Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.667261 | 0.385244 | 0.192622 | − | 0.981273i | \(-0.438301\pi\) | ||||
0.192622 | + | 0.981273i | \(0.438301\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.307121 | 0.137349 | 0.0686743 | − | 0.997639i | \(-0.478123\pi\) | ||||
0.0686743 | + | 0.997639i | \(0.478123\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.25072 | −1.60662 | −0.803311 | − | 0.595560i | \(-0.796930\pi\) | ||||
−0.803311 | + | 0.595560i | \(0.796930\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.55476 | −0.851587 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.721001 | −0.217390 | −0.108695 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108695 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.50964 | −1.25075 | −0.625375 | − | 0.780325i | \(-0.715054\pi\) | ||||
−0.625375 | + | 0.780325i | \(0.715054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.204930 | 0.0529127 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.96970 | 1.93294 | 0.966468 | − | 0.256786i | \(-0.0826635\pi\) | ||||
0.966468 | + | 0.256786i | \(0.0826635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.29804 | 1.44487 | 0.722435 | − | 0.691439i | \(-0.243023\pi\) | ||||
0.722435 | + | 0.691439i | \(0.243023\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.83634 | −0.618941 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.88211 | 1.01799 | 0.508995 | − | 0.860769i | \(-0.330017\pi\) | ||||
0.508995 | + | 0.860769i | \(0.330017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90568 | −0.981135 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.70648 | −0.713312 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.38483 | 1.37133 | 0.685664 | − | 0.727918i | \(-0.259512\pi\) | ||||
0.685664 | + | 0.727918i | \(0.259512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.57254 | 1.53967 | 0.769837 | − | 0.638241i | \(-0.220337\pi\) | ||||
0.769837 | + | 0.638241i | \(0.220337\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.481096 | −0.0837480 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.30549 | −0.220667 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.903054 | −0.148461 | −0.0742306 | − | 0.997241i | \(-0.523650\pi\) | ||||
−0.0742306 | + | 0.997241i | \(0.523650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00911 | −0.481843 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.48154 | −1.48077 | −0.740384 | − | 0.672184i | \(-0.765356\pi\) | ||||
−0.740384 | + | 0.672184i | \(0.765356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86056 | 0.283732 | 0.141866 | − | 0.989886i | \(-0.454690\pi\) | ||||
0.141866 | + | 0.989886i | \(0.454690\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.784621 | −0.116964 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.432654 | 0.0631090 | 0.0315545 | − | 0.999502i | \(-0.489954\pi\) | ||||
0.0315545 | + | 0.999502i | \(0.489954\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0686 | 1.58123 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.31787 | 0.744651 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1315 | −1.80375 | −0.901876 | − | 0.431994i | \(-0.857810\pi\) | ||||
−0.901876 | + | 0.431994i | \(0.857810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.221434 | −0.0298582 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.20244 | 0.556627 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.80194 | −0.494971 | −0.247485 | − | 0.968892i | \(-0.579604\pi\) | ||||
−0.247485 | + | 0.968892i | \(0.579604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.98011 | −0.893712 | −0.446856 | − | 0.894606i | \(-0.647456\pi\) | ||||
−0.446856 | + | 0.894606i | \(0.647456\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.8596 | 1.36818 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.38501 | −0.171789 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.59763 | −0.561690 | −0.280845 | − | 0.959753i | \(-0.590615\pi\) | ||||
−0.280845 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.25764 | 0.392174 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.98521 | −0.235601 | −0.117800 | − | 0.993037i | \(-0.537584\pi\) | ||||
−0.117800 | + | 0.993037i | \(0.537584\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.07898 | 0.360368 | 0.180184 | − | 0.983633i | \(-0.442331\pi\) | ||||
0.180184 | + | 0.983633i | \(0.442331\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.27337 | −0.377976 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.06477 | 0.349263 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.39903 | −0.157403 | −0.0787014 | − | 0.996898i | \(-0.525077\pi\) | ||||
−0.0787014 | + | 0.996898i | \(0.525077\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.19110 | 0.576789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.69377 | 0.954265 | 0.477132 | − | 0.878831i | \(-0.341676\pi\) | ||||
0.477132 | + | 0.878831i | \(0.341676\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.44766 | 0.265486 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.92761 | 0.528296 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.04116 | 0.322362 | 0.161181 | − | 0.986925i | \(-0.448470\pi\) | ||||
0.161181 | + | 0.986925i | \(0.448470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.1692 | 2.00948 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.72013 | 0.593149 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.93426 | 0.198451 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.67187 | −0.575891 | −0.287945 | − | 0.957647i | \(-0.592972\pi\) | ||||
−0.287945 | + | 0.957647i | \(0.592972\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.84199 | 0.185126 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.91983 | 0.688548 | 0.344274 | − | 0.938869i | \(-0.388125\pi\) | ||||
0.344274 | + | 0.938869i | \(0.388125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.40902 | 0.138835 | 0.0694174 | − | 0.997588i | \(-0.477886\pi\) | ||||
0.0694174 | + | 0.997588i | \(0.477886\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.871100 | −0.0850106 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.70772 | 0.358439 | 0.179220 | − | 0.983809i | \(-0.442643\pi\) | ||||
0.179220 | + | 0.983809i | \(0.442643\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.48992 | −0.621622 | −0.310811 | − | 0.950472i | \(-0.600601\pi\) | ||||
−0.310811 | + | 0.950472i | \(0.600601\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.602573 | −0.0571937 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0417 | −0.944645 | −0.472322 | − | 0.881426i | \(-0.656584\pi\) | ||||
−0.472322 | + | 0.881426i | \(0.656584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.49940 | 0.139820 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.5211 | 1.06512 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −33.8770 | −3.10550 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4802 | −0.952742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.32667 | −0.570456 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.04224 | −0.272106 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.2654 | −1.70953 | −0.854764 | − | 0.519018i | \(-0.826298\pi\) | ||||
−0.854764 | + | 0.519018i | \(0.826298\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.24148 | 0.109306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.1144 | −1.75740 | −0.878701 | − | 0.477372i | \(-0.841589\pi\) | ||||
−0.878701 | + | 0.477372i | \(0.841589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.7712 | −2.32136 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.13834 | −0.0979725 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4500 | 1.40542 | 0.702711 | − | 0.711476i | \(-0.251973\pi\) | ||||
0.702711 | + | 0.711476i | \(0.251973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.60624 | 0.814791 | 0.407395 | − | 0.913252i | \(-0.366437\pi\) | ||||
0.407395 | + | 0.913252i | \(0.366437\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.288693 | 0.0243124 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.25145 | 0.271900 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.26804 | 0.188350 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.38567 | 0.609160 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.3862 | −1.83395 | −0.916974 | − | 0.398947i | \(-0.869376\pi\) | ||||
−0.916974 | + | 0.398947i | \(0.869376\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8741 | −0.966297 | −0.483149 | − | 0.875538i | \(-0.660507\pi\) | ||||
−0.483149 | + | 0.875538i | \(0.660507\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.3607 | −1.64606 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.63281 | 0.211472 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.8085 | −1.50108 | −0.750540 | − | 0.660825i | \(-0.770207\pi\) | ||||
−0.750540 | + | 0.660825i | \(0.770207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.76215 | −0.694884 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.7525 | −1.63552 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.9259 | 1.87402 | 0.937012 | − | 0.349297i | \(-0.113580\pi\) | ||||
0.937012 | + | 0.349297i | \(0.113580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.147755 | −0.0115027 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.9339 | −1.23301 | −0.616503 | − | 0.787353i | \(-0.711451\pi\) | ||||
−0.616503 | + | 0.787353i | \(0.711451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.33686 | 0.564374 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.0900 | −1.23043 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.77409 | −0.515024 | −0.257512 | − | 0.966275i | \(-0.582903\pi\) | ||||
−0.257512 | + | 0.966275i | \(0.582903\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.8527 | 1.57631 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.53689 | −0.190684 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.7988 | 0.807142 | 0.403571 | − | 0.914948i | \(-0.367769\pi\) | ||||
0.403571 | + | 0.914948i | \(0.367769\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9864 | 0.965269 | 0.482635 | − | 0.875822i | \(-0.339680\pi\) | ||||
0.482635 | + | 0.875822i | \(0.339680\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.65756 | −0.344297 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.277347 | −0.0203909 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.74616 | −0.420201 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.7552 | 1.14602 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7261 | 0.993188 | 0.496594 | − | 0.867983i | \(-0.334584\pi\) | ||||
0.496594 | + | 0.867983i | \(0.334584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4246 | 0.966324 | 0.483162 | − | 0.875531i | \(-0.339488\pi\) | ||||
0.483162 | + | 0.875531i | \(0.339488\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.924160 | −0.0661805 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.99175 | −0.640635 | −0.320318 | − | 0.947310i | \(-0.603790\pi\) | ||||
−0.320318 | + | 0.947310i | \(0.603790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5387 | −1.03062 | −0.515311 | − | 0.857003i | \(-0.672324\pi\) | ||||
−0.515311 | + | 0.857003i | \(0.672324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.06782 | −0.216387 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −31.3909 | −2.20321 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.91198 | −0.203382 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.4726 | −0.866908 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.54089 | −0.314100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.55378 | 0.106966 | 0.0534832 | − | 0.998569i | \(-0.482968\pi\) | ||||
0.0534832 | + | 0.998569i | \(0.482968\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.32465 | −0.0907636 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.571416 | 0.0389702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −36.4395 | −2.47367 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.05449 | 0.138829 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.9405 | −2.41762 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.7987 | −1.05796 | −0.528978 | − | 0.848635i | \(-0.677425\pi\) | ||||
−0.528978 | + | 0.848635i | \(0.677425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.5328 | 0.835523 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.1142 | 1.33502 | 0.667512 | − | 0.744599i | \(-0.267359\pi\) | ||||
0.667512 | + | 0.744599i | \(0.267359\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.478210 | −0.0316010 | −0.0158005 | − | 0.999875i | \(-0.505030\pi\) | ||||
−0.0158005 | + | 0.999875i | \(0.505030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.04500 | 0.134551 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.9502 | −1.76557 | −0.882783 | − | 0.469781i | \(-0.844333\pi\) | ||||
−0.882783 | + | 0.469781i | \(0.844333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.132877 | 0.00866794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.933516 | −0.0606384 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.77549 | −0.179532 | −0.0897659 | − | 0.995963i | \(-0.528612\pi\) | ||||
−0.0897659 | + | 0.995963i | \(0.528612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.65974 | 0.300160 | 0.150080 | − | 0.988674i | \(-0.452047\pi\) | ||||
0.150080 | + | 0.988674i | \(0.452047\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5833 | 0.935516 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.39941 | 0.217180 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.4019 | −1.80717 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.80101 | 0.367624 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.0865 | −1.26785 | −0.633926 | − | 0.773394i | \(-0.718558\pi\) | ||||
−0.633926 | + | 0.773394i | \(0.718558\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.52000 | −0.221301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.63323 | 0.102277 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3177 | −0.768358 | −0.384179 | − | 0.923259i | \(-0.625515\pi\) | ||||
−0.384179 | + | 0.923259i | \(0.625515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.83863 | 0.238521 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.8665 | −1.16781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.98111 | −0.368811 | −0.184406 | − | 0.982850i | \(-0.559036\pi\) | ||||
−0.184406 | + | 0.982850i | \(0.559036\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.03296 | −0.247743 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.02925 | 0.124188 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.6549 | −1.07644 | −0.538218 | − | 0.842806i | \(-0.680902\pi\) | ||||
−0.538218 | + | 0.842806i | \(0.680902\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3089 | 0.990694 | 0.495347 | − | 0.868695i | \(-0.335041\pi\) | ||||
0.495347 | + | 0.868695i | \(0.335041\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.7909 | 0.774139 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.53700 | 0.213289 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.18714 | −0.491917 | −0.245959 | − | 0.969280i | \(-0.579103\pi\) | ||||
−0.245959 | + | 0.969280i | \(0.579103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.9008 | −1.31117 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.6880 | −1.23414 | −0.617070 | − | 0.786908i | \(-0.711681\pi\) | ||||
−0.617070 | + | 0.786908i | \(0.711681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.937311 | −0.0557174 | −0.0278587 | − | 0.999612i | \(-0.508869\pi\) | ||||
−0.0278587 | + | 0.999612i | \(0.508869\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.29066 | 0.0764520 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.3034 | 2.37903 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.5162 | 2.73624 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.78462 | −0.221858 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.9140 | −0.929707 | −0.464854 | − | 0.885387i | \(-0.653893\pi\) | ||||
−0.464854 | + | 0.885387i | \(0.653893\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.16766 | −0.0679836 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.67237 | 0.155067 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.0166 | −1.27325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.90871 | −0.455850 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.61733 | 0.265259 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.14374 | −0.122750 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.1293 | −0.692258 | −0.346129 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346129 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.940184 | 0.0534852 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.73181 | 0.551840 | 0.275920 | − | 0.961181i | \(-0.411017\pi\) | ||||
0.275920 | + | 0.961181i | \(0.411017\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.94322 | −0.505501 | −0.252750 | − | 0.967532i | \(-0.581335\pi\) | ||||
−0.252750 | + | 0.967532i | \(0.581335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.33520 | 0.187917 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.7836 | −1.78515 | −0.892573 | − | 0.450902i | \(-0.851102\pi\) | ||||
−0.892573 | + | 0.450902i | \(0.851102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.32447 | −0.298113 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.47402 | 0.138086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 50.1935 | 2.79284 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.1228 | 1.22715 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.33047 | −0.239476 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.83909 | −0.101392 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.60674 | −0.308174 | −0.154087 | − | 0.988057i | \(-0.549244\pi\) | ||||
−0.154087 | + | 0.988057i | \(0.549244\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.30709 | 0.126428 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.41203 | −0.0771474 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7356 | 0.802701 | 0.401350 | − | 0.915925i | \(-0.368541\pi\) | ||||
0.401350 | + | 0.915925i | \(0.368541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.70044 | −0.363918 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.18081 | −0.334710 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2946 | −0.933821 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00049 | 0.0538646 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.2441 | 1.14044 | 0.570222 | − | 0.821491i | \(-0.306857\pi\) | ||||
0.570222 | + | 0.821491i | \(0.306857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.58047 | 0.298716 | 0.149358 | − | 0.988783i | \(-0.452279\pi\) | ||||
0.149358 | + | 0.988783i | \(0.452279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.7149 | 0.892175 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.5258 | −1.25215 | −0.626075 | − | 0.779763i | \(-0.715340\pi\) | ||||
−0.626075 | + | 0.779763i | \(0.715340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.609698 | −0.0323594 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.6048 | −1.19637 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.93140 | −0.207492 | −0.103746 | − | 0.994604i | \(-0.533083\pi\) | ||||
−0.103746 | + | 0.994604i | \(0.533083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.6654 | 1.08765 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.99300 | −0.367038 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.945621 | 0.0494960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.7574 | 1.76212 | 0.881061 | − | 0.473003i | \(-0.156830\pi\) | ||||
0.881061 | + | 0.473003i | \(0.156830\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.2231 | 1.26100 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 55.8184 | 2.89795 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.9721 | 1.13767 | 0.568836 | − | 0.822451i | \(-0.307394\pi\) | ||||
0.568836 | + | 0.822451i | \(0.307394\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.02997 | −0.104827 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.3029 | −1.71519 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.9373 | 1.89734 | 0.948672 | − | 0.316262i | \(-0.102428\pi\) | ||||
0.948672 | + | 0.316262i | \(0.102428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.8551 | −0.658584 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −38.3731 | −1.96077 | −0.980387 | − | 0.197084i | \(-0.936853\pi\) | ||||
−0.980387 | + | 0.197084i | \(0.936853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.941256 | 0.0479708 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.75328 | −0.241623 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.13829 | 0.159117 | 0.0795587 | − | 0.996830i | \(-0.474649\pi\) | ||||
0.0795587 | + | 0.996830i | \(0.474649\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.9090 | 1.96771 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.4216 | −0.677028 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.429670 | −0.0216191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.6226 | −0.633509 | −0.316755 | − | 0.948508i | \(-0.602593\pi\) | ||||
−0.316755 | + | 0.948508i | \(0.602593\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.8634 | −0.894289 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1940 | −0.658874 | −0.329437 | − | 0.944177i | \(-0.606859\pi\) | ||||
−0.329437 | + | 0.944177i | \(0.606859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.6591 | −1.92575 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.59429 | 0.0792211 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.651103 | 0.0322740 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.6687 | 0.923110 | 0.461555 | − | 0.887112i | \(-0.347292\pi\) | ||||
0.461555 | + | 0.887112i | \(0.347292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.9765 | 0.541430 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.1610 | 0.795231 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.67004 | 0.131067 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.40987 | 0.313893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.8992 | −1.16755 | −0.583777 | − | 0.811914i | \(-0.698426\pi\) | ||||
−0.583777 | + | 0.811914i | \(0.698426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2272 | 0.595915 | 0.297958 | − | 0.954579i | \(-0.403695\pi\) | ||||
0.297958 | + | 0.954579i | \(0.403695\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.10533 | −0.0537429 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −39.0968 | −1.89647 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.6705 | 1.43586 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.16957 | 0.104748 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6741 | −0.610491 | −0.305246 | − | 0.952274i | \(-0.598739\pi\) | ||||
−0.305246 | + | 0.952274i | \(0.598739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.0284 | −1.63530 | −0.817651 | − | 0.575714i | \(-0.804724\pi\) | ||||
−0.817651 | + | 0.575714i | \(0.804724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.51337 | 0.0725607 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.7477 | 1.47086 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.6920 | 1.17849 | 0.589244 | − | 0.807956i | \(-0.299426\pi\) | ||||
0.589244 | + | 0.807956i | \(0.299426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28.2777 | −1.34656 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.5906 | 1.16833 | 0.584167 | − | 0.811633i | \(-0.301421\pi\) | ||||
0.584167 | + | 0.811633i | \(0.301421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.934002 | 0.0442760 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.9374 | −0.706517 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.17674 | −0.338691 | −0.169346 | − | 0.985557i | \(-0.554165\pi\) | ||||
−0.169346 | + | 0.985557i | \(0.554165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.83620 | 0.321904 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.92310 | −0.372260 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.88727 | 0.275999 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.1927 | 1.08491 | 0.542455 | − | 0.840085i | \(-0.317495\pi\) | ||||
0.542455 | + | 0.840085i | \(0.317495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.5395 | −1.37879 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.75291 | −0.267940 | −0.133970 | − | 0.990985i | \(-0.542773\pi\) | ||||
−0.133970 | + | 0.990985i | \(0.542773\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8464 | −0.922342 | −0.461171 | − | 0.887311i | \(-0.652571\pi\) | ||||
−0.461171 | + | 0.887311i | \(0.652571\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.75677 | 0.0814683 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3506 | 0.617792 | 0.308896 | − | 0.951096i | \(-0.400040\pi\) | ||||
0.308896 | + | 0.951096i | \(0.400040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.5432 | 0.902423 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.5502 | −0.578282 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.34146 | −0.0616805 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.8962 | −1.41761 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.5479 | 1.53605 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.17837 | 0.373679 | 0.186840 | − | 0.982390i | \(-0.440176\pi\) | ||||
0.186840 | + | 0.982390i | \(0.440176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.07245 | 0.185688 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.8473 | −0.630075 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.74195 | −0.0790978 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0826 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.9649 | 0.721956 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.3077 | −1.77393 | −0.886965 | − | 0.461836i | \(-0.847191\pi\) | ||||
−0.886965 | + | 0.461836i | \(0.847191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 58.8549 | 2.65069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.565712 | 0.0254269 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.43855 | 0.378521 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.2872 | 0.952947 | 0.476474 | − | 0.879189i | \(-0.341915\pi\) | ||||
0.476474 | + | 0.879189i | \(0.341915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6321 | −0.475008 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.12522 | 0.0945712 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.89560 | 0.217421 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.9814 | 1.46187 | 0.730937 | − | 0.682445i | \(-0.239083\pi\) | ||||
0.730937 | + | 0.682445i | \(0.239083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0879 | −0.578975 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.3436 | −1.03064 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.432739 | 0.0190688 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.311944 | −0.0137193 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.52009 | −0.198410 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 43.6614 | 1.91284 | 0.956421 | − | 0.291990i | \(-0.0943175\pi\) | ||||
0.956421 | + | 0.291990i | \(0.0943175\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.6035 | −0.769748 | −0.384874 | − | 0.922969i | \(-0.625755\pi\) | ||||
−0.384874 | + | 0.922969i | \(0.625755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.9142 | 0.607264 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 68.3206 | 2.97609 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.834992 | 0.0363040 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.71306 | 0.421511 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.7584 | 1.85207 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.13872 | 0.0492311 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.20564 | 0.310946 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.98049 | −0.343744 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.7313 | −0.547361 | −0.273681 | − | 0.961821i | \(-0.588241\pi\) | ||||
−0.273681 | + | 0.961821i | \(0.588241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.66530 | 0.371864 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.99319 | −0.0853789 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.99668 | −0.384670 | −0.192335 | − | 0.981329i | \(-0.561606\pi\) | ||||
−0.192335 | + | 0.981329i | \(0.561606\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.8325 | 0.761074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.5100 | 1.98139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.94687 | 0.252887 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.185063 | −0.00785548 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.6045 | 0.661182 | 0.330591 | − | 0.943774i | \(-0.392752\pi\) | ||||
0.330591 | + | 0.943774i | \(0.392752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.39044 | −0.354878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.83419 | −0.161880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.8071 | −1.29837 | −0.649183 | − | 0.760632i | \(-0.724889\pi\) | ||||
−0.649183 | + | 0.760632i | \(0.724889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.08402 | −0.129746 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0659 | −0.926681 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.3008 | 0.515677 | 0.257838 | − | 0.966188i | \(-0.416990\pi\) | ||||
0.257838 | + | 0.966188i | \(0.416990\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.1173 | −1.46961 | −0.734807 | − | 0.678276i | \(-0.762727\pi\) | ||||
−0.734807 | + | 0.678276i | \(0.762727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.15892 | 0.382619 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.9501 | −0.998786 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.6086 | −0.649796 | −0.324898 | − | 0.945749i | \(-0.605330\pi\) | ||||
−0.324898 | + | 0.945749i | \(0.605330\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.95772 | 0.372270 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.9548 | −1.53314 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.46783 | 0.392118 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.53836 | 0.146293 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0930 | −0.581681 | −0.290841 | − | 0.956771i | \(-0.593935\pi\) | ||||
−0.290841 | + | 0.956771i | \(0.593935\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.9902 | 2.22463 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.99984 | −0.246801 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.74557 | −0.153812 | −0.0769060 | − | 0.997038i | \(-0.524504\pi\) | ||||
−0.0769060 | + | 0.997038i | \(0.524504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4043 | −0.426536 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.70112 | −0.397040 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.31104 | −0.176144 | −0.0880722 | − | 0.996114i | \(-0.528071\pi\) | ||||
−0.0880722 | + | 0.996114i | \(0.528071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.45071 | −0.385503 | −0.192751 | − | 0.981248i | \(-0.561741\pi\) | ||||
−0.192751 | + | 0.981248i | \(0.561741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7459 | 0.478328 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.21868 | −0.130858 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.0664 | −1.66683 | −0.833417 | − | 0.552645i | \(-0.813619\pi\) | ||||
−0.833417 | + | 0.552645i | \(0.813619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.9459 | −0.848771 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.95111 | −0.0789336 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.03276 | −0.243661 | −0.121831 | − | 0.992551i | \(-0.538876\pi\) | ||||
−0.121831 | + | 0.992551i | \(0.538876\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.94305 | −0.0783514 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.88785 | −0.156519 | −0.0782595 | − | 0.996933i | \(-0.524936\pi\) | ||||
−0.0782595 | + | 0.996933i | \(0.524936\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.1723 | −0.690213 | −0.345107 | − | 0.938563i | \(-0.612157\pi\) | ||||
−0.345107 | + | 0.938563i | \(0.612157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0954 | −0.726145 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.9271 | −0.517913 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5940 | 0.943762 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.02996 | −0.121005 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.19707 | −0.286966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.9300 | −0.634165 | −0.317082 | − | 0.948398i | \(-0.602703\pi\) | ||||
−0.317082 | + | 0.948398i | \(0.602703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.03677 | 0.0412081 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.91681 | −0.234801 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −49.9155 | −1.97773 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.07173 | 0.200634 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.4598 | 1.55857 | 0.779284 | − | 0.626671i | \(-0.215583\pi\) | ||||
0.779284 | + | 0.626671i | \(0.215583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.1011 | 0.713836 | 0.356918 | − | 0.934136i | \(-0.383828\pi\) | ||||
0.356918 | + | 0.934136i | \(0.383828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.381284 | 0.0150130 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.6770 | 1.95301 | 0.976503 | − | 0.215504i | \(-0.0691394\pi\) | ||||
0.976503 | + | 0.215504i | \(0.0691394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.74120 | 0.107602 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.3147 | −0.952967 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.61404 | −0.180561 | −0.0902807 | − | 0.995916i | \(-0.528776\pi\) | ||||
−0.0902807 | + | 0.995916i | \(0.528776\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.17755 | −0.241377 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.86607 | −0.306885 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.5534 | −0.800646 | −0.400323 | − | 0.916374i | \(-0.631102\pi\) | ||||
−0.400323 | + | 0.916374i | \(0.631102\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5211 | 0.759282 | 0.379641 | − | 0.925134i | \(-0.376047\pi\) | ||||
0.379641 | + | 0.925134i | \(0.376047\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.9817 | −0.931372 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.22200 | −0.318836 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.0536 | 1.39600 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.5418 | −0.407571 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.03267 | 0.194284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.6149 | 1.56559 | 0.782794 | − | 0.622281i | \(-0.213794\pi\) | ||||
0.782794 | + | 0.622281i | \(0.213794\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.1828 | 0.699856 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.7650 | 0.721199 | 0.360599 | − | 0.932721i | \(-0.382572\pi\) | ||||
0.360599 | + | 0.932721i | \(0.382572\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.1095 | 0.925238 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.4214 | 0.514310 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.4215 | −0.628353 | −0.314176 | − | 0.949365i | \(-0.601728\pi\) | ||||
−0.314176 | + | 0.949365i | \(0.601728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.05215 | 0.193033 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.319091 | −0.0121741 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.2184 | 2.25604 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.3456 | 0.431606 | 0.215803 | − | 0.976437i | \(-0.430763\pi\) | ||||
0.215803 | + | 0.976437i | \(0.430763\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.82977 | −0.297428 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.95028 | 0.111910 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −75.5651 | −2.86223 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.9828 | −0.680173 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.66016 | 0.100473 | 0.0502364 | − | 0.998737i | \(-0.484003\pi\) | ||||
0.0502364 | + | 0.998737i | \(0.484003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.68747 | −0.214507 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0886637 | 0.00333927 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.4142 | −1.10624 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.7288 | −1.49205 | −0.746024 | − | 0.665919i | \(-0.768040\pi\) | ||||
−0.746024 | + | 0.665919i | \(0.768040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.57418 | 0.134042 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.8521 | 1.56737 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.998590 | 0.0373451 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.85198 | −0.0691635 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.3195 | 0.459441 | 0.229721 | − | 0.973257i | \(-0.426219\pi\) | ||||
0.229721 | + | 0.973257i | \(0.426219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.98935 | −0.223055 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.10927 | 0.115635 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36.2276 | −1.34546 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.3154 | −0.938897 | −0.469449 | − | 0.882960i | \(-0.655547\pi\) | ||||
−0.469449 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.84245 | −0.216387 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.8281 | 0.548436 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.5561 | −1.05474 | −0.527372 | − | 0.849634i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849634i | \(0.676823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.26829 | 0.0836672 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.31490 | 0.122106 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0882 | 0.886100 | 0.443050 | − | 0.896497i | \(-0.353896\pi\) | ||||
0.443050 | + | 0.896497i | \(0.353896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.9515 | −0.696201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.2680 | 1.18380 | 0.591899 | − | 0.806012i | \(-0.298378\pi\) | ||||
0.591899 | + | 0.806012i | \(0.298378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.87527 | −0.251890 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.2105 | −0.812640 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.7605 | −0.575876 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.9809 | −1.02104 | −0.510519 | − | 0.859867i | \(-0.670547\pi\) | ||||
−0.510519 | + | 0.859867i | \(0.670547\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.4030 | −0.488432 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.64677 | −0.132720 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00964 | 0.291115 | 0.145558 | − | 0.989350i | \(-0.453502\pi\) | ||||
0.145558 | + | 0.989350i | \(0.453502\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.34876 | −0.0852547 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.9041 | 0.902775 | 0.451387 | − | 0.892328i | \(-0.350929\pi\) | ||||
0.451387 | + | 0.892328i | \(0.350929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.5868 | 0.998710 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.25320 | −0.226085 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.1454 | 0.619085 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.8461 | −1.22052 | −0.610261 | − | 0.792200i | \(-0.708935\pi\) | ||||
−0.610261 | + | 0.792200i | \(0.708935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.21914 | −0.296005 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.6404 | −1.64157 | −0.820786 | − | 0.571236i | \(-0.806464\pi\) | ||||
−0.820786 | + | 0.571236i | \(0.806464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.0541 | −1.51063 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.56137 | 0.0918886 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.7152 | −2.13952 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.43133 | 0.0512172 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.3717 | −0.978185 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.77648 | −0.206171 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.2047 | −1.50444 | −0.752218 | − | 0.658914i | \(-0.771016\pi\) | ||||
−0.752218 | + | 0.658914i | \(0.771016\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.99097 | −0.142082 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.6845 | 1.51769 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.4778 | 1.11781 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.69104 | −0.0954414 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.9132 | −0.882471 | −0.441236 | − | 0.897391i | \(-0.645460\pi\) | ||||
−0.441236 | + | 0.897391i | \(0.645460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.44812 | 0.121986 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.76943 | −0.274519 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.21995 | −0.0783403 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.37352 | −0.224637 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.7804 | −0.414690 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.3047 | −1.69830 | −0.849152 | − | 0.528148i | \(-0.822887\pi\) | ||||
−0.849152 | + | 0.528148i | \(0.822887\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.98459 | 0.175033 | 0.0875163 | − | 0.996163i | \(-0.472107\pi\) | ||||
0.0875163 | + | 0.996163i | \(0.472107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.8823 | 0.381658 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.34815 | 0.257395 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.7179 | 0.409956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −48.9728 | −1.71125 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.6862 | 0.721954 | 0.360977 | − | 0.932575i | \(-0.382443\pi\) | ||||
0.360977 | + | 0.932575i | \(0.382443\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0734 | −0.420853 | −0.210427 | − | 0.977610i | \(-0.567485\pi\) | ||||
−0.210427 | + | 0.977610i | \(0.567485\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.36010 | 0.0821682 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.2071 | −1.18950 | −0.594748 | − | 0.803912i | \(-0.702748\pi\) | ||||
−0.594748 | + | 0.803912i | \(0.702748\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.2677 | −1.64168 | −0.820838 | − | 0.571161i | \(-0.806493\pi\) | ||||
−0.820838 | + | 0.571161i | \(0.806493\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.46296 | −0.189508 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 88.2137 | 3.05642 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.89365 | −0.169352 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.7739 | −1.09827 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.6906 | 1.26670 | 0.633350 | − | 0.773865i | \(-0.281679\pi\) | ||||
0.633350 | + | 0.773865i | \(0.281679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.5357 | 0.880543 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.8043 | −0.475445 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.25330 | 0.0775160 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.5482 | 1.53070 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.625431 | −0.0214648 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.40881 | −0.151132 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9228 | 0.579427 | 0.289713 | − | 0.957113i | \(-0.406440\pi\) | ||||
0.289713 | + | 0.957113i | \(0.406440\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.94158 | −0.168998 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.3955 | 1.10661 | 0.553305 | − | 0.832979i | \(-0.313367\pi\) | ||||
0.553305 | + | 0.832979i | \(0.313367\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.2728 | −1.44233 | −0.721164 | − | 0.692764i | \(-0.756393\pi\) | ||||
−0.721164 | + | 0.692764i | \(0.756393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.8929 | 0.916508 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5450 | 0.563198 | 0.281599 | − | 0.959532i | \(-0.409135\pi\) | ||||
0.281599 | + | 0.959532i | \(0.409135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.08046 | −0.0707379 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.0384 | 1.05412 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.00870 | 0.0342178 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.7337 | 0.702534 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.4903 | 0.490421 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.9317 | 0.437172 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.41710 | 0.250458 | 0.125229 | − | 0.992128i | \(-0.460033\pi\) | ||||
0.125229 | + | 0.992128i | \(0.460033\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.6188 | −0.358164 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.5860 | 1.23261 | 0.616307 | − | 0.787506i | \(-0.288628\pi\) | ||||
0.616307 | + | 0.787506i | \(0.288628\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.76867 | −0.160479 | −0.0802393 | − | 0.996776i | \(-0.525568\pi\) | ||||
−0.0802393 | + | 0.996776i | \(0.525568\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.779132 | −0.0261902 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.5077 | −0.487120 | −0.243560 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243560 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 81.8918 | 2.74656 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.74278 | −0.125388 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.72487 | 0.0911844 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.31655 | 0.110860 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.6908 | −0.490512 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 63.3068 | 2.11140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −104.654 | −3.48654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.27717 | −0.175613 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.98839 | 0.132578 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.98338 | −0.198675 | −0.0993374 | − | 0.995054i | \(-0.531672\pi\) | ||||
−0.0993374 | + | 0.995054i | \(0.531672\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.6785 | −0.586359 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6582 | −0.750701 | −0.375350 | − | 0.926883i | \(-0.622478\pi\) | ||||
−0.375350 | + | 0.926883i | \(0.622478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.26821 | −0.207448 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.43043 | −0.0472887 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 85.5006 | 2.82348 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.10778 | 0.267451 | 0.133726 | − | 0.991018i | \(-0.457306\pi\) | ||||
0.133726 | + | 0.991018i | \(0.457306\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.09344 | −0.266688 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.95256 | 0.294677 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.43009 | 0.145660 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.59971 | −0.118230 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.57905 | 0.314278 | 0.157139 | − | 0.987576i | \(-0.449773\pi\) | ||||
0.157139 | + | 0.987576i | \(0.449773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 69.7107 | 2.28468 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.49366 | 0.212593 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.76477 | −0.0577140 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.196050 | 0.00640467 | 0.00320234 | − | 0.999995i | \(-0.498981\pi\) | ||||
0.00320234 | + | 0.999995i | \(0.498981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.96746 | −0.194741 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.893569 | 0.0291295 | 0.0145648 | − | 0.999894i | \(-0.495364\pi\) | ||||
0.0145648 | + | 0.999894i | \(0.495364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.2899 | −1.50741 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.83875 | 0.157405 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.2934 | 1.11439 | 0.557193 | − | 0.830383i | \(-0.311878\pi\) | ||||
0.557193 | + | 0.830383i | \(0.311878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.8851 | −0.450730 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.2080 | −0.687716 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0568 | 0.455346 | 0.227673 | − | 0.973738i | \(-0.426888\pi\) | ||||
0.227673 | + | 0.973738i | \(0.426888\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.21558 | 0.136413 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.55281 | −0.114846 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −69.9245 | −2.25798 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.4885 | 1.37060 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.47235 | −0.305242 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.12298 | 0.132723 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.9849 | −1.18935 | −0.594677 | − | 0.803965i | \(-0.702720\pi\) | ||||
−0.594677 | + | 0.803965i | \(0.702720\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.4922 | 1.07592 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.2185 | 1.00185 | 0.500924 | − | 0.865491i | \(-0.332993\pi\) | ||||
0.500924 | + | 0.865491i | \(0.332993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.8334 | −1.30906 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.7617 | 0.472753 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.1478 | 0.612593 | 0.306297 | − | 0.951936i | \(-0.400910\pi\) | ||||
0.306297 | + | 0.951936i | \(0.400910\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.19268 | −0.0700782 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.5802 | 0.529365 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.2033 | 0.516805 | 0.258402 | − | 0.966037i | \(-0.416804\pi\) | ||||
0.258402 | + | 0.966037i | \(0.416804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.76155 | −0.0879904 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.22715 | −0.0390607 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.08344 | 0.288837 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.9646 | 1.42835 | 0.714174 | − | 0.699968i | \(-0.246802\pi\) | ||||
0.714174 | + | 0.699968i | \(0.246802\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.74116 | −0.118722 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.46514 | −0.141555 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.1546 | 1.52507 | 0.762536 | − | 0.646946i | \(-0.223954\pi\) | ||||
0.762536 | + | 0.646946i | \(0.223954\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.34715 | 0.105899 |
(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 | 8048.2.a.v.1.18 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.11 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.11 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.18 | 28 | 1.1 | even | 1 | trivial |