Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,3,Mod(189,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.189");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.g (of order \(2\), degree \(1\), 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: | \(10.3542500457\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20x^{10} + 44x^{8} - 270x^{6} + 36676x^{4} - 71664x^{2} + 687241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 189.10 | ||
Root | \(-1.63363 - 1.34185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.189 |
Dual form | 380.3.g.c.189.9 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.26725 | 1.08908 | 0.544542 | − | 0.838733i | \(-0.316703\pi\) | ||||
0.544542 | + | 0.838733i | \(0.316703\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.26535 | + | 2.60898i | 0.853070 | + | 0.521796i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.30368i | − | 0.900525i | −0.892896 | − | 0.450263i | \(-0.851330\pi\) | ||
0.892896 | − | 0.450263i | \(-0.148670\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.67495 | 0.186105 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.53070 | 0.411882 | 0.205941 | − | 0.978564i | \(-0.433974\pi\) | ||||
0.205941 | + | 0.978564i | \(0.433974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.5357 | 0.887362 | 0.443681 | − | 0.896185i | \(-0.353672\pi\) | ||||
0.443681 | + | 0.896185i | \(0.353672\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.9360 | + | 8.52420i | 0.929066 | + | 0.568280i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.08572i | 0.0638659i | 0.999490 | + | 0.0319330i | \(0.0101663\pi\) | ||||
−0.999490 | + | 0.0319330i | \(0.989834\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.8558 | − | 8.76832i | 0.887145 | − | 0.461491i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 20.5957i | − | 0.980748i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 31.5184i | − | 1.37036i | −0.728372 | − | 0.685182i | \(-0.759722\pi\) | ||
0.728372 | − | 0.685182i | \(-0.240278\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.3865 | + | 22.2564i | 0.455458 | + | 0.890257i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −23.9328 | −0.886400 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38.1324i | 1.31491i | 0.753494 | + | 0.657454i | \(0.228367\pi\) | ||||
−0.753494 | + | 0.657454i | \(0.771633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58.2398i | 1.87870i | 0.342955 | + | 0.939352i | \(0.388572\pi\) | ||||
−0.342955 | + | 0.939352i | \(0.611428\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.8030 | 0.448575 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.4462 | − | 26.8874i | 0.469890 | − | 0.768212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.2691 | −1.08835 | −0.544177 | − | 0.838971i | \(-0.683158\pi\) | ||||
−0.544177 | + | 0.838971i | \(0.683158\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 37.6901 | 0.966413 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 18.0249i | − | 0.439632i | −0.975541 | − | 0.219816i | \(-0.929454\pi\) | ||
0.975541 | − | 0.219816i | \(-0.0705456\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.74764i | − | 0.0638986i | −0.999489 | − | 0.0319493i | \(-0.989828\pi\) | ||
0.999489 | − | 0.0319493i | \(-0.0101715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.14424 | + | 4.36990i | 0.158761 | + | 0.0971090i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 76.1195i | − | 1.61956i | −0.586731 | − | 0.809782i | \(-0.699586\pi\) | ||
0.586731 | − | 0.809782i | \(-0.300414\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.26364 | 0.189054 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.54733i | 0.0695554i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.06781 | 0.152223 | 0.0761115 | − | 0.997099i | \(-0.475750\pi\) | ||||
0.0761115 | + | 0.997099i | \(0.475750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.3251 | + | 11.8205i | 0.351365 | + | 0.214918i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 55.0720 | − | 28.6483i | 0.966176 | − | 0.502602i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 95.3957i | 1.61688i | 0.588581 | + | 0.808438i | \(0.299687\pi\) | ||||
−0.588581 | + | 0.808438i | \(0.700313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.28507 | −0.0702470 | −0.0351235 | − | 0.999383i | \(-0.511182\pi\) | ||||
−0.0351235 | + | 0.999383i | \(0.511182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 10.5583i | − | 0.167593i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 49.2039 | + | 30.0964i | 0.756982 | + | 0.463022i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −70.7364 | −1.05577 | −0.527883 | − | 0.849317i | \(-0.677014\pi\) | ||||
−0.527883 | + | 0.849317i | \(0.677014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 102.979i | − | 1.49244i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 93.3131i | − | 1.31427i | −0.753773 | − | 0.657135i | \(-0.771768\pi\) | ||
0.753773 | − | 0.657135i | \(-0.228232\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.2908i | − | 0.195765i | −0.995198 | − | 0.0978824i | \(-0.968793\pi\) | ||
0.995198 | − | 0.0978824i | \(-0.0312069\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 37.2025 | + | 72.7174i | 0.496033 | + | 0.969565i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 28.5601i | − | 0.370910i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.11815i | − | 0.0774449i | −0.999250 | − | 0.0387224i | \(-0.987671\pi\) | ||
0.999250 | − | 0.0387224i | \(-0.0123288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −93.2691 | −1.15147 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 89.0257i | 1.07260i | 0.844028 | + | 0.536299i | \(0.180178\pi\) | ||||
−0.844028 | + | 0.536299i | \(0.819822\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.83262 | + | 4.63098i | −0.0333250 | + | 0.0544821i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 124.588i | 1.43205i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 92.3366i | − | 1.03749i | −0.854929 | − | 0.518745i | \(-0.826399\pi\) | ||
0.854929 | − | 0.518745i | \(-0.173601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 72.7174i | − | 0.799092i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 190.284i | 2.04607i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 94.7721 | + | 6.57633i | 0.997601 | + | 0.0692245i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −64.6843 | −0.666849 | −0.333424 | − | 0.942777i | \(-0.608204\pi\) | ||||
−0.333424 | + | 0.942777i | \(0.608204\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.58869 | 0.0766535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −155.672 | −1.54131 | −0.770654 | − | 0.637254i | \(-0.780070\pi\) | ||||
−0.770654 | + | 0.637254i | \(0.780070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 130.821 | 1.27010 | 0.635052 | − | 0.772469i | \(-0.280978\pi\) | ||||
0.635052 | + | 0.772469i | \(0.280978\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 53.7338 | − | 87.8480i | 0.511750 | − | 0.836648i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −95.1516 | −0.889268 | −0.444634 | − | 0.895712i | \(-0.646666\pi\) | ||||
−0.444634 | + | 0.895712i | \(0.646666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 155.589i | 1.42742i | 0.700443 | + | 0.713709i | \(0.252986\pi\) | ||||
−0.700443 | + | 0.713709i | \(0.747014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −131.569 | −1.18531 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −174.840 | −1.54725 | −0.773626 | − | 0.633642i | \(-0.781559\pi\) | ||||
−0.773626 | + | 0.633642i | \(0.781559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 82.2308 | − | 134.437i | 0.715050 | − | 1.16902i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.3217 | 0.165143 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.84404 | 0.0575129 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −100.473 | −0.830353 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 58.8919i | − | 0.478796i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.49927 | + | 124.639i | −0.0759941 | + | 0.997108i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 80.8200 | 0.636378 | 0.318189 | − | 0.948027i | \(-0.396925\pi\) | ||||
0.318189 | + | 0.948027i | \(0.396925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.97723i | − | 0.0695910i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −129.957 | −0.992039 | −0.496020 | − | 0.868311i | \(-0.665206\pi\) | ||||
−0.496020 | + | 0.868311i | \(0.665206\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −55.2727 | − | 106.253i | −0.415584 | − | 0.798897i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −102.082 | − | 62.4402i | −0.756162 | − | 0.462520i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 58.8037i | − | 0.429224i | −0.976699 | − | 0.214612i | \(-0.931151\pi\) | ||
0.976699 | − | 0.214612i | \(-0.0688487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.48444 | 0.0178736 | 0.00893682 | − | 0.999960i | \(-0.497155\pi\) | ||||
0.00893682 | + | 0.999960i | \(0.497155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 248.702i | − | 1.76384i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 52.2649 | 0.365489 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −99.4865 | + | 162.648i | −0.686114 | + | 1.12171i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 30.2667 | 0.205896 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −90.8294 | −0.609594 | −0.304797 | − | 0.952417i | \(-0.598589\pi\) | ||||
−0.304797 | + | 0.952417i | \(0.598589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 44.1209i | − | 0.292192i | −0.989270 | − | 0.146096i | \(-0.953329\pi\) | ||
0.989270 | − | 0.146096i | \(-0.0466708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.81853i | 0.0118858i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −151.946 | + | 248.413i | −0.980300 | + | 1.60267i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.36283i | − | 0.0596358i | −0.999555 | − | 0.0298179i | \(-0.990507\pi\) | ||
0.999555 | − | 0.0298179i | \(-0.00949275\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.3596 | 0.165784 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −198.682 | −1.23405 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 35.8739i | − | 0.220085i | −0.993927 | − | 0.110043i | \(-0.964901\pi\) | ||
0.993927 | − | 0.110043i | \(-0.0350987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 63.1399 | + | 38.6206i | 0.382666 | + | 0.234064i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 195.223 | 1.16900 | 0.584501 | − | 0.811393i | \(-0.301290\pi\) | ||||
0.584501 | + | 0.811393i | \(0.301290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.9274 | −0.212588 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 28.2325 | − | 14.6865i | 0.165102 | − | 0.0858859i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −236.304 | −1.36592 | −0.682960 | − | 0.730455i | \(-0.739308\pi\) | ||||
−0.682960 | + | 0.730455i | \(0.739308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 140.297 | − | 71.7766i | 0.801699 | − | 0.410152i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 311.682i | 1.76091i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 125.945i | − | 0.703604i | −0.936074 | − | 0.351802i | \(-0.885569\pi\) | ||
0.936074 | − | 0.351802i | \(-0.114431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.4185i | − | 0.0630856i | −0.999502 | − | 0.0315428i | \(-0.989958\pi\) | ||
0.999502 | − | 0.0315428i | \(-0.0100421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0004 | −0.0765049 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −171.762 | − | 105.061i | −0.928442 | − | 0.567898i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.91908i | 0.0263052i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 150.865i | 0.798226i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 36.3733 | 0.190436 | 0.0952180 | − | 0.995456i | \(-0.469645\pi\) | ||||
0.0952180 | + | 0.995456i | \(0.469645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −150.814 | −0.781422 | −0.390711 | − | 0.920513i | \(-0.627771\pi\) | ||||
−0.390711 | + | 0.920513i | \(0.627771\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 160.762 | + | 98.3326i | 0.824418 | + | 0.504270i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 257.585i | 1.30754i | 0.756695 | + | 0.653768i | \(0.226813\pi\) | ||||
−0.756695 | + | 0.653768i | \(0.773187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 128.758 | 0.647027 | 0.323513 | − | 0.946224i | \(-0.395136\pi\) | ||||
0.323513 | + | 0.946224i | \(0.395136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −231.114 | −1.14982 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 240.374 | 1.18411 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 47.0266 | − | 76.8825i | 0.229398 | − | 0.375037i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 52.7917i | − | 0.255032i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 76.3685 | − | 39.7267i | 0.365399 | − | 0.190080i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 161.636i | 0.766048i | 0.923738 | + | 0.383024i | \(0.125117\pi\) | ||||
−0.923738 | + | 0.383024i | \(0.874883\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 304.878i | − | 1.43135i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.16853 | − | 11.7196i | 0.0333420 | − | 0.0545100i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 367.125 | 1.69182 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 46.6918i | − | 0.213204i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.5246i | 0.0566722i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 386.480 | 1.73310 | 0.866548 | − | 0.499094i | \(-0.166334\pi\) | ||||
0.866548 | + | 0.499094i | \(0.166334\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.0717 | + | 37.2784i | 0.0847632 | + | 0.165682i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −52.4767 | −0.231175 | −0.115587 | − | 0.993297i | \(-0.536875\pi\) | ||||
−0.115587 | + | 0.993297i | \(0.536875\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 394.025 | 1.72063 | 0.860316 | − | 0.509762i | \(-0.170266\pi\) | ||||
0.860316 | + | 0.509762i | \(0.170266\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 93.3131i | − | 0.403953i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 22.2691i | − | 0.0955754i | −0.998858 | − | 0.0477877i | \(-0.984783\pi\) | ||
0.998858 | − | 0.0477877i | \(-0.0152171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 198.594 | − | 324.676i | 0.845081 | − | 1.38160i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 19.9895i | − | 0.0843440i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 83.5976 | 0.349781 | 0.174890 | − | 0.984588i | \(-0.444043\pi\) | ||||
0.174890 | + | 0.984588i | \(0.444043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 214.605i | − | 0.890477i | −0.895412 | − | 0.445238i | \(-0.853119\pi\) | ||
0.895412 | − | 0.445238i | \(-0.146881\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −89.3385 | −0.367648 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 39.5127 | + | 24.1686i | 0.161276 | + | 0.0986475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 194.443 | − | 101.149i | 0.787219 | − | 0.409509i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 290.870i | 1.16815i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.6770 | −0.0983146 | −0.0491573 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491573 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 142.801i | − | 0.564429i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.25490 | + | 15.1306i | −0.0362937 | + | 0.0593357i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 152.548 | 0.593573 | 0.296787 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296787 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 253.843i | 0.980090i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 63.8697i | 0.244712i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 345.570i | 1.31395i | 0.753911 | + | 0.656977i | \(0.228165\pi\) | ||||
−0.753911 | + | 0.656977i | \(0.771835\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.4121 | + | 21.0488i | 0.129857 | + | 0.0794293i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 301.687i | − | 1.12991i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.39433i | 0.00518338i | 0.999997 | + | 0.00259169i | \(0.000824962\pi\) | ||||
−0.999997 | + | 0.00259169i | \(0.999175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 407.864 | 1.50503 | 0.752516 | − | 0.658574i | \(-0.228840\pi\) | ||||
0.752516 | + | 0.658574i | \(0.228840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 237.586i | − | 0.870279i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 51.5887 | + | 100.837i | 0.187595 | + | 0.366681i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 330.614i | − | 1.19355i | −0.802407 | − | 0.596777i | \(-0.796448\pi\) | ||
0.802407 | − | 0.596777i | \(-0.203552\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 97.5487i | 0.349637i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 79.1238i | − | 0.281579i | −0.990040 | − | 0.140790i | \(-0.955036\pi\) | ||
0.990040 | − | 0.140790i | \(-0.0449641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 15.0236i | − | 0.0530870i | −0.999648 | − | 0.0265435i | \(-0.991550\pi\) | ||
0.999648 | − | 0.0265435i | \(-0.00845006\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 309.645 | + | 21.4865i | 1.08647 | + | 0.0753913i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −113.623 | −0.395899 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 287.821 | 0.995921 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −211.340 | −0.726255 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 77.7057 | 0.265207 | 0.132604 | − | 0.991169i | \(-0.457666\pi\) | ||||
0.132604 | + | 0.991169i | \(0.457666\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −248.885 | + | 406.896i | −0.843679 | + | 1.37931i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −108.432 | −0.365092 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 363.587i | − | 1.21601i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3202 | −0.0575423 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −508.620 | −1.67861 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.2773 | − | 11.1796i | −0.0599256 | − | 0.0366546i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −212.669 | −0.692734 | −0.346367 | − | 0.938099i | \(-0.612585\pi\) | ||||
−0.346367 | + | 0.938099i | \(0.612585\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 427.425 | 1.38325 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 104.314 | 0.335415 | 0.167707 | − | 0.985837i | \(-0.446364\pi\) | ||||
0.167707 | + | 0.985837i | \(0.446364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 489.532i | 1.56400i | 0.623279 | + | 0.781999i | \(0.285800\pi\) | ||||
−0.623279 | + | 0.781999i | \(0.714200\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 27.5465 | − | 45.0350i | 0.0874491 | − | 0.142968i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 146.496 | 0.462133 | 0.231067 | − | 0.972938i | \(-0.425778\pi\) | ||||
0.231067 | + | 0.972938i | \(0.425778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 172.766i | 0.541588i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −310.885 | −0.968488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.51995 | + | 18.3006i | 0.0294735 | + | 0.0566584i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 131.351 | + | 256.744i | 0.404157 | + | 0.789980i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 508.347i | 1.55458i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −479.833 | −1.45846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 319.048i | 0.963892i | 0.876201 | + | 0.481946i | \(0.160070\pi\) | ||||
−0.876201 | + | 0.481946i | \(0.839930\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −67.4486 | −0.202548 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −301.716 | − | 184.550i | −0.900644 | − | 0.550895i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −386.447 | −1.14673 | −0.573363 | − | 0.819301i | \(-0.694362\pi\) | ||||
−0.573363 | + | 0.819301i | \(0.694362\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −571.245 | −1.68509 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 263.867i | 0.773805i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 367.275i | − | 1.07077i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 268.669 | − | 439.240i | 0.778750 | − | 1.27316i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 624.138i | − | 1.79867i | −0.437262 | − | 0.899334i | \(-0.644052\pi\) | ||
0.437262 | − | 0.899334i | \(-0.355948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 509.597 | 1.46016 | 0.730081 | − | 0.683360i | \(-0.239482\pi\) | ||||
0.730081 | + | 0.683360i | \(0.239482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −276.082 | −0.786558 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 65.8979i | 0.186680i | 0.995634 | + | 0.0933398i | \(0.0297543\pi\) | ||||
−0.995634 | + | 0.0933398i | \(0.970246\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 243.452 | − | 398.013i | 0.685780 | − | 1.12116i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.3612 | 0.0626364 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −548.958 | −1.52913 | −0.764566 | − | 0.644546i | \(-0.777047\pi\) | ||||
−0.764566 | + | 0.644546i | \(0.777047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 207.233 | − | 295.593i | 0.574053 | − | 0.818818i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −328.270 | −0.904325 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.2845 | − | 60.9554i | 0.102149 | − | 0.167001i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 234.257i | 0.638303i | 0.947704 | + | 0.319151i | \(0.103398\pi\) | ||||
−0.947704 | + | 0.319151i | \(0.896602\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 30.1908i | − | 0.0818178i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 50.8569i | − | 0.137081i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 167.444 | 0.448911 | 0.224455 | − | 0.974484i | \(-0.427940\pi\) | ||||
0.224455 | + | 0.974484i | \(0.427940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.0365 | + | 407.226i | −0.0827641 | + | 1.08594i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 439.884i | 1.16680i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 69.3701i | 0.183034i | 0.995803 | + | 0.0915172i | \(0.0291717\pi\) | ||||
−0.995803 | + | 0.0915172i | \(0.970828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 264.059 | 0.693069 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 547.099 | 1.42846 | 0.714229 | − | 0.699912i | \(-0.246777\pi\) | ||||
0.714229 | + | 0.699912i | \(0.246777\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 74.5127 | − | 121.819i | 0.193539 | − | 0.316413i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4.60215i | − | 0.0118919i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 49.2968 | 0.126727 | 0.0633635 | − | 0.997991i | \(-0.479817\pi\) | ||||
0.0633635 | + | 0.997991i | \(0.479817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.2202 | 0.0875196 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −424.603 | −1.08041 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.9621 | − | 26.0961i | 0.0404104 | − | 0.0660660i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 333.006i | − | 0.838805i | −0.907800 | − | 0.419402i | \(-0.862240\pi\) | ||
0.907800 | − | 0.419402i | \(-0.137760\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −180.590 | − | 347.156i | −0.452606 | − | 0.870066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 338.509i | − | 0.844161i | −0.906558 | − | 0.422081i | \(-0.861300\pi\) | ||
0.906558 | − | 0.422081i | \(-0.138700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 671.838i | 1.66709i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −397.825 | − | 243.337i | −0.982285 | − | 0.600832i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −182.447 | −0.448273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 162.742i | − | 0.397903i | −0.980009 | − | 0.198951i | \(-0.936246\pi\) | ||
0.980009 | − | 0.198951i | \(-0.0637536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 192.127i | − | 0.467461i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 601.344 | 1.45604 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −232.266 | + | 379.726i | −0.559677 | + | 0.915002i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.11728 | 0.0194659 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −240.614 | −0.574257 | −0.287128 | − | 0.957892i | \(-0.592701\pi\) | ||||
−0.287128 | + | 0.957892i | \(0.592701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 753.729i | 1.79033i | 0.445735 | + | 0.895165i | \(0.352943\pi\) | ||||
−0.445735 | + | 0.895165i | \(0.647057\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 127.496i | − | 0.301409i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.1643 | + | 12.3625i | −0.0568571 | + | 0.0290883i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.0117i | 0.0632592i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 170.763 | 0.398048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 198.792i | − | 0.461235i | −0.973045 | − | 0.230617i | \(-0.925925\pi\) | ||
0.973045 | − | 0.230617i | \(-0.0740745\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 592.322 | 1.36795 | 0.683975 | − | 0.729506i | \(-0.260250\pi\) | ||||
0.683975 | + | 0.729506i | \(0.260250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −325.048 | + | 531.412i | −0.747236 | + | 1.22164i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −276.363 | − | 531.266i | −0.632410 | − | 1.21571i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 837.288i | − | 1.90726i | −0.300977 | − | 0.953631i | \(-0.597313\pi\) | ||
0.300977 | − | 0.953631i | \(-0.402687\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.5161 | 0.0351839 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 736.917i | 1.66347i | 0.555174 | + | 0.831734i | \(0.312652\pi\) | ||||
−0.555174 | + | 0.831734i | \(0.687348\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 240.904 | − | 393.848i | 0.541358 | − | 0.885052i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −296.763 | −0.663899 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 369.746i | 0.823489i | 0.911299 | + | 0.411744i | \(0.135080\pi\) | ||||
−0.911299 | + | 0.411744i | \(0.864920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 81.6655i | − | 0.181076i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 144.154i | − | 0.318221i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 189.718 | − | 310.165i | 0.416963 | − | 0.681682i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 799.508i | 1.74947i | 0.484601 | + | 0.874735i | \(0.338965\pi\) | ||||
−0.484601 | + | 0.874735i | \(0.661035\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 25.9843i | − | 0.0566108i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 721.581 | 1.56525 | 0.782625 | − | 0.622493i | \(-0.213880\pi\) | ||||
0.782625 | + | 0.622493i | \(0.213880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 850.242i | − | 1.83638i | −0.396145 | − | 0.918188i | \(-0.629652\pi\) | ||
0.396145 | − | 0.918188i | \(-0.370348\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −496.448 | + | 811.630i | −1.06763 | + | 1.74544i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 125.893i | − | 0.269579i | −0.990874 | − | 0.134789i | \(-0.956964\pi\) | ||
0.990874 | − | 0.134789i | \(-0.0430358\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 445.899i | 0.950745i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 30.5907i | − | 0.0649485i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.4487i | − | 0.0263187i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 387.079 | + | 275.309i | 0.814903 | + | 0.579597i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.5132 | 0.0283295 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −549.803 | −1.14782 | −0.573908 | − | 0.818920i | \(-0.694573\pi\) | ||||
−0.573908 | + | 0.818920i | \(0.694573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −464.532 | −0.965764 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −649.144 | −1.34398 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −275.901 | − | 168.760i | −0.568869 | − | 0.347959i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −165.606 | −0.340054 | −0.170027 | − | 0.985439i | \(-0.554385\pi\) | ||||
−0.170027 | + | 0.985439i | \(0.554385\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 117.209i | − | 0.239692i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −344.284 | −0.701190 | −0.350595 | − | 0.936527i | \(-0.614021\pi\) | ||||
−0.350595 | + | 0.936527i | \(0.614021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.4011 | −0.0839779 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32.3685 | + | 19.7987i | 0.0653908 | + | 0.0399975i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −588.216 | −1.18353 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 136.376 | 0.273298 | 0.136649 | − | 0.990620i | \(-0.456367\pi\) | ||||
0.136649 | + | 0.990620i | \(0.456367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 637.844 | 1.27314 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 175.677i | 0.349258i | 0.984634 | + | 0.174629i | \(0.0558726\pi\) | ||||
−0.984634 | + | 0.174629i | \(0.944127\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −663.996 | − | 406.145i | −1.31484 | − | 0.804248i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −117.384 | −0.231527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 374.070i | − | 0.734912i | −0.930041 | − | 0.367456i | \(-0.880229\pi\) | ||
0.930041 | − | 0.367456i | \(-0.119771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −90.0848 | −0.176291 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −403.406 | + | 209.851i | −0.786366 | + | 0.409065i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 557.997 | + | 341.309i | 1.08349 | + | 0.662735i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 344.875i | − | 0.667069i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −772.066 | −1.48760 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 160.601i | 0.308255i | 0.988051 | + | 0.154127i | \(0.0492566\pi\) | ||||
−0.988051 | + | 0.154127i | \(0.950743\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 671.370 | 1.28369 | 0.641845 | − | 0.766834i | \(-0.278169\pi\) | ||||
0.641845 | + | 0.766834i | \(0.278169\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 458.387 | − | 234.512i | 0.873118 | − | 0.446690i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −63.2322 | −0.119985 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −464.409 | −0.877900 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 159.783i | 0.300909i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 207.930i | − | 0.390112i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −405.855 | − | 248.249i | −0.758608 | − | 0.464016i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 411.495i | − | 0.766284i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.9708 | 0.0778680 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 59.9401 | 0.110795 | 0.0553975 | − | 0.998464i | \(-0.482357\pi\) | ||||
0.0553975 | + | 0.998464i | \(0.482357\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 37.3071i | − | 0.0687056i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −405.927 | + | 663.640i | −0.744820 | + | 1.21769i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −754.492 | −1.37933 | −0.689664 | − | 0.724130i | \(-0.742242\pi\) | ||||
−0.689664 | + | 0.724130i | \(0.742242\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.17726 | −0.0130733 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 334.357 | + | 642.750i | 0.606818 | + | 1.16652i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.5668 | −0.0697411 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −561.189 | − | 343.261i | −1.01115 | − | 0.618489i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 758.951i | 1.36257i | 0.732018 | + | 0.681285i | \(0.238579\pi\) | ||||
−0.732018 | + | 0.681285i | \(0.761421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31.6960i | − | 0.0567012i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0719i | 0.0286486i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 200.922 | 0.356877 | 0.178438 | − | 0.983951i | \(-0.442895\pi\) | ||||
0.178438 | + | 0.983951i | \(0.442895\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −745.752 | − | 456.153i | −1.31992 | − | 0.807350i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 587.938i | 1.03693i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 353.921i | − | 0.622006i | −0.950409 | − | 0.311003i | \(-0.899335\pi\) | ||
0.950409 | − | 0.311003i | \(-0.100665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 820.990 | 1.43781 | 0.718905 | − | 0.695108i | \(-0.244643\pi\) | ||||
0.718905 | + | 0.695108i | \(0.244643\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 118.841 | 0.207401 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 701.487 | − | 358.883i | 1.21998 | − | 0.624144i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 549.666i | − | 0.952627i | −0.879276 | − | 0.476314i | \(-0.841973\pi\) | ||
0.879276 | − | 0.476314i | \(-0.158027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −492.749 | −0.851035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 561.189 | 0.965903 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.5529 | 0.0626979 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 82.4139 | + | 50.4099i | 0.140878 | + | 0.0861708i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 206.107i | 0.351120i | 0.984469 | + | 0.175560i | \(0.0561736\pi\) | ||||
−0.984469 | + | 0.175560i | \(0.943826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 510.666 | + | 981.676i | 0.867004 | + | 1.66668i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 841.594i | 1.42402i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 332.865i | − | 0.561324i | −0.959807 | − | 0.280662i | \(-0.909446\pi\) | ||
0.959807 | − | 0.280662i | \(-0.0905540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.1922 | + | 17.8559i | 0.0490626 | + | 0.0300100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 420.686 | 0.704667 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 77.8882i | − | 0.130030i | −0.997884 | − | 0.0650152i | \(-0.979290\pi\) | ||
0.997884 | − | 0.0650152i | \(-0.0207096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 454.271i | − | 0.755859i | −0.925834 | − | 0.377929i | \(-0.876636\pi\) | ||
0.925834 | − | 0.377929i | \(-0.123364\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −118.480 | −0.196484 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −428.552 | − | 262.131i | −0.708350 | − | 0.433275i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 874.377 | 1.44049 | 0.720245 | − | 0.693720i | \(-0.244029\pi\) | ||||
0.720245 | + | 0.693720i | \(0.244029\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 785.363 | 1.28959 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 878.092i | − | 1.43714i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 980.965i | − | 1.60027i | −0.599821 | − | 0.800134i | \(-0.704761\pi\) | ||
0.599821 | − | 0.800134i | \(-0.295239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 153.648 | − | 251.195i | 0.249834 | − | 0.408447i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 806.424i | − | 1.30701i | −0.756923 | − | 0.653504i | \(-0.773298\pi\) | ||
0.756923 | − | 0.653504i | \(-0.226702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 221.549 | 0.357915 | 0.178957 | − | 0.983857i | \(-0.442728\pi\) | ||||
0.178957 | + | 0.983857i | \(0.442728\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 754.323i | 1.21469i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −582.060 | −0.934286 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −365.697 | + | 506.844i | −0.585115 | + | 0.810950i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 249.515 | − | 129.797i | 0.397951 | − | 0.207013i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 43.7210i | − | 0.0695087i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 590.815 | 0.936316 | 0.468158 | − | 0.883645i | \(-0.344918\pi\) | ||||
0.468158 | + | 0.883645i | \(0.344918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 528.107i | 0.834292i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 344.726 | + | 210.858i | 0.542875 | + | 0.332059i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 106.863 | 0.167759 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 156.295i | − | 0.244592i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1110.32i | 1.73217i | 0.499896 | + | 0.866086i | \(0.333372\pi\) | ||||
−0.499896 | + | 0.866086i | \(0.666628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 430.490i | 0.669503i | 0.942306 | + | 0.334752i | \(0.108652\pi\) | ||||
−0.942306 | + | 0.334752i | \(0.891348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.4214 | − | 38.2911i | 0.0363123 | − | 0.0593660i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 102.290i | − | 0.158099i | −0.996871 | − | 0.0790497i | \(-0.974811\pi\) | ||
0.996871 | − | 0.0790497i | \(-0.0251886\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 432.210i | 0.665962i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1199.49 | 1.84254 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 71.2294i | − | 0.109080i | −0.998512 | − | 0.0545401i | \(-0.982631\pi\) | ||
0.998512 | − | 0.0545401i | \(-0.0173693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −554.313 | − | 339.055i | −0.846279 | − | 0.517642i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 23.9364i | − | 0.0364329i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1003.48i | − | 1.52273i | −0.648325 | − | 0.761364i | \(-0.724530\pi\) | ||
0.648325 | − | 0.761364i | \(-0.275470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 620.531i | 0.938775i | 0.882992 | + | 0.469388i | \(0.155525\pi\) | ||||
−0.882992 | + | 0.469388i | \(0.844475\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 40.9209i | 0.0617208i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41.4550 | − | 597.413i | 0.0623384 | − | 0.898365i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1201.87 | 1.80190 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1262.73 | 1.88749 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.4144 | −0.0289335 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −973.102 | −1.44592 | −0.722959 | − | 0.690891i | \(-0.757218\pi\) | ||||
−0.722959 | + | 0.690891i | \(0.757218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −272.510 | − | 532.659i | −0.403718 | − | 0.789124i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 518.327 | 0.765623 | 0.382811 | − | 0.923827i | \(-0.374956\pi\) | ||||
0.382811 | + | 0.923827i | \(0.374956\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 407.749i | 0.600514i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −171.455 | −0.251769 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 423.707 | 0.620362 | 0.310181 | − | 0.950678i | \(-0.399610\pi\) | ||||
0.310181 | + | 0.950678i | \(0.399610\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 153.418 | − | 250.818i | 0.223967 | − | 0.366158i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1287.38 | 1.87391 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 93.0680 | 0.135077 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 789.329 | 1.14230 | 0.571150 | − | 0.820846i | \(-0.306498\pi\) | ||||
0.571150 | + | 0.820846i | \(0.306498\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 47.8367i | − | 0.0690284i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.5970 | + | 6.48184i | 0.0152475 | + | 0.00932639i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.5700 | 0.0280775 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 72.7587i | − | 0.104090i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 307.669 | 0.438900 | 0.219450 | − | 0.975624i | \(-0.429574\pi\) | ||||
0.219450 | + | 0.975624i | \(0.429574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −678.766 | + | 353.092i | −0.965527 | + | 0.502265i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 648.857 | − | 1060.80i | 0.920365 | − | 1.50468i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 981.307i | 1.38799i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −767.955 | −1.08315 | −0.541576 | − | 0.840651i | \(-0.682172\pi\) | ||||
−0.541576 | + | 0.840651i | \(0.682172\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10.2476i | − | 0.0144129i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1835.63 | 2.57451 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 222.928 | + | 136.358i | 0.311788 | + | 0.190710i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 273.134 | 0.380941 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1329.40 | −1.84895 | −0.924476 | − | 0.381239i | \(-0.875497\pi\) | ||||
−0.924476 | + | 0.381239i | \(0.875497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 824.652i | − | 1.14376i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 701.169i | − | 0.969804i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −848.690 | + | 434.193i | −1.17061 | + | 0.598886i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1117.94i | − | 1.53775i | −0.639399 | − | 0.768875i | \(-0.720817\pi\) | ||
0.639399 | − | 0.768875i | \(-0.279183\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 547.530 | 0.751070 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.98317 | 0.00408094 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1173.92i | 1.60153i | 0.598976 | + | 0.800767i | \(0.295575\pi\) | ||||
−0.598976 | + | 0.800767i | \(0.704425\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 129.098 | + | 78.9651i | 0.175644 | + | 0.107436i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −320.486 | −0.434852 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −415.270 | −0.561935 | −0.280968 | − | 0.959717i | \(-0.590655\pi\) | ||||
−0.280968 | + | 0.959717i | \(0.590655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 635.295 | − | 330.479i | 0.857348 | − | 0.445990i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1113.69 | −1.49892 | −0.749458 | − | 0.662052i | \(-0.769686\pi\) | ||||
−0.749458 | + | 0.662052i | \(0.769686\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −387.420 | − | 236.972i | −0.520026 | − | 0.318083i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 149.113i | 0.199616i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 599.805i | 0.800808i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 434.422i | 0.578458i | 0.957260 | + | 0.289229i | \(0.0933989\pi\) | ||||
−0.957260 | + | 0.289229i | \(0.906601\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −80.6259 | −0.107073 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 115.111 | − | 188.191i | 0.152464 | − | 0.249260i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 90.2103i | − | 0.119168i | −0.998223 | − | 0.0595841i | \(-0.981023\pi\) | ||
0.998223 | − | 0.0595841i | \(-0.0189774\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 466.566i | − | 0.614711i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 846.768 | 1.11270 | 0.556352 | − | 0.830947i | \(-0.312201\pi\) | ||||
0.556352 | + | 0.830947i | \(0.312201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 980.780 | 1.28543 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.74450 | + | 7.75665i | −0.00620195 | + | 0.0101394i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1100.46i | 1.43475i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 154.558 | 0.200986 | 0.100493 | − | 0.994938i | \(-0.467958\pi\) | ||||
0.100493 | + | 0.994938i | \(0.467958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 498.414 | 0.646452 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1094.68 | −1.41615 | −0.708076 | − | 0.706137i | \(-0.750436\pi\) | ||||
−0.708076 | + | 0.706137i | \(0.750436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1296.21 | + | 663.146i | −1.67253 | + | 0.855672i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 829.370i | 1.06740i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −158.048 | − | 303.823i | −0.202886 | − | 0.390017i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 422.774i | − | 0.541324i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 912.614i | − | 1.16554i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.4274 | − | 39.9358i | 0.0311177 | − | 0.0508736i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1085.31 | −1.37905 | −0.689524 | − | 0.724262i | \(-0.742180\pi\) | ||||
−0.689524 | + | 0.724262i | \(0.742180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1129.06i | 1.43101i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1102.13i | 1.39334i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.4313 | −0.0623345 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 112.433 | + | 68.7716i | 0.141425 | + | 0.0865052i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 788.528 | 0.989370 | 0.494685 | − | 0.869072i | \(-0.335283\pi\) | ||||
0.494685 | + | 0.869072i | \(0.335283\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 82.6445 | 0.103435 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 154.659i | − | 0.193082i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 64.7475i | − | 0.0806320i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −847.448 | − | 518.357i | −1.05273 | − | 0.643921i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.55563i | 0.00564514i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 159.009 | 0.196550 | 0.0982752 | − | 0.995159i | \(-0.468667\pi\) | ||||
0.0982752 | + | 0.995159i | \(0.468667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 948.179i | 1.16915i | 0.811340 | + | 0.584574i | \(0.198738\pi\) | ||||
−0.811340 | + | 0.584574i | \(0.801262\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1332.59 | 1.63911 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 93.5943 | − | 153.015i | 0.114840 | − | 0.187748i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0922 | − | 46.3135i | −0.0294886 | − | 0.0566873i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 121.798i | − | 0.148715i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 352.733 | 0.429638 | 0.214819 | − | 0.976654i | \(-0.431084\pi\) | ||||
0.214819 | + | 0.976654i | \(0.431084\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 993.008i | − | 1.20657i | −0.797525 | − | 0.603286i | \(-0.793858\pi\) | ||
0.797525 | − | 0.603286i | \(-0.206142\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 168.553 | + | 329.461i | 0.204307 | + | 0.399347i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1388.92 | −1.67947 | −0.839737 | − | 0.542994i | \(-0.817291\pi\) | ||||
−0.839737 | + | 0.542994i | \(0.817291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1346.99i | − | 1.62483i | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||
0.583077 | − | 0.812417i | \(-0.301849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1080.20i | − | 1.29988i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0577i | 0.0120741i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 832.696 | + | 509.333i | 0.997241 | + | 0.609980i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1393.84i | − | 1.66528i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 23.1544i | − | 0.0275976i | −0.999905 | − | 0.0137988i | \(-0.995608\pi\) | ||
0.999905 | − | 0.0137988i | \(-0.00439244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −613.077 | −0.728986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 258.518i | − | 0.306664i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −153.243 | − | 93.7339i | −0.181353 | − | 0.110928i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 633.348i | 0.747754i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 49.0860i | − | 0.0578163i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1269.22i | 1.49144i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1344.49i | 1.57619i | 0.615551 | + | 0.788097i | \(0.288933\pi\) | ||||
−0.615551 | + | 0.788097i | \(0.711067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 158.738 | + | 11.0150i | 0.185659 | + | 0.0128830i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 612.032 | 0.714156 | 0.357078 | − | 0.934074i | \(-0.383773\pi\) | ||||
0.357078 | + | 0.934074i | \(0.383773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 405.145 | 0.471647 | 0.235824 | − | 0.971796i | \(-0.424221\pi\) | ||||
0.235824 | + | 0.971796i | \(0.424221\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −371.236 | −0.431168 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1715.67 | −1.98802 | −0.994012 | − | 0.109267i | \(-0.965150\pi\) | ||||
−0.994012 | + | 0.109267i | \(0.965150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1007.92 | − | 616.513i | −1.16523 | − | 0.712732i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 940.385 | 1.08464 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 27.7195i | − | 0.0318982i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −815.994 | −0.936848 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −108.343 | −0.124104 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 785.681 | + | 59.8803i | 0.897921 | + | 0.0684347i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −806.571 | −0.919693 | −0.459847 | − | 0.887998i | \(-0.652096\pi\) | ||||
−0.459847 | + | 0.887998i | \(0.652096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 253.884 | 0.288833 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −762.909 | −0.865958 | −0.432979 | − | 0.901404i | \(-0.642538\pi\) | ||||
−0.432979 | + | 0.901404i | \(0.642538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 292.155i | 0.330866i | 0.986221 | + | 0.165433i | \(0.0529022\pi\) | ||||
−0.986221 | + | 0.165433i | \(0.947098\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −813.171 | + | 1329.43i | −0.918838 | + | 1.50218i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.76046 | −0.00762171 | −0.00381086 | − | 0.999993i | \(-0.501213\pi\) | ||||
−0.00381086 | + | 0.999993i | \(0.501213\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 509.463i | − | 0.573074i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −422.575 | −0.474270 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −667.440 | − | 1283.05i | −0.747413 | − | 1.43679i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 328.588 | − | 537.200i | 0.367138 | − | 0.600224i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1187.93i | − | 1.32434i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2220.82 | −2.47032 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.75940i | 0.00972186i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −56.5896 | −0.0626684 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.7906 | − | 48.7039i | 0.0329178 | − | 0.0538165i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −123.248 | −0.135885 | −0.0679425 | − | 0.997689i | \(-0.521643\pi\) | ||||
−0.0679425 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −260.743 | −0.286846 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 102.149i | − | 0.112129i | −0.998427 | − | 0.0560645i | \(-0.982145\pi\) | ||
0.998427 | − | 0.0560645i | \(-0.0178552\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 403.349i | 0.441784i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −59.7166 | − | 36.5267i | −0.0652641 | − | 0.0399199i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 819.208i | 0.893357i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 793.186 | 0.863096 | 0.431548 | − | 0.902090i | \(-0.357967\pi\) | ||||
0.431548 | + | 0.902090i | \(0.357967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −694.844 | −0.754446 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1076.43i | − | 1.16623i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −458.522 | − | 896.246i | −0.495700 | − | 0.968914i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 219.118 | 0.236373 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −527.324 | −0.567625 | −0.283813 | − | 0.958880i | \(-0.591599\pi\) | ||||
−0.283813 | + | 0.958880i | \(0.591599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 156.146 | − | 81.2266i | 0.167718 | − | 0.0872466i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 340.820 | 0.365295 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.8338 | + | 20.9816i | −0.0137260 | + | 0.0224402i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1358.67i | 1.45002i | 0.688736 | + | 0.725012i | \(0.258166\pi\) | ||||
−0.688736 | + | 0.725012i | \(0.741834\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1599.42i | 1.70333i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 767.460i | − | 0.815579i | −0.913076 | − | 0.407790i | \(-0.866300\pi\) | ||
0.913076 | − | 0.407790i | \(-0.133700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −568.116 | −0.602456 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −393.603 | + | 643.491i | −0.416511 | + | 0.680943i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 588.458i | − | 0.621392i | −0.950509 | − | 0.310696i | \(-0.899438\pi\) | ||
0.950509 | − | 0.310696i | \(-0.100562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 164.855i | − | 0.173714i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 478.641 | 0.503302 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1523.39 | 1.59852 | 0.799259 | − | 0.600987i | \(-0.205226\pi\) | ||||
0.799259 | + | 0.600987i | \(0.205226\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 155.145 | + | 94.8971i | 0.162455 | + | 0.0993687i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 564.472i | 0.589835i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −370.679 | −0.386527 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2430.88 | −2.52953 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −159.374 | −0.165497 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −643.277 | − | 393.472i | −0.666608 | − | 0.407743i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3510i | 0.0189772i | 0.999955 | + | 0.00948861i | \(0.00302036\pi\) | ||||
−0.999955 | + | 0.00948861i | \(0.996980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.1041 | + | 59.7929i | 0.0320992 | + | 0.0617057i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1560.15i | − | 1.60675i | −0.595476 | − | 0.803373i | \(-0.703036\pi\) | ||
0.595476 | − | 0.803373i | \(-0.296964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15.6611i | − | 0.0160957i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 429.157 | + | 838.847i | 0.440161 | + | 0.860356i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 577.097 | 0.590683 | 0.295341 | − | 0.955392i | \(-0.404567\pi\) | ||||
0.295341 | + | 0.955392i | \(0.404567\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 418.350i | − | 0.427324i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 260.603i | 0.265650i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1162.84 | 1.18295 | 0.591474 | − | 0.806324i | \(-0.298546\pi\) | ||||
0.591474 | + | 0.806324i | \(0.298546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −672.033 | + | 1098.69i | −0.682267 | + | 1.11542i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1567.74 | −1.58838 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −86.6012 | −0.0875644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 469.236i | − | 0.473497i | −0.971571 | − | 0.236749i | \(-0.923918\pi\) | ||
0.971571 | − | 0.236749i | \(-0.0760818\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1042.41i | 1.04976i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 549.200 | + | 335.928i | 0.551959 | + | 0.337616i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1618.73i | 1.62360i | 0.583933 | + | 0.811802i | \(0.301513\pi\) | ||||
−0.583933 | + | 0.811802i | \(0.698487\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 963.752 | 0.964717 |
(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 | 380.3.g.c.189.10 | yes | 12 | |
3.2 | odd | 2 | 3420.3.h.e.2089.2 | 12 | |||
5.2 | odd | 4 | 1900.3.e.e.1101.4 | 12 | |||
5.3 | odd | 4 | 1900.3.e.e.1101.9 | 12 | |||
5.4 | even | 2 | inner | 380.3.g.c.189.3 | ✓ | 12 | |
15.14 | odd | 2 | 3420.3.h.e.2089.3 | 12 | |||
19.18 | odd | 2 | inner | 380.3.g.c.189.4 | yes | 12 | |
57.56 | even | 2 | 3420.3.h.e.2089.1 | 12 | |||
95.18 | even | 4 | 1900.3.e.e.1101.3 | 12 | |||
95.37 | even | 4 | 1900.3.e.e.1101.10 | 12 | |||
95.94 | odd | 2 | inner | 380.3.g.c.189.9 | yes | 12 | |
285.284 | even | 2 | 3420.3.h.e.2089.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.g.c.189.3 | ✓ | 12 | 5.4 | even | 2 | inner | |
380.3.g.c.189.4 | yes | 12 | 19.18 | odd | 2 | inner | |
380.3.g.c.189.9 | yes | 12 | 95.94 | odd | 2 | inner | |
380.3.g.c.189.10 | yes | 12 | 1.1 | even | 1 | trivial | |
1900.3.e.e.1101.3 | 12 | 95.18 | even | 4 | |||
1900.3.e.e.1101.4 | 12 | 5.2 | odd | 4 | |||
1900.3.e.e.1101.9 | 12 | 5.3 | odd | 4 | |||
1900.3.e.e.1101.10 | 12 | 95.37 | even | 4 | |||
3420.3.h.e.2089.1 | 12 | 57.56 | even | 2 | |||
3420.3.h.e.2089.2 | 12 | 3.2 | odd | 2 | |||
3420.3.h.e.2089.3 | 12 | 15.14 | odd | 2 | |||
3420.3.h.e.2089.4 | 12 | 285.284 | even | 2 |