Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, 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("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.253565184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 20x^{3} + 22x^{2} - 32x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.366738\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | −0.366738 | −0.211736 | −0.105868 | − | 0.994380i | \(-0.533762\pi\) | ||||
−0.105868 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.08675 | 1.16668 | 0.583341 | − | 0.812227i | \(-0.301745\pi\) | ||||
0.583341 | + | 0.812227i | \(0.301745\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.86550 | −0.955168 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.94567 | −1.49118 | −0.745588 | − | 0.666407i | \(-0.767831\pi\) | ||||
−0.745588 | + | 0.666407i | \(0.767831\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.79016 | −1.05120 | −0.525601 | − | 0.850731i | \(-0.676160\pi\) | ||||
−0.525601 | + | 0.850731i | \(0.676160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.97713 | 0.964596 | 0.482298 | − | 0.876007i | \(-0.339802\pi\) | ||||
0.482298 | + | 0.876007i | \(0.339802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.13203 | −0.247029 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.56426 | 1.36874 | 0.684372 | − | 0.729133i | \(-0.260077\pi\) | ||||
0.684372 | + | 0.729133i | \(0.260077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.15110 | 0.413980 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.14084 | 0.954630 | 0.477315 | − | 0.878732i | \(-0.341610\pi\) | ||||
0.477315 | + | 0.878732i | \(0.341610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.25626 | 0.764447 | 0.382224 | − | 0.924070i | \(-0.375158\pi\) | ||||
0.382224 | + | 0.924070i | \(0.375158\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.81376 | 0.315736 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.75503 | −1.27492 | −0.637459 | − | 0.770484i | \(-0.720015\pi\) | ||||
−0.637459 | + | 0.770484i | \(0.720015\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.39000 | 0.222577 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.25626 | −0.352369 | −0.176184 | − | 0.984357i | \(-0.556376\pi\) | ||||
−0.176184 | + | 0.984357i | \(0.556376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2276 | −1.55969 | −0.779846 | − | 0.625971i | \(-0.784703\pi\) | ||||
−0.779846 | + | 0.625971i | \(0.784703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.935652 | 0.136479 | 0.0682395 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682395 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.52804 | 0.361149 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.45856 | −0.204240 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.52117 | −1.03311 | −0.516556 | − | 0.856253i | \(-0.672786\pi\) | ||||
−0.516556 | + | 0.856253i | \(0.672786\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.366738 | −0.0485756 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4356 | −1.35860 | −0.679298 | − | 0.733863i | \(-0.737715\pi\) | ||||
−0.679298 | + | 0.733863i | \(0.737715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9163 | 1.39769 | 0.698847 | − | 0.715271i | \(-0.253697\pi\) | ||||
0.698847 | + | 0.715271i | \(0.253697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.84510 | −1.11438 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.80924 | −0.831881 | −0.415940 | − | 0.909392i | \(-0.636547\pi\) | ||||
−0.415940 | + | 0.909392i | \(0.636547\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.40736 | −0.289812 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.98093 | −0.353771 | −0.176886 | − | 0.984231i | \(-0.556602\pi\) | ||||
−0.176886 | + | 0.984231i | \(0.556602\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.19638 | −0.257066 | −0.128533 | − | 0.991705i | \(-0.541027\pi\) | ||||
−0.128533 | + | 0.991705i | \(0.541027\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.2661 | −1.73973 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.26652 | −0.367513 | −0.183756 | − | 0.982972i | \(-0.558826\pi\) | ||||
−0.183756 | + | 0.982972i | \(0.558826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.80762 | 0.867513 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.09936 | −0.449963 | −0.224982 | − | 0.974363i | \(-0.572232\pi\) | ||||
−0.224982 | + | 0.974363i | \(0.572232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.88534 | −0.202129 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4134 | −1.31581 | −0.657907 | − | 0.753099i | \(-0.728558\pi\) | ||||
−0.657907 | + | 0.753099i | \(0.728558\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.6993 | −1.22642 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.56093 | −0.161861 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6172 | −1.07801 | −0.539007 | − | 0.842302i | \(-0.681200\pi\) | ||||
−0.539007 | + | 0.842302i | \(0.681200\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.1718 | 1.42432 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1119 | −1.30469 | −0.652343 | − | 0.757924i | \(-0.726214\pi\) | ||||
−0.652343 | + | 0.757924i | \(0.726214\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.95691 | −0.488419 | −0.244209 | − | 0.969723i | \(-0.578528\pi\) | ||||
−0.244209 | + | 0.969723i | \(0.578528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.9142 | −1.82850 | −0.914251 | − | 0.405148i | \(-0.867220\pi\) | ||||
−0.914251 | + | 0.405148i | \(0.867220\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.90118 | 0.852578 | 0.426289 | − | 0.904587i | \(-0.359821\pi\) | ||||
0.426289 | + | 0.904587i | \(0.359821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.84406 | 0.269946 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.85071 | 0.926677 | 0.463339 | − | 0.886181i | \(-0.346651\pi\) | ||||
0.463339 | + | 0.886181i | \(0.346651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.8607 | 1.00407 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.2764 | 1.12538 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.4596 | 1.22360 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.827456 | 0.0746092 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.76384 | 0.333987 | 0.166993 | − | 0.985958i | \(-0.446594\pi\) | ||||
0.166993 | + | 0.985958i | \(0.446594\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.75084 | 0.330243 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0488 | 0.877966 | 0.438983 | − | 0.898495i | \(-0.355339\pi\) | ||||
0.438983 | + | 0.898495i | \(0.355339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.08675 | 0.267655 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6244 | −1.24945 | −0.624724 | − | 0.780845i | \(-0.714789\pi\) | ||||
−0.624724 | + | 0.780845i | \(0.714789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0773 | −1.02438 | −0.512191 | − | 0.858872i | \(-0.671166\pi\) | ||||
−0.512191 | + | 0.858872i | \(0.671166\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.343139 | −0.0288975 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.7449 | 1.56753 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.927129 | −0.0764683 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.5739 | 1.03009 | 0.515046 | − | 0.857162i | \(-0.327775\pi\) | ||||
0.515046 | + | 0.857162i | \(0.327775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.390336 | −0.0317651 | −0.0158826 | − | 0.999874i | \(-0.505056\pi\) | ||||
−0.0158826 | + | 0.999874i | \(0.505056\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.3965 | −0.921351 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6517 | −1.40876 | −0.704379 | − | 0.709824i | \(-0.748774\pi\) | ||||
−0.704379 | + | 0.709824i | \(0.748774\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.75830 | 0.218747 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.2623 | 1.59689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.72733 | −0.448599 | −0.224300 | − | 0.974520i | \(-0.572009\pi\) | ||||
−0.224300 | + | 0.974520i | \(0.572009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.22343 | −0.636348 | −0.318174 | − | 0.948032i | \(-0.603070\pi\) | ||||
−0.318174 | + | 0.948032i | \(0.603070\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.36534 | 0.105027 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.86550 | −0.219131 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1427 | 1.15127 | 0.575637 | − | 0.817705i | \(-0.304754\pi\) | ||||
0.575637 | + | 0.817705i | \(0.304754\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.82712 | 0.287664 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.07415 | 0.304516 | 0.152258 | − | 0.988341i | \(-0.451346\pi\) | ||||
0.152258 | + | 0.988341i | \(0.451346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.92981 | 0.217771 | 0.108885 | − | 0.994054i | \(-0.465272\pi\) | ||||
0.108885 | + | 0.994054i | \(0.465272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.00343 | −0.295942 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.6696 | −1.43838 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.63992 | 0.482983 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.41644 | −0.391920 | −0.195960 | − | 0.980612i | \(-0.562782\pi\) | ||||
−0.195960 | + | 0.980612i | \(0.562782\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.6275 | 1.77273 | 0.886363 | − | 0.462991i | \(-0.153224\pi\) | ||||
0.886363 | + | 0.462991i | \(0.153224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.93923 | 0.280658 | 0.140329 | − | 0.990105i | \(-0.455184\pi\) | ||||
0.140329 | + | 0.990105i | \(0.455184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.8079 | −1.47504 | −0.737518 | − | 0.675328i | \(-0.764002\pi\) | ||||
−0.737518 | + | 0.675328i | \(0.764002\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.49720 | 0.176139 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.8685 | 1.11375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.8099 | −1.30738 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.94567 | −0.342099 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.9069 | −1.57698 | −0.788488 | − | 0.615050i | \(-0.789136\pi\) | ||||
−0.788488 | + | 0.615050i | \(0.789136\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.09322 | 0.0749061 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.1380 | 0.891868 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.805494 | 0.0544302 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0740 | −1.01399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.6488 | −1.11489 | −0.557444 | − | 0.830214i | \(-0.688218\pi\) | ||||
−0.557444 | + | 0.830214i | \(0.688218\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8343 | 0.785469 | 0.392735 | − | 0.919652i | \(-0.371529\pi\) | ||||
0.392735 | + | 0.919652i | \(0.371529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.84288 | 0.320026 | 0.160013 | − | 0.987115i | \(-0.448846\pi\) | ||||
0.160013 | + | 0.987115i | \(0.448846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.59864 | 0.368363 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.60851 | −0.629474 | −0.314737 | − | 0.949179i | \(-0.601916\pi\) | ||||
−0.314737 | + | 0.949179i | \(0.601916\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.19796 | 0.0778157 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.49984 | −0.614493 | −0.307247 | − | 0.951630i | \(-0.599408\pi\) | ||||
−0.307247 | + | 0.951630i | \(0.599408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8687 | −1.40868 | −0.704342 | − | 0.709860i | \(-0.748758\pi\) | ||||
−0.704342 | + | 0.709860i | \(0.748758\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.31665 | −0.597663 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.79016 | −0.241162 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.50339 | 0.0952734 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.03109 | 0.128201 | 0.0641007 | − | 0.997943i | \(-0.479582\pi\) | ||||
0.0641007 | + | 0.997943i | \(0.479582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.4647 | −2.04104 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.62917 | −0.475894 | −0.237947 | − | 0.971278i | \(-0.576475\pi\) | ||||
−0.237947 | + | 0.971278i | \(0.576475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.9379 | −1.48743 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.7311 | −0.911831 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.3299 | 1.87022 | 0.935112 | − | 0.354352i | \(-0.115298\pi\) | ||||
0.935112 | + | 0.354352i | \(0.115298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.55245 | 0.278605 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.3382 | 1.48393 | 0.741963 | − | 0.670441i | \(-0.233895\pi\) | ||||
0.741963 | + | 0.670441i | \(0.233895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.62084 | 0.219951 | 0.109975 | − | 0.993934i | \(-0.464923\pi\) | ||||
0.109975 | + | 0.993934i | \(0.464923\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.29057 | 0.259677 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.6842 | 1.78355 | 0.891776 | − | 0.452477i | \(-0.149459\pi\) | ||||
0.891776 | + | 0.452477i | \(0.149459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.1963 | −0.730175 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.1363 | 1.73813 | 0.869064 | − | 0.494700i | \(-0.164722\pi\) | ||||
0.869064 | + | 0.494700i | \(0.164722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.2081 | −1.43902 | −0.719511 | − | 0.694481i | \(-0.755634\pi\) | ||||
−0.719511 | + | 0.694481i | \(0.755634\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.96452 | −0.411103 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.18244 | −0.0695551 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.89373 | 0.228254 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.9338 | 0.930865 | 0.465433 | − | 0.885083i | \(-0.345899\pi\) | ||||
0.465433 | + | 0.885083i | \(0.345899\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.6386 | −0.617316 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.8796 | −1.43883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.5700 | −1.81967 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.80864 | 0.276249 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9373 | −1.48032 | −0.740161 | − | 0.672429i | \(-0.765251\pi\) | ||||
−0.740161 | + | 0.672429i | \(0.765251\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.81788 | 0.103416 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.58526 | −0.146597 | −0.0732983 | − | 0.997310i | \(-0.523353\pi\) | ||||
−0.0732983 | + | 0.997310i | \(0.523353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1027 | −0.966701 | −0.483351 | − | 0.875427i | \(-0.660580\pi\) | ||||
−0.483351 | + | 0.875427i | \(0.660580\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.5591 | −1.37938 | −0.689690 | − | 0.724105i | \(-0.742253\pi\) | ||||
−0.689690 | + | 0.724105i | \(0.742253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.4249 | −1.42352 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.93654 | 0.387160 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.97713 | 0.221293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.26440 | −0.180522 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.88813 | 0.159228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.4328 | 0.903227 | 0.451614 | − | 0.892214i | \(-0.350849\pi\) | ||||
0.451614 | + | 0.892214i | \(0.350849\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.2221 | 1.21776 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.0174 | 0.654627 | 0.327314 | − | 0.944916i | \(-0.393857\pi\) | ||||
0.327314 | + | 0.944916i | \(0.393857\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.61263 | −0.196211 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.0501 | −1.13992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8038 | −0.745336 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.3681 | −1.52288 | −0.761439 | − | 0.648236i | \(-0.775507\pi\) | ||||
−0.761439 | + | 0.648236i | \(0.775507\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.9733 | 1.81855 | 0.909275 | − | 0.416195i | \(-0.136637\pi\) | ||||
0.909275 | + | 0.416195i | \(0.136637\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.15302 | −0.435176 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.6181 | −1.41674 | −0.708369 | − | 0.705842i | \(-0.750569\pi\) | ||||
−0.708369 | + | 0.705842i | \(0.750569\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.50222 | −0.238283 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.84964 | 0.308732 | 0.154366 | − | 0.988014i | \(-0.450666\pi\) | ||||
0.154366 | + | 0.988014i | \(0.450666\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.93616 | −0.259081 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.41146 | −0.125877 | −0.0629385 | − | 0.998017i | \(-0.520047\pi\) | ||||
−0.0629385 | + | 0.998017i | \(0.520047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.46533 | 0.336571 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.2160 | −1.20531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.2074 | −1.40874 | −0.704372 | − | 0.709831i | \(-0.748771\pi\) | ||||
−0.704372 | + | 0.709831i | \(0.748771\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.4846 | −1.00351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.0749 | −1.90441 | −0.952204 | − | 0.305461i | \(-0.901189\pi\) | ||||
−0.952204 | + | 0.305461i | \(0.901189\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.38034 | −0.0707170 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.238749 | 0.0121995 | 0.00609975 | − | 0.999981i | \(-0.498058\pi\) | ||||
0.00609975 | + | 0.999981i | \(0.498058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.3072 | 1.48977 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.3399 | 1.08197 | 0.540987 | − | 0.841031i | \(-0.318051\pi\) | ||||
0.540987 | + | 0.841031i | \(0.318051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.1069 | 1.32028 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.68527 | −0.185897 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7416 | 0.890424 | 0.445212 | − | 0.895425i | \(-0.353128\pi\) | ||||
0.445212 | + | 0.895425i | \(0.353128\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.13203 | −0.0566723 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.4310 | 1.81928 | 0.909638 | − | 0.415401i | \(-0.136359\pi\) | ||||
0.909638 | + | 0.415401i | \(0.136359\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.1319 | −0.803589 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.3538 | 1.90113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.530833 | −0.0262480 | −0.0131240 | − | 0.999914i | \(-0.504178\pi\) | ||||
−0.0131240 | + | 0.999914i | \(0.504178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.36332 | 0.264553 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.2120 | −1.58505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.42919 | 0.216898 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.3816 | 1.43538 | 0.717692 | − | 0.696361i | \(-0.245199\pi\) | ||||
0.717692 | + | 0.696361i | \(0.245199\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.95912 | 0.144219 | 0.0721093 | − | 0.997397i | \(-0.477027\pi\) | ||||
0.0721093 | + | 0.997397i | \(0.477027\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.68112 | −0.130360 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.6960 | 1.63067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.87446 | −0.331902 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.4518 | −1.56315 | −0.781573 | − | 0.623814i | \(-0.785582\pi\) | ||||
−0.781573 | + | 0.623814i | \(0.785582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.7821 | −1.33512 | −0.667562 | − | 0.744554i | \(-0.732662\pi\) | ||||
−0.667562 | + | 0.744554i | \(0.732662\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.56426 | 0.314011 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0388357 | −0.00185352 | −0.000926762 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000926762 | 1.00000i | \(0.500295\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.24412 | −0.344958 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.98842 | −0.189496 | −0.0947479 | − | 0.995501i | \(-0.530204\pi\) | ||||
−0.0947479 | + | 0.995501i | \(0.530204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.61132 | −0.218108 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.1695 | 1.09343 | 0.546717 | − | 0.837317i | \(-0.315877\pi\) | ||||
0.546717 | + | 0.837317i | \(0.315877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.1587 | 0.525444 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.143151 | 0.00672582 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5398 | −0.539811 | −0.269905 | − | 0.962887i | \(-0.586992\pi\) | ||||
−0.269905 | + | 0.962887i | \(0.586992\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.55521 | 0.399323 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.96090 | 0.417351 | 0.208675 | − | 0.977985i | \(-0.433085\pi\) | ||||
0.208675 | + | 0.977985i | \(0.433085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.43012 | 0.205885 | 0.102943 | − | 0.994687i | \(-0.467174\pi\) | ||||
0.102943 | + | 0.994687i | \(0.467174\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.6874 | 1.42004 | 0.710021 | − | 0.704180i | \(-0.248685\pi\) | ||||
0.710021 | + | 0.704180i | \(0.248685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.0184 | −0.970541 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.47354 | 0.298285 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.5823 | 2.32578 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.5519 | 0.986796 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0047 | −0.822657 | −0.411328 | − | 0.911487i | \(-0.634935\pi\) | ||||
−0.411328 | + | 0.911487i | \(0.634935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.3928 | 1.34020 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.43093 | −0.338119 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7434 | 0.668087 | 0.334043 | − | 0.942558i | \(-0.391587\pi\) | ||||
0.334043 | + | 0.942558i | \(0.391587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.10043 | 0.0949847 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.0805 | 1.80881 | 0.904404 | − | 0.426677i | \(-0.140316\pi\) | ||||
0.904404 | + | 0.426677i | \(0.140316\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.4458 | 0.920832 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.20139 | −0.412739 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.7838 | 0.572282 | 0.286141 | − | 0.958188i | \(-0.407627\pi\) | ||||
0.286141 | + | 0.958188i | \(0.407627\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.01584 | 0.134738 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.9101 | 0.531046 | 0.265523 | − | 0.964105i | \(-0.414455\pi\) | ||||
0.265523 | + | 0.964105i | \(0.414455\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.500723 | −0.0222379 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7374 | 0.697549 | 0.348775 | − | 0.937207i | \(-0.386598\pi\) | ||||
0.348775 | + | 0.937207i | \(0.386598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.77967 | −0.299915 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.15110 | 0.0949734 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.62743 | −0.203514 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.55338 | −0.243766 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.67909 | 0.248806 | 0.124403 | − | 0.992232i | \(-0.460299\pi\) | ||||
0.124403 | + | 0.992232i | \(0.460299\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.8094 | 1.60956 | 0.804781 | − | 0.593572i | \(-0.202283\pi\) | ||||
0.804781 | + | 0.593572i | \(0.202283\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9277 | 0.737382 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.0896 | 0.873459 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.9032 | 1.29769 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.55160 | 0.370411 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.49414 | −0.0644770 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.5029 | −0.538537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.9051 | −1.07076 | −0.535378 | − | 0.844613i | \(-0.679831\pi\) | ||||
−0.535378 | + | 0.844613i | \(0.679831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.07447 | −0.0461100 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.17066 | −0.392109 | −0.196055 | − | 0.980593i | \(-0.562813\pi\) | ||||
−0.196055 | + | 0.980593i | \(0.562813\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.2808 | −1.33503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.14084 | 0.219007 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0830 | −0.428771 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.3168 | 0.691364 | 0.345682 | − | 0.938352i | \(-0.387648\pi\) | ||||
0.345682 | + | 0.938352i | \(0.387648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.7642 | 1.63955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.21357 | 0.304557 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.4254 | −0.987264 | −0.493632 | − | 0.869671i | \(-0.664331\pi\) | ||||
−0.493632 | + | 0.869671i | \(0.664331\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.1002 | 1.01211 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.5994 | −0.905495 | −0.452748 | − | 0.891639i | \(-0.649556\pi\) | ||||
−0.452748 | + | 0.891639i | \(0.649556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.9099 | −0.582111 | −0.291055 | − | 0.956706i | \(-0.594006\pi\) | ||||
−0.291055 | + | 0.956706i | \(0.594006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.98641 | 0.0829836 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0208 | 1.12489 | 0.562445 | − | 0.826834i | \(-0.309861\pi\) | ||||
0.562445 | + | 0.826834i | \(0.309861\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.03183 | −0.375350 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.6537 | −0.524964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.1972 | 1.54055 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.29463 | −0.0947096 | −0.0473548 | − | 0.998878i | \(-0.515079\pi\) | ||||
−0.0473548 | + | 0.998878i | \(0.515079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.25626 | 0.175376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.44466 | −0.0594255 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.6929 | 0.931888 | 0.465944 | − | 0.884814i | \(-0.345715\pi\) | ||||
0.465944 | + | 0.884814i | \(0.345715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.63105 | 0.312318 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.95675 | −0.202527 | −0.101264 | − | 0.994860i | \(-0.532289\pi\) | ||||
−0.101264 | + | 0.994860i | \(0.532289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.5372 | −1.36801 | −0.684005 | − | 0.729477i | \(-0.739763\pi\) | ||||
−0.684005 | + | 0.729477i | \(0.739763\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.5119 | 0.794586 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.9103 | −1.33579 | −0.667893 | − | 0.744257i | \(-0.732804\pi\) | ||||
−0.667893 | + | 0.744257i | \(0.732804\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.81957 | −0.235821 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.54628 | −0.143467 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.4090 | 1.79366 | 0.896831 | − | 0.442374i | \(-0.145863\pi\) | ||||
0.896831 | + | 0.442374i | \(0.145863\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.2962 | −0.736579 | −0.368290 | − | 0.929711i | \(-0.620056\pi\) | ||||
−0.368290 | + | 0.929711i | \(0.620056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.76770 | 0.111243 | 0.0556216 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556216 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.1204 | 0.566632 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.3170 | −1.53514 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.81376 | 0.0724347 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.8428 | −1.22978 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.74488 | −0.228700 | −0.114350 | − | 0.993441i | \(-0.536479\pi\) | ||||
−0.114350 | + | 0.993441i | \(0.536479\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.40083 | 0.333903 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.58170 | −0.379641 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.54186 | 0.337911 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.3436 | 0.764028 | 0.382014 | − | 0.924157i | \(-0.375231\pi\) | ||||
0.382014 | + | 0.924157i | \(0.375231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0400 | 0.435375 | 0.217687 | − | 0.976019i | \(-0.430149\pi\) | ||||
0.217687 | + | 0.976019i | \(0.430149\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.35938 | −0.132071 | −0.0660353 | − | 0.997817i | \(-0.521035\pi\) | ||||
−0.0660353 | + | 0.997817i | \(0.521035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.6109 | 2.02590 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.81821 | −0.188841 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −44.1434 | −1.72747 | −0.863733 | − | 0.503950i | \(-0.831879\pi\) | ||||
−0.863733 | + | 0.503950i | \(0.831879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.29372 | 0.245542 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.1874 | 1.37071 | 0.685354 | − | 0.728210i | \(-0.259648\pi\) | ||||
0.685354 | + | 0.728210i | \(0.259648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.3574 | 0.402855 | 0.201428 | − | 0.979503i | \(-0.435442\pi\) | ||||
0.201428 | + | 0.979503i | \(0.435442\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.52819 | 0.214697 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.7458 | 1.30664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.10575 | 0.236062 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −53.9886 | −2.08421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0384 | −1.38918 | −0.694589 | − | 0.719407i | \(-0.744414\pi\) | ||||
−0.694589 | + | 0.719407i | \(0.744414\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.4531 | −0.440177 | −0.220089 | − | 0.975480i | \(-0.570635\pi\) | ||||
−0.220089 | + | 0.975480i | \(0.570635\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.7727 | −1.25770 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.34008 | −0.166312 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.9554 | 1.64364 | 0.821821 | − | 0.569745i | \(-0.192958\pi\) | ||||
0.821821 | + | 0.569745i | \(0.192958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.77607 | −0.0677611 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.5065 | 1.08601 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.23235 | 0.199048 | 0.0995241 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995241 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 43.7449 | 1.66173 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.97345 | −0.339894 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.52380 | 0.133282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.3930 | −0.656925 | −0.328463 | − | 0.944517i | \(-0.606531\pi\) | ||||
−0.328463 | + | 0.944517i | \(0.606531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.75503 | −0.292486 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.4733 | −1.52215 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5383 | −0.808888 | −0.404444 | − | 0.914563i | \(-0.632535\pi\) | ||||
−0.404444 | + | 0.914563i | \(0.632535\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.36024 | 0.351036 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.9392 | 1.04633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.48395 | 0.130110 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.8923 | 1.15209 | 0.576044 | − | 0.817418i | \(-0.304596\pi\) | ||||
0.576044 | + | 0.817418i | \(0.304596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3007 | −0.569830 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.02006 | 0.298269 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.9947 | −0.778649 | −0.389325 | − | 0.921101i | \(-0.627292\pi\) | ||||
−0.389325 | + | 0.921101i | \(0.627292\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0061 | −0.740967 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.6765 | −1.50447 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0911 | 0.815955 | 0.407978 | − | 0.912992i | \(-0.366234\pi\) | ||||
0.407978 | + | 0.912992i | \(0.366234\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.6762 | 1.24048 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.81209 | −0.287372 | −0.143686 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143686 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.39000 | 0.0510628 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.9012 | 0.656731 | 0.328365 | − | 0.944551i | \(-0.393502\pi\) | ||||
0.328365 | + | 0.944551i | \(0.393502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.7467 | 0.429790 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −58.3834 | −2.13328 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.8802 | −1.78366 | −0.891832 | − | 0.452367i | \(-0.850580\pi\) | ||||
−0.891832 | + | 0.452367i | \(0.850580\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.744878 | −0.0271449 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.75011 | 0.245337 | 0.122668 | − | 0.992448i | \(-0.460855\pi\) | ||||
0.122668 | + | 0.992448i | \(0.460855\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.9060 | 0.432161 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.5563 | 1.72392 | 0.861958 | − | 0.506980i | \(-0.169238\pi\) | ||||
0.861958 | + | 0.506980i | \(0.169238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.4757 | 0.994689 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.5525 | 1.42816 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.849714 | −0.0306415 | −0.0153207 | − | 0.999883i | \(-0.504877\pi\) | ||||
−0.0153207 | + | 0.999883i | \(0.504877\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.79790 | 0.100764 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.74109 | −0.170525 | −0.0852627 | − | 0.996359i | \(-0.527173\pi\) | ||||
−0.0852627 | + | 0.996359i | \(0.527173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.77891 | 0.314942 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.25626 | −0.0808390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.7427 | 0.527535 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.0585 | 0.395197 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0208 | −0.678018 | −0.339009 | − | 0.940783i | \(-0.610092\pi\) | ||||
−0.339009 | + | 0.940783i | \(0.610092\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.1231 | −0.395994 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.4067 | 1.08114 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.3747 | −1.46926 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.8784 | −0.668706 | −0.334353 | − | 0.942448i | \(-0.608518\pi\) | ||||
−0.334353 | + | 0.942448i | \(0.608518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.72121 | 0.131647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.5705 | 1.25682 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.8625 | 0.383331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.92573 | −0.314201 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.68753 | −0.0593305 | −0.0296652 | − | 0.999560i | \(-0.509444\pi\) | ||||
−0.0296652 | + | 0.999560i | \(0.509444\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.3960 | 1.34827 | 0.674133 | − | 0.738610i | \(-0.264517\pi\) | ||||
0.674133 | + | 0.738610i | \(0.264517\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.32790 | −0.0465715 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2276 | −0.357818 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.5244 | 1.17144 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.4671 | −0.400204 | −0.200102 | − | 0.979775i | \(-0.564127\pi\) | ||||
−0.200102 | + | 0.979775i | \(0.564127\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.0927 | −1.60669 | −0.803345 | − | 0.595515i | \(-0.796948\pi\) | ||||
−0.803345 | + | 0.595515i | \(0.796948\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.44674 | −0.0503081 | −0.0251540 | − | 0.999684i | \(-0.508008\pi\) | ||||
−0.0251540 | + | 0.999684i | \(0.508008\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.8553 | −1.52316 | −0.761578 | − | 0.648073i | \(-0.775575\pi\) | ||||
−0.761578 | + | 0.648073i | \(0.775575\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.8863 | −0.377642 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0544 | 0.348363 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.15565 | 0.316465 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.7264 | −1.57865 | −0.789325 | − | 0.613976i | \(-0.789569\pi\) | ||||
−0.789325 | + | 0.613976i | \(0.789569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.57179 | −0.0886824 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.6854 | −0.368024 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.5466 | 1.42756 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.87802 | 0.304693 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.9061 | −1.74504 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.3388 | 0.970303 | 0.485151 | − | 0.874430i | \(-0.338764\pi\) | ||||
0.485151 | + | 0.874430i | \(0.338764\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.7526 | 0.640575 | 0.320288 | − | 0.947320i | \(-0.396220\pi\) | ||||
0.320288 | + | 0.947320i | \(0.396220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2675 | −0.486801 | −0.243401 | − | 0.969926i | \(-0.578263\pi\) | ||||
−0.243401 | + | 0.969926i | \(0.578263\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.55415 | 0.0870453 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.9573 | −1.12188 | −0.560940 | − | 0.827857i | \(-0.689560\pi\) | ||||
−0.560940 | + | 0.827857i | \(0.689560\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.433644 | 0.0147273 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.1552 | 0.548026 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.8081 | 0.874475 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.4236 | 1.02968 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.9346 | −1.41603 | −0.708016 | − | 0.706197i | \(-0.750409\pi\) | ||||
−0.708016 | + | 0.706197i | \(0.750409\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.84354 | −0.197098 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.69223 | 0.259158 | 0.129579 | − | 0.991569i | \(-0.458637\pi\) | ||||
0.129579 | + | 0.991569i | \(0.458637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.8546 | −1.10565 | −0.552823 | − | 0.833299i | \(-0.686449\pi\) | ||||
−0.552823 | + | 0.833299i | \(0.686449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.97358 | −0.0662664 | −0.0331332 | − | 0.999451i | \(-0.510549\pi\) | ||||
−0.0331332 | + | 0.999451i | \(0.510549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6180 | 0.389656 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.6139 | −1.29361 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.935652 | 0.0313104 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.12430 | 0.304651 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.8808 | 0.729764 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.9127 | −0.996536 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5779 | 0.385289 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.21342 | 0.206313 | 0.103157 | − | 0.994665i | \(-0.467106\pi\) | ||||
0.103157 | + | 0.994665i | \(0.467106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.5723 | 1.24619 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.4200 | −1.33917 | −0.669586 | − | 0.742734i | \(-0.733529\pi\) | ||||
−0.669586 | + | 0.742734i | \(0.733529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.2741 | 0.670974 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.0181 | 1.02431 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.0177 | 1.74889 | 0.874446 | − | 0.485122i | \(-0.161225\pi\) | ||||
0.874446 | + | 0.485122i | \(0.161225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.51220 | 0.313438 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.2982 | 0.371885 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2040 | 0.466522 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.0520 | 1.24845 | 0.624224 | − | 0.781246i | \(-0.285415\pi\) | ||||
0.624224 | + | 0.781246i | \(0.285415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.52804 | 0.0828533 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.948112 | 0.0310398 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.8035 | −0.418271 | −0.209135 | − | 0.977887i | \(-0.567065\pi\) | ||||
−0.209135 | + | 0.977887i | \(0.567065\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.27220 | 0.204686 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.1622 | 1.30925 | 0.654625 | − | 0.755954i | \(-0.272827\pi\) | ||||
0.654625 | + | 0.755954i | \(0.272827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8107 | −0.482303 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.3713 | 0.824458 | 0.412229 | − | 0.911080i | \(-0.364750\pi\) | ||||
0.412229 | + | 0.911080i | \(0.364750\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.32463 | 0.270229 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.00676 | 0.292064 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.25884 | −0.202744 | −0.101372 | − | 0.994849i | \(-0.532323\pi\) | ||||
−0.101372 | + | 0.994849i | \(0.532323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.32426 | 0.301411 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.1420 | −1.45771 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.8842 | −0.415620 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 54.1986 | 1.74653 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6425 | 0.535186 | 0.267593 | − | 0.963532i | \(-0.413772\pi\) | ||||
0.267593 | + | 0.963532i | \(0.413772\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.45856 | −0.0468558 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.5468 | −0.659377 | −0.329688 | − | 0.944090i | \(-0.606944\pi\) | ||||
−0.329688 | + | 0.944090i | \(0.606944\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37.2796 | −1.19513 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.7487 | 1.55961 | 0.779804 | − | 0.626024i | \(-0.215319\pi\) | ||||
0.779804 | + | 0.626024i | \(0.215319\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61.3924 | 1.96211 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5064 | −0.814355 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.9881 | 1.11595 | 0.557973 | − | 0.829859i | \(-0.311579\pi\) | ||||
0.557973 | + | 0.829859i | \(0.311579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.05919 | −0.0337142 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −67.1366 | −2.13482 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4515 | 0.395535 | 0.197768 | − | 0.980249i | \(-0.436631\pi\) | ||||
0.197768 | + | 0.980249i | \(0.436631\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.02652 | −0.191246 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.4889 | 0.427199 | 0.213599 | − | 0.976921i | \(-0.431481\pi\) | ||||
0.213599 | + | 0.976921i | \(0.431481\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.6818 | −0.527790 |
(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 | 3800.2.a.z.1.4 | 6 | ||
4.3 | odd | 2 | 7600.2.a.cn.1.3 | 6 | |||
5.2 | odd | 4 | 760.2.d.e.609.7 | yes | 12 | ||
5.3 | odd | 4 | 760.2.d.e.609.6 | ✓ | 12 | ||
5.4 | even | 2 | 3800.2.a.be.1.3 | 6 | |||
20.3 | even | 4 | 1520.2.d.k.609.7 | 12 | |||
20.7 | even | 4 | 1520.2.d.k.609.6 | 12 | |||
20.19 | odd | 2 | 7600.2.a.cg.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.e.609.6 | ✓ | 12 | 5.3 | odd | 4 | ||
760.2.d.e.609.7 | yes | 12 | 5.2 | odd | 4 | ||
1520.2.d.k.609.6 | 12 | 20.7 | even | 4 | |||
1520.2.d.k.609.7 | 12 | 20.3 | even | 4 | |||
3800.2.a.z.1.4 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.a.be.1.3 | 6 | 5.4 | even | 2 | |||
7600.2.a.cg.1.4 | 6 | 20.19 | odd | 2 | |||
7600.2.a.cn.1.3 | 6 | 4.3 | odd | 2 |