Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(49,1500)]
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, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.o (of order \(10\), 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 \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 949.1 | ||
Character | \(\chi\) | \(=\) | 1500.949 |
Dual form | 1500.2.o.c.49.1 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.951057 | − | 0.309017i | −0.549093 | − | 0.178411i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.78808i | 1.43176i | 0.698223 | + | 0.715880i | \(0.253974\pi\) | ||||
−0.698223 | + | 0.715880i | \(0.746026\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.653426 | − | 0.474742i | 0.197015 | − | 0.143140i | −0.484904 | − | 0.874567i | \(-0.661145\pi\) |
0.681919 | + | 0.731427i | \(0.261145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.79168 | + | 3.84242i | −0.774274 | + | 1.06570i | 0.221617 | + | 0.975134i | \(0.428867\pi\) |
−0.995891 | + | 0.0905626i | \(0.971133\pi\) | |||||||
\(14\) | 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 | ||||||||
\(21\) | 1.17058 | − | 3.60268i | 0.255442 | − | 0.786169i | ||||
\(22\) | 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 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.587785 | − | 0.809017i | −0.113119 | − | 0.155695i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.14365 | + | 3.51978i | −0.212370 | + | 0.653607i | 0.786960 | + | 0.617004i | \(0.211654\pi\) |
−0.999330 | + | 0.0366030i | \(0.988346\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | −0.768148 | + | 0.249586i | −0.133717 | + | 0.0434474i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.02074 | + | 6.91045i | −0.825404 | + | 1.13607i | 0.163357 | + | 0.986567i | \(0.447768\pi\) |
−0.988761 | + | 0.149504i | \(0.952232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.84242 | − | 2.79168i | 0.615280 | − | 0.447027i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.30279 | − | 6.75887i | −1.45285 | − | 1.05556i | −0.985155 | − | 0.171669i | \(-0.945084\pi\) |
−0.467697 | − | 0.883889i | \(-0.654916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.2458i | − | 1.56247i | −0.624238 | − | 0.781234i | \(-0.714591\pi\) | ||
0.624238 | − | 0.781234i | \(-0.285409\pi\) | |||||||
\(44\) | 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 | ||||||||
\(51\) | −1.14884 | −0.160870 | ||||||||
\(52\) | 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 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0150112i | 0.00198828i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.25803 | + | 6.72635i | 1.20529 | + | 0.875696i | 0.994795 | − | 0.101898i | \(-0.0324916\pi\) |
0.210498 | + | 0.977594i | \(0.432492\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −2.22658 | + | 3.06462i | −0.280523 | + | 0.386106i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6312 | + | 4.10412i | −1.54314 | + | 0.501398i | −0.952241 | − | 0.305346i | \(-0.901228\pi\) |
−0.590901 | + | 0.806744i | \(0.701228\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.93691 | + | 5.96119i | 0.233176 | + | 0.717643i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.51826 | + | 4.67271i | −0.180184 | + | 0.554549i | −0.999832 | − | 0.0183179i | \(-0.994169\pi\) |
0.819648 | + | 0.572867i | \(0.194169\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.75001 | − | 3.78507i | −0.321865 | − | 0.443009i | 0.617171 | − | 0.786829i | \(-0.288279\pi\) |
−0.939035 | + | 0.343820i | \(0.888279\pi\) | |||||||
\(74\) | 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 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 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 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.17534 | − | 2.99410i | 0.233221 | − | 0.321002i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.0306 | + | 9.46730i | −1.38124 | + | 1.00353i | −0.384480 | + | 0.923133i | \(0.625619\pi\) |
−0.996763 | + | 0.0803985i | \(0.974381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.5554 | − | 10.5751i | −1.52582 | − | 1.10857i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.58209i | 0.164055i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.66744 | + | 2.49130i | 0.778511 | + | 0.252954i | 0.671204 | − | 0.741272i | \(-0.265777\pi\) |
0.107307 | + | 0.994226i | \(0.465777\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.807679 | 0.0811748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6496 | 1.15918 | 0.579590 | − | 0.814908i | \(-0.303213\pi\) | ||||
0.579590 | + | 0.814908i | \(0.303213\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.9216 | − | 5.82307i | −1.76587 | − | 0.573764i | −0.768084 | − | 0.640349i | \(-0.778790\pi\) |
−0.997781 | + | 0.0665845i | \(0.978790\pi\) | |||||||
\(104\) | 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 | ||||||||
\(111\) | 6.91045 | − | 5.02074i | 0.655911 | − | 0.476547i | ||||
\(112\) | 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 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.51704 | + | 1.46767i | −0.417600 | + | 0.135687i | ||||
\(118\) | 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 | ||||||||
\(123\) | 6.75887 | + | 9.30279i | 0.609427 | + | 0.838804i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.34592 | + | 1.85250i | 0.119431 | + | 0.164382i | 0.864547 | − | 0.502553i | \(-0.167606\pi\) |
−0.745116 | + | 0.666935i | \(0.767606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.16612 | + | 9.74432i | −0.278762 | + | 0.857940i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.17840 | − | 6.70444i | −0.190328 | − | 0.585769i | 0.809671 | − | 0.586883i | \(-0.199645\pi\) |
−0.999999 | + | 0.00111420i | \(0.999645\pi\) | |||||||
\(132\) | 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 | ||||||||
\(141\) | 0.425771 | + | 0.309341i | 0.0358564 | + | 0.0260512i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.83607i | 0.320788i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.98985 | + | 2.27114i | 0.576513 | + | 0.187321i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9712 | 1.14457 | 0.572284 | − | 0.820056i | \(-0.306058\pi\) | ||||
0.572284 | + | 0.820056i | \(0.306058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1871 | −1.64280 | −0.821400 | − | 0.570352i | \(-0.806807\pi\) | ||||
−0.821400 | + | 0.570352i | \(0.806807\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.09262 | + | 0.355012i | 0.0883328 | + | 0.0287011i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.76546i | 0.619751i | 0.950777 | + | 0.309876i | \(0.100287\pi\) | ||||
−0.950777 | + | 0.309876i | \(0.899713\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.38641 | − | 1.73383i | −0.189255 | − | 0.137502i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.2090 | − | 13.9561i | 1.51388 | − | 1.09990i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.16480 | − | 11.2379i | 0.639517 | − | 0.880219i | −0.359073 | − | 0.933310i | \(-0.616907\pi\) |
0.998590 | + | 0.0530901i | \(0.0169070\pi\) | |||||||
\(164\) | 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 | ||||||||
\(171\) | 0.00463870 | − | 0.0142765i | 0.000354730 | − | 0.00109175i | ||||
\(172\) | 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 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.72635 | − | 9.25803i | −0.505583 | − | 0.695876i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.20182 | − | 22.1649i | 0.538290 | − | 1.65669i | −0.198142 | − | 0.980173i | \(-0.563491\pi\) |
0.736432 | − | 0.676512i | \(-0.236509\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 2.98833 | − | 0.970968i | 0.220904 | − | 0.0717760i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.545404 | − | 0.750685i | 0.0398839 | − | 0.0548955i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.06462 | − | 2.22658i | 0.222919 | − | 0.161960i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.57575 | − | 5.50411i | −0.548162 | − | 0.398263i | 0.278945 | − | 0.960307i | \(-0.410015\pi\) |
−0.827107 | + | 0.562044i | \(0.810015\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.9309i | − | 1.36268i | −0.731969 | − | 0.681338i | \(-0.761398\pi\) | ||
0.731969 | − | 0.681338i | \(-0.238602\pi\) | |||||||
\(194\) | 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 | ||||||||
\(201\) | 13.2812 | 0.936783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.3332 | − | 4.33223i | −0.935808 | − | 0.304063i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.26797i | − | 0.435654i | ||||||
\(208\) | 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 | ||||||||
\(213\) | 2.88790 | − | 3.97485i | 0.197875 | − | 0.272352i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.69977 | − | 1.85197i | 0.386926 | − | 0.125720i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.44577 | + | 4.44962i | 0.0976960 | + | 0.300677i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.68613 | + | 5.18938i | −0.113421 | + | 0.349075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.25091 | + | 11.3564i | 0.552522 | + | 0.760481i | 0.990352 | − | 0.138577i | \(-0.0442527\pi\) |
−0.437830 | + | 0.899058i | \(0.644253\pi\) | |||||||
\(224\) | 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 | ||||||||
\(231\) | −0.945454 | − | 2.90981i | −0.0622063 | − | 0.191451i | ||||
\(232\) | 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 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.44968 | − | 7.50084i | 0.353995 | − | 0.487232i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.03839 | + | 4.38714i | −0.390591 | + | 0.283781i | −0.765698 | − | 0.643201i | \(-0.777606\pi\) |
0.375107 | + | 0.926982i | \(0.377606\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0678060 | + | 0.0220315i | 0.00431439 | + | 0.00140183i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.42370 | −0.0902231 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.5809 | 1.23593 | 0.617967 | − | 0.786204i | \(-0.287956\pi\) | ||||
0.617967 | + | 0.786204i | \(0.287956\pi\) | |||||||
\(252\) | 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 | ||||||||
\(261\) | −2.99410 | + | 2.17534i | −0.185330 | + | 0.134650i | ||||
\(262\) | 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 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.3184 | − | 4.97725i | 0.937472 | − | 0.304603i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.97152 | − | 9.14540i | −0.181177 | − | 0.557605i | 0.818685 | − | 0.574243i | \(-0.194704\pi\) |
−0.999862 | + | 0.0166382i | \(0.994704\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 10.5751 | + | 14.5554i | 0.640036 | + | 0.880934i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.23436 | + | 5.82810i | 0.254418 | + | 0.350176i | 0.917052 | − | 0.398767i | \(-0.130562\pi\) |
−0.662634 | + | 0.748943i | \(0.730562\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.488893 | − | 1.50466i | 0.0292693 | − | 0.0900815i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.20758 | + | 28.3380i | 0.549278 | + | 1.69050i | 0.710594 | + | 0.703602i | \(0.248426\pi\) |
−0.161316 | + | 0.986903i | \(0.551574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.39215 | − | 2.72677i | 0.498861 | − | 0.162090i | −0.0487693 | − | 0.998810i | \(-0.515530\pi\) |
0.547631 | + | 0.836720i | \(0.315530\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | −6.52232 | − | 4.73874i | −0.382345 | − | 0.277790i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.20743i | 0.245800i | 0.992419 | + | 0.122900i | \(0.0392195\pi\) | ||||
−0.992419 | + | 0.122900i | \(0.960780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.768148 | − | 0.249586i | −0.0445725 | − | 0.0144825i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.7697 | 1.72163 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.8119 | 2.23708 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.0794 | − | 3.59993i | −0.636497 | − | 0.206811i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.41109i | 0.251754i | 0.992046 | + | 0.125877i | \(0.0401745\pi\) | ||||
−0.992046 | + | 0.125877i | \(0.959825\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.2450 | + | 11.0761i | 0.867258 | + | 0.630100i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.11346 | − | 3.71514i | 0.289958 | − | 0.210667i | −0.433291 | − | 0.901254i | \(-0.642648\pi\) |
0.723249 | + | 0.690587i | \(0.242648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00753 | − | 12.3978i | 0.509136 | − | 0.700765i | −0.474638 | − | 0.880181i | \(-0.657421\pi\) |
0.983773 | + | 0.179416i | \(0.0574208\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | −4.44851 | + | 13.6911i | −0.248292 | + | 0.764164i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0101366 | − | 0.0139519i | −0.000564018 | − | 0.000776304i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.38673 | + | 4.66144i | 0.187287 | + | 0.257778i | ||||
\(328\) | 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 | ||||||||
\(333\) | −8.12372 | + | 2.63956i | −0.445177 | + | 0.144647i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.89780 | + | 8.11762i | −0.321274 | + | 0.442195i | −0.938856 | − | 0.344311i | \(-0.888112\pi\) |
0.617582 | + | 0.786507i | \(0.288112\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.5027 | − | 10.5368i | 0.787680 | − | 0.572283i | ||||
\(340\) | 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 | ||||||||
\(351\) | 4.74950 | 0.253509 | ||||||||
\(352\) | 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 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 4.35192i | − | 0.230328i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.3910 | − | 11.1823i | −0.812308 | − | 0.590177i | 0.102191 | − | 0.994765i | \(-0.467415\pi\) |
−0.914499 | + | 0.404588i | \(0.867415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3711 | − | 11.1678i | 0.809007 | − | 0.587778i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.08220 | − | 8.37143i | 0.319233 | − | 0.439386i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.927465 | + | 0.301352i | −0.0484133 | + | 0.0157304i | −0.333124 | − | 0.942883i | \(-0.608103\pi\) |
0.284710 | + | 0.958614i | \(0.408103\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.55335 | − | 10.9361i | −0.184980 | − | 0.569310i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.45294 | + | 10.6271i | −0.179268 | + | 0.551729i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0341 | + | 15.1871i | 0.571324 | + | 0.786360i | 0.992711 | − | 0.120521i | \(-0.0384566\pi\) |
−0.421387 | + | 0.906881i | \(0.638457\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | −0.707591 | − | 2.17774i | −0.0362510 | − | 0.111569i | ||||
\(382\) | 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 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.02232 | − | 8.28902i | 0.306132 | − | 0.421354i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.94232 | − | 5.77044i | 0.402692 | − | 0.292573i | −0.367945 | − | 0.929848i | \(-0.619938\pi\) |
0.770637 | + | 0.637275i | \(0.219938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.82567 | − | 4.23259i | −0.294617 | − | 0.214051i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.04946i | 0.355598i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0447 | − | 3.58865i | −0.554319 | − | 0.180109i | 0.0184443 | − | 0.999830i | \(-0.494129\pi\) |
−0.572763 | + | 0.819721i | \(0.694129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0568635 | −0.00284674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.4145 | −1.26914 | −0.634570 | − | 0.772865i | \(-0.718823\pi\) | ||||
−0.634570 | + | 0.772865i | \(0.718823\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 17.7441 | − | 12.8918i | 0.875251 | − | 0.635907i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.4800 | + | 35.0702i | −1.25379 | + | 1.72569i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.24200 | + | 3.00291i | −0.452583 | + | 0.147053i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.31956 | + | 19.4496i | 0.308731 | + | 0.950176i | 0.978259 | + | 0.207389i | \(0.0664965\pi\) |
−0.669528 | + | 0.742787i | \(0.733503\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −0.309341 | − | 0.425771i | −0.0150407 | − | 0.0207017i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.99618 | − | 9.62941i | −0.338569 | − | 0.466000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.18541 | − | 3.64832i | 0.0572321 | − | 0.176142i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.85900 | − | 8.79908i | −0.137713 | − | 0.423837i | 0.858289 | − | 0.513166i | \(-0.171528\pi\) |
−0.996002 | + | 0.0893294i | \(0.971528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.223727 | + | 0.0726932i | −0.0107516 | + | 0.00349341i | −0.314388 | − | 0.949295i | \(-0.601799\pi\) |
0.303636 | + | 0.952788i | \(0.401799\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | −5.94593 | − | 4.31997i | −0.283139 | − | 0.205713i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.3862i | − | 1.15862i | −0.815106 | − | 0.579311i | \(-0.803322\pi\) | ||
0.815106 | − | 0.579311i | \(-0.196678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.2874 | − | 4.31735i | −0.628474 | − | 0.204203i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.9483 | −1.13019 | −0.565096 | − | 0.825025i | \(-0.691161\pi\) | ||||
−0.565096 | + | 0.825025i | \(0.691161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.28740 | −0.437327 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.1990 | + | 6.23815i | 0.902050 | + | 0.293094i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.91244i | 0.183016i | 0.995804 | + | 0.0915082i | \(0.0291688\pi\) | ||||
−0.995804 | + | 0.0915082i | \(0.970831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.929435 | − | 0.675274i | −0.0433823 | − | 0.0315191i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.09170 | − | 1.51971i | 0.0974202 | − | 0.0707799i | −0.538009 | − | 0.842939i | \(-0.680823\pi\) |
0.635429 | + | 0.772159i | \(0.280823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8777 | + | 17.7247i | −0.598478 | + | 0.823734i | −0.995568 | − | 0.0940453i | \(-0.970020\pi\) |
0.397090 | + | 0.917780i | \(0.370020\pi\) | |||||||
\(464\) | 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 | ||||||||
\(471\) | 2.39966 | − | 7.38539i | 0.110570 | − | 0.340301i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.86410 | − | 6.69486i | −0.223652 | − | 0.307830i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.73383 | + | 2.38641i | 0.0793865 | + | 0.109266i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.90100 | − | 5.85067i | 0.0868588 | − | 0.267324i | −0.898188 | − | 0.439612i | \(-0.855116\pi\) |
0.985047 | + | 0.172288i | \(0.0551160\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5366 | − | 38.5836i | −0.571618 | − | 1.75926i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.5815 | + | 7.33717i | −1.02749 | + | 0.333853i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.69230 | − | 5.08201i | 0.167314 | − | 0.230288i | −0.717124 | − | 0.696945i | \(-0.754542\pi\) |
0.884438 | + | 0.466658i | \(0.154542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.2379 | + | 8.16480i | −0.508195 | + | 0.369225i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.22591 | + | 1.61722i | 0.100454 | + | 0.0729840i | 0.636878 | − | 0.770964i | \(-0.280225\pi\) |
−0.536424 | + | 0.843948i | \(0.680225\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | −2.89787 | −0.129467 | ||||||||
\(502\) | 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 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.55771i | 0.424473i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.50277 | − | 6.17763i | −0.376879 | − | 0.273818i | 0.383179 | − | 0.923674i | \(-0.374829\pi\) |
−0.760058 | + | 0.649856i | \(0.774829\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3382 | − | 10.4173i | 0.634283 | − | 0.460833i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.00882334 | + | 0.0121443i | −0.000389560 | + | 0.000536183i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.404263 | + | 0.131353i | −0.0177795 | + | 0.00577690i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.70752 | − | 14.4882i | −0.206637 | − | 0.635963i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.41778 | + | 7.44115i | −0.105925 | + | 0.326003i | −0.989946 | − | 0.141443i | \(-0.954826\pi\) |
0.884022 | + | 0.467446i | \(0.154826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9592 | + | 17.8368i | 0.566665 | + | 0.779947i | 0.992155 | − | 0.125016i | \(-0.0398982\pi\) |
−0.425490 | + | 0.904963i | \(0.639898\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 3.53625 | + | 10.8835i | 0.153460 | + | 0.472302i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.9409 | − | 16.8766i | 2.24981 | − | 0.731007i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.6987 | + | 18.8546i | −0.591142 | + | 0.813637i | ||||
\(538\) | 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 | ||||||||
\(543\) | − | 17.6985i | − | 0.759514i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.39292 | + | 0.777505i | 0.102314 | + | 0.0332437i | 0.359726 | − | 0.933058i | \(-0.382870\pi\) |
−0.257413 | + | 0.966302i | \(0.582870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.14212 | −0.134102 | ||||||||
\(550\) | 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 | ||||||||
\(561\) | −0.750685 | + | 0.545404i | −0.0316939 | + | 0.0230270i | ||||
\(562\) | 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 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.60268 | + | 1.17058i | −0.151298 | + | 0.0491598i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.9892 | + | 36.8991i | 0.502615 | + | 1.54689i | 0.804743 | + | 0.593623i | \(0.202303\pi\) |
−0.302128 | + | 0.953267i | \(0.597697\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 5.50411 | + | 7.57575i | 0.229937 | + | 0.316482i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.8962 | + | 20.5029i | 0.620139 | + | 0.853548i | 0.997363 | − | 0.0725741i | \(-0.0231214\pi\) |
−0.377224 | + | 0.926122i | \(0.623121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.84997 | + | 18.0044i | −0.243116 | + | 0.748236i | ||||
\(580\) | 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 | ||||||||
\(591\) | 6.10288 | + | 4.43400i | 0.251039 | + | 0.182390i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7.14389i | − | 0.293364i | −0.989184 | − | 0.146682i | \(-0.953141\pi\) | ||
0.989184 | − | 0.146682i | \(-0.0468595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.41011 | + | 1.10801i | 0.139566 | + | 0.0453479i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.6627 | −0.966833 | −0.483417 | − | 0.875390i | \(-0.660604\pi\) | ||||
−0.483417 | + | 0.875390i | \(0.660604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.98023 | −0.325520 | −0.162760 | − | 0.986666i | \(-0.552040\pi\) | ||||
−0.162760 | + | 0.986666i | \(0.552040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.6312 | − | 4.10412i | −0.514381 | − | 0.167133i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.2004i | − | 0.698144i | −0.937096 | − | 0.349072i | \(-0.886497\pi\) | ||
0.937096 | − | 0.349072i | \(-0.113503\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.3419 | + | 8.24038i | 0.459597 | + | 0.333917i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.02220 | − | 1.46921i | 0.0818094 | − | 0.0594380i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.67810 | + | 11.9444i | −0.350505 | + | 0.482429i | −0.947473 | − | 0.319836i | \(-0.896372\pi\) |
0.596968 | + | 0.802265i | \(0.296372\pi\) | |||||||
\(614\) | 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 | ||||||||
\(621\) | −1.93691 | + | 5.96119i | −0.0777254 | + | 0.239214i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.8629 | − | 49.3611i | −1.43682 | − | 1.97761i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.00712642 | + | 0.00980868i | 0.000284602 | + | 0.000391721i | ||||
\(628\) | 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 | ||||||||
\(633\) | 1.98289 | − | 0.644279i | 0.0788126 | − | 0.0256078i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.5177 | − | 28.2401i | 0.812940 | − | 1.11892i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.97485 | + | 2.88790i | −0.157243 | + | 0.114243i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.12903 | + | 2.27338i | 0.123589 | + | 0.0897930i | 0.647863 | − | 0.761757i | \(-0.275663\pi\) |
−0.524273 | + | 0.851550i | \(0.675663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 23.2212i | − | 0.915756i | −0.889015 | − | 0.457878i | \(-0.848610\pi\) | ||
0.889015 | − | 0.457878i | \(-0.151390\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −5.99309 | −0.234888 | ||||||||
\(652\) | 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 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.67860i | − | 0.182530i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.9288 | − | 24.6507i | −1.32168 | − | 0.960255i | −0.999910 | − | 0.0134358i | \(-0.995723\pi\) |
−0.321767 | − | 0.946819i | \(-0.604277\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 3.20721 | − | 4.41435i | 0.124558 | − | 0.171439i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.0619 | − | 7.16833i | 0.854239 | − | 0.277559i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.33776 | − | 13.3503i | −0.167708 | − | 0.516151i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.784230 | + | 2.41361i | −0.0302749 | + | 0.0931765i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1017 | − | 23.5385i | −0.659223 | − | 0.907343i | 0.340232 | − | 0.940341i | \(-0.389494\pi\) |
−0.999455 | + | 0.0329986i | \(0.989494\pi\) | |||||||
\(674\) | 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 | ||||||||
\(681\) | −0.783313 | − | 2.41079i | −0.0300166 | − | 0.0923817i | ||||
\(682\) | 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 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.71385 | + | 13.3700i | −0.370607 | + | 0.510096i | ||||
\(688\) | 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 | ||||||||
\(693\) | 3.05955i | 0.116223i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5639 | − | 4.08225i | −0.475890 | − | 0.154626i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.5208 | −1.00311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.3495 | −0.881898 | −0.440949 | − | 0.897532i | \(-0.645358\pi\) | ||||
−0.440949 | + | 0.897532i | \(0.645358\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | −7.50084 | + | 5.44968i | −0.281303 | + | 0.204379i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.82877 | + | 8.02261i | −0.218289 | + | 0.300449i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.09855 | − | 2.30646i | 0.265100 | − | 0.0861363i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.55488 | + | 14.0185i | 0.169868 | + | 0.522801i | 0.999362 | − | 0.0357149i | \(-0.0113708\pi\) |
−0.829494 | + | 0.558516i | \(0.811371\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0583 | − | 67.8884i | 0.821493 | − | 2.52830i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.05288 | + | 8.33107i | 0.225109 | + | 0.309836i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.6698 | − | 24.3204i | −0.655336 | − | 0.901993i | 0.343979 | − | 0.938977i | \(-0.388225\pi\) |
−0.999316 | + | 0.0369839i | \(0.988225\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.63738 | − | 11.1947i | −0.134533 | − | 0.414051i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.5355 | + | 6.99732i | −0.795433 | + | 0.258452i | −0.678416 | − | 0.734678i | \(-0.737333\pi\) |
−0.117017 | + | 0.993130i | \(0.537333\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | −0.0576792 | − | 0.0419064i | −0.00211890 | − | 0.00153947i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.9796i | 0.916411i | 0.888846 | + | 0.458205i | \(0.151508\pi\) | ||||
−0.888846 | + | 0.458205i | \(0.848492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.35402 | + | 0.439947i | 0.0495409 | + | 0.0160968i | ||||
\(748\) | 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 | ||||||||
\(753\) | −18.6225 | − | 6.05083i | −0.678643 | − | 0.220504i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.91474i | − | 0.360357i | −0.983634 | − | 0.180179i | \(-0.942332\pi\) | ||
0.983634 | − | 0.180179i | \(-0.0576676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.09565 | + | 2.97566i | 0.148663 | + | 0.108010i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.6076 | − | 18.6050i | 0.928273 | − | 0.674430i | −0.0172961 | − | 0.999850i | \(-0.505506\pi\) |
0.945569 | + | 0.325420i | \(0.105506\pi\) | |||||||
\(762\) | 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 | ||||||||
\(771\) | −1.84801 | + | 5.68760i | −0.0665546 | + | 0.204834i | ||||
\(772\) | 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 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.0190 | + | 26.1774i | 0.682302 | + | 0.939108i | ||||
\(778\) | 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 | ||||||||
\(783\) | 3.51978 | − | 1.14365i | 0.125787 | − | 0.0408706i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.2038 | + | 22.3026i | −0.577603 | + | 0.795002i | −0.993430 | − | 0.114442i | \(-0.963492\pi\) |
0.415827 | + | 0.909444i | \(0.363492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.91104 | − | 3.56808i | 0.174838 | − | 0.127027i | ||||
\(790\) | 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 | ||||||||
\(801\) | −16.1067 | −0.569103 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.59386 | − | 1.16772i | −0.126825 | − | 0.0412078i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.61605i | 0.338501i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.36960 | − | 0.995071i | −0.0481525 | − | 0.0349848i | 0.563449 | − | 0.826151i | \(-0.309474\pi\) |
−0.611601 | + | 0.791166i | \(0.709474\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 17.8849 | − | 24.6164i | 0.627250 | − | 0.863335i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.146274 | + | 0.0475272i | −0.00511746 | + | 0.00166277i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.55967 | − | 17.1109i | −0.194271 | − | 0.597904i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.2235 | + | 43.7754i | −0.496403 | + | 1.52777i | 0.318356 | + | 0.947971i | \(0.396869\pi\) |
−0.814759 | + | 0.579800i | \(0.803131\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.9082 | + | 45.2942i | 1.14711 | + | 1.57886i | 0.750502 | + | 0.660868i | \(0.229812\pi\) |
0.396605 | + | 0.917990i | \(0.370188\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | −2.22614 | − | 6.85134i | −0.0772238 | − | 0.237670i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.03026 | + | 2.60919i | −0.278232 | + | 0.0904030i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.929930 | + | 1.27994i | −0.0321431 | + | 0.0442412i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.2783 | − | 30.7170i | 1.45961 | − | 1.06047i | 0.476146 | − | 0.879366i | \(-0.342034\pi\) |
0.983464 | − | 0.181102i | \(-0.0579665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3806 | + | 8.99501i | 0.426916 | + | 0.310173i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 29.7964i | − | 1.02624i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.2793 | − | 12.1128i | −1.28093 | − | 0.416200i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.82402 | −0.302840 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.5397 | 1.83532 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.7010 | + | 5.42649i | 0.571832 | + | 0.185799i | 0.580638 | − | 0.814162i | \(-0.302803\pi\) |
−0.00880614 | + | 0.999961i | \(0.502803\pi\) | |||||||
\(854\) | 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 | ||||||||
\(861\) | −35.2397 | + | 25.6032i | −1.20097 | + | 0.872553i | ||||
\(862\) | 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 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.9127 | − | 4.84543i | 0.506462 | − | 0.164560i | ||||
\(868\) | 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 | ||||||||
\(873\) | 4.73874 | + | 6.52232i | 0.160382 | + | 0.220747i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3126 | + | 30.7106i | 0.753442 | + | 1.03702i | 0.997731 | + | 0.0673215i | \(0.0214453\pi\) |
−0.244289 | + | 0.969702i | \(0.578555\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.30017 | − | 4.00150i | 0.0438535 | − | 0.134967i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3378 | − | 34.8942i | −0.381981 | − | 1.17562i | −0.938647 | − | 0.344879i | \(-0.887920\pi\) |
0.556666 | − | 0.830736i | \(-0.312080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5128 | + | 6.98993i | −0.723964 | + | 0.235230i | −0.647741 | − | 0.761861i | \(-0.724286\pi\) |
−0.0762228 | + | 0.997091i | \(0.524286\pi\) | |||||||
\(884\) | 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 | ||||||||
\(891\) | 0.653426 | + | 0.474742i | 0.0218906 | + | 0.0159044i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.00790011i | 0.000264367i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.3126 | − | 9.19934i | −0.945332 | − | 0.307157i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.85519 | 0.195281 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.38882 | 0.112898 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.9123 | − | 11.9935i | −1.22836 | − | 0.399120i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.7792i | 1.08842i | 0.838950 | + | 0.544208i | \(0.183170\pi\) | ||||
−0.838950 | + | 0.544208i | \(0.816830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.42474 | + | 6.84747i | 0.312599 | + | 0.227116i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0778 | + | 16.0405i | −0.731470 | + | 0.531444i | −0.890028 | − | 0.455906i | \(-0.849315\pi\) |
0.158558 | + | 0.987350i | \(0.449315\pi\) | |||||||
\(912\) | 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 | ||||||||
\(921\) | 1.36310 | − | 4.19520i | 0.0449158 | − | 0.138236i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.7161 | − | 18.8785i | −0.451469 | − | 0.621394i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.0761 | − | 15.2450i | −0.363788 | − | 0.500711i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.4151 | − | 32.0542i | 0.341707 | − | 1.05167i | −0.621616 | − | 0.783322i | \(-0.713524\pi\) |
0.963323 | − | 0.268344i | \(-0.0864763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0340925 | + | 0.104926i | 0.00111734 | + | 0.00343880i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.01123 | + | 1.95317i | −0.196799 | + | 0.0639438i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.614857 | + | 0.846278i | −0.0200865 | + | 0.0276467i | −0.818942 | − | 0.573876i | \(-0.805439\pi\) |
0.798856 | + | 0.601523i | \(0.205439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.3978 | + | 9.00753i | −0.404587 | + | 0.293950i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.62928 | − | 3.36337i | −0.150910 | − | 0.109643i | 0.509768 | − | 0.860312i | \(-0.329731\pi\) |
−0.660678 | + | 0.750669i | \(0.729731\pi\) | |||||||
\(942\) | 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 | ||||||||
\(951\) | −21.3155 | −0.691204 | ||||||||
\(952\) | 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 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2.98915i | − | 0.0966255i | ||||||
\(958\) | 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 | ||||||||
\(963\) | 8.46158 | − | 11.6464i | 0.272671 | − | 0.375299i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.40935 | + | 2.73236i | −0.270427 | + | 0.0878669i | −0.441091 | − | 0.897462i | \(-0.645409\pi\) |
0.170665 | + | 0.985329i | \(0.445409\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.00532915 | + | 0.0164014i | 0.000171197 | + | 0.000526890i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0493 | − | 49.3945i | 0.515045 | − | 1.58515i | −0.268155 | − | 0.963376i | \(-0.586414\pi\) |
0.783200 | − | 0.621770i | \(-0.213586\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | −1.78051 | − | 5.47985i | −0.0568473 | − | 0.174958i | ||||
\(982\) | 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 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.17181 | + | 1.61286i | −0.0372991 | + | 0.0513378i | ||||
\(988\) | 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 | ||||||||
\(993\) | − | 19.8124i | − | 0.628728i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.5746 | + | 12.2087i | 1.19000 | + | 0.386654i | 0.836072 | − | 0.548619i | \(-0.184846\pi\) |
0.353927 | + | 0.935273i | \(0.384846\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.54179 | 0.270250 |
(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.o.c.949.1 | 24 | ||
5.2 | odd | 4 | 1500.2.m.d.301.2 | 24 | |||
5.3 | odd | 4 | 1500.2.m.c.301.5 | 24 | |||
5.4 | even | 2 | 300.2.o.a.289.5 | yes | 24 | ||
15.14 | odd | 2 | 900.2.w.c.289.4 | 24 | |||
25.3 | odd | 20 | 7500.2.a.n.1.9 | 12 | |||
25.4 | even | 10 | 7500.2.d.g.1249.16 | 24 | |||
25.9 | even | 10 | inner | 1500.2.o.c.49.1 | 24 | ||
25.12 | odd | 20 | 1500.2.m.d.1201.2 | 24 | |||
25.13 | odd | 20 | 1500.2.m.c.1201.5 | 24 | |||
25.16 | even | 5 | 300.2.o.a.109.5 | ✓ | 24 | ||
25.21 | even | 5 | 7500.2.d.g.1249.9 | 24 | |||
25.22 | odd | 20 | 7500.2.a.m.1.4 | 12 | |||
75.41 | odd | 10 | 900.2.w.c.109.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.5 | ✓ | 24 | 25.16 | even | 5 | ||
300.2.o.a.289.5 | yes | 24 | 5.4 | even | 2 | ||
900.2.w.c.109.4 | 24 | 75.41 | odd | 10 | |||
900.2.w.c.289.4 | 24 | 15.14 | odd | 2 | |||
1500.2.m.c.301.5 | 24 | 5.3 | odd | 4 | |||
1500.2.m.c.1201.5 | 24 | 25.13 | odd | 20 | |||
1500.2.m.d.301.2 | 24 | 5.2 | odd | 4 | |||
1500.2.m.d.1201.2 | 24 | 25.12 | odd | 20 | |||
1500.2.o.c.49.1 | 24 | 25.9 | even | 10 | inner | ||
1500.2.o.c.949.1 | 24 | 1.1 | even | 1 | trivial | ||
7500.2.a.m.1.4 | 12 | 25.22 | odd | 20 | |||
7500.2.a.n.1.9 | 12 | 25.3 | odd | 20 | |||
7500.2.d.g.1249.9 | 24 | 25.21 | even | 5 | |||
7500.2.d.g.1249.16 | 24 | 25.4 | even | 10 |