Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.7457527933.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.52358\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.07710 | 1.46873 | 0.734367 | − | 0.678753i | \(-0.237479\pi\) | ||||
0.734367 | + | 0.678753i | \(0.237479\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.31436 | 1.15718 | ||||||||
\(5\) | 2.30039 | 1.02877 | 0.514383 | − | 0.857561i | \(-0.328021\pi\) | ||||
0.514383 | + | 0.857561i | \(0.328021\pi\) | |||||||
\(6\) | −2.07710 | −0.847974 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.652949 | 0.230852 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.77814 | 1.51098 | ||||||||
\(11\) | −2.24173 | −0.675906 | −0.337953 | − | 0.941163i | \(-0.609735\pi\) | ||||
−0.337953 | + | 0.941163i | \(0.609735\pi\) | |||||||
\(12\) | −2.31436 | −0.668097 | ||||||||
\(13\) | −4.05386 | −1.12434 | −0.562169 | − | 0.827022i | \(-0.690033\pi\) | ||||
−0.562169 | + | 0.827022i | \(0.690033\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.30039 | −0.593958 | ||||||||
\(16\) | −3.27247 | −0.818117 | ||||||||
\(17\) | −1.22520 | −0.297156 | −0.148578 | − | 0.988901i | \(-0.547470\pi\) | ||||
−0.148578 | + | 0.988901i | \(0.547470\pi\) | |||||||
\(18\) | 2.07710 | 0.489578 | ||||||||
\(19\) | −4.41144 | −1.01205 | −0.506026 | − | 0.862518i | \(-0.668886\pi\) | ||||
−0.506026 | + | 0.862518i | \(0.668886\pi\) | |||||||
\(20\) | 5.32392 | 1.19046 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.65630 | −0.992726 | ||||||||
\(23\) | 6.56124 | 1.36811 | 0.684056 | − | 0.729429i | \(-0.260214\pi\) | ||||
0.684056 | + | 0.729429i | \(0.260214\pi\) | |||||||
\(24\) | −0.652949 | −0.133283 | ||||||||
\(25\) | 0.291790 | 0.0583580 | ||||||||
\(26\) | −8.42028 | −1.65135 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.41695 | 0.634511 | 0.317255 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317255 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(30\) | −4.77814 | −0.872366 | ||||||||
\(31\) | 1.07464 | 0.193011 | 0.0965056 | − | 0.995332i | \(-0.469233\pi\) | ||||
0.0965056 | + | 0.995332i | \(0.469233\pi\) | |||||||
\(32\) | −8.10315 | −1.43245 | ||||||||
\(33\) | 2.24173 | 0.390235 | ||||||||
\(34\) | −2.54488 | −0.436443 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.31436 | 0.385726 | ||||||||
\(37\) | −1.63983 | −0.269587 | −0.134793 | − | 0.990874i | \(-0.543037\pi\) | ||||
−0.134793 | + | 0.990874i | \(0.543037\pi\) | |||||||
\(38\) | −9.16300 | −1.48644 | ||||||||
\(39\) | 4.05386 | 0.649137 | ||||||||
\(40\) | 1.50204 | 0.237493 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.67207 | −0.712484 | −0.356242 | − | 0.934394i | \(-0.615942\pi\) | ||||
−0.356242 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(44\) | −5.18815 | −0.782144 | ||||||||
\(45\) | 2.30039 | 0.342922 | ||||||||
\(46\) | 13.6284 | 2.00939 | ||||||||
\(47\) | −10.9409 | −1.59589 | −0.797947 | − | 0.602727i | \(-0.794081\pi\) | ||||
−0.797947 | + | 0.602727i | \(0.794081\pi\) | |||||||
\(48\) | 3.27247 | 0.472340 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.606078 | 0.0857123 | ||||||||
\(51\) | 1.22520 | 0.171563 | ||||||||
\(52\) | −9.38207 | −1.30106 | ||||||||
\(53\) | −3.43644 | −0.472032 | −0.236016 | − | 0.971749i | \(-0.575842\pi\) | ||||
−0.236016 | + | 0.971749i | \(0.575842\pi\) | |||||||
\(54\) | −2.07710 | −0.282658 | ||||||||
\(55\) | −5.15684 | −0.695349 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.41144 | 0.584309 | ||||||||
\(58\) | 7.09735 | 0.931927 | ||||||||
\(59\) | −9.90021 | −1.28890 | −0.644449 | − | 0.764648i | \(-0.722913\pi\) | ||||
−0.644449 | + | 0.764648i | \(0.722913\pi\) | |||||||
\(60\) | −5.32392 | −0.687315 | ||||||||
\(61\) | −5.18833 | −0.664298 | −0.332149 | − | 0.943227i | \(-0.607774\pi\) | ||||
−0.332149 | + | 0.943227i | \(0.607774\pi\) | |||||||
\(62\) | 2.23214 | 0.283482 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.2861 | −1.28577 | ||||||||
\(65\) | −9.32545 | −1.15668 | ||||||||
\(66\) | 4.65630 | 0.573151 | ||||||||
\(67\) | 10.9161 | 1.33361 | 0.666806 | − | 0.745231i | \(-0.267661\pi\) | ||||
0.666806 | + | 0.745231i | \(0.267661\pi\) | |||||||
\(68\) | −2.83556 | −0.343862 | ||||||||
\(69\) | −6.56124 | −0.789880 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.24347 | −0.622286 | −0.311143 | − | 0.950363i | \(-0.600712\pi\) | ||||
−0.311143 | + | 0.950363i | \(0.600712\pi\) | |||||||
\(72\) | 0.652949 | 0.0769507 | ||||||||
\(73\) | −5.69973 | −0.667103 | −0.333551 | − | 0.942732i | \(-0.608247\pi\) | ||||
−0.333551 | + | 0.942732i | \(0.608247\pi\) | |||||||
\(74\) | −3.40610 | −0.395951 | ||||||||
\(75\) | −0.291790 | −0.0336930 | ||||||||
\(76\) | −10.2096 | −1.17112 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.42028 | 0.953409 | ||||||||
\(79\) | 3.55265 | 0.399704 | 0.199852 | − | 0.979826i | \(-0.435954\pi\) | ||||
0.199852 | + | 0.979826i | \(0.435954\pi\) | |||||||
\(80\) | −7.52795 | −0.841651 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.07710 | −0.229378 | ||||||||
\(83\) | −2.44743 | −0.268640 | −0.134320 | − | 0.990938i | \(-0.542885\pi\) | ||||
−0.134320 | + | 0.990938i | \(0.542885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.81845 | −0.305703 | ||||||||
\(86\) | −9.70437 | −1.04645 | ||||||||
\(87\) | −3.41695 | −0.366335 | ||||||||
\(88\) | −1.46373 | −0.156034 | ||||||||
\(89\) | −5.51735 | −0.584837 | −0.292419 | − | 0.956290i | \(-0.594460\pi\) | ||||
−0.292419 | + | 0.956290i | \(0.594460\pi\) | |||||||
\(90\) | 4.77814 | 0.503661 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.1850 | 1.58315 | ||||||||
\(93\) | −1.07464 | −0.111435 | ||||||||
\(94\) | −22.7254 | −2.34394 | ||||||||
\(95\) | −10.1480 | −1.04116 | ||||||||
\(96\) | 8.10315 | 0.827025 | ||||||||
\(97\) | 3.88945 | 0.394914 | 0.197457 | − | 0.980312i | \(-0.436732\pi\) | ||||
0.197457 | + | 0.980312i | \(0.436732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.24173 | −0.225302 | ||||||||
\(100\) | 0.675306 | 0.0675306 | ||||||||
\(101\) | −11.7539 | −1.16956 | −0.584780 | − | 0.811192i | \(-0.698819\pi\) | ||||
−0.584780 | + | 0.811192i | \(0.698819\pi\) | |||||||
\(102\) | 2.54488 | 0.251980 | ||||||||
\(103\) | 7.81801 | 0.770331 | 0.385165 | − | 0.922848i | \(-0.374144\pi\) | ||||
0.385165 | + | 0.922848i | \(0.374144\pi\) | |||||||
\(104\) | −2.64696 | −0.259556 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.13785 | −0.693289 | ||||||||
\(107\) | 14.9202 | 1.44239 | 0.721193 | − | 0.692734i | \(-0.243594\pi\) | ||||
0.721193 | + | 0.692734i | \(0.243594\pi\) | |||||||
\(108\) | −2.31436 | −0.222699 | ||||||||
\(109\) | −2.44790 | −0.234466 | −0.117233 | − | 0.993104i | \(-0.537402\pi\) | ||||
−0.117233 | + | 0.993104i | \(0.537402\pi\) | |||||||
\(110\) | −10.7113 | −1.02128 | ||||||||
\(111\) | 1.63983 | 0.155646 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.66753 | −0.533156 | −0.266578 | − | 0.963813i | \(-0.585893\pi\) | ||||
−0.266578 | + | 0.963813i | \(0.585893\pi\) | |||||||
\(114\) | 9.16300 | 0.858194 | ||||||||
\(115\) | 15.0934 | 1.40747 | ||||||||
\(116\) | 7.90803 | 0.734242 | ||||||||
\(117\) | −4.05386 | −0.374779 | ||||||||
\(118\) | −20.5637 | −1.89305 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.50204 | −0.137116 | ||||||||
\(121\) | −5.97466 | −0.543151 | ||||||||
\(122\) | −10.7767 | −0.975676 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 2.48710 | 0.223348 | ||||||||
\(125\) | −10.8307 | −0.968729 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.81071 | 0.515617 | 0.257809 | − | 0.966196i | \(-0.417000\pi\) | ||||
0.257809 | + | 0.966196i | \(0.417000\pi\) | |||||||
\(128\) | −5.15907 | −0.456001 | ||||||||
\(129\) | 4.67207 | 0.411353 | ||||||||
\(130\) | −19.3699 | −1.69885 | ||||||||
\(131\) | −14.4403 | −1.26165 | −0.630826 | − | 0.775925i | \(-0.717284\pi\) | ||||
−0.630826 | + | 0.775925i | \(0.717284\pi\) | |||||||
\(132\) | 5.18815 | 0.451571 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 22.6738 | 1.95872 | ||||||||
\(135\) | −2.30039 | −0.197986 | ||||||||
\(136\) | −0.799996 | −0.0685991 | ||||||||
\(137\) | 7.95642 | 0.679762 | 0.339881 | − | 0.940468i | \(-0.389613\pi\) | ||||
0.339881 | + | 0.940468i | \(0.389613\pi\) | |||||||
\(138\) | −13.6284 | −1.16012 | ||||||||
\(139\) | 8.96101 | 0.760063 | 0.380031 | − | 0.924974i | \(-0.375913\pi\) | ||||
0.380031 | + | 0.924974i | \(0.375913\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.9409 | 0.921390 | ||||||||
\(142\) | −10.8912 | −0.913972 | ||||||||
\(143\) | 9.08764 | 0.759947 | ||||||||
\(144\) | −3.27247 | −0.272706 | ||||||||
\(145\) | 7.86030 | 0.652763 | ||||||||
\(146\) | −11.8389 | −0.979796 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.79515 | −0.311960 | ||||||||
\(149\) | −3.54749 | −0.290622 | −0.145311 | − | 0.989386i | \(-0.546418\pi\) | ||||
−0.145311 | + | 0.989386i | \(0.546418\pi\) | |||||||
\(150\) | −0.606078 | −0.0494860 | ||||||||
\(151\) | −8.99035 | −0.731624 | −0.365812 | − | 0.930689i | \(-0.619209\pi\) | ||||
−0.365812 | + | 0.930689i | \(0.619209\pi\) | |||||||
\(152\) | −2.88044 | −0.233635 | ||||||||
\(153\) | −1.22520 | −0.0990519 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.47209 | 0.198563 | ||||||||
\(156\) | 9.38207 | 0.751166 | ||||||||
\(157\) | 7.01626 | 0.559958 | 0.279979 | − | 0.960006i | \(-0.409672\pi\) | ||||
0.279979 | + | 0.960006i | \(0.409672\pi\) | |||||||
\(158\) | 7.37921 | 0.587059 | ||||||||
\(159\) | 3.43644 | 0.272528 | ||||||||
\(160\) | −18.6404 | −1.47365 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.07710 | 0.163193 | ||||||||
\(163\) | 18.5576 | 1.45355 | 0.726773 | − | 0.686878i | \(-0.241019\pi\) | ||||
0.726773 | + | 0.686878i | \(0.241019\pi\) | |||||||
\(164\) | −2.31436 | −0.180721 | ||||||||
\(165\) | 5.15684 | 0.401460 | ||||||||
\(166\) | −5.08356 | −0.394561 | ||||||||
\(167\) | −14.8071 | −1.14581 | −0.572905 | − | 0.819622i | \(-0.694184\pi\) | ||||
−0.572905 | + | 0.819622i | \(0.694184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.43376 | 0.264135 | ||||||||
\(170\) | −5.85420 | −0.448997 | ||||||||
\(171\) | −4.41144 | −0.337351 | ||||||||
\(172\) | −10.8128 | −0.824470 | ||||||||
\(173\) | 21.1741 | 1.60984 | 0.804920 | − | 0.593383i | \(-0.202208\pi\) | ||||
0.804920 | + | 0.593383i | \(0.202208\pi\) | |||||||
\(174\) | −7.09735 | −0.538049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.33598 | 0.552971 | ||||||||
\(177\) | 9.90021 | 0.744145 | ||||||||
\(178\) | −11.4601 | −0.858970 | ||||||||
\(179\) | 7.08941 | 0.529887 | 0.264944 | − | 0.964264i | \(-0.414647\pi\) | ||||
0.264944 | + | 0.964264i | \(0.414647\pi\) | |||||||
\(180\) | 5.32392 | 0.396821 | ||||||||
\(181\) | −24.0383 | −1.78675 | −0.893375 | − | 0.449312i | \(-0.851669\pi\) | ||||
−0.893375 | + | 0.449312i | \(0.851669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.18833 | 0.383532 | ||||||||
\(184\) | 4.28415 | 0.315832 | ||||||||
\(185\) | −3.77225 | −0.277341 | ||||||||
\(186\) | −2.23214 | −0.163668 | ||||||||
\(187\) | 2.74657 | 0.200849 | ||||||||
\(188\) | −25.3211 | −1.84673 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.0785 | −1.52919 | ||||||||
\(191\) | 19.7740 | 1.43080 | 0.715399 | − | 0.698716i | \(-0.246245\pi\) | ||||
0.715399 | + | 0.698716i | \(0.246245\pi\) | |||||||
\(192\) | 10.2861 | 0.742338 | ||||||||
\(193\) | −10.7386 | −0.772985 | −0.386492 | − | 0.922293i | \(-0.626313\pi\) | ||||
−0.386492 | + | 0.922293i | \(0.626313\pi\) | |||||||
\(194\) | 8.07879 | 0.580023 | ||||||||
\(195\) | 9.32545 | 0.667809 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.6837 | −1.82989 | −0.914944 | − | 0.403580i | \(-0.867766\pi\) | ||||
−0.914944 | + | 0.403580i | \(0.867766\pi\) | |||||||
\(198\) | −4.65630 | −0.330909 | ||||||||
\(199\) | −12.3661 | −0.876611 | −0.438305 | − | 0.898826i | \(-0.644421\pi\) | ||||
−0.438305 | + | 0.898826i | \(0.644421\pi\) | |||||||
\(200\) | 0.190524 | 0.0134721 | ||||||||
\(201\) | −10.9161 | −0.769961 | ||||||||
\(202\) | −24.4141 | −1.71777 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.83556 | 0.198529 | ||||||||
\(205\) | −2.30039 | −0.160666 | ||||||||
\(206\) | 16.2388 | 1.13141 | ||||||||
\(207\) | 6.56124 | 0.456037 | ||||||||
\(208\) | 13.2661 | 0.919840 | ||||||||
\(209\) | 9.88923 | 0.684053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7379 | −0.876916 | −0.438458 | − | 0.898752i | \(-0.644475\pi\) | ||||
−0.438458 | + | 0.898752i | \(0.644475\pi\) | |||||||
\(212\) | −7.95315 | −0.546225 | ||||||||
\(213\) | 5.24347 | 0.359277 | ||||||||
\(214\) | 30.9907 | 2.11848 | ||||||||
\(215\) | −10.7476 | −0.732979 | ||||||||
\(216\) | −0.652949 | −0.0444275 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.08454 | −0.344368 | ||||||||
\(219\) | 5.69973 | 0.385152 | ||||||||
\(220\) | −11.9348 | −0.804642 | ||||||||
\(221\) | 4.96680 | 0.334103 | ||||||||
\(222\) | 3.40610 | 0.228602 | ||||||||
\(223\) | 14.5408 | 0.973721 | 0.486861 | − | 0.873480i | \(-0.338142\pi\) | ||||
0.486861 | + | 0.873480i | \(0.338142\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.291790 | 0.0194527 | ||||||||
\(226\) | −11.7720 | −0.783064 | ||||||||
\(227\) | 12.7598 | 0.846898 | 0.423449 | − | 0.905920i | \(-0.360819\pi\) | ||||
0.423449 | + | 0.905920i | \(0.360819\pi\) | |||||||
\(228\) | 10.2096 | 0.676149 | ||||||||
\(229\) | 16.3536 | 1.08067 | 0.540337 | − | 0.841448i | \(-0.318297\pi\) | ||||
0.540337 | + | 0.841448i | \(0.318297\pi\) | |||||||
\(230\) | 31.3505 | 2.06719 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.23109 | 0.146478 | ||||||||
\(233\) | 25.6813 | 1.68244 | 0.841218 | − | 0.540696i | \(-0.181839\pi\) | ||||
0.841218 | + | 0.540696i | \(0.181839\pi\) | |||||||
\(234\) | −8.42028 | −0.550451 | ||||||||
\(235\) | −25.1683 | −1.64180 | ||||||||
\(236\) | −22.9126 | −1.49148 | ||||||||
\(237\) | −3.55265 | −0.230769 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.68343 | −0.432315 | −0.216158 | − | 0.976359i | \(-0.569352\pi\) | ||||
−0.216158 | + | 0.976359i | \(0.569352\pi\) | |||||||
\(240\) | 7.52795 | 0.485927 | ||||||||
\(241\) | 12.8119 | 0.825289 | 0.412645 | − | 0.910892i | \(-0.364605\pi\) | ||||
0.412645 | + | 0.910892i | \(0.364605\pi\) | |||||||
\(242\) | −12.4100 | −0.797744 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.0076 | −0.768711 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.07710 | 0.132431 | ||||||||
\(247\) | 17.8833 | 1.13789 | ||||||||
\(248\) | 0.701685 | 0.0445570 | ||||||||
\(249\) | 2.44743 | 0.155099 | ||||||||
\(250\) | −22.4965 | −1.42280 | ||||||||
\(251\) | 20.6747 | 1.30498 | 0.652488 | − | 0.757799i | \(-0.273725\pi\) | ||||
0.652488 | + | 0.757799i | \(0.273725\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.7085 | −0.924716 | ||||||||
\(254\) | 12.0694 | 0.757304 | ||||||||
\(255\) | 2.81845 | 0.176498 | ||||||||
\(256\) | 9.85637 | 0.616023 | ||||||||
\(257\) | −26.3985 | −1.64669 | −0.823345 | − | 0.567541i | \(-0.807895\pi\) | ||||
−0.823345 | + | 0.567541i | \(0.807895\pi\) | |||||||
\(258\) | 9.70437 | 0.604167 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −21.5824 | −1.33848 | ||||||||
\(261\) | 3.41695 | 0.211504 | ||||||||
\(262\) | −29.9939 | −1.85303 | ||||||||
\(263\) | −4.26169 | −0.262787 | −0.131393 | − | 0.991330i | \(-0.541945\pi\) | ||||
−0.131393 | + | 0.991330i | \(0.541945\pi\) | |||||||
\(264\) | 1.46373 | 0.0900865 | ||||||||
\(265\) | −7.90516 | −0.485610 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.51735 | 0.337656 | ||||||||
\(268\) | 25.2637 | 1.54323 | ||||||||
\(269\) | 14.8791 | 0.907193 | 0.453597 | − | 0.891207i | \(-0.350141\pi\) | ||||
0.453597 | + | 0.891207i | \(0.350141\pi\) | |||||||
\(270\) | −4.77814 | −0.290789 | ||||||||
\(271\) | 24.8652 | 1.51045 | 0.755225 | − | 0.655465i | \(-0.227527\pi\) | ||||
0.755225 | + | 0.655465i | \(0.227527\pi\) | |||||||
\(272\) | 4.00944 | 0.243108 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5263 | 0.998390 | ||||||||
\(275\) | −0.654114 | −0.0394445 | ||||||||
\(276\) | −15.1850 | −0.914032 | ||||||||
\(277\) | −24.1746 | −1.45251 | −0.726256 | − | 0.687425i | \(-0.758741\pi\) | ||||
−0.726256 | + | 0.687425i | \(0.758741\pi\) | |||||||
\(278\) | 18.6129 | 1.11633 | ||||||||
\(279\) | 1.07464 | 0.0643370 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0063 | −0.656583 | −0.328291 | − | 0.944576i | \(-0.606473\pi\) | ||||
−0.328291 | + | 0.944576i | \(0.606473\pi\) | |||||||
\(282\) | 22.7254 | 1.35328 | ||||||||
\(283\) | 16.1057 | 0.957387 | 0.478694 | − | 0.877982i | \(-0.341110\pi\) | ||||
0.478694 | + | 0.877982i | \(0.341110\pi\) | |||||||
\(284\) | −12.1353 | −0.720095 | ||||||||
\(285\) | 10.1480 | 0.601117 | ||||||||
\(286\) | 18.8760 | 1.11616 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8.10315 | −0.477483 | ||||||||
\(289\) | −15.4989 | −0.911698 | ||||||||
\(290\) | 16.3267 | 0.958735 | ||||||||
\(291\) | −3.88945 | −0.228004 | ||||||||
\(292\) | −13.1912 | −0.771957 | ||||||||
\(293\) | −12.6292 | −0.737808 | −0.368904 | − | 0.929467i | \(-0.620267\pi\) | ||||
−0.368904 | + | 0.929467i | \(0.620267\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.7743 | −1.32597 | ||||||||
\(296\) | −1.07073 | −0.0622347 | ||||||||
\(297\) | 2.24173 | 0.130078 | ||||||||
\(298\) | −7.36851 | −0.426846 | ||||||||
\(299\) | −26.5983 | −1.53822 | ||||||||
\(300\) | −0.675306 | −0.0389888 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −18.6739 | −1.07456 | ||||||||
\(303\) | 11.7539 | 0.675246 | ||||||||
\(304\) | 14.4363 | 0.827978 | ||||||||
\(305\) | −11.9352 | −0.683406 | ||||||||
\(306\) | −2.54488 | −0.145481 | ||||||||
\(307\) | 23.2927 | 1.32939 | 0.664693 | − | 0.747116i | \(-0.268562\pi\) | ||||
0.664693 | + | 0.747116i | \(0.268562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.81801 | −0.444751 | ||||||||
\(310\) | 5.13479 | 0.291636 | ||||||||
\(311\) | −8.17595 | −0.463616 | −0.231808 | − | 0.972762i | \(-0.574464\pi\) | ||||
−0.231808 | + | 0.972762i | \(0.574464\pi\) | |||||||
\(312\) | 2.64696 | 0.149855 | ||||||||
\(313\) | −16.9412 | −0.957576 | −0.478788 | − | 0.877931i | \(-0.658924\pi\) | ||||
−0.478788 | + | 0.877931i | \(0.658924\pi\) | |||||||
\(314\) | 14.5735 | 0.822429 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.22209 | 0.462529 | ||||||||
\(317\) | 10.8754 | 0.610824 | 0.305412 | − | 0.952220i | \(-0.401206\pi\) | ||||
0.305412 | + | 0.952220i | \(0.401206\pi\) | |||||||
\(318\) | 7.13785 | 0.400271 | ||||||||
\(319\) | −7.65986 | −0.428870 | ||||||||
\(320\) | −23.6621 | −1.32275 | ||||||||
\(321\) | −14.9202 | −0.832762 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.40491 | 0.300737 | ||||||||
\(324\) | 2.31436 | 0.128575 | ||||||||
\(325\) | −1.18288 | −0.0656141 | ||||||||
\(326\) | 38.5461 | 2.13487 | ||||||||
\(327\) | 2.44790 | 0.135369 | ||||||||
\(328\) | −0.652949 | −0.0360531 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.7113 | 0.589637 | ||||||||
\(331\) | −12.5272 | −0.688557 | −0.344278 | − | 0.938868i | \(-0.611876\pi\) | ||||
−0.344278 | + | 0.938868i | \(0.611876\pi\) | |||||||
\(332\) | −5.66422 | −0.310864 | ||||||||
\(333\) | −1.63983 | −0.0898622 | ||||||||
\(334\) | −30.7559 | −1.68289 | ||||||||
\(335\) | 25.1112 | 1.37197 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.0009 | 0.817152 | 0.408576 | − | 0.912724i | \(-0.366026\pi\) | ||||
0.408576 | + | 0.912724i | \(0.366026\pi\) | |||||||
\(338\) | 7.13227 | 0.387944 | ||||||||
\(339\) | 5.66753 | 0.307818 | ||||||||
\(340\) | −6.52289 | −0.353753 | ||||||||
\(341\) | −2.40905 | −0.130457 | ||||||||
\(342\) | −9.16300 | −0.495479 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.05062 | −0.164478 | ||||||||
\(345\) | −15.0934 | −0.812601 | ||||||||
\(346\) | 43.9809 | 2.36443 | ||||||||
\(347\) | −35.5777 | −1.90991 | −0.954955 | − | 0.296752i | \(-0.904097\pi\) | ||||
−0.954955 | + | 0.296752i | \(0.904097\pi\) | |||||||
\(348\) | −7.90803 | −0.423915 | ||||||||
\(349\) | 24.7802 | 1.32646 | 0.663228 | − | 0.748418i | \(-0.269186\pi\) | ||||
0.663228 | + | 0.748418i | \(0.269186\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.05386 | 0.216379 | ||||||||
\(352\) | 18.1651 | 0.968201 | ||||||||
\(353\) | 8.42011 | 0.448157 | 0.224079 | − | 0.974571i | \(-0.428063\pi\) | ||||
0.224079 | + | 0.974571i | \(0.428063\pi\) | |||||||
\(354\) | 20.5637 | 1.09295 | ||||||||
\(355\) | −12.0620 | −0.640186 | ||||||||
\(356\) | −12.7691 | −0.676761 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.7254 | 0.778263 | ||||||||
\(359\) | 20.6533 | 1.09004 | 0.545019 | − | 0.838424i | \(-0.316522\pi\) | ||||
0.545019 | + | 0.838424i | \(0.316522\pi\) | |||||||
\(360\) | 1.50204 | 0.0791642 | ||||||||
\(361\) | 0.460761 | 0.0242506 | ||||||||
\(362\) | −49.9299 | −2.62426 | ||||||||
\(363\) | 5.97466 | 0.313588 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.1116 | −0.686292 | ||||||||
\(366\) | 10.7767 | 0.563307 | ||||||||
\(367\) | −29.3148 | −1.53022 | −0.765111 | − | 0.643898i | \(-0.777316\pi\) | ||||
−0.765111 | + | 0.643898i | \(0.777316\pi\) | |||||||
\(368\) | −21.4714 | −1.11928 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −7.83535 | −0.407340 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.48710 | −0.128950 | ||||||||
\(373\) | −25.6244 | −1.32678 | −0.663391 | − | 0.748273i | \(-0.730883\pi\) | ||||
−0.663391 | + | 0.748273i | \(0.730883\pi\) | |||||||
\(374\) | 5.70492 | 0.294994 | ||||||||
\(375\) | 10.8307 | 0.559296 | ||||||||
\(376\) | −7.14385 | −0.368416 | ||||||||
\(377\) | −13.8518 | −0.713405 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.09331 | −0.467092 | −0.233546 | − | 0.972346i | \(-0.575033\pi\) | ||||
−0.233546 | + | 0.972346i | \(0.575033\pi\) | |||||||
\(380\) | −23.4861 | −1.20481 | ||||||||
\(381\) | −5.81071 | −0.297692 | ||||||||
\(382\) | 41.0727 | 2.10146 | ||||||||
\(383\) | 10.4624 | 0.534603 | 0.267302 | − | 0.963613i | \(-0.413868\pi\) | ||||
0.267302 | + | 0.963613i | \(0.413868\pi\) | |||||||
\(384\) | 5.15907 | 0.263272 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.3053 | −1.13531 | ||||||||
\(387\) | −4.67207 | −0.237495 | ||||||||
\(388\) | 9.00158 | 0.456986 | ||||||||
\(389\) | −22.4569 | −1.13861 | −0.569304 | − | 0.822127i | \(-0.692787\pi\) | ||||
−0.569304 | + | 0.822127i | \(0.692787\pi\) | |||||||
\(390\) | 19.3699 | 0.980834 | ||||||||
\(391\) | −8.03886 | −0.406542 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.4403 | 0.728415 | ||||||||
\(394\) | −53.3477 | −2.68762 | ||||||||
\(395\) | 8.17247 | 0.411202 | ||||||||
\(396\) | −5.18815 | −0.260715 | ||||||||
\(397\) | −34.0978 | −1.71132 | −0.855659 | − | 0.517540i | \(-0.826848\pi\) | ||||
−0.855659 | + | 0.517540i | \(0.826848\pi\) | |||||||
\(398\) | −25.6857 | −1.28751 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.954874 | −0.0477437 | ||||||||
\(401\) | 26.2661 | 1.31167 | 0.655833 | − | 0.754906i | \(-0.272318\pi\) | ||||
0.655833 | + | 0.754906i | \(0.272318\pi\) | |||||||
\(402\) | −22.6738 | −1.13087 | ||||||||
\(403\) | −4.35644 | −0.217010 | ||||||||
\(404\) | −27.2028 | −1.35339 | ||||||||
\(405\) | 2.30039 | 0.114307 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.67605 | 0.182215 | ||||||||
\(408\) | 0.799996 | 0.0396057 | ||||||||
\(409\) | 13.7222 | 0.678517 | 0.339259 | − | 0.940693i | \(-0.389824\pi\) | ||||
0.339259 | + | 0.940693i | \(0.389824\pi\) | |||||||
\(410\) | −4.77814 | −0.235976 | ||||||||
\(411\) | −7.95642 | −0.392461 | ||||||||
\(412\) | 18.0936 | 0.891410 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 13.6284 | 0.669797 | ||||||||
\(415\) | −5.63004 | −0.276368 | ||||||||
\(416\) | 32.8490 | 1.61056 | ||||||||
\(417\) | −8.96101 | −0.438823 | ||||||||
\(418\) | 20.5410 | 1.00469 | ||||||||
\(419\) | 5.03172 | 0.245815 | 0.122908 | − | 0.992418i | \(-0.460778\pi\) | ||||
0.122908 | + | 0.992418i | \(0.460778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.3421 | 1.72247 | 0.861234 | − | 0.508209i | \(-0.169692\pi\) | ||||
0.861234 | + | 0.508209i | \(0.169692\pi\) | |||||||
\(422\) | −26.4580 | −1.28796 | ||||||||
\(423\) | −10.9409 | −0.531965 | ||||||||
\(424\) | −2.24382 | −0.108970 | ||||||||
\(425\) | −0.357502 | −0.0173414 | ||||||||
\(426\) | 10.8912 | 0.527682 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 34.5305 | 1.66910 | ||||||||
\(429\) | −9.08764 | −0.438755 | ||||||||
\(430\) | −22.3238 | −1.07655 | ||||||||
\(431\) | −10.0032 | −0.481838 | −0.240919 | − | 0.970545i | \(-0.577449\pi\) | ||||
−0.240919 | + | 0.970545i | \(0.577449\pi\) | |||||||
\(432\) | 3.27247 | 0.157447 | ||||||||
\(433\) | −0.228599 | −0.0109858 | −0.00549289 | − | 0.999985i | \(-0.501748\pi\) | ||||
−0.00549289 | + | 0.999985i | \(0.501748\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.86030 | −0.376873 | ||||||||
\(436\) | −5.66531 | −0.271319 | ||||||||
\(437\) | −28.9445 | −1.38460 | ||||||||
\(438\) | 11.8389 | 0.565686 | ||||||||
\(439\) | 6.63796 | 0.316812 | 0.158406 | − | 0.987374i | \(-0.449364\pi\) | ||||
0.158406 | + | 0.987374i | \(0.449364\pi\) | |||||||
\(440\) | −3.36715 | −0.160523 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.3166 | 0.490709 | ||||||||
\(443\) | −34.2893 | −1.62913 | −0.814567 | − | 0.580069i | \(-0.803025\pi\) | ||||
−0.814567 | + | 0.580069i | \(0.803025\pi\) | |||||||
\(444\) | 3.79515 | 0.180110 | ||||||||
\(445\) | −12.6920 | −0.601660 | ||||||||
\(446\) | 30.2026 | 1.43014 | ||||||||
\(447\) | 3.54749 | 0.167791 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.8006 | −1.12322 | −0.561609 | − | 0.827403i | \(-0.689817\pi\) | ||||
−0.561609 | + | 0.827403i | \(0.689817\pi\) | |||||||
\(450\) | 0.606078 | 0.0285708 | ||||||||
\(451\) | 2.24173 | 0.105559 | ||||||||
\(452\) | −13.1167 | −0.616956 | ||||||||
\(453\) | 8.99035 | 0.422403 | ||||||||
\(454\) | 26.5034 | 1.24387 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.88044 | 0.134889 | ||||||||
\(457\) | 3.89804 | 0.182343 | 0.0911713 | − | 0.995835i | \(-0.470939\pi\) | ||||
0.0911713 | + | 0.995835i | \(0.470939\pi\) | |||||||
\(458\) | 33.9681 | 1.58722 | ||||||||
\(459\) | 1.22520 | 0.0571876 | ||||||||
\(460\) | 34.9315 | 1.62869 | ||||||||
\(461\) | −8.82325 | −0.410940 | −0.205470 | − | 0.978663i | \(-0.565872\pi\) | ||||
−0.205470 | + | 0.978663i | \(0.565872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.1088 | −1.25985 | −0.629925 | − | 0.776656i | \(-0.716915\pi\) | ||||
−0.629925 | + | 0.776656i | \(0.716915\pi\) | |||||||
\(464\) | −11.1819 | −0.519104 | ||||||||
\(465\) | −2.47209 | −0.114640 | ||||||||
\(466\) | 53.3426 | 2.47105 | ||||||||
\(467\) | −39.6617 | −1.83532 | −0.917662 | − | 0.397361i | \(-0.869926\pi\) | ||||
−0.917662 | + | 0.397361i | \(0.869926\pi\) | |||||||
\(468\) | −9.38207 | −0.433686 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −52.2772 | −2.41137 | ||||||||
\(471\) | −7.01626 | −0.323292 | ||||||||
\(472\) | −6.46433 | −0.297545 | ||||||||
\(473\) | 10.4735 | 0.481572 | ||||||||
\(474\) | −7.37921 | −0.338938 | ||||||||
\(475\) | −1.28721 | −0.0590614 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.43644 | −0.157344 | ||||||||
\(478\) | −13.8822 | −0.634956 | ||||||||
\(479\) | 0.661325 | 0.0302167 | 0.0151084 | − | 0.999886i | \(-0.495191\pi\) | ||||
0.0151084 | + | 0.999886i | \(0.495191\pi\) | |||||||
\(480\) | 18.6404 | 0.850814 | ||||||||
\(481\) | 6.64764 | 0.303106 | ||||||||
\(482\) | 26.6117 | 1.21213 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.8275 | −0.628522 | ||||||||
\(485\) | 8.94725 | 0.406274 | ||||||||
\(486\) | −2.07710 | −0.0942193 | ||||||||
\(487\) | −12.0841 | −0.547582 | −0.273791 | − | 0.961789i | \(-0.588278\pi\) | ||||
−0.273791 | + | 0.961789i | \(0.588278\pi\) | |||||||
\(488\) | −3.38771 | −0.153355 | ||||||||
\(489\) | −18.5576 | −0.839205 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.89624 | −0.266094 | −0.133047 | − | 0.991110i | \(-0.542476\pi\) | ||||
−0.133047 | + | 0.991110i | \(0.542476\pi\) | |||||||
\(492\) | 2.31436 | 0.104339 | ||||||||
\(493\) | −4.18646 | −0.188549 | ||||||||
\(494\) | 37.1455 | 1.67126 | ||||||||
\(495\) | −5.15684 | −0.231783 | ||||||||
\(496\) | −3.51673 | −0.157906 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.08356 | 0.227800 | ||||||||
\(499\) | −9.66766 | −0.432784 | −0.216392 | − | 0.976307i | \(-0.569429\pi\) | ||||
−0.216392 | + | 0.976307i | \(0.569429\pi\) | |||||||
\(500\) | −25.0661 | −1.12099 | ||||||||
\(501\) | 14.8071 | 0.661534 | ||||||||
\(502\) | 42.9435 | 1.91666 | ||||||||
\(503\) | 35.1796 | 1.56858 | 0.784290 | − | 0.620395i | \(-0.213028\pi\) | ||||
0.784290 | + | 0.620395i | \(0.213028\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0386 | −1.20320 | ||||||||
\(506\) | −30.5511 | −1.35816 | ||||||||
\(507\) | −3.43376 | −0.152499 | ||||||||
\(508\) | 13.4481 | 0.596661 | ||||||||
\(509\) | −2.79729 | −0.123988 | −0.0619938 | − | 0.998077i | \(-0.519746\pi\) | ||||
−0.0619938 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(510\) | 5.85420 | 0.259228 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 30.7908 | 1.36078 | ||||||||
\(513\) | 4.41144 | 0.194770 | ||||||||
\(514\) | −54.8323 | −2.41855 | ||||||||
\(515\) | 17.9845 | 0.792490 | ||||||||
\(516\) | 10.8128 | 0.476008 | ||||||||
\(517\) | 24.5265 | 1.07867 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.1741 | −0.929442 | ||||||||
\(520\) | −6.08904 | −0.267022 | ||||||||
\(521\) | 29.5199 | 1.29329 | 0.646645 | − | 0.762791i | \(-0.276171\pi\) | ||||
0.646645 | + | 0.762791i | \(0.276171\pi\) | |||||||
\(522\) | 7.09735 | 0.310642 | ||||||||
\(523\) | 29.5127 | 1.29050 | 0.645250 | − | 0.763971i | \(-0.276753\pi\) | ||||
0.645250 | + | 0.763971i | \(0.276753\pi\) | |||||||
\(524\) | −33.4199 | −1.45995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.85196 | −0.385964 | ||||||||
\(527\) | −1.31665 | −0.0573544 | ||||||||
\(528\) | −7.33598 | −0.319258 | ||||||||
\(529\) | 20.0498 | 0.871732 | ||||||||
\(530\) | −16.4198 | −0.713232 | ||||||||
\(531\) | −9.90021 | −0.429632 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.05386 | 0.175592 | ||||||||
\(534\) | 11.4601 | 0.495927 | ||||||||
\(535\) | 34.3222 | 1.48388 | ||||||||
\(536\) | 7.12764 | 0.307867 | ||||||||
\(537\) | −7.08941 | −0.305930 | ||||||||
\(538\) | 30.9054 | 1.33242 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.32392 | −0.229105 | ||||||||
\(541\) | 35.9810 | 1.54695 | 0.773473 | − | 0.633830i | \(-0.218518\pi\) | ||||
0.773473 | + | 0.633830i | \(0.218518\pi\) | |||||||
\(542\) | 51.6475 | 2.21845 | ||||||||
\(543\) | 24.0383 | 1.03158 | ||||||||
\(544\) | 9.92802 | 0.425660 | ||||||||
\(545\) | −5.63112 | −0.241211 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5998 | 0.838028 | 0.419014 | − | 0.907980i | \(-0.362376\pi\) | ||||
0.419014 | + | 0.907980i | \(0.362376\pi\) | |||||||
\(548\) | 18.4140 | 0.786606 | ||||||||
\(549\) | −5.18833 | −0.221433 | ||||||||
\(550\) | −1.35866 | −0.0579335 | ||||||||
\(551\) | −15.0736 | −0.642158 | ||||||||
\(552\) | −4.28415 | −0.182346 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −50.2131 | −2.13335 | ||||||||
\(555\) | 3.77225 | 0.160123 | ||||||||
\(556\) | 20.7390 | 0.879528 | ||||||||
\(557\) | 14.9938 | 0.635306 | 0.317653 | − | 0.948207i | \(-0.397105\pi\) | ||||
0.317653 | + | 0.948207i | \(0.397105\pi\) | |||||||
\(558\) | 2.23214 | 0.0944939 | ||||||||
\(559\) | 18.9399 | 0.801072 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.74657 | −0.115960 | ||||||||
\(562\) | −22.8613 | −0.964345 | ||||||||
\(563\) | −35.7951 | −1.50858 | −0.754291 | − | 0.656540i | \(-0.772019\pi\) | ||||
−0.754291 | + | 0.656540i | \(0.772019\pi\) | |||||||
\(564\) | 25.3211 | 1.06621 | ||||||||
\(565\) | −13.0375 | −0.548492 | ||||||||
\(566\) | 33.4533 | 1.40615 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.42372 | −0.143656 | ||||||||
\(569\) | 25.4501 | 1.06692 | 0.533461 | − | 0.845825i | \(-0.320891\pi\) | ||||
0.533461 | + | 0.845825i | \(0.320891\pi\) | |||||||
\(570\) | 21.0785 | 0.882880 | ||||||||
\(571\) | −22.1799 | −0.928200 | −0.464100 | − | 0.885783i | \(-0.653622\pi\) | ||||
−0.464100 | + | 0.885783i | \(0.653622\pi\) | |||||||
\(572\) | 21.0320 | 0.879393 | ||||||||
\(573\) | −19.7740 | −0.826072 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.91450 | 0.0798403 | ||||||||
\(576\) | −10.2861 | −0.428589 | ||||||||
\(577\) | −30.2462 | −1.25917 | −0.629583 | − | 0.776933i | \(-0.716774\pi\) | ||||
−0.629583 | + | 0.776933i | \(0.716774\pi\) | |||||||
\(578\) | −32.1928 | −1.33904 | ||||||||
\(579\) | 10.7386 | 0.446283 | ||||||||
\(580\) | 18.1915 | 0.755363 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.07879 | −0.334877 | ||||||||
\(583\) | 7.70357 | 0.319049 | ||||||||
\(584\) | −3.72163 | −0.154002 | ||||||||
\(585\) | −9.32545 | −0.385560 | ||||||||
\(586\) | −26.2322 | −1.08364 | ||||||||
\(587\) | 2.37388 | 0.0979804 | 0.0489902 | − | 0.998799i | \(-0.484400\pi\) | ||||
0.0489902 | + | 0.998799i | \(0.484400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.74071 | −0.195337 | ||||||||
\(590\) | −47.3046 | −1.94750 | ||||||||
\(591\) | 25.6837 | 1.05649 | ||||||||
\(592\) | 5.36630 | 0.220553 | ||||||||
\(593\) | −11.6657 | −0.479051 | −0.239525 | − | 0.970890i | \(-0.576992\pi\) | ||||
−0.239525 | + | 0.970890i | \(0.576992\pi\) | |||||||
\(594\) | 4.65630 | 0.191050 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.21016 | −0.336301 | ||||||||
\(597\) | 12.3661 | 0.506112 | ||||||||
\(598\) | −55.2474 | −2.25924 | ||||||||
\(599\) | 15.5533 | 0.635489 | 0.317744 | − | 0.948176i | \(-0.397075\pi\) | ||||
0.317744 | + | 0.948176i | \(0.397075\pi\) | |||||||
\(600\) | −0.190524 | −0.00777811 | ||||||||
\(601\) | 22.3375 | 0.911166 | 0.455583 | − | 0.890193i | \(-0.349431\pi\) | ||||
0.455583 | + | 0.890193i | \(0.349431\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.9161 | 0.444537 | ||||||||
\(604\) | −20.8069 | −0.846619 | ||||||||
\(605\) | −13.7440 | −0.558775 | ||||||||
\(606\) | 24.4141 | 0.991756 | ||||||||
\(607\) | 37.4654 | 1.52067 | 0.760337 | − | 0.649528i | \(-0.225034\pi\) | ||||
0.760337 | + | 0.649528i | \(0.225034\pi\) | |||||||
\(608\) | 35.7465 | 1.44971 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.7906 | −1.00374 | ||||||||
\(611\) | 44.3528 | 1.79432 | ||||||||
\(612\) | −2.83556 | −0.114621 | ||||||||
\(613\) | 47.2820 | 1.90970 | 0.954852 | − | 0.297083i | \(-0.0960139\pi\) | ||||
0.954852 | + | 0.297083i | \(0.0960139\pi\) | |||||||
\(614\) | 48.3814 | 1.95251 | ||||||||
\(615\) | 2.30039 | 0.0927606 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.52799 | −0.262807 | −0.131404 | − | 0.991329i | \(-0.541948\pi\) | ||||
−0.131404 | + | 0.991329i | \(0.541948\pi\) | |||||||
\(618\) | −16.2388 | −0.653220 | ||||||||
\(619\) | −43.1677 | −1.73506 | −0.867528 | − | 0.497389i | \(-0.834292\pi\) | ||||
−0.867528 | + | 0.497389i | \(0.834292\pi\) | |||||||
\(620\) | 5.72130 | 0.229773 | ||||||||
\(621\) | −6.56124 | −0.263293 | ||||||||
\(622\) | −16.9823 | −0.680928 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −13.2661 | −0.531070 | ||||||||
\(625\) | −26.3738 | −1.05495 | ||||||||
\(626\) | −35.1887 | −1.40642 | ||||||||
\(627\) | −9.88923 | −0.394938 | ||||||||
\(628\) | 16.2381 | 0.647971 | ||||||||
\(629\) | 2.00913 | 0.0801092 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.2725 | 1.36437 | 0.682183 | − | 0.731182i | \(-0.261031\pi\) | ||||
0.682183 | + | 0.731182i | \(0.261031\pi\) | |||||||
\(632\) | 2.31970 | 0.0922725 | ||||||||
\(633\) | 12.7379 | 0.506288 | ||||||||
\(634\) | 22.5893 | 0.897137 | ||||||||
\(635\) | 13.3669 | 0.530449 | ||||||||
\(636\) | 7.95315 | 0.315363 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.9103 | −0.629895 | ||||||||
\(639\) | −5.24347 | −0.207429 | ||||||||
\(640\) | −11.8679 | −0.469118 | ||||||||
\(641\) | 29.6706 | 1.17192 | 0.585960 | − | 0.810340i | \(-0.300718\pi\) | ||||
0.585960 | + | 0.810340i | \(0.300718\pi\) | |||||||
\(642\) | −30.9907 | −1.22311 | ||||||||
\(643\) | −0.491928 | −0.0193997 | −0.00969987 | − | 0.999953i | \(-0.503088\pi\) | ||||
−0.00969987 | + | 0.999953i | \(0.503088\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.7476 | 0.423185 | ||||||||
\(646\) | 11.2266 | 0.441703 | ||||||||
\(647\) | 17.2939 | 0.679895 | 0.339948 | − | 0.940444i | \(-0.389591\pi\) | ||||
0.339948 | + | 0.940444i | \(0.389591\pi\) | |||||||
\(648\) | 0.652949 | 0.0256502 | ||||||||
\(649\) | 22.1936 | 0.871174 | ||||||||
\(650\) | −2.45695 | −0.0963696 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.9489 | 1.68201 | ||||||||
\(653\) | −5.95097 | −0.232879 | −0.116440 | − | 0.993198i | \(-0.537148\pi\) | ||||
−0.116440 | + | 0.993198i | \(0.537148\pi\) | |||||||
\(654\) | 5.08454 | 0.198821 | ||||||||
\(655\) | −33.2182 | −1.29794 | ||||||||
\(656\) | 3.27247 | 0.127768 | ||||||||
\(657\) | −5.69973 | −0.222368 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.3637 | 1.88398 | 0.941992 | − | 0.335635i | \(-0.108951\pi\) | ||||
0.941992 | + | 0.335635i | \(0.108951\pi\) | |||||||
\(660\) | 11.9348 | 0.464560 | ||||||||
\(661\) | 15.9158 | 0.619054 | 0.309527 | − | 0.950891i | \(-0.399829\pi\) | ||||
0.309527 | + | 0.950891i | \(0.399829\pi\) | |||||||
\(662\) | −26.0203 | −1.01131 | ||||||||
\(663\) | −4.96680 | −0.192895 | ||||||||
\(664\) | −1.59804 | −0.0620162 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.40610 | −0.131984 | ||||||||
\(667\) | 22.4194 | 0.868082 | ||||||||
\(668\) | −34.2690 | −1.32591 | ||||||||
\(669\) | −14.5408 | −0.562178 | ||||||||
\(670\) | 52.1586 | 2.01506 | ||||||||
\(671\) | 11.6308 | 0.449003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.6199 | −0.833387 | −0.416693 | − | 0.909047i | \(-0.636811\pi\) | ||||
−0.416693 | + | 0.909047i | \(0.636811\pi\) | |||||||
\(674\) | 31.1584 | 1.20018 | ||||||||
\(675\) | −0.291790 | −0.0112310 | ||||||||
\(676\) | 7.94694 | 0.305651 | ||||||||
\(677\) | 10.1041 | 0.388331 | 0.194166 | − | 0.980969i | \(-0.437800\pi\) | ||||
0.194166 | + | 0.980969i | \(0.437800\pi\) | |||||||
\(678\) | 11.7720 | 0.452102 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.84030 | −0.0705723 | ||||||||
\(681\) | −12.7598 | −0.488957 | ||||||||
\(682\) | −5.00385 | −0.191607 | ||||||||
\(683\) | −44.1322 | −1.68867 | −0.844336 | − | 0.535813i | \(-0.820005\pi\) | ||||
−0.844336 | + | 0.535813i | \(0.820005\pi\) | |||||||
\(684\) | −10.2096 | −0.390375 | ||||||||
\(685\) | 18.3029 | 0.699316 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3536 | −0.623928 | ||||||||
\(688\) | 15.2892 | 0.582895 | ||||||||
\(689\) | 13.9309 | 0.530723 | ||||||||
\(690\) | −31.3505 | −1.19349 | ||||||||
\(691\) | 6.85734 | 0.260865 | 0.130433 | − | 0.991457i | \(-0.458363\pi\) | ||||
0.130433 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(692\) | 49.0045 | 1.86287 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −73.8985 | −2.80515 | ||||||||
\(695\) | 20.6138 | 0.781926 | ||||||||
\(696\) | −2.23109 | −0.0845693 | ||||||||
\(697\) | 1.22520 | 0.0464079 | ||||||||
\(698\) | 51.4711 | 1.94821 | ||||||||
\(699\) | −25.6813 | −0.971355 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.8246 | 1.88185 | 0.940925 | − | 0.338615i | \(-0.109958\pi\) | ||||
0.940925 | + | 0.338615i | \(0.109958\pi\) | |||||||
\(702\) | 8.42028 | 0.317803 | ||||||||
\(703\) | 7.23401 | 0.272836 | ||||||||
\(704\) | 23.0587 | 0.869058 | ||||||||
\(705\) | 25.1683 | 0.947894 | ||||||||
\(706\) | 17.4894 | 0.658223 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 22.9126 | 0.861108 | ||||||||
\(709\) | −46.7512 | −1.75578 | −0.877889 | − | 0.478865i | \(-0.841048\pi\) | ||||
−0.877889 | + | 0.478865i | \(0.841048\pi\) | |||||||
\(710\) | −25.0541 | −0.940263 | ||||||||
\(711\) | 3.55265 | 0.133235 | ||||||||
\(712\) | −3.60254 | −0.135011 | ||||||||
\(713\) | 7.05097 | 0.264061 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.9051 | 0.781807 | ||||||||
\(716\) | 16.4074 | 0.613174 | ||||||||
\(717\) | 6.68343 | 0.249597 | ||||||||
\(718\) | 42.8990 | 1.60098 | ||||||||
\(719\) | 17.2085 | 0.641769 | 0.320884 | − | 0.947118i | \(-0.396020\pi\) | ||||
0.320884 | + | 0.947118i | \(0.396020\pi\) | |||||||
\(720\) | −7.52795 | −0.280550 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.957049 | 0.0356177 | ||||||||
\(723\) | −12.8119 | −0.476481 | ||||||||
\(724\) | −55.6331 | −2.06759 | ||||||||
\(725\) | 0.997031 | 0.0370288 | ||||||||
\(726\) | 12.4100 | 0.460578 | ||||||||
\(727\) | 14.0624 | 0.521547 | 0.260773 | − | 0.965400i | \(-0.416022\pi\) | ||||
0.260773 | + | 0.965400i | \(0.416022\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.2341 | −1.00798 | ||||||||
\(731\) | 5.72424 | 0.211719 | ||||||||
\(732\) | 12.0076 | 0.443815 | ||||||||
\(733\) | −44.3042 | −1.63641 | −0.818206 | − | 0.574925i | \(-0.805031\pi\) | ||||
−0.818206 | + | 0.574925i | \(0.805031\pi\) | |||||||
\(734\) | −60.8899 | −2.24749 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53.1667 | −1.95975 | ||||||||
\(737\) | −24.4709 | −0.901397 | ||||||||
\(738\) | −2.07710 | −0.0764592 | ||||||||
\(739\) | 37.1616 | 1.36701 | 0.683506 | − | 0.729945i | \(-0.260455\pi\) | ||||
0.683506 | + | 0.729945i | \(0.260455\pi\) | |||||||
\(740\) | −8.73033 | −0.320933 | ||||||||
\(741\) | −17.8833 | −0.656960 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.6676 | 0.648161 | 0.324080 | − | 0.946030i | \(-0.394945\pi\) | ||||
0.324080 | + | 0.946030i | \(0.394945\pi\) | |||||||
\(744\) | −0.701685 | −0.0257250 | ||||||||
\(745\) | −8.16062 | −0.298982 | ||||||||
\(746\) | −53.2246 | −1.94869 | ||||||||
\(747\) | −2.44743 | −0.0895467 | ||||||||
\(748\) | 6.35655 | 0.232418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 22.4965 | 0.821456 | ||||||||
\(751\) | 23.3385 | 0.851635 | 0.425817 | − | 0.904809i | \(-0.359987\pi\) | ||||
0.425817 | + | 0.904809i | \(0.359987\pi\) | |||||||
\(752\) | 35.8038 | 1.30563 | ||||||||
\(753\) | −20.6747 | −0.753428 | ||||||||
\(754\) | −28.7716 | −1.04780 | ||||||||
\(755\) | −20.6813 | −0.752670 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.81661 | −0.102371 | −0.0511857 | − | 0.998689i | \(-0.516300\pi\) | ||||
−0.0511857 | + | 0.998689i | \(0.516300\pi\) | |||||||
\(758\) | −18.8877 | −0.686034 | ||||||||
\(759\) | 14.7085 | 0.533885 | ||||||||
\(760\) | −6.62613 | −0.240355 | ||||||||
\(761\) | 25.8866 | 0.938389 | 0.469194 | − | 0.883095i | \(-0.344544\pi\) | ||||
0.469194 | + | 0.883095i | \(0.344544\pi\) | |||||||
\(762\) | −12.0694 | −0.437230 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 45.7641 | 1.65569 | ||||||||
\(765\) | −2.81845 | −0.101901 | ||||||||
\(766\) | 21.7315 | 0.785189 | ||||||||
\(767\) | 40.1340 | 1.44916 | ||||||||
\(768\) | −9.85637 | −0.355661 | ||||||||
\(769\) | −21.1931 | −0.764243 | −0.382121 | − | 0.924112i | \(-0.624806\pi\) | ||||
−0.382121 | + | 0.924112i | \(0.624806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.3985 | 0.950717 | ||||||||
\(772\) | −24.8530 | −0.894481 | ||||||||
\(773\) | 30.2026 | 1.08631 | 0.543155 | − | 0.839632i | \(-0.317229\pi\) | ||||
0.543155 | + | 0.839632i | \(0.317229\pi\) | |||||||
\(774\) | −9.70437 | −0.348816 | ||||||||
\(775\) | 0.313569 | 0.0112637 | ||||||||
\(776\) | 2.53961 | 0.0911668 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −46.6452 | −1.67231 | ||||||||
\(779\) | 4.41144 | 0.158056 | ||||||||
\(780\) | 21.5824 | 0.772774 | ||||||||
\(781\) | 11.7544 | 0.420607 | ||||||||
\(782\) | −16.6975 | −0.597102 | ||||||||
\(783\) | −3.41695 | −0.122112 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1401 | 0.576066 | ||||||||
\(786\) | 29.9939 | 1.06985 | ||||||||
\(787\) | 22.0228 | 0.785027 | 0.392513 | − | 0.919746i | \(-0.371606\pi\) | ||||
0.392513 | + | 0.919746i | \(0.371606\pi\) | |||||||
\(788\) | −59.4412 | −2.11751 | ||||||||
\(789\) | 4.26169 | 0.151720 | ||||||||
\(790\) | 16.9751 | 0.603945 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.46373 | −0.0520115 | ||||||||
\(793\) | 21.0328 | 0.746895 | ||||||||
\(794\) | −70.8245 | −2.51347 | ||||||||
\(795\) | 7.90516 | 0.280367 | ||||||||
\(796\) | −28.6196 | −1.01439 | ||||||||
\(797\) | 16.6446 | 0.589583 | 0.294791 | − | 0.955562i | \(-0.404750\pi\) | ||||
0.294791 | + | 0.955562i | \(0.404750\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4048 | 0.474229 | ||||||||
\(800\) | −2.36442 | −0.0835948 | ||||||||
\(801\) | −5.51735 | −0.194946 | ||||||||
\(802\) | 54.5573 | 1.92649 | ||||||||
\(803\) | 12.7772 | 0.450899 | ||||||||
\(804\) | −25.2637 | −0.890982 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.04877 | −0.318729 | ||||||||
\(807\) | −14.8791 | −0.523768 | ||||||||
\(808\) | −7.67472 | −0.269996 | ||||||||
\(809\) | −20.1468 | −0.708323 | −0.354162 | − | 0.935184i | \(-0.615234\pi\) | ||||
−0.354162 | + | 0.935184i | \(0.615234\pi\) | |||||||
\(810\) | 4.77814 | 0.167887 | ||||||||
\(811\) | −34.5884 | −1.21456 | −0.607282 | − | 0.794487i | \(-0.707740\pi\) | ||||
−0.607282 | + | 0.794487i | \(0.707740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.8652 | −0.872059 | ||||||||
\(814\) | 7.63554 | 0.267626 | ||||||||
\(815\) | 42.6898 | 1.49536 | ||||||||
\(816\) | −4.00944 | −0.140359 | ||||||||
\(817\) | 20.6105 | 0.721071 | ||||||||
\(818\) | 28.5024 | 0.996561 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.32392 | −0.185919 | ||||||||
\(821\) | −31.8361 | −1.11109 | −0.555543 | − | 0.831488i | \(-0.687490\pi\) | ||||
−0.555543 | + | 0.831488i | \(0.687490\pi\) | |||||||
\(822\) | −16.5263 | −0.576421 | ||||||||
\(823\) | 3.12481 | 0.108924 | 0.0544620 | − | 0.998516i | \(-0.482656\pi\) | ||||
0.0544620 | + | 0.998516i | \(0.482656\pi\) | |||||||
\(824\) | 5.10476 | 0.177833 | ||||||||
\(825\) | 0.654114 | 0.0227733 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.35195 | 0.325199 | 0.162600 | − | 0.986692i | \(-0.448012\pi\) | ||||
0.162600 | + | 0.986692i | \(0.448012\pi\) | |||||||
\(828\) | 15.1850 | 0.527716 | ||||||||
\(829\) | −12.0702 | −0.419215 | −0.209608 | − | 0.977786i | \(-0.567219\pi\) | ||||
−0.209608 | + | 0.977786i | \(0.567219\pi\) | |||||||
\(830\) | −11.6942 | −0.405910 | ||||||||
\(831\) | 24.1746 | 0.838608 | ||||||||
\(832\) | 41.6985 | 1.44564 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −18.6129 | −0.644513 | ||||||||
\(835\) | −34.0622 | −1.17877 | ||||||||
\(836\) | 22.8872 | 0.791570 | ||||||||
\(837\) | −1.07464 | −0.0371450 | ||||||||
\(838\) | 10.4514 | 0.361037 | ||||||||
\(839\) | −14.1488 | −0.488472 | −0.244236 | − | 0.969716i | \(-0.578537\pi\) | ||||
−0.244236 | + | 0.969716i | \(0.578537\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.3245 | −0.597396 | ||||||||
\(842\) | 73.4091 | 2.52985 | ||||||||
\(843\) | 11.0063 | 0.379078 | ||||||||
\(844\) | −29.4801 | −1.01475 | ||||||||
\(845\) | 7.89898 | 0.271733 | ||||||||
\(846\) | −22.7254 | −0.781314 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.2457 | 0.386178 | ||||||||
\(849\) | −16.1057 | −0.552748 | ||||||||
\(850\) | −0.742569 | −0.0254699 | ||||||||
\(851\) | −10.7593 | −0.368825 | ||||||||
\(852\) | 12.1353 | 0.415747 | ||||||||
\(853\) | −51.9016 | −1.77708 | −0.888538 | − | 0.458804i | \(-0.848278\pi\) | ||||
−0.888538 | + | 0.458804i | \(0.848278\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.1480 | −0.347055 | ||||||||
\(856\) | 9.74210 | 0.332978 | ||||||||
\(857\) | −26.5421 | −0.906662 | −0.453331 | − | 0.891342i | \(-0.649764\pi\) | ||||
−0.453331 | + | 0.891342i | \(0.649764\pi\) | |||||||
\(858\) | −18.8760 | −0.644415 | ||||||||
\(859\) | −24.1629 | −0.824427 | −0.412214 | − | 0.911087i | \(-0.635244\pi\) | ||||
−0.412214 | + | 0.911087i | \(0.635244\pi\) | |||||||
\(860\) | −24.8737 | −0.848187 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.7777 | −0.707692 | ||||||||
\(863\) | 49.6475 | 1.69002 | 0.845011 | − | 0.534749i | \(-0.179594\pi\) | ||||
0.845011 | + | 0.534749i | \(0.179594\pi\) | |||||||
\(864\) | 8.10315 | 0.275675 | ||||||||
\(865\) | 48.7088 | 1.65615 | ||||||||
\(866\) | −0.474824 | −0.0161352 | ||||||||
\(867\) | 15.4989 | 0.526369 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.96406 | −0.270162 | ||||||||
\(870\) | −16.3267 | −0.553526 | ||||||||
\(871\) | −44.2523 | −1.49943 | ||||||||
\(872\) | −1.59835 | −0.0541270 | ||||||||
\(873\) | 3.88945 | 0.131638 | ||||||||
\(874\) | −60.1206 | −2.03361 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.1912 | 0.445689 | ||||||||
\(877\) | −0.127968 | −0.00432118 | −0.00216059 | − | 0.999998i | \(-0.500688\pi\) | ||||
−0.00216059 | + | 0.999998i | \(0.500688\pi\) | |||||||
\(878\) | 13.7877 | 0.465313 | ||||||||
\(879\) | 12.6292 | 0.425974 | ||||||||
\(880\) | 16.8756 | 0.568877 | ||||||||
\(881\) | 35.9413 | 1.21089 | 0.605446 | − | 0.795886i | \(-0.292995\pi\) | ||||
0.605446 | + | 0.795886i | \(0.292995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.5574 | 0.422590 | 0.211295 | − | 0.977422i | \(-0.432232\pi\) | ||||
0.211295 | + | 0.977422i | \(0.432232\pi\) | |||||||
\(884\) | 11.4949 | 0.386617 | ||||||||
\(885\) | 22.7743 | 0.765551 | ||||||||
\(886\) | −71.2224 | −2.39276 | ||||||||
\(887\) | 13.9193 | 0.467364 | 0.233682 | − | 0.972313i | \(-0.424922\pi\) | ||||
0.233682 | + | 0.972313i | \(0.424922\pi\) | |||||||
\(888\) | 1.07073 | 0.0359312 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −26.3627 | −0.883679 | ||||||||
\(891\) | −2.24173 | −0.0751007 | ||||||||
\(892\) | 33.6525 | 1.12677 | ||||||||
\(893\) | 48.2651 | 1.61513 | ||||||||
\(894\) | 7.36851 | 0.246440 | ||||||||
\(895\) | 16.3084 | 0.545129 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.5983 | 0.888092 | ||||||||
\(898\) | −49.4362 | −1.64971 | ||||||||
\(899\) | 3.67199 | 0.122468 | ||||||||
\(900\) | 0.675306 | 0.0225102 | ||||||||
\(901\) | 4.21035 | 0.140267 | ||||||||
\(902\) | 4.65630 | 0.155038 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.70060 | −0.123080 | ||||||||
\(905\) | −55.2974 | −1.83815 | ||||||||
\(906\) | 18.6739 | 0.620398 | ||||||||
\(907\) | −44.7454 | −1.48575 | −0.742874 | − | 0.669431i | \(-0.766538\pi\) | ||||
−0.742874 | + | 0.669431i | \(0.766538\pi\) | |||||||
\(908\) | 29.5307 | 0.980011 | ||||||||
\(909\) | −11.7539 | −0.389853 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4251 | −0.345400 | −0.172700 | − | 0.984975i | \(-0.555249\pi\) | ||||
−0.172700 | + | 0.984975i | \(0.555249\pi\) | |||||||
\(912\) | −14.4363 | −0.478033 | ||||||||
\(913\) | 5.48647 | 0.181576 | ||||||||
\(914\) | 8.09663 | 0.267813 | ||||||||
\(915\) | 11.9352 | 0.394565 | ||||||||
\(916\) | 37.8480 | 1.25053 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.54488 | 0.0839934 | ||||||||
\(919\) | 24.6925 | 0.814532 | 0.407266 | − | 0.913310i | \(-0.366482\pi\) | ||||
0.407266 | + | 0.913310i | \(0.366482\pi\) | |||||||
\(920\) | 9.85521 | 0.324917 | ||||||||
\(921\) | −23.2927 | −0.767522 | ||||||||
\(922\) | −18.3268 | −0.603561 | ||||||||
\(923\) | 21.2563 | 0.699659 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.478486 | −0.0157325 | ||||||||
\(926\) | −56.3077 | −1.85039 | ||||||||
\(927\) | 7.81801 | 0.256777 | ||||||||
\(928\) | −27.6880 | −0.908904 | ||||||||
\(929\) | −0.159923 | −0.00524692 | −0.00262346 | − | 0.999997i | \(-0.500835\pi\) | ||||
−0.00262346 | + | 0.999997i | \(0.500835\pi\) | |||||||
\(930\) | −5.13479 | −0.168376 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 59.4356 | 1.94688 | ||||||||
\(933\) | 8.17595 | 0.267669 | ||||||||
\(934\) | −82.3814 | −2.69560 | ||||||||
\(935\) | 6.31819 | 0.206627 | ||||||||
\(936\) | −2.64696 | −0.0865186 | ||||||||
\(937\) | 28.2710 | 0.923572 | 0.461786 | − | 0.886991i | \(-0.347209\pi\) | ||||
0.461786 | + | 0.886991i | \(0.347209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9412 | 0.552857 | ||||||||
\(940\) | −58.2485 | −1.89986 | ||||||||
\(941\) | 12.0075 | 0.391434 | 0.195717 | − | 0.980660i | \(-0.437297\pi\) | ||||
0.195717 | + | 0.980660i | \(0.437297\pi\) | |||||||
\(942\) | −14.5735 | −0.474830 | ||||||||
\(943\) | −6.56124 | −0.213663 | ||||||||
\(944\) | 32.3981 | 1.05447 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.7545 | 0.707301 | ||||||||
\(947\) | 1.30006 | 0.0422463 | 0.0211232 | − | 0.999777i | \(-0.493276\pi\) | ||||
0.0211232 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(948\) | −8.22209 | −0.267041 | ||||||||
\(949\) | 23.1059 | 0.750049 | ||||||||
\(950\) | −2.67367 | −0.0867454 | ||||||||
\(951\) | −10.8754 | −0.352659 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.2749 | −1.88771 | −0.943854 | − | 0.330363i | \(-0.892829\pi\) | ||||
−0.943854 | + | 0.330363i | \(0.892829\pi\) | |||||||
\(954\) | −7.13785 | −0.231096 | ||||||||
\(955\) | 45.4880 | 1.47196 | ||||||||
\(956\) | −15.4678 | −0.500265 | ||||||||
\(957\) | 7.65986 | 0.247608 | ||||||||
\(958\) | 1.37364 | 0.0443803 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 23.6621 | 0.763692 | ||||||||
\(961\) | −29.8451 | −0.962747 | ||||||||
\(962\) | 13.8078 | 0.445182 | ||||||||
\(963\) | 14.9202 | 0.480795 | ||||||||
\(964\) | 29.6514 | 0.955006 | ||||||||
\(965\) | −24.7031 | −0.795220 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.2902 | 1.26349 | 0.631743 | − | 0.775178i | \(-0.282340\pi\) | ||||
0.631743 | + | 0.775178i | \(0.282340\pi\) | |||||||
\(968\) | −3.90115 | −0.125388 | ||||||||
\(969\) | −5.40491 | −0.173631 | ||||||||
\(970\) | 18.5844 | 0.596708 | ||||||||
\(971\) | −56.1663 | −1.80246 | −0.901232 | − | 0.433338i | \(-0.857336\pi\) | ||||
−0.901232 | + | 0.433338i | \(0.857336\pi\) | |||||||
\(972\) | −2.31436 | −0.0742330 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −25.0999 | −0.804251 | ||||||||
\(975\) | 1.18288 | 0.0378823 | ||||||||
\(976\) | 16.9787 | 0.543474 | ||||||||
\(977\) | −14.6676 | −0.469259 | −0.234629 | − | 0.972085i | \(-0.575388\pi\) | ||||
−0.234629 | + | 0.972085i | \(0.575388\pi\) | |||||||
\(978\) | −38.5461 | −1.23257 | ||||||||
\(979\) | 12.3684 | 0.395295 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.44790 | −0.0781554 | ||||||||
\(982\) | −12.2471 | −0.390821 | ||||||||
\(983\) | 29.8488 | 0.952027 | 0.476014 | − | 0.879438i | \(-0.342081\pi\) | ||||
0.476014 | + | 0.879438i | \(0.342081\pi\) | |||||||
\(984\) | 0.652949 | 0.0208152 | ||||||||
\(985\) | −59.0825 | −1.88253 | ||||||||
\(986\) | −8.69570 | −0.276928 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 41.3884 | 1.31674 | ||||||||
\(989\) | −30.6546 | −0.974758 | ||||||||
\(990\) | −10.7113 | −0.340427 | ||||||||
\(991\) | −48.8390 | −1.55142 | −0.775710 | − | 0.631089i | \(-0.782608\pi\) | ||||
−0.775710 | + | 0.631089i | \(0.782608\pi\) | |||||||
\(992\) | −8.70797 | −0.276478 | ||||||||
\(993\) | 12.5272 | 0.397539 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.4469 | −0.901827 | ||||||||
\(996\) | 5.66422 | 0.179478 | ||||||||
\(997\) | 43.4145 | 1.37495 | 0.687475 | − | 0.726208i | \(-0.258719\pi\) | ||||
0.687475 | + | 0.726208i | \(0.258719\pi\) | |||||||
\(998\) | −20.0807 | −0.635644 | ||||||||
\(999\) | 1.63983 | 0.0518820 |
(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 | 6027.2.a.bb.1.7 | 8 | ||
7.2 | even | 3 | 861.2.i.d.739.2 | yes | 16 | ||
7.4 | even | 3 | 861.2.i.d.247.2 | ✓ | 16 | ||
7.6 | odd | 2 | 6027.2.a.bc.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.d.247.2 | ✓ | 16 | 7.4 | even | 3 | ||
861.2.i.d.739.2 | yes | 16 | 7.2 | even | 3 | ||
6027.2.a.bb.1.7 | 8 | 1.1 | even | 1 | trivial | ||
6027.2.a.bc.1.7 | 8 | 7.6 | odd | 2 |