Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
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: | \( x^{9} - 3x^{8} - 19x^{7} + 51x^{6} + 116x^{5} - 247x^{4} - 249x^{3} + 288x^{2} + 189x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.56319\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.56319 | −1.47986 | −0.739930 | − | 0.672684i | \(-0.765141\pi\) | ||||
−0.739930 | + | 0.672684i | \(0.765141\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.31026 | −0.585966 | −0.292983 | − | 0.956118i | \(-0.594648\pi\) | ||||
−0.292983 | + | 0.956118i | \(0.594648\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56996 | 1.18999 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.35845 | 0.867148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.78120 | −0.432006 | −0.216003 | − | 0.976393i | \(-0.569302\pi\) | ||||
−0.216003 | + | 0.976393i | \(0.569302\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.55568 | 1.04514 | 0.522572 | − | 0.852595i | \(-0.324972\pi\) | ||||
0.522572 | + | 0.852595i | \(0.324972\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.56319 | −0.559335 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.54866 | −1.15697 | −0.578487 | − | 0.815691i | \(-0.696357\pi\) | ||||
−0.578487 | + | 0.815691i | \(0.696357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.28322 | −0.656643 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.46091 | −0.281153 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.85706 | 0.530543 | 0.265271 | − | 0.964174i | \(-0.414538\pi\) | ||||
0.265271 | + | 0.964174i | \(0.414538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.25463 | 1.66218 | 0.831090 | − | 0.556138i | \(-0.187717\pi\) | ||||
0.831090 | + | 0.556138i | \(0.187717\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.56319 | −0.446195 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.31026 | −0.221475 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.67962 | −0.604926 | −0.302463 | − | 0.953161i | \(-0.597809\pi\) | ||||
−0.302463 | + | 0.953161i | \(0.597809\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.56319 | 0.410439 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.34204 | 0.678113 | 0.339057 | − | 0.940766i | \(-0.389892\pi\) | ||||
0.339057 | + | 0.940766i | \(0.389892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.19868 | 0.182797 | 0.0913983 | − | 0.995814i | \(-0.470866\pi\) | ||||
0.0913983 | + | 0.995814i | \(0.470866\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.67758 | −0.697292 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.6383 | −1.69762 | −0.848810 | − | 0.528697i | \(-0.822681\pi\) | ||||
−0.848810 | + | 0.528697i | \(0.822681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.56557 | 0.639308 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.45384 | −0.886503 | −0.443251 | − | 0.896397i | \(-0.646175\pi\) | ||||
−0.443251 | + | 0.896397i | \(0.646175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.31026 | −0.176676 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.6771 | −1.54667 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.985627 | −0.128318 | −0.0641589 | − | 0.997940i | \(-0.520436\pi\) | ||||
−0.0641589 | + | 0.997940i | \(0.520436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.869309 | −0.111304 | −0.0556518 | − | 0.998450i | \(-0.517724\pi\) | ||||
−0.0556518 | + | 0.998450i | \(0.517724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.56996 | 0.449772 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.31026 | 0.162518 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.06256 | −0.374152 | −0.187076 | − | 0.982345i | \(-0.559901\pi\) | ||||
−0.187076 | + | 0.982345i | \(0.559901\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.2223 | 1.71216 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6102 | −1.49656 | −0.748278 | − | 0.663386i | \(-0.769119\pi\) | ||||
−0.748278 | + | 0.663386i | \(0.769119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6810 | 1.71828 | 0.859138 | − | 0.511743i | \(-0.171000\pi\) | ||||
0.859138 | + | 0.511743i | \(0.171000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.41552 | 0.971740 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.88790 | −0.662440 | −0.331220 | − | 0.943554i | \(-0.607460\pi\) | ||||
−0.331220 | + | 0.943554i | \(0.607460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.96527 | −0.773919 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.74429 | −0.630518 | −0.315259 | − | 0.949006i | \(-0.602091\pi\) | ||||
−0.315259 | + | 0.949006i | \(0.602091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.33384 | 0.253141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.32319 | −0.785129 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.5572 | 1.33106 | 0.665532 | − | 0.746370i | \(-0.268205\pi\) | ||||
0.665532 | + | 0.746370i | \(0.268205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.7214 | −2.45979 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.96913 | −0.612420 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.505117 | −0.0512869 | −0.0256434 | − | 0.999671i | \(-0.508163\pi\) | ||||
−0.0256434 | + | 0.999671i | \(0.508163\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.56996 | 0.358794 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0920 | 1.50171 | 0.750855 | − | 0.660467i | \(-0.229642\pi\) | ||||
0.750855 | + | 0.660467i | \(0.229642\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.3268 | −1.51020 | −0.755099 | − | 0.655611i | \(-0.772411\pi\) | ||||
−0.755099 | + | 0.655611i | \(0.772411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.35845 | 0.327751 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.90090 | −0.377115 | −0.188557 | − | 0.982062i | \(-0.560381\pi\) | ||||
−0.188557 | + | 0.982062i | \(0.560381\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.33805 | 0.511293 | 0.255646 | − | 0.966770i | \(-0.417712\pi\) | ||||
0.255646 | + | 0.966770i | \(0.417712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.43158 | 0.895206 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.947829 | 0.0891642 | 0.0445821 | − | 0.999006i | \(-0.485804\pi\) | ||||
0.0445821 | + | 0.999006i | \(0.485804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.27019 | 0.677948 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.56996 | −0.330043 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.78120 | −0.163283 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.1295 | −1.00351 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8532 | 0.970737 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.7001 | −1.65936 | −0.829682 | − | 0.558237i | \(-0.811478\pi\) | ||||
−0.829682 | + | 0.558237i | \(0.811478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.07244 | −0.270513 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7408 | −1.20054 | −0.600270 | − | 0.799797i | \(-0.704940\pi\) | ||||
−0.600270 | + | 0.799797i | \(0.704940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.55568 | 0.395028 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.91418 | 0.164746 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.49101 | −0.212821 | −0.106411 | − | 0.994322i | \(-0.533936\pi\) | ||||
−0.106411 | + | 0.994322i | \(0.533936\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.3501 | 1.47162 | 0.735808 | − | 0.677190i | \(-0.236803\pi\) | ||||
0.735808 | + | 0.677190i | \(0.236803\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.8312 | 2.51224 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.74349 | −0.310880 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.56319 | −0.211409 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.55721 | 0.291418 | 0.145709 | − | 0.989328i | \(-0.453454\pi\) | ||||
0.145709 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.0951 | 1.79807 | 0.899035 | − | 0.437876i | \(-0.144269\pi\) | ||||
0.899035 | + | 0.437876i | \(0.144269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.35883 | −0.514081 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.1260 | −0.973982 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00759 | 0.718884 | 0.359442 | − | 0.933167i | \(-0.382967\pi\) | ||||
0.359442 | + | 0.933167i | \(0.382967\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.5424 | 1.31190 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.54866 | −0.437295 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.4943 | 1.52691 | 0.763454 | − | 0.645862i | \(-0.223502\pi\) | ||||
0.763454 | + | 0.645862i | \(0.223502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.35845 | 0.261455 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.38652 | 0.726351 | 0.363175 | − | 0.931721i | \(-0.381693\pi\) | ||||
0.363175 | + | 0.931721i | \(0.381693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.2636 | 1.24371 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4594 | 1.09933 | 0.549664 | − | 0.835386i | \(-0.314756\pi\) | ||||
0.549664 | + | 0.835386i | \(0.314756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.28322 | −0.248188 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.52635 | 0.189892 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.3448 | 1.37115 | 0.685576 | − | 0.728001i | \(-0.259550\pi\) | ||||
0.685576 | + | 0.728001i | \(0.259550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.34152 | 0.620020 | 0.310010 | − | 0.950733i | \(-0.399668\pi\) | ||||
0.310010 | + | 0.950733i | \(0.399668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.22821 | 0.164714 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.82127 | 0.354466 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.78120 | −0.130255 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.46091 | −0.106266 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.42461 | 0.320154 | 0.160077 | − | 0.987105i | \(-0.448826\pi\) | ||||
0.160077 | + | 0.987105i | \(0.448826\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.2387 | 1.96068 | 0.980341 | − | 0.197308i | \(-0.0632200\pi\) | ||||
0.980341 | + | 0.197308i | \(0.0632200\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.35845 | −0.240504 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.3664 | 1.37980 | 0.689899 | − | 0.723906i | \(-0.257655\pi\) | ||||
0.689899 | + | 0.723906i | \(0.257655\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2746 | −1.22457 | −0.612283 | − | 0.790639i | \(-0.709748\pi\) | ||||
−0.612283 | + | 0.790639i | \(0.709748\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.84995 | 0.553692 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.85706 | 0.200526 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.68921 | −0.397351 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.8085 | −1.37678 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.55568 | 0.315123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8093 | −0.744141 | −0.372071 | − | 0.928204i | \(-0.621352\pi\) | ||||
−0.372071 | + | 0.928204i | \(0.621352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 32.3224 | 2.21469 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.57058 | −0.107113 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.25463 | 0.628245 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −37.6301 | −2.54281 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.78120 | 0.119817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3461 | 1.16158 | 0.580791 | − | 0.814052i | \(-0.302743\pi\) | ||||
0.580791 | + | 0.814052i | \(0.302743\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.7209 | −0.781396 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.5753 | 1.36563 | 0.682816 | − | 0.730591i | \(-0.260755\pi\) | ||||
0.682816 | + | 0.730591i | \(0.260755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.1895 | −1.46633 | −0.733163 | − | 0.680053i | \(-0.761957\pi\) | ||||
−0.733163 | + | 0.680053i | \(0.761957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.56319 | −0.168646 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9095 | −0.976752 | −0.488376 | − | 0.872633i | \(-0.662411\pi\) | ||||
−0.488376 | + | 0.872633i | \(0.662411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.2492 | 0.994749 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.0918 | 0.980319 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.691072 | 0.0447017 | 0.0223509 | − | 0.999750i | \(-0.492885\pi\) | ||||
0.0223509 | + | 0.999750i | \(0.492885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3788 | −0.861803 | −0.430901 | − | 0.902399i | \(-0.641804\pi\) | ||||
−0.430901 | + | 0.902399i | \(0.641804\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2361 | 1.42645 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.31026 | −0.0837095 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.55568 | −0.289871 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.7237 | 0.933079 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.6773 | −0.800181 | −0.400091 | − | 0.916476i | \(-0.631021\pi\) | ||||
−0.400091 | + | 0.916476i | \(0.631021\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.54866 | −0.348841 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.98209 | −0.374613 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.5981 | 1.84628 | 0.923139 | − | 0.384466i | \(-0.125615\pi\) | ||||
0.923139 | + | 0.384466i | \(0.125615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.67962 | −0.228641 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1996 | 0.631338 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.62856 | −0.532060 | −0.266030 | − | 0.963965i | \(-0.585712\pi\) | ||||
−0.266030 | + | 0.963965i | \(0.585712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.45621 | 0.519461 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.1866 | −1.96979 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.81761 | 0.232764 | 0.116382 | − | 0.993205i | \(-0.462870\pi\) | ||||
0.116382 | + | 0.993205i | \(0.462870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0096 | 1.45848 | 0.729239 | − | 0.684259i | \(-0.239874\pi\) | ||||
0.729239 | + | 0.684259i | \(0.239874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.56319 | 0.155131 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.28322 | −0.197985 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8449 | 0.952025 | 0.476013 | − | 0.879438i | \(-0.342082\pi\) | ||||
0.476013 | + | 0.879438i | \(0.342082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.0386 | 1.97797 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4112 | 1.33694 | 0.668469 | − | 0.743740i | \(-0.266950\pi\) | ||||
0.668469 | + | 0.743740i | \(0.266950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2106 | 0.725844 | 0.362922 | − | 0.931820i | \(-0.381779\pi\) | ||||
0.362922 | + | 0.931820i | \(0.381779\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.3000 | 0.906296 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.34204 | 0.256303 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.8273 | −0.813371 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.29471 | 0.0758974 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.0366 | −1.22897 | −0.614485 | − | 0.788929i | \(-0.710636\pi\) | ||||
−0.614485 | + | 0.788929i | \(0.710636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.29143 | 0.0751899 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.46091 | −0.0847708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.54866 | 0.320887 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.19868 | 0.0690906 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −38.6837 | −2.22232 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.13902 | 0.0652202 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.3712 | 1.96167 | 0.980834 | − | 0.194846i | \(-0.0624207\pi\) | ||||
0.980834 | + | 0.194846i | \(0.0624207\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.2856 | 2.23488 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.07674 | −0.0610561 | −0.0305281 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305281 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.94415 | −0.222937 | −0.111468 | − | 0.993768i | \(-0.535555\pi\) | ||||
−0.111468 | + | 0.993768i | \(0.535555\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.67758 | −0.263552 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.9574 | −0.783925 | −0.391963 | − | 0.919981i | \(-0.628204\pi\) | ||||
−0.391963 | + | 0.919981i | \(0.628204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.85706 | 0.159965 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.99877 | 0.558077 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.11460 | −0.451508 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.28322 | 0.182120 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.6825 | −0.756642 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.6383 | −0.641640 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.54436 | 0.139851 | 0.0699253 | − | 0.997552i | \(-0.477724\pi\) | ||||
0.0699253 | + | 0.997552i | \(0.477724\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.1361 | −0.719854 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.01276 | 0.219240 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.41277 | 0.294853 | 0.147426 | − | 0.989073i | \(-0.452901\pi\) | ||||
0.147426 | + | 0.989073i | \(0.452901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.42947 | −0.131951 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.25463 | 0.501166 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.6349 | −1.00327 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.22519 | 0.387868 | 0.193934 | − | 0.981015i | \(-0.437875\pi\) | ||||
0.193934 | + | 0.981015i | \(0.437875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7011 | 1.37575 | 0.687873 | − | 0.725831i | \(-0.258544\pi\) | ||||
0.687873 | + | 0.725831i | \(0.258544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.46091 | 0.0779778 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.21680 | −0.437336 | −0.218668 | − | 0.975799i | \(-0.570171\pi\) | ||||
−0.218668 | + | 0.975799i | \(0.570171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.5227 | 0.876931 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.56557 | 0.241636 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.6194 | −1.61603 | −0.808015 | − | 0.589162i | \(-0.799458\pi\) | ||||
−0.808015 | + | 0.589162i | \(0.799458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.75422 | 0.0923275 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.56319 | −0.134533 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.2359 | −1.00685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.8533 | −1.29733 | −0.648666 | − | 0.761073i | \(-0.724673\pi\) | ||||
−0.648666 | + | 0.761073i | \(0.724673\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.5009 | 0.806945 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.45384 | −0.335067 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6264 | 1.79289 | 0.896443 | − | 0.443159i | \(-0.146142\pi\) | ||||
0.896443 | + | 0.443159i | \(0.146142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.8188 | −1.43656 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.85706 | −0.147146 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5528 | 1.00436 | 0.502180 | − | 0.864763i | \(-0.332531\pi\) | ||||
0.502180 | + | 0.864763i | \(0.332531\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 47.9319 | 2.45563 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0689 | 0.821083 | 0.410541 | − | 0.911842i | \(-0.365340\pi\) | ||||
0.410541 | + | 0.911842i | \(0.365340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.31026 | −0.0667771 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.27923 | 0.217525 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.40934 | −0.324967 | −0.162483 | − | 0.986711i | \(-0.551950\pi\) | ||||
−0.162483 | + | 0.986711i | \(0.551950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.88329 | 0.499820 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.2204 | 1.77663 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.71468 | 0.388168 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.5510 | −1.53331 | −0.766655 | − | 0.642059i | \(-0.778080\pi\) | ||||
−0.766655 | + | 0.642059i | \(0.778080\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.6771 | −0.584586 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.8673 | 1.54144 | 0.770718 | − | 0.637176i | \(-0.219898\pi\) | ||||
0.770718 | + | 0.637176i | \(0.219898\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.25463 | −0.461006 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.12632 | 0.453491 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.67962 | −0.182392 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.3423 | −1.00586 | −0.502931 | − | 0.864327i | \(-0.667745\pi\) | ||||
−0.502931 | + | 0.864327i | \(0.667745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.38494 | 0.314946 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.985627 | −0.0484996 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.52652 | 0.369462 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −44.4716 | −2.17779 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.4488 | 0.998987 | 0.499494 | − | 0.866318i | \(-0.333519\pi\) | ||||
0.499494 | + | 0.866318i | \(0.333519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6834 | 0.666889 | 0.333444 | − | 0.942770i | \(-0.391789\pi\) | ||||
0.333444 | + | 0.942770i | \(0.391789\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −41.5483 | −2.02015 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.84808 | 0.283674 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.869309 | −0.0420688 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.56319 | 0.123752 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.8211 | −1.05109 | −0.525543 | − | 0.850767i | \(-0.676138\pi\) | ||||
−0.525543 | + | 0.850767i | \(0.676138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1888 | 0.633813 | 0.316907 | − | 0.948457i | \(-0.397356\pi\) | ||||
0.316907 | + | 0.948457i | \(0.397356\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.59530 | 0.460059 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.2779 | −1.20921 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8562 | −0.899959 | −0.449980 | − | 0.893039i | \(-0.648569\pi\) | ||||
−0.449980 | + | 0.893039i | \(0.648569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56996 | 0.169998 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.7795 | 0.892240 | 0.446120 | − | 0.894973i | \(-0.352805\pi\) | ||||
0.446120 | + | 0.894973i | \(0.352805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.4532 | −0.779959 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.11781 | −0.431258 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.6859 | −1.35377 | −0.676886 | − | 0.736088i | \(-0.736671\pi\) | ||||
−0.676886 | + | 0.736088i | \(0.736671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.34204 | 0.204459 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −56.6339 | −2.66089 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.31026 | 0.0614260 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.25967 | 0.292815 | 0.146408 | − | 0.989224i | \(-0.453229\pi\) | ||||
0.146408 | + | 0.989224i | \(0.453229\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.60219 | 0.121460 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.2302 | 1.36139 | 0.680694 | − | 0.732568i | \(-0.261678\pi\) | ||||
0.680694 | + | 0.732568i | \(0.261678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2108 | 0.613958 | 0.306979 | − | 0.951716i | \(-0.400682\pi\) | ||||
0.306979 | + | 0.951716i | \(0.400682\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.0812 | 1.44136 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.1731 | −1.44252 | −0.721260 | − | 0.692664i | \(-0.756437\pi\) | ||||
−0.721260 | + | 0.692664i | \(0.756437\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.06256 | −0.141416 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.0882 | −1.06385 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.19868 | 0.0551152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.9573 | −0.686287 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.0399 | −1.05493 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.4088 | 1.02388 | 0.511941 | − | 0.859020i | \(-0.328926\pi\) | ||||
0.511941 | + | 0.859020i | \(0.328926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.67962 | 0.167776 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.2223 | 0.647136 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.661835 | 0.0300524 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.1399 | −0.776684 | −0.388342 | − | 0.921515i | \(-0.626952\pi\) | ||||
−0.388342 | + | 0.921515i | \(0.626952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −49.9675 | −2.25961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.74433 | −0.123850 | −0.0619250 | − | 0.998081i | \(-0.519724\pi\) | ||||
−0.0619250 | + | 0.998081i | \(0.519724\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.08901 | −0.229197 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.67758 | −0.210241 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.6102 | −0.565645 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.28958 | 0.326326 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.0595 | −1.07490 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.7200 | 1.72644 | 0.863220 | − | 0.504829i | \(-0.168444\pi\) | ||||
0.863220 | + | 0.504829i | \(0.168444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.7744 | −0.879951 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.56319 | −0.113835 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.5527 | −1.30990 | −0.654950 | − | 0.755672i | \(-0.727310\pi\) | ||||
−0.654950 | + | 0.755672i | \(0.727310\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6810 | 0.649448 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.65546 | −0.293846 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.0822 | 0.884926 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6383 | −0.511852 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.0622 | −1.62685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.5726 | 1.25179 | 0.625895 | − | 0.779908i | \(-0.284734\pi\) | ||||
0.625895 | + | 0.779908i | \(0.284734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.20207 | −0.227471 | −0.113735 | − | 0.993511i | \(-0.536282\pi\) | ||||
−0.113735 | + | 0.993511i | \(0.536282\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.41552 | 0.367283 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.4844 | −0.718071 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.78759 | 0.338591 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.51865 | −0.152696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.34204 | −0.188075 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.11120 | 0.220977 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −47.0212 | −2.02911 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5568 | 0.539858 | 0.269929 | − | 0.962880i | \(-0.413000\pi\) | ||||
0.269929 | + | 0.962880i | \(0.413000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.3809 | −0.917543 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.99424 | −0.299600 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6383 | −0.839673 | −0.419837 | − | 0.907600i | \(-0.637913\pi\) | ||||
−0.419837 | + | 0.907600i | \(0.637913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.10340 | −0.132450 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.0158 | 0.554494 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.88790 | −0.250379 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.3578 | −0.524561 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.6785 | 0.833806 | 0.416903 | − | 0.908951i | \(-0.363115\pi\) | ||||
0.416903 | + | 0.908951i | \(0.363115\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.19868 | −0.0506987 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.56557 | 0.192759 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0392 | −0.633825 | −0.316912 | − | 0.948455i | \(-0.602646\pi\) | ||||
−0.316912 | + | 0.948455i | \(0.602646\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.24190 | −0.0522472 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.96527 | −0.292514 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.8104 | 1.29164 | 0.645819 | − | 0.763491i | \(-0.276516\pi\) | ||||
0.645819 | + | 0.763491i | \(0.276516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.26472 | 0.345868 | 0.172934 | − | 0.984933i | \(-0.444675\pi\) | ||||
0.172934 | + | 0.984933i | \(0.444675\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.3411 | −0.473782 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.2174 | 0.759720 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.9355 | −0.788296 | −0.394148 | − | 0.919047i | \(-0.628960\pi\) | ||||
−0.394148 | + | 0.919047i | \(0.628960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −69.8180 | −2.90154 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.74429 | −0.238313 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.45384 | −0.267291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.67758 | 0.193394 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.8825 | −0.903187 | −0.451593 | − | 0.892224i | \(-0.649144\pi\) | ||||
−0.451593 | + | 0.892224i | \(0.649144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.1611 | 1.73722 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −49.6398 | −2.04191 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.74145 | −0.276838 | −0.138419 | − | 0.990374i | \(-0.544202\pi\) | ||||
−0.138419 | + | 0.990374i | \(0.544202\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.33384 | 0.0956782 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.2782 | 1.81219 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.2426 | −0.786232 | −0.393116 | − | 0.919489i | \(-0.628603\pi\) | ||||
−0.393116 | + | 0.919489i | \(0.628603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.875564 | −0.0357150 | −0.0178575 | − | 0.999841i | \(-0.505685\pi\) | ||||
−0.0178575 | + | 0.999841i | \(0.505685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9332 | −0.445236 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.31026 | −0.0532697 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.57093 | −0.347883 | −0.173942 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173942 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.32319 | −0.296751 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.6383 | 0.470835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.2024 | 1.78532 | 0.892659 | − | 0.450732i | \(-0.148837\pi\) | ||||
0.892659 | + | 0.450732i | \(0.148837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.5825 | 0.588025 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.16468 | −0.248181 | −0.124090 | − | 0.992271i | \(-0.539601\pi\) | ||||
−0.124090 | + | 0.992271i | \(0.539601\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2516 | 0.613014 | 0.306507 | − | 0.951868i | \(-0.400840\pi\) | ||||
0.306507 | + | 0.951868i | \(0.400840\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.10611 | 0.325287 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.5572 | 0.503095 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.19559 | 0.0878237 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.6771 | −0.466338 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.55416 | 0.261332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4365 | 0.813564 | 0.406782 | − | 0.913525i | \(-0.366651\pi\) | ||||
0.406782 | + | 0.913525i | \(0.366651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.7063 | 1.10123 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.5020 | 0.972331 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.0179 | −1.78088 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.1968 | −0.955715 | −0.477857 | − | 0.878437i | \(-0.658586\pi\) | ||||
−0.477857 | + | 0.878437i | \(0.658586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5221 | 0.572694 | 0.286347 | − | 0.958126i | \(-0.407559\pi\) | ||||
0.286347 | + | 0.958126i | \(0.407559\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.02570 | 0.158512 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.9009 | −1.25415 | −0.627077 | − | 0.778958i | \(-0.715749\pi\) | ||||
−0.627077 | + | 0.778958i | \(0.715749\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.985627 | −0.0386893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.7214 | −0.929715 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3097 | 0.442584 | 0.221292 | − | 0.975208i | \(-0.428973\pi\) | ||||
0.221292 | + | 0.975208i | \(0.428973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0040 | 0.703476 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 52.4104 | 2.04473 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.30187 | 0.323395 | 0.161697 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161697 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.3382 | 0.946646 | 0.473323 | − | 0.880889i | \(-0.343054\pi\) | ||||
0.473323 | + | 0.880889i | \(0.343054\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.56557 | −0.177312 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.96913 | −0.231473 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.8528 | −0.613824 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −44.4615 | −1.71898 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.869309 | −0.0335593 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.6886 | 0.604753 | 0.302376 | − | 0.953189i | \(-0.402220\pi\) | ||||
0.302376 | + | 0.953189i | \(0.402220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.79650 | 0.184617 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.1034 | 1.31070 | 0.655350 | − | 0.755325i | \(-0.272521\pi\) | ||||
0.655350 | + | 0.755325i | \(0.272521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.505117 | −0.0193846 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −52.7385 | −2.02094 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2714 | 0.469550 | 0.234775 | − | 0.972050i | \(-0.424565\pi\) | ||||
0.234775 | + | 0.972050i | \(0.424565\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.26387 | 0.124706 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 56.8761 | 2.16996 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.45384 | 0.245872 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.5281 | −1.16134 | −0.580671 | − | 0.814138i | \(-0.697210\pi\) | ||||
−0.580671 | + | 0.814138i | \(0.697210\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.56996 | 0.135612 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.7331 | −0.862317 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.73407 | −0.292949 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.2159 | 1.44546 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.0064 | −1.28440 | −0.642202 | − | 0.766535i | \(-0.721979\pi\) | ||||
−0.642202 | + | 0.766535i | \(0.721979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.7632 | −0.632235 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39.0867 | −1.47209 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.0920 | 0.567593 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.1256 | −0.680723 | −0.340361 | − | 0.940295i | \(-0.610549\pi\) | ||||
−0.340361 | + | 0.940295i | \(0.610549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.0195 | −0.788294 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −51.3507 | −1.92310 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.31026 | 0.0490010 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.77135 | −0.0661523 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.6444 | −1.59037 | −0.795184 | − | 0.606368i | \(-0.792626\pi\) | ||||
−0.795184 | + | 0.606368i | \(0.792626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3268 | −0.570801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.2924 | 1.27535 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.38034 | −0.348377 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.2366 | 1.82608 | 0.913041 | − | 0.407867i | \(-0.133727\pi\) | ||||
0.913041 | + | 0.407867i | \(0.133727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.0995 | −1.33702 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.13509 | −0.0789692 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.5000 | 1.08961 | 0.544804 | − | 0.838563i | \(-0.316604\pi\) | ||||
0.544804 | + | 0.838563i | \(0.316604\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.35845 | 0.123878 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.06256 | −0.112811 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.5493 | 1.23413 | 0.617066 | − | 0.786912i | \(-0.288321\pi\) | ||||
0.617066 | + | 0.786912i | \(0.288321\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6771 | 0.428969 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.847165 | 0.0310795 | 0.0155397 | − | 0.999879i | \(-0.495053\pi\) | ||||
0.0155397 | + | 0.999879i | \(0.495053\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.66087 | −0.170761 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.5069 | −0.750308 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.90090 | −0.142536 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.01203 | −0.255873 | −0.127936 | − | 0.991782i | \(-0.540835\pi\) | ||||
−0.127936 | + | 0.991782i | \(0.540835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.4943 | 1.18416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.9503 | −1.05361 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.6194 | 1.58537 | 0.792686 | − | 0.609630i | \(-0.208682\pi\) | ||||
0.792686 | + | 0.609630i | \(0.208682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.2223 | 0.516236 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.4859 | −0.778863 | −0.389432 | − | 0.921055i | \(-0.627329\pi\) | ||||
−0.389432 | + | 0.921055i | \(0.627329\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.33805 | 0.193251 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.33172 | 0.301234 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.985627 | 0.0355889 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0566 | −0.579014 | −0.289507 | − | 0.957176i | \(-0.593491\pi\) | ||||
−0.289507 | + | 0.957176i | \(0.593491\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −75.8656 | −2.73223 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.3606 | 0.876189 | 0.438094 | − | 0.898929i | \(-0.355654\pi\) | ||||
0.438094 | + | 0.898929i | \(0.355654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.3849 | −1.09146 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.43158 | 0.338356 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.7810 | 0.708726 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6102 | −0.451228 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.17392 | −0.149164 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.8023 | −0.421242 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.9081 | 0.495769 | 0.247884 | − | 0.968790i | \(-0.420265\pi\) | ||||
0.247884 | + | 0.968790i | \(0.420265\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.1167 | 0.787374 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.947829 | 0.0337009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.869309 | 0.0308701 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.6749 | −0.768729 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.9063 | −1.51982 | −0.759910 | − | 0.650029i | \(-0.774757\pi\) | ||||
−0.759910 | + | 0.650029i | \(0.774757\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7302 | 0.733382 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.8288 | 1.58395 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.6810 | 0.518080 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.27019 | 0.256240 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.78527 | −0.344458 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.6998 | −0.727766 | −0.363883 | − | 0.931445i | \(-0.618549\pi\) | ||||
−0.363883 | + | 0.931445i | \(0.618549\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.1031 | 1.72424 | 0.862122 | − | 0.506700i | \(-0.169135\pi\) | ||||
0.862122 | + | 0.506700i | \(0.169135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −61.5412 | −2.15834 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.5426 | −0.894717 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.46079 | 0.191049 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.56996 | −0.124744 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.33958 | −0.116552 | −0.0582760 | − | 0.998301i | \(-0.518560\pi\) | ||||
−0.0582760 | + | 0.998301i | \(0.518560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.2624 | −1.15945 | −0.579727 | − | 0.814811i | \(-0.696841\pi\) | ||||
−0.579727 | + | 0.814811i | \(0.696841\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.41552 | 0.292991 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.9417 | −0.971629 | −0.485815 | − | 0.874062i | \(-0.661477\pi\) | ||||
−0.485815 | + | 0.874062i | \(0.661477\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9194 | 1.31699 | 0.658497 | − | 0.752583i | \(-0.271192\pi\) | ||||
0.658497 | + | 0.752583i | \(0.271192\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.6134 | −1.40886 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.78120 | −0.0617151 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.2988 | −0.425617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5202 | −0.467327 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.8122 | −0.649469 | −0.324734 | − | 0.945805i | \(-0.605275\pi\) | ||||
−0.324734 | + | 0.945805i | \(0.605275\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.8372 | −0.718525 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −57.4442 | −1.97848 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.31026 | −0.0450743 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.2981 | −1.07415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.4170 | 0.699884 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6216 | 0.397918 | 0.198959 | − | 0.980008i | \(-0.436244\pi\) | ||||
0.198959 | + | 0.980008i | \(0.436244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.3095 | −0.728771 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.52571 | −0.188755 | −0.0943773 | − | 0.995537i | \(-0.530086\pi\) | ||||
−0.0943773 | + | 0.995537i | \(0.530086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.6294 | −1.21566 | −0.607829 | − | 0.794068i | \(-0.707959\pi\) | ||||
−0.607829 | + | 0.794068i | \(0.707959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.1295 | −0.379292 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.3791 | −1.20432 | −0.602159 | − | 0.798377i | \(-0.705692\pi\) | ||||
−0.602159 | + | 0.798377i | \(0.705692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.9456 | −0.644169 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.4421 | 1.20368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.88790 | −0.199733 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.06256 | 0.103771 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.80325 | −0.0610307 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.8532 | 0.366904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1409 | 0.545039 | 0.272519 | − | 0.962150i | \(-0.412143\pi\) | ||||
0.272519 | + | 0.962150i | \(0.412143\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 53.9208 | 1.81870 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.0910 | 1.48546 | 0.742732 | − | 0.669589i | \(-0.233530\pi\) | ||||
0.742732 | + | 0.669589i | \(0.233530\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.23103 | −0.176038 | −0.0880191 | − | 0.996119i | \(-0.528054\pi\) | ||||
−0.0880191 | + | 0.996119i | \(0.528054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.31018 | −0.111271 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.1171 | −1.07839 | −0.539193 | − | 0.842182i | \(-0.681271\pi\) | ||||
−0.539193 | + | 0.842182i | \(0.681271\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.7001 | −0.627180 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.96527 | −0.233345 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −53.0204 | −1.77426 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0364 | −0.803449 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.2223 | −0.474868 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.4410 | 0.881857 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.4956 | 0.382974 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.07244 | −0.102244 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.9296 | −0.363311 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.4967 | −1.87594 | −0.937970 | − | 0.346716i | \(-0.887297\pi\) | ||||
−0.937970 | + | 0.346716i | \(0.887297\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 53.8778 | 1.78701 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.7887 | 1.25200 | 0.625998 | − | 0.779825i | \(-0.284692\pi\) | ||||
0.625998 | + | 0.779825i | \(0.284692\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.74429 | −0.190108 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.91953 | −0.0965168 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.7408 | −0.453762 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.9068 | −0.623679 | −0.311839 | − | 0.950135i | \(-0.600945\pi\) | ||||
−0.311839 | + | 0.950135i | \(0.600945\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −88.1000 | −2.90299 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.6102 | 0.415070 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0810 | 0.397221 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −54.7162 | −1.79712 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.1699 | −1.28512 | −0.642561 | − | 0.766234i | \(-0.722128\pi\) | ||||
−0.642561 | + | 0.766234i | \(0.722128\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.55568 | 0.149306 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.75988 | 0.0903545 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.33384 | 0.0763248 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.9573 | 1.20734 | 0.603672 | − | 0.797233i | \(-0.293704\pi\) | ||||
0.603672 | + | 0.797233i | \(0.293704\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.1096 | 0.329915 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.1026 | 1.47030 | 0.735152 | − | 0.677902i | \(-0.237111\pi\) | ||||
0.735152 | + | 0.677902i | \(0.237111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0925 | −0.784560 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.91418 | 0.0622682 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.8420 | 0.644777 | 0.322389 | − | 0.946607i | \(-0.395514\pi\) | ||||
0.322389 | + | 0.946607i | \(0.395514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.6810 | −0.476564 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.7755 | 1.16010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.0626 | 1.00622 | 0.503108 | − | 0.864223i | \(-0.332190\pi\) | ||||
0.503108 | + | 0.864223i | \(0.332190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.79739 | −0.187599 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.32319 | −0.236725 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.49101 | −0.0804389 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.6481 | 1.76284 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.9261 | −0.448761 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.6898 | −1.14889 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.5885 | −0.469136 | −0.234568 | − | 0.972100i | \(-0.575368\pi\) | ||||
−0.234568 | + | 0.972100i | \(0.575368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.7993 | 0.668169 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.03851 | 0.257968 | 0.128984 | − | 0.991647i | \(-0.458828\pi\) | ||||
0.128984 | + | 0.991647i | \(0.458828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.3501 | 0.556218 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.41552 | −0.269512 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.4864 | 0.687410 | 0.343705 | − | 0.939078i | \(-0.388318\pi\) | ||||
0.343705 | + | 0.939078i | \(0.388318\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.5572 | 0.401331 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.0566 | 0.608431 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.4025 | 1.67138 | 0.835691 | − | 0.549201i | \(-0.185068\pi\) | ||||
0.835691 | + | 0.549201i | \(0.185068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.3750 | −0.808515 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.8312 | 0.949538 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.65105 | −0.211491 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.2504 | 1.05623 | 0.528117 | − | 0.849172i | \(-0.322898\pi\) | ||||
0.528117 | + | 0.849172i | \(0.322898\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.52168 | −0.206959 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.6343 | 0.717554 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0215 | 0.412394 | 0.206197 | − | 0.978510i | \(-0.433891\pi\) | ||||
0.206197 | + | 0.978510i | \(0.433891\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.37561 | 0.170077 |
(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 | 4004.2.a.h.1.2 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.h.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial |