Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1889,4032)]
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([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.i (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: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.20 | ||
Character | \(\chi\) | \(=\) | 4032.1889 |
Dual form | 4032.2.i.c.1889.19 |
$q$-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 | ||||||||
\(5\) | 1.77767i | 0.795000i | 0.917602 | + | 0.397500i | \(0.130122\pi\) | ||||
−0.917602 | + | 0.397500i | \(0.869878\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.39248 | − | 1.12962i | −0.904272 | − | 0.426957i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.85226 | 1.16150 | 0.580749 | − | 0.814082i | \(-0.302760\pi\) | ||||
0.580749 | + | 0.814082i | \(0.302760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.59329 | −1.82865 | −0.914324 | − | 0.404983i | \(-0.867277\pi\) | ||||
−0.914324 | + | 0.404983i | \(0.867277\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.56507 | 1.10719 | 0.553596 | − | 0.832785i | \(-0.313255\pi\) | ||||
0.553596 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.05080 | −0.241069 | −0.120535 | − | 0.992709i | \(-0.538461\pi\) | ||||
−0.120535 | + | 0.992709i | \(0.538461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.0946494i | − | 0.0197358i | −0.999951 | − | 0.00986789i | \(-0.996859\pi\) | ||
0.999951 | − | 0.00986789i | \(-0.00314110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.83988 | 0.367976 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.31746 | −0.801733 | −0.400866 | − | 0.916137i | \(-0.631291\pi\) | ||||
−0.400866 | + | 0.916137i | \(0.631291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.07928i | − | 0.732660i | −0.930485 | − | 0.366330i | \(-0.880614\pi\) | ||
0.930485 | − | 0.366330i | \(-0.119386\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00810 | − | 4.25305i | 0.339430 | − | 0.718896i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.65110i | − | 0.764637i | −0.924031 | − | 0.382318i | \(-0.875126\pi\) | ||
0.924031 | − | 0.382318i | \(-0.124874\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.5851 | −1.80929 | −0.904645 | − | 0.426165i | \(-0.859864\pi\) | ||||
−0.904645 | + | 0.426165i | \(0.859864\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.28779i | 0.958879i | 0.877575 | + | 0.479440i | \(0.159160\pi\) | ||||
−0.877575 | + | 0.479440i | \(0.840840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.12926 | 0.894045 | 0.447022 | − | 0.894523i | \(-0.352484\pi\) | ||||
0.447022 | + | 0.894523i | \(0.352484\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.44791 | + | 5.40519i | 0.635416 | + | 0.772170i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | −0.336463 | −0.168232 | − | 0.985747i | \(-0.553806\pi\) | ||||
−0.168232 | + | 0.985747i | \(0.553806\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.84805i | 0.923391i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 13.1781i | − | 1.71564i | −0.513950 | − | 0.857820i | \(-0.671818\pi\) | ||
0.513950 | − | 0.857820i | \(-0.328182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.58881 | 0.587537 | 0.293769 | − | 0.955877i | \(-0.405091\pi\) | ||||
0.293769 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 11.7207i | − | 1.45377i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.83988i | 0.591285i | 0.955299 | + | 0.295643i | \(0.0955337\pi\) | ||||
−0.955299 | + | 0.295643i | \(0.904466\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.5713i | − | 1.37326i | −0.727008 | − | 0.686629i | \(-0.759090\pi\) | ||
0.727008 | − | 0.686629i | \(-0.240910\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.25280i | − | 0.263670i | −0.991272 | − | 0.131835i | \(-0.957913\pi\) | ||
0.991272 | − | 0.131835i | \(-0.0420869\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.21644 | − | 4.35159i | −1.05031 | − | 0.495910i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.2210 | 1.59999 | 0.799995 | − | 0.600007i | \(-0.204835\pi\) | ||||
0.799995 | + | 0.600007i | \(0.204835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6162i | 1.16528i | 0.812731 | + | 0.582639i | \(0.197980\pi\) | ||||
−0.812731 | + | 0.582639i | \(0.802020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.11521i | 0.880218i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.61301 | −0.912977 | −0.456489 | − | 0.889729i | \(-0.650893\pi\) | ||||
−0.456489 | + | 0.889729i | \(0.650893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.7743 | + | 7.44791i | 1.65360 | + | 0.780753i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.86797i | − | 0.191650i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.2822i | − | 1.45014i | −0.688675 | − | 0.725070i | \(-0.741807\pi\) | ||
0.688675 | − | 0.725070i | \(-0.258193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 5.33302i | − | 0.530655i | −0.964158 | − | 0.265328i | \(-0.914520\pi\) | ||
0.964158 | − | 0.265328i | \(-0.0854801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.1353i | − | 1.39279i | −0.717657 | − | 0.696397i | \(-0.754785\pi\) | ||
0.717657 | − | 0.696397i | \(-0.245215\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5730 | 1.50550 | 0.752748 | − | 0.658309i | \(-0.228728\pi\) | ||||
0.752748 | + | 0.658309i | \(0.228728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.0340i | − | 1.24843i | −0.781252 | − | 0.624216i | \(-0.785418\pi\) | ||
0.781252 | − | 0.624216i | \(-0.214582\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.9633i | − | 1.50171i | −0.660470 | − | 0.750853i | \(-0.729643\pi\) | ||
0.660470 | − | 0.750853i | \(-0.270357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.168256 | 0.0156899 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.9218 | − | 5.15680i | −1.00120 | − | 0.472723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.83988 | 0.349080 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1591i | 1.08754i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.27710 | 0.202060 | 0.101030 | − | 0.994883i | \(-0.467786\pi\) | ||||
0.101030 | + | 0.994883i | \(0.467786\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.624051i | 0.0545236i | 0.999628 | + | 0.0272618i | \(0.00867877\pi\) | ||||
−0.999628 | + | 0.0272618i | \(0.991321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.51401 | + | 1.18700i | 0.217992 | + | 0.102926i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.1826i | − | 1.29714i | −0.761157 | − | 0.648568i | \(-0.775368\pi\) | ||
0.761157 | − | 0.648568i | \(-0.224632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9120 | −1.09518 | −0.547590 | − | 0.836747i | \(-0.684454\pi\) | ||||
−0.547590 | + | 0.836747i | \(0.684454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.3990 | −2.12397 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.67504i | − | 0.637377i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.02714 | 0.739532 | 0.369766 | − | 0.929125i | \(-0.379438\pi\) | ||||
0.369766 | + | 0.929125i | \(0.379438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.42667 | 0.604374 | 0.302187 | − | 0.953249i | \(-0.402283\pi\) | ||||
0.302187 | + | 0.953249i | \(0.402283\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.25162 | 0.582464 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.46723 | −0.436332 | −0.218166 | − | 0.975912i | \(-0.570007\pi\) | ||||
−0.218166 | + | 0.975912i | \(0.570007\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.106918 | + | 0.226447i | −0.00842632 | + | 0.0178465i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.839878i | 0.0657843i | 0.999459 | + | 0.0328922i | \(0.0104718\pi\) | ||||
−0.999459 | + | 0.0328922i | \(0.989528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.57392 | 0.199176 | 0.0995878 | − | 0.995029i | \(-0.468248\pi\) | ||||
0.0995878 | + | 0.995029i | \(0.468248\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.4714 | 2.34395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.4921i | 1.32990i | 0.746888 | + | 0.664949i | \(0.231547\pi\) | ||||
−0.746888 | + | 0.664949i | \(0.768453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.40187 | − | 2.07836i | −0.332750 | − | 0.157110i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.3699 | 1.52252 | 0.761260 | − | 0.648447i | \(-0.224581\pi\) | ||||
0.761260 | + | 0.648447i | \(0.224581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.56527 | 0.116345 | 0.0581726 | − | 0.998307i | \(-0.481473\pi\) | ||||
0.0581726 | + | 0.998307i | \(0.481473\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.26814 | 0.607886 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.5858 | 1.28600 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.80433i | − | 0.347629i | −0.984778 | − | 0.173815i | \(-0.944391\pi\) | ||
0.984778 | − | 0.173815i | \(-0.0556093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.05595 | 0.435917 | 0.217958 | − | 0.975958i | \(-0.430060\pi\) | ||||
0.217958 | + | 0.975958i | \(0.430060\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4367 | 0.886082 | 0.443041 | − | 0.896501i | \(-0.353900\pi\) | ||||
0.443041 | + | 0.896501i | \(0.353900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.9553i | 1.13104i | 0.824733 | + | 0.565522i | \(0.191325\pi\) | ||||
−0.824733 | + | 0.565522i | \(0.808675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3294 | + | 4.87710i | 0.724985 | + | 0.342305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 20.5945i | − | 1.43839i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.04794 | −0.280002 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.608035i | 0.0418589i | 0.999781 | + | 0.0209294i | \(0.00666253\pi\) | ||||
−0.999781 | + | 0.0209294i | \(0.993337\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.1776 | −0.762309 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.60804 | + | 9.75958i | −0.312814 | + | 0.662524i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.0988 | −2.02467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.28726i | − | 0.487991i | −0.969776 | − | 0.243996i | \(-0.921542\pi\) | ||
0.969776 | − | 0.243996i | \(-0.0784582\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 19.3361i | − | 1.28338i | −0.766963 | − | 0.641692i | \(-0.778233\pi\) | ||
0.766963 | − | 0.641692i | \(-0.221767\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.95322 | 0.195154 | 0.0975771 | − | 0.995228i | \(-0.468891\pi\) | ||||
0.0975771 | + | 0.995228i | \(0.468891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.9472i | − | 0.782684i | −0.920245 | − | 0.391342i | \(-0.872011\pi\) | ||
0.920245 | − | 0.391342i | \(-0.127989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8958i | 0.710765i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 28.3255i | − | 1.83222i | −0.400923 | − | 0.916112i | \(-0.631310\pi\) | ||
0.400923 | − | 0.916112i | \(-0.368690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.9910i | − | 1.48098i | −0.672067 | − | 0.740491i | \(-0.734593\pi\) | ||
0.672067 | − | 0.740491i | \(-0.265407\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.60866 | + | 7.90694i | −0.613875 | + | 0.505156i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820 | 0.440831 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.8222i | − | 1.31428i | −0.753767 | − | 0.657142i | \(-0.771765\pi\) | ||
0.753767 | − | 0.657142i | \(-0.228235\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.364614i | − | 0.0229231i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.7432 | −1.10679 | −0.553394 | − | 0.832920i | \(-0.686668\pi\) | ||||
−0.553394 | + | 0.832920i | \(0.686668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.25398 | + | 11.1277i | −0.326467 | + | 0.691440i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.4703i | 1.01560i | 0.861475 | + | 0.507800i | \(0.169541\pi\) | ||||
−0.861475 | + | 0.507800i | \(0.830459\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.35439i | − | 0.267488i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.67822i | 0.102323i | 0.998690 | + | 0.0511613i | \(0.0162923\pi\) | ||||
−0.998690 | + | 0.0511613i | \(0.983708\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.8034i | 1.38521i | 0.721318 | + | 0.692604i | \(0.243537\pi\) | ||||
−0.721318 | + | 0.692604i | \(0.756463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.08768 | 0.427403 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.47349i | − | 0.328870i | −0.986388 | − | 0.164435i | \(-0.947420\pi\) | ||
0.986388 | − | 0.164435i | \(-0.0525801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.03960i | − | 0.539258i | −0.962964 | − | 0.269629i | \(-0.913099\pi\) | ||
0.962964 | − | 0.269629i | \(-0.0869010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.55639 | −0.330293 | −0.165147 | − | 0.986269i | \(-0.552810\pi\) | ||||
−0.165147 | + | 0.986269i | \(0.552810\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.7171 | + | 13.0868i | 1.63609 | + | 0.772489i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.83988 | 0.225875 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.3814i | − | 0.606488i | −0.952913 | − | 0.303244i | \(-0.901930\pi\) | ||
0.952913 | − | 0.303244i | \(-0.0980696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.4263 | 1.36393 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.624051i | 0.0360898i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.10282 | − | 15.0434i | 0.409400 | − | 0.867088i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.15741i | 0.467092i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8906 | 1.36351 | 0.681754 | − | 0.731581i | \(-0.261217\pi\) | ||||
0.681754 | + | 0.731581i | \(0.261217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.1208 | 1.87811 | 0.939053 | − | 0.343772i | \(-0.111705\pi\) | ||||
0.939053 | + | 0.343772i | \(0.111705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8239i | 1.45966i | 0.683631 | + | 0.729828i | \(0.260400\pi\) | ||||
−0.683631 | + | 0.729828i | \(0.739600\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.2970 | −1.47699 | −0.738493 | − | 0.674261i | \(-0.764462\pi\) | ||||
−0.738493 | + | 0.674261i | \(0.764462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.6320 | −0.931212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.79696 | −0.266910 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1308 | −0.672898 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.6641 | − | 6.92374i | −0.808460 | − | 0.381718i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.9675i | 0.877656i | 0.898571 | + | 0.438828i | \(0.144606\pi\) | ||||
−0.898571 | + | 0.438828i | \(0.855394\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.60372 | −0.470072 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7917 | −0.751279 | −0.375640 | − | 0.926766i | \(-0.622577\pi\) | ||||
−0.375640 | + | 0.926766i | \(0.622577\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.7144i | − | 0.850983i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.53572 | − | 17.9563i | −0.244906 | − | 0.969547i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.85226 | 0.206800 | 0.103400 | − | 0.994640i | \(-0.467028\pi\) | ||||
0.103400 | + | 0.994640i | \(0.467028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.44816 | −0.238104 | −0.119052 | − | 0.992888i | \(-0.537986\pi\) | ||||
−0.119052 | + | 0.992888i | \(0.537986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.39917 | −0.447043 | −0.223521 | − | 0.974699i | \(-0.571755\pi\) | ||||
−0.223521 | + | 0.974699i | \(0.571755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.5700 | 1.09174 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.5713i | − | 0.610709i | −0.952239 | − | 0.305354i | \(-0.901225\pi\) | ||
0.952239 | − | 0.305354i | \(-0.0987750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8958 | −0.941886 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00474 | 0.209618 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.90826i | − | 0.517207i | −0.965984 | − | 0.258603i | \(-0.916738\pi\) | ||
0.965984 | − | 0.258603i | \(-0.0832623\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.86035 | + | 2.76699i | 0.304254 | + | 0.143655i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.6380i | 1.84526i | 0.385682 | + | 0.922632i | \(0.373966\pi\) | ||||
−0.385682 | + | 0.922632i | \(0.626034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.4663 | 1.46609 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.6080i | − | 0.853097i | −0.904465 | − | 0.426549i | \(-0.859729\pi\) | ||
0.904465 | − | 0.426549i | \(-0.140271\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.08089 | −0.0552308 | −0.0276154 | − | 0.999619i | \(-0.508791\pi\) | ||||
−0.0276154 | + | 0.999619i | \(0.508791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.73570 | − | 16.3838i | 0.394248 | − | 0.834997i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.73208 | 0.493436 | 0.246718 | − | 0.969087i | \(-0.420648\pi\) | ||||
0.246718 | + | 0.969087i | \(0.420648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.432081i | − | 0.0218513i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.2803i | 1.27199i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.4524 | −1.52836 | −0.764181 | − | 0.645001i | \(-0.776857\pi\) | ||||
−0.764181 | + | 0.645001i | \(0.776857\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 0.226447i | − | 0.0113082i | −0.999984 | − | 0.00565411i | \(-0.998200\pi\) | ||
0.999984 | − | 0.00565411i | \(-0.00179977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.8958i | 1.33978i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 17.9172i | − | 0.888125i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.2664i | − | 0.853767i | −0.904307 | − | 0.426883i | \(-0.859611\pi\) | ||
0.904307 | − | 0.426883i | \(-0.140389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.8862 | + | 31.5283i | −0.732504 | + | 1.55141i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.8721 | −0.926396 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 26.1423i | − | 1.27714i | −0.769565 | − | 0.638568i | \(-0.779527\pi\) | ||
0.769565 | − | 0.638568i | \(-0.220473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.2393i | 1.08388i | 0.840418 | + | 0.541939i | \(0.182310\pi\) | ||||
−0.840418 | + | 0.541939i | \(0.817690\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.39917 | 0.407420 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.9786 | − | 5.18362i | −0.531293 | − | 0.250853i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.15666i | 0.296556i | 0.988946 | + | 0.148278i | \(0.0473730\pi\) | ||||
−0.988946 | + | 0.148278i | \(0.952627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.7676i | 1.57471i | 0.616498 | + | 0.787356i | \(0.288551\pi\) | ||||
−0.616498 | + | 0.787356i | \(0.711449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0994573i | 0.00475769i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 35.0484i | − | 1.67277i | −0.548145 | − | 0.836383i | \(-0.684666\pi\) | ||
0.548145 | − | 0.836383i | \(-0.315334\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.4967 | −1.06885 | −0.534425 | − | 0.845216i | \(-0.679472\pi\) | ||||
−0.534425 | + | 0.845216i | \(0.679472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 15.3111i | − | 0.725817i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.8253i | − | 1.50193i | −0.660344 | − | 0.750964i | \(-0.729589\pi\) | ||
0.660344 | − | 0.750964i | \(-0.270411\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.6288 | −2.10149 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.2400 | + | 28.0415i | −0.620699 | + | 1.31461i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.7917 | 1.20648 | 0.603241 | − | 0.797559i | \(-0.293876\pi\) | ||||
0.603241 | + | 0.797559i | \(0.293876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 10.4809i | − | 0.488142i | −0.969757 | − | 0.244071i | \(-0.921517\pi\) | ||
0.969757 | − | 0.244071i | \(-0.0784830\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.8097 | 1.29243 | 0.646214 | − | 0.763157i | \(-0.276352\pi\) | ||||
0.646214 | + | 0.763157i | \(0.276352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.50609i | 0.393615i | 0.980442 | + | 0.196808i | \(0.0630574\pi\) | ||||
−0.980442 | + | 0.196808i | \(0.936943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.46723 | − | 11.5793i | 0.252453 | − | 0.534683i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.2222i | 1.11374i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.93334 | −0.0887076 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.9246 | −1.04745 | −0.523725 | − | 0.851887i | \(-0.675458\pi\) | ||||
−0.523725 | + | 0.851887i | \(0.675458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.6661i | 1.39825i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.3891 | 1.15286 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.2113 | −1.27838 | −0.639188 | − | 0.769051i | \(-0.720729\pi\) | ||||
−0.639188 | + | 0.769051i | \(0.720729\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.5435 | −1.46867 | −0.734334 | − | 0.678788i | \(-0.762506\pi\) | ||||
−0.734334 | + | 0.678788i | \(0.762506\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.7095 | −0.887673 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.0712 | + | 27.6841i | −0.586322 | + | 1.24180i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.0717i | − | 0.764235i | −0.924114 | − | 0.382118i | \(-0.875195\pi\) | ||
0.924114 | − | 0.382118i | \(-0.124805\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.3506 | −0.907391 | −0.453695 | − | 0.891157i | \(-0.649895\pi\) | ||||
−0.453695 | + | 0.891157i | \(0.649895\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.48037 | 0.421871 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 22.7394i | − | 1.00791i | −0.863731 | − | 0.503953i | \(-0.831879\pi\) | ||
0.863731 | − | 0.503953i | \(-0.168121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.54481 | + | 5.38977i | −0.112576 | + | 0.238430i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.1280 | 1.10727 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.6115 | 1.03843 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.9834 | −1.26979 | −0.634893 | − | 0.772600i | \(-0.718956\pi\) | ||||
−0.634893 | + | 0.772600i | \(0.718956\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6661 | −1.34093 | −0.670466 | − | 0.741940i | \(-0.733906\pi\) | ||||
−0.670466 | + | 0.741940i | \(0.733906\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 18.6222i | − | 0.811195i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9910 | 0.999610 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 76.3839 | 3.30856 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.6836i | 1.19687i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.1345 | + | 20.8222i | 0.738035 | + | 0.896875i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.3268i | 0.873919i | 0.899481 | + | 0.436959i | \(0.143945\pi\) | ||||
−0.899481 | + | 0.436959i | \(0.856055\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.1702 | 0.992503 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.48037i | − | 0.234324i | −0.993113 | − | 0.117162i | \(-0.962620\pi\) | ||
0.993113 | − | 0.117162i | \(-0.0373796\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.53678 | 0.193273 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.0235 | − | 16.0644i | −1.44683 | − | 0.683126i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.1570 | −1.78625 | −0.893124 | − | 0.449810i | \(-0.851492\pi\) | ||||
−0.893124 | + | 0.449810i | \(0.851492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 41.4572i | − | 1.75345i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.42389i | 0.144300i | 0.997394 | + | 0.0721498i | \(0.0229860\pi\) | ||||
−0.997394 | + | 0.0721498i | \(0.977014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.3776 | 1.19386 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.3238i | 0.810095i | 0.914296 | + | 0.405048i | \(0.132745\pi\) | ||||
−0.914296 | + | 0.405048i | \(0.867255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 37.5274i | − | 1.57047i | −0.619197 | − | 0.785235i | \(-0.712542\pi\) | ||
0.619197 | − | 0.785235i | \(-0.287458\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.174143i | − | 0.00726228i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.92784i | 0.413301i | 0.978415 | + | 0.206651i | \(0.0662563\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.9923 | − | 25.3990i | 0.497523 | − | 1.05373i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.43606 | −0.390802 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.43026i | − | 0.306679i | −0.988174 | − | 0.153340i | \(-0.950997\pi\) | ||
0.988174 | − | 0.153340i | \(-0.0490029\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.28649i | 0.176622i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.7911 | 0.894853 | 0.447426 | − | 0.894321i | \(-0.352341\pi\) | ||||
0.447426 | + | 0.894321i | \(0.352341\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.16711 | − | 19.4155i | 0.375815 | − | 0.795956i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.47799i | 0.182966i | 0.995807 | + | 0.0914828i | \(0.0291606\pi\) | ||||
−0.995807 | + | 0.0914828i | \(0.970839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.0294i | − | 0.490691i | −0.969436 | − | 0.245345i | \(-0.921099\pi\) | ||
0.969436 | − | 0.245345i | \(-0.0789014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.82605i | 0.277518i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.4083i | 1.27482i | 0.770524 | + | 0.637412i | \(0.219995\pi\) | ||||
−0.770524 | + | 0.637412i | \(0.780005\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.4120 | −1.63489 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5856i | 0.589108i | 0.955635 | + | 0.294554i | \(0.0951711\pi\) | ||||
−0.955635 | + | 0.294554i | \(0.904829\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.69730i | 0.269623i | 0.990871 | + | 0.134812i | \(0.0430429\pi\) | ||||
−0.990871 | + | 0.134812i | \(0.956957\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.6366 | 0.749069 | 0.374535 | − | 0.927213i | \(-0.377803\pi\) | ||||
0.374535 | + | 0.927213i | \(0.377803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.6064 | + | 9.72944i | 0.825580 | + | 0.389802i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4155 | −0.496618 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 21.2326i | − | 0.846600i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7940 | 0.907415 | 0.453707 | − | 0.891151i | \(-0.350101\pi\) | ||||
0.453707 | + | 0.891151i | \(0.350101\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.04794i | 0.160638i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.3264 | − | 35.6380i | −1.16195 | − | 1.41203i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.7927i | 1.13724i | 0.822599 | + | 0.568622i | \(0.192523\pi\) | ||||
−0.822599 | + | 0.568622i | \(0.807477\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.89291 | −0.232394 | −0.116197 | − | 0.993226i | \(-0.537070\pi\) | ||||
−0.116197 | + | 0.993226i | \(0.537070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2326 | 0.834740 | 0.417370 | − | 0.908737i | \(-0.362952\pi\) | ||||
0.417370 | + | 0.908737i | \(0.362952\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 50.7653i | − | 1.99271i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.44949 | 0.0958559 | 0.0479280 | − | 0.998851i | \(-0.484738\pi\) | ||||
0.0479280 | + | 0.998851i | \(0.484738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.10936 | −0.0433462 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.8066 | −0.654693 | −0.327347 | − | 0.944904i | \(-0.606154\pi\) | ||||
−0.327347 | + | 0.944904i | \(0.606154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.6908 | 1.07705 | 0.538523 | − | 0.842611i | \(-0.318983\pi\) | ||||
0.538523 | + | 0.842611i | \(0.318983\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.11010 | + | 4.46909i | −0.0818262 | + | 0.173304i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.408645i | 0.0158228i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.6773 | 0.682424 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.95177 | −0.190877 | −0.0954384 | − | 0.995435i | \(-0.530425\pi\) | ||||
−0.0954384 | + | 0.995435i | \(0.530425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.5803i | 0.406634i | 0.979113 | + | 0.203317i | \(0.0651722\pi\) | ||||
−0.979113 | + | 0.203317i | \(0.934828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.1335 | + | 34.1699i | −0.619147 | + | 1.31132i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.1718 | −1.80498 | −0.902489 | − | 0.430713i | \(-0.858262\pi\) | ||||
−0.902489 | + | 0.430713i | \(0.858262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.9897 | 1.03122 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.1502 | 0.615273 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0589 | 0.915242 | 0.457621 | − | 0.889147i | \(-0.348702\pi\) | ||||
0.457621 | + | 0.889147i | \(0.348702\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 22.9533i | − | 0.870667i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.8869 | −2.00323 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.2657 | 0.954273 | 0.477136 | − | 0.878829i | \(-0.341675\pi\) | ||||
0.477136 | + | 0.878829i | \(0.341675\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.88737i | 0.184330i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.02429 | + | 12.7591i | −0.226567 | + | 0.479857i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.3362i | 0.838855i | 0.907789 | + | 0.419427i | \(0.137769\pi\) | ||||
−0.907789 | + | 0.419427i | \(0.862231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.386101 | −0.0144596 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 45.1512i | − | 1.68856i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.74032 | 0.251371 | 0.125686 | − | 0.992070i | \(-0.459887\pi\) | ||||
0.125686 | + | 0.992070i | \(0.459887\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9675 | + | 33.8184i | −0.594663 | + | 1.25946i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.94361 | −0.295018 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.4995i | 1.35369i | 0.736125 | + | 0.676846i | \(0.236654\pi\) | ||||
−0.736125 | + | 0.676846i | \(0.763346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.7042i | 1.06166i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.6065 | 1.35209 | 0.676046 | − | 0.736860i | \(-0.263692\pi\) | ||||
0.676046 | + | 0.736860i | \(0.263692\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.6444i | 0.686777i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.36847i | 0.0503400i | 0.999683 | + | 0.0251700i | \(0.00801270\pi\) | ||||
−0.999683 | + | 0.0251700i | \(0.991987\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.31969i | − | 0.268534i | −0.990945 | − | 0.134267i | \(-0.957132\pi\) | ||
0.990945 | − | 0.134267i | \(-0.0428679\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.0473i | 0.587928i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.2580 | − | 17.5915i | −1.36138 | − | 0.642781i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.87247 | −0.104818 | −0.0524090 | − | 0.998626i | \(-0.516690\pi\) | ||||
−0.0524090 | + | 0.998626i | \(0.516690\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.2022i | 0.480477i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.3167i | 1.82879i | 0.404819 | + | 0.914397i | \(0.367334\pi\) | ||||
−0.404819 | + | 0.914397i | \(0.632666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.68885 | 0.351220 | 0.175610 | − | 0.984460i | \(-0.443810\pi\) | ||||
0.175610 | + | 0.984460i | \(0.443810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.7235 | + | 31.1836i | −0.533026 | + | 1.12892i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 86.8868i | 3.13730i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.82624i | 0.282222i | 0.989994 | + | 0.141111i | \(0.0450674\pi\) | ||||
−0.989994 | + | 0.141111i | \(0.954933\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 17.3926i | − | 0.625569i | −0.949824 | − | 0.312785i | \(-0.898738\pi\) | ||
0.949824 | − | 0.312785i | \(-0.101262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.50537i | − | 0.269601i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.1736 | 0.436164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 44.5755i | − | 1.59504i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9.71894i | − | 0.346884i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8961 | 0.566635 | 0.283318 | − | 0.959026i | \(-0.408565\pi\) | ||||
0.283318 | + | 0.959026i | \(0.408565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0325 | + | 38.1920i | −0.641163 | + | 1.35795i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.2553 | −1.07440 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.1581i | 0.997412i | 0.866771 | + | 0.498706i | \(0.166191\pi\) | ||||
−0.866771 | + | 0.498706i | \(0.833809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.9805 | 0.989880 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 8.67836i | − | 0.306253i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.402548 | − | 0.190065i | −0.0141880 | − | 0.00669892i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.4324i | 0.718366i | 0.933267 | + | 0.359183i | \(0.116945\pi\) | ||||
−0.933267 | + | 0.359183i | \(0.883055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.9977 | 0.631985 | 0.315992 | − | 0.948762i | \(-0.397663\pi\) | ||||
0.315992 | + | 0.948762i | \(0.397663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.49303 | −0.0522985 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.60719i | − | 0.231156i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.1600 | 0.912989 | 0.456494 | − | 0.889726i | \(-0.349105\pi\) | ||||
0.456494 | + | 0.889726i | \(0.349105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.2891 | −1.40439 | −0.702194 | − | 0.711986i | \(-0.747796\pi\) | ||||
−0.702194 | + | 0.711986i | \(0.747796\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.3729 | −1.57777 | −0.788885 | − | 0.614541i | \(-0.789341\pi\) | ||||
−0.788885 | + | 0.614541i | \(0.789341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.98124 | 0.277200 | 0.138600 | − | 0.990348i | \(-0.455740\pi\) | ||||
0.138600 | + | 0.990348i | \(0.455740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.3050 | + | 24.6751i | 0.703528 | + | 0.854941i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.57558i | 0.158345i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.58515 | 0.330916 | 0.165458 | − | 0.986217i | \(-0.447090\pi\) | ||||
0.165458 | + | 0.986217i | \(0.447090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.3595 | −0.357225 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 54.1682i | 1.86344i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.18683 | − | 4.33761i | −0.315663 | − | 0.149042i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.440224 | −0.0150907 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.1676 | −1.54651 | −0.773254 | − | 0.634096i | \(-0.781372\pi\) | ||||
−0.773254 | + | 0.634096i | \(0.781372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.9055 | 1.73890 | 0.869450 | − | 0.494021i | \(-0.164474\pi\) | ||||
0.869450 | + | 0.494021i | \(0.164474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.1930 | −0.825455 | −0.412728 | − | 0.910855i | \(-0.635424\pi\) | ||||
−0.412728 | + | 0.910855i | \(0.635424\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.6081i | 1.21211i | 0.795421 | + | 0.606057i | \(0.207250\pi\) | ||||
−0.795421 | + | 0.606057i | \(0.792750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.0952 | −1.05727 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.7830 | 1.85839 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 31.9107i | − | 1.08125i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.7351 | − | 29.0903i | 0.464332 | − | 0.983432i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.84069i | 0.298529i | 0.988797 | + | 0.149264i | \(0.0476906\pi\) | ||||
−0.988797 | + | 0.149264i | \(0.952309\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.32334 | −0.246730 | −0.123365 | − | 0.992361i | \(-0.539369\pi\) | ||||
−0.123365 | + | 0.992361i | \(0.539369\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 51.4390i | − | 1.73106i | −0.500858 | − | 0.865529i | \(-0.666982\pi\) | ||
0.500858 | − | 0.865529i | \(-0.333018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6475 | 0.391084 | 0.195542 | − | 0.980695i | \(-0.437353\pi\) | ||||
0.195542 | + | 0.980695i | \(0.437353\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.44791 | − | 2.57226i | −0.182717 | − | 0.0862708i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.44061 | −0.215527 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.2111i | 1.21040i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.6121i | 0.587397i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1821 | −0.372530 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.78253i | 0.0924945i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.6550i | 1.08429i | 0.840284 | + | 0.542146i | \(0.182388\pi\) | ||||
−0.840284 | + | 0.542146i | \(0.817612\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 49.9787i | − | 1.65587i | −0.560826 | − | 0.827934i | \(-0.689516\pi\) | ||
0.560826 | − | 0.827934i | \(-0.310484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.8963i | 1.35347i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.704941 | − | 1.49303i | 0.0232792 | − | 0.0493041i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.15896 | 0.236152 | 0.118076 | − | 0.993005i | \(-0.462327\pi\) | ||||
0.118076 | + | 0.993005i | \(0.462327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 76.2928i | 2.51121i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 8.55746i | − | 0.281368i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.730969 | 0.0239823 | 0.0119912 | − | 0.999928i | \(-0.496183\pi\) | ||||
0.0119912 | + | 0.999928i | \(0.496183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.67385 | − | 5.67976i | −0.153179 | − | 0.186146i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.2619i | 1.02237i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.3748i | 1.28632i | 0.765732 | + | 0.643160i | \(0.222377\pi\) | ||||
−0.765732 | + | 0.643160i | \(0.777623\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.1198i | 1.60126i | 0.599159 | + | 0.800630i | \(0.295502\pi\) | ||||
−0.599159 | + | 0.800630i | \(0.704498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.09652i | 0.0357078i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.7171 | −1.45311 | −0.726556 | − | 0.687108i | \(-0.758880\pi\) | ||||
−0.726556 | + | 0.687108i | \(0.758880\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.8533i | 0.482160i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.1681i | 0.426558i | 0.976991 | + | 0.213279i | \(0.0684143\pi\) | ||||
−0.976991 | + | 0.213279i | \(0.931586\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.54053 | 0.276365 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1506 | + | 36.3240i | −0.553820 | + | 1.17296i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.3595 | 0.463210 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.7655i | 0.346554i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8067 | −0.926360 | −0.463180 | − | 0.886264i | \(-0.653292\pi\) | ||||
−0.463180 | + | 0.886264i | \(0.653292\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 26.5284i | − | 0.851338i | −0.904879 | − | 0.425669i | \(-0.860039\pi\) | ||
0.904879 | − | 0.425669i | \(-0.139961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.8916 | + | 14.5856i | 0.990340 | + | 0.467594i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.3105i | 1.28965i | 0.764331 | + | 0.644824i | \(0.223069\pi\) | ||||
−0.764331 | + | 0.644824i | \(0.776931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.1795 | −1.06042 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.57392 | −0.0820952 | −0.0410476 | − | 0.999157i | \(-0.513070\pi\) | ||||
−0.0410476 | + | 0.999157i | \(0.513070\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.1085i | 0.704435i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.595136 | 0.0189242 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.0332 | −1.04933 | −0.524667 | − | 0.851308i | \(-0.675810\pi\) | ||||
−0.524667 | + | 0.851308i | \(0.675810\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.3634 | −0.899180 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.8123 | 0.849156 | 0.424578 | − | 0.905391i | \(-0.360423\pi\) | ||||
0.424578 | + | 0.905391i | \(0.360423\pi\) | |||||||
\(998\) | 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.i.c.1889.20 | yes | 48 | |
3.2 | odd | 2 | inner | 4032.2.i.c.1889.1 | ✓ | 48 | |
4.3 | odd | 2 | inner | 4032.2.i.c.1889.12 | yes | 48 | |
7.6 | odd | 2 | inner | 4032.2.i.c.1889.37 | yes | 48 | |
8.3 | odd | 2 | inner | 4032.2.i.c.1889.47 | yes | 48 | |
8.5 | even | 2 | inner | 4032.2.i.c.1889.5 | yes | 48 | |
12.11 | even | 2 | inner | 4032.2.i.c.1889.43 | yes | 48 | |
21.20 | even | 2 | inner | 4032.2.i.c.1889.6 | yes | 48 | |
24.5 | odd | 2 | inner | 4032.2.i.c.1889.38 | yes | 48 | |
24.11 | even | 2 | inner | 4032.2.i.c.1889.30 | yes | 48 | |
28.27 | even | 2 | inner | 4032.2.i.c.1889.29 | yes | 48 | |
56.13 | odd | 2 | inner | 4032.2.i.c.1889.2 | yes | 48 | |
56.27 | even | 2 | inner | 4032.2.i.c.1889.44 | yes | 48 | |
84.83 | odd | 2 | inner | 4032.2.i.c.1889.48 | yes | 48 | |
168.83 | odd | 2 | inner | 4032.2.i.c.1889.11 | yes | 48 | |
168.125 | even | 2 | inner | 4032.2.i.c.1889.19 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.i.c.1889.1 | ✓ | 48 | 3.2 | odd | 2 | inner | |
4032.2.i.c.1889.2 | yes | 48 | 56.13 | odd | 2 | inner | |
4032.2.i.c.1889.5 | yes | 48 | 8.5 | even | 2 | inner | |
4032.2.i.c.1889.6 | yes | 48 | 21.20 | even | 2 | inner | |
4032.2.i.c.1889.11 | yes | 48 | 168.83 | odd | 2 | inner | |
4032.2.i.c.1889.12 | yes | 48 | 4.3 | odd | 2 | inner | |
4032.2.i.c.1889.19 | yes | 48 | 168.125 | even | 2 | inner | |
4032.2.i.c.1889.20 | yes | 48 | 1.1 | even | 1 | trivial | |
4032.2.i.c.1889.29 | yes | 48 | 28.27 | even | 2 | inner | |
4032.2.i.c.1889.30 | yes | 48 | 24.11 | even | 2 | inner | |
4032.2.i.c.1889.37 | yes | 48 | 7.6 | odd | 2 | inner | |
4032.2.i.c.1889.38 | yes | 48 | 24.5 | odd | 2 | inner | |
4032.2.i.c.1889.43 | yes | 48 | 12.11 | even | 2 | inner | |
4032.2.i.c.1889.44 | yes | 48 | 56.27 | even | 2 | inner | |
4032.2.i.c.1889.47 | yes | 48 | 8.3 | odd | 2 | inner | |
4032.2.i.c.1889.48 | yes | 48 | 84.83 | odd | 2 | inner |