Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(301,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.m (of order \(5\), degree \(4\), 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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.2 | ||
Character | \(\chi\) | \(=\) | 1500.301 |
Dual form | 1500.2.m.c.1201.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.31873 | −0.498431 | −0.249216 | − | 0.968448i | \(-0.580173\pi\) | ||||
−0.249216 | + | 0.968448i | \(0.580173\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.25737 | + | 0.913532i | −0.379111 | + | 0.275440i | −0.760979 | − | 0.648777i | \(-0.775281\pi\) |
0.381868 | + | 0.924217i | \(0.375281\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.96447 | − | 1.42727i | −0.544846 | − | 0.395854i | 0.281036 | − | 0.959697i | \(-0.409322\pi\) |
−0.825882 | + | 0.563844i | \(0.809322\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.406161 | − | 1.25004i | −0.0985085 | − | 0.303178i | 0.889644 | − | 0.456655i | \(-0.150953\pi\) |
−0.988152 | + | 0.153477i | \(0.950953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.315522 | − | 0.971077i | −0.0723857 | − | 0.222780i | 0.908318 | − | 0.418280i | \(-0.137367\pi\) |
−0.980704 | + | 0.195500i | \(0.937367\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.407508 | + | 1.25418i | −0.0889256 | + | 0.273685i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.05137 | + | 2.94350i | −0.844770 | + | 0.613761i | −0.923699 | − | 0.383119i | \(-0.874850\pi\) |
0.0789291 | + | 0.996880i | \(0.474850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.82443 | + | 5.61503i | −0.338789 | + | 1.04268i | 0.626037 | + | 0.779794i | \(0.284676\pi\) |
−0.964825 | + | 0.262891i | \(0.915324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.73547 | + | 8.41891i | 0.491305 | + | 1.51208i | 0.822637 | + | 0.568567i | \(0.192502\pi\) |
−0.331332 | + | 0.943514i | \(0.607498\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.480272 | + | 1.47813i | 0.0836047 | + | 0.257309i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.06542 | − | 2.95370i | −0.668352 | − | 0.485586i | 0.201121 | − | 0.979566i | \(-0.435541\pi\) |
−0.869473 | + | 0.493981i | \(0.835541\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.96447 | + | 1.42727i | −0.314567 | + | 0.228546i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.43499 | − | 4.67529i | −1.00498 | − | 0.730158i | −0.0418271 | − | 0.999125i | \(-0.513318\pi\) |
−0.963150 | + | 0.268967i | \(0.913318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.84831 | −1.04436 | −0.522179 | − | 0.852836i | \(-0.674881\pi\) | ||||
−0.522179 | + | 0.852836i | \(0.674881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.39575 | − | 7.37336i | 0.349456 | − | 1.07552i | −0.609698 | − | 0.792633i | \(-0.708709\pi\) |
0.959155 | − | 0.282882i | \(-0.0912906\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.26096 | −0.751566 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.31436 | −0.184048 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.22067 | + | 3.75685i | −0.167673 | + | 0.516043i | −0.999223 | − | 0.0394057i | \(-0.987454\pi\) |
0.831551 | + | 0.555449i | \(0.187454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.02105 | −0.135241 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.35355 | + | 4.61613i | 0.827162 | + | 0.600969i | 0.918755 | − | 0.394828i | \(-0.129196\pi\) |
−0.0915928 | + | 0.995797i | \(0.529196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.83287 | − | 2.05820i | 0.362711 | − | 0.263525i | −0.391471 | − | 0.920191i | \(-0.628034\pi\) |
0.754182 | + | 0.656665i | \(0.228034\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.06687 | + | 0.775127i | 0.134413 | + | 0.0976568i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.57475 | − | 7.92426i | −0.314555 | − | 0.968102i | −0.975937 | − | 0.218052i | \(-0.930030\pi\) |
0.661382 | − | 0.750050i | \(-0.269970\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.54749 | + | 4.76268i | 0.186296 | + | 0.573359i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00454 | + | 12.3247i | −0.475252 | + | 1.46267i | 0.370366 | + | 0.928886i | \(0.379232\pi\) |
−0.845618 | + | 0.533788i | \(0.820768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2862 | + | 7.47339i | −1.20391 | + | 0.874694i | −0.994664 | − | 0.103168i | \(-0.967102\pi\) |
−0.209249 | + | 0.977862i | \(0.567102\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.65812 | − | 1.20470i | 0.188961 | − | 0.137288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.386585 | + | 1.18979i | −0.0434942 | + | 0.133861i | −0.970446 | − | 0.241320i | \(-0.922420\pi\) |
0.926951 | + | 0.375182i | \(0.122420\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.53607 | + | 7.80521i | 0.278370 | + | 0.856734i | 0.988308 | + | 0.152470i | \(0.0487227\pi\) |
−0.709939 | + | 0.704264i | \(0.751277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.77643 | + | 3.47028i | 0.512087 | + | 0.372053i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.74667 | + | 5.62829i | −0.821146 | + | 0.596597i | −0.917040 | − | 0.398794i | \(-0.869429\pi\) |
0.0958948 | + | 0.995391i | \(0.469429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.59059 | + | 1.88218i | 0.271568 | + | 0.197306i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.85217 | 0.917927 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.02874 | − | 15.4769i | 0.510591 | − | 1.57144i | −0.280573 | − | 0.959833i | \(-0.590524\pi\) |
0.791164 | − | 0.611604i | \(-0.209476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.55419 | 0.156202 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.63722 | 0.560925 | 0.280462 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280462 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.59994 | − | 8.00179i | 0.256179 | − | 0.788439i | −0.737415 | − | 0.675439i | \(-0.763954\pi\) |
0.993595 | − | 0.113000i | \(-0.0360460\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.06196 | −0.199337 | −0.0996687 | − | 0.995021i | \(-0.531778\pi\) | ||||
−0.0996687 | + | 0.995021i | \(0.531778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3052 | − | 8.21372i | −1.08284 | − | 0.786731i | −0.104666 | − | 0.994507i | \(-0.533377\pi\) |
−0.978176 | + | 0.207776i | \(0.933377\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.06542 | + | 2.95370i | −0.385873 | + | 0.280353i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.81862 | − | 3.50093i | −0.453297 | − | 0.329340i | 0.337599 | − | 0.941290i | \(-0.390385\pi\) |
−0.790896 | + | 0.611950i | \(0.790385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.750360 | + | 2.30937i | 0.0693708 | + | 0.213502i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.535615 | + | 1.64845i | 0.0490997 | + | 0.151113i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.65275 | + | 8.16433i | −0.241159 | + | 0.742211i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.43499 | + | 4.67529i | −0.580224 | + | 0.421557i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.96004 | − | 1.42406i | 0.173926 | − | 0.126364i | −0.497417 | − | 0.867512i | \(-0.665718\pi\) |
0.671342 | + | 0.741147i | \(0.265718\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.11624 | + | 6.51313i | −0.186325 | + | 0.573449i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.37948 | + | 10.4010i | 0.295267 | + | 0.908737i | 0.983132 | + | 0.182899i | \(0.0585481\pi\) |
−0.687865 | + | 0.725839i | \(0.741452\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.416087 | + | 1.28058i | 0.0360793 | + | 0.111041i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.02256 | + | 2.19602i | 0.258235 | + | 0.187618i | 0.709368 | − | 0.704838i | \(-0.248980\pi\) |
−0.451134 | + | 0.892456i | \(0.648980\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.73765 | − | 1.26247i | 0.147385 | − | 0.107082i | −0.511649 | − | 0.859194i | \(-0.670965\pi\) |
0.659034 | + | 0.752113i | \(0.270965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.27216 | − | 4.55699i | −0.528211 | − | 0.383768i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.77392 | 0.315591 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.62573 | + | 5.00347i | −0.134088 | + | 0.412680i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.85344 | −0.643379 | −0.321690 | − | 0.946845i | \(-0.604251\pi\) | ||||
−0.321690 | + | 0.946845i | \(0.604251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5124 | 1.83203 | 0.916016 | − | 0.401141i | \(-0.131386\pi\) | ||||
0.916016 | + | 0.401141i | \(0.131386\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.406161 | + | 1.25004i | −0.0328362 | + | 0.101059i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.4083 | −1.54895 | −0.774477 | − | 0.632602i | \(-0.781987\pi\) | ||||
−0.774477 | + | 0.632602i | \(0.781987\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.19577 | + | 2.32186i | 0.253441 | + | 0.184136i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.34265 | − | 3.88166i | 0.421060 | − | 0.305918i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2473 | − | 8.89817i | −0.959281 | − | 0.696959i | −0.00629741 | − | 0.999980i | \(-0.502005\pi\) |
−0.952984 | + | 0.303022i | \(0.902005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.84227 | + | 17.9807i | 0.452089 | + | 1.39139i | 0.874519 | + | 0.484990i | \(0.161177\pi\) |
−0.422431 | + | 0.906395i | \(0.638823\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.19518 | − | 6.75608i | −0.168860 | − | 0.519698i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.315522 | + | 0.971077i | −0.0241286 | + | 0.0742601i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.4729 | − | 14.1479i | 1.48050 | − | 1.07564i | 0.503100 | − | 0.864228i | \(-0.332193\pi\) |
0.977396 | − | 0.211415i | \(-0.0678072\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.35355 | − | 4.61613i | 0.477562 | − | 0.346969i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.461162 | − | 1.41931i | 0.0344689 | − | 0.106084i | −0.932342 | − | 0.361578i | \(-0.882238\pi\) |
0.966811 | + | 0.255494i | \(0.0822381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.809018 | − | 2.48990i | −0.0601338 | − | 0.185073i | 0.916477 | − | 0.400087i | \(-0.131020\pi\) |
−0.976611 | + | 0.215014i | \(0.931020\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.08206 | − | 3.33023i | −0.0799881 | − | 0.246178i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.65264 | + | 1.20071i | 0.120853 | + | 0.0878050i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.06687 | − | 0.775127i | 0.0776035 | − | 0.0563822i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6599 | − | 12.1041i | −1.20547 | − | 0.875824i | −0.210657 | − | 0.977560i | \(-0.567560\pi\) |
−0.994811 | + | 0.101736i | \(0.967560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.15953 | 0.371391 | 0.185696 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185696 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.24799 | + | 9.99630i | −0.231410 | + | 0.712207i | 0.766167 | + | 0.642641i | \(0.222161\pi\) |
−0.997577 | + | 0.0695657i | \(0.977839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.65216 | 0.258895 | 0.129447 | − | 0.991586i | \(-0.458680\pi\) | ||||
0.129447 | + | 0.991586i | \(0.458680\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.33206 | −0.587698 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.40593 | − | 7.40468i | 0.168863 | − | 0.519707i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.00777 | 0.348064 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.28384 | + | 0.932763i | 0.0888049 | + | 0.0645206i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3259 | − | 15.4941i | 1.46813 | − | 1.06666i | 0.486983 | − | 0.873411i | \(-0.338097\pi\) |
0.981150 | − | 0.193249i | \(-0.0619026\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.4840 | + | 7.61709i | 0.718354 | + | 0.521914i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.60733 | − | 11.1022i | −0.244882 | − | 0.753669i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.92899 | + | 12.0922i | 0.265497 | + | 0.817115i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.986247 | + | 3.03536i | −0.0663422 | + | 0.204180i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.9621 | + | 10.8706i | −1.00194 | + | 0.727950i | −0.962503 | − | 0.271272i | \(-0.912556\pi\) |
−0.0394348 | + | 0.999222i | \(0.512556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0976 | + | 10.9690i | −1.00206 | + | 0.728039i | −0.962529 | − | 0.271179i | \(-0.912586\pi\) |
−0.0395311 | + | 0.999218i | \(0.512586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.63423 | − | 26.5734i | 0.570566 | − | 1.75602i | −0.0802368 | − | 0.996776i | \(-0.525568\pi\) |
0.650803 | − | 0.759247i | \(-0.274432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.633347 | − | 1.94924i | −0.0416712 | − | 0.128251i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.65043 | + | 23.5456i | 0.501196 | + | 1.54252i | 0.807073 | + | 0.590452i | \(0.201050\pi\) |
−0.305877 | + | 0.952071i | \(0.598950\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.01209 | + | 0.735329i | 0.0657425 | + | 0.0477647i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.47102 | − | 6.88110i | 0.612629 | − | 0.445101i | −0.237710 | − | 0.971336i | \(-0.576397\pi\) |
0.850339 | + | 0.526235i | \(0.176397\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.1221 | − | 17.5257i | −1.55384 | − | 1.12893i | −0.940842 | − | 0.338846i | \(-0.889963\pi\) |
−0.612998 | − | 0.790084i | \(-0.710037\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.766156 | + | 2.35799i | −0.0487493 | + | 0.150035i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.20689 | 0.520090 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.87297 | −0.181340 | −0.0906700 | − | 0.995881i | \(-0.528901\pi\) | ||||
−0.0906700 | + | 0.995881i | \(0.528901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.40510 | − | 7.40212i | 0.151207 | − | 0.465367i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.11716 | 0.506334 | 0.253167 | − | 0.967423i | \(-0.418528\pi\) | ||||
0.253167 | + | 0.967423i | \(0.418528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.36118 | + | 3.89512i | 0.333127 | + | 0.242031i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.77643 | − | 3.47028i | 0.295654 | − | 0.214805i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0467 | − | 13.1117i | −1.11281 | − | 0.808501i | −0.129703 | − | 0.991553i | \(-0.541403\pi\) |
−0.983103 | + | 0.183051i | \(0.941403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.95897 | + | 9.10676i | 0.181086 | + | 0.557325i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.53369 | − | 7.79789i | −0.154482 | − | 0.475446i | 0.843626 | − | 0.536931i | \(-0.180416\pi\) |
−0.998108 | + | 0.0614851i | \(0.980416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.93158 | + | 9.02246i | −0.178081 | + | 0.548075i | −0.999761 | − | 0.0218733i | \(-0.993037\pi\) |
0.821680 | + | 0.569949i | \(0.193037\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.59059 | − | 1.88218i | 0.156790 | − | 0.113915i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.371885 | + | 0.270190i | −0.0223444 | + | 0.0162341i | −0.598901 | − | 0.800823i | \(-0.704396\pi\) |
0.576557 | + | 0.817057i | \(0.304396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.73547 | − | 8.41891i | 0.163768 | − | 0.504027i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.71493 | − | 14.5111i | −0.281269 | − | 0.865658i | −0.987492 | − | 0.157668i | \(-0.949602\pi\) |
0.706223 | − | 0.707990i | \(-0.250398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.29800 | − | 10.1502i | −0.196046 | − | 0.603366i | −0.999963 | − | 0.00862506i | \(-0.997255\pi\) |
0.803917 | − | 0.594741i | \(-0.202745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48598 | + | 6.16543i | 0.500912 | + | 0.363934i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3557 | − | 8.97692i | 0.726804 | − | 0.528054i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1654 | − | 9.56522i | −0.771770 | − | 0.560723i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.8334 | 1.80130 | 0.900652 | − | 0.434541i | \(-0.143089\pi\) | ||||
0.900652 | + | 0.434541i | \(0.143089\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.480272 | − | 1.47813i | 0.0278682 | − | 0.0857696i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.1600 | 0.703229 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.03104 | 0.520541 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.74200 | − | 5.36132i | 0.100075 | − | 0.308000i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8634 | 1.01952 | 0.509758 | − | 0.860318i | \(-0.329735\pi\) | ||||
0.509758 | + | 0.860318i | \(0.329735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.80673 | − | 4.94538i | −0.387221 | − | 0.281333i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.75942 | − | 7.09063i | 0.553406 | − | 0.402073i | −0.275634 | − | 0.961263i | \(-0.588888\pi\) |
0.829040 | + | 0.559190i | \(0.188888\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.1766 | − | 11.0264i | −0.857830 | − | 0.623250i | 0.0694641 | − | 0.997584i | \(-0.477871\pi\) |
−0.927294 | + | 0.374335i | \(0.877871\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.31133 | − | 10.1912i | −0.185983 | − | 0.572395i | 0.813981 | − | 0.580891i | \(-0.197296\pi\) |
−0.999964 | + | 0.00849553i | \(0.997296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.83552 | − | 8.72685i | −0.158759 | − | 0.488610i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.637181 | + | 1.96104i | −0.0355640 | + | 0.109455i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.08573 | + | 0.788827i | −0.0604115 | + | 0.0438915i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.3052 | + | 8.21372i | −0.625179 | + | 0.454219i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.15934 | + | 9.72344i | −0.174180 | + | 0.536071i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.671547 | + | 2.06681i | 0.0369116 | + | 0.113602i | 0.967815 | − | 0.251664i | \(-0.0809779\pi\) |
−0.930903 | + | 0.365266i | \(0.880978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.55285 | + | 4.77919i | 0.0850959 | + | 0.261898i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.14603 | − | 5.91844i | −0.443743 | − | 0.322398i | 0.343378 | − | 0.939197i | \(-0.388429\pi\) |
−0.787120 | + | 0.616800i | \(0.788429\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.81862 | + | 3.50093i | −0.261711 | + | 0.190144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.1304 | − | 8.08674i | −0.602747 | − | 0.437922i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1688 | 0.873035 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.53489 | + | 13.9570i | −0.243446 | + | 0.749249i | 0.752442 | + | 0.658658i | \(0.228876\pi\) |
−0.995888 | + | 0.0905912i | \(0.971124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.5685 | 0.993949 | 0.496974 | − | 0.867765i | \(-0.334444\pi\) | ||||
0.496974 | + | 0.867765i | \(0.334444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.42822 | 0.129609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.70763 | − | 17.5663i | 0.303787 | − | 0.934959i | −0.676340 | − | 0.736589i | \(-0.736435\pi\) |
0.980127 | − | 0.198370i | \(-0.0635648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.73329 | 0.0917352 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.9550 | + | 14.4981i | 1.05318 | + | 0.765182i | 0.972815 | − | 0.231583i | \(-0.0743906\pi\) |
0.0803676 | + | 0.996765i | \(0.474391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5279 | − | 10.5551i | 0.764626 | − | 0.555533i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.94499 | + | 5.04583i | 0.364517 | + | 0.264837i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.04423 | + | 12.4469i | 0.211107 | + | 0.649721i | 0.999407 | + | 0.0344301i | \(0.0109616\pi\) |
−0.788300 | + | 0.615291i | \(0.789038\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.45795 | + | 7.56478i | 0.127956 | + | 0.393807i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.60973 | − | 4.95425i | 0.0835733 | − | 0.257212i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.239599 | + | 0.174079i | −0.0124060 | + | 0.00901348i | −0.593971 | − | 0.804486i | \(-0.702441\pi\) |
0.581565 | + | 0.813500i | \(0.302441\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.5982 | − | 8.42659i | 0.597338 | − | 0.433992i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.41901 | − | 7.44495i | 0.124256 | − | 0.382421i | −0.869509 | − | 0.493918i | \(-0.835564\pi\) |
0.993765 | + | 0.111496i | \(0.0355644\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.748670 | − | 2.30417i | −0.0383555 | − | 0.118046i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.44294 | + | 19.8293i | 0.329219 | + | 1.01323i | 0.969500 | + | 0.245090i | \(0.0788177\pi\) |
−0.640282 | + | 0.768140i | \(0.721182\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.54040 | + | 4.02534i | 0.281634 | + | 0.204619i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.6010 | − | 16.4206i | 1.14592 | − | 0.832558i | 0.157985 | − | 0.987441i | \(-0.449500\pi\) |
0.987933 | + | 0.154883i | \(0.0495001\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.32498 | + | 3.86883i | 0.269296 | + | 0.195655i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9362 | 0.551660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.95418 | + | 30.6358i | −0.499586 | + | 1.53757i | 0.310100 | + | 0.950704i | \(0.399637\pi\) |
−0.809686 | + | 0.586863i | \(0.800363\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.34649 | 0.0674086 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3441 | −0.516562 | −0.258281 | − | 0.966070i | \(-0.583156\pi\) | ||||
−0.258281 | + | 0.966070i | \(0.583156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.64232 | − | 20.4429i | 0.330877 | − | 1.01834i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.81004 | 0.387129 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.7399 | − | 21.6073i | −1.47054 | − | 1.06841i | −0.980456 | − | 0.196739i | \(-0.936965\pi\) |
−0.490087 | − | 0.871673i | \(-0.663035\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.02256 | − | 2.19602i | 0.149092 | − | 0.108322i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.37859 | − | 6.08740i | −0.412284 | − | 0.299542i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.663721 | − | 2.04272i | −0.0325026 | − | 0.100033i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.74262 | − | 26.9070i | −0.427105 | − | 1.31449i | −0.900964 | − | 0.433894i | \(-0.857139\pi\) |
0.473859 | − | 0.880601i | \(-0.342861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.392142 | − | 1.20689i | 0.0191118 | − | 0.0588202i | −0.941046 | − | 0.338279i | \(-0.890155\pi\) |
0.960158 | + | 0.279459i | \(0.0901551\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.27216 | + | 4.55699i | −0.304963 | + | 0.221568i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.73577 | + | 2.71420i | −0.180787 | + | 0.131349i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.16621 | − | 3.58921i | 0.0563049 | − | 0.173289i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.24011 | + | 6.89434i | 0.107902 | + | 0.332089i | 0.990401 | − | 0.138226i | \(-0.0441402\pi\) |
−0.882498 | + | 0.470315i | \(0.844140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.18592 | − | 3.64988i | −0.0569916 | − | 0.175402i | 0.918508 | − | 0.395401i | \(-0.129394\pi\) |
−0.975500 | + | 0.219999i | \(0.929394\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.13666 | + | 3.00546i | 0.197883 | + | 0.143771i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.5358 | + | 18.5528i | −1.21876 | + | 0.885479i | −0.995996 | − | 0.0893940i | \(-0.971507\pi\) |
−0.222761 | + | 0.974873i | \(0.571507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.25621 | + | 3.09232i | 0.202677 | + | 0.147253i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.65284 | −0.126040 | −0.0630200 | − | 0.998012i | \(-0.520073\pi\) | ||||
−0.0630200 | + | 0.998012i | \(0.520073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.42685 | + | 7.46907i | −0.114786 | + | 0.353275i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3646 | −1.29142 | −0.645709 | − | 0.763584i | \(-0.723438\pi\) | ||||
−0.645709 | + | 0.763584i | \(0.723438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.3622 | 0.582113 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.95671 | − | 21.4106i | 0.326855 | − | 1.00596i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.66698 | −0.0779781 | −0.0389891 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389891 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.06334 | + | 0.772564i | 0.0496326 | + | 0.0360602i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.8272 | − | 20.2176i | 1.29604 | − | 0.941630i | 0.296133 | − | 0.955147i | \(-0.404303\pi\) |
0.999909 | + | 0.0135170i | \(0.00430273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.6204 | + | 20.7939i | 1.33010 | + | 0.966377i | 0.999746 | + | 0.0225205i | \(0.00716910\pi\) |
0.330357 | + | 0.943856i | \(0.392831\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.46057 | + | 22.9613i | 0.345234 | + | 1.06252i | 0.961458 | + | 0.274951i | \(0.0886615\pi\) |
−0.616224 | + | 0.787571i | \(0.711338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.39538 | + | 10.4499i | 0.156784 | + | 0.482532i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.99751 | + | 18.4584i | −0.276351 | + | 0.850520i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.61086 | − | 6.25615i | 0.395928 | − | 0.287658i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.19577 | − | 2.32186i | 0.146324 | − | 0.106311i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.03656 | + | 21.6563i | −0.321509 | + | 0.989502i | 0.651483 | + | 0.758663i | \(0.274147\pi\) |
−0.972992 | + | 0.230839i | \(0.925853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.77067 | + | 11.6049i | 0.171928 | + | 0.529139i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.04071 | − | 6.28066i | −0.0928555 | − | 0.285780i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.56973 | − | 5.49973i | −0.343017 | − | 0.249217i | 0.402917 | − | 0.915237i | \(-0.367996\pi\) |
−0.745934 | + | 0.666020i | \(0.767996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.2473 | + | 8.89817i | −0.553841 | + | 0.402389i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7363 | − | 10.7066i | −0.665042 | − | 0.483181i | 0.203320 | − | 0.979112i | \(-0.434827\pi\) |
−0.868362 | + | 0.495931i | \(0.834827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.76000 | 0.349493 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.28089 | − | 16.2529i | 0.236880 | − | 0.729043i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.14936 | 0.275283 | 0.137642 | − | 0.990482i | \(-0.456048\pi\) | ||||
0.137642 | + | 0.990482i | \(0.456048\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.9060 | 0.844657 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.89502 | + | 15.0653i | −0.218258 | + | 0.671730i | 0.780648 | + | 0.624971i | \(0.214889\pi\) |
−0.998906 | + | 0.0467590i | \(0.985111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.10376 | −0.315489 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.09898 | + | 2.97808i | 0.181684 | + | 0.132001i | 0.674910 | − | 0.737900i | \(-0.264182\pi\) |
−0.493226 | + | 0.869901i | \(0.664182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5647 | − | 9.85535i | 0.600068 | − | 0.435975i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.826047 | + | 0.600159i | 0.0364709 | + | 0.0264976i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.72346 | + | 11.4596i | 0.163758 | + | 0.503994i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.43798 | − | 22.8918i | −0.326491 | − | 1.00484i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2578 | + | 34.6481i | −0.493215 | + | 1.51796i | 0.326505 | + | 0.945195i | \(0.394129\pi\) |
−0.819720 | + | 0.572764i | \(0.805871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.36727 | + | 6.80572i | −0.409602 | + | 0.297593i | −0.773441 | − | 0.633869i | \(-0.781466\pi\) |
0.363839 | + | 0.931462i | \(0.381466\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.41289 | − | 6.83887i | 0.410032 | − | 0.297906i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.642075 | − | 1.97610i | 0.0279163 | − | 0.0859175i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.42684 | − | 7.46905i | −0.105316 | − | 0.324129i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.96843 | + | 18.3689i | 0.258521 | + | 0.795647i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.20734 | − | 0.877183i | −0.0521005 | − | 0.0378532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.61498 | − | 4.80606i | 0.284927 | − | 0.207012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2715 | − | 12.5485i | −0.742559 | − | 0.539500i | 0.150953 | − | 0.988541i | \(-0.451766\pi\) |
−0.893511 | + | 0.449041i | \(0.851766\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.61804 | −0.112351 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.83217 | − | 24.1049i | 0.334879 | − | 1.03065i | −0.631902 | − | 0.775048i | \(-0.717726\pi\) |
0.966781 | − | 0.255604i | \(-0.0822745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.50161 | −0.149445 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.02827 | 0.256813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.509800 | − | 1.56900i | 0.0216789 | − | 0.0667207i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.953134 | 0.0403856 | 0.0201928 | − | 0.999796i | \(-0.493572\pi\) | ||||
0.0201928 | + | 0.999796i | \(0.493572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.4533 | + | 9.77439i | 0.569014 | + | 0.413413i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.65264 | − | 1.20071i | 0.0697746 | − | 0.0506942i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.6806 | − | 17.9315i | −1.04016 | − | 0.755723i | −0.0698461 | − | 0.997558i | \(-0.522251\pi\) |
−0.970317 | + | 0.241835i | \(0.922251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.407508 | − | 1.25418i | −0.0171137 | − | 0.0526707i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.81510 | + | 30.2078i | 0.411471 | + | 1.26638i | 0.915370 | + | 0.402614i | \(0.131898\pi\) |
−0.503899 | + | 0.863762i | \(0.668102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.65796 | + | 26.6465i | −0.362324 | + | 1.11512i | 0.589315 | + | 0.807903i | \(0.299398\pi\) |
−0.951640 | + | 0.307217i | \(0.900602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.6599 | + | 12.1041i | −0.695977 | + | 0.505657i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.58593 | − | 3.33187i | 0.190915 | − | 0.138708i | −0.488222 | − | 0.872719i | \(-0.662354\pi\) |
0.679137 | + | 0.734012i | \(0.262354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.59438 | − | 4.90701i | 0.0662603 | − | 0.203928i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.34438 | − | 10.2929i | −0.138748 | − | 0.427023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.89717 | − | 5.83888i | −0.0785726 | − | 0.241822i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.5206 | − | 19.9949i | −1.13590 | − | 0.825278i | −0.149355 | − | 0.988784i | \(-0.547720\pi\) |
−0.986542 | + | 0.163506i | \(0.947720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.31231 | − | 5.31270i | 0.301298 | − | 0.218906i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.50336 | + | 6.17805i | 0.349781 | + | 0.254131i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.9225 | −0.941313 | −0.470657 | − | 0.882316i | \(-0.655983\pi\) | ||||
−0.470657 | + | 0.882316i | \(0.655983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.12858 | − | 3.47341i | 0.0461896 | − | 0.142157i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.7017 | −0.723270 | −0.361635 | − | 0.932320i | \(-0.617781\pi\) | ||||
−0.361635 | + | 0.932320i | \(0.617781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.8773 | −1.17793 | −0.588964 | − | 0.808159i | \(-0.700464\pi\) | ||||
−0.588964 | + | 0.808159i | \(0.700464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.57475 | + | 7.92426i | −0.104852 | + | 0.322701i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5926 | 0.470528 | 0.235264 | − | 0.971932i | \(-0.424405\pi\) | ||||
0.235264 | + | 0.971932i | \(0.424405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.29880 | − | 4.57634i | −0.255240 | − | 0.185443i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.2302 | + | 11.0654i | −0.616146 | + | 0.447657i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.2970 | + | 7.48123i | 0.415893 | + | 0.302164i | 0.775983 | − | 0.630754i | \(-0.217254\pi\) |
−0.360090 | + | 0.932917i | \(0.617254\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2451 | − | 40.7643i | −0.533229 | − | 1.64111i | −0.747446 | − | 0.664323i | \(-0.768720\pi\) |
0.214217 | − | 0.976786i | \(-0.431280\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.30448 | + | 13.2478i | 0.173012 | + | 0.532475i | 0.999537 | − | 0.0304242i | \(-0.00968580\pi\) |
−0.826525 | + | 0.562899i | \(0.809686\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.54749 | − | 4.76268i | 0.0620985 | − | 0.191120i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.2157 | − | 7.42216i | 0.409285 | − | 0.297363i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.28384 | − | 0.932763i | 0.0512715 | − | 0.0372510i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.04102 | + | 6.28160i | −0.0813806 | + | 0.250464i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.66089 | − | 8.18939i | −0.105928 | − | 0.326014i | 0.884019 | − | 0.467451i | \(-0.154828\pi\) |
−0.989947 | + | 0.141437i | \(0.954828\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.14575 | − | 25.0701i | −0.323765 | − | 0.996445i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.3350 | + | 7.50882i | 0.409488 | + | 0.297510i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.4840 | − | 7.61709i | 0.414742 | − | 0.301327i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0591 | + | 12.3942i | 0.673794 | + | 0.489540i | 0.871293 | − | 0.490763i | \(-0.163282\pi\) |
−0.197499 | + | 0.980303i | \(0.563282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2412 | 0.482747 | 0.241374 | − | 0.970432i | \(-0.422402\pi\) | ||||
0.241374 | + | 0.970432i | \(0.422402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.49162 | + | 10.7461i | −0.137270 | + | 0.422472i | −0.995936 | − | 0.0900623i | \(-0.971293\pi\) |
0.858667 | + | 0.512535i | \(0.171293\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.2057 | −0.479117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.6736 | −0.457524 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.57373 | + | 20.2319i | −0.257250 | + | 0.791734i | 0.736128 | + | 0.676842i | \(0.236652\pi\) |
−0.993378 | + | 0.114892i | \(0.963348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.7145 | 0.496039 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.9986 | + | 10.8971i | 0.584263 | + | 0.424492i | 0.840258 | − | 0.542186i | \(-0.182403\pi\) |
−0.255995 | + | 0.966678i | \(0.582403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0800 | + | 11.6828i | −0.625441 | + | 0.454409i | −0.854818 | − | 0.518928i | \(-0.826331\pi\) |
0.229377 | + | 0.973338i | \(0.426331\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.58203 | + | 1.87595i | 0.100278 | + | 0.0728560i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.13635 | − | 28.1188i | −0.353761 | − | 1.08876i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.71502 | + | 17.5890i | 0.220955 | + | 0.680031i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.68173 | + | 5.17583i | −0.0649224 | + | 0.199811i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.2430 | + | 25.6055i | −1.35852 | + | 0.987021i | −0.359980 | + | 0.932960i | \(0.617216\pi\) |
−0.998538 | + | 0.0540603i | \(0.982784\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.76996 | − | 2.73904i | 0.144891 | − | 0.105270i | −0.512978 | − | 0.858402i | \(-0.671458\pi\) |
0.657870 | + | 0.753132i | \(0.271458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.63152 | + | 20.4097i | −0.254494 | + | 0.783253i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.76675 | + | 17.7482i | 0.220982 | + | 0.680114i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0299 | + | 37.0242i | 0.460311 | + | 1.41669i | 0.864786 | + | 0.502141i | \(0.167454\pi\) |
−0.404475 | + | 0.914549i | \(0.632546\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.6047 | − | 16.4233i | −0.862424 | − | 0.626588i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.76002 | − | 5.63798i | 0.295633 | − | 0.214790i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.81060 | + | 5.67473i | 0.297129 | + | 0.215877i | 0.726354 | − | 0.687321i | \(-0.241213\pi\) |
−0.429225 | + | 0.903198i | \(0.641213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.04956 | −0.0778562 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.23064 | + | 9.94289i | −0.122369 | + | 0.376614i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.7573 | 0.936407 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.6430 | 0.704135 | 0.352068 | − | 0.935975i | \(-0.385479\pi\) | ||||
0.352068 | + | 0.935975i | \(0.385479\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.58554 | + | 4.87980i | −0.0597999 | + | 0.184045i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.43395 | −0.279582 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.85935 | + | 7.16324i | 0.370276 | + | 0.269021i | 0.757325 | − | 0.653038i | \(-0.226506\pi\) |
−0.387050 | + | 0.922059i | \(0.626506\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.01209 | − | 0.735329i | 0.0379565 | − | 0.0275770i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.8634 | − | 26.0563i | −1.34310 | − | 0.975817i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.61761 | − | 11.1338i | −0.135102 | − | 0.415801i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.2311 | − | 40.7210i | −0.493435 | − | 1.51864i | −0.819382 | − | 0.573248i | \(-0.805683\pi\) |
0.325947 | − | 0.945388i | \(-0.394317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.42860 | + | 10.5522i | −0.127688 | + | 0.392983i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.1221 | + | 17.5257i | −0.897110 | + | 0.651788i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.868548 | + | 0.631037i | −0.0322126 | + | 0.0234039i | −0.603775 | − | 0.797155i | \(-0.706337\pi\) |
0.571562 | + | 0.820559i | \(0.306337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.78152 | + | 8.56063i | 0.102878 | + | 0.316626i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.251338 | − | 0.773538i | −0.00928337 | − | 0.0285713i | 0.946308 | − | 0.323268i | \(-0.104781\pi\) |
−0.955591 | + | 0.294696i | \(0.904781\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4765 | + | 7.61160i | 0.385906 | + | 0.280377i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.6000 | + | 22.2322i | −1.12564 | + | 0.817824i | −0.985054 | − | 0.172244i | \(-0.944898\pi\) |
−0.140585 | + | 0.990069i | \(0.544898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00582 | + | 1.45732i | 0.0736857 | + | 0.0535358i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.7517 | −1.67847 | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||||
−0.839233 | + | 0.543772i | \(0.816996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.53607 | − | 7.80521i | 0.0927899 | − | 0.285578i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.71916 | 0.0993560 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.1925 | −1.43016 | −0.715078 | − | 0.699045i | \(-0.753609\pi\) | ||||
−0.715078 | + | 0.699045i | \(0.753609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.887796 | + | 2.73235i | −0.0323531 | + | 0.0995725i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.48615 | −0.163052 | −0.0815259 | − | 0.996671i | \(-0.525979\pi\) | ||||
−0.0815259 | + | 0.996671i | \(0.525979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.29662 | − | 4.57476i | −0.228553 | − | 0.166053i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2776 | + | 12.5529i | −0.626312 | + | 0.455043i | −0.855121 | − | 0.518429i | \(-0.826517\pi\) |
0.228808 | + | 0.973471i | \(0.426517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.9085 | + | 10.8316i | 0.539723 | + | 0.392131i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.89290 | − | 18.1365i | −0.212780 | − | 0.654870i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.94179 | + | 24.4423i | 0.286388 | + | 0.881413i | 0.985979 | + | 0.166869i | \(0.0533657\pi\) |
−0.699591 | + | 0.714544i | \(0.746634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.50834 | − | 7.71988i | 0.0903357 | − | 0.278025i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.9797 | − | 17.4223i | 0.862490 | − | 0.626636i | −0.0660712 | − | 0.997815i | \(-0.521046\pi\) |
0.928561 | + | 0.371179i | \(0.121046\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.36118 | − | 3.89512i | 0.192331 | − | 0.139737i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.50969 | + | 7.72403i | −0.0899189 | + | 0.276742i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.22383 | − | 19.1550i | −0.222706 | − | 0.685420i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.82443 | − | 5.61503i | −0.0651999 | − | 0.200665i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.50148 | − | 4.72360i | −0.231753 | − | 0.168378i | 0.465848 | − | 0.884865i | \(-0.345749\pi\) |
−0.697601 | + | 0.716486i | \(0.745749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.0467 | + | 13.1117i | −0.642479 | + | 0.466789i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.35443 | + | 4.61676i | 0.225938 | + | 0.164153i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.50268 | −0.301939 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.07628 | + | 15.6232i | −0.179811 | + | 0.553401i | −0.999820 | − | 0.0189486i | \(-0.993968\pi\) |
0.820009 | + | 0.572350i | \(0.193968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.1900 | −0.360497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.57541 | 0.338331 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.10642 | − | 18.7936i | 0.215491 | − | 0.663213i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.19918 | −0.288625 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.2743 | − | 28.5344i | −1.38081 | − | 1.00322i | −0.996804 | − | 0.0798870i | \(-0.974544\pi\) |
−0.384006 | − | 0.923330i | \(-0.625456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2584 | + | 12.5390i | −0.606024 | + | 0.440302i | −0.848012 | − | 0.529977i | \(-0.822201\pi\) |
0.241988 | + | 0.970279i | \(0.422201\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.67496 | + | 5.57619i | 0.269173 | + | 0.195565i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.16079 | + | 6.65024i | 0.0755966 | + | 0.232662i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.989519 | − | 3.04543i | −0.0345766 | − | 0.106416i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.922371 | − | 2.83877i | 0.0321910 | − | 0.0990736i | −0.933670 | − | 0.358134i | \(-0.883413\pi\) |
0.965861 | + | 0.259061i | \(0.0834130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.76974 | + | 2.01233i | −0.0965469 | + | 0.0701455i | −0.635011 | − | 0.772503i | \(-0.719005\pi\) |
0.538464 | + | 0.842648i | \(0.319005\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.30639 | + | 4.58186i | −0.219295 | + | 0.159327i | −0.692009 | − | 0.721889i | \(-0.743274\pi\) |
0.472715 | + | 0.881216i | \(0.343274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.65047 | + | 20.4680i | −0.230980 | + | 0.710884i | 0.766649 | + | 0.642067i | \(0.221923\pi\) |
−0.997629 | + | 0.0688179i | \(0.978077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.142047 | + | 0.437177i | 0.00492757 | + | 0.0151655i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.13680 | + | 6.57639i | 0.0740357 | + | 0.227858i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.16155 | − | 5.20317i | −0.247540 | − | 0.179848i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.31004 | + | 2.40488i | −0.114275 | + | 0.0830258i | −0.643455 | − | 0.765484i | \(-0.722500\pi\) |
0.529180 | + | 0.848510i | \(0.322500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.73850 | − | 3.44272i | −0.163397 | − | 0.118715i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.2578 | −0.525508 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.49825 | − | 10.7665i | 0.120201 | − | 0.369941i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.6725 | −0.366281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.1648 | 0.862637 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.75958 | + | 23.8815i | −0.265683 | + | 0.817688i | 0.725852 | + | 0.687850i | \(0.241446\pi\) |
−0.991535 | + | 0.129837i | \(0.958554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.8315 | −1.22398 | −0.611991 | − | 0.790865i | \(-0.709631\pi\) | ||||
−0.611991 | + | 0.790865i | \(0.709631\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.2363 | + | 16.8821i | 0.792811 | + | 0.576011i | 0.908796 | − | 0.417240i | \(-0.137003\pi\) |
−0.115985 | + | 0.993251i | \(0.537003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.48598 | − | 6.16543i | 0.289202 | − | 0.210117i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.0119 | − | 12.3598i | −0.579090 | − | 0.420734i | 0.259306 | − | 0.965795i | \(-0.416506\pi\) |
−0.838396 | + | 0.545062i | \(0.816506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.71945 | − | 14.5250i | −0.160281 | − | 0.493293i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.600828 | − | 1.84916i | −0.0203817 | − | 0.0627284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.25204 | + | 19.2418i | −0.211842 | + | 0.651984i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.1654 | + | 9.56522i | −0.445581 | + | 0.323734i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.69384 | + | 4.13682i | −0.192267 | + | 0.139690i | −0.679754 | − | 0.733440i | \(-0.737914\pi\) |
0.487487 | + | 0.873130i | \(0.337914\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.52803 | − | 29.3243i | 0.321373 | − | 0.989083i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.1220 | + | 46.5406i | 0.509472 | + | 1.56799i | 0.793121 | + | 0.609064i | \(0.208455\pi\) |
−0.283649 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.62862 | + | 8.09007i | 0.0884602 | + | 0.272252i | 0.985494 | − | 0.169709i | \(-0.0542828\pi\) |
−0.897034 | + | 0.441961i | \(0.854283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.2500 | − | 19.7983i | −0.914966 | − | 0.664761i | 0.0273002 | − | 0.999627i | \(-0.491309\pi\) |
−0.942266 | + | 0.334866i | \(0.891309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.58476 | + | 1.87794i | −0.0866901 | + | 0.0629840i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.25737 | − | 0.913532i | −0.0421235 | − | 0.0306045i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.91602 | −0.264899 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.75764 | − | 11.5648i | 0.125464 | − | 0.386138i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −52.2631 | −1.74307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.19199 | 0.172970 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.79075 | − | 8.58903i | 0.0928702 | − | 0.285825i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.2382 | 1.40250 | 0.701248 | − | 0.712918i | \(-0.252627\pi\) | ||||
0.701248 | + | 0.712918i | \(0.252627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.56061 | − | 3.31348i | −0.151266 | − | 0.109901i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4371 | − | 22.1138i | 1.00843 | − | 0.732664i | 0.0445478 | − | 0.999007i | \(-0.485815\pi\) |
0.963878 | + | 0.266343i | \(0.0858153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3191 | − | 7.49726i | −0.341512 | − | 0.248123i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.45661 | − | 13.7160i | −0.147170 | − | 0.452943i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7537 | + | 36.1742i | 0.387719 | + | 1.19328i | 0.934488 | + | 0.355993i | \(0.115857\pi\) |
−0.546769 | + | 0.837283i | \(0.684143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.52009 | − | 16.9891i | 0.181893 | − | 0.559809i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.4575 | − | 18.4960i | 0.837944 | − | 0.608802i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.80673 | + | 4.94538i | −0.223562 | + | 0.162427i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.91592 | + | 24.3627i | −0.259713 | + | 0.799314i | 0.733152 | + | 0.680065i | \(0.238049\pi\) |
−0.992864 | + | 0.119249i | \(0.961951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65995 | + | 5.10880i | 0.0544027 | + | 0.167434i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.72777 | − | 11.4729i | −0.122042 | − | 0.375605i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.7367 | + | 22.3315i | 1.00412 | + | 0.729538i | 0.962968 | − | 0.269614i | \(-0.0868962\pi\) |
0.0411552 | + | 0.999153i | \(0.486896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.1766 | + | 11.0264i | −0.495268 | + | 0.359833i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.3522 | + | 22.0522i | 0.989454 | + | 0.718881i | 0.959802 | − | 0.280680i | \(-0.0905598\pi\) |
0.0296528 | + | 0.999560i | \(0.490560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.8323 | 1.29712 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.8650 | − | 33.4391i | 0.353066 | − | 1.08663i | −0.604056 | − | 0.796942i | \(-0.706450\pi\) |
0.957122 | − | 0.289684i | \(-0.0935503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.8735 | 1.00220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.7157 | −0.347480 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1044 | + | 49.5641i | −0.521671 | + | 1.60554i | 0.249134 | + | 0.968469i | \(0.419854\pi\) |
−0.770805 | + | 0.637071i | \(0.780146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.17595 | −0.296616 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.98593 | − | 2.89594i | −0.128712 | − | 0.0935149i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38.3157 | + | 27.8380i | −1.23599 | + | 0.898001i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.66816 | + | 1.21199i | 0.0537558 | + | 0.0390559i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.9083 | + | 39.7277i | 0.415103 | + | 1.27756i | 0.912158 | + | 0.409838i | \(0.134415\pi\) |
−0.497055 | + | 0.867719i | \(0.665585\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.414711 | + | 1.27635i | 0.0133224 | + | 0.0410022i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.141561 | − | 0.435679i | 0.00454289 | − | 0.0139816i | −0.948759 | − | 0.315999i | \(-0.897660\pi\) |
0.953302 | + | 0.302018i | \(0.0976602\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.29148 | + | 1.66486i | −0.0734614 | + | 0.0533728i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.15300 | − | 2.29079i | 0.100873 | − | 0.0732888i | −0.536205 | − | 0.844088i | \(-0.680143\pi\) |
0.637079 | + | 0.770799i | \(0.280143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.59881 | − | 14.1537i | 0.146979 | − | 0.452353i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.31821 | + | 13.2901i | 0.137870 | + | 0.424319i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.3958 | − | 53.5388i | −0.554841 | − | 1.70762i | −0.696364 | − | 0.717689i | \(-0.745200\pi\) |
0.141523 | − | 0.989935i | \(-0.454800\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.27125 | + | 6.00942i | 0.263277 | + | 0.191282i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7451 | − | 20.1580i | 0.882242 | − | 0.640986i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5804 | − | 12.7729i | −0.558460 | − | 0.405745i | 0.272435 | − | 0.962174i | \(-0.412171\pi\) |
−0.830895 | + | 0.556429i | \(0.812171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.17317 | 0.0689636 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9066 | + | 36.6447i | −0.377085 | + | 1.16055i | 0.564976 | + | 0.825107i | \(0.308885\pi\) |
−0.942061 | + | 0.335441i | \(0.891115\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.02514 | 0.158988 |
(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 | 1500.2.m.c.301.2 | 24 | ||
5.2 | odd | 4 | 1500.2.o.c.949.2 | 24 | |||
5.3 | odd | 4 | 300.2.o.a.289.6 | yes | 24 | ||
5.4 | even | 2 | 1500.2.m.d.301.5 | 24 | |||
15.8 | even | 4 | 900.2.w.c.289.1 | 24 | |||
25.3 | odd | 20 | 7500.2.d.g.1249.21 | 24 | |||
25.4 | even | 10 | 7500.2.a.m.1.9 | 12 | |||
25.9 | even | 10 | 1500.2.m.d.1201.5 | 24 | |||
25.12 | odd | 20 | 300.2.o.a.109.6 | ✓ | 24 | ||
25.13 | odd | 20 | 1500.2.o.c.49.2 | 24 | |||
25.16 | even | 5 | inner | 1500.2.m.c.1201.2 | 24 | ||
25.21 | even | 5 | 7500.2.a.n.1.4 | 12 | |||
25.22 | odd | 20 | 7500.2.d.g.1249.4 | 24 | |||
75.62 | even | 20 | 900.2.w.c.109.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.6 | ✓ | 24 | 25.12 | odd | 20 | ||
300.2.o.a.289.6 | yes | 24 | 5.3 | odd | 4 | ||
900.2.w.c.109.1 | 24 | 75.62 | even | 20 | |||
900.2.w.c.289.1 | 24 | 15.8 | even | 4 | |||
1500.2.m.c.301.2 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.c.1201.2 | 24 | 25.16 | even | 5 | inner | ||
1500.2.m.d.301.5 | 24 | 5.4 | even | 2 | |||
1500.2.m.d.1201.5 | 24 | 25.9 | even | 10 | |||
1500.2.o.c.49.2 | 24 | 25.13 | odd | 20 | |||
1500.2.o.c.949.2 | 24 | 5.2 | odd | 4 | |||
7500.2.a.m.1.9 | 12 | 25.4 | even | 10 | |||
7500.2.a.n.1.4 | 12 | 25.21 | even | 5 | |||
7500.2.d.g.1249.4 | 24 | 25.22 | odd | 20 | |||
7500.2.d.g.1249.21 | 24 | 25.3 | odd | 20 |