Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(2645,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2646.2645");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2645.8 | ||
Root | \(0.991445 + 0.130526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2645 |
Dual form | 2646.2.d.e.2645.16 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 4.29725 | 1.92179 | 0.960894 | − | 0.276916i | \(-0.0893125\pi\) | ||||
0.960894 | + | 0.276916i | \(0.0893125\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 4.29725i | − 1.35891i | ||||||||
\(11\) | − 5.20041i | − 1.56798i | −0.620771 | − | 0.783992i | \(-0.713180\pi\) | ||||
0.620771 | − | 0.783992i | \(-0.286820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81444i | 0.780586i | 0.920691 | + | 0.390293i | \(0.127626\pi\) | ||||
−0.920691 | + | 0.390293i | \(0.872374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.02815 | −0.976970 | −0.488485 | − | 0.872572i | \(-0.662450\pi\) | ||||
−0.488485 | + | 0.872572i | \(0.662450\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.77998i | − 0.408355i | −0.978934 | − | 0.204178i | \(-0.934548\pi\) | ||||
0.978934 | − | 0.204178i | \(-0.0654520\pi\) | |||||||
\(20\) | −4.29725 | −0.960894 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.20041 | −1.10873 | ||||||||
\(23\) | − 7.70319i | − 1.60623i | −0.595827 | − | 0.803113i | \(-0.703176\pi\) | ||||
0.595827 | − | 0.803113i | \(-0.296824\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.4663 | 2.69327 | ||||||||
\(26\) | 2.81444 | 0.551958 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5.02884i | − 0.933832i | −0.884302 | − | 0.466916i | \(-0.845365\pi\) | ||||
0.884302 | − | 0.466916i | \(-0.154635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.25139i | − 0.224756i | −0.993666 | − | 0.112378i | \(-0.964153\pi\) | ||||
0.993666 | − | 0.112378i | \(-0.0358468\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.02815i | 0.690822i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.17738 | −1.50875 | −0.754376 | − | 0.656443i | \(-0.772060\pi\) | ||||
−0.754376 | + | 0.656443i | \(0.772060\pi\) | |||||||
\(38\) | −1.77998 | −0.288751 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.29725i | 0.679455i | ||||||||
\(41\) | −5.29403 | −0.826789 | −0.413394 | − | 0.910552i | \(-0.635657\pi\) | ||||
−0.413394 | + | 0.910552i | \(0.635657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.53572 | −0.691690 | −0.345845 | − | 0.938292i | \(-0.612408\pi\) | ||||
−0.345845 | + | 0.938292i | \(0.612408\pi\) | |||||||
\(44\) | 5.20041i | 0.783992i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.70319 | −1.13577 | ||||||||
\(47\) | 7.59771 | 1.10824 | 0.554120 | − | 0.832437i | \(-0.313055\pi\) | ||||
0.554120 | + | 0.832437i | \(0.313055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 13.4663i | − 1.90443i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.81444i | − 0.390293i | ||||||||
\(53\) | 0.167470i | 0.0230037i | 0.999934 | + | 0.0115019i | \(0.00366124\pi\) | ||||
−0.999934 | + | 0.0115019i | \(0.996339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 22.3475i | − 3.01333i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.02884 | −0.660319 | ||||||||
\(59\) | 5.99698 | 0.780740 | 0.390370 | − | 0.920658i | \(-0.372347\pi\) | ||||
0.390370 | + | 0.920658i | \(0.372347\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.79367i | − 0.997877i | −0.866637 | − | 0.498939i | \(-0.833723\pi\) | ||||
0.866637 | − | 0.498939i | \(-0.166277\pi\) | |||||||
\(62\) | −1.25139 | −0.158927 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 12.0944i | 1.50012i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3778 | 1.39002 | 0.695009 | − | 0.719001i | \(-0.255400\pi\) | ||||
0.695009 | + | 0.719001i | \(0.255400\pi\) | |||||||
\(68\) | 4.02815 | 0.488485 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.539455i | 0.0640216i | 0.999488 | + | 0.0320108i | \(0.0101911\pi\) | ||||
−0.999488 | + | 0.0320108i | \(0.989809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 3.80634i | − 0.445498i | −0.974876 | − | 0.222749i | \(-0.928497\pi\) | ||||
0.974876 | − | 0.222749i | \(-0.0715031\pi\) | |||||||
\(74\) | 9.17738i | 1.06685i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.77998i | 0.204178i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.99590 | 0.224556 | 0.112278 | − | 0.993677i | \(-0.464185\pi\) | ||||
0.112278 | + | 0.993677i | \(0.464185\pi\) | |||||||
\(80\) | 4.29725 | 0.480447 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.29403i | 0.584628i | ||||||||
\(83\) | 16.0388 | 1.76049 | 0.880245 | − | 0.474520i | \(-0.157378\pi\) | ||||
0.880245 | + | 0.474520i | \(0.157378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.3100 | −1.87753 | ||||||||
\(86\) | 4.53572i | 0.489099i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.20041 | 0.554366 | ||||||||
\(89\) | −1.29396 | −0.137159 | −0.0685795 | − | 0.997646i | \(-0.521847\pi\) | ||||
−0.0685795 | + | 0.997646i | \(0.521847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.70319i | 0.803113i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 7.59771i | − 0.783644i | ||||||||
\(95\) | − 7.64901i | − 0.784772i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.2596i | 1.75245i | 0.481902 | + | 0.876225i | \(0.339946\pi\) | ||||
−0.481902 | + | 0.876225i | \(0.660054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.4663 | −1.34663 | ||||||||
\(101\) | 14.1659 | 1.40955 | 0.704777 | − | 0.709429i | \(-0.251047\pi\) | ||||
0.704777 | + | 0.709429i | \(0.251047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.817539i | 0.0805545i | 0.999189 | + | 0.0402773i | \(0.0128241\pi\) | ||||
−0.999189 | + | 0.0402773i | \(0.987176\pi\) | |||||||
\(104\) | −2.81444 | −0.275979 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.167470 | 0.0162661 | ||||||||
\(107\) | 12.5586i | 1.21409i | 0.794667 | + | 0.607045i | \(0.207645\pi\) | ||||
−0.794667 | + | 0.607045i | \(0.792355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.395023 | −0.0378363 | −0.0189181 | − | 0.999821i | \(-0.506022\pi\) | ||||
−0.0189181 | + | 0.999821i | \(0.506022\pi\) | |||||||
\(110\) | −22.3475 | −2.13075 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.1520i | 1.51946i | 0.650241 | + | 0.759728i | \(0.274668\pi\) | ||||
−0.650241 | + | 0.759728i | \(0.725332\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 33.1025i | − 3.08682i | ||||||||
\(116\) | 5.02884i | 0.466916i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 5.99698i | − 0.552067i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0443 | −1.45857 | ||||||||
\(122\) | −7.79367 | −0.705606 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.25139i | 0.112378i | ||||||||
\(125\) | 36.3820 | 3.25411 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.04803 | 0.802883 | 0.401441 | − | 0.915885i | \(-0.368509\pi\) | ||||
0.401441 | + | 0.915885i | \(0.368509\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.0944 | 1.06075 | ||||||||
\(131\) | −1.75412 | −0.153259 | −0.0766293 | − | 0.997060i | \(-0.524416\pi\) | ||||
−0.0766293 | + | 0.997060i | \(0.524416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 11.3778i | − 0.982891i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 4.02815i | − 0.345411i | ||||||||
\(137\) | − 16.4433i | − 1.40485i | −0.711759 | − | 0.702423i | \(-0.752101\pi\) | ||||
0.711759 | − | 0.702423i | \(-0.247899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 17.6373i | − 1.49598i | −0.663710 | − | 0.747990i | \(-0.731019\pi\) | ||||
0.663710 | − | 0.747990i | \(-0.268981\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.539455 | 0.0452701 | ||||||||
\(143\) | 14.6363 | 1.22395 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 21.6102i | − 1.79463i | ||||||||
\(146\) | −3.80634 | −0.315015 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.17738 | 0.754376 | ||||||||
\(149\) | − 12.2115i | − 1.00041i | −0.865908 | − | 0.500203i | \(-0.833259\pi\) | ||||
0.865908 | − | 0.500203i | \(-0.166741\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.44860 | −0.687537 | −0.343769 | − | 0.939054i | \(-0.611704\pi\) | ||||
−0.343769 | + | 0.939054i | \(0.611704\pi\) | |||||||
\(152\) | 1.77998 | 0.144375 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5.37753i | − 0.431934i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.97105i | − 0.157307i | −0.996902 | − | 0.0786534i | \(-0.974938\pi\) | ||||
0.996902 | − | 0.0786534i | \(-0.0250620\pi\) | |||||||
\(158\) | − 1.99590i | − 0.158785i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 4.29725i | − 0.339727i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.67231 | −0.600941 | −0.300471 | − | 0.953791i | \(-0.597144\pi\) | ||||
−0.300471 | + | 0.953791i | \(0.597144\pi\) | |||||||
\(164\) | 5.29403 | 0.413394 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 16.0388i | − 1.24485i | ||||||||
\(167\) | −6.19782 | −0.479602 | −0.239801 | − | 0.970822i | \(-0.577082\pi\) | ||||
−0.239801 | + | 0.970822i | \(0.577082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.07891 | 0.390685 | ||||||||
\(170\) | 17.3100i | 1.32761i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.53572 | 0.345845 | ||||||||
\(173\) | −1.17825 | −0.0895805 | −0.0447903 | − | 0.998996i | \(-0.514262\pi\) | ||||
−0.0447903 | + | 0.998996i | \(0.514262\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 5.20041i | − 0.391996i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.29396i | 0.0969861i | ||||||||
\(179\) | 15.3425i | 1.14676i | 0.819291 | + | 0.573378i | \(0.194367\pi\) | ||||
−0.819291 | + | 0.573378i | \(0.805633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.24186i | 0.389624i | 0.980841 | + | 0.194812i | \(0.0624097\pi\) | ||||
−0.980841 | + | 0.194812i | \(0.937590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.70319 | 0.567886 | ||||||||
\(185\) | −39.4375 | −2.89950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9480i | 1.53187i | ||||||||
\(188\) | −7.59771 | −0.554120 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.64901 | −0.554918 | ||||||||
\(191\) | − 4.63237i | − 0.335187i | −0.985856 | − | 0.167593i | \(-0.946400\pi\) | ||||
0.985856 | − | 0.167593i | \(-0.0535996\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.34315 | −0.528571 | −0.264286 | − | 0.964444i | \(-0.585136\pi\) | ||||
−0.264286 | + | 0.964444i | \(0.585136\pi\) | |||||||
\(194\) | 17.2596 | 1.23917 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.5456i | 1.67756i | 0.544474 | + | 0.838778i | \(0.316729\pi\) | ||||
−0.544474 | + | 0.838778i | \(0.683271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 7.28291i | − 0.516272i | −0.966109 | − | 0.258136i | \(-0.916892\pi\) | ||||
0.966109 | − | 0.258136i | \(-0.0831082\pi\) | |||||||
\(200\) | 13.4663i | 0.952215i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 14.1659i | − 0.996706i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.7498 | −1.58891 | ||||||||
\(206\) | 0.817539 | 0.0569607 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.81444i | 0.195147i | ||||||||
\(209\) | −9.25662 | −0.640294 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7862 | −0.880238 | −0.440119 | − | 0.897939i | \(-0.645064\pi\) | ||||
−0.440119 | + | 0.897939i | \(0.645064\pi\) | |||||||
\(212\) | − 0.167470i | − 0.0115019i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.5586 | 0.858491 | ||||||||
\(215\) | −19.4911 | −1.32928 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.395023i | 0.0267543i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.3475i | 1.50667i | ||||||||
\(221\) | − 11.3370i | − 0.762609i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.38874i | 0.226927i | 0.993542 | + | 0.113463i | \(0.0361945\pi\) | ||||
−0.993542 | + | 0.113463i | \(0.963806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.1520 | 1.07442 | ||||||||
\(227\) | −1.21149 | −0.0804093 | −0.0402046 | − | 0.999191i | \(-0.512801\pi\) | ||||
−0.0402046 | + | 0.999191i | \(0.512801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6590i | 1.29910i | 0.760318 | + | 0.649551i | \(0.225043\pi\) | ||||
−0.760318 | + | 0.649551i | \(0.774957\pi\) | |||||||
\(230\) | −33.1025 | −2.18271 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.02884 | 0.330160 | ||||||||
\(233\) | − 15.2758i | − 1.00075i | −0.865808 | − | 0.500377i | \(-0.833195\pi\) | ||||
0.865808 | − | 0.500377i | \(-0.166805\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.6493 | 2.12980 | ||||||||
\(236\) | −5.99698 | −0.390370 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.539712i | 0.0349111i | 0.999848 | + | 0.0174555i | \(0.00555655\pi\) | ||||
−0.999848 | + | 0.0174555i | \(0.994443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 9.37436i | − 0.603855i | −0.953331 | − | 0.301928i | \(-0.902370\pi\) | ||||
0.953331 | − | 0.301928i | \(-0.0976301\pi\) | |||||||
\(242\) | 16.0443i | 1.03137i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.79367i | 0.498939i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.00965 | 0.318756 | ||||||||
\(248\) | 1.25139 | 0.0794633 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 36.3820i | − 2.30100i | ||||||||
\(251\) | −12.2724 | −0.774626 | −0.387313 | − | 0.921948i | \(-0.626597\pi\) | ||||
−0.387313 | + | 0.921948i | \(0.626597\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −40.0597 | −2.51853 | ||||||||
\(254\) | − 9.04803i | − 0.567724i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.4783 | 0.840754 | 0.420377 | − | 0.907350i | \(-0.361898\pi\) | ||||
0.420377 | + | 0.907350i | \(0.361898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 12.0944i | − 0.750060i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.75412i | 0.108370i | ||||||||
\(263\) | 12.5893i | 0.776289i | 0.921599 | + | 0.388144i | \(0.126884\pi\) | ||||
−0.921599 | + | 0.388144i | \(0.873116\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.719659i | 0.0442083i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.3778 | −0.695009 | ||||||||
\(269\) | 6.85395 | 0.417892 | 0.208946 | − | 0.977927i | \(-0.432997\pi\) | ||||
0.208946 | + | 0.977927i | \(0.432997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.8899i | 1.81568i | 0.419317 | + | 0.907840i | \(0.362270\pi\) | ||||
−0.419317 | + | 0.907840i | \(0.637730\pi\) | |||||||
\(272\) | −4.02815 | −0.244243 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4433 | −0.993377 | ||||||||
\(275\) | − 70.0306i | − 4.22300i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.7992 | −1.85055 | −0.925274 | − | 0.379300i | \(-0.876165\pi\) | ||||
−0.925274 | + | 0.379300i | \(0.876165\pi\) | |||||||
\(278\) | −17.6373 | −1.05782 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.44161i | 0.384274i | 0.981368 | + | 0.192137i | \(0.0615418\pi\) | ||||
−0.981368 | + | 0.192137i | \(0.938458\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 13.5392i | − 0.804821i | −0.915459 | − | 0.402410i | \(-0.868172\pi\) | ||||
0.915459 | − | 0.402410i | \(-0.131828\pi\) | |||||||
\(284\) | − 0.539455i | − 0.0320108i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 14.6363i | − 0.865460i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.773996 | −0.0455292 | ||||||||
\(290\) | −21.6102 | −1.26899 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.80634i | 0.222749i | ||||||||
\(293\) | −26.3170 | −1.53745 | −0.768727 | − | 0.639577i | \(-0.779109\pi\) | ||||
−0.768727 | + | 0.639577i | \(0.779109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.7705 | 1.50042 | ||||||||
\(296\) | − 9.17738i | − 0.533424i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2115 | −0.707393 | ||||||||
\(299\) | 21.6802 | 1.25380 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.44860i | 0.486162i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 1.77998i | − 0.102089i | ||||||||
\(305\) | − 33.4913i | − 1.91771i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.4207i | 1.10840i | 0.832385 | + | 0.554198i | \(0.186975\pi\) | ||||
−0.832385 | + | 0.554198i | \(0.813025\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.37753 | −0.305423 | ||||||||
\(311\) | −3.58894 | −0.203510 | −0.101755 | − | 0.994809i | \(-0.532446\pi\) | ||||
−0.101755 | + | 0.994809i | \(0.532446\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 12.9198i | − 0.730272i | −0.930954 | − | 0.365136i | \(-0.881023\pi\) | ||||
0.930954 | − | 0.365136i | \(-0.118977\pi\) | |||||||
\(314\) | −1.97105 | −0.111233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.99590 | −0.112278 | ||||||||
\(317\) | 12.0384i | 0.676143i | 0.941120 | + | 0.338071i | \(0.109775\pi\) | ||||
−0.941120 | + | 0.338071i | \(0.890225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.1520 | −1.46423 | ||||||||
\(320\) | −4.29725 | −0.240224 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.17002i | 0.398951i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.9003i | 2.10233i | ||||||||
\(326\) | 7.67231i | 0.424930i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 5.29403i | − 0.292314i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8226 | 1.41934 | 0.709671 | − | 0.704534i | \(-0.248844\pi\) | ||||
0.709671 | + | 0.704534i | \(0.248844\pi\) | |||||||
\(332\) | −16.0388 | −0.880245 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.19782i | 0.339130i | ||||||||
\(335\) | 48.8932 | 2.67132 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.5378 | 1.88139 | 0.940696 | − | 0.339250i | \(-0.110173\pi\) | ||||
0.940696 | + | 0.339250i | \(0.110173\pi\) | |||||||
\(338\) | − 5.07891i | − 0.276256i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 17.3100 | 0.938765 | ||||||||
\(341\) | −6.50774 | −0.352414 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 4.53572i | − 0.244549i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.17825i | 0.0633430i | ||||||||
\(347\) | − 11.4390i | − 0.614075i | −0.951697 | − | 0.307038i | \(-0.900662\pi\) | ||||
0.951697 | − | 0.307038i | \(-0.0993377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9.93436i | − 0.531774i | −0.964004 | − | 0.265887i | \(-0.914335\pi\) | ||||
0.964004 | − | 0.265887i | \(-0.0856648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.20041 | −0.277183 | ||||||||
\(353\) | −2.80734 | −0.149419 | −0.0747097 | − | 0.997205i | \(-0.523803\pi\) | ||||
−0.0747097 | + | 0.997205i | \(0.523803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.31817i | 0.123036i | ||||||||
\(356\) | 1.29396 | 0.0685795 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.3425 | 0.810879 | ||||||||
\(359\) | 3.70282i | 0.195427i | 0.995215 | + | 0.0977137i | \(0.0311530\pi\) | ||||
−0.995215 | + | 0.0977137i | \(0.968847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8317 | 0.833246 | ||||||||
\(362\) | 5.24186 | 0.275506 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 16.3568i | − 0.856154i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.3176i | 0.695171i | 0.937648 | + | 0.347586i | \(0.112998\pi\) | ||||
−0.937648 | + | 0.347586i | \(0.887002\pi\) | |||||||
\(368\) | − 7.70319i | − 0.401556i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 39.4375i | 2.05026i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.09640 | −0.108548 | −0.0542738 | − | 0.998526i | \(-0.517284\pi\) | ||||
−0.0542738 | + | 0.998526i | \(0.517284\pi\) | |||||||
\(374\) | 20.9480 | 1.08320 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.59771i | 0.391822i | ||||||||
\(377\) | 14.1534 | 0.728936 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5916 | −0.544053 | −0.272027 | − | 0.962290i | \(-0.587694\pi\) | ||||
−0.272027 | + | 0.962290i | \(0.587694\pi\) | |||||||
\(380\) | 7.64901i | 0.392386i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.63237 | −0.237013 | ||||||||
\(383\) | 29.3742 | 1.50095 | 0.750476 | − | 0.660898i | \(-0.229825\pi\) | ||||
0.750476 | + | 0.660898i | \(0.229825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.34315i | 0.373756i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 17.2596i | − 0.876225i | ||||||||
\(389\) | − 0.139250i | − 0.00706028i | −0.999994 | − | 0.00353014i | \(-0.998876\pi\) | ||||
0.999994 | − | 0.00353014i | \(-0.00112368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.0296i | 1.56923i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.5456 | 1.18621 | ||||||||
\(395\) | 8.57687 | 0.431549 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.13731i | − 0.257834i | −0.991655 | − | 0.128917i | \(-0.958850\pi\) | ||||
0.991655 | − | 0.128917i | \(-0.0411501\pi\) | |||||||
\(398\) | −7.28291 | −0.365059 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.4663 | 0.673317 | ||||||||
\(401\) | − 10.0437i | − 0.501557i | −0.968044 | − | 0.250778i | \(-0.919313\pi\) | ||||
0.968044 | − | 0.250778i | \(-0.0806866\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.52196 | 0.175442 | ||||||||
\(404\) | −14.1659 | −0.704777 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.7261i | 2.36570i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 9.66617i | − 0.477961i | −0.971024 | − | 0.238981i | \(-0.923187\pi\) | ||||
0.971024 | − | 0.238981i | \(-0.0768132\pi\) | |||||||
\(410\) | 22.7498i | 1.12353i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 0.817539i | − 0.0402773i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 68.9228 | 3.38329 | ||||||||
\(416\) | 2.81444 | 0.137989 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.25662i | 0.452756i | ||||||||
\(419\) | 17.8462 | 0.871846 | 0.435923 | − | 0.899984i | \(-0.356422\pi\) | ||||
0.435923 | + | 0.899984i | \(0.356422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.87102 | 0.286136 | 0.143068 | − | 0.989713i | \(-0.454303\pi\) | ||||
0.143068 | + | 0.989713i | \(0.454303\pi\) | |||||||
\(422\) | 12.7862i | 0.622422i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.167470 | −0.00813305 | ||||||||
\(425\) | −54.2445 | −2.63124 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 12.5586i | − 0.607045i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.4911i | 0.939944i | ||||||||
\(431\) | 26.1698i | 1.26055i | 0.776370 | + | 0.630277i | \(0.217059\pi\) | ||||
−0.776370 | + | 0.630277i | \(0.782941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.2277i | 0.779852i | 0.920846 | + | 0.389926i | \(0.127499\pi\) | ||||
−0.920846 | + | 0.389926i | \(0.872501\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.395023 | 0.0189181 | ||||||||
\(437\) | −13.7115 | −0.655910 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 33.8953i | − 1.61773i | −0.587991 | − | 0.808867i | \(-0.700081\pi\) | ||||
0.587991 | − | 0.808867i | \(-0.299919\pi\) | |||||||
\(440\) | 22.3475 | 1.06537 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.3370 | −0.539246 | ||||||||
\(443\) | 6.11944i | 0.290743i | 0.989377 | + | 0.145372i | \(0.0464378\pi\) | ||||
−0.989377 | + | 0.145372i | \(0.953562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.56045 | −0.263591 | ||||||||
\(446\) | 3.38874 | 0.160461 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.0982i | 1.84516i | 0.385806 | + | 0.922580i | \(0.373923\pi\) | ||||
−0.385806 | + | 0.922580i | \(0.626077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.5312i | 1.29639i | ||||||||
\(452\) | − 16.1520i | − 0.759728i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.21149i | 0.0568579i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.24264 | −0.245240 | −0.122620 | − | 0.992454i | \(-0.539130\pi\) | ||||
−0.122620 | + | 0.992454i | \(0.539130\pi\) | |||||||
\(458\) | 19.6590 | 0.918604 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 33.1025i | 1.54341i | ||||||||
\(461\) | −22.4583 | −1.04599 | −0.522993 | − | 0.852337i | \(-0.675185\pi\) | ||||
−0.522993 | + | 0.852337i | \(0.675185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5278 | −0.768110 | −0.384055 | − | 0.923310i | \(-0.625473\pi\) | ||||
−0.384055 | + | 0.923310i | \(0.625473\pi\) | |||||||
\(464\) | − 5.02884i | − 0.233458i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.2758 | −0.707640 | ||||||||
\(467\) | −30.1761 | −1.39638 | −0.698192 | − | 0.715910i | \(-0.746012\pi\) | ||||
−0.698192 | + | 0.715910i | \(0.746012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 32.6493i | − 1.50600i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.99698i | 0.276033i | ||||||||
\(473\) | 23.5876i | 1.08456i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 23.9698i | − 1.09981i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.539712 | 0.0246859 | ||||||||
\(479\) | 35.4561 | 1.62003 | 0.810016 | − | 0.586408i | \(-0.199458\pi\) | ||||
0.810016 | + | 0.586408i | \(0.199458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 25.8292i | − 1.17771i | ||||||||
\(482\) | −9.37436 | −0.426990 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.0443 | 0.729286 | ||||||||
\(485\) | 74.1690i | 3.36784i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.6313 | 0.889577 | 0.444789 | − | 0.895636i | \(-0.353279\pi\) | ||||
0.444789 | + | 0.895636i | \(0.353279\pi\) | |||||||
\(488\) | 7.79367 | 0.352803 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 13.8081i | − 0.623149i | −0.950222 | − | 0.311574i | \(-0.899144\pi\) | ||||
0.950222 | − | 0.311574i | \(-0.100856\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.2569i | 0.912326i | ||||||||
\(494\) | − 5.00965i | − 0.225395i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 1.25139i | − 0.0561890i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7029 | −0.702960 | −0.351480 | − | 0.936195i | \(-0.614321\pi\) | ||||
−0.351480 | + | 0.936195i | \(0.614321\pi\) | |||||||
\(500\) | −36.3820 | −1.62705 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.2724i | 0.547743i | ||||||||
\(503\) | 9.82270 | 0.437972 | 0.218986 | − | 0.975728i | \(-0.429725\pi\) | ||||
0.218986 | + | 0.975728i | \(0.429725\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 60.8742 | 2.70887 | ||||||||
\(506\) | 40.0597i | 1.78087i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.04803 | −0.401441 | ||||||||
\(509\) | 7.79995 | 0.345727 | 0.172863 | − | 0.984946i | \(-0.444698\pi\) | ||||
0.172863 | + | 0.984946i | \(0.444698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 13.4783i | − 0.594503i | ||||||||
\(515\) | 3.51317i | 0.154809i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 39.5112i | − 1.73770i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.0944 | −0.530373 | ||||||||
\(521\) | 13.3093 | 0.583092 | 0.291546 | − | 0.956557i | \(-0.405830\pi\) | ||||
0.291546 | + | 0.956557i | \(0.405830\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 43.5992i | − 1.90646i | −0.302249 | − | 0.953229i | \(-0.597737\pi\) | ||||
0.302249 | − | 0.953229i | \(-0.402263\pi\) | |||||||
\(524\) | 1.75412 | 0.0766293 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.5893 | 0.548919 | ||||||||
\(527\) | 5.04079i | 0.219580i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −36.3391 | −1.57996 | ||||||||
\(530\) | 0.719659 | 0.0312600 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 14.8998i | − 0.645380i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.9676i | 2.33322i | ||||||||
\(536\) | 11.3778i | 0.491446i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 6.85395i | − 0.295495i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.54936 | 0.152599 | 0.0762995 | − | 0.997085i | \(-0.475689\pi\) | ||||
0.0762995 | + | 0.997085i | \(0.475689\pi\) | |||||||
\(542\) | 29.8899 | 1.28388 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.02815i | 0.172706i | ||||||||
\(545\) | −1.69751 | −0.0727134 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3055 | −0.996471 | −0.498236 | − | 0.867042i | \(-0.666019\pi\) | ||||
−0.498236 | + | 0.867042i | \(0.666019\pi\) | |||||||
\(548\) | 16.4433i | 0.702423i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −70.0306 | −2.98611 | ||||||||
\(551\) | −8.95123 | −0.381335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.7992i | 1.30853i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.6373i | 0.747990i | ||||||||
\(557\) | − 25.4845i | − 1.07981i | −0.841726 | − | 0.539906i | \(-0.818460\pi\) | ||||
0.841726 | − | 0.539906i | \(-0.181540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 12.7655i | − 0.539924i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.44161 | 0.271723 | ||||||||
\(563\) | 27.9806 | 1.17924 | 0.589621 | − | 0.807680i | \(-0.299277\pi\) | ||||
0.589621 | + | 0.807680i | \(0.299277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 69.4093i | 2.92007i | ||||||||
\(566\) | −13.5392 | −0.569094 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.539455 | −0.0226350 | ||||||||
\(569\) | 12.7865i | 0.536036i | 0.963414 | + | 0.268018i | \(0.0863687\pi\) | ||||
−0.963414 | + | 0.268018i | \(0.913631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9288 | −1.04324 | −0.521620 | − | 0.853178i | \(-0.674672\pi\) | ||||
−0.521620 | + | 0.853178i | \(0.674672\pi\) | |||||||
\(572\) | −14.6363 | −0.611973 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 103.734i | − 4.32600i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.1318i | 0.671576i | 0.941938 | + | 0.335788i | \(0.109003\pi\) | ||||
−0.941938 | + | 0.335788i | \(0.890997\pi\) | |||||||
\(578\) | 0.773996i | 0.0321940i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.6102i | 0.897314i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.870912 | 0.0360695 | ||||||||
\(584\) | 3.80634 | 0.157507 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.3170i | 1.08714i | ||||||||
\(587\) | 22.9149 | 0.945797 | 0.472899 | − | 0.881117i | \(-0.343208\pi\) | ||||
0.472899 | + | 0.881117i | \(0.343208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.22745 | −0.0917803 | ||||||||
\(590\) | − 25.7705i | − 1.06096i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.17738 | −0.377188 | ||||||||
\(593\) | 14.0878 | 0.578518 | 0.289259 | − | 0.957251i | \(-0.406591\pi\) | ||||
0.289259 | + | 0.957251i | \(0.406591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.2115i | 0.500203i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 21.6802i | − 0.886568i | ||||||||
\(599\) | − 33.5681i | − 1.37155i | −0.727812 | − | 0.685777i | \(-0.759463\pi\) | ||||
0.727812 | − | 0.685777i | \(-0.240537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9839i | 1.05990i | 0.848027 | + | 0.529952i | \(0.177790\pi\) | ||||
−0.848027 | + | 0.529952i | \(0.822210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.44860 | 0.343769 | ||||||||
\(605\) | −68.9463 | −2.80307 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.8701i | 0.725324i | 0.931921 | + | 0.362662i | \(0.118132\pi\) | ||||
−0.931921 | + | 0.362662i | \(0.881868\pi\) | |||||||
\(608\) | −1.77998 | −0.0721877 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −33.4913 | −1.35602 | ||||||||
\(611\) | 21.3833i | 0.865077i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0387 | 0.405460 | 0.202730 | − | 0.979235i | \(-0.435019\pi\) | ||||
0.202730 | + | 0.979235i | \(0.435019\pi\) | |||||||
\(614\) | 19.4207 | 0.783754 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 5.79319i | − 0.233225i | −0.993177 | − | 0.116612i | \(-0.962796\pi\) | ||||
0.993177 | − | 0.116612i | \(-0.0372035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.3424i | 1.13918i | 0.821930 | + | 0.569589i | \(0.192898\pi\) | ||||
−0.821930 | + | 0.569589i | \(0.807102\pi\) | |||||||
\(620\) | 5.37753i | 0.215967i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.58894i | 0.143903i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 89.0108 | 3.56043 | ||||||||
\(626\) | −12.9198 | −0.516380 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.97105i | 0.0786534i | ||||||||
\(629\) | 36.9679 | 1.47401 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.3316 | 0.889005 | 0.444503 | − | 0.895777i | \(-0.353380\pi\) | ||||
0.444503 | + | 0.895777i | \(0.353380\pi\) | |||||||
\(632\) | 1.99590i | 0.0793925i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0384 | 0.478105 | ||||||||
\(635\) | 38.8816 | 1.54297 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.1520i | 1.03537i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.29725i | 0.169864i | ||||||||
\(641\) | 30.2138i | 1.19337i | 0.802474 | + | 0.596687i | \(0.203517\pi\) | ||||
−0.802474 | + | 0.596687i | \(0.796483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.0613i | 1.10663i | 0.832972 | + | 0.553315i | \(0.186637\pi\) | ||||
−0.832972 | + | 0.553315i | \(0.813363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.17002 | 0.282101 | ||||||||
\(647\) | 24.9682 | 0.981600 | 0.490800 | − | 0.871272i | \(-0.336705\pi\) | ||||
0.490800 | + | 0.871272i | \(0.336705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 31.1868i | − 1.22419i | ||||||||
\(650\) | 37.9003 | 1.48657 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.67231 | 0.300471 | ||||||||
\(653\) | 35.2971i | 1.38128i | 0.723198 | + | 0.690641i | \(0.242672\pi\) | ||||
−0.723198 | + | 0.690641i | \(0.757328\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.53791 | −0.294530 | ||||||||
\(656\) | −5.29403 | −0.206697 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.73576i | 0.340297i | 0.985418 | + | 0.170149i | \(0.0544248\pi\) | ||||
−0.985418 | + | 0.170149i | \(0.945575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.5348i | 1.38214i | 0.722785 | + | 0.691072i | \(0.242861\pi\) | ||||
−0.722785 | + | 0.691072i | \(0.757139\pi\) | |||||||
\(662\) | − 25.8226i | − 1.00363i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.0388i | 0.622427i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.7381 | −1.49994 | ||||||||
\(668\) | 6.19782 | 0.239801 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 48.8932i | − 1.88891i | ||||||||
\(671\) | −40.5303 | −1.56465 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.14709 | 0.275500 | 0.137750 | − | 0.990467i | \(-0.456013\pi\) | ||||
0.137750 | + | 0.990467i | \(0.456013\pi\) | |||||||
\(674\) | − 34.5378i | − 1.33035i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.07891 | −0.195343 | ||||||||
\(677\) | 20.1163 | 0.773132 | 0.386566 | − | 0.922262i | \(-0.373661\pi\) | ||||
0.386566 | + | 0.922262i | \(0.373661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 17.3100i | − 0.663807i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.50774i | 0.249194i | ||||||||
\(683\) | 18.7325i | 0.716781i | 0.933572 | + | 0.358390i | \(0.116674\pi\) | ||||
−0.933572 | + | 0.358390i | \(0.883326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 70.6610i | − 2.69982i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.53572 | −0.172923 | ||||||||
\(689\) | −0.471334 | −0.0179564 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.9637i | 1.21596i | 0.793954 | + | 0.607978i | \(0.208019\pi\) | ||||
−0.793954 | + | 0.607978i | \(0.791981\pi\) | |||||||
\(692\) | 1.17825 | 0.0447903 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.4390 | −0.434217 | ||||||||
\(695\) | − 75.7920i | − 2.87496i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.3252 | 0.807748 | ||||||||
\(698\) | −9.93436 | −0.376021 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.1148i | 0.910805i | 0.890286 | + | 0.455403i | \(0.150505\pi\) | ||||
−0.890286 | + | 0.455403i | \(0.849495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3355i | 0.616106i | ||||||||
\(704\) | 5.20041i | 0.195998i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.80734i | 0.105655i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0545 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(710\) | 2.31817 | 0.0869995 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 1.29396i | − 0.0484931i | ||||||||
\(713\) | −9.63968 | −0.361009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.8957 | 2.35216 | ||||||||
\(716\) | − 15.3425i | − 0.573378i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.70282 | 0.138188 | ||||||||
\(719\) | 31.4581 | 1.17319 | 0.586594 | − | 0.809881i | \(-0.300468\pi\) | ||||
0.586594 | + | 0.809881i | \(0.300468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 15.8317i | − 0.589194i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 5.24186i | − 0.194812i | ||||||||
\(725\) | − 67.7201i | − 2.51506i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.9687i | 1.33400i | 0.745056 | + | 0.667002i | \(0.232423\pi\) | ||||
−0.745056 | + | 0.667002i | \(0.767577\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −16.3568 | −0.605392 | ||||||||
\(731\) | 18.2705 | 0.675761 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2830i | 0.490619i | 0.969445 | + | 0.245309i | \(0.0788895\pi\) | ||||
−0.969445 | + | 0.245309i | \(0.921110\pi\) | |||||||
\(734\) | 13.3176 | 0.491560 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.70319 | −0.283943 | ||||||||
\(737\) | − 59.1692i | − 2.17953i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.1049 | −1.58564 | −0.792819 | − | 0.609457i | \(-0.791388\pi\) | ||||
−0.792819 | + | 0.609457i | \(0.791388\pi\) | |||||||
\(740\) | 39.4375 | 1.44975 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.1826i | 0.410248i | 0.978736 | + | 0.205124i | \(0.0657598\pi\) | ||||
−0.978736 | + | 0.205124i | \(0.934240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 52.4759i | − 1.92257i | ||||||||
\(746\) | 2.09640i | 0.0767547i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 20.9480i | − 0.765937i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.3361 | −1.39891 | −0.699453 | − | 0.714679i | \(-0.746573\pi\) | ||||
−0.699453 | + | 0.714679i | \(0.746573\pi\) | |||||||
\(752\) | 7.59771 | 0.277060 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 14.1534i | − 0.515436i | ||||||||
\(755\) | −36.3057 | −1.32130 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.1806 | 1.71481 | 0.857405 | − | 0.514642i | \(-0.172075\pi\) | ||||
0.857405 | + | 0.514642i | \(0.172075\pi\) | |||||||
\(758\) | 10.5916i | 0.384704i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.64901 | 0.277459 | ||||||||
\(761\) | 28.0668 | 1.01742 | 0.508711 | − | 0.860937i | \(-0.330122\pi\) | ||||
0.508711 | + | 0.860937i | \(0.330122\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.63237i | 0.167593i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 29.3742i | − 1.06133i | ||||||||
\(767\) | 16.8782i | 0.609435i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.9545i | 0.935944i | 0.883743 | + | 0.467972i | \(0.155015\pi\) | ||||
−0.883743 | + | 0.467972i | \(0.844985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.34315 | 0.264286 | ||||||||
\(773\) | −21.0644 | −0.757634 | −0.378817 | − | 0.925472i | \(-0.623669\pi\) | ||||
−0.378817 | + | 0.925472i | \(0.623669\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 16.8516i | − 0.605329i | ||||||||
\(776\) | −17.2596 | −0.619585 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.139250 | −0.00499237 | ||||||||
\(779\) | 9.42326i | 0.337623i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.80539 | 0.100385 | ||||||||
\(782\) | 31.0296 | 1.10962 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 8.47009i | − 0.302310i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 19.2179i | − 0.685046i | −0.939510 | − | 0.342523i | \(-0.888719\pi\) | ||||
0.939510 | − | 0.342523i | \(-0.111281\pi\) | |||||||
\(788\) | − 23.5456i | − 0.838778i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 8.57687i | − 0.305151i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.9348 | 0.778929 | ||||||||
\(794\) | −5.13731 | −0.182316 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.28291i | 0.258136i | ||||||||
\(797\) | −32.2444 | −1.14216 | −0.571078 | − | 0.820896i | \(-0.693475\pi\) | ||||
−0.571078 | + | 0.820896i | \(0.693475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.6047 | −1.08272 | ||||||||
\(800\) | − 13.4663i | − 0.476107i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.0437 | −0.354654 | ||||||||
\(803\) | −19.7945 | −0.698534 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 3.52196i | − 0.124056i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.1659i | 0.498353i | ||||||||
\(809\) | − 45.0695i | − 1.58456i | −0.610157 | − | 0.792280i | \(-0.708894\pi\) | ||||
0.610157 | − | 0.792280i | \(-0.291106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 30.5466i | − 1.07264i | −0.844016 | − | 0.536319i | \(-0.819815\pi\) | ||||
0.844016 | − | 0.536319i | \(-0.180185\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 47.7261 | 1.67280 | ||||||||
\(815\) | −32.9698 | −1.15488 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.07348i | 0.282455i | ||||||||
\(818\) | −9.66617 | −0.337970 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.7498 | 0.794457 | ||||||||
\(821\) | 26.9642i | 0.941057i | 0.882385 | + | 0.470528i | \(0.155937\pi\) | ||||
−0.882385 | + | 0.470528i | \(0.844063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.86392 | 0.308977 | 0.154488 | − | 0.987995i | \(-0.450627\pi\) | ||||
0.154488 | + | 0.987995i | \(0.450627\pi\) | |||||||
\(824\) | −0.817539 | −0.0284803 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 37.8611i | − 1.31656i | −0.752773 | − | 0.658280i | \(-0.771284\pi\) | ||||
0.752773 | − | 0.658280i | \(-0.228716\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9864i | 0.624694i | 0.949968 | + | 0.312347i | \(0.101115\pi\) | ||||
−0.949968 | + | 0.312347i | \(0.898885\pi\) | |||||||
\(830\) | − 68.9228i | − 2.39235i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 2.81444i | − 0.0975733i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.6336 | −0.921693 | ||||||||
\(836\) | 9.25662 | 0.320147 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 17.8462i | − 0.616488i | ||||||||
\(839\) | −46.9701 | −1.62159 | −0.810793 | − | 0.585332i | \(-0.800964\pi\) | ||||
−0.810793 | + | 0.585332i | \(0.800964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.71077 | 0.127958 | ||||||||
\(842\) | − 5.87102i | − 0.202329i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.7862 | 0.440119 | ||||||||
\(845\) | 21.8253 | 0.750815 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.167470i | 0.00575094i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 54.2445i | 1.86057i | ||||||||
\(851\) | 70.6950i | 2.42339i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5809i | 0.533479i | 0.963769 | + | 0.266740i | \(0.0859463\pi\) | ||||
−0.963769 | + | 0.266740i | \(0.914054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.5586 | −0.429246 | ||||||||
\(857\) | 9.43539 | 0.322307 | 0.161153 | − | 0.986929i | \(-0.448479\pi\) | ||||
0.161153 | + | 0.986929i | \(0.448479\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 47.2724i | − 1.61291i | −0.591293 | − | 0.806457i | \(-0.701382\pi\) | ||||
0.591293 | − | 0.806457i | \(-0.298618\pi\) | |||||||
\(860\) | 19.4911 | 0.664641 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.1698 | 0.891347 | ||||||||
\(863\) | − 20.3117i | − 0.691417i | −0.938342 | − | 0.345709i | \(-0.887639\pi\) | ||||
0.938342 | − | 0.345709i | \(-0.112361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.06323 | −0.172155 | ||||||||
\(866\) | 16.2277 | 0.551439 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 10.3795i | − 0.352100i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0221i | 1.08503i | ||||||||
\(872\) | − 0.395023i | − 0.0133772i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.7115i | 0.463799i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.2321 | 0.919564 | 0.459782 | − | 0.888032i | \(-0.347928\pi\) | ||||
0.459782 | + | 0.888032i | \(0.347928\pi\) | |||||||
\(878\) | −33.8953 | −1.14391 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 22.3475i | − 0.753333i | ||||||||
\(881\) | −13.3664 | −0.450326 | −0.225163 | − | 0.974321i | \(-0.572291\pi\) | ||||
−0.225163 | + | 0.974321i | \(0.572291\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.6560 | 0.627824 | 0.313912 | − | 0.949452i | \(-0.398360\pi\) | ||||
0.313912 | + | 0.949452i | \(0.398360\pi\) | |||||||
\(884\) | 11.3370i | 0.381305i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.11944 | 0.205587 | ||||||||
\(887\) | −3.12571 | −0.104951 | −0.0524756 | − | 0.998622i | \(-0.516711\pi\) | ||||
−0.0524756 | + | 0.998622i | \(0.516711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.56045i | 0.186387i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 3.38874i | − 0.113463i | ||||||||
\(893\) | − 13.5238i | − 0.452556i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 65.9307i | 2.20382i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.0982 | 1.30472 | ||||||||
\(899\) | −6.29304 | −0.209885 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 0.674594i | − 0.0224740i | ||||||||
\(902\) | 27.5312 | 0.916687 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.1520 | −0.537209 | ||||||||
\(905\) | 22.5256i | 0.748775i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.81672 | −0.126732 | −0.0633660 | − | 0.997990i | \(-0.520184\pi\) | ||||
−0.0633660 | + | 0.997990i | \(0.520184\pi\) | |||||||
\(908\) | 1.21149 | 0.0402046 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 48.5006i | − 1.60690i | −0.595373 | − | 0.803449i | \(-0.702996\pi\) | ||||
0.595373 | − | 0.803449i | \(-0.297004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 83.4085i | − 2.76042i | ||||||||
\(914\) | 5.24264i | 0.173411i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 19.6590i | − 0.649551i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.8847 | −0.721908 | −0.360954 | − | 0.932584i | \(-0.617549\pi\) | ||||
−0.360954 | + | 0.932584i | \(0.617549\pi\) | |||||||
\(920\) | 33.1025 | 1.09136 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.4583i | 0.739624i | ||||||||
\(923\) | −1.51827 | −0.0499743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −123.586 | −4.06347 | ||||||||
\(926\) | 16.5278i | 0.543136i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.02884 | −0.165080 | ||||||||
\(929\) | −23.6339 | −0.775402 | −0.387701 | − | 0.921785i | \(-0.626731\pi\) | ||||
−0.387701 | + | 0.921785i | \(0.626731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.2758i | 0.500377i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.1761i | 0.987393i | ||||||||
\(935\) | 90.0190i | 2.94394i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9674i | 1.14234i | 0.820833 | + | 0.571168i | \(0.193509\pi\) | ||||
−0.820833 | + | 0.571168i | \(0.806491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −32.6493 | −1.06490 | ||||||||
\(941\) | −12.7640 | −0.416093 | −0.208047 | − | 0.978119i | \(-0.566711\pi\) | ||||
−0.208047 | + | 0.978119i | \(0.566711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.7809i | 1.32801i | ||||||||
\(944\) | 5.99698 | 0.195185 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.5876 | 0.766899 | ||||||||
\(947\) | − 4.45356i | − 0.144721i | −0.997379 | − | 0.0723606i | \(-0.976947\pi\) | ||||
0.997379 | − | 0.0723606i | \(-0.0230532\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.7127 | 0.347750 | ||||||||
\(950\) | −23.9698 | −0.777683 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.5722i | 0.666398i | 0.942857 | + | 0.333199i | \(0.108128\pi\) | ||||
−0.942857 | + | 0.333199i | \(0.891872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 19.9065i | − 0.644158i | ||||||||
\(956\) | − 0.539712i | − 0.0174555i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 35.4561i | − 1.14554i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4340 | 0.949485 | ||||||||
\(962\) | −25.8292 | −0.832767 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.37436i | 0.301928i | ||||||||
\(965\) | −31.5553 | −1.01580 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.6779 | −1.01869 | −0.509346 | − | 0.860562i | \(-0.670112\pi\) | ||||
−0.509346 | + | 0.860562i | \(0.670112\pi\) | |||||||
\(968\) | − 16.0443i | − 0.515683i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 74.1690 | 2.38142 | ||||||||
\(971\) | −9.60450 | −0.308223 | −0.154112 | − | 0.988053i | \(-0.549252\pi\) | ||||
−0.154112 | + | 0.988053i | \(0.549252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 19.6313i | − 0.629026i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 7.79367i | − 0.249469i | ||||||||
\(977\) | 40.5256i | 1.29653i | 0.761416 | + | 0.648264i | \(0.224505\pi\) | ||||
−0.761416 | + | 0.648264i | \(0.775495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.72911i | 0.215063i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.8081 | −0.440633 | ||||||||
\(983\) | 25.2959 | 0.806815 | 0.403407 | − | 0.915021i | \(-0.367826\pi\) | ||||
0.403407 | + | 0.915021i | \(0.367826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 101.181i | 3.22391i | ||||||||
\(986\) | 20.2569 | 0.645112 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.00965 | −0.159378 | ||||||||
\(989\) | 34.9395i | 1.11101i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.6706 | −0.720156 | −0.360078 | − | 0.932922i | \(-0.617250\pi\) | ||||
−0.360078 | + | 0.932922i | \(0.617250\pi\) | |||||||
\(992\) | −1.25139 | −0.0397316 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 31.2965i | − 0.992165i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.0079i | 1.52042i | 0.649675 | + | 0.760212i | \(0.274905\pi\) | ||||
−0.649675 | + | 0.760212i | \(0.725095\pi\) | |||||||
\(998\) | 15.7029i | 0.497068i | ||||||||
\(999\) | 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 | 2646.2.d.e.2645.8 | yes | 16 | |
3.2 | odd | 2 | inner | 2646.2.d.e.2645.9 | yes | 16 | |
7.6 | odd | 2 | inner | 2646.2.d.e.2645.1 | ✓ | 16 | |
21.20 | even | 2 | inner | 2646.2.d.e.2645.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.d.e.2645.1 | ✓ | 16 | 7.6 | odd | 2 | inner | |
2646.2.d.e.2645.8 | yes | 16 | 1.1 | even | 1 | trivial | |
2646.2.d.e.2645.9 | yes | 16 | 3.2 | odd | 2 | inner | |
2646.2.d.e.2645.16 | yes | 16 | 21.20 | even | 2 | inner |