Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(18.7808145554\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.585786 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.24264 | 0.543920 | 0.271960 | − | 0.962309i | \(-0.412328\pi\) | ||||
0.271960 | + | 0.962309i | \(0.412328\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.82843 | −1.56655 | −0.783274 | − | 0.621676i | \(-0.786452\pi\) | ||||
−0.783274 | + | 0.621676i | \(0.786452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528 | 1.57568 | 0.787839 | − | 0.615882i | \(-0.211200\pi\) | ||||
0.787839 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.17157 | −0.928842 | −0.464421 | − | 0.885615i | \(-0.653738\pi\) | ||||
−0.464421 | + | 0.885615i | \(0.653738\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.828427 | −0.144211 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.65685 | 0.272385 | 0.136193 | − | 0.990682i | \(-0.456513\pi\) | ||||
0.136193 | + | 0.990682i | \(0.456513\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.41421 | 0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.585786 | −0.0914845 | −0.0457422 | − | 0.998953i | \(-0.514565\pi\) | ||||
−0.0457422 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.585786 | 0.0873239 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.82843 | −0.996028 | −0.498014 | − | 0.867169i | \(-0.665937\pi\) | ||||
−0.498014 | + | 0.867169i | \(0.665937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.24264 | −0.314033 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.3137 | −1.82878 | −0.914389 | − | 0.404836i | \(-0.867329\pi\) | ||||
−0.914389 | + | 0.404836i | \(0.867329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.485281 | 0.0654353 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.82843 | 0.904447 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.17157 | −0.673281 | −0.336641 | − | 0.941633i | \(-0.609291\pi\) | ||||
−0.336641 | + | 0.941633i | \(0.609291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8995 | 1.77965 | 0.889824 | − | 0.456304i | \(-0.150827\pi\) | ||||
0.889824 | + | 0.456304i | \(0.150827\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.828427 | −0.102754 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.82843 | 0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.828427 | 0.0983162 | 0.0491581 | − | 0.998791i | \(-0.484346\pi\) | ||||
0.0491581 | + | 0.998791i | \(0.484346\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0711 | −1.29577 | −0.647885 | − | 0.761738i | \(-0.724346\pi\) | ||||
−0.647885 | + | 0.761738i | \(0.724346\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.65685 | 0.537727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.34315 | 0.263624 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.3137 | −1.68090 | −0.840449 | − | 0.541891i | \(-0.817709\pi\) | ||||
−0.840449 | + | 0.541891i | \(0.817709\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.31371 | 0.142492 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.48528 | −0.909718 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.7279 | −1.13716 | −0.568579 | − | 0.822629i | \(-0.692507\pi\) | ||||
−0.568579 | + | 0.822629i | \(0.692507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.17157 | 0.536267 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | −0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.75736 | −0.787641 | −0.393820 | − | 0.919187i | \(-0.628847\pi\) | ||||
−0.393820 | + | 0.919187i | \(0.628847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.828427 | 0.0832601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.41421 | 0.339727 | 0.169863 | − | 0.985468i | \(-0.445667\pi\) | ||||
0.169863 | + | 0.985468i | \(0.445667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8284 | −1.06696 | −0.533478 | − | 0.845814i | \(-0.679115\pi\) | ||||
−0.533478 | + | 0.845814i | \(0.679115\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.4853 | −1.40035 | −0.700173 | − | 0.713974i | \(-0.746894\pi\) | ||||
−0.700173 | + | 0.713974i | \(0.746894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3137 | −1.08366 | −0.541828 | − | 0.840489i | \(-0.682268\pi\) | ||||
−0.541828 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.65685 | −0.157262 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82843 | −0.263752 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | −0.130744 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.585786 | 0.0528186 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3137 | 1.35887 | 0.679436 | − | 0.733735i | \(-0.262225\pi\) | ||||
0.679436 | + | 0.733735i | \(0.262225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.31371 | 0.639002 | 0.319501 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319501 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.585786 | −0.0504165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.48528 | 0.383203 | 0.191602 | − | 0.981473i | \(-0.438632\pi\) | ||||
0.191602 | + | 0.981473i | \(0.438632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.65685 | 0.140533 | 0.0702663 | − | 0.997528i | \(-0.477615\pi\) | ||||
0.0702663 | + | 0.997528i | \(0.477615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.82843 | 0.575057 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.17157 | −0.0979718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.97056 | 0.412783 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.65685 | −0.785864 | −0.392932 | − | 0.919568i | \(-0.628539\pi\) | ||||
−0.392932 | + | 0.919568i | \(0.628539\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.24264 | 0.181307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.02944 | −0.243330 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8995 | −1.10930 | −0.554650 | − | 0.832084i | \(-0.687148\pi\) | ||||
−0.554650 | + | 0.832084i | \(0.687148\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.3137 | 1.05585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6569 | 1.06969 | 0.534844 | − | 0.844951i | \(-0.320370\pi\) | ||||
0.534844 | + | 0.844951i | \(0.320370\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.485281 | −0.0377791 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.17157 | −0.0906590 | −0.0453295 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453295 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.82843 | −0.522183 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.41421 | −0.259578 | −0.129789 | − | 0.991542i | \(-0.541430\pi\) | ||||
−0.129789 | + | 0.991542i | \(0.541430\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.17157 | 0.388719 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.7990 | −1.33036 | −0.665179 | − | 0.746684i | \(-0.731645\pi\) | ||||
−0.665179 | + | 0.746684i | \(0.731645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.89949 | −0.735824 | −0.367912 | − | 0.929861i | \(-0.619927\pi\) | ||||
−0.367912 | + | 0.929861i | \(0.619927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8995 | −1.02748 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.970563 | 0.0713572 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.85786 | 0.135860 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1716 | −1.09778 | −0.548888 | − | 0.835896i | \(-0.684949\pi\) | ||||
−0.548888 | + | 0.835896i | \(0.684949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.6274 | 1.77272 | 0.886360 | − | 0.462996i | \(-0.153226\pi\) | ||||
0.886360 | + | 0.462996i | \(0.153226\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.828427 | 0.0593249 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.65685 | −0.401004 | −0.200502 | − | 0.979693i | \(-0.564257\pi\) | ||||
−0.200502 | + | 0.979693i | \(0.564257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.343146 | −0.0239663 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.82843 | −0.335599 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3431 | 0.987423 | 0.493711 | − | 0.869626i | \(-0.335640\pi\) | ||||
0.493711 | + | 0.869626i | \(0.335640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.828427 | −0.0567629 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.68629 | 0.319602 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.0711 | 0.748113 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.17157 | −0.213343 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6569 | 0.914531 | 0.457265 | − | 0.889330i | \(-0.348829\pi\) | ||||
0.457265 | + | 0.889330i | \(0.348829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.7990 | 1.31411 | 0.657053 | − | 0.753845i | \(-0.271803\pi\) | ||||
0.657053 | + | 0.753845i | \(0.271803\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0711 | 0.995924 | 0.497962 | − | 0.867199i | \(-0.334082\pi\) | ||||
0.497962 | + | 0.867199i | \(0.334082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.4853 | −1.86613 | −0.933066 | − | 0.359704i | \(-0.882878\pi\) | ||||
−0.933066 | + | 0.359704i | \(0.882878\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | −0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.34315 | −0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.17157 | 0.205152 | 0.102576 | − | 0.994725i | \(-0.467292\pi\) | ||||
0.102576 | + | 0.994725i | \(0.467292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8995 | −1.41067 | −0.705335 | − | 0.708874i | \(-0.749204\pi\) | ||||
−0.705335 | + | 0.708874i | \(0.749204\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.65685 | 0.614451 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.3137 | 0.970467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.48528 | −0.535586 | −0.267793 | − | 0.963476i | \(-0.586294\pi\) | ||||
−0.267793 | + | 0.963476i | \(0.586294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.31371 | −0.0822676 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.2426 | −1.88648 | −0.943242 | − | 0.332106i | \(-0.892241\pi\) | ||||
−0.943242 | + | 0.332106i | \(0.892241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.48528 | 0.525226 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.8284 | −1.53099 | −0.765493 | − | 0.643444i | \(-0.777505\pi\) | ||||
−0.765493 | + | 0.643444i | \(0.777505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.79899 | −0.479088 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7279 | 0.656538 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.0416 | 1.83167 | 0.915835 | − | 0.401554i | \(-0.131530\pi\) | ||||
0.915835 | + | 0.401554i | \(0.131530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.1716 | 0.800116 | 0.400058 | − | 0.916490i | \(-0.368990\pi\) | ||||
0.400058 | + | 0.916490i | \(0.368990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.85786 | −0.232638 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.00000 | −0.360505 | −0.180253 | − | 0.983620i | \(-0.557691\pi\) | ||||
−0.180253 | + | 0.983620i | \(0.557691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.17157 | −0.309614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4853 | −0.744809 | −0.372405 | − | 0.928070i | \(-0.621467\pi\) | ||||
−0.372405 | + | 0.928070i | \(0.621467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8284 | 0.881458 | 0.440729 | − | 0.897640i | \(-0.354720\pi\) | ||||
0.440729 | + | 0.897640i | \(0.354720\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9706 | −0.704151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.75736 | 0.454744 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.07107 | 0.0625724 | 0.0312862 | − | 0.999510i | \(-0.490040\pi\) | ||||
0.0312862 | + | 0.999510i | \(0.490040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.02944 | −0.176381 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.828427 | −0.0480702 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.82843 | 0.394898 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.41421 | −0.196141 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.14214 | 0.466217 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5147 | 0.657180 | 0.328590 | − | 0.944473i | \(-0.393427\pi\) | ||||
0.328590 | + | 0.944473i | \(0.393427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8284 | 0.616008 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.1421 | 1.48238 | 0.741192 | − | 0.671293i | \(-0.234261\pi\) | ||||
0.741192 | + | 0.671293i | \(0.234261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4142 | −0.984310 | −0.492155 | − | 0.870508i | \(-0.663791\pi\) | ||||
−0.492155 | + | 0.870508i | \(0.663791\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.3137 | 1.19710 | 0.598549 | − | 0.801087i | \(-0.295744\pi\) | ||||
0.598549 | + | 0.801087i | \(0.295744\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.02944 | 0.393573 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.4853 | 0.808490 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3137 | −0.852078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.58579 | 0.365314 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.3137 | 0.625650 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.68629 | 0.477442 | 0.238721 | − | 0.971088i | \(-0.423272\pi\) | ||||
0.238721 | + | 0.971088i | \(0.423272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.65685 | 0.0907951 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.68629 | 0.256039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.9706 | −0.924445 | −0.462223 | − | 0.886764i | \(-0.652948\pi\) | ||||
−0.462223 | + | 0.886764i | \(0.652948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.28427 | −0.232006 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.82843 | 0.152277 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.14214 | 0.222361 | 0.111181 | − | 0.993800i | \(-0.464537\pi\) | ||||
0.111181 | + | 0.993800i | \(0.464537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3848 | 1.62646 | 0.813230 | − | 0.581943i | \(-0.197707\pi\) | ||||
0.813230 | + | 0.581943i | \(0.197707\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41421 | 0.0754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8995 | −0.846245 | −0.423122 | − | 0.906073i | \(-0.639066\pi\) | ||||
−0.423122 | + | 0.906073i | \(0.639066\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.485281 | 0.0257561 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.4558 | 1.87129 | 0.935644 | − | 0.352945i | \(-0.114820\pi\) | ||||
0.935644 | + | 0.352945i | \(0.114820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6274 | 1.45407 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.3137 | 0.541329 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.48528 | −0.339455 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.585786 | −0.0304948 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6863 | 0.760427 | 0.380214 | − | 0.924899i | \(-0.375850\pi\) | ||||
0.380214 | + | 0.924899i | \(0.375850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.686292 | 0.0352524 | 0.0176262 | − | 0.999845i | \(-0.494389\pi\) | ||||
0.0176262 | + | 0.999845i | \(0.494389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.3137 | −0.784545 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.9706 | −1.27594 | −0.637968 | − | 0.770063i | \(-0.720225\pi\) | ||||
−0.637968 | + | 0.770063i | \(0.720225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.00000 | 0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1421 | −0.717035 | −0.358517 | − | 0.933523i | \(-0.616718\pi\) | ||||
−0.358517 | + | 0.933523i | \(0.616718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8284 | −0.547617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.31371 | −0.368928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.37258 | 0.0690621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.27208 | 0.364975 | 0.182488 | − | 0.983208i | \(-0.441585\pi\) | ||||
0.182488 | + | 0.983208i | \(0.441585\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4853 | −0.623485 | −0.311743 | − | 0.950167i | \(-0.600913\pi\) | ||||
−0.311743 | + | 0.950167i | \(0.600913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.31371 | 0.364322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.585786 | 0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.37258 | 0.0680364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2426 | 0.803147 | 0.401573 | − | 0.915827i | \(-0.368463\pi\) | ||||
0.401573 | + | 0.915827i | \(0.368463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.48528 | −0.221243 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.97056 | −0.440348 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.65685 | −0.0811365 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.8284 | −0.529003 | −0.264502 | − | 0.964385i | \(-0.585207\pi\) | ||||
−0.264502 | + | 0.964385i | \(0.585207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.68629 | 0.325870 | 0.162935 | − | 0.986637i | \(-0.447904\pi\) | ||||
0.162935 | + | 0.986637i | \(0.447904\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.82843 | −0.332009 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.4437 | −0.506591 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.17157 | 0.0565641 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.4853 | 1.46842 | 0.734212 | − | 0.678920i | \(-0.237552\pi\) | ||||
0.734212 | + | 0.678920i | \(0.237552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3848 | 1.26797 | 0.633986 | − | 0.773345i | \(-0.281418\pi\) | ||||
0.633986 | + | 0.773345i | \(0.281418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.97056 | −0.238320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.9706 | 1.57720 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.31371 | 0.158155 | 0.0790773 | − | 0.996868i | \(-0.474803\pi\) | ||||
0.0790773 | + | 0.996868i | \(0.474803\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.4853 | −1.82849 | −0.914245 | − | 0.405161i | \(-0.867216\pi\) | ||||
−0.914245 | + | 0.405161i | \(0.867216\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.28427 | −0.297903 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.485281 | −0.0228510 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.65685 | 0.453719 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6274 | 0.964910 | 0.482455 | − | 0.875921i | \(-0.339745\pi\) | ||||
0.482455 | + | 0.875921i | \(0.339745\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.24264 | −0.104678 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.2426 | 0.849644 | 0.424822 | − | 0.905277i | \(-0.360337\pi\) | ||||
0.424822 | + | 0.905277i | \(0.360337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9706 | −0.974585 | −0.487292 | − | 0.873239i | \(-0.662015\pi\) | ||||
−0.487292 | + | 0.873239i | \(0.662015\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.02944 | 0.140487 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8284 | 0.501080 | 0.250540 | − | 0.968106i | \(-0.419392\pi\) | ||||
0.250540 | + | 0.968106i | \(0.419392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8995 | 0.640455 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.62742 | 0.304729 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.7990 | 1.45904 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.3137 | −0.609593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 43.1127 | 1.96987 | 0.984935 | − | 0.172926i | \(-0.0553223\pi\) | ||||
0.984935 | + | 0.172926i | \(0.0553223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.34315 | −0.106838 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.54416 | −0.206339 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.9706 | 0.950267 | 0.475133 | − | 0.879914i | \(-0.342400\pi\) | ||||
0.475133 | + | 0.879914i | \(0.342400\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.6569 | −0.617584 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.1421 | −1.08952 | −0.544760 | − | 0.838592i | \(-0.683379\pi\) | ||||
−0.544760 | + | 0.838592i | \(0.683379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.0294 | 0.857043 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.485281 | 0.0218118 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.2843 | 1.26618 | 0.633089 | − | 0.774079i | \(-0.281787\pi\) | ||||
0.633089 | + | 0.774079i | \(0.281787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.17157 | 0.0523420 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6274 | 0.652204 | 0.326102 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326102 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.0000 | 0.488527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.0711 | 1.64315 | 0.821573 | − | 0.570103i | \(-0.193097\pi\) | ||||
0.821573 | + | 0.570103i | \(0.193097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.82843 | 0.301482 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.34315 | −0.279512 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.41421 | 0.149867 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.7279 | 1.34621 | 0.673107 | − | 0.739545i | \(-0.264959\pi\) | ||||
0.673107 | + | 0.739545i | \(0.264959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.65685 | −0.422265 | −0.211132 | − | 0.977457i | \(-0.567715\pi\) | ||||
−0.211132 | + | 0.977457i | \(0.567715\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.5980 | −0.505216 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.17157 | −0.224427 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.828427 | 0.0358832 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.48528 | −0.366851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.7990 | 0.768083 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.6274 | 1.57474 | 0.787368 | − | 0.616483i | \(-0.211443\pi\) | ||||
0.787368 | + | 0.616483i | \(0.211443\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.89949 | 0.424828 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.62742 | −0.283887 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9706 | −1.23869 | −0.619346 | − | 0.785118i | \(-0.712602\pi\) | ||||
−0.619346 | + | 0.785118i | \(0.712602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.8995 | 0.593216 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −57.9411 | −2.46837 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.970563 | −0.0411981 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.9411 | −1.01442 | −0.507209 | − | 0.861823i | \(-0.669323\pi\) | ||||
−0.507209 | + | 0.861823i | \(0.669323\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.3137 | −0.478519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.85786 | −0.0784391 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.1716 | −0.892275 | −0.446138 | − | 0.894964i | \(-0.647201\pi\) | ||||
−0.446138 | + | 0.894964i | \(0.647201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.51472 | 0.147865 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.17157 | 0.0491149 | 0.0245574 | − | 0.999698i | \(-0.492182\pi\) | ||||
0.0245574 | + | 0.999698i | \(0.492182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2843 | 0.681476 | 0.340738 | − | 0.940158i | \(-0.389323\pi\) | ||||
0.340738 | + | 0.940158i | \(0.389323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.1716 | 0.633802 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.4853 | 0.937701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.58579 | −0.274170 | −0.137085 | − | 0.990559i | \(-0.543773\pi\) | ||||
−0.137085 | + | 0.990559i | \(0.543773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.6274 | −1.02348 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.0294 | −0.456793 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.828427 | −0.0342512 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1716 | 0.873844 | 0.436922 | − | 0.899499i | \(-0.356069\pi\) | ||||
0.436922 | + | 0.899499i | \(0.356069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.3137 | 1.45508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00000 | −0.0822690 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.9289 | 0.613058 | 0.306529 | − | 0.951861i | \(-0.400832\pi\) | ||||
0.306529 | + | 0.951861i | \(0.400832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65685 | 0.231520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.1421 | 0.496114 | 0.248057 | − | 0.968745i | \(-0.420208\pi\) | ||||
0.248057 | + | 0.968745i | \(0.420208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.75736 | −0.153266 | −0.0766329 | − | 0.997059i | \(-0.524417\pi\) | ||||
−0.0766329 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.04163 | −0.245627 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.5980 | 1.93194 | 0.965971 | − | 0.258650i | \(-0.0832775\pi\) | ||||
0.965971 | + | 0.258650i | \(0.0832775\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.65685 | 0.390675 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6569 | −0.551595 | −0.275798 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275798 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.343146 | 0.0138370 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.4558 | −1.18585 | −0.592924 | − | 0.805259i | \(-0.702026\pi\) | ||||
−0.592924 | + | 0.805259i | \(0.702026\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.2843 | −0.654520 | −0.327260 | − | 0.944934i | \(-0.606125\pi\) | ||||
−0.327260 | + | 0.944934i | \(0.606125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.82843 | 0.193758 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.65685 | 0.225913 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.71573 | 0.148156 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.2843 | −1.92217 | −0.961083 | − | 0.276259i | \(-0.910905\pi\) | ||||
−0.961083 | + | 0.276259i | \(0.910905\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.3431 | −0.570089 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.97056 | 0.355986 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.828427 | 0.0327721 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.8284 | 1.21765 | 0.608825 | − | 0.793305i | \(-0.291641\pi\) | ||||
0.608825 | + | 0.793305i | \(0.291641\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.4853 | −1.43884 | −0.719420 | − | 0.694576i | \(-0.755592\pi\) | ||||
−0.719420 | + | 0.694576i | \(0.755592\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.68629 | −0.184523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.17157 | −0.360572 | −0.180286 | − | 0.983614i | \(-0.557702\pi\) | ||||
−0.180286 | + | 0.983614i | \(0.557702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.28427 | −0.168172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.82843 | −0.110685 | −0.0553425 | − | 0.998467i | \(-0.517625\pi\) | ||||
−0.0553425 | + | 0.998467i | \(0.517625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.28427 | 0.167400 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.0711 | −0.431923 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.4853 | −1.65499 | −0.827496 | − | 0.561472i | \(-0.810235\pi\) | ||||
−0.827496 | + | 0.561472i | \(0.810235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.3553 | 1.84191 | 0.920955 | − | 0.389670i | \(-0.127411\pi\) | ||||
0.920955 | + | 0.389670i | \(0.127411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.17157 | 0.123174 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.9706 | −1.58639 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.6569 | −0.528004 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5147 | 0.444521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.31371 | −0.281923 | −0.140961 | − | 0.990015i | \(-0.545019\pi\) | ||||
−0.140961 | + | 0.990015i | \(0.545019\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.65685 | 0.179242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.5563 | 1.13594 | 0.567971 | − | 0.823048i | \(-0.307728\pi\) | ||||
0.567971 | + | 0.823048i | \(0.307728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.7990 | −0.758699 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.1421 | 0.617662 | 0.308831 | − | 0.951117i | \(-0.400062\pi\) | ||||
0.308831 | + | 0.951117i | \(0.400062\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.62742 | 0.100388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.0711 | −0.574997 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.8284 | 0.717306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.970563 | 0.0368155 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.31371 | −0.0497603 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.4853 | 1.07741 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.17157 | −0.195328 | −0.0976638 | − | 0.995219i | \(-0.531137\pi\) | ||||
−0.0976638 | + | 0.995219i | \(0.531137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.3137 | −0.426705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.00000 | −0.300446 | −0.150223 | − | 0.988652i | \(-0.547999\pi\) | ||||
−0.150223 | + | 0.988652i | \(0.547999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.34315 | 0.0878748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.9706 | 0.935155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.686292 | −0.0256658 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.17157 | −0.118445 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.68629 | 0.174769 | 0.0873846 | − | 0.996175i | \(-0.472149\pi\) | ||||
0.0873846 | + | 0.996175i | \(0.472149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.8995 | 0.814451 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.5147 | −1.46754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4558 | −0.944105 | −0.472052 | − | 0.881570i | \(-0.656487\pi\) | ||||
−0.472052 | + | 0.881570i | \(0.656487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.9411 | 0.663576 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.7574 | 0.434268 | 0.217134 | − | 0.976142i | \(-0.430329\pi\) | ||||
0.217134 | + | 0.976142i | \(0.430329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.62742 | 0.244124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.2843 | −0.746169 | −0.373084 | − | 0.927797i | \(-0.621700\pi\) | ||||
−0.373084 | + | 0.927797i | \(0.621700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.65685 | −0.354753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.1716 | 0.409845 | 0.204923 | − | 0.978778i | \(-0.434306\pi\) | ||||
0.204923 | + | 0.978778i | \(0.434306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.85786 | −0.214616 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.3137 | −0.560299 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.6569 | −1.08219 | −0.541097 | − | 0.840960i | \(-0.681991\pi\) | ||||
−0.541097 | + | 0.840960i | \(0.681991\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.48528 | 0.309221 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | −0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3137 | −0.411204 | −0.205602 | − | 0.978636i | \(-0.565915\pi\) | ||||
−0.205602 | + | 0.978636i | \(0.565915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.75736 | −0.353704 | −0.176852 | − | 0.984237i | \(-0.556591\pi\) | ||||
−0.176852 | + | 0.984237i | \(0.556591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.31371 | 0.0474972 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.31371 | 0.264083 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0711 | 0.543477 | 0.271738 | − | 0.962371i | \(-0.412401\pi\) | ||||
0.271738 | + | 0.962371i | \(0.412401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.2426 | 1.08916 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.41421 | −0.122801 | −0.0614004 | − | 0.998113i | \(-0.519557\pi\) | ||||
−0.0614004 | + | 0.998113i | \(0.519557\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.0833 | 0.865096 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.00000 | 0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.686292 | 0.0245574 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.48528 | −0.303239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.14214 | −0.290605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6274 | 0.378827 | 0.189413 | − | 0.981897i | \(-0.439341\pi\) | ||||
0.189413 | + | 0.981897i | \(0.439341\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.8284 | 0.883915 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.6569 | −0.698035 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.79899 | 0.276602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.2132 | −1.53069 | −0.765345 | − | 0.643620i | \(-0.777432\pi\) | ||||
−0.765345 | + | 0.643620i | \(0.777432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.3137 | −0.541760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.7279 | −0.379052 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.17157 | −0.323658 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.0416 | −1.05752 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9706 | 0.736376 | 0.368188 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368188 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.1716 | −0.461947 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.6274 | −1.91117 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0000 | 0.349002 | 0.174501 | − | 0.984657i | \(-0.444169\pi\) | ||||
0.174501 | + | 0.984657i | \(0.444169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.34315 | 0.0816769 | 0.0408385 | − | 0.999166i | \(-0.486997\pi\) | ||||
0.0408385 | + | 0.999166i | \(0.486997\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.85786 | 0.134314 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4558 | 0.676546 | 0.338273 | − | 0.941048i | \(-0.390157\pi\) | ||||
0.338273 | + | 0.941048i | \(0.390157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.27208 | 0.113644 | 0.0568220 | − | 0.998384i | \(-0.481903\pi\) | ||||
0.0568220 | + | 0.998384i | \(0.481903\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.00000 | 0.208138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.686292 | −0.0237501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.17157 | 0.178756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.1716 | −1.69759 | −0.848796 | − | 0.528721i | \(-0.822672\pi\) | ||||
−0.848796 | + | 0.528721i | \(0.822672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.4853 | 0.430016 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.44365 | −0.221668 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.8284 | −0.508910 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.0416 | 1.23404 | 0.617021 | − | 0.786947i | \(-0.288339\pi\) | ||||
0.617021 | + | 0.786947i | \(0.288339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.6985 | −1.49271 | −0.746356 | − | 0.665547i | \(-0.768198\pi\) | ||||
−0.746356 | + | 0.665547i | \(0.768198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.8284 | 1.32481 | 0.662404 | − | 0.749146i | \(-0.269536\pi\) | ||||
0.662404 | + | 0.749146i | \(0.269536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.5147 | 1.00469 | 0.502346 | − | 0.864666i | \(-0.332470\pi\) | ||||
0.502346 | + | 0.864666i | \(0.332470\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00000 | −0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9706 | 0.406542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.94113 | 0.0658482 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3137 | −0.383350 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.75736 | −0.262547 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.2843 | 0.684951 | 0.342476 | − | 0.939527i | \(-0.388735\pi\) | ||||
0.342476 | + | 0.939527i | \(0.388735\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.07107 | −0.0361262 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0711 | −0.844666 | −0.422333 | − | 0.906441i | \(-0.638789\pi\) | ||||
−0.422333 | + | 0.906441i | \(0.638789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.3431 | −0.617296 | −0.308648 | − | 0.951176i | \(-0.599877\pi\) | ||||
−0.308648 | + | 0.951176i | \(0.599877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.02944 | 0.101833 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.4558 | −0.720417 | −0.360208 | − | 0.932872i | \(-0.617294\pi\) | ||||
−0.360208 | + | 0.932872i | \(0.617294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.828427 | 0.0277534 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.6274 | 1.56033 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.4264 | −0.348516 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.82843 | −0.227995 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43.8823 | −1.46356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8579 | −0.994710 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.79899 | −0.192765 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.02944 | 0.233409 | 0.116704 | − | 0.993167i | \(-0.462767\pi\) | ||||
0.116704 | + | 0.993167i | \(0.462767\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.41421 | 0.113242 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.4853 | 1.80518 | 0.902589 | − | 0.430503i | \(-0.141664\pi\) | ||||
0.902589 | + | 0.430503i | \(0.141664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.6863 | −0.419855 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.14214 | −0.269171 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.2548 | 1.62477 | 0.812384 | − | 0.583123i | \(-0.198170\pi\) | ||||
0.812384 | + | 0.583123i | \(0.198170\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.5147 | −0.379423 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.17157 | −0.0385628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.71573 | −0.253692 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.8284 | −0.355652 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 60.8701 | 1.99708 | 0.998541 | − | 0.0540006i | \(-0.0171973\pi\) | ||||
0.998541 | + | 0.0540006i | \(0.0171973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.1421 | −0.855855 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.08831 | 0.0355916 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.10051 | −0.199295 | −0.0996474 | − | 0.995023i | \(-0.531771\pi\) | ||||
−0.0996474 | + | 0.995023i | \(0.531771\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.4142 | 0.568291 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.8995 | −1.43108 | −0.715541 | − | 0.698570i | \(-0.753820\pi\) | ||||
−0.715541 | + | 0.698570i | \(0.753820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.82843 | 0.0921063 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.1421 | −0.654531 | −0.327266 | − | 0.944932i | \(-0.606127\pi\) | ||||
−0.327266 | + | 0.944932i | \(0.606127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6569 | 0.508243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.3137 | −0.691144 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.37258 | −0.238821 | −0.119411 | − | 0.992845i | \(-0.538101\pi\) | ||||
−0.119411 | + | 0.992845i | \(0.538101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.88730 | −0.287586 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.02944 | −0.227229 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.25483 | −0.137253 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.4853 | −0.466782 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.4264 | 0.464402 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.6274 | 1.11354 | 0.556771 | − | 0.830666i | \(-0.312040\pi\) | ||||
0.556771 | + | 0.830666i | \(0.312040\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.3137 | 0.491947 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.2548 | 1.83740 | 0.918698 | − | 0.394962i | \(-0.129242\pi\) | ||||
0.918698 | + | 0.394962i | \(0.129242\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.58579 | −0.210914 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.8579 | 0.699295 | 0.349648 | − | 0.936881i | \(-0.386301\pi\) | ||||
0.349648 | + | 0.936881i | \(0.386301\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.88730 | −0.284039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3137 | −0.361219 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.6274 | 0.466542 | 0.233271 | − | 0.972412i | \(-0.425057\pi\) | ||||
0.233271 | + | 0.972412i | \(0.425057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.17157 | 0.0373294 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.6274 | −1.22828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.3137 | −0.740584 | −0.370292 | − | 0.928915i | \(-0.620742\pi\) | ||||
−0.370292 | + | 0.928915i | \(0.620742\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.68629 | −0.275651 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.31371 | −0.105052 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.5858 | −1.09534 | −0.547671 | − | 0.836693i | \(-0.684486\pi\) | ||||
−0.547671 | + | 0.836693i | \(0.684486\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.65685 | −0.0524205 |
(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 | 2352.2.a.bb.1.1 | 2 | ||
3.2 | odd | 2 | 7056.2.a.cg.1.2 | 2 | |||
4.3 | odd | 2 | 1176.2.a.o.1.1 | yes | 2 | ||
7.2 | even | 3 | 2352.2.q.be.1537.2 | 4 | |||
7.3 | odd | 6 | 2352.2.q.bc.961.1 | 4 | |||
7.4 | even | 3 | 2352.2.q.be.961.2 | 4 | |||
7.5 | odd | 6 | 2352.2.q.bc.1537.1 | 4 | |||
7.6 | odd | 2 | 2352.2.a.bd.1.2 | 2 | |||
8.3 | odd | 2 | 9408.2.a.dg.1.2 | 2 | |||
8.5 | even | 2 | 9408.2.a.du.1.2 | 2 | |||
12.11 | even | 2 | 3528.2.a.bb.1.2 | 2 | |||
21.20 | even | 2 | 7056.2.a.cx.1.1 | 2 | |||
28.3 | even | 6 | 1176.2.q.o.961.1 | 4 | |||
28.11 | odd | 6 | 1176.2.q.k.961.2 | 4 | |||
28.19 | even | 6 | 1176.2.q.o.361.1 | 4 | |||
28.23 | odd | 6 | 1176.2.q.k.361.2 | 4 | |||
28.27 | even | 2 | 1176.2.a.j.1.2 | ✓ | 2 | ||
56.13 | odd | 2 | 9408.2.a.ds.1.1 | 2 | |||
56.27 | even | 2 | 9408.2.a.ee.1.1 | 2 | |||
84.11 | even | 6 | 3528.2.s.bm.3313.1 | 4 | |||
84.23 | even | 6 | 3528.2.s.bm.361.1 | 4 | |||
84.47 | odd | 6 | 3528.2.s.bd.361.2 | 4 | |||
84.59 | odd | 6 | 3528.2.s.bd.3313.2 | 4 | |||
84.83 | odd | 2 | 3528.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.j.1.2 | ✓ | 2 | 28.27 | even | 2 | ||
1176.2.a.o.1.1 | yes | 2 | 4.3 | odd | 2 | ||
1176.2.q.k.361.2 | 4 | 28.23 | odd | 6 | |||
1176.2.q.k.961.2 | 4 | 28.11 | odd | 6 | |||
1176.2.q.o.361.1 | 4 | 28.19 | even | 6 | |||
1176.2.q.o.961.1 | 4 | 28.3 | even | 6 | |||
2352.2.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.2.a.bd.1.2 | 2 | 7.6 | odd | 2 | |||
2352.2.q.bc.961.1 | 4 | 7.3 | odd | 6 | |||
2352.2.q.bc.1537.1 | 4 | 7.5 | odd | 6 | |||
2352.2.q.be.961.2 | 4 | 7.4 | even | 3 | |||
2352.2.q.be.1537.2 | 4 | 7.2 | even | 3 | |||
3528.2.a.bb.1.2 | 2 | 12.11 | even | 2 | |||
3528.2.a.bl.1.1 | 2 | 84.83 | odd | 2 | |||
3528.2.s.bd.361.2 | 4 | 84.47 | odd | 6 | |||
3528.2.s.bd.3313.2 | 4 | 84.59 | odd | 6 | |||
3528.2.s.bm.361.1 | 4 | 84.23 | even | 6 | |||
3528.2.s.bm.3313.1 | 4 | 84.11 | even | 6 | |||
7056.2.a.cg.1.2 | 2 | 3.2 | odd | 2 | |||
7056.2.a.cx.1.1 | 2 | 21.20 | even | 2 | |||
9408.2.a.dg.1.2 | 2 | 8.3 | odd | 2 | |||
9408.2.a.ds.1.1 | 2 | 56.13 | odd | 2 | |||
9408.2.a.du.1.2 | 2 | 8.5 | even | 2 | |||
9408.2.a.ee.1.1 | 2 | 56.27 | even | 2 |