Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(415,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.415");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.m (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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 415.4 | ||
Root | \(-1.25564 - 1.55672i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.415 |
Dual form | 1152.3.m.f.991.4 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.909023 | + | 0.909023i | 0.181805 | + | 0.181805i | 0.792142 | − | 0.610337i | \(-0.208966\pi\) |
−0.610337 | + | 0.792142i | \(0.708966\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.654713 | −0.0935305 | −0.0467652 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467652 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.3760 | + | 13.3760i | −1.21600 | + | 1.21600i | −0.246980 | + | 0.969021i | \(0.579438\pi\) |
−0.969021 | + | 0.246980i | \(0.920562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.32795 | + | 8.32795i | −0.640612 | + | 0.640612i | −0.950706 | − | 0.310094i | \(-0.899639\pi\) |
0.310094 | + | 0.950706i | \(0.399639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.93529 | 0.231488 | 0.115744 | − | 0.993279i | \(-0.463075\pi\) | ||||
0.115744 | + | 0.993279i | \(0.463075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.8974 | − | 16.8974i | −0.889336 | − | 0.889336i | 0.105123 | − | 0.994459i | \(-0.466476\pi\) |
−0.994459 | + | 0.105123i | \(0.966476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.1787 | 1.00777 | 0.503884 | − | 0.863771i | \(-0.331904\pi\) | ||||
0.503884 | + | 0.863771i | \(0.331904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 23.3474i | − | 0.933894i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.6105 | − | 35.6105i | 1.22795 | − | 1.22795i | 0.263209 | − | 0.964739i | \(-0.415219\pi\) |
0.964739 | − | 0.263209i | \(-0.0847809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 45.5687i | − | 1.46996i | −0.678089 | − | 0.734980i | \(-0.737192\pi\) | ||
0.678089 | − | 0.734980i | \(-0.262808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.595149 | − | 0.595149i | −0.0170043 | − | 0.0170043i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1527 | − | 10.1527i | −0.274398 | − | 0.274398i | 0.556470 | − | 0.830868i | \(-0.312156\pi\) |
−0.830868 | + | 0.556470i | \(0.812156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 28.4661i | − | 0.694295i | −0.937811 | − | 0.347148i | \(-0.887150\pi\) | ||
0.937811 | − | 0.347148i | \(-0.112850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.7354 | + | 22.7354i | −0.528730 | + | 0.528730i | −0.920194 | − | 0.391464i | \(-0.871969\pi\) |
0.391464 | + | 0.920194i | \(0.371969\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.7746i | 0.229247i | 0.993409 | + | 0.114623i | \(0.0365661\pi\) | ||||
−0.993409 | + | 0.114623i | \(0.963434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.5714 | −0.991252 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 41.5142 | + | 41.5142i | 0.783287 | + | 0.783287i | 0.980384 | − | 0.197097i | \(-0.0631514\pi\) |
−0.197097 | + | 0.980384i | \(0.563151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.3182 | −0.442149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −21.0646 | + | 21.0646i | −0.357027 | + | 0.357027i | −0.862716 | − | 0.505689i | \(-0.831238\pi\) |
0.505689 | + | 0.862716i | \(0.331238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68.7531 | − | 68.7531i | 1.12710 | − | 1.12710i | 0.136453 | − | 0.990647i | \(-0.456430\pi\) |
0.990647 | − | 0.136453i | \(-0.0435703\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.1406 | −0.232932 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −67.8242 | − | 67.8242i | −1.01230 | − | 1.01230i | −0.999923 | − | 0.0123779i | \(-0.996060\pi\) |
−0.0123779 | − | 0.999923i | \(-0.503940\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −33.3094 | −0.469147 | −0.234573 | − | 0.972098i | \(-0.575369\pi\) | ||||
−0.234573 | + | 0.972098i | \(0.575369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.6331i | 0.255248i | 0.991823 | + | 0.127624i | \(0.0407351\pi\) | ||||
−0.991823 | + | 0.127624i | \(0.959265\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.75745 | − | 8.75745i | 0.113733 | − | 0.113733i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.29222i | − | 0.0796483i | −0.999207 | − | 0.0398242i | \(-0.987320\pi\) | ||
0.999207 | − | 0.0398242i | \(-0.0126798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −72.0774 | − | 72.0774i | −0.868402 | − | 0.868402i | 0.123894 | − | 0.992296i | \(-0.460462\pi\) |
−0.992296 | + | 0.123894i | \(0.960462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.57727 | + | 3.57727i | 0.0420855 | + | 0.0420855i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6131i | 0.119248i | 0.998221 | + | 0.0596240i | \(0.0189902\pi\) | ||||
−0.998221 | + | 0.0596240i | \(0.981010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.45242 | − | 5.45242i | 0.0599167 | − | 0.0599167i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 30.7202i | − | 0.323371i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 143.631 | 1.48073 | 0.740366 | − | 0.672204i | \(-0.234652\pi\) | ||||
0.740366 | + | 0.672204i | \(0.234652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −90.3100 | − | 90.3100i | −0.894159 | − | 0.894159i | 0.100753 | − | 0.994912i | \(-0.467875\pi\) |
−0.994912 | + | 0.100753i | \(0.967875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −95.1656 | −0.923938 | −0.461969 | − | 0.886896i | \(-0.652857\pi\) | ||||
−0.461969 | + | 0.886896i | \(0.652857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 27.2524 | − | 27.2524i | 0.254695 | − | 0.254695i | −0.568197 | − | 0.822892i | \(-0.692359\pi\) |
0.822892 | + | 0.568197i | \(0.192359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 132.413 | − | 132.413i | 1.21480 | − | 1.21480i | 0.245366 | − | 0.969430i | \(-0.421092\pi\) |
0.969430 | − | 0.245366i | \(-0.0789082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −37.9551 | −0.335886 | −0.167943 | − | 0.985797i | \(-0.553712\pi\) | ||||
−0.167943 | + | 0.985797i | \(0.553712\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.0699 | + | 21.0699i | 0.183217 | + | 0.183217i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.57649 | −0.0216512 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 236.835i | − | 1.95731i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 43.9488 | − | 43.9488i | 0.351591 | − | 0.351591i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 96.5399i | 0.760157i | 0.924954 | + | 0.380078i | \(0.124103\pi\) | ||||
−0.924954 | + | 0.380078i | \(0.875897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −54.5082 | − | 54.5082i | −0.416093 | − | 0.416093i | 0.467762 | − | 0.883855i | \(-0.345061\pi\) |
−0.883855 | + | 0.467762i | \(0.845061\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.0629 | + | 11.0629i | 0.0831801 | + | 0.0831801i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 25.9333i | − | 0.189294i | −0.995511 | − | 0.0946471i | \(-0.969828\pi\) | ||
0.995511 | − | 0.0946471i | \(-0.0301723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.64066 | + | 3.64066i | −0.0261918 | + | 0.0261918i | −0.720081 | − | 0.693890i | \(-0.755896\pi\) |
0.693890 | + | 0.720081i | \(0.255896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 222.789i | − | 1.55797i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 64.7415 | 0.446493 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.9718 | − | 18.9718i | −0.127328 | − | 0.127328i | 0.640571 | − | 0.767899i | \(-0.278698\pi\) |
−0.767899 | + | 0.640571i | \(0.778698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −103.209 | −0.683503 | −0.341751 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341751 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 41.4230 | − | 41.4230i | 0.267245 | − | 0.267245i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −88.2067 | + | 88.2067i | −0.561826 | + | 0.561826i | −0.929826 | − | 0.368000i | \(-0.880043\pi\) |
0.368000 | + | 0.929826i | \(0.380043\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.1754 | −0.0942571 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.8038 | − | 18.8038i | −0.115361 | − | 0.115361i | 0.647070 | − | 0.762431i | \(-0.275994\pi\) |
−0.762431 | + | 0.647070i | \(0.775994\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −267.105 | −1.59943 | −0.799715 | − | 0.600380i | \(-0.795016\pi\) | ||||
−0.799715 | + | 0.600380i | \(0.795016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.2905i | 0.179234i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −153.520 | + | 153.520i | −0.887396 | + | 0.887396i | −0.994272 | − | 0.106876i | \(-0.965915\pi\) |
0.106876 | + | 0.994272i | \(0.465915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.2858i | 0.0873476i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 123.581 | + | 123.581i | 0.690399 | + | 0.690399i | 0.962320 | − | 0.271921i | \(-0.0876589\pi\) |
−0.271921 | + | 0.962320i | \(0.587659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −122.965 | − | 122.965i | −0.679364 | − | 0.679364i | 0.280493 | − | 0.959856i | \(-0.409502\pi\) |
−0.959856 | + | 0.280493i | \(0.909502\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 18.4581i | − | 0.0997737i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −52.6385 | + | 52.6385i | −0.281489 | + | 0.281489i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 193.992i | 1.01566i | 0.861456 | + | 0.507832i | \(0.169553\pi\) | ||||
−0.861456 | + | 0.507832i | \(0.830447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 141.555 | 0.733444 | 0.366722 | − | 0.930331i | \(-0.380480\pi\) | ||||
0.366722 | + | 0.930331i | \(0.380480\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 28.9507 | + | 28.9507i | 0.146958 | + | 0.146958i | 0.776758 | − | 0.629800i | \(-0.216863\pi\) |
−0.629800 | + | 0.776758i | \(0.716863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.6253 | −0.138821 | −0.0694104 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694104 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.3147 | + | 23.3147i | −0.114851 | + | 0.114851i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.8763 | − | 25.8763i | 0.126226 | − | 0.126226i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 452.039 | 2.16287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.35041 | − | 7.35041i | −0.0348361 | − | 0.0348361i | 0.689474 | − | 0.724310i | \(-0.257842\pi\) |
−0.724310 | + | 0.689474i | \(0.757842\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −41.3340 | −0.192251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.8345i | 0.137486i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.7729 | + | 32.7729i | −0.148294 | + | 0.148294i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 386.106i | − | 1.73142i | −0.500549 | − | 0.865708i | \(-0.666869\pi\) | ||
0.500549 | − | 0.865708i | \(-0.333131\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −49.7286 | − | 49.7286i | −0.219069 | − | 0.219069i | 0.589037 | − | 0.808106i | \(-0.299507\pi\) |
−0.808106 | + | 0.589037i | \(0.799507\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 191.870 | + | 191.870i | 0.837861 | + | 0.837861i | 0.988577 | − | 0.150716i | \(-0.0481579\pi\) |
−0.150716 | + | 0.988577i | \(0.548158\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 298.610i | − | 1.28159i | −0.767712 | − | 0.640795i | \(-0.778605\pi\) | ||
0.767712 | − | 0.640795i | \(-0.221395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.79435 | + | 9.79435i | −0.0416781 | + | 0.0416781i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 247.352i | 1.03495i | 0.855700 | + | 0.517473i | \(0.173127\pi\) | ||||
−0.855700 | + | 0.517473i | \(0.826873\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −220.337 | −0.914260 | −0.457130 | − | 0.889400i | \(-0.651123\pi\) | ||||
−0.457130 | + | 0.889400i | \(0.651123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −44.1525 | − | 44.1525i | −0.180214 | − | 0.180214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 281.441 | 1.13944 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 162.716 | − | 162.716i | 0.648272 | − | 0.648272i | −0.304303 | − | 0.952575i | \(-0.598424\pi\) |
0.952575 | + | 0.304303i | \(0.0984235\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −310.038 | + | 310.038i | −1.22545 | + | 1.22545i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −101.165 | −0.393637 | −0.196819 | − | 0.980440i | \(-0.563061\pi\) | ||||
−0.196819 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.64713 | + | 6.64713i | 0.0256646 | + | 0.0256646i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 323.635 | 1.23055 | 0.615276 | − | 0.788312i | \(-0.289045\pi\) | ||||
0.615276 | + | 0.788312i | \(0.289045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 75.4747i | 0.284810i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.51275 | − | 1.51275i | 0.00562361 | − | 0.00562361i | −0.704289 | − | 0.709913i | \(-0.748734\pi\) |
0.709913 | + | 0.704289i | \(0.248734\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 166.098i | − | 0.612909i | −0.951885 | − | 0.306454i | \(-0.900857\pi\) | ||
0.951885 | − | 0.306454i | \(-0.0991427\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 312.294 | + | 312.294i | 1.13562 | + | 1.13562i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −317.830 | − | 317.830i | −1.14740 | − | 1.14740i | −0.987062 | − | 0.160338i | \(-0.948741\pi\) |
−0.160338 | − | 0.987062i | \(-0.551259\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 402.790i | 1.43342i | 0.697374 | + | 0.716708i | \(0.254352\pi\) | ||||
−0.697374 | + | 0.716708i | \(0.745648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 192.406 | − | 192.406i | 0.679881 | − | 0.679881i | −0.280092 | − | 0.959973i | \(-0.590365\pi\) |
0.959973 | + | 0.280092i | \(0.0903649\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.6371i | 0.0649378i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −273.513 | −0.946413 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −75.3645 | − | 75.3645i | −0.257217 | − | 0.257217i | 0.566704 | − | 0.823921i | \(-0.308218\pi\) |
−0.823921 | + | 0.566704i | \(0.808218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.2964 | −0.129818 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −193.031 | + | 193.031i | −0.645588 | + | 0.645588i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.8852 | − | 14.8852i | 0.0494524 | − | 0.0494524i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 124.996 | 0.409824 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 111.544 | + | 111.544i | 0.363337 | + | 0.363337i | 0.865040 | − | 0.501703i | \(-0.167293\pi\) |
−0.501703 | + | 0.865040i | \(0.667293\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 224.484 | 0.721813 | 0.360906 | − | 0.932602i | \(-0.382467\pi\) | ||||
0.360906 | + | 0.932602i | \(0.382467\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 488.339i | 1.56019i | 0.625661 | + | 0.780095i | \(0.284829\pi\) | ||||
−0.625661 | + | 0.780095i | \(0.715171\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 257.361 | − | 257.361i | 0.811863 | − | 0.811863i | −0.173050 | − | 0.984913i | \(-0.555362\pi\) |
0.984913 | + | 0.173050i | \(0.0553621\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 952.652i | 2.98637i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −66.4962 | − | 66.4962i | −0.205871 | − | 0.205871i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 194.436 | + | 194.436i | 0.598263 | + | 0.598263i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.05427i | − | 0.0214416i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 123.553 | − | 123.553i | 0.373271 | − | 0.373271i | −0.495396 | − | 0.868667i | \(-0.664977\pi\) |
0.868667 | + | 0.495396i | \(0.164977\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 123.307i | − | 0.368082i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −246.234 | −0.730665 | −0.365333 | − | 0.930877i | \(-0.619045\pi\) | ||||
−0.365333 | + | 0.930877i | \(0.619045\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 609.528 | + | 609.528i | 1.78747 | + | 1.78747i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 63.8813 | 0.186243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −123.212 | + | 123.212i | −0.355076 | + | 0.355076i | −0.861994 | − | 0.506918i | \(-0.830785\pi\) |
0.506918 | + | 0.861994i | \(0.330785\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −115.371 | + | 115.371i | −0.330575 | + | 0.330575i | −0.852805 | − | 0.522230i | \(-0.825100\pi\) |
0.522230 | + | 0.852805i | \(0.325100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −650.544 | −1.84290 | −0.921451 | − | 0.388495i | \(-0.872995\pi\) | ||||
−0.921451 | + | 0.388495i | \(0.872995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.2790 | − | 30.2790i | −0.0852930 | − | 0.0852930i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −94.4878 | −0.263197 | −0.131599 | − | 0.991303i | \(-0.542011\pi\) | ||||
−0.131599 | + | 0.991303i | \(0.542011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 210.044i | 0.581838i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.9379 | + | 16.9379i | −0.0464053 | + | 0.0464053i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 131.379i | − | 0.357982i | −0.983851 | − | 0.178991i | \(-0.942717\pi\) | ||
0.983851 | − | 0.178991i | \(-0.0572832\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.1799 | − | 27.1799i | −0.0732612 | − | 0.0732612i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 275.796 | + | 275.796i | 0.739400 | + | 0.739400i | 0.972462 | − | 0.233062i | \(-0.0748745\pi\) |
−0.233062 | + | 0.972462i | \(0.574874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 593.125i | 1.57328i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0427 | − | 13.0427i | 0.0344135 | − | 0.0344135i | −0.689691 | − | 0.724104i | \(-0.742253\pi\) |
0.724104 | + | 0.689691i | \(0.242253\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 121.974i | 0.318470i | 0.987241 | + | 0.159235i | \(0.0509027\pi\) | ||||
−0.987241 | + | 0.159235i | \(0.949097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.9214 | 0.0413544 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −233.267 | − | 233.267i | −0.599659 | − | 0.599659i | 0.340563 | − | 0.940222i | \(-0.389382\pi\) |
−0.940222 | + | 0.340563i | \(0.889382\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 91.2149 | 0.233286 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.71977 | − | 5.71977i | 0.0144804 | − | 0.0144804i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 83.7693 | − | 83.7693i | 0.211006 | − | 0.211006i | −0.593689 | − | 0.804695i | \(-0.702329\pi\) |
0.804695 | + | 0.593689i | \(0.202329\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −589.134 | −1.46916 | −0.734581 | − | 0.678521i | \(-0.762621\pi\) | ||||
−0.734581 | + | 0.678521i | \(0.762621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 379.494 | + | 379.494i | 0.941673 | + | 0.941673i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 271.606 | 0.667337 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 449.285i | − | 1.09850i | −0.835659 | − | 0.549248i | \(-0.814914\pi\) | ||
0.835659 | − | 0.549248i | \(-0.185086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7913 | − | 13.7913i | 0.0333929 | − | 0.0333929i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 131.040i | − | 0.315759i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −218.639 | − | 218.639i | −0.521811 | − | 0.521811i | 0.396307 | − | 0.918118i | \(-0.370292\pi\) |
−0.918118 | + | 0.396307i | \(0.870292\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 61.2101 | + | 61.2101i | 0.145392 | + | 0.145392i | 0.776056 | − | 0.630664i | \(-0.217217\pi\) |
−0.630664 | + | 0.776056i | \(0.717217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 91.8787i | − | 0.216185i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −45.0136 | + | 45.0136i | −0.105418 | + | 0.105418i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 501.119i | − | 1.16269i | −0.813657 | − | 0.581345i | \(-0.802527\pi\) | ||
0.813657 | − | 0.581345i | \(-0.197473\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 75.5505 | 0.174482 | 0.0872408 | − | 0.996187i | \(-0.472195\pi\) | ||||
0.0872408 | + | 0.996187i | \(0.472195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −391.659 | − | 391.659i | −0.896245 | − | 0.896245i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 717.251 | 1.63383 | 0.816915 | − | 0.576758i | \(-0.195682\pi\) | ||||
0.816915 | + | 0.576758i | \(0.195682\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 299.093 | − | 299.093i | 0.675153 | − | 0.675153i | −0.283746 | − | 0.958899i | \(-0.591577\pi\) |
0.958899 | + | 0.283746i | \(0.0915773\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.64753 | + | 9.64753i | −0.0216798 | + | 0.0216798i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 44.5560 | 0.0992339 | 0.0496170 | − | 0.998768i | \(-0.484200\pi\) | ||||
0.0496170 | + | 0.998768i | \(0.484200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 380.763 | + | 380.763i | 0.844263 | + | 0.844263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.91275 | 0.0217863 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 641.227i | 1.40312i | 0.712609 | + | 0.701562i | \(0.247514\pi\) | ||||
−0.712609 | + | 0.701562i | \(0.752486\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −393.690 | + | 393.690i | −0.853991 | + | 0.853991i | −0.990622 | − | 0.136631i | \(-0.956373\pi\) |
0.136631 | + | 0.990622i | \(0.456373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 395.861i | 0.854991i | 0.904018 | + | 0.427495i | \(0.140604\pi\) | ||||
−0.904018 | + | 0.427495i | \(0.859396\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −83.1457 | − | 83.1457i | −0.178042 | − | 0.178042i | 0.612460 | − | 0.790502i | \(-0.290180\pi\) |
−0.790502 | + | 0.612460i | \(0.790180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 44.4054 | + | 44.4054i | 0.0946810 | + | 0.0946810i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 608.217i | − | 1.28587i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −394.509 | + | 394.509i | −0.830546 | + | 0.830546i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 430.043i | 0.897793i | 0.893584 | + | 0.448896i | \(0.148183\pi\) | ||||
−0.893584 | + | 0.448896i | \(0.851817\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 169.103 | 0.351565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 130.564 | + | 130.564i | 0.269204 | + | 0.269204i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 573.790 | 1.17821 | 0.589107 | − | 0.808055i | \(-0.299480\pi\) | ||||
0.589107 | + | 0.808055i | \(0.299480\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −489.133 | + | 489.133i | −0.996197 | + | 0.996197i | −0.999993 | − | 0.00379588i | \(-0.998792\pi\) |
0.00379588 | + | 0.999993i | \(0.498792\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 140.138 | − | 140.138i | 0.284255 | − | 0.284255i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.8081 | 0.0438795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −260.469 | − | 260.469i | −0.521982 | − | 0.521982i | 0.396188 | − | 0.918170i | \(-0.370333\pi\) |
−0.918170 | + | 0.396188i | \(0.870333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 975.416 | 1.93920 | 0.969598 | − | 0.244701i | \(-0.0786900\pi\) | ||||
0.969598 | + | 0.244701i | \(0.0786900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 164.188i | − | 0.325124i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −420.191 | + | 420.191i | −0.825523 | + | 0.825523i | −0.986894 | − | 0.161371i | \(-0.948408\pi\) |
0.161371 | + | 0.986894i | \(0.448408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.1994i | − | 0.0238735i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −86.5077 | − | 86.5077i | −0.167976 | − | 0.167976i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −144.121 | − | 144.121i | −0.278764 | − | 0.278764i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 396.333i | 0.760716i | 0.924839 | + | 0.380358i | \(0.124199\pi\) | ||||
−0.924839 | + | 0.380358i | \(0.875801\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −564.600 | + | 564.600i | −1.07954 | + | 1.07954i | −0.0829913 | + | 0.996550i | \(0.526447\pi\) |
−0.996550 | + | 0.0829913i | \(0.973553\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 179.326i | − | 0.340278i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.25115 | 0.0155976 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 237.064 | + | 237.064i | 0.444773 | + | 0.444773i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.5461 | 0.0926095 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 649.691 | − | 649.691i | 1.20536 | − | 1.20536i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.5601 | − | 29.5601i | 0.0546398 | − | 0.0546398i | −0.679259 | − | 0.733899i | \(-0.737699\pi\) |
0.733899 | + | 0.679259i | \(0.237699\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 240.733 | 0.441711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 138.608 | + | 138.608i | 0.253397 | + | 0.253397i | 0.822362 | − | 0.568965i | \(-0.192656\pi\) |
−0.568965 | + | 0.822362i | \(0.692656\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1203.45 | −2.18412 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.11960i | 0.00744955i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 60.4400 | − | 60.4400i | 0.108510 | − | 0.108510i | −0.650767 | − | 0.759277i | \(-0.725553\pi\) |
0.759277 | + | 0.650767i | \(0.225553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 378.678i | − | 0.677421i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 267.325 | + | 267.325i | 0.474822 | + | 0.474822i | 0.903471 | − | 0.428649i | \(-0.141010\pi\) |
−0.428649 | + | 0.903471i | \(0.641010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.5021 | − | 34.5021i | −0.0610656 | − | 0.0610656i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 315.715i | − | 0.554859i | −0.960746 | − | 0.277429i | \(-0.910518\pi\) | ||
0.960746 | − | 0.277429i | \(-0.0894825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 670.572 | − | 670.572i | 1.17438 | − | 1.17438i | 0.193228 | − | 0.981154i | \(-0.438104\pi\) |
0.981154 | − | 0.193228i | \(-0.0618956\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 541.161i | − | 0.941149i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 413.628 | 0.716859 | 0.358430 | − | 0.933557i | \(-0.383312\pi\) | ||||
0.358430 | + | 0.933557i | \(0.383312\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 47.1900 | + | 47.1900i | 0.0812220 | + | 0.0812220i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1110.59 | −1.90495 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −420.085 | + | 420.085i | −0.715647 | + | 0.715647i | −0.967711 | − | 0.252064i | \(-0.918891\pi\) |
0.252064 | + | 0.967711i | \(0.418891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −769.993 | + | 769.993i | −1.30729 | + | 1.30729i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 740.798 | 1.24924 | 0.624619 | − | 0.780930i | \(-0.285254\pi\) | ||||
0.624619 | + | 0.780930i | \(0.285254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34209 | − | 2.34209i | −0.00393628 | − | 0.00393628i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −435.161 | −0.726479 | −0.363240 | − | 0.931696i | \(-0.618329\pi\) | ||||
−0.363240 | + | 0.931696i | \(0.618329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 380.001i | − | 0.632280i | −0.948712 | − | 0.316140i | \(-0.897613\pi\) | ||
0.948712 | − | 0.316140i | \(-0.102387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 215.288 | − | 215.288i | 0.355849 | − | 0.355849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 181.813i | − | 0.299527i | −0.988722 | − | 0.149763i | \(-0.952149\pi\) | ||
0.988722 | − | 0.149763i | \(-0.0478512\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −89.7303 | − | 89.7303i | −0.146858 | − | 0.146858i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −55.1479 | − | 55.1479i | −0.0899640 | − | 0.0899640i | 0.660693 | − | 0.750657i | \(-0.270263\pi\) |
−0.750657 | + | 0.660693i | \(0.770263\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 579.674i | 0.939504i | 0.882798 | + | 0.469752i | \(0.155657\pi\) | ||||
−0.882798 | + | 0.469752i | \(0.844343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −91.1070 | + | 91.1070i | −0.147184 | + | 0.147184i | −0.776859 | − | 0.629675i | \(-0.783188\pi\) |
0.629675 | + | 0.776859i | \(0.283188\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.94852i | − | 0.0111533i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −503.783 | −0.806053 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39.9540 | − | 39.9540i | −0.0635199 | − | 0.0635199i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −693.474 | −1.09901 | −0.549504 | − | 0.835491i | \(-0.685183\pi\) | ||||
−0.549504 | + | 0.835491i | \(0.685183\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −87.7570 | + | 87.7570i | −0.138200 | + | 0.138200i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 404.500 | − | 404.500i | 0.635007 | − | 0.635007i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 218.329 | 0.340607 | 0.170304 | − | 0.985392i | \(-0.445525\pi\) | ||||
0.170304 | + | 0.985392i | \(0.445525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −887.430 | − | 887.430i | −1.38014 | − | 1.38014i | −0.844353 | − | 0.535787i | \(-0.820015\pi\) |
−0.535787 | − | 0.844353i | \(-0.679985\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 223.177 | 0.344941 | 0.172470 | − | 0.985015i | \(-0.444825\pi\) | ||||
0.172470 | + | 0.985015i | \(0.444825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 563.520i | − | 0.868290i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 539.691 | − | 539.691i | 0.826479 | − | 0.826479i | −0.160549 | − | 0.987028i | \(-0.551326\pi\) |
0.987028 | + | 0.160549i | \(0.0513264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 99.0983i | − | 0.151295i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 625.166 | + | 625.166i | 0.948659 | + | 0.948659i | 0.998745 | − | 0.0500862i | \(-0.0159496\pi\) |
−0.0500862 | + | 0.998745i | \(0.515950\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 326.893 | + | 326.893i | 0.494544 | + | 0.494544i | 0.909734 | − | 0.415191i | \(-0.136285\pi\) |
−0.415191 | + | 0.909734i | \(0.636285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.1129i | 0.0302450i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 825.404 | − | 825.404i | 1.23749 | − | 1.23749i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1839.28i | 2.74111i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 422.147 | 0.627262 | 0.313631 | − | 0.949545i | \(-0.398455\pi\) | ||||
0.313631 | + | 0.949545i | \(0.398455\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −126.017 | − | 126.017i | −0.186140 | − | 0.186140i | 0.607885 | − | 0.794025i | \(-0.292018\pi\) |
−0.794025 | + | 0.607885i | \(0.792018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −94.0372 | −0.138494 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 621.906 | − | 621.906i | 0.910551 | − | 0.910551i | −0.0857647 | − | 0.996315i | \(-0.527333\pi\) |
0.996315 | + | 0.0857647i | \(0.0273333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.5740 | − | 23.5740i | 0.0344145 | − | 0.0344145i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −691.456 | −1.00357 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 403.376 | + | 403.376i | 0.583758 | + | 0.583758i | 0.935934 | − | 0.352176i | \(-0.114558\pi\) |
−0.352176 | + | 0.935934i | \(0.614558\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.61889 | −0.00952359 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 112.022i | − | 0.160721i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 466.593 | − | 466.593i | 0.665611 | − | 0.665611i | −0.291086 | − | 0.956697i | \(-0.594017\pi\) |
0.956697 | + | 0.291086i | \(0.0940166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 343.109i | 0.488065i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 59.1272 | + | 59.1272i | 0.0836311 | + | 0.0836311i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −822.764 | − | 822.764i | −1.16046 | − | 1.16046i | −0.984376 | − | 0.176081i | \(-0.943658\pi\) |
−0.176081 | − | 0.984376i | \(-0.556342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1056.22i | − | 1.48138i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 202.521 | − | 202.521i | 0.283246 | − | 0.283246i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 710.142i | − | 0.987681i | −0.869553 | − | 0.493840i | \(-0.835593\pi\) | ||
0.869553 | − | 0.493840i | \(-0.164407\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.3062 | 0.0864164 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −831.411 | − | 831.411i | −1.14677 | − | 1.14677i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −214.095 | −0.294490 | −0.147245 | − | 0.989100i | \(-0.547041\pi\) | ||||
−0.147245 | + | 0.989100i | \(0.547041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −89.4704 | + | 89.4704i | −0.122395 | + | 0.122395i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 96.1768 | − | 96.1768i | 0.131210 | − | 0.131210i | −0.638452 | − | 0.769662i | \(-0.720425\pi\) |
0.769662 | + | 0.638452i | \(0.220425\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1814.43 | 2.46192 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −885.341 | − | 885.341i | −1.19803 | − | 1.19803i | −0.974757 | − | 0.223268i | \(-0.928327\pi\) |
−0.223268 | − | 0.974757i | \(-0.571673\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −906.258 | −1.21973 | −0.609864 | − | 0.792506i | \(-0.708776\pi\) | ||||
−0.609864 | + | 0.792506i | \(0.708776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 34.4917i | − | 0.0462976i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.8425 | + | 17.8425i | −0.0238218 | + | 0.0238218i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1147.02i | − | 1.52732i | −0.645618 | − | 0.763661i | \(-0.723400\pi\) | ||
0.645618 | − | 0.763661i | \(-0.276600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −93.8192 | − | 93.8192i | −0.124264 | − | 0.124264i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −525.591 | − | 525.591i | −0.694308 | − | 0.694308i | 0.268869 | − | 0.963177i | \(-0.413350\pi\) |
−0.963177 | + | 0.268869i | \(0.913350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 788.107i | − | 1.03562i | −0.855495 | − | 0.517810i | \(-0.826747\pi\) | ||
0.855495 | − | 0.517810i | \(-0.173253\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −86.6925 | + | 86.6925i | −0.113621 | + | 0.113621i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 350.850i | − | 0.457431i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −768.187 | −0.998943 | −0.499471 | − | 0.866330i | \(-0.666472\pi\) | ||||
−0.499471 | + | 0.866330i | \(0.666472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 275.915 | + | 275.915i | 0.356941 | + | 0.356941i | 0.862684 | − | 0.505743i | \(-0.168782\pi\) |
−0.505743 | + | 0.862684i | \(0.668782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1063.91 | −1.37279 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −481.003 | + | 481.003i | −0.617462 | + | 0.617462i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 445.547 | − | 445.547i | 0.570483 | − | 0.570483i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −160.364 | −0.204285 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −240.824 | − | 240.824i | −0.306002 | − | 0.306002i | 0.537354 | − | 0.843356i | \(-0.319424\pi\) |
−0.843356 | + | 0.537354i | \(0.819424\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.8497 | 0.0314156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1145.14i | 1.44407i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −681.033 | + | 681.033i | −0.854496 | + | 0.854496i | −0.990683 | − | 0.136187i | \(-0.956515\pi\) |
0.136187 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.4012i | 0.0530678i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −249.237 | − | 249.237i | −0.310382 | − | 0.310382i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7948 | − | 13.7948i | −0.0171364 | − | 0.0171364i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 445.322i | 0.550459i | 0.961379 | + | 0.275230i | \(0.0887539\pi\) | ||||
−0.961379 | + | 0.275230i | \(0.911246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −223.787 | + | 223.787i | −0.275939 | + | 0.275939i | −0.831485 | − | 0.555546i | \(-0.812509\pi\) |
0.555546 | + | 0.831485i | \(0.312509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 34.1861i | − | 0.0419462i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 768.337 | 0.940437 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 382.528 | + | 382.528i | 0.465929 | + | 0.465929i | 0.900593 | − | 0.434664i | \(-0.143133\pi\) |
−0.434664 | + | 0.900593i | \(0.643133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −730.046 | −0.887055 | −0.443527 | − | 0.896261i | \(-0.646273\pi\) | ||||
−0.443527 | + | 0.896261i | \(0.646273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 252.094 | − | 252.094i | 0.304829 | − | 0.304829i | −0.538071 | − | 0.842900i | \(-0.680847\pi\) |
0.842900 | + | 0.538071i | \(0.180847\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 870.285 | − | 870.285i | 1.04980 | − | 1.04980i | 0.0511072 | − | 0.998693i | \(-0.483725\pi\) |
0.998693 | − | 0.0511072i | \(-0.0162750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −191.143 | −0.229463 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −242.804 | − | 242.804i | −0.290784 | − | 0.290784i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −550.145 | −0.655715 | −0.327858 | − | 0.944727i | \(-0.606327\pi\) | ||||
−0.327858 | + | 0.944727i | \(0.606327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1695.21i | − | 2.01571i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.5348 | + | 27.5348i | −0.0325855 | + | 0.0325855i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 155.059i | 0.183069i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −235.327 | − | 235.327i | −0.276530 | − | 0.276530i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 676.266 | + | 676.266i | 0.792809 | + | 0.792809i | 0.981950 | − | 0.189141i | \(-0.0605703\pi\) |
−0.189141 | + | 0.981950i | \(0.560570\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 291.272i | 0.339874i | 0.985455 | + | 0.169937i | \(0.0543563\pi\) | ||||
−0.985455 | + | 0.169937i | \(0.945644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −988.357 | + | 988.357i | −1.15059 | + | 1.15059i | −0.164156 | + | 0.986434i | \(0.552490\pi\) |
−0.986434 | + | 0.164156i | \(0.947510\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 922.512i | 1.06896i | 0.845181 | + | 0.534480i | \(0.179492\pi\) | ||||
−0.845181 | + | 0.534480i | \(0.820508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −279.105 | −0.322665 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 84.1648 | + | 84.1648i | 0.0968524 | + | 0.0968524i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1129.67 | 1.29698 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.7739 | + | 28.7739i | −0.0328845 | + | 0.0328845i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 406.278 | − | 406.278i | 0.463259 | − | 0.463259i | −0.436463 | − | 0.899722i | \(-0.643769\pi\) |
0.899722 | + | 0.436463i | \(0.143769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1009.42 | 1.14577 | 0.572884 | − | 0.819637i | \(-0.305825\pi\) | ||||
0.572884 | + | 0.819637i | \(0.305825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.3792 | − | 56.3792i | −0.0638496 | − | 0.0638496i | 0.674461 | − | 0.738311i | \(-0.264376\pi\) |
−0.738311 | + | 0.674461i | \(0.764376\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.0431 | −0.0237239 | −0.0118620 | − | 0.999930i | \(-0.503776\pi\) | ||||
−0.0118620 | + | 0.999930i | \(0.503776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 63.2060i | − | 0.0710978i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 182.063 | − | 182.063i | 0.203877 | − | 0.203877i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 224.677i | 0.251035i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1622.72 | − | 1622.72i | −1.80503 | − | 1.80503i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 163.371 | + | 163.371i | 0.181321 | + | 0.181321i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 223.556i | − | 0.247023i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −496.202 | + | 496.202i | −0.547080 | + | 0.547080i | −0.925595 | − | 0.378515i | \(-0.876435\pi\) |
0.378515 | + | 0.925595i | \(0.376435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1532.15i | − | 1.68183i | −0.541163 | − | 0.840917i | \(-0.682016\pi\) | ||
0.541163 | − | 0.840917i | \(-0.317984\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1928.21 | 2.11195 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35.6872 | + | 35.6872i | 0.0389174 | + | 0.0389174i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 727.639 | 0.791773 | 0.395886 | − | 0.918299i | \(-0.370437\pi\) | ||||
0.395886 | + | 0.918299i | \(0.370437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 277.399 | − | 277.399i | 0.300541 | − | 0.300541i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −237.040 | + | 237.040i | −0.256259 | + | 0.256259i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1544.59 | −1.66264 | −0.831318 | − | 0.555797i | \(-0.812413\pi\) | ||||
−0.831318 | + | 0.555797i | \(0.812413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 820.729 | + | 820.729i | 0.881556 | + | 0.881556i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −95.6992 | −0.102352 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 716.111i | − | 0.764259i | −0.924109 | − | 0.382130i | \(-0.875191\pi\) | ||
0.924109 | − | 0.382130i | \(-0.124809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 537.759 | − | 537.759i | 0.571476 | − | 0.571476i | −0.361065 | − | 0.932541i | \(-0.617587\pi\) |
0.932541 | + | 0.361065i | \(0.117587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 659.807i | − | 0.699689i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 734.420 | + | 734.420i | 0.775523 | + | 0.775523i | 0.979066 | − | 0.203543i | \(-0.0652457\pi\) |
−0.203543 | + | 0.979066i | \(0.565246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −155.176 | − | 155.176i | −0.163515 | − | 0.163515i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 138.512i | 0.145343i | 0.997356 | + | 0.0726714i | \(0.0231524\pi\) | ||||
−0.997356 | + | 0.0726714i | \(0.976848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −176.343 | + | 176.343i | −0.184652 | + | 0.184652i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9789i | 0.0177048i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1115.51 | −1.16078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 128.676 | + | 128.676i | 0.133343 | + | 0.133343i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −701.820 | −0.725770 | −0.362885 | − | 0.931834i | \(-0.618208\pi\) | ||||
−0.362885 | + | 0.931834i | \(0.618208\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −62.5684 | + | 62.5684i | −0.0644371 | + | 0.0644371i | −0.738591 | − | 0.674154i | \(-0.764508\pi\) |
0.674154 | + | 0.738591i | \(0.264508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.38359 | − | 2.38359i | 0.00244973 | − | 0.00244973i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1740.21 | −1.78117 | −0.890587 | − | 0.454814i | \(-0.849706\pi\) | ||||
−0.890587 | + | 0.454814i | \(0.849706\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −141.961 | − | 141.961i | −0.145006 | − | 0.145006i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1451.81 | 1.47692 | 0.738460 | − | 0.674298i | \(-0.235554\pi\) | ||||
0.738460 | + | 0.674298i | \(0.235554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.6337i | 0.0534353i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −526.976 | + | 526.976i | −0.532837 | + | 0.532837i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.1684i | 0.0223698i | 0.999937 | + | 0.0111849i | \(0.00356033\pi\) | ||||
−0.999937 | + | 0.0111849i | \(0.996440\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.1121 | − | 25.1121i | −0.0252382 | − | 0.0252382i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.5020 | − | 13.5020i | −0.0135426 | − | 0.0135426i | 0.700303 | − | 0.713846i | \(-0.253048\pi\) |
−0.713846 | + | 0.700303i | \(0.753048\pi\) | |||||||
\(998\) | 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 | 1152.3.m.f.415.4 | 16 | ||
3.2 | odd | 2 | 384.3.l.a.31.3 | 16 | |||
4.3 | odd | 2 | 1152.3.m.c.415.4 | 16 | |||
8.3 | odd | 2 | 576.3.m.c.271.5 | 16 | |||
8.5 | even | 2 | 144.3.m.c.91.3 | 16 | |||
12.11 | even | 2 | 384.3.l.b.31.7 | 16 | |||
16.3 | odd | 4 | inner | 1152.3.m.f.991.4 | 16 | ||
16.5 | even | 4 | 576.3.m.c.559.5 | 16 | |||
16.11 | odd | 4 | 144.3.m.c.19.3 | 16 | |||
16.13 | even | 4 | 1152.3.m.c.991.4 | 16 | |||
24.5 | odd | 2 | 48.3.l.a.43.6 | yes | 16 | ||
24.11 | even | 2 | 192.3.l.a.79.2 | 16 | |||
48.5 | odd | 4 | 192.3.l.a.175.2 | 16 | |||
48.11 | even | 4 | 48.3.l.a.19.6 | ✓ | 16 | ||
48.29 | odd | 4 | 384.3.l.b.223.7 | 16 | |||
48.35 | even | 4 | 384.3.l.a.223.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.6 | ✓ | 16 | 48.11 | even | 4 | ||
48.3.l.a.43.6 | yes | 16 | 24.5 | odd | 2 | ||
144.3.m.c.19.3 | 16 | 16.11 | odd | 4 | |||
144.3.m.c.91.3 | 16 | 8.5 | even | 2 | |||
192.3.l.a.79.2 | 16 | 24.11 | even | 2 | |||
192.3.l.a.175.2 | 16 | 48.5 | odd | 4 | |||
384.3.l.a.31.3 | 16 | 3.2 | odd | 2 | |||
384.3.l.a.223.3 | 16 | 48.35 | even | 4 | |||
384.3.l.b.31.7 | 16 | 12.11 | even | 2 | |||
384.3.l.b.223.7 | 16 | 48.29 | odd | 4 | |||
576.3.m.c.271.5 | 16 | 8.3 | odd | 2 | |||
576.3.m.c.559.5 | 16 | 16.5 | even | 4 | |||
1152.3.m.c.415.4 | 16 | 4.3 | odd | 2 | |||
1152.3.m.c.991.4 | 16 | 16.13 | even | 4 | |||
1152.3.m.f.415.4 | 16 | 1.1 | even | 1 | trivial | ||
1152.3.m.f.991.4 | 16 | 16.3 | odd | 4 | inner |