Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (of order \(6\), degree \(2\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.6 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.a.2591.6 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.420258 | − | 0.242636i | −0.187945 | − | 0.108510i | 0.403075 | − | 0.915167i | \(-0.367941\pi\) |
−0.591020 | + | 0.806657i | \(0.701275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.92619i | 0.728032i | 0.931393 | + | 0.364016i | \(0.118595\pi\) | ||||
−0.931393 | + | 0.364016i | \(0.881405\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.610994 | −0.184222 | −0.0921109 | − | 0.995749i | \(-0.529361\pi\) | ||||
−0.0921109 | + | 0.995749i | \(0.529361\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.889419 | − | 1.54052i | −0.246680 | − | 0.427263i | 0.715922 | − | 0.698180i | \(-0.246006\pi\) |
−0.962603 | + | 0.270917i | \(0.912673\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.89960 | + | 2.25144i | 0.945792 | + | 0.546053i | 0.891771 | − | 0.452487i | \(-0.149463\pi\) |
0.0540208 | + | 0.998540i | \(0.482796\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.30176 | − | 4.15998i | −0.298643 | − | 0.954365i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.121114 | − | 0.209776i | −0.0252540 | − | 0.0437413i | 0.853122 | − | 0.521711i | \(-0.174706\pi\) |
−0.878376 | + | 0.477970i | \(0.841373\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.38226 | − | 4.12619i | −0.476451 | − | 0.825237i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.18126 | − | 2.99140i | 0.962136 | − | 0.555490i | 0.0653063 | − | 0.997865i | \(-0.479198\pi\) |
0.896830 | + | 0.442376i | \(0.145864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.423054i | − | 0.0759827i | −0.999278 | − | 0.0379913i | \(-0.987904\pi\) | ||
0.999278 | − | 0.0379913i | \(-0.0120959\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.467363 | − | 0.809497i | 0.0789988 | − | 0.136830i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.98567 | −0.326443 | −0.163221 | − | 0.986589i | \(-0.552188\pi\) | ||||
−0.163221 | + | 0.986589i | \(0.552188\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.42417 | + | 3.13165i | 0.847114 | + | 0.489081i | 0.859676 | − | 0.510840i | \(-0.170665\pi\) |
−0.0125623 | + | 0.999921i | \(0.503999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24844 | + | 1.87549i | 0.495382 | + | 0.286009i | 0.726805 | − | 0.686844i | \(-0.241005\pi\) |
−0.231422 | + | 0.972853i | \(0.574338\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.88383 | + | 4.99494i | 0.420649 | + | 0.728586i | 0.996003 | − | 0.0893185i | \(-0.0284689\pi\) |
−0.575354 | + | 0.817905i | \(0.695136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.28979 | 0.469970 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.85356 | − | 1.64750i | 0.391966 | − | 0.226302i | −0.291045 | − | 0.956709i | \(-0.594003\pi\) |
0.683012 | + | 0.730407i | \(0.260670\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.256775 | + | 0.148249i | 0.0346236 | + | 0.0199899i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.16651 | + | 3.75250i | −0.282056 | + | 0.488534i | −0.971891 | − | 0.235432i | \(-0.924350\pi\) |
0.689835 | + | 0.723966i | \(0.257683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.59275 | − | 2.75873i | −0.203931 | − | 0.353219i | 0.745861 | − | 0.666102i | \(-0.232038\pi\) |
−0.949792 | + | 0.312883i | \(0.898705\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.863220i | 0.107069i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.13814 | − | 2.38916i | 0.505554 | − | 0.291882i | −0.225450 | − | 0.974255i | \(-0.572385\pi\) |
0.731004 | + | 0.682373i | \(0.239052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.60211 | + | 13.1672i | −0.902205 | + | 1.56266i | −0.0775785 | + | 0.996986i | \(0.524719\pi\) |
−0.824626 | + | 0.565678i | \(0.808614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.34087 | − | 5.78656i | 0.391019 | − | 0.677265i | −0.601565 | − | 0.798824i | \(-0.705456\pi\) |
0.992584 | + | 0.121558i | \(0.0387892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.17689i | − | 0.134119i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3701 | + | 7.71920i | 1.50425 | + | 0.868478i | 0.999988 | + | 0.00492653i | \(0.00156817\pi\) |
0.504260 | + | 0.863552i | \(0.331765\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.99578 | 0.987415 | 0.493707 | − | 0.869628i | \(-0.335641\pi\) | ||||
0.493707 | + | 0.869628i | \(0.335641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.09256 | − | 1.89237i | −0.118505 | − | 0.205256i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.14682 | − | 4.70357i | 0.863562 | − | 0.498578i | −0.00164176 | − | 0.999999i | \(-0.500523\pi\) |
0.865203 | + | 0.501421i | \(0.167189\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.96733 | − | 1.71319i | 0.311061 | − | 0.179591i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.462288 | + | 2.06412i | −0.0474298 | + | 0.211774i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.18910 | − | 5.52368i | 0.323804 | − | 0.560845i | −0.657466 | − | 0.753484i | \(-0.728372\pi\) |
0.981270 | + | 0.192640i | \(0.0617049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.61192 | − | 2.66269i | 0.458903 | − | 0.264948i | −0.252680 | − | 0.967550i | \(-0.581312\pi\) |
0.711583 | + | 0.702602i | \(0.247979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.57269i | − | 0.352027i | −0.984388 | − | 0.176014i | \(-0.943680\pi\) | ||
0.984388 | − | 0.176014i | \(-0.0563203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.12772 | 0.399042 | 0.199521 | − | 0.979894i | \(-0.436061\pi\) | ||||
0.199521 | + | 0.979894i | \(0.436061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.62369 | − | 9.74051i | 0.538652 | − | 0.932972i | −0.460325 | − | 0.887750i | \(-0.652267\pi\) |
0.998977 | − | 0.0452218i | \(-0.0143995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.15441i | 0.578958i | 0.957184 | + | 0.289479i | \(0.0934820\pi\) | ||||
−0.957184 | + | 0.289479i | \(0.906518\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.117547i | 0.0109613i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.33669 | + | 7.51138i | −0.397544 | + | 0.688567i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6267 | −0.966062 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.73845i | 0.423819i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.925602 | − | 0.534397i | 0.0821339 | − | 0.0474200i | −0.458371 | − | 0.888761i | \(-0.651567\pi\) |
0.540504 | + | 0.841341i | \(0.318233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.48949 | + | 2.57987i | −0.130137 | + | 0.225404i | −0.923729 | − | 0.383046i | \(-0.874875\pi\) |
0.793592 | + | 0.608450i | \(0.208208\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.01292 | − | 2.50743i | 0.694808 | − | 0.217422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.9996 | − | 9.23737i | 1.36694 | − | 0.789202i | 0.376402 | − | 0.926456i | \(-0.377161\pi\) |
0.990536 | + | 0.137254i | \(0.0438277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.89522 | + | 4.55831i | −0.669664 | + | 0.386631i | −0.795949 | − | 0.605363i | \(-0.793028\pi\) |
0.126285 | + | 0.991994i | \(0.459695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.543430 | + | 0.941248i | 0.0454439 | + | 0.0787111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.90329 | −0.241105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3348 | + | 7.12152i | 1.01051 | + | 0.583418i | 0.911341 | − | 0.411653i | \(-0.135048\pi\) |
0.0991686 | + | 0.995071i | \(0.468382\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.84107i | 0.800855i | 0.916329 | + | 0.400427i | \(0.131138\pi\) | ||||
−0.916329 | + | 0.400427i | \(0.868862\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.102648 | + | 0.177792i | −0.00824489 | + | 0.0142806i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.26706 | + | 5.65872i | −0.260740 | + | 0.451615i | −0.966439 | − | 0.256897i | \(-0.917300\pi\) |
0.705699 | + | 0.708512i | \(0.250633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.404068 | − | 0.233289i | 0.0318450 | − | 0.0183857i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.0135i | − | 1.17595i | −0.808879 | − | 0.587975i | \(-0.799925\pi\) | ||
0.808879 | − | 0.587975i | \(-0.200075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.15701 | − | 5.46810i | −0.244297 | − | 0.423134i | 0.717637 | − | 0.696417i | \(-0.245224\pi\) |
−0.961934 | + | 0.273283i | \(0.911890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.91787 | − | 8.51800i | 0.378298 | − | 0.655231i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.1182 | + | 6.41908i | 0.845299 | + | 0.488033i | 0.859062 | − | 0.511872i | \(-0.171048\pi\) |
−0.0137631 | + | 0.999905i | \(0.504381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.94782 | − | 4.58868i | 0.600799 | − | 0.346872i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.4674 | 0.857115 | 0.428558 | − | 0.903514i | \(-0.359022\pi\) | ||||
0.428558 | + | 0.903514i | \(0.359022\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.87538 | − | 11.9085i | −0.511043 | − | 0.885152i | −0.999918 | − | 0.0127983i | \(-0.995926\pi\) |
0.488875 | − | 0.872354i | \(-0.337407\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.834495 | + | 0.481796i | 0.0613533 | + | 0.0354223i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.38263 | − | 1.37561i | −0.174235 | − | 0.100595i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.4411 | −1.26199 | −0.630996 | − | 0.775786i | \(-0.717353\pi\) | ||||
−0.630996 | + | 0.775786i | \(0.717353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.48115 | − | 6.02954i | 0.250579 | − | 0.434016i | −0.713106 | − | 0.701056i | \(-0.752712\pi\) |
0.963685 | + | 0.267040i | \(0.0860457\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.58982i | − | 0.683246i | −0.939837 | − | 0.341623i | \(-0.889023\pi\) | ||
0.939837 | − | 0.341623i | \(-0.110977\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.32171 | + | 1.91779i | −0.235470 | + | 0.135948i | −0.613093 | − | 0.790011i | \(-0.710075\pi\) |
0.377623 | + | 0.925959i | \(0.376741\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.76201 | + | 9.98010i | 0.404414 | + | 0.700466i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.51970 | − | 2.63220i | −0.106141 | − | 0.183841i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.795365 | + | 2.54172i | 0.0550165 | + | 0.175815i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.19164 | + | 5.30679i | 0.632778 | + | 0.365335i | 0.781827 | − | 0.623495i | \(-0.214288\pi\) |
−0.149049 | + | 0.988830i | \(0.547621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.910122 | − | 1.57638i | −0.0620698 | − | 0.107508i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.814882 | 0.0553178 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.00988i | − | 0.538803i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.06628 | + | 3.50237i | 0.406228 | + | 0.234536i | 0.689168 | − | 0.724602i | \(-0.257976\pi\) |
−0.282940 | + | 0.959138i | \(0.591310\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.1861 | 0.742450 | 0.371225 | − | 0.928543i | \(-0.378938\pi\) | ||||
0.371225 | + | 0.928543i | \(0.378938\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5605 | −0.697859 | −0.348930 | − | 0.937149i | \(-0.613455\pi\) | ||||
−0.348930 | + | 0.937149i | \(0.613455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.49728 | − | 3.17386i | −0.360139 | − | 0.207926i | 0.309003 | − | 0.951061i | \(-0.400005\pi\) |
−0.669142 | + | 0.743135i | \(0.733338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.79888i | − | 0.182579i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.69586 | 0.174381 | 0.0871904 | − | 0.996192i | \(-0.472211\pi\) | ||||
0.0871904 | + | 0.996192i | \(0.472211\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.667812 | + | 1.15668i | 0.0430175 | + | 0.0745086i | 0.886733 | − | 0.462283i | \(-0.152970\pi\) |
−0.843715 | + | 0.536791i | \(0.819636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.38256 | − | 0.798222i | −0.0883285 | − | 0.0509965i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.25072 | + | 5.70534i | −0.334095 | + | 0.363022i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.08912 | − | 8.81462i | −0.321223 | − | 0.556374i | 0.659518 | − | 0.751689i | \(-0.270760\pi\) |
−0.980741 | + | 0.195315i | \(0.937427\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0740000 | + | 0.128172i | 0.00465234 | + | 0.00805809i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.9876 | − | 8.07575i | 0.872523 | − | 0.503751i | 0.00433712 | − | 0.999991i | \(-0.498619\pi\) |
0.868186 | + | 0.496239i | \(0.165286\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.82479i | − | 0.237661i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.492663 | − | 0.853317i | 0.0303789 | − | 0.0526178i | −0.850436 | − | 0.526078i | \(-0.823662\pi\) |
0.880815 | + | 0.473460i | \(0.156995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.59897 | −0.0982242 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8778 | + | 9.16706i | 0.968087 | + | 0.558926i | 0.898653 | − | 0.438661i | \(-0.144547\pi\) |
0.0694348 | + | 0.997586i | \(0.477880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.22963 | + | 4.17403i | 0.439169 | + | 0.253554i | 0.703245 | − | 0.710948i | \(-0.251734\pi\) |
−0.264076 | + | 0.964502i | \(0.585067\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.45554 | + | 2.52108i | 0.0877726 | + | 0.152027i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1188 | 1.32899 | 0.664494 | − | 0.747293i | \(-0.268647\pi\) | ||||
0.664494 | + | 0.747293i | \(0.268647\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.79959 | + | 5.65780i | −0.584595 | + | 0.337516i | −0.762957 | − | 0.646449i | \(-0.776253\pi\) |
0.178363 | + | 0.983965i | \(0.442920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.12442 | − | 5.26799i | −0.542390 | − | 0.313149i | 0.203657 | − | 0.979042i | \(-0.434717\pi\) |
−0.746047 | + | 0.665893i | \(0.768051\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.03215 | + | 10.4480i | −0.356067 | + | 0.616726i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.63792 | + | 2.83697i | 0.0963484 | + | 0.166880i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.28078i | − | 0.366927i | −0.983027 | − | 0.183464i | \(-0.941269\pi\) | ||
0.983027 | − | 0.183464i | \(-0.0587309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.82099 | − | 1.05135i | 0.106022 | − | 0.0612118i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.215442 | + | 0.373157i | −0.0124593 | + | 0.0215802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.61255 | + | 6.25711i | −0.208224 | + | 0.360654i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.54584i | 0.0885143i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0020 | − | 6.92933i | −0.684988 | − | 0.395478i | 0.116744 | − | 0.993162i | \(-0.462754\pi\) |
−0.801732 | + | 0.597684i | \(0.796088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.69554 | −0.493079 | −0.246539 | − | 0.969133i | \(-0.579293\pi\) | ||||
−0.246539 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.278745 | − | 0.482801i | −0.0157556 | − | 0.0272895i | 0.858040 | − | 0.513583i | \(-0.171682\pi\) |
−0.873796 | + | 0.486293i | \(0.838349\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.9649 | + | 14.4135i | −1.40217 | + | 0.809542i | −0.994615 | − | 0.103639i | \(-0.966951\pi\) |
−0.407553 | + | 0.913182i | \(0.633618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16572 | + | 1.82773i | −0.177246 | + | 0.102333i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.28960 | − | 19.1531i | 0.238680 | − | 1.06571i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.23765 | + | 7.33982i | −0.235062 | + | 0.407140i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.62120 | + | 5.55480i | −0.530434 | + | 0.306246i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6.62797i | − | 0.364306i | −0.983270 | − | 0.182153i | \(-0.941693\pi\) | ||
0.983270 | − | 0.182153i | \(-0.0583067\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.31878 | −0.126689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.92757 | + | 10.2668i | −0.322895 | + | 0.559271i | −0.981084 | − | 0.193582i | \(-0.937989\pi\) |
0.658189 | + | 0.752853i | \(0.271323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.258483i | 0.0139977i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8201i | 1.07018i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.2261 | − | 22.9084i | 0.710017 | − | 1.22979i | −0.254833 | − | 0.966985i | \(-0.582021\pi\) |
0.964850 | − | 0.262800i | \(-0.0846460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9308 | 0.799226 | 0.399613 | − | 0.916684i | \(-0.369145\pi\) | ||||
0.399613 | + | 0.916684i | \(0.369145\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.4562i | 1.03555i | 0.855517 | + | 0.517775i | \(0.173240\pi\) | ||||
−0.855517 | + | 0.517775i | \(0.826760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.38970 | − | 3.68909i | 0.339130 | − | 0.195797i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.7512 | + | 18.6215i | −0.567424 | + | 0.982808i | 0.429395 | + | 0.903117i | \(0.358727\pi\) |
−0.996820 | + | 0.0796910i | \(0.974607\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6109 | + | 10.8306i | −0.821625 | + | 0.570029i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.80806 | + | 1.62123i | −0.146980 | + | 0.0848592i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.60649 | + | 4.96896i | −0.449255 | + | 0.259378i | −0.707516 | − | 0.706698i | \(-0.750184\pi\) |
0.258260 | + | 0.966075i | \(0.416851\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.17340 | + | 5.49650i | 0.164755 | + | 0.285364i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4225 | −0.953881 | −0.476941 | − | 0.878936i | \(-0.658254\pi\) | ||||
−0.476941 | + | 0.878936i | \(0.658254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.21662 | − | 5.32122i | −0.474680 | − | 0.274057i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.7734i | − | 1.06706i | −0.845783 | − | 0.533528i | \(-0.820866\pi\) | ||
0.845783 | − | 0.533528i | \(-0.179134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.3400 | + | 23.1055i | −0.681642 | + | 1.18064i | 0.292838 | + | 0.956162i | \(0.405400\pi\) |
−0.974480 | + | 0.224476i | \(0.927933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.285556 | + | 0.494598i | −0.0145533 | + | 0.0252071i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.27614 | + | 3.04618i | −0.267511 | + | 0.154447i | −0.627756 | − | 0.778410i | \(-0.716026\pi\) |
0.360245 | + | 0.932858i | \(0.382693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.09072i | − | 0.0551602i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.74591 | − | 6.48811i | −0.188477 | − | 0.326452i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.32784 | + | 9.22810i | −0.267397 | + | 0.463145i | −0.968189 | − | 0.250221i | \(-0.919497\pi\) |
0.700792 | + | 0.713366i | \(0.252830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.9567 | − | 13.2540i | −1.14640 | − | 0.661875i | −0.198393 | − | 0.980123i | \(-0.563572\pi\) |
−0.948008 | + | 0.318248i | \(0.896906\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.651722 | + | 0.376272i | −0.0324646 | + | 0.0187434i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.21324 | 0.0601378 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.19512 | + | 3.80206i | 0.108542 | + | 0.188000i | 0.915180 | − | 0.403046i | \(-0.132049\pi\) |
−0.806638 | + | 0.591046i | \(0.798715\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.22804 | − | 4.17311i | −0.355669 | − | 0.205345i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.78055 | − | 2.18270i | −0.185580 | − | 0.107145i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.42844 | 0.265197 | 0.132598 | − | 0.991170i | \(-0.457668\pi\) | ||||
0.132598 | + | 0.991170i | \(0.457668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.57871 | − | 4.46646i | 0.125679 | − | 0.217682i | −0.796319 | − | 0.604876i | \(-0.793223\pi\) |
0.921998 | + | 0.387195i | \(0.126556\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 21.4540i | − | 1.04067i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.31383 | − | 3.06794i | 0.257154 | − | 0.148468i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.18928 | + | 15.9163i | 0.442632 | + | 0.766661i | 0.997884 | − | 0.0650209i | \(-0.0207114\pi\) |
−0.555252 | + | 0.831682i | \(0.687378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.1096 | + | 19.2424i | 0.533894 | + | 0.924732i | 0.999216 | + | 0.0395901i | \(0.0126052\pi\) |
−0.465322 | + | 0.885141i | \(0.654061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.715002 | + | 0.776909i | −0.0342032 | + | 0.0371646i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.6789 | + | 14.8257i | 1.22558 | + | 0.707592i | 0.966103 | − | 0.258156i | \(-0.0831150\pi\) |
0.259482 | + | 0.965748i | \(0.416448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.3830 | − | 19.7160i | −0.540824 | − | 0.936734i | −0.998857 | − | 0.0477989i | \(-0.984779\pi\) |
0.458033 | − | 0.888935i | \(-0.348554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.56502 | −0.216403 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.46867i | − | 0.210889i | −0.994425 | − | 0.105445i | \(-0.966373\pi\) | ||
0.994425 | − | 0.105445i | \(-0.0336266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.31414 | − | 1.91342i | −0.156057 | − | 0.0900994i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.66273 | −0.0779499 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.85292 | 0.273788 | 0.136894 | − | 0.990586i | \(-0.456288\pi\) | ||||
0.136894 | + | 0.990586i | \(0.456288\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.0016 | − | 7.50646i | −0.605544 | − | 0.349611i | 0.165676 | − | 0.986180i | \(-0.447020\pi\) |
−0.771219 | + | 0.636569i | \(0.780353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.11830i | 0.0519719i | 0.999662 | + | 0.0259860i | \(0.00827252\pi\) | ||||
−0.999662 | + | 0.0259860i | \(0.991727\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.5205 | 1.92134 | 0.960671 | − | 0.277691i | \(-0.0895690\pi\) | ||||
0.960671 | + | 0.277691i | \(0.0895690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.60197 | + | 7.97085i | 0.212499 | + | 0.368060i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.98478 | − | 1.14591i | −0.0912602 | − | 0.0526891i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0637 | + | 15.2814i | −0.645289 | + | 0.701160i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.83998 | − | 13.5792i | −0.358218 | − | 0.620451i | 0.629445 | − | 0.777045i | \(-0.283282\pi\) |
−0.987663 | + | 0.156593i | \(0.949949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.76610 | + | 3.05897i | 0.0805270 | + | 0.139477i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.68049 | + | 1.54758i | −0.121715 | + | 0.0702720i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.04224i | 0.0925427i | 0.998929 | + | 0.0462714i | \(0.0147339\pi\) | ||||
−0.998929 | + | 0.0462714i | \(0.985266\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2695 | − | 22.9835i | 0.598846 | − | 1.03723i | −0.394145 | − | 0.919048i | \(-0.628959\pi\) |
0.992992 | − | 0.118184i | \(-0.0377073\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.9398 | 1.21331 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.3626 | − | 14.6431i | −1.13767 | − | 0.656834i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.9939 | − | 17.3170i | −1.34271 | − | 0.775214i | −0.355506 | − | 0.934674i | \(-0.615691\pi\) |
−0.987204 | + | 0.159460i | \(0.949025\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.9791 | − | 27.6765i | −0.712471 | − | 1.23404i | −0.963927 | − | 0.266168i | \(-0.914243\pi\) |
0.251456 | − | 0.967869i | \(-0.419091\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.58426 | −0.114998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.7589 | + | 11.4078i | −0.875799 | + | 0.505643i | −0.869271 | − | 0.494336i | \(-0.835411\pi\) |
−0.00652823 | + | 0.999979i | \(0.502078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1460 | + | 6.43516i | 0.493071 | + | 0.284675i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.866863 | + | 1.50145i | −0.0381985 | + | 0.0661618i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.76200 | − | 3.05188i | −0.0774928 | − | 0.134221i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.09569i | 0.223246i | 0.993751 | + | 0.111623i | \(0.0356050\pi\) | ||||
−0.993751 | + | 0.111623i | \(0.964395\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.1712 | + | 12.2232i | −0.925752 | + | 0.534483i | −0.885466 | − | 0.464705i | \(-0.846160\pi\) |
−0.0402866 | + | 0.999188i | \(0.512827\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.952478 | − | 1.64974i | 0.0414906 | − | 0.0718638i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4707 | − | 19.8678i | 0.498724 | − | 0.863816i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.1414i | − | 0.482587i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.73471 | − | 1.00153i | −0.0749980 | − | 0.0433001i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.01004 | −0.0865787 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0409 | + | 26.0516i | 0.646659 | + | 1.12005i | 0.983916 | + | 0.178633i | \(0.0571675\pi\) |
−0.337257 | + | 0.941413i | \(0.609499\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.72680 | + | 2.72902i | −0.202474 | + | 0.116898i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.2592 | + | 9.96461i | −0.737951 | + | 0.426056i | −0.821324 | − | 0.570462i | \(-0.806764\pi\) |
0.0833729 | + | 0.996518i | \(0.473431\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.1889 | − | 17.6599i | −0.817475 | − | 0.752336i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8687 | + | 25.7533i | −0.632280 | + | 1.09514i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.34354 | + | 4.81715i | −0.353527 | + | 0.204109i | −0.666238 | − | 0.745739i | \(-0.732096\pi\) |
0.312710 | + | 0.949849i | \(0.398763\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.67237i | − | 0.282211i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.81914 | −0.0766677 | −0.0383339 | − | 0.999265i | \(-0.512205\pi\) | ||||
−0.0383339 | + | 0.999265i | \(0.512205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.49328 | − | 2.58644i | 0.0628228 | − | 0.108812i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0388i | 0.672382i | 0.941794 | + | 0.336191i | \(0.109139\pi\) | ||||
−0.941794 | + | 0.336191i | \(0.890861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.71146i | − | 0.155320i | −0.996980 | − | 0.0776598i | \(-0.975255\pi\) | ||
0.996980 | − | 0.0776598i | \(-0.0247448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.577049 | + | 0.999478i | −0.0240646 | + | 0.0416811i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.9587 | −1.95492 | −0.977459 | − | 0.211126i | \(-0.932287\pi\) | ||||
−0.977459 | + | 0.211126i | \(0.932287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.3276i | 0.718869i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.74351 | + | 1.00661i | −0.0722087 | + | 0.0416897i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0431 | − | 38.1798i | 0.909816 | − | 1.57585i | 0.0954964 | − | 0.995430i | \(-0.469556\pi\) |
0.814319 | − | 0.580417i | \(-0.197110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.75989 | + | 0.550712i | −0.0725152 | + | 0.0226917i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.9625 | + | 6.32922i | −0.450177 | + | 0.259910i | −0.707905 | − | 0.706308i | \(-0.750359\pi\) |
0.257728 | + | 0.966218i | \(0.417026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.64506 | − | 2.10448i | 0.149433 | − | 0.0862752i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.2828 | − | 42.0590i | −0.992168 | − | 1.71849i | −0.604260 | − | 0.796787i | \(-0.706531\pi\) |
−0.387908 | − | 0.921698i | \(-0.626802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2147 | 1.02853 | 0.514264 | − | 0.857632i | \(-0.328065\pi\) | ||||
0.514264 | + | 0.857632i | \(0.328065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.46595 | + | 2.57842i | 0.181567 | + | 0.104828i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 34.9811i | − | 1.41984i | −0.704283 | − | 0.709919i | \(-0.748731\pi\) | ||
0.704283 | − | 0.709919i | \(-0.251269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.12986 | − | 8.88518i | 0.207532 | − | 0.359456i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.9896 | + | 24.2307i | −0.565035 | + | 0.978670i | 0.432011 | + | 0.901868i | \(0.357804\pi\) |
−0.997046 | + | 0.0768017i | \(0.975529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0668 | + | 9.27615i | −0.646824 | + | 0.373444i | −0.787238 | − | 0.616649i | \(-0.788490\pi\) |
0.140415 | + | 0.990093i | \(0.455156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.22585i | 0.129658i | 0.997896 | + | 0.0648290i | \(0.0206502\pi\) | ||||
−0.997896 | + | 0.0648290i | \(0.979350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.05998 | + | 15.6923i | 0.362980 | + | 0.628700i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.7616 | + | 18.6396i | −0.430462 | + | 0.745583i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.74333 | − | 4.47062i | −0.308747 | − | 0.178255i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.6237 | + | 17.6806i | −1.21911 | + | 0.703852i | −0.964727 | − | 0.263252i | \(-0.915205\pi\) |
−0.254381 | + | 0.967104i | \(0.581872\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.518656 | −0.0205822 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.92600 | − | 5.06798i | −0.115932 | − | 0.200801i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.15028 | + | 0.664116i | 0.0454334 | + | 0.0262310i | 0.522545 | − | 0.852612i | \(-0.324983\pi\) |
−0.477111 | + | 0.878843i | \(0.658316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.3711 | − | 13.4933i | −0.921666 | − | 0.532124i | −0.0374997 | − | 0.999297i | \(-0.511939\pi\) |
−0.884166 | + | 0.467173i | \(0.845273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.9228 | −1.09776 | −0.548878 | − | 0.835902i | \(-0.684945\pi\) | ||||
−0.548878 | + | 0.835902i | \(0.684945\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.32373 | − | 2.29276i | 0.0519608 | − | 0.0899987i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.51311i | 0.0592127i | 0.999562 | + | 0.0296064i | \(0.00942538\pi\) | ||||
−0.999562 | + | 0.0296064i | \(0.990575\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.25194 | − | 0.722808i | 0.0489174 | − | 0.0282424i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1199 | + | 24.4564i | 0.550033 | + | 0.952686i | 0.998271 | + | 0.0587714i | \(0.0187183\pi\) |
−0.448238 | + | 0.893914i | \(0.647948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.30326 | − | 7.45347i | −0.167377 | − | 0.289906i | 0.770120 | − | 0.637900i | \(-0.220197\pi\) |
−0.937497 | + | 0.347993i | \(0.886863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.97589 | − | 0.890455i | −0.154178 | − | 0.0345304i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.25505 | − | 0.724602i | −0.0485956 | − | 0.0280567i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.973162 | + | 1.68557i | 0.0375685 | + | 0.0650706i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.3199 | 0.976009 | 0.488005 | − | 0.872841i | \(-0.337725\pi\) | ||||
0.488005 | + | 0.872841i | \(0.337725\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 18.7436i | − | 0.720376i | −0.932880 | − | 0.360188i | \(-0.882713\pi\) | ||
0.932880 | − | 0.360188i | \(-0.117287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.6397 | + | 6.14281i | 0.408313 | + | 0.235739i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.71791 | −0.295318 | −0.147659 | − | 0.989038i | \(-0.547174\pi\) | ||||
−0.147659 | + | 0.989038i | \(0.547174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.96528 | −0.342546 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.07602 | − | 2.93064i | −0.193381 | − | 0.111648i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.59423i | 0.212814i | 0.994323 | + | 0.106407i | \(0.0339347\pi\) | ||||
−0.994323 | + | 0.106407i | \(0.966065\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.42404 | 0.167813 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.1014 | + | 24.4244i | 0.534129 | + | 0.925138i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.9559 | − | 15.5630i | −1.01811 | − | 0.587807i | −0.104555 | − | 0.994519i | \(-0.533342\pi\) |
−0.913556 | + | 0.406713i | \(0.866675\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.58486 | + | 8.26036i | 0.0974899 | + | 0.311545i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.12886 | + | 8.88344i | 0.192891 | + | 0.334096i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.5873 | + | 18.3377i | 0.397614 | + | 0.688688i | 0.993431 | − | 0.114432i | \(-0.0365049\pi\) |
−0.595817 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.0887463 | + | 0.0512377i | −0.00332358 | + | 0.00191887i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.527423i | − | 0.0197245i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0882 | − | 27.8656i | 0.599988 | − | 1.03921i | −0.392834 | − | 0.919609i | \(-0.628505\pi\) |
0.992822 | − | 0.119600i | \(-0.0381613\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.88168 | 0.256287 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.6862 | − | 14.2526i | −0.916822 | − | 0.529327i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00241 | + | 4.62020i | 0.296793 | + | 0.171354i | 0.641001 | − | 0.767540i | \(-0.278519\pi\) |
−0.344208 | + | 0.938893i | \(0.611853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.44507 | + | 14.6273i | 0.312352 | + | 0.541010i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.4170 | −0.717184 | −0.358592 | − | 0.933494i | \(-0.616743\pi\) | ||||
−0.358592 | + | 0.933494i | \(0.616743\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.52838 | + | 1.45976i | −0.0931341 | + | 0.0537710i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.33473 | + | 3.08001i | 0.196241 | + | 0.113300i | 0.594901 | − | 0.803799i | \(-0.297191\pi\) |
−0.398660 | + | 0.917099i | \(0.630525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0767 | + | 27.8457i | −0.589798 | + | 1.02156i | 0.404461 | + | 0.914555i | \(0.367459\pi\) |
−0.994259 | + | 0.107004i | \(0.965874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.45588 | − | 5.98575i | −0.126614 | − | 0.219301i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.95078i | 0.290515i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.9837 | + | 11.5376i | −0.729216 | + | 0.421013i | −0.818135 | − | 0.575026i | \(-0.804992\pi\) |
0.0889190 | + | 0.996039i | \(0.471659\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.38780 | − | 4.13579i | 0.0869009 | − | 0.150517i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.0252 | + | 19.0963i | −0.400719 | + | 0.694066i | −0.993813 | − | 0.111067i | \(-0.964573\pi\) |
0.593093 | + | 0.805134i | \(0.297906\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.20390i | − | 0.261141i | −0.991439 | − | 0.130571i | \(-0.958319\pi\) | ||
0.991439 | − | 0.130571i | \(-0.0416809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.7621 | + | 10.8323i | 0.679233 | + | 0.392156i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.70774 | 0.278310 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.60217 | + | 9.70323i | 0.202019 | + | 0.349908i | 0.949179 | − | 0.314737i | \(-0.101916\pi\) |
−0.747160 | + | 0.664645i | \(0.768583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.0909 | + | 13.9089i | −0.866491 | + | 0.500269i | −0.866181 | − | 0.499731i | \(-0.833432\pi\) |
−0.000310458 | 1.00000i | \(0.500099\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.74560 | + | 1.00782i | −0.0627037 | + | 0.0362020i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.96665 | − | 26.6411i | 0.213777 | − | 0.954516i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.64485 | − | 8.04511i | 0.166206 | − | 0.287877i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.74602 | − | 1.58542i | 0.0980096 | − | 0.0565859i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 49.1575i | − | 1.75228i | −0.482060 | − | 0.876138i | \(-0.660111\pi\) | ||
0.482060 | − | 0.876138i | \(-0.339889\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.8546 | −0.421500 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.83325 | + | 4.90733i | −0.100612 | + | 0.174264i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.13639i | − | 0.181940i | −0.995854 | − | 0.0909701i | \(-0.971003\pi\) | ||
0.995854 | − | 0.0909701i | \(-0.0289968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.9710i | 0.918788i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.04125 | + | 3.53555i | −0.0720343 | + | 0.124767i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.226417 | −0.00798015 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.9399i | 0.947156i | 0.880752 | + | 0.473578i | \(0.157038\pi\) | ||||
−0.880752 | + | 0.473578i | \(0.842962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4757 | − | 13.5537i | 0.824345 | − | 0.475936i | −0.0275678 | − | 0.999620i | \(-0.508776\pi\) |
0.851912 | + | 0.523684i | \(0.175443\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.64282 | + | 6.30955i | −0.127602 | + | 0.221014i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.57332 | − | 15.9549i | 0.125015 | − | 0.558190i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.06111 | + | 0.612630i | −0.0370329 | + | 0.0213809i | −0.518402 | − | 0.855137i | \(-0.673473\pi\) |
0.481369 | + | 0.876518i | \(0.340140\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.98619 | + | 4.61083i | −0.278381 | + | 0.160723i | −0.632690 | − | 0.774405i | \(-0.718049\pi\) |
0.354309 | + | 0.935128i | \(0.384716\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.1285 | − | 24.4713i | −0.491297 | − | 0.850951i | 0.508653 | − | 0.860972i | \(-0.330144\pi\) |
−0.999950 | + | 0.0100207i | \(0.996810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.20848 | −0.146167 | −0.0730833 | − | 0.997326i | \(-0.523284\pi\) | ||||
−0.0730833 | + | 0.997326i | \(0.523284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.8289 | + | 7.40675i | 0.444494 | + | 0.256629i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.06402i | 0.106035i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.7781 | + | 35.9888i | −0.717341 | + | 1.24247i | 0.244709 | + | 0.969597i | \(0.421308\pi\) |
−0.962050 | + | 0.272874i | \(0.912026\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.39698 | − | 5.88374i | 0.117137 | − | 0.202888i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.13355 | + | 2.38650i | −0.142198 | + | 0.0820983i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.4690i | − | 0.703324i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.240493 | + | 0.416546i | 0.00824399 | + | 0.0142790i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.60095 | − | 14.8973i | 0.294491 | − | 0.510073i | −0.680376 | − | 0.732864i | \(-0.738183\pi\) |
0.974866 | + | 0.222791i | \(0.0715166\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.5845 | − | 16.5032i | −0.976426 | − | 0.563740i | −0.0752371 | − | 0.997166i | \(-0.523971\pi\) |
−0.901189 | + | 0.433426i | \(0.857305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.1602 | + | 17.9904i | −1.06317 | + | 0.613824i | −0.926308 | − | 0.376766i | \(-0.877036\pi\) |
−0.136865 | + | 0.990590i | \(0.543703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.3018 | 1.03149 | 0.515743 | − | 0.856744i | \(-0.327516\pi\) | ||||
0.515743 | + | 0.856744i | \(0.327516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.11500 | − | 5.39534i | −0.105913 | − | 0.183447i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.16903 | − | 4.71639i | −0.277115 | − | 0.159993i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.36108 | − | 4.24992i | −0.249421 | − | 0.144003i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.12715 | −0.308554 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6100 | + | 39.1616i | −0.763485 | + | 1.32239i | 0.177559 | + | 0.984110i | \(0.443180\pi\) |
−0.941044 | + | 0.338284i | \(0.890153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.91740i | 0.199362i | 0.995019 | + | 0.0996812i | \(0.0317823\pi\) | ||||
−0.995019 | + | 0.0996812i | \(0.968218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.5219 | − | 22.2406i | 1.29637 | − | 0.748457i | 0.316591 | − | 0.948562i | \(-0.397462\pi\) |
0.979774 | + | 0.200105i | \(0.0641285\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.69968 | − | 4.67598i | −0.0906463 | − | 0.157004i | 0.817137 | − | 0.576444i | \(-0.195560\pi\) |
−0.907783 | + | 0.419440i | \(0.862227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.02935 | + | 1.78289i | 0.0345233 | + | 0.0597961i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.0248 | − | 18.4988i | 0.569713 | − | 0.619040i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.81928 | − | 2.78241i | −0.161091 | − | 0.0930057i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.26552 | − | 2.19195i | −0.0422076 | − | 0.0731057i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.8370 | 0.494291 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.67286i | 0.221813i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.958413 | + | 0.553340i | 0.0318236 | + | 0.0183734i | 0.515827 | − | 0.856693i | \(-0.327485\pi\) |
−0.484004 | + | 0.875066i | \(0.660818\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4474 | 0.379268 | 0.189634 | − | 0.981855i | \(-0.439270\pi\) | ||||
0.189634 | + | 0.981855i | \(0.439270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.49637 | −0.181903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.96933 | − | 2.86904i | −0.164102 | − | 0.0947441i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.6358i | 0.944607i | 0.881436 | + | 0.472303i | \(0.156577\pi\) | ||||
−0.881436 | + | 0.472303i | \(0.843423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.0458 | 0.890225 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.73038 | + | 8.19326i | 0.155534 | + | 0.269393i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.0773 | + | 19.0972i | 1.08523 | + | 0.626558i | 0.932302 | − | 0.361680i | \(-0.117797\pi\) |
0.152928 | + | 0.988237i | \(0.451130\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.28250 | − | 13.6855i | −0.140353 | − | 0.448523i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.667547 | + | 1.15623i | 0.0218311 | + | 0.0378126i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.0248 | − | 34.6840i | −0.654182 | − | 1.13308i | −0.982098 | − | 0.188370i | \(-0.939680\pi\) |
0.327916 | − | 0.944707i | \(-0.393654\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.0454 | − | 18.5014i | 1.04465 | − | 0.603128i | 0.123502 | − | 0.992344i | \(-0.460587\pi\) |
0.921147 | + | 0.389216i | \(0.127254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.51715i | − | 0.0494051i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.1399 | − | 43.5436i | 0.816938 | − | 1.41498i | −0.0909907 | − | 0.995852i | \(-0.529003\pi\) |
0.907928 | − | 0.419126i | \(-0.137663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.8857 | −0.385827 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.70820 | + | 2.14093i | 0.120121 | + | 0.0693516i | 0.558856 | − | 0.829264i | \(-0.311240\pi\) |
−0.438736 | + | 0.898616i | \(0.644574\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.32975 | + | 4.23183i | 0.237185 | + | 0.136939i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.7929 | + | 30.8183i | 0.574564 | + | 0.995174i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8210 | 0.994227 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.92597 | + | 1.68931i | −0.0941902 | + | 0.0543807i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.59550 | + | 3.80791i | 0.212097 | + | 0.122454i | 0.602286 | − | 0.798281i | \(-0.294257\pi\) |
−0.390189 | + | 0.920735i | \(0.627590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.8677 | + | 39.6080i | −0.733858 | + | 1.27108i | 0.221364 | + | 0.975191i | \(0.428949\pi\) |
−0.955222 | + | 0.295888i | \(0.904384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.78017 | − | 15.2077i | −0.281479 | − | 0.487537i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.3130i | 0.841827i | 0.907101 | + | 0.420913i | \(0.138290\pi\) | ||||
−0.907101 | + | 0.420913i | \(0.861710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.97766 | + | 2.87386i | −0.159087 | + | 0.0918488i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.15030 | + | 10.6526i | −0.196164 | + | 0.339766i | −0.947281 | − | 0.320403i | \(-0.896182\pi\) |
0.751117 | + | 0.660169i | \(0.229515\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.32684 | + | 4.03020i | −0.0741392 | + | 0.128413i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.908591i | − | 0.0288915i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.9492 | + | 8.63095i | 0.474879 | + | 0.274171i | 0.718280 | − | 0.695754i | \(-0.244930\pi\) |
−0.243401 | + | 0.969926i | \(0.578263\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.86130 | 0.0590072 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.95927 | − | 6.85765i | −0.125391 | − | 0.217184i | 0.796495 | − | 0.604646i | \(-0.206685\pi\) |
−0.921886 | + | 0.387462i | \(0.873352\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.cg.a.1151.6 | ✓ | 24 | |
3.2 | odd | 2 | inner | 2736.2.cg.a.1151.7 | yes | 24 | |
4.3 | odd | 2 | 2736.2.cg.b.1151.6 | yes | 24 | ||
12.11 | even | 2 | 2736.2.cg.b.1151.7 | yes | 24 | ||
19.7 | even | 3 | 2736.2.cg.b.2591.7 | yes | 24 | ||
57.26 | odd | 6 | 2736.2.cg.b.2591.6 | yes | 24 | ||
76.7 | odd | 6 | inner | 2736.2.cg.a.2591.7 | yes | 24 | |
228.83 | even | 6 | inner | 2736.2.cg.a.2591.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.a.1151.6 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2736.2.cg.a.1151.7 | yes | 24 | 3.2 | odd | 2 | inner | |
2736.2.cg.a.2591.6 | yes | 24 | 228.83 | even | 6 | inner | |
2736.2.cg.a.2591.7 | yes | 24 | 76.7 | odd | 6 | inner | |
2736.2.cg.b.1151.6 | yes | 24 | 4.3 | odd | 2 | ||
2736.2.cg.b.1151.7 | yes | 24 | 12.11 | even | 2 | ||
2736.2.cg.b.2591.6 | yes | 24 | 57.26 | odd | 6 | ||
2736.2.cg.b.2591.7 | yes | 24 | 19.7 | even | 3 |