Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not 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: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.9 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.9 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(5\) | −0.111394 | − | 0.111394i | −0.0498168 | − | 0.0498168i | 0.681760 | − | 0.731576i | \(-0.261215\pi\) |
−0.731576 | + | 0.681760i | \(0.761215\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.61173 | + | 3.61173i | −1.08898 | + | 1.08898i | −0.0933436 | + | 0.995634i | \(0.529755\pi\) |
−0.995634 | + | 0.0933436i | \(0.970245\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.94473 | − | 1.94473i | −0.539372 | − | 0.539372i | 0.383973 | − | 0.923344i | \(-0.374556\pi\) |
−0.923344 | + | 0.383973i | \(0.874556\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.79732i | 1.16352i | 0.813360 | + | 0.581761i | \(0.197636\pi\) | ||||
−0.813360 | + | 0.581761i | \(0.802364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.03275 | + | 3.03275i | −0.695761 | + | 0.695761i | −0.963493 | − | 0.267732i | \(-0.913726\pi\) |
0.267732 | + | 0.963493i | \(0.413726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.58652i | − | 1.37339i | −0.726948 | − | 0.686693i | \(-0.759062\pi\) | ||
0.726948 | − | 0.686693i | \(-0.240938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.97518i | − | 0.995037i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.53154 | − | 1.53154i | 0.284399 | − | 0.284399i | −0.550462 | − | 0.834861i | \(-0.685548\pi\) |
0.834861 | + | 0.550462i | \(0.185548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.26529i | − | 0.586464i | −0.956041 | − | 0.293232i | \(-0.905269\pi\) | ||
0.956041 | − | 0.293232i | \(-0.0947308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.111394 | + | 0.111394i | 0.0188290 | + | 0.0188290i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.05597 | − | 1.05597i | 0.173601 | − | 0.173601i | −0.614959 | − | 0.788559i | \(-0.710827\pi\) |
0.788559 | + | 0.614959i | \(0.210827\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.26613 | −0.197737 | −0.0988684 | − | 0.995101i | \(-0.531522\pi\) | ||||
−0.0988684 | + | 0.995101i | \(0.531522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.484499 | − | 0.484499i | −0.0738855 | − | 0.0738855i | 0.669198 | − | 0.743084i | \(-0.266638\pi\) |
−0.743084 | + | 0.669198i | \(0.766638\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2247 | 1.63729 | 0.818644 | − | 0.574301i | \(-0.194726\pi\) | ||||
0.818644 | + | 0.574301i | \(0.194726\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00870 | + | 4.00870i | 0.550637 | + | 0.550637i | 0.926625 | − | 0.375988i | \(-0.122697\pi\) |
−0.375988 | + | 0.926625i | \(0.622697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.804648 | 0.108499 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.61474 | − | 7.61474i | 0.991354 | − | 0.991354i | −0.00860874 | − | 0.999963i | \(-0.502740\pi\) |
0.999963 | + | 0.00860874i | \(0.00274028\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.44215 | + | 5.44215i | 0.696796 | + | 0.696796i | 0.963718 | − | 0.266922i | \(-0.0860066\pi\) |
−0.266922 | + | 0.963718i | \(0.586007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.433262i | 0.0537395i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.897143 | − | 0.897143i | 0.109603 | − | 0.109603i | −0.650178 | − | 0.759782i | \(-0.725306\pi\) |
0.759782 | + | 0.650178i | \(0.225306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.83052i | − | 0.335921i | −0.985794 | − | 0.167960i | \(-0.946282\pi\) | ||
0.985794 | − | 0.167960i | \(-0.0537181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.7394i | − | 1.84216i | −0.389372 | − | 0.921080i | \(-0.627308\pi\) | ||
0.389372 | − | 0.921080i | \(-0.372692\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.61173 | − | 3.61173i | 0.411595 | − | 0.411595i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4151i | 1.73433i | 0.498020 | + | 0.867165i | \(0.334061\pi\) | ||||
−0.498020 | + | 0.867165i | \(0.665939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.57988 | + | 7.57988i | 0.832000 | + | 0.832000i | 0.987790 | − | 0.155790i | \(-0.0497924\pi\) |
−0.155790 | + | 0.987790i | \(0.549792\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.534392 | − | 0.534392i | 0.0579629 | − | 0.0579629i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.1420 | 1.39305 | 0.696525 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696525 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.94473 | + | 1.94473i | 0.203863 | + | 0.203863i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.675660 | 0.0693212 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4839 | −1.06447 | −0.532237 | − | 0.846595i | \(-0.678648\pi\) | ||||
−0.532237 | + | 0.846595i | \(0.678648\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.472060 | + | 0.472060i | 0.0469717 | + | 0.0469717i | 0.730202 | − | 0.683231i | \(-0.239426\pi\) |
−0.683231 | + | 0.730202i | \(0.739426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5554 | 1.63125 | 0.815624 | − | 0.578583i | \(-0.196394\pi\) | ||||
0.815624 | + | 0.578583i | \(0.196394\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.98789 | − | 7.98789i | 0.772218 | − | 0.772218i | −0.206276 | − | 0.978494i | \(-0.566134\pi\) |
0.978494 | + | 0.206276i | \(0.0661343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.01886 | − | 6.01886i | −0.576502 | − | 0.576502i | 0.357436 | − | 0.933938i | \(-0.383651\pi\) |
−0.933938 | + | 0.357436i | \(0.883651\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.81071i | − | 0.734770i | −0.930069 | − | 0.367385i | \(-0.880253\pi\) | ||
0.930069 | − | 0.367385i | \(-0.119747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.733698 | + | 0.733698i | −0.0684177 | + | 0.0684177i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.79732i | − | 0.439770i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 15.0892i | − | 1.37174i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.11117 | + | 1.11117i | −0.0993863 | + | 0.0993863i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.59439i | − | 0.585157i | −0.956241 | − | 0.292579i | \(-0.905487\pi\) | ||
0.956241 | − | 0.292579i | \(-0.0945133\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.27211 | − | 6.27211i | −0.547997 | − | 0.547997i | 0.377864 | − | 0.925861i | \(-0.376659\pi\) |
−0.925861 | + | 0.377864i | \(0.876659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.03275 | − | 3.03275i | 0.262973 | − | 0.262973i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.4152 | −1.91506 | −0.957530 | − | 0.288333i | \(-0.906899\pi\) | ||||
−0.957530 | + | 0.288333i | \(0.906899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.44120 | − | 9.44120i | −0.800792 | − | 0.800792i | 0.182427 | − | 0.983219i | \(-0.441605\pi\) |
−0.983219 | + | 0.182427i | \(0.941605\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.0477 | 1.17473 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.341207 | −0.0283357 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6024 | + | 10.6024i | 0.868581 | + | 0.868581i | 0.992315 | − | 0.123735i | \(-0.0394872\pi\) |
−0.123735 | + | 0.992315i | \(0.539487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.651929 | 0.0530532 | 0.0265266 | − | 0.999648i | \(-0.491555\pi\) | ||||
0.0265266 | + | 0.999648i | \(0.491555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.363733 | + | 0.363733i | −0.0292157 | + | 0.0292157i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6768 | − | 15.6768i | −1.25114 | − | 1.25114i | −0.955209 | − | 0.295934i | \(-0.904369\pi\) |
−0.295934 | − | 0.955209i | \(-0.595631\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.58652i | 0.519091i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.07211 | − | 4.07211i | 0.318952 | − | 0.318952i | −0.529412 | − | 0.848365i | \(-0.677588\pi\) |
0.848365 | + | 0.529412i | \(0.177588\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.04509i | 0.622548i | 0.950320 | + | 0.311274i | \(0.100756\pi\) | ||||
−0.950320 | + | 0.311274i | \(0.899244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.43603i | − | 0.418156i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.546907 | + | 0.546907i | −0.0415806 | + | 0.0415806i | −0.727591 | − | 0.686011i | \(-0.759360\pi\) |
0.686011 | + | 0.727591i | \(0.259360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.97518i | 0.376088i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.4071 | + | 15.4071i | 1.15158 | + | 1.15158i | 0.986236 | + | 0.165345i | \(0.0528739\pi\) |
0.165345 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.10925 | + | 4.10925i | −0.305438 | + | 0.305438i | −0.843137 | − | 0.537699i | \(-0.819294\pi\) |
0.537699 | + | 0.843137i | \(0.319294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.235257 | −0.0172965 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.3266 | − | 17.3266i | −1.26705 | − | 1.26705i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.56461 | 0.547356 | 0.273678 | − | 0.961821i | \(-0.411760\pi\) | ||||
0.273678 | + | 0.961821i | \(0.411760\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0355 | 1.01030 | 0.505149 | − | 0.863032i | \(-0.331438\pi\) | ||||
0.505149 | + | 0.863032i | \(0.331438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.59894 | + | 9.59894i | 0.683896 | + | 0.683896i | 0.960876 | − | 0.276980i | \(-0.0893335\pi\) |
−0.276980 | + | 0.960876i | \(0.589334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5176 | 0.887349 | 0.443675 | − | 0.896188i | \(-0.353675\pi\) | ||||
0.443675 | + | 0.896188i | \(0.353675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.53154 | + | 1.53154i | −0.107493 | + | 0.107493i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.141039 | + | 0.141039i | 0.00985062 | + | 0.00985062i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 21.9070i | − | 1.51534i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.19384 | + | 6.19384i | −0.426401 | + | 0.426401i | −0.887401 | − | 0.460999i | \(-0.847491\pi\) |
0.460999 | + | 0.887401i | \(0.347491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.107940i | 0.00736148i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.26529i | 0.221662i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.32951 | − | 9.32951i | 0.627571 | − | 0.627571i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.4809i | − | 1.57240i | −0.617972 | − | 0.786200i | \(-0.712045\pi\) | ||
0.617972 | − | 0.786200i | \(-0.287955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.8869 | + | 13.8869i | 0.921707 | + | 0.921707i | 0.997150 | − | 0.0754430i | \(-0.0240371\pi\) |
−0.0754430 | + | 0.997150i | \(0.524037\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.96200 | + | 2.96200i | −0.195735 | + | 0.195735i | −0.798169 | − | 0.602434i | \(-0.794198\pi\) |
0.602434 | + | 0.798169i | \(0.294198\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.94090 | 0.127153 | 0.0635763 | − | 0.997977i | \(-0.479749\pi\) | ||||
0.0635763 | + | 0.997977i | \(0.479749\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.25036 | − | 1.25036i | −0.0815645 | − | 0.0815645i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.73260 | −0.241442 | −0.120721 | − | 0.992686i | \(-0.538521\pi\) | ||||
−0.120721 | + | 0.992686i | \(0.538521\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.72519 | −0.433208 | −0.216604 | − | 0.976260i | \(-0.569498\pi\) | ||||
−0.216604 | + | 0.976260i | \(0.569498\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.111394 | − | 0.111394i | −0.00711669 | − | 0.00711669i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.7958 | 0.750548 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.29389 | + | 7.29389i | −0.460387 | + | 0.460387i | −0.898782 | − | 0.438396i | \(-0.855547\pi\) |
0.438396 | + | 0.898782i | \(0.355547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.7887 | + | 23.7887i | 1.49559 | + | 1.49559i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.33778i | − | 0.208205i | −0.994567 | − | 0.104103i | \(-0.966803\pi\) | ||
0.994567 | − | 0.104103i | \(-0.0331970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.05597 | + | 1.05597i | −0.0656149 | + | 0.0656149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.2784i | − | 1.00377i | −0.864934 | − | 0.501886i | \(-0.832640\pi\) | ||
0.864934 | − | 0.501886i | \(-0.167360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.893087i | − | 0.0548619i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6895 | − | 16.6895i | 1.01758 | − | 1.01758i | 0.0177322 | − | 0.999843i | \(-0.494355\pi\) |
0.999843 | − | 0.0177322i | \(-0.00564465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.4291i | − | 1.18023i | −0.807318 | − | 0.590116i | \(-0.799082\pi\) | ||
0.807318 | − | 0.590116i | \(-0.200918\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.9690 | + | 17.9690i | 1.08357 | + | 1.08357i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.2943 | + | 20.2943i | −1.21937 | + | 1.21937i | −0.251511 | + | 0.967854i | \(0.580927\pi\) |
−0.967854 | + | 0.251511i | \(0.919073\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.67930 | 0.517763 | 0.258882 | − | 0.965909i | \(-0.416646\pi\) | ||||
0.258882 | + | 0.965909i | \(0.416646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.11240 | + | 5.11240i | 0.303901 | + | 0.303901i | 0.842538 | − | 0.538637i | \(-0.181061\pi\) |
−0.538637 | + | 0.842538i | \(0.681061\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.26613 | 0.0747375 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.01430 | −0.353782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.21225 | − | 4.21225i | −0.246082 | − | 0.246082i | 0.573279 | − | 0.819361i | \(-0.305671\pi\) |
−0.819361 | + | 0.573279i | \(0.805671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.69647 | −0.0987722 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.8090 | + | 12.8090i | −0.740765 | + | 0.740765i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.484499 | + | 0.484499i | 0.0279261 | + | 0.0279261i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.21244i | − | 0.0694243i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.47769 | + | 5.47769i | −0.312628 | + | 0.312628i | −0.845927 | − | 0.533299i | \(-0.820952\pi\) |
0.533299 | + | 0.845927i | \(0.320952\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 10.8058i | − | 0.612740i | −0.951913 | − | 0.306370i | \(-0.900886\pi\) | ||
0.951913 | − | 0.306370i | \(-0.0991144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 26.1747i | − | 1.47948i | −0.672893 | − | 0.739740i | \(-0.734949\pi\) | ||
0.672893 | − | 0.739740i | \(-0.265051\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7908 | − | 14.7908i | 0.830735 | − | 0.830735i | −0.156883 | − | 0.987617i | \(-0.550144\pi\) |
0.987617 | + | 0.156883i | \(0.0501444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.0630i | 0.619408i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5491 | − | 14.5491i | −0.809533 | − | 0.809533i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.67540 | + | 9.67540i | −0.536695 | + | 0.536695i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.2247 | −0.618837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8239 | − | 12.8239i | −0.704868 | − | 0.704868i | 0.260583 | − | 0.965451i | \(-0.416085\pi\) |
−0.965451 | + | 0.260583i | \(0.916085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.199872 | −0.0109202 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.5576 | 0.629582 | 0.314791 | − | 0.949161i | \(-0.398066\pi\) | ||||
0.314791 | + | 0.949161i | \(0.398066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7934 | + | 11.7934i | 0.638646 | + | 0.638646i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.89704 | − | 2.89704i | 0.155521 | − | 0.155521i | −0.625058 | − | 0.780579i | \(-0.714924\pi\) |
0.780579 | + | 0.625058i | \(0.214924\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.35296 | + | 8.35296i | 0.447124 | + | 0.447124i | 0.894397 | − | 0.447273i | \(-0.147605\pi\) |
−0.447273 | + | 0.894397i | \(0.647605\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.6486i | − | 0.619993i | −0.950738 | − | 0.309996i | \(-0.899672\pi\) | ||
0.950738 | − | 0.309996i | \(-0.100328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.315302 | + | 0.315302i | −0.0167345 | + | 0.0167345i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.0137i | − | 1.26739i | −0.773582 | − | 0.633696i | \(-0.781537\pi\) | ||
0.773582 | − | 0.633696i | \(-0.218463\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.604810i | 0.0318321i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.75327 | + | 1.75327i | −0.0917706 | + | 0.0917706i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.1938i | − | 0.636510i | −0.948005 | − | 0.318255i | \(-0.896903\pi\) | ||
0.948005 | − | 0.318255i | \(-0.103097\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00870 | − | 4.00870i | −0.208121 | − | 0.208121i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.3599 | − | 17.3599i | 0.898859 | − | 0.898859i | −0.0964762 | − | 0.995335i | \(-0.530757\pi\) |
0.995335 | + | 0.0964762i | \(0.0307572\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.95685 | −0.306794 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.2388 | − | 16.2388i | −0.834130 | − | 0.834130i | 0.153949 | − | 0.988079i | \(-0.450801\pi\) |
−0.988079 | + | 0.153949i | \(0.950801\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0190 | −0.614141 | −0.307070 | − | 0.951687i | \(-0.599349\pi\) | ||||
−0.307070 | + | 0.951687i | \(0.599349\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.804648 | −0.0410087 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.2292 | − | 13.2292i | −0.670749 | − | 0.670749i | 0.287140 | − | 0.957889i | \(-0.407296\pi\) |
−0.957889 | + | 0.287140i | \(0.907296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.5977 | 1.59796 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.71714 | − | 1.71714i | 0.0863988 | − | 0.0863988i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.8846 | + | 21.8846i | 1.09836 | + | 1.09836i | 0.994603 | + | 0.103756i | \(0.0330860\pi\) |
0.103756 | + | 0.994603i | \(0.466914\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.8646i | 1.39149i | 0.718288 | + | 0.695746i | \(0.244926\pi\) | ||||
−0.718288 | + | 0.695746i | \(0.755074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.35012 | + | 6.35012i | −0.316322 | + | 0.316322i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.62778i | 0.378095i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.57933i | − | 0.473667i | −0.971550 | − | 0.236834i | \(-0.923890\pi\) | ||
0.971550 | − | 0.236834i | \(-0.0761097\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.61474 | + | 7.61474i | −0.374697 | + | 0.374697i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.68870i | − | 0.0828952i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.53866 | + | 6.53866i | 0.319435 | + | 0.319435i | 0.848550 | − | 0.529115i | \(-0.177476\pi\) |
−0.529115 | + | 0.848550i | \(0.677476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8801 | + | 17.8801i | −0.871424 | + | 0.871424i | −0.992628 | − | 0.121204i | \(-0.961325\pi\) |
0.121204 | + | 0.992628i | \(0.461325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.8676 | 1.15775 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.44215 | − | 5.44215i | −0.263364 | − | 0.263364i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.02619 | −0.145766 | −0.0728832 | − | 0.997340i | \(-0.523220\pi\) | ||||
−0.0728832 | + | 0.997340i | \(0.523220\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.3339 | 1.60192 | 0.800962 | − | 0.598715i | \(-0.204322\pi\) | ||||
0.800962 | + | 0.598715i | \(0.204322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.9753 | + | 19.9753i | 0.955549 | + | 0.955549i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0388 | −1.19504 | −0.597519 | − | 0.801855i | \(-0.703847\pi\) | ||||
−0.597519 | + | 0.801855i | \(0.703847\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.5230 | + | 11.5230i | −0.547473 | + | 0.547473i | −0.925709 | − | 0.378236i | \(-0.876531\pi\) |
0.378236 | + | 0.925709i | \(0.376531\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.46394 | − | 1.46394i | −0.0693973 | − | 0.0693973i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.9666i | 1.17825i | 0.808042 | + | 0.589124i | \(0.200527\pi\) | ||||
−0.808042 | + | 0.589124i | \(0.799473\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.57293 | − | 4.57293i | 0.215331 | − | 0.215331i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.433262i | − | 0.0203116i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.0783i | − | 0.705333i | −0.935749 | − | 0.352666i | \(-0.885275\pi\) | ||
0.935749 | − | 0.352666i | \(-0.114725\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.98842 | + | 1.98842i | −0.0926101 | + | 0.0926101i | −0.751894 | − | 0.659284i | \(-0.770860\pi\) |
0.659284 | + | 0.751894i | \(0.270860\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8131i | 0.641949i | 0.947088 | + | 0.320975i | \(0.104010\pi\) | ||||
−0.947088 | + | 0.320975i | \(0.895990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8035 | − | 27.8035i | −1.28659 | − | 1.28659i | −0.936842 | − | 0.349753i | \(-0.886266\pi\) |
−0.349753 | − | 0.936842i | \(-0.613734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.897143 | + | 0.897143i | −0.0414262 | + | 0.0414262i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.49976 | 0.160919 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.0885 | + | 15.0885i | 0.692308 | + | 0.692308i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.4026 | 0.977909 | 0.488954 | − | 0.872309i | \(-0.337378\pi\) | ||||
0.488954 | + | 0.872309i | \(0.337378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.10717 | −0.187271 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.16784 | + | 1.16784i | 0.0530287 | + | 0.0530287i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.9883 | 1.26827 | 0.634136 | − | 0.773222i | \(-0.281356\pi\) | ||||
0.634136 | + | 0.773222i | \(0.281356\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0491 | + | 22.0491i | −0.995063 | + | 0.995063i | −0.999988 | − | 0.00492464i | \(-0.998432\pi\) |
0.00492464 | + | 0.999988i | \(0.498432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.34727 | + | 7.34727i | 0.330904 | + | 0.330904i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.83052i | 0.126966i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.60480 | + | 5.60480i | −0.250905 | + | 0.250905i | −0.821342 | − | 0.570436i | \(-0.806774\pi\) |
0.570436 | + | 0.821342i | \(0.306774\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.02371i | − | 0.223996i | −0.993708 | − | 0.111998i | \(-0.964275\pi\) | ||
0.993708 | − | 0.111998i | \(-0.0357250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.105169i | − | 0.00467996i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.3372 | − | 26.3372i | 1.16738 | − | 1.16738i | 0.184555 | − | 0.982822i | \(-0.440915\pi\) |
0.982822 | − | 0.184555i | \(-0.0590845\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.7394i | 0.696271i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.84416 | − | 1.84416i | −0.0812635 | − | 0.0812635i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.5405 | + | 40.5405i | −1.78297 | + | 1.78297i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.453686 | 0.0198763 | 0.00993817 | − | 0.999951i | \(-0.496837\pi\) | ||||
0.00993817 | + | 0.999951i | \(0.496837\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.5974 | − | 26.5974i | −1.16302 | − | 1.16302i | −0.983810 | − | 0.179214i | \(-0.942645\pi\) |
−0.179214 | − | 0.983810i | \(-0.557355\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.6647 | 0.682363 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3823 | −0.886187 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.46229 | + | 2.46229i | 0.106654 | + | 0.106654i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.77960 | −0.0769389 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.61173 | + | 3.61173i | −0.155568 | + | 0.155568i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5559 | − | 17.5559i | −0.754785 | − | 0.754785i | 0.220583 | − | 0.975368i | \(-0.429204\pi\) |
−0.975368 | + | 0.220583i | \(0.929204\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.34093i | 0.0574390i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.76713 | + | 6.76713i | −0.289342 | + | 0.289342i | −0.836820 | − | 0.547478i | \(-0.815588\pi\) |
0.547478 | + | 0.836820i | \(0.315588\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.28954i | 0.395748i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.4151i | − | 0.655515i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.6889 | + | 29.6889i | −1.25796 | + | 1.25796i | −0.305893 | + | 0.952066i | \(0.598955\pi\) |
−0.952066 | + | 0.305893i | \(0.901045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.88444i | 0.0797035i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.1503 | + | 25.1503i | 1.05996 | + | 1.05996i | 0.998084 | + | 0.0618753i | \(0.0197081\pi\) |
0.0618753 | + | 0.998084i | \(0.480292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.870065 | + | 0.870065i | −0.0366039 | + | 0.0366039i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.4528 | −0.731660 | −0.365830 | − | 0.930682i | \(-0.619215\pi\) | ||||
−0.365830 | + | 0.930682i | \(0.619215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4569 | + | 22.4569i | 0.939793 | + | 0.939793i | 0.998288 | − | 0.0584947i | \(-0.0186301\pi\) |
−0.0584947 | + | 0.998288i | \(0.518630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.7692 | −1.36657 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.6265 | 1.69130 | 0.845652 | − | 0.533734i | \(-0.179212\pi\) | ||||
0.845652 | + | 0.533734i | \(0.179212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.57988 | − | 7.57988i | −0.314466 | − | 0.314466i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.9567 | −1.19926 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.79577 | − | 1.79577i | 0.0741194 | − | 0.0741194i | −0.669075 | − | 0.743195i | \(-0.733310\pi\) |
0.743195 | + | 0.669075i | \(0.233310\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.90283 | + | 9.90283i | 0.408039 | + | 0.408039i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.4046i | − | 0.468331i | −0.972197 | − | 0.234165i | \(-0.924764\pi\) | ||
0.972197 | − | 0.234165i | \(-0.0752357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.534392 | + | 0.534392i | −0.0219079 | + | 0.0219079i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.81649i | 0.319373i | 0.987168 | + | 0.159687i | \(0.0510484\pi\) | ||||
−0.987168 | + | 0.159687i | \(0.948952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.2752i | 0.908625i | 0.890842 | + | 0.454313i | \(0.150115\pi\) | ||||
−0.890842 | + | 0.454313i | \(0.849885\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.68084 | + | 1.68084i | −0.0683359 | + | 0.0683359i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 11.5129i | − | 0.467293i | −0.972322 | − | 0.233646i | \(-0.924934\pi\) | ||
0.972322 | − | 0.233646i | \(-0.0750658\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.8290 | − | 21.8290i | −0.883107 | − | 0.883107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.6256 | − | 24.6256i | 0.994618 | − | 0.994618i | −0.00536742 | − | 0.999986i | \(-0.501709\pi\) |
0.999986 | + | 0.00536742i | \(0.00170851\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3630 | −1.18211 | −0.591054 | − | 0.806632i | \(-0.701288\pi\) | ||||
−0.591054 | + | 0.806632i | \(0.701288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.5316 | − | 32.5316i | −1.30756 | − | 1.30756i | −0.923173 | − | 0.384384i | \(-0.874414\pi\) |
−0.384384 | − | 0.923173i | \(-0.625586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.1420 | −0.526524 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.6284 | −0.985134 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.06584 | + | 5.06584i | 0.201988 | + | 0.201988i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.4307 | 0.415240 | 0.207620 | − | 0.978210i | \(-0.433428\pi\) | ||||
0.207620 | + | 0.978210i | \(0.433428\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.734574 | + | 0.734574i | −0.0291507 | + | 0.0291507i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.94473 | − | 1.94473i | −0.0770531 | − | 0.0770531i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 26.3287i | − | 1.03992i | −0.854191 | − | 0.519960i | \(-0.825947\pi\) | ||
0.854191 | − | 0.519960i | \(-0.174053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1662 | + | 10.1662i | −0.400917 | + | 0.400917i | −0.878556 | − | 0.477639i | \(-0.841493\pi\) |
0.477639 | + | 0.878556i | \(0.341493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.4560i | − | 1.19735i | −0.800992 | − | 0.598675i | \(-0.795694\pi\) | ||
0.800992 | − | 0.598675i | \(-0.204306\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.0047i | 2.15912i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.424352 | − | 0.424352i | 0.0166062 | − | 0.0166062i | −0.698755 | − | 0.715361i | \(-0.746262\pi\) |
0.715361 | + | 0.698755i | \(0.246262\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.39735i | 0.0545989i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.4421 | − | 21.4421i | −0.835268 | − | 0.835268i | 0.152964 | − | 0.988232i | \(-0.451118\pi\) |
−0.988232 | + | 0.152964i | \(0.951118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6529 | − | 29.6529i | 1.15337 | − | 1.15337i | 0.167492 | − | 0.985873i | \(-0.446433\pi\) |
0.985873 | − | 0.167492i | \(-0.0535668\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.675660 | −0.0262010 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0875 | − | 10.0875i | −0.390589 | − | 0.390589i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39.3112 | −1.51759 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.5720 | −1.29410 | −0.647052 | − | 0.762446i | \(-0.723998\pi\) | ||||
−0.647052 | + | 0.762446i | \(0.723998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.4845 | + | 23.4845i | 0.902584 | + | 0.902584i | 0.995659 | − | 0.0930751i | \(-0.0296697\pi\) |
−0.0930751 | + | 0.995659i | \(0.529670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.4839 | 0.402333 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.90491 | − | 4.90491i | 0.187681 | − | 0.187681i | −0.607012 | − | 0.794693i | \(-0.707632\pi\) |
0.794693 | + | 0.607012i | \(0.207632\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.49691 | + | 2.49691i | 0.0954022 | + | 0.0954022i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15.5917i | − | 0.593996i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1177 | − | 19.1177i | 0.727272 | − | 0.727272i | −0.242804 | − | 0.970075i | \(-0.578067\pi\) |
0.970075 | + | 0.242804i | \(0.0780671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.10338i | 0.0797858i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.07405i | − | 0.230071i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.01355 | − | 6.01355i | 0.227129 | − | 0.227129i | −0.584363 | − | 0.811492i | \(-0.698656\pi\) |
0.811492 | + | 0.584363i | \(0.198656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.40501i | 0.241570i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.472060 | − | 0.472060i | −0.0177536 | − | 0.0177536i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.33448 | + | 6.33448i | −0.237896 | + | 0.237896i | −0.815979 | − | 0.578082i | \(-0.803801\pi\) |
0.578082 | + | 0.815979i | \(0.303801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.5069 | −0.805441 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.56483 | − | 1.56483i | −0.0585212 | − | 0.0585212i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.8643 | −0.740814 | −0.370407 | − | 0.928869i | \(-0.620782\pi\) | ||||
−0.370407 | + | 0.928869i | \(0.620782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5554 | −0.616554 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.61967 | − | 7.61967i | −0.282987 | − | 0.282987i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0880 | 0.633759 | 0.316879 | − | 0.948466i | \(-0.397365\pi\) | ||||
0.316879 | + | 0.948466i | \(0.397365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.32430 | − | 2.32430i | 0.0859673 | − | 0.0859673i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.4896 | + | 27.4896i | 1.01535 | + | 1.01535i | 0.999880 | + | 0.0154724i | \(0.00492520\pi\) |
0.0154724 | + | 0.999880i | \(0.495075\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.48048i | 0.238711i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.4666 | + | 33.4666i | −1.23109 | + | 1.23109i | −0.267542 | + | 0.963546i | \(0.586212\pi\) |
−0.963546 | + | 0.267542i | \(0.913788\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.720828i | 0.0264446i | 0.999913 | + | 0.0132223i | \(0.00420892\pi\) | ||||
−0.999913 | + | 0.0132223i | \(0.995791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.36208i | − | 0.0865398i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.98789 | + | 7.98789i | −0.291871 | + | 0.291871i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.54158i | 0.311687i | 0.987782 | + | 0.155843i | \(0.0498095\pi\) | ||||
−0.987782 | + | 0.155843i | \(0.950190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0726208 | − | 0.0726208i | −0.00264294 | − | 0.00264294i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.80744 | − | 5.80744i | 0.211075 | − | 0.211075i | −0.593649 | − | 0.804724i | \(-0.702313\pi\) |
0.804724 | + | 0.593649i | \(0.202313\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.8670 | −0.720179 | −0.360090 | − | 0.932918i | \(-0.617254\pi\) | ||||
−0.360090 | + | 0.932918i | \(0.617254\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.01886 | + | 6.01886i | 0.217897 | + | 0.217897i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.6172 | −1.06942 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.4781 | 1.85635 | 0.928173 | − | 0.372148i | \(-0.121379\pi\) | ||||
0.928173 | + | 0.372148i | \(0.121379\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.8748 | + | 17.8748i | 0.642913 | + | 0.642913i | 0.951271 | − | 0.308358i | \(-0.0997793\pi\) |
−0.308358 | + | 0.951271i | \(0.599779\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.2454 | −0.583553 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.83987 | − | 3.83987i | 0.137578 | − | 0.137578i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2231 | + | 10.2231i | 0.365810 | + | 0.365810i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.49259i | 0.124656i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.93955 | − | 9.93955i | 0.354307 | − | 0.354307i | −0.507403 | − | 0.861709i | \(-0.669394\pi\) |
0.861709 | + | 0.507403i | \(0.169394\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.81071i | 0.277717i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 21.1671i | − | 0.751664i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.30890 | + | 1.30890i | −0.0463636 | + | 0.0463636i | −0.729908 | − | 0.683545i | \(-0.760437\pi\) |
0.683545 | + | 0.729908i | \(0.260437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.8484i | 1.90502i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.8466 | + | 56.8466i | 2.00607 | + | 2.00607i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.733698 | − | 0.733698i | 0.0258594 | − | 0.0258594i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.4014 | −1.35012 | −0.675060 | − | 0.737763i | \(-0.735882\pi\) | ||||
−0.675060 | + | 0.737763i | \(0.735882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4504 | + | 32.4504i | 1.13949 | + | 1.13949i | 0.988542 | + | 0.150946i | \(0.0482319\pi\) |
0.150946 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.907215 | −0.0317784 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.93873 | 0.102813 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.9023 | − | 13.9023i | −0.485194 | − | 0.485194i | 0.421592 | − | 0.906786i | \(-0.361472\pi\) |
−0.906786 | + | 0.421592i | \(0.861472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.7710 | 0.549744 | 0.274872 | − | 0.961481i | \(-0.411365\pi\) | ||||
0.274872 | + | 0.961481i | \(0.411365\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.4573 | + | 25.4573i | −0.885237 | + | 0.885237i | −0.994061 | − | 0.108824i | \(-0.965291\pi\) |
0.108824 | + | 0.994061i | \(0.465291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0084 | − | 18.0084i | −0.625459 | − | 0.625459i | 0.321463 | − | 0.946922i | \(-0.395825\pi\) |
−0.946922 | + | 0.321463i | \(0.895825\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.79732i | 0.166217i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.896173 | − | 0.896173i | 0.0310133 | − | 0.0310133i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.91080i | 0.238587i | 0.992859 | + | 0.119294i | \(0.0380630\pi\) | ||||
−0.992859 | + | 0.119294i | \(0.961937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.3088i | 0.838234i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.605540 | + | 0.605540i | −0.0208312 | + | 0.0208312i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.0892i | 0.518471i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.95519 | − | 6.95519i | −0.238421 | − | 0.238421i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.91240 | + | 8.91240i | −0.305155 | + | 0.305155i | −0.843027 | − | 0.537872i | \(-0.819228\pi\) |
0.537872 | + | 0.843027i | \(0.319228\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.4916 | 1.00741 | 0.503706 | − | 0.863875i | \(-0.331969\pi\) | ||||
0.503706 | + | 0.863875i | \(0.331969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9280 | + | 11.9280i | 0.406977 | + | 0.406977i | 0.880683 | − | 0.473706i | \(-0.157084\pi\) |
−0.473706 | + | 0.880683i | \(0.657084\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.3343 | 1.54320 | 0.771598 | − | 0.636110i | \(-0.219458\pi\) | ||||
0.771598 | + | 0.636110i | \(0.219458\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.121844 | 0.00414282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −55.6751 | − | 55.6751i | −1.88865 | − | 1.88865i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.48941 | −0.118234 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.11117 | − | 1.11117i | 0.0375645 | − | 0.0375645i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.3609 | + | 31.3609i | 1.05898 | + | 1.05898i | 0.998148 | + | 0.0608358i | \(0.0193766\pi\) |
0.0608358 | + | 0.998148i | \(0.480623\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 51.6409i | − | 1.73983i | −0.493204 | − | 0.869913i | \(-0.664175\pi\) | ||
0.493204 | − | 0.869913i | \(-0.335825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.8785 | − | 21.8785i | 0.736269 | − | 0.736269i | −0.235585 | − | 0.971854i | \(-0.575701\pi\) |
0.971854 | + | 0.235585i | \(0.0757006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 19.7592i | − | 0.663449i | −0.943376 | − | 0.331725i | \(-0.892370\pi\) | ||
0.943376 | − | 0.331725i | \(-0.107630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.59439i | 0.221169i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.0417 | + | 34.0417i | −1.13916 | + | 1.13916i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.43251i | − | 0.114736i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.00091 | − | 5.00091i | −0.166790 | − | 0.166790i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.2310 | + | 19.2310i | −0.640678 | + | 0.640678i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.915490 | 0.0304319 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.5036 | + | 31.5036i | 1.04606 | + | 1.04606i | 0.998887 | + | 0.0471723i | \(0.0150210\pi\) |
0.0471723 | + | 0.998887i | \(0.484979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.7479 | 0.521752 | 0.260876 | − | 0.965372i | \(-0.415989\pi\) | ||||
0.260876 | + | 0.965372i | \(0.415989\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.7530 | −1.81206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.27211 | + | 6.27211i | 0.207123 | + | 0.207123i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.5809 | 1.04176 | 0.520880 | − | 0.853630i | \(-0.325604\pi\) | ||||
0.520880 | + | 0.853630i | \(0.325604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.50460 | + | 5.50460i | −0.181186 | + | 0.181186i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.25366 | − | 5.25366i | −0.172739 | − | 0.172739i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.4061i | 1.03040i | 0.857070 | + | 0.515200i | \(0.172282\pi\) | ||||
−0.857070 | + | 0.515200i | \(0.827718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.03275 | + | 3.03275i | −0.0993945 | + | 0.0993945i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.86016i | 0.126241i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9239i | 0.487544i | 0.969833 | + | 0.243772i | \(0.0783848\pi\) | ||||
−0.969833 | + | 0.243772i | \(0.921615\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.4870 | − | 13.4870i | 0.439664 | − | 0.439664i | −0.452235 | − | 0.891899i | \(-0.649373\pi\) |
0.891899 | + | 0.452235i | \(0.149373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.33942i | 0.271569i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.6554 | − | 28.6554i | −0.931174 | − | 0.931174i | 0.0666054 | − | 0.997779i | \(-0.478783\pi\) |
−0.997779 | + | 0.0666054i | \(0.978783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.6090 | + | 30.6090i | −0.993609 | + | 0.993609i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.9378 | −1.58525 | −0.792626 | − | 0.609709i | \(-0.791286\pi\) | ||||
−0.792626 | + | 0.609709i | \(0.791286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.842651 | − | 0.842651i | −0.0272675 | − | 0.0272675i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.4152 | 0.723825 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.3379 | 0.656060 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.56347 | − | 1.56347i | −0.0503298 | − | 0.0503298i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.50595 | 0.273533 | 0.136767 | − | 0.990603i | \(-0.456329\pi\) | ||||
0.136767 | + | 0.990603i | \(0.456329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.52407 | + | 8.52407i | −0.273550 | + | 0.273550i | −0.830528 | − | 0.556977i | \(-0.811961\pi\) |
0.556977 | + | 0.830528i | \(0.311961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.44120 | + | 9.44120i | 0.302671 | + | 0.302671i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.2469i | 0.967685i | 0.875155 | + | 0.483842i | \(0.160759\pi\) | ||||
−0.875155 | + | 0.483842i | \(0.839241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47.4654 | + | 47.4654i | −1.51700 | + | 1.51700i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.8151i | 1.58886i | 0.607358 | + | 0.794428i | \(0.292229\pi\) | ||||
−0.607358 | + | 0.794428i | \(0.707771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.13852i | − | 0.0681390i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.19117 | + | 3.19117i | −0.101473 | + | 0.101473i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.1968i | 0.832167i | 0.909326 | + | 0.416084i | \(0.136598\pi\) | ||||
−0.909326 | + | 0.416084i | \(0.863402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.39438 | − | 1.39438i | −0.0442049 | − | 0.0442049i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.13429 | + | 5.13429i | −0.162604 | + | 0.162604i | −0.783719 | − | 0.621115i | \(-0.786680\pi\) |
0.621115 | + | 0.783719i | \(0.286680\pi\) | |||||||
\(998\) | 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.v.e.1583.9 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.12 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.18 | yes | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.3 | ✓ | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.3 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.12 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.18 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.9 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.3 | ✓ | 40 | 12.11 | even | 2 | ||
1008.2.v.e.323.18 | yes | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.827.3 | yes | 40 | 16.5 | even | 4 | ||
1008.2.v.e.827.18 | yes | 40 | 48.5 | odd | 4 | ||
4032.2.v.e.1583.9 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.1583.12 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.3599.9 | 40 | 48.11 | even | 4 | inner | ||
4032.2.v.e.3599.12 | 40 | 16.11 | odd | 4 | inner |