Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.71099\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.71099 | −1.21239 | −0.606195 | − | 0.795316i | \(-0.707305\pi\) | ||||
−0.606195 | + | 0.795316i | \(0.707305\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.775439 | −0.293088 | −0.146544 | − | 0.989204i | \(-0.546815\pi\) | ||||
−0.146544 | + | 0.989204i | \(0.546815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.70739 | 1.11782 | 0.558911 | − | 0.829228i | \(-0.311219\pi\) | ||||
0.558911 | + | 0.829228i | \(0.311219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.16847 | −1.71083 | −0.855413 | − | 0.517947i | \(-0.826697\pi\) | ||||
−0.855413 | + | 0.517947i | \(0.826697\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.71099 | −0.699974 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.36353 | 1.54338 | 0.771691 | − | 0.635998i | \(-0.219411\pi\) | ||||
0.771691 | + | 0.635998i | \(0.219411\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.922209 | 0.211569 | 0.105785 | − | 0.994389i | \(-0.466265\pi\) | ||||
0.105785 | + | 0.994389i | \(0.466265\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.775439 | −0.169215 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.47047 | −0.932157 | −0.466079 | − | 0.884743i | \(-0.654334\pi\) | ||||
−0.466079 | + | 0.884743i | \(0.654334\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.34945 | 0.469889 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.18433 | −0.962705 | −0.481353 | − | 0.876527i | \(-0.659854\pi\) | ||||
−0.481353 | + | 0.876527i | \(0.659854\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.35539 | 0.243436 | 0.121718 | − | 0.992565i | \(-0.461160\pi\) | ||||
0.121718 | + | 0.992565i | \(0.461160\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.70739 | 0.645375 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.10220 | 0.355337 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.5076 | 1.89183 | 0.945915 | − | 0.324414i | \(-0.105167\pi\) | ||||
0.945915 | + | 0.324414i | \(0.105167\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.16847 | −0.987746 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.90644 | −1.39095 | −0.695476 | − | 0.718549i | \(-0.744806\pi\) | ||||
−0.695476 | + | 0.718549i | \(0.744806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.52092 | 0.841933 | 0.420966 | − | 0.907076i | \(-0.361691\pi\) | ||||
0.420966 | + | 0.907076i | \(0.361691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.71099 | −0.404130 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.07634 | 1.17806 | 0.589028 | − | 0.808113i | \(-0.299511\pi\) | ||||
0.589028 | + | 0.808113i | \(0.299511\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.39869 | −0.914099 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.36353 | 0.891072 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.23790 | −0.307399 | −0.153700 | − | 0.988118i | \(-0.549119\pi\) | ||||
−0.153700 | + | 0.988118i | \(0.549119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0507 | −1.35524 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.922209 | 0.122150 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3284 | 1.60502 | 0.802509 | − | 0.596640i | \(-0.203498\pi\) | ||||
0.802509 | + | 0.596640i | \(0.203498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.08112 | −0.650571 | −0.325285 | − | 0.945616i | \(-0.605460\pi\) | ||||
−0.325285 | + | 0.945616i | \(0.605460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.775439 | −0.0976961 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.7226 | 2.07419 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.628889 | 0.0768311 | 0.0384155 | − | 0.999262i | \(-0.487769\pi\) | ||||
0.0384155 | + | 0.999262i | \(0.487769\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.47047 | −0.538181 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.07457 | 0.364884 | 0.182442 | − | 0.983217i | \(-0.441600\pi\) | ||||
0.182442 | + | 0.983217i | \(0.441600\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.83167 | 0.448463 | 0.224232 | − | 0.974536i | \(-0.428013\pi\) | ||||
0.224232 | + | 0.974536i | \(0.428013\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.34945 | 0.271291 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.87486 | −0.327620 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8763 | 1.78622 | 0.893111 | − | 0.449837i | \(-0.148518\pi\) | ||||
0.893111 | + | 0.449837i | \(0.148518\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.76483 | −0.523009 | −0.261504 | − | 0.965202i | \(-0.584219\pi\) | ||||
−0.261504 | + | 0.965202i | \(0.584219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.2514 | −1.87118 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.18433 | −0.555818 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.390848 | 0.0414298 | 0.0207149 | − | 0.999785i | \(-0.493406\pi\) | ||||
0.0207149 | + | 0.999785i | \(0.493406\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.78327 | 0.501423 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.35539 | 0.140548 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.50010 | −0.256504 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.5125 | 1.57506 | 0.787529 | − | 0.616277i | \(-0.211360\pi\) | ||||
0.787529 | + | 0.616277i | \(0.211360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.70739 | 0.372607 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.2133 | 1.41428 | 0.707140 | − | 0.707074i | \(-0.249985\pi\) | ||||
0.707140 | + | 0.707074i | \(0.249985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.6148 | −1.14444 | −0.572219 | − | 0.820101i | \(-0.693917\pi\) | ||||
−0.572219 | + | 0.820101i | \(0.693917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.10220 | 0.205154 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1267 | 1.26901 | 0.634503 | − | 0.772920i | \(-0.281205\pi\) | ||||
0.634503 | + | 0.772920i | \(0.281205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.37165 | 0.322945 | 0.161473 | − | 0.986877i | \(-0.448376\pi\) | ||||
0.161473 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.5076 | 1.09225 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9419 | −1.21747 | −0.608735 | − | 0.793374i | \(-0.708323\pi\) | ||||
−0.608735 | + | 0.793374i | \(0.708323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.1194 | 1.13014 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.16847 | −0.570275 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.93452 | −0.452347 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.74477 | 0.249525 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.90644 | −0.803066 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.18562 | 0.642701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.24079 | −0.465045 | −0.232522 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232522 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.52092 | 0.486090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.29290 | 0.375072 | 0.187536 | − | 0.982258i | \(-0.439950\pi\) | ||||
0.187536 | + | 0.982258i | \(0.439950\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.715117 | −0.0620085 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.71099 | −0.233325 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.17341 | −0.185687 | −0.0928433 | − | 0.995681i | \(-0.529596\pi\) | ||||
−0.0928433 | + | 0.995681i | \(0.529596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.0691 | 1.53260 | 0.766300 | − | 0.642483i | \(-0.222096\pi\) | ||||
0.766300 | + | 0.642483i | \(0.222096\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.07634 | 0.680150 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.8689 | −1.91240 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.0546 | 1.16717 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.39869 | −0.527755 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.330735 | −0.0270949 | −0.0135474 | − | 0.999908i | \(-0.504312\pi\) | ||||
−0.0135474 | + | 0.999908i | \(0.504312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.69073 | −0.300347 | −0.150174 | − | 0.988660i | \(-0.547983\pi\) | ||||
−0.150174 | + | 0.988660i | \(0.547983\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.36353 | 0.514461 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.67445 | −0.295139 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7517 | 1.25712 | 0.628560 | − | 0.777761i | \(-0.283645\pi\) | ||||
0.628560 | + | 0.777761i | \(0.283645\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.23790 | −0.177477 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46657 | 0.273204 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.5320 | 1.21656 | 0.608280 | − | 0.793722i | \(-0.291860\pi\) | ||||
0.608280 | + | 0.793722i | \(0.291860\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.0507 | −0.782446 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.0500 | 1.92692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.922209 | 0.0705231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8363 | 1.28004 | 0.640020 | − | 0.768358i | \(-0.278926\pi\) | ||||
0.640020 | + | 0.768358i | \(0.278926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.82185 | −0.137719 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.3284 | 0.926658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.7443 | −1.10204 | −0.551020 | − | 0.834492i | \(-0.685761\pi\) | ||||
−0.551020 | + | 0.834492i | \(0.685761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7286 | 0.871783 | 0.435891 | − | 0.899999i | \(-0.356433\pi\) | ||||
0.435891 | + | 0.899999i | \(0.356433\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.08112 | −0.375607 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.1968 | −2.29364 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.5921 | 1.72523 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.775439 | −0.0564049 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.61629 | 0.116951 | 0.0584753 | − | 0.998289i | \(-0.481376\pi\) | ||||
0.0584753 | + | 0.998289i | \(0.481376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7212 | 1.34758 | 0.673792 | − | 0.738921i | \(-0.264664\pi\) | ||||
0.673792 | + | 0.738921i | \(0.264664\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.7226 | 1.19753 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.1950 | −0.868856 | −0.434428 | − | 0.900707i | \(-0.643049\pi\) | ||||
−0.434428 | + | 0.900707i | \(0.643049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.48491 | −0.105262 | −0.0526312 | − | 0.998614i | \(-0.516761\pi\) | ||||
−0.0526312 | + | 0.998614i | \(0.516761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.628889 | 0.0443584 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.02013 | 0.282158 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.1452 | 1.68638 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.47047 | −0.310719 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.41899 | 0.236497 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9344 | 1.02813 | 0.514063 | − | 0.857752i | \(-0.328140\pi\) | ||||
0.514063 | + | 0.857752i | \(0.328140\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.07457 | 0.210666 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.9671 | −1.02075 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.05102 | −0.0713482 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.83167 | 0.258920 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.2532 | −2.64046 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3483 | −0.692975 | −0.346487 | − | 0.938055i | \(-0.612626\pi\) | ||||
−0.346487 | + | 0.938055i | \(0.612626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.34945 | 0.156630 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.31500 | −0.485513 | −0.242757 | − | 0.970087i | \(-0.578052\pi\) | ||||
−0.242757 | + | 0.970087i | \(0.578052\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3272 | 1.14502 | 0.572508 | − | 0.819899i | \(-0.305970\pi\) | ||||
0.572508 | + | 0.819899i | \(0.305970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.87486 | −0.189152 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.4242 | −1.07599 | −0.537994 | − | 0.842949i | \(-0.680818\pi\) | ||||
−0.537994 | + | 0.842949i | \(0.680818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.8948 | −1.42826 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.8763 | 1.03128 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.16870 | −0.269651 | −0.134825 | − | 0.990869i | \(-0.543047\pi\) | ||||
−0.134825 | + | 0.990869i | \(0.543047\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1175 | 0.651725 | 0.325862 | − | 0.945417i | \(-0.394345\pi\) | ||||
0.325862 | + | 0.945417i | \(0.394345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.3468 | 1.10824 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.68862 | −0.361958 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.76483 | −0.301959 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.9898 | 0.756790 | 0.378395 | − | 0.925644i | \(-0.376476\pi\) | ||||
0.378395 | + | 0.925644i | \(0.376476\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.5738 | −1.04199 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.2514 | −1.08033 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.0253 | 0.750117 | 0.375059 | − | 0.927001i | \(-0.377623\pi\) | ||||
0.375059 | + | 0.927001i | \(0.377623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.92340 | −0.554473 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.18433 | −0.320902 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.941771 | −0.0580721 | −0.0290360 | − | 0.999578i | \(-0.509244\pi\) | ||||
−0.0290360 | + | 0.999578i | \(0.509244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.06691 | 0.372688 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.390848 | 0.0239195 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.56306 | 0.217243 | 0.108622 | − | 0.994083i | \(-0.465356\pi\) | ||||
0.108622 | + | 0.994083i | \(0.465356\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3869 | 1.29916 | 0.649582 | − | 0.760292i | \(-0.274944\pi\) | ||||
0.649582 | + | 0.760292i | \(0.274944\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.78327 | 0.289497 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.71032 | 0.525252 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.5165 | 1.71339 | 0.856695 | − | 0.515823i | \(-0.172514\pi\) | ||||
0.856695 | + | 0.515823i | \(0.172514\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.35539 | 0.0811453 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.7452 | −1.59549 | −0.797744 | − | 0.602997i | \(-0.793973\pi\) | ||||
−0.797744 | + | 0.602997i | \(0.793973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.76889 | −0.164594 | −0.0822968 | − | 0.996608i | \(-0.526226\pi\) | ||||
−0.0822968 | + | 0.996608i | \(0.526226\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.50010 | −0.148093 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.90640 | 0.407672 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.4945 | 1.38203 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.5125 | 0.909360 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.3417 | −1.01311 | −0.506555 | − | 0.862208i | \(-0.669081\pi\) | ||||
−0.506555 | + | 0.862208i | \(0.669081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.4221 | −1.94591 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.70739 | 0.215125 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.5759 | 1.59476 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.28114 | −0.246761 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.2133 | 0.816535 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.7748 | 0.788745 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.3038 | −0.987578 | −0.493789 | − | 0.869582i | \(-0.664388\pi\) | ||||
−0.493789 | + | 0.869582i | \(0.664388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6148 | −0.660742 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.3959 | 1.32666 | 0.663329 | − | 0.748328i | \(-0.269143\pi\) | ||||
0.663329 | + | 0.748328i | \(0.269143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.191470 | 0.0108225 | 0.00541127 | − | 0.999985i | \(-0.498278\pi\) | ||||
0.00541127 | + | 0.999985i | \(0.498278\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.10220 | 0.118446 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.25612 | −0.182882 | −0.0914410 | − | 0.995810i | \(-0.529147\pi\) | ||||
−0.0914410 | + | 0.995810i | \(0.529147\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.2203 | −1.07613 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.1267 | 0.732661 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.86850 | 0.326532 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.4925 | −0.803898 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.37165 | 0.186452 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.26271 | −0.345274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.7585 | −1.69064 | −0.845320 | − | 0.534260i | \(-0.820590\pi\) | ||||
−0.845320 | + | 0.534260i | \(0.820590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.5076 | 0.630610 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.70491 | −0.0931492 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.60466 | 0.141885 | 0.0709425 | − | 0.997480i | \(-0.477399\pi\) | ||||
0.0709425 | + | 0.997480i | \(0.477399\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.9419 | −0.702906 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.02498 | 0.272118 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.3899 | 0.561000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.1194 | 0.652485 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.1851 | −1.08359 | −0.541796 | − | 0.840510i | \(-0.682255\pi\) | ||||
−0.541796 | + | 0.840510i | \(0.682255\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.7950 | 0.738431 | 0.369216 | − | 0.929344i | \(-0.379626\pi\) | ||||
0.369216 | + | 0.929344i | \(0.379626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.16847 | −0.329249 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.65454 | −0.354185 | −0.177093 | − | 0.984194i | \(-0.556669\pi\) | ||||
−0.177093 | + | 0.984194i | \(0.556669\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.33510 | −0.442381 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.93452 | −0.261163 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.5216 | 0.977535 | 0.488768 | − | 0.872414i | \(-0.337447\pi\) | ||||
0.488768 | + | 0.872414i | \(0.337447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1495 | −0.955238 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.74477 | 0.144063 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.3876 | −0.543712 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.6276 | −0.920152 | −0.460076 | − | 0.887880i | \(-0.652178\pi\) | ||||
−0.460076 | + | 0.887880i | \(0.652178\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.90644 | −0.463651 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.73535 | 0.0900951 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.37087 | 0.226315 | 0.113158 | − | 0.993577i | \(-0.463904\pi\) | ||||
0.113158 | + | 0.993577i | \(0.463904\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.18562 | 0.371064 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.9794 | 1.64702 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.2802 | −1.60676 | −0.803379 | − | 0.595468i | \(-0.796967\pi\) | ||||
−0.803379 | + | 0.595468i | \(0.796967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.24079 | −0.268494 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.10351 | −0.311875 | −0.155937 | − | 0.987767i | \(-0.549840\pi\) | ||||
−0.155937 | + | 0.987767i | \(0.549840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.79370 | 0.397204 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.52092 | 0.280644 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.97649 | −0.404424 | −0.202212 | − | 0.979342i | \(-0.564813\pi\) | ||||
−0.202212 | + | 0.979342i | \(0.564813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.4479 | −1.43867 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.29290 | 0.216548 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −43.0404 | −2.16560 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2101 | 1.21507 | 0.607535 | − | 0.794293i | \(-0.292158\pi\) | ||||
0.607535 | + | 0.794293i | \(0.292158\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.715117 | −0.0358006 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.9420 | −0.895982 | −0.447991 | − | 0.894038i | \(-0.647860\pi\) | ||||
−0.447991 | + | 0.894038i | \(0.647860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.36071 | −0.416476 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.71099 | −0.134710 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.6630 | 2.11473 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9929 | −0.543562 | −0.271781 | − | 0.962359i | \(-0.587613\pi\) | ||||
−0.271781 | + | 0.962359i | \(0.587613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.17341 | −0.107206 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.55990 | −0.470412 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9174 | 0.634090 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.0691 | 0.884847 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.5571 | −1.00428 | −0.502139 | − | 0.864787i | \(-0.667453\pi\) | ||||
−0.502139 | + | 0.864787i | \(0.667453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.2776 | 0.744583 | 0.372291 | − | 0.928116i | \(-0.378572\pi\) | ||||
0.372291 | + | 0.928116i | \(0.378572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.07634 | 0.392685 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.9508 | 0.725218 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.94010 | 0.190675 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.8689 | −1.10412 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.6247 | −1.18613 | −0.593066 | − | 0.805154i | \(-0.702083\pi\) | ||||
−0.593066 | + | 0.805154i | \(0.702083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.2365 | −1.45307 | −0.726537 | − | 0.687127i | \(-0.758872\pi\) | ||||
−0.726537 | + | 0.687127i | \(0.758872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.0546 | 0.673868 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.12271 | −0.197216 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.07328 | 0.242134 | 0.121067 | − | 0.992644i | \(-0.461368\pi\) | ||||
0.121067 | + | 0.992644i | \(0.461368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.39869 | −0.304700 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.3097 | −0.537339 | −0.268670 | − | 0.963232i | \(-0.586584\pi\) | ||||
−0.268670 | + | 0.963232i | \(0.586584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.05958 | −0.0502291 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.330735 | −0.0156432 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.0503 | −1.08781 | −0.543906 | − | 0.839146i | \(-0.683055\pi\) | ||||
−0.543906 | + | 0.839146i | \(0.683055\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.0197 | −1.55484 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.69073 | −0.173406 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.9674 | −0.607920 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.1775 | 1.78587 | 0.892935 | − | 0.450185i | \(-0.148642\pi\) | ||||
0.892935 | + | 0.450185i | \(0.148642\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.36353 | 0.297024 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.19692 | −0.148895 | −0.0744477 | − | 0.997225i | \(-0.523719\pi\) | ||||
−0.0744477 | + | 0.997225i | \(0.523719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.8591 | 1.38767 | 0.693834 | − | 0.720135i | \(-0.255920\pi\) | ||||
0.693834 | + | 0.720135i | \(0.255920\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.67445 | −0.170399 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.0326 | −1.57484 | −0.787421 | − | 0.616415i | \(-0.788584\pi\) | ||||
−0.787421 | + | 0.616415i | \(0.788584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.487665 | −0.0225183 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.7517 | 0.725798 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.4682 | 0.941131 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.16668 | 0.0994141 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.23790 | −0.102466 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.2683 | −1.38300 | −0.691498 | − | 0.722378i | \(-0.743049\pi\) | ||||
−0.691498 | + | 0.722378i | \(0.743049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −70.9840 | −3.23659 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.46657 | 0.157735 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −42.0542 | −1.90958 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.1702 | −0.823369 | −0.411684 | − | 0.911327i | \(-0.635059\pi\) | ||||
−0.411684 | + | 0.911327i | \(0.635059\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.5320 | 0.702381 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.7025 | −1.47584 | −0.737922 | − | 0.674886i | \(-0.764193\pi\) | ||||
−0.737922 | + | 0.674886i | \(0.764193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.9906 | −1.48582 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.0507 | −0.451745 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.38414 | −0.106943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.70087 | −0.165674 | −0.0828368 | − | 0.996563i | \(-0.526398\pi\) | ||||
−0.0828368 | + | 0.996563i | \(0.526398\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.4615 | 0.778569 | 0.389285 | − | 0.921118i | \(-0.372722\pi\) | ||||
0.389285 | + | 0.921118i | \(0.372722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.5322 | −1.71466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.0500 | 1.11251 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8296 | 0.568662 | 0.284331 | − | 0.958726i | \(-0.408229\pi\) | ||||
0.284331 | + | 0.958726i | \(0.408229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.97123 | −0.131439 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.922209 | 0.0407165 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.4875 | 1.38751 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.9422 | 1.31686 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.8363 | 0.739032 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.7753 | 0.647316 | 0.323658 | − | 0.946174i | \(-0.395087\pi\) | ||||
0.323658 | + | 0.946174i | \(0.395087\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.6247 | 0.814402 | 0.407201 | − | 0.913339i | \(-0.366505\pi\) | ||||
0.407201 | + | 0.913339i | \(0.366505\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.82185 | −0.0795121 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.62508 | 0.375715 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.01492 | −0.131083 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.3284 | 0.535006 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 54.9391 | 2.37968 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.5863 | −1.53853 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.7443 | −0.636263 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.7225 | −1.02180 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5963 | 0.541558 | 0.270779 | − | 0.962641i | \(-0.412719\pi\) | ||||
0.270779 | + | 0.962641i | \(0.412719\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.7286 | 0.503324 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.14048 | −0.391535 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.0198 | 0.471172 | 0.235586 | − | 0.971853i | \(-0.424299\pi\) | ||||
0.235586 | + | 0.971853i | \(0.424299\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.08112 | −0.216857 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.78103 | −0.203679 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.3111 | −0.523521 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −31.1968 | −1.32423 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.8382 | 1.09480 | 0.547401 | − | 0.836871i | \(-0.315617\pi\) | ||||
0.547401 | + | 0.836871i | \(0.315617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.0556 | −1.44040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.5921 | 0.996059 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.8221 | 1.46757 | 0.733787 | − | 0.679379i | \(-0.237751\pi\) | ||||
0.733787 | + | 0.679379i | \(0.237751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.0853 | 1.47605 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.775439 | −0.0325654 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.62357 | −0.109986 | −0.0549929 | − | 0.998487i | \(-0.517514\pi\) | ||||
−0.0549929 | + | 0.998487i | \(0.517514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.52229 | 0.398495 | 0.199248 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199248 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.61629 | 0.0675215 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.5031 | −0.438010 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.2255 | 1.29994 | 0.649968 | − | 0.759962i | \(-0.274782\pi\) | ||||
0.649968 | + | 0.759962i | \(0.274782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.7212 | 0.778028 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.69484 | 0.153288 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.29678 | −0.343617 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.7226 | 0.691396 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.02985 | 0.248878 | 0.124439 | − | 0.992227i | \(-0.460287\pi\) | ||||
0.124439 | + | 0.992227i | \(0.460287\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.24996 | 0.0515036 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1950 | −0.501634 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.7573 | 1.13986 | 0.569929 | − | 0.821694i | \(-0.306971\pi\) | ||||
0.569929 | + | 0.821694i | \(0.306971\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.3774 | 0.548421 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.48491 | −0.0607733 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.4573 | −1.44874 | −0.724372 | − | 0.689409i | \(-0.757870\pi\) | ||||
−0.724372 | + | 0.689409i | \(0.757870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.3416 | 1.27845 | 0.639225 | − | 0.769020i | \(-0.279255\pi\) | ||||
0.639225 | + | 0.769020i | \(0.279255\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.628889 | 0.0256104 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.44104 | −0.302521 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.9080 | −1.29510 | −0.647552 | − | 0.762021i | \(-0.724207\pi\) | ||||
−0.647552 | + | 0.762021i | \(0.724207\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.02013 | 0.162904 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.8187 | −2.01545 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.53486 | 0.142772 | 0.0713859 | − | 0.997449i | \(-0.477258\pi\) | ||||
0.0713859 | + | 0.997449i | \(0.477258\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.1452 | 0.973630 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.53527 | −0.263100 | −0.131550 | − | 0.991310i | \(-0.541995\pi\) | ||||
−0.131550 | + | 0.991310i | \(0.541995\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.3866 | −1.10076 | −0.550381 | − | 0.834914i | \(-0.685517\pi\) | ||||
−0.550381 | + | 0.834914i | \(0.685517\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.47047 | −0.179394 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.303079 | −0.0121426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2273 | −1.24909 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.41899 | 0.136541 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 73.2286 | 2.91982 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8036 | −0.509704 | −0.254852 | − | 0.966980i | \(-0.582027\pi\) | ||||
−0.254852 | + | 0.966980i | \(0.582027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.9344 | 0.593589 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.2077 | 0.563815 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.4702 | 1.56386 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.07457 | 0.121628 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.32208 | −0.0917165 | −0.0458583 | − | 0.998948i | \(-0.514602\pi\) | ||||
−0.0458583 | + | 0.998948i | \(0.514602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.60321 | 0.0632245 | 0.0316122 | − | 0.999500i | \(-0.489936\pi\) | ||||
0.0316122 | + | 0.999500i | \(0.489936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.9671 | −0.589331 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.0337 | 1.69183 | 0.845915 | − | 0.533317i | \(-0.179055\pi\) | ||||
0.845915 | + | 0.533317i | \(0.179055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.7062 | 1.79412 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.05102 | −0.0411929 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.3118 | 0.716596 | 0.358298 | − | 0.933607i | \(-0.383357\pi\) | ||||
0.358298 | + | 0.933607i | \(0.383357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.6380 | −0.454734 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.83167 | 0.149488 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.81736 | 0.187658 | 0.0938289 | − | 0.995588i | \(-0.470089\pi\) | ||||
0.0938289 | + | 0.995588i | \(0.470089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.4346 | 1.65051 | 0.825257 | − | 0.564757i | \(-0.191030\pi\) | ||||
0.825257 | + | 0.564757i | \(0.191030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.2532 | −1.52447 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.93867 | 0.0751785 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.1764 | 0.897392 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.3483 | −0.400089 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.8377 | −0.727222 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.4211 | 0.902815 | 0.451408 | − | 0.892318i | \(-0.350922\pi\) | ||||
0.451408 | + | 0.892318i | \(0.350922\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.34945 | 0.0904302 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.8529 | 1.22421 | 0.612104 | − | 0.790777i | \(-0.290323\pi\) | ||||
0.612104 | + | 0.790777i | \(0.290323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0290 | −0.461631 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.31500 | −0.280311 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.9939 | 1.37727 | 0.688635 | − | 0.725108i | \(-0.258210\pi\) | ||||
0.688635 | + | 0.725108i | \(0.258210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.89207 | 0.225124 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.3272 | 0.661076 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8044 | 0.525906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.9417 | −1.06295 | −0.531476 | − | 0.847073i | \(-0.678362\pi\) | ||||
−0.531476 | + | 0.847073i | \(0.678362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.87486 | −0.109207 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −48.9850 | −1.85811 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −56.6763 | −2.14677 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.4242 | −0.621222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.3135 | −0.427306 | −0.213653 | − | 0.976910i | \(-0.568536\pi\) | ||||
−0.213653 | + | 0.976910i | \(0.568536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6124 | 0.400253 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.8948 | −0.824607 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.0216 | −0.414509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.8151 | −1.26995 | −0.634976 | − | 0.772532i | \(-0.718990\pi\) | ||||
−0.634976 | + | 0.772532i | \(0.718990\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.8763 | 0.595407 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.05924 | −0.226920 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 61.9974 | 2.31857 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.16870 | −0.155683 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.3845 | −1.43150 | −0.715749 | − | 0.698357i | \(-0.753915\pi\) | ||||
−0.715749 | + | 0.698357i | \(0.753915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.00655 | 0.335421 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.1175 | 0.376273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.1803 | −0.452365 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.6807 | −0.470301 | −0.235150 | − | 0.971959i | \(-0.575558\pi\) | ||||
−0.235150 | + | 0.971959i | \(0.575558\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.1325 | 1.29942 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.51823 | 0.166885 | 0.0834423 | − | 0.996513i | \(-0.473409\pi\) | ||||
0.0834423 | + | 0.996513i | \(0.473409\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.3468 | 0.639845 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.33154 | 0.0858834 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.4318 | 1.81838 | 0.909189 | − | 0.416383i | \(-0.136703\pi\) | ||||
0.909189 | + | 0.416383i | \(0.136703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.68862 | −0.208977 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.0292 | −0.404623 | −0.202312 | − | 0.979321i | \(-0.564845\pi\) | ||||
−0.202312 | + | 0.979321i | \(0.564845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.896619 | 0.0328496 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.76483 | −0.174336 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1790 | −0.371931 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.2471 | 1.83354 | 0.916771 | − | 0.399412i | \(-0.130786\pi\) | ||||
0.916771 | + | 0.399412i | \(0.130786\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.9898 | 0.436933 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0055 | 0.364138 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.6067 | −1.47588 | −0.737938 | − | 0.674869i | \(-0.764200\pi\) | ||||
−0.737938 | + | 0.674869i | \(0.764200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.5738 | −0.601590 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3817 | −1.06509 | −0.532543 | − | 0.846403i | \(-0.678764\pi\) | ||||
−0.532543 | + | 0.846403i | \(0.678764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.61450 | −0.0946514 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.2514 | −0.623727 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −76.0473 | −2.74591 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.1206 | 1.05012 | 0.525058 | − | 0.851067i | \(-0.324044\pi\) | ||||
0.525058 | + | 0.851067i | \(0.324044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0253 | 0.433081 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.665280 | −0.0239285 | −0.0119642 | − | 0.999928i | \(-0.503808\pi\) | ||||
−0.0119642 | + | 0.999928i | \(0.503808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.18442 | 0.114388 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.92340 | −0.320125 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.21360 | −0.294283 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3986 | 0.407875 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.18433 | −0.185273 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.7025 | −1.52412 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.0421 | −1.14218 | −0.571089 | − | 0.820888i | \(-0.693479\pi\) | ||||
−0.571089 | + | 0.820888i | \(0.693479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.941771 | −0.0335279 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0356 | 0.356826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.3427 | 1.11301 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.06691 | 0.215171 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.1598 | −1.45795 | −0.728977 | − | 0.684538i | \(-0.760004\pi\) | ||||
−0.728977 | + | 0.684538i | \(0.760004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.3940 | 1.81819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.390848 | 0.0138099 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.2055 | 0.501302 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.39783 | −0.331230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.56306 | 0.125426 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.4775 | 1.10669 | 0.553345 | − | 0.832952i | \(-0.313351\pi\) | ||||
0.553345 | + | 0.832952i | \(0.313351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.1659 | −0.532546 | −0.266273 | − | 0.963898i | \(-0.585792\pi\) | ||||
−0.266273 | + | 0.963898i | \(0.585792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.3869 | 0.750072 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.1070 | −1.47495 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.09145 | 0.178127 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.78327 | 0.167141 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.3086 | −1.75578 | −0.877890 | − | 0.478862i | \(-0.841050\pi\) | ||||
−0.877890 | + | 0.478862i | \(0.841050\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.2887 | −1.09066 | −0.545328 | − | 0.838222i | \(-0.683595\pi\) | ||||
−0.545328 | + | 0.838222i | \(0.683595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.71032 | 0.303254 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.5291 | 0.748639 | 0.374320 | − | 0.927300i | \(-0.377876\pi\) | ||||
0.374320 | + | 0.927300i | \(0.377876\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.7206 | −1.06697 | −0.533486 | − | 0.845809i | \(-0.679118\pi\) | ||||
−0.533486 | + | 0.845809i | \(0.679118\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.5165 | 0.989227 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −40.7183 | −1.41080 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.71099 | 0.0938175 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.35539 | 0.0468493 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.94057 | 0.239615 | 0.119808 | − | 0.992797i | \(-0.461772\pi\) | ||||
0.119808 | + | 0.992797i | \(0.461772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.12277 | −0.0731989 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.7452 | −0.921155 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −67.9103 | −2.33618 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.12840 | −0.0731328 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.76889 | −0.0950281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51.4442 | −1.76348 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.88185 | −0.201391 | −0.100695 | − | 0.994917i | \(-0.532107\pi\) | ||||
−0.100695 | + | 0.994917i | \(0.532107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.50010 | −0.0855015 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.9088 | −0.850869 | −0.425435 | − | 0.904989i | \(-0.639879\pi\) | ||||
−0.425435 | + | 0.904989i | \(0.639879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.86029 | 0.336429 | 0.168214 | − | 0.985750i | \(-0.446200\pi\) | ||||
0.168214 | + | 0.985750i | \(0.446200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.90640 | 0.235369 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.4522 | 1.27489 | 0.637444 | − | 0.770497i | \(-0.279992\pi\) | ||||
0.637444 | + | 0.770497i | \(0.279992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.6430 | −1.55191 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.4945 | 0.797914 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.8597 | 1.99668 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.87928 | −0.131445 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.5125 | 0.525019 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.57200 | −0.188368 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.7918 | −1.14107 | −0.570534 | − | 0.821274i | \(-0.693264\pi\) | ||||
−0.570534 | + | 0.821274i | \(0.693264\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.3417 | −0.584920 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.8128 | 1.71193 | 0.855963 | − | 0.517038i | \(-0.172965\pi\) | ||||
0.855963 | + | 0.517038i | \(0.172965\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.4246 | 1.56231 | 0.781156 | − | 0.624336i | \(-0.214630\pi\) | ||||
0.781156 | + | 0.624336i | \(0.214630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.4221 | −1.12347 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.20134 | 0.241797 | 0.120899 | − | 0.992665i | \(-0.461422\pi\) | ||||
0.120899 | + | 0.992665i | \(0.461422\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.06391 | 0.136299 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.70739 | 0.124202 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.44807 | 0.249240 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.9716 | 1.33610 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.5759 | 0.920734 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.02680 | −0.234357 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2409 | −0.474434 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.28114 | −0.142467 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.7962 | −1.05694 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.0271 | −1.16305 | −0.581527 | − | 0.813527i | \(-0.697545\pi\) | ||||
−0.581527 | + | 0.813527i | \(0.697545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.2133 | 0.471427 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.7886 | −1.02007 | −0.510036 | − | 0.860153i | \(-0.670368\pi\) | ||||
−0.510036 | + | 0.860153i | \(0.670368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.6651 | −0.584630 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.7748 | 0.455382 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.32888 | −0.109929 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.8564 | 0.786949 | 0.393474 | − | 0.919336i | \(-0.371273\pi\) | ||||
0.393474 | + | 0.919336i | \(0.371273\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.3038 | −0.570178 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.9654 | −0.624252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.0364 | 0.888951 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.6148 | −0.381479 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.8969 | −1.37459 | −0.687297 | − | 0.726377i | \(-0.741203\pi\) | ||||
−0.687297 | + | 0.726377i | \(0.741203\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.90094 | −0.193395 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.3959 | 0.765947 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −63.9579 | −2.09165 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.6906 | −1.26397 | −0.631983 | − | 0.774983i | \(-0.717759\pi\) | ||||
−0.631983 | + | 0.774983i | \(0.717759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.191470 | 0.00624839 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.1394 | −1.60190 | −0.800949 | − | 0.598732i | \(-0.795671\pi\) | ||||
−0.800949 | + | 0.598732i | \(0.795671\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.8159 | 1.29659 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.10220 | 0.0683847 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 60.1778 | 1.95552 | 0.977758 | − | 0.209736i | \(-0.0672604\pi\) | ||||
0.977758 | + | 0.209736i | \(0.0672604\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.6355 | −0.767242 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.25612 | −0.105587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.03764 | 0.195578 | 0.0977892 | − | 0.995207i | \(-0.468823\pi\) | ||||
0.0977892 | + | 0.995207i | \(0.468823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.38174 | −0.141790 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.2203 | −0.621305 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.68534 | 0.0544225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1629 | −0.940739 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.1267 | 0.423002 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −50.7530 | −1.63380 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.4074 | −0.559785 | −0.279892 | − | 0.960031i | \(-0.590299\pi\) | ||||
−0.279892 | + | 0.960031i | \(0.590299\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.86850 | 0.188523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.2201 | −0.584711 | −0.292356 | − | 0.956310i | \(-0.594439\pi\) | ||||
−0.292356 | + | 0.956310i | \(0.594439\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0115 | −0.449187 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.4925 | −0.464131 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.7926 | −1.30507 | −0.652535 | − | 0.757758i | \(-0.726295\pi\) | ||||
−0.652535 | + | 0.757758i | \(0.726295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.44903 | 0.0463111 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.37165 | 0.107648 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.5978 | 1.80519 | 0.902594 | − | 0.430492i | \(-0.141660\pi\) | ||||
0.902594 | + | 0.430492i | \(0.141660\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.0604 | 1.05339 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.26271 | −0.199344 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.6811 | −0.784814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.0500 | −0.478081 | −0.239040 | − | 0.971010i | \(-0.576833\pi\) | ||||
−0.239040 | + | 0.971010i | \(0.576833\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.7585 | −0.976092 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.02557 | 0.127619 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.2414 | −0.736063 | −0.368031 | − | 0.929813i | \(-0.619968\pi\) | ||||
−0.368031 | + | 0.929813i | \(0.619968\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.5076 | 0.364083 |
(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 | 4008.2.a.m.1.4 | ✓ | 13 | |
4.3 | odd | 2 | 8016.2.a.bg.1.4 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.4 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8016.2.a.bg.1.4 | 13 | 4.3 | odd | 2 |