Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1400) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.347296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.34730 | 0.777862 | 0.388931 | − | 0.921267i | \(-0.372844\pi\) | ||||
0.388931 | + | 0.921267i | \(0.372844\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.18479 | −0.394931 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41147 | 0.425575 | 0.212788 | − | 0.977098i | \(-0.431746\pi\) | ||||
0.212788 | + | 0.977098i | \(0.431746\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.47565 | −1.79602 | −0.898011 | − | 0.439972i | \(-0.854988\pi\) | ||||
−0.898011 | + | 0.439972i | \(0.854988\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.59627 | 0.629687 | 0.314844 | − | 0.949144i | \(-0.398048\pi\) | ||||
0.314844 | + | 0.949144i | \(0.398048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.16250 | 0.266697 | 0.133348 | − | 0.991069i | \(-0.457427\pi\) | ||||
0.133348 | + | 0.991069i | \(0.457427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.57398 | −0.328197 | −0.164099 | − | 0.986444i | \(-0.552472\pi\) | ||||
−0.164099 | + | 0.986444i | \(0.552472\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.63816 | −1.08506 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.22668 | 1.15627 | 0.578133 | − | 0.815943i | \(-0.303782\pi\) | ||||
0.578133 | + | 0.815943i | \(0.303782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.98545 | 0.895414 | 0.447707 | − | 0.894180i | \(-0.352241\pi\) | ||||
0.447707 | + | 0.894180i | \(0.352241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.90167 | 0.331039 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.47565 | −1.39339 | −0.696694 | − | 0.717368i | \(-0.745347\pi\) | ||||
−0.696694 | + | 0.717368i | \(0.745347\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.72462 | −1.39706 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.57398 | 0.558162 | 0.279081 | − | 0.960268i | \(-0.409970\pi\) | ||||
0.279081 | + | 0.960268i | \(0.409970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.24897 | −1.10546 | −0.552729 | − | 0.833361i | \(-0.686413\pi\) | ||||
−0.552729 | + | 0.833361i | \(0.686413\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9436 | 1.59628 | 0.798141 | − | 0.602470i | \(-0.205817\pi\) | ||||
0.798141 | + | 0.602470i | \(0.205817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.49794 | 0.489810 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.7861 | 1.75631 | 0.878154 | − | 0.478378i | \(-0.158775\pi\) | ||||
0.878154 | + | 0.478378i | \(0.158775\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.56624 | 0.207453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.04189 | −0.265831 | −0.132916 | − | 0.991127i | \(-0.542434\pi\) | ||||
−0.132916 | + | 0.991127i | \(0.542434\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.615867 | −0.0788537 | −0.0394268 | − | 0.999222i | \(-0.512553\pi\) | ||||
−0.0394268 | + | 0.999222i | \(0.512553\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.08378 | 0.743252 | 0.371626 | − | 0.928383i | \(-0.378800\pi\) | ||||
0.371626 | + | 0.928383i | \(0.378800\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.12061 | −0.255292 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.27631 | −0.982217 | −0.491109 | − | 0.871098i | \(-0.663408\pi\) | ||||
−0.491109 | + | 0.871098i | \(0.663408\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.51754 | 0.411697 | 0.205849 | − | 0.978584i | \(-0.434005\pi\) | ||||
0.205849 | + | 0.978584i | \(0.434005\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.879385 | 0.0989386 | 0.0494693 | − | 0.998776i | \(-0.484247\pi\) | ||||
0.0494693 | + | 0.998776i | \(0.484247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.04189 | −0.449099 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.90167 | −0.428264 | −0.214132 | − | 0.976805i | \(-0.568692\pi\) | ||||
−0.214132 | + | 0.976805i | \(0.568692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.38919 | 0.899415 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.96316 | 0.632094 | 0.316047 | − | 0.948744i | \(-0.397644\pi\) | ||||
0.316047 | + | 0.948744i | \(0.397644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.71688 | 0.696508 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.23442 | 0.328406 | 0.164203 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164203 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.67230 | −0.168073 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5321 | 1.44600 | 0.722998 | − | 0.690850i | \(-0.242763\pi\) | ||||
0.722998 | + | 0.690850i | \(0.242763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9736 | −1.57392 | −0.786962 | − | 0.617001i | \(-0.788347\pi\) | ||||
−0.786962 | + | 0.617001i | \(0.788347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.8307 | 1.72376 | 0.861879 | − | 0.507114i | \(-0.169288\pi\) | ||||
0.861879 | + | 0.507114i | \(0.169288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2344 | 1.17185 | 0.585923 | − | 0.810367i | \(-0.300732\pi\) | ||||
0.585923 | + | 0.810367i | \(0.300732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.4192 | −1.08386 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.29086 | −0.403650 | −0.201825 | − | 0.979422i | \(-0.564687\pi\) | ||||
−0.201825 | + | 0.979422i | \(0.564687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.67230 | 0.709305 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00774 | −0.818886 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.81521 | 0.434173 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.89899 | 0.878393 | 0.439196 | − | 0.898391i | \(-0.355263\pi\) | ||||
0.439196 | + | 0.898391i | \(0.355263\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.76651 | −0.859893 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9659 | 1.39494 | 0.697471 | − | 0.716613i | \(-0.254308\pi\) | ||||
0.697471 | + | 0.716613i | \(0.254308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.7219 | 1.08691 | 0.543454 | − | 0.839439i | \(-0.317116\pi\) | ||||
0.543454 | + | 0.839439i | \(0.317116\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.65270 | 0.649094 | 0.324547 | − | 0.945870i | \(-0.394788\pi\) | ||||
0.324547 | + | 0.945870i | \(0.394788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.7442 | 1.24169 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.14022 | −0.764343 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.29086 | 0.269598 | 0.134799 | − | 0.990873i | \(-0.456961\pi\) | ||||
0.134799 | + | 0.990873i | \(0.456961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7246 | −1.52379 | −0.761894 | − | 0.647702i | \(-0.775730\pi\) | ||||
−0.761894 | + | 0.647702i | \(0.775730\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.07604 | −0.248683 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.7074 | −1.49301 | −0.746506 | − | 0.665379i | \(-0.768270\pi\) | ||||
−0.746506 | + | 0.665379i | \(0.768270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.2267 | 1.36616 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.87939 | −0.147205 | −0.0736024 | − | 0.997288i | \(-0.523450\pi\) | ||||
−0.0736024 | + | 0.997288i | \(0.523450\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.25402 | −0.0970392 | −0.0485196 | − | 0.998822i | \(-0.515450\pi\) | ||||
−0.0485196 | + | 0.998822i | \(0.515450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.9341 | 2.22570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.37733 | −0.105327 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.35504 | 0.103022 | 0.0515108 | − | 0.998672i | \(-0.483596\pi\) | ||||
0.0515108 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.75103 | −0.206780 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.4047 | 0.852425 | 0.426212 | − | 0.904623i | \(-0.359848\pi\) | ||||
0.426212 | + | 0.904623i | \(0.359848\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.40373 | 0.698974 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.829755 | −0.0613373 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.66456 | 0.267979 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.7743 | −1.79260 | −0.896301 | − | 0.443446i | \(-0.853756\pi\) | ||||
−0.896301 | + | 0.443446i | \(0.853756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9786 | −0.790260 | −0.395130 | − | 0.918625i | \(-0.629300\pi\) | ||||
−0.395130 | + | 0.918625i | \(0.629300\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.1019 | 1.71719 | 0.858596 | − | 0.512652i | \(-0.171337\pi\) | ||||
0.858596 | + | 0.512652i | \(0.171337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79561 | 0.694392 | 0.347196 | − | 0.937793i | \(-0.387134\pi\) | ||||
0.347196 | + | 0.937793i | \(0.387134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.19665 | 0.578147 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.86484 | 0.129615 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.64084 | 0.113500 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.68954 | 0.460527 | 0.230263 | − | 0.973128i | \(-0.426041\pi\) | ||||
0.230263 | + | 0.973128i | \(0.426041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.1506 | −0.764030 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.73917 | 0.320243 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.8125 | −1.13093 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4911 | 1.70701 | 0.853506 | − | 0.521083i | \(-0.174472\pi\) | ||||
0.853506 | + | 0.521083i | \(0.174472\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.3396 | 0.752633 | 0.376316 | − | 0.926491i | \(-0.377191\pi\) | ||||
0.376316 | + | 0.926491i | \(0.377191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.64321 | −0.372914 | −0.186457 | − | 0.982463i | \(-0.559700\pi\) | ||||
−0.186457 | + | 0.982463i | \(0.559700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.3601 | 0.678712 | 0.339356 | − | 0.940658i | \(-0.389791\pi\) | ||||
0.339356 | + | 0.940658i | \(0.389791\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.18479 | 0.0769605 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2422 | −0.791880 | −0.395940 | − | 0.918276i | \(-0.629581\pi\) | ||||
−0.395940 | + | 0.918276i | \(0.629581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.8598 | 1.15045 | 0.575225 | − | 0.817995i | \(-0.304915\pi\) | ||||
0.575225 | + | 0.817995i | \(0.304915\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.4688 | 0.735727 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.52797 | −0.478993 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.25671 | −0.333131 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7888 | 1.05970 | 0.529850 | − | 0.848091i | \(-0.322248\pi\) | ||||
0.529850 | + | 0.848091i | \(0.322248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.22163 | −0.139673 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.3250 | 1.14308 | 0.571541 | − | 0.820573i | \(-0.306346\pi\) | ||||
0.571541 | + | 0.820573i | \(0.306346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.37733 | −0.456645 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5202 | 0.833693 | 0.416847 | − | 0.908977i | \(-0.363135\pi\) | ||||
0.416847 | + | 0.908977i | \(0.363135\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.03415 | 0.491682 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.7648 | 1.69285 | 0.846424 | − | 0.532510i | \(-0.178751\pi\) | ||||
0.846424 | + | 0.532510i | \(0.178751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8794 | 0.964604 | 0.482302 | − | 0.876005i | \(-0.339801\pi\) | ||||
0.482302 | + | 0.876005i | \(0.339801\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7074 | −1.00385 | −0.501925 | − | 0.864911i | \(-0.667375\pi\) | ||||
−0.501925 | + | 0.864911i | \(0.667375\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.90673 | −0.353626 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.0155 | 1.90988 | 0.954942 | − | 0.296793i | \(-0.0959172\pi\) | ||||
0.954942 | + | 0.296793i | \(0.0959172\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7074 | −0.636488 | −0.318244 | − | 0.948009i | \(-0.603093\pi\) | ||||
−0.318244 | + | 0.948009i | \(0.603093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2594 | −0.603494 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.35773 | 0.255454 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.20439 | −0.479306 | −0.239653 | − | 0.970859i | \(-0.577034\pi\) | ||||
−0.239653 | + | 0.970859i | \(0.577034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.95811 | −0.461776 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.1925 | 0.589449 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.5790 | 1.12479 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.3678 | 1.50489 | 0.752446 | − | 0.658654i | \(-0.228874\pi\) | ||||
0.752446 | + | 0.658654i | \(0.228874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.5212 | −1.22430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6655 | −0.831604 | −0.415802 | − | 0.909455i | \(-0.636499\pi\) | ||||
−0.415802 | + | 0.909455i | \(0.636499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.5202 | −1.72511 | −0.862553 | − | 0.505967i | \(-0.831136\pi\) | ||||
−0.862553 | + | 0.505967i | \(0.831136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.8716 | −0.947606 | −0.473803 | − | 0.880631i | \(-0.657119\pi\) | ||||
−0.473803 | + | 0.880631i | \(0.657119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.78880 | 0.492078 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0232 | 1.34085 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.01817 | 0.167935 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.4834 | 0.911534 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3756 | 0.790153 | 0.395076 | − | 0.918648i | \(-0.370718\pi\) | ||||
0.395076 | + | 0.918648i | \(0.370718\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0419 | 0.550292 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.2909 | 0.996367 | 0.498183 | − | 0.867072i | \(-0.334001\pi\) | ||||
0.498183 | + | 0.867072i | \(0.334001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.78106 | −0.313984 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.03684 | 0.381066 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.0378 | −1.66619 | −0.833097 | − | 0.553126i | \(-0.813435\pi\) | ||||
−0.833097 | + | 0.553126i | \(0.813435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3286 | −1.14170 | −0.570848 | − | 0.821056i | \(-0.693385\pi\) | ||||
−0.570848 | + | 0.821056i | \(0.693385\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.5107 | 1.94880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.6313 | −1.84324 | −0.921620 | − | 0.388093i | \(-0.873134\pi\) | ||||
−0.921620 | + | 0.388093i | \(0.873134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.7151 | −1.19886 | −0.599429 | − | 0.800428i | \(-0.704606\pi\) | ||||
−0.599429 | + | 0.800428i | \(0.704606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6486 | −0.928873 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.1361 | −0.636980 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.7050 | 1.60279 | 0.801395 | − | 0.598136i | \(-0.204092\pi\) | ||||
0.801395 | + | 0.598136i | \(0.204092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.23442 | −0.220435 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.3705 | −0.899411 | −0.449706 | − | 0.893177i | \(-0.648471\pi\) | ||||
−0.449706 | + | 0.893177i | \(0.648471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.3218 | −2.07668 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.78880 | 0.143251 | 0.0716255 | − | 0.997432i | \(-0.477181\pi\) | ||||
0.0716255 | + | 0.997432i | \(0.477181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.3369 | 0.683268 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.07098 | −0.259115 | −0.129558 | − | 0.991572i | \(-0.541356\pi\) | ||||
−0.129558 | + | 0.991572i | \(0.541356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.58853 | 0.436579 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.59896 | −0.435984 | −0.217992 | − | 0.975951i | \(-0.569951\pi\) | ||||
−0.217992 | + | 0.975951i | \(0.569951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.08647 | −0.206661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.5107 | 1.08507 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.57398 | 0.129184 | 0.0645921 | − | 0.997912i | \(-0.479425\pi\) | ||||
0.0645921 | + | 0.997912i | \(0.479425\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.4620 | 1.47126 | 0.735632 | − | 0.677381i | \(-0.236885\pi\) | ||||
0.735632 | + | 0.677381i | \(0.236885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.2841 | −1.60818 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.9632 | −0.592992 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.85204 | 0.289365 | 0.144682 | − | 0.989478i | \(-0.453784\pi\) | ||||
0.144682 | + | 0.989478i | \(0.453784\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.1402 | 0.845464 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.3105 | 0.504905 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.03952 | −0.0507841 | −0.0253921 | − | 0.999678i | \(-0.508083\pi\) | ||||
−0.0253921 | + | 0.999678i | \(0.508083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1566 | −1.56722 | −0.783609 | − | 0.621254i | \(-0.786623\pi\) | ||||
−0.783609 | + | 0.621254i | \(0.786623\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.9659 | −0.630421 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.3146 | −0.594553 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.460170 | 0.0221656 | 0.0110828 | − | 0.999939i | \(-0.496472\pi\) | ||||
0.0110828 | + | 0.999939i | \(0.496472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.6509 | 1.18465 | 0.592325 | − | 0.805699i | \(-0.298210\pi\) | ||||
0.592325 | + | 0.805699i | \(0.298210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.82976 | −0.0875291 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.9145 | 1.42774 | 0.713870 | − | 0.700278i | \(-0.246941\pi\) | ||||
0.713870 | + | 0.700278i | \(0.246941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.5868 | −0.598016 | −0.299008 | − | 0.954251i | \(-0.596656\pi\) | ||||
−0.299008 | + | 0.954251i | \(0.596656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.43376 | 0.209710 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4783 | 1.15520 | 0.577602 | − | 0.816318i | \(-0.303989\pi\) | ||||
0.577602 | + | 0.816318i | \(0.303989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.04458 | 0.237540 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.2276 | −1.18530 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.4611 | −1.89269 | −0.946345 | − | 0.323157i | \(-0.895256\pi\) | ||||
−0.946345 | + | 0.323157i | \(0.895256\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.6382 | −0.683251 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.22668 | −0.243431 | −0.121715 | − | 0.992565i | \(-0.538840\pi\) | ||||
−0.121715 | + | 0.992565i | \(0.538840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.0547 | −1.86150 | −0.930749 | − | 0.365658i | \(-0.880844\pi\) | ||||
−0.930749 | + | 0.365658i | \(0.880844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.5767 | 0.952175 | 0.476087 | − | 0.879398i | \(-0.342055\pi\) | ||||
0.476087 | + | 0.879398i | \(0.342055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.2044 | −1.16136 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.2317 | −0.470456 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.1489 | −0.693620 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6040 | 1.03280 | 0.516402 | − | 0.856346i | \(-0.327271\pi\) | ||||
0.516402 | + | 0.856346i | \(0.327271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.8854 | 2.50256 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.9118 | −1.17417 | −0.587087 | − | 0.809524i | \(-0.699726\pi\) | ||||
−0.587087 | + | 0.809524i | \(0.699726\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.53209 | −0.114505 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.7297 | 1.79298 | 0.896488 | − | 0.443069i | \(-0.146110\pi\) | ||||
0.896488 | + | 0.443069i | \(0.146110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.1661 | 0.728086 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.1925 | 0.903942 | 0.451971 | − | 0.892033i | \(-0.350721\pi\) | ||||
0.451971 | + | 0.892033i | \(0.350721\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.68954 | −0.0754831 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.29086 | −0.325083 | −0.162542 | − | 0.986702i | \(-0.551969\pi\) | ||||
−0.162542 | + | 0.986702i | \(0.551969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.9828 | 1.73129 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.54252 | 0.289992 | 0.144996 | − | 0.989432i | \(-0.453683\pi\) | ||||
0.144996 | + | 0.989432i | \(0.453683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.55438 | −0.289383 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.4466 | 0.679339 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.82564 | 0.0801366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7588 | 0.515161 | 0.257581 | − | 0.966257i | \(-0.417075\pi\) | ||||
0.257581 | + | 0.966257i | \(0.417075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.984518 | 0.0430500 | 0.0215250 | − | 0.999768i | \(-0.493148\pi\) | ||||
0.0215250 | + | 0.999768i | \(0.493148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9436 | 0.563830 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5226 | −0.892287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.41921 | 0.104985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.1438 | −1.00247 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.3655 | 0.663069 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.2098 | 0.696912 | 0.348456 | − | 0.937325i | \(-0.386706\pi\) | ||||
0.348456 | + | 0.937325i | \(0.386706\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6696 | 0.543705 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3337 | 1.25422 | 0.627109 | − | 0.778932i | \(-0.284238\pi\) | ||||
0.627109 | + | 0.778932i | \(0.284238\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.729675 | 0.0311418 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.23854 | 0.308372 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.0469 | −0.552817 | −0.276408 | − | 0.961040i | \(-0.589144\pi\) | ||||
−0.276408 | + | 0.961040i | \(0.589144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.9418 | 1.98543 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.93725 | 0.208451 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.9418 | 1.13546 | 0.567731 | − | 0.823214i | \(-0.307821\pi\) | ||||
0.567731 | + | 0.823214i | \(0.307821\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2327 | 0.554742 | 0.277371 | − | 0.960763i | \(-0.410537\pi\) | ||||
0.277371 | + | 0.960763i | \(0.410537\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.32770 | −0.264806 | −0.132403 | − | 0.991196i | \(-0.542269\pi\) | ||||
−0.132403 | + | 0.991196i | \(0.542269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.3783 | −1.39440 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.19160 | −0.257760 | −0.128880 | − | 0.991660i | \(-0.541138\pi\) | ||||
−0.128880 | + | 0.991660i | \(0.541138\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.7915 | −0.614713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0473 | 0.747441 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.6186 | 1.09867 | 0.549333 | − | 0.835604i | \(-0.314882\pi\) | ||||
0.549333 | + | 0.835604i | \(0.314882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.79561 | 0.238804 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.4725 | 1.33574 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.5466 | −0.556294 | −0.278147 | − | 0.960539i | \(-0.589720\pi\) | ||||
−0.278147 | + | 0.960539i | \(0.589720\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.1976 | 0.540141 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.6013 | −1.20948 | −0.604739 | − | 0.796424i | \(-0.706722\pi\) | ||||
−0.604739 | + | 0.796424i | \(0.706722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9050 | −0.852732 | −0.426366 | − | 0.904551i | \(-0.640206\pi\) | ||||
−0.426366 | + | 0.904551i | \(0.640206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.20801 | −0.293533 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.2036 | −1.51005 | −0.755023 | − | 0.655698i | \(-0.772374\pi\) | ||||
−0.755023 | + | 0.655698i | \(0.772374\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −70.8667 | −2.86696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.1138 | 1.05473 | 0.527363 | − | 0.849640i | \(-0.323181\pi\) | ||||
0.527363 | + | 0.849640i | \(0.323181\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4698 | −1.02537 | −0.512687 | − | 0.858575i | \(-0.671350\pi\) | ||||
−0.512687 | + | 0.858575i | \(0.671350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0291 | 0.604070 | 0.302035 | − | 0.953297i | \(-0.402334\pi\) | ||||
0.302035 | + | 0.953297i | \(0.402334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.87433 | 0.356115 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.21070 | 0.0882870 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.0051 | −0.877399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.605762 | 0.0241150 | 0.0120575 | − | 0.999927i | \(-0.496162\pi\) | ||||
0.0120575 | + | 0.999927i | \(0.496162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.01279 | 0.358226 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.80571 | 0.387908 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.7543 | 0.898742 | 0.449371 | − | 0.893345i | \(-0.351648\pi\) | ||||
0.449371 | + | 0.893345i | \(0.351648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.85204 | 0.0730375 | 0.0365187 | − | 0.999333i | \(-0.488373\pi\) | ||||
0.0365187 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.68685 | 0.262887 | 0.131444 | − | 0.991324i | \(-0.458039\pi\) | ||||
0.131444 | + | 0.991324i | \(0.458039\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.88207 | −0.113131 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.0327 | 0.431744 | 0.215872 | − | 0.976422i | \(-0.430741\pi\) | ||||
0.215872 | + | 0.976422i | \(0.430741\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.16756 | −0.162592 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.5202 | −0.526673 | −0.263337 | − | 0.964704i | \(-0.584823\pi\) | ||||
−0.263337 | + | 0.964704i | \(0.584823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.1385 | 1.63900 | 0.819498 | − | 0.573082i | \(-0.194252\pi\) | ||||
0.819498 | + | 0.573082i | \(0.194252\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.6514 | −0.879709 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.80066 | −0.379483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.3441 | 1.32782 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.869280 | −0.0335582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.8494 | −0.726589 | −0.363295 | − | 0.931674i | \(-0.618348\pi\) | ||||
−0.363295 | + | 0.931674i | \(0.618348\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.9760 | −0.959904 | −0.479952 | − | 0.877295i | \(-0.659346\pi\) | ||||
−0.479952 | + | 0.877295i | \(0.659346\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.2777 | 0.585444 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.1266 | 0.655331 | 0.327666 | − | 0.944794i | \(-0.393738\pi\) | ||||
0.327666 | + | 0.944794i | \(0.393738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.60307 | −0.290075 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −82.7984 | −3.15437 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.6100 | −0.517749 | −0.258874 | − | 0.965911i | \(-0.583352\pi\) | ||||
−0.258874 | + | 0.965911i | \(0.583352\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.27900 | 0.351467 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.9581 | 0.527944 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.86247 | 0.145884 | 0.0729418 | − | 0.997336i | \(-0.476761\pi\) | ||||
0.0729418 | + | 0.997336i | \(0.476761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.85298 | −0.371612 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7870 | −0.818230 | −0.409115 | − | 0.912483i | \(-0.634162\pi\) | ||||
−0.409115 | + | 0.912483i | \(0.634162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04189 | −0.0390739 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.84699 | −0.293872 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.4938 | −0.615973 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.7853 | −1.89397 | −0.946986 | − | 0.321275i | \(-0.895889\pi\) | ||||
−0.946986 | + | 0.321275i | \(0.895889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.0624 | 0.894891 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1607 | 1.41530 | 0.707652 | − | 0.706561i | \(-0.249755\pi\) | ||||
0.707652 | + | 0.706561i | \(0.249755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.5776 | 1.02139 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.8203 | −0.696092 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.3942 | −0.568599 | −0.284300 | − | 0.958735i | \(-0.591761\pi\) | ||||
−0.284300 | + | 0.958735i | \(0.591761\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.58710 | 0.316310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.1498 | −1.62408 | −0.812039 | − | 0.583604i | \(-0.801642\pi\) | ||||
−0.812039 | + | 0.583604i | \(0.801642\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1424 | −0.372591 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −53.0378 | −1.94577 | −0.972884 | − | 0.231296i | \(-0.925704\pi\) | ||||
−0.972884 | + | 0.231296i | \(0.925704\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.62267 | 0.169135 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.71688 | 0.354574 | 0.177287 | − | 0.984159i | \(-0.443268\pi\) | ||||
0.177287 | + | 0.984159i | \(0.443268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.6195 | 0.824300 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.2030 | 0.806980 | 0.403490 | − | 0.914984i | \(-0.367797\pi\) | ||||
0.403490 | + | 0.914984i | \(0.367797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.99319 | −0.108646 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.0547 | 1.34323 | 0.671616 | − | 0.740900i | \(-0.265601\pi\) | ||||
0.671616 | + | 0.740900i | \(0.265601\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2226 | 0.477439 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.7948 | 1.50716 | 0.753579 | − | 0.657357i | \(-0.228326\pi\) | ||||
0.753579 | + | 0.657357i | \(0.228326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6892 | 0.889160 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.3381 | −1.12715 | −0.563577 | − | 0.826064i | \(-0.690575\pi\) | ||||
−0.563577 | + | 0.826064i | \(0.690575\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.15476 | 0.148860 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6818 | −0.418008 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.1070 | −1.25462 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.7719 | 0.883022 | 0.441511 | − | 0.897256i | \(-0.354443\pi\) | ||||
0.441511 | + | 0.897256i | \(0.354443\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.2158 | 0.648498 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.98814 | 0.141623 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.07697 | 0.179836 | 0.0899178 | − | 0.995949i | \(-0.471340\pi\) | ||||
0.0899178 | + | 0.995949i | \(0.471340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.4124 | 1.00516 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.06511 | −0.249633 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.96492 | 0.175208 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.4074 | 1.31680 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.95037 | 0.103729 | 0.0518647 | − | 0.998654i | \(-0.483484\pi\) | ||||
0.0518647 | + | 0.998654i | \(0.483484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1753 | −0.462647 | −0.231324 | − | 0.972877i | \(-0.574306\pi\) | ||||
−0.231324 | + | 0.972877i | \(0.574306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.3942 | 0.750329 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.42696 | −0.294822 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.6064 | −0.823868 | −0.411934 | − | 0.911214i | \(-0.635147\pi\) | ||||
−0.411934 | + | 0.911214i | \(0.635147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.64084 | 0.196627 | 0.0983137 | − | 0.995155i | \(-0.468655\pi\) | ||||
0.0983137 | + | 0.995155i | \(0.468655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.2368 | −0.668929 | −0.334464 | − | 0.942408i | \(-0.608555\pi\) | ||||
−0.334464 | + | 0.942408i | \(0.608555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.3523 | 0.949986 | 0.474993 | − | 0.879989i | \(-0.342451\pi\) | ||||
0.474993 | + | 0.879989i | \(0.342451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.5098 | −0.780856 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.1088 | −0.971581 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.5425 | 0.571111 | 0.285556 | − | 0.958362i | \(-0.407822\pi\) | ||||
0.285556 | + | 0.958362i | \(0.407822\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.77156 | 0.336950 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.1343 | 1.48563 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.4260 | −0.495100 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.3405 | 0.457306 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.633103 | −0.0216770 | −0.0108385 | − | 0.999941i | \(-0.503450\pi\) | ||||
−0.0108385 | + | 0.999941i | \(0.503450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.15570 | 0.210275 | 0.105137 | − | 0.994458i | \(-0.466472\pi\) | ||||
0.105137 | + | 0.994458i | \(0.466472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.5107 | −0.870415 | −0.435208 | − | 0.900330i | \(-0.643325\pi\) | ||||
−0.435208 | + | 0.900330i | \(0.643325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.7469 | 0.433910 | 0.216955 | − | 0.976182i | \(-0.430388\pi\) | ||||
0.216955 | + | 0.976182i | \(0.430388\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.8225 | −0.469435 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.24123 | 0.0421058 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.3964 | −1.33490 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.83212 | −0.129698 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.5817 | −1.43788 | −0.718941 | − | 0.695071i | \(-0.755373\pi\) | ||||
−0.718941 | + | 0.695071i | \(0.755373\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.0537 | −0.372834 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0033 | −0.775001 | −0.387500 | − | 0.921870i | \(-0.626661\pi\) | ||||
−0.387500 | + | 0.921870i | \(0.626661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.92303 | 0.0647151 | 0.0323575 | − | 0.999476i | \(-0.489698\pi\) | ||||
0.0323575 | + | 0.999476i | \(0.489698\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.7529 | 0.696814 | 0.348407 | − | 0.937343i | \(-0.386723\pi\) | ||||
0.348407 | + | 0.937343i | \(0.386723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.70502 | −0.191125 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7219 | 0.425723 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.7324 | 0.458510 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.0428 | 1.03534 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.1962 | 1.10592 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.76289 | −0.124945 | −0.0624723 | − | 0.998047i | \(-0.519899\pi\) | ||||
−0.0624723 | + | 0.998047i | \(0.519899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.2175 | −0.571069 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.0618 | −0.631546 | −0.315773 | − | 0.948835i | \(-0.602264\pi\) | ||||
−0.315773 | + | 0.948835i | \(0.602264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.50711 | −0.182259 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.2267 | 0.634230 | 0.317115 | − | 0.948387i | \(-0.397286\pi\) | ||||
0.317115 | + | 0.948387i | \(0.397286\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.5253 | 1.17060 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 53.5945 | 1.76408 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.9254 | 0.621591 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.3242 | 1.71670 | 0.858350 | − | 0.513064i | \(-0.171490\pi\) | ||||
0.858350 | + | 0.513064i | \(0.171490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.7588 | −0.646873 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.0145 | −1.17654 | −0.588272 | − | 0.808663i | \(-0.700192\pi\) | ||||
−0.588272 | + | 0.808663i | \(0.700192\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.1198 | −1.34189 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8215 | 1.00475 | 0.502376 | − | 0.864649i | \(-0.332459\pi\) | ||||
0.502376 | + | 0.864649i | \(0.332459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.62536 | −0.183187 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.96679 | −0.226390 | −0.113195 | − | 0.993573i | \(-0.536108\pi\) | ||||
−0.113195 | + | 0.993573i | \(0.536108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.7784 | −0.739417 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.7311 | −0.737107 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.84491 | −0.221728 | −0.110864 | − | 0.993836i | \(-0.535362\pi\) | ||||
−0.110864 | + | 0.993836i | \(0.535362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.8411 | 0.382769 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.14527 | −0.198234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.1257 | −0.680765 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.2909 | −0.620352 | −0.310176 | − | 0.950679i | \(-0.600388\pi\) | ||||
−0.310176 | + | 0.950679i | \(0.600388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.06637 | 0.130631 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.7452 | 1.37176 | 0.685879 | − | 0.727716i | \(-0.259418\pi\) | ||||
0.685879 | + | 0.727716i | \(0.259418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.5149 | 0.400386 | 0.200193 | − | 0.979757i | \(-0.435843\pi\) | ||||
0.200193 | + | 0.979757i | \(0.435843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.41685 | 0.269004 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.4953 | −0.462798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.1370 | 0.929327 | 0.464663 | − | 0.885487i | \(-0.346175\pi\) | ||||
0.464663 | + | 0.885487i | \(0.346175\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4097 | 0.362808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.0215 | 1.90664 | 0.953322 | − | 0.301954i | \(-0.0976390\pi\) | ||||
0.953322 | + | 0.301954i | \(0.0976390\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.3682 | 0.614630 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.5990 | −1.12743 | −0.563715 | − | 0.825969i | \(-0.690628\pi\) | ||||
−0.563715 | + | 0.825969i | \(0.690628\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 47.7870 | 1.51192 |
(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 | 9800.2.a.ci.1.2 | 3 | ||
5.4 | even | 2 | 9800.2.a.cc.1.2 | 3 | |||
7.2 | even | 3 | 1400.2.q.i.1201.2 | yes | 6 | ||
7.4 | even | 3 | 1400.2.q.i.401.2 | ✓ | 6 | ||
7.6 | odd | 2 | 9800.2.a.cb.1.2 | 3 | |||
35.2 | odd | 12 | 1400.2.bh.h.249.5 | 12 | |||
35.4 | even | 6 | 1400.2.q.k.401.2 | yes | 6 | ||
35.9 | even | 6 | 1400.2.q.k.1201.2 | yes | 6 | ||
35.18 | odd | 12 | 1400.2.bh.h.849.5 | 12 | |||
35.23 | odd | 12 | 1400.2.bh.h.249.2 | 12 | |||
35.32 | odd | 12 | 1400.2.bh.h.849.2 | 12 | |||
35.34 | odd | 2 | 9800.2.a.ch.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.i.401.2 | ✓ | 6 | 7.4 | even | 3 | ||
1400.2.q.i.1201.2 | yes | 6 | 7.2 | even | 3 | ||
1400.2.q.k.401.2 | yes | 6 | 35.4 | even | 6 | ||
1400.2.q.k.1201.2 | yes | 6 | 35.9 | even | 6 | ||
1400.2.bh.h.249.2 | 12 | 35.23 | odd | 12 | |||
1400.2.bh.h.249.5 | 12 | 35.2 | odd | 12 | |||
1400.2.bh.h.849.2 | 12 | 35.32 | odd | 12 | |||
1400.2.bh.h.849.5 | 12 | 35.18 | odd | 12 | |||
9800.2.a.cb.1.2 | 3 | 7.6 | odd | 2 | |||
9800.2.a.cc.1.2 | 3 | 5.4 | even | 2 | |||
9800.2.a.ch.1.2 | 3 | 35.34 | odd | 2 | |||
9800.2.a.ci.1.2 | 3 | 1.1 | even | 1 | trivial |