Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | −2.53334 | −1.46263 | −0.731314 | − | 0.682041i | \(-0.761092\pi\) | ||||
−0.731314 | + | 0.682041i | \(0.761092\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50187 | 0.671655 | 0.335828 | − | 0.941923i | \(-0.390984\pi\) | ||||
0.335828 | + | 0.941923i | \(0.390984\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.478852 | −0.180989 | −0.0904946 | − | 0.995897i | \(-0.528845\pi\) | ||||
−0.0904946 | + | 0.995897i | \(0.528845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.41783 | 1.13928 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.20287 | −1.26721 | −0.633607 | − | 0.773655i | \(-0.718426\pi\) | ||||
−0.633607 | + | 0.773655i | \(0.718426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.32908 | 1.20067 | 0.600336 | − | 0.799748i | \(-0.295034\pi\) | ||||
0.600336 | + | 0.799748i | \(0.295034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.80475 | −0.982381 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.05558 | 0.498551 | 0.249275 | − | 0.968433i | \(-0.419808\pi\) | ||||
0.249275 | + | 0.968433i | \(0.419808\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.535658 | −0.122888 | −0.0614442 | − | 0.998111i | \(-0.519571\pi\) | ||||
−0.0614442 | + | 0.998111i | \(0.519571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.21310 | 0.264720 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.64982 | 1.38658 | 0.693292 | − | 0.720657i | \(-0.256160\pi\) | ||||
0.693292 | + | 0.720657i | \(0.256160\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.74440 | −0.548879 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.05852 | −0.203712 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.258982 | 0.0480917 | 0.0240459 | − | 0.999711i | \(-0.492345\pi\) | ||||
0.0240459 | + | 0.999711i | \(0.492345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.57844 | −0.822311 | −0.411156 | − | 0.911565i | \(-0.634875\pi\) | ||||
−0.411156 | + | 0.911565i | \(0.634875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.6473 | 1.85346 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.719173 | −0.121562 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8796 | −1.95300 | −0.976500 | − | 0.215518i | \(-0.930856\pi\) | ||||
−0.976500 | + | 0.215518i | \(0.930856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.9671 | −1.75614 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.23725 | −0.817921 | −0.408961 | − | 0.912552i | \(-0.634109\pi\) | ||||
−0.408961 | + | 0.912552i | \(0.634109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.69198 | 1.32552 | 0.662758 | − | 0.748834i | \(-0.269386\pi\) | ||||
0.662758 | + | 0.748834i | \(0.269386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.13313 | 0.765202 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.5859 | 1.68998 | 0.844990 | − | 0.534783i | \(-0.179607\pi\) | ||||
0.844990 | + | 0.534783i | \(0.179607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77070 | −0.967243 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.20748 | −0.729194 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2460 | 1.68211 | 0.841056 | − | 0.540948i | \(-0.181934\pi\) | ||||
0.841056 | + | 0.540948i | \(0.181934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.31216 | −0.851131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.35701 | 0.179740 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.96974 | −0.516816 | −0.258408 | − | 0.966036i | \(-0.583198\pi\) | ||||
−0.258408 | + | 0.966036i | \(0.583198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.23862 | 0.542699 | 0.271350 | − | 0.962481i | \(-0.412530\pi\) | ||||
0.271350 | + | 0.962481i | \(0.412530\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.63664 | −0.206197 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.50171 | 0.806438 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.8609 | −1.81555 | −0.907773 | − | 0.419461i | \(-0.862219\pi\) | ||||
−0.907773 | + | 0.419461i | \(0.862219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.8463 | −2.02805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3598 | 1.94155 | 0.970773 | − | 0.240001i | \(-0.0771478\pi\) | ||||
0.970773 | + | 0.240001i | \(0.0771478\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.11513 | 0.715722 | 0.357861 | − | 0.933775i | \(-0.383506\pi\) | ||||
0.357861 | + | 0.933775i | \(0.383506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.95250 | 0.802805 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.01256 | 0.229352 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5582 | −1.18789 | −0.593944 | − | 0.804506i | \(-0.702430\pi\) | ||||
−0.593944 | + | 0.804506i | \(0.702430\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.57191 | −0.841324 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1519 | −1.33384 | −0.666920 | − | 0.745130i | \(-0.732388\pi\) | ||||
−0.666920 | + | 0.745130i | \(0.732388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.08720 | 0.334854 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.656090 | −0.0703403 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.39741 | 0.572124 | 0.286062 | − | 0.958211i | \(-0.407654\pi\) | ||||
0.286062 | + | 0.958211i | \(0.407654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.07299 | −0.217309 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.5988 | 1.20274 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.804488 | −0.0825387 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0202 | 1.42354 | 0.711768 | − | 0.702414i | \(-0.247895\pi\) | ||||
0.711768 | + | 0.702414i | \(0.247895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.3647 | −1.44371 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0962519 | −0.00957742 | −0.00478871 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478871 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7390 | 1.05814 | 0.529072 | − | 0.848577i | \(-0.322540\pi\) | ||||
0.529072 | + | 0.848577i | \(0.322540\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.82191 | 0.177800 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.4866 | −1.88384 | −0.941920 | − | 0.335836i | \(-0.890981\pi\) | ||||
−0.941920 | + | 0.335836i | \(0.890981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0525721 | 0.00503549 | 0.00251775 | − | 0.999997i | \(-0.499199\pi\) | ||||
0.00251775 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30.0952 | 2.85651 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.74548 | 0.258273 | 0.129136 | − | 0.991627i | \(-0.458780\pi\) | ||||
0.129136 | + | 0.991627i | \(0.458780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.98715 | 0.931306 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.7961 | 1.36790 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.984318 | −0.0902323 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.66414 | 0.605831 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.2678 | 1.19631 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.6311 | −1.04031 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4193 | 1.36824 | 0.684122 | − | 0.729367i | \(-0.260185\pi\) | ||||
0.684122 | + | 0.729367i | \(0.260185\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.0198 | −1.93873 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8641 | −1.21131 | −0.605656 | − | 0.795727i | \(-0.707089\pi\) | ||||
−0.605656 | + | 0.795727i | \(0.707089\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.256501 | 0.0222415 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.58975 | −0.136824 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4346 | −1.23323 | −0.616613 | − | 0.787266i | \(-0.711496\pi\) | ||||
−0.616613 | + | 0.787266i | \(0.711496\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.9011 | 1.94244 | 0.971221 | − | 0.238179i | \(-0.0765505\pi\) | ||||
0.971221 | + | 0.238179i | \(0.0765505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.3511 | −2.47181 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.1946 | −1.52151 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.388956 | 0.0323011 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.1525 | 1.41472 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.40542 | −0.770522 | −0.385261 | − | 0.922808i | \(-0.625889\pi\) | ||||
−0.385261 | + | 0.922808i | \(0.625889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.32090 | 0.595766 | 0.297883 | − | 0.954602i | \(-0.403719\pi\) | ||||
0.297883 | + | 0.954602i | \(0.403719\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.02562 | 0.567988 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.87620 | −0.552310 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.11074 | 0.567499 | 0.283749 | − | 0.958898i | \(-0.408422\pi\) | ||||
0.283749 | + | 0.958898i | \(0.408422\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −31.0232 | −2.46030 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.18428 | −0.250957 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.35460 | 0.497730 | 0.248865 | − | 0.968538i | \(-0.419942\pi\) | ||||
0.248865 | + | 0.968538i | \(0.419942\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.9909 | 1.24489 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.47308 | 0.655667 | 0.327833 | − | 0.944736i | \(-0.393682\pi\) | ||||
0.327833 | + | 0.944736i | \(0.393682\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.74097 | 0.441613 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.83079 | −0.140004 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.2270 | 1.08166 | 0.540828 | − | 0.841133i | \(-0.318111\pi\) | ||||
0.540828 | + | 0.841133i | \(0.318111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.31416 | 0.0993412 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0567 | 0.755909 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.07057 | 0.603223 | 0.301611 | − | 0.953431i | \(-0.402476\pi\) | ||||
0.301611 | + | 0.953431i | \(0.402476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.9756 | 1.33612 | 0.668060 | − | 0.744108i | \(-0.267125\pi\) | ||||
0.668060 | + | 0.744108i | \(0.267125\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7379 | −0.793766 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.8416 | −1.31174 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.63933 | −0.631770 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.506874 | 0.0368696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.0431 | 1.37791 | 0.688954 | − | 0.724805i | \(-0.258070\pi\) | ||||
0.688954 | + | 0.724805i | \(0.258070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.70949 | −0.195033 | −0.0975166 | − | 0.995234i | \(-0.531090\pi\) | ||||
−0.0975166 | + | 0.995234i | \(0.531090\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.4711 | −1.17952 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3153 | −0.948674 | −0.474337 | − | 0.880343i | \(-0.657312\pi\) | ||||
−0.474337 | + | 0.880343i | \(0.657312\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.68736 | −0.190502 | −0.0952510 | − | 0.995453i | \(-0.530365\pi\) | ||||
−0.0952510 | + | 0.995453i | \(0.530365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37.6477 | 2.65547 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.124014 | −0.00870408 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.86566 | −0.549361 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.7280 | 1.57970 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.25130 | 0.155726 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.55720 | 0.657945 | 0.328973 | − | 0.944339i | \(-0.393298\pi\) | ||||
0.328973 | + | 0.944339i | \(0.393298\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −41.4449 | −2.83976 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.0542 | 0.890289 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.19240 | 0.148829 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.4917 | −1.04683 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.89876 | 0.598596 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.23789 | −0.283790 | −0.141895 | − | 0.989882i | \(-0.545320\pi\) | ||||
−0.141895 | + | 0.989882i | \(0.545320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.37989 | −0.625326 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.23005 | 0.148013 | 0.0740067 | − | 0.997258i | \(-0.476421\pi\) | ||||
0.0740067 | + | 0.997258i | \(0.476421\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.2320 | 1.79954 | 0.899769 | − | 0.436366i | \(-0.143735\pi\) | ||||
0.899769 | + | 0.436366i | \(0.143735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.09850 | −0.335456 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.4212 | 1.14130 | 0.570649 | − | 0.821194i | \(-0.306692\pi\) | ||||
0.570649 | + | 0.821194i | \(0.306692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.4005 | 1.13508 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.7475 | 1.73744 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.2187 | 1.89000 | 0.945002 | − | 0.327066i | \(-0.106060\pi\) | ||||
0.945002 | + | 0.327066i | \(0.106060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.793095 | −0.0510877 | −0.0255439 | − | 0.999674i | \(-0.508132\pi\) | ||||
−0.0255439 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3578 | 1.43425 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.1687 | −0.649654 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.31891 | −0.147549 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.7848 | 1.95091 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.9484 | −1.75710 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.82095 | −0.489767 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.86990 | −0.366154 | −0.183077 | − | 0.983099i | \(-0.558606\pi\) | ||||
−0.183077 | + | 0.983099i | \(0.558606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.68859 | 0.353472 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.885157 | 0.0547898 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2437 | 1.00163 | 0.500815 | − | 0.865554i | \(-0.333034\pi\) | ||||
0.500815 | + | 0.865554i | \(0.333034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.3918 | 1.12980 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.6735 | −0.836804 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.6368 | 1.25825 | 0.629125 | − | 0.777304i | \(-0.283413\pi\) | ||||
0.629125 | + | 0.777304i | \(0.283413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.0148 | 1.88401 | 0.942007 | − | 0.335593i | \(-0.108937\pi\) | ||||
0.942007 | + | 0.335593i | \(0.108937\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.25160 | 0.317841 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.5343 | 0.695547 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.90285 | 0.294584 | 0.147292 | − | 0.989093i | \(-0.452944\pi\) | ||||
0.147292 | + | 0.989093i | \(0.452944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.6483 | −0.936841 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7041 | 0.936827 | 0.468413 | − | 0.883509i | \(-0.344826\pi\) | ||||
0.468413 | + | 0.883509i | \(0.344826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.2286 | −1.08358 | −0.541790 | − | 0.840514i | \(-0.682253\pi\) | ||||
−0.541790 | + | 0.840514i | \(0.682253\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.03804 | 0.120723 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.50787 | 0.148035 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.7746 | −0.751447 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.5180 | −2.08210 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.47789 | −0.0863394 | −0.0431697 | − | 0.999068i | \(-0.513746\pi\) | ||||
−0.0431697 | + | 0.999068i | \(0.513746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.96202 | −0.347122 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.44882 | 0.258147 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.7876 | 1.66483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.16218 | −0.239904 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.243839 | 0.0140082 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.36584 | 0.364507 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7263 | 1.63950 | 0.819748 | − | 0.572725i | \(-0.194114\pi\) | ||||
0.819748 | + | 0.572725i | \(0.194114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.2056 | −1.54767 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8515 | −1.01227 | −0.506133 | − | 0.862455i | \(-0.668926\pi\) | ||||
−0.506133 | + | 0.862455i | \(0.668926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.9352 | −0.787662 | −0.393831 | − | 0.919183i | \(-0.628850\pi\) | ||||
−0.393831 | + | 0.919183i | \(0.628850\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.45801 | −0.138493 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.6130 | 0.989247 | 0.494623 | − | 0.869107i | \(-0.335306\pi\) | ||||
0.494623 | + | 0.869107i | \(0.335306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08847 | −0.0609425 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 49.3663 | 2.75536 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.10109 | −0.0612661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.8807 | −0.659024 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.133183 | −0.00736505 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.54794 | −0.305868 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0310 | 0.661284 | 0.330642 | − | 0.943756i | \(-0.392735\pi\) | ||||
0.330642 | + | 0.943756i | \(0.392735\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −40.6026 | −2.22501 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.3191 | −1.21942 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3931 | 0.947463 | 0.473732 | − | 0.880669i | \(-0.342907\pi\) | ||||
0.473732 | + | 0.880669i | \(0.342907\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.95524 | −0.377757 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.2426 | 1.04204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.59413 | 0.356050 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.3009 | −1.36215 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.6671 | −0.841054 | −0.420527 | − | 0.907280i | \(-0.638155\pi\) | ||||
−0.420527 | + | 0.907280i | \(0.638155\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.9367 | 1.17425 | 0.587123 | − | 0.809498i | \(-0.300260\pi\) | ||||
0.587123 | + | 0.809498i | \(0.300260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.58241 | −0.244591 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.9804 | 1.75537 | 0.877686 | − | 0.479237i | \(-0.159087\pi\) | ||||
0.877686 | + | 0.479237i | \(0.159087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.5702 | 1.30405 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.49362 | 0.131976 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.6493 | 0.931493 | 0.465746 | − | 0.884918i | \(-0.345786\pi\) | ||||
0.465746 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7131 | −0.984898 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.8826 | −0.886105 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.18411 | 0.480718 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.5782 | 1.64837 | 0.824183 | − | 0.566323i | \(-0.191634\pi\) | ||||
0.824183 | + | 0.566323i | \(0.191634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.9001 | −0.931840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.86401 | −0.304444 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7157 | 0.761949 | 0.380975 | − | 0.924585i | \(-0.375589\pi\) | ||||
0.380975 | + | 0.924585i | \(0.375589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.4655 | 1.52159 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12115 | 0.0577424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6456 | −1.31732 | −0.658662 | − | 0.752439i | \(-0.728877\pi\) | ||||
−0.658662 | + | 0.752439i | \(0.728877\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.0625 | −2.00123 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.6100 | −0.746537 | −0.373268 | − | 0.927723i | \(-0.621763\pi\) | ||||
−0.373268 | + | 0.927723i | \(0.621763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.02259 | 0.154046 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.7078 | 1.51013 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.94533 | −0.402844 | −0.201422 | − | 0.979505i | \(-0.564556\pi\) | ||||
−0.201422 | + | 0.979505i | \(0.564556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6692 | 0.691282 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.1225 | 1.77170 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.8570 | −0.797852 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.55835 | −0.329154 | −0.164577 | − | 0.986364i | \(-0.552626\pi\) | ||||
−0.164577 | + | 0.986364i | \(0.552626\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.649806 | −0.0325310 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.20130 | −0.259741 | −0.129870 | − | 0.991531i | \(-0.541456\pi\) | ||||
−0.129870 | + | 0.991531i | \(0.541456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.8204 | −0.987326 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.3720 | −0.565079 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.9286 | 2.47487 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7419 | 0.728939 | 0.364470 | − | 0.931215i | \(-0.381250\pi\) | ||||
0.364470 | + | 0.931215i | \(0.381250\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.5677 | 1.80375 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.90092 | 0.0935382 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2505 | −0.895880 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −58.0163 | −2.84107 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.9425 | −1.46279 | −0.731394 | − | 0.681955i | \(-0.761130\pi\) | ||||
−0.731394 | + | 0.681955i | \(0.761130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.851309 | −0.0414903 | −0.0207451 | − | 0.999785i | \(-0.506604\pi\) | ||||
−0.0207451 | + | 0.999785i | \(0.506604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 39.5987 | 1.92536 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.64132 | −0.273644 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.02967 | −0.0982227 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 46.0932 | 2.22540 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.5827 | −0.606086 | −0.303043 | − | 0.952977i | \(-0.598003\pi\) | ||||
−0.303043 | + | 0.952977i | \(0.598003\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.9864 | −0.527974 | −0.263987 | − | 0.964526i | \(-0.585038\pi\) | ||||
−0.263987 | + | 0.964526i | \(0.585038\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.985360 | −0.0472444 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.56203 | −0.170395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3714 | 1.02000 | 0.510000 | − | 0.860175i | \(-0.329645\pi\) | ||||
0.510000 | + | 0.860175i | \(0.329645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.1411 | −1.10196 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.4243 | −1.77808 | −0.889040 | − | 0.457829i | \(-0.848627\pi\) | ||||
−0.889040 | + | 0.457829i | \(0.848627\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.10618 | 0.384270 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.8272 | 1.12699 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.9688 | 1.46151 | 0.730755 | − | 0.682640i | \(-0.239168\pi\) | ||||
0.730755 | + | 0.682640i | \(0.239168\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.0115 | 1.03648 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.5464 | −0.871384 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.11336 | −0.145957 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.39062 | −0.439275 | −0.219637 | − | 0.975582i | \(-0.570487\pi\) | ||||
−0.219637 | + | 0.975582i | \(0.570487\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.17587 | −0.101561 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.75111 | −0.267856 | −0.133928 | − | 0.990991i | \(-0.542759\pi\) | ||||
−0.133928 | + | 0.990991i | \(0.542759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7631 | 1.19731 | 0.598656 | − | 0.801006i | \(-0.295701\pi\) | ||||
0.598656 | + | 0.801006i | \(0.295701\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.4198 | 0.807823 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.5070 | −1.36542 | −0.682710 | − | 0.730689i | \(-0.739199\pi\) | ||||
−0.682710 | + | 0.730689i | \(0.739199\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.11617 | 0.328594 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0139 | −0.830039 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.5313 | −1.67971 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.47006 | 0.0674509 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 41.8547 | 1.91639 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6959 | −0.899927 | −0.449963 | − | 0.893047i | \(-0.648563\pi\) | ||||
−0.449963 | + | 0.893047i | \(0.648563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.4279 | −2.34491 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.06688 | 0.367056 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0565 | 0.956126 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1758 | −0.461108 | −0.230554 | − | 0.973060i | \(-0.574054\pi\) | ||||
−0.230554 | + | 0.973060i | \(0.574054\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0984 | −0.727994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0822 | 1.35759 | 0.678796 | − | 0.734327i | \(-0.262502\pi\) | ||||
0.678796 | + | 0.734327i | \(0.262502\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.532357 | 0.0239762 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.5739 | −0.969675 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.83391 | −0.351399 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6262 | 1.28149 | 0.640743 | − | 0.767756i | \(-0.278627\pi\) | ||||
0.640743 | + | 0.767756i | \(0.278627\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.4652 | −0.958996 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.95326 | 0.265443 | 0.132721 | − | 0.991153i | \(-0.457628\pi\) | ||||
0.132721 | + | 0.991153i | \(0.457628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.144558 | −0.00643273 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.5438 | −0.645915 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.90797 | −0.439163 | −0.219582 | − | 0.975594i | \(-0.570469\pi\) | ||||
−0.219582 | + | 0.975594i | \(0.570469\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.92824 | −0.129538 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.567004 | 0.0250338 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.1285 | 0.710709 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −48.6941 | −2.14157 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.0418 | −1.58206 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.43628 | 0.106735 | 0.0533677 | − | 0.998575i | \(-0.483004\pi\) | ||||
0.0533677 | + | 0.998575i | \(0.483004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.7452 | −1.38812 | −0.694061 | − | 0.719916i | \(-0.744180\pi\) | ||||
−0.694061 | + | 0.719916i | \(0.744180\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.32922 | −0.145299 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.41133 | −0.409964 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2201 | 0.922614 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.5679 | −0.588797 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.6725 | −0.982055 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.2663 | −1.26529 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.4455 | −0.882290 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.4564 | 1.22570 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.211389 | 0.00908834 | 0.00454417 | − | 0.999990i | \(-0.498554\pi\) | ||||
0.00454417 | + | 0.999990i | \(0.498554\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −45.5385 | −1.95424 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0789563 | 0.00338212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.20570 | 0.350850 | 0.175425 | − | 0.984493i | \(-0.443870\pi\) | ||||
0.175425 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4869 | 0.618285 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.138726 | −0.00590992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.05581 | 0.214995 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 45.1990 | 1.91859 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.8194 | −1.68720 | −0.843602 | − | 0.536970i | \(-0.819569\pi\) | ||||
−0.843602 | + | 0.536970i | \(0.819569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.6283 | 1.59151 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.8864 | 0.924044 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.24909 | −0.221223 | −0.110611 | − | 0.993864i | \(-0.535281\pi\) | ||||
−0.110611 | + | 0.993864i | \(0.535281\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.12334 | 0.173470 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.62583 | 0.152270 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.91025 | −0.373537 | −0.186769 | − | 0.982404i | \(-0.559801\pi\) | ||||
−0.186769 | + | 0.982404i | \(0.559801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0518 | 0.588051 | 0.294025 | − | 0.955798i | \(-0.405005\pi\) | ||||
0.294025 | + | 0.955798i | \(0.405005\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −48.2426 | −2.01536 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.2497 | −0.761067 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.31977 | 0.0965735 | 0.0482867 | − | 0.998834i | \(-0.484624\pi\) | ||||
0.0482867 | + | 0.998834i | \(0.484624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.86407 | 0.285261 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.81894 | 0.241410 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.4682 | −2.13160 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.2218 | 0.918757 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.53569 | 0.311031 | 0.155516 | − | 0.987833i | \(-0.450296\pi\) | ||||
0.155516 | + | 0.987833i | \(0.450296\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.45248 | 0.101053 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.7322 | 1.38756 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.1818 | 0.828768 | 0.414384 | − | 0.910102i | \(-0.363997\pi\) | ||||
0.414384 | + | 0.910102i | \(0.363997\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.47831 | −0.0606050 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.80802 | 0.278634 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.2813 | 0.460943 | 0.230471 | − | 0.973079i | \(-0.425973\pi\) | ||||
0.230471 | + | 0.973079i | \(0.425973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.6425 | −1.53547 | −0.767734 | − | 0.640769i | \(-0.778616\pi\) | ||||
−0.767734 | + | 0.640769i | \(0.778616\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −50.7921 | −2.06841 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0087 | 0.406910 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.9414 | 1.58058 | 0.790291 | − | 0.612732i | \(-0.209929\pi\) | ||||
0.790291 | + | 0.612732i | \(0.209929\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.314170 | 0.0127308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.1564 | 2.02911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.6687 | −1.35987 | −0.679934 | − | 0.733274i | \(-0.737991\pi\) | ||||
−0.679934 | + | 0.733274i | \(0.737991\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.9264 | 0.803511 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.86536 | 0.276389 | 0.138194 | − | 0.990405i | \(-0.455870\pi\) | ||||
0.138194 | + | 0.990405i | \(0.455870\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.3773 | 0.577873 | 0.288936 | − | 0.957348i | \(-0.406698\pi\) | ||||
0.288936 | + | 0.957348i | \(0.406698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.03895 | −0.282464 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.58456 | −0.103548 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.74632 | −0.149853 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.70333 | −0.227769 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.4195 | −0.973669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1422 | −0.921278 | −0.460639 | − | 0.887588i | \(-0.652380\pi\) | ||||
−0.460639 | + | 0.887588i | \(0.652380\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.2117 | −0.962328 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.1578 | 0.918989 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.3109 | −1.16134 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 55.9149 | 2.21196 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.5776 | 1.01026 | 0.505128 | − | 0.863045i | \(-0.331445\pi\) | ||||
0.505128 | + | 0.863045i | \(0.331445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.45113 | −0.0966633 | −0.0483316 | − | 0.998831i | \(-0.515390\pi\) | ||||
−0.0483316 | + | 0.998831i | \(0.515390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.0708 | −1.30216 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.9315 | −1.72712 | −0.863562 | − | 0.504243i | \(-0.831772\pi\) | ||||
−0.863562 | + | 0.504243i | \(0.831772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6843 | 0.654917 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.55409 | −0.217682 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.4190 | 1.38605 | 0.693025 | − | 0.720913i | \(-0.256277\pi\) | ||||
0.693025 | + | 0.720913i | \(0.256277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.8220 | −0.813584 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.9005 | 0.815406 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.6085 | −1.58188 | −0.790940 | − | 0.611893i | \(-0.790408\pi\) | ||||
−0.790940 | + | 0.611893i | \(0.790408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.84140 | 0.343891 | 0.171945 | − | 0.985106i | \(-0.444995\pi\) | ||||
0.171945 | + | 0.985106i | \(0.444995\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.5436 | −0.875522 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.385231 | 0.0149386 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.72218 | 0.0666832 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.7360 | 0.415079 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.8144 | −0.687716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.8126 | 1.68885 | 0.844426 | − | 0.535672i | \(-0.179942\pi\) | ||||
0.844426 | + | 0.535672i | \(0.179942\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.90499 | 0.111813 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.7378 | −1.25822 | −0.629109 | − | 0.777317i | \(-0.716580\pi\) | ||||
−0.629109 | + | 0.777317i | \(0.716580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.71361 | −0.257645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.64948 | −0.216488 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.2997 | 0.700218 | 0.350109 | − | 0.936709i | \(-0.386145\pi\) | ||||
0.350109 | + | 0.936709i | \(0.386145\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.6788 | −0.828303 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −68.9879 | −2.63205 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 53.0138 | 2.01966 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0415 | −0.724372 | −0.362186 | − | 0.932106i | \(-0.617969\pi\) | ||||
−0.362186 | + | 0.932106i | \(0.617969\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.87858 | 0.261296 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34.3943 | 1.30465 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.7656 | −0.407775 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −44.1338 | −1.66929 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.8488 | −1.61838 | −0.809189 | − | 0.587549i | \(-0.800093\pi\) | ||||
−0.809189 | + | 0.587549i | \(0.800093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.36343 | 0.240001 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −44.0815 | −1.66020 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0460905 | 0.00173341 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.0324 | −1.24056 | −0.620279 | − | 0.784382i | \(-0.712980\pi\) | ||||
−0.620279 | + | 0.784382i | \(0.712980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.0861 | −1.35334 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.4458 | −1.14020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.3259 | −1.02193 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −74.0211 | −2.76437 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.0194 | −1.64165 | −0.820824 | − | 0.571182i | \(-0.806485\pi\) | ||||
−0.820824 | + | 0.571182i | \(0.806485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.14239 | −0.191513 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00918 | 0.0747223 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.710749 | −0.0263965 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.1168 | 0.412300 | 0.206150 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206150 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.9243 | −1.25646 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.8670 | 0.660836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.6867 | −0.431659 | −0.215829 | − | 0.976431i | \(-0.569246\pi\) | ||||
−0.215829 | + | 0.976431i | \(0.569246\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.7608 | 0.950201 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 62.4584 | 2.30069 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.9919 | 1.65505 | 0.827527 | − | 0.561426i | \(-0.189747\pi\) | ||||
0.827527 | + | 0.561426i | \(0.189747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.87460 | 0.215809 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7461 | −0.981220 | −0.490610 | − | 0.871379i | \(-0.663226\pi\) | ||||
−0.490610 | + | 0.871379i | \(0.663226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.1257 | −0.517525 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −41.5330 | −1.51961 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.33121 | 0.340955 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7444 | 0.465049 | 0.232525 | − | 0.972591i | \(-0.425301\pi\) | ||||
0.232525 | + | 0.972591i | \(0.425301\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.53334 | −0.0923202 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.9950 | 0.400150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2279 | 0.371739 | 0.185870 | − | 0.982574i | \(-0.440490\pi\) | ||||
0.185870 | + | 0.982574i | \(0.440490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 70.8028 | 2.56998 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1670 | 0.803555 | 0.401777 | − | 0.915737i | \(-0.368393\pi\) | ||||
0.401777 | + | 0.915737i | \(0.368393\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0251743 | −0.000911370 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.5515 | 0.381492 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.1853 | −0.620527 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.3208 | 1.85067 | 0.925337 | − | 0.379146i | \(-0.123782\pi\) | ||||
0.925337 | + | 0.379146i | \(0.123782\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.8705 | 0.535547 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.17332 | 0.222039 | 0.111019 | − | 0.993818i | \(-0.464588\pi\) | ||||
0.111019 | + | 0.993818i | \(0.464588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.5650 | 0.451350 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.4112 | −0.516997 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.80538 | 0.100513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68.7580 | −2.46035 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.274137 | −0.00979686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.6794 | 0.381164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7681 | −0.704658 | −0.352329 | − | 0.935876i | \(-0.614610\pi\) | ||||
−0.352329 | + | 0.935876i | \(0.614610\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.1509 | −1.46501 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.31468 | −0.0467446 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.3493 | 0.651604 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −46.5928 | −1.65248 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.193962 | −0.00687048 | −0.00343524 | − | 0.999994i | \(-0.501093\pi\) | ||||
−0.00343524 | + | 0.999994i | \(0.501093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.8157 | 0.842540 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.4474 | 0.651808 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.7011 | −0.906973 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.78237 | −0.168556 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −52.2802 | −1.84035 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.7244 | −0.904422 | −0.452211 | − | 0.891911i | \(-0.649365\pi\) | ||||
−0.452211 | + | 0.891911i | \(0.649365\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.3805 | −0.961459 | −0.480730 | − | 0.876869i | \(-0.659628\pi\) | ||||
−0.480730 | + | 0.876869i | \(0.659628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −78.5711 | −2.75561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.54376 | 0.334303 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.65593 | −0.162891 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.08514 | −0.247575 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.8188 | −0.796380 | −0.398190 | − | 0.917303i | \(-0.630362\pi\) | ||||
−0.398190 | + | 0.917303i | \(0.630362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.9298 | −1.21758 | −0.608789 | − | 0.793332i | \(-0.708344\pi\) | ||||
−0.608789 | + | 0.793332i | \(0.708344\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.2205 | −1.01733 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.95134 | −0.311269 | −0.155634 | − | 0.987815i | \(-0.549742\pi\) | ||||
−0.155634 | + | 0.987815i | \(0.549742\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.6186 | 1.41074 | 0.705372 | − | 0.708838i | \(-0.250780\pi\) | ||||
0.705372 | + | 0.708838i | \(0.250780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.4206 | −0.430866 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.9177 | −0.482220 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.7254 | 0.440382 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.84636 | 0.167515 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.2914 | −0.804108 | −0.402054 | − | 0.915616i | \(-0.631704\pi\) | ||||
−0.402054 | + | 0.915616i | \(0.631704\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9329 | −0.997687 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −39.7838 | −1.37023 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.62217 | 0.296612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.19114 | −0.109649 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46.1794 | 1.58487 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −78.9974 | −2.70800 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.70196 | 0.195231 | 0.0976157 | − | 0.995224i | \(-0.468878\pi\) | ||||
0.0976157 | + | 0.995224i | \(0.468878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.74961 | −0.0940345 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.35878 | 0.114734 | 0.0573669 | − | 0.998353i | \(-0.481730\pi\) | ||||
0.0573669 | + | 0.998353i | \(0.481730\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.73347 | 0.332102 | 0.166051 | − | 0.986117i | \(-0.446898\pi\) | ||||
0.166051 | + | 0.986117i | \(0.446898\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.35330 | −0.216520 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.75375 | 0.332022 | 0.166011 | − | 0.986124i | \(-0.446911\pi\) | ||||
0.166011 | + | 0.986124i | \(0.446911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.3670 | 0.726500 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32.3625 | 1.09909 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.3747 | 1.50531 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −64.3340 | −2.17988 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 47.9187 | 1.62180 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.56956 | 0.188285 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.7419 | −0.396495 | −0.198247 | − | 0.980152i | \(-0.563525\pi\) | ||||
−0.198247 | + | 0.980152i | \(0.563525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.74401 | 0.126282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.1291 | 1.25091 | 0.625456 | − | 0.780259i | \(-0.284913\pi\) | ||||
0.625456 | + | 0.780259i | \(0.284913\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9646 | 0.638210 | 0.319105 | − | 0.947719i | \(-0.396618\pi\) | ||||
0.319105 | + | 0.947719i | \(0.396618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.1039 | 0.507711 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.0150 | 0.772770 | 0.386385 | − | 0.922338i | \(-0.373724\pi\) | ||||
0.386385 | + | 0.922338i | \(0.373724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.38359 | −0.247638 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.8238 | 1.06614 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.20609 | −0.207679 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.1209 | 0.405158 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −72.9290 | −2.43503 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.18573 | −0.0395464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1725 | 0.838618 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.5442 | 0.350890 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.9970 | 0.897411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.5773 | 0.782873 | 0.391436 | − | 0.920205i | \(-0.371978\pi\) | ||||
0.391436 | + | 0.920205i | \(0.371978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.328973 | −0.0109114 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.6900 | 0.685492 | 0.342746 | − | 0.939428i | \(-0.388643\pi\) | ||||
0.342746 | + | 0.939428i | \(0.388643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.0727 | 1.69026 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.1269 | −0.533137 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.63886 | 0.219234 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.6254 | −1.30712 | −0.653560 | − | 0.756875i | \(-0.726725\pi\) | ||||
−0.653560 | + | 0.756875i | \(0.726725\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −72.7736 | −2.39797 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 70.8227 | 2.33116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.6024 | 1.07196 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.7041 | 1.20552 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.16495 | −0.267883 | −0.133942 | − | 0.990989i | \(-0.542763\pi\) | ||||
−0.133942 | + | 0.990989i | \(0.542763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.62678 | 0.118863 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 45.2240 | 1.48057 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.9751 | −0.424332 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2089 | −0.496853 | −0.248426 | − | 0.968651i | \(-0.579913\pi\) | ||||
−0.248426 | + | 0.968651i | \(0.579913\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.3026 | 1.15206 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.5538 | 0.930827 | 0.465414 | − | 0.885093i | \(-0.345906\pi\) | ||||
0.465414 | + | 0.885093i | \(0.345906\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.8268 | −1.13412 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.761257 | 0.0247637 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8580 | −0.515317 | −0.257658 | − | 0.966236i | \(-0.582951\pi\) | ||||
−0.257658 | + | 0.966236i | \(0.582951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.4729 | 0.859347 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.6199 | −1.44690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.4793 | −0.501423 | −0.250711 | − | 0.968062i | \(-0.580665\pi\) | ||||
−0.250711 | + | 0.968062i | \(0.580665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6001 | 0.925479 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.75746 | 0.0891361 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.91202 | 0.223201 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0379 | −0.323804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −66.6020 | −2.14622 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.06929 | −0.130995 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.7818 | 1.50440 | 0.752201 | − | 0.658933i | \(-0.228992\pi\) | ||||
0.752201 | + | 0.658933i | \(0.228992\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.78943 | 0.0896095 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.16808 | −0.133760 | −0.0668801 | − | 0.997761i | \(-0.521304\pi\) | ||||
−0.0668801 | + | 0.997761i | \(0.521304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.9662 | −0.351561 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.0980 | 0.963906 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.8271 | 0.346389 | 0.173195 | − | 0.984888i | \(-0.444591\pi\) | ||||
0.173195 | + | 0.984888i | \(0.444591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.6846 | −0.725003 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.179683 | 0.00573683 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.8392 | −0.983616 | −0.491808 | − | 0.870704i | \(-0.663664\pi\) | ||||
−0.491808 | + | 0.870704i | \(0.663664\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.9978 | −0.637182 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.0548 | 0.447371 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.8001 | 1.83794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.0982 | 0.701973 | 0.350987 | − | 0.936380i | \(-0.385846\pi\) | ||||
0.350987 | + | 0.936380i | \(0.385846\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.4787 | −0.967212 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.03606 | −0.127952 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.31981 | 0.168480 | 0.0842400 | − | 0.996445i | \(-0.473154\pi\) | ||||
0.0842400 | + | 0.996445i | \(0.473154\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.5748 | 0.397849 |
(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 | 4016.2.a.m.1.5 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.19 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.19 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.5 | 23 | 1.1 | even | 1 | trivial |