Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.692297\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.307703 | 0.137609 | 0.0688044 | − | 0.997630i | \(-0.478082\pi\) | ||||
0.0688044 | + | 0.997630i | \(0.478082\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.307703 | −0.0973041 | ||||||||
\(11\) | 1.25714 | 0.379042 | 0.189521 | − | 0.981877i | \(-0.439306\pi\) | ||||
0.189521 | + | 0.981877i | \(0.439306\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.307703 | 0.0794485 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.64173 | −0.640715 | −0.320357 | − | 0.947297i | \(-0.603803\pi\) | ||||
−0.320357 | + | 0.947297i | \(0.603803\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −7.86343 | −1.80399 | −0.901997 | − | 0.431741i | \(-0.857899\pi\) | ||||
−0.901997 | + | 0.431741i | \(0.857899\pi\) | |||||||
\(20\) | 0.307703 | 0.0688044 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.25714 | −0.268023 | ||||||||
\(23\) | −6.47884 | −1.35093 | −0.675465 | − | 0.737392i | \(-0.736057\pi\) | ||||
−0.675465 | + | 0.737392i | \(0.736057\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.90532 | −0.981064 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.88438 | 1.64979 | 0.824894 | − | 0.565288i | \(-0.191235\pi\) | ||||
0.824894 | + | 0.565288i | \(0.191235\pi\) | |||||||
\(30\) | −0.307703 | −0.0561786 | ||||||||
\(31\) | 5.22170 | 0.937844 | 0.468922 | − | 0.883239i | \(-0.344642\pi\) | ||||
0.468922 | + | 0.883239i | \(0.344642\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.25714 | 0.218840 | ||||||||
\(34\) | 2.64173 | 0.453054 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.44922 | 1.38904 | 0.694521 | − | 0.719472i | \(-0.255616\pi\) | ||||
0.694521 | + | 0.719472i | \(0.255616\pi\) | |||||||
\(38\) | 7.86343 | 1.27562 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.307703 | −0.0486521 | ||||||||
\(41\) | 0.192517 | 0.0300660 | 0.0150330 | − | 0.999887i | \(-0.495215\pi\) | ||||
0.0150330 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4788 | 1.59801 | 0.799004 | − | 0.601326i | \(-0.205361\pi\) | ||||
0.799004 | + | 0.601326i | \(0.205361\pi\) | |||||||
\(44\) | 1.25714 | 0.189521 | ||||||||
\(45\) | 0.307703 | 0.0458696 | ||||||||
\(46\) | 6.47884 | 0.955252 | ||||||||
\(47\) | 9.74825 | 1.42193 | 0.710964 | − | 0.703229i | \(-0.248259\pi\) | ||||
0.710964 | + | 0.703229i | \(0.248259\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.90532 | 0.693717 | ||||||||
\(51\) | −2.64173 | −0.369917 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 7.74825 | 1.06430 | 0.532152 | − | 0.846649i | \(-0.321384\pi\) | ||||
0.532152 | + | 0.846649i | \(0.321384\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.386825 | 0.0521595 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.86343 | −1.04154 | ||||||||
\(58\) | −8.88438 | −1.16658 | ||||||||
\(59\) | 10.0920 | 1.31387 | 0.656934 | − | 0.753948i | \(-0.271853\pi\) | ||||
0.656934 | + | 0.753948i | \(0.271853\pi\) | |||||||
\(60\) | 0.307703 | 0.0397242 | ||||||||
\(61\) | 9.38639 | 1.20180 | 0.600902 | − | 0.799323i | \(-0.294808\pi\) | ||||
0.600902 | + | 0.799323i | \(0.294808\pi\) | |||||||
\(62\) | −5.22170 | −0.663156 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.307703 | −0.0381658 | ||||||||
\(66\) | −1.25714 | −0.154743 | ||||||||
\(67\) | 9.62724 | 1.17615 | 0.588077 | − | 0.808805i | \(-0.299885\pi\) | ||||
0.588077 | + | 0.808805i | \(0.299885\pi\) | |||||||
\(68\) | −2.64173 | −0.320357 | ||||||||
\(69\) | −6.47884 | −0.779960 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.56484 | −0.185713 | −0.0928563 | − | 0.995680i | \(-0.529600\pi\) | ||||
−0.0928563 | + | 0.995680i | \(0.529600\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 6.83487 | 0.799961 | 0.399981 | − | 0.916524i | \(-0.369017\pi\) | ||||
0.399981 | + | 0.916524i | \(0.369017\pi\) | |||||||
\(74\) | −8.44922 | −0.982202 | ||||||||
\(75\) | −4.90532 | −0.566417 | ||||||||
\(76\) | −7.86343 | −0.901997 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −16.0082 | −1.80107 | −0.900534 | − | 0.434786i | \(-0.856824\pi\) | ||||
−0.900534 | + | 0.434786i | \(0.856824\pi\) | |||||||
\(80\) | 0.307703 | 0.0344022 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.192517 | −0.0212599 | ||||||||
\(83\) | −1.04145 | −0.114314 | −0.0571569 | − | 0.998365i | \(-0.518204\pi\) | ||||
−0.0571569 | + | 0.998365i | \(0.518204\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.812869 | −0.0881680 | ||||||||
\(86\) | −10.4788 | −1.12996 | ||||||||
\(87\) | 8.88438 | 0.952505 | ||||||||
\(88\) | −1.25714 | −0.134012 | ||||||||
\(89\) | 1.24308 | 0.131766 | 0.0658831 | − | 0.997827i | \(-0.479014\pi\) | ||||
0.0658831 | + | 0.997827i | \(0.479014\pi\) | |||||||
\(90\) | −0.307703 | −0.0324347 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.47884 | −0.675465 | ||||||||
\(93\) | 5.22170 | 0.541465 | ||||||||
\(94\) | −9.74825 | −1.00545 | ||||||||
\(95\) | −2.41960 | −0.248246 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −15.7688 | −1.60107 | −0.800537 | − | 0.599283i | \(-0.795452\pi\) | ||||
−0.800537 | + | 0.599283i | \(0.795452\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.25714 | 0.126347 | ||||||||
\(100\) | −4.90532 | −0.490532 | ||||||||
\(101\) | 19.3509 | 1.92549 | 0.962745 | − | 0.270409i | \(-0.0871591\pi\) | ||||
0.962745 | + | 0.270409i | \(0.0871591\pi\) | |||||||
\(102\) | 2.64173 | 0.261571 | ||||||||
\(103\) | −18.0642 | −1.77992 | −0.889959 | − | 0.456042i | \(-0.849267\pi\) | ||||
−0.889959 | + | 0.456042i | \(0.849267\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.74825 | −0.752576 | ||||||||
\(107\) | 16.0577 | 1.55236 | 0.776180 | − | 0.630511i | \(-0.217155\pi\) | ||||
0.776180 | + | 0.630511i | \(0.217155\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.8053 | 1.03496 | 0.517478 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517478 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(110\) | −0.386825 | −0.0368824 | ||||||||
\(111\) | 8.44922 | 0.801964 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.8367 | 1.39572 | 0.697858 | − | 0.716236i | \(-0.254137\pi\) | ||||
0.697858 | + | 0.716236i | \(0.254137\pi\) | |||||||
\(114\) | 7.86343 | 0.736478 | ||||||||
\(115\) | −1.99356 | −0.185900 | ||||||||
\(116\) | 8.88438 | 0.824894 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −10.0920 | −0.929045 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.307703 | −0.0280893 | ||||||||
\(121\) | −9.41960 | −0.856327 | ||||||||
\(122\) | −9.38639 | −0.849804 | ||||||||
\(123\) | 0.192517 | 0.0173586 | ||||||||
\(124\) | 5.22170 | 0.468922 | ||||||||
\(125\) | −3.04789 | −0.272612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.53584 | −0.136284 | −0.0681421 | − | 0.997676i | \(-0.521707\pi\) | ||||
−0.0681421 | + | 0.997676i | \(0.521707\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.4788 | 0.922610 | ||||||||
\(130\) | 0.307703 | 0.0269873 | ||||||||
\(131\) | 2.16934 | 0.189536 | 0.0947682 | − | 0.995499i | \(-0.469789\pi\) | ||||
0.0947682 | + | 0.995499i | \(0.469789\pi\) | |||||||
\(132\) | 1.25714 | 0.109420 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.62724 | −0.831666 | ||||||||
\(135\) | 0.307703 | 0.0264828 | ||||||||
\(136\) | 2.64173 | 0.226527 | ||||||||
\(137\) | −8.46972 | −0.723617 | −0.361809 | − | 0.932252i | \(-0.617841\pi\) | ||||
−0.361809 | + | 0.932252i | \(0.617841\pi\) | |||||||
\(138\) | 6.47884 | 0.551515 | ||||||||
\(139\) | −12.4015 | −1.05188 | −0.525941 | − | 0.850521i | \(-0.676287\pi\) | ||||
−0.525941 | + | 0.850521i | \(0.676287\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.74825 | 0.820950 | ||||||||
\(142\) | 1.56484 | 0.131319 | ||||||||
\(143\) | −1.25714 | −0.105127 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.73375 | 0.227025 | ||||||||
\(146\) | −6.83487 | −0.565658 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.44922 | 0.694521 | ||||||||
\(149\) | 0.213022 | 0.0174514 | 0.00872571 | − | 0.999962i | \(-0.497222\pi\) | ||||
0.00872571 | + | 0.999962i | \(0.497222\pi\) | |||||||
\(150\) | 4.90532 | 0.400518 | ||||||||
\(151\) | 12.5116 | 1.01818 | 0.509090 | − | 0.860713i | \(-0.329982\pi\) | ||||
0.509090 | + | 0.860713i | \(0.329982\pi\) | |||||||
\(152\) | 7.86343 | 0.637809 | ||||||||
\(153\) | −2.64173 | −0.213572 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.60673 | 0.129056 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −2.21569 | −0.176831 | −0.0884157 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884157 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(158\) | 16.0082 | 1.27355 | ||||||||
\(159\) | 7.74825 | 0.614476 | ||||||||
\(160\) | −0.307703 | −0.0243260 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 16.4337 | 1.28718 | 0.643592 | − | 0.765369i | \(-0.277443\pi\) | ||||
0.643592 | + | 0.765369i | \(0.277443\pi\) | |||||||
\(164\) | 0.192517 | 0.0150330 | ||||||||
\(165\) | 0.386825 | 0.0301143 | ||||||||
\(166\) | 1.04145 | 0.0808321 | ||||||||
\(167\) | 12.9544 | 1.00244 | 0.501220 | − | 0.865320i | \(-0.332885\pi\) | ||||
0.501220 | + | 0.865320i | \(0.332885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.812869 | 0.0623442 | ||||||||
\(171\) | −7.86343 | −0.601332 | ||||||||
\(172\) | 10.4788 | 0.799004 | ||||||||
\(173\) | 2.74930 | 0.209026 | 0.104513 | − | 0.994524i | \(-0.466672\pi\) | ||||
0.104513 | + | 0.994524i | \(0.466672\pi\) | |||||||
\(174\) | −8.88438 | −0.673523 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.25714 | 0.0947605 | ||||||||
\(177\) | 10.0920 | 0.758562 | ||||||||
\(178\) | −1.24308 | −0.0931727 | ||||||||
\(179\) | −3.10007 | −0.231710 | −0.115855 | − | 0.993266i | \(-0.536961\pi\) | ||||
−0.115855 | + | 0.993266i | \(0.536961\pi\) | |||||||
\(180\) | 0.307703 | 0.0229348 | ||||||||
\(181\) | 4.94032 | 0.367211 | 0.183606 | − | 0.983000i | \(-0.441223\pi\) | ||||
0.183606 | + | 0.983000i | \(0.441223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.38639 | 0.693862 | ||||||||
\(184\) | 6.47884 | 0.477626 | ||||||||
\(185\) | 2.59985 | 0.191145 | ||||||||
\(186\) | −5.22170 | −0.382873 | ||||||||
\(187\) | −3.32103 | −0.242858 | ||||||||
\(188\) | 9.74825 | 0.710964 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.41960 | 0.175536 | ||||||||
\(191\) | −24.4187 | −1.76688 | −0.883438 | − | 0.468547i | \(-0.844778\pi\) | ||||
−0.883438 | + | 0.468547i | \(0.844778\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −8.43428 | −0.607113 | −0.303556 | − | 0.952813i | \(-0.598174\pi\) | ||||
−0.303556 | + | 0.952813i | \(0.598174\pi\) | |||||||
\(194\) | 15.7688 | 1.13213 | ||||||||
\(195\) | −0.307703 | −0.0220350 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4770 | 0.888953 | 0.444476 | − | 0.895791i | \(-0.353390\pi\) | ||||
0.444476 | + | 0.895791i | \(0.353390\pi\) | |||||||
\(198\) | −1.25714 | −0.0893410 | ||||||||
\(199\) | 5.44878 | 0.386254 | 0.193127 | − | 0.981174i | \(-0.438137\pi\) | ||||
0.193127 | + | 0.981174i | \(0.438137\pi\) | |||||||
\(200\) | 4.90532 | 0.346858 | ||||||||
\(201\) | 9.62724 | 0.679053 | ||||||||
\(202\) | −19.3509 | −1.36153 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.64173 | −0.184958 | ||||||||
\(205\) | 0.0592379 | 0.00413735 | ||||||||
\(206\) | 18.0642 | 1.25859 | ||||||||
\(207\) | −6.47884 | −0.450310 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −9.88543 | −0.683790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8763 | −0.955285 | −0.477643 | − | 0.878554i | \(-0.658509\pi\) | ||||
−0.477643 | + | 0.878554i | \(0.658509\pi\) | |||||||
\(212\) | 7.74825 | 0.532152 | ||||||||
\(213\) | −1.56484 | −0.107221 | ||||||||
\(214\) | −16.0577 | −1.09768 | ||||||||
\(215\) | 3.22437 | 0.219900 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.8053 | −0.731824 | ||||||||
\(219\) | 6.83487 | 0.461858 | ||||||||
\(220\) | 0.386825 | 0.0260798 | ||||||||
\(221\) | 2.64173 | 0.177702 | ||||||||
\(222\) | −8.44922 | −0.567074 | ||||||||
\(223\) | −13.2589 | −0.887884 | −0.443942 | − | 0.896056i | \(-0.646420\pi\) | ||||
−0.443942 | + | 0.896056i | \(0.646420\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.90532 | −0.327021 | ||||||||
\(226\) | −14.8367 | −0.986920 | ||||||||
\(227\) | 18.4459 | 1.22430 | 0.612150 | − | 0.790742i | \(-0.290305\pi\) | ||||
0.612150 | + | 0.790742i | \(0.290305\pi\) | |||||||
\(228\) | −7.86343 | −0.520768 | ||||||||
\(229\) | −12.5471 | −0.829133 | −0.414566 | − | 0.910019i | \(-0.636067\pi\) | ||||
−0.414566 | + | 0.910019i | \(0.636067\pi\) | |||||||
\(230\) | 1.99356 | 0.131451 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.88438 | −0.583288 | ||||||||
\(233\) | 9.52761 | 0.624174 | 0.312087 | − | 0.950053i | \(-0.398972\pi\) | ||||
0.312087 | + | 0.950053i | \(0.398972\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 2.99956 | 0.195670 | ||||||||
\(236\) | 10.0920 | 0.656934 | ||||||||
\(237\) | −16.0082 | −1.03985 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6651 | 1.14266 | 0.571330 | − | 0.820721i | \(-0.306428\pi\) | ||||
0.571330 | + | 0.820721i | \(0.306428\pi\) | |||||||
\(240\) | 0.307703 | 0.0198621 | ||||||||
\(241\) | −0.986672 | −0.0635572 | −0.0317786 | − | 0.999495i | \(-0.510117\pi\) | ||||
−0.0317786 | + | 0.999495i | \(0.510117\pi\) | |||||||
\(242\) | 9.41960 | 0.605515 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.38639 | 0.600902 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.192517 | −0.0122744 | ||||||||
\(247\) | 7.86343 | 0.500338 | ||||||||
\(248\) | −5.22170 | −0.331578 | ||||||||
\(249\) | −1.04145 | −0.0659991 | ||||||||
\(250\) | 3.04789 | 0.192766 | ||||||||
\(251\) | −14.7117 | −0.928597 | −0.464299 | − | 0.885679i | \(-0.653694\pi\) | ||||
−0.464299 | + | 0.885679i | \(0.653694\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.14481 | −0.512060 | ||||||||
\(254\) | 1.53584 | 0.0963674 | ||||||||
\(255\) | −0.812869 | −0.0509038 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.8280 | −1.23684 | −0.618418 | − | 0.785849i | \(-0.712226\pi\) | ||||
−0.618418 | + | 0.785849i | \(0.712226\pi\) | |||||||
\(258\) | −10.4788 | −0.652384 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.307703 | −0.0190829 | ||||||||
\(261\) | 8.88438 | 0.549929 | ||||||||
\(262\) | −2.16934 | −0.134022 | ||||||||
\(263\) | 20.4260 | 1.25952 | 0.629762 | − | 0.776788i | \(-0.283152\pi\) | ||||
0.629762 | + | 0.776788i | \(0.283152\pi\) | |||||||
\(264\) | −1.25714 | −0.0773716 | ||||||||
\(265\) | 2.38416 | 0.146458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.24308 | 0.0760752 | ||||||||
\(268\) | 9.62724 | 0.588077 | ||||||||
\(269\) | −20.6344 | −1.25810 | −0.629051 | − | 0.777364i | \(-0.716556\pi\) | ||||
−0.629051 | + | 0.777364i | \(0.716556\pi\) | |||||||
\(270\) | −0.307703 | −0.0187262 | ||||||||
\(271\) | −2.28137 | −0.138584 | −0.0692918 | − | 0.997596i | \(-0.522074\pi\) | ||||
−0.0692918 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(272\) | −2.64173 | −0.160179 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.46972 | 0.511675 | ||||||||
\(275\) | −6.16667 | −0.371864 | ||||||||
\(276\) | −6.47884 | −0.389980 | ||||||||
\(277\) | 23.6232 | 1.41938 | 0.709690 | − | 0.704514i | \(-0.248835\pi\) | ||||
0.709690 | + | 0.704514i | \(0.248835\pi\) | |||||||
\(278\) | 12.4015 | 0.743793 | ||||||||
\(279\) | 5.22170 | 0.312615 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.92911 | −0.234391 | −0.117196 | − | 0.993109i | \(-0.537390\pi\) | ||||
−0.117196 | + | 0.993109i | \(0.537390\pi\) | |||||||
\(282\) | −9.74825 | −0.580500 | ||||||||
\(283\) | −20.1002 | −1.19484 | −0.597418 | − | 0.801930i | \(-0.703807\pi\) | ||||
−0.597418 | + | 0.801930i | \(0.703807\pi\) | |||||||
\(284\) | −1.56484 | −0.0928563 | ||||||||
\(285\) | −2.41960 | −0.143325 | ||||||||
\(286\) | 1.25714 | 0.0743362 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −10.0212 | −0.589485 | ||||||||
\(290\) | −2.73375 | −0.160531 | ||||||||
\(291\) | −15.7688 | −0.924381 | ||||||||
\(292\) | 6.83487 | 0.399981 | ||||||||
\(293\) | 2.75842 | 0.161149 | 0.0805743 | − | 0.996749i | \(-0.474325\pi\) | ||||
0.0805743 | + | 0.996749i | \(0.474325\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.10534 | 0.180800 | ||||||||
\(296\) | −8.44922 | −0.491101 | ||||||||
\(297\) | 1.25714 | 0.0729467 | ||||||||
\(298\) | −0.213022 | −0.0123400 | ||||||||
\(299\) | 6.47884 | 0.374681 | ||||||||
\(300\) | −4.90532 | −0.283209 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.5116 | −0.719962 | ||||||||
\(303\) | 19.3509 | 1.11168 | ||||||||
\(304\) | −7.86343 | −0.450999 | ||||||||
\(305\) | 2.88822 | 0.165379 | ||||||||
\(306\) | 2.64173 | 0.151018 | ||||||||
\(307\) | 5.64397 | 0.322118 | 0.161059 | − | 0.986945i | \(-0.448509\pi\) | ||||
0.161059 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.0642 | −1.02764 | ||||||||
\(310\) | −1.60673 | −0.0912561 | ||||||||
\(311\) | −24.9822 | −1.41661 | −0.708306 | − | 0.705906i | \(-0.750540\pi\) | ||||
−0.708306 | + | 0.705906i | \(0.750540\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −27.5680 | −1.55824 | −0.779118 | − | 0.626878i | \(-0.784333\pi\) | ||||
−0.779118 | + | 0.626878i | \(0.784333\pi\) | |||||||
\(314\) | 2.21569 | 0.125039 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0082 | −0.900534 | ||||||||
\(317\) | 0.274794 | 0.0154340 | 0.00771699 | − | 0.999970i | \(-0.497544\pi\) | ||||
0.00771699 | + | 0.999970i | \(0.497544\pi\) | |||||||
\(318\) | −7.74825 | −0.434500 | ||||||||
\(319\) | 11.1689 | 0.625339 | ||||||||
\(320\) | 0.307703 | 0.0172011 | ||||||||
\(321\) | 16.0577 | 0.896256 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.7731 | 1.15585 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.90532 | 0.272098 | ||||||||
\(326\) | −16.4337 | −0.910176 | ||||||||
\(327\) | 10.8053 | 0.597532 | ||||||||
\(328\) | −0.192517 | −0.0106300 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.386825 | −0.0212940 | ||||||||
\(331\) | 21.4660 | 1.17988 | 0.589939 | − | 0.807448i | \(-0.299152\pi\) | ||||
0.589939 | + | 0.807448i | \(0.299152\pi\) | |||||||
\(332\) | −1.04145 | −0.0571569 | ||||||||
\(333\) | 8.44922 | 0.463014 | ||||||||
\(334\) | −12.9544 | −0.708832 | ||||||||
\(335\) | 2.96233 | 0.161849 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0350 | 1.25480 | 0.627398 | − | 0.778698i | \(-0.284120\pi\) | ||||
0.627398 | + | 0.778698i | \(0.284120\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 14.8367 | 0.805817 | ||||||||
\(340\) | −0.812869 | −0.0440840 | ||||||||
\(341\) | 6.56440 | 0.355482 | ||||||||
\(342\) | 7.86343 | 0.425206 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.4788 | −0.564981 | ||||||||
\(345\) | −1.99356 | −0.107329 | ||||||||
\(346\) | −2.74930 | −0.147804 | ||||||||
\(347\) | −1.68647 | −0.0905346 | −0.0452673 | − | 0.998975i | \(-0.514414\pi\) | ||||
−0.0452673 | + | 0.998975i | \(0.514414\pi\) | |||||||
\(348\) | 8.88438 | 0.476253 | ||||||||
\(349\) | −22.2877 | −1.19303 | −0.596516 | − | 0.802601i | \(-0.703449\pi\) | ||||
−0.596516 | + | 0.802601i | \(0.703449\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.25714 | −0.0670058 | ||||||||
\(353\) | 13.0664 | 0.695455 | 0.347728 | − | 0.937596i | \(-0.386953\pi\) | ||||
0.347728 | + | 0.937596i | \(0.386953\pi\) | |||||||
\(354\) | −10.0920 | −0.536384 | ||||||||
\(355\) | −0.481506 | −0.0255557 | ||||||||
\(356\) | 1.24308 | 0.0658831 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.10007 | 0.163844 | ||||||||
\(359\) | 3.70320 | 0.195448 | 0.0977238 | − | 0.995214i | \(-0.468844\pi\) | ||||
0.0977238 | + | 0.995214i | \(0.468844\pi\) | |||||||
\(360\) | −0.307703 | −0.0162174 | ||||||||
\(361\) | 42.8336 | 2.25440 | ||||||||
\(362\) | −4.94032 | −0.259658 | ||||||||
\(363\) | −9.41960 | −0.494401 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.10311 | 0.110082 | ||||||||
\(366\) | −9.38639 | −0.490634 | ||||||||
\(367\) | 4.32176 | 0.225594 | 0.112797 | − | 0.993618i | \(-0.464019\pi\) | ||||
0.112797 | + | 0.993618i | \(0.464019\pi\) | |||||||
\(368\) | −6.47884 | −0.337733 | ||||||||
\(369\) | 0.192517 | 0.0100220 | ||||||||
\(370\) | −2.59985 | −0.135160 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.22170 | 0.270732 | ||||||||
\(373\) | 23.6349 | 1.22377 | 0.611883 | − | 0.790948i | \(-0.290412\pi\) | ||||
0.611883 | + | 0.790948i | \(0.290412\pi\) | |||||||
\(374\) | 3.32103 | 0.171726 | ||||||||
\(375\) | −3.04789 | −0.157393 | ||||||||
\(376\) | −9.74825 | −0.502727 | ||||||||
\(377\) | −8.88438 | −0.457569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.21196 | 0.164987 | 0.0824937 | − | 0.996592i | \(-0.473712\pi\) | ||||
0.0824937 | + | 0.996592i | \(0.473712\pi\) | |||||||
\(380\) | −2.41960 | −0.124123 | ||||||||
\(381\) | −1.53584 | −0.0786837 | ||||||||
\(382\) | 24.4187 | 1.24937 | ||||||||
\(383\) | 37.3559 | 1.90880 | 0.954398 | − | 0.298536i | \(-0.0964982\pi\) | ||||
0.954398 | + | 0.298536i | \(0.0964982\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.43428 | 0.429294 | ||||||||
\(387\) | 10.4788 | 0.532669 | ||||||||
\(388\) | −15.7688 | −0.800537 | ||||||||
\(389\) | −10.0334 | −0.508713 | −0.254357 | − | 0.967110i | \(-0.581864\pi\) | ||||
−0.254357 | + | 0.967110i | \(0.581864\pi\) | |||||||
\(390\) | 0.307703 | 0.0155811 | ||||||||
\(391\) | 17.1154 | 0.865561 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.16934 | 0.109429 | ||||||||
\(394\) | −12.4770 | −0.628584 | ||||||||
\(395\) | −4.92578 | −0.247843 | ||||||||
\(396\) | 1.25714 | 0.0631737 | ||||||||
\(397\) | −24.3552 | −1.22235 | −0.611175 | − | 0.791495i | \(-0.709303\pi\) | ||||
−0.611175 | + | 0.791495i | \(0.709303\pi\) | |||||||
\(398\) | −5.44878 | −0.273123 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.90532 | −0.245266 | ||||||||
\(401\) | 22.4434 | 1.12077 | 0.560385 | − | 0.828232i | \(-0.310653\pi\) | ||||
0.560385 | + | 0.828232i | \(0.310653\pi\) | |||||||
\(402\) | −9.62724 | −0.480163 | ||||||||
\(403\) | −5.22170 | −0.260111 | ||||||||
\(404\) | 19.3509 | 0.962745 | ||||||||
\(405\) | 0.307703 | 0.0152899 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6218 | 0.526506 | ||||||||
\(408\) | 2.64173 | 0.130785 | ||||||||
\(409\) | −17.5729 | −0.868926 | −0.434463 | − | 0.900690i | \(-0.643062\pi\) | ||||
−0.434463 | + | 0.900690i | \(0.643062\pi\) | |||||||
\(410\) | −0.0592379 | −0.00292555 | ||||||||
\(411\) | −8.46972 | −0.417781 | ||||||||
\(412\) | −18.0642 | −0.889959 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.47884 | 0.318417 | ||||||||
\(415\) | −0.320457 | −0.0157306 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −12.4015 | −0.607304 | ||||||||
\(418\) | 9.88543 | 0.483512 | ||||||||
\(419\) | 8.69651 | 0.424852 | 0.212426 | − | 0.977177i | \(-0.431863\pi\) | ||||
0.212426 | + | 0.977177i | \(0.431863\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.83648 | 0.479401 | 0.239700 | − | 0.970847i | \(-0.422951\pi\) | ||||
0.239700 | + | 0.970847i | \(0.422951\pi\) | |||||||
\(422\) | 13.8763 | 0.675489 | ||||||||
\(423\) | 9.74825 | 0.473976 | ||||||||
\(424\) | −7.74825 | −0.376288 | ||||||||
\(425\) | 12.9586 | 0.628582 | ||||||||
\(426\) | 1.56484 | 0.0758169 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.0577 | 0.776180 | ||||||||
\(429\) | −1.25714 | −0.0606953 | ||||||||
\(430\) | −3.22437 | −0.155493 | ||||||||
\(431\) | −30.0518 | −1.44754 | −0.723772 | − | 0.690040i | \(-0.757593\pi\) | ||||
−0.723772 | + | 0.690040i | \(0.757593\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −6.83816 | −0.328621 | −0.164311 | − | 0.986409i | \(-0.552540\pi\) | ||||
−0.164311 | + | 0.986409i | \(0.552540\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.73375 | 0.131073 | ||||||||
\(436\) | 10.8053 | 0.517478 | ||||||||
\(437\) | 50.9459 | 2.43707 | ||||||||
\(438\) | −6.83487 | −0.326583 | ||||||||
\(439\) | 1.19387 | 0.0569803 | 0.0284902 | − | 0.999594i | \(-0.490930\pi\) | ||||
0.0284902 | + | 0.999594i | \(0.490930\pi\) | |||||||
\(440\) | −0.386825 | −0.0184412 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.64173 | −0.125655 | ||||||||
\(443\) | 2.07404 | 0.0985407 | 0.0492703 | − | 0.998785i | \(-0.484310\pi\) | ||||
0.0492703 | + | 0.998785i | \(0.484310\pi\) | |||||||
\(444\) | 8.44922 | 0.400982 | ||||||||
\(445\) | 0.382499 | 0.0181322 | ||||||||
\(446\) | 13.2589 | 0.627829 | ||||||||
\(447\) | 0.213022 | 0.0100756 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.2736 | 1.47589 | 0.737947 | − | 0.674859i | \(-0.235796\pi\) | ||||
0.737947 | + | 0.674859i | \(0.235796\pi\) | |||||||
\(450\) | 4.90532 | 0.231239 | ||||||||
\(451\) | 0.242020 | 0.0113963 | ||||||||
\(452\) | 14.8367 | 0.697858 | ||||||||
\(453\) | 12.5116 | 0.587847 | ||||||||
\(454\) | −18.4459 | −0.865710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.86343 | 0.368239 | ||||||||
\(457\) | 1.30635 | 0.0611084 | 0.0305542 | − | 0.999533i | \(-0.490273\pi\) | ||||
0.0305542 | + | 0.999533i | \(0.490273\pi\) | |||||||
\(458\) | 12.5471 | 0.586285 | ||||||||
\(459\) | −2.64173 | −0.123306 | ||||||||
\(460\) | −1.99356 | −0.0929500 | ||||||||
\(461\) | 12.4723 | 0.580891 | 0.290445 | − | 0.956892i | \(-0.406197\pi\) | ||||
0.290445 | + | 0.956892i | \(0.406197\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.7415 | −1.47515 | −0.737577 | − | 0.675263i | \(-0.764030\pi\) | ||||
−0.737577 | + | 0.675263i | \(0.764030\pi\) | |||||||
\(464\) | 8.88438 | 0.412447 | ||||||||
\(465\) | 1.60673 | 0.0745103 | ||||||||
\(466\) | −9.52761 | −0.441358 | ||||||||
\(467\) | −31.6006 | −1.46230 | −0.731152 | − | 0.682215i | \(-0.761017\pi\) | ||||
−0.731152 | + | 0.682215i | \(0.761017\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.99956 | −0.138359 | ||||||||
\(471\) | −2.21569 | −0.102094 | ||||||||
\(472\) | −10.0920 | −0.464522 | ||||||||
\(473\) | 13.1734 | 0.605712 | ||||||||
\(474\) | 16.0082 | 0.735283 | ||||||||
\(475\) | 38.5726 | 1.76983 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.74825 | 0.354768 | ||||||||
\(478\) | −17.6651 | −0.807982 | ||||||||
\(479\) | −19.1429 | −0.874660 | −0.437330 | − | 0.899301i | \(-0.644076\pi\) | ||||
−0.437330 | + | 0.899301i | \(0.644076\pi\) | |||||||
\(480\) | −0.307703 | −0.0140446 | ||||||||
\(481\) | −8.44922 | −0.385251 | ||||||||
\(482\) | 0.986672 | 0.0449417 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.41960 | −0.428164 | ||||||||
\(485\) | −4.85209 | −0.220322 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −18.7563 | −0.849929 | −0.424965 | − | 0.905210i | \(-0.639713\pi\) | ||||
−0.424965 | + | 0.905210i | \(0.639713\pi\) | |||||||
\(488\) | −9.38639 | −0.424902 | ||||||||
\(489\) | 16.4337 | 0.743156 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2050 | −0.956967 | −0.478483 | − | 0.878097i | \(-0.658813\pi\) | ||||
−0.478483 | + | 0.878097i | \(0.658813\pi\) | |||||||
\(492\) | 0.192517 | 0.00867932 | ||||||||
\(493\) | −23.4702 | −1.05704 | ||||||||
\(494\) | −7.86343 | −0.353793 | ||||||||
\(495\) | 0.386825 | 0.0173865 | ||||||||
\(496\) | 5.22170 | 0.234461 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.04145 | 0.0466684 | ||||||||
\(499\) | −38.9864 | −1.74527 | −0.872636 | − | 0.488371i | \(-0.837591\pi\) | ||||
−0.872636 | + | 0.488371i | \(0.837591\pi\) | |||||||
\(500\) | −3.04789 | −0.136306 | ||||||||
\(501\) | 12.9544 | 0.578759 | ||||||||
\(502\) | 14.7117 | 0.656617 | ||||||||
\(503\) | 36.1321 | 1.61105 | 0.805526 | − | 0.592560i | \(-0.201883\pi\) | ||||
0.805526 | + | 0.592560i | \(0.201883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.95434 | 0.264965 | ||||||||
\(506\) | 8.14481 | 0.362081 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −1.53584 | −0.0681421 | ||||||||
\(509\) | −11.2053 | −0.496664 | −0.248332 | − | 0.968675i | \(-0.579882\pi\) | ||||
−0.248332 | + | 0.968675i | \(0.579882\pi\) | |||||||
\(510\) | 0.812869 | 0.0359944 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.86343 | −0.347179 | ||||||||
\(514\) | 19.8280 | 0.874575 | ||||||||
\(515\) | −5.55840 | −0.244932 | ||||||||
\(516\) | 10.4788 | 0.461305 | ||||||||
\(517\) | 12.2549 | 0.538970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.74930 | 0.120681 | ||||||||
\(520\) | 0.307703 | 0.0134937 | ||||||||
\(521\) | −24.2741 | −1.06347 | −0.531733 | − | 0.846912i | \(-0.678459\pi\) | ||||
−0.531733 | + | 0.846912i | \(0.678459\pi\) | |||||||
\(522\) | −8.88438 | −0.388859 | ||||||||
\(523\) | −10.9494 | −0.478785 | −0.239393 | − | 0.970923i | \(-0.576948\pi\) | ||||
−0.239393 | + | 0.970923i | \(0.576948\pi\) | |||||||
\(524\) | 2.16934 | 0.0947682 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.4260 | −0.890618 | ||||||||
\(527\) | −13.7943 | −0.600891 | ||||||||
\(528\) | 1.25714 | 0.0547100 | ||||||||
\(529\) | 18.9753 | 0.825014 | ||||||||
\(530\) | −2.38416 | −0.103561 | ||||||||
\(531\) | 10.0920 | 0.437956 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.192517 | −0.00833882 | ||||||||
\(534\) | −1.24308 | −0.0537933 | ||||||||
\(535\) | 4.94101 | 0.213618 | ||||||||
\(536\) | −9.62724 | −0.415833 | ||||||||
\(537\) | −3.10007 | −0.133778 | ||||||||
\(538\) | 20.6344 | 0.889613 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.307703 | 0.0132414 | ||||||||
\(541\) | −8.63858 | −0.371402 | −0.185701 | − | 0.982606i | \(-0.559456\pi\) | ||||
−0.185701 | + | 0.982606i | \(0.559456\pi\) | |||||||
\(542\) | 2.28137 | 0.0979934 | ||||||||
\(543\) | 4.94032 | 0.212010 | ||||||||
\(544\) | 2.64173 | 0.113263 | ||||||||
\(545\) | 3.32481 | 0.142419 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.32536 | 0.142182 | 0.0710910 | − | 0.997470i | \(-0.477352\pi\) | ||||
0.0710910 | + | 0.997470i | \(0.477352\pi\) | |||||||
\(548\) | −8.46972 | −0.361809 | ||||||||
\(549\) | 9.38639 | 0.400601 | ||||||||
\(550\) | 6.16667 | 0.262948 | ||||||||
\(551\) | −69.8617 | −2.97621 | ||||||||
\(552\) | 6.47884 | 0.275758 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −23.6232 | −1.00365 | ||||||||
\(555\) | 2.59985 | 0.110357 | ||||||||
\(556\) | −12.4015 | −0.525941 | ||||||||
\(557\) | −26.5544 | −1.12515 | −0.562573 | − | 0.826747i | \(-0.690189\pi\) | ||||
−0.562573 | + | 0.826747i | \(0.690189\pi\) | |||||||
\(558\) | −5.22170 | −0.221052 | ||||||||
\(559\) | −10.4788 | −0.443208 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.32103 | −0.140214 | ||||||||
\(562\) | 3.92911 | 0.165740 | ||||||||
\(563\) | −30.5664 | −1.28822 | −0.644110 | − | 0.764933i | \(-0.722772\pi\) | ||||
−0.644110 | + | 0.764933i | \(0.722772\pi\) | |||||||
\(564\) | 9.74825 | 0.410475 | ||||||||
\(565\) | 4.56528 | 0.192063 | ||||||||
\(566\) | 20.1002 | 0.844876 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.56484 | 0.0656593 | ||||||||
\(569\) | 40.6092 | 1.70243 | 0.851213 | − | 0.524821i | \(-0.175868\pi\) | ||||
0.851213 | + | 0.524821i | \(0.175868\pi\) | |||||||
\(570\) | 2.41960 | 0.101346 | ||||||||
\(571\) | 12.3552 | 0.517047 | 0.258524 | − | 0.966005i | \(-0.416764\pi\) | ||||
0.258524 | + | 0.966005i | \(0.416764\pi\) | |||||||
\(572\) | −1.25714 | −0.0525637 | ||||||||
\(573\) | −24.4187 | −1.02011 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.7808 | 1.32535 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −13.2006 | −0.549547 | −0.274773 | − | 0.961509i | \(-0.588603\pi\) | ||||
−0.274773 | + | 0.961509i | \(0.588603\pi\) | |||||||
\(578\) | 10.0212 | 0.416829 | ||||||||
\(579\) | −8.43428 | −0.350517 | ||||||||
\(580\) | 2.73375 | 0.113513 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 15.7688 | 0.653636 | ||||||||
\(583\) | 9.74063 | 0.403416 | ||||||||
\(584\) | −6.83487 | −0.282829 | ||||||||
\(585\) | −0.307703 | −0.0127219 | ||||||||
\(586\) | −2.75842 | −0.113949 | ||||||||
\(587\) | 29.6452 | 1.22359 | 0.611794 | − | 0.791017i | \(-0.290448\pi\) | ||||
0.611794 | + | 0.791017i | \(0.290448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.0605 | −1.69187 | ||||||||
\(590\) | −3.10534 | −0.127845 | ||||||||
\(591\) | 12.4770 | 0.513237 | ||||||||
\(592\) | 8.44922 | 0.347261 | ||||||||
\(593\) | 28.7560 | 1.18087 | 0.590435 | − | 0.807085i | \(-0.298956\pi\) | ||||
0.590435 | + | 0.807085i | \(0.298956\pi\) | |||||||
\(594\) | −1.25714 | −0.0515811 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.213022 | 0.00872571 | ||||||||
\(597\) | 5.44878 | 0.223004 | ||||||||
\(598\) | −6.47884 | −0.264939 | ||||||||
\(599\) | 1.11790 | 0.0456762 | 0.0228381 | − | 0.999739i | \(-0.492730\pi\) | ||||
0.0228381 | + | 0.999739i | \(0.492730\pi\) | |||||||
\(600\) | 4.90532 | 0.200259 | ||||||||
\(601\) | −18.4091 | −0.750924 | −0.375462 | − | 0.926838i | \(-0.622516\pi\) | ||||
−0.375462 | + | 0.926838i | \(0.622516\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.62724 | 0.392051 | ||||||||
\(604\) | 12.5116 | 0.509090 | ||||||||
\(605\) | −2.89844 | −0.117838 | ||||||||
\(606\) | −19.3509 | −0.786078 | ||||||||
\(607\) | 2.75978 | 0.112016 | 0.0560080 | − | 0.998430i | \(-0.482163\pi\) | ||||
0.0560080 | + | 0.998430i | \(0.482163\pi\) | |||||||
\(608\) | 7.86343 | 0.318904 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.88822 | −0.116940 | ||||||||
\(611\) | −9.74825 | −0.394372 | ||||||||
\(612\) | −2.64173 | −0.106786 | ||||||||
\(613\) | 37.3489 | 1.50851 | 0.754254 | − | 0.656583i | \(-0.227999\pi\) | ||||
0.754254 | + | 0.656583i | \(0.227999\pi\) | |||||||
\(614\) | −5.64397 | −0.227772 | ||||||||
\(615\) | 0.0592379 | 0.00238870 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.4033 | 1.30451 | 0.652254 | − | 0.758001i | \(-0.273824\pi\) | ||||
0.652254 | + | 0.758001i | \(0.273824\pi\) | |||||||
\(618\) | 18.0642 | 0.726648 | ||||||||
\(619\) | 31.5448 | 1.26789 | 0.633947 | − | 0.773377i | \(-0.281434\pi\) | ||||
0.633947 | + | 0.773377i | \(0.281434\pi\) | |||||||
\(620\) | 1.60673 | 0.0645278 | ||||||||
\(621\) | −6.47884 | −0.259987 | ||||||||
\(622\) | 24.9822 | 1.00170 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 23.5888 | 0.943550 | ||||||||
\(626\) | 27.5680 | 1.10184 | ||||||||
\(627\) | −9.88543 | −0.394786 | ||||||||
\(628\) | −2.21569 | −0.0884157 | ||||||||
\(629\) | −22.3206 | −0.889980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.7900 | −0.867447 | −0.433723 | − | 0.901046i | \(-0.642800\pi\) | ||||
−0.433723 | + | 0.901046i | \(0.642800\pi\) | |||||||
\(632\) | 16.0082 | 0.636773 | ||||||||
\(633\) | −13.8763 | −0.551534 | ||||||||
\(634\) | −0.274794 | −0.0109135 | ||||||||
\(635\) | −0.472583 | −0.0187539 | ||||||||
\(636\) | 7.74825 | 0.307238 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.1689 | −0.442181 | ||||||||
\(639\) | −1.56484 | −0.0619042 | ||||||||
\(640\) | −0.307703 | −0.0121630 | ||||||||
\(641\) | 32.3750 | 1.27874 | 0.639369 | − | 0.768900i | \(-0.279196\pi\) | ||||
0.639369 | + | 0.768900i | \(0.279196\pi\) | |||||||
\(642\) | −16.0577 | −0.633748 | ||||||||
\(643\) | 47.4249 | 1.87025 | 0.935127 | − | 0.354313i | \(-0.115285\pi\) | ||||
0.935127 | + | 0.354313i | \(0.115285\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.22437 | 0.126959 | ||||||||
\(646\) | −20.7731 | −0.817307 | ||||||||
\(647\) | −33.7131 | −1.32540 | −0.662699 | − | 0.748886i | \(-0.730589\pi\) | ||||
−0.662699 | + | 0.748886i | \(0.730589\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 12.6871 | 0.498011 | ||||||||
\(650\) | −4.90532 | −0.192402 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.4337 | 0.643592 | ||||||||
\(653\) | −39.3341 | −1.53926 | −0.769631 | − | 0.638489i | \(-0.779560\pi\) | ||||
−0.769631 | + | 0.638489i | \(0.779560\pi\) | |||||||
\(654\) | −10.8053 | −0.422519 | ||||||||
\(655\) | 0.667512 | 0.0260819 | ||||||||
\(656\) | 0.192517 | 0.00751651 | ||||||||
\(657\) | 6.83487 | 0.266654 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.61944 | −0.335766 | −0.167883 | − | 0.985807i | \(-0.553693\pi\) | ||||
−0.167883 | + | 0.985807i | \(0.553693\pi\) | |||||||
\(660\) | 0.386825 | 0.0150572 | ||||||||
\(661\) | 37.4537 | 1.45678 | 0.728391 | − | 0.685162i | \(-0.240269\pi\) | ||||
0.728391 | + | 0.685162i | \(0.240269\pi\) | |||||||
\(662\) | −21.4660 | −0.834300 | ||||||||
\(663\) | 2.64173 | 0.102596 | ||||||||
\(664\) | 1.04145 | 0.0404161 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.44922 | −0.327401 | ||||||||
\(667\) | −57.5604 | −2.22875 | ||||||||
\(668\) | 12.9544 | 0.501220 | ||||||||
\(669\) | −13.2589 | −0.512620 | ||||||||
\(670\) | −2.96233 | −0.114445 | ||||||||
\(671\) | 11.8000 | 0.455534 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.4792 | −1.71455 | −0.857274 | − | 0.514861i | \(-0.827843\pi\) | ||||
−0.857274 | + | 0.514861i | \(0.827843\pi\) | |||||||
\(674\) | −23.0350 | −0.887275 | ||||||||
\(675\) | −4.90532 | −0.188806 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 21.6604 | 0.832478 | 0.416239 | − | 0.909255i | \(-0.363348\pi\) | ||||
0.416239 | + | 0.909255i | \(0.363348\pi\) | |||||||
\(678\) | −14.8367 | −0.569799 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.812869 | 0.0311721 | ||||||||
\(681\) | 18.4459 | 0.706850 | ||||||||
\(682\) | −6.56440 | −0.251364 | ||||||||
\(683\) | 3.19702 | 0.122331 | 0.0611654 | − | 0.998128i | \(-0.480518\pi\) | ||||
0.0611654 | + | 0.998128i | \(0.480518\pi\) | |||||||
\(684\) | −7.86343 | −0.300666 | ||||||||
\(685\) | −2.60616 | −0.0995761 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.5471 | −0.478700 | ||||||||
\(688\) | 10.4788 | 0.399502 | ||||||||
\(689\) | −7.74825 | −0.295185 | ||||||||
\(690\) | 1.99356 | 0.0758934 | ||||||||
\(691\) | −6.51428 | −0.247815 | −0.123907 | − | 0.992294i | \(-0.539543\pi\) | ||||
−0.123907 | + | 0.992294i | \(0.539543\pi\) | |||||||
\(692\) | 2.74930 | 0.104513 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.68647 | 0.0640176 | ||||||||
\(695\) | −3.81598 | −0.144748 | ||||||||
\(696\) | −8.88438 | −0.336761 | ||||||||
\(697\) | −0.508578 | −0.0192638 | ||||||||
\(698\) | 22.2877 | 0.843601 | ||||||||
\(699\) | 9.52761 | 0.360367 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.4705 | 0.924237 | 0.462119 | − | 0.886818i | \(-0.347089\pi\) | ||||
0.462119 | + | 0.886818i | \(0.347089\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −66.4398 | −2.50583 | ||||||||
\(704\) | 1.25714 | 0.0473802 | ||||||||
\(705\) | 2.99956 | 0.112970 | ||||||||
\(706\) | −13.0664 | −0.491761 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.0920 | 0.379281 | ||||||||
\(709\) | −24.9327 | −0.936367 | −0.468184 | − | 0.883631i | \(-0.655091\pi\) | ||||
−0.468184 | + | 0.883631i | \(0.655091\pi\) | |||||||
\(710\) | 0.481506 | 0.0180706 | ||||||||
\(711\) | −16.0082 | −0.600356 | ||||||||
\(712\) | −1.24308 | −0.0465864 | ||||||||
\(713\) | −33.8305 | −1.26696 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.386825 | −0.0144664 | ||||||||
\(716\) | −3.10007 | −0.115855 | ||||||||
\(717\) | 17.6651 | 0.659715 | ||||||||
\(718\) | −3.70320 | −0.138202 | ||||||||
\(719\) | −24.2084 | −0.902820 | −0.451410 | − | 0.892317i | \(-0.649079\pi\) | ||||
−0.451410 | + | 0.892317i | \(0.649079\pi\) | |||||||
\(720\) | 0.307703 | 0.0114674 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −42.8336 | −1.59410 | ||||||||
\(723\) | −0.986672 | −0.0366947 | ||||||||
\(724\) | 4.94032 | 0.183606 | ||||||||
\(725\) | −43.5807 | −1.61855 | ||||||||
\(726\) | 9.41960 | 0.349594 | ||||||||
\(727\) | 30.5312 | 1.13234 | 0.566170 | − | 0.824288i | \(-0.308424\pi\) | ||||
0.566170 | + | 0.824288i | \(0.308424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.10311 | −0.0778395 | ||||||||
\(731\) | −27.6823 | −1.02387 | ||||||||
\(732\) | 9.38639 | 0.346931 | ||||||||
\(733\) | −15.1098 | −0.558093 | −0.279047 | − | 0.960278i | \(-0.590018\pi\) | ||||
−0.279047 | + | 0.960278i | \(0.590018\pi\) | |||||||
\(734\) | −4.32176 | −0.159519 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.47884 | 0.238813 | ||||||||
\(737\) | 12.1028 | 0.445812 | ||||||||
\(738\) | −0.192517 | −0.00708664 | ||||||||
\(739\) | 12.9782 | 0.477410 | 0.238705 | − | 0.971092i | \(-0.423277\pi\) | ||||
0.238705 | + | 0.971092i | \(0.423277\pi\) | |||||||
\(740\) | 2.59985 | 0.0955723 | ||||||||
\(741\) | 7.86343 | 0.288870 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.44171 | −0.199637 | −0.0998186 | − | 0.995006i | \(-0.531826\pi\) | ||||
−0.0998186 | + | 0.995006i | \(0.531826\pi\) | |||||||
\(744\) | −5.22170 | −0.191437 | ||||||||
\(745\) | 0.0655474 | 0.00240147 | ||||||||
\(746\) | −23.6349 | −0.865333 | ||||||||
\(747\) | −1.04145 | −0.0381046 | ||||||||
\(748\) | −3.32103 | −0.121429 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.04789 | 0.111293 | ||||||||
\(751\) | 32.3086 | 1.17896 | 0.589479 | − | 0.807784i | \(-0.299333\pi\) | ||||
0.589479 | + | 0.807784i | \(0.299333\pi\) | |||||||
\(752\) | 9.74825 | 0.355482 | ||||||||
\(753\) | −14.7117 | −0.536126 | ||||||||
\(754\) | 8.88438 | 0.323550 | ||||||||
\(755\) | 3.84986 | 0.140111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.8745 | −0.576970 | −0.288485 | − | 0.957484i | \(-0.593151\pi\) | ||||
−0.288485 | + | 0.957484i | \(0.593151\pi\) | |||||||
\(758\) | −3.21196 | −0.116664 | ||||||||
\(759\) | −8.14481 | −0.295638 | ||||||||
\(760\) | 2.41960 | 0.0877681 | ||||||||
\(761\) | 41.2621 | 1.49575 | 0.747875 | − | 0.663840i | \(-0.231074\pi\) | ||||
0.747875 | + | 0.663840i | \(0.231074\pi\) | |||||||
\(762\) | 1.53584 | 0.0556378 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.4187 | −0.883438 | ||||||||
\(765\) | −0.812869 | −0.0293893 | ||||||||
\(766\) | −37.3559 | −1.34972 | ||||||||
\(767\) | −10.0920 | −0.364401 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 48.1001 | 1.73453 | 0.867267 | − | 0.497843i | \(-0.165874\pi\) | ||||
0.867267 | + | 0.497843i | \(0.165874\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.8280 | −0.714088 | ||||||||
\(772\) | −8.43428 | −0.303556 | ||||||||
\(773\) | −9.45474 | −0.340063 | −0.170032 | − | 0.985439i | \(-0.554387\pi\) | ||||
−0.170032 | + | 0.985439i | \(0.554387\pi\) | |||||||
\(774\) | −10.4788 | −0.376654 | ||||||||
\(775\) | −25.6141 | −0.920085 | ||||||||
\(776\) | 15.7688 | 0.566065 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0334 | 0.359715 | ||||||||
\(779\) | −1.51384 | −0.0542390 | ||||||||
\(780\) | −0.307703 | −0.0110175 | ||||||||
\(781\) | −1.96723 | −0.0703929 | ||||||||
\(782\) | −17.1154 | −0.612044 | ||||||||
\(783\) | 8.88438 | 0.317502 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.681774 | −0.0243336 | ||||||||
\(786\) | −2.16934 | −0.0773779 | ||||||||
\(787\) | 39.2061 | 1.39755 | 0.698774 | − | 0.715343i | \(-0.253729\pi\) | ||||
0.698774 | + | 0.715343i | \(0.253729\pi\) | |||||||
\(788\) | 12.4770 | 0.444476 | ||||||||
\(789\) | 20.4260 | 0.727186 | ||||||||
\(790\) | 4.92578 | 0.175251 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.25714 | −0.0446705 | ||||||||
\(793\) | −9.38639 | −0.333320 | ||||||||
\(794\) | 24.3552 | 0.864332 | ||||||||
\(795\) | 2.38416 | 0.0845573 | ||||||||
\(796\) | 5.44878 | 0.193127 | ||||||||
\(797\) | 18.1246 | 0.642006 | 0.321003 | − | 0.947078i | \(-0.395980\pi\) | ||||
0.321003 | + | 0.947078i | \(0.395980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.7523 | −0.911050 | ||||||||
\(800\) | 4.90532 | 0.173429 | ||||||||
\(801\) | 1.24308 | 0.0439220 | ||||||||
\(802\) | −22.4434 | −0.792504 | ||||||||
\(803\) | 8.59239 | 0.303219 | ||||||||
\(804\) | 9.62724 | 0.339526 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.22170 | 0.183926 | ||||||||
\(807\) | −20.6344 | −0.726366 | ||||||||
\(808\) | −19.3509 | −0.680764 | ||||||||
\(809\) | −47.5457 | −1.67162 | −0.835810 | − | 0.549019i | \(-0.815001\pi\) | ||||
−0.835810 | + | 0.549019i | \(0.815001\pi\) | |||||||
\(810\) | −0.307703 | −0.0108116 | ||||||||
\(811\) | −5.91697 | −0.207773 | −0.103886 | − | 0.994589i | \(-0.533128\pi\) | ||||
−0.103886 | + | 0.994589i | \(0.533128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.28137 | −0.0800113 | ||||||||
\(814\) | −10.6218 | −0.372296 | ||||||||
\(815\) | 5.05668 | 0.177128 | ||||||||
\(816\) | −2.64173 | −0.0924792 | ||||||||
\(817\) | −82.3996 | −2.88280 | ||||||||
\(818\) | 17.5729 | 0.614424 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0592379 | 0.00206868 | ||||||||
\(821\) | 23.2754 | 0.812317 | 0.406159 | − | 0.913803i | \(-0.366868\pi\) | ||||
0.406159 | + | 0.913803i | \(0.366868\pi\) | |||||||
\(822\) | 8.46972 | 0.295416 | ||||||||
\(823\) | −33.2570 | −1.15927 | −0.579633 | − | 0.814878i | \(-0.696804\pi\) | ||||
−0.579633 | + | 0.814878i | \(0.696804\pi\) | |||||||
\(824\) | 18.0642 | 0.629296 | ||||||||
\(825\) | −6.16667 | −0.214696 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.6956 | −0.997845 | −0.498922 | − | 0.866647i | \(-0.666271\pi\) | ||||
−0.498922 | + | 0.866647i | \(0.666271\pi\) | |||||||
\(828\) | −6.47884 | −0.225155 | ||||||||
\(829\) | 33.3026 | 1.15665 | 0.578324 | − | 0.815807i | \(-0.303707\pi\) | ||||
0.578324 | + | 0.815807i | \(0.303707\pi\) | |||||||
\(830\) | 0.320457 | 0.0111232 | ||||||||
\(831\) | 23.6232 | 0.819480 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.4015 | 0.429429 | ||||||||
\(835\) | 3.98610 | 0.137945 | ||||||||
\(836\) | −9.88543 | −0.341895 | ||||||||
\(837\) | 5.22170 | 0.180488 | ||||||||
\(838\) | −8.69651 | −0.300416 | ||||||||
\(839\) | 33.1610 | 1.14484 | 0.572422 | − | 0.819959i | \(-0.306004\pi\) | ||||
0.572422 | + | 0.819959i | \(0.306004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.9321 | 1.72180 | ||||||||
\(842\) | −9.83648 | −0.338988 | ||||||||
\(843\) | −3.92911 | −0.135326 | ||||||||
\(844\) | −13.8763 | −0.477643 | ||||||||
\(845\) | 0.307703 | 0.0105853 | ||||||||
\(846\) | −9.74825 | −0.335152 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.74825 | 0.266076 | ||||||||
\(849\) | −20.1002 | −0.689839 | ||||||||
\(850\) | −12.9586 | −0.444475 | ||||||||
\(851\) | −54.7411 | −1.87650 | ||||||||
\(852\) | −1.56484 | −0.0536106 | ||||||||
\(853\) | −17.3008 | −0.592369 | −0.296184 | − | 0.955131i | \(-0.595714\pi\) | ||||
−0.296184 | + | 0.955131i | \(0.595714\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.41960 | −0.0827485 | ||||||||
\(856\) | −16.0577 | −0.548842 | ||||||||
\(857\) | 45.6377 | 1.55896 | 0.779478 | − | 0.626430i | \(-0.215484\pi\) | ||||
0.779478 | + | 0.626430i | \(0.215484\pi\) | |||||||
\(858\) | 1.25714 | 0.0429181 | ||||||||
\(859\) | 10.2247 | 0.348861 | 0.174431 | − | 0.984669i | \(-0.444192\pi\) | ||||
0.174431 | + | 0.984669i | \(0.444192\pi\) | |||||||
\(860\) | 3.22437 | 0.109950 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.0518 | 1.02357 | ||||||||
\(863\) | −49.9830 | −1.70144 | −0.850721 | − | 0.525618i | \(-0.823834\pi\) | ||||
−0.850721 | + | 0.525618i | \(0.823834\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0.845968 | 0.0287638 | ||||||||
\(866\) | 6.83816 | 0.232370 | ||||||||
\(867\) | −10.0212 | −0.340339 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.1246 | −0.682680 | ||||||||
\(870\) | −2.73375 | −0.0926827 | ||||||||
\(871\) | −9.62724 | −0.326206 | ||||||||
\(872\) | −10.8053 | −0.365912 | ||||||||
\(873\) | −15.7688 | −0.533691 | ||||||||
\(874\) | −50.9459 | −1.72327 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.83487 | 0.230929 | ||||||||
\(877\) | −13.2274 | −0.446657 | −0.223329 | − | 0.974743i | \(-0.571692\pi\) | ||||
−0.223329 | + | 0.974743i | \(0.571692\pi\) | |||||||
\(878\) | −1.19387 | −0.0402912 | ||||||||
\(879\) | 2.75842 | 0.0930391 | ||||||||
\(880\) | 0.386825 | 0.0130399 | ||||||||
\(881\) | −4.45983 | −0.150255 | −0.0751277 | − | 0.997174i | \(-0.523936\pi\) | ||||
−0.0751277 | + | 0.997174i | \(0.523936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.38980 | −0.315992 | −0.157996 | − | 0.987440i | \(-0.550503\pi\) | ||||
−0.157996 | + | 0.987440i | \(0.550503\pi\) | |||||||
\(884\) | 2.64173 | 0.0888512 | ||||||||
\(885\) | 3.10534 | 0.104385 | ||||||||
\(886\) | −2.07404 | −0.0696788 | ||||||||
\(887\) | −7.68051 | −0.257886 | −0.128943 | − | 0.991652i | \(-0.541158\pi\) | ||||
−0.128943 | + | 0.991652i | \(0.541158\pi\) | |||||||
\(888\) | −8.44922 | −0.283537 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.382499 | −0.0128214 | ||||||||
\(891\) | 1.25714 | 0.0421158 | ||||||||
\(892\) | −13.2589 | −0.443942 | ||||||||
\(893\) | −76.6547 | −2.56515 | ||||||||
\(894\) | −0.213022 | −0.00712451 | ||||||||
\(895\) | −0.953899 | −0.0318853 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.47884 | 0.216322 | ||||||||
\(898\) | −31.2736 | −1.04361 | ||||||||
\(899\) | 46.3915 | 1.54724 | ||||||||
\(900\) | −4.90532 | −0.163511 | ||||||||
\(901\) | −20.4688 | −0.681915 | ||||||||
\(902\) | −0.242020 | −0.00805840 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.8367 | −0.493460 | ||||||||
\(905\) | 1.52015 | 0.0505315 | ||||||||
\(906\) | −12.5116 | −0.415670 | ||||||||
\(907\) | 52.6792 | 1.74918 | 0.874592 | − | 0.484860i | \(-0.161129\pi\) | ||||
0.874592 | + | 0.484860i | \(0.161129\pi\) | |||||||
\(908\) | 18.4459 | 0.612150 | ||||||||
\(909\) | 19.3509 | 0.641830 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.37413 | −0.144921 | −0.0724607 | − | 0.997371i | \(-0.523085\pi\) | ||||
−0.0724607 | + | 0.997371i | \(0.523085\pi\) | |||||||
\(912\) | −7.86343 | −0.260384 | ||||||||
\(913\) | −1.30925 | −0.0433298 | ||||||||
\(914\) | −1.30635 | −0.0432102 | ||||||||
\(915\) | 2.88822 | 0.0954815 | ||||||||
\(916\) | −12.5471 | −0.414566 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.64173 | 0.0871902 | ||||||||
\(919\) | −22.0592 | −0.727667 | −0.363834 | − | 0.931464i | \(-0.618532\pi\) | ||||
−0.363834 | + | 0.931464i | \(0.618532\pi\) | |||||||
\(920\) | 1.99356 | 0.0657256 | ||||||||
\(921\) | 5.64397 | 0.185975 | ||||||||
\(922\) | −12.4723 | −0.410752 | ||||||||
\(923\) | 1.56484 | 0.0515074 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.4461 | −1.36274 | ||||||||
\(926\) | 31.7415 | 1.04309 | ||||||||
\(927\) | −18.0642 | −0.593306 | ||||||||
\(928\) | −8.88438 | −0.291644 | ||||||||
\(929\) | 7.47152 | 0.245133 | 0.122566 | − | 0.992460i | \(-0.460888\pi\) | ||||
0.122566 | + | 0.992460i | \(0.460888\pi\) | |||||||
\(930\) | −1.60673 | −0.0526868 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.52761 | 0.312087 | ||||||||
\(933\) | −24.9822 | −0.817881 | ||||||||
\(934\) | 31.6006 | 1.03400 | ||||||||
\(935\) | −1.02189 | −0.0334194 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 10.5523 | 0.344729 | 0.172365 | − | 0.985033i | \(-0.444859\pi\) | ||||
0.172365 | + | 0.985033i | \(0.444859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.5680 | −0.899648 | ||||||||
\(940\) | 2.99956 | 0.0978349 | ||||||||
\(941\) | −40.0419 | −1.30533 | −0.652664 | − | 0.757647i | \(-0.726349\pi\) | ||||
−0.652664 | + | 0.757647i | \(0.726349\pi\) | |||||||
\(942\) | 2.21569 | 0.0721911 | ||||||||
\(943\) | −1.24728 | −0.0406172 | ||||||||
\(944\) | 10.0920 | 0.328467 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.1734 | −0.428303 | ||||||||
\(947\) | 26.8315 | 0.871905 | 0.435953 | − | 0.899970i | \(-0.356412\pi\) | ||||
0.435953 | + | 0.899970i | \(0.356412\pi\) | |||||||
\(948\) | −16.0082 | −0.519923 | ||||||||
\(949\) | −6.83487 | −0.221869 | ||||||||
\(950\) | −38.5726 | −1.25146 | ||||||||
\(951\) | 0.274794 | 0.00891081 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.9987 | 0.485855 | 0.242928 | − | 0.970044i | \(-0.421892\pi\) | ||||
0.242928 | + | 0.970044i | \(0.421892\pi\) | |||||||
\(954\) | −7.74825 | −0.250859 | ||||||||
\(955\) | −7.51371 | −0.243138 | ||||||||
\(956\) | 17.6651 | 0.571330 | ||||||||
\(957\) | 11.1689 | 0.361039 | ||||||||
\(958\) | 19.1429 | 0.618478 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.307703 | 0.00993106 | ||||||||
\(961\) | −3.73388 | −0.120448 | ||||||||
\(962\) | 8.44922 | 0.272414 | ||||||||
\(963\) | 16.0577 | 0.517453 | ||||||||
\(964\) | −0.986672 | −0.0317786 | ||||||||
\(965\) | −2.59525 | −0.0835441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.4407 | 0.785961 | 0.392980 | − | 0.919547i | \(-0.371444\pi\) | ||||
0.392980 | + | 0.919547i | \(0.371444\pi\) | |||||||
\(968\) | 9.41960 | 0.302757 | ||||||||
\(969\) | 20.7731 | 0.667328 | ||||||||
\(970\) | 4.85209 | 0.155791 | ||||||||
\(971\) | −6.27014 | −0.201218 | −0.100609 | − | 0.994926i | \(-0.532079\pi\) | ||||
−0.100609 | + | 0.994926i | \(0.532079\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.7563 | 0.600991 | ||||||||
\(975\) | 4.90532 | 0.157096 | ||||||||
\(976\) | 9.38639 | 0.300451 | ||||||||
\(977\) | 53.5154 | 1.71211 | 0.856054 | − | 0.516886i | \(-0.172909\pi\) | ||||
0.856054 | + | 0.516886i | \(0.172909\pi\) | |||||||
\(978\) | −16.4337 | −0.525490 | ||||||||
\(979\) | 1.56272 | 0.0499449 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.8053 | 0.344985 | ||||||||
\(982\) | 21.2050 | 0.676678 | ||||||||
\(983\) | −41.7110 | −1.33038 | −0.665188 | − | 0.746676i | \(-0.731649\pi\) | ||||
−0.665188 | + | 0.746676i | \(0.731649\pi\) | |||||||
\(984\) | −0.192517 | −0.00613721 | ||||||||
\(985\) | 3.83922 | 0.122328 | ||||||||
\(986\) | 23.4702 | 0.747442 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.86343 | 0.250169 | ||||||||
\(989\) | −67.8907 | −2.15880 | ||||||||
\(990\) | −0.386825 | −0.0122941 | ||||||||
\(991\) | −4.84665 | −0.153959 | −0.0769795 | − | 0.997033i | \(-0.524528\pi\) | ||||
−0.0769795 | + | 0.997033i | \(0.524528\pi\) | |||||||
\(992\) | −5.22170 | −0.165789 | ||||||||
\(993\) | 21.4660 | 0.681203 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.67660 | 0.0531519 | ||||||||
\(996\) | −1.04145 | −0.0329996 | ||||||||
\(997\) | −10.0643 | −0.318740 | −0.159370 | − | 0.987219i | \(-0.550946\pi\) | ||||
−0.159370 | + | 0.987219i | \(0.550946\pi\) | |||||||
\(998\) | 38.9864 | 1.23409 | ||||||||
\(999\) | 8.44922 | 0.267321 |
(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 | 3822.2.a.by.1.2 | yes | 4 | |
7.6 | odd | 2 | 3822.2.a.bx.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3822.2.a.bx.1.3 | ✓ | 4 | 7.6 | odd | 2 | ||
3822.2.a.by.1.2 | yes | 4 | 1.1 | even | 1 | trivial |