Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.1 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1057 |
Dual form | 1200.3.bg.a.193.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.77526 | − | 4.77526i | −0.682179 | − | 0.682179i | 0.278312 | − | 0.960491i | \(-0.410225\pi\) |
−0.960491 | + | 0.278312i | \(0.910225\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.6969 | −1.88154 | −0.940770 | − | 0.339046i | \(-0.889896\pi\) | ||||
−0.940770 | + | 0.339046i | \(0.889896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.32577 | + | 8.32577i | −0.640443 | + | 0.640443i | −0.950664 | − | 0.310221i | \(-0.899597\pi\) |
0.310221 | + | 0.950664i | \(0.399597\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.34847 | − | 1.34847i | −0.0793217 | − | 0.0793217i | 0.666333 | − | 0.745654i | \(-0.267863\pi\) |
−0.745654 | + | 0.666333i | \(0.767863\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33.6969i | 1.77352i | 0.462227 | + | 0.886762i | \(0.347050\pi\) | ||||
−0.462227 | + | 0.886762i | \(0.652950\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.6969 | 0.556997 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.0454 | − | 16.0454i | 0.697626 | − | 0.697626i | −0.266272 | − | 0.963898i | \(-0.585792\pi\) |
0.963898 | + | 0.266272i | \(0.0857918\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.69694i | 0.299894i | 0.988694 | + | 0.149947i | \(0.0479104\pi\) | ||||
−0.988694 | + | 0.149947i | \(0.952090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 49.0908 | 1.58357 | 0.791787 | − | 0.610797i | \(-0.209151\pi\) | ||||
0.791787 | + | 0.610797i | \(0.209151\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 25.3485 | − | 25.3485i | 0.768135 | − | 0.768135i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −36.4949 | − | 36.4949i | −0.986349 | − | 0.986349i | 0.0135595 | − | 0.999908i | \(-0.495684\pi\) |
−0.999908 | + | 0.0135595i | \(0.995684\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 20.3939i | − | 0.522920i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.3031 | 0.812270 | 0.406135 | − | 0.913813i | \(-0.366876\pi\) | ||||
0.406135 | + | 0.913813i | \(0.366876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.1237 | − | 24.1237i | 0.561017 | − | 0.561017i | −0.368579 | − | 0.929596i | \(-0.620156\pi\) |
0.929596 | + | 0.368579i | \(0.120156\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.9546 | + | 13.9546i | 0.296906 | + | 0.296906i | 0.839801 | − | 0.542895i | \(-0.182672\pi\) |
−0.542895 | + | 0.839801i | \(0.682672\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.39388i | − | 0.0692628i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.30306 | 0.0647659 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 59.3939 | − | 59.3939i | 1.12064 | − | 1.12064i | 0.128994 | − | 0.991645i | \(-0.458825\pi\) |
0.991645 | − | 0.128994i | \(-0.0411747\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −41.2702 | − | 41.2702i | −0.724038 | − | 0.724038i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 30.0000i | 0.508475i | 0.967142 | + | 0.254237i | \(0.0818244\pi\) | ||||
−0.967142 | + | 0.254237i | \(0.918176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −47.7878 | −0.783406 | −0.391703 | − | 0.920092i | \(-0.628114\pi\) | ||||
−0.391703 | + | 0.920092i | \(0.628114\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.3258 | + | 14.3258i | −0.227393 | + | 0.227393i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −17.0227 | − | 17.0227i | −0.254070 | − | 0.254070i | 0.568567 | − | 0.822637i | \(-0.307498\pi\) |
−0.822637 | + | 0.568567i | \(0.807498\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 39.3031i | 0.569610i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.30306 | 0.131029 | 0.0655145 | − | 0.997852i | \(-0.479131\pi\) | ||||
0.0655145 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22.2929 | − | 22.2929i | 0.305382 | − | 0.305382i | −0.537733 | − | 0.843115i | \(-0.680719\pi\) |
0.843115 | + | 0.537733i | \(0.180719\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 98.8332 | + | 98.8332i | 1.28355 | + | 1.28355i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 27.3939i | − | 0.346758i | −0.984855 | − | 0.173379i | \(-0.944531\pi\) | ||
0.984855 | − | 0.173379i | \(-0.0554685\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 63.4393 | − | 63.4393i | 0.764329 | − | 0.764329i | −0.212773 | − | 0.977102i | \(-0.568249\pi\) |
0.977102 | + | 0.212773i | \(0.0682495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.6515 | − | 10.6515i | −0.122431 | − | 0.122431i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.3939i | 0.195437i | 0.995214 | + | 0.0977184i | \(0.0311545\pi\) | ||||
−0.995214 | + | 0.0977184i | \(0.968846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 79.5153 | 0.873795 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −60.1237 | + | 60.1237i | −0.646492 | + | 0.646492i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 41.8763 | + | 41.8763i | 0.431714 | + | 0.431714i | 0.889211 | − | 0.457497i | \(-0.151254\pi\) |
−0.457497 | + | 0.889211i | \(0.651254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 62.0908i | 0.627180i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 162.879 | 1.61266 | 0.806330 | − | 0.591467i | \(-0.201451\pi\) | ||||
0.806330 | + | 0.591467i | \(0.201451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 36.9898 | − | 36.9898i | 0.359124 | − | 0.359124i | −0.504366 | − | 0.863490i | \(-0.668274\pi\) |
0.863490 | + | 0.504366i | \(0.168274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −134.091 | − | 134.091i | −1.25319 | − | 1.25319i | −0.954284 | − | 0.298901i | \(-0.903380\pi\) |
−0.298901 | − | 0.954284i | \(-0.596620\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 145.000i | 1.33028i | 0.746721 | + | 0.665138i | \(0.231627\pi\) | ||||
−0.746721 | + | 0.665138i | \(0.768373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 89.3939 | 0.805350 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.2122 | + | 13.2122i | −0.116923 | + | 0.116923i | −0.763147 | − | 0.646225i | \(-0.776347\pi\) |
0.646225 | + | 0.763147i | \(0.276347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24.9773 | + | 24.9773i | 0.213481 | + | 0.213481i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.8786i | 0.108223i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 307.363 | 2.54019 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −40.7878 | + | 40.7878i | −0.331608 | + | 0.331608i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 50.6969 | + | 50.6969i | 0.399188 | + | 0.399188i | 0.877947 | − | 0.478758i | \(-0.158913\pi\) |
−0.478758 | + | 0.877947i | \(0.658913\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 59.0908i | 0.458068i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 156.272 | 1.19292 | 0.596460 | − | 0.802643i | \(-0.296574\pi\) | ||||
0.596460 | + | 0.802643i | \(0.296574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 160.911 | − | 160.911i | 1.20986 | − | 1.20986i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −91.3485 | − | 91.3485i | −0.666777 | − | 0.666777i | 0.290191 | − | 0.956969i | \(-0.406281\pi\) |
−0.956969 | + | 0.290191i | \(0.906281\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 35.2122i | 0.253326i | 0.991946 | + | 0.126663i | \(0.0404266\pi\) | ||||
−0.991946 | + | 0.126663i | \(0.959573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −34.1816 | −0.242423 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 172.318 | − | 172.318i | 1.20502 | − | 1.20502i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.15663 | + | 4.15663i | 0.0282764 | + | 0.0282764i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.78775i | − | 0.0321326i | −0.999871 | − | 0.0160663i | \(-0.994886\pi\) | ||
0.999871 | − | 0.0160663i | \(-0.00511428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37.8786 | −0.250851 | −0.125426 | − | 0.992103i | \(-0.540030\pi\) | ||||
−0.125426 | + | 0.992103i | \(0.540030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.04541 | + | 4.04541i | −0.0264406 | + | 0.0264406i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −29.1339 | − | 29.1339i | −0.185566 | − | 0.185566i | 0.608210 | − | 0.793776i | \(-0.291888\pi\) |
−0.793776 | + | 0.608210i | \(0.791888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 145.485i | 0.914998i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −153.242 | −0.951813 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −193.856 | + | 193.856i | −1.18930 | + | 1.18930i | −0.212038 | + | 0.977261i | \(0.568010\pi\) |
−0.977261 | + | 0.212038i | \(0.931990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 167.666 | + | 167.666i | 1.00399 | + | 1.00399i | 0.999992 | + | 0.00399795i | \(0.00127259\pi\) |
0.00399795 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.3633i | 0.179664i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 101.091 | 0.591174 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 74.8332 | − | 74.8332i | 0.432562 | − | 0.432562i | −0.456937 | − | 0.889499i | \(-0.651054\pi\) |
0.889499 | + | 0.456937i | \(0.151054\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −36.7423 | − | 36.7423i | −0.207584 | − | 0.207584i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 229.151i | − | 1.28017i | −0.768303 | − | 0.640087i | \(-0.778898\pi\) | ||
0.768303 | − | 0.640087i | \(-0.221102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −135.182 | −0.746860 | −0.373430 | − | 0.927658i | \(-0.621818\pi\) | ||||
−0.373430 | + | 0.927658i | \(0.621818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 58.5278 | − | 58.5278i | 0.319824 | − | 0.319824i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.9092 | + | 27.9092i | 0.149247 | + | 0.149247i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 35.0908i | − | 0.185666i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.9092 | 0.114708 | 0.0573539 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573539 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −98.4870 | + | 98.4870i | −0.510295 | + | 0.510295i | −0.914617 | − | 0.404322i | \(-0.867508\pi\) |
0.404322 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 63.4393 | + | 63.4393i | 0.322027 | + | 0.322027i | 0.849544 | − | 0.527517i | \(-0.176877\pi\) |
−0.527517 | + | 0.849544i | \(0.676877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 181.091i | 0.910004i | 0.890490 | + | 0.455002i | \(0.150361\pi\) | ||||
−0.890490 | + | 0.455002i | \(0.849639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.6969 | 0.207447 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 41.5301 | − | 41.5301i | 0.204582 | − | 0.204582i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −48.1362 | − | 48.1362i | −0.232542 | − | 0.232542i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 697.423i | − | 3.33695i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.7276 | −0.136150 | −0.0680748 | − | 0.997680i | \(-0.521686\pi\) | ||||
−0.0680748 | + | 0.997680i | \(0.521686\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.3939 | + | 11.3939i | −0.0534924 | + | 0.0534924i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −234.421 | − | 234.421i | −1.08028 | − | 1.08028i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 54.6061i | 0.249343i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.4541 | 0.101602 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 33.1793 | − | 33.1793i | 0.148786 | − | 0.148786i | −0.628789 | − | 0.777576i | \(-0.716449\pi\) |
0.777576 | + | 0.628789i | \(0.216449\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 252.879 | + | 252.879i | 1.11400 | + | 1.11400i | 0.992604 | + | 0.121399i | \(0.0387380\pi\) |
0.121399 | + | 0.992604i | \(0.461262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 275.000i | 1.20087i | 0.799672 | + | 0.600437i | \(0.205007\pi\) | ||||
−0.799672 | + | 0.600437i | \(0.794993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −242.091 | −1.04801 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 223.757 | − | 223.757i | 0.960331 | − | 0.960331i | −0.0389116 | − | 0.999243i | \(-0.512389\pi\) |
0.999243 | + | 0.0389116i | \(0.0123891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.5505 | + | 33.5505i | 0.141563 | + | 0.141563i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 305.666i | − | 1.27894i | −0.768817 | − | 0.639469i | \(-0.779154\pi\) | ||
0.768817 | − | 0.639469i | \(-0.220846\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 167.000 | 0.692946 | 0.346473 | − | 0.938060i | \(-0.387379\pi\) | ||||
0.346473 | + | 0.938060i | \(0.387379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −280.553 | − | 280.553i | −1.13584 | − | 1.13584i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 155.394i | 0.624072i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −261.576 | −1.04213 | −0.521067 | − | 0.853516i | \(-0.674466\pi\) | ||||
−0.521067 | + | 0.853516i | \(0.674466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −332.091 | + | 332.091i | −1.31261 | + | 1.31261i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 94.5153 | + | 94.5153i | 0.367764 | + | 0.367764i | 0.866661 | − | 0.498897i | \(-0.166262\pi\) |
−0.498897 | + | 0.866661i | \(0.666262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 348.545i | 1.34573i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.0908 | 0.0999648 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −34.1816 | + | 34.1816i | −0.129968 | + | 0.129968i | −0.769098 | − | 0.639130i | \(-0.779294\pi\) |
0.639130 | + | 0.769098i | \(0.279294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.3031 | − | 21.3031i | −0.0797867 | − | 0.0797867i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 389.605i | 1.44835i | 0.689618 | + | 0.724173i | \(0.257778\pi\) | ||||
−0.689618 | + | 0.724173i | \(0.742222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −156.788 | −0.578553 | −0.289276 | − | 0.957246i | \(-0.593415\pi\) | ||||
−0.289276 | + | 0.957246i | \(0.593415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −97.3860 | + | 97.3860i | −0.356725 | + | 0.356725i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 285.588 | + | 285.588i | 1.03100 | + | 1.03100i | 0.999504 | + | 0.0314999i | \(0.0100284\pi\) |
0.0314999 | + | 0.999504i | \(0.489972\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 147.272i | − | 0.527858i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.1520 | −0.0717155 | −0.0358577 | − | 0.999357i | \(-0.511416\pi\) | ||||
−0.0358577 | + | 0.999357i | \(0.511416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 170.573 | − | 170.573i | 0.602732 | − | 0.602732i | −0.338304 | − | 0.941037i | \(-0.609853\pi\) |
0.941037 | + | 0.338304i | \(0.109853\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −159.031 | − | 159.031i | −0.554114 | − | 0.554114i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 285.363i | − | 0.987416i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −102.576 | −0.352493 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 259.621 | − | 259.621i | 0.886078 | − | 0.886078i | −0.108066 | − | 0.994144i | \(-0.534466\pi\) |
0.994144 | + | 0.108066i | \(0.0344656\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −76.0454 | − | 76.0454i | −0.256045 | − | 0.256045i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 267.181i | 0.893581i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −230.394 | −0.765428 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −199.485 | + | 199.485i | −0.658365 | + | 0.658365i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −118.911 | − | 118.911i | −0.387334 | − | 0.387334i | 0.486402 | − | 0.873735i | \(-0.338309\pi\) |
−0.873735 | + | 0.486402i | \(0.838309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 90.6061i | 0.293224i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 52.7878 | 0.169736 | 0.0848678 | − | 0.996392i | \(-0.472953\pi\) | ||||
0.0848678 | + | 0.996392i | \(0.472953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −238.553 | + | 238.553i | −0.762150 | + | 0.762150i | −0.976711 | − | 0.214561i | \(-0.931168\pi\) |
0.214561 | + | 0.976711i | \(0.431168\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −48.9398 | − | 48.9398i | −0.154384 | − | 0.154384i | 0.625689 | − | 0.780073i | \(-0.284818\pi\) |
−0.780073 | + | 0.625689i | \(0.784818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 180.000i | − | 0.564263i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 328.454 | 1.02322 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.4393 | − | 45.4393i | 0.140679 | − | 0.140679i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −177.588 | − | 177.588i | −0.543083 | − | 0.543083i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 133.273i | − | 0.405087i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 291.939 | 0.881990 | 0.440995 | − | 0.897510i | \(-0.354626\pi\) | ||||
0.440995 | + | 0.897510i | \(0.354626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −109.485 | + | 109.485i | −0.328783 | + | 0.328783i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −266.462 | − | 266.462i | −0.790688 | − | 0.790688i | 0.190918 | − | 0.981606i | \(-0.438854\pi\) |
−0.981606 | + | 0.190918i | \(0.938854\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 32.3633i | − | 0.0954668i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1016.03 | −2.97956 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −250.194 | + | 250.194i | −0.729429 | + | 0.729429i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 141.773 | + | 141.773i | 0.408568 | + | 0.408568i | 0.881239 | − | 0.472671i | \(-0.156710\pi\) |
−0.472671 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 183.939i | − | 0.527045i | −0.964653 | − | 0.263523i | \(-0.915116\pi\) | ||
0.964653 | − | 0.263523i | \(-0.0848844\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −61.1816 | −0.174307 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −54.7423 | + | 54.7423i | −0.155077 | + | 0.155077i | −0.780381 | − | 0.625304i | \(-0.784975\pi\) |
0.625304 | + | 0.780381i | \(0.284975\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.7730 | − | 15.7730i | −0.0441820 | − | 0.0441820i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 648.272i | − | 1.80577i | −0.429879 | − | 0.902886i | \(-0.641444\pi\) | ||
0.429879 | − | 0.902886i | \(-0.358556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −774.484 | −2.14538 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −376.442 | + | 376.442i | −1.03703 | + | 1.03703i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 56.6594 | + | 56.6594i | 0.154385 | + | 0.154385i | 0.780073 | − | 0.625688i | \(-0.215182\pi\) |
−0.625688 | + | 0.780073i | \(0.715182\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 99.9092i | − | 0.270757i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −567.242 | −1.52895 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −155.815 | + | 155.815i | −0.417735 | + | 0.417735i | −0.884422 | − | 0.466688i | \(-0.845447\pi\) |
0.466688 | + | 0.884422i | \(0.345447\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −72.4087 | − | 72.4087i | −0.192065 | − | 0.192065i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 674.181i | − | 1.77884i | −0.457090 | − | 0.889420i | \(-0.651108\pi\) | ||
0.457090 | − | 0.889420i | \(-0.348892\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −124.182 | −0.325936 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −244.182 | + | 244.182i | −0.637550 | + | 0.637550i | −0.949950 | − | 0.312401i | \(-0.898867\pi\) |
0.312401 | + | 0.949950i | \(0.398867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −72.3712 | − | 72.3712i | −0.187006 | − | 0.187006i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 44.7582i | 0.115060i | 0.998344 | + | 0.0575298i | \(0.0183224\pi\) | ||||
−0.998344 | + | 0.0575298i | \(0.981678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.2735 | −0.110674 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −191.394 | + | 191.394i | −0.487007 | + | 0.487007i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 548.648 | + | 548.648i | 1.38199 | + | 1.38199i | 0.841090 | + | 0.540896i | \(0.181915\pi\) |
0.540896 | + | 0.841090i | \(0.318085\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 394.151i | 0.987847i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 273.303 | 0.681554 | 0.340777 | − | 0.940144i | \(-0.389310\pi\) | ||||
0.340777 | + | 0.940144i | \(0.389310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −408.719 | + | 408.719i | −1.01419 | + | 1.01419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 755.333 | + | 755.333i | 1.85585 | + | 1.85585i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 197.182i | − | 0.482107i | −0.970512 | − | 0.241053i | \(-0.922507\pi\) | ||
0.970512 | − | 0.241053i | \(-0.0774929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 223.757 | 0.544421 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 143.258 | − | 143.258i | 0.346871 | − | 0.346871i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −43.1260 | − | 43.1260i | −0.103420 | − | 0.103420i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 613.485i | − | 1.46416i | −0.681217 | − | 0.732082i | \(-0.738549\pi\) | ||
0.681217 | − | 0.732082i | \(-0.261451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 128.120 | 0.304324 | 0.152162 | − | 0.988356i | \(-0.451376\pi\) | ||||
0.152162 | + | 0.988356i | \(0.451376\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 41.8638 | − | 41.8638i | 0.0989687 | − | 0.0989687i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 228.199 | + | 228.199i | 0.534423 | + | 0.534423i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 422.091i | 0.983895i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 393.242 | 0.912394 | 0.456197 | − | 0.889879i | \(-0.349211\pi\) | ||||
0.456197 | + | 0.889879i | \(0.349211\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 221.381 | − | 221.381i | 0.511273 | − | 0.511273i | −0.403643 | − | 0.914917i | \(-0.632256\pi\) |
0.914917 | + | 0.403643i | \(0.132256\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 540.681 | + | 540.681i | 1.23726 | + | 1.23726i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 361.091i | 0.822530i | 0.911516 | + | 0.411265i | \(0.134913\pi\) | ||||
−0.911516 | + | 0.411265i | \(0.865087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.1816 | −0.0230876 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 440.636 | − | 440.636i | 0.994663 | − | 0.994663i | −0.00532284 | − | 0.999986i | \(-0.501694\pi\) |
0.999986 | + | 0.00532284i | \(0.00169432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.86378 | + | 5.86378i | 0.0131181 | + | 0.0131181i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 280.849i | − | 0.625499i | −0.949836 | − | 0.312749i | \(-0.898750\pi\) | ||
0.949836 | − | 0.312749i | \(-0.101250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −689.271 | −1.52832 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 46.3916 | − | 46.3916i | 0.102410 | − | 0.102410i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −261.576 | − | 261.576i | −0.572375 | − | 0.572375i | 0.360416 | − | 0.932792i | \(-0.382635\pi\) |
−0.932792 | + | 0.360416i | \(0.882635\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 9.90918i | − | 0.0215886i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.30306 | −0.0201802 | −0.0100901 | − | 0.999949i | \(-0.503212\pi\) | ||||
−0.0100901 | + | 0.999949i | \(0.503212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 252.495 | − | 252.495i | 0.545345 | − | 0.545345i | −0.379746 | − | 0.925091i | \(-0.623988\pi\) |
0.925091 | + | 0.379746i | \(0.123988\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −366.470 | − | 366.470i | −0.784732 | − | 0.784732i | 0.195893 | − | 0.980625i | \(-0.437239\pi\) |
−0.980625 | + | 0.195893i | \(0.937239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 162.576i | 0.346643i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 71.3633 | 0.151514 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −499.287 | + | 499.287i | −1.05558 | + | 1.05558i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −178.182 | − | 178.182i | −0.373546 | − | 0.373546i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 442.182i | 0.923135i | 0.887105 | + | 0.461567i | \(0.152713\pi\) | ||||
−0.887105 | + | 0.461567i | \(0.847287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 607.696 | 1.26340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 187.682 | − | 187.682i | 0.388576 | − | 0.388576i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −100.083 | − | 100.083i | −0.205509 | − | 0.205509i | 0.596846 | − | 0.802355i | \(-0.296420\pi\) |
−0.802355 | + | 0.596846i | \(0.796420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 474.848i | − | 0.971059i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −286.788 | −0.584089 | −0.292045 | − | 0.956405i | \(-0.594336\pi\) | ||||
−0.292045 | + | 0.956405i | \(0.594336\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.7276 | − | 11.7276i | 0.0237881 | − | 0.0237881i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −44.4245 | − | 44.4245i | −0.0893853 | − | 0.0893853i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 82.3643i | − | 0.165059i | −0.996589 | − | 0.0825294i | \(-0.973700\pi\) | ||
0.996589 | − | 0.0825294i | \(-0.0262998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −410.697 | −0.819754 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −219.848 | + | 219.848i | −0.437073 | + | 0.437073i | −0.891026 | − | 0.453952i | \(-0.850014\pi\) |
0.453952 | + | 0.891026i | \(0.350014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.1872 | − | 37.1872i | −0.0733476 | − | 0.0733476i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 805.696i | − | 1.58290i | −0.611234 | − | 0.791450i | \(-0.709327\pi\) | ||
0.611234 | − | 0.791450i | \(-0.290673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −212.908 | −0.416650 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −123.810 | + | 123.810i | −0.241346 | + | 0.241346i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −288.817 | − | 288.817i | −0.558641 | − | 0.558641i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 183.303i | 0.353185i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 372.879 | 0.715698 | 0.357849 | − | 0.933779i | \(-0.383510\pi\) | ||||
0.357849 | + | 0.933779i | \(0.383510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −56.1395 | + | 56.1395i | −0.107341 | + | 0.107341i | −0.758738 | − | 0.651396i | \(-0.774184\pi\) |
0.651396 | + | 0.758738i | \(0.274184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −66.1975 | − | 66.1975i | −0.125612 | − | 0.125612i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0898i | 0.0266348i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 90.0000 | 0.169492 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −277.273 | + | 277.273i | −0.520213 | + | 0.520213i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 280.652 | + | 280.652i | 0.522629 | + | 0.522629i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 70.2429i | 0.130321i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 633.120 | 1.17028 | 0.585139 | − | 0.810933i | \(-0.301040\pi\) | ||||
0.585139 | + | 0.810933i | \(0.301040\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 165.563 | − | 165.563i | 0.304904 | − | 0.304904i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0408 | − | 32.0408i | −0.0585755 | − | 0.0585755i | 0.677212 | − | 0.735788i | \(-0.263188\pi\) |
−0.735788 | + | 0.677212i | \(0.763188\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 143.363i | 0.261135i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −293.060 | −0.531870 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −130.813 | + | 130.813i | −0.236551 | + | 0.236551i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 701.741 | + | 701.741i | 1.25986 | + | 1.25986i | 0.951160 | + | 0.308699i | \(0.0998936\pi\) |
0.308699 | + | 0.951160i | \(0.400106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 401.697i | 0.718599i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −68.3633 | −0.121860 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 265.621 | − | 265.621i | 0.471796 | − | 0.471796i | −0.430700 | − | 0.902495i | \(-0.641733\pi\) |
0.902495 | + | 0.430700i | \(0.141733\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.9773 | + | 42.9773i | 0.0757977 | + | 0.0757977i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 946.999i | − | 1.66432i | −0.554534 | − | 0.832161i | \(-0.687104\pi\) | ||
0.554534 | − | 0.832161i | \(-0.312896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 337.334 | 0.590777 | 0.295389 | − | 0.955377i | \(-0.404551\pi\) | ||||
0.295389 | + | 0.955377i | \(0.404551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.8332 | + | 26.8332i | −0.0468293 | + | 0.0468293i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −325.547 | − | 325.547i | −0.564207 | − | 0.564207i | 0.366293 | − | 0.930500i | \(-0.380627\pi\) |
−0.930500 | + | 0.366293i | \(0.880627\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 241.243i | − | 0.416654i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −605.878 | −1.04282 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1229.27 | + | 1229.27i | −2.10853 | + | 2.10853i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −381.514 | − | 381.514i | −0.649939 | − | 0.649939i | 0.303039 | − | 0.952978i | \(-0.401999\pi\) |
−0.952978 | + | 0.303039i | \(0.901999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1654.21i | 2.80851i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −155.394 | −0.262934 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 200.697 | − | 200.697i | 0.338443 | − | 0.338443i | −0.517338 | − | 0.855781i | \(-0.673077\pi\) |
0.855781 | + | 0.517338i | \(0.173077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −221.790 | − | 221.790i | −0.371508 | − | 0.371508i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 112.182i | 0.187282i | 0.995606 | + | 0.0936408i | \(0.0298505\pi\) | ||||
−0.995606 | + | 0.0936408i | \(0.970149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −59.5449 | −0.0990764 | −0.0495382 | − | 0.998772i | \(-0.515775\pi\) | ||||
−0.0495382 | + | 0.998772i | \(0.515775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −51.0681 | + | 51.0681i | −0.0846901 | + | 0.0846901i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 406.070 | + | 406.070i | 0.668979 | + | 0.668979i | 0.957480 | − | 0.288500i | \(-0.0931567\pi\) |
−0.288500 | + | 0.957480i | \(0.593157\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 101.728i | 0.167040i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −232.365 | −0.380303 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −81.7480 | + | 81.7480i | −0.133357 | + | 0.133357i | −0.770635 | − | 0.637277i | \(-0.780061\pi\) |
0.637277 | + | 0.770635i | \(0.280061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −734.636 | − | 734.636i | −1.19066 | − | 1.19066i | −0.976883 | − | 0.213775i | \(-0.931424\pi\) |
−0.213775 | − | 0.976883i | \(-0.568576\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 266.303i | 0.430215i | 0.976590 | + | 0.215107i | \(0.0690102\pi\) | ||||
−0.976590 | + | 0.215107i | \(0.930990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 117.909 | 0.189870 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 83.0602 | − | 83.0602i | 0.133323 | − | 0.133323i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 854.166 | + | 854.166i | 1.36231 | + | 1.36231i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 98.4245i | 0.156478i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −456.546 | −0.723528 | −0.361764 | − | 0.932270i | \(-0.617825\pi\) | ||||
−0.361764 | + | 0.932270i | \(0.617825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35.1839 | − | 35.1839i | 0.0555828 | − | 0.0555828i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2566 | + | 28.2566i | 0.0443589 | + | 0.0443589i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 27.9092i | − | 0.0436763i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 538.120 | 0.839501 | 0.419751 | − | 0.907639i | \(-0.362118\pi\) | ||||
0.419751 | + | 0.907639i | \(0.362118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.5459 | + | 31.5459i | −0.0490605 | + | 0.0490605i | −0.731211 | − | 0.682151i | \(-0.761045\pi\) |
0.682151 | + | 0.731211i | \(0.261045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 112.849 | + | 112.849i | 0.174419 | + | 0.174419i | 0.788918 | − | 0.614499i | \(-0.210642\pi\) |
−0.614499 | + | 0.788918i | \(0.710642\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 620.908i | − | 0.956715i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 574.212 | 0.882046 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 491.803 | − | 491.803i | 0.753143 | − | 0.753143i | −0.221921 | − | 0.975065i | \(-0.571233\pi\) |
0.975065 | + | 0.221921i | \(0.0712328\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −66.8786 | − | 66.8786i | −0.101794 | − | 0.101794i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 471.787i | − | 0.715913i | −0.933738 | − | 0.357957i | \(-0.883474\pi\) | ||
0.933738 | − | 0.357957i | \(-0.116526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −897.151 | −1.35726 | −0.678632 | − | 0.734479i | \(-0.737427\pi\) | ||||
−0.678632 | + | 0.734479i | \(0.737427\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.5005 | + | 27.5005i | −0.0414789 | + | 0.0414789i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 139.546 | + | 139.546i | 0.209214 | + | 0.209214i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 81.2724i | 0.121483i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 989.060 | 1.47401 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −105.526 | + | 105.526i | −0.156799 | + | 0.156799i | −0.781146 | − | 0.624348i | \(-0.785365\pi\) |
0.624348 | + | 0.781146i | \(0.285365\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −547.015 | − | 547.015i | −0.807998 | − | 0.807998i | 0.176332 | − | 0.984331i | \(-0.443577\pi\) |
−0.984331 | + | 0.176332i | \(0.943577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 399.940i | − | 0.589013i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −619.423 | −0.909579 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 533.271 | − | 533.271i | 0.780778 | − | 0.780778i | −0.199184 | − | 0.979962i | \(-0.563829\pi\) |
0.979962 | + | 0.199184i | \(0.0638292\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −336.805 | − | 336.805i | −0.490254 | − | 0.490254i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 988.999i | 1.43541i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1191.09 | 1.72372 | 0.861859 | − | 0.507147i | \(-0.169300\pi\) | ||||
0.861859 | + | 0.507147i | \(0.169300\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 296.499 | − | 296.499i | 0.427849 | − | 0.427849i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.9082 | − | 44.9082i | −0.0644306 | − | 0.0644306i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 548.091i | 0.784107i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 717.242 | 1.02317 | 0.511585 | − | 0.859233i | \(-0.329059\pi\) | ||||
0.511585 | + | 0.859233i | \(0.329059\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1229.77 | − | 1229.77i | 1.74931 | − | 1.74931i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −777.787 | − | 777.787i | −1.10012 | − | 1.10012i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 148.514i | − | 0.209470i | −0.994500 | − | 0.104735i | \(-0.966601\pi\) | ||
0.994500 | − | 0.104735i | \(-0.0333994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −82.1816 | −0.115586 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 787.682 | − | 787.682i | 1.10474 | − | 1.10474i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 374.363 | + | 374.363i | 0.522124 | + | 0.522124i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 43.4847i | − | 0.0604794i | −0.999543 | − | 0.0302397i | \(-0.990373\pi\) | ||
0.999543 | − | 0.0302397i | \(-0.00962706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −353.271 | −0.489974 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −204.532 | + | 204.532i | −0.282894 | + | 0.282894i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −817.608 | − | 817.608i | −1.12463 | − | 1.12463i | −0.991036 | − | 0.133598i | \(-0.957347\pi\) |
−0.133598 | − | 0.991036i | \(-0.542653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −65.0602 | −0.0890016 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 842.030 | − | 842.030i | 1.14874 | − | 1.14874i | 0.161944 | − | 0.986800i | \(-0.448223\pi\) |
0.986800 | − | 0.161944i | \(-0.0517765\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 352.318 | + | 352.318i | 0.478043 | + | 0.478043i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 406.545i | 0.550128i | 0.961426 | + | 0.275064i | \(0.0886991\pi\) | ||||
−0.961426 | + | 0.275064i | \(0.911301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 687.211 | 0.927411 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 394.515 | − | 394.515i | 0.530976 | − | 0.530976i | −0.389887 | − | 0.920863i | \(-0.627486\pi\) |
0.920863 | + | 0.389887i | \(0.127486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −190.318 | − | 190.318i | −0.254776 | − | 0.254776i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1280.64i | 1.70979i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 612.788 | 0.815962 | 0.407981 | − | 0.912990i | \(-0.366233\pi\) | ||||
0.407981 | + | 0.912990i | \(0.366233\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 320.363 | − | 320.363i | 0.425449 | − | 0.425449i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 181.547 | + | 181.547i | 0.239825 | + | 0.239825i | 0.816777 | − | 0.576953i | \(-0.195758\pi\) |
−0.576953 | + | 0.816777i | \(0.695758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 813.453i | − | 1.07174i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 497.271 | 0.653445 | 0.326722 | − | 0.945120i | \(-0.394056\pi\) | ||||
0.326722 | + | 0.945120i | \(0.394056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 692.412 | − | 692.412i | 0.907486 | − | 0.907486i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −249.773 | − | 249.773i | −0.325649 | − | 0.325649i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 220.271i | − | 0.286439i | −0.989691 | − | 0.143219i | \(-0.954255\pi\) | ||
0.989691 | − | 0.143219i | \(-0.0457455\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −231.514 | −0.300278 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −917.605 | + | 917.605i | −1.18707 | + | 1.18707i | −0.209196 | + | 0.977874i | \(0.567085\pi\) |
−0.977874 | + | 0.209196i | \(0.932915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −426.879 | − | 426.879i | −0.549393 | − | 0.549393i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1122.21i | 1.44058i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −192.545 | −0.246536 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.9546 | + | 31.9546i | −0.0408105 | + | 0.0408105i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 862.194 | + | 862.194i | 1.09555 | + | 1.09555i | 0.994925 | + | 0.100620i | \(0.0320828\pi\) |
0.100620 | + | 0.994925i | \(0.467917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 83.7276i | − | 0.106119i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 126.184 | 0.159524 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 397.870 | − | 397.870i | 0.501727 | − | 0.501727i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 175.818 | + | 175.818i | 0.220600 | + | 0.220600i | 0.808751 | − | 0.588151i | \(-0.200144\pi\) |
−0.588151 | + | 0.808751i | \(0.700144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 37.6347i | − | 0.0471022i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 52.1816 | 0.0651456 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −461.394 | + | 461.394i | −0.574588 | + | 0.574588i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −477.167 | − | 477.167i | −0.591285 | − | 0.591285i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 828.272i | 1.02382i | 0.859038 | + | 0.511911i | \(0.171062\pi\) | ||||
−0.859038 | + | 0.511911i | \(0.828938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 116.909 | 0.144154 | 0.0720772 | − | 0.997399i | \(-0.477037\pi\) | ||||
0.0720772 | + | 0.997399i | \(0.477037\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 192.025 | − | 192.025i | 0.236193 | − | 0.236193i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 812.896 | + | 812.896i | 0.994976 | + | 0.994976i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 238.546i | − | 0.291265i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 632.424 | 0.770310 | 0.385155 | − | 0.922852i | \(-0.374148\pi\) | ||||
0.385155 | + | 0.922852i | \(0.374148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1028.81 | − | 1028.81i | 1.25007 | − | 1.25007i | 0.294385 | − | 0.955687i | \(-0.404885\pi\) |
0.955687 | − | 0.294385i | \(-0.0951149\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 348.061 | + | 348.061i | 0.420872 | + | 0.420872i | 0.885504 | − | 0.464632i | \(-0.153813\pi\) |
−0.464632 | + | 0.885504i | \(0.653813\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 901.392i | − | 1.08732i | −0.839304 | − | 0.543662i | \(-0.817037\pi\) | ||
0.839304 | − | 0.543662i | \(-0.182963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −699.545 | −0.841811 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.57654 | + | 4.57654i | −0.00549404 | + | 0.00549404i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 180.371 | + | 180.371i | 0.215497 | + | 0.215497i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 99.1806i | 0.118213i | 0.998252 | + | 0.0591064i | \(0.0188251\pi\) | ||||
−0.998252 | + | 0.0591064i | \(0.981175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 765.363 | 0.910063 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.6811 | − | 24.6811i | 0.0292777 | − | 0.0292777i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1467.74 | − | 1467.74i | −1.73287 | − | 1.73287i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 417.817i | 0.492129i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1171.15 | −1.37621 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 662.612 | − | 662.612i | 0.776802 | − | 0.776802i | −0.202484 | − | 0.979286i | \(-0.564901\pi\) |
0.979286 | + | 0.202484i | \(0.0649013\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 487.546 | + | 487.546i | 0.568898 | + | 0.568898i | 0.931820 | − | 0.362921i | \(-0.118221\pi\) |
−0.362921 | + | 0.931820i | \(0.618221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 110.849i | − | 0.129044i | −0.997916 | − | 0.0645221i | \(-0.979448\pi\) | ||
0.997916 | − | 0.0645221i | \(-0.0205523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 389.544 | 0.452432 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −917.271 | + | 917.271i | −1.06289 | + | 1.06289i | −0.0650018 | + | 0.997885i | \(0.520705\pi\) |
−0.997885 | + | 0.0650018i | \(0.979295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 349.497 | + | 349.497i | 0.403111 | + | 0.403111i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 566.969i | 0.652439i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 283.454 | 0.325435 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 125.629 | − | 125.629i | 0.143905 | − | 0.143905i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.7538 | − | 53.7538i | −0.0612928 | − | 0.0612928i | 0.675796 | − | 0.737089i | \(-0.263800\pi\) |
−0.737089 | + | 0.675796i | \(0.763800\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 635.939i | 0.723480i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 648.545 | 0.736146 | 0.368073 | − | 0.929797i | \(-0.380018\pi\) | ||||
0.368073 | + | 0.929797i | \(0.380018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −191.381 | + | 191.381i | −0.216740 | + | 0.216740i | −0.807123 | − | 0.590383i | \(-0.798977\pi\) |
0.590383 | + | 0.807123i | \(0.298977\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 468.347 | + | 468.347i | 0.528013 | + | 0.528013i | 0.919979 | − | 0.391967i | \(-0.128205\pi\) |
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 484.182i | − | 0.544636i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 186.272 | 0.209060 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −470.227 | + | 470.227i | −0.526570 | + | 0.526570i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −327.228 | − | 327.228i | −0.364803 | − | 0.364803i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 426.940i | 0.474905i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −160.182 | −0.177782 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 282.174 | − | 282.174i | 0.312485 | − | 0.312485i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 359.160 | + | 359.160i | 0.395987 | + | 0.395987i | 0.876815 | − | 0.480828i | \(-0.159664\pi\) |
−0.480828 | + | 0.876815i | \(0.659664\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 488.636i | − | 0.537553i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1698.00 | 1.86389 | 0.931943 | − | 0.362605i | \(-0.118113\pi\) | ||||
0.931943 | + | 0.362605i | \(0.118113\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1313.00 | + | 1313.00i | −1.43811 | + | 1.43811i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −746.241 | − | 746.241i | −0.813785 | − | 0.813785i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 316.728i | − | 0.344644i | −0.985041 | − | 0.172322i | \(-0.944873\pi\) | ||
0.985041 | − | 0.172322i | \(-0.0551269\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 291.272 | 0.316257 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −77.4551 | + | 77.4551i | −0.0839167 | + | 0.0839167i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −110.969 | − | 110.969i | −0.119708 | − | 0.119708i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 123.426i | − | 0.132858i | −0.997791 | − | 0.0664292i | \(-0.978839\pi\) | ||
0.997791 | − | 0.0664292i | \(-0.0211607\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 114.363 | 0.122839 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −64.6515 | + | 64.6515i | −0.0692942 | + | 0.0692942i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −261.513 | − | 261.513i | −0.279096 | − | 0.279096i | 0.553652 | − | 0.832748i | \(-0.313234\pi\) |
−0.832748 | + | 0.553652i | \(0.813234\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 584.333i | − | 0.622292i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −942.422 | −1.00151 | −0.500756 | − | 0.865589i | \(-0.666945\pi\) | ||||
−0.500756 | + | 0.865589i | \(0.666945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 534.361 | − | 534.361i | 0.566661 | − | 0.566661i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −986.983 | − | 986.983i | −1.04222 | − | 1.04222i | −0.999069 | − | 0.0431523i | \(-0.986260\pi\) |
−0.0431523 | − | 0.999069i | \(-0.513740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 371.210i | 0.391159i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 119.878 | 0.126054 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 112.454 | − | 112.454i | 0.118000 | − | 0.118000i | −0.645641 | − | 0.763641i | \(-0.723410\pi\) |
0.763641 | + | 0.645641i | \(0.223410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 220.454 | + | 220.454i | 0.230360 | + | 0.230360i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 872.424i | 0.909723i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1448.91 | 1.50771 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −402.272 | + | 402.272i | −0.417728 | + | 0.417728i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 700.009 | + | 700.009i | 0.723898 | + | 0.723898i | 0.969397 | − | 0.245499i | \(-0.0789518\pi\) |
−0.245499 | + | 0.969397i | \(0.578952\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 111.303i | 0.114864i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1450.18 | 1.49349 | 0.746746 | − | 0.665109i | \(-0.231615\pi\) | ||||
0.746746 | + | 0.665109i | \(0.231615\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 168.147 | − | 168.147i | 0.172813 | − | 0.172813i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1146.14 | − | 1146.14i | −1.17312 | − | 1.17312i | −0.981462 | − | 0.191656i | \(-0.938614\pi\) |
−0.191656 | − | 0.981462i | \(-0.561386\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 360.000i | − | 0.367722i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 435.000 | 0.443425 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −760.332 | + | 760.332i | −0.773481 | + | 0.773481i | −0.978713 | − | 0.205232i | \(-0.934205\pi\) |
0.205232 | + | 0.978713i | \(0.434205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 163.226 | + | 163.226i | 0.165376 | + | 0.165376i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 774.150i | − | 0.782760i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 222.605 | 0.224627 | 0.112313 | − | 0.993673i | \(-0.464174\pi\) | ||||
0.112313 | + | 0.993673i | \(0.464174\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −357.551 | + | 357.551i | −0.360071 | + | 0.360071i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −467.183 | − | 467.183i | −0.468588 | − | 0.468588i | 0.432869 | − | 0.901457i | \(-0.357501\pi\) |
−0.901457 | + | 0.432869i | \(0.857501\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 268.182i | − | 0.268450i |
(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 | 1200.3.bg.a.1057.1 | 4 | ||
4.3 | odd | 2 | 150.3.f.c.7.2 | yes | 4 | ||
5.2 | odd | 4 | 1200.3.bg.p.193.2 | 4 | |||
5.3 | odd | 4 | inner | 1200.3.bg.a.193.1 | 4 | ||
5.4 | even | 2 | 1200.3.bg.p.1057.2 | 4 | |||
12.11 | even | 2 | 450.3.g.g.307.1 | 4 | |||
20.3 | even | 4 | 150.3.f.c.43.2 | yes | 4 | ||
20.7 | even | 4 | 150.3.f.a.43.1 | yes | 4 | ||
20.19 | odd | 2 | 150.3.f.a.7.1 | ✓ | 4 | ||
60.23 | odd | 4 | 450.3.g.g.343.1 | 4 | |||
60.47 | odd | 4 | 450.3.g.h.343.2 | 4 | |||
60.59 | even | 2 | 450.3.g.h.307.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.3.f.a.7.1 | ✓ | 4 | 20.19 | odd | 2 | ||
150.3.f.a.43.1 | yes | 4 | 20.7 | even | 4 | ||
150.3.f.c.7.2 | yes | 4 | 4.3 | odd | 2 | ||
150.3.f.c.43.2 | yes | 4 | 20.3 | even | 4 | ||
450.3.g.g.307.1 | 4 | 12.11 | even | 2 | |||
450.3.g.g.343.1 | 4 | 60.23 | odd | 4 | |||
450.3.g.h.307.2 | 4 | 60.59 | even | 2 | |||
450.3.g.h.343.2 | 4 | 60.47 | odd | 4 | |||
1200.3.bg.a.193.1 | 4 | 5.3 | odd | 4 | inner | ||
1200.3.bg.a.1057.1 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.p.193.2 | 4 | 5.2 | odd | 4 | |||
1200.3.bg.p.1057.2 | 4 | 5.4 | even | 2 |