Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1224,2,Mod(145,1224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1224.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1224.bq (of order \(8\), 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: | \(9.77368920740\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 36x^{14} + 466x^{12} + 2956x^{10} + 10049x^{8} + 18032x^{6} + 14800x^{4} + 3200x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 408) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 865.4 | ||
Root | \(-1.71472i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1224.865 |
Dual form | 1224.2.bq.e.433.4 |
$q$-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 \(\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times\).
\(n\) | \(137\) | \(613\) | \(649\) | \(919\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50807 | − | 1.03888i | 1.12164 | − | 0.464600i | 0.256711 | − | 0.966488i | \(-0.417361\pi\) |
0.864933 | + | 0.501888i | \(0.167361\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.22010 | + | 0.919595i | 0.839118 | + | 0.347574i | 0.760506 | − | 0.649331i | \(-0.224951\pi\) |
0.0786124 | + | 0.996905i | \(0.474951\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.87280 | − | 4.52134i | 0.564671 | − | 1.36324i | −0.341324 | − | 0.939946i | \(-0.610875\pi\) |
0.905994 | − | 0.423290i | \(-0.139125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.07051i | − | 0.296906i | −0.988920 | − | 0.148453i | \(-0.952571\pi\) | ||
0.988920 | − | 0.148453i | \(-0.0474293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.25570 | − | 2.52991i | −0.789622 | − | 0.613593i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.61272 | + | 1.61272i | 0.369984 | + | 0.369984i | 0.867471 | − | 0.497487i | \(-0.165744\pi\) |
−0.497487 | + | 0.867471i | \(0.665744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.41400 | − | 5.82790i | 0.503353 | − | 1.21520i | −0.444294 | − | 0.895881i | \(-0.646545\pi\) |
0.947647 | − | 0.319321i | \(-0.103455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.67562 | − | 1.67562i | 0.335125 | − | 0.335125i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.13555 | + | 1.29879i | −0.582257 | + | 0.241179i | −0.654315 | − | 0.756222i | \(-0.727043\pi\) |
0.0720587 | + | 0.997400i | \(0.477043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.67656 | + | 6.46178i | 0.480724 | + | 1.16057i | 0.959266 | + | 0.282506i | \(0.0911656\pi\) |
−0.478542 | + | 0.878065i | \(0.658834\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.52351 | 1.10267 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.63047 | − | 3.93630i | −0.268047 | − | 0.647123i | 0.731344 | − | 0.682009i | \(-0.238893\pi\) |
−0.999391 | + | 0.0348855i | \(0.988893\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.08028 | − | 2.93275i | −1.10575 | − | 0.458018i | −0.246280 | − | 0.969199i | \(-0.579208\pi\) |
−0.859473 | + | 0.511180i | \(0.829208\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.37197 | + | 4.37197i | −0.666719 | + | 0.666719i | −0.956955 | − | 0.290236i | \(-0.906266\pi\) |
0.290236 | + | 0.956955i | \(0.406266\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.19868i | 1.19590i | 0.801533 | + | 0.597950i | \(0.204018\pi\) | ||||
−0.801533 | + | 0.597950i | \(0.795982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.866566 | − | 0.866566i | −0.123795 | − | 0.123795i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.97888 | + | 7.97888i | 1.09598 | + | 1.09598i | 0.994875 | + | 0.101108i | \(0.0322389\pi\) |
0.101108 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13.2855i | − | 1.79141i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.89888 | − | 8.89888i | 1.15854 | − | 1.15854i | 0.173745 | − | 0.984791i | \(-0.444413\pi\) |
0.984791 | − | 0.173745i | \(-0.0555869\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.52414 | − | 1.04553i | −0.323183 | − | 0.133867i | 0.215193 | − | 0.976572i | \(-0.430962\pi\) |
−0.538376 | + | 0.842705i | \(0.680962\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.11213 | − | 2.68491i | −0.137942 | − | 0.333022i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8012 | 1.56392 | 0.781958 | − | 0.623331i | \(-0.214221\pi\) | ||||
0.781958 | + | 0.623331i | \(0.214221\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.62627 | + | 3.92615i | 0.193002 | + | 0.465948i | 0.990524 | − | 0.137342i | \(-0.0438559\pi\) |
−0.797521 | + | 0.603291i | \(0.793856\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.47623 | + | 3.92518i | −1.10911 | + | 0.459408i | −0.860631 | − | 0.509229i | \(-0.829931\pi\) |
−0.248478 | + | 0.968637i | \(0.579931\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.31560 | − | 8.31560i | 0.947651 | − | 0.947651i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.464750 | − | 1.12200i | 0.0522884 | − | 0.126235i | −0.895577 | − | 0.444907i | \(-0.853237\pi\) |
0.947865 | + | 0.318672i | \(0.103237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.92403 | − | 2.92403i | −0.320954 | − | 0.320954i | 0.528179 | − | 0.849133i | \(-0.322875\pi\) |
−0.849133 | + | 0.528179i | \(0.822875\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.7938 | − | 2.96293i | −1.17075 | − | 0.321374i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.96634i | − | 0.314431i | −0.987564 | − | 0.157216i | \(-0.949748\pi\) | ||
0.987564 | − | 0.157216i | \(-0.0502518\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.984434 | − | 2.37663i | 0.103197 | − | 0.249139i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.72025 | + | 2.36941i | 0.586886 | + | 0.243096i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.8658 | − | 6.98605i | 1.71247 | − | 0.709326i | 0.712495 | − | 0.701678i | \(-0.247565\pi\) |
0.999971 | − | 0.00764885i | \(-0.00243473\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.04503 | 0.900014 | 0.450007 | − | 0.893025i | \(-0.351421\pi\) | ||||
0.450007 | + | 0.893025i | \(0.351421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.23568 | −0.220288 | −0.110144 | − | 0.993916i | \(-0.535131\pi\) | ||||
−0.110144 | + | 0.993916i | \(0.535131\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.04118 | + | 2.08813i | −0.487350 | + | 0.201867i | −0.612808 | − | 0.790232i | \(-0.709960\pi\) |
0.125458 | + | 0.992099i | \(0.459960\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.44258 | − | 1.01175i | −0.233956 | − | 0.0969079i | 0.262625 | − | 0.964898i | \(-0.415412\pi\) |
−0.496582 | + | 0.867990i | \(0.665412\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.35434 | + | 12.9265i | −0.503694 | + | 1.21602i | 0.443764 | + | 0.896144i | \(0.353643\pi\) |
−0.947458 | + | 0.319880i | \(0.896357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 17.1246i | − | 1.59688i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.90147 | − | 8.61057i | −0.449317 | − | 0.789330i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.15696 | − | 9.15696i | −0.832451 | − | 0.832451i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.73257 | + | 6.59701i | −0.244409 | + | 0.590054i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2828 | − | 10.2828i | 0.912449 | − | 0.912449i | −0.0840159 | − | 0.996464i | \(-0.526775\pi\) |
0.996464 | + | 0.0840159i | \(0.0267746\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.23079 | − | 0.924024i | 0.194905 | − | 0.0807323i | −0.283096 | − | 0.959092i | \(-0.591361\pi\) |
0.478001 | + | 0.878359i | \(0.341361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.09735 | + | 5.06346i | 0.181864 | + | 0.439058i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.42184 | 0.121476 | 0.0607382 | − | 0.998154i | \(-0.480655\pi\) | ||||
0.0607382 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.94425 | + | 14.3507i | 0.504184 | + | 1.21721i | 0.947185 | + | 0.320687i | \(0.103914\pi\) |
−0.443001 | + | 0.896521i | \(0.646086\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.84013 | − | 2.00485i | −0.404752 | − | 0.167654i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.51490 | + | 6.51490i | −0.541033 | + | 0.541033i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.2390i | 1.33035i | 0.746687 | + | 0.665176i | \(0.231643\pi\) | ||||
−0.746687 | + | 0.665176i | \(0.768357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.48539 | + | 2.48539i | 0.202258 | + | 0.202258i | 0.800967 | − | 0.598709i | \(-0.204319\pi\) |
−0.598709 | + | 0.800967i | \(0.704319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.4260 | + | 13.4260i | 1.07840 | + | 1.07840i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.3904i | 1.70714i | 0.520975 | + | 0.853572i | \(0.325568\pi\) | ||||
−0.520975 | + | 0.853572i | \(0.674432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7186 | − | 10.7186i | 0.844746 | − | 0.844746i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3602 | + | 7.60506i | 1.43809 | + | 0.595675i | 0.959333 | − | 0.282275i | \(-0.0910892\pi\) |
0.478752 | + | 0.877950i | \(0.341089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.03768 | − | 7.33360i | −0.235063 | − | 0.567491i | 0.761697 | − | 0.647934i | \(-0.224367\pi\) |
−0.996759 | + | 0.0804426i | \(0.974367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8540 | 0.911847 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.18012 | − | 22.1628i | −0.697951 | − | 1.68500i | −0.728112 | − | 0.685458i | \(-0.759602\pi\) |
0.0301604 | − | 0.999545i | \(-0.490398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.26094 | − | 2.17915i | 0.397690 | − | 0.164728i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.0828 | + | 17.0828i | −1.27683 | + | 1.27683i | −0.334392 | + | 0.942434i | \(0.608531\pi\) |
−0.942434 | + | 0.334392i | \(0.891469\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.65785 | − | 11.2451i | 0.346216 | − | 0.835838i | −0.650844 | − | 0.759211i | \(-0.725585\pi\) |
0.997060 | − | 0.0766270i | \(-0.0244151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.17866 | − | 8.17866i | −0.601307 | − | 0.601307i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5359 | + | 9.98209i | −1.28235 | + | 0.729963i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.27804i | − | 0.237191i | −0.992943 | − | 0.118595i | \(-0.962161\pi\) | ||
0.992943 | − | 0.118595i | \(-0.0378392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.94091 | + | 19.1711i | −0.571599 | + | 1.37996i | 0.328593 | + | 0.944472i | \(0.393425\pi\) |
−0.900193 | + | 0.435492i | \(0.856575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.2135 | − | 7.54429i | −1.29766 | − | 0.537508i | −0.376401 | − | 0.926457i | \(-0.622838\pi\) |
−0.921259 | + | 0.388949i | \(0.872838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0934 | + | 5.83768i | −0.999055 | + | 0.413822i | −0.821451 | − | 0.570280i | \(-0.806835\pi\) |
−0.177605 | + | 0.984102i | \(0.556835\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.15558 | −0.572410 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.8046 | −1.45306 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3120 | − | 4.27137i | 0.713295 | − | 0.295457i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5631 | − | 4.78961i | −0.796039 | − | 0.329730i | −0.0526704 | − | 0.998612i | \(-0.516773\pi\) |
−0.743369 | + | 0.668882i | \(0.766773\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.42327 | + | 15.5071i | −0.438063 | + | 1.05758i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.8071i | 1.14094i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.70829 | + | 3.48525i | −0.182179 | + | 0.234443i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.32288 | − | 5.32288i | −0.356446 | − | 0.356446i | 0.506055 | − | 0.862501i | \(-0.331103\pi\) |
−0.862501 | + | 0.506055i | \(0.831103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.83963 | + | 4.44126i | −0.122101 | + | 0.294777i | −0.973097 | − | 0.230394i | \(-0.925999\pi\) |
0.850997 | + | 0.525171i | \(0.175999\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.47732 | + | 9.47732i | −0.626279 | + | 0.626279i | −0.947130 | − | 0.320851i | \(-0.896031\pi\) |
0.320851 | + | 0.947130i | \(0.396031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7306 | + | 5.27318i | −0.834008 | + | 0.345457i | −0.758488 | − | 0.651687i | \(-0.774062\pi\) |
−0.0755198 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.51742 | + | 20.5629i | 0.555616 | + | 1.34137i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0060 | 1.10003 | 0.550014 | − | 0.835155i | \(-0.314622\pi\) | ||||
0.550014 | + | 0.835155i | \(0.314622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.42077 | − | 17.9153i | −0.478014 | − | 1.15403i | −0.960539 | − | 0.278145i | \(-0.910280\pi\) |
0.482525 | − | 0.875882i | \(-0.339720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.07366 | − | 1.27315i | −0.196369 | − | 0.0813388i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.72644 | − | 1.72644i | 0.109850 | − | 0.109850i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5316i | 1.35906i | 0.733646 | + | 0.679532i | \(0.237817\pi\) | ||||
−0.733646 | + | 0.679532i | \(0.762183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.8290 | − | 21.8290i | −1.37238 | − | 1.37238i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5195 | − | 13.5195i | −0.843324 | − | 0.843324i | 0.145966 | − | 0.989290i | \(-0.453371\pi\) |
−0.989290 | + | 0.145966i | \(0.953371\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 10.2383i | − | 0.636179i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.83952 | + | 7.83952i | −0.483406 | + | 0.483406i | −0.906218 | − | 0.422812i | \(-0.861043\pi\) |
0.422812 | + | 0.906218i | \(0.361043\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.3007 | + | 11.7225i | 1.73850 | + | 0.720109i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.69352 | − | 4.08852i | −0.103256 | − | 0.249282i | 0.863805 | − | 0.503826i | \(-0.168075\pi\) |
−0.967061 | + | 0.254544i | \(0.918075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2476 | 0.986973 | 0.493486 | − | 0.869753i | \(-0.335722\pi\) | ||||
0.493486 | + | 0.869753i | \(0.335722\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.43795 | − | 10.7142i | −0.267619 | − | 0.646089i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.591916 | + | 0.245180i | −0.0355648 | + | 0.0147314i | −0.400395 | − | 0.916343i | \(-0.631127\pi\) |
0.364830 | + | 0.931074i | \(0.381127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0521155 | + | 0.0521155i | −0.00310895 | + | 0.00310895i | −0.708660 | − | 0.705551i | \(-0.750700\pi\) |
0.705551 | + | 0.708660i | \(0.250700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.82868 | + | 18.9001i | −0.465367 | + | 1.12350i | 0.500797 | + | 0.865565i | \(0.333040\pi\) |
−0.966164 | + | 0.257930i | \(0.916960\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.0220 | − | 13.0220i | −0.768663 | − | 0.768663i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.19911 | + | 16.4732i | 0.247007 | + | 0.969014i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.88796i | 0.460820i | 0.973094 | + | 0.230410i | \(0.0740067\pi\) | ||||
−0.973094 | + | 0.230410i | \(0.925993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0742 | − | 31.5639i | 0.761209 | − | 1.83772i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.23882 | − | 2.58420i | −0.360800 | − | 0.149448i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.7266 | + | 5.68576i | −0.791190 | + | 0.327722i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.41691 | −0.424691 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.63954 | −0.264793 | −0.132396 | − | 0.991197i | \(-0.542267\pi\) | ||||
−0.132396 | + | 0.991197i | \(0.542267\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.16892 | − | 2.14104i | 0.293103 | − | 0.121407i | −0.231287 | − | 0.972886i | \(-0.574294\pi\) |
0.524389 | + | 0.851479i | \(0.324294\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.810266 | + | 0.335623i | 0.0457990 | + | 0.0189705i | 0.405465 | − | 0.914110i | \(-0.367109\pi\) |
−0.359666 | + | 0.933081i | \(0.617109\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.3854 | + | 27.4867i | −0.639467 | + | 1.54381i | 0.187925 | + | 0.982183i | \(0.439824\pi\) |
−0.827392 | + | 0.561625i | \(0.810176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.6092i | 0.929939i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.17049 | − | 9.33059i | −0.0651280 | − | 0.519168i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.79377 | − | 1.79377i | −0.0995003 | − | 0.0995003i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.53947 | + | 18.2019i | −0.415664 | + | 1.00350i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.18438 | + | 8.18438i | −0.449854 | + | 0.449854i | −0.895306 | − | 0.445452i | \(-0.853043\pi\) |
0.445452 | + | 0.895306i | \(0.353043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.1063 | − | 13.2989i | 1.75416 | − | 0.726595i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.47644 | + | 15.6355i | 0.352794 | + | 0.851720i | 0.996273 | + | 0.0862562i | \(0.0274904\pi\) |
−0.643479 | + | 0.765464i | \(0.722510\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.2286 | 1.85358 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.56414 | − | 18.2614i | −0.408425 | − | 0.986025i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.02695 | + | 0.839592i | 0.108813 | + | 0.0450716i | 0.436426 | − | 0.899740i | \(-0.356244\pi\) |
−0.327613 | + | 0.944812i | \(0.606244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.7192 | − | 18.7192i | 1.00201 | − | 1.00201i | 0.00201610 | − | 0.999998i | \(-0.499358\pi\) |
0.999998 | − | 0.00201610i | \(-0.000641744\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9345i | 1.32713i | 0.748120 | + | 0.663564i | \(0.230957\pi\) | ||||
−0.748120 | + | 0.663564i | \(0.769043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.15758 | + | 8.15758i | 0.432959 | + | 0.432959i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.09699 | − | 2.09699i | −0.110675 | − | 0.110675i | 0.649601 | − | 0.760276i | \(-0.274936\pi\) |
−0.760276 | + | 0.649601i | \(0.774936\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.7982i | − | 0.726223i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.6893 | + | 19.6893i | −1.03058 | + | 1.03058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.6341 | − | 8.96114i | −1.12929 | − | 0.467768i | −0.261751 | − | 0.965135i | \(-0.584300\pi\) |
−0.867540 | + | 0.497368i | \(0.834300\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3766 | + | 25.0512i | 0.538724 | + | 1.30060i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.4720 | 1.57778 | 0.788890 | − | 0.614534i | \(-0.210656\pi\) | ||||
0.788890 | + | 0.614534i | \(0.210656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.39036 | + | 3.35663i | 0.0716073 | + | 0.172875i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.43151 | + | 1.00717i | −0.124898 | + | 0.0517346i | −0.444257 | − | 0.895899i | \(-0.646532\pi\) |
0.319359 | + | 0.947634i | \(0.396532\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.8259 | + | 13.8259i | −0.706473 | + | 0.706473i | −0.965792 | − | 0.259319i | \(-0.916502\pi\) |
0.259319 | + | 0.965792i | \(0.416502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.2172 | − | 29.4950i | 0.622648 | − | 1.50321i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.3694 | + | 10.3694i | 0.525748 | + | 0.525748i | 0.919302 | − | 0.393553i | \(-0.128754\pi\) |
−0.393553 | + | 0.919302i | \(0.628754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.6033 | + | 12.8667i | −1.14310 | + | 0.650696i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.29689i | − | 0.165884i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.12132 | − | 12.3639i | 0.257031 | − | 0.620529i | −0.741708 | − | 0.670723i | \(-0.765984\pi\) |
0.998739 | + | 0.0501941i | \(0.0159840\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.03313 | + | 2.49900i | 0.301280 | + | 0.124794i | 0.528202 | − | 0.849119i | \(-0.322866\pi\) |
−0.226922 | + | 0.973913i | \(0.572866\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.91739 | − | 2.86528i | 0.344580 | − | 0.142730i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.8509 | −1.03354 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.45254 | −0.319058 | −0.159529 | − | 0.987193i | \(-0.550997\pi\) | ||||
−0.159529 | + | 0.987193i | \(0.550997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.9398 | − | 11.5730i | 1.37483 | − | 0.569471i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.3714 | − | 4.29596i | −0.509111 | − | 0.210881i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.77323 | + | 21.1805i | −0.428600 | + | 1.03473i | 0.551131 | + | 0.834419i | \(0.314196\pi\) |
−0.979732 | + | 0.200314i | \(0.935804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.8644i | − | 1.30929i | −0.755936 | − | 0.654645i | \(-0.772818\pi\) | ||
0.755936 | − | 0.654645i | \(-0.227182\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.69449 | + | 1.21614i | −0.470252 | + | 0.0589917i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.64238 | − | 4.64238i | −0.224660 | − | 0.224660i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8232 | − | 35.7865i | 0.714010 | − | 1.72377i | 0.0242809 | − | 0.999705i | \(-0.492270\pi\) |
0.689729 | − | 0.724068i | \(-0.257730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.6205 | + | 21.6205i | −1.03901 | + | 1.03901i | −0.0398071 | + | 0.999207i | \(0.512674\pi\) |
−0.999207 | + | 0.0398071i | \(0.987326\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.2919 | − | 5.50569i | 0.635839 | − | 0.263373i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.602318 | − | 1.45412i | −0.0287471 | − | 0.0694016i | 0.908854 | − | 0.417114i | \(-0.136958\pi\) |
−0.937601 | + | 0.347713i | \(0.886958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7788 | −0.702164 | −0.351082 | − | 0.936345i | \(-0.614186\pi\) | ||||
−0.351082 | + | 0.936345i | \(0.614186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.08166 | − | 7.43979i | −0.146085 | − | 0.352680i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.04315 | + | 3.74579i | 0.426773 | + | 0.176775i | 0.585722 | − | 0.810512i | \(-0.300811\pi\) |
−0.158950 | + | 0.987287i | \(0.550811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.5199 | + | 26.5199i | −1.24877 | + | 1.24877i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 6.98347i | − | 0.327390i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3054 | − | 17.3054i | −0.809513 | − | 0.809513i | 0.175047 | − | 0.984560i | \(-0.443992\pi\) |
−0.984560 | + | 0.175047i | \(0.943992\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.62092 | − | 9.62092i | −0.448091 | − | 0.448091i | 0.446629 | − | 0.894719i | \(-0.352625\pi\) |
−0.894719 | + | 0.446629i | \(0.852625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.8498i | − | 0.504233i | −0.967697 | − | 0.252117i | \(-0.918873\pi\) | ||
0.967697 | − | 0.252117i | \(-0.0811267\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.9692 | + | 10.9692i | −0.507594 | + | 0.507594i | −0.913787 | − | 0.406193i | \(-0.866856\pi\) |
0.406193 | + | 0.913787i | \(0.366856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.4199 | + | 11.7719i | 1.31231 | + | 0.543577i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.5793 | + | 27.9550i | 0.532418 | + | 1.28537i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.40464 | 0.247982 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.4855 | − | 39.7996i | −0.753244 | − | 1.81849i | −0.540407 | − | 0.841403i | \(-0.681730\pi\) |
−0.212836 | − | 0.977088i | \(-0.568270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.21384 | + | 1.74543i | −0.192134 | + | 0.0795847i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.0430 | − | 35.0430i | 1.59122 | − | 1.59122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.2097 | − | 39.1337i | 0.734531 | − | 1.77331i | 0.107666 | − | 0.994187i | \(-0.465662\pi\) |
0.626865 | − | 0.779128i | \(-0.284338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.65738 | − | 3.65738i | −0.165055 | − | 0.165055i | 0.619747 | − | 0.784802i | \(-0.287235\pi\) |
−0.784802 | + | 0.619747i | \(0.787235\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4942 | + | 3.70420i | 0.607748 | + | 0.166829i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.2119i | 0.458068i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.48908 | + | 20.4945i | −0.380023 | + | 0.917458i | 0.611937 | + | 0.790907i | \(0.290391\pi\) |
−0.991960 | + | 0.126551i | \(0.959609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.0563 | + | 10.3786i | 1.11720 | + | 0.462761i | 0.863413 | − | 0.504498i | \(-0.168322\pi\) |
0.253791 | + | 0.967259i | \(0.418322\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.6856 | − | 9.39667i | 1.00950 | − | 0.418147i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.9336 | −1.14949 | −0.574743 | − | 0.818334i | \(-0.694898\pi\) | ||||
−0.574743 | + | 0.818334i | \(0.694898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.6478 | −1.09035 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.60724 | + | 2.32259i | −0.247084 | + | 0.102346i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.0690 | + | 15.3545i | 1.63029 | + | 0.675290i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.8942 | − | 35.9578i | 0.652527 | − | 1.57534i | −0.156573 | − | 0.987666i | \(-0.550045\pi\) |
0.809099 | − | 0.587672i | \(-0.199955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.2087i | 1.27721i | 0.769536 | + | 0.638603i | \(0.220488\pi\) | ||||
−0.769536 | + | 0.638603i | \(0.779512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.63367 | − | 27.8091i | 0.332528 | − | 1.21138i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.8736 | − | 11.8736i | −0.516244 | − | 0.516244i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.13953 | + | 7.57950i | −0.135988 | + | 0.328304i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.4743 | + | 10.4743i | −0.452845 | + | 0.452845i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.54094 | + | 2.29513i | −0.238665 | + | 0.0988584i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.71438 | + | 13.7957i | 0.245680 | + | 0.593125i | 0.997828 | − | 0.0658697i | \(-0.0209822\pi\) |
−0.752148 | + | 0.658994i | \(0.770982\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.17724 | −0.307439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00943 | + | 19.3365i | 0.342458 | + | 0.826767i | 0.997466 | + | 0.0711452i | \(0.0226654\pi\) |
−0.655008 | + | 0.755622i | \(0.727335\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.15136 | − | 2.96219i | −0.304658 | − | 0.126194i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.06358 | − | 2.06358i | 0.0877523 | − | 0.0877523i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 11.4512i | − | 0.485203i | −0.970126 | − | 0.242602i | \(-0.921999\pi\) | ||
0.970126 | − | 0.242602i | \(-0.0780008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.68023 | + | 4.68023i | 0.197952 | + | 0.197952i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.1023 | + | 16.1023i | 0.678629 | + | 0.678629i | 0.959690 | − | 0.281061i | \(-0.0906862\pi\) |
−0.281061 | + | 0.959690i | \(0.590686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.9831i | 1.59796i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.4856 | − | 22.4856i | 0.942644 | − | 0.942644i | −0.0557985 | − | 0.998442i | \(-0.517770\pi\) |
0.998442 | + | 0.0557985i | \(0.0177704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.9087 | − | 15.2881i | −1.54458 | − | 0.639787i | −0.562256 | − | 0.826963i | \(-0.690067\pi\) |
−0.982326 | + | 0.187176i | \(0.940067\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.72042 | − | 13.8103i | −0.238558 | − | 0.575930i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.3973 | 1.18219 | 0.591097 | − | 0.806600i | \(-0.298695\pi\) | ||||
0.591097 | + | 0.806600i | \(0.298695\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.80271 | − | 9.18055i | −0.157763 | − | 0.380873i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.0181 | − | 21.1324i | 2.11295 | − | 0.875214i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.76184 | − | 7.76184i | 0.320365 | − | 0.320365i | −0.528542 | − | 0.848907i | \(-0.677261\pi\) |
0.848907 | + | 0.528542i | \(0.177261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.10453 | + | 14.7376i | −0.251533 | + | 0.607254i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.22864 | + | 2.22864i | 0.0915194 | + | 0.0915194i | 0.751384 | − | 0.659865i | \(-0.229387\pi\) |
−0.659865 | + | 0.751384i | \(0.729387\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.2386 | − | 16.5039i | −0.870696 | − | 0.676594i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.4176i | 0.629945i | 0.949101 | + | 0.314972i | \(0.101995\pi\) | ||||
−0.949101 | + | 0.314972i | \(0.898005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.10132 | − | 19.5583i | 0.330460 | − | 0.797801i | −0.668096 | − | 0.744075i | \(-0.732890\pi\) |
0.998556 | − | 0.0537256i | \(-0.0171096\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.4793 | − | 13.4534i | −1.32047 | − | 0.546957i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0086 | + | 5.80253i | −0.568590 | + | 0.235518i | −0.648409 | − | 0.761292i | \(-0.724565\pi\) |
0.0798199 | + | 0.996809i | \(0.474565\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.77676 | 0.355070 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.4543 | 1.75510 | 0.877551 | − | 0.479484i | \(-0.159176\pi\) | ||||
0.877551 | + | 0.479484i | \(0.159176\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.3420 | − | 15.0534i | 1.46307 | − | 0.606025i | 0.497807 | − | 0.867288i | \(-0.334139\pi\) |
0.965268 | + | 0.261263i | \(0.0841388\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.69556 | + | 4.01603i | 0.389697 | + | 0.161418i | 0.568924 | − | 0.822390i | \(-0.307360\pi\) |
−0.179227 | + | 0.983808i | \(0.557360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.72783 | − | 6.58557i | 0.109288 | − | 0.263845i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.2330i | 1.24932i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.65017 | + | 16.9403i | −0.185414 | + | 0.675455i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.2236 | − | 32.2236i | −1.28280 | − | 1.28280i | −0.939067 | − | 0.343734i | \(-0.888308\pi\) |
−0.343734 | − | 0.939067i | \(-0.611692\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.1074 | − | 36.4725i | 0.599519 | − | 1.44737i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.927666 | + | 0.927666i | −0.0367555 | + | 0.0367555i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.8538 | + | 5.73842i | −0.547191 | + | 0.226654i | −0.639114 | − | 0.769112i | \(-0.720699\pi\) |
0.0919230 | + | 0.995766i | \(0.470699\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.89107 | + | 19.0507i | 0.311193 | + | 0.751287i | 0.999661 | + | 0.0260206i | \(0.00828356\pi\) |
−0.688468 | + | 0.725267i | \(0.741716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.8160 | −1.05424 | −0.527122 | − | 0.849790i | \(-0.676729\pi\) | ||||
−0.527122 | + | 0.849790i | \(0.676729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.5690 | − | 56.9007i | −0.925166 | − | 2.23355i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.6601 | + | 5.24399i | 0.495428 | + | 0.205213i | 0.616385 | − | 0.787445i | \(-0.288596\pi\) |
−0.120957 | + | 0.992658i | \(0.538596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.63504 | − | 4.63504i | 0.181106 | − | 0.181106i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20.2130i | − | 0.787388i | −0.919241 | − | 0.393694i | \(-0.871197\pi\) | ||
0.919241 | − | 0.393694i | \(-0.128803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.04254 | + | 5.04254i | 0.196132 | + | 0.196132i | 0.798340 | − | 0.602208i | \(-0.205712\pi\) |
−0.602208 | + | 0.798340i | \(0.705712\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.5206 | + | 10.5206i | 0.407972 | + | 0.407972i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.4089i | 0.828957i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.45443 | + | 9.45443i | −0.364984 | + | 0.364984i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.6300 | − | 14.3442i | −1.33489 | − | 0.552929i | −0.402844 | − | 0.915269i | \(-0.631978\pi\) |
−0.932046 | + | 0.362339i | \(0.881978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.0912 | − | 34.0193i | −0.541571 | − | 1.30747i | −0.923614 | − | 0.383323i | \(-0.874780\pi\) |
0.382044 | − | 0.924144i | \(-0.375220\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.8681 | 1.68350 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.42199 | − | 15.5041i | −0.245731 | − | 0.593246i | 0.752102 | − | 0.659047i | \(-0.229040\pi\) |
−0.997833 | + | 0.0658003i | \(0.979040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.56609 | − | 1.47712i | 0.136253 | − | 0.0564379i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.54146 | − | 8.54146i | 0.325404 | − | 0.325404i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.24785 | − | 12.6694i | 0.199638 | − | 0.481968i | −0.792078 | − | 0.610420i | \(-0.791001\pi\) |
0.991716 | + | 0.128452i | \(0.0410007\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.8172 | + | 29.8172i | 1.13103 | + | 1.13103i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.6316 | + | 27.4606i | 0.592091 | + | 1.04014i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 11.5629i | − | 0.436724i | −0.975868 | − | 0.218362i | \(-0.929929\pi\) | ||
0.975868 | − | 0.218362i | \(-0.0700713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.71867 | − | 8.97766i | 0.140252 | − | 0.338599i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0809 | + | 8.31776i | 0.755218 | + | 0.312822i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.9142 | + | 5.76346i | −0.522560 | + | 0.216451i | −0.628341 | − | 0.777938i | \(-0.716266\pi\) |
0.105781 | + | 0.994389i | \(0.466266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44.1199 | 1.65230 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.2222 | −0.531880 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.76251 | + | 0.730055i | −0.0657305 | + | 0.0272264i | −0.415306 | − | 0.909682i | \(-0.636326\pi\) |
0.349576 | + | 0.936908i | \(0.386326\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.96342 | − | 2.05592i | −0.184847 | − | 0.0765663i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.07772 | + | 7.43027i | −0.114304 | + | 0.275953i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.61649i | − | 0.171216i | −0.996329 | − | 0.0856082i | \(-0.972717\pi\) | ||
0.996329 | − | 0.0856082i | \(-0.0272833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.2945 | − | 3.17311i | 0.935550 | − | 0.117362i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.76113 | + | 4.76113i | 0.175856 | + | 0.175856i | 0.789547 | − | 0.613691i | \(-0.210316\pi\) |
−0.613691 | + | 0.789547i | \(0.710316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.9741 | − | 57.8786i | 0.883097 | − | 2.13199i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.49918 | − | 6.49918i | 0.239076 | − | 0.239076i | −0.577391 | − | 0.816468i | \(-0.695929\pi\) |
0.816468 | + | 0.577391i | \(0.195929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.90655 | + | 3.27500i | −0.290063 | + | 0.120148i | −0.522970 | − | 0.852351i | \(-0.675176\pi\) |
0.232907 | + | 0.972499i | \(0.425176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.8703 | + | 40.7286i | 0.618081 | + | 1.49218i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.1122 | −0.479108 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.59617 | + | 8.68192i | 0.131226 | + | 0.316808i | 0.975812 | − | 0.218613i | \(-0.0701532\pi\) |
−0.844586 | + | 0.535420i | \(0.820153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.81554 | + | 3.65151i | 0.320830 | + | 0.132892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.9701 | + | 30.9701i | −1.12563 | + | 1.12563i | −0.134750 | + | 0.990880i | \(0.543023\pi\) |
−0.990880 | + | 0.134750i | \(0.956977\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.85599i | 0.284779i | 0.989811 | + | 0.142390i | \(0.0454786\pi\) | ||||
−0.989811 | + | 0.142390i | \(0.954521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.49236 | − | 4.49236i | −0.162634 | − | 0.162634i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.52632 | − | 9.52632i | −0.343976 | − | 0.343976i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 33.7233i | − | 1.21609i | −0.793901 | − | 0.608047i | \(-0.791953\pi\) | ||
0.793901 | − | 0.608047i | \(-0.208047\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.9064 | + | 19.9064i | −0.715983 | + | 0.715983i | −0.967780 | − | 0.251797i | \(-0.918978\pi\) |
0.251797 | + | 0.967780i | \(0.418978\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.3124 | + | 6.34261i | 0.550038 | + | 0.227833i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.68883 | − | 16.1483i | −0.239652 | − | 0.578571i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7971 | 0.744180 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.2220 | + | 53.6488i | 0.793139 | + | 1.91481i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.9518 | − | 13.2349i | 1.13896 | − | 0.471772i | 0.268141 | − | 0.963380i | \(-0.413591\pi\) |
0.870817 | + | 0.491608i | \(0.163591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.7743 | + | 23.7743i | −0.845317 | + | 0.845317i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.11925 | + | 2.70211i | −0.0397458 | + | 0.0959549i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.8112 | − | 31.8112i | −1.12681 | − | 1.12681i | −0.990692 | − | 0.136119i | \(-0.956537\pi\) |
−0.136119 | − | 0.990692i | \(-0.543463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7419 | − | 26.6924i | 0.733797 | − | 0.944310i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.1964i | 1.77139i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.7477 | − | 38.0184i | 0.555035 | − | 1.33997i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.7452 | − | 11.9066i | −1.01063 | − | 0.418615i | −0.184943 | − | 0.982749i | \(-0.559210\pi\) |
−0.825683 | + | 0.564134i | \(0.809210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.6958 | − | 18.5136i | 1.56948 | − | 0.650101i | 0.582779 | − | 0.812631i | \(-0.301965\pi\) |
0.986704 | + | 0.162529i | \(0.0519653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.9495 | 1.88977 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1016 | −0.493351 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2625 | − | 8.80722i | 0.742067 | − | 0.307374i | 0.0205669 | − | 0.999788i | \(-0.493453\pi\) |
0.721500 | + | 0.692414i | \(0.243453\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0413 | + | 4.15925i | 0.350018 | + | 0.144982i | 0.550764 | − | 0.834661i | \(-0.314336\pi\) |
−0.200746 | + | 0.979643i | \(0.564336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.2934 | + | 29.6790i | −0.427485 | + | 1.03204i | 0.552598 | + | 0.833448i | \(0.313637\pi\) |
−0.980082 | + | 0.198591i | \(0.936363\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.0657i | 0.731642i | 0.930685 | + | 0.365821i | \(0.119212\pi\) | ||||
−0.930685 | + | 0.365821i | \(0.880788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.628942 | + | 5.01361i | 0.0217915 | + | 0.173711i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.2374 | − | 15.2374i | −0.527313 | − | 0.527313i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.3781 | − | 39.5402i | 0.565435 | − | 1.36508i | −0.339932 | − | 0.940450i | \(-0.610404\pi\) |
0.905367 | − | 0.424631i | \(-0.139596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3613 | + | 12.3613i | −0.426251 | + | 0.426251i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.7307 | − | 12.3149i | 1.02277 | − | 0.423644i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.9087 | − | 28.7500i | −0.409186 | − | 0.987863i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.8763 | −0.921307 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.75449 | + | 13.8926i | 0.197030 | + | 0.475673i | 0.991256 | − | 0.131949i | \(-0.0421236\pi\) |
−0.794226 | + | 0.607622i | \(0.792124\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.2462 | − | 4.65833i | −0.384163 | − | 0.159126i | 0.182240 | − | 0.983254i | \(-0.441665\pi\) |
−0.566403 | + | 0.824129i | \(0.691665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.12775 | − | 9.12775i | 0.311435 | − | 0.311435i | −0.534030 | − | 0.845465i | \(-0.679323\pi\) |
0.845465 | + | 0.534030i | \(0.179323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.4811i | 0.731226i | 0.930767 | + | 0.365613i | \(0.119141\pi\) | ||||
−0.930767 | + | 0.365613i | \(0.880859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.0488 | − | 46.0488i | −1.56571 | − | 1.56571i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.20258 | − | 4.20258i | −0.142563 | − | 0.142563i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.7038i | − | 0.464335i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1332 | + | 12.1332i | −0.410175 | + | 0.410175i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.3960 | − | 19.6321i | −1.60045 | − | 0.662928i | −0.608971 | − | 0.793192i | \(-0.708417\pi\) |
−0.991479 | + | 0.130264i | \(0.958417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.5491 | + | 37.5388i | 0.523861 | + | 1.26471i | 0.935487 | + | 0.353361i | \(0.114961\pi\) |
−0.411626 | + | 0.911353i | \(0.635039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.59541 | 0.120995 | 0.0604975 | − | 0.998168i | \(-0.480731\pi\) | ||||
0.0604975 | + | 0.998168i | \(0.480731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.3637 | + | 37.0913i | 0.515864 | + | 1.24540i | 0.940424 | + | 0.340005i | \(0.110429\pi\) |
−0.424560 | + | 0.905400i | \(0.639571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.2848 | − | 13.3728i | 1.08280 | − | 0.448509i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.2222 | + | 13.2222i | −0.442465 | + | 0.442465i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.0979 | + | 60.5917i | −0.838930 | + | 2.02536i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.7850 | − | 16.7850i | −0.559810 | − | 0.559810i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.79096 | − | 46.1627i | −0.192925 | − | 1.53790i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 33.0423i | − | 1.09836i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.9424 | − | 40.9026i | 0.562563 | − | 1.35815i | −0.345147 | − | 0.938549i | \(-0.612171\pi\) |
0.907710 | − | 0.419599i | \(-0.137829\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.08964 | − | 3.35084i | −0.268022 | − | 0.111018i | 0.244625 | − | 0.969618i | \(-0.421335\pi\) |
−0.512647 | + | 0.858599i | \(0.671335\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.6966 | + | 7.74440i | −0.618768 | + | 0.256302i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.80230 | 0.191609 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.6562 | −1.07723 | −0.538615 | − | 0.842552i | \(-0.681052\pi\) | ||||
−0.538615 | + | 0.842552i | \(0.681052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.20298 | − | 1.74093i | 0.138343 | − | 0.0573034i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.32780 | − | 3.86370i | −0.306696 | − | 0.127038i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.8006 | − | 45.3888i | 0.616829 | − | 1.48916i | −0.238537 | − | 0.971133i | \(-0.576668\pi\) |
0.855366 | − | 0.518024i | \(-0.173332\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.79506i | − | 0.0916045i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −33.6110 | + | 43.2534i | −1.09920 | + | 1.41454i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6009 | + | 28.6009i | 0.934352 | + | 0.934352i | 0.997974 | − | 0.0636224i | \(-0.0202653\pi\) |
−0.0636224 | + | 0.997974i | \(0.520265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.10983 | + | 2.67938i | −0.0361796 | + | 0.0873452i | −0.940937 | − | 0.338583i | \(-0.890052\pi\) |
0.904757 | + | 0.425928i | \(0.140052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.1835 | + | 34.1835i | −1.11317 | + | 1.11317i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.7742 | − | 17.3034i | 1.35748 | − | 0.562286i | 0.419114 | − | 0.907934i | \(-0.362341\pi\) |
0.938364 | + | 0.345648i | \(0.112341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.20194 | + | 10.1444i | 0.136401 | + | 0.329301i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.8145 | −0.577069 | −0.288534 | − | 0.957470i | \(-0.593168\pi\) | ||||
−0.288534 | + | 0.957470i | \(0.593168\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.40549 | − | 8.22157i | −0.110199 | − | 0.266044i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.15663 | + | 1.30752i | 0.101933 | + | 0.0422221i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6704 | + | 12.6704i | −0.408722 | + | 0.408722i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 56.3320i | 1.81339i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1664 | + | 19.1664i | 0.616349 | + | 0.616349i | 0.944593 | − | 0.328244i | \(-0.106457\pi\) |
−0.328244 | + | 0.944593i | \(0.606457\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.02700 | − | 1.02700i | −0.0329582 | − | 0.0329582i | 0.690436 | − | 0.723394i | \(-0.257419\pi\) |
−0.723394 | + | 0.690436i | \(0.757419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.3262i | 1.19662i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.2951 | + | 34.2951i | −1.09720 | + | 1.09720i | −0.102462 | + | 0.994737i | \(0.532672\pi\) |
−0.994737 | + | 0.102462i | \(0.967328\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.4118 | − | 5.55536i | −0.428644 | − | 0.177550i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.76821 | − | 16.3399i | −0.215872 | − | 0.521162i | 0.778433 | − | 0.627727i | \(-0.216015\pi\) |
−0.994306 | + | 0.106565i | \(0.966015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53.5184 | −1.70524 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.9255 | + | 36.0333i | 0.474603 | + | 1.14579i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.3051 | + | 10.8959i | −0.835610 | + | 0.346121i | −0.759121 | − | 0.650950i | \(-0.774371\pi\) |
−0.0764888 | + | 0.997070i | \(0.524371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.2826 | + | 29.2826i | −0.928322 | + | 0.928322i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.92753 | + | 11.8961i | −0.156056 | + | 0.376753i | −0.982499 | − | 0.186267i | \(-0.940361\pi\) |
0.826443 | + | 0.563021i | \(0.190361\pi\) | |||||||
\(998\) | 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 | 1224.2.bq.e.865.4 | 16 | ||
3.2 | odd | 2 | 408.2.ba.a.49.1 | yes | 16 | ||
12.11 | even | 2 | 816.2.bq.f.49.3 | 16 | |||
17.8 | even | 8 | inner | 1224.2.bq.e.433.4 | 16 | ||
51.5 | even | 16 | 6936.2.a.bo.1.7 | 8 | |||
51.8 | odd | 8 | 408.2.ba.a.25.1 | ✓ | 16 | ||
51.29 | even | 16 | 6936.2.a.bl.1.2 | 8 | |||
204.59 | even | 8 | 816.2.bq.f.433.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
408.2.ba.a.25.1 | ✓ | 16 | 51.8 | odd | 8 | ||
408.2.ba.a.49.1 | yes | 16 | 3.2 | odd | 2 | ||
816.2.bq.f.49.3 | 16 | 12.11 | even | 2 | |||
816.2.bq.f.433.3 | 16 | 204.59 | even | 8 | |||
1224.2.bq.e.433.4 | 16 | 17.8 | even | 8 | inner | ||
1224.2.bq.e.865.4 | 16 | 1.1 | even | 1 | trivial | ||
6936.2.a.bl.1.2 | 8 | 51.29 | even | 16 | |||
6936.2.a.bo.1.7 | 8 | 51.5 | even | 16 |