Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, 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("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16693 | 1.53225 | 0.766126 | − | 0.642691i | \(-0.222182\pi\) | ||||
0.766126 | + | 0.642691i | \(0.222182\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.69559 | 1.34779 | ||||||||
\(5\) | 1.04157 | 0.465804 | 0.232902 | − | 0.972500i | \(-0.425178\pi\) | ||||
0.232902 | + | 0.972500i | \(0.425178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.90919 | 1.47754 | 0.738768 | − | 0.673960i | \(-0.235408\pi\) | ||||
0.738768 | + | 0.673960i | \(0.235408\pi\) | |||||||
\(8\) | 1.50729 | 0.532908 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.25701 | 0.713728 | ||||||||
\(11\) | 4.40000 | 1.32665 | 0.663325 | − | 0.748331i | \(-0.269145\pi\) | ||||
0.663325 | + | 0.748331i | \(0.269145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.894885 | 0.248196 | 0.124098 | − | 0.992270i | \(-0.460396\pi\) | ||||
0.124098 | + | 0.992270i | \(0.460396\pi\) | |||||||
\(14\) | 8.47095 | 2.26396 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.12498 | −0.531245 | ||||||||
\(17\) | −0.522546 | −0.126736 | −0.0633680 | − | 0.997990i | \(-0.520184\pi\) | ||||
−0.0633680 | + | 0.997990i | \(0.520184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.99593 | 1.60498 | 0.802489 | − | 0.596668i | \(-0.203509\pi\) | ||||
0.802489 | + | 0.596668i | \(0.203509\pi\) | |||||||
\(20\) | 2.80764 | 0.627807 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.53450 | 2.03276 | ||||||||
\(23\) | −0.550269 | −0.114739 | −0.0573695 | − | 0.998353i | \(-0.518271\pi\) | ||||
−0.0573695 | + | 0.998353i | \(0.518271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.91514 | −0.783027 | ||||||||
\(26\) | 1.93915 | 0.380299 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.5376 | 1.99141 | ||||||||
\(29\) | 2.59234 | 0.481386 | 0.240693 | − | 0.970601i | \(-0.422625\pi\) | ||||
0.240693 | + | 0.970601i | \(0.422625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.61206 | −1.36717 | −0.683583 | − | 0.729873i | \(-0.739579\pi\) | ||||
−0.683583 | + | 0.729873i | \(0.739579\pi\) | |||||||
\(32\) | −7.61927 | −1.34691 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.13232 | −0.194191 | ||||||||
\(35\) | 4.07169 | 0.688241 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.30590 | −1.03668 | −0.518342 | − | 0.855173i | \(-0.673451\pi\) | ||||
−0.518342 | + | 0.855173i | \(0.673451\pi\) | |||||||
\(38\) | 15.1597 | 2.45923 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.56995 | 0.248230 | ||||||||
\(41\) | −1.60738 | −0.251031 | −0.125516 | − | 0.992092i | \(-0.540059\pi\) | ||||
−0.125516 | + | 0.992092i | \(0.540059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.85677 | 0.740650 | 0.370325 | − | 0.928902i | \(-0.379246\pi\) | ||||
0.370325 | + | 0.928902i | \(0.379246\pi\) | |||||||
\(44\) | 11.8606 | 1.78805 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.19240 | −0.175809 | ||||||||
\(47\) | −5.35226 | −0.780707 | −0.390353 | − | 0.920665i | \(-0.627647\pi\) | ||||
−0.390353 | + | 0.920665i | \(0.627647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.28179 | 1.18311 | ||||||||
\(50\) | −8.48383 | −1.19979 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.41224 | 0.334518 | ||||||||
\(53\) | −5.20098 | −0.714409 | −0.357205 | − | 0.934026i | \(-0.616270\pi\) | ||||
−0.357205 | + | 0.934026i | \(0.616270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.58290 | 0.617959 | ||||||||
\(56\) | 5.89229 | 0.787391 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.61742 | 0.737604 | ||||||||
\(59\) | 14.6701 | 1.90988 | 0.954940 | − | 0.296799i | \(-0.0959190\pi\) | ||||
0.954940 | + | 0.296799i | \(0.0959190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4981 | −1.34415 | −0.672073 | − | 0.740485i | \(-0.734596\pi\) | ||||
−0.672073 | + | 0.740485i | \(0.734596\pi\) | |||||||
\(62\) | −16.4948 | −2.09484 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.2605 | −1.53256 | ||||||||
\(65\) | 0.932084 | 0.115611 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.37983 | −0.168572 | −0.0842862 | − | 0.996442i | \(-0.526861\pi\) | ||||
−0.0842862 | + | 0.996442i | \(0.526861\pi\) | |||||||
\(68\) | −1.40857 | −0.170814 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.82307 | 1.05456 | ||||||||
\(71\) | 14.5938 | 1.73196 | 0.865981 | − | 0.500077i | \(-0.166695\pi\) | ||||
0.865981 | + | 0.500077i | \(0.166695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.06639 | −0.710017 | −0.355008 | − | 0.934863i | \(-0.615522\pi\) | ||||
−0.355008 | + | 0.934863i | \(0.615522\pi\) | |||||||
\(74\) | −13.6645 | −1.58846 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 18.8582 | 2.16318 | ||||||||
\(77\) | 17.2005 | 1.96017 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.16664 | −0.693802 | −0.346901 | − | 0.937902i | \(-0.612766\pi\) | ||||
−0.346901 | + | 0.937902i | \(0.612766\pi\) | |||||||
\(80\) | −2.21331 | −0.247456 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.48309 | −0.384643 | ||||||||
\(83\) | 0.0347730 | 0.00381683 | 0.00190842 | − | 0.999998i | \(-0.499393\pi\) | ||||
0.00190842 | + | 0.999998i | \(0.499393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.544267 | −0.0590340 | ||||||||
\(86\) | 10.5243 | 1.13486 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.63209 | 0.706983 | ||||||||
\(89\) | −11.6153 | −1.23122 | −0.615611 | − | 0.788050i | \(-0.711091\pi\) | ||||
−0.615611 | + | 0.788050i | \(0.711091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.49828 | 0.366719 | ||||||||
\(92\) | −1.48330 | −0.154645 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.5980 | −1.19624 | ||||||||
\(95\) | 7.28674 | 0.747604 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.41450 | −0.651293 | −0.325647 | − | 0.945492i | \(-0.605582\pi\) | ||||
−0.325647 | + | 0.945492i | \(0.605582\pi\) | |||||||
\(98\) | 17.9461 | 1.81283 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.5536 | −1.05536 | ||||||||
\(101\) | −4.52301 | −0.450057 | −0.225028 | − | 0.974352i | \(-0.572247\pi\) | ||||
−0.225028 | + | 0.974352i | \(0.572247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0379 | 1.38319 | 0.691597 | − | 0.722283i | \(-0.256907\pi\) | ||||
0.691597 | + | 0.722283i | \(0.256907\pi\) | |||||||
\(104\) | 1.34885 | 0.132266 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.2702 | −1.09465 | ||||||||
\(107\) | 4.28189 | 0.413946 | 0.206973 | − | 0.978347i | \(-0.433639\pi\) | ||||
0.206973 | + | 0.978347i | \(0.433639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.06151 | 0.580588 | 0.290294 | − | 0.956938i | \(-0.406247\pi\) | ||||
0.290294 | + | 0.956938i | \(0.406247\pi\) | |||||||
\(110\) | 9.93083 | 0.946868 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.30696 | −0.784934 | ||||||||
\(113\) | −3.10269 | −0.291877 | −0.145938 | − | 0.989294i | \(-0.546620\pi\) | ||||
−0.145938 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.573143 | −0.0534459 | ||||||||
\(116\) | 6.98789 | 0.648809 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 31.7890 | 2.92642 | ||||||||
\(119\) | −2.04273 | −0.187257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.36003 | 0.760002 | ||||||||
\(122\) | −22.7487 | −2.05957 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −20.5190 | −1.84266 | ||||||||
\(125\) | −9.28572 | −0.830540 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.30013 | −0.292839 | −0.146420 | − | 0.989223i | \(-0.546775\pi\) | ||||
−0.146420 | + | 0.989223i | \(0.546775\pi\) | |||||||
\(128\) | −11.3290 | −1.00136 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.01976 | 0.177145 | ||||||||
\(131\) | 22.5168 | 1.96730 | 0.983652 | − | 0.180081i | \(-0.0576361\pi\) | ||||
0.983652 | + | 0.180081i | \(0.0576361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.3484 | 2.37141 | ||||||||
\(134\) | −2.98999 | −0.258295 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.787628 | −0.0675386 | ||||||||
\(137\) | 8.93145 | 0.763065 | 0.381533 | − | 0.924355i | \(-0.375396\pi\) | ||||
0.381533 | + | 0.924355i | \(0.375396\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.53862 | 0.469780 | 0.234890 | − | 0.972022i | \(-0.424527\pi\) | ||||
0.234890 | + | 0.972022i | \(0.424527\pi\) | |||||||
\(140\) | 10.9756 | 0.927608 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 31.6237 | 2.65380 | ||||||||
\(143\) | 3.93750 | 0.329270 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.70010 | 0.224231 | ||||||||
\(146\) | −13.1454 | −1.08792 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.9981 | −1.39724 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4454 | −1.17555 | −0.587773 | − | 0.809026i | \(-0.699995\pi\) | ||||
−0.587773 | + | 0.809026i | \(0.699995\pi\) | |||||||
\(152\) | 10.5449 | 0.855305 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 37.2722 | 3.00348 | ||||||||
\(155\) | −7.92848 | −0.636831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.82968 | −0.465260 | −0.232630 | − | 0.972565i | \(-0.574733\pi\) | ||||
−0.232630 | + | 0.972565i | \(0.574733\pi\) | |||||||
\(158\) | −13.3627 | −1.06308 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.93599 | −0.627395 | ||||||||
\(161\) | −2.15111 | −0.169531 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.3142 | 1.90444 | 0.952218 | − | 0.305418i | \(-0.0987963\pi\) | ||||
0.952218 | + | 0.305418i | \(0.0987963\pi\) | |||||||
\(164\) | −4.33284 | −0.338338 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0753507 | 0.00584835 | ||||||||
\(167\) | −5.65206 | −0.437370 | −0.218685 | − | 0.975796i | \(-0.570177\pi\) | ||||
−0.218685 | + | 0.975796i | \(0.570177\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1992 | −0.938399 | ||||||||
\(170\) | −1.17939 | −0.0904550 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.0919 | 0.998244 | ||||||||
\(173\) | −0.710082 | −0.0539865 | −0.0269933 | − | 0.999636i | \(-0.508593\pi\) | ||||
−0.0269933 | + | 0.999636i | \(0.508593\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.3050 | −1.15695 | ||||||||
\(176\) | −9.34992 | −0.704777 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.1696 | −1.88654 | ||||||||
\(179\) | −17.9600 | −1.34239 | −0.671197 | − | 0.741279i | \(-0.734220\pi\) | ||||
−0.671197 | + | 0.741279i | \(0.734220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.0568 | 1.71380 | 0.856900 | − | 0.515483i | \(-0.172387\pi\) | ||||
0.856900 | + | 0.515483i | \(0.172387\pi\) | |||||||
\(182\) | 7.58052 | 0.561906 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.829416 | −0.0611454 | ||||||||
\(185\) | −6.56803 | −0.482891 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.29920 | −0.168134 | ||||||||
\(188\) | −14.4275 | −1.05223 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.7899 | 1.14552 | ||||||||
\(191\) | −12.3628 | −0.894543 | −0.447271 | − | 0.894398i | \(-0.647604\pi\) | ||||
−0.447271 | + | 0.894398i | \(0.647604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6611 | 0.911369 | 0.455685 | − | 0.890141i | \(-0.349395\pi\) | ||||
0.455685 | + | 0.890141i | \(0.349395\pi\) | |||||||
\(194\) | −13.8998 | −0.997945 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.3243 | 1.59459 | ||||||||
\(197\) | −7.34898 | −0.523593 | −0.261797 | − | 0.965123i | \(-0.584315\pi\) | ||||
−0.261797 | + | 0.965123i | \(0.584315\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8165 | −0.908539 | −0.454270 | − | 0.890864i | \(-0.650100\pi\) | ||||
−0.454270 | + | 0.890864i | \(0.650100\pi\) | |||||||
\(200\) | −5.90125 | −0.417281 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.80106 | −0.689600 | ||||||||
\(203\) | 10.1340 | 0.711265 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.67420 | −0.116931 | ||||||||
\(206\) | 30.4191 | 2.11940 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.90161 | −0.131853 | ||||||||
\(209\) | 30.7821 | 2.12924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6603 | −1.00926 | −0.504628 | − | 0.863337i | \(-0.668370\pi\) | ||||
−0.504628 | + | 0.863337i | \(0.668370\pi\) | |||||||
\(212\) | −14.0197 | −0.962876 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.27855 | 0.634269 | ||||||||
\(215\) | 5.05866 | 0.344998 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.7570 | −2.02004 | ||||||||
\(218\) | 13.1349 | 0.889606 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.3536 | 0.832881 | ||||||||
\(221\) | −0.467618 | −0.0314554 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.68334 | −0.179690 | −0.0898449 | − | 0.995956i | \(-0.528637\pi\) | ||||
−0.0898449 | + | 0.995956i | \(0.528637\pi\) | |||||||
\(224\) | −29.7852 | −1.99011 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.72332 | −0.447229 | ||||||||
\(227\) | 14.3651 | 0.953447 | 0.476723 | − | 0.879053i | \(-0.341824\pi\) | ||||
0.476723 | + | 0.879053i | \(0.341824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.39520 | −0.488688 | −0.244344 | − | 0.969689i | \(-0.578573\pi\) | ||||
−0.244344 | + | 0.969689i | \(0.578573\pi\) | |||||||
\(230\) | −1.24196 | −0.0818925 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.90741 | 0.256534 | ||||||||
\(233\) | 7.14901 | 0.468347 | 0.234173 | − | 0.972195i | \(-0.424762\pi\) | ||||
0.234173 | + | 0.972195i | \(0.424762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.57474 | −0.363656 | ||||||||
\(236\) | 39.5445 | 2.57413 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.42646 | −0.286925 | ||||||||
\(239\) | −7.17639 | −0.464202 | −0.232101 | − | 0.972692i | \(-0.574560\pi\) | ||||
−0.232101 | + | 0.972692i | \(0.574560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.4307 | −1.05840 | −0.529198 | − | 0.848499i | \(-0.677507\pi\) | ||||
−0.529198 | + | 0.848499i | \(0.677507\pi\) | |||||||
\(242\) | 18.1156 | 1.16451 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −28.2986 | −1.81163 | ||||||||
\(245\) | 8.62605 | 0.551098 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.26055 | 0.398350 | ||||||||
\(248\) | −11.4736 | −0.728574 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −20.1215 | −1.27260 | ||||||||
\(251\) | 19.6270 | 1.23884 | 0.619421 | − | 0.785059i | \(-0.287367\pi\) | ||||
0.619421 | + | 0.785059i | \(0.287367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.42119 | −0.152219 | ||||||||
\(254\) | −7.15115 | −0.448703 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.0283131 | −0.00176957 | ||||||||
\(257\) | 29.7981 | 1.85875 | 0.929377 | − | 0.369133i | \(-0.120345\pi\) | ||||
0.929377 | + | 0.369133i | \(0.120345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.6510 | −1.53174 | ||||||||
\(260\) | 2.51251 | 0.155819 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 48.7924 | 3.01440 | ||||||||
\(263\) | −2.53032 | −0.156026 | −0.0780132 | − | 0.996952i | \(-0.524858\pi\) | ||||
−0.0780132 | + | 0.996952i | \(0.524858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.41717 | −0.332774 | ||||||||
\(266\) | 59.2622 | 3.63360 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.71944 | −0.227201 | ||||||||
\(269\) | −25.1431 | −1.53300 | −0.766500 | − | 0.642244i | \(-0.778004\pi\) | ||||
−0.766500 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7640 | −0.775359 | −0.387680 | − | 0.921794i | \(-0.626723\pi\) | ||||
−0.387680 | + | 0.921794i | \(0.626723\pi\) | |||||||
\(272\) | 1.11040 | 0.0673278 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.3538 | 1.16921 | ||||||||
\(275\) | −17.2266 | −1.03880 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.7932 | −0.708585 | −0.354292 | − | 0.935135i | \(-0.615278\pi\) | ||||
−0.354292 | + | 0.935135i | \(0.615278\pi\) | |||||||
\(278\) | 12.0018 | 0.719821 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.13723 | 0.366769 | ||||||||
\(281\) | 8.82307 | 0.526340 | 0.263170 | − | 0.964749i | \(-0.415232\pi\) | ||||
0.263170 | + | 0.964749i | \(0.415232\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4334 | 1.03631 | 0.518154 | − | 0.855287i | \(-0.326619\pi\) | ||||
0.518154 | + | 0.855287i | \(0.326619\pi\) | |||||||
\(284\) | 39.3388 | 2.33433 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.53228 | 0.504524 | ||||||||
\(287\) | −6.28357 | −0.370908 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7269 | −0.983938 | ||||||||
\(290\) | 5.85093 | 0.343579 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.3525 | −0.956956 | ||||||||
\(293\) | −29.1516 | −1.70306 | −0.851528 | − | 0.524308i | \(-0.824324\pi\) | ||||
−0.851528 | + | 0.524308i | \(0.824324\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2799 | 0.889629 | ||||||||
\(296\) | −9.50484 | −0.552457 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.16693 | 0.125527 | ||||||||
\(299\) | −0.492428 | −0.0284778 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.9860 | 1.09434 | ||||||||
\(302\) | −31.3021 | −1.80123 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.8662 | −0.852636 | ||||||||
\(305\) | −10.9345 | −0.626108 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.9202 | 0.908616 | 0.454308 | − | 0.890845i | \(-0.349887\pi\) | ||||
0.454308 | + | 0.890845i | \(0.349887\pi\) | |||||||
\(308\) | 46.3654 | 2.64191 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.1805 | −0.975785 | ||||||||
\(311\) | −5.14780 | −0.291905 | −0.145953 | − | 0.989292i | \(-0.546625\pi\) | ||||
−0.145953 | + | 0.989292i | \(0.546625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.2791 | −1.54191 | −0.770954 | − | 0.636891i | \(-0.780220\pi\) | ||||
−0.770954 | + | 0.636891i | \(0.780220\pi\) | |||||||
\(314\) | −12.6325 | −0.712894 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.6227 | −0.935102 | ||||||||
\(317\) | −4.80296 | −0.269761 | −0.134881 | − | 0.990862i | \(-0.543065\pi\) | ||||
−0.134881 | + | 0.990862i | \(0.543065\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4063 | 0.638631 | ||||||||
\(320\) | −12.7701 | −0.713871 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.66130 | −0.259764 | ||||||||
\(323\) | −3.65569 | −0.203408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.50360 | −0.194345 | ||||||||
\(326\) | 52.6872 | 2.91808 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.42280 | −0.133777 | ||||||||
\(329\) | −20.9230 | −1.15352 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.01121 | 0.0555810 | 0.0277905 | − | 0.999614i | \(-0.491153\pi\) | ||||
0.0277905 | + | 0.999614i | \(0.491153\pi\) | |||||||
\(332\) | 0.0937337 | 0.00514431 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.2476 | −0.670160 | ||||||||
\(335\) | −1.43718 | −0.0785216 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.19738 | −0.228646 | −0.114323 | − | 0.993444i | \(-0.536470\pi\) | ||||
−0.114323 | + | 0.993444i | \(0.536470\pi\) | |||||||
\(338\) | −26.4348 | −1.43786 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.46712 | −0.0795657 | ||||||||
\(341\) | −33.4931 | −1.81375 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.01075 | 0.270555 | ||||||||
\(344\) | 7.32057 | 0.394699 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.53870 | −0.0827209 | ||||||||
\(347\) | 33.1031 | 1.77707 | 0.888534 | − | 0.458811i | \(-0.151724\pi\) | ||||
0.888534 | + | 0.458811i | \(0.151724\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.53808 | 0.349975 | 0.174988 | − | 0.984571i | \(-0.444011\pi\) | ||||
0.174988 | + | 0.984571i | \(0.444011\pi\) | |||||||
\(350\) | −33.1649 | −1.77274 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −33.5248 | −1.78688 | ||||||||
\(353\) | −2.29484 | −0.122142 | −0.0610710 | − | 0.998133i | \(-0.519452\pi\) | ||||
−0.0610710 | + | 0.998133i | \(0.519452\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.2004 | 0.806754 | ||||||||
\(356\) | −31.3101 | −1.65943 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.9181 | −2.05689 | ||||||||
\(359\) | 23.2158 | 1.22528 | 0.612642 | − | 0.790360i | \(-0.290107\pi\) | ||||
0.612642 | + | 0.790360i | \(0.290107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.9431 | 1.57595 | ||||||||
\(362\) | 49.9625 | 2.62597 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.42992 | 0.494262 | ||||||||
\(365\) | −6.31856 | −0.330728 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.9970 | −0.991636 | −0.495818 | − | 0.868427i | \(-0.665132\pi\) | ||||
−0.495818 | + | 0.868427i | \(0.665132\pi\) | |||||||
\(368\) | 1.16931 | 0.0609546 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.2325 | −0.739911 | ||||||||
\(371\) | −20.3316 | −1.05557 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1963 | −1.20106 | −0.600528 | − | 0.799603i | \(-0.705043\pi\) | ||||
−0.600528 | + | 0.799603i | \(0.705043\pi\) | |||||||
\(374\) | −4.98221 | −0.257624 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.06741 | −0.416045 | ||||||||
\(377\) | 2.31985 | 0.119478 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.93900 | 0.305066 | 0.152533 | − | 0.988298i | \(-0.451257\pi\) | ||||
0.152533 | + | 0.988298i | \(0.451257\pi\) | |||||||
\(380\) | 19.6421 | 1.00762 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.7894 | −1.37066 | ||||||||
\(383\) | 23.3659 | 1.19394 | 0.596971 | − | 0.802263i | \(-0.296371\pi\) | ||||
0.596971 | + | 0.802263i | \(0.296371\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.9155 | 0.913056 | ||||||||
\(386\) | 27.4358 | 1.39645 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.2908 | −0.877809 | ||||||||
\(389\) | 13.2562 | 0.672116 | 0.336058 | − | 0.941841i | \(-0.390906\pi\) | ||||
0.336058 | + | 0.941841i | \(0.390906\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.287541 | 0.0145416 | ||||||||
\(392\) | 12.4831 | 0.630490 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.9247 | −0.802276 | ||||||||
\(395\) | −6.42298 | −0.323175 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.940682 | −0.0472115 | −0.0236057 | − | 0.999721i | \(-0.507515\pi\) | ||||
−0.0236057 | + | 0.999721i | \(0.507515\pi\) | |||||||
\(398\) | −27.7725 | −1.39211 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.31959 | 0.415979 | ||||||||
\(401\) | −22.0549 | −1.10137 | −0.550684 | − | 0.834714i | \(-0.685633\pi\) | ||||
−0.550684 | + | 0.834714i | \(0.685633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.81192 | −0.339326 | ||||||||
\(404\) | −12.1922 | −0.606584 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.9596 | 1.08984 | ||||||||
\(407\) | −27.7460 | −1.37532 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.0975 | −1.48823 | −0.744113 | − | 0.668054i | \(-0.767127\pi\) | ||||
−0.744113 | + | 0.668054i | \(0.767127\pi\) | |||||||
\(410\) | −3.62787 | −0.179168 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 37.8404 | 1.86426 | ||||||||
\(413\) | 57.3481 | 2.82192 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0362185 | 0.00177789 | ||||||||
\(416\) | −6.81837 | −0.334298 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 66.7027 | 3.26254 | ||||||||
\(419\) | 1.12681 | 0.0550483 | 0.0275242 | − | 0.999621i | \(-0.491238\pi\) | ||||
0.0275242 | + | 0.999621i | \(0.491238\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.9434 | −1.02072 | −0.510359 | − | 0.859962i | \(-0.670487\pi\) | ||||
−0.510359 | + | 0.859962i | \(0.670487\pi\) | |||||||
\(422\) | −31.7678 | −1.54643 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.83939 | −0.380714 | ||||||||
\(425\) | 2.04584 | 0.0992377 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41.0391 | −1.98602 | ||||||||
\(428\) | 11.5422 | 0.557913 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.9618 | 0.528623 | ||||||||
\(431\) | 31.1729 | 1.50155 | 0.750773 | − | 0.660560i | \(-0.229681\pi\) | ||||
0.750773 | + | 0.660560i | \(0.229681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.4854 | −0.696126 | −0.348063 | − | 0.937471i | \(-0.613161\pi\) | ||||
−0.348063 | + | 0.937471i | \(0.613161\pi\) | |||||||
\(434\) | −64.4814 | −3.09521 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.3393 | 0.782513 | ||||||||
\(437\) | −3.84965 | −0.184154 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.0226 | −1.33744 | −0.668722 | − | 0.743512i | \(-0.733158\pi\) | ||||
−0.668722 | + | 0.743512i | \(0.733158\pi\) | |||||||
\(440\) | 6.90777 | 0.329315 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.01330 | −0.0481976 | ||||||||
\(443\) | −7.24134 | −0.344047 | −0.172023 | − | 0.985093i | \(-0.555030\pi\) | ||||
−0.172023 | + | 0.985093i | \(0.555030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0982 | −0.573508 | ||||||||
\(446\) | −5.81461 | −0.275330 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −47.9285 | −2.26441 | ||||||||
\(449\) | 15.9677 | 0.753564 | 0.376782 | − | 0.926302i | \(-0.377031\pi\) | ||||
0.376782 | + | 0.926302i | \(0.377031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.07249 | −0.333031 | ||||||||
\(452\) | −8.36359 | −0.393390 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 31.1282 | 1.46092 | ||||||||
\(455\) | 3.64369 | 0.170819 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.9449 | 1.77499 | 0.887494 | − | 0.460820i | \(-0.152445\pi\) | ||||
0.887494 | + | 0.460820i | \(0.152445\pi\) | |||||||
\(458\) | −16.0249 | −0.748794 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.54496 | −0.0720340 | ||||||||
\(461\) | 28.5037 | 1.32755 | 0.663776 | − | 0.747932i | \(-0.268953\pi\) | ||||
0.663776 | + | 0.747932i | \(0.268953\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.5846 | −1.28196 | −0.640982 | − | 0.767556i | \(-0.721473\pi\) | ||||
−0.640982 | + | 0.767556i | \(0.721473\pi\) | |||||||
\(464\) | −5.50868 | −0.255734 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.4914 | 0.717625 | ||||||||
\(467\) | −6.54931 | −0.303066 | −0.151533 | − | 0.988452i | \(-0.548421\pi\) | ||||
−0.151533 | + | 0.988452i | \(0.548421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.39400 | −0.249072 | ||||||||
\(470\) | −12.0801 | −0.557212 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22.1121 | 1.01779 | ||||||||
\(473\) | 21.3698 | 0.982584 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.3900 | −1.25674 | ||||||||
\(476\) | −5.50636 | −0.252384 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.5507 | −0.711274 | ||||||||
\(479\) | 14.2398 | 0.650634 | 0.325317 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325317 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.64306 | −0.257301 | ||||||||
\(482\) | −35.6042 | −1.62173 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.5352 | 1.02433 | ||||||||
\(485\) | −6.68114 | −0.303375 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.4567 | −1.28950 | −0.644748 | − | 0.764395i | \(-0.723038\pi\) | ||||
−0.644748 | + | 0.764395i | \(0.723038\pi\) | |||||||
\(488\) | −15.8237 | −0.716306 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.6920 | 0.844421 | ||||||||
\(491\) | 4.56080 | 0.205826 | 0.102913 | − | 0.994690i | \(-0.467184\pi\) | ||||
0.102913 | + | 0.994690i | \(0.467184\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.35462 | −0.0610089 | ||||||||
\(494\) | 13.5662 | 0.610372 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.1755 | 0.726300 | ||||||||
\(497\) | 57.0499 | 2.55904 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8353 | 0.932718 | 0.466359 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466359 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(500\) | −25.0305 | −1.11940 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 42.5302 | 1.89822 | ||||||||
\(503\) | −0.585197 | −0.0260927 | −0.0130463 | − | 0.999915i | \(-0.504153\pi\) | ||||
−0.0130463 | + | 0.999915i | \(0.504153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.71103 | −0.209638 | ||||||||
\(506\) | −5.24654 | −0.233237 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.89579 | −0.394687 | ||||||||
\(509\) | −19.5396 | −0.866077 | −0.433039 | − | 0.901375i | \(-0.642559\pi\) | ||||
−0.433039 | + | 0.901375i | \(0.642559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.7147 | −1.04908 | ||||||||
\(512\) | 22.5967 | 0.998644 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 64.5704 | 2.84808 | ||||||||
\(515\) | 14.6214 | 0.644297 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.5499 | −1.03573 | ||||||||
\(518\) | −53.4170 | −2.34701 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.40492 | 0.0616099 | ||||||||
\(521\) | −33.7281 | −1.47765 | −0.738827 | − | 0.673895i | \(-0.764620\pi\) | ||||
−0.738827 | + | 0.673895i | \(0.764620\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.5821 | 1.81826 | 0.909129 | − | 0.416515i | \(-0.136749\pi\) | ||||
0.909129 | + | 0.416515i | \(0.136749\pi\) | |||||||
\(524\) | 60.6961 | 2.65152 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.48303 | −0.239072 | ||||||||
\(527\) | 3.97765 | 0.173269 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6972 | −0.986835 | ||||||||
\(530\) | −11.7386 | −0.509894 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 73.7202 | 3.19617 | ||||||||
\(533\) | −1.43842 | −0.0623050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.45988 | 0.192817 | ||||||||
\(536\) | −2.07980 | −0.0898336 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −54.4833 | −2.34894 | ||||||||
\(539\) | 36.4399 | 1.56958 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3236 | 0.701805 | 0.350903 | − | 0.936412i | \(-0.385875\pi\) | ||||
0.350903 | + | 0.936412i | \(0.385875\pi\) | |||||||
\(542\) | −27.6588 | −1.18805 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.98141 | 0.170702 | ||||||||
\(545\) | 6.31348 | 0.270440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.63939 | 0.241123 | 0.120562 | − | 0.992706i | \(-0.461531\pi\) | ||||
0.120562 | + | 0.992706i | \(0.461531\pi\) | |||||||
\(548\) | 24.0755 | 1.02845 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −37.3289 | −1.59171 | ||||||||
\(551\) | 18.1358 | 0.772613 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.1066 | −1.02512 | ||||||||
\(554\) | −25.5551 | −1.08573 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.9298 | 0.633166 | ||||||||
\(557\) | 7.09526 | 0.300636 | 0.150318 | − | 0.988638i | \(-0.451970\pi\) | ||||
0.150318 | + | 0.988638i | \(0.451970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.34625 | 0.183827 | ||||||||
\(560\) | −8.65226 | −0.365625 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.1190 | 0.806485 | ||||||||
\(563\) | −23.6261 | −0.995719 | −0.497860 | − | 0.867258i | \(-0.665881\pi\) | ||||
−0.497860 | + | 0.867258i | \(0.665881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.23167 | −0.135957 | ||||||||
\(566\) | 37.7770 | 1.58788 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.9971 | 0.922976 | ||||||||
\(569\) | −14.4892 | −0.607419 | −0.303710 | − | 0.952765i | \(-0.598225\pi\) | ||||
−0.303710 | + | 0.952765i | \(0.598225\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.7666 | −1.12015 | −0.560074 | − | 0.828443i | \(-0.689227\pi\) | ||||
−0.560074 | + | 0.828443i | \(0.689227\pi\) | |||||||
\(572\) | 10.6139 | 0.443788 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.6161 | −0.568324 | ||||||||
\(575\) | 2.15438 | 0.0898438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.44997 | −0.185255 | −0.0926273 | − | 0.995701i | \(-0.529527\pi\) | ||||
−0.0926273 | + | 0.995701i | \(0.529527\pi\) | |||||||
\(578\) | −36.2461 | −1.50764 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.27836 | 0.302217 | ||||||||
\(581\) | 0.135934 | 0.00563951 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.8843 | −0.947771 | ||||||||
\(584\) | −9.14381 | −0.378374 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −63.1696 | −2.60951 | ||||||||
\(587\) | 43.0988 | 1.77888 | 0.889440 | − | 0.457052i | \(-0.151095\pi\) | ||||
0.889440 | + | 0.457052i | \(0.151095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.2535 | −2.19427 | ||||||||
\(590\) | 33.1104 | 1.36314 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.3999 | 0.550733 | ||||||||
\(593\) | 26.2454 | 1.07777 | 0.538884 | − | 0.842380i | \(-0.318846\pi\) | ||||
0.538884 | + | 0.842380i | \(0.318846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.12764 | −0.0872249 | ||||||||
\(596\) | 2.69559 | 0.110416 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.06706 | −0.0436352 | ||||||||
\(599\) | −12.6767 | −0.517957 | −0.258979 | − | 0.965883i | \(-0.583386\pi\) | ||||
−0.258979 | + | 0.965883i | \(0.583386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.8133 | −1.95035 | −0.975173 | − | 0.221443i | \(-0.928923\pi\) | ||||
−0.975173 | + | 0.221443i | \(0.928923\pi\) | |||||||
\(602\) | 41.1414 | 1.67680 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −38.9387 | −1.58439 | ||||||||
\(605\) | 8.70754 | 0.354012 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.46055 | −0.262226 | −0.131113 | − | 0.991367i | \(-0.541855\pi\) | ||||
−0.131113 | + | 0.991367i | \(0.541855\pi\) | |||||||
\(608\) | −53.3039 | −2.16176 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.6943 | −0.959354 | ||||||||
\(611\) | −4.78965 | −0.193769 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.7535 | −0.636279 | −0.318140 | − | 0.948044i | \(-0.603058\pi\) | ||||
−0.318140 | + | 0.948044i | \(0.603058\pi\) | |||||||
\(614\) | 34.4981 | 1.39223 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.9261 | 1.04459 | ||||||||
\(617\) | −14.6509 | −0.589823 | −0.294912 | − | 0.955525i | \(-0.595290\pi\) | ||||
−0.294912 | + | 0.955525i | \(0.595290\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6842 | 1.39408 | 0.697038 | − | 0.717034i | \(-0.254501\pi\) | ||||
0.697038 | + | 0.717034i | \(0.254501\pi\) | |||||||
\(620\) | −21.3719 | −0.858317 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.1549 | −0.447272 | ||||||||
\(623\) | −45.4065 | −1.81917 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.90396 | 0.396159 | ||||||||
\(626\) | −59.1120 | −2.36259 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.7144 | −0.627074 | ||||||||
\(629\) | 3.29512 | 0.131385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0133 | −0.717099 | −0.358550 | − | 0.933511i | \(-0.616729\pi\) | ||||
−0.358550 | + | 0.933511i | \(0.616729\pi\) | |||||||
\(632\) | −9.29493 | −0.369732 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.4077 | −0.413342 | ||||||||
\(635\) | −3.43731 | −0.136405 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.41125 | 0.293644 | ||||||||
\(638\) | 24.7167 | 0.978543 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.8000 | −0.466435 | ||||||||
\(641\) | −20.5414 | −0.811336 | −0.405668 | − | 0.914020i | \(-0.632961\pi\) | ||||
−0.405668 | + | 0.914020i | \(0.632961\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.7792 | −0.701144 | −0.350572 | − | 0.936536i | \(-0.614013\pi\) | ||||
−0.350572 | + | 0.936536i | \(0.614013\pi\) | |||||||
\(644\) | −5.79850 | −0.228493 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.92163 | −0.311673 | ||||||||
\(647\) | 5.81065 | 0.228440 | 0.114220 | − | 0.993455i | \(-0.463563\pi\) | ||||
0.114220 | + | 0.993455i | \(0.463563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 64.5483 | 2.53374 | ||||||||
\(650\) | −7.59205 | −0.297785 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 65.5411 | 2.56679 | ||||||||
\(653\) | 45.7938 | 1.79205 | 0.896026 | − | 0.444003i | \(-0.146442\pi\) | ||||
0.896026 | + | 0.444003i | \(0.146442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.4528 | 0.916377 | ||||||||
\(656\) | 3.41566 | 0.133359 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −45.3387 | −1.76749 | ||||||||
\(659\) | 26.2093 | 1.02097 | 0.510485 | − | 0.859886i | \(-0.329466\pi\) | ||||
0.510485 | + | 0.859886i | \(0.329466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.3919 | −0.715360 | −0.357680 | − | 0.933844i | \(-0.616432\pi\) | ||||
−0.357680 | + | 0.933844i | \(0.616432\pi\) | |||||||
\(662\) | 2.19122 | 0.0851640 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0524131 | 0.00203402 | ||||||||
\(665\) | 28.4853 | 1.10461 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.42649 | −0.0552338 | ||||||||
\(668\) | −15.2356 | −0.589484 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.11427 | −0.120315 | ||||||||
\(671\) | −46.1917 | −1.78321 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.8082 | 0.802095 | 0.401048 | − | 0.916057i | \(-0.368646\pi\) | ||||
0.401048 | + | 0.916057i | \(0.368646\pi\) | |||||||
\(674\) | −9.09543 | −0.350343 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −32.8840 | −1.26477 | ||||||||
\(677\) | 4.30973 | 0.165636 | 0.0828182 | − | 0.996565i | \(-0.473608\pi\) | ||||
0.0828182 | + | 0.996565i | \(0.473608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.0755 | −0.962309 | ||||||||
\(680\) | −0.820369 | −0.0314597 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −72.5772 | −2.77912 | ||||||||
\(683\) | −10.4576 | −0.400149 | −0.200074 | − | 0.979781i | \(-0.564118\pi\) | ||||
−0.200074 | + | 0.979781i | \(0.564118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.30271 | 0.355438 | ||||||||
\(686\) | 10.8580 | 0.414559 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.3205 | −0.393467 | ||||||||
\(689\) | −4.65428 | −0.177314 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.4319 | 0.815310 | 0.407655 | − | 0.913136i | \(-0.366347\pi\) | ||||
0.407655 | + | 0.913136i | \(0.366347\pi\) | |||||||
\(692\) | −1.91409 | −0.0727627 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 71.7321 | 2.72291 | ||||||||
\(695\) | 5.76885 | 0.218825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.839931 | 0.0318147 | ||||||||
\(698\) | 14.1676 | 0.536250 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −41.2560 | −1.55933 | ||||||||
\(701\) | −14.0193 | −0.529501 | −0.264751 | − | 0.964317i | \(-0.585290\pi\) | ||||
−0.264751 | + | 0.964317i | \(0.585290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.1157 | −1.66385 | ||||||||
\(704\) | −53.9461 | −2.03317 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.97276 | −0.187152 | ||||||||
\(707\) | −17.6813 | −0.664975 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7062 | 0.552303 | 0.276152 | − | 0.961114i | \(-0.410941\pi\) | ||||
0.276152 | + | 0.961114i | \(0.410941\pi\) | |||||||
\(710\) | 32.9382 | 1.23615 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.5077 | −0.656128 | ||||||||
\(713\) | 4.18868 | 0.156867 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.10117 | 0.153375 | ||||||||
\(716\) | −48.4128 | −1.80927 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 50.3071 | 1.87744 | ||||||||
\(719\) | −33.4489 | −1.24743 | −0.623717 | − | 0.781650i | \(-0.714378\pi\) | ||||
−0.623717 | + | 0.781650i | \(0.714378\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 54.8768 | 2.04372 | ||||||||
\(722\) | 64.8846 | 2.41475 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 62.1517 | 2.30985 | ||||||||
\(725\) | −10.1494 | −0.376938 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.5885 | 0.392706 | 0.196353 | − | 0.980533i | \(-0.437090\pi\) | ||||
0.196353 | + | 0.980533i | \(0.437090\pi\) | |||||||
\(728\) | 5.27292 | 0.195428 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.6919 | −0.506759 | ||||||||
\(731\) | −2.53788 | −0.0938670 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.9577 | −1.66055 | −0.830275 | − | 0.557354i | \(-0.811816\pi\) | ||||
−0.830275 | + | 0.557354i | \(0.811816\pi\) | |||||||
\(734\) | −41.1652 | −1.51943 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.19265 | 0.154543 | ||||||||
\(737\) | −6.07123 | −0.223637 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2482 | 0.965557 | 0.482778 | − | 0.875743i | \(-0.339628\pi\) | ||||
0.482778 | + | 0.875743i | \(0.339628\pi\) | |||||||
\(740\) | −17.7047 | −0.650838 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −44.0572 | −1.61739 | ||||||||
\(743\) | 5.27632 | 0.193570 | 0.0967848 | − | 0.995305i | \(-0.469144\pi\) | ||||
0.0967848 | + | 0.995305i | \(0.469144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.04157 | 0.0381601 | ||||||||
\(746\) | −50.2647 | −1.84032 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.19770 | −0.226610 | ||||||||
\(749\) | 16.7387 | 0.611620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.33884 | 0.0488548 | 0.0244274 | − | 0.999702i | \(-0.492224\pi\) | ||||
0.0244274 | + | 0.999702i | \(0.492224\pi\) | |||||||
\(752\) | 11.3734 | 0.414747 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.02695 | 0.183071 | ||||||||
\(755\) | −15.0458 | −0.547573 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.9065 | 1.66850 | 0.834250 | − | 0.551386i | \(-0.185901\pi\) | ||||
0.834250 | + | 0.551386i | \(0.185901\pi\) | |||||||
\(758\) | 12.8694 | 0.467437 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.9832 | 0.398404 | ||||||||
\(761\) | −33.5900 | −1.21764 | −0.608818 | − | 0.793310i | \(-0.708356\pi\) | ||||
−0.608818 | + | 0.793310i | \(0.708356\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.6956 | 0.857839 | ||||||||
\(764\) | −33.3251 | −1.20566 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.6323 | 1.82942 | ||||||||
\(767\) | 13.1280 | 0.474025 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.8859 | −0.572860 | −0.286430 | − | 0.958101i | \(-0.592469\pi\) | ||||
−0.286430 | + | 0.958101i | \(0.592469\pi\) | |||||||
\(770\) | 38.8215 | 1.39903 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 34.1292 | 1.22834 | ||||||||
\(773\) | 44.3575 | 1.59543 | 0.797715 | − | 0.603035i | \(-0.206042\pi\) | ||||
0.797715 | + | 0.603035i | \(0.206042\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.8022 | 1.07053 | ||||||||
\(776\) | −9.66851 | −0.347079 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.7253 | 1.02985 | ||||||||
\(779\) | −11.2451 | −0.402899 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.2126 | 2.29771 | ||||||||
\(782\) | 0.623081 | 0.0222813 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.5986 | −0.628523 | ||||||||
\(785\) | −6.07202 | −0.216720 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.6686 | −0.879341 | −0.439670 | − | 0.898159i | \(-0.644905\pi\) | ||||
−0.439670 | + | 0.898159i | \(0.644905\pi\) | |||||||
\(788\) | −19.8098 | −0.705696 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.9182 | −0.495186 | ||||||||
\(791\) | −12.1290 | −0.431259 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.39460 | −0.333612 | ||||||||
\(794\) | −2.03839 | −0.0723399 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.5481 | −1.22452 | ||||||||
\(797\) | 27.8639 | 0.986990 | 0.493495 | − | 0.869749i | \(-0.335719\pi\) | ||||
0.493495 | + | 0.869749i | \(0.335719\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.79680 | 0.0989436 | ||||||||
\(800\) | 29.8305 | 1.05467 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −47.7914 | −1.68757 | ||||||||
\(803\) | −26.6921 | −0.941944 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.24053 | −0.0789682 | ||||||||
\(806\) | −14.7610 | −0.519932 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.81750 | −0.239839 | ||||||||
\(809\) | 22.3244 | 0.784885 | 0.392442 | − | 0.919777i | \(-0.371630\pi\) | ||||
0.392442 | + | 0.919777i | \(0.371630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0587 | −0.423439 | −0.211719 | − | 0.977331i | \(-0.567906\pi\) | ||||
−0.211719 | + | 0.977331i | \(0.567906\pi\) | |||||||
\(812\) | 27.3170 | 0.958638 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −60.1237 | −2.10733 | ||||||||
\(815\) | 25.3249 | 0.887093 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.9776 | 1.18873 | ||||||||
\(818\) | −65.2192 | −2.28033 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.51295 | −0.157599 | ||||||||
\(821\) | −33.7012 | −1.17618 | −0.588090 | − | 0.808795i | \(-0.700120\pi\) | ||||
−0.588090 | + | 0.808795i | \(0.700120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.4094 | 0.432566 | 0.216283 | − | 0.976331i | \(-0.430607\pi\) | ||||
0.216283 | + | 0.976331i | \(0.430607\pi\) | |||||||
\(824\) | 21.1592 | 0.737116 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 124.269 | 4.32389 | ||||||||
\(827\) | 11.4120 | 0.396836 | 0.198418 | − | 0.980118i | \(-0.436420\pi\) | ||||
0.198418 | + | 0.980118i | \(0.436420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.6469 | −0.856024 | −0.428012 | − | 0.903773i | \(-0.640786\pi\) | ||||
−0.428012 | + | 0.903773i | \(0.640786\pi\) | |||||||
\(830\) | 0.0784829 | 0.00272418 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.9717 | −0.380375 | ||||||||
\(833\) | −4.32761 | −0.149943 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.88701 | −0.203728 | ||||||||
\(836\) | 82.9759 | 2.86978 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.44172 | 0.0843478 | ||||||||
\(839\) | −49.4638 | −1.70768 | −0.853841 | − | 0.520534i | \(-0.825733\pi\) | ||||
−0.853841 | + | 0.520534i | \(0.825733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2798 | −0.768268 | ||||||||
\(842\) | −45.3828 | −1.56400 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −39.5181 | −1.36027 | ||||||||
\(845\) | −12.7063 | −0.437109 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.6809 | 1.12293 | ||||||||
\(848\) | 11.0520 | 0.379526 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.43319 | 0.152057 | ||||||||
\(851\) | 3.46995 | 0.118948 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.4674 | −0.495354 | −0.247677 | − | 0.968843i | \(-0.579667\pi\) | ||||
−0.247677 | + | 0.968843i | \(0.579667\pi\) | |||||||
\(854\) | −88.9290 | −3.04309 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.45405 | 0.220595 | ||||||||
\(857\) | −52.3900 | −1.78961 | −0.894805 | − | 0.446458i | \(-0.852685\pi\) | ||||
−0.894805 | + | 0.446458i | \(0.852685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.34885 | 0.250740 | 0.125370 | − | 0.992110i | \(-0.459988\pi\) | ||||
0.125370 | + | 0.992110i | \(0.459988\pi\) | |||||||
\(860\) | 13.6361 | 0.464986 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 67.5495 | 2.30075 | ||||||||
\(863\) | −40.1142 | −1.36550 | −0.682752 | − | 0.730651i | \(-0.739217\pi\) | ||||
−0.682752 | + | 0.730651i | \(0.739217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.739598 | −0.0251471 | ||||||||
\(866\) | −31.3890 | −1.06664 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −80.2126 | −2.72259 | ||||||||
\(869\) | −27.1333 | −0.920432 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.23478 | −0.0418391 | ||||||||
\(872\) | 9.13647 | 0.309400 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.34192 | −0.282170 | ||||||||
\(875\) | −36.2997 | −1.22715 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.9947 | 1.55313 | 0.776565 | − | 0.630038i | \(-0.216961\pi\) | ||||
0.776565 | + | 0.630038i | \(0.216961\pi\) | |||||||
\(878\) | −60.7230 | −2.04930 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.73858 | −0.328287 | ||||||||
\(881\) | 0.747769 | 0.0251930 | 0.0125965 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125965 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.5270 | 0.926357 | 0.463179 | − | 0.886265i | \(-0.346709\pi\) | ||||
0.463179 | + | 0.886265i | \(0.346709\pi\) | |||||||
\(884\) | −1.26051 | −0.0423954 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.6915 | −0.527166 | ||||||||
\(887\) | 23.3996 | 0.785681 | 0.392841 | − | 0.919607i | \(-0.371492\pi\) | ||||
0.392841 | + | 0.919607i | \(0.371492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9008 | −0.432680 | ||||||||
\(890\) | −26.2159 | −0.878758 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.23318 | −0.242185 | ||||||||
\(893\) | −37.4440 | −1.25302 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.7066 | −0.625292 | ||||||||
\(896\) | −44.2874 | −1.47954 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.6010 | 1.15465 | ||||||||
\(899\) | −19.7331 | −0.658134 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.71775 | 0.0905413 | ||||||||
\(902\) | −15.3256 | −0.510287 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.67667 | −0.155544 | ||||||||
\(905\) | 24.0152 | 0.798294 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.2183 | −0.936975 | −0.468487 | − | 0.883470i | \(-0.655201\pi\) | ||||
−0.468487 | + | 0.883470i | \(0.655201\pi\) | |||||||
\(908\) | 38.7225 | 1.28505 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.89563 | 0.261738 | ||||||||
\(911\) | −3.89740 | −0.129127 | −0.0645634 | − | 0.997914i | \(-0.520565\pi\) | ||||
−0.0645634 | + | 0.997914i | \(0.520565\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.153001 | 0.00506361 | ||||||||
\(914\) | 82.2239 | 2.71973 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.9344 | −0.658651 | ||||||||
\(917\) | 88.0226 | 2.90676 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.3546 | 0.935332 | 0.467666 | − | 0.883905i | \(-0.345095\pi\) | ||||
0.467666 | + | 0.883905i | \(0.345095\pi\) | |||||||
\(920\) | −0.863894 | −0.0284817 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 61.7656 | 2.03414 | ||||||||
\(923\) | 13.0597 | 0.429867 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.6885 | 0.811752 | ||||||||
\(926\) | −59.7739 | −1.96429 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19.7517 | −0.648383 | ||||||||
\(929\) | −21.0993 | −0.692245 | −0.346122 | − | 0.938189i | \(-0.612502\pi\) | ||||
−0.346122 | + | 0.938189i | \(0.612502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 57.9388 | 1.89887 | ||||||||
\(932\) | 19.2708 | 0.631235 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.1919 | −0.464373 | ||||||||
\(935\) | −2.39478 | −0.0783175 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.4404 | −1.48447 | −0.742237 | − | 0.670137i | \(-0.766235\pi\) | ||||
−0.742237 | + | 0.670137i | \(0.766235\pi\) | |||||||
\(938\) | −11.6884 | −0.381641 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.0272 | −0.490133 | ||||||||
\(941\) | 39.4685 | 1.28664 | 0.643318 | − | 0.765599i | \(-0.277557\pi\) | ||||
0.643318 | + | 0.765599i | \(0.277557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.884494 | 0.0288031 | ||||||||
\(944\) | −31.1736 | −1.01461 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.3069 | 1.50557 | ||||||||
\(947\) | 13.6395 | 0.443223 | 0.221612 | − | 0.975135i | \(-0.428868\pi\) | ||||
0.221612 | + | 0.975135i | \(0.428868\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.42872 | −0.176224 | ||||||||
\(950\) | −59.3523 | −1.92564 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.07899 | −0.0997907 | ||||||||
\(953\) | 55.9418 | 1.81213 | 0.906066 | − | 0.423136i | \(-0.139071\pi\) | ||||
0.906066 | + | 0.423136i | \(0.139071\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.8767 | −0.416681 | ||||||||
\(956\) | −19.3446 | −0.625649 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.8567 | 0.996935 | ||||||||
\(959\) | 34.9148 | 1.12746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.9435 | 0.869144 | ||||||||
\(962\) | −12.2281 | −0.394250 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −44.2904 | −1.42650 | ||||||||
\(965\) | 13.1874 | 0.424519 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.6707 | 1.75809 | 0.879045 | − | 0.476739i | \(-0.158181\pi\) | ||||
0.879045 | + | 0.476739i | \(0.158181\pi\) | |||||||
\(968\) | 12.6010 | 0.405011 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.4776 | −0.464846 | ||||||||
\(971\) | 49.5192 | 1.58915 | 0.794573 | − | 0.607169i | \(-0.207695\pi\) | ||||
0.794573 | + | 0.607169i | \(0.207695\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.6515 | 0.694117 | ||||||||
\(974\) | −61.6637 | −1.97583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.3083 | 0.714071 | ||||||||
\(977\) | 7.53020 | 0.240912 | 0.120456 | − | 0.992719i | \(-0.461564\pi\) | ||||
0.120456 | + | 0.992719i | \(0.461564\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.1075 | −1.63340 | ||||||||
\(980\) | 23.2523 | 0.742767 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.88293 | 0.315377 | ||||||||
\(983\) | 13.6448 | 0.435201 | 0.217600 | − | 0.976038i | \(-0.430177\pi\) | ||||
0.217600 | + | 0.976038i | \(0.430177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.65446 | −0.243892 | ||||||||
\(986\) | −2.93536 | −0.0934809 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.8759 | 0.536893 | ||||||||
\(989\) | −2.67253 | −0.0849815 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.1923 | 0.609663 | 0.304832 | − | 0.952406i | \(-0.401400\pi\) | ||||
0.304832 | + | 0.952406i | \(0.401400\pi\) | |||||||
\(992\) | 57.9983 | 1.84145 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 123.623 | 3.92109 | ||||||||
\(995\) | −13.3493 | −0.423201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.2777 | 1.33895 | 0.669473 | − | 0.742836i | \(-0.266520\pi\) | ||||
0.669473 | + | 0.742836i | \(0.266520\pi\) | |||||||
\(998\) | 45.1487 | 1.42916 | ||||||||
\(999\) | 0 | 0 |
(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 | 4023.2.a.f.1.20 | yes | 25 | |
3.2 | odd | 2 | 4023.2.a.e.1.6 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.6 | ✓ | 25 | 3.2 | odd | 2 | ||
4023.2.a.f.1.20 | yes | 25 | 1.1 | even | 1 | trivial |