Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + 5490 x^{8} - 2787 x^{7} - 10540 x^{6} + 1919 x^{5} + 10822 x^{4} + 132 x^{3} + \cdots + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.861451\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.138549 | 0.0799913 | 0.0399957 | − | 0.999200i | \(-0.487266\pi\) | ||||
0.0399957 | + | 0.999200i | \(0.487266\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.13854 | 0.509169 | 0.254584 | − | 0.967051i | \(-0.418061\pi\) | ||||
0.254584 | + | 0.967051i | \(0.418061\pi\) | |||||||
\(6\) | 0.138549 | 0.0565624 | ||||||||
\(7\) | −2.28657 | −0.864244 | −0.432122 | − | 0.901815i | \(-0.642235\pi\) | ||||
−0.432122 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.98080 | −0.993601 | ||||||||
\(10\) | 1.13854 | 0.360037 | ||||||||
\(11\) | 4.66208 | 1.40567 | 0.702835 | − | 0.711353i | \(-0.251917\pi\) | ||||
0.702835 | + | 0.711353i | \(0.251917\pi\) | |||||||
\(12\) | 0.138549 | 0.0399957 | ||||||||
\(13\) | 1.82268 | 0.505521 | 0.252760 | − | 0.967529i | \(-0.418662\pi\) | ||||
0.252760 | + | 0.967529i | \(0.418662\pi\) | |||||||
\(14\) | −2.28657 | −0.611113 | ||||||||
\(15\) | 0.157743 | 0.0407291 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.36722 | 1.30174 | 0.650871 | − | 0.759189i | \(-0.274404\pi\) | ||||
0.650871 | + | 0.759189i | \(0.274404\pi\) | |||||||
\(18\) | −2.98080 | −0.702582 | ||||||||
\(19\) | −1.97980 | −0.454197 | −0.227098 | − | 0.973872i | \(-0.572924\pi\) | ||||
−0.227098 | + | 0.973872i | \(0.572924\pi\) | |||||||
\(20\) | 1.13854 | 0.254584 | ||||||||
\(21\) | −0.316803 | −0.0691320 | ||||||||
\(22\) | 4.66208 | 0.993958 | ||||||||
\(23\) | 4.84322 | 1.00988 | 0.504940 | − | 0.863154i | \(-0.331514\pi\) | ||||
0.504940 | + | 0.863154i | \(0.331514\pi\) | |||||||
\(24\) | 0.138549 | 0.0282812 | ||||||||
\(25\) | −3.70374 | −0.740747 | ||||||||
\(26\) | 1.82268 | 0.357457 | ||||||||
\(27\) | −0.828635 | −0.159471 | ||||||||
\(28\) | −2.28657 | −0.432122 | ||||||||
\(29\) | 3.73505 | 0.693581 | 0.346791 | − | 0.937943i | \(-0.387271\pi\) | ||||
0.346791 | + | 0.937943i | \(0.387271\pi\) | |||||||
\(30\) | 0.157743 | 0.0287998 | ||||||||
\(31\) | 2.93872 | 0.527810 | 0.263905 | − | 0.964549i | \(-0.414989\pi\) | ||||
0.263905 | + | 0.964549i | \(0.414989\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.645926 | 0.112441 | ||||||||
\(34\) | 5.36722 | 0.920470 | ||||||||
\(35\) | −2.60335 | −0.440046 | ||||||||
\(36\) | −2.98080 | −0.496801 | ||||||||
\(37\) | 4.76643 | 0.783596 | 0.391798 | − | 0.920051i | \(-0.371853\pi\) | ||||
0.391798 | + | 0.920051i | \(0.371853\pi\) | |||||||
\(38\) | −1.97980 | −0.321166 | ||||||||
\(39\) | 0.252531 | 0.0404373 | ||||||||
\(40\) | 1.13854 | 0.180018 | ||||||||
\(41\) | 3.64130 | 0.568676 | 0.284338 | − | 0.958724i | \(-0.408226\pi\) | ||||
0.284338 | + | 0.958724i | \(0.408226\pi\) | |||||||
\(42\) | −0.316803 | −0.0488837 | ||||||||
\(43\) | 6.16489 | 0.940136 | 0.470068 | − | 0.882630i | \(-0.344229\pi\) | ||||
0.470068 | + | 0.882630i | \(0.344229\pi\) | |||||||
\(44\) | 4.66208 | 0.702835 | ||||||||
\(45\) | −3.39375 | −0.505911 | ||||||||
\(46\) | 4.84322 | 0.714094 | ||||||||
\(47\) | 0.388521 | 0.0566716 | 0.0283358 | − | 0.999598i | \(-0.490979\pi\) | ||||
0.0283358 | + | 0.999598i | \(0.490979\pi\) | |||||||
\(48\) | 0.138549 | 0.0199978 | ||||||||
\(49\) | −1.77158 | −0.253082 | ||||||||
\(50\) | −3.70374 | −0.523787 | ||||||||
\(51\) | 0.743623 | 0.104128 | ||||||||
\(52\) | 1.82268 | 0.252760 | ||||||||
\(53\) | −0.525829 | −0.0722282 | −0.0361141 | − | 0.999348i | \(-0.511498\pi\) | ||||
−0.0361141 | + | 0.999348i | \(0.511498\pi\) | |||||||
\(54\) | −0.828635 | −0.112763 | ||||||||
\(55\) | 5.30794 | 0.715723 | ||||||||
\(56\) | −2.28657 | −0.305556 | ||||||||
\(57\) | −0.274299 | −0.0363318 | ||||||||
\(58\) | 3.73505 | 0.490436 | ||||||||
\(59\) | 14.4444 | 1.88050 | 0.940248 | − | 0.340490i | \(-0.110593\pi\) | ||||
0.940248 | + | 0.340490i | \(0.110593\pi\) | |||||||
\(60\) | 0.157743 | 0.0203645 | ||||||||
\(61\) | −10.2226 | −1.30888 | −0.654438 | − | 0.756116i | \(-0.727095\pi\) | ||||
−0.654438 | + | 0.756116i | \(0.727095\pi\) | |||||||
\(62\) | 2.93872 | 0.373218 | ||||||||
\(63\) | 6.81583 | 0.858714 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.07519 | 0.257395 | ||||||||
\(66\) | 0.645926 | 0.0795080 | ||||||||
\(67\) | −10.4758 | −1.27982 | −0.639910 | − | 0.768450i | \(-0.721028\pi\) | ||||
−0.639910 | + | 0.768450i | \(0.721028\pi\) | |||||||
\(68\) | 5.36722 | 0.650871 | ||||||||
\(69\) | 0.671023 | 0.0807817 | ||||||||
\(70\) | −2.60335 | −0.311160 | ||||||||
\(71\) | −0.842117 | −0.0999409 | −0.0499704 | − | 0.998751i | \(-0.515913\pi\) | ||||
−0.0499704 | + | 0.998751i | \(0.515913\pi\) | |||||||
\(72\) | −2.98080 | −0.351291 | ||||||||
\(73\) | −7.06349 | −0.826718 | −0.413359 | − | 0.910568i | \(-0.635645\pi\) | ||||
−0.413359 | + | 0.910568i | \(0.635645\pi\) | |||||||
\(74\) | 4.76643 | 0.554086 | ||||||||
\(75\) | −0.513149 | −0.0592533 | ||||||||
\(76\) | −1.97980 | −0.227098 | ||||||||
\(77\) | −10.6602 | −1.21484 | ||||||||
\(78\) | 0.252531 | 0.0285935 | ||||||||
\(79\) | −3.58053 | −0.402841 | −0.201420 | − | 0.979505i | \(-0.564556\pi\) | ||||
−0.201420 | + | 0.979505i | \(0.564556\pi\) | |||||||
\(80\) | 1.13854 | 0.127292 | ||||||||
\(81\) | 8.82761 | 0.980845 | ||||||||
\(82\) | 3.64130 | 0.402115 | ||||||||
\(83\) | 5.10442 | 0.560283 | 0.280142 | − | 0.959959i | \(-0.409619\pi\) | ||||
0.280142 | + | 0.959959i | \(0.409619\pi\) | |||||||
\(84\) | −0.316803 | −0.0345660 | ||||||||
\(85\) | 6.11077 | 0.662806 | ||||||||
\(86\) | 6.16489 | 0.664777 | ||||||||
\(87\) | 0.517488 | 0.0554805 | ||||||||
\(88\) | 4.66208 | 0.496979 | ||||||||
\(89\) | −0.209053 | −0.0221596 | −0.0110798 | − | 0.999939i | \(-0.503527\pi\) | ||||
−0.0110798 | + | 0.999939i | \(0.503527\pi\) | |||||||
\(90\) | −3.39375 | −0.357733 | ||||||||
\(91\) | −4.16770 | −0.436894 | ||||||||
\(92\) | 4.84322 | 0.504940 | ||||||||
\(93\) | 0.407157 | 0.0422202 | ||||||||
\(94\) | 0.388521 | 0.0400729 | ||||||||
\(95\) | −2.25407 | −0.231263 | ||||||||
\(96\) | 0.138549 | 0.0141406 | ||||||||
\(97\) | −10.5510 | −1.07129 | −0.535646 | − | 0.844443i | \(-0.679932\pi\) | ||||
−0.535646 | + | 0.844443i | \(0.679932\pi\) | |||||||
\(98\) | −1.77158 | −0.178956 | ||||||||
\(99\) | −13.8967 | −1.39667 | ||||||||
\(100\) | −3.70374 | −0.370374 | ||||||||
\(101\) | 8.90464 | 0.886045 | 0.443023 | − | 0.896510i | \(-0.353906\pi\) | ||||
0.443023 | + | 0.896510i | \(0.353906\pi\) | |||||||
\(102\) | 0.743623 | 0.0736296 | ||||||||
\(103\) | −10.6656 | −1.05091 | −0.525455 | − | 0.850822i | \(-0.676105\pi\) | ||||
−0.525455 | + | 0.850822i | \(0.676105\pi\) | |||||||
\(104\) | 1.82268 | 0.178729 | ||||||||
\(105\) | −0.360691 | −0.0351999 | ||||||||
\(106\) | −0.525829 | −0.0510730 | ||||||||
\(107\) | −10.7423 | −1.03849 | −0.519246 | − | 0.854625i | \(-0.673787\pi\) | ||||
−0.519246 | + | 0.854625i | \(0.673787\pi\) | |||||||
\(108\) | −0.828635 | −0.0797354 | ||||||||
\(109\) | −11.6993 | −1.12059 | −0.560297 | − | 0.828292i | \(-0.689313\pi\) | ||||
−0.560297 | + | 0.828292i | \(0.689313\pi\) | |||||||
\(110\) | 5.30794 | 0.506092 | ||||||||
\(111\) | 0.660384 | 0.0626809 | ||||||||
\(112\) | −2.28657 | −0.216061 | ||||||||
\(113\) | 15.2792 | 1.43735 | 0.718675 | − | 0.695346i | \(-0.244749\pi\) | ||||
0.718675 | + | 0.695346i | \(0.244749\pi\) | |||||||
\(114\) | −0.274299 | −0.0256905 | ||||||||
\(115\) | 5.51418 | 0.514200 | ||||||||
\(116\) | 3.73505 | 0.346791 | ||||||||
\(117\) | −5.43306 | −0.502286 | ||||||||
\(118\) | 14.4444 | 1.32971 | ||||||||
\(119\) | −12.2725 | −1.12502 | ||||||||
\(120\) | 0.157743 | 0.0143999 | ||||||||
\(121\) | 10.7350 | 0.975906 | ||||||||
\(122\) | −10.2226 | −0.925515 | ||||||||
\(123\) | 0.504499 | 0.0454891 | ||||||||
\(124\) | 2.93872 | 0.263905 | ||||||||
\(125\) | −9.90952 | −0.886334 | ||||||||
\(126\) | 6.81583 | 0.607203 | ||||||||
\(127\) | −6.13297 | −0.544213 | −0.272107 | − | 0.962267i | \(-0.587720\pi\) | ||||
−0.272107 | + | 0.962267i | \(0.587720\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.854139 | 0.0752027 | ||||||||
\(130\) | 2.07519 | 0.182006 | ||||||||
\(131\) | −7.17094 | −0.626528 | −0.313264 | − | 0.949666i | \(-0.601422\pi\) | ||||
−0.313264 | + | 0.949666i | \(0.601422\pi\) | |||||||
\(132\) | 0.645926 | 0.0562207 | ||||||||
\(133\) | 4.52696 | 0.392537 | ||||||||
\(134\) | −10.4758 | −0.904969 | ||||||||
\(135\) | −0.943430 | −0.0811975 | ||||||||
\(136\) | 5.36722 | 0.460235 | ||||||||
\(137\) | −2.24576 | −0.191868 | −0.0959340 | − | 0.995388i | \(-0.530584\pi\) | ||||
−0.0959340 | + | 0.995388i | \(0.530584\pi\) | |||||||
\(138\) | 0.671023 | 0.0571213 | ||||||||
\(139\) | 12.4554 | 1.05645 | 0.528226 | − | 0.849104i | \(-0.322857\pi\) | ||||
0.528226 | + | 0.849104i | \(0.322857\pi\) | |||||||
\(140\) | −2.60335 | −0.220023 | ||||||||
\(141\) | 0.0538292 | 0.00453323 | ||||||||
\(142\) | −0.842117 | −0.0706689 | ||||||||
\(143\) | 8.49748 | 0.710595 | ||||||||
\(144\) | −2.98080 | −0.248400 | ||||||||
\(145\) | 4.25249 | 0.353150 | ||||||||
\(146\) | −7.06349 | −0.584578 | ||||||||
\(147\) | −0.245450 | −0.0202444 | ||||||||
\(148\) | 4.76643 | 0.391798 | ||||||||
\(149\) | −15.6328 | −1.28069 | −0.640343 | − | 0.768089i | \(-0.721208\pi\) | ||||
−0.640343 | + | 0.768089i | \(0.721208\pi\) | |||||||
\(150\) | −0.513149 | −0.0418984 | ||||||||
\(151\) | 13.1386 | 1.06920 | 0.534602 | − | 0.845104i | \(-0.320462\pi\) | ||||
0.534602 | + | 0.845104i | \(0.320462\pi\) | |||||||
\(152\) | −1.97980 | −0.160583 | ||||||||
\(153\) | −15.9986 | −1.29341 | ||||||||
\(154\) | −10.6602 | −0.859022 | ||||||||
\(155\) | 3.34584 | 0.268744 | ||||||||
\(156\) | 0.252531 | 0.0202186 | ||||||||
\(157\) | −17.4965 | −1.39638 | −0.698188 | − | 0.715914i | \(-0.746010\pi\) | ||||
−0.698188 | + | 0.715914i | \(0.746010\pi\) | |||||||
\(158\) | −3.58053 | −0.284851 | ||||||||
\(159\) | −0.0728531 | −0.00577762 | ||||||||
\(160\) | 1.13854 | 0.0900092 | ||||||||
\(161\) | −11.0744 | −0.872783 | ||||||||
\(162\) | 8.82761 | 0.693562 | ||||||||
\(163\) | −5.75782 | −0.450987 | −0.225494 | − | 0.974245i | \(-0.572399\pi\) | ||||
−0.225494 | + | 0.974245i | \(0.572399\pi\) | |||||||
\(164\) | 3.64130 | 0.284338 | ||||||||
\(165\) | 0.735410 | 0.0572516 | ||||||||
\(166\) | 5.10442 | 0.396180 | ||||||||
\(167\) | 16.6673 | 1.28975 | 0.644876 | − | 0.764287i | \(-0.276909\pi\) | ||||
0.644876 | + | 0.764287i | \(0.276909\pi\) | |||||||
\(168\) | −0.316803 | −0.0244419 | ||||||||
\(169\) | −9.67783 | −0.744449 | ||||||||
\(170\) | 6.11077 | 0.468675 | ||||||||
\(171\) | 5.90139 | 0.451291 | ||||||||
\(172\) | 6.16489 | 0.470068 | ||||||||
\(173\) | −5.18347 | −0.394092 | −0.197046 | − | 0.980394i | \(-0.563135\pi\) | ||||
−0.197046 | + | 0.980394i | \(0.563135\pi\) | |||||||
\(174\) | 0.517488 | 0.0392306 | ||||||||
\(175\) | 8.46887 | 0.640186 | ||||||||
\(176\) | 4.66208 | 0.351417 | ||||||||
\(177\) | 2.00125 | 0.150423 | ||||||||
\(178\) | −0.209053 | −0.0156692 | ||||||||
\(179\) | −1.73198 | −0.129455 | −0.0647273 | − | 0.997903i | \(-0.520618\pi\) | ||||
−0.0647273 | + | 0.997903i | \(0.520618\pi\) | |||||||
\(180\) | −3.39375 | −0.252955 | ||||||||
\(181\) | 17.2557 | 1.28261 | 0.641303 | − | 0.767288i | \(-0.278394\pi\) | ||||
0.641303 | + | 0.767288i | \(0.278394\pi\) | |||||||
\(182\) | −4.16770 | −0.308930 | ||||||||
\(183\) | −1.41634 | −0.104699 | ||||||||
\(184\) | 4.84322 | 0.357047 | ||||||||
\(185\) | 5.42675 | 0.398983 | ||||||||
\(186\) | 0.407157 | 0.0298542 | ||||||||
\(187\) | 25.0224 | 1.82982 | ||||||||
\(188\) | 0.388521 | 0.0283358 | ||||||||
\(189\) | 1.89473 | 0.137822 | ||||||||
\(190\) | −2.25407 | −0.163528 | ||||||||
\(191\) | 23.1592 | 1.67574 | 0.837872 | − | 0.545867i | \(-0.183800\pi\) | ||||
0.837872 | + | 0.545867i | \(0.183800\pi\) | |||||||
\(192\) | 0.138549 | 0.00999891 | ||||||||
\(193\) | 1.10413 | 0.0794771 | 0.0397386 | − | 0.999210i | \(-0.487347\pi\) | ||||
0.0397386 | + | 0.999210i | \(0.487347\pi\) | |||||||
\(194\) | −10.5510 | −0.757518 | ||||||||
\(195\) | 0.287515 | 0.0205894 | ||||||||
\(196\) | −1.77158 | −0.126541 | ||||||||
\(197\) | −4.14299 | −0.295176 | −0.147588 | − | 0.989049i | \(-0.547151\pi\) | ||||
−0.147588 | + | 0.989049i | \(0.547151\pi\) | |||||||
\(198\) | −13.8967 | −0.987598 | ||||||||
\(199\) | 9.85628 | 0.698693 | 0.349347 | − | 0.936994i | \(-0.386404\pi\) | ||||
0.349347 | + | 0.936994i | \(0.386404\pi\) | |||||||
\(200\) | −3.70374 | −0.261894 | ||||||||
\(201\) | −1.45141 | −0.102374 | ||||||||
\(202\) | 8.90464 | 0.626528 | ||||||||
\(203\) | −8.54047 | −0.599424 | ||||||||
\(204\) | 0.743623 | 0.0520640 | ||||||||
\(205\) | 4.14575 | 0.289552 | ||||||||
\(206\) | −10.6656 | −0.743105 | ||||||||
\(207\) | −14.4367 | −1.00342 | ||||||||
\(208\) | 1.82268 | 0.126380 | ||||||||
\(209\) | −9.22997 | −0.638451 | ||||||||
\(210\) | −0.360691 | −0.0248901 | ||||||||
\(211\) | −18.3543 | −1.26356 | −0.631780 | − | 0.775148i | \(-0.717675\pi\) | ||||
−0.631780 | + | 0.775148i | \(0.717675\pi\) | |||||||
\(212\) | −0.525829 | −0.0361141 | ||||||||
\(213\) | −0.116674 | −0.00799440 | ||||||||
\(214\) | −10.7423 | −0.734325 | ||||||||
\(215\) | 7.01894 | 0.478688 | ||||||||
\(216\) | −0.828635 | −0.0563814 | ||||||||
\(217\) | −6.71961 | −0.456157 | ||||||||
\(218\) | −11.6993 | −0.792379 | ||||||||
\(219\) | −0.978639 | −0.0661303 | ||||||||
\(220\) | 5.30794 | 0.357861 | ||||||||
\(221\) | 9.78273 | 0.658058 | ||||||||
\(222\) | 0.660384 | 0.0443221 | ||||||||
\(223\) | −1.09531 | −0.0733471 | −0.0366735 | − | 0.999327i | \(-0.511676\pi\) | ||||
−0.0366735 | + | 0.999327i | \(0.511676\pi\) | |||||||
\(224\) | −2.28657 | −0.152778 | ||||||||
\(225\) | 11.0401 | 0.736007 | ||||||||
\(226\) | 15.2792 | 1.01636 | ||||||||
\(227\) | −2.25099 | −0.149404 | −0.0747018 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747018 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(228\) | −0.274299 | −0.0181659 | ||||||||
\(229\) | −13.2224 | −0.873764 | −0.436882 | − | 0.899519i | \(-0.643917\pi\) | ||||
−0.436882 | + | 0.899519i | \(0.643917\pi\) | |||||||
\(230\) | 5.51418 | 0.363594 | ||||||||
\(231\) | −1.47696 | −0.0971767 | ||||||||
\(232\) | 3.73505 | 0.245218 | ||||||||
\(233\) | −4.72089 | −0.309276 | −0.154638 | − | 0.987971i | \(-0.549421\pi\) | ||||
−0.154638 | + | 0.987971i | \(0.549421\pi\) | |||||||
\(234\) | −5.43306 | −0.355170 | ||||||||
\(235\) | 0.442345 | 0.0288554 | ||||||||
\(236\) | 14.4444 | 0.940248 | ||||||||
\(237\) | −0.496078 | −0.0322237 | ||||||||
\(238\) | −12.2725 | −0.795511 | ||||||||
\(239\) | 5.84687 | 0.378203 | 0.189101 | − | 0.981958i | \(-0.439443\pi\) | ||||
0.189101 | + | 0.981958i | \(0.439443\pi\) | |||||||
\(240\) | 0.157743 | 0.0101823 | ||||||||
\(241\) | −0.115891 | −0.00746520 | −0.00373260 | − | 0.999993i | \(-0.501188\pi\) | ||||
−0.00373260 | + | 0.999993i | \(0.501188\pi\) | |||||||
\(242\) | 10.7350 | 0.690070 | ||||||||
\(243\) | 3.70896 | 0.237930 | ||||||||
\(244\) | −10.2226 | −0.654438 | ||||||||
\(245\) | −2.01700 | −0.128862 | ||||||||
\(246\) | 0.504499 | 0.0321657 | ||||||||
\(247\) | −3.60854 | −0.229606 | ||||||||
\(248\) | 2.93872 | 0.186609 | ||||||||
\(249\) | 0.707213 | 0.0448178 | ||||||||
\(250\) | −9.90952 | −0.626733 | ||||||||
\(251\) | −7.68083 | −0.484809 | −0.242405 | − | 0.970175i | \(-0.577936\pi\) | ||||
−0.242405 | + | 0.970175i | \(0.577936\pi\) | |||||||
\(252\) | 6.81583 | 0.429357 | ||||||||
\(253\) | 22.5795 | 1.41956 | ||||||||
\(254\) | −6.13297 | −0.384817 | ||||||||
\(255\) | 0.846641 | 0.0530187 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.7498 | −1.41909 | −0.709546 | − | 0.704660i | \(-0.751100\pi\) | ||||
−0.709546 | + | 0.704660i | \(0.751100\pi\) | |||||||
\(258\) | 0.854139 | 0.0531764 | ||||||||
\(259\) | −10.8988 | −0.677218 | ||||||||
\(260\) | 2.07519 | 0.128698 | ||||||||
\(261\) | −11.1335 | −0.689143 | ||||||||
\(262\) | −7.17094 | −0.443022 | ||||||||
\(263\) | 28.3260 | 1.74666 | 0.873329 | − | 0.487130i | \(-0.161956\pi\) | ||||
0.873329 | + | 0.487130i | \(0.161956\pi\) | |||||||
\(264\) | 0.645926 | 0.0397540 | ||||||||
\(265\) | −0.598675 | −0.0367763 | ||||||||
\(266\) | 4.52696 | 0.277566 | ||||||||
\(267\) | −0.0289641 | −0.00177257 | ||||||||
\(268\) | −10.4758 | −0.639910 | ||||||||
\(269\) | −25.1503 | −1.53344 | −0.766721 | − | 0.641981i | \(-0.778113\pi\) | ||||
−0.766721 | + | 0.641981i | \(0.778113\pi\) | |||||||
\(270\) | −0.943430 | −0.0574153 | ||||||||
\(271\) | −21.3951 | −1.29966 | −0.649829 | − | 0.760080i | \(-0.725160\pi\) | ||||
−0.649829 | + | 0.760080i | \(0.725160\pi\) | |||||||
\(272\) | 5.36722 | 0.325435 | ||||||||
\(273\) | −0.577431 | −0.0349477 | ||||||||
\(274\) | −2.24576 | −0.135671 | ||||||||
\(275\) | −17.2671 | −1.04125 | ||||||||
\(276\) | 0.671023 | 0.0403908 | ||||||||
\(277\) | −9.82730 | −0.590465 | −0.295233 | − | 0.955425i | \(-0.595397\pi\) | ||||
−0.295233 | + | 0.955425i | \(0.595397\pi\) | |||||||
\(278\) | 12.4554 | 0.747025 | ||||||||
\(279\) | −8.75976 | −0.524433 | ||||||||
\(280\) | −2.60335 | −0.155580 | ||||||||
\(281\) | −17.7452 | −1.05859 | −0.529295 | − | 0.848438i | \(-0.677544\pi\) | ||||
−0.529295 | + | 0.848438i | \(0.677544\pi\) | |||||||
\(282\) | 0.0538292 | 0.00320548 | ||||||||
\(283\) | −27.8139 | −1.65336 | −0.826682 | − | 0.562669i | \(-0.809774\pi\) | ||||
−0.826682 | + | 0.562669i | \(0.809774\pi\) | |||||||
\(284\) | −0.842117 | −0.0499704 | ||||||||
\(285\) | −0.312299 | −0.0184990 | ||||||||
\(286\) | 8.49748 | 0.502467 | ||||||||
\(287\) | −8.32611 | −0.491475 | ||||||||
\(288\) | −2.98080 | −0.175646 | ||||||||
\(289\) | 11.8070 | 0.694530 | ||||||||
\(290\) | 4.25249 | 0.249715 | ||||||||
\(291\) | −1.46183 | −0.0856940 | ||||||||
\(292\) | −7.06349 | −0.413359 | ||||||||
\(293\) | 0.342825 | 0.0200281 | 0.0100140 | − | 0.999950i | \(-0.496812\pi\) | ||||
0.0100140 | + | 0.999950i | \(0.496812\pi\) | |||||||
\(294\) | −0.245450 | −0.0143149 | ||||||||
\(295\) | 16.4454 | 0.957490 | ||||||||
\(296\) | 4.76643 | 0.277043 | ||||||||
\(297\) | −3.86316 | −0.224163 | ||||||||
\(298\) | −15.6328 | −0.905582 | ||||||||
\(299\) | 8.82765 | 0.510516 | ||||||||
\(300\) | −0.513149 | −0.0296267 | ||||||||
\(301\) | −14.0965 | −0.812507 | ||||||||
\(302\) | 13.1386 | 0.756041 | ||||||||
\(303\) | 1.23373 | 0.0708759 | ||||||||
\(304\) | −1.97980 | −0.113549 | ||||||||
\(305\) | −11.6389 | −0.666439 | ||||||||
\(306\) | −15.9986 | −0.914580 | ||||||||
\(307\) | 19.5763 | 1.11728 | 0.558640 | − | 0.829410i | \(-0.311323\pi\) | ||||
0.558640 | + | 0.829410i | \(0.311323\pi\) | |||||||
\(308\) | −10.6602 | −0.607421 | ||||||||
\(309\) | −1.47770 | −0.0840636 | ||||||||
\(310\) | 3.34584 | 0.190031 | ||||||||
\(311\) | −23.1403 | −1.31217 | −0.656084 | − | 0.754688i | \(-0.727788\pi\) | ||||
−0.656084 | + | 0.754688i | \(0.727788\pi\) | |||||||
\(312\) | 0.252531 | 0.0142967 | ||||||||
\(313\) | 7.89543 | 0.446276 | 0.223138 | − | 0.974787i | \(-0.428370\pi\) | ||||
0.223138 | + | 0.974787i | \(0.428370\pi\) | |||||||
\(314\) | −17.4965 | −0.987387 | ||||||||
\(315\) | 7.76007 | 0.437230 | ||||||||
\(316\) | −3.58053 | −0.201420 | ||||||||
\(317\) | −9.95610 | −0.559190 | −0.279595 | − | 0.960118i | \(-0.590200\pi\) | ||||
−0.279595 | + | 0.960118i | \(0.590200\pi\) | |||||||
\(318\) | −0.0728531 | −0.00408540 | ||||||||
\(319\) | 17.4131 | 0.974946 | ||||||||
\(320\) | 1.13854 | 0.0636461 | ||||||||
\(321\) | −1.48833 | −0.0830704 | ||||||||
\(322\) | −11.0744 | −0.617151 | ||||||||
\(323\) | −10.6260 | −0.591247 | ||||||||
\(324\) | 8.82761 | 0.490423 | ||||||||
\(325\) | −6.75073 | −0.374463 | ||||||||
\(326\) | −5.75782 | −0.318896 | ||||||||
\(327\) | −1.62093 | −0.0896377 | ||||||||
\(328\) | 3.64130 | 0.201057 | ||||||||
\(329\) | −0.888382 | −0.0489781 | ||||||||
\(330\) | 0.735410 | 0.0404830 | ||||||||
\(331\) | −14.4038 | −0.791704 | −0.395852 | − | 0.918314i | \(-0.629551\pi\) | ||||
−0.395852 | + | 0.918314i | \(0.629551\pi\) | |||||||
\(332\) | 5.10442 | 0.280142 | ||||||||
\(333\) | −14.2078 | −0.778582 | ||||||||
\(334\) | 16.6673 | 0.911992 | ||||||||
\(335\) | −11.9270 | −0.651644 | ||||||||
\(336\) | −0.316803 | −0.0172830 | ||||||||
\(337\) | −1.71653 | −0.0935056 | −0.0467528 | − | 0.998906i | \(-0.514887\pi\) | ||||
−0.0467528 | + | 0.998906i | \(0.514887\pi\) | |||||||
\(338\) | −9.67783 | −0.526405 | ||||||||
\(339\) | 2.11692 | 0.114976 | ||||||||
\(340\) | 6.11077 | 0.331403 | ||||||||
\(341\) | 13.7006 | 0.741927 | ||||||||
\(342\) | 5.90139 | 0.319111 | ||||||||
\(343\) | 20.0569 | 1.08297 | ||||||||
\(344\) | 6.16489 | 0.332388 | ||||||||
\(345\) | 0.763984 | 0.0411315 | ||||||||
\(346\) | −5.18347 | −0.278665 | ||||||||
\(347\) | 10.7239 | 0.575689 | 0.287845 | − | 0.957677i | \(-0.407061\pi\) | ||||
0.287845 | + | 0.957677i | \(0.407061\pi\) | |||||||
\(348\) | 0.517488 | 0.0277402 | ||||||||
\(349\) | 13.0689 | 0.699563 | 0.349782 | − | 0.936831i | \(-0.386256\pi\) | ||||
0.349782 | + | 0.936831i | \(0.386256\pi\) | |||||||
\(350\) | 8.46887 | 0.452680 | ||||||||
\(351\) | −1.51034 | −0.0806158 | ||||||||
\(352\) | 4.66208 | 0.248490 | ||||||||
\(353\) | 10.7805 | 0.573788 | 0.286894 | − | 0.957962i | \(-0.407377\pi\) | ||||
0.286894 | + | 0.957962i | \(0.407377\pi\) | |||||||
\(354\) | 2.00125 | 0.106365 | ||||||||
\(355\) | −0.958780 | −0.0508868 | ||||||||
\(356\) | −0.209053 | −0.0110798 | ||||||||
\(357\) | −1.70035 | −0.0899920 | ||||||||
\(358\) | −1.73198 | −0.0915382 | ||||||||
\(359\) | 2.01409 | 0.106299 | 0.0531497 | − | 0.998587i | \(-0.483074\pi\) | ||||
0.0531497 | + | 0.998587i | \(0.483074\pi\) | |||||||
\(360\) | −3.39375 | −0.178866 | ||||||||
\(361\) | −15.0804 | −0.793705 | ||||||||
\(362\) | 17.2557 | 0.906939 | ||||||||
\(363\) | 1.48732 | 0.0780640 | ||||||||
\(364\) | −4.16770 | −0.218447 | ||||||||
\(365\) | −8.04203 | −0.420939 | ||||||||
\(366\) | −1.41634 | −0.0740332 | ||||||||
\(367\) | −8.65410 | −0.451740 | −0.225870 | − | 0.974157i | \(-0.572523\pi\) | ||||
−0.225870 | + | 0.974157i | \(0.572523\pi\) | |||||||
\(368\) | 4.84322 | 0.252470 | ||||||||
\(369\) | −10.8540 | −0.565037 | ||||||||
\(370\) | 5.42675 | 0.282123 | ||||||||
\(371\) | 1.20235 | 0.0624227 | ||||||||
\(372\) | 0.407157 | 0.0211101 | ||||||||
\(373\) | 1.86032 | 0.0963239 | 0.0481619 | − | 0.998840i | \(-0.484664\pi\) | ||||
0.0481619 | + | 0.998840i | \(0.484664\pi\) | |||||||
\(374\) | 25.0224 | 1.29388 | ||||||||
\(375\) | −1.37295 | −0.0708990 | ||||||||
\(376\) | 0.388521 | 0.0200364 | ||||||||
\(377\) | 6.80781 | 0.350620 | ||||||||
\(378\) | 1.89473 | 0.0974546 | ||||||||
\(379\) | −31.4273 | −1.61431 | −0.807157 | − | 0.590337i | \(-0.798995\pi\) | ||||
−0.807157 | + | 0.590337i | \(0.798995\pi\) | |||||||
\(380\) | −2.25407 | −0.115631 | ||||||||
\(381\) | −0.849717 | −0.0435323 | ||||||||
\(382\) | 23.1592 | 1.18493 | ||||||||
\(383\) | −4.84782 | −0.247712 | −0.123856 | − | 0.992300i | \(-0.539526\pi\) | ||||
−0.123856 | + | 0.992300i | \(0.539526\pi\) | |||||||
\(384\) | 0.138549 | 0.00707030 | ||||||||
\(385\) | −12.1370 | −0.618559 | ||||||||
\(386\) | 1.10413 | 0.0561988 | ||||||||
\(387\) | −18.3763 | −0.934121 | ||||||||
\(388\) | −10.5510 | −0.535646 | ||||||||
\(389\) | −15.2510 | −0.773256 | −0.386628 | − | 0.922236i | \(-0.626360\pi\) | ||||
−0.386628 | + | 0.922236i | \(0.626360\pi\) | |||||||
\(390\) | 0.287515 | 0.0145589 | ||||||||
\(391\) | 25.9946 | 1.31460 | ||||||||
\(392\) | −1.77158 | −0.0894781 | ||||||||
\(393\) | −0.993527 | −0.0501168 | ||||||||
\(394\) | −4.14299 | −0.208721 | ||||||||
\(395\) | −4.07656 | −0.205114 | ||||||||
\(396\) | −13.8967 | −0.698337 | ||||||||
\(397\) | 17.2077 | 0.863630 | 0.431815 | − | 0.901962i | \(-0.357873\pi\) | ||||
0.431815 | + | 0.901962i | \(0.357873\pi\) | |||||||
\(398\) | 9.85628 | 0.494051 | ||||||||
\(399\) | 0.627206 | 0.0313996 | ||||||||
\(400\) | −3.70374 | −0.185187 | ||||||||
\(401\) | 36.1817 | 1.80683 | 0.903413 | − | 0.428771i | \(-0.141053\pi\) | ||||
0.903413 | + | 0.428771i | \(0.141053\pi\) | |||||||
\(402\) | −1.45141 | −0.0723897 | ||||||||
\(403\) | 5.35636 | 0.266819 | ||||||||
\(404\) | 8.90464 | 0.443023 | ||||||||
\(405\) | 10.0505 | 0.499416 | ||||||||
\(406\) | −8.54047 | −0.423856 | ||||||||
\(407\) | 22.2215 | 1.10148 | ||||||||
\(408\) | 0.743623 | 0.0368148 | ||||||||
\(409\) | −16.9164 | −0.836463 | −0.418232 | − | 0.908340i | \(-0.637350\pi\) | ||||
−0.418232 | + | 0.908340i | \(0.637350\pi\) | |||||||
\(410\) | 4.14575 | 0.204744 | ||||||||
\(411\) | −0.311147 | −0.0153478 | ||||||||
\(412\) | −10.6656 | −0.525455 | ||||||||
\(413\) | −33.0281 | −1.62521 | ||||||||
\(414\) | −14.4367 | −0.709524 | ||||||||
\(415\) | 5.81157 | 0.285279 | ||||||||
\(416\) | 1.82268 | 0.0893643 | ||||||||
\(417\) | 1.72568 | 0.0845070 | ||||||||
\(418\) | −9.22997 | −0.451453 | ||||||||
\(419\) | 25.6805 | 1.25458 | 0.627288 | − | 0.778787i | \(-0.284165\pi\) | ||||
0.627288 | + | 0.778787i | \(0.284165\pi\) | |||||||
\(420\) | −0.360691 | −0.0175999 | ||||||||
\(421\) | 15.1695 | 0.739315 | 0.369657 | − | 0.929168i | \(-0.379475\pi\) | ||||
0.369657 | + | 0.929168i | \(0.379475\pi\) | |||||||
\(422\) | −18.3543 | −0.893472 | ||||||||
\(423\) | −1.15810 | −0.0563090 | ||||||||
\(424\) | −0.525829 | −0.0255365 | ||||||||
\(425\) | −19.8788 | −0.964261 | ||||||||
\(426\) | −0.116674 | −0.00565289 | ||||||||
\(427\) | 23.3749 | 1.13119 | ||||||||
\(428\) | −10.7423 | −0.519246 | ||||||||
\(429\) | 1.17732 | 0.0568415 | ||||||||
\(430\) | 7.01894 | 0.338484 | ||||||||
\(431\) | −22.0541 | −1.06231 | −0.531153 | − | 0.847276i | \(-0.678241\pi\) | ||||
−0.531153 | + | 0.847276i | \(0.678241\pi\) | |||||||
\(432\) | −0.828635 | −0.0398677 | ||||||||
\(433\) | 16.9027 | 0.812293 | 0.406147 | − | 0.913808i | \(-0.366872\pi\) | ||||
0.406147 | + | 0.913808i | \(0.366872\pi\) | |||||||
\(434\) | −6.71961 | −0.322552 | ||||||||
\(435\) | 0.589178 | 0.0282489 | ||||||||
\(436\) | −11.6993 | −0.560297 | ||||||||
\(437\) | −9.58860 | −0.458685 | ||||||||
\(438\) | −0.978639 | −0.0467612 | ||||||||
\(439\) | 39.1863 | 1.87026 | 0.935131 | − | 0.354302i | \(-0.115281\pi\) | ||||
0.935131 | + | 0.354302i | \(0.115281\pi\) | |||||||
\(440\) | 5.30794 | 0.253046 | ||||||||
\(441\) | 5.28072 | 0.251463 | ||||||||
\(442\) | 9.78273 | 0.465317 | ||||||||
\(443\) | −26.0277 | −1.23661 | −0.618307 | − | 0.785936i | \(-0.712181\pi\) | ||||
−0.618307 | + | 0.785936i | \(0.712181\pi\) | |||||||
\(444\) | 0.660384 | 0.0313404 | ||||||||
\(445\) | −0.238014 | −0.0112830 | ||||||||
\(446\) | −1.09531 | −0.0518642 | ||||||||
\(447\) | −2.16591 | −0.102444 | ||||||||
\(448\) | −2.28657 | −0.108031 | ||||||||
\(449\) | −24.2305 | −1.14351 | −0.571754 | − | 0.820425i | \(-0.693737\pi\) | ||||
−0.571754 | + | 0.820425i | \(0.693737\pi\) | |||||||
\(450\) | 11.0401 | 0.520436 | ||||||||
\(451\) | 16.9760 | 0.799370 | ||||||||
\(452\) | 15.2792 | 0.718675 | ||||||||
\(453\) | 1.82034 | 0.0855270 | ||||||||
\(454\) | −2.25099 | −0.105644 | ||||||||
\(455\) | −4.74507 | −0.222452 | ||||||||
\(456\) | −0.274299 | −0.0128452 | ||||||||
\(457\) | −29.9564 | −1.40130 | −0.700650 | − | 0.713505i | \(-0.747107\pi\) | ||||
−0.700650 | + | 0.713505i | \(0.747107\pi\) | |||||||
\(458\) | −13.2224 | −0.617844 | ||||||||
\(459\) | −4.44746 | −0.207590 | ||||||||
\(460\) | 5.51418 | 0.257100 | ||||||||
\(461\) | 7.05161 | 0.328426 | 0.164213 | − | 0.986425i | \(-0.447492\pi\) | ||||
0.164213 | + | 0.986425i | \(0.447492\pi\) | |||||||
\(462\) | −1.47696 | −0.0687143 | ||||||||
\(463\) | 33.0534 | 1.53612 | 0.768060 | − | 0.640378i | \(-0.221222\pi\) | ||||
0.768060 | + | 0.640378i | \(0.221222\pi\) | |||||||
\(464\) | 3.73505 | 0.173395 | ||||||||
\(465\) | 0.463563 | 0.0214972 | ||||||||
\(466\) | −4.72089 | −0.218691 | ||||||||
\(467\) | 32.7686 | 1.51635 | 0.758175 | − | 0.652051i | \(-0.226091\pi\) | ||||
0.758175 | + | 0.652051i | \(0.226091\pi\) | |||||||
\(468\) | −5.43306 | −0.251143 | ||||||||
\(469\) | 23.9536 | 1.10608 | ||||||||
\(470\) | 0.442345 | 0.0204038 | ||||||||
\(471\) | −2.42413 | −0.111698 | ||||||||
\(472\) | 14.4444 | 0.664856 | ||||||||
\(473\) | 28.7412 | 1.32152 | ||||||||
\(474\) | −0.496078 | −0.0227856 | ||||||||
\(475\) | 7.33265 | 0.336445 | ||||||||
\(476\) | −12.2725 | −0.562511 | ||||||||
\(477\) | 1.56739 | 0.0717660 | ||||||||
\(478\) | 5.84687 | 0.267430 | ||||||||
\(479\) | −17.9402 | −0.819710 | −0.409855 | − | 0.912151i | \(-0.634421\pi\) | ||||
−0.409855 | + | 0.912151i | \(0.634421\pi\) | |||||||
\(480\) | 0.157743 | 0.00719995 | ||||||||
\(481\) | 8.68768 | 0.396124 | ||||||||
\(482\) | −0.115891 | −0.00527869 | ||||||||
\(483\) | −1.53434 | −0.0698151 | ||||||||
\(484\) | 10.7350 | 0.487953 | ||||||||
\(485\) | −12.0127 | −0.545468 | ||||||||
\(486\) | 3.70896 | 0.168242 | ||||||||
\(487\) | 34.1072 | 1.54555 | 0.772773 | − | 0.634682i | \(-0.218869\pi\) | ||||
0.772773 | + | 0.634682i | \(0.218869\pi\) | |||||||
\(488\) | −10.2226 | −0.462758 | ||||||||
\(489\) | −0.797740 | −0.0360750 | ||||||||
\(490\) | −2.01700 | −0.0911189 | ||||||||
\(491\) | 5.20616 | 0.234951 | 0.117475 | − | 0.993076i | \(-0.462520\pi\) | ||||
0.117475 | + | 0.993076i | \(0.462520\pi\) | |||||||
\(492\) | 0.504499 | 0.0227446 | ||||||||
\(493\) | 20.0468 | 0.902864 | ||||||||
\(494\) | −3.60854 | −0.162356 | ||||||||
\(495\) | −15.8219 | −0.711143 | ||||||||
\(496\) | 2.93872 | 0.131953 | ||||||||
\(497\) | 1.92556 | 0.0863733 | ||||||||
\(498\) | 0.707213 | 0.0316910 | ||||||||
\(499\) | −15.5744 | −0.697206 | −0.348603 | − | 0.937271i | \(-0.613344\pi\) | ||||
−0.348603 | + | 0.937271i | \(0.613344\pi\) | |||||||
\(500\) | −9.90952 | −0.443167 | ||||||||
\(501\) | 2.30923 | 0.103169 | ||||||||
\(502\) | −7.68083 | −0.342812 | ||||||||
\(503\) | 28.1844 | 1.25668 | 0.628341 | − | 0.777938i | \(-0.283734\pi\) | ||||
0.628341 | + | 0.777938i | \(0.283734\pi\) | |||||||
\(504\) | 6.81583 | 0.303601 | ||||||||
\(505\) | 10.1383 | 0.451146 | ||||||||
\(506\) | 22.5795 | 1.00378 | ||||||||
\(507\) | −1.34085 | −0.0595494 | ||||||||
\(508\) | −6.13297 | −0.272107 | ||||||||
\(509\) | −26.7550 | −1.18589 | −0.592947 | − | 0.805241i | \(-0.702036\pi\) | ||||
−0.592947 | + | 0.805241i | \(0.702036\pi\) | |||||||
\(510\) | 0.846641 | 0.0374899 | ||||||||
\(511\) | 16.1512 | 0.714486 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.64053 | 0.0724311 | ||||||||
\(514\) | −22.7498 | −1.00345 | ||||||||
\(515\) | −12.1431 | −0.535090 | ||||||||
\(516\) | 0.854139 | 0.0376014 | ||||||||
\(517\) | 1.81131 | 0.0796615 | ||||||||
\(518\) | −10.8988 | −0.478866 | ||||||||
\(519\) | −0.718164 | −0.0315239 | ||||||||
\(520\) | 2.07519 | 0.0910030 | ||||||||
\(521\) | −38.9717 | −1.70738 | −0.853690 | − | 0.520782i | \(-0.825640\pi\) | ||||
−0.853690 | + | 0.520782i | \(0.825640\pi\) | |||||||
\(522\) | −11.1335 | −0.487298 | ||||||||
\(523\) | 22.3230 | 0.976116 | 0.488058 | − | 0.872811i | \(-0.337706\pi\) | ||||
0.488058 | + | 0.872811i | \(0.337706\pi\) | |||||||
\(524\) | −7.17094 | −0.313264 | ||||||||
\(525\) | 1.17335 | 0.0512094 | ||||||||
\(526\) | 28.3260 | 1.23507 | ||||||||
\(527\) | 15.7728 | 0.687072 | ||||||||
\(528\) | 0.645926 | 0.0281103 | ||||||||
\(529\) | 0.456764 | 0.0198593 | ||||||||
\(530\) | −0.598675 | −0.0260048 | ||||||||
\(531\) | −43.0558 | −1.86846 | ||||||||
\(532\) | 4.52696 | 0.196269 | ||||||||
\(533\) | 6.63694 | 0.287478 | ||||||||
\(534\) | −0.0289641 | −0.00125340 | ||||||||
\(535\) | −12.2304 | −0.528768 | ||||||||
\(536\) | −10.4758 | −0.452484 | ||||||||
\(537\) | −0.239965 | −0.0103552 | ||||||||
\(538\) | −25.1503 | −1.08431 | ||||||||
\(539\) | −8.25922 | −0.355750 | ||||||||
\(540\) | −0.943430 | −0.0405988 | ||||||||
\(541\) | 35.1038 | 1.50923 | 0.754616 | − | 0.656167i | \(-0.227823\pi\) | ||||
0.754616 | + | 0.656167i | \(0.227823\pi\) | |||||||
\(542\) | −21.3951 | −0.918998 | ||||||||
\(543\) | 2.39076 | 0.102597 | ||||||||
\(544\) | 5.36722 | 0.230118 | ||||||||
\(545\) | −13.3201 | −0.570571 | ||||||||
\(546\) | −0.577431 | −0.0247117 | ||||||||
\(547\) | −9.37171 | −0.400705 | −0.200353 | − | 0.979724i | \(-0.564209\pi\) | ||||
−0.200353 | + | 0.979724i | \(0.564209\pi\) | |||||||
\(548\) | −2.24576 | −0.0959340 | ||||||||
\(549\) | 30.4717 | 1.30050 | ||||||||
\(550\) | −17.2671 | −0.736272 | ||||||||
\(551\) | −7.39465 | −0.315023 | ||||||||
\(552\) | 0.671023 | 0.0285606 | ||||||||
\(553\) | 8.18714 | 0.348153 | ||||||||
\(554\) | −9.82730 | −0.417522 | ||||||||
\(555\) | 0.751871 | 0.0319151 | ||||||||
\(556\) | 12.4554 | 0.528226 | ||||||||
\(557\) | −22.4550 | −0.951450 | −0.475725 | − | 0.879594i | \(-0.657814\pi\) | ||||
−0.475725 | + | 0.879594i | \(0.657814\pi\) | |||||||
\(558\) | −8.75976 | −0.370830 | ||||||||
\(559\) | 11.2366 | 0.475259 | ||||||||
\(560\) | −2.60335 | −0.110012 | ||||||||
\(561\) | 3.46683 | 0.146370 | ||||||||
\(562\) | −17.7452 | −0.748536 | ||||||||
\(563\) | 17.6918 | 0.745622 | 0.372811 | − | 0.927907i | \(-0.378394\pi\) | ||||
0.372811 | + | 0.927907i | \(0.378394\pi\) | |||||||
\(564\) | 0.0538292 | 0.00226662 | ||||||||
\(565\) | 17.3960 | 0.731854 | ||||||||
\(566\) | −27.8139 | −1.16911 | ||||||||
\(567\) | −20.1850 | −0.847690 | ||||||||
\(568\) | −0.842117 | −0.0353344 | ||||||||
\(569\) | 1.79786 | 0.0753701 | 0.0376851 | − | 0.999290i | \(-0.488002\pi\) | ||||
0.0376851 | + | 0.999290i | \(0.488002\pi\) | |||||||
\(570\) | −0.312299 | −0.0130808 | ||||||||
\(571\) | −20.4821 | −0.857150 | −0.428575 | − | 0.903506i | \(-0.640984\pi\) | ||||
−0.428575 | + | 0.903506i | \(0.640984\pi\) | |||||||
\(572\) | 8.49748 | 0.355298 | ||||||||
\(573\) | 3.20869 | 0.134045 | ||||||||
\(574\) | −8.32611 | −0.347525 | ||||||||
\(575\) | −17.9380 | −0.748066 | ||||||||
\(576\) | −2.98080 | −0.124200 | ||||||||
\(577\) | −2.55098 | −0.106199 | −0.0530993 | − | 0.998589i | \(-0.516910\pi\) | ||||
−0.0530993 | + | 0.998589i | \(0.516910\pi\) | |||||||
\(578\) | 11.8070 | 0.491107 | ||||||||
\(579\) | 0.152976 | 0.00635748 | ||||||||
\(580\) | 4.25249 | 0.176575 | ||||||||
\(581\) | −11.6716 | −0.484221 | ||||||||
\(582\) | −1.46183 | −0.0605948 | ||||||||
\(583\) | −2.45145 | −0.101529 | ||||||||
\(584\) | −7.06349 | −0.292289 | ||||||||
\(585\) | −6.18573 | −0.255748 | ||||||||
\(586\) | 0.342825 | 0.0141620 | ||||||||
\(587\) | 30.7292 | 1.26833 | 0.634166 | − | 0.773197i | \(-0.281344\pi\) | ||||
0.634166 | + | 0.773197i | \(0.281344\pi\) | |||||||
\(588\) | −0.245450 | −0.0101222 | ||||||||
\(589\) | −5.81808 | −0.239730 | ||||||||
\(590\) | 16.4454 | 0.677047 | ||||||||
\(591\) | −0.574007 | −0.0236115 | ||||||||
\(592\) | 4.76643 | 0.195899 | ||||||||
\(593\) | 8.38904 | 0.344496 | 0.172248 | − | 0.985054i | \(-0.444897\pi\) | ||||
0.172248 | + | 0.985054i | \(0.444897\pi\) | |||||||
\(594\) | −3.86316 | −0.158507 | ||||||||
\(595\) | −13.9727 | −0.572826 | ||||||||
\(596\) | −15.6328 | −0.640343 | ||||||||
\(597\) | 1.36558 | 0.0558894 | ||||||||
\(598\) | 8.82765 | 0.360989 | ||||||||
\(599\) | 32.1056 | 1.31180 | 0.655899 | − | 0.754849i | \(-0.272290\pi\) | ||||
0.655899 | + | 0.754849i | \(0.272290\pi\) | |||||||
\(600\) | −0.513149 | −0.0209492 | ||||||||
\(601\) | −10.6968 | −0.436333 | −0.218166 | − | 0.975912i | \(-0.570008\pi\) | ||||
−0.218166 | + | 0.975912i | \(0.570008\pi\) | |||||||
\(602\) | −14.0965 | −0.574529 | ||||||||
\(603\) | 31.2262 | 1.27163 | ||||||||
\(604\) | 13.1386 | 0.534602 | ||||||||
\(605\) | 12.2221 | 0.496901 | ||||||||
\(606\) | 1.23373 | 0.0501168 | ||||||||
\(607\) | −9.33240 | −0.378790 | −0.189395 | − | 0.981901i | \(-0.560653\pi\) | ||||
−0.189395 | + | 0.981901i | \(0.560653\pi\) | |||||||
\(608\) | −1.97980 | −0.0802914 | ||||||||
\(609\) | −1.18327 | −0.0479487 | ||||||||
\(610\) | −11.6389 | −0.471243 | ||||||||
\(611\) | 0.708150 | 0.0286487 | ||||||||
\(612\) | −15.9986 | −0.646706 | ||||||||
\(613\) | 26.3233 | 1.06319 | 0.531595 | − | 0.846999i | \(-0.321593\pi\) | ||||
0.531595 | + | 0.846999i | \(0.321593\pi\) | |||||||
\(614\) | 19.5763 | 0.790036 | ||||||||
\(615\) | 0.574390 | 0.0231616 | ||||||||
\(616\) | −10.6602 | −0.429511 | ||||||||
\(617\) | 23.1241 | 0.930940 | 0.465470 | − | 0.885064i | \(-0.345885\pi\) | ||||
0.465470 | + | 0.885064i | \(0.345885\pi\) | |||||||
\(618\) | −1.47770 | −0.0594420 | ||||||||
\(619\) | −36.0721 | −1.44986 | −0.724930 | − | 0.688822i | \(-0.758128\pi\) | ||||
−0.724930 | + | 0.688822i | \(0.758128\pi\) | |||||||
\(620\) | 3.34584 | 0.134372 | ||||||||
\(621\) | −4.01326 | −0.161047 | ||||||||
\(622\) | −23.1403 | −0.927843 | ||||||||
\(623\) | 0.478015 | 0.0191513 | ||||||||
\(624\) | 0.252531 | 0.0101093 | ||||||||
\(625\) | 7.23634 | 0.289454 | ||||||||
\(626\) | 7.89543 | 0.315565 | ||||||||
\(627\) | −1.27880 | −0.0510705 | ||||||||
\(628\) | −17.4965 | −0.698188 | ||||||||
\(629\) | 25.5825 | 1.02004 | ||||||||
\(630\) | 7.76007 | 0.309169 | ||||||||
\(631\) | −24.5142 | −0.975896 | −0.487948 | − | 0.872873i | \(-0.662254\pi\) | ||||
−0.487948 | + | 0.872873i | \(0.662254\pi\) | |||||||
\(632\) | −3.58053 | −0.142426 | ||||||||
\(633\) | −2.54297 | −0.101074 | ||||||||
\(634\) | −9.95610 | −0.395407 | ||||||||
\(635\) | −6.98261 | −0.277096 | ||||||||
\(636\) | −0.0728531 | −0.00288881 | ||||||||
\(637\) | −3.22902 | −0.127938 | ||||||||
\(638\) | 17.4131 | 0.689391 | ||||||||
\(639\) | 2.51018 | 0.0993014 | ||||||||
\(640\) | 1.13854 | 0.0450046 | ||||||||
\(641\) | 3.57085 | 0.141040 | 0.0705201 | − | 0.997510i | \(-0.477534\pi\) | ||||
0.0705201 | + | 0.997510i | \(0.477534\pi\) | |||||||
\(642\) | −1.48833 | −0.0587396 | ||||||||
\(643\) | −5.61347 | −0.221374 | −0.110687 | − | 0.993855i | \(-0.535305\pi\) | ||||
−0.110687 | + | 0.993855i | \(0.535305\pi\) | |||||||
\(644\) | −11.0744 | −0.436392 | ||||||||
\(645\) | 0.972468 | 0.0382909 | ||||||||
\(646\) | −10.6260 | −0.418075 | ||||||||
\(647\) | 44.9967 | 1.76900 | 0.884501 | − | 0.466538i | \(-0.154499\pi\) | ||||
0.884501 | + | 0.466538i | \(0.154499\pi\) | |||||||
\(648\) | 8.82761 | 0.346781 | ||||||||
\(649\) | 67.3407 | 2.64336 | ||||||||
\(650\) | −6.75073 | −0.264786 | ||||||||
\(651\) | −0.930995 | −0.0364886 | ||||||||
\(652\) | −5.75782 | −0.225494 | ||||||||
\(653\) | 3.02430 | 0.118350 | 0.0591749 | − | 0.998248i | \(-0.481153\pi\) | ||||
0.0591749 | + | 0.998248i | \(0.481153\pi\) | |||||||
\(654\) | −1.62093 | −0.0633835 | ||||||||
\(655\) | −8.16437 | −0.319009 | ||||||||
\(656\) | 3.64130 | 0.142169 | ||||||||
\(657\) | 21.0549 | 0.821429 | ||||||||
\(658\) | −0.888382 | −0.0346327 | ||||||||
\(659\) | 14.2081 | 0.553467 | 0.276734 | − | 0.960947i | \(-0.410748\pi\) | ||||
0.276734 | + | 0.960947i | \(0.410748\pi\) | |||||||
\(660\) | 0.735410 | 0.0286258 | ||||||||
\(661\) | 0.681590 | 0.0265108 | 0.0132554 | − | 0.999912i | \(-0.495781\pi\) | ||||
0.0132554 | + | 0.999912i | \(0.495781\pi\) | |||||||
\(662\) | −14.4038 | −0.559819 | ||||||||
\(663\) | 1.35539 | 0.0526389 | ||||||||
\(664\) | 5.10442 | 0.198090 | ||||||||
\(665\) | 5.15410 | 0.199868 | ||||||||
\(666\) | −14.2078 | −0.550541 | ||||||||
\(667\) | 18.0897 | 0.700435 | ||||||||
\(668\) | 16.6673 | 0.644876 | ||||||||
\(669\) | −0.151754 | −0.00586713 | ||||||||
\(670\) | −11.9270 | −0.460782 | ||||||||
\(671\) | −47.6588 | −1.83985 | ||||||||
\(672\) | −0.316803 | −0.0122209 | ||||||||
\(673\) | −7.02794 | −0.270907 | −0.135454 | − | 0.990784i | \(-0.543249\pi\) | ||||
−0.135454 | + | 0.990784i | \(0.543249\pi\) | |||||||
\(674\) | −1.71653 | −0.0661184 | ||||||||
\(675\) | 3.06904 | 0.118128 | ||||||||
\(676\) | −9.67783 | −0.372224 | ||||||||
\(677\) | −9.53803 | −0.366576 | −0.183288 | − | 0.983059i | \(-0.558674\pi\) | ||||
−0.183288 | + | 0.983059i | \(0.558674\pi\) | |||||||
\(678\) | 2.11692 | 0.0813000 | ||||||||
\(679\) | 24.1256 | 0.925857 | ||||||||
\(680\) | 6.11077 | 0.234337 | ||||||||
\(681\) | −0.311873 | −0.0119510 | ||||||||
\(682\) | 13.7006 | 0.524621 | ||||||||
\(683\) | 20.8725 | 0.798663 | 0.399332 | − | 0.916807i | \(-0.369242\pi\) | ||||
0.399332 | + | 0.916807i | \(0.369242\pi\) | |||||||
\(684\) | 5.90139 | 0.225645 | ||||||||
\(685\) | −2.55687 | −0.0976932 | ||||||||
\(686\) | 20.0569 | 0.765775 | ||||||||
\(687\) | −1.83196 | −0.0698935 | ||||||||
\(688\) | 6.16489 | 0.235034 | ||||||||
\(689\) | −0.958419 | −0.0365128 | ||||||||
\(690\) | 0.763984 | 0.0290844 | ||||||||
\(691\) | 19.9094 | 0.757391 | 0.378695 | − | 0.925521i | \(-0.376373\pi\) | ||||
0.378695 | + | 0.925521i | \(0.376373\pi\) | |||||||
\(692\) | −5.18347 | −0.197046 | ||||||||
\(693\) | 31.7759 | 1.20707 | ||||||||
\(694\) | 10.7239 | 0.407074 | ||||||||
\(695\) | 14.1809 | 0.537913 | ||||||||
\(696\) | 0.517488 | 0.0196153 | ||||||||
\(697\) | 19.5437 | 0.740269 | ||||||||
\(698\) | 13.0689 | 0.494666 | ||||||||
\(699\) | −0.654075 | −0.0247394 | ||||||||
\(700\) | 8.46887 | 0.320093 | ||||||||
\(701\) | 27.8722 | 1.05272 | 0.526359 | − | 0.850262i | \(-0.323557\pi\) | ||||
0.526359 | + | 0.850262i | \(0.323557\pi\) | |||||||
\(702\) | −1.51034 | −0.0570040 | ||||||||
\(703\) | −9.43657 | −0.355907 | ||||||||
\(704\) | 4.66208 | 0.175709 | ||||||||
\(705\) | 0.0612864 | 0.00230818 | ||||||||
\(706\) | 10.7805 | 0.405729 | ||||||||
\(707\) | −20.3611 | −0.765759 | ||||||||
\(708\) | 2.00125 | 0.0752117 | ||||||||
\(709\) | −47.6371 | −1.78905 | −0.894524 | − | 0.447021i | \(-0.852485\pi\) | ||||
−0.894524 | + | 0.447021i | \(0.852485\pi\) | |||||||
\(710\) | −0.958780 | −0.0359824 | ||||||||
\(711\) | 10.6728 | 0.400263 | ||||||||
\(712\) | −0.209053 | −0.00783459 | ||||||||
\(713\) | 14.2329 | 0.533025 | ||||||||
\(714\) | −1.70035 | −0.0636340 | ||||||||
\(715\) | 9.67469 | 0.361813 | ||||||||
\(716\) | −1.73198 | −0.0647273 | ||||||||
\(717\) | 0.810078 | 0.0302529 | ||||||||
\(718\) | 2.01409 | 0.0751650 | ||||||||
\(719\) | −23.7039 | −0.884008 | −0.442004 | − | 0.897013i | \(-0.645732\pi\) | ||||
−0.442004 | + | 0.897013i | \(0.645732\pi\) | |||||||
\(720\) | −3.39375 | −0.126478 | ||||||||
\(721\) | 24.3876 | 0.908242 | ||||||||
\(722\) | −15.0804 | −0.561234 | ||||||||
\(723\) | −0.0160566 | −0.000597151 0 | ||||||||
\(724\) | 17.2557 | 0.641303 | ||||||||
\(725\) | −13.8336 | −0.513769 | ||||||||
\(726\) | 1.48732 | 0.0551996 | ||||||||
\(727\) | 0.112244 | 0.00416292 | 0.00208146 | − | 0.999998i | \(-0.499337\pi\) | ||||
0.00208146 | + | 0.999998i | \(0.499337\pi\) | |||||||
\(728\) | −4.16770 | −0.154465 | ||||||||
\(729\) | −25.9689 | −0.961813 | ||||||||
\(730\) | −8.04203 | −0.297649 | ||||||||
\(731\) | 33.0883 | 1.22381 | ||||||||
\(732\) | −1.41634 | −0.0523494 | ||||||||
\(733\) | 12.7854 | 0.472238 | 0.236119 | − | 0.971724i | \(-0.424124\pi\) | ||||
0.236119 | + | 0.971724i | \(0.424124\pi\) | |||||||
\(734\) | −8.65410 | −0.319429 | ||||||||
\(735\) | −0.279454 | −0.0103078 | ||||||||
\(736\) | 4.84322 | 0.178523 | ||||||||
\(737\) | −48.8389 | −1.79900 | ||||||||
\(738\) | −10.8540 | −0.399542 | ||||||||
\(739\) | −43.9324 | −1.61608 | −0.808039 | − | 0.589128i | \(-0.799471\pi\) | ||||
−0.808039 | + | 0.589128i | \(0.799471\pi\) | |||||||
\(740\) | 5.42675 | 0.199491 | ||||||||
\(741\) | −0.499960 | −0.0183665 | ||||||||
\(742\) | 1.20235 | 0.0441395 | ||||||||
\(743\) | −17.7507 | −0.651210 | −0.325605 | − | 0.945506i | \(-0.605568\pi\) | ||||
−0.325605 | + | 0.945506i | \(0.605568\pi\) | |||||||
\(744\) | 0.407157 | 0.0149271 | ||||||||
\(745\) | −17.7985 | −0.652086 | ||||||||
\(746\) | 1.86032 | 0.0681113 | ||||||||
\(747\) | −15.2153 | −0.556698 | ||||||||
\(748\) | 25.0224 | 0.914909 | ||||||||
\(749\) | 24.5630 | 0.897511 | ||||||||
\(750\) | −1.37295 | −0.0501332 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0.388521 | 0.0141679 | ||||||||
\(753\) | −1.06417 | −0.0387805 | ||||||||
\(754\) | 6.80781 | 0.247926 | ||||||||
\(755\) | 14.9588 | 0.544405 | ||||||||
\(756\) | 1.89473 | 0.0689108 | ||||||||
\(757\) | 25.6276 | 0.931450 | 0.465725 | − | 0.884930i | \(-0.345794\pi\) | ||||
0.465725 | + | 0.884930i | \(0.345794\pi\) | |||||||
\(758\) | −31.4273 | −1.14149 | ||||||||
\(759\) | 3.12836 | 0.113552 | ||||||||
\(760\) | −2.25407 | −0.0817638 | ||||||||
\(761\) | 3.12192 | 0.113170 | 0.0565848 | − | 0.998398i | \(-0.481979\pi\) | ||||
0.0565848 | + | 0.998398i | \(0.481979\pi\) | |||||||
\(762\) | −0.849717 | −0.0307820 | ||||||||
\(763\) | 26.7514 | 0.968466 | ||||||||
\(764\) | 23.1592 | 0.837872 | ||||||||
\(765\) | −18.2150 | −0.658565 | ||||||||
\(766\) | −4.84782 | −0.175159 | ||||||||
\(767\) | 26.3275 | 0.950630 | ||||||||
\(768\) | 0.138549 | 0.00499946 | ||||||||
\(769\) | 39.8944 | 1.43863 | 0.719314 | − | 0.694685i | \(-0.244456\pi\) | ||||
0.719314 | + | 0.694685i | \(0.244456\pi\) | |||||||
\(770\) | −12.1370 | −0.437387 | ||||||||
\(771\) | −3.15196 | −0.113515 | ||||||||
\(772\) | 1.10413 | 0.0397386 | ||||||||
\(773\) | −34.2216 | −1.23087 | −0.615433 | − | 0.788190i | \(-0.711019\pi\) | ||||
−0.615433 | + | 0.788190i | \(0.711019\pi\) | |||||||
\(774\) | −18.3763 | −0.660523 | ||||||||
\(775\) | −10.8843 | −0.390974 | ||||||||
\(776\) | −10.5510 | −0.378759 | ||||||||
\(777\) | −1.51002 | −0.0541716 | ||||||||
\(778\) | −15.2510 | −0.546774 | ||||||||
\(779\) | −7.20905 | −0.258291 | ||||||||
\(780\) | 0.287515 | 0.0102947 | ||||||||
\(781\) | −3.92601 | −0.140484 | ||||||||
\(782\) | 25.9946 | 0.929565 | ||||||||
\(783\) | −3.09499 | −0.110606 | ||||||||
\(784\) | −1.77158 | −0.0632706 | ||||||||
\(785\) | −19.9204 | −0.710991 | ||||||||
\(786\) | −0.993527 | −0.0354379 | ||||||||
\(787\) | −2.56575 | −0.0914591 | −0.0457296 | − | 0.998954i | \(-0.514561\pi\) | ||||
−0.0457296 | + | 0.998954i | \(0.514561\pi\) | |||||||
\(788\) | −4.14299 | −0.147588 | ||||||||
\(789\) | 3.92454 | 0.139718 | ||||||||
\(790\) | −4.07656 | −0.145037 | ||||||||
\(791\) | −34.9371 | −1.24222 | ||||||||
\(792\) | −13.8967 | −0.493799 | ||||||||
\(793\) | −18.6326 | −0.661664 | ||||||||
\(794\) | 17.2077 | 0.610679 | ||||||||
\(795\) | −0.0829458 | −0.00294179 | ||||||||
\(796\) | 9.85628 | 0.349347 | ||||||||
\(797\) | −4.15598 | −0.147212 | −0.0736062 | − | 0.997287i | \(-0.523451\pi\) | ||||
−0.0736062 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(798\) | 0.627206 | 0.0222028 | ||||||||
\(799\) | 2.08528 | 0.0737717 | ||||||||
\(800\) | −3.70374 | −0.130947 | ||||||||
\(801\) | 0.623146 | 0.0220178 | ||||||||
\(802\) | 36.1817 | 1.27762 | ||||||||
\(803\) | −32.9305 | −1.16209 | ||||||||
\(804\) | −1.45141 | −0.0511872 | ||||||||
\(805\) | −12.6086 | −0.444394 | ||||||||
\(806\) | 5.35636 | 0.188670 | ||||||||
\(807\) | −3.48455 | −0.122662 | ||||||||
\(808\) | 8.90464 | 0.313264 | ||||||||
\(809\) | 21.2844 | 0.748319 | 0.374159 | − | 0.927364i | \(-0.377931\pi\) | ||||
0.374159 | + | 0.927364i | \(0.377931\pi\) | |||||||
\(810\) | 10.0505 | 0.353140 | ||||||||
\(811\) | −19.8330 | −0.696432 | −0.348216 | − | 0.937414i | \(-0.613212\pi\) | ||||
−0.348216 | + | 0.937414i | \(0.613212\pi\) | |||||||
\(812\) | −8.54047 | −0.299712 | ||||||||
\(813\) | −2.96427 | −0.103961 | ||||||||
\(814\) | 22.2215 | 0.778862 | ||||||||
\(815\) | −6.55548 | −0.229628 | ||||||||
\(816\) | 0.743623 | 0.0260320 | ||||||||
\(817\) | −12.2052 | −0.427007 | ||||||||
\(818\) | −16.9164 | −0.591469 | ||||||||
\(819\) | 12.4231 | 0.434098 | ||||||||
\(820\) | 4.14575 | 0.144776 | ||||||||
\(821\) | −17.1919 | −0.600001 | −0.300001 | − | 0.953939i | \(-0.596987\pi\) | ||||
−0.300001 | + | 0.953939i | \(0.596987\pi\) | |||||||
\(822\) | −0.311147 | −0.0108525 | ||||||||
\(823\) | −26.3722 | −0.919277 | −0.459639 | − | 0.888106i | \(-0.652021\pi\) | ||||
−0.459639 | + | 0.888106i | \(0.652021\pi\) | |||||||
\(824\) | −10.6656 | −0.371553 | ||||||||
\(825\) | −2.39234 | −0.0832906 | ||||||||
\(826\) | −33.0281 | −1.14920 | ||||||||
\(827\) | 18.8219 | 0.654500 | 0.327250 | − | 0.944938i | \(-0.393878\pi\) | ||||
0.327250 | + | 0.944938i | \(0.393878\pi\) | |||||||
\(828\) | −14.4367 | −0.501710 | ||||||||
\(829\) | −5.71767 | −0.198583 | −0.0992915 | − | 0.995058i | \(-0.531658\pi\) | ||||
−0.0992915 | + | 0.995058i | \(0.531658\pi\) | |||||||
\(830\) | 5.81157 | 0.201723 | ||||||||
\(831\) | −1.36156 | −0.0472321 | ||||||||
\(832\) | 1.82268 | 0.0631901 | ||||||||
\(833\) | −9.50843 | −0.329448 | ||||||||
\(834\) | 1.72568 | 0.0597555 | ||||||||
\(835\) | 18.9763 | 0.656701 | ||||||||
\(836\) | −9.22997 | −0.319225 | ||||||||
\(837\) | −2.43513 | −0.0841703 | ||||||||
\(838\) | 25.6805 | 0.887119 | ||||||||
\(839\) | 52.0932 | 1.79846 | 0.899228 | − | 0.437481i | \(-0.144129\pi\) | ||||
0.899228 | + | 0.437481i | \(0.144129\pi\) | |||||||
\(840\) | −0.360691 | −0.0124450 | ||||||||
\(841\) | −15.0494 | −0.518945 | ||||||||
\(842\) | 15.1695 | 0.522774 | ||||||||
\(843\) | −2.45858 | −0.0846780 | ||||||||
\(844\) | −18.3543 | −0.631780 | ||||||||
\(845\) | −11.0186 | −0.379050 | ||||||||
\(846\) | −1.15810 | −0.0398165 | ||||||||
\(847\) | −24.5463 | −0.843421 | ||||||||
\(848\) | −0.525829 | −0.0180570 | ||||||||
\(849\) | −3.85359 | −0.132255 | ||||||||
\(850\) | −19.8788 | −0.681836 | ||||||||
\(851\) | 23.0849 | 0.791339 | ||||||||
\(852\) | −0.116674 | −0.00399720 | ||||||||
\(853\) | 37.6986 | 1.29077 | 0.645387 | − | 0.763855i | \(-0.276696\pi\) | ||||
0.645387 | + | 0.763855i | \(0.276696\pi\) | |||||||
\(854\) | 23.3749 | 0.799871 | ||||||||
\(855\) | 6.71895 | 0.229783 | ||||||||
\(856\) | −10.7423 | −0.367163 | ||||||||
\(857\) | 2.71656 | 0.0927959 | 0.0463980 | − | 0.998923i | \(-0.485226\pi\) | ||||
0.0463980 | + | 0.998923i | \(0.485226\pi\) | |||||||
\(858\) | 1.17732 | 0.0401930 | ||||||||
\(859\) | 11.3921 | 0.388692 | 0.194346 | − | 0.980933i | \(-0.437742\pi\) | ||||
0.194346 | + | 0.980933i | \(0.437742\pi\) | |||||||
\(860\) | 7.01894 | 0.239344 | ||||||||
\(861\) | −1.15357 | −0.0393137 | ||||||||
\(862\) | −22.0541 | −0.751164 | ||||||||
\(863\) | −17.5668 | −0.597981 | −0.298991 | − | 0.954256i | \(-0.596650\pi\) | ||||
−0.298991 | + | 0.954256i | \(0.596650\pi\) | |||||||
\(864\) | −0.828635 | −0.0281907 | ||||||||
\(865\) | −5.90156 | −0.200659 | ||||||||
\(866\) | 16.9027 | 0.574378 | ||||||||
\(867\) | 1.63585 | 0.0555564 | ||||||||
\(868\) | −6.71961 | −0.228078 | ||||||||
\(869\) | −16.6927 | −0.566261 | ||||||||
\(870\) | 0.589178 | 0.0199750 | ||||||||
\(871\) | −19.0940 | −0.646976 | ||||||||
\(872\) | −11.6993 | −0.396190 | ||||||||
\(873\) | 31.4505 | 1.06444 | ||||||||
\(874\) | −9.58860 | −0.324339 | ||||||||
\(875\) | 22.6588 | 0.766009 | ||||||||
\(876\) | −0.978639 | −0.0330651 | ||||||||
\(877\) | −2.40801 | −0.0813126 | −0.0406563 | − | 0.999173i | \(-0.512945\pi\) | ||||
−0.0406563 | + | 0.999173i | \(0.512945\pi\) | |||||||
\(878\) | 39.1863 | 1.32248 | ||||||||
\(879\) | 0.0474981 | 0.00160207 | ||||||||
\(880\) | 5.30794 | 0.178931 | ||||||||
\(881\) | −41.5528 | −1.39995 | −0.699975 | − | 0.714168i | \(-0.746805\pi\) | ||||
−0.699975 | + | 0.714168i | \(0.746805\pi\) | |||||||
\(882\) | 5.28072 | 0.177811 | ||||||||
\(883\) | 49.8958 | 1.67913 | 0.839563 | − | 0.543262i | \(-0.182811\pi\) | ||||
0.839563 | + | 0.543262i | \(0.182811\pi\) | |||||||
\(884\) | 9.78273 | 0.329029 | ||||||||
\(885\) | 2.27850 | 0.0765909 | ||||||||
\(886\) | −26.0277 | −0.874419 | ||||||||
\(887\) | −26.4940 | −0.889583 | −0.444792 | − | 0.895634i | \(-0.646722\pi\) | ||||
−0.444792 | + | 0.895634i | \(0.646722\pi\) | |||||||
\(888\) | 0.660384 | 0.0221610 | ||||||||
\(889\) | 14.0235 | 0.470333 | ||||||||
\(890\) | −0.238014 | −0.00797825 | ||||||||
\(891\) | 41.1550 | 1.37874 | ||||||||
\(892\) | −1.09531 | −0.0366735 | ||||||||
\(893\) | −0.769193 | −0.0257401 | ||||||||
\(894\) | −2.16591 | −0.0724387 | ||||||||
\(895\) | −1.97193 | −0.0659142 | ||||||||
\(896\) | −2.28657 | −0.0763891 | ||||||||
\(897\) | 1.22306 | 0.0408368 | ||||||||
\(898\) | −24.2305 | −0.808582 | ||||||||
\(899\) | 10.9763 | 0.366079 | ||||||||
\(900\) | 11.0401 | 0.368004 | ||||||||
\(901\) | −2.82224 | −0.0940224 | ||||||||
\(902\) | 16.9760 | 0.565240 | ||||||||
\(903\) | −1.95305 | −0.0649935 | ||||||||
\(904\) | 15.2792 | 0.508180 | ||||||||
\(905\) | 19.6462 | 0.653063 | ||||||||
\(906\) | 1.82034 | 0.0604767 | ||||||||
\(907\) | 46.7312 | 1.55168 | 0.775841 | − | 0.630928i | \(-0.217326\pi\) | ||||
0.775841 | + | 0.630928i | \(0.217326\pi\) | |||||||
\(908\) | −2.25099 | −0.0747018 | ||||||||
\(909\) | −26.5430 | −0.880376 | ||||||||
\(910\) | −4.74507 | −0.157298 | ||||||||
\(911\) | 3.07178 | 0.101772 | 0.0508862 | − | 0.998704i | \(-0.483795\pi\) | ||||
0.0508862 | + | 0.998704i | \(0.483795\pi\) | |||||||
\(912\) | −0.274299 | −0.00908295 | ||||||||
\(913\) | 23.7972 | 0.787573 | ||||||||
\(914\) | −29.9564 | −0.990869 | ||||||||
\(915\) | −1.61255 | −0.0533093 | ||||||||
\(916\) | −13.2224 | −0.436882 | ||||||||
\(917\) | 16.3969 | 0.541473 | ||||||||
\(918\) | −4.44746 | −0.146788 | ||||||||
\(919\) | −10.7399 | −0.354278 | −0.177139 | − | 0.984186i | \(-0.556684\pi\) | ||||
−0.177139 | + | 0.984186i | \(0.556684\pi\) | |||||||
\(920\) | 5.51418 | 0.181797 | ||||||||
\(921\) | 2.71228 | 0.0893727 | ||||||||
\(922\) | 7.05161 | 0.232232 | ||||||||
\(923\) | −1.53491 | −0.0505222 | ||||||||
\(924\) | −1.47696 | −0.0485884 | ||||||||
\(925\) | −17.6536 | −0.580447 | ||||||||
\(926\) | 33.0534 | 1.08620 | ||||||||
\(927\) | 31.7920 | 1.04419 | ||||||||
\(928\) | 3.73505 | 0.122609 | ||||||||
\(929\) | 23.3730 | 0.766844 | 0.383422 | − | 0.923573i | \(-0.374745\pi\) | ||||
0.383422 | + | 0.923573i | \(0.374745\pi\) | |||||||
\(930\) | 0.463563 | 0.0152008 | ||||||||
\(931\) | 3.50736 | 0.114949 | ||||||||
\(932\) | −4.72089 | −0.154638 | ||||||||
\(933\) | −3.20607 | −0.104962 | ||||||||
\(934\) | 32.7686 | 1.07222 | ||||||||
\(935\) | 28.4889 | 0.931686 | ||||||||
\(936\) | −5.43306 | −0.177585 | ||||||||
\(937\) | 21.9987 | 0.718666 | 0.359333 | − | 0.933209i | \(-0.383004\pi\) | ||||
0.359333 | + | 0.933209i | \(0.383004\pi\) | |||||||
\(938\) | 23.9536 | 0.782114 | ||||||||
\(939\) | 1.09390 | 0.0356982 | ||||||||
\(940\) | 0.442345 | 0.0144277 | ||||||||
\(941\) | 28.3308 | 0.923559 | 0.461780 | − | 0.886995i | \(-0.347211\pi\) | ||||
0.461780 | + | 0.886995i | \(0.347211\pi\) | |||||||
\(942\) | −2.42413 | −0.0789824 | ||||||||
\(943\) | 17.6356 | 0.574295 | ||||||||
\(944\) | 14.4444 | 0.470124 | ||||||||
\(945\) | 2.15722 | 0.0701745 | ||||||||
\(946\) | 28.7412 | 0.934456 | ||||||||
\(947\) | −21.5386 | −0.699910 | −0.349955 | − | 0.936767i | \(-0.613803\pi\) | ||||
−0.349955 | + | 0.936767i | \(0.613803\pi\) | |||||||
\(948\) | −0.496078 | −0.0161119 | ||||||||
\(949\) | −12.8745 | −0.417924 | ||||||||
\(950\) | 7.33265 | 0.237903 | ||||||||
\(951\) | −1.37941 | −0.0447304 | ||||||||
\(952\) | −12.2725 | −0.397755 | ||||||||
\(953\) | −60.3153 | −1.95380 | −0.976902 | − | 0.213688i | \(-0.931453\pi\) | ||||
−0.976902 | + | 0.213688i | \(0.931453\pi\) | |||||||
\(954\) | 1.56739 | 0.0507462 | ||||||||
\(955\) | 26.3676 | 0.853236 | ||||||||
\(956\) | 5.84687 | 0.189101 | ||||||||
\(957\) | 2.41257 | 0.0779872 | ||||||||
\(958\) | −17.9402 | −0.579622 | ||||||||
\(959\) | 5.13509 | 0.165821 | ||||||||
\(960\) | 0.157743 | 0.00509113 | ||||||||
\(961\) | −22.3639 | −0.721416 | ||||||||
\(962\) | 8.68768 | 0.280102 | ||||||||
\(963\) | 32.0205 | 1.03185 | ||||||||
\(964\) | −0.115891 | −0.00373260 | ||||||||
\(965\) | 1.25709 | 0.0404673 | ||||||||
\(966\) | −1.53434 | −0.0493667 | ||||||||
\(967\) | 4.86306 | 0.156386 | 0.0781928 | − | 0.996938i | \(-0.475085\pi\) | ||||
0.0781928 | + | 0.996938i | \(0.475085\pi\) | |||||||
\(968\) | 10.7350 | 0.345035 | ||||||||
\(969\) | −1.47222 | −0.0472946 | ||||||||
\(970\) | −12.0127 | −0.385704 | ||||||||
\(971\) | 38.1127 | 1.22310 | 0.611548 | − | 0.791208i | \(-0.290547\pi\) | ||||
0.611548 | + | 0.791208i | \(0.290547\pi\) | |||||||
\(972\) | 3.70896 | 0.118965 | ||||||||
\(973\) | −28.4802 | −0.913033 | ||||||||
\(974\) | 34.1072 | 1.09287 | ||||||||
\(975\) | −0.935307 | −0.0299538 | ||||||||
\(976\) | −10.2226 | −0.327219 | ||||||||
\(977\) | −60.7118 | −1.94234 | −0.971171 | − | 0.238384i | \(-0.923382\pi\) | ||||
−0.971171 | + | 0.238384i | \(0.923382\pi\) | |||||||
\(978\) | −0.797740 | −0.0255089 | ||||||||
\(979\) | −0.974620 | −0.0311490 | ||||||||
\(980\) | −2.01700 | −0.0644308 | ||||||||
\(981\) | 34.8734 | 1.11342 | ||||||||
\(982\) | 5.20616 | 0.166135 | ||||||||
\(983\) | 43.8145 | 1.39747 | 0.698733 | − | 0.715383i | \(-0.253748\pi\) | ||||
0.698733 | + | 0.715383i | \(0.253748\pi\) | |||||||
\(984\) | 0.504499 | 0.0160828 | ||||||||
\(985\) | −4.71694 | −0.150294 | ||||||||
\(986\) | 20.0468 | 0.638421 | ||||||||
\(987\) | −0.123084 | −0.00391782 | ||||||||
\(988\) | −3.60854 | −0.114803 | ||||||||
\(989\) | 29.8579 | 0.949426 | ||||||||
\(990\) | −15.8219 | −0.502854 | ||||||||
\(991\) | −3.06703 | −0.0974274 | −0.0487137 | − | 0.998813i | \(-0.515512\pi\) | ||||
−0.0487137 | + | 0.998813i | \(0.515512\pi\) | |||||||
\(992\) | 2.93872 | 0.0933045 | ||||||||
\(993\) | −1.99563 | −0.0633295 | ||||||||
\(994\) | 1.92556 | 0.0610751 | ||||||||
\(995\) | 11.2217 | 0.355753 | ||||||||
\(996\) | 0.707213 | 0.0224089 | ||||||||
\(997\) | 15.7466 | 0.498700 | 0.249350 | − | 0.968413i | \(-0.419783\pi\) | ||||
0.249350 | + | 0.968413i | \(0.419783\pi\) | |||||||
\(998\) | −15.5744 | −0.492999 | ||||||||
\(999\) | −3.94963 | −0.124961 |
(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 | 1502.2.a.g.1.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.g.1.7 | ✓ | 16 | 1.1 | even | 1 | trivial |