Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(1,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, 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("2070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.43163\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.08719 | 1.16685 | 0.583424 | − | 0.812168i | \(-0.301713\pi\) | ||||
0.583424 | + | 0.812168i | \(0.301713\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 6.46926 | 1.95056 | 0.975278 | − | 0.220983i | \(-0.0709265\pi\) | ||||
0.975278 | + | 0.220983i | \(0.0709265\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.95044 | 1.09566 | 0.547828 | − | 0.836591i | \(-0.315455\pi\) | ||||
0.547828 | + | 0.836591i | \(0.315455\pi\) | |||||||
\(14\) | −3.08719 | −0.825086 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.43163 | 0.832292 | 0.416146 | − | 0.909298i | \(-0.363381\pi\) | ||||
0.416146 | + | 0.909298i | \(0.363381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.08719 | 0.708250 | 0.354125 | − | 0.935198i | \(-0.384779\pi\) | ||||
0.354125 | + | 0.935198i | \(0.384779\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.46926 | −1.37925 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.95044 | −0.774746 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.08719 | 0.583424 | ||||||||
\(29\) | −0.863254 | −0.160302 | −0.0801511 | − | 0.996783i | \(-0.525540\pi\) | ||||
−0.0801511 | + | 0.996783i | \(0.525540\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.95044 | −1.06873 | −0.534366 | − | 0.845253i | \(-0.679449\pi\) | ||||
−0.534366 | + | 0.845253i | \(0.679449\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.43163 | −0.588519 | ||||||||
\(35\) | 3.08719 | 0.521830 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.03763 | −1.15698 | −0.578490 | − | 0.815690i | \(-0.696358\pi\) | ||||
−0.578490 | + | 0.815690i | \(0.696358\pi\) | |||||||
\(38\) | −3.08719 | −0.500808 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.60601 | −0.875511 | −0.437756 | − | 0.899094i | \(-0.644226\pi\) | ||||
−0.437756 | + | 0.899094i | \(0.644226\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 6.46926 | 0.975278 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −3.90089 | −0.569003 | −0.284501 | − | 0.958676i | \(-0.591828\pi\) | ||||
−0.284501 | + | 0.958676i | \(0.591828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.53074 | 0.361534 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.95044 | 0.547828 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.46926 | 0.872315 | ||||||||
\(56\) | −3.08719 | −0.412543 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.863254 | 0.113351 | ||||||||
\(59\) | −6.86325 | −0.893520 | −0.446760 | − | 0.894654i | \(-0.647422\pi\) | ||||
−0.446760 | + | 0.894654i | \(0.647422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5069 | −1.72938 | −0.864690 | − | 0.502305i | \(-0.832485\pi\) | ||||
−0.864690 | + | 0.502305i | \(0.832485\pi\) | |||||||
\(62\) | 5.95044 | 0.755707 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.95044 | 0.489992 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0753 | −1.23089 | −0.615445 | − | 0.788180i | \(-0.711024\pi\) | ||||
−0.615445 | + | 0.788180i | \(0.711024\pi\) | |||||||
\(68\) | 3.43163 | 0.416146 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.08719 | −0.368990 | ||||||||
\(71\) | −2.56837 | −0.304810 | −0.152405 | − | 0.988318i | \(-0.548702\pi\) | ||||
−0.152405 | + | 0.988318i | \(0.548702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.90089 | 0.690647 | 0.345323 | − | 0.938484i | \(-0.387769\pi\) | ||||
0.345323 | + | 0.938484i | \(0.387769\pi\) | |||||||
\(74\) | 7.03763 | 0.818108 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.08719 | 0.354125 | ||||||||
\(77\) | 19.9718 | 2.27600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8018 | 1.77784 | 0.888919 | − | 0.458064i | \(-0.151457\pi\) | ||||
0.888919 | + | 0.458064i | \(0.151457\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.60601 | 0.619080 | ||||||||
\(83\) | −9.03763 | −0.992009 | −0.496005 | − | 0.868320i | \(-0.665200\pi\) | ||||
−0.496005 | + | 0.868320i | \(0.665200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.43163 | 0.372212 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.46926 | −0.689625 | ||||||||
\(89\) | −16.7641 | −1.77700 | −0.888498 | − | 0.458881i | \(-0.848250\pi\) | ||||
−0.888498 | + | 0.458881i | \(0.848250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1958 | 1.27846 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.90089 | 0.402346 | ||||||||
\(95\) | 3.08719 | 0.316739 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2949 | −1.45143 | −0.725713 | − | 0.687998i | \(-0.758490\pi\) | ||||
−0.725713 | + | 0.687998i | \(0.758490\pi\) | |||||||
\(98\) | −2.53074 | −0.255643 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −0.863254 | −0.0858970 | −0.0429485 | − | 0.999077i | \(-0.513675\pi\) | ||||
−0.0429485 | + | 0.999077i | \(0.513675\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.53074 | 0.150828 | 0.0754141 | − | 0.997152i | \(-0.475972\pi\) | ||||
0.0754141 | + | 0.997152i | \(0.475972\pi\) | |||||||
\(104\) | −3.95044 | −0.387373 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −17.6274 | −1.70410 | −0.852052 | − | 0.523457i | \(-0.824642\pi\) | ||||
−0.852052 | + | 0.523457i | \(0.824642\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.91281 | −0.278997 | −0.139498 | − | 0.990222i | \(-0.544549\pi\) | ||||
−0.139498 | + | 0.990222i | \(0.544549\pi\) | |||||||
\(110\) | −6.46926 | −0.616820 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.08719 | 0.291712 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | −0.863254 | −0.0801511 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.86325 | 0.631814 | ||||||||
\(119\) | 10.5941 | 0.971158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8513 | 2.80467 | ||||||||
\(122\) | 13.5069 | 1.22286 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.95044 | −0.534366 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9385 | 1.85799 | 0.928997 | − | 0.370088i | \(-0.120673\pi\) | ||||
0.928997 | + | 0.370088i | \(0.120673\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.95044 | −0.346477 | ||||||||
\(131\) | −10.7641 | −0.940467 | −0.470234 | − | 0.882542i | \(-0.655830\pi\) | ||||
−0.470234 | + | 0.882542i | \(0.655830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.53074 | 0.826420 | ||||||||
\(134\) | 10.0753 | 0.870370 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.43163 | −0.294260 | ||||||||
\(137\) | −3.26157 | −0.278655 | −0.139327 | − | 0.990246i | \(-0.544494\pi\) | ||||
−0.139327 | + | 0.990246i | \(0.544494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9385 | −1.43671 | −0.718353 | − | 0.695678i | \(-0.755104\pi\) | ||||
−0.718353 | + | 0.695678i | \(0.755104\pi\) | |||||||
\(140\) | 3.08719 | 0.260915 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.56837 | 0.215533 | ||||||||
\(143\) | 25.5565 | 2.13714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.863254 | −0.0716894 | ||||||||
\(146\) | −5.90089 | −0.488361 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.03763 | −0.578490 | ||||||||
\(149\) | −3.26157 | −0.267198 | −0.133599 | − | 0.991035i | \(-0.542653\pi\) | ||||
−0.133599 | + | 0.991035i | \(0.542653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.294881 | 0.0239971 | 0.0119986 | − | 0.999928i | \(-0.496181\pi\) | ||||
0.0119986 | + | 0.999928i | \(0.496181\pi\) | |||||||
\(152\) | −3.08719 | −0.250404 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −19.9718 | −1.60938 | ||||||||
\(155\) | −5.95044 | −0.477951 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.13675 | 0.569574 | 0.284787 | − | 0.958591i | \(-0.408077\pi\) | ||||
0.284787 | + | 0.958591i | \(0.408077\pi\) | |||||||
\(158\) | −15.8018 | −1.25712 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 3.08719 | 0.243305 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.12482 | −0.636385 | −0.318193 | − | 0.948026i | \(-0.603076\pi\) | ||||
−0.318193 | + | 0.948026i | \(0.603076\pi\) | |||||||
\(164\) | −5.60601 | −0.437756 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.03763 | 0.701456 | ||||||||
\(167\) | 7.80178 | 0.603719 | 0.301860 | − | 0.953352i | \(-0.402393\pi\) | ||||
0.301860 | + | 0.953352i | \(0.402393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.60601 | 0.200462 | ||||||||
\(170\) | −3.43163 | −0.263194 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 19.3325 | 1.46982 | 0.734912 | − | 0.678163i | \(-0.237223\pi\) | ||||
0.734912 | + | 0.678163i | \(0.237223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.08719 | 0.233370 | ||||||||
\(176\) | 6.46926 | 0.487639 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.7641 | 1.25653 | ||||||||
\(179\) | −2.17438 | −0.162521 | −0.0812604 | − | 0.996693i | \(-0.525895\pi\) | ||||
−0.0812604 | + | 0.996693i | \(0.525895\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.26157 | −0.539748 | −0.269874 | − | 0.962896i | \(-0.586982\pi\) | ||||
−0.269874 | + | 0.962896i | \(0.586982\pi\) | |||||||
\(182\) | −12.1958 | −0.904011 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −7.03763 | −0.517417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.2001 | 1.62343 | ||||||||
\(188\) | −3.90089 | −0.284501 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.08719 | −0.223968 | ||||||||
\(191\) | −8.58976 | −0.621533 | −0.310767 | − | 0.950486i | \(-0.600586\pi\) | ||||
−0.310767 | + | 0.950486i | \(0.600586\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.44787 | 0.176202 | 0.0881008 | − | 0.996112i | \(-0.471920\pi\) | ||||
0.0881008 | + | 0.996112i | \(0.471920\pi\) | |||||||
\(194\) | 14.2949 | 1.02631 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.53074 | 0.180767 | ||||||||
\(197\) | 10.7428 | 0.765389 | 0.382695 | − | 0.923875i | \(-0.374996\pi\) | ||||
0.382695 | + | 0.923875i | \(0.374996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3111 | −0.801824 | −0.400912 | − | 0.916116i | \(-0.631307\pi\) | ||||
−0.400912 | + | 0.916116i | \(0.631307\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.863254 | 0.0607384 | ||||||||
\(203\) | −2.66503 | −0.187048 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.60601 | −0.391540 | ||||||||
\(206\) | −1.53074 | −0.106652 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.95044 | 0.273914 | ||||||||
\(209\) | 19.9718 | 1.38148 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.1129 | 1.59116 | 0.795579 | − | 0.605850i | \(-0.207167\pi\) | ||||
0.795579 | + | 0.605850i | \(0.207167\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.6274 | 1.20498 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.3701 | −1.24705 | ||||||||
\(218\) | 2.91281 | 0.197280 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.46926 | 0.436157 | ||||||||
\(221\) | 13.5565 | 0.911906 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.72651 | −0.383475 | −0.191738 | − | 0.981446i | \(-0.561412\pi\) | ||||
−0.191738 | + | 0.981446i | \(0.561412\pi\) | |||||||
\(224\) | −3.08719 | −0.206272 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 17.6274 | 1.16997 | 0.584986 | − | 0.811044i | \(-0.301100\pi\) | ||||
0.584986 | + | 0.811044i | \(0.301100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.0753 | −1.06228 | −0.531142 | − | 0.847283i | \(-0.678237\pi\) | ||||
−0.531142 | + | 0.847283i | \(0.678237\pi\) | |||||||
\(230\) | −1.00000 | −0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.863254 | 0.0566754 | ||||||||
\(233\) | 6.44787 | 0.422414 | 0.211207 | − | 0.977441i | \(-0.432261\pi\) | ||||
0.211207 | + | 0.977441i | \(0.432261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.90089 | −0.254466 | ||||||||
\(236\) | −6.86325 | −0.446760 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.5941 | −0.686712 | ||||||||
\(239\) | −4.34876 | −0.281298 | −0.140649 | − | 0.990060i | \(-0.544919\pi\) | ||||
−0.140649 | + | 0.990060i | \(0.544919\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.764142 | 0.0492227 | 0.0246114 | − | 0.999697i | \(-0.492165\pi\) | ||||
0.0246114 | + | 0.999697i | \(0.492165\pi\) | |||||||
\(242\) | −30.8513 | −1.98320 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.5069 | −0.864690 | ||||||||
\(245\) | 2.53074 | 0.161683 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1958 | 0.775998 | ||||||||
\(248\) | 5.95044 | 0.377854 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 22.5402 | 1.42273 | 0.711363 | − | 0.702825i | \(-0.248078\pi\) | ||||
0.711363 | + | 0.702825i | \(0.248078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.46926 | 0.406719 | ||||||||
\(254\) | −20.9385 | −1.31380 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.90089 | 0.617600 | 0.308800 | − | 0.951127i | \(-0.400073\pi\) | ||||
0.308800 | + | 0.951127i | \(0.400073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.7265 | −1.35002 | ||||||||
\(260\) | 3.95044 | 0.244996 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.7641 | 0.665011 | ||||||||
\(263\) | 7.25725 | 0.447501 | 0.223751 | − | 0.974646i | \(-0.428170\pi\) | ||||
0.223751 | + | 0.974646i | \(0.428170\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −9.53074 | −0.584367 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.0753 | −0.615445 | ||||||||
\(269\) | 6.93852 | 0.423049 | 0.211525 | − | 0.977373i | \(-0.432157\pi\) | ||||
0.211525 | + | 0.977373i | \(0.432157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2992 | −0.625632 | −0.312816 | − | 0.949814i | \(-0.601272\pi\) | ||||
−0.312816 | + | 0.949814i | \(0.601272\pi\) | |||||||
\(272\) | 3.43163 | 0.208073 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.26157 | 0.197039 | ||||||||
\(275\) | 6.46926 | 0.390111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8018 | −1.06961 | −0.534803 | − | 0.844977i | \(-0.679614\pi\) | ||||
−0.534803 | + | 0.844977i | \(0.679614\pi\) | |||||||
\(278\) | 16.9385 | 1.01590 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.08719 | −0.184495 | ||||||||
\(281\) | 18.9385 | 1.12978 | 0.564889 | − | 0.825167i | \(-0.308919\pi\) | ||||
0.564889 | + | 0.825167i | \(0.308919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.6889 | 0.754275 | 0.377138 | − | 0.926157i | \(-0.376908\pi\) | ||||
0.377138 | + | 0.926157i | \(0.376908\pi\) | |||||||
\(284\) | −2.56837 | −0.152405 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −25.5565 | −1.51118 | ||||||||
\(287\) | −17.3068 | −1.02159 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.22394 | −0.307290 | ||||||||
\(290\) | 0.863254 | 0.0506920 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.90089 | 0.345323 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.86325 | −0.399594 | ||||||||
\(296\) | 7.03763 | 0.409054 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.26157 | 0.188938 | ||||||||
\(299\) | 3.95044 | 0.228460 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.6975 | 1.42354 | ||||||||
\(302\) | −0.294881 | −0.0169685 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.08719 | 0.177062 | ||||||||
\(305\) | −13.5069 | −0.773402 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9599 | −1.31039 | −0.655196 | − | 0.755459i | \(-0.727414\pi\) | ||||
−0.655196 | + | 0.755459i | \(0.727414\pi\) | |||||||
\(308\) | 19.9718 | 1.13800 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.95044 | 0.337962 | ||||||||
\(311\) | −18.0753 | −1.02495 | −0.512477 | − | 0.858701i | \(-0.671272\pi\) | ||||
−0.512477 | + | 0.858701i | \(0.671272\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1625 | 0.857033 | 0.428516 | − | 0.903534i | \(-0.359036\pi\) | ||||
0.428516 | + | 0.903534i | \(0.359036\pi\) | |||||||
\(314\) | −7.13675 | −0.402750 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.8018 | 0.888919 | ||||||||
\(317\) | −14.0257 | −0.787762 | −0.393881 | − | 0.919161i | \(-0.628868\pi\) | ||||
−0.393881 | + | 0.919161i | \(0.628868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.58462 | −0.312678 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.08719 | −0.172042 | ||||||||
\(323\) | 10.5941 | 0.589471 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.95044 | 0.219131 | ||||||||
\(326\) | 8.12482 | 0.449992 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.60601 | 0.309540 | ||||||||
\(329\) | −12.0428 | −0.663940 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.7403 | −1.35985 | −0.679925 | − | 0.733282i | \(-0.737988\pi\) | ||||
−0.679925 | + | 0.733282i | \(0.737988\pi\) | |||||||
\(332\) | −9.03763 | −0.496005 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.80178 | −0.426894 | ||||||||
\(335\) | −10.0753 | −0.550471 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7146 | 0.801555 | 0.400777 | − | 0.916176i | \(-0.368740\pi\) | ||||
0.400777 | + | 0.916176i | \(0.368740\pi\) | |||||||
\(338\) | −2.60601 | −0.141748 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.43163 | 0.186106 | ||||||||
\(341\) | −38.4950 | −2.08462 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.7975 | −0.744993 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.3325 | −1.03932 | ||||||||
\(347\) | −9.43163 | −0.506316 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.3488 | 0.982187 | 0.491093 | − | 0.871107i | \(-0.336597\pi\) | ||||
0.491093 | + | 0.871107i | \(0.336597\pi\) | |||||||
\(350\) | −3.08719 | −0.165017 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.46926 | −0.344813 | ||||||||
\(353\) | 33.1129 | 1.76242 | 0.881211 | − | 0.472723i | \(-0.156729\pi\) | ||||
0.881211 | + | 0.472723i | \(0.156729\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.56837 | −0.136315 | ||||||||
\(356\) | −16.7641 | −0.888498 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.17438 | 0.114920 | ||||||||
\(359\) | −33.0376 | −1.74366 | −0.871830 | − | 0.489809i | \(-0.837067\pi\) | ||||
−0.871830 | + | 0.489809i | \(0.837067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.46926 | −0.498382 | ||||||||
\(362\) | 7.26157 | 0.381660 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.1958 | 0.639232 | ||||||||
\(365\) | 5.90089 | 0.308867 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.27349 | −0.118675 | −0.0593376 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593376 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.03763 | 0.365869 | ||||||||
\(371\) | 18.5231 | 0.961673 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.9762 | 1.24144 | 0.620719 | − | 0.784033i | \(-0.286841\pi\) | ||||
0.620719 | + | 0.784033i | \(0.286841\pi\) | |||||||
\(374\) | −22.2001 | −1.14794 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.90089 | 0.201173 | ||||||||
\(377\) | −3.41024 | −0.175636 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.8795 | −0.712942 | −0.356471 | − | 0.934306i | \(-0.616020\pi\) | ||||
−0.356471 | + | 0.934306i | \(0.616020\pi\) | |||||||
\(380\) | 3.08719 | 0.158369 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.58976 | 0.439490 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.9718 | 1.01786 | ||||||||
\(386\) | −2.44787 | −0.124593 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.2949 | −0.725713 | ||||||||
\(389\) | 26.6436 | 1.35089 | 0.675443 | − | 0.737412i | \(-0.263952\pi\) | ||||
0.675443 | + | 0.737412i | \(0.263952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.43163 | 0.173545 | ||||||||
\(392\) | −2.53074 | −0.127822 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.7428 | −0.541212 | ||||||||
\(395\) | 15.8018 | 0.795074 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.66749 | −0.435009 | −0.217504 | − | 0.976059i | \(-0.569792\pi\) | ||||
−0.217504 | + | 0.976059i | \(0.569792\pi\) | |||||||
\(398\) | 11.3111 | 0.566975 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −39.9762 | −1.99631 | −0.998157 | − | 0.0606854i | \(-0.980671\pi\) | ||||
−0.998157 | + | 0.0606854i | \(0.980671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.5069 | −1.17096 | ||||||||
\(404\) | −0.863254 | −0.0429485 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.66503 | 0.132263 | ||||||||
\(407\) | −45.5283 | −2.25675 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.1248 | 1.48958 | 0.744788 | − | 0.667301i | \(-0.232550\pi\) | ||||
0.744788 | + | 0.667301i | \(0.232550\pi\) | |||||||
\(410\) | 5.60601 | 0.276861 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.53074 | 0.0754141 | ||||||||
\(413\) | −21.1882 | −1.04260 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.03763 | −0.443640 | ||||||||
\(416\) | −3.95044 | −0.193686 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −19.9718 | −0.976854 | ||||||||
\(419\) | −25.8770 | −1.26418 | −0.632088 | − | 0.774897i | \(-0.717802\pi\) | ||||
−0.632088 | + | 0.774897i | \(0.717802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7146 | −0.522197 | −0.261098 | − | 0.965312i | \(-0.584085\pi\) | ||||
−0.261098 | + | 0.965312i | \(0.584085\pi\) | |||||||
\(422\) | −23.1129 | −1.12512 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 3.43163 | 0.166458 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41.6983 | −2.01792 | ||||||||
\(428\) | −17.6274 | −0.852052 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | −32.2496 | −1.55341 | −0.776705 | − | 0.629864i | \(-0.783111\pi\) | ||||
−0.776705 | + | 0.629864i | \(0.783111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6393 | 0.991862 | 0.495931 | − | 0.868362i | \(-0.334827\pi\) | ||||
0.495931 | + | 0.868362i | \(0.334827\pi\) | |||||||
\(434\) | 18.3701 | 0.881795 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.91281 | −0.139498 | ||||||||
\(437\) | 3.08719 | 0.147680 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2239 | −0.774326 | −0.387163 | − | 0.922011i | \(-0.626545\pi\) | ||||
−0.387163 | + | 0.922011i | \(0.626545\pi\) | |||||||
\(440\) | −6.46926 | −0.308410 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.5565 | −0.644815 | ||||||||
\(443\) | 15.6770 | 0.744834 | 0.372417 | − | 0.928065i | \(-0.378529\pi\) | ||||
0.372417 | + | 0.928065i | \(0.378529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.7641 | −0.794697 | ||||||||
\(446\) | 5.72651 | 0.271158 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.08719 | 0.145856 | ||||||||
\(449\) | −22.5727 | −1.06527 | −0.532636 | − | 0.846345i | \(-0.678798\pi\) | ||||
−0.532636 | + | 0.846345i | \(0.678798\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.2667 | −1.70773 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.6274 | −0.827295 | ||||||||
\(455\) | 12.1958 | 0.571746 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.45302 | −0.0679693 | −0.0339846 | − | 0.999422i | \(-0.510820\pi\) | ||||
−0.0339846 | + | 0.999422i | \(0.510820\pi\) | |||||||
\(458\) | 16.0753 | 0.751148 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.00000 | 0.0466252 | ||||||||
\(461\) | 29.7027 | 1.38339 | 0.691695 | − | 0.722189i | \(-0.256864\pi\) | ||||
0.691695 | + | 0.722189i | \(0.256864\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.9624 | 1.06715 | 0.533576 | − | 0.845752i | \(-0.320848\pi\) | ||||
0.533576 | + | 0.845752i | \(0.320848\pi\) | |||||||
\(464\) | −0.863254 | −0.0400756 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.44787 | −0.298692 | ||||||||
\(467\) | −9.48550 | −0.438937 | −0.219468 | − | 0.975620i | \(-0.570432\pi\) | ||||
−0.219468 | + | 0.975620i | \(0.570432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.1043 | −1.43626 | ||||||||
\(470\) | 3.90089 | 0.179935 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.86325 | 0.315907 | ||||||||
\(473\) | 51.7541 | 2.37966 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.08719 | 0.141650 | ||||||||
\(476\) | 10.5941 | 0.485579 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.34876 | 0.198908 | ||||||||
\(479\) | 30.5659 | 1.39659 | 0.698296 | − | 0.715809i | \(-0.253942\pi\) | ||||
0.698296 | + | 0.715809i | \(0.253942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8018 | −1.26765 | ||||||||
\(482\) | −0.764142 | −0.0348057 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.8513 | 1.40233 | ||||||||
\(485\) | −14.2949 | −0.649097 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.1367 | −0.957797 | −0.478899 | − | 0.877870i | \(-0.658964\pi\) | ||||
−0.478899 | + | 0.877870i | \(0.658964\pi\) | |||||||
\(488\) | 13.5069 | 0.611428 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.53074 | −0.114327 | ||||||||
\(491\) | 28.0514 | 1.26594 | 0.632971 | − | 0.774175i | \(-0.281835\pi\) | ||||
0.632971 | + | 0.774175i | \(0.281835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.96237 | −0.133418 | ||||||||
\(494\) | −12.1958 | −0.548714 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.95044 | −0.267183 | ||||||||
\(497\) | −7.92905 | −0.355667 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.80178 | 0.170191 | 0.0850954 | − | 0.996373i | \(-0.472880\pi\) | ||||
0.0850954 | + | 0.996373i | \(0.472880\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.5402 | −1.00602 | ||||||||
\(503\) | −19.0872 | −0.851056 | −0.425528 | − | 0.904945i | \(-0.639912\pi\) | ||||
−0.425528 | + | 0.904945i | \(0.639912\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.863254 | −0.0384143 | ||||||||
\(506\) | −6.46926 | −0.287594 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.9385 | 0.928997 | ||||||||
\(509\) | 9.41024 | 0.417101 | 0.208551 | − | 0.978012i | \(-0.433125\pi\) | ||||
0.208551 | + | 0.978012i | \(0.433125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.2172 | 0.805880 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.90089 | −0.436709 | ||||||||
\(515\) | 1.53074 | 0.0674524 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.2359 | −1.10987 | ||||||||
\(518\) | 21.7265 | 0.954608 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.95044 | −0.173238 | ||||||||
\(521\) | −25.8018 | −1.13040 | −0.565198 | − | 0.824955i | \(-0.691200\pi\) | ||||
−0.565198 | + | 0.824955i | \(0.691200\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.1129 | −0.835749 | −0.417874 | − | 0.908505i | \(-0.637225\pi\) | ||||
−0.417874 | + | 0.908505i | \(0.637225\pi\) | |||||||
\(524\) | −10.7641 | −0.470234 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.25725 | −0.316431 | ||||||||
\(527\) | −20.4197 | −0.889496 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.53074 | 0.413210 | ||||||||
\(533\) | −22.1462 | −0.959259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.6274 | −0.762099 | ||||||||
\(536\) | 10.0753 | 0.435185 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.93852 | −0.299141 | ||||||||
\(539\) | 16.3720 | 0.705193 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8394 | 1.32589 | 0.662945 | − | 0.748668i | \(-0.269306\pi\) | ||||
0.662945 | + | 0.748668i | \(0.269306\pi\) | |||||||
\(542\) | 10.2992 | 0.442389 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.43163 | −0.147130 | ||||||||
\(545\) | −2.91281 | −0.124771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8513 | 0.592240 | 0.296120 | − | 0.955151i | \(-0.404307\pi\) | ||||
0.296120 | + | 0.955151i | \(0.404307\pi\) | |||||||
\(548\) | −3.26157 | −0.139327 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.46926 | −0.275850 | ||||||||
\(551\) | −2.66503 | −0.113534 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 48.7831 | 2.07447 | ||||||||
\(554\) | 17.8018 | 0.756325 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.9385 | −0.718353 | ||||||||
\(557\) | 28.7641 | 1.21878 | 0.609388 | − | 0.792872i | \(-0.291415\pi\) | ||||
0.609388 | + | 0.792872i | \(0.291415\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.6036 | 1.33669 | ||||||||
\(560\) | 3.08719 | 0.130458 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.9385 | −0.798873 | ||||||||
\(563\) | −36.1505 | −1.52356 | −0.761782 | − | 0.647834i | \(-0.775675\pi\) | ||||
−0.761782 | + | 0.647834i | \(0.775675\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | 0.252422 | ||||||||
\(566\) | −12.6889 | −0.533353 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.56837 | 0.107767 | ||||||||
\(569\) | 10.3488 | 0.433843 | 0.216921 | − | 0.976189i | \(-0.430399\pi\) | ||||
0.216921 | + | 0.976189i | \(0.430399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6060 | 0.820486 | 0.410243 | − | 0.911976i | \(-0.365444\pi\) | ||||
0.410243 | + | 0.911976i | \(0.365444\pi\) | |||||||
\(572\) | 25.5565 | 1.06857 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.3068 | 0.722372 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.1505 | −1.42171 | −0.710853 | − | 0.703341i | \(-0.751691\pi\) | ||||
−0.710853 | + | 0.703341i | \(0.751691\pi\) | |||||||
\(578\) | 5.22394 | 0.217287 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.863254 | −0.0358447 | ||||||||
\(581\) | −27.9009 | −1.15752 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.8156 | 1.60758 | ||||||||
\(584\) | −5.90089 | −0.244180 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 5.19062 | 0.214240 | 0.107120 | − | 0.994246i | \(-0.465837\pi\) | ||||
0.107120 | + | 0.994246i | \(0.465837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.3701 | −0.756929 | ||||||||
\(590\) | 6.86325 | 0.282556 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.03763 | −0.289245 | ||||||||
\(593\) | 2.09911 | 0.0862002 | 0.0431001 | − | 0.999071i | \(-0.486277\pi\) | ||||
0.0431001 | + | 0.999071i | \(0.486277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5941 | 0.434315 | ||||||||
\(596\) | −3.26157 | −0.133599 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.95044 | −0.161546 | ||||||||
\(599\) | −11.1581 | −0.455909 | −0.227955 | − | 0.973672i | \(-0.573204\pi\) | ||||
−0.227955 | + | 0.973672i | \(0.573204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.57784 | 0.390688 | 0.195344 | − | 0.980735i | \(-0.437418\pi\) | ||||
0.195344 | + | 0.980735i | \(0.437418\pi\) | |||||||
\(602\) | −24.6975 | −1.00660 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.294881 | 0.0119986 | ||||||||
\(605\) | 30.8513 | 1.25428 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.6975 | −1.00244 | −0.501221 | − | 0.865320i | \(-0.667115\pi\) | ||||
−0.501221 | + | 0.865320i | \(0.667115\pi\) | |||||||
\(608\) | −3.08719 | −0.125202 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.5069 | 0.546878 | ||||||||
\(611\) | −15.4102 | −0.623431 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.3488 | −1.06422 | −0.532108 | − | 0.846676i | \(-0.678600\pi\) | ||||
−0.532108 | + | 0.846676i | \(0.678600\pi\) | |||||||
\(614\) | 22.9599 | 0.926587 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.9718 | −0.804688 | ||||||||
\(617\) | −5.94612 | −0.239382 | −0.119691 | − | 0.992811i | \(-0.538190\pi\) | ||||
−0.119691 | + | 0.992811i | \(0.538190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.6856 | 1.59510 | 0.797549 | − | 0.603254i | \(-0.206129\pi\) | ||||
0.797549 | + | 0.603254i | \(0.206129\pi\) | |||||||
\(620\) | −5.95044 | −0.238976 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0753 | 0.724752 | ||||||||
\(623\) | −51.7541 | −2.07348 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.1625 | −0.606014 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.13675 | 0.284787 | ||||||||
\(629\) | −24.1505 | −0.962945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0138 | −0.916164 | −0.458082 | − | 0.888910i | \(-0.651463\pi\) | ||||
−0.458082 | + | 0.888910i | \(0.651463\pi\) | |||||||
\(632\) | −15.8018 | −0.628561 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0257 | 0.557032 | ||||||||
\(635\) | 20.9385 | 0.830920 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.99754 | 0.396117 | ||||||||
\(638\) | 5.58462 | 0.221097 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −25.4617 | −1.00568 | −0.502838 | − | 0.864381i | \(-0.667711\pi\) | ||||
−0.502838 | + | 0.864381i | \(0.667711\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.4479 | −0.648641 | −0.324320 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324320 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(644\) | 3.08719 | 0.121652 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5941 | −0.416819 | ||||||||
\(647\) | 34.9147 | 1.37264 | 0.686319 | − | 0.727301i | \(-0.259226\pi\) | ||||
0.686319 | + | 0.727301i | \(0.259226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.4002 | −1.74286 | ||||||||
\(650\) | −3.95044 | −0.154949 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.12482 | −0.318193 | ||||||||
\(653\) | 34.2754 | 1.34130 | 0.670649 | − | 0.741775i | \(-0.266016\pi\) | ||||
0.670649 | + | 0.741775i | \(0.266016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7641 | −0.420590 | ||||||||
\(656\) | −5.60601 | −0.218878 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0428 | 0.469476 | ||||||||
\(659\) | −35.2548 | −1.37333 | −0.686666 | − | 0.726973i | \(-0.740926\pi\) | ||||
−0.686666 | + | 0.726973i | \(0.740926\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.5684 | 1.11118 | 0.555590 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555590 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(662\) | 24.7403 | 0.961559 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.03763 | 0.350728 | ||||||||
\(665\) | 9.53074 | 0.369586 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.863254 | −0.0334253 | ||||||||
\(668\) | 7.80178 | 0.301860 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0753 | 0.389242 | ||||||||
\(671\) | −87.3796 | −3.37325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.8770 | −0.920392 | −0.460196 | − | 0.887817i | \(-0.652221\pi\) | ||||
−0.460196 | + | 0.887817i | \(0.652221\pi\) | |||||||
\(674\) | −14.7146 | −0.566785 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.60601 | 0.100231 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −44.1310 | −1.69359 | ||||||||
\(680\) | −3.43163 | −0.131597 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 38.4950 | 1.47405 | ||||||||
\(683\) | −34.6480 | −1.32577 | −0.662884 | − | 0.748722i | \(-0.730668\pi\) | ||||
−0.662884 | + | 0.748722i | \(0.730668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.26157 | −0.124618 | ||||||||
\(686\) | 13.7975 | 0.526789 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 23.7027 | 0.903000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.1744 | −0.691386 | −0.345693 | − | 0.938348i | \(-0.612356\pi\) | ||||
−0.345693 | + | 0.938348i | \(0.612356\pi\) | |||||||
\(692\) | 19.3325 | 0.734912 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.43163 | 0.358020 | ||||||||
\(695\) | −16.9385 | −0.642515 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.2377 | −0.728681 | ||||||||
\(698\) | −18.3488 | −0.694511 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.08719 | 0.116685 | ||||||||
\(701\) | 40.6907 | 1.53687 | 0.768434 | − | 0.639929i | \(-0.221036\pi\) | ||||
0.768434 | + | 0.639929i | \(0.221036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.7265 | −0.819431 | ||||||||
\(704\) | 6.46926 | 0.243819 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.1129 | −1.24622 | ||||||||
\(707\) | −2.66503 | −0.100229 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.4454 | −0.993178 | −0.496589 | − | 0.867986i | \(-0.665414\pi\) | ||||
−0.496589 | + | 0.867986i | \(0.665414\pi\) | |||||||
\(710\) | 2.56837 | 0.0963893 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.7641 | 0.628263 | ||||||||
\(713\) | −5.95044 | −0.222846 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.5565 | 0.955757 | ||||||||
\(716\) | −2.17438 | −0.0812604 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.0376 | 1.23295 | ||||||||
\(719\) | 2.24778 | 0.0838281 | 0.0419140 | − | 0.999121i | \(-0.486654\pi\) | ||||
0.0419140 | + | 0.999121i | \(0.486654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.72568 | 0.175994 | ||||||||
\(722\) | 9.46926 | 0.352409 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.26157 | −0.269874 | ||||||||
\(725\) | −0.863254 | −0.0320605 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.4830 | 0.796762 | 0.398381 | − | 0.917220i | \(-0.369572\pi\) | ||||
0.398381 | + | 0.917220i | \(0.369572\pi\) | |||||||
\(728\) | −12.1958 | −0.452005 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.90089 | −0.218402 | ||||||||
\(731\) | 27.4530 | 1.01539 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.3778 | 0.420247 | 0.210123 | − | 0.977675i | \(-0.432613\pi\) | ||||
0.210123 | + | 0.977675i | \(0.432613\pi\) | |||||||
\(734\) | 2.27349 | 0.0839161 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −65.1795 | −2.40092 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.8770 | 0.804760 | 0.402380 | − | 0.915473i | \(-0.368183\pi\) | ||||
0.402380 | + | 0.915473i | \(0.368183\pi\) | |||||||
\(740\) | −7.03763 | −0.258709 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.5231 | −0.680006 | ||||||||
\(743\) | −5.36068 | −0.196664 | −0.0983322 | − | 0.995154i | \(-0.531351\pi\) | ||||
−0.0983322 | + | 0.995154i | \(0.531351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.26157 | −0.119495 | ||||||||
\(746\) | −23.9762 | −0.877829 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.2001 | 0.811716 | ||||||||
\(749\) | −54.4191 | −1.98843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.3915 | 0.890060 | 0.445030 | − | 0.895516i | \(-0.353193\pi\) | ||||
0.445030 | + | 0.895516i | \(0.353193\pi\) | |||||||
\(752\) | −3.90089 | −0.142251 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.41024 | 0.124194 | ||||||||
\(755\) | 0.294881 | 0.0107318 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.9437 | 1.52447 | 0.762234 | − | 0.647301i | \(-0.224102\pi\) | ||||
0.762234 | + | 0.647301i | \(0.224102\pi\) | |||||||
\(758\) | 13.8795 | 0.504126 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.08719 | −0.111984 | ||||||||
\(761\) | 18.3745 | 0.666074 | 0.333037 | − | 0.942914i | \(-0.391927\pi\) | ||||
0.333037 | + | 0.942914i | \(0.391927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.99240 | −0.325547 | ||||||||
\(764\) | −8.58976 | −0.310767 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.1129 | −0.978990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.4993 | 1.53256 | 0.766282 | − | 0.642505i | \(-0.222105\pi\) | ||||
0.766282 | + | 0.642505i | \(0.222105\pi\) | |||||||
\(770\) | −19.9718 | −0.719735 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.44787 | 0.0881008 | ||||||||
\(773\) | 15.0376 | 0.540866 | 0.270433 | − | 0.962739i | \(-0.412833\pi\) | ||||
0.270433 | + | 0.962739i | \(0.412833\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.95044 | −0.213746 | ||||||||
\(776\) | 14.2949 | 0.513156 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.6436 | −0.955221 | ||||||||
\(779\) | −17.3068 | −0.620081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.6155 | −0.594548 | ||||||||
\(782\) | −3.43163 | −0.122715 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.53074 | 0.0903836 | ||||||||
\(785\) | 7.13675 | 0.254721 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.39154 | −0.299126 | −0.149563 | − | 0.988752i | \(-0.547787\pi\) | ||||
−0.149563 | + | 0.988752i | \(0.547787\pi\) | |||||||
\(788\) | 10.7428 | 0.382695 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.8018 | −0.562202 | ||||||||
\(791\) | 18.5231 | 0.658607 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.3582 | −1.89481 | ||||||||
\(794\) | 8.66749 | 0.307598 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.3111 | −0.400912 | ||||||||
\(797\) | 22.0514 | 0.781101 | 0.390551 | − | 0.920581i | \(-0.372285\pi\) | ||||
0.390551 | + | 0.920581i | \(0.372285\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.3864 | −0.473576 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.9762 | 1.41161 | ||||||||
\(803\) | 38.1744 | 1.34714 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.08719 | 0.108809 | ||||||||
\(806\) | 23.5069 | 0.827995 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.863254 | 0.0303692 | ||||||||
\(809\) | −2.04524 | −0.0719066 | −0.0359533 | − | 0.999353i | \(-0.511447\pi\) | ||||
−0.0359533 | + | 0.999353i | \(0.511447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.24965 | 0.149225 | 0.0746126 | − | 0.997213i | \(-0.476228\pi\) | ||||
0.0746126 | + | 0.997213i | \(0.476228\pi\) | |||||||
\(812\) | −2.66503 | −0.0935242 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 45.5283 | 1.59577 | ||||||||
\(815\) | −8.12482 | −0.284600 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.6975 | 0.864057 | ||||||||
\(818\) | −30.1248 | −1.05329 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.60601 | −0.195770 | ||||||||
\(821\) | 29.2548 | 1.02100 | 0.510500 | − | 0.859878i | \(-0.329460\pi\) | ||||
0.510500 | + | 0.859878i | \(0.329460\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5846 | 0.473530 | 0.236765 | − | 0.971567i | \(-0.423913\pi\) | ||||
0.236765 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(824\) | −1.53074 | −0.0533258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.1882 | 0.737231 | ||||||||
\(827\) | −24.7880 | −0.861963 | −0.430981 | − | 0.902361i | \(-0.641833\pi\) | ||||
−0.430981 | + | 0.902361i | \(0.641833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.1505 | 0.908246 | 0.454123 | − | 0.890939i | \(-0.349953\pi\) | ||||
0.454123 | + | 0.890939i | \(0.349953\pi\) | |||||||
\(830\) | 9.03763 | 0.313701 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.95044 | 0.136957 | ||||||||
\(833\) | 8.68455 | 0.300902 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.80178 | 0.269992 | ||||||||
\(836\) | 19.9718 | 0.690740 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.8770 | 0.893908 | ||||||||
\(839\) | −6.37260 | −0.220007 | −0.110003 | − | 0.993931i | \(-0.535086\pi\) | ||||
−0.110003 | + | 0.993931i | \(0.535086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2548 | −0.974303 | ||||||||
\(842\) | 10.7146 | 0.369249 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.1129 | 0.795579 | ||||||||
\(845\) | 2.60601 | 0.0896493 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 95.2439 | 3.27262 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.43163 | −0.117704 | ||||||||
\(851\) | −7.03763 | −0.241247 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.6293 | −1.15144 | −0.575722 | − | 0.817646i | \(-0.695279\pi\) | ||||
−0.575722 | + | 0.817646i | \(0.695279\pi\) | |||||||
\(854\) | 41.6983 | 1.42689 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.6274 | 0.602492 | ||||||||
\(857\) | −11.1795 | −0.381885 | −0.190943 | − | 0.981601i | \(-0.561154\pi\) | ||||
−0.190943 | + | 0.981601i | \(0.561154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.9009 | 1.63436 | 0.817179 | − | 0.576385i | \(-0.195537\pi\) | ||||
0.817179 | + | 0.576385i | \(0.195537\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.2496 | 1.09843 | ||||||||
\(863\) | 30.1180 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.3325 | 0.657325 | ||||||||
\(866\) | −20.6393 | −0.701353 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.3701 | −0.623523 | ||||||||
\(869\) | 102.226 | 3.46777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.8018 | −1.34863 | ||||||||
\(872\) | 2.91281 | 0.0986402 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.08719 | −0.104426 | ||||||||
\(875\) | 3.08719 | 0.104366 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3940 | −0.756191 | −0.378096 | − | 0.925767i | \(-0.623421\pi\) | ||||
−0.378096 | + | 0.925767i | \(0.623421\pi\) | |||||||
\(878\) | 16.2239 | 0.547531 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.46926 | 0.218079 | ||||||||
\(881\) | −21.1129 | −0.711312 | −0.355656 | − | 0.934617i | \(-0.615742\pi\) | ||||
−0.355656 | + | 0.934617i | \(0.615742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.1061 | 1.65255 | 0.826276 | − | 0.563265i | \(-0.190455\pi\) | ||||
0.826276 | + | 0.563265i | \(0.190455\pi\) | |||||||
\(884\) | 13.5565 | 0.455953 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.6770 | −0.526678 | ||||||||
\(887\) | 43.0566 | 1.44570 | 0.722849 | − | 0.691006i | \(-0.242832\pi\) | ||||
0.722849 | + | 0.691006i | \(0.242832\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 64.6412 | 2.16800 | ||||||||
\(890\) | 16.7641 | 0.561935 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.72651 | −0.191738 | ||||||||
\(893\) | −12.0428 | −0.402996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.17438 | −0.0726815 | ||||||||
\(896\) | −3.08719 | −0.103136 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.5727 | 0.753261 | ||||||||
\(899\) | 5.13675 | 0.171320 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.5898 | 0.685944 | ||||||||
\(902\) | 36.2667 | 1.20755 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −7.26157 | −0.241383 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.9762 | −1.26098 | −0.630489 | − | 0.776198i | \(-0.717146\pi\) | ||||
−0.630489 | + | 0.776198i | \(0.717146\pi\) | |||||||
\(908\) | 17.6274 | 0.584986 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.1958 | −0.404286 | ||||||||
\(911\) | 15.7504 | 0.521833 | 0.260916 | − | 0.965361i | \(-0.415975\pi\) | ||||
0.260916 | + | 0.965361i | \(0.415975\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.4668 | −1.93497 | ||||||||
\(914\) | 1.45302 | 0.0480615 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0753 | −0.531142 | ||||||||
\(917\) | −33.2309 | −1.09738 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.4240 | 1.00360 | 0.501798 | − | 0.864985i | \(-0.332672\pi\) | ||||
0.501798 | + | 0.864985i | \(0.332672\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.7027 | −0.978205 | ||||||||
\(923\) | −10.1462 | −0.333967 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.03763 | −0.231396 | ||||||||
\(926\) | −22.9624 | −0.754590 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.863254 | 0.0283377 | ||||||||
\(929\) | 37.8018 | 1.24024 | 0.620118 | − | 0.784509i | \(-0.287085\pi\) | ||||
0.620118 | + | 0.784509i | \(0.287085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.81287 | 0.256057 | ||||||||
\(932\) | 6.44787 | 0.211207 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.48550 | 0.310375 | ||||||||
\(935\) | 22.2001 | 0.726021 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.6907 | −1.06796 | −0.533980 | − | 0.845497i | \(-0.679304\pi\) | ||||
−0.533980 | + | 0.845497i | \(0.679304\pi\) | |||||||
\(938\) | 31.1043 | 1.01559 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.90089 | −0.127233 | ||||||||
\(941\) | 46.4882 | 1.51547 | 0.757736 | − | 0.652561i | \(-0.226306\pi\) | ||||
0.757736 | + | 0.652561i | \(0.226306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.60601 | −0.182557 | ||||||||
\(944\) | −6.86325 | −0.223380 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.7541 | −1.68267 | ||||||||
\(947\) | 37.2052 | 1.20901 | 0.604504 | − | 0.796602i | \(-0.293371\pi\) | ||||
0.604504 | + | 0.796602i | \(0.293371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.3111 | 0.756711 | ||||||||
\(950\) | −3.08719 | −0.100162 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.5941 | −0.343356 | ||||||||
\(953\) | −49.1104 | −1.59084 | −0.795422 | − | 0.606056i | \(-0.792751\pi\) | ||||
−0.795422 | + | 0.606056i | \(0.792751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.58976 | −0.277958 | ||||||||
\(956\) | −4.34876 | −0.140649 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.5659 | −0.987540 | ||||||||
\(959\) | −10.0691 | −0.325148 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.40778 | 0.142187 | ||||||||
\(962\) | 27.8018 | 0.896365 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.764142 | 0.0246114 | ||||||||
\(965\) | 2.44787 | 0.0787997 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.96751 | 0.0632709 | 0.0316355 | − | 0.999499i | \(-0.489928\pi\) | ||||
0.0316355 | + | 0.999499i | \(0.489928\pi\) | |||||||
\(968\) | −30.8513 | −0.991599 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.2949 | 0.458981 | ||||||||
\(971\) | −26.1205 | −0.838247 | −0.419123 | − | 0.907929i | \(-0.637663\pi\) | ||||
−0.419123 | + | 0.907929i | \(0.637663\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −52.2924 | −1.67642 | ||||||||
\(974\) | 21.1367 | 0.677265 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.5069 | −0.432345 | ||||||||
\(977\) | 0.639319 | 0.0204536 | 0.0102268 | − | 0.999948i | \(-0.496745\pi\) | ||||
0.0102268 | + | 0.999948i | \(0.496745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −108.452 | −3.46613 | ||||||||
\(980\) | 2.53074 | 0.0808415 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.0514 | −0.895157 | ||||||||
\(983\) | 6.46926 | 0.206337 | 0.103169 | − | 0.994664i | \(-0.467102\pi\) | ||||
0.103169 | + | 0.994664i | \(0.467102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7428 | 0.342293 | ||||||||
\(986\) | 2.96237 | 0.0943410 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.1958 | 0.387999 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.2334 | 1.18276 | 0.591379 | − | 0.806394i | \(-0.298584\pi\) | ||||
0.591379 | + | 0.806394i | \(0.298584\pi\) | |||||||
\(992\) | 5.95044 | 0.188927 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.92905 | 0.251494 | ||||||||
\(995\) | −11.3111 | −0.358587 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.65124 | 0.305658 | 0.152829 | − | 0.988253i | \(-0.451162\pi\) | ||||
0.152829 | + | 0.988253i | \(0.451162\pi\) | |||||||
\(998\) | −3.80178 | −0.120343 | ||||||||
\(999\) | 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 | 2070.2.a.z.1.2 | 3 | ||
3.2 | odd | 2 | 230.2.a.d.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 1840.2.a.r.1.2 | 3 | |||
15.2 | even | 4 | 1150.2.b.j.599.5 | 6 | |||
15.8 | even | 4 | 1150.2.b.j.599.2 | 6 | |||
15.14 | odd | 2 | 1150.2.a.q.1.2 | 3 | |||
24.5 | odd | 2 | 7360.2.a.bz.1.2 | 3 | |||
24.11 | even | 2 | 7360.2.a.ce.1.2 | 3 | |||
60.59 | even | 2 | 9200.2.a.cf.1.2 | 3 | |||
69.68 | even | 2 | 5290.2.a.r.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.d.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
1150.2.a.q.1.2 | 3 | 15.14 | odd | 2 | |||
1150.2.b.j.599.2 | 6 | 15.8 | even | 4 | |||
1150.2.b.j.599.5 | 6 | 15.2 | even | 4 | |||
1840.2.a.r.1.2 | 3 | 12.11 | even | 2 | |||
2070.2.a.z.1.2 | 3 | 1.1 | even | 1 | trivial | ||
5290.2.a.r.1.2 | 3 | 69.68 | even | 2 | |||
7360.2.a.bz.1.2 | 3 | 24.5 | odd | 2 | |||
7360.2.a.ce.1.2 | 3 | 24.11 | even | 2 | |||
9200.2.a.cf.1.2 | 3 | 60.59 | even | 2 |