Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (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: | \(10.4632421514\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 223.3 | ||
Root | \(-1.25564 + 1.55672i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.223 |
Dual form | 384.3.l.a.31.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.909023 | + | 0.909023i | −0.181805 | + | 0.181805i | −0.792142 | − | 0.610337i | \(-0.791034\pi\) |
0.610337 | + | 0.792142i | \(0.291034\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.654713 | −0.0935305 | −0.0467652 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467652 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.3760 | + | 13.3760i | 1.21600 | + | 1.21600i | 0.969021 | + | 0.246980i | \(0.0794382\pi\) |
0.246980 | + | 0.969021i | \(0.420562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.32795 | − | 8.32795i | −0.640612 | − | 0.640612i | 0.310094 | − | 0.950706i | \(-0.399639\pi\) |
−0.950706 | + | 0.310094i | \(0.899639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.22664i | − | 0.148443i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.93529 | −0.231488 | −0.115744 | − | 0.993279i | \(-0.536925\pi\) | ||||
−0.115744 | + | 0.993279i | \(0.536925\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.8974 | + | 16.8974i | −0.889336 | + | 0.889336i | −0.994459 | − | 0.105123i | \(-0.966476\pi\) |
0.105123 | + | 0.994459i | \(0.466476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.801857 | − | 0.801857i | 0.0381837 | − | 0.0381837i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.1787 | −1.00777 | −0.503884 | − | 0.863771i | \(-0.668096\pi\) | ||||
−0.503884 | + | 0.863771i | \(0.668096\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.3474i | 0.933894i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −35.6105 | − | 35.6105i | −1.22795 | − | 1.22795i | −0.964739 | − | 0.263209i | \(-0.915219\pi\) |
−0.263209 | − | 0.964739i | \(-0.584781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 45.5687i | 1.46996i | 0.678089 | + | 0.734980i | \(0.262808\pi\) | ||||
−0.678089 | + | 0.734980i | \(0.737192\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −32.7644 | −0.992860 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.595149 | − | 0.595149i | 0.0170043 | − | 0.0170043i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1527 | + | 10.1527i | −0.274398 | + | 0.274398i | −0.830868 | − | 0.556470i | \(-0.812156\pi\) |
0.556470 | + | 0.830868i | \(0.312156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 20.3992 | 0.523057 | ||||||||
\(40\) | 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 | 0.391464 | − | 0.920194i | \(-0.371969\pi\) |
−0.920194 | + | 0.391464i | \(0.871969\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.72707 | + | 2.72707i | 0.0606015 | + | 0.0606015i | ||||
\(46\) | 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 | ||||||||
\(51\) | 4.81973 | − | 4.81973i | 0.0945045 | − | 0.0945045i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −41.5142 | + | 41.5142i | −0.783287 | + | 0.783287i | −0.980384 | − | 0.197097i | \(-0.936849\pi\) |
0.197097 | + | 0.980384i | \(0.436849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.3182 | −0.442149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 41.3900i | − | 0.726140i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 21.0646 | + | 21.0646i | 0.357027 | + | 0.357027i | 0.862716 | − | 0.505689i | \(-0.168762\pi\) |
−0.505689 | + | 0.862716i | \(0.668762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68.7531 | + | 68.7531i | 1.12710 | + | 1.12710i | 0.990647 | + | 0.136453i | \(0.0435703\pi\) |
0.136453 | + | 0.990647i | \(0.456430\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.96414i | 0.0311768i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.1406 | 0.232932 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −67.8242 | + | 67.8242i | −1.01230 | + | 1.01230i | −0.0123779 | + | 0.999923i | \(0.503940\pi\) |
−0.999923 | + | 0.0123779i | \(0.996060\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 28.3880 | − | 28.3880i | 0.411420 | − | 0.411420i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33.3094 | 0.469147 | 0.234573 | − | 0.972098i | \(-0.424631\pi\) | ||||
0.234573 | + | 0.972098i | \(0.424631\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 18.6331i | − | 0.255248i | −0.991823 | − | 0.127624i | \(-0.959265\pi\) | ||
0.991823 | − | 0.127624i | \(-0.0407351\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −28.5946 | − | 28.5946i | −0.381261 | − | 0.381261i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.75745 | − | 8.75745i | −0.113733 | − | 0.113733i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.29222i | 0.0796483i | 0.999207 | + | 0.0398242i | \(0.0126798\pi\) | ||||
−0.999207 | + | 0.0398242i | \(0.987320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 72.0774 | − | 72.0774i | 0.868402 | − | 0.868402i | −0.123894 | − | 0.992296i | \(-0.539538\pi\) |
0.992296 | + | 0.123894i | \(0.0395382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.57727 | − | 3.57727i | 0.0420855 | − | 0.0420855i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 87.2275 | 1.00262 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | −55.8101 | − | 55.8101i | −0.600108 | − | 0.600108i | ||||
\(94\) | 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 | ||||||||
\(99\) | 40.1280 | − | 40.1280i | 0.405334 | − | 0.405334i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 90.3100 | − | 90.3100i | 0.894159 | − | 0.894159i | −0.100753 | − | 0.994912i | \(-0.532125\pi\) |
0.994912 | + | 0.100753i | \(0.0321251\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −95.1656 | −0.923938 | −0.461969 | − | 0.886896i | \(-0.652857\pi\) | ||||
−0.461969 | + | 0.886896i | \(0.652857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.45781i | 0.0138839i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −27.2524 | − | 27.2524i | −0.254695 | − | 0.254695i | 0.568197 | − | 0.822892i | \(-0.307641\pi\) |
−0.822892 | + | 0.568197i | \(0.807641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 132.413 | + | 132.413i | 1.21480 | + | 1.21480i | 0.969430 | + | 0.245366i | \(0.0789082\pi\) |
0.245366 | + | 0.969430i | \(0.421092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 24.8690i | − | 0.224045i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 37.9551 | 0.335886 | 0.167943 | − | 0.985797i | \(-0.446288\pi\) | ||||
0.167943 | + | 0.985797i | \(0.446288\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.0699 | − | 21.0699i | 0.183217 | − | 0.183217i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −24.9838 | + | 24.9838i | −0.213537 | + | 0.213537i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.57649 | 0.0216512 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 236.835i | 1.95731i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 34.8637 | + | 34.8637i | 0.283445 | + | 0.283445i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −43.9488 | − | 43.9488i | −0.351591 | − | 0.351591i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 96.5399i | − | 0.760157i | −0.924954 | − | 0.380078i | \(-0.875897\pi\) | ||
0.924954 | − | 0.380078i | \(-0.124103\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 55.6901 | 0.431706 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 54.5082 | − | 54.5082i | 0.416093 | − | 0.416093i | −0.467762 | − | 0.883855i | \(-0.654939\pi\) |
0.883855 | + | 0.467762i | \(0.154939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.0629 | − | 11.0629i | 0.0831801 | − | 0.0831801i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.67992 | −0.0494809 | ||||||||
\(136\) | 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 | 0.693890 | − | 0.720081i | \(-0.255896\pi\) |
−0.720081 | + | 0.693890i | \(0.755896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.1961 | − | 13.1961i | −0.0935896 | − | 0.0935896i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 222.789i | − | 1.55797i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 64.7415 | 0.446493 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 59.4875 | − | 59.4875i | 0.404677 | − | 0.404677i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.9718 | − | 18.9718i | 0.127328 | − | 0.127328i | −0.640571 | − | 0.767899i | \(-0.721302\pi\) |
0.767899 | + | 0.640571i | \(0.221302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −103.209 | −0.683503 | −0.341751 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341751 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.8059i | 0.0771626i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −41.4230 | − | 41.4230i | −0.267245 | − | 0.267245i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −88.2067 | − | 88.2067i | −0.561826 | − | 0.561826i | 0.368000 | − | 0.929826i | \(-0.380043\pi\) |
−0.929826 | + | 0.368000i | \(0.880043\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 101.689i | − | 0.639551i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.1754 | 0.0942571 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.8038 | + | 18.8038i | −0.115361 | + | 0.115361i | −0.762431 | − | 0.647070i | \(-0.775994\pi\) |
0.647070 | + | 0.762431i | \(0.275994\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 29.7836 | − | 29.7836i | 0.180507 | − | 0.180507i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 267.105 | 1.59943 | 0.799715 | − | 0.600380i | \(-0.204984\pi\) | ||||
0.799715 | + | 0.600380i | \(0.204984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 30.2905i | − | 0.179234i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 50.6922 | + | 50.6922i | 0.296445 | + | 0.296445i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 153.520 | + | 153.520i | 0.887396 | + | 0.887396i | 0.994272 | − | 0.106876i | \(-0.0340849\pi\) |
−0.106876 | + | 0.994272i | \(0.534085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 15.2858i | − | 0.0873476i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −51.5975 | −0.291511 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −123.581 | + | 123.581i | −0.690399 | + | 0.690399i | −0.962320 | − | 0.271921i | \(-0.912341\pi\) |
0.271921 | + | 0.962320i | \(0.412341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −122.965 | + | 122.965i | −0.679364 | + | 0.679364i | −0.959856 | − | 0.280493i | \(-0.909502\pi\) |
0.280493 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −168.410 | −0.920273 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 18.4581i | − | 0.0997737i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −52.6385 | − | 52.6385i | −0.281489 | − | 0.281489i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.40557 | − | 2.40557i | −0.0127279 | − | 0.0127279i | ||||
\(190\) | 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 | ||||||||
\(195\) | −18.5434 | + | 18.5434i | −0.0950942 | + | 0.0950942i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −28.9507 | + | 28.9507i | −0.146958 | + | 0.146958i | −0.776758 | − | 0.629800i | \(-0.783137\pi\) |
0.629800 | + | 0.776758i | \(0.283137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.6253 | −0.138821 | −0.0694104 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694104 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 166.135i | − | 0.826541i | ||||||
\(202\) | 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 | ||||||||
\(207\) | 69.5360i | 0.335923i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −452.039 | −2.16287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.35041 | + | 7.35041i | −0.0348361 | + | 0.0348361i | −0.724310 | − | 0.689474i | \(-0.757842\pi\) |
0.689474 | + | 0.724310i | \(0.257842\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −40.7955 | + | 40.7955i | −0.191528 | + | 0.191528i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 41.3340 | 0.192251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 29.8345i | − | 0.137486i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.8208 | + | 22.8208i | 0.104205 | + | 0.104205i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.7729 | + | 32.7729i | 0.148294 | + | 0.148294i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 386.106i | 1.73142i | 0.500549 | + | 0.865708i | \(0.333131\pi\) | ||||
−0.500549 | + | 0.865708i | \(0.666869\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 70.0421 | 0.311298 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 49.7286 | − | 49.7286i | 0.219069 | − | 0.219069i | −0.589037 | − | 0.808106i | \(-0.700493\pi\) |
0.808106 | + | 0.589037i | \(0.200493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 191.870 | − | 191.870i | 0.837861 | − | 0.837861i | −0.150716 | − | 0.988577i | \(-0.548158\pi\) |
0.988577 | + | 0.150716i | \(0.0481579\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.4513 | 0.0928627 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | −7.70636 | − | 7.70636i | −0.0325163 | − | 0.0325163i | ||||
\(238\) | 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 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 44.1525 | − | 44.1525i | 0.180214 | − | 0.180214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 281.441 | 1.13944 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 176.553i | 0.709047i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −162.716 | − | 162.716i | −0.648272 | − | 0.648272i | 0.304303 | − | 0.952575i | \(-0.401576\pi\) |
−0.952575 | + | 0.304303i | \(0.901576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −310.038 | − | 310.038i | −1.22545 | − | 1.22545i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.76249i | 0.0343627i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 101.165 | 0.393637 | 0.196819 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196819 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.64713 | − | 6.64713i | 0.0256646 | − | 0.0256646i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −106.831 | + | 106.831i | −0.409316 | + | 0.409316i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −323.635 | −1.23055 | −0.615276 | − | 0.788312i | \(-0.710955\pi\) | ||||
−0.615276 | + | 0.788312i | \(0.710955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 75.4747i | − | 0.284810i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9983 | − | 12.9983i | −0.0486828 | − | 0.0486828i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.51275 | − | 1.51275i | −0.00562361 | − | 0.00562361i | 0.704289 | − | 0.709913i | \(-0.251266\pi\) |
−0.709913 | + | 0.704289i | \(0.751266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 166.098i | 0.612909i | 0.951885 | + | 0.306454i | \(0.0991427\pi\) | ||||
−0.951885 | + | 0.306454i | \(0.900857\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.3556 | −0.0489218 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −312.294 | + | 312.294i | −1.13562 | + | 1.13562i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −317.830 | + | 317.830i | −1.14740 | + | 1.14740i | −0.160338 | + | 0.987062i | \(0.551259\pi\) |
−0.987062 | + | 0.160338i | \(0.948741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 136.706 | 0.489986 | ||||||||
\(280\) | 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 | 0.959973 | − | 0.280092i | \(-0.0903649\pi\) |
−0.280092 | + | 0.959973i | \(0.590365\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 37.6244 | + | 37.6244i | 0.132016 | + | 0.132016i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.6371i | 0.0649378i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −273.513 | −0.946413 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −175.911 | + | 175.911i | −0.604506 | + | 0.604506i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 75.3645 | − | 75.3645i | 0.257217 | − | 0.257217i | −0.566704 | − | 0.823921i | \(-0.691782\pi\) |
0.823921 | + | 0.566704i | \(0.191782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.2964 | −0.129818 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 98.2932i | 0.330953i | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 221.214i | 0.730078i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −124.996 | −0.409824 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 111.544 | − | 111.544i | 0.363337 | − | 0.363337i | −0.501703 | − | 0.865040i | \(-0.667293\pi\) |
0.865040 | + | 0.501703i | \(0.167293\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 116.554 | − | 116.554i | 0.377196 | − | 0.377196i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −224.484 | −0.721813 | −0.360906 | − | 0.932602i | \(-0.617533\pi\) | ||||
−0.360906 | + | 0.932602i | \(0.617533\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 488.339i | − | 1.56019i | −0.625661 | − | 0.780095i | \(-0.715171\pi\) | ||
0.625661 | − | 0.780095i | \(-0.284829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.78545 | − | 1.78545i | −0.00566809 | − | 0.00566809i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −257.361 | − | 257.361i | −0.811863 | − | 0.811863i | 0.173050 | − | 0.984913i | \(-0.444638\pi\) |
−0.984913 | + | 0.173050i | \(0.944638\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 952.652i | − | 2.98637i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 66.7545 | 0.207958 | ||||||||
\(322\) | 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 | ||||||||
\(327\) | −324.344 | −0.991877 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.05427i | − | 0.0214416i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 123.553 | + | 123.553i | 0.373271 | + | 0.373271i | 0.868667 | − | 0.495396i | \(-0.164977\pi\) |
−0.495396 | + | 0.868667i | \(0.664977\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.4582 | + | 30.4582i | 0.0914661 | + | 0.0914661i | ||||
\(334\) | 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 | ||||||||
\(339\) | −46.4853 | + | 46.4853i | −0.137125 | + | 0.137125i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −609.528 | + | 609.528i | −1.78747 | + | 1.78747i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 63.8813 | 0.186243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 51.6106i | 0.149596i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 123.212 | + | 123.212i | 0.355076 | + | 0.355076i | 0.861994 | − | 0.506918i | \(-0.169215\pi\) |
−0.506918 | + | 0.861994i | \(0.669215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −115.371 | − | 115.371i | −0.330575 | − | 0.330575i | 0.522230 | − | 0.852805i | \(-0.325100\pi\) |
−0.852805 | + | 0.522230i | \(0.825100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 61.1977i | − | 0.174352i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 650.544 | 1.84290 | 0.921451 | − | 0.388495i | \(-0.127005\pi\) | ||||
0.921451 | + | 0.388495i | \(0.127005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.2790 | + | 30.2790i | −0.0852930 | + | 0.0852930i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.15554 | + | 3.15554i | −0.00883906 | + | 0.00883906i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 94.4878 | 0.263197 | 0.131599 | − | 0.991303i | \(-0.457989\pi\) | ||||
0.131599 | + | 0.991303i | \(0.457989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 210.044i | − | 0.581838i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −290.063 | − | 290.063i | −0.799070 | − | 0.799070i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9379 | + | 16.9379i | 0.0464053 | + | 0.0464053i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 131.379i | 0.357982i | 0.983851 | + | 0.178991i | \(0.0572832\pi\) | ||||
−0.983851 | + | 0.178991i | \(0.942717\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −85.3983 | −0.231432 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.1799 | − | 27.1799i | 0.0732612 | − | 0.0732612i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 275.796 | − | 275.796i | 0.739400 | − | 0.739400i | −0.233062 | − | 0.972462i | \(-0.574874\pi\) |
0.972462 | + | 0.233062i | \(0.0748745\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 107.652 | 0.287073 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 593.125i | 1.57328i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0427 | + | 13.0427i | 0.0344135 | + | 0.0344135i | 0.724104 | − | 0.689691i | \(-0.242253\pi\) |
−0.689691 | + | 0.724104i | \(0.742253\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 118.237 | + | 118.237i | 0.310333 | + | 0.310333i | ||||
\(382\) | 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 | ||||||||
\(387\) | −68.2062 | + | 68.2062i | −0.176243 | + | 0.176243i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 233.267 | − | 233.267i | 0.599659 | − | 0.599659i | −0.340563 | − | 0.940222i | \(-0.610618\pi\) |
0.940222 | + | 0.340563i | \(0.110618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 91.2149 | 0.233286 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 133.517i | 0.339738i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.71977 | − | 5.71977i | −0.0144804 | − | 0.0144804i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 83.7693 | + | 83.7693i | 0.211006 | + | 0.211006i | 0.804695 | − | 0.593689i | \(-0.202329\pi\) |
−0.593689 | + | 0.804695i | \(0.702329\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.0986i | 0.0679162i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 589.134 | 1.46916 | 0.734581 | − | 0.678521i | \(-0.237379\pi\) | ||||
0.734581 | + | 0.678521i | \(0.237379\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 379.494 | − | 379.494i | 0.941673 | − | 0.941673i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.18120 | − | 8.18120i | 0.0202005 | − | 0.0202005i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −271.606 | −0.667337 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 449.285i | 1.09850i | 0.835659 | + | 0.549248i | \(0.185086\pi\) | ||||
−0.835659 | + | 0.549248i | \(0.814914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.7617 | + | 31.7617i | 0.0772790 | + | 0.0772790i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.7913 | − | 13.7913i | −0.0333929 | − | 0.0333929i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 131.040i | 0.315759i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.91777 | 0.0213855 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 218.639 | − | 218.639i | 0.521811 | − | 0.521811i | −0.396307 | − | 0.918118i | \(-0.629708\pi\) |
0.918118 | + | 0.396307i | \(0.129708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 61.2101 | − | 61.2101i | 0.145392 | − | 0.145392i | −0.630664 | − | 0.776056i | \(-0.717217\pi\) |
0.776056 | + | 0.630664i | \(0.217217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 32.3238 | 0.0764156 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 91.8787i | − | 0.216185i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −45.0136 | − | 45.0136i | −0.105418 | − | 0.105418i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 272.860 | + | 272.860i | 0.636038 | + | 0.636038i | ||||
\(430\) | 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 | ||||||||
\(435\) | −79.2918 | + | 79.2918i | −0.182280 | + | 0.182280i | ||||
\(436\) | 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 | ||||||||
\(441\) | 145.714i | 0.330417i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −299.093 | − | 299.093i | −0.675153 | − | 0.675153i | 0.283746 | − | 0.958899i | \(-0.408423\pi\) |
−0.958899 | + | 0.283746i | \(0.908423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.64753 | − | 9.64753i | −0.0216798 | − | 0.0216798i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 46.4714i | 0.103963i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −44.5560 | −0.0992339 | −0.0496170 | − | 0.998768i | \(-0.515800\pi\) | ||||
−0.0496170 | + | 0.998768i | \(0.515800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 380.763 | − | 380.763i | 0.844263 | − | 0.844263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 126.405 | − | 126.405i | 0.279039 | − | 0.279039i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.91275 | −0.0217863 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 641.227i | − | 1.40312i | −0.712609 | − | 0.701562i | \(-0.752486\pi\) | ||
0.712609 | − | 0.701562i | \(-0.247514\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.4592 | − | 14.4592i | −0.0315015 | − | 0.0315015i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 393.690 | + | 393.690i | 0.853991 | + | 0.853991i | 0.990622 | − | 0.136631i | \(-0.0436273\pi\) |
−0.136631 | + | 0.990622i | \(0.543627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 395.861i | − | 0.854991i | −0.904018 | − | 0.427495i | \(-0.859396\pi\) | ||
0.904018 | − | 0.427495i | \(-0.140604\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 101.465 | 0.218205 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 83.1457 | − | 83.1457i | 0.178042 | − | 0.178042i | −0.612460 | − | 0.790502i | \(-0.709820\pi\) |
0.790502 | + | 0.612460i | \(0.209820\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 44.4054 | − | 44.4054i | 0.0946810 | − | 0.0946810i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 216.061 | 0.458729 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 608.217i | − | 1.28587i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −394.509 | − | 394.509i | −0.830546 | − | 0.830546i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 124.543 | + | 124.543i | 0.261096 | + | 0.261096i | ||||
\(478\) | 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 | ||||||||
\(483\) | −18.5860 | + | 18.5860i | −0.0384803 | + | 0.0384803i | ||||
\(484\) | 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 | ||||||||
\(489\) | − | 46.0597i | − | 0.0941916i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 489.133 | + | 489.133i | 0.996197 | + | 0.996197i | 0.999993 | − | 0.00379588i | \(-0.00120827\pi\) |
−0.00379588 | + | 0.999993i | \(0.501208\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 140.138 | + | 140.138i | 0.284255 | + | 0.284255i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 72.9546i | 0.147383i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.8081 | −0.0438795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −260.469 | + | 260.469i | −0.521982 | + | 0.521982i | −0.918170 | − | 0.396188i | \(-0.870333\pi\) |
0.396188 | + | 0.918170i | \(0.370333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −327.135 | + | 327.135i | −0.652965 | + | 0.652965i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −975.416 | −1.93920 | −0.969598 | − | 0.244701i | \(-0.921310\pi\) | ||||
−0.969598 | + | 0.244701i | \(0.921310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 164.188i | 0.325124i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.0981 | + | 37.0981i | 0.0731719 | + | 0.0731719i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 420.191 | + | 420.191i | 0.825523 | + | 0.825523i | 0.986894 | − | 0.161371i | \(-0.0515916\pi\) |
−0.161371 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1994i | 0.0238735i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −124.170 | −0.242047 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | −376.044 | −0.724556 | ||||||||
\(520\) | 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 | −0.996550 | − | 0.0829913i | \(-0.973553\pi\) |
−0.0829913 | − | 0.996550i | \(-0.526447\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.7212 | + | 18.7212i | 0.0356595 | + | 0.0356595i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 179.326i | − | 0.340278i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.25115 | 0.0155976 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63.1938 | − | 63.1938i | 0.119009 | − | 0.119009i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −237.064 | + | 237.064i | −0.444773 | + | 0.444773i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.5461 | 0.0926095 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 302.711i | − | 0.563708i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −649.691 | − | 649.691i | −1.20536 | − | 1.20536i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.5601 | + | 29.5601i | 0.0546398 | + | 0.0546398i | 0.733899 | − | 0.679259i | \(-0.237699\pi\) |
−0.679259 | + | 0.733899i | \(0.737699\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 301.201i | − | 0.554698i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −240.733 | −0.441711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 138.608 | − | 138.608i | 0.253397 | − | 0.253397i | −0.568965 | − | 0.822362i | \(-0.692656\pi\) |
0.822362 | + | 0.568965i | \(0.192656\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 206.259 | − | 206.259i | 0.375700 | − | 0.375700i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1203.45 | 2.18412 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.11960i | − | 0.00744955i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.6065 | + | 22.6065i | 0.0407324 | + | 0.0407324i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −60.4400 | − | 60.4400i | −0.108510 | − | 0.108510i | 0.650767 | − | 0.759277i | \(-0.274447\pi\) |
−0.759277 | + | 0.650767i | \(0.774447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 378.678i | 0.677421i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 128.938 | 0.229835 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −267.325 | + | 267.325i | −0.474822 | + | 0.474822i | −0.903471 | − | 0.428649i | \(-0.858990\pi\) |
0.428649 | + | 0.903471i | \(0.358990\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.5021 | + | 34.5021i | −0.0610656 | + | 0.0610656i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.89242 | 0.0103923 | ||||||||
\(568\) | 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 | 0.981154 | + | 0.193228i | \(0.0618956\pi\) |
0.193228 | + | 0.981154i | \(0.438104\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −237.591 | − | 237.591i | −0.414643 | − | 0.414643i | ||||
\(574\) | 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 | ||||||||
\(579\) | −173.368 | + | 173.368i | −0.299427 | + | 0.299427i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −47.1900 | + | 47.1900i | −0.0812220 | + | 0.0812220i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1110.59 | −1.90495 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 45.4218i | − | 0.0776441i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 420.085 | + | 420.085i | 0.715647 | + | 0.715647i | 0.967711 | − | 0.252064i | \(-0.0811093\pi\) |
−0.252064 | + | 0.967711i | \(0.581109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −769.993 | − | 769.993i | −1.30729 | − | 1.30729i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 70.9145i | − | 0.119991i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −740.798 | −1.24924 | −0.624619 | − | 0.780930i | \(-0.714746\pi\) | ||||
−0.624619 | + | 0.780930i | \(0.714746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34209 | + | 2.34209i | −0.00393628 | + | 0.00393628i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.8340 | − | 33.8340i | 0.0566733 | − | 0.0566733i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 435.161 | 0.726479 | 0.363240 | − | 0.931696i | \(-0.381671\pi\) | ||||
0.363240 | + | 0.931696i | \(0.381671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 380.001i | 0.632280i | 0.948712 | + | 0.316140i | \(0.102387\pi\) | ||||
−0.948712 | + | 0.316140i | \(0.897613\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 203.473 | + | 203.473i | 0.337434 | + | 0.337434i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −215.288 | − | 215.288i | −0.355849 | − | 0.355849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 181.813i | 0.299527i | 0.988722 | + | 0.149763i | \(0.0478512\pi\) | ||||
−0.988722 | + | 0.149763i | \(0.952149\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −57.1090 | −0.0937751 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 89.7303 | − | 89.7303i | 0.146858 | − | 0.146858i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −55.1479 | + | 55.1479i | −0.0899640 | + | 0.0899640i | −0.750657 | − | 0.660693i | \(-0.770263\pi\) |
0.660693 | + | 0.750657i | \(0.270263\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −63.3838 | −0.103063 | ||||||||
\(616\) | 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 | 0.629675 | − | 0.776859i | \(-0.283188\pi\) |
−0.776859 | + | 0.629675i | \(0.783188\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −85.1639 | − | 85.1639i | −0.137140 | − | 0.137140i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.94852i | − | 0.0111533i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −503.783 | −0.806053 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 553.633 | − | 553.633i | 0.882987 | − | 0.882987i | ||||
\(628\) | 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 | ||||||||
\(633\) | − | 18.0048i | − | 0.0284435i | ||||||
\(634\) | 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 | ||||||||
\(639\) | − | 99.9283i | − | 0.156382i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −218.329 | −0.340607 | −0.170304 | − | 0.985392i | \(-0.554475\pi\) | ||||
−0.170304 | + | 0.985392i | \(0.554475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −887.430 | + | 887.430i | −1.38014 | + | 1.38014i | −0.535787 | + | 0.844353i | \(0.679985\pi\) |
−0.844353 | + | 0.535787i | \(0.820015\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −50.6236 | + | 50.6236i | −0.0784861 | + | 0.0784861i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −223.177 | −0.344941 | −0.172470 | − | 0.985015i | \(-0.555175\pi\) | ||||
−0.172470 | + | 0.985015i | \(0.555175\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 563.520i | 0.868290i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.5396 | + | 36.5396i | 0.0561284 | + | 0.0561284i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −539.691 | − | 539.691i | −0.826479 | − | 0.826479i | 0.160549 | − | 0.987028i | \(-0.448674\pi\) |
−0.987028 | + | 0.160549i | \(0.948674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 99.0983i | 0.151295i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −55.8994 | −0.0850828 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −625.166 | + | 625.166i | −0.948659 | + | 0.948659i | −0.998745 | − | 0.0500862i | \(-0.984050\pi\) |
0.0500862 | + | 0.998745i | \(0.484050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 326.893 | − | 326.893i | 0.494544 | − | 0.494544i | −0.415191 | − | 0.909734i | \(-0.636285\pi\) |
0.909734 | + | 0.415191i | \(0.136285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −80.2770 | −0.121081 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.1129i | 0.0302450i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 825.404 | + | 825.404i | 1.23749 | + | 1.23749i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −472.881 | − | 472.881i | −0.706848 | − | 0.706848i | ||||
\(670\) | 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 | ||||||||
\(675\) | −85.7837 | + | 85.7837i | −0.127087 | + | 0.127087i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 126.017 | − | 126.017i | 0.186140 | − | 0.186140i | −0.607885 | − | 0.794025i | \(-0.707982\pi\) |
0.794025 | + | 0.607885i | \(0.207982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −94.0372 | −0.138494 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 121.810i | 0.178869i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −621.906 | − | 621.906i | −0.910551 | − | 0.910551i | 0.0857647 | − | 0.996315i | \(-0.472667\pi\) |
−0.996315 | + | 0.0857647i | \(0.972667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.5740 | + | 23.5740i | 0.0344145 | + | 0.0344145i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 469.984i | 0.684111i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 691.456 | 1.00357 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 403.376 | − | 403.376i | 0.583758 | − | 0.583758i | −0.352176 | − | 0.935934i | \(-0.614558\pi\) |
0.935934 | + | 0.352176i | \(0.114558\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.2724 | + | 26.2724i | −0.0379110 | + | 0.0379110i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.61889 | 0.00952359 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 112.022i | 0.160721i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 365.722 | + | 365.722i | 0.523207 | + | 0.523207i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −466.593 | − | 466.593i | −0.665611 | − | 0.665611i | 0.291086 | − | 0.956697i | \(-0.405983\pi\) |
−0.956697 | + | 0.291086i | \(0.905983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 343.109i | − | 0.488065i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.9912 | 0.0340300 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −59.1272 | + | 59.1272i | −0.0836311 | + | 0.0836311i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −822.764 | + | 822.764i | −1.16046 | + | 1.16046i | −0.176081 | + | 0.984376i | \(0.556342\pi\) |
−0.984376 | + | 0.176081i | \(0.943658\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.8767 | 0.0265494 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1056.22i | − | 1.48138i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 202.521 | + | 202.521i | 0.283246 | + | 0.283246i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −302.943 | − | 302.943i | −0.422515 | − | 0.422515i | ||||
\(718\) | 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 | ||||||||
\(723\) | 269.856 | − | 269.856i | 0.373245 | − | 0.373245i | ||||
\(724\) | 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 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 89.4704 | + | 89.4704i | 0.122395 | + | 0.122395i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 96.1768 | + | 96.1768i | 0.131210 | + | 0.131210i | 0.769662 | − | 0.638452i | \(-0.220425\pi\) |
−0.638452 | + | 0.769662i | \(0.720425\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 108.151i | 0.147144i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1814.43 | −2.46192 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −885.341 | + | 885.341i | −1.19803 | + | 1.19803i | −0.223268 | + | 0.974757i | \(0.571673\pi\) |
−0.974757 | + | 0.223268i | \(0.928327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −344.694 | + | 344.694i | −0.465174 | + | 0.465174i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 906.258 | 1.21973 | 0.609864 | − | 0.792506i | \(-0.291224\pi\) | ||||
0.609864 | + | 0.792506i | \(0.291224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.4917i | 0.0462976i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −216.232 | − | 216.232i | −0.289467 | − | 0.289467i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.8425 | + | 17.8425i | 0.0238218 | + | 0.0238218i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1147.02i | 1.52732i | 0.645618 | + | 0.763661i | \(0.276600\pi\) | ||||
−0.645618 | + | 0.763661i | \(0.723400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 398.572 | 0.529312 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 93.8192 | − | 93.8192i | 0.124264 | − | 0.124264i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −525.591 | + | 525.591i | −0.694308 | + | 0.694308i | −0.963177 | − | 0.268869i | \(-0.913350\pi\) |
0.268869 | + | 0.963177i | \(0.413350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 759.435 | 1.00057 | ||||||||
\(760\) | 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 | ||||||||
\(765\) | −10.7318 | − | 10.7318i | −0.0140285 | − | 0.0140285i | ||||
\(766\) | 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 | ||||||||
\(771\) | −123.901 | + | 123.901i | −0.160702 | + | 0.160702i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −275.915 | + | 275.915i | −0.356941 | + | 0.356941i | −0.862684 | − | 0.505743i | \(-0.831218\pi\) |
0.505743 | + | 0.862684i | \(0.331218\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1063.91 | −1.37279 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.2821i | 0.0209551i | ||||||||
\(778\) | 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 | ||||||||
\(783\) | − | 261.683i | − | 0.334205i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 160.364 | 0.204285 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −240.824 | + | 240.824i | −0.306002 | + | 0.306002i | −0.843356 | − | 0.537354i | \(-0.819424\pi\) |
0.537354 | + | 0.843356i | \(0.319424\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 396.371 | − | 396.371i | 0.502371 | − | 0.502371i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.8497 | −0.0314156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1145.14i | − | 1.44407i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 92.4373 | + | 92.4373i | 0.116273 | + | 0.116273i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 681.033 | + | 681.033i | 0.854496 | + | 0.854496i | 0.990683 | − | 0.136187i | \(-0.0434848\pi\) |
−0.136187 | + | 0.990683i | \(0.543485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 42.4012i | − | 0.0530678i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.8392 | 0.0397493 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | 3.70547 | 0.00459166 | ||||||||
\(808\) | 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 | 0.555546 | − | 0.831485i | \(-0.312509\pi\) |
−0.831485 | + | 0.555546i | \(0.812509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −203.428 | − | 203.428i | −0.250219 | − | 0.250219i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 34.1861i | − | 0.0419462i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 768.337 | 0.940437 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.3573 | − | 16.3573i | 0.0199722 | − | 0.0199722i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −382.528 | + | 382.528i | −0.465929 | + | 0.465929i | −0.900593 | − | 0.434664i | \(-0.856867\pi\) |
0.434664 | + | 0.900593i | \(0.356867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −730.046 | −0.887055 | −0.443527 | − | 0.896261i | \(-0.646273\pi\) | ||||
−0.443527 | + | 0.896261i | \(0.646273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 764.962i | − | 0.927227i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −252.094 | − | 252.094i | −0.304829 | − | 0.304829i | 0.538071 | − | 0.842900i | \(-0.319153\pi\) |
−0.842900 | + | 0.538071i | \(0.819153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 870.285 | + | 870.285i | 1.04980 | + | 1.04980i | 0.998693 | + | 0.0511072i | \(0.0162750\pi\) |
0.0511072 | + | 0.998693i | \(0.483725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 778.521i | − | 0.936849i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 191.143 | 0.229463 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −242.804 | + | 242.804i | −0.290784 | + | 0.290784i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −167.430 | + | 167.430i | −0.200036 | + | 0.200036i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 550.145 | 0.655715 | 0.327858 | − | 0.944727i | \(-0.393673\pi\) | ||||
0.327858 | + | 0.944727i | \(0.393673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1695.21i | 2.01571i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −493.315 | − | 493.315i | −0.585189 | − | 0.585189i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.5348 | + | 27.5348i | 0.0325855 | + | 0.0325855i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 155.059i | − | 0.183069i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −471.298 | −0.555121 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 235.327 | − | 235.327i | 0.276530 | − | 0.276530i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 676.266 | − | 676.266i | 0.792809 | − | 0.792809i | −0.189141 | − | 0.981950i | \(-0.560570\pi\) |
0.981950 | + | 0.189141i | \(0.0605703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −92.1607 | −0.107790 | ||||||||
\(856\) | 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 | −0.986434 | − | 0.164156i | \(-0.947510\pi\) |
−0.164156 | − | 0.986434i | \(-0.552490\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.8257 | − | 22.8257i | −0.0265107 | − | 0.0265107i | ||||
\(862\) | 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 | ||||||||
\(867\) | 334.984 | − | 334.984i | 0.386372 | − | 0.386372i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −84.1648 | + | 84.1648i | −0.0968524 | + | 0.0968524i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1129.67 | 1.29698 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 430.893i | − | 0.493577i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.7739 | + | 28.7739i | 0.0328845 | + | 0.0328845i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 406.278 | + | 406.278i | 0.463259 | + | 0.463259i | 0.899722 | − | 0.436463i | \(-0.143769\pi\) |
−0.436463 | + | 0.899722i | \(0.643769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 184.605i | 0.210017i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1009.42 | −1.14577 | −0.572884 | − | 0.819637i | \(-0.694175\pi\) | ||||
−0.572884 | + | 0.819637i | \(0.694175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.3792 | + | 56.3792i | −0.0638496 | + | 0.0638496i | −0.738311 | − | 0.674461i | \(-0.764376\pi\) |
0.674461 | + | 0.738311i | \(0.264376\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.9033 | − | 46.9033i | 0.0529981 | − | 0.0529981i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0431 | 0.0237239 | 0.0118620 | − | 0.999930i | \(-0.496224\pi\) | ||||
0.0118620 | + | 0.999930i | \(0.496224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.2060i | 0.0710978i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −120.384 | − | 120.384i | −0.135111 | − | 0.135111i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −182.063 | − | 182.063i | −0.203877 | − | 0.203877i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 224.677i | − | 0.251035i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −472.827 | −0.527121 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | −36.4610 | −0.0403777 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 223.556i | − | 0.247023i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −496.202 | − | 496.202i | −0.547080 | − | 0.547080i | 0.378515 | − | 0.925595i | \(-0.376435\pi\) |
−0.925595 | + | 0.378515i | \(0.876435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −270.930 | − | 270.930i | −0.298053 | − | 0.298053i | ||||
\(910\) | 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 | ||||||||
\(915\) | 153.088 | − | 153.088i | 0.167310 | − | 0.167310i | ||||
\(916\) | 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 | ||||||||
\(921\) | 273.227i | 0.296663i | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 285.497i | 0.307979i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1544.59 | 1.66264 | 0.831318 | − | 0.555797i | \(-0.187587\pi\) | ||||
0.831318 | + | 0.555797i | \(0.187587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 820.729 | − | 820.729i | 0.881556 | − | 0.881556i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 274.935 | − | 274.935i | 0.294679 | − | 0.294679i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 95.6992 | 0.102352 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 716.111i | 0.764259i | 0.924109 | + | 0.382130i | \(0.124809\pi\) | ||||
−0.924109 | + | 0.382130i | \(0.875191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 598.091 | + | 598.091i | 0.636945 | + | 0.636945i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −537.759 | − | 537.759i | −0.571476 | − | 0.571476i | 0.361065 | − | 0.932541i | \(-0.382413\pi\) |
−0.932541 | + | 0.361065i | \(0.882413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 659.807i | 0.699689i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.37344 | 0.00462797 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −734.420 | + | 734.420i | −0.775523 | + | 0.775523i | −0.979066 | − | 0.203543i | \(-0.934754\pi\) |
0.203543 | + | 0.979066i | \(0.434754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −155.176 | + | 155.176i | −0.163515 | + | 0.163515i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 630.402 | 0.662884 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 1166.76 | + | 1166.76i | 1.21918 | + | 1.21918i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9789i | 0.0177048i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1115.51 | −1.16078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −81.7572 | + | 81.7572i | −0.0848984 | + | 0.0848984i | ||||
\(964\) | 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 | ||||||||
\(969\) | 162.882i | 0.168093i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 62.5684 | + | 62.5684i | 0.0644371 | + | 0.0644371i | 0.738591 | − | 0.674154i | \(-0.235492\pi\) |
−0.674154 | + | 0.738591i | \(0.735492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.38359 | + | 2.38359i | 0.00244973 | + | 0.00244973i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 476.268i | 0.488480i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1740.21 | 1.78117 | 0.890587 | − | 0.454814i | \(-0.150294\pi\) | ||||
0.890587 | + | 0.454814i | \(0.150294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −141.961 | + | 141.961i | −0.145006 | + | 0.145006i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 397.239 | − | 397.239i | 0.404932 | − | 0.404932i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1451.81 | −1.47692 | −0.738460 | − | 0.674298i | \(-0.764446\pi\) | ||||
−0.738460 | + | 0.674298i | \(0.764446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 52.6337i | − | 0.0534353i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.63968 | + | 8.63968i | 0.00875348 | + | 0.00875348i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 526.976 | + | 526.976i | 0.532837 | + | 0.532837i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 22.1684i | − | 0.0223698i | −0.999937 | − | 0.0111849i | \(-0.996440\pi\) | ||
0.999937 | − | 0.0111849i | \(-0.00356033\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −302.641 | −0.304775 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.1121 | − | 25.1121i | 0.0252382 | − | 0.0252382i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.5020 | + | 13.5020i | −0.0135426 | + | 0.0135426i | −0.713846 | − | 0.700303i | \(-0.753048\pi\) |
0.700303 | + | 0.713846i | \(0.253048\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −74.6071 | −0.0746817 |
(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 | 384.3.l.a.223.3 | 16 | ||
3.2 | odd | 2 | 1152.3.m.f.991.4 | 16 | |||
4.3 | odd | 2 | 384.3.l.b.223.7 | 16 | |||
8.3 | odd | 2 | 192.3.l.a.175.2 | 16 | |||
8.5 | even | 2 | 48.3.l.a.19.6 | ✓ | 16 | ||
12.11 | even | 2 | 1152.3.m.c.991.4 | 16 | |||
16.3 | odd | 4 | 48.3.l.a.43.6 | yes | 16 | ||
16.5 | even | 4 | 384.3.l.b.31.7 | 16 | |||
16.11 | odd | 4 | inner | 384.3.l.a.31.3 | 16 | ||
16.13 | even | 4 | 192.3.l.a.79.2 | 16 | |||
24.5 | odd | 2 | 144.3.m.c.19.3 | 16 | |||
24.11 | even | 2 | 576.3.m.c.559.5 | 16 | |||
48.5 | odd | 4 | 1152.3.m.c.415.4 | 16 | |||
48.11 | even | 4 | 1152.3.m.f.415.4 | 16 | |||
48.29 | odd | 4 | 576.3.m.c.271.5 | 16 | |||
48.35 | even | 4 | 144.3.m.c.91.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.6 | ✓ | 16 | 8.5 | even | 2 | ||
48.3.l.a.43.6 | yes | 16 | 16.3 | odd | 4 | ||
144.3.m.c.19.3 | 16 | 24.5 | odd | 2 | |||
144.3.m.c.91.3 | 16 | 48.35 | even | 4 | |||
192.3.l.a.79.2 | 16 | 16.13 | even | 4 | |||
192.3.l.a.175.2 | 16 | 8.3 | odd | 2 | |||
384.3.l.a.31.3 | 16 | 16.11 | odd | 4 | inner | ||
384.3.l.a.223.3 | 16 | 1.1 | even | 1 | trivial | ||
384.3.l.b.31.7 | 16 | 16.5 | even | 4 | |||
384.3.l.b.223.7 | 16 | 4.3 | odd | 2 | |||
576.3.m.c.271.5 | 16 | 48.29 | odd | 4 | |||
576.3.m.c.559.5 | 16 | 24.11 | even | 2 | |||
1152.3.m.c.415.4 | 16 | 48.5 | odd | 4 | |||
1152.3.m.c.991.4 | 16 | 12.11 | even | 2 | |||
1152.3.m.f.415.4 | 16 | 48.11 | even | 4 | |||
1152.3.m.f.991.4 | 16 | 3.2 | odd | 2 |