Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26259 | 1.59989 | 0.799946 | − | 0.600072i | \(-0.204862\pi\) | ||||
0.799946 | + | 0.600072i | \(0.204862\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.11931 | 1.55965 | ||||||||
\(5\) | −3.51535 | −1.57211 | −0.786056 | − | 0.618155i | \(-0.787880\pi\) | ||||
−0.786056 | + | 0.618155i | \(0.787880\pi\) | |||||||
\(6\) | −2.26259 | −0.923698 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.53253 | 0.895383 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −7.95379 | −2.51521 | ||||||||
\(11\) | −3.79341 | −1.14376 | −0.571878 | − | 0.820339i | \(-0.693785\pi\) | ||||
−0.571878 | + | 0.820339i | \(0.693785\pi\) | |||||||
\(12\) | −3.11931 | −0.900466 | ||||||||
\(13\) | −1.46159 | −0.405373 | −0.202687 | − | 0.979244i | \(-0.564967\pi\) | ||||
−0.202687 | + | 0.979244i | \(0.564967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.51535 | 0.907659 | ||||||||
\(16\) | −0.508546 | −0.127136 | ||||||||
\(17\) | −6.67693 | −1.61939 | −0.809697 | − | 0.586848i | \(-0.800369\pi\) | ||||
−0.809697 | + | 0.586848i | \(0.800369\pi\) | |||||||
\(18\) | 2.26259 | 0.533297 | ||||||||
\(19\) | 2.27770 | 0.522540 | 0.261270 | − | 0.965266i | \(-0.415859\pi\) | ||||
0.261270 | + | 0.965266i | \(0.415859\pi\) | |||||||
\(20\) | −10.9654 | −2.45195 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.58292 | −1.82988 | ||||||||
\(23\) | 8.49274 | 1.77086 | 0.885429 | − | 0.464774i | \(-0.153864\pi\) | ||||
0.885429 | + | 0.464774i | \(0.153864\pi\) | |||||||
\(24\) | −2.53253 | −0.516950 | ||||||||
\(25\) | 7.35768 | 1.47154 | ||||||||
\(26\) | −3.30698 | −0.648553 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.04769 | −0.937332 | −0.468666 | − | 0.883376i | \(-0.655265\pi\) | ||||
−0.468666 | + | 0.883376i | \(0.655265\pi\) | |||||||
\(30\) | 7.95379 | 1.45216 | ||||||||
\(31\) | 1.44795 | 0.260059 | 0.130029 | − | 0.991510i | \(-0.458493\pi\) | ||||
0.130029 | + | 0.991510i | \(0.458493\pi\) | |||||||
\(32\) | −6.21568 | −1.09879 | ||||||||
\(33\) | 3.79341 | 0.660348 | ||||||||
\(34\) | −15.1071 | −2.59085 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.11931 | 0.519884 | ||||||||
\(37\) | −0.996436 | −0.163813 | −0.0819066 | − | 0.996640i | \(-0.526101\pi\) | ||||
−0.0819066 | + | 0.996640i | \(0.526101\pi\) | |||||||
\(38\) | 5.15350 | 0.836008 | ||||||||
\(39\) | 1.46159 | 0.234042 | ||||||||
\(40\) | −8.90272 | −1.40764 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8446 | 1.65379 | 0.826893 | − | 0.562359i | \(-0.190106\pi\) | ||||
0.826893 | + | 0.562359i | \(0.190106\pi\) | |||||||
\(44\) | −11.8328 | −1.78386 | ||||||||
\(45\) | −3.51535 | −0.524037 | ||||||||
\(46\) | 19.2156 | 2.83318 | ||||||||
\(47\) | 0.748913 | 0.109240 | 0.0546201 | − | 0.998507i | \(-0.482605\pi\) | ||||
0.0546201 | + | 0.998507i | \(0.482605\pi\) | |||||||
\(48\) | 0.508546 | 0.0734023 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 16.6474 | 2.35430 | ||||||||
\(51\) | 6.67693 | 0.934958 | ||||||||
\(52\) | −4.55916 | −0.632241 | ||||||||
\(53\) | 9.47305 | 1.30122 | 0.650611 | − | 0.759411i | \(-0.274513\pi\) | ||||
0.650611 | + | 0.759411i | \(0.274513\pi\) | |||||||
\(54\) | −2.26259 | −0.307899 | ||||||||
\(55\) | 13.3352 | 1.79811 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.27770 | −0.301689 | ||||||||
\(58\) | −11.4208 | −1.49963 | ||||||||
\(59\) | 9.62699 | 1.25333 | 0.626664 | − | 0.779290i | \(-0.284420\pi\) | ||||
0.626664 | + | 0.779290i | \(0.284420\pi\) | |||||||
\(60\) | 10.9654 | 1.41563 | ||||||||
\(61\) | 13.5721 | 1.73773 | 0.868867 | − | 0.495046i | \(-0.164849\pi\) | ||||
0.868867 | + | 0.495046i | \(0.164849\pi\) | |||||||
\(62\) | 3.27611 | 0.416066 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0464 | −1.63080 | ||||||||
\(65\) | 5.13801 | 0.637292 | ||||||||
\(66\) | 8.58292 | 1.05648 | ||||||||
\(67\) | 8.40378 | 1.02668 | 0.513342 | − | 0.858184i | \(-0.328407\pi\) | ||||
0.513342 | + | 0.858184i | \(0.328407\pi\) | |||||||
\(68\) | −20.8274 | −2.52569 | ||||||||
\(69\) | −8.49274 | −1.02241 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.50992 | −0.772585 | −0.386293 | − | 0.922376i | \(-0.626245\pi\) | ||||
−0.386293 | + | 0.922376i | \(0.626245\pi\) | |||||||
\(72\) | 2.53253 | 0.298461 | ||||||||
\(73\) | 2.28092 | 0.266962 | 0.133481 | − | 0.991051i | \(-0.457385\pi\) | ||||
0.133481 | + | 0.991051i | \(0.457385\pi\) | |||||||
\(74\) | −2.25452 | −0.262083 | ||||||||
\(75\) | −7.35768 | −0.849592 | ||||||||
\(76\) | 7.10484 | 0.814982 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.30698 | 0.374442 | ||||||||
\(79\) | −1.03517 | −0.116466 | −0.0582331 | − | 0.998303i | \(-0.518547\pi\) | ||||
−0.0582331 | + | 0.998303i | \(0.518547\pi\) | |||||||
\(80\) | 1.78772 | 0.199873 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.26259 | 0.249861 | ||||||||
\(83\) | 1.84818 | 0.202865 | 0.101432 | − | 0.994842i | \(-0.467657\pi\) | ||||
0.101432 | + | 0.994842i | \(0.467657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.4718 | 2.54587 | ||||||||
\(86\) | 24.5369 | 2.64588 | ||||||||
\(87\) | 5.04769 | 0.541169 | ||||||||
\(88\) | −9.60691 | −1.02410 | ||||||||
\(89\) | 1.76420 | 0.187005 | 0.0935023 | − | 0.995619i | \(-0.470194\pi\) | ||||
0.0935023 | + | 0.995619i | \(0.470194\pi\) | |||||||
\(90\) | −7.95379 | −0.838403 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 26.4914 | 2.76192 | ||||||||
\(93\) | −1.44795 | −0.150145 | ||||||||
\(94\) | 1.69448 | 0.174773 | ||||||||
\(95\) | −8.00692 | −0.821492 | ||||||||
\(96\) | 6.21568 | 0.634385 | ||||||||
\(97\) | −17.4604 | −1.77284 | −0.886419 | − | 0.462883i | \(-0.846815\pi\) | ||||
−0.886419 | + | 0.462883i | \(0.846815\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.79341 | −0.381252 | ||||||||
\(100\) | 22.9509 | 2.29509 | ||||||||
\(101\) | −19.4496 | −1.93531 | −0.967653 | − | 0.252287i | \(-0.918817\pi\) | ||||
−0.967653 | + | 0.252287i | \(0.918817\pi\) | |||||||
\(102\) | 15.1071 | 1.49583 | ||||||||
\(103\) | 4.41489 | 0.435012 | 0.217506 | − | 0.976059i | \(-0.430208\pi\) | ||||
0.217506 | + | 0.976059i | \(0.430208\pi\) | |||||||
\(104\) | −3.70152 | −0.362964 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.4336 | 2.08182 | ||||||||
\(107\) | −15.1587 | −1.46544 | −0.732721 | − | 0.680529i | \(-0.761750\pi\) | ||||
−0.732721 | + | 0.680529i | \(0.761750\pi\) | |||||||
\(108\) | −3.11931 | −0.300155 | ||||||||
\(109\) | −9.37929 | −0.898374 | −0.449187 | − | 0.893438i | \(-0.648286\pi\) | ||||
−0.449187 | + | 0.893438i | \(0.648286\pi\) | |||||||
\(110\) | 30.1720 | 2.87678 | ||||||||
\(111\) | 0.996436 | 0.0945775 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.40865 | 0.132515 | 0.0662574 | − | 0.997803i | \(-0.478894\pi\) | ||||
0.0662574 | + | 0.997803i | \(0.478894\pi\) | |||||||
\(114\) | −5.15350 | −0.482669 | ||||||||
\(115\) | −29.8549 | −2.78399 | ||||||||
\(116\) | −15.7453 | −1.46191 | ||||||||
\(117\) | −1.46159 | −0.135124 | ||||||||
\(118\) | 21.7819 | 2.00519 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.90272 | 0.812703 | ||||||||
\(121\) | 3.38994 | 0.308177 | ||||||||
\(122\) | 30.7081 | 2.78018 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 4.51659 | 0.405601 | ||||||||
\(125\) | −8.28808 | −0.741309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.83967 | −0.251980 | −0.125990 | − | 0.992032i | \(-0.540211\pi\) | ||||
−0.125990 | + | 0.992032i | \(0.540211\pi\) | |||||||
\(128\) | −17.0874 | −1.51032 | ||||||||
\(129\) | −10.8446 | −0.954814 | ||||||||
\(130\) | 11.6252 | 1.01960 | ||||||||
\(131\) | 14.7028 | 1.28459 | 0.642295 | − | 0.766458i | \(-0.277982\pi\) | ||||
0.642295 | + | 0.766458i | \(0.277982\pi\) | |||||||
\(132\) | 11.8328 | 1.02991 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 19.0143 | 1.64258 | ||||||||
\(135\) | 3.51535 | 0.302553 | ||||||||
\(136\) | −16.9095 | −1.44998 | ||||||||
\(137\) | −9.39271 | −0.802474 | −0.401237 | − | 0.915974i | \(-0.631420\pi\) | ||||
−0.401237 | + | 0.915974i | \(0.631420\pi\) | |||||||
\(138\) | −19.2156 | −1.63574 | ||||||||
\(139\) | 11.1571 | 0.946333 | 0.473166 | − | 0.880973i | \(-0.343111\pi\) | ||||
0.473166 | + | 0.880973i | \(0.343111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.748913 | −0.0630699 | ||||||||
\(142\) | −14.7293 | −1.23605 | ||||||||
\(143\) | 5.54442 | 0.463648 | ||||||||
\(144\) | −0.508546 | −0.0423788 | ||||||||
\(145\) | 17.7444 | 1.47359 | ||||||||
\(146\) | 5.16078 | 0.427109 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.10819 | −0.255492 | ||||||||
\(149\) | 0.818797 | 0.0670785 | 0.0335392 | − | 0.999437i | \(-0.489322\pi\) | ||||
0.0335392 | + | 0.999437i | \(0.489322\pi\) | |||||||
\(150\) | −16.6474 | −1.35926 | ||||||||
\(151\) | 20.6578 | 1.68111 | 0.840554 | − | 0.541728i | \(-0.182230\pi\) | ||||
0.840554 | + | 0.541728i | \(0.182230\pi\) | |||||||
\(152\) | 5.76834 | 0.467874 | ||||||||
\(153\) | −6.67693 | −0.539798 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.09004 | −0.408842 | ||||||||
\(156\) | 4.55916 | 0.365025 | ||||||||
\(157\) | 3.57661 | 0.285445 | 0.142722 | − | 0.989763i | \(-0.454414\pi\) | ||||
0.142722 | + | 0.989763i | \(0.454414\pi\) | |||||||
\(158\) | −2.34217 | −0.186333 | ||||||||
\(159\) | −9.47305 | −0.751261 | ||||||||
\(160\) | 21.8503 | 1.72742 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.26259 | 0.177766 | ||||||||
\(163\) | 12.6245 | 0.988830 | 0.494415 | − | 0.869226i | \(-0.335382\pi\) | ||||
0.494415 | + | 0.869226i | \(0.335382\pi\) | |||||||
\(164\) | 3.11931 | 0.243577 | ||||||||
\(165\) | −13.3352 | −1.03814 | ||||||||
\(166\) | 4.18168 | 0.324561 | ||||||||
\(167\) | −4.48125 | −0.346770 | −0.173385 | − | 0.984854i | \(-0.555470\pi\) | ||||
−0.173385 | + | 0.984854i | \(0.555470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8637 | −0.835673 | ||||||||
\(170\) | 53.1069 | 4.07311 | ||||||||
\(171\) | 2.27770 | 0.174180 | ||||||||
\(172\) | 33.8276 | 2.57933 | ||||||||
\(173\) | 22.5618 | 1.71534 | 0.857670 | − | 0.514201i | \(-0.171911\pi\) | ||||
0.857670 | + | 0.514201i | \(0.171911\pi\) | |||||||
\(174\) | 11.4208 | 0.865811 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.92912 | 0.145413 | ||||||||
\(177\) | −9.62699 | −0.723609 | ||||||||
\(178\) | 3.99165 | 0.299187 | ||||||||
\(179\) | 14.9892 | 1.12035 | 0.560173 | − | 0.828375i | \(-0.310735\pi\) | ||||
0.560173 | + | 0.828375i | \(0.310735\pi\) | |||||||
\(180\) | −10.9654 | −0.817316 | ||||||||
\(181\) | −1.00879 | −0.0749830 | −0.0374915 | − | 0.999297i | \(-0.511937\pi\) | ||||
−0.0374915 | + | 0.999297i | \(0.511937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.5721 | −1.00328 | ||||||||
\(184\) | 21.5081 | 1.58560 | ||||||||
\(185\) | 3.50282 | 0.257533 | ||||||||
\(186\) | −3.27611 | −0.240216 | ||||||||
\(187\) | 25.3283 | 1.85219 | ||||||||
\(188\) | 2.33609 | 0.170377 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.1164 | −1.31430 | ||||||||
\(191\) | 20.0147 | 1.44821 | 0.724106 | − | 0.689689i | \(-0.242253\pi\) | ||||
0.724106 | + | 0.689689i | \(0.242253\pi\) | |||||||
\(192\) | 13.0464 | 0.941546 | ||||||||
\(193\) | 3.47028 | 0.249796 | 0.124898 | − | 0.992170i | \(-0.460140\pi\) | ||||
0.124898 | + | 0.992170i | \(0.460140\pi\) | |||||||
\(194\) | −39.5058 | −2.83635 | ||||||||
\(195\) | −5.13801 | −0.367941 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6030 | 0.826681 | 0.413340 | − | 0.910577i | \(-0.364362\pi\) | ||||
0.413340 | + | 0.910577i | \(0.364362\pi\) | |||||||
\(198\) | −8.58292 | −0.609962 | ||||||||
\(199\) | 7.82824 | 0.554929 | 0.277464 | − | 0.960736i | \(-0.410506\pi\) | ||||
0.277464 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(200\) | 18.6335 | 1.31759 | ||||||||
\(201\) | −8.40378 | −0.592757 | ||||||||
\(202\) | −44.0064 | −3.09628 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 20.8274 | 1.45821 | ||||||||
\(205\) | −3.51535 | −0.245523 | ||||||||
\(206\) | 9.98908 | 0.695972 | ||||||||
\(207\) | 8.49274 | 0.590286 | ||||||||
\(208\) | 0.743287 | 0.0515377 | ||||||||
\(209\) | −8.64025 | −0.597659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.767110 | −0.0528100 | −0.0264050 | − | 0.999651i | \(-0.508406\pi\) | ||||
−0.0264050 | + | 0.999651i | \(0.508406\pi\) | |||||||
\(212\) | 29.5493 | 2.02946 | ||||||||
\(213\) | 6.50992 | 0.446052 | ||||||||
\(214\) | −34.2978 | −2.34455 | ||||||||
\(215\) | −38.1226 | −2.59994 | ||||||||
\(216\) | −2.53253 | −0.172317 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −21.2215 | −1.43730 | ||||||||
\(219\) | −2.28092 | −0.154130 | ||||||||
\(220\) | 41.5964 | 2.80443 | ||||||||
\(221\) | 9.75896 | 0.656459 | ||||||||
\(222\) | 2.25452 | 0.151314 | ||||||||
\(223\) | 5.48934 | 0.367594 | 0.183797 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183797 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.35768 | 0.490512 | ||||||||
\(226\) | 3.18720 | 0.212009 | ||||||||
\(227\) | 24.0590 | 1.59685 | 0.798426 | − | 0.602093i | \(-0.205666\pi\) | ||||
0.798426 | + | 0.602093i | \(0.205666\pi\) | |||||||
\(228\) | −7.10484 | −0.470530 | ||||||||
\(229\) | 10.3429 | 0.683476 | 0.341738 | − | 0.939795i | \(-0.388985\pi\) | ||||
0.341738 | + | 0.939795i | \(0.388985\pi\) | |||||||
\(230\) | −67.5495 | −4.45408 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.7834 | −0.839271 | ||||||||
\(233\) | −17.3807 | −1.13865 | −0.569325 | − | 0.822112i | \(-0.692795\pi\) | ||||
−0.569325 | + | 0.822112i | \(0.692795\pi\) | |||||||
\(234\) | −3.30698 | −0.216184 | ||||||||
\(235\) | −2.63269 | −0.171738 | ||||||||
\(236\) | 30.0295 | 1.95476 | ||||||||
\(237\) | 1.03517 | 0.0672418 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.43783 | −0.481113 | −0.240557 | − | 0.970635i | \(-0.577330\pi\) | ||||
−0.240557 | + | 0.970635i | \(0.577330\pi\) | |||||||
\(240\) | −1.78772 | −0.115397 | ||||||||
\(241\) | 7.82930 | 0.504329 | 0.252165 | − | 0.967684i | \(-0.418858\pi\) | ||||
0.252165 | + | 0.967684i | \(0.418858\pi\) | |||||||
\(242\) | 7.67005 | 0.493049 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 42.3356 | 2.71026 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.26259 | −0.144257 | ||||||||
\(247\) | −3.32907 | −0.211824 | ||||||||
\(248\) | 3.66696 | 0.232852 | ||||||||
\(249\) | −1.84818 | −0.117124 | ||||||||
\(250\) | −18.7525 | −1.18601 | ||||||||
\(251\) | 11.4230 | 0.721012 | 0.360506 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360506 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.2164 | −2.02543 | ||||||||
\(254\) | −6.42500 | −0.403141 | ||||||||
\(255\) | −23.4718 | −1.46986 | ||||||||
\(256\) | −12.5688 | −0.785548 | ||||||||
\(257\) | 14.8155 | 0.924168 | 0.462084 | − | 0.886836i | \(-0.347102\pi\) | ||||
0.462084 | + | 0.886836i | \(0.347102\pi\) | |||||||
\(258\) | −24.5369 | −1.52760 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.0270 | 0.993954 | ||||||||
\(261\) | −5.04769 | −0.312444 | ||||||||
\(262\) | 33.2664 | 2.05520 | ||||||||
\(263\) | −21.3829 | −1.31853 | −0.659264 | − | 0.751912i | \(-0.729132\pi\) | ||||
−0.659264 | + | 0.751912i | \(0.729132\pi\) | |||||||
\(264\) | 9.60691 | 0.591264 | ||||||||
\(265\) | −33.3011 | −2.04567 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.76420 | −0.107967 | ||||||||
\(268\) | 26.2139 | 1.60127 | ||||||||
\(269\) | −29.0758 | −1.77278 | −0.886391 | − | 0.462937i | \(-0.846796\pi\) | ||||
−0.886391 | + | 0.462937i | \(0.846796\pi\) | |||||||
\(270\) | 7.95379 | 0.484052 | ||||||||
\(271\) | 21.8299 | 1.32607 | 0.663035 | − | 0.748588i | \(-0.269268\pi\) | ||||
0.663035 | + | 0.748588i | \(0.269268\pi\) | |||||||
\(272\) | 3.39553 | 0.205884 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.2518 | −1.28387 | ||||||||
\(275\) | −27.9107 | −1.68308 | ||||||||
\(276\) | −26.4914 | −1.59460 | ||||||||
\(277\) | −26.3880 | −1.58550 | −0.792751 | − | 0.609546i | \(-0.791352\pi\) | ||||
−0.792751 | + | 0.609546i | \(0.791352\pi\) | |||||||
\(278\) | 25.2439 | 1.51403 | ||||||||
\(279\) | 1.44795 | 0.0866863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.8668 | 0.648256 | 0.324128 | − | 0.946013i | \(-0.394929\pi\) | ||||
0.324128 | + | 0.946013i | \(0.394929\pi\) | |||||||
\(282\) | −1.69448 | −0.100905 | ||||||||
\(283\) | 30.8486 | 1.83376 | 0.916879 | − | 0.399165i | \(-0.130700\pi\) | ||||
0.916879 | + | 0.399165i | \(0.130700\pi\) | |||||||
\(284\) | −20.3064 | −1.20496 | ||||||||
\(285\) | 8.00692 | 0.474289 | ||||||||
\(286\) | 12.5447 | 0.741786 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.21568 | −0.366263 | ||||||||
\(289\) | 27.5814 | 1.62244 | ||||||||
\(290\) | 40.1482 | 2.35759 | ||||||||
\(291\) | 17.4604 | 1.02355 | ||||||||
\(292\) | 7.11489 | 0.416367 | ||||||||
\(293\) | −10.1999 | −0.595885 | −0.297942 | − | 0.954584i | \(-0.596300\pi\) | ||||
−0.297942 | + | 0.954584i | \(0.596300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.8422 | −1.97037 | ||||||||
\(296\) | −2.52350 | −0.146676 | ||||||||
\(297\) | 3.79341 | 0.220116 | ||||||||
\(298\) | 1.85260 | 0.107318 | ||||||||
\(299\) | −12.4129 | −0.717858 | ||||||||
\(300\) | −22.9509 | −1.32507 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 46.7401 | 2.68959 | ||||||||
\(303\) | 19.4496 | 1.11735 | ||||||||
\(304\) | −1.15832 | −0.0664340 | ||||||||
\(305\) | −47.7108 | −2.73191 | ||||||||
\(306\) | −15.1071 | −0.863618 | ||||||||
\(307\) | −22.0097 | −1.25616 | −0.628081 | − | 0.778148i | \(-0.716159\pi\) | ||||
−0.628081 | + | 0.778148i | \(0.716159\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.41489 | −0.251154 | ||||||||
\(310\) | −11.5167 | −0.654102 | ||||||||
\(311\) | 0.628039 | 0.0356128 | 0.0178064 | − | 0.999841i | \(-0.494332\pi\) | ||||
0.0178064 | + | 0.999841i | \(0.494332\pi\) | |||||||
\(312\) | 3.70152 | 0.209557 | ||||||||
\(313\) | −17.9356 | −1.01378 | −0.506891 | − | 0.862010i | \(-0.669205\pi\) | ||||
−0.506891 | + | 0.862010i | \(0.669205\pi\) | |||||||
\(314\) | 8.09240 | 0.456681 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.22902 | −0.181647 | ||||||||
\(317\) | 15.2704 | 0.857668 | 0.428834 | − | 0.903383i | \(-0.358924\pi\) | ||||
0.428834 | + | 0.903383i | \(0.358924\pi\) | |||||||
\(318\) | −21.4336 | −1.20194 | ||||||||
\(319\) | 19.1479 | 1.07208 | ||||||||
\(320\) | 45.8628 | 2.56381 | ||||||||
\(321\) | 15.1587 | 0.846074 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.2081 | −0.846199 | ||||||||
\(324\) | 3.11931 | 0.173295 | ||||||||
\(325\) | −10.7539 | −0.596521 | ||||||||
\(326\) | 28.5641 | 1.58202 | ||||||||
\(327\) | 9.37929 | 0.518676 | ||||||||
\(328\) | 2.53253 | 0.139835 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −30.1720 | −1.66091 | ||||||||
\(331\) | 30.8713 | 1.69684 | 0.848421 | − | 0.529322i | \(-0.177554\pi\) | ||||
0.848421 | + | 0.529322i | \(0.177554\pi\) | |||||||
\(332\) | 5.76505 | 0.316398 | ||||||||
\(333\) | −0.996436 | −0.0546044 | ||||||||
\(334\) | −10.1392 | −0.554794 | ||||||||
\(335\) | −29.5422 | −1.61406 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7318 | −0.748017 | −0.374008 | − | 0.927425i | \(-0.622017\pi\) | ||||
−0.374008 | + | 0.927425i | \(0.622017\pi\) | |||||||
\(338\) | −24.5802 | −1.33699 | ||||||||
\(339\) | −1.40865 | −0.0765074 | ||||||||
\(340\) | 73.2156 | 3.97067 | ||||||||
\(341\) | −5.49265 | −0.297444 | ||||||||
\(342\) | 5.15350 | 0.278669 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 27.4642 | 1.48077 | ||||||||
\(345\) | 29.8549 | 1.60734 | ||||||||
\(346\) | 51.0480 | 2.74436 | ||||||||
\(347\) | −16.9673 | −0.910854 | −0.455427 | − | 0.890273i | \(-0.650513\pi\) | ||||
−0.455427 | + | 0.890273i | \(0.650513\pi\) | |||||||
\(348\) | 15.7453 | 0.844035 | ||||||||
\(349\) | −5.94969 | −0.318479 | −0.159240 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159240 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.46159 | 0.0780141 | ||||||||
\(352\) | 23.5786 | 1.25674 | ||||||||
\(353\) | 5.44568 | 0.289844 | 0.144922 | − | 0.989443i | \(-0.453707\pi\) | ||||
0.144922 | + | 0.989443i | \(0.453707\pi\) | |||||||
\(354\) | −21.7819 | −1.15770 | ||||||||
\(355\) | 22.8846 | 1.21459 | ||||||||
\(356\) | 5.50307 | 0.291662 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 33.9144 | 1.79243 | ||||||||
\(359\) | −23.9295 | −1.26295 | −0.631476 | − | 0.775396i | \(-0.717550\pi\) | ||||
−0.631476 | + | 0.775396i | \(0.717550\pi\) | |||||||
\(360\) | −8.90272 | −0.469214 | ||||||||
\(361\) | −13.8121 | −0.726951 | ||||||||
\(362\) | −2.28248 | −0.119965 | ||||||||
\(363\) | −3.38994 | −0.177926 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.01823 | −0.419694 | ||||||||
\(366\) | −30.7081 | −1.60514 | ||||||||
\(367\) | 3.62240 | 0.189088 | 0.0945438 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945438 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(368\) | −4.31895 | −0.225141 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 7.92544 | 0.412024 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.51659 | −0.234174 | ||||||||
\(373\) | 30.5324 | 1.58091 | 0.790455 | − | 0.612521i | \(-0.209844\pi\) | ||||
0.790455 | + | 0.612521i | \(0.209844\pi\) | |||||||
\(374\) | 57.3076 | 2.96330 | ||||||||
\(375\) | 8.28808 | 0.427995 | ||||||||
\(376\) | 1.89664 | 0.0978119 | ||||||||
\(377\) | 7.37766 | 0.379969 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5620 | −0.748002 | −0.374001 | − | 0.927428i | \(-0.622014\pi\) | ||||
−0.374001 | + | 0.927428i | \(0.622014\pi\) | |||||||
\(380\) | −24.9760 | −1.28124 | ||||||||
\(381\) | 2.83967 | 0.145481 | ||||||||
\(382\) | 45.2850 | 2.31698 | ||||||||
\(383\) | 4.84686 | 0.247663 | 0.123831 | − | 0.992303i | \(-0.460482\pi\) | ||||
0.123831 | + | 0.992303i | \(0.460482\pi\) | |||||||
\(384\) | 17.0874 | 0.871985 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.85181 | 0.399646 | ||||||||
\(387\) | 10.8446 | 0.551262 | ||||||||
\(388\) | −54.4644 | −2.76501 | ||||||||
\(389\) | −0.685686 | −0.0347657 | −0.0173828 | − | 0.999849i | \(-0.505533\pi\) | ||||
−0.0173828 | + | 0.999849i | \(0.505533\pi\) | |||||||
\(390\) | −11.6252 | −0.588665 | ||||||||
\(391\) | −56.7054 | −2.86772 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.7028 | −0.741658 | ||||||||
\(394\) | 26.2529 | 1.32260 | ||||||||
\(395\) | 3.63900 | 0.183098 | ||||||||
\(396\) | −11.8328 | −0.594620 | ||||||||
\(397\) | −0.404290 | −0.0202907 | −0.0101454 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101454 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(398\) | 17.7121 | 0.887826 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.74172 | −0.187086 | ||||||||
\(401\) | −28.1364 | −1.40506 | −0.702532 | − | 0.711652i | \(-0.747947\pi\) | ||||
−0.702532 | + | 0.711652i | \(0.747947\pi\) | |||||||
\(402\) | −19.0143 | −0.948347 | ||||||||
\(403\) | −2.11631 | −0.105421 | ||||||||
\(404\) | −60.6692 | −3.01840 | ||||||||
\(405\) | −3.51535 | −0.174679 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.77989 | 0.187362 | ||||||||
\(408\) | 16.9095 | 0.837145 | ||||||||
\(409\) | 16.9935 | 0.840273 | 0.420137 | − | 0.907461i | \(-0.361982\pi\) | ||||
0.420137 | + | 0.907461i | \(0.361982\pi\) | |||||||
\(410\) | −7.95379 | −0.392810 | ||||||||
\(411\) | 9.39271 | 0.463308 | ||||||||
\(412\) | 13.7714 | 0.678468 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 19.2156 | 0.944394 | ||||||||
\(415\) | −6.49702 | −0.318926 | ||||||||
\(416\) | 9.08480 | 0.445419 | ||||||||
\(417\) | −11.1571 | −0.546366 | ||||||||
\(418\) | −19.5493 | −0.956189 | ||||||||
\(419\) | −10.1348 | −0.495116 | −0.247558 | − | 0.968873i | \(-0.579628\pi\) | ||||
−0.247558 | + | 0.968873i | \(0.579628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.95651 | 0.387777 | 0.193888 | − | 0.981024i | \(-0.437890\pi\) | ||||
0.193888 | + | 0.981024i | \(0.437890\pi\) | |||||||
\(422\) | −1.73565 | −0.0844903 | ||||||||
\(423\) | 0.748913 | 0.0364134 | ||||||||
\(424\) | 23.9907 | 1.16509 | ||||||||
\(425\) | −49.1268 | −2.38300 | ||||||||
\(426\) | 14.7293 | 0.713635 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −47.2845 | −2.28558 | ||||||||
\(429\) | −5.54442 | −0.267687 | ||||||||
\(430\) | −86.2557 | −4.15962 | ||||||||
\(431\) | −27.1478 | −1.30766 | −0.653832 | − | 0.756640i | \(-0.726840\pi\) | ||||
−0.653832 | + | 0.756640i | \(0.726840\pi\) | |||||||
\(432\) | 0.508546 | 0.0244674 | ||||||||
\(433\) | −27.6879 | −1.33060 | −0.665298 | − | 0.746578i | \(-0.731696\pi\) | ||||
−0.665298 | + | 0.746578i | \(0.731696\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.7444 | −0.850778 | ||||||||
\(436\) | −29.2569 | −1.40115 | ||||||||
\(437\) | 19.3439 | 0.925345 | ||||||||
\(438\) | −5.16078 | −0.246592 | ||||||||
\(439\) | 8.75911 | 0.418049 | 0.209025 | − | 0.977910i | \(-0.432971\pi\) | ||||
0.209025 | + | 0.977910i | \(0.432971\pi\) | |||||||
\(440\) | 33.7716 | 1.61000 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.0805 | 1.05026 | ||||||||
\(443\) | −35.5985 | −1.69133 | −0.845667 | − | 0.533711i | \(-0.820797\pi\) | ||||
−0.845667 | + | 0.533711i | \(0.820797\pi\) | |||||||
\(444\) | 3.10819 | 0.147508 | ||||||||
\(445\) | −6.20177 | −0.293992 | ||||||||
\(446\) | 12.4201 | 0.588110 | ||||||||
\(447\) | −0.818797 | −0.0387278 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.3648 | 1.66897 | 0.834484 | − | 0.551032i | \(-0.185766\pi\) | ||||
0.834484 | + | 0.551032i | \(0.185766\pi\) | |||||||
\(450\) | 16.6474 | 0.784766 | ||||||||
\(451\) | −3.79341 | −0.178625 | ||||||||
\(452\) | 4.39401 | 0.206677 | ||||||||
\(453\) | −20.6578 | −0.970588 | ||||||||
\(454\) | 54.4356 | 2.55479 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.76834 | −0.270127 | ||||||||
\(457\) | 19.7650 | 0.924570 | 0.462285 | − | 0.886731i | \(-0.347030\pi\) | ||||
0.462285 | + | 0.886731i | \(0.347030\pi\) | |||||||
\(458\) | 23.4016 | 1.09349 | ||||||||
\(459\) | 6.67693 | 0.311653 | ||||||||
\(460\) | −93.1267 | −4.34205 | ||||||||
\(461\) | −10.7489 | −0.500626 | −0.250313 | − | 0.968165i | \(-0.580534\pi\) | ||||
−0.250313 | + | 0.968165i | \(0.580534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.89539 | 0.134560 | 0.0672801 | − | 0.997734i | \(-0.478568\pi\) | ||||
0.0672801 | + | 0.997734i | \(0.478568\pi\) | |||||||
\(464\) | 2.56698 | 0.119169 | ||||||||
\(465\) | 5.09004 | 0.236045 | ||||||||
\(466\) | −39.3255 | −1.82172 | ||||||||
\(467\) | 5.98144 | 0.276788 | 0.138394 | − | 0.990377i | \(-0.455806\pi\) | ||||
0.138394 | + | 0.990377i | \(0.455806\pi\) | |||||||
\(468\) | −4.55916 | −0.210747 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.95670 | −0.274762 | ||||||||
\(471\) | −3.57661 | −0.164802 | ||||||||
\(472\) | 24.3806 | 1.12221 | ||||||||
\(473\) | −41.1380 | −1.89153 | ||||||||
\(474\) | 2.34217 | 0.107580 | ||||||||
\(475\) | 16.7586 | 0.768937 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.47305 | 0.433741 | ||||||||
\(478\) | −16.8287 | −0.769729 | ||||||||
\(479\) | 15.0728 | 0.688693 | 0.344346 | − | 0.938843i | \(-0.388101\pi\) | ||||
0.344346 | + | 0.938843i | \(0.388101\pi\) | |||||||
\(480\) | −21.8503 | −0.997325 | ||||||||
\(481\) | 1.45638 | 0.0664054 | ||||||||
\(482\) | 17.7145 | 0.806872 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.5743 | 0.480649 | ||||||||
\(485\) | 61.3795 | 2.78710 | ||||||||
\(486\) | −2.26259 | −0.102633 | ||||||||
\(487\) | −26.7979 | −1.21433 | −0.607165 | − | 0.794576i | \(-0.707693\pi\) | ||||
−0.607165 | + | 0.794576i | \(0.707693\pi\) | |||||||
\(488\) | 34.3718 | 1.55594 | ||||||||
\(489\) | −12.6245 | −0.570901 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6716 | 0.662120 | 0.331060 | − | 0.943610i | \(-0.392594\pi\) | ||||
0.331060 | + | 0.943610i | \(0.392594\pi\) | |||||||
\(492\) | −3.11931 | −0.140629 | ||||||||
\(493\) | 33.7031 | 1.51791 | ||||||||
\(494\) | −7.53232 | −0.338895 | ||||||||
\(495\) | 13.3352 | 0.599371 | ||||||||
\(496\) | −0.736347 | −0.0330630 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.18168 | −0.187386 | ||||||||
\(499\) | 33.3116 | 1.49123 | 0.745616 | − | 0.666376i | \(-0.232155\pi\) | ||||
0.745616 | + | 0.666376i | \(0.232155\pi\) | |||||||
\(500\) | −25.8531 | −1.15618 | ||||||||
\(501\) | 4.48125 | 0.200208 | ||||||||
\(502\) | 25.8455 | 1.15354 | ||||||||
\(503\) | 36.2073 | 1.61440 | 0.807201 | − | 0.590277i | \(-0.200981\pi\) | ||||
0.807201 | + | 0.590277i | \(0.200981\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 68.3721 | 3.04252 | ||||||||
\(506\) | −72.8925 | −3.24047 | ||||||||
\(507\) | 10.8637 | 0.482476 | ||||||||
\(508\) | −8.85780 | −0.393001 | ||||||||
\(509\) | −17.9330 | −0.794867 | −0.397433 | − | 0.917631i | \(-0.630099\pi\) | ||||
−0.397433 | + | 0.917631i | \(0.630099\pi\) | |||||||
\(510\) | −53.1069 | −2.35161 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.73677 | 0.253532 | ||||||||
\(513\) | −2.27770 | −0.100563 | ||||||||
\(514\) | 33.5215 | 1.47857 | ||||||||
\(515\) | −15.5199 | −0.683888 | ||||||||
\(516\) | −33.8276 | −1.48918 | ||||||||
\(517\) | −2.84093 | −0.124944 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.5618 | −0.990352 | ||||||||
\(520\) | 13.0121 | 0.570621 | ||||||||
\(521\) | −34.4137 | −1.50769 | −0.753846 | − | 0.657051i | \(-0.771803\pi\) | ||||
−0.753846 | + | 0.657051i | \(0.771803\pi\) | |||||||
\(522\) | −11.4208 | −0.499876 | ||||||||
\(523\) | −1.82322 | −0.0797237 | −0.0398618 | − | 0.999205i | \(-0.512692\pi\) | ||||
−0.0398618 | + | 0.999205i | \(0.512692\pi\) | |||||||
\(524\) | 45.8625 | 2.00351 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −48.3808 | −2.10950 | ||||||||
\(527\) | −9.66784 | −0.421138 | ||||||||
\(528\) | −1.92912 | −0.0839543 | ||||||||
\(529\) | 49.1266 | 2.13594 | ||||||||
\(530\) | −75.3466 | −3.27285 | ||||||||
\(531\) | 9.62699 | 0.417776 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.46159 | −0.0633086 | ||||||||
\(534\) | −3.99165 | −0.172736 | ||||||||
\(535\) | 53.2880 | 2.30384 | ||||||||
\(536\) | 21.2828 | 0.919277 | ||||||||
\(537\) | −14.9892 | −0.646832 | ||||||||
\(538\) | −65.7865 | −2.83626 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.9654 | 0.471878 | ||||||||
\(541\) | 31.9421 | 1.37330 | 0.686650 | − | 0.726988i | \(-0.259080\pi\) | ||||
0.686650 | + | 0.726988i | \(0.259080\pi\) | |||||||
\(542\) | 49.3920 | 2.12157 | ||||||||
\(543\) | 1.00879 | 0.0432915 | ||||||||
\(544\) | 41.5017 | 1.77937 | ||||||||
\(545\) | 32.9715 | 1.41234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.486837 | −0.0208156 | −0.0104078 | − | 0.999946i | \(-0.503313\pi\) | ||||
−0.0104078 | + | 0.999946i | \(0.503313\pi\) | |||||||
\(548\) | −29.2987 | −1.25158 | ||||||||
\(549\) | 13.5721 | 0.579244 | ||||||||
\(550\) | −63.1504 | −2.69274 | ||||||||
\(551\) | −11.4971 | −0.489794 | ||||||||
\(552\) | −21.5081 | −0.915445 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −59.7052 | −2.53663 | ||||||||
\(555\) | −3.50282 | −0.148687 | ||||||||
\(556\) | 34.8024 | 1.47595 | ||||||||
\(557\) | 22.0350 | 0.933653 | 0.466827 | − | 0.884349i | \(-0.345397\pi\) | ||||
0.466827 | + | 0.884349i | \(0.345397\pi\) | |||||||
\(558\) | 3.27611 | 0.138689 | ||||||||
\(559\) | −15.8504 | −0.670400 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.3283 | −1.06936 | ||||||||
\(562\) | 24.5870 | 1.03714 | ||||||||
\(563\) | −2.55811 | −0.107812 | −0.0539058 | − | 0.998546i | \(-0.517167\pi\) | ||||
−0.0539058 | + | 0.998546i | \(0.517167\pi\) | |||||||
\(564\) | −2.33609 | −0.0983671 | ||||||||
\(565\) | −4.95190 | −0.208328 | ||||||||
\(566\) | 69.7976 | 2.93381 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.4865 | −0.691760 | ||||||||
\(569\) | 31.6305 | 1.32602 | 0.663010 | − | 0.748610i | \(-0.269279\pi\) | ||||
0.663010 | + | 0.748610i | \(0.269279\pi\) | |||||||
\(570\) | 18.1164 | 0.758810 | ||||||||
\(571\) | −34.5220 | −1.44470 | −0.722349 | − | 0.691528i | \(-0.756938\pi\) | ||||
−0.722349 | + | 0.691528i | \(0.756938\pi\) | |||||||
\(572\) | 17.2947 | 0.723129 | ||||||||
\(573\) | −20.0147 | −0.836125 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 62.4869 | 2.60588 | ||||||||
\(576\) | −13.0464 | −0.543602 | ||||||||
\(577\) | −41.9733 | −1.74737 | −0.873686 | − | 0.486491i | \(-0.838277\pi\) | ||||
−0.873686 | + | 0.486491i | \(0.838277\pi\) | |||||||
\(578\) | 62.4054 | 2.59572 | ||||||||
\(579\) | −3.47028 | −0.144220 | ||||||||
\(580\) | 55.3501 | 2.29829 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 39.5058 | 1.63757 | ||||||||
\(583\) | −35.9351 | −1.48828 | ||||||||
\(584\) | 5.77649 | 0.239033 | ||||||||
\(585\) | 5.13801 | 0.212431 | ||||||||
\(586\) | −23.0782 | −0.953351 | ||||||||
\(587\) | −27.5287 | −1.13623 | −0.568115 | − | 0.822949i | \(-0.692327\pi\) | ||||
−0.568115 | + | 0.822949i | \(0.692327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.29799 | 0.135891 | ||||||||
\(590\) | −76.5710 | −3.15238 | ||||||||
\(591\) | −11.6030 | −0.477284 | ||||||||
\(592\) | 0.506734 | 0.0208266 | ||||||||
\(593\) | 2.59633 | 0.106618 | 0.0533092 | − | 0.998578i | \(-0.483023\pi\) | ||||
0.0533092 | + | 0.998578i | \(0.483023\pi\) | |||||||
\(594\) | 8.58292 | 0.352161 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.55408 | 0.104619 | ||||||||
\(597\) | −7.82824 | −0.320388 | ||||||||
\(598\) | −28.0853 | −1.14850 | ||||||||
\(599\) | −7.58409 | −0.309878 | −0.154939 | − | 0.987924i | \(-0.549518\pi\) | ||||
−0.154939 | + | 0.987924i | \(0.549518\pi\) | |||||||
\(600\) | −18.6335 | −0.760711 | ||||||||
\(601\) | 25.1438 | 1.02564 | 0.512818 | − | 0.858497i | \(-0.328602\pi\) | ||||
0.512818 | + | 0.858497i | \(0.328602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.40378 | 0.342228 | ||||||||
\(604\) | 64.4380 | 2.62194 | ||||||||
\(605\) | −11.9168 | −0.484488 | ||||||||
\(606\) | 44.0064 | 1.78764 | ||||||||
\(607\) | −36.2667 | −1.47202 | −0.736011 | − | 0.676970i | \(-0.763293\pi\) | ||||
−0.736011 | + | 0.676970i | \(0.763293\pi\) | |||||||
\(608\) | −14.1575 | −0.574161 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −107.950 | −4.37076 | ||||||||
\(611\) | −1.09461 | −0.0442830 | ||||||||
\(612\) | −20.8274 | −0.841897 | ||||||||
\(613\) | 42.1617 | 1.70290 | 0.851448 | − | 0.524439i | \(-0.175725\pi\) | ||||
0.851448 | + | 0.524439i | \(0.175725\pi\) | |||||||
\(614\) | −49.7990 | −2.00972 | ||||||||
\(615\) | 3.51535 | 0.141753 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.94775 | −0.239447 | −0.119724 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119724 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(618\) | −9.98908 | −0.401820 | ||||||||
\(619\) | 11.3756 | 0.457224 | 0.228612 | − | 0.973518i | \(-0.426581\pi\) | ||||
0.228612 | + | 0.973518i | \(0.426581\pi\) | |||||||
\(620\) | −15.8774 | −0.637651 | ||||||||
\(621\) | −8.49274 | −0.340802 | ||||||||
\(622\) | 1.42099 | 0.0569766 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.743287 | −0.0297553 | ||||||||
\(625\) | −7.65291 | −0.306116 | ||||||||
\(626\) | −40.5810 | −1.62194 | ||||||||
\(627\) | 8.64025 | 0.345058 | ||||||||
\(628\) | 11.1565 | 0.445195 | ||||||||
\(629\) | 6.65314 | 0.265278 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.5226 | 1.37432 | 0.687161 | − | 0.726505i | \(-0.258857\pi\) | ||||
0.687161 | + | 0.726505i | \(0.258857\pi\) | |||||||
\(632\) | −2.62161 | −0.104282 | ||||||||
\(633\) | 0.767110 | 0.0304899 | ||||||||
\(634\) | 34.5505 | 1.37218 | ||||||||
\(635\) | 9.98243 | 0.396141 | ||||||||
\(636\) | −29.5493 | −1.17171 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 43.3239 | 1.71521 | ||||||||
\(639\) | −6.50992 | −0.257528 | ||||||||
\(640\) | 60.0680 | 2.37440 | ||||||||
\(641\) | −10.2549 | −0.405044 | −0.202522 | − | 0.979278i | \(-0.564914\pi\) | ||||
−0.202522 | + | 0.979278i | \(0.564914\pi\) | |||||||
\(642\) | 34.2978 | 1.35363 | ||||||||
\(643\) | 14.0531 | 0.554199 | 0.277100 | − | 0.960841i | \(-0.410627\pi\) | ||||
0.277100 | + | 0.960841i | \(0.410627\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.1226 | 1.50107 | ||||||||
\(646\) | −34.4096 | −1.35383 | ||||||||
\(647\) | 12.1956 | 0.479458 | 0.239729 | − | 0.970840i | \(-0.422941\pi\) | ||||
0.239729 | + | 0.970840i | \(0.422941\pi\) | |||||||
\(648\) | 2.53253 | 0.0994870 | ||||||||
\(649\) | −36.5191 | −1.43350 | ||||||||
\(650\) | −24.3317 | −0.954369 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 39.3798 | 1.54223 | ||||||||
\(653\) | 3.31551 | 0.129746 | 0.0648729 | − | 0.997894i | \(-0.479336\pi\) | ||||
0.0648729 | + | 0.997894i | \(0.479336\pi\) | |||||||
\(654\) | 21.2215 | 0.829826 | ||||||||
\(655\) | −51.6855 | −2.01952 | ||||||||
\(656\) | −0.508546 | −0.0198554 | ||||||||
\(657\) | 2.28092 | 0.0889872 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.07950 | −0.314733 | −0.157366 | − | 0.987540i | \(-0.550300\pi\) | ||||
−0.157366 | + | 0.987540i | \(0.550300\pi\) | |||||||
\(660\) | −41.5964 | −1.61914 | ||||||||
\(661\) | −33.3359 | −1.29661 | −0.648307 | − | 0.761379i | \(-0.724523\pi\) | ||||
−0.648307 | + | 0.761379i | \(0.724523\pi\) | |||||||
\(662\) | 69.8491 | 2.71476 | ||||||||
\(663\) | −9.75896 | −0.379007 | ||||||||
\(664\) | 4.68058 | 0.181642 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.25452 | −0.0873611 | ||||||||
\(667\) | −42.8687 | −1.65988 | ||||||||
\(668\) | −13.9784 | −0.540841 | ||||||||
\(669\) | −5.48934 | −0.212230 | ||||||||
\(670\) | −66.8419 | −2.58233 | ||||||||
\(671\) | −51.4846 | −1.98754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8487 | 0.649469 | 0.324735 | − | 0.945805i | \(-0.394725\pi\) | ||||
0.324735 | + | 0.945805i | \(0.394725\pi\) | |||||||
\(674\) | −31.0693 | −1.19675 | ||||||||
\(675\) | −7.35768 | −0.283197 | ||||||||
\(676\) | −33.8873 | −1.30336 | ||||||||
\(677\) | −28.5473 | −1.09716 | −0.548580 | − | 0.836098i | \(-0.684831\pi\) | ||||
−0.548580 | + | 0.836098i | \(0.684831\pi\) | |||||||
\(678\) | −3.18720 | −0.122404 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 59.4428 | 2.27953 | ||||||||
\(681\) | −24.0590 | −0.921943 | ||||||||
\(682\) | −12.4276 | −0.475878 | ||||||||
\(683\) | 18.4684 | 0.706674 | 0.353337 | − | 0.935496i | \(-0.385047\pi\) | ||||
0.353337 | + | 0.935496i | \(0.385047\pi\) | |||||||
\(684\) | 7.10484 | 0.271661 | ||||||||
\(685\) | 33.0187 | 1.26158 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.3429 | −0.394605 | ||||||||
\(688\) | −5.51498 | −0.210257 | ||||||||
\(689\) | −13.8457 | −0.527481 | ||||||||
\(690\) | 67.5495 | 2.57156 | ||||||||
\(691\) | 33.1686 | 1.26179 | 0.630896 | − | 0.775868i | \(-0.282688\pi\) | ||||
0.630896 | + | 0.775868i | \(0.282688\pi\) | |||||||
\(692\) | 70.3770 | 2.67533 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.3901 | −1.45727 | ||||||||
\(695\) | −39.2211 | −1.48774 | ||||||||
\(696\) | 12.7834 | 0.484553 | ||||||||
\(697\) | −6.67693 | −0.252907 | ||||||||
\(698\) | −13.4617 | −0.509533 | ||||||||
\(699\) | 17.3807 | 0.657400 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.1339 | 1.66692 | 0.833458 | − | 0.552583i | \(-0.186358\pi\) | ||||
0.833458 | + | 0.552583i | \(0.186358\pi\) | |||||||
\(702\) | 3.30698 | 0.124814 | ||||||||
\(703\) | −2.26958 | −0.0855990 | ||||||||
\(704\) | 49.4905 | 1.86524 | ||||||||
\(705\) | 2.63269 | 0.0991529 | ||||||||
\(706\) | 12.3213 | 0.463719 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −30.0295 | −1.12858 | ||||||||
\(709\) | −22.1547 | −0.832039 | −0.416019 | − | 0.909356i | \(-0.636575\pi\) | ||||
−0.416019 | + | 0.909356i | \(0.636575\pi\) | |||||||
\(710\) | 51.7785 | 1.94321 | ||||||||
\(711\) | −1.03517 | −0.0388221 | ||||||||
\(712\) | 4.46788 | 0.167441 | ||||||||
\(713\) | 12.2970 | 0.460528 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.4906 | −0.728906 | ||||||||
\(716\) | 46.7559 | 1.74735 | ||||||||
\(717\) | 7.43783 | 0.277771 | ||||||||
\(718\) | −54.1426 | −2.02059 | ||||||||
\(719\) | −2.80563 | −0.104633 | −0.0523163 | − | 0.998631i | \(-0.516660\pi\) | ||||
−0.0523163 | + | 0.998631i | \(0.516660\pi\) | |||||||
\(720\) | 1.78772 | 0.0666243 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −31.2510 | −1.16304 | ||||||||
\(723\) | −7.82930 | −0.291175 | ||||||||
\(724\) | −3.14674 | −0.116947 | ||||||||
\(725\) | −37.1393 | −1.37932 | ||||||||
\(726\) | −7.67005 | −0.284662 | ||||||||
\(727\) | 25.3472 | 0.940076 | 0.470038 | − | 0.882646i | \(-0.344240\pi\) | ||||
0.470038 | + | 0.882646i | \(0.344240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.1420 | −0.671464 | ||||||||
\(731\) | −72.4087 | −2.67813 | ||||||||
\(732\) | −42.3356 | −1.56477 | ||||||||
\(733\) | 10.8205 | 0.399664 | 0.199832 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199832 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(734\) | 8.19600 | 0.302520 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −52.7882 | −1.94580 | ||||||||
\(737\) | −31.8790 | −1.17428 | ||||||||
\(738\) | 2.26259 | 0.0832870 | ||||||||
\(739\) | 15.7485 | 0.579318 | 0.289659 | − | 0.957130i | \(-0.406458\pi\) | ||||
0.289659 | + | 0.957130i | \(0.406458\pi\) | |||||||
\(740\) | 10.9264 | 0.401661 | ||||||||
\(741\) | 3.32907 | 0.122297 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.4834 | −1.11833 | −0.559164 | − | 0.829057i | \(-0.688878\pi\) | ||||
−0.559164 | + | 0.829057i | \(0.688878\pi\) | |||||||
\(744\) | −3.66696 | −0.134437 | ||||||||
\(745\) | −2.87836 | −0.105455 | ||||||||
\(746\) | 69.0823 | 2.52928 | ||||||||
\(747\) | 1.84818 | 0.0676215 | ||||||||
\(748\) | 79.0068 | 2.88877 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 18.7525 | 0.684745 | ||||||||
\(751\) | −34.4554 | −1.25729 | −0.628647 | − | 0.777690i | \(-0.716391\pi\) | ||||
−0.628647 | + | 0.777690i | \(0.716391\pi\) | |||||||
\(752\) | −0.380857 | −0.0138884 | ||||||||
\(753\) | −11.4230 | −0.416276 | ||||||||
\(754\) | 16.6926 | 0.607909 | ||||||||
\(755\) | −72.6194 | −2.64289 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.0474 | −1.09209 | −0.546045 | − | 0.837756i | \(-0.683867\pi\) | ||||
−0.546045 | + | 0.837756i | \(0.683867\pi\) | |||||||
\(758\) | −32.9479 | −1.19672 | ||||||||
\(759\) | 32.2164 | 1.16938 | ||||||||
\(760\) | −20.2777 | −0.735550 | ||||||||
\(761\) | 38.0425 | 1.37904 | 0.689520 | − | 0.724266i | \(-0.257821\pi\) | ||||
0.689520 | + | 0.724266i | \(0.257821\pi\) | |||||||
\(762\) | 6.42500 | 0.232753 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 62.4319 | 2.25871 | ||||||||
\(765\) | 23.4718 | 0.848623 | ||||||||
\(766\) | 10.9664 | 0.396234 | ||||||||
\(767\) | −14.0707 | −0.508065 | ||||||||
\(768\) | 12.5688 | 0.453536 | ||||||||
\(769\) | −44.6290 | −1.60936 | −0.804681 | − | 0.593708i | \(-0.797663\pi\) | ||||
−0.804681 | + | 0.593708i | \(0.797663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.8155 | −0.533569 | ||||||||
\(772\) | 10.8249 | 0.389595 | ||||||||
\(773\) | −9.92149 | −0.356851 | −0.178426 | − | 0.983953i | \(-0.557100\pi\) | ||||
−0.178426 | + | 0.983953i | \(0.557100\pi\) | |||||||
\(774\) | 24.5369 | 0.881960 | ||||||||
\(775\) | 10.6535 | 0.382686 | ||||||||
\(776\) | −44.2190 | −1.58737 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.55142 | −0.0556213 | ||||||||
\(779\) | 2.27770 | 0.0816071 | ||||||||
\(780\) | −16.0270 | −0.573860 | ||||||||
\(781\) | 24.6948 | 0.883649 | ||||||||
\(782\) | −128.301 | −4.58804 | ||||||||
\(783\) | 5.04769 | 0.180390 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.5730 | −0.448751 | ||||||||
\(786\) | −33.2664 | −1.18657 | ||||||||
\(787\) | 9.83436 | 0.350557 | 0.175279 | − | 0.984519i | \(-0.443917\pi\) | ||||
0.175279 | + | 0.984519i | \(0.443917\pi\) | |||||||
\(788\) | 36.1934 | 1.28934 | ||||||||
\(789\) | 21.3829 | 0.761253 | ||||||||
\(790\) | 8.23356 | 0.292937 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.60691 | −0.341367 | ||||||||
\(793\) | −19.8369 | −0.704430 | ||||||||
\(794\) | −0.914742 | −0.0324630 | ||||||||
\(795\) | 33.3011 | 1.18107 | ||||||||
\(796\) | 24.4187 | 0.865496 | ||||||||
\(797\) | 37.5618 | 1.33051 | 0.665253 | − | 0.746618i | \(-0.268323\pi\) | ||||
0.665253 | + | 0.746618i | \(0.268323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.00044 | −0.176903 | ||||||||
\(800\) | −45.7330 | −1.61691 | ||||||||
\(801\) | 1.76420 | 0.0623348 | ||||||||
\(802\) | −63.6611 | −2.24795 | ||||||||
\(803\) | −8.65246 | −0.305339 | ||||||||
\(804\) | −26.2139 | −0.924495 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.78834 | −0.168662 | ||||||||
\(807\) | 29.0758 | 1.02352 | ||||||||
\(808\) | −49.2566 | −1.73284 | ||||||||
\(809\) | 21.9434 | 0.771489 | 0.385744 | − | 0.922606i | \(-0.373945\pi\) | ||||
0.385744 | + | 0.922606i | \(0.373945\pi\) | |||||||
\(810\) | −7.95379 | −0.279468 | ||||||||
\(811\) | −1.08414 | −0.0380692 | −0.0190346 | − | 0.999819i | \(-0.506059\pi\) | ||||
−0.0190346 | + | 0.999819i | \(0.506059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.8299 | −0.765607 | ||||||||
\(814\) | 8.55233 | 0.299759 | ||||||||
\(815\) | −44.3796 | −1.55455 | ||||||||
\(816\) | −3.39553 | −0.118867 | ||||||||
\(817\) | 24.7008 | 0.864170 | ||||||||
\(818\) | 38.4492 | 1.34435 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.9654 | −0.382930 | ||||||||
\(821\) | 30.1425 | 1.05198 | 0.525990 | − | 0.850491i | \(-0.323695\pi\) | ||||
0.525990 | + | 0.850491i | \(0.323695\pi\) | |||||||
\(822\) | 21.2518 | 0.741243 | ||||||||
\(823\) | 8.54130 | 0.297731 | 0.148866 | − | 0.988857i | \(-0.452438\pi\) | ||||
0.148866 | + | 0.988857i | \(0.452438\pi\) | |||||||
\(824\) | 11.1808 | 0.389503 | ||||||||
\(825\) | 27.9107 | 0.971726 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.6006 | 1.58569 | 0.792843 | − | 0.609426i | \(-0.208600\pi\) | ||||
0.792843 | + | 0.609426i | \(0.208600\pi\) | |||||||
\(828\) | 26.4914 | 0.920641 | ||||||||
\(829\) | −34.3490 | −1.19299 | −0.596495 | − | 0.802617i | \(-0.703440\pi\) | ||||
−0.596495 | + | 0.802617i | \(0.703440\pi\) | |||||||
\(830\) | −14.7001 | −0.510247 | ||||||||
\(831\) | 26.3880 | 0.915390 | ||||||||
\(832\) | 19.0686 | 0.661084 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −25.2439 | −0.874126 | ||||||||
\(835\) | 15.7532 | 0.545161 | ||||||||
\(836\) | −26.9516 | −0.932140 | ||||||||
\(837\) | −1.44795 | −0.0500484 | ||||||||
\(838\) | −22.9308 | −0.792131 | ||||||||
\(839\) | 40.4048 | 1.39493 | 0.697464 | − | 0.716619i | \(-0.254312\pi\) | ||||
0.697464 | + | 0.716619i | \(0.254312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.52086 | −0.121409 | ||||||||
\(842\) | 18.0023 | 0.620401 | ||||||||
\(843\) | −10.8668 | −0.374271 | ||||||||
\(844\) | −2.39285 | −0.0823653 | ||||||||
\(845\) | 38.1899 | 1.31377 | ||||||||
\(846\) | 1.69448 | 0.0582575 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.81748 | −0.165433 | ||||||||
\(849\) | −30.8486 | −1.05872 | ||||||||
\(850\) | −111.154 | −3.81254 | ||||||||
\(851\) | −8.46247 | −0.290090 | ||||||||
\(852\) | 20.3064 | 0.695687 | ||||||||
\(853\) | −3.69729 | −0.126593 | −0.0632965 | − | 0.997995i | \(-0.520161\pi\) | ||||
−0.0632965 | + | 0.997995i | \(0.520161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00692 | −0.273831 | ||||||||
\(856\) | −38.3897 | −1.31213 | ||||||||
\(857\) | −5.08270 | −0.173622 | −0.0868108 | − | 0.996225i | \(-0.527668\pi\) | ||||
−0.0868108 | + | 0.996225i | \(0.527668\pi\) | |||||||
\(858\) | −12.5447 | −0.428270 | ||||||||
\(859\) | −47.7419 | −1.62893 | −0.814467 | − | 0.580210i | \(-0.802970\pi\) | ||||
−0.814467 | + | 0.580210i | \(0.802970\pi\) | |||||||
\(860\) | −118.916 | −4.05500 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −61.4243 | −2.09212 | ||||||||
\(863\) | 16.7136 | 0.568938 | 0.284469 | − | 0.958685i | \(-0.408183\pi\) | ||||
0.284469 | + | 0.958685i | \(0.408183\pi\) | |||||||
\(864\) | 6.21568 | 0.211462 | ||||||||
\(865\) | −79.3125 | −2.69671 | ||||||||
\(866\) | −62.6464 | −2.12881 | ||||||||
\(867\) | −27.5814 | −0.936714 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.92684 | 0.133209 | ||||||||
\(870\) | −40.1482 | −1.36115 | ||||||||
\(871\) | −12.2829 | −0.416190 | ||||||||
\(872\) | −23.7533 | −0.804389 | ||||||||
\(873\) | −17.4604 | −0.590946 | ||||||||
\(874\) | 43.7673 | 1.48045 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.11489 | −0.240390 | ||||||||
\(877\) | −8.44843 | −0.285283 | −0.142642 | − | 0.989774i | \(-0.545560\pi\) | ||||
−0.142642 | + | 0.989774i | \(0.545560\pi\) | |||||||
\(878\) | 19.8183 | 0.668834 | ||||||||
\(879\) | 10.1999 | 0.344034 | ||||||||
\(880\) | −6.78154 | −0.228606 | ||||||||
\(881\) | −25.5874 | −0.862062 | −0.431031 | − | 0.902337i | \(-0.641850\pi\) | ||||
−0.431031 | + | 0.902337i | \(0.641850\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.4322 | 1.83179 | 0.915895 | − | 0.401418i | \(-0.131483\pi\) | ||||
0.915895 | + | 0.401418i | \(0.131483\pi\) | |||||||
\(884\) | 30.4412 | 1.02385 | ||||||||
\(885\) | 33.8422 | 1.13759 | ||||||||
\(886\) | −80.5446 | −2.70595 | ||||||||
\(887\) | 54.1148 | 1.81700 | 0.908498 | − | 0.417889i | \(-0.137230\pi\) | ||||
0.908498 | + | 0.417889i | \(0.137230\pi\) | |||||||
\(888\) | 2.52350 | 0.0846832 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.0321 | −0.470355 | ||||||||
\(891\) | −3.79341 | −0.127084 | ||||||||
\(892\) | 17.1229 | 0.573318 | ||||||||
\(893\) | 1.70580 | 0.0570824 | ||||||||
\(894\) | −1.85260 | −0.0619602 | ||||||||
\(895\) | −52.6923 | −1.76131 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.4129 | 0.414456 | ||||||||
\(898\) | 80.0160 | 2.67017 | ||||||||
\(899\) | −7.30878 | −0.243761 | ||||||||
\(900\) | 22.9509 | 0.765029 | ||||||||
\(901\) | −63.2509 | −2.10719 | ||||||||
\(902\) | −8.58292 | −0.285780 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.56745 | 0.118651 | ||||||||
\(905\) | 3.54626 | 0.117882 | ||||||||
\(906\) | −46.7401 | −1.55284 | ||||||||
\(907\) | −5.56564 | −0.184804 | −0.0924021 | − | 0.995722i | \(-0.529455\pi\) | ||||
−0.0924021 | + | 0.995722i | \(0.529455\pi\) | |||||||
\(908\) | 75.0474 | 2.49053 | ||||||||
\(909\) | −19.4496 | −0.645102 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.67651 | 0.287466 | 0.143733 | − | 0.989617i | \(-0.454089\pi\) | ||||
0.143733 | + | 0.989617i | \(0.454089\pi\) | |||||||
\(912\) | 1.15832 | 0.0383557 | ||||||||
\(913\) | −7.01092 | −0.232028 | ||||||||
\(914\) | 44.7202 | 1.47921 | ||||||||
\(915\) | 47.7108 | 1.57727 | ||||||||
\(916\) | 32.2626 | 1.06598 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 15.1071 | 0.498610 | ||||||||
\(919\) | 31.0314 | 1.02363 | 0.511816 | − | 0.859095i | \(-0.328973\pi\) | ||||
0.511816 | + | 0.859095i | \(0.328973\pi\) | |||||||
\(920\) | −75.6084 | −2.49274 | ||||||||
\(921\) | 22.0097 | 0.725246 | ||||||||
\(922\) | −24.3203 | −0.800947 | ||||||||
\(923\) | 9.51486 | 0.313185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.33146 | −0.241057 | ||||||||
\(926\) | 6.55107 | 0.215282 | ||||||||
\(927\) | 4.41489 | 0.145004 | ||||||||
\(928\) | 31.3748 | 1.02993 | ||||||||
\(929\) | −0.0908696 | −0.00298133 | −0.00149067 | − | 0.999999i | \(-0.500474\pi\) | ||||
−0.00149067 | + | 0.999999i | \(0.500474\pi\) | |||||||
\(930\) | 11.5167 | 0.377646 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −54.2158 | −1.77590 | ||||||||
\(933\) | −0.628039 | −0.0205611 | ||||||||
\(934\) | 13.5335 | 0.442831 | ||||||||
\(935\) | −89.0379 | −2.91185 | ||||||||
\(936\) | −3.70152 | −0.120988 | ||||||||
\(937\) | 39.5068 | 1.29063 | 0.645316 | − | 0.763916i | \(-0.276726\pi\) | ||||
0.645316 | + | 0.763916i | \(0.276726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.9356 | 0.585308 | ||||||||
\(940\) | −8.21217 | −0.267851 | ||||||||
\(941\) | −1.91194 | −0.0623275 | −0.0311638 | − | 0.999514i | \(-0.509921\pi\) | ||||
−0.0311638 | + | 0.999514i | \(0.509921\pi\) | |||||||
\(942\) | −8.09240 | −0.263665 | ||||||||
\(943\) | 8.49274 | 0.276562 | ||||||||
\(944\) | −4.89577 | −0.159344 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −93.0784 | −3.02624 | ||||||||
\(947\) | 10.0939 | 0.328007 | 0.164004 | − | 0.986460i | \(-0.447559\pi\) | ||||
0.164004 | + | 0.986460i | \(0.447559\pi\) | |||||||
\(948\) | 3.22902 | 0.104874 | ||||||||
\(949\) | −3.33378 | −0.108219 | ||||||||
\(950\) | 37.9178 | 1.23022 | ||||||||
\(951\) | −15.2704 | −0.495175 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.1757 | 1.75492 | 0.877461 | − | 0.479647i | \(-0.159235\pi\) | ||||
0.877461 | + | 0.479647i | \(0.159235\pi\) | |||||||
\(954\) | 21.4336 | 0.693938 | ||||||||
\(955\) | −70.3586 | −2.27675 | ||||||||
\(956\) | −23.2009 | −0.750370 | ||||||||
\(957\) | −19.1479 | −0.618965 | ||||||||
\(958\) | 34.1035 | 1.10183 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −45.8628 | −1.48022 | ||||||||
\(961\) | −28.9035 | −0.932369 | ||||||||
\(962\) | 3.29520 | 0.106241 | ||||||||
\(963\) | −15.1587 | −0.488481 | ||||||||
\(964\) | 24.4220 | 0.786579 | ||||||||
\(965\) | −12.1992 | −0.392707 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.86574 | −0.0599983 | −0.0299991 | − | 0.999550i | \(-0.509550\pi\) | ||||
−0.0299991 | + | 0.999550i | \(0.509550\pi\) | |||||||
\(968\) | 8.58512 | 0.275936 | ||||||||
\(969\) | 15.2081 | 0.488553 | ||||||||
\(970\) | 138.877 | 4.45906 | ||||||||
\(971\) | 35.0800 | 1.12577 | 0.562886 | − | 0.826535i | \(-0.309691\pi\) | ||||
0.562886 | + | 0.826535i | \(0.309691\pi\) | |||||||
\(972\) | −3.11931 | −0.100052 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −60.6327 | −1.94280 | ||||||||
\(975\) | 10.7539 | 0.344402 | ||||||||
\(976\) | −6.90205 | −0.220929 | ||||||||
\(977\) | −3.77558 | −0.120792 | −0.0603958 | − | 0.998175i | \(-0.519236\pi\) | ||||
−0.0603958 | + | 0.998175i | \(0.519236\pi\) | |||||||
\(978\) | −28.5641 | −0.913380 | ||||||||
\(979\) | −6.69232 | −0.213887 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.37929 | −0.299458 | ||||||||
\(982\) | 33.1958 | 1.05932 | ||||||||
\(983\) | 30.5146 | 0.973265 | 0.486632 | − | 0.873607i | \(-0.338225\pi\) | ||||
0.486632 | + | 0.873607i | \(0.338225\pi\) | |||||||
\(984\) | −2.53253 | −0.0807340 | ||||||||
\(985\) | −40.7887 | −1.29964 | ||||||||
\(986\) | 76.2561 | 2.42849 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.3844 | −0.330372 | ||||||||
\(989\) | 92.1004 | 2.92862 | ||||||||
\(990\) | 30.1720 | 0.958928 | ||||||||
\(991\) | −3.83662 | −0.121874 | −0.0609371 | − | 0.998142i | \(-0.519409\pi\) | ||||
−0.0609371 | + | 0.998142i | \(0.519409\pi\) | |||||||
\(992\) | −8.99998 | −0.285750 | ||||||||
\(993\) | −30.8713 | −0.979672 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.5190 | −0.872411 | ||||||||
\(996\) | −5.76505 | −0.182673 | ||||||||
\(997\) | −0.932058 | −0.0295186 | −0.0147593 | − | 0.999891i | \(-0.504698\pi\) | ||||
−0.0147593 | + | 0.999891i | \(0.504698\pi\) | |||||||
\(998\) | 75.3705 | 2.38581 | ||||||||
\(999\) | 0.996436 | 0.0315258 |
(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 | 6027.2.a.bn.1.19 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.19 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.19 | yes | 24 | 7.6 | odd | 2 |