Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,2,Mod(99,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2450.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.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: | \(19.5633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 490) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.99 |
Dual form | 2450.2.c.t.99.3 |
$q$-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 \(\left(\mathbb{Z}/2450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | − 0.585786i | − 0.338204i | −0.985599 | − | 0.169102i | \(-0.945913\pi\) | ||||
0.985599 | − | 0.169102i | \(-0.0540867\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.585786 | −0.239146 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.65685 | 0.885618 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | 0.585786i | 0.169102i | ||||||||
\(13\) | − 0.828427i | − 0.229764i | −0.993379 | − | 0.114882i | \(-0.963351\pi\) | ||||
0.993379 | − | 0.114882i | \(-0.0366490\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.41421i | 1.31314i | 0.754265 | + | 0.656570i | \(0.227993\pi\) | ||||
−0.754265 | + | 0.656570i | \(0.772007\pi\) | |||||||
\(18\) | − 2.65685i | − 0.626227i | ||||||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 4.82843i | − 1.02942i | ||||||||
\(23\) | 6.82843i | 1.42383i | 0.702268 | + | 0.711913i | \(0.252171\pi\) | ||||
−0.702268 | + | 0.711913i | \(0.747829\pi\) | |||||||
\(24\) | 0.585786 | 0.119573 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.828427 | −0.162468 | ||||||||
\(27\) | − 3.31371i | − 0.637723i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82843 | 0.508001 | 0.254000 | − | 0.967204i | \(-0.418254\pi\) | ||||
0.254000 | + | 0.967204i | \(0.418254\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 2.82843i | − 0.492366i | ||||||||
\(34\) | 5.41421 | 0.928530 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.65685 | −0.442809 | ||||||||
\(37\) | 3.65685i | 0.601183i | 0.953753 | + | 0.300592i | \(0.0971841\pi\) | ||||
−0.953753 | + | 0.300592i | \(0.902816\pi\) | |||||||
\(38\) | 3.41421i | 0.553859i | ||||||||
\(39\) | −0.485281 | −0.0777072 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.0711 | 1.72901 | 0.864505 | − | 0.502624i | \(-0.167632\pi\) | ||||
0.864505 | + | 0.502624i | \(0.167632\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.17157i | 0.483660i | 0.970319 | + | 0.241830i | \(0.0777477\pi\) | ||||
−0.970319 | + | 0.241830i | \(0.922252\pi\) | |||||||
\(44\) | −4.82843 | −0.727913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.82843 | 1.00680 | ||||||||
\(47\) | 10.8284i | 1.57949i | 0.613436 | + | 0.789744i | \(0.289787\pi\) | ||||
−0.613436 | + | 0.789744i | \(0.710213\pi\) | |||||||
\(48\) | − 0.585786i | − 0.0845510i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.17157 | 0.444109 | ||||||||
\(52\) | 0.828427i | 0.114882i | ||||||||
\(53\) | 10.4853i | 1.44026i | 0.693837 | + | 0.720132i | \(0.255919\pi\) | ||||
−0.693837 | + | 0.720132i | \(0.744081\pi\) | |||||||
\(54\) | −3.31371 | −0.450939 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | 0.828427i | 0.108778i | ||||||||
\(59\) | −11.4142 | −1.48600 | −0.743002 | − | 0.669289i | \(-0.766599\pi\) | ||||
−0.743002 | + | 0.669289i | \(0.766599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.3137 | −1.70465 | −0.852323 | − | 0.523016i | \(-0.824807\pi\) | ||||
−0.852323 | + | 0.523016i | \(0.824807\pi\) | |||||||
\(62\) | − 2.82843i | − 0.359211i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.82843 | −0.348155 | ||||||||
\(67\) | − 9.65685i | − 1.17977i | −0.807486 | − | 0.589886i | \(-0.799173\pi\) | ||||
0.807486 | − | 0.589886i | \(-0.200827\pi\) | |||||||
\(68\) | − 5.41421i | − 0.656570i | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4853 | 1.48173 | 0.740865 | − | 0.671654i | \(-0.234416\pi\) | ||||
0.740865 | + | 0.671654i | \(0.234416\pi\) | |||||||
\(72\) | 2.65685i | 0.313113i | ||||||||
\(73\) | 6.58579i | 0.770808i | 0.922748 | + | 0.385404i | \(0.125938\pi\) | ||||
−0.922748 | + | 0.385404i | \(0.874062\pi\) | |||||||
\(74\) | 3.65685 | 0.425101 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.41421 | 0.391637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.485281i | 0.0549473i | ||||||||
\(79\) | 1.17157 | 0.131812 | 0.0659061 | − | 0.997826i | \(-0.479006\pi\) | ||||
0.0659061 | + | 0.997826i | \(0.479006\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.02944 | 0.669937 | ||||||||
\(82\) | − 11.0711i | − 1.22259i | ||||||||
\(83\) | − 6.24264i | − 0.685219i | −0.939478 | − | 0.342609i | \(-0.888689\pi\) | ||||
0.939478 | − | 0.342609i | \(-0.111311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.17157 | 0.341999 | ||||||||
\(87\) | 0.485281i | 0.0520276i | ||||||||
\(88\) | 4.82843i | 0.514712i | ||||||||
\(89\) | 12.7279 | 1.34916 | 0.674579 | − | 0.738203i | \(-0.264325\pi\) | ||||
0.674579 | + | 0.738203i | \(0.264325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 6.82843i | − 0.711913i | ||||||||
\(93\) | − 1.65685i | − 0.171808i | ||||||||
\(94\) | 10.8284 | 1.11687 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.585786 | −0.0597866 | ||||||||
\(97\) | − 16.2426i | − 1.64919i | −0.565723 | − | 0.824595i | \(-0.691403\pi\) | ||||
0.565723 | − | 0.824595i | \(-0.308597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.8284 | 1.28931 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.31371 | −0.926749 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(102\) | − 3.17157i | − 0.314033i | ||||||||
\(103\) | 9.17157i | 0.903702i | 0.892093 | + | 0.451851i | \(0.149236\pi\) | ||||
−0.892093 | + | 0.451851i | \(0.850764\pi\) | |||||||
\(104\) | 0.828427 | 0.0812340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4853 | 1.01842 | ||||||||
\(107\) | − 1.65685i | − 0.160174i | −0.996788 | − | 0.0800871i | \(-0.974480\pi\) | ||||
0.996788 | − | 0.0800871i | \(-0.0255198\pi\) | |||||||
\(108\) | 3.31371i | 0.318862i | ||||||||
\(109\) | 14.4853 | 1.38744 | 0.693719 | − | 0.720246i | \(-0.255971\pi\) | ||||
0.693719 | + | 0.720246i | \(0.255971\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.14214 | 0.203323 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 7.31371i | − 0.688016i | −0.938967 | − | 0.344008i | \(-0.888215\pi\) | ||||
0.938967 | − | 0.344008i | \(-0.111785\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.828427 | 0.0769175 | ||||||||
\(117\) | − 2.20101i | − 0.203483i | ||||||||
\(118\) | 11.4142i | 1.05076i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 13.3137i | 1.20537i | ||||||||
\(123\) | − 6.48528i | − 0.584758i | ||||||||
\(124\) | −2.82843 | −0.254000 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.82843i | − 0.250982i | −0.992095 | − | 0.125491i | \(-0.959949\pi\) | ||||
0.992095 | − | 0.125491i | \(-0.0400507\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 1.85786 | 0.163576 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.24264 | 0.195940 | 0.0979702 | − | 0.995189i | \(-0.468765\pi\) | ||||
0.0979702 | + | 0.995189i | \(0.468765\pi\) | |||||||
\(132\) | 2.82843i | 0.246183i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.65685 | −0.834225 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.41421 | −0.464265 | ||||||||
\(137\) | − 16.0000i | − 1.36697i | −0.729964 | − | 0.683486i | \(-0.760463\pi\) | ||||
0.729964 | − | 0.683486i | \(-0.239537\pi\) | |||||||
\(138\) | − 4.00000i | − 0.340503i | ||||||||
\(139\) | −0.100505 | −0.00852473 | −0.00426236 | − | 0.999991i | \(-0.501357\pi\) | ||||
−0.00426236 | + | 0.999991i | \(0.501357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.34315 | 0.534189 | ||||||||
\(142\) | − 12.4853i | − 1.04774i | ||||||||
\(143\) | − 4.00000i | − 0.334497i | ||||||||
\(144\) | 2.65685 | 0.221405 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.58579 | 0.545044 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 3.65685i | − 0.300592i | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3137 | 0.920697 | 0.460348 | − | 0.887738i | \(-0.347725\pi\) | ||||
0.460348 | + | 0.887738i | \(0.347725\pi\) | |||||||
\(152\) | − 3.41421i | − 0.276929i | ||||||||
\(153\) | 14.3848i | 1.16294i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.485281 | 0.0388536 | ||||||||
\(157\) | − 10.4853i | − 0.836817i | −0.908259 | − | 0.418408i | \(-0.862588\pi\) | ||||
0.908259 | − | 0.418408i | \(-0.137412\pi\) | |||||||
\(158\) | − 1.17157i | − 0.0932053i | ||||||||
\(159\) | 6.14214 | 0.487103 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − 6.02944i | − 0.473717i | ||||||||
\(163\) | − 8.14214i | − 0.637741i | −0.947798 | − | 0.318871i | \(-0.896696\pi\) | ||||
0.947798 | − | 0.318871i | \(-0.103304\pi\) | |||||||
\(164\) | −11.0711 | −0.864505 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.24264 | −0.484523 | ||||||||
\(167\) | − 23.7990i | − 1.84162i | −0.390010 | − | 0.920811i | \(-0.627529\pi\) | ||||
0.390010 | − | 0.920811i | \(-0.372471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3137 | 0.947208 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.07107 | −0.693682 | ||||||||
\(172\) | − 3.17157i | − 0.241830i | ||||||||
\(173\) | 3.17157i | 0.241130i | 0.992705 | + | 0.120565i | \(0.0384707\pi\) | ||||
−0.992705 | + | 0.120565i | \(0.961529\pi\) | |||||||
\(174\) | 0.485281 | 0.0367891 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.82843 | 0.363956 | ||||||||
\(177\) | 6.68629i | 0.502572i | ||||||||
\(178\) | − 12.7279i | − 0.953998i | ||||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4853 | 1.07668 | 0.538341 | − | 0.842727i | \(-0.319051\pi\) | ||||
0.538341 | + | 0.842727i | \(0.319051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.79899i | 0.576518i | ||||||||
\(184\) | −6.82843 | −0.503398 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.65685 | −0.121486 | ||||||||
\(187\) | 26.1421i | 1.91170i | ||||||||
\(188\) | − 10.8284i | − 0.789744i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.1421 | −1.31272 | −0.656359 | − | 0.754448i | \(-0.727904\pi\) | ||||
−0.656359 | + | 0.754448i | \(0.727904\pi\) | |||||||
\(192\) | 0.585786i | 0.0422755i | ||||||||
\(193\) | 5.65685i | 0.407189i | 0.979055 | + | 0.203595i | \(0.0652625\pi\) | ||||
−0.979055 | + | 0.203595i | \(0.934738\pi\) | |||||||
\(194\) | −16.2426 | −1.16615 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7990i | 0.983137i | 0.870839 | + | 0.491569i | \(0.163576\pi\) | ||||
−0.870839 | + | 0.491569i | \(0.836424\pi\) | |||||||
\(198\) | − 12.8284i | − 0.911677i | ||||||||
\(199\) | 0.485281 | 0.0344007 | 0.0172003 | − | 0.999852i | \(-0.494525\pi\) | ||||
0.0172003 | + | 0.999852i | \(0.494525\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | 9.31371i | 0.655310i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.17157 | −0.222055 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.17157 | 0.639014 | ||||||||
\(207\) | 18.1421i | 1.26097i | ||||||||
\(208\) | − 0.828427i | − 0.0574411i | ||||||||
\(209\) | −16.4853 | −1.14031 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.6274 | −1.83311 | −0.916553 | − | 0.399912i | \(-0.869041\pi\) | ||||
−0.916553 | + | 0.399912i | \(0.869041\pi\) | |||||||
\(212\) | − 10.4853i | − 0.720132i | ||||||||
\(213\) | − 7.31371i | − 0.501127i | ||||||||
\(214\) | −1.65685 | −0.113260 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.31371 | 0.225469 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 14.4853i | − 0.981067i | ||||||||
\(219\) | 3.85786 | 0.260690 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.48528 | 0.301713 | ||||||||
\(222\) | − 2.14214i | − 0.143771i | ||||||||
\(223\) | − 15.3137i | − 1.02548i | −0.858543 | − | 0.512741i | \(-0.828630\pi\) | ||||
0.858543 | − | 0.512741i | \(-0.171370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.31371 | −0.486501 | ||||||||
\(227\) | 9.75736i | 0.647619i | 0.946122 | + | 0.323809i | \(0.104964\pi\) | ||||
−0.946122 | + | 0.323809i | \(0.895036\pi\) | |||||||
\(228\) | − 2.00000i | − 0.132453i | ||||||||
\(229\) | −12.1421 | −0.802375 | −0.401187 | − | 0.915996i | \(-0.631402\pi\) | ||||
−0.401187 | + | 0.915996i | \(0.631402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 0.828427i | − 0.0543889i | ||||||||
\(233\) | − 0.686292i | − 0.0449605i | −0.999747 | − | 0.0224802i | \(-0.992844\pi\) | ||||
0.999747 | − | 0.0224802i | \(-0.00715628\pi\) | |||||||
\(234\) | −2.20101 | −0.143885 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.4142 | 0.743002 | ||||||||
\(237\) | − 0.686292i | − 0.0445794i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.65685 | 0.624650 | 0.312325 | − | 0.949975i | \(-0.398892\pi\) | ||||
0.312325 | + | 0.949975i | \(0.398892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5858 | −0.681890 | −0.340945 | − | 0.940083i | \(-0.610747\pi\) | ||||
−0.340945 | + | 0.940083i | \(0.610747\pi\) | |||||||
\(242\) | − 12.3137i | − 0.791555i | ||||||||
\(243\) | − 13.4731i | − 0.864299i | ||||||||
\(244\) | 13.3137 | 0.852323 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.48528 | −0.413486 | ||||||||
\(247\) | 2.82843i | 0.179969i | ||||||||
\(248\) | 2.82843i | 0.179605i | ||||||||
\(249\) | −3.65685 | −0.231744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.41421 | 0.215503 | 0.107752 | − | 0.994178i | \(-0.465635\pi\) | ||||
0.107752 | + | 0.994178i | \(0.465635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.9706i | 2.07284i | ||||||||
\(254\) | −2.82843 | −0.177471 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.89949i | 0.617514i | 0.951141 | + | 0.308757i | \(0.0999129\pi\) | ||||
−0.951141 | + | 0.308757i | \(0.900087\pi\) | |||||||
\(258\) | − 1.85786i | − 0.115666i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.20101 | −0.136239 | ||||||||
\(262\) | − 2.24264i | − 0.138551i | ||||||||
\(263\) | − 28.0000i | − 1.72655i | −0.504730 | − | 0.863277i | \(-0.668408\pi\) | ||||
0.504730 | − | 0.863277i | \(-0.331592\pi\) | |||||||
\(264\) | 2.82843 | 0.174078 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 7.45584i | − 0.456290i | ||||||||
\(268\) | 9.65685i | 0.589886i | ||||||||
\(269\) | −1.51472 | −0.0923540 | −0.0461770 | − | 0.998933i | \(-0.514704\pi\) | ||||
−0.0461770 | + | 0.998933i | \(0.514704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 5.41421i | 0.328285i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.00000 | −0.240772 | ||||||||
\(277\) | 20.1421i | 1.21022i | 0.796140 | + | 0.605112i | \(0.206872\pi\) | ||||
−0.796140 | + | 0.605112i | \(0.793128\pi\) | |||||||
\(278\) | 0.100505i | 0.00602789i | ||||||||
\(279\) | 7.51472 | 0.449894 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | − 6.34315i | − 0.377729i | ||||||||
\(283\) | − 6.24264i | − 0.371086i | −0.982636 | − | 0.185543i | \(-0.940596\pi\) | ||||
0.982636 | − | 0.185543i | \(-0.0594045\pi\) | |||||||
\(284\) | −12.4853 | −0.740865 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − 2.65685i | − 0.156557i | ||||||||
\(289\) | −12.3137 | −0.724336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.51472 | −0.557763 | ||||||||
\(292\) | − 6.58579i | − 0.385404i | ||||||||
\(293\) | 19.6569i | 1.14837i | 0.818727 | + | 0.574183i | \(0.194680\pi\) | ||||
−0.818727 | + | 0.574183i | \(0.805320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.65685 | −0.212550 | ||||||||
\(297\) | − 16.0000i | − 0.928414i | ||||||||
\(298\) | − 6.00000i | − 0.347571i | ||||||||
\(299\) | 5.65685 | 0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 11.3137i | − 0.651031i | ||||||||
\(303\) | 5.45584i | 0.313430i | ||||||||
\(304\) | −3.41421 | −0.195819 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 14.3848 | 0.822323 | ||||||||
\(307\) | 29.0711i | 1.65917i | 0.558378 | + | 0.829587i | \(0.311424\pi\) | ||||
−0.558378 | + | 0.829587i | \(0.688576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.37258 | 0.305636 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | − 0.485281i | − 0.0274736i | ||||||||
\(313\) | 22.3848i | 1.26526i | 0.774453 | + | 0.632631i | \(0.218025\pi\) | ||||
−0.774453 | + | 0.632631i | \(0.781975\pi\) | |||||||
\(314\) | −10.4853 | −0.591719 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.17157 | −0.0659061 | ||||||||
\(317\) | − 6.48528i | − 0.364250i | −0.983275 | − | 0.182125i | \(-0.941702\pi\) | ||||
0.983275 | − | 0.182125i | \(-0.0582975\pi\) | |||||||
\(318\) | − 6.14214i | − 0.344434i | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.970563 | −0.0541715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 18.4853i | − 1.02855i | ||||||||
\(324\) | −6.02944 | −0.334969 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.14214 | −0.450951 | ||||||||
\(327\) | − 8.48528i | − 0.469237i | ||||||||
\(328\) | 11.0711i | 0.611297i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.79899 | −0.318741 | −0.159371 | − | 0.987219i | \(-0.550946\pi\) | ||||
−0.159371 | + | 0.987219i | \(0.550946\pi\) | |||||||
\(332\) | 6.24264i | 0.342609i | ||||||||
\(333\) | 9.71573i | 0.532419i | ||||||||
\(334\) | −23.7990 | −1.30222 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000i | 0.326841i | 0.986557 | + | 0.163420i | \(0.0522527\pi\) | ||||
−0.986557 | + | 0.163420i | \(0.947747\pi\) | |||||||
\(338\) | − 12.3137i | − 0.669777i | ||||||||
\(339\) | −4.28427 | −0.232690 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.6569 | 0.739560 | ||||||||
\(342\) | 9.07107i | 0.490507i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.17157 | −0.171000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.17157 | 0.170505 | ||||||||
\(347\) | − 8.82843i | − 0.473935i | −0.971518 | − | 0.236967i | \(-0.923847\pi\) | ||||
0.971518 | − | 0.236967i | \(-0.0761535\pi\) | |||||||
\(348\) | − 0.485281i | − 0.0260138i | ||||||||
\(349\) | 14.4853 | 0.775379 | 0.387690 | − | 0.921790i | \(-0.373273\pi\) | ||||
0.387690 | + | 0.921790i | \(0.373273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.74517 | −0.146526 | ||||||||
\(352\) | − 4.82843i | − 0.257356i | ||||||||
\(353\) | − 34.3848i | − 1.83012i | −0.403321 | − | 0.915058i | \(-0.632144\pi\) | ||||
0.403321 | − | 0.915058i | \(-0.367856\pi\) | |||||||
\(354\) | 6.68629 | 0.355372 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.7279 | −0.674579 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000i | 0.211407i | ||||||||
\(359\) | 28.2843 | 1.49279 | 0.746393 | − | 0.665505i | \(-0.231784\pi\) | ||||
0.746393 | + | 0.665505i | \(0.231784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | − 14.4853i | − 0.761329i | ||||||||
\(363\) | − 7.21320i | − 0.378595i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.79899 | 0.407660 | ||||||||
\(367\) | − 8.97056i | − 0.468260i | −0.972205 | − | 0.234130i | \(-0.924776\pi\) | ||||
0.972205 | − | 0.234130i | \(-0.0752241\pi\) | |||||||
\(368\) | 6.82843i | 0.355956i | ||||||||
\(369\) | 29.4142 | 1.53124 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.65685i | 0.0859039i | ||||||||
\(373\) | 13.5147i | 0.699766i | 0.936793 | + | 0.349883i | \(0.113779\pi\) | ||||
−0.936793 | + | 0.349883i | \(0.886221\pi\) | |||||||
\(374\) | 26.1421 | 1.35178 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.8284 | −0.558433 | ||||||||
\(377\) | 0.686292i | 0.0353458i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.5147 | −0.899671 | −0.449835 | − | 0.893112i | \(-0.648517\pi\) | ||||
−0.449835 | + | 0.893112i | \(0.648517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.65685 | −0.0848832 | ||||||||
\(382\) | 18.1421i | 0.928232i | ||||||||
\(383\) | 15.5147i | 0.792765i | 0.918085 | + | 0.396383i | \(0.129735\pi\) | ||||
−0.918085 | + | 0.396383i | \(0.870265\pi\) | |||||||
\(384\) | 0.585786 | 0.0298933 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.65685 | 0.287926 | ||||||||
\(387\) | 8.42641i | 0.428338i | ||||||||
\(388\) | 16.2426i | 0.824595i | ||||||||
\(389\) | 0.142136 | 0.00720656 | 0.00360328 | − | 0.999994i | \(-0.498853\pi\) | ||||
0.00360328 | + | 0.999994i | \(0.498853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.9706 | −1.86968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.31371i | − 0.0662678i | ||||||||
\(394\) | 13.7990 | 0.695183 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.8284 | −0.644653 | ||||||||
\(397\) | − 5.79899i | − 0.291043i | −0.989355 | − | 0.145521i | \(-0.953514\pi\) | ||||
0.989355 | − | 0.145521i | \(-0.0464860\pi\) | |||||||
\(398\) | − 0.485281i | − 0.0243250i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 5.65685i | 0.282138i | ||||||||
\(403\) | − 2.34315i | − 0.116720i | ||||||||
\(404\) | 9.31371 | 0.463374 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.6569i | 0.875218i | ||||||||
\(408\) | 3.17157i | 0.157016i | ||||||||
\(409\) | 13.4142 | 0.663290 | 0.331645 | − | 0.943404i | \(-0.392396\pi\) | ||||
0.331645 | + | 0.943404i | \(0.392396\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.37258 | −0.462315 | ||||||||
\(412\) | − 9.17157i | − 0.451851i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.1421 | 0.891637 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.828427 | −0.0406170 | ||||||||
\(417\) | 0.0588745i | 0.00288310i | ||||||||
\(418\) | 16.4853i | 0.806321i | ||||||||
\(419\) | −32.8701 | −1.60581 | −0.802904 | − | 0.596109i | \(-0.796713\pi\) | ||||
−0.802904 | + | 0.596109i | \(0.796713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.31371 | −0.258974 | −0.129487 | − | 0.991581i | \(-0.541333\pi\) | ||||
−0.129487 | + | 0.991581i | \(0.541333\pi\) | |||||||
\(422\) | 26.6274i | 1.29620i | ||||||||
\(423\) | 28.7696i | 1.39882i | ||||||||
\(424\) | −10.4853 | −0.509210 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.31371 | −0.354350 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.65685i | 0.0800871i | ||||||||
\(429\) | −2.34315 | −0.113128 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.6569 | −1.62119 | −0.810597 | − | 0.585605i | \(-0.800857\pi\) | ||||
−0.810597 | + | 0.585605i | \(0.800857\pi\) | |||||||
\(432\) | − 3.31371i | − 0.159431i | ||||||||
\(433\) | − 13.4142i | − 0.644646i | −0.946630 | − | 0.322323i | \(-0.895536\pi\) | ||||
0.946630 | − | 0.322323i | \(-0.104464\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.4853 | −0.693719 | ||||||||
\(437\) | − 23.3137i | − 1.11525i | ||||||||
\(438\) | − 3.85786i | − 0.184336i | ||||||||
\(439\) | −8.97056 | −0.428142 | −0.214071 | − | 0.976818i | \(-0.568672\pi\) | ||||
−0.214071 | + | 0.976818i | \(0.568672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 4.48528i | − 0.213343i | ||||||||
\(443\) | − 36.9706i | − 1.75652i | −0.478179 | − | 0.878262i | \(-0.658703\pi\) | ||||
0.478179 | − | 0.878262i | \(-0.341297\pi\) | |||||||
\(444\) | −2.14214 | −0.101661 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.3137 | −0.725125 | ||||||||
\(447\) | − 3.51472i | − 0.166240i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.6274 | −1.35101 | −0.675506 | − | 0.737355i | \(-0.736075\pi\) | ||||
−0.675506 | + | 0.737355i | \(0.736075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53.4558 | 2.51714 | ||||||||
\(452\) | 7.31371i | 0.344008i | ||||||||
\(453\) | − 6.62742i | − 0.311383i | ||||||||
\(454\) | 9.75736 | 0.457936 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 10.3431i | 0.483832i | 0.970297 | + | 0.241916i | \(0.0777758\pi\) | ||||
−0.970297 | + | 0.241916i | \(0.922224\pi\) | |||||||
\(458\) | 12.1421i | 0.567365i | ||||||||
\(459\) | 17.9411 | 0.837420 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.17157 | −0.334013 | −0.167007 | − | 0.985956i | \(-0.553410\pi\) | ||||
−0.167007 | + | 0.985956i | \(0.553410\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 16.9706i | − 0.788689i | −0.918963 | − | 0.394344i | \(-0.870972\pi\) | ||||
0.918963 | − | 0.394344i | \(-0.129028\pi\) | |||||||
\(464\) | −0.828427 | −0.0384588 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.686292 | −0.0317918 | ||||||||
\(467\) | 3.89949i | 0.180447i | 0.995922 | + | 0.0902236i | \(0.0287582\pi\) | ||||
−0.995922 | + | 0.0902236i | \(0.971242\pi\) | |||||||
\(468\) | 2.20101i | 0.101742i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.14214 | −0.283015 | ||||||||
\(472\) | − 11.4142i | − 0.525382i | ||||||||
\(473\) | 15.3137i | 0.704125i | ||||||||
\(474\) | −0.686292 | −0.0315224 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.8579i | 1.27552i | ||||||||
\(478\) | − 9.65685i | − 0.441694i | ||||||||
\(479\) | 22.8284 | 1.04306 | 0.521529 | − | 0.853234i | \(-0.325362\pi\) | ||||
0.521529 | + | 0.853234i | \(0.325362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.02944 | 0.138130 | ||||||||
\(482\) | 10.5858i | 0.482169i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.3137 | −0.559714 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.4731 | −0.611152 | ||||||||
\(487\) | − 7.79899i | − 0.353406i | −0.984264 | − | 0.176703i | \(-0.943457\pi\) | ||||
0.984264 | − | 0.176703i | \(-0.0565432\pi\) | |||||||
\(488\) | − 13.3137i | − 0.602683i | ||||||||
\(489\) | −4.76955 | −0.215687 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2843 | −1.09593 | −0.547967 | − | 0.836500i | \(-0.684598\pi\) | ||||
−0.547967 | + | 0.836500i | \(0.684598\pi\) | |||||||
\(492\) | 6.48528i | 0.292379i | ||||||||
\(493\) | − 4.48528i | − 0.202007i | ||||||||
\(494\) | 2.82843 | 0.127257 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.82843 | 0.127000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.65685i | 0.163868i | ||||||||
\(499\) | −41.6569 | −1.86482 | −0.932408 | − | 0.361406i | \(-0.882297\pi\) | ||||
−0.932408 | + | 0.361406i | \(0.882297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.9411 | −0.622844 | ||||||||
\(502\) | − 3.41421i | − 0.152384i | ||||||||
\(503\) | − 6.34315i | − 0.282827i | −0.989951 | − | 0.141413i | \(-0.954835\pi\) | ||||
0.989951 | − | 0.141413i | \(-0.0451647\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 32.9706 | 1.46572 | ||||||||
\(507\) | − 7.21320i | − 0.320350i | ||||||||
\(508\) | 2.82843i | 0.125491i | ||||||||
\(509\) | 33.7990 | 1.49811 | 0.749057 | − | 0.662506i | \(-0.230507\pi\) | ||||
0.749057 | + | 0.662506i | \(0.230507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 11.3137i | 0.499512i | ||||||||
\(514\) | 9.89949 | 0.436648 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.85786 | −0.0817879 | ||||||||
\(517\) | 52.2843i | 2.29946i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.85786 | 0.0815512 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.92893 | 0.215940 | 0.107970 | − | 0.994154i | \(-0.465565\pi\) | ||||
0.107970 | + | 0.994154i | \(0.465565\pi\) | |||||||
\(522\) | 2.20101i | 0.0963356i | ||||||||
\(523\) | − 4.10051i | − 0.179303i | −0.995973 | − | 0.0896513i | \(-0.971425\pi\) | ||||
0.995973 | − | 0.0896513i | \(-0.0285753\pi\) | |||||||
\(524\) | −2.24264 | −0.0979702 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0000 | −1.22086 | ||||||||
\(527\) | 15.3137i | 0.667076i | ||||||||
\(528\) | − 2.82843i | − 0.123091i | ||||||||
\(529\) | −23.6274 | −1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.3259 | −1.31603 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.17157i | − 0.397265i | ||||||||
\(534\) | −7.45584 | −0.322646 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.65685 | 0.417113 | ||||||||
\(537\) | 2.34315i | 0.101114i | ||||||||
\(538\) | 1.51472i | 0.0653042i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9706 | 0.815608 | 0.407804 | − | 0.913069i | \(-0.366295\pi\) | ||||
0.407804 | + | 0.913069i | \(0.366295\pi\) | |||||||
\(542\) | − 12.0000i | − 0.515444i | ||||||||
\(543\) | − 8.48528i | − 0.364138i | ||||||||
\(544\) | 5.41421 | 0.232132 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.48528i | 0.277291i | 0.990342 | + | 0.138645i | \(0.0442748\pi\) | ||||
−0.990342 | + | 0.138645i | \(0.955725\pi\) | |||||||
\(548\) | 16.0000i | 0.683486i | ||||||||
\(549\) | −35.3726 | −1.50967 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.82843 | 0.120495 | ||||||||
\(552\) | 4.00000i | 0.170251i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.1421 | 0.855757 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.100505 | 0.00426236 | ||||||||
\(557\) | 20.8284i | 0.882529i | 0.897377 | + | 0.441264i | \(0.145470\pi\) | ||||
−0.897377 | + | 0.441264i | \(0.854530\pi\) | |||||||
\(558\) | − 7.51472i | − 0.318123i | ||||||||
\(559\) | 2.62742 | 0.111128 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.3137 | 0.646545 | ||||||||
\(562\) | − 8.00000i | − 0.337460i | ||||||||
\(563\) | 39.4142i | 1.66111i | 0.556936 | + | 0.830556i | \(0.311977\pi\) | ||||
−0.556936 | + | 0.830556i | \(0.688023\pi\) | |||||||
\(564\) | −6.34315 | −0.267095 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.24264 | −0.262398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.4853i | 0.523871i | ||||||||
\(569\) | 6.68629 | 0.280304 | 0.140152 | − | 0.990130i | \(-0.455241\pi\) | ||||
0.140152 | + | 0.990130i | \(0.455241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.7990 | −1.74923 | −0.874617 | − | 0.484815i | \(-0.838887\pi\) | ||||
−0.874617 | + | 0.484815i | \(0.838887\pi\) | |||||||
\(572\) | 4.00000i | 0.167248i | ||||||||
\(573\) | 10.6274i | 0.443967i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.65685 | −0.110702 | ||||||||
\(577\) | 25.8995i | 1.07821i | 0.842239 | + | 0.539105i | \(0.181237\pi\) | ||||
−0.842239 | + | 0.539105i | \(0.818763\pi\) | |||||||
\(578\) | 12.3137i | 0.512183i | ||||||||
\(579\) | 3.31371 | 0.137713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.51472i | 0.394398i | ||||||||
\(583\) | 50.6274i | 2.09677i | ||||||||
\(584\) | −6.58579 | −0.272522 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.6569 | 0.812017 | ||||||||
\(587\) | 2.92893i | 0.120890i | 0.998172 | + | 0.0604450i | \(0.0192520\pi\) | ||||
−0.998172 | + | 0.0604450i | \(0.980748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.65685 | −0.397904 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.08326 | 0.332501 | ||||||||
\(592\) | 3.65685i | 0.150296i | ||||||||
\(593\) | − 28.7279i | − 1.17971i | −0.807508 | − | 0.589857i | \(-0.799184\pi\) | ||||
0.807508 | − | 0.589857i | \(-0.200816\pi\) | |||||||
\(594\) | −16.0000 | −0.656488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | − 0.284271i | − 0.0116344i | ||||||||
\(598\) | − 5.65685i | − 0.231326i | ||||||||
\(599\) | 5.17157 | 0.211305 | 0.105652 | − | 0.994403i | \(-0.466307\pi\) | ||||
0.105652 | + | 0.994403i | \(0.466307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.41421 | 0.384014 | 0.192007 | − | 0.981394i | \(-0.438500\pi\) | ||||
0.192007 | + | 0.981394i | \(0.438500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 25.6569i | − 1.04483i | ||||||||
\(604\) | −11.3137 | −0.460348 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.45584 | 0.221629 | ||||||||
\(607\) | − 40.2843i | − 1.63509i | −0.575866 | − | 0.817544i | \(-0.695335\pi\) | ||||
0.575866 | − | 0.817544i | \(-0.304665\pi\) | |||||||
\(608\) | 3.41421i | 0.138465i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.97056 | 0.362910 | ||||||||
\(612\) | − 14.3848i | − 0.581470i | ||||||||
\(613\) | 23.6569i | 0.955491i | 0.878498 | + | 0.477746i | \(0.158546\pi\) | ||||
−0.878498 | + | 0.477746i | \(0.841454\pi\) | |||||||
\(614\) | 29.0711 | 1.17321 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 10.6863i | − 0.430214i | −0.976590 | − | 0.215107i | \(-0.930990\pi\) | ||||
0.976590 | − | 0.215107i | \(-0.0690100\pi\) | |||||||
\(618\) | − 5.37258i | − 0.216117i | ||||||||
\(619\) | −14.9289 | −0.600044 | −0.300022 | − | 0.953932i | \(-0.596994\pi\) | ||||
−0.300022 | + | 0.953932i | \(0.596994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.6274 | 0.908007 | ||||||||
\(622\) | − 4.00000i | − 0.160385i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.485281 | −0.0194268 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.3848 | 0.894676 | ||||||||
\(627\) | 9.65685i | 0.385658i | ||||||||
\(628\) | 10.4853i | 0.418408i | ||||||||
\(629\) | −19.7990 | −0.789437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.48528 | 0.178556 | 0.0892781 | − | 0.996007i | \(-0.471544\pi\) | ||||
0.0892781 | + | 0.996007i | \(0.471544\pi\) | |||||||
\(632\) | 1.17157i | 0.0466027i | ||||||||
\(633\) | 15.5980i | 0.619964i | ||||||||
\(634\) | −6.48528 | −0.257563 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.14214 | −0.243552 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.00000i | 0.158362i | ||||||||
\(639\) | 33.1716 | 1.31225 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.6274 | 0.814734 | 0.407367 | − | 0.913265i | \(-0.366447\pi\) | ||||
0.407367 | + | 0.913265i | \(0.366447\pi\) | |||||||
\(642\) | 0.970563i | 0.0383051i | ||||||||
\(643\) | − 47.2132i | − 1.86191i | −0.365138 | − | 0.930953i | \(-0.618978\pi\) | ||||
0.365138 | − | 0.930953i | \(-0.381022\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.4853 | −0.727294 | ||||||||
\(647\) | 39.1127i | 1.53768i | 0.639442 | + | 0.768839i | \(0.279165\pi\) | ||||
−0.639442 | + | 0.768839i | \(0.720835\pi\) | |||||||
\(648\) | 6.02944i | 0.236859i | ||||||||
\(649\) | −55.1127 | −2.16336 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.14214i | 0.318871i | ||||||||
\(653\) | − 15.6569i | − 0.612700i | −0.951919 | − | 0.306350i | \(-0.900892\pi\) | ||||
0.951919 | − | 0.306350i | \(-0.0991078\pi\) | |||||||
\(654\) | −8.48528 | −0.331801 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.0711 | 0.432253 | ||||||||
\(657\) | 17.4975i | 0.682642i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.8284 | 1.27881 | 0.639407 | − | 0.768868i | \(-0.279180\pi\) | ||||
0.639407 | + | 0.768868i | \(0.279180\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.2843 | 0.711176 | 0.355588 | − | 0.934643i | \(-0.384281\pi\) | ||||
0.355588 | + | 0.934643i | \(0.384281\pi\) | |||||||
\(662\) | 5.79899i | 0.225384i | ||||||||
\(663\) | − 2.62742i | − 0.102040i | ||||||||
\(664\) | 6.24264 | 0.242261 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.71573 | 0.376477 | ||||||||
\(667\) | − 5.65685i | − 0.219034i | ||||||||
\(668\) | 23.7990i | 0.920811i | ||||||||
\(669\) | −8.97056 | −0.346822 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −64.2843 | −2.48167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.0000i | 1.85026i | 0.379646 | + | 0.925132i | \(0.376046\pi\) | ||||
−0.379646 | + | 0.925132i | \(0.623954\pi\) | |||||||
\(674\) | 6.00000 | 0.231111 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3137 | −0.473604 | ||||||||
\(677\) | − 11.4558i | − 0.440284i | −0.975468 | − | 0.220142i | \(-0.929348\pi\) | ||||
0.975468 | − | 0.220142i | \(-0.0706521\pi\) | |||||||
\(678\) | 4.28427i | 0.164536i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.71573 | 0.219027 | ||||||||
\(682\) | − 13.6569i | − 0.522948i | ||||||||
\(683\) | − 22.3431i | − 0.854937i | −0.904030 | − | 0.427468i | \(-0.859406\pi\) | ||||
0.904030 | − | 0.427468i | \(-0.140594\pi\) | |||||||
\(684\) | 9.07107 | 0.346841 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.11270i | 0.271366i | ||||||||
\(688\) | 3.17157i | 0.120915i | ||||||||
\(689\) | 8.68629 | 0.330921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.2426 | 0.389648 | 0.194824 | − | 0.980838i | \(-0.437586\pi\) | ||||
0.194824 | + | 0.980838i | \(0.437586\pi\) | |||||||
\(692\) | − 3.17157i | − 0.120565i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.82843 | −0.335123 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.485281 | −0.0183945 | ||||||||
\(697\) | 59.9411i | 2.27043i | ||||||||
\(698\) | − 14.4853i | − 0.548276i | ||||||||
\(699\) | −0.402020 | −0.0152058 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.4853 | −0.547102 | −0.273551 | − | 0.961858i | \(-0.588198\pi\) | ||||
−0.273551 | + | 0.961858i | \(0.588198\pi\) | |||||||
\(702\) | 2.74517i | 0.103610i | ||||||||
\(703\) | − 12.4853i | − 0.470891i | ||||||||
\(704\) | −4.82843 | −0.181978 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.3848 | −1.29409 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − 6.68629i | − 0.251286i | ||||||||
\(709\) | 17.1127 | 0.642681 | 0.321340 | − | 0.946964i | \(-0.395867\pi\) | ||||
0.321340 | + | 0.946964i | \(0.395867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.11270 | 0.116735 | ||||||||
\(712\) | 12.7279i | 0.476999i | ||||||||
\(713\) | 19.3137i | 0.723304i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | − 5.65685i | − 0.211259i | ||||||||
\(718\) | − 28.2843i | − 1.05556i | ||||||||
\(719\) | 9.45584 | 0.352643 | 0.176322 | − | 0.984333i | \(-0.443580\pi\) | ||||
0.176322 | + | 0.984333i | \(0.443580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.34315i | 0.273284i | ||||||||
\(723\) | 6.20101i | 0.230618i | ||||||||
\(724\) | −14.4853 | −0.538341 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.21320 | −0.267707 | ||||||||
\(727\) | − 20.4853i | − 0.759757i | −0.925036 | − | 0.379879i | \(-0.875966\pi\) | ||||
0.925036 | − | 0.379879i | \(-0.124034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.1960 | 0.377628 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.1716 | −0.635114 | ||||||||
\(732\) | − 7.79899i | − 0.288259i | ||||||||
\(733\) | − 34.0000i | − 1.25582i | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||||
0.778287 | − | 0.627909i | \(-0.216089\pi\) | |||||||
\(734\) | −8.97056 | −0.331110 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.82843 | 0.251699 | ||||||||
\(737\) | − 46.6274i | − 1.71754i | ||||||||
\(738\) | − 29.4142i | − 1.08275i | ||||||||
\(739\) | −8.82843 | −0.324759 | −0.162379 | − | 0.986728i | \(-0.551917\pi\) | ||||
−0.162379 | + | 0.986728i | \(0.551917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.65685 | 0.0608661 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 12.2010i | − 0.447612i | −0.974634 | − | 0.223806i | \(-0.928152\pi\) | ||||
0.974634 | − | 0.223806i | \(-0.0718481\pi\) | |||||||
\(744\) | 1.65685 | 0.0607432 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.5147 | 0.494809 | ||||||||
\(747\) | − 16.5858i | − 0.606842i | ||||||||
\(748\) | − 26.1421i | − 0.955851i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.6863 | −0.608891 | −0.304446 | − | 0.952530i | \(-0.598471\pi\) | ||||
−0.304446 | + | 0.952530i | \(0.598471\pi\) | |||||||
\(752\) | 10.8284i | 0.394872i | ||||||||
\(753\) | − 2.00000i | − 0.0728841i | ||||||||
\(754\) | 0.686292 | 0.0249933 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 7.65685i | − 0.278293i | −0.990272 | − | 0.139147i | \(-0.955564\pi\) | ||||
0.990272 | − | 0.139147i | \(-0.0444359\pi\) | |||||||
\(758\) | 17.5147i | 0.636163i | ||||||||
\(759\) | 19.3137 | 0.701043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.3848 | −0.521448 | −0.260724 | − | 0.965413i | \(-0.583961\pi\) | ||||
−0.260724 | + | 0.965413i | \(0.583961\pi\) | |||||||
\(762\) | 1.65685i | 0.0600215i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.1421 | 0.656359 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.5147 | 0.560570 | ||||||||
\(767\) | 9.45584i | 0.341431i | ||||||||
\(768\) | − 0.585786i | − 0.0211377i | ||||||||
\(769\) | 11.5563 | 0.416733 | 0.208366 | − | 0.978051i | \(-0.433185\pi\) | ||||
0.208366 | + | 0.978051i | \(0.433185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.79899 | 0.208846 | ||||||||
\(772\) | − 5.65685i | − 0.203595i | ||||||||
\(773\) | 2.00000i | 0.0719350i | 0.999353 | + | 0.0359675i | \(0.0114513\pi\) | ||||
−0.999353 | + | 0.0359675i | \(0.988549\pi\) | |||||||
\(774\) | 8.42641 | 0.302881 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.2426 | 0.583077 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 0.142136i | − 0.00509581i | ||||||||
\(779\) | −37.7990 | −1.35429 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.2843 | 2.15714 | ||||||||
\(782\) | 36.9706i | 1.32206i | ||||||||
\(783\) | 2.74517i | 0.0981042i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.31371 | −0.0468584 | ||||||||
\(787\) | − 26.7279i | − 0.952748i | −0.879243 | − | 0.476374i | \(-0.841951\pi\) | ||||
0.879243 | − | 0.476374i | \(-0.158049\pi\) | |||||||
\(788\) | − 13.7990i | − 0.491569i | ||||||||
\(789\) | −16.4020 | −0.583927 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.8284i | 0.455838i | ||||||||
\(793\) | 11.0294i | 0.391667i | ||||||||
\(794\) | −5.79899 | −0.205798 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.485281 | −0.0172003 | ||||||||
\(797\) | − 2.20101i | − 0.0779638i | −0.999240 | − | 0.0389819i | \(-0.987589\pi\) | ||||
0.999240 | − | 0.0389819i | \(-0.0124115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58.6274 | −2.07409 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.8162 | 1.19484 | ||||||||
\(802\) | 6.00000i | 0.211867i | ||||||||
\(803\) | 31.7990i | 1.12216i | ||||||||
\(804\) | 5.65685 | 0.199502 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.34315 | −0.0825338 | ||||||||
\(807\) | 0.887302i | 0.0312345i | ||||||||
\(808\) | − 9.31371i | − 0.327655i | ||||||||
\(809\) | −36.9706 | −1.29982 | −0.649908 | − | 0.760013i | \(-0.725193\pi\) | ||||
−0.649908 | + | 0.760013i | \(0.725193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.4142 | 1.24356 | 0.621781 | − | 0.783191i | \(-0.286410\pi\) | ||||
0.621781 | + | 0.783191i | \(0.286410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.02944i | − 0.246533i | ||||||||
\(814\) | 17.6569 | 0.618872 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.17157 | 0.111027 | ||||||||
\(817\) | − 10.8284i | − 0.378839i | ||||||||
\(818\) | − 13.4142i | − 0.469017i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.31371 | −0.185450 | −0.0927249 | − | 0.995692i | \(-0.529558\pi\) | ||||
−0.0927249 | + | 0.995692i | \(0.529558\pi\) | |||||||
\(822\) | 9.37258i | 0.326906i | ||||||||
\(823\) | 36.2843i | 1.26479i | 0.774646 | + | 0.632395i | \(0.217928\pi\) | ||||
−0.774646 | + | 0.632395i | \(0.782072\pi\) | |||||||
\(824\) | −9.17157 | −0.319507 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 50.6274i | − 1.76049i | −0.474522 | − | 0.880244i | \(-0.657379\pi\) | ||||
0.474522 | − | 0.880244i | \(-0.342621\pi\) | |||||||
\(828\) | − 18.1421i | − 0.630483i | ||||||||
\(829\) | 38.9706 | 1.35350 | 0.676752 | − | 0.736211i | \(-0.263387\pi\) | ||||
0.676752 | + | 0.736211i | \(0.263387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.7990 | 0.409302 | ||||||||
\(832\) | 0.828427i | 0.0287205i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.0588745 | 0.00203866 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.4853 | 0.570155 | ||||||||
\(837\) | − 9.37258i | − 0.323964i | ||||||||
\(838\) | 32.8701i | 1.13548i | ||||||||
\(839\) | 13.8579 | 0.478427 | 0.239213 | − | 0.970967i | \(-0.423110\pi\) | ||||
0.239213 | + | 0.970967i | \(0.423110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | 5.31371i | 0.183122i | ||||||||
\(843\) | − 4.68629i | − 0.161404i | ||||||||
\(844\) | 26.6274 | 0.916553 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 28.7696 | 0.989118 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.4853i | 0.360066i | ||||||||
\(849\) | −3.65685 | −0.125503 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.9706 | −0.855980 | ||||||||
\(852\) | 7.31371i | 0.250564i | ||||||||
\(853\) | 48.8284i | 1.67185i | 0.548841 | + | 0.835927i | \(0.315069\pi\) | ||||
−0.548841 | + | 0.835927i | \(0.684931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.65685 | 0.0566301 | ||||||||
\(857\) | − 19.0711i | − 0.651455i | −0.945464 | − | 0.325728i | \(-0.894391\pi\) | ||||
0.945464 | − | 0.325728i | \(-0.105609\pi\) | |||||||
\(858\) | 2.34315i | 0.0799937i | ||||||||
\(859\) | −35.2132 | −1.20146 | −0.600729 | − | 0.799452i | \(-0.705123\pi\) | ||||
−0.600729 | + | 0.799452i | \(0.705123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.6569i | 1.14636i | ||||||||
\(863\) | − 28.9706i | − 0.986169i | −0.869981 | − | 0.493085i | \(-0.835869\pi\) | ||||
0.869981 | − | 0.493085i | \(-0.164131\pi\) | |||||||
\(864\) | −3.31371 | −0.112735 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.4142 | −0.455834 | ||||||||
\(867\) | 7.21320i | 0.244973i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.65685 | 0.191896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | 14.4853i | 0.490534i | ||||||||
\(873\) | − 43.1543i | − 1.46055i | ||||||||
\(874\) | −23.3137 | −0.788598 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.85786 | −0.130345 | ||||||||
\(877\) | 26.2843i | 0.887557i | 0.896137 | + | 0.443778i | \(0.146362\pi\) | ||||
−0.896137 | + | 0.443778i | \(0.853638\pi\) | |||||||
\(878\) | 8.97056i | 0.302742i | ||||||||
\(879\) | 11.5147 | 0.388382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3848 | 1.15845 | 0.579226 | − | 0.815167i | \(-0.303355\pi\) | ||||
0.579226 | + | 0.815167i | \(0.303355\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.3431i | 1.02113i | 0.859840 | + | 0.510564i | \(0.170563\pi\) | ||||
−0.859840 | + | 0.510564i | \(0.829437\pi\) | |||||||
\(884\) | −4.48528 | −0.150856 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.9706 | −1.24205 | ||||||||
\(887\) | 7.11270i | 0.238821i | 0.992845 | + | 0.119411i | \(0.0381005\pi\) | ||||
−0.992845 | + | 0.119411i | \(0.961900\pi\) | |||||||
\(888\) | 2.14214i | 0.0718854i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.1127 | 0.975312 | ||||||||
\(892\) | 15.3137i | 0.512741i | ||||||||
\(893\) | − 36.9706i | − 1.23717i | ||||||||
\(894\) | −3.51472 | −0.117550 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 3.31371i | − 0.110642i | ||||||||
\(898\) | 28.6274i | 0.955309i | ||||||||
\(899\) | −2.34315 | −0.0781483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −56.7696 | −1.89127 | ||||||||
\(902\) | − 53.4558i | − 1.77988i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.31371 | 0.243250 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.62742 | −0.220181 | ||||||||
\(907\) | − 56.2843i | − 1.86889i | −0.356109 | − | 0.934444i | \(-0.615897\pi\) | ||||
0.356109 | − | 0.934444i | \(-0.384103\pi\) | |||||||
\(908\) | − 9.75736i | − 0.323809i | ||||||||
\(909\) | −24.7452 | −0.820745 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.2843 | −0.672048 | −0.336024 | − | 0.941853i | \(-0.609082\pi\) | ||||
−0.336024 | + | 0.941853i | \(0.609082\pi\) | |||||||
\(912\) | 2.00000i | 0.0662266i | ||||||||
\(913\) | − 30.1421i | − 0.997559i | ||||||||
\(914\) | 10.3431 | 0.342121 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.1421 | 0.401187 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 17.9411i | − 0.592145i | ||||||||
\(919\) | −32.4853 | −1.07159 | −0.535795 | − | 0.844348i | \(-0.679988\pi\) | ||||
−0.535795 | + | 0.844348i | \(0.679988\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.0294 | 0.561139 | ||||||||
\(922\) | 7.17157i | 0.236183i | ||||||||
\(923\) | − 10.3431i | − 0.340449i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.9706 | −0.557687 | ||||||||
\(927\) | 24.3675i | 0.800335i | ||||||||
\(928\) | 0.828427i | 0.0271945i | ||||||||
\(929\) | −25.2132 | −0.827218 | −0.413609 | − | 0.910455i | \(-0.635732\pi\) | ||||
−0.413609 | + | 0.910455i | \(0.635732\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.686292i | 0.0224802i | ||||||||
\(933\) | − 2.34315i | − 0.0767111i | ||||||||
\(934\) | 3.89949 | 0.127595 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.20101 | 0.0719423 | ||||||||
\(937\) | 11.7574i | 0.384096i | 0.981386 | + | 0.192048i | \(0.0615130\pi\) | ||||
−0.981386 | + | 0.192048i | \(0.938487\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.1127 | 0.427917 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.0000 | −1.62995 | −0.814977 | − | 0.579494i | \(-0.803250\pi\) | ||||
−0.814977 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(942\) | 6.14214i | 0.200122i | ||||||||
\(943\) | 75.5980i | 2.46181i | ||||||||
\(944\) | −11.4142 | −0.371501 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.3137 | 0.497892 | ||||||||
\(947\) | 0.828427i | 0.0269203i | 0.999909 | + | 0.0134601i | \(0.00428462\pi\) | ||||
−0.999909 | + | 0.0134601i | \(0.995715\pi\) | |||||||
\(948\) | 0.686292i | 0.0222897i | ||||||||
\(949\) | 5.45584 | 0.177104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.79899 | −0.123191 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 11.6569i | − 0.377603i | −0.982015 | − | 0.188801i | \(-0.939540\pi\) | ||||
0.982015 | − | 0.188801i | \(-0.0604602\pi\) | |||||||
\(954\) | 27.8579 | 0.901932 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.65685 | −0.312325 | ||||||||
\(957\) | 2.34315i | 0.0757431i | ||||||||
\(958\) | − 22.8284i | − 0.737553i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | − 3.02944i | − 0.0976730i | ||||||||
\(963\) | − 4.40202i | − 0.141853i | ||||||||
\(964\) | 10.5858 | 0.340945 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.4558i | 0.432711i | 0.976315 | + | 0.216355i | \(0.0694170\pi\) | ||||
−0.976315 | + | 0.216355i | \(0.930583\pi\) | |||||||
\(968\) | 12.3137i | 0.395778i | ||||||||
\(969\) | −10.8284 | −0.347859 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.3553 | 1.19879 | 0.599395 | − | 0.800453i | \(-0.295408\pi\) | ||||
0.599395 | + | 0.800453i | \(0.295408\pi\) | |||||||
\(972\) | 13.4731i | 0.432150i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.79899 | −0.249896 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.3137 | −0.426161 | ||||||||
\(977\) | − 35.3137i | − 1.12979i | −0.825164 | − | 0.564893i | \(-0.808918\pi\) | ||||
0.825164 | − | 0.564893i | \(-0.191082\pi\) | |||||||
\(978\) | 4.76955i | 0.152513i | ||||||||
\(979\) | 61.4558 | 1.96414 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.4853 | 1.22874 | ||||||||
\(982\) | 24.2843i | 0.774942i | ||||||||
\(983\) | 51.7990i | 1.65213i | 0.563574 | + | 0.826066i | \(0.309426\pi\) | ||||
−0.563574 | + | 0.826066i | \(0.690574\pi\) | |||||||
\(984\) | 6.48528 | 0.206743 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.48528 | −0.142840 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 2.82843i | − 0.0899843i | ||||||||
\(989\) | −21.6569 | −0.688648 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.7696 | −0.913895 | −0.456947 | − | 0.889494i | \(-0.651057\pi\) | ||||
−0.456947 | + | 0.889494i | \(0.651057\pi\) | |||||||
\(992\) | − 2.82843i | − 0.0898027i | ||||||||
\(993\) | 3.39697i | 0.107800i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.65685 | 0.115872 | ||||||||
\(997\) | 38.2843i | 1.21248i | 0.795284 | + | 0.606238i | \(0.207322\pi\) | ||||
−0.795284 | + | 0.606238i | \(0.792678\pi\) | |||||||
\(998\) | 41.6569i | 1.31862i | ||||||||
\(999\) | 12.1177 | 0.383389 |
(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 | 2450.2.c.t.99.2 | 4 | ||
5.2 | odd | 4 | 2450.2.a.bn.1.2 | 2 | |||
5.3 | odd | 4 | 490.2.a.m.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 2450.2.c.t.99.3 | 4 | ||
7.6 | odd | 2 | 2450.2.c.w.99.1 | 4 | |||
15.8 | even | 4 | 4410.2.a.bt.1.1 | 2 | |||
20.3 | even | 4 | 3920.2.a.bm.1.2 | 2 | |||
35.3 | even | 12 | 490.2.e.j.471.1 | 4 | |||
35.13 | even | 4 | 490.2.a.l.1.2 | ✓ | 2 | ||
35.18 | odd | 12 | 490.2.e.i.471.2 | 4 | |||
35.23 | odd | 12 | 490.2.e.i.361.2 | 4 | |||
35.27 | even | 4 | 2450.2.a.bs.1.1 | 2 | |||
35.33 | even | 12 | 490.2.e.j.361.1 | 4 | |||
35.34 | odd | 2 | 2450.2.c.w.99.4 | 4 | |||
105.83 | odd | 4 | 4410.2.a.by.1.1 | 2 | |||
140.83 | odd | 4 | 3920.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.2.a.l.1.2 | ✓ | 2 | 35.13 | even | 4 | ||
490.2.a.m.1.1 | yes | 2 | 5.3 | odd | 4 | ||
490.2.e.i.361.2 | 4 | 35.23 | odd | 12 | |||
490.2.e.i.471.2 | 4 | 35.18 | odd | 12 | |||
490.2.e.j.361.1 | 4 | 35.33 | even | 12 | |||
490.2.e.j.471.1 | 4 | 35.3 | even | 12 | |||
2450.2.a.bn.1.2 | 2 | 5.2 | odd | 4 | |||
2450.2.a.bs.1.1 | 2 | 35.27 | even | 4 | |||
2450.2.c.t.99.2 | 4 | 1.1 | even | 1 | trivial | ||
2450.2.c.t.99.3 | 4 | 5.4 | even | 2 | inner | ||
2450.2.c.w.99.1 | 4 | 7.6 | odd | 2 | |||
2450.2.c.w.99.4 | 4 | 35.34 | odd | 2 | |||
3920.2.a.bm.1.2 | 2 | 20.3 | even | 4 | |||
3920.2.a.ca.1.1 | 2 | 140.83 | odd | 4 | |||
4410.2.a.bt.1.1 | 2 | 15.8 | even | 4 | |||
4410.2.a.by.1.1 | 2 | 105.83 | odd | 4 |