Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,2,Mod(109,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.w (of order \(10\), degree \(4\), 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: | \(7.18653618192\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Character | \(\chi\) | \(=\) | 900.289 |
Dual form | 900.2.w.c.109.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.64247 | + | 1.51733i | 0.734535 | + | 0.678571i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.78808i | − | 1.43176i | −0.698223 | − | 0.715880i | \(-0.746026\pi\) | ||
0.698223 | − | 0.715880i | \(-0.253974\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.653426 | + | 0.474742i | −0.197015 | + | 0.143140i | −0.681919 | − | 0.731427i | \(-0.738855\pi\) |
0.484904 | + | 0.874567i | \(0.338855\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.79168 | − | 3.84242i | 0.774274 | − | 1.06570i | −0.221617 | − | 0.975134i | \(-0.571133\pi\) |
0.995891 | − | 0.0905626i | \(-0.0288665\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.09262 | − | 0.355012i | 0.264998 | − | 0.0861032i | −0.173504 | − | 0.984833i | \(-0.555509\pi\) |
0.438503 | + | 0.898730i | \(0.355509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.00463870 | − | 0.0142765i | −0.00106419 | − | 0.00327524i | 0.950523 | − | 0.310654i | \(-0.100548\pi\) |
−0.951587 | + | 0.307379i | \(0.900548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.68422 | − | 5.07089i | −0.768213 | − | 1.05735i | −0.996486 | − | 0.0837569i | \(-0.973308\pi\) |
0.228274 | − | 0.973597i | \(-0.426692\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.395416 | + | 4.98434i | 0.0790832 | + | 0.996868i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.14365 | − | 3.51978i | 0.212370 | − | 0.653607i | −0.786960 | − | 0.617004i | \(-0.788346\pi\) |
0.999330 | − | 0.0366030i | \(-0.0116537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.488893 | − | 1.50466i | −0.0878078 | − | 0.270245i | 0.897505 | − | 0.441005i | \(-0.145378\pi\) |
−0.985313 | + | 0.170760i | \(0.945378\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.74777 | − | 6.22181i | 0.971551 | − | 1.05168i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.02074 | − | 6.91045i | 0.825404 | − | 1.13607i | −0.163357 | − | 0.986567i | \(-0.552232\pi\) |
0.988761 | − | 0.149504i | \(-0.0477678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.30279 | + | 6.75887i | 1.45285 | + | 1.05556i | 0.985155 | + | 0.171669i | \(0.0549160\pi\) |
0.467697 | + | 0.883889i | \(0.345084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2458i | 1.56247i | 0.624238 | + | 0.781234i | \(0.285409\pi\) | ||||
−0.624238 | + | 0.781234i | \(0.714591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.500524 | − | 0.162630i | −0.0730090 | − | 0.0237221i | 0.272285 | − | 0.962217i | \(-0.412221\pi\) |
−0.345294 | + | 0.938495i | \(0.612221\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.34957 | −1.04994 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.80539 | + | 0.911527i | 0.385350 | + | 0.125208i | 0.495284 | − | 0.868731i | \(-0.335064\pi\) |
−0.109934 | + | 0.993939i | \(0.535064\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.79357 | − | 0.211714i | −0.241845 | − | 0.0285475i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.25803 | − | 6.72635i | −1.20529 | − | 0.875696i | −0.210498 | − | 0.977594i | \(-0.567508\pi\) |
−0.994795 | + | 0.101898i | \(0.967508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.54203 | + | 1.84689i | −0.325473 | + | 0.236470i | −0.738507 | − | 0.674245i | \(-0.764469\pi\) |
0.413034 | + | 0.910716i | \(0.364469\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.4155 | − | 2.07516i | 1.29188 | − | 0.257392i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6312 | − | 4.10412i | 1.54314 | − | 0.501398i | 0.590901 | − | 0.806744i | \(-0.298772\pi\) |
0.952241 | + | 0.305346i | \(0.0987722\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.51826 | − | 4.67271i | 0.180184 | − | 0.554549i | −0.819648 | − | 0.572867i | \(-0.805831\pi\) |
0.999832 | + | 0.0183179i | \(0.00583110\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.75001 | + | 3.78507i | 0.321865 | + | 0.443009i | 0.939035 | − | 0.343820i | \(-0.111721\pi\) |
−0.617171 | + | 0.786829i | \(0.711721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.79836 | + | 2.47523i | 0.204942 | + | 0.282079i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.86507 | + | 8.81777i | −0.322345 | + | 0.992076i | 0.650280 | + | 0.759695i | \(0.274652\pi\) |
−0.972625 | + | 0.232381i | \(0.925348\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.35402 | − | 0.439947i | 0.148623 | − | 0.0482904i | −0.233761 | − | 0.972294i | \(-0.575103\pi\) |
0.382384 | + | 0.924004i | \(0.375103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.33326 | + | 1.07476i | 0.253078 | + | 0.116574i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0306 | − | 9.46730i | 1.38124 | − | 1.00353i | 0.384480 | − | 0.923133i | \(-0.374381\pi\) |
0.996763 | − | 0.0803985i | \(-0.0256193\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.5554 | − | 10.5751i | −1.52582 | − | 1.10857i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0140432 | − | 0.0304871i | 0.00144080 | − | 0.00312791i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.66744 | − | 2.49130i | −0.778511 | − | 0.252954i | −0.107307 | − | 0.994226i | \(-0.534223\pi\) |
−0.671204 | + | 0.741272i | \(0.734223\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6496 | −1.15918 | −0.579590 | − | 0.814908i | \(-0.696787\pi\) | ||||
−0.579590 | + | 0.814908i | \(0.696787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9216 | + | 5.82307i | 1.76587 | + | 0.573764i | 0.997781 | − | 0.0665845i | \(-0.0212102\pi\) |
0.768084 | + | 0.640349i | \(0.221210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.3957i | − | 1.39168i | −0.718195 | − | 0.695842i | \(-0.755031\pi\) | ||
0.718195 | − | 0.695842i | \(-0.244969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.66144 | − | 3.38673i | −0.446485 | − | 0.324390i | 0.341722 | − | 0.939801i | \(-0.388990\pi\) |
−0.788206 | + | 0.615411i | \(0.788990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5368 | + | 14.5027i | −0.991223 | + | 1.36430i | −0.0606641 | + | 0.998158i | \(0.519322\pi\) |
−0.930559 | + | 0.366143i | \(0.880678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.64300 | − | 13.9190i | 0.153211 | − | 1.29795i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.34482 | − | 4.13892i | −0.123279 | − | 0.379414i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.19760 | + | 9.84120i | −0.290691 | + | 0.894655i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.91343 | + | 8.78661i | −0.618356 | + | 0.785898i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.34592 | − | 1.85250i | −0.119431 | − | 0.164382i | 0.745116 | − | 0.666935i | \(-0.232394\pi\) |
−0.864547 | + | 0.502553i | \(0.832394\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.17840 | + | 6.70444i | 0.190328 | + | 0.585769i | 0.999999 | − | 0.00111420i | \(-0.000354661\pi\) |
−0.809671 | + | 0.586883i | \(0.800355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0540804 | + | 0.0175718i | −0.00468937 | + | 0.00152367i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8918 | + | 17.7441i | −1.10142 | + | 1.51598i | −0.267940 | + | 0.963436i | \(0.586343\pi\) |
−0.833484 | + | 0.552544i | \(0.813657\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.86171 | − | 5.71187i | 0.666822 | − | 0.484474i | −0.202138 | − | 0.979357i | \(-0.564789\pi\) |
0.868960 | + | 0.494883i | \(0.164789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.83607i | 0.320788i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.21907 | − | 4.04584i | 0.599512 | − | 0.335989i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9712 | −1.14457 | −0.572284 | − | 0.820056i | \(-0.693942\pi\) | ||||
−0.572284 | + | 0.820056i | \(0.693942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1871 | −1.64280 | −0.821400 | − | 0.570352i | \(-0.806807\pi\) | ||||
−0.821400 | + | 0.570352i | \(0.806807\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.48007 | − | 3.21317i | 0.118882 | − | 0.258088i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.76546i | − | 0.619751i | −0.950777 | − | 0.309876i | \(-0.899713\pi\) | ||
0.950777 | − | 0.309876i | \(-0.100287\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.2090 | + | 13.9561i | −1.51388 | + | 1.09990i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.16480 | + | 11.2379i | −0.639517 | + | 0.880219i | −0.998590 | − | 0.0530901i | \(-0.983093\pi\) |
0.359073 | + | 0.933310i | \(0.383093\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.75604 | − | 0.895491i | 0.213269 | − | 0.0692952i | −0.200434 | − | 0.979707i | \(-0.564235\pi\) |
0.413703 | + | 0.910412i | \(0.364235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.95350 | − | 9.08992i | −0.227192 | − | 0.699225i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.95423 | + | 12.3244i | 0.680777 | + | 0.937009i | 0.999943 | − | 0.0106895i | \(-0.00340264\pi\) |
−0.319166 | + | 0.947699i | \(0.603403\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.8811 | − | 1.49787i | 1.42728 | − | 0.113228i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.20182 | + | 22.1649i | −0.538290 | + | 1.65669i | 0.198142 | + | 0.980173i | \(0.436509\pi\) |
−0.736432 | + | 0.676512i | \(0.763491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.46913 | + | 16.8322i | 0.406517 | + | 1.25113i | 0.919622 | + | 0.392805i | \(0.128495\pi\) |
−0.513105 | + | 0.858326i | \(0.671505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.7319 | − | 3.73209i | 1.37719 | − | 0.274389i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.545404 | + | 0.750685i | −0.0398839 | + | 0.0548955i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.57575 | + | 5.50411i | 0.548162 | + | 0.398263i | 0.827107 | − | 0.562044i | \(-0.189985\pi\) |
−0.278945 | + | 0.960307i | \(0.589985\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9309i | 1.36268i | 0.731969 | + | 0.681338i | \(0.238602\pi\) | ||||
−0.731969 | + | 0.681338i | \(0.761398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.17436 | − | 2.33109i | −0.511152 | − | 0.166083i | 0.0420739 | − | 0.999114i | \(-0.486603\pi\) |
−0.553226 | + | 0.833031i | \(0.686603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.58560 | −0.254176 | −0.127088 | − | 0.991891i | \(-0.540563\pi\) | ||||
−0.127088 | + | 0.991891i | \(0.540563\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.3332 | − | 4.33223i | −0.935808 | − | 0.304063i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.02411 | + | 25.2166i | 0.350899 | + | 1.76121i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.00980868 | + | 0.00712642i | 0.000678480 | + | 0.000492945i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.68674 | + | 1.22549i | −0.116120 | + | 0.0843663i | −0.644330 | − | 0.764748i | \(-0.722864\pi\) |
0.528210 | + | 0.849114i | \(0.322864\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.5462 | + | 16.8284i | −1.06025 | + | 1.14769i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.69977 | + | 1.85197i | −0.386926 | + | 0.125720i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.68613 | − | 5.18938i | 0.113421 | − | 0.349075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.25091 | − | 11.3564i | −0.552522 | − | 0.760481i | 0.437830 | − | 0.899058i | \(-0.355747\pi\) |
−0.990352 | + | 0.138577i | \(0.955747\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.48995 | + | 2.05074i | 0.0988915 | + | 0.136112i | 0.855595 | − | 0.517646i | \(-0.173191\pi\) |
−0.756704 | + | 0.653758i | \(0.773191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.10687 | − | 15.7173i | 0.337472 | − | 1.03863i | −0.628020 | − | 0.778197i | \(-0.716134\pi\) |
0.965492 | − | 0.260434i | \(-0.0838656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.2228 | − | 8.19539i | 1.65240 | − | 0.536898i | 0.673143 | − | 0.739512i | \(-0.264944\pi\) |
0.979259 | + | 0.202614i | \(0.0649437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.575332 | − | 1.02658i | −0.0375305 | − | 0.0669664i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.03839 | − | 4.38714i | 0.390591 | − | 0.283781i | −0.375107 | − | 0.926982i | \(-0.622394\pi\) |
0.765698 | + | 0.643201i | \(0.222394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.33107 | − | 6.05288i | −0.536651 | − | 0.389900i | 0.286189 | − | 0.958173i | \(-0.407612\pi\) |
−0.822840 | + | 0.568273i | \(0.807612\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.0714 | − | 11.1517i | −0.771216 | − | 0.712458i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0678060 | − | 0.0220315i | −0.00431439 | − | 0.00140183i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.5809 | −1.23593 | −0.617967 | − | 0.786204i | \(-0.712044\pi\) | ||||
−0.617967 | + | 0.786204i | \(0.712044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.81473 | + | 1.56440i | 0.302699 | + | 0.0983530i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.98030i | − | 0.373041i | −0.982451 | − | 0.186520i | \(-0.940279\pi\) | ||
0.982451 | − | 0.186520i | \(-0.0597210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.1774 | − | 19.0190i | −1.62658 | − | 1.18178i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.56808 | + | 4.91104i | −0.220017 | + | 0.302827i | −0.904730 | − | 0.425985i | \(-0.859928\pi\) |
0.684713 | + | 0.728813i | \(0.259928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.22469 | + | 5.75386i | 0.198091 | + | 0.353457i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.97152 | + | 9.14540i | 0.181177 | + | 0.557605i | 0.999862 | − | 0.0166382i | \(-0.00529635\pi\) |
−0.818685 | + | 0.574243i | \(0.805296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.40263 | + | 28.9383i | −0.571169 | + | 1.75788i | 0.0776990 | + | 0.996977i | \(0.475243\pi\) |
−0.648868 | + | 0.760901i | \(0.724757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.62465 | − | 3.06918i | −0.158272 | − | 0.185078i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.23436 | − | 5.82810i | −0.254418 | − | 0.350176i | 0.662634 | − | 0.748943i | \(-0.269438\pi\) |
−0.917052 | + | 0.398767i | \(0.869438\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.20758 | − | 28.3380i | −0.549278 | − | 1.69050i | −0.710594 | − | 0.703602i | \(-0.751574\pi\) |
0.161316 | − | 0.986903i | \(-0.448426\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.39215 | + | 2.72677i | −0.498861 | + | 0.162090i | −0.547631 | − | 0.836720i | \(-0.684470\pi\) |
0.0487693 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.6032 | − | 35.2397i | 1.51131 | − | 2.08014i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.6855 | + | 9.21656i | −0.746207 | + | 0.542151i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.20743i | 0.245800i | 0.992419 | + | 0.122900i | \(0.0392195\pi\) | ||||
−0.992419 | + | 0.122900i | \(0.960780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.99993 | − | 25.0953i | −0.291107 | − | 1.46111i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.7697 | −1.72163 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.8119 | 2.23708 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.97755 | − | 0.823633i | −0.399533 | − | 0.0471611i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.41109i | − | 0.251754i | −0.992046 | − | 0.125877i | \(-0.959825\pi\) | ||
0.992046 | − | 0.125877i | \(-0.0401745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.11346 | + | 3.71514i | −0.289958 | + | 0.210667i | −0.723249 | − | 0.690587i | \(-0.757352\pi\) |
0.433291 | + | 0.901254i | \(0.357352\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.00753 | + | 12.3978i | −0.509136 | + | 0.700765i | −0.983773 | − | 0.179416i | \(-0.942579\pi\) |
0.474638 | + | 0.880181i | \(0.342579\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.2723 | − | 6.58686i | 1.13860 | − | 0.369955i | 0.321765 | − | 0.946820i | \(-0.395724\pi\) |
0.816840 | + | 0.576864i | \(0.195724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.923699 | + | 2.84285i | 0.0517172 | + | 0.159169i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0101366 | − | 0.0139519i | −0.000564018 | − | 0.000776304i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.2558 | + | 12.3953i | 1.12359 | + | 0.687570i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.616057 | + | 1.89603i | −0.0339643 | + | 0.104531i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.12237 | + | 18.8427i | 0.336516 | + | 1.03569i | 0.965970 | + | 0.258652i | \(0.0832785\pi\) |
−0.629454 | + | 0.777037i | \(0.716722\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.9736 | + | 12.4248i | 1.47373 | + | 0.678838i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.89780 | − | 8.11762i | 0.321274 | − | 0.442195i | −0.617582 | − | 0.786507i | \(-0.711888\pi\) |
0.938856 | + | 0.344311i | \(0.111888\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.03378 | + | 0.751085i | 0.0559823 | + | 0.0406735i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.32419i | 0.0714997i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.1885 | + | 4.28519i | 0.707994 | + | 0.230041i | 0.640810 | − | 0.767700i | \(-0.278599\pi\) |
0.0671837 | + | 0.997741i | \(0.478599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.2533 | −1.45883 | −0.729417 | − | 0.684069i | \(-0.760209\pi\) | ||||
−0.729417 | + | 0.684069i | \(0.760209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.8063 | + | 3.83609i | 0.628384 | + | 0.204174i | 0.605859 | − | 0.795572i | \(-0.292830\pi\) |
0.0225248 | + | 0.999746i | \(0.492830\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.58374 | − | 5.37110i | 0.508652 | − | 0.285068i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.3910 | + | 11.1823i | 0.812308 | + | 0.590177i | 0.914499 | − | 0.404588i | \(-0.132585\pi\) |
−0.102191 | + | 0.994765i | \(0.532585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3711 | − | 11.1678i | 0.809007 | − | 0.587778i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.22639 | + | 10.3895i | −0.0641920 | + | 0.543814i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.927465 | − | 0.301352i | 0.0484133 | − | 0.0157304i | −0.284710 | − | 0.958614i | \(-0.591897\pi\) |
0.333124 | + | 0.942883i | \(0.391897\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.45294 | − | 10.6271i | 0.179268 | − | 0.551729i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0341 | − | 15.1871i | −0.571324 | − | 0.786360i | 0.421387 | − | 0.906881i | \(-0.361543\pi\) |
−0.992711 | + | 0.120521i | \(0.961543\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3318 | − | 14.2205i | −0.532114 | − | 0.732392i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.06536 | − | 3.27883i | 0.0547236 | − | 0.168422i | −0.919959 | − | 0.392014i | \(-0.871778\pi\) |
0.974683 | + | 0.223592i | \(0.0717784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.9681 | − | 8.43755i | 1.32691 | − | 0.431139i | 0.442046 | − | 0.896992i | \(-0.354253\pi\) |
0.884862 | + | 0.465854i | \(0.154253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.801990 | + | 6.79420i | −0.0408732 | + | 0.346264i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.94232 | + | 5.77044i | −0.402692 | + | 0.292573i | −0.770637 | − | 0.637275i | \(-0.780062\pi\) |
0.367945 | + | 0.929848i | \(0.380062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.82567 | − | 4.23259i | −0.294617 | − | 0.214051i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.0853 | + | 10.1357i | −0.909968 | + | 0.509981i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0447 | + | 3.58865i | 0.554319 | + | 0.180109i | 0.572763 | − | 0.819721i | \(-0.305871\pi\) |
−0.0184443 | + | 0.999830i | \(0.505871\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.4145 | 1.26914 | 0.634570 | − | 0.772865i | \(-0.281177\pi\) | ||||
0.634570 | + | 0.772865i | \(0.281177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.14637 | − | 2.32200i | −0.355986 | − | 0.115667i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.89902i | 0.341972i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9568 | + | 10.1402i | 0.690117 | + | 0.501399i | 0.876699 | − | 0.481040i | \(-0.159741\pi\) |
−0.186582 | + | 0.982439i | \(0.559741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.4800 | + | 35.0702i | −1.25379 | + | 1.72569i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.89148 | + | 1.33189i | 0.141937 | + | 0.0653800i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.31956 | − | 19.4496i | −0.308731 | − | 0.950176i | −0.978259 | − | 0.207389i | \(-0.933503\pi\) |
0.669528 | − | 0.742787i | \(-0.266497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.46100 | + | 19.8849i | −0.314890 | + | 0.969132i | 0.660910 | + | 0.750466i | \(0.270171\pi\) |
−0.975800 | + | 0.218666i | \(0.929829\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.20154 | + | 5.30559i | 0.106790 | + | 0.257359i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.99618 | + | 9.62941i | 0.338569 | + | 0.466000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.85900 | + | 8.79908i | 0.137713 | + | 0.423837i | 0.996002 | − | 0.0893294i | \(-0.0284724\pi\) |
−0.858289 | + | 0.513166i | \(0.828472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.223727 | − | 0.0726932i | 0.0107516 | − | 0.00349341i | −0.303636 | − | 0.952788i | \(-0.598201\pi\) |
0.314388 | + | 0.949295i | \(0.398201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0553044 | + | 0.0761199i | −0.00264557 | + | 0.00364131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.2424 | − | 18.3396i | 1.20475 | − | 0.875304i | 0.210008 | − | 0.977700i | \(-0.432651\pi\) |
0.994744 | + | 0.102396i | \(0.0326509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.3862i | − | 1.15862i | −0.815106 | − | 0.579311i | \(-0.803322\pi\) | ||
0.815106 | − | 0.579311i | \(-0.196678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.7674 | + | 4.22200i | 1.69554 | + | 0.200142i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.9483 | 1.13019 | 0.565096 | − | 0.825025i | \(-0.308839\pi\) | ||||
0.565096 | + | 0.825025i | \(0.308839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.28740 | −0.437327 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.86087 | − | 39.4547i | −0.368523 | − | 1.84967i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.91244i | − | 0.183016i | −0.995804 | − | 0.0915082i | \(-0.970831\pi\) | ||
0.995804 | − | 0.0915082i | \(-0.0291688\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.09170 | + | 1.51971i | −0.0974202 | + | 0.0707799i | −0.635429 | − | 0.772159i | \(-0.719177\pi\) |
0.538009 | + | 0.842939i | \(0.319177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8777 | − | 17.7247i | 0.598478 | − | 0.823734i | −0.397090 | − | 0.917780i | \(-0.629980\pi\) |
0.995568 | + | 0.0940453i | \(0.0299799\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.79561 | + | 2.53295i | −0.360738 | + | 0.117211i | −0.483778 | − | 0.875191i | \(-0.660736\pi\) |
0.123040 | + | 0.992402i | \(0.460736\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5467 | − | 47.8479i | −0.717881 | − | 2.20941i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.86410 | − | 6.69486i | −0.223652 | − | 0.307830i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0693245 | − | 0.0287660i | 0.00318083 | − | 0.00131987i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.90100 | + | 5.85067i | −0.0868588 | + | 0.267324i | −0.985047 | − | 0.172288i | \(-0.944884\pi\) |
0.898188 | + | 0.439612i | \(0.144884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5366 | − | 38.5836i | −0.571618 | − | 1.75926i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.81342 | − | 15.7259i | −0.400197 | − | 0.714078i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.69230 | + | 5.08201i | −0.167314 | + | 0.230288i | −0.884438 | − | 0.466658i | \(-0.845458\pi\) |
0.717124 | + | 0.696945i | \(0.245458\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.22591 | − | 1.61722i | −0.100454 | − | 0.0729840i | 0.536424 | − | 0.843948i | \(-0.319775\pi\) |
−0.636878 | + | 0.770964i | \(0.719775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.25178i | − | 0.191490i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.7006 | − | 5.75128i | −0.793982 | − | 0.257980i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4263 | 0.735341 | 0.367670 | − | 0.929956i | \(-0.380156\pi\) | ||||
0.367670 | + | 0.929956i | \(0.380156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.6860 | + | 3.79701i | 0.521053 | + | 0.169300i | 0.557723 | − | 0.830027i | \(-0.311675\pi\) |
−0.0366701 | + | 0.999327i | \(0.511675\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.1341 | − | 17.6763i | −0.851458 | − | 0.786586i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.50277 | + | 6.17763i | 0.376879 | + | 0.273818i | 0.760058 | − | 0.649856i | \(-0.225171\pi\) |
−0.383179 | + | 0.923674i | \(0.625171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3382 | − | 10.4173i | 0.634283 | − | 0.460833i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.6001 | + | 36.7572i | 0.907750 | + | 1.61971i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.404263 | − | 0.131353i | 0.0177795 | − | 0.00577690i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.41778 | − | 7.44115i | 0.105925 | − | 0.326003i | −0.884022 | − | 0.467446i | \(-0.845174\pi\) |
0.989946 | + | 0.141443i | \(0.0451742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9592 | − | 17.8368i | −0.566665 | − | 0.779947i | 0.425490 | − | 0.904963i | \(-0.360102\pi\) |
−0.992155 | + | 0.125016i | \(0.960102\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.06834 | − | 1.47045i | −0.0465378 | − | 0.0640538i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.03308 | + | 15.4902i | −0.218830 | + | 0.673489i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.9409 | − | 16.8766i | 2.24981 | − | 0.731007i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.8430 | − | 23.6445i | 0.944357 | − | 1.02224i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.80240 | − | 3.48915i | 0.206854 | − | 0.150288i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0860 | − | 7.32791i | −0.433631 | − | 0.315052i | 0.349468 | − | 0.936948i | \(-0.386362\pi\) |
−0.783099 | + | 0.621897i | \(0.786362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.51748 | − | 12.6356i | −0.107837 | − | 0.541248i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.39292 | − | 0.777505i | −0.102314 | − | 0.0332437i | 0.257413 | − | 0.966302i | \(-0.417130\pi\) |
−0.359726 | + | 0.933058i | \(0.617130\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0555550 | −0.00236672 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.4024 | + | 10.8531i | 1.42042 | + | 0.461521i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.262544i | − | 0.0111244i | −0.999985 | − | 0.00556218i | \(-0.998229\pi\) | ||
0.999985 | − | 0.00556218i | \(-0.00177051\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.3687 | + | 28.6030i | 1.66512 | + | 1.20978i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0928 | + | 26.2790i | −0.804666 | + | 1.10753i | 0.187459 | + | 0.982272i | \(0.439975\pi\) |
−0.992125 | + | 0.125255i | \(0.960025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.3119 | + | 7.83241i | −1.65386 | + | 0.329512i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.9892 | − | 36.8991i | −0.502615 | − | 1.54689i | −0.804743 | − | 0.593623i | \(-0.797697\pi\) |
0.302128 | − | 0.953267i | \(-0.402303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0258 | + | 33.9338i | −0.461414 | + | 1.42009i | 0.402023 | + | 0.915629i | \(0.368307\pi\) |
−0.863437 | + | 0.504456i | \(0.831693\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.8182 | − | 20.3685i | 0.993290 | − | 0.849425i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.8962 | − | 20.5029i | −0.620139 | − | 0.853548i | 0.377224 | − | 0.926122i | \(-0.376879\pi\) |
−0.997363 | + | 0.0725741i | \(0.976879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.66655 | − | 5.12913i | −0.0691403 | − | 0.212792i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.26586 | + | 0.736221i | −0.0938422 | + | 0.0304912i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.303103 | − | 0.417186i | 0.0125104 | − | 0.0172191i | −0.802716 | − | 0.596362i | \(-0.796612\pi\) |
0.815226 | + | 0.579142i | \(0.196612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0192134 | + | 0.0139593i | −0.000791673 | + | 0.000575184i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7.14389i | − | 0.293364i | −0.989184 | − | 0.146682i | \(-0.953141\pi\) | ||
0.989184 | − | 0.146682i | \(-0.0468595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.07129 | − | 8.83858i | 0.166907 | − | 0.362347i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.6627 | 0.966833 | 0.483417 | − | 0.875390i | \(-0.339396\pi\) | ||||
0.483417 | + | 0.875390i | \(0.339396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.98023 | −0.325520 | −0.162760 | − | 0.986666i | \(-0.552040\pi\) | ||||
−0.162760 | + | 0.986666i | \(0.552040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.1843 | + | 11.3121i | −0.820610 | + | 0.459901i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2004i | 0.698144i | 0.937096 | + | 0.349072i | \(0.113503\pi\) | ||||
−0.937096 | + | 0.349072i | \(0.886497\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.02220 | + | 1.46921i | −0.0818094 | + | 0.0594380i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.67810 | − | 11.9444i | 0.350505 | − | 0.482429i | −0.596968 | − | 0.802265i | \(-0.703628\pi\) |
0.947473 | + | 0.319836i | \(0.103628\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.7142 | + | 4.78092i | −0.592370 | + | 0.192473i | −0.589834 | − | 0.807524i | \(-0.700807\pi\) |
−0.00253529 | + | 0.999997i | \(0.500807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5792 | + | 35.6370i | 0.465406 | + | 1.43237i | 0.858471 | + | 0.512861i | \(0.171414\pi\) |
−0.393066 | + | 0.919510i | \(0.628586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.8629 | − | 49.3611i | −1.43682 | − | 1.97761i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.6873 | + | 3.94177i | −0.987492 | + | 0.157671i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.03244 | − | 9.33290i | 0.120911 | − | 0.372127i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.468691 | − | 1.44248i | −0.0186583 | − | 0.0574244i | 0.941294 | − | 0.337588i | \(-0.109611\pi\) |
−0.959952 | + | 0.280164i | \(0.909611\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.600220 | − | 5.08487i | 0.0238190 | − | 0.201787i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.5177 | + | 28.2401i | −0.812940 | + | 1.11892i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.12903 | − | 2.27338i | −0.123589 | − | 0.0897930i | 0.524273 | − | 0.851550i | \(-0.324337\pi\) |
−0.647863 | + | 0.761757i | \(0.724337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.2212i | 0.915756i | 0.889015 | + | 0.457878i | \(0.151390\pi\) | ||||
−0.889015 | + | 0.457878i | \(0.848610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.8795 | + | 8.08384i | 0.978114 | + | 0.317808i | 0.754087 | − | 0.656775i | \(-0.228080\pi\) |
0.224027 | + | 0.974583i | \(0.428080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.24271 | 0.362808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.13602 | + | 2.64355i | 0.318387 | + | 0.103450i | 0.463851 | − | 0.885913i | \(-0.346467\pi\) |
−0.145464 | + | 0.989364i | \(0.546467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.59488 | + | 14.3172i | −0.257683 | + | 0.559419i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.9288 | + | 24.6507i | 1.32168 | + | 0.960255i | 0.999910 | + | 0.0134358i | \(0.00427688\pi\) |
0.321767 | + | 0.946819i | \(0.395723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.1713 | − | 10.2961i | 0.551201 | − | 0.400471i | −0.277027 | − | 0.960862i | \(-0.589349\pi\) |
0.828228 | + | 0.560391i | \(0.189349\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.115488 | − | 0.0531967i | −0.00447842 | − | 0.00206288i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.0619 | + | 7.16833i | −0.854239 | + | 0.277559i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.784230 | − | 2.41361i | 0.0302749 | − | 0.0931765i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.1017 | + | 23.5385i | 0.659223 | + | 0.907343i | 0.999455 | − | 0.0329986i | \(-0.0105057\pi\) |
−0.340232 | + | 0.940341i | \(0.610506\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.5667 | + | 24.1785i | 0.675143 | + | 0.929255i | 0.999863 | − | 0.0165555i | \(-0.00527003\pi\) |
−0.324720 | + | 0.945810i | \(0.605270\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.43726 | + | 29.0449i | −0.362169 | + | 1.11464i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.3984 | + | 11.5016i | −1.35448 | + | 0.440097i | −0.894197 | − | 0.447674i | \(-0.852252\pi\) |
−0.460284 | + | 0.887772i | \(0.652252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48.0981 | + | 9.58296i | −1.83773 | + | 0.366146i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3342 | − | 8.23481i | 0.431800 | − | 0.313721i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.6397 | − | 9.90980i | −0.518877 | − | 0.376986i | 0.297303 | − | 0.954783i | \(-0.403913\pi\) |
−0.816181 | + | 0.577797i | \(0.803913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.5794 | + | 2.54724i | 0.818554 | + | 0.0966225i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5639 | + | 4.08225i | 0.475890 | + | 0.154626i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.3495 | 0.881898 | 0.440949 | − | 0.897532i | \(-0.354642\pi\) | ||||
0.440949 | + | 0.897532i | \(0.354642\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.121947 | − | 0.0396228i | −0.00459930 | − | 0.00149440i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.1297i | 1.65967i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.4019 | + | 11.1901i | 0.578429 | + | 0.420253i | 0.838157 | − | 0.545428i | \(-0.183633\pi\) |
−0.259728 | + | 0.965682i | \(0.583633\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.82877 | + | 8.02261i | −0.218289 | + | 0.300449i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.82058 | + | 6.30063i | −0.217677 | + | 0.235630i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.55488 | − | 14.0185i | −0.169868 | − | 0.522801i | 0.829494 | − | 0.558516i | \(-0.188629\pi\) |
−0.999362 | + | 0.0357149i | \(0.988629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0583 | − | 67.8884i | 0.821493 | − | 2.52830i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.9960 | + | 4.30854i | 0.668355 | + | 0.160015i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6698 | + | 24.3204i | 0.655336 | + | 0.901993i | 0.999316 | − | 0.0369839i | \(-0.0117750\pi\) |
−0.343979 | + | 0.938977i | \(0.611775\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.63738 | + | 11.1947i | 0.134533 | + | 0.414051i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.5355 | − | 6.99732i | 0.795433 | − | 0.258452i | 0.117017 | − | 0.993130i | \(-0.462667\pi\) |
0.678416 | + | 0.734678i | \(0.262667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.30514 | + | 8.67828i | −0.232253 | + | 0.319668i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.7764 | + | 15.0949i | −0.764272 | + | 0.555276i | −0.900218 | − | 0.435440i | \(-0.856593\pi\) |
0.135946 | + | 0.990716i | \(0.456593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.9796i | 0.916411i | 0.888846 | + | 0.458205i | \(0.151508\pi\) | ||||
−0.888846 | + | 0.458205i | \(0.848492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.9473 | − | 21.1990i | −0.840725 | − | 0.776670i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.5321 | −1.99256 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9383 | 0.654580 | 0.327290 | − | 0.944924i | \(-0.393865\pi\) | ||||
0.327290 | + | 0.944924i | \(0.393865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.1567 | − | 30.6305i | −1.20669 | − | 1.11476i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.91474i | 0.360357i | 0.983634 | + | 0.180179i | \(0.0576676\pi\) | ||||
−0.983634 | + | 0.180179i | \(0.942332\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6076 | + | 18.6050i | −0.928273 | + | 0.674430i | −0.945569 | − | 0.325420i | \(-0.894494\pi\) |
0.0172961 | + | 0.999850i | \(0.494494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8292 | + | 17.6579i | −0.464449 | + | 0.639259i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −51.6910 | + | 16.7954i | −1.86645 | + | 0.606447i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.91430 | − | 21.2800i | −0.249336 | − | 0.767377i | −0.994893 | − | 0.100935i | \(-0.967816\pi\) |
0.745557 | − | 0.666442i | \(-0.232184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.1148 | − | 38.6967i | −1.01122 | − | 1.39182i | −0.918182 | − | 0.396160i | \(-0.870343\pi\) |
−0.0930367 | − | 0.995663i | \(-0.529657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.30641 | − | 3.03178i | 0.262454 | − | 0.108905i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0533399 | − | 0.164163i | 0.00191110 | − | 0.00588176i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.22626 | + | 3.77405i | 0.0438792 | + | 0.135046i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.7828 | − | 12.7545i | 0.420545 | − | 0.455229i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.2038 | − | 22.3026i | 0.577603 | − | 0.795002i | −0.415827 | − | 0.909444i | \(-0.636508\pi\) |
0.993430 | + | 0.114442i | \(0.0365079\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.9375 | + | 39.9144i | 1.95335 | + | 1.41919i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9235i | 0.529948i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.9712 | − | 7.13887i | −0.778260 | − | 0.252872i | −0.107163 | − | 0.994241i | \(-0.534177\pi\) |
−0.671097 | + | 0.741370i | \(0.734177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.604617 | −0.0213898 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.59386 | − | 1.16772i | −0.126825 | − | 0.0412078i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −52.7262 | − | 6.22382i | −1.85835 | − | 0.219361i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.36960 | + | 0.995071i | 0.0481525 | + | 0.0349848i | 0.611601 | − | 0.791166i | \(-0.290526\pi\) |
−0.563449 | + | 0.826151i | \(0.690526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.6435 | + | 12.0922i | −0.584434 | + | 0.424616i | −0.840320 | − | 0.542091i | \(-0.817633\pi\) |
0.255886 | + | 0.966707i | \(0.417633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.4620 | + | 6.06919i | −1.06704 | + | 0.212594i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.146274 | − | 0.0475272i | 0.00511746 | − | 0.00166277i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.2235 | − | 43.7754i | 0.496403 | − | 1.52777i | −0.318356 | − | 0.947971i | \(-0.603131\pi\) |
0.814759 | − | 0.579800i | \(-0.196869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.9082 | − | 45.2942i | −1.14711 | − | 1.57886i | −0.750502 | − | 0.660868i | \(-0.770188\pi\) |
−0.396605 | − | 0.917990i | \(-0.629812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.1319 | − | 16.6981i | −0.421866 | − | 0.580648i | 0.544196 | − | 0.838958i | \(-0.316835\pi\) |
−0.966062 | + | 0.258309i | \(0.916835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.599179 | − | 1.84408i | 0.0208103 | − | 0.0640476i | −0.940112 | − | 0.340866i | \(-0.889280\pi\) |
0.960922 | + | 0.276818i | \(0.0892799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.03026 | + | 2.60919i | −0.278232 | + | 0.0904030i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.88547 | + | 2.71100i | 0.203675 | + | 0.0938182i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.2783 | + | 30.7170i | −1.45961 | + | 1.06047i | −0.476146 | + | 0.879366i | \(0.657966\pi\) |
−0.983464 | + | 0.181102i | \(0.942034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3806 | + | 8.99501i | 0.426916 | + | 0.310173i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.94139 | − | 19.4114i | 0.307593 | − | 0.667771i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.2793 | + | 12.1128i | 1.28093 | + | 0.416200i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53.5397 | −1.83532 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7010 | − | 5.42649i | −0.571832 | − | 0.185799i | 0.00880614 | − | 0.999961i | \(-0.497197\pi\) |
−0.580638 | + | 0.814162i | \(0.697197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.9890i | 1.74175i | 0.491503 | + | 0.870876i | \(0.336448\pi\) | ||||
−0.491503 | + | 0.870876i | \(0.663552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0749 | + | 10.9525i | 0.514349 | + | 0.373696i | 0.814471 | − | 0.580205i | \(-0.197027\pi\) |
−0.300122 | + | 0.953901i | \(0.597027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.171716 | + | 0.236347i | −0.00584529 | + | 0.00804536i | −0.811930 | − | 0.583755i | \(-0.801583\pi\) |
0.806084 | + | 0.591801i | \(0.201583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.99319 | + | 33.8290i | −0.135773 | + | 1.15022i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.31405 | − | 7.12192i | −0.0784989 | − | 0.241595i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.4925 | − | 59.9917i | 0.660477 | − | 2.03274i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.2844 | + | 26.1887i | 1.12522 | + | 0.885338i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3126 | − | 30.7106i | −0.753442 | − | 1.03702i | −0.997731 | − | 0.0673215i | \(-0.978555\pi\) |
0.244289 | − | 0.969702i | \(-0.421445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.3378 | + | 34.8942i | 0.381981 | + | 1.17562i | 0.938647 | + | 0.344879i | \(0.112080\pi\) |
−0.556666 | + | 0.830736i | \(0.687920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5128 | − | 6.98993i | 0.723964 | − | 0.235230i | 0.0762228 | − | 0.997091i | \(-0.475714\pi\) |
0.647741 | + | 0.761861i | \(0.275714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.3643 | + | 19.7708i | −0.482306 | + | 0.663838i | −0.978946 | − | 0.204119i | \(-0.934567\pi\) |
0.496640 | + | 0.867957i | \(0.334567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.01741 | + | 5.09845i | −0.235356 | + | 0.170996i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.00790011i | 0.000264367i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.4603 | + | 25.4777i | −1.51957 | + | 0.851625i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.85519 | −0.195281 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.38882 | 0.112898 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.5572 | + | 35.9449i | −0.550380 | + | 1.19485i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 32.7792i | − | 1.08842i | −0.838950 | − | 0.544208i | \(-0.816830\pi\) | ||
0.838950 | − | 0.544208i | \(-0.183170\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0778 | − | 16.0405i | 0.731470 | − | 0.531444i | −0.158558 | − | 0.987350i | \(-0.550685\pi\) |
0.890028 | + | 0.455906i | \(0.150685\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.675888 | + | 0.930280i | −0.0223686 | + | 0.0307878i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.3970 | − | 8.25197i | 0.838681 | − | 0.272504i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.8923 | + | 39.6783i | 0.425277 | + | 1.30887i | 0.902729 | + | 0.430209i | \(0.141560\pi\) |
−0.477453 | + | 0.878658i | \(0.658440\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.7161 | − | 18.8785i | −0.451469 | − | 0.621394i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.4293 | + | 22.2926i | 1.19779 | + | 0.732975i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4151 | + | 32.0542i | −0.341707 | + | 1.05167i | 0.621616 | + | 0.783322i | \(0.286476\pi\) |
−0.963323 | + | 0.268344i | \(0.913524\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0340925 | + | 0.104926i | 0.00111734 | + | 0.00343880i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.03485 | + | 0.405418i | −0.0665466 | + | 0.0132586i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.614857 | − | 0.846278i | 0.0200865 | − | 0.0276467i | −0.798856 | − | 0.601523i | \(-0.794561\pi\) |
0.818942 | + | 0.573876i | \(0.194561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.62928 | + | 3.36337i | 0.150910 | + | 0.109643i | 0.660678 | − | 0.750669i | \(-0.270269\pi\) |
−0.509768 | + | 0.860312i | \(0.670269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 72.0746i | − | 2.34707i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.9783 | + | 3.89200i | 0.389244 | + | 0.126473i | 0.497099 | − | 0.867694i | \(-0.334398\pi\) |
−0.107856 | + | 0.994167i | \(0.534398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.2210 | 0.721325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.5813 | − | 17.7346i | −1.76806 | − | 0.574479i | −0.770079 | − | 0.637948i | \(-0.779783\pi\) |
−0.997984 | + | 0.0634695i | \(0.979783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.09140 | + | 20.5352i | 0.132395 | + | 0.664505i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 67.2161 | + | 48.8353i | 2.17052 | + | 1.57698i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0545 | − | 16.7501i | 0.743695 | − | 0.540326i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.7244 | + | 31.0934i | −0.924672 | + | 1.00093i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.40935 | − | 2.73236i | 0.270427 | − | 0.0878669i | −0.170665 | − | 0.985329i | \(-0.554591\pi\) |
0.441091 | + | 0.897462i | \(0.354591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0493 | + | 49.3945i | −0.515045 | + | 1.58515i | 0.268155 | + | 0.963376i | \(0.413586\pi\) |
−0.783200 | + | 0.621770i | \(0.786414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.6370 | − | 29.7808i | −0.693651 | − | 0.954729i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.8859 | − | 30.1234i | −0.700193 | − | 0.963732i | −0.999953 | − | 0.00971780i | \(-0.996907\pi\) |
0.299760 | − | 0.954015i | \(-0.403093\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.02002 | + | 12.3724i | −0.128480 | + | 0.395422i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.0107 | − | 11.0507i | 1.08477 | − | 0.352464i | 0.288548 | − | 0.957465i | \(-0.406827\pi\) |
0.796225 | + | 0.605001i | \(0.206827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.24664 | − | 14.7146i | −0.262760 | − | 0.468847i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.9553 | − | 37.7477i | 1.65208 | − | 1.20031i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.4505 | + | 25.7563i | 1.12612 | + | 0.818175i | 0.985126 | − | 0.171835i | \(-0.0549697\pi\) |
0.140996 | + | 0.990010i | \(0.454970\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.88924 | − | 5.44054i | −0.186701 | − | 0.172477i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.5746 | − | 12.2087i | −1.19000 | − | 0.386654i | −0.353927 | − | 0.935273i | \(-0.615154\pi\) |
−0.836072 | + | 0.548619i | \(0.815154\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.2.w.c.289.4 | 24 | ||
3.2 | odd | 2 | 300.2.o.a.289.5 | yes | 24 | ||
15.2 | even | 4 | 1500.2.m.c.301.5 | 24 | |||
15.8 | even | 4 | 1500.2.m.d.301.2 | 24 | |||
15.14 | odd | 2 | 1500.2.o.c.949.1 | 24 | |||
25.9 | even | 10 | inner | 900.2.w.c.109.4 | 24 | ||
75.29 | odd | 10 | 7500.2.d.g.1249.9 | 24 | |||
75.38 | even | 20 | 1500.2.m.d.1201.2 | 24 | |||
75.41 | odd | 10 | 1500.2.o.c.49.1 | 24 | |||
75.47 | even | 20 | 7500.2.a.n.1.9 | 12 | |||
75.53 | even | 20 | 7500.2.a.m.1.4 | 12 | |||
75.59 | odd | 10 | 300.2.o.a.109.5 | ✓ | 24 | ||
75.62 | even | 20 | 1500.2.m.c.1201.5 | 24 | |||
75.71 | odd | 10 | 7500.2.d.g.1249.16 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.5 | ✓ | 24 | 75.59 | odd | 10 | ||
300.2.o.a.289.5 | yes | 24 | 3.2 | odd | 2 | ||
900.2.w.c.109.4 | 24 | 25.9 | even | 10 | inner | ||
900.2.w.c.289.4 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.c.301.5 | 24 | 15.2 | even | 4 | |||
1500.2.m.c.1201.5 | 24 | 75.62 | even | 20 | |||
1500.2.m.d.301.2 | 24 | 15.8 | even | 4 | |||
1500.2.m.d.1201.2 | 24 | 75.38 | even | 20 | |||
1500.2.o.c.49.1 | 24 | 75.41 | odd | 10 | |||
1500.2.o.c.949.1 | 24 | 15.14 | odd | 2 | |||
7500.2.a.m.1.4 | 12 | 75.53 | even | 20 | |||
7500.2.a.n.1.9 | 12 | 75.47 | even | 20 | |||
7500.2.d.g.1249.9 | 24 | 75.29 | odd | 10 | |||
7500.2.d.g.1249.16 | 24 | 75.71 | odd | 10 |