Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,2,Mod(349,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, 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("1450.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.b (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: | \(11.5783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.4 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.349 |
Dual form | 1450.2.b.i.349.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.44949i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | −1.00000 | ||||||||
\(7\) | 4.44949i | 1.68175i | 0.541230 | + | 0.840875i | \(0.317959\pi\) | ||||
−0.541230 | + | 0.840875i | \(0.682041\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | − 2.44949i | − 0.707107i | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | −4.44949 | −1.18918 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 2.00000i | − 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | − 3.00000i | − 0.707107i | ||||||||
\(19\) | −6.44949 | −1.47961 | −0.739807 | − | 0.672819i | \(-0.765083\pi\) | ||||
−0.739807 | + | 0.672819i | \(0.765083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.8990 | −2.37835 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | 2.44949i | 0.510754i | 0.966842 | + | 0.255377i | \(0.0821996\pi\) | ||||
−0.966842 | + | 0.255377i | \(0.917800\pi\) | |||||||
\(24\) | 2.44949 | 0.500000 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.44949 | −0.480384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 4.44949i | − 0.840875i | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 4.89898i | 0.852803i | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | − 3.44949i | − 0.567093i | −0.958959 | − | 0.283546i | \(-0.908489\pi\) | ||||
0.958959 | − | 0.283546i | \(-0.0915110\pi\) | |||||||
\(38\) | − 6.44949i | − 1.04625i | ||||||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3485 | 1.77233 | 0.886167 | − | 0.463367i | \(-0.153359\pi\) | ||||
0.886167 | + | 0.463367i | \(0.153359\pi\) | |||||||
\(42\) | − 10.8990i | − 1.68175i | ||||||||
\(43\) | 8.89898i | 1.35708i | 0.734563 | + | 0.678541i | \(0.237387\pi\) | ||||
−0.734563 | + | 0.678541i | \(0.762613\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.44949 | −0.361158 | ||||||||
\(47\) | 5.89898i | 0.860455i | 0.902721 | + | 0.430227i | \(0.141567\pi\) | ||||
−0.902721 | + | 0.430227i | \(0.858433\pi\) | |||||||
\(48\) | 2.44949i | 0.353553i | ||||||||
\(49\) | −12.7980 | −1.82828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.89898 | 0.685994 | ||||||||
\(52\) | − 2.44949i | − 0.339683i | ||||||||
\(53\) | − 10.4495i | − 1.43535i | −0.696379 | − | 0.717674i | \(-0.745207\pi\) | ||||
0.696379 | − | 0.717674i | \(-0.254793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.44949 | 0.594588 | ||||||||
\(57\) | − 15.7980i | − 2.09249i | ||||||||
\(58\) | 1.00000i | 0.131306i | ||||||||
\(59\) | −8.55051 | −1.11318 | −0.556591 | − | 0.830787i | \(-0.687891\pi\) | ||||
−0.556591 | + | 0.830787i | \(0.687891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.44949 | 0.441662 | 0.220831 | − | 0.975312i | \(-0.429123\pi\) | ||||
0.220831 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(62\) | − 3.00000i | − 0.381000i | ||||||||
\(63\) | − 13.3485i | − 1.68175i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.89898 | −0.603023 | ||||||||
\(67\) | − 13.4495i | − 1.64312i | −0.570124 | − | 0.821558i | \(-0.693105\pi\) | ||||
0.570124 | − | 0.821558i | \(-0.306895\pi\) | |||||||
\(68\) | 2.00000i | 0.242536i | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3485 | 1.34682 | 0.673408 | − | 0.739271i | \(-0.264830\pi\) | ||||
0.673408 | + | 0.739271i | \(0.264830\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | − 13.3485i | − 1.56232i | −0.624331 | − | 0.781160i | \(-0.714628\pi\) | ||||
0.624331 | − | 0.781160i | \(-0.285372\pi\) | |||||||
\(74\) | 3.44949 | 0.400995 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.44949 | 0.739807 | ||||||||
\(77\) | 8.89898i | 1.01413i | ||||||||
\(78\) | − 6.00000i | − 0.679366i | ||||||||
\(79\) | 2.89898 | 0.326161 | 0.163080 | − | 0.986613i | \(-0.447857\pi\) | ||||
0.163080 | + | 0.986613i | \(0.447857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 11.3485i | 1.25323i | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 10.8990 | 1.18918 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.89898 | −0.959602 | ||||||||
\(87\) | 2.44949i | 0.262613i | ||||||||
\(88\) | − 2.00000i | − 0.213201i | ||||||||
\(89\) | −3.55051 | −0.376353 | −0.188177 | − | 0.982135i | \(-0.560258\pi\) | ||||
−0.188177 | + | 0.982135i | \(0.560258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8990 | −1.14252 | ||||||||
\(92\) | − 2.44949i | − 0.255377i | ||||||||
\(93\) | − 7.34847i | − 0.762001i | ||||||||
\(94\) | −5.89898 | −0.608433 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.44949 | −0.250000 | ||||||||
\(97\) | 7.34847i | 0.746124i | 0.927806 | + | 0.373062i | \(0.121692\pi\) | ||||
−0.927806 | + | 0.373062i | \(0.878308\pi\) | |||||||
\(98\) | − 12.7980i | − 1.29279i | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4495 | 1.33827 | 0.669137 | − | 0.743139i | \(-0.266664\pi\) | ||||
0.669137 | + | 0.743139i | \(0.266664\pi\) | |||||||
\(102\) | 4.89898i | 0.485071i | ||||||||
\(103\) | 2.44949i | 0.241355i | 0.992692 | + | 0.120678i | \(0.0385068\pi\) | ||||
−0.992692 | + | 0.120678i | \(0.961493\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4495 | 1.01494 | ||||||||
\(107\) | 5.24745i | 0.507290i | 0.967297 | + | 0.253645i | \(0.0816295\pi\) | ||||
−0.967297 | + | 0.253645i | \(0.918370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.34847 | 0.895421 | 0.447710 | − | 0.894179i | \(-0.352240\pi\) | ||||
0.447710 | + | 0.894179i | \(0.352240\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.44949 | 0.801990 | ||||||||
\(112\) | 4.44949i | 0.420437i | ||||||||
\(113\) | − 6.24745i | − 0.587711i | −0.955850 | − | 0.293855i | \(-0.905062\pi\) | ||||
0.955850 | − | 0.293855i | \(-0.0949384\pi\) | |||||||
\(114\) | 15.7980 | 1.47961 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | − 7.34847i | − 0.679366i | ||||||||
\(118\) | − 8.55051i | − 0.787138i | ||||||||
\(119\) | 8.89898 | 0.815768 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 3.44949i | 0.312302i | ||||||||
\(123\) | 27.7980i | 2.50646i | ||||||||
\(124\) | 3.00000 | 0.269408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.3485 | 1.18918 | ||||||||
\(127\) | 8.79796i | 0.780693i | 0.920668 | + | 0.390346i | \(0.127645\pi\) | ||||
−0.920668 | + | 0.390346i | \(0.872355\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −21.7980 | −1.91920 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.34847 | −0.642039 | −0.321019 | − | 0.947073i | \(-0.604025\pi\) | ||||
−0.321019 | + | 0.947073i | \(0.604025\pi\) | |||||||
\(132\) | − 4.89898i | − 0.426401i | ||||||||
\(133\) | − 28.6969i | − 2.48834i | ||||||||
\(134\) | 13.4495 | 1.16186 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 0.898979i | 0.0768050i | 0.999262 | + | 0.0384025i | \(0.0122269\pi\) | ||||
−0.999262 | + | 0.0384025i | \(0.987773\pi\) | |||||||
\(138\) | − 6.00000i | − 0.510754i | ||||||||
\(139\) | 11.4495 | 0.971133 | 0.485567 | − | 0.874200i | \(-0.338613\pi\) | ||||
0.485567 | + | 0.874200i | \(0.338613\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.4495 | −1.21687 | ||||||||
\(142\) | 11.3485i | 0.952342i | ||||||||
\(143\) | 4.89898i | 0.409673i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.3485 | 1.10473 | ||||||||
\(147\) | − 31.3485i | − 2.58558i | ||||||||
\(148\) | 3.44949i | 0.283546i | ||||||||
\(149\) | −15.7980 | −1.29422 | −0.647110 | − | 0.762397i | \(-0.724022\pi\) | ||||
−0.647110 | + | 0.762397i | \(0.724022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3485 | 0.923525 | 0.461763 | − | 0.887004i | \(-0.347217\pi\) | ||||
0.461763 | + | 0.887004i | \(0.347217\pi\) | |||||||
\(152\) | 6.44949i | 0.523123i | ||||||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | −8.89898 | −0.717100 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | 12.3485i | 0.985515i | 0.870167 | + | 0.492758i | \(0.164011\pi\) | ||||
−0.870167 | + | 0.492758i | \(0.835989\pi\) | |||||||
\(158\) | 2.89898i | 0.230630i | ||||||||
\(159\) | 25.5959 | 2.02989 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8990 | −0.858960 | ||||||||
\(162\) | − 9.00000i | − 0.707107i | ||||||||
\(163\) | 12.4495i | 0.975119i | 0.873090 | + | 0.487560i | \(0.162113\pi\) | ||||
−0.873090 | + | 0.487560i | \(0.837887\pi\) | |||||||
\(164\) | −11.3485 | −0.886167 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | − 17.7980i | − 1.37725i | −0.725119 | − | 0.688624i | \(-0.758215\pi\) | ||||
0.725119 | − | 0.688624i | \(-0.241785\pi\) | |||||||
\(168\) | 10.8990i | 0.840875i | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.3485 | 1.47961 | ||||||||
\(172\) | − 8.89898i | − 0.678541i | ||||||||
\(173\) | 16.0000i | 1.21646i | 0.793762 | + | 0.608229i | \(0.208120\pi\) | ||||
−0.793762 | + | 0.608229i | \(0.791880\pi\) | |||||||
\(174\) | −2.44949 | −0.185695 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | − 20.9444i | − 1.57428i | ||||||||
\(178\) | − 3.55051i | − 0.266122i | ||||||||
\(179\) | 17.2474 | 1.28913 | 0.644567 | − | 0.764547i | \(-0.277038\pi\) | ||||
0.644567 | + | 0.764547i | \(0.277038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.0454 | −1.93594 | −0.967970 | − | 0.251066i | \(-0.919219\pi\) | ||||
−0.967970 | + | 0.251066i | \(0.919219\pi\) | |||||||
\(182\) | − 10.8990i | − 0.807886i | ||||||||
\(183\) | 8.44949i | 0.624604i | ||||||||
\(184\) | 2.44949 | 0.180579 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.34847 | 0.538816 | ||||||||
\(187\) | − 4.00000i | − 0.292509i | ||||||||
\(188\) | − 5.89898i | − 0.430227i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6969 | −0.846361 | −0.423180 | − | 0.906045i | \(-0.639086\pi\) | ||||
−0.423180 | + | 0.906045i | \(0.639086\pi\) | |||||||
\(192\) | − 2.44949i | − 0.176777i | ||||||||
\(193\) | 5.34847i | 0.384991i | 0.981298 | + | 0.192496i | \(0.0616581\pi\) | ||||
−0.981298 | + | 0.192496i | \(0.938342\pi\) | |||||||
\(194\) | −7.34847 | −0.527589 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.7980 | 0.914140 | ||||||||
\(197\) | 5.10102i | 0.363433i | 0.983351 | + | 0.181716i | \(0.0581653\pi\) | ||||
−0.983351 | + | 0.181716i | \(0.941835\pi\) | |||||||
\(198\) | − 6.00000i | − 0.426401i | ||||||||
\(199\) | 0.651531 | 0.0461858 | 0.0230929 | − | 0.999733i | \(-0.492649\pi\) | ||||
0.0230929 | + | 0.999733i | \(0.492649\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.9444 | 2.32372 | ||||||||
\(202\) | 13.4495i | 0.946303i | ||||||||
\(203\) | 4.44949i | 0.312293i | ||||||||
\(204\) | −4.89898 | −0.342997 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.44949 | −0.170664 | ||||||||
\(207\) | − 7.34847i | − 0.510754i | ||||||||
\(208\) | 2.44949i | 0.169842i | ||||||||
\(209\) | −12.8990 | −0.892241 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4949 | −1.54861 | −0.774306 | − | 0.632811i | \(-0.781901\pi\) | ||||
−0.774306 | + | 0.632811i | \(0.781901\pi\) | |||||||
\(212\) | 10.4495i | 0.717674i | ||||||||
\(213\) | 27.7980i | 1.90468i | ||||||||
\(214\) | −5.24745 | −0.358708 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 13.3485i | − 0.906153i | ||||||||
\(218\) | 9.34847i | 0.633158i | ||||||||
\(219\) | 32.6969 | 2.20945 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.89898 | 0.329541 | ||||||||
\(222\) | 8.44949i | 0.567093i | ||||||||
\(223\) | − 4.00000i | − 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | −4.44949 | −0.297294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.24745 | 0.415574 | ||||||||
\(227\) | 15.2474i | 1.01201i | 0.862531 | + | 0.506004i | \(0.168878\pi\) | ||||
−0.862531 | + | 0.506004i | \(0.831122\pi\) | |||||||
\(228\) | 15.7980i | 1.04625i | ||||||||
\(229\) | 17.1010 | 1.13007 | 0.565034 | − | 0.825068i | \(-0.308863\pi\) | ||||
0.565034 | + | 0.825068i | \(0.308863\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.7980 | −1.43420 | ||||||||
\(232\) | − 1.00000i | − 0.0656532i | ||||||||
\(233\) | 11.0000i | 0.720634i | 0.932830 | + | 0.360317i | \(0.117331\pi\) | ||||
−0.932830 | + | 0.360317i | \(0.882669\pi\) | |||||||
\(234\) | 7.34847 | 0.480384 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.55051 | 0.556591 | ||||||||
\(237\) | 7.10102i | 0.461261i | ||||||||
\(238\) | 8.89898i | 0.576835i | ||||||||
\(239\) | −21.5959 | −1.39692 | −0.698462 | − | 0.715647i | \(-0.746132\pi\) | ||||
−0.698462 | + | 0.715647i | \(0.746132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0000 | 1.09507 | 0.547533 | − | 0.836784i | \(-0.315567\pi\) | ||||
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | − 7.00000i | − 0.449977i | ||||||||
\(243\) | − 22.0454i | − 1.41421i | ||||||||
\(244\) | −3.44949 | −0.220831 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −27.7980 | −1.77233 | ||||||||
\(247\) | − 15.7980i | − 1.00520i | ||||||||
\(248\) | 3.00000i | 0.190500i | ||||||||
\(249\) | −14.6969 | −0.931381 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.14643 | −0.198601 | −0.0993004 | − | 0.995058i | \(-0.531660\pi\) | ||||
−0.0993004 | + | 0.995058i | \(0.531660\pi\) | |||||||
\(252\) | 13.3485i | 0.840875i | ||||||||
\(253\) | 4.89898i | 0.307996i | ||||||||
\(254\) | −8.79796 | −0.552033 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.6969i | 1.66531i | 0.553793 | + | 0.832655i | \(0.313180\pi\) | ||||
−0.553793 | + | 0.832655i | \(0.686820\pi\) | |||||||
\(258\) | − 21.7980i | − 1.35708i | ||||||||
\(259\) | 15.3485 | 0.953707 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | − 7.34847i | − 0.453990i | ||||||||
\(263\) | 16.7980i | 1.03581i | 0.855439 | + | 0.517903i | \(0.173287\pi\) | ||||
−0.855439 | + | 0.517903i | \(0.826713\pi\) | |||||||
\(264\) | 4.89898 | 0.301511 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 28.6969 | 1.75952 | ||||||||
\(267\) | − 8.69694i | − 0.532244i | ||||||||
\(268\) | 13.4495i | 0.821558i | ||||||||
\(269\) | −24.3485 | −1.48455 | −0.742276 | − | 0.670094i | \(-0.766254\pi\) | ||||
−0.742276 | + | 0.670094i | \(0.766254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6969 | 0.953521 | 0.476761 | − | 0.879033i | \(-0.341811\pi\) | ||||
0.476761 | + | 0.879033i | \(0.341811\pi\) | |||||||
\(272\) | − 2.00000i | − 0.121268i | ||||||||
\(273\) | − 26.6969i | − 1.61577i | ||||||||
\(274\) | −0.898979 | −0.0543093 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | − 22.9444i | − 1.37859i | −0.724479 | − | 0.689297i | \(-0.757919\pi\) | ||||
0.724479 | − | 0.689297i | \(-0.242081\pi\) | |||||||
\(278\) | 11.4495i | 0.686695i | ||||||||
\(279\) | 9.00000 | 0.538816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.7980 | −1.71794 | −0.858971 | − | 0.512024i | \(-0.828896\pi\) | ||||
−0.858971 | + | 0.512024i | \(0.828896\pi\) | |||||||
\(282\) | − 14.4495i | − 0.860455i | ||||||||
\(283\) | − 24.0000i | − 1.42665i | −0.700832 | − | 0.713326i | \(-0.747188\pi\) | ||||
0.700832 | − | 0.713326i | \(-0.252812\pi\) | |||||||
\(284\) | −11.3485 | −0.673408 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.89898 | −0.289683 | ||||||||
\(287\) | 50.4949i | 2.98062i | ||||||||
\(288\) | − 3.00000i | − 0.176777i | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.0000 | −1.05518 | ||||||||
\(292\) | 13.3485i | 0.781160i | ||||||||
\(293\) | 7.44949i | 0.435204i | 0.976038 | + | 0.217602i | \(0.0698235\pi\) | ||||
−0.976038 | + | 0.217602i | \(0.930177\pi\) | |||||||
\(294\) | 31.3485 | 1.82828 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.44949 | −0.200498 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 15.7980i | − 0.915151i | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −39.5959 | −2.28227 | ||||||||
\(302\) | 11.3485i | 0.653031i | ||||||||
\(303\) | 32.9444i | 1.89261i | ||||||||
\(304\) | −6.44949 | −0.369904 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.00000 | −0.342997 | ||||||||
\(307\) | 25.3939i | 1.44931i | 0.689114 | + | 0.724653i | \(0.258000\pi\) | ||||
−0.689114 | + | 0.724653i | \(0.742000\pi\) | |||||||
\(308\) | − 8.89898i | − 0.507066i | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.5959 | −1.11118 | −0.555591 | − | 0.831456i | \(-0.687508\pi\) | ||||
−0.555591 | + | 0.831456i | \(0.687508\pi\) | |||||||
\(312\) | 6.00000i | 0.339683i | ||||||||
\(313\) | 32.5959i | 1.84243i | 0.389054 | + | 0.921215i | \(0.372802\pi\) | ||||
−0.389054 | + | 0.921215i | \(0.627198\pi\) | |||||||
\(314\) | −12.3485 | −0.696864 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.89898 | −0.163080 | ||||||||
\(317\) | 13.6515i | 0.766746i | 0.923594 | + | 0.383373i | \(0.125238\pi\) | ||||
−0.923594 | + | 0.383373i | \(0.874762\pi\) | |||||||
\(318\) | 25.5959i | 1.43535i | ||||||||
\(319\) | 2.00000 | 0.111979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8536 | −0.717416 | ||||||||
\(322\) | − 10.8990i | − 0.607376i | ||||||||
\(323\) | 12.8990i | 0.717718i | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.4495 | −0.689513 | ||||||||
\(327\) | 22.8990i | 1.26632i | ||||||||
\(328\) | − 11.3485i | − 0.626614i | ||||||||
\(329\) | −26.2474 | −1.44707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.2474 | −1.66255 | −0.831275 | − | 0.555861i | \(-0.812389\pi\) | ||||
−0.831275 | + | 0.555861i | \(0.812389\pi\) | |||||||
\(332\) | − 6.00000i | − 0.329293i | ||||||||
\(333\) | 10.3485i | 0.567093i | ||||||||
\(334\) | 17.7980 | 0.973861 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.8990 | −0.594588 | ||||||||
\(337\) | 23.7980i | 1.29636i | 0.761488 | + | 0.648179i | \(0.224469\pi\) | ||||
−0.761488 | + | 0.648179i | \(0.775531\pi\) | |||||||
\(338\) | 7.00000i | 0.380750i | ||||||||
\(339\) | 15.3031 | 0.831148 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 19.3485i | 1.04625i | ||||||||
\(343\) | − 25.7980i | − 1.39296i | ||||||||
\(344\) | 8.89898 | 0.479801 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.0000 | −0.860165 | ||||||||
\(347\) | − 25.0454i | − 1.34451i | −0.740321 | − | 0.672254i | \(-0.765326\pi\) | ||||
0.740321 | − | 0.672254i | \(-0.234674\pi\) | |||||||
\(348\) | − 2.44949i | − 0.131306i | ||||||||
\(349\) | 30.9444 | 1.65642 | 0.828208 | − | 0.560422i | \(-0.189361\pi\) | ||||
0.828208 | + | 0.560422i | \(0.189361\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000i | 0.106600i | ||||||||
\(353\) | 16.7980i | 0.894065i | 0.894518 | + | 0.447033i | \(0.147519\pi\) | ||||
−0.894518 | + | 0.447033i | \(0.852481\pi\) | |||||||
\(354\) | 20.9444 | 1.11318 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.55051 | 0.188177 | ||||||||
\(357\) | 21.7980i | 1.15367i | ||||||||
\(358\) | 17.2474i | 0.911556i | ||||||||
\(359\) | 16.5959 | 0.875899 | 0.437950 | − | 0.899000i | \(-0.355705\pi\) | ||||
0.437950 | + | 0.899000i | \(0.355705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5959 | 1.18926 | ||||||||
\(362\) | − 26.0454i | − 1.36892i | ||||||||
\(363\) | − 17.1464i | − 0.899954i | ||||||||
\(364\) | 10.8990 | 0.571262 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.44949 | −0.441662 | ||||||||
\(367\) | − 1.20204i | − 0.0627460i | −0.999508 | − | 0.0313730i | \(-0.990012\pi\) | ||||
0.999508 | − | 0.0313730i | \(-0.00998798\pi\) | |||||||
\(368\) | 2.44949i | 0.127688i | ||||||||
\(369\) | −34.0454 | −1.77233 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.4949 | 2.41389 | ||||||||
\(372\) | 7.34847i | 0.381000i | ||||||||
\(373\) | − 28.4949i | − 1.47541i | −0.675123 | − | 0.737705i | \(-0.735910\pi\) | ||||
0.675123 | − | 0.737705i | \(-0.264090\pi\) | |||||||
\(374\) | 4.00000 | 0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.89898 | 0.304217 | ||||||||
\(377\) | 2.44949i | 0.126155i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.1464 | −1.29169 | −0.645843 | − | 0.763471i | \(-0.723494\pi\) | ||||
−0.645843 | + | 0.763471i | \(0.723494\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.5505 | −1.10407 | ||||||||
\(382\) | − 11.6969i | − 0.598467i | ||||||||
\(383\) | 11.7980i | 0.602848i | 0.953490 | + | 0.301424i | \(0.0974619\pi\) | ||||
−0.953490 | + | 0.301424i | \(0.902538\pi\) | |||||||
\(384\) | 2.44949 | 0.125000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.34847 | −0.272230 | ||||||||
\(387\) | − 26.6969i | − 1.35708i | ||||||||
\(388\) | − 7.34847i | − 0.373062i | ||||||||
\(389\) | 24.3485 | 1.23452 | 0.617258 | − | 0.786761i | \(-0.288243\pi\) | ||||
0.617258 | + | 0.786761i | \(0.288243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.89898 | 0.247752 | ||||||||
\(392\) | 12.7980i | 0.646395i | ||||||||
\(393\) | − 18.0000i | − 0.907980i | ||||||||
\(394\) | −5.10102 | −0.256986 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.00000 | 0.301511 | ||||||||
\(397\) | 13.1464i | 0.659800i | 0.944016 | + | 0.329900i | \(0.107015\pi\) | ||||
−0.944016 | + | 0.329900i | \(0.892985\pi\) | |||||||
\(398\) | 0.651531i | 0.0326583i | ||||||||
\(399\) | 70.2929 | 3.51904 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.5959 | 1.92739 | 0.963694 | − | 0.267009i | \(-0.0860353\pi\) | ||||
0.963694 | + | 0.267009i | \(0.0860353\pi\) | |||||||
\(402\) | 32.9444i | 1.64312i | ||||||||
\(403\) | − 7.34847i | − 0.366053i | ||||||||
\(404\) | −13.4495 | −0.669137 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.44949 | −0.220824 | ||||||||
\(407\) | − 6.89898i | − 0.341970i | ||||||||
\(408\) | − 4.89898i | − 0.242536i | ||||||||
\(409\) | 5.79796 | 0.286691 | 0.143345 | − | 0.989673i | \(-0.454214\pi\) | ||||
0.143345 | + | 0.989673i | \(0.454214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.20204 | −0.108619 | ||||||||
\(412\) | − 2.44949i | − 0.120678i | ||||||||
\(413\) | − 38.0454i | − 1.87209i | ||||||||
\(414\) | 7.34847 | 0.361158 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.44949 | −0.120096 | ||||||||
\(417\) | 28.0454i | 1.37339i | ||||||||
\(418\) | − 12.8990i | − 0.630910i | ||||||||
\(419\) | 10.1464 | 0.495685 | 0.247843 | − | 0.968800i | \(-0.420278\pi\) | ||||
0.247843 | + | 0.968800i | \(0.420278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4495 | 0.655488 | 0.327744 | − | 0.944767i | \(-0.393712\pi\) | ||||
0.327744 | + | 0.944767i | \(0.393712\pi\) | |||||||
\(422\) | − 22.4949i | − 1.09503i | ||||||||
\(423\) | − 17.6969i | − 0.860455i | ||||||||
\(424\) | −10.4495 | −0.507472 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −27.7980 | −1.34682 | ||||||||
\(427\) | 15.3485i | 0.742764i | ||||||||
\(428\) | − 5.24745i | − 0.253645i | ||||||||
\(429\) | −12.0000 | −0.579365 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4495 | 0.888681 | 0.444340 | − | 0.895858i | \(-0.353438\pi\) | ||||
0.444340 | + | 0.895858i | \(0.353438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 30.4495i | − 1.46331i | −0.681676 | − | 0.731655i | \(-0.738748\pi\) | ||||
0.681676 | − | 0.731655i | \(-0.261252\pi\) | |||||||
\(434\) | 13.3485 | 0.640747 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.34847 | −0.447710 | ||||||||
\(437\) | − 15.7980i | − 0.755719i | ||||||||
\(438\) | 32.6969i | 1.56232i | ||||||||
\(439\) | −18.6969 | −0.892356 | −0.446178 | − | 0.894944i | \(-0.647215\pi\) | ||||
−0.446178 | + | 0.894944i | \(0.647215\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38.3939 | 1.82828 | ||||||||
\(442\) | 4.89898i | 0.233021i | ||||||||
\(443\) | 13.1010i | 0.622448i | 0.950337 | + | 0.311224i | \(0.100739\pi\) | ||||
−0.950337 | + | 0.311224i | \(0.899261\pi\) | |||||||
\(444\) | −8.44949 | −0.400995 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | − 38.6969i | − 1.83030i | ||||||||
\(448\) | − 4.44949i | − 0.210219i | ||||||||
\(449\) | −25.7980 | −1.21748 | −0.608740 | − | 0.793369i | \(-0.708325\pi\) | ||||
−0.608740 | + | 0.793369i | \(0.708325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6969 | 1.06876 | ||||||||
\(452\) | 6.24745i | 0.293855i | ||||||||
\(453\) | 27.7980i | 1.30606i | ||||||||
\(454\) | −15.2474 | −0.715598 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.7980 | −0.739807 | ||||||||
\(457\) | − 17.7980i | − 0.832553i | −0.909238 | − | 0.416277i | \(-0.863335\pi\) | ||||
0.909238 | − | 0.416277i | \(-0.136665\pi\) | |||||||
\(458\) | 17.1010i | 0.799078i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.2929 | −1.31773 | −0.658865 | − | 0.752261i | \(-0.728963\pi\) | ||||
−0.658865 | + | 0.752261i | \(0.728963\pi\) | |||||||
\(462\) | − 21.7980i | − 1.01413i | ||||||||
\(463\) | 3.10102i | 0.144117i | 0.997400 | + | 0.0720583i | \(0.0229568\pi\) | ||||
−0.997400 | + | 0.0720583i | \(0.977043\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0000 | −0.509565 | ||||||||
\(467\) | − 22.9444i | − 1.06174i | −0.847453 | − | 0.530870i | \(-0.821865\pi\) | ||||
0.847453 | − | 0.530870i | \(-0.178135\pi\) | |||||||
\(468\) | 7.34847i | 0.339683i | ||||||||
\(469\) | 59.8434 | 2.76331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.2474 | −1.39373 | ||||||||
\(472\) | 8.55051i | 0.393569i | ||||||||
\(473\) | 17.7980i | 0.818351i | ||||||||
\(474\) | −7.10102 | −0.326161 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.89898 | −0.407884 | ||||||||
\(477\) | 31.3485i | 1.43535i | ||||||||
\(478\) | − 21.5959i | − 0.987774i | ||||||||
\(479\) | 4.20204 | 0.191996 | 0.0959981 | − | 0.995382i | \(-0.469396\pi\) | ||||
0.0959981 | + | 0.995382i | \(0.469396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.44949 | 0.385264 | ||||||||
\(482\) | 17.0000i | 0.774329i | ||||||||
\(483\) | − 26.6969i | − 1.21475i | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | 1.00000 | ||||||||
\(487\) | − 9.10102i | − 0.412407i | −0.978509 | − | 0.206203i | \(-0.933889\pi\) | ||||
0.978509 | − | 0.206203i | \(-0.0661108\pi\) | |||||||
\(488\) | − 3.44949i | − 0.156151i | ||||||||
\(489\) | −30.4949 | −1.37903 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.4949 | 1.19570 | 0.597849 | − | 0.801609i | \(-0.296022\pi\) | ||||
0.597849 | + | 0.801609i | \(0.296022\pi\) | |||||||
\(492\) | − 27.7980i | − 1.25323i | ||||||||
\(493\) | − 2.00000i | − 0.0900755i | ||||||||
\(494\) | 15.7980 | 0.710784 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | −0.134704 | ||||||||
\(497\) | 50.4949i | 2.26501i | ||||||||
\(498\) | − 14.6969i | − 0.658586i | ||||||||
\(499\) | 24.3485 | 1.08999 | 0.544994 | − | 0.838440i | \(-0.316532\pi\) | ||||
0.544994 | + | 0.838440i | \(0.316532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.5959 | 1.94772 | ||||||||
\(502\) | − 3.14643i | − 0.140432i | ||||||||
\(503\) | − 4.79796i | − 0.213930i | −0.994263 | − | 0.106965i | \(-0.965887\pi\) | ||||
0.994263 | − | 0.106965i | \(-0.0341133\pi\) | |||||||
\(504\) | −13.3485 | −0.594588 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.89898 | −0.217786 | ||||||||
\(507\) | 17.1464i | 0.761500i | ||||||||
\(508\) | − 8.79796i | − 0.390346i | ||||||||
\(509\) | 17.3939 | 0.770970 | 0.385485 | − | 0.922714i | \(-0.374034\pi\) | ||||
0.385485 | + | 0.922714i | \(0.374034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.3939 | 2.62743 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.6969 | −1.17755 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.7980 | 0.959602 | ||||||||
\(517\) | 11.7980i | 0.518874i | ||||||||
\(518\) | 15.3485i | 0.674373i | ||||||||
\(519\) | −39.1918 | −1.72033 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.1010 | −0.442534 | −0.221267 | − | 0.975213i | \(-0.571019\pi\) | ||||
−0.221267 | + | 0.975213i | \(0.571019\pi\) | |||||||
\(522\) | − 3.00000i | − 0.131306i | ||||||||
\(523\) | 27.4495i | 1.20028i | 0.799894 | + | 0.600141i | \(0.204889\pi\) | ||||
−0.799894 | + | 0.600141i | \(0.795111\pi\) | |||||||
\(524\) | 7.34847 | 0.321019 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.7980 | −0.732426 | ||||||||
\(527\) | 6.00000i | 0.261364i | ||||||||
\(528\) | 4.89898i | 0.213201i | ||||||||
\(529\) | 17.0000 | 0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.6515 | 1.11318 | ||||||||
\(532\) | 28.6969i | 1.24417i | ||||||||
\(533\) | 27.7980i | 1.20406i | ||||||||
\(534\) | 8.69694 | 0.376353 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.4495 | −0.580929 | ||||||||
\(537\) | 42.2474i | 1.82311i | ||||||||
\(538\) | − 24.3485i | − 1.04974i | ||||||||
\(539\) | −25.5959 | −1.10249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0454 | −0.904813 | −0.452406 | − | 0.891812i | \(-0.649434\pi\) | ||||
−0.452406 | + | 0.891812i | \(0.649434\pi\) | |||||||
\(542\) | 15.6969i | 0.674241i | ||||||||
\(543\) | − 63.7980i | − 2.73783i | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 26.6969 | 1.14252 | ||||||||
\(547\) | − 22.0000i | − 0.940652i | −0.882493 | − | 0.470326i | \(-0.844136\pi\) | ||||
0.882493 | − | 0.470326i | \(-0.155864\pi\) | |||||||
\(548\) | − 0.898979i | − 0.0384025i | ||||||||
\(549\) | −10.3485 | −0.441662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.44949 | −0.274758 | ||||||||
\(552\) | 6.00000i | 0.255377i | ||||||||
\(553\) | 12.8990i | 0.548520i | ||||||||
\(554\) | 22.9444 | 0.974814 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4495 | −0.485567 | ||||||||
\(557\) | − 6.49490i | − 0.275198i | −0.990488 | − | 0.137599i | \(-0.956062\pi\) | ||||
0.990488 | − | 0.137599i | \(-0.0439385\pi\) | |||||||
\(558\) | 9.00000i | 0.381000i | ||||||||
\(559\) | −21.7980 | −0.921955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.79796 | 0.413670 | ||||||||
\(562\) | − 28.7980i | − 1.21477i | ||||||||
\(563\) | 21.7980i | 0.918674i | 0.888262 | + | 0.459337i | \(0.151913\pi\) | ||||
−0.888262 | + | 0.459337i | \(0.848087\pi\) | |||||||
\(564\) | 14.4495 | 0.608433 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | − 40.0454i | − 1.68175i | ||||||||
\(568\) | − 11.3485i | − 0.476171i | ||||||||
\(569\) | 8.69694 | 0.364595 | 0.182297 | − | 0.983243i | \(-0.441647\pi\) | ||||
0.182297 | + | 0.983243i | \(0.441647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.0454 | 1.04812 | 0.524059 | − | 0.851682i | \(-0.324417\pi\) | ||||
0.524059 | + | 0.851682i | \(0.324417\pi\) | |||||||
\(572\) | − 4.89898i | − 0.204837i | ||||||||
\(573\) | − 28.6515i | − 1.19693i | ||||||||
\(574\) | −50.4949 | −2.10762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | 28.9444i | 1.20497i | 0.798130 | + | 0.602485i | \(0.205823\pi\) | ||||
−0.798130 | + | 0.602485i | \(0.794177\pi\) | |||||||
\(578\) | 13.0000i | 0.540729i | ||||||||
\(579\) | −13.1010 | −0.544460 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.6969 | −1.10758 | ||||||||
\(582\) | − 18.0000i | − 0.746124i | ||||||||
\(583\) | − 20.8990i | − 0.865547i | ||||||||
\(584\) | −13.3485 | −0.552364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.44949 | −0.307736 | ||||||||
\(587\) | − 14.7526i | − 0.608903i | −0.952528 | − | 0.304451i | \(-0.901527\pi\) | ||||
0.952528 | − | 0.304451i | \(-0.0984731\pi\) | |||||||
\(588\) | 31.3485i | 1.29279i | ||||||||
\(589\) | 19.3485 | 0.797240 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4949 | −0.513971 | ||||||||
\(592\) | − 3.44949i | − 0.141773i | ||||||||
\(593\) | 18.3939i | 0.755346i | 0.925939 | + | 0.377673i | \(0.123276\pi\) | ||||
−0.925939 | + | 0.377673i | \(0.876724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.7980 | 0.647110 | ||||||||
\(597\) | 1.59592i | 0.0653166i | ||||||||
\(598\) | − 6.00000i | − 0.245358i | ||||||||
\(599\) | 12.1010 | 0.494434 | 0.247217 | − | 0.968960i | \(-0.420484\pi\) | ||||
0.247217 | + | 0.968960i | \(0.420484\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.69694 | −0.273174 | −0.136587 | − | 0.990628i | \(-0.543613\pi\) | ||||
−0.136587 | + | 0.990628i | \(0.543613\pi\) | |||||||
\(602\) | − 39.5959i | − 1.61381i | ||||||||
\(603\) | 40.3485i | 1.64312i | ||||||||
\(604\) | −11.3485 | −0.461763 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −32.9444 | −1.33827 | ||||||||
\(607\) | − 34.3939i | − 1.39600i | −0.716096 | − | 0.698002i | \(-0.754073\pi\) | ||||
0.716096 | − | 0.698002i | \(-0.245927\pi\) | |||||||
\(608\) | − 6.44949i | − 0.261561i | ||||||||
\(609\) | −10.8990 | −0.441649 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.4495 | −0.584564 | ||||||||
\(612\) | − 6.00000i | − 0.242536i | ||||||||
\(613\) | − 46.8990i | − 1.89423i | −0.320891 | − | 0.947116i | \(-0.603982\pi\) | ||||
0.320891 | − | 0.947116i | \(-0.396018\pi\) | |||||||
\(614\) | −25.3939 | −1.02481 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.89898 | 0.358550 | ||||||||
\(617\) | 14.4495i | 0.581715i | 0.956766 | + | 0.290857i | \(0.0939405\pi\) | ||||
−0.956766 | + | 0.290857i | \(0.906060\pi\) | |||||||
\(618\) | − 6.00000i | − 0.241355i | ||||||||
\(619\) | −2.89898 | −0.116520 | −0.0582599 | − | 0.998301i | \(-0.518555\pi\) | ||||
−0.0582599 | + | 0.998301i | \(0.518555\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 19.5959i | − 0.785725i | ||||||||
\(623\) | − 15.7980i | − 0.632932i | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.5959 | −1.30279 | ||||||||
\(627\) | − 31.5959i | − 1.26182i | ||||||||
\(628\) | − 12.3485i | − 0.492758i | ||||||||
\(629\) | −6.89898 | −0.275080 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | − 2.89898i | − 0.115315i | ||||||||
\(633\) | − 55.1010i | − 2.19007i | ||||||||
\(634\) | −13.6515 | −0.542172 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −25.5959 | −1.01494 | ||||||||
\(637\) | − 31.3485i | − 1.24207i | ||||||||
\(638\) | 2.00000i | 0.0791808i | ||||||||
\(639\) | −34.0454 | −1.34682 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.2474 | 0.957717 | 0.478858 | − | 0.877892i | \(-0.341051\pi\) | ||||
0.478858 | + | 0.877892i | \(0.341051\pi\) | |||||||
\(642\) | − 12.8536i | − 0.507290i | ||||||||
\(643\) | 24.8434i | 0.979727i | 0.871799 | + | 0.489863i | \(0.162953\pi\) | ||||
−0.871799 | + | 0.489863i | \(0.837047\pi\) | |||||||
\(644\) | 10.8990 | 0.429480 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.8990 | −0.507504 | ||||||||
\(647\) | 39.5959i | 1.55668i | 0.627845 | + | 0.778338i | \(0.283937\pi\) | ||||
−0.627845 | + | 0.778338i | \(0.716063\pi\) | |||||||
\(648\) | 9.00000i | 0.353553i | ||||||||
\(649\) | −17.1010 | −0.671274 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.6969 | 1.28149 | ||||||||
\(652\) | − 12.4495i | − 0.487560i | ||||||||
\(653\) | − 11.2474i | − 0.440147i | −0.975483 | − | 0.220073i | \(-0.929370\pi\) | ||||
0.975483 | − | 0.220073i | \(-0.0706297\pi\) | |||||||
\(654\) | −22.8990 | −0.895421 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.3485 | 0.443083 | ||||||||
\(657\) | 40.0454i | 1.56232i | ||||||||
\(658\) | − 26.2474i | − 1.02323i | ||||||||
\(659\) | 38.6969 | 1.50742 | 0.753709 | − | 0.657208i | \(-0.228263\pi\) | ||||
0.753709 | + | 0.657208i | \(0.228263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.75255 | 0.379330 | 0.189665 | − | 0.981849i | \(-0.439260\pi\) | ||||
0.189665 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(662\) | − 30.2474i | − 1.17560i | ||||||||
\(663\) | 12.0000i | 0.466041i | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.3485 | −0.400995 | ||||||||
\(667\) | 2.44949i | 0.0948446i | ||||||||
\(668\) | 17.7980i | 0.688624i | ||||||||
\(669\) | 9.79796 | 0.378811 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.89898 | 0.266332 | ||||||||
\(672\) | − 10.8990i | − 0.420437i | ||||||||
\(673\) | 16.7980i | 0.647514i | 0.946140 | + | 0.323757i | \(0.104946\pi\) | ||||
−0.946140 | + | 0.323757i | \(0.895054\pi\) | |||||||
\(674\) | −23.7980 | −0.916663 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | − 25.0454i | − 0.962573i | −0.876563 | − | 0.481287i | \(-0.840170\pi\) | ||||
0.876563 | − | 0.481287i | \(-0.159830\pi\) | |||||||
\(678\) | 15.3031i | 0.587711i | ||||||||
\(679\) | −32.6969 | −1.25479 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.3485 | −1.43120 | ||||||||
\(682\) | − 6.00000i | − 0.229752i | ||||||||
\(683\) | − 11.1010i | − 0.424769i | −0.977186 | − | 0.212384i | \(-0.931877\pi\) | ||||
0.977186 | − | 0.212384i | \(-0.0681229\pi\) | |||||||
\(684\) | −19.3485 | −0.739807 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.7980 | 0.984971 | ||||||||
\(687\) | 41.8888i | 1.59816i | ||||||||
\(688\) | 8.89898i | 0.339270i | ||||||||
\(689\) | 25.5959 | 0.975127 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.9444 | −1.67172 | −0.835862 | − | 0.548940i | \(-0.815031\pi\) | ||||
−0.835862 | + | 0.548940i | \(0.815031\pi\) | |||||||
\(692\) | − 16.0000i | − 0.608229i | ||||||||
\(693\) | − 26.6969i | − 1.01413i | ||||||||
\(694\) | 25.0454 | 0.950711 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.44949 | 0.0928477 | ||||||||
\(697\) | − 22.6969i | − 0.859708i | ||||||||
\(698\) | 30.9444i | 1.17126i | ||||||||
\(699\) | −26.9444 | −1.01913 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.3939 | −0.959113 | −0.479557 | − | 0.877511i | \(-0.659203\pi\) | ||||
−0.479557 | + | 0.877511i | \(0.659203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.2474i | 0.839078i | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.7980 | −0.632200 | ||||||||
\(707\) | 59.8434i | 2.25064i | ||||||||
\(708\) | 20.9444i | 0.787138i | ||||||||
\(709\) | 27.3939 | 1.02880 | 0.514399 | − | 0.857551i | \(-0.328015\pi\) | ||||
0.514399 | + | 0.857551i | \(0.328015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.69694 | −0.326161 | ||||||||
\(712\) | 3.55051i | 0.133061i | ||||||||
\(713\) | − 7.34847i | − 0.275202i | ||||||||
\(714\) | −21.7980 | −0.815768 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.2474 | −0.644567 | ||||||||
\(717\) | − 52.8990i | − 1.97555i | ||||||||
\(718\) | 16.5959i | 0.619354i | ||||||||
\(719\) | 36.7423 | 1.37026 | 0.685129 | − | 0.728422i | \(-0.259746\pi\) | ||||
0.685129 | + | 0.728422i | \(0.259746\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8990 | −0.405899 | ||||||||
\(722\) | 22.5959i | 0.840933i | ||||||||
\(723\) | 41.6413i | 1.54866i | ||||||||
\(724\) | 26.0454 | 0.967970 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.1464 | 0.636364 | ||||||||
\(727\) | − 33.5959i | − 1.24600i | −0.782220 | − | 0.623002i | \(-0.785913\pi\) | ||||
0.782220 | − | 0.623002i | \(-0.214087\pi\) | |||||||
\(728\) | 10.8990i | 0.403943i | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.7980 | 0.658281 | ||||||||
\(732\) | − 8.44949i | − 0.312302i | ||||||||
\(733\) | − 1.10102i | − 0.0406671i | −0.999793 | − | 0.0203336i | \(-0.993527\pi\) | ||||
0.999793 | − | 0.0203336i | \(-0.00647282\pi\) | |||||||
\(734\) | 1.20204 | 0.0443681 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.44949 | −0.0902894 | ||||||||
\(737\) | − 26.8990i | − 0.990837i | ||||||||
\(738\) | − 34.0454i | − 1.25323i | ||||||||
\(739\) | −10.0000 | −0.367856 | −0.183928 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183928 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.6969 | 1.42157 | ||||||||
\(742\) | 46.4949i | 1.70688i | ||||||||
\(743\) | − 12.6969i | − 0.465805i | −0.972500 | − | 0.232903i | \(-0.925178\pi\) | ||||
0.972500 | − | 0.232903i | \(-0.0748224\pi\) | |||||||
\(744\) | −7.34847 | −0.269408 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.4949 | 1.04327 | ||||||||
\(747\) | − 18.0000i | − 0.658586i | ||||||||
\(748\) | 4.00000i | 0.146254i | ||||||||
\(749\) | −23.3485 | −0.853134 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.1010 | 0.879459 | 0.439729 | − | 0.898130i | \(-0.355074\pi\) | ||||
0.439729 | + | 0.898130i | \(0.355074\pi\) | |||||||
\(752\) | 5.89898i | 0.215114i | ||||||||
\(753\) | − 7.70714i | − 0.280864i | ||||||||
\(754\) | −2.44949 | −0.0892052 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 19.3939i | − 0.704882i | −0.935834 | − | 0.352441i | \(-0.885352\pi\) | ||||
0.935834 | − | 0.352441i | \(-0.114648\pi\) | |||||||
\(758\) | − 25.1464i | − 0.913359i | ||||||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1010 | 0.511162 | 0.255581 | − | 0.966788i | \(-0.417733\pi\) | ||||
0.255581 | + | 0.966788i | \(0.417733\pi\) | |||||||
\(762\) | − 21.5505i | − 0.780693i | ||||||||
\(763\) | 41.5959i | 1.50587i | ||||||||
\(764\) | 11.6969 | 0.423180 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.7980 | −0.426278 | ||||||||
\(767\) | − 20.9444i | − 0.756258i | ||||||||
\(768\) | 2.44949i | 0.0883883i | ||||||||
\(769\) | 3.55051 | 0.128035 | 0.0640173 | − | 0.997949i | \(-0.479609\pi\) | ||||
0.0640173 | + | 0.997949i | \(0.479609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.3939 | −2.35510 | ||||||||
\(772\) | − 5.34847i | − 0.192496i | ||||||||
\(773\) | 17.4495i | 0.627615i | 0.949487 | + | 0.313807i | \(0.101605\pi\) | ||||
−0.949487 | + | 0.313807i | \(0.898395\pi\) | |||||||
\(774\) | 26.6969 | 0.959602 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.34847 | 0.263795 | ||||||||
\(777\) | 37.5959i | 1.34875i | ||||||||
\(778\) | 24.3485i | 0.872935i | ||||||||
\(779\) | −73.1918 | −2.62237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6969 | 0.812160 | ||||||||
\(782\) | 4.89898i | 0.175187i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.7980 | −0.457070 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.0000 | 0.642039 | ||||||||
\(787\) | − 40.5505i | − 1.44547i | −0.691125 | − | 0.722735i | \(-0.742885\pi\) | ||||
0.691125 | − | 0.722735i | \(-0.257115\pi\) | |||||||
\(788\) | − 5.10102i | − 0.181716i | ||||||||
\(789\) | −41.1464 | −1.46485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.7980 | 0.988382 | ||||||||
\(792\) | 6.00000i | 0.213201i | ||||||||
\(793\) | 8.44949i | 0.300050i | ||||||||
\(794\) | −13.1464 | −0.466549 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.651531 | −0.0230929 | ||||||||
\(797\) | 18.0000i | 0.637593i | 0.947823 | + | 0.318796i | \(0.103279\pi\) | ||||
−0.947823 | + | 0.318796i | \(0.896721\pi\) | |||||||
\(798\) | 70.2929i | 2.48834i | ||||||||
\(799\) | 11.7980 | 0.417382 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.6515 | 0.376353 | ||||||||
\(802\) | 38.5959i | 1.36287i | ||||||||
\(803\) | − 26.6969i | − 0.942114i | ||||||||
\(804\) | −32.9444 | −1.16186 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.34847 | 0.258839 | ||||||||
\(807\) | − 59.6413i | − 2.09947i | ||||||||
\(808\) | − 13.4495i | − 0.473151i | ||||||||
\(809\) | −31.5959 | −1.11085 | −0.555427 | − | 0.831566i | \(-0.687445\pi\) | ||||
−0.555427 | + | 0.831566i | \(0.687445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.4495 | −1.03411 | −0.517056 | − | 0.855952i | \(-0.672972\pi\) | ||||
−0.517056 | + | 0.855952i | \(0.672972\pi\) | |||||||
\(812\) | − 4.44949i | − 0.156146i | ||||||||
\(813\) | 38.4495i | 1.34848i | ||||||||
\(814\) | 6.89898 | 0.241809 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.89898 | 0.171499 | ||||||||
\(817\) | − 57.3939i | − 2.00796i | ||||||||
\(818\) | 5.79796i | 0.202721i | ||||||||
\(819\) | 32.6969 | 1.14252 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7526 | 0.689369 | 0.344684 | − | 0.938719i | \(-0.387986\pi\) | ||||
0.344684 | + | 0.938719i | \(0.387986\pi\) | |||||||
\(822\) | − 2.20204i | − 0.0768050i | ||||||||
\(823\) | 11.7980i | 0.411251i | 0.978631 | + | 0.205625i | \(0.0659229\pi\) | ||||
−0.978631 | + | 0.205625i | \(0.934077\pi\) | |||||||
\(824\) | 2.44949 | 0.0853320 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 38.0454 | 1.32377 | ||||||||
\(827\) | 19.3031i | 0.671233i | 0.941999 | + | 0.335617i | \(0.108945\pi\) | ||||
−0.941999 | + | 0.335617i | \(0.891055\pi\) | |||||||
\(828\) | 7.34847i | 0.255377i | ||||||||
\(829\) | −14.4949 | −0.503429 | −0.251714 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251714 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.2020 | 1.94963 | ||||||||
\(832\) | − 2.44949i | − 0.0849208i | ||||||||
\(833\) | 25.5959i | 0.886846i | ||||||||
\(834\) | −28.0454 | −0.971133 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.8990 | 0.446121 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.1464i | 0.350503i | ||||||||
\(839\) | 30.7980 | 1.06326 | 0.531632 | − | 0.846976i | \(-0.321579\pi\) | ||||
0.531632 | + | 0.846976i | \(0.321579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 13.4495i | 0.463500i | ||||||||
\(843\) | − 70.5403i | − 2.42954i | ||||||||
\(844\) | 22.4949 | 0.774306 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.6969 | 0.608433 | ||||||||
\(847\) | − 31.1464i | − 1.07020i | ||||||||
\(848\) | − 10.4495i | − 0.358837i | ||||||||
\(849\) | 58.7878 | 2.01759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.44949 | 0.289645 | ||||||||
\(852\) | − 27.7980i | − 0.952342i | ||||||||
\(853\) | − 8.20204i | − 0.280833i | −0.990093 | − | 0.140416i | \(-0.955156\pi\) | ||||
0.990093 | − | 0.140416i | \(-0.0448441\pi\) | |||||||
\(854\) | −15.3485 | −0.525214 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.24745 | 0.179354 | ||||||||
\(857\) | − 39.3939i | − 1.34567i | −0.739793 | − | 0.672835i | \(-0.765077\pi\) | ||||
0.739793 | − | 0.672835i | \(-0.234923\pi\) | |||||||
\(858\) | − 12.0000i | − 0.409673i | ||||||||
\(859\) | −22.8990 | −0.781303 | −0.390652 | − | 0.920539i | \(-0.627750\pi\) | ||||
−0.390652 | + | 0.920539i | \(0.627750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −123.687 | −4.21523 | ||||||||
\(862\) | 18.4495i | 0.628392i | ||||||||
\(863\) | − 11.7526i | − 0.400061i | −0.979790 | − | 0.200031i | \(-0.935896\pi\) | ||||
0.979790 | − | 0.200031i | \(-0.0641042\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.4495 | 1.03472 | ||||||||
\(867\) | 31.8434i | 1.08146i | ||||||||
\(868\) | 13.3485i | 0.453077i | ||||||||
\(869\) | 5.79796 | 0.196682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.9444 | 1.11628 | ||||||||
\(872\) | − 9.34847i | − 0.316579i | ||||||||
\(873\) | − 22.0454i | − 0.746124i | ||||||||
\(874\) | 15.7980 | 0.534374 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.6969 | −1.10473 | ||||||||
\(877\) | 8.00000i | 0.270141i | 0.990836 | + | 0.135070i | \(0.0431261\pi\) | ||||
−0.990836 | + | 0.135070i | \(0.956874\pi\) | |||||||
\(878\) | − 18.6969i | − 0.630991i | ||||||||
\(879\) | −18.2474 | −0.615471 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 38.3939i | 1.29279i | ||||||||
\(883\) | − 29.9444i | − 1.00771i | −0.863789 | − | 0.503854i | \(-0.831915\pi\) | ||||
0.863789 | − | 0.503854i | \(-0.168085\pi\) | |||||||
\(884\) | −4.89898 | −0.164771 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.1010 | −0.440137 | ||||||||
\(887\) | − 47.7980i | − 1.60490i | −0.596720 | − | 0.802449i | \(-0.703530\pi\) | ||||
0.596720 | − | 0.802449i | \(-0.296470\pi\) | |||||||
\(888\) | − 8.44949i | − 0.283546i | ||||||||
\(889\) | −39.1464 | −1.31293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | −0.603023 | ||||||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | − 38.0454i | − 1.27314i | ||||||||
\(894\) | 38.6969 | 1.29422 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.44949 | 0.148647 | ||||||||
\(897\) | − 14.6969i | − 0.490716i | ||||||||
\(898\) | − 25.7980i | − 0.860889i | ||||||||
\(899\) | −3.00000 | −0.100056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.8990 | −0.696246 | ||||||||
\(902\) | 22.6969i | 0.755725i | ||||||||
\(903\) | − 96.9898i | − 3.22762i | ||||||||
\(904\) | −6.24745 | −0.207787 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −27.7980 | −0.923525 | ||||||||
\(907\) | − 21.3485i | − 0.708864i | −0.935082 | − | 0.354432i | \(-0.884674\pi\) | ||||
0.935082 | − | 0.354432i | \(-0.115326\pi\) | |||||||
\(908\) | − 15.2474i | − 0.506004i | ||||||||
\(909\) | −40.3485 | −1.33827 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.4949 | 1.70610 | 0.853051 | − | 0.521827i | \(-0.174750\pi\) | ||||
0.853051 | + | 0.521827i | \(0.174750\pi\) | |||||||
\(912\) | − 15.7980i | − 0.523123i | ||||||||
\(913\) | 12.0000i | 0.397142i | ||||||||
\(914\) | 17.7980 | 0.588704 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.1010 | −0.565034 | ||||||||
\(917\) | − 32.6969i | − 1.07975i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8536 | 0.819844 | 0.409922 | − | 0.912121i | \(-0.365556\pi\) | ||||
0.409922 | + | 0.912121i | \(0.365556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −62.2020 | −2.04963 | ||||||||
\(922\) | − 28.2929i | − 0.931776i | ||||||||
\(923\) | 27.7980i | 0.914981i | ||||||||
\(924\) | 21.7980 | 0.717100 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.10102 | −0.101906 | ||||||||
\(927\) | − 7.34847i | − 0.241355i | ||||||||
\(928\) | 1.00000i | 0.0328266i | ||||||||
\(929\) | 39.4949 | 1.29579 | 0.647893 | − | 0.761732i | \(-0.275650\pi\) | ||||
0.647893 | + | 0.761732i | \(0.275650\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.5403 | 2.70515 | ||||||||
\(932\) | − 11.0000i | − 0.360317i | ||||||||
\(933\) | − 48.0000i | − 1.57145i | ||||||||
\(934\) | 22.9444 | 0.750763 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.34847 | −0.240192 | ||||||||
\(937\) | 53.2929i | 1.74100i | 0.492167 | + | 0.870501i | \(0.336205\pi\) | ||||
−0.492167 | + | 0.870501i | \(0.663795\pi\) | |||||||
\(938\) | 59.8434i | 1.95396i | ||||||||
\(939\) | −79.8434 | −2.60559 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.44949 | 0.275445 | 0.137723 | − | 0.990471i | \(-0.456022\pi\) | ||||
0.137723 | + | 0.990471i | \(0.456022\pi\) | |||||||
\(942\) | − 30.2474i | − 0.985515i | ||||||||
\(943\) | 27.7980i | 0.905226i | ||||||||
\(944\) | −8.55051 | −0.278295 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.7980 | −0.578662 | ||||||||
\(947\) | 37.3485i | 1.21366i | 0.794831 | + | 0.606831i | \(0.207560\pi\) | ||||
−0.794831 | + | 0.606831i | \(0.792440\pi\) | |||||||
\(948\) | − 7.10102i | − 0.230630i | ||||||||
\(949\) | 32.6969 | 1.06139 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.4393 | −1.08434 | ||||||||
\(952\) | − 8.89898i | − 0.288418i | ||||||||
\(953\) | − 34.2929i | − 1.11085i | −0.831565 | − | 0.555427i | \(-0.812555\pi\) | ||||
0.831565 | − | 0.555427i | \(-0.187445\pi\) | |||||||
\(954\) | −31.3485 | −1.01494 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21.5959 | 0.698462 | ||||||||
\(957\) | 4.89898i | 0.158362i | ||||||||
\(958\) | 4.20204i | 0.135762i | ||||||||
\(959\) | −4.00000 | −0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 8.44949i | 0.272422i | ||||||||
\(963\) | − 15.7423i | − 0.507290i | ||||||||
\(964\) | −17.0000 | −0.547533 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 26.6969 | 0.858960 | ||||||||
\(967\) | 28.0000i | 0.900419i | 0.892923 | + | 0.450210i | \(0.148651\pi\) | ||||
−0.892923 | + | 0.450210i | \(0.851349\pi\) | |||||||
\(968\) | 7.00000i | 0.224989i | ||||||||
\(969\) | −31.5959 | −1.01501 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9444 | 0.736320 | 0.368160 | − | 0.929762i | \(-0.379988\pi\) | ||||
0.368160 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(972\) | 22.0454i | 0.707107i | ||||||||
\(973\) | 50.9444i | 1.63320i | ||||||||
\(974\) | 9.10102 | 0.291616 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.44949 | 0.110415 | ||||||||
\(977\) | 0.101021i | 0.00323193i | 0.999999 | + | 0.00161597i | \(0.000514378\pi\) | ||||
−0.999999 | + | 0.00161597i | \(0.999486\pi\) | |||||||
\(978\) | − 30.4949i | − 0.975119i | ||||||||
\(979\) | −7.10102 | −0.226950 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.0454 | −0.895421 | ||||||||
\(982\) | 26.4949i | 0.845486i | ||||||||
\(983\) | − 39.0000i | − 1.24391i | −0.783054 | − | 0.621953i | \(-0.786339\pi\) | ||||
0.783054 | − | 0.621953i | \(-0.213661\pi\) | |||||||
\(984\) | 27.7980 | 0.886167 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.00000 | 0.0636930 | ||||||||
\(987\) | − 64.2929i | − 2.04646i | ||||||||
\(988\) | 15.7980i | 0.502600i | ||||||||
\(989\) | −21.7980 | −0.693135 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.50510 | −0.111343 | −0.0556716 | − | 0.998449i | \(-0.517730\pi\) | ||||
−0.0556716 | + | 0.998449i | \(0.517730\pi\) | |||||||
\(992\) | − 3.00000i | − 0.0952501i | ||||||||
\(993\) | − 74.0908i | − 2.35120i | ||||||||
\(994\) | −50.4949 | −1.60160 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.6969 | 0.465690 | ||||||||
\(997\) | 29.7423i | 0.941950i | 0.882147 | + | 0.470975i | \(0.156098\pi\) | ||||
−0.882147 | + | 0.470975i | \(0.843902\pi\) | |||||||
\(998\) | 24.3485i | 0.770737i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1450.2.b.i.349.4 | 4 | ||
5.2 | odd | 4 | 1450.2.a.j.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1450.2.a.o.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1450.2.b.i.349.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1450.2.a.j.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
1450.2.a.o.1.1 | yes | 2 | 5.3 | odd | 4 | ||
1450.2.b.i.349.1 | 4 | 5.4 | even | 2 | inner | ||
1450.2.b.i.349.4 | 4 | 1.1 | even | 1 | trivial |