | −4.93120 | −0.410934 | ||||||||
\(145\) | 2.53878 | 0.210834 | ||||||||
\(146\) | 22.6073 | 1.87100 | ||||||||
\(147\) | −3.15195 | −0.259969 | ||||||||
\(148\) | 32.9009 | 2.70444 | ||||||||
\(149\) | −14.9750 | −1.22680 | −0.613401 | − | 0.789772i | \(-0.710199\pi\) | ||||
−0.613401 | + | 0.789772i | \(0.710199\pi\) | |||||||
\(150\) | −19.8162 | −1.61799 | ||||||||
\(151\) | −6.58328 | −0.535740 | −0.267870 | − | 0.963455i | \(-0.586320\pi\) | ||||
−0.267870 | + | 0.963455i | \(0.586320\pi\) | |||||||
\(152\) | −6.28083 | −0.509442 | ||||||||
\(153\) | 31.9544 | 2.58336 | ||||||||
\(154\) | 4.06961 | 0.327938 | ||||||||
\(155\) | −2.97216 | −0.238729 | ||||||||
\(156\) | −1.14417 | −0.0916069 | ||||||||
\(157\) | −1.59429 | −0.127238 | −0.0636191 | − | 0.997974i | \(-0.520264\pi\) | ||||
−0.0636191 | + | 0.997974i | \(0.520264\pi\) | |||||||
\(158\) | 29.2378 | 2.32604 | ||||||||
\(159\) | 20.7804 | 1.64799 | ||||||||
\(160\) | 9.54692 | 0.754750 | ||||||||
\(161\) | 4.16764 | 0.328456 | ||||||||
\(162\) | −41.1805 | −3.23545 | ||||||||
\(163\) | 3.40652 | 0.266819 | 0.133410 | − | 0.991061i | \(-0.457407\pi\) | ||||
0.133410 | + | 0.991061i | \(0.457407\pi\) | |||||||
\(164\) | −2.25533 | −0.176112 | ||||||||
\(165\) | 8.46446 | 0.658957 | ||||||||
\(166\) | 29.4011 | 2.28197 | ||||||||
\(167\) | 24.0584 | 1.86170 | 0.930849 | − | 0.365404i | \(-0.119069\pi\) | ||||
0.930849 | + | 0.365404i | \(0.119069\pi\) | |||||||
\(168\) | 7.60156 | 0.586473 | ||||||||
\(169\) | −12.9860 | −0.998925 | ||||||||
\(170\) | −15.4189 | −1.18258 | ||||||||
\(171\) | 18.0604 | 1.38112 | ||||||||
\(172\) | −14.1879 | −1.08182 | ||||||||
\(173\) | 22.3753 | 1.70116 | 0.850581 | − | 0.525845i | \(-0.176251\pi\) | ||||
0.850581 | + | 0.525845i | \(0.176251\pi\) | |||||||
\(174\) | 12.1266 | 0.919312 | ||||||||
\(175\) | −2.79187 | −0.211045 | ||||||||
\(176\) | 1.28506 | 0.0968654 | ||||||||
\(177\) | −11.4603 | −0.861412 | ||||||||
\(178\) | 21.4275 | 1.60606 | ||||||||
\(179\) | 13.7150 | 1.02511 | 0.512553 | − | 0.858656i | \(-0.328700\pi\) | ||||
0.512553 | + | 0.858656i | \(0.328700\pi\) | |||||||
\(180\) | 31.6463 | 2.35878 | ||||||||
\(181\) | −1.89955 | −0.141192 | −0.0705962 | − | 0.997505i | \(-0.522490\pi\) | ||||
−0.0705962 | + | 0.997505i | \(0.522490\pi\) | |||||||
\(182\) | −0.266183 | −0.0197308 | ||||||||
\(183\) | −21.2471 | −1.57063 | ||||||||
\(184\) | −10.0511 | −0.740976 | ||||||||
\(185\) | 15.9201 | 1.17047 | ||||||||
\(186\) | −14.1966 | −1.04095 | ||||||||
\(187\) | −8.32728 | −0.608951 | ||||||||
\(188\) | −28.4242 | −2.07305 | ||||||||
\(189\) | −12.4023 | −0.902137 | ||||||||
\(190\) | −8.71468 | −0.632230 | ||||||||
\(191\) | 3.58967 | 0.259739 | 0.129870 | − | 0.991531i | \(-0.458544\pi\) | ||||
0.129870 | + | 0.991531i | \(0.458544\pi\) | |||||||
\(192\) | 41.1186 | 2.96748 | ||||||||
\(193\) | 7.55714 | 0.543975 | 0.271987 | − | 0.962301i | \(-0.412319\pi\) | ||||
0.271987 | + | 0.962301i | \(0.412319\pi\) | |||||||
\(194\) | −8.19290 | −0.588216 | ||||||||
\(195\) | −0.553640 | −0.0396470 | ||||||||
\(196\) | 3.07097 | 0.219355 | ||||||||
\(197\) | −4.54289 | −0.323667 | −0.161834 | − | 0.986818i | \(-0.551741\pi\) | ||||
−0.161834 | + | 0.986818i | \(0.551741\pi\) | |||||||
\(198\) | 28.2219 | 2.00565 | ||||||||
\(199\) | −23.8856 | −1.69321 | −0.846603 | − | 0.532225i | \(-0.821356\pi\) | ||||
−0.846603 | + | 0.532225i | \(0.821356\pi\) | |||||||
\(200\) | 6.73315 | 0.476105 | ||||||||
\(201\) | −10.7479 | −0.758098 | ||||||||
\(202\) | 19.0097 | 1.33752 | ||||||||
\(203\) | 1.70849 | 0.119912 | ||||||||
\(204\) | −44.6018 | −3.12275 | ||||||||
\(205\) | −1.09131 | −0.0762203 | ||||||||
\(206\) | −6.99698 | −0.487503 | ||||||||
\(207\) | 28.9018 | 2.00881 | ||||||||
\(208\) | −0.0840530 | −0.00582803 | ||||||||
\(209\) | −4.70652 | −0.325557 | ||||||||
\(210\) | 10.5472 | 0.727827 | ||||||||
\(211\) | −18.8760 | −1.29948 | −0.649738 | − | 0.760158i | \(-0.725121\pi\) | ||||
−0.649738 | + | 0.760158i | \(0.725121\pi\) | |||||||
\(212\) | −20.2465 | −1.39053 | ||||||||
\(213\) | 34.7835 | 2.38333 | ||||||||
\(214\) | 33.4008 | 2.28323 | ||||||||
\(215\) | −6.86524 | −0.468205 | ||||||||
\(216\) | 29.9107 | 2.03517 | ||||||||
\(217\) | −2.00013 | −0.135778 | ||||||||
\(218\) | 1.79042 | 0.121262 | ||||||||
\(219\) | 31.6435 | 2.13827 | ||||||||
\(220\) | −8.24698 | −0.556011 | ||||||||
\(221\) | 0.544667 | 0.0366383 | ||||||||
\(222\) | 76.0427 | 5.10365 | ||||||||
\(223\) | 12.8415 | 0.859929 | 0.429965 | − | 0.902846i | \(-0.358526\pi\) | ||||
0.429965 | + | 0.902846i | \(0.358526\pi\) | |||||||
\(224\) | 6.42467 | 0.429266 | ||||||||
\(225\) | −19.3611 | −1.29074 | ||||||||
\(226\) | −21.8675 | −1.45460 | ||||||||
\(227\) | 22.2024 | 1.47362 | 0.736812 | − | 0.676097i | \(-0.236330\pi\) | ||||
0.736812 | + | 0.676097i | \(0.236330\pi\) | |||||||
\(228\) | −25.2086 | −1.66948 | ||||||||
\(229\) | −22.1015 | −1.46051 | −0.730255 | − | 0.683175i | \(-0.760599\pi\) | ||||
−0.730255 | + | 0.683175i | \(0.760599\pi\) | |||||||
\(230\) | −13.9459 | −0.919569 | ||||||||
\(231\) | 5.69622 | 0.374784 | ||||||||
\(232\) | −4.12036 | −0.270515 | ||||||||
\(233\) | 6.53757 | 0.428290 | 0.214145 | − | 0.976802i | \(-0.431303\pi\) | ||||
0.214145 | + | 0.976802i | \(0.431303\pi\) | |||||||
\(234\) | −1.84593 | −0.120672 | ||||||||
\(235\) | −13.7539 | −0.897204 | ||||||||
\(236\) | 11.1659 | 0.726838 | ||||||||
\(237\) | 40.9241 | 2.65831 | ||||||||
\(238\) | −10.3763 | −0.672595 | ||||||||
\(239\) | −8.06523 | −0.521696 | −0.260848 | − | 0.965380i | \(-0.584002\pi\) | ||||
−0.260848 | + | 0.965380i | \(0.584002\pi\) | |||||||
\(240\) | 3.33051 | 0.214983 | ||||||||
\(241\) | 25.2744 | 1.62807 | 0.814035 | − | 0.580816i | \(-0.197266\pi\) | ||||
0.814035 | + | 0.580816i | \(0.197266\pi\) | |||||||
\(242\) | 17.4161 | 1.11955 | ||||||||
\(243\) | −20.4333 | −1.31079 | ||||||||
\(244\) | 20.7012 | 1.32526 | ||||||||
\(245\) | 1.48598 | 0.0949357 | ||||||||
\(246\) | −5.21267 | −0.332348 | ||||||||
\(247\) | 0.307842 | 0.0195875 | ||||||||
\(248\) | 4.82372 | 0.306307 | ||||||||
\(249\) | 41.1526 | 2.60794 | ||||||||
\(250\) | 26.0735 | 1.64903 | ||||||||
\(251\) | 4.42774 | 0.279476 | 0.139738 | − | 0.990188i | \(-0.455374\pi\) | ||||
0.139738 | + | 0.990188i | \(0.455374\pi\) | |||||||
\(252\) | 21.2966 | 1.34156 | ||||||||
\(253\) | −7.53176 | −0.473518 | ||||||||
\(254\) | 24.8972 | 1.56219 | ||||||||
\(255\) | −21.5819 | −1.35151 | ||||||||
\(256\) | −11.1270 | −0.695435 | ||||||||
\(257\) | −9.32220 | −0.581503 | −0.290752 | − | 0.956799i | \(-0.593905\pi\) | ||||
−0.290752 | + | 0.956799i | \(0.593905\pi\) | |||||||
\(258\) | −32.7920 | −2.04154 | ||||||||
\(259\) | 10.7135 | 0.665706 | ||||||||
\(260\) | 0.539415 | 0.0334531 | ||||||||
\(261\) | 11.8480 | 0.733376 | ||||||||
\(262\) | −44.4873 | −2.74843 | ||||||||
\(263\) | 26.5234 | 1.63550 | 0.817751 | − | 0.575572i | \(-0.195221\pi\) | ||||
0.817751 | + | 0.575572i | \(0.195221\pi\) | |||||||
\(264\) | −13.7376 | −0.845489 | ||||||||
\(265\) | −9.79684 | −0.601815 | ||||||||
\(266\) | −5.86461 | −0.359582 | ||||||||
\(267\) | 29.9920 | 1.83548 | ||||||||
\(268\) | 10.4718 | 0.639664 | ||||||||
\(269\) | −11.8921 | −0.725071 | −0.362536 | − | 0.931970i | \(-0.618089\pi\) | ||||
−0.362536 | + | 0.931970i | \(0.618089\pi\) | |||||||
\(270\) | 41.5013 | 2.52569 | ||||||||
\(271\) | 12.5010 | 0.759379 | 0.379690 | − | 0.925114i | \(-0.376031\pi\) | ||||
0.379690 | + | 0.925114i | \(0.376031\pi\) | |||||||
\(272\) | −3.27653 | −0.198669 | ||||||||
\(273\) | −0.372576 | −0.0225493 | ||||||||
\(274\) | −8.27147 | −0.499698 | ||||||||
\(275\) | 5.04547 | 0.304253 | ||||||||
\(276\) | −40.3409 | −2.42824 | ||||||||
\(277\) | 10.4051 | 0.625184 | 0.312592 | − | 0.949887i | \(-0.398803\pi\) | ||||
0.312592 | + | 0.949887i | \(0.398803\pi\) | |||||||
\(278\) | 44.2182 | 2.65203 | ||||||||
\(279\) | −13.8705 | −0.830408 | ||||||||
\(280\) | −3.58373 | −0.214169 | ||||||||
\(281\) | 8.67708 | 0.517631 | 0.258816 | − | 0.965927i | \(-0.416668\pi\) | ||||
0.258816 | + | 0.965927i | \(0.416668\pi\) | |||||||
\(282\) | −65.6959 | −3.91213 | ||||||||
\(283\) | −31.6052 | −1.87874 | −0.939368 | − | 0.342912i | \(-0.888587\pi\) | ||||
−0.939368 | + | 0.342912i | \(0.888587\pi\) | |||||||
\(284\) | −33.8898 | −2.01099 | ||||||||
\(285\) | −12.1979 | −0.722543 | ||||||||
\(286\) | 0.481047 | 0.0284449 | ||||||||
\(287\) | −0.734404 | −0.0433505 | ||||||||
\(288\) | 44.5538 | 2.62536 | ||||||||
\(289\) | 4.23210 | 0.248947 | ||||||||
\(290\) | −5.71703 | −0.335715 | ||||||||
\(291\) | −11.4676 | −0.672242 | ||||||||
\(292\) | −30.8304 | −1.80422 | ||||||||
\(293\) | 0.256704 | 0.0149968 | 0.00749841 | − | 0.999972i | \(-0.497613\pi\) | ||||
0.00749841 | + | 0.999972i | \(0.497613\pi\) | |||||||
\(294\) | 7.09783 | 0.413954 | ||||||||
\(295\) | 5.40294 | 0.314572 | ||||||||
\(296\) | −25.8378 | −1.50179 | ||||||||
\(297\) | 22.4135 | 1.30057 | ||||||||
\(298\) | 33.7220 | 1.95346 | ||||||||
\(299\) | 0.492635 | 0.0284898 | ||||||||
\(300\) | 27.0240 | 1.56023 | ||||||||
\(301\) | −4.62001 | −0.266293 | ||||||||
\(302\) | 14.8248 | 0.853069 | ||||||||
\(303\) | 26.6078 | 1.52858 | ||||||||
\(304\) | −1.85188 | −0.106212 | ||||||||
\(305\) | 10.0169 | 0.573566 | ||||||||
\(306\) | −71.9576 | −4.11354 | ||||||||
\(307\) | −21.6675 | −1.23663 | −0.618316 | − | 0.785930i | \(-0.712185\pi\) | ||||
−0.618316 | + | 0.785930i | \(0.712185\pi\) | |||||||
\(308\) | −5.54987 | −0.316233 | ||||||||
\(309\) | −9.79366 | −0.557142 | ||||||||
\(310\) | 6.69294 | 0.380134 | ||||||||
\(311\) | 10.8042 | 0.612652 | 0.306326 | − | 0.951927i | \(-0.400900\pi\) | ||||
0.306326 | + | 0.951927i | \(0.400900\pi\) | |||||||
\(312\) | 0.898541 | 0.0508699 | ||||||||
\(313\) | 11.1276 | 0.628971 | 0.314485 | − | 0.949262i | \(-0.398168\pi\) | ||||
0.314485 | + | 0.949262i | \(0.398168\pi\) | |||||||
\(314\) | 3.59015 | 0.202604 | ||||||||
\(315\) | 10.3050 | 0.580620 | ||||||||
\(316\) | −39.8727 | −2.24301 | ||||||||
\(317\) | −18.3815 | −1.03241 | −0.516205 | − | 0.856465i | \(-0.672656\pi\) | ||||
−0.516205 | + | 0.856465i | \(0.672656\pi\) | |||||||
\(318\) | −46.7949 | −2.62413 | ||||||||
\(319\) | −3.08759 | −0.172872 | ||||||||
\(320\) | −19.3852 | −1.08367 | ||||||||
\(321\) | 46.7510 | 2.60938 | ||||||||
\(322\) | −9.38503 | −0.523007 | ||||||||
\(323\) | 12.0002 | 0.667711 | ||||||||
\(324\) | 56.1593 | 3.11996 | ||||||||
\(325\) | −0.330012 | −0.0183058 | ||||||||
\(326\) | −7.67108 | −0.424862 | ||||||||
\(327\) | 2.50604 | 0.138584 | ||||||||
\(328\) | 1.77116 | 0.0977960 | ||||||||
\(329\) | −9.25577 | −0.510287 | ||||||||
\(330\) | −19.0610 | −1.04927 | ||||||||
\(331\) | −11.6571 | −0.640730 | −0.320365 | − | 0.947294i | \(-0.603805\pi\) | ||||
−0.320365 | + | 0.947294i | \(0.603805\pi\) | |||||||
\(332\) | −40.0953 | −2.20052 | ||||||||
\(333\) | 74.2962 | 4.07141 | ||||||||
\(334\) | −54.1768 | −2.96442 | ||||||||
\(335\) | 5.06706 | 0.276843 | ||||||||
\(336\) | 2.24129 | 0.122272 | ||||||||
\(337\) | −4.97204 | −0.270844 | −0.135422 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135422 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(338\) | 29.2430 | 1.59061 | ||||||||
\(339\) | −30.6079 | −1.66239 | ||||||||
\(340\) | 21.0274 | 1.14037 | ||||||||
\(341\) | 3.61465 | 0.195744 | ||||||||
\(342\) | −40.6700 | −2.19918 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.1421 | 0.600741 | ||||||||
\(345\) | −19.5201 | −1.05093 | ||||||||
\(346\) | −50.3865 | −2.70879 | ||||||||
\(347\) | 25.4043 | 1.36378 | 0.681888 | − | 0.731456i | \(-0.261159\pi\) | ||||
0.681888 | + | 0.731456i | \(0.261159\pi\) | |||||||
\(348\) | −16.5374 | −0.886499 | ||||||||
\(349\) | −4.68626 | −0.250850 | −0.125425 | − | 0.992103i | \(-0.540029\pi\) | ||||
−0.125425 | + | 0.992103i | \(0.540029\pi\) | |||||||
\(350\) | 6.28696 | 0.336052 | ||||||||
\(351\) | −1.46602 | −0.0782501 | ||||||||
\(352\) | −11.6107 | −0.618851 | ||||||||
\(353\) | 7.76895 | 0.413499 | 0.206750 | − | 0.978394i | \(-0.433711\pi\) | ||||
0.206750 | + | 0.978394i | \(0.433711\pi\) | |||||||
\(354\) | 25.8073 | 1.37164 | ||||||||
\(355\) | −16.3986 | −0.870346 | ||||||||
\(356\) | −29.2214 | −1.54873 | ||||||||
\(357\) | −14.5237 | −0.768674 | ||||||||
\(358\) | −30.8845 | −1.63230 | ||||||||
\(359\) | −3.90140 | −0.205908 | −0.102954 | − | 0.994686i | \(-0.532829\pi\) | ||||
−0.102954 | + | 0.994686i | \(0.532829\pi\) | |||||||
\(360\) | −24.8525 | −1.30984 | ||||||||
\(361\) | −12.2175 | −0.643029 | ||||||||
\(362\) | 4.27756 | 0.224823 | ||||||||
\(363\) | 24.3773 | 1.27947 | ||||||||
\(364\) | 0.363003 | 0.0190265 | ||||||||
\(365\) | −14.9182 | −0.780855 | ||||||||
\(366\) | 47.8460 | 2.50095 | ||||||||
\(367\) | −36.7223 | −1.91689 | −0.958446 | − | 0.285276i | \(-0.907915\pi\) | ||||
−0.958446 | + | 0.285276i | \(0.907915\pi\) | |||||||
\(368\) | −2.96352 | −0.154484 | ||||||||
\(369\) | −5.09295 | −0.265128 | ||||||||
\(370\) | −35.8501 | −1.86376 | ||||||||
\(371\) | −6.59285 | −0.342284 | ||||||||
\(372\) | 19.3604 | 1.00379 | ||||||||
\(373\) | 12.1354 | 0.628346 | 0.314173 | − | 0.949366i | \(-0.398273\pi\) | ||||
0.314173 | + | 0.949366i | \(0.398273\pi\) | |||||||
\(374\) | 18.7520 | 0.969645 | ||||||||
\(375\) | 36.4950 | 1.88460 | ||||||||
\(376\) | 22.3221 | 1.15118 | ||||||||
\(377\) | 0.201952 | 0.0104010 | ||||||||
\(378\) | 27.9286 | 1.43649 | ||||||||
\(379\) | −28.3692 | −1.45723 | −0.728614 | − | 0.684924i | \(-0.759835\pi\) | ||||
−0.728614 | + | 0.684924i | \(0.759835\pi\) | |||||||
\(380\) | 11.8845 | 0.609663 | ||||||||
\(381\) | 34.8486 | 1.78535 | ||||||||
\(382\) | −8.08350 | −0.413588 | ||||||||
\(383\) | −11.2115 | −0.572880 | −0.286440 | − | 0.958098i | \(-0.592472\pi\) | ||||
−0.286440 | + | 0.958098i | \(0.592472\pi\) | |||||||
\(384\) | −52.0937 | −2.65839 | ||||||||
\(385\) | −2.68546 | −0.136864 | ||||||||
\(386\) | −17.0178 | −0.866182 | ||||||||
\(387\) | −32.0389 | −1.62863 | ||||||||
\(388\) | 11.1729 | 0.567221 | ||||||||
\(389\) | 15.6303 | 0.792487 | 0.396244 | − | 0.918145i | \(-0.370314\pi\) | ||||
0.396244 | + | 0.918145i | \(0.370314\pi\) | |||||||
\(390\) | 1.24673 | 0.0631307 | ||||||||
\(391\) | 19.2038 | 0.971176 | ||||||||
\(392\) | −2.41170 | −0.121809 | ||||||||
\(393\) | −62.2687 | −3.14104 | ||||||||
\(394\) | 10.2300 | 0.515382 | ||||||||
\(395\) | −19.2936 | −0.970764 | ||||||||
\(396\) | −38.4873 | −1.93406 | ||||||||
\(397\) | 23.4557 | 1.17721 | 0.588604 | − | 0.808422i | \(-0.299678\pi\) | ||||
0.588604 | + | 0.808422i | \(0.299678\pi\) | |||||||
\(398\) | 53.7876 | 2.69613 | ||||||||
\(399\) | −8.20868 | −0.410948 | ||||||||
\(400\) | 1.98524 | 0.0992620 | ||||||||
\(401\) | 10.4508 | 0.521888 | 0.260944 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260944 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(402\) | 24.2030 | 1.20714 | ||||||||
\(403\) | −0.236425 | −0.0117772 | ||||||||
\(404\) | −25.9242 | −1.28978 | ||||||||
\(405\) | 27.1743 | 1.35030 | ||||||||
\(406\) | −3.84731 | −0.190939 | ||||||||
\(407\) | −19.3615 | −0.959714 | ||||||||
\(408\) | 35.0267 | 1.73408 | ||||||||
\(409\) | −6.69689 | −0.331140 | −0.165570 | − | 0.986198i | \(-0.552946\pi\) | ||||
−0.165570 | + | 0.986198i | \(0.552946\pi\) | |||||||
\(410\) | 2.45750 | 0.121367 | ||||||||
\(411\) | −11.5776 | −0.571079 | ||||||||
\(412\) | 9.54204 | 0.470102 | ||||||||
\(413\) | 3.63595 | 0.178913 | ||||||||
\(414\) | −65.0834 | −3.19867 | ||||||||
\(415\) | −19.4013 | −0.952372 | ||||||||
\(416\) | 0.759426 | 0.0372339 | ||||||||
\(417\) | 61.8922 | 3.03087 | ||||||||
\(418\) | 10.5985 | 0.518391 | ||||||||
\(419\) | 3.51411 | 0.171675 | 0.0858377 | − | 0.996309i | \(-0.472643\pi\) | ||||
0.0858377 | + | 0.996309i | \(0.472643\pi\) | |||||||
\(420\) | −14.3836 | −0.701849 | ||||||||
\(421\) | −21.5476 | −1.05016 | −0.525082 | − | 0.851052i | \(-0.675965\pi\) | ||||
−0.525082 | + | 0.851052i | \(0.675965\pi\) | |||||||
\(422\) | 42.5065 | 2.06918 | ||||||||
\(423\) | −64.1870 | −3.12088 | ||||||||
\(424\) | 15.9000 | 0.772171 | ||||||||
\(425\) | −12.8645 | −0.624018 | ||||||||
\(426\) | −78.3283 | −3.79502 | ||||||||
\(427\) | 6.74094 | 0.326217 | ||||||||
\(428\) | −45.5498 | −2.20173 | ||||||||
\(429\) | 0.673320 | 0.0325082 | ||||||||
\(430\) | 15.4597 | 0.745533 | ||||||||
\(431\) | −31.3170 | −1.50848 | −0.754242 | − | 0.656596i | \(-0.771996\pi\) | ||||
−0.754242 | + | 0.656596i | \(0.771996\pi\) | |||||||
\(432\) | 8.81905 | 0.424307 | ||||||||
\(433\) | −12.0671 | −0.579908 | −0.289954 | − | 0.957041i | \(-0.593640\pi\) | ||||
−0.289954 | + | 0.957041i | \(0.593640\pi\) | |||||||
\(434\) | 4.50406 | 0.216202 | ||||||||
\(435\) | −8.00211 | −0.383672 | ||||||||
\(436\) | −2.44165 | −0.116934 | ||||||||
\(437\) | 10.8538 | 0.519210 | ||||||||
\(438\) | −71.2573 | −3.40481 | ||||||||
\(439\) | 26.5970 | 1.26940 | 0.634702 | − | 0.772757i | \(-0.281123\pi\) | ||||
0.634702 | + | 0.772757i | \(0.281123\pi\) | |||||||
\(440\) | 6.47653 | 0.308757 | ||||||||
\(441\) | 6.93481 | 0.330229 | ||||||||
\(442\) | −1.22653 | −0.0583399 | ||||||||
\(443\) | 17.1679 | 0.815673 | 0.407837 | − | 0.913055i | \(-0.366283\pi\) | ||||
0.407837 | + | 0.913055i | \(0.366283\pi\) | |||||||
\(444\) | −103.702 | −4.92149 | ||||||||
\(445\) | −14.1396 | −0.670283 | ||||||||
\(446\) | −28.9175 | −1.36928 | ||||||||
\(447\) | 47.2006 | 2.23251 | ||||||||
\(448\) | −13.0454 | −0.616339 | ||||||||
\(449\) | 22.3309 | 1.05386 | 0.526931 | − | 0.849908i | \(-0.323343\pi\) | ||||
0.526931 | + | 0.849908i | \(0.323343\pi\) | |||||||
\(450\) | 43.5988 | 2.05527 | ||||||||
\(451\) | 1.32722 | 0.0624962 | ||||||||
\(452\) | 29.8215 | 1.40268 | ||||||||
\(453\) | 20.7502 | 0.974929 | ||||||||
\(454\) | −49.9972 | −2.34648 | ||||||||
\(455\) | 0.175650 | 0.00823459 | ||||||||
\(456\) | 19.7969 | 0.927073 | ||||||||
\(457\) | −22.1697 | −1.03705 | −0.518527 | − | 0.855061i | \(-0.673519\pi\) | ||||
−0.518527 | + | 0.855061i | \(0.673519\pi\) | |||||||
\(458\) | 49.7700 | 2.32560 | ||||||||
\(459\) | −57.1479 | −2.66743 | ||||||||
\(460\) | 19.0186 | 0.886746 | ||||||||
\(461\) | −4.59956 | −0.214223 | −0.107111 | − | 0.994247i | \(-0.534160\pi\) | ||||
−0.107111 | + | 0.994247i | \(0.534160\pi\) | |||||||
\(462\) | −12.8272 | −0.596776 | ||||||||
\(463\) | −31.2323 | −1.45149 | −0.725744 | − | 0.687965i | \(-0.758504\pi\) | ||||
−0.725744 | + | 0.687965i | \(0.758504\pi\) | |||||||
\(464\) | −1.21487 | −0.0563990 | ||||||||
\(465\) | 9.36810 | 0.434435 | ||||||||
\(466\) | −14.7218 | −0.681976 | ||||||||
\(467\) | −5.60616 | −0.259422 | −0.129711 | − | 0.991552i | \(-0.541405\pi\) | ||||
−0.129711 | + | 0.991552i | \(0.541405\pi\) | |||||||
\(468\) | 2.51736 | 0.116365 | ||||||||
\(469\) | 3.40992 | 0.157455 | ||||||||
\(470\) | 30.9721 | 1.42864 | ||||||||
\(471\) | 5.02513 | 0.231546 | ||||||||
\(472\) | −8.76882 | −0.403618 | ||||||||
\(473\) | 8.34929 | 0.383901 | ||||||||
\(474\) | −92.1563 | −4.23288 | ||||||||
\(475\) | −7.27090 | −0.333612 | ||||||||
\(476\) | 14.1505 | 0.648588 | ||||||||
\(477\) | −45.7202 | −2.09338 | ||||||||
\(478\) | 18.1619 | 0.830707 | ||||||||
\(479\) | −3.99643 | −0.182602 | −0.0913009 | − | 0.995823i | \(-0.529102\pi\) | ||||
−0.0913009 | + | 0.995823i | \(0.529102\pi\) | |||||||
\(480\) | −30.0914 | −1.37348 | ||||||||
\(481\) | 1.26639 | 0.0577424 | ||||||||
\(482\) | −56.9150 | −2.59241 | ||||||||
\(483\) | −13.1362 | −0.597718 | ||||||||
\(484\) | −23.7510 | −1.07959 | ||||||||
\(485\) | 5.40636 | 0.245490 | ||||||||
\(486\) | 46.0133 | 2.08721 | ||||||||
\(487\) | 26.6685 | 1.20847 | 0.604234 | − | 0.796807i | \(-0.293479\pi\) | ||||
0.604234 | + | 0.796807i | \(0.293479\pi\) | |||||||
\(488\) | −16.2571 | −0.735926 | ||||||||
\(489\) | −10.7372 | −0.485553 | ||||||||
\(490\) | −3.34625 | −0.151168 | ||||||||
\(491\) | 7.72807 | 0.348763 | 0.174381 | − | 0.984678i | \(-0.444207\pi\) | ||||
0.174381 | + | 0.984678i | \(0.444207\pi\) | |||||||
\(492\) | 7.10870 | 0.320485 | ||||||||
\(493\) | 7.87243 | 0.354556 | ||||||||
\(494\) | −0.693225 | −0.0311897 | ||||||||
\(495\) | −18.6232 | −0.837050 | ||||||||
\(496\) | 1.42225 | 0.0638611 | ||||||||
\(497\) | −11.0355 | −0.495012 | ||||||||
\(498\) | −92.6709 | −4.15268 | ||||||||
\(499\) | 0.0786257 | 0.00351977 | 0.00175989 | − | 0.999998i | \(-0.499440\pi\) | ||||
0.00175989 | + | 0.999998i | \(0.499440\pi\) | |||||||
\(500\) | −35.5574 | −1.59017 | ||||||||
\(501\) | −75.8311 | −3.38788 | ||||||||
\(502\) | −9.97074 | −0.445016 | ||||||||
\(503\) | −21.3721 | −0.952936 | −0.476468 | − | 0.879192i | \(-0.658083\pi\) | ||||
−0.476468 | + | 0.879192i | \(0.658083\pi\) | |||||||
\(504\) | −16.7247 | −0.744976 | ||||||||
\(505\) | −12.5442 | −0.558208 | ||||||||
\(506\) | 16.9606 | 0.753992 | ||||||||
\(507\) | 40.9314 | 1.81783 | ||||||||
\(508\) | −33.9532 | −1.50643 | ||||||||
\(509\) | −24.0236 | −1.06483 | −0.532415 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532415 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(510\) | 48.5998 | 2.15203 | ||||||||
\(511\) | −10.0393 | −0.444113 | ||||||||
\(512\) | −7.99827 | −0.353477 | ||||||||
\(513\) | −32.2996 | −1.42606 | ||||||||
\(514\) | 20.9925 | 0.925940 | ||||||||
\(515\) | 4.61719 | 0.203458 | ||||||||
\(516\) | 44.7197 | 1.96867 | ||||||||
\(517\) | 16.7271 | 0.735655 | ||||||||
\(518\) | −24.1256 | −1.06002 | ||||||||
\(519\) | −70.5258 | −3.09574 | ||||||||
\(520\) | −0.423614 | −0.0185767 | ||||||||
\(521\) | 7.44491 | 0.326167 | 0.163084 | − | 0.986612i | \(-0.447856\pi\) | ||||
0.163084 | + | 0.986612i | \(0.447856\pi\) | |||||||
\(522\) | −26.6804 | −1.16777 | ||||||||
\(523\) | −8.03508 | −0.351349 | −0.175675 | − | 0.984448i | \(-0.556211\pi\) | ||||
−0.175675 | + | 0.984448i | \(0.556211\pi\) | |||||||
\(524\) | 60.6689 | 2.65033 | ||||||||
\(525\) | 8.79984 | 0.384056 | ||||||||
\(526\) | −59.7275 | −2.60424 | ||||||||
\(527\) | −9.21628 | −0.401467 | ||||||||
\(528\) | −4.05046 | −0.176274 | ||||||||
\(529\) | −5.63080 | −0.244817 | ||||||||
\(530\) | 22.0613 | 0.958283 | ||||||||
\(531\) | 25.2146 | 1.09422 | ||||||||
\(532\) | 7.99778 | 0.346748 | ||||||||
\(533\) | −0.0868100 | −0.00376016 | ||||||||
\(534\) | −67.5384 | −2.92267 | ||||||||
\(535\) | −22.0406 | −0.952898 | ||||||||
\(536\) | −8.22370 | −0.355210 | ||||||||
\(537\) | −43.2290 | −1.86547 | ||||||||
\(538\) | 26.7795 | 1.15455 | ||||||||
\(539\) | −1.80720 | −0.0778417 | ||||||||
\(540\) | −56.5968 | −2.43554 | ||||||||
\(541\) | −4.06658 | −0.174836 | −0.0874180 | − | 0.996172i | \(-0.527862\pi\) | ||||
−0.0874180 | + | 0.996172i | \(0.527862\pi\) | |||||||
\(542\) | −28.1507 | −1.20918 | ||||||||
\(543\) | 5.98729 | 0.256939 | ||||||||
\(544\) | 29.6038 | 1.26925 | ||||||||
\(545\) | −1.18146 | −0.0506084 | ||||||||
\(546\) | 0.838997 | 0.0359057 | ||||||||
\(547\) | 29.9747 | 1.28163 | 0.640813 | − | 0.767697i | \(-0.278597\pi\) | ||||
0.640813 | + | 0.767697i | \(0.278597\pi\) | |||||||
\(548\) | 11.2801 | 0.481862 | ||||||||
\(549\) | 46.7472 | 1.99512 | ||||||||
\(550\) | −11.3618 | −0.484469 | ||||||||
\(551\) | 4.44944 | 0.189553 | ||||||||
\(552\) | 31.6806 | 1.34841 | ||||||||
\(553\) | −12.9837 | −0.552125 | ||||||||
\(554\) | −23.4311 | −0.995493 | ||||||||
\(555\) | −50.1793 | −2.12999 | ||||||||
\(556\) | −60.3020 | −2.55737 | ||||||||
\(557\) | −3.14757 | −0.133367 | −0.0666833 | − | 0.997774i | \(-0.521242\pi\) | ||||
−0.0666833 | + | 0.997774i | \(0.521242\pi\) | |||||||
\(558\) | 31.2348 | 1.32228 | ||||||||
\(559\) | −0.546107 | −0.0230979 | ||||||||
\(560\) | −1.05665 | −0.0446516 | ||||||||
\(561\) | 26.2472 | 1.10816 | ||||||||
\(562\) | −19.5398 | −0.824235 | ||||||||
\(563\) | 9.24699 | 0.389714 | 0.194857 | − | 0.980832i | \(-0.437576\pi\) | ||||
0.194857 | + | 0.980832i | \(0.437576\pi\) | |||||||
\(564\) | 89.5918 | 3.77250 | ||||||||
\(565\) | 14.4300 | 0.607074 | ||||||||
\(566\) | 71.1712 | 2.99155 | ||||||||
\(567\) | 18.2872 | 0.767989 | ||||||||
\(568\) | 26.6144 | 1.11672 | ||||||||
\(569\) | −26.8669 | −1.12632 | −0.563159 | − | 0.826349i | \(-0.690414\pi\) | ||||
−0.563159 | + | 0.826349i | \(0.690414\pi\) | |||||||
\(570\) | 27.4683 | 1.15052 | ||||||||
\(571\) | −16.9462 | −0.709177 | −0.354589 | − | 0.935022i | \(-0.615379\pi\) | ||||
−0.354589 | + | 0.935022i | \(0.615379\pi\) | |||||||
\(572\) | −0.656020 | −0.0274296 | ||||||||
\(573\) | −11.3145 | −0.472668 | ||||||||
\(574\) | 1.65379 | 0.0690279 | ||||||||
\(575\) | −11.6355 | −0.485234 | ||||||||
\(576\) | −90.4676 | −3.76948 | ||||||||
\(577\) | 6.92784 | 0.288410 | 0.144205 | − | 0.989548i | \(-0.453938\pi\) | ||||
0.144205 | + | 0.989548i | \(0.453938\pi\) | |||||||
\(578\) | −9.53018 | −0.396403 | ||||||||
\(579\) | −23.8197 | −0.989915 | ||||||||
\(580\) | 7.79651 | 0.323733 | ||||||||
\(581\) | −13.0562 | −0.541664 | ||||||||
\(582\) | 25.8236 | 1.07042 | ||||||||
\(583\) | 11.9146 | 0.493453 | ||||||||
\(584\) | 24.2118 | 1.00189 | ||||||||
\(585\) | 1.21810 | 0.0503621 | ||||||||
\(586\) | −0.578068 | −0.0238798 | ||||||||
\(587\) | −29.6401 | −1.22338 | −0.611689 | − | 0.791098i | \(-0.709510\pi\) | ||||
−0.611689 | + | 0.791098i | \(0.709510\pi\) | |||||||
\(588\) | −9.67956 | −0.399178 | ||||||||
\(589\) | −5.20898 | −0.214632 | ||||||||
\(590\) | −12.1668 | −0.500899 | ||||||||
\(591\) | 14.3190 | 0.589004 | ||||||||
\(592\) | −7.61817 | −0.313105 | ||||||||
\(593\) | −17.5073 | −0.718940 | −0.359470 | − | 0.933157i | \(-0.617042\pi\) | ||||
−0.359470 | + | 0.933157i | \(0.617042\pi\) | |||||||
\(594\) | −50.4726 | −2.07092 | ||||||||
\(595\) | 6.84714 | 0.280705 | ||||||||
\(596\) | −45.9878 | −1.88374 | ||||||||
\(597\) | 75.2863 | 3.08126 | ||||||||
\(598\) | −1.10935 | −0.0453649 | ||||||||
\(599\) | 3.33470 | 0.136252 | 0.0681260 | − | 0.997677i | \(-0.478298\pi\) | ||||
0.0681260 | + | 0.997677i | \(0.478298\pi\) | |||||||
\(600\) | −21.2226 | −0.866407 | ||||||||
\(601\) | 2.40141 | 0.0979556 | 0.0489778 | − | 0.998800i | \(-0.484404\pi\) | ||||
0.0489778 | + | 0.998800i | \(0.484404\pi\) | |||||||
\(602\) | 10.4037 | 0.424024 | ||||||||
\(603\) | 23.6471 | 0.962985 | ||||||||
\(604\) | −20.2171 | −0.822620 | ||||||||
\(605\) | −11.4926 | −0.467240 | ||||||||
\(606\) | −59.9176 | −2.43399 | ||||||||
\(607\) | −10.0650 | −0.408525 | −0.204262 | − | 0.978916i | \(-0.565480\pi\) | ||||
−0.204262 | + | 0.978916i | \(0.565480\pi\) | |||||||
\(608\) | 16.7319 | 0.678566 | ||||||||
\(609\) | −5.38508 | −0.218214 | ||||||||
\(610\) | −22.5569 | −0.913301 | ||||||||
\(611\) | −1.09408 | −0.0442616 | ||||||||
\(612\) | 98.1311 | 3.96671 | ||||||||
\(613\) | −4.46403 | −0.180300 | −0.0901502 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901502 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(614\) | 48.7927 | 1.96911 | ||||||||
\(615\) | 3.43975 | 0.138704 | ||||||||
\(616\) | 4.35843 | 0.175606 | ||||||||
\(617\) | −15.8111 | −0.636530 | −0.318265 | − | 0.948002i | \(-0.603100\pi\) | ||||
−0.318265 | + | 0.948002i | \(0.603100\pi\) | |||||||
\(618\) | 22.0542 | 0.887149 | ||||||||
\(619\) | 29.7501 | 1.19576 | 0.597879 | − | 0.801586i | \(-0.296010\pi\) | ||||
0.597879 | + | 0.801586i | \(0.296010\pi\) | |||||||
\(620\) | −9.12740 | −0.366565 | ||||||||
\(621\) | −51.6884 | −2.07419 | ||||||||
\(622\) | −24.3299 | −0.975538 | ||||||||
\(623\) | −9.51537 | −0.381225 | ||||||||
\(624\) | 0.264931 | 0.0106057 | ||||||||
\(625\) | −3.24614 | −0.129846 | ||||||||
\(626\) | −25.0581 | −1.00152 | ||||||||
\(627\) | 14.8347 | 0.592443 | ||||||||
\(628\) | −4.89602 | −0.195372 | ||||||||
\(629\) | 49.3661 | 1.96835 | ||||||||
\(630\) | −23.2056 | −0.924533 | ||||||||
\(631\) | 31.8015 | 1.26600 | 0.632999 | − | 0.774153i | \(-0.281824\pi\) | ||||
0.632999 | + | 0.774153i | \(0.281824\pi\) | |||||||
\(632\) | 31.3129 | 1.24556 | ||||||||
\(633\) | 59.4962 | 2.36476 | ||||||||
\(634\) | 41.3931 | 1.64393 | ||||||||
\(635\) | −16.4293 | −0.651975 | ||||||||
\(636\) | 63.8159 | 2.53047 | ||||||||
\(637\) | 0.118205 | 0.00468344 | ||||||||
\(638\) | 6.95288 | 0.275267 | ||||||||
\(639\) | −76.5294 | −3.02745 | ||||||||
\(640\) | 24.5594 | 0.970796 | ||||||||
\(641\) | 16.4744 | 0.650699 | 0.325350 | − | 0.945594i | \(-0.394518\pi\) | ||||
0.325350 | + | 0.945594i | \(0.394518\pi\) | |||||||
\(642\) | −105.278 | −4.15498 | ||||||||
\(643\) | 13.0067 | 0.512932 | 0.256466 | − | 0.966553i | \(-0.417442\pi\) | ||||
0.256466 | + | 0.966553i | \(0.417442\pi\) | |||||||
\(644\) | 12.7987 | 0.504339 | ||||||||
\(645\) | 21.6389 | 0.852031 | ||||||||
\(646\) | −27.0231 | −1.06321 | ||||||||
\(647\) | −37.1849 | −1.46189 | −0.730944 | − | 0.682438i | \(-0.760920\pi\) | ||||
−0.730944 | + | 0.682438i | \(0.760920\pi\) | |||||||
\(648\) | −44.1031 | −1.73253 | ||||||||
\(649\) | −6.57090 | −0.257930 | ||||||||
\(650\) | 0.743148 | 0.0291487 | ||||||||
\(651\) | 6.30433 | 0.247086 | ||||||||
\(652\) | 10.4613 | 0.409697 | ||||||||
\(653\) | 40.4935 | 1.58463 | 0.792317 | − | 0.610110i | \(-0.208875\pi\) | ||||
0.792317 | + | 0.610110i | \(0.208875\pi\) | |||||||
\(654\) | −5.64331 | −0.220671 | ||||||||
\(655\) | 29.3564 | 1.14705 | ||||||||
\(656\) | 0.522220 | 0.0203892 | ||||||||
\(657\) | −69.6207 | −2.71616 | ||||||||
\(658\) | 20.8429 | 0.812541 | ||||||||
\(659\) | 20.5019 | 0.798640 | 0.399320 | − | 0.916812i | \(-0.369246\pi\) | ||||
0.399320 | + | 0.916812i | \(0.369246\pi\) | |||||||
\(660\) | 25.9941 | 1.01182 | ||||||||
\(661\) | 31.8266 | 1.23791 | 0.618956 | − | 0.785426i | \(-0.287556\pi\) | ||||
0.618956 | + | 0.785426i | \(0.287556\pi\) | |||||||
\(662\) | 26.2503 | 1.02025 | ||||||||
\(663\) | −1.71677 | −0.0666737 | ||||||||
\(664\) | 31.4877 | 1.22196 | ||||||||
\(665\) | 3.86996 | 0.150070 | ||||||||
\(666\) | −167.306 | −6.48299 | ||||||||
\(667\) | 7.12036 | 0.275702 | ||||||||
\(668\) | 73.8828 | 2.85861 | ||||||||
\(669\) | −40.4758 | −1.56488 | ||||||||
\(670\) | −11.4104 | −0.440823 | ||||||||
\(671\) | −12.1822 | −0.470290 | ||||||||
\(672\) | −20.2502 | −0.781170 | ||||||||
\(673\) | −29.7117 | −1.14530 | −0.572651 | − | 0.819800i | \(-0.694085\pi\) | ||||
−0.572651 | + | 0.819800i | \(0.694085\pi\) | |||||||
\(674\) | 11.1965 | 0.431271 | ||||||||
\(675\) | 34.6257 | 1.33274 | ||||||||
\(676\) | −39.8797 | −1.53384 | ||||||||
\(677\) | 40.7669 | 1.56680 | 0.783400 | − | 0.621517i | \(-0.213484\pi\) | ||||
0.783400 | + | 0.621517i | \(0.213484\pi\) | |||||||
\(678\) | 68.9253 | 2.64706 | ||||||||
\(679\) | 3.63825 | 0.139623 | ||||||||
\(680\) | −16.5132 | −0.633254 | ||||||||
\(681\) | −69.9809 | −2.68167 | ||||||||
\(682\) | −8.13976 | −0.311687 | ||||||||
\(683\) | 18.2699 | 0.699079 | 0.349539 | − | 0.936922i | \(-0.386338\pi\) | ||||
0.349539 | + | 0.936922i | \(0.386338\pi\) | |||||||
\(684\) | 55.4631 | 2.12068 | ||||||||
\(685\) | 5.45820 | 0.208547 | ||||||||
\(686\) | −2.25188 | −0.0859772 | ||||||||
\(687\) | 69.6630 | 2.65781 | ||||||||
\(688\) | 3.28520 | 0.125247 | ||||||||
\(689\) | −0.779307 | −0.0296892 | ||||||||
\(690\) | 43.9570 | 1.67341 | ||||||||
\(691\) | 42.6438 | 1.62225 | 0.811123 | − | 0.584876i | \(-0.198857\pi\) | ||||
0.811123 | + | 0.584876i | \(0.198857\pi\) | |||||||
\(692\) | 68.7138 | 2.61211 | ||||||||
\(693\) | −12.5326 | −0.476074 | ||||||||
\(694\) | −57.2076 | −2.17157 | ||||||||
\(695\) | −29.1789 | −1.10682 | ||||||||
\(696\) | 12.9872 | 0.492278 | ||||||||
\(697\) | −3.38401 | −0.128178 | ||||||||
\(698\) | 10.5529 | 0.399434 | ||||||||
\(699\) | −20.6061 | −0.779395 | ||||||||
\(700\) | −8.57374 | −0.324057 | ||||||||
\(701\) | 7.66940 | 0.289669 | 0.144835 | − | 0.989456i | \(-0.453735\pi\) | ||||
0.144835 | + | 0.989456i | \(0.453735\pi\) | |||||||
\(702\) | 3.30129 | 0.124599 | ||||||||
\(703\) | 27.9014 | 1.05232 | ||||||||
\(704\) | 23.5757 | 0.888544 | ||||||||
\(705\) | 43.3516 | 1.63272 | ||||||||
\(706\) | −17.4948 | −0.658424 | ||||||||
\(707\) | −8.44168 | −0.317482 | ||||||||
\(708\) | −35.1944 | −1.32269 | ||||||||
\(709\) | −22.5595 | −0.847239 | −0.423620 | − | 0.905840i | \(-0.639241\pi\) | ||||
−0.423620 | + | 0.905840i | \(0.639241\pi\) | |||||||
\(710\) | 36.9276 | 1.38587 | ||||||||
\(711\) | −90.0398 | −3.37676 | ||||||||
\(712\) | 22.9482 | 0.860020 | ||||||||
\(713\) | −8.33583 | −0.312179 | ||||||||
\(714\) | 32.7056 | 1.22398 | ||||||||
\(715\) | −0.317435 | −0.0118714 | ||||||||
\(716\) | 42.1183 | 1.57403 | ||||||||
\(717\) | 25.4212 | 0.949373 | ||||||||
\(718\) | 8.78550 | 0.327872 | ||||||||
\(719\) | −14.3607 | −0.535564 | −0.267782 | − | 0.963479i | \(-0.586291\pi\) | ||||
−0.267782 | + | 0.963479i | \(0.586291\pi\) | |||||||
\(720\) | −7.32766 | −0.273086 | ||||||||
\(721\) | 3.10717 | 0.115717 | ||||||||
\(722\) | 27.5125 | 1.02391 | ||||||||
\(723\) | −79.6639 | −2.96273 | ||||||||
\(724\) | −5.83346 | −0.216799 | ||||||||
\(725\) | −4.76987 | −0.177149 | ||||||||
\(726\) | −54.8947 | −2.03733 | ||||||||
\(727\) | 33.5933 | 1.24591 | 0.622953 | − | 0.782260i | \(-0.285933\pi\) | ||||
0.622953 | + | 0.782260i | \(0.285933\pi\) | |||||||
\(728\) | −0.285074 | −0.0105656 | ||||||||
\(729\) | 9.54321 | 0.353452 | ||||||||
\(730\) | 33.5940 | 1.24337 | ||||||||
\(731\) | −21.2882 | −0.787373 | ||||||||
\(732\) | −65.2493 | −2.41169 | ||||||||
\(733\) | 42.9532 | 1.58651 | 0.793257 | − | 0.608887i | \(-0.208384\pi\) | ||||
0.793257 | + | 0.608887i | \(0.208384\pi\) | |||||||
\(734\) | 82.6944 | 3.05231 | ||||||||
\(735\) | −4.68374 | −0.172762 | ||||||||
\(736\) | 26.7757 | 0.986965 | ||||||||
\(737\) | −6.16241 | −0.226995 | ||||||||
\(738\) | 11.4687 | 0.422169 | ||||||||
\(739\) | −24.1401 | −0.888009 | −0.444005 | − | 0.896025i | \(-0.646443\pi\) | ||||
−0.444005 | + | 0.896025i | \(0.646443\pi\) | |||||||
\(740\) | 48.8901 | 1.79723 | ||||||||
\(741\) | −0.970305 | −0.0356450 | ||||||||
\(742\) | 14.8463 | 0.545026 | ||||||||
\(743\) | 3.72572 | 0.136683 | 0.0683416 | − | 0.997662i | \(-0.478229\pi\) | ||||
0.0683416 | + | 0.997662i | \(0.478229\pi\) | |||||||
\(744\) | −15.2041 | −0.557411 | ||||||||
\(745\) | −22.2526 | −0.815271 | ||||||||
\(746\) | −27.3275 | −1.00053 | ||||||||
\(747\) | −90.5425 | −3.31278 | ||||||||
\(748\) | −25.5728 | −0.935035 | ||||||||
\(749\) | −14.8324 | −0.541963 | ||||||||
\(750\) | −82.1825 | −3.00088 | ||||||||
\(751\) | −51.1766 | −1.86746 | −0.933731 | − | 0.357975i | \(-0.883467\pi\) | ||||
−0.933731 | + | 0.357975i | \(0.883467\pi\) | |||||||
\(752\) | 6.58159 | 0.240006 | ||||||||
\(753\) | −13.9560 | −0.508586 | ||||||||
\(754\) | −0.454771 | −0.0165618 | ||||||||
\(755\) | −9.78261 | −0.356026 | ||||||||
\(756\) | −38.0872 | −1.38522 | ||||||||
\(757\) | −0.103777 | −0.00377182 | −0.00188591 | − | 0.999998i | \(-0.500600\pi\) | ||||
−0.00188591 | + | 0.999998i | \(0.500600\pi\) | |||||||
\(758\) | 63.8841 | 2.32038 | ||||||||
\(759\) | 23.7398 | 0.861699 | ||||||||
\(760\) | −9.33317 | −0.338550 | ||||||||
\(761\) | −49.4710 | −1.79332 | −0.896661 | − | 0.442718i | \(-0.854014\pi\) | ||||
−0.896661 | + | 0.442718i | \(0.854014\pi\) | |||||||
\(762\) | −78.4749 | −2.84284 | ||||||||
\(763\) | −0.795075 | −0.0287837 | ||||||||
\(764\) | 11.0238 | 0.398826 | ||||||||
\(765\) | 47.4836 | 1.71677 | ||||||||
\(766\) | 25.2469 | 0.912209 | ||||||||
\(767\) | 0.429787 | 0.0155187 | ||||||||
\(768\) | 35.0716 | 1.26554 | ||||||||
\(769\) | 12.2913 | 0.443234 | 0.221617 | − | 0.975134i | \(-0.428867\pi\) | ||||
0.221617 | + | 0.975134i | \(0.428867\pi\) | |||||||
\(770\) | 6.04735 | 0.217931 | ||||||||
\(771\) | 29.3832 | 1.05821 | ||||||||
\(772\) | 23.2077 | 0.835265 | ||||||||
\(773\) | 47.0409 | 1.69194 | 0.845972 | − | 0.533228i | \(-0.179021\pi\) | ||||
0.845972 | + | 0.533228i | \(0.179021\pi\) | |||||||
\(774\) | 72.1478 | 2.59330 | ||||||||
\(775\) | 5.58411 | 0.200587 | ||||||||
\(776\) | −8.77436 | −0.314981 | ||||||||
\(777\) | −33.7685 | −1.21144 | ||||||||
\(778\) | −35.1976 | −1.26189 | ||||||||
\(779\) | −1.91262 | −0.0685267 | ||||||||
\(780\) | −1.70021 | −0.0608773 | ||||||||
\(781\) | 19.9434 | 0.713633 | ||||||||
\(782\) | −43.2446 | −1.54642 | ||||||||
\(783\) | −21.1893 | −0.757242 | ||||||||
\(784\) | −0.711080 | −0.0253957 | ||||||||
\(785\) | −2.36908 | −0.0845561 | ||||||||
\(786\) | 140.222 | 5.00155 | ||||||||
\(787\) | −27.0970 | −0.965904 | −0.482952 | − | 0.875647i | \(-0.660435\pi\) | ||||
−0.482952 | + | 0.875647i | \(0.660435\pi\) | |||||||
\(788\) | −13.9511 | −0.496987 | ||||||||
\(789\) | −83.6005 | −2.97626 | ||||||||
\(790\) | 43.4468 | 1.54577 | ||||||||
\(791\) | 9.71076 | 0.345275 | ||||||||
\(792\) | 30.2249 | 1.07399 | ||||||||
\(793\) | 0.796812 | 0.0282956 | ||||||||
\(794\) | −52.8194 | −1.87449 | ||||||||
\(795\) | 30.8792 | 1.09517 | ||||||||
\(796\) | −73.3520 | −2.59989 | ||||||||
\(797\) | 9.52599 | 0.337428 | 0.168714 | − | 0.985665i | \(-0.446039\pi\) | ||||
0.168714 | + | 0.985665i | \(0.446039\pi\) | |||||||
\(798\) | 18.4850 | 0.654361 | ||||||||
\(799\) | −42.6490 | −1.50881 | ||||||||
\(800\) | −17.9368 | −0.634162 | ||||||||
\(801\) | −65.9873 | −2.33154 | ||||||||
\(802\) | −23.5340 | −0.831013 | ||||||||
\(803\) | 18.1431 | 0.640255 | ||||||||
\(804\) | −33.0065 | −1.16405 | ||||||||
\(805\) | 6.19302 | 0.218275 | ||||||||
\(806\) | 0.532402 | 0.0187531 | ||||||||
\(807\) | 37.4832 | 1.31947 | ||||||||
\(808\) | 20.3588 | 0.716220 | ||||||||
\(809\) | −34.7609 | −1.22213 | −0.611065 | − | 0.791581i | \(-0.709259\pi\) | ||||
−0.611065 | + | 0.791581i | \(0.709259\pi\) | |||||||
\(810\) | −61.1934 | −2.15012 | ||||||||
\(811\) | 4.50178 | 0.158079 | 0.0790394 | − | 0.996871i | \(-0.474815\pi\) | ||||
0.0790394 | + | 0.996871i | \(0.474815\pi\) | |||||||
\(812\) | 5.24672 | 0.184124 | ||||||||
\(813\) | −39.4025 | −1.38190 | ||||||||
\(814\) | 43.5998 | 1.52817 | ||||||||
\(815\) | 5.06202 | 0.177315 | ||||||||
\(816\) | 10.3275 | 0.361534 | ||||||||
\(817\) | −12.0320 | −0.420945 | ||||||||
\(818\) | 15.0806 | 0.527281 | ||||||||
\(819\) | 0.819728 | 0.0286436 | ||||||||
\(820\) | −3.35138 | −0.117035 | ||||||||
\(821\) | −31.0748 | −1.08452 | −0.542259 | − | 0.840212i | \(-0.682431\pi\) | ||||
−0.542259 | + | 0.840212i | \(0.682431\pi\) | |||||||
\(822\) | 26.0713 | 0.909340 | ||||||||
\(823\) | −19.0671 | −0.664636 | −0.332318 | − | 0.943167i | \(-0.607831\pi\) | ||||
−0.332318 | + | 0.943167i | \(0.607831\pi\) | |||||||
\(824\) | −7.49357 | −0.261051 | ||||||||
\(825\) | −15.9031 | −0.553674 | ||||||||
\(826\) | −8.18773 | −0.284888 | ||||||||
\(827\) | 11.2551 | 0.391379 | 0.195689 | − | 0.980666i | \(-0.437306\pi\) | ||||
0.195689 | + | 0.980666i | \(0.437306\pi\) | |||||||
\(828\) | 88.7565 | 3.08450 | ||||||||
\(829\) | 25.6029 | 0.889227 | 0.444613 | − | 0.895723i | \(-0.353341\pi\) | ||||
0.444613 | + | 0.895723i | \(0.353341\pi\) | |||||||
\(830\) | 43.6894 | 1.51648 | ||||||||
\(831\) | −32.7965 | −1.13770 | ||||||||
\(832\) | −1.54203 | −0.0534603 | ||||||||
\(833\) | 4.60783 | 0.159652 | ||||||||
\(834\) | −139.374 | −4.82612 | ||||||||
\(835\) | 35.7503 | 1.23719 | ||||||||
\(836\) | −14.4536 | −0.499888 | ||||||||
\(837\) | 24.8063 | 0.857432 | ||||||||
\(838\) | −7.91335 | −0.273362 | ||||||||
\(839\) | −36.0320 | −1.24396 | −0.621981 | − | 0.783032i | \(-0.713672\pi\) | ||||
−0.621981 | + | 0.783032i | \(0.713672\pi\) | |||||||
\(840\) | 11.2958 | 0.389741 | ||||||||
\(841\) | −26.0811 | −0.899347 | ||||||||
\(842\) | 48.5225 | 1.67220 | ||||||||
\(843\) | −27.3498 | −0.941976 | ||||||||
\(844\) | −57.9676 | −1.99533 | ||||||||
\(845\) | −19.2970 | −0.663836 | ||||||||
\(846\) | 144.542 | 4.96944 | ||||||||
\(847\) | −7.73402 | −0.265744 | ||||||||
\(848\) | 4.68804 | 0.160988 | ||||||||
\(849\) | 99.6182 | 3.41889 | ||||||||
\(850\) | 28.9692 | 0.993636 | ||||||||
\(851\) | 44.6501 | 1.53059 | ||||||||
\(852\) | 106.819 | 3.65956 | ||||||||
\(853\) | 12.6237 | 0.432226 | 0.216113 | − | 0.976368i | \(-0.430662\pi\) | ||||
0.216113 | + | 0.976368i | \(0.430662\pi\) | |||||||
\(854\) | −15.1798 | −0.519442 | ||||||||
\(855\) | 26.8374 | 0.917820 | ||||||||
\(856\) | 35.7712 | 1.22264 | ||||||||
\(857\) | −25.3711 | −0.866660 | −0.433330 | − | 0.901235i | \(-0.642661\pi\) | ||||
−0.433330 | + | 0.901235i | \(0.642661\pi\) | |||||||
\(858\) | −1.51624 | −0.0517635 | ||||||||
\(859\) | −1.50264 | −0.0512694 | −0.0256347 | − | 0.999671i | \(-0.508161\pi\) | ||||
−0.0256347 | + | 0.999671i | \(0.508161\pi\) | |||||||
\(860\) | −21.0829 | −0.718922 | ||||||||
\(861\) | 2.31481 | 0.0788884 | ||||||||
\(862\) | 70.5221 | 2.40199 | ||||||||
\(863\) | 1.00000 | 0.0340404 | ||||||||
\(864\) | −79.6809 | −2.71080 | ||||||||
\(865\) | 33.2492 | 1.13051 | ||||||||
\(866\) | 27.1737 | 0.923399 | ||||||||
\(867\) | −13.3394 | −0.453029 | ||||||||
\(868\) | −6.14235 | −0.208485 | ||||||||
\(869\) | 23.4642 | 0.795970 | ||||||||
\(870\) | 18.0198 | 0.610929 | ||||||||
\(871\) | 0.403068 | 0.0136575 | ||||||||
\(872\) | 1.91748 | 0.0649342 | ||||||||
\(873\) | 25.2305 | 0.853925 | ||||||||
\(874\) | −24.4416 | −0.826748 | ||||||||
\(875\) | −11.5785 | −0.391426 | ||||||||
\(876\) | 97.1761 | 3.28328 | ||||||||
\(877\) | −54.6977 | −1.84701 | −0.923505 | − | 0.383587i | \(-0.874689\pi\) | ||||
−0.923505 | + | 0.383587i | \(0.874689\pi\) | |||||||
\(878\) | −59.8932 | −2.02130 | ||||||||
\(879\) | −0.809120 | −0.0272909 | ||||||||
\(880\) | 1.90958 | 0.0643719 | ||||||||
\(881\) | 15.4681 | 0.521135 | 0.260567 | − | 0.965456i | \(-0.416090\pi\) | ||||
0.260567 | + | 0.965456i | \(0.416090\pi\) | |||||||
\(882\) | −15.6164 | −0.525831 | ||||||||
\(883\) | −48.4282 | −1.62974 | −0.814869 | − | 0.579645i | \(-0.803191\pi\) | ||||
−0.814869 | + | 0.579645i | \(0.803191\pi\) | |||||||
\(884\) | 1.67266 | 0.0562576 | ||||||||
\(885\) | −17.0298 | −0.572451 | ||||||||
\(886\) | −38.6602 | −1.29881 | ||||||||
\(887\) | 24.2238 | 0.813357 | 0.406679 | − | 0.913571i | \(-0.366687\pi\) | ||||
0.406679 | + | 0.913571i | \(0.366687\pi\) | |||||||
\(888\) | 81.4395 | 2.73293 | ||||||||
\(889\) | −11.0562 | −0.370812 | ||||||||
\(890\) | 31.8408 | 1.06731 | ||||||||
\(891\) | −33.0486 | −1.10717 | ||||||||
\(892\) | 39.4358 | 1.32041 | ||||||||
\(893\) | −24.1050 | −0.806642 | ||||||||
\(894\) | −106.290 | −3.55487 | ||||||||
\(895\) | 20.3802 | 0.681234 | ||||||||
\(896\) | 16.5274 | 0.552143 | ||||||||
\(897\) | −1.55276 | −0.0518452 | ||||||||
\(898\) | −50.2866 | −1.67809 | ||||||||
\(899\) | −3.41721 | −0.113970 | ||||||||
\(900\) | −59.4573 | −1.98191 | ||||||||
\(901\) | −30.3787 | −1.01206 | ||||||||
\(902\) | −2.98873 | −0.0995139 | ||||||||
\(903\) | 14.5621 | 0.484595 | ||||||||
\(904\) | −23.4194 | −0.778919 | ||||||||
\(905\) | −2.82269 | −0.0938293 | ||||||||
\(906\) | −46.7270 | −1.55240 | ||||||||
\(907\) | 12.8585 | 0.426959 | 0.213479 | − | 0.976948i | \(-0.431520\pi\) | ||||
0.213479 | + | 0.976948i | \(0.431520\pi\) | |||||||
\(908\) | 68.1829 | 2.26273 | ||||||||
\(909\) | −58.5415 | −1.94170 | ||||||||
\(910\) | −0.395542 | −0.0131121 | ||||||||
\(911\) | −14.4293 | −0.478064 | −0.239032 | − | 0.971012i | \(-0.576830\pi\) | ||||
−0.239032 | + | 0.971012i | \(0.576830\pi\) | |||||||
\(912\) | 5.83703 | 0.193283 | ||||||||
\(913\) | 23.5953 | 0.780889 | ||||||||
\(914\) | 49.9235 | 1.65132 | ||||||||
\(915\) | −31.5728 | −1.04376 | ||||||||
\(916\) | −67.8731 | −2.24259 | ||||||||
\(917\) | 19.7556 | 0.652387 | ||||||||
\(918\) | 128.690 | 4.24741 | ||||||||
\(919\) | −47.4295 | −1.56455 | −0.782277 | − | 0.622930i | \(-0.785942\pi\) | ||||
−0.782277 | + | 0.622930i | \(0.785942\pi\) | |||||||
\(920\) | −14.9357 | −0.492416 | ||||||||
\(921\) | 68.2950 | 2.25040 | ||||||||
\(922\) | 10.3577 | 0.341112 | ||||||||
\(923\) | −1.30445 | −0.0429366 | ||||||||
\(924\) | 17.4929 | 0.575475 | ||||||||
\(925\) | −29.9107 | −0.983459 | ||||||||
\(926\) | 70.3314 | 2.31123 | ||||||||
\(927\) | 21.5477 | 0.707718 | ||||||||
\(928\) | 10.9765 | 0.360320 | ||||||||
\(929\) | 32.9381 | 1.08066 | 0.540332 | − | 0.841452i | \(-0.318299\pi\) | ||||
0.540332 | + | 0.841452i | \(0.318299\pi\) | |||||||
\(930\) | −21.0958 | −0.691760 | ||||||||
\(931\) | 2.60432 | 0.0853530 | ||||||||
\(932\) | 20.0767 | 0.657634 | ||||||||
\(933\) | −34.0544 | −1.11489 | ||||||||
\(934\) | 12.6244 | 0.413084 | ||||||||
\(935\) | −12.3742 | −0.404678 | ||||||||
\(936\) | −1.97694 | −0.0646182 | ||||||||
\(937\) | −39.4371 | −1.28835 | −0.644177 | − | 0.764877i | \(-0.722800\pi\) | ||||
−0.644177 | + | 0.764877i | \(0.722800\pi\) | |||||||
\(938\) | −7.67873 | −0.250719 | ||||||||
\(939\) | −35.0738 | −1.14459 | ||||||||
\(940\) | −42.2378 | −1.37764 | ||||||||
\(941\) | 45.7441 | 1.49121 | 0.745607 | − | 0.666386i | \(-0.232160\pi\) | ||||
0.745607 | + | 0.666386i | \(0.232160\pi\) | |||||||
\(942\) | −11.3160 | −0.368695 | ||||||||
\(943\) | −3.06073 | −0.0996710 | ||||||||
\(944\) | −2.58545 | −0.0841492 | ||||||||
\(945\) | −18.4296 | −0.599515 | ||||||||
\(946\) | −18.8016 | −0.611293 | ||||||||
\(947\) | −2.09714 | −0.0681479 | −0.0340740 | − | 0.999419i | \(-0.510848\pi\) | ||||
−0.0340740 | + | 0.999419i | \(0.510848\pi\) | |||||||
\(948\) | 125.677 | 4.08179 | ||||||||
\(949\) | −1.18669 | −0.0385217 | ||||||||
\(950\) | 16.3732 | 0.531217 | ||||||||
\(951\) | 57.9378 | 1.87876 | ||||||||
\(952\) | −11.1127 | −0.360165 | ||||||||
\(953\) | 16.5559 | 0.536300 | 0.268150 | − | 0.963377i | \(-0.413588\pi\) | ||||
0.268150 | + | 0.963377i | \(0.413588\pi\) | |||||||
\(954\) | 102.956 | 3.33334 | ||||||||
\(955\) | 5.33417 | 0.172610 | ||||||||
\(956\) | −24.7681 | −0.801057 | ||||||||
\(957\) | 9.73192 | 0.314588 | ||||||||
\(958\) | 8.99950 | 0.290761 | ||||||||
\(959\) | 3.67314 | 0.118612 | ||||||||
\(960\) | 61.1013 | 1.97204 | ||||||||
\(961\) | −26.9995 | −0.870950 | ||||||||
\(962\) | −2.85176 | −0.0919444 | ||||||||
\(963\) | −102.860 | −3.31461 | ||||||||
\(964\) | 77.6171 | 2.49988 | ||||||||
\(965\) | 11.2297 | 0.361498 | ||||||||
\(966\) | 29.5812 | 0.951758 | ||||||||
\(967\) | −19.0406 | −0.612303 | −0.306151 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(968\) | 18.6521 | 0.599502 | ||||||||
\(969\) | −37.8242 | −1.21509 | ||||||||
\(970\) | −12.1745 | −0.390899 | ||||||||
\(971\) | 14.5439 | 0.466736 | 0.233368 | − | 0.972389i | \(-0.425025\pi\) | ||||
0.233368 | + | 0.972389i | \(0.425025\pi\) | |||||||
\(972\) | −62.7500 | −2.01271 | ||||||||
\(973\) | −19.6361 | −0.629505 | ||||||||
\(974\) | −60.0544 | −1.92427 | ||||||||
\(975\) | 1.04018 | 0.0333125 | ||||||||
\(976\) | −4.79335 | −0.153431 | ||||||||
\(977\) | 4.82827 | 0.154470 | 0.0772350 | − | 0.997013i | \(-0.475391\pi\) | ||||
0.0772350 | + | 0.997013i | \(0.475391\pi\) | |||||||
\(978\) | 24.1789 | 0.773156 | ||||||||
\(979\) | 17.1962 | 0.549593 | ||||||||
\(980\) | 4.56340 | 0.145772 | ||||||||
\(981\) | −5.51370 | −0.176039 | ||||||||
\(982\) | −17.4027 | −0.555343 | ||||||||
\(983\) | −16.6018 | −0.529515 | −0.264758 | − | 0.964315i | \(-0.585292\pi\) | ||||
−0.264758 | + | 0.964315i | \(0.585292\pi\) | |||||||
\(984\) | −5.58262 | −0.177967 | ||||||||
\(985\) | −6.75064 | −0.215093 | ||||||||
\(986\) | −17.7278 | −0.564567 | ||||||||
\(987\) | 29.1738 | 0.928611 | ||||||||
\(988\) | 0.945375 | 0.0300764 | ||||||||
\(989\) | −19.2545 | −0.612258 | ||||||||
\(990\) | 41.9372 | 1.33285 | ||||||||
\(991\) | 11.7533 | 0.373357 | 0.186679 | − | 0.982421i | \(-0.440228\pi\) | ||||
0.186679 | + | 0.982421i | \(0.440228\pi\) | |||||||
\(992\) | −12.8502 | −0.407994 | ||||||||
\(993\) | 36.7425 | 1.16599 | ||||||||
\(994\) | 24.8507 | 0.788217 | ||||||||
\(995\) | −35.4935 | −1.12522 | ||||||||
\(996\) | 126.379 | 4.00446 | ||||||||
\(997\) | −36.3309 | −1.15061 | −0.575306 | − | 0.817938i | \(-0.695117\pi\) | ||||
−0.575306 | + | 0.817938i | \(0.695117\pi\) | |||||||
\(998\) | −0.177056 | −0.00560460 | ||||||||
\(999\) | −132.873 | −4.20391 |
(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 | 6041.2.a.c.1.9 | ✓ | 83 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.c.1.9 | ✓ | 83 | 1.1 | even | 1 | trivial |