Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 2x^{8} - 12x^{7} + 21x^{6} + 48x^{5} - 68x^{4} - 73x^{3} + 66x^{2} + 40x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.200649\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.200649 | 0.141880 | 0.0709400 | − | 0.997481i | \(-0.477400\pi\) | ||||
0.0709400 | + | 0.997481i | \(0.477400\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.95974 | −0.979870 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.775135 | −0.292974 | −0.146487 | − | 0.989213i | \(-0.546797\pi\) | ||||
−0.146487 | + | 0.989213i | \(0.546797\pi\) | |||||||
\(8\) | −0.794517 | −0.280904 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.45447 | −1.34307 | −0.671537 | − | 0.740971i | \(-0.734365\pi\) | ||||
−0.671537 | + | 0.740971i | \(0.734365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.67934 | −1.02046 | −0.510232 | − | 0.860037i | \(-0.670441\pi\) | ||||
−0.510232 | + | 0.860037i | \(0.670441\pi\) | |||||||
\(14\) | −0.155530 | −0.0415671 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.76006 | 0.940015 | ||||||||
\(17\) | 1.05645 | 0.256226 | 0.128113 | − | 0.991760i | \(-0.459108\pi\) | ||||
0.128113 | + | 0.991760i | \(0.459108\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.76245 | 0.863166 | 0.431583 | − | 0.902073i | \(-0.357955\pi\) | ||||
0.431583 | + | 0.902073i | \(0.357955\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.893784 | −0.190555 | ||||||||
\(23\) | 6.21538 | 1.29600 | 0.647998 | − | 0.761642i | \(-0.275607\pi\) | ||||
0.647998 | + | 0.761642i | \(0.275607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.738254 | −0.144784 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.51906 | 0.287076 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.96384 | −0.711927 | −0.355963 | − | 0.934500i | \(-0.615847\pi\) | ||||
−0.355963 | + | 0.934500i | \(0.615847\pi\) | |||||||
\(32\) | 2.34348 | 0.414273 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.211974 | 0.0363533 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.64473 | −0.434790 | −0.217395 | − | 0.976084i | \(-0.569756\pi\) | ||||
−0.217395 | + | 0.976084i | \(0.569756\pi\) | |||||||
\(38\) | 0.754931 | 0.122466 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.67607 | −1.04263 | −0.521314 | − | 0.853365i | \(-0.674558\pi\) | ||||
−0.521314 | + | 0.853365i | \(0.674558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.96230 | −1.51924 | −0.759618 | − | 0.650369i | \(-0.774614\pi\) | ||||
−0.759618 | + | 0.650369i | \(0.774614\pi\) | |||||||
\(44\) | 8.72961 | 1.31604 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.24711 | 0.183876 | ||||||||
\(47\) | −12.6272 | −1.84187 | −0.920936 | − | 0.389715i | \(-0.872574\pi\) | ||||
−0.920936 | + | 0.389715i | \(0.872574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.39917 | −0.914166 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.21054 | 0.999922 | ||||||||
\(53\) | −2.87463 | −0.394860 | −0.197430 | − | 0.980317i | \(-0.563260\pi\) | ||||
−0.197430 | + | 0.980317i | \(0.563260\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.615858 | 0.0822975 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.200649 | −0.0263465 | ||||||||
\(59\) | 7.92534 | 1.03179 | 0.515896 | − | 0.856651i | \(-0.327459\pi\) | ||||
0.515896 | + | 0.856651i | \(0.327459\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.22149 | −0.284432 | −0.142216 | − | 0.989836i | \(-0.545423\pi\) | ||||
−0.142216 | + | 0.989836i | \(0.545423\pi\) | |||||||
\(62\) | −0.795340 | −0.101008 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.04991 | −0.881238 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.12604 | 0.504077 | 0.252038 | − | 0.967717i | \(-0.418899\pi\) | ||||
0.252038 | + | 0.967717i | \(0.418899\pi\) | |||||||
\(68\) | −2.07036 | −0.251068 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6161 | −1.61593 | −0.807966 | − | 0.589229i | \(-0.799432\pi\) | ||||
−0.807966 | + | 0.589229i | \(0.799432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.60138 | 1.00672 | 0.503358 | − | 0.864078i | \(-0.332098\pi\) | ||||
0.503358 | + | 0.864078i | \(0.332098\pi\) | |||||||
\(74\) | −0.530661 | −0.0616881 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.37343 | −0.845790 | ||||||||
\(77\) | 3.45282 | 0.393485 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.97979 | 0.785288 | 0.392644 | − | 0.919691i | \(-0.371560\pi\) | ||||
0.392644 | + | 0.919691i | \(0.371560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.33955 | −0.147928 | ||||||||
\(83\) | 2.90876 | 0.319278 | 0.159639 | − | 0.987175i | \(-0.448967\pi\) | ||||
0.159639 | + | 0.987175i | \(0.448967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.99892 | −0.215549 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.53915 | 0.377275 | ||||||||
\(89\) | 4.30975 | 0.456833 | 0.228416 | − | 0.973564i | \(-0.426645\pi\) | ||||
0.228416 | + | 0.973564i | \(0.426645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.85198 | 0.298969 | ||||||||
\(92\) | −12.1805 | −1.26991 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.53364 | −0.261325 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.82019 | −0.387881 | −0.193941 | − | 0.981013i | \(-0.562127\pi\) | ||||
−0.193941 | + | 0.981013i | \(0.562127\pi\) | |||||||
\(98\) | −1.28398 | −0.129702 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.79941 | 0.179048 | 0.0895241 | − | 0.995985i | \(-0.471465\pi\) | ||||
0.0895241 | + | 0.995985i | \(0.471465\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.658227 | 0.0648570 | 0.0324285 | − | 0.999474i | \(-0.489676\pi\) | ||||
0.0324285 | + | 0.999474i | \(0.489676\pi\) | |||||||
\(104\) | 2.92329 | 0.286653 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.576790 | −0.0560228 | ||||||||
\(107\) | −6.24882 | −0.604097 | −0.302048 | − | 0.953293i | \(-0.597670\pi\) | ||||
−0.302048 | + | 0.953293i | \(0.597670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.44434 | 0.713039 | 0.356519 | − | 0.934288i | \(-0.383963\pi\) | ||||
0.356519 | + | 0.934288i | \(0.383963\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.91456 | −0.275400 | ||||||||
\(113\) | 21.0265 | 1.97801 | 0.989003 | − | 0.147896i | \(-0.0472500\pi\) | ||||
0.989003 | + | 0.147896i | \(0.0472500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.95974 | 0.181957 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.59021 | 0.146391 | ||||||||
\(119\) | −0.818888 | −0.0750673 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.84231 | 0.803847 | ||||||||
\(122\) | −0.445738 | −0.0403552 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.76810 | 0.697596 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9855 | 1.06354 | 0.531771 | − | 0.846888i | \(-0.321527\pi\) | ||||
0.531771 | + | 0.846888i | \(0.321527\pi\) | |||||||
\(128\) | −6.10152 | −0.539304 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6387 | 1.19162 | 0.595810 | − | 0.803126i | \(-0.296831\pi\) | ||||
0.595810 | + | 0.803126i | \(0.296831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.91641 | −0.252885 | ||||||||
\(134\) | 0.827885 | 0.0715184 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.839363 | −0.0719748 | ||||||||
\(137\) | 5.55942 | 0.474974 | 0.237487 | − | 0.971391i | \(-0.423676\pi\) | ||||
0.237487 | + | 0.971391i | \(0.423676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.0649 | 1.87152 | 0.935759 | − | 0.352639i | \(-0.114716\pi\) | ||||
0.935759 | + | 0.352639i | \(0.114716\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.73205 | −0.229269 | ||||||||
\(143\) | 16.3895 | 1.37056 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.72586 | 0.142833 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.18298 | 0.426038 | ||||||||
\(149\) | 8.92269 | 0.730975 | 0.365488 | − | 0.930816i | \(-0.380902\pi\) | ||||
0.365488 | + | 0.930816i | \(0.380902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.84172 | −0.638150 | −0.319075 | − | 0.947729i | \(-0.603372\pi\) | ||||
−0.319075 | + | 0.947729i | \(0.603372\pi\) | |||||||
\(152\) | −2.98933 | −0.242467 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.692803 | 0.0558277 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.8114 | −1.42150 | −0.710751 | − | 0.703444i | \(-0.751645\pi\) | ||||
−0.710751 | + | 0.703444i | \(0.751645\pi\) | |||||||
\(158\) | 1.40049 | 0.111417 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.81776 | −0.379693 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3040 | 0.963724 | 0.481862 | − | 0.876247i | \(-0.339961\pi\) | ||||
0.481862 | + | 0.876247i | \(0.339961\pi\) | |||||||
\(164\) | 13.0834 | 1.02164 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.583640 | 0.0452992 | ||||||||
\(167\) | 21.6643 | 1.67643 | 0.838216 | − | 0.545338i | \(-0.183599\pi\) | ||||
0.838216 | + | 0.545338i | \(0.183599\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.537513 | 0.0413471 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 19.5235 | 1.48865 | ||||||||
\(173\) | 4.25059 | 0.323167 | 0.161583 | − | 0.986859i | \(-0.448340\pi\) | ||||
0.161583 | + | 0.986859i | \(0.448340\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.7491 | −1.26251 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.864746 | 0.0648154 | ||||||||
\(179\) | 23.2124 | 1.73497 | 0.867487 | − | 0.497460i | \(-0.165734\pi\) | ||||
0.867487 | + | 0.497460i | \(0.165734\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.68131 | 0.719606 | 0.359803 | − | 0.933028i | \(-0.382844\pi\) | ||||
0.359803 | + | 0.933028i | \(0.382844\pi\) | |||||||
\(182\) | 0.572247 | 0.0424177 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.93822 | −0.364050 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.70590 | −0.344130 | ||||||||
\(188\) | 24.7461 | 1.80479 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.1664 | −1.53155 | −0.765775 | − | 0.643109i | \(-0.777644\pi\) | ||||
−0.765775 | + | 0.643109i | \(0.777644\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.6231 | 1.26854 | 0.634269 | − | 0.773112i | \(-0.281301\pi\) | ||||
0.634269 | + | 0.773112i | \(0.281301\pi\) | |||||||
\(194\) | −0.766516 | −0.0550326 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.5407 | 0.895764 | ||||||||
\(197\) | 12.6217 | 0.899257 | 0.449628 | − | 0.893216i | \(-0.351556\pi\) | ||||
0.449628 | + | 0.893216i | \(0.351556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9741 | −1.48681 | −0.743406 | − | 0.668841i | \(-0.766791\pi\) | ||||
−0.743406 | + | 0.668841i | \(0.766791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.361050 | 0.0254034 | ||||||||
\(203\) | 0.775135 | 0.0544038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.132072 | 0.00920191 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.8345 | −0.959252 | ||||||||
\(209\) | −16.7597 | −1.15930 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.1750 | −1.73312 | −0.866558 | − | 0.499077i | \(-0.833672\pi\) | ||||
−0.866558 | + | 0.499077i | \(0.833672\pi\) | |||||||
\(212\) | 5.63352 | 0.386912 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.25382 | −0.0857093 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.07251 | 0.208576 | ||||||||
\(218\) | 1.49370 | 0.101166 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.88702 | −0.261469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.225647 | −0.0151104 | −0.00755521 | − | 0.999971i | \(-0.502405\pi\) | ||||
−0.00755521 | + | 0.999971i | \(0.502405\pi\) | |||||||
\(224\) | −1.81652 | −0.121371 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.21894 | 0.280640 | ||||||||
\(227\) | 26.3772 | 1.75072 | 0.875359 | − | 0.483474i | \(-0.160625\pi\) | ||||
0.875359 | + | 0.483474i | \(0.160625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.12235 | −0.206331 | −0.103165 | − | 0.994664i | \(-0.532897\pi\) | ||||
−0.103165 | + | 0.994664i | \(0.532897\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.794517 | 0.0521626 | ||||||||
\(233\) | 12.4808 | 0.817644 | 0.408822 | − | 0.912614i | \(-0.365940\pi\) | ||||
0.408822 | + | 0.912614i | \(0.365940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.5316 | −1.01102 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.164309 | −0.0106506 | ||||||||
\(239\) | 12.6664 | 0.819321 | 0.409660 | − | 0.912238i | \(-0.365647\pi\) | ||||
0.409660 | + | 0.912238i | \(0.365647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.738241 | −0.0475543 | −0.0237771 | − | 0.999717i | \(-0.507569\pi\) | ||||
−0.0237771 | + | 0.999717i | \(0.507569\pi\) | |||||||
\(242\) | 1.77420 | 0.114050 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.35354 | 0.278707 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8433 | −0.880830 | ||||||||
\(248\) | 3.14934 | 0.199983 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3549 | −0.779832 | −0.389916 | − | 0.920850i | \(-0.627496\pi\) | ||||
−0.389916 | + | 0.920850i | \(0.627496\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.6862 | −1.74062 | ||||||||
\(254\) | 2.40488 | 0.150895 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.8755 | 0.804722 | ||||||||
\(257\) | 17.5823 | 1.09675 | 0.548377 | − | 0.836231i | \(-0.315246\pi\) | ||||
0.548377 | + | 0.836231i | \(0.315246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.05002 | 0.127382 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.73659 | 0.169067 | ||||||||
\(263\) | 11.3491 | 0.699816 | 0.349908 | − | 0.936784i | \(-0.386213\pi\) | ||||
0.349908 | + | 0.936784i | \(0.386213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.585174 | −0.0358793 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.08597 | −0.493930 | ||||||||
\(269\) | −14.3872 | −0.877201 | −0.438601 | − | 0.898682i | \(-0.644526\pi\) | ||||
−0.438601 | + | 0.898682i | \(0.644526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32554 | 0.384249 | 0.192124 | − | 0.981371i | \(-0.438462\pi\) | ||||
0.192124 | + | 0.981371i | \(0.438462\pi\) | |||||||
\(272\) | 3.97230 | 0.240856 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.11549 | 0.0673893 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.3726 | 1.10390 | 0.551952 | − | 0.833876i | \(-0.313883\pi\) | ||||
0.551952 | + | 0.833876i | \(0.313883\pi\) | |||||||
\(278\) | 4.42729 | 0.265531 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.1207 | 1.02133 | 0.510667 | − | 0.859778i | \(-0.329398\pi\) | ||||
0.510667 | + | 0.859778i | \(0.329398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.6804 | −1.70487 | −0.852435 | − | 0.522833i | \(-0.824875\pi\) | ||||
−0.852435 | + | 0.522833i | \(0.824875\pi\) | |||||||
\(284\) | 26.6840 | 1.58340 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.28853 | 0.194455 | ||||||||
\(287\) | 5.17486 | 0.305462 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8839 | −0.934348 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.8565 | −0.986450 | ||||||||
\(293\) | 9.71695 | 0.567670 | 0.283835 | − | 0.958873i | \(-0.408393\pi\) | ||||
0.283835 | + | 0.958873i | \(0.408393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.10128 | 0.122134 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.79033 | 0.103711 | ||||||||
\(299\) | −22.8685 | −1.32252 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.72213 | 0.445096 | ||||||||
\(302\) | −1.57343 | −0.0905408 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.1471 | 0.811389 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.56349 | 0.488744 | 0.244372 | − | 0.969682i | \(-0.421418\pi\) | ||||
0.244372 | + | 0.969682i | \(0.421418\pi\) | |||||||
\(308\) | −6.76663 | −0.385564 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.1647 | −0.973324 | −0.486662 | − | 0.873590i | \(-0.661786\pi\) | ||||
−0.486662 | + | 0.873590i | \(0.661786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.40045 | −0.192205 | −0.0961025 | − | 0.995371i | \(-0.530638\pi\) | ||||
−0.0961025 | + | 0.995371i | \(0.530638\pi\) | |||||||
\(314\) | −3.57383 | −0.201683 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.6786 | −0.769480 | ||||||||
\(317\) | −23.0876 | −1.29673 | −0.648365 | − | 0.761329i | \(-0.724547\pi\) | ||||
−0.648365 | + | 0.761329i | \(0.724547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.45447 | 0.249403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.966677 | −0.0538708 | ||||||||
\(323\) | 3.97482 | 0.221165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.46878 | 0.136733 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.30425 | 0.292878 | ||||||||
\(329\) | 9.78781 | 0.539620 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.3051 | −0.841245 | −0.420623 | − | 0.907236i | \(-0.638188\pi\) | ||||
−0.420623 | + | 0.907236i | \(0.638188\pi\) | |||||||
\(332\) | −5.70042 | −0.312851 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.34691 | 0.237852 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.93351 | −0.159799 | −0.0798994 | − | 0.996803i | \(-0.525460\pi\) | ||||
−0.0798994 | + | 0.996803i | \(0.525460\pi\) | |||||||
\(338\) | 0.107851 | 0.00586634 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.6568 | 0.956170 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.3862 | 0.560800 | ||||||||
\(344\) | 7.91521 | 0.426760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.852876 | 0.0458509 | ||||||||
\(347\) | 31.0176 | 1.66511 | 0.832555 | − | 0.553942i | \(-0.186877\pi\) | ||||
0.832555 | + | 0.553942i | \(0.186877\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.15838 | −0.436708 | −0.218354 | − | 0.975870i | \(-0.570069\pi\) | ||||
−0.218354 | + | 0.975870i | \(0.570069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.4390 | −0.556400 | ||||||||
\(353\) | 1.25800 | 0.0669568 | 0.0334784 | − | 0.999439i | \(-0.489342\pi\) | ||||
0.0334784 | + | 0.999439i | \(0.489342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.44599 | −0.447637 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.65753 | 0.246158 | ||||||||
\(359\) | −3.64864 | −0.192568 | −0.0962838 | − | 0.995354i | \(-0.530696\pi\) | ||||
−0.0962838 | + | 0.995354i | \(0.530696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.84396 | −0.254945 | ||||||||
\(362\) | 1.94254 | 0.102098 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.58915 | −0.292951 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.1323 | 0.685503 | 0.342751 | − | 0.939426i | \(-0.388641\pi\) | ||||
0.342751 | + | 0.939426i | \(0.388641\pi\) | |||||||
\(368\) | 23.3702 | 1.21826 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.22822 | 0.115684 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.58444 | −0.392707 | −0.196354 | − | 0.980533i | \(-0.562910\pi\) | ||||
−0.196354 | + | 0.980533i | \(0.562910\pi\) | |||||||
\(374\) | −0.944233 | −0.0488251 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.0325 | 0.517389 | ||||||||
\(377\) | 3.67934 | 0.189495 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.8949 | −1.43287 | −0.716434 | − | 0.697655i | \(-0.754227\pi\) | ||||
−0.716434 | + | 0.697655i | \(0.754227\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.24702 | −0.217296 | ||||||||
\(383\) | 12.0440 | 0.615418 | 0.307709 | − | 0.951481i | \(-0.400438\pi\) | ||||
0.307709 | + | 0.951481i | \(0.400438\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.53605 | 0.179980 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.48658 | 0.380073 | ||||||||
\(389\) | 29.0575 | 1.47327 | 0.736636 | − | 0.676290i | \(-0.236413\pi\) | ||||
0.736636 | + | 0.676290i | \(0.236413\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.56620 | 0.332067 | ||||||||
\(392\) | 5.08424 | 0.256793 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.53252 | 0.127587 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1050 | −0.557346 | −0.278673 | − | 0.960386i | \(-0.589895\pi\) | ||||
−0.278673 | + | 0.960386i | \(0.589895\pi\) | |||||||
\(398\) | −4.20842 | −0.210949 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.9928 | 0.748703 | 0.374352 | − | 0.927287i | \(-0.377865\pi\) | ||||
0.374352 | + | 0.927287i | \(0.377865\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.5843 | 0.726496 | ||||||||
\(404\) | −3.52638 | −0.175444 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.155530 | 0.00771882 | ||||||||
\(407\) | 11.7809 | 0.583955 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3994 | 1.30537 | 0.652684 | − | 0.757631i | \(-0.273643\pi\) | ||||
0.652684 | + | 0.757631i | \(0.273643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.28995 | −0.0635514 | ||||||||
\(413\) | −6.14321 | −0.302288 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.62247 | −0.422751 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.36282 | −0.164481 | ||||||||
\(419\) | −15.1863 | −0.741901 | −0.370950 | − | 0.928653i | \(-0.620968\pi\) | ||||
−0.370950 | + | 0.928653i | \(0.620968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.51805 | 0.220196 | 0.110098 | − | 0.993921i | \(-0.464883\pi\) | ||||
0.110098 | + | 0.993921i | \(0.464883\pi\) | |||||||
\(422\) | −5.05132 | −0.245894 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.28394 | 0.110918 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.72195 | 0.0833311 | ||||||||
\(428\) | 12.2461 | 0.591936 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.10385 | 0.149507 | 0.0747536 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747536 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.92413 | −0.428866 | −0.214433 | − | 0.976739i | \(-0.568790\pi\) | ||||
−0.214433 | + | 0.976739i | \(0.568790\pi\) | |||||||
\(434\) | 0.616496 | 0.0295927 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.5890 | −0.698685 | ||||||||
\(437\) | 23.3851 | 1.11866 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.6862 | −1.56003 | −0.780013 | − | 0.625764i | \(-0.784787\pi\) | ||||
−0.780013 | + | 0.625764i | \(0.784787\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.779925 | −0.0370972 | ||||||||
\(443\) | 14.9791 | 0.711677 | 0.355838 | − | 0.934548i | \(-0.384195\pi\) | ||||
0.355838 | + | 0.934548i | \(0.384195\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.0452757 | −0.00214387 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.46463 | 0.258180 | ||||||||
\(449\) | −34.4130 | −1.62405 | −0.812024 | − | 0.583623i | \(-0.801634\pi\) | ||||
−0.812024 | + | 0.583623i | \(0.801634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.7384 | 1.40033 | ||||||||
\(452\) | −41.2065 | −1.93819 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.29256 | 0.248392 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.7364 | −1.39101 | −0.695506 | − | 0.718520i | \(-0.744820\pi\) | ||||
−0.695506 | + | 0.718520i | \(0.744820\pi\) | |||||||
\(458\) | −0.626496 | −0.0292742 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.01736 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0818 | 0.747384 | 0.373692 | − | 0.927553i | \(-0.378092\pi\) | ||||
0.373692 | + | 0.927553i | \(0.378092\pi\) | |||||||
\(464\) | −3.76006 | −0.174556 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.50425 | 0.116007 | ||||||||
\(467\) | 21.5438 | 0.996928 | 0.498464 | − | 0.866910i | \(-0.333898\pi\) | ||||
0.498464 | + | 0.866910i | \(0.333898\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.19824 | −0.147681 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.29681 | −0.289834 | ||||||||
\(473\) | 44.3768 | 2.04045 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.60481 | 0.0735562 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.54149 | 0.116245 | ||||||||
\(479\) | 14.2131 | 0.649414 | 0.324707 | − | 0.945815i | \(-0.394734\pi\) | ||||
0.324707 | + | 0.945815i | \(0.394734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.73084 | 0.443688 | ||||||||
\(482\) | −0.148127 | −0.00674700 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.3286 | −0.787665 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.1443 | 0.867512 | 0.433756 | − | 0.901030i | \(-0.357188\pi\) | ||||
0.433756 | + | 0.901030i | \(0.357188\pi\) | |||||||
\(488\) | 1.76501 | 0.0798981 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.2694 | −1.45630 | −0.728148 | − | 0.685420i | \(-0.759619\pi\) | ||||
−0.728148 | + | 0.685420i | \(0.759619\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.05645 | −0.0475799 | ||||||||
\(494\) | −2.77764 | −0.124972 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.9043 | −0.669222 | ||||||||
\(497\) | 10.5543 | 0.473426 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.4860 | 0.917078 | 0.458539 | − | 0.888674i | \(-0.348373\pi\) | ||||
0.458539 | + | 0.888674i | \(0.348373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.47899 | −0.110643 | ||||||||
\(503\) | −3.42204 | −0.152581 | −0.0762905 | − | 0.997086i | \(-0.524308\pi\) | ||||
−0.0762905 | + | 0.997086i | \(0.524308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.55520 | −0.246959 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.4885 | −1.04213 | ||||||||
\(509\) | 21.5512 | 0.955238 | 0.477619 | − | 0.878567i | \(-0.341500\pi\) | ||||
0.477619 | + | 0.878567i | \(0.341500\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.66723 | −0.294941 | ||||||||
\(512\) | 14.7865 | 0.653478 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.52787 | 0.155608 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 56.2476 | 2.47377 | ||||||||
\(518\) | 0.411334 | 0.0180730 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.7978 | 1.39309 | 0.696544 | − | 0.717514i | \(-0.254720\pi\) | ||||
0.696544 | + | 0.717514i | \(0.254720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.5953 | 1.73138 | 0.865691 | − | 0.500579i | \(-0.166879\pi\) | ||||
0.865691 | + | 0.500579i | \(0.166879\pi\) | |||||||
\(524\) | −26.7283 | −1.16763 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.27718 | 0.0992900 | ||||||||
\(527\) | −4.18758 | −0.182414 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.6309 | 0.679605 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.71540 | 0.247794 | ||||||||
\(533\) | 24.5635 | 1.06396 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.27821 | −0.141597 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.88677 | −0.124457 | ||||||||
\(539\) | 28.5049 | 1.22779 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.5906 | −1.10023 | −0.550113 | − | 0.835090i | \(-0.685415\pi\) | ||||
−0.550113 | + | 0.835090i | \(0.685415\pi\) | |||||||
\(542\) | 1.26921 | 0.0545173 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.47576 | 0.106147 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.96642 | 0.255106 | 0.127553 | − | 0.991832i | \(-0.459288\pi\) | ||||
0.127553 | + | 0.991832i | \(0.459288\pi\) | |||||||
\(548\) | −10.8950 | −0.465412 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.76245 | −0.160286 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.41028 | −0.230069 | ||||||||
\(554\) | 3.68645 | 0.156622 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −43.2414 | −1.83385 | ||||||||
\(557\) | 15.5091 | 0.657143 | 0.328572 | − | 0.944479i | \(-0.393433\pi\) | ||||
0.328572 | + | 0.944479i | \(0.393433\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.6547 | 1.55033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.43524 | 0.144907 | ||||||||
\(563\) | 8.67282 | 0.365516 | 0.182758 | − | 0.983158i | \(-0.441498\pi\) | ||||
0.182758 | + | 0.983158i | \(0.441498\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.75468 | −0.241887 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.8182 | 0.453922 | ||||||||
\(569\) | −2.05132 | −0.0859959 | −0.0429980 | − | 0.999075i | \(-0.513691\pi\) | ||||
−0.0429980 | + | 0.999075i | \(0.513691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.72574 | −0.114069 | −0.0570344 | − | 0.998372i | \(-0.518164\pi\) | ||||
−0.0570344 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(572\) | −32.1192 | −1.34297 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.03833 | 0.0433390 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.3626 | −1.01423 | −0.507115 | − | 0.861879i | \(-0.669288\pi\) | ||||
−0.507115 | + | 0.861879i | \(0.669288\pi\) | |||||||
\(578\) | −3.18709 | −0.132565 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.25469 | −0.0935401 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.8049 | 0.530326 | ||||||||
\(584\) | −6.83394 | −0.282790 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.94969 | 0.0805411 | ||||||||
\(587\) | 4.29753 | 0.177378 | 0.0886890 | − | 0.996059i | \(-0.471732\pi\) | ||||
0.0886890 | + | 0.996059i | \(0.471732\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.9138 | −0.614511 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.94433 | −0.408710 | ||||||||
\(593\) | 20.7059 | 0.850291 | 0.425146 | − | 0.905125i | \(-0.360223\pi\) | ||||
0.425146 | + | 0.905125i | \(0.360223\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.4862 | −0.716261 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.58853 | −0.187639 | ||||||||
\(599\) | −2.58646 | −0.105680 | −0.0528399 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528399 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.6870 | 1.04779 | 0.523897 | − | 0.851782i | \(-0.324478\pi\) | ||||
0.523897 | + | 0.851782i | \(0.324478\pi\) | |||||||
\(602\) | 1.54944 | 0.0631503 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.3677 | 0.625304 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.6725 | 0.757893 | 0.378947 | − | 0.925419i | \(-0.376286\pi\) | ||||
0.378947 | + | 0.925419i | \(0.376286\pi\) | |||||||
\(608\) | 8.81725 | 0.357587 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.4598 | 1.87956 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.5152 | −1.15172 | −0.575858 | − | 0.817549i | \(-0.695332\pi\) | ||||
−0.575858 | + | 0.817549i | \(0.695332\pi\) | |||||||
\(614\) | 1.71825 | 0.0693430 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.74332 | −0.110532 | ||||||||
\(617\) | −31.7077 | −1.27651 | −0.638253 | − | 0.769827i | \(-0.720343\pi\) | ||||
−0.638253 | + | 0.769827i | \(0.720343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.0039 | 1.32654 | 0.663269 | − | 0.748381i | \(-0.269169\pi\) | ||||
0.663269 | + | 0.748381i | \(0.269169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.44408 | −0.138095 | ||||||||
\(623\) | −3.34064 | −0.133840 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.682297 | −0.0272701 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 34.9057 | 1.39289 | ||||||||
\(629\) | −2.79401 | −0.111404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.7586 | −0.468102 | −0.234051 | − | 0.972224i | \(-0.575198\pi\) | ||||
−0.234051 | + | 0.972224i | \(0.575198\pi\) | |||||||
\(632\) | −5.54556 | −0.220591 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.63250 | −0.183980 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.5447 | 0.932874 | ||||||||
\(638\) | 0.893784 | 0.0353852 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.63965 | −0.143758 | −0.0718788 | − | 0.997413i | \(-0.522899\pi\) | ||||
−0.0718788 | + | 0.997413i | \(0.522899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.1571 | 1.30759 | 0.653794 | − | 0.756673i | \(-0.273176\pi\) | ||||
0.653794 | + | 0.756673i | \(0.273176\pi\) | |||||||
\(644\) | 9.44155 | 0.372049 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.797543 | 0.0313789 | ||||||||
\(647\) | 47.8411 | 1.88083 | 0.940413 | − | 0.340034i | \(-0.110439\pi\) | ||||
0.940413 | + | 0.340034i | \(0.110439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.3032 | −1.38577 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.1127 | −0.944325 | ||||||||
\(653\) | −10.3879 | −0.406512 | −0.203256 | − | 0.979126i | \(-0.565152\pi\) | ||||
−0.203256 | + | 0.979126i | \(0.565152\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −25.1024 | −0.980086 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.96391 | 0.0765612 | ||||||||
\(659\) | 33.5433 | 1.30666 | 0.653331 | − | 0.757073i | \(-0.273371\pi\) | ||||
0.653331 | + | 0.757073i | \(0.273371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.6291 | −0.724589 | −0.362294 | − | 0.932064i | \(-0.618006\pi\) | ||||
−0.362294 | + | 0.932064i | \(0.618006\pi\) | |||||||
\(662\) | −3.07095 | −0.119356 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.31106 | −0.0896866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.21538 | −0.240660 | ||||||||
\(668\) | −42.4564 | −1.64269 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.89555 | 0.382013 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.3062 | −1.12967 | −0.564835 | − | 0.825204i | \(-0.691060\pi\) | ||||
−0.564835 | + | 0.825204i | \(0.691060\pi\) | |||||||
\(674\) | −0.588606 | −0.0226723 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.05339 | −0.0405148 | ||||||||
\(677\) | −20.8134 | −0.799925 | −0.399962 | − | 0.916532i | \(-0.630977\pi\) | ||||
−0.399962 | + | 0.916532i | \(0.630977\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.96116 | 0.113639 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.54282 | 0.135661 | ||||||||
\(683\) | −26.6885 | −1.02121 | −0.510604 | − | 0.859816i | \(-0.670578\pi\) | ||||
−0.510604 | + | 0.859816i | \(0.670578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.08397 | 0.0795664 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.4589 | −1.42811 | ||||||||
\(689\) | 10.5767 | 0.402941 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.2486 | −1.30288 | −0.651439 | − | 0.758701i | \(-0.725834\pi\) | ||||
−0.651439 | + | 0.758701i | \(0.725834\pi\) | |||||||
\(692\) | −8.33006 | −0.316661 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.22363 | 0.236246 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.05290 | −0.267148 | ||||||||
\(698\) | −1.63697 | −0.0619601 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.4457 | −1.07438 | −0.537190 | − | 0.843461i | \(-0.680514\pi\) | ||||
−0.537190 | + | 0.843461i | \(0.680514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.95066 | −0.375296 | ||||||||
\(704\) | 31.4036 | 1.18357 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.252417 | 0.00949983 | ||||||||
\(707\) | −1.39479 | −0.0524564 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4260 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.42417 | −0.128326 | ||||||||
\(713\) | −24.6368 | −0.922654 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −45.4902 | −1.70005 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.732094 | −0.0273215 | ||||||||
\(719\) | −28.3986 | −1.05909 | −0.529545 | − | 0.848282i | \(-0.677637\pi\) | ||||
−0.529545 | + | 0.848282i | \(0.677637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.510215 | −0.0190014 | ||||||||
\(722\) | −0.971933 | −0.0361716 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.9729 | −0.705120 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.50646 | −0.130047 | −0.0650236 | − | 0.997884i | \(-0.520712\pi\) | ||||
−0.0650236 | + | 0.997884i | \(0.520712\pi\) | |||||||
\(728\) | −2.26595 | −0.0839816 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.5246 | −0.389267 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.8907 | 1.36259 | 0.681295 | − | 0.732009i | \(-0.261417\pi\) | ||||
0.681295 | + | 0.732009i | \(0.261417\pi\) | |||||||
\(734\) | 2.63499 | 0.0972592 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.5656 | 0.536897 | ||||||||
\(737\) | −18.3793 | −0.677012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.5756 | −0.462603 | −0.231301 | − | 0.972882i | \(-0.574298\pi\) | ||||
−0.231301 | + | 0.972882i | \(0.574298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.447090 | 0.0164132 | ||||||||
\(743\) | 36.2579 | 1.33017 | 0.665086 | − | 0.746767i | \(-0.268395\pi\) | ||||
0.665086 | + | 0.746767i | \(0.268395\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.52181 | −0.0557173 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.22235 | 0.337202 | ||||||||
\(749\) | 4.84368 | 0.176984 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2839 | 0.813151 | 0.406576 | − | 0.913617i | \(-0.366723\pi\) | ||||
0.406576 | + | 0.913617i | \(0.366723\pi\) | |||||||
\(752\) | −47.4792 | −1.73139 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.738254 | 0.0268856 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1631 | 0.805530 | 0.402765 | − | 0.915303i | \(-0.368049\pi\) | ||||
0.402765 | + | 0.915303i | \(0.368049\pi\) | |||||||
\(758\) | −5.59708 | −0.203295 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.6078 | −1.58078 | −0.790391 | − | 0.612603i | \(-0.790123\pi\) | ||||
−0.790391 | + | 0.612603i | \(0.790123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.77037 | −0.208901 | ||||||||
\(764\) | 41.4807 | 1.50072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.41660 | 0.0873155 | ||||||||
\(767\) | −29.1600 | −1.05291 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.84025 | −0.210605 | −0.105302 | − | 0.994440i | \(-0.533581\pi\) | ||||
−0.105302 | + | 0.994440i | \(0.533581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −34.5367 | −1.24300 | ||||||||
\(773\) | −19.9643 | −0.718067 | −0.359034 | − | 0.933325i | \(-0.616894\pi\) | ||||
−0.359034 | + | 0.933325i | \(0.616894\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.03520 | 0.108957 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.83034 | 0.209028 | ||||||||
\(779\) | −25.1184 | −0.899960 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.6525 | 2.17032 | ||||||||
\(782\) | 1.31750 | 0.0471137 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.0613 | −0.859331 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.1482 | −0.932081 | −0.466041 | − | 0.884763i | \(-0.654320\pi\) | ||||
−0.466041 | + | 0.884763i | \(0.654320\pi\) | |||||||
\(788\) | −24.7352 | −0.881155 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.2984 | −0.579503 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.17359 | 0.290253 | ||||||||
\(794\) | −2.22821 | −0.0790763 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41.1037 | 1.45688 | ||||||||
\(797\) | 43.5293 | 1.54189 | 0.770944 | − | 0.636903i | \(-0.219785\pi\) | ||||
0.770944 | + | 0.636903i | \(0.219785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.3400 | −0.471934 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.00828 | 0.106226 | ||||||||
\(803\) | −38.3146 | −1.35209 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.92632 | 0.103075 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.42966 | −0.0502954 | ||||||||
\(809\) | −43.8436 | −1.54146 | −0.770729 | − | 0.637164i | \(-0.780108\pi\) | ||||
−0.770729 | + | 0.637164i | \(0.780108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.2295 | 0.534778 | 0.267389 | − | 0.963589i | \(-0.413839\pi\) | ||||
0.267389 | + | 0.963589i | \(0.413839\pi\) | |||||||
\(812\) | −1.51906 | −0.0533087 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.36381 | 0.0828516 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.4827 | −1.31135 | ||||||||
\(818\) | 5.29701 | 0.185206 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.3792 | 0.501837 | 0.250919 | − | 0.968008i | \(-0.419267\pi\) | ||||
0.250919 | + | 0.968008i | \(0.419267\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.68581 | 0.337626 | 0.168813 | − | 0.985648i | \(-0.446007\pi\) | ||||
0.168813 | + | 0.985648i | \(0.446007\pi\) | |||||||
\(824\) | −0.522972 | −0.0182186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.23263 | −0.0428886 | ||||||||
\(827\) | 30.2089 | 1.05047 | 0.525233 | − | 0.850958i | \(-0.323978\pi\) | ||||
0.525233 | + | 0.850958i | \(0.323978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.9917 | 1.35424 | 0.677119 | − | 0.735874i | \(-0.263228\pi\) | ||||
0.677119 | + | 0.735874i | \(0.263228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.9390 | 0.899272 | ||||||||
\(833\) | −6.76037 | −0.234233 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.8447 | 1.13596 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.04712 | −0.105261 | ||||||||
\(839\) | −9.74245 | −0.336347 | −0.168173 | − | 0.985757i | \(-0.553787\pi\) | ||||
−0.168173 | + | 0.985757i | \(0.553787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0.906541 | 0.0312415 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 49.3364 | 1.69823 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.85399 | −0.235506 | ||||||||
\(848\) | −10.8088 | −0.371175 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.4380 | −0.563486 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.4478 | −1.76154 | −0.880769 | − | 0.473545i | \(-0.842974\pi\) | ||||
−0.880769 | + | 0.473545i | \(0.842974\pi\) | |||||||
\(854\) | 0.345507 | 0.0118230 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.96479 | 0.169693 | ||||||||
\(857\) | −48.8308 | −1.66803 | −0.834014 | − | 0.551743i | \(-0.813963\pi\) | ||||
−0.834014 | + | 0.551743i | \(0.813963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6720 | −0.568841 | −0.284421 | − | 0.958700i | \(-0.591801\pi\) | ||||
−0.284421 | + | 0.958700i | \(0.591801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.622783 | 0.0212121 | ||||||||
\(863\) | 2.90194 | 0.0987831 | 0.0493915 | − | 0.998779i | \(-0.484272\pi\) | ||||
0.0493915 | + | 0.998779i | \(0.484272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.79061 | −0.0608476 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.02133 | −0.204377 | ||||||||
\(869\) | −31.0913 | −1.05470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.1811 | −0.514392 | ||||||||
\(872\) | −5.91465 | −0.200295 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.69218 | 0.158715 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.4418 | 1.26432 | 0.632160 | − | 0.774838i | \(-0.282169\pi\) | ||||
0.632160 | + | 0.774838i | \(0.282169\pi\) | |||||||
\(878\) | −6.55843 | −0.221336 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.8351 | 1.07255 | 0.536275 | − | 0.844043i | \(-0.319831\pi\) | ||||
0.536275 | + | 0.844043i | \(0.319831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.4903 | 0.554942 | 0.277471 | − | 0.960734i | \(-0.410504\pi\) | ||||
0.277471 | + | 0.960734i | \(0.410504\pi\) | |||||||
\(884\) | 7.61754 | 0.256206 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.00553 | 0.100973 | ||||||||
\(887\) | −8.78785 | −0.295067 | −0.147534 | − | 0.989057i | \(-0.547133\pi\) | ||||
−0.147534 | + | 0.989057i | \(0.547133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.29039 | −0.311590 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.442209 | 0.0148062 | ||||||||
\(893\) | −47.5094 | −1.58984 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.72951 | 0.158002 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.90492 | −0.230420 | ||||||||
\(899\) | 3.96384 | 0.132202 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.03688 | −0.101173 | ||||||||
\(902\) | 5.96697 | 0.198678 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.7059 | −0.555630 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.51166 | −0.216216 | −0.108108 | − | 0.994139i | \(-0.534479\pi\) | ||||
−0.108108 | + | 0.994139i | \(0.534479\pi\) | |||||||
\(908\) | −51.6925 | −1.71548 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.3746 | 0.741304 | 0.370652 | − | 0.928772i | \(-0.379134\pi\) | ||||
0.370652 | + | 0.928772i | \(0.379134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.9570 | −0.428814 | ||||||||
\(914\) | −5.96658 | −0.197357 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.11900 | 0.202178 | ||||||||
\(917\) | −10.5718 | −0.349113 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.2078 | 0.732568 | 0.366284 | − | 0.930503i | \(-0.380630\pi\) | ||||
0.366284 | + | 0.930503i | \(0.380630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.00673 | 0.0331548 | ||||||||
\(923\) | 50.0982 | 1.64900 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.22679 | 0.106039 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.34348 | −0.0769287 | ||||||||
\(929\) | 35.0239 | 1.14910 | 0.574548 | − | 0.818471i | \(-0.305178\pi\) | ||||
0.574548 | + | 0.818471i | \(0.305178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0766 | −0.789077 | ||||||||
\(932\) | −24.4591 | −0.801184 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.32274 | 0.141444 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.4983 | −1.84572 | −0.922860 | − | 0.385136i | \(-0.874155\pi\) | ||||
−0.922860 | + | 0.385136i | \(0.874155\pi\) | |||||||
\(938\) | −0.641723 | −0.0209530 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.3736 | 1.28354 | 0.641771 | − | 0.766896i | \(-0.278200\pi\) | ||||
0.641771 | + | 0.766896i | \(0.278200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.4943 | −1.35124 | ||||||||
\(944\) | 29.7998 | 0.969900 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.90414 | 0.289499 | ||||||||
\(947\) | −58.9377 | −1.91522 | −0.957610 | − | 0.288069i | \(-0.906987\pi\) | ||||
−0.957610 | + | 0.288069i | \(0.906987\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.6474 | −1.02732 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.650620 | 0.0210867 | ||||||||
\(953\) | 23.3111 | 0.755120 | 0.377560 | − | 0.925985i | \(-0.376763\pi\) | ||||
0.377560 | + | 0.925985i | \(0.376763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.8228 | −0.802828 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.85184 | 0.0921389 | ||||||||
\(959\) | −4.30930 | −0.139155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2880 | −0.493160 | ||||||||
\(962\) | 1.95248 | 0.0629505 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.44676 | 0.0465970 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.7227 | −0.441293 | −0.220646 | − | 0.975354i | \(-0.570817\pi\) | ||||
−0.220646 | + | 0.975354i | \(0.570817\pi\) | |||||||
\(968\) | −7.02537 | −0.225804 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.1078 | 1.89686 | 0.948430 | − | 0.316985i | \(-0.102671\pi\) | ||||
0.948430 | + | 0.316985i | \(0.102671\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1033 | −0.548306 | ||||||||
\(974\) | 3.84128 | 0.123083 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.35292 | −0.267371 | ||||||||
\(977\) | 25.0687 | 0.802018 | 0.401009 | − | 0.916074i | \(-0.368660\pi\) | ||||
0.401009 | + | 0.916074i | \(0.368660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.1977 | −0.613560 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.47480 | −0.206619 | ||||||||
\(983\) | −28.3475 | −0.904146 | −0.452073 | − | 0.891981i | \(-0.649315\pi\) | ||||
−0.452073 | + | 0.891981i | \(0.649315\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.211974 | −0.00675064 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27.1293 | 0.863099 | ||||||||
\(989\) | −61.9195 | −1.96892 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.81196 | −0.152857 | −0.0764285 | − | 0.997075i | \(-0.524352\pi\) | ||||
−0.0764285 | + | 0.997075i | \(0.524352\pi\) | |||||||
\(992\) | −9.28920 | −0.294932 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.11771 | 0.0671696 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.9930 | −0.601514 | −0.300757 | − | 0.953701i | \(-0.597239\pi\) | ||||
−0.300757 | + | 0.953701i | \(0.597239\pi\) | |||||||
\(998\) | 4.11048 | 0.130115 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6525.2.a.cc.1.5 | yes | 9 | |
3.2 | odd | 2 | 6525.2.a.ca.1.5 | ✓ | 9 | ||
5.4 | even | 2 | 6525.2.a.cb.1.5 | yes | 9 | ||
15.14 | odd | 2 | 6525.2.a.cd.1.5 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6525.2.a.ca.1.5 | ✓ | 9 | 3.2 | odd | 2 | ||
6525.2.a.cb.1.5 | yes | 9 | 5.4 | even | 2 | ||
6525.2.a.cc.1.5 | yes | 9 | 1.1 | even | 1 | trivial | |
6525.2.a.cd.1.5 | yes | 9 | 15.14 | odd | 2 |