Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(973,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([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("1620.973");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.l (of order \(4\), degree \(2\), 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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 973.10 | ||
Character | \(\chi\) | \(=\) | 1620.973 |
Dual form | 1620.3.l.g.1297.10 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.87041 | − | 3.16543i | 0.774082 | − | 0.633086i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.43863 | − | 3.43863i | 0.491233 | − | 0.491233i | −0.417462 | − | 0.908695i | \(-0.637080\pi\) |
0.908695 | + | 0.417462i | \(0.137080\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.26535 | −0.660487 | −0.330243 | − | 0.943896i | \(-0.607131\pi\) | ||||
−0.330243 | + | 0.943896i | \(0.607131\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.06083 | − | 3.06083i | −0.235448 | − | 0.235448i | 0.579514 | − | 0.814962i | \(-0.303242\pi\) |
−0.814962 | + | 0.579514i | \(0.803242\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.69512 | − | 4.69512i | 0.276184 | − | 0.276184i | −0.555400 | − | 0.831584i | \(-0.687435\pi\) |
0.831584 | + | 0.555400i | \(0.187435\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.1112i | 0.532169i | 0.963950 | + | 0.266084i | \(0.0857300\pi\) | ||||
−0.963950 | + | 0.266084i | \(0.914270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.8592 | + | 29.8592i | 1.29822 | + | 1.29822i | 0.929564 | + | 0.368660i | \(0.120183\pi\) |
0.368660 | + | 0.929564i | \(0.379817\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.96012 | − | 24.5030i | 0.198405 | − | 0.980120i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 33.7361i | − | 1.16332i | −0.813434 | − | 0.581658i | \(-0.802404\pi\) | ||
0.813434 | − | 0.581658i | \(-0.197596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23.3466 | 0.753116 | 0.376558 | − | 0.926393i | \(-0.377108\pi\) | ||||
0.376558 | + | 0.926393i | \(0.377108\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.42417 | − | 24.1937i | 0.0692619 | − | 0.691247i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.1926 | − | 40.1926i | 1.08629 | − | 1.08629i | 0.0903805 | − | 0.995907i | \(-0.471192\pi\) |
0.995907 | − | 0.0903805i | \(-0.0288083\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5684 | 0.257766 | 0.128883 | − | 0.991660i | \(-0.458861\pi\) | ||||
0.128883 | + | 0.991660i | \(0.458861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −52.7100 | − | 52.7100i | −1.22581 | − | 1.22581i | −0.965533 | − | 0.260280i | \(-0.916185\pi\) |
−0.260280 | − | 0.965533i | \(-0.583815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17.0667 | − | 17.0667i | 0.363121 | − | 0.363121i | −0.501840 | − | 0.864961i | \(-0.667343\pi\) |
0.864961 | + | 0.501840i | \(0.167343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.3516i | 0.517380i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −44.6296 | − | 44.6296i | −0.842069 | − | 0.842069i | 0.147059 | − | 0.989128i | \(-0.453019\pi\) |
−0.989128 | + | 0.147059i | \(0.953019\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −28.1199 | + | 22.9980i | −0.511271 | + | 0.418145i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.1167i | 0.222318i | 0.993803 | + | 0.111159i | \(0.0354562\pi\) | ||||
−0.993803 | + | 0.111159i | \(0.964544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −54.2365 | −0.889123 | −0.444561 | − | 0.895748i | \(-0.646640\pi\) | ||||
−0.444561 | + | 0.895748i | \(0.646640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.5355 | − | 2.15782i | −0.331315 | − | 0.0331973i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 46.6532 | − | 46.6532i | 0.696317 | − | 0.696317i | −0.267297 | − | 0.963614i | \(-0.586131\pi\) |
0.963614 | + | 0.267297i | \(0.0861306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1754 | 0.213737 | 0.106869 | − | 0.994273i | \(-0.465918\pi\) | ||||
0.106869 | + | 0.994273i | \(0.465918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 31.1199 | + | 31.1199i | 0.426300 | + | 0.426300i | 0.887366 | − | 0.461066i | \(-0.152533\pi\) |
−0.461066 | + | 0.887366i | \(0.652533\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.9829 | + | 24.9829i | −0.324453 | + | 0.324453i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 144.092i | − | 1.82395i | −0.410249 | − | 0.911973i | \(-0.634558\pi\) | ||
0.410249 | − | 0.911973i | \(-0.365442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 58.5951 | + | 58.5951i | 0.705965 | + | 0.705965i | 0.965684 | − | 0.259719i | \(-0.0836299\pi\) |
−0.259719 | + | 0.965684i | \(0.583630\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.30997 | − | 33.0341i | 0.0389408 | − | 0.388637i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 124.203i | 1.39554i | 0.716324 | + | 0.697768i | \(0.245823\pi\) | ||||
−0.716324 | + | 0.697768i | \(0.754177\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.0501 | −0.231320 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.0063 | + | 39.1345i | 0.336909 | + | 0.411942i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −20.8047 | + | 20.8047i | −0.214481 | + | 0.214481i | −0.806168 | − | 0.591687i | \(-0.798462\pi\) |
0.591687 | + | 0.806168i | \(0.298462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −136.461 | −1.35110 | −0.675549 | − | 0.737315i | \(-0.736093\pi\) | ||||
−0.675549 | + | 0.737315i | \(0.736093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −49.0738 | − | 49.0738i | −0.476445 | − | 0.476445i | 0.427548 | − | 0.903993i | \(-0.359378\pi\) |
−0.903993 | + | 0.427548i | \(0.859378\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −28.8128 | + | 28.8128i | −0.269279 | + | 0.269279i | −0.828810 | − | 0.559531i | \(-0.810981\pi\) |
0.559531 | + | 0.828810i | \(0.310981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 178.917i | − | 1.64144i | −0.571332 | − | 0.820719i | \(-0.693573\pi\) | ||
0.571332 | − | 0.820719i | \(-0.306427\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 25.6615 | + | 25.6615i | 0.227093 | + | 0.227093i | 0.811477 | − | 0.584384i | \(-0.198664\pi\) |
−0.584384 | + | 0.811477i | \(0.698664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 210.084 | + | 21.0501i | 1.82682 | + | 0.183044i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 32.2896i | − | 0.271341i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −68.2147 | −0.563758 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −58.3648 | − | 110.538i | −0.466918 | − | 0.884300i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 82.5876 | − | 82.5876i | 0.650296 | − | 0.650296i | −0.302768 | − | 0.953064i | \(-0.597911\pi\) |
0.953064 | + | 0.302768i | \(0.0979108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −146.464 | −1.11805 | −0.559024 | − | 0.829152i | \(-0.688824\pi\) | ||||
−0.559024 | + | 0.829152i | \(0.688824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.7687 | + | 34.7687i | 0.261419 | + | 0.261419i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −116.396 | + | 116.396i | −0.849606 | + | 0.849606i | −0.990084 | − | 0.140478i | \(-0.955136\pi\) |
0.140478 | + | 0.990084i | \(0.455136\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 167.551i | − | 1.20541i | −0.797966 | − | 0.602703i | \(-0.794090\pi\) | ||
0.797966 | − | 0.602703i | \(-0.205910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.2380 | + | 22.2380i | 0.155511 | + | 0.155511i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −106.789 | − | 130.573i | −0.736478 | − | 0.900501i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 187.948i | − | 1.26140i | −0.776028 | − | 0.630699i | \(-0.782768\pi\) | ||
0.776028 | − | 0.630699i | \(-0.217232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 77.7893 | 0.515161 | 0.257580 | − | 0.966257i | \(-0.417075\pi\) | ||||
0.257580 | + | 0.966257i | \(0.417075\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 90.3608 | − | 73.9020i | 0.582973 | − | 0.476787i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 97.9050 | − | 97.9050i | 0.623599 | − | 0.623599i | −0.322851 | − | 0.946450i | \(-0.604641\pi\) |
0.946450 | + | 0.322851i | \(0.104641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 205.349 | 1.27546 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −160.492 | − | 160.492i | −0.984616 | − | 0.984616i | 0.0152671 | − | 0.999883i | \(-0.495140\pi\) |
−0.999883 | + | 0.0152671i | \(0.995140\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −36.7194 | + | 36.7194i | −0.219877 | + | 0.219877i | −0.808446 | − | 0.588570i | \(-0.799691\pi\) |
0.588570 | + | 0.808446i | \(0.299691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 150.263i | − | 0.889128i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 118.749 | + | 118.749i | 0.686411 | + | 0.686411i | 0.961437 | − | 0.275026i | \(-0.0886865\pi\) |
−0.275026 | + | 0.961437i | \(0.588686\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −67.2008 | − | 101.313i | −0.384004 | − | 0.578930i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 293.293i | 1.63851i | 0.573429 | + | 0.819255i | \(0.305613\pi\) | ||||
−0.573429 | + | 0.819255i | \(0.694387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 182.818 | 1.01005 | 0.505023 | − | 0.863106i | \(-0.331484\pi\) | ||||
0.505023 | + | 0.863106i | \(0.331484\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 28.3350 | − | 282.789i | 0.153162 | − | 1.52859i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.1117 | + | 34.1117i | −0.182416 | + | 0.182416i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 289.810 | 1.51733 | 0.758666 | − | 0.651480i | \(-0.225851\pi\) | ||||
0.758666 | + | 0.651480i | \(0.225851\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −196.785 | − | 196.785i | −1.01961 | − | 1.01961i | −0.999804 | − | 0.0198065i | \(-0.993695\pi\) |
−0.0198065 | − | 0.999804i | \(-0.506305\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 181.377 | − | 181.377i | 0.920694 | − | 0.920694i | −0.0763840 | − | 0.997078i | \(-0.524337\pi\) |
0.997078 | + | 0.0763840i | \(0.0243375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 160.532i | 0.806694i | 0.915047 | + | 0.403347i | \(0.132153\pi\) | ||||
−0.915047 | + | 0.403347i | \(0.867847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −116.006 | − | 116.006i | −0.571459 | − | 0.571459i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.9040 | − | 33.4535i | 0.199532 | − | 0.163188i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 73.4615i | − | 0.351490i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 404.607 | 1.91757 | 0.958783 | − | 0.284138i | \(-0.0917074\pi\) | ||||
0.958783 | + | 0.284138i | \(0.0917074\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −370.859 | − | 37.1595i | −1.72492 | − | 0.172835i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 80.2803 | − | 80.2803i | 0.369955 | − | 0.369955i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.7419 | −0.130054 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 207.081 | + | 207.081i | 0.928614 | + | 0.928614i | 0.997616 | − | 0.0690026i | \(-0.0219817\pi\) |
−0.0690026 | + | 0.997616i | \(0.521982\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.85057 | + | 9.85057i | −0.0433946 | + | 0.0433946i | −0.728471 | − | 0.685077i | \(-0.759769\pi\) |
0.685077 | + | 0.728471i | \(0.259769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 119.872i | 0.523459i | 0.965141 | + | 0.261729i | \(0.0842928\pi\) | ||||
−0.965141 | + | 0.261729i | \(0.915707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 37.3376 | + | 37.3376i | 0.160247 | + | 0.160247i | 0.782676 | − | 0.622429i | \(-0.213854\pi\) |
−0.622429 | + | 0.782676i | \(0.713854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0317 | − | 120.078i | 0.0511986 | − | 0.510972i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 176.707i | − | 0.739359i | −0.929159 | − | 0.369679i | \(-0.879468\pi\) | ||
0.929159 | − | 0.369679i | \(-0.120532\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −292.782 | −1.21486 | −0.607431 | − | 0.794372i | \(-0.707800\pi\) | ||||
−0.607431 | + | 0.794372i | \(0.707800\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 80.2488 | + | 98.1212i | 0.327546 | + | 0.400495i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.9487 | − | 30.9487i | 0.125298 | − | 0.125298i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 279.420 | 1.11323 | 0.556614 | − | 0.830771i | \(-0.312100\pi\) | ||||
0.556614 | + | 0.830771i | \(0.312100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −216.937 | − | 216.937i | −0.857460 | − | 0.857460i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −183.160 | + | 183.160i | −0.712684 | + | 0.712684i | −0.967096 | − | 0.254412i | \(-0.918118\pi\) |
0.254412 | + | 0.967096i | \(0.418118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 276.415i | − | 1.06724i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −125.277 | − | 125.277i | −0.476340 | − | 0.476340i | 0.427619 | − | 0.903959i | \(-0.359353\pi\) |
−0.903959 | + | 0.427619i | \(0.859353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −314.007 | − | 31.4630i | −1.18493 | − | 0.118728i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 232.364i | − | 0.863806i | −0.901920 | − | 0.431903i | \(-0.857842\pi\) | ||
0.901920 | − | 0.431903i | \(-0.142158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.09756 | 0.00774009 | 0.00387005 | − | 0.999993i | \(-0.498768\pi\) | ||||
0.00387005 | + | 0.999993i | \(0.498768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.0370 | + | 178.023i | −0.131044 | + | 0.647356i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −127.091 | + | 127.091i | −0.458812 | + | 0.458812i | −0.898265 | − | 0.439453i | \(-0.855172\pi\) |
0.439453 | + | 0.898265i | \(0.355172\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −47.6809 | −0.169683 | −0.0848414 | − | 0.996394i | \(-0.527038\pi\) | ||||
−0.0848414 | + | 0.996394i | \(0.527038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 172.324 | + | 172.324i | 0.608919 | + | 0.608919i | 0.942664 | − | 0.333744i | \(-0.108312\pi\) |
−0.333744 | + | 0.942664i | \(0.608312\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 36.3408 | − | 36.3408i | 0.126623 | − | 0.126623i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 244.912i | 0.847445i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 397.647 | + | 397.647i | 1.35716 | + | 1.35716i | 0.877402 | + | 0.479755i | \(0.159275\pi\) |
0.479755 | + | 0.877402i | \(0.340725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.5201 | + | 50.7671i | 0.140746 | + | 0.172092i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 182.788i | − | 0.611330i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −362.500 | −1.20432 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −209.917 | + | 171.682i | −0.688253 | + | 0.562891i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0548 | + | 25.0548i | −0.0816117 | + | 0.0816117i | −0.746734 | − | 0.665123i | \(-0.768379\pi\) |
0.665123 | + | 0.746734i | \(0.268379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 549.785 | 1.76780 | 0.883899 | − | 0.467678i | \(-0.154909\pi\) | ||||
0.883899 | + | 0.467678i | \(0.154909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 47.6266 | + | 47.6266i | 0.152162 | + | 0.152162i | 0.779083 | − | 0.626921i | \(-0.215685\pi\) |
−0.626921 | + | 0.779083i | \(0.715685\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −343.911 | + | 343.911i | −1.08489 | + | 1.08489i | −0.0888492 | + | 0.996045i | \(0.528319\pi\) |
−0.996045 | + | 0.0888492i | \(0.971681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 245.105i | 0.768354i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.4734 | + | 47.4734i | 0.146976 | + | 0.146976i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −90.1816 | + | 59.8174i | −0.277482 | + | 0.184054i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 117.372i | − | 0.356754i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.2220 | −0.0882840 | −0.0441420 | − | 0.999025i | \(-0.514055\pi\) | ||||
−0.0441420 | + | 0.999025i | \(0.514055\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.8896 | − | 328.244i | 0.0981779 | − | 0.979834i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 77.9144 | − | 77.9144i | 0.231200 | − | 0.231200i | −0.581993 | − | 0.813193i | \(-0.697727\pi\) |
0.813193 | + | 0.581993i | \(0.197727\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −169.621 | −0.497423 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 255.668 | + | 255.668i | 0.745387 | + | 0.745387i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −279.836 | + | 279.836i | −0.806445 | + | 0.806445i | −0.984094 | − | 0.177649i | \(-0.943151\pi\) |
0.177649 | + | 0.984094i | \(0.443151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 660.500i | − | 1.89255i | −0.323361 | − | 0.946276i | \(-0.604813\pi\) | ||
0.323361 | − | 0.946276i | \(-0.395187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −79.8004 | − | 79.8004i | −0.226063 | − | 0.226063i | 0.584983 | − | 0.811046i | \(-0.301101\pi\) |
−0.811046 | + | 0.584983i | \(0.801101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 58.7348 | − | 48.0365i | 0.165450 | − | 0.135314i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7.67587i | − | 0.0213812i | −0.999943 | − | 0.0106906i | \(-0.996597\pi\) | ||
0.999943 | − | 0.0106906i | \(-0.00340299\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 258.763 | 0.716796 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 218.955 | + | 21.9389i | 0.599875 | + | 0.0601066i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.7561 | − | 31.7561i | 0.0865288 | − | 0.0865288i | −0.662518 | − | 0.749046i | \(-0.730512\pi\) |
0.749046 | + | 0.662518i | \(0.230512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −306.930 | −0.827304 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 209.534 | + | 209.534i | 0.561754 | + | 0.561754i | 0.929805 | − | 0.368052i | \(-0.119975\pi\) |
−0.368052 | + | 0.929805i | \(0.619975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −103.261 | + | 103.261i | −0.273901 | + | 0.273901i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 509.263i | 1.34370i | 0.740686 | + | 0.671851i | \(0.234500\pi\) | ||||
−0.740686 | + | 0.671851i | \(0.765500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −82.6383 | − | 82.6383i | −0.215766 | − | 0.215766i | 0.590946 | − | 0.806711i | \(-0.298755\pi\) |
−0.806711 | + | 0.590946i | \(0.798755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.6124 | + | 175.775i | −0.0457465 | + | 0.456559i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 222.388i | − | 0.571692i | −0.958276 | − | 0.285846i | \(-0.907725\pi\) | ||
0.958276 | − | 0.285846i | \(-0.0922747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 280.385 | 0.717097 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −456.112 | − | 557.694i | −1.15471 | − | 1.41188i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −282.792 | + | 282.792i | −0.712323 | + | 0.712323i | −0.967021 | − | 0.254698i | \(-0.918024\pi\) |
0.254698 | + | 0.967021i | \(0.418024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −104.462 | −0.260504 | −0.130252 | − | 0.991481i | \(-0.541579\pi\) | ||||
−0.130252 | + | 0.991481i | \(0.541579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −71.4599 | − | 71.4599i | −0.177320 | − | 0.177320i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −292.014 | + | 292.014i | −0.717478 | + | 0.717478i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 198.833i | 0.486144i | 0.970008 | + | 0.243072i | \(0.0781551\pi\) | ||||
−0.970008 | + | 0.243072i | \(0.921845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.1036 | + | 45.1036i | 0.109210 | + | 0.109210i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 412.266 | + | 41.3084i | 0.993412 | + | 0.0995383i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 205.468i | 0.490377i | 0.969475 | + | 0.245189i | \(0.0788499\pi\) | ||||
−0.969475 | + | 0.245189i | \(0.921150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −628.299 | −1.49240 | −0.746199 | − | 0.665723i | \(-0.768123\pi\) | ||||
−0.746199 | + | 0.665723i | \(0.768123\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −91.7562 | − | 138.333i | −0.215897 | − | 0.325490i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −186.499 | + | 186.499i | −0.436766 | + | 0.436766i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 325.388 | 0.754961 | 0.377481 | − | 0.926017i | \(-0.376790\pi\) | ||||
0.377481 | + | 0.926017i | \(0.376790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −42.3633 | − | 42.3633i | −0.0978366 | − | 0.0978366i | 0.656494 | − | 0.754331i | \(-0.272039\pi\) |
−0.754331 | + | 0.656494i | \(0.772039\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −301.912 | + | 301.912i | −0.690875 | + | 0.690875i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 239.832i | 0.546315i | 0.961969 | + | 0.273158i | \(0.0880681\pi\) | ||||
−0.961969 | + | 0.273158i | \(0.911932\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 345.233 | + | 345.233i | 0.779307 | + | 0.779307i | 0.979713 | − | 0.200406i | \(-0.0642261\pi\) |
−0.200406 | + | 0.979713i | \(0.564226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 393.155 | + | 480.715i | 0.883494 | + | 1.08026i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.5708i | 0.0658593i | 0.999458 | + | 0.0329296i | \(0.0104837\pi\) | ||||
−0.999458 | + | 0.0329296i | \(0.989516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −76.7831 | −0.170251 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −81.4726 | + | 66.6327i | −0.179061 | + | 0.146445i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −351.775 | + | 351.775i | −0.769749 | + | 0.769749i | −0.978062 | − | 0.208313i | \(-0.933203\pi\) |
0.208313 | + | 0.978062i | \(0.433203\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 832.442 | 1.80573 | 0.902865 | − | 0.429923i | \(-0.141459\pi\) | ||||
0.902865 | + | 0.429923i | \(0.141459\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 129.749 | + | 129.749i | 0.280235 | + | 0.280235i | 0.833203 | − | 0.552968i | \(-0.186505\pi\) |
−0.552968 | + | 0.833203i | \(0.686505\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −310.447 | + | 310.447i | −0.664769 | + | 0.664769i | −0.956500 | − | 0.291731i | \(-0.905769\pi\) |
0.291731 | + | 0.956500i | \(0.405769\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 320.846i | − | 0.684108i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 382.956 | + | 382.956i | 0.809633 | + | 0.809633i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 247.755 | + | 50.1529i | 0.521590 | + | 0.105585i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 137.105i | − | 0.286231i | −0.989706 | − | 0.143115i | \(-0.954288\pi\) | ||
0.989706 | − | 0.143115i | \(-0.0457120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −246.046 | −0.511529 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.6669 | + | 146.378i | −0.0302410 | + | 0.301811i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 187.010 | − | 187.010i | 0.384003 | − | 0.384003i | −0.488539 | − | 0.872542i | \(-0.662470\pi\) |
0.872542 | + | 0.488539i | \(0.162470\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 97.2541 | 0.198073 | 0.0990367 | − | 0.995084i | \(-0.468424\pi\) | ||||
0.0990367 | + | 0.995084i | \(0.468424\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −158.395 | − | 158.395i | −0.321289 | − | 0.321289i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 52.1824 | − | 52.1824i | 0.104995 | − | 0.104995i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 175.306i | 0.351314i | 0.984451 | + | 0.175657i | \(0.0562049\pi\) | ||||
−0.984451 | + | 0.175657i | \(0.943795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −252.151 | − | 252.151i | −0.501293 | − | 0.501293i | 0.410546 | − | 0.911840i | \(-0.365338\pi\) |
−0.911840 | + | 0.410546i | \(0.865338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −528.159 | + | 431.957i | −1.04586 | + | 0.855361i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 185.839i | − | 0.365106i | −0.983196 | − | 0.182553i | \(-0.941564\pi\) | ||
0.983196 | − | 0.182553i | \(-0.0584362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 214.020 | 0.418825 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −345.275 | − | 34.5960i | −0.670437 | − | 0.0671768i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −123.996 | + | 123.996i | −0.239837 | + | 0.239837i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 877.064 | 1.68343 | 0.841713 | − | 0.539926i | \(-0.181548\pi\) | ||||
0.841713 | + | 0.539926i | \(0.181548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 526.019 | + | 526.019i | 1.00577 | + | 1.00577i | 0.999983 | + | 0.00578841i | \(0.00184252\pi\) |
0.00578841 | + | 0.999983i | \(0.498157\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 109.615 | − | 109.615i | 0.207998 | − | 0.207998i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1254.14i | 2.37077i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.3481 | − | 32.3481i | −0.0606905 | − | 0.0606905i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.3125 | + | 202.723i | −0.0379673 | + | 0.378921i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 184.188i | − | 0.341723i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −253.279 | −0.468168 | −0.234084 | − | 0.972216i | \(-0.575209\pi\) | ||||
−0.234084 | + | 0.972216i | \(0.575209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −566.348 | − | 692.481i | −1.03917 | − | 1.27061i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 58.1608 | − | 58.1608i | 0.106327 | − | 0.106327i | −0.651942 | − | 0.758269i | \(-0.726045\pi\) |
0.758269 | + | 0.651942i | \(0.226045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 341.113 | 0.619080 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −495.479 | − | 495.479i | −0.895983 | − | 0.895983i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −595.191 | + | 595.191i | −1.06857 | + | 1.06857i | −0.0710965 | + | 0.997469i | \(0.522650\pi\) |
−0.997469 | + | 0.0710965i | \(0.977350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 322.672i | 0.577232i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −353.520 | − | 353.520i | −0.627922 | − | 0.627922i | 0.319623 | − | 0.947545i | \(-0.396444\pi\) |
−0.947545 | + | 0.319623i | \(0.896444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 180.550 | + | 18.0909i | 0.319558 | + | 0.0320192i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 513.090i | − | 0.901739i | −0.892590 | − | 0.450870i | \(-0.851114\pi\) | ||
0.892590 | − | 0.450870i | \(-0.148886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 135.817 | 0.237858 | 0.118929 | − | 0.992903i | \(-0.462054\pi\) | ||||
0.118929 | + | 0.992903i | \(0.462054\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 879.744 | − | 583.534i | 1.52999 | − | 1.01484i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −610.805 | + | 610.805i | −1.05859 | + | 1.05859i | −0.0604145 | + | 0.998173i | \(0.519242\pi\) |
−0.998173 | + | 0.0604145i | \(0.980758\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 402.974 | 0.693587 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 324.250 | + | 324.250i | 0.556175 | + | 0.556175i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −394.607 | + | 394.607i | −0.672243 | + | 0.672243i | −0.958233 | − | 0.285989i | \(-0.907678\pi\) |
0.285989 | + | 0.958233i | \(0.407678\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 236.062i | 0.400785i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 343.990 | + | 343.990i | 0.580084 | + | 0.580084i | 0.934926 | − | 0.354842i | \(-0.115465\pi\) |
−0.354842 | + | 0.934926i | \(0.615465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −102.210 | − | 124.974i | −0.171782 | − | 0.210040i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 852.943i | − | 1.42395i | −0.702207 | − | 0.711973i | \(-0.747802\pi\) | ||
0.702207 | − | 0.711973i | \(-0.252198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 708.388 | 1.17868 | 0.589341 | − | 0.807885i | \(-0.299388\pi\) | ||||
0.589341 | + | 0.807885i | \(0.299388\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −264.019 | + | 215.929i | −0.436394 | + | 0.356907i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −345.248 | + | 345.248i | −0.568778 | + | 0.568778i | −0.931786 | − | 0.363008i | \(-0.881750\pi\) |
0.363008 | + | 0.931786i | \(0.381750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −104.476 | −0.170993 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −375.137 | − | 375.137i | −0.611969 | − | 0.611969i | 0.331489 | − | 0.943459i | \(-0.392449\pi\) |
−0.943459 | + | 0.331489i | \(0.892449\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 147.878 | − | 147.878i | 0.239673 | − | 0.239673i | −0.577042 | − | 0.816715i | \(-0.695793\pi\) |
0.816715 | + | 0.577042i | \(0.195793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1013.22i | 1.63686i | 0.574606 | + | 0.818430i | \(0.305155\pi\) | ||||
−0.574606 | + | 0.818430i | \(0.694845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 427.087 | + | 427.087i | 0.685533 | + | 0.685533i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −575.794 | − | 243.076i | −0.921271 | − | 0.388921i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 377.419i | − | 0.600030i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −656.253 | −1.04002 | −0.520010 | − | 0.854160i | \(-0.674072\pi\) | ||||
−0.520010 | + | 0.854160i | \(0.674072\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.2226 | − | 581.073i | 0.0916891 | − | 0.915075i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 77.5970 | − | 77.5970i | 0.121816 | − | 0.121816i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 64.9961 | 0.101398 | 0.0506990 | − | 0.998714i | \(-0.483855\pi\) | ||||
0.0506990 | + | 0.998714i | \(0.483855\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −183.525 | − | 183.525i | −0.285420 | − | 0.285420i | 0.549846 | − | 0.835266i | \(-0.314686\pi\) |
−0.835266 | + | 0.549846i | \(0.814686\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −153.861 | + | 153.861i | −0.237807 | + | 0.237807i | −0.815941 | − | 0.578135i | \(-0.803781\pi\) |
0.578135 | + | 0.815941i | \(0.303781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 95.2977i | − | 0.146838i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −51.2563 | − | 51.2563i | −0.0784935 | − | 0.0784935i | 0.666770 | − | 0.745264i | \(-0.267676\pi\) |
−0.745264 | + | 0.666770i | \(0.767676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −566.876 | + | 463.622i | −0.865460 | + | 0.707820i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 577.821i | 0.876815i | 0.898776 | + | 0.438407i | \(0.144457\pi\) | ||||
−0.898776 | + | 0.438407i | \(0.855543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −376.303 | −0.569294 | −0.284647 | − | 0.958632i | \(-0.591876\pi\) | ||||
−0.284647 | + | 0.958632i | \(0.591876\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 244.627 | + | 24.5113i | 0.367860 | + | 0.0368590i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1007.33 | − | 1007.33i | 1.51024 | − | 1.51024i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 394.047 | 0.587253 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 321.691 | + | 321.691i | 0.477996 | + | 0.477996i | 0.904490 | − | 0.426494i | \(-0.140252\pi\) |
−0.426494 | + | 0.904490i | \(0.640252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 600.196 | − | 600.196i | 0.886552 | − | 0.886552i | −0.107638 | − | 0.994190i | \(-0.534329\pi\) |
0.994190 | + | 0.107638i | \(0.0343288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 143.079i | 0.210721i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 731.092 | + | 731.092i | 1.07041 | + | 1.07041i | 0.997326 | + | 0.0730866i | \(0.0232850\pi\) |
0.0730866 | + | 0.997326i | \(0.476715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −82.0569 | + | 818.943i | −0.119791 | + | 1.19554i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 273.207i | 0.396527i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1104.64 | 1.59862 | 0.799308 | − | 0.600921i | \(-0.205199\pi\) | ||||
0.799308 | + | 0.600921i | \(0.205199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −530.372 | − | 648.493i | −0.763125 | − | 0.933083i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.6199 | − | 49.6199i | 0.0711907 | − | 0.0711907i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −664.424 | −0.947823 | −0.473911 | − | 0.880573i | \(-0.657158\pi\) | ||||
−0.473911 | + | 0.880573i | \(0.657158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 406.396 | + | 406.396i | 0.578089 | + | 0.578089i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −469.239 | + | 469.239i | −0.663704 | + | 0.663704i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 647.253i | 0.912909i | 0.889747 | + | 0.456455i | \(0.150881\pi\) | ||||
−0.889747 | + | 0.456455i | \(0.849119\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 697.110 | + | 697.110i | 0.977713 | + | 0.977713i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 156.463 | + | 15.6773i | 0.218829 | + | 0.0219264i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 42.0429i | − | 0.0584742i | −0.999573 | − | 0.0292371i | \(-0.990692\pi\) | ||
0.999573 | − | 0.0292371i | \(-0.00930778\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −337.493 | −0.468091 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −826.637 | − | 167.335i | −1.14019 | − | 0.230807i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −193.225 | + | 193.225i | −0.265784 | + | 0.265784i | −0.827399 | − | 0.561615i | \(-0.810180\pi\) |
0.561615 | + | 0.827399i | \(0.310180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −494.960 | −0.677099 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 951.899 | + | 951.899i | 1.29863 | + | 1.29863i | 0.929294 | + | 0.369340i | \(0.120416\pi\) |
0.369340 | + | 0.929294i | \(0.379584\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −338.952 | + | 338.952i | −0.459908 | + | 0.459908i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1019.58i | − | 1.37968i | −0.723963 | − | 0.689839i | \(-0.757681\pi\) | ||
0.723963 | − | 0.689839i | \(-0.242319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 418.295 | + | 418.295i | 0.562981 | + | 0.562981i | 0.930153 | − | 0.367172i | \(-0.119674\pi\) |
−0.367172 | + | 0.930153i | \(0.619674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −594.937 | − | 727.436i | −0.798573 | − | 0.976424i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 198.154i | 0.264557i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.35093 | 0.00978818 | 0.00489409 | − | 0.999988i | \(-0.498442\pi\) | ||||
0.00489409 | + | 0.999988i | \(0.498442\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 301.076 | − | 246.236i | 0.398777 | − | 0.326141i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −575.920 | + | 575.920i | −0.760793 | + | 0.760793i | −0.976466 | − | 0.215673i | \(-0.930806\pi\) |
0.215673 | + | 0.976466i | \(0.430806\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1243.54 | −1.63408 | −0.817042 | − | 0.576578i | \(-0.804388\pi\) | ||||
−0.817042 | + | 0.576578i | \(0.804388\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −615.229 | − | 615.229i | −0.806329 | − | 0.806329i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.1481 | − | 40.1481i | 0.0523443 | − | 0.0523443i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 872.201i | − | 1.13420i | −0.823648 | − | 0.567101i | \(-0.808065\pi\) | ||
0.823648 | − | 0.567101i | \(-0.191935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −502.677 | − | 502.677i | −0.650294 | − | 0.650294i | 0.302770 | − | 0.953064i | \(-0.402089\pi\) |
−0.953064 | + | 0.302770i | \(0.902089\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 115.802 | − | 572.062i | 0.149422 | − | 0.738144i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 106.859i | 0.137175i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −110.254 | −0.141171 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 69.0210 | − | 688.843i | 0.0879249 | − | 0.877508i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 249.776 | − | 249.776i | 0.317377 | − | 0.317377i | −0.530382 | − | 0.847759i | \(-0.677951\pi\) |
0.847759 | + | 0.530382i | \(0.177951\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 176.481 | 0.223111 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 166.009 | + | 166.009i | 0.209342 | + | 0.209342i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.2255 | + | 21.2255i | −0.0266317 | + | 0.0266317i | −0.720297 | − | 0.693666i | \(-0.755995\pi\) |
0.693666 | + | 0.720297i | \(0.255995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 160.260i | − | 0.200576i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −226.097 | − | 226.097i | −0.281565 | − | 0.281565i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 794.786 | − | 650.019i | 0.987311 | − | 0.807476i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 218.418i | − | 0.269986i | −0.990847 | − | 0.134993i | \(-0.956899\pi\) | ||
0.990847 | − | 0.134993i | \(-0.0431011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 708.023 | 0.873024 | 0.436512 | − | 0.899698i | \(-0.356214\pi\) | ||||
0.436512 | + | 0.899698i | \(0.356214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1129.20 | − | 113.144i | −1.38552 | − | 0.138827i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 532.962 | − | 532.962i | 0.652340 | − | 0.652340i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1021.92 | 1.24472 | 0.622361 | − | 0.782731i | \(-0.286174\pi\) | ||||
0.622361 | + | 0.782731i | \(0.286174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 196.702 | + | 196.702i | 0.239007 | + | 0.239007i | 0.816439 | − | 0.577432i | \(-0.195945\pi\) |
−0.577432 | + | 0.816439i | \(0.695945\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −870.595 | + | 870.595i | −1.05271 | + | 1.05271i | −0.0541833 | + | 0.998531i | \(0.517256\pi\) |
−0.998531 | + | 0.0541833i | \(0.982744\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 460.400i | − | 0.555368i | −0.960672 | − | 0.277684i | \(-0.910433\pi\) | ||
0.960672 | − | 0.277684i | \(-0.0895668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 119.029 | + | 119.029i | 0.142892 | + | 0.142892i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.8864 | + | 258.352i | −0.0310017 | + | 0.309403i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1386.65i | 1.65274i | 0.563130 | + | 0.826368i | \(0.309597\pi\) | ||||
−0.563130 | + | 0.826368i | \(0.690403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −297.127 | −0.353302 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −475.646 | − | 581.578i | −0.562894 | − | 0.688258i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −234.565 | + | 234.565i | −0.276936 | + | 0.276936i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2400.24 | 2.82049 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −808.704 | − | 808.704i | −0.948070 | − | 0.948070i | 0.0506467 | − | 0.998717i | \(-0.483872\pi\) |
−0.998717 | + | 0.0506467i | \(0.983872\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −945.140 | + | 945.140i | −1.10285 | + | 1.10285i | −0.108781 | + | 0.994066i | \(0.534695\pi\) |
−0.994066 | + | 0.108781i | \(0.965305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 924.339i | − | 1.07606i | −0.842924 | − | 0.538032i | \(-0.819168\pi\) | ||
0.842924 | − | 0.538032i | \(-0.180832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 788.779 | + | 788.779i | 0.913997 | + | 0.913997i | 0.996584 | − | 0.0825868i | \(-0.0263182\pi\) |
−0.0825868 | + | 0.996584i | \(0.526318\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 835.499 | + | 83.7157i | 0.965895 | + | 0.0967812i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1046.88i | 1.20469i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −285.595 | −0.327893 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −580.793 | − | 179.403i | −0.663763 | − | 0.205032i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −862.503 | + | 862.503i | −0.983470 | + | 0.983470i | −0.999866 | − | 0.0163953i | \(-0.994781\pi\) |
0.0163953 | + | 0.999866i | \(0.494781\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −356.941 | −0.405154 | −0.202577 | − | 0.979266i | \(-0.564932\pi\) | ||||
−0.202577 | + | 0.979266i | \(0.564932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 314.661 | + | 314.661i | 0.356354 | + | 0.356354i | 0.862467 | − | 0.506113i | \(-0.168918\pi\) |
−0.506113 | + | 0.862467i | \(0.668918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −407.418 | + | 407.418i | −0.459321 | + | 0.459321i | −0.898432 | − | 0.439112i | \(-0.855293\pi\) |
0.439112 | + | 0.898432i | \(0.355293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 567.977i | − | 0.638894i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 172.565 | + | 172.565i | 0.193242 | + | 0.193242i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 928.399 | + | 1135.17i | 1.03732 | + | 1.26834i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 787.624i | − | 0.876111i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −419.083 | −0.465131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 707.581 | − | 578.698i | 0.781858 | − | 0.639445i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 361.599 | − | 361.599i | 0.398676 | − | 0.398676i | −0.479090 | − | 0.877766i | \(-0.659033\pi\) |
0.877766 | + | 0.479090i | \(0.159033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.3980 | −0.0652009 | −0.0326004 | − | 0.999468i | \(-0.510379\pi\) | ||||
−0.0326004 | + | 0.999468i | \(0.510379\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −425.714 | − | 425.714i | −0.466281 | − | 0.466281i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −503.636 | + | 503.636i | −0.549222 | + | 0.549222i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 272.183i | 0.296173i | 0.988974 | + | 0.148087i | \(0.0473115\pi\) | ||||
−0.988974 | + | 0.148087i | \(0.952689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.4492 | − | 46.4492i | −0.0503241 | − | 0.0503241i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −785.480 | − | 1184.20i | −0.849168 | − | 1.28022i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1690.97i | − | 1.82020i | −0.414383 | − | 0.910102i | \(-0.636003\pi\) | ||
0.414383 | − | 0.910102i | \(-0.363997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −256.336 | −0.275334 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.0481 | + | 240.005i | −0.0257199 | + | 0.256689i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −658.662 | + | 658.662i | −0.702947 | + | 0.702947i | −0.965042 | − | 0.262095i | \(-0.915587\pi\) |
0.262095 | + | 0.965042i | \(0.415587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −155.326 | −0.165065 | −0.0825326 | − | 0.996588i | \(-0.526301\pi\) | ||||
−0.0825326 | + | 0.996588i | \(0.526301\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 315.563 | + | 315.563i | 0.334638 | + | 0.334638i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 125.521 | − | 125.521i | 0.132546 | − | 0.132546i | −0.637721 | − | 0.770267i | \(-0.720123\pi\) |
0.770267 | + | 0.637721i | \(0.220123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 190.505i | − | 0.200743i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1133.35 | + | 1133.35i | 1.18924 | + | 1.18924i | 0.977277 | + | 0.211965i | \(0.0679863\pi\) |
0.211965 | + | 0.977277i | \(0.432014\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1121.68 | − | 917.374i | 1.17454 | − | 0.960601i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 800.486i | 0.834709i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −415.937 | −0.432817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1384.55 | − | 138.729i | −1.43476 | − | 0.143761i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 112.878 | − | 112.878i | 0.116730 | − | 0.116730i | −0.646329 | − | 0.763059i | \(-0.723697\pi\) |
0.763059 | + | 0.646329i | \(0.223697\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1054.48 | −1.08597 | −0.542986 | − | 0.839742i | \(-0.682706\pi\) | ||||
−0.542986 | + | 0.839742i | \(0.682706\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −576.148 | − | 576.148i | −0.592135 | − | 0.592135i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 277.019 | − | 277.019i | 0.283540 | − | 0.283540i | −0.550979 | − | 0.834519i | \(-0.685746\pi\) |
0.834519 | + | 0.550979i | \(0.185746\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 902.376i | − | 0.921733i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −824.165 | − | 824.165i | −0.838418 | − | 0.838418i | 0.150233 | − | 0.988651i | \(-0.451998\pi\) |
−0.988651 | + | 0.150233i | \(0.951998\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 127.867 | − | 1276.14i | 0.129814 | − | 1.29557i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3147.75i | − | 3.18276i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 130.497 | 0.131682 | 0.0658412 | − | 0.997830i | \(-0.479027\pi\) | ||||
0.0658412 | + | 0.997830i | \(0.479027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 508.153 | + | 621.325i | 0.510706 | + | 0.624447i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1139.64 | − | 1139.64i | 1.14306 | − | 1.14306i | 0.155178 | − | 0.987887i | \(-0.450405\pi\) |
0.987887 | − | 0.155178i | \(-0.0495951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.3.l.g.973.10 | 24 | ||
3.2 | odd | 2 | 1620.3.l.f.973.3 | 24 | |||
5.2 | odd | 4 | inner | 1620.3.l.g.1297.10 | 24 | ||
9.2 | odd | 6 | 180.3.u.a.13.10 | ✓ | 48 | ||
9.4 | even | 3 | 540.3.v.a.73.3 | 48 | |||
9.5 | odd | 6 | 180.3.u.a.133.4 | yes | 48 | ||
9.7 | even | 3 | 540.3.v.a.253.6 | 48 | |||
15.2 | even | 4 | 1620.3.l.f.1297.3 | 24 | |||
45.2 | even | 12 | 180.3.u.a.157.4 | yes | 48 | ||
45.7 | odd | 12 | 540.3.v.a.37.3 | 48 | |||
45.22 | odd | 12 | 540.3.v.a.397.6 | 48 | |||
45.32 | even | 12 | 180.3.u.a.97.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.u.a.13.10 | ✓ | 48 | 9.2 | odd | 6 | ||
180.3.u.a.97.10 | yes | 48 | 45.32 | even | 12 | ||
180.3.u.a.133.4 | yes | 48 | 9.5 | odd | 6 | ||
180.3.u.a.157.4 | yes | 48 | 45.2 | even | 12 | ||
540.3.v.a.37.3 | 48 | 45.7 | odd | 12 | |||
540.3.v.a.73.3 | 48 | 9.4 | even | 3 | |||
540.3.v.a.253.6 | 48 | 9.7 | even | 3 | |||
540.3.v.a.397.6 | 48 | 45.22 | odd | 12 | |||
1620.3.l.f.973.3 | 24 | 3.2 | odd | 2 | |||
1620.3.l.f.1297.3 | 24 | 15.2 | even | 4 | |||
1620.3.l.g.973.10 | 24 | 1.1 | even | 1 | trivial | ||
1620.3.l.g.1297.10 | 24 | 5.2 | odd | 4 | inner |