Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 19x^{7} + 16x^{6} + 106x^{5} - 87x^{4} - 153x^{3} + 149x^{2} - 26x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.52382\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −2.52382 | −1.45713 | −0.728565 | − | 0.684977i | \(-0.759812\pi\) | ||||
−0.728565 | + | 0.684977i | \(0.759812\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.54727 | 1.71871 | 0.859353 | − | 0.511383i | \(-0.170867\pi\) | ||||
0.859353 | + | 0.511383i | \(0.170867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.36968 | 1.12323 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.52395 | 0.760999 | 0.380499 | − | 0.924781i | \(-0.375752\pi\) | ||||
0.380499 | + | 0.924781i | \(0.375752\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.52382 | 0.651648 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.14630 | 1.24816 | 0.624081 | − | 0.781360i | \(-0.285474\pi\) | ||||
0.624081 | + | 0.781360i | \(0.285474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.52781 | 1.72700 | 0.863499 | − | 0.504350i | \(-0.168268\pi\) | ||||
0.863499 | + | 0.504350i | \(0.168268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.4765 | −2.50438 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.63662 | 0.549774 | 0.274887 | − | 0.961477i | \(-0.411360\pi\) | ||||
0.274887 | + | 0.961477i | \(0.411360\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.933014 | −0.179559 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.61995 | −1.60068 | −0.800342 | − | 0.599544i | \(-0.795349\pi\) | ||||
−0.800342 | + | 0.599544i | \(0.795349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.44094 | 1.51604 | 0.758018 | − | 0.652233i | \(-0.226168\pi\) | ||||
0.758018 | + | 0.652233i | \(0.226168\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.37000 | −1.10887 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.54727 | −0.768629 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.98381 | 1.14813 | 0.574065 | − | 0.818810i | \(-0.305366\pi\) | ||||
0.574065 | + | 0.818810i | \(0.305366\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66091 | 0.415564 | 0.207782 | − | 0.978175i | \(-0.433376\pi\) | ||||
0.207782 | + | 0.978175i | \(0.433376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.74401 | −1.48595 | −0.742974 | − | 0.669320i | \(-0.766585\pi\) | ||||
−0.742974 | + | 0.669320i | \(0.766585\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.36968 | −0.502323 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.15221 | −1.18912 | −0.594561 | − | 0.804051i | \(-0.702674\pi\) | ||||
−0.594561 | + | 0.804051i | \(0.702674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.6776 | 1.95395 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.9884 | −1.81873 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.43808 | −0.197535 | −0.0987677 | − | 0.995111i | \(-0.531490\pi\) | ||||
−0.0987677 | + | 0.995111i | \(0.531490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.52395 | −0.340329 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.9989 | −2.51646 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0833281 | 0.0108484 | 0.00542420 | − | 0.999985i | \(-0.498273\pi\) | ||||
0.00542420 | + | 0.999985i | \(0.498273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.818691 | −0.104823 | −0.0524113 | − | 0.998626i | \(-0.516691\pi\) | ||||
−0.0524113 | + | 0.998626i | \(0.516691\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.3229 | 1.93050 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.08761 | 0.621550 | 0.310775 | − | 0.950483i | \(-0.399411\pi\) | ||||
0.310775 | + | 0.950483i | \(0.399411\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.65437 | −0.801092 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.78118 | −0.923456 | −0.461728 | − | 0.887021i | \(-0.652770\pi\) | ||||
−0.461728 | + | 0.887021i | \(0.652770\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.148454 | 0.0173753 | 0.00868764 | − | 0.999962i | \(-0.497235\pi\) | ||||
0.00868764 | + | 0.999962i | \(0.497235\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.52382 | −0.291426 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.4771 | 1.30793 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.18836 | 0.808754 | 0.404377 | − | 0.914592i | \(-0.367488\pi\) | ||||
0.404377 | + | 0.914592i | \(0.367488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.75429 | −0.861587 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.9198 | −1.85719 | −0.928597 | − | 0.371089i | \(-0.878984\pi\) | ||||
−0.928597 | + | 0.371089i | \(0.878984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.14630 | −0.558195 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.7552 | 2.33240 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.05664 | 0.324003 | 0.162002 | − | 0.986790i | \(-0.448205\pi\) | ||||
0.162002 | + | 0.986790i | \(0.448205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.3034 | −2.20906 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.52781 | −0.772337 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.27717 | 0.840419 | 0.420209 | − | 0.907427i | \(-0.361957\pi\) | ||||
0.420209 | + | 0.907427i | \(0.361957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.50490 | 0.854775 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.46123 | 0.244902 | 0.122451 | − | 0.992475i | \(-0.460925\pi\) | ||||
0.122451 | + | 0.992475i | \(0.460925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6923 | −1.05355 | −0.526773 | − | 0.850006i | \(-0.676598\pi\) | ||||
−0.526773 | + | 0.850006i | \(0.676598\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.4765 | 1.11999 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.880036 | −0.0850763 | −0.0425381 | − | 0.999095i | \(-0.513544\pi\) | ||||
−0.0425381 | + | 0.999095i | \(0.513544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.54141 | −0.147640 | −0.0738201 | − | 0.997272i | \(-0.523519\pi\) | ||||
−0.0738201 | + | 0.997272i | \(0.523519\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.6259 | −1.67298 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7763 | 1.01375 | 0.506874 | − | 0.862020i | \(-0.330801\pi\) | ||||
0.506874 | + | 0.862020i | \(0.330801\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.63662 | −0.245866 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.4016 | 2.14522 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.62969 | −0.420881 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.71566 | −0.605531 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.09528 | 0.540868 | 0.270434 | − | 0.962738i | \(-0.412833\pi\) | ||||
0.270434 | + | 0.962738i | \(0.412833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.5922 | 2.16522 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4044 | 0.909039 | 0.454520 | − | 0.890737i | \(-0.349811\pi\) | ||||
0.454520 | + | 0.890737i | \(0.349811\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.2310 | 2.96820 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.933014 | 0.0803011 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.89180 | 0.417934 | 0.208967 | − | 0.977923i | \(-0.432990\pi\) | ||||
0.208967 | + | 0.977923i | \(0.432990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.4823 | −1.90692 | −0.953460 | − | 0.301519i | \(-0.902506\pi\) | ||||
−0.953460 | + | 0.301519i | \(0.902506\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.5747 | 1.73270 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.61995 | 0.715848 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −34.5200 | −2.84716 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.4563 | 1.67584 | 0.837922 | − | 0.545790i | \(-0.183770\pi\) | ||||
0.837922 | + | 0.545790i | \(0.183770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0637311 | −0.00518637 | −0.00259318 | − | 0.999997i | \(-0.500825\pi\) | ||||
−0.00259318 | + | 0.999997i | \(0.500825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.3414 | 1.40197 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.44094 | −0.677992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0591648 | −0.00472187 | −0.00236093 | − | 0.999997i | \(-0.500752\pi\) | ||||
−0.00236093 | + | 0.999997i | \(0.500752\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.62946 | 0.287835 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.9894 | 0.944900 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9234 | −1.24721 | −0.623607 | − | 0.781738i | \(-0.714334\pi\) | ||||
−0.623607 | + | 0.781738i | \(0.714334\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.37000 | 0.495904 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.1436 | −1.71352 | −0.856762 | − | 0.515711i | \(-0.827528\pi\) | ||||
−0.856762 | + | 0.515711i | \(0.827528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 25.3663 | 1.93981 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.7289 | 1.42393 | 0.711966 | − | 0.702214i | \(-0.247805\pi\) | ||||
0.711966 | + | 0.702214i | \(0.247805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.54727 | 0.343741 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.210305 | −0.0158075 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.89212 | 0.664628 | 0.332314 | − | 0.943169i | \(-0.392171\pi\) | ||||
0.332314 | + | 0.943169i | \(0.392171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.90674 | −0.290386 | −0.145193 | − | 0.989403i | \(-0.546380\pi\) | ||||
−0.145193 | + | 0.989403i | \(0.546380\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.06623 | 0.152740 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.98381 | −0.513460 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9890 | 0.949850 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.24267 | −0.308609 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.0068 | 1.59236 | 0.796179 | − | 0.605061i | \(-0.206851\pi\) | ||||
0.796179 | + | 0.605061i | \(0.206851\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.46062 | −0.465046 | −0.232523 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232523 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.2295 | −1.37004 | −0.685021 | − | 0.728523i | \(-0.740207\pi\) | ||||
−0.685021 | + | 0.728523i | \(0.740207\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3145 | 1.15651 | 0.578253 | − | 0.815858i | \(-0.303735\pi\) | ||||
0.578253 | + | 0.815858i | \(0.303735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.8402 | −0.905679 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −39.1972 | −2.75111 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.66091 | −0.185846 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.88458 | 0.617521 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.9998 | 1.31424 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.2686 | 1.46419 | 0.732094 | − | 0.681204i | \(-0.238543\pi\) | ||||
0.732094 | + | 0.681204i | \(0.238543\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.6383 | 1.34560 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.74401 | 0.664536 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 38.3832 | 2.60562 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.374673 | −0.0253180 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.75386 | 0.653167 | 0.326583 | − | 0.945168i | \(-0.394103\pi\) | ||||
0.326583 | + | 0.945168i | \(0.394103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.36968 | 0.224646 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.0411 | −1.72841 | −0.864205 | − | 0.503140i | \(-0.832178\pi\) | ||||
−0.864205 | + | 0.503140i | \(0.832178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.9818 | 1.05610 | 0.528052 | − | 0.849212i | \(-0.322923\pi\) | ||||
0.528052 | + | 0.849212i | \(0.322923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.9661 | −1.90583 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.67734 | −0.502960 | −0.251480 | − | 0.967863i | \(-0.580917\pi\) | ||||
−0.251480 | + | 0.967863i | \(0.580917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.15221 | 0.531791 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.1422 | −1.17846 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.1981 | 1.17714 | 0.588570 | − | 0.808446i | \(-0.299691\pi\) | ||||
0.588570 | + | 0.808446i | \(0.299691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7693 | −0.886958 | −0.443479 | − | 0.896285i | \(-0.646256\pi\) | ||||
−0.443479 | + | 0.896285i | \(0.646256\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3695 | 1.43500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.6776 | −0.873833 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 42.7027 | 2.70617 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.54318 | 0.602360 | 0.301180 | − | 0.953567i | \(-0.402619\pi\) | ||||
0.301180 | + | 0.953567i | \(0.402619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.65470 | 0.418377 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.9884 | 0.813363 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.56768 | −0.596816 | −0.298408 | − | 0.954438i | \(-0.596456\pi\) | ||||
−0.298408 | + | 0.954438i | \(0.596456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.7572 | 1.97330 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.0465 | −1.79793 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.2418 | 1.30982 | 0.654912 | − | 0.755705i | \(-0.272705\pi\) | ||||
0.654912 | + | 0.755705i | \(0.272705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.43808 | 0.0883405 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.71442 | −0.472115 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.1110 | 1.47008 | 0.735038 | − | 0.678026i | \(-0.237164\pi\) | ||||
0.735038 | + | 0.678026i | \(0.237164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.12699 | 0.129205 | 0.0646026 | − | 0.997911i | \(-0.479422\pi\) | ||||
0.0646026 | + | 0.997911i | \(0.479422\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.52395 | 0.152200 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.5197 | 1.47325 | 0.736623 | − | 0.676303i | \(-0.236419\pi\) | ||||
0.736623 | + | 0.676303i | \(0.236419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.4433 | 1.70285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.63729 | 0.574913 | 0.287456 | − | 0.957794i | \(-0.407190\pi\) | ||||
0.287456 | + | 0.957794i | \(0.407190\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.5987 | −1.40280 | −0.701400 | − | 0.712768i | \(-0.747441\pi\) | ||||
−0.701400 | + | 0.712768i | \(0.747441\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.9989 | 1.12540 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0999 | 0.714232 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.48444 | 0.557908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.8901 | −1.22460 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.38348 | 0.314506 | 0.157253 | − | 0.987558i | \(-0.449736\pi\) | ||||
0.157253 | + | 0.987558i | \(0.449736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0833281 | −0.00485155 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.35488 | −0.136644 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −44.3086 | −2.55391 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.21171 | −0.356854 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.818691 | 0.0468781 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.1743 | −0.694825 | −0.347413 | − | 0.937712i | \(-0.612940\pi\) | ||||
−0.347413 | + | 0.937712i | \(0.612940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.9855 | 1.53515 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.2103 | −0.749085 | −0.374543 | − | 0.927210i | \(-0.622200\pi\) | ||||
−0.374543 | + | 0.927210i | \(0.622200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.1485 | −1.36495 | −0.682476 | − | 0.730908i | \(-0.739097\pi\) | ||||
−0.682476 | + | 0.730908i | \(0.739097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.3229 | −0.863345 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.42443 | −0.360832 | −0.180416 | − | 0.983590i | \(-0.557744\pi\) | ||||
−0.180416 | + | 0.983590i | \(0.557744\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.7563 | −1.21812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.22105 | 0.123967 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 38.7404 | 2.15557 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.89024 | 0.215131 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.0703 | −2.04375 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8105 | 1.19881 | 0.599407 | − | 0.800444i | \(-0.295403\pi\) | ||||
0.599407 | + | 0.800444i | \(0.295403\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.5332 | 1.28961 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.08761 | −0.277966 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.94670 | 0.323937 | 0.161969 | − | 0.986796i | \(-0.448216\pi\) | ||||
0.161969 | + | 0.986796i | \(0.448216\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.1975 | −1.47716 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.3045 | 1.15370 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30.3651 | 1.63956 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.65437 | 0.358259 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7097 | −1.11175 | −0.555877 | − | 0.831264i | \(-0.687618\pi\) | ||||
−0.555877 | + | 0.831264i | \(0.687618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.05214 | −0.431021 | −0.215511 | − | 0.976502i | \(-0.569142\pi\) | ||||
−0.215511 | + | 0.976502i | \(0.569142\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.11032 | −0.378444 | −0.189222 | − | 0.981934i | \(-0.560597\pi\) | ||||
−0.189222 | + | 0.981934i | \(0.560597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.78118 | 0.412982 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −59.0616 | −3.12587 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.26310 | −0.330554 | −0.165277 | − | 0.986247i | \(-0.552852\pi\) | ||||
−0.165277 | + | 0.986247i | \(0.552852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.6679 | 1.98252 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.6845 | 0.613278 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.148454 | −0.00777046 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.9522 | 0.832697 | 0.416349 | − | 0.909205i | \(-0.363310\pi\) | ||||
0.416349 | + | 0.909205i | \(0.363310\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.96642 | 0.466773 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.53934 | −0.339505 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.42611 | −0.0738410 | −0.0369205 | − | 0.999318i | \(-0.511755\pi\) | ||||
−0.0369205 | + | 0.999318i | \(0.511755\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.52382 | 0.130330 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.57360 | 0.183564 | 0.0917818 | − | 0.995779i | \(-0.470744\pi\) | ||||
0.0917818 | + | 0.995779i | \(0.470744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.3834 | −0.788115 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.84620 | 0.247629 | 0.123815 | − | 0.992305i | \(-0.460487\pi\) | ||||
0.123815 | + | 0.992305i | \(0.460487\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.4771 | −0.584925 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.8342 | −1.66906 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.7772 | −1.71257 | −0.856285 | − | 0.516503i | \(-0.827233\pi\) | ||||
−0.856285 | + | 0.516503i | \(0.827233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5689 | 0.686207 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.2589 | −1.32459 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.18836 | −0.361686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.483569 | 0.0242696 | 0.0121348 | − | 0.999926i | \(-0.496137\pi\) | ||||
0.0121348 | + | 0.999926i | \(0.496137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −86.3929 | −4.32506 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0902 | −0.903380 | −0.451690 | − | 0.892175i | \(-0.649179\pi\) | ||||
−0.451690 | + | 0.892175i | \(0.649179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.75429 | 0.385314 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.6268 | 0.873726 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.5327 | 1.70753 | 0.853766 | − | 0.520657i | \(-0.174313\pi\) | ||||
0.853766 | + | 0.520657i | \(0.174313\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3460 | −0.608985 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.378915 | 0.0186452 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.9198 | 0.830563 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 56.7412 | 2.77863 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.0215 | −1.12467 | −0.562337 | − | 0.826908i | \(-0.690098\pi\) | ||||
−0.562337 | + | 0.826908i | \(0.690098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.63811 | −0.372259 | −0.186129 | − | 0.982525i | \(-0.559594\pi\) | ||||
−0.186129 | + | 0.982525i | \(0.559594\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.4704 | −1.33565 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.14630 | 0.249632 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.72281 | −0.180159 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3076 | −1.07452 | −0.537260 | − | 0.843417i | \(-0.680541\pi\) | ||||
−0.537260 | + | 0.843417i | \(0.680541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.01305 | 0.0486838 | 0.0243419 | − | 0.999704i | \(-0.492251\pi\) | ||||
0.0243419 | + | 0.999704i | \(0.492251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.7552 | −1.04308 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.8480 | 0.949459 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.1466 | −1.91609 | −0.958046 | − | 0.286613i | \(-0.907471\pi\) | ||||
−0.958046 | + | 0.286613i | \(0.907471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 46.0893 | 2.19473 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.0607 | −1.76080 | −0.880402 | − | 0.474228i | \(-0.842727\pi\) | ||||
−0.880402 | + | 0.474228i | \(0.842727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.05664 | −0.144899 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −51.6281 | −2.44192 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.4726 | −0.541424 | −0.270712 | − | 0.962660i | \(-0.587259\pi\) | ||||
−0.270712 | + | 0.962660i | \(0.587259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.71599 | 0.316244 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.160846 | 0.00755721 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.21789 | 0.431195 | 0.215597 | − | 0.976482i | \(-0.430830\pi\) | ||||
0.215597 | + | 0.976482i | \(0.430830\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.80157 | −0.224118 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.78265 | 0.176176 | 0.0880878 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880878 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.59710 | −0.120698 | −0.0603488 | − | 0.998177i | \(-0.519221\pi\) | ||||
−0.0603488 | + | 0.998177i | \(0.519221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.3034 | 0.987923 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.2664 | −1.81703 | −0.908516 | − | 0.417849i | \(-0.862784\pi\) | ||||
−0.908516 | + | 0.417849i | \(0.862784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1347 | 1.06826 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.149321 | 0.00688037 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.5934 | −1.13080 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.52781 | 0.345400 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.84587 | −0.221877 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.8940 | −1.64004 | −0.820019 | − | 0.572337i | \(-0.806037\pi\) | ||||
−0.820019 | + | 0.572337i | \(0.806037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.2592 | −1.37684 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.27717 | −0.375847 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.6683 | −1.38971 | −0.694856 | − | 0.719149i | \(-0.744532\pi\) | ||||
−0.694856 | + | 0.719149i | \(0.744532\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.1878 | 1.81735 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.2621 | 1.36571 | 0.682856 | − | 0.730553i | \(-0.260738\pi\) | ||||
0.682856 | + | 0.730553i | \(0.260738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.3609 | −1.99791 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.50490 | −0.382267 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.3831 | −1.58715 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.5036 | 0.514973 | 0.257486 | − | 0.966282i | \(-0.417106\pi\) | ||||
0.257486 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 55.8866 | 2.49683 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.0889 | −0.628195 | −0.314097 | − | 0.949391i | \(-0.601702\pi\) | ||||
−0.314097 | + | 0.949391i | \(0.601702\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.46123 | −0.109523 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.07854 | −0.358075 | −0.179037 | − | 0.983842i | \(-0.557298\pi\) | ||||
−0.179037 | + | 0.983842i | \(0.557298\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.675062 | 0.0298630 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.02355 | −0.310097 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.6923 | 0.471160 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.5757 | −0.904920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −47.2684 | −2.07485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.6830 | 1.38806 | 0.694028 | − | 0.719948i | \(-0.255834\pi\) | ||||
0.694028 | + | 0.719948i | \(0.255834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.56717 | 0.243435 | 0.121718 | − | 0.992565i | \(-0.461160\pi\) | ||||
0.121718 | + | 0.992565i | \(0.461160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.4765 | −0.500876 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.4396 | 1.89226 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0482 | −0.697749 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.280789 | 0.0121852 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.880036 | 0.0380473 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.4421 | −0.968449 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.5217 | 1.48695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.01207 | 0.129499 | 0.0647496 | − | 0.997902i | \(-0.479375\pi\) | ||||
0.0647496 | + | 0.997902i | \(0.479375\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.85992 | 0.423130 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.54141 | 0.0660267 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1320 | 0.989053 | 0.494527 | − | 0.869163i | \(-0.335341\pi\) | ||||
0.494527 | + | 0.869163i | \(0.335341\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.75873 | −0.117740 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −64.8893 | −2.76438 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.6874 | 1.39001 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.6259 | 0.748177 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.18919 | 0.304616 | 0.152308 | − | 0.988333i | \(-0.451329\pi\) | ||||
0.152308 | + | 0.988333i | \(0.451329\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.7819 | −1.38405 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.32860 | 0.224574 | 0.112287 | − | 0.993676i | \(-0.464182\pi\) | ||||
0.112287 | + | 0.993676i | \(0.464182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7763 | −0.453362 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.2608 | −1.48082 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.8437 | 1.67034 | 0.835168 | − | 0.549995i | \(-0.185370\pi\) | ||||
0.835168 | + | 0.549995i | \(0.185370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.28735 | 0.137571 | 0.0687857 | − | 0.997631i | \(-0.478088\pi\) | ||||
0.0687857 | + | 0.997631i | \(0.478088\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.5414 | −2.32027 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.63662 | 0.109955 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.3187 | 0.679358 | 0.339679 | − | 0.940541i | \(-0.389682\pi\) | ||||
0.339679 | + | 0.940541i | \(0.389682\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.3055 | 0.677632 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −76.9391 | −3.19197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.62964 | −0.150324 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.3533 | 0.881344 | 0.440672 | − | 0.897668i | \(-0.354740\pi\) | ||||
0.440672 | + | 0.897668i | \(0.354740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 63.5418 | 2.61819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 48.5317 | 1.99633 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.2461 | −1.07780 | −0.538898 | − | 0.842371i | \(-0.681159\pi\) | ||||
−0.538898 | + | 0.842371i | \(0.681159\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.4016 | −0.959373 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −41.1750 | −1.68518 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6381 | −1.04754 | −0.523772 | − | 0.851858i | \(-0.675476\pi\) | ||||
−0.523772 | + | 0.851858i | \(0.675476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.6633 | 0.598128 | 0.299064 | − | 0.954233i | \(-0.403326\pi\) | ||||
0.299064 | + | 0.954233i | \(0.403326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.1436 | 0.698142 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.62969 | 0.188224 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.8341 | 0.602100 | 0.301050 | − | 0.953608i | \(-0.402663\pi\) | ||||
0.301050 | + | 0.953608i | \(0.402663\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 98.9268 | 4.00872 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.253642 | 0.0102445 | 0.00512225 | − | 0.999987i | \(-0.498370\pi\) | ||||
0.00512225 | + | 0.999987i | \(0.498370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.71566 | 0.270802 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.99816 | 0.402511 | 0.201255 | − | 0.979539i | \(-0.435498\pi\) | ||||
0.201255 | + | 0.979539i | \(0.435498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.07953 | −0.244357 | −0.122178 | − | 0.992508i | \(-0.538988\pi\) | ||||
−0.122178 | + | 0.992508i | \(0.538988\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.46001 | −0.0987167 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8994 | 0.556866 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −47.9521 | −1.91502 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.9408 | 1.43305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.4143 | 1.60887 | 0.804434 | − | 0.594041i | \(-0.202468\pi\) | ||||
0.804434 | + | 0.594041i | \(0.202468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −53.6781 | −2.13351 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.09528 | −0.241884 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.2201 | −1.03725 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.7514 | 0.424653 | 0.212327 | − | 0.977199i | \(-0.431896\pi\) | ||||
0.212327 | + | 0.977199i | \(0.431896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.7425 | 0.620823 | 0.310412 | − | 0.950602i | \(-0.399533\pi\) | ||||
0.310412 | + | 0.950602i | \(0.399533\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.5922 | −0.968315 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.4404 | −0.528399 | −0.264199 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264199 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.210316 | 0.00825562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −96.8724 | −3.79673 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.21367 | 0.0474948 | 0.0237474 | − | 0.999718i | \(-0.492440\pi\) | ||||
0.0237474 | + | 0.999718i | \(0.492440\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4044 | −0.406535 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.500245 | 0.0195164 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.8299 | −0.460827 | −0.230413 | − | 0.973093i | \(-0.574008\pi\) | ||||
−0.230413 | + | 0.973093i | \(0.574008\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.4477 | −1.72882 | −0.864409 | − | 0.502790i | \(-0.832307\pi\) | ||||
−0.864409 | + | 0.502790i | \(0.832307\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −34.2310 | −1.32742 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.7276 | −0.880015 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.6170 | −0.951749 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.06633 | −0.0797699 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2950 | 0.473936 | 0.236968 | − | 0.971517i | \(-0.423846\pi\) | ||||
0.236968 | + | 0.971517i | \(0.423846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.933014 | −0.0359117 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.57026 | −0.290949 | −0.145474 | − | 0.989362i | \(-0.546471\pi\) | ||||
−0.145474 | + | 0.989362i | \(0.546471\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.6385 | 1.44443 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 65.7232 | 2.51852 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7077 | 0.639303 | 0.319651 | − | 0.947535i | \(-0.396434\pi\) | ||||
0.319651 | + | 0.947535i | \(0.396434\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.89180 | −0.186906 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.3351 | −1.53888 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5620 | 0.706131 | 0.353065 | − | 0.935599i | \(-0.385139\pi\) | ||||
0.353065 | + | 0.935599i | \(0.385139\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 38.6741 | 1.46911 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.4823 | 0.852801 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.6938 | 0.518691 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.3763 | 0.732877 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.7585 | 0.972886 | 0.486443 | − | 0.873712i | \(-0.338294\pi\) | ||||
0.486443 | + | 0.873712i | \(0.338294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.5728 | 1.98282 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.5747 | −0.774889 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.1919 | 0.420914 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.33378 | 0.200314 | 0.100157 | − | 0.994972i | \(-0.468065\pi\) | ||||
0.100157 | + | 0.994972i | \(0.468065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.2225 | 0.908415 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.2556 | 0.833478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −45.9289 | −1.71525 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.5517 | −0.691861 | −0.345930 | − | 0.938260i | \(-0.612437\pi\) | ||||
−0.345930 | + | 0.938260i | \(0.612437\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.6208 | −1.81073 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.7513 | 1.29241 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.61995 | −0.320137 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5977 | 0.541400 | 0.270700 | − | 0.962664i | \(-0.412745\pi\) | ||||
0.270700 | + | 0.962664i | \(0.412745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.1938 | −1.22940 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50.1456 | −1.85470 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.2807 | 1.04457 | 0.522286 | − | 0.852770i | \(-0.325079\pi\) | ||||
0.522286 | + | 0.852770i | \(0.325079\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.5200 | 1.27329 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.8409 | 0.472999 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.37192 | 0.0872523 | 0.0436262 | − | 0.999048i | \(-0.486109\pi\) | ||||
0.0436262 | + | 0.999048i | \(0.486109\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.4361 | 0.969845 | 0.484923 | − | 0.874557i | \(-0.338848\pi\) | ||||
0.484923 | + | 0.874557i | \(0.338848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.4563 | −0.749460 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −57.0145 | −2.08605 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00176 | −0.146221 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0414 | −0.475889 | −0.237944 | − | 0.971279i | \(-0.576474\pi\) | ||||
−0.237944 | + | 0.971279i | \(0.576474\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.0853 | −0.877717 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0637311 | 0.00231941 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.6023 | −1.58475 | −0.792377 | − | 0.610032i | \(-0.791157\pi\) | ||||
−0.792377 | + | 0.610032i | \(0.791157\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.7953 | −0.609630 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2976 | −0.627038 | −0.313519 | − | 0.949582i | \(-0.601508\pi\) | ||||
−0.313519 | + | 0.949582i | \(0.601508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.00920 | −0.253750 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.3414 | −0.626980 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.3193 | 0.985158 | 0.492579 | − | 0.870268i | \(-0.336054\pi\) | ||||
0.492579 | + | 0.870268i | \(0.336054\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1471 | 0.869638 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.4675 | −0.772131 | −0.386066 | − | 0.922471i | \(-0.626166\pi\) | ||||
−0.386066 | + | 0.922471i | \(0.626166\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.44094 | 0.303207 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −80.1497 | −2.87535 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0308 | 0.717678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.6393 | −0.702749 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.04253 | 0.287417 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0591648 | 0.00211168 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4097 | 0.763174 | 0.381587 | − | 0.924333i | \(-0.375378\pi\) | ||||
0.381587 | + | 0.924333i | \(0.375378\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −53.6105 | −1.90859 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 49.0027 | 1.74234 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.62946 | −0.128724 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.0647 | 0.533617 | 0.266809 | − | 0.963750i | \(-0.414031\pi\) | ||||
0.266809 | + | 0.963750i | \(0.414031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.9537 | −1.48422 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2999 | 0.363930 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.374691 | 0.0132226 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.9894 | −0.422572 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −60.8520 | −2.14209 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.7046 | 0.938885 | 0.469442 | − | 0.882963i | \(-0.344455\pi\) | ||||
0.469442 | + | 0.882963i | \(0.344455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.8145 | −0.766011 | −0.383005 | − | 0.923746i | \(-0.625111\pi\) | ||||
−0.383005 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.36814 | −0.188269 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9234 | 0.557771 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −73.3511 | −2.56623 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.0913 | 1.01529 | 0.507646 | − | 0.861565i | \(-0.330516\pi\) | ||||
0.507646 | + | 0.861565i | \(0.330516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.4597 | −0.713182 | −0.356591 | − | 0.934261i | \(-0.616061\pi\) | ||||
−0.356591 | + | 0.934261i | \(0.616061\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.37000 | −0.221775 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.2164 | −0.842086 | −0.421043 | − | 0.907041i | \(-0.638336\pi\) | ||||
−0.421043 | + | 0.907041i | \(0.638336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.77286 | −0.131037 | −0.0655185 | − | 0.997851i | \(-0.520870\pi\) | ||||
−0.0655185 | + | 0.997851i | \(0.520870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −61.8834 | −2.14671 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 70.3893 | 2.43885 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.1436 | 0.766312 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.87551 | −0.272218 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0985 | 0.417685 | 0.208843 | − | 0.977949i | \(-0.433030\pi\) | ||||
0.208843 | + | 0.977949i | \(0.433030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.3035 | 1.56219 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.3228 | −0.837723 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0524 | −0.723370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 59.5591 | 2.04406 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.4137 | 0.631212 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.2655 | 1.54986 | 0.774930 | − | 0.632047i | \(-0.217785\pi\) | ||||
0.774930 | + | 0.632047i | \(0.217785\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.3663 | −0.867510 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.4321 | −0.390514 | −0.195257 | − | 0.980752i | \(-0.562554\pi\) | ||||
−0.195257 | + | 0.980752i | \(0.562554\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.9331 | −1.66957 | −0.834787 | − | 0.550573i | \(-0.814409\pi\) | ||||
−0.834787 | + | 0.550573i | \(0.814409\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.5379 | −1.04073 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.25636 | −0.247009 | −0.123505 | − | 0.992344i | \(-0.539413\pi\) | ||||
−0.123505 | + | 0.992344i | \(0.539413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7289 | −0.636802 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.9371 | −0.812945 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.1430 | 0.615461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.8914 | 0.943982 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.54727 | −0.153726 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.2767 | −0.414555 | −0.207277 | − | 0.978282i | \(-0.566460\pi\) | ||||
−0.207277 | + | 0.978282i | \(0.566460\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.5869 | −0.458276 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.2767 | −0.750520 | −0.375260 | − | 0.926920i | \(-0.622447\pi\) | ||||
−0.375260 | + | 0.926920i | \(0.622447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.4148 | 1.42737 | 0.713686 | − | 0.700465i | \(-0.247024\pi\) | ||||
0.713686 | + | 0.700465i | \(0.247024\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.210305 | 0.00706934 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.44309 | −0.115608 | −0.0578038 | − | 0.998328i | \(-0.518410\pi\) | ||||
−0.0578038 | + | 0.998328i | \(0.518410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.7169 | 0.929594 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.5714 | −0.655667 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −61.3683 | −2.05361 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.89212 | −0.297231 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72.7604 | −2.42670 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.40080 | −0.246556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 111.827 | 3.72138 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.90674 | 0.129864 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.8493 | −0.825108 | −0.412554 | − | 0.910933i | \(-0.635363\pi\) | ||||
−0.412554 | + | 0.910933i | \(0.635363\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.29357 | 0.275080 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5928 | 0.417218 | 0.208609 | − | 0.977999i | \(-0.433106\pi\) | ||||
0.208609 | + | 0.977999i | \(0.433106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.7048 | −1.41332 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.06623 | −0.0683075 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.3117 | 1.56237 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.6595 | 1.30825 | 0.654124 | − | 0.756388i | \(-0.273038\pi\) | ||||
0.654124 | + | 0.756388i | \(0.273038\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.7258 | 1.01245 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.98381 | 0.229626 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.0297 | −1.18337 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.5553 | 1.36338 | 0.681692 | − | 0.731639i | \(-0.261244\pi\) | ||||
0.681692 | + | 0.731639i | \(0.261244\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 102.963 | 3.37447 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.3404 | 1.09151 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.9890 | −0.424786 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.57744 | −0.182207 | −0.0911035 | − | 0.995841i | \(-0.529039\pi\) | ||||
−0.0911035 | + | 0.995841i | \(0.529039\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.9465 | 1.98891 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.7230 | 0.642951 | 0.321475 | − | 0.946918i | \(-0.395821\pi\) | ||||
0.321475 | + | 0.946918i | \(0.395821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.01581 | 0.228466 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.24267 | 0.138014 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.4631 | −0.794943 | −0.397471 | − | 0.917615i | \(-0.630112\pi\) | ||||
−0.397471 | + | 0.917615i | \(0.630112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2141 | 0.525779 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.5402 | 1.79912 | 0.899562 | − | 0.436794i | \(-0.143886\pi\) | ||||
0.899562 | + | 0.436794i | \(0.143886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.0068 | −0.712125 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 54.9090 | 1.77496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.2443 | 0.718306 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.2494 | 1.29837 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.96544 | −0.0955600 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.46062 | 0.207975 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.1787 | −0.584589 | −0.292294 | − | 0.956328i | \(-0.594419\pi\) | ||||
−0.292294 | + | 0.956328i | \(0.594419\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −97.7739 | −3.14095 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.7938 | −1.37332 | −0.686660 | − | 0.726979i | \(-0.740924\pi\) | ||||
−0.686660 | + | 0.726979i | \(0.740924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −102.233 | −3.27743 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.7715 | 0.888488 | 0.444244 | − | 0.895906i | \(-0.353472\pi\) | ||||
0.444244 | + | 0.895906i | \(0.353472\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.71480 | 0.246566 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.19406 | −0.165834 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.1593 | 0.834351 | 0.417176 | − | 0.908826i | \(-0.363020\pi\) | ||||
0.417176 | + | 0.908826i | \(0.363020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.2295 | 0.612701 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 93.5588 | 2.97801 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.6913 | −0.816936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.2217 | 1.59535 | 0.797673 | − | 0.603090i | \(-0.206064\pi\) | ||||
0.797673 | + | 0.603090i | \(0.206064\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −55.0459 | −1.74683 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.3145 | −0.517205 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.5985 | 1.41245 | 0.706224 | − | 0.707989i | \(-0.250397\pi\) | ||||
0.706224 | + | 0.707989i | \(0.250397\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.51599 | −0.206157 |
(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 | 3380.2.a.r.1.2 | ✓ | 9 | |
13.5 | odd | 4 | 3380.2.f.j.3041.4 | 18 | |||
13.8 | odd | 4 | 3380.2.f.j.3041.3 | 18 | |||
13.12 | even | 2 | 3380.2.a.s.1.2 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.r.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial | |
3380.2.a.s.1.2 | yes | 9 | 13.12 | even | 2 | ||
3380.2.f.j.3041.3 | 18 | 13.8 | odd | 4 | |||
3380.2.f.j.3041.4 | 18 | 13.5 | odd | 4 |