Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(506,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.506");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.c (of order \(2\), degree \(1\), 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 506.3 | ||
Root | \(-1.27597 + 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.506 |
Dual form | 845.2.c.g.506.6 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.21969i | − 0.862449i | −0.902245 | − | 0.431224i | \(-0.858082\pi\) | ||||
0.902245 | − | 0.431224i | \(-0.141918\pi\) | |||||||
\(3\) | 2.33225 | 1.34652 | 0.673262 | − | 0.739404i | \(-0.264893\pi\) | ||||
0.673262 | + | 0.739404i | \(0.264893\pi\) | |||||||
\(4\) | 0.512364 | 0.256182 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − 2.84461i | − 1.16131i | ||||||||
\(7\) | 3.60020i | 1.36075i | 0.732866 | + | 0.680373i | \(0.238182\pi\) | ||||
−0.732866 | + | 0.680373i | \(0.761818\pi\) | |||||||
\(8\) | − 3.06430i | − 1.08339i | ||||||||
\(9\) | 2.43937 | 0.813125 | ||||||||
\(10\) | 1.21969 | 0.385699 | ||||||||
\(11\) | 5.37182i | 1.61966i | 0.586662 | + | 0.809832i | \(0.300442\pi\) | ||||
−0.586662 | + | 0.809832i | \(0.699558\pi\) | |||||||
\(12\) | 1.19496 | 0.344955 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.39111 | 1.17357 | ||||||||
\(15\) | 2.33225i | 0.602183i | ||||||||
\(16\) | −2.71276 | −0.678189 | ||||||||
\(17\) | 1.13186 | 0.274515 | 0.137258 | − | 0.990535i | \(-0.456171\pi\) | ||||
0.137258 | + | 0.990535i | \(0.456171\pi\) | |||||||
\(18\) | − 2.97527i | − 0.701278i | ||||||||
\(19\) | − 2.26795i | − 0.520303i | −0.965568 | − | 0.260152i | \(-0.916227\pi\) | ||||
0.965568 | − | 0.260152i | \(-0.0837725\pi\) | |||||||
\(20\) | 0.512364i | 0.114568i | ||||||||
\(21\) | 8.39654i | 1.83228i | ||||||||
\(22\) | 6.55193 | 1.39688 | ||||||||
\(23\) | 3.89287 | 0.811720 | 0.405860 | − | 0.913935i | \(-0.366972\pi\) | ||||
0.405860 | + | 0.913935i | \(0.366972\pi\) | |||||||
\(24\) | − 7.14670i | − 1.45881i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.30752 | −0.251632 | ||||||||
\(28\) | 1.84461i | 0.348599i | ||||||||
\(29\) | −0.0247279 | −0.00459185 | −0.00229593 | − | 0.999997i | \(-0.500731\pi\) | ||||
−0.00229593 | + | 0.999997i | \(0.500731\pi\) | |||||||
\(30\) | 2.84461 | 0.519352 | ||||||||
\(31\) | − 5.46410i | − 0.981382i | −0.871334 | − | 0.490691i | \(-0.836744\pi\) | ||||
0.871334 | − | 0.490691i | \(-0.163256\pi\) | |||||||
\(32\) | − 2.81988i | − 0.498490i | ||||||||
\(33\) | 12.5284i | 2.18091i | ||||||||
\(34\) | − 1.38051i | − 0.236755i | ||||||||
\(35\) | −3.60020 | −0.608544 | ||||||||
\(36\) | 1.24985 | 0.208308 | ||||||||
\(37\) | − 8.70406i | − 1.43094i | −0.698644 | − | 0.715470i | \(-0.746213\pi\) | ||||
0.698644 | − | 0.715470i | \(-0.253787\pi\) | |||||||
\(38\) | −2.76619 | −0.448735 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.06430 | 0.484508 | ||||||||
\(41\) | − 3.73205i | − 0.582848i | −0.956594 | − | 0.291424i | \(-0.905871\pi\) | ||||
0.956594 | − | 0.291424i | \(-0.0941291\pi\) | |||||||
\(42\) | 10.2412 | 1.58024 | ||||||||
\(43\) | 1.13186 | 0.172606 | 0.0863031 | − | 0.996269i | \(-0.472495\pi\) | ||||
0.0863031 | + | 0.996269i | \(0.472495\pi\) | |||||||
\(44\) | 2.75232i | 0.414929i | ||||||||
\(45\) | 2.43937i | 0.363640i | ||||||||
\(46\) | − 4.74809i | − 0.700067i | ||||||||
\(47\) | 2.58535i | 0.377113i | 0.982062 | + | 0.188556i | \(0.0603808\pi\) | ||||
−0.982062 | + | 0.188556i | \(0.939619\pi\) | |||||||
\(48\) | −6.32681 | −0.913197 | ||||||||
\(49\) | −5.96141 | −0.851630 | ||||||||
\(50\) | 1.21969i | 0.172490i | ||||||||
\(51\) | 2.63977 | 0.369641 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.43937 | −0.609795 | −0.304897 | − | 0.952385i | \(-0.598622\pi\) | ||||
−0.304897 | + | 0.952385i | \(0.598622\pi\) | |||||||
\(54\) | 1.59476i | 0.217020i | ||||||||
\(55\) | −5.37182 | −0.724336 | ||||||||
\(56\) | 11.0321 | 1.47422 | ||||||||
\(57\) | − 5.28942i | − 0.700600i | ||||||||
\(58\) | 0.0301603i | 0.00396024i | ||||||||
\(59\) | − 0.171425i | − 0.0223176i | −0.999938 | − | 0.0111588i | \(-0.996448\pi\) | ||||
0.999938 | − | 0.0111588i | \(-0.00355203\pi\) | |||||||
\(60\) | 1.19496i | 0.154269i | ||||||||
\(61\) | 3.36023 | 0.430234 | 0.215117 | − | 0.976588i | \(-0.430987\pi\) | ||||
0.215117 | + | 0.976588i | \(0.430987\pi\) | |||||||
\(62\) | −6.66449 | −0.846391 | ||||||||
\(63\) | 8.78222i | 1.10646i | ||||||||
\(64\) | −8.86488 | −1.10811 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.2807 | 1.88093 | ||||||||
\(67\) | − 6.39980i | − 0.781861i | −0.920420 | − | 0.390930i | \(-0.872153\pi\) | ||||
0.920420 | − | 0.390930i | \(-0.127847\pi\) | |||||||
\(68\) | 0.579922 | 0.0703258 | ||||||||
\(69\) | 9.07914 | 1.09300 | ||||||||
\(70\) | 4.39111i | 0.524838i | ||||||||
\(71\) | 10.7973i | 1.28141i | 0.767788 | + | 0.640703i | \(0.221357\pi\) | ||||
−0.767788 | + | 0.640703i | \(0.778643\pi\) | |||||||
\(72\) | − 7.47497i | − 0.880933i | ||||||||
\(73\) | − 4.70308i | − 0.550454i | −0.961379 | − | 0.275227i | \(-0.911247\pi\) | ||||
0.961379 | − | 0.275227i | \(-0.0887531\pi\) | |||||||
\(74\) | −10.6162 | −1.23411 | ||||||||
\(75\) | −2.33225 | −0.269305 | ||||||||
\(76\) | − 1.16202i | − 0.133292i | ||||||||
\(77\) | −19.3396 | −2.20395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9826 | −1.34815 | −0.674075 | − | 0.738663i | \(-0.735457\pi\) | ||||
−0.674075 | + | 0.738663i | \(0.735457\pi\) | |||||||
\(80\) | − 2.71276i | − 0.303295i | ||||||||
\(81\) | −10.3676 | −1.15195 | ||||||||
\(82\) | −4.55193 | −0.502677 | ||||||||
\(83\) | 12.1286i | 1.33129i | 0.746270 | + | 0.665643i | \(0.231843\pi\) | ||||
−0.746270 | + | 0.665643i | \(0.768157\pi\) | |||||||
\(84\) | 4.30209i | 0.469396i | ||||||||
\(85\) | 1.13186i | 0.122767i | ||||||||
\(86\) | − 1.38051i | − 0.148864i | ||||||||
\(87\) | −0.0576715 | −0.00618303 | ||||||||
\(88\) | 16.4608 | 1.75473 | ||||||||
\(89\) | − 16.1540i | − 1.71232i | −0.516707 | − | 0.856162i | \(-0.672842\pi\) | ||||
0.516707 | − | 0.856162i | \(-0.327158\pi\) | |||||||
\(90\) | 2.97527 | 0.313621 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.99457 | 0.207948 | ||||||||
\(93\) | − 12.7436i | − 1.32145i | ||||||||
\(94\) | 3.15332 | 0.325240 | ||||||||
\(95\) | 2.26795 | 0.232687 | ||||||||
\(96\) | − 6.57666i | − 0.671228i | ||||||||
\(97\) | − 12.1682i | − 1.23549i | −0.786379 | − | 0.617745i | \(-0.788046\pi\) | ||||
0.786379 | − | 0.617745i | \(-0.211954\pi\) | |||||||
\(98\) | 7.27105i | 0.734487i | ||||||||
\(99\) | 13.1039i | 1.31699i | ||||||||
\(100\) | −0.512364 | −0.0512364 | ||||||||
\(101\) | 4.05441 | 0.403429 | 0.201714 | − | 0.979444i | \(-0.435349\pi\) | ||||
0.201714 | + | 0.979444i | \(0.435349\pi\) | |||||||
\(102\) | − 3.21969i | − 0.318797i | ||||||||
\(103\) | 17.9035 | 1.76408 | 0.882041 | − | 0.471173i | \(-0.156169\pi\) | ||||
0.882041 | + | 0.471173i | \(0.156169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.39654 | −0.819419 | ||||||||
\(106\) | 5.41465i | 0.525917i | ||||||||
\(107\) | −9.13186 | −0.882810 | −0.441405 | − | 0.897308i | \(-0.645520\pi\) | ||||
−0.441405 | + | 0.897308i | \(0.645520\pi\) | |||||||
\(108\) | −0.669925 | −0.0644636 | ||||||||
\(109\) | − 7.37605i | − 0.706498i | −0.935529 | − | 0.353249i | \(-0.885077\pi\) | ||||
0.935529 | − | 0.353249i | \(-0.114923\pi\) | |||||||
\(110\) | 6.55193i | 0.624702i | ||||||||
\(111\) | − 20.3000i | − 1.92679i | ||||||||
\(112\) | − 9.76645i | − 0.922843i | ||||||||
\(113\) | 7.07588 | 0.665643 | 0.332821 | − | 0.942990i | \(-0.391999\pi\) | ||||
0.332821 | + | 0.942990i | \(0.391999\pi\) | |||||||
\(114\) | −6.45143 | −0.604232 | ||||||||
\(115\) | 3.89287i | 0.363012i | ||||||||
\(116\) | −0.0126697 | −0.00117635 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.209084 | −0.0192478 | ||||||||
\(119\) | 4.07490i | 0.373545i | ||||||||
\(120\) | 7.14670 | 0.652401 | ||||||||
\(121\) | −17.8564 | −1.62331 | ||||||||
\(122\) | − 4.09843i | − 0.371055i | ||||||||
\(123\) | − 8.70406i | − 0.784819i | ||||||||
\(124\) | − 2.79961i | − 0.251412i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 10.7116 | 0.954262 | ||||||||
\(127\) | 11.4361 | 1.01479 | 0.507395 | − | 0.861713i | \(-0.330608\pi\) | ||||
0.507395 | + | 0.861713i | \(0.330608\pi\) | |||||||
\(128\) | 5.17262i | 0.457199i | ||||||||
\(129\) | 2.63977 | 0.232418 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5680 | −0.923328 | −0.461664 | − | 0.887055i | \(-0.652747\pi\) | ||||
−0.461664 | + | 0.887055i | \(0.652747\pi\) | |||||||
\(132\) | 6.41910i | 0.558711i | ||||||||
\(133\) | 8.16506 | 0.708001 | ||||||||
\(134\) | −7.80576 | −0.674315 | ||||||||
\(135\) | − 1.30752i | − 0.112533i | ||||||||
\(136\) | − 3.46834i | − 0.297408i | ||||||||
\(137\) | 3.78672i | 0.323522i | 0.986830 | + | 0.161761i | \(0.0517173\pi\) | ||||
−0.986830 | + | 0.161761i | \(0.948283\pi\) | |||||||
\(138\) | − 11.0737i | − 0.942656i | ||||||||
\(139\) | 2.01386 | 0.170814 | 0.0854068 | − | 0.996346i | \(-0.472781\pi\) | ||||
0.0854068 | + | 0.996346i | \(0.472781\pi\) | |||||||
\(140\) | −1.84461 | −0.155898 | ||||||||
\(141\) | 6.02968i | 0.507791i | ||||||||
\(142\) | 13.1694 | 1.10515 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.61742 | −0.551452 | ||||||||
\(145\) | − 0.0247279i | − 0.00205354i | ||||||||
\(146\) | −5.73629 | −0.474739 | ||||||||
\(147\) | −13.9035 | −1.14674 | ||||||||
\(148\) | − 4.45965i | − 0.366581i | ||||||||
\(149\) | 5.51780i | 0.452035i | 0.974123 | + | 0.226018i | \(0.0725707\pi\) | ||||
−0.974123 | + | 0.226018i | \(0.927429\pi\) | |||||||
\(150\) | 2.84461i | 0.232261i | ||||||||
\(151\) | − 4.88961i | − 0.397911i | −0.980009 | − | 0.198956i | \(-0.936245\pi\) | ||||
0.980009 | − | 0.198956i | \(-0.0637549\pi\) | |||||||
\(152\) | −6.94967 | −0.563693 | ||||||||
\(153\) | 2.76102 | 0.223215 | ||||||||
\(154\) | 23.5882i | 1.90079i | ||||||||
\(155\) | 5.46410 | 0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0405 | 0.801323 | 0.400661 | − | 0.916226i | \(-0.368780\pi\) | ||||
0.400661 | + | 0.916226i | \(0.368780\pi\) | |||||||
\(158\) | 14.6150i | 1.16271i | ||||||||
\(159\) | −10.3537 | −0.821103 | ||||||||
\(160\) | 2.81988 | 0.222931 | ||||||||
\(161\) | 14.0151i | 1.10454i | ||||||||
\(162\) | 12.6452i | 0.993501i | ||||||||
\(163\) | 6.78124i | 0.531148i | 0.964090 | + | 0.265574i | \(0.0855615\pi\) | ||||
−0.964090 | + | 0.265574i | \(0.914439\pi\) | |||||||
\(164\) | − 1.91217i | − 0.149315i | ||||||||
\(165\) | −12.5284 | −0.975335 | ||||||||
\(166\) | 14.7931 | 1.14817 | ||||||||
\(167\) | 10.4898i | 0.811726i | 0.913934 | + | 0.405863i | \(0.133029\pi\) | ||||
−0.913934 | + | 0.405863i | \(0.866971\pi\) | |||||||
\(168\) | 25.7295 | 1.98507 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.38051 | 0.105880 | ||||||||
\(171\) | − 5.53238i | − 0.423071i | ||||||||
\(172\) | 0.579922 | 0.0442186 | ||||||||
\(173\) | 4.45845 | 0.338970 | 0.169485 | − | 0.985533i | \(-0.445790\pi\) | ||||
0.169485 | + | 0.985533i | \(0.445790\pi\) | |||||||
\(174\) | 0.0703412i | 0.00533255i | ||||||||
\(175\) | − 3.60020i | − 0.272149i | ||||||||
\(176\) | − 14.5724i | − 1.09844i | ||||||||
\(177\) | − 0.399804i | − 0.0300511i | ||||||||
\(178\) | −19.7029 | −1.47679 | ||||||||
\(179\) | −18.6313 | −1.39257 | −0.696284 | − | 0.717766i | \(-0.745165\pi\) | ||||
−0.696284 | + | 0.717766i | \(0.745165\pi\) | |||||||
\(180\) | 1.24985i | 0.0931581i | ||||||||
\(181\) | −18.0900 | −1.34462 | −0.672310 | − | 0.740270i | \(-0.734698\pi\) | ||||
−0.672310 | + | 0.740270i | \(0.734698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.83690 | 0.579320 | ||||||||
\(184\) | − 11.9289i | − 0.879412i | ||||||||
\(185\) | 8.70406 | 0.639935 | ||||||||
\(186\) | −15.5432 | −1.13969 | ||||||||
\(187\) | 6.08012i | 0.444622i | ||||||||
\(188\) | 1.32464i | 0.0966095i | ||||||||
\(189\) | − 4.70732i | − 0.342407i | ||||||||
\(190\) | − 2.76619i | − 0.200680i | ||||||||
\(191\) | 27.3363 | 1.97799 | 0.988994 | − | 0.147958i | \(-0.0472701\pi\) | ||||
0.988994 | + | 0.147958i | \(0.0472701\pi\) | |||||||
\(192\) | −20.6751 | −1.49210 | ||||||||
\(193\) | 21.7674i | 1.56685i | 0.621486 | + | 0.783425i | \(0.286529\pi\) | ||||
−0.621486 | + | 0.783425i | \(0.713471\pi\) | |||||||
\(194\) | −14.8413 | −1.06555 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.05441 | −0.218172 | ||||||||
\(197\) | 1.69672i | 0.120886i | 0.998172 | + | 0.0604432i | \(0.0192514\pi\) | ||||
−0.998172 | + | 0.0604432i | \(0.980749\pi\) | |||||||
\(198\) | 15.9826 | 1.13583 | ||||||||
\(199\) | −25.3255 | −1.79527 | −0.897637 | − | 0.440735i | \(-0.854718\pi\) | ||||
−0.897637 | + | 0.440735i | \(0.854718\pi\) | |||||||
\(200\) | 3.06430i | 0.216679i | ||||||||
\(201\) | − 14.9259i | − 1.05279i | ||||||||
\(202\) | − 4.94511i | − 0.347937i | ||||||||
\(203\) | − 0.0890252i | − 0.00624834i | ||||||||
\(204\) | 1.35252 | 0.0946954 | ||||||||
\(205\) | 3.73205 | 0.260658 | ||||||||
\(206\) | − 21.8366i | − 1.52143i | ||||||||
\(207\) | 9.49617 | 0.660030 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.1830 | 0.842716 | ||||||||
\(210\) | 10.2412i | 0.706707i | ||||||||
\(211\) | −0.335507 | −0.0230973 | −0.0115486 | − | 0.999933i | \(-0.503676\pi\) | ||||
−0.0115486 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(212\) | −2.27458 | −0.156218 | ||||||||
\(213\) | 25.1820i | 1.72544i | ||||||||
\(214\) | 11.1380i | 0.761378i | ||||||||
\(215\) | 1.13186i | 0.0771919i | ||||||||
\(216\) | 4.00663i | 0.272616i | ||||||||
\(217\) | 19.6718 | 1.33541 | ||||||||
\(218\) | −8.99648 | −0.609318 | ||||||||
\(219\) | − 10.9688i | − 0.741200i | ||||||||
\(220\) | −2.75232 | −0.185562 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −24.7597 | −1.66176 | ||||||||
\(223\) | 12.2968i | 0.823452i | 0.911308 | + | 0.411726i | \(0.135074\pi\) | ||||
−0.911308 | + | 0.411726i | \(0.864926\pi\) | |||||||
\(224\) | 10.1521 | 0.678318 | ||||||||
\(225\) | −2.43937 | −0.162625 | ||||||||
\(226\) | − 8.63036i | − 0.574083i | ||||||||
\(227\) | 7.63227i | 0.506571i | 0.967392 | + | 0.253286i | \(0.0815112\pi\) | ||||
−0.967392 | + | 0.253286i | \(0.918489\pi\) | |||||||
\(228\) | − 2.71011i | − 0.179481i | ||||||||
\(229\) | − 14.4008i | − 0.951631i | −0.879545 | − | 0.475815i | \(-0.842153\pi\) | ||||
0.879545 | − | 0.475815i | \(-0.157847\pi\) | |||||||
\(230\) | 4.74809 | 0.313080 | ||||||||
\(231\) | −45.1047 | −2.96767 | ||||||||
\(232\) | 0.0757736i | 0.00497478i | ||||||||
\(233\) | −9.49617 | −0.622115 | −0.311057 | − | 0.950391i | \(-0.600683\pi\) | ||||
−0.311057 | + | 0.950391i | \(0.600683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.58535 | −0.168650 | ||||||||
\(236\) | − 0.0878318i | − 0.00571736i | ||||||||
\(237\) | −27.9464 | −1.81531 | ||||||||
\(238\) | 4.97010 | 0.322164 | ||||||||
\(239\) | 19.9143i | 1.28815i | 0.764962 | + | 0.644076i | \(0.222758\pi\) | ||||
−0.764962 | + | 0.644076i | \(0.777242\pi\) | |||||||
\(240\) | − 6.32681i | − 0.408394i | ||||||||
\(241\) | 23.2664i | 1.49872i | 0.662163 | + | 0.749360i | \(0.269639\pi\) | ||||
−0.662163 | + | 0.749360i | \(0.730361\pi\) | |||||||
\(242\) | 21.7792i | 1.40002i | ||||||||
\(243\) | −20.2572 | −1.29950 | ||||||||
\(244\) | 1.72166 | 0.110218 | ||||||||
\(245\) | − 5.96141i | − 0.380860i | ||||||||
\(246\) | −10.6162 | −0.676866 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.7436 | −1.06322 | ||||||||
\(249\) | 28.2869i | 1.79261i | ||||||||
\(250\) | −1.21969 | −0.0771398 | ||||||||
\(251\) | −11.8402 | −0.747344 | −0.373672 | − | 0.927561i | \(-0.621901\pi\) | ||||
−0.373672 | + | 0.927561i | \(0.621901\pi\) | |||||||
\(252\) | 4.49969i | 0.283454i | ||||||||
\(253\) | 20.9118i | 1.31471i | ||||||||
\(254\) | − 13.9485i | − 0.875205i | ||||||||
\(255\) | 2.63977i | 0.165309i | ||||||||
\(256\) | −11.4208 | −0.713800 | ||||||||
\(257\) | 5.55002 | 0.346201 | 0.173100 | − | 0.984904i | \(-0.444621\pi\) | ||||
0.173100 | + | 0.984904i | \(0.444621\pi\) | |||||||
\(258\) | − 3.21969i | − 0.200449i | ||||||||
\(259\) | 31.3363 | 1.94714 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0603205 | −0.00373375 | ||||||||
\(262\) | 12.8896i | 0.796323i | ||||||||
\(263\) | 6.85967 | 0.422985 | 0.211493 | − | 0.977380i | \(-0.432168\pi\) | ||||
0.211493 | + | 0.977380i | \(0.432168\pi\) | |||||||
\(264\) | 38.3907 | 2.36279 | ||||||||
\(265\) | − 4.43937i | − 0.272709i | ||||||||
\(266\) | − 9.95882i | − 0.610614i | ||||||||
\(267\) | − 37.6752i | − 2.30568i | ||||||||
\(268\) | − 3.27903i | − 0.200299i | ||||||||
\(269\) | −1.42199 | −0.0867001 | −0.0433501 | − | 0.999060i | \(-0.513803\pi\) | ||||
−0.0433501 | + | 0.999060i | \(0.513803\pi\) | |||||||
\(270\) | −1.59476 | −0.0970542 | ||||||||
\(271\) | − 9.96947i | − 0.605602i | −0.953054 | − | 0.302801i | \(-0.902078\pi\) | ||||
0.953054 | − | 0.302801i | \(-0.0979218\pi\) | |||||||
\(272\) | −3.07045 | −0.186173 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.61862 | 0.279021 | ||||||||
\(275\) | − 5.37182i | − 0.323933i | ||||||||
\(276\) | 4.65182 | 0.280007 | ||||||||
\(277\) | 17.5237 | 1.05290 | 0.526449 | − | 0.850206i | \(-0.323523\pi\) | ||||
0.526449 | + | 0.850206i | \(0.323523\pi\) | |||||||
\(278\) | − 2.45628i | − 0.147318i | ||||||||
\(279\) | − 13.3290i | − 0.797986i | ||||||||
\(280\) | 11.0321i | 0.659292i | ||||||||
\(281\) | 10.7352i | 0.640406i | 0.947349 | + | 0.320203i | \(0.103751\pi\) | ||||
−0.947349 | + | 0.320203i | \(0.896249\pi\) | |||||||
\(282\) | 7.35433 | 0.437944 | ||||||||
\(283\) | −1.31838 | −0.0783698 | −0.0391849 | − | 0.999232i | \(-0.512476\pi\) | ||||
−0.0391849 | + | 0.999232i | \(0.512476\pi\) | |||||||
\(284\) | 5.53216i | 0.328273i | ||||||||
\(285\) | 5.28942 | 0.313318 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.4361 | 0.793109 | ||||||||
\(288\) | − 6.87875i | − 0.405334i | ||||||||
\(289\) | −15.7189 | −0.924641 | ||||||||
\(290\) | −0.0301603 | −0.00177107 | ||||||||
\(291\) | − 28.3792i | − 1.66362i | ||||||||
\(292\) | − 2.40969i | − 0.141016i | ||||||||
\(293\) | 18.7427i | 1.09496i | 0.836820 | + | 0.547479i | \(0.184412\pi\) | ||||
−0.836820 | + | 0.547479i | \(0.815588\pi\) | |||||||
\(294\) | 16.9579i | 0.989004i | ||||||||
\(295\) | 0.171425 | 0.00998072 | ||||||||
\(296\) | −26.6718 | −1.55027 | ||||||||
\(297\) | − 7.02375i | − 0.407559i | ||||||||
\(298\) | 6.72998 | 0.389857 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.19496 | −0.0689910 | ||||||||
\(301\) | 4.07490i | 0.234873i | ||||||||
\(302\) | −5.96380 | −0.343178 | ||||||||
\(303\) | 9.45589 | 0.543226 | ||||||||
\(304\) | 6.15239i | 0.352864i | ||||||||
\(305\) | 3.36023i | 0.192406i | ||||||||
\(306\) | − 3.36758i | − 0.192512i | ||||||||
\(307\) | 14.3043i | 0.816387i | 0.912895 | + | 0.408194i | \(0.133841\pi\) | ||||
−0.912895 | + | 0.408194i | \(0.866159\pi\) | |||||||
\(308\) | −9.90891 | −0.564612 | ||||||||
\(309\) | 41.7553 | 2.37538 | ||||||||
\(310\) | − 6.66449i | − 0.378518i | ||||||||
\(311\) | −2.76102 | −0.156563 | −0.0782815 | − | 0.996931i | \(-0.524943\pi\) | ||||
−0.0782815 | + | 0.996931i | \(0.524943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3858 | −0.926179 | −0.463090 | − | 0.886311i | \(-0.653259\pi\) | ||||
−0.463090 | + | 0.886311i | \(0.653259\pi\) | |||||||
\(314\) | − 12.2463i | − 0.691100i | ||||||||
\(315\) | −8.78222 | −0.494822 | ||||||||
\(316\) | −6.13946 | −0.345372 | ||||||||
\(317\) | − 1.78575i | − 0.100297i | −0.998742 | − | 0.0501487i | \(-0.984030\pi\) | ||||
0.998742 | − | 0.0501487i | \(-0.0159695\pi\) | |||||||
\(318\) | 12.6283i | 0.708159i | ||||||||
\(319\) | − 0.132834i | − 0.00743725i | ||||||||
\(320\) | − 8.86488i | − 0.495562i | ||||||||
\(321\) | −21.2977 | −1.18872 | ||||||||
\(322\) | 17.0940 | 0.952613 | ||||||||
\(323\) | − 2.56699i | − 0.142831i | ||||||||
\(324\) | −5.31197 | −0.295110 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.27099 | 0.458088 | ||||||||
\(327\) | − 17.2028i | − 0.951316i | ||||||||
\(328\) | −11.4361 | −0.631454 | ||||||||
\(329\) | −9.30778 | −0.513155 | ||||||||
\(330\) | 15.2807i | 0.841176i | ||||||||
\(331\) | − 7.22440i | − 0.397089i | −0.980092 | − | 0.198545i | \(-0.936379\pi\) | ||||
0.980092 | − | 0.198545i | \(-0.0636215\pi\) | |||||||
\(332\) | 6.21425i | 0.341052i | ||||||||
\(333\) | − 21.2325i | − 1.16353i | ||||||||
\(334\) | 12.7943 | 0.700072 | ||||||||
\(335\) | 6.39980 | 0.349659 | ||||||||
\(336\) | − 22.7778i | − 1.24263i | ||||||||
\(337\) | 4.36219 | 0.237624 | 0.118812 | − | 0.992917i | \(-0.462091\pi\) | ||||
0.118812 | + | 0.992917i | \(0.462091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.5027 | 0.896303 | ||||||||
\(340\) | 0.579922i | 0.0314507i | ||||||||
\(341\) | 29.3521 | 1.58951 | ||||||||
\(342\) | −6.74777 | −0.364877 | ||||||||
\(343\) | 3.73913i | 0.201894i | ||||||||
\(344\) | − 3.46834i | − 0.187000i | ||||||||
\(345\) | 9.07914i | 0.488804i | ||||||||
\(346\) | − 5.43792i | − 0.292344i | ||||||||
\(347\) | −26.7072 | −1.43372 | −0.716858 | − | 0.697219i | \(-0.754420\pi\) | ||||
−0.716858 | + | 0.697219i | \(0.754420\pi\) | |||||||
\(348\) | −0.0295488 | −0.00158398 | ||||||||
\(349\) | 23.5711i | 1.26173i | 0.775892 | + | 0.630865i | \(0.217300\pi\) | ||||
−0.775892 | + | 0.630865i | \(0.782700\pi\) | |||||||
\(350\) | −4.39111 | −0.234715 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.1479 | 0.807385 | ||||||||
\(353\) | − 5.73727i | − 0.305364i | −0.988275 | − | 0.152682i | \(-0.951209\pi\) | ||||
0.988275 | − | 0.152682i | \(-0.0487910\pi\) | |||||||
\(354\) | −0.487636 | −0.0259176 | ||||||||
\(355\) | −10.7973 | −0.573063 | ||||||||
\(356\) | − 8.27675i | − 0.438667i | ||||||||
\(357\) | 9.50367i | 0.502988i | ||||||||
\(358\) | 22.7243i | 1.20102i | ||||||||
\(359\) | − 24.7583i | − 1.30669i | −0.757059 | − | 0.653347i | \(-0.773364\pi\) | ||||
0.757059 | − | 0.653347i | \(-0.226636\pi\) | |||||||
\(360\) | 7.47497 | 0.393965 | ||||||||
\(361\) | 13.8564 | 0.729285 | ||||||||
\(362\) | 22.0641i | 1.15967i | ||||||||
\(363\) | −41.6455 | −2.18582 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.70308 | 0.246171 | ||||||||
\(366\) | − 9.55856i | − 0.499634i | ||||||||
\(367\) | 26.0535 | 1.35998 | 0.679992 | − | 0.733220i | \(-0.261983\pi\) | ||||
0.679992 | + | 0.733220i | \(0.261983\pi\) | |||||||
\(368\) | −10.5604 | −0.550499 | ||||||||
\(369\) | − 9.10387i | − 0.473928i | ||||||||
\(370\) | − 10.6162i | − 0.551912i | ||||||||
\(371\) | − 15.9826i | − 0.829776i | ||||||||
\(372\) | − 6.52938i | − 0.338532i | ||||||||
\(373\) | 13.2045 | 0.683702 | 0.341851 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341851 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(374\) | 7.41584 | 0.383464 | ||||||||
\(375\) | − 2.33225i | − 0.120437i | ||||||||
\(376\) | 7.92229 | 0.408561 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.74146 | −0.295309 | ||||||||
\(379\) | − 25.9977i | − 1.33541i | −0.744425 | − | 0.667707i | \(-0.767276\pi\) | ||||
0.744425 | − | 0.667707i | \(-0.232724\pi\) | |||||||
\(380\) | 1.16202 | 0.0596101 | ||||||||
\(381\) | 26.6718 | 1.36644 | ||||||||
\(382\) | − 33.3418i | − 1.70591i | ||||||||
\(383\) | 9.60020i | 0.490547i | 0.969454 | + | 0.245274i | \(0.0788778\pi\) | ||||
−0.969454 | + | 0.245274i | \(0.921122\pi\) | |||||||
\(384\) | 12.0638i | 0.615629i | ||||||||
\(385\) | − 19.3396i | − 0.985637i | ||||||||
\(386\) | 26.5494 | 1.35133 | ||||||||
\(387\) | 2.76102 | 0.140350 | ||||||||
\(388\) | − 6.23453i | − 0.316510i | ||||||||
\(389\) | −5.63129 | −0.285518 | −0.142759 | − | 0.989758i | \(-0.545597\pi\) | ||||
−0.142759 | + | 0.989758i | \(0.545597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40617 | 0.222829 | ||||||||
\(392\) | 18.2675i | 0.922650i | ||||||||
\(393\) | −24.6471 | −1.24328 | ||||||||
\(394\) | 2.06947 | 0.104258 | ||||||||
\(395\) | − 11.9826i | − 0.602911i | ||||||||
\(396\) | 6.71395i | 0.337389i | ||||||||
\(397\) | − 16.7658i | − 0.841452i | −0.907188 | − | 0.420726i | \(-0.861775\pi\) | ||||
0.907188 | − | 0.420726i | \(-0.138225\pi\) | |||||||
\(398\) | 30.8891i | 1.54833i | ||||||||
\(399\) | 19.0429 | 0.953339 | ||||||||
\(400\) | 2.71276 | 0.135638 | ||||||||
\(401\) | − 13.8780i | − 0.693036i | −0.938043 | − | 0.346518i | \(-0.887364\pi\) | ||||
0.938043 | − | 0.346518i | \(-0.112636\pi\) | |||||||
\(402\) | −18.2050 | −0.907980 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.07733 | 0.103351 | ||||||||
\(405\) | − 10.3676i | − 0.515169i | ||||||||
\(406\) | −0.108583 | −0.00538888 | ||||||||
\(407\) | 46.7566 | 2.31764 | ||||||||
\(408\) | − 8.08903i | − 0.400466i | ||||||||
\(409\) | − 29.4251i | − 1.45498i | −0.686120 | − | 0.727489i | \(-0.740687\pi\) | ||||
0.686120 | − | 0.727489i | \(-0.259313\pi\) | |||||||
\(410\) | − 4.55193i | − 0.224804i | ||||||||
\(411\) | 8.83157i | 0.435629i | ||||||||
\(412\) | 9.17310 | 0.451926 | ||||||||
\(413\) | 0.617162 | 0.0303686 | ||||||||
\(414\) | − 11.5824i | − 0.569242i | ||||||||
\(415\) | −12.1286 | −0.595369 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.69683 | 0.230005 | ||||||||
\(418\) | − 14.8595i | − 0.726800i | ||||||||
\(419\) | 6.96793 | 0.340406 | 0.170203 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170203 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(420\) | −4.30209 | −0.209920 | ||||||||
\(421\) | − 7.12125i | − 0.347069i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) | ||||
0.984828 | − | 0.173534i | \(-0.0555188\pi\) | |||||||
\(422\) | 0.409213i | 0.0199202i | ||||||||
\(423\) | 6.30664i | 0.306640i | ||||||||
\(424\) | 13.6036i | 0.660647i | ||||||||
\(425\) | −1.13186 | −0.0549030 | ||||||||
\(426\) | 30.7142 | 1.48811 | ||||||||
\(427\) | 12.0975i | 0.585439i | ||||||||
\(428\) | −4.67883 | −0.226160 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.38051 | 0.0665740 | ||||||||
\(431\) | − 30.2144i | − 1.45537i | −0.685909 | − | 0.727687i | \(-0.740595\pi\) | ||||
0.685909 | − | 0.727687i | \(-0.259405\pi\) | |||||||
\(432\) | 3.54698 | 0.170654 | ||||||||
\(433\) | −1.20013 | −0.0576745 | −0.0288373 | − | 0.999584i | \(-0.509180\pi\) | ||||
−0.0288373 | + | 0.999584i | \(0.509180\pi\) | |||||||
\(434\) | − 23.9935i | − 1.15172i | ||||||||
\(435\) | − 0.0576715i | − 0.00276514i | ||||||||
\(436\) | − 3.77922i | − 0.180992i | ||||||||
\(437\) | − 8.82884i | − 0.422341i | ||||||||
\(438\) | −13.3784 | −0.639247 | ||||||||
\(439\) | 16.5541 | 0.790084 | 0.395042 | − | 0.918663i | \(-0.370730\pi\) | ||||
0.395042 | + | 0.918663i | \(0.370730\pi\) | |||||||
\(440\) | 16.4608i | 0.784740i | ||||||||
\(441\) | −14.5421 | −0.692481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.55949 | 0.216628 | 0.108314 | − | 0.994117i | \(-0.465455\pi\) | ||||
0.108314 | + | 0.994117i | \(0.465455\pi\) | |||||||
\(444\) | − 10.4010i | − 0.493610i | ||||||||
\(445\) | 16.1540 | 0.765775 | ||||||||
\(446\) | 14.9982 | 0.710185 | ||||||||
\(447\) | 12.8689i | 0.608676i | ||||||||
\(448\) | − 31.9153i | − 1.50786i | ||||||||
\(449\) | 13.8522i | 0.653724i | 0.945072 | + | 0.326862i | \(0.105991\pi\) | ||||
−0.945072 | + | 0.326862i | \(0.894009\pi\) | |||||||
\(450\) | 2.97527i | 0.140256i | ||||||||
\(451\) | 20.0479 | 0.944018 | ||||||||
\(452\) | 3.62542 | 0.170526 | ||||||||
\(453\) | − 11.4038i | − 0.535796i | ||||||||
\(454\) | 9.30897 | 0.436892 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.2083 | −0.759025 | ||||||||
\(457\) | − 40.1146i | − 1.87648i | −0.345984 | − | 0.938240i | \(-0.612455\pi\) | ||||
0.345984 | − | 0.938240i | \(-0.387545\pi\) | |||||||
\(458\) | −17.5644 | −0.820733 | ||||||||
\(459\) | −1.47992 | −0.0690768 | ||||||||
\(460\) | 1.99457i | 0.0929972i | ||||||||
\(461\) | 7.53900i | 0.351126i | 0.984468 | + | 0.175563i | \(0.0561746\pi\) | ||||
−0.984468 | + | 0.175563i | \(0.943825\pi\) | |||||||
\(462\) | 55.0136i | 2.55946i | ||||||||
\(463\) | 23.3031i | 1.08299i | 0.840705 | + | 0.541494i | \(0.182141\pi\) | ||||
−0.840705 | + | 0.541494i | \(0.817859\pi\) | |||||||
\(464\) | 0.0670807 | 0.00311414 | ||||||||
\(465\) | 12.7436 | 0.590972 | ||||||||
\(466\) | 11.5824i | 0.536542i | ||||||||
\(467\) | 22.6297 | 1.04718 | 0.523589 | − | 0.851971i | \(-0.324593\pi\) | ||||
0.523589 | + | 0.851971i | \(0.324593\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.0405 | 1.06391 | ||||||||
\(470\) | 3.15332i | 0.145452i | ||||||||
\(471\) | 23.4170 | 1.07900 | ||||||||
\(472\) | −0.525296 | −0.0241787 | ||||||||
\(473\) | 6.08012i | 0.279564i | ||||||||
\(474\) | 34.0859i | 1.56562i | ||||||||
\(475\) | 2.26795i | 0.104061i | ||||||||
\(476\) | 2.08783i | 0.0956956i | ||||||||
\(477\) | −10.8293 | −0.495839 | ||||||||
\(478\) | 24.2893 | 1.11096 | ||||||||
\(479\) | 20.6448i | 0.943286i | 0.881790 | + | 0.471643i | \(0.156339\pi\) | ||||
−0.881790 | + | 0.471643i | \(0.843661\pi\) | |||||||
\(480\) | 6.57666 | 0.300182 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 28.3777 | 1.29257 | ||||||||
\(483\) | 32.6867i | 1.48730i | ||||||||
\(484\) | −9.14898 | −0.415863 | ||||||||
\(485\) | 12.1682 | 0.552528 | ||||||||
\(486\) | 24.7074i | 1.12075i | ||||||||
\(487\) | − 3.03605i | − 0.137576i | −0.997631 | − | 0.0687882i | \(-0.978087\pi\) | ||||
0.997631 | − | 0.0687882i | \(-0.0219133\pi\) | |||||||
\(488\) | − 10.2968i | − 0.466112i | ||||||||
\(489\) | 15.8155i | 0.715203i | ||||||||
\(490\) | −7.27105 | −0.328473 | ||||||||
\(491\) | −10.6680 | −0.481441 | −0.240720 | − | 0.970595i | \(-0.577384\pi\) | ||||
−0.240720 | + | 0.970595i | \(0.577384\pi\) | |||||||
\(492\) | − 4.45965i | − 0.201056i | ||||||||
\(493\) | −0.0279884 | −0.00126053 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.1039 | −0.588975 | ||||||||
\(496\) | 14.8228i | 0.665562i | ||||||||
\(497\) | −38.8725 | −1.74367 | ||||||||
\(498\) | 34.5011 | 1.54603 | ||||||||
\(499\) | − 33.9143i | − 1.51821i | −0.650966 | − | 0.759107i | \(-0.725636\pi\) | ||||
0.650966 | − | 0.759107i | \(-0.274364\pi\) | |||||||
\(500\) | − 0.512364i | − 0.0229136i | ||||||||
\(501\) | 24.4648i | 1.09301i | ||||||||
\(502\) | 14.4413i | 0.644546i | ||||||||
\(503\) | −12.6276 | −0.563037 | −0.281518 | − | 0.959556i | \(-0.590838\pi\) | ||||
−0.281518 | + | 0.959556i | \(0.590838\pi\) | |||||||
\(504\) | 26.9113 | 1.19873 | ||||||||
\(505\) | 4.05441i | 0.180419i | ||||||||
\(506\) | 25.5058 | 1.13387 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.85945 | 0.259971 | ||||||||
\(509\) | 24.1526i | 1.07055i | 0.844679 | + | 0.535273i | \(0.179791\pi\) | ||||
−0.844679 | + | 0.535273i | \(0.820209\pi\) | |||||||
\(510\) | 3.21969 | 0.142570 | ||||||||
\(511\) | 16.9320 | 0.749029 | ||||||||
\(512\) | 24.2750i | 1.07281i | ||||||||
\(513\) | 2.96539i | 0.130925i | ||||||||
\(514\) | − 6.76929i | − 0.298581i | ||||||||
\(515\) | 17.9035i | 0.788921i | ||||||||
\(516\) | 1.35252 | 0.0595414 | ||||||||
\(517\) | −13.8880 | −0.610796 | ||||||||
\(518\) | − 38.2205i | − 1.67931i | ||||||||
\(519\) | 10.3982 | 0.456431 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7521 | −1.08441 | −0.542205 | − | 0.840246i | \(-0.682410\pi\) | ||||
−0.542205 | + | 0.840246i | \(0.682410\pi\) | |||||||
\(522\) | 0.0735722i | 0.00322017i | ||||||||
\(523\) | 37.0326 | 1.61932 | 0.809662 | − | 0.586897i | \(-0.199650\pi\) | ||||
0.809662 | + | 0.586897i | \(0.199650\pi\) | |||||||
\(524\) | −5.41465 | −0.236540 | ||||||||
\(525\) | − 8.39654i | − 0.366455i | ||||||||
\(526\) | − 8.36665i | − 0.364803i | ||||||||
\(527\) | − 6.18457i | − 0.269404i | ||||||||
\(528\) | − 33.9865i | − 1.47907i | ||||||||
\(529\) | −7.84554 | −0.341111 | ||||||||
\(530\) | −5.41465 | −0.235197 | ||||||||
\(531\) | − 0.418169i | − 0.0181470i | ||||||||
\(532\) | 4.18348 | 0.181377 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −45.9519 | −1.98854 | ||||||||
\(535\) | − 9.13186i | − 0.394805i | ||||||||
\(536\) | −19.6109 | −0.847062 | ||||||||
\(537\) | −43.4528 | −1.87512 | ||||||||
\(538\) | 1.73438i | 0.0747744i | ||||||||
\(539\) | − 32.0236i | − 1.37935i | ||||||||
\(540\) | − 0.669925i | − 0.0288290i | ||||||||
\(541\) | − 8.38144i | − 0.360346i | −0.983635 | − | 0.180173i | \(-0.942334\pi\) | ||||
0.983635 | − | 0.180173i | \(-0.0576658\pi\) | |||||||
\(542\) | −12.1596 | −0.522301 | ||||||||
\(543\) | −42.1903 | −1.81056 | ||||||||
\(544\) | − 3.19170i | − 0.136843i | ||||||||
\(545\) | 7.37605 | 0.315955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.7842 | −0.974181 | −0.487091 | − | 0.873351i | \(-0.661942\pi\) | ||||
−0.487091 | + | 0.873351i | \(0.661942\pi\) | |||||||
\(548\) | 1.94018i | 0.0828804i | ||||||||
\(549\) | 8.19687 | 0.349834 | ||||||||
\(550\) | −6.55193 | −0.279375 | ||||||||
\(551\) | 0.0560816i | 0.00238915i | ||||||||
\(552\) | − 27.8212i | − 1.18415i | ||||||||
\(553\) | − 43.1398i | − 1.83449i | ||||||||
\(554\) | − 21.3735i | − 0.908071i | ||||||||
\(555\) | 20.3000 | 0.861688 | ||||||||
\(556\) | 1.03183 | 0.0437594 | ||||||||
\(557\) | − 28.1527i | − 1.19287i | −0.802662 | − | 0.596435i | \(-0.796583\pi\) | ||||
0.802662 | − | 0.596435i | \(-0.203417\pi\) | |||||||
\(558\) | −16.2572 | −0.688222 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 9.76645 | 0.412708 | ||||||||
\(561\) | 14.1803i | 0.598694i | ||||||||
\(562\) | 13.0935 | 0.552317 | ||||||||
\(563\) | 18.1303 | 0.764101 | 0.382050 | − | 0.924142i | \(-0.375218\pi\) | ||||
0.382050 | + | 0.924142i | \(0.375218\pi\) | |||||||
\(564\) | 3.08939i | 0.130087i | ||||||||
\(565\) | 7.07588i | 0.297684i | ||||||||
\(566\) | 1.60801i | 0.0675899i | ||||||||
\(567\) | − 37.3253i | − 1.56752i | ||||||||
\(568\) | 33.0862 | 1.38827 | ||||||||
\(569\) | −40.5985 | −1.70198 | −0.850988 | − | 0.525185i | \(-0.823996\pi\) | ||||
−0.850988 | + | 0.525185i | \(0.823996\pi\) | |||||||
\(570\) | − 6.45143i | − 0.270221i | ||||||||
\(571\) | −24.7159 | −1.03433 | −0.517164 | − | 0.855886i | \(-0.673012\pi\) | ||||
−0.517164 | + | 0.855886i | \(0.673012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 63.7551 | 2.66341 | ||||||||
\(574\) | − 16.3879i | − 0.684016i | ||||||||
\(575\) | −3.89287 | −0.162344 | ||||||||
\(576\) | −21.6248 | −0.901032 | ||||||||
\(577\) | − 23.0691i | − 0.960379i | −0.877165 | − | 0.480189i | \(-0.840568\pi\) | ||||
0.877165 | − | 0.480189i | \(-0.159432\pi\) | |||||||
\(578\) | 19.1721i | 0.797456i | ||||||||
\(579\) | 50.7669i | 2.10980i | ||||||||
\(580\) | − 0.0126697i | 0 0.000526079i | ||||||||
\(581\) | −43.6653 | −1.81154 | ||||||||
\(582\) | −34.6137 | −1.43478 | ||||||||
\(583\) | − 23.8475i | − 0.987662i | ||||||||
\(584\) | −14.4116 | −0.596358 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.8602 | 0.944345 | ||||||||
\(587\) | 20.3523i | 0.840030i | 0.907517 | + | 0.420015i | \(0.137975\pi\) | ||||
−0.907517 | + | 0.420015i | \(0.862025\pi\) | |||||||
\(588\) | −7.12364 | −0.293774 | ||||||||
\(589\) | −12.3923 | −0.510616 | ||||||||
\(590\) | − 0.209084i | − 0.00860786i | ||||||||
\(591\) | 3.95717i | 0.162776i | ||||||||
\(592\) | 23.6120i | 0.970447i | ||||||||
\(593\) | 10.3834i | 0.426395i | 0.977009 | + | 0.213198i | \(0.0683878\pi\) | ||||
−0.977009 | + | 0.213198i | \(0.931612\pi\) | |||||||
\(594\) | −8.56677 | −0.351499 | ||||||||
\(595\) | −4.07490 | −0.167055 | ||||||||
\(596\) | 2.82712i | 0.115803i | ||||||||
\(597\) | −59.0652 | −2.41738 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.5965 | −1.29100 | −0.645499 | − | 0.763761i | \(-0.723351\pi\) | ||||
−0.645499 | + | 0.763761i | \(0.723351\pi\) | |||||||
\(600\) | 7.14670i | 0.291763i | ||||||||
\(601\) | −43.8845 | −1.79009 | −0.895044 | − | 0.445979i | \(-0.852856\pi\) | ||||
−0.895044 | + | 0.445979i | \(0.852856\pi\) | |||||||
\(602\) | 4.97010 | 0.202566 | ||||||||
\(603\) | − 15.6115i | − 0.635750i | ||||||||
\(604\) | − 2.50526i | − 0.101938i | ||||||||
\(605\) | − 17.8564i | − 0.725966i | ||||||||
\(606\) | − 11.5332i | − 0.468505i | ||||||||
\(607\) | 2.17540 | 0.0882968 | 0.0441484 | − | 0.999025i | \(-0.485943\pi\) | ||||
0.0441484 | + | 0.999025i | \(0.485943\pi\) | |||||||
\(608\) | −6.39535 | −0.259366 | ||||||||
\(609\) | − 0.207629i | − 0.00841354i | ||||||||
\(610\) | 4.09843 | 0.165941 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.41465 | 0.0571837 | ||||||||
\(613\) | 14.7620i | 0.596231i | 0.954530 | + | 0.298116i | \(0.0963581\pi\) | ||||
−0.954530 | + | 0.298116i | \(0.903642\pi\) | |||||||
\(614\) | 17.4467 | 0.704092 | ||||||||
\(615\) | 8.70406 | 0.350982 | ||||||||
\(616\) | 59.2622i | 2.38774i | ||||||||
\(617\) | 20.2972i | 0.817134i | 0.912728 | + | 0.408567i | \(0.133971\pi\) | ||||
−0.912728 | + | 0.408567i | \(0.866029\pi\) | |||||||
\(618\) | − 50.9284i | − 2.04864i | ||||||||
\(619\) | 9.94207i | 0.399605i | 0.979836 | + | 0.199803i | \(0.0640301\pi\) | ||||
−0.979836 | + | 0.199803i | \(0.935970\pi\) | |||||||
\(620\) | 2.79961 | 0.112435 | ||||||||
\(621\) | −5.09000 | −0.204255 | ||||||||
\(622\) | 3.36758i | 0.135028i | ||||||||
\(623\) | 58.1577 | 2.33004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.9855i | 0.798782i | ||||||||
\(627\) | 28.4138 | 1.13474 | ||||||||
\(628\) | 5.14441 | 0.205284 | ||||||||
\(629\) | − 9.85174i | − 0.392815i | ||||||||
\(630\) | 10.7116i | 0.426759i | ||||||||
\(631\) | 0.973420i | 0.0387512i | 0.999812 | + | 0.0193756i | \(0.00616784\pi\) | ||||
−0.999812 | + | 0.0193756i | \(0.993832\pi\) | |||||||
\(632\) | 36.7183i | 1.46058i | ||||||||
\(633\) | −0.782485 | −0.0311010 | ||||||||
\(634\) | −2.17805 | −0.0865014 | ||||||||
\(635\) | 11.4361i | 0.453828i | ||||||||
\(636\) | −5.30487 | −0.210352 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.162015 | −0.00641425 | ||||||||
\(639\) | 26.3387i | 1.04194i | ||||||||
\(640\) | −5.17262 | −0.204466 | ||||||||
\(641\) | 12.6209 | 0.498497 | 0.249249 | − | 0.968440i | \(-0.419816\pi\) | ||||
0.249249 | + | 0.968440i | \(0.419816\pi\) | |||||||
\(642\) | 25.9766i | 1.02521i | ||||||||
\(643\) | − 9.96043i | − 0.392801i | −0.980524 | − | 0.196401i | \(-0.937075\pi\) | ||||
0.980524 | − | 0.196401i | \(-0.0629253\pi\) | |||||||
\(644\) | 7.18083i | 0.282964i | ||||||||
\(645\) | 2.63977i | 0.103941i | ||||||||
\(646\) | −3.13092 | −0.123185 | ||||||||
\(647\) | 36.2763 | 1.42617 | 0.713084 | − | 0.701079i | \(-0.247298\pi\) | ||||
0.713084 | + | 0.701079i | \(0.247298\pi\) | |||||||
\(648\) | 31.7693i | 1.24802i | ||||||||
\(649\) | 0.920861 | 0.0361470 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.8796 | 1.79816 | ||||||||
\(652\) | 3.47447i | 0.136071i | ||||||||
\(653\) | 13.7554 | 0.538289 | 0.269145 | − | 0.963100i | \(-0.413259\pi\) | ||||
0.269145 | + | 0.963100i | \(0.413259\pi\) | |||||||
\(654\) | −20.9820 | −0.820461 | ||||||||
\(655\) | − 10.5680i | − 0.412925i | ||||||||
\(656\) | 10.1241i | 0.395281i | ||||||||
\(657\) | − 11.4726i | − 0.447588i | ||||||||
\(658\) | 11.3526i | 0.442570i | ||||||||
\(659\) | −2.58183 | −0.100574 | −0.0502869 | − | 0.998735i | \(-0.516014\pi\) | ||||
−0.0502869 | + | 0.998735i | \(0.516014\pi\) | |||||||
\(660\) | −6.41910 | −0.249863 | ||||||||
\(661\) | 24.8765i | 0.967582i | 0.875183 | + | 0.483791i | \(0.160741\pi\) | ||||
−0.875183 | + | 0.483791i | \(0.839259\pi\) | |||||||
\(662\) | −8.81151 | −0.342469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 37.1656 | 1.44231 | ||||||||
\(665\) | 8.16506i | 0.316627i | ||||||||
\(666\) | −25.8970 | −1.00349 | ||||||||
\(667\) | −0.0962625 | −0.00372730 | ||||||||
\(668\) | 5.37460i | 0.207949i | ||||||||
\(669\) | 28.6791i | 1.10880i | ||||||||
\(670\) | − 7.80576i | − 0.301563i | ||||||||
\(671\) | 18.0506i | 0.696834i | ||||||||
\(672\) | 23.6773 | 0.913370 | ||||||||
\(673\) | −43.3222 | −1.66995 | −0.834974 | − | 0.550289i | \(-0.814517\pi\) | ||||
−0.834974 | + | 0.550289i | \(0.814517\pi\) | |||||||
\(674\) | − 5.32051i | − 0.204938i | ||||||||
\(675\) | 1.30752 | 0.0503264 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.3625 | −1.58969 | −0.794845 | − | 0.606813i | \(-0.792448\pi\) | ||||
−0.794845 | + | 0.606813i | \(0.792448\pi\) | |||||||
\(678\) | − 20.1281i | − 0.773016i | ||||||||
\(679\) | 43.8078 | 1.68119 | ||||||||
\(680\) | 3.46834 | 0.133005 | ||||||||
\(681\) | 17.8003i | 0.682110i | ||||||||
\(682\) | − 35.8004i | − 1.37087i | ||||||||
\(683\) | 2.62688i | 0.100515i | 0.998736 | + | 0.0502574i | \(0.0160042\pi\) | ||||
−0.998736 | + | 0.0502574i | \(0.983996\pi\) | |||||||
\(684\) | − 2.83459i | − 0.108383i | ||||||||
\(685\) | −3.78672 | −0.144683 | ||||||||
\(686\) | 4.56057 | 0.174123 | ||||||||
\(687\) | − 33.5862i | − 1.28139i | ||||||||
\(688\) | −3.07045 | −0.117060 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 11.0737 | 0.421569 | ||||||||
\(691\) | 15.2753i | 0.581099i | 0.956860 | + | 0.290550i | \(0.0938382\pi\) | ||||
−0.956860 | + | 0.290550i | \(0.906162\pi\) | |||||||
\(692\) | 2.28435 | 0.0868380 | ||||||||
\(693\) | −47.1765 | −1.79209 | ||||||||
\(694\) | 32.5744i | 1.23651i | ||||||||
\(695\) | 2.01386i | 0.0763902i | ||||||||
\(696\) | 0.176723i | 0.00669865i | ||||||||
\(697\) | − 4.22414i | − 0.160001i | ||||||||
\(698\) | 28.7493 | 1.08818 | ||||||||
\(699\) | −22.1474 | −0.837692 | ||||||||
\(700\) | − 1.84461i | − 0.0697197i | ||||||||
\(701\) | 48.1947 | 1.82029 | 0.910144 | − | 0.414292i | \(-0.135971\pi\) | ||||
0.910144 | + | 0.414292i | \(0.135971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.7404 | −0.744522 | ||||||||
\(704\) | − 47.6205i | − 1.79477i | ||||||||
\(705\) | −6.02968 | −0.227091 | ||||||||
\(706\) | −6.99767 | −0.263361 | ||||||||
\(707\) | 14.5967i | 0.548964i | ||||||||
\(708\) | − 0.204845i | − 0.00769856i | ||||||||
\(709\) | − 38.8699i | − 1.45979i | −0.683559 | − | 0.729896i | \(-0.739569\pi\) | ||||
0.683559 | − | 0.729896i | \(-0.260431\pi\) | |||||||
\(710\) | 13.1694i | 0.494237i | ||||||||
\(711\) | −29.2301 | −1.09621 | ||||||||
\(712\) | −49.5008 | −1.85512 | ||||||||
\(713\) | − 21.2711i | − 0.796607i | ||||||||
\(714\) | 11.5915 | 0.433801 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.54600 | −0.356751 | ||||||||
\(717\) | 46.4452i | 1.73453i | ||||||||
\(718\) | −30.1974 | −1.12696 | ||||||||
\(719\) | −6.61660 | −0.246758 | −0.123379 | − | 0.992360i | \(-0.539373\pi\) | ||||
−0.123379 | + | 0.992360i | \(0.539373\pi\) | |||||||
\(720\) | − 6.61742i | − 0.246617i | ||||||||
\(721\) | 64.4560i | 2.40047i | ||||||||
\(722\) | − 16.9005i | − 0.628971i | ||||||||
\(723\) | 54.2629i | 2.01806i | ||||||||
\(724\) | −9.26867 | −0.344467 | ||||||||
\(725\) | 0.0247279 | 0.000918370 0 | ||||||||
\(726\) | 50.7945i | 1.88516i | ||||||||
\(727\) | 18.3735 | 0.681435 | 0.340717 | − | 0.940166i | \(-0.389330\pi\) | ||||
0.340717 | + | 0.940166i | \(0.389330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.1420 | −0.597853 | ||||||||
\(730\) | − 5.73629i | − 0.212310i | ||||||||
\(731\) | 1.28110 | 0.0473830 | ||||||||
\(732\) | 4.01534 | 0.148411 | ||||||||
\(733\) | − 0.791131i | − 0.0292211i | −0.999893 | − | 0.0146105i | \(-0.995349\pi\) | ||||
0.999893 | − | 0.0146105i | \(-0.00465084\pi\) | |||||||
\(734\) | − 31.7772i | − 1.17292i | ||||||||
\(735\) | − 13.9035i | − 0.512837i | ||||||||
\(736\) | − 10.9774i | − 0.404634i | ||||||||
\(737\) | 34.3786 | 1.26635 | ||||||||
\(738\) | −11.1039 | −0.408739 | ||||||||
\(739\) | 31.1853i | 1.14717i | 0.819146 | + | 0.573585i | \(0.194448\pi\) | ||||
−0.819146 | + | 0.573585i | \(0.805552\pi\) | |||||||
\(740\) | 4.45965 | 0.163940 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.4938 | −0.715639 | ||||||||
\(743\) | − 5.56304i | − 0.204088i | −0.994780 | − | 0.102044i | \(-0.967462\pi\) | ||||
0.994780 | − | 0.102044i | \(-0.0325383\pi\) | |||||||
\(744\) | −39.0503 | −1.43165 | ||||||||
\(745\) | −5.51780 | −0.202156 | ||||||||
\(746\) | − 16.1053i | − 0.589658i | ||||||||
\(747\) | 29.5862i | 1.08250i | ||||||||
\(748\) | 3.11523i | 0.113904i | ||||||||
\(749\) | − 32.8765i | − 1.20128i | ||||||||
\(750\) | −2.84461 | −0.103870 | ||||||||
\(751\) | 35.2097 | 1.28482 | 0.642410 | − | 0.766361i | \(-0.277935\pi\) | ||||
0.642410 | + | 0.766361i | \(0.277935\pi\) | |||||||
\(752\) | − 7.01343i | − 0.255754i | ||||||||
\(753\) | −27.6142 | −1.00632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.88961 | 0.177951 | ||||||||
\(756\) | − 2.41186i | − 0.0877186i | ||||||||
\(757\) | 50.0446 | 1.81890 | 0.909451 | − | 0.415810i | \(-0.136502\pi\) | ||||
0.909451 | + | 0.415810i | \(0.136502\pi\) | |||||||
\(758\) | −31.7091 | −1.15173 | ||||||||
\(759\) | 48.7715i | 1.77029i | ||||||||
\(760\) | − 6.94967i | − 0.252091i | ||||||||
\(761\) | 44.8209i | 1.62476i | 0.583130 | + | 0.812379i | \(0.301828\pi\) | ||||
−0.583130 | + | 0.812379i | \(0.698172\pi\) | |||||||
\(762\) | − 32.5313i | − 1.17848i | ||||||||
\(763\) | 26.5552 | 0.961364 | ||||||||
\(764\) | 14.0061 | 0.506725 | ||||||||
\(765\) | 2.76102i | 0.0998248i | ||||||||
\(766\) | 11.7092 | 0.423072 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −26.6361 | −0.961148 | ||||||||
\(769\) | 39.3633i | 1.41948i | 0.704465 | + | 0.709739i | \(0.251187\pi\) | ||||
−0.704465 | + | 0.709739i | \(0.748813\pi\) | |||||||
\(770\) | −23.5882 | −0.850061 | ||||||||
\(771\) | 12.9440 | 0.466168 | ||||||||
\(772\) | 11.1528i | 0.401399i | ||||||||
\(773\) | − 48.7805i | − 1.75451i | −0.480022 | − | 0.877256i | \(-0.659371\pi\) | ||||
0.480022 | − | 0.877256i | \(-0.340629\pi\) | |||||||
\(774\) | − 3.36758i | − 0.121045i | ||||||||
\(775\) | 5.46410i | 0.196276i | ||||||||
\(776\) | −37.2869 | −1.33852 | ||||||||
\(777\) | 73.0840 | 2.62188 | ||||||||
\(778\) | 6.86841i | 0.246244i | ||||||||
\(779\) | −8.46410 | −0.303258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −58.0013 | −2.07545 | ||||||||
\(782\) | − 5.37415i | − 0.192179i | ||||||||
\(783\) | 0.0323322 | 0.00115546 | ||||||||
\(784\) | 16.1718 | 0.577566 | ||||||||
\(785\) | 10.0405i | 0.358363i | ||||||||
\(786\) | 30.0618i | 1.07227i | ||||||||
\(787\) | 39.8608i | 1.42088i | 0.703756 | + | 0.710442i | \(0.251505\pi\) | ||||
−0.703756 | + | 0.710442i | \(0.748495\pi\) | |||||||
\(788\) | 0.869338i | 0.0309689i | ||||||||
\(789\) | 15.9984 | 0.569559 | ||||||||
\(790\) | −14.6150 | −0.519980 | ||||||||
\(791\) | 25.4745i | 0.905771i | ||||||||
\(792\) | 40.1541 | 1.42682 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.4490 | −0.725709 | ||||||||
\(795\) | − 10.3537i | − 0.367208i | ||||||||
\(796\) | −12.9759 | −0.459917 | ||||||||
\(797\) | −26.2118 | −0.928470 | −0.464235 | − | 0.885712i | \(-0.653671\pi\) | ||||
−0.464235 | + | 0.885712i | \(0.653671\pi\) | |||||||
\(798\) | − 23.2264i | − 0.822206i | ||||||||
\(799\) | 2.92625i | 0.103523i | ||||||||
\(800\) | 2.81988i | 0.0996979i | ||||||||
\(801\) | − 39.4057i | − 1.39233i | ||||||||
\(802\) | −16.9269 | −0.597708 | ||||||||
\(803\) | 25.2641 | 0.891551 | ||||||||
\(804\) | − 7.64750i | − 0.269707i | ||||||||
\(805\) | −14.0151 | −0.493968 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.31643 | −0.116744 | ||||||||
\(808\) | − 12.4239i | − 0.437072i | ||||||||
\(809\) | 22.2136 | 0.780990 | 0.390495 | − | 0.920605i | \(-0.372304\pi\) | ||||
0.390495 | + | 0.920605i | \(0.372304\pi\) | |||||||
\(810\) | −12.6452 | −0.444307 | ||||||||
\(811\) | − 19.0950i | − 0.670515i | −0.942127 | − | 0.335257i | \(-0.891177\pi\) | ||||
0.942127 | − | 0.335257i | \(-0.108823\pi\) | |||||||
\(812\) | − 0.0456133i | − 0.00160071i | ||||||||
\(813\) | − 23.2513i | − 0.815457i | ||||||||
\(814\) | − 57.0284i | − 1.99885i | ||||||||
\(815\) | −6.78124 | −0.237537 | ||||||||
\(816\) | −7.16104 | −0.250686 | ||||||||
\(817\) | − 2.56699i | − 0.0898076i | ||||||||
\(818\) | −35.8894 | −1.25484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.91217 | 0.0667758 | ||||||||
\(821\) | 34.1584i | 1.19214i | 0.802934 | + | 0.596068i | \(0.203271\pi\) | ||||
−0.802934 | + | 0.596068i | \(0.796729\pi\) | |||||||
\(822\) | 10.7718 | 0.375708 | ||||||||
\(823\) | −4.07940 | −0.142199 | −0.0710995 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0710995 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(824\) | − 54.8616i | − 1.91119i | ||||||||
\(825\) | − 12.5284i | − 0.436183i | ||||||||
\(826\) | − 0.752744i | − 0.0261913i | ||||||||
\(827\) | − 54.8780i | − 1.90830i | −0.299337 | − | 0.954148i | \(-0.596765\pi\) | ||||
0.299337 | − | 0.954148i | \(-0.403235\pi\) | |||||||
\(828\) | 4.86550 | 0.169088 | ||||||||
\(829\) | −8.14950 | −0.283044 | −0.141522 | − | 0.989935i | \(-0.545200\pi\) | ||||
−0.141522 | + | 0.989935i | \(0.545200\pi\) | |||||||
\(830\) | 14.7931i | 0.513476i | ||||||||
\(831\) | 40.8697 | 1.41775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.74745 | −0.233785 | ||||||||
\(834\) | − 5.72866i | − 0.198367i | ||||||||
\(835\) | −10.4898 | −0.363015 | ||||||||
\(836\) | 6.24213 | 0.215889 | ||||||||
\(837\) | 7.14441i | 0.246947i | ||||||||
\(838\) | − 8.49869i | − 0.293582i | ||||||||
\(839\) | − 21.8865i | − 0.755606i | −0.925886 | − | 0.377803i | \(-0.876680\pi\) | ||||
0.925886 | − | 0.377803i | \(-0.123320\pi\) | |||||||
\(840\) | 25.7295i | 0.887752i | ||||||||
\(841\) | −28.9994 | −0.999979 | ||||||||
\(842\) | −8.68570 | −0.299329 | ||||||||
\(843\) | 25.0370i | 0.862321i | ||||||||
\(844\) | −0.171902 | −0.00591710 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.69213 | 0.264461 | ||||||||
\(847\) | − 64.2866i | − 2.20891i | ||||||||
\(848\) | 12.0429 | 0.413556 | ||||||||
\(849\) | −3.07480 | −0.105527 | ||||||||
\(850\) | 1.38051i | 0.0473511i | ||||||||
\(851\) | − 33.8838i | − 1.16152i | ||||||||
\(852\) | 12.9024i | 0.442028i | ||||||||
\(853\) | − 19.2240i | − 0.658217i | −0.944292 | − | 0.329108i | \(-0.893252\pi\) | ||||
0.944292 | − | 0.329108i | \(-0.106748\pi\) | |||||||
\(854\) | 14.7552 | 0.504911 | ||||||||
\(855\) | 5.53238 | 0.189203 | ||||||||
\(856\) | 27.9827i | 0.956430i | ||||||||
\(857\) | 27.8197 | 0.950302 | 0.475151 | − | 0.879904i | \(-0.342393\pi\) | ||||
0.475151 | + | 0.879904i | \(0.342393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.7355 | 1.56048 | 0.780238 | − | 0.625482i | \(-0.215098\pi\) | ||||
0.780238 | + | 0.625482i | \(0.215098\pi\) | |||||||
\(860\) | 0.579922i | 0.0197752i | ||||||||
\(861\) | 31.3363 | 1.06794 | ||||||||
\(862\) | −36.8521 | −1.25519 | ||||||||
\(863\) | − 54.8186i | − 1.86605i | −0.359814 | − | 0.933024i | \(-0.617160\pi\) | ||||
0.359814 | − | 0.933024i | \(-0.382840\pi\) | |||||||
\(864\) | 3.68705i | 0.125436i | ||||||||
\(865\) | 4.45845i | 0.151592i | ||||||||
\(866\) | 1.46378i | 0.0497413i | ||||||||
\(867\) | −36.6604 | −1.24505 | ||||||||
\(868\) | 10.0791 | 0.342108 | ||||||||
\(869\) | − 64.3684i | − 2.18355i | ||||||||
\(870\) | −0.0703412 | −0.00238479 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22.6024 | −0.765415 | ||||||||
\(873\) | − 29.6827i | − 1.00461i | ||||||||
\(874\) | −10.7684 | −0.364247 | ||||||||
\(875\) | 3.60020 | 0.121709 | ||||||||
\(876\) | − 5.61999i | − 0.189882i | ||||||||
\(877\) | 27.3794i | 0.924537i | 0.886740 | + | 0.462269i | \(0.152964\pi\) | ||||
−0.886740 | + | 0.462269i | \(0.847036\pi\) | |||||||
\(878\) | − 20.1908i | − 0.681407i | ||||||||
\(879\) | 43.7125i | 1.47439i | ||||||||
\(880\) | 14.5724 | 0.491236 | ||||||||
\(881\) | 34.4426 | 1.16040 | 0.580200 | − | 0.814474i | \(-0.302974\pi\) | ||||
0.580200 | + | 0.814474i | \(0.302974\pi\) | |||||||
\(882\) | 17.7368i | 0.597230i | ||||||||
\(883\) | 17.3592 | 0.584183 | 0.292092 | − | 0.956390i | \(-0.405649\pi\) | ||||
0.292092 | + | 0.956390i | \(0.405649\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.399804 | 0.0134393 | ||||||||
\(886\) | − 5.56115i | − 0.186831i | ||||||||
\(887\) | −31.1427 | −1.04567 | −0.522835 | − | 0.852434i | \(-0.675126\pi\) | ||||
−0.522835 | + | 0.852434i | \(0.675126\pi\) | |||||||
\(888\) | −62.2053 | −2.08747 | ||||||||
\(889\) | 41.1722i | 1.38087i | ||||||||
\(890\) | − 19.7029i | − 0.660442i | ||||||||
\(891\) | − 55.6927i | − 1.86578i | ||||||||
\(892\) | 6.30042i | 0.210954i | ||||||||
\(893\) | 5.86345 | 0.196213 | ||||||||
\(894\) | 15.6960 | 0.524952 | ||||||||
\(895\) | − 18.6313i | − 0.622775i | ||||||||
\(896\) | −18.6224 | −0.622132 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.8953 | 0.563804 | ||||||||
\(899\) | 0.135116i | 0.00450636i | ||||||||
\(900\) | −1.24985 | −0.0416616 | ||||||||
\(901\) | −5.02473 | −0.167398 | ||||||||
\(902\) | − 24.4521i | − 0.814167i | ||||||||
\(903\) | 9.50367i | 0.316262i | ||||||||
\(904\) | − 21.6826i | − 0.721152i | ||||||||
\(905\) | − 18.0900i | − 0.601332i | ||||||||
\(906\) | −13.9090 | −0.462097 | ||||||||
\(907\) | −17.6057 | −0.584587 | −0.292294 | − | 0.956329i | \(-0.594418\pi\) | ||||
−0.292294 | + | 0.956329i | \(0.594418\pi\) | |||||||
\(908\) | 3.91050i | 0.129774i | ||||||||
\(909\) | 9.89022 | 0.328038 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.0232 | 1.65734 | 0.828671 | − | 0.559737i | \(-0.189098\pi\) | ||||
0.828671 | + | 0.559737i | \(0.189098\pi\) | |||||||
\(912\) | 14.3489i | 0.475139i | ||||||||
\(913\) | −65.1526 | −2.15624 | ||||||||
\(914\) | −48.9272 | −1.61837 | ||||||||
\(915\) | 7.83690i | 0.259080i | ||||||||
\(916\) | − 7.37844i | − 0.243791i | ||||||||
\(917\) | − 38.0468i | − 1.25641i | ||||||||
\(918\) | 1.80504i | 0.0595752i | ||||||||
\(919\) | −7.61556 | −0.251214 | −0.125607 | − | 0.992080i | \(-0.540088\pi\) | ||||
−0.125607 | + | 0.992080i | \(0.540088\pi\) | |||||||
\(920\) | 11.9289 | 0.393285 | ||||||||
\(921\) | 33.3611i | 1.09928i | ||||||||
\(922\) | 9.19522 | 0.302828 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −23.1100 | −0.760264 | ||||||||
\(925\) | 8.70406i | 0.286188i | ||||||||
\(926\) | 28.4225 | 0.934022 | ||||||||
\(927\) | 43.6733 | 1.43442 | ||||||||
\(928\) | 0.0697297i | 0.00228899i | ||||||||
\(929\) | 14.1239i | 0.463391i | 0.972788 | + | 0.231695i | \(0.0744273\pi\) | ||||
−0.972788 | + | 0.231695i | \(0.925573\pi\) | |||||||
\(930\) | − 15.5432i | − 0.509683i | ||||||||
\(931\) | 13.5202i | 0.443106i | ||||||||
\(932\) | −4.86550 | −0.159375 | ||||||||
\(933\) | −6.43937 | −0.210816 | ||||||||
\(934\) | − 27.6012i | − 0.903138i | ||||||||
\(935\) | −6.08012 | −0.198841 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9317 | −0.781815 | −0.390908 | − | 0.920430i | \(-0.627839\pi\) | ||||
−0.390908 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(938\) | − 28.1023i | − 0.917571i | ||||||||
\(939\) | −38.2157 | −1.24712 | ||||||||
\(940\) | −1.32464 | −0.0432051 | ||||||||
\(941\) | 25.3591i | 0.826683i | 0.910576 | + | 0.413342i | \(0.135638\pi\) | ||||
−0.910576 | + | 0.413342i | \(0.864362\pi\) | |||||||
\(942\) | − 28.5614i | − 0.930582i | ||||||||
\(943\) | − 14.5284i | − 0.473110i | ||||||||
\(944\) | 0.465033i | 0.0151355i | ||||||||
\(945\) | 4.70732 | 0.153129 | ||||||||
\(946\) | 7.41584 | 0.241110 | ||||||||
\(947\) | 41.4223i | 1.34604i | 0.739623 | + | 0.673021i | \(0.235004\pi\) | ||||
−0.739623 | + | 0.673021i | \(0.764996\pi\) | |||||||
\(948\) | −14.3187 | −0.465051 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.76619 | 0.0897470 | ||||||||
\(951\) | − 4.16480i | − 0.135053i | ||||||||
\(952\) | 12.4867 | 0.404696 | ||||||||
\(953\) | −24.3026 | −0.787237 | −0.393619 | − | 0.919274i | \(-0.628777\pi\) | ||||
−0.393619 | + | 0.919274i | \(0.628777\pi\) | |||||||
\(954\) | 13.2083i | 0.427636i | ||||||||
\(955\) | 27.3363i | 0.884583i | ||||||||
\(956\) | 10.2034i | 0.330001i | ||||||||
\(957\) | − 0.309801i | − 0.0100144i | ||||||||
\(958\) | 25.1802 | 0.813536 | ||||||||
\(959\) | −13.6329 | −0.440231 | ||||||||
\(960\) | − 20.6751i | − 0.667286i | ||||||||
\(961\) | 1.14359 | 0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.2760 | −0.717834 | ||||||||
\(964\) | 11.9209i | 0.383945i | ||||||||
\(965\) | −21.7674 | −0.700717 | ||||||||
\(966\) | 39.8675 | 1.28272 | ||||||||
\(967\) | − 23.6784i | − 0.761445i | −0.924689 | − | 0.380722i | \(-0.875675\pi\) | ||||
0.924689 | − | 0.380722i | \(-0.124325\pi\) | |||||||
\(968\) | 54.7173i | 1.75868i | ||||||||
\(969\) | − 5.98685i | − 0.192325i | ||||||||
\(970\) | − 14.8413i | − 0.476527i | ||||||||
\(971\) | −16.9722 | −0.544663 | −0.272332 | − | 0.962203i | \(-0.587795\pi\) | ||||
−0.272332 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(972\) | −10.3791 | −0.332908 | ||||||||
\(973\) | 7.25030i | 0.232434i | ||||||||
\(974\) | −3.70303 | −0.118653 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.11550 | −0.291780 | ||||||||
\(977\) | − 24.9994i | − 0.799802i | −0.916558 | − | 0.399901i | \(-0.869044\pi\) | ||||
0.916558 | − | 0.399901i | \(-0.130956\pi\) | |||||||
\(978\) | 19.2900 | 0.616826 | ||||||||
\(979\) | 86.7765 | 2.77339 | ||||||||
\(980\) | − 3.05441i | − 0.0975696i | ||||||||
\(981\) | − 17.9930i | − 0.574471i | ||||||||
\(982\) | 13.0116i | 0.415218i | ||||||||
\(983\) | − 27.3418i | − 0.872068i | −0.899930 | − | 0.436034i | \(-0.856383\pi\) | ||||
0.899930 | − | 0.436034i | \(-0.143617\pi\) | |||||||
\(984\) | −26.6718 | −0.850267 | ||||||||
\(985\) | −1.69672 | −0.0540620 | ||||||||
\(986\) | 0.0341370i | 0.00108715i | ||||||||
\(987\) | −21.7080 | −0.690975 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.40617 | 0.140108 | ||||||||
\(990\) | 15.9826i | 0.507961i | ||||||||
\(991\) | 16.0760 | 0.510672 | 0.255336 | − | 0.966852i | \(-0.417814\pi\) | ||||
0.255336 | + | 0.966852i | \(0.417814\pi\) | |||||||
\(992\) | −15.4081 | −0.489208 | ||||||||
\(993\) | − 16.8491i | − 0.534690i | ||||||||
\(994\) | 47.4123i | 1.50383i | ||||||||
\(995\) | − 25.3255i | − 0.802871i | ||||||||
\(996\) | 14.4932i | 0.459234i | ||||||||
\(997\) | −34.5612 | −1.09456 | −0.547282 | − | 0.836948i | \(-0.684337\pi\) | ||||
−0.547282 | + | 0.836948i | \(0.684337\pi\) | |||||||
\(998\) | −41.3649 | −1.30938 | ||||||||
\(999\) | 11.3807i | 0.360070i |
(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 | 845.2.c.g.506.3 | 8 | ||
13.2 | odd | 12 | 845.2.e.n.191.3 | 8 | |||
13.3 | even | 3 | 65.2.m.a.56.3 | yes | 8 | ||
13.4 | even | 6 | 65.2.m.a.36.3 | ✓ | 8 | ||
13.5 | odd | 4 | 845.2.a.l.1.2 | 4 | |||
13.6 | odd | 12 | 845.2.e.n.146.3 | 8 | |||
13.7 | odd | 12 | 845.2.e.m.146.2 | 8 | |||
13.8 | odd | 4 | 845.2.a.m.1.3 | 4 | |||
13.9 | even | 3 | 845.2.m.g.361.2 | 8 | |||
13.10 | even | 6 | 845.2.m.g.316.2 | 8 | |||
13.11 | odd | 12 | 845.2.e.m.191.2 | 8 | |||
13.12 | even | 2 | inner | 845.2.c.g.506.6 | 8 | ||
39.5 | even | 4 | 7605.2.a.cj.1.3 | 4 | |||
39.8 | even | 4 | 7605.2.a.cf.1.2 | 4 | |||
39.17 | odd | 6 | 585.2.bu.c.361.2 | 8 | |||
39.29 | odd | 6 | 585.2.bu.c.316.2 | 8 | |||
52.3 | odd | 6 | 1040.2.da.b.641.4 | 8 | |||
52.43 | odd | 6 | 1040.2.da.b.881.4 | 8 | |||
65.3 | odd | 12 | 325.2.m.c.199.3 | 8 | |||
65.4 | even | 6 | 325.2.n.d.101.2 | 8 | |||
65.17 | odd | 12 | 325.2.m.c.49.3 | 8 | |||
65.29 | even | 6 | 325.2.n.d.251.2 | 8 | |||
65.34 | odd | 4 | 4225.2.a.bi.1.2 | 4 | |||
65.42 | odd | 12 | 325.2.m.b.199.2 | 8 | |||
65.43 | odd | 12 | 325.2.m.b.49.2 | 8 | |||
65.44 | odd | 4 | 4225.2.a.bl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.3 | ✓ | 8 | 13.4 | even | 6 | ||
65.2.m.a.56.3 | yes | 8 | 13.3 | even | 3 | ||
325.2.m.b.49.2 | 8 | 65.43 | odd | 12 | |||
325.2.m.b.199.2 | 8 | 65.42 | odd | 12 | |||
325.2.m.c.49.3 | 8 | 65.17 | odd | 12 | |||
325.2.m.c.199.3 | 8 | 65.3 | odd | 12 | |||
325.2.n.d.101.2 | 8 | 65.4 | even | 6 | |||
325.2.n.d.251.2 | 8 | 65.29 | even | 6 | |||
585.2.bu.c.316.2 | 8 | 39.29 | odd | 6 | |||
585.2.bu.c.361.2 | 8 | 39.17 | odd | 6 | |||
845.2.a.l.1.2 | 4 | 13.5 | odd | 4 | |||
845.2.a.m.1.3 | 4 | 13.8 | odd | 4 | |||
845.2.c.g.506.3 | 8 | 1.1 | even | 1 | trivial | ||
845.2.c.g.506.6 | 8 | 13.12 | even | 2 | inner | ||
845.2.e.m.146.2 | 8 | 13.7 | odd | 12 | |||
845.2.e.m.191.2 | 8 | 13.11 | odd | 12 | |||
845.2.e.n.146.3 | 8 | 13.6 | odd | 12 | |||
845.2.e.n.191.3 | 8 | 13.2 | odd | 12 | |||
845.2.m.g.316.2 | 8 | 13.10 | even | 6 | |||
845.2.m.g.361.2 | 8 | 13.9 | even | 3 | |||
1040.2.da.b.641.4 | 8 | 52.3 | odd | 6 | |||
1040.2.da.b.881.4 | 8 | 52.43 | odd | 6 | |||
4225.2.a.bi.1.2 | 4 | 65.34 | odd | 4 | |||
4225.2.a.bl.1.3 | 4 | 65.44 | odd | 4 | |||
7605.2.a.cf.1.2 | 4 | 39.8 | even | 4 | |||
7605.2.a.cj.1.3 | 4 | 39.5 | even | 4 |