Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7056,2,Mod(1,7056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7056, 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("7056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7056.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: | \(56.3424436662\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7056.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.41421 | 1.79821 | 0.899105 | − | 0.437732i | \(-0.144218\pi\) | ||||
0.899105 | + | 0.437732i | \(0.144218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.82843 | 1.56655 | 0.783274 | − | 0.621676i | \(-0.213548\pi\) | ||||
0.783274 | + | 0.621676i | \(0.213548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82843 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | −0.508001 | −0.254000 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.254000 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.65685 | −0.272385 | −0.136193 | − | 0.990682i | \(-0.543487\pi\) | ||||
−0.136193 | + | 0.990682i | \(0.543487\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2426 | 1.59963 | 0.799816 | − | 0.600245i | \(-0.204930\pi\) | ||||
0.799816 | + | 0.600245i | \(0.204930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3137 | 1.72532 | 0.862662 | − | 0.505781i | \(-0.168795\pi\) | ||||
0.862662 | + | 0.505781i | \(0.168795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.48528 | 0.654246 | 0.327123 | − | 0.944982i | \(-0.393921\pi\) | ||||
0.327123 | + | 0.944982i | \(0.393921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.48528 | −1.10469 | −0.552345 | − | 0.833616i | \(-0.686267\pi\) | ||||
−0.552345 | + | 0.833616i | \(0.686267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0711 | −1.41750 | −0.708752 | − | 0.705457i | \(-0.750742\pi\) | ||||
−0.708752 | + | 0.705457i | \(0.750742\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4853 | 1.79668 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3137 | −1.38219 | −0.691095 | − | 0.722764i | \(-0.742871\pi\) | ||||
−0.691095 | + | 0.722764i | \(0.742871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4853 | −1.24437 | −0.622187 | − | 0.782869i | \(-0.713756\pi\) | ||||
−0.622187 | + | 0.782869i | \(0.713756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.75736 | −0.907930 | −0.453965 | − | 0.891019i | \(-0.649991\pi\) | ||||
−0.453965 | + | 0.891019i | \(0.649991\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6569 | −1.53652 | −0.768258 | − | 0.640140i | \(-0.778876\pi\) | ||||
−0.768258 | + | 0.640140i | \(0.778876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.3137 | 2.74566 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.75736 | 0.610279 | 0.305139 | − | 0.952308i | \(-0.401297\pi\) | ||||
0.305139 | + | 0.952308i | \(0.401297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.3137 | 2.39194 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.242641 | 0.0246364 | 0.0123182 | − | 0.999924i | \(-0.496079\pi\) | ||||
0.0123182 | + | 0.999924i | \(0.496079\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7279 | −1.06747 | −0.533734 | − | 0.845652i | \(-0.679212\pi\) | ||||
−0.533734 | + | 0.845652i | \(0.679212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1421 | 1.39347 | 0.696733 | − | 0.717331i | \(-0.254636\pi\) | ||||
0.696733 | + | 0.717331i | \(0.254636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8284 | 1.24017 | 0.620085 | − | 0.784534i | \(-0.287098\pi\) | ||||
0.620085 | + | 0.784534i | \(0.287098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.31371 | −0.317396 | −0.158698 | − | 0.987327i | \(-0.550730\pi\) | ||||
−0.158698 | + | 0.987327i | \(0.550730\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.4853 | −1.53726 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.0000 | −1.77471 | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.17157 | 0.783580 | 0.391790 | − | 0.920055i | \(-0.371856\pi\) | ||||
0.391790 | + | 0.920055i | \(0.371856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.9706 | −1.77870 | −0.889350 | − | 0.457227i | \(-0.848843\pi\) | ||||
−0.889350 | + | 0.457227i | \(0.848843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.51472 | 0.293916 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.65685 | −0.801958 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.31371 | −0.107623 | −0.0538116 | − | 0.998551i | \(-0.517137\pi\) | ||||
−0.0538116 | + | 0.998551i | \(0.517137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.65685 | 0.785864 | 0.392932 | − | 0.919568i | \(-0.371461\pi\) | ||||
0.392932 | + | 0.919568i | \(0.371461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.65685 | −0.775657 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.242641 | −0.0193648 | −0.00968242 | − | 0.999953i | \(-0.503082\pi\) | ||||
−0.00968242 | + | 0.999953i | \(0.503082\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.65685 | −0.443079 | −0.221540 | − | 0.975151i | \(-0.571108\pi\) | ||||
−0.221540 | + | 0.975151i | \(0.571108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.8284 | 1.14746 | 0.573729 | − | 0.819045i | \(-0.305496\pi\) | ||||
0.573729 | + | 0.819045i | \(0.305496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.5858 | −1.26099 | −0.630497 | − | 0.776192i | \(-0.717149\pi\) | ||||
−0.630497 | + | 0.776192i | \(0.717149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.48528 | −0.484733 | −0.242366 | − | 0.970185i | \(-0.577924\pi\) | ||||
−0.242366 | + | 0.970185i | \(0.577924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.07107 | 0.525588 | 0.262794 | − | 0.964852i | \(-0.415356\pi\) | ||||
0.262794 | + | 0.964852i | \(0.415356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.65685 | −0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.14214 | 0.449157 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.1421 | 0.878574 | 0.439287 | − | 0.898347i | \(-0.355231\pi\) | ||||
0.439287 | + | 0.898347i | \(0.355231\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.68629 | 0.191390 | 0.0956952 | − | 0.995411i | \(-0.469493\pi\) | ||||
0.0956952 | + | 0.995411i | \(0.469493\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.65685 | −0.401004 | −0.200502 | − | 0.979693i | \(-0.564257\pi\) | ||||
−0.200502 | + | 0.979693i | \(0.564257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.9706 | 2.44245 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.65685 | −0.114063 | −0.0570313 | − | 0.998372i | \(-0.518163\pi\) | ||||
−0.0570313 | + | 0.998372i | \(0.518163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 38.6274 | 2.63437 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.4558 | 2.11595 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6569 | 0.914531 | 0.457265 | − | 0.889330i | \(-0.348829\pi\) | ||||
0.457265 | + | 0.889330i | \(0.348829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.17157 | 0.343249 | 0.171625 | − | 0.985162i | \(-0.445098\pi\) | ||||
0.171625 | + | 0.985162i | \(0.445098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4142 | 1.67942 | 0.839709 | − | 0.543036i | \(-0.182725\pi\) | ||||
0.839709 | + | 0.543036i | \(0.182725\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.8284 | 0.971443 | 0.485721 | − | 0.874114i | \(-0.338557\pi\) | ||||
0.485721 | + | 0.874114i | \(0.338557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.3137 | 0.998956 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8284 | −0.829802 | −0.414901 | − | 0.909867i | \(-0.636184\pi\) | ||||
−0.414901 | + | 0.909867i | \(0.636184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.8995 | −0.895345 | −0.447673 | − | 0.894198i | \(-0.647747\pi\) | ||||
−0.447673 | + | 0.894198i | \(0.647747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.9706 | 1.84335 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.14214 | 0.387688 | 0.193844 | − | 0.981032i | \(-0.437904\pi\) | ||||
0.193844 | + | 0.981032i | \(0.437904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.41421 | −0.212973 | −0.106486 | − | 0.994314i | \(-0.533960\pi\) | ||||
−0.106486 | + | 0.994314i | \(0.533960\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.1421 | −1.24202 | −0.621009 | − | 0.783804i | \(-0.713277\pi\) | ||||
−0.621009 | + | 0.783804i | \(0.713277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.82843 | 0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.100505 | −0.00612790 | −0.00306395 | − | 0.999995i | \(-0.500975\pi\) | ||||
−0.00306395 | + | 0.999995i | \(0.500975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.14214 | 0.373108 | 0.186554 | − | 0.982445i | \(-0.440268\pi\) | ||||
0.186554 | + | 0.982445i | \(0.440268\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.51472 | 0.332550 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.6274 | −1.72005 | −0.860027 | − | 0.510248i | \(-0.829554\pi\) | ||||
−0.860027 | + | 0.510248i | \(0.829554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.17157 | −0.0698902 | −0.0349451 | − | 0.999389i | \(-0.511126\pi\) | ||||
−0.0349451 | + | 0.999389i | \(0.511126\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.1421 | −1.55399 | −0.776994 | − | 0.629508i | \(-0.783257\pi\) | ||||
−0.776994 | + | 0.629508i | \(0.783257\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.9706 | 2.23356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.75736 | −0.102666 | −0.0513330 | − | 0.998682i | \(-0.516347\pi\) | ||||
−0.0513330 | + | 0.998682i | \(0.516347\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.9706 | −1.68673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.4853 | −1.18469 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −37.7990 | −2.16436 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5147 | −0.657180 | −0.328590 | − | 0.944473i | \(-0.606573\pi\) | ||||
−0.328590 | + | 0.944473i | \(0.606573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.7990 | −1.34952 | −0.674758 | − | 0.738039i | \(-0.735752\pi\) | ||||
−0.674758 | + | 0.738039i | \(0.735752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.7279 | −1.62380 | −0.811899 | − | 0.583798i | \(-0.801566\pi\) | ||||
−0.811899 | + | 0.583798i | \(0.801566\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.0000 | 1.23564 | 0.617822 | − | 0.786318i | \(-0.288015\pi\) | ||||
0.617822 | + | 0.786318i | \(0.288015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.34315 | −0.131191 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 50.6274 | 2.81698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.2426 | 1.56662 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.31371 | −0.401998 | −0.200999 | − | 0.979591i | \(-0.564419\pi\) | ||||
−0.200999 | + | 0.979591i | \(0.564419\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −38.6274 | −2.11044 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3431 | 0.563427 | 0.281714 | − | 0.959499i | \(-0.409097\pi\) | ||||
0.281714 | + | 0.959499i | \(0.409097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.34315 | −0.126888 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.48528 | −0.133417 | −0.0667084 | − | 0.997773i | \(-0.521250\pi\) | ||||
−0.0667084 | + | 0.997773i | \(0.521250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5858 | −0.566644 | −0.283322 | − | 0.959025i | \(-0.591437\pi\) | ||||
−0.283322 | + | 0.959025i | \(0.591437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.6985 | −1.47424 | −0.737121 | − | 0.675761i | \(-0.763815\pi\) | ||||
−0.737121 | + | 0.675761i | \(0.763815\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −35.7990 | −1.90001 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.8284 | 1.52151 | 0.760753 | − | 0.649041i | \(-0.224830\pi\) | ||||
0.760753 | + | 0.649041i | \(0.224830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6274 | 1.45407 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.4853 | −1.38630 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.68629 | 0.244622 | 0.122311 | − | 0.992492i | \(-0.460969\pi\) | ||||
0.122311 | + | 0.992492i | \(0.460969\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.31371 | 0.275133 | 0.137567 | − | 0.990493i | \(-0.456072\pi\) | ||||
0.137567 | + | 0.990493i | \(0.456072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3137 | 1.19754 | 0.598772 | − | 0.800919i | \(-0.295655\pi\) | ||||
0.598772 | + | 0.800919i | \(0.295655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.97056 | 0.458374 | 0.229187 | − | 0.973382i | \(-0.426393\pi\) | ||||
0.229187 | + | 0.973382i | \(0.426393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.7990 | 1.81508 | 0.907540 | − | 0.419965i | \(-0.137958\pi\) | ||||
0.907540 | + | 0.419965i | \(0.137958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.7990 | −1.81043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −46.6274 | −2.34608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2426 | 0.815195 | 0.407597 | − | 0.913162i | \(-0.366367\pi\) | ||||
0.407597 | + | 0.913162i | \(0.366367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.17157 | −0.0585056 | −0.0292528 | − | 0.999572i | \(-0.509313\pi\) | ||||
−0.0292528 | + | 0.999572i | \(0.509313\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | −0.597763 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.37258 | −0.0680364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.24264 | 0.407572 | 0.203786 | − | 0.979015i | \(-0.434675\pi\) | ||||
0.203786 | + | 0.979015i | \(0.434675\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.6569 | 0.670389 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.51472 | −0.367118 | −0.183559 | − | 0.983009i | \(-0.558762\pi\) | ||||
−0.183559 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3137 | −1.23371 | −0.616857 | − | 0.787075i | \(-0.711594\pi\) | ||||
−0.616857 | + | 0.787075i | \(0.711594\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 49.3553 | 2.39409 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.14214 | −0.392193 | −0.196096 | − | 0.980585i | \(-0.562827\pi\) | ||||
−0.196096 | + | 0.980585i | \(0.562827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.928932 | −0.0446416 | −0.0223208 | − | 0.999751i | \(-0.507106\pi\) | ||||
−0.0223208 | + | 0.999751i | \(0.507106\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.9706 | −1.57720 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6863 | 0.605484 | 0.302742 | − | 0.953073i | \(-0.402098\pi\) | ||||
0.302742 | + | 0.953073i | \(0.402098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1716 | −0.530777 | −0.265389 | − | 0.964141i | \(-0.585500\pi\) | ||||
−0.265389 | + | 0.964141i | \(0.585500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.6569 | 0.931824 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.6274 | 0.784696 | 0.392348 | − | 0.919817i | \(-0.371663\pi\) | ||||
0.392348 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.48528 | 0.399556 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.6274 | −1.15202 | −0.576011 | − | 0.817442i | \(-0.695391\pi\) | ||||
−0.576011 | + | 0.817442i | \(0.695391\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.3848 | 0.763115 | 0.381558 | − | 0.924345i | \(-0.375388\pi\) | ||||
0.381558 | + | 0.924345i | \(0.375388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.65685 | −0.0770005 | −0.0385003 | − | 0.999259i | \(-0.512258\pi\) | ||||
−0.0385003 | + | 0.999259i | \(0.512258\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.8284 | 0.871276 | 0.435638 | − | 0.900122i | \(-0.356523\pi\) | ||||
0.435638 | + | 0.900122i | \(0.356523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.37258 | 0.430952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 45.4558 | 2.08566 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.8284 | −1.04306 | −0.521529 | − | 0.853234i | \(-0.674638\pi\) | ||||
−0.521529 | + | 0.853234i | \(0.674638\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.02944 | −0.320515 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.828427 | 0.0376169 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.97056 | −0.225238 | −0.112619 | − | 0.993638i | \(-0.535924\pi\) | ||||
−0.112619 | + | 0.993638i | \(0.535924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.1716 | 0.865201 | 0.432600 | − | 0.901586i | \(-0.357596\pi\) | ||||
0.432600 | + | 0.901586i | \(0.357596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.9706 | −0.944467 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9706 | 1.11784 | 0.558918 | − | 0.829223i | \(-0.311217\pi\) | ||||
0.558918 | + | 0.829223i | \(0.311217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.3137 | 0.861156 | 0.430578 | − | 0.902553i | \(-0.358310\pi\) | ||||
0.430578 | + | 0.902553i | \(0.358310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.6274 | −1.62990 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.3848 | −1.61273 | −0.806363 | − | 0.591420i | \(-0.798567\pi\) | ||||
−0.806363 | + | 0.591420i | \(0.798567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 48.2843 | 2.12766 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.71573 | 0.163418 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.2426 | 0.623981 | 0.311991 | − | 0.950085i | \(-0.399004\pi\) | ||||
0.311991 | + | 0.950085i | \(0.399004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.97056 | −0.217348 | −0.108674 | − | 0.994077i | \(-0.534660\pi\) | ||||
−0.108674 | + | 0.994077i | \(0.534660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.9706 | −0.913492 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.4558 | 1.88228 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.7990 | 1.89360 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.3137 | −0.484626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.02944 | 0.129529 | 0.0647647 | − | 0.997901i | \(-0.479370\pi\) | ||||
0.0647647 | + | 0.997901i | \(0.479370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.3137 | −0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.6274 | −1.38247 | −0.691234 | − | 0.722631i | \(-0.742933\pi\) | ||||
−0.691234 | + | 0.722631i | \(0.742933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.0000 | 2.03018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.85786 | −0.0782996 | −0.0391498 | − | 0.999233i | \(-0.512465\pi\) | ||||
−0.0391498 | + | 0.999233i | \(0.512465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.1421 | 1.43637 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.85786 | 0.245574 | 0.122787 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122787 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.6569 | 1.74329 | 0.871643 | − | 0.490142i | \(-0.163055\pi\) | ||||
0.871643 | + | 0.490142i | \(0.163055\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.1421 | −1.34042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.2132 | −0.550073 | −0.275036 | − | 0.961434i | \(-0.588690\pi\) | ||||
−0.275036 | + | 0.961434i | \(0.588690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.65685 | 0.0686199 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.7990 | 1.47758 | 0.738791 | − | 0.673934i | \(-0.235397\pi\) | ||||
0.738791 | + | 0.673934i | \(0.235397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3137 | −0.795807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 47.4142 | 1.94707 | 0.973534 | − | 0.228541i | \(-0.0733956\pi\) | ||||
0.973534 | + | 0.228541i | \(0.0733956\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.4558 | 0.958380 | 0.479190 | − | 0.877711i | \(-0.340931\pi\) | ||||
0.479190 | + | 0.877711i | \(0.340931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.2426 | 0.499388 | 0.249694 | − | 0.968325i | \(-0.419670\pi\) | ||||
0.249694 | + | 0.968325i | \(0.419670\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.2132 | −1.43162 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.9706 | 1.01352 | 0.506762 | − | 0.862086i | \(-0.330842\pi\) | ||||
0.506762 | + | 0.862086i | \(0.330842\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.0294 | 0.769849 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.3431 | −0.417756 | −0.208878 | − | 0.977942i | \(-0.566981\pi\) | ||||
−0.208878 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.48528 | 0.180571 | 0.0902853 | − | 0.995916i | \(-0.471222\pi\) | ||||
0.0902853 | + | 0.995916i | \(0.471222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.6569 | 1.35278 | 0.676392 | − | 0.736542i | \(-0.263543\pi\) | ||||
0.676392 | + | 0.736542i | \(0.263543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.2843 | −0.489806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.02944 | 0.120600 | 0.0603000 | − | 0.998180i | \(-0.480794\pi\) | ||||
0.0603000 | + | 0.998180i | \(0.480794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −68.2843 | −2.70978 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.1127 | −1.38687 | −0.693434 | − | 0.720520i | \(-0.743903\pi\) | ||||
−0.693434 | + | 0.720520i | \(0.743903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.7990 | 1.25403 | 0.627015 | − | 0.779007i | \(-0.284277\pi\) | ||||
0.627015 | + | 0.779007i | \(0.284277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.201010 | 0.00790252 | 0.00395126 | − | 0.999992i | \(-0.498742\pi\) | ||||
0.00395126 | + | 0.999992i | \(0.498742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.02944 | −0.275930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −46.1421 | −1.80568 | −0.902841 | − | 0.429975i | \(-0.858522\pi\) | ||||
−0.902841 | + | 0.429975i | \(0.858522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.6569 | 0.533617 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5147 | 0.838094 | 0.419047 | − | 0.907964i | \(-0.362364\pi\) | ||||
0.419047 | + | 0.907964i | \(0.362364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.92893 | −0.191713 | −0.0958566 | − | 0.995395i | \(-0.530559\pi\) | ||||
−0.0958566 | + | 0.995395i | \(0.530559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6569 | 0.528796 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.17157 | −0.354065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.3137 | −0.898677 | −0.449339 | − | 0.893361i | \(-0.648340\pi\) | ||||
−0.449339 | + | 0.893361i | \(0.648340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.6985 | 1.06454 | 0.532270 | − | 0.846575i | \(-0.321339\pi\) | ||||
0.532270 | + | 0.846575i | \(0.321339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.79899 | −0.0688364 | −0.0344182 | − | 0.999408i | \(-0.510958\pi\) | ||||
−0.0344182 | + | 0.999408i | \(0.510958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.3137 | 1.19644 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.48528 | 0.323263 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.68629 | 0.330442 | 0.165221 | − | 0.986257i | \(-0.447166\pi\) | ||||
0.165221 | + | 0.986257i | \(0.447166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −71.5980 | −2.71587 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 75.9411 | 2.87648 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.14214 | 0.231985 | 0.115993 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115993 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.3137 | −0.426705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.62742 | 0.248898 | 0.124449 | − | 0.992226i | \(-0.460284\pi\) | ||||
0.124449 | + | 0.992226i | \(0.460284\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.6569 | 0.511453 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.62742 | 0.247161 | 0.123580 | − | 0.992335i | \(-0.460562\pi\) | ||||
0.123580 | + | 0.992335i | \(0.460562\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.8284 | −0.699270 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.85786 | −0.365608 | −0.182804 | − | 0.983149i | \(-0.558517\pi\) | ||||
−0.182804 | + | 0.983149i | \(0.558517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 83.8823 | 3.10250 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.04163 | 0.297024 | 0.148512 | − | 0.988911i | \(-0.452552\pi\) | ||||
0.148512 | + | 0.988911i | \(0.452552\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.37258 | −0.345244 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.9706 | −1.21284 | −0.606421 | − | 0.795144i | \(-0.707395\pi\) | ||||
−0.606421 | + | 0.795144i | \(0.707395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.82843 | −0.177138 | −0.0885689 | − | 0.996070i | \(-0.528229\pi\) | ||||
−0.0885689 | + | 0.996070i | \(0.528229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.48528 | −0.164328 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.2843 | −0.740184 | −0.370092 | − | 0.928995i | \(-0.620674\pi\) | ||||
−0.370092 | + | 0.928995i | \(0.620674\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.9706 | 1.19992 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.9411 | 1.52438 | 0.762188 | − | 0.647356i | \(-0.224125\pi\) | ||||
0.762188 | + | 0.647356i | \(0.224125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.8995 | −1.15636 | −0.578178 | − | 0.815911i | \(-0.696236\pi\) | ||||
−0.578178 | + | 0.815911i | \(0.696236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.0000 | −1.29988 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.8701 | −1.25745 | −0.628723 | − | 0.777629i | \(-0.716422\pi\) | ||||
−0.628723 | + | 0.777629i | \(0.716422\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.3553 | 1.19971 | 0.599854 | − | 0.800109i | \(-0.295225\pi\) | ||||
0.599854 | + | 0.800109i | \(0.295225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.8284 | −0.676337 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 69.9411 | 2.50590 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.68629 | −0.310820 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.828427 | −0.0295678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.3137 | 0.545875 | 0.272937 | − | 0.962032i | \(-0.412005\pi\) | ||||
0.272937 | + | 0.962032i | \(0.412005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.9706 | −1.66797 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.4142 | −1.39612 | −0.698062 | − | 0.716038i | \(-0.745954\pi\) | ||||
−0.698062 | + | 0.716038i | \(0.745954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.2548 | 1.17647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.42641 | −0.226783 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.62742 | 0.162691 | 0.0813457 | − | 0.996686i | \(-0.474078\pi\) | ||||
0.0813457 | + | 0.996686i | \(0.474078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6569 | 0.900934 | 0.450467 | − | 0.892793i | \(-0.351257\pi\) | ||||
0.450467 | + | 0.892793i | \(0.351257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.3137 | −0.676530 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 77.2548 | 2.70280 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.6863 | 0.372954 | 0.186477 | − | 0.982459i | \(-0.440293\pi\) | ||||
0.186477 | + | 0.982459i | \(0.440293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.9706 | 0.870419 | 0.435210 | − | 0.900329i | \(-0.356674\pi\) | ||||
0.435210 | + | 0.900329i | \(0.356674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.1421 | 1.39588 | 0.697939 | − | 0.716157i | \(-0.254100\pi\) | ||||
0.697939 | + | 0.716157i | \(0.254100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.3848 | −1.19423 | −0.597116 | − | 0.802155i | \(-0.703687\pi\) | ||||
−0.597116 | + | 0.802155i | \(0.703687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 50.6274 | 1.75203 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.7990 | −0.821632 | −0.410816 | − | 0.911718i | \(-0.634756\pi\) | ||||
−0.410816 | + | 0.911718i | \(0.634756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.0711 | 0.587263 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.92893 | −0.168763 | −0.0843817 | − | 0.996434i | \(-0.526892\pi\) | ||||
−0.0843817 | + | 0.996434i | \(0.526892\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.2132 | −0.383036 | −0.191518 | − | 0.981489i | \(-0.561341\pi\) | ||||
−0.191518 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.54416 | 0.0868055 | 0.0434027 | − | 0.999058i | \(-0.486180\pi\) | ||||
0.0434027 | + | 0.999058i | \(0.486180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.0833 | 1.84102 | 0.920508 | − | 0.390724i | \(-0.127775\pi\) | ||||
0.920508 | + | 0.390724i | \(0.127775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.6274 | −1.92539 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.3137 | −0.383791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2843 | −0.955092 | −0.477546 | − | 0.878607i | \(-0.658474\pi\) | ||||
−0.477546 | + | 0.878607i | \(0.658474\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0416 | 1.01213 | 0.506064 | − | 0.862496i | \(-0.331100\pi\) | ||||
0.506064 | + | 0.862496i | \(0.331100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3431 | 0.348075 | 0.174037 | − | 0.984739i | \(-0.444319\pi\) | ||||
0.174037 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.7990 | 1.33632 | 0.668160 | − | 0.744018i | \(-0.267082\pi\) | ||||
0.668160 | + | 0.744018i | \(0.267082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.6274 | 1.02491 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.1421 | −0.740130 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.00000 | 0.266815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.8284 | 0.494007 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.1421 | 0.802512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.6569 | −1.78165 | −0.890823 | − | 0.454350i | \(-0.849872\pi\) | ||||
−0.890823 | + | 0.454350i | \(0.849872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.48528 | 0.214867 | 0.107433 | − | 0.994212i | \(-0.465737\pi\) | ||||
0.107433 | + | 0.994212i | \(0.465737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.31371 | 0.109668 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.3137 | −1.03294 | −0.516472 | − | 0.856304i | \(-0.672755\pi\) | ||||
−0.516472 | + | 0.856304i | \(0.672755\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.4853 | −1.46425 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0294 | −0.362646 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8995 | −0.521646 | −0.260823 | − | 0.965387i | \(-0.583994\pi\) | ||||
−0.260823 | + | 0.965387i | \(0.583994\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.9706 | 0.685811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.3553 | −1.67771 | −0.838853 | − | 0.544358i | \(-0.816773\pi\) | ||||
−0.838853 | + | 0.544358i | \(0.816773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.7279 | −0.480117 | −0.240058 | − | 0.970758i | \(-0.577167\pi\) | ||||
−0.240058 | + | 0.970758i | \(0.577167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.4558 | −1.61050 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −58.7696 | −1.90975 | −0.954877 | − | 0.297002i | \(-0.904013\pi\) | ||||
−0.954877 | + | 0.297002i | \(0.904013\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.9117 | −1.06836 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00000 | −0.0647864 | −0.0323932 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323932 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.4558 | 1.34148 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.82843 | 0.219815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.3137 | 1.00698 | 0.503490 | − | 0.864001i | \(-0.332049\pi\) | ||||
0.503490 | + | 0.864001i | \(0.332049\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.79899 | 0.249512 | 0.124756 | − | 0.992187i | \(-0.460185\pi\) | ||||
0.124756 | + | 0.992187i | \(0.460185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.76955 | 0.152436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.37258 | −0.0437786 | −0.0218893 | − | 0.999760i | \(-0.506968\pi\) | ||||
−0.0218893 | + | 0.999760i | \(0.506968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.17157 | 0.292231 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −54.6274 | −1.73705 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.6274 | 0.591719 | 0.295860 | − | 0.955231i | \(-0.404394\pi\) | ||||
0.295860 | + | 0.955231i | \(0.404394\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.3137 | −0.612286 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.3848 | 1.72238 | 0.861192 | − | 0.508281i | \(-0.169719\pi\) | ||||
0.861192 | + | 0.508281i | \(0.169719\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7056.2.a.cw.1.2 | 2 | ||
3.2 | odd | 2 | 2352.2.a.z.1.1 | 2 | |||
4.3 | odd | 2 | 3528.2.a.bm.1.2 | 2 | |||
7.6 | odd | 2 | 7056.2.a.ce.1.1 | 2 | |||
12.11 | even | 2 | 1176.2.a.m.1.1 | yes | 2 | ||
21.2 | odd | 6 | 2352.2.q.bg.1537.2 | 4 | |||
21.5 | even | 6 | 2352.2.q.ba.1537.1 | 4 | |||
21.11 | odd | 6 | 2352.2.q.bg.961.2 | 4 | |||
21.17 | even | 6 | 2352.2.q.ba.961.1 | 4 | |||
21.20 | even | 2 | 2352.2.a.bg.1.2 | 2 | |||
24.5 | odd | 2 | 9408.2.a.ed.1.2 | 2 | |||
24.11 | even | 2 | 9408.2.a.dr.1.2 | 2 | |||
28.3 | even | 6 | 3528.2.s.bl.3313.2 | 4 | |||
28.11 | odd | 6 | 3528.2.s.bc.3313.1 | 4 | |||
28.19 | even | 6 | 3528.2.s.bl.361.2 | 4 | |||
28.23 | odd | 6 | 3528.2.s.bc.361.1 | 4 | |||
28.27 | even | 2 | 3528.2.a.bc.1.1 | 2 | |||
84.11 | even | 6 | 1176.2.q.m.961.2 | 4 | |||
84.23 | even | 6 | 1176.2.q.m.361.2 | 4 | |||
84.47 | odd | 6 | 1176.2.q.n.361.1 | 4 | |||
84.59 | odd | 6 | 1176.2.q.n.961.1 | 4 | |||
84.83 | odd | 2 | 1176.2.a.l.1.2 | ✓ | 2 | ||
168.83 | odd | 2 | 9408.2.a.dv.1.1 | 2 | |||
168.125 | even | 2 | 9408.2.a.dh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.l.1.2 | ✓ | 2 | 84.83 | odd | 2 | ||
1176.2.a.m.1.1 | yes | 2 | 12.11 | even | 2 | ||
1176.2.q.m.361.2 | 4 | 84.23 | even | 6 | |||
1176.2.q.m.961.2 | 4 | 84.11 | even | 6 | |||
1176.2.q.n.361.1 | 4 | 84.47 | odd | 6 | |||
1176.2.q.n.961.1 | 4 | 84.59 | odd | 6 | |||
2352.2.a.z.1.1 | 2 | 3.2 | odd | 2 | |||
2352.2.a.bg.1.2 | 2 | 21.20 | even | 2 | |||
2352.2.q.ba.961.1 | 4 | 21.17 | even | 6 | |||
2352.2.q.ba.1537.1 | 4 | 21.5 | even | 6 | |||
2352.2.q.bg.961.2 | 4 | 21.11 | odd | 6 | |||
2352.2.q.bg.1537.2 | 4 | 21.2 | odd | 6 | |||
3528.2.a.bc.1.1 | 2 | 28.27 | even | 2 | |||
3528.2.a.bm.1.2 | 2 | 4.3 | odd | 2 | |||
3528.2.s.bc.361.1 | 4 | 28.23 | odd | 6 | |||
3528.2.s.bc.3313.1 | 4 | 28.11 | odd | 6 | |||
3528.2.s.bl.361.2 | 4 | 28.19 | even | 6 | |||
3528.2.s.bl.3313.2 | 4 | 28.3 | even | 6 | |||
7056.2.a.ce.1.1 | 2 | 7.6 | odd | 2 | |||
7056.2.a.cw.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9408.2.a.dh.1.1 | 2 | 168.125 | even | 2 | |||
9408.2.a.dr.1.2 | 2 | 24.11 | even | 2 | |||
9408.2.a.dv.1.1 | 2 | 168.83 | odd | 2 | |||
9408.2.a.ed.1.2 | 2 | 24.5 | odd | 2 |