Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, 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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
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: | \( x^{9} - x^{8} - 31x^{7} + 24x^{6} + 293x^{5} - 101x^{4} - 864x^{3} - 278x^{2} + 24x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.94765\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | ||||||||
\(5\) | 2.94765 | 1.31823 | 0.659115 | − | 0.752042i | \(-0.270931\pi\) | ||||
0.659115 | + | 0.752042i | \(0.270931\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.65088 | 1.75787 | 0.878934 | − | 0.476944i | \(-0.158256\pi\) | ||||
0.878934 | + | 0.476944i | \(0.158256\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.56158 | 1.67688 | 0.838440 | − | 0.544993i | \(-0.183468\pi\) | ||||
0.838440 | + | 0.544993i | \(0.183468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.393514 | −0.109141 | −0.0545706 | − | 0.998510i | \(-0.517379\pi\) | ||||
−0.0545706 | + | 0.998510i | \(0.517379\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.257869 | 0.0625424 | 0.0312712 | − | 0.999511i | \(-0.490044\pi\) | ||||
0.0312712 | + | 0.999511i | \(0.490044\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.11137 | 0.484381 | 0.242191 | − | 0.970229i | \(-0.422134\pi\) | ||||
0.242191 | + | 0.970229i | \(0.422134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.38988 | −1.12387 | −0.561934 | − | 0.827182i | \(-0.689943\pi\) | ||||
−0.561934 | + | 0.827182i | \(0.689943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.68866 | 0.737731 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.101053 | 0.0187651 | 0.00938257 | − | 0.999956i | \(-0.497013\pi\) | ||||
0.00938257 | + | 0.999956i | \(0.497013\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.82473 | −0.686941 | −0.343471 | − | 0.939163i | \(-0.611603\pi\) | ||||
−0.343471 | + | 0.939163i | \(0.611603\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.7092 | 2.31727 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.36787 | −0.224876 | −0.112438 | − | 0.993659i | \(-0.535866\pi\) | ||||
−0.112438 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.79375 | 0.904832 | 0.452416 | − | 0.891807i | \(-0.350562\pi\) | ||||
0.452416 | + | 0.891807i | \(0.350562\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.94402 | 1.21145 | 0.605726 | − | 0.795673i | \(-0.292883\pi\) | ||||
0.605726 | + | 0.795673i | \(0.292883\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.64008 | −0.822691 | −0.411345 | − | 0.911480i | \(-0.634941\pi\) | ||||
−0.411345 | + | 0.911480i | \(0.634941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.6307 | 2.09010 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.37285 | 0.600657 | 0.300329 | − | 0.953836i | \(-0.402904\pi\) | ||||
0.300329 | + | 0.953836i | \(0.402904\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3936 | 2.21052 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.40379 | −0.963891 | −0.481946 | − | 0.876201i | \(-0.660070\pi\) | ||||
−0.481946 | + | 0.876201i | \(0.660070\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.23267 | 0.541938 | 0.270969 | − | 0.962588i | \(-0.412656\pi\) | ||||
0.270969 | + | 0.962588i | \(0.412656\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.15994 | −0.143873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.79684 | −0.586027 | −0.293014 | − | 0.956108i | \(-0.594658\pi\) | ||||
−0.293014 | + | 0.956108i | \(0.594658\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.11410 | 0.844288 | 0.422144 | − | 0.906529i | \(-0.361278\pi\) | ||||
0.422144 | + | 0.906529i | \(0.361278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79959 | 1.14696 | 0.573478 | − | 0.819221i | \(-0.305594\pi\) | ||||
0.573478 | + | 0.819221i | \(0.305594\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25.8663 | 2.94773 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.39883 | −0.494907 | −0.247453 | − | 0.968900i | \(-0.579594\pi\) | ||||
−0.247453 | + | 0.968900i | \(0.579594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.64462 | −1.05863 | −0.529317 | − | 0.848424i | \(-0.677552\pi\) | ||||
−0.529317 | + | 0.848424i | \(0.677552\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.760108 | 0.0824453 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6901 | −1.13315 | −0.566575 | − | 0.824010i | \(-0.691732\pi\) | ||||
−0.566575 | + | 0.824010i | \(0.691732\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.83019 | −0.191856 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.22358 | 0.638526 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.54716 | −0.563229 | −0.281614 | − | 0.959528i | \(-0.590870\pi\) | ||||
−0.281614 | + | 0.959528i | \(0.590870\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0543 | −1.39846 | −0.699230 | − | 0.714897i | \(-0.746474\pi\) | ||||
−0.699230 | + | 0.714897i | \(0.746474\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.68601 | 0.658792 | 0.329396 | − | 0.944192i | \(-0.393155\pi\) | ||||
0.329396 | + | 0.944192i | \(0.393155\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.5825 | −1.79644 | −0.898220 | − | 0.439546i | \(-0.855139\pi\) | ||||
−0.898220 | + | 0.439546i | \(0.855139\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.80580 | 0.460312 | 0.230156 | − | 0.973154i | \(-0.426076\pi\) | ||||
0.230156 | + | 0.973154i | \(0.426076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0810 | −1.04242 | −0.521208 | − | 0.853430i | \(-0.674518\pi\) | ||||
−0.521208 | + | 0.853430i | \(0.674518\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8875 | −1.48152 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.19932 | 0.109941 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.9312 | 1.81193 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.86538 | −0.345730 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.5991 | 1.82787 | 0.913937 | − | 0.405856i | \(-0.133026\pi\) | ||||
0.913937 | + | 0.405856i | \(0.133026\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.89118 | 0.514715 | 0.257358 | − | 0.966316i | \(-0.417148\pi\) | ||||
0.257358 | + | 0.966316i | \(0.417148\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.81972 | 0.851478 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.9620 | −1.70547 | −0.852736 | − | 0.522342i | \(-0.825059\pi\) | ||||
−0.852736 | + | 0.522342i | \(0.825059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.24509 | −0.784158 | −0.392079 | − | 0.919931i | \(-0.628244\pi\) | ||||
−0.392079 | + | 0.919931i | \(0.628244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.18856 | −0.183017 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.297870 | 0.0247368 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.57188 | 0.210696 | 0.105348 | − | 0.994435i | \(-0.466404\pi\) | ||||
0.105348 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.44717 | −0.768800 | −0.384400 | − | 0.923167i | \(-0.625592\pi\) | ||||
−0.384400 | + | 0.923167i | \(0.625592\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.2740 | −0.905547 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0957 | 0.885533 | 0.442766 | − | 0.896637i | \(-0.353997\pi\) | ||||
0.442766 | + | 0.896637i | \(0.353997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.0677 | −1.97561 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.4423 | 0.896233 | 0.448116 | − | 0.893975i | \(-0.352095\pi\) | ||||
0.448116 | + | 0.893975i | \(0.352095\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8451 | −0.988088 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.0924 | −1.07142 | −0.535712 | − | 0.844401i | \(-0.679957\pi\) | ||||
−0.535712 | + | 0.844401i | \(0.679957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.1555 | 1.29683 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.89743 | 0.515538 | 0.257769 | − | 0.966207i | \(-0.417013\pi\) | ||||
0.257769 | + | 0.966207i | \(0.417013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0876 | −1.41877 | −0.709384 | − | 0.704822i | \(-0.751027\pi\) | ||||
−0.709384 | + | 0.704822i | \(0.751027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.03200 | −0.296439 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.43416 | 0.104876 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.60862 | −0.116396 | −0.0581979 | − | 0.998305i | \(-0.518535\pi\) | ||||
−0.0581979 | + | 0.998305i | \(0.518535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7119 | 1.34692 | 0.673458 | − | 0.739226i | \(-0.264808\pi\) | ||||
0.673458 | + | 0.739226i | \(0.264808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.93111 | 0.137586 | 0.0687928 | − | 0.997631i | \(-0.478085\pi\) | ||||
0.0687928 | + | 0.997631i | \(0.478085\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.3394 | −1.37093 | −0.685465 | − | 0.728105i | \(-0.740401\pi\) | ||||
−0.685465 | + | 0.728105i | \(0.740401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.469987 | 0.0329866 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.0780 | 1.19278 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.7426 | 0.812250 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9760 | −1.09983 | −0.549916 | − | 0.835220i | \(-0.685340\pi\) | ||||
−0.549916 | + | 0.835220i | \(0.685340\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.4162 | 1.59697 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.7883 | −1.20755 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.101475 | −0.00682595 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.3254 | 1.69592 | 0.847958 | − | 0.530064i | \(-0.177832\pi\) | ||||
0.847958 | + | 0.530064i | \(0.177832\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.37245 | −0.422954 | −0.211477 | − | 0.977383i | \(-0.567827\pi\) | ||||
−0.211477 | + | 0.977383i | \(0.567827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.56881 | 0.103670 | 0.0518351 | − | 0.998656i | \(-0.483493\pi\) | ||||
0.0518351 | + | 0.998656i | \(0.483493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.4918 | 1.67002 | 0.835012 | − | 0.550232i | \(-0.185461\pi\) | ||||
0.835012 | + | 0.550232i | \(0.185461\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.6250 | −1.08450 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.23855 | 0.144800 | 0.0723998 | − | 0.997376i | \(-0.476934\pi\) | ||||
0.0723998 | + | 0.997376i | \(0.476934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.73714 | 0.627224 | 0.313612 | − | 0.949551i | \(-0.398461\pi\) | ||||
0.313612 | + | 0.949551i | \(0.398461\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 43.1262 | 2.75523 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.830853 | −0.0528659 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7392 | 0.804090 | 0.402045 | − | 0.915620i | \(-0.368300\pi\) | ||||
0.402045 | + | 0.915620i | \(0.368300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.9763 | −1.88459 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.4381 | −0.713486 | −0.356743 | − | 0.934203i | \(-0.616113\pi\) | ||||
−0.356743 | + | 0.934203i | \(0.616113\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.36179 | −0.395302 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.7134 | 1.46223 | 0.731116 | − | 0.682253i | \(-0.239000\pi\) | ||||
0.731116 | + | 0.682253i | \(0.239000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.8896 | 0.791805 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.3877 | −1.24306 | −0.621529 | − | 0.783391i | \(-0.713488\pi\) | ||||
−0.621529 | + | 0.783391i | \(0.713488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.753640 | 0.0457804 | 0.0228902 | − | 0.999738i | \(-0.492713\pi\) | ||||
0.0228902 | + | 0.999738i | \(0.492713\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.5148 | 1.23709 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.2696 | −1.57839 | −0.789195 | − | 0.614143i | \(-0.789502\pi\) | ||||
−0.789195 | + | 0.614143i | \(0.789502\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7488 | −1.11846 | −0.559230 | − | 0.829013i | \(-0.688903\pi\) | ||||
−0.559230 | + | 0.829013i | \(0.688903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.8657 | −1.83478 | −0.917389 | − | 0.397992i | \(-0.869707\pi\) | ||||
−0.917389 | + | 0.397992i | \(0.869707\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.9460 | 1.59057 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9335 | −0.996088 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.54329 | 0.557525 | 0.278763 | − | 0.960360i | \(-0.410076\pi\) | ||||
0.278763 | + | 0.960360i | \(0.410076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.8238 | −1.27063 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.12099 | 0.122660 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.9467 | 2.12957 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4764 | 0.714399 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4454 | −1.05273 | −0.526366 | − | 0.850258i | \(-0.676446\pi\) | ||||
−0.526366 | + | 0.850258i | \(0.676446\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.89773 | 0.164315 | 0.0821575 | − | 0.996619i | \(-0.473819\pi\) | ||||
0.0821575 | + | 0.996619i | \(0.473819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.39954 | 0.135630 | 0.0678149 | − | 0.997698i | \(-0.478397\pi\) | ||||
0.0678149 | + | 0.997698i | \(0.478397\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.3953 | −0.583860 | −0.291930 | − | 0.956440i | \(-0.594297\pi\) | ||||
−0.291930 | + | 0.956440i | \(0.594297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.562017 | 0.0314669 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.544456 | 0.0302944 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.45154 | −0.0805169 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.2313 | −1.44618 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0622 | 0.717965 | 0.358983 | − | 0.933344i | \(-0.383124\pi\) | ||||
0.358983 | + | 0.933344i | \(0.383124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.1394 | −0.772519 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6914 | 1.50845 | 0.754224 | − | 0.656618i | \(-0.228013\pi\) | ||||
0.754224 | + | 0.656618i | \(0.228013\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.2715 | −1.15192 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 35.4894 | 1.91625 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.6196 | 1.64374 | 0.821872 | − | 0.569672i | \(-0.192930\pi\) | ||||
0.821872 | + | 0.569672i | \(0.192930\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.7482 | 1.43180 | 0.715898 | − | 0.698204i | \(-0.246017\pi\) | ||||
0.715898 | + | 0.698204i | \(0.246017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.7882 | −1.37257 | −0.686283 | − | 0.727335i | \(-0.740759\pi\) | ||||
−0.686283 | + | 0.727335i | \(0.740759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.9699 | 1.11297 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.2661 | 1.38627 | 0.693135 | − | 0.720808i | \(-0.256229\pi\) | ||||
0.693135 | + | 0.720808i | \(0.256229\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5421 | −0.765375 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.8858 | 1.51195 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.6384 | −0.555323 | −0.277661 | − | 0.960679i | \(-0.589559\pi\) | ||||
−0.277661 | + | 0.960679i | \(0.589559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3376 | 1.05588 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9912 | −0.724435 | −0.362217 | − | 0.932094i | \(-0.617980\pi\) | ||||
−0.362217 | + | 0.932094i | \(0.617980\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0397659 | −0.00204805 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4396 | −0.638979 | −0.319490 | − | 0.947590i | \(-0.603511\pi\) | ||||
−0.319490 | + | 0.947590i | \(0.603511\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.12077 | 0.108366 | 0.0541830 | − | 0.998531i | \(-0.482745\pi\) | ||||
0.0541830 | + | 0.998531i | \(0.482745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 76.2448 | 3.88579 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.6819 | −1.30212 | −0.651062 | − | 0.759025i | \(-0.725676\pi\) | ||||
−0.651062 | + | 0.759025i | \(0.725676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.38988 | −0.0702894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.9662 | −0.652401 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.9235 | 1.25087 | 0.625437 | − | 0.780274i | \(-0.284921\pi\) | ||||
0.625437 | + | 0.780274i | \(0.284921\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.9408 | −1.04574 | −0.522868 | − | 0.852414i | \(-0.675138\pi\) | ||||
−0.522868 | + | 0.852414i | \(0.675138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.50508 | 0.0749736 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.60751 | −0.377091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0301 | 0.693742 | 0.346871 | − | 0.937913i | \(-0.387244\pi\) | ||||
0.346871 | + | 0.937913i | \(0.387244\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.4341 | −1.69439 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.4290 | −1.39552 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.6278 | 0.861173 | 0.430586 | − | 0.902549i | \(-0.358307\pi\) | ||||
0.430586 | + | 0.902549i | \(0.358307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.22755 | −0.157301 | −0.0786505 | − | 0.996902i | \(-0.525061\pi\) | ||||
−0.0786505 | + | 0.996902i | \(0.525061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.951190 | 0.0461395 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.6856 | 0.952654 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.25080 | 0.0602491 | 0.0301246 | − | 0.999546i | \(-0.490410\pi\) | ||||
0.0301246 | + | 0.999546i | \(0.490410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.8700 | 0.522381 | 0.261191 | − | 0.965287i | \(-0.415885\pi\) | ||||
0.261191 | + | 0.965287i | \(0.415885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.3800 | −0.544381 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.2789 | 1.92241 | 0.961204 | − | 0.275838i | \(-0.0889554\pi\) | ||||
0.961204 | + | 0.275838i | \(0.0889554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.0259 | 0.998970 | 0.499485 | − | 0.866323i | \(-0.333523\pi\) | ||||
0.499485 | + | 0.866323i | \(0.333523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.5107 | −1.49375 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.3177 | 1.38359 | 0.691794 | − | 0.722095i | \(-0.256821\pi\) | ||||
0.691794 | + | 0.722095i | \(0.256821\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.2224 | 1.51729 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.39475 | −0.252910 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.2568 | −1.64924 | −0.824622 | − | 0.565685i | \(-0.808612\pi\) | ||||
−0.824622 | + | 0.565685i | \(0.808612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.33399 | −0.341578 | −0.170789 | − | 0.985308i | \(-0.554632\pi\) | ||||
−0.170789 | + | 0.985308i | \(0.554632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.77568 | −0.314892 | −0.157446 | − | 0.987528i | \(-0.550326\pi\) | ||||
−0.157446 | + | 0.987528i | \(0.550326\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.8308 | 1.01021 | 0.505104 | − | 0.863058i | \(-0.331454\pi\) | ||||
0.505104 | + | 0.863058i | \(0.331454\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.3095 | −1.03016 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.1814 | 2.03146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.78812 | 0.357343 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.8655 | −0.861985 | −0.430992 | − | 0.902356i | \(-0.641836\pi\) | ||||
−0.430992 | + | 0.902356i | \(0.641836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.538275 | 0.0245432 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.3511 | −0.742465 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.2690 | −1.00911 | −0.504553 | − | 0.863381i | \(-0.668343\pi\) | ||||
−0.504553 | + | 0.863381i | \(0.668343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.3929 | −1.19110 | −0.595549 | − | 0.803319i | \(-0.703065\pi\) | ||||
−0.595549 | + | 0.803319i | \(0.703065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0260585 | 0.00117362 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.0868 | 1.48415 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.2798 | 0.863085 | 0.431542 | − | 0.902093i | \(-0.357970\pi\) | ||||
0.431542 | + | 0.902093i | \(0.357970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 44.5066 | 1.98445 | 0.992225 | − | 0.124456i | \(-0.0397186\pi\) | ||||
0.992225 | + | 0.124456i | \(0.0397186\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.4273 | −1.84349 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.4138 | −0.505906 | −0.252953 | − | 0.967479i | \(-0.581402\pi\) | ||||
−0.252953 | + | 0.967479i | \(0.581402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.5767 | 2.01620 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.7080 | 0.868440 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.3678 | −1.37955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.1737 | −0.927638 | −0.463819 | − | 0.885930i | \(-0.653521\pi\) | ||||
−0.463819 | + | 0.885930i | \(0.653521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.6063 | 1.77559 | 0.887795 | − | 0.460239i | \(-0.152236\pi\) | ||||
0.887795 | + | 0.460239i | \(0.152236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.986278 | −0.0429630 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.05084 | 0.263080 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.27992 | −0.0987544 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −54.7748 | −2.36812 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 81.3698 | 3.50484 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.70757 | 0.159401 | 0.0797004 | − | 0.996819i | \(-0.474604\pi\) | ||||
0.0797004 | + | 0.996819i | \(0.474604\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.1658 | 0.606798 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.265318 | −0.0113442 | −0.00567208 | − | 0.999984i | \(-0.501805\pi\) | ||||
−0.00567208 | + | 0.999984i | \(0.501805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.213361 | 0.00908948 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.4584 | −0.869981 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.5449 | 0.446802 | 0.223401 | − | 0.974727i | \(-0.428284\pi\) | ||||
0.223401 | + | 0.974727i | \(0.428284\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.12608 | −0.132219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.6916 | 1.33564 | 0.667821 | − | 0.744322i | \(-0.267227\pi\) | ||||
0.667821 | + | 0.744322i | \(0.267227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.6630 | −1.37414 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.6165 | 1.70273 | 0.851365 | − | 0.524573i | \(-0.175775\pi\) | ||||
0.851365 | + | 0.524573i | \(0.175775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.2878 | 1.05826 | 0.529131 | − | 0.848540i | \(-0.322518\pi\) | ||||
0.529131 | + | 0.848540i | \(0.322518\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.8814 | −0.829113 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.3694 | −1.84712 | −0.923561 | − | 0.383452i | \(-0.874735\pi\) | ||||
−0.923561 | + | 0.383452i | \(0.874735\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.8560 | −1.86094 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.3200 | 1.00723 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.9324 | 0.616325 | 0.308162 | − | 0.951334i | \(-0.400286\pi\) | ||||
0.308162 | + | 0.951334i | \(0.400286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.07541 | −0.332741 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.70449 | 0.0699948 | 0.0349974 | − | 0.999387i | \(-0.488858\pi\) | ||||
0.0349974 | + | 0.999387i | \(0.488858\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.53517 | 0.144928 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.0511 | −1.14614 | −0.573069 | − | 0.819507i | \(-0.694247\pi\) | ||||
−0.573069 | + | 0.819507i | \(0.694247\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.3274 | −1.60420 | −0.802099 | − | 0.597191i | \(-0.796283\pi\) | ||||
−0.802099 | + | 0.597191i | \(0.796283\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 58.7503 | 2.38854 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.5448 | 1.36154 | 0.680771 | − | 0.732496i | \(-0.261645\pi\) | ||||
0.680771 | + | 0.732496i | \(0.261645\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.21945 | 0.0897894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.5000 | 1.71656 | 0.858280 | − | 0.513182i | \(-0.171533\pi\) | ||||
0.858280 | + | 0.513182i | \(0.171533\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.95453 | −0.279979 | −0.139989 | − | 0.990153i | \(-0.544707\pi\) | ||||
−0.139989 | + | 0.990153i | \(0.544707\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.29546 | 0.333423 | 0.166711 | − | 0.986006i | \(-0.446685\pi\) | ||||
0.166711 | + | 0.986006i | \(0.446685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −49.7184 | −1.99193 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.8371 | −1.19348 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.352731 | −0.0140643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.7880 | 1.66355 | 0.831777 | − | 0.555110i | \(-0.187324\pi\) | ||||
0.831777 | + | 0.555110i | \(0.187324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 60.7190 | 2.40956 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.75738 | −0.228116 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.5081 | −0.889018 | −0.444509 | − | 0.895774i | \(-0.646622\pi\) | ||||
−0.444509 | + | 0.895774i | \(0.646622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.1894 | −0.638446 | −0.319223 | − | 0.947680i | \(-0.603422\pi\) | ||||
−0.319223 | + | 0.947680i | \(0.603422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.9895 | −1.61146 | −0.805731 | − | 0.592282i | \(-0.798227\pi\) | ||||
−0.805731 | + | 0.592282i | \(0.798227\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.1768 | −1.61633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.8116 | 0.618756 | 0.309378 | − | 0.950939i | \(-0.399879\pi\) | ||||
0.309378 | + | 0.950939i | \(0.399879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.3652 | 0.678513 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.9906 | −0.739768 | −0.369884 | − | 0.929078i | \(-0.620603\pi\) | ||||
−0.369884 | + | 0.929078i | \(0.620603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.4650 | 1.49611 | 0.748057 | − | 0.663634i | \(-0.230987\pi\) | ||||
0.748057 | + | 0.663634i | \(0.230987\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.9451 | 1.12244 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.544666 | −0.0210896 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.5403 | 0.908765 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.8458 | 1.53594 | 0.767970 | − | 0.640485i | \(-0.221267\pi\) | ||||
0.767970 | + | 0.640485i | \(0.221267\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.8601 | −0.917019 | −0.458509 | − | 0.888690i | \(-0.651616\pi\) | ||||
−0.458509 | + | 0.888690i | \(0.651616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.7992 | −0.990081 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.5117 | 0.631804 | 0.315902 | − | 0.948792i | \(-0.397693\pi\) | ||||
0.315902 | + | 0.948792i | \(0.397693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −58.8412 | −2.24821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.72078 | −0.0655564 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4923 | −0.703481 | −0.351741 | − | 0.936098i | \(-0.614410\pi\) | ||||
−0.351741 | + | 0.936098i | \(0.614410\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.2513 | −1.03370 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.49403 | 0.0565903 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7230 | 0.782696 | 0.391348 | − | 0.920243i | \(-0.372009\pi\) | ||||
0.391348 | + | 0.920243i | \(0.372009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.88807 | −0.108926 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −65.3651 | −2.45831 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.5876 | −0.622961 | −0.311480 | − | 0.950253i | \(-0.600825\pi\) | ||||
−0.311480 | + | 0.950253i | \(0.600825\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.6148 | 0.772032 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.45112 | −0.241258 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0418 | −1.04578 | −0.522890 | − | 0.852400i | \(-0.675146\pi\) | ||||
−0.522890 | + | 0.852400i | \(0.675146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.0958 | 1.15807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.372751 | 0.0138436 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.0096 | −1.81766 | −0.908832 | − | 0.417162i | \(-0.863025\pi\) | ||||
−0.908832 | + | 0.417162i | \(0.863025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.04852 | 0.0757671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.39596 | −0.199304 | −0.0996522 | − | 0.995022i | \(-0.531773\pi\) | ||||
−0.0996522 | + | 0.995022i | \(0.531773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.6780 | −0.982698 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.9366 | 1.43231 | 0.716153 | − | 0.697943i | \(-0.245901\pi\) | ||||
0.716153 | + | 0.697943i | \(0.245901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.0681 | 0.919659 | 0.459829 | − | 0.888007i | \(-0.347911\pi\) | ||||
0.459829 | + | 0.888007i | \(0.347911\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.58100 | 0.277746 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −86.4251 | −3.15790 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3068 | −0.668023 | −0.334012 | − | 0.942569i | \(-0.608403\pi\) | ||||
−0.334012 | + | 0.942569i | \(0.608403\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.8470 | −1.01346 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.04280 | −0.183284 | −0.0916418 | − | 0.995792i | \(-0.529211\pi\) | ||||
−0.0916418 | + | 0.995792i | \(0.529211\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.64107 | −0.0594889 | −0.0297444 | − | 0.999558i | \(-0.509469\pi\) | ||||
−0.0297444 | + | 0.999558i | \(0.509469\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.3512 | 0.809168 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.91349 | 0.105200 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.6826 | −0.673713 | −0.336856 | − | 0.941556i | \(-0.609364\pi\) | ||||
−0.336856 | + | 0.941556i | \(0.609364\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.3488 | 0.516091 | 0.258046 | − | 0.966133i | \(-0.416922\pi\) | ||||
0.258046 | + | 0.966133i | \(0.416922\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.1081 | −0.506778 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.2327 | 0.438283 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.5656 | 1.41577 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.7063 | 1.16734 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.2812 | 1.15070 | 0.575351 | − | 0.817907i | \(-0.304866\pi\) | ||||
0.575351 | + | 0.817907i | \(0.304866\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51.5366 | −1.83243 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.66561 | −0.0591477 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.26106 | −0.221778 | −0.110889 | − | 0.993833i | \(-0.535370\pi\) | ||||
−0.110889 | + | 0.993833i | \(0.535370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45440 | −0.0514530 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.5013 | 1.92331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −73.8909 | −2.60431 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.5687 | 1.18021 | 0.590106 | − | 0.807326i | \(-0.299086\pi\) | ||||
0.590106 | + | 0.807326i | \(0.299086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9961 | 0.491469 | 0.245735 | − | 0.969337i | \(-0.420971\pi\) | ||||
0.245735 | + | 0.969337i | \(0.420971\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.7280 | 1.18144 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.7728 | 0.586805 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.67995 | 0.163331 | 0.0816656 | − | 0.996660i | \(-0.473976\pi\) | ||||
0.0816656 | + | 0.996660i | \(0.473976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5726 | 0.856548 | 0.428274 | − | 0.903649i | \(-0.359122\pi\) | ||||
0.428274 | + | 0.903649i | \(0.359122\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.9433 | −1.11078 | −0.555388 | − | 0.831591i | \(-0.687430\pi\) | ||||
−0.555388 | + | 0.831591i | \(0.687430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.4234 | 0.605140 | 0.302570 | − | 0.953127i | \(-0.402155\pi\) | ||||
0.302570 | + | 0.953127i | \(0.402155\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.77280 | 0.130720 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.94765 | 0.102008 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.29713 | 0.217401 | 0.108701 | − | 0.994075i | \(-0.465331\pi\) | ||||
0.108701 | + | 0.994075i | \(0.465331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9898 | −0.999648 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −37.8630 | −1.30253 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 92.6977 | 3.18513 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.37265 | 0.252731 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.7750 | 1.73850 | 0.869251 | − | 0.494371i | \(-0.164602\pi\) | ||||
0.869251 | + | 0.494371i | \(0.164602\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.83360 | −0.301750 | −0.150875 | − | 0.988553i | \(-0.548209\pi\) | ||||
−0.150875 | + | 0.988553i | \(0.548209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0835075 | 0.00284924 | 0.00142462 | − | 0.999999i | \(-0.499547\pi\) | ||||
0.00142462 | + | 0.999999i | \(0.499547\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.00419 | 0.238425 | 0.119213 | − | 0.992869i | \(-0.461963\pi\) | ||||
0.119213 | + | 0.992869i | \(0.461963\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −41.5394 | −1.41238 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.4645 | −0.829900 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.88762 | 0.0639597 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.9774 | −0.607748 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7259 | −0.564792 | −0.282396 | − | 0.959298i | \(-0.591129\pi\) | ||||
−0.282396 | + | 0.959298i | \(0.591129\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.6420 | 1.43665 | 0.718324 | − | 0.695709i | \(-0.244910\pi\) | ||||
0.718324 | + | 0.695709i | \(0.244910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.4022 | −1.46060 | −0.730300 | − | 0.683126i | \(-0.760620\pi\) | ||||
−0.730300 | + | 0.683126i | \(0.760620\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0250 | −0.940986 | −0.470493 | − | 0.882404i | \(-0.655924\pi\) | ||||
−0.470493 | + | 0.882404i | \(0.655924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 95.8039 | 3.21316 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.9083 | −0.398496 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.3312 | 0.679598 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.386502 | −0.0128906 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12762 | 0.0375665 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −56.2635 | −1.87026 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.56086 | −0.151441 | −0.0757205 | − | 0.997129i | \(-0.524126\pi\) | ||||
−0.0757205 | + | 0.997129i | \(0.524126\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.27413 | 0.0753454 | 0.0376727 | − | 0.999290i | \(-0.488006\pi\) | ||||
0.0376727 | + | 0.999290i | \(0.488006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −53.6394 | −1.77520 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.3992 | 0.904801 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0412 | −0.793046 | −0.396523 | − | 0.918025i | \(-0.629783\pi\) | ||||
−0.396523 | + | 0.918025i | \(0.629783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.79950 | −0.0921466 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.04560 | −0.165898 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.4175 | 0.669875 | 0.334938 | − | 0.942240i | \(-0.391285\pi\) | ||||
0.334938 | + | 0.942240i | \(0.391285\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.8908 | 1.01240 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.22740 | 0.138251 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.5945 | −1.42417 | −0.712085 | − | 0.702094i | \(-0.752249\pi\) | ||||
−0.712085 | + | 0.702094i | \(0.752249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.3081 | −0.857619 | −0.428810 | − | 0.903395i | \(-0.641067\pi\) | ||||
−0.428810 | + | 0.903395i | \(0.641067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.2276 | −1.01691 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.0868 | −1.62760 | −0.813801 | − | 0.581144i | \(-0.802605\pi\) | ||||
−0.813801 | + | 0.581144i | \(0.802605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.85628 | −0.125180 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.1095 | −0.619018 | −0.309509 | − | 0.950896i | \(-0.600165\pi\) | ||||
−0.309509 | + | 0.950896i | \(0.600165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.74166 | −0.153437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −92.8411 | −2.99799 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.3715 | −0.528112 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 55.1563 | 1.77554 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.4846 | −0.980320 | −0.490160 | − | 0.871633i | \(-0.663062\pi\) | ||||
−0.490160 | + | 0.871633i | \(0.663062\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.783562 | −0.0251457 | −0.0125728 | − | 0.999921i | \(-0.504002\pi\) | ||||
−0.0125728 | + | 0.999921i | \(0.504002\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.9978 | −1.37845 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.80461 | −0.0577347 | −0.0288673 | − | 0.999583i | \(-0.509190\pi\) | ||||
−0.0288673 | + | 0.999583i | \(0.509190\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59.4539 | −1.90016 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.5566 | −1.26166 | −0.630830 | − | 0.775921i | \(-0.717286\pi\) | ||||
−0.630830 | + | 0.775921i | \(0.717286\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.69223 | 0.181370 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.8174 | −1.36151 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.8643 | −1.07574 | −0.537868 | − | 0.843029i | \(-0.680770\pi\) | ||||
−0.537868 | + | 0.843029i | \(0.680770\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −57.0057 | −1.80720 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8336 | 0.818160 | 0.409080 | − | 0.912499i | \(-0.365850\pi\) | ||||
0.409080 | + | 0.912499i | \(0.365850\pi\) | |||||||
\(998\) | 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 | 6012.2.a.i.1.8 | 9 | ||
3.2 | odd | 2 | 2004.2.a.c.1.2 | ✓ | 9 | ||
12.11 | even | 2 | 8016.2.a.bc.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.c.1.2 | ✓ | 9 | 3.2 | odd | 2 | ||
6012.2.a.i.1.8 | 9 | 1.1 | even | 1 | trivial | ||
8016.2.a.bc.1.2 | 9 | 12.11 | even | 2 |