Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(289,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bw (of order \(6\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.7 | ||
Character | \(\chi\) | \(=\) | 560.289 |
Dual form | 560.2.bw.f.529.7 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.277116 | − | 0.159993i | 0.159993 | − | 0.0923721i | −0.417866 | − | 0.908509i | \(-0.637222\pi\) |
0.577859 | + | 0.816137i | \(0.303888\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00685 | − | 0.986173i | −0.897492 | − | 0.441030i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.50695 | + | 2.17465i | 0.569573 | + | 0.821941i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.44880 | + | 2.50940i | −0.482935 | + | 0.836468i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.08301 | + | 3.60788i | 0.628052 | + | 1.08782i | 0.987942 | + | 0.154823i | \(0.0494808\pi\) |
−0.359890 | + | 0.932995i | \(0.617186\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.89761i | − | 0.803652i | −0.915716 | − | 0.401826i | \(-0.868376\pi\) | ||
0.915716 | − | 0.401826i | \(-0.131624\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.713913 | + | 0.0477982i | −0.184332 | + | 0.0123414i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.72628 | + | 2.15137i | −0.903756 | + | 0.521784i | −0.878417 | − | 0.477895i | \(-0.841400\pi\) |
−0.0253388 | + | 0.999679i | \(0.508066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.979442 | + | 1.69644i | −0.224700 | + | 0.389191i | −0.956229 | − | 0.292619i | \(-0.905473\pi\) |
0.731530 | + | 0.681810i | \(0.238807\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.765529 | + | 0.361529i | 0.167052 | + | 0.0788922i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.23229 | + | 1.28881i | 0.465464 | + | 0.268736i | 0.714339 | − | 0.699800i | \(-0.246728\pi\) |
−0.248875 | + | 0.968536i | \(0.580061\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.05492 | + | 3.95821i | 0.610985 | + | 0.791642i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.88715i | 0.363183i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.96541 | 1.10775 | 0.553874 | − | 0.832600i | \(-0.313149\pi\) | ||||
0.553874 | + | 0.832600i | \(0.313149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.71509 | + | 8.16678i | 0.846856 | + | 1.46680i | 0.884000 | + | 0.467487i | \(0.154840\pi\) |
−0.0371445 | + | 0.999310i | \(0.511826\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.15447 | + | 0.666536i | 0.200968 | + | 0.116029i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.879645 | − | 5.85032i | −0.148687 | − | 0.988884i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.48144 | + | 3.16471i | 0.901143 | + | 0.520275i | 0.877571 | − | 0.479447i | \(-0.159163\pi\) |
0.0235722 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.463598 | − | 0.802975i | −0.0742350 | − | 0.128579i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.19271 | −1.12331 | −0.561656 | − | 0.827371i | \(-0.689836\pi\) | ||||
−0.561656 | + | 0.827371i | \(0.689836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.73966i | − | 0.722792i | −0.932412 | − | 0.361396i | \(-0.882300\pi\) | ||
0.932412 | − | 0.361396i | \(-0.117700\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.38224 | − | 3.60723i | 0.802338 | − | 0.537734i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.84122 | − | 2.21773i | −0.560300 | − | 0.323489i | 0.192966 | − | 0.981205i | \(-0.438189\pi\) |
−0.753266 | + | 0.657716i | \(0.771523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.45821 | + | 6.55418i | −0.351172 | + | 0.936311i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.688409 | + | 1.19236i | −0.0963965 | + | 0.166964i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.37373 | + | 3.67988i | −0.875500 | + | 0.505470i | −0.869172 | − | 0.494510i | \(-0.835348\pi\) |
−0.00632781 | + | 0.999980i | \(0.502014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.622303 | − | 9.29471i | −0.0839113 | − | 1.25330i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.626816i | 0.0830239i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.61034 | + | 2.78920i | 0.209649 | + | 0.363122i | 0.951604 | − | 0.307327i | \(-0.0994346\pi\) |
−0.741955 | + | 0.670450i | \(0.766101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.94998 | − | 10.3057i | 0.761817 | − | 1.31951i | −0.180096 | − | 0.983649i | \(-0.557641\pi\) |
0.941913 | − | 0.335857i | \(-0.109026\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.64035 | + | 0.630900i | −0.962593 | + | 0.0794859i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.85754 | + | 5.81508i | −0.354435 | + | 0.721272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1172 | + | 5.84119i | −1.23602 | + | 0.713614i | −0.968278 | − | 0.249877i | \(-0.919610\pi\) |
−0.267739 | + | 0.963492i | \(0.586276\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.824804 | 0.0992947 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.58808 | −0.900539 | −0.450270 | − | 0.892893i | \(-0.648672\pi\) | ||||
−0.450270 | + | 0.892893i | \(0.648672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.57951 | − | 4.95338i | 1.00416 | − | 0.579749i | 0.0946803 | − | 0.995508i | \(-0.469817\pi\) |
0.909475 | + | 0.415758i | \(0.136484\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.47986 | + | 0.608118i | 0.170879 | + | 0.0702194i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.70689 | + | 9.96672i | −0.536400 | + | 1.13581i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.41634 | − | 11.1134i | 0.721895 | − | 1.25036i | −0.238345 | − | 0.971181i | \(-0.576605\pi\) |
0.960239 | − | 0.279178i | \(-0.0900619\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.04448 | − | 7.00525i | −0.449387 | − | 0.778361i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.75180i | − | 0.631342i | −0.948869 | − | 0.315671i | \(-0.897770\pi\) | ||
0.948869 | − | 0.315671i | \(-0.102230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.59972 | − | 0.642724i | 1.04124 | − | 0.0697132i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.65311 | − | 0.954424i | 0.177232 | − | 0.102325i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50907 | + | 2.61379i | −0.159961 | + | 0.277061i | −0.934855 | − | 0.355031i | \(-0.884470\pi\) |
0.774893 | + | 0.632092i | \(0.217804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.30129 | − | 4.36655i | 0.660554 | − | 0.457739i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.61326 | + | 1.50877i | 0.270982 | + | 0.156452i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.63859 | − | 2.43861i | 0.373311 | − | 0.250197i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.414281i | 0.0420639i | 0.999779 | + | 0.0210320i | \(0.00669517\pi\) | ||||
−0.999779 | + | 0.0210320i | \(0.993305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0715 | −1.21323 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.99935 | − | 13.8553i | −0.795965 | − | 1.37865i | −0.922224 | − | 0.386655i | \(-0.873630\pi\) |
0.126259 | − | 0.991997i | \(-0.459703\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.24596 | + | 1.29670i | 0.221301 | + | 0.127768i | 0.606552 | − | 0.795043i | \(-0.292552\pi\) |
−0.385252 | + | 0.922812i | \(0.625885\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.17977 | − | 1.48048i | −0.115134 | − | 0.144480i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.0917 | + | 9.86787i | 1.65231 | + | 0.953963i | 0.976118 | + | 0.217239i | \(0.0697052\pi\) |
0.676194 | + | 0.736724i | \(0.263628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.69235 | − | 8.12738i | −0.449445 | − | 0.778462i | 0.548905 | − | 0.835885i | \(-0.315045\pi\) |
−0.998350 | + | 0.0574228i | \(0.981712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.02533 | 0.192236 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.61401i | − | 0.245906i | −0.992413 | − | 0.122953i | \(-0.960764\pi\) | ||
0.992413 | − | 0.122953i | \(-0.0392364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.20888 | − | 4.78788i | −0.299230 | − | 0.446472i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.27127 | + | 4.19807i | 0.672229 | + | 0.388112i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.2938 | − | 4.86135i | −0.943630 | − | 0.445639i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.17788 | + | 5.50426i | −0.288899 | + | 0.500387i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.99322 | + | 1.15078i | −0.179722 | + | 0.103763i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.22730 | − | 10.9562i | −0.199216 | − | 0.979956i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3587i | 1.80655i | 0.429067 | + | 0.903273i | \(0.358843\pi\) | ||||
−0.429067 | + | 0.903273i | \(0.641157\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.758314 | − | 1.31344i | −0.0667658 | − | 0.115642i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.82538 | + | 3.16165i | −0.159484 | + | 0.276234i | −0.934683 | − | 0.355483i | \(-0.884316\pi\) |
0.775199 | + | 0.631717i | \(0.217650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.16514 | + | 0.426511i | −0.447875 | + | 0.0369832i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.86106 | − | 3.78724i | 0.160175 | − | 0.325954i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.24192 | + | 5.33582i | −0.789590 | + | 0.455870i | −0.839818 | − | 0.542868i | \(-0.817339\pi\) |
0.0502281 | + | 0.998738i | \(0.484005\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0047 | 1.01823 | 0.509113 | − | 0.860699i | \(-0.329973\pi\) | ||||
0.509113 | + | 0.860699i | \(0.329973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.41929 | −0.119526 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.4542 | − | 6.03576i | 0.874227 | − | 0.504735i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.9717 | − | 5.88293i | −0.994196 | − | 0.488550i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.367414 | + | 2.20957i | 0.0303038 | + | 0.182242i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.71251 | − | 11.6264i | 0.549910 | − | 0.952472i | −0.448370 | − | 0.893848i | \(-0.647995\pi\) |
0.998280 | − | 0.0586242i | \(-0.0186714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.28727 | − | 5.69371i | −0.267514 | − | 0.463348i | 0.700705 | − | 0.713451i | \(-0.252869\pi\) |
−0.968219 | + | 0.250103i | \(0.919535\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 12.4676i | − | 1.00795i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.40864 | − | 21.0394i | −0.113145 | − | 1.68993i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.55523 | + | 1.47526i | −0.203930 | + | 0.117739i | −0.598487 | − | 0.801132i | \(-0.704231\pi\) |
0.394558 | + | 0.918871i | \(0.370898\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.17751 | + | 2.03951i | −0.0933827 | + | 0.161744i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.561229 | + | 6.79662i | 0.0442311 | + | 0.535648i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.62597 | + | 2.67080i | 0.362334 | + | 0.209194i | 0.670104 | − | 0.742267i | \(-0.266249\pi\) |
−0.307770 | + | 0.951461i | \(0.599583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.65954 | − | 2.47615i | −0.129195 | − | 0.192768i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.56009i | 0.120724i | 0.998177 | + | 0.0603618i | \(0.0192254\pi\) | ||||
−0.998177 | + | 0.0603618i | \(0.980775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.60386 | 0.354143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.83804 | − | 4.91563i | −0.217030 | − | 0.375908i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.6101 | − | 7.85781i | −1.03476 | − | 0.597418i | −0.116414 | − | 0.993201i | \(-0.537140\pi\) |
−0.918344 | + | 0.395783i | \(0.870473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00411 | + | 12.6082i | −0.302682 | + | 0.953092i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.892504 | + | 0.515288i | 0.0670847 | + | 0.0387314i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.53583 | − | 9.58834i | −0.413767 | − | 0.716666i | 0.581531 | − | 0.813524i | \(-0.302454\pi\) |
−0.995298 | + | 0.0968583i | \(0.969121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8950 | 1.10713 | 0.553567 | − | 0.832805i | \(-0.313266\pi\) | ||||
0.553567 | + | 0.832805i | \(0.313266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.80783i | − | 0.281483i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.87949 | − | 11.7568i | −0.579312 | − | 0.864374i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5238 | − | 8.96266i | −1.13521 | − | 0.655414i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.10390 | + | 2.84385i | −0.298515 | + | 0.206859i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.506772 | + | 0.877755i | −0.0366688 | + | 0.0635121i | −0.883777 | − | 0.467908i | \(-0.845008\pi\) |
0.847109 | + | 0.531420i | \(0.178341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.53206 | − | 3.77129i | 0.470188 | − | 0.271463i | −0.246131 | − | 0.969237i | \(-0.579159\pi\) |
0.716318 | + | 0.697774i | \(0.245826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.138500 | + | 2.06864i | 0.00991822 | + | 0.148138i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.26180i | − | 0.659876i | −0.944003 | − | 0.329938i | \(-0.892972\pi\) | ||
0.944003 | − | 0.329938i | \(-0.107028\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.04961 | + | 13.9423i | 0.570622 | + | 0.988346i | 0.996502 | + | 0.0835668i | \(0.0266312\pi\) |
−0.425880 | + | 0.904780i | \(0.640035\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.86910 | + | 3.23738i | −0.131836 | + | 0.228347i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.98957 | + | 12.9727i | 0.630944 | + | 0.910503i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4347 | + | 7.09326i | 1.00816 | + | 0.495415i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.46829 | + | 3.73447i | −0.449577 | + | 0.259564i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.16076 | −0.564492 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.20349 | −0.220537 | −0.110269 | − | 0.993902i | \(-0.535171\pi\) | ||||
−0.110269 | + | 0.993902i | \(0.535171\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.10278 | + | 1.21404i | −0.144080 | + | 0.0831847i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.67413 | + | 9.51181i | −0.318773 | + | 0.648700i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6545 | + | 22.5606i | −0.723273 | + | 1.53151i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.58501 | − | 2.74533i | 0.107105 | − | 0.185512i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.23382 | + | 10.7973i | 0.419332 | + | 0.726305i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.7564i | − | 1.25602i | −0.778206 | − | 0.628010i | \(-0.783870\pi\) | ||
0.778206 | − | 0.628010i | \(-0.216130\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.3587 | + | 1.93136i | −0.957249 | + | 0.128757i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.85380 | − | 3.37969i | 0.388530 | − | 0.224318i | −0.292993 | − | 0.956115i | \(-0.594651\pi\) |
0.681523 | + | 0.731797i | \(0.261318\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.0815770 | − | 0.141295i | 0.00539076 | − | 0.00933707i | −0.863317 | − | 0.504661i | \(-0.831617\pi\) |
0.868708 | + | 0.495324i | \(0.164951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.290251 | + | 3.51501i | 0.0190971 | + | 0.231271i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.6872 | + | 13.6758i | 1.55180 | + | 0.895931i | 0.997996 | + | 0.0632829i | \(0.0201571\pi\) |
0.553802 | + | 0.832648i | \(0.313176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.52171 | + | 8.23877i | 0.360196 | + | 0.537438i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 4.10628i | − | 0.266732i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3226 | 1.24988 | 0.624938 | − | 0.780674i | \(-0.285124\pi\) | ||||
0.624938 | + | 0.780674i | \(0.285124\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1760 | + | 21.0894i | 0.784323 | + | 1.35849i | 0.929403 | + | 0.369067i | \(0.120323\pi\) |
−0.145080 | + | 0.989420i | \(0.546344\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.14455 | − | 4.12491i | −0.458323 | − | 0.264613i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.3968 | − | 10.7291i | 0.728116 | − | 0.685454i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.91563 | + | 2.83804i | 0.312774 | + | 0.180580i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.920248 | − | 1.59392i | −0.0583184 | − | 0.101010i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.53106 | 0.538476 | 0.269238 | − | 0.963074i | \(-0.413228\pi\) | ||||
0.269238 | + | 0.963074i | \(0.413228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.7384i | 0.675120i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.55741 | − | 1.71400i | 0.160151 | − | 0.107335i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.9948 | + | 10.9666i | 1.18486 | + | 0.684080i | 0.957134 | − | 0.289645i | \(-0.0935371\pi\) |
0.227728 | + | 0.973725i | \(0.426870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.37811 | + | 16.6893i | 0.0856318 | + | 1.03702i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.64271 | + | 14.9696i | −0.534970 | + | 0.926596i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.39051 | + | 5.42162i | −0.579044 | + | 0.334311i | −0.760753 | − | 0.649041i | \(-0.775170\pi\) |
0.181709 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4202 | − | 1.09937i | 1.00868 | − | 0.0675336i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.965765i | 0.0591039i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.58343 | + | 16.5990i | 0.584312 | + | 1.01206i | 0.994961 | + | 0.100265i | \(0.0319690\pi\) |
−0.410649 | + | 0.911794i | \(0.634698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.95683 | − | 10.3175i | 0.361851 | − | 0.626745i | −0.626414 | − | 0.779490i | \(-0.715478\pi\) |
0.988266 | + | 0.152745i | \(0.0488115\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.04757 | − | 2.21820i | 0.0634019 | − | 0.134252i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.91732 | + | 19.2668i | −0.477433 | + | 1.16183i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.13327 | − | 4.69574i | 0.488681 | − | 0.282140i | −0.235346 | − | 0.971912i | \(-0.575622\pi\) |
0.724027 | + | 0.689772i | \(0.242289\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.3250 | −1.63590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.15248 | 0.0687513 | 0.0343756 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343756 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.2525 | + | 10.5381i | −1.08500 | + | 0.626424i | −0.932240 | − | 0.361840i | \(-0.882149\pi\) |
−0.152758 | + | 0.988264i | \(0.548815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.618150 | − | 1.25793i | 0.0366160 | − | 0.0745133i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.8390 | − | 15.6416i | −0.639809 | − | 0.923296i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.756773 | − | 1.31077i | 0.0445161 | − | 0.0771041i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0662822 | + | 0.114804i | 0.00388553 | + | 0.00672994i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.92590i | 0.579877i | 0.957045 | + | 0.289939i | \(0.0936349\pi\) | ||||
−0.957045 | + | 0.289939i | \(0.906365\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.481092 | − | 7.18558i | −0.0280102 | − | 0.418361i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.80863 | + | 3.93097i | −0.395077 | + | 0.228098i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.73447 | − | 6.46829i | 0.215970 | − | 0.374071i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3071 | − | 7.14243i | 0.594092 | − | 0.411683i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.43350 | − | 2.55968i | −0.254698 | − | 0.147050i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.1039 | + | 14.8143i | −1.26567 | + | 0.848262i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.94680i | − | 0.168183i | −0.996458 | − | 0.0840915i | \(-0.973201\pi\) | ||
0.996458 | − | 0.0840915i | \(-0.0267988\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.829856 | 0.0472088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5413 | − | 18.2580i | −0.597740 | − | 1.03532i | −0.993154 | − | 0.116812i | \(-0.962732\pi\) |
0.395414 | − | 0.918503i | \(-0.370601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0686 | − | 6.39048i | −0.625637 | − | 0.361211i | 0.153424 | − | 0.988160i | \(-0.450970\pi\) |
−0.779060 | + | 0.626949i | \(0.784303\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.9552 | + | 6.26858i | 0.898976 | + | 0.353195i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.15548 | − | 3.55387i | −0.345726 | − | 0.199605i | 0.317075 | − | 0.948400i | \(-0.397299\pi\) |
−0.662801 | + | 0.748795i | \(0.730633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4260 | + | 21.5225i | 0.695724 | + | 1.20503i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.31517 | 0.352478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.42857i | − | 0.468978i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.4693 | − | 8.85197i | 0.636205 | − | 0.491019i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.60065 | − | 1.50149i | −0.143816 | − | 0.0830324i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.965739 | − | 11.6953i | −0.0532429 | − | 0.644784i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.70602 | + | 4.68696i | −0.148736 | + | 0.257619i | −0.930761 | − | 0.365629i | \(-0.880854\pi\) |
0.782024 | + | 0.623248i | \(0.214187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.8831 | + | 9.17009i | −0.870387 | + | 0.502518i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.0642 | − | 1.74506i | 1.42404 | − | 0.0953429i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.9764i | − | 0.924765i | −0.886681 | − | 0.462382i | \(-0.846995\pi\) | ||
0.886681 | − | 0.462382i | \(-0.153005\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.418224 | − | 0.724385i | −0.0227148 | − | 0.0393432i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.6432 | + | 34.0230i | −1.06374 | + | 1.84245i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.9574 | + | 4.53107i | −0.969610 | + | 0.244655i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.65526 | − | 0.813400i | −0.0891163 | − | 0.0437920i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.7424 | + | 7.93415i | −0.737728 | + | 0.425928i | −0.821243 | − | 0.570579i | \(-0.806719\pi\) |
0.0835145 | + | 0.996507i | \(0.473385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.1130 | −1.02309 | −0.511547 | − | 0.859255i | \(-0.670927\pi\) | ||||
−0.511547 | + | 0.859255i | \(0.670927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.46823 | 0.291873 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.6110 | − | 13.0545i | 1.20346 | − | 0.694820i | 0.242140 | − | 0.970241i | \(-0.422151\pi\) |
0.961324 | + | 0.275422i | \(0.0888174\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.2282 | + | 7.48316i | 0.808227 | + | 0.397165i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.63036 | + | 0.299776i | −0.192139 | + | 0.0158658i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.5067 | + | 19.9301i | −0.607298 | + | 1.05187i | 0.384386 | + | 0.923173i | \(0.374413\pi\) |
−0.991684 | + | 0.128699i | \(0.958920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.58139 | + | 13.1313i | 0.399020 | + | 0.691123i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.03376i | 0.106745i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.1027 | + | 1.47983i | −1.15691 | + | 0.0774578i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.2865 | − | 16.3312i | 1.47654 | − | 0.852482i | 0.476893 | − | 0.878961i | \(-0.341763\pi\) |
0.999649 | + | 0.0264790i | \(0.00842952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.4208 | − | 18.0494i | 0.542487 | − | 0.939614i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.6073 | − | 8.31525i | −0.914128 | − | 0.431707i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.9128 | − | 12.0740i | −1.08282 | − | 0.625169i | −0.151168 | − | 0.988508i | \(-0.548303\pi\) |
−0.931657 | + | 0.363339i | \(0.881637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.37014 | − | 2.67980i | −0.122394 | − | 0.138384i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 17.2854i | − | 0.890244i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6614 | 1.57497 | 0.787484 | − | 0.616335i | \(-0.211383\pi\) | ||||
0.787484 | + | 0.616335i | \(0.211383\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.25726 | + | 5.64174i | 0.166874 | + | 0.289035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.6910 | + | 15.9874i | 1.41494 | + | 0.816919i | 0.995849 | − | 0.0910234i | \(-0.0290138\pi\) |
0.419096 | + | 0.907942i | \(0.362347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.2750 | − | 15.3599i | 0.982343 | − | 0.782815i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.8937 | + | 6.86684i | 0.604592 | + | 0.349061i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.72442 | + | 11.6470i | 0.340942 | + | 0.590528i | 0.984608 | − | 0.174778i | \(-0.0559208\pi\) |
−0.643666 | + | 0.765306i | \(0.722587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0908 | −0.560887 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.16819i | 0.0589275i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.8364 | + | 15.9754i | −1.19934 | + | 0.803810i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3921 | + | 5.99988i | 0.521564 | + | 0.301125i | 0.737574 | − | 0.675266i | \(-0.235971\pi\) |
−0.216010 | + | 0.976391i | \(0.569304\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.36311 | + | 0.944581i | −0.0682407 | + | 0.0472882i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.4468 | − | 28.4867i | 0.821315 | − | 1.42256i | −0.0833891 | − | 0.996517i | \(-0.526574\pi\) |
0.904704 | − | 0.426041i | \(-0.140092\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.6641 | − | 13.6625i | 1.17879 | − | 0.680577i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.20829 | + | 18.0471i | 0.0600406 | + | 0.896766i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.3685i | 1.30704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.2012 | + | 17.6690i | 0.504416 | + | 0.873674i | 0.999987 | + | 0.00510650i | \(0.00162546\pi\) |
−0.495571 | + | 0.868567i | \(0.665041\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.70739 | + | 2.95729i | −0.0842194 | + | 0.145872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.63882 | + | 7.70511i | −0.179055 | + | 0.379144i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.67227 | + | 11.5430i | −0.278441 | + | 0.566624i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.32670 | − | 1.92067i | 0.162909 | − | 0.0940557i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0820 | −1.37190 | −0.685949 | − | 0.727650i | \(-0.740613\pi\) | ||||
−0.685949 | + | 0.727650i | \(0.740613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.4438 | −0.703949 | −0.351974 | − | 0.936010i | \(-0.614490\pi\) | ||||
−0.351974 | + | 0.936010i | \(0.614490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.1304 | − | 6.42612i | 0.541177 | − | 0.312449i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.8991 | − | 8.17714i | −0.965247 | − | 0.396649i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.3776 | − | 2.59100i | 1.51847 | − | 0.125387i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.93136 | − | 3.34521i | 0.0932469 | − | 0.161508i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.67280 | − | 11.5576i | −0.321417 | − | 0.556711i | 0.659363 | − | 0.751824i | \(-0.270826\pi\) |
−0.980781 | + | 0.195113i | \(0.937493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.96912i | − | 0.142687i | −0.997452 | − | 0.0713434i | \(-0.977271\pi\) | ||
0.997452 | − | 0.0713434i | \(-0.0227286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.25878 | + | 0.285135i | −0.204193 | + | 0.0136712i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.37279 | + | 2.52463i | −0.209179 | + | 0.120770i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2690 | − | 24.7146i | 0.681023 | − | 1.17957i | −0.293647 | − | 0.955914i | \(-0.594869\pi\) |
0.974669 | − | 0.223652i | \(-0.0717978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.8856 | − | 15.6644i | −0.613600 | − | 0.745921i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.02118 | + | 3.47633i | 0.286075 | + | 0.165165i | 0.636170 | − | 0.771549i | \(-0.280518\pi\) |
−0.350096 | + | 0.936714i | \(0.613851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.60614 | − | 3.75729i | 0.265756 | − | 0.178113i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.29582i | − | 0.203185i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.33832 | −0.251931 | −0.125965 | − | 0.992035i | \(-0.540203\pi\) | ||||
−0.125965 | + | 0.992035i | \(0.540203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.9825 | − | 25.9505i | −0.705499 | − | 1.22196i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.82191 | − | 1.05188i | −0.0856008 | − | 0.0494216i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.9519 | + | 2.54887i | −0.794719 | + | 0.119493i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.14044 | − | 2.39048i | −0.193681 | − | 0.111822i | 0.400023 | − | 0.916505i | \(-0.369002\pi\) |
−0.593705 | + | 0.804683i | \(0.702335\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.05996 | − | 7.03206i | −0.189503 | − | 0.328229i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.39398 | −0.0649242 | −0.0324621 | − | 0.999473i | \(-0.510335\pi\) | ||||
−0.0324621 | + | 0.999473i | \(0.510335\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4620i | 1.27627i | 0.769925 | + | 0.638135i | \(0.220294\pi\) | ||||
−0.769925 | + | 0.638135i | \(0.779706\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.75652 | − | 5.60500i | −0.174205 | − | 0.259925i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.9868 | − | 19.6223i | −1.57272 | − | 0.908012i | −0.995834 | − | 0.0911889i | \(-0.970933\pi\) |
−0.576889 | − | 0.816823i | \(-0.695733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.9487 | − | 13.1991i | −1.29055 | − | 0.609476i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.472064 | + | 0.817639i | −0.0217516 | + | 0.0376748i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.1002 | − | 9.87278i | 0.786266 | − | 0.453951i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.70701 | + | 1.30567i | −0.445388 | + | 0.0599081i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 21.3257i | − | 0.976436i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.64068 | + | 8.03789i | 0.212038 | + | 0.367260i | 0.952352 | − | 0.305000i | \(-0.0986566\pi\) |
−0.740314 | + | 0.672261i | \(0.765323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.17009 | − | 15.8831i | 0.418120 | − | 0.724205i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.24294 | + | 1.79366i | 0.0565556 | + | 0.0816144i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.408553 | − | 0.831402i | 0.0185515 | − | 0.0377520i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.3578 | − | 5.98006i | 0.469356 | − | 0.270983i | −0.246614 | − | 0.969114i | \(-0.579318\pi\) |
0.715970 | + | 0.698131i | \(0.245985\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.70924 | 0.0772946 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.6956 | 1.74631 | 0.873153 | − | 0.487446i | \(-0.162072\pi\) | ||||
0.873153 | + | 0.487446i | \(0.162072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.2288 | + | 12.8338i | −1.00113 | + | 0.578005i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 24.2258 | + | 11.9046i | 1.08887 | + | 0.535072i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.4348 | − | 16.5014i | −0.512923 | − | 0.740190i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.1441 | − | 24.4983i | 0.633177 | − | 1.09669i | −0.353722 | − | 0.935351i | \(-0.615084\pi\) |
0.986898 | − | 0.161344i | \(-0.0515827\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.249604 | + | 0.432327i | 0.0111515 | + | 0.0193149i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.88492i | 0.396159i | 0.980186 | + | 0.198079i | \(0.0634704\pi\) | ||||
−0.980186 | + | 0.198079i | \(0.936530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.38982 | + | 35.6943i | 0.106345 | + | 1.58837i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.27581 | − | 0.736587i | 0.0566605 | − | 0.0327130i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.08158 | − | 1.87336i | 0.0479404 | − | 0.0830352i | −0.841059 | − | 0.540943i | \(-0.818068\pi\) |
0.889000 | + | 0.457908i | \(0.151401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7008 | + | 11.1929i | 1.04846 | + | 0.495146i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.20145 | − | 1.84836i | −0.141348 | − | 0.0816070i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.22853 | − | 4.81720i | −0.142266 | − | 0.212271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 18.4783i | − | 0.812673i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.02878 | −0.220739 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8513 | − | 25.7232i | −0.650646 | − | 1.12695i | −0.982966 | − | 0.183786i | \(-0.941165\pi\) |
0.332320 | − | 0.943167i | \(-0.392169\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.3578 | − | 5.98006i | −0.452914 | − | 0.261490i | 0.256146 | − | 0.966638i | \(-0.417547\pi\) |
−0.709060 | + | 0.705148i | \(0.750880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.907624 | + | 4.13457i | 0.0396120 | + | 0.180448i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.1395 | − | 20.2878i | −1.53070 | − | 0.883750i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.17793 | − | 14.1646i | −0.355562 | − | 0.615852i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.33229 | −0.404987 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.8417i | 0.902752i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.5690 | − | 36.6587i | −1.06221 | − | 1.58489i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.06814 | − | 1.77139i | −0.132400 | − | 0.0764411i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.7672 | + | 4.78351i | −1.23909 | + | 0.206040i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.48408 | + | 9.49871i | −0.235779 | + | 0.408381i | −0.959499 | − | 0.281713i | \(-0.909098\pi\) |
0.723720 | + | 0.690094i | \(0.242431\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.12764 | − | 2.38309i | 0.177134 | − | 0.102268i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.40184 | + | 20.9379i | 0.0600484 | + | 0.896883i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 30.4206i | − | 1.30069i | −0.759638 | − | 0.650346i | \(-0.774624\pi\) | ||
0.759638 | − | 0.650346i | \(-0.225376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.2407 | + | 29.8618i | 0.735816 | + | 1.27447i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.84277 | + | 10.1200i | −0.248910 | + | 0.431126i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.8369 | − | 2.79408i | 1.43889 | − | 0.118816i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.06454 | − | 1.99732i | −0.172530 | − | 0.0847817i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.0596 | − | 19.0870i | 1.40078 | − | 0.808742i | 0.406309 | − | 0.913736i | \(-0.366816\pi\) |
0.994473 | + | 0.104994i | \(0.0334824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7337 | −0.580873 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.73586 | −0.242168 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.3320 | + | 9.42926i | −0.688310 | + | 0.397396i | −0.802979 | − | 0.596008i | \(-0.796753\pi\) |
0.114669 | + | 0.993404i | \(0.463419\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.57787 | + | 5.24594i | −0.108452 | + | 0.220698i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.13913 | − | 19.3519i | 0.383808 | − | 0.812703i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.7747 | − | 37.7149i | 0.912844 | − | 1.58109i | 0.102816 | − | 0.994700i | \(-0.467215\pi\) |
0.810028 | − | 0.586392i | \(-0.199452\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.21437 | + | 12.4957i | 0.301912 | + | 0.522927i | 0.976569 | − | 0.215205i | \(-0.0690418\pi\) |
−0.674657 | + | 0.738131i | \(0.735708\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.324320i | 0.0135487i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.71808 | + | 12.7731i | 0.0716488 | + | 0.532674i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.8841 | + | 17.2536i | −1.24409 | + | 0.718276i | −0.969925 | − | 0.243406i | \(-0.921735\pi\) |
−0.274167 | + | 0.961682i | \(0.588402\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.20676 | − | 2.09017i | 0.0501512 | − | 0.0868645i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.5081 | − | 8.66767i | 0.518925 | − | 0.359595i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.5531 | − | 15.3305i | −1.09972 | − | 0.634923i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.4523 | − | 15.5956i | −0.432151 | − | 0.644800i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.37071i | 0.386771i | 0.981123 | + | 0.193385i | \(0.0619468\pi\) | ||||
−0.981123 | + | 0.193385i | \(0.938053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.4726 | −0.761152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.48182 | − | 2.56660i | −0.0609541 | − | 0.105576i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.4505 | + | 20.4674i | 1.45578 | + | 0.840494i | 0.998800 | − | 0.0489841i | \(-0.0155984\pi\) |
0.456978 | + | 0.889478i | \(0.348932\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.8640 | + | 19.9075i | 0.650360 | + | 0.816127i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.46136 | + | 2.57577i | 0.182591 | + | 0.105419i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.8224 | − | 30.8693i | −0.728203 | − | 1.26128i | −0.957642 | − | 0.287961i | \(-0.907023\pi\) |
0.229440 | − | 0.973323i | \(-0.426311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3323 | 0.625417 | 0.312708 | − | 0.949849i | \(-0.398764\pi\) | ||||
0.312708 | + | 0.949849i | \(0.398764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 33.8509i | − | 1.37852i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.8057 | − | 7.91229i | 0.479970 | − | 0.321680i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.4036 | − | 11.2026i | −0.787566 | − | 0.454701i | 0.0515389 | − | 0.998671i | \(-0.483587\pi\) |
−0.839105 | + | 0.543969i | \(0.816921\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.56670 | + | 2.15667i | 0.185052 | + | 0.0873927i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.42612 | + | 11.1304i | −0.259973 | + | 0.450286i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.4159 | + | 14.0965i | −0.986148 | + | 0.569353i | −0.904121 | − | 0.427277i | \(-0.859473\pi\) |
−0.0820275 | + | 0.996630i | \(0.526140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.13497 | − | 0.343798i | 0.207062 | − | 0.0138633i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 31.0381i | − | 1.24955i | −0.780807 | − | 0.624773i | \(-0.785192\pi\) | ||
0.780807 | − | 0.624773i | \(-0.214808\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0231 | + | 26.0208i | 0.603829 | + | 1.04586i | 0.992235 | + | 0.124374i | \(0.0396924\pi\) |
−0.388406 | + | 0.921488i | \(0.626974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.43219 | + | 4.21267i | −0.0976002 | + | 0.169049i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.95818 | + | 0.657145i | −0.318838 | + | 0.0263279i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.33488 | + | 24.1841i | −0.253395 | + | 0.967363i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.26148 | + | 1.30567i | −0.0903148 | + | 0.0521433i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.2338 | −1.08588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4263 | −1.05201 | −0.526007 | − | 0.850480i | \(-0.676312\pi\) | ||||
−0.526007 | + | 0.850480i | \(0.676312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.887739 | + | 0.512537i | −0.0352845 | + | 0.0203715i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.0772 | − | 40.8570i | 0.796741 | − | 1.62136i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.9914 | + | 7.12292i | 0.752468 | + | 0.282220i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.9936 | − | 19.0415i | 0.434902 | − | 0.753272i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.50488 | − | 6.07064i | −0.138435 | − | 0.239776i | 0.788470 | − | 0.615074i | \(-0.210874\pi\) |
−0.926904 | + | 0.375298i | \(0.877540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.0207i | 1.26277i | 0.775469 | + | 0.631386i | \(0.217514\pi\) | ||||
−0.775469 | + | 0.631386i | \(0.782486\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.226547 | + | 3.38371i | 0.00892028 | + | 0.133233i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.8513 | − | 13.7706i | 0.937692 | − | 0.541377i | 0.0484560 | − | 0.998825i | \(-0.484570\pi\) |
0.889236 | + | 0.457449i | \(0.151237\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.70873 | + | 11.6199i | −0.263341 | + | 0.456119i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.657011 | + | 7.95655i | 0.0257503 | + | 0.311842i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.2012 | + | 5.88965i | 0.399203 | + | 0.230480i | 0.686140 | − | 0.727470i | \(-0.259304\pi\) |
−0.286937 | + | 0.957949i | \(0.592637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.78119 | − | 4.54482i | 0.264963 | − | 0.177581i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.7059i | 1.11992i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.11635 | −0.277214 | −0.138607 | − | 0.990347i | \(-0.544262\pi\) | ||||
−0.138607 | + | 0.990347i | \(0.544262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9523 | − | 25.8982i | −0.581579 | − | 1.00732i | −0.995292 | − | 0.0969168i | \(-0.969102\pi\) |
0.413714 | − | 0.910407i | \(-0.364231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.45499 | + | 1.99474i | 0.134181 | + | 0.0774692i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.7863 | + | 4.23778i | 0.418275 | + | 0.164334i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.3165 | + | 7.68828i | 0.515617 | + | 0.297692i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.00089 | − | 5.19770i | −0.116021 | − | 0.200955i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.5756 | 1.91384 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.8573i | 0.418520i | 0.977860 | + | 0.209260i | \(0.0671054\pi\) | ||||
−0.977860 | + | 0.209260i | \(0.932895\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.46976 | + | 5.76511i | −0.287511 | + | 0.221899i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.4549 | + | 10.6549i | 0.709279 | + | 0.409503i | 0.810794 | − | 0.585332i | \(-0.199036\pi\) |
−0.101515 | + | 0.994834i | \(0.532369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.900917 | + | 0.624301i | −0.0345740 | + | 0.0239585i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.08145 | − | 1.87313i | 0.0414414 | − | 0.0717787i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3777 | + | 8.87831i | −0.588411 | + | 0.339719i | −0.764469 | − | 0.644661i | \(-0.776999\pi\) |
0.176058 | + | 0.984380i | \(0.443665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.8092 | − | 1.59408i | 0.909704 | − | 0.0609068i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 0.0522070i | − | 0.00199182i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.6628 | + | 18.4686i | 0.406222 | + | 0.703597i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.78672 | + | 16.9511i | −0.372304 | + | 0.644850i | −0.989920 | − | 0.141630i | \(-0.954766\pi\) |
0.617615 | + | 0.786480i | \(0.288099\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.1912 | − | 26.2513i | −0.691025 | − | 0.997205i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.0917 | − | 11.8387i | −0.913851 | − | 0.449069i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.8020 | − | 15.4742i | 1.01520 | − | 0.586126i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.75213 | 0.331036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.10176 | −0.154921 | −0.0774607 | − | 0.996995i | \(-0.524681\pi\) | ||||
−0.0774607 | + | 0.996995i | \(0.524681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7375 | + | 6.19930i | −0.404973 | + | 0.233811i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.84830 | + | 1.39966i | 0.107273 | + | 0.0527144i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0758 | − | 38.2750i | 0.679810 | − | 1.43948i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.87393 | − | 11.9060i | 0.258156 | − | 0.447139i | −0.707592 | − | 0.706621i | \(-0.750219\pi\) |
0.965748 | + | 0.259482i | \(0.0835519\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.5920 | + | 32.2024i | 0.697256 | + | 1.20768i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.3075i | 0.910321i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.9324 | + | 1.80319i | −1.00722 | + | 0.0674355i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.35461 | − | 3.09149i | 0.199972 | − | 0.115454i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.59297 | + | 13.1514i | −0.283170 | + | 0.490465i | −0.972164 | − | 0.234302i | \(-0.924719\pi\) |
0.688994 | + | 0.724767i | \(0.258053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.564666 | + | 6.83824i | 0.0210293 | + | 0.254669i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.74832 | + | 3.89614i | 0.250973 | + | 0.144899i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.2239 | + | 23.6123i | 0.676817 | + | 0.876941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.68973i | − | 0.0997565i | −0.998755 | − | 0.0498783i | \(-0.984117\pi\) | ||
0.998755 | − | 0.0498783i | \(-0.0158833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.6271 | 0.801002 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1968 | + | 17.6613i | 0.377141 | + | 0.653227i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.4602 | − | 16.4315i | −1.05120 | − | 0.606911i | −0.128216 | − | 0.991746i | \(-0.540925\pi\) |
−0.922985 | + | 0.384835i | \(0.874258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.44167 | − | 4.79661i | 0.0531767 | − | 0.176926i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.1486 | − | 24.3345i | −1.55257 | − | 0.896374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.5981 | − | 23.5527i | −0.500216 | − | 0.866399i | −1.00000 | 0.000248947i | \(-0.999921\pi\) | |
0.499784 | − | 0.866150i | \(-0.333413\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.81627 | 0.0667223 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.8026i | 0.873233i | 0.899648 | + | 0.436617i | \(0.143823\pi\) | ||||
−0.899648 | + | 0.436617i | \(0.856177\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.9367 | + | 16.7128i | −0.913609 | + | 0.612310i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.4336 | + | 8.33323i | 0.528097 | + | 0.304897i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.29709 | + | 52.0387i | 0.157012 | + | 1.90145i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7271 | + | 22.0441i | −0.464420 | + | 0.804399i | −0.999175 | − | 0.0406078i | \(-0.987071\pi\) |
0.534755 | + | 0.845007i | \(0.320404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.36410 | − | 1.36491i | 0.0861524 | − | 0.0497401i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.982075 | + | 14.6683i | 0.0357414 | + | 0.533833i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 21.9982i | − | 0.799537i | −0.916616 | − | 0.399769i | \(-0.869091\pi\) | ||
0.916616 | − | 0.399769i | \(-0.130909\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.71808 | + | 2.97580i | 0.0623623 | + | 0.108015i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.38991 | + | 4.13945i | −0.0866343 | + | 0.150055i | −0.906086 | − | 0.423093i | \(-0.860945\pi\) |
0.819452 | + | 0.573148i | \(0.194278\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6031 | − | 22.4518i | 0.383858 | − | 0.812809i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.2953 | + | 25.0207i | −0.444536 | + | 0.904627i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.08200 | − | 4.66614i | 0.291824 | − | 0.168485i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.775623 | −0.0279697 | −0.0139848 | − | 0.999902i | \(-0.504452\pi\) | ||||
−0.0139848 | + | 0.999902i | \(0.504452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.01835 | 0.252760 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.95332 | + | 1.12775i | −0.0702560 | + | 0.0405623i | −0.534716 | − | 0.845032i | \(-0.679582\pi\) |
0.464461 | + | 0.885594i | \(0.346248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.9216 | + | 43.6122i | −0.643763 | + | 1.56660i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.05207 | + | 4.40438i | 0.109492 | + | 0.158006i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.04484 | − | 12.2020i | 0.252408 | − | 0.437183i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8061 | − | 27.3769i | −0.565585 | − | 0.979623i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.2576i | 0.402315i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.58284 | − | 0.440736i | 0.234952 | − | 0.0157306i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.1429 | + | 22.0218i | −1.35965 | + | 0.784993i | −0.989576 | − | 0.144010i | \(-0.954000\pi\) |
−0.370072 | + | 0.929003i | \(0.620667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.73484 | + | 3.00484i | −0.0617620 | + | 0.106975i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.68456 | − | 3.93918i | 0.202120 | − | 0.140061i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.8618 | − | 17.2407i | −1.06042 | − | 0.612236i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.37440 | − | 2.93176i | 0.155144 | − | 0.103979i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.05089i | − | 0.0372245i | −0.999827 | − | 0.0186122i | \(-0.994075\pi\) | ||
0.999827 | − | 0.0186122i | \(-0.00592480\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.0846 | 0.675166 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.37270 | − | 7.57374i | −0.154502 | − | 0.267605i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.7424 | + | 20.6359i | 1.26132 | + | 0.728226i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.57634 | − | 14.1933i | 0.196540 | − | 0.500247i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.31145 | + | 3.06657i | 0.186972 | + | 0.107948i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.27506 | + | 12.6008i | 0.255777 | + | 0.443019i | 0.965106 | − | 0.261858i | \(-0.0843353\pi\) |
−0.709329 | + | 0.704878i | \(0.751002\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0148 | −0.457010 | −0.228505 | − | 0.973543i | \(-0.573384\pi\) | ||||
−0.228505 | + | 0.973543i | \(0.573384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.81221i | − | 0.133700i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.64977 | − | 9.92192i | −0.232931 | − | 0.347550i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.04057 | + | 4.64223i | 0.281304 | + | 0.162411i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.82810 | + | 22.1387i | 0.0638790 | + | 0.773590i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.75766 | − | 3.04435i | 0.0613427 | − | 0.106249i | −0.833723 | − | 0.552183i | \(-0.813795\pi\) |
0.895066 | + | 0.445934i | \(0.147128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.7049 | − | 20.6142i | 1.24459 | − | 0.718567i | 0.274568 | − | 0.961568i | \(-0.411465\pi\) |
0.970026 | + | 0.243001i | \(0.0781319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.888540 | + | 6.60587i | 0.0309350 | + | 0.229987i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.21314i | 0.216052i | 0.994148 | + | 0.108026i | \(0.0344530\pi\) | ||||
−0.994148 | + | 0.108026i | \(0.965547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.76940 | − | 6.52879i | −0.130917 | − | 0.226754i | 0.793114 | − | 0.609074i | \(-0.208459\pi\) |
−0.924030 | + | 0.382320i | \(0.875125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.50257 | − | 2.60254i | 0.0521237 | − | 0.0902809i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.94048 | − | 29.7112i | −0.171177 | − | 1.02943i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53852 | − | 3.13088i | 0.0532427 | − | 0.108348i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.4120 | + | 8.89811i | −0.532716 | + | 0.307564i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.2861 | 0.562259 | 0.281129 | − | 0.959670i | \(-0.409291\pi\) | ||||
0.281129 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.58608 | 0.227106 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.319371 | − | 0.184389i | 0.0109997 | − | 0.00635070i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.23928 | − | 4.54021i | −0.317841 | − | 0.156188i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.7587 | + | 1.38385i | −0.575837 | + | 0.0475496i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.37204 | + | 5.84055i | −0.115728 | + | 0.200447i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.15743 | + | 14.1291i | 0.279633 | + | 0.484339i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0261i | 1.02808i | 0.857768 | + | 0.514038i | \(0.171851\pi\) | ||||
−0.857768 | + | 0.514038i | \(0.828149\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.847868 | + | 12.6638i | 0.0289965 | + | 0.433091i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.2379 | − | 11.1070i | 0.657153 | − | 0.379407i | −0.134038 | − | 0.990976i | \(-0.542795\pi\) |
0.791191 | + | 0.611569i | \(0.209461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7242 | + | 22.0390i | −0.434146 | + | 0.751962i | −0.997225 | − | 0.0744403i | \(-0.976283\pi\) |
0.563080 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.50623 | − | 2.60038i | −0.187652 | − | 0.0886206i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.41308 | − | 4.27994i | −0.252344 | − | 0.145691i | 0.368493 | − | 0.929630i | \(-0.379874\pi\) |
−0.620837 | + | 0.783940i | \(0.713207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.5644 | + | 29.1914i | 0.665208 | + | 0.992538i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 0.484314i | − | 0.0164482i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.4613 | 1.81355 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9255 | + | 29.3158i | 0.573498 | + | 0.993327i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.03960 | − | 0.600213i | −0.0351851 | − | 0.0203141i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.4696 | − | 21.3541i | 0.691997 | − | 0.721900i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.9702 | − | 21.3447i | −1.24839 | − | 0.720760i | −0.277604 | − | 0.960695i | \(-0.589540\pi\) |
−0.970789 | + | 0.239935i | \(0.922874\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.58808 | + | 2.75063i | 0.0535645 | + | 0.0927764i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0315 | −0.674879 | −0.337439 | − | 0.941347i | \(-0.609561\pi\) | ||||
−0.337439 | + | 0.941347i | \(0.609561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.5719i | − | 0.456730i | −0.973576 | − | 0.228365i | \(-0.926662\pi\) | ||
0.973576 | − | 0.228365i | \(-0.0733380\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.28296 | − | 1.91427i | −0.0431263 | − | 0.0643475i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.2508 | + | 14.5786i | 0.847839 | + | 0.489500i | 0.859921 | − | 0.510427i | \(-0.170513\pi\) |
−0.0120824 | + | 0.999927i | \(0.503846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.2731 | + | 30.6796i | −1.48487 | + | 1.02896i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.8494 | − | 29.1840i | 0.564477 | − | 0.977702i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.52451 | − | 4.34428i | 0.251798 | − | 0.145376i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.65384 | + | 24.7017i | 0.0552816 | + | 0.825686i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.38996i | − | 0.0797984i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.1274 | + | 48.7182i | 0.938103 | + | 1.62484i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8335 | − | 27.4245i | 0.527492 | − | 0.913643i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.71353 | − | 3.62835i | 0.0570226 | − | 0.120744i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.8920 | − | 14.6890i | −0.993644 | − | 0.488279i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.5469 | − | 23.9871i | 1.37954 | − | 0.796479i | 0.387439 | − | 0.921896i | \(-0.373360\pi\) |
0.992104 | + | 0.125416i | \(0.0400266\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.3580 | 1.53760 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2832 | −1.40091 | −0.700453 | − | 0.713699i | \(-0.747019\pi\) | ||||
−0.700453 | + | 0.713699i | \(0.747019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.7518 | − | 11.9811i | 0.686785 | − | 0.396516i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.75518 | + | 7.64175i | −0.124142 | + | 0.252629i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.62622 | + | 0.794883i | −0.317886 | + | 0.0262494i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.9821 | − | 32.8780i | 0.626162 | − | 1.08454i | −0.362153 | − | 0.932119i | \(-0.617958\pi\) |
0.988315 | − | 0.152426i | \(-0.0487085\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.471468 | − | 0.816607i | −0.0155354 | − | 0.0269081i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.9873i | 0.723720i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.21878 | + | 31.3646i | 0.138713 | + | 1.03126i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.50791 | + | 3.75734i | −0.213748 | + | 0.123407i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.26381 | + | 2.18899i | −0.0414643 | + | 0.0718183i | −0.886013 | − | 0.463661i | \(-0.846536\pi\) |
0.844548 | + | 0.535479i | \(0.179869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.71112 | − | 10.5896i | −0.285495 | − | 0.347062i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.84231 | − | 3.37306i | −0.191268 | − | 0.110429i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.3152 | + | 33.2959i | 0.729786 | + | 1.08889i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.05740i | − | 0.0345438i | −0.999851 | − | 0.0172719i | \(-0.994502\pi\) | ||
0.999851 | − | 0.0172719i | \(-0.00549809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.08973 | −0.133463 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.33792 | + | 9.24555i | 0.174011 | + | 0.301396i | 0.939819 | − | 0.341674i | \(-0.110994\pi\) |
−0.765807 | + | 0.643070i | \(0.777660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0562 | − | 9.27004i | −0.522861 | − | 0.301874i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.0405 | − | 1.66003i | 0.359146 | − | 0.0540006i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.3370 | − | 14.6283i | −0.823341 | − | 0.475356i | 0.0282263 | − | 0.999602i | \(-0.491014\pi\) |
−0.851567 | + | 0.524245i | \(0.824347\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.3530 | − | 24.8601i | −0.465917 | − | 0.806992i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.27438 | −0.0737517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.31630i | 0.204605i | 0.994753 | + | 0.102302i | \(0.0326209\pi\) | ||||
−0.994753 | + | 0.102302i | \(0.967379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.88264 | − | 1.26176i | 0.0609207 | − | 0.0408296i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.88691 | + | 3.97616i | 0.222622 | + | 0.128531i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.5306 | − | 12.0571i | −0.824428 | − | 0.389345i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9642 | + | 50.1674i | −0.934329 | + | 1.61830i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −49.5249 | + | 28.5932i | −1.59592 | + | 0.921404i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.8280 | + | 1.12668i | −0.541713 | + | 0.0362690i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.2185i | 1.74355i | 0.489906 | + | 0.871775i | \(0.337031\pi\) | ||||
−0.489906 | + | 0.871775i | \(0.662969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.34851 | − | 2.33569i | −0.0433205 | − | 0.0750333i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.20395 | + | 12.4776i | −0.231186 | + | 0.400426i | −0.958157 | − | 0.286242i | \(-0.907594\pi\) |
0.726971 | + | 0.686668i | \(0.240927\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0905 | + | 26.1061i | 0.579955 | + | 0.836922i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.76209 | − | 4.28804i | 0.0564320 | − | 0.137327i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0650 | + | 12.1619i | −0.673929 | + | 0.389093i | −0.797564 | − | 0.603235i | \(-0.793878\pi\) |
0.123635 | + | 0.992328i | \(0.460545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5737 | −0.401856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.1932 | 0.868211 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.2591 | − | 11.1192i | 0.614270 | − | 0.354649i | −0.160365 | − | 0.987058i | \(-0.551267\pi\) |
0.774635 | + | 0.632409i | \(0.217934\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.13374 | + | 18.5871i | −0.291025 | + | 0.592234i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.13879 | − | 3.08645i | −0.0680786 | − | 0.0982429i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.10853 | − | 10.5803i | 0.194240 | − | 0.336433i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.13274 | − | 10.6222i | −0.194813 | − | 0.337426i | 0.752026 | − | 0.659133i | \(-0.229077\pi\) |
−0.946839 | + | 0.321707i | \(0.895743\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.73178i | 0.0549563i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.40483 | − | 35.9186i | −0.0762383 | − | 1.13869i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.18103 | + | 2.41392i | −0.132414 | + | 0.0764495i | −0.564744 | − | 0.825266i | \(-0.691025\pi\) |
0.432330 | + | 0.901716i | \(0.357692\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.97230 | + | 10.3443i | −0.188955 | + | 0.327280i |
(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 | 560.2.bw.f.289.7 | 24 | ||
4.3 | odd | 2 | 280.2.bg.a.9.6 | ✓ | 24 | ||
5.4 | even | 2 | inner | 560.2.bw.f.289.6 | 24 | ||
7.4 | even | 3 | inner | 560.2.bw.f.529.6 | 24 | ||
20.3 | even | 4 | 1400.2.q.o.401.3 | 12 | |||
20.7 | even | 4 | 1400.2.q.n.401.4 | 12 | |||
20.19 | odd | 2 | 280.2.bg.a.9.7 | yes | 24 | ||
28.11 | odd | 6 | 280.2.bg.a.249.7 | yes | 24 | ||
28.19 | even | 6 | 1960.2.g.e.1569.7 | 12 | |||
28.23 | odd | 6 | 1960.2.g.f.1569.6 | 12 | |||
35.4 | even | 6 | inner | 560.2.bw.f.529.7 | 24 | ||
140.19 | even | 6 | 1960.2.g.e.1569.6 | 12 | |||
140.23 | even | 12 | 9800.2.a.cv.1.4 | 6 | |||
140.39 | odd | 6 | 280.2.bg.a.249.6 | yes | 24 | ||
140.47 | odd | 12 | 9800.2.a.cw.1.4 | 6 | |||
140.67 | even | 12 | 1400.2.q.n.1201.4 | 12 | |||
140.79 | odd | 6 | 1960.2.g.f.1569.7 | 12 | |||
140.103 | odd | 12 | 9800.2.a.cy.1.3 | 6 | |||
140.107 | even | 12 | 9800.2.a.cx.1.3 | 6 | |||
140.123 | even | 12 | 1400.2.q.o.1201.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.6 | ✓ | 24 | 4.3 | odd | 2 | ||
280.2.bg.a.9.7 | yes | 24 | 20.19 | odd | 2 | ||
280.2.bg.a.249.6 | yes | 24 | 140.39 | odd | 6 | ||
280.2.bg.a.249.7 | yes | 24 | 28.11 | odd | 6 | ||
560.2.bw.f.289.6 | 24 | 5.4 | even | 2 | inner | ||
560.2.bw.f.289.7 | 24 | 1.1 | even | 1 | trivial | ||
560.2.bw.f.529.6 | 24 | 7.4 | even | 3 | inner | ||
560.2.bw.f.529.7 | 24 | 35.4 | even | 6 | inner | ||
1400.2.q.n.401.4 | 12 | 20.7 | even | 4 | |||
1400.2.q.n.1201.4 | 12 | 140.67 | even | 12 | |||
1400.2.q.o.401.3 | 12 | 20.3 | even | 4 | |||
1400.2.q.o.1201.3 | 12 | 140.123 | even | 12 | |||
1960.2.g.e.1569.6 | 12 | 140.19 | even | 6 | |||
1960.2.g.e.1569.7 | 12 | 28.19 | even | 6 | |||
1960.2.g.f.1569.6 | 12 | 28.23 | odd | 6 | |||
1960.2.g.f.1569.7 | 12 | 140.79 | odd | 6 | |||
9800.2.a.cv.1.4 | 6 | 140.23 | even | 12 | |||
9800.2.a.cw.1.4 | 6 | 140.47 | odd | 12 | |||
9800.2.a.cx.1.3 | 6 | 140.107 | even | 12 | |||
9800.2.a.cy.1.3 | 6 | 140.103 | odd | 12 |