Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2541) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56155 | −1.10418 | −0.552092 | − | 0.833783i | \(-0.686170\pi\) | ||||
−0.552092 | + | 0.833783i | \(0.686170\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.43845 | 0.862121 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.56155 | 0.493806 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.56155 | −1.54250 | −0.771249 | − | 0.636534i | \(-0.780367\pi\) | ||||
−0.771249 | + | 0.636534i | \(0.780367\pi\) | |||||||
\(14\) | 1.56155 | 0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 4.12311 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | −0.438447 | −0.0980398 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 8.68466 | 1.70320 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.438447 | −0.0828587 | ||||||||
\(29\) | 6.68466 | 1.24131 | 0.620655 | − | 0.784084i | \(-0.286867\pi\) | ||||
0.620655 | + | 0.784084i | \(0.286867\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.24621 | 1.48106 | 0.740532 | − | 0.672022i | \(-0.234574\pi\) | ||||
0.740532 | + | 0.672022i | \(0.234574\pi\) | |||||||
\(32\) | 2.43845 | 0.431061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.43845 | −1.10418 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.68466 | −0.441355 | −0.220678 | − | 0.975347i | \(-0.570827\pi\) | ||||
−0.220678 | + | 0.975347i | \(0.570827\pi\) | |||||||
\(38\) | 9.36932 | 1.51990 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.43845 | −0.385552 | ||||||||
\(41\) | −7.56155 | −1.18092 | −0.590458 | − | 0.807068i | \(-0.701053\pi\) | ||||
−0.590458 | + | 0.807068i | \(0.701053\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.68466 | 0.866902 | 0.433451 | − | 0.901177i | \(-0.357296\pi\) | ||||
0.433451 | + | 0.901177i | \(0.357296\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.24621 | −0.920954 | ||||||||
\(47\) | −3.43845 | −0.501549 | −0.250775 | − | 0.968046i | \(-0.580685\pi\) | ||||
−0.250775 | + | 0.968046i | \(0.580685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.24621 | 0.883348 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.43845 | −0.338152 | ||||||||
\(53\) | −7.80776 | −1.07248 | −0.536239 | − | 0.844066i | \(-0.680156\pi\) | ||||
−0.536239 | + | 0.844066i | \(0.680156\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.43845 | −0.325851 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.4384 | −1.37064 | ||||||||
\(59\) | 12.5616 | 1.63537 | 0.817687 | − | 0.575662i | \(-0.195256\pi\) | ||||
0.817687 | + | 0.575662i | \(0.195256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3693 | 1.71177 | 0.855883 | − | 0.517170i | \(-0.173014\pi\) | ||||
0.855883 | + | 0.517170i | \(0.173014\pi\) | |||||||
\(62\) | −12.8769 | −1.63537 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 5.56155 | 0.689826 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.80776 | 1.07604 | 0.538020 | − | 0.842932i | \(-0.319173\pi\) | ||||
0.538020 | + | 0.842932i | \(0.319173\pi\) | |||||||
\(68\) | 1.80776 | 0.219224 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.56155 | −0.186641 | ||||||||
\(71\) | −3.12311 | −0.370644 | −0.185322 | − | 0.982678i | \(-0.559333\pi\) | ||||
−0.185322 | + | 0.982678i | \(0.559333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.12311 | −0.833696 | −0.416848 | − | 0.908976i | \(-0.636865\pi\) | ||||
−0.416848 | + | 0.908976i | \(0.636865\pi\) | |||||||
\(74\) | 4.19224 | 0.487338 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.63068 | −0.301760 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.12311 | −0.351377 | −0.175688 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175688 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(80\) | 4.68466 | 0.523761 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.8078 | 1.30395 | ||||||||
\(83\) | −8.80776 | −0.966778 | −0.483389 | − | 0.875406i | \(-0.660594\pi\) | ||||
−0.483389 | + | 0.875406i | \(0.660594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.12311 | −0.447214 | ||||||||
\(86\) | −8.87689 | −0.957220 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.2462 | 1.19210 | 0.596048 | − | 0.802949i | \(-0.296737\pi\) | ||||
0.596048 | + | 0.802949i | \(0.296737\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.56155 | 0.583009 | ||||||||
\(92\) | 1.75379 | 0.182845 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.36932 | 0.553803 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31534 | 0.133553 | 0.0667764 | − | 0.997768i | \(-0.478729\pi\) | ||||
0.0667764 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(98\) | −1.56155 | −0.157741 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.75379 | −0.175379 | ||||||||
\(101\) | 4.56155 | 0.453891 | 0.226946 | − | 0.973907i | \(-0.427126\pi\) | ||||
0.226946 | + | 0.973907i | \(0.427126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | −13.5616 | −1.32982 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.1922 | 1.18421 | ||||||||
\(107\) | −3.12311 | −0.301922 | −0.150961 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150961 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.87689 | −0.371339 | −0.185670 | − | 0.982612i | \(-0.559445\pi\) | ||||
−0.185670 | + | 0.982612i | \(0.559445\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.68466 | 0.442659 | ||||||||
\(113\) | 8.93087 | 0.840146 | 0.420073 | − | 0.907490i | \(-0.362005\pi\) | ||||
0.420073 | + | 0.907490i | \(0.362005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 2.93087 | 0.272124 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.6155 | −1.80576 | ||||||||
\(119\) | −4.12311 | −0.377964 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −20.8769 | −1.89011 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.61553 | 0.324684 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.9309 | −1.94605 | −0.973025 | − | 0.230700i | \(-0.925899\pi\) | ||||
−0.973025 | + | 0.230700i | \(0.925899\pi\) | |||||||
\(128\) | −13.5616 | −1.19868 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.68466 | −0.761695 | ||||||||
\(131\) | −2.56155 | −0.223804 | −0.111902 | − | 0.993719i | \(-0.535694\pi\) | ||||
−0.111902 | + | 0.993719i | \(0.535694\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | −13.7538 | −1.18815 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.0540 | 0.862121 | ||||||||
\(137\) | 14.0000 | 1.19610 | 0.598050 | − | 0.801459i | \(-0.295942\pi\) | ||||
0.598050 | + | 0.801459i | \(0.295942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.24621 | −0.529797 | −0.264898 | − | 0.964276i | \(-0.585338\pi\) | ||||
−0.264898 | + | 0.964276i | \(0.585338\pi\) | |||||||
\(140\) | 0.438447 | 0.0370556 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.87689 | 0.409260 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.68466 | −0.555131 | ||||||||
\(146\) | 11.1231 | 0.920555 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.17708 | −0.0967555 | ||||||||
\(149\) | −5.31534 | −0.435450 | −0.217725 | − | 0.976010i | \(-0.569864\pi\) | ||||
−0.217725 | + | 0.976010i | \(0.569864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4384 | −0.930848 | −0.465424 | − | 0.885088i | \(-0.654098\pi\) | ||||
−0.465424 | + | 0.885088i | \(0.654098\pi\) | |||||||
\(152\) | −14.6307 | −1.18671 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.24621 | −0.662352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.36932 | −0.428518 | −0.214259 | − | 0.976777i | \(-0.568734\pi\) | ||||
−0.214259 | + | 0.976777i | \(0.568734\pi\) | |||||||
\(158\) | 4.87689 | 0.387985 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.43845 | −0.192776 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3693 | 1.36047 | 0.680235 | − | 0.732994i | \(-0.261878\pi\) | ||||
0.680235 | + | 0.732994i | \(0.261878\pi\) | |||||||
\(164\) | −3.31534 | −0.258885 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.7538 | 1.06750 | ||||||||
\(167\) | −12.8078 | −0.991095 | −0.495547 | − | 0.868581i | \(-0.665032\pi\) | ||||
−0.495547 | + | 0.868581i | \(0.665032\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.9309 | 1.37930 | ||||||||
\(170\) | 6.43845 | 0.493806 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.49242 | 0.190045 | ||||||||
\(173\) | 12.5616 | 0.955037 | 0.477519 | − | 0.878622i | \(-0.341536\pi\) | ||||
0.477519 | + | 0.878622i | \(0.341536\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.5616 | −1.31629 | ||||||||
\(179\) | 4.87689 | 0.364516 | 0.182258 | − | 0.983251i | \(-0.441659\pi\) | ||||
0.182258 | + | 0.983251i | \(0.441659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.192236 | −0.0142888 | −0.00714439 | − | 0.999974i | \(-0.502274\pi\) | ||||
−0.00714439 | + | 0.999974i | \(0.502274\pi\) | |||||||
\(182\) | −8.68466 | −0.643750 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.75379 | 0.719059 | ||||||||
\(185\) | 2.68466 | 0.197380 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.50758 | −0.109951 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.36932 | −0.679722 | ||||||||
\(191\) | 12.2462 | 0.886105 | 0.443052 | − | 0.896496i | \(-0.353896\pi\) | ||||
0.443052 | + | 0.896496i | \(0.353896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2462 | 1.09745 | 0.548723 | − | 0.836004i | \(-0.315114\pi\) | ||||
0.548723 | + | 0.836004i | \(0.315114\pi\) | |||||||
\(194\) | −2.05398 | −0.147467 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.438447 | 0.0313177 | ||||||||
\(197\) | 27.1771 | 1.93629 | 0.968143 | − | 0.250396i | \(-0.0805609\pi\) | ||||
0.968143 | + | 0.250396i | \(0.0805609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.12311 | −0.504944 | −0.252472 | − | 0.967604i | \(-0.581243\pi\) | ||||
−0.252472 | + | 0.967604i | \(0.581243\pi\) | |||||||
\(200\) | −9.75379 | −0.689697 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.12311 | −0.501180 | ||||||||
\(203\) | −6.68466 | −0.469171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.56155 | 0.528122 | ||||||||
\(206\) | 12.4924 | 0.870388 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 26.0540 | 1.80652 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.0540 | −1.86247 | −0.931236 | − | 0.364416i | \(-0.881269\pi\) | ||||
−0.931236 | + | 0.364416i | \(0.881269\pi\) | |||||||
\(212\) | −3.42329 | −0.235113 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.87689 | 0.333378 | ||||||||
\(215\) | −5.68466 | −0.387690 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.24621 | −0.559789 | ||||||||
\(218\) | 6.05398 | 0.410027 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.9309 | −1.54250 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | −2.43845 | −0.162926 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.9460 | −0.927676 | ||||||||
\(227\) | 5.68466 | 0.377304 | 0.188652 | − | 0.982044i | \(-0.439588\pi\) | ||||
0.188652 | + | 0.982044i | \(0.439588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.19224 | −0.277031 | −0.138515 | − | 0.990360i | \(-0.544233\pi\) | ||||
−0.138515 | + | 0.990360i | \(0.544233\pi\) | |||||||
\(230\) | 6.24621 | 0.411863 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.3002 | 1.07016 | ||||||||
\(233\) | −27.1771 | −1.78043 | −0.890215 | − | 0.455541i | \(-0.849446\pi\) | ||||
−0.890215 | + | 0.455541i | \(0.849446\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.43845 | 0.224300 | ||||||||
\(236\) | 5.50758 | 0.358513 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.43845 | 0.417343 | ||||||||
\(239\) | −19.3693 | −1.25290 | −0.626448 | − | 0.779463i | \(-0.715492\pi\) | ||||
−0.626448 | + | 0.779463i | \(0.715492\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2462 | 0.788848 | 0.394424 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394424 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.86174 | 0.375259 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.3693 | 2.12324 | ||||||||
\(248\) | 20.1080 | 1.27686 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.0540 | −0.888851 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 34.2462 | 2.14880 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | −23.0000 | −1.43470 | −0.717350 | − | 0.696713i | \(-0.754645\pi\) | ||||
−0.717350 | + | 0.696713i | \(0.754645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.68466 | 0.166817 | ||||||||
\(260\) | 2.43845 | 0.151226 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | 30.7386 | 1.89543 | 0.947713 | − | 0.319125i | \(-0.103389\pi\) | ||||
0.947713 | + | 0.319125i | \(0.103389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.80776 | 0.479627 | ||||||||
\(266\) | −9.36932 | −0.574470 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.86174 | 0.235893 | ||||||||
\(269\) | 4.43845 | 0.270617 | 0.135308 | − | 0.990804i | \(-0.456797\pi\) | ||||
0.135308 | + | 0.990804i | \(0.456797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | −19.3153 | −1.17116 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.8617 | −1.32072 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.2462 | 0.795888 | 0.397944 | − | 0.917410i | \(-0.369724\pi\) | ||||
0.397944 | + | 0.917410i | \(0.369724\pi\) | |||||||
\(278\) | 9.75379 | 0.584993 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.43845 | 0.145725 | ||||||||
\(281\) | 20.8769 | 1.24541 | 0.622706 | − | 0.782456i | \(-0.286033\pi\) | ||||
0.622706 | + | 0.782456i | \(0.286033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1231 | −0.898975 | −0.449488 | − | 0.893287i | \(-0.648393\pi\) | ||||
−0.449488 | + | 0.893287i | \(0.648393\pi\) | |||||||
\(284\) | −1.36932 | −0.0812540 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.56155 | 0.446344 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 10.4384 | 0.612967 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.12311 | −0.182766 | ||||||||
\(293\) | −22.3693 | −1.30683 | −0.653415 | − | 0.757000i | \(-0.726664\pi\) | ||||
−0.653415 | + | 0.757000i | \(0.726664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.5616 | −0.731362 | ||||||||
\(296\) | −6.54640 | −0.380502 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.30019 | 0.480817 | ||||||||
\(299\) | −22.2462 | −1.28653 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.68466 | −0.327658 | ||||||||
\(302\) | 17.8617 | 1.02783 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 28.1080 | 1.61210 | ||||||||
\(305\) | −13.3693 | −0.765525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.8769 | −1.30565 | −0.652827 | − | 0.757507i | \(-0.726417\pi\) | ||||
−0.652827 | + | 0.757507i | \(0.726417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.8769 | 0.731358 | ||||||||
\(311\) | −4.56155 | −0.258662 | −0.129331 | − | 0.991601i | \(-0.541283\pi\) | ||||
−0.129331 | + | 0.991601i | \(0.541283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.43845 | 0.137829 | 0.0689146 | − | 0.997623i | \(-0.478046\pi\) | ||||
0.0689146 | + | 0.997623i | \(0.478046\pi\) | |||||||
\(314\) | 8.38447 | 0.473163 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.36932 | −0.0770301 | ||||||||
\(317\) | 27.1231 | 1.52339 | 0.761693 | − | 0.647938i | \(-0.224369\pi\) | ||||
0.761693 | + | 0.647938i | \(0.224369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −5.56155 | −0.310900 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.24621 | 0.348088 | ||||||||
\(323\) | −24.7386 | −1.37649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.2462 | 1.23400 | ||||||||
\(326\) | −27.1231 | −1.50221 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.4384 | −1.01809 | ||||||||
\(329\) | 3.43845 | 0.189568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6847 | −0.972037 | −0.486018 | − | 0.873949i | \(-0.661551\pi\) | ||||
−0.486018 | + | 0.873949i | \(0.661551\pi\) | |||||||
\(332\) | −3.86174 | −0.211940 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0000 | 1.09435 | ||||||||
\(335\) | −8.80776 | −0.481220 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1771 | −1.48043 | −0.740215 | − | 0.672370i | \(-0.765276\pi\) | ||||
−0.740215 | + | 0.672370i | \(0.765276\pi\) | |||||||
\(338\) | −28.0000 | −1.52300 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.80776 | −0.0980398 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 13.8617 | 0.747375 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.6155 | −1.05454 | ||||||||
\(347\) | −14.0000 | −0.751559 | −0.375780 | − | 0.926709i | \(-0.622625\pi\) | ||||
−0.375780 | + | 0.926709i | \(0.622625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.05398 | 0.431119 | 0.215560 | − | 0.976491i | \(-0.430842\pi\) | ||||
0.215560 | + | 0.976491i | \(0.430842\pi\) | |||||||
\(350\) | −6.24621 | −0.333874 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.1771 | −1.23359 | −0.616796 | − | 0.787123i | \(-0.711570\pi\) | ||||
−0.616796 | + | 0.787123i | \(0.711570\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.12311 | 0.165757 | ||||||||
\(356\) | 4.93087 | 0.261336 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.61553 | −0.402493 | ||||||||
\(359\) | 28.0000 | 1.47778 | 0.738892 | − | 0.673824i | \(-0.235349\pi\) | ||||
0.738892 | + | 0.673824i | \(0.235349\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0.300187 | 0.0157775 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.43845 | 0.127809 | ||||||||
\(365\) | 7.12311 | 0.372840 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4924 | 0.756498 | 0.378249 | − | 0.925704i | \(-0.376526\pi\) | ||||
0.378249 | + | 0.925704i | \(0.376526\pi\) | |||||||
\(368\) | −18.7386 | −0.976819 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.19224 | −0.217944 | ||||||||
\(371\) | 7.80776 | 0.405359 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.80776 | −0.352493 | −0.176246 | − | 0.984346i | \(-0.556396\pi\) | ||||
−0.176246 | + | 0.984346i | \(0.556396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.38447 | −0.432396 | ||||||||
\(377\) | −37.1771 | −1.91472 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5616 | −0.747977 | −0.373988 | − | 0.927433i | \(-0.622010\pi\) | ||||
−0.373988 | + | 0.927433i | \(0.622010\pi\) | |||||||
\(380\) | 2.63068 | 0.134951 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.1231 | −0.978423 | ||||||||
\(383\) | −17.4384 | −0.891063 | −0.445532 | − | 0.895266i | \(-0.646985\pi\) | ||||
−0.445532 | + | 0.895266i | \(0.646985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.8078 | −1.21178 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.576708 | 0.0292779 | ||||||||
\(389\) | −17.5616 | −0.890406 | −0.445203 | − | 0.895430i | \(-0.646868\pi\) | ||||
−0.445203 | + | 0.895430i | \(0.646868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4924 | 0.834058 | ||||||||
\(392\) | 2.43845 | 0.123160 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −42.4384 | −2.13802 | ||||||||
\(395\) | 3.12311 | 0.157140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3153 | −0.668278 | −0.334139 | − | 0.942524i | \(-0.608445\pi\) | ||||
−0.334139 | + | 0.942524i | \(0.608445\pi\) | |||||||
\(398\) | 11.1231 | 0.557551 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.7386 | 0.936932 | ||||||||
\(401\) | 15.3153 | 0.764812 | 0.382406 | − | 0.923994i | \(-0.375096\pi\) | ||||
0.382406 | + | 0.923994i | \(0.375096\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.8617 | −2.28454 | ||||||||
\(404\) | 2.00000 | 0.0995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.4384 | 0.518051 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.3002 | −1.69604 | −0.848018 | − | 0.529968i | \(-0.822204\pi\) | ||||
−0.848018 | + | 0.529968i | \(0.822204\pi\) | |||||||
\(410\) | −11.8078 | −0.583144 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.50758 | −0.172806 | ||||||||
\(413\) | −12.5616 | −0.618114 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.80776 | 0.432356 | ||||||||
\(416\) | −13.5616 | −0.664910 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.3002 | 1.04058 | 0.520291 | − | 0.853989i | \(-0.325823\pi\) | ||||
0.520291 | + | 0.853989i | \(0.325823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00000 | −0.341159 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(422\) | 42.2462 | 2.05651 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −19.0388 | −0.924607 | ||||||||
\(425\) | −16.4924 | −0.800000 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.3693 | −0.646987 | ||||||||
\(428\) | −1.36932 | −0.0661884 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.87689 | 0.428082 | ||||||||
\(431\) | 10.6307 | 0.512062 | 0.256031 | − | 0.966669i | \(-0.417585\pi\) | ||||
0.256031 | + | 0.966669i | \(0.417585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.9309 | −0.621418 | −0.310709 | − | 0.950505i | \(-0.600566\pi\) | ||||
−0.310709 | + | 0.950505i | \(0.600566\pi\) | |||||||
\(434\) | 12.8769 | 0.618111 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.69981 | −0.0814063 | ||||||||
\(437\) | −24.0000 | −1.14808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.12311 | 0.0536029 | 0.0268015 | − | 0.999641i | \(-0.491468\pi\) | ||||
0.0268015 | + | 0.999641i | \(0.491468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.8078 | 1.70320 | ||||||||
\(443\) | 8.49242 | 0.403487 | 0.201744 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201744 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.2462 | −0.533122 | ||||||||
\(446\) | −37.4773 | −1.77460 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.56155 | −0.262759 | ||||||||
\(449\) | −28.0540 | −1.32395 | −0.661974 | − | 0.749526i | \(-0.730281\pi\) | ||||
−0.661974 | + | 0.749526i | \(0.730281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.91571 | 0.184180 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.87689 | −0.416613 | ||||||||
\(455\) | −5.56155 | −0.260730 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.6155 | 0.496573 | 0.248287 | − | 0.968687i | \(-0.420132\pi\) | ||||
0.248287 | + | 0.968687i | \(0.420132\pi\) | |||||||
\(458\) | 6.54640 | 0.305893 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.75379 | −0.0817708 | ||||||||
\(461\) | −10.3693 | −0.482947 | −0.241474 | − | 0.970407i | \(-0.577631\pi\) | ||||
−0.241474 | + | 0.970407i | \(0.577631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.876894 | 0.0407527 | 0.0203764 | − | 0.999792i | \(-0.493514\pi\) | ||||
0.0203764 | + | 0.999792i | \(0.493514\pi\) | |||||||
\(464\) | −31.3153 | −1.45378 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 42.4384 | 1.96592 | ||||||||
\(467\) | 21.7538 | 1.00665 | 0.503323 | − | 0.864099i | \(-0.332111\pi\) | ||||
0.503323 | + | 0.864099i | \(0.332111\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.80776 | −0.406705 | ||||||||
\(470\) | −5.36932 | −0.247668 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 30.6307 | 1.40989 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0000 | 1.10120 | ||||||||
\(476\) | −1.80776 | −0.0828587 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 30.2462 | 1.38343 | ||||||||
\(479\) | −29.6847 | −1.35633 | −0.678163 | − | 0.734911i | \(-0.737224\pi\) | ||||
−0.678163 | + | 0.734911i | \(0.737224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9309 | 0.680789 | ||||||||
\(482\) | −19.1231 | −0.871034 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.31534 | −0.0597266 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.4384 | 0.880840 | 0.440420 | − | 0.897792i | \(-0.354830\pi\) | ||||
0.440420 | + | 0.897792i | \(0.354830\pi\) | |||||||
\(488\) | 32.6004 | 1.47575 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.56155 | 0.0705438 | ||||||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.5616 | 1.24131 | ||||||||
\(494\) | −52.1080 | −2.34445 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −38.6307 | −1.73457 | ||||||||
\(497\) | 3.12311 | 0.140090 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.5464 | −1.77034 | −0.885170 | − | 0.465268i | \(-0.845958\pi\) | ||||
−0.885170 | + | 0.465268i | \(0.845958\pi\) | |||||||
\(500\) | 3.94602 | 0.176472 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.24621 | 0.278782 | ||||||||
\(503\) | −19.6847 | −0.877696 | −0.438848 | − | 0.898561i | \(-0.644613\pi\) | ||||
−0.438848 | + | 0.898561i | \(0.644613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.56155 | −0.202986 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.61553 | −0.426620 | ||||||||
\(509\) | −25.6847 | −1.13845 | −0.569226 | − | 0.822181i | \(-0.692757\pi\) | ||||
−0.569226 | + | 0.822181i | \(0.692757\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.12311 | 0.315108 | ||||||||
\(512\) | 11.4233 | 0.504843 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 35.9157 | 1.58417 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.19224 | −0.184196 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.5616 | 0.594713 | ||||||||
\(521\) | −43.9309 | −1.92465 | −0.962323 | − | 0.271908i | \(-0.912345\pi\) | ||||
−0.962323 | + | 0.271908i | \(0.912345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.1231 | 1.09856 | 0.549278 | − | 0.835639i | \(-0.314903\pi\) | ||||
0.549278 | + | 0.835639i | \(0.314903\pi\) | |||||||
\(524\) | −1.12311 | −0.0490631 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −48.0000 | −2.09290 | ||||||||
\(527\) | 34.0000 | 1.48106 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −12.1922 | −0.529597 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.63068 | 0.114055 | ||||||||
\(533\) | 42.0540 | 1.82156 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.12311 | 0.135024 | ||||||||
\(536\) | 21.4773 | 0.927677 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.93087 | −0.298811 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9309 | −0.512948 | −0.256474 | − | 0.966551i | \(-0.582561\pi\) | ||||
−0.256474 | + | 0.966551i | \(0.582561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.0540 | 0.431061 | ||||||||
\(545\) | 3.87689 | 0.166068 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.3693 | 0.913686 | 0.456843 | − | 0.889547i | \(-0.348980\pi\) | ||||
0.456843 | + | 0.889547i | \(0.348980\pi\) | |||||||
\(548\) | 6.13826 | 0.262213 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.1080 | −1.70866 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.12311 | 0.132808 | ||||||||
\(554\) | −20.6847 | −0.878807 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.73863 | −0.116144 | ||||||||
\(557\) | −42.4924 | −1.80046 | −0.900231 | − | 0.435413i | \(-0.856602\pi\) | ||||
−0.900231 | + | 0.435413i | \(0.856602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.6155 | −1.33719 | ||||||||
\(560\) | −4.68466 | −0.197963 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.6004 | −1.37516 | ||||||||
\(563\) | 6.80776 | 0.286913 | 0.143457 | − | 0.989657i | \(-0.454178\pi\) | ||||
0.143457 | + | 0.989657i | \(0.454178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.93087 | −0.375725 | ||||||||
\(566\) | 23.6155 | 0.992635 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.61553 | −0.319540 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2462 | 0.428791 | 0.214395 | − | 0.976747i | \(-0.431222\pi\) | ||||
0.214395 | + | 0.976747i | \(0.431222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.8078 | −0.492847 | ||||||||
\(575\) | −16.0000 | −0.667246 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.8078 | −1.15765 | −0.578826 | − | 0.815451i | \(-0.696489\pi\) | ||||
−0.578826 | + | 0.815451i | \(0.696489\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.93087 | −0.121698 | ||||||||
\(581\) | 8.80776 | 0.365408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −17.3693 | −0.718747 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.9309 | 1.44298 | ||||||||
\(587\) | 3.43845 | 0.141920 | 0.0709600 | − | 0.997479i | \(-0.477394\pi\) | ||||
0.0709600 | + | 0.997479i | \(0.477394\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.4773 | −2.03868 | ||||||||
\(590\) | 19.6155 | 0.807559 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.5767 | 0.516900 | ||||||||
\(593\) | −44.3693 | −1.82203 | −0.911015 | − | 0.412374i | \(-0.864700\pi\) | ||||
−0.911015 | + | 0.412374i | \(0.864700\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.12311 | 0.169031 | ||||||||
\(596\) | −2.33050 | −0.0954609 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.7386 | 1.42057 | ||||||||
\(599\) | 41.2311 | 1.68466 | 0.842328 | − | 0.538966i | \(-0.181185\pi\) | ||||
0.842328 | + | 0.538966i | \(0.181185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.68466 | −0.191091 | −0.0955456 | − | 0.995425i | \(-0.530460\pi\) | ||||
−0.0955456 | + | 0.995425i | \(0.530460\pi\) | |||||||
\(602\) | 8.87689 | 0.361795 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.01515 | −0.204064 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.2462 | 0.578236 | 0.289118 | − | 0.957293i | \(-0.406638\pi\) | ||||
0.289118 | + | 0.957293i | \(0.406638\pi\) | |||||||
\(608\) | −14.6307 | −0.593353 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.8769 | 0.845281 | ||||||||
\(611\) | 19.1231 | 0.773638 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.4924 | 1.11041 | 0.555204 | − | 0.831714i | \(-0.312640\pi\) | ||||
0.555204 | + | 0.831714i | \(0.312640\pi\) | |||||||
\(614\) | 35.7235 | 1.44168 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.1771 | 1.89928 | 0.949639 | − | 0.313346i | \(-0.101450\pi\) | ||||
0.949639 | + | 0.313346i | \(0.101450\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.4924 | −1.86869 | −0.934344 | − | 0.356372i | \(-0.884014\pi\) | ||||
−0.934344 | + | 0.356372i | \(0.884014\pi\) | |||||||
\(620\) | −3.61553 | −0.145203 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.12311 | 0.285611 | ||||||||
\(623\) | −11.2462 | −0.450570 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −3.80776 | −0.152189 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.35416 | −0.0939413 | ||||||||
\(629\) | −11.0691 | −0.441355 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −47.9309 | −1.90810 | −0.954049 | − | 0.299651i | \(-0.903130\pi\) | ||||
−0.954049 | + | 0.299651i | \(0.903130\pi\) | |||||||
\(632\) | −7.61553 | −0.302929 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −42.3542 | −1.68210 | ||||||||
\(635\) | 21.9309 | 0.870300 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.56155 | −0.220357 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13.5616 | 0.536067 | ||||||||
\(641\) | 14.6847 | 0.580009 | 0.290005 | − | 0.957025i | \(-0.406343\pi\) | ||||
0.290005 | + | 0.957025i | \(0.406343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.7386 | −0.423490 | −0.211745 | − | 0.977325i | \(-0.567915\pi\) | ||||
−0.211745 | + | 0.977325i | \(0.567915\pi\) | |||||||
\(644\) | −1.75379 | −0.0691090 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.6307 | 1.51990 | ||||||||
\(647\) | −13.9309 | −0.547679 | −0.273840 | − | 0.961775i | \(-0.588294\pi\) | ||||
−0.273840 | + | 0.961775i | \(0.588294\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −34.7386 | −1.36256 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.61553 | 0.298247 | ||||||||
\(653\) | −8.24621 | −0.322699 | −0.161350 | − | 0.986897i | \(-0.551585\pi\) | ||||
−0.161350 | + | 0.986897i | \(0.551585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.56155 | 0.100088 | ||||||||
\(656\) | 35.4233 | 1.38305 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.36932 | −0.209318 | ||||||||
\(659\) | −10.0000 | −0.389545 | −0.194772 | − | 0.980848i | \(-0.562397\pi\) | ||||
−0.194772 | + | 0.980848i | \(0.562397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.4233 | −1.22222 | −0.611112 | − | 0.791544i | \(-0.709278\pi\) | ||||
−0.611112 | + | 0.791544i | \(0.709278\pi\) | |||||||
\(662\) | 27.6155 | 1.07331 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.4773 | −0.833480 | ||||||||
\(665\) | −6.00000 | −0.232670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.7386 | 1.03532 | ||||||||
\(668\) | −5.61553 | −0.217271 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.7538 | 0.531355 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.9309 | −1.07666 | −0.538328 | − | 0.842735i | \(-0.680944\pi\) | ||||
−0.538328 | + | 0.842735i | \(0.680944\pi\) | |||||||
\(674\) | 42.4384 | 1.63467 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.86174 | 0.302375 | ||||||||
\(677\) | −22.8617 | −0.878648 | −0.439324 | − | 0.898329i | \(-0.644782\pi\) | ||||
−0.439324 | + | 0.898329i | \(0.644782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.31534 | −0.0504782 | ||||||||
\(680\) | −10.0540 | −0.385552 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6155 | −0.520984 | −0.260492 | − | 0.965476i | \(-0.583885\pi\) | ||||
−0.260492 | + | 0.965476i | \(0.583885\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0000 | −0.534913 | ||||||||
\(686\) | 1.56155 | 0.0596204 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.6307 | −1.01529 | ||||||||
\(689\) | 43.4233 | 1.65430 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1080 | 1.37361 | 0.686806 | − | 0.726841i | \(-0.259012\pi\) | ||||
0.686806 | + | 0.726841i | \(0.259012\pi\) | |||||||
\(692\) | 5.50758 | 0.209367 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8617 | 0.829860 | ||||||||
\(695\) | 6.24621 | 0.236932 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.1771 | −1.18092 | ||||||||
\(698\) | −12.5767 | −0.476035 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.75379 | 0.0662870 | ||||||||
\(701\) | 7.17708 | 0.271075 | 0.135537 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135537 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.1080 | 0.607523 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.1922 | 1.36211 | ||||||||
\(707\) | −4.56155 | −0.171555 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.9309 | −1.34941 | −0.674706 | − | 0.738087i | \(-0.735730\pi\) | ||||
−0.674706 | + | 0.738087i | \(0.735730\pi\) | |||||||
\(710\) | −4.87689 | −0.183027 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.4233 | 1.02773 | ||||||||
\(713\) | 32.9848 | 1.23529 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.13826 | 0.0799106 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −43.7235 | −1.63175 | ||||||||
\(719\) | 21.8617 | 0.815305 | 0.407653 | − | 0.913137i | \(-0.366347\pi\) | ||||
0.407653 | + | 0.913137i | \(0.366347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | −26.5464 | −0.987955 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.0842853 | −0.00313244 | ||||||||
\(725\) | −26.7386 | −0.993048 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.2311 | −1.82588 | −0.912939 | − | 0.408095i | \(-0.866193\pi\) | ||||
−0.912939 | + | 0.408095i | \(0.866193\pi\) | |||||||
\(728\) | 13.5616 | 0.502625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.1231 | −0.411685 | ||||||||
\(731\) | 23.4384 | 0.866902 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.4384 | 1.27201 | 0.636007 | − | 0.771684i | \(-0.280585\pi\) | ||||
0.636007 | + | 0.771684i | \(0.280585\pi\) | |||||||
\(734\) | −22.6307 | −0.835314 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.75379 | 0.359529 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.38447 | −0.308428 | −0.154214 | − | 0.988037i | \(-0.549284\pi\) | ||||
−0.154214 | + | 0.988037i | \(0.549284\pi\) | |||||||
\(740\) | 1.17708 | 0.0432704 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.1922 | −0.447591 | ||||||||
\(743\) | −32.8769 | −1.20614 | −0.603068 | − | 0.797690i | \(-0.706055\pi\) | ||||
−0.603068 | + | 0.797690i | \(0.706055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.31534 | 0.194739 | ||||||||
\(746\) | 10.6307 | 0.389217 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.12311 | 0.114116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5616 | 0.458378 | 0.229189 | − | 0.973382i | \(-0.426393\pi\) | ||||
0.229189 | + | 0.973382i | \(0.426393\pi\) | |||||||
\(752\) | 16.1080 | 0.587397 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 58.0540 | 2.11420 | ||||||||
\(755\) | 11.4384 | 0.416288 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.615528 | −0.0223718 | −0.0111859 | − | 0.999937i | \(-0.503561\pi\) | ||||
−0.0111859 | + | 0.999937i | \(0.503561\pi\) | |||||||
\(758\) | 22.7386 | 0.825904 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.6307 | 0.530711 | ||||||||
\(761\) | −13.9848 | −0.506950 | −0.253475 | − | 0.967342i | \(-0.581574\pi\) | ||||
−0.253475 | + | 0.967342i | \(0.581574\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.87689 | 0.140353 | ||||||||
\(764\) | 5.36932 | 0.194255 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.2311 | 0.983898 | ||||||||
\(767\) | −69.8617 | −2.52256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3002 | 0.732043 | 0.366022 | − | 0.930606i | \(-0.380720\pi\) | ||||
0.366022 | + | 0.930606i | \(0.380720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.68466 | 0.240586 | ||||||||
\(773\) | −29.5464 | −1.06271 | −0.531355 | − | 0.847149i | \(-0.678317\pi\) | ||||
−0.531355 | + | 0.847149i | \(0.678317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.9848 | −1.18485 | ||||||||
\(776\) | 3.20739 | 0.115139 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.4233 | 0.983173 | ||||||||
\(779\) | 45.3693 | 1.62552 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −25.7538 | −0.920954 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.68466 | −0.167309 | ||||||||
\(785\) | 5.36932 | 0.191639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.1231 | −1.32330 | −0.661648 | − | 0.749815i | \(-0.730143\pi\) | ||||
−0.661648 | + | 0.749815i | \(0.730143\pi\) | |||||||
\(788\) | 11.9157 | 0.424480 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.87689 | −0.173512 | ||||||||
\(791\) | −8.93087 | −0.317545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −74.3542 | −2.64039 | ||||||||
\(794\) | 20.7926 | 0.737902 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.12311 | −0.110696 | ||||||||
\(797\) | −39.3002 | −1.39208 | −0.696042 | − | 0.718001i | \(-0.745057\pi\) | ||||
−0.696042 | + | 0.718001i | \(0.745057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.1771 | −0.501549 | ||||||||
\(800\) | −9.75379 | −0.344849 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.9157 | −0.844493 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 71.6155 | 2.52255 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.1231 | 0.391309 | ||||||||
\(809\) | 45.8617 | 1.61241 | 0.806206 | − | 0.591634i | \(-0.201517\pi\) | ||||
0.806206 | + | 0.591634i | \(0.201517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | −2.93087 | −0.102853 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.3693 | −0.608421 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.1080 | −1.19329 | ||||||||
\(818\) | 53.5616 | 1.87274 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.31534 | 0.115777 | ||||||||
\(821\) | −1.50758 | −0.0526148 | −0.0263074 | − | 0.999654i | \(-0.508375\pi\) | ||||
−0.0263074 | + | 0.999654i | \(0.508375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.2462 | −1.33318 | −0.666590 | − | 0.745425i | \(-0.732247\pi\) | ||||
−0.666590 | + | 0.745425i | \(0.732247\pi\) | |||||||
\(824\) | −19.5076 | −0.679579 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.6155 | 0.682512 | ||||||||
\(827\) | −39.1231 | −1.36044 | −0.680222 | − | 0.733006i | \(-0.738117\pi\) | ||||
−0.680222 | + | 0.733006i | \(0.738117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.8078 | 1.66043 | 0.830216 | − | 0.557442i | \(-0.188217\pi\) | ||||
0.830216 | + | 0.557442i | \(0.188217\pi\) | |||||||
\(830\) | −13.7538 | −0.477401 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −30.9309 | −1.07233 | ||||||||
\(833\) | 4.12311 | 0.142857 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.8078 | 0.443231 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.2614 | −1.14899 | ||||||||
\(839\) | −57.0540 | −1.96972 | −0.984861 | − | 0.173346i | \(-0.944542\pi\) | ||||
−0.984861 | + | 0.173346i | \(0.944542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6847 | 0.540850 | ||||||||
\(842\) | 10.9309 | 0.376703 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.8617 | −0.408298 | ||||||||
\(845\) | −17.9309 | −0.616841 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 36.5767 | 1.25605 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25.7538 | 0.883348 | ||||||||
\(851\) | −10.7386 | −0.368116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.7926 | −1.80758 | −0.903792 | − | 0.427971i | \(-0.859228\pi\) | ||||
−0.903792 | + | 0.427971i | \(0.859228\pi\) | |||||||
\(854\) | 20.8769 | 0.714393 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.61553 | −0.260293 | ||||||||
\(857\) | −9.19224 | −0.314001 | −0.157000 | − | 0.987599i | \(-0.550182\pi\) | ||||
−0.157000 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.6307 | 0.567432 | 0.283716 | − | 0.958908i | \(-0.408433\pi\) | ||||
0.283716 | + | 0.958908i | \(0.408433\pi\) | |||||||
\(860\) | −2.49242 | −0.0849909 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.6004 | −0.565411 | ||||||||
\(863\) | −36.2462 | −1.23384 | −0.616918 | − | 0.787028i | \(-0.711619\pi\) | ||||
−0.616918 | + | 0.787028i | \(0.711619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.5616 | −0.427106 | ||||||||
\(866\) | 20.1922 | 0.686160 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.61553 | −0.122719 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.9848 | −1.65979 | ||||||||
\(872\) | −9.45360 | −0.320139 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.4773 | 1.26769 | ||||||||
\(875\) | −9.00000 | −0.304256 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.4233 | 1.80398 | 0.901988 | − | 0.431761i | \(-0.142107\pi\) | ||||
0.901988 | + | 0.431761i | \(0.142107\pi\) | |||||||
\(878\) | −1.75379 | −0.0591875 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.0691 | 0.642455 | 0.321228 | − | 0.947002i | \(-0.395905\pi\) | ||||
0.321228 | + | 0.947002i | \(0.395905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.17708 | −0.0732646 | −0.0366323 | − | 0.999329i | \(-0.511663\pi\) | ||||
−0.0366323 | + | 0.999329i | \(0.511663\pi\) | |||||||
\(884\) | −10.0540 | −0.338152 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.2614 | −0.445524 | ||||||||
\(887\) | 7.19224 | 0.241492 | 0.120746 | − | 0.992683i | \(-0.461471\pi\) | ||||
0.120746 | + | 0.992683i | \(0.461471\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.9309 | 0.735538 | ||||||||
\(890\) | 17.5616 | 0.588665 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.5227 | 0.352327 | ||||||||
\(893\) | 20.6307 | 0.690379 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.87689 | −0.163017 | ||||||||
\(896\) | 13.5616 | 0.453060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 43.8078 | 1.46188 | ||||||||
\(899\) | 55.1231 | 1.83846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.1922 | −1.07248 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.7775 | 0.724307 | ||||||||
\(905\) | 0.192236 | 0.00639014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.6307 | 0.618622 | 0.309311 | − | 0.950961i | \(-0.399902\pi\) | ||||
0.309311 | + | 0.950961i | \(0.399902\pi\) | |||||||
\(908\) | 2.49242 | 0.0827139 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.68466 | 0.287894 | ||||||||
\(911\) | 19.3693 | 0.641734 | 0.320867 | − | 0.947124i | \(-0.396026\pi\) | ||||
0.320867 | + | 0.947124i | \(0.396026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −16.5767 | −0.548309 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.83807 | −0.0607317 | ||||||||
\(917\) | 2.56155 | 0.0845899 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6155 | −0.383161 | −0.191580 | − | 0.981477i | \(-0.561361\pi\) | ||||
−0.191580 | + | 0.981477i | \(0.561361\pi\) | |||||||
\(920\) | −9.75379 | −0.321573 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.1922 | 0.533263 | ||||||||
\(923\) | 17.3693 | 0.571718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7386 | 0.353084 | ||||||||
\(926\) | −1.36932 | −0.0449985 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.3002 | 0.535080 | ||||||||
\(929\) | −2.50758 | −0.0822709 | −0.0411355 | − | 0.999154i | \(-0.513098\pi\) | ||||
−0.0411355 | + | 0.999154i | \(0.513098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | −11.9157 | −0.390312 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.9697 | −1.11152 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.93087 | 0.161084 | 0.0805422 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805422 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(938\) | 13.7538 | 0.449077 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.50758 | 0.0491718 | ||||||||
\(941\) | −28.4384 | −0.927067 | −0.463533 | − | 0.886079i | \(-0.653419\pi\) | ||||
−0.463533 | + | 0.886079i | \(0.653419\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.2462 | −0.984952 | ||||||||
\(944\) | −58.8466 | −1.91529 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.00000 | −0.0649913 | −0.0324956 | − | 0.999472i | \(-0.510346\pi\) | ||||
−0.0324956 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.6155 | 1.28597 | ||||||||
\(950\) | −37.4773 | −1.21592 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.0540 | −0.325851 | ||||||||
\(953\) | −43.6695 | −1.41459 | −0.707297 | − | 0.706917i | \(-0.750086\pi\) | ||||
−0.707297 | + | 0.706917i | \(0.750086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.2462 | −0.396278 | ||||||||
\(956\) | −8.49242 | −0.274665 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 46.3542 | 1.49763 | ||||||||
\(959\) | −14.0000 | −0.452084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.0000 | 1.19355 | ||||||||
\(962\) | −23.3153 | −0.751717 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.36932 | 0.172934 | ||||||||
\(965\) | −15.2462 | −0.490793 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.3002 | −0.620652 | −0.310326 | − | 0.950630i | \(-0.600438\pi\) | ||||
−0.310326 | + | 0.950630i | \(0.600438\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.05398 | 0.0659492 | ||||||||
\(971\) | −16.3153 | −0.523584 | −0.261792 | − | 0.965124i | \(-0.584313\pi\) | ||||
−0.261792 | + | 0.965124i | \(0.584313\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.24621 | 0.200244 | ||||||||
\(974\) | −30.3542 | −0.972610 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −62.6307 | −2.00476 | ||||||||
\(977\) | −57.6695 | −1.84501 | −0.922505 | − | 0.385984i | \(-0.873862\pi\) | ||||
−0.922505 | + | 0.385984i | \(0.873862\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.438447 | −0.0140057 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.2311 | −0.996623 | ||||||||
\(983\) | 6.63068 | 0.211486 | 0.105743 | − | 0.994393i | \(-0.466278\pi\) | ||||
0.105743 | + | 0.994393i | \(0.466278\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.1771 | −0.865934 | ||||||||
\(986\) | −43.0388 | −1.37064 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.6307 | 0.465464 | ||||||||
\(989\) | 22.7386 | 0.723046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.8617 | 1.96510 | 0.982551 | − | 0.185991i | \(-0.0595495\pi\) | ||||
0.982551 | + | 0.185991i | \(0.0595495\pi\) | |||||||
\(992\) | 20.1080 | 0.638428 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.87689 | −0.154686 | ||||||||
\(995\) | 7.12311 | 0.225818 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0388 | 1.29971 | 0.649856 | − | 0.760057i | \(-0.274829\pi\) | ||||
0.649856 | + | 0.760057i | \(0.274829\pi\) | |||||||
\(998\) | 61.7538 | 1.95478 | ||||||||
\(999\) | 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 | 7623.2.a.bt.1.1 | 2 | ||
3.2 | odd | 2 | 2541.2.a.u.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 7623.2.a.be.1.2 | 2 | |||
33.32 | even | 2 | 2541.2.a.bc.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.u.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
2541.2.a.bc.1.1 | yes | 2 | 33.32 | even | 2 | ||
7623.2.a.be.1.2 | 2 | 11.10 | odd | 2 | |||
7623.2.a.bt.1.1 | 2 | 1.1 | even | 1 | trivial |