Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(865,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.310217769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2053.4 | ||
Root | \(0.346911 + 0.600868i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.2053 |
Dual form | 2268.2.i.m.865.4 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00677 | + | 3.47583i | 0.897456 | + | 1.55444i | 0.830735 | + | 0.556669i | \(0.187921\pi\) |
0.0667218 | + | 0.997772i | \(0.478746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.89234 | + | 1.84906i | −0.715239 | + | 0.698880i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.885571 | + | 1.53385i | −0.267010 | + | 0.462474i | −0.968088 | − | 0.250610i | \(-0.919369\pi\) |
0.701079 | + | 0.713084i | \(0.252702\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.114429 | + | 0.198197i | −0.0317369 | + | 0.0549699i | −0.881458 | − | 0.472263i | \(-0.843437\pi\) |
0.849721 | + | 0.527233i | \(0.176771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.04751 | − | 5.27844i | −0.739129 | − | 1.28021i | −0.952888 | − | 0.303323i | \(-0.901904\pi\) |
0.213759 | − | 0.976886i | \(-0.431429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.27792 | + | 5.67752i | −0.752005 | + | 1.30251i | 0.194844 | + | 0.980834i | \(0.437580\pi\) |
−0.946849 | + | 0.321677i | \(0.895753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.769592 | − | 1.33297i | −0.160471 | − | 0.277944i | 0.774567 | − | 0.632492i | \(-0.217968\pi\) |
−0.935038 | + | 0.354548i | \(0.884635\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.55428 | + | 9.62030i | −1.11086 | + | 1.92406i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.271142 | − | 0.469632i | −0.0503498 | − | 0.0872084i | 0.839752 | − | 0.542970i | \(-0.182700\pi\) |
−0.890102 | + | 0.455762i | \(0.849367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.55273 | 0.817695 | 0.408847 | − | 0.912603i | \(-0.365931\pi\) | ||||
0.408847 | + | 0.912603i | \(0.365931\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.2245 | − | 2.86683i | −1.72826 | − | 0.484582i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.54073 | − | 2.66863i | 0.253295 | − | 0.438720i | −0.711136 | − | 0.703054i | \(-0.751819\pi\) |
0.964431 | + | 0.264335i | \(0.0851523\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.43985 | + | 7.69005i | −0.693388 | + | 1.20098i | 0.277333 | + | 0.960774i | \(0.410550\pi\) |
−0.970721 | + | 0.240210i | \(0.922784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.12120 | − | 3.67403i | −0.323480 | − | 0.560284i | 0.657723 | − | 0.753260i | \(-0.271520\pi\) |
−0.981204 | + | 0.192975i | \(0.938186\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.757595 | 0.110507 | 0.0552533 | − | 0.998472i | \(-0.482403\pi\) | ||||
0.0552533 | + | 0.998472i | \(0.482403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.161936 | − | 6.99813i | 0.0231338 | − | 0.999732i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.19645 | + | 5.53641i | 0.439066 | + | 0.760485i | 0.997618 | − | 0.0689852i | \(-0.0219761\pi\) |
−0.558552 | + | 0.829470i | \(0.688643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.10856 | −0.958518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.17648 | −0.673921 | −0.336960 | − | 0.941519i | \(-0.609399\pi\) | ||||
−0.336960 | + | 0.941519i | \(0.609399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5015 | 1.60065 | 0.800324 | − | 0.599568i | \(-0.204661\pi\) | ||||
0.800324 | + | 0.599568i | \(0.204661\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.918533 | −0.113930 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.18803 | −0.755989 | −0.377994 | − | 0.925808i | \(-0.623386\pi\) | ||||
−0.377994 | + | 0.925808i | \(0.623386\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.9068 | −1.65043 | −0.825217 | − | 0.564816i | \(-0.808947\pi\) | ||||
−0.825217 | + | 0.564816i | \(0.808947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.08824 | − | 8.81309i | −0.595534 | − | 1.03149i | −0.993471 | − | 0.114082i | \(-0.963607\pi\) |
0.397938 | − | 0.917412i | \(-0.369726\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.16039 | − | 4.54006i | −0.132238 | − | 0.517387i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5829 | 1.30318 | 0.651590 | − | 0.758571i | \(-0.274102\pi\) | ||||
0.651590 | + | 0.758571i | \(0.274102\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.66871 | − | 15.0146i | −0.951515 | − | 1.64807i | −0.742150 | − | 0.670234i | \(-0.766194\pi\) |
−0.209365 | − | 0.977838i | \(-0.567140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.2313 | − | 21.1853i | 1.32667 | − | 2.29786i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.04596 | − | 8.73985i | 0.534870 | − | 0.926423i | −0.464299 | − | 0.885678i | \(-0.653694\pi\) |
0.999170 | − | 0.0407443i | \(-0.0129729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.149939 | − | 0.586643i | −0.0157179 | − | 0.0614969i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.3121 | −2.69957 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.91267 | + | 8.50899i | 0.498806 | + | 0.863957i | 0.999999 | − | 0.00137861i | \(-0.000438824\pi\) |
−0.501193 | + | 0.865335i | \(0.667105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.730408 | + | 1.26510i | −0.0726783 | + | 0.125883i | −0.900074 | − | 0.435736i | \(-0.856488\pi\) |
0.827396 | + | 0.561619i | \(0.189821\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.68226 | + | 15.0381i | 0.855488 | + | 1.48175i | 0.876191 | + | 0.481963i | \(0.160076\pi\) |
−0.0207031 | + | 0.999786i | \(0.506590\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.97436 | + | 6.88380i | −0.384216 | + | 0.665482i | −0.991660 | − | 0.128881i | \(-0.958862\pi\) |
0.607444 | + | 0.794363i | \(0.292195\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.83065 | − | 15.2951i | −0.845823 | − | 1.46501i | −0.884905 | − | 0.465772i | \(-0.845777\pi\) |
0.0390825 | − | 0.999236i | \(-0.487556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.97381 | + | 8.61490i | −0.467897 | + | 0.810421i | −0.999327 | − | 0.0366810i | \(-0.988321\pi\) |
0.531430 | + | 0.847102i | \(0.321655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.08879 | − | 5.34995i | 0.288031 | − | 0.498885i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.5271 | + | 4.35359i | 1.42337 | + | 0.399093i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.93153 | + | 6.80961i | 0.357412 | + | 0.619055i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −24.5170 | −2.19287 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4189 | −1.01326 | −0.506631 | − | 0.862163i | \(-0.669109\pi\) | ||||
−0.506631 | + | 0.862163i | \(0.669109\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.16249 | + | 2.01349i | 0.101567 | + | 0.175919i | 0.912330 | − | 0.409455i | \(-0.134281\pi\) |
−0.810763 | + | 0.585374i | \(0.800948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.29514 | − | 16.8049i | −0.372436 | − | 1.45717i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.12366 | − | 15.8026i | 0.779487 | − | 1.35011i | −0.152751 | − | 0.988265i | \(-0.548813\pi\) |
0.932238 | − | 0.361846i | \(-0.117853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.08202 | + | 8.80232i | −0.431051 | + | 0.746603i | −0.996964 | − | 0.0778624i | \(-0.975191\pi\) |
0.565913 | + | 0.824465i | \(0.308524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.202670 | − | 0.351035i | −0.0169481 | − | 0.0293550i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.08824 | − | 1.88489i | 0.0903735 | − | 0.156531i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.18226 | + | 14.1721i | 0.670317 | + | 1.16102i | 0.977814 | + | 0.209474i | \(0.0671750\pi\) |
−0.307498 | + | 0.951549i | \(0.599492\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.6483 | + | 20.1754i | −0.947925 | + | 1.64185i | −0.198139 | + | 0.980174i | \(0.563490\pi\) |
−0.749786 | + | 0.661680i | \(0.769844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.13630 | + | 15.8245i | 0.733845 | + | 1.27106i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3541 | 1.06577 | 0.532885 | − | 0.846187i | \(-0.321108\pi\) | ||||
0.532885 | + | 0.846187i | \(0.321108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.92108 | + | 1.09942i | 0.309024 | + | 0.0866464i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.31865 | + | 2.28397i | −0.103285 | + | 0.178894i | −0.913036 | − | 0.407879i | \(-0.866269\pi\) |
0.809751 | + | 0.586773i | \(0.199602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.75073 | + | 6.49645i | −0.290240 | + | 0.502711i | −0.973866 | − | 0.227122i | \(-0.927069\pi\) |
0.683626 | + | 0.729832i | \(0.260402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.47381 | + | 11.2130i | 0.497986 | + | 0.862536i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.04374 | −0.383469 | −0.191734 | − | 0.981447i | \(-0.561411\pi\) | ||||
−0.191734 | + | 0.981447i | \(0.561411\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.27792 | − | 28.4751i | −0.550159 | − | 2.15252i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.35938 | − | 2.35452i | −0.101605 | − | 0.175985i | 0.810741 | − | 0.585405i | \(-0.199064\pi\) |
−0.912346 | + | 0.409420i | \(0.865731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5527 | 1.23035 | 0.615177 | − | 0.788389i | \(-0.289084\pi\) | ||||
0.615177 | + | 0.788389i | \(0.289084\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.3676 | 0.909285 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7951 | 0.789419 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.0426 | −1.59495 | −0.797475 | − | 0.603352i | \(-0.793831\pi\) | ||||
−0.797475 | + | 0.603352i | \(0.793831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7470 | −0.917547 | −0.458773 | − | 0.888553i | \(-0.651711\pi\) | ||||
−0.458773 | + | 0.888553i | \(0.651711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.35097 | −0.666229 | −0.333114 | − | 0.942886i | \(-0.608100\pi\) | ||||
−0.333114 | + | 0.942886i | \(0.608100\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.48059 | + | 12.9568i | 0.530285 | + | 0.918480i | 0.999376 | + | 0.0353302i | \(0.0112483\pi\) |
−0.469091 | + | 0.883150i | \(0.655418\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.38147 | + | 0.387347i | 0.0969603 | + | 0.0271864i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.6391 | −2.48914 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.80565 | − | 10.0557i | −0.401585 | − | 0.695566i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.70167 | − | 8.14353i | 0.323676 | − | 0.560624i | −0.657567 | − | 0.753396i | \(-0.728414\pi\) |
0.981244 | + | 0.192772i | \(0.0617477\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.51355 | − | 14.7459i | 0.580619 | − | 1.00566i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.61534 | + | 8.41828i | −0.584847 | + | 0.571470i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.39489 | 0.0938307 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.877799 | − | 1.52039i | −0.0587818 | − | 0.101813i | 0.835137 | − | 0.550042i | \(-0.185388\pi\) |
−0.893919 | + | 0.448229i | \(0.852055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1823 | + | 19.3682i | −0.742192 | + | 1.28552i | 0.209303 | + | 0.977851i | \(0.432881\pi\) |
−0.951495 | + | 0.307664i | \(0.900453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.45340 | + | 7.71351i | 0.294289 | + | 0.509723i | 0.974819 | − | 0.222997i | \(-0.0715839\pi\) |
−0.680530 | + | 0.732720i | \(0.738251\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.91267 | − | 5.04488i | 0.190815 | − | 0.330501i | −0.754706 | − | 0.656064i | \(-0.772220\pi\) |
0.945521 | + | 0.325562i | \(0.105554\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.52032 | + | 2.63327i | 0.0991748 | + | 0.171776i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.92475 | − | 6.79787i | 0.253871 | − | 0.439718i | −0.710717 | − | 0.703478i | \(-0.751629\pi\) |
0.964588 | + | 0.263760i | \(0.0849627\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9957 | + | 22.5092i | −0.837126 | + | 1.44994i | 0.0551625 | + | 0.998477i | \(0.482432\pi\) |
−0.892288 | + | 0.451467i | \(0.850901\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.6493 | − | 13.4808i | 1.57479 | − | 0.861256i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.750177 | − | 1.29935i | −0.0477326 | − | 0.0826754i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.64593 | −0.419488 | −0.209744 | − | 0.977756i | \(-0.567263\pi\) | ||||
−0.209744 | + | 0.977756i | \(0.567263\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.72611 | 0.171389 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5621 | + | 18.2940i | 0.658843 | + | 1.14115i | 0.980916 | + | 0.194434i | \(0.0622871\pi\) |
−0.322073 | + | 0.946715i | \(0.604380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.01886 | + | 7.89888i | 0.125446 | + | 0.490812i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0966 | + | 22.6839i | −0.807569 | + | 1.39875i | 0.106974 | + | 0.994262i | \(0.465884\pi\) |
−0.914543 | + | 0.404488i | \(0.867450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.8291 | + | 22.2206i | −0.788085 | + | 1.36500i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.13475 | − | 14.0898i | −0.495984 | − | 0.859070i | 0.504005 | − | 0.863701i | \(-0.331859\pi\) |
−0.999989 | + | 0.00463056i | \(0.998526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.55950 | + | 9.62934i | −0.337716 | + | 0.584941i | −0.984003 | − | 0.178154i | \(-0.942988\pi\) |
0.646287 | + | 0.763095i | \(0.276321\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.83742 | − | 17.0389i | −0.593219 | − | 1.02749i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.600882 | + | 1.04076i | −0.0361035 | + | 0.0625331i | −0.883513 | − | 0.468407i | \(-0.844828\pi\) |
0.847409 | + | 0.530941i | \(0.178161\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.23141 | + | 7.32901i | 0.252425 | + | 0.437212i | 0.964193 | − | 0.265202i | \(-0.0854387\pi\) |
−0.711768 | + | 0.702414i | \(0.752105\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.552731 | −0.0328564 | −0.0164282 | − | 0.999865i | \(-0.505229\pi\) | ||||
−0.0164282 | + | 0.999865i | \(0.505229\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.81765 | − | 22.7618i | −0.343405 | − | 1.34359i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0746 | + | 17.4497i | −0.592624 | + | 1.02645i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.6921 | − | 23.7155i | 0.799903 | − | 1.38547i | −0.119776 | − | 0.992801i | \(-0.538218\pi\) |
0.919679 | − | 0.392671i | \(-0.128449\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3880 | − | 17.9926i | −0.604814 | − | 1.04757i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.352255 | 0.0203714 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8076 | + | 3.03030i | 0.622937 | + | 0.174663i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.0876 | + | 43.4530i | 1.43651 | + | 2.48811i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.4899 | 0.884056 | 0.442028 | − | 0.897001i | \(-0.354259\pi\) | ||||
0.442028 | + | 0.897001i | \(0.354259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.7710 | −1.00770 | −0.503849 | − | 0.863792i | \(-0.668083\pi\) | ||||
−0.503849 | + | 0.863792i | \(0.668083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6897 | 0.943356 | 0.471678 | − | 0.881771i | \(-0.343648\pi\) | ||||
0.471678 | + | 0.881771i | \(0.343648\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.55383 | −0.536597 | −0.268298 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268298 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.960462 | 0.0537755 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.9579 | 2.22332 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.27114 | − | 2.20168i | −0.0705103 | − | 0.122127i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.43363 | + | 1.40084i | −0.0790386 | + | 0.0772308i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.8815 | 1.36761 | 0.683806 | − | 0.729664i | \(-0.260323\pi\) | ||||
0.683806 | + | 0.729664i | \(0.260323\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.4180 | − | 21.5086i | −0.678467 | − | 1.17514i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.2668 | + | 17.7827i | −0.559270 | + | 0.968683i | 0.438288 | + | 0.898835i | \(0.355585\pi\) |
−0.997558 | + | 0.0698488i | \(0.977748\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.03177 | + | 6.98322i | −0.218332 | + | 0.378163i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6335 | + | 13.5423i | 0.682147 | + | 0.731215i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.9716 | 0.696353 | 0.348176 | − | 0.937429i | \(-0.386801\pi\) | ||||
0.348176 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.38657 | − | 14.5260i | −0.448923 | − | 0.777557i | 0.549393 | − | 0.835564i | \(-0.314859\pi\) |
−0.998316 | + | 0.0580068i | \(0.981526\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.94973 | − | 12.0373i | 0.369897 | − | 0.640680i | −0.619652 | − | 0.784876i | \(-0.712726\pi\) |
0.989549 | + | 0.144197i | \(0.0460598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.9078 | − | 48.3377i | −1.48119 | − | 2.56550i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.88247 | + | 3.26053i | −0.0993530 | + | 0.172084i | −0.911417 | − | 0.411484i | \(-0.865011\pi\) |
0.812064 | + | 0.583568i | \(0.198344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.9895 | − | 20.7664i | −0.631024 | − | 1.09297i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.4219 | − | 35.3718i | 1.06893 | − | 1.85144i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.6283 | − | 30.5332i | 0.920191 | − | 1.59382i | 0.121074 | − | 0.992644i | \(-0.461366\pi\) |
0.799118 | − | 0.601175i | \(-0.205300\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.2860 | − | 4.56636i | −0.845524 | − | 0.237074i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.26683 | + | 14.3186i | 0.428040 | + | 0.741387i | 0.996699 | − | 0.0811864i | \(-0.0258709\pi\) |
−0.568659 | + | 0.822573i | \(0.692538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.124106 | 0.00639179 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.51811 | 0.334813 | 0.167406 | − | 0.985888i | \(-0.446461\pi\) | ||||
0.167406 | + | 0.985888i | \(0.446461\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.44663 | − | 5.96973i | −0.176114 | − | 0.305039i | 0.764432 | − | 0.644704i | \(-0.223020\pi\) |
−0.940546 | + | 0.339665i | \(0.889686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4518 | − | 13.1442i | 0.685570 | − | 0.669889i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.8516 | + | 23.9917i | −0.702305 | + | 1.21643i | 0.265351 | + | 0.964152i | \(0.414512\pi\) |
−0.967656 | + | 0.252275i | \(0.918821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.69067 | + | 8.12448i | −0.237218 | + | 0.410873i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.2443 | + | 40.2603i | 1.16955 | + | 2.02572i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.75604 | + | 6.50566i | −0.188510 | + | 0.326510i | −0.944754 | − | 0.327781i | \(-0.893699\pi\) |
0.756243 | + | 0.654290i | \(0.227033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.428407 | − | 0.742022i | −0.0213936 | − | 0.0370548i | 0.855130 | − | 0.518413i | \(-0.173477\pi\) |
−0.876524 | + | 0.481358i | \(0.840144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.520965 | + | 0.902337i | −0.0259511 | + | 0.0449486i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.72886 | + | 4.72652i | 0.135264 | + | 0.234285i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.49544 | 0.0739448 | 0.0369724 | − | 0.999316i | \(-0.488229\pi\) | ||||
0.0369724 | + | 0.999316i | \(0.488229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.79569 | − | 9.57164i | 0.482014 | − | 0.470990i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.7923 | − | 60.2620i | 1.70789 | − | 2.95814i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.97436 | + | 12.0800i | −0.340720 | + | 0.590144i | −0.984567 | − | 0.175010i | \(-0.944004\pi\) |
0.643847 | + | 0.765155i | \(0.277337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.86405 | − | 10.1568i | −0.285797 | − | 0.495014i | 0.687005 | − | 0.726652i | \(-0.258925\pi\) |
−0.972802 | + | 0.231638i | \(0.925591\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 67.7068 | 3.28426 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.6571 | + | 23.1160i | −1.14485 | + | 1.11866i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.69844 | + | 15.0661i | 0.418989 | + | 0.725711i | 0.995838 | − | 0.0911402i | \(-0.0290511\pi\) |
−0.576849 | + | 0.816851i | \(0.695718\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.99800 | 0.480473 | 0.240237 | − | 0.970714i | \(-0.422775\pi\) | ||||
0.240237 | + | 0.970714i | \(0.422775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0906 | 0.482700 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.62575 | 0.268502 | 0.134251 | − | 0.990947i | \(-0.457137\pi\) | ||||
0.134251 | + | 0.990947i | \(0.457137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.1250 | 1.38377 | 0.691886 | − | 0.722007i | \(-0.256780\pi\) | ||||
0.691886 | + | 0.722007i | \(0.256780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.5044 | 1.92009 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.9088 | 0.845168 | 0.422584 | − | 0.906324i | \(-0.361123\pi\) | ||||
0.422584 | + | 0.906324i | \(0.361123\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.86361 | − | 13.6202i | −0.370283 | − | 0.641349i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.73818 | − | 1.69842i | 0.0814871 | − | 0.0796234i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.03554 | −0.329109 | −0.164554 | − | 0.986368i | \(-0.552619\pi\) | ||||
−0.164554 | + | 0.986368i | \(0.552619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.02409 | − | 12.1661i | −0.327144 | − | 0.566631i | 0.654800 | − | 0.755802i | \(-0.272753\pi\) |
−0.981944 | + | 0.189172i | \(0.939420\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.64208 | + | 9.77236i | −0.262209 | + | 0.454160i | −0.966829 | − | 0.255425i | \(-0.917784\pi\) |
0.704619 | + | 0.709586i | \(0.251118\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.8813 | − | 32.7033i | 0.873720 | − | 1.51333i | 0.0156005 | − | 0.999878i | \(-0.495034\pi\) |
0.858120 | − | 0.513450i | \(-0.171633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.7099 | − | 11.4421i | 0.540712 | − | 0.528345i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.51390 | 0.345490 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.4129 | − | 63.0690i | −1.67074 | − | 2.89381i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.61956 | − | 16.6616i | 0.439529 | − | 0.761286i | −0.558124 | − | 0.829757i | \(-0.688479\pi\) |
0.997653 | + | 0.0684710i | \(0.0218121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.352609 | + | 0.610737i | 0.0160776 | + | 0.0278472i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.7172 | + | 34.1512i | −0.895313 | + | 1.55073i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.06196 | + | 12.2317i | 0.320008 | + | 0.554270i | 0.980489 | − | 0.196572i | \(-0.0629811\pi\) |
−0.660481 | + | 0.750842i | \(0.729648\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9592 | + | 22.4459i | −0.584839 | + | 1.01297i | 0.410056 | + | 0.912060i | \(0.365509\pi\) |
−0.994895 | + | 0.100911i | \(0.967824\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.65261 | + | 2.86241i | −0.0744300 | + | 0.128917i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.3165 | − | 25.7145i | 1.18045 | − | 1.15345i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.43208 | + | 14.6048i | 0.377472 | + | 0.653800i | 0.990694 | − | 0.136110i | \(-0.0434602\pi\) |
−0.613222 | + | 0.789911i | \(0.710127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.12392 | 0.317640 | 0.158820 | − | 0.987308i | \(-0.449231\pi\) | ||||
0.158820 | + | 0.987308i | \(0.449231\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.86306 | −0.260903 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.79201 | − | 6.56796i | −0.168078 | − | 0.291120i | 0.769666 | − | 0.638447i | \(-0.220423\pi\) |
−0.937744 | + | 0.347327i | \(0.887089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.9247 | + | 7.26893i | 1.14684 | + | 0.321559i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −34.8467 | + | 60.3562i | −1.53553 | + | 2.65961i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.670904 | + | 1.16204i | −0.0295063 | + | 0.0511064i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.6691 | + | 23.6755i | 0.598853 | + | 1.03724i | 0.992991 | + | 0.118192i | \(0.0377098\pi\) |
−0.394138 | + | 0.919051i | \(0.628957\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.12652 | + | 1.95119i | −0.0492592 | + | 0.0853194i | −0.889604 | − | 0.456733i | \(-0.849019\pi\) |
0.840344 | + | 0.542053i | \(0.182353\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.8745 | − | 24.0313i | −0.604382 | − | 1.04682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.3155 | − | 17.8669i | 0.448498 | − | 0.776822i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.01610 | − | 1.75993i | −0.0440120 | − | 0.0762310i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.9026 | −1.37927 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.5907 | + | 6.44572i | 0.456174 | + | 0.277637i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.33120 | + | 16.1621i | −0.401180 | + | 0.694863i | −0.993869 | − | 0.110568i | \(-0.964733\pi\) |
0.592689 | + | 0.805431i | \(0.298066\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.4422 | − | 61.3877i | 1.51818 | − | 2.62956i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8979 | + | 34.4642i | 0.850774 | + | 1.47358i | 0.880511 | + | 0.474026i | \(0.157200\pi\) |
−0.0297373 | + | 0.999558i | \(0.509467\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.55512 | 0.151453 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.9189 | + | 21.4176i | −0.932086 | + | 0.910767i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.86525 | + | 6.69481i | 0.163776 | + | 0.283668i | 0.936220 | − | 0.351415i | \(-0.114299\pi\) |
−0.772444 | + | 0.635083i | \(0.780966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.970909 | 0.0410651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.8631 | 1.00571 | 0.502854 | − | 0.864371i | \(-0.332283\pi\) | ||||
0.502854 | + | 0.864371i | \(0.332283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.9253 | −1.67967 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.5132 | −0.650347 | −0.325173 | − | 0.945654i | \(-0.605423\pi\) | ||||
−0.325173 | + | 0.945654i | \(0.605423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.5934 | 1.32214 | 0.661071 | − | 0.750324i | \(-0.270102\pi\) | ||||
0.661071 | + | 0.750324i | \(0.270102\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.0981 | 0.713041 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.33842 | + | 10.9785i | 0.263872 | + | 0.457039i | 0.967267 | − | 0.253759i | \(-0.0816671\pi\) |
−0.703396 | + | 0.710799i | \(0.748334\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.1672 | + | 12.3839i | 1.83236 | + | 0.513771i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3227 | −0.468939 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8041 | − | 23.9094i | −0.569756 | − | 0.986847i | −0.996590 | − | 0.0825166i | \(-0.973704\pi\) |
0.426833 | − | 0.904330i | \(-0.359629\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.9235 | + | 25.8482i | −0.614911 | + | 1.06506i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.4142 | − | 19.7700i | 0.468726 | − | 0.811857i | −0.530635 | − | 0.847600i | \(-0.678047\pi\) |
0.999361 | + | 0.0357436i | \(0.0113800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0270 | + | 62.7063i | 0.657043 | + | 2.57071i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.8105 | 1.42232 | 0.711159 | − | 0.703031i | \(-0.248171\pi\) | ||||
0.711159 | + | 0.703031i | \(0.248171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.892988 | − | 1.54670i | −0.0364257 | − | 0.0630912i | 0.847238 | − | 0.531214i | \(-0.178264\pi\) |
−0.883664 | + | 0.468123i | \(0.844931\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.7794 | + | 27.3307i | −0.641523 | + | 1.11115i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.63997 | − | 14.9649i | −0.350686 | − | 0.607405i | 0.635684 | − | 0.771949i | \(-0.280718\pi\) |
−0.986370 | + | 0.164544i | \(0.947385\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0866908 | + | 0.150153i | −0.00350714 | + | 0.00607454i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.73973 | + | 3.01330i | 0.0702671 | + | 0.121706i | 0.899018 | − | 0.437911i | \(-0.144282\pi\) |
−0.828751 | + | 0.559617i | \(0.810948\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.8562 | + | 41.3201i | −0.960414 | + | 1.66349i | −0.238953 | + | 0.971031i | \(0.576804\pi\) |
−0.721461 | + | 0.692455i | \(0.756529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.35261 | − | 2.34279i | 0.0543660 | − | 0.0941646i | −0.837562 | − | 0.546343i | \(-0.816020\pi\) |
0.891928 | + | 0.452178i | \(0.149353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.61185 | + | 25.8691i | 0.264898 | + | 1.03642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4287 | − | 37.1155i | −0.857147 | − | 1.48462i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.7816 | −0.748871 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.45861 | 0.0580663 | 0.0290332 | − | 0.999578i | \(-0.490757\pi\) | ||||
0.0290332 | + | 0.999578i | \(0.490757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.9151 | − | 39.6902i | −0.909359 | − | 1.57506i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.36848 | + | 0.832884i | 0.0542210 | + | 0.0330001i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.8155 | + | 20.4651i | −0.466686 | + | 0.808324i | −0.999276 | − | 0.0380495i | \(-0.987886\pi\) |
0.532590 | + | 0.846374i | \(0.321219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.12220 | + | 7.13986i | −0.162564 | + | 0.281569i | −0.935787 | − | 0.352565i | \(-0.885310\pi\) |
0.773224 | + | 0.634133i | \(0.218643\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.10644 | − | 3.64846i | −0.0828127 | − | 0.143436i | 0.821644 | − | 0.570000i | \(-0.193057\pi\) |
−0.904457 | + | 0.426565i | \(0.859724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.58414 | − | 7.93997i | 0.179943 | − | 0.311671i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.6534 | + | 34.0407i | 0.769097 | + | 1.33211i | 0.938053 | + | 0.346491i | \(0.112627\pi\) |
−0.168956 | + | 0.985624i | \(0.554040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.66570 | + | 8.08123i | −0.182304 | + | 0.315760i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.5076 | − | 32.0561i | −0.720953 | − | 1.24873i | −0.960618 | − | 0.277872i | \(-0.910371\pi\) |
0.239665 | − | 0.970856i | \(-0.422962\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.03954 | −0.234911 | −0.117455 | − | 0.993078i | \(-0.537474\pi\) | ||||
−0.117455 | + | 0.993078i | \(0.537474\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 49.7916 | − | 48.6528i | 1.93084 | − | 1.88667i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.417337 | + | 0.722849i | −0.0161594 | + | 0.0279888i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.0709 | + | 19.1754i | −0.427388 | + | 0.740259i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4194 | + | 30.1714i | 0.671470 | + | 1.16302i | 0.977487 | + | 0.210994i | \(0.0676701\pi\) |
−0.306017 | + | 0.952026i | \(0.598997\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.1024 | 1.04163 | 0.520814 | − | 0.853670i | \(-0.325628\pi\) | ||||
0.520814 | + | 0.853670i | \(0.325628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.0301 | − | 7.01811i | −0.960567 | − | 0.269330i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0557 | − | 19.1491i | −0.423036 | − | 0.732720i | 0.573199 | − | 0.819416i | \(-0.305702\pi\) |
−0.996235 | + | 0.0866964i | \(0.972369\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 73.2365 | 2.79822 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.46307 | −0.0557384 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.5186 | −1.54140 | −0.770701 | − | 0.637197i | \(-0.780094\pi\) | ||||
−0.770701 | + | 0.637197i | \(0.780094\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −40.7938 | −1.54740 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.1219 | 2.05001 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.5703 | 1.19239 | 0.596197 | − | 0.802838i | \(-0.296678\pi\) | ||||
0.596197 | + | 0.802838i | \(0.296678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1008 | + | 17.4951i | 0.380959 | + | 0.659839i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.957073 | − | 3.74458i | −0.0359944 | − | 0.140830i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.0708 | −0.753776 | −0.376888 | − | 0.926259i | \(-0.623006\pi\) | ||||
−0.376888 | + | 0.926259i | \(0.623006\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.50374 | − | 6.06866i | −0.131216 | − | 0.227273i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.813426 | − | 1.40889i | 0.0304204 | − | 0.0526897i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.08603 | + | 12.2734i | −0.264264 | + | 0.457719i | −0.967371 | − | 0.253366i | \(-0.918462\pi\) |
0.703106 | + | 0.711085i | \(0.251796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.2362 | − | 12.4033i | −1.64744 | − | 0.461921i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.02399 | 0.223726 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.5067 | − | 21.6622i | −0.463847 | − | 0.803407i | 0.535302 | − | 0.844661i | \(-0.320198\pi\) |
−0.999149 | + | 0.0412542i | \(0.986865\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9288 | + | 22.3933i | −0.478188 | + | 0.828245i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.3515 | − | 31.7858i | −0.677829 | − | 1.17403i | −0.975633 | − | 0.219407i | \(-0.929588\pi\) |
0.297805 | − | 0.954627i | \(-0.403746\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.47994 | − | 9.49154i | 0.201856 | − | 0.349625i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.70944 | + | 9.88905i | 0.210025 | + | 0.363774i | 0.951722 | − | 0.306961i | \(-0.0993120\pi\) |
−0.741697 | + | 0.670735i | \(0.765979\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.3645 | − | 38.7365i | 0.820474 | − | 1.42110i | −0.0848549 | − | 0.996393i | \(-0.527043\pi\) |
0.905329 | − | 0.424710i | \(-0.139624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.8399 | + | 56.8803i | −1.20316 | + | 2.08393i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.20771 | − | 20.3754i | −0.190286 | − | 0.744500i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6654 | + | 27.1333i | 0.571638 | + | 0.990107i | 0.996398 | + | 0.0848004i | \(0.0270253\pi\) |
−0.424760 | + | 0.905306i | \(0.639641\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −93.5020 | −3.40289 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.8242 | −1.19302 | −0.596508 | − | 0.802607i | \(-0.703446\pi\) | ||||
−0.596508 | + | 0.802607i | \(0.703446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.70422 | − | 4.68385i | −0.0980279 | − | 0.169789i | 0.812840 | − | 0.582486i | \(-0.197920\pi\) |
−0.910868 | + | 0.412697i | \(0.864587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.9923 | + | 12.6152i | 1.62883 | + | 0.456702i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.592340 | − | 1.02596i | 0.0213882 | − | 0.0370454i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.54660 | + | 2.67879i | −0.0557718 | + | 0.0965997i | −0.892563 | − | 0.450922i | \(-0.851095\pi\) |
0.836792 | + | 0.547522i | \(0.184429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0166 | + | 19.0812i | 0.396238 | + | 0.686304i | 0.993258 | − | 0.115922i | \(-0.0369822\pi\) |
−0.597020 | + | 0.802226i | \(0.703649\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.2871 | + | 43.7986i | −0.908341 | + | 1.57329i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.1069 | − | 50.4147i | −1.04286 | − | 1.80629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.3155 | − | 21.3310i | 0.440682 | − | 0.763283i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.7986 | + | 46.4165i | 0.956483 | + | 1.65668i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.6704 | −1.27151 | −0.635756 | − | 0.771890i | \(-0.719312\pi\) | ||||
−0.635756 | + | 0.771890i | \(0.719312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.51731 | − | 25.4992i | −0.231729 | − | 0.906649i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.43053 | + | 2.47775i | −0.0507996 | + | 0.0879875i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.95927 | − | 13.7859i | 0.281932 | − | 0.488320i | −0.689929 | − | 0.723877i | \(-0.742358\pi\) |
0.971860 | + | 0.235557i | \(0.0756915\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.30878 | − | 3.99892i | −0.0816786 | − | 0.141471i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.0240 | 0.636053 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.04732 | + | 15.8353i | 0.142649 | + | 0.558121i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.52433 | − | 13.0325i | −0.264541 | − | 0.458199i | 0.702902 | − | 0.711287i | \(-0.251887\pi\) |
−0.967443 | + | 0.253088i | \(0.918554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.8358 | −0.415610 | −0.207805 | − | 0.978170i | \(-0.566632\pi\) | ||||
−0.207805 | + | 0.978170i | \(0.566632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.5849 | −0.370774 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.8125 | 0.973036 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.9514 | −1.70842 | −0.854208 | − | 0.519931i | \(-0.825958\pi\) | ||||
−0.854208 | + | 0.519931i | \(0.825958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.3157 | 0.464155 | 0.232078 | − | 0.972697i | \(-0.425448\pi\) | ||||
0.232078 | + | 0.972697i | \(0.425448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.3154 | 0.949850 | 0.474925 | − | 0.880026i | \(-0.342475\pi\) | ||||
0.474925 | + | 0.880026i | \(0.342475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.36003 | − | 9.28384i | −0.186161 | − | 0.322441i | 0.757806 | − | 0.652480i | \(-0.226271\pi\) |
−0.943967 | + | 0.330039i | \(0.892938\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.4327 | + | 20.4721i | −1.29697 | + | 0.709315i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.1075 | −1.04191 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.96082 | − | 15.5206i | −0.309362 | − | 0.535830i | 0.668861 | − | 0.743387i | \(-0.266782\pi\) |
−0.978223 | + | 0.207557i | \(0.933449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3530 | − | 24.8601i | 0.494930 | − | 0.857244i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.9830 | + | 45.0038i | −0.893841 | + | 1.54818i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0312 | − | 5.61648i | −0.688280 | − | 0.192985i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.74294 | −0.162586 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.13174 | − | 8.88844i | −0.175707 | − | 0.304334i | 0.764698 | − | 0.644388i | \(-0.222888\pi\) |
−0.940406 | + | 0.340054i | \(0.889555\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.3185 | − | 28.2644i | 0.557428 | − | 0.965494i | −0.440282 | − | 0.897860i | \(-0.645122\pi\) |
0.997710 | − | 0.0676344i | \(-0.0215451\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.71212 | − | 4.69753i | −0.0925363 | − | 0.160278i | 0.816041 | − | 0.577993i | \(-0.196164\pi\) |
−0.908578 | + | 0.417716i | \(0.862831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.27005 | + | 16.0562i | −0.315556 | + | 0.546559i | −0.979556 | − | 0.201174i | \(-0.935524\pi\) |
0.663999 | + | 0.747733i | \(0.268858\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.1216 | − | 17.5312i | −0.344146 | − | 0.596079i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.2575 | + | 17.7665i | −0.347962 | + | 0.602688i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.708091 | − | 1.22645i | 0.0239927 | − | 0.0415566i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 46.3946 | − | 45.3335i | 1.56842 | − | 1.53255i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.40689 | − | 14.5612i | −0.283881 | − | 0.491695i | 0.688457 | − | 0.725278i | \(-0.258289\pi\) |
−0.972337 | + | 0.233582i | \(0.924955\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.86926 | 0.130359 | 0.0651793 | − | 0.997874i | \(-0.479238\pi\) | ||||
0.0651793 | + | 0.997874i | \(0.479238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.9696 | 1.17682 | 0.588411 | − | 0.808562i | \(-0.299754\pi\) | ||||
0.588411 | + | 0.808562i | \(0.299754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.7381 | + | 32.4553i | 0.629163 | + | 1.08974i | 0.987720 | + | 0.156235i | \(0.0499357\pi\) |
−0.358556 | + | 0.933508i | \(0.616731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.6085 | − | 21.1142i | 0.724725 | − | 0.708149i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.48333 | + | 4.30126i | −0.0831015 | + | 0.143936i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.45595 | − | 9.44998i | 0.182372 | − | 0.315878i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.23444 | − | 2.13811i | −0.0411708 | − | 0.0713098i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.4824 | − | 33.7445i | 0.649053 | − | 1.12419i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.2176 | + | 57.5345i | 1.10419 | + | 1.91251i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.3273 | − | 33.4759i | 0.641753 | − | 1.11155i | −0.343288 | − | 0.939230i | \(-0.611541\pi\) |
0.985041 | − | 0.172319i | \(-0.0551261\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4700 | + | 44.1153i | 0.843857 | + | 1.46160i | 0.886610 | + | 0.462518i | \(0.153054\pi\) |
−0.0427526 | + | 0.999086i | \(0.513613\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.7070 | 1.01625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.92289 | − | 1.66070i | −0.195591 | − | 0.0548412i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.71044 | + | 6.42667i | −0.122396 | + | 0.211996i | −0.920712 | − | 0.390242i | \(-0.872391\pi\) |
0.798316 | + | 0.602239i | \(0.205725\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.59134 | − | 2.75628i | 0.0523796 | − | 0.0907242i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1153 | + | 29.6446i | 0.562749 | + | 0.974709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.9829 | 0.852472 | 0.426236 | − | 0.904612i | \(-0.359839\pi\) | ||||
0.426236 | + | 0.904612i | \(0.359839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39.2012 | + | 23.8587i | 1.28477 | + | 0.781936i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.6634 | + | 37.5221i | 0.708469 | + | 1.22710i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.0972 | 0.819891 | 0.409945 | − | 0.912110i | \(-0.365548\pi\) | ||||
0.409945 | + | 0.912110i | \(0.365548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.3308 | −1.67334 | −0.836668 | − | 0.547711i | \(-0.815499\pi\) | ||||
−0.836668 | + | 0.547711i | \(0.815499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.6675 | 0.445075 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.9808 | 1.46168 | 0.730839 | − | 0.682549i | \(-0.239129\pi\) | ||||
0.730839 | + | 0.682549i | \(0.239129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.32897 | 0.0756016 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.6027 | −0.375847 | −0.187924 | − | 0.982184i | \(-0.560176\pi\) | ||||
−0.187924 | + | 0.982184i | \(0.560176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.2346 | − | 76.6166i | −1.43140 | − | 2.47925i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.9550 | + | 46.7743i | 0.386046 | + | 1.51042i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.2726 | −0.331376 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.5803 | − | 44.3063i | −0.823458 | − | 1.42627i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.52123 | + | 16.4912i | −0.306182 | + | 0.530323i | −0.977524 | − | 0.210825i | \(-0.932385\pi\) |
0.671342 | + | 0.741148i | \(0.265718\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.39580 | + | 14.5420i | −0.269434 | + | 0.466673i | −0.968716 | − | 0.248173i | \(-0.920170\pi\) |
0.699282 | + | 0.714846i | \(0.253503\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.65910 | − | 26.0540i | −0.213481 | − | 0.835252i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.66019 | −0.277064 | −0.138532 | − | 0.990358i | \(-0.544238\pi\) | ||||
−0.138532 | + | 0.990358i | \(0.544238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.93711 | + | 15.4795i | 0.285631 | + | 0.494728i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.34851 | + | 12.7280i | −0.234381 | + | 0.405960i | −0.959093 | − | 0.283092i | \(-0.908640\pi\) |
0.724712 | + | 0.689052i | \(0.241973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.7653 | − | 32.5024i | −0.597911 | − | 1.03561i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.26492 | + | 5.65501i | −0.103818 | + | 0.179819i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.9319 | − | 36.2551i | −0.664923 | − | 1.15168i | −0.979306 | − | 0.202384i | \(-0.935131\pi\) |
0.314383 | − | 0.949296i | \(-0.398202\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.0237 | + | 52.0025i | −0.951815 | + | 1.64859i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.77891 | − | 13.4735i | 0.246361 | − | 0.426709i | −0.716153 | − | 0.697944i | \(-0.754099\pi\) |
0.962513 | + | 0.271235i | \(0.0874319\pi\) | |||||||
\(998\) | 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 | 2268.2.i.m.2053.4 | 8 | ||
3.2 | odd | 2 | 2268.2.i.l.2053.1 | 8 | |||
7.4 | even | 3 | 2268.2.l.l.109.1 | 8 | |||
9.2 | odd | 6 | 2268.2.l.m.541.4 | 8 | |||
9.4 | even | 3 | 2268.2.k.d.1297.4 | yes | 8 | ||
9.5 | odd | 6 | 2268.2.k.c.1297.1 | ✓ | 8 | ||
9.7 | even | 3 | 2268.2.l.l.541.1 | 8 | |||
21.11 | odd | 6 | 2268.2.l.m.109.4 | 8 | |||
63.4 | even | 3 | 2268.2.k.d.1621.4 | yes | 8 | ||
63.11 | odd | 6 | 2268.2.i.l.865.1 | 8 | |||
63.25 | even | 3 | inner | 2268.2.i.m.865.4 | 8 | ||
63.32 | odd | 6 | 2268.2.k.c.1621.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.l.865.1 | 8 | 63.11 | odd | 6 | |||
2268.2.i.l.2053.1 | 8 | 3.2 | odd | 2 | |||
2268.2.i.m.865.4 | 8 | 63.25 | even | 3 | inner | ||
2268.2.i.m.2053.4 | 8 | 1.1 | even | 1 | trivial | ||
2268.2.k.c.1297.1 | ✓ | 8 | 9.5 | odd | 6 | ||
2268.2.k.c.1621.1 | yes | 8 | 63.32 | odd | 6 | ||
2268.2.k.d.1297.4 | yes | 8 | 9.4 | even | 3 | ||
2268.2.k.d.1621.4 | yes | 8 | 63.4 | even | 3 | ||
2268.2.l.l.109.1 | 8 | 7.4 | even | 3 | |||
2268.2.l.l.541.1 | 8 | 9.7 | even | 3 | |||
2268.2.l.m.109.4 | 8 | 21.11 | odd | 6 | |||
2268.2.l.m.541.4 | 8 | 9.2 | odd | 6 |