Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.5 | ||
Root | \(-0.385124 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.2.p.c.223.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.76873 | 1.23822 | 0.619108 | − | 0.785306i | \(-0.287494\pi\) | ||||
0.619108 | + | 0.785306i | \(0.287494\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.480901 | + | 2.60168i | −0.181763 | + | 0.983342i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.75739 | −1.73592 | −0.867959 | − | 0.496635i | \(-0.834569\pi\) | ||||
−0.867959 | + | 0.496635i | \(0.834569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.76873i | − | 0.714884i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.71919i | 1.62964i | 0.579712 | + | 0.814822i | \(0.303165\pi\) | ||||
−0.579712 | + | 0.814822i | \(0.696835\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.20336i | 1.19373i | 0.802341 | + | 0.596866i | \(0.203588\pi\) | ||||
−0.802341 | + | 0.596866i | \(0.796412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.60168 | + | 0.480901i | 0.567733 | + | 0.104941i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43462i | 0.924683i | 0.886702 | + | 0.462342i | \(0.152991\pi\) | ||||
−0.886702 | + | 0.462342i | \(0.847009\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.66589 | 0.533178 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.54050i | 0.286063i | 0.989718 | + | 0.143032i | \(0.0456851\pi\) | ||||
−0.989718 | + | 0.143032i | \(0.954315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.05068 | −1.44594 | −0.722972 | − | 0.690877i | \(-0.757225\pi\) | ||||
−0.722972 | + | 0.690877i | \(0.757225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.75739i | 1.00223i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.33149 | + | 7.20336i | −0.225062 | + | 1.21759i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.42590i | − | 0.727614i | −0.931474 | − | 0.363807i | \(-0.881477\pi\) | ||
0.931474 | − | 0.363807i | \(-0.118523\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000i | 0.320256i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.209011i | − | 0.0326420i | −0.999867 | − | 0.0163210i | \(-0.994805\pi\) | ||
0.999867 | − | 0.0163210i | \(-0.00519537\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5530 | 1.60931 | 0.804657 | − | 0.593740i | \(-0.202349\pi\) | ||||
0.804657 | + | 0.593740i | \(0.202349\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.76873 | −0.412739 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.58658 | −0.669021 | −0.334511 | − | 0.942392i | \(-0.608571\pi\) | ||||
−0.334511 | + | 0.942392i | \(0.608571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.53747 | − | 2.50230i | −0.933924 | − | 0.357471i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.71919 | 0.940875 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.05068i | − | 1.10585i | −0.833232 | − | 0.552923i | \(-0.813512\pi\) | ||
0.833232 | − | 0.552923i | \(-0.186488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.9407 | −2.14944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.20336 | 0.689202 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.53747i | − | 0.720917i | −0.932775 | − | 0.360459i | \(-0.882620\pi\) | ||
0.932775 | − | 0.360459i | \(-0.117380\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8692 | 1.39166 | 0.695832 | − | 0.718204i | \(-0.255036\pi\) | ||||
0.695832 | + | 0.718204i | \(0.255036\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.480901 | − | 2.60168i | 0.0605878 | − | 0.327781i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.53747 | −0.686838 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.04280 | −0.493906 | −0.246953 | − | 0.969027i | \(-0.579429\pi\) | ||||
−0.246953 | + | 0.969027i | \(0.579429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.43462 | 0.533866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.10284i | − | 0.130884i | −0.997856 | − | 0.0654418i | \(-0.979154\pi\) | ||
0.997856 | − | 0.0654418i | \(-0.0208457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.59118i | 1.12256i | 0.827625 | + | 0.561281i | \(0.189691\pi\) | ||||
−0.827625 | + | 0.561281i | \(0.810309\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 2.66589i | − | 0.307830i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.76873 | − | 14.9789i | 0.315527 | − | 1.70700i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.7408i | − | 1.65847i | −0.558898 | − | 0.829236i | \(-0.688776\pi\) | ||
0.558898 | − | 0.829236i | \(-0.311224\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.86925i | 0.973526i | 0.873534 | + | 0.486763i | \(0.161823\pi\) | ||||
−0.873534 | + | 0.486763i | \(0.838177\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.6037i | 2.01785i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.54050 | 0.165159 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.6474i | 1.44662i | 0.690523 | + | 0.723311i | \(0.257380\pi\) | ||||
−0.690523 | + | 0.723311i | \(0.742620\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.961802 | − | 5.20336i | 0.100824 | − | 0.545460i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.05068i | 0.834817i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.4067i | 1.47810i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.58658i | 0.465696i | 0.972513 | + | 0.232848i | \(0.0748045\pi\) | ||||
−0.972513 | + | 0.232848i | \(0.925195\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.75739 | 0.578639 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.76873 | 0.275499 | 0.137750 | − | 0.990467i | \(-0.456013\pi\) | ||||
0.137750 | + | 0.990467i | \(0.456013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.9835 | 1.96903 | 0.984515 | − | 0.175298i | \(-0.0560888\pi\) | ||||
0.984515 | + | 0.175298i | \(0.0560888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.20336 | + | 1.33149i | 0.702976 | + | 0.129940i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.752791 | −0.0727750 | −0.0363875 | − | 0.999338i | \(-0.511585\pi\) | ||||
−0.0363875 | + | 0.999338i | \(0.511585\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.85181i | 0.847849i | 0.905697 | + | 0.423925i | \(0.139348\pi\) | ||||
−0.905697 | + | 0.423925i | \(0.860652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.42590 | −0.420088 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.5375 | 1.08535 | 0.542677 | − | 0.839942i | \(-0.317411\pi\) | ||||
0.542677 | + | 0.839942i | \(0.317411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2783i | 1.14496i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.4812 | − | 3.23127i | −1.60250 | − | 0.296210i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.1475 | 2.01341 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.209011 | −0.0188459 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.46253 | −0.578026 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.66589i | 0.325295i | 0.986684 | + | 0.162648i | \(0.0520034\pi\) | ||||
−0.986684 | + | 0.162648i | \(0.947997\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 10.5530i | − | 0.929138i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.13075i | − | 0.273535i | −0.990603 | − | 0.136768i | \(-0.956329\pi\) | ||
0.990603 | − | 0.136768i | \(-0.0436713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5375 | − | 2.50230i | −1.17385 | − | 0.216977i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.76873i | 0.238295i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.4817 | −1.66443 | −0.832215 | − | 0.554453i | \(-0.812927\pi\) | ||||
−0.832215 | + | 0.554453i | \(0.812927\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.66822i | 0.395953i | 0.980207 | + | 0.197977i | \(0.0634370\pi\) | ||||
−0.980207 | + | 0.197977i | \(0.936563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.58658i | 0.386259i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5148 | 0.962914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.26523i | 0.354208i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.50230 | + | 6.53747i | −0.206386 | + | 0.539201i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.97428i | − | 0.817125i | −0.912730 | − | 0.408563i | \(-0.866030\pi\) | ||
0.912730 | − | 0.408563i | \(-0.133970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.79664i | 0.227587i | 0.993504 | + | 0.113794i | \(0.0363003\pi\) | ||||
−0.993504 | + | 0.113794i | \(0.963700\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.71919i | − | 0.543214i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.2902 | −1.79039 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.9442 | 1.75134 | 0.875668 | − | 0.482913i | \(-0.160421\pi\) | ||||
0.875668 | + | 0.482913i | \(0.160421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.05068 | −0.638460 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.5375 | − | 2.13261i | −0.909280 | − | 0.168074i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.89001 | 0.617993 | 0.308996 | − | 0.951063i | \(-0.400007\pi\) | ||||
0.308996 | + | 0.951063i | \(0.400007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.9407i | 1.24098i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.00460 | −0.387268 | −0.193634 | − | 0.981074i | \(-0.562027\pi\) | ||||
−0.193634 | + | 0.981074i | \(0.562027\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.20336i | − | 0.397911i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.50723 | −0.646793 | −0.323396 | − | 0.946264i | \(-0.604825\pi\) | ||||
−0.323396 | + | 0.946264i | \(0.604825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.28203 | + | 6.93579i | −0.0969123 | + | 0.524296i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.53747 | −0.416222 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3440 | −0.773144 | −0.386572 | − | 0.922259i | \(-0.626341\pi\) | ||||
−0.386572 | + | 0.922259i | \(0.626341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.8692i | − | 0.803478i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.2542i | − | 0.900943i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 38.6850i | − | 2.82893i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.60168 | − | 0.480901i | −0.189244 | − | 0.0349804i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.50956i | 0.253943i | 0.991906 | + | 0.126971i | \(0.0405257\pi\) | ||||
−0.991906 | + | 0.126971i | \(0.959474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4090 | 0.965204 | 0.482602 | − | 0.875840i | \(-0.339692\pi\) | ||||
0.482602 | + | 0.875840i | \(0.339692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.53747i | 0.396546i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.70905i | − | 0.406753i | −0.979101 | − | 0.203377i | \(-0.934808\pi\) | ||
0.979101 | − | 0.203377i | \(-0.0651916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.80901 | 0.340902 | 0.170451 | − | 0.985366i | \(-0.445478\pi\) | ||||
0.170451 | + | 0.985366i | \(0.445478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.04280i | 0.285157i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.00788 | − | 0.740827i | −0.281298 | − | 0.0519959i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 0.578696i | − | 0.0404179i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 4.43462i | − | 0.308228i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 29.9578i | − | 2.07222i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4002 | 0.991350 | 0.495675 | − | 0.868508i | \(-0.334921\pi\) | ||||
0.495675 | + | 0.868508i | \(0.334921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.10284 | −0.0755657 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.2184 | 1.99268 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.87158 | − | 20.9453i | 0.262820 | − | 1.42186i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.59118 | 0.648112 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.4384i | − | 0.903964i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0586 | 0.807501 | 0.403750 | − | 0.914869i | \(-0.367706\pi\) | ||||
0.403750 | + | 0.914869i | \(0.367706\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.66589 | −0.177726 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.7385i | 1.17735i | 0.808372 | + | 0.588673i | \(0.200349\pi\) | ||||
−0.808372 | + | 0.588673i | \(0.799651\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4817 | −0.758729 | −0.379365 | − | 0.925247i | \(-0.623857\pi\) | ||||
−0.379365 | + | 0.925247i | \(0.623857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.9789 | − | 2.76873i | −0.985538 | − | 0.182169i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.6077 | −1.35006 | −0.675029 | − | 0.737791i | \(-0.735869\pi\) | ||||
−0.675029 | + | 0.737791i | \(0.735869\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.6990 | −0.828392 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7408 | −0.957520 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.6403i | 1.20574i | 0.797839 | + | 0.602871i | \(0.205977\pi\) | ||||
−0.797839 | + | 0.602871i | \(0.794023\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5958i | 0.940197i | 0.882614 | + | 0.470098i | \(0.155782\pi\) | ||||
−0.882614 | + | 0.470098i | \(0.844218\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.1005 | − | 6.92820i | −1.15640 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 10.4067i | − | 0.662164i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.86925 | 0.562066 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.4817i | − | 0.850954i | −0.904969 | − | 0.425477i | \(-0.860106\pi\) | ||
0.904969 | − | 0.425477i | \(-0.139894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 25.5319i | − | 1.60517i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.6037 | 1.16501 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.6566i | 1.47566i | 0.674988 | + | 0.737829i | \(0.264149\pi\) | ||||
−0.674988 | + | 0.737829i | \(0.735851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.5148 | + | 2.12842i | 0.715494 | + | 0.132254i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1.54050i | − | 0.0953544i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.8972i | − | 0.671947i | −0.941871 | − | 0.335974i | \(-0.890935\pi\) | ||
0.941871 | − | 0.335974i | \(-0.109065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 22.2902i | − | 1.36928i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.6474 | 0.835207 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0447 | −0.856320 | −0.428160 | − | 0.903703i | \(-0.640838\pi\) | ||||
−0.428160 | + | 0.903703i | \(0.640838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9117 | 1.63477 | 0.817384 | − | 0.576093i | \(-0.195423\pi\) | ||||
0.817384 | + | 0.576093i | \(0.195423\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.20336 | − | 0.961802i | −0.314922 | − | 0.0582109i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.3486 | −0.925553 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.50230i | 0.150349i | 0.997170 | + | 0.0751743i | \(0.0239513\pi\) | ||||
−0.997170 | + | 0.0751743i | \(0.976049\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.05068 | 0.481982 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.3509 | −0.975413 | −0.487707 | − | 0.873008i | \(-0.662166\pi\) | ||||
−0.487707 | + | 0.873008i | \(0.662166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.9419i | − | 0.888201i | −0.895977 | − | 0.444101i | \(-0.853523\pi\) | ||
0.895977 | − | 0.444101i | \(-0.146477\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.4067 | 0.853380 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.543780 | + | 0.100514i | 0.0320983 | + | 0.00593313i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.1475 | −1.65574 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.58658 | 0.268870 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.50723 | −0.496998 | −0.248499 | − | 0.968632i | \(-0.579937\pi\) | ||||
−0.248499 | + | 0.968632i | \(0.579937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 15.3318i | − | 0.892651i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.75739i | − | 0.334078i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 8.86925i | − | 0.512922i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.07494 | + | 27.4555i | −0.292515 | + | 1.58251i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.76873i | − | 0.159060i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30.0941 | 1.72318 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.5351i | 0.715418i | 0.933833 | + | 0.357709i | \(0.116442\pi\) | ||||
−0.933833 | + | 0.357709i | \(0.883558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 19.9835i | − | 1.13682i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5194 | 0.936728 | 0.468364 | − | 0.883536i | \(-0.344844\pi\) | ||||
0.468364 | + | 0.883536i | \(0.344844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.68325i | 0.264713i | 0.991202 | + | 0.132357i | \(0.0422544\pi\) | ||||
−0.991202 | + | 0.132357i | \(0.957746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.33149 | − | 7.20336i | 0.0750208 | − | 0.405863i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.97428i | − | 0.560212i | −0.959969 | − | 0.280106i | \(-0.909630\pi\) | ||
0.959969 | − | 0.280106i | \(-0.0903695\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.86925i | − | 0.496583i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.752791i | 0.0420167i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.9624 | −1.94536 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.33178 | −0.295754 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.85181 | 0.489506 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.20569 | − | 11.9328i | 0.121604 | − | 0.657877i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.62478 | 0.199236 | 0.0996178 | − | 0.995026i | \(-0.468238\pi\) | ||||
0.0996178 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.42590i | 0.242538i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.1934 | −0.611563 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 11.5375i | − | 0.626629i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 46.3509 | 2.51004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.65406 | − | 15.8050i | 0.521270 | − | 0.853392i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.2783 | 0.661041 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.7666 | 0.846395 | 0.423197 | − | 0.906037i | \(-0.360908\pi\) | ||||
0.423197 | + | 0.906037i | \(0.360908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1308 | −0.916988 | −0.458494 | − | 0.888697i | \(-0.651611\pi\) | ||||
−0.458494 | + | 0.888697i | \(0.651611\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.00000i | − | 0.106752i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.6678i | − | 1.41938i | −0.704513 | − | 0.709691i | \(-0.748835\pi\) | ||
0.704513 | − | 0.709691i | \(-0.251165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.05348i | − | 0.162062i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.23127 | + | 17.4812i | −0.171017 | + | 0.925202i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.1028i | 1.32488i | 0.749116 | + | 0.662439i | \(0.230479\pi\) | ||||
−0.749116 | + | 0.662439i | \(0.769521\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.07494 | −0.424997 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 22.1475i | − | 1.16244i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.5554i | 1.38997i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0678 | −1.15193 | −0.575964 | − | 0.817475i | \(-0.695373\pi\) | ||||
−0.575964 | + | 0.817475i | \(0.695373\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.209011i | 0.0108807i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.9453 | + | 3.87158i | 1.08742 | + | 0.201002i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.9486i | 1.03290i | 0.856318 | + | 0.516449i | \(0.172746\pi\) | ||||
−0.856318 | + | 0.516449i | \(0.827254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.46253i | 0.333724i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.08100i | − | 0.158679i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6497 | −1.11207 | −0.556036 | − | 0.831158i | \(-0.687678\pi\) | ||||
−0.556036 | + | 0.831158i | \(0.687678\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.66589 | 0.187809 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.2184 | 1.49299 | 0.746495 | − | 0.665391i | \(-0.231735\pi\) | ||||
0.746495 | + | 0.665391i | \(0.231735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.66589 | − | 41.4725i | 0.390690 | − | 2.11364i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.5530 | −0.536438 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.70905i | 0.289460i | 0.989471 | + | 0.144730i | \(0.0462314\pi\) | ||||
−0.989471 | + | 0.144730i | \(0.953769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.7971 | −1.50690 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.13075 | −0.157926 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 40.8134i | − | 2.05355i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2760 | −0.666302 | −0.333151 | − | 0.942874i | \(-0.608112\pi\) | ||||
−0.333151 | + | 0.942874i | \(0.608112\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.50230 | + | 13.5375i | −0.125272 | + | 0.677721i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1452 | 1.30563 | 0.652815 | − | 0.757518i | \(-0.273588\pi\) | ||||
0.652815 | + | 0.757518i | \(0.273588\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.1014 | 0.802066 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.76873 | 0.137580 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.4817i | 1.26308i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.5958i | 0.721715i | 0.932621 | + | 0.360857i | \(0.117516\pi\) | ||||
−0.932621 | + | 0.360857i | \(0.882484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.4817i | 0.960959i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.4067 | + | 2.66297i | 0.708908 | + | 0.131036i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.5566i | 1.20544i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.66822 | 0.228604 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.6124i | 1.39781i | 0.715216 | + | 0.698904i | \(0.246328\pi\) | ||||
−0.715216 | + | 0.698904i | \(0.753672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.5115i | − | 0.609773i | −0.952389 | − | 0.304887i | \(-0.901381\pi\) | ||
0.952389 | − | 0.304887i | \(-0.0986186\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.58658 | 0.223007 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.9126i | 0.868890i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.22703 | + | 28.2783i | −0.252954 | + | 1.36848i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 11.5148i | − | 0.555939i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 35.4537i | − | 1.70775i | −0.520481 | − | 0.853873i | \(-0.674247\pi\) | ||
0.520481 | − | 0.853873i | \(-0.325753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.8860i | − | 1.77263i | −0.463086 | − | 0.886313i | \(-0.653258\pi\) | ||
0.463086 | − | 0.886313i | \(-0.346742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.26523 | 0.204502 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.0749 | −1.10382 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9710 | 0.523617 | 0.261809 | − | 0.965120i | \(-0.415681\pi\) | ||||
0.261809 | + | 0.965120i | \(0.415681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.53747 | + | 2.50230i | 0.311308 | + | 0.119157i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.5374 | −1.02327 | −0.511636 | − | 0.859202i | \(-0.670961\pi\) | ||||
−0.511636 | + | 0.859202i | \(0.670961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.7860i | 1.79123i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.97428 | −0.471767 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.2760 | 0.815303 | 0.407652 | − | 0.913138i | \(-0.366348\pi\) | ||||
0.407652 | + | 0.913138i | \(0.366348\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20336i | 0.0566639i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.79664 | 0.131398 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.66297 | − | 14.4067i | 0.124842 | − | 0.675397i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | 0.0935561 | 0.0467780 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467780 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.71919 | −0.313625 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.8437 | −1.76256 | −0.881278 | − | 0.472599i | \(-0.843316\pi\) | ||||
−0.881278 | + | 0.472599i | \(0.843316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.99767i | − | 0.139313i | −0.997571 | − | 0.0696567i | \(-0.977810\pi\) | ||
0.997571 | − | 0.0696567i | \(-0.0221904\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.2902i | 1.03368i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 8.66822i | − | 0.401117i | −0.979682 | − | 0.200559i | \(-0.935724\pi\) | ||
0.979682 | − | 0.200559i | \(-0.0642757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.94419 | − | 10.5181i | 0.0897741 | − | 0.485679i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 21.9442i | − | 1.01113i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −60.7576 | −2.79364 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8716i | 0.636472i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.05068i | 0.368615i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.26523 | 0.194883 | 0.0974417 | − | 0.995241i | \(-0.468934\pi\) | ||||
0.0974417 | + | 0.995241i | \(0.468934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.85181i | 0.403608i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.13261 | + | 11.5375i | −0.0970373 | + | 0.524973i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.6990i | 0.576633i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.9419i | 1.03959i | 0.854290 | + | 0.519797i | \(0.173993\pi\) | ||||
−0.854290 | + | 0.519797i | \(0.826007\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.89001i | − | 0.356798i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.25641 | −0.417736 | −0.208868 | − | 0.977944i | \(-0.566978\pi\) | ||||
−0.208868 | + | 0.977944i | \(0.566978\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3509 | −0.466181 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.9407 | 0.716480 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.86925 | + | 0.530359i | 0.128703 | + | 0.0237899i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.54838 | 0.248380 | 0.124190 | − | 0.992258i | \(-0.460367\pi\) | ||||
0.124190 | + | 0.992258i | \(0.460367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.00460i | 0.223589i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.26983 | −0.413321 | −0.206661 | − | 0.978413i | \(-0.566260\pi\) | ||||
−0.206661 | + | 0.978413i | \(0.566260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.66589 | 0.341128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000i | 0.399704i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.0447 | 1.15441 | 0.577205 | − | 0.816599i | \(-0.304143\pi\) | ||||
0.577205 | + | 0.816599i | \(0.304143\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.9532 | − | 4.61241i | −1.10386 | − | 0.204041i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.20336 | −0.229734 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 55.3290 | 2.43808 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.4067 | 1.16137 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.50723i | 0.373426i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.5960i | 1.47187i | 0.677054 | + | 0.735933i | \(0.263256\pi\) | ||||
−0.677054 | + | 0.735933i | \(0.736744\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 26.8181i | − | 1.17267i | −0.810067 | − | 0.586337i | \(-0.800570\pi\) | ||
0.810067 | − | 0.586337i | \(-0.199430\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.93579 | + | 1.28203i | 0.302703 | + | 0.0559523i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 54.0941i | − | 2.35637i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.33411 | 0.144961 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.53747i | 0.240306i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.418022i | 0.0181065i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.08428 | −0.0901112 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.3440i | 0.446375i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.6388 | + | 14.4067i | 1.62122 | + | 0.620541i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 28.2217i | − | 1.21334i | −0.794952 | − | 0.606672i | \(-0.792504\pi\) | ||
0.794952 | − | 0.606672i | \(-0.207496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.00000i | − | 0.0858282i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5083i | 1.04982i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.28315 | −0.0548635 | −0.0274318 | − | 0.999624i | \(-0.508733\pi\) | ||||
−0.0274318 | + | 0.999624i | \(0.508733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.8692 | −0.463888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.01576 | −0.341483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.3509 | + | 7.08888i | 1.63085 | + | 0.301450i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.2542 | −0.520160 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 40.7681i | − | 1.72740i | −0.504007 | − | 0.863700i | \(-0.668141\pi\) | ||
0.504007 | − | 0.863700i | \(-0.331859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.1060 | −0.892687 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.6850 | −1.63328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 19.9442i | − | 0.840547i | −0.907397 | − | 0.420274i | \(-0.861934\pi\) | ||
0.907397 | − | 0.420274i | \(-0.138066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.9442 | 1.34390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.480901 | + | 2.60168i | −0.0201959 | + | 0.109260i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.8692 | 1.12642 | 0.563209 | − | 0.826315i | \(-0.309567\pi\) | ||||
0.563209 | + | 0.826315i | \(0.309567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.7622 | 1.24551 | 0.622754 | − | 0.782418i | \(-0.286014\pi\) | ||||
0.622754 | + | 0.782418i | \(0.286014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.50956 | 0.146614 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.8222i | 0.493021i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.7240i | 1.27906i | 0.768768 | + | 0.639528i | \(0.220870\pi\) | ||||
−0.768768 | + | 0.639528i | \(0.779130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 13.4090i | − | 0.557261i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.0749 | − | 4.26523i | −0.957310 | − | 0.176952i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.3509i | 1.91966i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.53747 | 0.228946 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.33178i | 0.137517i | 0.997633 | + | 0.0687586i | \(0.0219038\pi\) | ||||
−0.997633 | + | 0.0687586i | \(0.978096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 41.8906i | − | 1.72607i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.70905 | −0.234839 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.29001i | 0.135104i | 0.997716 | + | 0.0675522i | \(0.0215189\pi\) | ||||
−0.997716 | + | 0.0675522i | \(0.978481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −48.4007 | − | 8.94652i | −1.98424 | − | 0.366771i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.80901i | − | 0.196820i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.71059i | 0.151611i | 0.997123 | + | 0.0758053i | \(0.0241527\pi\) | ||||
−0.997123 | + | 0.0758053i | \(0.975847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3417i | 0.544220i | 0.962266 | + | 0.272110i | \(0.0877214\pi\) | ||||
−0.962266 | + | 0.272110i | \(0.912279\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.04280 | 0.164635 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 61.3207 | 2.49304 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.7510 | 1.08579 | 0.542895 | − | 0.839801i | \(-0.317328\pi\) | ||||
0.542895 | + | 0.839801i | \(0.317328\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.740827 | + | 4.00788i | −0.0300198 | + | 0.162408i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.17315 | 0.371106 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 30.2791i | − | 1.22296i | −0.791259 | − | 0.611481i | \(-0.790574\pi\) | ||
0.791259 | − | 0.611481i | \(-0.209426\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.578696 | −0.0233353 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.48165 | −0.301200 | −0.150600 | − | 0.988595i | \(-0.548121\pi\) | ||||
−0.150600 | + | 0.988595i | \(0.548121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1452i | 0.648931i | 0.945898 | + | 0.324465i | \(0.105184\pi\) | ||||
−0.945898 | + | 0.324465i | \(0.894816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.43462 | −0.177955 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.5061 | − | 6.56305i | −1.42252 | − | 0.262943i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2225 | −1.24890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29.9578 | −1.19640 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.7385 | 1.18575 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.00233i | − | 0.199140i | −0.995031 | − | 0.0995698i | \(-0.968253\pi\) | ||
0.995031 | − | 0.0995698i | \(-0.0317467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 14.4002i | − | 0.572356i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.1499i | 0.402785i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.0749 | + | 5.00460i | 0.518048 | + | 0.198289i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.10284i | 0.0436279i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.5519 | 1.12773 | 0.563867 | − | 0.825866i | \(-0.309313\pi\) | ||||
0.563867 | + | 0.825866i | \(0.309313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.27830i | − | 0.326464i | −0.986588 | − | 0.163232i | \(-0.947808\pi\) | ||
0.986588 | − | 0.163232i | \(-0.0521919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 29.2184i | − | 1.15047i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.9486 | −0.784259 | −0.392130 | − | 0.919910i | \(-0.628261\pi\) | ||||
−0.392130 | + | 0.919910i | \(0.628261\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.8814i | 1.25145i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.9453 | − | 3.87158i | −0.820910 | − | 0.151739i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.6825i | 1.27896i | 0.768806 | + | 0.639482i | \(0.220851\pi\) | ||||
−0.768806 | + | 0.639482i | \(0.779149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.66822i | − | 0.338695i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 9.59118i | − | 0.374187i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.93046 | −0.153109 | −0.0765545 | − | 0.997065i | \(-0.524392\pi\) | ||||
−0.0765545 | + | 0.997065i | \(0.524392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6827 | 0.454404 | 0.227202 | − | 0.973848i | \(-0.427042\pi\) | ||||
0.227202 | + | 0.973848i | \(0.427042\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.4384 | −0.521904 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −37.4817 | − | 6.92820i | −1.45348 | − | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.83153 | −0.264518 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 12.0586i | − | 0.466211i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −62.5785 | −2.41582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6659 | −0.680970 | −0.340485 | − | 0.940250i | \(-0.610591\pi\) | ||||
−0.340485 | + | 0.940250i | \(0.610591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.66589i | 0.102610i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.6571 | −1.17825 | −0.589124 | − | 0.808043i | \(-0.700527\pi\) | ||||
−0.589124 | + | 0.808043i | \(0.700527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.9328 | − | 2.20569i | −0.457939 | − | 0.0846466i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.7385 | 0.679741 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.8790 | 0.913706 | 0.456853 | − | 0.889542i | \(-0.348977\pi\) | ||||
0.456853 | + | 0.889542i | \(0.348977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −53.9395 | −2.06092 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.4817i | 0.438052i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.1014i | 0.613413i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.5566i | 1.69501i | 0.530785 | + | 0.847506i | \(0.321897\pi\) | ||||
−0.530785 | + | 0.847506i | \(0.678103\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.76873 | + | 14.9789i | −0.105176 | + | 0.569001i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9251i | 0.490276i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.40439 | 0.0531949 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.6077i | 0.779456i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.0940i | 1.74095i | 0.492215 | + | 0.870474i | \(0.336188\pi\) | ||||
−0.492215 | + | 0.870474i | \(0.663812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.0296 | 0.868576 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.6990i | 0.478273i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.33149 | + | 7.20336i | −0.0500757 | + | 0.270910i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.8656i | 0.896292i | 0.893960 | + | 0.448146i | \(0.147915\pi\) | ||||
−0.893960 | + | 0.448146i | \(0.852085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.7408i | 0.552824i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 35.7017i | − | 1.33704i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.8814 | 1.19230 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.6403 | 0.696135 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.42919 | −0.127887 | −0.0639435 | − | 0.997954i | \(-0.520368\pi\) | ||||
−0.0639435 | + | 0.997954i | \(0.520368\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.61007 | + | 51.9906i | −0.357898 | + | 1.93623i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.5958 | 0.542823 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.10680i | 0.152523i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0553 | 0.484193 | 0.242097 | − | 0.970252i | \(-0.422165\pi\) | ||||
0.242097 | + | 0.970252i | \(0.422165\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 70.9075i | 2.62261i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.1452 | 0.670209 | 0.335104 | − | 0.942181i | \(-0.391228\pi\) | ||||
0.335104 | + | 0.942181i | \(0.391228\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.92820 | + | 18.1005i | −0.255551 | + | 0.667648i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.2760 | 0.857381 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −53.1131 | −1.95380 | −0.976898 | − | 0.213705i | \(-0.931447\pi\) | ||||
−0.976898 | + | 0.213705i | \(0.931447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.4067 | −0.382300 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.2481i | − | 0.779516i | −0.920917 | − | 0.389758i | \(-0.872559\pi\) | ||
0.920917 | − | 0.389758i | \(-0.127441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 27.6161i | − | 1.01178i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 8.86925i | − | 0.324509i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.362018 | − | 1.95852i | 0.0132278 | − | 0.0715628i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 9.61474i | − | 0.350847i | −0.984493 | − | 0.175423i | \(-0.943871\pi\) | ||
0.984493 | − | 0.175423i | \(-0.0561294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.4817 | −0.491299 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.74316i | 0.281802i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 16.8676i | − | 0.613062i | −0.951861 | − | 0.306531i | \(-0.900832\pi\) | ||
0.951861 | − | 0.306531i | \(-0.0991684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.5319 | −0.926748 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.1576i | 0.730712i | 0.930868 | + | 0.365356i | \(0.119053\pi\) | ||||
−0.930868 | + | 0.365356i | \(0.880947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.0296 | − | 4.25684i | −0.833726 | − | 0.154108i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 18.6037i | − | 0.672617i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.0749i | 0.399893i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7286i | 1.28841i | 0.764855 | + | 0.644203i | \(0.222811\pi\) | ||||
−0.764855 | + | 0.644203i | \(0.777189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.6566 | 0.851971 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.6938 | −0.564467 | −0.282233 | − | 0.959346i | \(-0.591075\pi\) | ||||
−0.282233 | + | 0.959346i | \(0.591075\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.4622 | −0.770946 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.12842 | − | 11.5148i | 0.0763567 | − | 0.413090i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.08756 | 0.0389659 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.34951i | 0.227203i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.54050 | −0.0550529 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.7576 | 2.16853 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.00000i | − | 0.142585i | −0.997455 | − | 0.0712923i | \(-0.977288\pi\) | ||
0.997455 | − | 0.0712923i | \(-0.0227123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.8972 | −0.387949 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.54838 | + | 30.0168i | −0.197278 | + | 1.06727i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.7385 | −0.771957 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −22.2902 | −0.790552 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.4705 | 1.25643 | 0.628215 | − | 0.778039i | \(-0.283786\pi\) | ||||
0.628215 | + | 0.778039i | \(0.283786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 30.8181i | − | 1.09027i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.6474i | − | 0.482207i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 55.2201i | − | 1.94868i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.9442 | − | 5.90464i | −1.12588 | − | 0.208111i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.0447i | 0.494397i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.6077 | 0.724530 | 0.362265 | − | 0.932075i | \(-0.382004\pi\) | ||||
0.362265 | + | 0.932075i | \(0.382004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.2201i | 1.23675i | 0.785884 | + | 0.618373i | \(0.212208\pi\) | ||||
−0.785884 | + | 0.618373i | \(0.787792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 26.9117i | − | 0.943834i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.8453 | 0.765208 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.9109i | 1.92109i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.961802 | + | 5.20336i | −0.0336081 | + | 0.181820i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.1612i | 1.19224i | 0.802897 | + | 0.596118i | \(0.203291\pi\) | ||||
−0.802897 | + | 0.596118i | \(0.796709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7.81110i | − | 0.272278i | −0.990690 | − | 0.136139i | \(-0.956531\pi\) | ||
0.990690 | − | 0.136139i | \(-0.0434694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.3486i | 0.534369i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.66072 | 0.196842 | 0.0984212 | − | 0.995145i | \(-0.468621\pi\) | ||||
0.0984212 | + | 0.995145i | \(0.468621\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.5566 | 1.75590 | 0.877951 | − | 0.478750i | \(-0.158910\pi\) | ||||
0.877951 | + | 0.478750i | \(0.158910\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.50230 | 0.0868038 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.8134 | − | 43.9265i | 0.582551 | − | 1.52196i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.8564 | −0.479521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 8.05068i | − | 0.278272i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.2679 | 0.941394 | 0.470697 | − | 0.882295i | \(-0.344002\pi\) | ||||
0.470697 | + | 0.882295i | \(0.344002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6269 | 0.918168 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.3509i | 0.563155i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.9186 | −0.857226 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.6508 | + | 57.6208i | −0.365965 | + | 1.97987i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.9419 | −0.512803 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.6272 | 0.672812 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.8692 | 1.19390 | 0.596950 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596950 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 14.4067i | − | 0.492699i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.6363i | 0.739082i | 0.929214 | + | 0.369541i | \(0.120485\pi\) | ||||
−0.929214 | + | 0.369541i | \(0.879515\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22.5398i | − | 0.769048i | −0.923115 | − | 0.384524i | \(-0.874366\pi\) | ||
0.923115 | − | 0.384524i | \(-0.125634\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.100514 | − | 0.543780i | 0.00342549 | − | 0.0185320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.6594i | 0.873457i | 0.899593 | + | 0.436729i | \(0.143863\pi\) | ||||
−0.899593 | + | 0.436729i | \(0.856137\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.5543 | −0.800869 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.1475i | 0.955941i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 84.8687i | 2.87897i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.08560 | 0.273970 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.58658i | − | 0.155232i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.10784 | − | 16.8134i | 0.105064 | − | 0.568398i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.9440i | 0.504622i | 0.967646 | + | 0.252311i | \(0.0811906\pi\) | ||||
−0.967646 | + | 0.252311i | \(0.918809\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.50723i | 0.286942i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.9844i | − | 0.370075i | −0.982732 | − | 0.185037i | \(-0.940759\pi\) | ||
0.982732 | − | 0.185037i | \(-0.0592406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.613612 | 0.0206497 | 0.0103249 | − | 0.999947i | \(-0.496713\pi\) | ||||
0.0103249 | + | 0.999947i | \(0.496713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.3318 | −0.515372 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.0545 | −1.37848 | −0.689238 | − | 0.724535i | \(-0.742055\pi\) | ||||
−0.689238 | + | 0.724535i | \(0.742055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.53747 | − | 1.76293i | −0.319876 | − | 0.0591268i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.75739 | −0.192880 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 23.8656i | − | 0.798632i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.6397 | −0.957320 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.86925 | −0.296136 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 12.4021i | − | 0.413632i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.0941 | 1.80213 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.4555 | + | 5.07494i | 0.913661 | + | 0.168883i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.53747 | 0.184072 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.6681 | −1.38357 | −0.691784 | − | 0.722105i | \(-0.743175\pi\) | ||||
−0.691784 | + | 0.722105i | \(0.743175\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.76873 | −0.0918331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.8972i | 1.15619i | 0.815968 | + | 0.578097i | \(0.196205\pi\) | ||||
−0.815968 | + | 0.578097i | \(0.803795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 51.0637i | − | 1.68996i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 30.0941i | − | 0.994879i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.14521 | + | 1.50558i | 0.268979 | + | 0.0497187i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.5398i | − | 0.479624i | −0.970819 | − | 0.239812i | \(-0.922914\pi\) | ||
0.970819 | − | 0.239812i | \(-0.0770858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.5351 | 0.413047 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.20569i | 0.0726011i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 11.7990i | − | 0.387948i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.9835 | −0.656344 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.38217i | 0.307819i | 0.988085 | + | 0.153909i | \(0.0491864\pi\) | ||||
−0.988085 | + | 0.153909i | \(0.950814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.0204 | − | 34.0168i | 0.426725 | − | 1.11486i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 16.5194i | − | 0.540820i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 107.109i | − | 3.50282i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.321348i | − | 0.0104980i | −0.999986 | − | 0.00524899i | \(-0.998329\pi\) | ||
0.999986 | − | 0.00524899i | \(-0.00167081\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.68325 | 0.152832 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.6938 | 0.902792 | 0.451396 | − | 0.892324i | \(-0.350926\pi\) | ||||
0.451396 | + | 0.892324i | \(0.350926\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.926885 | 0.0301835 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.20336 | − | 1.33149i | −0.234325 | − | 0.0433133i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.8587 | 0.710314 | 0.355157 | − | 0.934807i | \(-0.384427\pi\) | ||||
0.355157 | + | 0.934807i | \(0.384427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 19.1824i | − | 0.622686i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.97428 | −0.323438 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.7432 | 1.22262 | 0.611310 | − | 0.791391i | \(-0.290643\pi\) | ||||
0.611310 | + | 0.791391i | \(0.290643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.71704i | 0.314436i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.86925 | −0.286702 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.36875 | − | 50.6850i | 0.302533 | − | 1.63670i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.8134 | 1.09076 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.752791 | 0.0242583 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.1261 | 1.19513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.4840i | − | 1.10893i | −0.832207 | − | 0.554465i | \(-0.812923\pi\) | ||
0.832207 | − | 0.554465i | \(-0.187077\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.9624i | 1.12315i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.9633i | 1.63549i | 0.575580 | + | 0.817745i | \(0.304776\pi\) | ||||
−0.575580 | + | 0.817745i | \(0.695224\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.1452 | − | 2.24495i | −0.389358 | − | 0.0719698i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.33178i | 0.170754i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.6124 | −1.49126 | −0.745631 | − | 0.666359i | \(-0.767852\pi\) | ||||
−0.745631 | + | 0.666359i | \(0.767852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 78.5734i | − | 2.51122i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 8.85181i | − | 0.282616i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.31938 | −0.233452 | −0.116726 | − | 0.993164i | \(-0.537240\pi\) | ||||
−0.116726 | + | 0.993164i | \(0.537240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 15.8069i | − | 0.503648i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.9328 | − | 2.20569i | −0.379825 | − | 0.0702079i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.7985i | 1.48811i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.0917i | 1.17826i | 0.808039 | + | 0.589129i | \(0.200529\pi\) | ||||
−0.808039 | + | 0.589129i | \(0.799471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.62478i | − | 0.115029i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.3149 | 0.422110 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.0191 | −1.67913 | −0.839566 | − | 0.543257i | \(-0.817191\pi\) | ||||
−0.839566 | + | 0.543257i | \(0.817191\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.42590 | 0.140029 |
(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 | 1344.2.p.c.223.5 | ✓ | 12 | |
3.2 | odd | 2 | 4032.2.p.j.1567.2 | 12 | |||
4.3 | odd | 2 | inner | 1344.2.p.c.223.12 | yes | 12 | |
7.6 | odd | 2 | 1344.2.p.d.223.8 | yes | 12 | ||
8.3 | odd | 2 | 1344.2.p.d.223.2 | yes | 12 | ||
8.5 | even | 2 | 1344.2.p.d.223.7 | yes | 12 | ||
12.11 | even | 2 | 4032.2.p.j.1567.3 | 12 | |||
21.20 | even | 2 | 4032.2.p.k.1567.12 | 12 | |||
24.5 | odd | 2 | 4032.2.p.k.1567.10 | 12 | |||
24.11 | even | 2 | 4032.2.p.k.1567.11 | 12 | |||
28.27 | even | 2 | 1344.2.p.d.223.1 | yes | 12 | ||
56.13 | odd | 2 | inner | 1344.2.p.c.223.6 | yes | 12 | |
56.27 | even | 2 | inner | 1344.2.p.c.223.11 | yes | 12 | |
84.83 | odd | 2 | 4032.2.p.k.1567.9 | 12 | |||
168.83 | odd | 2 | 4032.2.p.j.1567.1 | 12 | |||
168.125 | even | 2 | 4032.2.p.j.1567.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.p.c.223.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1344.2.p.c.223.6 | yes | 12 | 56.13 | odd | 2 | inner | |
1344.2.p.c.223.11 | yes | 12 | 56.27 | even | 2 | inner | |
1344.2.p.c.223.12 | yes | 12 | 4.3 | odd | 2 | inner | |
1344.2.p.d.223.1 | yes | 12 | 28.27 | even | 2 | ||
1344.2.p.d.223.2 | yes | 12 | 8.3 | odd | 2 | ||
1344.2.p.d.223.7 | yes | 12 | 8.5 | even | 2 | ||
1344.2.p.d.223.8 | yes | 12 | 7.6 | odd | 2 | ||
4032.2.p.j.1567.1 | 12 | 168.83 | odd | 2 | |||
4032.2.p.j.1567.2 | 12 | 3.2 | odd | 2 | |||
4032.2.p.j.1567.3 | 12 | 12.11 | even | 2 | |||
4032.2.p.j.1567.4 | 12 | 168.125 | even | 2 | |||
4032.2.p.k.1567.9 | 12 | 84.83 | odd | 2 | |||
4032.2.p.k.1567.10 | 12 | 24.5 | odd | 2 | |||
4032.2.p.k.1567.11 | 12 | 24.11 | even | 2 | |||
4032.2.p.k.1567.12 | 12 | 21.20 | even | 2 |