Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41110 | −1.70490 | −0.852452 | − | 0.522805i | \(-0.824886\pi\) | ||||
−0.852452 | + | 0.522805i | \(0.824886\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.81340 | 1.90670 | ||||||||
\(5\) | −2.91376 | −1.30307 | −0.651536 | − | 0.758618i | \(-0.725875\pi\) | ||||
−0.651536 | + | 0.758618i | \(0.725875\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −4.37229 | −1.54584 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.02536 | 2.22161 | ||||||||
\(11\) | 4.84187 | 1.45988 | 0.729940 | − | 0.683512i | \(-0.239548\pi\) | ||||
0.729940 | + | 0.683512i | \(0.239548\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.92231 | −1.64255 | −0.821277 | − | 0.570530i | \(-0.806738\pi\) | ||||
−0.821277 | + | 0.570530i | \(0.806738\pi\) | |||||||
\(14\) | 2.41110 | 0.644393 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.91522 | 0.728806 | ||||||||
\(17\) | 7.70060 | 1.86767 | 0.933835 | − | 0.357705i | \(-0.116441\pi\) | ||||
0.933835 | + | 0.357705i | \(0.116441\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.16283 | −1.64327 | −0.821633 | − | 0.570016i | \(-0.806937\pi\) | ||||
−0.821633 | + | 0.570016i | \(0.806937\pi\) | |||||||
\(20\) | −11.1113 | −2.48457 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.6742 | −2.48896 | ||||||||
\(23\) | −6.74473 | −1.40637 | −0.703187 | − | 0.711005i | \(-0.748240\pi\) | ||||
−0.703187 | + | 0.711005i | \(0.748240\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.48998 | 0.697995 | ||||||||
\(26\) | 14.2793 | 2.80040 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.81340 | −0.720665 | ||||||||
\(29\) | 1.16404 | 0.216156 | 0.108078 | − | 0.994142i | \(-0.465530\pi\) | ||||
0.108078 | + | 0.994142i | \(0.465530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.19532 | −0.573896 | −0.286948 | − | 0.957946i | \(-0.592641\pi\) | ||||
−0.286948 | + | 0.957946i | \(0.592641\pi\) | |||||||
\(32\) | 1.71568 | 0.303293 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.5669 | −3.18420 | ||||||||
\(35\) | 2.91376 | 0.492515 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.23173 | 1.02449 | 0.512245 | − | 0.858840i | \(-0.328814\pi\) | ||||
0.512245 | + | 0.858840i | \(0.328814\pi\) | |||||||
\(38\) | 17.2703 | 2.80161 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.7398 | 2.01434 | ||||||||
\(41\) | −1.69054 | −0.264019 | −0.132009 | − | 0.991248i | \(-0.542143\pi\) | ||||
−0.132009 | + | 0.991248i | \(0.542143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5590 | 1.61023 | 0.805115 | − | 0.593119i | \(-0.202104\pi\) | ||||
0.805115 | + | 0.593119i | \(0.202104\pi\) | |||||||
\(44\) | 18.4640 | 2.78355 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.2622 | 2.39773 | ||||||||
\(47\) | 4.01302 | 0.585359 | 0.292680 | − | 0.956211i | \(-0.405453\pi\) | ||||
0.292680 | + | 0.956211i | \(0.405453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.41468 | −1.19002 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −22.5841 | −3.13186 | ||||||||
\(53\) | 4.73182 | 0.649965 | 0.324982 | − | 0.945720i | \(-0.394642\pi\) | ||||
0.324982 | + | 0.945720i | \(0.394642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.1080 | −1.90233 | ||||||||
\(56\) | 4.37229 | 0.584272 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.80661 | −0.368526 | ||||||||
\(59\) | 1.42000 | 0.184868 | 0.0924338 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924338 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.30923 | 0.679777 | 0.339888 | − | 0.940466i | \(-0.389611\pi\) | ||||
0.339888 | + | 0.940466i | \(0.389611\pi\) | |||||||
\(62\) | 7.70423 | 0.978439 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.96713 | −1.24589 | ||||||||
\(65\) | 17.2562 | 2.14036 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.727254 | 0.0888482 | 0.0444241 | − | 0.999013i | \(-0.485855\pi\) | ||||
0.0444241 | + | 0.999013i | \(0.485855\pi\) | |||||||
\(68\) | 29.3655 | 3.56109 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.02536 | −0.839691 | ||||||||
\(71\) | −6.03872 | −0.716664 | −0.358332 | − | 0.933594i | \(-0.616654\pi\) | ||||
−0.358332 | + | 0.933594i | \(0.616654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.68043 | −0.898926 | −0.449463 | − | 0.893299i | \(-0.648385\pi\) | ||||
−0.449463 | + | 0.893299i | \(0.648385\pi\) | |||||||
\(74\) | −15.0253 | −1.74666 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27.3148 | −3.13322 | ||||||||
\(77\) | −4.84187 | −0.551782 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.20331 | −0.472909 | −0.236455 | − | 0.971643i | \(-0.575985\pi\) | ||||
−0.236455 | + | 0.971643i | \(0.575985\pi\) | |||||||
\(80\) | −8.49425 | −0.949686 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.07607 | 0.450127 | ||||||||
\(83\) | −14.0855 | −1.54608 | −0.773040 | − | 0.634358i | \(-0.781265\pi\) | ||||
−0.773040 | + | 0.634358i | \(0.781265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.4377 | −2.43371 | ||||||||
\(86\) | −25.4588 | −2.74529 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −21.1701 | −2.25674 | ||||||||
\(89\) | 13.2348 | 1.40289 | 0.701444 | − | 0.712725i | \(-0.252539\pi\) | ||||
0.701444 | + | 0.712725i | \(0.252539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.92231 | 0.620827 | ||||||||
\(92\) | −25.7204 | −2.68153 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.67580 | −0.997982 | ||||||||
\(95\) | 20.8708 | 2.14129 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0256030 | −0.00259960 | −0.00129980 | − | 0.999999i | \(-0.500414\pi\) | ||||
−0.00129980 | + | 0.999999i | \(0.500414\pi\) | |||||||
\(98\) | −2.41110 | −0.243558 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.3087 | 1.33087 | ||||||||
\(101\) | −8.54546 | −0.850305 | −0.425152 | − | 0.905122i | \(-0.639780\pi\) | ||||
−0.425152 | + | 0.905122i | \(0.639780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8304 | −1.26421 | −0.632107 | − | 0.774881i | \(-0.717810\pi\) | ||||
−0.632107 | + | 0.774881i | \(0.717810\pi\) | |||||||
\(104\) | 25.8941 | 2.53912 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.4089 | −1.10813 | ||||||||
\(107\) | 14.8632 | 1.43688 | 0.718441 | − | 0.695587i | \(-0.244856\pi\) | ||||
0.718441 | + | 0.695587i | \(0.244856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.94497 | 0.282077 | 0.141039 | − | 0.990004i | \(-0.454956\pi\) | ||||
0.141039 | + | 0.990004i | \(0.454956\pi\) | |||||||
\(110\) | 34.0159 | 3.24329 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.91522 | −0.275463 | ||||||||
\(113\) | 10.5406 | 0.991577 | 0.495789 | − | 0.868443i | \(-0.334879\pi\) | ||||
0.495789 | + | 0.868443i | \(0.334879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.6525 | 1.83260 | ||||||||
\(116\) | 4.43894 | 0.412145 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.42375 | −0.315182 | ||||||||
\(119\) | −7.70060 | −0.705913 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4437 | 1.13125 | ||||||||
\(122\) | −12.8011 | −1.15895 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.1850 | −1.09425 | ||||||||
\(125\) | 4.39984 | 0.393534 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 20.6004 | 1.82083 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −41.6064 | −3.64912 | ||||||||
\(131\) | −19.9073 | −1.73931 | −0.869655 | − | 0.493659i | \(-0.835659\pi\) | ||||
−0.869655 | + | 0.493659i | \(0.835659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.16283 | 0.621096 | ||||||||
\(134\) | −1.75348 | −0.151478 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −33.6692 | −2.88711 | ||||||||
\(137\) | −1.07424 | −0.0917787 | −0.0458894 | − | 0.998947i | \(-0.514612\pi\) | ||||
−0.0458894 | + | 0.998947i | \(0.514612\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.35399 | −0.454120 | −0.227060 | − | 0.973881i | \(-0.572911\pi\) | ||||
−0.227060 | + | 0.973881i | \(0.572911\pi\) | |||||||
\(140\) | 11.1113 | 0.939078 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.5600 | 1.22184 | ||||||||
\(143\) | −28.6751 | −2.39793 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.39172 | −0.281667 | ||||||||
\(146\) | 18.5183 | 1.53258 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.7641 | 1.95339 | ||||||||
\(149\) | 3.75043 | 0.307247 | 0.153623 | − | 0.988129i | \(-0.450906\pi\) | ||||
0.153623 | + | 0.988129i | \(0.450906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.64734 | −0.296817 | −0.148408 | − | 0.988926i | \(-0.547415\pi\) | ||||
−0.148408 | + | 0.988926i | \(0.547415\pi\) | |||||||
\(152\) | 31.3180 | 2.54022 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.6742 | 0.940737 | ||||||||
\(155\) | 9.31038 | 0.747828 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.4878 | 1.39568 | 0.697841 | − | 0.716253i | \(-0.254144\pi\) | ||||
0.697841 | + | 0.716253i | \(0.254144\pi\) | |||||||
\(158\) | 10.1346 | 0.806265 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.99909 | −0.395213 | ||||||||
\(161\) | 6.74473 | 0.531559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.22206 | −0.409023 | −0.204512 | − | 0.978864i | \(-0.565561\pi\) | ||||
−0.204512 | + | 0.978864i | \(0.565561\pi\) | |||||||
\(164\) | −6.44672 | −0.503405 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 33.9614 | 2.63592 | ||||||||
\(167\) | −10.5060 | −0.812979 | −0.406489 | − | 0.913655i | \(-0.633247\pi\) | ||||
−0.406489 | + | 0.913655i | \(0.633247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.0738 | 1.69798 | ||||||||
\(170\) | 54.0994 | 4.14924 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 40.2656 | 3.07023 | ||||||||
\(173\) | 1.45272 | 0.110448 | 0.0552240 | − | 0.998474i | \(-0.482413\pi\) | ||||
0.0552240 | + | 0.998474i | \(0.482413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.48998 | −0.263817 | ||||||||
\(176\) | 14.1151 | 1.06397 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −31.9105 | −2.39179 | ||||||||
\(179\) | 15.7102 | 1.17423 | 0.587117 | − | 0.809502i | \(-0.300263\pi\) | ||||
0.587117 | + | 0.809502i | \(0.300263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3252 | 1.28777 | 0.643886 | − | 0.765121i | \(-0.277321\pi\) | ||||
0.643886 | + | 0.765121i | \(0.277321\pi\) | |||||||
\(182\) | −14.2793 | −1.05845 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 29.4899 | 2.17403 | ||||||||
\(185\) | −18.1577 | −1.33498 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 37.2853 | 2.72657 | ||||||||
\(188\) | 15.3033 | 1.11611 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −50.3215 | −3.65070 | ||||||||
\(191\) | −10.6002 | −0.767002 | −0.383501 | − | 0.923541i | \(-0.625282\pi\) | ||||
−0.383501 | + | 0.923541i | \(0.625282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.0481 | 1.80300 | 0.901500 | − | 0.432779i | \(-0.142467\pi\) | ||||
0.901500 | + | 0.432779i | \(0.142467\pi\) | |||||||
\(194\) | 0.0617315 | 0.00443206 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.81340 | 0.272386 | ||||||||
\(197\) | 14.5870 | 1.03928 | 0.519641 | − | 0.854385i | \(-0.326066\pi\) | ||||
0.519641 | + | 0.854385i | \(0.326066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8687 | 1.40846 | 0.704228 | − | 0.709974i | \(-0.251293\pi\) | ||||
0.704228 | + | 0.709974i | \(0.251293\pi\) | |||||||
\(200\) | −15.2592 | −1.07899 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.6039 | 1.44969 | ||||||||
\(203\) | −1.16404 | −0.0816994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.92584 | 0.344035 | ||||||||
\(206\) | 30.9353 | 2.15537 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −17.2649 | −1.19710 | ||||||||
\(209\) | −34.6815 | −2.39897 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8972 | −1.16325 | −0.581624 | − | 0.813458i | \(-0.697582\pi\) | ||||
−0.581624 | + | 0.813458i | \(0.697582\pi\) | |||||||
\(212\) | 18.0443 | 1.23929 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −35.8367 | −2.44975 | ||||||||
\(215\) | −30.7663 | −2.09824 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.19532 | 0.216912 | ||||||||
\(218\) | −7.10062 | −0.480914 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −53.7996 | −3.62717 | ||||||||
\(221\) | −45.6053 | −3.06775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.68685 | −0.246890 | −0.123445 | − | 0.992351i | \(-0.539394\pi\) | ||||
−0.123445 | + | 0.992351i | \(0.539394\pi\) | |||||||
\(224\) | −1.71568 | −0.114634 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.4145 | −1.69054 | ||||||||
\(227\) | 23.4616 | 1.55720 | 0.778602 | − | 0.627518i | \(-0.215929\pi\) | ||||
0.778602 | + | 0.627518i | \(0.215929\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.9869 | −1.71726 | −0.858631 | − | 0.512595i | \(-0.828684\pi\) | ||||
−0.858631 | + | 0.512595i | \(0.828684\pi\) | |||||||
\(230\) | −47.3841 | −3.12442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.08951 | −0.334143 | ||||||||
\(233\) | −24.6677 | −1.61604 | −0.808018 | − | 0.589158i | \(-0.799459\pi\) | ||||
−0.808018 | + | 0.589158i | \(0.799459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6930 | −0.762765 | ||||||||
\(236\) | 5.41501 | 0.352487 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.5669 | 1.20351 | ||||||||
\(239\) | 20.9419 | 1.35462 | 0.677310 | − | 0.735698i | \(-0.263146\pi\) | ||||
0.677310 | + | 0.735698i | \(0.263146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.75038 | −0.177167 | −0.0885837 | − | 0.996069i | \(-0.528234\pi\) | ||||
−0.0885837 | + | 0.996069i | \(0.528234\pi\) | |||||||
\(242\) | −30.0031 | −1.92867 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.2462 | 1.29613 | ||||||||
\(245\) | −2.91376 | −0.186153 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.4205 | 2.69915 | ||||||||
\(248\) | 13.9709 | 0.887151 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.6085 | −0.670937 | ||||||||
\(251\) | 12.4711 | 0.787171 | 0.393586 | − | 0.919288i | \(-0.371234\pi\) | ||||
0.393586 | + | 0.919288i | \(0.371234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.6571 | −2.05314 | ||||||||
\(254\) | 2.41110 | 0.151286 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.7353 | −1.85846 | ||||||||
\(257\) | 27.8640 | 1.73811 | 0.869053 | − | 0.494718i | \(-0.164729\pi\) | ||||
0.869053 | + | 0.494718i | \(0.164729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.23173 | −0.387221 | ||||||||
\(260\) | 65.8047 | 4.08103 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 47.9985 | 2.96536 | ||||||||
\(263\) | −9.19650 | −0.567081 | −0.283540 | − | 0.958960i | \(-0.591509\pi\) | ||||
−0.283540 | + | 0.958960i | \(0.591509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.7874 | −0.846951 | ||||||||
\(266\) | −17.2703 | −1.05891 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.77331 | 0.169407 | ||||||||
\(269\) | −16.8197 | −1.02552 | −0.512759 | − | 0.858533i | \(-0.671376\pi\) | ||||
−0.512759 | + | 0.858533i | \(0.671376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.27897 | −0.138438 | −0.0692188 | − | 0.997602i | \(-0.522051\pi\) | ||||
−0.0692188 | + | 0.997602i | \(0.522051\pi\) | |||||||
\(272\) | 22.4490 | 1.36117 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.59011 | 0.156474 | ||||||||
\(275\) | 16.8980 | 1.01899 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00040 | 0.120192 | 0.0600961 | − | 0.998193i | \(-0.480859\pi\) | ||||
0.0600961 | + | 0.998193i | \(0.480859\pi\) | |||||||
\(278\) | 12.9090 | 0.774231 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.7398 | −0.761348 | ||||||||
\(281\) | 14.6564 | 0.874325 | 0.437162 | − | 0.899383i | \(-0.355984\pi\) | ||||
0.437162 | + | 0.899383i | \(0.355984\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.9212 | −1.30308 | −0.651539 | − | 0.758615i | \(-0.725876\pi\) | ||||
−0.651539 | + | 0.758615i | \(0.725876\pi\) | |||||||
\(284\) | −23.0281 | −1.36646 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 69.1385 | 4.08824 | ||||||||
\(287\) | 1.69054 | 0.0997897 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.2992 | 2.48819 | ||||||||
\(290\) | 8.17778 | 0.480216 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.2885 | −1.71398 | ||||||||
\(293\) | 15.8863 | 0.928089 | 0.464044 | − | 0.885812i | \(-0.346398\pi\) | ||||
0.464044 | + | 0.885812i | \(0.346398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.13752 | −0.240896 | ||||||||
\(296\) | −27.2469 | −1.58369 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.04265 | −0.523827 | ||||||||
\(299\) | 39.9444 | 2.31004 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5590 | −0.608610 | ||||||||
\(302\) | 8.79411 | 0.506044 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.8813 | −1.19762 | ||||||||
\(305\) | −15.4698 | −0.885798 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9610 | −0.968014 | −0.484007 | − | 0.875064i | \(-0.660819\pi\) | ||||
−0.484007 | + | 0.875064i | \(0.660819\pi\) | |||||||
\(308\) | −18.4640 | −1.05208 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −22.4483 | −1.27498 | ||||||||
\(311\) | 10.4649 | 0.593408 | 0.296704 | − | 0.954969i | \(-0.404112\pi\) | ||||
0.296704 | + | 0.954969i | \(0.404112\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9768 | 0.733494 | 0.366747 | − | 0.930321i | \(-0.380471\pi\) | ||||
0.366747 | + | 0.930321i | \(0.380471\pi\) | |||||||
\(314\) | −42.1649 | −2.37950 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0289 | −0.901696 | ||||||||
\(317\) | −33.4039 | −1.87615 | −0.938076 | − | 0.346430i | \(-0.887394\pi\) | ||||
−0.938076 | + | 0.346430i | \(0.887394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.63612 | 0.315562 | ||||||||
\(320\) | 29.0418 | 1.62349 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.2622 | −0.906258 | ||||||||
\(323\) | −55.1581 | −3.06908 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.6687 | −1.14649 | ||||||||
\(326\) | 12.5909 | 0.697346 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.39155 | 0.408130 | ||||||||
\(329\) | −4.01302 | −0.221245 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8998 | −0.928896 | −0.464448 | − | 0.885600i | \(-0.653747\pi\) | ||||
−0.464448 | + | 0.885600i | \(0.653747\pi\) | |||||||
\(332\) | −53.7135 | −2.94791 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.3310 | 1.38605 | ||||||||
\(335\) | −2.11904 | −0.115776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.1038 | 1.14960 | 0.574799 | − | 0.818295i | \(-0.305080\pi\) | ||||
0.574799 | + | 0.818295i | \(0.305080\pi\) | |||||||
\(338\) | −53.2221 | −2.89490 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −85.5638 | −4.64035 | ||||||||
\(341\) | −15.4713 | −0.837819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −46.1669 | −2.48915 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.50264 | −0.188303 | ||||||||
\(347\) | −14.5910 | −0.783287 | −0.391644 | − | 0.920117i | \(-0.628093\pi\) | ||||
−0.391644 | + | 0.920117i | \(0.628093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.54477 | 0.136218 | 0.0681091 | − | 0.997678i | \(-0.478303\pi\) | ||||
0.0681091 | + | 0.997678i | \(0.478303\pi\) | |||||||
\(350\) | 8.41468 | 0.449784 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.30712 | 0.442771 | ||||||||
\(353\) | 34.5501 | 1.83892 | 0.919458 | − | 0.393188i | \(-0.128628\pi\) | ||||
0.919458 | + | 0.393188i | \(0.128628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.5954 | 0.933864 | ||||||||
\(356\) | 50.4697 | 2.67489 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −37.8788 | −2.00196 | ||||||||
\(359\) | 11.9986 | 0.633260 | 0.316630 | − | 0.948549i | \(-0.397449\pi\) | ||||
0.316630 | + | 0.948549i | \(0.397449\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.3062 | 1.70033 | ||||||||
\(362\) | −41.7728 | −2.19553 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 22.5841 | 1.18373 | ||||||||
\(365\) | 22.3789 | 1.17136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.64367 | −0.190198 | −0.0950989 | − | 0.995468i | \(-0.530317\pi\) | ||||
−0.0950989 | + | 0.995468i | \(0.530317\pi\) | |||||||
\(368\) | −19.6624 | −1.02497 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 43.7801 | 2.27602 | ||||||||
\(371\) | −4.73182 | −0.245664 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.2311 | 1.04753 | 0.523765 | − | 0.851863i | \(-0.324527\pi\) | ||||
0.523765 | + | 0.851863i | \(0.324527\pi\) | |||||||
\(374\) | −89.8986 | −4.64854 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.5461 | −0.904871 | ||||||||
\(377\) | −6.89379 | −0.355048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3071 | −0.991739 | −0.495870 | − | 0.868397i | \(-0.665151\pi\) | ||||
−0.495870 | + | 0.868397i | \(0.665151\pi\) | |||||||
\(380\) | 79.5886 | 4.08281 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 25.5581 | 1.30767 | ||||||||
\(383\) | −17.7304 | −0.905981 | −0.452991 | − | 0.891515i | \(-0.649643\pi\) | ||||
−0.452991 | + | 0.891515i | \(0.649643\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.1080 | 0.719012 | ||||||||
\(386\) | −60.3934 | −3.07394 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0976347 | −0.00495665 | ||||||||
\(389\) | −31.0388 | −1.57373 | −0.786865 | − | 0.617125i | \(-0.788297\pi\) | ||||
−0.786865 | + | 0.617125i | \(0.788297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.9384 | −2.62664 | ||||||||
\(392\) | −4.37229 | −0.220834 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −35.1708 | −1.77188 | ||||||||
\(395\) | 12.2474 | 0.616234 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.66235 | −0.334374 | −0.167187 | − | 0.985925i | \(-0.553468\pi\) | ||||
−0.167187 | + | 0.985925i | \(0.553468\pi\) | |||||||
\(398\) | −47.9054 | −2.40128 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.1741 | 0.508703 | ||||||||
\(401\) | −28.5013 | −1.42329 | −0.711643 | − | 0.702541i | \(-0.752049\pi\) | ||||
−0.711643 | + | 0.702541i | \(0.752049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.9237 | 0.942655 | ||||||||
\(404\) | −32.5873 | −1.62128 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.80661 | 0.139290 | ||||||||
\(407\) | 30.1732 | 1.49563 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0751 | −1.28933 | −0.644665 | − | 0.764465i | \(-0.723003\pi\) | ||||
−0.644665 | + | 0.764465i | \(0.723003\pi\) | |||||||
\(410\) | −11.8767 | −0.586547 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −48.9274 | −2.41048 | ||||||||
\(413\) | −1.42000 | −0.0698734 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.0416 | 2.01465 | ||||||||
\(416\) | −10.1608 | −0.498175 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 83.6206 | 4.09002 | ||||||||
\(419\) | −15.1006 | −0.737714 | −0.368857 | − | 0.929486i | \(-0.620251\pi\) | ||||
−0.368857 | + | 0.929486i | \(0.620251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.28830 | −0.355210 | −0.177605 | − | 0.984102i | \(-0.556835\pi\) | ||||
−0.177605 | + | 0.984102i | \(0.556835\pi\) | |||||||
\(422\) | 40.7407 | 1.98323 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.6889 | −1.00474 | ||||||||
\(425\) | 26.8749 | 1.30362 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.30923 | −0.256931 | ||||||||
\(428\) | 56.6795 | 2.73971 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 74.1806 | 3.57731 | ||||||||
\(431\) | −18.7701 | −0.904123 | −0.452062 | − | 0.891987i | \(-0.649311\pi\) | ||||
−0.452062 | + | 0.891987i | \(0.649311\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.2440 | −1.50149 | −0.750747 | − | 0.660590i | \(-0.770306\pi\) | ||||
−0.750747 | + | 0.660590i | \(0.770306\pi\) | |||||||
\(434\) | −7.70423 | −0.369815 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.2304 | 0.537836 | ||||||||
\(437\) | 48.3114 | 2.31105 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.7246 | −0.655039 | −0.327520 | − | 0.944844i | \(-0.606213\pi\) | ||||
−0.327520 | + | 0.944844i | \(0.606213\pi\) | |||||||
\(440\) | 61.6844 | 2.94069 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 109.959 | 5.23022 | ||||||||
\(443\) | 30.9731 | 1.47158 | 0.735789 | − | 0.677211i | \(-0.236811\pi\) | ||||
0.735789 | + | 0.677211i | \(0.236811\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.5630 | −1.82806 | ||||||||
\(446\) | 8.88936 | 0.420923 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.96713 | 0.470903 | ||||||||
\(449\) | −18.9463 | −0.894130 | −0.447065 | − | 0.894502i | \(-0.647531\pi\) | ||||
−0.447065 | + | 0.894502i | \(0.647531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.18540 | −0.385435 | ||||||||
\(452\) | 40.1956 | 1.89064 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −56.5684 | −2.65488 | ||||||||
\(455\) | −17.2562 | −0.808982 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.49341 | −0.303749 | −0.151874 | − | 0.988400i | \(-0.548531\pi\) | ||||
−0.151874 | + | 0.988400i | \(0.548531\pi\) | |||||||
\(458\) | 62.6570 | 2.92777 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 74.9429 | 3.49423 | ||||||||
\(461\) | 28.4651 | 1.32575 | 0.662876 | − | 0.748729i | \(-0.269336\pi\) | ||||
0.662876 | + | 0.748729i | \(0.269336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.49350 | −0.208831 | −0.104415 | − | 0.994534i | \(-0.533297\pi\) | ||||
−0.104415 | + | 0.994534i | \(0.533297\pi\) | |||||||
\(464\) | 3.39343 | 0.157536 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 59.4763 | 2.75519 | ||||||||
\(467\) | −1.30117 | −0.0602111 | −0.0301055 | − | 0.999547i | \(-0.509584\pi\) | ||||
−0.0301055 | + | 0.999547i | \(0.509584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.727254 | −0.0335815 | ||||||||
\(470\) | 28.1929 | 1.30044 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.20863 | −0.285775 | ||||||||
\(473\) | 51.1252 | 2.35074 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.9981 | −1.14699 | ||||||||
\(476\) | −29.3655 | −1.34596 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −50.4930 | −2.30950 | ||||||||
\(479\) | 24.2021 | 1.10582 | 0.552910 | − | 0.833241i | \(-0.313517\pi\) | ||||
0.552910 | + | 0.833241i | \(0.313517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.9062 | −1.68278 | ||||||||
\(482\) | 6.63143 | 0.302054 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 47.4529 | 2.15695 | ||||||||
\(485\) | 0.0746010 | 0.00338746 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.8759 | −0.764722 | −0.382361 | − | 0.924013i | \(-0.624889\pi\) | ||||
−0.382361 | + | 0.924013i | \(0.624889\pi\) | |||||||
\(488\) | −23.2135 | −1.05082 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.02536 | 0.317373 | ||||||||
\(491\) | 5.48154 | 0.247379 | 0.123689 | − | 0.992321i | \(-0.460527\pi\) | ||||
0.123689 | + | 0.992321i | \(0.460527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.96378 | 0.403709 | ||||||||
\(494\) | −102.280 | −4.60180 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.31507 | −0.418259 | ||||||||
\(497\) | 6.03872 | 0.270874 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1726 | −0.813517 | −0.406759 | − | 0.913536i | \(-0.633341\pi\) | ||||
−0.406759 | + | 0.913536i | \(0.633341\pi\) | |||||||
\(500\) | 16.7784 | 0.750351 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.0692 | −1.34205 | ||||||||
\(503\) | 12.4515 | 0.555183 | 0.277592 | − | 0.960699i | \(-0.410464\pi\) | ||||
0.277592 | + | 0.960699i | \(0.410464\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.8994 | 1.10801 | ||||||||
\(506\) | 78.7396 | 3.50040 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.81340 | −0.169192 | ||||||||
\(509\) | −20.7279 | −0.918749 | −0.459375 | − | 0.888243i | \(-0.651926\pi\) | ||||
−0.459375 | + | 0.888243i | \(0.651926\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.68043 | 0.339762 | ||||||||
\(512\) | 30.4940 | 1.34766 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −67.1828 | −2.96331 | ||||||||
\(515\) | 37.3846 | 1.64736 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.4305 | 0.854554 | ||||||||
\(518\) | 15.0253 | 0.660174 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −75.4490 | −3.30866 | ||||||||
\(521\) | −31.8644 | −1.39600 | −0.698002 | − | 0.716096i | \(-0.745927\pi\) | ||||
−0.698002 | + | 0.716096i | \(0.745927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.9579 | 1.39742 | 0.698710 | − | 0.715405i | \(-0.253758\pi\) | ||||
0.698710 | + | 0.715405i | \(0.253758\pi\) | |||||||
\(524\) | −75.9146 | −3.31634 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1737 | 0.966819 | ||||||||
\(527\) | −24.6059 | −1.07185 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4914 | 0.977886 | ||||||||
\(530\) | 33.2427 | 1.44397 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.3148 | 1.18424 | ||||||||
\(533\) | 10.0119 | 0.433665 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.3078 | −1.87236 | ||||||||
\(536\) | −3.17977 | −0.137345 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.5541 | 1.74841 | ||||||||
\(539\) | 4.84187 | 0.208554 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1995 | −1.85729 | −0.928646 | − | 0.370967i | \(-0.879026\pi\) | ||||
−0.928646 | + | 0.370967i | \(0.879026\pi\) | |||||||
\(542\) | 5.49482 | 0.236023 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.2118 | 0.566451 | ||||||||
\(545\) | −8.58093 | −0.367567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00358 | 0.256695 | 0.128347 | − | 0.991729i | \(-0.459033\pi\) | ||||
0.128347 | + | 0.991729i | \(0.459033\pi\) | |||||||
\(548\) | −4.09652 | −0.174995 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −40.7428 | −1.73728 | ||||||||
\(551\) | −8.33781 | −0.355203 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.20331 | 0.178743 | ||||||||
\(554\) | −4.82316 | −0.204916 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4169 | −0.865870 | ||||||||
\(557\) | 11.8692 | 0.502914 | 0.251457 | − | 0.967868i | \(-0.419090\pi\) | ||||
0.251457 | + | 0.967868i | \(0.419090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.5336 | −2.64489 | ||||||||
\(560\) | 8.49425 | 0.358948 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.3379 | −1.49064 | ||||||||
\(563\) | 24.3997 | 1.02832 | 0.514162 | − | 0.857693i | \(-0.328103\pi\) | ||||
0.514162 | + | 0.857693i | \(0.328103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.7128 | −1.29210 | ||||||||
\(566\) | 52.8541 | 2.22162 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.4030 | 1.10785 | ||||||||
\(569\) | −6.37571 | −0.267284 | −0.133642 | − | 0.991030i | \(-0.542667\pi\) | ||||
−0.133642 | + | 0.991030i | \(0.542667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.76600 | 0.199451 | 0.0997255 | − | 0.995015i | \(-0.468204\pi\) | ||||
0.0997255 | + | 0.995015i | \(0.468204\pi\) | |||||||
\(572\) | −109.350 | −4.57213 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.07607 | −0.170132 | ||||||||
\(575\) | −23.5389 | −0.981642 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.7666 | 0.448220 | 0.224110 | − | 0.974564i | \(-0.428053\pi\) | ||||
0.224110 | + | 0.974564i | \(0.428053\pi\) | |||||||
\(578\) | −101.988 | −4.24212 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.9340 | −0.537055 | ||||||||
\(581\) | 14.0855 | 0.584363 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.9108 | 0.948870 | ||||||||
\(584\) | 33.5810 | 1.38959 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.3035 | −1.58230 | ||||||||
\(587\) | 0.0116818 | 0.000482159 0 | 0.000241079 | − | 1.00000i | \(-0.499923\pi\) | ||||
0.000241079 | 1.00000i | \(0.499923\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.8875 | 0.943065 | ||||||||
\(590\) | 9.97597 | 0.410704 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.1669 | 0.746654 | ||||||||
\(593\) | −37.5294 | −1.54115 | −0.770573 | − | 0.637351i | \(-0.780030\pi\) | ||||
−0.770573 | + | 0.637351i | \(0.780030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.4377 | 0.919855 | ||||||||
\(596\) | 14.3019 | 0.585828 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −96.3099 | −3.93840 | ||||||||
\(599\) | −28.8340 | −1.17812 | −0.589062 | − | 0.808088i | \(-0.700503\pi\) | ||||
−0.589062 | + | 0.808088i | \(0.700503\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.9469 | 1.34393 | 0.671966 | − | 0.740582i | \(-0.265450\pi\) | ||||
0.671966 | + | 0.740582i | \(0.265450\pi\) | |||||||
\(602\) | 25.4588 | 1.03762 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.9088 | −0.565940 | ||||||||
\(605\) | −36.2580 | −1.47410 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.9893 | −1.54194 | −0.770970 | − | 0.636872i | \(-0.780228\pi\) | ||||
−0.770970 | + | 0.636872i | \(0.780228\pi\) | |||||||
\(608\) | −12.2892 | −0.498391 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.2992 | 1.51020 | ||||||||
\(611\) | −23.7664 | −0.961484 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.9743 | −0.725975 | −0.362987 | − | 0.931794i | \(-0.618243\pi\) | ||||
−0.362987 | + | 0.931794i | \(0.618243\pi\) | |||||||
\(614\) | 40.8946 | 1.65037 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.1701 | 0.852966 | ||||||||
\(617\) | 25.2975 | 1.01844 | 0.509220 | − | 0.860637i | \(-0.329934\pi\) | ||||
0.509220 | + | 0.860637i | \(0.329934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1324 | 0.809190 | 0.404595 | − | 0.914496i | \(-0.367412\pi\) | ||||
0.404595 | + | 0.914496i | \(0.367412\pi\) | |||||||
\(620\) | 35.5042 | 1.42588 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.2318 | −1.01170 | ||||||||
\(623\) | −13.2348 | −0.530242 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2699 | −1.21080 | ||||||||
\(626\) | −31.2884 | −1.25054 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 66.6882 | 2.66115 | ||||||||
\(629\) | 47.9880 | 1.91341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.4163 | −0.454476 | −0.227238 | − | 0.973839i | \(-0.572969\pi\) | ||||
−0.227238 | + | 0.973839i | \(0.572969\pi\) | |||||||
\(632\) | 18.3781 | 0.731041 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 80.5402 | 3.19866 | ||||||||
\(635\) | 2.91376 | 0.115629 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.92231 | −0.234651 | ||||||||
\(638\) | −13.5892 | −0.538003 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −60.0245 | −2.37268 | ||||||||
\(641\) | 19.5013 | 0.770256 | 0.385128 | − | 0.922863i | \(-0.374157\pi\) | ||||
0.385128 | + | 0.922863i | \(0.374157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.5234 | −1.95301 | −0.976506 | − | 0.215492i | \(-0.930864\pi\) | ||||
−0.976506 | + | 0.215492i | \(0.930864\pi\) | |||||||
\(644\) | 25.7204 | 1.01352 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 132.992 | 5.23249 | ||||||||
\(647\) | 13.2292 | 0.520095 | 0.260047 | − | 0.965596i | \(-0.416262\pi\) | ||||
0.260047 | + | 0.965596i | \(0.416262\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.87544 | 0.269884 | ||||||||
\(650\) | 49.8344 | 1.95466 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.9138 | −0.779885 | ||||||||
\(653\) | 5.45442 | 0.213448 | 0.106724 | − | 0.994289i | \(-0.465964\pi\) | ||||
0.106724 | + | 0.994289i | \(0.465964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58.0051 | 2.26645 | ||||||||
\(656\) | −4.92832 | −0.192418 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.67580 | 0.377202 | ||||||||
\(659\) | 12.0550 | 0.469596 | 0.234798 | − | 0.972044i | \(-0.424557\pi\) | ||||
0.234798 | + | 0.972044i | \(0.424557\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.99457 | −0.0775799 | −0.0387900 | − | 0.999247i | \(-0.512350\pi\) | ||||
−0.0387900 | + | 0.999247i | \(0.512350\pi\) | |||||||
\(662\) | 40.7471 | 1.58368 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 61.5857 | 2.38999 | ||||||||
\(665\) | −20.8708 | −0.809333 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.85112 | −0.303997 | ||||||||
\(668\) | −40.0636 | −1.55011 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.10922 | 0.197386 | ||||||||
\(671\) | 25.7066 | 0.992392 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.7995 | −0.416289 | −0.208144 | − | 0.978098i | \(-0.566742\pi\) | ||||
−0.208144 | + | 0.978098i | \(0.566742\pi\) | |||||||
\(674\) | −50.8834 | −1.95995 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 84.1762 | 3.23754 | ||||||||
\(677\) | −15.9165 | −0.611722 | −0.305861 | − | 0.952076i | \(-0.598944\pi\) | ||||
−0.305861 | + | 0.952076i | \(0.598944\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0256030 | 0.000982555 0 | ||||||||
\(680\) | 98.1040 | 3.76212 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 37.3029 | 1.42840 | ||||||||
\(683\) | −2.33667 | −0.0894101 | −0.0447050 | − | 0.999000i | \(-0.514235\pi\) | ||||
−0.0447050 | + | 0.999000i | \(0.514235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.13008 | 0.119594 | ||||||||
\(686\) | 2.41110 | 0.0920562 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.7818 | 1.17355 | ||||||||
\(689\) | −28.0233 | −1.06760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.2180 | −0.502837 | −0.251419 | − | 0.967878i | \(-0.580897\pi\) | ||||
−0.251419 | + | 0.967878i | \(0.580897\pi\) | |||||||
\(692\) | 5.53979 | 0.210591 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.1804 | 1.33543 | ||||||||
\(695\) | 15.6002 | 0.591750 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.0182 | −0.493100 | ||||||||
\(698\) | −6.13568 | −0.232239 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.3087 | −0.503021 | ||||||||
\(701\) | −11.0311 | −0.416639 | −0.208320 | − | 0.978061i | \(-0.566799\pi\) | ||||
−0.208320 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.6368 | −1.68351 | ||||||||
\(704\) | −48.2596 | −1.81885 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −83.3037 | −3.13518 | ||||||||
\(707\) | 8.54546 | 0.321385 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.7628 | −1.68110 | −0.840550 | − | 0.541733i | \(-0.817768\pi\) | ||||
−0.840550 | + | 0.541733i | \(0.817768\pi\) | |||||||
\(710\) | −42.4242 | −1.59215 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −57.8665 | −2.16864 | ||||||||
\(713\) | 21.5516 | 0.807112 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 83.5522 | 3.12467 | ||||||||
\(716\) | 59.9092 | 2.23891 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.9297 | −1.07965 | ||||||||
\(719\) | −22.5152 | −0.839674 | −0.419837 | − | 0.907599i | \(-0.637913\pi\) | ||||
−0.419837 | + | 0.907599i | \(0.637913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8304 | 0.477828 | ||||||||
\(722\) | −77.8934 | −2.89889 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 66.0680 | 2.45540 | ||||||||
\(725\) | 4.06246 | 0.150876 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.2526 | 1.67832 | 0.839162 | − | 0.543881i | \(-0.183046\pi\) | ||||
0.839162 | + | 0.543881i | \(0.183046\pi\) | |||||||
\(728\) | −25.8941 | −0.959698 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −53.9577 | −1.99707 | ||||||||
\(731\) | 81.3105 | 3.00738 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.823994 | −0.0304349 | −0.0152175 | − | 0.999884i | \(-0.504844\pi\) | ||||
−0.0152175 | + | 0.999884i | \(0.504844\pi\) | |||||||
\(734\) | 8.78524 | 0.324269 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.5718 | −0.426543 | ||||||||
\(737\) | 3.52127 | 0.129708 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.7283 | −1.24071 | −0.620357 | − | 0.784320i | \(-0.713012\pi\) | ||||
−0.620357 | + | 0.784320i | \(0.713012\pi\) | |||||||
\(740\) | −69.2427 | −2.54541 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.4089 | 0.418833 | ||||||||
\(743\) | 42.3307 | 1.55296 | 0.776481 | − | 0.630141i | \(-0.217003\pi\) | ||||
0.776481 | + | 0.630141i | \(0.217003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.9278 | −0.400365 | ||||||||
\(746\) | −48.7793 | −1.78594 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 142.184 | 5.19875 | ||||||||
\(749\) | −14.8632 | −0.543091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.1432 | 0.880997 | 0.440498 | − | 0.897753i | \(-0.354802\pi\) | ||||
0.440498 | + | 0.897753i | \(0.354802\pi\) | |||||||
\(752\) | 11.6989 | 0.426613 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.6216 | 0.605324 | ||||||||
\(755\) | 10.6275 | 0.386773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.4792 | −1.25317 | −0.626585 | − | 0.779353i | \(-0.715548\pi\) | ||||
−0.626585 | + | 0.779353i | \(0.715548\pi\) | |||||||
\(758\) | 46.5513 | 1.69082 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −91.2530 | −3.31009 | ||||||||
\(761\) | 21.9434 | 0.795447 | 0.397724 | − | 0.917505i | \(-0.369800\pi\) | ||||
0.397724 | + | 0.917505i | \(0.369800\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.94497 | −0.106615 | ||||||||
\(764\) | −40.4227 | −1.46244 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.7498 | 1.54461 | ||||||||
\(767\) | −8.40966 | −0.303655 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9123 | −1.04260 | −0.521302 | − | 0.853372i | \(-0.674554\pi\) | ||||
−0.521302 | + | 0.853372i | \(0.674554\pi\) | |||||||
\(770\) | −34.0159 | −1.22585 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 95.5184 | 3.43778 | ||||||||
\(773\) | −37.5638 | −1.35108 | −0.675538 | − | 0.737325i | \(-0.736089\pi\) | ||||
−0.675538 | + | 0.737325i | \(0.736089\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.1516 | −0.400577 | ||||||||
\(776\) | 0.111944 | 0.00401855 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 74.8377 | 2.68306 | ||||||||
\(779\) | 12.1091 | 0.433853 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.2387 | −1.04624 | ||||||||
\(782\) | 125.229 | 4.47817 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.91522 | 0.104115 | ||||||||
\(785\) | −50.9553 | −1.81867 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.93126 | −0.247073 | −0.123536 | − | 0.992340i | \(-0.539424\pi\) | ||||
−0.123536 | + | 0.992340i | \(0.539424\pi\) | |||||||
\(788\) | 55.6261 | 1.98160 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −29.5297 | −1.05062 | ||||||||
\(791\) | −10.5406 | −0.374781 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.4429 | −1.11657 | ||||||||
\(794\) | 16.0636 | 0.570075 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 75.7674 | 2.68550 | ||||||||
\(797\) | −19.9833 | −0.707847 | −0.353923 | − | 0.935274i | \(-0.615153\pi\) | ||||
−0.353923 | + | 0.935274i | \(0.615153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.9027 | 1.09326 | ||||||||
\(800\) | 5.98770 | 0.211697 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 68.7194 | 2.42657 | ||||||||
\(803\) | −37.1876 | −1.31232 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.6525 | −0.692660 | ||||||||
\(806\) | −45.6269 | −1.60714 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 37.3632 | 1.31443 | ||||||||
\(809\) | −36.8912 | −1.29702 | −0.648512 | − | 0.761204i | \(-0.724609\pi\) | ||||
−0.648512 | + | 0.761204i | \(0.724609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.0117 | −1.75615 | −0.878075 | − | 0.478524i | \(-0.841172\pi\) | ||||
−0.878075 | + | 0.478524i | \(0.841172\pi\) | |||||||
\(812\) | −4.43894 | −0.155776 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −72.7506 | −2.54991 | ||||||||
\(815\) | 15.2158 | 0.532987 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −75.6323 | −2.64604 | ||||||||
\(818\) | 62.8696 | 2.19818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.7842 | 0.655972 | ||||||||
\(821\) | −41.7480 | −1.45702 | −0.728508 | − | 0.685037i | \(-0.759786\pi\) | ||||
−0.728508 | + | 0.685037i | \(0.759786\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.5077 | 1.13315 | 0.566574 | − | 0.824011i | \(-0.308269\pi\) | ||||
0.566574 | + | 0.824011i | \(0.308269\pi\) | |||||||
\(824\) | 56.0981 | 1.95427 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.42375 | 0.119128 | ||||||||
\(827\) | 41.7566 | 1.45202 | 0.726010 | − | 0.687685i | \(-0.241373\pi\) | ||||
0.726010 | + | 0.687685i | \(0.241373\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.4492 | 1.40486 | 0.702430 | − | 0.711753i | \(-0.252098\pi\) | ||||
0.702430 | + | 0.711753i | \(0.252098\pi\) | |||||||
\(830\) | −98.9553 | −3.43479 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 59.0285 | 2.04644 | ||||||||
\(833\) | 7.70060 | 0.266810 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.6119 | 1.05937 | ||||||||
\(836\) | −132.255 | −4.57412 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.4091 | 1.25773 | ||||||||
\(839\) | −28.2930 | −0.976782 | −0.488391 | − | 0.872625i | \(-0.662416\pi\) | ||||
−0.488391 | + | 0.872625i | \(0.662416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6450 | −0.953276 | ||||||||
\(842\) | 17.5728 | 0.605600 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −64.4356 | −2.21797 | ||||||||
\(845\) | −64.3176 | −2.21259 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.4437 | −0.427571 | ||||||||
\(848\) | 13.7943 | 0.473698 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −64.7981 | −2.22256 | ||||||||
\(851\) | −42.0313 | −1.44081 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.1811 | −0.348594 | −0.174297 | − | 0.984693i | \(-0.555765\pi\) | ||||
−0.174297 | + | 0.984693i | \(0.555765\pi\) | |||||||
\(854\) | 12.8011 | 0.438044 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −64.9864 | −2.22119 | ||||||||
\(857\) | −36.0529 | −1.23154 | −0.615772 | − | 0.787925i | \(-0.711156\pi\) | ||||
−0.615772 | + | 0.787925i | \(0.711156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.2611 | 0.930138 | 0.465069 | − | 0.885274i | \(-0.346029\pi\) | ||||
0.465069 | + | 0.885274i | \(0.346029\pi\) | |||||||
\(860\) | −117.324 | −4.00072 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 45.2566 | 1.54144 | ||||||||
\(863\) | −47.4525 | −1.61530 | −0.807651 | − | 0.589661i | \(-0.799261\pi\) | ||||
−0.807651 | + | 0.589661i | \(0.799261\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.23286 | −0.143922 | ||||||||
\(866\) | 75.3325 | 2.55990 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.1850 | 0.413587 | ||||||||
\(869\) | −20.3519 | −0.690390 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.30703 | −0.145938 | ||||||||
\(872\) | −12.8763 | −0.436045 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −116.484 | −3.94011 | ||||||||
\(875\) | −4.39984 | −0.148742 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7097 | 0.395410 | 0.197705 | − | 0.980262i | \(-0.436651\pi\) | ||||
0.197705 | + | 0.980262i | \(0.436651\pi\) | |||||||
\(878\) | 33.0914 | 1.11678 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −41.1281 | −1.38643 | ||||||||
\(881\) | −34.8353 | −1.17363 | −0.586815 | − | 0.809721i | \(-0.699618\pi\) | ||||
−0.586815 | + | 0.809721i | \(0.699618\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.0139 | −1.01005 | −0.505025 | − | 0.863105i | \(-0.668517\pi\) | ||||
−0.505025 | + | 0.863105i | \(0.668517\pi\) | |||||||
\(884\) | −173.911 | −5.84927 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −74.6793 | −2.50890 | ||||||||
\(887\) | 17.5113 | 0.587971 | 0.293986 | − | 0.955810i | \(-0.405018\pi\) | ||||
0.293986 | + | 0.955810i | \(0.405018\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 92.9793 | 3.11667 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.0594 | −0.470745 | ||||||||
\(893\) | −28.7446 | −0.961902 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.7756 | −1.53011 | ||||||||
\(896\) | −20.6004 | −0.688210 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45.6813 | 1.52441 | ||||||||
\(899\) | −3.71947 | −0.124051 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.4378 | 1.21392 | ||||||||
\(902\) | 19.7358 | 0.657131 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −46.0866 | −1.53282 | ||||||||
\(905\) | −50.4814 | −1.67806 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.82321 | 0.193356 | 0.0966782 | − | 0.995316i | \(-0.469178\pi\) | ||||
0.0966782 | + | 0.995316i | \(0.469178\pi\) | |||||||
\(908\) | 89.4687 | 2.96912 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41.6064 | 1.37924 | ||||||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −68.1999 | −2.25709 | ||||||||
\(914\) | 15.6563 | 0.517863 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −99.0984 | −3.27430 | ||||||||
\(917\) | 19.9073 | 0.657398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.7463 | −1.87189 | −0.935944 | − | 0.352148i | \(-0.885451\pi\) | ||||
−0.935944 | + | 0.352148i | \(0.885451\pi\) | |||||||
\(920\) | −85.9264 | −2.83291 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −68.6322 | −2.26028 | ||||||||
\(923\) | 35.7632 | 1.17716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.7486 | 0.715089 | ||||||||
\(926\) | 10.8343 | 0.356037 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.99712 | 0.0655587 | ||||||||
\(929\) | −17.9985 | −0.590512 | −0.295256 | − | 0.955418i | \(-0.595405\pi\) | ||||
−0.295256 | + | 0.955418i | \(0.595405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.16283 | −0.234752 | ||||||||
\(932\) | −94.0679 | −3.08130 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.13726 | 0.102654 | ||||||||
\(935\) | −108.640 | −3.55292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.5134 | −1.71554 | −0.857768 | − | 0.514036i | \(-0.828150\pi\) | ||||
−0.857768 | + | 0.514036i | \(0.828150\pi\) | |||||||
\(938\) | 1.75348 | 0.0572532 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −44.5900 | −1.45436 | ||||||||
\(941\) | −10.8023 | −0.352144 | −0.176072 | − | 0.984377i | \(-0.556339\pi\) | ||||
−0.176072 | + | 0.984377i | \(0.556339\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4023 | 0.371309 | ||||||||
\(944\) | 4.13960 | 0.134733 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −123.268 | −4.00779 | ||||||||
\(947\) | 9.48649 | 0.308269 | 0.154135 | − | 0.988050i | \(-0.450741\pi\) | ||||
0.154135 | + | 0.988050i | \(0.450741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.4859 | 1.47653 | ||||||||
\(950\) | 60.2730 | 1.95551 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 33.6692 | 1.09123 | ||||||||
\(953\) | 43.7726 | 1.41793 | 0.708966 | − | 0.705242i | \(-0.249162\pi\) | ||||
0.708966 | + | 0.705242i | \(0.249162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.8863 | 0.999458 | ||||||||
\(956\) | 79.8599 | 2.58285 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −58.3536 | −1.88532 | ||||||||
\(959\) | 1.07424 | 0.0346891 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7899 | −0.670643 | ||||||||
\(962\) | 88.9846 | 2.86898 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.4883 | −0.337805 | ||||||||
\(965\) | −72.9840 | −2.34944 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.9435 | −0.544865 | −0.272432 | − | 0.962175i | \(-0.587828\pi\) | ||||
−0.272432 | + | 0.962175i | \(0.587828\pi\) | |||||||
\(968\) | −54.4076 | −1.74873 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.179871 | −0.00577529 | ||||||||
\(971\) | −32.4646 | −1.04184 | −0.520919 | − | 0.853606i | \(-0.674411\pi\) | ||||
−0.520919 | + | 0.853606i | \(0.674411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.35399 | 0.171641 | ||||||||
\(974\) | 40.6896 | 1.30378 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.4776 | 0.495425 | ||||||||
\(977\) | −30.0860 | −0.962535 | −0.481268 | − | 0.876574i | \(-0.659823\pi\) | ||||
−0.481268 | + | 0.876574i | \(0.659823\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.0813 | 2.04805 | ||||||||
\(980\) | −11.1113 | −0.354938 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.2165 | −0.421757 | ||||||||
\(983\) | −36.4707 | −1.16323 | −0.581617 | − | 0.813462i | \(-0.697580\pi\) | ||||
−0.581617 | + | 0.813462i | \(0.697580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.5030 | −1.35426 | ||||||||
\(986\) | −21.6126 | −0.688285 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 161.767 | 5.14648 | ||||||||
\(989\) | −71.2175 | −2.26458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.7882 | 1.16862 | 0.584308 | − | 0.811532i | \(-0.301366\pi\) | ||||
0.584308 | + | 0.811532i | \(0.301366\pi\) | |||||||
\(992\) | −5.48216 | −0.174059 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.5600 | −0.461814 | ||||||||
\(995\) | −57.8926 | −1.83532 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.17533 | −0.195575 | −0.0977873 | − | 0.995207i | \(-0.531176\pi\) | ||||
−0.0977873 | + | 0.995207i | \(0.531176\pi\) | |||||||
\(998\) | 43.8159 | 1.38697 | ||||||||
\(999\) | 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 | 8001.2.a.z.1.4 | ✓ | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.29 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
8001.2.a.z.1.29 | yes | 32 | 3.2 | odd | 2 | inner |