Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 22x^{7} + 22x^{6} + 152x^{5} - 136x^{4} - 341x^{3} + 169x^{2} + 196x + 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-3.22348\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.22348 | 1.86108 | 0.930540 | − | 0.366191i | \(-0.119338\pi\) | ||||
0.930540 | + | 0.366191i | \(0.119338\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.96048 | −0.876753 | −0.438377 | − | 0.898791i | \(-0.644446\pi\) | ||||
−0.438377 | + | 0.898791i | \(0.644446\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.83651 | −1.45006 | −0.725032 | − | 0.688715i | \(-0.758175\pi\) | ||||
−0.725032 | + | 0.688715i | \(0.758175\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.39085 | 2.46362 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.08725 | −1.13360 | −0.566800 | − | 0.823855i | \(-0.691819\pi\) | ||||
−0.566800 | + | 0.823855i | \(0.691819\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.31957 | −1.63171 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.84309 | 1.65969 | 0.829847 | − | 0.557991i | \(-0.188428\pi\) | ||||
0.829847 | + | 0.557991i | \(0.188428\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.3669 | −2.69868 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.67929 | 1.39273 | 0.696364 | − | 0.717689i | \(-0.254800\pi\) | ||||
0.696364 | + | 0.717689i | \(0.254800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.15652 | −0.231304 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.1538 | 2.72391 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.43658 | 0.638157 | 0.319079 | − | 0.947728i | \(-0.396627\pi\) | ||||
0.319079 | + | 0.947728i | \(0.396627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.74398 | 1.03165 | 0.515825 | − | 0.856694i | \(-0.327486\pi\) | ||||
0.515825 | + | 0.856694i | \(0.327486\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.22348 | −0.561137 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.52140 | 1.27135 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.55434 | 0.748729 | 0.374364 | − | 0.927282i | \(-0.377861\pi\) | ||||
0.374364 | + | 0.927282i | \(0.377861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.1752 | −2.10972 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.970944 | −0.151636 | −0.0758180 | − | 0.997122i | \(-0.524157\pi\) | ||||
−0.0758180 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.42713 | 0.980128 | 0.490064 | − | 0.871687i | \(-0.336973\pi\) | ||||
0.490064 | + | 0.871687i | \(0.336973\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.4896 | −2.15998 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.92096 | −1.15539 | −0.577695 | − | 0.816252i | \(-0.696048\pi\) | ||||
−0.577695 | + | 0.816252i | \(0.696048\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.71881 | 1.10269 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 22.0586 | 3.08882 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4503 | 1.84754 | 0.923771 | − | 0.382946i | \(-0.125090\pi\) | ||||
0.923771 | + | 0.382946i | \(0.125090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.96048 | 0.264351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.22348 | 0.426961 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7764 | 1.53315 | 0.766577 | − | 0.642153i | \(-0.221958\pi\) | ||||
0.766577 | + | 0.642153i | \(0.221958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.76071 | 1.24973 | 0.624865 | − | 0.780732i | \(-0.285154\pi\) | ||||
0.624865 | + | 0.780732i | \(0.285154\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −28.3551 | −3.57240 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.01298 | 0.993888 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.19392 | −1.12322 | −0.561608 | − | 0.827403i | \(-0.689817\pi\) | ||||
−0.561608 | + | 0.827403i | \(0.689817\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.5306 | 2.59198 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.97888 | 0.946919 | 0.473460 | − | 0.880815i | \(-0.343005\pi\) | ||||
0.473460 | + | 0.880815i | \(0.343005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.01922 | 0.470414 | 0.235207 | − | 0.971945i | \(-0.424423\pi\) | ||||
0.235207 | + | 0.971945i | \(0.424423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.72802 | −0.430475 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.83651 | 0.437211 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.07742 | −0.796272 | −0.398136 | − | 0.917326i | \(-0.630343\pi\) | ||||
−0.398136 | + | 0.917326i | \(0.630343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.4521 | 2.60579 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2436 | −1.34391 | −0.671957 | − | 0.740590i | \(-0.734546\pi\) | ||||
−0.671957 | + | 0.740590i | \(0.734546\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.4157 | −1.45514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.0778 | 1.18766 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.57690 | −0.803150 | −0.401575 | − | 0.915826i | \(-0.631537\pi\) | ||||
−0.401575 | + | 0.915826i | \(0.631537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.6808 | 1.64379 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.5156 | 1.91998 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.96048 | −0.201141 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.3311 | −1.75971 | −0.879853 | − | 0.475245i | \(-0.842359\pi\) | ||||
−0.879853 | + | 0.475245i | \(0.842359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.39085 | −0.742808 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.21441 | −0.518853 | −0.259426 | − | 0.965763i | \(-0.583533\pi\) | ||||
−0.259426 | + | 0.965763i | \(0.583533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.55783 | −0.449096 | −0.224548 | − | 0.974463i | \(-0.572091\pi\) | ||||
−0.224548 | + | 0.974463i | \(0.572091\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 24.2451 | 2.36608 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.15529 | −0.595054 | −0.297527 | − | 0.954713i | \(-0.596162\pi\) | ||||
−0.297527 | + | 0.954713i | \(0.596162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.26716 | 0.408720 | 0.204360 | − | 0.978896i | \(-0.434489\pi\) | ||||
0.204360 | + | 0.978896i | \(0.434489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.6808 | 1.39344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.1642 | 1.61467 | 0.807336 | − | 0.590092i | \(-0.200909\pi\) | ||||
0.807336 | + | 0.590092i | \(0.200909\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.0946 | −1.22108 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −30.2083 | −2.79276 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.2536 | −2.40666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.12982 | −0.282207 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0697 | 1.07955 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.39705 | −0.212703 | −0.106352 | − | 0.994329i | \(-0.533917\pi\) | ||||
−0.106352 | + | 0.994329i | \(0.533917\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.7177 | 1.82410 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.81445 | −0.595381 | −0.297691 | − | 0.954662i | \(-0.596216\pi\) | ||||
−0.297691 | + | 0.954662i | \(0.596216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.83651 | −0.332668 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −27.7483 | −2.38819 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.9984 | 1.79401 | 0.897007 | − | 0.442016i | \(-0.145736\pi\) | ||||
0.897007 | + | 0.442016i | \(0.145736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.323311 | −0.0274229 | −0.0137115 | − | 0.999906i | \(-0.504365\pi\) | ||||
−0.0137115 | + | 0.999906i | \(0.504365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −25.5331 | −2.15027 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.08725 | 0.341793 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.73735 | −0.559506 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.8815 | 2.05219 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4092 | 1.01660 | 0.508301 | − | 0.861180i | \(-0.330274\pi\) | ||||
0.508301 | + | 0.861180i | \(0.330274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.41414 | −0.521975 | −0.260987 | − | 0.965342i | \(-0.584048\pi\) | ||||
−0.260987 | + | 0.965342i | \(0.584048\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 50.5762 | 4.08885 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.2610 | −0.904502 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5680 | −0.843421 | −0.421710 | − | 0.906731i | \(-0.638570\pi\) | ||||
−0.421710 | + | 0.906731i | \(0.638570\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 43.3568 | 3.43842 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.6252 | −2.01955 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.57594 | 0.750046 | 0.375023 | − | 0.927016i | \(-0.377635\pi\) | ||||
0.375023 | + | 0.927016i | \(0.377635\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.31957 | 0.491978 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0810 | −0.857474 | −0.428737 | − | 0.903429i | \(-0.641041\pi\) | ||||
−0.428737 | + | 0.903429i | \(0.641041\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.70565 | 0.285050 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.39085 | 0.565192 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.79409 | 0.516545 | 0.258273 | − | 0.966072i | \(-0.416847\pi\) | ||||
0.258273 | + | 0.966072i | \(0.416847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.43700 | 0.335406 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 37.9610 | 2.85332 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.70621 | 0.725476 | 0.362738 | − | 0.931891i | \(-0.381842\pi\) | ||||
0.362738 | + | 0.931891i | \(0.381842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.42537 | 0.403264 | 0.201632 | − | 0.979461i | \(-0.435375\pi\) | ||||
0.201632 | + | 0.979461i | \(0.435375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.4635 | 2.32585 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.92869 | −0.656450 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.84309 | −0.500416 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −54.3013 | −3.94984 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.12045 | 0.587575 | 0.293787 | − | 0.955871i | \(-0.405084\pi\) | ||||
0.293787 | + | 0.955871i | \(0.405084\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0898 | −0.726283 | −0.363142 | − | 0.931734i | \(-0.618296\pi\) | ||||
−0.363142 | + | 0.931734i | \(0.618296\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 25.8297 | 1.84970 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.2693 | 1.72912 | 0.864559 | − | 0.502532i | \(-0.167598\pi\) | ||||
0.864559 | + | 0.502532i | \(0.167598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.49321 | −0.247627 | −0.123814 | − | 0.992305i | \(-0.539512\pi\) | ||||
−0.123814 | + | 0.992305i | \(0.539512\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.6365 | −2.09039 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.1845 | −0.925369 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.90352 | 0.132947 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 49.3656 | 3.43115 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.2427 | −1.32472 | −0.662360 | − | 0.749186i | \(-0.730445\pi\) | ||||
−0.662360 | + | 0.749186i | \(0.730445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.7198 | 1.76229 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.6003 | −0.859330 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.0368 | −1.49596 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.9559 | 0.875478 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.9695 | −1.88143 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.1209 | 1.01257 | 0.506286 | − | 0.862366i | \(-0.331018\pi\) | ||||
0.506286 | + | 0.862366i | \(0.331018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.54767 | −0.569844 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.7270 | −1.77393 | −0.886966 | − | 0.461835i | \(-0.847191\pi\) | ||||
−0.886966 | + | 0.461835i | \(0.847191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.06443 | 0.268585 | 0.134292 | − | 0.990942i | \(-0.457124\pi\) | ||||
0.134292 | + | 0.990942i | \(0.457124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.3669 | 0.813684 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.23599 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.5289 | 1.01299 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.8139 | −1.48193 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.8455 | −1.54243 | −0.771217 | − | 0.636572i | \(-0.780352\pi\) | ||||
−0.771217 | + | 0.636572i | \(0.780352\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.90120 | −0.637792 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 33.1360 | 2.12567 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.1326 | −0.966784 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.08725 | −0.260066 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.4672 | −2.50113 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.21310 | −0.139690 | −0.0698448 | − | 0.997558i | \(-0.522250\pi\) | ||||
−0.0698448 | + | 0.997558i | \(0.522250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.67929 | −0.419923 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −43.2454 | −2.70813 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.9604 | −1.49461 | −0.747303 | − | 0.664484i | \(-0.768652\pi\) | ||||
−0.747303 | + | 0.664484i | \(0.768652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.4728 | −1.08570 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.3993 | 1.57217 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.95541 | −0.490552 | −0.245276 | − | 0.969453i | \(-0.578879\pi\) | ||||
−0.245276 | + | 0.969453i | \(0.578879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.3691 | −1.61984 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.4240 | −1.49473 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.9571 | −0.850979 | −0.425490 | − | 0.904963i | \(-0.639898\pi\) | ||||
−0.425490 | + | 0.904963i | \(0.639898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.9194 | 0.967033 | 0.483516 | − | 0.875335i | \(-0.339359\pi\) | ||||
0.483516 | + | 0.875335i | \(0.339359\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 50.5468 | 3.05923 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.15652 | 0.0697408 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.5440 | −1.17428 | −0.587141 | − | 0.809485i | \(-0.699747\pi\) | ||||
−0.587141 | + | 0.809485i | \(0.699747\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 42.4529 | 2.54159 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.4707 | 1.16152 | 0.580761 | − | 0.814074i | \(-0.302755\pi\) | ||||
0.580761 | + | 0.814074i | \(0.302755\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.48498 | 0.266604 | 0.133302 | − | 0.991075i | \(-0.457442\pi\) | ||||
0.133302 | + | 0.991075i | \(0.457442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.31957 | −0.374339 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.72504 | 0.219882 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.8279 | 1.75458 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −55.8665 | −3.27495 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.2958 | 1.76990 | 0.884951 | − | 0.465685i | \(-0.154192\pi\) | ||||
0.884951 | + | 0.465685i | \(0.154192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.0873 | −1.34420 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.1538 | −0.821288 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.2999 | −1.57880 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.6577 | −1.42125 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.8086 | −0.965626 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.1357 | −1.09571 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.31088 | 0.246035 | 0.123018 | − | 0.992404i | \(-0.460743\pi\) | ||||
0.123018 | + | 0.992404i | \(0.460743\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.6921 | −0.835804 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.7973 | −1.06590 | −0.532948 | − | 0.846148i | \(-0.678916\pi\) | ||||
−0.532948 | + | 0.846148i | \(0.678916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.5192 | 0.707627 | 0.353814 | − | 0.935316i | \(-0.384885\pi\) | ||||
0.353814 | + | 0.935316i | \(0.384885\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 55.5895 | 3.13211 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.1197 | 0.961541 | 0.480770 | − | 0.876847i | \(-0.340357\pi\) | ||||
0.480770 | + | 0.876847i | \(0.340357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.43658 | −0.192412 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.8415 | −1.10744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.84309 | 0.380760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.72699 | 0.262206 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.7551 | 0.760660 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.3888 | 1.67539 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9080 | 0.599556 | 0.299778 | − | 0.954009i | \(-0.403087\pi\) | ||||
0.299778 | + | 0.954009i | \(0.403087\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33.6604 | 1.84458 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.0245 | 0.984783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.5700 | 1.12052 | 0.560260 | − | 0.828317i | \(-0.310701\pi\) | ||||
0.560260 | + | 0.828317i | \(0.310701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 55.3285 | 3.00503 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.74398 | −0.311054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.75771 | −0.148903 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −42.2103 | −2.27252 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.2051 | −1.03098 | −0.515492 | − | 0.856895i | \(-0.672391\pi\) | ||||
−0.515492 | + | 0.856895i | \(0.672391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.3696 | 1.67918 | 0.839588 | − | 0.543223i | \(-0.182796\pi\) | ||||
0.839588 | + | 0.543223i | \(0.182796\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −57.8503 | −3.08782 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.0842 | −1.54800 | −0.773998 | − | 0.633188i | \(-0.781746\pi\) | ||||
−0.773998 | + | 0.633188i | \(0.781746\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.6424 | −0.830214 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −84.6280 | −4.47899 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.2593 | −1.59703 | −0.798514 | − | 0.601977i | \(-0.794380\pi\) | ||||
−0.798514 | + | 0.601977i | \(0.794380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.22348 | 0.169189 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.87960 | −0.412437 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.28222 | −0.119131 | −0.0595654 | − | 0.998224i | \(-0.518971\pi\) | ||||
−0.0595654 | + | 0.998224i | \(0.518971\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.17610 | −0.373573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −51.6022 | −2.67905 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.7646 | 0.557368 | 0.278684 | − | 0.960383i | \(-0.410102\pi\) | ||||
0.278684 | + | 0.960383i | \(0.410102\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38.9066 | 2.00913 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.0462 | −0.723415 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4988 | 1.15568 | 0.577842 | − | 0.816149i | \(-0.303895\pi\) | ||||
0.577842 | + | 0.816149i | \(0.303895\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.72684 | −0.395858 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.04990 | −0.206940 | −0.103470 | − | 0.994633i | \(-0.532995\pi\) | ||||
−0.103470 | + | 0.994633i | \(0.532995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.52140 | −0.383326 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 47.5019 | 2.41466 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.9676 | −0.556078 | −0.278039 | − | 0.960570i | \(-0.589684\pi\) | ||||
−0.278039 | + | 0.960570i | \(0.589684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.7070 | 2.31150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.9663 | −1.10805 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.8751 | 0.698134 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.2611 | −1.31801 | −0.659004 | − | 0.752140i | \(-0.729022\pi\) | ||||
−0.659004 | + | 0.752140i | \(0.729022\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.3669 | −0.619121 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.5194 | −1.32431 | −0.662157 | − | 0.749365i | \(-0.730359\pi\) | ||||
−0.662157 | + | 0.749365i | \(0.730359\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.4771 | −1.16948 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −45.9774 | −2.28463 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.55434 | −0.225750 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3338 | 0.708763 | 0.354381 | − | 0.935101i | \(-0.384691\pi\) | ||||
0.354381 | + | 0.935101i | \(0.384691\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 67.6880 | 3.33880 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −45.1802 | −2.22317 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0034 | 1.17828 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.04219 | −0.0510362 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.708329 | 0.0346042 | 0.0173021 | − | 0.999850i | \(-0.494492\pi\) | ||||
0.0173021 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.40268 | −0.117100 | −0.0585498 | − | 0.998284i | \(-0.518648\pi\) | ||||
−0.0585498 | + | 0.998284i | \(0.518648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −58.5426 | −2.84644 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.91417 | −0.383894 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.4471 | −1.81219 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.1752 | 0.636105 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.38612 | −0.355777 | −0.177888 | − | 0.984051i | \(-0.556927\pi\) | ||||
−0.177888 | + | 0.984051i | \(0.556927\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.68213 | 0.369180 | 0.184590 | − | 0.982816i | \(-0.440904\pi\) | ||||
0.184590 | + | 0.982816i | \(0.440904\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.7177 | −1.04129 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.67929 | 0.319514 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.2370 | −0.679493 | −0.339747 | − | 0.940517i | \(-0.610341\pi\) | ||||
−0.339747 | + | 0.940517i | \(0.610341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 57.0485 | 2.71660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.846194 | 0.0402039 | 0.0201019 | − | 0.999798i | \(-0.493601\pi\) | ||||
0.0201019 | + | 0.999798i | \(0.493601\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.8544 | 0.704164 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 40.0009 | 1.89198 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.8778 | 0.607742 | 0.303871 | − | 0.952713i | \(-0.401721\pi\) | ||||
0.303871 | + | 0.952713i | \(0.401721\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.970944 | 0.0457200 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.6759 | −0.971437 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.7419 | −1.44120 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.4303 | 1.47025 | 0.735124 | − | 0.677932i | \(-0.237124\pi\) | ||||
0.735124 | + | 0.677932i | \(0.237124\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 96.8559 | 4.52085 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.1045 | 0.889788 | 0.444894 | − | 0.895583i | \(-0.353241\pi\) | ||||
0.444894 | + | 0.895583i | \(0.353241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8763 | 0.830782 | 0.415391 | − | 0.909643i | \(-0.363645\pi\) | ||||
0.415391 | + | 0.909643i | \(0.363645\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −36.2995 | −1.68335 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.4325 | 0.852956 | 0.426478 | − | 0.904498i | \(-0.359754\pi\) | ||||
0.426478 | + | 0.904498i | \(0.359754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.2726 | 1.62874 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.0659 | −1.56967 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.42713 | −0.295520 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.15652 | −0.0530648 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 99.4092 | 4.55163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.2766 | 0.698005 | 0.349002 | − | 0.937122i | \(-0.386521\pi\) | ||||
0.349002 | + | 0.937122i | \(0.386521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.6147 | −0.848759 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −82.6023 | −3.75853 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.9773 | 1.54283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.8012 | −1.57699 | −0.788496 | − | 0.615040i | \(-0.789140\pi\) | ||||
−0.788496 | + | 0.615040i | \(0.789140\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.8679 | 1.39589 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8170 | 0.894327 | 0.447164 | − | 0.894452i | \(-0.352434\pi\) | ||||
0.447164 | + | 0.894452i | \(0.352434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.5168 | 1.05915 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.4896 | 0.651259 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.6111 | −1.37309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.3775 | 0.822692 | 0.411346 | − | 0.911479i | \(-0.365059\pi\) | ||||
0.411346 | + | 0.911479i | \(0.365059\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.7195 | −1.59583 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.6934 | −0.655148 | −0.327574 | − | 0.944826i | \(-0.606231\pi\) | ||||
−0.327574 | + | 0.944826i | \(0.606231\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2227 | 0.454906 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.9451 | 0.530500 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.1430 | −1.29174 | −0.645870 | − | 0.763448i | \(-0.723505\pi\) | ||||
−0.645870 | + | 0.763448i | \(0.723505\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4198 | −0.682131 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.1538 | 0.624907 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.93553 | 0.393747 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.92096 | 0.348363 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.9007 | 0.961332 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.48195 | −0.108736 | −0.0543680 | − | 0.998521i | \(-0.517314\pi\) | ||||
−0.0543680 | + | 0.998521i | \(0.517314\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.967311 | 0.0422976 | 0.0211488 | − | 0.999776i | \(-0.493268\pi\) | ||||
0.0211488 | + | 0.999776i | \(0.493268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.3026 | 0.624217 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.3066 | 1.71222 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6129 | 0.939691 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 87.0374 | 3.77710 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.96849 | 0.171895 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0673 | 0.521715 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.2878 | 1.35017 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.71881 | −0.332473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.9523 | −1.07278 | −0.536391 | − | 0.843970i | \(-0.680213\pi\) | ||||
−0.536391 | + | 0.843970i | \(0.680213\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.4886 | 0.750507 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.36568 | −0.358346 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.1506 | −1.67396 | −0.836979 | − | 0.547234i | \(-0.815681\pi\) | ||||
−0.836979 | + | 0.547234i | \(0.815681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 72.1399 | 3.07886 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.43658 | 0.146403 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.1526 | 1.15465 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28.7815 | −1.22171 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.2091 | −0.559686 | −0.279843 | − | 0.960046i | \(-0.590282\pi\) | ||||
−0.279843 | + | 0.960046i | \(0.590282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.2693 | −1.11107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.0586 | −0.931315 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.54591 | −0.360167 | −0.180084 | − | 0.983651i | \(-0.557637\pi\) | ||||
−0.180084 | + | 0.983651i | \(0.557637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.6501 | −1.41567 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −89.9742 | −3.77856 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.4177 | −1.35902 | −0.679511 | − | 0.733665i | \(-0.737808\pi\) | ||||
−0.679511 | + | 0.733665i | \(0.737808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1261 | 1.09334 | 0.546672 | − | 0.837347i | \(-0.315895\pi\) | ||||
0.546672 | + | 0.837347i | \(0.315895\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.1761 | 1.09352 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.72473 | −0.322144 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.4296 | 1.72474 | 0.862369 | − | 0.506281i | \(-0.168980\pi\) | ||||
0.862369 | + | 0.506281i | \(0.168980\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.5245 | −1.35167 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 46.9729 | 1.94876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.4503 | −0.557055 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 59.2227 | 2.44856 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.4492 | −0.926577 | −0.463289 | − | 0.886207i | \(-0.653331\pi\) | ||||
−0.463289 | + | 0.886207i | \(0.653331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.74398 | 0.236677 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 78.2318 | 3.21802 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.79617 | −0.402281 | −0.201140 | − | 0.979562i | \(-0.564465\pi\) | ||||
−0.201140 | + | 0.979562i | \(0.564465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 51.4696 | 2.11005 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.2603 | −0.460854 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.65509 | 0.108484 | 0.0542420 | − | 0.998528i | \(-0.482726\pi\) | ||||
0.0542420 | + | 0.998528i | \(0.482726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.1960 | 1.02777 | 0.513884 | − | 0.857860i | \(-0.328206\pi\) | ||||
0.513884 | + | 0.857860i | \(0.328206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −67.9509 | −2.76717 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.96048 | −0.0797048 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.4327 | 1.35699 | 0.678496 | − | 0.734605i | \(-0.262632\pi\) | ||||
0.678496 | + | 0.734605i | \(0.262632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −42.5000 | −1.72219 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.3750 | 1.30975 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3061 | −0.698987 | −0.349494 | − | 0.936939i | \(-0.613646\pi\) | ||||
−0.349494 | + | 0.936939i | \(0.613646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.13595 | 0.247425 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.5384 | 0.585294 | 0.292647 | − | 0.956221i | \(-0.405464\pi\) | ||||
0.292647 | + | 0.956221i | \(0.405464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.0886 | 1.89265 | 0.946325 | − | 0.323217i | \(-0.104764\pi\) | ||||
0.946325 | + | 0.323217i | \(0.104764\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 94.5375 | 3.79366 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.0688 | 1.16462 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.8799 | −0.715194 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.22348 | −0.128734 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.1658 | 1.24266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.2723 | 0.727411 | 0.363705 | − | 0.931514i | \(-0.381512\pi\) | ||||
0.363705 | + | 0.931514i | \(0.381512\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −62.0284 | −2.46541 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.69936 | 0.186488 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.5487 | −1.25001 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 58.9707 | 2.33285 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.2261 | 0.759384 | 0.379692 | − | 0.925113i | \(-0.376030\pi\) | ||||
0.379692 | + | 0.925113i | \(0.376030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.4887 | −0.729123 | −0.364561 | − | 0.931179i | \(-0.618781\pi\) | ||||
−0.364561 | + | 0.931179i | \(0.618781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.6167 | −1.59928 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.57015 | 0.258299 | 0.129150 | − | 0.991625i | \(-0.458775\pi\) | ||||
0.129150 | + | 0.991625i | \(0.458775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.7764 | −0.462263 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −71.0354 | −2.78410 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.56134 | 0.295898 | 0.147949 | − | 0.988995i | \(-0.452733\pi\) | ||||
0.147949 | + | 0.988995i | \(0.452733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.3596 | 0.522002 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.7055 | 1.15892 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.9806 | 1.12892 | 0.564461 | − | 0.825460i | \(-0.309084\pi\) | ||||
0.564461 | + | 0.825460i | \(0.309084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.3680 | 1.37566 | 0.687828 | − | 0.725873i | \(-0.258564\pi\) | ||||
0.687828 | + | 0.725873i | \(0.258564\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −90.1591 | −3.50149 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.52140 | 0.291667 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.9539 | 0.888780 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 48.7421 | 1.88448 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.76071 | −0.376808 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.20026 | 0.316097 | 0.158048 | − | 0.987431i | \(-0.449480\pi\) | ||||
0.158048 | + | 0.987431i | \(0.449480\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.3692 | −0.630050 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.6685 | −0.448455 | −0.224228 | − | 0.974537i | \(-0.571986\pi\) | ||||
−0.224228 | + | 0.974537i | \(0.571986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 66.4909 | 2.55169 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −86.1540 | −3.30143 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.25446 | 0.239320 | 0.119660 | − | 0.992815i | \(-0.461820\pi\) | ||||
0.119660 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.1669 | −1.57291 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.1016 | 0.499858 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.9748 | −2.09437 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.7580 | −1.32226 | −0.661128 | − | 0.750273i | \(-0.729922\pi\) | ||||
−0.661128 | + | 0.750273i | \(0.729922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.3551 | 1.07712 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.633845 | 0.0240431 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.64426 | −0.251669 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.3251 | −0.882236 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.6407 | 1.00621 | 0.503103 | − | 0.864227i | \(-0.332192\pi\) | ||||
0.503103 | + | 0.864227i | \(0.332192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.55434 | 0.171770 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 50.0571 | 1.88526 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0051 | 0.752370 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.4732 | −0.919110 | −0.459555 | − | 0.888149i | \(-0.651991\pi\) | ||||
−0.459555 | + | 0.888149i | \(0.651991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −52.3081 | −1.96171 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.3657 | 1.43681 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.01298 | −0.299668 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −76.8654 | −2.87059 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.82314 | 0.366341 | 0.183171 | − | 0.983081i | \(-0.441364\pi\) | ||||
0.183171 | + | 0.983081i | \(0.441364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.4862 | 0.651219 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.9164 | −1.18698 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.97448 | −0.147608 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.8971 | −1.44262 | −0.721308 | − | 0.692615i | \(-0.756459\pi\) | ||||
−0.721308 | + | 0.692615i | \(0.756459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.4570 | 1.35026 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.9814 | 1.62671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.2696 | −1.15497 | −0.577485 | − | 0.816402i | \(-0.695966\pi\) | ||||
−0.577485 | + | 0.816402i | \(0.695966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −48.7796 | −1.79926 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.19392 | 0.338662 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.2935 | −0.746510 | −0.373255 | − | 0.927729i | \(-0.621758\pi\) | ||||
−0.373255 | + | 0.927729i | \(0.621758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.1752 | −0.484003 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.7900 | −1.12958 | −0.564788 | − | 0.825236i | \(-0.691042\pi\) | ||||
−0.564788 | + | 0.825236i | \(0.691042\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.3280 | −0.891308 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −90.4909 | −3.31089 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.6148 | 0.862867 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.6425 | −0.899218 | −0.449609 | − | 0.893226i | \(-0.648437\pi\) | ||||
−0.449609 | + | 0.893226i | \(0.648437\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.13389 | −0.259973 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5748 | 0.457643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.2119 | −0.661924 | −0.330962 | − | 0.943644i | \(-0.607373\pi\) | ||||
−0.330962 | + | 0.943644i | \(0.607373\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.5306 | −0.781510 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.7014 | −1.47542 | −0.737712 | − | 0.675115i | \(-0.764094\pi\) | ||||
−0.737712 | + | 0.675115i | \(0.764094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.3710 | −0.592670 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −99.1537 | −3.58491 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.1330 | −1.73798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.3969 | −0.663409 | −0.331704 | − | 0.943383i | \(-0.607624\pi\) | ||||
−0.331704 | + | 0.943383i | \(0.607624\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −77.2358 | −2.78158 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.0262 | −0.864162 | −0.432081 | − | 0.901835i | \(-0.642221\pi\) | ||||
−0.432081 | + | 0.901835i | \(0.642221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.64303 | −0.238625 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −56.3232 | −2.02058 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.970944 | −0.0347877 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.97888 | −0.285507 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 48.6408 | 1.73828 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.7184 | 0.739472 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.4174 | 1.69025 | 0.845125 | − | 0.534569i | \(-0.179526\pi\) | ||||
0.845125 | + | 0.534569i | \(0.179526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.6441 | −0.912956 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.8506 | −2.34138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.8945 | −1.41670 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −85.0002 | −3.01465 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.3765 | 1.43021 | 0.715105 | − | 0.699017i | \(-0.246379\pi\) | ||||
0.715105 | + | 0.699017i | \(0.246379\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54.2038 | −1.91759 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −55.9997 | −1.97865 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.01922 | −0.141835 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 50.2376 | 1.77064 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −44.9905 | −1.58374 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.4740 | −1.21204 | −0.606020 | − | 0.795449i | \(-0.707235\pi\) | ||||
−0.606020 | + | 0.795449i | \(0.707235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.8683 | 0.697670 | 0.348835 | − | 0.937184i | \(-0.386577\pi\) | ||||
0.348835 | + | 0.937184i | \(0.386577\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.3158 | 1.79973 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7734 | −0.657605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.42713 | 0.224857 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 115.894 | 4.04968 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.4349 | −1.72529 | −0.862644 | − | 0.505811i | \(-0.831193\pi\) | ||||
−0.862644 | + | 0.505811i | \(0.831193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.8830 | −0.902224 | −0.451112 | − | 0.892467i | \(-0.648972\pi\) | ||||
−0.451112 | + | 0.892467i | \(0.648972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.72802 | 0.129793 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0775 | 0.593844 | 0.296922 | − | 0.954902i | \(-0.404040\pi\) | ||||
0.296922 | + | 0.954902i | \(0.404040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.94722 | 0.0676298 | 0.0338149 | − | 0.999428i | \(-0.489234\pi\) | ||||
0.0338149 | + | 0.999428i | \(0.489234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −62.9996 | −2.18543 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 52.8205 | 1.83012 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.7241 | 0.751793 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 81.2993 | 2.81012 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.09414 | 0.279441 | 0.139720 | − | 0.990191i | \(-0.455380\pi\) | ||||
0.139720 | + | 0.990191i | \(0.455380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1899 | −0.592755 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 62.7633 | 2.16168 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.26484 | −0.249918 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.83651 | −0.131824 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.4573 | 0.496172 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.4197 | 1.04278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.3021 | 1.61959 | 0.809797 | − | 0.586710i | \(-0.199577\pi\) | ||||
0.809797 | + | 0.586710i | \(0.199577\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.4896 | −0.495534 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.2751 | −0.624265 | −0.312133 | − | 0.950039i | \(-0.601043\pi\) | ||||
−0.312133 | + | 0.950039i | \(0.601043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 58.5032 | 1.99610 | 0.998051 | − | 0.0624014i | \(-0.0198759\pi\) | ||||
0.998051 | + | 0.0624014i | \(0.0198759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0076 | 0.409218 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.5843 | 0.938981 | 0.469491 | − | 0.882938i | \(-0.344438\pi\) | ||||
0.469491 | + | 0.882938i | \(0.344438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.3197 | −0.452883 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 96.1497 | 3.26542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.07742 | 0.240085 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.5779 | 1.27328 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −128.092 | −4.33524 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −46.3056 | −1.56542 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.7574 | 0.363252 | 0.181626 | − | 0.983368i | \(-0.441864\pi\) | ||||
0.181626 | + | 0.983368i | \(0.441864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 97.6581 | 3.29393 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.3314 | −1.56094 | −0.780472 | − | 0.625191i | \(-0.785021\pi\) | ||||
−0.780472 | + | 0.625191i | \(0.785021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.2331 | −0.512636 | −0.256318 | − | 0.966593i | \(-0.582509\pi\) | ||||
−0.256318 | + | 0.966593i | \(0.582509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −74.4217 | −2.50166 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.6277 | −0.793341 | −0.396671 | − | 0.917961i | \(-0.629835\pi\) | ||||
−0.396671 | + | 0.917961i | \(0.629835\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.19629 | 0.308434 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.4521 | −0.785675 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.92096 | −0.265065 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.0288 | −0.636064 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −88.0009 | −2.93827 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.7397 | 0.658355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 92.0417 | 3.06635 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −79.4838 | −2.64506 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.6363 | −0.353563 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.7451 | 0.556013 | 0.278006 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278006 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38.5389 | −1.27825 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.40911 | −0.112949 | −0.0564744 | − | 0.998404i | \(-0.517986\pi\) | ||||
−0.0564744 | + | 0.998404i | \(0.517986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2436 | 0.405205 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −61.6835 | −2.03919 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.1437 | 0.863341 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.14196 | 0.268578 | 0.134289 | − | 0.990942i | \(-0.457125\pi\) | ||||
0.134289 | + | 0.990942i | \(0.457125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8961 | 0.457891 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.6117 | −1.07343 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.26718 | −0.173184 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.6862 | −1.10640 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.6605 | 1.46526 | 0.732632 | − | 0.680625i | \(-0.238292\pi\) | ||||
0.732632 | + | 0.680625i | \(0.238292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.71881 | 0.252974 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −60.5927 | −1.98372 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.4157 | 0.438742 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0422 | 0.883429 | 0.441714 | − | 0.897156i | \(-0.354370\pi\) | ||||
0.441714 | + | 0.897156i | \(0.354370\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.3555 | 1.31695 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.5097 | 0.766395 | 0.383197 | − | 0.923666i | \(-0.374823\pi\) | ||||
0.383197 | + | 0.923666i | \(0.374823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.48521 | −0.211188 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 106.457 | 3.46303 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.7025 | −1.38765 | −0.693823 | − | 0.720146i | \(-0.744075\pi\) | ||||
−0.693823 | + | 0.720146i | \(0.744075\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.4276 | −0.533262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 55.1852 | 1.78950 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.2708 | −0.818600 | −0.409300 | − | 0.912400i | \(-0.634227\pi\) | ||||
−0.409300 | + | 0.912400i | \(0.634227\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.9200 | −0.515158 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0778 | −0.358093 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −80.5606 | −2.60144 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.99332 | 0.0643006 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.4928 | −1.46598 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.7809 | 0.636771 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.78722 | −0.250420 | −0.125210 | − | 0.992130i | \(-0.539960\pi\) | ||||
−0.125210 | + | 0.992130i | \(0.539960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.0586 | 0.708624 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.0683640 | −0.00219390 | −0.00109695 | − | 0.999999i | \(-0.500349\pi\) | ||||
−0.00109695 | + | 0.999999i | \(0.500349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.24039 | 0.0397650 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.2374 | 0.487987 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.2460 | −0.903668 | −0.451834 | − | 0.892102i | \(-0.649230\pi\) | ||||
−0.451834 | + | 0.892102i | \(0.649230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.57690 | 0.242159 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.5379 | 1.00693 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −60.3323 | −1.92430 | −0.962151 | − | 0.272518i | \(-0.912143\pi\) | ||||
−0.962151 | + | 0.272518i | \(0.912143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.5795 | −1.51601 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 97.9579 | 3.11804 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.9286 | 1.36505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9051 | −0.409944 | −0.204972 | − | 0.978768i | \(-0.565710\pi\) | ||||
−0.204972 | + | 0.978768i | \(0.565710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.1617 | 1.11582 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.84837 | 0.217108 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.28960 | −0.230864 | −0.115432 | − | 0.993315i | \(-0.536825\pi\) | ||||
−0.115432 | + | 0.993315i | \(0.536825\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 64.4613 | 2.03947 |
(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 | 3344.2.a.bb.1.9 | 9 | ||
4.3 | odd | 2 | 1672.2.a.k.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.k.1.1 | ✓ | 9 | 4.3 | odd | 2 | ||
3344.2.a.bb.1.9 | 9 | 1.1 | even | 1 | trivial |