Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62932 | −1.85921 | −0.929606 | − | 0.368556i | \(-0.879852\pi\) | ||||
−0.929606 | + | 0.368556i | \(0.879852\pi\) | |||||||
\(3\) | 0.928194 | 0.535893 | 0.267947 | − | 0.963434i | \(-0.413655\pi\) | ||||
0.267947 | + | 0.963434i | \(0.413655\pi\) | |||||||
\(4\) | 4.91333 | 2.45667 | ||||||||
\(5\) | 1.81764 | 0.812874 | 0.406437 | − | 0.913679i | \(-0.366771\pi\) | ||||
0.406437 | + | 0.913679i | \(0.366771\pi\) | |||||||
\(6\) | −2.44052 | −0.996339 | ||||||||
\(7\) | 3.79843 | 1.43567 | 0.717835 | − | 0.696213i | \(-0.245133\pi\) | ||||
0.717835 | + | 0.696213i | \(0.245133\pi\) | |||||||
\(8\) | −7.66009 | −2.70825 | ||||||||
\(9\) | −2.13846 | −0.712818 | ||||||||
\(10\) | −4.77917 | −1.51131 | ||||||||
\(11\) | 0.597155 | 0.180049 | 0.0900244 | − | 0.995940i | \(-0.471305\pi\) | ||||
0.0900244 | + | 0.995940i | \(0.471305\pi\) | |||||||
\(12\) | 4.56053 | 1.31651 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −9.98729 | −2.66921 | ||||||||
\(15\) | 1.68713 | 0.435614 | ||||||||
\(16\) | 10.3142 | 2.57854 | ||||||||
\(17\) | −6.29148 | −1.52591 | −0.762954 | − | 0.646452i | \(-0.776252\pi\) | ||||
−0.762954 | + | 0.646452i | \(0.776252\pi\) | |||||||
\(18\) | 5.62269 | 1.32528 | ||||||||
\(19\) | 3.84371 | 0.881809 | 0.440904 | − | 0.897554i | \(-0.354658\pi\) | ||||
0.440904 | + | 0.897554i | \(0.354658\pi\) | |||||||
\(20\) | 8.93068 | 1.99696 | ||||||||
\(21\) | 3.52568 | 0.769366 | ||||||||
\(22\) | −1.57011 | −0.334749 | ||||||||
\(23\) | −1.64780 | −0.343590 | −0.171795 | − | 0.985133i | \(-0.554957\pi\) | ||||
−0.171795 | + | 0.985133i | \(0.554957\pi\) | |||||||
\(24\) | −7.11005 | −1.45133 | ||||||||
\(25\) | −1.69618 | −0.339235 | ||||||||
\(26\) | 2.62932 | 0.515652 | ||||||||
\(27\) | −4.76948 | −0.917888 | ||||||||
\(28\) | 18.6629 | 3.52696 | ||||||||
\(29\) | −7.96027 | −1.47819 | −0.739093 | − | 0.673604i | \(-0.764746\pi\) | ||||
−0.739093 | + | 0.673604i | \(0.764746\pi\) | |||||||
\(30\) | −4.43600 | −0.809898 | ||||||||
\(31\) | −2.25637 | −0.405256 | −0.202628 | − | 0.979256i | \(-0.564948\pi\) | ||||
−0.202628 | + | 0.979256i | \(0.564948\pi\) | |||||||
\(32\) | −11.7991 | −2.08581 | ||||||||
\(33\) | 0.554275 | 0.0964870 | ||||||||
\(34\) | 16.5423 | 2.83699 | ||||||||
\(35\) | 6.90418 | 1.16702 | ||||||||
\(36\) | −10.5069 | −1.75116 | ||||||||
\(37\) | −3.94507 | −0.648565 | −0.324283 | − | 0.945960i | \(-0.605123\pi\) | ||||
−0.324283 | + | 0.945960i | \(0.605123\pi\) | |||||||
\(38\) | −10.1064 | −1.63947 | ||||||||
\(39\) | −0.928194 | −0.148630 | ||||||||
\(40\) | −13.9233 | −2.20147 | ||||||||
\(41\) | 2.09558 | 0.327274 | 0.163637 | − | 0.986521i | \(-0.447677\pi\) | ||||
0.163637 | + | 0.986521i | \(0.447677\pi\) | |||||||
\(42\) | −9.27014 | −1.43041 | ||||||||
\(43\) | −2.01409 | −0.307145 | −0.153573 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153573 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(44\) | 2.93402 | 0.442320 | ||||||||
\(45\) | −3.88695 | −0.579432 | ||||||||
\(46\) | 4.33259 | 0.638806 | ||||||||
\(47\) | 1.57582 | 0.229857 | 0.114928 | − | 0.993374i | \(-0.463336\pi\) | ||||
0.114928 | + | 0.993374i | \(0.463336\pi\) | |||||||
\(48\) | 9.57355 | 1.38182 | ||||||||
\(49\) | 7.42805 | 1.06115 | ||||||||
\(50\) | 4.45979 | 0.630710 | ||||||||
\(51\) | −5.83972 | −0.817724 | ||||||||
\(52\) | −4.91333 | −0.681357 | ||||||||
\(53\) | 4.25474 | 0.584433 | 0.292217 | − | 0.956352i | \(-0.405607\pi\) | ||||
0.292217 | + | 0.956352i | \(0.405607\pi\) | |||||||
\(54\) | 12.5405 | 1.70655 | ||||||||
\(55\) | 1.08541 | 0.146357 | ||||||||
\(56\) | −29.0963 | −3.88816 | ||||||||
\(57\) | 3.56771 | 0.472555 | ||||||||
\(58\) | 20.9301 | 2.74826 | ||||||||
\(59\) | −3.74510 | −0.487571 | −0.243785 | − | 0.969829i | \(-0.578389\pi\) | ||||
−0.243785 | + | 0.969829i | \(0.578389\pi\) | |||||||
\(60\) | 8.28941 | 1.07016 | ||||||||
\(61\) | −2.61101 | −0.334306 | −0.167153 | − | 0.985931i | \(-0.553457\pi\) | ||||
−0.167153 | + | 0.985931i | \(0.553457\pi\) | |||||||
\(62\) | 5.93272 | 0.753456 | ||||||||
\(63\) | −8.12277 | −1.02337 | ||||||||
\(64\) | 10.3953 | 1.29941 | ||||||||
\(65\) | −1.81764 | −0.225451 | ||||||||
\(66\) | −1.45737 | −0.179390 | ||||||||
\(67\) | 7.44967 | 0.910122 | 0.455061 | − | 0.890460i | \(-0.349617\pi\) | ||||
0.455061 | + | 0.890460i | \(0.349617\pi\) | |||||||
\(68\) | −30.9121 | −3.74865 | ||||||||
\(69\) | −1.52948 | −0.184127 | ||||||||
\(70\) | −18.1533 | −2.16974 | ||||||||
\(71\) | −5.97636 | −0.709264 | −0.354632 | − | 0.935006i | \(-0.615394\pi\) | ||||
−0.354632 | + | 0.935006i | \(0.615394\pi\) | |||||||
\(72\) | 16.3808 | 1.93049 | ||||||||
\(73\) | 5.55999 | 0.650747 | 0.325374 | − | 0.945586i | \(-0.394510\pi\) | ||||
0.325374 | + | 0.945586i | \(0.394510\pi\) | |||||||
\(74\) | 10.3729 | 1.20582 | ||||||||
\(75\) | −1.57438 | −0.181794 | ||||||||
\(76\) | 18.8854 | 2.16631 | ||||||||
\(77\) | 2.26825 | 0.258491 | ||||||||
\(78\) | 2.44052 | 0.276335 | ||||||||
\(79\) | 4.70309 | 0.529139 | 0.264569 | − | 0.964367i | \(-0.414770\pi\) | ||||
0.264569 | + | 0.964367i | \(0.414770\pi\) | |||||||
\(80\) | 18.7475 | 2.09603 | ||||||||
\(81\) | 1.98836 | 0.220929 | ||||||||
\(82\) | −5.50995 | −0.608472 | ||||||||
\(83\) | −7.03268 | −0.771936 | −0.385968 | − | 0.922512i | \(-0.626133\pi\) | ||||
−0.385968 | + | 0.922512i | \(0.626133\pi\) | |||||||
\(84\) | 17.3228 | 1.89008 | ||||||||
\(85\) | −11.4357 | −1.24037 | ||||||||
\(86\) | 5.29568 | 0.571048 | ||||||||
\(87\) | −7.38868 | −0.792150 | ||||||||
\(88\) | −4.57426 | −0.487617 | ||||||||
\(89\) | −11.6459 | −1.23446 | −0.617230 | − | 0.786783i | \(-0.711745\pi\) | ||||
−0.617230 | + | 0.786783i | \(0.711745\pi\) | |||||||
\(90\) | 10.2200 | 1.07729 | ||||||||
\(91\) | −3.79843 | −0.398183 | ||||||||
\(92\) | −8.09619 | −0.844086 | ||||||||
\(93\) | −2.09435 | −0.217174 | ||||||||
\(94\) | −4.14334 | −0.427353 | ||||||||
\(95\) | 6.98650 | 0.716800 | ||||||||
\(96\) | −10.9519 | −1.11777 | ||||||||
\(97\) | 16.6462 | 1.69017 | 0.845083 | − | 0.534636i | \(-0.179551\pi\) | ||||
0.845083 | + | 0.534636i | \(0.179551\pi\) | |||||||
\(98\) | −19.5307 | −1.97290 | ||||||||
\(99\) | −1.27699 | −0.128342 | ||||||||
\(100\) | −8.33388 | −0.833388 | ||||||||
\(101\) | 14.3705 | 1.42992 | 0.714959 | − | 0.699166i | \(-0.246445\pi\) | ||||
0.714959 | + | 0.699166i | \(0.246445\pi\) | |||||||
\(102\) | 15.3545 | 1.52032 | ||||||||
\(103\) | −6.51358 | −0.641802 | −0.320901 | − | 0.947113i | \(-0.603986\pi\) | ||||
−0.320901 | + | 0.947113i | \(0.603986\pi\) | |||||||
\(104\) | 7.66009 | 0.751133 | ||||||||
\(105\) | 6.40842 | 0.625398 | ||||||||
\(106\) | −11.1871 | −1.08658 | ||||||||
\(107\) | 2.24666 | 0.217192 | 0.108596 | − | 0.994086i | \(-0.465364\pi\) | ||||
0.108596 | + | 0.994086i | \(0.465364\pi\) | |||||||
\(108\) | −23.4341 | −2.25494 | ||||||||
\(109\) | −7.82159 | −0.749173 | −0.374586 | − | 0.927192i | \(-0.622215\pi\) | ||||
−0.374586 | + | 0.927192i | \(0.622215\pi\) | |||||||
\(110\) | −2.85390 | −0.272109 | ||||||||
\(111\) | −3.66179 | −0.347562 | ||||||||
\(112\) | 39.1776 | 3.70194 | ||||||||
\(113\) | −7.39754 | −0.695902 | −0.347951 | − | 0.937513i | \(-0.613122\pi\) | ||||
−0.347951 | + | 0.937513i | \(0.613122\pi\) | |||||||
\(114\) | −9.38067 | −0.878580 | ||||||||
\(115\) | −2.99511 | −0.279295 | ||||||||
\(116\) | −39.1115 | −3.63141 | ||||||||
\(117\) | 2.13846 | 0.197700 | ||||||||
\(118\) | 9.84708 | 0.906497 | ||||||||
\(119\) | −23.8977 | −2.19070 | ||||||||
\(120\) | −12.9235 | −1.17975 | ||||||||
\(121\) | −10.6434 | −0.967582 | ||||||||
\(122\) | 6.86519 | 0.621545 | ||||||||
\(123\) | 1.94510 | 0.175384 | ||||||||
\(124\) | −11.0863 | −0.995578 | ||||||||
\(125\) | −12.1713 | −1.08863 | ||||||||
\(126\) | 21.3574 | 1.90267 | ||||||||
\(127\) | −6.85015 | −0.607852 | −0.303926 | − | 0.952696i | \(-0.598298\pi\) | ||||
−0.303926 | + | 0.952696i | \(0.598298\pi\) | |||||||
\(128\) | −3.73434 | −0.330072 | ||||||||
\(129\) | −1.86946 | −0.164597 | ||||||||
\(130\) | 4.77917 | 0.419161 | ||||||||
\(131\) | −10.8310 | −0.946309 | −0.473155 | − | 0.880979i | \(-0.656885\pi\) | ||||
−0.473155 | + | 0.880979i | \(0.656885\pi\) | |||||||
\(132\) | 2.72334 | 0.237036 | ||||||||
\(133\) | 14.6001 | 1.26599 | ||||||||
\(134\) | −19.5876 | −1.69211 | ||||||||
\(135\) | −8.66922 | −0.746128 | ||||||||
\(136\) | 48.1933 | 4.13254 | ||||||||
\(137\) | −13.9910 | −1.19533 | −0.597666 | − | 0.801746i | \(-0.703905\pi\) | ||||
−0.597666 | + | 0.801746i | \(0.703905\pi\) | |||||||
\(138\) | 4.02149 | 0.342332 | ||||||||
\(139\) | −10.7896 | −0.915165 | −0.457583 | − | 0.889167i | \(-0.651285\pi\) | ||||
−0.457583 | + | 0.889167i | \(0.651285\pi\) | |||||||
\(140\) | 33.9225 | 2.86698 | ||||||||
\(141\) | 1.46267 | 0.123179 | ||||||||
\(142\) | 15.7138 | 1.31867 | ||||||||
\(143\) | −0.597155 | −0.0499366 | ||||||||
\(144\) | −22.0564 | −1.83803 | ||||||||
\(145\) | −14.4689 | −1.20158 | ||||||||
\(146\) | −14.6190 | −1.20988 | ||||||||
\(147\) | 6.89467 | 0.568663 | ||||||||
\(148\) | −19.3834 | −1.59331 | ||||||||
\(149\) | −7.58507 | −0.621393 | −0.310696 | − | 0.950509i | \(-0.600562\pi\) | ||||
−0.310696 | + | 0.950509i | \(0.600562\pi\) | |||||||
\(150\) | 4.13955 | 0.337993 | ||||||||
\(151\) | −18.7979 | −1.52975 | −0.764875 | − | 0.644179i | \(-0.777199\pi\) | ||||
−0.764875 | + | 0.644179i | \(0.777199\pi\) | |||||||
\(152\) | −29.4432 | −2.38816 | ||||||||
\(153\) | 13.4541 | 1.08770 | ||||||||
\(154\) | −5.96395 | −0.480589 | ||||||||
\(155\) | −4.10127 | −0.329422 | ||||||||
\(156\) | −4.56053 | −0.365134 | ||||||||
\(157\) | −12.9440 | −1.03304 | −0.516521 | − | 0.856275i | \(-0.672773\pi\) | ||||
−0.516521 | + | 0.856275i | \(0.672773\pi\) | |||||||
\(158\) | −12.3659 | −0.983780 | ||||||||
\(159\) | 3.94922 | 0.313194 | ||||||||
\(160\) | −21.4465 | −1.69550 | ||||||||
\(161\) | −6.25905 | −0.493282 | ||||||||
\(162\) | −5.22803 | −0.410753 | ||||||||
\(163\) | 4.80617 | 0.376448 | 0.188224 | − | 0.982126i | \(-0.439727\pi\) | ||||
0.188224 | + | 0.982126i | \(0.439727\pi\) | |||||||
\(164\) | 10.2963 | 0.804004 | ||||||||
\(165\) | 1.00747 | 0.0784318 | ||||||||
\(166\) | 18.4912 | 1.43519 | ||||||||
\(167\) | −0.994647 | −0.0769681 | −0.0384840 | − | 0.999259i | \(-0.512253\pi\) | ||||
−0.0384840 | + | 0.999259i | \(0.512253\pi\) | |||||||
\(168\) | −27.0070 | −2.08364 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 30.0680 | 2.30611 | ||||||||
\(171\) | −8.21961 | −0.628569 | ||||||||
\(172\) | −9.89587 | −0.754553 | ||||||||
\(173\) | −14.6709 | −1.11541 | −0.557705 | − | 0.830039i | \(-0.688318\pi\) | ||||
−0.557705 | + | 0.830039i | \(0.688318\pi\) | |||||||
\(174\) | 19.4272 | 1.47277 | ||||||||
\(175\) | −6.44280 | −0.487030 | ||||||||
\(176\) | 6.15915 | 0.464264 | ||||||||
\(177\) | −3.47618 | −0.261286 | ||||||||
\(178\) | 30.6208 | 2.29512 | ||||||||
\(179\) | −0.555342 | −0.0415082 | −0.0207541 | − | 0.999785i | \(-0.506607\pi\) | ||||
−0.0207541 | + | 0.999785i | \(0.506607\pi\) | |||||||
\(180\) | −19.0979 | −1.42347 | ||||||||
\(181\) | 24.1279 | 1.79341 | 0.896706 | − | 0.442626i | \(-0.145953\pi\) | ||||
0.896706 | + | 0.442626i | \(0.145953\pi\) | |||||||
\(182\) | 9.98729 | 0.740307 | ||||||||
\(183\) | −2.42353 | −0.179152 | ||||||||
\(184\) | 12.6223 | 0.930527 | ||||||||
\(185\) | −7.17073 | −0.527202 | ||||||||
\(186\) | 5.50672 | 0.403772 | ||||||||
\(187\) | −3.75699 | −0.274738 | ||||||||
\(188\) | 7.74253 | 0.564682 | ||||||||
\(189\) | −18.1165 | −1.31778 | ||||||||
\(190\) | −18.3698 | −1.33268 | ||||||||
\(191\) | 13.5152 | 0.977922 | 0.488961 | − | 0.872306i | \(-0.337376\pi\) | ||||
0.488961 | + | 0.872306i | \(0.337376\pi\) | |||||||
\(192\) | 9.64884 | 0.696345 | ||||||||
\(193\) | 19.7479 | 1.42148 | 0.710742 | − | 0.703453i | \(-0.248359\pi\) | ||||
0.710742 | + | 0.703453i | \(0.248359\pi\) | |||||||
\(194\) | −43.7682 | −3.14237 | ||||||||
\(195\) | −1.68713 | −0.120818 | ||||||||
\(196\) | 36.4965 | 2.60689 | ||||||||
\(197\) | −6.46596 | −0.460681 | −0.230340 | − | 0.973110i | \(-0.573984\pi\) | ||||
−0.230340 | + | 0.973110i | \(0.573984\pi\) | |||||||
\(198\) | 3.35761 | 0.238615 | ||||||||
\(199\) | −8.21724 | −0.582505 | −0.291252 | − | 0.956646i | \(-0.594072\pi\) | ||||
−0.291252 | + | 0.956646i | \(0.594072\pi\) | |||||||
\(200\) | 12.9929 | 0.918734 | ||||||||
\(201\) | 6.91474 | 0.487728 | ||||||||
\(202\) | −37.7847 | −2.65852 | ||||||||
\(203\) | −30.2365 | −2.12219 | ||||||||
\(204\) | −28.6925 | −2.00888 | ||||||||
\(205\) | 3.80901 | 0.266033 | ||||||||
\(206\) | 17.1263 | 1.19325 | ||||||||
\(207\) | 3.52374 | 0.244917 | ||||||||
\(208\) | −10.3142 | −0.715159 | ||||||||
\(209\) | 2.29529 | 0.158769 | ||||||||
\(210\) | −16.8498 | −1.16275 | ||||||||
\(211\) | −1.12780 | −0.0776410 | −0.0388205 | − | 0.999246i | \(-0.512360\pi\) | ||||
−0.0388205 | + | 0.999246i | \(0.512360\pi\) | |||||||
\(212\) | 20.9049 | 1.43576 | ||||||||
\(213\) | −5.54723 | −0.380090 | ||||||||
\(214\) | −5.90718 | −0.403806 | ||||||||
\(215\) | −3.66089 | −0.249670 | ||||||||
\(216\) | 36.5347 | 2.48587 | ||||||||
\(217\) | −8.57065 | −0.581814 | ||||||||
\(218\) | 20.5655 | 1.39287 | ||||||||
\(219\) | 5.16075 | 0.348731 | ||||||||
\(220\) | 5.33300 | 0.359551 | ||||||||
\(221\) | 6.29148 | 0.423211 | ||||||||
\(222\) | 9.62803 | 0.646191 | ||||||||
\(223\) | −25.6995 | −1.72097 | −0.860484 | − | 0.509478i | \(-0.829838\pi\) | ||||
−0.860484 | + | 0.509478i | \(0.829838\pi\) | |||||||
\(224\) | −44.8180 | −2.99453 | ||||||||
\(225\) | 3.62720 | 0.241813 | ||||||||
\(226\) | 19.4505 | 1.29383 | ||||||||
\(227\) | 8.19413 | 0.543863 | 0.271932 | − | 0.962317i | \(-0.412338\pi\) | ||||
0.271932 | + | 0.962317i | \(0.412338\pi\) | |||||||
\(228\) | 17.5294 | 1.16091 | ||||||||
\(229\) | −16.0732 | −1.06215 | −0.531073 | − | 0.847326i | \(-0.678211\pi\) | ||||
−0.531073 | + | 0.847326i | \(0.678211\pi\) | |||||||
\(230\) | 7.87511 | 0.519269 | ||||||||
\(231\) | 2.10537 | 0.138524 | ||||||||
\(232\) | 60.9764 | 4.00330 | ||||||||
\(233\) | −15.4720 | −1.01361 | −0.506803 | − | 0.862062i | \(-0.669173\pi\) | ||||
−0.506803 | + | 0.862062i | \(0.669173\pi\) | |||||||
\(234\) | −5.62269 | −0.367567 | ||||||||
\(235\) | 2.86428 | 0.186845 | ||||||||
\(236\) | −18.4009 | −1.19780 | ||||||||
\(237\) | 4.36538 | 0.283562 | ||||||||
\(238\) | 62.8348 | 4.07298 | ||||||||
\(239\) | −10.4146 | −0.673665 | −0.336833 | − | 0.941565i | \(-0.609356\pi\) | ||||
−0.336833 | + | 0.941565i | \(0.609356\pi\) | |||||||
\(240\) | 17.4013 | 1.12325 | ||||||||
\(241\) | −4.52938 | −0.291763 | −0.145881 | − | 0.989302i | \(-0.546602\pi\) | ||||
−0.145881 | + | 0.989302i | \(0.546602\pi\) | |||||||
\(242\) | 27.9849 | 1.79894 | ||||||||
\(243\) | 16.1540 | 1.03628 | ||||||||
\(244\) | −12.8288 | −0.821278 | ||||||||
\(245\) | 13.5015 | 0.862582 | ||||||||
\(246\) | −5.11430 | −0.326076 | ||||||||
\(247\) | −3.84371 | −0.244570 | ||||||||
\(248\) | 17.2840 | 1.09753 | ||||||||
\(249\) | −6.52769 | −0.413676 | ||||||||
\(250\) | 32.0021 | 2.02399 | ||||||||
\(251\) | −6.90516 | −0.435850 | −0.217925 | − | 0.975966i | \(-0.569929\pi\) | ||||
−0.217925 | + | 0.975966i | \(0.569929\pi\) | |||||||
\(252\) | −39.9099 | −2.51408 | ||||||||
\(253\) | −0.983991 | −0.0618630 | ||||||||
\(254\) | 18.0112 | 1.13013 | ||||||||
\(255\) | −10.6145 | −0.664707 | ||||||||
\(256\) | −10.9718 | −0.685736 | ||||||||
\(257\) | 28.2197 | 1.76030 | 0.880150 | − | 0.474696i | \(-0.157442\pi\) | ||||
0.880150 | + | 0.474696i | \(0.157442\pi\) | |||||||
\(258\) | 4.91542 | 0.306021 | ||||||||
\(259\) | −14.9851 | −0.931126 | ||||||||
\(260\) | −8.93068 | −0.553857 | ||||||||
\(261\) | 17.0227 | 1.05368 | ||||||||
\(262\) | 28.4782 | 1.75939 | ||||||||
\(263\) | −12.4078 | −0.765097 | −0.382549 | − | 0.923935i | \(-0.624954\pi\) | ||||
−0.382549 | + | 0.923935i | \(0.624954\pi\) | |||||||
\(264\) | −4.24580 | −0.261311 | ||||||||
\(265\) | 7.73359 | 0.475071 | ||||||||
\(266\) | −38.3883 | −2.35374 | ||||||||
\(267\) | −10.8096 | −0.661539 | ||||||||
\(268\) | 36.6027 | 2.23587 | ||||||||
\(269\) | 6.06078 | 0.369532 | 0.184766 | − | 0.982783i | \(-0.440847\pi\) | ||||
0.184766 | + | 0.982783i | \(0.440847\pi\) | |||||||
\(270\) | 22.7942 | 1.38721 | ||||||||
\(271\) | 7.27201 | 0.441743 | 0.220872 | − | 0.975303i | \(-0.429110\pi\) | ||||
0.220872 | + | 0.975303i | \(0.429110\pi\) | |||||||
\(272\) | −64.8914 | −3.93462 | ||||||||
\(273\) | −3.52568 | −0.213384 | ||||||||
\(274\) | 36.7868 | 2.22237 | ||||||||
\(275\) | −1.01288 | −0.0610789 | ||||||||
\(276\) | −7.51483 | −0.452340 | ||||||||
\(277\) | 21.1748 | 1.27227 | 0.636135 | − | 0.771578i | \(-0.280532\pi\) | ||||
0.636135 | + | 0.771578i | \(0.280532\pi\) | |||||||
\(278\) | 28.3694 | 1.70149 | ||||||||
\(279\) | 4.82514 | 0.288874 | ||||||||
\(280\) | −52.8867 | −3.16058 | ||||||||
\(281\) | 21.8837 | 1.30547 | 0.652736 | − | 0.757585i | \(-0.273621\pi\) | ||||
0.652736 | + | 0.757585i | \(0.273621\pi\) | |||||||
\(282\) | −3.84582 | −0.229015 | ||||||||
\(283\) | 24.2867 | 1.44369 | 0.721846 | − | 0.692054i | \(-0.243294\pi\) | ||||
0.721846 | + | 0.692054i | \(0.243294\pi\) | |||||||
\(284\) | −29.3639 | −1.74242 | ||||||||
\(285\) | 6.48483 | 0.384128 | ||||||||
\(286\) | 1.57011 | 0.0928426 | ||||||||
\(287\) | 7.95990 | 0.469858 | ||||||||
\(288\) | 25.2318 | 1.48680 | ||||||||
\(289\) | 22.5828 | 1.32840 | ||||||||
\(290\) | 38.0435 | 2.23399 | ||||||||
\(291\) | 15.4509 | 0.905748 | ||||||||
\(292\) | 27.3181 | 1.59867 | ||||||||
\(293\) | 3.82656 | 0.223550 | 0.111775 | − | 0.993734i | \(-0.464346\pi\) | ||||
0.111775 | + | 0.993734i | \(0.464346\pi\) | |||||||
\(294\) | −18.1283 | −1.05726 | ||||||||
\(295\) | −6.80726 | −0.396334 | ||||||||
\(296\) | 30.2196 | 1.75648 | ||||||||
\(297\) | −2.84812 | −0.165265 | ||||||||
\(298\) | 19.9436 | 1.15530 | ||||||||
\(299\) | 1.64780 | 0.0952947 | ||||||||
\(300\) | −7.73546 | −0.446607 | ||||||||
\(301\) | −7.65036 | −0.440959 | ||||||||
\(302\) | 49.4257 | 2.84413 | ||||||||
\(303\) | 13.3386 | 0.766283 | ||||||||
\(304\) | 39.6447 | 2.27378 | ||||||||
\(305\) | −4.74589 | −0.271749 | ||||||||
\(306\) | −35.3750 | −2.02226 | ||||||||
\(307\) | −4.14652 | −0.236654 | −0.118327 | − | 0.992975i | \(-0.537753\pi\) | ||||
−0.118327 | + | 0.992975i | \(0.537753\pi\) | |||||||
\(308\) | 11.1447 | 0.635026 | ||||||||
\(309\) | −6.04587 | −0.343938 | ||||||||
\(310\) | 10.7836 | 0.612465 | ||||||||
\(311\) | −19.7040 | −1.11731 | −0.558654 | − | 0.829401i | \(-0.688682\pi\) | ||||
−0.558654 | + | 0.829401i | \(0.688682\pi\) | |||||||
\(312\) | 7.11005 | 0.402527 | ||||||||
\(313\) | −11.6856 | −0.660511 | −0.330255 | − | 0.943892i | \(-0.607135\pi\) | ||||
−0.330255 | + | 0.943892i | \(0.607135\pi\) | |||||||
\(314\) | 34.0339 | 1.92064 | ||||||||
\(315\) | −14.7643 | −0.831873 | ||||||||
\(316\) | 23.1078 | 1.29992 | ||||||||
\(317\) | −15.0907 | −0.847576 | −0.423788 | − | 0.905761i | \(-0.639300\pi\) | ||||
−0.423788 | + | 0.905761i | \(0.639300\pi\) | |||||||
\(318\) | −10.3838 | −0.582293 | ||||||||
\(319\) | −4.75351 | −0.266146 | ||||||||
\(320\) | 18.8949 | 1.05626 | ||||||||
\(321\) | 2.08533 | 0.116392 | ||||||||
\(322\) | 16.4570 | 0.917115 | ||||||||
\(323\) | −24.1827 | −1.34556 | ||||||||
\(324\) | 9.76946 | 0.542748 | ||||||||
\(325\) | 1.69618 | 0.0940869 | ||||||||
\(326\) | −12.6370 | −0.699897 | ||||||||
\(327\) | −7.25996 | −0.401477 | ||||||||
\(328\) | −16.0523 | −0.886341 | ||||||||
\(329\) | 5.98564 | 0.329999 | ||||||||
\(330\) | −2.64897 | −0.145821 | ||||||||
\(331\) | −12.0351 | −0.661508 | −0.330754 | − | 0.943717i | \(-0.607303\pi\) | ||||
−0.330754 | + | 0.943717i | \(0.607303\pi\) | |||||||
\(332\) | −34.5539 | −1.89639 | ||||||||
\(333\) | 8.43635 | 0.462309 | ||||||||
\(334\) | 2.61525 | 0.143100 | ||||||||
\(335\) | 13.5408 | 0.739815 | ||||||||
\(336\) | 36.3645 | 1.98384 | ||||||||
\(337\) | −15.0586 | −0.820296 | −0.410148 | − | 0.912019i | \(-0.634523\pi\) | ||||
−0.410148 | + | 0.912019i | \(0.634523\pi\) | |||||||
\(338\) | −2.62932 | −0.143016 | ||||||||
\(339\) | −6.86635 | −0.372929 | ||||||||
\(340\) | −56.1872 | −3.04718 | ||||||||
\(341\) | −1.34740 | −0.0729658 | ||||||||
\(342\) | 21.6120 | 1.16864 | ||||||||
\(343\) | 1.62592 | 0.0877914 | ||||||||
\(344\) | 15.4281 | 0.831826 | ||||||||
\(345\) | −2.78004 | −0.149673 | ||||||||
\(346\) | 38.5746 | 2.07378 | ||||||||
\(347\) | −22.9679 | −1.23298 | −0.616492 | − | 0.787361i | \(-0.711447\pi\) | ||||
−0.616492 | + | 0.787361i | \(0.711447\pi\) | |||||||
\(348\) | −36.3030 | −1.94605 | ||||||||
\(349\) | −2.01351 | −0.107781 | −0.0538904 | − | 0.998547i | \(-0.517162\pi\) | ||||
−0.0538904 | + | 0.998547i | \(0.517162\pi\) | |||||||
\(350\) | 16.9402 | 0.905492 | ||||||||
\(351\) | 4.76948 | 0.254576 | ||||||||
\(352\) | −7.04588 | −0.375547 | ||||||||
\(353\) | 3.70839 | 0.197378 | 0.0986888 | − | 0.995118i | \(-0.468535\pi\) | ||||
0.0986888 | + | 0.995118i | \(0.468535\pi\) | |||||||
\(354\) | 9.14000 | 0.485786 | ||||||||
\(355\) | −10.8629 | −0.576542 | ||||||||
\(356\) | −57.2201 | −3.03266 | ||||||||
\(357\) | −22.1817 | −1.17398 | ||||||||
\(358\) | 1.46017 | 0.0771725 | ||||||||
\(359\) | 4.67697 | 0.246841 | 0.123420 | − | 0.992354i | \(-0.460614\pi\) | ||||
0.123420 | + | 0.992354i | \(0.460614\pi\) | |||||||
\(360\) | 29.7744 | 1.56925 | ||||||||
\(361\) | −4.22586 | −0.222414 | ||||||||
\(362\) | −63.4400 | −3.33433 | ||||||||
\(363\) | −9.87915 | −0.518521 | ||||||||
\(364\) | −18.6629 | −0.978204 | ||||||||
\(365\) | 10.1061 | 0.528976 | ||||||||
\(366\) | 6.37223 | 0.333082 | ||||||||
\(367\) | −2.88746 | −0.150724 | −0.0753622 | − | 0.997156i | \(-0.524011\pi\) | ||||
−0.0753622 | + | 0.997156i | \(0.524011\pi\) | |||||||
\(368\) | −16.9957 | −0.885961 | ||||||||
\(369\) | −4.48130 | −0.233287 | ||||||||
\(370\) | 18.8541 | 0.980180 | ||||||||
\(371\) | 16.1613 | 0.839053 | ||||||||
\(372\) | −10.2902 | −0.533524 | ||||||||
\(373\) | 31.0683 | 1.60866 | 0.804329 | − | 0.594184i | \(-0.202525\pi\) | ||||
0.804329 | + | 0.594184i | \(0.202525\pi\) | |||||||
\(374\) | 9.87833 | 0.510796 | ||||||||
\(375\) | −11.2973 | −0.583389 | ||||||||
\(376\) | −12.0709 | −0.622510 | ||||||||
\(377\) | 7.96027 | 0.409975 | ||||||||
\(378\) | 47.6342 | 2.45004 | ||||||||
\(379\) | 4.11997 | 0.211628 | 0.105814 | − | 0.994386i | \(-0.466255\pi\) | ||||
0.105814 | + | 0.994386i | \(0.466255\pi\) | |||||||
\(380\) | 34.3270 | 1.76094 | ||||||||
\(381\) | −6.35827 | −0.325744 | ||||||||
\(382\) | −35.5357 | −1.81816 | ||||||||
\(383\) | −0.560735 | −0.0286522 | −0.0143261 | − | 0.999897i | \(-0.504560\pi\) | ||||
−0.0143261 | + | 0.999897i | \(0.504560\pi\) | |||||||
\(384\) | −3.46619 | −0.176883 | ||||||||
\(385\) | 4.12286 | 0.210121 | ||||||||
\(386\) | −51.9236 | −2.64284 | ||||||||
\(387\) | 4.30703 | 0.218939 | ||||||||
\(388\) | 81.7883 | 4.15217 | ||||||||
\(389\) | 19.8640 | 1.00714 | 0.503572 | − | 0.863953i | \(-0.332019\pi\) | ||||
0.503572 | + | 0.863953i | \(0.332019\pi\) | |||||||
\(390\) | 4.43600 | 0.224625 | ||||||||
\(391\) | 10.3671 | 0.524287 | ||||||||
\(392\) | −56.8995 | −2.87386 | ||||||||
\(393\) | −10.0533 | −0.507121 | ||||||||
\(394\) | 17.0011 | 0.856502 | ||||||||
\(395\) | 8.54853 | 0.430123 | ||||||||
\(396\) | −6.27427 | −0.315294 | ||||||||
\(397\) | 1.71307 | 0.0859766 | 0.0429883 | − | 0.999076i | \(-0.486312\pi\) | ||||
0.0429883 | + | 0.999076i | \(0.486312\pi\) | |||||||
\(398\) | 21.6058 | 1.08300 | ||||||||
\(399\) | 13.5517 | 0.678434 | ||||||||
\(400\) | −17.4946 | −0.874732 | ||||||||
\(401\) | 26.2570 | 1.31121 | 0.655606 | − | 0.755103i | \(-0.272413\pi\) | ||||
0.655606 | + | 0.755103i | \(0.272413\pi\) | |||||||
\(402\) | −18.1811 | −0.906790 | ||||||||
\(403\) | 2.25637 | 0.112398 | ||||||||
\(404\) | 70.6070 | 3.51283 | ||||||||
\(405\) | 3.61412 | 0.179587 | ||||||||
\(406\) | 79.5015 | 3.94560 | ||||||||
\(407\) | −2.35582 | −0.116773 | ||||||||
\(408\) | 44.7328 | 2.21460 | ||||||||
\(409\) | 15.0583 | 0.744584 | 0.372292 | − | 0.928116i | \(-0.378572\pi\) | ||||
0.372292 | + | 0.928116i | \(0.378572\pi\) | |||||||
\(410\) | −10.0151 | −0.494611 | ||||||||
\(411\) | −12.9864 | −0.640570 | ||||||||
\(412\) | −32.0034 | −1.57669 | ||||||||
\(413\) | −14.2255 | −0.699991 | ||||||||
\(414\) | −9.26506 | −0.455353 | ||||||||
\(415\) | −12.7829 | −0.627487 | ||||||||
\(416\) | 11.7991 | 0.578498 | ||||||||
\(417\) | −10.0149 | −0.490431 | ||||||||
\(418\) | −6.03506 | −0.295184 | ||||||||
\(419\) | −8.08717 | −0.395084 | −0.197542 | − | 0.980294i | \(-0.563296\pi\) | ||||
−0.197542 | + | 0.980294i | \(0.563296\pi\) | |||||||
\(420\) | 31.4867 | 1.53639 | ||||||||
\(421\) | −24.7564 | −1.20655 | −0.603276 | − | 0.797532i | \(-0.706138\pi\) | ||||
−0.603276 | + | 0.797532i | \(0.706138\pi\) | |||||||
\(422\) | 2.96535 | 0.144351 | ||||||||
\(423\) | −3.36982 | −0.163846 | ||||||||
\(424\) | −32.5917 | −1.58279 | ||||||||
\(425\) | 10.6715 | 0.517642 | ||||||||
\(426\) | 14.5854 | 0.706667 | ||||||||
\(427\) | −9.91774 | −0.479953 | ||||||||
\(428\) | 11.0386 | 0.533569 | ||||||||
\(429\) | −0.554275 | −0.0267607 | ||||||||
\(430\) | 9.62565 | 0.464190 | ||||||||
\(431\) | 28.6227 | 1.37871 | 0.689354 | − | 0.724425i | \(-0.257895\pi\) | ||||
0.689354 | + | 0.724425i | \(0.257895\pi\) | |||||||
\(432\) | −49.1933 | −2.36681 | ||||||||
\(433\) | −2.93982 | −0.141279 | −0.0706394 | − | 0.997502i | \(-0.522504\pi\) | ||||
−0.0706394 | + | 0.997502i | \(0.522504\pi\) | |||||||
\(434\) | 22.5350 | 1.08171 | ||||||||
\(435\) | −13.4300 | −0.643918 | ||||||||
\(436\) | −38.4301 | −1.84047 | ||||||||
\(437\) | −6.33367 | −0.302981 | ||||||||
\(438\) | −13.5693 | −0.648365 | ||||||||
\(439\) | 3.26546 | 0.155852 | 0.0779260 | − | 0.996959i | \(-0.475170\pi\) | ||||
0.0779260 | + | 0.996959i | \(0.475170\pi\) | |||||||
\(440\) | −8.31436 | −0.396372 | ||||||||
\(441\) | −15.8846 | −0.756407 | ||||||||
\(442\) | −16.5423 | −0.786838 | ||||||||
\(443\) | −11.3376 | −0.538668 | −0.269334 | − | 0.963047i | \(-0.586803\pi\) | ||||
−0.269334 | + | 0.963047i | \(0.586803\pi\) | |||||||
\(444\) | −17.9916 | −0.853843 | ||||||||
\(445\) | −21.1680 | −1.00346 | ||||||||
\(446\) | 67.5723 | 3.19964 | ||||||||
\(447\) | −7.04042 | −0.333000 | ||||||||
\(448\) | 39.4857 | 1.86552 | ||||||||
\(449\) | 25.4093 | 1.19914 | 0.599570 | − | 0.800322i | \(-0.295338\pi\) | ||||
0.599570 | + | 0.800322i | \(0.295338\pi\) | |||||||
\(450\) | −9.53707 | −0.449582 | ||||||||
\(451\) | 1.25138 | 0.0589254 | ||||||||
\(452\) | −36.3466 | −1.70960 | ||||||||
\(453\) | −17.4481 | −0.819782 | ||||||||
\(454\) | −21.5450 | −1.01116 | ||||||||
\(455\) | −6.90418 | −0.323673 | ||||||||
\(456\) | −27.3290 | −1.27980 | ||||||||
\(457\) | 18.5014 | 0.865461 | 0.432730 | − | 0.901523i | \(-0.357550\pi\) | ||||
0.432730 | + | 0.901523i | \(0.357550\pi\) | |||||||
\(458\) | 42.2616 | 1.97475 | ||||||||
\(459\) | 30.0071 | 1.40061 | ||||||||
\(460\) | −14.7160 | −0.686136 | ||||||||
\(461\) | −30.3524 | −1.41365 | −0.706826 | − | 0.707388i | \(-0.749874\pi\) | ||||
−0.706826 | + | 0.707388i | \(0.749874\pi\) | |||||||
\(462\) | −5.53571 | −0.257544 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | −82.1036 | −3.81156 | ||||||||
\(465\) | −3.80678 | −0.176535 | ||||||||
\(466\) | 40.6809 | 1.88451 | ||||||||
\(467\) | 17.7439 | 0.821088 | 0.410544 | − | 0.911841i | \(-0.365339\pi\) | ||||
0.410544 | + | 0.911841i | \(0.365339\pi\) | |||||||
\(468\) | 10.5069 | 0.485684 | ||||||||
\(469\) | 28.2970 | 1.30664 | ||||||||
\(470\) | −7.53111 | −0.347384 | ||||||||
\(471\) | −12.0145 | −0.553600 | ||||||||
\(472\) | 28.6878 | 1.32046 | ||||||||
\(473\) | −1.20272 | −0.0553011 | ||||||||
\(474\) | −11.4780 | −0.527201 | ||||||||
\(475\) | −6.51962 | −0.299140 | ||||||||
\(476\) | −117.418 | −5.38182 | ||||||||
\(477\) | −9.09857 | −0.416595 | ||||||||
\(478\) | 27.3834 | 1.25249 | ||||||||
\(479\) | 19.0719 | 0.871417 | 0.435709 | − | 0.900088i | \(-0.356498\pi\) | ||||
0.435709 | + | 0.900088i | \(0.356498\pi\) | |||||||
\(480\) | −19.9066 | −0.908606 | ||||||||
\(481\) | 3.94507 | 0.179880 | ||||||||
\(482\) | 11.9092 | 0.542449 | ||||||||
\(483\) | −5.80961 | −0.264346 | ||||||||
\(484\) | −52.2946 | −2.37703 | ||||||||
\(485\) | 30.2568 | 1.37389 | ||||||||
\(486\) | −42.4742 | −1.92667 | ||||||||
\(487\) | −22.2951 | −1.01029 | −0.505143 | − | 0.863036i | \(-0.668560\pi\) | ||||
−0.505143 | + | 0.863036i | \(0.668560\pi\) | |||||||
\(488\) | 20.0006 | 0.905384 | ||||||||
\(489\) | 4.46106 | 0.201736 | ||||||||
\(490\) | −35.4999 | −1.60372 | ||||||||
\(491\) | 24.7232 | 1.11574 | 0.557871 | − | 0.829927i | \(-0.311618\pi\) | ||||
0.557871 | + | 0.829927i | \(0.311618\pi\) | |||||||
\(492\) | 9.55694 | 0.430860 | ||||||||
\(493\) | 50.0819 | 2.25558 | ||||||||
\(494\) | 10.1064 | 0.454707 | ||||||||
\(495\) | −2.32111 | −0.104326 | ||||||||
\(496\) | −23.2726 | −1.04497 | ||||||||
\(497\) | −22.7008 | −1.01827 | ||||||||
\(498\) | 17.1634 | 0.769110 | ||||||||
\(499\) | 28.3063 | 1.26717 | 0.633583 | − | 0.773675i | \(-0.281583\pi\) | ||||
0.633583 | + | 0.773675i | \(0.281583\pi\) | |||||||
\(500\) | −59.8014 | −2.67440 | ||||||||
\(501\) | −0.923225 | −0.0412467 | ||||||||
\(502\) | 18.1559 | 0.810337 | ||||||||
\(503\) | −9.48245 | −0.422802 | −0.211401 | − | 0.977399i | \(-0.567803\pi\) | ||||
−0.211401 | + | 0.977399i | \(0.567803\pi\) | |||||||
\(504\) | 62.2211 | 2.77155 | ||||||||
\(505\) | 26.1204 | 1.16234 | ||||||||
\(506\) | 2.58723 | 0.115016 | ||||||||
\(507\) | 0.928194 | 0.0412226 | ||||||||
\(508\) | −33.6570 | −1.49329 | ||||||||
\(509\) | −10.0831 | −0.446926 | −0.223463 | − | 0.974712i | \(-0.571736\pi\) | ||||
−0.223463 | + | 0.974712i | \(0.571736\pi\) | |||||||
\(510\) | 27.9090 | 1.23583 | ||||||||
\(511\) | 21.1192 | 0.934258 | ||||||||
\(512\) | 36.3170 | 1.60500 | ||||||||
\(513\) | −18.3325 | −0.809401 | ||||||||
\(514\) | −74.1988 | −3.27277 | ||||||||
\(515\) | −11.8394 | −0.521705 | ||||||||
\(516\) | −9.18529 | −0.404360 | ||||||||
\(517\) | 0.941008 | 0.0413855 | ||||||||
\(518\) | 39.4005 | 1.73116 | ||||||||
\(519\) | −13.6175 | −0.597741 | ||||||||
\(520\) | 13.9233 | 0.610577 | ||||||||
\(521\) | 20.7233 | 0.907902 | 0.453951 | − | 0.891027i | \(-0.350014\pi\) | ||||
0.453951 | + | 0.891027i | \(0.350014\pi\) | |||||||
\(522\) | −44.7581 | −1.95901 | ||||||||
\(523\) | 14.9854 | 0.655264 | 0.327632 | − | 0.944805i | \(-0.393749\pi\) | ||||
0.327632 | + | 0.944805i | \(0.393749\pi\) | |||||||
\(524\) | −53.2163 | −2.32477 | ||||||||
\(525\) | −5.98017 | −0.260996 | ||||||||
\(526\) | 32.6241 | 1.42248 | ||||||||
\(527\) | 14.1959 | 0.618383 | ||||||||
\(528\) | 5.71689 | 0.248796 | ||||||||
\(529\) | −20.2848 | −0.881946 | ||||||||
\(530\) | −20.3341 | −0.883257 | ||||||||
\(531\) | 8.00874 | 0.347550 | ||||||||
\(532\) | 71.7350 | 3.11011 | ||||||||
\(533\) | −2.09558 | −0.0907696 | ||||||||
\(534\) | 28.4220 | 1.22994 | ||||||||
\(535\) | 4.08362 | 0.176550 | ||||||||
\(536\) | −57.0651 | −2.46484 | ||||||||
\(537\) | −0.515465 | −0.0222440 | ||||||||
\(538\) | −15.9357 | −0.687039 | ||||||||
\(539\) | 4.43569 | 0.191059 | ||||||||
\(540\) | −42.5948 | −1.83299 | ||||||||
\(541\) | 13.6275 | 0.585893 | 0.292946 | − | 0.956129i | \(-0.405364\pi\) | ||||
0.292946 | + | 0.956129i | \(0.405364\pi\) | |||||||
\(542\) | −19.1205 | −0.821294 | ||||||||
\(543\) | 22.3954 | 0.961078 | ||||||||
\(544\) | 74.2338 | 3.18275 | ||||||||
\(545\) | −14.2169 | −0.608983 | ||||||||
\(546\) | 9.27014 | 0.396726 | ||||||||
\(547\) | −25.9183 | −1.10819 | −0.554094 | − | 0.832454i | \(-0.686935\pi\) | ||||
−0.554094 | + | 0.832454i | \(0.686935\pi\) | |||||||
\(548\) | −68.7424 | −2.93653 | ||||||||
\(549\) | 5.58353 | 0.238299 | ||||||||
\(550\) | 2.66318 | 0.113559 | ||||||||
\(551\) | −30.5970 | −1.30348 | ||||||||
\(552\) | 11.7159 | 0.498663 | ||||||||
\(553\) | 17.8643 | 0.759669 | ||||||||
\(554\) | −55.6753 | −2.36542 | ||||||||
\(555\) | −6.65583 | −0.282524 | ||||||||
\(556\) | −53.0131 | −2.24826 | ||||||||
\(557\) | 0.345068 | 0.0146210 | 0.00731050 | − | 0.999973i | \(-0.497673\pi\) | ||||
0.00731050 | + | 0.999973i | \(0.497673\pi\) | |||||||
\(558\) | −12.6869 | −0.537077 | ||||||||
\(559\) | 2.01409 | 0.0851867 | ||||||||
\(560\) | 71.2109 | 3.00921 | ||||||||
\(561\) | −3.48721 | −0.147230 | ||||||||
\(562\) | −57.5393 | −2.42715 | ||||||||
\(563\) | 7.18860 | 0.302963 | 0.151482 | − | 0.988460i | \(-0.451596\pi\) | ||||
0.151482 | + | 0.988460i | \(0.451596\pi\) | |||||||
\(564\) | 7.18657 | 0.302609 | ||||||||
\(565\) | −13.4461 | −0.565681 | ||||||||
\(566\) | −63.8574 | −2.68413 | ||||||||
\(567\) | 7.55263 | 0.317181 | ||||||||
\(568\) | 45.7795 | 1.92086 | ||||||||
\(569\) | −12.0933 | −0.506977 | −0.253489 | − | 0.967338i | \(-0.581578\pi\) | ||||
−0.253489 | + | 0.967338i | \(0.581578\pi\) | |||||||
\(570\) | −17.0507 | −0.714175 | ||||||||
\(571\) | −7.81091 | −0.326876 | −0.163438 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163438 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(572\) | −2.93402 | −0.122677 | ||||||||
\(573\) | 12.5447 | 0.524062 | ||||||||
\(574\) | −20.9291 | −0.873565 | ||||||||
\(575\) | 2.79496 | 0.116558 | ||||||||
\(576\) | −22.2298 | −0.926243 | ||||||||
\(577\) | −26.7558 | −1.11386 | −0.556929 | − | 0.830560i | \(-0.688021\pi\) | ||||
−0.556929 | + | 0.830560i | \(0.688021\pi\) | |||||||
\(578\) | −59.3773 | −2.46977 | ||||||||
\(579\) | 18.3299 | 0.761764 | ||||||||
\(580\) | −71.0907 | −2.95188 | ||||||||
\(581\) | −26.7131 | −1.10825 | ||||||||
\(582\) | −40.6254 | −1.68398 | ||||||||
\(583\) | 2.54074 | 0.105227 | ||||||||
\(584\) | −42.5900 | −1.76239 | ||||||||
\(585\) | 3.88695 | 0.160705 | ||||||||
\(586\) | −10.0613 | −0.415626 | ||||||||
\(587\) | −2.66043 | −0.109808 | −0.0549039 | − | 0.998492i | \(-0.517485\pi\) | ||||
−0.0549039 | + | 0.998492i | \(0.517485\pi\) | |||||||
\(588\) | 33.8758 | 1.39702 | ||||||||
\(589\) | −8.67284 | −0.357358 | ||||||||
\(590\) | 17.8985 | 0.736868 | ||||||||
\(591\) | −6.00167 | −0.246876 | ||||||||
\(592\) | −40.6901 | −1.67235 | ||||||||
\(593\) | 43.4373 | 1.78375 | 0.891877 | − | 0.452277i | \(-0.149388\pi\) | ||||
0.891877 | + | 0.452277i | \(0.149388\pi\) | |||||||
\(594\) | 7.48862 | 0.307262 | ||||||||
\(595\) | −43.4375 | −1.78077 | ||||||||
\(596\) | −37.2680 | −1.52656 | ||||||||
\(597\) | −7.62719 | −0.312160 | ||||||||
\(598\) | −4.33259 | −0.177173 | ||||||||
\(599\) | −21.3712 | −0.873205 | −0.436602 | − | 0.899655i | \(-0.643818\pi\) | ||||
−0.436602 | + | 0.899655i | \(0.643818\pi\) | |||||||
\(600\) | 12.0599 | 0.492343 | ||||||||
\(601\) | −16.5101 | −0.673461 | −0.336731 | − | 0.941601i | \(-0.609321\pi\) | ||||
−0.336731 | + | 0.941601i | \(0.609321\pi\) | |||||||
\(602\) | 20.1152 | 0.819836 | ||||||||
\(603\) | −15.9308 | −0.648752 | ||||||||
\(604\) | −92.3602 | −3.75808 | ||||||||
\(605\) | −19.3459 | −0.786523 | ||||||||
\(606\) | −35.0715 | −1.42468 | ||||||||
\(607\) | 41.0526 | 1.66627 | 0.833136 | − | 0.553068i | \(-0.186543\pi\) | ||||
0.833136 | + | 0.553068i | \(0.186543\pi\) | |||||||
\(608\) | −45.3524 | −1.83928 | ||||||||
\(609\) | −28.0654 | −1.13727 | ||||||||
\(610\) | 12.4785 | 0.505238 | ||||||||
\(611\) | −1.57582 | −0.0637509 | ||||||||
\(612\) | 66.1042 | 2.67211 | ||||||||
\(613\) | 26.8724 | 1.08536 | 0.542682 | − | 0.839938i | \(-0.317409\pi\) | ||||
0.542682 | + | 0.839938i | \(0.317409\pi\) | |||||||
\(614\) | 10.9025 | 0.439990 | ||||||||
\(615\) | 3.53550 | 0.142565 | ||||||||
\(616\) | −17.3750 | −0.700058 | ||||||||
\(617\) | −35.3571 | −1.42342 | −0.711712 | − | 0.702471i | \(-0.752080\pi\) | ||||
−0.711712 | + | 0.702471i | \(0.752080\pi\) | |||||||
\(618\) | 15.8965 | 0.639453 | ||||||||
\(619\) | −20.1091 | −0.808252 | −0.404126 | − | 0.914703i | \(-0.632424\pi\) | ||||
−0.404126 | + | 0.914703i | \(0.632424\pi\) | |||||||
\(620\) | −20.1509 | −0.809280 | ||||||||
\(621\) | 7.85915 | 0.315377 | ||||||||
\(622\) | 51.8080 | 2.07731 | ||||||||
\(623\) | −44.2360 | −1.77228 | ||||||||
\(624\) | −9.57355 | −0.383249 | ||||||||
\(625\) | −13.6421 | −0.545684 | ||||||||
\(626\) | 30.7253 | 1.22803 | ||||||||
\(627\) | 2.13048 | 0.0850830 | ||||||||
\(628\) | −63.5980 | −2.53784 | ||||||||
\(629\) | 24.8203 | 0.989652 | ||||||||
\(630\) | 38.8201 | 1.54663 | ||||||||
\(631\) | 1.90161 | 0.0757020 | 0.0378510 | − | 0.999283i | \(-0.487949\pi\) | ||||
0.0378510 | + | 0.999283i | \(0.487949\pi\) | |||||||
\(632\) | −36.0261 | −1.43304 | ||||||||
\(633\) | −1.04682 | −0.0416073 | ||||||||
\(634\) | 39.6782 | 1.57582 | ||||||||
\(635\) | −12.4511 | −0.494107 | ||||||||
\(636\) | 19.4038 | 0.769413 | ||||||||
\(637\) | −7.42805 | −0.294310 | ||||||||
\(638\) | 12.4985 | 0.494821 | ||||||||
\(639\) | 12.7802 | 0.505576 | ||||||||
\(640\) | −6.78769 | −0.268307 | ||||||||
\(641\) | −31.4869 | −1.24366 | −0.621830 | − | 0.783153i | \(-0.713610\pi\) | ||||
−0.621830 | + | 0.783153i | \(0.713610\pi\) | |||||||
\(642\) | −5.48301 | −0.216397 | ||||||||
\(643\) | 9.04150 | 0.356562 | 0.178281 | − | 0.983980i | \(-0.442946\pi\) | ||||
0.178281 | + | 0.983980i | \(0.442946\pi\) | |||||||
\(644\) | −30.7528 | −1.21183 | ||||||||
\(645\) | −3.39801 | −0.133797 | ||||||||
\(646\) | 63.5840 | 2.50168 | ||||||||
\(647\) | 23.4677 | 0.922609 | 0.461304 | − | 0.887242i | \(-0.347382\pi\) | ||||
0.461304 | + | 0.887242i | \(0.347382\pi\) | |||||||
\(648\) | −15.2310 | −0.598330 | ||||||||
\(649\) | −2.23641 | −0.0877866 | ||||||||
\(650\) | −4.45979 | −0.174927 | ||||||||
\(651\) | −7.95523 | −0.311790 | ||||||||
\(652\) | 23.6143 | 0.924808 | ||||||||
\(653\) | −46.6335 | −1.82491 | −0.912455 | − | 0.409178i | \(-0.865816\pi\) | ||||
−0.912455 | + | 0.409178i | \(0.865816\pi\) | |||||||
\(654\) | 19.0888 | 0.746430 | ||||||||
\(655\) | −19.6869 | −0.769230 | ||||||||
\(656\) | 21.6141 | 0.843891 | ||||||||
\(657\) | −11.8898 | −0.463865 | ||||||||
\(658\) | −15.7382 | −0.613538 | ||||||||
\(659\) | −26.9078 | −1.04818 | −0.524089 | − | 0.851663i | \(-0.675594\pi\) | ||||
−0.524089 | + | 0.851663i | \(0.675594\pi\) | |||||||
\(660\) | 4.95006 | 0.192681 | ||||||||
\(661\) | −34.2933 | −1.33385 | −0.666927 | − | 0.745123i | \(-0.732391\pi\) | ||||
−0.666927 | + | 0.745123i | \(0.732391\pi\) | |||||||
\(662\) | 31.6441 | 1.22988 | ||||||||
\(663\) | 5.83972 | 0.226796 | ||||||||
\(664\) | 53.8709 | 2.09060 | ||||||||
\(665\) | 26.5377 | 1.02909 | ||||||||
\(666\) | −22.1819 | −0.859531 | ||||||||
\(667\) | 13.1169 | 0.507890 | ||||||||
\(668\) | −4.88703 | −0.189085 | ||||||||
\(669\) | −23.8541 | −0.922255 | ||||||||
\(670\) | −35.6032 | −1.37547 | ||||||||
\(671\) | −1.55918 | −0.0601914 | ||||||||
\(672\) | −41.5998 | −1.60475 | ||||||||
\(673\) | 41.5895 | 1.60316 | 0.801579 | − | 0.597889i | \(-0.203994\pi\) | ||||
0.801579 | + | 0.597889i | \(0.203994\pi\) | |||||||
\(674\) | 39.5940 | 1.52510 | ||||||||
\(675\) | 8.08988 | 0.311380 | ||||||||
\(676\) | 4.91333 | 0.188974 | ||||||||
\(677\) | 39.5259 | 1.51910 | 0.759552 | − | 0.650446i | \(-0.225418\pi\) | ||||
0.759552 | + | 0.650446i | \(0.225418\pi\) | |||||||
\(678\) | 18.0538 | 0.693354 | ||||||||
\(679\) | 63.2294 | 2.42652 | ||||||||
\(680\) | 87.5982 | 3.35924 | ||||||||
\(681\) | 7.60574 | 0.291453 | ||||||||
\(682\) | 3.54275 | 0.135659 | ||||||||
\(683\) | 4.80529 | 0.183869 | 0.0919347 | − | 0.995765i | \(-0.470695\pi\) | ||||
0.0919347 | + | 0.995765i | \(0.470695\pi\) | |||||||
\(684\) | −40.3857 | −1.54419 | ||||||||
\(685\) | −25.4306 | −0.971654 | ||||||||
\(686\) | −4.27507 | −0.163223 | ||||||||
\(687\) | −14.9190 | −0.569197 | ||||||||
\(688\) | −20.7736 | −0.791987 | ||||||||
\(689\) | −4.25474 | −0.162093 | ||||||||
\(690\) | 7.30963 | 0.278273 | ||||||||
\(691\) | −32.9368 | −1.25298 | −0.626488 | − | 0.779431i | \(-0.715508\pi\) | ||||
−0.626488 | + | 0.779431i | \(0.715508\pi\) | |||||||
\(692\) | −72.0831 | −2.74019 | ||||||||
\(693\) | −4.85055 | −0.184257 | ||||||||
\(694\) | 60.3901 | 2.29238 | ||||||||
\(695\) | −19.6117 | −0.743914 | ||||||||
\(696\) | 56.5979 | 2.14534 | ||||||||
\(697\) | −13.1843 | −0.499391 | ||||||||
\(698\) | 5.29417 | 0.200387 | ||||||||
\(699\) | −14.3610 | −0.543184 | ||||||||
\(700\) | −31.6556 | −1.19647 | ||||||||
\(701\) | −6.83127 | −0.258014 | −0.129007 | − | 0.991644i | \(-0.541179\pi\) | ||||
−0.129007 | + | 0.991644i | \(0.541179\pi\) | |||||||
\(702\) | −12.5405 | −0.473311 | ||||||||
\(703\) | −15.1637 | −0.571911 | ||||||||
\(704\) | 6.20759 | 0.233957 | ||||||||
\(705\) | 2.65861 | 0.100129 | ||||||||
\(706\) | −9.75054 | −0.366967 | ||||||||
\(707\) | 54.5853 | 2.05289 | ||||||||
\(708\) | −17.0796 | −0.641892 | ||||||||
\(709\) | 7.35350 | 0.276167 | 0.138083 | − | 0.990421i | \(-0.455906\pi\) | ||||
0.138083 | + | 0.990421i | \(0.455906\pi\) | |||||||
\(710\) | 28.5620 | 1.07191 | ||||||||
\(711\) | −10.0573 | −0.377180 | ||||||||
\(712\) | 89.2084 | 3.34323 | ||||||||
\(713\) | 3.71804 | 0.139242 | ||||||||
\(714\) | 58.3229 | 2.18268 | ||||||||
\(715\) | −1.08541 | −0.0405922 | ||||||||
\(716\) | −2.72858 | −0.101972 | ||||||||
\(717\) | −9.66678 | −0.361013 | ||||||||
\(718\) | −12.2973 | −0.458929 | ||||||||
\(719\) | −47.2443 | −1.76191 | −0.880957 | − | 0.473196i | \(-0.843100\pi\) | ||||
−0.880957 | + | 0.473196i | \(0.843100\pi\) | |||||||
\(720\) | −40.0906 | −1.49409 | ||||||||
\(721\) | −24.7414 | −0.921417 | ||||||||
\(722\) | 11.1111 | 0.413514 | ||||||||
\(723\) | −4.20414 | −0.156354 | ||||||||
\(724\) | 118.548 | 4.40582 | ||||||||
\(725\) | 13.5020 | 0.501453 | ||||||||
\(726\) | 25.9755 | 0.964040 | ||||||||
\(727\) | 33.1859 | 1.23080 | 0.615398 | − | 0.788217i | \(-0.288995\pi\) | ||||
0.615398 | + | 0.788217i | \(0.288995\pi\) | |||||||
\(728\) | 29.0963 | 1.07838 | ||||||||
\(729\) | 9.02901 | 0.334408 | ||||||||
\(730\) | −26.5721 | −0.983477 | ||||||||
\(731\) | 12.6716 | 0.468675 | ||||||||
\(732\) | −11.9076 | −0.440117 | ||||||||
\(733\) | 22.3900 | 0.826993 | 0.413496 | − | 0.910506i | \(-0.364307\pi\) | ||||
0.413496 | + | 0.910506i | \(0.364307\pi\) | |||||||
\(734\) | 7.59207 | 0.280228 | ||||||||
\(735\) | 12.5321 | 0.462252 | ||||||||
\(736\) | 19.4425 | 0.716662 | ||||||||
\(737\) | 4.44860 | 0.163866 | ||||||||
\(738\) | 11.7828 | 0.433730 | ||||||||
\(739\) | −21.4240 | −0.788095 | −0.394047 | − | 0.919090i | \(-0.628925\pi\) | ||||
−0.394047 | + | 0.919090i | \(0.628925\pi\) | |||||||
\(740\) | −35.2322 | −1.29516 | ||||||||
\(741\) | −3.56771 | −0.131063 | ||||||||
\(742\) | −42.4933 | −1.55998 | ||||||||
\(743\) | −45.8313 | −1.68139 | −0.840695 | − | 0.541510i | \(-0.817853\pi\) | ||||
−0.840695 | + | 0.541510i | \(0.817853\pi\) | |||||||
\(744\) | 16.0429 | 0.588161 | ||||||||
\(745\) | −13.7869 | −0.505114 | ||||||||
\(746\) | −81.6887 | −2.99083 | ||||||||
\(747\) | 15.0391 | 0.550251 | ||||||||
\(748\) | −18.4593 | −0.674940 | ||||||||
\(749\) | 8.53376 | 0.311817 | ||||||||
\(750\) | 29.7042 | 1.08464 | ||||||||
\(751\) | 17.4634 | 0.637247 | 0.318623 | − | 0.947881i | \(-0.396779\pi\) | ||||
0.318623 | + | 0.947881i | \(0.396779\pi\) | |||||||
\(752\) | 16.2533 | 0.592696 | ||||||||
\(753\) | −6.40933 | −0.233569 | ||||||||
\(754\) | −20.9301 | −0.762230 | ||||||||
\(755\) | −34.1678 | −1.24349 | ||||||||
\(756\) | −89.0126 | −3.23736 | ||||||||
\(757\) | 25.3201 | 0.920274 | 0.460137 | − | 0.887848i | \(-0.347800\pi\) | ||||
0.460137 | + | 0.887848i | \(0.347800\pi\) | |||||||
\(758\) | −10.8327 | −0.393462 | ||||||||
\(759\) | −0.913335 | −0.0331519 | ||||||||
\(760\) | −53.5172 | −1.94127 | ||||||||
\(761\) | −14.8624 | −0.538763 | −0.269382 | − | 0.963034i | \(-0.586819\pi\) | ||||
−0.269382 | + | 0.963034i | \(0.586819\pi\) | |||||||
\(762\) | 16.7179 | 0.605627 | ||||||||
\(763\) | −29.7098 | −1.07557 | ||||||||
\(764\) | 66.4044 | 2.40243 | ||||||||
\(765\) | 24.4547 | 0.884160 | ||||||||
\(766\) | 1.47435 | 0.0532705 | ||||||||
\(767\) | 3.74510 | 0.135228 | ||||||||
\(768\) | −10.1839 | −0.367481 | ||||||||
\(769\) | −0.317481 | −0.0114487 | −0.00572433 | − | 0.999984i | \(-0.501822\pi\) | ||||
−0.00572433 | + | 0.999984i | \(0.501822\pi\) | |||||||
\(770\) | −10.8403 | −0.390659 | ||||||||
\(771\) | 26.1934 | 0.943333 | ||||||||
\(772\) | 97.0279 | 3.49211 | ||||||||
\(773\) | −6.87615 | −0.247318 | −0.123659 | − | 0.992325i | \(-0.539463\pi\) | ||||
−0.123659 | + | 0.992325i | \(0.539463\pi\) | |||||||
\(774\) | −11.3246 | −0.407053 | ||||||||
\(775\) | 3.82720 | 0.137477 | ||||||||
\(776\) | −127.511 | −4.57739 | ||||||||
\(777\) | −13.9090 | −0.498984 | ||||||||
\(778\) | −52.2288 | −1.87249 | ||||||||
\(779\) | 8.05480 | 0.288593 | ||||||||
\(780\) | −8.28941 | −0.296808 | ||||||||
\(781\) | −3.56881 | −0.127702 | ||||||||
\(782\) | −27.2584 | −0.974760 | ||||||||
\(783\) | 37.9664 | 1.35681 | ||||||||
\(784\) | 76.6142 | 2.73622 | ||||||||
\(785\) | −23.5275 | −0.839733 | ||||||||
\(786\) | 26.4333 | 0.942844 | ||||||||
\(787\) | −23.2841 | −0.829989 | −0.414995 | − | 0.909824i | \(-0.636217\pi\) | ||||
−0.414995 | + | 0.909824i | \(0.636217\pi\) | |||||||
\(788\) | −31.7694 | −1.13174 | ||||||||
\(789\) | −11.5168 | −0.410010 | ||||||||
\(790\) | −22.4768 | −0.799690 | ||||||||
\(791\) | −28.0990 | −0.999085 | ||||||||
\(792\) | 9.78184 | 0.347583 | ||||||||
\(793\) | 2.61101 | 0.0927197 | ||||||||
\(794\) | −4.50422 | −0.159849 | ||||||||
\(795\) | 7.17828 | 0.254587 | ||||||||
\(796\) | −40.3740 | −1.43102 | ||||||||
\(797\) | −4.86891 | −0.172466 | −0.0862328 | − | 0.996275i | \(-0.527483\pi\) | ||||
−0.0862328 | + | 0.996275i | \(0.527483\pi\) | |||||||
\(798\) | −35.6318 | −1.26135 | ||||||||
\(799\) | −9.91425 | −0.350741 | ||||||||
\(800\) | 20.0133 | 0.707578 | ||||||||
\(801\) | 24.9042 | 0.879946 | ||||||||
\(802\) | −69.0381 | −2.43782 | ||||||||
\(803\) | 3.32017 | 0.117166 | ||||||||
\(804\) | 33.9744 | 1.19819 | ||||||||
\(805\) | −11.3767 | −0.400976 | ||||||||
\(806\) | −5.93272 | −0.208971 | ||||||||
\(807\) | 5.62558 | 0.198030 | ||||||||
\(808\) | −110.079 | −3.87258 | ||||||||
\(809\) | −6.82863 | −0.240082 | −0.120041 | − | 0.992769i | \(-0.538303\pi\) | ||||
−0.120041 | + | 0.992769i | \(0.538303\pi\) | |||||||
\(810\) | −9.50269 | −0.333891 | ||||||||
\(811\) | −55.7435 | −1.95742 | −0.978710 | − | 0.205248i | \(-0.934200\pi\) | ||||
−0.978710 | + | 0.205248i | \(0.934200\pi\) | |||||||
\(812\) | −148.562 | −5.21351 | ||||||||
\(813\) | 6.74984 | 0.236727 | ||||||||
\(814\) | 6.19420 | 0.217107 | ||||||||
\(815\) | 8.73590 | 0.306005 | ||||||||
\(816\) | −60.2319 | −2.10854 | ||||||||
\(817\) | −7.74157 | −0.270843 | ||||||||
\(818\) | −39.5931 | −1.38434 | ||||||||
\(819\) | 8.12277 | 0.283832 | ||||||||
\(820\) | 18.7149 | 0.653554 | ||||||||
\(821\) | −5.97522 | −0.208537 | −0.104268 | − | 0.994549i | \(-0.533250\pi\) | ||||
−0.104268 | + | 0.994549i | \(0.533250\pi\) | |||||||
\(822\) | 34.1453 | 1.19095 | ||||||||
\(823\) | −6.90000 | −0.240519 | −0.120259 | − | 0.992743i | \(-0.538373\pi\) | ||||
−0.120259 | + | 0.992743i | \(0.538373\pi\) | |||||||
\(824\) | 49.8946 | 1.73816 | ||||||||
\(825\) | −0.940149 | −0.0327318 | ||||||||
\(826\) | 37.4034 | 1.30143 | ||||||||
\(827\) | 4.63798 | 0.161278 | 0.0806392 | − | 0.996743i | \(-0.474304\pi\) | ||||
0.0806392 | + | 0.996743i | \(0.474304\pi\) | |||||||
\(828\) | 17.3133 | 0.601680 | ||||||||
\(829\) | −4.60847 | −0.160059 | −0.0800294 | − | 0.996793i | \(-0.525501\pi\) | ||||
−0.0800294 | + | 0.996793i | \(0.525501\pi\) | |||||||
\(830\) | 33.6103 | 1.16663 | ||||||||
\(831\) | 19.6543 | 0.681801 | ||||||||
\(832\) | −10.3953 | −0.360391 | ||||||||
\(833\) | −46.7335 | −1.61922 | ||||||||
\(834\) | 26.3323 | 0.911814 | ||||||||
\(835\) | −1.80791 | −0.0625654 | ||||||||
\(836\) | 11.2775 | 0.390042 | ||||||||
\(837\) | 10.7617 | 0.371979 | ||||||||
\(838\) | 21.2638 | 0.734545 | ||||||||
\(839\) | 23.7001 | 0.818219 | 0.409110 | − | 0.912485i | \(-0.365839\pi\) | ||||
0.409110 | + | 0.912485i | \(0.365839\pi\) | |||||||
\(840\) | −49.0891 | −1.69373 | ||||||||
\(841\) | 34.3660 | 1.18503 | ||||||||
\(842\) | 65.0925 | 2.24324 | ||||||||
\(843\) | 20.3123 | 0.699594 | ||||||||
\(844\) | −5.54126 | −0.190738 | ||||||||
\(845\) | 1.81764 | 0.0625288 | ||||||||
\(846\) | 8.86034 | 0.304625 | ||||||||
\(847\) | −40.4282 | −1.38913 | ||||||||
\(848\) | 43.8841 | 1.50699 | ||||||||
\(849\) | 22.5427 | 0.773665 | ||||||||
\(850\) | −28.0587 | −0.962406 | ||||||||
\(851\) | 6.50068 | 0.222841 | ||||||||
\(852\) | −27.2554 | −0.933753 | ||||||||
\(853\) | 1.58740 | 0.0543515 | 0.0271757 | − | 0.999631i | \(-0.491349\pi\) | ||||
0.0271757 | + | 0.999631i | \(0.491349\pi\) | |||||||
\(854\) | 26.0769 | 0.892334 | ||||||||
\(855\) | −14.9403 | −0.510948 | ||||||||
\(856\) | −17.2096 | −0.588211 | ||||||||
\(857\) | −20.5758 | −0.702857 | −0.351428 | − | 0.936215i | \(-0.614304\pi\) | ||||
−0.351428 | + | 0.936215i | \(0.614304\pi\) | |||||||
\(858\) | 1.45737 | 0.0497537 | ||||||||
\(859\) | −17.8949 | −0.610564 | −0.305282 | − | 0.952262i | \(-0.598751\pi\) | ||||
−0.305282 | + | 0.952262i | \(0.598751\pi\) | |||||||
\(860\) | −17.9872 | −0.613357 | ||||||||
\(861\) | 7.38833 | 0.251794 | ||||||||
\(862\) | −75.2583 | −2.56331 | ||||||||
\(863\) | 47.6149 | 1.62083 | 0.810415 | − | 0.585856i | \(-0.199241\pi\) | ||||
0.810415 | + | 0.585856i | \(0.199241\pi\) | |||||||
\(864\) | 56.2756 | 1.91454 | ||||||||
\(865\) | −26.6665 | −0.906688 | ||||||||
\(866\) | 7.72973 | 0.262667 | ||||||||
\(867\) | 20.9612 | 0.711879 | ||||||||
\(868\) | −42.1105 | −1.42932 | ||||||||
\(869\) | 2.80847 | 0.0952708 | ||||||||
\(870\) | 35.3117 | 1.19718 | ||||||||
\(871\) | −7.44967 | −0.252422 | ||||||||
\(872\) | 59.9141 | 2.02895 | ||||||||
\(873\) | −35.5971 | −1.20478 | ||||||||
\(874\) | 16.6533 | 0.563305 | ||||||||
\(875\) | −46.2316 | −1.56291 | ||||||||
\(876\) | 25.3565 | 0.856716 | ||||||||
\(877\) | 6.33667 | 0.213974 | 0.106987 | − | 0.994260i | \(-0.465880\pi\) | ||||
0.106987 | + | 0.994260i | \(0.465880\pi\) | |||||||
\(878\) | −8.58595 | −0.289762 | ||||||||
\(879\) | 3.55179 | 0.119799 | ||||||||
\(880\) | 11.1951 | 0.377388 | ||||||||
\(881\) | 19.7425 | 0.665143 | 0.332572 | − | 0.943078i | \(-0.392084\pi\) | ||||
0.332572 | + | 0.943078i | \(0.392084\pi\) | |||||||
\(882\) | 41.7656 | 1.40632 | ||||||||
\(883\) | −49.3588 | −1.66106 | −0.830528 | − | 0.556978i | \(-0.811961\pi\) | ||||
−0.830528 | + | 0.556978i | \(0.811961\pi\) | |||||||
\(884\) | 30.9121 | 1.03969 | ||||||||
\(885\) | −6.31846 | −0.212393 | ||||||||
\(886\) | 29.8103 | 1.00150 | ||||||||
\(887\) | −49.0977 | −1.64854 | −0.824269 | − | 0.566198i | \(-0.808414\pi\) | ||||
−0.824269 | + | 0.566198i | \(0.808414\pi\) | |||||||
\(888\) | 28.0496 | 0.941284 | ||||||||
\(889\) | −26.0198 | −0.872675 | ||||||||
\(890\) | 55.6576 | 1.86565 | ||||||||
\(891\) | 1.18736 | 0.0397779 | ||||||||
\(892\) | −126.270 | −4.22784 | ||||||||
\(893\) | 6.05700 | 0.202690 | ||||||||
\(894\) | 18.5115 | 0.619118 | ||||||||
\(895\) | −1.00941 | −0.0337409 | ||||||||
\(896\) | −14.1846 | −0.473875 | ||||||||
\(897\) | 1.52948 | 0.0510678 | ||||||||
\(898\) | −66.8093 | −2.22946 | ||||||||
\(899\) | 17.9613 | 0.599043 | ||||||||
\(900\) | 17.8216 | 0.594054 | ||||||||
\(901\) | −26.7686 | −0.891792 | ||||||||
\(902\) | −3.29029 | −0.109555 | ||||||||
\(903\) | −7.10102 | −0.236307 | ||||||||
\(904\) | 56.6658 | 1.88468 | ||||||||
\(905\) | 43.8559 | 1.45782 | ||||||||
\(906\) | 45.8766 | 1.52415 | ||||||||
\(907\) | 52.4797 | 1.74256 | 0.871279 | − | 0.490787i | \(-0.163291\pi\) | ||||
0.871279 | + | 0.490787i | \(0.163291\pi\) | |||||||
\(908\) | 40.2605 | 1.33609 | ||||||||
\(909\) | −30.7307 | −1.01927 | ||||||||
\(910\) | 18.1533 | 0.601777 | ||||||||
\(911\) | 14.5061 | 0.480607 | 0.240304 | − | 0.970698i | \(-0.422753\pi\) | ||||
0.240304 | + | 0.970698i | \(0.422753\pi\) | |||||||
\(912\) | 36.7980 | 1.21850 | ||||||||
\(913\) | −4.19959 | −0.138986 | ||||||||
\(914\) | −48.6462 | −1.60907 | ||||||||
\(915\) | −4.40510 | −0.145628 | ||||||||
\(916\) | −78.9729 | −2.60934 | ||||||||
\(917\) | −41.1408 | −1.35859 | ||||||||
\(918\) | −78.8984 | −2.60404 | ||||||||
\(919\) | −26.6560 | −0.879299 | −0.439649 | − | 0.898169i | \(-0.644897\pi\) | ||||
−0.439649 | + | 0.898169i | \(0.644897\pi\) | |||||||
\(920\) | 22.9428 | 0.756402 | ||||||||
\(921\) | −3.84877 | −0.126821 | ||||||||
\(922\) | 79.8062 | 2.62828 | ||||||||
\(923\) | 5.97636 | 0.196714 | ||||||||
\(924\) | 10.3444 | 0.340306 | ||||||||
\(925\) | 6.69153 | 0.220016 | ||||||||
\(926\) | 2.62932 | 0.0864049 | ||||||||
\(927\) | 13.9290 | 0.457489 | ||||||||
\(928\) | 93.9240 | 3.08321 | ||||||||
\(929\) | −16.7601 | −0.549880 | −0.274940 | − | 0.961461i | \(-0.588658\pi\) | ||||
−0.274940 | + | 0.961461i | \(0.588658\pi\) | |||||||
\(930\) | 10.0092 | 0.328216 | ||||||||
\(931\) | 28.5513 | 0.935731 | ||||||||
\(932\) | −76.0192 | −2.49009 | ||||||||
\(933\) | −18.2891 | −0.598758 | ||||||||
\(934\) | −46.6543 | −1.52658 | ||||||||
\(935\) | −6.82886 | −0.223328 | ||||||||
\(936\) | −16.3808 | −0.535422 | ||||||||
\(937\) | 8.12095 | 0.265300 | 0.132650 | − | 0.991163i | \(-0.457651\pi\) | ||||
0.132650 | + | 0.991163i | \(0.457651\pi\) | |||||||
\(938\) | −74.4020 | −2.42931 | ||||||||
\(939\) | −10.8465 | −0.353963 | ||||||||
\(940\) | 14.0731 | 0.459015 | ||||||||
\(941\) | −30.7369 | −1.00200 | −0.500998 | − | 0.865448i | \(-0.667034\pi\) | ||||
−0.500998 | + | 0.865448i | \(0.667034\pi\) | |||||||
\(942\) | 31.5900 | 1.02926 | ||||||||
\(943\) | −3.45309 | −0.112448 | ||||||||
\(944\) | −38.6276 | −1.25722 | ||||||||
\(945\) | −32.9294 | −1.07119 | ||||||||
\(946\) | 3.16234 | 0.102816 | ||||||||
\(947\) | 21.6274 | 0.702797 | 0.351399 | − | 0.936226i | \(-0.385706\pi\) | ||||
0.351399 | + | 0.936226i | \(0.385706\pi\) | |||||||
\(948\) | 21.4486 | 0.696617 | ||||||||
\(949\) | −5.55999 | −0.180485 | ||||||||
\(950\) | 17.1422 | 0.556165 | ||||||||
\(951\) | −14.0071 | −0.454210 | ||||||||
\(952\) | 183.059 | 5.93297 | ||||||||
\(953\) | −25.8796 | −0.838323 | −0.419161 | − | 0.907912i | \(-0.637676\pi\) | ||||
−0.419161 | + | 0.907912i | \(0.637676\pi\) | |||||||
\(954\) | 23.9231 | 0.774538 | ||||||||
\(955\) | 24.5657 | 0.794928 | ||||||||
\(956\) | −51.1705 | −1.65497 | ||||||||
\(957\) | −4.41218 | −0.142626 | ||||||||
\(958\) | −50.1462 | −1.62015 | ||||||||
\(959\) | −53.1438 | −1.71610 | ||||||||
\(960\) | 17.5381 | 0.566041 | ||||||||
\(961\) | −25.9088 | −0.835768 | ||||||||
\(962\) | −10.3729 | −0.334434 | ||||||||
\(963\) | −4.80437 | −0.154819 | ||||||||
\(964\) | −22.2543 | −0.716764 | ||||||||
\(965\) | 35.8946 | 1.15549 | ||||||||
\(966\) | 15.2753 | 0.491476 | ||||||||
\(967\) | 51.1530 | 1.64497 | 0.822484 | − | 0.568788i | \(-0.192587\pi\) | ||||
0.822484 | + | 0.568788i | \(0.192587\pi\) | |||||||
\(968\) | 81.5294 | 2.62046 | ||||||||
\(969\) | −22.4462 | −0.721076 | ||||||||
\(970\) | −79.5549 | −2.55436 | ||||||||
\(971\) | −23.5987 | −0.757320 | −0.378660 | − | 0.925536i | \(-0.623615\pi\) | ||||
−0.378660 | + | 0.925536i | \(0.623615\pi\) | |||||||
\(972\) | 79.3702 | 2.54580 | ||||||||
\(973\) | −40.9837 | −1.31388 | ||||||||
\(974\) | 58.6209 | 1.87834 | ||||||||
\(975\) | 1.57438 | 0.0504205 | ||||||||
\(976\) | −26.9304 | −0.862022 | ||||||||
\(977\) | 61.9423 | 1.98171 | 0.990855 | − | 0.134930i | \(-0.0430809\pi\) | ||||
0.990855 | + | 0.134930i | \(0.0430809\pi\) | |||||||
\(978\) | −11.7296 | −0.375070 | ||||||||
\(979\) | −6.95439 | −0.222263 | ||||||||
\(980\) | 66.3376 | 2.11908 | ||||||||
\(981\) | 16.7261 | 0.534024 | ||||||||
\(982\) | −65.0053 | −2.07440 | ||||||||
\(983\) | −18.7550 | −0.598193 | −0.299097 | − | 0.954223i | \(-0.596685\pi\) | ||||
−0.299097 | + | 0.954223i | \(0.596685\pi\) | |||||||
\(984\) | −14.8997 | −0.474984 | ||||||||
\(985\) | −11.7528 | −0.374475 | ||||||||
\(986\) | −131.681 | −4.19359 | ||||||||
\(987\) | 5.55584 | 0.176844 | ||||||||
\(988\) | −18.8854 | −0.600826 | ||||||||
\(989\) | 3.31881 | 0.105532 | ||||||||
\(990\) | 6.10294 | 0.193964 | ||||||||
\(991\) | −34.1265 | −1.08406 | −0.542032 | − | 0.840358i | \(-0.682345\pi\) | ||||
−0.542032 | + | 0.840358i | \(0.682345\pi\) | |||||||
\(992\) | 26.6231 | 0.845284 | ||||||||
\(993\) | −11.1709 | −0.354498 | ||||||||
\(994\) | 59.6876 | 1.89318 | ||||||||
\(995\) | −14.9360 | −0.473503 | ||||||||
\(996\) | −32.0727 | −1.01626 | ||||||||
\(997\) | −28.2205 | −0.893754 | −0.446877 | − | 0.894596i | \(-0.647464\pi\) | ||||
−0.446877 | + | 0.894596i | \(0.647464\pi\) | |||||||
\(998\) | −74.4265 | −2.35593 | ||||||||
\(999\) | 18.8159 | 0.595310 |
(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 | 6019.2.a.c.1.4 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.4 | ✓ | 108 | 1.1 | even | 1 | trivial |