Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(145,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.y (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 34x^{6} + 921x^{4} - 7990x^{2} + 55225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(2.69047 + 1.55335i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.145 |
Dual form | 684.3.y.g.217.2 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.19676 | − | 3.80490i | −0.439352 | − | 0.760981i | 0.558287 | − | 0.829648i | \(-0.311459\pi\) |
−0.997640 | + | 0.0686670i | \(0.978125\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.44949 | 0.207070 | 0.103535 | − | 0.994626i | \(-0.466985\pi\) | ||||
0.103535 | + | 0.994626i | \(0.466985\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.1554 | 1.37777 | 0.688883 | − | 0.724873i | \(-0.258102\pi\) | ||||
0.688883 | + | 0.724873i | \(0.258102\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.8485 | − | 8.57277i | −1.14219 | − | 0.659444i | −0.195218 | − | 0.980760i | \(-0.562541\pi\) |
−0.946972 | + | 0.321316i | \(0.895875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.77447 | + | 16.9299i | 0.574969 | + | 0.995875i | 0.996045 | + | 0.0888501i | \(0.0283192\pi\) |
−0.421076 | + | 0.907025i | \(0.638347\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.34847 | − | 18.7026i | −0.176235 | − | 0.984348i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.19676 | + | 3.80490i | −0.0955114 | + | 0.165431i | −0.909822 | − | 0.414999i | \(-0.863782\pi\) |
0.814311 | + | 0.580429i | \(0.197115\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.84847 | − | 4.93369i | 0.113939 | − | 0.197348i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.3234 | − | 16.9299i | −1.01115 | − | 0.583789i | −0.0996235 | − | 0.995025i | \(-0.531764\pi\) |
−0.911529 | + | 0.411236i | \(0.865097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.62475i | − | 0.181443i | −0.995876 | − | 0.0907217i | \(-0.971083\pi\) | ||
0.995876 | − | 0.0907217i | \(-0.0289174\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.18418 | − | 5.51517i | −0.0909767 | − | 0.157576i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 23.7238i | − | 0.641184i | −0.947217 | − | 0.320592i | \(-0.896118\pi\) | ||
0.947217 | − | 0.320592i | \(-0.103882\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −32.2857 | + | 18.6401i | −0.787456 | + | 0.454638i | −0.839066 | − | 0.544030i | \(-0.816898\pi\) |
0.0516104 | + | 0.998667i | \(0.483565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15.9722 | − | 27.6647i | −0.371446 | − | 0.643364i | 0.618342 | − | 0.785909i | \(-0.287805\pi\) |
−0.989788 | + | 0.142545i | \(0.954471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.0979 | − | 67.7195i | 0.831870 | − | 1.44084i | −0.0646836 | − | 0.997906i | \(-0.520604\pi\) |
0.896554 | − | 0.442935i | \(-0.146063\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −46.8990 | −0.957122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.55255 | − | 5.51517i | −0.180237 | − | 0.104060i | 0.407167 | − | 0.913354i | \(-0.366517\pi\) |
−0.587404 | + | 0.809294i | \(0.699850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −33.2929 | − | 57.6649i | −0.605325 | − | 1.04845i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −78.4177 | + | 45.2745i | −1.32911 | + | 0.767364i | −0.985163 | − | 0.171624i | \(-0.945099\pi\) |
−0.343951 | + | 0.938988i | \(0.611765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.1413 | − | 98.9717i | 0.936743 | − | 1.62249i | 0.165247 | − | 0.986252i | \(-0.447158\pi\) |
0.771496 | − | 0.636234i | \(-0.219509\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 75.3293i | 1.15891i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −98.3105 | − | 56.7596i | −1.46732 | − | 0.847158i | −0.467989 | − | 0.883734i | \(-0.655021\pi\) |
−0.999331 | + | 0.0365763i | \(0.988355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 87.9702 | − | 50.7896i | 1.23902 | − | 0.715347i | 0.270124 | − | 0.962825i | \(-0.412935\pi\) |
0.968893 | + | 0.247478i | \(0.0796019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0505 | + | 17.4080i | 0.137678 | + | 0.238466i | 0.926617 | − | 0.376006i | \(-0.122703\pi\) |
−0.788939 | + | 0.614471i | \(0.789369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.9676 | 0.285294 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −45.8258 | + | 26.4575i | −0.580073 | + | 0.334905i | −0.761162 | − | 0.648561i | \(-0.775371\pi\) |
0.181089 | + | 0.983467i | \(0.442038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −29.2237 | −0.352092 | −0.176046 | − | 0.984382i | \(-0.556331\pi\) | ||||
−0.176046 | + | 0.984382i | \(0.556331\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 42.9444 | − | 74.3819i | 0.505228 | − | 0.875081i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 126.846 | + | 73.2347i | 1.42524 | + | 0.822862i | 0.996740 | − | 0.0806807i | \(-0.0257094\pi\) |
0.428498 | + | 0.903543i | \(0.359043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.5227 | − | 12.4261i | −0.236513 | − | 0.136551i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −63.8059 | + | 53.8258i | −0.671641 | + | 0.566587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 27.0000 | − | 15.5885i | 0.278351 | − | 0.160706i | −0.354326 | − | 0.935122i | \(-0.615290\pi\) |
0.632676 | + | 0.774416i | \(0.281956\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66.0026 | − | 114.320i | 0.653491 | − | 1.13188i | −0.328778 | − | 0.944407i | \(-0.606637\pi\) |
0.982270 | − | 0.187473i | \(-0.0600297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41.3156i | 0.401122i | 0.979681 | + | 0.200561i | \(0.0642765\pi\) | ||||
−0.979681 | + | 0.200561i | \(0.935723\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 33.8598i | − | 0.316446i | −0.987403 | − | 0.158223i | \(-0.949423\pi\) | ||
0.987403 | − | 0.158223i | \(-0.0505766\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −30.3031 | + | 17.4955i | −0.278010 | + | 0.160509i | −0.632522 | − | 0.774542i | \(-0.717980\pi\) |
0.354512 | + | 0.935051i | \(0.384647\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 163.227i | − | 1.44448i | −0.691641 | − | 0.722241i | \(-0.743112\pi\) | ||
0.691641 | − | 0.722241i | \(-0.256888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.3031 | 0.167853 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.1680 | + | 24.5397i | 0.119059 | + | 0.206216i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 108.687 | 0.898237 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −134.868 | −1.07894 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −135.576 | − | 78.2746i | −1.06752 | − | 0.616335i | −0.140020 | − | 0.990149i | \(-0.544717\pi\) |
−0.927504 | + | 0.373814i | \(0.878050\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 107.963 | + | 186.997i | 0.824145 | + | 1.42746i | 0.902571 | + | 0.430541i | \(0.141677\pi\) |
−0.0784255 | + | 0.996920i | \(0.524989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.85357 | − | 27.1092i | −0.0364930 | − | 0.203829i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −29.7673 | + | 51.5584i | −0.217279 | + | 0.376339i | −0.953975 | − | 0.299885i | \(-0.903052\pi\) |
0.736696 | + | 0.676224i | \(0.236385\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.82577 | + | 3.16232i | −0.0131350 | + | 0.0227505i | −0.872518 | − | 0.488582i | \(-0.837514\pi\) |
0.859383 | + | 0.511332i | \(0.170848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −225.035 | − | 129.924i | −1.57367 | − | 0.908559i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 148.764i | 1.02596i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 29.0017 | + | 50.2325i | 0.194643 | + | 0.337131i | 0.946783 | − | 0.321872i | \(-0.104312\pi\) |
−0.752141 | + | 0.659003i | \(0.770979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.64258i | 0.0572356i | 0.999590 | + | 0.0286178i | \(0.00911058\pi\) | ||||
−0.999590 | + | 0.0286178i | \(0.990889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.4016 | + | 12.3562i | −0.138075 | + | 0.0797176i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60.0301 | + | 103.975i | 0.382357 | + | 0.662262i | 0.991399 | − | 0.130876i | \(-0.0417790\pi\) |
−0.609041 | + | 0.793138i | \(0.708446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.18418 | + | 5.51517i | −0.0197775 | + | 0.0342557i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −51.8332 | −0.317995 | −0.158997 | − | 0.987279i | \(-0.550826\pi\) | ||||
−0.158997 | + | 0.987279i | \(0.550826\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 125.215 | + | 72.2932i | 0.749793 | + | 0.432893i | 0.825619 | − | 0.564228i | \(-0.190826\pi\) |
−0.0758260 | + | 0.997121i | \(0.524159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 62.4847 | + | 108.227i | 0.369732 | + | 0.640394i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −57.0161 | + | 32.9182i | −0.329573 | + | 0.190279i | −0.655651 | − | 0.755064i | \(-0.727606\pi\) |
0.326079 | + | 0.945343i | \(0.394273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.12883 | − | 7.15134i | 0.0235933 | − | 0.0408648i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 60.1097i | − | 0.335808i | −0.985803 | − | 0.167904i | \(-0.946300\pi\) | ||
0.985803 | − | 0.167904i | \(-0.0536999\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 218.530 | + | 126.168i | 1.20735 | + | 0.697063i | 0.962179 | − | 0.272417i | \(-0.0878231\pi\) |
0.245169 | + | 0.969480i | \(0.421156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −90.2668 | + | 52.1155i | −0.487928 | + | 0.281706i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 148.136 | + | 256.579i | 0.792172 | + | 1.37208i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 211.533 | 1.10750 | 0.553750 | − | 0.832683i | \(-0.313196\pi\) | ||||
0.553750 | + | 0.832683i | \(0.313196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 48.4546 | − | 27.9753i | 0.251060 | − | 0.144950i | −0.369189 | − | 0.929354i | \(-0.620365\pi\) |
0.620250 | + | 0.784405i | \(0.287031\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −95.1265 | −0.482876 | −0.241438 | − | 0.970416i | \(-0.577619\pi\) | ||||
−0.241438 | + | 0.970416i | \(0.577619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −40.4115 | + | 69.9947i | −0.203073 | + | 0.351732i | −0.949517 | − | 0.313716i | \(-0.898426\pi\) |
0.746444 | + | 0.665448i | \(0.231759\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −42.5040 | − | 24.5397i | −0.209379 | − | 0.120885i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 141.848 | + | 81.8960i | 0.691941 | + | 0.399492i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −50.7475 | − | 283.446i | −0.242811 | − | 1.35620i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −46.0982 | + | 26.6148i | −0.218475 | + | 0.126137i | −0.605244 | − | 0.796040i | \(-0.706924\pi\) |
0.386769 | + | 0.922177i | \(0.373591\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −70.1742 | + | 121.545i | −0.326392 | + | 0.565327i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.15301i | − | 0.0375715i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 335.177i | − | 1.51664i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −171.356 | + | 98.9324i | −0.768412 | + | 0.443643i | −0.832308 | − | 0.554314i | \(-0.812981\pi\) |
0.0638959 | + | 0.997957i | \(0.479647\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 125.946i | − | 0.554829i | −0.960750 | − | 0.277415i | \(-0.910522\pi\) | ||
0.960750 | − | 0.277415i | \(-0.0894775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 193.586 | 0.845352 | 0.422676 | − | 0.906281i | \(-0.361091\pi\) | ||||
0.422676 | + | 0.906281i | \(0.361091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 148.592 | + | 257.369i | 0.637734 | + | 1.10459i | 0.985929 | + | 0.167165i | \(0.0534613\pi\) |
−0.348195 | + | 0.937422i | \(0.613205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −343.555 | −1.46194 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −104.801 | −0.438499 | −0.219250 | − | 0.975669i | \(-0.570361\pi\) | ||||
−0.219250 | + | 0.975669i | \(0.570361\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 356.787 | + | 205.991i | 1.48044 | + | 0.854735i | 0.999755 | − | 0.0221551i | \(-0.00705275\pi\) |
0.480690 | + | 0.876890i | \(0.340386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 103.026 | + | 178.446i | 0.420514 | + | 0.728352i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −110.614 | + | 306.411i | −0.447828 | + | 1.24053i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −87.8705 | + | 152.196i | −0.350082 | + | 0.606359i | −0.986263 | − | 0.165180i | \(-0.947180\pi\) |
0.636182 | + | 0.771539i | \(0.280513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.2929 | + | 57.6649i | −0.131592 | + | 0.227925i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 373.283 | + | 215.515i | 1.45246 | + | 0.838579i | 0.998621 | − | 0.0525037i | \(-0.0167201\pi\) |
0.453841 | + | 0.891083i | \(0.350053\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 34.3874i | − | 0.132770i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 60.0781 | + | 104.058i | 0.228434 | + | 0.395659i | 0.957344 | − | 0.288950i | \(-0.0933062\pi\) |
−0.728910 | + | 0.684609i | \(0.759973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.4621i | 0.182876i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 415.487 | − | 239.882i | 1.54456 | − | 0.891754i | 0.546021 | − | 0.837772i | \(-0.316142\pi\) |
0.998542 | − | 0.0539820i | \(-0.0171914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −63.0908 | − | 109.276i | −0.232807 | − | 0.403234i | 0.725826 | − | 0.687879i | \(-0.241458\pi\) |
−0.958633 | + | 0.284644i | \(0.908125\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 43.1697 | − | 74.7722i | 0.156981 | − | 0.271899i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 459.918 | 1.66036 | 0.830178 | − | 0.557499i | \(-0.188239\pi\) | ||||
0.830178 | + | 0.557499i | \(0.188239\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 65.2371 | + | 37.6647i | 0.232161 | + | 0.134038i | 0.611568 | − | 0.791192i | \(-0.290539\pi\) |
−0.379408 | + | 0.925230i | \(0.623872\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 178.753 | + | 309.609i | 0.631634 | + | 1.09402i | 0.987218 | + | 0.159378i | \(0.0509490\pi\) |
−0.355583 | + | 0.934645i | \(0.615718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −46.7978 | + | 27.0187i | −0.163058 | + | 0.0941418i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −46.5806 | + | 80.6800i | −0.161179 | + | 0.279169i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 228.294i | 0.779161i | 0.920992 | + | 0.389581i | \(0.127380\pi\) | ||||
−0.920992 | + | 0.389581i | \(0.872620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 344.530 | + | 198.915i | 1.16790 | + | 0.674287i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 65.2371 | − | 37.6647i | 0.218184 | − | 0.125969i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.1515 | − | 40.0996i | −0.0769154 | − | 0.133221i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −502.104 | −1.64624 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −83.6969 | + | 48.3224i | −0.272628 | + | 0.157402i | −0.630082 | − | 0.776529i | \(-0.716979\pi\) |
0.357453 | + | 0.933931i | \(0.383645\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −414.722 | −1.33351 | −0.666755 | − | 0.745277i | \(-0.732317\pi\) | ||||
−0.666755 | + | 0.745277i | \(0.732317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 164.000 | − | 284.056i | 0.523962 | − | 0.907528i | −0.475649 | − | 0.879635i | \(-0.657787\pi\) |
0.999611 | − | 0.0278932i | \(-0.00887983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −461.253 | − | 266.304i | −1.45506 | − | 0.840077i | −0.456295 | − | 0.889829i | \(-0.650824\pi\) |
−0.998762 | + | 0.0497515i | \(0.984157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −444.409 | − | 256.579i | −1.39313 | − | 0.804324i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 283.904 | − | 239.497i | 0.878958 | − | 0.741478i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −84.5908 | + | 48.8385i | −0.260279 | + | 0.150272i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 56.6720 | − | 98.1588i | 0.172255 | − | 0.298355i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 138.310i | − | 0.417856i | −0.977931 | − | 0.208928i | \(-0.933003\pi\) | ||
0.977931 | − | 0.208928i | \(-0.0669975\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 498.749i | 1.48880i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −200.409 | + | 115.706i | −0.594686 | + | 0.343342i | −0.766948 | − | 0.641709i | \(-0.778226\pi\) |
0.172262 | + | 0.985051i | \(0.444892\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 85.2454i | − | 0.249986i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −139.005 | −0.405261 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −291.137 | − | 504.264i | −0.839012 | − | 1.45321i | −0.890722 | − | 0.454549i | \(-0.849800\pi\) |
0.0517097 | − | 0.998662i | \(-0.483533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 160.444 | 0.459725 | 0.229862 | − | 0.973223i | \(-0.426172\pi\) | ||||
0.229862 | + | 0.973223i | \(0.426172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −162.959 | −0.461641 | −0.230821 | − | 0.972996i | \(-0.574141\pi\) | ||||
−0.230821 | + | 0.972996i | \(0.574141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −386.499 | − | 223.146i | −1.08873 | − | 0.628579i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −130.674 | − | 226.334i | −0.363994 | − | 0.630456i | 0.624620 | − | 0.780928i | \(-0.285254\pi\) |
−0.988614 | + | 0.150473i | \(0.951920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −338.576 | + | 125.250i | −0.937882 | + | 0.346954i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.1572 | − | 76.4825i | 0.120979 | − | 0.209541i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 229.750 | − | 397.938i | 0.626021 | − | 1.08430i | −0.362321 | − | 0.932053i | \(-0.618016\pi\) |
0.988342 | − | 0.152247i | \(-0.0486510\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8463 | − | 7.99418i | −0.0373216 | − | 0.0215477i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 48.6194i | − | 0.130347i | −0.997874 | − | 0.0651734i | \(-0.979240\pi\) | ||
0.997874 | − | 0.0651734i | \(-0.0207601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 290.272 | + | 502.766i | 0.769952 | + | 1.33360i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 523.962i | − | 1.38249i | −0.722622 | − | 0.691243i | \(-0.757063\pi\) | ||
0.722622 | − | 0.691243i | \(-0.242937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 339.665 | − | 196.106i | 0.886855 | − | 0.512026i | 0.0139424 | − | 0.999903i | \(-0.495562\pi\) |
0.872912 | + | 0.487877i | \(0.162229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −48.2577 | − | 83.5847i | −0.125345 | − | 0.217103i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −266.108 | + | 460.912i | −0.684081 | + | 1.18486i | 0.289644 | + | 0.957135i | \(0.406463\pi\) |
−0.973725 | + | 0.227729i | \(0.926870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −85.8888 | −0.219664 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 201.337 | + | 116.242i | 0.509713 | + | 0.294283i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −62.3332 | − | 107.964i | −0.157010 | − | 0.271950i | 0.776779 | − | 0.629774i | \(-0.216852\pi\) |
−0.933789 | + | 0.357823i | \(0.883519\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −174.975 | + | 101.022i | −0.436348 | + | 0.251926i | −0.702047 | − | 0.712130i | \(-0.747730\pi\) |
0.265699 | + | 0.964056i | \(0.414397\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.2196 | + | 83.5189i | −0.119652 | + | 0.207243i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 359.544i | − | 0.883401i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 473.091 | + | 273.139i | 1.15670 | + | 0.667822i | 0.950511 | − | 0.310690i | \(-0.100560\pi\) |
0.206190 | + | 0.978512i | \(0.433893\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −113.666 | + | 65.6249i | −0.275219 | + | 0.158898i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 64.1975 | + | 111.193i | 0.154693 | + | 0.267936i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 529.552 | 1.26385 | 0.631924 | − | 0.775031i | \(-0.282266\pi\) | ||||
0.631924 | + | 0.775031i | \(0.282266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 225.681 | − | 130.297i | 0.536060 | − | 0.309494i | −0.207421 | − | 0.978252i | \(-0.566507\pi\) |
0.743480 | + | 0.668758i | \(0.233174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 111.369 | 0.262045 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 82.8258 | − | 143.458i | 0.193971 | − | 0.335968i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 208.226 | + | 120.219i | 0.483123 | + | 0.278931i | 0.721717 | − | 0.692188i | \(-0.243353\pi\) |
−0.238594 | + | 0.971119i | \(0.576686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −715.847 | − | 413.295i | −1.65323 | − | 0.954491i | −0.975733 | − | 0.218963i | \(-0.929733\pi\) |
−0.677494 | − | 0.735528i | \(-0.736934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 78.5174 | + | 28.3446i | 0.179674 | + | 0.0648618i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 516.901 | − | 298.433i | 1.17745 | − | 0.679801i | 0.222027 | − | 0.975040i | \(-0.428733\pi\) |
0.955423 | + | 0.295239i | \(0.0953993\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −259.517 | + | 449.497i | −0.585818 | + | 1.01467i | 0.408955 | + | 0.912554i | \(0.365893\pi\) |
−0.994773 | + | 0.102112i | \(0.967440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 643.517i | − | 1.44611i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 50.6169i | − | 0.112732i | −0.998410 | − | 0.0563662i | \(-0.982049\pi\) | ||
0.998410 | − | 0.0563662i | \(-0.0179514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −489.303 | + | 282.499i | −1.08493 | + | 0.626384i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 109.189i | 0.239976i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 219.788 | 0.480936 | 0.240468 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240468 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.1770 | − | 40.1437i | −0.0502754 | − | 0.0870796i | 0.839793 | − | 0.542907i | \(-0.182677\pi\) |
−0.890068 | + | 0.455828i | \(0.849343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −678.308 | −1.46503 | −0.732514 | − | 0.680752i | \(-0.761653\pi\) | ||||
−0.732514 | + | 0.680752i | \(0.761653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 687.475 | 1.47211 | 0.736054 | − | 0.676923i | \(-0.236687\pi\) | ||||
0.736054 | + | 0.676923i | \(0.236687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −142.500 | − | 82.2724i | −0.303838 | − | 0.175421i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −242.065 | − | 419.269i | −0.511766 | − | 0.886405i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −101.811 | − | 36.7535i | −0.214339 | − | 0.0773758i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −194.946 | + | 337.656i | −0.406985 | + | 0.704919i | −0.994550 | − | 0.104258i | \(-0.966753\pi\) |
0.587565 | + | 0.809177i | \(0.300087\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −203.379 | + | 352.262i | −0.422824 | + | 0.732353i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −118.625 | − | 68.4883i | −0.244588 | − | 0.141213i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 179.520i | − | 0.368624i | −0.982868 | − | 0.184312i | \(-0.940994\pi\) | ||
0.982868 | − | 0.184312i | \(-0.0590057\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −253.593 | − | 439.235i | −0.516482 | − | 0.894573i | −0.999817 | − | 0.0191376i | \(-0.993908\pi\) |
0.483335 | − | 0.875436i | \(-0.339425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 661.923i | − | 1.34264i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 127.512 | − | 73.6191i | 0.256563 | − | 0.148127i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −359.729 | − | 623.069i | −0.720900 | − | 1.24864i | −0.960639 | − | 0.277799i | \(-0.910395\pi\) |
0.239739 | − | 0.970837i | \(-0.422938\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 315.102 | − | 545.773i | 0.626445 | − | 1.08504i | −0.361814 | − | 0.932250i | \(-0.617842\pi\) |
0.988259 | − | 0.152785i | \(-0.0488242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −579.968 | −1.14845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −83.0780 | − | 47.9651i | −0.163218 | − | 0.0942340i | 0.416166 | − | 0.909289i | \(-0.363374\pi\) |
−0.579384 | + | 0.815055i | \(0.696707\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5681 | + | 25.2327i | 0.0285090 | + | 0.0493791i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 157.202 | − | 90.7606i | 0.305246 | − | 0.176234i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 592.545 | − | 1026.32i | 1.14612 | − | 1.98514i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 253.352i | − | 0.486281i | −0.969991 | − | 0.243140i | \(-0.921822\pi\) | ||
0.969991 | − | 0.243140i | \(-0.0781776\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −406.309 | − | 234.583i | −0.776882 | − | 0.448533i | 0.0584420 | − | 0.998291i | \(-0.481387\pi\) |
−0.835324 | + | 0.549758i | \(0.814720\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 95.2263 | − | 54.9789i | 0.180695 | − | 0.104324i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 254.848 | + | 441.410i | 0.481755 | + | 0.834424i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 639.191 | 1.19923 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −128.833 | + | 74.3819i | −0.240810 | + | 0.139032i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −710.774 | −1.31869 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 461.257 | − | 798.921i | 0.852601 | − | 1.47675i | −0.0262519 | − | 0.999655i | \(-0.508357\pi\) |
0.878853 | − | 0.477093i | \(-0.158309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 133.137 | + | 76.8668i | 0.244289 | + | 0.141040i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 159.901 | + | 92.3187i | 0.292323 | + | 0.168773i | 0.638989 | − | 0.769216i | \(-0.279353\pi\) |
−0.346666 | + | 0.937989i | \(0.612686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −218.444 | + | 605.114i | −0.396451 | + | 1.09821i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −66.4240 | + | 38.3499i | −0.120116 | + | 0.0693488i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −392.410 | + | 679.674i | −0.704507 | + | 1.22024i | 0.262363 | + | 0.964969i | \(0.415498\pi\) |
−0.966869 | + | 0.255272i | \(0.917835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 547.704i | 0.979792i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 700.448i | 1.24413i | 0.782964 | + | 0.622067i | \(0.213707\pi\) | ||||
−0.782964 | + | 0.622067i | \(0.786293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −621.061 | + | 358.570i | −1.09922 | + | 0.634637i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 251.046i | − | 0.441206i | −0.975364 | − | 0.220603i | \(-0.929198\pi\) | ||
0.975364 | − | 0.220603i | \(-0.0708025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 728.378 | 1.27562 | 0.637809 | − | 0.770194i | \(-0.279841\pi\) | ||||
0.637809 | + | 0.770194i | \(0.279841\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.5148 | + | 21.6763i | 0.0217649 | + | 0.0376979i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −200.504 | −0.347494 | −0.173747 | − | 0.984790i | \(-0.555588\pi\) | ||||
−0.173747 | + | 0.984790i | \(0.555588\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.3594 | −0.0729078 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −144.773 | − | 83.5847i | −0.248324 | − | 0.143370i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −257.221 | − | 445.519i | −0.438195 | − | 0.758977i | 0.559355 | − | 0.828928i | \(-0.311049\pi\) |
−0.997550 | + | 0.0699515i | \(0.977716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −105.197 | + | 18.8343i | −0.178603 | + | 0.0319767i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 399.444 | − | 691.858i | 0.673599 | − | 1.16671i | −0.303277 | − | 0.952902i | \(-0.598081\pi\) |
0.976876 | − | 0.213805i | \(-0.0685859\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 62.2474 | − | 107.816i | 0.104618 | − | 0.181203i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −147.881 | − | 85.3793i | −0.246880 | − | 0.142536i | 0.371455 | − | 0.928451i | \(-0.378859\pi\) |
−0.618335 | + | 0.785915i | \(0.712192\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 836.789i | 1.39233i | 0.717883 | + | 0.696164i | \(0.245111\pi\) | ||||
−0.717883 | + | 0.696164i | \(0.754889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −238.759 | − | 413.543i | −0.394643 | − | 0.683542i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 285.238i | − | 0.469914i | −0.972006 | − | 0.234957i | \(-0.924505\pi\) | ||
0.972006 | − | 0.234957i | \(-0.0754949\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1161.09 | + | 670.354i | −1.90031 | + | 1.09714i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −330.388 | − | 572.249i | −0.538969 | − | 0.933522i | −0.998960 | − | 0.0455986i | \(-0.985480\pi\) |
0.459990 | − | 0.887924i | \(-0.347853\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −372.340 | + | 644.912i | −0.603468 | + | 1.04524i | 0.388823 | + | 0.921312i | \(0.372882\pi\) |
−0.992292 | + | 0.123926i | \(0.960452\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 94.1964 | 0.152175 | 0.0760876 | − | 0.997101i | \(-0.475757\pi\) | ||||
0.0760876 | + | 0.997101i | \(0.475757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 183.862 | + | 106.153i | 0.295124 | + | 0.170390i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 225.061 | + | 389.817i | 0.360097 | + | 0.623707i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 401.641 | − | 231.888i | 0.638539 | − | 0.368661i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 284.195 | − | 492.240i | 0.450388 | − | 0.780094i | −0.548022 | − | 0.836464i | \(-0.684619\pi\) |
0.998410 | + | 0.0563693i | \(0.0179524\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 687.802i | 1.08315i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 696.378 | + | 402.054i | 1.09322 | + | 0.631168i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 233.256 | − | 134.670i | 0.363894 | − | 0.210094i | −0.306894 | − | 0.951744i | \(-0.599290\pi\) |
0.670787 | + | 0.741650i | \(0.265956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 577.725 | + | 1000.65i | 0.898483 | + | 1.55622i | 0.829434 | + | 0.558605i | \(0.188663\pi\) |
0.0690498 | + | 0.997613i | \(0.478003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1039.16 | −1.60611 | −0.803057 | − | 0.595902i | \(-0.796795\pi\) | ||||
−0.803057 | + | 0.595902i | \(0.796795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1188.45 | + | 686.154i | −1.83121 | + | 1.05725i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1115.67 | 1.70852 | 0.854262 | − | 0.519843i | \(-0.174009\pi\) | ||||
0.854262 | + | 0.519843i | \(0.174009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 474.338 | − | 821.578i | 0.724181 | − | 1.25432i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −86.7060 | − | 50.0597i | −0.131572 | − | 0.0759632i | 0.432769 | − | 0.901505i | \(-0.357536\pi\) |
−0.564341 | + | 0.825542i | \(0.690870\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −759.303 | − | 438.384i | −1.14872 | − | 0.663213i | −0.200144 | − | 0.979766i | \(-0.564141\pi\) |
−0.948575 | + | 0.316553i | \(0.897474\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −92.4859 | + | 78.0200i | −0.139077 | + | 0.117323i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 128.833 | − | 74.3819i | 0.193153 | − | 0.111517i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 866.001 | − | 1499.96i | 1.29061 | − | 2.23541i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 838.032i | 1.24522i | 0.782533 | + | 0.622609i | \(0.213927\pi\) | ||||
−0.782533 | + | 0.622609i | \(0.786073\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 572.195i | − | 0.845193i | −0.906318 | − | 0.422596i | \(-0.861119\pi\) | ||
0.906318 | − | 0.422596i | \(-0.138881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.1362 | − | 22.5953i | 0.0576380 | − | 0.0332773i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 191.437i | 0.280289i | 0.990131 | + | 0.140144i | \(0.0447567\pi\) | ||||
−0.990131 | + | 0.140144i | \(0.955243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 261.566 | 0.381849 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 94.5605 | + | 163.784i | 0.137243 | + | 0.237712i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1090.79 | 1.57856 | 0.789281 | − | 0.614033i | \(-0.210454\pi\) | ||||
0.789281 | + | 0.614033i | \(0.210454\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0431 | 0.0230836 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −631.151 | − | 364.395i | −0.905525 | − | 0.522805i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 404.337 | + | 700.331i | 0.576800 | + | 0.999046i | 0.995844 | + | 0.0910803i | \(0.0290320\pi\) |
−0.419044 | + | 0.907966i | \(0.637635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −443.697 | + | 79.4384i | −0.631148 | + | 0.112999i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 95.6701 | − | 165.706i | 0.135318 | − | 0.234378i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 153.803 | − | 266.395i | 0.216930 | − | 0.375733i | −0.736938 | − | 0.675960i | \(-0.763729\pi\) |
0.953868 | + | 0.300227i | \(0.0970625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.4016 | + | 12.3562i | 0.0300163 | + | 0.0173299i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1141.65i | 1.59671i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 156.569 | + | 271.185i | 0.217759 | + | 0.377169i | 0.954122 | − | 0.299417i | \(-0.0967920\pi\) |
−0.736364 | + | 0.676586i | \(0.763459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.8865i | 0.0830604i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −167.054 | + | 96.4485i | −0.230419 | + | 0.133032i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 295.082 | + | 511.098i | 0.405890 | + | 0.703023i | 0.994425 | − | 0.105449i | \(-0.0336281\pi\) |
−0.588534 | + | 0.808472i | \(0.700295\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 312.240 | − | 540.815i | 0.427140 | − | 0.739829i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −775.514 | −1.05800 | −0.529000 | − | 0.848622i | \(-0.677433\pi\) | ||||
−0.529000 | + | 0.848622i | \(0.677433\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1489.94 | − | 860.215i | −2.02162 | − | 1.16718i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 473.628 | + | 820.348i | 0.640904 | + | 1.11008i | 0.985231 | + | 0.171229i | \(0.0547738\pi\) |
−0.344327 | + | 0.938850i | \(0.611893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −487.913 | + | 281.697i | −0.656680 | + | 0.379134i | −0.791011 | − | 0.611802i | \(-0.790445\pi\) |
0.134331 | + | 0.990937i | \(0.457112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 127.420 | − | 220.698i | 0.171033 | − | 0.296239i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 49.0794i | − | 0.0655265i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 863.689 | + | 498.651i | 1.15005 | + | 0.663982i | 0.948900 | − | 0.315578i | \(-0.102198\pi\) |
0.201152 | + | 0.979560i | \(0.435532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.8842 | − | 18.9857i | 0.0435552 | − | 0.0251466i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 595.954 | + | 1032.22i | 0.787258 | + | 1.36357i | 0.927641 | + | 0.373473i | \(0.121833\pi\) |
−0.140383 | + | 0.990097i | \(0.544833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −516.905 | −0.679244 | −0.339622 | − | 0.940562i | \(-0.610299\pi\) | ||||
−0.339622 | + | 0.940562i | \(0.610299\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.9240 | + | 25.3595i | −0.0575675 | + | 0.0332366i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1552.51 | 2.02413 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −142.307 | + | 246.483i | −0.185055 | + | 0.320524i | −0.943595 | − | 0.331102i | \(-0.892580\pi\) |
0.758540 | + | 0.651626i | \(0.225913\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 792.031 | + | 457.280i | 1.02462 | + | 0.591565i | 0.915439 | − | 0.402457i | \(-0.131844\pi\) |
0.109181 | + | 0.994022i | \(0.465177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.7508 | − | 16.0219i | −0.0358074 | − | 0.0206734i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 456.727 | + | 541.411i | 0.586299 | + | 0.695007i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1333.23 | − | 769.738i | 1.70708 | − | 0.985581i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 263.744 | − | 456.818i | 0.335979 | − | 0.581933i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 199.823i | 0.253905i | 0.991909 | + | 0.126952i | \(0.0405195\pi\) | ||||
−0.991909 | + | 0.126952i | \(0.959480\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 236.595i | − | 0.299109i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1696.92 | + | 979.719i | −2.13988 | + | 1.23546i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1490.18i | 1.86973i | 0.355003 | + | 0.934865i | \(0.384480\pi\) | ||||
−0.355003 | + | 0.934865i | \(0.615520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1528.64 | 1.91320 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 152.320 | + | 263.825i | 0.189688 | + | 0.328550i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.9796 | 0.0347573 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 235.121 | 0.290631 | 0.145316 | − | 0.989385i | \(-0.453580\pi\) | ||||
0.145316 | + | 0.989385i | \(0.453580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 406.665 | + | 234.788i | 0.501437 | + | 0.289505i | 0.729307 | − | 0.684187i | \(-0.239843\pi\) |
−0.227870 | + | 0.973692i | \(0.573176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 113.865 | + | 197.220i | 0.139712 | + | 0.241988i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −463.919 | + | 391.356i | −0.567832 | + | 0.479016i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −370.642 | + | 641.971i | −0.451452 | + | 0.781938i | −0.998476 | − | 0.0551789i | \(-0.982427\pi\) |
0.547025 | + | 0.837117i | \(0.315760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −514.242 | + | 890.693i | −0.624838 | + | 1.08225i | 0.363734 | + | 0.931503i | \(0.381502\pi\) |
−0.988572 | + | 0.150749i | \(0.951832\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 613.862 | + | 354.413i | 0.742275 | + | 0.428553i | 0.822896 | − | 0.568192i | \(-0.192357\pi\) |
−0.0806207 | + | 0.996745i | \(0.525690\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 695.252i | 0.838664i | 0.907833 | + | 0.419332i | \(0.137736\pi\) | ||||
−0.907833 | + | 0.419332i | \(0.862264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −458.413 | − | 793.994i | −0.550315 | − | 0.953174i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 635.244i | − | 0.760771i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −747.665 | + | 431.664i | −0.891138 | + | 0.514499i | −0.874315 | − | 0.485360i | \(-0.838689\pi\) |
−0.0168234 | + | 0.999858i | \(0.505355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 152.742 | + | 264.557i | 0.181619 | + | 0.314574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 274.528 | − | 475.497i | 0.324885 | − | 0.562718i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 157.540 | 0.185998 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 90.2668 | + | 52.1155i | 0.106071 | + | 0.0612404i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −92.1663 | − | 159.637i | −0.108050 | − | 0.187147i | 0.806930 | − | 0.590646i | \(-0.201127\pi\) |
−0.914980 | + | 0.403499i | \(0.867794\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 684.058 | − | 394.941i | 0.798201 | − | 0.460842i | −0.0446406 | − | 0.999003i | \(-0.514214\pi\) |
0.842842 | + | 0.538161i | \(0.180881\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 627.043 | − | 1086.07i | 0.729968 | − | 1.26434i | −0.226928 | − | 0.973912i | \(-0.572868\pi\) |
0.956896 | − | 0.290430i | \(-0.0937984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1094.97i | − | 1.26879i | −0.773009 | − | 0.634395i | \(-0.781249\pi\) | ||
0.773009 | − | 0.634395i | \(-0.218751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 250.502 | + | 144.627i | 0.289597 | + | 0.167199i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −694.509 | + | 400.975i | −0.799204 | + | 0.461421i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 973.173 | + | 1685.59i | 1.11731 | + | 1.93523i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −195.489 | −0.223417 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.6520 | + | 9.03671i | −0.0178473 | + | 0.0103041i | −0.508897 | − | 0.860827i | \(-0.669947\pi\) |
0.491050 | + | 0.871131i | \(0.336613\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 362.089 | 0.410998 | 0.205499 | − | 0.978657i | \(-0.434118\pi\) | ||||
0.205499 | + | 0.978657i | \(0.434118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 517.836 | − | 896.918i | 0.586451 | − | 1.01576i | −0.408242 | − | 0.912874i | \(-0.633858\pi\) |
0.994693 | − | 0.102889i | \(-0.0328086\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −374.913 | − | 216.456i | −0.422676 | − | 0.244032i | 0.273546 | − | 0.961859i | \(-0.411804\pi\) |
−0.696221 | + | 0.717827i | \(0.745137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −196.515 | − | 113.458i | −0.221052 | − | 0.127624i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1397.45 | − | 504.476i | −1.56489 | − | 0.564923i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −228.712 | + | 132.047i | −0.255544 | + | 0.147538i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −95.2263 | + | 164.937i | −0.105925 | + | 0.183467i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 215.631i | − | 0.239325i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1108.65i | − | 1.22503i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1446.74 | + | 835.277i | −1.59509 | + | 0.920923i | −0.602670 | + | 0.797990i | \(0.705897\pi\) |
−0.992415 | + | 0.122933i | \(0.960770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1087.43i | 1.19367i | 0.802364 | + | 0.596835i | \(0.203575\pi\) | ||||
−0.802364 | + | 0.596835i | \(0.796425\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −442.897 | −0.485101 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 156.491 | + | 271.051i | 0.170656 | + | 0.295584i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −984.258 | −1.07101 | −0.535505 | − | 0.844532i | \(-0.679879\pi\) | ||||
−0.535505 | + | 0.844532i | \(0.679879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1741.63 | −1.88692 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −117.046 | − | 67.5765i | −0.126536 | − | 0.0730557i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 223.803 | + | 387.638i | 0.240907 | + | 0.417264i | 0.960973 | − | 0.276642i | \(-0.0892216\pi\) |
−0.720066 | + | 0.693906i | \(0.755888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 157.040 | + | 877.133i | 0.168679 | + | 0.942141i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 650.840 | − | 1127.29i | 0.696086 | − | 1.20566i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −153.045 | + | 265.082i | −0.163335 | + | 0.282905i | −0.936063 | − | 0.351833i | \(-0.885558\pi\) |
0.772728 | + | 0.634738i | \(0.218892\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −739.908 | − | 427.186i | −0.786299 | − | 0.453970i | 0.0523588 | − | 0.998628i | \(-0.483326\pi\) |
−0.838658 | + | 0.544658i | \(0.816659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 163.792i | − | 0.173692i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −573.188 | − | 992.791i | −0.605267 | − | 1.04835i | −0.992009 | − | 0.126166i | \(-0.959733\pi\) |
0.386742 | − | 0.922188i | \(-0.373600\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 344.643i | − | 0.363164i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −675.404 | + | 389.944i | −0.708713 | + | 0.409176i | −0.810584 | − | 0.585622i | \(-0.800850\pi\) |
0.101871 | + | 0.994798i | \(0.467517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −464.687 | − | 804.861i | −0.486583 | − | 0.842786i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.1473 | + | 74.7334i | −0.0449920 | + | 0.0779284i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 929.362 | 0.967078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −212.886 | − | 122.910i | −0.220608 | − | 0.127368i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 687.674 | + | 1191.09i | 0.711141 | + | 1.23173i | 0.964429 | + | 0.264342i | \(0.0851548\pi\) |
−0.253288 | + | 0.967391i | \(0.581512\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1484.68 | − | 857.179i | 1.52902 | − | 0.882780i | 0.529616 | − | 0.848238i | \(-0.322336\pi\) |
0.999403 | − | 0.0345418i | \(-0.0109972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.64643 | + | 4.58375i | −0.00271986 | + | 0.00471094i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1792.68i | 1.83489i | 0.397866 | + | 0.917443i | \(0.369751\pi\) | ||||
−0.397866 | + | 0.917443i | \(0.630249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1922.41 | + | 1109.90i | 1.96364 | + | 1.13371i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −487.315 | + | 281.351i | −0.495742 | + | 0.286217i | −0.726954 | − | 0.686687i | \(-0.759064\pi\) |
0.231211 | + | 0.972904i | \(0.425731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 208.970 | + | 361.947i | 0.212153 | + | 0.367459i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 140.348 | 0.141909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1085.70 | − | 626.830i | 1.09556 | − | 0.632523i | 0.160510 | − | 0.987034i | \(-0.448686\pi\) |
0.935052 | + | 0.354511i | \(0.115353\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 355.098 | 0.356882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 502.212 | − | 869.856i | 0.503723 | − | 0.872474i | −0.496268 | − | 0.868169i | \(-0.665297\pi\) |
0.999991 | − | 0.00430418i | \(-0.00137007\pi\) | |||||||
\(998\) | 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 | 684.3.y.g.145.2 | ✓ | 8 | |
3.2 | odd | 2 | inner | 684.3.y.g.145.3 | yes | 8 | |
19.8 | odd | 6 | inner | 684.3.y.g.217.2 | yes | 8 | |
57.8 | even | 6 | inner | 684.3.y.g.217.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.y.g.145.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
684.3.y.g.145.3 | yes | 8 | 3.2 | odd | 2 | inner | |
684.3.y.g.217.2 | yes | 8 | 19.8 | odd | 6 | inner | |
684.3.y.g.217.3 | yes | 8 | 57.8 | even | 6 | inner |