Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1567,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, 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("4032.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.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: | \(32.1956820950\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1344) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.9 | ||
Root | \(-0.385124 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1567 |
Dual form | 4032.2.p.k.1567.10 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 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 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.54050i | − | 0.286063i | −0.989718 | − | 0.143032i | \(-0.954315\pi\) | ||
0.989718 | − | 0.143032i | \(-0.0456851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.05068 | −1.44594 | −0.722972 | − | 0.690877i | \(-0.757225\pi\) | ||||
−0.722972 | + | 0.690877i | \(0.757225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | \(-0.797651\pi\) | ||||
−0.804657 | + | 0.593740i | \(0.797651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.58658 | 0.669021 | 0.334511 | − | 0.942392i | \(-0.391429\pi\) | ||||
0.334511 | + | 0.942392i | \(0.391429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.53747 | + | 2.50230i | −0.933924 | + | 0.357471i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.05068i | 1.10585i | 0.833232 | + | 0.552923i | \(0.186488\pi\) | ||||
−0.833232 | + | 0.552923i | \(0.813512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.9407 | −2.14944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.53747i | 0.720917i | 0.932775 | + | 0.360459i | \(0.117380\pi\) | ||||
−0.932775 | + | 0.360459i | \(0.882620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8692 | −1.39166 | −0.695832 | − | 0.718204i | \(-0.744964\pi\) | ||||
−0.695832 | + | 0.718204i | \(0.744964\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.53747 | 0.686838 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.04280 | 0.493906 | 0.246953 | − | 0.969027i | \(-0.420571\pi\) | ||||
0.246953 | + | 0.969027i | \(0.420571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.810309\pi\) | ||
0.827625 | − | 0.561281i | \(-0.189691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.76873 | + | 14.9789i | 0.315527 | + | 1.70700i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7408i | 1.65847i | 0.558898 | + | 0.829236i | \(0.311224\pi\) | ||||
−0.558898 | + | 0.829236i | \(0.688776\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.86925i | − | 0.973526i | −0.873534 | − | 0.486763i | \(-0.838177\pi\) | ||
0.873534 | − | 0.486763i | \(-0.161823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.6037i | 2.01785i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.4067i | 1.47810i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.58658i | − | 0.465696i | −0.972513 | − | 0.232848i | \(-0.925195\pi\) | ||
0.972513 | − | 0.232848i | \(-0.0748045\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5375 | −1.08535 | −0.542677 | − | 0.839942i | \(-0.682589\pi\) | ||||
−0.542677 | + | 0.839942i | \(0.682589\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2783i | 1.14496i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.4812 | − | 3.23127i | 1.60250 | − | 0.296210i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.1475 | 2.01341 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.46253 | −0.578026 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.66589i | − | 0.325295i | −0.986684 | − | 0.162648i | \(-0.947997\pi\) | ||
0.986684 | − | 0.162648i | \(-0.0520034\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.13075i | 0.273535i | 0.990603 | + | 0.136768i | \(0.0436713\pi\) | ||||
−0.990603 | + | 0.136768i | \(0.956329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5375 | − | 2.50230i | 1.17385 | − | 0.216977i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.4817 | 1.66443 | 0.832215 | − | 0.554453i | \(-0.187073\pi\) | ||||
0.832215 | + | 0.554453i | \(0.187073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.66822i | 0.395953i | 0.980207 | + | 0.197977i | \(0.0634370\pi\) | ||||
−0.980207 | + | 0.197977i | \(0.936563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.5148 | −0.962914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.26523i | − | 0.354208i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.97428i | 0.817125i | 0.912730 | + | 0.408563i | \(0.133970\pi\) | ||||
−0.912730 | + | 0.408563i | \(0.866030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.79664i | − | 0.227587i | −0.993504 | − | 0.113794i | \(-0.963700\pi\) | ||
0.993504 | − | 0.113794i | \(-0.0363003\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.2902 | −1.79039 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.9442 | −1.75134 | −0.875668 | − | 0.482913i | \(-0.839579\pi\) | ||||
−0.875668 | + | 0.482913i | \(0.839579\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.5375 | − | 2.13261i | 0.909280 | − | 0.168074i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.89001 | −0.617993 | −0.308996 | − | 0.951063i | \(-0.599993\pi\) | ||||
−0.308996 | + | 0.951063i | \(0.599993\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.00460 | 0.387268 | 0.193634 | − | 0.981074i | \(-0.437973\pi\) | ||||
0.193634 | + | 0.981074i | \(0.437973\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.2542i | − | 0.900943i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 38.6850i | − | 2.82893i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.70905i | 0.406753i | 0.979101 | + | 0.203377i | \(0.0651916\pi\) | ||||
−0.979101 | + | 0.203377i | \(0.934808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.80901 | 0.340902 | 0.170451 | − | 0.985366i | \(-0.445478\pi\) | ||||
0.170451 | + | 0.985366i | \(0.445478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.00788 | + | 0.740827i | −0.281298 | + | 0.0519959i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 0.578696i | − | 0.0404179i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 29.9578i | − | 2.07222i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.4002 | −0.991350 | −0.495675 | − | 0.868508i | \(-0.665079\pi\) | ||||
−0.495675 | + | 0.868508i | \(0.665079\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.2184 | −1.99268 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.87158 | + | 20.9453i | 0.262820 | + | 1.42186i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 17.7385i | − | 1.17735i | −0.808372 | − | 0.588673i | \(-0.799651\pi\) | ||
0.808372 | − | 0.588673i | \(-0.200349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4817 | 0.758729 | 0.379365 | − | 0.925247i | \(-0.376143\pi\) | ||||
0.379365 | + | 0.925247i | \(0.376143\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.6077 | 1.35006 | 0.675029 | − | 0.737791i | \(-0.264131\pi\) | ||||
0.675029 | + | 0.737791i | \(0.264131\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.6990 | 0.828392 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | \(-0.844218\pi\) | ||
0.882614 | − | 0.470098i | \(-0.155782\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.1005 | + | 6.92820i | −1.15640 | + | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.4067i | 0.662164i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4817i | 0.850954i | 0.904969 | + | 0.425477i | \(0.139894\pi\) | ||||
−0.904969 | + | 0.425477i | \(0.860106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 25.5319i | − | 1.60517i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3509 | 0.975413 | 0.487707 | − | 0.873008i | \(-0.337834\pi\) | ||||
0.487707 | + | 0.873008i | \(0.337834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.9419i | − | 0.888201i | −0.895977 | − | 0.444101i | \(-0.853523\pi\) | ||
0.895977 | − | 0.444101i | \(-0.146477\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.543780 | + | 0.100514i | −0.0320983 | + | 0.00593313i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.1475 | −1.65574 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.86925i | 0.512922i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.07494 | + | 27.4555i | 0.292515 | + | 1.58251i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.5194 | −0.936728 | −0.468364 | − | 0.883536i | \(-0.655156\pi\) | ||||
−0.468364 | + | 0.883536i | \(0.655156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.68325i | − | 0.264713i | −0.991202 | − | 0.132357i | \(-0.957746\pi\) | ||
0.991202 | − | 0.132357i | \(-0.0422544\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.97428i | 0.560212i | 0.959969 | + | 0.280106i | \(0.0903695\pi\) | ||||
−0.959969 | + | 0.280106i | \(0.909630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.86925i | 0.496583i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.9624 | −1.94536 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.33178 | 0.295754 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.20569 | − | 11.9328i | −0.121604 | − | 0.657877i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.62478 | −0.199236 | −0.0996178 | − | 0.995026i | \(-0.531762\pi\) | ||||
−0.0996178 | + | 0.995026i | \(0.531762\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 46.3509 | 2.51004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.65406 | + | 15.8050i | 0.521270 | + | 0.853392i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | \(-0.348389\pi\) | ||||
0.458494 | + | 0.888697i | \(0.348389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 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 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.08100i | − | 0.158679i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6497 | 1.11207 | 0.556036 | − | 0.831158i | \(-0.312322\pi\) | ||||
0.556036 | + | 0.831158i | \(0.312322\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.2184 | −1.49299 | −0.746495 | − | 0.665391i | \(-0.768265\pi\) | ||||
−0.746495 | + | 0.665391i | \(0.768265\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.66589 | + | 41.4725i | 0.390690 | + | 2.11364i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 5.70905i | − | 0.289460i | −0.989471 | − | 0.144730i | \(-0.953769\pi\) | ||
0.989471 | − | 0.144730i | \(-0.0462314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.7971 | −1.50690 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.8134i | 2.05355i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.2760 | 0.666302 | 0.333151 | − | 0.942874i | \(-0.391888\pi\) | ||||
0.333151 | + | 0.942874i | \(0.391888\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.1452 | −1.30563 | −0.652815 | − | 0.757518i | \(-0.726412\pi\) | ||||
−0.652815 | + | 0.757518i | \(0.726412\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.1014 | −0.802066 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.4817i | 1.26308i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.5958i | − | 0.721715i | −0.932621 | − | 0.360857i | \(-0.882484\pi\) | ||
0.932621 | − | 0.360857i | \(-0.117516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.4067 | − | 2.66297i | 0.708908 | − | 0.131036i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 24.5566i | − | 1.20544i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 28.6124i | − | 1.39781i | −0.715216 | − | 0.698904i | \(-0.753672\pi\) | ||
0.715216 | − | 0.698904i | \(-0.246328\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.5115i | − | 0.609773i | −0.952389 | − | 0.304887i | \(-0.901381\pi\) | ||
0.952389 | − | 0.304887i | \(-0.0986186\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.9126i | 0.868890i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.22703 | + | 28.2783i | 0.252954 | + | 1.36848i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(0.346742\pi\) | ||||
−0.463086 | + | 0.886313i | \(0.653258\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.2760 | −0.815303 | −0.407652 | − | 0.913138i | \(-0.633652\pi\) | ||||
−0.407652 | + | 0.913138i | \(0.633652\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20336i | 0.0566639i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | \(0.0221904\pi\) | ||||
−0.997571 | + | 0.0696567i | \(0.977810\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.66822i | 0.401117i | 0.979682 | + | 0.200559i | \(0.0642757\pi\) | ||||
−0.979682 | + | 0.200559i | \(0.935724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.94419 | − | 10.5181i | −0.0897741 | − | 0.485679i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 60.7576 | 2.79364 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8716i | 0.636472i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.26523 | −0.194883 | −0.0974417 | − | 0.995241i | \(-0.531066\pi\) | ||||
−0.0974417 | + | 0.995241i | \(0.531066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 8.85181i | − | 0.403608i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.6990i | − | 0.576633i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.9419i | − | 1.03959i | −0.854290 | − | 0.519797i | \(-0.826007\pi\) | ||
0.854290 | − | 0.519797i | \(-0.173993\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.86925 | + | 0.530359i | −0.128703 | + | 0.0237899i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.54838 | −0.248380 | −0.124190 | − | 0.992258i | \(-0.539633\pi\) | ||||
−0.124190 | + | 0.992258i | \(0.539633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.26983 | 0.413321 | 0.206661 | − | 0.978413i | \(-0.433740\pi\) | ||||
0.206661 | + | 0.978413i | \(0.433740\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.66589 | 0.341128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 55.3290 | 2.43808 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.4067 | −1.16137 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 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 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 54.0941i | − | 2.35637i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.33411 | 0.144961 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.418022i | − | 0.0181065i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.08428 | −0.0901112 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5083i | 1.04982i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.28315 | 0.0548635 | 0.0274318 | − | 0.999624i | \(-0.491267\pi\) | ||||
0.0274318 | + | 0.999624i | \(0.491267\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.01576 | 0.341483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.3509 | − | 7.08888i | 1.63085 | − | 0.301450i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.7681i | 1.72740i | 0.504007 | + | 0.863700i | \(0.331859\pi\) | ||||
−0.504007 | + | 0.863700i | \(0.668141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.1060 | −0.892687 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.9442i | 0.840547i | 0.907397 | + | 0.420274i | \(0.138066\pi\) | ||||
−0.907397 | + | 0.420274i | \(0.861934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31.9442 | −1.34390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.8692 | −1.12642 | −0.563209 | − | 0.826315i | \(-0.690433\pi\) | ||||
−0.563209 | + | 0.826315i | \(0.690433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.7622 | −1.24551 | −0.622754 | − | 0.782418i | \(-0.713986\pi\) | ||||
−0.622754 | + | 0.782418i | \(0.713986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.8222i | 0.493021i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 30.7240i | − | 1.27906i | −0.768768 | − | 0.639528i | \(-0.779130\pi\) | ||
0.768768 | − | 0.639528i | \(-0.220870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.0749 | + | 4.26523i | −0.957310 | + | 0.176952i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 46.3509i | − | 1.91966i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.33178i | − | 0.137517i | −0.997633 | − | 0.0687586i | \(-0.978096\pi\) | ||
0.997633 | − | 0.0687586i | \(-0.0219038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 41.8906i | − | 1.72607i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | \(-0.912279\pi\) | ||
0.962266 | − | 0.272110i | \(-0.0877214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | 0 | ||||||||
\(610\) | 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 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.48165 | 0.301200 | 0.150600 | − | 0.988595i | \(-0.451879\pi\) | ||||
0.150600 | + | 0.988595i | \(0.451879\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1452i | 0.648931i | 0.945898 | + | 0.324465i | \(0.105184\pi\) | ||||
−0.945898 | + | 0.324465i | \(0.894816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.5061 | − | 6.56305i | 1.42252 | − | 0.262943i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2225 | −1.24890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.7385 | 1.18575 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00233i | 0.199140i | 0.995031 | + | 0.0995698i | \(0.0317467\pi\) | ||||
−0.995031 | + | 0.0995698i | \(0.968253\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 10.1499i | − | 0.402785i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0749 | + | 5.00460i | −0.518048 | + | 0.198289i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.5519 | −1.12773 | −0.563867 | − | 0.825866i | \(-0.690687\pi\) | ||||
−0.563867 | + | 0.825866i | \(0.690687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.27830i | − | 0.326464i | −0.986588 | − | 0.163232i | \(-0.947808\pi\) | ||
0.986588 | − | 0.163232i | \(-0.0521919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.9486 | 0.784259 | 0.392130 | − | 0.919910i | \(-0.371739\pi\) | ||||
0.392130 | + | 0.919910i | \(0.371739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 31.8814i | − | 1.25145i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 32.6825i | − | 1.27896i | −0.768806 | − | 0.639482i | \(-0.779149\pi\) | ||
0.768806 | − | 0.639482i | \(-0.220851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.66822i | 0.338695i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | \(-0.572958\pi\) | ||||
−0.227202 | + | 0.973848i | \(0.572958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 37.4817 | − | 6.92820i | 1.45348 | − | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.83153 | 0.264518 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9251i | 0.490276i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.40439 | 0.0531949 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 46.0940i | − | 1.74095i | −0.492215 | − | 0.870474i | \(-0.663812\pi\) | ||
0.492215 | − | 0.870474i | \(-0.336188\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.0296 | 0.868576 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 35.7017i | − | 1.33704i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.8814 | −1.19230 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.42919 | 0.127887 | 0.0639435 | − | 0.997954i | \(-0.479632\pi\) | ||||
0.0639435 | + | 0.997954i | \(0.479632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.61007 | − | 51.9906i | −0.357898 | − | 1.93623i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 70.9075i | − | 2.62261i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.1452 | −0.670209 | −0.335104 | − | 0.942181i | \(-0.608772\pi\) | ||||
−0.335104 | + | 0.942181i | \(0.608772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.2760 | −0.857381 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.1131 | 1.95380 | 0.976898 | − | 0.213705i | \(-0.0685532\pi\) | ||||
0.976898 | + | 0.213705i | \(0.0685532\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.362018 | + | 1.95852i | 0.0132278 | + | 0.0715628i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.61474i | 0.350847i | 0.984493 | + | 0.175423i | \(0.0561294\pi\) | ||||
−0.984493 | + | 0.175423i | \(0.943871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 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 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.0749i | 0.399893i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35.7286i | − | 1.28841i | −0.764855 | − | 0.644203i | \(-0.777189\pi\) | ||
0.764855 | − | 0.644203i | \(-0.222811\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.08756 | 0.0389659 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.34951i | 0.227203i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.54838 | + | 30.0168i | 0.197278 | + | 1.06727i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.7385 | −0.771957 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 55.2201i | 1.94868i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.9442 | − | 5.90464i | 1.12588 | − | 0.208111i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.6077 | −0.724530 | −0.362265 | − | 0.932075i | \(-0.617996\pi\) | ||||
−0.362265 | + | 0.932075i | \(0.617996\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.2201i | 1.23675i | 0.785884 | + | 0.618373i | \(0.212208\pi\) | ||||
−0.785884 | + | 0.618373i | \(0.787792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.8453 | −0.765208 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 54.9109i | − | 1.92109i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 34.1612i | − | 1.19224i | −0.802897 | − | 0.596118i | \(-0.796709\pi\) | ||
0.802897 | − | 0.596118i | \(-0.203291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.81110i | 0.272278i | 0.990690 | + | 0.136139i | \(0.0434694\pi\) | ||||
−0.990690 | + | 0.136139i | \(0.956531\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | \(-0.841090\pi\) | ||||
−0.877951 | + | 0.478750i | \(0.841090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.8134 | − | 43.9265i | −0.582551 | − | 1.52196i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.8564 | 0.479521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.2679 | −0.941394 | −0.470697 | − | 0.882295i | \(-0.655998\pi\) | ||||
−0.470697 | + | 0.882295i | \(0.655998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6269 | 0.918168 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.9186 | −0.857226 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.6508 | − | 57.6208i | −0.365965 | − | 1.97987i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.6272 | 0.672812 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.8692 | −1.19390 | −0.596950 | − | 0.802278i | \(-0.703621\pi\) | ||||
−0.596950 | + | 0.802278i | \(0.703621\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 84.8687i | − | 2.87897i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.08560 | 0.273970 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | \(-0.503287\pi\) | ||||
−0.0103249 | + | 0.999947i | \(0.503287\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.0545 | 1.37848 | 0.689238 | − | 0.724535i | \(-0.257945\pi\) | ||||
0.689238 | + | 0.724535i | \(0.257945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.53747 | + | 1.76293i | −0.319876 | + | 0.0591268i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.8656i | 0.798632i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.6397 | −0.957320 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.4021i | 0.413632i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.0941 | −1.80213 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.53747 | −0.184072 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.6681 | 1.38357 | 0.691784 | − | 0.722105i | \(-0.256825\pi\) | ||||
0.691784 | + | 0.722105i | \(0.256825\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.14521 | − | 1.50558i | 0.268979 | − | 0.0497187i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5398i | 0.479624i | 0.970819 | + | 0.239812i | \(0.0770858\pi\) | ||||
−0.970819 | + | 0.239812i | \(0.922914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.20569i | − | 0.0726011i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 11.7990i | − | 0.387948i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 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 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 107.109i | − | 3.50282i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.321348i | 0.0104980i | 0.999986 | + | 0.00524899i | \(0.00167081\pi\) | ||||
−0.999986 | + | 0.00524899i | \(0.998329\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.7432 | −1.22262 | −0.611310 | − | 0.791391i | \(-0.709357\pi\) | ||||
−0.611310 | + | 0.791391i | \(0.709357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.71704i | 0.314436i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.36875 | − | 50.6850i | −0.302533 | − | 1.63670i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.8134 | 1.09076 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.1261 | 1.19513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.4840i | 1.10893i | 0.832207 | + | 0.554465i | \(0.187077\pi\) | ||||
−0.832207 | + | 0.554465i | \(0.812923\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 50.9633i | − | 1.63549i | −0.575580 | − | 0.817745i | \(-0.695224\pi\) | ||
0.575580 | − | 0.817745i | \(-0.304776\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.1452 | − | 2.24495i | 0.389358 | − | 0.0719698i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.6124 | 1.49126 | 0.745631 | − | 0.666359i | \(-0.232148\pi\) | ||||
0.745631 | + | 0.666359i | \(0.232148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 78.5734i | − | 2.51122i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.31938 | 0.233452 | 0.116726 | − | 0.993164i | \(-0.462760\pi\) | ||||
0.116726 | + | 0.993164i | \(0.462760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.8069i | 0.503648i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 46.7985i | − | 1.48811i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 37.0917i | − | 1.17826i | −0.808039 | − | 0.589129i | \(-0.799471\pi\) | ||
0.808039 | − | 0.589129i | \(-0.200529\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.3149 | 0.422110 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.0191 | 1.67913 | 0.839566 | − | 0.543257i | \(-0.182809\pi\) | ||||
0.839566 | + | 0.543257i | \(0.182809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.p.k.1567.9 | 12 | ||
3.2 | odd | 2 | 1344.2.p.d.223.1 | yes | 12 | ||
4.3 | odd | 2 | inner | 4032.2.p.k.1567.12 | 12 | ||
7.6 | odd | 2 | 4032.2.p.j.1567.3 | 12 | |||
8.3 | odd | 2 | 4032.2.p.j.1567.4 | 12 | |||
8.5 | even | 2 | 4032.2.p.j.1567.1 | 12 | |||
12.11 | even | 2 | 1344.2.p.d.223.8 | yes | 12 | ||
21.20 | even | 2 | 1344.2.p.c.223.12 | yes | 12 | ||
24.5 | odd | 2 | 1344.2.p.c.223.11 | yes | 12 | ||
24.11 | even | 2 | 1344.2.p.c.223.6 | yes | 12 | ||
28.27 | even | 2 | 4032.2.p.j.1567.2 | 12 | |||
56.13 | odd | 2 | inner | 4032.2.p.k.1567.11 | 12 | ||
56.27 | even | 2 | inner | 4032.2.p.k.1567.10 | 12 | ||
84.83 | odd | 2 | 1344.2.p.c.223.5 | ✓ | 12 | ||
168.83 | odd | 2 | 1344.2.p.d.223.7 | yes | 12 | ||
168.125 | even | 2 | 1344.2.p.d.223.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.p.c.223.5 | ✓ | 12 | 84.83 | odd | 2 | ||
1344.2.p.c.223.6 | yes | 12 | 24.11 | even | 2 | ||
1344.2.p.c.223.11 | yes | 12 | 24.5 | odd | 2 | ||
1344.2.p.c.223.12 | yes | 12 | 21.20 | even | 2 | ||
1344.2.p.d.223.1 | yes | 12 | 3.2 | odd | 2 | ||
1344.2.p.d.223.2 | yes | 12 | 168.125 | even | 2 | ||
1344.2.p.d.223.7 | yes | 12 | 168.83 | odd | 2 | ||
1344.2.p.d.223.8 | yes | 12 | 12.11 | even | 2 | ||
4032.2.p.j.1567.1 | 12 | 8.5 | even | 2 | |||
4032.2.p.j.1567.2 | 12 | 28.27 | even | 2 | |||
4032.2.p.j.1567.3 | 12 | 7.6 | odd | 2 | |||
4032.2.p.j.1567.4 | 12 | 8.3 | odd | 2 | |||
4032.2.p.k.1567.9 | 12 | 1.1 | even | 1 | trivial | ||
4032.2.p.k.1567.10 | 12 | 56.27 | even | 2 | inner | ||
4032.2.p.k.1567.11 | 12 | 56.13 | odd | 2 | inner | ||
4032.2.p.k.1567.12 | 12 | 4.3 | odd | 2 | inner |