Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.373 |
Dual form | 588.4.i.c.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 5.19615i | 0.268328 | − | 0.464758i | −0.700102 | − | 0.714043i | \(-0.746862\pi\) |
0.968430 | + | 0.249285i | \(0.0801955\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.0000 | − | 31.1769i | −0.493382 | − | 0.854563i | 0.506589 | − | 0.862188i | \(-0.330906\pi\) |
−0.999971 | + | 0.00762479i | \(0.997573\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −62.0000 | −1.32275 | −0.661373 | − | 0.750057i | \(-0.730026\pi\) | ||||
−0.661373 | + | 0.750057i | \(0.730026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.0000 | −0.309839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 57.0000 | + | 98.7269i | 0.813208 | + | 1.40852i | 0.910608 | + | 0.413272i | \(0.135614\pi\) |
−0.0974001 | + | 0.995245i | \(0.531053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −38.0000 | + | 65.8179i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.0000 | − | 20.7846i | 0.108790 | − | 0.188430i | −0.806490 | − | 0.591247i | \(-0.798636\pi\) |
0.915280 | + | 0.402817i | \(0.131969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.5000 | + | 77.0763i | 0.356000 | + | 0.616610i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 54.0000 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −56.0000 | − | 96.9948i | −0.324448 | − | 0.561961i | 0.656952 | − | 0.753932i | \(-0.271845\pi\) |
−0.981401 | + | 0.191971i | \(0.938512\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −54.0000 | + | 93.5307i | −0.284854 | + | 0.493382i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 89.0000 | − | 154.153i | 0.395446 | − | 0.684933i | −0.597712 | − | 0.801711i | \(-0.703923\pi\) |
0.993158 | + | 0.116778i | \(0.0372566\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 93.0000 | + | 161.081i | 0.381844 | + | 0.661373i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −378.000 | −1.43985 | −0.719923 | − | 0.694054i | \(-0.755823\pi\) | ||||
−0.719923 | + | 0.694054i | \(0.755823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −172.000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.0000 | + | 46.7654i | 0.0894427 | + | 0.154919i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −96.0000 | + | 166.277i | −0.297937 | + | 0.516042i | −0.975664 | − | 0.219272i | \(-0.929632\pi\) |
0.677727 | + | 0.735314i | \(0.262965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 171.000 | − | 296.181i | 0.469506 | − | 0.813208i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 201.000 | + | 348.142i | 0.520933 | + | 0.902283i | 0.999704 | + | 0.0243430i | \(0.00774937\pi\) |
−0.478770 | + | 0.877940i | \(0.658917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −216.000 | −0.529553 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 228.000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 198.000 | + | 342.946i | 0.436905 | + | 0.756742i | 0.997449 | − | 0.0713828i | \(-0.0227412\pi\) |
−0.560544 | + | 0.828125i | \(0.689408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 127.000 | − | 219.970i | 0.266569 | − | 0.461710i | −0.701405 | − | 0.712763i | \(-0.747443\pi\) |
0.967973 | + | 0.251053i | \(0.0807768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −186.000 | + | 322.161i | −0.354930 | + | 0.614757i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 506.000 | + | 876.418i | 0.922653 | + | 1.59808i | 0.795293 | + | 0.606225i | \(0.207317\pi\) |
0.127360 | + | 0.991857i | \(0.459350\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −72.0000 | −0.125620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 840.000 | 1.40408 | 0.702040 | − | 0.712138i | \(-0.252273\pi\) | ||||
0.702040 | + | 0.712138i | \(0.252273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 445.000 | + | 770.763i | 0.713470 | + | 1.23577i | 0.963547 | + | 0.267540i | \(0.0862108\pi\) |
−0.250077 | + | 0.968226i | \(0.580456\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 133.500 | − | 231.229i | 0.205537 | − | 0.356000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40.0000 | + | 69.2820i | −0.0569665 | + | 0.0986688i | −0.893102 | − | 0.449854i | \(-0.851476\pi\) |
0.836136 | + | 0.548522i | \(0.184809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 108.000 | 0.142826 | 0.0714129 | − | 0.997447i | \(-0.477249\pi\) | ||||
0.0714129 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 684.000 | 0.872826 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −81.0000 | − | 140.296i | −0.0998174 | − | 0.172889i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −819.000 | + | 1418.55i | −0.975436 | + | 1.68951i | −0.296948 | + | 0.954894i | \(0.595969\pi\) |
−0.678488 | + | 0.734612i | \(0.737364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −168.000 | + | 290.985i | −0.187320 | + | 0.324448i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 228.000 | + | 394.908i | 0.246235 | + | 0.426491i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1010.00 | −1.05722 | −0.528608 | − | 0.848866i | \(-0.677286\pi\) | ||||
−0.528608 | + | 0.848866i | \(0.677286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 324.000 | 0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 5.19615i | 0.00295556 | + | 0.00511917i | 0.867499 | − | 0.497438i | \(-0.165726\pi\) |
−0.864544 | + | 0.502557i | \(0.832393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −236.000 | + | 408.764i | −0.225765 | + | 0.391036i | −0.956549 | − | 0.291573i | \(-0.905821\pi\) |
0.730784 | + | 0.682609i | \(0.239155\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 486.000 | − | 841.777i | 0.439097 | − | 0.760539i | −0.558523 | − | 0.829489i | \(-0.688632\pi\) |
0.997620 | + | 0.0689505i | \(0.0219651\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 893.000 | + | 1546.72i | 0.784715 | + | 1.35917i | 0.929169 | + | 0.369654i | \(0.120524\pi\) |
−0.144455 | + | 0.989511i | \(0.546143\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −534.000 | −0.456622 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2286.00 | −1.90309 | −0.951543 | − | 0.307515i | \(-0.900503\pi\) | ||||
−0.951543 | + | 0.307515i | \(0.900503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −72.0000 | − | 124.708i | −0.0583829 | − | 0.101122i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 279.000 | − | 483.242i | 0.220458 | − | 0.381844i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5000 | − | 30.3109i | 0.0131480 | − | 0.0227730i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 567.000 | + | 982.073i | 0.415648 | + | 0.719923i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1328.00 | 0.927881 | 0.463941 | − | 0.885866i | \(-0.346435\pi\) | ||||
0.463941 | + | 0.885866i | \(0.346435\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 258.000 | + | 446.869i | 0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −606.000 | + | 1049.62i | −0.404171 | + | 0.700046i | −0.994225 | − | 0.107319i | \(-0.965773\pi\) |
0.590053 | + | 0.807364i | \(0.299107\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 81.0000 | − | 140.296i | 0.0516398 | − | 0.0894427i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 627.000 | + | 1086.00i | 0.391009 | + | 0.677247i | 0.992583 | − | 0.121570i | \(-0.0387928\pi\) |
−0.601574 | + | 0.798817i | \(0.705459\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 340.000 | 0.207471 | 0.103735 | − | 0.994605i | \(-0.466921\pi\) | ||||
0.103735 | + | 0.994605i | \(0.466921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 576.000 | 0.344028 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1116.00 | + | 1932.97i | 0.652620 | + | 1.13037i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 162.000 | − | 280.592i | 0.0927818 | − | 0.160703i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −519.000 | + | 898.934i | −0.285357 | + | 0.494252i | −0.972696 | − | 0.232085i | \(-0.925445\pi\) |
0.687339 | + | 0.726337i | \(0.258779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1468.00 | − | 2542.65i | −0.791153 | − | 1.37032i | −0.925253 | − | 0.379350i | \(-0.876148\pi\) |
0.134100 | − | 0.990968i | \(-0.457186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1026.00 | −0.542138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −672.000 | −0.348234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −665.000 | − | 1151.81i | −0.338043 | − | 0.585508i | 0.646021 | − | 0.763319i | \(-0.276432\pi\) |
−0.984065 | + | 0.177811i | \(0.943098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 603.000 | − | 1044.43i | 0.300761 | − | 0.520933i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1682.00 | − | 2913.31i | 0.808248 | − | 1.39993i | −0.105828 | − | 0.994384i | \(-0.533749\pi\) |
0.914076 | − | 0.405542i | \(-0.132917\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 324.000 | + | 561.184i | 0.152869 | + | 0.264777i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3048.00 | −1.41234 | −0.706172 | − | 0.708041i | \(-0.749579\pi\) | ||||
−0.706172 | + | 0.708041i | \(0.749579\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1647.00 | 0.749659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −342.000 | − | 592.361i | −0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1353.00 | + | 2343.46i | −0.594605 | + | 1.02989i | 0.398997 | + | 0.916952i | \(0.369358\pi\) |
−0.993602 | + | 0.112934i | \(0.963975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 594.000 | − | 1028.84i | 0.252247 | − | 0.436905i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2358.00 | − | 4084.18i | −0.984610 | − | 1.70539i | −0.643657 | − | 0.765314i | \(-0.722584\pi\) |
−0.340953 | − | 0.940080i | \(-0.610750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1910.00 | −0.784360 | −0.392180 | − | 0.919888i | \(-0.628279\pi\) | ||||
−0.392180 | + | 0.919888i | \(0.628279\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −762.000 | −0.307807 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −534.000 | − | 924.915i | −0.212219 | − | 0.367574i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2052.00 | − | 3554.17i | 0.802444 | − | 1.38987i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2040.00 | + | 3533.38i | −0.772823 | + | 1.33857i | 0.163187 | + | 0.986595i | \(0.447823\pi\) |
−0.936010 | + | 0.351974i | \(0.885511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1343.00 | + | 2326.14i | 0.500887 | + | 0.867562i | 0.999999 | + | 0.00102491i | \(0.000326238\pi\) |
−0.499112 | + | 0.866537i | \(0.666340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1116.00 | 0.409838 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 510.000 | 0.184447 | 0.0922233 | − | 0.995738i | \(-0.470603\pi\) | ||||
0.0922233 | + | 0.995738i | \(0.470603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 676.000 | + | 1170.87i | 0.240806 | + | 0.417088i | 0.960944 | − | 0.276743i | \(-0.0892550\pi\) |
−0.720138 | + | 0.693831i | \(0.755922\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1518.00 | − | 2629.25i | 0.532694 | − | 0.922653i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1134.00 | + | 1964.15i | −0.386351 | + | 0.669180i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 108.000 | + | 187.061i | 0.0362634 | + | 0.0628100i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2736.00 | 0.905517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3364.00 | −1.09757 | −0.548785 | − | 0.835963i | \(-0.684909\pi\) | ||||
−0.548785 | + | 0.835963i | \(0.684909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1260.00 | − | 2182.38i | −0.405323 | − | 0.702040i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −516.000 | + | 893.738i | −0.163679 | + | 0.283500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1335.00 | − | 2312.29i | 0.411922 | − | 0.713470i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3534.00 | − | 6121.07i | −1.07567 | − | 1.86311i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4768.00 | 1.43179 | 0.715894 | − | 0.698209i | \(-0.246019\pi\) | ||||
0.715894 | + | 0.698209i | \(0.246019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 210.000 | + | 363.731i | 0.0614017 | + | 0.106351i | 0.895092 | − | 0.445881i | \(-0.147110\pi\) |
−0.833690 | + | 0.552232i | \(0.813776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −941.000 | + | 1629.86i | −0.271542 | + | 0.470324i | −0.969257 | − | 0.246051i | \(-0.920867\pi\) |
0.697715 | + | 0.716375i | \(0.254200\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2541.00 | + | 4401.14i | −0.714448 | + | 1.23746i | 0.248724 | + | 0.968574i | \(0.419989\pi\) |
−0.963172 | + | 0.268886i | \(0.913344\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 576.000 | + | 997.661i | 0.159890 | + | 0.276937i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 240.000 | 0.0657792 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5424.00 | −1.46799 | −0.733995 | − | 0.679155i | \(-0.762346\pi\) | ||||
−0.733995 | + | 0.679155i | \(0.762346\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1295.00 | − | 2243.01i | −0.346134 | − | 0.599522i | 0.639425 | − | 0.768853i | \(-0.279172\pi\) |
−0.985559 | + | 0.169332i | \(0.945839\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2356.00 | − | 4080.71i | 0.606918 | − | 1.05121i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −162.000 | − | 280.592i | −0.0412303 | − | 0.0714129i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4932.00 | 1.24026 | 0.620130 | − | 0.784499i | \(-0.287080\pi\) | ||||
0.620130 | + | 0.784499i | \(0.287080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −864.000 | −0.214700 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1026.00 | − | 1777.08i | −0.251963 | − | 0.436413i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1719.00 | + | 2977.40i | −0.417231 | + | 0.722665i | −0.995660 | − | 0.0930680i | \(-0.970333\pi\) |
0.578429 | + | 0.815733i | \(0.303666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −243.000 | + | 420.888i | −0.0576296 | + | 0.0998174i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3060.00 | − | 5300.08i | −0.717444 | − | 1.24265i | −0.962009 | − | 0.273016i | \(-0.911979\pi\) |
0.244566 | − | 0.969633i | \(-0.421355\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2412.00 | 0.559124 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4914.00 | 1.12634 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | − | 15.5885i | −0.00203992 | − | 0.00353325i | 0.865004 | − | 0.501766i | \(-0.167316\pi\) |
−0.867044 | + | 0.498232i | \(0.833983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3448.00 | − | 5972.11i | 0.772882 | − | 1.33867i | −0.163095 | − | 0.986610i | \(-0.552148\pi\) |
0.935977 | − | 0.352061i | \(-0.114519\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1602.00 | − | 2774.75i | 0.351288 | − | 0.608449i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3127.00 | − | 5416.12i | −0.678279 | − | 1.17481i | −0.975499 | − | 0.220004i | \(-0.929393\pi\) |
0.297220 | − | 0.954809i | \(-0.403940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1008.00 | 0.216299 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1194.00 | 0.253481 | 0.126740 | − | 0.991936i | \(-0.459549\pi\) | ||||
0.126740 | + | 0.991936i | \(0.459549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3578.00 | − | 6197.28i | −0.751555 | − | 1.30173i | −0.947069 | − | 0.321030i | \(-0.895971\pi\) |
0.195514 | − | 0.980701i | \(-0.437362\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 684.000 | − | 1184.72i | 0.142164 | − | 0.246235i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4041.50 | + | 7000.08i | −0.822613 | + | 1.42481i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1515.00 | + | 2624.06i | 0.305192 | + | 0.528608i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3738.00 | 0.745312 | 0.372656 | − | 0.927970i | \(-0.378447\pi\) | ||||
0.372656 | + | 0.927970i | \(0.378447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2376.00 | 0.468936 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −486.000 | − | 841.777i | −0.0949514 | − | 0.164461i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −744.000 | + | 1288.65i | −0.143902 | + | 0.249245i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | − | 15.5885i | 0.00170639 | − | 0.00295556i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −762.000 | − | 1319.82i | −0.143056 | − | 0.247780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 844.000 | 0.156904 | 0.0784522 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784522 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1416.00 | 0.260691 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3156.00 | + | 5466.35i | 0.575435 | + | 0.996683i | 0.995994 | + | 0.0894178i | \(0.0285006\pi\) |
−0.420559 | + | 0.907265i | \(0.638166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4141.00 | − | 7172.42i | 0.747806 | − | 1.29524i | −0.201067 | − | 0.979578i | \(-0.564441\pi\) |
0.948872 | − | 0.315660i | \(-0.102226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4659.00 | + | 8069.62i | −0.825475 | + | 1.42976i | 0.0760811 | + | 0.997102i | \(0.475759\pi\) |
−0.901556 | + | 0.432663i | \(0.857574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −972.000 | − | 1683.55i | −0.170600 | − | 0.295489i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2916.00 | −0.507026 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8664.00 | −1.49250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2759.00 | − | 4778.73i | −0.470898 | − | 0.815619i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2679.00 | − | 4640.16i | 0.453055 | − | 0.784715i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −826.000 | + | 1430.67i | −0.137163 | + | 0.237574i | −0.926422 | − | 0.376487i | \(-0.877132\pi\) |
0.789258 | + | 0.614061i | \(0.210465\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 801.000 | + | 1387.37i | 0.131815 | + | 0.228311i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6072.00 | 0.990295 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1294.00 | −0.209165 | −0.104583 | − | 0.994516i | \(-0.533351\pi\) | ||||
−0.104583 | + | 0.994516i | \(0.533351\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3429.00 | + | 5939.20i | 0.549374 | + | 0.951543i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2016.00 | + | 3491.81i | −0.320154 | + | 0.554523i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −216.000 | + | 374.123i | −0.0337074 | + | 0.0583829i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1818.00 | − | 3148.87i | −0.281255 | − | 0.487147i | 0.690439 | − | 0.723390i | \(-0.257417\pi\) |
−0.971694 | + | 0.236243i | \(0.924084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10478.0 | −1.60709 | −0.803545 | − | 0.595244i | \(-0.797055\pi\) | ||||
−0.803545 | + | 0.595244i | \(0.797055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1674.00 | −0.254563 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3783.00 | − | 6552.35i | −0.570393 | − | 0.987950i | −0.996525 | − | 0.0832890i | \(-0.973458\pi\) |
0.426132 | − | 0.904661i | \(-0.359876\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2520.00 | − | 4364.77i | 0.376754 | − | 0.652557i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4020.00 | − | 6962.84i | 0.590996 | − | 1.02363i | −0.403103 | − | 0.915155i | \(-0.632068\pi\) |
0.994099 | − | 0.108480i | \(-0.0345984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 541.500 | + | 937.906i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −105.000 | −0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5340.00 | 0.765776 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3784.00 | + | 6554.08i | 0.538210 | + | 0.932208i | 0.999001 | + | 0.0446985i | \(0.0142327\pi\) |
−0.460790 | + | 0.887509i | \(0.652434\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1701.00 | − | 2946.22i | 0.239974 | − | 0.415648i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6761.00 | − | 11710.4i | 0.938529 | − | 1.62558i | 0.170312 | − | 0.985390i | \(-0.445522\pi\) |
0.768217 | − | 0.640190i | \(-0.221144\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1926.00 | − | 3335.93i | −0.265222 | − | 0.459378i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3348.00 | −0.457376 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2468.00 | 0.334492 | 0.167246 | − | 0.985915i | \(-0.446513\pi\) | ||||
0.167246 | + | 0.985915i | \(0.446513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1992.00 | − | 3450.25i | −0.267856 | − | 0.463941i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6168.00 | + | 10683.3i | −0.822898 | + | 1.42530i | 0.0806166 | + | 0.996745i | \(0.474311\pi\) |
−0.903515 | + | 0.428557i | \(0.859022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 774.000 | − | 1340.61i | 0.101666 | − | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1881.00 | + | 3257.99i | 0.245168 | + | 0.424644i | 0.962179 | − | 0.272418i | \(-0.0878234\pi\) |
−0.717011 | + | 0.697062i | \(0.754490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2736.00 | 0.353876 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3636.00 | 0.466697 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 240.000 | + | 415.692i | 0.0305714 | + | 0.0529513i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4385.00 | + | 7595.04i | −0.554350 | + | 0.960162i | 0.443604 | + | 0.896223i | \(0.353700\pi\) |
−0.997954 | + | 0.0639390i | \(0.979634\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3321.00 | + | 5752.14i | −0.413573 | + | 0.716330i | −0.995277 | − | 0.0970706i | \(-0.969053\pi\) |
0.581704 | + | 0.813400i | \(0.302386\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3472.00 | + | 6013.68i | 0.429163 | + | 0.743332i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −486.000 | −0.0596285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6408.00 | −0.780424 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −755.000 | − | 1307.70i | −0.0912771 | − | 0.158097i | 0.816772 | − | 0.576961i | \(-0.195762\pi\) |
−0.908049 | + | 0.418864i | \(0.862428\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1881.00 | − | 3257.99i | 0.225749 | − | 0.391009i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 324.000 | − | 561.184i | 0.0383242 | − | 0.0663794i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −510.000 | − | 883.346i | −0.0598916 | − | 0.103735i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1260.00 | 0.146909 | 0.0734547 | − | 0.997299i | \(-0.476598\pi\) | ||||
0.0734547 | + | 0.997299i | \(0.476598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3998.00 | 0.462828 | 0.231414 | − | 0.972855i | \(-0.425665\pi\) | ||||
0.231414 | + | 0.972855i | \(0.425665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −864.000 | − | 1496.49i | −0.0993123 | − | 0.172014i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5073.00 | + | 8786.69i | −0.579004 | + | 1.00286i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3348.00 | − | 5798.91i | 0.376790 | − | 0.652620i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1368.00 | + | 2369.45i | 0.152887 | + | 0.264808i | 0.932288 | − | 0.361718i | \(-0.117810\pi\) |
−0.779401 | + | 0.626526i | \(0.784476\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2690.00 | −0.298552 | −0.149276 | − | 0.988796i | \(-0.547694\pi\) | ||||
−0.149276 | + | 0.988796i | \(0.547694\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −972.000 | −0.107135 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 912.000 | + | 1579.63i | 0.0998327 | + | 0.172915i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −620.000 | + | 1073.87i | −0.0674054 | + | 0.116750i | −0.897758 | − | 0.440488i | \(-0.854805\pi\) |
0.830353 | + | 0.557238i | \(0.188139\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1950.00 | − | 3377.50i | 0.209136 | − | 0.362234i | −0.742307 | − | 0.670060i | \(-0.766268\pi\) |
0.951443 | + | 0.307826i | \(0.0996015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4914.00 | + | 8511.30i | 0.523474 | + | 0.906684i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3114.00 | 0.329501 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10878.0 | −1.14335 | −0.571675 | − | 0.820480i | \(-0.693706\pi\) | ||||
−0.571675 | + | 0.820480i | \(0.693706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6804.00 | + | 11784.9i | 0.710394 | + | 1.23044i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4404.00 | + | 7627.95i | −0.456773 | + | 0.791153i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1165.00 | + | 2017.84i | −0.119248 | + | 0.206544i | −0.919470 | − | 0.393160i | \(-0.871382\pi\) |
0.800222 | + | 0.599704i | \(0.204715\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1539.00 | + | 2665.63i | 0.156502 | + | 0.271069i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15150.0 | −1.53060 | −0.765299 | − | 0.643675i | \(-0.777409\pi\) | ||||
−0.765299 | + | 0.643675i | \(0.777409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2992.00 | −0.300324 | −0.150162 | − | 0.988661i | \(-0.547980\pi\) | ||||
−0.150162 | + | 0.988661i | \(0.547980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1008.00 | + | 1745.91i | 0.100527 | + | 0.174117i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4362.00 | − | 7555.21i | 0.432225 | − | 0.748636i | −0.564839 | − | 0.825201i | \(-0.691062\pi\) |
0.997065 | + | 0.0765646i | \(0.0243951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1995.00 | + | 3455.44i | −0.195169 | + | 0.338043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3096.00 | + | 5362.43i | 0.300960 | + | 0.521279i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6764.00 | −0.653376 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3618.00 | −0.347289 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4872.00 | + | 8438.55i | 0.464734 | + | 0.804942i | 0.999189 | − | 0.0402542i | \(-0.0128168\pi\) |
−0.534456 | + | 0.845196i | \(0.679483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5518.00 | + | 9557.46i | −0.523075 | + | 0.905993i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3030.00 | + | 5248.11i | −0.283681 | + | 0.491350i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2068.00 | − | 3581.88i | −0.192423 | − | 0.333286i | 0.753630 | − | 0.657299i | \(-0.228301\pi\) |
−0.946053 | + | 0.324013i | \(0.894968\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10092.0 | −0.933284 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16212.0 | 1.49010 | 0.745048 | − | 0.667011i | \(-0.232426\pi\) | ||||
0.745048 | + | 0.667011i | \(0.232426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3078.00 | + | 5331.25i | 0.281189 | + | 0.487034i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 972.000 | − | 1683.55i | 0.0882589 | − | 0.152869i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1198.00 | + | 2075.00i | −0.107475 | + | 0.186152i | −0.914747 | − | 0.404028i | \(-0.867610\pi\) |
0.807272 | + | 0.590180i | \(0.200943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4572.00 | + | 7918.94i | 0.407708 | + | 0.706172i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13128.0 | −1.16371 | −0.581857 | − | 0.813291i | \(-0.697674\pi\) | ||||
−0.581857 | + | 0.813291i | \(0.697674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 0.00317224 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2470.50 | − | 4279.03i | −0.216408 | − | 0.374829i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6399.00 | − | 11083.4i | 0.557231 | − | 0.965153i | −0.440495 | − | 0.897755i | \(-0.645197\pi\) |
0.997726 | − | 0.0673977i | \(-0.0214696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1026.00 | + | 1777.08i | −0.0883022 | + | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1416.00 | + | 2452.58i | 0.121158 | + | 0.209852i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6912.00 | 0.587987 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8118.00 | 0.686591 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3693.00 | + | 6396.46i | 0.310544 | + | 0.537877i | 0.978480 | − | 0.206341i | \(-0.0661556\pi\) |
−0.667936 | + | 0.744218i | \(0.732822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2590.00 | − | 4486.01i | 0.216545 | − | 0.375066i | −0.737205 | − | 0.675669i | \(-0.763855\pi\) |
0.953749 | + | 0.300603i | \(0.0971880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6384.00 | − | 11057.4i | 0.527688 | − | 0.913982i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5795.50 | + | 10038.1i | 0.476329 | + | 0.825027i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3564.00 | −0.291270 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23436.0 | 1.90455 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2916.00 | − | 5050.66i | −0.235644 | − | 0.408148i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7074.00 | + | 12252.5i | −0.568465 | + | 0.984610i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2035.00 | + | 3524.72i | −0.161722 | + | 0.280110i | −0.935486 | − | 0.353363i | \(-0.885038\pi\) |
0.773764 | + | 0.633473i | \(0.218371\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2865.00 | + | 4962.33i | 0.226425 | + | 0.392180i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10716.0 | 0.842244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14780.0 | 1.15530 | 0.577648 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577648 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1143.00 | + | 1979.73i | 0.0888562 | + | 0.153903i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2052.00 | + | 3554.17i | −0.158654 | + | 0.274796i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1602.00 | + | 2774.75i | −0.122525 | + | 0.212219i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3429.00 | + | 5939.20i | 0.260846 | + | 0.451799i | 0.966467 | − | 0.256791i | \(-0.0826651\pi\) |
−0.705621 | + | 0.708590i | \(0.749332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10664.0 | 0.806868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12312.0 | −0.926583 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3330.00 | + | 5767.73i | 0.249277 | + | 0.431760i | 0.963325 | − | 0.268336i | \(-0.0864738\pi\) |
−0.714049 | + | 0.700096i | \(0.753140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6858.00 | + | 11878.4i | −0.510652 | + | 0.884475i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 75.0000 | − | 129.904i | 0.00552577 | − | 0.00957092i | −0.863249 | − | 0.504778i | \(-0.831574\pi\) |
0.868775 | + | 0.495207i | \(0.164908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4094.00 | + | 7091.02i | 0.300050 | + | 0.519702i | 0.976147 | − | 0.217111i | \(-0.0696633\pi\) |
−0.676097 | + | 0.736813i | \(0.736330\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12240.0 | 0.892379 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2136.00 | 0.154917 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2927.00 | − | 5069.71i | −0.211183 | − | 0.365780i | 0.740902 | − | 0.671613i | \(-0.234398\pi\) |
−0.952085 | + | 0.305833i | \(0.901065\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4029.00 | − | 6978.43i | 0.289187 | − | 0.500887i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7236.00 | − | 12533.1i | 0.514039 | − | 0.890341i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1674.00 | − | 2899.45i | −0.118310 | − | 0.204919i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17580.0 | −1.23612 | −0.618062 | − | 0.786130i | \(-0.712082\pi\) | ||||
−0.618062 | + | 0.786130i | \(0.712082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8512.00 | 0.595468 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −765.000 | − | 1325.02i | −0.0532452 | − | 0.0922233i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8577.00 | − | 14855.8i | 0.593955 | − | 1.02876i | −0.399739 | − | 0.916629i | \(-0.630899\pi\) |
0.993693 | − | 0.112131i | \(-0.0357675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2028.00 | − | 3512.60i | 0.139029 | − | 0.240806i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9060.00 | + | 15692.4i | 0.617999 | + | 1.07041i | 0.989850 | + | 0.142114i | \(0.0453899\pi\) |
−0.371851 | + | 0.928292i | \(0.621277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17546.0 | −1.19088 | −0.595438 | − | 0.803401i | \(-0.703021\pi\) | ||||
−0.595438 | + | 0.803401i | \(0.703021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9108.00 | −0.615102 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −105.000 | − | 181.865i | −0.00705596 | − | 0.0122213i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7280.00 | + | 12609.3i | −0.486798 | + | 0.843158i | −0.999885 | − | 0.0151784i | \(-0.995168\pi\) |
0.513087 | + | 0.858336i | \(0.328502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5952.00 | − | 10309.2i | 0.394095 | − | 0.682593i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2249.00 | + | 3895.38i | 0.148183 | + | 0.256661i | 0.930556 | − | 0.366150i | \(-0.119324\pi\) |
−0.782373 | + | 0.622810i | \(0.785991\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6804.00 | 0.446120 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5478.00 | −0.357433 | −0.178716 | − | 0.983901i | \(-0.557194\pi\) | ||||
−0.178716 | + | 0.983901i | \(0.557194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3022.00 | + | 5234.26i | 0.196227 | + | 0.339875i | 0.947302 | − | 0.320342i | \(-0.103798\pi\) |
−0.751075 | + | 0.660217i | \(0.770464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 324.000 | − | 561.184i | 0.0209367 | − | 0.0362634i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1710.50 | + | 2962.67i | −0.109472 | + | 0.189611i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4104.00 | − | 7108.34i | −0.261400 | − | 0.452759i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20292.0 | 1.28632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15352.0 | −0.968547 | −0.484274 | − | 0.874917i | \(-0.660916\pi\) | ||||
−0.484274 | + | 0.874917i | \(0.660916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5046.00 | + | 8739.93i | 0.316841 | + | 0.548785i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3984.00 | − | 6900.49i | 0.248977 | − | 0.431240i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3780.00 | + | 6547.15i | −0.234013 | + | 0.405323i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11199.0 | + | 19397.2i | 0.690068 | + | 1.19523i | 0.971815 | + | 0.235745i | \(0.0757530\pi\) |
−0.281746 | + | 0.959489i | \(0.590914\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3764.00 | −0.230852 | −0.115426 | − | 0.993316i | \(-0.536823\pi\) | ||||
−0.115426 | + | 0.993316i | \(0.536823\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3096.00 | 0.189000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8844.00 | − | 15318.3i | −0.537393 | − | 0.930793i | −0.999043 | − | 0.0437305i | \(-0.986076\pi\) |
0.461650 | − | 0.887062i | \(-0.347258\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7128.00 | − | 12346.1i | 0.431122 | − | 0.746726i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9939.00 | + | 17214.9i | −0.595625 | + | 1.03165i | 0.397833 | + | 0.917458i | \(0.369762\pi\) |
−0.993458 | + | 0.114195i | \(0.963571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3636.00 | + | 6297.74i | 0.216901 | + | 0.375684i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8010.00 | −0.475647 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20004.0 | −1.18247 | −0.591233 | − | 0.806501i | \(-0.701359\pi\) | ||||
−0.591233 | + | 0.806501i | \(0.701359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −653.000 | − | 1131.03i | −0.0384247 | − | 0.0665536i | 0.846173 | − | 0.532908i | \(-0.178901\pi\) |
−0.884598 | + | 0.466354i | \(0.845567\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10602.0 | + | 18363.2i | −0.621037 | + | 1.07567i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 648.000 | − | 1122.37i | 0.0376172 | − | 0.0651549i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7152.00 | − | 12387.6i | −0.413322 | − | 0.715894i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9144.00 | −0.526081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13054.0 | −0.747689 | −0.373845 | − | 0.927491i | \(-0.621961\pi\) | ||||
−0.373845 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1201.50 | + | 2081.06i | 0.0685122 | + | 0.118667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2523.00 | − | 4369.96i | 0.143230 | − | 0.248082i | −0.785481 | − | 0.618886i | \(-0.787584\pi\) |
0.928711 | + | 0.370804i | \(0.120918\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 630.000 | − | 1091.19i | 0.0354503 | − | 0.0614017i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6234.00 | − | 10797.6i | −0.349249 | − | 0.604918i | 0.636867 | − | 0.770974i | \(-0.280230\pi\) |
−0.986116 | + | 0.166056i | \(0.946897\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7524.00 | 0.419675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5646.00 | 0.313549 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12462.0 | − | 21584.8i | −0.689063 | − | 1.19349i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11606.0 | + | 20102.2i | −0.638948 | + | 1.10669i | 0.346716 | + | 0.937970i | \(0.387297\pi\) |
−0.985664 | + | 0.168720i | \(0.946037\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1020.00 | − | 1766.69i | 0.0556702 | − | 0.0964237i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21546.0 | − | 37318.8i | −1.17089 | − | 2.02805i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15246.0 | 0.824974 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35958.0 | 1.93740 | 0.968698 | − | 0.248241i | \(-0.0798526\pi\) | ||||
0.968698 | + | 0.248241i | \(0.0798526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6764.00 | + | 11715.6i | 0.362886 | + | 0.628538i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1728.00 | − | 2992.98i | 0.0923124 | − | 0.159890i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3223.00 | + | 5582.40i | −0.170723 | + | 0.295700i | −0.938673 | − | 0.344809i | \(-0.887944\pi\) |
0.767950 | + | 0.640510i | \(0.221277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −360.000 | − | 623.538i | −0.0189888 | − | 0.0328896i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2688.00 | −0.141187 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13392.0 | 0.700465 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8136.00 | + | 14092.0i | 0.423772 | + | 0.733995i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2352.00 | + | 4073.78i | −0.121996 | + | 0.211302i | −0.920555 | − | 0.390614i | \(-0.872263\pi\) |
0.798559 | + | 0.601917i | \(0.205596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3885.00 | + | 6729.02i | −0.199841 | + | 0.346134i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2403.00 | + | 4162.12i | 0.123097 | + | 0.213210i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10600.0 | 0.540760 | 0.270380 | − | 0.962754i | \(-0.412851\pi\) | ||||
0.270380 | + | 0.962754i | \(0.412851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9804.00 | − | 16981.0i | −0.496052 | − | 0.859187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6271.00 | − | 10861.7i | 0.315995 | − | 0.547320i | −0.663653 | − | 0.748040i | \(-0.730995\pi\) |
0.979649 | + | 0.200720i | \(0.0643282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18216.0 | − | 31551.0i | 0.910441 | − | 1.57693i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11662.0 | − | 20199.2i | −0.580506 | − | 1.00547i | −0.995419 | − | 0.0956044i | \(-0.969522\pi\) |
0.414914 | − | 0.909861i | \(-0.363812\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14136.0 | −0.700808 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6312.00 | −0.311662 | −0.155831 | − | 0.987784i | \(-0.549806\pi\) | ||||
−0.155831 | + | 0.987784i | \(0.549806\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3114.00 | + | 5393.61i | 0.153138 | + | 0.265244i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −486.000 | + | 841.777i | −0.0238043 | + | 0.0412303i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17920.0 | + | 31038.4i | −0.870719 | + | 1.50813i | −0.00946509 | + | 0.999955i | \(0.503013\pi\) |
−0.861254 | + | 0.508175i | \(0.830320\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7398.00 | − | 12813.7i | −0.358032 | − | 0.620130i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17616.0 | −0.849155 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34594.0 | −1.66095 | −0.830476 | − | 0.557055i | \(-0.811931\pi\) | ||||
−0.830476 | + | 0.557055i | \(0.811931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1296.00 | + | 2244.74i | 0.0619787 | + | 0.107350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11973.0 | − | 20737.8i | 0.570330 | − | 0.987840i | −0.426202 | − | 0.904628i | \(-0.640149\pi\) |
0.996532 | − | 0.0832121i | \(-0.0265179\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3078.00 | + | 5331.25i | −0.145471 | + | 0.251963i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12276.0 | − | 21262.7i | −0.577915 | − | 1.00098i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18770.0 | −0.880187 | −0.440093 | − | 0.897952i | \(-0.645055\pi\) | ||||
−0.440093 | + | 0.897952i | \(0.645055\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10314.0 | 0.481776 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15171.0 | + | 26276.9i | 0.705903 | + | 1.22266i | 0.966365 | + | 0.257176i | \(0.0827919\pi\) |
−0.260462 | + | 0.965484i | \(0.583875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4984.00 | − | 8632.54i | 0.231007 | − | 0.400116i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14364.0 | − | 24879.2i | 0.660647 | − | 1.14427i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15120.0 | − | 26188.6i | −0.692748 | − | 1.19987i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1458.00 | 0.0665449 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7980.00 | −0.362826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13094.0 | − | 22679.5i | −0.593076 | − | 1.02724i | −0.993815 | − | 0.111045i | \(-0.964580\pi\) |
0.400739 | − | 0.916192i | \(-0.368753\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9180.00 | + | 15900.2i | −0.414216 | + | 0.717444i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7874.00 | + | 13638.2i | −0.352603 | + | 0.610726i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3618.00 | − | 6266.56i | −0.161405 | − | 0.279562i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34818.0 | 1.54745 | 0.773724 | − | 0.633522i | \(-0.218391\pi\) | ||||
0.773724 | + | 0.633522i | \(0.218391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21888.0 | −0.969139 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7371.00 | − | 12766.9i | −0.325145 | − | 0.563168i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16020.0 | − | 27747.5i | 0.704027 | − | 1.21941i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.0000 | + | 46.7654i | −0.00117775 | + | 0.00203992i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10851.0 | + | 18794.5i | 0.471571 | + | 0.816785i | 0.999471 | − | 0.0325217i | \(-0.0103538\pi\) |
−0.527900 | + | 0.849306i | \(0.677020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20356.0 | 0.881376 | 0.440688 | − | 0.897660i | \(-0.354735\pi\) | ||||
0.440688 | + | 0.897660i | \(0.354735\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20688.0 | −0.892448 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10092.0 | − | 17479.9i | −0.433751 | − | 0.751279i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6536.00 | − | 11320.7i | 0.279885 | − | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9945.00 | − | 17225.2i | 0.422756 | − | 0.732235i | −0.573452 | − | 0.819239i | \(-0.694396\pi\) |
0.996208 | + | 0.0870040i | \(0.0277293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2116.00 | − | 3665.02i | −0.0896223 | − | 0.155230i | 0.817729 | − | 0.575603i | \(-0.195233\pi\) |
−0.907352 | + | 0.420373i | \(0.861899\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9612.00 | −0.405633 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9636.00 | 0.405171 | 0.202586 | − | 0.979265i | \(-0.435066\pi\) | ||||
0.202586 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17647.0 | + | 30565.5i | 0.739331 | + | 1.28056i | 0.952797 | + | 0.303609i | \(0.0981916\pi\) |
−0.213465 | + | 0.976951i | \(0.568475\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9381.00 | + | 16248.4i | −0.391604 | + | 0.678279i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9144.00 | + | 15837.9i | −0.378971 | + | 0.656398i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1512.00 | − | 2618.86i | −0.0624401 | − | 0.108149i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3768.00 | 0.155049 | 0.0775243 | − | 0.996990i | \(-0.475298\pi\) | ||||
0.0775243 | + | 0.996990i | \(0.475298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1791.00 | − | 3102.10i | −0.0731736 | − | 0.126740i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4941.00 | − | 8558.06i | 0.201155 | − | 0.348410i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10734.0 | + | 18591.8i | −0.433910 | + | 0.751555i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2136.00 | − | 3699.66i | −0.0860413 | − | 0.149028i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39466.0 | 1.58416 | 0.792081 | − | 0.610416i | \(-0.208998\pi\) | ||||
0.792081 | + | 0.610416i | \(0.208998\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4104.00 | −0.164157 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17019.0 | − | 29477.8i | −0.678364 | − | 1.17496i | −0.975473 | − | 0.220117i | \(-0.929356\pi\) |
0.297109 | − | 0.954843i | \(-0.403977\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1682.00 | + | 2913.31i | −0.0668092 | + | 0.115717i | −0.897495 | − | 0.441024i | \(-0.854615\pi\) |
0.830686 | + | 0.556741i | \(0.187949\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6552.00 | + | 11348.4i | −0.258439 | + | 0.447629i | −0.965824 | − | 0.259199i | \(-0.916541\pi\) |
0.707385 | + | 0.706828i | \(0.249875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8118.00 | + | 14060.8i | 0.319099 | + | 0.552695i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24249.0 | 0.949872 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2880.00 | 0.112425 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31372.0 | − | 54337.9i | −1.22044 | − | 2.11386i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4545.00 | − | 7872.17i | 0.176203 | − | 0.305192i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20429.0 | − | 35384.1i | 0.786589 | − | 1.36241i | −0.141457 | − | 0.989944i | \(-0.545179\pi\) |
0.928045 | − | 0.372467i | \(-0.121488\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5607.00 | − | 9711.61i | −0.215153 | − | 0.372656i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37374.0 | 1.42924 | 0.714621 | − | 0.699512i | \(-0.246599\pi\) | ||||
0.714621 | + | 0.699512i | \(0.246599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9788.00 | 0.373038 | 0.186519 | − | 0.982451i | \(-0.440279\pi\) | ||||
0.186519 | + | 0.982451i | \(0.440279\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3564.00 | − | 6173.03i | −0.135370 | − | 0.234468i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25212.0 | − | 43668.5i | 0.954381 | − | 1.65304i | 0.218603 | − | 0.975814i | \(-0.429850\pi\) |
0.735778 | − | 0.677223i | \(-0.236817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1458.00 | + | 2525.33i | −0.0548202 | + | 0.0949514i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7296.00 | − | 12637.0i | −0.273406 | − | 0.473553i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28296.0 | −1.05679 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4464.00 | 0.166163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3024.00 | − | 5237.72i | −0.112187 | − | 0.194313i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22914.0 | + | 39688.2i | −0.847254 | + | 1.46749i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5730.00 | + | 9924.65i | −0.210466 | + | 0.364538i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6206.00 | + | 10749.1i | 0.227196 | + | 0.393515i | 0.956976 | − | 0.290167i | \(-0.0937108\pi\) |
−0.729780 | + | 0.683682i | \(0.760378\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −54.0000 | −0.00197037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6576.00 | 0.239158 | 0.119579 | − | 0.992825i | \(-0.461846\pi\) | ||||
0.119579 | + | 0.992825i | \(0.461846\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1944.00 | − | 3367.11i | −0.0704677 | − | 0.122054i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2286.00 | + | 3959.47i | −0.0825933 | + | 0.143056i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4132.00 | + | 7156.83i | −0.148316 | + | 0.256890i | −0.930605 | − | 0.366025i | \(-0.880718\pi\) |
0.782289 | + | 0.622915i | \(0.214052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1266.00 | − | 2192.78i | −0.0452944 | − | 0.0784522i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −52080.0 | −1.85724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15842.0 | 0.563115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2124.00 | − | 3678.88i | −0.0752549 | − | 0.130345i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19713.0 | − | 34143.9i | 0.696192 | − | 1.20584i | −0.273585 | − | 0.961848i | \(-0.588209\pi\) |
0.969777 | − | 0.243992i | \(-0.0784572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9468.00 | − | 16399.1i | 0.332228 | − | 0.575435i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12312.0 | − | 21325.0i | −0.430637 | − | 0.745885i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4678.00 | 0.163099 | 0.0815494 | − | 0.996669i | \(-0.474013\pi\) | ||||
0.0815494 | + | 0.996669i | \(0.474013\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24846.0 | −0.863492 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8673.00 | − | 15022.1i | −0.300459 | − | 0.520410i | 0.675781 | − | 0.737102i | \(-0.263806\pi\) |
−0.976240 | + | 0.216692i | \(0.930473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4536.00 | + | 7856.58i | −0.156641 | + | 0.271310i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9726.00 | + | 16845.9i | −0.333741 | + | 0.578056i | −0.983242 | − | 0.182304i | \(-0.941644\pi\) |
0.649501 | + | 0.760360i | \(0.274978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27590.0 | − | 47787.3i | −0.943740 | − | 1.63461i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27954.0 | 0.953176 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4458.00 | 0.151531 | 0.0757654 | − | 0.997126i | \(-0.475860\pi\) | ||||
0.0757654 | + | 0.997126i | \(0.475860\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12240.0 | + | 21200.3i | 0.414740 | + | 0.718351i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2916.00 | + | 5050.66i | −0.0984962 | + | 0.170600i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8623.50 | − | 14936.3i | 0.289467 | − | 0.501371i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4374.00 | + | 7575.99i | 0.146366 | + | 0.253513i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16116.0 | 0.537609 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52520.0 | 1.74657 | 0.873283 | − | 0.487213i | \(-0.161987\pi\) | ||||
0.873283 | + | 0.487213i | \(0.161987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12996.0 | + | 22509.7i | 0.430848 | + | 0.746251i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5202.00 | + | 9010.13i | −0.171926 | + | 0.297785i | −0.939093 | − | 0.343663i | \(-0.888332\pi\) |
0.767167 | + | 0.641447i | \(0.221666\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8277.00 | + | 14336.2i | −0.271873 | + | 0.470898i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3783.00 | + | 6552.35i | 0.123878 | + | 0.214563i | 0.921294 | − | 0.388867i | \(-0.127133\pi\) |
−0.797416 | + | 0.603430i | \(0.793800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58968.0 | 1.92505 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16074.0 | −0.523143 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22188.0 | + | 38430.7i | 0.719926 | + | 1.24695i | 0.961029 | + | 0.276449i | \(0.0891576\pi\) |
−0.241103 | + | 0.970500i | \(0.577509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1530.00 | − | 2650.04i | 0.0494922 | − | 0.0857231i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2064.00 | + | 3574.95i | −0.0663614 | + | 0.114941i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13664.0 | + | 23666.7i | 0.437993 | + | 0.758626i | 0.997535 | − | 0.0701759i | \(-0.0223561\pi\) |
−0.559541 | + | 0.828802i | \(0.689023\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4956.00 | 0.158383 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8112.00 | 0.258460 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1387.00 | + | 2402.35i | 0.0440589 | + | 0.0763123i | 0.887214 | − | 0.461358i | \(-0.152638\pi\) |
−0.843155 | + | 0.537671i | \(0.819304\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2403.00 | − | 4162.12i | 0.0761037 | − | 0.131815i |
(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 | 588.4.i.c.373.1 | 2 | ||
3.2 | odd | 2 | 1764.4.k.f.1549.1 | 2 | |||
7.2 | even | 3 | 588.4.a.d.1.1 | 1 | |||
7.3 | odd | 6 | 588.4.i.f.361.1 | 2 | |||
7.4 | even | 3 | inner | 588.4.i.c.361.1 | 2 | ||
7.5 | odd | 6 | 84.4.a.a.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 588.4.i.f.373.1 | 2 | |||
21.2 | odd | 6 | 1764.4.a.j.1.1 | 1 | |||
21.5 | even | 6 | 252.4.a.b.1.1 | 1 | |||
21.11 | odd | 6 | 1764.4.k.f.361.1 | 2 | |||
21.17 | even | 6 | 1764.4.k.l.361.1 | 2 | |||
21.20 | even | 2 | 1764.4.k.l.1549.1 | 2 | |||
28.19 | even | 6 | 336.4.a.k.1.1 | 1 | |||
28.23 | odd | 6 | 2352.4.a.d.1.1 | 1 | |||
35.12 | even | 12 | 2100.4.k.j.1849.2 | 2 | |||
35.19 | odd | 6 | 2100.4.a.l.1.1 | 1 | |||
35.33 | even | 12 | 2100.4.k.j.1849.1 | 2 | |||
56.5 | odd | 6 | 1344.4.a.q.1.1 | 1 | |||
56.19 | even | 6 | 1344.4.a.d.1.1 | 1 | |||
84.47 | odd | 6 | 1008.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.a.a.1.1 | ✓ | 1 | 7.5 | odd | 6 | ||
252.4.a.b.1.1 | 1 | 21.5 | even | 6 | |||
336.4.a.k.1.1 | 1 | 28.19 | even | 6 | |||
588.4.a.d.1.1 | 1 | 7.2 | even | 3 | |||
588.4.i.c.361.1 | 2 | 7.4 | even | 3 | inner | ||
588.4.i.c.373.1 | 2 | 1.1 | even | 1 | trivial | ||
588.4.i.f.361.1 | 2 | 7.3 | odd | 6 | |||
588.4.i.f.373.1 | 2 | 7.6 | odd | 2 | |||
1008.4.a.h.1.1 | 1 | 84.47 | odd | 6 | |||
1344.4.a.d.1.1 | 1 | 56.19 | even | 6 | |||
1344.4.a.q.1.1 | 1 | 56.5 | odd | 6 | |||
1764.4.a.j.1.1 | 1 | 21.2 | odd | 6 | |||
1764.4.k.f.361.1 | 2 | 21.11 | odd | 6 | |||
1764.4.k.f.1549.1 | 2 | 3.2 | odd | 2 | |||
1764.4.k.l.361.1 | 2 | 21.17 | even | 6 | |||
1764.4.k.l.1549.1 | 2 | 21.20 | even | 2 | |||
2100.4.a.l.1.1 | 1 | 35.19 | odd | 6 | |||
2100.4.k.j.1849.1 | 2 | 35.33 | even | 12 | |||
2100.4.k.j.1849.2 | 2 | 35.12 | even | 12 | |||
2352.4.a.d.1.1 | 1 | 28.23 | odd | 6 |