Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(865,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.i (of order \(3\), 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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 756) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2053.3 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.2053 |
Dual form | 2268.2.i.k.865.3 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.14400 | + | 3.71351i | 0.958824 | + | 1.66073i | 0.725364 | + | 0.688366i | \(0.241672\pi\) |
0.233461 | + | 0.972366i | \(0.424995\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23855 | − | 2.33795i | 0.468128 | − | 0.883661i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.90545 | − | 3.30033i | 0.574514 | − | 0.995087i | −0.421581 | − | 0.906791i | \(-0.638525\pi\) |
0.996094 | − | 0.0882959i | \(-0.0281421\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.64400 | + | 2.84748i | −0.455962 | + | 0.789750i | −0.998743 | − | 0.0501244i | \(-0.984038\pi\) |
0.542781 | + | 0.839875i | \(0.317372\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.405446 | + | 0.702253i | 0.0983351 | + | 0.170321i | 0.910996 | − | 0.412416i | \(-0.135315\pi\) |
−0.812661 | + | 0.582737i | \(0.801982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.54944 | + | 6.14781i | −0.814298 | + | 1.41041i | 0.0955331 | + | 0.995426i | \(0.469544\pi\) |
−0.909831 | + | 0.414979i | \(0.863789\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.23855 | + | 5.60933i | 0.675284 | + | 1.16963i | 0.976386 | + | 0.216035i | \(0.0693124\pi\) |
−0.301101 | + | 0.953592i | \(0.597354\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.69344 | + | 11.5934i | −1.33869 | + | 2.31868i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.90545 | − | 3.30033i | −0.353832 | − | 0.612856i | 0.633085 | − | 0.774082i | \(-0.281788\pi\) |
−0.986917 | + | 0.161227i | \(0.948455\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28799 | 0.590541 | 0.295270 | − | 0.955414i | \(-0.404590\pi\) | ||||
0.295270 | + | 0.955414i | \(0.404590\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.3374 | − | 0.413181i | 1.91638 | − | 0.0698403i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.88255 | − | 4.99272i | 0.473888 | − | 0.820797i | −0.525665 | − | 0.850691i | \(-0.676184\pi\) |
0.999553 | + | 0.0298939i | \(0.00951695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.04944 | + | 1.81769i | −0.163895 | + | 0.283875i | −0.936262 | − | 0.351301i | \(-0.885739\pi\) |
0.772367 | + | 0.635176i | \(0.219073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.38255 | + | 7.59079i | 0.668332 | + | 1.15758i | 0.978370 | + | 0.206861i | \(0.0663248\pi\) |
−0.310038 | + | 0.950724i | \(0.600342\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.33379 | 0.486284 | 0.243142 | − | 0.969991i | \(-0.421822\pi\) | ||||
0.243142 | + | 0.969991i | \(0.421822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.93199 | − | 5.79133i | −0.561713 | − | 0.827332i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.93199 | − | 8.54245i | −0.677461 | − | 1.17340i | −0.975743 | − | 0.218919i | \(-0.929747\pi\) |
0.298282 | − | 0.954478i | \(-0.403586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3411 | 2.20343 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.47710 | 0.452680 | 0.226340 | − | 0.974048i | \(-0.427324\pi\) | ||||
0.226340 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.95420 | 0.762357 | 0.381179 | − | 0.924501i | \(-0.375518\pi\) | ||||
0.381179 | + | 0.924501i | \(0.375518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.0989 | −1.74875 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.52290 | −0.430391 | −0.215195 | − | 0.976571i | \(-0.569039\pi\) | ||||
−0.215195 | + | 0.976571i | \(0.569039\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.05308 | 0.718369 | 0.359184 | − | 0.933267i | \(-0.383055\pi\) | ||||
0.359184 | + | 0.933267i | \(0.383055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.19344 | + | 8.99530i | 0.607846 | + | 1.05282i | 0.991595 | + | 0.129383i | \(0.0412995\pi\) |
−0.383749 | + | 0.923438i | \(0.625367\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.35600 | − | 8.54245i | −0.610373 | − | 0.973503i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.14468 | −0.578822 | −0.289411 | − | 0.957205i | \(-0.593459\pi\) | ||||
−0.289411 | + | 0.957205i | \(0.593459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.856004 | + | 1.48264i | 0.0939586 | + | 0.162741i | 0.909174 | − | 0.416417i | \(-0.136715\pi\) |
−0.815215 | + | 0.579159i | \(0.803381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.73855 | + | 3.01126i | −0.188572 | + | 0.326617i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.26509 | + | 10.8515i | −0.664098 | + | 1.15025i | 0.315430 | + | 0.948949i | \(0.397851\pi\) |
−0.979529 | + | 0.201304i | \(0.935482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.62110 | + | 7.37033i | 0.484422 | + | 0.772620i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −30.4400 | −3.12307 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.522900 | − | 0.905690i | −0.0530925 | − | 0.0919589i | 0.838258 | − | 0.545274i | \(-0.183574\pi\) |
−0.891350 | + | 0.453315i | \(0.850241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.95489 | + | 15.5103i | −0.891045 | + | 1.54333i | −0.0524199 | + | 0.998625i | \(0.516693\pi\) |
−0.838625 | + | 0.544710i | \(0.816640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.50000 | + | 6.06218i | 0.344865 | + | 0.597324i | 0.985329 | − | 0.170664i | \(-0.0545913\pi\) |
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.45056 | − | 5.97654i | 0.333578 | − | 0.577774i | −0.649633 | − | 0.760248i | \(-0.725077\pi\) |
0.983211 | + | 0.182474i | \(0.0584106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.81089 | + | 4.86861i | 0.269235 | + | 0.466328i | 0.968664 | − | 0.248373i | \(-0.0798959\pi\) |
−0.699430 | + | 0.714701i | \(0.746563\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0760 | − | 17.4521i | 0.947869 | − | 1.64176i | 0.197966 | − | 0.980209i | \(-0.436566\pi\) |
0.749903 | − | 0.661548i | \(-0.230100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.8869 | + | 24.0528i | −1.29496 | + | 2.24293i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.14400 | − | 0.0781356i | 0.196540 | − | 0.00716268i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.76145 | − | 3.05092i | −0.160132 | − | 0.277356i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −35.9629 | −3.21662 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.14468 | −0.190310 | −0.0951550 | − | 0.995462i | \(-0.530335\pi\) | ||||
−0.0951550 | + | 0.995462i | \(0.530335\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.69344 | + | 2.93312i | 0.147956 | + | 0.256268i | 0.930472 | − | 0.366363i | \(-0.119397\pi\) |
−0.782516 | + | 0.622631i | \(0.786064\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.97710 | + | 15.9128i | 0.865124 | + | 1.37981i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.47710 | − | 11.2187i | 0.553376 | − | 0.958475i | −0.444652 | − | 0.895703i | \(-0.646673\pi\) |
0.998028 | − | 0.0627719i | \(-0.0199941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.64400 | − | 14.9718i | 0.733174 | − | 1.26989i | −0.222346 | − | 0.974968i | \(-0.571371\pi\) |
0.955520 | − | 0.294927i | \(-0.0952953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.26509 | + | 10.8515i | 0.523913 | + | 0.907444i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.17054 | − | 14.1518i | 0.678526 | − | 1.17524i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.784350 | + | 1.35853i | 0.0642565 | + | 0.111295i | 0.896364 | − | 0.443319i | \(-0.146199\pi\) |
−0.832107 | + | 0.554614i | \(0.812866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.693438 | − | 1.20107i | 0.0564312 | − | 0.0977417i | −0.836430 | − | 0.548074i | \(-0.815361\pi\) |
0.892861 | + | 0.450332i | \(0.148695\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.04944 | + | 12.2100i | 0.566225 | + | 0.980730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8640 | −1.34589 | −0.672946 | − | 0.739692i | \(-0.734971\pi\) | ||||
−0.672946 | + | 0.739692i | \(0.734971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.1254 | − | 0.624118i | 1.34967 | − | 0.0491874i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.64833 | + | 14.9793i | −0.677389 | + | 1.17327i | 0.298375 | + | 0.954449i | \(0.403555\pi\) |
−0.975764 | + | 0.218824i | \(0.929778\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.97779 | − | 12.0859i | 0.539957 | − | 0.935234i | −0.458948 | − | 0.888463i | \(-0.651774\pi\) |
0.998906 | − | 0.0467708i | \(-0.0148930\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.09455 | + | 1.89582i | 0.0841964 | + | 0.145833i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.14331 | 0.695153 | 0.347576 | − | 0.937652i | \(-0.387005\pi\) | ||||
0.347576 | + | 0.937652i | \(0.387005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.8145 | + | 30.0079i | 1.42225 | + | 2.26838i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.53087 | − | 14.7759i | −0.637627 | − | 1.10440i | −0.985952 | − | 0.167029i | \(-0.946583\pi\) |
0.348325 | − | 0.937374i | \(-0.386751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4400 | −1.22197 | −0.610986 | − | 0.791641i | \(-0.709227\pi\) | ||||
−0.610986 | + | 0.791641i | \(0.709227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.7207 | 1.81750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.09022 | 0.225980 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.96286 | 0.214385 | 0.107193 | − | 0.994238i | \(-0.465814\pi\) | ||||
0.107193 | + | 0.994238i | \(0.465814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.4313 | −1.25473 | −0.627366 | − | 0.778724i | \(-0.715867\pi\) | ||||
−0.627366 | + | 0.778724i | \(0.715867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2880 | 0.732989 | 0.366495 | − | 0.930420i | \(-0.380558\pi\) | ||||
0.366495 | + | 0.930420i | \(0.380558\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | + | 6.06218i | 0.248108 | + | 0.429736i | 0.963001 | − | 0.269498i | \(-0.0868577\pi\) |
−0.714893 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0760 | + | 0.367208i | −0.707195 | + | 0.0257730i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.5265 | + | 23.4287i | 0.935650 | + | 1.62059i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.21634 | + | 14.2311i | −0.565636 | + | 0.979710i | 0.431354 | + | 0.902183i | \(0.358036\pi\) |
−0.996990 | + | 0.0775277i | \(0.975297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.7923 | + | 32.5493i | −1.28163 | + | 2.21984i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.07234 | − | 7.68715i | 0.276449 | − | 0.521838i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.66621 | −0.179349 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.06801 | − | 3.58190i | −0.138484 | − | 0.239862i | 0.788439 | − | 0.615113i | \(-0.210890\pi\) |
−0.926923 | + | 0.375251i | \(0.877556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.6483 | − | 18.4434i | 0.706754 | − | 1.22413i | −0.259300 | − | 0.965797i | \(-0.583492\pi\) |
0.966055 | − | 0.258338i | \(-0.0831747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.92766 | + | 5.07085i | 0.193465 | + | 0.335091i | 0.946396 | − | 0.323008i | \(-0.104694\pi\) |
−0.752931 | + | 0.658099i | \(0.771361\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.02290 | − | 6.96787i | 0.263549 | − | 0.456480i | −0.703633 | − | 0.710563i | \(-0.748440\pi\) |
0.967182 | + | 0.254083i | \(0.0817736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.14764 | + | 12.3801i | 0.466260 | + | 0.807587i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.04944 | − | 12.2100i | 0.455991 | − | 0.789799i | −0.542754 | − | 0.839892i | \(-0.682618\pi\) |
0.998745 | + | 0.0500930i | \(0.0159518\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3640 | − | 23.1471i | 0.860849 | − | 1.49103i | −0.0102608 | − | 0.999947i | \(-0.503266\pi\) |
0.871110 | − | 0.491088i | \(-0.163400\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.0760 | − | 27.0181i | 0.835394 | − | 1.72612i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.6705 | − | 20.2140i | −0.742579 | − | 1.28618i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.43268 | 0.153549 | 0.0767746 | − | 0.997048i | \(-0.475538\pi\) | ||||
0.0767746 | + | 0.997048i | \(0.475538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6835 | 1.55184 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.26509 | + | 10.8515i | 0.390806 | + | 0.676895i | 0.992556 | − | 0.121789i | \(-0.0388631\pi\) |
−0.601750 | + | 0.798684i | \(0.705530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.10253 | − | 12.9230i | −0.503466 | − | 0.802994i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.45056 | − | 5.97654i | 0.212771 | − | 0.368529i | −0.739810 | − | 0.672816i | \(-0.765085\pi\) |
0.952581 | + | 0.304286i | \(0.0984180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.1483 | − | 36.6300i | 1.29913 | − | 2.25016i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.9054 | − | 18.8888i | −0.664917 | − | 1.15167i | −0.979308 | − | 0.202376i | \(-0.935134\pi\) |
0.314391 | − | 0.949294i | \(-0.398200\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.76145 | + | 6.51502i | −0.228492 | + | 0.395759i | −0.957361 | − | 0.288893i | \(-0.906713\pi\) |
0.728870 | + | 0.684653i | \(0.240046\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.5080 | + | 44.1811i | 1.53819 | + | 2.66422i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.61745 | + | 7.99766i | −0.277436 | + | 0.480533i | −0.970747 | − | 0.240106i | \(-0.922818\pi\) |
0.693311 | + | 0.720639i | \(0.256151\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.83743 | + | 11.8428i | 0.407887 | + | 0.706481i | 0.994653 | − | 0.103276i | \(-0.0329323\pi\) |
−0.586766 | + | 0.809757i | \(0.699599\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.14331 | 0.127406 | 0.0637032 | − | 0.997969i | \(-0.479709\pi\) | ||||
0.0637032 | + | 0.997969i | \(0.479709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.94987 | + | 4.70484i | 0.174125 | + | 0.277718i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17123 | − | 14.1530i | 0.480660 | − | 0.832528i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.64833 | + | 8.05114i | −0.271558 | + | 0.470353i | −0.969261 | − | 0.246035i | \(-0.920872\pi\) |
0.697703 | + | 0.716387i | \(0.254206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.45489 | + | 12.9122i | 0.434040 | + | 0.751780i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.2967 | −1.23162 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.1749 | − | 0.844583i | 1.33578 | − | 0.0486810i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.7658 | + | 22.1110i | 0.730966 | + | 1.26607i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3869 | −0.592810 | −0.296405 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296405 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.57598 | 0.146071 | 0.0730353 | − | 0.997329i | \(-0.476731\pi\) | ||||
0.0730353 | + | 0.997329i | \(0.476731\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.4844 | −0.649136 | −0.324568 | − | 0.945862i | \(-0.605219\pi\) | ||||
−0.324568 | + | 0.945862i | \(0.605219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1964 | −0.853514 | −0.426757 | − | 0.904366i | \(-0.640344\pi\) | ||||
−0.426757 | + | 0.904366i | \(0.640344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.5229 | −0.813126 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.75643 | −0.320296 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.0080 | − | 38.1189i | −1.22078 | − | 2.11446i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.12907 | − | 7.79423i | 0.227643 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5316 | 0.853692 | 0.426846 | − | 0.904324i | \(-0.359625\pi\) | ||||
0.426846 | + | 0.904324i | \(0.359625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.55308 | − | 13.0823i | −0.412669 | − | 0.714764i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.50433 | − | 2.60558i | 0.0819461 | − | 0.141935i | −0.822140 | − | 0.569286i | \(-0.807220\pi\) |
0.904086 | + | 0.427351i | \(0.140553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.26509 | − | 10.8515i | 0.339274 | − | 0.587639i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4098 | + | 2.01993i | −0.994035 | + | 0.109066i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.8654 | −1.22748 | −0.613738 | − | 0.789510i | \(-0.710335\pi\) | ||||
−0.613738 | + | 0.789510i | \(0.710335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.52221 | − | 7.83270i | −0.242068 | − | 0.419275i | 0.719235 | − | 0.694767i | \(-0.244493\pi\) |
−0.961303 | + | 0.275492i | \(0.911159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.09820 | + | 15.7585i | −0.484248 | + | 0.838742i | −0.999836 | − | 0.0180942i | \(-0.994240\pi\) |
0.515588 | + | 0.856837i | \(0.327573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.9778 | + | 22.4782i | 0.688789 | + | 1.19302i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1934 | − | 21.1197i | 0.643545 | − | 1.11465i | −0.341090 | − | 0.940030i | \(-0.610796\pi\) |
0.984636 | − | 0.174622i | \(-0.0558704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6971 | − | 27.1881i | −0.826162 | − | 1.43095i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.2694 | + | 38.5718i | −1.16563 | + | 2.01894i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.43268 | − | 7.67762i | 0.231384 | − | 0.400769i | −0.726832 | − | 0.686816i | \(-0.759008\pi\) |
0.958216 | + | 0.286047i | \(0.0923413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.0803 | + | 0.950469i | −1.35402 | + | 0.0493459i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.57598 | + | 2.72968i | 0.0816014 | + | 0.141338i | 0.903938 | − | 0.427664i | \(-0.140663\pi\) |
−0.822337 | + | 0.569001i | \(0.807330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.5302 | 0.645337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.28799 | −0.117526 | −0.0587631 | − | 0.998272i | \(-0.518716\pi\) | ||||
−0.0587631 | + | 0.998272i | \(0.518716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.1254 | − | 24.4660i | −0.721776 | − | 1.25015i | −0.960287 | − | 0.279012i | \(-0.909993\pi\) |
0.238512 | − | 0.971140i | \(-0.423340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.2392 | − | 38.2046i | 1.03149 | − | 1.94708i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.360335 | − | 0.624118i | 0.0182697 | − | 0.0316440i | −0.856746 | − | 0.515739i | \(-0.827518\pi\) |
0.875016 | + | 0.484095i | \(0.160851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.62612 | + | 4.54856i | −0.132808 | + | 0.230031i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.0302 | − | 19.1048i | −0.554989 | − | 0.961269i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5753 | + | 18.3169i | −0.530759 | + | 0.919301i | 0.468597 | + | 0.883412i | \(0.344760\pi\) |
−0.999356 | + | 0.0358892i | \(0.988574\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.2472 | − | 24.6769i | −0.711472 | − | 1.23231i | −0.964305 | − | 0.264795i | \(-0.914696\pi\) |
0.252833 | − | 0.967510i | \(-0.418638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.40545 | + | 9.36251i | −0.269264 | + | 0.466380i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9851 | − | 19.0267i | −0.544510 | − | 0.943119i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7637 | −0.532231 | −0.266116 | − | 0.963941i | \(-0.585740\pi\) | ||||
−0.266116 | + | 0.963941i | \(0.585740\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.30656 | − | 8.12927i | 0.211912 | − | 0.400015i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.67054 | + | 6.35756i | −0.180180 | + | 0.312080i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.0302 | − | 29.4971i | 0.831979 | − | 1.44103i | −0.0644877 | − | 0.997919i | \(-0.520541\pi\) |
0.896467 | − | 0.443111i | \(-0.146125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2916 | − | 17.8256i | −0.501584 | − | 0.868768i | −0.999998 | − | 0.00182949i | \(-0.999418\pi\) |
0.498415 | − | 0.866939i | \(-0.333916\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8553 | −0.526560 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.37457 | − | 13.9206i | 0.356881 | − | 0.673665i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.9814 | + | 20.7524i | 0.577125 | + | 0.999610i | 0.995807 | + | 0.0914772i | \(0.0291589\pi\) |
−0.418682 | + | 0.908133i | \(0.637508\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.9642 | 1.43999 | 0.719995 | − | 0.693980i | \(-0.244144\pi\) | ||||
0.719995 | + | 0.693980i | \(0.244144\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45.9802 | −2.19953 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.8196 | 1.37548 | 0.687741 | − | 0.725956i | \(-0.258602\pi\) | ||||
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.0087 | −1.52078 | −0.760389 | − | 0.649468i | \(-0.774992\pi\) | ||||
−0.760389 | + | 0.649468i | \(0.774992\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −53.7293 | −2.54701 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.0087 | 1.51058 | 0.755291 | − | 0.655390i | \(-0.227496\pi\) | ||||
0.755291 | + | 0.655390i | \(0.227496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.99931 | + | 6.92701i | 0.188320 | + | 0.326180i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.4622 | + | 32.9624i | −0.818639 | + | 1.54530i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.8553 | −0.975570 | −0.487785 | − | 0.872964i | \(-0.662195\pi\) | ||||
−0.487785 | + | 0.872964i | \(0.662195\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.6254 | + | 21.8679i | 0.588025 | + | 1.01849i | 0.994491 | + | 0.104823i | \(0.0334276\pi\) |
−0.406466 | + | 0.913666i | \(0.633239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5760 | − | 18.3181i | 0.491508 | − | 0.851316i | −0.508445 | − | 0.861095i | \(-0.669779\pi\) |
0.999952 | + | 0.00977849i | \(0.00311264\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.95853 | − | 13.7846i | 0.368277 | − | 0.637874i | −0.621019 | − | 0.783795i | \(-0.713281\pi\) |
0.989296 | + | 0.145921i | \(0.0466145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.36329 | + | 8.23635i | −0.201478 | + | 0.380319i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.4028 | 1.53586 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −47.5159 | − | 82.3000i | −2.18018 | − | 3.77618i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.977789 | + | 1.69358i | −0.0446763 | + | 0.0773816i | −0.887499 | − | 0.460810i | \(-0.847559\pi\) |
0.842823 | + | 0.538192i | \(0.180892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.47779 | + | 16.4160i | 0.432150 | + | 0.748506i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.24219 | − | 3.88359i | 0.101813 | − | 0.176345i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.98143 | − | 17.2883i | −0.452302 | − | 0.783410i | 0.546227 | − | 0.837637i | \(-0.316064\pi\) |
−0.998529 | + | 0.0542276i | \(0.982730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0488 | − | 19.1370i | 0.498623 | − | 0.863641i | −0.501375 | − | 0.865230i | \(-0.667172\pi\) |
0.999999 | + | 0.00158899i | \(0.000505790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.54511 | − | 2.67621i | 0.0695883 | − | 0.120531i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.49705 | − | 14.1518i | 0.336289 | − | 0.634794i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5574 | + | 28.6783i | 0.741212 | + | 1.28382i | 0.951944 | + | 0.306272i | \(0.0990819\pi\) |
−0.210732 | + | 0.977544i | \(0.567585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.76509 | 0.212465 | 0.106232 | − | 0.994341i | \(-0.466121\pi\) | ||||
0.106232 | + | 0.994341i | \(0.466121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −76.7970 | −3.41742 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.38255 | − | 9.32284i | −0.238577 | − | 0.413228i | 0.721729 | − | 0.692176i | \(-0.243348\pi\) |
−0.960306 | + | 0.278948i | \(0.910014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.4629 | − | 1.00085i | 1.21489 | − | 0.0442752i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0080 | + | 25.9946i | −0.661330 | + | 1.14546i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.35236 | − | 11.0026i | 0.279377 | − | 0.483894i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.617454 | − | 1.06946i | −0.0270512 | − | 0.0468540i | 0.852183 | − | 0.523244i | \(-0.175278\pi\) |
−0.879234 | + | 0.476390i | \(0.841945\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.28435 | − | 7.42071i | 0.187342 | − | 0.324485i | −0.757022 | − | 0.653390i | \(-0.773346\pi\) |
0.944363 | + | 0.328905i | \(0.106680\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.33310 | + | 2.30900i | 0.0580709 | + | 0.100582i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.47641 | + | 16.4136i | −0.412018 | + | 0.713636i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.45056 | − | 5.97654i | −0.149460 | − | 0.258873i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.5919 | 1.27937 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.6055 | + | 1.94180i | −1.14598 | + | 0.0836390i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.50433 | − | 12.9979i | 0.322636 | − | 0.558823i | −0.658395 | − | 0.752673i | \(-0.728764\pi\) |
0.981031 | + | 0.193850i | \(0.0620976\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0531 | + | 20.8766i | −0.516297 | + | 0.894253i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.12543 | − | 10.6095i | −0.261904 | − | 0.453632i | 0.704844 | − | 0.709363i | \(-0.251017\pi\) |
−0.966748 | + | 0.255731i | \(0.917684\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.0531 | 1.15250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.37195 | + | 12.0280i | −0.270963 | + | 0.511483i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.8905 | + | 22.3270i | 0.546189 | + | 0.946027i | 0.998531 | + | 0.0541823i | \(0.0172552\pi\) |
−0.452342 | + | 0.891844i | \(0.649411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.8196 | −1.21894 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.6835 | 1.04029 | 0.520143 | − | 0.854079i | \(-0.325879\pi\) | ||||
0.520143 | + | 0.854079i | \(0.325879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 86.4115 | 3.63536 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2335 | 0.512856 | 0.256428 | − | 0.966563i | \(-0.417454\pi\) | ||||
0.256428 | + | 0.966563i | \(0.417454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3126 | 1.47779 | 0.738893 | − | 0.673823i | \(-0.235349\pi\) | ||||
0.738893 | + | 0.673823i | \(0.235349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −86.7081 | −3.61598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.52221 | − | 7.83270i | −0.188262 | − | 0.326080i | 0.756409 | − | 0.654099i | \(-0.226952\pi\) |
−0.944671 | + | 0.328020i | \(0.893619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.52654 | − | 0.164965i | 0.187793 | − | 0.00684390i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.5906 | −1.55684 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.9098 | − | 31.0206i | −0.739216 | − | 1.28036i | −0.952849 | − | 0.303445i | \(-0.901863\pi\) |
0.213633 | − | 0.976914i | \(-0.431470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.6705 | + | 20.2140i | −0.480876 | + | 0.832902i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.0309 | − | 38.1586i | 0.904700 | − | 1.56699i | 0.0833794 | − | 0.996518i | \(-0.473429\pi\) |
0.821320 | − | 0.570468i | \(-0.193238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.88688 | + | 7.79423i | 0.200342 | + | 0.319532i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0631 | 1.22835 | 0.614173 | − | 0.789171i | \(-0.289490\pi\) | ||||
0.614173 | + | 0.789171i | \(0.289490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5982 | − | 25.2848i | −0.595473 | − | 1.03139i | −0.993480 | − | 0.114007i | \(-0.963631\pi\) |
0.398007 | − | 0.917382i | \(-0.369702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.55308 | − | 13.0823i | 0.307077 | − | 0.531872i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.07165 | + | 13.9805i | 0.327618 | + | 0.567452i | 0.982039 | − | 0.188679i | \(-0.0604207\pi\) |
−0.654420 | + | 0.756131i | \(0.727087\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.48074 | + | 9.49292i | −0.221727 | + | 0.384043i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5581 | − | 40.8038i | −0.951503 | − | 1.64805i | −0.742175 | − | 0.670206i | \(-0.766206\pi\) |
−0.209327 | − | 0.977846i | \(-0.567127\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.0073 | + | 32.9216i | −0.765204 | + | 1.32537i | 0.174934 | + | 0.984580i | \(0.444029\pi\) |
−0.940138 | + | 0.340793i | \(0.889305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.09091 | + | 10.5498i | −0.244814 | + | 0.424031i | −0.962079 | − | 0.272769i | \(-0.912060\pi\) |
0.717265 | + | 0.696800i | \(0.245394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.6105 | + | 28.0875i | 0.705550 | + | 1.12530i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −43.6370 | − | 75.5816i | −1.74548 | − | 3.02326i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.67487 | 0.186399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.8640 | −0.432488 | −0.216244 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216244 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.59820 | − | 7.96431i | −0.182474 | − | 0.316054i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.9549 | − | 1.67536i | 0.909506 | − | 0.0663801i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.2200 | − | 26.3618i | 0.601153 | − | 1.04123i | −0.391494 | − | 0.920181i | \(-0.628042\pi\) |
0.992647 | − | 0.121047i | \(-0.0386251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.9320 | − | 32.7912i | 0.746605 | − | 1.29316i | −0.202837 | − | 0.979213i | \(-0.565016\pi\) |
0.949441 | − | 0.313945i | \(-0.101651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0982 | + | 31.3470i | 0.711513 | + | 1.23238i | 0.964289 | + | 0.264853i | \(0.0853233\pi\) |
−0.252775 | + | 0.967525i | \(0.581343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.62543 | − | 11.4756i | 0.260071 | − | 0.450456i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0488 | − | 19.1370i | −0.432371 | − | 0.748889i | 0.564706 | − | 0.825292i | \(-0.308990\pi\) |
−0.997077 | + | 0.0764035i | \(0.975656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.26145 | + | 12.5772i | −0.283728 | + | 0.491432i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0338 | + | 38.1637i | 0.858316 | + | 1.48665i | 0.873534 | + | 0.486763i | \(0.161822\pi\) |
−0.0152182 | + | 0.999884i | \(0.504844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.90702 | 0.229757 | 0.114878 | − | 0.993380i | \(-0.463352\pi\) | ||||
0.114878 | + | 0.993380i | \(0.463352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −37.7014 | + | 71.1670i | −1.46200 | + | 2.75974i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.3418 | − | 21.3766i | 0.477875 | − | 0.827704i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.3454 | − | 19.6508i | 0.437985 | − | 0.758612i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.09888 | + | 1.90332i | 0.0423589 | + | 0.0733677i | 0.886428 | − | 0.462867i | \(-0.153179\pi\) |
−0.844069 | + | 0.536235i | \(0.819846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0631 | 1.15542 | 0.577710 | − | 0.816242i | \(-0.303947\pi\) | ||||
0.577710 | + | 0.816242i | \(0.303947\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.76509 | + | 0.100771i | −0.106114 | + | 0.00386723i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.14764 | + | 7.18392i | 0.158705 | + | 0.274885i | 0.934402 | − | 0.356221i | \(-0.115935\pi\) |
−0.775697 | + | 0.631106i | \(0.782601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.5475 | 2.12236 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.4327 | 1.23559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.19639 | −0.0455129 | −0.0227564 | − | 0.999741i | \(-0.507244\pi\) | ||||
−0.0227564 | + | 0.999741i | \(0.507244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 74.1308 | 2.81194 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.70197 | −0.0644667 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.8813 | −1.20414 | −0.602070 | − | 0.798443i | \(-0.705657\pi\) | ||||
−0.602070 | + | 0.798443i | \(0.705657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.4629 | + | 35.4427i | 0.771771 | + | 1.33675i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.1712 | + | 40.1464i | 0.946661 | + | 1.50986i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.4327 | −0.804921 | −0.402461 | − | 0.915437i | \(-0.631845\pi\) | ||||
−0.402461 | + | 0.915437i | \(0.631845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.6483 | + | 18.4434i | 0.398783 | + | 0.690712i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.8647 | + | 46.5310i | −1.00468 | + | 1.74016i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.6304 | − | 37.4650i | 0.806680 | − | 1.39721i | −0.108472 | − | 0.994100i | \(-0.534596\pi\) |
0.915151 | − | 0.403110i | \(-0.132071\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.5080 | − | 0.674503i | 0.689273 | − | 0.0251198i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 51.0159 | 1.89468 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.09091 | − | 10.5498i | −0.225899 | − | 0.391269i | 0.730689 | − | 0.682710i | \(-0.239199\pi\) |
−0.956589 | + | 0.291441i | \(0.905865\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.55377 | + | 6.15532i | −0.131441 | + | 0.227663i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.72431 | − | 11.6468i | −0.248368 | − | 0.430186i | 0.714705 | − | 0.699426i | \(-0.246561\pi\) |
−0.963073 | + | 0.269240i | \(0.913228\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.71270 | + | 11.6267i | −0.247265 | + | 0.428276i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.93632 | + | 8.54995i | 0.181585 | + | 0.314515i | 0.942421 | − | 0.334430i | \(-0.108544\pi\) |
−0.760835 | + | 0.648945i | \(0.775210\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.2844 | − | 19.5451i | 0.413983 | − | 0.717039i | −0.581338 | − | 0.813662i | \(-0.697471\pi\) |
0.995321 | + | 0.0966229i | \(0.0308041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.36329 | + | 5.82539i | −0.123221 | + | 0.213426i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.69915 | − | 15.4695i | −0.354399 | − | 0.565242i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.287992 | + | 0.498817i | 0.0105090 | + | 0.0182021i | 0.871232 | − | 0.490871i | \(-0.163321\pi\) |
−0.860723 | + | 0.509073i | \(0.829988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.94692 | 0.216430 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.8196 | 0.829391 | 0.414695 | − | 0.909960i | \(-0.363888\pi\) | ||||
0.414695 | + | 0.909960i | \(0.363888\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.89052 | − | 17.1309i | −0.358531 | − | 0.620994i | 0.629185 | − | 0.777256i | \(-0.283389\pi\) |
−0.987716 | + | 0.156262i | \(0.950056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8640 | − | 0.541702i | 0.538112 | − | 0.0196109i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.71634 | + | 9.90099i | −0.206405 | + | 0.357504i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.3603 | − | 24.8728i | 0.517847 | − | 0.896937i | −0.481938 | − | 0.876205i | \(-0.660067\pi\) |
0.999785 | − | 0.0207319i | \(-0.00659965\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.10253 | − | 7.10578i | −0.147558 | − | 0.255577i | 0.782767 | − | 0.622315i | \(-0.213808\pi\) |
−0.930324 | + | 0.366738i | \(0.880475\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.0080 | + | 38.1189i | −0.790550 | + | 1.36927i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.44987 | − | 12.9036i | −0.266919 | − | 0.462318i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5338 | − | 19.9772i | 0.412713 | − | 0.714839i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.1563 | − | 62.6245i | −1.29047 | − | 2.23517i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.6364 | −1.87628 | −0.938142 | − | 0.346252i | \(-0.887454\pi\) | ||||
−0.938142 | + | 0.346252i | \(0.887454\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.3225 | − | 45.1724i | −1.00703 | − | 1.60615i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.78868 | + | 16.9545i | −0.347606 | + | 0.602072i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.76647 | − | 15.1840i | 0.310524 | − | 0.537844i | −0.667952 | − | 0.744205i | \(-0.732829\pi\) |
0.978476 | + | 0.206361i | \(0.0661621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.35167 | + | 2.34117i | 0.0478188 | + | 0.0828245i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.5833 | 1.39686 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39.0345 | + | 62.2573i | 1.37579 | + | 2.19428i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.57530 | + | 6.19259i | 0.125701 | + | 0.217720i | 0.922007 | − | 0.387174i | \(-0.126549\pi\) |
−0.796306 | + | 0.604894i | \(0.793215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.6835 | −1.11256 | −0.556280 | − | 0.830995i | \(-0.687772\pi\) | ||||
−0.556280 | + | 0.830995i | \(0.687772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −74.1679 | −2.59799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.2224 | −2.17689 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0690 | −0.525913 | −0.262956 | − | 0.964808i | \(-0.584698\pi\) | ||||
−0.262956 | + | 0.964808i | \(0.584698\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.9556 | −0.730465 | −0.365233 | − | 0.930916i | \(-0.619011\pi\) | ||||
−0.365233 | + | 0.930916i | \(0.619011\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.7897 | 1.27930 | 0.639652 | − | 0.768665i | \(-0.279079\pi\) | ||||
0.639652 | + | 0.768665i | \(0.279079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.1527 | − | 40.1016i | −0.804125 | − | 1.39279i | −0.916880 | − | 0.399163i | \(-0.869301\pi\) |
0.112755 | − | 0.993623i | \(-0.464032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.47277 | − | 5.10932i | 0.0856764 | − | 0.177028i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59.8414 | 2.07090 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.8189 | + | 22.2029i | 0.442556 | + | 0.766530i | 0.997878 | − | 0.0651053i | \(-0.0207383\pi\) |
−0.555322 | + | 0.831635i | \(0.687405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.23855 | − | 12.5375i | 0.249605 | − | 0.432329i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.69344 | + | 8.12927i | −0.161459 | + | 0.279656i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.31453 | + | 0.339458i | −0.320051 | + | 0.0116639i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.3411 | 1.28004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.71565 | + | 4.70364i | 0.0929821 | + | 0.161050i | 0.908765 | − | 0.417309i | \(-0.137027\pi\) |
−0.815783 | + | 0.578359i | \(0.803693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.61745 | + | 6.26561i | −0.123570 | + | 0.214029i | −0.921173 | − | 0.389153i | \(-0.872768\pi\) |
0.797603 | + | 0.603183i | \(0.206101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.71565 | + | 4.70364i | 0.0926568 | + | 0.160486i | 0.908628 | − | 0.417606i | \(-0.137131\pi\) |
−0.815971 | + | 0.578092i | \(0.803797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.35600 | + | 9.27687i | −0.182320 | + | 0.315788i | −0.942670 | − | 0.333725i | \(-0.891694\pi\) |
0.760350 | + | 0.649514i | \(0.225028\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.6032 | + | 33.9538i | 0.666529 | + | 1.15446i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.80292 | + | 16.9792i | −0.332541 | + | 0.575978i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.79163 | − | 10.0314i | 0.196242 | − | 0.339901i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −44.5418 | + | 84.0792i | −1.50579 | + | 2.84240i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.90840 | + | 11.9657i | 0.233280 | + | 0.404053i | 0.958771 | − | 0.284178i | \(-0.0917208\pi\) |
−0.725491 | + | 0.688231i | \(0.758387\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.6662 | 0.797335 | 0.398667 | − | 0.917096i | \(-0.369473\pi\) | ||||
0.398667 | + | 0.917096i | \(0.369473\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9615 | 0.638105 | 0.319052 | − | 0.947737i | \(-0.396635\pi\) | ||||
0.319052 | + | 0.947737i | \(0.396635\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.1978 | − | 17.6631i | −0.342408 | − | 0.593067i | 0.642472 | − | 0.766309i | \(-0.277909\pi\) |
−0.984879 | + | 0.173242i | \(0.944576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.65630 | + | 5.01416i | −0.0890894 | + | 0.168169i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.8331 | + | 20.4955i | −0.395980 | + | 0.685857i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.5803 | − | 63.3590i | 1.22275 | − | 2.11786i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.26509 | − | 10.8515i | −0.208953 | − | 0.361916i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.99931 | − | 6.92701i | 0.133236 | − | 0.230772i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.2472 | − | 61.0500i | −1.17166 | − | 2.02937i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.0073 | + | 34.6536i | −0.664331 | + | 1.15065i | 0.315135 | + | 0.949047i | \(0.397950\pi\) |
−0.979466 | + | 0.201608i | \(0.935383\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.41342 | − | 11.1084i | −0.212486 | − | 0.368037i | 0.740006 | − | 0.672600i | \(-0.234823\pi\) |
−0.952492 | + | 0.304564i | \(0.901489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.52428 | 0.215922 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.95489 | − | 0.326351i | 0.295716 | − | 0.0107771i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.9771 | − | 38.0655i | 0.724958 | − | 1.25566i | −0.234034 | − | 0.972228i | \(-0.575193\pi\) |
0.958991 | − | 0.283435i | \(-0.0914740\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.95125 | + | 17.2361i | −0.327549 | + | 0.567332i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.5883 | + | 66.8369i | 1.26878 | + | 2.19758i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.2349 | −1.32006 | −0.660032 | − | 0.751237i | \(-0.729457\pi\) | ||||
−0.660032 | + | 0.751237i | \(0.729457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.5604 | − | 3.61715i | 1.62428 | − | 0.118547i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.62543 | + | 11.4756i | 0.216675 | + | 0.375291i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.06175 | −0.100023 | −0.0500114 | − | 0.998749i | \(-0.515926\pi\) | ||||
−0.0500114 | + | 0.998749i | \(0.515926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.1891 | −0.658146 | −0.329073 | − | 0.944304i | \(-0.606736\pi\) | ||||
−0.329073 | + | 0.944304i | \(0.606736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.5947 | −0.442704 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.14468 | 0.0371973 | 0.0185986 | − | 0.999827i | \(-0.494080\pi\) | ||||
0.0185986 | + | 0.999827i | \(0.494080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.1520 | −1.10862 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.9701 | −1.39194 | −0.695970 | − | 0.718071i | \(-0.745025\pi\) | ||||
−0.695970 | + | 0.718071i | \(0.745025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.35236 | + | 11.0026i | 0.205558 | + | 0.356036i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.2064 | − | 29.0380i | −0.587916 | − | 0.937686i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1891 | −0.651262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37.3726 | − | 64.7313i | −1.20307 | − | 2.08377i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.99931 | + | 8.65906i | −0.160767 | + | 0.278457i | −0.935144 | − | 0.354268i | \(-0.884730\pi\) |
0.774377 | + | 0.632725i | \(0.218063\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.3145 | − | 28.2576i | 0.523558 | − | 0.906830i | −0.476066 | − | 0.879410i | \(-0.657938\pi\) |
0.999624 | − | 0.0274199i | \(-0.00872911\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.2973 | − | 38.7526i | −0.778937 | − | 1.24235i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.4958 | −1.32757 | −0.663784 | − | 0.747924i | \(-0.731051\pi\) | ||||
−0.663784 | + | 0.747924i | \(0.731051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.8756 | + | 41.3537i | 0.763067 | + | 1.32167i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.7163 | − | 30.6856i | 0.565063 | − | 0.978719i | −0.431980 | − | 0.901883i | \(-0.642185\pi\) |
0.997044 | − | 0.0768356i | \(-0.0244816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.0574 | + | 38.2046i | 0.702808 | + | 1.21730i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.3862 | + | 49.1663i | −0.902628 | + | 1.56340i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2960 | + | 42.0818i | 0.771787 | + | 1.33677i | 0.936583 | + | 0.350446i | \(0.113970\pi\) |
−0.164796 | + | 0.986328i | \(0.552697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.0080 | + | 25.9946i | −0.475785 | + | 0.824083i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.5130 | + | 40.7257i | −0.744664 | + | 1.28980i | 0.205688 | + | 0.978618i | \(0.434057\pi\) |
−0.950352 | + | 0.311178i | \(0.899276\pi\) | |||||||
\(998\) | 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 | 2268.2.i.k.2053.3 | 6 | ||
3.2 | odd | 2 | 2268.2.i.j.2053.1 | 6 | |||
7.4 | even | 3 | 2268.2.l.j.109.1 | 6 | |||
9.2 | odd | 6 | 2268.2.l.k.541.3 | 6 | |||
9.4 | even | 3 | 756.2.k.f.541.3 | yes | 6 | ||
9.5 | odd | 6 | 756.2.k.e.541.1 | yes | 6 | ||
9.7 | even | 3 | 2268.2.l.j.541.1 | 6 | |||
21.11 | odd | 6 | 2268.2.l.k.109.3 | 6 | |||
63.4 | even | 3 | 756.2.k.f.109.3 | yes | 6 | ||
63.5 | even | 6 | 5292.2.a.v.1.1 | 3 | |||
63.11 | odd | 6 | 2268.2.i.j.865.1 | 6 | |||
63.23 | odd | 6 | 5292.2.a.x.1.3 | 3 | |||
63.25 | even | 3 | inner | 2268.2.i.k.865.3 | 6 | ||
63.32 | odd | 6 | 756.2.k.e.109.1 | ✓ | 6 | ||
63.40 | odd | 6 | 5292.2.a.w.1.3 | 3 | |||
63.58 | even | 3 | 5292.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.k.e.109.1 | ✓ | 6 | 63.32 | odd | 6 | ||
756.2.k.e.541.1 | yes | 6 | 9.5 | odd | 6 | ||
756.2.k.f.109.3 | yes | 6 | 63.4 | even | 3 | ||
756.2.k.f.541.3 | yes | 6 | 9.4 | even | 3 | ||
2268.2.i.j.865.1 | 6 | 63.11 | odd | 6 | |||
2268.2.i.j.2053.1 | 6 | 3.2 | odd | 2 | |||
2268.2.i.k.865.3 | 6 | 63.25 | even | 3 | inner | ||
2268.2.i.k.2053.3 | 6 | 1.1 | even | 1 | trivial | ||
2268.2.l.j.109.1 | 6 | 7.4 | even | 3 | |||
2268.2.l.j.541.1 | 6 | 9.7 | even | 3 | |||
2268.2.l.k.109.3 | 6 | 21.11 | odd | 6 | |||
2268.2.l.k.541.3 | 6 | 9.2 | odd | 6 | |||
5292.2.a.u.1.1 | 3 | 63.58 | even | 3 | |||
5292.2.a.v.1.1 | 3 | 63.5 | even | 6 | |||
5292.2.a.w.1.3 | 3 | 63.40 | odd | 6 | |||
5292.2.a.x.1.3 | 3 | 63.23 | odd | 6 |