Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.195727752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 15x^{4} - 25x^{3} - 3x^{2} + 9x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.33297\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.15496 | 1.19246 | 0.596231 | − | 0.802813i | \(-0.296664\pi\) | ||||
0.596231 | + | 0.802813i | \(0.296664\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.98752 | 0.900772 | 0.450386 | − | 0.892834i | \(-0.351286\pi\) | ||||
0.450386 | + | 0.892834i | \(0.351286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.285913 | 0.0792980 | 0.0396490 | − | 0.999214i | \(-0.487376\pi\) | ||||
0.0396490 | + | 0.999214i | \(0.487376\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.60830 | 0.875142 | 0.437571 | − | 0.899184i | \(-0.355839\pi\) | ||||
0.437571 | + | 0.899184i | \(0.355839\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.827332 | −0.189803 | −0.0949014 | − | 0.995487i | \(-0.530254\pi\) | ||||
−0.0949014 | + | 0.995487i | \(0.530254\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.15496 | 0.688468 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.54034 | 1.78078 | 0.890392 | − | 0.455195i | \(-0.150431\pi\) | ||||
0.890392 | + | 0.455195i | \(0.150431\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.01509 | −1.30267 | −0.651335 | − | 0.758790i | \(-0.725791\pi\) | ||||
−0.651335 | + | 0.758790i | \(0.725791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.11929 | −0.919452 | −0.459726 | − | 0.888061i | \(-0.652052\pi\) | ||||
−0.459726 | + | 0.888061i | \(0.652052\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.98752 | 0.520061 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.15496 | −0.533285 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.86013 | 1.29220 | 0.646099 | − | 0.763254i | \(-0.276399\pi\) | ||||
0.646099 | + | 0.763254i | \(0.276399\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.285913 | 0.0457827 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.299088 | −0.0467097 | −0.0233549 | − | 0.999727i | \(-0.507435\pi\) | ||||
−0.0233549 | + | 0.999727i | \(0.507435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.325033 | −0.0495671 | −0.0247835 | − | 0.999693i | \(-0.507890\pi\) | ||||
−0.0247835 | + | 0.999693i | \(0.507890\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.94740 | 1.01338 | 0.506691 | − | 0.862128i | \(-0.330869\pi\) | ||||
0.506691 | + | 0.862128i | \(0.330869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.95375 | 0.421964 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.60830 | 0.505263 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00050 | −1.09895 | −0.549477 | − | 0.835509i | \(-0.685173\pi\) | ||||
−0.549477 | + | 0.835509i | \(0.685173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.98752 | −0.402838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.827332 | −0.109583 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.59664 | −0.988998 | −0.494499 | − | 0.869178i | \(-0.664648\pi\) | ||||
−0.494499 | + | 0.869178i | \(0.664648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.05522 | −0.903328 | −0.451664 | − | 0.892188i | \(-0.649169\pi\) | ||||
−0.451664 | + | 0.892188i | \(0.649169\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.15496 | 0.397487 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.285913 | −0.0354631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.54034 | 1.02814 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9890 | 1.77887 | 0.889436 | − | 0.457061i | \(-0.151098\pi\) | ||||
0.889436 | + | 0.457061i | \(0.151098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.66984 | −0.663604 | −0.331802 | − | 0.943349i | \(-0.607657\pi\) | ||||
−0.331802 | + | 0.943349i | \(0.607657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.42551 | 1.07414 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.40186 | −0.157722 | −0.0788609 | − | 0.996886i | \(-0.525128\pi\) | ||||
−0.0788609 | + | 0.996886i | \(0.525128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.16743 | 0.457435 | 0.228718 | − | 0.973493i | \(-0.426547\pi\) | ||||
0.228718 | + | 0.973493i | \(0.426547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.60830 | −0.391375 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.01509 | −0.752097 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.37544 | 0.463796 | 0.231898 | − | 0.972740i | \(-0.425506\pi\) | ||||
0.231898 | + | 0.972740i | \(0.425506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.902043 | 0.0945598 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.11929 | −0.530846 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.827332 | 0.0848824 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52023 | 0.357425 | 0.178713 | − | 0.983901i | \(-0.442807\pi\) | ||||
0.178713 | + | 0.983901i | \(0.442807\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.98752 | 0.300257 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.93919 | −0.889482 | −0.444741 | − | 0.895659i | \(-0.646704\pi\) | ||||
−0.444741 | + | 0.895659i | \(0.646704\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5575 | 1.13880 | 0.569398 | − | 0.822062i | \(-0.307176\pi\) | ||||
0.569398 | + | 0.822062i | \(0.307176\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.15496 | −0.307892 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.378522 | 0.0365931 | 0.0182966 | − | 0.999833i | \(-0.494176\pi\) | ||||
0.0182966 | + | 0.999833i | \(0.494176\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.16387 | 0.398827 | 0.199413 | − | 0.979915i | \(-0.436096\pi\) | ||||
0.199413 | + | 0.979915i | \(0.436096\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.86013 | 0.746051 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.08719 | −0.290418 | −0.145209 | − | 0.989401i | \(-0.546385\pi\) | ||||
−0.145209 | + | 0.989401i | \(0.546385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.54034 | −0.796391 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.285913 | 0.0264327 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3840 | 1.04357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.07470 | −0.188609 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.299088 | −0.0269679 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.16100 | −0.457965 | −0.228983 | − | 0.973431i | \(-0.573540\pi\) | ||||
−0.228983 | + | 0.973431i | \(0.573540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.325033 | −0.0286176 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.2863 | 1.77243 | 0.886213 | − | 0.463278i | \(-0.153327\pi\) | ||||
0.886213 | + | 0.463278i | \(0.153327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.61020 | −0.226333 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.78286 | 0.323192 | 0.161596 | − | 0.986857i | \(-0.448336\pi\) | ||||
0.161596 | + | 0.986857i | \(0.448336\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.25651 | −0.191395 | −0.0956975 | − | 0.995410i | \(-0.530508\pi\) | ||||
−0.0956975 | + | 0.995410i | \(0.530508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.94740 | 0.585076 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.854172 | 0.0714294 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.01509 | 0.582572 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.95375 | 0.243621 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5973 | 0.868163 | 0.434082 | − | 0.900874i | \(-0.357073\pi\) | ||||
0.434082 | + | 0.900874i | \(0.357073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.20194 | −0.667465 | −0.333732 | − | 0.942668i | \(-0.608308\pi\) | ||||
−0.333732 | + | 0.942668i | \(0.608308\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.60830 | 0.291714 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.11929 | 0.411191 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.3258 | −1.62218 | −0.811088 | − | 0.584924i | \(-0.801124\pi\) | ||||
−0.811088 | + | 0.584924i | \(0.801124\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.00050 | −0.634481 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.9444 | 2.12352 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.7073 | −0.838660 | −0.419330 | − | 0.907834i | \(-0.637735\pi\) | ||||
−0.419330 | + | 0.907834i | \(0.637735\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.98752 | −0.232578 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.8494 | 1.84552 | 0.922760 | − | 0.385376i | \(-0.125928\pi\) | ||||
0.922760 | + | 0.385376i | \(0.125928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9183 | −0.993712 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.827332 | −0.0632676 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.7835 | 1.42808 | 0.714042 | − | 0.700103i | \(-0.246863\pi\) | ||||
0.714042 | + | 0.700103i | \(0.246863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.15496 | 0.238492 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.59664 | −0.570998 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.89439 | −0.216337 | −0.108168 | − | 0.994133i | \(-0.534499\pi\) | ||||
−0.108168 | + | 0.994133i | \(0.534499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.61165 | 0.565769 | 0.282885 | − | 0.959154i | \(-0.408709\pi\) | ||||
0.282885 | + | 0.959154i | \(0.408709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.05522 | −0.521537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.86013 | −0.577889 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7799 | 0.788304 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.15496 | 0.229489 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.14590 | 0.227629 | 0.113815 | − | 0.993502i | \(-0.463693\pi\) | ||||
0.113815 | + | 0.993502i | \(0.463693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.62036 | −0.692489 | −0.346244 | − | 0.938144i | \(-0.612543\pi\) | ||||
−0.346244 | + | 0.938144i | \(0.612543\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.285913 | −0.0204747 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.2285 | −1.44122 | −0.720612 | − | 0.693339i | \(-0.756139\pi\) | ||||
−0.720612 | + | 0.693339i | \(0.756139\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.64854 | 0.258638 | 0.129319 | − | 0.991603i | \(-0.458721\pi\) | ||||
0.129319 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.1323 | −1.55338 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.299088 | 0.0208892 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.54034 | 0.593594 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.47167 | −0.170969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.82327 | −0.538576 | −0.269288 | − | 0.963060i | \(-0.586788\pi\) | ||||
−0.269288 | + | 0.963060i | \(0.586788\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.9890 | 1.02703 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.325033 | 0.0221671 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.1511 | −1.09641 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.66984 | −0.383132 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.03166 | 0.0693970 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.55347 | 0.170993 | 0.0854966 | − | 0.996338i | \(-0.472752\pi\) | ||||
0.0854966 | + | 0.996338i | \(0.472752\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.2142 | 1.34167 | 0.670833 | − | 0.741608i | \(-0.265937\pi\) | ||||
0.670833 | + | 0.741608i | \(0.265937\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.86312 | 0.255282 | 0.127641 | − | 0.991820i | \(-0.459259\pi\) | ||||
0.127641 | + | 0.991820i | \(0.459259\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.42551 | 0.620153 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.98051 | 0.195260 | 0.0976298 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976298 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.94740 | −0.453198 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.40186 | −0.0910607 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.31022 | 0.472859 | 0.236429 | − | 0.971649i | \(-0.424023\pi\) | ||||
0.236429 | + | 0.971649i | \(0.424023\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.4246 | 1.63774 | 0.818871 | − | 0.573978i | \(-0.194600\pi\) | ||||
0.818871 | + | 0.573978i | \(0.194600\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.95375 | −0.188708 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.236545 | −0.0150510 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.16743 | 0.264100 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.6780 | −1.87326 | −0.936630 | − | 0.350321i | \(-0.886073\pi\) | ||||
−0.936630 | + | 0.350321i | \(0.886073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.5145 | 1.60408 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.60830 | −0.225961 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6045 | 1.09814 | 0.549068 | − | 0.835778i | \(-0.314983\pi\) | ||||
0.549068 | + | 0.835778i | \(0.314983\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.7984 | 1.54090 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.01509 | −0.434223 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.47086 | 0.460673 | 0.230337 | − | 0.973111i | \(-0.426017\pi\) | ||||
0.230337 | + | 0.973111i | \(0.426017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00050 | 0.491467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.37544 | 0.267773 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.84115 | 0.112257 | 0.0561285 | − | 0.998424i | \(-0.482124\pi\) | ||||
0.0561285 | + | 0.998424i | \(0.482124\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6863 | 0.831386 | 0.415693 | − | 0.909505i | \(-0.363539\pi\) | ||||
0.415693 | + | 0.909505i | \(0.363539\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.902043 | 0.0545941 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.98752 | 0.180154 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.01952 | 0.421762 | 0.210881 | − | 0.977512i | \(-0.432367\pi\) | ||||
0.210881 | + | 0.977512i | \(0.432367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.11929 | −0.306484 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.76047 | 0.343641 | 0.171820 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171820 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.2822 | 1.68120 | 0.840601 | − | 0.541655i | \(-0.182202\pi\) | ||||
0.840601 | + | 0.541655i | \(0.182202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.827332 | 0.0490069 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.943611 | −0.0556996 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.98015 | −0.234127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.52023 | 0.206360 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.17258 | 0.535868 | 0.267934 | − | 0.963437i | \(-0.413659\pi\) | ||||
0.267934 | + | 0.963437i | \(0.413659\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.59664 | 0.442293 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.98752 | 0.173354 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.44179 | 0.141213 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.02547 | −0.0591068 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.93919 | −0.513543 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.05522 | 0.403981 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.81781 | −0.332040 | −0.166020 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166020 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.5575 | 0.657484 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.795437 | −0.0451051 | −0.0225525 | − | 0.999746i | \(-0.507179\pi\) | ||||
−0.0225525 | + | 0.999746i | \(0.507179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.8364 | −1.46036 | −0.730181 | − | 0.683254i | \(-0.760564\pi\) | ||||
−0.730181 | + | 0.683254i | \(0.760564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.15496 | −0.177762 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.0724 | 1.12738 | 0.563688 | − | 0.825987i | \(-0.309382\pi\) | ||||
0.563688 | + | 0.825987i | \(0.309382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.9578 | −1.17341 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.378522 | 0.0211271 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.98526 | −0.166104 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.285913 | 0.0158596 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.16387 | 0.230263 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.9187 | 1.20842 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6748 | −1.35625 | −0.678126 | − | 0.734946i | \(-0.737207\pi\) | ||||
−0.678126 | + | 0.734946i | \(0.737207\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.86013 | 0.430733 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.95874 | 0.488014 | 0.244007 | − | 0.969774i | \(-0.421538\pi\) | ||||
0.244007 | + | 0.969774i | \(0.421538\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.08719 | −0.167673 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.2940 | −0.828217 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.7657 | −0.689285 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.54034 | −0.459796 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.7693 | −1.06127 | −0.530635 | − | 0.847601i | \(-0.678046\pi\) | ||||
−0.530635 | + | 0.847601i | \(0.678046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1902 | −0.545470 | −0.272735 | − | 0.962089i | \(-0.587928\pi\) | ||||
−0.272735 | + | 0.962089i | \(0.587928\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.285913 | 0.0152609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.2854 | −1.07968 | −0.539842 | − | 0.841767i | \(-0.681516\pi\) | ||||
−0.539842 | + | 0.841767i | \(0.681516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.9890 | −0.795535 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.3840 | 0.602507 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.6854 | −1.25007 | −0.625034 | − | 0.780598i | \(-0.714915\pi\) | ||||
−0.625034 | + | 0.780598i | \(0.714915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3155 | −0.963975 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.07470 | −0.108894 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.66984 | 0.296773 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.98082 | 0.520994 | 0.260497 | − | 0.965475i | \(-0.416114\pi\) | ||||
0.260497 | + | 0.965475i | \(0.416114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.299088 | −0.0155699 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.2412 | −1.31046 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.8677 | −1.13227 | −0.566133 | − | 0.824314i | \(-0.691561\pi\) | ||||
−0.566133 | + | 0.824314i | \(0.691561\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00571 | −0.103299 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.2895 | 0.631270 | 0.315635 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315635 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.16100 | −0.264406 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.13827 | −0.364749 | −0.182374 | − | 0.983229i | \(-0.558378\pi\) | ||||
−0.182374 | + | 0.983229i | \(0.558378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.42551 | −0.480368 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.325033 | −0.0165224 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.63393 | −0.488459 | −0.244230 | − | 0.969717i | \(-0.578535\pi\) | ||||
−0.244230 | + | 0.969717i | \(0.578535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.8161 | 1.55844 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.2863 | 1.02331 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.40186 | 0.0705353 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3923 | 1.52534 | 0.762672 | − | 0.646786i | \(-0.223887\pi\) | ||||
0.762672 | + | 0.646786i | \(0.223887\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.61020 | −0.130673 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.1718 | −1.40683 | −0.703415 | − | 0.710779i | \(-0.748343\pi\) | ||||
−0.703415 | + | 0.710779i | \(0.748343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.46367 | −0.0729107 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.4823 | 1.16398 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.98115 | 0.196855 | 0.0984275 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984275 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.78286 | 0.186595 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.9671 | −1.17934 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.16743 | −0.204571 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.25651 | −0.110502 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.5070 | 0.562152 | 0.281076 | − | 0.959686i | \(-0.409309\pi\) | ||||
0.281076 | + | 0.959686i | \(0.409309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00861 | −0.292842 | −0.146421 | − | 0.989222i | \(-0.546775\pi\) | ||||
−0.146421 | + | 0.989222i | \(0.546775\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.94740 | 0.337794 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.60830 | 0.175028 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.2589 | −1.07718 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.854172 | 0.0412398 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.782291 | 0.0376816 | 0.0188408 | − | 0.999822i | \(-0.494002\pi\) | ||||
0.0188408 | + | 0.999822i | \(0.494002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.2474 | −1.35748 | −0.678742 | − | 0.734376i | \(-0.737475\pi\) | ||||
−0.678742 | + | 0.734376i | \(0.737475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.01509 | 0.336348 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.06569 | −0.337998 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5072 | −0.644664 | −0.322332 | − | 0.946627i | \(-0.604467\pi\) | ||||
−0.322332 | + | 0.946627i | \(0.604467\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.95375 | 0.140655 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.7621 | −1.79413 | −0.897066 | − | 0.441897i | \(-0.854306\pi\) | ||||
−0.897066 | + | 0.441897i | \(0.854306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.37544 | −0.207416 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5973 | 0.501234 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.5523 | 1.91378 | 0.956890 | − | 0.290452i | \(-0.0938056\pi\) | ||||
0.956890 | + | 0.290452i | \(0.0938056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.893533 | −0.0420748 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.20194 | −0.385361 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.902043 | −0.0422884 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.83602 | 0.0858855 | 0.0429427 | − | 0.999078i | \(-0.486327\pi\) | ||||
0.0429427 | + | 0.999078i | \(0.486327\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.60830 | 0.168421 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.1909 | 0.521213 | 0.260606 | − | 0.965445i | \(-0.416078\pi\) | ||||
0.260606 | + | 0.965445i | \(0.416078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.88392 | −0.226975 | −0.113488 | − | 0.993539i | \(-0.536202\pi\) | ||||
−0.113488 | + | 0.993539i | \(0.536202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.11929 | 0.237401 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.42945 | −0.251245 | −0.125622 | − | 0.992078i | \(-0.540093\pi\) | ||||
−0.125622 | + | 0.992078i | \(0.540093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.15496 | 0.145682 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.3258 | −0.936564 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.971044 | −0.0446487 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.827332 | −0.0379606 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.00050 | −0.366318 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.0597 | −1.32777 | −0.663886 | − | 0.747834i | \(-0.731094\pi\) | ||||
−0.663886 | + | 0.747834i | \(0.731094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.24731 | 0.102469 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.9444 | 1.22601 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.52023 | −0.159845 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.6239 | −0.798614 | −0.399307 | − | 0.916817i | \(-0.630749\pi\) | ||||
−0.399307 | + | 0.916817i | \(0.630749\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7073 | −0.484200 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2557 | 0.598219 | 0.299110 | − | 0.954219i | \(-0.403310\pi\) | ||||
0.299110 | + | 0.954219i | \(0.403310\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.3126 | −1.14002 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.98752 | −0.134279 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.2898 | 2.12124 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.82162 | 0.394910 | 0.197455 | − | 0.980312i | \(-0.436732\pi\) | ||||
0.197455 | + | 0.980312i | \(0.436732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.8494 | 1.06551 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.7640 | −1.19335 | −0.596674 | − | 0.802484i | \(-0.703511\pi\) | ||||
−0.596674 | + | 0.802484i | \(0.703511\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.93919 | 0.397789 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9183 | −0.573720 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.2099 | −0.585520 | −0.292760 | − | 0.956186i | \(-0.594574\pi\) | ||||
−0.292760 | + | 0.956186i | \(0.594574\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.8881 | −0.791323 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.827332 | −0.0365276 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.5575 | −0.509285 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7555 | 0.912826 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.7835 | 0.824505 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.07464 | −0.0908915 | −0.0454458 | − | 0.998967i | \(-0.514471\pi\) | ||||
−0.0454458 | + | 0.998967i | \(0.514471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0122 | −0.875072 | −0.437536 | − | 0.899201i | \(-0.644149\pi\) | ||||
−0.437536 | + | 0.899201i | \(0.644149\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.15496 | 0.137694 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.4720 | −0.804651 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.9374 | 2.17119 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.59664 | −0.329666 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0855132 | −0.00370399 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.378522 | −0.0163649 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.89439 | −0.124902 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.82440 | 0.380094 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.3776 | 0.919097 | 0.459548 | − | 0.888153i | \(-0.348011\pi\) | ||||
0.459548 | + | 0.888153i | \(0.348011\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.61165 | 0.326647 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.16387 | −0.178361 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.86325 | −0.421722 | −0.210861 | − | 0.977516i | \(-0.567627\pi\) | ||||
−0.210861 | + | 0.977516i | \(0.567627\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.05522 | −0.301109 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.80381 | 0.247250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.42281 | −0.188077 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.86013 | −0.333644 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.0273 | 0.890955 | 0.445478 | − | 0.895293i | \(-0.353034\pi\) | ||||
0.445478 | + | 0.895293i | \(0.353034\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0929312 | −0.00393057 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.7799 | 0.455127 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.9495 | 0.714337 | 0.357169 | − | 0.934040i | \(-0.383742\pi\) | ||||
0.357169 | + | 0.934040i | \(0.383742\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.08719 | 0.129879 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.15496 | 0.132496 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.64662 | −0.362485 | −0.181243 | − | 0.983438i | \(-0.558012\pi\) | ||||
−0.181243 | + | 0.983438i | \(0.558012\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.7902 | −1.49777 | −0.748887 | − | 0.662698i | \(-0.769411\pi\) | ||||
−0.748887 | + | 0.662698i | \(0.769411\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.14590 | 0.131422 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.54034 | 0.356157 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.73298 | −0.197037 | −0.0985183 | − | 0.995135i | \(-0.531410\pi\) | ||||
−0.0985183 | + | 0.995135i | \(0.531410\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.62036 | −0.399808 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.1481 | 0.545474 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.9017 | −0.989907 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.285913 | −0.0118210 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.7594 | 1.59977 | 0.799886 | − | 0.600151i | \(-0.204893\pi\) | ||||
0.799886 | + | 0.600151i | \(0.204893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.23535 | 0.174515 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.2285 | −0.832091 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.562880 | 0.0231147 | 0.0115574 | − | 0.999933i | \(-0.496321\pi\) | ||||
0.0115574 | + | 0.999933i | \(0.496321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.3840 | −0.466700 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.64854 | 0.149325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.8815 | 1.09835 | 0.549174 | − | 0.835708i | \(-0.314943\pi\) | ||||
0.549174 | + | 0.835708i | \(0.314943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.1263 | 1.43283 | 0.716416 | − | 0.697673i | \(-0.245781\pi\) | ||||
0.716416 | + | 0.697673i | \(0.245781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.07470 | 0.0843486 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.9876 | 0.689506 | 0.344753 | − | 0.938693i | \(-0.387963\pi\) | ||||
0.344753 | + | 0.938693i | \(0.387963\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.1323 | −0.896846 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.98635 | 0.0803591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.17805 | 0.168750 | 0.0843750 | − | 0.996434i | \(-0.473111\pi\) | ||||
0.0843750 | + | 0.996434i | \(0.473111\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.299088 | 0.0120604 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.7969 | −1.72294 | −0.861469 | − | 0.507810i | \(-0.830455\pi\) | ||||
−0.861469 | + | 0.507810i | \(0.830455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.4662 | −1.38531 | −0.692656 | − | 0.721268i | \(-0.743560\pi\) | ||||
−0.692656 | + | 0.721268i | \(0.743560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.54034 | 0.342712 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8043 | 0.553059 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.47167 | −0.0987091 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.3617 | 1.13086 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.5909 | −1.25762 | −0.628808 | − | 0.777561i | \(-0.716457\pi\) | ||||
−0.628808 | + | 0.777561i | \(0.716457\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.82327 | −0.310947 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.16100 | 0.204808 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.844516 | 0.0334609 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.9890 | 0.592957 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.9149 | 1.65554 | 0.827770 | − | 0.561068i | \(-0.189609\pi\) | ||||
0.827770 | + | 0.561068i | \(0.189609\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.2476 | −1.86326 | −0.931631 | − | 0.363405i | \(-0.881614\pi\) | ||||
−0.931631 | + | 0.363405i | \(0.881614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.325033 | 0.0127982 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.69644 | 0.184636 | 0.0923181 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923181 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.6951 | −0.890862 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.1511 | −0.633013 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.0808 | 0.433625 | 0.216813 | − | 0.976213i | \(-0.430434\pi\) | ||||
0.216813 | + | 0.976213i | \(0.430434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.2863 | −0.792653 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.66984 | −0.221201 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.6262 | 0.530801 | 0.265401 | − | 0.964138i | \(-0.414496\pi\) | ||||
0.265401 | + | 0.964138i | \(0.414496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.1582 | 1.44529 | 0.722643 | − | 0.691221i | \(-0.242927\pi\) | ||||
0.722643 | + | 0.691221i | \(0.242927\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.03166 | 0.0400664 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.61020 | 0.101219 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −59.9112 | −2.31977 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.55347 | 0.0987230 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0776 | −0.813693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.8829 | −1.34464 | −0.672319 | − | 0.740262i | \(-0.734702\pi\) | ||||
−0.672319 | + | 0.740262i | \(0.734702\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.33989 | −0.166796 | −0.0833978 | − | 0.996516i | \(-0.526577\pi\) | ||||
−0.0833978 | + | 0.996516i | \(0.526577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.1062 | 0.426216 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.2142 | 0.774611 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.8172 | −1.56183 | −0.780913 | − | 0.624640i | \(-0.785246\pi\) | ||||
−0.780913 | + | 0.624640i | \(0.785246\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.78286 | −0.144536 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.86312 | 0.147387 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.28745 | −0.0871448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.7801 | 0.600303 | 0.300151 | − | 0.953892i | \(-0.402963\pi\) | ||||
0.300151 | + | 0.953892i | \(0.402963\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.42551 | 0.358045 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.25651 | 0.0855944 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.07920 | −0.0408777 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.98051 | 0.112733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.0045 | −0.982177 | −0.491088 | − | 0.871110i | \(-0.663401\pi\) | ||||
−0.491088 | + | 0.871110i | \(0.663401\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.50294 | −0.245263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.94740 | −0.261654 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.2027 | −1.06067 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.80831 | −0.255691 | −0.127846 | − | 0.991794i | \(-0.540806\pi\) | ||||
−0.127846 | + | 0.991794i | \(0.540806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.40186 | −0.0525739 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.7205 | −1.63734 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.854172 | −0.0319442 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.31022 | 0.273005 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.8383 | −1.18737 | −0.593684 | − | 0.804698i | \(-0.702327\pi\) | ||||
−0.593684 | + | 0.804698i | \(0.702327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.4635 | 1.35797 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.4246 | 0.945551 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.01509 | −0.260534 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.7120 | 0.990694 | 0.495347 | − | 0.868695i | \(-0.335041\pi\) | ||||
0.495347 | + | 0.868695i | \(0.335041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.17282 | −0.0433782 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.50114 | 0.277061 | 0.138530 | − | 0.990358i | \(-0.455762\pi\) | ||||
0.138530 | + | 0.990358i | \(0.455762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.95375 | −0.108951 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.98752 | 0.110047 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.5034 | −1.71066 | −0.855328 | − | 0.518087i | \(-0.826644\pi\) | ||||
−0.855328 | + | 0.518087i | \(0.826644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.236545 | −0.00868969 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.8678 | −0.765567 | −0.382783 | − | 0.923838i | \(-0.625034\pi\) | ||||
−0.382783 | + | 0.923838i | \(0.625034\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5973 | −0.388254 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.16743 | 0.152478 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.19422 | 0.0436359 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7525 | 0.720779 | 0.360390 | − | 0.932802i | \(-0.382644\pi\) | ||||
0.360390 | + | 0.932802i | \(0.382644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.6780 | −1.08153 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.20194 | 0.298499 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5601 | −0.819961 | −0.409981 | − | 0.912094i | \(-0.634465\pi\) | ||||
−0.409981 | + | 0.912094i | \(0.634465\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.5145 | 0.926116 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.24842 | 0.154005 | 0.0770026 | − | 0.997031i | \(-0.475465\pi\) | ||||
0.0770026 | + | 0.997031i | \(0.475465\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.1368 | 0.475585 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.60830 | −0.130458 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.17198 | −0.0784255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.1223 | 0.725627 | 0.362814 | − | 0.931862i | \(-0.381816\pi\) | ||||
0.362814 | + | 0.931862i | \(0.381816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6045 | 0.634009 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.02404 | −0.180702 | −0.0903511 | − | 0.995910i | \(-0.528799\pi\) | ||||
−0.0903511 | + | 0.995910i | \(0.528799\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.11929 | −0.183890 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.7984 | 0.889637 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.247445 | 0.00886564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.7801 | 1.60236 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.01509 | −0.250699 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.3258 | 0.725459 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.10979 | 0.182144 | 0.0910721 | − | 0.995844i | \(-0.470971\pi\) | ||||
0.0910721 | + | 0.995844i | \(0.470971\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.47086 | 0.265970 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.73994 | −0.346313 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.01718 | −0.0716321 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.00050 | 0.283749 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.3566 | −1.25239 | −0.626197 | − | 0.779665i | \(-0.715389\pi\) | ||||
−0.626197 | + | 0.779665i | \(0.715389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.0683 | 0.886853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.37544 | 0.154599 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.9388 | −0.597756 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.9444 | −0.949665 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.84115 | 0.0648116 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.85483 | 0.311319 | 0.155660 | − | 0.987811i | \(-0.450250\pi\) | ||||
0.155660 | + | 0.987811i | \(0.450250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.8145 | −0.906471 | −0.453236 | − | 0.891391i | \(-0.649730\pi\) | ||||
−0.453236 | + | 0.891391i | \(0.649730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.6863 | 0.480001 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.7073 | 0.375060 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.268910 | 0.00940798 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.902043 | 0.0315199 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2283 | 0.671073 | 0.335536 | − | 0.942027i | \(-0.391082\pi\) | ||||
0.335536 | + | 0.942027i | \(0.391082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.1086 | 1.57239 | 0.786193 | − | 0.617981i | \(-0.212049\pi\) | ||||
0.786193 | + | 0.617981i | \(0.212049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.98752 | 0.104012 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6280 | 0.369573 | 0.184787 | − | 0.982779i | \(-0.440841\pi\) | ||||
0.184787 | + | 0.982779i | \(0.440841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.25278 | 0.0435110 | 0.0217555 | − | 0.999763i | \(-0.493074\pi\) | ||||
0.0217555 | + | 0.999763i | \(0.493074\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.01952 | 0.243504 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.6580 | 0.369279 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.8494 | −0.825341 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.11929 | −0.176949 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.38362 | 0.151339 | 0.0756696 | − | 0.997133i | \(-0.475891\pi\) | ||||
0.0756696 | + | 0.997133i | \(0.475891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.2115 | 0.696948 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.76047 | 0.198401 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.9183 | 0.444401 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.54559 | −0.224909 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.2822 | 0.970642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.1282 | 2.30113 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.7363 | −0.607280 | −0.303640 | − | 0.952787i | \(-0.598202\pi\) | ||||
−0.303640 | + | 0.952787i | \(0.598202\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.827332 | 0.0282941 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.03497 | 0.308629 | 0.154314 | − | 0.988022i | \(-0.450683\pi\) | ||||
0.154314 | + | 0.988022i | \(0.450683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.9596 | −1.29516 | −0.647582 | − | 0.761996i | \(-0.724220\pi\) | ||||
−0.647582 | + | 0.761996i | \(0.724220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.943611 | −0.0321582 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.6735 | −0.942017 | −0.471008 | − | 0.882129i | \(-0.656110\pi\) | ||||
−0.471008 | + | 0.882129i | \(0.656110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7835 | −0.638659 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.98015 | −0.135173 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.18809 | −0.142071 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.285913 | 0.00968779 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.52023 | 0.119142 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.15496 | −0.106657 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.1259 | −0.814673 | −0.407337 | − | 0.913278i | \(-0.633542\pi\) | ||||
−0.407337 | + | 0.913278i | \(0.633542\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.17258 | 0.309383 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.512416 | 0.0172637 | 0.00863187 | − | 0.999963i | \(-0.497252\pi\) | ||||
0.00863187 | + | 0.999963i | \(0.497252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.3694 | −1.05567 | −0.527833 | − | 0.849348i | \(-0.676995\pi\) | ||||
−0.527833 | + | 0.849348i | \(0.676995\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.59664 | 0.255358 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.1787 | 0.946148 | 0.473074 | − | 0.881023i | \(-0.343144\pi\) | ||||
0.473074 | + | 0.881023i | \(0.343144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.2827 | −0.546106 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.98752 | 0.100086 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.74780 | −0.192343 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.89439 | 0.0967487 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.44179 | 0.0815291 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.9123 | 1.19774 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.8682 | −0.961740 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.02547 | −0.0341254 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.61165 | −0.253020 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.52920 | 0.117185 | 0.0585926 | − | 0.998282i | \(-0.481339\pi\) | ||||
0.0585926 | + | 0.998282i | \(0.481339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.93919 | −0.296494 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.394566 | −0.0130726 | −0.00653628 | − | 0.999979i | \(-0.502081\pi\) | ||||
−0.00653628 | + | 0.999979i | \(0.502081\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.4503 | 0.412045 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.05522 | 0.233238 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 64.0025 | 2.11355 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.3198 | −1.06613 | −0.533066 | − | 0.846074i | \(-0.678960\pi\) | ||||
−0.533066 | + | 0.846074i | \(0.678960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.81781 | −0.191703 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.28556 | 0.141061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.86013 | 0.258440 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.5575 | 0.379599 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.0133 | −0.820661 | −0.410330 | − | 0.911937i | \(-0.634587\pi\) | ||||
−0.410330 | + | 0.911937i | \(0.634587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.44373 | −0.0800901 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.795437 | −0.0260414 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.7799 | −0.352540 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.2156 | −0.431733 | −0.215867 | − | 0.976423i | \(-0.569258\pi\) | ||||
−0.215867 | + | 0.976423i | \(0.569258\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.8364 | −0.843140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.6504 | −0.966574 | −0.483287 | − | 0.875462i | \(-0.660557\pi\) | ||||
−0.483287 | + | 0.875462i | \(0.660557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.55432 | −0.0831799 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.15496 | −0.102631 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7923 | 0.643162 | 0.321581 | − | 0.946882i | \(-0.395786\pi\) | ||||
0.321581 | + | 0.946882i | \(0.395786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.62108 | −0.0526225 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.0724 | 0.650891 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.2637 | −1.40145 | −0.700724 | − | 0.713432i | \(-0.747140\pi\) | ||||
−0.700724 | + | 0.713432i | \(0.747140\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.14590 | −0.101799 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.9578 | −0.677468 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.9348 | 0.385394 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.79286 | −0.154608 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.378522 | 0.0121977 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.62036 | 0.309690 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.1463 | −0.615703 | −0.307852 | − | 0.951434i | \(-0.599610\pi\) | ||||
−0.307852 | + | 0.951434i | \(0.599610\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.98526 | −0.0959004 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.8352 | −1.53510 | −0.767552 | − | 0.640987i | \(-0.778525\pi\) | ||||
−0.767552 | + | 0.640987i | \(0.778525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.11920 | −0.228231 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.285913 | 0.00915654 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.2324 | −1.19117 | −0.595585 | − | 0.803292i | \(-0.703080\pi\) | ||||
−0.595585 | + | 0.803292i | \(0.703080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.0717 | 0.417774 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.16387 | 0.132942 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −60.4931 | −1.92943 | −0.964715 | − | 0.263297i | \(-0.915190\pi\) | ||||
−0.964715 | + | 0.263297i | \(0.915190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.2285 | 0.644535 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.9187 | 0.697681 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.77589 | −0.0882683 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.9987 | −0.794111 | −0.397055 | − | 0.917795i | \(-0.629968\pi\) | ||||
−0.397055 | + | 0.917795i | \(0.629968\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.6748 | −0.783032 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.64854 | −0.115667 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.9031 | −1.35875 | −0.679377 | − | 0.733789i | \(-0.737750\pi\) | ||||
−0.679377 | + | 0.733789i | \(0.737750\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.86013 | 0.248684 |
(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 | 4020.2.a.g.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.g.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial |