Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.a (trivial) |
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: | yes |
Analytic conductor: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.117688.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.97382\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.27510 | 1.89088 | 0.945441 | − | 0.325793i | \(-0.105631\pi\) | ||||
0.945441 | + | 0.325793i | \(0.105631\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.27510 | −1.33706 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.72630 | 2.57543 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.27510 | 0.945441 | ||||||||
\(13\) | −6.46446 | −1.79292 | −0.896460 | − | 0.443125i | \(-0.853870\pi\) | ||||
−0.896460 | + | 0.443125i | \(0.853870\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.38123 | −0.820069 | −0.410035 | − | 0.912070i | \(-0.634483\pi\) | ||||
−0.410035 | + | 0.912070i | \(0.634483\pi\) | |||||||
\(18\) | −7.72630 | −1.82111 | ||||||||
\(19\) | 6.62018 | 1.51877 | 0.759386 | − | 0.650640i | \(-0.225499\pi\) | ||||
0.759386 | + | 0.650640i | \(0.225499\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.27510 | 0.714686 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 5.53694 | 1.15453 | 0.577266 | − | 0.816556i | \(-0.304119\pi\) | ||||
0.577266 | + | 0.816556i | \(0.304119\pi\) | |||||||
\(24\) | −3.27510 | −0.668528 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.46446 | 1.26779 | ||||||||
\(27\) | 15.4791 | 2.97896 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.01326 | −0.188158 | −0.0940792 | − | 0.995565i | \(-0.529991\pi\) | ||||
−0.0940792 | + | 0.995565i | \(0.529991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.72630 | −0.489659 | −0.244829 | − | 0.969566i | \(-0.578732\pi\) | ||||
−0.244829 | + | 0.969566i | \(0.578732\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.27510 | 0.570122 | ||||||||
\(34\) | 3.38123 | 0.579877 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.72630 | 1.28772 | ||||||||
\(37\) | −2.15571 | −0.354397 | −0.177198 | − | 0.984175i | \(-0.556703\pi\) | ||||
−0.177198 | + | 0.984175i | \(0.556703\pi\) | |||||||
\(38\) | −6.62018 | −1.07393 | ||||||||
\(39\) | −21.1718 | −3.39020 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.81064 | 0.438948 | 0.219474 | − | 0.975618i | \(-0.429566\pi\) | ||||
0.219474 | + | 0.975618i | \(0.429566\pi\) | |||||||
\(42\) | −3.27510 | −0.505359 | ||||||||
\(43\) | 12.4190 | 1.89387 | 0.946937 | − | 0.321420i | \(-0.104160\pi\) | ||||
0.946937 | + | 0.321420i | \(0.104160\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.53694 | −0.816378 | ||||||||
\(47\) | −2.82139 | −0.411542 | −0.205771 | − | 0.978600i | \(-0.565970\pi\) | ||||
−0.205771 | + | 0.978600i | \(0.565970\pi\) | |||||||
\(48\) | 3.27510 | 0.472720 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.0739 | −1.55065 | ||||||||
\(52\) | −6.46446 | −0.896460 | ||||||||
\(53\) | 8.39450 | 1.15307 | 0.576536 | − | 0.817071i | \(-0.304404\pi\) | ||||
0.576536 | + | 0.817071i | \(0.304404\pi\) | |||||||
\(54\) | −15.4791 | −2.10644 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 21.6818 | 2.87182 | ||||||||
\(58\) | 1.01326 | 0.133048 | ||||||||
\(59\) | 11.4308 | 1.48817 | 0.744083 | − | 0.668088i | \(-0.232887\pi\) | ||||
0.744083 | + | 0.668088i | \(0.232887\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.64307 | 0.722521 | 0.361261 | − | 0.932465i | \(-0.382346\pi\) | ||||
0.361261 | + | 0.932465i | \(0.382346\pi\) | |||||||
\(62\) | 2.72630 | 0.346241 | ||||||||
\(63\) | 7.72630 | 0.973423 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.27510 | −0.403137 | ||||||||
\(67\) | −3.16897 | −0.387152 | −0.193576 | − | 0.981085i | \(-0.562009\pi\) | ||||
−0.193576 | + | 0.981085i | \(0.562009\pi\) | |||||||
\(68\) | −3.38123 | −0.410035 | ||||||||
\(69\) | 18.1341 | 2.18308 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.85755 | 0.576485 | 0.288243 | − | 0.957557i | \(-0.406929\pi\) | ||||
0.288243 | + | 0.957557i | \(0.406929\pi\) | |||||||
\(72\) | −7.72630 | −0.910554 | ||||||||
\(73\) | −0.831025 | −0.0972641 | −0.0486321 | − | 0.998817i | \(-0.515486\pi\) | ||||
−0.0486321 | + | 0.998817i | \(0.515486\pi\) | |||||||
\(74\) | 2.15571 | 0.250596 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.62018 | 0.759386 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 21.1718 | 2.39723 | ||||||||
\(79\) | −10.5610 | −1.18820 | −0.594100 | − | 0.804391i | \(-0.702492\pi\) | ||||
−0.594100 | + | 0.804391i | \(0.702492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 27.5169 | 3.05743 | ||||||||
\(82\) | −2.81064 | −0.310383 | ||||||||
\(83\) | −4.81205 | −0.528191 | −0.264095 | − | 0.964497i | \(-0.585073\pi\) | ||||
−0.264095 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(84\) | 3.27510 | 0.357343 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.4190 | −1.33917 | ||||||||
\(87\) | −3.31854 | −0.355785 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 8.02653 | 0.850810 | 0.425405 | − | 0.905003i | \(-0.360132\pi\) | ||||
0.425405 | + | 0.905003i | \(0.360132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.46446 | −0.677660 | ||||||||
\(92\) | 5.53694 | 0.577266 | ||||||||
\(93\) | −8.92893 | −0.925887 | ||||||||
\(94\) | 2.82139 | 0.291004 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.27510 | −0.334264 | ||||||||
\(97\) | 11.3961 | 1.15709 | 0.578547 | − | 0.815649i | \(-0.303620\pi\) | ||||
0.578547 | + | 0.815649i | \(0.303620\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 7.72630 | 0.776523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.47159 | −0.146428 | −0.0732141 | − | 0.997316i | \(-0.523326\pi\) | ||||
−0.0732141 | + | 0.997316i | \(0.523326\pi\) | |||||||
\(102\) | 11.0739 | 1.09648 | ||||||||
\(103\) | −5.49003 | −0.540949 | −0.270474 | − | 0.962727i | \(-0.587181\pi\) | ||||
−0.270474 | + | 0.962727i | \(0.587181\pi\) | |||||||
\(104\) | 6.46446 | 0.633893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.39450 | −0.815346 | ||||||||
\(107\) | −10.1341 | −0.979697 | −0.489848 | − | 0.871808i | \(-0.662948\pi\) | ||||
−0.489848 | + | 0.871808i | \(0.662948\pi\) | |||||||
\(108\) | 15.4791 | 1.48948 | ||||||||
\(109\) | 11.5635 | 1.10758 | 0.553790 | − | 0.832656i | \(-0.313181\pi\) | ||||
0.553790 | + | 0.832656i | \(0.313181\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.06018 | −0.670122 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 2.47883 | 0.233189 | 0.116594 | − | 0.993180i | \(-0.462802\pi\) | ||||
0.116594 | + | 0.993180i | \(0.462802\pi\) | |||||||
\(114\) | −21.6818 | −2.03068 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.01326 | −0.0940792 | ||||||||
\(117\) | −49.9464 | −4.61755 | ||||||||
\(118\) | −11.4308 | −1.05229 | ||||||||
\(119\) | −3.38123 | −0.309957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.64307 | −0.510900 | ||||||||
\(123\) | 9.20514 | 0.829999 | ||||||||
\(124\) | −2.72630 | −0.244829 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.72630 | −0.688314 | ||||||||
\(127\) | −9.78648 | −0.868410 | −0.434205 | − | 0.900814i | \(-0.642971\pi\) | ||||
−0.434205 | + | 0.900814i | \(0.642971\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 40.6734 | 3.58109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.64670 | 0.755466 | 0.377733 | − | 0.925915i | \(-0.376704\pi\) | ||||
0.377733 | + | 0.925915i | \(0.376704\pi\) | |||||||
\(132\) | 3.27510 | 0.285061 | ||||||||
\(133\) | 6.62018 | 0.574042 | ||||||||
\(134\) | 3.16897 | 0.273758 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.38123 | 0.289938 | ||||||||
\(137\) | −2.95264 | −0.252261 | −0.126131 | − | 0.992014i | \(-0.540256\pi\) | ||||
−0.126131 | + | 0.992014i | \(0.540256\pi\) | |||||||
\(138\) | −18.1341 | −1.54367 | ||||||||
\(139\) | −17.9063 | −1.51879 | −0.759397 | − | 0.650627i | \(-0.774506\pi\) | ||||
−0.759397 | + | 0.650627i | \(0.774506\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.24035 | −0.778178 | ||||||||
\(142\) | −4.85755 | −0.407637 | ||||||||
\(143\) | −6.46446 | −0.540586 | ||||||||
\(144\) | 7.72630 | 0.643859 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.831025 | 0.0687761 | ||||||||
\(147\) | 3.27510 | 0.270126 | ||||||||
\(148\) | −2.15571 | −0.177198 | ||||||||
\(149\) | 10.9867 | 0.900069 | 0.450034 | − | 0.893011i | \(-0.351412\pi\) | ||||
0.450034 | + | 0.893011i | \(0.351412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.15320 | −0.582119 | −0.291060 | − | 0.956705i | \(-0.594008\pi\) | ||||
−0.291060 | + | 0.956705i | \(0.594008\pi\) | |||||||
\(152\) | −6.62018 | −0.536967 | ||||||||
\(153\) | −26.1244 | −2.11204 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −21.1718 | −1.69510 | ||||||||
\(157\) | −11.8905 | −0.948969 | −0.474484 | − | 0.880264i | \(-0.657365\pi\) | ||||
−0.474484 | + | 0.880264i | \(0.657365\pi\) | |||||||
\(158\) | 10.5610 | 0.840185 | ||||||||
\(159\) | 27.4928 | 2.18032 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.53694 | 0.436372 | ||||||||
\(162\) | −27.5169 | −2.16193 | ||||||||
\(163\) | 6.47381 | 0.507068 | 0.253534 | − | 0.967326i | \(-0.418407\pi\) | ||||
0.253534 | + | 0.967326i | \(0.418407\pi\) | |||||||
\(164\) | 2.81064 | 0.219474 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.81205 | 0.373487 | ||||||||
\(167\) | −13.6241 | −1.05426 | −0.527132 | − | 0.849783i | \(-0.676733\pi\) | ||||
−0.527132 | + | 0.849783i | \(0.676733\pi\) | |||||||
\(168\) | −3.27510 | −0.252680 | ||||||||
\(169\) | 28.7893 | 2.21456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 51.1495 | 3.91150 | ||||||||
\(172\) | 12.4190 | 0.946937 | ||||||||
\(173\) | −3.05209 | −0.232046 | −0.116023 | − | 0.993247i | \(-0.537015\pi\) | ||||
−0.116023 | + | 0.993247i | \(0.537015\pi\) | |||||||
\(174\) | 3.31854 | 0.251578 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 37.4371 | 2.81394 | ||||||||
\(178\) | −8.02653 | −0.601614 | ||||||||
\(179\) | −17.4417 | −1.30365 | −0.651827 | − | 0.758367i | \(-0.725997\pi\) | ||||
−0.651827 | + | 0.758367i | \(0.725997\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.9813 | −1.85685 | −0.928424 | − | 0.371523i | \(-0.878836\pi\) | ||||
−0.928424 | + | 0.371523i | \(0.878836\pi\) | |||||||
\(182\) | 6.46446 | 0.479178 | ||||||||
\(183\) | 18.4816 | 1.36620 | ||||||||
\(184\) | −5.53694 | −0.408189 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.92893 | 0.654701 | ||||||||
\(187\) | −3.38123 | −0.247260 | ||||||||
\(188\) | −2.82139 | −0.205771 | ||||||||
\(189\) | 15.4791 | 1.12594 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.6624 | 1.35036 | 0.675180 | − | 0.737653i | \(-0.264066\pi\) | ||||
0.675180 | + | 0.737653i | \(0.264066\pi\) | |||||||
\(192\) | 3.27510 | 0.236360 | ||||||||
\(193\) | −4.82641 | −0.347413 | −0.173706 | − | 0.984797i | \(-0.555574\pi\) | ||||
−0.173706 | + | 0.984797i | \(0.555574\pi\) | |||||||
\(194\) | −11.3961 | −0.818190 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 13.1677 | 0.938161 | 0.469080 | − | 0.883155i | \(-0.344585\pi\) | ||||
0.469080 | + | 0.883155i | \(0.344585\pi\) | |||||||
\(198\) | −7.72630 | −0.549085 | ||||||||
\(199\) | −17.6955 | −1.25440 | −0.627199 | − | 0.778859i | \(-0.715799\pi\) | ||||
−0.627199 | + | 0.778859i | \(0.715799\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.3787 | −0.732059 | ||||||||
\(202\) | 1.47159 | 0.103540 | ||||||||
\(203\) | −1.01326 | −0.0711172 | ||||||||
\(204\) | −11.0739 | −0.775327 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.49003 | 0.382509 | ||||||||
\(207\) | 42.7801 | 2.97342 | ||||||||
\(208\) | −6.46446 | −0.448230 | ||||||||
\(209\) | 6.62018 | 0.457927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2669 | 0.775644 | 0.387822 | − | 0.921734i | \(-0.373228\pi\) | ||||
0.387822 | + | 0.921734i | \(0.373228\pi\) | |||||||
\(212\) | 8.39450 | 0.576536 | ||||||||
\(213\) | 15.9090 | 1.09007 | ||||||||
\(214\) | 10.1341 | 0.692750 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −15.4791 | −1.05322 | ||||||||
\(217\) | −2.72630 | −0.185074 | ||||||||
\(218\) | −11.5635 | −0.783177 | ||||||||
\(219\) | −2.72169 | −0.183915 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.8579 | 1.47032 | ||||||||
\(222\) | 7.06018 | 0.473848 | ||||||||
\(223\) | 24.2768 | 1.62570 | 0.812848 | − | 0.582476i | \(-0.197916\pi\) | ||||
0.812848 | + | 0.582476i | \(0.197916\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.47883 | −0.164889 | ||||||||
\(227\) | −19.9074 | −1.32130 | −0.660652 | − | 0.750693i | \(-0.729720\pi\) | ||||
−0.660652 | + | 0.750693i | \(0.729720\pi\) | |||||||
\(228\) | 21.6818 | 1.43591 | ||||||||
\(229\) | −10.9196 | −0.721586 | −0.360793 | − | 0.932646i | \(-0.617494\pi\) | ||||
−0.360793 | + | 0.932646i | \(0.617494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.27510 | 0.215486 | ||||||||
\(232\) | 1.01326 | 0.0665240 | ||||||||
\(233\) | −6.86037 | −0.449438 | −0.224719 | − | 0.974424i | \(-0.572146\pi\) | ||||
−0.224719 | + | 0.974424i | \(0.572146\pi\) | |||||||
\(234\) | 49.9464 | 3.26510 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.4308 | 0.744083 | ||||||||
\(237\) | −34.5882 | −2.24675 | ||||||||
\(238\) | 3.38123 | 0.219173 | ||||||||
\(239\) | 19.0161 | 1.23005 | 0.615024 | − | 0.788508i | \(-0.289146\pi\) | ||||
0.615024 | + | 0.788508i | \(0.289146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.59461 | −0.618043 | −0.309022 | − | 0.951055i | \(-0.600002\pi\) | ||||
−0.309022 | + | 0.951055i | \(0.600002\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 43.6832 | 2.80228 | ||||||||
\(244\) | 5.64307 | 0.361261 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.20514 | −0.586898 | ||||||||
\(247\) | −42.7959 | −2.72304 | ||||||||
\(248\) | 2.72630 | 0.173120 | ||||||||
\(249\) | −15.7600 | −0.998746 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9823 | −1.45063 | −0.725314 | − | 0.688418i | \(-0.758305\pi\) | ||||
−0.725314 | + | 0.688418i | \(0.758305\pi\) | |||||||
\(252\) | 7.72630 | 0.486711 | ||||||||
\(253\) | 5.53694 | 0.348105 | ||||||||
\(254\) | 9.78648 | 0.614058 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.18067 | −0.0736484 | −0.0368242 | − | 0.999322i | \(-0.511724\pi\) | ||||
−0.0368242 | + | 0.999322i | \(0.511724\pi\) | |||||||
\(258\) | −40.6734 | −2.53221 | ||||||||
\(259\) | −2.15571 | −0.133949 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.82878 | −0.484590 | ||||||||
\(262\) | −8.64670 | −0.534195 | ||||||||
\(263\) | −26.9368 | −1.66099 | −0.830496 | − | 0.557024i | \(-0.811943\pi\) | ||||
−0.830496 | + | 0.557024i | \(0.811943\pi\) | |||||||
\(264\) | −3.27510 | −0.201569 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.62018 | −0.405909 | ||||||||
\(267\) | 26.2877 | 1.60878 | ||||||||
\(268\) | −3.16897 | −0.193576 | ||||||||
\(269\) | −20.4439 | −1.24649 | −0.623244 | − | 0.782027i | \(-0.714186\pi\) | ||||
−0.623244 | + | 0.782027i | \(0.714186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6269 | 1.55672 | 0.778362 | − | 0.627816i | \(-0.216051\pi\) | ||||
0.778362 | + | 0.627816i | \(0.216051\pi\) | |||||||
\(272\) | −3.38123 | −0.205017 | ||||||||
\(273\) | −21.1718 | −1.28138 | ||||||||
\(274\) | 2.95264 | 0.178376 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18.1341 | 1.09154 | ||||||||
\(277\) | −16.3408 | −0.981821 | −0.490911 | − | 0.871210i | \(-0.663336\pi\) | ||||
−0.490911 | + | 0.871210i | \(0.663336\pi\) | |||||||
\(278\) | 17.9063 | 1.07395 | ||||||||
\(279\) | −21.0643 | −1.26108 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.37872 | 0.261213 | 0.130606 | − | 0.991434i | \(-0.458308\pi\) | ||||
0.130606 | + | 0.991434i | \(0.458308\pi\) | |||||||
\(282\) | 9.24035 | 0.550255 | ||||||||
\(283\) | −15.1500 | −0.900574 | −0.450287 | − | 0.892884i | \(-0.648678\pi\) | ||||
−0.450287 | + | 0.892884i | \(0.648678\pi\) | |||||||
\(284\) | 4.85755 | 0.288243 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.46446 | 0.382252 | ||||||||
\(287\) | 2.81064 | 0.165907 | ||||||||
\(288\) | −7.72630 | −0.455277 | ||||||||
\(289\) | −5.56727 | −0.327486 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.3233 | 2.18793 | ||||||||
\(292\) | −0.831025 | −0.0486321 | ||||||||
\(293\) | 0.630927 | 0.0368592 | 0.0184296 | − | 0.999830i | \(-0.494133\pi\) | ||||
0.0184296 | + | 0.999830i | \(0.494133\pi\) | |||||||
\(294\) | −3.27510 | −0.191008 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.15571 | 0.125298 | ||||||||
\(297\) | 15.4791 | 0.898191 | ||||||||
\(298\) | −10.9867 | −0.636445 | ||||||||
\(299\) | −35.7934 | −2.06998 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.4190 | 0.715817 | ||||||||
\(302\) | 7.15320 | 0.411620 | ||||||||
\(303\) | −4.81960 | −0.276879 | ||||||||
\(304\) | 6.62018 | 0.379693 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 26.1244 | 1.49343 | ||||||||
\(307\) | −17.5287 | −1.00042 | −0.500208 | − | 0.865905i | \(-0.666743\pi\) | ||||
−0.500208 | + | 0.865905i | \(0.666743\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | −17.9804 | −1.02287 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.0181 | 1.64547 | 0.822734 | − | 0.568427i | \(-0.192448\pi\) | ||||
0.822734 | + | 0.568427i | \(0.192448\pi\) | |||||||
\(312\) | 21.1718 | 1.19862 | ||||||||
\(313\) | −26.9475 | −1.52316 | −0.761582 | − | 0.648069i | \(-0.775577\pi\) | ||||
−0.761582 | + | 0.648069i | \(0.775577\pi\) | |||||||
\(314\) | 11.8905 | 0.671022 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.5610 | −0.594100 | ||||||||
\(317\) | −16.7087 | −0.938456 | −0.469228 | − | 0.883077i | \(-0.655468\pi\) | ||||
−0.469228 | + | 0.883077i | \(0.655468\pi\) | |||||||
\(318\) | −27.4928 | −1.54172 | ||||||||
\(319\) | −1.01326 | −0.0567319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.1901 | −1.85249 | ||||||||
\(322\) | −5.53694 | −0.308562 | ||||||||
\(323\) | −22.3844 | −1.24550 | ||||||||
\(324\) | 27.5169 | 1.52871 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.47381 | −0.358551 | ||||||||
\(327\) | 37.8716 | 2.09430 | ||||||||
\(328\) | −2.81064 | −0.155192 | ||||||||
\(329\) | −2.82139 | −0.155548 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.0222 | −1.70514 | −0.852568 | − | 0.522617i | \(-0.824956\pi\) | ||||
−0.852568 | + | 0.522617i | \(0.824956\pi\) | |||||||
\(332\) | −4.81205 | −0.264095 | ||||||||
\(333\) | −16.6557 | −0.912726 | ||||||||
\(334\) | 13.6241 | 0.745477 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.27510 | 0.178672 | ||||||||
\(337\) | 14.1958 | 0.773295 | 0.386647 | − | 0.922228i | \(-0.373633\pi\) | ||||
0.386647 | + | 0.922228i | \(0.373633\pi\) | |||||||
\(338\) | −28.7893 | −1.56593 | ||||||||
\(339\) | 8.11843 | 0.440933 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.72630 | −0.147638 | ||||||||
\(342\) | −51.1495 | −2.76585 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.4190 | −0.669585 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.05209 | 0.164082 | ||||||||
\(347\) | 5.38584 | 0.289127 | 0.144564 | − | 0.989496i | \(-0.453822\pi\) | ||||
0.144564 | + | 0.989496i | \(0.453822\pi\) | |||||||
\(348\) | −3.31854 | −0.177893 | ||||||||
\(349\) | −22.9557 | −1.22879 | −0.614396 | − | 0.788997i | \(-0.710600\pi\) | ||||
−0.614396 | + | 0.788997i | \(0.710600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −100.064 | −5.34104 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 2.80195 | 0.149133 | 0.0745664 | − | 0.997216i | \(-0.476243\pi\) | ||||
0.0745664 | + | 0.997216i | \(0.476243\pi\) | |||||||
\(354\) | −37.4371 | −1.98976 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.02653 | 0.425405 | ||||||||
\(357\) | −11.0739 | −0.586092 | ||||||||
\(358\) | 17.4417 | 0.921823 | ||||||||
\(359\) | 9.53192 | 0.503076 | 0.251538 | − | 0.967847i | \(-0.419064\pi\) | ||||
0.251538 | + | 0.967847i | \(0.419064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.8267 | 1.30667 | ||||||||
\(362\) | 24.9813 | 1.31299 | ||||||||
\(363\) | 3.27510 | 0.171898 | ||||||||
\(364\) | −6.46446 | −0.338830 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −18.4816 | −0.966051 | ||||||||
\(367\) | −11.8716 | −0.619691 | −0.309845 | − | 0.950787i | \(-0.600277\pi\) | ||||
−0.309845 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(368\) | 5.53694 | 0.288633 | ||||||||
\(369\) | 21.7159 | 1.13048 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.39450 | 0.435821 | ||||||||
\(372\) | −8.92893 | −0.462943 | ||||||||
\(373\) | −12.3379 | −0.638835 | −0.319417 | − | 0.947614i | \(-0.603487\pi\) | ||||
−0.319417 | + | 0.947614i | \(0.603487\pi\) | |||||||
\(374\) | 3.38123 | 0.174839 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.82139 | 0.145502 | ||||||||
\(377\) | 6.55021 | 0.337353 | ||||||||
\(378\) | −15.4791 | −0.796161 | ||||||||
\(379\) | −23.2669 | −1.19514 | −0.597570 | − | 0.801817i | \(-0.703867\pi\) | ||||
−0.597570 | + | 0.801817i | \(0.703867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.0517 | −1.64206 | ||||||||
\(382\) | −18.6624 | −0.954849 | ||||||||
\(383\) | −9.41519 | −0.481094 | −0.240547 | − | 0.970638i | \(-0.577327\pi\) | ||||
−0.240547 | + | 0.970638i | \(0.577327\pi\) | |||||||
\(384\) | −3.27510 | −0.167132 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.82641 | 0.245658 | ||||||||
\(387\) | 95.9526 | 4.87755 | ||||||||
\(388\) | 11.3961 | 0.578547 | ||||||||
\(389\) | 24.7245 | 1.25358 | 0.626791 | − | 0.779187i | \(-0.284368\pi\) | ||||
0.626791 | + | 0.779187i | \(0.284368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.7217 | −0.946797 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 28.3188 | 1.42850 | ||||||||
\(394\) | −13.1677 | −0.663380 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.72630 | 0.388261 | ||||||||
\(397\) | 0.894317 | 0.0448845 | 0.0224423 | − | 0.999748i | \(-0.492856\pi\) | ||||
0.0224423 | + | 0.999748i | \(0.492856\pi\) | |||||||
\(398\) | 17.6955 | 0.886994 | ||||||||
\(399\) | 21.6818 | 1.08545 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.60662 | 0.180106 | 0.0900531 | − | 0.995937i | \(-0.471296\pi\) | ||||
0.0900531 | + | 0.995937i | \(0.471296\pi\) | |||||||
\(402\) | 10.3787 | 0.517644 | ||||||||
\(403\) | 17.6241 | 0.877919 | ||||||||
\(404\) | −1.47159 | −0.0732141 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.01326 | 0.0502874 | ||||||||
\(407\) | −2.15571 | −0.106855 | ||||||||
\(408\) | 11.0739 | 0.548239 | ||||||||
\(409\) | 24.4591 | 1.20942 | 0.604711 | − | 0.796445i | \(-0.293289\pi\) | ||||
0.604711 | + | 0.796445i | \(0.293289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.67020 | −0.476996 | ||||||||
\(412\) | −5.49003 | −0.270474 | ||||||||
\(413\) | 11.4308 | 0.562474 | ||||||||
\(414\) | −42.7801 | −2.10253 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.46446 | 0.316946 | ||||||||
\(417\) | −58.6451 | −2.87186 | ||||||||
\(418\) | −6.62018 | −0.323803 | ||||||||
\(419\) | 4.70912 | 0.230056 | 0.115028 | − | 0.993362i | \(-0.463304\pi\) | ||||
0.115028 | + | 0.993362i | \(0.463304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1731 | 0.642015 | 0.321008 | − | 0.947077i | \(-0.395978\pi\) | ||||
0.321008 | + | 0.947077i | \(0.395978\pi\) | |||||||
\(422\) | −11.2669 | −0.548463 | ||||||||
\(423\) | −21.7989 | −1.05990 | ||||||||
\(424\) | −8.39450 | −0.407673 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.9090 | −0.770793 | ||||||||
\(427\) | 5.64307 | 0.273087 | ||||||||
\(428\) | −10.1341 | −0.489848 | ||||||||
\(429\) | −21.1718 | −1.02218 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.96302 | −0.335397 | −0.167699 | − | 0.985838i | \(-0.553634\pi\) | ||||
−0.167699 | + | 0.985838i | \(0.553634\pi\) | |||||||
\(432\) | 15.4791 | 0.744740 | ||||||||
\(433\) | −3.53318 | −0.169794 | −0.0848969 | − | 0.996390i | \(-0.527056\pi\) | ||||
−0.0848969 | + | 0.996390i | \(0.527056\pi\) | |||||||
\(434\) | 2.72630 | 0.130867 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.5635 | 0.553790 | ||||||||
\(437\) | 36.6555 | 1.75347 | ||||||||
\(438\) | 2.72169 | 0.130048 | ||||||||
\(439\) | 32.6519 | 1.55839 | 0.779194 | − | 0.626782i | \(-0.215628\pi\) | ||||
0.779194 | + | 0.626782i | \(0.215628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.72630 | 0.367919 | ||||||||
\(442\) | −21.8579 | −1.03967 | ||||||||
\(443\) | 40.9084 | 1.94362 | 0.971808 | − | 0.235772i | \(-0.0757619\pi\) | ||||
0.971808 | + | 0.235772i | \(0.0757619\pi\) | |||||||
\(444\) | −7.06018 | −0.335061 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.2768 | −1.14954 | ||||||||
\(447\) | 35.9827 | 1.70192 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −29.6135 | −1.39755 | −0.698774 | − | 0.715342i | \(-0.746271\pi\) | ||||
−0.698774 | + | 0.715342i | \(0.746271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.81064 | 0.132348 | ||||||||
\(452\) | 2.47883 | 0.116594 | ||||||||
\(453\) | −23.4275 | −1.10072 | ||||||||
\(454\) | 19.9074 | 0.934302 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.6818 | −1.01534 | ||||||||
\(457\) | 15.4719 | 0.723744 | 0.361872 | − | 0.932228i | \(-0.382138\pi\) | ||||
0.361872 | + | 0.932228i | \(0.382138\pi\) | |||||||
\(458\) | 10.9196 | 0.510239 | ||||||||
\(459\) | −52.3386 | −2.44295 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.231236 | 0.0107697 | 0.00538486 | − | 0.999986i | \(-0.498286\pi\) | ||||
0.00538486 | + | 0.999986i | \(0.498286\pi\) | |||||||
\(462\) | −3.27510 | −0.152372 | ||||||||
\(463\) | −0.741666 | −0.0344682 | −0.0172341 | − | 0.999851i | \(-0.505486\pi\) | ||||
−0.0172341 | + | 0.999851i | \(0.505486\pi\) | |||||||
\(464\) | −1.01326 | −0.0470396 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.86037 | 0.317800 | ||||||||
\(467\) | 35.1500 | 1.62655 | 0.813274 | − | 0.581880i | \(-0.197683\pi\) | ||||
0.813274 | + | 0.581880i | \(0.197683\pi\) | |||||||
\(468\) | −49.9464 | −2.30877 | ||||||||
\(469\) | −3.16897 | −0.146330 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −38.9428 | −1.79439 | ||||||||
\(472\) | −11.4308 | −0.526146 | ||||||||
\(473\) | 12.4190 | 0.571024 | ||||||||
\(474\) | 34.5882 | 1.58869 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.38123 | −0.154979 | ||||||||
\(477\) | 64.8584 | 2.96966 | ||||||||
\(478\) | −19.0161 | −0.869775 | ||||||||
\(479\) | 7.82851 | 0.357694 | 0.178847 | − | 0.983877i | \(-0.442763\pi\) | ||||
0.178847 | + | 0.983877i | \(0.442763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9355 | 0.635405 | ||||||||
\(482\) | 9.59461 | 0.437022 | ||||||||
\(483\) | 18.1341 | 0.825128 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −43.6832 | −1.98151 | ||||||||
\(487\) | −38.4687 | −1.74318 | −0.871591 | − | 0.490233i | \(-0.836912\pi\) | ||||
−0.871591 | + | 0.490233i | \(0.836912\pi\) | |||||||
\(488\) | −5.64307 | −0.255450 | ||||||||
\(489\) | 21.2024 | 0.958805 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.04234 | 0.317816 | 0.158908 | − | 0.987293i | \(-0.449203\pi\) | ||||
0.158908 | + | 0.987293i | \(0.449203\pi\) | |||||||
\(492\) | 9.20514 | 0.415000 | ||||||||
\(493\) | 3.42608 | 0.154303 | ||||||||
\(494\) | 42.7959 | 1.92548 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.72630 | −0.122415 | ||||||||
\(497\) | 4.85755 | 0.217891 | ||||||||
\(498\) | 15.7600 | 0.706220 | ||||||||
\(499\) | −10.7080 | −0.479355 | −0.239678 | − | 0.970853i | \(-0.577042\pi\) | ||||
−0.239678 | + | 0.970853i | \(0.577042\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −44.6203 | −1.99349 | ||||||||
\(502\) | 22.9823 | 1.02575 | ||||||||
\(503\) | −1.57235 | −0.0701078 | −0.0350539 | − | 0.999385i | \(-0.511160\pi\) | ||||
−0.0350539 | + | 0.999385i | \(0.511160\pi\) | |||||||
\(504\) | −7.72630 | −0.344157 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.53694 | −0.246147 | ||||||||
\(507\) | 94.2879 | 4.18747 | ||||||||
\(508\) | −9.78648 | −0.434205 | ||||||||
\(509\) | 18.1484 | 0.804415 | 0.402208 | − | 0.915549i | \(-0.368243\pi\) | ||||
0.402208 | + | 0.915549i | \(0.368243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.831025 | −0.0367624 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 102.475 | 4.52436 | ||||||||
\(514\) | 1.18067 | 0.0520773 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 40.6734 | 1.79055 | ||||||||
\(517\) | −2.82139 | −0.124085 | ||||||||
\(518\) | 2.15571 | 0.0947165 | ||||||||
\(519\) | −9.99592 | −0.438772 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.77193 | 0.384305 | 0.192153 | − | 0.981365i | \(-0.438453\pi\) | ||||
0.192153 | + | 0.981365i | \(0.438453\pi\) | |||||||
\(522\) | 7.82878 | 0.342657 | ||||||||
\(523\) | −15.0998 | −0.660266 | −0.330133 | − | 0.943934i | \(-0.607094\pi\) | ||||
−0.330133 | + | 0.943934i | \(0.607094\pi\) | |||||||
\(524\) | 8.64670 | 0.377733 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.9368 | 1.17450 | ||||||||
\(527\) | 9.21827 | 0.401554 | ||||||||
\(528\) | 3.27510 | 0.142531 | ||||||||
\(529\) | 7.65774 | 0.332945 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 88.3179 | 3.83267 | ||||||||
\(532\) | 6.62018 | 0.287021 | ||||||||
\(533\) | −18.1693 | −0.786999 | ||||||||
\(534\) | −26.2877 | −1.13758 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.16897 | 0.136879 | ||||||||
\(537\) | −57.1234 | −2.46506 | ||||||||
\(538\) | 20.4439 | 0.881401 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8143 | 0.765896 | 0.382948 | − | 0.923770i | \(-0.374909\pi\) | ||||
0.382948 | + | 0.923770i | \(0.374909\pi\) | |||||||
\(542\) | −25.6269 | −1.10077 | ||||||||
\(543\) | −81.8164 | −3.51108 | ||||||||
\(544\) | 3.38123 | 0.144969 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 21.1718 | 0.906069 | ||||||||
\(547\) | −39.7962 | −1.70156 | −0.850781 | − | 0.525520i | \(-0.823871\pi\) | ||||
−0.850781 | + | 0.525520i | \(0.823871\pi\) | |||||||
\(548\) | −2.95264 | −0.126131 | ||||||||
\(549\) | 43.6001 | 1.86081 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.70798 | −0.285770 | ||||||||
\(552\) | −18.1341 | −0.771837 | ||||||||
\(553\) | −10.5610 | −0.449098 | ||||||||
\(554\) | 16.3408 | 0.694253 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.9063 | −0.759397 | ||||||||
\(557\) | −5.61626 | −0.237968 | −0.118984 | − | 0.992896i | \(-0.537964\pi\) | ||||
−0.118984 | + | 0.992896i | \(0.537964\pi\) | |||||||
\(558\) | 21.0643 | 0.891721 | ||||||||
\(559\) | −80.2819 | −3.39556 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0739 | −0.467540 | ||||||||
\(562\) | −4.37872 | −0.184705 | ||||||||
\(563\) | 27.4346 | 1.15623 | 0.578115 | − | 0.815955i | \(-0.303789\pi\) | ||||
0.578115 | + | 0.815955i | \(0.303789\pi\) | |||||||
\(564\) | −9.24035 | −0.389089 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.1500 | 0.636802 | ||||||||
\(567\) | 27.5169 | 1.15560 | ||||||||
\(568\) | −4.85755 | −0.203818 | ||||||||
\(569\) | 6.02245 | 0.252474 | 0.126237 | − | 0.992000i | \(-0.459710\pi\) | ||||
0.126237 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.38374 | 0.350849 | 0.175424 | − | 0.984493i | \(-0.443870\pi\) | ||||
0.175424 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(572\) | −6.46446 | −0.270293 | ||||||||
\(573\) | 61.1211 | 2.55337 | ||||||||
\(574\) | −2.81064 | −0.117314 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.72630 | 0.321929 | ||||||||
\(577\) | −1.12762 | −0.0469434 | −0.0234717 | − | 0.999725i | \(-0.507472\pi\) | ||||
−0.0234717 | + | 0.999725i | \(0.507472\pi\) | |||||||
\(578\) | 5.56727 | 0.231568 | ||||||||
\(579\) | −15.8070 | −0.656917 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.81205 | −0.199637 | ||||||||
\(582\) | −37.3233 | −1.54710 | ||||||||
\(583\) | 8.39450 | 0.347665 | ||||||||
\(584\) | 0.831025 | 0.0343881 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.630927 | −0.0260634 | ||||||||
\(587\) | −11.3187 | −0.467172 | −0.233586 | − | 0.972336i | \(-0.575046\pi\) | ||||
−0.233586 | + | 0.972336i | \(0.575046\pi\) | |||||||
\(588\) | 3.27510 | 0.135063 | ||||||||
\(589\) | −18.0486 | −0.743680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 43.1256 | 1.77395 | ||||||||
\(592\) | −2.15571 | −0.0885992 | ||||||||
\(593\) | −19.0319 | −0.781545 | −0.390772 | − | 0.920487i | \(-0.627792\pi\) | ||||
−0.390772 | + | 0.920487i | \(0.627792\pi\) | |||||||
\(594\) | −15.4791 | −0.635117 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.9867 | 0.450034 | ||||||||
\(597\) | −57.9545 | −2.37192 | ||||||||
\(598\) | 35.7934 | 1.46370 | ||||||||
\(599\) | −12.8576 | −0.525345 | −0.262673 | − | 0.964885i | \(-0.584604\pi\) | ||||
−0.262673 | + | 0.964885i | \(0.584604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.16565 | 0.129129 | 0.0645647 | − | 0.997914i | \(-0.479434\pi\) | ||||
0.0645647 | + | 0.997914i | \(0.479434\pi\) | |||||||
\(602\) | −12.4190 | −0.506159 | ||||||||
\(603\) | −24.4845 | −0.997084 | ||||||||
\(604\) | −7.15320 | −0.291060 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.81960 | 0.195783 | ||||||||
\(607\) | −2.18017 | −0.0884905 | −0.0442453 | − | 0.999021i | \(-0.514088\pi\) | ||||
−0.0442453 | + | 0.999021i | \(0.514088\pi\) | |||||||
\(608\) | −6.62018 | −0.268484 | ||||||||
\(609\) | −3.31854 | −0.134474 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.2388 | 0.737862 | ||||||||
\(612\) | −26.1244 | −1.05602 | ||||||||
\(613\) | 32.4835 | 1.31200 | 0.655998 | − | 0.754762i | \(-0.272248\pi\) | ||||
0.655998 | + | 0.754762i | \(0.272248\pi\) | |||||||
\(614\) | 17.5287 | 0.707401 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 8.85755 | 0.356592 | 0.178296 | − | 0.983977i | \(-0.442942\pi\) | ||||
0.178296 | + | 0.983977i | \(0.442942\pi\) | |||||||
\(618\) | 17.9804 | 0.723279 | ||||||||
\(619\) | 28.4997 | 1.14550 | 0.572749 | − | 0.819731i | \(-0.305877\pi\) | ||||
0.572749 | + | 0.819731i | \(0.305877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 85.7071 | 3.43931 | ||||||||
\(622\) | −29.0181 | −1.16352 | ||||||||
\(623\) | 8.02653 | 0.321576 | ||||||||
\(624\) | −21.1718 | −0.847550 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.9475 | 1.07704 | ||||||||
\(627\) | 21.6818 | 0.865886 | ||||||||
\(628\) | −11.8905 | −0.474484 | ||||||||
\(629\) | 7.28896 | 0.290630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.8847 | −1.78683 | −0.893416 | − | 0.449231i | \(-0.851698\pi\) | ||||
−0.893416 | + | 0.449231i | \(0.851698\pi\) | |||||||
\(632\) | 10.5610 | 0.420092 | ||||||||
\(633\) | 36.9002 | 1.46665 | ||||||||
\(634\) | 16.7087 | 0.663589 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 27.4928 | 1.09016 | ||||||||
\(637\) | −6.46446 | −0.256131 | ||||||||
\(638\) | 1.01326 | 0.0401155 | ||||||||
\(639\) | 37.5309 | 1.48470 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.3641 | 1.51529 | 0.757646 | − | 0.652666i | \(-0.226350\pi\) | ||||
0.757646 | + | 0.652666i | \(0.226350\pi\) | |||||||
\(642\) | 33.1901 | 1.30991 | ||||||||
\(643\) | −7.61526 | −0.300317 | −0.150158 | − | 0.988662i | \(-0.547978\pi\) | ||||
−0.150158 | + | 0.988662i | \(0.547978\pi\) | |||||||
\(644\) | 5.53694 | 0.218186 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.3844 | 0.880701 | ||||||||
\(647\) | 30.7250 | 1.20793 | 0.603963 | − | 0.797012i | \(-0.293587\pi\) | ||||
0.603963 | + | 0.797012i | \(0.293587\pi\) | |||||||
\(648\) | −27.5169 | −1.08096 | ||||||||
\(649\) | 11.4308 | 0.448699 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.92893 | −0.349952 | ||||||||
\(652\) | 6.47381 | 0.253534 | ||||||||
\(653\) | 37.5653 | 1.47005 | 0.735023 | − | 0.678043i | \(-0.237171\pi\) | ||||
0.735023 | + | 0.678043i | \(0.237171\pi\) | |||||||
\(654\) | −37.8716 | −1.48090 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.81064 | 0.109737 | ||||||||
\(657\) | −6.42075 | −0.250497 | ||||||||
\(658\) | 2.82139 | 0.109989 | ||||||||
\(659\) | −39.9380 | −1.55576 | −0.777882 | − | 0.628410i | \(-0.783706\pi\) | ||||
−0.777882 | + | 0.628410i | \(0.783706\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.3398 | −1.41345 | −0.706727 | − | 0.707486i | \(-0.749829\pi\) | ||||
−0.706727 | + | 0.707486i | \(0.749829\pi\) | |||||||
\(662\) | 31.0222 | 1.20571 | ||||||||
\(663\) | 71.5867 | 2.78020 | ||||||||
\(664\) | 4.81205 | 0.186744 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.6557 | 0.645394 | ||||||||
\(667\) | −5.61038 | −0.217235 | ||||||||
\(668\) | −13.6241 | −0.527132 | ||||||||
\(669\) | 79.5091 | 3.07400 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.64307 | 0.217848 | ||||||||
\(672\) | −3.27510 | −0.126340 | ||||||||
\(673\) | 33.8212 | 1.30371 | 0.651855 | − | 0.758344i | \(-0.273991\pi\) | ||||
0.651855 | + | 0.758344i | \(0.273991\pi\) | |||||||
\(674\) | −14.1958 | −0.546802 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.7893 | 1.10728 | ||||||||
\(677\) | −47.8344 | −1.83843 | −0.919213 | − | 0.393760i | \(-0.871174\pi\) | ||||
−0.919213 | + | 0.393760i | \(0.871174\pi\) | |||||||
\(678\) | −8.11843 | −0.311786 | ||||||||
\(679\) | 11.3961 | 0.437341 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −65.1989 | −2.49843 | ||||||||
\(682\) | 2.72630 | 0.104396 | ||||||||
\(683\) | 44.6775 | 1.70954 | 0.854768 | − | 0.519011i | \(-0.173700\pi\) | ||||
0.854768 | + | 0.519011i | \(0.173700\pi\) | |||||||
\(684\) | 51.1495 | 1.95575 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −35.7628 | −1.36443 | ||||||||
\(688\) | 12.4190 | 0.473468 | ||||||||
\(689\) | −54.2659 | −2.06737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.08364 | −0.345558 | −0.172779 | − | 0.984961i | \(-0.555275\pi\) | ||||
−0.172779 | + | 0.984961i | \(0.555275\pi\) | |||||||
\(692\) | −3.05209 | −0.116023 | ||||||||
\(693\) | 7.72630 | 0.293498 | ||||||||
\(694\) | −5.38584 | −0.204444 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.31854 | 0.125789 | ||||||||
\(697\) | −9.50343 | −0.359968 | ||||||||
\(698\) | 22.9557 | 0.868888 | ||||||||
\(699\) | −22.4684 | −0.849834 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.5344 | 0.813344 | 0.406672 | − | 0.913574i | \(-0.366689\pi\) | ||||
0.406672 | + | 0.913574i | \(0.366689\pi\) | |||||||
\(702\) | 100.064 | 3.77668 | ||||||||
\(703\) | −14.2712 | −0.538248 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.80195 | −0.105453 | ||||||||
\(707\) | −1.47159 | −0.0553447 | ||||||||
\(708\) | 37.4371 | 1.40697 | ||||||||
\(709\) | −0.0726367 | −0.00272793 | −0.00136396 | − | 0.999999i | \(-0.500434\pi\) | ||||
−0.00136396 | + | 0.999999i | \(0.500434\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −81.5972 | −3.06013 | ||||||||
\(712\) | −8.02653 | −0.300807 | ||||||||
\(713\) | −15.0954 | −0.565327 | ||||||||
\(714\) | 11.0739 | 0.414430 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.4417 | −0.651827 | ||||||||
\(717\) | 62.2796 | 2.32588 | ||||||||
\(718\) | −9.53192 | −0.355728 | ||||||||
\(719\) | −14.8626 | −0.554281 | −0.277140 | − | 0.960829i | \(-0.589387\pi\) | ||||
−0.277140 | + | 0.960829i | \(0.589387\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.49003 | −0.204459 | ||||||||
\(722\) | −24.8267 | −0.923955 | ||||||||
\(723\) | −31.4233 | −1.16865 | ||||||||
\(724\) | −24.9813 | −0.928424 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.27510 | −0.121550 | ||||||||
\(727\) | −14.3413 | −0.531889 | −0.265945 | − | 0.963988i | \(-0.585684\pi\) | ||||
−0.265945 | + | 0.963988i | \(0.585684\pi\) | |||||||
\(728\) | 6.46446 | 0.239589 | ||||||||
\(729\) | 60.5163 | 2.24135 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.9914 | −1.55311 | ||||||||
\(732\) | 18.4816 | 0.683101 | ||||||||
\(733\) | 38.0104 | 1.40394 | 0.701972 | − | 0.712204i | \(-0.252303\pi\) | ||||
0.701972 | + | 0.712204i | \(0.252303\pi\) | |||||||
\(734\) | 11.8716 | 0.438188 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.53694 | −0.204094 | ||||||||
\(737\) | −3.16897 | −0.116731 | ||||||||
\(738\) | −21.7159 | −0.799372 | ||||||||
\(739\) | 8.83792 | 0.325108 | 0.162554 | − | 0.986700i | \(-0.448027\pi\) | ||||
0.162554 | + | 0.986700i | \(0.448027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −140.161 | −5.14894 | ||||||||
\(742\) | −8.39450 | −0.308172 | ||||||||
\(743\) | −32.2049 | −1.18148 | −0.590742 | − | 0.806861i | \(-0.701165\pi\) | ||||
−0.590742 | + | 0.806861i | \(0.701165\pi\) | |||||||
\(744\) | 8.92893 | 0.327350 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.3379 | 0.451724 | ||||||||
\(747\) | −37.1793 | −1.36032 | ||||||||
\(748\) | −3.38123 | −0.123630 | ||||||||
\(749\) | −10.1341 | −0.370291 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.1493 | −1.35560 | −0.677799 | − | 0.735247i | \(-0.737066\pi\) | ||||
−0.677799 | + | 0.735247i | \(0.737066\pi\) | |||||||
\(752\) | −2.82139 | −0.102886 | ||||||||
\(753\) | −75.2693 | −2.74297 | ||||||||
\(754\) | −6.55021 | −0.238544 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15.4791 | 0.562971 | ||||||||
\(757\) | 3.34714 | 0.121654 | 0.0608269 | − | 0.998148i | \(-0.480626\pi\) | ||||
0.0608269 | + | 0.998148i | \(0.480626\pi\) | |||||||
\(758\) | 23.2669 | 0.845091 | ||||||||
\(759\) | 18.1341 | 0.658225 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.7682 | 0.897848 | 0.448924 | − | 0.893570i | \(-0.351807\pi\) | ||||
0.448924 | + | 0.893570i | \(0.351807\pi\) | |||||||
\(762\) | 32.0517 | 1.16111 | ||||||||
\(763\) | 11.5635 | 0.418626 | ||||||||
\(764\) | 18.6624 | 0.675180 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.41519 | 0.340184 | ||||||||
\(767\) | −73.8941 | −2.66816 | ||||||||
\(768\) | 3.27510 | 0.118180 | ||||||||
\(769\) | −13.2016 | −0.476063 | −0.238032 | − | 0.971257i | \(-0.576502\pi\) | ||||
−0.238032 | + | 0.971257i | \(0.576502\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.86683 | −0.139260 | ||||||||
\(772\) | −4.82641 | −0.173706 | ||||||||
\(773\) | −5.00683 | −0.180083 | −0.0900416 | − | 0.995938i | \(-0.528700\pi\) | ||||
−0.0900416 | + | 0.995938i | \(0.528700\pi\) | |||||||
\(774\) | −95.9526 | −3.44895 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.3961 | −0.409095 | ||||||||
\(777\) | −7.06018 | −0.253282 | ||||||||
\(778\) | −24.7245 | −0.886417 | ||||||||
\(779\) | 18.6069 | 0.666662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.85755 | 0.173817 | ||||||||
\(782\) | 18.7217 | 0.669486 | ||||||||
\(783\) | −15.6844 | −0.560516 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −28.3188 | −1.01010 | ||||||||
\(787\) | 20.5280 | 0.731746 | 0.365873 | − | 0.930665i | \(-0.380770\pi\) | ||||
0.365873 | + | 0.930665i | \(0.380770\pi\) | |||||||
\(788\) | 13.1677 | 0.469080 | ||||||||
\(789\) | −88.2207 | −3.14074 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.47883 | 0.0881371 | ||||||||
\(792\) | −7.72630 | −0.274542 | ||||||||
\(793\) | −36.4794 | −1.29542 | ||||||||
\(794\) | −0.894317 | −0.0317381 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.6955 | −0.627199 | ||||||||
\(797\) | 4.72846 | 0.167491 | 0.0837454 | − | 0.996487i | \(-0.473312\pi\) | ||||
0.0837454 | + | 0.996487i | \(0.473312\pi\) | |||||||
\(798\) | −21.6818 | −0.767526 | ||||||||
\(799\) | 9.53978 | 0.337493 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 62.0154 | 2.19121 | ||||||||
\(802\) | −3.60662 | −0.127354 | ||||||||
\(803\) | −0.831025 | −0.0293262 | ||||||||
\(804\) | −10.3787 | −0.366029 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.6241 | −0.620782 | ||||||||
\(807\) | −66.9560 | −2.35696 | ||||||||
\(808\) | 1.47159 | 0.0517702 | ||||||||
\(809\) | −31.1911 | −1.09662 | −0.548310 | − | 0.836275i | \(-0.684728\pi\) | ||||
−0.548310 | + | 0.836275i | \(0.684728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.74209 | 0.131403 | 0.0657013 | − | 0.997839i | \(-0.479072\pi\) | ||||
0.0657013 | + | 0.997839i | \(0.479072\pi\) | |||||||
\(812\) | −1.01326 | −0.0355586 | ||||||||
\(813\) | 83.9308 | 2.94358 | ||||||||
\(814\) | 2.15571 | 0.0755576 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −11.0739 | −0.387664 | ||||||||
\(817\) | 82.2157 | 2.87636 | ||||||||
\(818\) | −24.4591 | −0.855191 | ||||||||
\(819\) | −49.9464 | −1.74527 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.1553 | 0.563825 | 0.281913 | − | 0.959440i | \(-0.409031\pi\) | ||||
0.281913 | + | 0.959440i | \(0.409031\pi\) | |||||||
\(822\) | 9.67020 | 0.337287 | ||||||||
\(823\) | −1.62701 | −0.0567139 | −0.0283570 | − | 0.999598i | \(-0.509028\pi\) | ||||
−0.0283570 | + | 0.999598i | \(0.509028\pi\) | |||||||
\(824\) | 5.49003 | 0.191254 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.4308 | −0.397729 | ||||||||
\(827\) | 28.5580 | 0.993061 | 0.496530 | − | 0.868019i | \(-0.334607\pi\) | ||||
0.496530 | + | 0.868019i | \(0.334607\pi\) | |||||||
\(828\) | 42.7801 | 1.48671 | ||||||||
\(829\) | 18.7101 | 0.649830 | 0.324915 | − | 0.945743i | \(-0.394664\pi\) | ||||
0.324915 | + | 0.945743i | \(0.394664\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −53.5177 | −1.85651 | ||||||||
\(832\) | −6.46446 | −0.224115 | ||||||||
\(833\) | −3.38123 | −0.117153 | ||||||||
\(834\) | 58.6451 | 2.03071 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.62018 | 0.228964 | ||||||||
\(837\) | −42.2008 | −1.45867 | ||||||||
\(838\) | −4.70912 | −0.162674 | ||||||||
\(839\) | 36.4414 | 1.25810 | 0.629049 | − | 0.777366i | \(-0.283445\pi\) | ||||
0.629049 | + | 0.777366i | \(0.283445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9733 | −0.964596 | ||||||||
\(842\) | −13.1731 | −0.453973 | ||||||||
\(843\) | 14.3408 | 0.493922 | ||||||||
\(844\) | 11.2669 | 0.387822 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 21.7989 | 0.749463 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 8.39450 | 0.288268 | ||||||||
\(849\) | −49.6178 | −1.70288 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.9361 | −0.409163 | ||||||||
\(852\) | 15.9090 | 0.545033 | ||||||||
\(853\) | −25.9043 | −0.886945 | −0.443472 | − | 0.896288i | \(-0.646254\pi\) | ||||
−0.443472 | + | 0.896288i | \(0.646254\pi\) | |||||||
\(854\) | −5.64307 | −0.193102 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1341 | 0.346375 | ||||||||
\(857\) | 15.6452 | 0.534431 | 0.267215 | − | 0.963637i | \(-0.413896\pi\) | ||||
0.267215 | + | 0.963637i | \(0.413896\pi\) | |||||||
\(858\) | 21.1718 | 0.722793 | ||||||||
\(859\) | −31.7666 | −1.08386 | −0.541930 | − | 0.840423i | \(-0.682306\pi\) | ||||
−0.541930 | + | 0.840423i | \(0.682306\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.20514 | 0.313710 | ||||||||
\(862\) | 6.96302 | 0.237162 | ||||||||
\(863\) | 7.07738 | 0.240917 | 0.120458 | − | 0.992718i | \(-0.461564\pi\) | ||||
0.120458 | + | 0.992718i | \(0.461564\pi\) | |||||||
\(864\) | −15.4791 | −0.526611 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.53318 | 0.120062 | ||||||||
\(867\) | −18.2334 | −0.619238 | ||||||||
\(868\) | −2.72630 | −0.0925368 | ||||||||
\(869\) | −10.5610 | −0.358256 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.4857 | 0.694132 | ||||||||
\(872\) | −11.5635 | −0.391589 | ||||||||
\(873\) | 88.0494 | 2.98002 | ||||||||
\(874\) | −36.6555 | −1.23989 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.72169 | −0.0919575 | ||||||||
\(877\) | −13.7101 | −0.462957 | −0.231478 | − | 0.972840i | \(-0.574356\pi\) | ||||
−0.231478 | + | 0.972840i | \(0.574356\pi\) | |||||||
\(878\) | −32.6519 | −1.10195 | ||||||||
\(879\) | 2.06635 | 0.0696963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.9858 | −0.538574 | −0.269287 | − | 0.963060i | \(-0.586788\pi\) | ||||
−0.269287 | + | 0.963060i | \(0.586788\pi\) | |||||||
\(882\) | −7.72630 | −0.260158 | ||||||||
\(883\) | −44.0546 | −1.48256 | −0.741278 | − | 0.671198i | \(-0.765780\pi\) | ||||
−0.741278 | + | 0.671198i | \(0.765780\pi\) | |||||||
\(884\) | 21.8579 | 0.735159 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.9084 | −1.37434 | ||||||||
\(887\) | −51.9962 | −1.74586 | −0.872930 | − | 0.487845i | \(-0.837783\pi\) | ||||
−0.872930 | + | 0.487845i | \(0.837783\pi\) | |||||||
\(888\) | 7.06018 | 0.236924 | ||||||||
\(889\) | −9.78648 | −0.328228 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.5169 | 0.921850 | ||||||||
\(892\) | 24.2768 | 0.812848 | ||||||||
\(893\) | −18.6781 | −0.625039 | ||||||||
\(894\) | −35.9827 | −1.20344 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −117.227 | −3.91410 | ||||||||
\(898\) | 29.6135 | 0.988216 | ||||||||
\(899\) | 2.76247 | 0.0921334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.3837 | −0.945600 | ||||||||
\(902\) | −2.81064 | −0.0935841 | ||||||||
\(903\) | 40.6734 | 1.35353 | ||||||||
\(904\) | −2.47883 | −0.0824447 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 23.4275 | 0.778326 | ||||||||
\(907\) | 25.8158 | 0.857200 | 0.428600 | − | 0.903494i | \(-0.359007\pi\) | ||||
0.428600 | + | 0.903494i | \(0.359007\pi\) | |||||||
\(908\) | −19.9074 | −0.660652 | ||||||||
\(909\) | −11.3699 | −0.377116 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.2763 | 1.86452 | 0.932258 | − | 0.361794i | \(-0.117836\pi\) | ||||
0.932258 | + | 0.361794i | \(0.117836\pi\) | |||||||
\(912\) | 21.6818 | 0.717955 | ||||||||
\(913\) | −4.81205 | −0.159256 | ||||||||
\(914\) | −15.4719 | −0.511764 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.9196 | −0.360793 | ||||||||
\(917\) | 8.64670 | 0.285539 | ||||||||
\(918\) | 52.3386 | 1.72743 | ||||||||
\(919\) | −21.0335 | −0.693831 | −0.346916 | − | 0.937896i | \(-0.612771\pi\) | ||||
−0.346916 | + | 0.937896i | \(0.612771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −57.4084 | −1.89167 | ||||||||
\(922\) | −0.231236 | −0.00761534 | ||||||||
\(923\) | −31.4015 | −1.03359 | ||||||||
\(924\) | 3.27510 | 0.107743 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.741666 | 0.0243727 | ||||||||
\(927\) | −42.4176 | −1.39318 | ||||||||
\(928\) | 1.01326 | 0.0332620 | ||||||||
\(929\) | −17.0767 | −0.560268 | −0.280134 | − | 0.959961i | \(-0.590379\pi\) | ||||
−0.280134 | + | 0.959961i | \(0.590379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.62018 | 0.216967 | ||||||||
\(932\) | −6.86037 | −0.224719 | ||||||||
\(933\) | 95.0374 | 3.11139 | ||||||||
\(934\) | −35.1500 | −1.15014 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 49.9464 | 1.63255 | ||||||||
\(937\) | 4.00689 | 0.130899 | 0.0654497 | − | 0.997856i | \(-0.479152\pi\) | ||||
0.0654497 | + | 0.997856i | \(0.479152\pi\) | |||||||
\(938\) | 3.16897 | 0.103471 | ||||||||
\(939\) | −88.2559 | −2.88012 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.4810 | −0.472067 | −0.236033 | − | 0.971745i | \(-0.575847\pi\) | ||||
−0.236033 | + | 0.971745i | \(0.575847\pi\) | |||||||
\(942\) | 38.9428 | 1.26882 | ||||||||
\(943\) | 15.5624 | 0.506780 | ||||||||
\(944\) | 11.4308 | 0.372041 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4190 | −0.403775 | ||||||||
\(947\) | −34.1301 | −1.10908 | −0.554539 | − | 0.832158i | \(-0.687105\pi\) | ||||
−0.554539 | + | 0.832158i | \(0.687105\pi\) | |||||||
\(948\) | −34.5882 | −1.12337 | ||||||||
\(949\) | 5.37213 | 0.174387 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.7228 | −1.77451 | ||||||||
\(952\) | 3.38123 | 0.109586 | ||||||||
\(953\) | −6.31885 | −0.204688 | −0.102344 | − | 0.994749i | \(-0.532634\pi\) | ||||
−0.102344 | + | 0.994749i | \(0.532634\pi\) | |||||||
\(954\) | −64.8584 | −2.09987 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 19.0161 | 0.615024 | ||||||||
\(957\) | −3.31854 | −0.107273 | ||||||||
\(958\) | −7.82851 | −0.252928 | ||||||||
\(959\) | −2.95264 | −0.0953457 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5673 | −0.760234 | ||||||||
\(962\) | −13.9355 | −0.449299 | ||||||||
\(963\) | −78.2989 | −2.52315 | ||||||||
\(964\) | −9.59461 | −0.309022 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.1341 | −0.583454 | ||||||||
\(967\) | 32.6668 | 1.05049 | 0.525247 | − | 0.850950i | \(-0.323973\pi\) | ||||
0.525247 | + | 0.850950i | \(0.323973\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −73.3111 | −2.35509 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.9801 | −1.05838 | −0.529190 | − | 0.848503i | \(-0.677504\pi\) | ||||
−0.529190 | + | 0.848503i | \(0.677504\pi\) | |||||||
\(972\) | 43.6832 | 1.40114 | ||||||||
\(973\) | −17.9063 | −0.574050 | ||||||||
\(974\) | 38.4687 | 1.23262 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.64307 | 0.180630 | ||||||||
\(977\) | −5.50566 | −0.176142 | −0.0880709 | − | 0.996114i | \(-0.528070\pi\) | ||||
−0.0880709 | + | 0.996114i | \(0.528070\pi\) | |||||||
\(978\) | −21.2024 | −0.677978 | ||||||||
\(979\) | 8.02653 | 0.256529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 89.3429 | 2.85250 | ||||||||
\(982\) | −7.04234 | −0.224730 | ||||||||
\(983\) | 15.5437 | 0.495767 | 0.247883 | − | 0.968790i | \(-0.420265\pi\) | ||||
0.247883 | + | 0.968790i | \(0.420265\pi\) | |||||||
\(984\) | −9.20514 | −0.293449 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.42608 | −0.109109 | ||||||||
\(987\) | −9.24035 | −0.294124 | ||||||||
\(988\) | −42.7959 | −1.36152 | ||||||||
\(989\) | 68.7631 | 2.18654 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.47470 | −0.0786115 | −0.0393057 | − | 0.999227i | \(-0.512515\pi\) | ||||
−0.0393057 | + | 0.999227i | \(0.512515\pi\) | |||||||
\(992\) | 2.72630 | 0.0865602 | ||||||||
\(993\) | −101.601 | −3.22421 | ||||||||
\(994\) | −4.85755 | −0.154072 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.7600 | −0.499373 | ||||||||
\(997\) | 13.9735 | 0.442544 | 0.221272 | − | 0.975212i | \(-0.428979\pi\) | ||||
0.221272 | + | 0.975212i | \(0.428979\pi\) | |||||||
\(998\) | 10.7080 | 0.338955 | ||||||||
\(999\) | −33.3685 | −1.05573 |
(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 | 3850.2.a.bz.1.5 | 5 | ||
5.2 | odd | 4 | 770.2.c.f.309.1 | ✓ | 10 | ||
5.3 | odd | 4 | 770.2.c.f.309.10 | yes | 10 | ||
5.4 | even | 2 | 3850.2.a.ca.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.c.f.309.1 | ✓ | 10 | 5.2 | odd | 4 | ||
770.2.c.f.309.10 | yes | 10 | 5.3 | odd | 4 | ||
3850.2.a.bz.1.5 | 5 | 1.1 | even | 1 | trivial | ||
3850.2.a.ca.1.1 | 5 | 5.4 | even | 2 |