Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.77462 | 1.25484 | 0.627422 | − | 0.778680i | \(-0.284110\pi\) | ||||
0.627422 | + | 0.778680i | \(0.284110\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.14926 | 0.574631 | ||||||||
\(5\) | −1.38341 | −0.618682 | −0.309341 | − | 0.950951i | \(-0.600108\pi\) | ||||
−0.309341 | + | 0.950951i | \(0.600108\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00047 | −1.13407 | −0.567035 | − | 0.823694i | \(-0.691909\pi\) | ||||
−0.567035 | + | 0.823694i | \(0.691909\pi\) | |||||||
\(8\) | −1.50973 | −0.533771 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.45503 | −0.776349 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.91001 | 0.529743 | 0.264871 | − | 0.964284i | \(-0.414671\pi\) | ||||
0.264871 | + | 0.964284i | \(0.414671\pi\) | |||||||
\(14\) | −5.32467 | −1.42308 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.97772 | −1.24443 | ||||||||
\(17\) | −5.53610 | −1.34270 | −0.671351 | − | 0.741140i | \(-0.734286\pi\) | ||||
−0.671351 | + | 0.741140i | \(0.734286\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.26949 | 0.750074 | 0.375037 | − | 0.927010i | \(-0.377630\pi\) | ||||
0.375037 | + | 0.927010i | \(0.377630\pi\) | |||||||
\(20\) | −1.58991 | −0.355514 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.77462 | 0.378349 | ||||||||
\(23\) | 1.92659 | 0.401722 | 0.200861 | − | 0.979620i | \(-0.435626\pi\) | ||||
0.200861 | + | 0.979620i | \(0.435626\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.08616 | −0.617233 | ||||||||
\(26\) | 3.38954 | 0.664744 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.44832 | −0.651672 | ||||||||
\(29\) | 5.32737 | 0.989269 | 0.494634 | − | 0.869101i | \(-0.335302\pi\) | ||||
0.494634 | + | 0.869101i | \(0.335302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.87230 | 1.23430 | 0.617151 | − | 0.786845i | \(-0.288287\pi\) | ||||
0.617151 | + | 0.786845i | \(0.288287\pi\) | |||||||
\(32\) | −5.81408 | −1.02779 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.82445 | −1.68488 | ||||||||
\(35\) | 4.15089 | 0.701628 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.70575 | −0.609222 | −0.304611 | − | 0.952477i | \(-0.598527\pi\) | ||||
−0.304611 | + | 0.952477i | \(0.598527\pi\) | |||||||
\(38\) | 5.80210 | 0.941225 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.08859 | 0.330235 | ||||||||
\(41\) | 9.75741 | 1.52385 | 0.761926 | − | 0.647664i | \(-0.224254\pi\) | ||||
0.761926 | + | 0.647664i | \(0.224254\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.90873 | −1.35857 | −0.679285 | − | 0.733875i | \(-0.737710\pi\) | ||||
−0.679285 | + | 0.733875i | \(0.737710\pi\) | |||||||
\(44\) | 1.14926 | 0.173258 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.41896 | 0.504098 | ||||||||
\(47\) | −1.73547 | −0.253144 | −0.126572 | − | 0.991957i | \(-0.540398\pi\) | ||||
−0.126572 | + | 0.991957i | \(0.540398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00280 | 0.286114 | ||||||||
\(50\) | −5.47676 | −0.774530 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.19511 | 0.304407 | ||||||||
\(53\) | 3.45951 | 0.475200 | 0.237600 | − | 0.971363i | \(-0.423639\pi\) | ||||
0.237600 | + | 0.971363i | \(0.423639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.38341 | −0.186540 | ||||||||
\(56\) | 4.52990 | 0.605334 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.45404 | 1.24138 | ||||||||
\(59\) | −13.9936 | −1.82182 | −0.910909 | − | 0.412608i | \(-0.864618\pi\) | ||||
−0.910909 | + | 0.412608i | \(0.864618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 12.1957 | 1.54886 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.362312 | −0.0452890 | ||||||||
\(65\) | −2.64234 | −0.327742 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.30997 | 0.160038 | 0.0800189 | − | 0.996793i | \(-0.474502\pi\) | ||||
0.0800189 | + | 0.996793i | \(0.474502\pi\) | |||||||
\(68\) | −6.36243 | −0.771558 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.36623 | 0.880433 | ||||||||
\(71\) | 14.4465 | 1.71449 | 0.857244 | − | 0.514911i | \(-0.172175\pi\) | ||||
0.857244 | + | 0.514911i | \(0.172175\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.37902 | 0.629567 | 0.314783 | − | 0.949164i | \(-0.398068\pi\) | ||||
0.314783 | + | 0.949164i | \(0.398068\pi\) | |||||||
\(74\) | −6.57629 | −0.764478 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.75751 | 0.431016 | ||||||||
\(77\) | −3.00047 | −0.341935 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7016 | 1.65406 | 0.827029 | − | 0.562159i | \(-0.190029\pi\) | ||||
0.827029 | + | 0.562159i | \(0.190029\pi\) | |||||||
\(80\) | 6.88625 | 0.769906 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.3157 | 1.91219 | ||||||||
\(83\) | −5.37220 | −0.589676 | −0.294838 | − | 0.955547i | \(-0.595266\pi\) | ||||
−0.294838 | + | 0.955547i | \(0.595266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.65872 | 0.830705 | ||||||||
\(86\) | −15.8096 | −1.70479 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.50973 | −0.160938 | ||||||||
\(89\) | 5.99196 | 0.635146 | 0.317573 | − | 0.948234i | \(-0.397132\pi\) | ||||
0.317573 | + | 0.948234i | \(0.397132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.73093 | −0.600765 | ||||||||
\(92\) | 2.21416 | 0.230842 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.07979 | −0.317657 | ||||||||
\(95\) | −4.52307 | −0.464057 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.5252 | 1.88095 | 0.940473 | − | 0.339867i | \(-0.110382\pi\) | ||||
0.940473 | + | 0.339867i | \(0.110382\pi\) | |||||||
\(98\) | 3.55419 | 0.359028 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.54681 | −0.354681 | ||||||||
\(101\) | 10.5775 | 1.05251 | 0.526253 | − | 0.850328i | \(-0.323597\pi\) | ||||
0.526253 | + | 0.850328i | \(0.323597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.331727 | −0.0326861 | −0.0163430 | − | 0.999866i | \(-0.505202\pi\) | ||||
−0.0163430 | + | 0.999866i | \(0.505202\pi\) | |||||||
\(104\) | −2.88361 | −0.282761 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.13930 | 0.596302 | ||||||||
\(107\) | 20.2776 | 1.96031 | 0.980153 | − | 0.198240i | \(-0.0635226\pi\) | ||||
0.980153 | + | 0.198240i | \(0.0635226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.79571 | 0.171998 | 0.0859991 | − | 0.996295i | \(-0.472592\pi\) | ||||
0.0859991 | + | 0.996295i | \(0.472592\pi\) | |||||||
\(110\) | −2.45503 | −0.234078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 14.9355 | 1.41127 | ||||||||
\(113\) | 12.2151 | 1.14910 | 0.574548 | − | 0.818471i | \(-0.305178\pi\) | ||||
0.574548 | + | 0.818471i | \(0.305178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.66527 | −0.248538 | ||||||||
\(116\) | 6.12255 | 0.568464 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.8333 | −2.28610 | ||||||||
\(119\) | 16.6109 | 1.52272 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.77462 | −0.160666 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.89808 | 0.709268 | ||||||||
\(125\) | 11.1865 | 1.00055 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.31827 | −0.116978 | −0.0584888 | − | 0.998288i | \(-0.518628\pi\) | ||||
−0.0584888 | + | 0.998288i | \(0.518628\pi\) | |||||||
\(128\) | 10.9852 | 0.970963 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.68914 | −0.411265 | ||||||||
\(131\) | −4.60086 | −0.401979 | −0.200990 | − | 0.979593i | \(-0.564416\pi\) | ||||
−0.200990 | + | 0.979593i | \(0.564416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.81001 | −0.850636 | ||||||||
\(134\) | 2.32469 | 0.200822 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.35803 | 0.716696 | ||||||||
\(137\) | 1.93120 | 0.164994 | 0.0824969 | − | 0.996591i | \(-0.473711\pi\) | ||||
0.0824969 | + | 0.996591i | \(0.473711\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.524643 | 0.0444996 | 0.0222498 | − | 0.999752i | \(-0.492917\pi\) | ||||
0.0222498 | + | 0.999752i | \(0.492917\pi\) | |||||||
\(140\) | 4.77046 | 0.403177 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.6370 | 2.15141 | ||||||||
\(143\) | 1.91001 | 0.159723 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.36997 | −0.612042 | ||||||||
\(146\) | 9.54569 | 0.790007 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.25888 | −0.350078 | ||||||||
\(149\) | −20.5293 | −1.68182 | −0.840912 | − | 0.541171i | \(-0.817981\pi\) | ||||
−0.840912 | + | 0.541171i | \(0.817981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2387 | 1.32149 | 0.660743 | − | 0.750612i | \(-0.270241\pi\) | ||||
0.660743 | + | 0.750612i | \(0.270241\pi\) | |||||||
\(152\) | −4.93606 | −0.400368 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.32467 | −0.429075 | ||||||||
\(155\) | −9.50724 | −0.763640 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0781 | 0.884127 | 0.442063 | − | 0.896984i | \(-0.354247\pi\) | ||||
0.442063 | + | 0.896984i | \(0.354247\pi\) | |||||||
\(158\) | 26.0897 | 2.07558 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.04328 | 0.635877 | ||||||||
\(161\) | −5.78067 | −0.455580 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.840249 | 0.0658134 | 0.0329067 | − | 0.999458i | \(-0.489524\pi\) | ||||
0.0329067 | + | 0.999458i | \(0.489524\pi\) | |||||||
\(164\) | 11.2138 | 0.875652 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.53359 | −0.739950 | ||||||||
\(167\) | 2.15956 | 0.167112 | 0.0835559 | − | 0.996503i | \(-0.473372\pi\) | ||||
0.0835559 | + | 0.996503i | \(0.473372\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.35184 | −0.719373 | ||||||||
\(170\) | 13.5913 | 1.04240 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.2385 | −0.780676 | ||||||||
\(173\) | 8.83539 | 0.671742 | 0.335871 | − | 0.941908i | \(-0.390969\pi\) | ||||
0.335871 | + | 0.941908i | \(0.390969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.25993 | 0.699985 | ||||||||
\(176\) | −4.97772 | −0.375210 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.6334 | 0.797008 | ||||||||
\(179\) | −2.24198 | −0.167574 | −0.0837868 | − | 0.996484i | \(-0.526701\pi\) | ||||
−0.0837868 | + | 0.996484i | \(0.526701\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.43057 | −0.254992 | −0.127496 | − | 0.991839i | \(-0.540694\pi\) | ||||
−0.127496 | + | 0.991839i | \(0.540694\pi\) | |||||||
\(182\) | −10.1702 | −0.753866 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.90864 | −0.214428 | ||||||||
\(185\) | 5.12659 | 0.376915 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.53610 | −0.404840 | ||||||||
\(188\) | −1.99451 | −0.145465 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.02671 | −0.582319 | ||||||||
\(191\) | 11.0429 | 0.799036 | 0.399518 | − | 0.916725i | \(-0.369177\pi\) | ||||
0.399518 | + | 0.916725i | \(0.369177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8007 | −0.777453 | −0.388726 | − | 0.921353i | \(-0.627085\pi\) | ||||
−0.388726 | + | 0.921353i | \(0.627085\pi\) | |||||||
\(194\) | 32.8751 | 2.36029 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.30174 | 0.164410 | ||||||||
\(197\) | 2.66347 | 0.189764 | 0.0948822 | − | 0.995489i | \(-0.469753\pi\) | ||||
0.0948822 | + | 0.995489i | \(0.469753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.50042 | −0.531691 | −0.265845 | − | 0.964016i | \(-0.585651\pi\) | ||||
−0.265845 | + | 0.964016i | \(0.585651\pi\) | |||||||
\(200\) | 4.65928 | 0.329461 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.7711 | 1.32073 | ||||||||
\(203\) | −15.9846 | −1.12190 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.4985 | −0.942779 | ||||||||
\(206\) | −0.588689 | −0.0410159 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.50752 | −0.659228 | ||||||||
\(209\) | 3.26949 | 0.226156 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.6852 | −1.14866 | −0.574328 | − | 0.818625i | \(-0.694737\pi\) | ||||
−0.574328 | + | 0.818625i | \(0.694737\pi\) | |||||||
\(212\) | 3.97588 | 0.273065 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 35.9849 | 2.45988 | ||||||||
\(215\) | 12.3245 | 0.840522 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.6201 | −1.39978 | ||||||||
\(218\) | 3.18670 | 0.215831 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.58991 | −0.107191 | ||||||||
\(221\) | −10.5740 | −0.711286 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5951 | −0.910397 | −0.455198 | − | 0.890390i | \(-0.650432\pi\) | ||||
−0.455198 | + | 0.890390i | \(0.650432\pi\) | |||||||
\(224\) | 17.4449 | 1.16559 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.6770 | 1.44194 | ||||||||
\(227\) | 0.528432 | 0.0350733 | 0.0175366 | − | 0.999846i | \(-0.494418\pi\) | ||||
0.0175366 | + | 0.999846i | \(0.494418\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.67417 | 0.176714 | 0.0883571 | − | 0.996089i | \(-0.471838\pi\) | ||||
0.0883571 | + | 0.996089i | \(0.471838\pi\) | |||||||
\(230\) | −4.72984 | −0.311876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.04291 | −0.528043 | ||||||||
\(233\) | −27.0368 | −1.77124 | −0.885621 | − | 0.464408i | \(-0.846267\pi\) | ||||
−0.885621 | + | 0.464408i | \(0.846267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.40088 | 0.156616 | ||||||||
\(236\) | −16.0824 | −1.04687 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 29.4779 | 1.91077 | ||||||||
\(239\) | 12.4532 | 0.805533 | 0.402767 | − | 0.915303i | \(-0.368049\pi\) | ||||
0.402767 | + | 0.915303i | \(0.368049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.41293 | −0.541924 | −0.270962 | − | 0.962590i | \(-0.587342\pi\) | ||||
−0.270962 | + | 0.962590i | \(0.587342\pi\) | |||||||
\(242\) | 1.77462 | 0.114077 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.14926 | −0.0735740 | ||||||||
\(245\) | −2.77070 | −0.177013 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.24478 | 0.397346 | ||||||||
\(248\) | −10.3753 | −0.658835 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.8518 | 1.25554 | ||||||||
\(251\) | 15.1182 | 0.954254 | 0.477127 | − | 0.878834i | \(-0.341678\pi\) | ||||
0.477127 | + | 0.878834i | \(0.341678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.92659 | 0.121124 | ||||||||
\(254\) | −2.33943 | −0.146789 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.2191 | 1.26369 | ||||||||
\(257\) | 18.1387 | 1.13146 | 0.565732 | − | 0.824589i | \(-0.308594\pi\) | ||||
0.565732 | + | 0.824589i | \(0.308594\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1190 | 0.690900 | ||||||||
\(260\) | −3.03674 | −0.188331 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.16477 | −0.504421 | ||||||||
\(263\) | −11.1417 | −0.687027 | −0.343514 | − | 0.939148i | \(-0.611617\pi\) | ||||
−0.343514 | + | 0.939148i | \(0.611617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.78594 | −0.293998 | ||||||||
\(266\) | −17.4090 | −1.06741 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.50549 | 0.0919627 | ||||||||
\(269\) | 4.30607 | 0.262546 | 0.131273 | − | 0.991346i | \(-0.458094\pi\) | ||||
0.131273 | + | 0.991346i | \(0.458094\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9322 | 0.664083 | 0.332042 | − | 0.943265i | \(-0.392263\pi\) | ||||
0.332042 | + | 0.943265i | \(0.392263\pi\) | |||||||
\(272\) | 27.5572 | 1.67090 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.42714 | 0.207041 | ||||||||
\(275\) | −3.08616 | −0.186103 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4176 | −1.46711 | −0.733557 | − | 0.679628i | \(-0.762141\pi\) | ||||
−0.733557 | + | 0.679628i | \(0.762141\pi\) | |||||||
\(278\) | 0.931039 | 0.0558400 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.26673 | −0.374509 | ||||||||
\(281\) | −0.333656 | −0.0199042 | −0.00995212 | − | 0.999950i | \(-0.503168\pi\) | ||||
−0.00995212 | + | 0.999950i | \(0.503168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.36506 | 0.259476 | 0.129738 | − | 0.991548i | \(-0.458586\pi\) | ||||
0.129738 | + | 0.991548i | \(0.458586\pi\) | |||||||
\(284\) | 16.6028 | 0.985198 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.38954 | 0.200428 | ||||||||
\(287\) | −29.2768 | −1.72815 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.6484 | 0.802848 | ||||||||
\(290\) | −13.0789 | −0.768017 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.18190 | 0.361768 | ||||||||
\(293\) | −23.9647 | −1.40003 | −0.700016 | − | 0.714127i | \(-0.746824\pi\) | ||||
−0.700016 | + | 0.714127i | \(0.746824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.3590 | 1.12713 | ||||||||
\(296\) | 5.59470 | 0.325185 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −36.4316 | −2.11043 | ||||||||
\(299\) | 3.67982 | 0.212809 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.7303 | 1.54071 | ||||||||
\(302\) | 28.8174 | 1.65826 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.2746 | −0.933414 | ||||||||
\(305\) | 1.38341 | 0.0792141 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0771 | 1.26000 | 0.630002 | − | 0.776593i | \(-0.283054\pi\) | ||||
0.630002 | + | 0.776593i | \(0.283054\pi\) | |||||||
\(308\) | −3.44832 | −0.196486 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.8717 | −0.958249 | ||||||||
\(311\) | 4.88561 | 0.277037 | 0.138519 | − | 0.990360i | \(-0.455766\pi\) | ||||
0.138519 | + | 0.990360i | \(0.455766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8503 | −0.895914 | −0.447957 | − | 0.894055i | \(-0.647848\pi\) | ||||
−0.447957 | + | 0.894055i | \(0.647848\pi\) | |||||||
\(314\) | 19.6593 | 1.10944 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.8960 | 0.950473 | ||||||||
\(317\) | −12.4684 | −0.700295 | −0.350148 | − | 0.936694i | \(-0.613869\pi\) | ||||
−0.350148 | + | 0.936694i | \(0.613869\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.32737 | 0.298276 | ||||||||
\(320\) | 0.501228 | 0.0280195 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.2585 | −0.571682 | ||||||||
\(323\) | −18.1003 | −1.00712 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.89462 | −0.326975 | ||||||||
\(326\) | 1.49112 | 0.0825855 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.7311 | −0.813388 | ||||||||
\(329\) | 5.20722 | 0.287083 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.37223 | 0.0754245 | 0.0377123 | − | 0.999289i | \(-0.487993\pi\) | ||||
0.0377123 | + | 0.999289i | \(0.487993\pi\) | |||||||
\(332\) | −6.17407 | −0.338846 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.83239 | 0.209699 | ||||||||
\(335\) | −1.81223 | −0.0990125 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.72751 | 0.203051 | 0.101525 | − | 0.994833i | \(-0.467628\pi\) | ||||
0.101525 | + | 0.994833i | \(0.467628\pi\) | |||||||
\(338\) | −16.5959 | −0.902700 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.80188 | 0.477349 | ||||||||
\(341\) | 6.87230 | 0.372156 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.9939 | 0.809597 | ||||||||
\(344\) | 13.4498 | 0.725165 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.6794 | 0.842931 | ||||||||
\(347\) | 9.56283 | 0.513360 | 0.256680 | − | 0.966497i | \(-0.417371\pi\) | ||||
0.256680 | + | 0.966497i | \(0.417371\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5888 | −0.995038 | −0.497519 | − | 0.867453i | \(-0.665756\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665756\pi\) | |||||||
\(350\) | 16.4328 | 0.878371 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.81408 | −0.309891 | ||||||||
\(353\) | 7.34062 | 0.390702 | 0.195351 | − | 0.980733i | \(-0.437415\pi\) | ||||
0.195351 | + | 0.980733i | \(0.437415\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.9855 | −1.06072 | ||||||||
\(356\) | 6.88633 | 0.364975 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.97866 | −0.210278 | ||||||||
\(359\) | 7.51165 | 0.396450 | 0.198225 | − | 0.980157i | \(-0.436482\pi\) | ||||
0.198225 | + | 0.980157i | \(0.436482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.31040 | −0.437390 | ||||||||
\(362\) | −6.08795 | −0.319975 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.58634 | −0.345218 | ||||||||
\(365\) | −7.44141 | −0.389501 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.0261 | −1.82835 | −0.914175 | − | 0.405320i | \(-0.867160\pi\) | ||||
−0.914175 | + | 0.405320i | \(0.867160\pi\) | |||||||
\(368\) | −9.59003 | −0.499915 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.09774 | 0.472969 | ||||||||
\(371\) | −10.3801 | −0.538910 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.0943 | 1.66178 | 0.830891 | − | 0.556436i | \(-0.187832\pi\) | ||||
0.830891 | + | 0.556436i | \(0.187832\pi\) | |||||||
\(374\) | −9.82445 | −0.508010 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.62010 | 0.135121 | ||||||||
\(377\) | 10.1754 | 0.524058 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9206 | 0.663688 | 0.331844 | − | 0.943334i | \(-0.392329\pi\) | ||||
0.331844 | + | 0.943334i | \(0.392329\pi\) | |||||||
\(380\) | −5.19819 | −0.266661 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.5969 | 1.00267 | ||||||||
\(383\) | 11.4054 | 0.582789 | 0.291395 | − | 0.956603i | \(-0.405881\pi\) | ||||
0.291395 | + | 0.956603i | \(0.405881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.15089 | 0.211549 | ||||||||
\(386\) | −19.1671 | −0.975581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.2903 | 1.08085 | ||||||||
\(389\) | 21.1661 | 1.07316 | 0.536582 | − | 0.843848i | \(-0.319715\pi\) | ||||
0.536582 | + | 0.843848i | \(0.319715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.6658 | −0.539393 | ||||||||
\(392\) | −3.02369 | −0.152719 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.72664 | 0.238125 | ||||||||
\(395\) | −20.3384 | −1.02334 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.05003 | 0.102888 | 0.0514441 | − | 0.998676i | \(-0.483618\pi\) | ||||
0.0514441 | + | 0.998676i | \(0.483618\pi\) | |||||||
\(398\) | −13.3104 | −0.667188 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.3621 | 0.768103 | ||||||||
\(401\) | 28.6494 | 1.43068 | 0.715342 | − | 0.698774i | \(-0.246271\pi\) | ||||
0.715342 | + | 0.698774i | \(0.246271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.1262 | 0.653863 | ||||||||
\(404\) | 12.1564 | 0.604802 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28.3665 | −1.40781 | ||||||||
\(407\) | −3.70575 | −0.183687 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.34125 | 0.0663204 | 0.0331602 | − | 0.999450i | \(-0.489443\pi\) | ||||
0.0331602 | + | 0.999450i | \(0.489443\pi\) | |||||||
\(410\) | −23.9547 | −1.18304 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.381242 | −0.0187824 | ||||||||
\(413\) | 41.9875 | 2.06607 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.43198 | 0.364822 | ||||||||
\(416\) | −11.1050 | −0.544466 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.80210 | 0.283790 | ||||||||
\(419\) | 16.6723 | 0.814495 | 0.407247 | − | 0.913318i | \(-0.366489\pi\) | ||||
0.407247 | + | 0.913318i | \(0.366489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.9609 | −1.70389 | −0.851946 | − | 0.523630i | \(-0.824577\pi\) | ||||
−0.851946 | + | 0.523630i | \(0.824577\pi\) | |||||||
\(422\) | −29.6098 | −1.44138 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.22294 | −0.253648 | ||||||||
\(425\) | 17.0853 | 0.828760 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.00047 | 0.145203 | ||||||||
\(428\) | 23.3042 | 1.12645 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.8712 | 1.05472 | ||||||||
\(431\) | 1.32377 | 0.0637638 | 0.0318819 | − | 0.999492i | \(-0.489850\pi\) | ||||
0.0318819 | + | 0.999492i | \(0.489850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.4879 | −1.22487 | −0.612436 | − | 0.790520i | \(-0.709810\pi\) | ||||
−0.612436 | + | 0.790520i | \(0.709810\pi\) | |||||||
\(434\) | −36.5928 | −1.75651 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.06375 | 0.0988356 | ||||||||
\(437\) | 6.29898 | 0.301321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.3742 | 1.73605 | 0.868023 | − | 0.496525i | \(-0.165391\pi\) | ||||
0.868023 | + | 0.496525i | \(0.165391\pi\) | |||||||
\(440\) | 2.08859 | 0.0995695 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.7648 | −0.892553 | ||||||||
\(443\) | 11.7349 | 0.557542 | 0.278771 | − | 0.960358i | \(-0.410073\pi\) | ||||
0.278771 | + | 0.960358i | \(0.410073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.28936 | −0.392953 | ||||||||
\(446\) | −24.1261 | −1.14240 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.08711 | 0.0513609 | ||||||||
\(449\) | 5.50937 | 0.260003 | 0.130002 | − | 0.991514i | \(-0.458502\pi\) | ||||
0.130002 | + | 0.991514i | \(0.458502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.75741 | 0.459458 | ||||||||
\(452\) | 14.0383 | 0.660306 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.937764 | 0.0440114 | ||||||||
\(455\) | 7.92826 | 0.371682 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.412085 | −0.0192765 | −0.00963827 | − | 0.999954i | \(-0.503068\pi\) | ||||
−0.00963827 | + | 0.999954i | \(0.503068\pi\) | |||||||
\(458\) | 4.74563 | 0.221748 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.06310 | −0.142818 | ||||||||
\(461\) | −20.4352 | −0.951764 | −0.475882 | − | 0.879509i | \(-0.657871\pi\) | ||||
−0.475882 | + | 0.879509i | \(0.657871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.9214 | −1.39057 | −0.695283 | − | 0.718736i | \(-0.744721\pi\) | ||||
−0.695283 | + | 0.718736i | \(0.744721\pi\) | |||||||
\(464\) | −26.5182 | −1.23108 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.9800 | −2.22263 | ||||||||
\(467\) | −8.83738 | −0.408945 | −0.204473 | − | 0.978872i | \(-0.565548\pi\) | ||||
−0.204473 | + | 0.978872i | \(0.565548\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.93051 | −0.181494 | ||||||||
\(470\) | 4.26063 | 0.196528 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.1267 | 0.972434 | ||||||||
\(473\) | −8.90873 | −0.409624 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0902 | −0.462970 | ||||||||
\(476\) | 19.0903 | 0.875000 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.0997 | 1.01082 | ||||||||
\(479\) | −13.5867 | −0.620793 | −0.310397 | − | 0.950607i | \(-0.600462\pi\) | ||||
−0.310397 | + | 0.950607i | \(0.600462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.07805 | −0.322731 | ||||||||
\(482\) | −14.9297 | −0.680030 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.14926 | 0.0522392 | ||||||||
\(485\) | −25.6280 | −1.16371 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.43282 | −0.200870 | −0.100435 | − | 0.994944i | \(-0.532024\pi\) | ||||
−0.100435 | + | 0.994944i | \(0.532024\pi\) | |||||||
\(488\) | 1.50973 | 0.0683424 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.91692 | −0.222124 | ||||||||
\(491\) | −11.8780 | −0.536049 | −0.268024 | − | 0.963412i | \(-0.586371\pi\) | ||||
−0.268024 | + | 0.963412i | \(0.586371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.4929 | −1.32829 | ||||||||
\(494\) | 11.0821 | 0.498607 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.2084 | −1.53600 | ||||||||
\(497\) | −43.3463 | −1.94435 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8417 | −0.753940 | −0.376970 | − | 0.926225i | \(-0.623034\pi\) | ||||
−0.376970 | + | 0.926225i | \(0.623034\pi\) | |||||||
\(500\) | 12.8562 | 0.574949 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.8290 | 1.19744 | ||||||||
\(503\) | −28.5265 | −1.27193 | −0.635967 | − | 0.771716i | \(-0.719399\pi\) | ||||
−0.635967 | + | 0.771716i | \(0.719399\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6331 | −0.651166 | ||||||||
\(506\) | 3.41896 | 0.151991 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.51504 | −0.0672190 | ||||||||
\(509\) | 32.0469 | 1.42045 | 0.710227 | − | 0.703973i | \(-0.248592\pi\) | ||||
0.710227 | + | 0.703973i | \(0.248592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.1396 | −0.713972 | ||||||||
\(512\) | 13.9108 | 0.614776 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.1893 | 1.41981 | ||||||||
\(515\) | 0.458916 | 0.0202223 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.73547 | −0.0763259 | ||||||||
\(518\) | 19.7319 | 0.866972 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.98923 | 0.174939 | ||||||||
\(521\) | 29.7095 | 1.30159 | 0.650797 | − | 0.759251i | \(-0.274435\pi\) | ||||
0.650797 | + | 0.759251i | \(0.274435\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6258 | −1.33917 | −0.669587 | − | 0.742734i | \(-0.733529\pi\) | ||||
−0.669587 | + | 0.742734i | \(0.733529\pi\) | |||||||
\(524\) | −5.28760 | −0.230990 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.7723 | −0.862112 | ||||||||
\(527\) | −38.0458 | −1.65730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2883 | −0.838620 | ||||||||
\(530\) | −8.49320 | −0.368921 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.2743 | −0.488802 | ||||||||
\(533\) | 18.6368 | 0.807249 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.0523 | −1.21281 | ||||||||
\(536\) | −1.97770 | −0.0854236 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.64162 | 0.329454 | ||||||||
\(539\) | 2.00280 | 0.0862665 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.0599 | −0.518494 | −0.259247 | − | 0.965811i | \(-0.583474\pi\) | ||||
−0.259247 | + | 0.965811i | \(0.583474\pi\) | |||||||
\(542\) | 19.4004 | 0.833320 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.1873 | 1.38002 | ||||||||
\(545\) | −2.48422 | −0.106412 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.6713 | 0.670056 | 0.335028 | − | 0.942208i | \(-0.391254\pi\) | ||||
0.335028 | + | 0.942208i | \(0.391254\pi\) | |||||||
\(548\) | 2.21946 | 0.0948106 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.47676 | −0.233530 | ||||||||
\(551\) | 17.4178 | 0.742024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −44.1116 | −1.87582 | ||||||||
\(554\) | −43.3319 | −1.84100 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.602952 | 0.0255709 | ||||||||
\(557\) | 21.7950 | 0.923485 | 0.461742 | − | 0.887014i | \(-0.347224\pi\) | ||||
0.461742 | + | 0.887014i | \(0.347224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.0158 | −0.719692 | ||||||||
\(560\) | −20.6620 | −0.873127 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.592111 | −0.0249767 | ||||||||
\(563\) | 40.1440 | 1.69187 | 0.845933 | − | 0.533289i | \(-0.179044\pi\) | ||||
0.845933 | + | 0.533289i | \(0.179044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.8985 | −0.710925 | ||||||||
\(566\) | 7.74631 | 0.325602 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.8104 | −0.915144 | ||||||||
\(569\) | 27.1384 | 1.13770 | 0.568850 | − | 0.822442i | \(-0.307389\pi\) | ||||
0.568850 | + | 0.822442i | \(0.307389\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.8310 | 0.829901 | 0.414950 | − | 0.909844i | \(-0.363799\pi\) | ||||
0.414950 | + | 0.909844i | \(0.363799\pi\) | |||||||
\(572\) | 2.19511 | 0.0917820 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −51.9550 | −2.16856 | ||||||||
\(575\) | −5.94577 | −0.247956 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3627 | −1.51380 | −0.756899 | − | 0.653532i | \(-0.773287\pi\) | ||||
−0.756899 | + | 0.653532i | \(0.773287\pi\) | |||||||
\(578\) | 24.2207 | 1.00745 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.47002 | −0.351699 | ||||||||
\(581\) | 16.1191 | 0.668733 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.45951 | 0.143278 | ||||||||
\(584\) | −8.12088 | −0.336045 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −42.5281 | −1.75682 | ||||||||
\(587\) | −18.8007 | −0.775990 | −0.387995 | − | 0.921661i | \(-0.626832\pi\) | ||||
−0.387995 | + | 0.921661i | \(0.626832\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.4690 | 0.925817 | ||||||||
\(590\) | 34.3548 | 1.41437 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.4462 | 0.758135 | ||||||||
\(593\) | −9.65046 | −0.396297 | −0.198148 | − | 0.980172i | \(-0.563493\pi\) | ||||
−0.198148 | + | 0.980172i | \(0.563493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.9797 | −0.942077 | ||||||||
\(596\) | −23.5935 | −0.966429 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.53026 | 0.267042 | ||||||||
\(599\) | −3.84944 | −0.157284 | −0.0786420 | − | 0.996903i | \(-0.525058\pi\) | ||||
−0.0786420 | + | 0.996903i | \(0.525058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.79246 | 0.154698 | 0.0773488 | − | 0.997004i | \(-0.475355\pi\) | ||||
0.0773488 | + | 0.997004i | \(0.475355\pi\) | |||||||
\(602\) | 47.4361 | 1.93335 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.6625 | 0.759367 | ||||||||
\(605\) | −1.38341 | −0.0562438 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.42952 | −0.342144 | −0.171072 | − | 0.985259i | \(-0.554723\pi\) | ||||
−0.171072 | + | 0.985259i | \(0.554723\pi\) | |||||||
\(608\) | −19.0091 | −0.770921 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.45503 | 0.0994012 | ||||||||
\(611\) | −3.31477 | −0.134101 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.9296 | −1.37040 | −0.685202 | − | 0.728353i | \(-0.740286\pi\) | ||||
−0.685202 | + | 0.728353i | \(0.740286\pi\) | |||||||
\(614\) | 39.1783 | 1.58111 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.52990 | 0.182515 | ||||||||
\(617\) | 33.4620 | 1.34713 | 0.673564 | − | 0.739129i | \(-0.264762\pi\) | ||||
0.673564 | + | 0.739129i | \(0.264762\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.1918 | −1.77622 | −0.888109 | − | 0.459633i | \(-0.847981\pi\) | ||||
−0.888109 | + | 0.459633i | \(0.847981\pi\) | |||||||
\(620\) | −10.9263 | −0.438811 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.67008 | 0.347638 | ||||||||
\(623\) | −17.9787 | −0.720300 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.0447694 | −0.00179078 | ||||||||
\(626\) | −28.1283 | −1.12423 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.7316 | 0.508047 | ||||||||
\(629\) | 20.5154 | 0.818004 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.2349 | 1.76096 | 0.880482 | − | 0.474079i | \(-0.157219\pi\) | ||||
0.880482 | + | 0.474079i | \(0.157219\pi\) | |||||||
\(632\) | −22.1955 | −0.882889 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.1266 | −0.878761 | ||||||||
\(635\) | 1.82372 | 0.0723720 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.82537 | 0.151567 | ||||||||
\(638\) | 9.45404 | 0.374289 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.1971 | −0.600717 | ||||||||
\(641\) | 7.36324 | 0.290831 | 0.145415 | − | 0.989371i | \(-0.453548\pi\) | ||||
0.145415 | + | 0.989371i | \(0.453548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.6344 | 1.52359 | 0.761795 | − | 0.647818i | \(-0.224318\pi\) | ||||
0.761795 | + | 0.647818i | \(0.224318\pi\) | |||||||
\(644\) | −6.64350 | −0.261791 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32.1210 | −1.26378 | ||||||||
\(647\) | −16.0672 | −0.631667 | −0.315834 | − | 0.948815i | \(-0.602284\pi\) | ||||
−0.315834 | + | 0.948815i | \(0.602284\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9936 | −0.549299 | ||||||||
\(650\) | −10.4607 | −0.410302 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.965667 | 0.0378184 | ||||||||
\(653\) | −29.4442 | −1.15224 | −0.576120 | − | 0.817365i | \(-0.695434\pi\) | ||||
−0.576120 | + | 0.817365i | \(0.695434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.36490 | 0.248697 | ||||||||
\(656\) | −48.5697 | −1.89633 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.24082 | 0.360245 | ||||||||
\(659\) | −2.22704 | −0.0867532 | −0.0433766 | − | 0.999059i | \(-0.513812\pi\) | ||||
−0.0433766 | + | 0.999059i | \(0.513812\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.78984 | −0.186303 | −0.0931515 | − | 0.995652i | \(-0.529694\pi\) | ||||
−0.0931515 | + | 0.995652i | \(0.529694\pi\) | |||||||
\(662\) | 2.43518 | 0.0946459 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.11059 | 0.314752 | ||||||||
\(665\) | 13.5713 | 0.526273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.2637 | 0.397411 | ||||||||
\(668\) | 2.48190 | 0.0960276 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.21601 | −0.124245 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.9084 | 1.46126 | 0.730630 | − | 0.682773i | \(-0.239226\pi\) | ||||
0.730630 | + | 0.682773i | \(0.239226\pi\) | |||||||
\(674\) | 6.61491 | 0.254797 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.7477 | −0.413374 | ||||||||
\(677\) | 46.7699 | 1.79751 | 0.898756 | − | 0.438448i | \(-0.144472\pi\) | ||||
0.898756 | + | 0.438448i | \(0.144472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −55.5842 | −2.13312 | ||||||||
\(680\) | −11.5626 | −0.443406 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.1957 | 0.466997 | ||||||||
\(683\) | −20.7596 | −0.794343 | −0.397171 | − | 0.917744i | \(-0.630008\pi\) | ||||
−0.397171 | + | 0.917744i | \(0.630008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.67165 | −0.102079 | ||||||||
\(686\) | 26.6085 | 1.01592 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 44.3452 | 1.69064 | ||||||||
\(689\) | 6.60771 | 0.251734 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0782 | 1.14423 | 0.572115 | − | 0.820173i | \(-0.306123\pi\) | ||||
0.572115 | + | 0.820173i | \(0.306123\pi\) | |||||||
\(692\) | 10.1542 | 0.386004 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.9703 | 0.644186 | ||||||||
\(695\) | −0.725798 | −0.0275311 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −54.0180 | −2.04608 | ||||||||
\(698\) | −32.9881 | −1.24862 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.6421 | 0.402233 | ||||||||
\(701\) | 19.9910 | 0.755048 | 0.377524 | − | 0.926000i | \(-0.376776\pi\) | ||||
0.377524 | + | 0.926000i | \(0.376776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.1159 | −0.456962 | ||||||||
\(704\) | −0.362312 | −0.0136552 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.0268 | 0.490269 | ||||||||
\(707\) | −31.7376 | −1.19361 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.8223 | −1.45800 | −0.729001 | − | 0.684513i | \(-0.760015\pi\) | ||||
−0.729001 | + | 0.684513i | \(0.760015\pi\) | |||||||
\(710\) | −35.4667 | −1.33104 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.04625 | −0.339023 | ||||||||
\(713\) | 13.2401 | 0.495846 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.64234 | −0.0988180 | ||||||||
\(716\) | −2.57662 | −0.0962930 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.3303 | 0.497482 | ||||||||
\(719\) | 39.1271 | 1.45919 | 0.729597 | − | 0.683877i | \(-0.239708\pi\) | ||||
0.729597 | + | 0.683877i | \(0.239708\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.995336 | 0.0370683 | ||||||||
\(722\) | −14.7478 | −0.548855 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.94263 | −0.146527 | ||||||||
\(725\) | −16.4412 | −0.610609 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.6521 | −0.617592 | −0.308796 | − | 0.951128i | \(-0.599926\pi\) | ||||
−0.308796 | + | 0.951128i | \(0.599926\pi\) | |||||||
\(728\) | 8.65218 | 0.320671 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.2056 | −0.488763 | ||||||||
\(731\) | 49.3196 | 1.82415 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.5747 | 1.16624 | 0.583119 | − | 0.812387i | \(-0.301832\pi\) | ||||
0.583119 | + | 0.812387i | \(0.301832\pi\) | |||||||
\(734\) | −62.1580 | −2.29429 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.2013 | −0.412887 | ||||||||
\(737\) | 1.30997 | 0.0482532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.2375 | −1.29623 | −0.648117 | − | 0.761541i | \(-0.724443\pi\) | ||||
−0.648117 | + | 0.761541i | \(0.724443\pi\) | |||||||
\(740\) | 5.89180 | 0.216587 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.4208 | −0.676247 | ||||||||
\(743\) | 22.9658 | 0.842534 | 0.421267 | − | 0.906937i | \(-0.361585\pi\) | ||||
0.421267 | + | 0.906937i | \(0.361585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.4005 | 1.04051 | ||||||||
\(746\) | 56.9551 | 2.08527 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.36243 | −0.232633 | ||||||||
\(749\) | −60.8422 | −2.22312 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.4722 | 1.65930 | 0.829652 | − | 0.558281i | \(-0.188539\pi\) | ||||
0.829652 | + | 0.558281i | \(0.188539\pi\) | |||||||
\(752\) | 8.63869 | 0.315021 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.0574 | 0.657610 | ||||||||
\(755\) | −22.4648 | −0.817579 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.4333 | 0.524588 | 0.262294 | − | 0.964988i | \(-0.415521\pi\) | ||||
0.262294 | + | 0.964988i | \(0.415521\pi\) | |||||||
\(758\) | 22.9291 | 0.832824 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.82862 | 0.247700 | ||||||||
\(761\) | 47.1071 | 1.70763 | 0.853815 | − | 0.520576i | \(-0.174283\pi\) | ||||
0.853815 | + | 0.520576i | \(0.174283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.38798 | −0.195058 | ||||||||
\(764\) | 12.6912 | 0.459151 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.2402 | 0.731309 | ||||||||
\(767\) | −26.7281 | −0.965095 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.9030 | 1.54712 | 0.773561 | − | 0.633721i | \(-0.218473\pi\) | ||||
0.773561 | + | 0.633721i | \(0.218473\pi\) | |||||||
\(770\) | 7.36623 | 0.265461 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.4129 | −0.446748 | ||||||||
\(773\) | 44.2757 | 1.59249 | 0.796243 | − | 0.604976i | \(-0.206817\pi\) | ||||
0.796243 | + | 0.604976i | \(0.206817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.2091 | −0.761852 | ||||||||
\(776\) | −27.9681 | −1.00400 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.5617 | 1.34665 | ||||||||
\(779\) | 31.9018 | 1.14300 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4465 | 0.516937 | ||||||||
\(782\) | −18.9277 | −0.676853 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.96936 | −0.356048 | ||||||||
\(785\) | −15.3256 | −0.546993 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.5288 | −0.517896 | −0.258948 | − | 0.965891i | \(-0.583376\pi\) | ||||
−0.258948 | + | 0.965891i | \(0.583376\pi\) | |||||||
\(788\) | 3.06103 | 0.109045 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −36.0928 | −1.28413 | ||||||||
\(791\) | −36.6509 | −1.30315 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.91001 | −0.0678266 | ||||||||
\(794\) | 3.63802 | 0.129109 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.61995 | −0.305526 | ||||||||
\(797\) | 41.9535 | 1.48607 | 0.743034 | − | 0.669253i | \(-0.233386\pi\) | ||||
0.743034 | + | 0.669253i | \(0.233386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.60774 | 0.339897 | ||||||||
\(800\) | 17.9432 | 0.634388 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 50.8418 | 1.79528 | ||||||||
\(803\) | 5.37902 | 0.189821 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.99706 | 0.281859 | ||||||||
\(806\) | 23.2940 | 0.820495 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.9693 | −0.561797 | ||||||||
\(809\) | 26.4843 | 0.931140 | 0.465570 | − | 0.885011i | \(-0.345849\pi\) | ||||
0.465570 | + | 0.885011i | \(0.345849\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.8378 | 0.766828 | 0.383414 | − | 0.923577i | \(-0.374748\pi\) | ||||
0.383414 | + | 0.923577i | \(0.374748\pi\) | |||||||
\(812\) | −18.3705 | −0.644678 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.57629 | −0.230499 | ||||||||
\(815\) | −1.16241 | −0.0407176 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.1271 | −1.01903 | ||||||||
\(818\) | 2.38020 | 0.0832217 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.5134 | −0.541750 | ||||||||
\(821\) | 47.3362 | 1.65205 | 0.826023 | − | 0.563636i | \(-0.190598\pi\) | ||||
0.826023 | + | 0.563636i | \(0.190598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.0471 | −0.524508 | −0.262254 | − | 0.964999i | \(-0.584466\pi\) | ||||
−0.262254 | + | 0.964999i | \(0.584466\pi\) | |||||||
\(824\) | 0.500820 | 0.0174469 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 74.5116 | 2.59259 | ||||||||
\(827\) | 14.8054 | 0.514835 | 0.257418 | − | 0.966300i | \(-0.417128\pi\) | ||||
0.257418 | + | 0.966300i | \(0.417128\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.6278 | −1.02901 | −0.514507 | − | 0.857486i | \(-0.672025\pi\) | ||||
−0.514507 | + | 0.857486i | \(0.672025\pi\) | |||||||
\(830\) | 13.1889 | 0.457794 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.692022 | −0.0239915 | ||||||||
\(833\) | −11.0877 | −0.384165 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.98757 | −0.103389 | ||||||||
\(836\) | 3.75751 | 0.129956 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.5869 | 1.02206 | ||||||||
\(839\) | 23.2760 | 0.803578 | 0.401789 | − | 0.915732i | \(-0.368389\pi\) | ||||
0.401789 | + | 0.915732i | \(0.368389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.619079 | −0.0213475 | ||||||||
\(842\) | −62.0422 | −2.13812 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.1757 | −0.660054 | ||||||||
\(845\) | 12.9375 | 0.445063 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.00047 | −0.103097 | ||||||||
\(848\) | −17.2205 | −0.591353 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.3199 | 1.03996 | ||||||||
\(851\) | −7.13947 | −0.244738 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.24162 | 0.0425122 | 0.0212561 | − | 0.999774i | \(-0.493233\pi\) | ||||
0.0212561 | + | 0.999774i | \(0.493233\pi\) | |||||||
\(854\) | 5.32467 | 0.182207 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.6137 | −1.04636 | ||||||||
\(857\) | −6.05692 | −0.206900 | −0.103450 | − | 0.994635i | \(-0.532988\pi\) | ||||
−0.103450 | + | 0.994635i | \(0.532988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.5519 | −1.86129 | −0.930643 | − | 0.365928i | \(-0.880752\pi\) | ||||
−0.930643 | + | 0.365928i | \(0.880752\pi\) | |||||||
\(860\) | 14.1640 | 0.482990 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.34919 | 0.0800136 | ||||||||
\(863\) | −29.1925 | −0.993726 | −0.496863 | − | 0.867829i | \(-0.665515\pi\) | ||||
−0.496863 | + | 0.867829i | \(0.665515\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.2230 | −0.415595 | ||||||||
\(866\) | −45.2313 | −1.53702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −23.6979 | −0.804360 | ||||||||
\(869\) | 14.7016 | 0.498717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.50205 | 0.0847789 | ||||||||
\(872\) | −2.71105 | −0.0918078 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.1783 | 0.378110 | ||||||||
\(875\) | −33.5648 | −1.13470 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.8509 | 1.10930 | 0.554649 | − | 0.832085i | \(-0.312853\pi\) | ||||
0.554649 | + | 0.832085i | \(0.312853\pi\) | |||||||
\(878\) | 64.5502 | 2.17846 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.88625 | 0.232135 | ||||||||
\(881\) | −36.5828 | −1.23251 | −0.616254 | − | 0.787548i | \(-0.711350\pi\) | ||||
−0.616254 | + | 0.787548i | \(0.711350\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.2412 | 0.984045 | 0.492022 | − | 0.870583i | \(-0.336258\pi\) | ||||
0.492022 | + | 0.870583i | \(0.336258\pi\) | |||||||
\(884\) | −12.1523 | −0.408727 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.8250 | 0.699628 | ||||||||
\(887\) | −34.0633 | −1.14373 | −0.571866 | − | 0.820347i | \(-0.693780\pi\) | ||||
−0.571866 | + | 0.820347i | \(0.693780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.95543 | 0.132661 | ||||||||
\(890\) | −14.7104 | −0.493095 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.6244 | −0.523142 | ||||||||
\(893\) | −5.67411 | −0.189877 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.10159 | 0.103675 | ||||||||
\(896\) | −32.9607 | −1.10114 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.77702 | 0.326263 | ||||||||
\(899\) | 36.6113 | 1.22106 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.1522 | −0.638052 | ||||||||
\(902\) | 17.3157 | 0.576548 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.4415 | −0.613354 | ||||||||
\(905\) | 4.74590 | 0.157759 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.07580 | 0.301357 | 0.150679 | − | 0.988583i | \(-0.451854\pi\) | ||||
0.150679 | + | 0.988583i | \(0.451854\pi\) | |||||||
\(908\) | 0.607307 | 0.0201542 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.0696 | 0.466403 | ||||||||
\(911\) | 31.1996 | 1.03369 | 0.516845 | − | 0.856079i | \(-0.327106\pi\) | ||||
0.516845 | + | 0.856079i | \(0.327106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.37220 | −0.177794 | ||||||||
\(914\) | −0.731293 | −0.0241890 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.07332 | 0.101545 | ||||||||
\(917\) | 13.8047 | 0.455872 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.8654 | −1.77686 | −0.888429 | − | 0.459015i | \(-0.848202\pi\) | ||||
−0.888429 | + | 0.459015i | \(0.848202\pi\) | |||||||
\(920\) | 4.02385 | 0.132662 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.2647 | −1.19431 | ||||||||
\(923\) | 27.5931 | 0.908237 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.4366 | 0.376032 | ||||||||
\(926\) | −53.0990 | −1.74494 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30.9738 | −1.01676 | ||||||||
\(929\) | −3.87844 | −0.127248 | −0.0636238 | − | 0.997974i | \(-0.520266\pi\) | ||||
−0.0636238 | + | 0.997974i | \(0.520266\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.54813 | 0.214606 | ||||||||
\(932\) | −31.0724 | −1.01781 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.6830 | −0.513162 | ||||||||
\(935\) | 7.65872 | 0.250467 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.9089 | 0.977083 | 0.488541 | − | 0.872541i | \(-0.337529\pi\) | ||||
0.488541 | + | 0.872541i | \(0.337529\pi\) | |||||||
\(938\) | −6.97514 | −0.227747 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.75924 | 0.0899963 | ||||||||
\(941\) | 31.0364 | 1.01176 | 0.505878 | − | 0.862605i | \(-0.331169\pi\) | ||||
0.505878 | + | 0.862605i | \(0.331169\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.7985 | 0.612164 | ||||||||
\(944\) | 69.6565 | 2.26712 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.8096 | −0.514014 | ||||||||
\(947\) | −24.5563 | −0.797974 | −0.398987 | − | 0.916957i | \(-0.630638\pi\) | ||||
−0.398987 | + | 0.916957i | \(0.630638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2740 | 0.333508 | ||||||||
\(950\) | −17.9062 | −0.580955 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.0780 | −0.812783 | ||||||||
\(953\) | 16.9959 | 0.550551 | 0.275276 | − | 0.961365i | \(-0.411231\pi\) | ||||
0.275276 | + | 0.961365i | \(0.411231\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.2769 | −0.494349 | ||||||||
\(956\) | 14.3120 | 0.462885 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.1112 | −0.778998 | ||||||||
\(959\) | −5.79451 | −0.187114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.2286 | 0.523502 | ||||||||
\(962\) | −12.5608 | −0.404977 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.66866 | −0.311407 | ||||||||
\(965\) | 14.9419 | 0.480996 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.6372 | −0.792278 | −0.396139 | − | 0.918191i | \(-0.629650\pi\) | ||||
−0.396139 | + | 0.918191i | \(0.629650\pi\) | |||||||
\(968\) | −1.50973 | −0.0485247 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −45.4799 | −1.46027 | ||||||||
\(971\) | −23.2628 | −0.746539 | −0.373270 | − | 0.927723i | \(-0.621763\pi\) | ||||
−0.373270 | + | 0.927723i | \(0.621763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.57417 | −0.0504656 | ||||||||
\(974\) | −7.86656 | −0.252061 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.97772 | 0.159333 | ||||||||
\(977\) | −3.96648 | −0.126899 | −0.0634494 | − | 0.997985i | \(-0.520210\pi\) | ||||
−0.0634494 | + | 0.997985i | \(0.520210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.99196 | 0.191504 | ||||||||
\(980\) | −3.18426 | −0.101717 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.0790 | −0.672657 | ||||||||
\(983\) | −28.3662 | −0.904742 | −0.452371 | − | 0.891830i | \(-0.649422\pi\) | ||||
−0.452371 | + | 0.891830i | \(0.649422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.68468 | −0.117404 | ||||||||
\(986\) | −52.3385 | −1.66680 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.17689 | 0.228327 | ||||||||
\(989\) | −17.1635 | −0.545767 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.0031 | 1.77900 | 0.889499 | − | 0.456937i | \(-0.151053\pi\) | ||||
0.889499 | + | 0.456937i | \(0.151053\pi\) | |||||||
\(992\) | −39.9561 | −1.26861 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −76.9231 | −2.43985 | ||||||||
\(995\) | 10.3762 | 0.328947 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.2007 | 0.354729 | 0.177365 | − | 0.984145i | \(-0.443243\pi\) | ||||
0.177365 | + | 0.984145i | \(0.443243\pi\) | |||||||
\(998\) | −29.8876 | −0.946076 | ||||||||
\(999\) | 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 | 6039.2.a.o.1.19 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.n.1.7 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.7 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.o.1.19 | yes | 25 | 1.1 | even | 1 | trivial |