Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 13x^{6} + 24x^{5} + 48x^{4} - 68x^{3} - 62x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.77833\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 2.32921 | 1.34477 | 0.672385 | − | 0.740201i | \(-0.265270\pi\) | ||||
0.672385 | + | 0.740201i | \(0.265270\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.13887 | −1.40375 | −0.701873 | − | 0.712302i | \(-0.747653\pi\) | ||||
−0.701873 | + | 0.712302i | \(0.747653\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.535658 | 0.202460 | 0.101230 | − | 0.994863i | \(-0.467722\pi\) | ||||
0.101230 | + | 0.994863i | \(0.467722\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.42523 | 0.808409 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.425227 | 0.128211 | 0.0641054 | − | 0.997943i | \(-0.479581\pi\) | ||||
0.0641054 | + | 0.997943i | \(0.479581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.65786 | −1.84656 | −0.923279 | − | 0.384129i | \(-0.874502\pi\) | ||||
−0.923279 | + | 0.384129i | \(0.874502\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.31110 | −1.88772 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.33239 | 1.77837 | 0.889183 | − | 0.457552i | \(-0.151273\pi\) | ||||
0.889183 | + | 0.457552i | \(0.151273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.24766 | 0.272262 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.90033 | 1.23030 | 0.615152 | − | 0.788408i | \(-0.289095\pi\) | ||||
0.615152 | + | 0.788408i | \(0.289095\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.85252 | 0.970503 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.33877 | −0.257646 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.837037 | −0.155434 | −0.0777170 | − | 0.996975i | \(-0.524763\pi\) | ||||
−0.0777170 | + | 0.996975i | \(0.524763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.16999 | −0.569347 | −0.284674 | − | 0.958625i | \(-0.591885\pi\) | ||||
−0.284674 | + | 0.958625i | \(0.591885\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.990444 | 0.172414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.68136 | −0.284202 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.49490 | −0.574558 | −0.287279 | − | 0.957847i | \(-0.592751\pi\) | ||||
−0.287279 | + | 0.957847i | \(0.592751\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.5076 | −2.48320 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.123059 | 0.0192186 | 0.00960932 | − | 0.999954i | \(-0.496941\pi\) | ||||
0.00960932 | + | 0.999954i | \(0.496941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.39744 | −0.823101 | −0.411551 | − | 0.911387i | \(-0.635013\pi\) | ||||
−0.411551 | + | 0.911387i | \(0.635013\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.61248 | −1.13480 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.02928 | −0.296001 | −0.148000 | − | 0.988987i | \(-0.547284\pi\) | ||||
−0.148000 | + | 0.988987i | \(0.547284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.71307 | −0.959010 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.0787 | 2.39150 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.82785 | 0.800517 | 0.400259 | − | 0.916402i | \(-0.368920\pi\) | ||||
0.400259 | + | 0.916402i | \(0.368920\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.33473 | −0.179975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.32921 | −0.308512 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.56633 | −0.724675 | −0.362337 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362337 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.99606 | 0.895753 | 0.447877 | − | 0.894095i | \(-0.352180\pi\) | ||||
0.447877 | + | 0.894095i | \(0.352180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.29909 | 0.163670 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.8982 | 2.59210 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.3777 | −1.51217 | −0.756087 | − | 0.654471i | \(-0.772891\pi\) | ||||
−0.756087 | + | 0.654471i | \(0.772891\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.7431 | 1.65448 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1786 | −1.44534 | −0.722669 | − | 0.691194i | \(-0.757085\pi\) | ||||
−0.722669 | + | 0.691194i | \(0.757085\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.99382 | 0.818565 | 0.409282 | − | 0.912408i | \(-0.365779\pi\) | ||||
0.409282 | + | 0.912408i | \(0.365779\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.3025 | 1.30510 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.227776 | 0.0259575 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.07996 | 0.234014 | 0.117007 | − | 0.993131i | \(-0.462670\pi\) | ||||
0.117007 | + | 0.993131i | \(0.462670\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3940 | −1.15488 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.8227 | −1.29771 | −0.648853 | − | 0.760914i | \(-0.724751\pi\) | ||||
−0.648853 | + | 0.760914i | \(0.724751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.0154 | −2.49637 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.94964 | −0.209023 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.7684 | −1.45945 | −0.729723 | − | 0.683743i | \(-0.760351\pi\) | ||||
−0.729723 | + | 0.683743i | \(0.760351\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.56633 | −0.373853 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.38358 | −0.765641 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.13887 | 0.322041 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.801240 | 0.0813536 | 0.0406768 | − | 0.999172i | \(-0.487049\pi\) | ||||
0.0406768 | + | 0.999172i | \(0.487049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.03127 | 0.103647 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4171 | −1.23555 | −0.617773 | − | 0.786356i | \(-0.711965\pi\) | ||||
−0.617773 | + | 0.786356i | \(0.711965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.84869 | 0.280690 | 0.140345 | − | 0.990103i | \(-0.455179\pi\) | ||||
0.140345 | + | 0.990103i | \(0.455179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.91624 | −0.382186 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.288142 | 0.0278557 | 0.0139278 | − | 0.999903i | \(-0.495566\pi\) | ||||
0.0139278 | + | 0.999903i | \(0.495566\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.91873 | 0.183781 | 0.0918905 | − | 0.995769i | \(-0.470709\pi\) | ||||
0.0918905 | + | 0.995769i | \(0.470709\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.14036 | −0.772649 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.4370 | −1.26405 | −0.632024 | − | 0.774949i | \(-0.717776\pi\) | ||||
−0.632024 | + | 0.774949i | \(0.717776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.5204 | −1.72704 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.1468 | −1.49277 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.92765 | 0.360047 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8192 | −0.983562 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.286631 | 0.0258447 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.462931 | 0.0414058 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.9992 | −1.68591 | −0.842953 | − | 0.537987i | \(-0.819185\pi\) | ||||
−0.842953 | + | 0.537987i | \(0.819185\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.5718 | −1.10688 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1330 | 0.885322 | 0.442661 | − | 0.896689i | \(-0.354035\pi\) | ||||
0.442661 | + | 0.896689i | \(0.354035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.535658 | −0.0464474 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.20222 | 0.361670 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.28221 | 0.280418 | 0.140209 | − | 0.990122i | \(-0.455222\pi\) | ||||
0.140209 | + | 0.990122i | \(0.455222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.5345 | 0.893527 | 0.446763 | − | 0.894652i | \(-0.352577\pi\) | ||||
0.446763 | + | 0.894652i | \(0.352577\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.72662 | −0.398053 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.83110 | −0.236749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.62735 | 0.218190 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.6362 | −1.28965 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.93244 | −0.486005 | −0.243002 | − | 0.970026i | \(-0.578132\pi\) | ||||
−0.243002 | + | 0.970026i | \(0.578132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.57907 | −0.372639 | −0.186320 | − | 0.982489i | \(-0.559656\pi\) | ||||
−0.186320 | + | 0.982489i | \(0.559656\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.7827 | 1.43765 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.95019 | 0.799219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.80861 | −0.303960 | −0.151980 | − | 0.988384i | \(-0.548565\pi\) | ||||
−0.151980 | + | 0.988384i | \(0.548565\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.5743 | 1.07651 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.16056 | 0.249087 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.9293 | 1.40433 | 0.702164 | − | 0.712016i | \(-0.252217\pi\) | ||||
0.702164 | + | 0.712016i | \(0.252217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.10888 | −0.242026 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.8189 | −1.45625 | −0.728123 | − | 0.685446i | \(-0.759607\pi\) | ||||
−0.728123 | + | 0.685446i | \(0.759607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.3271 | 2.40978 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.42523 | −0.185462 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.87750 | −0.446858 | −0.223429 | − | 0.974720i | \(-0.571725\pi\) | ||||
−0.223429 | + | 0.974720i | \(0.571725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.59929 | 0.196488 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.9652 | −0.974522 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9245 | 1.41448 | 0.707241 | − | 0.706973i | \(-0.249940\pi\) | ||||
0.707241 | + | 0.706973i | \(0.249940\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5330 | 0.782914 | 0.391457 | − | 0.920196i | \(-0.371971\pi\) | ||||
0.391457 | + | 0.920196i | \(0.371971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.2953 | 1.20458 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.9700 | 0.806534 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.11793 | 0.228006 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.717121 | −0.0521629 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.60481 | 0.116120 | 0.0580600 | − | 0.998313i | \(-0.481509\pi\) | ||||
0.0580600 | + | 0.998313i | \(0.481509\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.2889 | −0.956554 | −0.478277 | − | 0.878209i | \(-0.658739\pi\) | ||||
−0.478277 | + | 0.878209i | \(0.658739\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 48.6763 | 3.48578 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.06689 | −0.289754 | −0.144877 | − | 0.989450i | \(-0.546279\pi\) | ||||
−0.144877 | + | 0.989450i | \(0.546279\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8273 | −0.909307 | −0.454653 | − | 0.890668i | \(-0.650237\pi\) | ||||
−0.454653 | + | 0.890668i | \(0.650237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.8302 | −2.03353 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.448365 | −0.0314691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.386268 | −0.0269781 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.3096 | 0.994589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.425227 | −0.0294136 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9906 | −1.10084 | −0.550420 | − | 0.834888i | \(-0.685532\pi\) | ||||
−0.550420 | + | 0.834888i | \(0.685532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.3666 | −1.94365 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.9419 | 1.15543 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.69803 | −0.115270 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.2901 | 1.10078 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −48.8181 | −3.28386 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1424 | 1.41580 | 0.707899 | − | 0.706314i | \(-0.249643\pi\) | ||||
0.707899 | + | 0.706314i | \(0.249643\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7685 | 0.784564 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.2056 | −1.47384 | −0.736918 | − | 0.675982i | \(-0.763720\pi\) | ||||
−0.736918 | + | 0.675982i | \(0.763720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6331 | −0.834816 | −0.417408 | − | 0.908719i | \(-0.637061\pi\) | ||||
−0.417408 | + | 0.908719i | \(0.637061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.530539 | 0.0349069 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.01852 | −0.197750 | −0.0988749 | − | 0.995100i | \(-0.531524\pi\) | ||||
−0.0988749 | + | 0.995100i | \(0.531524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.36965 | 0.415510 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.84468 | 0.314695 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7156 | 0.822504 | 0.411252 | − | 0.911522i | \(-0.365092\pi\) | ||||
0.411252 | + | 0.911522i | \(0.365092\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.05734 | −0.0681091 | −0.0340545 | − | 0.999420i | \(-0.510842\pi\) | ||||
−0.0340545 | + | 0.999420i | \(0.510842\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.1934 | −1.29541 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.0715 | 1.34621 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.65786 | 0.423630 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.5375 | −1.74512 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4689 | −0.850151 | −0.425076 | − | 0.905158i | \(-0.639752\pi\) | ||||
−0.425076 | + | 0.905158i | \(0.639752\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.50898 | 0.157738 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −53.6078 | −3.35705 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.1631 | 1.19536 | 0.597680 | − | 0.801734i | \(-0.296089\pi\) | ||||
0.597680 | + | 0.801734i | \(0.296089\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.87207 | −0.116325 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.03001 | −0.125654 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.55940 | 0.157819 | 0.0789097 | − | 0.996882i | \(-0.474856\pi\) | ||||
0.0789097 | + | 0.996882i | \(0.474856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.2929 | −1.12372 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.0695 | −1.96262 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.88596 | 0.297902 | 0.148951 | − | 0.988845i | \(-0.452410\pi\) | ||||
0.148951 | + | 0.988845i | \(0.452410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.1299 | 1.95175 | 0.975875 | − | 0.218329i | \(-0.0700604\pi\) | ||||
0.975875 | + | 0.218329i | \(0.0700604\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.30675 | −0.502747 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.06342 | 0.124429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.46639 | 0.448612 | 0.224306 | − | 0.974519i | \(-0.427988\pi\) | ||||
0.224306 | + | 0.974519i | \(0.427988\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.68795 | −0.460265 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.9770 | −1.13208 | −0.566038 | − | 0.824379i | \(-0.691524\pi\) | ||||
−0.566038 | + | 0.824379i | \(0.691524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.24321 | −0.0739012 | −0.0369506 | − | 0.999317i | \(-0.511764\pi\) | ||||
−0.0369506 | + | 0.999317i | \(0.511764\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.31110 | 0.433072 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0659177 | 0.00389100 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.7640 | 2.16259 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.86626 | 0.109402 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.35018 | −0.312561 | −0.156280 | − | 0.987713i | \(-0.549950\pi\) | ||||
−0.156280 | + | 0.987713i | \(0.549950\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4720 | 1.01726 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.569280 | −0.0330330 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −39.2836 | −2.27183 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.89118 | −0.166645 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.9220 | −1.66153 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.9597 | −1.25741 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4800 | −0.598123 | −0.299062 | − | 0.954234i | \(-0.596674\pi\) | ||||
−0.299062 | + | 0.954234i | \(0.596674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.63521 | 0.377464 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.3720 | 1.55212 | 0.776061 | − | 0.630658i | \(-0.217215\pi\) | ||||
0.776061 | + | 0.630658i | \(0.217215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9214 | 0.956451 | 0.478226 | − | 0.878237i | \(-0.341280\pi\) | ||||
0.478226 | + | 0.878237i | \(0.341280\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.07768 | −0.229751 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.82118 | −0.214619 | −0.107309 | − | 0.994226i | \(-0.534224\pi\) | ||||
−0.107309 | + | 0.994226i | \(0.534224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.355931 | −0.0199283 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.671143 | 0.0374595 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.33239 | −0.407985 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.3074 | −1.79209 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.46913 | 0.247143 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.08700 | −0.0599282 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.6082 | 1.46252 | 0.731258 | − | 0.682101i | \(-0.238933\pi\) | ||||
0.731258 | + | 0.682101i | \(0.238933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.47592 | −0.464478 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.8520 | 2.12271 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6884 | −0.636707 | −0.318354 | − | 0.947972i | \(-0.603130\pi\) | ||||
−0.318354 | + | 0.947972i | \(0.603130\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.2976 | −1.69985 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.34797 | −0.0729964 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34551 | −0.396620 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −43.1379 | −2.32247 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.2573 | 0.872739 | 0.436370 | − | 0.899767i | \(-0.356264\pi\) | ||||
0.436370 | + | 0.899767i | \(0.356264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.5885 | −1.20913 | −0.604567 | − | 0.796554i | \(-0.706654\pi\) | ||||
−0.604567 | + | 0.796554i | \(0.706654\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.91333 | 0.475758 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.2804 | −0.547169 | −0.273584 | − | 0.961848i | \(-0.588209\pi\) | ||||
−0.273584 | + | 0.961848i | \(0.588209\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.2272 | 2.02889 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.14833 | 0.484181 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1694 | 0.853386 | 0.426693 | − | 0.904397i | \(-0.359679\pi\) | ||||
0.426693 | + | 0.904397i | \(0.359679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.2002 | −1.32267 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.9527 | −1.14906 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.5371 | 1.01983 | 0.509914 | − | 0.860225i | \(-0.329677\pi\) | ||||
0.509914 | + | 0.860225i | \(0.329677\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.298447 | 0.0155365 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.12173 | 0.162072 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.9672 | −0.671418 | −0.335709 | − | 0.941966i | \(-0.608976\pi\) | ||||
−0.335709 | + | 0.941966i | \(0.608976\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.07826 | 0.0556813 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.57288 | 0.287018 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.229262 | 0.0117764 | 0.00588821 | − | 0.999983i | \(-0.498126\pi\) | ||||
0.00588821 | + | 0.999983i | \(0.498126\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −44.2532 | −2.26716 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.9168 | −0.966601 | −0.483301 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483301 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.714960 | −0.0364377 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.0900 | −0.665403 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.38404 | −0.475790 | −0.237895 | − | 0.971291i | \(-0.576457\pi\) | ||||
−0.237895 | + | 0.971291i | \(0.576457\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.2636 | 2.18793 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.6018 | 1.19055 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.52874 | −0.328496 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3307 | 0.919990 | 0.459995 | − | 0.887921i | \(-0.347851\pi\) | ||||
0.459995 | + | 0.887921i | \(0.347851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.24766 | −0.0624611 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.7518 | −1.13617 | −0.568085 | − | 0.822970i | \(-0.692316\pi\) | ||||
−0.568085 | + | 0.822970i | \(0.692316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.1054 | 1.05133 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.6253 | 1.62116 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.48613 | −0.0736645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3401 | 0.956305 | 0.478152 | − | 0.878277i | \(-0.341307\pi\) | ||||
0.478152 | + | 0.878277i | \(0.341307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.64497 | 0.377099 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.98165 | −0.146717 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.1098 | 1.82165 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.5371 | 1.20159 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0225 | 1.36899 | 0.684495 | − | 0.729017i | \(-0.260023\pi\) | ||||
0.684495 | + | 0.729017i | \(0.260023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5487 | 0.757798 | 0.378899 | − | 0.925438i | \(-0.376303\pi\) | ||||
0.378899 | + | 0.925438i | \(0.376303\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.92146 | −0.239290 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 35.5806 | 1.72591 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.74749 | 0.181354 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.59424 | −0.318373 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5573 | 0.749368 | 0.374684 | − | 0.927153i | \(-0.377751\pi\) | ||||
0.374684 | + | 0.927153i | \(0.377751\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.16219 | 0.200022 | 0.100011 | − | 0.994986i | \(-0.468112\pi\) | ||||
0.100011 | + | 0.994986i | \(0.468112\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.11966 | 0.293415 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.90033 | −0.282251 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.6600 | −1.17696 | −0.588478 | − | 0.808513i | \(-0.700273\pi\) | ||||
−0.588478 | + | 0.808513i | \(0.700273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.2807 | −0.775272 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.7595 | 0.938801 | 0.469401 | − | 0.882985i | \(-0.344470\pi\) | ||||
0.469401 | + | 0.882985i | \(0.344470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43.2172 | 2.04869 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.8179 | −0.653565 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.4826 | −0.777862 | −0.388931 | − | 0.921267i | \(-0.627156\pi\) | ||||
−0.388931 | + | 0.921267i | \(0.627156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0523282 | 0.00246404 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.6656 | −0.501115 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.1943 | 0.524795 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.44504 | −0.348264 | −0.174132 | − | 0.984722i | \(-0.555712\pi\) | ||||
−0.174132 | + | 0.984722i | \(0.555712\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.81637 | −0.458189 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.9337 | 0.695532 | 0.347766 | − | 0.937581i | \(-0.386940\pi\) | ||||
0.347766 | + | 0.937581i | \(0.386940\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.6042 | −1.09698 | −0.548491 | − | 0.836156i | \(-0.684798\pi\) | ||||
−0.548491 | + | 0.836156i | \(0.684798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.1761 | 1.07477 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.808996 | 0.0374359 | 0.0187179 | − | 0.999825i | \(-0.494042\pi\) | ||||
0.0187179 | + | 0.999825i | \(0.494042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.63020 | −0.306154 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.87106 | −0.408757 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.29514 | −0.105530 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.85252 | −0.222649 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.1339 | 0.647145 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.2547 | −0.559933 | −0.279966 | − | 0.960010i | \(-0.590323\pi\) | ||||
−0.279966 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.2686 | 1.06095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.36161 | 0.334965 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.51499 | −0.114200 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.1692 | −1.04990 | −0.524948 | − | 0.851134i | \(-0.675915\pi\) | ||||
−0.524948 | + | 0.851134i | \(0.675915\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.7610 | 1.88850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.6669 | −0.932684 | −0.466342 | − | 0.884605i | \(-0.654428\pi\) | ||||
−0.466342 | + | 0.884605i | \(0.654428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.13749 | −0.276418 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.23703 | −0.145494 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.52358 | −0.292623 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.36134 | −0.240007 | −0.120003 | − | 0.992773i | \(-0.538291\pi\) | ||||
−0.120003 | + | 0.992773i | \(0.538291\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −43.8331 | −1.95832 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.6878 | 1.14536 | 0.572681 | − | 0.819778i | \(-0.305903\pi\) | ||||
0.572681 | + | 0.819778i | \(0.305903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.9757 | 1.73439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 72.9675 | 3.24060 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.2273 | 0.719261 | 0.359631 | − | 0.933095i | \(-0.382903\pi\) | ||||
0.359631 | + | 0.933095i | \(0.382903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.74629 | 0.165726 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.33877 | 0.0591080 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.94168 | −0.394017 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.862904 | −0.0379505 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.6899 | −0.600922 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.4863 | −1.42325 | −0.711626 | − | 0.702559i | \(-0.752041\pi\) | ||||
−0.711626 | + | 0.702559i | \(0.752041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1406 | 0.487143 | 0.243571 | − | 0.969883i | \(-0.421681\pi\) | ||||
0.243571 | + | 0.969883i | \(0.421681\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.05429 | 0.264231 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.2436 | −1.01251 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.8139 | 0.513649 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.4996 | −0.585834 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.819312 | −0.0354884 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.904439 | −0.0391023 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 44.0791 | 1.90215 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.85458 | −0.122955 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.33136 | 0.0572394 | 0.0286197 | − | 0.999590i | \(-0.490889\pi\) | ||||
0.0286197 | + | 0.999590i | \(0.490889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.5336 | 1.05284 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.02264 | −0.257982 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1345 | 0.903644 | 0.451822 | − | 0.892108i | \(-0.350774\pi\) | ||||
0.451822 | + | 0.892108i | \(0.350774\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.9670 | 0.724135 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.837037 | 0.0356590 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.11415 | 0.0473784 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.5515 | 1.08460 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.60875 | −0.280022 | −0.140011 | − | 0.990150i | \(-0.544714\pi\) | ||||
−0.140011 | + | 0.990150i | \(0.544714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.9354 | 1.51991 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.26232 | 0.306615 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.42073 | −0.186312 | −0.0931559 | − | 0.995652i | \(-0.529695\pi\) | ||||
−0.0931559 | + | 0.995652i | \(0.529695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42.1771 | 1.77440 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.56760 | −0.233817 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.59442 | −0.360297 | −0.180149 | − | 0.983639i | \(-0.557658\pi\) | ||||
−0.180149 | + | 0.983639i | \(0.557658\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.6802 | −1.45132 | −0.725661 | − | 0.688052i | \(-0.758466\pi\) | ||||
−0.725661 | + | 0.688052i | \(0.758466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.73794 | 0.156155 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.6315 | 1.19401 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.2877 | 1.09437 | 0.547185 | − | 0.837012i | \(-0.315699\pi\) | ||||
0.547185 | + | 0.837012i | \(0.315699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.9526 | −1.28635 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.33290 | −0.262733 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.47816 | 0.102635 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 50.6828 | 2.09548 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.01067 | 0.289361 | 0.144681 | − | 0.989478i | \(-0.453785\pi\) | ||||
0.144681 | + | 0.989478i | \(0.453785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.16999 | 0.130617 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.47265 | −0.389653 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.7115 | 1.42543 | 0.712716 | − | 0.701453i | \(-0.247465\pi\) | ||||
0.712716 | + | 0.701453i | \(0.247465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.3284 | −0.505415 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.8776 | −1.22281 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.4456 | 1.32569 | 0.662845 | − | 0.748757i | \(-0.269349\pi\) | ||||
0.662845 | + | 0.748757i | \(0.269349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2901 | 1.48030 | 0.740152 | − | 0.672440i | \(-0.234754\pi\) | ||||
0.740152 | + | 0.672440i | \(0.234754\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.0187 | −1.22246 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.9600 | 1.38067 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.54708 | 0.225149 | 0.112575 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112575 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.04434 | −0.0423187 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5107 | 0.546583 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.7239 | 1.68521 | 0.842606 | − | 0.538530i | \(-0.181020\pi\) | ||||
0.842606 | + | 0.538530i | \(0.181020\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.899699 | −0.0362794 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0859 | −0.647593 | −0.323797 | − | 0.946127i | \(-0.604959\pi\) | ||||
−0.323797 | + | 0.946127i | \(0.604959\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.93257 | −0.117870 | −0.0589349 | − | 0.998262i | \(-0.518770\pi\) | ||||
−0.0589349 | + | 0.998262i | \(0.518770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.89918 | −0.316983 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.37514 | −0.295479 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.7157 | −1.02863 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.990444 | −0.0395545 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.6260 | −1.02177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0095 | 0.915994 | 0.457997 | − | 0.888954i | \(-0.348567\pi\) | ||||
0.457997 | + | 0.888954i | \(0.348567\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.2455 | −1.48038 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 59.6361 | 2.36658 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 44.6947 | 1.77087 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.5360 | −1.16842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.00476234 | −0.000188101 0 | −9.40506e−5 | − | 1.00000i | \(-0.500030\pi\) | ||||
−9.40506e−5 | 1.00000i | \(0.500030\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.6587 | −1.48511 | −0.742557 | − | 0.669783i | \(-0.766387\pi\) | ||||
−0.742557 | + | 0.669783i | \(0.766387\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 39.4612 | 1.55378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.3744 | −0.997570 | −0.498785 | − | 0.866726i | \(-0.666220\pi\) | ||||
−0.498785 | + | 0.866726i | \(0.666220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.36696 | −0.0929111 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.95507 | −0.155011 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.5548 | −0.882637 | −0.441319 | − | 0.897350i | \(-0.645489\pi\) | ||||
−0.441319 | + | 0.897350i | \(0.645489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.8061 | −1.24277 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.9616 | 0.661735 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.3990 | −0.716724 | −0.358362 | − | 0.933583i | \(-0.616665\pi\) | ||||
−0.358362 | + | 0.933583i | \(0.616665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.9383 | 1.55342 | 0.776710 | − | 0.629859i | \(-0.216887\pi\) | ||||
0.776710 | + | 0.629859i | \(0.216887\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −113.708 | −4.41604 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.68136 | 0.0652004 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.93880 | −0.191231 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 49.2451 | 1.90392 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.97491 | 0.114845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.04663 | −0.155986 | −0.0779931 | − | 0.996954i | \(-0.524851\pi\) | ||||
−0.0779931 | + | 0.996954i | \(0.524851\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.49639 | −0.250046 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.8041 | −1.64509 | −0.822547 | − | 0.568697i | \(-0.807448\pi\) | ||||
−0.822547 | + | 0.568697i | \(0.807448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.429190 | 0.0164708 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −51.7215 | −1.98197 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.33556 | −0.242423 | −0.121212 | − | 0.992627i | \(-0.538678\pi\) | ||||
−0.121212 | + | 0.992627i | \(0.538678\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.3024 | −0.393636 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.4251 | −1.12264 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.8010 | −1.47820 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.3700 | −0.584702 | −0.292351 | − | 0.956311i | \(-0.594438\pi\) | ||||
−0.292351 | + | 0.956311i | \(0.594438\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.552409 | 0.0209843 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.0665 | −1.25428 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.902320 | 0.0341778 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.03077 | −0.265928 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.0602 | −1.36197 | −0.680987 | − | 0.732296i | \(-0.738449\pi\) | ||||
−0.680987 | + | 0.732296i | \(0.738449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.49490 | 0.131813 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.8363 | 0.558766 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.65131 | −0.250148 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.1426 | 0.681360 | 0.340680 | − | 0.940179i | \(-0.389343\pi\) | ||||
0.340680 | + | 0.940179i | \(0.389343\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.04438 | 0.189179 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.7040 | −0.700470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.88647 | 0.332335 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.6173 | 1.10608 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.2801 | −1.42761 | −0.713804 | − | 0.700345i | \(-0.753029\pi\) | ||||
−0.713804 | + | 0.700345i | \(0.753029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.52592 | 0.0568284 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.46276 | −0.0915911 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.06174 | −0.150849 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.4550 | −0.869897 | −0.434949 | − | 0.900455i | \(-0.643233\pi\) | ||||
−0.434949 | + | 0.900455i | \(0.643233\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.8529 | −0.587144 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.5761 | −1.46378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.3814 | 0.715870 | 0.357935 | − | 0.933747i | \(-0.383481\pi\) | ||||
0.357935 | + | 0.933747i | \(0.383481\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 49.0799 | 1.81034 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.26332 | −0.193877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1161 | 0.445697 | 0.222848 | − | 0.974853i | \(-0.428464\pi\) | ||||
0.222848 | + | 0.974853i | \(0.428464\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.5076 | 0.569685 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.1148 | 1.06812 | 0.534060 | − | 0.845447i | \(-0.320666\pi\) | ||||
0.534060 | + | 0.845447i | \(0.320666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6212 | 0.682227 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.6726 | −1.04908 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.154345 | 0.00563965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.09618 | −0.0764906 | −0.0382453 | − | 0.999268i | \(-0.512177\pi\) | ||||
−0.0382453 | + | 0.999268i | \(0.512177\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.3720 | −1.14326 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.3731 | 0.523091 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.7044 | 1.33404 | 0.667022 | − | 0.745038i | \(-0.267569\pi\) | ||||
0.667022 | + | 0.745038i | \(0.267569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.84395 | 0.212122 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.8362 | −0.972812 | −0.486406 | − | 0.873733i | \(-0.661692\pi\) | ||||
−0.486406 | + | 0.873733i | \(0.661692\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.02778 | 0.0372082 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −55.8177 | −2.01809 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.0599 | 1.33815 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.3434 | 0.553299 | 0.276649 | − | 0.960971i | \(-0.410776\pi\) | ||||
0.276649 | + | 0.960971i | \(0.410776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.6349 | 1.60749 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −54.9160 | −1.97519 | −0.987596 | − | 0.157017i | \(-0.949812\pi\) | ||||
−0.987596 | + | 0.157017i | \(0.949812\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.3824 | −0.552553 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.36045 | −0.156430 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.123059 | −0.00440906 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.17869 | −0.185308 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.12060 | 0.0400469 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.9547 | 0.426683 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.2826 | −0.580413 | −0.290206 | − | 0.956964i | \(-0.593724\pi\) | ||||
−0.290206 | + | 0.956964i | \(0.593724\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.96139 | 0.212231 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.19764 | −0.255918 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.5788 | −1.65406 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −42.6080 | −1.51115 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.2945 | 0.718867 | 0.359434 | − | 0.933171i | \(-0.382970\pi\) | ||||
0.359434 | + | 0.933171i | \(0.382970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.8795 | −0.526398 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.3915 | −1.17983 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.97396 | 0.104949 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.92059 | −0.349655 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.3804 | 0.400610 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.57944 | 0.196163 | 0.0980813 | − | 0.995178i | \(-0.468729\pi\) | ||||
0.0980813 | + | 0.995178i | \(0.468729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.4695 | 0.999699 | 0.499849 | − | 0.866112i | \(-0.333389\pi\) | ||||
0.499849 | + | 0.866112i | \(0.333389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 74.8373 | 2.62466 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −56.2776 | −1.97132 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.39744 | 0.188832 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.64917 | −0.302226 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.41291 | 0.119111 | 0.0595556 | − | 0.998225i | \(-0.481032\pi\) | ||||
0.0595556 | + | 0.998225i | \(0.481032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8444 | 0.447729 | 0.223865 | − | 0.974620i | \(-0.428133\pi\) | ||||
0.223865 | + | 0.974620i | \(0.428133\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.80615 | 0.167328 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.4599 | −0.398501 | −0.199251 | − | 0.979949i | \(-0.563851\pi\) | ||||
−0.199251 | + | 0.979949i | \(0.563851\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6953 | 0.545119 | 0.272559 | − | 0.962139i | \(-0.412130\pi\) | ||||
0.272559 | + | 0.962139i | \(0.412130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.3908 | 0.603280 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.2229 | −1.70547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59.0700 | 2.04420 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.24388 | 0.146690 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.4629 | −1.39693 | −0.698467 | − | 0.715642i | \(-0.746134\pi\) | ||||
−0.698467 | + | 0.715642i | \(0.746134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2994 | −0.975840 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.2016 | −1.52238 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −98.3318 | −3.38272 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.79538 | −0.199131 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.89570 | −0.0993802 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.6211 | −0.706881 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.22071 | −0.0417962 | −0.0208981 | − | 0.999782i | \(-0.506653\pi\) | ||||
−0.0208981 | + | 0.999782i | \(0.506653\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.61248 | 0.260341 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.3646 | 1.68626 | 0.843131 | − | 0.537709i | \(-0.180710\pi\) | ||||
0.843131 | + | 0.537709i | \(0.180710\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.6828 | 1.42220 | 0.711099 | − | 0.703092i | \(-0.248198\pi\) | ||||
0.711099 | + | 0.703092i | \(0.248198\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.153536 | 0.00523250 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.0429 | −0.750348 | −0.375174 | − | 0.926954i | \(-0.622417\pi\) | ||||
−0.375174 | + | 0.926954i | \(0.622417\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.4487 | 0.627275 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 85.6311 | 2.90818 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.884457 | 0.0300031 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 82.4089 | 2.79232 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.94319 | 0.0657670 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.247973 | 0.00838300 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.7237 | −1.13877 | −0.569385 | − | 0.822071i | \(-0.692819\pi\) | ||||
−0.569385 | + | 0.822071i | \(0.692819\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.4617 | −0.420323 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.24781 | 0.244185 | 0.122092 | − | 0.992519i | \(-0.461040\pi\) | ||||
0.122092 | + | 0.992519i | \(0.461040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.1525 | −0.812797 | −0.406398 | − | 0.913696i | \(-0.633215\pi\) | ||||
−0.406398 | + | 0.913696i | \(0.633215\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 40.6960 | 1.36798 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.3957 | −0.684821 | −0.342411 | − | 0.939550i | \(-0.611243\pi\) | ||||
−0.342411 | + | 0.939550i | \(0.611243\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.1771 | −0.341328 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.41979 | −0.148069 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.02928 | 0.0679072 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −59.4015 | −1.98557 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −91.4998 | −3.05509 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.65340 | 0.0884959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.7321 | 1.42361 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.73416 | −0.224099 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.0618 | −1.09901 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.56562 | −0.218008 | −0.109004 | − | 0.994041i | \(-0.534766\pi\) | ||||
−0.109004 | + | 0.994041i | \(0.534766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.1143 | −0.998827 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.98339 | 0.231370 | 0.115685 | − | 0.993286i | \(-0.463094\pi\) | ||||
0.115685 | + | 0.993286i | \(0.463094\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.02732 | −0.166380 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −51.1488 | −1.69093 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.42780 | 0.179242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.4237 | −0.409819 | −0.204910 | − | 0.978781i | \(-0.565690\pi\) | ||||
−0.204910 | + | 0.978781i | \(0.565690\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.4101 | −0.804339 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 81.0837 | 2.66890 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.9591 | −0.557610 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.90873 | 0.226912 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.0649 | −0.756735 | −0.378367 | − | 0.925655i | \(-0.623514\pi\) | ||||
−0.378367 | + | 0.925655i | \(0.623514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.71307 | 0.220012 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 63.7551 | 2.08725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.78679 | −0.320062 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.2747 | 0.662347 | 0.331173 | − | 0.943570i | \(-0.392555\pi\) | ||||
0.331173 | + | 0.943570i | \(0.392555\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39.4134 | 1.28621 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.8390 | 1.10312 | 0.551559 | − | 0.834136i | \(-0.314033\pi\) | ||||
0.551559 | + | 0.834136i | \(0.314033\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.726091 | 0.0236448 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.25095 | 0.0732234 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.4208 | 1.80093 | 0.900466 | − | 0.434926i | \(-0.143225\pi\) | ||||
0.900466 | + | 0.434926i | \(0.143225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46.5639 | −1.51153 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.90033 | −0.288613 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.8530 | 0.643102 | 0.321551 | − | 0.946892i | \(-0.395796\pi\) | ||||
0.321551 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.03729 | −0.163003 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.829039 | −0.0267990 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.75814 | 0.0567734 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9512 | −0.675844 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.698809 | 0.0225188 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.7121 | 1.34276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.95336 | 0.191447 | 0.0957236 | − | 0.995408i | \(-0.469484\pi\) | ||||
0.0957236 | + | 0.995408i | \(0.469484\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.0787 | −0.548647 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.33267 | 0.171134 | 0.0855668 | − | 0.996332i | \(-0.472730\pi\) | ||||
0.0855668 | + | 0.996332i | \(0.472730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.64290 | 0.180903 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −75.2507 | −2.40995 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.6063 | −0.403312 | −0.201656 | − | 0.979456i | \(-0.564632\pi\) | ||||
−0.201656 | + | 0.979456i | \(0.564632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.85469 | −0.187117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.65335 | 0.148570 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.8397 | 0.632788 | 0.316394 | − | 0.948628i | \(-0.397528\pi\) | ||||
0.316394 | + | 0.948628i | \(0.397528\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.7655 | 0.406741 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.53185 | −0.0805897 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.8467 | −1.01267 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.9425 | −1.71354 | −0.856770 | − | 0.515699i | \(-0.827532\pi\) | ||||
−0.856770 | + | 0.515699i | \(0.827532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.9760 | 1.96675 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.2634 | 1.27644 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.6213 | −0.653084 | −0.326542 | − | 0.945183i | \(-0.605884\pi\) | ||||
−0.326542 | + | 0.945183i | \(0.605884\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.67886 | 0.148033 |
(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 | 4864.2.a.bo.1.7 | 8 | ||
4.3 | odd | 2 | 4864.2.a.bn.1.2 | 8 | |||
8.3 | odd | 2 | 4864.2.a.bp.1.7 | 8 | |||
8.5 | even | 2 | 4864.2.a.bq.1.2 | 8 | |||
16.3 | odd | 4 | 608.2.c.b.305.3 | 16 | |||
16.5 | even | 4 | 152.2.c.b.77.14 | yes | 16 | ||
16.11 | odd | 4 | 608.2.c.b.305.14 | 16 | |||
16.13 | even | 4 | 152.2.c.b.77.13 | ✓ | 16 | ||
48.5 | odd | 4 | 1368.2.g.b.685.3 | 16 | |||
48.11 | even | 4 | 5472.2.g.b.2737.14 | 16 | |||
48.29 | odd | 4 | 1368.2.g.b.685.4 | 16 | |||
48.35 | even | 4 | 5472.2.g.b.2737.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.13 | ✓ | 16 | 16.13 | even | 4 | ||
152.2.c.b.77.14 | yes | 16 | 16.5 | even | 4 | ||
608.2.c.b.305.3 | 16 | 16.3 | odd | 4 | |||
608.2.c.b.305.14 | 16 | 16.11 | odd | 4 | |||
1368.2.g.b.685.3 | 16 | 48.5 | odd | 4 | |||
1368.2.g.b.685.4 | 16 | 48.29 | odd | 4 | |||
4864.2.a.bn.1.2 | 8 | 4.3 | odd | 2 | |||
4864.2.a.bo.1.7 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.bp.1.7 | 8 | 8.3 | odd | 2 | |||
4864.2.a.bq.1.2 | 8 | 8.5 | even | 2 | |||
5472.2.g.b.2737.3 | 16 | 48.35 | even | 4 | |||
5472.2.g.b.2737.14 | 16 | 48.11 | even | 4 |