Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 15x^{6} + 56x^{5} + 87x^{4} - 248x^{3} - 241x^{2} + 340x + 248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.654712\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.654712 | −0.292796 | −0.146398 | − | 0.989226i | \(-0.546768\pi\) | ||||
−0.146398 | + | 0.989226i | \(0.546768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24646 | −0.849081 | −0.424540 | − | 0.905409i | \(-0.639564\pi\) | ||||
−0.424540 | + | 0.905409i | \(0.639564\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24164 | 1.27890 | 0.639452 | − | 0.768831i | \(-0.279161\pi\) | ||||
0.639452 | + | 0.768831i | \(0.279161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.30857 | −1.19498 | −0.597491 | − | 0.801876i | \(-0.703835\pi\) | ||||
−0.597491 | + | 0.801876i | \(0.703835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.04162 | −0.980238 | −0.490119 | − | 0.871656i | \(-0.663047\pi\) | ||||
−0.490119 | + | 0.871656i | \(0.663047\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.93647 | −0.612295 | −0.306148 | − | 0.951984i | \(-0.599040\pi\) | ||||
−0.306148 | + | 0.951984i | \(0.599040\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.57135 | −0.914270 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.01990 | 0.189390 | 0.0946952 | − | 0.995506i | \(-0.469812\pi\) | ||||
0.0946952 | + | 0.995506i | \(0.469812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.52340 | 1.53085 | 0.765423 | − | 0.643527i | \(-0.222530\pi\) | ||||
0.765423 | + | 0.643527i | \(0.222530\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.47078 | 0.248608 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.68866 | −1.42841 | −0.714203 | − | 0.699938i | \(-0.753211\pi\) | ||||
−0.714203 | + | 0.699938i | \(0.753211\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.95657 | −1.55495 | −0.777477 | − | 0.628911i | \(-0.783501\pi\) | ||||
−0.777477 | + | 0.628911i | \(0.783501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.61782 | 0.704212 | 0.352106 | − | 0.935960i | \(-0.385466\pi\) | ||||
0.352106 | + | 0.935960i | \(0.385466\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.96414 | 0.292796 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.53741 | 1.39117 | 0.695587 | − | 0.718442i | \(-0.255144\pi\) | ||||
0.695587 | + | 0.718442i | \(0.255144\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.95344 | −0.279062 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.71778 | 0.510677 | 0.255338 | − | 0.966852i | \(-0.417813\pi\) | ||||
0.255338 | + | 0.966852i | \(0.417813\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.77705 | −0.374458 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.335151 | 0.0436329 | 0.0218164 | − | 0.999762i | \(-0.493055\pi\) | ||||
0.0218164 | + | 0.999762i | \(0.493055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.24078 | 0.927087 | 0.463544 | − | 0.886074i | \(-0.346578\pi\) | ||||
0.463544 | + | 0.886074i | \(0.346578\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.73937 | 0.849081 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.82087 | 0.349886 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.613087 | 0.0749005 | 0.0374503 | − | 0.999298i | \(-0.488076\pi\) | ||||
0.0374503 | + | 0.999298i | \(0.488076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.70518 | 0.914436 | 0.457218 | − | 0.889355i | \(-0.348846\pi\) | ||||
0.457218 | + | 0.889355i | \(0.348846\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41742 | 0.165897 | 0.0829483 | − | 0.996554i | \(-0.473566\pi\) | ||||
0.0829483 | + | 0.996554i | \(0.473566\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.52866 | −1.08589 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.5845 | −1.27157 | −0.635784 | − | 0.771867i | \(-0.719323\pi\) | ||||
−0.635784 | + | 0.771867i | \(0.719323\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.64610 | 0.287010 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.60392 | −0.276015 | −0.138007 | − | 0.990431i | \(-0.544070\pi\) | ||||
−0.138007 | + | 0.990431i | \(0.544070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.67900 | 1.01464 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.654712 | −0.0671721 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5210 | 1.27132 | 0.635658 | − | 0.771971i | \(-0.280729\pi\) | ||||
0.635658 | + | 0.771971i | \(0.280729\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.7249 | −1.27890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2322 | −1.11765 | −0.558823 | − | 0.829287i | \(-0.688747\pi\) | ||||
−0.558823 | + | 0.829287i | \(0.688747\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.7998 | −1.35974 | −0.679869 | − | 0.733334i | \(-0.737963\pi\) | ||||
−0.679869 | + | 0.733334i | \(0.737963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.8460 | 1.82191 | 0.910957 | − | 0.412502i | \(-0.135345\pi\) | ||||
0.910957 | + | 0.412502i | \(0.135345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.40673 | −0.326305 | −0.163153 | − | 0.986601i | \(-0.552166\pi\) | ||||
−0.163153 | + | 0.986601i | \(0.552166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.77958 | −0.261481 | −0.130741 | − | 0.991417i | \(-0.541736\pi\) | ||||
−0.130741 | + | 0.991417i | \(0.541736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.92254 | 0.179278 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.9257 | 1.19498 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.07933 | 0.832301 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.99153 | 0.635593 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.26648 | 0.560491 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.2202 | 1.26184 | 0.630919 | − | 0.775849i | \(-0.282678\pi\) | ||||
0.630919 | + | 0.775849i | \(0.282678\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.83012 | −0.684120 | −0.342060 | − | 0.939678i | \(-0.611125\pi\) | ||||
−0.342060 | + | 0.939678i | \(0.611125\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.24646 | −0.194792 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.8506 | 1.26877 | 0.634387 | − | 0.773015i | \(-0.281253\pi\) | ||||
0.634387 | + | 0.773015i | \(0.281253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4740 | 1.22767 | 0.613835 | − | 0.789434i | \(-0.289626\pi\) | ||||
0.613835 | + | 0.789434i | \(0.289626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.2754 | −1.52827 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.667740 | −0.0554528 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.65984 | −0.217903 | −0.108951 | − | 0.994047i | \(-0.534749\pi\) | ||||
−0.108951 | + | 0.994047i | \(0.534749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0897947 | −0.00730739 | −0.00365369 | − | 0.999993i | \(-0.501163\pi\) | ||||
−0.00365369 | + | 0.999993i | \(0.501163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.1249 | 0.980238 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.58037 | −0.448226 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.84399 | 0.147167 | 0.0735833 | − | 0.997289i | \(-0.476557\pi\) | ||||
0.0735833 | + | 0.997289i | \(0.476557\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.59664 | 0.519888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.2171 | 1.89683 | 0.948416 | − | 0.317029i | \(-0.102685\pi\) | ||||
0.948416 | + | 0.317029i | \(0.102685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.8406 | −1.53531 | −0.767656 | − | 0.640862i | \(-0.778577\pi\) | ||||
−0.767656 | + | 0.640862i | \(0.778577\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.56374 | 0.427980 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.939402 | 0.0714214 | 0.0357107 | − | 0.999362i | \(-0.488631\pi\) | ||||
0.0357107 | + | 0.999362i | \(0.488631\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.2693 | 0.776289 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.9496 | 1.93957 | 0.969783 | − | 0.243967i | \(-0.0784490\pi\) | ||||
0.969783 | + | 0.243967i | \(0.0784490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5410 | 1.15515 | 0.577577 | − | 0.816336i | \(-0.303998\pi\) | ||||
0.577577 | + | 0.816336i | \(0.303998\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.68857 | 0.418232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.1431 | −1.25363 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.9972 | −1.59166 | −0.795832 | − | 0.605518i | \(-0.792966\pi\) | ||||
−0.795832 | + | 0.605518i | \(0.792966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.9817 | −1.87020 | −0.935101 | − | 0.354380i | \(-0.884692\pi\) | ||||
−0.935101 | + | 0.354380i | \(0.884692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7465 | 1.05065 | 0.525323 | − | 0.850903i | \(-0.323944\pi\) | ||||
0.525323 | + | 0.850903i | \(0.323944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1910 | −1.28952 | −0.644761 | − | 0.764384i | \(-0.723043\pi\) | ||||
−0.644761 | + | 0.764384i | \(0.723043\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.29116 | −0.160808 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.51869 | 0.455285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.80940 | 0.612295 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.24164 | 0.293401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.74717 | 0.602180 | 0.301090 | − | 0.953596i | \(-0.402650\pi\) | ||||
0.301090 | + | 0.953596i | \(0.402650\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.02335 | −0.206190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.1474 | −1.29981 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.4136 | 1.17137 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3996 | −0.897304 | −0.448652 | − | 0.893707i | \(-0.648096\pi\) | ||||
−0.448652 | + | 0.893707i | \(0.648096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.7141 | 0.914270 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.52766 | 0.632373 | 0.316187 | − | 0.948697i | \(-0.397597\pi\) | ||||
0.316187 | + | 0.948697i | \(0.397597\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.6995 | 1.83044 | 0.915219 | − | 0.402957i | \(-0.132018\pi\) | ||||
0.915219 | + | 0.402957i | \(0.132018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.8803 | −0.974843 | −0.487422 | − | 0.873167i | \(-0.662062\pi\) | ||||
−0.487422 | + | 0.873167i | \(0.662062\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.24426 | −0.407331 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.4292 | 1.64488 | 0.822440 | − | 0.568851i | \(-0.192612\pi\) | ||||
0.822440 | + | 0.568851i | \(0.192612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.08684 | 0.263257 | 0.131628 | − | 0.991299i | \(-0.457979\pi\) | ||||
0.131628 | + | 0.991299i | \(0.457979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.27894 | 0.0817084 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.30857 | −0.274147 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.7598 | 0.742271 | 0.371135 | − | 0.928579i | \(-0.378969\pi\) | ||||
0.371135 | + | 0.928579i | \(0.378969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.4554 | −0.783067 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.66944 | −0.416028 | −0.208014 | − | 0.978126i | \(-0.566700\pi\) | ||||
−0.208014 | + | 0.978126i | \(0.566700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.5187 | 1.21283 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.05970 | −0.189390 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.90137 | 0.425557 | 0.212778 | − | 0.977100i | \(-0.431749\pi\) | ||||
0.212778 | + | 0.977100i | \(0.431749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.43408 | −0.149524 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.2177 | 1.11075 | 0.555376 | − | 0.831599i | \(-0.312574\pi\) | ||||
0.555376 | + | 0.831599i | \(0.312574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.6723 | 1.31650 | 0.658249 | − | 0.752800i | \(-0.271297\pi\) | ||||
0.658249 | + | 0.752800i | \(0.271297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.3900 | −1.16926 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.5581 | 1.71589 | 0.857945 | − | 0.513741i | \(-0.171741\pi\) | ||||
0.857945 | + | 0.513741i | \(0.171741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.5702 | −1.53085 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2279 | 0.669802 | 0.334901 | − | 0.942253i | \(-0.391297\pi\) | ||||
0.334901 | + | 0.942253i | \(0.391297\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.31615 | −0.256569 | −0.128284 | − | 0.991737i | \(-0.540947\pi\) | ||||
−0.128284 | + | 0.991737i | \(0.540947\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.3670 | 1.32028 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.665267 | −0.0391334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.1197 | 0.941722 | 0.470861 | − | 0.882207i | \(-0.343943\pi\) | ||||
0.470861 | + | 0.882207i | \(0.343943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.219427 | −0.0127755 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.6520 | 0.731681 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3737 | −0.597932 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.74063 | −0.271448 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.6540 | 1.40708 | 0.703540 | − | 0.710656i | \(-0.251602\pi\) | ||||
0.703540 | + | 0.710656i | \(0.251602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.07763 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4576 | −1.43895 | −0.719473 | − | 0.694520i | \(-0.755617\pi\) | ||||
−0.719473 | + | 0.694520i | \(0.755617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.41235 | −0.248608 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.4618 | −1.65474 | −0.827368 | − | 0.561659i | \(-0.810163\pi\) | ||||
−0.827368 | + | 0.561659i | \(0.810163\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.32605 | 0.242212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.04162 | −0.224882 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.6960 | 1.09254 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.4254 | −1.18122 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4189 | −1.34218 | −0.671091 | − | 0.741375i | \(-0.734174\pi\) | ||||
−0.671091 | + | 0.741375i | \(0.734174\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.0660 | 1.42841 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.401396 | −0.0219306 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.8581 | 1.13621 | 0.568106 | − | 0.822956i | \(-0.307677\pi\) | ||||
0.568106 | + | 0.822956i | \(0.307677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.1532 | 1.95781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1135 | 1.08603 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.6997 | −1.48700 | −0.743498 | − | 0.668738i | \(-0.766835\pi\) | ||||
−0.743498 | + | 0.668738i | \(0.766835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.5168 | 1.25882 | 0.629412 | − | 0.777072i | \(-0.283296\pi\) | ||||
0.629412 | + | 0.777072i | \(0.283296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.4581 | −1.08888 | −0.544438 | − | 0.838801i | \(-0.683257\pi\) | ||||
−0.544438 | + | 0.838801i | \(0.683257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.04467 | −0.267743 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.37845 | −0.0727516 | −0.0363758 | − | 0.999338i | \(-0.511581\pi\) | ||||
−0.0363758 | + | 0.999338i | \(0.511581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.928003 | −0.0485739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.1590 | 1.10449 | 0.552247 | − | 0.833681i | \(-0.313771\pi\) | ||||
0.552247 | + | 0.833681i | \(0.313771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.8697 | 1.55495 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.35183 | −0.433606 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.83107 | 0.405478 | 0.202739 | − | 0.979233i | \(-0.435016\pi\) | ||||
0.202739 | + | 0.979233i | \(0.435016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.39430 | −0.226318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3241 | 0.735780 | 0.367890 | − | 0.929869i | \(-0.380080\pi\) | ||||
0.367890 | + | 0.929869i | \(0.380080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.13902 | 0.211494 | 0.105747 | − | 0.994393i | \(-0.466277\pi\) | ||||
0.105747 | + | 0.994393i | \(0.466277\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.23853 | 0.317945 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.8535 | −0.704212 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.24401 | 0.215180 | 0.107590 | − | 0.994195i | \(-0.465687\pi\) | ||||
0.107590 | + | 0.994195i | \(0.465687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8681 | 0.600195 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.654712 | −0.0329421 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.15641 | −0.359170 | −0.179585 | − | 0.983742i | \(-0.557475\pi\) | ||||
−0.179585 | + | 0.983742i | \(0.557475\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1289 | −0.555750 | −0.277875 | − | 0.960617i | \(-0.589630\pi\) | ||||
−0.277875 | + | 0.960617i | \(0.589630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.7236 | −1.82933 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.89241 | −0.292796 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.8542 | −1.82679 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.43950 | −0.318413 | −0.159207 | − | 0.987245i | \(-0.550894\pi\) | ||||
−0.159207 | + | 0.987245i | \(0.550894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.752901 | −0.0370478 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.58454 | 0.372310 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.4052 | 1.04571 | 0.522857 | − | 0.852420i | \(-0.324866\pi\) | ||||
0.522857 | + | 0.852420i | \(0.324866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.7376 | −1.59553 | −0.797767 | − | 0.602966i | \(-0.793985\pi\) | ||||
−0.797767 | + | 0.602966i | \(0.793985\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.6122 | −1.39117 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.4757 | 0.896203 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.2661 | −0.787172 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.5888 | 1.32891 | 0.664454 | − | 0.747329i | \(-0.268664\pi\) | ||||
0.664454 | + | 0.747329i | \(0.268664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.5252 | −1.17861 | −0.589304 | − | 0.807911i | \(-0.700598\pi\) | ||||
−0.589304 | + | 0.807911i | \(0.700598\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.93647 | −0.140470 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.62412 | 0.125242 | 0.0626212 | − | 0.998037i | \(-0.480054\pi\) | ||||
0.0626212 | + | 0.998037i | \(0.480054\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.86031 | 0.279062 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.6048 | −1.16901 | −0.584506 | − | 0.811390i | \(-0.698712\pi\) | ||||
−0.584506 | + | 0.811390i | \(0.698712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.70482 | 0.0808161 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.7548 | −0.932286 | −0.466143 | − | 0.884709i | \(-0.654357\pi\) | ||||
−0.466143 | + | 0.884709i | \(0.654357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.2322 | −1.98864 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.33696 | −0.297081 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.7733 | 1.11207 | 0.556035 | − | 0.831159i | \(-0.312322\pi\) | ||||
0.556035 | + | 0.831159i | \(0.312322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.8445 | 1.39000 | 0.694998 | − | 0.719011i | \(-0.255405\pi\) | ||||
0.694998 | + | 0.719011i | \(0.255405\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.38127 | −0.203615 | −0.101808 | − | 0.994804i | \(-0.532463\pi\) | ||||
−0.101808 | + | 0.994804i | \(0.532463\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.0911720 | −0.00421894 | −0.00210947 | − | 0.999998i | \(-0.500671\pi\) | ||||
−0.00210947 | + | 0.999998i | \(0.500671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.37727 | −0.0635966 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.5872 | 0.900618 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.57135 | −0.209748 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.1533 | −0.510677 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6605 | 1.03538 | 0.517692 | − | 0.855567i | \(-0.326791\pi\) | ||||
0.517692 | + | 0.855567i | \(0.326791\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.4357 | 1.70692 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.19766 | −0.372236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.34863 | 0.151741 | 0.0758706 | − | 0.997118i | \(-0.475826\pi\) | ||||
0.0758706 | + | 0.997118i | \(0.475826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.5521 | 1.10802 | 0.554010 | − | 0.832510i | \(-0.313097\pi\) | ||||
0.554010 | + | 0.832510i | \(0.313097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.12205 | −0.185648 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.33116 | 0.374458 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.3093 | −0.776430 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1104 | −1.03456 | −0.517282 | − | 0.855815i | \(-0.673056\pi\) | ||||
−0.517282 | + | 0.855815i | \(0.673056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.8628 | −1.73280 | −0.866402 | − | 0.499347i | \(-0.833573\pi\) | ||||
−0.866402 | + | 0.499347i | \(0.833573\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.35386 | 0.327242 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2610 | 0.499134 | 0.249567 | − | 0.968358i | \(-0.419712\pi\) | ||||
0.249567 | + | 0.968358i | \(0.419712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.18417 | −0.140860 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.03492 | 0.398126 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.4543 | 1.77918 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8461 | 0.694232 | 0.347116 | − | 0.937822i | \(-0.387161\pi\) | ||||
0.347116 | + | 0.937822i | \(0.387161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.6662 | −0.728761 | −0.364381 | − | 0.931250i | \(-0.618719\pi\) | ||||
−0.364381 | + | 0.931250i | \(0.618719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.4484 | −1.50059 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.3772 | −0.625094 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.00545 | −0.0436329 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.8985 | 1.85814 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3387 | −0.533449 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.28577 | −0.356894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0423 | −0.732707 | −0.366354 | − | 0.930476i | \(-0.619394\pi\) | ||||
−0.366354 | + | 0.930476i | \(0.619394\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.23042 | 0.0955409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.89279 | 0.337471 | 0.168736 | − | 0.985661i | \(-0.446032\pi\) | ||||
0.168736 | + | 0.985661i | \(0.446032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.7223 | −0.927087 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.01990 | 0.0434491 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.24646 | −0.0955290 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.8309 | 0.797893 | 0.398946 | − | 0.916974i | \(-0.369376\pi\) | ||||
0.398946 | + | 0.916974i | \(0.369376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.8962 | −0.841520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.22514 | 0.220213 | 0.110107 | − | 0.993920i | \(-0.464881\pi\) | ||||
0.110107 | + | 0.993920i | \(0.464881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.81983 | 0.0765607 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.2181 | −0.849081 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.7608 | −1.70878 | −0.854390 | − | 0.519632i | \(-0.826069\pi\) | ||||
−0.854390 | + | 0.519632i | \(0.826069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.5947 | 1.32220 | 0.661098 | − | 0.750300i | \(-0.270091\pi\) | ||||
0.661098 | + | 0.750300i | \(0.270091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.4236 | 0.559804 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.7485 | 0.822139 | 0.411070 | − | 0.911604i | \(-0.365155\pi\) | ||||
0.411070 | + | 0.911604i | \(0.365155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.0242 | 1.07966 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7695 | 0.653106 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.46261 | −0.349886 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.8829 | −1.64614 | −0.823071 | − | 0.567939i | \(-0.807741\pi\) | ||||
−0.823071 | + | 0.567939i | \(0.807741\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.52340 | 0.351200 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.8652 | 0.692569 | 0.346285 | − | 0.938129i | \(-0.387443\pi\) | ||||
0.346285 | + | 0.938129i | \(0.387443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.94435 | −0.243695 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.8685 | 1.66984 | 0.834920 | − | 0.550371i | \(-0.185514\pi\) | ||||
0.834920 | + | 0.550371i | \(0.185514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.3527 | −0.503877 | −0.251938 | − | 0.967743i | \(-0.581068\pi\) | ||||
−0.251938 | + | 0.967743i | \(0.581068\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.83926 | −0.0749005 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.57744 | −0.186099 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0787 | −0.409080 | −0.204540 | − | 0.978858i | \(-0.565570\pi\) | ||||
−0.204540 | + | 0.978858i | \(0.565570\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −41.0926 | −1.66243 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.27833 | 0.334359 | 0.167179 | − | 0.985927i | \(-0.446534\pi\) | ||||
0.167179 | + | 0.985927i | \(0.446534\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.6757 | −1.19470 | −0.597350 | − | 0.801981i | \(-0.703780\pi\) | ||||
−0.597350 | + | 0.801981i | \(0.703780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.2322 | 1.73765 | 0.868825 | − | 0.495119i | \(-0.164875\pi\) | ||||
0.868825 | + | 0.495119i | \(0.164875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.84959 | 0.234359 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.7540 | 0.750161 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.1163 | 1.40018 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.5753 | 0.580234 | 0.290117 | − | 0.956991i | \(-0.406306\pi\) | ||||
0.290117 | + | 0.956991i | \(0.406306\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.31013 | −0.369461 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.41651 | 0.333474 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.1155 | −0.914436 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.4479 | 0.531161 | 0.265581 | − | 0.964089i | \(-0.414436\pi\) | ||||
0.265581 | + | 0.964089i | \(0.414436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.0946 | −1.42343 | −0.711717 | − | 0.702467i | \(-0.752082\pi\) | ||||
−0.711717 | + | 0.702467i | \(0.752082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.3466 | 1.90070 | 0.950351 | − | 0.311181i | \(-0.100724\pi\) | ||||
0.950351 | + | 0.311181i | \(0.100724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.42159 | 0.0558022 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.2497 | −0.635902 | −0.317951 | − | 0.948107i | \(-0.602995\pi\) | ||||
−0.317951 | + | 0.948107i | \(0.602995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.12647 | 0.200308 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.25226 | −0.165897 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.8058 | −1.78434 | −0.892170 | − | 0.451700i | \(-0.850818\pi\) | ||||
−0.892170 | + | 0.451700i | \(0.850818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5919 | 0.762036 | 0.381018 | − | 0.924568i | \(-0.375574\pi\) | ||||
0.381018 | + | 0.924568i | \(0.375574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.47078 | 0.0570345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.99490 | −0.115963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.7128 | 1.18565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.3225 | 1.78560 | 0.892801 | − | 0.450451i | \(-0.148737\pi\) | ||||
0.892801 | + | 0.450451i | \(0.148737\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.62999 | −0.139512 | −0.0697560 | − | 0.997564i | \(-0.522222\pi\) | ||||
−0.0697560 | + | 0.997564i | \(0.522222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.1279 | −1.07945 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.7809 | 0.948215 | 0.474107 | − | 0.880467i | \(-0.342771\pi\) | ||||
0.474107 | + | 0.880467i | \(0.342771\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.72288 | −0.371492 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.0183 | −0.610249 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.6119 | −1.88733 | −0.943663 | − | 0.330907i | \(-0.892645\pi\) | ||||
−0.943663 | + | 0.330907i | \(0.892645\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.5860 | 1.08589 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.47632 | −0.359457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.2407 | 1.52423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.18305 | 0.0446834 | 0.0223417 | − | 0.999750i | \(-0.492888\pi\) | ||||
0.0223417 | + | 0.999750i | \(0.492888\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.68866 | −0.327699 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.2326 | 0.948971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.0883 | −1.31777 | −0.658885 | − | 0.752244i | \(-0.728972\pi\) | ||||
−0.658885 | + | 0.752244i | \(0.728972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.0287 | −0.937331 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9651 | 0.447470 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.0944 | 1.64444 | 0.822222 | − | 0.569168i | \(-0.192734\pi\) | ||||
0.822222 | + | 0.569168i | \(0.192734\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.0007 | 1.15453 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.66232 | −0.173154 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.5684 | −1.20790 | −0.603948 | − | 0.797024i | \(-0.706406\pi\) | ||||
−0.603948 | + | 0.797024i | \(0.706406\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.6635 | −0.690295 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.0263 | −1.47841 | −0.739203 | − | 0.673482i | \(-0.764798\pi\) | ||||
−0.739203 | + | 0.673482i | \(0.764798\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.60050 | 0.0957905 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.1669 | 0.594709 | 0.297354 | − | 0.954767i | \(-0.403896\pi\) | ||||
0.297354 | + | 0.954767i | \(0.403896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.331677 | −0.0121680 | −0.00608402 | − | 0.999981i | \(-0.501937\pi\) | ||||
−0.00608402 | + | 0.999981i | \(0.501937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.74143 | 0.0638011 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.7536 | 1.27157 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.3367 | −1.54695 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.31416 | −0.193917 | −0.0969583 | − | 0.995288i | \(-0.530911\pi\) | ||||
−0.0969583 | + | 0.995288i | \(0.530911\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0587897 | 0.00213958 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.3297 | 0.811588 | 0.405794 | − | 0.913965i | \(-0.366995\pi\) | ||||
0.405794 | + | 0.913965i | \(0.366995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.2979 | 0.373298 | 0.186649 | − | 0.982427i | \(-0.440237\pi\) | ||||
0.186649 | + | 0.982427i | \(0.440237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.65306 | 0.277059 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.93830 | −0.287010 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.44402 | −0.0521405 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.5275 | −1.28116 | −0.640578 | − | 0.767893i | \(-0.721305\pi\) | ||||
−0.640578 | + | 0.767893i | \(0.721305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.5918 | −1.31612 | −0.658058 | − | 0.752968i | \(-0.728622\pi\) | ||||
−0.658058 | + | 0.752968i | \(0.728622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.9634 | −1.39961 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.95657 | −0.356731 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.6826 | 1.16948 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.20728 | −0.0430898 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7961 | −0.705655 | −0.352827 | − | 0.935688i | \(-0.614780\pi\) | ||||
−0.352827 | + | 0.935688i | \(0.614780\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.24421 | 0.222019 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.1974 | −1.10785 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.1443 | 0.713549 | 0.356775 | − | 0.934190i | \(-0.383876\pi\) | ||||
0.356775 | + | 0.934190i | \(0.383876\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.5466 | −1.36368 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.81176 | 0.276015 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.01219 | 0.212166 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.31890 | −0.152221 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.8228 | 0.767247 | 0.383624 | − | 0.923490i | \(-0.374676\pi\) | ||||
0.383624 | + | 0.923490i | \(0.374676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6656 | 1.21727 | 0.608637 | − | 0.793449i | \(-0.291717\pi\) | ||||
0.608637 | + | 0.793449i | \(0.291717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.8553 | −0.555385 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.61782 | 0.161557 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.0370 | −1.01464 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.1315 | 0.702596 | 0.351298 | − | 0.936264i | \(-0.385740\pi\) | ||||
0.351298 | + | 0.936264i | \(0.385740\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.6505 | −0.440967 | −0.220483 | − | 0.975391i | \(-0.570764\pi\) | ||||
−0.220483 | + | 0.975391i | \(0.570764\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.5829 | −1.34166 | −0.670830 | − | 0.741611i | \(-0.734062\pi\) | ||||
−0.670830 | + | 0.741611i | \(0.734062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.7962 | −0.861207 | −0.430603 | − | 0.902541i | \(-0.641699\pi\) | ||||
−0.430603 | + | 0.902541i | \(0.641699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.89505 | 0.273547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.9899 | 0.449533 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.96886 | 0.206068 | 0.103034 | − | 0.994678i | \(-0.467145\pi\) | ||||
0.103034 | + | 0.994678i | \(0.467145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9598 | −0.964131 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.64265 | −0.125311 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.7062 | −0.539670 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.5139 | 0.874607 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.8056 | −1.22596 | −0.612981 | − | 0.790098i | \(-0.710030\pi\) | ||||
−0.612981 | + | 0.790098i | \(0.710030\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.96414 | 0.0671721 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.25594 | −0.0429021 | −0.0214511 | − | 0.999770i | \(-0.506829\pi\) | ||||
−0.0214511 | + | 0.999770i | \(0.506829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.3420 | 1.85413 | 0.927063 | − | 0.374905i | \(-0.122325\pi\) | ||||
0.927063 | + | 0.374905i | \(0.122325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.4058 | 1.00099 | 0.500493 | − | 0.865741i | \(-0.333152\pi\) | ||||
0.500493 | + | 0.865741i | \(0.333152\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.615038 | −0.0209119 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.24164 | 0.143888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.64153 | −0.0895047 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.5630 | −1.27132 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.0774 | −0.475902 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.2839 | 1.63043 | 0.815215 | − | 0.579158i | \(-0.196619\pi\) | ||||
0.815215 | + | 0.579158i | \(0.196619\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.5945 | 1.26659 | 0.633296 | − | 0.773910i | \(-0.281702\pi\) | ||||
0.633296 | + | 0.773910i | \(0.281702\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.21467 | −0.0408770 | −0.0204385 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204385 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.28546 | 0.211045 | 0.105523 | − | 0.994417i | \(-0.466348\pi\) | ||||
0.105523 | + | 0.994417i | \(0.466348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.9450 | −1.07140 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38.1748 | 1.27890 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.53741 | 0.319157 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9895 | −0.567898 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.69300 | 0.289928 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0259 | −0.500585 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.1749 | −0.338225 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.1998 | 0.670724 | 0.335362 | − | 0.942089i | \(-0.391141\pi\) | ||||
0.335362 | + | 0.942089i | \(0.391141\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.6966 | 1.11765 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3731 | 1.07257 | 0.536284 | − | 0.844038i | \(-0.319828\pi\) | ||||
0.536284 | + | 0.844038i | \(0.319828\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.1375 | −1.62621 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5900 | 0.580873 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.1700 | 1.35807 | 0.679036 | − | 0.734105i | \(-0.262398\pi\) | ||||
0.679036 | + | 0.734105i | \(0.262398\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.1983 | −1.09273 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.7189 | 1.30595 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.3995 | 1.35974 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.2050 | 1.48313 | 0.741564 | − | 0.670882i | \(-0.234084\pi\) | ||||
0.741564 | + | 0.670882i | \(0.234084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.95344 | −0.0640213 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.2238 | 0.367058 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.5610 | −1.65176 | −0.825878 | − | 0.563849i | \(-0.809320\pi\) | ||||
−0.825878 | + | 0.563849i | \(0.809320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.2818 | 1.67174 | 0.835870 | − | 0.548927i | \(-0.184964\pi\) | ||||
0.835870 | + | 0.548927i | \(0.184964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.2371 | 0.952092 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7081 | 0.640428 | 0.320214 | − | 0.947345i | \(-0.396245\pi\) | ||||
0.320214 | + | 0.947345i | \(0.396245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.10705 | −0.198243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.2773 | 1.82300 | 0.911500 | − | 0.411301i | \(-0.134926\pi\) | ||||
0.911500 | + | 0.411301i | \(0.134926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.4019 | 0.466033 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.3613 | −1.07729 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.6483 | 1.34349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56.5380 | −1.82191 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.0105 | 0.547588 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6609 | 0.889515 | 0.444757 | − | 0.895651i | \(-0.353290\pi\) | ||||
0.444757 | + | 0.895651i | \(0.353290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.00270 | −0.128453 | −0.0642264 | − | 0.997935i | \(-0.520458\pi\) | ||||
−0.0642264 | + | 0.997935i | \(0.520458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.5153 | −1.04239 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.3862 | −1.54801 | −0.774006 | − | 0.633178i | \(-0.781750\pi\) | ||||
−0.774006 | + | 0.633178i | \(0.781750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.0449 | −0.352996 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.2202 | 0.326305 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.7753 | 1.81085 | 0.905425 | − | 0.424506i | \(-0.139552\pi\) | ||||
0.905425 | + | 0.424506i | \(0.139552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.65473 | −0.307625 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.5601 | −0.431186 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.59162 | −0.209390 | −0.104695 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104695 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.9098 | 0.377567 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.9864 | −1.32972 | −0.664861 | − | 0.746967i | \(-0.731509\pi\) | ||||
−0.664861 | + | 0.746967i | \(0.731509\pi\) | |||||||
\(998\) | 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 | 6004.2.a.d.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.d.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial |