Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.37960\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37960 | 1.68263 | 0.841317 | − | 0.540542i | \(-0.181781\pi\) | ||||
0.841317 | + | 0.540542i | \(0.181781\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.66252 | 1.83126 | ||||||||
\(5\) | −2.55185 | −1.14122 | −0.570611 | − | 0.821221i | \(-0.693294\pi\) | ||||
−0.570611 | + | 0.821221i | \(0.693294\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.67712 | 0.633891 | 0.316945 | − | 0.948444i | \(-0.397343\pi\) | ||||
0.316945 | + | 0.948444i | \(0.397343\pi\) | |||||||
\(8\) | 3.95613 | 1.39870 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.07239 | −1.92026 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65147 | 1.56744 | 0.783718 | − | 0.621117i | \(-0.213321\pi\) | ||||
0.783718 | + | 0.621117i | \(0.213321\pi\) | |||||||
\(14\) | 3.99087 | 1.06661 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.08899 | 0.522248 | ||||||||
\(17\) | 4.01907 | 0.974767 | 0.487383 | − | 0.873188i | \(-0.337951\pi\) | ||||
0.487383 | + | 0.873188i | \(0.337951\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.77230 | 0.636010 | 0.318005 | − | 0.948089i | \(-0.396987\pi\) | ||||
0.318005 | + | 0.948089i | \(0.396987\pi\) | |||||||
\(20\) | −9.34619 | −2.08987 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.37960 | −0.507333 | ||||||||
\(23\) | −6.13877 | −1.28002 | −0.640011 | − | 0.768366i | \(-0.721070\pi\) | ||||
−0.640011 | + | 0.768366i | \(0.721070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.51194 | 0.302387 | ||||||||
\(26\) | 13.4483 | 2.63742 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.14247 | 1.16082 | ||||||||
\(29\) | −1.25605 | −0.233242 | −0.116621 | − | 0.993177i | \(-0.537206\pi\) | ||||
−0.116621 | + | 0.993177i | \(0.537206\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.37742 | 0.965814 | 0.482907 | − | 0.875672i | \(-0.339581\pi\) | ||||
0.482907 | + | 0.875672i | \(0.339581\pi\) | |||||||
\(32\) | −2.94129 | −0.519951 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.56379 | 1.64018 | ||||||||
\(35\) | −4.27975 | −0.723410 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.89012 | 0.475134 | 0.237567 | − | 0.971371i | \(-0.423650\pi\) | ||||
0.237567 | + | 0.971371i | \(0.423650\pi\) | |||||||
\(38\) | 6.59699 | 1.07017 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.0954 | −1.59623 | ||||||||
\(41\) | −6.31673 | −0.986508 | −0.493254 | − | 0.869885i | \(-0.664193\pi\) | ||||
−0.493254 | + | 0.869885i | \(0.664193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.33950 | 1.42426 | 0.712130 | − | 0.702047i | \(-0.247731\pi\) | ||||
0.712130 | + | 0.702047i | \(0.247731\pi\) | |||||||
\(44\) | −3.66252 | −0.552145 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.6078 | −2.15381 | ||||||||
\(47\) | 8.72405 | 1.27253 | 0.636267 | − | 0.771469i | \(-0.280478\pi\) | ||||
0.636267 | + | 0.771469i | \(0.280478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.18728 | −0.598183 | ||||||||
\(50\) | 3.59781 | 0.508807 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20.6986 | 2.87038 | ||||||||
\(53\) | 4.90573 | 0.673854 | 0.336927 | − | 0.941531i | \(-0.390612\pi\) | ||||
0.336927 | + | 0.941531i | \(0.390612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.55185 | 0.344091 | ||||||||
\(56\) | 6.63489 | 0.886625 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.98889 | −0.392461 | ||||||||
\(59\) | 4.68512 | 0.609951 | 0.304976 | − | 0.952360i | \(-0.401352\pi\) | ||||
0.304976 | + | 0.952360i | \(0.401352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 12.7961 | 1.62511 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.1771 | −1.39714 | ||||||||
\(65\) | −14.4217 | −1.78879 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.67098 | 0.692820 | 0.346410 | − | 0.938083i | \(-0.387401\pi\) | ||||
0.346410 | + | 0.938083i | \(0.387401\pi\) | |||||||
\(68\) | 14.7199 | 1.78505 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.1841 | −1.21723 | ||||||||
\(71\) | 2.71844 | 0.322620 | 0.161310 | − | 0.986904i | \(-0.448428\pi\) | ||||
0.161310 | + | 0.986904i | \(0.448428\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1095 | 1.76843 | 0.884215 | − | 0.467080i | \(-0.154694\pi\) | ||||
0.884215 | + | 0.467080i | \(0.154694\pi\) | |||||||
\(74\) | 6.87735 | 0.799476 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.1536 | 1.16470 | ||||||||
\(77\) | −1.67712 | −0.191125 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.47612 | −0.166076 | −0.0830381 | − | 0.996546i | \(-0.526462\pi\) | ||||
−0.0830381 | + | 0.996546i | \(0.526462\pi\) | |||||||
\(80\) | −5.33079 | −0.596001 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.0313 | −1.65993 | ||||||||
\(83\) | 2.19058 | 0.240448 | 0.120224 | − | 0.992747i | \(-0.461639\pi\) | ||||
0.120224 | + | 0.992747i | \(0.461639\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.2561 | −1.11243 | ||||||||
\(86\) | 22.2243 | 2.39651 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.95613 | −0.421725 | ||||||||
\(89\) | 13.1550 | 1.39442 | 0.697212 | − | 0.716865i | \(-0.254424\pi\) | ||||
0.697212 | + | 0.716865i | \(0.254424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.47818 | 0.993583 | ||||||||
\(92\) | −22.4833 | −2.34405 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20.7598 | 2.14121 | ||||||||
\(95\) | −7.07450 | −0.725829 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.84526 | −0.796565 | −0.398283 | − | 0.917263i | \(-0.630394\pi\) | ||||
−0.398283 | + | 0.917263i | \(0.630394\pi\) | |||||||
\(98\) | −9.96407 | −1.00652 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.53749 | 0.553749 | ||||||||
\(101\) | 3.23484 | 0.321879 | 0.160939 | − | 0.986964i | \(-0.448548\pi\) | ||||
0.160939 | + | 0.986964i | \(0.448548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.86347 | −0.774811 | −0.387405 | − | 0.921909i | \(-0.626629\pi\) | ||||
−0.387405 | + | 0.921909i | \(0.626629\pi\) | |||||||
\(104\) | 22.3580 | 2.19238 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.6737 | 1.13385 | ||||||||
\(107\) | 18.7522 | 1.81284 | 0.906420 | − | 0.422378i | \(-0.138805\pi\) | ||||
0.906420 | + | 0.422378i | \(0.138805\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.5666 | −1.87414 | −0.937070 | − | 0.349141i | \(-0.886473\pi\) | ||||
−0.937070 | + | 0.349141i | \(0.886473\pi\) | |||||||
\(110\) | 6.07239 | 0.578980 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.50348 | 0.331048 | ||||||||
\(113\) | −11.4456 | −1.07671 | −0.538356 | − | 0.842718i | \(-0.680954\pi\) | ||||
−0.538356 | + | 0.842718i | \(0.680954\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.6652 | 1.46079 | ||||||||
\(116\) | −4.60029 | −0.427126 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.1487 | 1.02632 | ||||||||
\(119\) | 6.74045 | 0.617896 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.37960 | −0.215439 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 19.6949 | 1.76865 | ||||||||
\(125\) | 8.90101 | 0.796131 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.63206 | 0.144822 | 0.0724109 | − | 0.997375i | \(-0.476931\pi\) | ||||
0.0724109 | + | 0.997375i | \(0.476931\pi\) | |||||||
\(128\) | −20.7145 | −1.83092 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −34.3179 | −3.00988 | ||||||||
\(131\) | −5.81437 | −0.508004 | −0.254002 | − | 0.967204i | \(-0.581747\pi\) | ||||
−0.254002 | + | 0.967204i | \(0.581747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.64948 | 0.403161 | ||||||||
\(134\) | 13.4947 | 1.16576 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.9000 | 1.36341 | ||||||||
\(137\) | 0.124547 | 0.0106407 | 0.00532037 | − | 0.999986i | \(-0.498306\pi\) | ||||
0.00532037 | + | 0.999986i | \(0.498306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.70439 | 0.483840 | 0.241920 | − | 0.970296i | \(-0.422223\pi\) | ||||
0.241920 | + | 0.970296i | \(0.422223\pi\) | |||||||
\(140\) | −15.6747 | −1.32475 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.46881 | 0.542851 | ||||||||
\(143\) | −5.65147 | −0.472600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.20524 | 0.266181 | ||||||||
\(146\) | 35.9546 | 2.97562 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5851 | 0.870092 | ||||||||
\(149\) | 20.0285 | 1.64080 | 0.820399 | − | 0.571792i | \(-0.193751\pi\) | ||||
0.820399 | + | 0.571792i | \(0.193751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.05186 | 0.655251 | 0.327626 | − | 0.944808i | \(-0.393752\pi\) | ||||
0.327626 | + | 0.944808i | \(0.393752\pi\) | |||||||
\(152\) | 10.9676 | 0.889589 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.99087 | −0.321594 | ||||||||
\(155\) | −13.7224 | −1.10221 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2781 | 0.820281 | 0.410141 | − | 0.912022i | \(-0.365480\pi\) | ||||
0.410141 | + | 0.912022i | \(0.365480\pi\) | |||||||
\(158\) | −3.51258 | −0.279446 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.50572 | 0.593379 | ||||||||
\(161\) | −10.2954 | −0.811394 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.68649 | −0.523727 | −0.261863 | − | 0.965105i | \(-0.584337\pi\) | ||||
−0.261863 | + | 0.965105i | \(0.584337\pi\) | |||||||
\(164\) | −23.1351 | −1.80655 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.21272 | 0.404585 | ||||||||
\(167\) | −14.0284 | −1.08555 | −0.542773 | − | 0.839879i | \(-0.682626\pi\) | ||||
−0.542773 | + | 0.839879i | \(0.682626\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.9391 | 1.45686 | ||||||||
\(170\) | −24.4054 | −1.87180 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 34.2061 | 2.60819 | ||||||||
\(173\) | −10.3570 | −0.787430 | −0.393715 | − | 0.919233i | \(-0.628810\pi\) | ||||
−0.393715 | + | 0.919233i | \(0.628810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.53569 | 0.191680 | ||||||||
\(176\) | −2.08899 | −0.157464 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 31.3036 | 2.34630 | ||||||||
\(179\) | 7.34446 | 0.548951 | 0.274476 | − | 0.961594i | \(-0.411496\pi\) | ||||
0.274476 | + | 0.961594i | \(0.411496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.531235 | −0.0394864 | −0.0197432 | − | 0.999805i | \(-0.506285\pi\) | ||||
−0.0197432 | + | 0.999805i | \(0.506285\pi\) | |||||||
\(182\) | 22.5543 | 1.67184 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −24.2858 | −1.79037 | ||||||||
\(185\) | −7.37516 | −0.542233 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.01907 | −0.293903 | ||||||||
\(188\) | 31.9520 | 2.33034 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.8345 | −1.22130 | ||||||||
\(191\) | −16.5231 | −1.19557 | −0.597785 | − | 0.801656i | \(-0.703952\pi\) | ||||
−0.597785 | + | 0.801656i | \(0.703952\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9043 | 1.28878 | 0.644391 | − | 0.764697i | \(-0.277111\pi\) | ||||
0.644391 | + | 0.764697i | \(0.277111\pi\) | |||||||
\(194\) | −18.6686 | −1.34033 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.3360 | −1.09543 | ||||||||
\(197\) | −9.54976 | −0.680392 | −0.340196 | − | 0.940355i | \(-0.610493\pi\) | ||||
−0.340196 | + | 0.940355i | \(0.610493\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.91086 | 0.560786 | 0.280393 | − | 0.959885i | \(-0.409535\pi\) | ||||
0.280393 | + | 0.959885i | \(0.409535\pi\) | |||||||
\(200\) | 5.98142 | 0.422950 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.69764 | 0.541604 | ||||||||
\(203\) | −2.10654 | −0.147850 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.1194 | 1.12582 | ||||||||
\(206\) | −18.7120 | −1.30372 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.8059 | 0.818590 | ||||||||
\(209\) | −2.77230 | −0.191764 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.64980 | −0.595477 | −0.297738 | − | 0.954648i | \(-0.596232\pi\) | ||||
−0.297738 | + | 0.954648i | \(0.596232\pi\) | |||||||
\(212\) | 17.9673 | 1.23400 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 44.6227 | 3.05035 | ||||||||
\(215\) | −23.8330 | −1.62540 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.01857 | 0.612220 | ||||||||
\(218\) | −46.5608 | −3.15349 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.34619 | 0.630120 | ||||||||
\(221\) | 22.7136 | 1.52788 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.83430 | 0.591588 | 0.295794 | − | 0.955252i | \(-0.404416\pi\) | ||||
0.295794 | + | 0.955252i | \(0.404416\pi\) | |||||||
\(224\) | −4.93288 | −0.329592 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.2360 | −1.81171 | ||||||||
\(227\) | −15.6307 | −1.03744 | −0.518722 | − | 0.854943i | \(-0.673592\pi\) | ||||
−0.518722 | + | 0.854943i | \(0.673592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.1402 | −0.868329 | −0.434164 | − | 0.900834i | \(-0.642956\pi\) | ||||
−0.434164 | + | 0.900834i | \(0.642956\pi\) | |||||||
\(230\) | 37.2770 | 2.45797 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.96908 | −0.326236 | ||||||||
\(233\) | 19.2138 | 1.25874 | 0.629368 | − | 0.777108i | \(-0.283314\pi\) | ||||
0.629368 | + | 0.777108i | \(0.283314\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.2625 | −1.45224 | ||||||||
\(236\) | 17.1593 | 1.11698 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.0396 | 1.03969 | ||||||||
\(239\) | −13.3971 | −0.866585 | −0.433293 | − | 0.901253i | \(-0.642648\pi\) | ||||
−0.433293 | + | 0.901253i | \(0.642648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.2756 | −1.62814 | −0.814072 | − | 0.580765i | \(-0.802754\pi\) | ||||
−0.814072 | + | 0.580765i | \(0.802754\pi\) | |||||||
\(242\) | 2.37960 | 0.152967 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.66252 | −0.234469 | ||||||||
\(245\) | 10.6853 | 0.682659 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.6676 | 0.996905 | ||||||||
\(248\) | 21.2738 | 1.35089 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 21.1809 | 1.33960 | ||||||||
\(251\) | −16.2067 | −1.02296 | −0.511480 | − | 0.859295i | \(-0.670903\pi\) | ||||
−0.511480 | + | 0.859295i | \(0.670903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.13877 | 0.385941 | ||||||||
\(254\) | 3.88366 | 0.243682 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.9380 | −1.68363 | ||||||||
\(257\) | 16.7068 | 1.04214 | 0.521072 | − | 0.853513i | \(-0.325532\pi\) | ||||
0.521072 | + | 0.853513i | \(0.325532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.84708 | 0.301183 | ||||||||
\(260\) | −52.8197 | −3.27574 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.8359 | −0.854785 | ||||||||
\(263\) | −10.1887 | −0.628263 | −0.314132 | − | 0.949379i | \(-0.601713\pi\) | ||||
−0.314132 | + | 0.949379i | \(0.601713\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.5187 | −0.769017 | ||||||||
\(266\) | 11.0639 | 0.678372 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 20.7700 | 1.26873 | ||||||||
\(269\) | −1.61445 | −0.0984350 | −0.0492175 | − | 0.998788i | \(-0.515673\pi\) | ||||
−0.0492175 | + | 0.998788i | \(0.515673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4804 | 1.54782 | 0.773912 | − | 0.633294i | \(-0.218297\pi\) | ||||
0.773912 | + | 0.633294i | \(0.218297\pi\) | |||||||
\(272\) | 8.39580 | 0.509070 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.296372 | 0.0179045 | ||||||||
\(275\) | −1.51194 | −0.0911732 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.4548 | 1.04876 | 0.524378 | − | 0.851486i | \(-0.324298\pi\) | ||||
0.524378 | + | 0.851486i | \(0.324298\pi\) | |||||||
\(278\) | 13.5742 | 0.814125 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −16.9312 | −1.01184 | ||||||||
\(281\) | 16.5498 | 0.987275 | 0.493638 | − | 0.869668i | \(-0.335667\pi\) | ||||
0.493638 | + | 0.869668i | \(0.335667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.5787 | 1.28272 | 0.641359 | − | 0.767241i | \(-0.278371\pi\) | ||||
0.641359 | + | 0.767241i | \(0.278371\pi\) | |||||||
\(284\) | 9.95633 | 0.590800 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.4483 | −0.795213 | ||||||||
\(287\) | −10.5939 | −0.625338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.847100 | −0.0498294 | ||||||||
\(290\) | 7.62720 | 0.447885 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 55.3387 | 3.23845 | ||||||||
\(293\) | 3.17063 | 0.185230 | 0.0926150 | − | 0.995702i | \(-0.470477\pi\) | ||||
0.0926150 | + | 0.995702i | \(0.470477\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9557 | −0.696090 | ||||||||
\(296\) | 11.4337 | 0.664571 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 47.6599 | 2.76086 | ||||||||
\(299\) | −34.6931 | −2.00635 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6634 | 0.902825 | ||||||||
\(302\) | 19.1602 | 1.10255 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.79132 | 0.332155 | ||||||||
\(305\) | 2.55185 | 0.146118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3935 | 0.650259 | 0.325130 | − | 0.945669i | \(-0.394592\pi\) | ||||
0.325130 | + | 0.945669i | \(0.394592\pi\) | |||||||
\(308\) | −6.14247 | −0.350000 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −32.6538 | −1.85461 | ||||||||
\(311\) | −13.0228 | −0.738456 | −0.369228 | − | 0.929339i | \(-0.620378\pi\) | ||||
−0.369228 | + | 0.929339i | \(0.620378\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.9422 | −1.80548 | −0.902740 | − | 0.430186i | \(-0.858448\pi\) | ||||
−0.902740 | + | 0.430186i | \(0.858448\pi\) | |||||||
\(314\) | 24.4578 | 1.38023 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.40631 | −0.304129 | ||||||||
\(317\) | −4.27975 | −0.240375 | −0.120187 | − | 0.992751i | \(-0.538350\pi\) | ||||
−0.120187 | + | 0.992751i | \(0.538350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.25605 | 0.0703250 | ||||||||
\(320\) | 28.5222 | 1.59444 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −24.4991 | −1.36528 | ||||||||
\(323\) | 11.1421 | 0.619962 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.54466 | 0.473973 | ||||||||
\(326\) | −15.9112 | −0.881240 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −24.9898 | −1.37983 | ||||||||
\(329\) | 14.6313 | 0.806647 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.6153 | −1.68277 | −0.841385 | − | 0.540436i | \(-0.818259\pi\) | ||||
−0.841385 | + | 0.540436i | \(0.818259\pi\) | |||||||
\(332\) | 8.02304 | 0.440321 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −33.3819 | −1.82658 | ||||||||
\(335\) | −14.4715 | −0.790662 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.1363 | 1.09689 | 0.548447 | − | 0.836185i | \(-0.315219\pi\) | ||||
0.548447 | + | 0.836185i | \(0.315219\pi\) | |||||||
\(338\) | 45.0676 | 2.45136 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −37.5630 | −2.03714 | ||||||||
\(341\) | −5.37742 | −0.291204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7624 | −1.01307 | ||||||||
\(344\) | 36.9483 | 1.99212 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.6456 | −1.32496 | ||||||||
\(347\) | 31.7798 | 1.70603 | 0.853015 | − | 0.521887i | \(-0.174772\pi\) | ||||
0.853015 | + | 0.521887i | \(0.174772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4164 | −1.52110 | −0.760548 | − | 0.649282i | \(-0.775069\pi\) | ||||
−0.760548 | + | 0.649282i | \(0.775069\pi\) | |||||||
\(350\) | 6.03395 | 0.322528 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.94129 | 0.156771 | ||||||||
\(353\) | −13.9859 | −0.744392 | −0.372196 | − | 0.928154i | \(-0.621395\pi\) | ||||
−0.372196 | + | 0.928154i | \(0.621395\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.93705 | −0.368180 | ||||||||
\(356\) | 48.1803 | 2.55355 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.4769 | 0.923684 | ||||||||
\(359\) | −9.57884 | −0.505552 | −0.252776 | − | 0.967525i | \(-0.581344\pi\) | ||||
−0.252776 | + | 0.967525i | \(0.581344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3143 | −0.595491 | ||||||||
\(362\) | −1.26413 | −0.0664412 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 34.7140 | 1.81951 | ||||||||
\(365\) | −38.5571 | −2.01817 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.5751 | −1.07401 | −0.537006 | − | 0.843578i | \(-0.680445\pi\) | ||||
−0.537006 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(368\) | −12.8238 | −0.668489 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.5500 | −0.912379 | ||||||||
\(371\) | 8.22749 | 0.427150 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.0493 | 1.40056 | 0.700280 | − | 0.713868i | \(-0.253058\pi\) | ||||
0.700280 | + | 0.713868i | \(0.253058\pi\) | |||||||
\(374\) | −9.56379 | −0.494532 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 34.5135 | 1.77990 | ||||||||
\(377\) | −7.09850 | −0.365592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5659 | −0.953665 | −0.476832 | − | 0.878994i | \(-0.658215\pi\) | ||||
−0.476832 | + | 0.878994i | \(0.658215\pi\) | |||||||
\(380\) | −25.9105 | −1.32918 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −39.3185 | −2.01171 | ||||||||
\(383\) | −3.36015 | −0.171696 | −0.0858478 | − | 0.996308i | \(-0.527360\pi\) | ||||
−0.0858478 | + | 0.996308i | \(0.527360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.27975 | 0.218116 | ||||||||
\(386\) | 42.6052 | 2.16855 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28.7334 | −1.45872 | ||||||||
\(389\) | −10.0729 | −0.510716 | −0.255358 | − | 0.966847i | \(-0.582193\pi\) | ||||
−0.255358 | + | 0.966847i | \(0.582193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.6721 | −1.24772 | ||||||||
\(392\) | −16.5654 | −0.836680 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.7246 | −1.14485 | ||||||||
\(395\) | 3.76683 | 0.189530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.9242 | −0.598461 | −0.299230 | − | 0.954181i | \(-0.596730\pi\) | ||||
−0.299230 | + | 0.954181i | \(0.596730\pi\) | |||||||
\(398\) | 18.8247 | 0.943598 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.15842 | 0.157921 | ||||||||
\(401\) | −11.2101 | −0.559804 | −0.279902 | − | 0.960029i | \(-0.590302\pi\) | ||||
−0.279902 | + | 0.960029i | \(0.590302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.3904 | 1.51385 | ||||||||
\(404\) | 11.8477 | 0.589443 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.01272 | −0.248777 | ||||||||
\(407\) | −2.89012 | −0.143258 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.5649 | −1.46189 | −0.730944 | − | 0.682437i | \(-0.760920\pi\) | ||||
−0.730944 | + | 0.682437i | \(0.760920\pi\) | |||||||
\(410\) | 38.3577 | 1.89435 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.8001 | −1.41888 | ||||||||
\(413\) | 7.85750 | 0.386642 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.59003 | −0.274404 | ||||||||
\(416\) | −16.6226 | −0.814990 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.59699 | −0.322669 | ||||||||
\(419\) | −13.1249 | −0.641194 | −0.320597 | − | 0.947216i | \(-0.603884\pi\) | ||||
−0.320597 | + | 0.947216i | \(0.603884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.4833 | −1.92430 | −0.962149 | − | 0.272524i | \(-0.912142\pi\) | ||||
−0.962149 | + | 0.272524i | \(0.912142\pi\) | |||||||
\(422\) | −20.5831 | −1.00197 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.4077 | 0.942522 | ||||||||
\(425\) | 6.07657 | 0.294757 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.67712 | −0.0811614 | ||||||||
\(428\) | 68.6801 | 3.31978 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −56.7131 | −2.73495 | ||||||||
\(431\) | −8.99935 | −0.433483 | −0.216742 | − | 0.976229i | \(-0.569543\pi\) | ||||
−0.216742 | + | 0.976229i | \(0.569543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.8497 | −0.953916 | −0.476958 | − | 0.878926i | \(-0.658261\pi\) | ||||
−0.476958 | + | 0.878926i | \(0.658261\pi\) | |||||||
\(434\) | 21.4606 | 1.03014 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −71.6630 | −3.43203 | ||||||||
\(437\) | −17.0185 | −0.814107 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7912 | 1.18322 | 0.591609 | − | 0.806225i | \(-0.298493\pi\) | ||||
0.591609 | + | 0.806225i | \(0.298493\pi\) | |||||||
\(440\) | 10.0954 | 0.481282 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 54.0495 | 2.57087 | ||||||||
\(443\) | −11.8657 | −0.563758 | −0.281879 | − | 0.959450i | \(-0.590958\pi\) | ||||
−0.281879 | + | 0.959450i | \(0.590958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.5695 | −1.59135 | ||||||||
\(446\) | 21.0221 | 0.995427 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18.7453 | −0.885631 | ||||||||
\(449\) | −5.23662 | −0.247132 | −0.123566 | − | 0.992336i | \(-0.539433\pi\) | ||||
−0.123566 | + | 0.992336i | \(0.539433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.31673 | 0.297443 | ||||||||
\(452\) | −41.9197 | −1.97174 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −37.1948 | −1.74564 | ||||||||
\(455\) | −24.1869 | −1.13390 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.12526 | 0.426862 | 0.213431 | − | 0.976958i | \(-0.431536\pi\) | ||||
0.213431 | + | 0.976958i | \(0.431536\pi\) | |||||||
\(458\) | −31.2685 | −1.46108 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 57.3741 | 2.67508 | ||||||||
\(461\) | −2.08183 | −0.0969604 | −0.0484802 | − | 0.998824i | \(-0.515438\pi\) | ||||
−0.0484802 | + | 0.998824i | \(0.515438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.5553 | 1.28060 | 0.640302 | − | 0.768124i | \(-0.278809\pi\) | ||||
0.640302 | + | 0.768124i | \(0.278809\pi\) | |||||||
\(464\) | −2.62387 | −0.121810 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 45.7211 | 2.11799 | ||||||||
\(467\) | −27.9889 | −1.29517 | −0.647587 | − | 0.761992i | \(-0.724222\pi\) | ||||
−0.647587 | + | 0.761992i | \(0.724222\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.51089 | 0.439172 | ||||||||
\(470\) | −52.9759 | −2.44359 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.5350 | 0.853141 | ||||||||
\(473\) | −9.33950 | −0.429431 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.19155 | 0.192321 | ||||||||
\(476\) | 24.6870 | 1.13153 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −31.8798 | −1.45815 | ||||||||
\(479\) | −0.953001 | −0.0435437 | −0.0217719 | − | 0.999763i | \(-0.506931\pi\) | ||||
−0.0217719 | + | 0.999763i | \(0.506931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.3335 | 0.744741 | ||||||||
\(482\) | −60.1459 | −2.73957 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.66252 | 0.166478 | ||||||||
\(485\) | 20.0199 | 0.909058 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.8346 | −0.581591 | −0.290796 | − | 0.956785i | \(-0.593920\pi\) | ||||
−0.290796 | + | 0.956785i | \(0.593920\pi\) | |||||||
\(488\) | −3.95613 | −0.179086 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 25.4268 | 1.14867 | ||||||||
\(491\) | −39.6400 | −1.78893 | −0.894465 | − | 0.447138i | \(-0.852443\pi\) | ||||
−0.894465 | + | 0.447138i | \(0.852443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.04813 | −0.227356 | ||||||||
\(494\) | 37.2827 | 1.67743 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.2334 | 0.504394 | ||||||||
\(497\) | 4.55914 | 0.204505 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.1235 | −1.57234 | −0.786172 | − | 0.618007i | \(-0.787940\pi\) | ||||
−0.786172 | + | 0.618007i | \(0.787940\pi\) | |||||||
\(500\) | 32.6001 | 1.45792 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −38.5656 | −1.72127 | ||||||||
\(503\) | −2.69005 | −0.119943 | −0.0599717 | − | 0.998200i | \(-0.519101\pi\) | ||||
−0.0599717 | + | 0.998200i | \(0.519101\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.25482 | −0.367335 | ||||||||
\(506\) | 14.6078 | 0.649398 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.97745 | 0.265206 | ||||||||
\(509\) | −22.4595 | −0.995500 | −0.497750 | − | 0.867321i | \(-0.665840\pi\) | ||||
−0.497750 | + | 0.867321i | \(0.665840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.3403 | 1.12099 | ||||||||
\(512\) | −22.6730 | −1.00201 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 39.7557 | 1.75355 | ||||||||
\(515\) | 20.0664 | 0.884231 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.72405 | −0.383683 | ||||||||
\(518\) | 11.5341 | 0.506780 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −57.0541 | −2.50199 | ||||||||
\(521\) | −24.9298 | −1.09219 | −0.546096 | − | 0.837722i | \(-0.683887\pi\) | ||||
−0.546096 | + | 0.837722i | \(0.683887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.1551 | −0.968775 | −0.484387 | − | 0.874854i | \(-0.660957\pi\) | ||||
−0.484387 | + | 0.874854i | \(0.660957\pi\) | |||||||
\(524\) | −21.2952 | −0.930287 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.2451 | −1.05714 | ||||||||
\(527\) | 21.6122 | 0.941444 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.6845 | 0.638456 | ||||||||
\(530\) | −29.7895 | −1.29397 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.0288 | 0.738292 | ||||||||
\(533\) | −35.6988 | −1.54629 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47.8527 | −2.06885 | ||||||||
\(536\) | 22.4351 | 0.969050 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.84176 | −0.165630 | ||||||||
\(539\) | 4.18728 | 0.180359 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.9763 | 1.50375 | 0.751874 | − | 0.659307i | \(-0.229150\pi\) | ||||
0.751874 | + | 0.659307i | \(0.229150\pi\) | |||||||
\(542\) | 60.6332 | 2.60442 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.8212 | −0.506831 | ||||||||
\(545\) | 49.9310 | 2.13881 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.5082 | 1.77476 | 0.887382 | − | 0.461035i | \(-0.152522\pi\) | ||||
0.887382 | + | 0.461035i | \(0.152522\pi\) | |||||||
\(548\) | 0.456154 | 0.0194859 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.59781 | −0.153411 | ||||||||
\(551\) | −3.48214 | −0.148344 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.47562 | −0.105274 | ||||||||
\(554\) | 41.5354 | 1.76467 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.8924 | 0.886036 | ||||||||
\(557\) | 13.4014 | 0.567836 | 0.283918 | − | 0.958849i | \(-0.408366\pi\) | ||||
0.283918 | + | 0.958849i | \(0.408366\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.7819 | 2.23244 | ||||||||
\(560\) | −8.94036 | −0.377799 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 39.3819 | 1.66122 | ||||||||
\(563\) | 10.6144 | 0.447343 | 0.223671 | − | 0.974665i | \(-0.428196\pi\) | ||||
0.223671 | + | 0.974665i | \(0.428196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.2074 | 1.22877 | ||||||||
\(566\) | 51.3486 | 2.15834 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.7545 | 0.451249 | ||||||||
\(569\) | 25.0719 | 1.05107 | 0.525535 | − | 0.850772i | \(-0.323865\pi\) | ||||
0.525535 | + | 0.850772i | \(0.323865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.81795 | −0.0760790 | −0.0380395 | − | 0.999276i | \(-0.512111\pi\) | ||||
−0.0380395 | + | 0.999276i | \(0.512111\pi\) | |||||||
\(572\) | −20.6986 | −0.865452 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25.2093 | −1.05222 | ||||||||
\(575\) | −9.28143 | −0.387062 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.7010 | 1.36136 | 0.680681 | − | 0.732580i | \(-0.261684\pi\) | ||||
0.680681 | + | 0.732580i | \(0.261684\pi\) | |||||||
\(578\) | −2.01576 | −0.0838447 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.7392 | 0.487445 | ||||||||
\(581\) | 3.67386 | 0.152417 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.90573 | −0.203175 | ||||||||
\(584\) | 59.7750 | 2.47351 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.54484 | 0.311674 | ||||||||
\(587\) | −24.0218 | −0.991488 | −0.495744 | − | 0.868469i | \(-0.665104\pi\) | ||||
−0.495744 | + | 0.868469i | \(0.665104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.9079 | 0.614268 | ||||||||
\(590\) | −28.4499 | −1.17126 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.03745 | 0.248138 | ||||||||
\(593\) | 3.62291 | 0.148775 | 0.0743875 | − | 0.997229i | \(-0.476300\pi\) | ||||
0.0743875 | + | 0.997229i | \(0.476300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.2006 | −0.705156 | ||||||||
\(596\) | 73.3547 | 3.00472 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −82.5558 | −3.37596 | ||||||||
\(599\) | −19.0751 | −0.779389 | −0.389695 | − | 0.920944i | \(-0.627419\pi\) | ||||
−0.389695 | + | 0.920944i | \(0.627419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.56199 | −0.390042 | −0.195021 | − | 0.980799i | \(-0.562477\pi\) | ||||
−0.195021 | + | 0.980799i | \(0.562477\pi\) | |||||||
\(602\) | 37.2728 | 1.51912 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 29.4901 | 1.19993 | ||||||||
\(605\) | −2.55185 | −0.103747 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.3670 | −1.35432 | −0.677162 | − | 0.735834i | \(-0.736790\pi\) | ||||
−0.677162 | + | 0.735834i | \(0.736790\pi\) | |||||||
\(608\) | −8.15414 | −0.330694 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.07239 | 0.245864 | ||||||||
\(611\) | 49.3037 | 1.99462 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0516 | 0.850268 | 0.425134 | − | 0.905131i | \(-0.360227\pi\) | ||||
0.425134 | + | 0.905131i | \(0.360227\pi\) | |||||||
\(614\) | 27.1119 | 1.09415 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.63489 | −0.267327 | ||||||||
\(617\) | −3.39567 | −0.136705 | −0.0683523 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683523 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.3446 | −0.455980 | −0.227990 | − | 0.973664i | \(-0.573215\pi\) | ||||
−0.227990 | + | 0.973664i | \(0.573215\pi\) | |||||||
\(620\) | −50.2584 | −2.01843 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.9892 | −1.24255 | ||||||||
\(623\) | 22.0624 | 0.883912 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2737 | −1.21095 | ||||||||
\(626\) | −76.0098 | −3.03796 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.6437 | 1.50215 | ||||||||
\(629\) | 11.6156 | 0.463144 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.0848 | 1.75499 | 0.877494 | − | 0.479587i | \(-0.159214\pi\) | ||||
0.877494 | + | 0.479587i | \(0.159214\pi\) | |||||||
\(632\) | −5.83972 | −0.232291 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.1841 | −0.404463 | ||||||||
\(635\) | −4.16477 | −0.165274 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.6643 | −0.937613 | ||||||||
\(638\) | 2.98889 | 0.118331 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 52.8602 | 2.08948 | ||||||||
\(641\) | 5.41854 | 0.214019 | 0.107010 | − | 0.994258i | \(-0.465872\pi\) | ||||
0.107010 | + | 0.994258i | \(0.465872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.3418 | 0.762768 | 0.381384 | − | 0.924417i | \(-0.375448\pi\) | ||||
0.381384 | + | 0.924417i | \(0.375448\pi\) | |||||||
\(644\) | −37.7072 | −1.48587 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.5137 | 1.04317 | ||||||||
\(647\) | −21.8968 | −0.860852 | −0.430426 | − | 0.902626i | \(-0.641637\pi\) | ||||
−0.430426 | + | 0.902626i | \(0.641637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.68512 | −0.183907 | ||||||||
\(650\) | 20.3329 | 0.797523 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.4894 | −0.959078 | ||||||||
\(653\) | 4.80308 | 0.187959 | 0.0939795 | − | 0.995574i | \(-0.470041\pi\) | ||||
0.0939795 | + | 0.995574i | \(0.470041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8374 | 0.579746 | ||||||||
\(656\) | −13.1956 | −0.515202 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 34.8166 | 1.35729 | ||||||||
\(659\) | 29.9093 | 1.16510 | 0.582550 | − | 0.812795i | \(-0.302055\pi\) | ||||
0.582550 | + | 0.812795i | \(0.302055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.4154 | −1.29971 | −0.649854 | − | 0.760059i | \(-0.725170\pi\) | ||||
−0.649854 | + | 0.760059i | \(0.725170\pi\) | |||||||
\(662\) | −72.8523 | −2.83149 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.66623 | 0.336315 | ||||||||
\(665\) | −11.8648 | −0.460096 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.71057 | 0.298555 | ||||||||
\(668\) | −51.3791 | −1.98792 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −34.4364 | −1.33039 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.76575 | −0.299348 | −0.149674 | − | 0.988735i | \(-0.547822\pi\) | ||||
−0.149674 | + | 0.988735i | \(0.547822\pi\) | |||||||
\(674\) | 47.9165 | 1.84567 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 69.3649 | 2.66788 | ||||||||
\(677\) | −32.9643 | −1.26692 | −0.633460 | − | 0.773775i | \(-0.718366\pi\) | ||||
−0.633460 | + | 0.773775i | \(0.718366\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.1574 | −0.504935 | ||||||||
\(680\) | −40.5743 | −1.55595 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.7961 | −0.489990 | ||||||||
\(683\) | 16.7372 | 0.640429 | 0.320215 | − | 0.947345i | \(-0.396245\pi\) | ||||
0.320215 | + | 0.947345i | \(0.396245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.317824 | −0.0121434 | ||||||||
\(686\) | −44.6470 | −1.70463 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.5101 | 0.743817 | ||||||||
\(689\) | 27.7246 | 1.05622 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.4790 | −0.664931 | −0.332465 | − | 0.943115i | \(-0.607880\pi\) | ||||
−0.332465 | + | 0.943115i | \(0.607880\pi\) | |||||||
\(692\) | −37.9328 | −1.44199 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 75.6233 | 2.87062 | ||||||||
\(695\) | −14.5567 | −0.552169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.3874 | −0.961616 | ||||||||
\(698\) | −67.6198 | −2.55945 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.28702 | 0.351016 | ||||||||
\(701\) | −20.9278 | −0.790434 | −0.395217 | − | 0.918588i | \(-0.629331\pi\) | ||||
−0.395217 | + | 0.918588i | \(0.629331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.01230 | 0.302190 | ||||||||
\(704\) | 11.1771 | 0.421252 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.2808 | −1.25254 | ||||||||
\(707\) | 5.42520 | 0.204036 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1466 | −0.906845 | −0.453423 | − | 0.891296i | \(-0.649797\pi\) | ||||
−0.453423 | + | 0.891296i | \(0.649797\pi\) | |||||||
\(710\) | −16.5074 | −0.619513 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 52.0427 | 1.95038 | ||||||||
\(713\) | −33.0108 | −1.23626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.4217 | 0.539341 | ||||||||
\(716\) | 26.8992 | 1.00527 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.7938 | −0.850659 | ||||||||
\(719\) | 32.0699 | 1.19601 | 0.598003 | − | 0.801494i | \(-0.295961\pi\) | ||||
0.598003 | + | 0.801494i | \(0.295961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.1880 | −0.491145 | ||||||||
\(722\) | −26.9236 | −1.00199 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.94566 | −0.0723098 | ||||||||
\(725\) | −1.89906 | −0.0705293 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.5250 | −0.835406 | −0.417703 | − | 0.908584i | \(-0.637165\pi\) | ||||
−0.417703 | + | 0.908584i | \(0.637165\pi\) | |||||||
\(728\) | 37.4969 | 1.38973 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −91.7506 | −3.39584 | ||||||||
\(731\) | 37.5361 | 1.38832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.0196 | 1.66284 | 0.831418 | − | 0.555648i | \(-0.187530\pi\) | ||||
0.831418 | + | 0.555648i | \(0.187530\pi\) | |||||||
\(734\) | −48.9606 | −1.80717 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.0559 | 0.665549 | ||||||||
\(737\) | −5.67098 | −0.208893 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.6313 | −1.42108 | −0.710539 | − | 0.703658i | \(-0.751549\pi\) | ||||
−0.710539 | + | 0.703658i | \(0.751549\pi\) | |||||||
\(740\) | −27.0117 | −0.992968 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.5782 | 0.718737 | ||||||||
\(743\) | 40.6081 | 1.48977 | 0.744884 | − | 0.667194i | \(-0.232505\pi\) | ||||
0.744884 | + | 0.667194i | \(0.232505\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −51.1097 | −1.87251 | ||||||||
\(746\) | 64.3666 | 2.35663 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.7199 | −0.538213 | ||||||||
\(749\) | 31.4496 | 1.14914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.7212 | 0.902088 | 0.451044 | − | 0.892502i | \(-0.351052\pi\) | ||||
0.451044 | + | 0.892502i | \(0.351052\pi\) | |||||||
\(752\) | 18.2245 | 0.664578 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.8916 | −0.615157 | ||||||||
\(755\) | −20.5471 | −0.747787 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0864 | 0.802743 | 0.401371 | − | 0.915915i | \(-0.368534\pi\) | ||||
0.401371 | + | 0.915915i | \(0.368534\pi\) | |||||||
\(758\) | −44.1794 | −1.60467 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −27.9877 | −1.01522 | ||||||||
\(761\) | 4.10116 | 0.148667 | 0.0743334 | − | 0.997233i | \(-0.476317\pi\) | ||||
0.0743334 | + | 0.997233i | \(0.476317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.8155 | −1.18800 | ||||||||
\(764\) | −60.5161 | −2.18940 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.99583 | −0.288901 | ||||||||
\(767\) | 26.4778 | 0.956060 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.84340 | −0.0664747 | −0.0332374 | − | 0.999447i | \(-0.510582\pi\) | ||||
−0.0332374 | + | 0.999447i | \(0.510582\pi\) | |||||||
\(770\) | 10.1841 | 0.367010 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 65.5749 | 2.36009 | ||||||||
\(773\) | 46.4688 | 1.67137 | 0.835684 | − | 0.549211i | \(-0.185072\pi\) | ||||
0.835684 | + | 0.549211i | \(0.185072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.13032 | 0.292050 | ||||||||
\(776\) | −31.0369 | −1.11416 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.9695 | −0.859348 | ||||||||
\(779\) | −17.5119 | −0.627429 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.71844 | −0.0972734 | ||||||||
\(782\) | −58.7099 | −2.09946 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.74719 | −0.312400 | ||||||||
\(785\) | −26.2281 | −0.936123 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.6731 | −0.950795 | −0.475397 | − | 0.879771i | \(-0.657696\pi\) | ||||
−0.475397 | + | 0.879771i | \(0.657696\pi\) | |||||||
\(788\) | −34.9761 | −1.24597 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.96357 | 0.318909 | ||||||||
\(791\) | −19.1956 | −0.682517 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.65147 | −0.200690 | ||||||||
\(794\) | −28.3750 | −1.00699 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.9737 | 1.02694 | ||||||||
\(797\) | 22.8323 | 0.808763 | 0.404381 | − | 0.914590i | \(-0.367487\pi\) | ||||
0.404381 | + | 0.914590i | \(0.367487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.0625 | 1.24042 | ||||||||
\(800\) | −4.44704 | −0.157227 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.6755 | −0.941945 | ||||||||
\(803\) | −15.1095 | −0.533202 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.2724 | 0.925980 | ||||||||
\(806\) | 72.3170 | 2.54726 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.7974 | 0.450213 | ||||||||
\(809\) | −5.39701 | −0.189749 | −0.0948744 | − | 0.995489i | \(-0.530245\pi\) | ||||
−0.0948744 | + | 0.995489i | \(0.530245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.8393 | −1.75009 | −0.875047 | − | 0.484037i | \(-0.839170\pi\) | ||||
−0.875047 | + | 0.484037i | \(0.839170\pi\) | |||||||
\(812\) | −7.71522 | −0.270751 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.87735 | −0.241051 | ||||||||
\(815\) | 17.0629 | 0.597688 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.8919 | 0.905844 | ||||||||
\(818\) | −70.3527 | −2.45982 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 59.0374 | 2.06168 | ||||||||
\(821\) | −17.3451 | −0.605347 | −0.302674 | − | 0.953094i | \(-0.597879\pi\) | ||||
−0.302674 | + | 0.953094i | \(0.597879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.8810 | −1.07644 | −0.538221 | − | 0.842804i | \(-0.680904\pi\) | ||||
−0.538221 | + | 0.842804i | \(0.680904\pi\) | |||||||
\(824\) | −31.1089 | −1.08373 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.6977 | 0.650578 | ||||||||
\(827\) | −52.0029 | −1.80832 | −0.904160 | − | 0.427195i | \(-0.859502\pi\) | ||||
−0.904160 | + | 0.427195i | \(0.859502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.0581 | 1.66913 | 0.834563 | − | 0.550912i | \(-0.185720\pi\) | ||||
0.834563 | + | 0.550912i | \(0.185720\pi\) | |||||||
\(830\) | −13.3021 | −0.461722 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −63.1670 | −2.18992 | ||||||||
\(833\) | −16.8290 | −0.583089 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.7983 | 1.23885 | ||||||||
\(836\) | −10.1536 | −0.351170 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.2321 | −1.07890 | ||||||||
\(839\) | 34.1026 | 1.17735 | 0.588676 | − | 0.808369i | \(-0.299649\pi\) | ||||
0.588676 | + | 0.808369i | \(0.299649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4223 | −0.945598 | ||||||||
\(842\) | −93.9546 | −3.23789 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −31.6800 | −1.09047 | ||||||||
\(845\) | −48.3298 | −1.66260 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.67712 | 0.0576264 | ||||||||
\(848\) | 10.2480 | 0.351919 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.4598 | 0.495968 | ||||||||
\(851\) | −17.7418 | −0.608181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.66881 | −0.0571391 | −0.0285695 | − | 0.999592i | \(-0.509095\pi\) | ||||
−0.0285695 | + | 0.999592i | \(0.509095\pi\) | |||||||
\(854\) | −3.99087 | −0.136565 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 74.1860 | 2.53562 | ||||||||
\(857\) | 52.5109 | 1.79374 | 0.896869 | − | 0.442297i | \(-0.145836\pi\) | ||||
0.896869 | + | 0.442297i | \(0.145836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.22377 | 0.246472 | 0.123236 | − | 0.992377i | \(-0.460673\pi\) | ||||
0.123236 | + | 0.992377i | \(0.460673\pi\) | |||||||
\(860\) | −87.2887 | −2.97652 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.4149 | −0.729394 | ||||||||
\(863\) | −47.7485 | −1.62538 | −0.812688 | − | 0.582698i | \(-0.801997\pi\) | ||||
−0.812688 | + | 0.582698i | \(0.801997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.4296 | 0.898632 | ||||||||
\(866\) | −47.2344 | −1.60509 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33.0307 | 1.12113 | ||||||||
\(869\) | 1.47612 | 0.0500739 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0494 | 1.08595 | ||||||||
\(872\) | −77.4080 | −2.62137 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −40.4974 | −1.36984 | ||||||||
\(875\) | 14.9280 | 0.504660 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.6923 | −0.597427 | −0.298714 | − | 0.954343i | \(-0.596558\pi\) | ||||
−0.298714 | + | 0.954343i | \(0.596558\pi\) | |||||||
\(878\) | 58.9932 | 1.99092 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.33079 | 0.179701 | ||||||||
\(881\) | −18.9137 | −0.637219 | −0.318610 | − | 0.947886i | \(-0.603216\pi\) | ||||
−0.318610 | + | 0.947886i | \(0.603216\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 59.1263 | 1.98976 | 0.994878 | − | 0.101079i | \(-0.0322294\pi\) | ||||
0.994878 | + | 0.101079i | \(0.0322294\pi\) | |||||||
\(884\) | 83.1891 | 2.79795 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.2357 | −0.948599 | ||||||||
\(887\) | 34.1377 | 1.14623 | 0.573117 | − | 0.819474i | \(-0.305734\pi\) | ||||
0.573117 | + | 0.819474i | \(0.305734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.73716 | 0.0918012 | ||||||||
\(890\) | −79.8821 | −2.67765 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 32.3558 | 1.08335 | ||||||||
\(893\) | 24.1857 | 0.809344 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.7420 | −0.626475 | ||||||||
\(896\) | −34.7406 | −1.16060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.4611 | −0.415832 | ||||||||
\(899\) | −6.75429 | −0.225268 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7165 | 0.656851 | ||||||||
\(902\) | 15.0313 | 0.500488 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −45.2803 | −1.50600 | ||||||||
\(905\) | 1.35563 | 0.0450628 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.40299 | 0.279017 | 0.139508 | − | 0.990221i | \(-0.455448\pi\) | ||||
0.139508 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(908\) | −57.2476 | −1.89983 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −57.5552 | −1.90794 | ||||||||
\(911\) | 12.5927 | 0.417214 | 0.208607 | − | 0.978000i | \(-0.433107\pi\) | ||||
0.208607 | + | 0.978000i | \(0.433107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.19058 | −0.0724977 | ||||||||
\(914\) | 21.7145 | 0.718252 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −48.1262 | −1.59013 | ||||||||
\(917\) | −9.75138 | −0.322019 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.7102 | 1.70576 | 0.852881 | − | 0.522105i | \(-0.174853\pi\) | ||||
0.852881 | + | 0.522105i | \(0.174853\pi\) | |||||||
\(920\) | 61.9736 | 2.04321 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.95393 | −0.163149 | ||||||||
\(923\) | 15.3632 | 0.505685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.36968 | 0.143674 | ||||||||
\(926\) | 65.5707 | 2.15479 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.69439 | 0.121274 | ||||||||
\(929\) | 43.9138 | 1.44076 | 0.720382 | − | 0.693577i | \(-0.243966\pi\) | ||||
0.720382 | + | 0.693577i | \(0.243966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.6084 | −0.380450 | ||||||||
\(932\) | 70.3707 | 2.30507 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −66.6026 | −2.17930 | ||||||||
\(935\) | 10.2561 | 0.335409 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6324 | 0.478021 | 0.239010 | − | 0.971017i | \(-0.423177\pi\) | ||||
0.239010 | + | 0.971017i | \(0.423177\pi\) | |||||||
\(938\) | 22.6322 | 0.738966 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −81.5366 | −2.65943 | ||||||||
\(941\) | −46.6148 | −1.51960 | −0.759799 | − | 0.650158i | \(-0.774703\pi\) | ||||
−0.759799 | + | 0.650158i | \(0.774703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.7770 | 1.26275 | ||||||||
\(944\) | 9.78719 | 0.318546 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.2243 | −0.722575 | ||||||||
\(947\) | −6.99474 | −0.227299 | −0.113649 | − | 0.993521i | \(-0.536254\pi\) | ||||
−0.113649 | + | 0.993521i | \(0.536254\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 85.3907 | 2.77190 | ||||||||
\(950\) | 9.97422 | 0.323607 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 26.6661 | 0.864253 | ||||||||
\(953\) | −39.6795 | −1.28534 | −0.642672 | − | 0.766142i | \(-0.722174\pi\) | ||||
−0.642672 | + | 0.766142i | \(0.722174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.1645 | 1.36441 | ||||||||
\(956\) | −49.0670 | −1.58694 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.26777 | −0.0732682 | ||||||||
\(959\) | 0.208879 | 0.00674506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.08330 | −0.0672033 | ||||||||
\(962\) | 38.8672 | 1.25313 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −92.5722 | −2.98155 | ||||||||
\(965\) | −45.6891 | −1.47079 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.5820 | −1.81956 | −0.909778 | − | 0.415096i | \(-0.863748\pi\) | ||||
−0.909778 | + | 0.415096i | \(0.863748\pi\) | |||||||
\(968\) | 3.95613 | 0.127155 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 47.6395 | 1.52961 | ||||||||
\(971\) | −23.7722 | −0.762885 | −0.381443 | − | 0.924392i | \(-0.624573\pi\) | ||||
−0.381443 | + | 0.924392i | \(0.624573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.56692 | 0.306702 | ||||||||
\(974\) | −30.5413 | −0.978605 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.08899 | −0.0668670 | ||||||||
\(977\) | 43.0284 | 1.37660 | 0.688300 | − | 0.725426i | \(-0.258357\pi\) | ||||
0.688300 | + | 0.725426i | \(0.258357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.1550 | −0.420434 | ||||||||
\(980\) | 39.1351 | 1.25013 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −94.3276 | −3.01011 | ||||||||
\(983\) | −28.8215 | −0.919263 | −0.459631 | − | 0.888110i | \(-0.652018\pi\) | ||||
−0.459631 | + | 0.888110i | \(0.652018\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.3695 | 0.776478 | ||||||||
\(986\) | −12.0126 | −0.382558 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 57.3828 | 1.82559 | ||||||||
\(989\) | −57.3330 | −1.82308 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.66098 | 0.179827 | 0.0899135 | − | 0.995950i | \(-0.471341\pi\) | ||||
0.0899135 | + | 0.995950i | \(0.471341\pi\) | |||||||
\(992\) | −15.8165 | −0.502176 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.8490 | 0.344108 | ||||||||
\(995\) | −20.1873 | −0.639981 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.8029 | −1.60894 | −0.804472 | − | 0.593991i | \(-0.797552\pi\) | ||||
−0.804472 | + | 0.593991i | \(0.797552\pi\) | |||||||
\(998\) | −83.5801 | −2.64568 | ||||||||
\(999\) | 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 | 6039.2.a.i.1.12 | 13 | ||
3.2 | odd | 2 | 2013.2.a.e.1.2 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.2 | ✓ | 13 | 3.2 | odd | 2 | ||
6039.2.a.i.1.12 | 13 | 1.1 | even | 1 | trivial |