Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + \cdots + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.09328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0932775 | −0.0417150 | −0.0208575 | − | 0.999782i | \(-0.506640\pi\) | ||||
−0.0208575 | + | 0.999782i | \(0.506640\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.86231 | −1.45982 | −0.729908 | − | 0.683545i | \(-0.760437\pi\) | ||||
−0.729908 | + | 0.683545i | \(0.760437\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.61303 | −1.39088 | −0.695441 | − | 0.718584i | \(-0.744791\pi\) | ||||
−0.695441 | + | 0.718584i | \(0.744791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.601864 | −0.166927 | −0.0834636 | − | 0.996511i | \(-0.526598\pi\) | ||||
−0.0834636 | + | 0.996511i | \(0.526598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0932775 | −0.0240842 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.832355 | −0.201876 | −0.100938 | − | 0.994893i | \(-0.532184\pi\) | ||||
−0.100938 | + | 0.994893i | \(0.532184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.67672 | −0.843497 | −0.421748 | − | 0.906713i | \(-0.638583\pi\) | ||||
−0.421748 | + | 0.906713i | \(0.638583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.86231 | −0.842825 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.30257 | −1.31418 | −0.657088 | − | 0.753814i | \(-0.728212\pi\) | ||||
−0.657088 | + | 0.753814i | \(0.728212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99130 | −0.998260 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.62585 | 0.858999 | 0.429500 | − | 0.903067i | \(-0.358690\pi\) | ||||
0.429500 | + | 0.903067i | \(0.358690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.74106 | −0.851519 | −0.425760 | − | 0.904836i | \(-0.639993\pi\) | ||||
−0.425760 | + | 0.904836i | \(0.639993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.61303 | −0.803026 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.360267 | 0.0608962 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.70292 | 0.937555 | 0.468777 | − | 0.883316i | \(-0.344695\pi\) | ||||
0.468777 | + | 0.883316i | \(0.344695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.601864 | −0.0963754 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.02105 | −0.627982 | −0.313991 | − | 0.949426i | \(-0.601666\pi\) | ||||
−0.313991 | + | 0.949426i | \(0.601666\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.85227 | 0.587466 | 0.293733 | − | 0.955887i | \(-0.405102\pi\) | ||||
0.293733 | + | 0.955887i | \(0.405102\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0932775 | −0.0139050 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.09137 | −0.305057 | −0.152529 | − | 0.988299i | \(-0.548742\pi\) | ||||
−0.152529 | + | 0.988299i | \(0.548742\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.91745 | 1.13106 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.832355 | −0.116553 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.76489 | 1.06659 | 0.533295 | − | 0.845930i | \(-0.320954\pi\) | ||||
0.533295 | + | 0.845930i | \(0.320954\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.430292 | 0.0580206 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.67672 | −0.486993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.38419 | 0.570772 | 0.285386 | − | 0.958413i | \(-0.407878\pi\) | ||||
0.285386 | + | 0.958413i | \(0.407878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.61504 | 0.206785 | 0.103393 | − | 0.994641i | \(-0.467030\pi\) | ||||
0.103393 | + | 0.994641i | \(0.467030\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.86231 | −0.486606 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0561404 | 0.00696336 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7662 | 1.55964 | 0.779821 | − | 0.626002i | \(-0.215310\pi\) | ||||
0.779821 | + | 0.626002i | \(0.215310\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.30257 | −0.758740 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.1673 | 1.56267 | 0.781337 | − | 0.624109i | \(-0.214538\pi\) | ||||
0.781337 | + | 0.624109i | \(0.214538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.17998 | 0.255147 | 0.127574 | − | 0.991829i | \(-0.459281\pi\) | ||||
0.127574 | + | 0.991829i | \(0.459281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.99130 | −0.576346 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.8170 | 2.03043 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.12808 | 0.914481 | 0.457240 | − | 0.889343i | \(-0.348838\pi\) | ||||
0.457240 | + | 0.889343i | \(0.348838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.46750 | 0.270844 | 0.135422 | − | 0.990788i | \(-0.456761\pi\) | ||||
0.135422 | + | 0.990788i | \(0.456761\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0776400 | 0.00842124 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.62585 | 0.495944 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.23125 | 0.448512 | 0.224256 | − | 0.974530i | \(-0.428005\pi\) | ||||
0.224256 | + | 0.974530i | \(0.428005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.32459 | 0.243683 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.74106 | −0.491625 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.342955 | 0.0351864 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.07885 | 0.312610 | 0.156305 | − | 0.987709i | \(-0.450042\pi\) | ||||
0.156305 | + | 0.987709i | \(0.450042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.61303 | −0.463627 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.37707 | 0.734046 | 0.367023 | − | 0.930212i | \(-0.380377\pi\) | ||||
0.367023 | + | 0.930212i | \(0.380377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.13078 | 0.505551 | 0.252775 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252775 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.360267 | 0.0351584 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.13448 | −0.399696 | −0.199848 | − | 0.979827i | \(-0.564045\pi\) | ||||
−0.199848 | + | 0.979827i | \(0.564045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.1790 | −1.54967 | −0.774833 | − | 0.632166i | \(-0.782166\pi\) | ||||
−0.774833 | + | 0.632166i | \(0.782166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.70292 | 0.541298 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0108 | −1.41210 | −0.706050 | − | 0.708162i | \(-0.749524\pi\) | ||||
−0.706050 | + | 0.708162i | \(0.749524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.587888 | 0.0548208 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.601864 | −0.0556424 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.21482 | 0.294702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2801 | 0.934551 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.02105 | −0.362565 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.931964 | 0.0833574 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.742937 | −0.0659250 | −0.0329625 | − | 0.999457i | \(-0.510494\pi\) | ||||
−0.0329625 | + | 0.999457i | \(0.510494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.85227 | 0.339174 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.4308 | −1.87242 | −0.936209 | − | 0.351444i | \(-0.885691\pi\) | ||||
−0.936209 | + | 0.351444i | \(0.885691\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.2006 | 1.23135 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0932775 | −0.00802805 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.6892 | 1.25498 | 0.627492 | − | 0.778623i | \(-0.284082\pi\) | ||||
0.627492 | + | 0.778623i | \(0.284082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.1246 | 1.45249 | 0.726247 | − | 0.687434i | \(-0.241263\pi\) | ||||
0.726247 | + | 0.687434i | \(0.241263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.09137 | −0.176125 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.77642 | 0.232176 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.431488 | −0.0358331 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.91745 | 0.653020 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.3475 | 1.33924 | 0.669620 | − | 0.742704i | \(-0.266457\pi\) | ||||
0.669620 | + | 0.742704i | \(0.266457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.37955 | 0.437782 | 0.218891 | − | 0.975749i | \(-0.429756\pi\) | ||||
0.218891 | + | 0.975749i | \(0.429756\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.832355 | −0.0672919 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.442234 | 0.0355211 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.59090 | −0.206776 | −0.103388 | − | 0.994641i | \(-0.532968\pi\) | ||||
−0.103388 | + | 0.994641i | \(0.532968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.76489 | 0.615796 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.3425 | 1.91846 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.8771 | −1.16526 | −0.582631 | − | 0.812737i | \(-0.697977\pi\) | ||||
−0.582631 | + | 0.812737i | \(0.697977\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.430292 | 0.0334982 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6378 | −0.972135 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.67672 | −0.281166 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.39765 | 0.182290 | 0.0911448 | − | 0.995838i | \(-0.470947\pi\) | ||||
0.0911448 | + | 0.995838i | \(0.470947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.2780 | 1.45728 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.38419 | 0.329536 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.24300 | 0.690854 | 0.345427 | − | 0.938446i | \(-0.387734\pi\) | ||||
0.345427 | + | 0.938446i | \(0.387734\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.04367 | 0.523552 | 0.261776 | − | 0.965129i | \(-0.415692\pi\) | ||||
0.261776 | + | 0.965129i | \(0.415692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.61504 | 0.119387 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.531955 | −0.0391101 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.83968 | 0.280785 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.86231 | −0.280942 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.2775 | −0.816009 | −0.408004 | − | 0.912980i | \(-0.633775\pi\) | ||||
−0.408004 | + | 0.912980i | \(0.633775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.525080 | −0.0377961 | −0.0188980 | − | 0.999821i | \(-0.506016\pi\) | ||||
−0.0188980 | + | 0.999821i | \(0.506016\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0561404 | 0.00402030 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.7353 | −1.26359 | −0.631795 | − | 0.775136i | \(-0.717681\pi\) | ||||
−0.631795 | + | 0.775136i | \(0.717681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8380 | −1.05184 | −0.525920 | − | 0.850534i | \(-0.676279\pi\) | ||||
−0.525920 | + | 0.850534i | \(0.676279\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.7662 | 0.900460 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.8665 | −1.25398 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.375073 | 0.0261962 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.30257 | −0.438059 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.9608 | 1.17320 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0538 | −1.72478 | −0.862388 | − | 0.506247i | \(-0.831032\pi\) | ||||
−0.862388 | + | 0.506247i | \(0.831032\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.1673 | 0.902210 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.359331 | −0.0245061 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.3114 | 1.24306 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.17998 | 0.147309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.500965 | 0.0336986 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.95620 | −0.465822 | −0.232911 | − | 0.972498i | \(-0.574825\pi\) | ||||
−0.232911 | + | 0.972498i | \(0.574825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99130 | −0.332753 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5654 | −0.701250 | −0.350625 | − | 0.936516i | \(-0.614031\pi\) | ||||
−0.350625 | + | 0.936516i | \(0.614031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.6950 | 1.16932 | 0.584660 | − | 0.811279i | \(-0.301228\pi\) | ||||
0.584660 | + | 0.811279i | \(0.301228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.8170 | 1.17227 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.03342 | 0.198726 | 0.0993628 | − | 0.995051i | \(-0.468320\pi\) | ||||
0.0993628 | + | 0.995051i | \(0.468320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.195078 | 0.0127255 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.12808 | 0.527976 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.47139 | 0.353915 | 0.176957 | − | 0.984219i | \(-0.443375\pi\) | ||||
0.176957 | + | 0.984219i | \(0.443375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.1326 | −1.29685 | −0.648427 | − | 0.761277i | \(-0.724573\pi\) | ||||
−0.648427 | + | 0.761277i | \(0.724573\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.738520 | −0.0471823 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.21288 | 0.140802 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.46750 | 0.156372 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.8256 | −0.746424 | −0.373212 | − | 0.927746i | \(-0.621744\pi\) | ||||
−0.373212 | + | 0.927746i | \(0.621744\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.0739 | 1.82786 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0776400 | 0.00486201 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.9960 | 1.74634 | 0.873172 | − | 0.487412i | \(-0.162059\pi\) | ||||
0.873172 | + | 0.487412i | \(0.162059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.0265 | −1.36866 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.62585 | 0.286333 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.13973 | −0.0702790 | −0.0351395 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351395 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.724289 | −0.0444927 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.23125 | 0.258948 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.10035 | 0.189031 | 0.0945157 | − | 0.995523i | \(-0.469870\pi\) | ||||
0.0945157 | + | 0.995523i | \(0.469870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9980 | 1.64001 | 0.820007 | − | 0.572354i | \(-0.193970\pi\) | ||||
0.820007 | + | 0.572354i | \(0.193970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.32459 | 0.140690 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.0250 | 1.38846 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.24414 | 0.555427 | 0.277713 | − | 0.960664i | \(-0.410423\pi\) | ||||
0.277713 | + | 0.960664i | \(0.410423\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.74106 | −0.283840 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.83309 | −0.109353 | −0.0546765 | − | 0.998504i | \(-0.517413\pi\) | ||||
−0.0546765 | + | 0.998504i | \(0.517413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.27493 | −0.135230 | −0.0676152 | − | 0.997711i | \(-0.521539\pi\) | ||||
−0.0676152 | + | 0.997711i | \(0.521539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.342955 | 0.0203149 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5305 | 0.916738 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3072 | −0.959246 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.07885 | 0.180485 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 33.0304 | 1.92966 | 0.964830 | − | 0.262876i | \(-0.0846711\pi\) | ||||
0.964830 | + | 0.262876i | \(0.0846711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.408946 | −0.0238098 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.61303 | −0.267675 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.79329 | 0.219372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.8787 | −0.857593 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.37707 | 0.423801 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.150647 | −0.00862603 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.54712 | −0.202445 | −0.101222 | − | 0.994864i | \(-0.532275\pi\) | ||||
−0.101222 | + | 0.994864i | \(0.532275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.13078 | 0.291880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.22270 | 0.522971 | 0.261486 | − | 0.965207i | \(-0.415788\pi\) | ||||
0.261486 | + | 0.965207i | \(0.415788\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6463 | −0.771335 | −0.385668 | − | 0.922638i | \(-0.626029\pi\) | ||||
−0.385668 | + | 0.922638i | \(0.626029\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.360267 | 0.0202987 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.8395 | 0.777304 | 0.388652 | − | 0.921385i | \(-0.372941\pi\) | ||||
0.388652 | + | 0.921385i | \(0.372941\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.3392 | −1.19477 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.13448 | −0.230764 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.06033 | 0.170282 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00409 | 0.166637 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.1790 | −0.894701 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.07752 | 0.445328 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.2468 | 1.82741 | 0.913705 | − | 0.406377i | \(-0.133208\pi\) | ||||
0.913705 | + | 0.406377i | \(0.133208\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.70292 | 0.312518 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.19080 | −0.0650604 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.7473 | 1.78386 | 0.891930 | − | 0.452174i | \(-0.149351\pi\) | ||||
0.891930 | + | 0.452174i | \(0.149351\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.0108 | −0.815276 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.8707 | 1.18436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.54348 | −0.191330 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.587888 | 0.0316508 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.842952 | −0.0452521 | −0.0226260 | − | 0.999744i | \(-0.507203\pi\) | ||||
−0.0226260 | + | 0.999744i | \(0.507203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.514223 | 0.0275257 | 0.0137629 | − | 0.999905i | \(-0.495619\pi\) | ||||
0.0137629 | + | 0.999905i | \(0.495619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.601864 | −0.0321251 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.5789 | −0.775958 | −0.387979 | − | 0.921668i | \(-0.626827\pi\) | ||||
−0.387979 | + | 0.921668i | \(0.626827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.22822 | −0.0651869 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.21482 | 0.170146 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.12726 | 0.165050 | 0.0825252 | − | 0.996589i | \(-0.473702\pi\) | ||||
0.0825252 | + | 0.996589i | \(0.473702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.48176 | −0.288514 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.2801 | 0.539563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.203343 | −0.0106435 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.4895 | −1.06955 | −0.534773 | − | 0.844996i | \(-0.679603\pi\) | ||||
−0.534773 | + | 0.844996i | \(0.679603\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.02105 | −0.209327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.9904 | −1.55702 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.4296 | −0.902470 | −0.451235 | − | 0.892405i | \(-0.649016\pi\) | ||||
−0.451235 | + | 0.892405i | \(0.649016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.931964 | 0.0481264 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.78414 | −0.143390 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3457 | 0.736890 | 0.368445 | − | 0.929650i | \(-0.379890\pi\) | ||||
0.368445 | + | 0.929650i | \(0.379890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.742937 | −0.0380618 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.3329 | 1.44774 | 0.723872 | − | 0.689934i | \(-0.242361\pi\) | ||||
0.723872 | + | 0.689934i | \(0.242361\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.66192 | −0.0846994 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.85227 | 0.195822 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.8631 | −0.854991 | −0.427496 | − | 0.904017i | \(-0.640604\pi\) | ||||
−0.427496 | + | 0.904017i | \(0.640604\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.24598 | 0.265300 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.4308 | −1.08104 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.758167 | −0.0381475 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3038 | 1.57109 | 0.785546 | − | 0.618803i | \(-0.212382\pi\) | ||||
0.785546 | + | 0.618803i | \(0.212382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.2006 | 0.710920 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.0449210 | −0.00224325 | −0.00112162 | − | 0.999999i | \(-0.500357\pi\) | ||||
−0.00112162 | + | 0.999999i | \(0.500357\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.85348 | 0.142142 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.0932775 | −0.00463500 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.3078 | −1.30403 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.4314 | 0.960821 | 0.480411 | − | 0.877044i | \(-0.340488\pi\) | ||||
0.480411 | + | 0.877044i | \(0.340488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.6892 | 0.724565 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.9331 | −0.833223 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.230163 | −0.0112982 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.1246 | 0.838597 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.5480 | −1.68778 | −0.843889 | − | 0.536517i | \(-0.819740\pi\) | ||||
−0.843889 | + | 0.536517i | \(0.819740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.22382 | 0.0596455 | 0.0298227 | − | 0.999555i | \(-0.490506\pi\) | ||||
0.0298227 | + | 0.999555i | \(0.490506\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.09137 | −0.101686 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.15453 | 0.201525 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.23780 | −0.301868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.77642 | 0.134047 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4784 | 0.601063 | 0.300531 | − | 0.953772i | \(-0.402836\pi\) | ||||
0.300531 | + | 0.953772i | \(0.402836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.8043 | −0.807565 | −0.403782 | − | 0.914855i | \(-0.632305\pi\) | ||||
−0.403782 | + | 0.914855i | \(0.632305\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.431488 | −0.0206883 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.1728 | 1.10850 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2911 | 0.634350 | 0.317175 | − | 0.948367i | \(-0.397266\pi\) | ||||
0.317175 | + | 0.948367i | \(0.397266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.91745 | 0.377021 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5380 | −1.11832 | −0.559162 | − | 0.829059i | \(-0.688877\pi\) | ||||
−0.559162 | + | 0.829059i | \(0.688877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.394681 | −0.0187097 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.3475 | 0.773211 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.0913 | −1.46729 | −0.733644 | − | 0.679534i | \(-0.762182\pi\) | ||||
−0.733644 | + | 0.679534i | \(0.762182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.5492 | 0.873448 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.37955 | 0.252753 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.216832 | −0.0101652 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.8267 | −1.11457 | −0.557283 | − | 0.830323i | \(-0.688156\pi\) | ||||
−0.557283 | + | 0.830323i | \(0.688156\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.832355 | −0.0388510 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.24371 | 0.383948 | 0.191974 | − | 0.981400i | \(-0.438511\pi\) | ||||
0.191974 | + | 0.981400i | \(0.438511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.22478 | 0.242816 | 0.121408 | − | 0.992603i | \(-0.461259\pi\) | ||||
0.121408 | + | 0.992603i | \(0.461259\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.442234 | 0.0205081 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.6902 | 0.772328 | 0.386164 | − | 0.922430i | \(-0.373800\pi\) | ||||
0.386164 | + | 0.922430i | \(0.373800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −49.3071 | −2.27679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.59090 | −0.119382 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.7707 | −0.817096 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.3516 | 0.842029 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.76489 | 0.355530 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.87991 | 0.451425 | 0.225712 | − | 0.974194i | \(-0.427529\pi\) | ||||
0.225712 | + | 0.974194i | \(0.427529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.43239 | −0.156503 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.3425 | 1.10762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.287187 | −0.0130405 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.04928 | 0.138176 | 0.0690881 | − | 0.997611i | \(-0.477991\pi\) | ||||
0.0690881 | + | 0.997611i | \(0.477991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.8771 | −0.672764 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.2489 | 1.41024 | 0.705121 | − | 0.709087i | \(-0.250893\pi\) | ||||
0.705121 | + | 0.709087i | \(0.250893\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.85035 | −0.173411 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.430292 | 0.0193402 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −50.8563 | −2.28122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0818 | −1.12282 | −0.561409 | − | 0.827539i | \(-0.689740\pi\) | ||||
−0.561409 | + | 0.827539i | \(0.689740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.7306 | −0.835155 | −0.417578 | − | 0.908641i | \(-0.637121\pi\) | ||||
−0.417578 | + | 0.908641i | \(0.637121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.688115 | −0.0306207 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6378 | −0.561263 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6596 | 0.694098 | 0.347049 | − | 0.937847i | \(-0.387184\pi\) | ||||
0.347049 | + | 0.937847i | \(0.387184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.41977 | −0.372468 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.67672 | −0.162331 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.478586 | −0.0210890 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.64755 | 0.424299 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.39765 | 0.105245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.7109 | 1.03879 | 0.519397 | − | 0.854533i | \(-0.326156\pi\) | ||||
0.519397 | + | 0.854533i | \(0.326156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.3744 | 1.19700 | 0.598500 | − | 0.801123i | \(-0.295764\pi\) | ||||
0.598500 | + | 0.801123i | \(0.295764\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.2780 | 0.841359 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.94625 | 0.171901 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.7224 | 0.727060 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.38419 | 0.190257 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.42012 | 0.104827 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.385654 | 0.0166733 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.24300 | 0.398865 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.5234 | −1.57318 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.8135 | −1.19580 | −0.597899 | − | 0.801572i | \(-0.703998\pi\) | ||||
−0.597899 | + | 0.801572i | \(0.703998\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.04367 | 0.302273 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.50914 | 0.0646443 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5049 | −0.577427 | −0.288714 | − | 0.957415i | \(-0.593228\pi\) | ||||
−0.288714 | + | 0.957415i | \(0.593228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.61504 | 0.0689283 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.0079 | −0.724563 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.3932 | −1.33497 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.531955 | −0.0225802 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.31791 | 0.394812 | 0.197406 | − | 0.980322i | \(-0.436748\pi\) | ||||
0.197406 | + | 0.980322i | \(0.436748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.31855 | −0.0980641 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.83968 | 0.162111 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.6760 | −1.33498 | −0.667492 | − | 0.744617i | \(-0.732632\pi\) | ||||
−0.667492 | + | 0.744617i | \(0.732632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.40017 | 0.0589057 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.86231 | −0.162202 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.3201 | −0.684175 | −0.342087 | − | 0.939668i | \(-0.611134\pi\) | ||||
−0.342087 | + | 0.939668i | \(0.611134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.0316 | −0.545357 | −0.272679 | − | 0.962105i | \(-0.587910\pi\) | ||||
−0.272679 | + | 0.962105i | \(0.587910\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.2775 | −0.471123 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.4580 | 1.31189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6936 | −0.486810 | −0.243405 | − | 0.969925i | \(-0.578264\pi\) | ||||
−0.243405 | + | 0.969925i | \(0.578264\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.525080 | −0.0218216 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.53027 | −0.395382 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.8197 | −1.48350 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0561404 | 0.00232112 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.9904 | 1.40294 | 0.701468 | − | 0.712701i | \(-0.252528\pi\) | ||||
0.701468 | + | 0.712701i | \(0.252528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.4315 | 0.718254 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.7353 | −0.729534 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.0891 | 1.11242 | 0.556208 | − | 0.831043i | \(-0.312256\pi\) | ||||
0.556208 | + | 0.831043i | \(0.312256\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.299870 | −0.0122935 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.8380 | −0.607280 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.6427 | 1.78319 | 0.891597 | − | 0.452830i | \(-0.149585\pi\) | ||||
0.891597 | + | 0.452830i | \(0.149585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.2968 | 0.623969 | 0.311984 | − | 0.950087i | \(-0.399006\pi\) | ||||
0.311984 | + | 0.950087i | \(0.399006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.7662 | 0.519881 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.958898 | −0.0389848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.1380 | −1.14208 | −0.571042 | − | 0.820921i | \(-0.693461\pi\) | ||||
−0.571042 | + | 0.820921i | \(0.693461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.8665 | −0.723987 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.25872 | 0.0509224 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.5990 | −1.84173 | −0.920864 | − | 0.389884i | \(-0.872515\pi\) | ||||
−0.920864 | + | 0.389884i | \(0.872515\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.375073 | 0.0151244 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.68654 | −0.389965 | −0.194983 | − | 0.980807i | \(-0.562465\pi\) | ||||
−0.194983 | + | 0.980807i | \(0.562465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.87505 | 0.155752 | 0.0778758 | − | 0.996963i | \(-0.475186\pi\) | ||||
0.0778758 | + | 0.996963i | \(0.475186\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.30257 | −0.252913 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.3424 | −0.654745 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8696 | 0.994783 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.9608 | 0.677349 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.74686 | −0.189270 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.6390 | 0.901244 | 0.450622 | − | 0.892715i | \(-0.351202\pi\) | ||||
0.450622 | + | 0.892715i | \(0.351202\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.0538 | −0.995800 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0692993 | 0.00275006 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.76523 | −0.188805 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1673 | 0.520891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.55587 | 0.219444 | 0.109722 | − | 0.993962i | \(-0.465004\pi\) | ||||
0.109722 | + | 0.993962i | \(0.465004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.1357 | 0.754639 | 0.377320 | − | 0.926083i | \(-0.376846\pi\) | ||||
0.377320 | + | 0.926083i | \(0.376846\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.359331 | −0.0141486 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.6418 | 0.418372 | 0.209186 | − | 0.977876i | \(-0.432919\pi\) | ||||
0.209186 | + | 0.977876i | \(0.432919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.2244 | −0.793876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.3114 | 0.717682 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.42895 | 0.251584 | 0.125792 | − | 0.992057i | \(-0.459853\pi\) | ||||
0.125792 | + | 0.992057i | \(0.459853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.99901 | 0.0781079 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.17998 | 0.0850492 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.838749 | 0.0326730 | 0.0163365 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163365 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.2337 | 0.592521 | 0.296261 | − | 0.955107i | \(-0.404260\pi\) | ||||
0.296261 | + | 0.955107i | \(0.404260\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.500965 | 0.0194559 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.32460 | −0.0513657 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.1548 | −1.12888 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.95620 | −0.268942 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.45024 | −0.287613 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.9761 | −1.38678 | −0.693388 | − | 0.720565i | \(-0.743883\pi\) | ||||
−0.693388 | + | 0.720565i | \(0.743883\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.99130 | −0.192115 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.27845 | 0.202867 | 0.101434 | − | 0.994842i | \(-0.467657\pi\) | ||||
0.101434 | + | 0.994842i | \(0.467657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.8915 | −0.456353 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5654 | −0.404867 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.0882 | 1.41914 | 0.709570 | − | 0.704635i | \(-0.248889\pi\) | ||||
0.709570 | + | 0.704635i | \(0.248889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.37017 | −0.0523516 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.6950 | 0.675107 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.67341 | −0.178043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.1700 | −0.386883 | −0.193442 | − | 0.981112i | \(-0.561965\pi\) | ||||
−0.193442 | + | 0.981112i | \(0.561965\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.8170 | 0.676810 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.59734 | −0.0605907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.34694 | 0.126774 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.03342 | 0.114734 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.3197 | 0.465310 | 0.232655 | − | 0.972559i | \(-0.425259\pi\) | ||||
0.232655 | + | 0.972559i | \(0.425259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.9680 | −0.790824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.195078 | 0.00734705 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.4925 | −1.07157 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.4565 | 0.542926 | 0.271463 | − | 0.962449i | \(-0.412493\pi\) | ||||
0.271463 | + | 0.962449i | \(0.412493\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.12808 | 0.304827 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.8809 | 1.11905 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.258978 | −0.00968521 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.47139 | 0.204333 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.61087 | −0.0600752 | −0.0300376 | − | 0.999549i | \(-0.509563\pi\) | ||||
−0.0300376 | + | 0.999549i | \(0.509563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.8167 | −0.738011 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.1326 | −0.748739 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.0890 | −0.857505 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.46431 | 0.0913961 | 0.0456981 | − | 0.998955i | \(-0.485449\pi\) | ||||
0.0456981 | + | 0.998955i | \(0.485449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.20646 | −0.118595 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.5980 | −0.871611 | −0.435806 | − | 0.900041i | \(-0.643537\pi\) | ||||
−0.435806 | + | 0.900041i | \(0.643537\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.738520 | −0.0272407 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −58.8910 | −2.16928 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −52.2196 | −1.92093 | −0.960464 | − | 0.278405i | \(-0.910194\pi\) | ||||
−0.960464 | + | 0.278405i | \(0.910194\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.21288 | 0.0812924 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.0041 | 1.28417 | 0.642087 | − | 0.766632i | \(-0.278069\pi\) | ||||
0.642087 | + | 0.766632i | \(0.278069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.52486 | −0.0558664 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.46750 | 0.0902813 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.9687 | 0.583482 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.6060 | 1.29928 | 0.649641 | − | 0.760241i | \(-0.274919\pi\) | ||||
0.649641 | + | 0.760241i | \(0.274919\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.8256 | −0.430948 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.501791 | −0.0182620 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.4806 | 0.962453 | 0.481227 | − | 0.876596i | \(-0.340191\pi\) | ||||
0.481227 | + | 0.876596i | \(0.340191\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.0739 | 1.05532 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.9119 | 1.26555 | 0.632777 | − | 0.774334i | \(-0.281915\pi\) | ||||
0.632777 | + | 0.774334i | \(0.281915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 62.4883 | 2.26223 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0776400 | 0.00280708 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.63869 | −0.0952774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.5078 | 0.703468 | 0.351734 | − | 0.936100i | \(-0.385592\pi\) | ||||
0.351734 | + | 0.936100i | \(0.385592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.9960 | 1.00825 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.7496 | −0.566475 | −0.283237 | − | 0.959050i | \(-0.591408\pi\) | ||||
−0.283237 | + | 0.959050i | \(0.591408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.6640 | 0.850038 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.0265 | −0.790195 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.7842 | 0.529700 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.7413 | −2.17349 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.62585 | 0.165315 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.241672 | 0.00862565 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.68308 | −0.131288 | −0.0656438 | − | 0.997843i | \(-0.520910\pi\) | ||||
−0.0656438 | + | 0.997843i | \(0.520910\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.13973 | −0.0405756 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.9765 | 2.06141 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.972037 | −0.0345180 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.724289 | −0.0256879 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.7204 | 1.76119 | 0.880593 | − | 0.473873i | \(-0.157144\pi\) | ||||
0.880593 | + | 0.473873i | \(0.157144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.74076 | 0.0615837 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.23125 | 0.149504 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.0563 | −0.354880 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.27061 | −0.0800284 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.10035 | 0.109137 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.2283 | 1.76593 | 0.882967 | − | 0.469436i | \(-0.155543\pi\) | ||||
0.882967 | + | 0.469436i | \(0.155543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.2989 | 1.59066 | 0.795329 | − | 0.606177i | \(-0.207298\pi\) | ||||
0.795329 | + | 0.606177i | \(0.207298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.9980 | 0.946862 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.38770 | 0.0486089 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1637 | −0.495526 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.32459 | 0.0812277 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.61746 | 0.126250 | 0.0631252 | − | 0.998006i | \(-0.479893\pi\) | ||||
0.0631252 | + | 0.998006i | \(0.479893\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.4501 | −1.13114 | −0.565570 | − | 0.824700i | \(-0.691344\pi\) | ||||
−0.565570 | + | 0.824700i | \(0.691344\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.0250 | 0.801628 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.1508 | −1.15277 | −0.576384 | − | 0.817179i | \(-0.695537\pi\) | ||||
−0.576384 | + | 0.817179i | \(0.695537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.9423 | −1.14413 | −0.572066 | − | 0.820208i | \(-0.693858\pi\) | ||||
−0.572066 | + | 0.820208i | \(0.693858\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.24414 | 0.320676 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.59013 | −0.228335 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0932775 | 0.00322800 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.74106 | −0.163875 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.4962 | 1.57070 | 0.785352 | − | 0.619050i | \(-0.212482\pi\) | ||||
0.785352 | + | 0.619050i | \(0.212482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.60148 | −0.262120 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.83309 | −0.0631350 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.17882 | 0.0405526 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.7048 | −1.36427 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.27493 | −0.0780753 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.9431 | −1.23211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.1984 | −0.760059 | −0.380029 | − | 0.924974i | \(-0.624086\pi\) | ||||
−0.380029 | + | 0.924974i | \(0.624086\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.342955 | 0.0117288 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.277939 | −0.00949421 | −0.00474710 | − | 0.999989i | \(-0.501511\pi\) | ||||
−0.00474710 | + | 0.999989i | \(0.501511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.8460 | −1.01833 | −0.509165 | − | 0.860669i | \(-0.670046\pi\) | ||||
−0.509165 | + | 0.860669i | \(0.670046\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.5305 | 0.529279 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.6018 | 1.27998 | 0.639990 | − | 0.768383i | \(-0.278938\pi\) | ||||
0.639990 | + | 0.768383i | \(0.278938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.223646 | −0.00760421 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.3072 | −0.553821 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.4951 | −1.27193 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.68354 | −0.260347 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.07885 | 0.104203 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.59953 | −0.121686 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.8596 | −0.805681 | −0.402840 | − | 0.915270i | \(-0.631977\pi\) | ||||
−0.402840 | + | 0.915270i | \(0.631977\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.0304 | 1.11409 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.20697 | −0.310191 | −0.155095 | − | 0.987900i | \(-0.549568\pi\) | ||||
−0.155095 | + | 0.987900i | \(0.549568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8744 | 0.668827 | 0.334414 | − | 0.942426i | \(-0.391462\pi\) | ||||
0.334414 | + | 0.942426i | \(0.391462\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.408946 | −0.0137466 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.76687 | 0.227209 | 0.113605 | − | 0.993526i | \(-0.463760\pi\) | ||||
0.113605 | + | 0.993526i | \(0.463760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.86945 | 0.0962384 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.61303 | −0.154542 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.68937 | 0.257315 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.862164 | −0.0288190 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.79329 | 0.126654 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.9314 | −0.731455 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.46314 | −0.215319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.8787 | −0.495132 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.657016 | −0.0218400 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.25694 | −0.141349 | −0.0706747 | − | 0.997499i | \(-0.522515\pi\) | ||||
−0.0706747 | + | 0.997499i | \(0.522515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.37707 | 0.244682 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.7840 | −0.456686 | −0.228343 | − | 0.973581i | \(-0.573331\pi\) | ||||
−0.228343 | + | 0.973581i | \(0.573331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3827 | −0.376712 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.150647 | −0.00498024 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 82.7724 | 2.73339 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.3999 | 0.376046 | 0.188023 | − | 0.982165i | \(-0.439792\pi\) | ||||
0.188023 | + | 0.982165i | \(0.439792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.54712 | −0.116881 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.92495 | −0.260853 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.4650 | −0.935923 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.13078 | 0.168517 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.6773 | 0.678399 | 0.339199 | − | 0.940715i | \(-0.389844\pi\) | ||||
0.339199 | + | 0.940715i | \(0.389844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.1102 | −0.954049 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.22270 | 0.301938 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.358156 | −0.0117129 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.4516 | −1.48484 | −0.742419 | − | 0.669936i | \(-0.766322\pi\) | ||||
−0.742419 | + | 0.669936i | \(0.766322\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.6463 | −0.445331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.11181 | 0.101442 | 0.0507211 | − | 0.998713i | \(-0.483848\pi\) | ||||
0.0507211 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3429 | 0.825279 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.360267 | 0.0117195 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.8799 | 0.808490 | 0.404245 | − | 0.914651i | \(-0.367534\pi\) | ||||
0.404245 | + | 0.914651i | \(0.367534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.31205 | −0.0425910 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.8395 | 0.448776 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.2552 | 1.14203 | 0.571013 | − | 0.820941i | \(-0.306551\pi\) | ||||
0.571013 | + | 0.820941i | \(0.306551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.05193 | 0.0340398 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.3392 | −0.689799 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56.7343 | −1.83205 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.52236 | −0.274915 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.13448 | −0.133232 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0489782 | 0.00157666 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5362 | 1.40003 | 0.700016 | − | 0.714128i | \(-0.253176\pi\) | ||||
0.700016 | + | 0.714128i | \(0.253176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.06033 | 0.0983121 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.29834 | 0.266306 | 0.133153 | − | 0.991095i | \(-0.457490\pi\) | ||||
0.133153 | + | 0.991095i | \(0.457490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −66.1407 | −2.12037 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00409 | 0.0962077 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.0429 | 0.609235 | 0.304618 | − | 0.952475i | \(-0.401471\pi\) | ||||
0.304618 | + | 0.952475i | \(0.401471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.5189 | −0.623827 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.1790 | −0.516556 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.70203 | 0.213761 | 0.106881 | − | 0.994272i | \(-0.465914\pi\) | ||||
0.106881 | + | 0.994272i | \(0.465914\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.65431 | 0.0527106 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.07752 | 0.257110 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.2792 | −0.772034 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.3822 | −0.838057 | −0.419029 | − | 0.907973i | \(-0.637629\pi\) | ||||
−0.419029 | + | 0.907973i | \(0.637629\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.2468 | 1.05506 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.38405 | 0.0438775 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.3122 | −1.46672 | −0.733361 | − | 0.679839i | \(-0.762050\pi\) | ||||
−0.733361 | + | 0.679839i | \(0.762050\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.70292 | 0.180433 |
(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 | 8016.2.a.be.1.5 | 11 | ||
4.3 | odd | 2 | 4008.2.a.k.1.5 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.5 | ✓ | 11 | 4.3 | odd | 2 | ||
8016.2.a.be.1.5 | 11 | 1.1 | even | 1 | trivial |