Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(361,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1260.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.s (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: | \(10.0611506547\) |
Analytic rank: | \(1\) |
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 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.541 |
Dual form | 1260.2.s.b.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 \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −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 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | + | 7.79423i | −0.938315 | + | 1.62521i | −0.169701 | + | 0.985496i | \(0.554280\pi\) |
−0.768613 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | + | 1.73205i | 0.338062 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | −0.780869 | −0.390434 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390434 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(42\) | 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 | ||||||||
\(47\) | 4.00000 | − | 6.92820i | 0.583460 | − | 1.01058i | −0.411606 | − | 0.911362i | \(-0.635032\pi\) |
0.995066 | − | 0.0992202i | \(-0.0316348\pi\) | |||||||
\(48\) | 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 | 0.970065 | − | 0.242846i | \(-0.0780811\pi\) |
−0.695344 | + | 0.718677i | \(0.744748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | + | 2.59808i | 0.183254 | + | 0.317406i | 0.942987 | − | 0.332830i | \(-0.108004\pi\) |
−0.759733 | + | 0.650236i | \(0.774670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | − | 12.1244i | −0.819288 | − | 1.41905i | −0.906208 | − | 0.422833i | \(-0.861036\pi\) |
0.0869195 | − | 0.996215i | \(-0.472298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.00000 | + | 1.73205i | −0.569803 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | + | 3.46410i | −0.225018 | + | 0.389742i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00000 | 0.109764 | 0.0548821 | − | 0.998493i | \(-0.482522\pi\) | ||||
0.0548821 | + | 0.998493i | \(0.482522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.50000 | − | 11.2583i | 0.688999 | − | 1.19338i | −0.283164 | − | 0.959072i | \(-0.591384\pi\) |
0.972162 | − | 0.234309i | \(-0.0752827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 15.5885i | −0.314485 | + | 1.63411i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.50000 | + | 11.2583i | −0.640464 | + | 1.10932i | 0.344865 | + | 0.938652i | \(0.387925\pi\) |
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.50000 | + | 12.9904i | −0.725052 | + | 1.25583i | 0.233900 | + | 0.972261i | \(0.424851\pi\) |
−0.958952 | + | 0.283567i | \(0.908482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50000 | − | 7.79423i | −0.431022 | − | 0.746552i | 0.565940 | − | 0.824447i | \(-0.308513\pi\) |
−0.996962 | + | 0.0778949i | \(0.975180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.50000 | − | 7.79423i | −0.419627 | − | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.00000 | − | 1.73205i | 0.458349 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.00000 | + | 3.46410i | −0.174741 | + | 0.302660i | −0.940072 | − | 0.340977i | \(-0.889242\pi\) |
0.765331 | + | 0.643637i | \(0.222575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | + | 10.3923i | 0.501745 | + | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50000 | − | 2.59808i | 0.124568 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00000 | + | 1.73205i | 0.0798087 | + | 0.138233i | 0.903167 | − | 0.429289i | \(-0.141236\pi\) |
−0.823359 | + | 0.567521i | \(0.807902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.0000 | + | 15.5885i | 1.41860 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | + | 6.92820i | −0.313304 | + | 0.542659i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.00000 | 0.696441 | 0.348220 | − | 0.937413i | \(-0.386786\pi\) | ||||
0.348220 | + | 0.937413i | \(0.386786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.00000 | + | 13.8564i | −0.608229 | + | 1.05348i | 0.383304 | + | 0.923622i | \(0.374786\pi\) |
−0.991532 | + | 0.129861i | \(0.958547\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | + | 0.866025i | −0.188982 | + | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00000 | 0.0743294 | 0.0371647 | − | 0.999309i | \(-0.488167\pi\) | ||||
0.0371647 | + | 0.999309i | \(0.488167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | − | 6.92820i | −0.294086 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 3.46410i | 0.146254 | − | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.73205i | −0.0719816 | − | 0.124676i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0000 | −0.997459 | −0.498729 | − | 0.866758i | \(-0.666200\pi\) | ||||
−0.498729 | + | 0.866758i | \(0.666200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | − | 17.3205i | −0.708881 | − | 1.22782i | −0.965272 | − | 0.261245i | \(-0.915867\pi\) |
0.256391 | − | 0.966573i | \(-0.417466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.50000 | + | 7.79423i | −0.105279 | + | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.50000 | − | 4.33013i | 0.174608 | − | 0.302429i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.500000 | + | 0.866025i | −0.0340997 | + | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.00000 | + | 1.73205i | −0.339422 | + | 0.117579i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.00000 | − | 3.46410i | −0.132745 | − | 0.229920i | 0.791989 | − | 0.610535i | \(-0.209046\pi\) |
−0.924734 | + | 0.380615i | \(0.875712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | − | 12.1244i | 0.462573 | − | 0.801200i | −0.536515 | − | 0.843891i | \(-0.680260\pi\) |
0.999088 | + | 0.0426906i | \(0.0135930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | + | 6.92820i | 0.260931 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0000 | 1.68180 | 0.840900 | − | 0.541190i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541190i | \(0.182026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.50000 | − | 4.33013i | 0.351382 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.0000 | −1.89358 | −0.946792 | − | 0.321847i | \(-0.895696\pi\) | ||||
−0.946792 | + | 0.321847i | \(0.895696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.00000 | − | 6.92820i | 0.249513 | − | 0.432169i | −0.713878 | − | 0.700270i | \(-0.753063\pi\) |
0.963391 | + | 0.268101i | \(0.0863961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0000 | + | 13.8564i | 0.994192 | + | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.50000 | + | 14.7224i | 0.524132 | + | 0.907824i | 0.999605 | + | 0.0280936i | \(0.00894366\pi\) |
−0.475473 | + | 0.879730i | \(0.657723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.50000 | + | 7.79423i | 0.274370 | + | 0.475223i | 0.969976 | − | 0.243201i | \(-0.0781974\pi\) |
−0.695606 | + | 0.718423i | \(0.744864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | − | 15.5885i | −0.540758 | − | 0.936620i | −0.998861 | − | 0.0477206i | \(-0.984804\pi\) |
0.458103 | − | 0.888899i | \(-0.348529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.50000 | + | 12.9904i | −0.147570 | + | 0.766798i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.00000 | −0.233682 | −0.116841 | − | 0.993151i | \(-0.537277\pi\) | ||||
−0.116841 | + | 0.993151i | \(0.537277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.0000 | − | 46.7654i | 1.56145 | − | 2.70451i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | − | 2.59808i | 0.0288195 | − | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.50000 | − | 6.06218i | −0.200409 | − | 0.347119i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00000 | 0.0570730 | 0.0285365 | − | 0.999593i | \(-0.490915\pi\) | ||||
0.0285365 | + | 0.999593i | \(0.490915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | − | 3.46410i | 0.113047 | − | 0.195803i | −0.803951 | − | 0.594696i | \(-0.797272\pi\) |
0.916997 | + | 0.398894i | \(0.130606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.00000 | − | 8.66025i | 0.280828 | − | 0.486408i | −0.690761 | − | 0.723083i | \(-0.742724\pi\) |
0.971589 | + | 0.236675i | \(0.0760576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | + | 5.19615i | 0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | + | 5.19615i | 0.166410 | + | 0.288231i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | − | 13.8564i | −0.882109 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | + | 8.66025i | −0.274825 | + | 0.476011i | −0.970091 | − | 0.242742i | \(-0.921953\pi\) |
0.695266 | + | 0.718752i | \(0.255287\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.00000 | −0.163908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.00000 | + | 3.46410i | −0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5000 | + | 21.6506i | 0.671035 | + | 1.16227i | 0.977611 | + | 0.210421i | \(0.0674834\pi\) |
−0.306576 | + | 0.951846i | \(0.599183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.0000 | −0.909989 | −0.454995 | − | 0.890494i | \(-0.650359\pi\) | ||||
−0.454995 | + | 0.890494i | \(0.650359\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | − | 31.1769i | −0.958043 | − | 1.65938i | −0.727245 | − | 0.686378i | \(-0.759200\pi\) |
−0.230799 | − | 0.973002i | \(-0.574134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | − | 6.92820i | 0.212298 | − | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.00000 | + | 8.66025i | −0.263890 | + | 0.457071i | −0.967272 | − | 0.253741i | \(-0.918339\pi\) |
0.703382 | + | 0.710812i | \(0.251672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.500000 | − | 0.866025i | −0.0260998 | − | 0.0452062i | 0.852680 | − | 0.522433i | \(-0.174975\pi\) |
−0.878780 | + | 0.477227i | \(0.841642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.0000 | − | 3.46410i | 0.519174 | − | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0000 | + | 27.7128i | −0.828449 | + | 1.43492i | 0.0708063 | + | 0.997490i | \(0.477443\pi\) |
−0.899255 | + | 0.437425i | \(0.855891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.0000 | 0.927047 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.50000 | + | 7.79423i | −0.229939 | + | 0.398266i | −0.957790 | − | 0.287469i | \(-0.907186\pi\) |
0.727851 | + | 0.685736i | \(0.240519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | − | 5.19615i | 0.0509647 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.00000 | − | 8.66025i | −0.253510 | − | 0.439092i | 0.710980 | − | 0.703213i | \(-0.248252\pi\) |
−0.964490 | + | 0.264120i | \(0.914918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.00000 | − | 3.46410i | −0.100631 | − | 0.174298i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.00000 | + | 8.66025i | −0.250943 | + | 0.434646i | −0.963786 | − | 0.266678i | \(-0.914074\pi\) |
0.712843 | + | 0.701324i | \(0.247407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.5000 | + | 25.1147i | −0.724095 | + | 1.25417i | 0.235250 | + | 0.971935i | \(0.424409\pi\) |
−0.959345 | + | 0.282235i | \(0.908924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | + | 10.3923i | 0.298881 | + | 0.517678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0000 | 0.793091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.50000 | − | 2.59808i | −0.0741702 | − | 0.128467i | 0.826555 | − | 0.562856i | \(-0.190297\pi\) |
−0.900725 | + | 0.434389i | \(0.856964\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.0000 | + | 6.92820i | −0.984136 | + | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.500000 | + | 0.866025i | −0.0245440 | + | 0.0425115i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.0000 | + | 12.1244i | 0.677507 | + | 0.586739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.00000 | + | 5.19615i | 0.144505 | + | 0.250290i | 0.929188 | − | 0.369607i | \(-0.120508\pi\) |
−0.784683 | + | 0.619897i | \(0.787174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.00000 | + | 3.46410i | −0.0954548 | + | 0.165333i | −0.909798 | − | 0.415051i | \(-0.863764\pi\) |
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5000 | − | 32.0429i | 0.878962 | − | 1.52241i | 0.0264796 | − | 0.999649i | \(-0.491570\pi\) |
0.852482 | − | 0.522757i | \(-0.175096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.50000 | + | 11.2583i | 0.308130 | + | 0.533696i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.00000 | + | 8.66025i | 0.235441 | + | 0.407795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | − | 10.3923i | −0.562569 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | + | 24.2487i | −0.654892 | + | 1.13431i | 0.327028 | + | 0.945015i | \(0.393953\pi\) |
−0.981921 | + | 0.189292i | \(0.939381\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.50000 | − | 4.33013i | 0.115686 | − | 0.200374i | −0.802368 | − | 0.596830i | \(-0.796427\pi\) |
0.918054 | + | 0.396456i | \(0.129760\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.50000 | − | 2.59808i | 0.346318 | − | 0.119968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00000 | − | 1.73205i | −0.0459800 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.0000 | − | 25.9808i | −0.685367 | − | 1.18709i | −0.973321 | − | 0.229447i | \(-0.926308\pi\) |
0.287954 | − | 0.957644i | \(-0.407025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | − | 41.5692i | 1.09431 | − | 1.89539i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.00000 | − | 8.66025i | 0.227038 | − | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | − | 27.7128i | −0.725029 | − | 1.25579i | −0.958962 | − | 0.283535i | \(-0.908493\pi\) |
0.233933 | − | 0.972253i | \(-0.424840\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.00000 | − | 5.19615i | −0.135113 | − | 0.234023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.00000 | + | 20.7846i | −0.179425 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.00000 | − | 5.19615i | 0.134298 | − | 0.232612i | −0.791031 | − | 0.611776i | \(-0.790455\pi\) |
0.925329 | + | 0.379165i | \(0.123789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.0000 | −1.20387 | −0.601935 | − | 0.798545i | \(-0.705603\pi\) | ||||
−0.601935 | + | 0.798545i | \(0.705603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | 0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.5000 | + | 35.5070i | −0.908647 | + | 1.57382i | −0.0927004 | + | 0.995694i | \(0.529550\pi\) |
−0.815946 | + | 0.578128i | \(0.803783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.0000 | + | 12.1244i | −1.54831 | + | 0.536350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.50000 | − | 11.2583i | −0.286424 | − | 0.496101i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.00000 | + | 12.1244i | 0.306676 | + | 0.531178i | 0.977633 | − | 0.210318i | \(-0.0674500\pi\) |
−0.670957 | + | 0.741496i | \(0.734117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.00000 | + | 3.46410i | −0.0874539 | + | 0.151475i | −0.906434 | − | 0.422347i | \(-0.861206\pi\) |
0.818980 | + | 0.573822i | \(0.194540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | − | 3.46410i | 0.0871214 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.0000 | 1.29944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.50000 | − | 12.9904i | −0.324253 | − | 0.561623i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | + | 13.8564i | 0.0861461 | + | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.5000 | + | 28.5788i | −0.709390 | + | 1.22870i | 0.255693 | + | 0.966758i | \(0.417696\pi\) |
−0.965084 | + | 0.261942i | \(0.915637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.0000 | −0.641354 | −0.320677 | − | 0.947189i | \(-0.603910\pi\) | ||||
−0.320677 | + | 0.947189i | \(0.603910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | + | 6.92820i | 0.340195 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.00000 | − | 1.73205i | −0.0423714 | − | 0.0733893i | 0.844062 | − | 0.536246i | \(-0.180158\pi\) |
−0.886433 | + | 0.462856i | \(0.846825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.50000 | − | 11.2583i | −0.273942 | − | 0.474482i | 0.695925 | − | 0.718114i | \(-0.254994\pi\) |
−0.969868 | + | 0.243632i | \(0.921661\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | + | 3.46410i | −0.0841406 | + | 0.145736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0000 | − | 25.9808i | 0.628833 | − | 1.08917i | −0.358954 | − | 0.933355i | \(-0.616866\pi\) |
0.987786 | − | 0.155815i | \(-0.0498003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | − | 20.7846i | −0.502184 | − | 0.869809i | −0.999997 | − | 0.00252413i | \(-0.999197\pi\) |
0.497812 | − | 0.867285i | \(-0.334137\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.00000 | 0.375326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.0000 | − | 19.0526i | −0.457936 | − | 0.793168i | 0.540916 | − | 0.841077i | \(-0.318078\pi\) |
−0.998852 | + | 0.0479084i | \(0.984744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.500000 | − | 2.59808i | 0.0207435 | − | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.0000 | −0.825488 | −0.412744 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | + | 31.1769i | −0.739171 | + | 1.28028i | 0.213697 | + | 0.976900i | \(0.431449\pi\) |
−0.952869 | + | 0.303383i | \(0.901884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.00000 | + | 5.19615i | −0.0409960 | + | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.50000 | + | 6.06218i | 0.142295 | + | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.500000 | + | 0.866025i | −0.0202944 | + | 0.0351509i | −0.875994 | − | 0.482322i | \(-0.839794\pi\) |
0.855700 | + | 0.517472i | \(0.173127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.0000 | + | 41.5692i | −0.970936 | + | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | + | 5.19615i | 0.121169 | + | 0.209871i | 0.920229 | − | 0.391381i | \(-0.128002\pi\) |
−0.799060 | + | 0.601251i | \(0.794669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0000 | −0.805170 | −0.402585 | − | 0.915383i | \(-0.631888\pi\) | ||||
−0.402585 | + | 0.915383i | \(0.631888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.0000 | − | 22.5167i | −1.04167 | − | 0.902111i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 13.8564i | −0.317470 | + | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.0000 | + | 15.5885i | 1.54524 | + | 0.617637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.5000 | − | 26.8468i | −0.612213 | − | 1.06038i | −0.990867 | − | 0.134846i | \(-0.956946\pi\) |
0.378653 | − | 0.925539i | \(-0.376387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.0000 | −0.788723 | −0.394362 | − | 0.918955i | \(-0.629034\pi\) | ||||
−0.394362 | + | 0.918955i | \(0.629034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.500000 | + | 0.866025i | 0.0196570 | + | 0.0340470i | 0.875687 | − | 0.482880i | \(-0.160409\pi\) |
−0.856030 | + | 0.516927i | \(0.827076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | + | 13.8564i | −0.314027 | + | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.0000 | + | 29.4449i | −0.665261 | + | 1.15227i | 0.313953 | + | 0.949439i | \(0.398347\pi\) |
−0.979214 | + | 0.202828i | \(0.934987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00000 | − | 3.46410i | −0.0781465 | − | 0.135354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5000 | − | 26.8468i | −0.602880 | − | 1.04422i | −0.992383 | − | 0.123194i | \(-0.960686\pi\) |
0.389503 | − | 0.921025i | \(-0.372647\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.5000 | − | 23.3827i | 0.522722 | − | 0.905381i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0000 | 0.540464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000 | 0.616755 | 0.308377 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308377 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.00000 | − | 5.19615i | 0.115299 | − | 0.199704i | −0.802600 | − | 0.596518i | \(-0.796551\pi\) |
0.917899 | + | 0.396813i | \(0.129884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.00000 | + | 25.9808i | −0.191882 | + | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.5000 | + | 25.1147i | 0.554827 | + | 0.960989i | 0.997917 | + | 0.0645115i | \(0.0205489\pi\) |
−0.443090 | + | 0.896477i | \(0.646118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | − | 20.7846i | −0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0000 | − | 22.5167i | 0.494543 | − | 0.856574i | −0.505437 | − | 0.862864i | \(-0.668669\pi\) |
0.999980 | + | 0.00628943i | \(0.00200200\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.00000 | + | 8.66025i | −0.189661 | + | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | − | 8.66025i | −0.189389 | − | 0.328031i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.0000 | 1.09531 | 0.547657 | − | 0.836703i | \(-0.315520\pi\) | ||||
0.547657 | + | 0.836703i | \(0.315520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.50000 | + | 2.59808i | −0.282067 | + | 0.0977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5000 | + | 26.8468i | −0.582115 | + | 1.00825i | 0.413114 | + | 0.910679i | \(0.364441\pi\) |
−0.995228 | + | 0.0975728i | \(0.968892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0000 | 0.674105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.0000 | + | 22.5167i | 0.968291 | + | 0.838564i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50000 | + | 2.59808i | 0.0557086 | + | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.00000 | 0.111264 | 0.0556319 | − | 0.998451i | \(-0.482283\pi\) | ||||
0.0556319 | + | 0.998451i | \(0.482283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.00000 | + | 1.73205i | 0.0369863 | + | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.0000 | + | 29.4449i | −0.627909 | + | 1.08757i | 0.360061 | + | 0.932929i | \(0.382756\pi\) |
−0.987971 | + | 0.154642i | \(0.950578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.00000 | − | 5.19615i | 0.110506 | − | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.00000 | − | 8.66025i | −0.183928 | − | 0.318573i | 0.759287 | − | 0.650756i | \(-0.225548\pi\) |
−0.943215 | + | 0.332184i | \(0.892215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | 0.110059 | 0.0550297 | − | 0.998485i | \(-0.482475\pi\) | ||||
0.0550297 | + | 0.998485i | \(0.482475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.50000 | + | 7.79423i | 0.164867 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0000 | + | 25.9808i | 1.09618 | + | 0.949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | + | 17.3205i | −0.364905 | + | 0.632034i | −0.988761 | − | 0.149505i | \(-0.952232\pi\) |
0.623856 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | − | 25.9808i | 0.543750 | − | 0.941802i | −0.454935 | − | 0.890525i | \(-0.650337\pi\) |
0.998684 | − | 0.0512772i | \(-0.0163292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.5000 | + | 7.79423i | −0.814555 | + | 0.282170i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000 | + | 41.5692i | 0.866590 | + | 1.50098i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | − | 15.5885i | −0.323708 | − | 0.560678i | 0.657542 | − | 0.753418i | \(-0.271596\pi\) |
−0.981250 | + | 0.192740i | \(0.938263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | + | 1.73205i | −0.0359211 | + | 0.0622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | + | 13.8564i | 0.286263 | + | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.50000 | + | 9.52628i | 0.196054 | + | 0.339575i | 0.947245 | − | 0.320509i | \(-0.103854\pi\) |
−0.751192 | + | 0.660084i | \(0.770521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00000 | − | 10.3923i | 0.0711118 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.0000 | − | 36.3731i | 0.745732 | − | 1.29165i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.0000 | −1.27519 | −0.637593 | − | 0.770374i | \(-0.720070\pi\) | ||||
−0.637593 | + | 0.770374i | \(0.720070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.0000 | + | 24.2487i | −0.494049 | + | 0.855718i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.5000 | + | 7.79423i | −0.793021 | + | 0.274710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.5000 | + | 38.9711i | 0.791058 | + | 1.37015i | 0.925312 | + | 0.379206i | \(0.123803\pi\) |
−0.134255 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.0000 | 1.75574 | 0.877869 | − | 0.478901i | \(-0.158965\pi\) | ||||
0.877869 | + | 0.478901i | \(0.158965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.50000 | − | 16.4545i | −0.331149 | − | 0.573567i | 0.651588 | − | 0.758573i | \(-0.274103\pi\) |
−0.982737 | + | 0.185006i | \(0.940770\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.0000 | −0.799788 | −0.399894 | − | 0.916561i | \(-0.630953\pi\) | ||||
−0.399894 | + | 0.916561i | \(0.630953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.00000 | + | 8.66025i | 0.173657 | + | 0.300783i | 0.939696 | − | 0.342012i | \(-0.111108\pi\) |
−0.766039 | + | 0.642795i | \(0.777775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | − | 13.8564i | −0.0692959 | − | 0.480096i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.50000 | + | 7.79423i | −0.155729 | + | 0.269730i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.0000 | −0.483334 | −0.241667 | − | 0.970359i | \(-0.577694\pi\) | ||||
−0.241667 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.5000 | + | 19.9186i | −0.395612 | + | 0.685220i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0000 | − | 12.1244i | −0.481046 | − | 0.416598i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | − | 62.3538i | −1.23406 | − | 2.13746i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.0000 | −1.36957 | −0.684787 | − | 0.728743i | \(-0.740105\pi\) | ||||
−0.684787 | + | 0.728743i | \(0.740105\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.0000 | − | 46.7654i | −0.922302 | − | 1.59747i | −0.795843 | − | 0.605503i | \(-0.792972\pi\) |
−0.126459 | − | 0.991972i | \(-0.540361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0000 | − | 31.1769i | 0.614152 | − | 1.06374i | −0.376381 | − | 0.926465i | \(-0.622831\pi\) |
0.990533 | − | 0.137277i | \(-0.0438352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.5000 | − | 32.0429i | 0.629747 | − | 1.09075i | −0.357855 | − | 0.933777i | \(-0.616492\pi\) |
0.987602 | − | 0.156977i | \(-0.0501749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | − | 13.8564i | −0.272008 | − | 0.471132i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.00000 | − | 15.5885i | −0.304953 | − | 0.528195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.500000 | − | 2.59808i | 0.0169031 | − | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.0000 | + | 27.7128i | −0.540282 | + | 0.935795i | 0.458606 | + | 0.888640i | \(0.348349\pi\) |
−0.998888 | + | 0.0471555i | \(0.984984\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0000 | 1.04442 | 0.522208 | − | 0.852818i | \(-0.325108\pi\) | ||||
0.522208 | + | 0.852818i | \(0.325108\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0000 | −1.21150 | −0.605748 | − | 0.795656i | \(-0.707126\pi\) | ||||
−0.605748 | + | 0.795656i | \(0.707126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.5000 | − | 45.8993i | 0.889783 | − | 1.54115i | 0.0496513 | − | 0.998767i | \(-0.484189\pi\) |
0.840132 | − | 0.542383i | \(-0.182478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | − | 41.5692i | 0.268311 | − | 1.39419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000 | 0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.00000 | + | 5.19615i | 0.100056 | + | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | + | 6.92820i | −0.133259 | + | 0.230812i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.500000 | + | 0.866025i | −0.0166206 | + | 0.0287877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | + | 32.0429i | 0.614282 | + | 1.06397i | 0.990510 | + | 0.137441i | \(0.0438878\pi\) |
−0.376228 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.0000 | −1.78910 | −0.894550 | − | 0.446968i | \(-0.852504\pi\) | ||||
−0.894550 | + | 0.446968i | \(0.852504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.00000 | − | 1.73205i | −0.0330952 | − | 0.0573225i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.00000 | + | 6.92820i | 0.264183 | + | 0.228789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | + | 27.7128i | −0.527791 | + | 0.914161i | 0.471684 | + | 0.881768i | \(0.343646\pi\) |
−0.999475 | + | 0.0323936i | \(0.989687\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0000 | 1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.50000 | + | 4.33013i | −0.0820223 | + | 0.142067i | −0.904118 | − | 0.427282i | \(-0.859471\pi\) |
0.822096 | + | 0.569349i | \(0.192805\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.00000 | + | 3.46410i | 0.0654070 | + | 0.113288i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.0000 | + | 32.9090i | 0.619382 | + | 1.07280i | 0.989599 | + | 0.143856i | \(0.0459502\pi\) |
−0.370216 | + | 0.928946i | \(0.620716\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.5000 | − | 38.9711i | 0.732701 | − | 1.26908i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.5000 | − | 25.1147i | 0.471187 | − | 0.816119i | −0.528270 | − | 0.849076i | \(-0.677159\pi\) |
0.999457 | + | 0.0329571i | \(0.0104925\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.0000 | + | 72.7461i | 1.36338 | + | 2.36144i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.0000 | 1.94359 | 0.971795 | − | 0.235826i | \(-0.0757795\pi\) | ||||
0.971795 | + | 0.235826i | \(0.0757795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00000 | + | 5.19615i | 0.0970777 | + | 0.168144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.0000 | + | 10.3923i | −0.968751 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.0000 | 1.18984 | 0.594920 | − | 0.803785i | \(-0.297184\pi\) | ||||
0.594920 | + | 0.803785i | \(0.297184\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.00000 | + | 10.3923i | −0.192549 | + | 0.333505i | −0.946094 | − | 0.323891i | \(-0.895009\pi\) |
0.753545 | + | 0.657396i | \(0.228342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.00000 | − | 25.9808i | 0.160293 | − | 0.832905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.00000 | − | 5.19615i | −0.0959785 | − | 0.166240i | 0.814038 | − | 0.580812i | \(-0.197265\pi\) |
−0.910017 | + | 0.414572i | \(0.863931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.0000 | −0.830964 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.50000 | − | 16.4545i | −0.303003 | − | 0.524816i | 0.673812 | − | 0.738903i | \(-0.264656\pi\) |
−0.976815 | + | 0.214087i | \(0.931323\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.00000 | − | 12.1244i | 0.223039 | − | 0.386314i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.50000 | + | 7.79423i | −0.143092 | + | 0.247842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | + | 32.9090i | 0.603555 | + | 1.04539i | 0.992278 | + | 0.124033i | \(0.0395829\pi\) |
−0.388723 | + | 0.921355i | \(0.627084\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0000 | 0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0000 | + | 34.6410i | 0.633406 | + | 1.09709i | 0.986850 | + | 0.161636i | \(0.0516771\pi\) |
−0.353444 | + | 0.935456i | \(0.614990\pi\) | |||||||
\(998\) | 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 | 1260.2.s.b.541.1 | 2 | ||
3.2 | odd | 2 | 140.2.i.b.121.1 | yes | 2 | ||
7.2 | even | 3 | 8820.2.a.w.1.1 | 1 | |||
7.4 | even | 3 | inner | 1260.2.s.b.361.1 | 2 | ||
7.5 | odd | 6 | 8820.2.a.k.1.1 | 1 | |||
12.11 | even | 2 | 560.2.q.a.401.1 | 2 | |||
15.2 | even | 4 | 700.2.r.c.149.2 | 4 | |||
15.8 | even | 4 | 700.2.r.c.149.1 | 4 | |||
15.14 | odd | 2 | 700.2.i.a.401.1 | 2 | |||
21.2 | odd | 6 | 980.2.a.a.1.1 | 1 | |||
21.5 | even | 6 | 980.2.a.i.1.1 | 1 | |||
21.11 | odd | 6 | 140.2.i.b.81.1 | ✓ | 2 | ||
21.17 | even | 6 | 980.2.i.a.361.1 | 2 | |||
21.20 | even | 2 | 980.2.i.a.961.1 | 2 | |||
84.11 | even | 6 | 560.2.q.a.81.1 | 2 | |||
84.23 | even | 6 | 3920.2.a.bi.1.1 | 1 | |||
84.47 | odd | 6 | 3920.2.a.d.1.1 | 1 | |||
105.2 | even | 12 | 4900.2.e.c.2549.2 | 2 | |||
105.23 | even | 12 | 4900.2.e.c.2549.1 | 2 | |||
105.32 | even | 12 | 700.2.r.c.249.1 | 4 | |||
105.44 | odd | 6 | 4900.2.a.v.1.1 | 1 | |||
105.47 | odd | 12 | 4900.2.e.b.2549.1 | 2 | |||
105.53 | even | 12 | 700.2.r.c.249.2 | 4 | |||
105.68 | odd | 12 | 4900.2.e.b.2549.2 | 2 | |||
105.74 | odd | 6 | 700.2.i.a.501.1 | 2 | |||
105.89 | even | 6 | 4900.2.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.i.b.81.1 | ✓ | 2 | 21.11 | odd | 6 | ||
140.2.i.b.121.1 | yes | 2 | 3.2 | odd | 2 | ||
560.2.q.a.81.1 | 2 | 84.11 | even | 6 | |||
560.2.q.a.401.1 | 2 | 12.11 | even | 2 | |||
700.2.i.a.401.1 | 2 | 15.14 | odd | 2 | |||
700.2.i.a.501.1 | 2 | 105.74 | odd | 6 | |||
700.2.r.c.149.1 | 4 | 15.8 | even | 4 | |||
700.2.r.c.149.2 | 4 | 15.2 | even | 4 | |||
700.2.r.c.249.1 | 4 | 105.32 | even | 12 | |||
700.2.r.c.249.2 | 4 | 105.53 | even | 12 | |||
980.2.a.a.1.1 | 1 | 21.2 | odd | 6 | |||
980.2.a.i.1.1 | 1 | 21.5 | even | 6 | |||
980.2.i.a.361.1 | 2 | 21.17 | even | 6 | |||
980.2.i.a.961.1 | 2 | 21.20 | even | 2 | |||
1260.2.s.b.361.1 | 2 | 7.4 | even | 3 | inner | ||
1260.2.s.b.541.1 | 2 | 1.1 | even | 1 | trivial | ||
3920.2.a.d.1.1 | 1 | 84.47 | odd | 6 | |||
3920.2.a.bi.1.1 | 1 | 84.23 | even | 6 | |||
4900.2.a.a.1.1 | 1 | 105.89 | even | 6 | |||
4900.2.a.v.1.1 | 1 | 105.44 | odd | 6 | |||
4900.2.e.b.2549.1 | 2 | 105.47 | odd | 12 | |||
4900.2.e.b.2549.2 | 2 | 105.68 | odd | 12 | |||
4900.2.e.c.2549.1 | 2 | 105.23 | even | 12 | |||
4900.2.e.c.2549.2 | 2 | 105.2 | even | 12 | |||
8820.2.a.k.1.1 | 1 | 7.5 | odd | 6 | |||
8820.2.a.w.1.1 | 1 | 7.2 | even | 3 |