Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (of order \(3\), 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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1801.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.1801 |
Dual form | 2520.2.bi.h.361.1 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | − | 1.73205i | 0.208514 | − | 0.361158i | −0.742732 | − | 0.669588i | \(-0.766471\pi\) |
0.951247 | + | 0.308431i | \(0.0998038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 7.79423i | 0.808224 | + | 1.39988i | 0.914093 | + | 0.405505i | \(0.132904\pi\) |
−0.105869 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.50000 | − | 0.866025i | −0.422577 | − | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.50000 | − | 9.52628i | 0.904194 | − | 1.56611i | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) |
0.821995 | − | 0.569495i | \(-0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.00000 | 1.24939 | 0.624695 | − | 0.780869i | \(-0.285223\pi\) | ||||
0.624695 | + | 0.780869i | \(0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | − | 3.46410i | −0.274721 | − | 0.475831i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
−0.970065 | + | 0.242846i | \(0.921919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | − | 12.1244i | 0.896258 | − | 1.55236i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.50000 | + | 4.33013i | −0.310087 | + | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.500000 | + | 0.866025i | 0.0610847 | + | 0.105802i | 0.894951 | − | 0.446165i | \(-0.147211\pi\) |
−0.833866 | + | 0.551967i | \(0.813877\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000 | − | 6.92820i | 0.911685 | − | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | − | 15.5885i | 0.953998 | − | 1.65237i | 0.217354 | − | 0.976093i | \(-0.430258\pi\) |
0.736644 | − | 0.676280i | \(-0.236409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | + | 12.9904i | 0.262071 | + | 1.36176i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.50000 | − | 4.33013i | −0.256495 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.0000 | −1.82762 | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.50000 | − | 9.52628i | 0.541931 | − | 0.938652i | −0.456862 | − | 0.889538i | \(-0.651027\pi\) |
0.998793 | − | 0.0491146i | \(-0.0156400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.00000 | + | 8.66025i | −0.483368 | + | 0.837218i | −0.999818 | − | 0.0190994i | \(-0.993920\pi\) |
0.516449 | + | 0.856318i | \(0.327253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | − | 4.33013i | −0.239457 | − | 0.414751i | 0.721102 | − | 0.692829i | \(-0.243636\pi\) |
−0.960558 | + | 0.278078i | \(0.910303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | − | 1.73205i | −0.0932505 | − | 0.161515i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0000 | − | 10.3923i | 1.10004 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | + | 1.73205i | −0.0873704 | + | 0.151330i | −0.906399 | − | 0.422423i | \(-0.861180\pi\) |
0.819028 | + | 0.573753i | \(0.194513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.5000 | − | 4.33013i | −1.08389 | − | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | + | 1.73205i | 0.0854358 | + | 0.147979i | 0.905577 | − | 0.424182i | \(-0.139438\pi\) |
−0.820141 | + | 0.572161i | \(0.806105\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0000 | 1.61156 | 0.805779 | − | 0.592216i | \(-0.201747\pi\) | ||||
0.805779 | + | 0.592216i | \(0.201747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0000 | − | 17.3205i | −0.836242 | − | 1.44841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | − | 1.73205i | 0.0830455 | − | 0.143839i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.00000 | 0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 15.5885i | 0.718278 | + | 1.24409i | 0.961681 | + | 0.274169i | \(0.0884028\pi\) |
−0.243403 | + | 0.969925i | \(0.578264\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.00000 | − | 1.73205i | −0.394055 | − | 0.136505i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0000 | 1.54765 | 0.773823 | − | 0.633402i | \(-0.218342\pi\) | ||||
0.773823 | + | 0.633402i | \(0.218342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | − | 3.46410i | 0.152057 | − | 0.263371i | −0.779926 | − | 0.625871i | \(-0.784744\pi\) |
0.931984 | + | 0.362500i | \(0.118077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 1.73205i | −0.151186 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.00000 | + | 15.5885i | 0.672692 | + | 1.16514i | 0.977138 | + | 0.212607i | \(0.0681952\pi\) |
−0.304446 | + | 0.952529i | \(0.598471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.50000 | − | 9.52628i | −0.404368 | − | 0.700386i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | + | 20.7846i | −0.877527 | + | 1.51992i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00000 | − | 1.73205i | 0.0723575 | − | 0.125327i | −0.827577 | − | 0.561353i | \(-0.810281\pi\) |
0.899934 | + | 0.436026i | \(0.143614\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.50000 | + | 2.59808i | 0.107972 | + | 0.187014i | 0.914949 | − | 0.403570i | \(-0.132231\pi\) |
−0.806976 | + | 0.590584i | \(0.798898\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | + | 6.92820i | 0.283552 | + | 0.491127i | 0.972257 | − | 0.233915i | \(-0.0751537\pi\) |
−0.688705 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.00000 | − | 5.19615i | −0.0701862 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | − | 6.92820i | 0.279372 | − | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.0000 | 1.38343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.500000 | − | 0.866025i | 0.0340997 | − | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | − | 15.5885i | 1.22192 | − | 1.05821i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | − | 25.9808i | −1.00901 | − | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | − | 6.92820i | −0.265489 | − | 0.459841i | 0.702202 | − | 0.711977i | \(-0.252200\pi\) |
−0.967692 | + | 0.252136i | \(0.918867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | + | 0.866025i | −0.0330409 | + | 0.0572286i | −0.882073 | − | 0.471113i | \(-0.843853\pi\) |
0.849032 | + | 0.528341i | \(0.177186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | − | 5.19615i | −0.195698 | − | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.0000 | −1.94054 | −0.970269 | − | 0.242028i | \(-0.922188\pi\) | ||||
−0.970269 | + | 0.242028i | \(0.922188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | + | 19.0526i | 0.708572 | + | 1.22728i | 0.965387 | + | 0.260822i | \(0.0839937\pi\) |
−0.256814 | + | 0.966461i | \(0.582673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | + | 6.92820i | −0.0638877 | + | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.5000 | + | 21.6506i | −0.795356 | + | 1.37760i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000 | 0.378717 | 0.189358 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189358 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.00000 | + | 10.3923i | −0.374270 | + | 0.648254i | −0.990217 | − | 0.139533i | \(-0.955440\pi\) |
0.615948 | + | 0.787787i | \(0.288773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.5000 | − | 9.52628i | −1.70877 | − | 0.591934i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.00000 | + | 3.46410i | 0.123325 | + | 0.213606i | 0.921077 | − | 0.389380i | \(-0.127311\pi\) |
−0.797752 | + | 0.602986i | \(0.793977\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.00000 | + | 5.19615i | 0.182913 | + | 0.316815i | 0.942871 | − | 0.333157i | \(-0.108114\pi\) |
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.50000 | − | 16.4545i | −0.570800 | − | 0.988654i | −0.996484 | − | 0.0837823i | \(-0.973300\pi\) |
0.425684 | − | 0.904872i | \(-0.360033\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0000 | −1.19310 | −0.596550 | − | 0.802576i | \(-0.703462\pi\) | ||||
−0.596550 | + | 0.802576i | \(0.703462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.50000 | − | 4.33013i | −0.148610 | − | 0.257399i | 0.782104 | − | 0.623148i | \(-0.214146\pi\) |
−0.930714 | + | 0.365748i | \(0.880813\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | − | 20.7846i | −0.236113 | − | 1.22688i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.0000 | 1.16841 | 0.584206 | − | 0.811605i | \(-0.301406\pi\) | ||||
0.584206 | + | 0.811605i | \(0.301406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.00000 | + | 8.66025i | −0.289157 | + | 0.500835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.500000 | − | 2.59808i | −0.0288195 | − | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00000 | − | 12.1244i | −0.400819 | − | 0.694239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | + | 13.8564i | 0.453638 | + | 0.785725i | 0.998609 | − | 0.0527306i | \(-0.0167924\pi\) |
−0.544970 | + | 0.838455i | \(0.683459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5000 | − | 26.8468i | 0.876112 | − | 1.51747i | 0.0205381 | − | 0.999789i | \(-0.493462\pi\) |
0.855574 | − | 0.517681i | \(-0.173205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0000 | + | 19.0526i | −0.617822 | + | 1.07010i | 0.372061 | + | 0.928208i | \(0.378651\pi\) |
−0.989882 | + | 0.141890i | \(0.954682\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.50000 | + | 4.33013i | 0.138675 | + | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0000 | − | 5.19615i | −0.826977 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5000 | − | 26.8468i | 0.851957 | − | 1.47563i | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) |
0.879440 | − | 0.476011i | \(-0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00000 | 0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.0000 | + | 31.1769i | −0.974755 | + | 1.68832i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.0000 | −1.60586 | −0.802932 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802932 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0000 | − | 20.7846i | −0.638696 | − | 1.10625i | −0.985719 | − | 0.168397i | \(-0.946141\pi\) |
0.347024 | − | 0.937856i | \(-0.387192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0000 | + | 25.9808i | −0.791670 | + | 1.37121i | 0.133263 | + | 0.991081i | \(0.457455\pi\) |
−0.924932 | + | 0.380131i | \(0.875879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.0000 | −0.575766 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.50000 | + | 14.7224i | 0.443696 | + | 0.768505i | 0.997960 | − | 0.0638362i | \(-0.0203335\pi\) |
−0.554264 | + | 0.832341i | \(0.687000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.00000 | + | 6.92820i | −0.415339 | + | 0.359694i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.50000 | − | 16.4545i | 0.491891 | − | 0.851981i | −0.508065 | − | 0.861319i | \(-0.669639\pi\) |
0.999956 | + | 0.00933789i | \(0.00297238\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0000 | −0.515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0000 | −0.770498 | −0.385249 | − | 0.922813i | \(-0.625884\pi\) | ||||
−0.385249 | + | 0.922813i | \(0.625884\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.00000 | − | 3.46410i | 0.102195 | − | 0.177007i | −0.810394 | − | 0.585886i | \(-0.800747\pi\) |
0.912589 | + | 0.408879i | \(0.134080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.00000 | − | 10.3923i | −0.101929 | − | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0000 | − | 17.3205i | −0.507020 | − | 0.878185i | −0.999967 | − | 0.00812520i | \(-0.997414\pi\) |
0.492947 | − | 0.870059i | \(-0.335920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.500000 | + | 0.866025i | 0.0251577 | + | 0.0435745i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.50000 | − | 6.06218i | 0.175660 | − | 0.304252i | −0.764730 | − | 0.644351i | \(-0.777127\pi\) |
0.940389 | + | 0.340099i | \(0.110461\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | + | 10.3923i | −0.299626 | + | 0.518967i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) |
0.676425 | + | 0.736512i | \(0.263528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.5000 | − | 38.9711i | −1.12080 | − | 1.94129i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.0000 | 2.18100 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5000 | − | 18.1865i | −0.519192 | − | 0.899266i | −0.999751 | − | 0.0223042i | \(-0.992900\pi\) |
0.480560 | − | 0.876962i | \(-0.340434\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | − | 10.3923i | 0.590481 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000 | − | 3.46410i | 0.0981761 | − | 0.170046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | 0.243685 | 0.121843 | − | 0.992549i | \(-0.461120\pi\) | ||||
0.121843 | + | 0.992549i | \(0.461120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.0000 | − | 12.1244i | −1.69377 | − | 0.586739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | + | 25.9808i | 0.722525 | + | 1.25145i | 0.959985 | + | 0.280052i | \(0.0903517\pi\) |
−0.237460 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.00000 | − | 8.66025i | −0.239182 | − | 0.414276i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | − | 24.2487i | 0.668184 | − | 1.15733i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0000 | + | 34.6410i | −0.950229 | + | 1.64584i | −0.205301 | + | 0.978699i | \(0.565817\pi\) |
−0.744927 | + | 0.667146i | \(0.767516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000 | + | 27.7128i | 0.753411 | + | 1.30495i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.5000 | + | 4.33013i | 0.586009 | + | 0.202999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.50000 | + | 2.59808i | −0.0701670 | + | 0.121533i | −0.898974 | − | 0.438001i | \(-0.855687\pi\) |
0.828807 | + | 0.559534i | \(0.189020\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0000 | −0.604161 | −0.302081 | − | 0.953282i | \(-0.597681\pi\) | ||||
−0.302081 | + | 0.953282i | \(0.597681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.00000 | − | 12.1244i | 0.323921 | − | 0.561048i | −0.657372 | − | 0.753566i | \(-0.728332\pi\) |
0.981293 | + | 0.192518i | \(0.0616653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | − | 1.73205i | 0.0923514 | − | 0.0799787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000 | + | 3.46410i | 0.0919601 | + | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.00000 | −0.229416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | + | 10.3923i | 0.274147 | + | 0.474837i | 0.969920 | − | 0.243426i | \(-0.0782712\pi\) |
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.5000 | + | 47.6314i | −1.25389 | + | 2.17180i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.00000 | + | 15.5885i | −0.408669 | + | 0.707835i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.50000 | − | 2.59808i | −0.0679715 | − | 0.117730i | 0.830037 | − | 0.557709i | \(-0.188319\pi\) |
−0.898008 | + | 0.439979i | \(0.854986\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.0000 | 1.26362 | 0.631811 | − | 0.775122i | \(-0.282312\pi\) | ||||
0.631811 | + | 0.775122i | \(0.282312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | + | 10.3923i | 0.270226 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.00000 | + | 31.1769i | 0.269137 | + | 1.39848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.50000 | + | 12.9904i | −0.335746 | + | 0.581529i | −0.983628 | − | 0.180212i | \(-0.942322\pi\) |
0.647882 | + | 0.761741i | \(0.275655\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.0000 | −1.69434 | −0.847168 | − | 0.531325i | \(-0.821694\pi\) | ||||
−0.847168 | + | 0.531325i | \(0.821694\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.00000 | + | 5.19615i | −0.132973 | + | 0.230315i | −0.924821 | − | 0.380402i | \(-0.875786\pi\) |
0.791849 | + | 0.610718i | \(0.209119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0000 | + | 19.0526i | −0.973223 | + | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.50000 | − | 9.52628i | −0.242359 | − | 0.419778i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000 | 1.05552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.0000 | + | 34.6410i | 0.876216 | + | 1.51765i | 0.855462 | + | 0.517866i | \(0.173273\pi\) |
0.0207541 | + | 0.999785i | \(0.493393\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5000 | − | 18.1865i | 0.459133 | − | 0.795242i | −0.539782 | − | 0.841805i | \(-0.681493\pi\) |
0.998915 | + | 0.0465630i | \(0.0148268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.0000 | + | 46.7654i | −1.17614 | + | 2.03713i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.0000 | −1.73259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.00000 | + | 8.66025i | 0.216169 | + | 0.374415i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.0000 | − | 17.3205i | −0.947607 | − | 0.746047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5000 | + | 21.6506i | −0.537417 | + | 0.930834i | 0.461625 | + | 0.887075i | \(0.347267\pi\) |
−0.999042 | + | 0.0437584i | \(0.986067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.00000 | −0.214176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.00000 | − | 8.66025i | 0.213007 | − | 0.368939i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.50000 | + | 0.866025i | 0.106311 | + | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00000 | + | 1.73205i | 0.0423714 | + | 0.0733893i | 0.886433 | − | 0.462856i | \(-0.153175\pi\) |
−0.844062 | + | 0.536246i | \(0.819842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.0000 | + | 25.9808i | 0.632175 | + | 1.09496i | 0.987106 | + | 0.160066i | \(0.0511708\pi\) |
−0.354932 | + | 0.934892i | \(0.615496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.00000 | − | 1.73205i | 0.0420703 | − | 0.0728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0000 | + | 31.1769i | −0.754599 | + | 1.30700i | 0.190974 | + | 0.981595i | \(0.438835\pi\) |
−0.945573 | + | 0.325409i | \(0.894498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5000 | + | 28.5788i | 0.690504 | + | 1.19599i | 0.971673 | + | 0.236329i | \(0.0759443\pi\) |
−0.281170 | + | 0.959658i | \(0.590722\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.50000 | + | 12.9904i | 0.312229 | + | 0.540797i | 0.978845 | − | 0.204605i | \(-0.0655910\pi\) |
−0.666616 | + | 0.745402i | \(0.732258\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.00000 | − | 10.3923i | −0.0829740 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.00000 | − | 13.8564i | 0.331326 | − | 0.573874i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.0000 | −1.23823 | −0.619116 | − | 0.785299i | \(-0.712509\pi\) | ||||
−0.619116 | + | 0.785299i | \(0.712509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.0000 | 1.85419 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.00000 | − | 15.5885i | −0.122988 | − | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.00000 | + | 3.46410i | 0.0817178 | + | 0.141539i | 0.903988 | − | 0.427558i | \(-0.140626\pi\) |
−0.822270 | + | 0.569097i | \(0.807293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.00000 | 0.285536 | 0.142768 | − | 0.989756i | \(-0.454400\pi\) | ||||
0.142768 | + | 0.989756i | \(0.454400\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50000 | + | 4.33013i | 0.101639 | + | 0.176045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5000 | + | 19.9186i | −0.466771 | + | 0.808470i | −0.999279 | − | 0.0379540i | \(-0.987916\pi\) |
0.532509 | + | 0.846424i | \(0.321249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | + | 25.9808i | −0.606835 | + | 1.05107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0000 | − | 39.8372i | −0.928961 | − | 1.60901i | −0.785063 | − | 0.619416i | \(-0.787370\pi\) |
−0.143898 | − | 0.989593i | \(-0.545964\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0000 | −0.885687 | −0.442843 | − | 0.896599i | \(-0.646030\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.5000 | − | 18.1865i | −0.422031 | − | 0.730978i | 0.574107 | − | 0.818780i | \(-0.305349\pi\) |
−0.996138 | + | 0.0878015i | \(0.972016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.0000 | − | 15.5885i | −1.80289 | − | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 66.0000 | 2.63159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.50000 | + | 6.06218i | −0.138893 | + | 0.240570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.5000 | − | 12.9904i | 1.28770 | − | 0.514698i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0000 | − | 19.0526i | −0.434474 | − | 0.752531i | 0.562779 | − | 0.826608i | \(-0.309732\pi\) |
−0.997253 | + | 0.0740768i | \(0.976399\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00000 | 0.0394362 | 0.0197181 | − | 0.999806i | \(-0.493723\pi\) | ||||
0.0197181 | + | 0.999806i | \(0.493723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0000 | − | 31.1769i | −0.707653 | − | 1.22569i | −0.965726 | − | 0.259565i | \(-0.916421\pi\) |
0.258073 | − | 0.966126i | \(-0.416913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | + | 20.7846i | −0.471041 | + | 0.815867i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0000 | − | 31.1769i | 0.704394 | − | 1.22005i | −0.262515 | − | 0.964928i | \(-0.584552\pi\) |
0.966910 | − | 0.255119i | \(-0.0821147\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00000 | + | 1.73205i | 0.0390732 | + | 0.0676768i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.0000 | −1.55818 | −0.779089 | − | 0.626913i | \(-0.784318\pi\) | ||||
−0.779089 | + | 0.626913i | \(0.784318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.5000 | + | 28.5788i | 0.641776 | + | 1.11159i | 0.985036 | + | 0.172348i | \(0.0551353\pi\) |
−0.343261 | + | 0.939240i | \(0.611531\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0000 | + | 8.66025i | −0.387783 | + | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.00000 | − | 3.46410i | 0.0774403 | − | 0.134131i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.0000 | 2.16186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0000 | −0.886585 | −0.443292 | − | 0.896377i | \(-0.646190\pi\) | ||||
−0.443292 | + | 0.896377i | \(0.646190\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.00000 | − | 15.5885i | 0.345898 | − | 0.599113i | −0.639618 | − | 0.768693i | \(-0.720908\pi\) |
0.985517 | + | 0.169580i | \(0.0542410\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.00000 | + | 46.7654i | 0.345388 | + | 1.79469i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.0000 | − | 22.5167i | −0.497431 | − | 0.861576i | 0.502564 | − | 0.864540i | \(-0.332390\pi\) |
−0.999996 | + | 0.00296369i | \(0.999057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.0000 | + | 17.3205i | 0.380970 | + | 0.659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5000 | − | 23.3827i | 0.513564 | − | 0.889519i | −0.486312 | − | 0.873785i | \(-0.661658\pi\) |
0.999876 | − | 0.0157341i | \(-0.00500851\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.50000 | − | 16.4545i | 0.360356 | − | 0.624154i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | + | 41.5692i | 0.909065 | + | 1.57455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.5000 | − | 47.6314i | −1.03718 | − | 1.79645i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.0000 | + | 20.7846i | −0.902613 | + | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0000 | 0.674105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.0000 | −0.747958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0000 | − | 29.4449i | 0.633993 | − | 1.09811i | −0.352735 | − | 0.935723i | \(-0.614748\pi\) |
0.986728 | − | 0.162385i | \(-0.0519185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.5000 | − | 9.52628i | −1.02415 | − | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | − | 1.73205i | −0.0371391 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0000 | 0.704671 | 0.352335 | − | 0.935874i | \(-0.385388\pi\) | ||||
0.352335 | + | 0.935874i | \(0.385388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | + | 5.19615i | 0.110959 | + | 0.192187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.500000 | − | 0.866025i | 0.0184679 | − | 0.0319874i | −0.856644 | − | 0.515908i | \(-0.827454\pi\) |
0.875112 | + | 0.483921i | \(0.160788\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.00000 | + | 3.46410i | −0.0736709 | + | 0.127602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.500000 | + | 0.866025i | 0.0183928 | + | 0.0318573i | 0.875075 | − | 0.483987i | \(-0.160812\pi\) |
−0.856683 | + | 0.515844i | \(0.827478\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0000 | −1.32071 | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||||
−0.660356 | + | 0.750953i | \(0.729595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.0000 | + | 8.66025i | 0.913480 | + | 0.316439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.500000 | − | 0.866025i | 0.0182453 | − | 0.0316017i | −0.856759 | − | 0.515718i | \(-0.827525\pi\) |
0.875004 | + | 0.484116i | \(0.160859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | + | 8.66025i | −0.362024 | + | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.0000 | − | 25.9808i | −0.541619 | − | 0.938111i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.00000 | + | 3.46410i | 0.0719350 | + | 0.124595i | 0.899749 | − | 0.436407i | \(-0.143749\pi\) |
−0.827814 | + | 0.561002i | \(0.810416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.50000 | − | 7.79423i | 0.161645 | − | 0.279977i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0000 | − | 34.6410i | 0.716574 | − | 1.24114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0000 | − | 41.5692i | −0.858788 | − | 1.48746i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.0000 | 0.642448 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0000 | + | 17.3205i | 0.356462 | + | 0.617409i | 0.987367 | − | 0.158450i | \(-0.0506498\pi\) |
−0.630905 | + | 0.775860i | \(0.717316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.00000 | − | 5.19615i | −0.0355559 | − | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0000 | + | 60.6218i | −1.24289 | + | 2.15274i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.00000 | −0.0708436 | −0.0354218 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354218 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.0000 | − | 38.1051i | 0.776363 | − | 1.34470i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | + | 3.46410i | −0.140981 | + | 0.122094i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.0000 | − | 29.4449i | −0.597688 | − | 1.03523i | −0.993161 | − | 0.116749i | \(-0.962753\pi\) |
0.395473 | − | 0.918477i | \(-0.370581\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.50000 | − | 4.33013i | 0.0874639 | − | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.0000 | −1.18230 | −0.591148 | − | 0.806563i | \(-0.701325\pi\) | ||||
−0.591148 | + | 0.806563i | \(0.701325\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.50000 | − | 14.7224i | −0.295217 | − | 0.511331i | 0.679818 | − | 0.733381i | \(-0.262059\pi\) |
−0.975035 | + | 0.222049i | \(0.928725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.0000 | − | 25.9808i | −1.14338 | − | 0.900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0000 | − | 17.3205i | 0.346064 | − | 0.599401i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.0000 | −1.17381 | −0.586905 | − | 0.809656i | \(-0.699654\pi\) | ||||
−0.586905 | + | 0.809656i | \(0.699654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.5000 | + | 4.33013i | 0.429505 | + | 0.148785i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0000 | − | 19.0526i | −0.377075 | − | 0.653113i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.0000 | 1.26686 | 0.633428 | − | 0.773802i | \(-0.281647\pi\) | ||||
0.633428 | + | 0.773802i | \(0.281647\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0000 | + | 32.9090i | 0.649028 | + | 1.12415i | 0.983355 | + | 0.181692i | \(0.0581574\pi\) |
−0.334328 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.00000 | + | 1.73205i | −0.0340404 | + | 0.0589597i | −0.882544 | − | 0.470230i | \(-0.844171\pi\) |
0.848503 | + | 0.529190i | \(0.177504\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00000 | − | 3.46410i | −0.0680020 | − | 0.117783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.00000 | −0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.50000 | − | 4.33013i | −0.0847093 | − | 0.146721i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.500000 | + | 2.59808i | 0.0169031 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.0000 | + | 43.3013i | −0.844190 | + | 1.46218i | 0.0421327 | + | 0.999112i | \(0.486585\pi\) |
−0.886323 | + | 0.463068i | \(0.846749\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.0000 | −0.539054 | −0.269527 | − | 0.962993i | \(-0.586867\pi\) | ||||
−0.269527 | + | 0.962993i | \(0.586867\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00000 | −0.0336527 | −0.0168263 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168263 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.50000 | + | 18.1865i | 0.117386 | + | 0.609957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.0000 | − | 25.9808i | −0.501956 | − | 0.869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | 0.601674 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | + | 15.5885i | 0.300167 | + | 0.519904i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | − | 20.7846i | 0.399778 | − | 0.692436i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.50000 | − | 4.33013i | 0.0831028 | − | 0.143938i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.50000 | + | 7.79423i | 0.149420 | + | 0.258803i | 0.931013 | − | 0.364985i | \(-0.118926\pi\) |
−0.781593 | + | 0.623788i | \(0.785593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.0000 | 1.25900 | 0.629498 | − | 0.777002i | \(-0.283261\pi\) | ||||
0.629498 | + | 0.777002i | \(0.283261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00000 | + | 13.8564i | 0.264761 | + | 0.458580i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.00000 | + | 1.73205i | 0.165115 | + | 0.0571974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.5000 | + | 32.0429i | −0.610259 | + | 1.05700i | 0.380938 | + | 0.924601i | \(0.375601\pi\) |
−0.991197 | + | 0.132398i | \(0.957732\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 60.0000 | 1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0000 | −0.361678 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.0000 | + | 24.2487i | −0.459325 | + | 0.795574i | −0.998925 | − | 0.0463469i | \(-0.985242\pi\) |
0.539600 | + | 0.841921i | \(0.318575\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | + | 34.6410i | −0.163868 | + | 1.13531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | + | 20.7846i | 0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0000 | 1.20874 | 0.604369 | − | 0.796705i | \(-0.293425\pi\) | ||||
0.604369 | + | 0.796705i | \(0.293425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.00000 | + | 15.5885i | 0.293392 | + | 0.508169i | 0.974609 | − | 0.223912i | \(-0.0718827\pi\) |
−0.681218 | + | 0.732081i | \(0.738549\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000 | − | 13.8564i | 0.260516 | − | 0.451227i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.00000 | + | 10.3923i | −0.194974 | + | 0.337705i | −0.946892 | − | 0.321552i | \(-0.895796\pi\) |
0.751918 | + | 0.659256i | \(0.229129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.5000 | + | 47.6314i | 0.892688 | + | 1.54618i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0000 | 0.388718 | 0.194359 | − | 0.980930i | \(-0.437737\pi\) | ||||
0.194359 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.00000 | − | 1.73205i | −0.0323592 | − | 0.0560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.00000 | − | 3.46410i | 0.129167 | − | 0.111862i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0000 | + | 43.3013i | −0.806452 | + | 1.39682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.00000 | 0.0965734 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.0000 | −1.18984 | −0.594920 | − | 0.803785i | \(-0.702816\pi\) | ||||
−0.594920 | + | 0.803785i | \(0.702816\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000 | − | 10.3923i | 0.192549 | − | 0.333505i | −0.753545 | − | 0.657396i | \(-0.771658\pi\) |
0.946094 | + | 0.323891i | \(0.104991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.50000 | − | 49.3634i | −0.304556 | − | 1.58252i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.0000 | 2.30113 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.0000 | + | 39.8372i | 0.733586 | + | 1.27061i | 0.955341 | + | 0.295506i | \(0.0954882\pi\) |
−0.221755 | + | 0.975102i | \(0.571178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | − | 15.5885i | 0.286764 | − | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.00000 | − | 1.73205i | 0.0317982 | − | 0.0550760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5000 | − | 33.7750i | −0.619438 | − | 1.07290i | −0.989588 | − | 0.143926i | \(-0.954027\pi\) |
0.370151 | − | 0.928972i | \(-0.379306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.00000 | 0.253617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50000 | − | 4.33013i | −0.0791758 | − | 0.137136i | 0.823719 | − | 0.566999i | \(-0.191896\pi\) |
−0.902895 | + | 0.429862i | \(0.858562\pi\) | |||||||
\(998\) | 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 | 2520.2.bi.h.1801.1 | 2 | ||
3.2 | odd | 2 | 840.2.bg.b.121.1 | ✓ | 2 | ||
7.4 | even | 3 | inner | 2520.2.bi.h.361.1 | 2 | ||
12.11 | even | 2 | 1680.2.bg.c.961.1 | 2 | |||
21.2 | odd | 6 | 5880.2.a.q.1.1 | 1 | |||
21.5 | even | 6 | 5880.2.a.ba.1.1 | 1 | |||
21.11 | odd | 6 | 840.2.bg.b.361.1 | yes | 2 | ||
84.11 | even | 6 | 1680.2.bg.c.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.bg.b.121.1 | ✓ | 2 | 3.2 | odd | 2 | ||
840.2.bg.b.361.1 | yes | 2 | 21.11 | odd | 6 | ||
1680.2.bg.c.961.1 | 2 | 12.11 | even | 2 | |||
1680.2.bg.c.1201.1 | 2 | 84.11 | even | 6 | |||
2520.2.bi.h.361.1 | 2 | 7.4 | even | 3 | inner | ||
2520.2.bi.h.1801.1 | 2 | 1.1 | even | 1 | trivial | ||
5880.2.a.q.1.1 | 1 | 21.2 | odd | 6 | |||
5880.2.a.ba.1.1 | 1 | 21.5 | even | 6 |