Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), 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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.1 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1057 |
Dual form | 1200.3.bg.h.193.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949 | + | 2.44949i | 0.349927 | + | 0.349927i | 0.860082 | − | 0.510155i | \(-0.170412\pi\) |
−0.510155 | + | 0.860082i | \(0.670412\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.00000 | −0.545455 | −0.272727 | − | 0.962091i | \(-0.587926\pi\) | ||||
−0.272727 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.2474 | − | 12.2474i | 0.942111 | − | 0.942111i | −0.0563023 | − | 0.998414i | \(-0.517931\pi\) |
0.998414 | + | 0.0563023i | \(0.0179311\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.6969 | − | 14.6969i | −0.864526 | − | 0.864526i | 0.127334 | − | 0.991860i | \(-0.459358\pi\) |
−0.991860 | + | 0.127334i | \(0.959358\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.0000i | 0.526316i | 0.964753 | + | 0.263158i | \(0.0847640\pi\) | ||||
−0.964753 | + | 0.263158i | \(0.915236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | −0.285714 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −29.3939 | + | 29.3939i | −1.27799 | + | 1.27799i | −0.336206 | + | 0.941788i | \(0.609144\pi\) |
−0.941788 | + | 0.336206i | \(0.890856\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 48.0000i | 1.65517i | 0.561339 | + | 0.827586i | \(0.310287\pi\) | ||||
−0.561339 | + | 0.827586i | \(0.689713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.0000 | 0.838710 | 0.419355 | − | 0.907822i | \(-0.362256\pi\) | ||||
0.419355 | + | 0.907822i | \(0.362256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.34847 | − | 7.34847i | 0.222681 | − | 0.222681i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −31.8434 | − | 31.8434i | −0.860632 | − | 0.860632i | 0.130780 | − | 0.991411i | \(-0.458252\pi\) |
−0.991411 | + | 0.130780i | \(0.958252\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.0000i | 0.769231i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 30.0000 | 0.731707 | 0.365854 | − | 0.930672i | \(-0.380777\pi\) | ||||
0.365854 | + | 0.930672i | \(0.380777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −29.3939 | + | 29.3939i | −0.683579 | + | 0.683579i | −0.960805 | − | 0.277226i | \(-0.910585\pi\) |
0.277226 | + | 0.960805i | \(0.410585\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −14.6969 | − | 14.6969i | −0.312701 | − | 0.312701i | 0.533254 | − | 0.845955i | \(-0.320969\pi\) |
−0.845955 | + | 0.533254i | \(0.820969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 37.0000i | − | 0.755102i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 36.0000 | 0.705882 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.6969 | + | 14.6969i | −0.277301 | + | 0.277301i | −0.832031 | − | 0.554730i | \(-0.812822\pi\) |
0.554730 | + | 0.832031i | \(0.312822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.2474 | − | 12.2474i | −0.214868 | − | 0.214868i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 78.0000i | − | 1.32203i | −0.750371 | − | 0.661017i | \(-0.770125\pi\) | ||
0.750371 | − | 0.661017i | \(-0.229875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.0327869 | 0.0163934 | − | 0.999866i | \(-0.494782\pi\) | ||||
0.0163934 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.34847 | − | 7.34847i | 0.116642 | − | 0.116642i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.6867 | − | 63.6867i | −0.950548 | − | 0.950548i | 0.0482853 | − | 0.998834i | \(-0.484624\pi\) |
−0.998834 | + | 0.0482853i | \(0.984624\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 72.0000i | − | 1.04348i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.000 | −1.69014 | −0.845070 | − | 0.534655i | \(-0.820442\pi\) | ||||
−0.845070 | + | 0.534655i | \(0.820442\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −83.2827 | + | 83.2827i | −1.14086 | + | 1.14086i | −0.152565 | + | 0.988293i | \(0.548753\pi\) |
−0.988293 | + | 0.152565i | \(0.951247\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.6969 | − | 14.6969i | −0.190869 | − | 0.190869i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.0000i | 0.936709i | 0.883541 | + | 0.468354i | \(0.155153\pi\) | ||||
−0.883541 | + | 0.468354i | \(0.844847\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 44.0908 | − | 44.0908i | 0.531215 | − | 0.531215i | −0.389719 | − | 0.920934i | \(-0.627428\pi\) |
0.920934 | + | 0.389719i | \(0.127428\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −58.7878 | − | 58.7878i | −0.675721 | − | 0.675721i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 150.000i | 1.68539i | 0.538389 | + | 0.842697i | \(0.319033\pi\) | ||||
−0.538389 | + | 0.842697i | \(0.680967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 60.0000 | 0.659341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −31.8434 | + | 31.8434i | −0.342402 | + | 0.342402i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89898 | − | 4.89898i | −0.0505049 | − | 0.0505049i | 0.681403 | − | 0.731908i | \(-0.261370\pi\) |
−0.731908 | + | 0.681403i | \(0.761370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.0000i | 0.181818i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | −0.118812 | −0.0594059 | − | 0.998234i | \(-0.518921\pi\) | ||||
−0.0594059 | + | 0.998234i | \(0.518921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41.6413 | − | 41.6413i | 0.404285 | − | 0.404285i | −0.475455 | − | 0.879740i | \(-0.657717\pi\) |
0.879740 | + | 0.475455i | \(0.157717\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −102.879 | − | 102.879i | −0.961482 | − | 0.961482i | 0.0378032 | − | 0.999285i | \(-0.487964\pi\) |
−0.999285 | + | 0.0378032i | \(0.987964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 74.0000i | − | 0.678899i | −0.940624 | − | 0.339450i | \(-0.889759\pi\) | ||
0.940624 | − | 0.339450i | \(-0.110241\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 78.0000 | 0.702703 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −132.272 | + | 132.272i | −1.17055 | + | 1.17055i | −0.188475 | + | 0.982078i | \(0.560354\pi\) |
−0.982078 | + | 0.188475i | \(0.939646\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −36.7423 | − | 36.7423i | −0.314037 | − | 0.314037i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 72.0000i | − | 0.605042i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.0000 | −0.702479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −36.7423 | + | 36.7423i | −0.298718 | + | 0.298718i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −95.5301 | − | 95.5301i | −0.752206 | − | 0.752206i | 0.222685 | − | 0.974890i | \(-0.428518\pi\) |
−0.974890 | + | 0.222685i | \(0.928518\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 72.0000i | − | 0.558140i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −102.000 | −0.778626 | −0.389313 | − | 0.921106i | \(-0.627288\pi\) | ||||
−0.389313 | + | 0.921106i | \(0.627288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.4949 | + | 24.4949i | −0.184172 | + | 0.184172i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −44.0908 | − | 44.0908i | −0.321831 | − | 0.321831i | 0.527638 | − | 0.849469i | \(-0.323078\pi\) |
−0.849469 | + | 0.527638i | \(0.823078\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 122.000i | − | 0.877698i | −0.898561 | − | 0.438849i | \(-0.855386\pi\) | ||
0.898561 | − | 0.438849i | \(-0.144614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.0000 | 0.255319 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −73.4847 | + | 73.4847i | −0.513879 | + | 0.513879i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 45.3156 | + | 45.3156i | 0.308269 | + | 0.308269i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 36.0000i | 0.241611i | 0.992676 | + | 0.120805i | \(0.0385477\pi\) | ||||
−0.992676 | + | 0.120805i | \(0.961452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −70.0000 | −0.463576 | −0.231788 | − | 0.972766i | \(-0.574458\pi\) | ||||
−0.231788 | + | 0.972766i | \(0.574458\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −44.0908 | + | 44.0908i | −0.288175 | + | 0.288175i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −139.621 | − | 139.621i | −0.889305 | − | 0.889305i | 0.105151 | − | 0.994456i | \(-0.466467\pi\) |
−0.994456 | + | 0.105151i | \(0.966467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 36.0000i | − | 0.226415i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −144.000 | −0.894410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −97.9796 | + | 97.9796i | −0.601102 | + | 0.601102i | −0.940605 | − | 0.339503i | \(-0.889741\pi\) |
0.339503 | + | 0.940605i | \(0.389741\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −29.3939 | − | 29.3939i | −0.176011 | − | 0.176011i | 0.613603 | − | 0.789614i | \(-0.289719\pi\) |
−0.789614 | + | 0.613603i | \(0.789719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 131.000i | − | 0.775148i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 30.0000 | 0.175439 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 191.060 | − | 191.060i | 1.10439 | − | 1.10439i | 0.110520 | − | 0.993874i | \(-0.464748\pi\) |
0.993874 | − | 0.110520i | \(-0.0352517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 95.5301 | + | 95.5301i | 0.539718 | + | 0.539718i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 222.000i | 1.24022i | 0.784514 | + | 0.620112i | \(0.212913\pi\) | ||||
−0.784514 | + | 0.620112i | \(0.787087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 190.000 | 1.04972 | 0.524862 | − | 0.851187i | \(-0.324117\pi\) | ||||
0.524862 | + | 0.851187i | \(0.324117\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.44949 | + | 2.44949i | −0.0133852 | + | 0.0133852i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 88.1816 | + | 88.1816i | 0.471560 | + | 0.471560i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.0000i | 0.0952381i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −204.000 | −1.06806 | −0.534031 | − | 0.845465i | \(-0.679324\pi\) | ||||
−0.534031 | + | 0.845465i | \(0.679324\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 68.5857 | − | 68.5857i | 0.355366 | − | 0.355366i | −0.506735 | − | 0.862102i | \(-0.669148\pi\) |
0.862102 | + | 0.506735i | \(0.169148\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −205.757 | − | 205.757i | −1.04445 | − | 1.04445i | −0.998965 | − | 0.0454876i | \(-0.985516\pi\) |
−0.0454876 | − | 0.998965i | \(-0.514484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 46.0000i | − | 0.231156i | −0.993298 | − | 0.115578i | \(-0.963128\pi\) | ||
0.993298 | − | 0.115578i | \(-0.0368720\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 156.000 | 0.776119 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −117.576 | + | 117.576i | −0.579190 | + | 0.579190i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 88.1816 | + | 88.1816i | 0.425998 | + | 0.425998i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 60.0000i | − | 0.287081i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 310.000 | 1.46919 | 0.734597 | − | 0.678504i | \(-0.237371\pi\) | ||||
0.734597 | + | 0.678504i | \(0.237371\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 146.969 | − | 146.969i | 0.689997 | − | 0.689997i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 63.6867 | + | 63.6867i | 0.293487 | + | 0.293487i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 204.000i | − | 0.931507i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −360.000 | −1.62896 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −183.712 | + | 183.712i | −0.823819 | + | 0.823819i | −0.986653 | − | 0.162834i | \(-0.947936\pi\) |
0.162834 | + | 0.986653i | \(0.447936\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 73.4847 | + | 73.4847i | 0.323721 | + | 0.323721i | 0.850193 | − | 0.526472i | \(-0.176485\pi\) |
−0.526472 | + | 0.850193i | \(0.676485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 242.000i | 1.05677i | 0.849005 | + | 0.528384i | \(0.177202\pi\) | ||||
−0.849005 | + | 0.528384i | \(0.822798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 36.0000 | 0.155844 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −73.4847 | + | 73.4847i | −0.315385 | + | 0.315385i | −0.846991 | − | 0.531607i | \(-0.821589\pi\) |
0.531607 | + | 0.846991i | \(0.321589\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −90.6311 | − | 90.6311i | −0.382410 | − | 0.382410i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 324.000i | 1.35565i | 0.735224 | + | 0.677824i | \(0.237077\pi\) | ||||
−0.735224 | + | 0.677824i | \(0.762923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 398.000 | 1.65145 | 0.825726 | − | 0.564071i | \(-0.190766\pi\) | ||||
0.825726 | + | 0.564071i | \(0.190766\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 122.474 | + | 122.474i | 0.495848 | + | 0.495848i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 108.000i | 0.433735i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 162.000 | 0.645418 | 0.322709 | − | 0.946498i | \(-0.395406\pi\) | ||||
0.322709 | + | 0.946498i | \(0.395406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 176.363 | − | 176.363i | 0.697088 | − | 0.697088i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 102.879 | + | 102.879i | 0.400306 | + | 0.400306i | 0.878341 | − | 0.478035i | \(-0.158651\pi\) |
−0.478035 | + | 0.878341i | \(0.658651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 156.000i | − | 0.602317i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 144.000 | 0.551724 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 117.576 | − | 117.576i | 0.447055 | − | 0.447055i | −0.447319 | − | 0.894374i | \(-0.647621\pi\) |
0.894374 | + | 0.447319i | \(0.147621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −183.712 | − | 183.712i | −0.688059 | − | 0.688059i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 48.0000i | − | 0.178439i | −0.996012 | − | 0.0892193i | \(-0.971563\pi\) | ||
0.996012 | − | 0.0892193i | \(-0.0284372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46.0000 | 0.169742 | 0.0848708 | − | 0.996392i | \(-0.472952\pi\) | ||||
0.0848708 | + | 0.996392i | \(0.472952\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −73.4847 | + | 73.4847i | −0.269175 | + | 0.269175i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 80.8332 | + | 80.8332i | 0.291816 | + | 0.291816i | 0.837798 | − | 0.545981i | \(-0.183843\pi\) |
−0.545981 | + | 0.837798i | \(0.683843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 78.0000i | − | 0.279570i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −414.000 | −1.47331 | −0.736655 | − | 0.676269i | \(-0.763596\pi\) | ||||
−0.736655 | + | 0.676269i | \(0.763596\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 279.242 | − | 279.242i | 0.986720 | − | 0.986720i | −0.0131927 | − | 0.999913i | \(-0.504199\pi\) |
0.999913 | + | 0.0131927i | \(0.00419950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 73.4847 | + | 73.4847i | 0.256044 | + | 0.256044i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 143.000i | 0.494810i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | 0.0412371 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 235.151 | − | 235.151i | 0.802563 | − | 0.802563i | −0.180932 | − | 0.983496i | \(-0.557912\pi\) |
0.983496 | + | 0.180932i | \(0.0579115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.0454 | − | 22.0454i | −0.0742270 | − | 0.0742270i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 720.000i | 2.40803i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −144.000 | −0.478405 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.6969 | − | 14.6969i | 0.0485047 | − | 0.0485047i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 44.0908 | + | 44.0908i | 0.143618 | + | 0.143618i | 0.775260 | − | 0.631642i | \(-0.217619\pi\) |
−0.631642 | + | 0.775260i | \(0.717619\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 102.000i | 0.330097i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −204.000 | −0.655949 | −0.327974 | − | 0.944687i | \(-0.606366\pi\) | ||||
−0.327974 | + | 0.944687i | \(0.606366\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −372.322 | + | 372.322i | −1.18953 | + | 1.18953i | −0.212331 | + | 0.977198i | \(0.568105\pi\) |
−0.977198 | + | 0.212331i | \(0.931895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 352.727 | + | 352.727i | 1.11270 | + | 1.11270i | 0.992784 | + | 0.119918i | \(0.0382632\pi\) |
0.119918 | + | 0.992784i | \(0.461737\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 288.000i | − | 0.902821i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 252.000 | 0.785047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 146.969 | − | 146.969i | 0.455014 | − | 0.455014i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 90.6311 | + | 90.6311i | 0.277159 | + | 0.277159i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 72.0000i | − | 0.218845i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −542.000 | −1.63746 | −0.818731 | − | 0.574177i | \(-0.805322\pi\) | ||||
−0.818731 | + | 0.574177i | \(0.805322\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −95.5301 | + | 95.5301i | −0.286877 | + | 0.286877i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 347.828 | + | 347.828i | 1.03213 | + | 1.03213i | 0.999466 | + | 0.0326628i | \(0.0103987\pi\) |
0.0326628 | + | 0.999466i | \(0.489601\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 324.000i | − | 0.955752i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −156.000 | −0.457478 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 210.656 | − | 210.656i | 0.614158 | − | 0.614158i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 191.060 | + | 191.060i | 0.550606 | + | 0.550606i | 0.926616 | − | 0.376010i | \(-0.122704\pi\) |
−0.376010 | + | 0.926616i | \(0.622704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 358.000i | − | 1.02579i | −0.858452 | − | 0.512894i | \(-0.828573\pi\) | ||
0.858452 | − | 0.512894i | \(-0.171427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 90.0000 | 0.256410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −426.211 | + | 426.211i | −1.20740 | + | 1.20740i | −0.235530 | + | 0.971867i | \(0.575683\pi\) |
−0.971867 | + | 0.235530i | \(0.924317\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 88.1816 | + | 88.1816i | 0.247007 | + | 0.247007i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 132.000i | 0.367688i | 0.982955 | + | 0.183844i | \(0.0588541\pi\) | ||||
−0.982955 | + | 0.183844i | \(0.941146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 261.000 | 0.722992 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 104.103 | − | 104.103i | 0.286786 | − | 0.286786i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −120.025 | − | 120.025i | −0.327044 | − | 0.327044i | 0.524418 | − | 0.851461i | \(-0.324283\pi\) |
−0.851461 | + | 0.524418i | \(0.824283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 90.0000i | − | 0.243902i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −72.0000 | −0.194070 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 409.065 | − | 409.065i | 1.09669 | − | 1.09669i | 0.101893 | − | 0.994795i | \(-0.467510\pi\) |
0.994795 | − | 0.101893i | \(-0.0324900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 587.878 | + | 587.878i | 1.55936 | + | 1.55936i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.0000i | − | 0.0686016i | −0.999412 | − | 0.0343008i | \(-0.989080\pi\) | ||
0.999412 | − | 0.0343008i | \(-0.0109204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 234.000 | 0.614173 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 426.211 | − | 426.211i | 1.11282 | − | 1.11282i | 0.120056 | − | 0.992767i | \(-0.461693\pi\) |
0.992767 | − | 0.120056i | \(-0.0383074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 88.1816 | + | 88.1816i | 0.227860 | + | 0.227860i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 72.0000i | 0.185090i | 0.995709 | + | 0.0925450i | \(0.0295002\pi\) | ||||
−0.995709 | + | 0.0925450i | \(0.970500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 864.000 | 2.20972 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 124.924 | − | 124.924i | 0.317873 | − | 0.317873i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −227.803 | − | 227.803i | −0.573810 | − | 0.573810i | 0.359381 | − | 0.933191i | \(-0.382988\pi\) |
−0.933191 | + | 0.359381i | \(0.882988\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 60.0000i | − | 0.150376i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −414.000 | −1.03242 | −0.516209 | − | 0.856462i | \(-0.672657\pi\) | ||||
−0.516209 | + | 0.856462i | \(0.672657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 318.434 | − | 318.434i | 0.790158 | − | 0.790158i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 191.060 | + | 191.060i | 0.469435 | + | 0.469435i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 482.000i | 1.17848i | 0.807957 | + | 0.589242i | \(0.200574\pi\) | ||||
−0.807957 | + | 0.589242i | \(0.799426\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 108.000 | 0.262774 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 191.060 | − | 191.060i | 0.462615 | − | 0.462615i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 149.419 | + | 149.419i | 0.358319 | + | 0.358319i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 126.000i | 0.300716i | 0.988632 | + | 0.150358i | \(0.0480426\pi\) | ||||
−0.988632 | + | 0.150358i | \(0.951957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 430.000 | 1.02138 | 0.510689 | − | 0.859766i | \(-0.329390\pi\) | ||||
0.510689 | + | 0.859766i | \(0.329390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −44.0908 | + | 44.0908i | −0.104234 | + | 0.104234i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.89898 | + | 4.89898i | 0.0114730 | + | 0.0114730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 180.000i | − | 0.419580i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −228.000 | −0.529002 | −0.264501 | − | 0.964385i | \(-0.585207\pi\) | ||||
−0.264501 | + | 0.964385i | \(0.585207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −249.848 | + | 249.848i | −0.577016 | + | 0.577016i | −0.934080 | − | 0.357064i | \(-0.883778\pi\) |
0.357064 | + | 0.934080i | \(0.383778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −293.939 | − | 293.939i | −0.672629 | − | 0.672629i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 194.000i | 0.441913i | 0.975284 | + | 0.220957i | \(0.0709180\pi\) | ||||
−0.975284 | + | 0.220957i | \(0.929082\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −111.000 | −0.251701 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −338.030 | + | 338.030i | −0.763046 | + | 0.763046i | −0.976872 | − | 0.213825i | \(-0.931408\pi\) |
0.213825 | + | 0.976872i | \(0.431408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −44.0908 | − | 44.0908i | −0.0986372 | − | 0.0986372i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000i | 0.0133630i | 0.999978 | + | 0.00668151i | \(0.00212681\pi\) | ||||
−0.999978 | + | 0.00668151i | \(0.997873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −180.000 | −0.399113 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 85.7321 | − | 85.7321i | 0.189254 | − | 0.189254i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 367.423 | + | 367.423i | 0.803990 | + | 0.803990i | 0.983717 | − | 0.179727i | \(-0.0575213\pi\) |
−0.179727 | + | 0.983717i | \(0.557521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 108.000i | − | 0.235294i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −204.000 | −0.442516 | −0.221258 | − | 0.975215i | \(-0.571016\pi\) | ||||
−0.221258 | + | 0.975215i | \(0.571016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −100.429 | + | 100.429i | −0.216909 | + | 0.216909i | −0.807195 | − | 0.590285i | \(-0.799015\pi\) |
0.590285 | + | 0.807195i | \(0.299015\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 191.060 | + | 191.060i | 0.409122 | + | 0.409122i | 0.881432 | − | 0.472310i | \(-0.156580\pi\) |
−0.472310 | + | 0.881432i | \(0.656580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 312.000i | − | 0.665245i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 342.000 | 0.726115 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 176.363 | − | 176.363i | 0.372861 | − | 0.372861i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 44.0908 | + | 44.0908i | 0.0924336 | + | 0.0924336i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 888.000i | − | 1.85386i | −0.375232 | − | 0.926931i | \(-0.622437\pi\) | ||
0.375232 | − | 0.926931i | \(-0.377563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −780.000 | −1.62162 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 176.363 | − | 176.363i | 0.365141 | − | 0.365141i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 531.539 | + | 531.539i | 1.09146 | + | 1.09146i | 0.995373 | + | 0.0960831i | \(0.0306315\pi\) |
0.0960831 | + | 0.995373i | \(0.469369\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 240.000i | − | 0.490798i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −534.000 | −1.08758 | −0.543788 | − | 0.839223i | \(-0.683011\pi\) | ||||
−0.543788 | + | 0.839223i | \(0.683011\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 705.453 | − | 705.453i | 1.43094 | − | 1.43094i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −293.939 | − | 293.939i | −0.591426 | − | 0.591426i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 658.000i | − | 1.31864i | −0.751864 | − | 0.659319i | \(-0.770845\pi\) | ||
0.751864 | − | 0.659319i | \(-0.229155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 72.0000 | 0.143713 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −191.060 | + | 191.060i | −0.379841 | + | 0.379841i | −0.871045 | − | 0.491203i | \(-0.836557\pi\) |
0.491203 | + | 0.871045i | \(0.336557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 160.442 | + | 160.442i | 0.316453 | + | 0.316453i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 324.000i | 0.636542i | 0.948000 | + | 0.318271i | \(0.103102\pi\) | ||||
−0.948000 | + | 0.318271i | \(0.896898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −408.000 | −0.798434 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −36.7423 | + | 36.7423i | −0.0716225 | + | 0.0716225i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 88.1816 | + | 88.1816i | 0.170564 | + | 0.170564i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 468.000i | 0.901734i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 342.000 | 0.656430 | 0.328215 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328215 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −578.080 | + | 578.080i | −1.10531 | + | 1.10531i | −0.111557 | + | 0.993758i | \(0.535584\pi\) |
−0.993758 | + | 0.111557i | \(0.964416\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −382.120 | − | 382.120i | −0.725086 | − | 0.725086i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1199.00i | − | 2.26654i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −234.000 | −0.440678 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 367.423 | − | 367.423i | 0.689350 | − | 0.689350i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −271.893 | − | 271.893i | −0.506319 | − | 0.506319i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 222.000i | 0.411874i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 98.0000 | 0.181146 | 0.0905730 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905730 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −232.702 | + | 232.702i | −0.428548 | + | 0.428548i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 519.292 | + | 519.292i | 0.949345 | + | 0.949345i | 0.998777 | − | 0.0494323i | \(-0.0157412\pi\) |
−0.0494323 | + | 0.998777i | \(0.515741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 6.00000i | − | 0.0109290i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −480.000 | −0.871143 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −181.262 | + | 181.262i | −0.327780 | + | 0.327780i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −396.817 | − | 396.817i | −0.712419 | − | 0.712419i | 0.254622 | − | 0.967041i | \(-0.418049\pi\) |
−0.967041 | + | 0.254622i | \(0.918049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 720.000i | 1.28801i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −216.000 | −0.385027 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 73.4847 | − | 73.4847i | 0.130523 | − | 0.130523i | −0.638827 | − | 0.769350i | \(-0.720580\pi\) |
0.769350 | + | 0.638827i | \(0.220580\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0454 | − | 22.0454i | −0.0388808 | − | 0.0388808i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 762.000i | 1.33919i | 0.742726 | + | 0.669596i | \(0.233533\pi\) | ||||
−0.742726 | + | 0.669596i | \(0.766467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 850.000 | 1.48862 | 0.744308 | − | 0.667836i | \(-0.232779\pi\) | ||||
0.744308 | + | 0.667836i | \(0.232779\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 249.848 | − | 249.848i | 0.436035 | − | 0.436035i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.89898 | − | 4.89898i | −0.00849043 | − | 0.00849043i | 0.702849 | − | 0.711339i | \(-0.251911\pi\) |
−0.711339 | + | 0.702849i | \(0.751911\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 168.000i | 0.290155i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 216.000 | 0.371773 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 88.1816 | − | 88.1816i | 0.151255 | − | 0.151255i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −132.272 | − | 132.272i | −0.225336 | − | 0.225336i | 0.585405 | − | 0.810741i | \(-0.300936\pi\) |
−0.810741 | + | 0.585405i | \(0.800936\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 260.000i | 0.441426i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 504.000 | 0.852792 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 102.879 | − | 102.879i | 0.173488 | − | 0.173488i | −0.615022 | − | 0.788510i | \(-0.710853\pi\) |
0.788510 | + | 0.615022i | \(0.210853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 56.3383 | + | 56.3383i | 0.0943690 | + | 0.0943690i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 732.000i | − | 1.22204i | −0.791616 | − | 0.611018i | \(-0.790760\pi\) | ||
0.791616 | − | 0.611018i | \(-0.209240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 778.000 | 1.29451 | 0.647255 | − | 0.762274i | \(-0.275917\pi\) | ||||
0.647255 | + | 0.762274i | \(0.275917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −191.060 | + | 191.060i | −0.316849 | + | 0.316849i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 105.328 | + | 105.328i | 0.173522 | + | 0.173522i | 0.788525 | − | 0.615003i | \(-0.210845\pi\) |
−0.615003 | + | 0.788525i | \(0.710845\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 288.000i | − | 0.472906i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −360.000 | −0.589198 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −71.0352 | + | 71.0352i | −0.115881 | + | 0.115881i | −0.762670 | − | 0.646788i | \(-0.776112\pi\) |
0.646788 | + | 0.762670i | \(0.276112\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 455.605 | + | 455.605i | 0.738420 | + | 0.738420i | 0.972272 | − | 0.233852i | \(-0.0751332\pi\) |
−0.233852 | + | 0.972272i | \(0.575133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 362.000i | 0.584814i | 0.956294 | + | 0.292407i | \(0.0944562\pi\) | ||||
−0.956294 | + | 0.292407i | \(0.905544\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −216.000 | −0.347826 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −367.423 | + | 367.423i | −0.589765 | + | 0.589765i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 73.4847 | + | 73.4847i | 0.117200 | + | 0.117200i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 936.000i | 1.48808i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 478.000 | 0.757528 | 0.378764 | − | 0.925493i | \(-0.376349\pi\) | ||||
0.378764 | + | 0.925493i | \(0.376349\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −379.671 | + | 379.671i | −0.599796 | + | 0.599796i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −453.156 | − | 453.156i | −0.711390 | − | 0.711390i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 360.000i | 0.563380i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 354.000 | 0.552262 | 0.276131 | − | 0.961120i | \(-0.410948\pi\) | ||||
0.276131 | + | 0.961120i | \(0.410948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −264.545 | + | 264.545i | −0.411423 | + | 0.411423i | −0.882234 | − | 0.470811i | \(-0.843961\pi\) |
0.470811 | + | 0.882234i | \(0.343961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 484.999 | + | 484.999i | 0.749612 | + | 0.749612i | 0.974406 | − | 0.224794i | \(-0.0721710\pi\) |
−0.224794 | + | 0.974406i | \(0.572171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 468.000i | 0.721109i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −156.000 | −0.239631 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.3939 | − | 29.3939i | 0.0450136 | − | 0.0450136i | −0.684242 | − | 0.729255i | \(-0.739867\pi\) |
0.729255 | + | 0.684242i | \(0.239867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 249.848 | + | 249.848i | 0.380286 | + | 0.380286i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 414.000i | 0.628225i | 0.949386 | + | 0.314112i | \(0.101707\pi\) | ||||
−0.949386 | + | 0.314112i | \(0.898293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1202.00 | −1.81846 | −0.909228 | − | 0.416298i | \(-0.863327\pi\) | ||||
−0.909228 | + | 0.416298i | \(0.863327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 440.908 | − | 440.908i | 0.665020 | − | 0.665020i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1410.91 | − | 1410.91i | −2.11530 | − | 2.11530i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 450.000i | − | 0.672646i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.0178838 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −171.464 | + | 171.464i | −0.254776 | + | 0.254776i | −0.822925 | − | 0.568149i | \(-0.807660\pi\) |
0.568149 | + | 0.822925i | \(0.307660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −235.151 | − | 235.151i | −0.347343 | − | 0.347343i | 0.511776 | − | 0.859119i | \(-0.328988\pi\) |
−0.859119 | + | 0.511776i | \(0.828988\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 24.0000i | − | 0.0353461i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −180.000 | −0.264317 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 690.756 | − | 690.756i | 1.01136 | − | 1.01136i | 0.0114212 | − | 0.999935i | \(-0.496364\pi\) |
0.999935 | − | 0.0114212i | \(-0.00363555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −296.388 | − | 296.388i | −0.431424 | − | 0.431424i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 360.000i | 0.522496i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −778.000 | −1.12590 | −0.562952 | − | 0.826489i | \(-0.690335\pi\) | ||||
−0.562952 | + | 0.826489i | \(0.690335\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −44.0908 | + | 44.0908i | −0.0636231 | + | 0.0636231i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −440.908 | − | 440.908i | −0.632580 | − | 0.632580i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 180.000i | − | 0.257511i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −84.0000 | −0.119829 | −0.0599144 | − | 0.998204i | \(-0.519083\pi\) | ||||
−0.0599144 | + | 0.998204i | \(0.519083\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 318.434 | − | 318.434i | 0.452964 | − | 0.452964i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.3939 | − | 29.3939i | −0.0415755 | − | 0.0415755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 502.000i | − | 0.708039i | −0.935238 | − | 0.354020i | \(-0.884815\pi\) | ||
0.935238 | − | 0.354020i | \(-0.115185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 222.000 | 0.312236 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −764.241 | + | 764.241i | −1.07187 | + | 1.07187i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −396.817 | − | 396.817i | −0.553441 | − | 0.553441i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1356.00i | − | 1.88595i | −0.332860 | − | 0.942976i | \(-0.608014\pi\) | ||
0.332860 | − | 0.942976i | \(-0.391986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 204.000 | 0.282940 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −487.448 | + | 487.448i | −0.674203 | + | 0.674203i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −815.680 | − | 815.680i | −1.12198 | − | 1.12198i | −0.991443 | − | 0.130537i | \(-0.958330\pi\) |
−0.130537 | − | 0.991443i | \(-0.541670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 864.000 | 1.18194 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −962.649 | + | 962.649i | −1.31330 | + | 1.31330i | −0.394333 | + | 0.918968i | \(0.629024\pi\) |
−0.918968 | + | 0.394333i | \(0.870976\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 382.120 | + | 382.120i | 0.518481 | + | 0.518481i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 610.000i | 0.825440i | 0.910858 | + | 0.412720i | \(0.135421\pi\) | ||||
−0.910858 | + | 0.412720i | \(0.864579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −300.000 | −0.404858 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.0908 | + | 44.0908i | −0.0593416 | + | 0.0593416i | −0.736155 | − | 0.676813i | \(-0.763360\pi\) |
0.676813 | + | 0.736155i | \(0.263360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −132.272 | − | 132.272i | −0.177072 | − | 0.177072i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 504.000i | − | 0.672897i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1058.00 | 1.40879 | 0.704394 | − | 0.709809i | \(-0.251219\pi\) | ||||
0.704394 | + | 0.709809i | \(0.251219\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −198.409 | + | 198.409i | −0.263491 | + | 0.263491i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.9444 | + | 26.9444i | 0.0355936 | + | 0.0355936i | 0.724680 | − | 0.689086i | \(-0.241988\pi\) |
−0.689086 | + | 0.724680i | \(0.741988\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 432.000i | 0.569170i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1122.00 | 1.47438 | 0.737188 | − | 0.675688i | \(-0.236153\pi\) | ||||
0.737188 | + | 0.675688i | \(0.236153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 181.262 | − | 181.262i | 0.237565 | − | 0.237565i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −955.301 | − | 955.301i | −1.24550 | − | 1.24550i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 274.000i | 0.356307i | 0.984003 | + | 0.178153i | \(0.0570123\pi\) | ||||
−0.984003 | + | 0.178153i | \(0.942988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −252.000 | −0.326848 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −382.120 | + | 382.120i | −0.494334 | + | 0.494334i | −0.909669 | − | 0.415334i | \(-0.863665\pi\) |
0.415334 | + | 0.909669i | \(0.363665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 191.060 | + | 191.060i | 0.245895 | + | 0.245895i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 300.000i | 0.385109i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 720.000 | 0.921895 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −176.363 | + | 176.363i | −0.225240 | + | 0.225240i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 421.312 | + | 421.312i | 0.535340 | + | 0.535340i | 0.922157 | − | 0.386817i | \(-0.126425\pi\) |
−0.386817 | + | 0.922157i | \(0.626425\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 288.000i | 0.365019i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −648.000 | −0.819216 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.4949 | − | 24.4949i | 0.0308889 | − | 0.0308889i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −396.817 | − | 396.817i | −0.497889 | − | 0.497889i | 0.412891 | − | 0.910780i | \(-0.364519\pi\) |
−0.910780 | + | 0.412891i | \(0.864519\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 432.000i | 0.540676i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 450.000 | 0.561798 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 499.696 | − | 499.696i | 0.622286 | − | 0.622286i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 58.7878 | + | 58.7878i | 0.0728473 | + | 0.0728473i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 618.000i | − | 0.763906i | −0.924182 | − | 0.381953i | \(-0.875252\pi\) | ||
0.924182 | − | 0.381953i | \(-0.124748\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −790.000 | −0.974106 | −0.487053 | − | 0.873372i | \(-0.661928\pi\) | ||||
−0.487053 | + | 0.873372i | \(0.661928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −56.3383 | + | 56.3383i | −0.0692968 | + | 0.0692968i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −293.939 | − | 293.939i | −0.359778 | − | 0.359778i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 180.000i | − | 0.219780i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1056.00 | 1.28624 | 0.643118 | − | 0.765767i | \(-0.277640\pi\) | ||||
0.643118 | + | 0.765767i | \(0.277640\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −75.9342 | + | 75.9342i | −0.0922651 | + | 0.0922651i | −0.751733 | − | 0.659468i | \(-0.770782\pi\) |
0.659468 | + | 0.751733i | \(0.270782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1072.88 | − | 1072.88i | −1.29731 | − | 1.29731i | −0.930162 | − | 0.367149i | \(-0.880334\pi\) |
−0.367149 | − | 0.930162i | \(-0.619666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 314.000i | 0.378770i | 0.981903 | + | 0.189385i | \(0.0606494\pi\) | ||||
−0.981903 | + | 0.189385i | \(0.939351\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −198.000 | −0.238267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −543.787 | + | 543.787i | −0.652805 | + | 0.652805i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 95.5301 | + | 95.5301i | 0.114134 | + | 0.114134i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 348.000i | − | 0.414779i | −0.978258 | − | 0.207390i | \(-0.933503\pi\) | ||
0.978258 | − | 0.207390i | \(-0.0664968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1463.00 | −1.73960 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 507.044 | − | 507.044i | 0.601476 | − | 0.601476i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −208.207 | − | 208.207i | −0.245817 | − | 0.245817i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 684.000i | 0.805654i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1872.00 | 2.19976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 144.520 | − | 144.520i | 0.169425 | − | 0.169425i | −0.617301 | − | 0.786727i | \(-0.711774\pi\) |
0.786727 | + | 0.617301i | \(0.211774\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −543.787 | − | 543.787i | −0.634524 | − | 0.634524i | 0.314676 | − | 0.949199i | \(-0.398104\pi\) |
−0.949199 | + | 0.314676i | \(0.898104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1030.00i | − | 1.19907i | −0.800349 | − | 0.599534i | \(-0.795352\pi\) | ||
0.800349 | − | 0.599534i | \(-0.204648\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −180.000 | −0.209059 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −940.604 | + | 940.604i | −1.08992 | + | 1.08992i | −0.0943881 | + | 0.995535i | \(0.530089\pi\) |
−0.995535 | + | 0.0943881i | \(0.969911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −175.139 | − | 175.139i | −0.202005 | − | 0.202005i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 444.000i | − | 0.510932i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1560.00 | −1.79104 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.6969 | + | 14.6969i | −0.0168350 | + | 0.0168350i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 688.307 | + | 688.307i | 0.784842 | + | 0.784842i | 0.980644 | − | 0.195801i | \(-0.0627308\pi\) |
−0.195801 | + | 0.980644i | \(0.562731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 576.000i | 0.655290i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1290.00 | −1.46425 | −0.732123 | − | 0.681173i | \(-0.761470\pi\) | ||||
−0.732123 | + | 0.681173i | \(0.761470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 333.131 | − | 333.131i | 0.377271 | − | 0.377271i | −0.492845 | − | 0.870117i | \(-0.664043\pi\) |
0.870117 | + | 0.492845i | \(0.164043\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 676.059 | + | 676.059i | 0.762186 | + | 0.762186i | 0.976717 | − | 0.214531i | \(-0.0688223\pi\) |
−0.214531 | + | 0.976717i | \(0.568822\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 468.000i | − | 0.526434i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54.0000 | 0.0606061 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 146.969 | − | 146.969i | 0.164579 | − | 0.164579i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −881.816 | − | 881.816i | −0.983073 | − | 0.983073i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1248.00i | 1.38821i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 432.000 | 0.479467 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 176.363 | − | 176.363i | 0.195308 | − | 0.195308i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 215.555 | + | 215.555i | 0.237657 | + | 0.237657i | 0.815879 | − | 0.578222i | \(-0.196253\pi\) |
−0.578222 | + | 0.815879i | \(0.696253\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.0000i | 0.0396040i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −408.000 | −0.447859 | −0.223930 | − | 0.974605i | \(-0.571889\pi\) | ||||
−0.223930 | + | 0.974605i | \(0.571889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −264.545 | + | 264.545i | −0.289753 | + | 0.289753i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −249.848 | − | 249.848i | −0.272462 | − | 0.272462i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 574.000i | 0.624592i | 0.949985 | + | 0.312296i | \(0.101098\pi\) | ||||
−0.949985 | + | 0.312296i | \(0.898902\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −108.000 | −0.117264 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1469.69 | + | 1469.69i | −1.59230 | + | 1.59230i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −124.924 | − | 124.924i | −0.134762 | − | 0.134762i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 474.000i | − | 0.510226i | −0.966911 | − | 0.255113i | \(-0.917887\pi\) | ||
0.966911 | − | 0.255113i | \(-0.0821127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 370.000 | 0.397422 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 249.848 | − | 249.848i | 0.267790 | − | 0.267790i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −362.524 | − | 362.524i | −0.386899 | − | 0.386899i | 0.486681 | − | 0.873580i | \(-0.338207\pi\) |
−0.873580 | + | 0.486681i | \(0.838207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 912.000i | − | 0.971246i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −881.816 | + | 881.816i | −0.935118 | + | 0.935118i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −102.879 | − | 102.879i | −0.108636 | − | 0.108636i | 0.650699 | − | 0.759336i | \(-0.274476\pi\) |
−0.759336 | + | 0.650699i | \(0.774476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2040.00i | 2.14963i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −864.000 | −0.908517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 338.030 | − | 338.030i | 0.354701 | − | 0.354701i | −0.507155 | − | 0.861855i | \(-0.669303\pi\) |
0.861855 | + | 0.507155i | \(0.169303\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 352.727 | + | 352.727i | 0.368575 | + | 0.368575i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 216.000i | − | 0.225235i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −285.000 | −0.296566 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −308.636 | + | 308.636i | −0.320494 | + | 0.320494i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −85.7321 | − | 85.7321i | −0.0886579 | − | 0.0886579i | 0.661387 | − | 0.750045i | \(-0.269968\pi\) |
−0.750045 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 360.000i | 0.371517i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1542.00 | 1.58805 | 0.794027 | − | 0.607883i | \(-0.207981\pi\) | ||||
0.794027 | + | 0.607883i | \(0.207981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 298.838 | − | 298.838i | 0.307130 | − | 0.307130i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −543.787 | − | 543.787i | −0.556588 | − | 0.556588i | 0.371746 | − | 0.928334i | \(-0.378759\pi\) |
−0.928334 | + | 0.371746i | \(0.878759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 900.000i | − | 0.919305i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −222.000 | −0.226300 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 426.211 | − | 426.211i | 0.433582 | − | 0.433582i | −0.456263 | − | 0.889845i | \(-0.650812\pi\) |
0.889845 | + | 0.456263i | \(0.150812\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 88.1816 | + | 88.1816i | 0.0893431 | + | 0.0893431i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1728.00i | − | 1.74722i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 262.000 | 0.264379 | 0.132190 | − | 0.991224i | \(-0.457799\pi\) | ||||
0.132190 | + | 0.991224i | \(0.457799\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 663.812 | − | 663.812i | 0.668491 | − | 0.668491i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1124.32 | − | 1124.32i | −1.12770 | − | 1.12770i | −0.990551 | − | 0.137148i | \(-0.956206\pi\) |
−0.137148 | − | 0.990551i | \(-0.543794\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 234.000i | − | 0.234234i |
(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 | 1200.3.bg.h.1057.1 | 4 | ||
4.3 | odd | 2 | 300.3.k.b.157.2 | yes | 4 | ||
5.2 | odd | 4 | inner | 1200.3.bg.h.193.2 | 4 | ||
5.3 | odd | 4 | inner | 1200.3.bg.h.193.1 | 4 | ||
5.4 | even | 2 | inner | 1200.3.bg.h.1057.2 | 4 | ||
12.11 | even | 2 | 900.3.l.c.757.1 | 4 | |||
20.3 | even | 4 | 300.3.k.b.193.2 | yes | 4 | ||
20.7 | even | 4 | 300.3.k.b.193.1 | yes | 4 | ||
20.19 | odd | 2 | 300.3.k.b.157.1 | ✓ | 4 | ||
60.23 | odd | 4 | 900.3.l.c.793.1 | 4 | |||
60.47 | odd | 4 | 900.3.l.c.793.2 | 4 | |||
60.59 | even | 2 | 900.3.l.c.757.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.k.b.157.1 | ✓ | 4 | 20.19 | odd | 2 | ||
300.3.k.b.157.2 | yes | 4 | 4.3 | odd | 2 | ||
300.3.k.b.193.1 | yes | 4 | 20.7 | even | 4 | ||
300.3.k.b.193.2 | yes | 4 | 20.3 | even | 4 | ||
900.3.l.c.757.1 | 4 | 12.11 | even | 2 | |||
900.3.l.c.757.2 | 4 | 60.59 | even | 2 | |||
900.3.l.c.793.1 | 4 | 60.23 | odd | 4 | |||
900.3.l.c.793.2 | 4 | 60.47 | odd | 4 | |||
1200.3.bg.h.193.1 | 4 | 5.3 | odd | 4 | inner | ||
1200.3.bg.h.193.2 | 4 | 5.2 | odd | 4 | inner | ||
1200.3.bg.h.1057.1 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.h.1057.2 | 4 | 5.4 | even | 2 | inner |