Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.9176805.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 12x^{3} + 7x^{2} + 30x - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.48204\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.48204 | 1.11000 | 0.555000 | − | 0.831850i | \(-0.312718\pi\) | ||||
0.555000 | + | 0.831850i | \(0.312718\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.57766 | 0.596300 | 0.298150 | − | 0.954519i | \(-0.403630\pi\) | ||||
0.298150 | + | 0.954519i | \(0.403630\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.48204 | −0.784889 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −4.97551 | −1.37996 | −0.689979 | − | 0.723830i | \(-0.742380\pi\) | ||||
−0.689979 | + | 0.723830i | \(0.742380\pi\) | |||||||
\(14\) | −1.57766 | −0.421648 | ||||||||
\(15\) | 2.48204 | 0.640859 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.22020 | 1.75116 | 0.875578 | − | 0.483077i | \(-0.160481\pi\) | ||||
0.875578 | + | 0.483077i | \(0.160481\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.46325 | 1.25336 | 0.626678 | − | 0.779278i | \(-0.284414\pi\) | ||||
0.626678 | + | 0.779278i | \(0.284414\pi\) | |||||||
\(20\) | 2.48204 | 0.555000 | ||||||||
\(21\) | 1.57766 | 0.344274 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −1.75531 | −0.366007 | −0.183004 | − | 0.983112i | \(-0.558582\pi\) | ||||
−0.183004 | + | 0.983112i | \(0.558582\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.16050 | 0.232101 | ||||||||
\(26\) | 4.97551 | 0.975777 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.57766 | 0.298150 | ||||||||
\(29\) | 2.32153 | 0.431098 | 0.215549 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215549 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(30\) | −2.48204 | −0.453156 | ||||||||
\(31\) | −2.23734 | −0.401839 | −0.200919 | − | 0.979608i | \(-0.564393\pi\) | ||||
−0.200919 | + | 0.979608i | \(0.564393\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −7.22020 | −1.23825 | ||||||||
\(35\) | 3.91581 | 0.661893 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.65450 | 0.600796 | 0.300398 | − | 0.953814i | \(-0.402880\pi\) | ||||
0.300398 | + | 0.953814i | \(0.402880\pi\) | |||||||
\(38\) | −5.46325 | −0.886257 | ||||||||
\(39\) | −4.97551 | −0.796719 | ||||||||
\(40\) | −2.48204 | −0.392444 | ||||||||
\(41\) | −0.0841890 | −0.0131481 | −0.00657406 | − | 0.999978i | \(-0.502093\pi\) | ||||
−0.00657406 | + | 0.999978i | \(0.502093\pi\) | |||||||
\(42\) | −1.57766 | −0.243438 | ||||||||
\(43\) | 3.92316 | 0.598276 | 0.299138 | − | 0.954210i | \(-0.403301\pi\) | ||||
0.299138 | + | 0.954210i | \(0.403301\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.48204 | 0.370000 | ||||||||
\(46\) | 1.75531 | 0.258806 | ||||||||
\(47\) | −5.61805 | −0.819476 | −0.409738 | − | 0.912203i | \(-0.634380\pi\) | ||||
−0.409738 | + | 0.912203i | \(0.634380\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.51099 | −0.644427 | ||||||||
\(50\) | −1.16050 | −0.164120 | ||||||||
\(51\) | 7.22020 | 1.01103 | ||||||||
\(52\) | −4.97551 | −0.689979 | ||||||||
\(53\) | 0.738164 | 0.101395 | 0.0506973 | − | 0.998714i | \(-0.483856\pi\) | ||||
0.0506973 | + | 0.998714i | \(0.483856\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.48204 | −0.334678 | ||||||||
\(56\) | −1.57766 | −0.210824 | ||||||||
\(57\) | 5.46325 | 0.723625 | ||||||||
\(58\) | −2.32153 | −0.304832 | ||||||||
\(59\) | 6.61123 | 0.860708 | 0.430354 | − | 0.902660i | \(-0.358389\pi\) | ||||
0.430354 | + | 0.902660i | \(0.358389\pi\) | |||||||
\(60\) | 2.48204 | 0.320429 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 2.23734 | 0.284143 | ||||||||
\(63\) | 1.57766 | 0.198767 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.3494 | −1.53175 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 7.08992 | 0.866171 | 0.433086 | − | 0.901353i | \(-0.357425\pi\) | ||||
0.433086 | + | 0.901353i | \(0.357425\pi\) | |||||||
\(68\) | 7.22020 | 0.875578 | ||||||||
\(69\) | −1.75531 | −0.211314 | ||||||||
\(70\) | −3.91581 | −0.468029 | ||||||||
\(71\) | 1.20142 | 0.142582 | 0.0712909 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712909 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 12.1189 | 1.41841 | 0.709203 | − | 0.705004i | \(-0.249055\pi\) | ||||
0.709203 | + | 0.705004i | \(0.249055\pi\) | |||||||
\(74\) | −3.65450 | −0.424827 | ||||||||
\(75\) | 1.16050 | 0.134003 | ||||||||
\(76\) | 5.46325 | 0.626678 | ||||||||
\(77\) | −1.57766 | −0.179791 | ||||||||
\(78\) | 4.97551 | 0.563365 | ||||||||
\(79\) | 10.4861 | 1.17978 | 0.589891 | − | 0.807483i | \(-0.299171\pi\) | ||||
0.589891 | + | 0.807483i | \(0.299171\pi\) | |||||||
\(80\) | 2.48204 | 0.277500 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.0841890 | 0.00929712 | ||||||||
\(83\) | 0.359100 | 0.0394164 | 0.0197082 | − | 0.999806i | \(-0.493726\pi\) | ||||
0.0197082 | + | 0.999806i | \(0.493726\pi\) | |||||||
\(84\) | 1.57766 | 0.172137 | ||||||||
\(85\) | 17.9208 | 1.94378 | ||||||||
\(86\) | −3.92316 | −0.423045 | ||||||||
\(87\) | 2.32153 | 0.248894 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 4.63572 | 0.491385 | 0.245693 | − | 0.969348i | \(-0.420985\pi\) | ||||
0.245693 | + | 0.969348i | \(0.420985\pi\) | |||||||
\(90\) | −2.48204 | −0.261630 | ||||||||
\(91\) | −7.84966 | −0.822868 | ||||||||
\(92\) | −1.75531 | −0.183004 | ||||||||
\(93\) | −2.23734 | −0.232002 | ||||||||
\(94\) | 5.61805 | 0.579457 | ||||||||
\(95\) | 13.5600 | 1.39123 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.94529 | 0.603653 | 0.301826 | − | 0.953363i | \(-0.402404\pi\) | ||||
0.301826 | + | 0.953363i | \(0.402404\pi\) | |||||||
\(98\) | 4.51099 | 0.455678 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 1.16050 | 0.116050 | ||||||||
\(101\) | −12.6243 | −1.25616 | −0.628082 | − | 0.778147i | \(-0.716160\pi\) | ||||
−0.628082 | + | 0.778147i | \(0.716160\pi\) | |||||||
\(102\) | −7.22020 | −0.714906 | ||||||||
\(103\) | 10.1900 | 1.00405 | 0.502024 | − | 0.864854i | \(-0.332589\pi\) | ||||
0.502024 | + | 0.864854i | \(0.332589\pi\) | |||||||
\(104\) | 4.97551 | 0.487889 | ||||||||
\(105\) | 3.91581 | 0.382144 | ||||||||
\(106\) | −0.738164 | −0.0716968 | ||||||||
\(107\) | −1.35801 | −0.131283 | −0.0656417 | − | 0.997843i | \(-0.520909\pi\) | ||||
−0.0656417 | + | 0.997843i | \(0.520909\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 6.58337 | 0.630572 | 0.315286 | − | 0.948997i | \(-0.397899\pi\) | ||||
0.315286 | + | 0.948997i | \(0.397899\pi\) | |||||||
\(110\) | 2.48204 | 0.236653 | ||||||||
\(111\) | 3.65450 | 0.346870 | ||||||||
\(112\) | 1.57766 | 0.149075 | ||||||||
\(113\) | −4.58448 | −0.431272 | −0.215636 | − | 0.976474i | \(-0.569182\pi\) | ||||
−0.215636 | + | 0.976474i | \(0.569182\pi\) | |||||||
\(114\) | −5.46325 | −0.511680 | ||||||||
\(115\) | −4.35674 | −0.406268 | ||||||||
\(116\) | 2.32153 | 0.215549 | ||||||||
\(117\) | −4.97551 | −0.459986 | ||||||||
\(118\) | −6.61123 | −0.608613 | ||||||||
\(119\) | 11.3910 | 1.04421 | ||||||||
\(120\) | −2.48204 | −0.226578 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | −0.0841890 | −0.00759107 | ||||||||
\(124\) | −2.23734 | −0.200919 | ||||||||
\(125\) | −9.52977 | −0.852369 | ||||||||
\(126\) | −1.57766 | −0.140549 | ||||||||
\(127\) | −6.83090 | −0.606144 | −0.303072 | − | 0.952968i | \(-0.598012\pi\) | ||||
−0.303072 | + | 0.952968i | \(0.598012\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.92316 | 0.345415 | ||||||||
\(130\) | 12.3494 | 1.08311 | ||||||||
\(131\) | 6.39323 | 0.558579 | 0.279290 | − | 0.960207i | \(-0.409901\pi\) | ||||
0.279290 | + | 0.960207i | \(0.409901\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 8.61916 | 0.747376 | ||||||||
\(134\) | −7.08992 | −0.612475 | ||||||||
\(135\) | 2.48204 | 0.213620 | ||||||||
\(136\) | −7.22020 | −0.619127 | ||||||||
\(137\) | −2.37624 | −0.203016 | −0.101508 | − | 0.994835i | \(-0.532367\pi\) | ||||
−0.101508 | + | 0.994835i | \(0.532367\pi\) | |||||||
\(138\) | 1.75531 | 0.149422 | ||||||||
\(139\) | 6.12294 | 0.519341 | 0.259670 | − | 0.965697i | \(-0.416386\pi\) | ||||
0.259670 | + | 0.965697i | \(0.416386\pi\) | |||||||
\(140\) | 3.91581 | 0.330946 | ||||||||
\(141\) | −5.61805 | −0.473125 | ||||||||
\(142\) | −1.20142 | −0.100821 | ||||||||
\(143\) | 4.97551 | 0.416073 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.76213 | 0.478519 | ||||||||
\(146\) | −12.1189 | −1.00296 | ||||||||
\(147\) | −4.51099 | −0.372060 | ||||||||
\(148\) | 3.65450 | 0.300398 | ||||||||
\(149\) | 14.0581 | 1.15168 | 0.575841 | − | 0.817562i | \(-0.304675\pi\) | ||||
0.575841 | + | 0.817562i | \(0.304675\pi\) | |||||||
\(150\) | −1.16050 | −0.0947547 | ||||||||
\(151\) | −10.2538 | −0.834440 | −0.417220 | − | 0.908806i | \(-0.636995\pi\) | ||||
−0.417220 | + | 0.908806i | \(0.636995\pi\) | |||||||
\(152\) | −5.46325 | −0.443128 | ||||||||
\(153\) | 7.22020 | 0.583719 | ||||||||
\(154\) | 1.57766 | 0.127132 | ||||||||
\(155\) | −5.55317 | −0.446041 | ||||||||
\(156\) | −4.97551 | −0.398359 | ||||||||
\(157\) | −8.82517 | −0.704325 | −0.352163 | − | 0.935939i | \(-0.614554\pi\) | ||||
−0.352163 | + | 0.935939i | \(0.614554\pi\) | |||||||
\(158\) | −10.4861 | −0.834231 | ||||||||
\(159\) | 0.738164 | 0.0585402 | ||||||||
\(160\) | −2.48204 | −0.196222 | ||||||||
\(161\) | −2.76928 | −0.218250 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.7260 | −0.918452 | −0.459226 | − | 0.888320i | \(-0.651873\pi\) | ||||
−0.459226 | + | 0.888320i | \(0.651873\pi\) | |||||||
\(164\) | −0.0841890 | −0.00657406 | ||||||||
\(165\) | −2.48204 | −0.193226 | ||||||||
\(166\) | −0.359100 | −0.0278716 | ||||||||
\(167\) | 3.73191 | 0.288784 | 0.144392 | − | 0.989521i | \(-0.453877\pi\) | ||||
0.144392 | + | 0.989521i | \(0.453877\pi\) | |||||||
\(168\) | −1.57766 | −0.121719 | ||||||||
\(169\) | 11.7557 | 0.904283 | ||||||||
\(170\) | −17.9208 | −1.37446 | ||||||||
\(171\) | 5.46325 | 0.417785 | ||||||||
\(172\) | 3.92316 | 0.299138 | ||||||||
\(173\) | −15.7364 | −1.19641 | −0.598207 | − | 0.801342i | \(-0.704120\pi\) | ||||
−0.598207 | + | 0.801342i | \(0.704120\pi\) | |||||||
\(174\) | −2.32153 | −0.175995 | ||||||||
\(175\) | 1.83088 | 0.138402 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 6.61123 | 0.496930 | ||||||||
\(178\) | −4.63572 | −0.347462 | ||||||||
\(179\) | −13.1480 | −0.982726 | −0.491363 | − | 0.870955i | \(-0.663501\pi\) | ||||
−0.491363 | + | 0.870955i | \(0.663501\pi\) | |||||||
\(180\) | 2.48204 | 0.185000 | ||||||||
\(181\) | −23.7767 | −1.76731 | −0.883655 | − | 0.468139i | \(-0.844925\pi\) | ||||
−0.883655 | + | 0.468139i | \(0.844925\pi\) | |||||||
\(182\) | 7.84966 | 0.581856 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 1.75531 | 0.129403 | ||||||||
\(185\) | 9.07061 | 0.666884 | ||||||||
\(186\) | 2.23734 | 0.164050 | ||||||||
\(187\) | −7.22020 | −0.527993 | ||||||||
\(188\) | −5.61805 | −0.409738 | ||||||||
\(189\) | 1.57766 | 0.114758 | ||||||||
\(190\) | −13.5600 | −0.983745 | ||||||||
\(191\) | −22.9311 | −1.65924 | −0.829619 | − | 0.558329i | \(-0.811443\pi\) | ||||
−0.829619 | + | 0.558329i | \(0.811443\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 15.2772 | 1.09967 | 0.549837 | − | 0.835272i | \(-0.314690\pi\) | ||||
0.549837 | + | 0.835272i | \(0.314690\pi\) | |||||||
\(194\) | −5.94529 | −0.426847 | ||||||||
\(195\) | −12.3494 | −0.884358 | ||||||||
\(196\) | −4.51099 | −0.322213 | ||||||||
\(197\) | −9.38641 | −0.668754 | −0.334377 | − | 0.942439i | \(-0.608526\pi\) | ||||
−0.334377 | + | 0.942439i | \(0.608526\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 11.3483 | 0.804461 | 0.402230 | − | 0.915538i | \(-0.368235\pi\) | ||||
0.402230 | + | 0.915538i | \(0.368235\pi\) | |||||||
\(200\) | −1.16050 | −0.0820600 | ||||||||
\(201\) | 7.08992 | 0.500084 | ||||||||
\(202\) | 12.6243 | 0.888243 | ||||||||
\(203\) | 3.66259 | 0.257064 | ||||||||
\(204\) | 7.22020 | 0.505515 | ||||||||
\(205\) | −0.208960 | −0.0145944 | ||||||||
\(206\) | −10.1900 | −0.709970 | ||||||||
\(207\) | −1.75531 | −0.122002 | ||||||||
\(208\) | −4.97551 | −0.344989 | ||||||||
\(209\) | −5.46325 | −0.377901 | ||||||||
\(210\) | −3.91581 | −0.270217 | ||||||||
\(211\) | 19.7222 | 1.35773 | 0.678866 | − | 0.734262i | \(-0.262472\pi\) | ||||
0.678866 | + | 0.734262i | \(0.262472\pi\) | |||||||
\(212\) | 0.738164 | 0.0506973 | ||||||||
\(213\) | 1.20142 | 0.0823197 | ||||||||
\(214\) | 1.35801 | 0.0928314 | ||||||||
\(215\) | 9.73742 | 0.664087 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.52977 | −0.239616 | ||||||||
\(218\) | −6.58337 | −0.445882 | ||||||||
\(219\) | 12.1189 | 0.818917 | ||||||||
\(220\) | −2.48204 | −0.167339 | ||||||||
\(221\) | −35.9242 | −2.41652 | ||||||||
\(222\) | −3.65450 | −0.245274 | ||||||||
\(223\) | −12.0039 | −0.803843 | −0.401921 | − | 0.915674i | \(-0.631657\pi\) | ||||
−0.401921 | + | 0.915674i | \(0.631657\pi\) | |||||||
\(224\) | −1.57766 | −0.105412 | ||||||||
\(225\) | 1.16050 | 0.0773669 | ||||||||
\(226\) | 4.58448 | 0.304955 | ||||||||
\(227\) | 3.72526 | 0.247254 | 0.123627 | − | 0.992329i | \(-0.460547\pi\) | ||||
0.123627 | + | 0.992329i | \(0.460547\pi\) | |||||||
\(228\) | 5.46325 | 0.361813 | ||||||||
\(229\) | 23.6720 | 1.56429 | 0.782146 | − | 0.623095i | \(-0.214125\pi\) | ||||
0.782146 | + | 0.623095i | \(0.214125\pi\) | |||||||
\(230\) | 4.35674 | 0.287275 | ||||||||
\(231\) | −1.57766 | −0.103802 | ||||||||
\(232\) | −2.32153 | −0.152416 | ||||||||
\(233\) | −10.8622 | −0.711607 | −0.355804 | − | 0.934561i | \(-0.615793\pi\) | ||||
−0.355804 | + | 0.934561i | \(0.615793\pi\) | |||||||
\(234\) | 4.97551 | 0.325259 | ||||||||
\(235\) | −13.9442 | −0.909619 | ||||||||
\(236\) | 6.61123 | 0.430354 | ||||||||
\(237\) | 10.4861 | 0.681147 | ||||||||
\(238\) | −11.3910 | −0.738371 | ||||||||
\(239\) | 1.82533 | 0.118071 | 0.0590353 | − | 0.998256i | \(-0.481198\pi\) | ||||
0.0590353 | + | 0.998256i | \(0.481198\pi\) | |||||||
\(240\) | 2.48204 | 0.160215 | ||||||||
\(241\) | 17.4546 | 1.12435 | 0.562176 | − | 0.827018i | \(-0.309964\pi\) | ||||
0.562176 | + | 0.827018i | \(0.309964\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −11.1964 | −0.715314 | ||||||||
\(246\) | 0.0841890 | 0.00536769 | ||||||||
\(247\) | −27.1825 | −1.72958 | ||||||||
\(248\) | 2.23734 | 0.142071 | ||||||||
\(249\) | 0.359100 | 0.0227571 | ||||||||
\(250\) | 9.52977 | 0.602716 | ||||||||
\(251\) | 20.2679 | 1.27930 | 0.639650 | − | 0.768666i | \(-0.279079\pi\) | ||||
0.639650 | + | 0.768666i | \(0.279079\pi\) | |||||||
\(252\) | 1.57766 | 0.0993833 | ||||||||
\(253\) | 1.75531 | 0.110355 | ||||||||
\(254\) | 6.83090 | 0.428609 | ||||||||
\(255\) | 17.9208 | 1.12224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.60217 | 0.474210 | 0.237105 | − | 0.971484i | \(-0.423801\pi\) | ||||
0.237105 | + | 0.971484i | \(0.423801\pi\) | |||||||
\(258\) | −3.92316 | −0.244245 | ||||||||
\(259\) | 5.76556 | 0.358255 | ||||||||
\(260\) | −12.3494 | −0.765877 | ||||||||
\(261\) | 2.32153 | 0.143699 | ||||||||
\(262\) | −6.39323 | −0.394975 | ||||||||
\(263\) | 4.33404 | 0.267248 | 0.133624 | − | 0.991032i | \(-0.457338\pi\) | ||||
0.133624 | + | 0.991032i | \(0.457338\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 1.83215 | 0.112548 | ||||||||
\(266\) | −8.61916 | −0.528475 | ||||||||
\(267\) | 4.63572 | 0.283701 | ||||||||
\(268\) | 7.08992 | 0.433086 | ||||||||
\(269\) | −11.4364 | −0.697289 | −0.348645 | − | 0.937255i | \(-0.613358\pi\) | ||||
−0.348645 | + | 0.937255i | \(0.613358\pi\) | |||||||
\(270\) | −2.48204 | −0.151052 | ||||||||
\(271\) | 6.09101 | 0.370002 | 0.185001 | − | 0.982738i | \(-0.440771\pi\) | ||||
0.185001 | + | 0.982738i | \(0.440771\pi\) | |||||||
\(272\) | 7.22020 | 0.437789 | ||||||||
\(273\) | −7.84966 | −0.475083 | ||||||||
\(274\) | 2.37624 | 0.143554 | ||||||||
\(275\) | −1.16050 | −0.0699810 | ||||||||
\(276\) | −1.75531 | −0.105657 | ||||||||
\(277\) | 9.24397 | 0.555416 | 0.277708 | − | 0.960665i | \(-0.410425\pi\) | ||||
0.277708 | + | 0.960665i | \(0.410425\pi\) | |||||||
\(278\) | −6.12294 | −0.367229 | ||||||||
\(279\) | −2.23734 | −0.133946 | ||||||||
\(280\) | −3.91581 | −0.234014 | ||||||||
\(281\) | 4.42234 | 0.263815 | 0.131907 | − | 0.991262i | \(-0.457890\pi\) | ||||
0.131907 | + | 0.991262i | \(0.457890\pi\) | |||||||
\(282\) | 5.61805 | 0.334550 | ||||||||
\(283\) | −12.6077 | −0.749449 | −0.374725 | − | 0.927136i | \(-0.622263\pi\) | ||||
−0.374725 | + | 0.927136i | \(0.622263\pi\) | |||||||
\(284\) | 1.20142 | 0.0712909 | ||||||||
\(285\) | 13.5600 | 0.803224 | ||||||||
\(286\) | −4.97551 | −0.294208 | ||||||||
\(287\) | −0.132822 | −0.00784022 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 35.1313 | 2.06655 | ||||||||
\(290\) | −5.76213 | −0.338364 | ||||||||
\(291\) | 5.94529 | 0.348519 | ||||||||
\(292\) | 12.1189 | 0.709203 | ||||||||
\(293\) | 5.90312 | 0.344864 | 0.172432 | − | 0.985021i | \(-0.444837\pi\) | ||||
0.172432 | + | 0.985021i | \(0.444837\pi\) | |||||||
\(294\) | 4.51099 | 0.263086 | ||||||||
\(295\) | 16.4093 | 0.955386 | ||||||||
\(296\) | −3.65450 | −0.212414 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −14.0581 | −0.814362 | ||||||||
\(299\) | 8.73355 | 0.505074 | ||||||||
\(300\) | 1.16050 | 0.0670017 | ||||||||
\(301\) | 6.18941 | 0.356752 | ||||||||
\(302\) | 10.2538 | 0.590038 | ||||||||
\(303\) | −12.6243 | −0.725247 | ||||||||
\(304\) | 5.46325 | 0.313339 | ||||||||
\(305\) | −2.48204 | −0.142121 | ||||||||
\(306\) | −7.22020 | −0.412751 | ||||||||
\(307\) | 18.1342 | 1.03497 | 0.517487 | − | 0.855691i | \(-0.326868\pi\) | ||||
0.517487 | + | 0.855691i | \(0.326868\pi\) | |||||||
\(308\) | −1.57766 | −0.0898956 | ||||||||
\(309\) | 10.1900 | 0.579688 | ||||||||
\(310\) | 5.55317 | 0.315399 | ||||||||
\(311\) | −14.9799 | −0.849435 | −0.424717 | − | 0.905326i | \(-0.639627\pi\) | ||||
−0.424717 | + | 0.905326i | \(0.639627\pi\) | |||||||
\(312\) | 4.97551 | 0.281683 | ||||||||
\(313\) | −12.9832 | −0.733855 | −0.366928 | − | 0.930249i | \(-0.619590\pi\) | ||||
−0.366928 | + | 0.930249i | \(0.619590\pi\) | |||||||
\(314\) | 8.82517 | 0.498033 | ||||||||
\(315\) | 3.91581 | 0.220631 | ||||||||
\(316\) | 10.4861 | 0.589891 | ||||||||
\(317\) | −29.4666 | −1.65501 | −0.827505 | − | 0.561458i | \(-0.810241\pi\) | ||||
−0.827505 | + | 0.561458i | \(0.810241\pi\) | |||||||
\(318\) | −0.738164 | −0.0413942 | ||||||||
\(319\) | −2.32153 | −0.129981 | ||||||||
\(320\) | 2.48204 | 0.138750 | ||||||||
\(321\) | −1.35801 | −0.0757966 | ||||||||
\(322\) | 2.76928 | 0.154326 | ||||||||
\(323\) | 39.4458 | 2.19482 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −5.77409 | −0.320289 | ||||||||
\(326\) | 11.7260 | 0.649443 | ||||||||
\(327\) | 6.58337 | 0.364061 | ||||||||
\(328\) | 0.0841890 | 0.00464856 | ||||||||
\(329\) | −8.86337 | −0.488654 | ||||||||
\(330\) | 2.48204 | 0.136632 | ||||||||
\(331\) | −13.0564 | −0.717642 | −0.358821 | − | 0.933406i | \(-0.616821\pi\) | ||||
−0.358821 | + | 0.933406i | \(0.616821\pi\) | |||||||
\(332\) | 0.359100 | 0.0197082 | ||||||||
\(333\) | 3.65450 | 0.200265 | ||||||||
\(334\) | −3.73191 | −0.204201 | ||||||||
\(335\) | 17.5974 | 0.961450 | ||||||||
\(336\) | 1.57766 | 0.0860685 | ||||||||
\(337\) | 5.16212 | 0.281199 | 0.140599 | − | 0.990067i | \(-0.455097\pi\) | ||||
0.140599 | + | 0.990067i | \(0.455097\pi\) | |||||||
\(338\) | −11.7557 | −0.639425 | ||||||||
\(339\) | −4.58448 | −0.248995 | ||||||||
\(340\) | 17.9208 | 0.971892 | ||||||||
\(341\) | 2.23734 | 0.121159 | ||||||||
\(342\) | −5.46325 | −0.295419 | ||||||||
\(343\) | −18.1604 | −0.980571 | ||||||||
\(344\) | −3.92316 | −0.211523 | ||||||||
\(345\) | −4.35674 | −0.234559 | ||||||||
\(346\) | 15.7364 | 0.845992 | ||||||||
\(347\) | 12.2368 | 0.656905 | 0.328452 | − | 0.944521i | \(-0.393473\pi\) | ||||
0.328452 | + | 0.944521i | \(0.393473\pi\) | |||||||
\(348\) | 2.32153 | 0.124447 | ||||||||
\(349\) | −18.5418 | −0.992521 | −0.496260 | − | 0.868174i | \(-0.665294\pi\) | ||||
−0.496260 | + | 0.868174i | \(0.665294\pi\) | |||||||
\(350\) | −1.83088 | −0.0978647 | ||||||||
\(351\) | −4.97551 | −0.265573 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 1.97315 | 0.105020 | 0.0525100 | − | 0.998620i | \(-0.483278\pi\) | ||||
0.0525100 | + | 0.998620i | \(0.483278\pi\) | |||||||
\(354\) | −6.61123 | −0.351383 | ||||||||
\(355\) | 2.98196 | 0.158266 | ||||||||
\(356\) | 4.63572 | 0.245693 | ||||||||
\(357\) | 11.3910 | 0.602877 | ||||||||
\(358\) | 13.1480 | 0.694892 | ||||||||
\(359\) | −9.23490 | −0.487399 | −0.243700 | − | 0.969851i | \(-0.578361\pi\) | ||||
−0.243700 | + | 0.969851i | \(0.578361\pi\) | |||||||
\(360\) | −2.48204 | −0.130815 | ||||||||
\(361\) | 10.8471 | 0.570901 | ||||||||
\(362\) | 23.7767 | 1.24968 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −7.84966 | −0.411434 | ||||||||
\(365\) | 30.0795 | 1.57443 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | 23.3975 | 1.22134 | 0.610670 | − | 0.791885i | \(-0.290900\pi\) | ||||
0.610670 | + | 0.791885i | \(0.290900\pi\) | |||||||
\(368\) | −1.75531 | −0.0915018 | ||||||||
\(369\) | −0.0841890 | −0.00438270 | ||||||||
\(370\) | −9.07061 | −0.471558 | ||||||||
\(371\) | 1.16457 | 0.0604616 | ||||||||
\(372\) | −2.23734 | −0.116001 | ||||||||
\(373\) | 6.44001 | 0.333451 | 0.166726 | − | 0.986003i | \(-0.446681\pi\) | ||||
0.166726 | + | 0.986003i | \(0.446681\pi\) | |||||||
\(374\) | 7.22020 | 0.373348 | ||||||||
\(375\) | −9.52977 | −0.492115 | ||||||||
\(376\) | 5.61805 | 0.289729 | ||||||||
\(377\) | −11.5508 | −0.594897 | ||||||||
\(378\) | −1.57766 | −0.0811461 | ||||||||
\(379\) | 13.5104 | 0.693985 | 0.346992 | − | 0.937868i | \(-0.387203\pi\) | ||||
0.346992 | + | 0.937868i | \(0.387203\pi\) | |||||||
\(380\) | 13.5600 | 0.695613 | ||||||||
\(381\) | −6.83090 | −0.349958 | ||||||||
\(382\) | 22.9311 | 1.17326 | ||||||||
\(383\) | −16.5203 | −0.844146 | −0.422073 | − | 0.906562i | \(-0.638697\pi\) | ||||
−0.422073 | + | 0.906562i | \(0.638697\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.91581 | −0.199568 | ||||||||
\(386\) | −15.2772 | −0.777587 | ||||||||
\(387\) | 3.92316 | 0.199425 | ||||||||
\(388\) | 5.94529 | 0.301826 | ||||||||
\(389\) | −11.1952 | −0.567617 | −0.283809 | − | 0.958881i | \(-0.591598\pi\) | ||||
−0.283809 | + | 0.958881i | \(0.591598\pi\) | |||||||
\(390\) | 12.3494 | 0.625336 | ||||||||
\(391\) | −12.6737 | −0.640935 | ||||||||
\(392\) | 4.51099 | 0.227839 | ||||||||
\(393\) | 6.39323 | 0.322496 | ||||||||
\(394\) | 9.38641 | 0.472881 | ||||||||
\(395\) | 26.0269 | 1.30956 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −21.6990 | −1.08904 | −0.544520 | − | 0.838748i | \(-0.683288\pi\) | ||||
−0.544520 | + | 0.838748i | \(0.683288\pi\) | |||||||
\(398\) | −11.3483 | −0.568840 | ||||||||
\(399\) | 8.61916 | 0.431498 | ||||||||
\(400\) | 1.16050 | 0.0580251 | ||||||||
\(401\) | −18.4153 | −0.919618 | −0.459809 | − | 0.888018i | \(-0.652082\pi\) | ||||
−0.459809 | + | 0.888018i | \(0.652082\pi\) | |||||||
\(402\) | −7.08992 | −0.353613 | ||||||||
\(403\) | 11.1319 | 0.554521 | ||||||||
\(404\) | −12.6243 | −0.628082 | ||||||||
\(405\) | 2.48204 | 0.123333 | ||||||||
\(406\) | −3.66259 | −0.181771 | ||||||||
\(407\) | −3.65450 | −0.181147 | ||||||||
\(408\) | −7.22020 | −0.357453 | ||||||||
\(409\) | 4.30492 | 0.212864 | 0.106432 | − | 0.994320i | \(-0.466057\pi\) | ||||
0.106432 | + | 0.994320i | \(0.466057\pi\) | |||||||
\(410\) | 0.208960 | 0.0103198 | ||||||||
\(411\) | −2.37624 | −0.117212 | ||||||||
\(412\) | 10.1900 | 0.502024 | ||||||||
\(413\) | 10.4303 | 0.513240 | ||||||||
\(414\) | 1.75531 | 0.0862687 | ||||||||
\(415\) | 0.891300 | 0.0437522 | ||||||||
\(416\) | 4.97551 | 0.243944 | ||||||||
\(417\) | 6.12294 | 0.299841 | ||||||||
\(418\) | 5.46325 | 0.267216 | ||||||||
\(419\) | −7.35619 | −0.359373 | −0.179687 | − | 0.983724i | \(-0.557508\pi\) | ||||
−0.179687 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(420\) | 3.91581 | 0.191072 | ||||||||
\(421\) | 26.5246 | 1.29273 | 0.646365 | − | 0.763028i | \(-0.276288\pi\) | ||||
0.646365 | + | 0.763028i | \(0.276288\pi\) | |||||||
\(422\) | −19.7222 | −0.960062 | ||||||||
\(423\) | −5.61805 | −0.273159 | ||||||||
\(424\) | −0.738164 | −0.0358484 | ||||||||
\(425\) | 8.37906 | 0.406444 | ||||||||
\(426\) | −1.20142 | −0.0582088 | ||||||||
\(427\) | −1.57766 | −0.0763484 | ||||||||
\(428\) | −1.35801 | −0.0656417 | ||||||||
\(429\) | 4.97551 | 0.240220 | ||||||||
\(430\) | −9.73742 | −0.469580 | ||||||||
\(431\) | 22.2025 | 1.06946 | 0.534729 | − | 0.845024i | \(-0.320414\pi\) | ||||
0.534729 | + | 0.845024i | \(0.320414\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 16.1513 | 0.776183 | 0.388091 | − | 0.921621i | \(-0.373134\pi\) | ||||
0.388091 | + | 0.921621i | \(0.373134\pi\) | |||||||
\(434\) | 3.52977 | 0.169434 | ||||||||
\(435\) | 5.76213 | 0.276273 | ||||||||
\(436\) | 6.58337 | 0.315286 | ||||||||
\(437\) | −9.58969 | −0.458737 | ||||||||
\(438\) | −12.1189 | −0.579062 | ||||||||
\(439\) | 3.76764 | 0.179820 | 0.0899099 | − | 0.995950i | \(-0.471342\pi\) | ||||
0.0899099 | + | 0.995950i | \(0.471342\pi\) | |||||||
\(440\) | 2.48204 | 0.118326 | ||||||||
\(441\) | −4.51099 | −0.214809 | ||||||||
\(442\) | 35.9242 | 1.70874 | ||||||||
\(443\) | −28.9033 | −1.37324 | −0.686618 | − | 0.727018i | \(-0.740906\pi\) | ||||
−0.686618 | + | 0.727018i | \(0.740906\pi\) | |||||||
\(444\) | 3.65450 | 0.173435 | ||||||||
\(445\) | 11.5060 | 0.545438 | ||||||||
\(446\) | 12.0039 | 0.568403 | ||||||||
\(447\) | 14.0581 | 0.664924 | ||||||||
\(448\) | 1.57766 | 0.0745375 | ||||||||
\(449\) | −17.3249 | −0.817612 | −0.408806 | − | 0.912621i | \(-0.634055\pi\) | ||||
−0.408806 | + | 0.912621i | \(0.634055\pi\) | |||||||
\(450\) | −1.16050 | −0.0547066 | ||||||||
\(451\) | 0.0841890 | 0.00396431 | ||||||||
\(452\) | −4.58448 | −0.215636 | ||||||||
\(453\) | −10.2538 | −0.481764 | ||||||||
\(454\) | −3.72526 | −0.174835 | ||||||||
\(455\) | −19.4831 | −0.913384 | ||||||||
\(456\) | −5.46325 | −0.255840 | ||||||||
\(457\) | −27.9527 | −1.30757 | −0.653787 | − | 0.756679i | \(-0.726821\pi\) | ||||
−0.653787 | + | 0.756679i | \(0.726821\pi\) | |||||||
\(458\) | −23.6720 | −1.10612 | ||||||||
\(459\) | 7.22020 | 0.337010 | ||||||||
\(460\) | −4.35674 | −0.203134 | ||||||||
\(461\) | −19.7301 | −0.918922 | −0.459461 | − | 0.888198i | \(-0.651957\pi\) | ||||
−0.459461 | + | 0.888198i | \(0.651957\pi\) | |||||||
\(462\) | 1.57766 | 0.0733994 | ||||||||
\(463\) | −35.0083 | −1.62698 | −0.813488 | − | 0.581582i | \(-0.802434\pi\) | ||||
−0.813488 | + | 0.581582i | \(0.802434\pi\) | |||||||
\(464\) | 2.32153 | 0.107774 | ||||||||
\(465\) | −5.55317 | −0.257522 | ||||||||
\(466\) | 10.8622 | 0.503182 | ||||||||
\(467\) | 2.95172 | 0.136589 | 0.0682947 | − | 0.997665i | \(-0.478244\pi\) | ||||
0.0682947 | + | 0.997665i | \(0.478244\pi\) | |||||||
\(468\) | −4.97551 | −0.229993 | ||||||||
\(469\) | 11.1855 | 0.516498 | ||||||||
\(470\) | 13.9442 | 0.643198 | ||||||||
\(471\) | −8.82517 | −0.406642 | ||||||||
\(472\) | −6.61123 | −0.304306 | ||||||||
\(473\) | −3.92316 | −0.180387 | ||||||||
\(474\) | −10.4861 | −0.481644 | ||||||||
\(475\) | 6.34012 | 0.290905 | ||||||||
\(476\) | 11.3910 | 0.522107 | ||||||||
\(477\) | 0.738164 | 0.0337982 | ||||||||
\(478\) | −1.82533 | −0.0834886 | ||||||||
\(479\) | 13.6000 | 0.621398 | 0.310699 | − | 0.950508i | \(-0.399437\pi\) | ||||
0.310699 | + | 0.950508i | \(0.399437\pi\) | |||||||
\(480\) | −2.48204 | −0.113289 | ||||||||
\(481\) | −18.1830 | −0.829074 | ||||||||
\(482\) | −17.4546 | −0.795037 | ||||||||
\(483\) | −2.76928 | −0.126007 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 14.7564 | 0.670055 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 29.5866 | 1.34070 | 0.670348 | − | 0.742047i | \(-0.266145\pi\) | ||||
0.670348 | + | 0.742047i | \(0.266145\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | −11.7260 | −0.530268 | ||||||||
\(490\) | 11.1964 | 0.505803 | ||||||||
\(491\) | −7.69301 | −0.347180 | −0.173590 | − | 0.984818i | \(-0.555537\pi\) | ||||
−0.173590 | + | 0.984818i | \(0.555537\pi\) | |||||||
\(492\) | −0.0841890 | −0.00379553 | ||||||||
\(493\) | 16.7619 | 0.754919 | ||||||||
\(494\) | 27.1825 | 1.22300 | ||||||||
\(495\) | −2.48204 | −0.111559 | ||||||||
\(496\) | −2.23734 | −0.100460 | ||||||||
\(497\) | 1.89543 | 0.0850215 | ||||||||
\(498\) | −0.359100 | −0.0160917 | ||||||||
\(499\) | −1.53213 | −0.0685877 | −0.0342938 | − | 0.999412i | \(-0.510918\pi\) | ||||
−0.0342938 | + | 0.999412i | \(0.510918\pi\) | |||||||
\(500\) | −9.52977 | −0.426184 | ||||||||
\(501\) | 3.73191 | 0.166729 | ||||||||
\(502\) | −20.2679 | −0.904602 | ||||||||
\(503\) | 11.5692 | 0.515846 | 0.257923 | − | 0.966165i | \(-0.416962\pi\) | ||||
0.257923 | + | 0.966165i | \(0.416962\pi\) | |||||||
\(504\) | −1.57766 | −0.0702746 | ||||||||
\(505\) | −31.3340 | −1.39434 | ||||||||
\(506\) | −1.75531 | −0.0780330 | ||||||||
\(507\) | 11.7557 | 0.522088 | ||||||||
\(508\) | −6.83090 | −0.303072 | ||||||||
\(509\) | 7.65272 | 0.339201 | 0.169601 | − | 0.985513i | \(-0.445752\pi\) | ||||
0.169601 | + | 0.985513i | \(0.445752\pi\) | |||||||
\(510\) | −17.9208 | −0.793546 | ||||||||
\(511\) | 19.1195 | 0.845795 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.46325 | 0.241208 | ||||||||
\(514\) | −7.60217 | −0.335317 | ||||||||
\(515\) | 25.2919 | 1.11449 | ||||||||
\(516\) | 3.92316 | 0.172707 | ||||||||
\(517\) | 5.61805 | 0.247081 | ||||||||
\(518\) | −5.76556 | −0.253324 | ||||||||
\(519\) | −15.7364 | −0.690750 | ||||||||
\(520\) | 12.3494 | 0.541557 | ||||||||
\(521\) | −13.2638 | −0.581099 | −0.290549 | − | 0.956860i | \(-0.593838\pi\) | ||||
−0.290549 | + | 0.956860i | \(0.593838\pi\) | |||||||
\(522\) | −2.32153 | −0.101611 | ||||||||
\(523\) | 12.6709 | 0.554061 | 0.277030 | − | 0.960861i | \(-0.410650\pi\) | ||||
0.277030 | + | 0.960861i | \(0.410650\pi\) | |||||||
\(524\) | 6.39323 | 0.279290 | ||||||||
\(525\) | 1.83088 | 0.0799062 | ||||||||
\(526\) | −4.33404 | −0.188973 | ||||||||
\(527\) | −16.1541 | −0.703682 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −19.9189 | −0.866039 | ||||||||
\(530\) | −1.83215 | −0.0795835 | ||||||||
\(531\) | 6.61123 | 0.286903 | ||||||||
\(532\) | 8.61916 | 0.373688 | ||||||||
\(533\) | 0.418883 | 0.0181438 | ||||||||
\(534\) | −4.63572 | −0.200607 | ||||||||
\(535\) | −3.37062 | −0.145725 | ||||||||
\(536\) | −7.08992 | −0.306238 | ||||||||
\(537\) | −13.1480 | −0.567377 | ||||||||
\(538\) | 11.4364 | 0.493058 | ||||||||
\(539\) | 4.51099 | 0.194302 | ||||||||
\(540\) | 2.48204 | 0.106810 | ||||||||
\(541\) | −1.05233 | −0.0452432 | −0.0226216 | − | 0.999744i | \(-0.507201\pi\) | ||||
−0.0226216 | + | 0.999744i | \(0.507201\pi\) | |||||||
\(542\) | −6.09101 | −0.261631 | ||||||||
\(543\) | −23.7767 | −1.02036 | ||||||||
\(544\) | −7.22020 | −0.309564 | ||||||||
\(545\) | 16.3402 | 0.699936 | ||||||||
\(546\) | 7.84966 | 0.335935 | ||||||||
\(547\) | 27.8952 | 1.19271 | 0.596357 | − | 0.802720i | \(-0.296614\pi\) | ||||
0.596357 | + | 0.802720i | \(0.296614\pi\) | |||||||
\(548\) | −2.37624 | −0.101508 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 1.16050 | 0.0494840 | ||||||||
\(551\) | 12.6831 | 0.540319 | ||||||||
\(552\) | 1.75531 | 0.0747109 | ||||||||
\(553\) | 16.5435 | 0.703503 | ||||||||
\(554\) | −9.24397 | −0.392739 | ||||||||
\(555\) | 9.07061 | 0.385026 | ||||||||
\(556\) | 6.12294 | 0.259670 | ||||||||
\(557\) | 12.6051 | 0.534097 | 0.267049 | − | 0.963683i | \(-0.413952\pi\) | ||||
0.267049 | + | 0.963683i | \(0.413952\pi\) | |||||||
\(558\) | 2.23734 | 0.0947143 | ||||||||
\(559\) | −19.5197 | −0.825596 | ||||||||
\(560\) | 3.91581 | 0.165473 | ||||||||
\(561\) | −7.22020 | −0.304837 | ||||||||
\(562\) | −4.42234 | −0.186545 | ||||||||
\(563\) | 33.6327 | 1.41745 | 0.708724 | − | 0.705486i | \(-0.249271\pi\) | ||||
0.708724 | + | 0.705486i | \(0.249271\pi\) | |||||||
\(564\) | −5.61805 | −0.236562 | ||||||||
\(565\) | −11.3788 | −0.478712 | ||||||||
\(566\) | 12.6077 | 0.529940 | ||||||||
\(567\) | 1.57766 | 0.0662555 | ||||||||
\(568\) | −1.20142 | −0.0504103 | ||||||||
\(569\) | 0.260216 | 0.0109088 | 0.00545440 | − | 0.999985i | \(-0.498264\pi\) | ||||
0.00545440 | + | 0.999985i | \(0.498264\pi\) | |||||||
\(570\) | −13.5600 | −0.567965 | ||||||||
\(571\) | 6.25904 | 0.261933 | 0.130966 | − | 0.991387i | \(-0.458192\pi\) | ||||
0.130966 | + | 0.991387i | \(0.458192\pi\) | |||||||
\(572\) | 4.97551 | 0.208036 | ||||||||
\(573\) | −22.9311 | −0.957962 | ||||||||
\(574\) | 0.132822 | 0.00554387 | ||||||||
\(575\) | −2.03704 | −0.0849504 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −41.0482 | −1.70886 | −0.854429 | − | 0.519568i | \(-0.826093\pi\) | ||||
−0.854429 | + | 0.519568i | \(0.826093\pi\) | |||||||
\(578\) | −35.1313 | −1.46127 | ||||||||
\(579\) | 15.2772 | 0.634897 | ||||||||
\(580\) | 5.76213 | 0.239259 | ||||||||
\(581\) | 0.566539 | 0.0235040 | ||||||||
\(582\) | −5.94529 | −0.246440 | ||||||||
\(583\) | −0.738164 | −0.0305716 | ||||||||
\(584\) | −12.1189 | −0.501482 | ||||||||
\(585\) | −12.3494 | −0.510584 | ||||||||
\(586\) | −5.90312 | −0.243856 | ||||||||
\(587\) | −44.9987 | −1.85730 | −0.928649 | − | 0.370961i | \(-0.879028\pi\) | ||||
−0.928649 | + | 0.370961i | \(0.879028\pi\) | |||||||
\(588\) | −4.51099 | −0.186030 | ||||||||
\(589\) | −12.2232 | −0.503647 | ||||||||
\(590\) | −16.4093 | −0.675560 | ||||||||
\(591\) | −9.38641 | −0.386105 | ||||||||
\(592\) | 3.65450 | 0.150199 | ||||||||
\(593\) | −38.2024 | −1.56878 | −0.784391 | − | 0.620266i | \(-0.787025\pi\) | ||||
−0.784391 | + | 0.620266i | \(0.787025\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 28.2729 | 1.15908 | ||||||||
\(596\) | 14.0581 | 0.575841 | ||||||||
\(597\) | 11.3483 | 0.464456 | ||||||||
\(598\) | −8.73355 | −0.357141 | ||||||||
\(599\) | 15.2200 | 0.621874 | 0.310937 | − | 0.950431i | \(-0.399357\pi\) | ||||
0.310937 | + | 0.950431i | \(0.399357\pi\) | |||||||
\(600\) | −1.16050 | −0.0473773 | ||||||||
\(601\) | −15.8396 | −0.646112 | −0.323056 | − | 0.946380i | \(-0.604710\pi\) | ||||
−0.323056 | + | 0.946380i | \(0.604710\pi\) | |||||||
\(602\) | −6.18941 | −0.252262 | ||||||||
\(603\) | 7.08992 | 0.288724 | ||||||||
\(604\) | −10.2538 | −0.417220 | ||||||||
\(605\) | 2.48204 | 0.100909 | ||||||||
\(606\) | 12.6243 | 0.512827 | ||||||||
\(607\) | 15.1823 | 0.616229 | 0.308115 | − | 0.951349i | \(-0.400302\pi\) | ||||
0.308115 | + | 0.951349i | \(0.400302\pi\) | |||||||
\(608\) | −5.46325 | −0.221564 | ||||||||
\(609\) | 3.66259 | 0.148416 | ||||||||
\(610\) | 2.48204 | 0.100495 | ||||||||
\(611\) | 27.9526 | 1.13084 | ||||||||
\(612\) | 7.22020 | 0.291859 | ||||||||
\(613\) | 3.87932 | 0.156684 | 0.0783421 | − | 0.996927i | \(-0.475037\pi\) | ||||
0.0783421 | + | 0.996927i | \(0.475037\pi\) | |||||||
\(614\) | −18.1342 | −0.731837 | ||||||||
\(615\) | −0.208960 | −0.00842609 | ||||||||
\(616\) | 1.57766 | 0.0635658 | ||||||||
\(617\) | 19.1740 | 0.771916 | 0.385958 | − | 0.922516i | \(-0.373871\pi\) | ||||
0.385958 | + | 0.922516i | \(0.373871\pi\) | |||||||
\(618\) | −10.1900 | −0.409901 | ||||||||
\(619\) | 7.44720 | 0.299328 | 0.149664 | − | 0.988737i | \(-0.452181\pi\) | ||||
0.149664 | + | 0.988737i | \(0.452181\pi\) | |||||||
\(620\) | −5.55317 | −0.223021 | ||||||||
\(621\) | −1.75531 | −0.0704381 | ||||||||
\(622\) | 14.9799 | 0.600641 | ||||||||
\(623\) | 7.31359 | 0.293013 | ||||||||
\(624\) | −4.97551 | −0.199180 | ||||||||
\(625\) | −29.4557 | −1.17823 | ||||||||
\(626\) | 12.9832 | 0.518914 | ||||||||
\(627\) | −5.46325 | −0.218181 | ||||||||
\(628\) | −8.82517 | −0.352163 | ||||||||
\(629\) | 26.3862 | 1.05209 | ||||||||
\(630\) | −3.91581 | −0.156010 | ||||||||
\(631\) | 4.60480 | 0.183314 | 0.0916570 | − | 0.995791i | \(-0.470784\pi\) | ||||
0.0916570 | + | 0.995791i | \(0.470784\pi\) | |||||||
\(632\) | −10.4861 | −0.417116 | ||||||||
\(633\) | 19.7222 | 0.783887 | ||||||||
\(634\) | 29.4666 | 1.17027 | ||||||||
\(635\) | −16.9545 | −0.672820 | ||||||||
\(636\) | 0.738164 | 0.0292701 | ||||||||
\(637\) | 22.4444 | 0.889281 | ||||||||
\(638\) | 2.32153 | 0.0919104 | ||||||||
\(639\) | 1.20142 | 0.0475273 | ||||||||
\(640\) | −2.48204 | −0.0981111 | ||||||||
\(641\) | −3.00269 | −0.118599 | −0.0592996 | − | 0.998240i | \(-0.518887\pi\) | ||||
−0.0592996 | + | 0.998240i | \(0.518887\pi\) | |||||||
\(642\) | 1.35801 | 0.0535963 | ||||||||
\(643\) | −18.0116 | −0.710310 | −0.355155 | − | 0.934807i | \(-0.615572\pi\) | ||||
−0.355155 | + | 0.934807i | \(0.615572\pi\) | |||||||
\(644\) | −2.76928 | −0.109125 | ||||||||
\(645\) | 9.73742 | 0.383411 | ||||||||
\(646\) | −39.4458 | −1.55197 | ||||||||
\(647\) | 49.1170 | 1.93099 | 0.965493 | − | 0.260427i | \(-0.0838634\pi\) | ||||
0.965493 | + | 0.260427i | \(0.0838634\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −6.61123 | −0.259513 | ||||||||
\(650\) | 5.77409 | 0.226479 | ||||||||
\(651\) | −3.52977 | −0.138343 | ||||||||
\(652\) | −11.7260 | −0.459226 | ||||||||
\(653\) | 17.1394 | 0.670718 | 0.335359 | − | 0.942090i | \(-0.391142\pi\) | ||||
0.335359 | + | 0.942090i | \(0.391142\pi\) | |||||||
\(654\) | −6.58337 | −0.257430 | ||||||||
\(655\) | 15.8682 | 0.620023 | ||||||||
\(656\) | −0.0841890 | −0.00328703 | ||||||||
\(657\) | 12.1189 | 0.472802 | ||||||||
\(658\) | 8.86337 | 0.345530 | ||||||||
\(659\) | 2.75457 | 0.107303 | 0.0536513 | − | 0.998560i | \(-0.482914\pi\) | ||||
0.0536513 | + | 0.998560i | \(0.482914\pi\) | |||||||
\(660\) | −2.48204 | −0.0966131 | ||||||||
\(661\) | 32.8559 | 1.27795 | 0.638973 | − | 0.769230i | \(-0.279360\pi\) | ||||
0.638973 | + | 0.769230i | \(0.279360\pi\) | |||||||
\(662\) | 13.0564 | 0.507449 | ||||||||
\(663\) | −35.9242 | −1.39518 | ||||||||
\(664\) | −0.359100 | −0.0139358 | ||||||||
\(665\) | 21.3931 | 0.829587 | ||||||||
\(666\) | −3.65450 | −0.141609 | ||||||||
\(667\) | −4.07501 | −0.157785 | ||||||||
\(668\) | 3.73191 | 0.144392 | ||||||||
\(669\) | −12.0039 | −0.464099 | ||||||||
\(670\) | −17.5974 | −0.679848 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −1.57766 | −0.0608596 | ||||||||
\(673\) | −2.74514 | −0.105817 | −0.0529087 | − | 0.998599i | \(-0.516849\pi\) | ||||
−0.0529087 | + | 0.998599i | \(0.516849\pi\) | |||||||
\(674\) | −5.16212 | −0.198838 | ||||||||
\(675\) | 1.16050 | 0.0446678 | ||||||||
\(676\) | 11.7557 | 0.452141 | ||||||||
\(677\) | −21.9923 | −0.845234 | −0.422617 | − | 0.906308i | \(-0.638888\pi\) | ||||
−0.422617 | + | 0.906308i | \(0.638888\pi\) | |||||||
\(678\) | 4.58448 | 0.176066 | ||||||||
\(679\) | 9.37965 | 0.359958 | ||||||||
\(680\) | −17.9208 | −0.687231 | ||||||||
\(681\) | 3.72526 | 0.142752 | ||||||||
\(682\) | −2.23734 | −0.0856723 | ||||||||
\(683\) | −35.2564 | −1.34905 | −0.674525 | − | 0.738252i | \(-0.735651\pi\) | ||||
−0.674525 | + | 0.738252i | \(0.735651\pi\) | |||||||
\(684\) | 5.46325 | 0.208893 | ||||||||
\(685\) | −5.89792 | −0.225348 | ||||||||
\(686\) | 18.1604 | 0.693369 | ||||||||
\(687\) | 23.6720 | 0.903144 | ||||||||
\(688\) | 3.92316 | 0.149569 | ||||||||
\(689\) | −3.67274 | −0.139920 | ||||||||
\(690\) | 4.35674 | 0.165858 | ||||||||
\(691\) | 28.0494 | 1.06705 | 0.533524 | − | 0.845785i | \(-0.320867\pi\) | ||||
0.533524 | + | 0.845785i | \(0.320867\pi\) | |||||||
\(692\) | −15.7364 | −0.598207 | ||||||||
\(693\) | −1.57766 | −0.0599304 | ||||||||
\(694\) | −12.2368 | −0.464502 | ||||||||
\(695\) | 15.1973 | 0.576468 | ||||||||
\(696\) | −2.32153 | −0.0879975 | ||||||||
\(697\) | −0.607861 | −0.0230244 | ||||||||
\(698\) | 18.5418 | 0.701818 | ||||||||
\(699\) | −10.8622 | −0.410847 | ||||||||
\(700\) | 1.83088 | 0.0692008 | ||||||||
\(701\) | 2.85019 | 0.107650 | 0.0538251 | − | 0.998550i | \(-0.482859\pi\) | ||||
0.0538251 | + | 0.998550i | \(0.482859\pi\) | |||||||
\(702\) | 4.97551 | 0.187788 | ||||||||
\(703\) | 19.9655 | 0.753012 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −13.9442 | −0.525169 | ||||||||
\(706\) | −1.97315 | −0.0742603 | ||||||||
\(707\) | −19.9169 | −0.749051 | ||||||||
\(708\) | 6.61123 | 0.248465 | ||||||||
\(709\) | 17.2618 | 0.648279 | 0.324140 | − | 0.946009i | \(-0.394925\pi\) | ||||
0.324140 | + | 0.946009i | \(0.394925\pi\) | |||||||
\(710\) | −2.98196 | −0.111911 | ||||||||
\(711\) | 10.4861 | 0.393260 | ||||||||
\(712\) | −4.63572 | −0.173731 | ||||||||
\(713\) | 3.92723 | 0.147076 | ||||||||
\(714\) | −11.3910 | −0.426298 | ||||||||
\(715\) | 12.3494 | 0.461841 | ||||||||
\(716\) | −13.1480 | −0.491363 | ||||||||
\(717\) | 1.82533 | 0.0681681 | ||||||||
\(718\) | 9.23490 | 0.344643 | ||||||||
\(719\) | 37.7255 | 1.40692 | 0.703462 | − | 0.710733i | \(-0.251637\pi\) | ||||
0.703462 | + | 0.710733i | \(0.251637\pi\) | |||||||
\(720\) | 2.48204 | 0.0925000 | ||||||||
\(721\) | 16.0763 | 0.598714 | ||||||||
\(722\) | −10.8471 | −0.403688 | ||||||||
\(723\) | 17.4546 | 0.649145 | ||||||||
\(724\) | −23.7767 | −0.883655 | ||||||||
\(725\) | 2.69415 | 0.100058 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −30.4200 | −1.12821 | −0.564107 | − | 0.825702i | \(-0.690780\pi\) | ||||
−0.564107 | + | 0.825702i | \(0.690780\pi\) | |||||||
\(728\) | 7.84966 | 0.290928 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −30.0795 | −1.11329 | ||||||||
\(731\) | 28.3260 | 1.04767 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 21.8473 | 0.806949 | 0.403475 | − | 0.914991i | \(-0.367802\pi\) | ||||
0.403475 | + | 0.914991i | \(0.367802\pi\) | |||||||
\(734\) | −23.3975 | −0.863617 | ||||||||
\(735\) | −11.1964 | −0.412987 | ||||||||
\(736\) | 1.75531 | 0.0647015 | ||||||||
\(737\) | −7.08992 | −0.261160 | ||||||||
\(738\) | 0.0841890 | 0.00309904 | ||||||||
\(739\) | 3.62541 | 0.133363 | 0.0666815 | − | 0.997774i | \(-0.478759\pi\) | ||||
0.0666815 | + | 0.997774i | \(0.478759\pi\) | |||||||
\(740\) | 9.07061 | 0.333442 | ||||||||
\(741\) | −27.1825 | −0.998572 | ||||||||
\(742\) | −1.16457 | −0.0427528 | ||||||||
\(743\) | −28.6055 | −1.04944 | −0.524718 | − | 0.851276i | \(-0.675829\pi\) | ||||
−0.524718 | + | 0.851276i | \(0.675829\pi\) | |||||||
\(744\) | 2.23734 | 0.0820250 | ||||||||
\(745\) | 34.8927 | 1.27837 | ||||||||
\(746\) | −6.44001 | −0.235786 | ||||||||
\(747\) | 0.359100 | 0.0131388 | ||||||||
\(748\) | −7.22020 | −0.263997 | ||||||||
\(749\) | −2.14247 | −0.0782843 | ||||||||
\(750\) | 9.52977 | 0.347978 | ||||||||
\(751\) | 4.90312 | 0.178918 | 0.0894588 | − | 0.995991i | \(-0.471486\pi\) | ||||
0.0894588 | + | 0.995991i | \(0.471486\pi\) | |||||||
\(752\) | −5.61805 | −0.204869 | ||||||||
\(753\) | 20.2679 | 0.738605 | ||||||||
\(754\) | 11.5508 | 0.420656 | ||||||||
\(755\) | −25.4502 | −0.926228 | ||||||||
\(756\) | 1.57766 | 0.0573790 | ||||||||
\(757\) | 45.3746 | 1.64917 | 0.824583 | − | 0.565741i | \(-0.191410\pi\) | ||||
0.824583 | + | 0.565741i | \(0.191410\pi\) | |||||||
\(758\) | −13.5104 | −0.490721 | ||||||||
\(759\) | 1.75531 | 0.0637136 | ||||||||
\(760\) | −13.5600 | −0.491873 | ||||||||
\(761\) | −32.0786 | −1.16285 | −0.581424 | − | 0.813601i | \(-0.697504\pi\) | ||||
−0.581424 | + | 0.813601i | \(0.697504\pi\) | |||||||
\(762\) | 6.83090 | 0.247457 | ||||||||
\(763\) | 10.3863 | 0.376010 | ||||||||
\(764\) | −22.9311 | −0.829619 | ||||||||
\(765\) | 17.9208 | 0.647928 | ||||||||
\(766\) | 16.5203 | 0.596901 | ||||||||
\(767\) | −32.8942 | −1.18774 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −22.0409 | −0.794815 | −0.397407 | − | 0.917642i | \(-0.630090\pi\) | ||||
−0.397407 | + | 0.917642i | \(0.630090\pi\) | |||||||
\(770\) | 3.91581 | 0.141116 | ||||||||
\(771\) | 7.60217 | 0.273786 | ||||||||
\(772\) | 15.2772 | 0.549837 | ||||||||
\(773\) | 1.84767 | 0.0664562 | 0.0332281 | − | 0.999448i | \(-0.489421\pi\) | ||||
0.0332281 | + | 0.999448i | \(0.489421\pi\) | |||||||
\(774\) | −3.92316 | −0.141015 | ||||||||
\(775\) | −2.59644 | −0.0932670 | ||||||||
\(776\) | −5.94529 | −0.213423 | ||||||||
\(777\) | 5.76556 | 0.206838 | ||||||||
\(778\) | 11.1952 | 0.401366 | ||||||||
\(779\) | −0.459946 | −0.0164793 | ||||||||
\(780\) | −12.3494 | −0.442179 | ||||||||
\(781\) | −1.20142 | −0.0429901 | ||||||||
\(782\) | 12.6737 | 0.453210 | ||||||||
\(783\) | 2.32153 | 0.0829648 | ||||||||
\(784\) | −4.51099 | −0.161107 | ||||||||
\(785\) | −21.9044 | −0.781801 | ||||||||
\(786\) | −6.39323 | −0.228039 | ||||||||
\(787\) | −35.6316 | −1.27013 | −0.635064 | − | 0.772459i | \(-0.719026\pi\) | ||||
−0.635064 | + | 0.772459i | \(0.719026\pi\) | |||||||
\(788\) | −9.38641 | −0.334377 | ||||||||
\(789\) | 4.33404 | 0.154296 | ||||||||
\(790\) | −26.0269 | −0.925997 | ||||||||
\(791\) | −7.23276 | −0.257167 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 4.97551 | 0.176685 | ||||||||
\(794\) | 21.6990 | 0.770068 | ||||||||
\(795\) | 1.83215 | 0.0649796 | ||||||||
\(796\) | 11.3483 | 0.402230 | ||||||||
\(797\) | −7.69723 | −0.272650 | −0.136325 | − | 0.990664i | \(-0.543529\pi\) | ||||
−0.136325 | + | 0.990664i | \(0.543529\pi\) | |||||||
\(798\) | −8.61916 | −0.305115 | ||||||||
\(799\) | −40.5634 | −1.43503 | ||||||||
\(800\) | −1.16050 | −0.0410300 | ||||||||
\(801\) | 4.63572 | 0.163795 | ||||||||
\(802\) | 18.4153 | 0.650268 | ||||||||
\(803\) | −12.1189 | −0.427666 | ||||||||
\(804\) | 7.08992 | 0.250042 | ||||||||
\(805\) | −6.87345 | −0.242257 | ||||||||
\(806\) | −11.1319 | −0.392105 | ||||||||
\(807\) | −11.4364 | −0.402580 | ||||||||
\(808\) | 12.6243 | 0.444121 | ||||||||
\(809\) | −25.4627 | −0.895222 | −0.447611 | − | 0.894228i | \(-0.647725\pi\) | ||||
−0.447611 | + | 0.894228i | \(0.647725\pi\) | |||||||
\(810\) | −2.48204 | −0.0872099 | ||||||||
\(811\) | −46.0069 | −1.61552 | −0.807760 | − | 0.589511i | \(-0.799321\pi\) | ||||
−0.807760 | + | 0.589511i | \(0.799321\pi\) | |||||||
\(812\) | 3.66259 | 0.128532 | ||||||||
\(813\) | 6.09101 | 0.213621 | ||||||||
\(814\) | 3.65450 | 0.128090 | ||||||||
\(815\) | −29.1044 | −1.01948 | ||||||||
\(816\) | 7.22020 | 0.252758 | ||||||||
\(817\) | 21.4332 | 0.749853 | ||||||||
\(818\) | −4.30492 | −0.150518 | ||||||||
\(819\) | −7.84966 | −0.274289 | ||||||||
\(820\) | −0.208960 | −0.00729720 | ||||||||
\(821\) | −55.5046 | −1.93712 | −0.968562 | − | 0.248771i | \(-0.919973\pi\) | ||||
−0.968562 | + | 0.248771i | \(0.919973\pi\) | |||||||
\(822\) | 2.37624 | 0.0828810 | ||||||||
\(823\) | 15.8969 | 0.554130 | 0.277065 | − | 0.960851i | \(-0.410638\pi\) | ||||
0.277065 | + | 0.960851i | \(0.410638\pi\) | |||||||
\(824\) | −10.1900 | −0.354985 | ||||||||
\(825\) | −1.16050 | −0.0404035 | ||||||||
\(826\) | −10.4303 | −0.362916 | ||||||||
\(827\) | 31.5467 | 1.09699 | 0.548493 | − | 0.836155i | \(-0.315202\pi\) | ||||
0.548493 | + | 0.836155i | \(0.315202\pi\) | |||||||
\(828\) | −1.75531 | −0.0610012 | ||||||||
\(829\) | 23.0397 | 0.800203 | 0.400101 | − | 0.916471i | \(-0.368975\pi\) | ||||
0.400101 | + | 0.916471i | \(0.368975\pi\) | |||||||
\(830\) | −0.891300 | −0.0309375 | ||||||||
\(831\) | 9.24397 | 0.320670 | ||||||||
\(832\) | −4.97551 | −0.172495 | ||||||||
\(833\) | −32.5702 | −1.12849 | ||||||||
\(834\) | −6.12294 | −0.212020 | ||||||||
\(835\) | 9.26273 | 0.320550 | ||||||||
\(836\) | −5.46325 | −0.188951 | ||||||||
\(837\) | −2.23734 | −0.0773339 | ||||||||
\(838\) | 7.35619 | 0.254115 | ||||||||
\(839\) | −18.9841 | −0.655405 | −0.327703 | − | 0.944781i | \(-0.606274\pi\) | ||||
−0.327703 | + | 0.944781i | \(0.606274\pi\) | |||||||
\(840\) | −3.91581 | −0.135108 | ||||||||
\(841\) | −23.6105 | −0.814155 | ||||||||
\(842\) | −26.5246 | −0.914098 | ||||||||
\(843\) | 4.42234 | 0.152313 | ||||||||
\(844\) | 19.7222 | 0.678866 | ||||||||
\(845\) | 29.1780 | 1.00375 | ||||||||
\(846\) | 5.61805 | 0.193152 | ||||||||
\(847\) | 1.57766 | 0.0542091 | ||||||||
\(848\) | 0.738164 | 0.0253486 | ||||||||
\(849\) | −12.6077 | −0.432695 | ||||||||
\(850\) | −8.37906 | −0.287400 | ||||||||
\(851\) | −6.41478 | −0.219896 | ||||||||
\(852\) | 1.20142 | 0.0411598 | ||||||||
\(853\) | −17.8157 | −0.610000 | −0.305000 | − | 0.952352i | \(-0.598656\pi\) | ||||
−0.305000 | + | 0.952352i | \(0.598656\pi\) | |||||||
\(854\) | 1.57766 | 0.0539864 | ||||||||
\(855\) | 13.5600 | 0.463742 | ||||||||
\(856\) | 1.35801 | 0.0464157 | ||||||||
\(857\) | −23.7992 | −0.812966 | −0.406483 | − | 0.913658i | \(-0.633245\pi\) | ||||
−0.406483 | + | 0.913658i | \(0.633245\pi\) | |||||||
\(858\) | −4.97551 | −0.169861 | ||||||||
\(859\) | −36.6484 | −1.25043 | −0.625214 | − | 0.780453i | \(-0.714988\pi\) | ||||
−0.625214 | + | 0.780453i | \(0.714988\pi\) | |||||||
\(860\) | 9.73742 | 0.332043 | ||||||||
\(861\) | −0.132822 | −0.00452655 | ||||||||
\(862\) | −22.2025 | −0.756221 | ||||||||
\(863\) | 2.33478 | 0.0794770 | 0.0397385 | − | 0.999210i | \(-0.487348\pi\) | ||||
0.0397385 | + | 0.999210i | \(0.487348\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −39.0582 | −1.32802 | ||||||||
\(866\) | −16.1513 | −0.548844 | ||||||||
\(867\) | 35.1313 | 1.19312 | ||||||||
\(868\) | −3.52977 | −0.119808 | ||||||||
\(869\) | −10.4861 | −0.355717 | ||||||||
\(870\) | −5.76213 | −0.195354 | ||||||||
\(871\) | −35.2759 | −1.19528 | ||||||||
\(872\) | −6.58337 | −0.222941 | ||||||||
\(873\) | 5.94529 | 0.201218 | ||||||||
\(874\) | 9.58969 | 0.324376 | ||||||||
\(875\) | −15.0347 | −0.508267 | ||||||||
\(876\) | 12.1189 | 0.409459 | ||||||||
\(877\) | −30.5720 | −1.03234 | −0.516172 | − | 0.856485i | \(-0.672644\pi\) | ||||
−0.516172 | + | 0.856485i | \(0.672644\pi\) | |||||||
\(878\) | −3.76764 | −0.127152 | ||||||||
\(879\) | 5.90312 | 0.199107 | ||||||||
\(880\) | −2.48204 | −0.0836694 | ||||||||
\(881\) | 39.6527 | 1.33593 | 0.667966 | − | 0.744192i | \(-0.267165\pi\) | ||||
0.667966 | + | 0.744192i | \(0.267165\pi\) | |||||||
\(882\) | 4.51099 | 0.151893 | ||||||||
\(883\) | 24.9384 | 0.839246 | 0.419623 | − | 0.907699i | \(-0.362162\pi\) | ||||
0.419623 | + | 0.907699i | \(0.362162\pi\) | |||||||
\(884\) | −35.9242 | −1.20826 | ||||||||
\(885\) | 16.4093 | 0.551593 | ||||||||
\(886\) | 28.9033 | 0.971025 | ||||||||
\(887\) | −35.3662 | −1.18748 | −0.593740 | − | 0.804657i | \(-0.702349\pi\) | ||||
−0.593740 | + | 0.804657i | \(0.702349\pi\) | |||||||
\(888\) | −3.65450 | −0.122637 | ||||||||
\(889\) | −10.7768 | −0.361444 | ||||||||
\(890\) | −11.5060 | −0.385683 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −12.0039 | −0.401921 | ||||||||
\(893\) | −30.6928 | −1.02710 | ||||||||
\(894\) | −14.0581 | −0.470172 | ||||||||
\(895\) | −32.6337 | −1.09083 | ||||||||
\(896\) | −1.57766 | −0.0527059 | ||||||||
\(897\) | 8.73355 | 0.291605 | ||||||||
\(898\) | 17.3249 | 0.578139 | ||||||||
\(899\) | −5.19407 | −0.173232 | ||||||||
\(900\) | 1.16050 | 0.0386834 | ||||||||
\(901\) | 5.32969 | 0.177558 | ||||||||
\(902\) | −0.0841890 | −0.00280319 | ||||||||
\(903\) | 6.18941 | 0.205971 | ||||||||
\(904\) | 4.58448 | 0.152478 | ||||||||
\(905\) | −59.0147 | −1.96171 | ||||||||
\(906\) | 10.2538 | 0.340659 | ||||||||
\(907\) | −24.1847 | −0.803041 | −0.401520 | − | 0.915850i | \(-0.631518\pi\) | ||||
−0.401520 | + | 0.915850i | \(0.631518\pi\) | |||||||
\(908\) | 3.72526 | 0.123627 | ||||||||
\(909\) | −12.6243 | −0.418722 | ||||||||
\(910\) | 19.4831 | 0.645860 | ||||||||
\(911\) | −30.1740 | −0.999710 | −0.499855 | − | 0.866109i | \(-0.666613\pi\) | ||||
−0.499855 | + | 0.866109i | \(0.666613\pi\) | |||||||
\(912\) | 5.46325 | 0.180906 | ||||||||
\(913\) | −0.359100 | −0.0118845 | ||||||||
\(914\) | 27.9527 | 0.924594 | ||||||||
\(915\) | −2.48204 | −0.0820536 | ||||||||
\(916\) | 23.6720 | 0.782146 | ||||||||
\(917\) | 10.0864 | 0.333081 | ||||||||
\(918\) | −7.22020 | −0.238302 | ||||||||
\(919\) | 44.9120 | 1.48151 | 0.740755 | − | 0.671775i | \(-0.234468\pi\) | ||||
0.740755 | + | 0.671775i | \(0.234468\pi\) | |||||||
\(920\) | 4.35674 | 0.143637 | ||||||||
\(921\) | 18.1342 | 0.597543 | ||||||||
\(922\) | 19.7301 | 0.649776 | ||||||||
\(923\) | −5.97766 | −0.196757 | ||||||||
\(924\) | −1.57766 | −0.0519012 | ||||||||
\(925\) | 4.24106 | 0.139445 | ||||||||
\(926\) | 35.0083 | 1.15045 | ||||||||
\(927\) | 10.1900 | 0.334683 | ||||||||
\(928\) | −2.32153 | −0.0762081 | ||||||||
\(929\) | −58.7619 | −1.92791 | −0.963957 | − | 0.266057i | \(-0.914279\pi\) | ||||
−0.963957 | + | 0.266057i | \(0.914279\pi\) | |||||||
\(930\) | 5.55317 | 0.182096 | ||||||||
\(931\) | −24.6447 | −0.807696 | ||||||||
\(932\) | −10.8622 | −0.355804 | ||||||||
\(933\) | −14.9799 | −0.490421 | ||||||||
\(934\) | −2.95172 | −0.0965832 | ||||||||
\(935\) | −17.9208 | −0.586073 | ||||||||
\(936\) | 4.97551 | 0.162630 | ||||||||
\(937\) | −40.8754 | −1.33534 | −0.667671 | − | 0.744457i | \(-0.732709\pi\) | ||||
−0.667671 | + | 0.744457i | \(0.732709\pi\) | |||||||
\(938\) | −11.1855 | −0.365219 | ||||||||
\(939\) | −12.9832 | −0.423692 | ||||||||
\(940\) | −13.9442 | −0.454809 | ||||||||
\(941\) | 2.90275 | 0.0946271 | 0.0473135 | − | 0.998880i | \(-0.484934\pi\) | ||||
0.0473135 | + | 0.998880i | \(0.484934\pi\) | |||||||
\(942\) | 8.82517 | 0.287540 | ||||||||
\(943\) | 0.147778 | 0.00481230 | ||||||||
\(944\) | 6.61123 | 0.215177 | ||||||||
\(945\) | 3.91581 | 0.127381 | ||||||||
\(946\) | 3.92316 | 0.127553 | ||||||||
\(947\) | 16.0737 | 0.522324 | 0.261162 | − | 0.965295i | \(-0.415894\pi\) | ||||
0.261162 | + | 0.965295i | \(0.415894\pi\) | |||||||
\(948\) | 10.4861 | 0.340573 | ||||||||
\(949\) | −60.2975 | −1.95734 | ||||||||
\(950\) | −6.34012 | −0.205701 | ||||||||
\(951\) | −29.4666 | −0.955521 | ||||||||
\(952\) | −11.3910 | −0.369185 | ||||||||
\(953\) | 49.3712 | 1.59929 | 0.799645 | − | 0.600473i | \(-0.205021\pi\) | ||||
0.799645 | + | 0.600473i | \(0.205021\pi\) | |||||||
\(954\) | −0.738164 | −0.0238989 | ||||||||
\(955\) | −56.9159 | −1.84176 | ||||||||
\(956\) | 1.82533 | 0.0590353 | ||||||||
\(957\) | −2.32153 | −0.0750445 | ||||||||
\(958\) | −13.6000 | −0.439395 | ||||||||
\(959\) | −3.74891 | −0.121059 | ||||||||
\(960\) | 2.48204 | 0.0801074 | ||||||||
\(961\) | −25.9943 | −0.838526 | ||||||||
\(962\) | 18.1830 | 0.586244 | ||||||||
\(963\) | −1.35801 | −0.0437612 | ||||||||
\(964\) | 17.4546 | 0.562176 | ||||||||
\(965\) | 37.9185 | 1.22064 | ||||||||
\(966\) | 2.76928 | 0.0891001 | ||||||||
\(967\) | 32.1599 | 1.03419 | 0.517096 | − | 0.855927i | \(-0.327013\pi\) | ||||
0.517096 | + | 0.855927i | \(0.327013\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 39.4458 | 1.26718 | ||||||||
\(970\) | −14.7564 | −0.473800 | ||||||||
\(971\) | −8.44075 | −0.270877 | −0.135438 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135438 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 9.65992 | 0.309683 | ||||||||
\(974\) | −29.5866 | −0.948015 | ||||||||
\(975\) | −5.77409 | −0.184919 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | −57.5522 | −1.84126 | −0.920629 | − | 0.390439i | \(-0.872323\pi\) | ||||
−0.920629 | + | 0.390439i | \(0.872323\pi\) | |||||||
\(978\) | 11.7260 | 0.374956 | ||||||||
\(979\) | −4.63572 | −0.148158 | ||||||||
\(980\) | −11.1964 | −0.357657 | ||||||||
\(981\) | 6.58337 | 0.210191 | ||||||||
\(982\) | 7.69301 | 0.245494 | ||||||||
\(983\) | −12.4597 | −0.397404 | −0.198702 | − | 0.980060i | \(-0.563673\pi\) | ||||
−0.198702 | + | 0.980060i | \(0.563673\pi\) | |||||||
\(984\) | 0.0841890 | 0.00268385 | ||||||||
\(985\) | −23.2974 | −0.742317 | ||||||||
\(986\) | −16.7619 | −0.533809 | ||||||||
\(987\) | −8.86337 | −0.282124 | ||||||||
\(988\) | −27.1825 | −0.864789 | ||||||||
\(989\) | −6.88635 | −0.218973 | ||||||||
\(990\) | 2.48204 | 0.0788843 | ||||||||
\(991\) | −27.3577 | −0.869046 | −0.434523 | − | 0.900661i | \(-0.643083\pi\) | ||||
−0.434523 | + | 0.900661i | \(0.643083\pi\) | |||||||
\(992\) | 2.23734 | 0.0710357 | ||||||||
\(993\) | −13.0564 | −0.414331 | ||||||||
\(994\) | −1.89543 | −0.0601193 | ||||||||
\(995\) | 28.1669 | 0.892952 | ||||||||
\(996\) | 0.359100 | 0.0113785 | ||||||||
\(997\) | −49.6451 | −1.57228 | −0.786138 | − | 0.618051i | \(-0.787922\pi\) | ||||
−0.786138 | + | 0.618051i | \(0.787922\pi\) | |||||||
\(998\) | 1.53213 | 0.0484988 | ||||||||
\(999\) | 3.65450 | 0.115623 |
(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 | 4026.2.a.u.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.u.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial |