Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,2,Mod(1,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.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: | \(9.12690095103\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 127) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.87939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1143.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.879385 | −0.621819 | −0.310910 | − | 0.950439i | \(-0.600634\pi\) | ||||
−0.310910 | + | 0.950439i | \(0.600634\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.22668 | −0.613341 | ||||||||
\(5\) | 2.34730 | 1.04974 | 0.524871 | − | 0.851182i | \(-0.324113\pi\) | ||||
0.524871 | + | 0.851182i | \(0.324113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.34730 | −0.509230 | −0.254615 | − | 0.967042i | \(-0.581949\pi\) | ||||
−0.254615 | + | 0.967042i | \(0.581949\pi\) | |||||||
\(8\) | 2.83750 | 1.00321 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.06418 | −0.652750 | ||||||||
\(11\) | −5.29086 | −1.59525 | −0.797627 | − | 0.603151i | \(-0.793912\pi\) | ||||
−0.797627 | + | 0.603151i | \(0.793912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.83750 | −0.509630 | −0.254815 | − | 0.966990i | \(-0.582015\pi\) | ||||
−0.254815 | + | 0.966990i | \(0.582015\pi\) | |||||||
\(14\) | 1.18479 | 0.316649 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0418891 | −0.0104723 | ||||||||
\(17\) | 7.87939 | 1.91103 | 0.955516 | − | 0.294940i | \(-0.0952996\pi\) | ||||
0.955516 | + | 0.294940i | \(0.0952996\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.652704 | 0.149740 | 0.0748702 | − | 0.997193i | \(-0.476146\pi\) | ||||
0.0748702 | + | 0.997193i | \(0.476146\pi\) | |||||||
\(20\) | −2.87939 | −0.643850 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.65270 | 0.991960 | ||||||||
\(23\) | 4.18479 | 0.872590 | 0.436295 | − | 0.899804i | \(-0.356290\pi\) | ||||
0.436295 | + | 0.899804i | \(0.356290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.509800 | 0.101960 | ||||||||
\(26\) | 1.61587 | 0.316898 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.65270 | 0.312332 | ||||||||
\(29\) | 3.10607 | 0.576782 | 0.288391 | − | 0.957513i | \(-0.406880\pi\) | ||||
0.288391 | + | 0.957513i | \(0.406880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.28312 | 0.230455 | 0.115227 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115227 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(32\) | −5.63816 | −0.996695 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.92902 | −1.18832 | ||||||||
\(35\) | −3.16250 | −0.534561 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.14796 | 0.846319 | 0.423159 | − | 0.906055i | \(-0.360921\pi\) | ||||
0.423159 | + | 0.906055i | \(0.360921\pi\) | |||||||
\(38\) | −0.573978 | −0.0931115 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.66044 | 1.05311 | ||||||||
\(41\) | 10.1284 | 1.58178 | 0.790892 | − | 0.611956i | \(-0.209617\pi\) | ||||
0.790892 | + | 0.611956i | \(0.209617\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.08378 | −0.775269 | −0.387634 | − | 0.921813i | \(-0.626708\pi\) | ||||
−0.387634 | + | 0.921813i | \(0.626708\pi\) | |||||||
\(44\) | 6.49020 | 0.978434 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.68004 | −0.542593 | ||||||||
\(47\) | −9.58172 | −1.39764 | −0.698819 | − | 0.715299i | \(-0.746291\pi\) | ||||
−0.698819 | + | 0.715299i | \(0.746291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.18479 | −0.740685 | ||||||||
\(50\) | −0.448311 | −0.0634007 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.25402 | 0.312577 | ||||||||
\(53\) | −0.448311 | −0.0615802 | −0.0307901 | − | 0.999526i | \(-0.509802\pi\) | ||||
−0.0307901 | + | 0.999526i | \(0.509802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.4192 | −1.67461 | ||||||||
\(56\) | −3.82295 | −0.510863 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.73143 | −0.358654 | ||||||||
\(59\) | 5.29086 | 0.688811 | 0.344406 | − | 0.938821i | \(-0.388080\pi\) | ||||
0.344406 | + | 0.938821i | \(0.388080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9513 | 1.53021 | 0.765104 | − | 0.643907i | \(-0.222688\pi\) | ||||
0.765104 | + | 0.643907i | \(0.222688\pi\) | |||||||
\(62\) | −1.12836 | −0.143301 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.04189 | 0.630236 | ||||||||
\(65\) | −4.31315 | −0.534980 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.652704 | −0.0797404 | −0.0398702 | − | 0.999205i | \(-0.512694\pi\) | ||||
−0.0398702 | + | 0.999205i | \(0.512694\pi\) | |||||||
\(68\) | −9.66550 | −1.17211 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.78106 | 0.332400 | ||||||||
\(71\) | 13.3405 | 1.58322 | 0.791612 | − | 0.611024i | \(-0.209242\pi\) | ||||
0.791612 | + | 0.611024i | \(0.209242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.32770 | 0.272436 | 0.136218 | − | 0.990679i | \(-0.456505\pi\) | ||||
0.136218 | + | 0.990679i | \(0.456505\pi\) | |||||||
\(74\) | −4.52704 | −0.526257 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.800660 | −0.0918419 | ||||||||
\(77\) | 7.12836 | 0.812352 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.1557 | 1.81766 | 0.908829 | − | 0.417169i | \(-0.136978\pi\) | ||||
0.908829 | + | 0.417169i | \(0.136978\pi\) | |||||||
\(80\) | −0.0983261 | −0.0109932 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.90673 | −0.983583 | ||||||||
\(83\) | 14.9368 | 1.63952 | 0.819761 | − | 0.572706i | \(-0.194106\pi\) | ||||
0.819761 | + | 0.572706i | \(0.194106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.4953 | 2.00609 | ||||||||
\(86\) | 4.47060 | 0.482077 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.0128 | −1.60037 | ||||||||
\(89\) | 17.3327 | 1.83727 | 0.918634 | − | 0.395110i | \(-0.129294\pi\) | ||||
0.918634 | + | 0.395110i | \(0.129294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.47565 | 0.259519 | ||||||||
\(92\) | −5.13341 | −0.535195 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.42602 | 0.869078 | ||||||||
\(95\) | 1.53209 | 0.157189 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.44562 | −0.146781 | −0.0733904 | − | 0.997303i | \(-0.523382\pi\) | ||||
−0.0733904 | + | 0.997303i | \(0.523382\pi\) | |||||||
\(98\) | 4.55943 | 0.460572 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.625362 | −0.0625362 | ||||||||
\(101\) | −7.15570 | −0.712018 | −0.356009 | − | 0.934482i | \(-0.615863\pi\) | ||||
−0.356009 | + | 0.934482i | \(0.615863\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.94356 | 0.585637 | 0.292818 | − | 0.956168i | \(-0.405407\pi\) | ||||
0.292818 | + | 0.956168i | \(0.405407\pi\) | |||||||
\(104\) | −5.21389 | −0.511264 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.394238 | 0.0382918 | ||||||||
\(107\) | −2.01455 | −0.194754 | −0.0973768 | − | 0.995248i | \(-0.531045\pi\) | ||||
−0.0973768 | + | 0.995248i | \(0.531045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.177052 | 0.0169585 | 0.00847924 | − | 0.999964i | \(-0.497301\pi\) | ||||
0.00847924 | + | 0.999964i | \(0.497301\pi\) | |||||||
\(110\) | 10.9213 | 1.04130 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0564370 | 0.00533279 | ||||||||
\(113\) | −3.70233 | −0.348286 | −0.174143 | − | 0.984720i | \(-0.555716\pi\) | ||||
−0.174143 | + | 0.984720i | \(0.555716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.82295 | 0.915995 | ||||||||
\(116\) | −3.81016 | −0.353764 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.65270 | −0.428316 | ||||||||
\(119\) | −10.6159 | −0.973155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.9932 | 1.54484 | ||||||||
\(122\) | −10.5098 | −0.951513 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.57398 | −0.141347 | ||||||||
\(125\) | −10.5398 | −0.942711 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 6.84255 | 0.604802 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.79292 | 0.332661 | ||||||||
\(131\) | −15.2395 | −1.33148 | −0.665740 | − | 0.746184i | \(-0.731884\pi\) | ||||
−0.665740 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.879385 | −0.0762524 | ||||||||
\(134\) | 0.573978 | 0.0495841 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 22.3577 | 1.91716 | ||||||||
\(137\) | 11.0000 | 0.939793 | 0.469897 | − | 0.882721i | \(-0.344291\pi\) | ||||
0.469897 | + | 0.882721i | \(0.344291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.221629 | −0.0187983 | −0.00939917 | − | 0.999956i | \(-0.502992\pi\) | ||||
−0.00939917 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(140\) | 3.87939 | 0.327868 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.7314 | −0.984480 | ||||||||
\(143\) | 9.72193 | 0.812989 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.29086 | 0.605473 | ||||||||
\(146\) | −2.04694 | −0.169406 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.31490 | −0.519082 | ||||||||
\(149\) | −2.19160 | −0.179543 | −0.0897714 | − | 0.995962i | \(-0.528614\pi\) | ||||
−0.0897714 | + | 0.995962i | \(0.528614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.5621 | −1.02229 | −0.511145 | − | 0.859494i | \(-0.670779\pi\) | ||||
−0.511145 | + | 0.859494i | \(0.670779\pi\) | |||||||
\(152\) | 1.85204 | 0.150221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.26857 | −0.505136 | ||||||||
\(155\) | 3.01186 | 0.241918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.32770 | −0.744431 | −0.372216 | − | 0.928146i | \(-0.621402\pi\) | ||||
−0.372216 | + | 0.928146i | \(0.621402\pi\) | |||||||
\(158\) | −14.2071 | −1.13025 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.2344 | −1.04627 | ||||||||
\(161\) | −5.63816 | −0.444349 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.8229 | −0.847719 | −0.423859 | − | 0.905728i | \(-0.639325\pi\) | ||||
−0.423859 | + | 0.905728i | \(0.639325\pi\) | |||||||
\(164\) | −12.4243 | −0.970172 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.1352 | −1.01949 | ||||||||
\(167\) | −1.36959 | −0.105982 | −0.0529908 | − | 0.998595i | \(-0.516875\pi\) | ||||
−0.0529908 | + | 0.998595i | \(0.516875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.62361 | −0.740278 | ||||||||
\(170\) | −16.2645 | −1.24743 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.23618 | 0.475504 | ||||||||
\(173\) | 16.6263 | 1.26407 | 0.632037 | − | 0.774938i | \(-0.282219\pi\) | ||||
0.632037 | + | 0.774938i | \(0.282219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.686852 | −0.0519211 | ||||||||
\(176\) | 0.221629 | 0.0167059 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.2422 | −1.14245 | ||||||||
\(179\) | −6.96316 | −0.520451 | −0.260226 | − | 0.965548i | \(-0.583797\pi\) | ||||
−0.260226 | + | 0.965548i | \(0.583797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.49020 | −0.185095 | −0.0925475 | − | 0.995708i | \(-0.529501\pi\) | ||||
−0.0925475 | + | 0.995708i | \(0.529501\pi\) | |||||||
\(182\) | −2.17705 | −0.161374 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.8743 | 0.875387 | ||||||||
\(185\) | 12.0838 | 0.888417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −41.6887 | −3.04858 | ||||||||
\(188\) | 11.7537 | 0.857228 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.34730 | −0.0977432 | ||||||||
\(191\) | 13.5398 | 0.979708 | 0.489854 | − | 0.871805i | \(-0.337050\pi\) | ||||
0.489854 | + | 0.871805i | \(0.337050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7888 | 1.56839 | 0.784196 | − | 0.620513i | \(-0.213076\pi\) | ||||
0.784196 | + | 0.620513i | \(0.213076\pi\) | |||||||
\(194\) | 1.27126 | 0.0912711 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.36009 | 0.454292 | ||||||||
\(197\) | 5.07192 | 0.361359 | 0.180680 | − | 0.983542i | \(-0.442170\pi\) | ||||
0.180680 | + | 0.983542i | \(0.442170\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.08378 | −0.502156 | −0.251078 | − | 0.967967i | \(-0.580785\pi\) | ||||
−0.251078 | + | 0.967967i | \(0.580785\pi\) | |||||||
\(200\) | 1.44656 | 0.102287 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.29261 | 0.442747 | ||||||||
\(203\) | −4.18479 | −0.293715 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.7743 | 1.66047 | ||||||||
\(206\) | −5.22668 | −0.364160 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0769710 | 0.00533698 | ||||||||
\(209\) | −3.45336 | −0.238874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.67230 | −0.252812 | −0.126406 | − | 0.991979i | \(-0.540344\pi\) | ||||
−0.126406 | + | 0.991979i | \(0.540344\pi\) | |||||||
\(212\) | 0.549935 | 0.0377697 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.77156 | 0.121102 | ||||||||
\(215\) | −11.9331 | −0.813833 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.72874 | −0.117355 | ||||||||
\(218\) | −0.155697 | −0.0105451 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.2344 | 1.02710 | ||||||||
\(221\) | −14.4783 | −0.973919 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.8753 | 1.66577 | 0.832886 | − | 0.553445i | \(-0.186687\pi\) | ||||
0.832886 | + | 0.553445i | \(0.186687\pi\) | |||||||
\(224\) | 7.59627 | 0.507547 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.25578 | 0.216571 | ||||||||
\(227\) | 10.5321 | 0.699039 | 0.349520 | − | 0.936929i | \(-0.386345\pi\) | ||||
0.349520 | + | 0.936929i | \(0.386345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.12061 | −0.470543 | −0.235272 | − | 0.971930i | \(-0.575598\pi\) | ||||
−0.235272 | + | 0.971930i | \(0.575598\pi\) | |||||||
\(230\) | −8.63816 | −0.569583 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.81345 | 0.578632 | ||||||||
\(233\) | −3.23442 | −0.211894 | −0.105947 | − | 0.994372i | \(-0.533787\pi\) | ||||
−0.105947 | + | 0.994372i | \(0.533787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4911 | −1.46716 | ||||||||
\(236\) | −6.49020 | −0.422476 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.33544 | 0.605126 | ||||||||
\(239\) | 8.00505 | 0.517804 | 0.258902 | − | 0.965904i | \(-0.416639\pi\) | ||||
0.258902 | + | 0.965904i | \(0.416639\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.5749 | −1.84067 | −0.920336 | − | 0.391129i | \(-0.872085\pi\) | ||||
−0.920336 | + | 0.391129i | \(0.872085\pi\) | |||||||
\(242\) | −14.9436 | −0.960609 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.6604 | −0.938539 | ||||||||
\(245\) | −12.1702 | −0.777528 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.19934 | −0.0763122 | ||||||||
\(248\) | 3.64084 | 0.231194 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.26857 | 0.586196 | ||||||||
\(251\) | −19.2540 | −1.21530 | −0.607652 | − | 0.794204i | \(-0.707888\pi\) | ||||
−0.607652 | + | 0.794204i | \(0.707888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.1411 | −1.39200 | ||||||||
\(254\) | 0.879385 | 0.0551775 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.1010 | −1.00631 | ||||||||
\(257\) | 20.1780 | 1.25867 | 0.629334 | − | 0.777135i | \(-0.283328\pi\) | ||||
0.629334 | + | 0.777135i | \(0.283328\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.93582 | −0.430971 | ||||||||
\(260\) | 5.29086 | 0.328125 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.4014 | 0.827939 | ||||||||
\(263\) | −7.52940 | −0.464283 | −0.232141 | − | 0.972682i | \(-0.574573\pi\) | ||||
−0.232141 | + | 0.972682i | \(0.574573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05232 | −0.0646434 | ||||||||
\(266\) | 0.773318 | 0.0474152 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.800660 | 0.0489081 | ||||||||
\(269\) | 13.3405 | 0.813384 | 0.406692 | − | 0.913565i | \(-0.366682\pi\) | ||||
0.406692 | + | 0.913565i | \(0.366682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.5226 | −1.61113 | −0.805566 | − | 0.592505i | \(-0.798139\pi\) | ||||
−0.805566 | + | 0.592505i | \(0.798139\pi\) | |||||||
\(272\) | −0.330060 | −0.0200128 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.67324 | −0.584382 | ||||||||
\(275\) | −2.69728 | −0.162652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.82800 | −0.530423 | −0.265212 | − | 0.964190i | \(-0.585442\pi\) | ||||
−0.265212 | + | 0.964190i | \(0.585442\pi\) | |||||||
\(278\) | 0.194897 | 0.0116892 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.97359 | −0.536275 | ||||||||
\(281\) | −17.8922 | −1.06736 | −0.533679 | − | 0.845687i | \(-0.679191\pi\) | ||||
−0.533679 | + | 0.845687i | \(0.679191\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4483 | 0.739975 | 0.369988 | − | 0.929037i | \(-0.379362\pi\) | ||||
0.369988 | + | 0.929037i | \(0.379362\pi\) | |||||||
\(284\) | −16.3645 | −0.971056 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.54933 | −0.505532 | ||||||||
\(287\) | −13.6459 | −0.805492 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.0847 | 2.65204 | ||||||||
\(290\) | −6.41147 | −0.376495 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.85534 | −0.167096 | ||||||||
\(293\) | −32.8316 | −1.91804 | −0.959022 | − | 0.283332i | \(-0.908560\pi\) | ||||
−0.959022 | + | 0.283332i | \(0.908560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.4192 | 0.723075 | ||||||||
\(296\) | 14.6073 | 0.849032 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.92726 | 0.111643 | ||||||||
\(299\) | −7.68954 | −0.444698 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.84936 | 0.394790 | ||||||||
\(302\) | 11.0469 | 0.635680 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0273411 | −0.00156812 | ||||||||
\(305\) | 28.0533 | 1.60632 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5125 | −0.942417 | −0.471209 | − | 0.882022i | \(-0.656182\pi\) | ||||
−0.471209 | + | 0.882022i | \(0.656182\pi\) | |||||||
\(308\) | −8.74422 | −0.498248 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.64858 | −0.150430 | ||||||||
\(311\) | −13.9290 | −0.789842 | −0.394921 | − | 0.918715i | \(-0.629228\pi\) | ||||
−0.394921 | + | 0.918715i | \(0.629228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1797 | −0.575393 | −0.287696 | − | 0.957722i | \(-0.592889\pi\) | ||||
−0.287696 | + | 0.957722i | \(0.592889\pi\) | |||||||
\(314\) | 8.20264 | 0.462902 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.8179 | −1.11484 | ||||||||
\(317\) | −19.9864 | −1.12255 | −0.561274 | − | 0.827630i | \(-0.689688\pi\) | ||||
−0.561274 | + | 0.827630i | \(0.689688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.4338 | −0.920114 | ||||||||
\(320\) | 11.8348 | 0.661586 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.95811 | 0.276305 | ||||||||
\(323\) | 5.14290 | 0.286159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.936756 | −0.0519619 | ||||||||
\(326\) | 9.51754 | 0.527128 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28.7392 | 1.58686 | ||||||||
\(329\) | 12.9094 | 0.711719 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.70140 | 0.368342 | 0.184171 | − | 0.982894i | \(-0.441040\pi\) | ||||
0.184171 | + | 0.982894i | \(0.441040\pi\) | |||||||
\(332\) | −18.3226 | −1.00559 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.20439 | 0.0659014 | ||||||||
\(335\) | −1.53209 | −0.0837070 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.524348 | 0.0285631 | 0.0142815 | − | 0.999898i | \(-0.495454\pi\) | ||||
0.0142815 | + | 0.999898i | \(0.495454\pi\) | |||||||
\(338\) | 8.46286 | 0.460319 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.6878 | −1.23042 | ||||||||
\(341\) | −6.78880 | −0.367634 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4165 | 0.886409 | ||||||||
\(344\) | −14.4252 | −0.777755 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.6209 | −0.786025 | ||||||||
\(347\) | 19.4037 | 1.04165 | 0.520823 | − | 0.853664i | \(-0.325625\pi\) | ||||
0.520823 | + | 0.853664i | \(0.325625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.5645 | −1.10079 | −0.550396 | − | 0.834904i | \(-0.685523\pi\) | ||||
−0.550396 | + | 0.834904i | \(0.685523\pi\) | |||||||
\(350\) | 0.604007 | 0.0322856 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 29.8307 | 1.58998 | ||||||||
\(353\) | −28.0925 | −1.49521 | −0.747605 | − | 0.664143i | \(-0.768796\pi\) | ||||
−0.747605 | + | 0.664143i | \(0.768796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.3141 | 1.66198 | ||||||||
\(356\) | −21.2618 | −1.12687 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.12330 | 0.323627 | ||||||||
\(359\) | −2.94356 | −0.155355 | −0.0776777 | − | 0.996979i | \(-0.524750\pi\) | ||||
−0.0776777 | + | 0.996979i | \(0.524750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5740 | −0.977578 | ||||||||
\(362\) | 2.18984 | 0.115096 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.03684 | −0.159173 | ||||||||
\(365\) | 5.46379 | 0.285988 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2668 | 0.953520 | 0.476760 | − | 0.879033i | \(-0.341811\pi\) | ||||
0.476760 | + | 0.879033i | \(0.341811\pi\) | |||||||
\(368\) | −0.175297 | −0.00913799 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.6263 | −0.552435 | ||||||||
\(371\) | 0.604007 | 0.0313585 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.05138 | 0.313329 | 0.156664 | − | 0.987652i | \(-0.449926\pi\) | ||||
0.156664 | + | 0.987652i | \(0.449926\pi\) | |||||||
\(374\) | 36.6604 | 1.89567 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.1881 | −1.40212 | ||||||||
\(377\) | −5.70739 | −0.293945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5449 | 0.695754 | 0.347877 | − | 0.937540i | \(-0.386903\pi\) | ||||
0.347877 | + | 0.937540i | \(0.386903\pi\) | |||||||
\(380\) | −1.87939 | −0.0964104 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.9067 | −0.609201 | ||||||||
\(383\) | 15.9504 | 0.815026 | 0.407513 | − | 0.913199i | \(-0.366396\pi\) | ||||
0.407513 | + | 0.913199i | \(0.366396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.7324 | 0.852760 | ||||||||
\(386\) | −19.1607 | −0.975256 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.77332 | 0.0900266 | ||||||||
\(389\) | 28.5226 | 1.44615 | 0.723076 | − | 0.690768i | \(-0.242727\pi\) | ||||
0.723076 | + | 0.690768i | \(0.242727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.9736 | 1.66755 | ||||||||
\(392\) | −14.7118 | −0.743060 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.46017 | −0.224700 | ||||||||
\(395\) | 37.9222 | 1.90807 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3182 | 0.718610 | 0.359305 | − | 0.933220i | \(-0.383014\pi\) | ||||
0.359305 | + | 0.933220i | \(0.383014\pi\) | |||||||
\(398\) | 6.22937 | 0.312250 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0213551 | −0.00106775 | ||||||||
\(401\) | −0.709141 | −0.0354128 | −0.0177064 | − | 0.999843i | \(-0.505636\pi\) | ||||
−0.0177064 | + | 0.999843i | \(0.505636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.35773 | −0.117447 | ||||||||
\(404\) | 8.77776 | 0.436710 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.68004 | 0.182638 | ||||||||
\(407\) | −27.2371 | −1.35009 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2472 | 1.14950 | 0.574750 | − | 0.818329i | \(-0.305099\pi\) | ||||
0.574750 | + | 0.818329i | \(0.305099\pi\) | |||||||
\(410\) | −20.9067 | −1.03251 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.29086 | −0.359195 | ||||||||
\(413\) | −7.12836 | −0.350763 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.0610 | 1.72108 | ||||||||
\(416\) | 10.3601 | 0.507945 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.03684 | 0.148537 | ||||||||
\(419\) | −2.32089 | −0.113383 | −0.0566914 | − | 0.998392i | \(-0.518055\pi\) | ||||
−0.0566914 | + | 0.998392i | \(0.518055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.1266 | −1.12712 | −0.563561 | − | 0.826075i | \(-0.690569\pi\) | ||||
−0.563561 | + | 0.826075i | \(0.690569\pi\) | |||||||
\(422\) | 3.22937 | 0.157203 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.27208 | −0.0617777 | ||||||||
\(425\) | 4.01691 | 0.194849 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.1019 | −0.779228 | ||||||||
\(428\) | 2.47121 | 0.119450 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.4938 | 0.506057 | ||||||||
\(431\) | −13.3105 | −0.641142 | −0.320571 | − | 0.947224i | \(-0.603875\pi\) | ||||
−0.320571 | + | 0.947224i | \(0.603875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.46522 | −0.406813 | −0.203406 | − | 0.979094i | \(-0.565201\pi\) | ||||
−0.203406 | + | 0.979094i | \(0.565201\pi\) | |||||||
\(434\) | 1.52023 | 0.0729733 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.217186 | −0.0104013 | ||||||||
\(437\) | 2.73143 | 0.130662 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.1952 | 0.820683 | 0.410342 | − | 0.911932i | \(-0.365409\pi\) | ||||
0.410342 | + | 0.911932i | \(0.365409\pi\) | |||||||
\(440\) | −35.2395 | −1.67998 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.7320 | 0.605601 | ||||||||
\(443\) | 28.8949 | 1.37284 | 0.686418 | − | 0.727207i | \(-0.259182\pi\) | ||||
0.686418 | + | 0.727207i | \(0.259182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.6851 | 1.92866 | ||||||||
\(446\) | −21.8749 | −1.03581 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.79292 | −0.320935 | ||||||||
\(449\) | 3.61081 | 0.170405 | 0.0852024 | − | 0.996364i | \(-0.472846\pi\) | ||||
0.0852024 | + | 0.996364i | \(0.472846\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.5877 | −2.52335 | ||||||||
\(452\) | 4.54158 | 0.213618 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.26176 | −0.434676 | ||||||||
\(455\) | 5.81109 | 0.272428 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.61175 | −0.309285 | −0.154642 | − | 0.987971i | \(-0.549422\pi\) | ||||
−0.154642 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(458\) | 6.26176 | 0.292593 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0496 | −0.561817 | ||||||||
\(461\) | −36.3141 | −1.69132 | −0.845658 | − | 0.533726i | \(-0.820792\pi\) | ||||
−0.845658 | + | 0.533726i | \(0.820792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.4688 | −0.997742 | −0.498871 | − | 0.866676i | \(-0.666252\pi\) | ||||
−0.498871 | + | 0.866676i | \(0.666252\pi\) | |||||||
\(464\) | −0.130110 | −0.00604022 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.84430 | 0.131760 | ||||||||
\(467\) | −33.4861 | −1.54955 | −0.774776 | − | 0.632236i | \(-0.782137\pi\) | ||||
−0.774776 | + | 0.632236i | \(0.782137\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.879385 | 0.0406062 | ||||||||
\(470\) | 19.7784 | 0.912308 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.0128 | 0.691020 | ||||||||
\(473\) | 26.8976 | 1.23675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.332748 | 0.0152675 | ||||||||
\(476\) | 13.0223 | 0.596876 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.03952 | −0.321980 | ||||||||
\(479\) | −31.1607 | −1.42377 | −0.711885 | − | 0.702296i | \(-0.752159\pi\) | ||||
−0.711885 | + | 0.702296i | \(0.752159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.45935 | −0.431309 | ||||||||
\(482\) | 25.1284 | 1.14457 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.8452 | −0.947511 | ||||||||
\(485\) | −3.39330 | −0.154082 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.54158 | 0.251113 | 0.125557 | − | 0.992086i | \(-0.459928\pi\) | ||||
0.125557 | + | 0.992086i | \(0.459928\pi\) | |||||||
\(488\) | 33.9118 | 1.53511 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.7023 | 0.483482 | ||||||||
\(491\) | −13.2618 | −0.598495 | −0.299248 | − | 0.954176i | \(-0.596736\pi\) | ||||
−0.299248 | + | 0.954176i | \(0.596736\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.4739 | 1.10225 | ||||||||
\(494\) | 1.05468 | 0.0474524 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.0537486 | −0.00241339 | ||||||||
\(497\) | −17.9736 | −0.806226 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.02465 | 0.314467 | 0.157233 | − | 0.987561i | \(-0.449743\pi\) | ||||
0.157233 | + | 0.987561i | \(0.449743\pi\) | |||||||
\(500\) | 12.9290 | 0.578203 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.9317 | 0.755699 | ||||||||
\(503\) | 12.5381 | 0.559045 | 0.279523 | − | 0.960139i | \(-0.409824\pi\) | ||||
0.279523 | + | 0.960139i | \(0.409824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.7965 | −0.747436 | ||||||||
\(506\) | 19.4706 | 0.865574 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.22668 | 0.0544252 | ||||||||
\(509\) | 17.4320 | 0.772660 | 0.386330 | − | 0.922361i | \(-0.373743\pi\) | ||||
0.386330 | + | 0.922361i | \(0.373743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.13610 | −0.138733 | ||||||||
\(512\) | 0.473897 | 0.0209435 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.7442 | −0.782664 | ||||||||
\(515\) | 13.9513 | 0.614768 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 50.6955 | 2.22959 | ||||||||
\(518\) | 6.09926 | 0.267986 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.2385 | −0.536696 | ||||||||
\(521\) | −13.8871 | −0.608406 | −0.304203 | − | 0.952607i | \(-0.598390\pi\) | ||||
−0.304203 | + | 0.952607i | \(0.598390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.05375 | 0.308439 | 0.154219 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154219 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(524\) | 18.6940 | 0.816650 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.62124 | 0.288700 | ||||||||
\(527\) | 10.1102 | 0.440407 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.48751 | −0.238587 | ||||||||
\(530\) | 0.925393 | 0.0401965 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.07873 | 0.0467687 | ||||||||
\(533\) | −18.6108 | −0.806124 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.72874 | −0.204441 | ||||||||
\(536\) | −1.85204 | −0.0799961 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.7314 | −0.505778 | ||||||||
\(539\) | 27.4320 | 1.18158 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3969 | 1.13489 | 0.567446 | − | 0.823410i | \(-0.307931\pi\) | ||||
0.567446 | + | 0.823410i | \(0.307931\pi\) | |||||||
\(542\) | 23.3236 | 1.00183 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −44.4252 | −1.90471 | ||||||||
\(545\) | 0.415593 | 0.0178020 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.4834 | −1.43165 | −0.715823 | − | 0.698282i | \(-0.753948\pi\) | ||||
−0.715823 | + | 0.698282i | \(0.753948\pi\) | |||||||
\(548\) | −13.4935 | −0.576414 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.37195 | 0.101140 | ||||||||
\(551\) | 2.02734 | 0.0863676 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.7665 | −0.925606 | ||||||||
\(554\) | 7.76321 | 0.329827 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.271868 | 0.0115298 | ||||||||
\(557\) | 27.6682 | 1.17234 | 0.586169 | − | 0.810189i | \(-0.300635\pi\) | ||||
0.586169 | + | 0.810189i | \(0.300635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.34142 | 0.395100 | ||||||||
\(560\) | 0.132474 | 0.00559806 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.7341 | 0.663704 | ||||||||
\(563\) | −2.64321 | −0.111398 | −0.0556990 | − | 0.998448i | \(-0.517739\pi\) | ||||
−0.0556990 | + | 0.998448i | \(0.517739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.69047 | −0.365611 | ||||||||
\(566\) | −10.9469 | −0.460131 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 37.8536 | 1.58830 | ||||||||
\(569\) | −11.8939 | −0.498620 | −0.249310 | − | 0.968424i | \(-0.580204\pi\) | ||||
−0.249310 | + | 0.968424i | \(0.580204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.1334 | −0.800708 | −0.400354 | − | 0.916361i | \(-0.631113\pi\) | ||||
−0.400354 | + | 0.916361i | \(0.631113\pi\) | |||||||
\(572\) | −11.9257 | −0.498639 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 2.13341 | 0.0889693 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7561 | −0.780826 | −0.390413 | − | 0.920640i | \(-0.627668\pi\) | ||||
−0.390413 | + | 0.920640i | \(0.627668\pi\) | |||||||
\(578\) | −39.6468 | −1.64909 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.94356 | −0.371361 | ||||||||
\(581\) | −20.1242 | −0.834894 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.37195 | 0.0982361 | ||||||||
\(584\) | 6.60483 | 0.273310 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.8716 | 1.19268 | ||||||||
\(587\) | 28.2909 | 1.16769 | 0.583844 | − | 0.811866i | \(-0.301548\pi\) | ||||
0.583844 | + | 0.811866i | \(0.301548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.837496 | 0.0345084 | ||||||||
\(590\) | −10.9213 | −0.449622 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.215643 | −0.00886288 | ||||||||
\(593\) | −7.34730 | −0.301717 | −0.150859 | − | 0.988555i | \(-0.548204\pi\) | ||||
−0.150859 | + | 0.988555i | \(0.548204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.9186 | −1.02156 | ||||||||
\(596\) | 2.68839 | 0.110121 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.76207 | 0.276522 | ||||||||
\(599\) | 28.8922 | 1.18050 | 0.590251 | − | 0.807220i | \(-0.299029\pi\) | ||||
0.590251 | + | 0.807220i | \(0.299029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.2249 | 0.824992 | 0.412496 | − | 0.910959i | \(-0.364657\pi\) | ||||
0.412496 | + | 0.910959i | \(0.364657\pi\) | |||||||
\(602\) | −6.02322 | −0.245488 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.4097 | 0.627013 | ||||||||
\(605\) | 39.8881 | 1.62168 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.7128 | −0.800116 | −0.400058 | − | 0.916490i | \(-0.631010\pi\) | ||||
−0.400058 | + | 0.916490i | \(0.631010\pi\) | |||||||
\(608\) | −3.68004 | −0.149246 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.6696 | −0.998844 | ||||||||
\(611\) | 17.6064 | 0.712278 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.69728 | 0.189721 | 0.0948607 | − | 0.995491i | \(-0.469759\pi\) | ||||
0.0948607 | + | 0.995491i | \(0.469759\pi\) | |||||||
\(614\) | 14.5208 | 0.586013 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.2267 | 0.814956 | ||||||||
\(617\) | 41.9368 | 1.68831 | 0.844155 | − | 0.536099i | \(-0.180103\pi\) | ||||
0.844155 | + | 0.536099i | \(0.180103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0814 | 0.807140 | 0.403570 | − | 0.914949i | \(-0.367769\pi\) | ||||
0.403570 | + | 0.914949i | \(0.367769\pi\) | |||||||
\(620\) | −3.69459 | −0.148378 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.2490 | 0.491139 | ||||||||
\(623\) | −23.3523 | −0.935592 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2891 | −1.09156 | ||||||||
\(626\) | 8.95191 | 0.357790 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.4421 | 0.456590 | ||||||||
\(629\) | 40.5627 | 1.61734 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.97090 | −0.396935 | −0.198468 | − | 0.980107i | \(-0.563596\pi\) | ||||
−0.198468 | + | 0.980107i | \(0.563596\pi\) | |||||||
\(632\) | 45.8417 | 1.82349 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.5757 | 0.698022 | ||||||||
\(635\) | −2.34730 | −0.0931496 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.52704 | 0.377475 | ||||||||
\(638\) | 14.4516 | 0.572145 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.0615 | 0.634886 | ||||||||
\(641\) | 11.9513 | 0.472048 | 0.236024 | − | 0.971747i | \(-0.424156\pi\) | ||||
0.236024 | + | 0.971747i | \(0.424156\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.2668 | −0.878118 | −0.439059 | − | 0.898458i | \(-0.644688\pi\) | ||||
−0.439059 | + | 0.898458i | \(0.644688\pi\) | |||||||
\(644\) | 6.91622 | 0.272537 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.52259 | −0.177939 | ||||||||
\(647\) | 2.62773 | 0.103307 | 0.0516533 | − | 0.998665i | \(-0.483551\pi\) | ||||
0.0516533 | + | 0.998665i | \(0.483551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.9932 | −1.09883 | ||||||||
\(650\) | 0.823769 | 0.0323109 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.2763 | 0.519940 | ||||||||
\(653\) | 39.9873 | 1.56482 | 0.782412 | − | 0.622761i | \(-0.213989\pi\) | ||||
0.782412 | + | 0.622761i | \(0.213989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.7716 | −1.39771 | ||||||||
\(656\) | −0.424267 | −0.0165649 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.3523 | −0.442561 | ||||||||
\(659\) | 20.4388 | 0.796183 | 0.398092 | − | 0.917346i | \(-0.369673\pi\) | ||||
0.398092 | + | 0.917346i | \(0.369673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5767 | −0.800340 | −0.400170 | − | 0.916441i | \(-0.631049\pi\) | ||||
−0.400170 | + | 0.916441i | \(0.631049\pi\) | |||||||
\(662\) | −5.89311 | −0.229042 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 42.3830 | 1.64478 | ||||||||
\(665\) | −2.06418 | −0.0800454 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.9982 | 0.503294 | ||||||||
\(668\) | 1.68004 | 0.0650029 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.34730 | 0.0520506 | ||||||||
\(671\) | −63.2327 | −2.44107 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.6064 | 1.06415 | 0.532074 | − | 0.846698i | \(-0.321413\pi\) | ||||
0.532074 | + | 0.846698i | \(0.321413\pi\) | |||||||
\(674\) | −0.461104 | −0.0177611 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8051 | 0.454042 | ||||||||
\(677\) | −21.5107 | −0.826725 | −0.413362 | − | 0.910567i | \(-0.635646\pi\) | ||||
−0.413362 | + | 0.910567i | \(0.635646\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.94768 | 0.0747452 | ||||||||
\(680\) | 52.4802 | 2.01252 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.96997 | 0.228602 | ||||||||
\(683\) | 27.7452 | 1.06164 | 0.530819 | − | 0.847485i | \(-0.321884\pi\) | ||||
0.530819 | + | 0.847485i | \(0.321884\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.8203 | 0.986541 | ||||||||
\(686\) | −14.4365 | −0.551186 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.212955 | 0.00811882 | ||||||||
\(689\) | 0.823769 | 0.0313831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.86989 | 0.0711340 | 0.0355670 | − | 0.999367i | \(-0.488676\pi\) | ||||
0.0355670 | + | 0.999367i | \(0.488676\pi\) | |||||||
\(692\) | −20.3952 | −0.775308 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.0634 | −0.647716 | ||||||||
\(695\) | −0.520229 | −0.0197334 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 79.8052 | 3.02284 | ||||||||
\(698\) | 18.0841 | 0.684493 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.842549 | 0.0318453 | ||||||||
\(701\) | 36.0036 | 1.35984 | 0.679919 | − | 0.733287i | \(-0.262015\pi\) | ||||
0.679919 | + | 0.733287i | \(0.262015\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.36009 | 0.126728 | ||||||||
\(704\) | −26.6759 | −1.00539 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.7041 | 0.929751 | ||||||||
\(707\) | 9.64084 | 0.362581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.6723 | 0.438363 | 0.219181 | − | 0.975684i | \(-0.429661\pi\) | ||||
0.219181 | + | 0.975684i | \(0.429661\pi\) | |||||||
\(710\) | −27.5371 | −1.03345 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 49.1816 | 1.84316 | ||||||||
\(713\) | 5.36959 | 0.201093 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.8203 | 0.853429 | ||||||||
\(716\) | 8.54158 | 0.319214 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.58853 | 0.0966029 | ||||||||
\(719\) | 45.8539 | 1.71006 | 0.855031 | − | 0.518577i | \(-0.173538\pi\) | ||||
0.855031 | + | 0.518577i | \(0.173538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00774 | −0.298224 | ||||||||
\(722\) | 16.3337 | 0.607877 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.05468 | 0.113526 | ||||||||
\(725\) | 1.58347 | 0.0588087 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.111444 | 0.00413321 | 0.00206661 | − | 0.999998i | \(-0.499342\pi\) | ||||
0.00206661 | + | 0.999998i | \(0.499342\pi\) | |||||||
\(728\) | 7.02465 | 0.260351 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.80478 | −0.177833 | ||||||||
\(731\) | −40.0570 | −1.48156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0983 | −0.890092 | −0.445046 | − | 0.895508i | \(-0.646813\pi\) | ||||
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(734\) | −16.0636 | −0.592917 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23.5945 | −0.869705 | ||||||||
\(737\) | 3.45336 | 0.127206 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.54570 | −0.314359 | −0.157179 | − | 0.987570i | \(-0.550240\pi\) | ||||
−0.157179 | + | 0.987570i | \(0.550240\pi\) | |||||||
\(740\) | −14.8229 | −0.544902 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.531155 | −0.0194993 | ||||||||
\(743\) | −34.0401 | −1.24881 | −0.624406 | − | 0.781100i | \(-0.714659\pi\) | ||||
−0.624406 | + | 0.781100i | \(0.714659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.14433 | −0.188474 | ||||||||
\(746\) | −5.32150 | −0.194834 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 51.1388 | 1.86982 | ||||||||
\(749\) | 2.71419 | 0.0991745 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.29591 | 0.339213 | 0.169606 | − | 0.985512i | \(-0.445750\pi\) | ||||
0.169606 | + | 0.985512i | \(0.445750\pi\) | |||||||
\(752\) | 0.401369 | 0.0146364 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.01899 | 0.182781 | ||||||||
\(755\) | −29.4870 | −1.07314 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.9436 | 1.08832 | 0.544159 | − | 0.838982i | \(-0.316849\pi\) | ||||
0.544159 | + | 0.838982i | \(0.316849\pi\) | |||||||
\(758\) | −11.9112 | −0.432633 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.34730 | 0.157693 | ||||||||
\(761\) | 6.83656 | 0.247825 | 0.123913 | − | 0.992293i | \(-0.460456\pi\) | ||||
0.123913 | + | 0.992293i | \(0.460456\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.238541 | −0.00863577 | ||||||||
\(764\) | −16.6091 | −0.600895 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.0265 | −0.506799 | ||||||||
\(767\) | −9.72193 | −0.351039 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5253 | −0.559856 | −0.279928 | − | 0.960021i | \(-0.590311\pi\) | ||||
−0.279928 | + | 0.960021i | \(0.590311\pi\) | |||||||
\(770\) | −14.7142 | −0.530263 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26.7279 | −0.961959 | ||||||||
\(773\) | −30.1857 | −1.08571 | −0.542853 | − | 0.839828i | \(-0.682656\pi\) | ||||
−0.542853 | + | 0.839828i | \(0.682656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.654134 | 0.0234972 | ||||||||
\(776\) | −4.10195 | −0.147251 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.0823 | −0.899246 | ||||||||
\(779\) | 6.61081 | 0.236857 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.5827 | −2.52565 | ||||||||
\(782\) | −28.9965 | −1.03691 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.217186 | 0.00775665 | ||||||||
\(785\) | −21.8949 | −0.781461 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.0906 | 0.680506 | 0.340253 | − | 0.940334i | \(-0.389487\pi\) | ||||
0.340253 | + | 0.940334i | \(0.389487\pi\) | |||||||
\(788\) | −6.22163 | −0.221636 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.3482 | −1.18648 | ||||||||
\(791\) | 4.98814 | 0.177358 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.9605 | −0.779839 | ||||||||
\(794\) | −12.5912 | −0.446845 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.68954 | 0.307993 | ||||||||
\(797\) | −27.0452 | −0.957990 | −0.478995 | − | 0.877818i | \(-0.658999\pi\) | ||||
−0.478995 | + | 0.877818i | \(0.658999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75.4981 | −2.67093 | ||||||||
\(800\) | −2.87433 | −0.101623 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.623608 | 0.0220204 | ||||||||
\(803\) | −12.3155 | −0.434605 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.2344 | −0.466452 | ||||||||
\(806\) | 2.07335 | 0.0730306 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.3043 | −0.714301 | ||||||||
\(809\) | −2.24628 | −0.0789751 | −0.0394875 | − | 0.999220i | \(-0.512573\pi\) | ||||
−0.0394875 | + | 0.999220i | \(0.512573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.5090 | 1.49269 | 0.746346 | − | 0.665558i | \(-0.231806\pi\) | ||||
0.746346 | + | 0.665558i | \(0.231806\pi\) | |||||||
\(812\) | 5.13341 | 0.180147 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.9519 | 0.839514 | ||||||||
\(815\) | −25.4047 | −0.889887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.31820 | −0.116089 | ||||||||
\(818\) | −20.4433 | −0.714782 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.1634 | −1.01843 | ||||||||
\(821\) | 43.2850 | 1.51066 | 0.755328 | − | 0.655347i | \(-0.227477\pi\) | ||||
0.755328 | + | 0.655347i | \(0.227477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.6340 | 0.928404 | 0.464202 | − | 0.885729i | \(-0.346341\pi\) | ||||
0.464202 | + | 0.885729i | \(0.346341\pi\) | |||||||
\(824\) | 16.8648 | 0.587514 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.26857 | 0.218111 | ||||||||
\(827\) | −44.9053 | −1.56151 | −0.780755 | − | 0.624837i | \(-0.785165\pi\) | ||||
−0.780755 | + | 0.624837i | \(0.785165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.1361 | −0.873013 | −0.436506 | − | 0.899701i | \(-0.643784\pi\) | ||||
−0.436506 | + | 0.899701i | \(0.643784\pi\) | |||||||
\(830\) | −30.8321 | −1.07020 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.26445 | −0.321187 | ||||||||
\(833\) | −40.8530 | −1.41547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.21482 | −0.111254 | ||||||||
\(836\) | 4.23618 | 0.146511 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.04096 | 0.0705036 | ||||||||
\(839\) | −17.1530 | −0.592188 | −0.296094 | − | 0.955159i | \(-0.595684\pi\) | ||||
−0.296094 | + | 0.955159i | \(0.595684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.3523 | −0.667322 | ||||||||
\(842\) | 20.3372 | 0.700866 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.50475 | 0.155060 | ||||||||
\(845\) | −22.5895 | −0.777101 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.8949 | −0.786677 | ||||||||
\(848\) | 0.0187793 | 0.000644884 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.53241 | −0.121161 | ||||||||
\(851\) | 21.5431 | 0.738489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0327 | 0.514710 | 0.257355 | − | 0.966317i | \(-0.417149\pi\) | ||||
0.257355 | + | 0.966317i | \(0.417149\pi\) | |||||||
\(854\) | 14.1598 | 0.484539 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.71627 | −0.195378 | ||||||||
\(857\) | 19.1916 | 0.655573 | 0.327786 | − | 0.944752i | \(-0.393697\pi\) | ||||
0.327786 | + | 0.944752i | \(0.393697\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3527 | 0.455587 | 0.227794 | − | 0.973709i | \(-0.426849\pi\) | ||||
0.227794 | + | 0.973709i | \(0.426849\pi\) | |||||||
\(860\) | 14.6382 | 0.499157 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.7050 | 0.398675 | ||||||||
\(863\) | −25.3577 | −0.863187 | −0.431594 | − | 0.902068i | \(-0.642049\pi\) | ||||
−0.431594 | + | 0.902068i | \(0.642049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.0268 | 1.32695 | ||||||||
\(866\) | 7.44419 | 0.252964 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.12061 | 0.0719784 | ||||||||
\(869\) | −85.4775 | −2.89963 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.19934 | 0.0406381 | ||||||||
\(872\) | 0.502384 | 0.0170129 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.40198 | −0.0812481 | ||||||||
\(875\) | 14.2003 | 0.480057 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.1257 | −0.814666 | −0.407333 | − | 0.913280i | \(-0.633541\pi\) | ||||
−0.407333 | + | 0.913280i | \(0.633541\pi\) | |||||||
\(878\) | −15.1212 | −0.510317 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.520229 | 0.0175369 | ||||||||
\(881\) | 42.7606 | 1.44064 | 0.720321 | − | 0.693641i | \(-0.243994\pi\) | ||||
0.720321 | + | 0.693641i | \(0.243994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.2983 | 0.716744 | 0.358372 | − | 0.933579i | \(-0.383332\pi\) | ||||
0.358372 | + | 0.933579i | \(0.383332\pi\) | |||||||
\(884\) | 17.7603 | 0.597344 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.4097 | −0.853656 | ||||||||
\(887\) | 27.9956 | 0.939999 | 0.469999 | − | 0.882667i | \(-0.344254\pi\) | ||||
0.469999 | + | 0.882667i | \(0.344254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.34730 | 0.0451869 | ||||||||
\(890\) | −35.7779 | −1.19928 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.5140 | −1.02169 | ||||||||
\(893\) | −6.25402 | −0.209283 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.3446 | −0.546340 | ||||||||
\(896\) | −9.21894 | −0.307983 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.17530 | −0.105961 | ||||||||
\(899\) | 3.98545 | 0.132922 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.53241 | −0.117682 | ||||||||
\(902\) | 47.1242 | 1.56907 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.5054 | −0.349403 | ||||||||
\(905\) | −5.84524 | −0.194302 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3750 | 0.610131 | 0.305065 | − | 0.952331i | \(-0.401322\pi\) | ||||
0.305065 | + | 0.952331i | \(0.401322\pi\) | |||||||
\(908\) | −12.9195 | −0.428749 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.11019 | −0.169401 | ||||||||
\(911\) | 16.3625 | 0.542112 | 0.271056 | − | 0.962564i | \(-0.412627\pi\) | ||||
0.271056 | + | 0.962564i | \(0.412627\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −79.0283 | −2.61545 | ||||||||
\(914\) | 5.81427 | 0.192319 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.73473 | 0.288604 | ||||||||
\(917\) | 20.5321 | 0.678029 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.5340 | −1.43605 | −0.718026 | − | 0.696016i | \(-0.754954\pi\) | ||||
−0.718026 | + | 0.696016i | \(0.754954\pi\) | |||||||
\(920\) | 27.8726 | 0.918932 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.9341 | 1.05169 | ||||||||
\(923\) | −24.5131 | −0.806858 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.62443 | 0.0862907 | ||||||||
\(926\) | 18.8794 | 0.620415 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.5125 | −0.574876 | ||||||||
\(929\) | −10.0368 | −0.329298 | −0.164649 | − | 0.986352i | \(-0.552649\pi\) | ||||
−0.164649 | + | 0.986352i | \(0.552649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.38413 | −0.110910 | ||||||||
\(932\) | 3.96761 | 0.129963 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.4472 | 0.963541 | ||||||||
\(935\) | −97.8558 | −3.20023 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.0865 | −1.01555 | −0.507775 | − | 0.861490i | \(-0.669532\pi\) | ||||
−0.507775 | + | 0.861490i | \(0.669532\pi\) | |||||||
\(938\) | −0.773318 | −0.0252497 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 27.5895 | 0.899869 | ||||||||
\(941\) | 14.1976 | 0.462828 | 0.231414 | − | 0.972855i | \(-0.425665\pi\) | ||||
0.231414 | + | 0.972855i | \(0.425665\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.3851 | 1.38025 | ||||||||
\(944\) | −0.221629 | −0.00721341 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.6533 | −0.769036 | ||||||||
\(947\) | −50.3236 | −1.63530 | −0.817648 | − | 0.575718i | \(-0.804723\pi\) | ||||
−0.817648 | + | 0.575718i | \(0.804723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.27713 | −0.138842 | ||||||||
\(950\) | −0.292614 | −0.00949365 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −30.1225 | −0.976275 | ||||||||
\(953\) | 34.1539 | 1.10635 | 0.553177 | − | 0.833064i | \(-0.313415\pi\) | ||||
0.553177 | + | 0.833064i | \(0.313415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.7820 | 1.02844 | ||||||||
\(956\) | −9.81965 | −0.317590 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.4023 | 0.885328 | ||||||||
\(959\) | −14.8203 | −0.478571 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3536 | −0.946891 | ||||||||
\(962\) | 8.31841 | 0.268196 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.0523 | 1.12896 | ||||||||
\(965\) | 51.1448 | 1.64641 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.47472 | 0.0795816 | 0.0397908 | − | 0.999208i | \(-0.487331\pi\) | ||||
0.0397908 | + | 0.999208i | \(0.487331\pi\) | |||||||
\(968\) | 48.2181 | 1.54979 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.98402 | 0.0958112 | ||||||||
\(971\) | −35.0770 | −1.12567 | −0.562837 | − | 0.826568i | \(-0.690290\pi\) | ||||
−0.562837 | + | 0.826568i | \(0.690290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.298600 | 0.00957268 | ||||||||
\(974\) | −4.87319 | −0.156147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.500629 | −0.0160247 | ||||||||
\(977\) | 16.6581 | 0.532939 | 0.266470 | − | 0.963843i | \(-0.414143\pi\) | ||||
0.266470 | + | 0.963843i | \(0.414143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −91.7051 | −2.93091 | ||||||||
\(980\) | 14.9290 | 0.476890 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.6622 | 0.372156 | ||||||||
\(983\) | 42.9009 | 1.36832 | 0.684162 | − | 0.729330i | \(-0.260168\pi\) | ||||
0.684162 | + | 0.729330i | \(0.260168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.9053 | 0.379334 | ||||||||
\(986\) | −21.5220 | −0.685400 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.47121 | 0.0468054 | ||||||||
\(989\) | −21.2746 | −0.676492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9213 | 0.791650 | 0.395825 | − | 0.918326i | \(-0.370459\pi\) | ||||
0.395825 | + | 0.918326i | \(0.370459\pi\) | |||||||
\(992\) | −7.23442 | −0.229693 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.8057 | 0.501327 | ||||||||
\(995\) | −16.6277 | −0.527134 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.6141 | 0.526174 | 0.263087 | − | 0.964772i | \(-0.415259\pi\) | ||||
0.263087 | + | 0.964772i | \(0.415259\pi\) | |||||||
\(998\) | −6.17738 | −0.195541 | ||||||||
\(999\) | 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 | 1143.2.a.e.1.1 | 3 | ||
3.2 | odd | 2 | 127.2.a.a.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 2032.2.a.k.1.3 | 3 | |||
15.14 | odd | 2 | 3175.2.a.h.1.1 | 3 | |||
21.20 | even | 2 | 6223.2.a.e.1.3 | 3 | |||
24.5 | odd | 2 | 8128.2.a.bd.1.3 | 3 | |||
24.11 | even | 2 | 8128.2.a.w.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
127.2.a.a.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1143.2.a.e.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2032.2.a.k.1.3 | 3 | 12.11 | even | 2 | |||
3175.2.a.h.1.1 | 3 | 15.14 | odd | 2 | |||
6223.2.a.e.1.3 | 3 | 21.20 | even | 2 | |||
8128.2.a.w.1.1 | 3 | 24.11 | even | 2 | |||
8128.2.a.bd.1.3 | 3 | 24.5 | odd | 2 |