Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8820,2,Mod(881,8820)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8820, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8820.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8820.d (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: | \(70.4280545828\) |
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: | \( x^{12} - 2 x^{11} - 9 x^{10} + 58 x^{9} - 78 x^{8} - 298 x^{7} + 1341 x^{6} - 2086 x^{5} - 3822 x^{4} + \cdots + 117649 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 1260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(-2.61674 + 0.390758i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8820.881 |
Dual form | 8820.2.d.a.881.10 |
$q$-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 \(\left(\mathbb{Z}/8820\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(4411\) | \(7057\) | \(7841\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.51357i | − 0.757869i | −0.925423 | − | 0.378935i | \(-0.876291\pi\) | ||||
0.925423 | − | 0.378935i | \(-0.123709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.11077i | − 0.585422i | −0.956201 | − | 0.292711i | \(-0.905443\pi\) | ||||
0.956201 | − | 0.292711i | \(-0.0945574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.49464 | −1.09011 | −0.545056 | − | 0.838400i | \(-0.683491\pi\) | ||||
−0.545056 | + | 0.838400i | \(0.683491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.65308i | − 1.29691i | −0.761255 | − | 0.648453i | \(-0.775416\pi\) | ||||
0.761255 | − | 0.648453i | \(-0.224584\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 7.98438i | − 1.66486i | −0.554131 | − | 0.832429i | \(-0.686949\pi\) | ||||
0.554131 | − | 0.832429i | \(-0.313051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.97264i | − 0.923396i | −0.887037 | − | 0.461698i | \(-0.847240\pi\) | ||||
0.887037 | − | 0.461698i | \(-0.152760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.08341i | 1.27222i | 0.771599 | + | 0.636109i | \(0.219457\pi\) | ||||
−0.771599 | + | 0.636109i | \(0.780543\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.35170 | −1.53741 | −0.768705 | − | 0.639604i | \(-0.779098\pi\) | ||||
−0.768705 | + | 0.639604i | \(0.779098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.23347 | 0.973505 | 0.486752 | − | 0.873540i | \(-0.338181\pi\) | ||||
0.486752 | + | 0.873540i | \(0.338181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.47185 | 1.44444 | 0.722222 | − | 0.691661i | \(-0.243121\pi\) | ||||
0.722222 | + | 0.691661i | \(0.243121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4442 | 1.52344 | 0.761718 | − | 0.647909i | \(-0.224356\pi\) | ||||
0.761718 | + | 0.647909i | \(0.224356\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 7.48621i | − 1.02831i | −0.857697 | − | 0.514155i | \(-0.828106\pi\) | ||||
0.857697 | − | 0.514155i | \(-0.171894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.51357i | 0.338929i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.376420 | −0.0490057 | −0.0245028 | − | 0.999700i | \(-0.507800\pi\) | ||||
−0.0245028 | + | 0.999700i | \(0.507800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.71345i | 1.24368i | 0.783144 | + | 0.621840i | \(0.213615\pi\) | ||||
−0.783144 | + | 0.621840i | \(0.786385\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.11077i | 0.261809i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.75582 | −0.458846 | −0.229423 | − | 0.973327i | \(-0.573684\pi\) | ||||
−0.229423 | + | 0.973327i | \(0.573684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.01312i | 1.06966i | 0.844959 | + | 0.534831i | \(0.179625\pi\) | ||||
−0.844959 | + | 0.534831i | \(0.820375\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4.92308i | − 0.576203i | −0.957600 | − | 0.288101i | \(-0.906976\pi\) | ||||
0.957600 | − | 0.288101i | \(-0.0930240\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9443 | −1.79388 | −0.896940 | − | 0.442153i | \(-0.854215\pi\) | ||||
−0.896940 | + | 0.442153i | \(0.854215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.29871 | −0.252316 | −0.126158 | − | 0.992010i | \(-0.540265\pi\) | ||||
−0.126158 | + | 0.992010i | \(0.540265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.49464 | 0.487513 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.7086 | −1.87710 | −0.938551 | − | 0.345140i | \(-0.887832\pi\) | ||||
−0.938551 | + | 0.345140i | \(0.887832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65308i | 0.579994i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.14156i | 0.420512i | 0.977646 | + | 0.210256i | \(0.0674297\pi\) | ||||
−0.977646 | + | 0.210256i | \(0.932570\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.56986 | −0.852733 | −0.426366 | − | 0.904551i | \(-0.640207\pi\) | ||||
−0.426366 | + | 0.904551i | \(0.640207\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0791i | 1.19019i | 0.803655 | + | 0.595095i | \(0.202886\pi\) | ||||
−0.803655 | + | 0.595095i | \(0.797114\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 0.493607i | − 0.0477188i | −0.999715 | − | 0.0238594i | \(-0.992405\pi\) | ||||
0.999715 | − | 0.0238594i | \(-0.00759540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.78497 | −0.554099 | −0.277050 | − | 0.960856i | \(-0.589357\pi\) | ||||
−0.277050 | + | 0.960856i | \(0.589357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.0862i | 1.60733i | 0.595081 | + | 0.803666i | \(0.297120\pi\) | ||||
−0.595081 | + | 0.803666i | \(0.702880\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.98438i | 0.744547i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.68198 | 0.425634 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.65596 | 0.501885 | 0.250943 | − | 0.968002i | \(-0.419259\pi\) | ||||
0.250943 | + | 0.968002i | \(0.419259\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.10944 | 0.0969324 | 0.0484662 | − | 0.998825i | \(-0.484567\pi\) | ||||
0.0484662 | + | 0.998825i | \(0.484567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 0.0920200i | − 0.00786180i | −0.999992 | − | 0.00393090i | \(-0.998749\pi\) | ||||
0.999992 | − | 0.00393090i | \(-0.00125125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.75255i | 0.827200i | 0.910459 | + | 0.413600i | \(0.135729\pi\) | ||||
−0.910459 | + | 0.413600i | \(0.864271\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.30556 | −0.443673 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.97264i | 0.412955i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 13.8953i | − 1.13835i | −0.822217 | − | 0.569175i | \(-0.807263\pi\) | ||||
0.822217 | − | 0.569175i | \(-0.192737\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.0645 | −1.22593 | −0.612966 | − | 0.790109i | \(-0.710024\pi\) | ||||
−0.612966 | + | 0.790109i | \(0.710024\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 7.08341i | − 0.568953i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.65850i | − 0.212172i | −0.994357 | − | 0.106086i | \(-0.966168\pi\) | ||||
0.994357 | − | 0.106086i | \(-0.0338318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.18178 | 0.719172 | 0.359586 | − | 0.933112i | \(-0.382918\pi\) | ||||
0.359586 | + | 0.933112i | \(0.382918\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.0924548 | 0.00715437 | 0.00357718 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357718 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.54466 | 0.657281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.322546 | 0.0245227 | 0.0122614 | − | 0.999925i | \(-0.496097\pi\) | ||||
0.0122614 | + | 0.999925i | \(0.496097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 5.23898i | − 0.391580i | −0.980646 | − | 0.195790i | \(-0.937273\pi\) | ||||
0.980646 | − | 0.195790i | \(-0.0627271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 20.3013i | − 1.50898i | −0.656310 | − | 0.754491i | \(-0.727884\pi\) | ||||
0.656310 | − | 0.754491i | \(-0.272116\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.35170 | 0.687550 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.2976i | 0.826162i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 8.60874i | − 0.622906i | −0.950261 | − | 0.311453i | \(-0.899184\pi\) | ||||
0.950261 | − | 0.311453i | \(-0.100816\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.93953 | 0.355555 | 0.177777 | − | 0.984071i | \(-0.443109\pi\) | ||||
0.177777 | + | 0.984071i | \(0.443109\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 7.78952i | − 0.554980i | −0.960729 | − | 0.277490i | \(-0.910497\pi\) | ||||
0.960729 | − | 0.277490i | \(-0.0895025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3381i | 1.08729i | 0.839316 | + | 0.543644i | \(0.182956\pi\) | ||||
−0.839316 | + | 0.543644i | \(0.817044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.23347 | −0.435365 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.2094 | −0.982885 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4987 | −1.20466 | −0.602329 | − | 0.798248i | \(-0.705761\pi\) | ||||
−0.602329 | + | 0.798248i | \(0.705761\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.47185 | −0.645975 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.48715i | 0.638175i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.4665i | 1.50447i | 0.658897 | + | 0.752234i | \(0.271023\pi\) | ||||
−0.658897 | + | 0.752234i | \(0.728977\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.20190 | 0.478007 | 0.239003 | − | 0.971019i | \(-0.423179\pi\) | ||||
0.239003 | + | 0.971019i | \(0.423179\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.7806i | 0.910645i | 0.890327 | + | 0.455323i | \(0.150476\pi\) | ||||
−0.890327 | + | 0.455323i | \(0.849524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.0572919i | 0.00375332i | 0.999998 | + | 0.00187666i | \(0.000597359\pi\) | ||||
−0.999998 | + | 0.00187666i | \(0.999403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.4442 | −0.681301 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 24.9150i | − 1.61162i | −0.592177 | − | 0.805808i | \(-0.701731\pi\) | ||||
0.592177 | − | 0.805808i | \(-0.298269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 21.5658i | − 1.38917i | −0.719409 | − | 0.694586i | \(-0.755587\pi\) | ||||
0.719409 | − | 0.694586i | \(-0.244413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.9323 | −0.759237 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6047 | −0.984962 | −0.492481 | − | 0.870323i | \(-0.663910\pi\) | ||||
−0.492481 | + | 0.870323i | \(0.663910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0693 | −1.26174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.8186 | −1.79766 | −0.898829 | − | 0.438300i | \(-0.855581\pi\) | ||||
−0.898829 | + | 0.438300i | \(0.855581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 31.5341i | − 1.94448i | −0.233994 | − | 0.972238i | \(-0.575180\pi\) | ||||
0.233994 | − | 0.972238i | \(-0.424820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.48621i | 0.459874i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.6359 | 1.92888 | 0.964438 | − | 0.264310i | \(-0.0851442\pi\) | ||||
0.964438 | + | 0.264310i | \(0.0851442\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.12729i | 0.372206i | 0.982530 | + | 0.186103i | \(0.0595858\pi\) | ||||
−0.982530 | + | 0.186103i | \(0.940414\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.51357i | − 0.151574i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7027 | −1.00357 | −0.501785 | − | 0.864992i | \(-0.667323\pi\) | ||||
−0.501785 | + | 0.864992i | \(0.667323\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.24284i | 0.372416i | 0.982510 | + | 0.186208i | \(0.0596199\pi\) | ||||
−0.982510 | + | 0.186208i | \(0.940380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.27390i | − 0.254057i | −0.991899 | − | 0.127028i | \(-0.959456\pi\) | ||||
0.991899 | − | 0.127028i | \(-0.0405440\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.20183 | 0.188343 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.5954 | 1.14478 | 0.572388 | − | 0.819983i | \(-0.306017\pi\) | ||||
0.572388 | + | 0.819983i | \(0.306017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.376420 | 0.0219160 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.8532 | −0.974644 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 9.71345i | − 0.556191i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7.74134i | − 0.441822i | −0.975294 | − | 0.220911i | \(-0.929097\pi\) | ||||
0.975294 | − | 0.220911i | \(-0.0709030\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.2244 | −0.806594 | −0.403297 | − | 0.915069i | \(-0.632136\pi\) | ||||
−0.403297 | + | 0.915069i | \(0.632136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0156i | 1.30092i | 0.759541 | + | 0.650460i | \(0.225424\pi\) | ||||
−0.759541 | + | 0.650460i | \(0.774576\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.72932i | − 0.209460i | −0.994501 | − | 0.104730i | \(-0.966602\pi\) | ||||
0.994501 | − | 0.104730i | \(-0.0333978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.4991 | −0.699814 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4086i | 1.41377i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.11077i | − 0.117084i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.5661 | −1.68006 | −0.840032 | − | 0.542537i | \(-0.817464\pi\) | ||||
−0.840032 | + | 0.542537i | \(0.817464\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.75582 | 0.205202 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.06846 | −0.221623 | −0.110812 | − | 0.993841i | \(-0.535345\pi\) | ||||
−0.110812 | + | 0.993841i | \(0.535345\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.8046 | 0.964175 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 21.6590i | − 1.16272i | −0.813648 | − | 0.581358i | \(-0.802522\pi\) | ||||
0.813648 | − | 0.581358i | \(-0.197478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3.23900i | − 0.173380i | −0.996235 | − | 0.0866900i | \(-0.972371\pi\) | ||||
0.996235 | − | 0.0866900i | \(-0.0276290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.95513 | 0.263735 | 0.131868 | − | 0.991267i | \(-0.457903\pi\) | ||||
0.131868 | + | 0.991267i | \(0.457903\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 9.01312i | − 0.478367i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.4123i | 1.23566i | 0.786313 | + | 0.617828i | \(0.211987\pi\) | ||||
−0.786313 | + | 0.617828i | \(0.788013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9573 | −0.681964 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.92308i | 0.257686i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 14.0977i | − 0.735896i | −0.929846 | − | 0.367948i | \(-0.880061\pi\) | ||||
0.929846 | − | 0.367948i | \(-0.119939\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.7643 | −1.17869 | −0.589345 | − | 0.807882i | \(-0.700614\pi\) | ||||
−0.589345 | + | 0.807882i | \(0.700614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.4961 | −0.540576 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.4861 | 1.20640 | 0.603200 | − | 0.797590i | \(-0.293892\pi\) | ||||
0.603200 | + | 0.797590i | \(0.293892\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.5996 | −1.25698 | −0.628490 | − | 0.777818i | \(-0.716327\pi\) | ||||
−0.628490 | + | 0.777818i | \(0.716327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.5993i | 1.19653i | 0.801297 | + | 0.598267i | \(0.204144\pi\) | ||||
−0.801297 | + | 0.598267i | \(0.795856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.8869i | 1.81488i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.9443 | 0.802247 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.0624i | 1.05709i | 0.848905 | + | 0.528545i | \(0.177262\pi\) | ||||
−0.848905 | + | 0.528545i | \(0.822738\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 13.7091i | − 0.684601i | −0.939591 | − | 0.342300i | \(-0.888794\pi\) | ||||
0.939591 | − | 0.342300i | \(-0.111206\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.9514 | 0.744784 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.5061i | 1.16516i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7044i | 0.677638i | 0.940852 | + | 0.338819i | \(0.110027\pi\) | ||||
−0.940852 | + | 0.338819i | \(0.889973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.29871 | 0.112839 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.10776 | 0.102971 | 0.0514855 | − | 0.998674i | \(-0.483604\pi\) | ||||
0.0514855 | + | 0.998674i | \(0.483604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3265 | 0.600756 | 0.300378 | − | 0.953820i | \(-0.402887\pi\) | ||||
0.300378 | + | 0.953820i | \(0.402887\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.49464 | −0.218022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.26225i | 0.157137i | 0.996909 | + | 0.0785685i | \(0.0250349\pi\) | ||||
−0.996909 | + | 0.0785685i | \(0.974965\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.4147i | 0.933013i | 0.884518 | + | 0.466506i | \(0.154488\pi\) | ||||
−0.884518 | + | 0.466506i | \(0.845512\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45.1363 | −2.15916 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 5.50383i | − 0.262683i | −0.991337 | − | 0.131342i | \(-0.958071\pi\) | ||||
0.991337 | − | 0.131342i | \(-0.0419285\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 26.7064i | − 1.26886i | −0.772981 | − | 0.634430i | \(-0.781235\pi\) | ||||
0.772981 | − | 0.634430i | \(-0.218765\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.7086 | 0.839466 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.96668i | 0.140006i | 0.997547 | + | 0.0700031i | \(0.0223009\pi\) | ||||
−0.997547 | + | 0.0700031i | \(0.977699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 15.6683i | − 0.737789i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.7057 | 1.29602 | 0.648010 | − | 0.761632i | \(-0.275601\pi\) | ||||
0.648010 | + | 0.761632i | \(0.275601\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.3720 | −1.83374 | −0.916868 | − | 0.399190i | \(-0.869291\pi\) | ||||
−0.916868 | + | 0.399190i | \(0.869291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.64212 | 0.448107 | 0.224054 | − | 0.974577i | \(-0.428071\pi\) | ||||
0.224054 | + | 0.974577i | \(0.428071\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.598126 | 0.0276780 | 0.0138390 | − | 0.999904i | \(-0.495595\pi\) | ||||
0.0138390 | + | 0.999904i | \(0.495595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 23.8081i | − 1.09470i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.65308i | − 0.259381i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5669 | −0.848343 | −0.424171 | − | 0.905582i | \(-0.639435\pi\) | ||||
−0.424171 | + | 0.905582i | \(0.639435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.7393i | 0.900033i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.14156i | − 0.188059i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.883324 | 0.0400272 | 0.0200136 | − | 0.999800i | \(-0.493629\pi\) | ||||
0.0200136 | + | 0.999800i | \(0.493629\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 6.63816i | − 0.299576i | −0.988718 | − | 0.149788i | \(-0.952141\pi\) | ||||
0.988718 | − | 0.149788i | \(-0.0478591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3503i | 1.00660i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8780 | −1.42705 | −0.713527 | − | 0.700627i | \(-0.752904\pi\) | ||||
−0.713527 | + | 0.700627i | \(0.752904\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.2668 | −1.12659 | −0.563294 | − | 0.826256i | \(-0.690466\pi\) | ||||
−0.563294 | + | 0.826256i | \(0.690466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.56986 | 0.381354 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.6705 | −0.827554 | −0.413777 | − | 0.910378i | \(-0.635791\pi\) | ||||
−0.413777 | + | 0.910378i | \(0.635791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 12.0791i | − 0.532269i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 26.2521i | − 1.15457i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.72658 | −0.338508 | −0.169254 | − | 0.985572i | \(-0.554136\pi\) | ||||
−0.169254 | + | 0.985572i | \(0.554136\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8777i | 0.606830i | 0.952859 | + | 0.303415i | \(0.0981268\pi\) | ||||
−0.952859 | + | 0.303415i | \(0.901873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 31.8374i | − 1.38686i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −40.7503 | −1.77175 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13.1574i | − 0.569911i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.493607i | 0.0213405i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.1678 | −1.46899 | −0.734495 | − | 0.678614i | \(-0.762581\pi\) | ||||
−0.734495 | + | 0.678614i | \(0.762581\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.78497 | 0.247801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.3564 | −0.742105 | −0.371052 | − | 0.928612i | \(-0.621003\pi\) | ||||
−0.371052 | + | 0.928612i | \(0.621003\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.1107 | −1.19756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.1372i | 0.895613i | 0.894130 | + | 0.447807i | \(0.147795\pi\) | ||||
−0.894130 | + | 0.447807i | \(0.852205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 19.9929i | − 0.845609i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.90359 | 0.333096 | 0.166548 | − | 0.986033i | \(-0.446738\pi\) | ||||
0.166548 | + | 0.986033i | \(0.446738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 17.0862i | − 0.718820i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.3161i | 1.39669i | 0.715764 | + | 0.698343i | \(0.246079\pi\) | ||||
−0.715764 | + | 0.698343i | \(0.753921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4241 | −1.18951 | −0.594756 | − | 0.803906i | \(-0.702751\pi\) | ||||
−0.594756 | + | 0.803906i | \(0.702751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 7.98438i | − 0.332972i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.9889i | 0.998671i | 0.866409 | + | 0.499335i | \(0.166422\pi\) | ||||
−0.866409 | + | 0.499335i | \(0.833578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.8171 | −0.779324 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.3522 | −1.21150 | −0.605748 | − | 0.795656i | \(-0.707126\pi\) | ||||
−0.605748 | + | 0.795656i | \(0.707126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.0431 | 1.64995 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.1757 | 1.03384 | 0.516922 | − | 0.856033i | \(-0.327078\pi\) | ||||
0.516922 | + | 0.856033i | \(0.327078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.2416i | 0.622753i | 0.950287 | + | 0.311377i | \(0.100790\pi\) | ||||
−0.950287 | + | 0.311377i | \(0.899210\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 35.1651i | − 1.43441i | −0.696861 | − | 0.717206i | \(-0.745421\pi\) | ||||
0.696861 | − | 0.717206i | \(-0.254579\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.68198 | −0.190349 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.0440i | 1.01650i | 0.861208 | + | 0.508252i | \(0.169708\pi\) | ||||
−0.861208 | + | 0.508252i | \(0.830292\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 22.0452i | − 0.891853i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.9794 | −0.483843 | −0.241921 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241921 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.8763i | 1.04174i | 0.853635 | + | 0.520871i | \(0.174393\pi\) | ||||
−0.853635 | + | 0.520871i | \(0.825607\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.81737i | 0.0730462i | 0.999333 | + | 0.0365231i | \(0.0116282\pi\) | ||||
−0.999333 | + | 0.0365231i | \(0.988372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.0325 | 1.67595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.129106 | 0.00513962 | 0.00256981 | − | 0.999997i | \(-0.499182\pi\) | ||||
0.00256981 | + | 0.999997i | \(0.499182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.65596 | −0.224450 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 33.1739i | − 1.31029i | −0.755503 | − | 0.655145i | \(-0.772608\pi\) | ||||
0.755503 | − | 0.655145i | \(-0.227392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.44358i | 0.0963653i | 0.998839 | + | 0.0481827i | \(0.0153430\pi\) | ||||
−0.998839 | + | 0.0481827i | \(0.984657\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.03938 | 0.237433 | 0.118716 | − | 0.992928i | \(-0.462122\pi\) | ||||
0.118716 | + | 0.992928i | \(0.462122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.946156i | 0.0371399i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 35.8589i | − 1.40327i | −0.712539 | − | 0.701633i | \(-0.752455\pi\) | ||||
0.712539 | − | 0.701633i | \(-0.247545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.10944 | −0.0433495 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3494i | 0.792702i | 0.918099 | + | 0.396351i | \(0.129724\pi\) | ||||
−0.918099 | + | 0.396351i | \(0.870276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.79588i | 0.303225i | 0.988440 | + | 0.151612i | \(0.0484465\pi\) | ||||
−0.988440 | + | 0.151612i | \(0.951553\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.7035 | −1.53732 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.4154 | 0.942547 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3705 | 0.631035 | 0.315517 | − | 0.948920i | \(-0.397822\pi\) | ||||
0.315517 | + | 0.948920i | \(0.397822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.34647 | −0.320781 | −0.160390 | − | 0.987054i | \(-0.551275\pi\) | ||||
−0.160390 | + | 0.987054i | \(0.551275\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.8039i | 0.413401i | 0.978404 | + | 0.206700i | \(0.0662725\pi\) | ||||
−0.978404 | + | 0.206700i | \(0.933728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0920200i | 0.00351590i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.8017 | −0.601995 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.53189i | 0.172401i | 0.996278 | + | 0.0862006i | \(0.0274726\pi\) | ||||
−0.996278 | + | 0.0862006i | \(0.972527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 9.75255i | − 0.369935i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0172 | −1.06123 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.7665i | 1.27534i | 0.770309 | + | 0.637671i | \(0.220102\pi\) | ||||
−0.770309 | + | 0.637671i | \(0.779898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.8659i | 1.99387i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0261738 | 0.000982978 0 | 0.000491489 | − | 1.00000i | \(-0.499844\pi\) | ||||
0.000491489 | 1.00000i | \(0.499844\pi\) | ||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 56.5566 | 2.11806 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.30556 | 0.198417 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.5721 | 1.06556 | 0.532780 | − | 0.846254i | \(-0.321147\pi\) | ||||
0.532780 | + | 0.846254i | \(0.321147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 4.97264i | − 0.184679i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.4387i | 1.24017i | 0.784533 | + | 0.620087i | \(0.212903\pi\) | ||||
−0.784533 | + | 0.620087i | \(0.787097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.5726 | −1.57460 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 20.1801i | − 0.745367i | −0.927958 | − | 0.372684i | \(-0.878438\pi\) | ||||
0.927958 | − | 0.372684i | \(-0.121562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.44050i | 0.347745i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.69879 | 0.356776 | 0.178388 | − | 0.983960i | \(-0.442912\pi\) | ||||
0.178388 | + | 0.983960i | \(0.442912\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 44.3997i | − 1.62887i | −0.580256 | − | 0.814434i | \(-0.697048\pi\) | ||||
0.580256 | − | 0.814434i | \(-0.302952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.8953i | 0.509085i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3681 | 0.816222 | 0.408111 | − | 0.912932i | \(-0.366188\pi\) | ||||
0.408111 | + | 0.912932i | \(0.366188\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0645 | 0.548253 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.9667 | 1.85242 | 0.926209 | − | 0.377011i | \(-0.123048\pi\) | ||||
0.926209 | + | 0.377011i | \(0.123048\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.2656 | 1.42338 | 0.711688 | − | 0.702495i | \(-0.247931\pi\) | ||||
0.711688 | + | 0.702495i | \(0.247931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.794535i | 0.0286890i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 3.86290i | − 0.139300i | −0.997572 | − | 0.0696498i | \(-0.977812\pi\) | ||||
0.997572 | − | 0.0696498i | \(-0.0221882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.4514 | 1.74267 | 0.871337 | − | 0.490684i | \(-0.163253\pi\) | ||||
0.871337 | + | 0.490684i | \(0.163253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.08341i | 0.254444i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 35.2383i | − 1.26254i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6551 | 0.810663 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.65850i | 0.0948860i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.1961i | 0.648619i | 0.945951 | + | 0.324310i | \(0.105132\pi\) | ||||
−0.945951 | + | 0.324310i | \(0.894868\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.5029 | 0.728078 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.3824 | 1.07620 | 0.538100 | − | 0.842881i | \(-0.319142\pi\) | ||||
0.538100 | + | 0.842881i | \(0.319142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.9427 | −1.66071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.3745 | −0.436686 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 51.7468i | − 1.81932i | −0.415354 | − | 0.909660i | \(-0.636342\pi\) | ||||
0.415354 | − | 0.909660i | \(-0.363658\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.2500i | 0.675958i | 0.941154 | + | 0.337979i | \(0.109743\pi\) | ||||
−0.941154 | + | 0.337979i | \(0.890257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.18178 | −0.321624 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 53.5451i | − 1.87331i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.1311i | 1.78449i | 0.451554 | + | 0.892244i | \(0.350870\pi\) | ||||
−0.451554 | + | 0.892244i | \(0.649130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.1691 | 1.46992 | 0.734962 | − | 0.678108i | \(-0.237200\pi\) | ||||
0.734962 | + | 0.678108i | \(0.237200\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.16301i | 0.179536i | 0.995963 | + | 0.0897678i | \(0.0286125\pi\) | ||||
−0.995963 | + | 0.0897678i | \(0.971388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 33.8307i | − 1.17499i | −0.809229 | − | 0.587494i | \(-0.800115\pi\) | ||||
0.809229 | − | 0.587494i | \(-0.199885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.0924548 | −0.00319953 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.5450 | −0.985483 | −0.492741 | − | 0.870176i | \(-0.664005\pi\) | ||||
−0.492741 | + | 0.870176i | \(0.664005\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.27283 | 0.147339 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.54466 | −0.293945 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 74.6675i | 2.55957i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 22.2041i | − 0.760252i | −0.924935 | − | 0.380126i | \(-0.875881\pi\) | ||||
0.924935 | − | 0.380126i | \(-0.124119\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.8369 | 0.575136 | 0.287568 | − | 0.957760i | \(-0.407153\pi\) | ||||
0.287568 | + | 0.957760i | \(0.407153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.2471i | 1.64617i | 0.567918 | + | 0.823085i | \(0.307749\pi\) | ||||
−0.567918 | + | 0.823085i | \(0.692251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 14.8184i | − 0.504425i | −0.967672 | − | 0.252213i | \(-0.918842\pi\) | ||||
0.967672 | − | 0.252213i | \(-0.0811582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.322546 | −0.0109669 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.0772i | 1.35953i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.92766i | 0.268618i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.2342 | −0.413120 | −0.206560 | − | 0.978434i | \(-0.566227\pi\) | ||||
−0.206560 | + | 0.978434i | \(0.566227\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7904 | −1.34057 | −0.670286 | − | 0.742103i | \(-0.733828\pi\) | ||||
−0.670286 | + | 0.742103i | \(0.733828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7168 | −1.16831 | −0.584156 | − | 0.811641i | \(-0.698574\pi\) | ||||
−0.584156 | + | 0.811641i | \(0.698574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.944675 | 0.0317191 | 0.0158595 | − | 0.999874i | \(-0.494952\pi\) | ||||
0.0158595 | + | 0.999874i | \(0.494952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 59.0416i | − 1.97575i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.23898i | 0.175120i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.2233 | 1.17476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.6478i | 1.12097i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.3013i | 0.674837i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.7762 | 0.822680 | 0.411340 | − | 0.911482i | \(-0.365061\pi\) | ||||
0.411340 | + | 0.911482i | \(0.365061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 14.5204i | − 0.481083i | −0.970639 | − | 0.240542i | \(-0.922675\pi\) | ||||
0.970639 | − | 0.240542i | \(-0.0773251\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.77795i | 0.191222i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.99364 | 0.230699 | 0.115350 | − | 0.993325i | \(-0.463201\pi\) | ||||
0.115350 | + | 0.993325i | \(0.463201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.0246 | 0.626203 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.35170 | −0.307482 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.7631 | 0.484360 | 0.242180 | − | 0.970231i | \(-0.422137\pi\) | ||||
0.242180 | + | 0.970231i | \(0.422137\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 11.2976i | − 0.369471i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.8385i | 1.59549i | 0.602998 | + | 0.797743i | \(0.293973\pi\) | ||||
−0.602998 | + | 0.797743i | \(0.706027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.0184 | −0.913372 | −0.456686 | − | 0.889628i | \(-0.650964\pi\) | ||||
−0.456686 | + | 0.889628i | \(0.650964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 49.7704i | − 1.62075i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.56957i | 0.0834997i | 0.999128 | + | 0.0417499i | \(0.0132933\pi\) | ||||
−0.999128 | + | 0.0417499i | \(0.986707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.3915 | −0.337322 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 12.9268i | − 0.418740i | −0.977837 | − | 0.209370i | \(-0.932859\pi\) | ||||
0.977837 | − | 0.209370i | \(-0.0671413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.60874i | 0.278572i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1747 | −0.618539 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.93953 | −0.159009 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.4481 | −0.914829 | −0.457414 | − | 0.889254i | \(-0.651224\pi\) | ||||
−0.457414 | + | 0.889254i | \(0.651224\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.9150 | −0.992109 | −0.496054 | − | 0.868291i | \(-0.665218\pi\) | ||||
−0.496054 | + | 0.868291i | \(0.665218\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.5984i | 1.61879i | 0.587267 | + | 0.809393i | \(0.300204\pi\) | ||||
−0.587267 | + | 0.809393i | \(0.699796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.5116i | 1.42260i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.1839 | 0.739453 | 0.369726 | − | 0.929141i | \(-0.379451\pi\) | ||||
0.369726 | + | 0.929141i | \(0.379451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.78952i | 0.248195i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 75.6269i | − 2.40479i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.3189 | −0.518388 | −0.259194 | − | 0.965825i | \(-0.583457\pi\) | ||||
−0.259194 | + | 0.965825i | \(0.583457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 15.3381i | − 0.486250i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 55.1372i | − 1.74621i | −0.487531 | − | 0.873106i | \(-0.662102\pi\) | ||||
0.487531 | − | 0.873106i | \(-0.337898\pi\) | |||||||
\(998\) | 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 | 8820.2.d.a.881.3 | 12 | ||
3.2 | odd | 2 | 8820.2.d.b.881.10 | 12 | |||
7.4 | even | 3 | 1260.2.cg.b.341.2 | yes | 12 | ||
7.5 | odd | 6 | 1260.2.cg.a.521.2 | yes | 12 | ||
7.6 | odd | 2 | 8820.2.d.b.881.3 | 12 | |||
21.5 | even | 6 | 1260.2.cg.b.521.2 | yes | 12 | ||
21.11 | odd | 6 | 1260.2.cg.a.341.2 | ✓ | 12 | ||
21.20 | even | 2 | inner | 8820.2.d.a.881.10 | 12 | ||
35.4 | even | 6 | 6300.2.ch.b.1601.5 | 12 | |||
35.12 | even | 12 | 6300.2.dd.c.4049.9 | 24 | |||
35.18 | odd | 12 | 6300.2.dd.b.1349.9 | 24 | |||
35.19 | odd | 6 | 6300.2.ch.c.4301.5 | 12 | |||
35.32 | odd | 12 | 6300.2.dd.b.1349.4 | 24 | |||
35.33 | even | 12 | 6300.2.dd.c.4049.4 | 24 | |||
105.32 | even | 12 | 6300.2.dd.c.1349.4 | 24 | |||
105.47 | odd | 12 | 6300.2.dd.b.4049.9 | 24 | |||
105.53 | even | 12 | 6300.2.dd.c.1349.9 | 24 | |||
105.68 | odd | 12 | 6300.2.dd.b.4049.4 | 24 | |||
105.74 | odd | 6 | 6300.2.ch.c.1601.5 | 12 | |||
105.89 | even | 6 | 6300.2.ch.b.4301.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.cg.a.341.2 | ✓ | 12 | 21.11 | odd | 6 | ||
1260.2.cg.a.521.2 | yes | 12 | 7.5 | odd | 6 | ||
1260.2.cg.b.341.2 | yes | 12 | 7.4 | even | 3 | ||
1260.2.cg.b.521.2 | yes | 12 | 21.5 | even | 6 | ||
6300.2.ch.b.1601.5 | 12 | 35.4 | even | 6 | |||
6300.2.ch.b.4301.5 | 12 | 105.89 | even | 6 | |||
6300.2.ch.c.1601.5 | 12 | 105.74 | odd | 6 | |||
6300.2.ch.c.4301.5 | 12 | 35.19 | odd | 6 | |||
6300.2.dd.b.1349.4 | 24 | 35.32 | odd | 12 | |||
6300.2.dd.b.1349.9 | 24 | 35.18 | odd | 12 | |||
6300.2.dd.b.4049.4 | 24 | 105.68 | odd | 12 | |||
6300.2.dd.b.4049.9 | 24 | 105.47 | odd | 12 | |||
6300.2.dd.c.1349.4 | 24 | 105.32 | even | 12 | |||
6300.2.dd.c.1349.9 | 24 | 105.53 | even | 12 | |||
6300.2.dd.c.4049.4 | 24 | 35.33 | even | 12 | |||
6300.2.dd.c.4049.9 | 24 | 35.12 | even | 12 | |||
8820.2.d.a.881.3 | 12 | 1.1 | even | 1 | trivial | ||
8820.2.d.a.881.10 | 12 | 21.20 | even | 2 | inner | ||
8820.2.d.b.881.3 | 12 | 7.6 | odd | 2 | |||
8820.2.d.b.881.10 | 12 | 3.2 | odd | 2 |