Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.23252.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.88474\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(5\) | −4.26056 | −1.90538 | −0.952689 | − | 0.303945i | \(-0.901696\pi\) | ||||
−0.952689 | + | 0.303945i | \(0.901696\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.26056 | −1.34731 | ||||||||
\(11\) | −3.76948 | −1.13654 | −0.568270 | − | 0.822842i | \(-0.692387\pi\) | ||||
−0.568270 | + | 0.822842i | \(0.692387\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.26056 | 0.626966 | 0.313483 | − | 0.949594i | \(-0.398504\pi\) | ||||
0.313483 | + | 0.949594i | \(0.398504\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.26056 | 1.10007 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.352835 | −0.0855752 | −0.0427876 | − | 0.999084i | \(-0.513624\pi\) | ||||
−0.0427876 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | −4.26056 | −0.952689 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.76948 | −0.803655 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 13.1523 | 2.63047 | ||||||||
\(26\) | 2.26056 | 0.443332 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.13451 | 1.69624 | 0.848118 | − | 0.529808i | \(-0.177736\pi\) | ||||
0.848118 | + | 0.529808i | \(0.177736\pi\) | |||||||
\(30\) | 4.26056 | 0.777868 | ||||||||
\(31\) | 7.89179 | 1.41741 | 0.708703 | − | 0.705507i | \(-0.249280\pi\) | ||||
0.708703 | + | 0.705507i | \(0.249280\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.76948 | 0.656181 | ||||||||
\(34\) | −0.352835 | −0.0605108 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.15608 | 0.518857 | 0.259428 | − | 0.965762i | \(-0.416466\pi\) | ||||
0.259428 | + | 0.965762i | \(0.416466\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | −2.26056 | −0.361979 | ||||||||
\(40\) | −4.26056 | −0.673653 | ||||||||
\(41\) | −5.90772 | −0.922631 | −0.461316 | − | 0.887236i | \(-0.652622\pi\) | ||||
−0.461316 | + | 0.887236i | \(0.652622\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.67720 | 1.47576 | 0.737879 | − | 0.674933i | \(-0.235827\pi\) | ||||
0.737879 | + | 0.674933i | \(0.235827\pi\) | |||||||
\(44\) | −3.76948 | −0.568270 | ||||||||
\(45\) | −4.26056 | −0.635126 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −9.27839 | −1.35339 | −0.676696 | − | 0.736262i | \(-0.736589\pi\) | ||||
−0.676696 | + | 0.736262i | \(0.736589\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.1523 | 1.86002 | ||||||||
\(51\) | 0.352835 | 0.0494068 | ||||||||
\(52\) | 2.26056 | 0.313483 | ||||||||
\(53\) | −10.2906 | −1.41352 | −0.706761 | − | 0.707453i | \(-0.749844\pi\) | ||||
−0.706761 | + | 0.707453i | \(0.749844\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 16.0601 | 2.16554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 9.13451 | 1.19942 | ||||||||
\(59\) | 9.74790 | 1.26907 | 0.634534 | − | 0.772895i | \(-0.281192\pi\) | ||||
0.634534 | + | 0.772895i | \(0.281192\pi\) | |||||||
\(60\) | 4.26056 | 0.550036 | ||||||||
\(61\) | −1.12605 | −0.144176 | −0.0720880 | − | 0.997398i | \(-0.522966\pi\) | ||||
−0.0720880 | + | 0.997398i | \(0.522966\pi\) | |||||||
\(62\) | 7.89179 | 1.00226 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.63123 | −1.19461 | ||||||||
\(66\) | 3.76948 | 0.463990 | ||||||||
\(67\) | −8.99626 | −1.09907 | −0.549534 | − | 0.835471i | \(-0.685195\pi\) | ||||
−0.549534 | + | 0.835471i | \(0.685195\pi\) | |||||||
\(68\) | −0.352835 | −0.0427876 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.29433 | 0.390965 | 0.195482 | − | 0.980707i | \(-0.437373\pi\) | ||||
0.195482 | + | 0.980707i | \(0.437373\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −3.01784 | −0.353211 | −0.176606 | − | 0.984282i | \(-0.556512\pi\) | ||||
−0.176606 | + | 0.984282i | \(0.556512\pi\) | |||||||
\(74\) | 3.15608 | 0.366887 | ||||||||
\(75\) | −13.1523 | −1.51870 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.26056 | −0.255958 | ||||||||
\(79\) | 3.01784 | 0.339533 | 0.169767 | − | 0.985484i | \(-0.445699\pi\) | ||||
0.169767 | + | 0.985484i | \(0.445699\pi\) | |||||||
\(80\) | −4.26056 | −0.476345 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.90772 | −0.652399 | ||||||||
\(83\) | −7.22678 | −0.793243 | −0.396621 | − | 0.917982i | \(-0.629817\pi\) | ||||
−0.396621 | + | 0.917982i | \(0.629817\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50328 | 0.163053 | ||||||||
\(86\) | 9.67720 | 1.04352 | ||||||||
\(87\) | −9.13451 | −0.979322 | ||||||||
\(88\) | −3.76948 | −0.401827 | ||||||||
\(89\) | −4.35284 | −0.461400 | −0.230700 | − | 0.973025i | \(-0.574102\pi\) | ||||
−0.230700 | + | 0.973025i | \(0.574102\pi\) | |||||||
\(90\) | −4.26056 | −0.449102 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −7.89179 | −0.818340 | ||||||||
\(94\) | −9.27839 | −0.956993 | ||||||||
\(95\) | 8.52111 | 0.874248 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −16.8173 | −1.70754 | −0.853771 | − | 0.520648i | \(-0.825690\pi\) | ||||
−0.853771 | + | 0.520648i | \(0.825690\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.76948 | −0.378847 | ||||||||
\(100\) | 13.1523 | 1.31523 | ||||||||
\(101\) | −10.1007 | −1.00506 | −0.502530 | − | 0.864560i | \(-0.667597\pi\) | ||||
−0.502530 | + | 0.864560i | \(0.667597\pi\) | |||||||
\(102\) | 0.352835 | 0.0349359 | ||||||||
\(103\) | −9.90772 | −0.976237 | −0.488118 | − | 0.872777i | \(-0.662317\pi\) | ||||
−0.488118 | + | 0.872777i | \(0.662317\pi\) | |||||||
\(104\) | 2.26056 | 0.221666 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.2906 | −0.999510 | ||||||||
\(107\) | 0.996260 | 0.0963121 | 0.0481560 | − | 0.998840i | \(-0.484666\pi\) | ||||
0.0481560 | + | 0.998840i | \(0.484666\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 11.4007 | 1.09199 | 0.545995 | − | 0.837789i | \(-0.316152\pi\) | ||||
0.545995 | + | 0.837789i | \(0.316152\pi\) | |||||||
\(110\) | 16.0601 | 1.53127 | ||||||||
\(111\) | −3.15608 | −0.299562 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.90772 | 0.367607 | 0.183804 | − | 0.982963i | \(-0.441159\pi\) | ||||
0.183804 | + | 0.982963i | \(0.441159\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 4.26056 | 0.397299 | ||||||||
\(116\) | 9.13451 | 0.848118 | ||||||||
\(117\) | 2.26056 | 0.208989 | ||||||||
\(118\) | 9.74790 | 0.897367 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.26056 | 0.388934 | ||||||||
\(121\) | 3.20895 | 0.291722 | ||||||||
\(122\) | −1.12605 | −0.101948 | ||||||||
\(123\) | 5.90772 | 0.532681 | ||||||||
\(124\) | 7.89179 | 0.708703 | ||||||||
\(125\) | −34.7335 | −3.10666 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.680937 | −0.0604234 | −0.0302117 | − | 0.999544i | \(-0.509618\pi\) | ||||
−0.0302117 | + | 0.999544i | \(0.509618\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.67720 | −0.852030 | ||||||||
\(130\) | −9.63123 | −0.844715 | ||||||||
\(131\) | 15.7836 | 1.37902 | 0.689509 | − | 0.724277i | \(-0.257827\pi\) | ||||
0.689509 | + | 0.724277i | \(0.257827\pi\) | |||||||
\(132\) | 3.76948 | 0.328091 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.99626 | −0.777158 | ||||||||
\(135\) | 4.26056 | 0.366690 | ||||||||
\(136\) | −0.352835 | −0.0302554 | ||||||||
\(137\) | −16.6735 | −1.42451 | −0.712255 | − | 0.701921i | \(-0.752326\pi\) | ||||
−0.712255 | + | 0.701921i | \(0.752326\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 2.09228 | 0.177465 | 0.0887324 | − | 0.996056i | \(-0.471718\pi\) | ||||
0.0887324 | + | 0.996056i | \(0.471718\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.27839 | 0.781382 | ||||||||
\(142\) | 3.29433 | 0.276454 | ||||||||
\(143\) | −8.52111 | −0.712571 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −38.9181 | −3.23197 | ||||||||
\(146\) | −3.01784 | −0.249758 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.15608 | 0.259428 | ||||||||
\(149\) | −2.50702 | −0.205383 | −0.102691 | − | 0.994713i | \(-0.532745\pi\) | ||||
−0.102691 | + | 0.994713i | \(0.532745\pi\) | |||||||
\(150\) | −13.1523 | −1.07388 | ||||||||
\(151\) | −14.4288 | −1.17420 | −0.587101 | − | 0.809514i | \(-0.699731\pi\) | ||||
−0.587101 | + | 0.809514i | \(0.699731\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | −0.352835 | −0.0285251 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.6234 | −2.70070 | ||||||||
\(156\) | −2.26056 | −0.180989 | ||||||||
\(157\) | 11.3951 | 0.909425 | 0.454712 | − | 0.890638i | \(-0.349742\pi\) | ||||
0.454712 | + | 0.890638i | \(0.349742\pi\) | |||||||
\(158\) | 3.01784 | 0.240086 | ||||||||
\(159\) | 10.2906 | 0.816097 | ||||||||
\(160\) | −4.26056 | −0.336827 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −19.7836 | −1.54957 | −0.774785 | − | 0.632225i | \(-0.782142\pi\) | ||||
−0.774785 | + | 0.632225i | \(0.782142\pi\) | |||||||
\(164\) | −5.90772 | −0.461316 | ||||||||
\(165\) | −16.0601 | −1.25027 | ||||||||
\(166\) | −7.22678 | −0.560907 | ||||||||
\(167\) | −1.85611 | −0.143630 | −0.0718151 | − | 0.997418i | \(-0.522879\pi\) | ||||
−0.0718151 | + | 0.997418i | \(0.522879\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.88988 | −0.606914 | ||||||||
\(170\) | 1.50328 | 0.115296 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 9.67720 | 0.737879 | ||||||||
\(173\) | 15.9519 | 1.21280 | 0.606398 | − | 0.795161i | \(-0.292614\pi\) | ||||
0.606398 | + | 0.795161i | \(0.292614\pi\) | |||||||
\(174\) | −9.13451 | −0.692485 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.76948 | −0.284135 | ||||||||
\(177\) | −9.74790 | −0.732697 | ||||||||
\(178\) | −4.35284 | −0.326259 | ||||||||
\(179\) | 22.6735 | 1.69469 | 0.847347 | − | 0.531040i | \(-0.178199\pi\) | ||||
0.847347 | + | 0.531040i | \(0.178199\pi\) | |||||||
\(180\) | −4.26056 | −0.317563 | ||||||||
\(181\) | 18.6894 | 1.38917 | 0.694586 | − | 0.719410i | \(-0.255588\pi\) | ||||
0.694586 | + | 0.719410i | \(0.255588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.12605 | 0.0832401 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −13.4467 | −0.988619 | ||||||||
\(186\) | −7.89179 | −0.578654 | ||||||||
\(187\) | 1.33000 | 0.0972596 | ||||||||
\(188\) | −9.27839 | −0.676696 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.52111 | 0.618187 | ||||||||
\(191\) | −17.7479 | −1.28419 | −0.642096 | − | 0.766624i | \(-0.721935\pi\) | ||||
−0.642096 | + | 0.766624i | \(0.721935\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −23.9678 | −1.72524 | −0.862619 | − | 0.505853i | \(-0.831178\pi\) | ||||
−0.862619 | + | 0.505853i | \(0.831178\pi\) | |||||||
\(194\) | −16.8173 | −1.20742 | ||||||||
\(195\) | 9.63123 | 0.689707 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.31906 | 0.0939794 | 0.0469897 | − | 0.998895i | \(-0.485037\pi\) | ||||
0.0469897 | + | 0.998895i | \(0.485037\pi\) | |||||||
\(198\) | −3.76948 | −0.267885 | ||||||||
\(199\) | 5.20205 | 0.368764 | 0.184382 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184382 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(200\) | 13.1523 | 0.930011 | ||||||||
\(201\) | 8.99626 | 0.634547 | ||||||||
\(202\) | −10.1007 | −0.710685 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.352835 | 0.0247034 | ||||||||
\(205\) | 25.1702 | 1.75796 | ||||||||
\(206\) | −9.90772 | −0.690304 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 2.26056 | 0.156741 | ||||||||
\(209\) | 7.53895 | 0.521480 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.982162 | −0.0676148 | −0.0338074 | − | 0.999428i | \(-0.510763\pi\) | ||||
−0.0338074 | + | 0.999428i | \(0.510763\pi\) | |||||||
\(212\) | −10.2906 | −0.706761 | ||||||||
\(213\) | −3.29433 | −0.225724 | ||||||||
\(214\) | 0.996260 | 0.0681029 | ||||||||
\(215\) | −41.2302 | −2.81188 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.4007 | 0.772153 | ||||||||
\(219\) | 3.01784 | 0.203927 | ||||||||
\(220\) | 16.0601 | 1.08277 | ||||||||
\(221\) | −0.797605 | −0.0536527 | ||||||||
\(222\) | −3.15608 | −0.211822 | ||||||||
\(223\) | 29.4551 | 1.97246 | 0.986231 | − | 0.165376i | \(-0.0528838\pi\) | ||||
0.986231 | + | 0.165376i | \(0.0528838\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.1523 | 0.876823 | ||||||||
\(226\) | 3.90772 | 0.259938 | ||||||||
\(227\) | 22.9856 | 1.52561 | 0.762805 | − | 0.646629i | \(-0.223822\pi\) | ||||
0.762805 | + | 0.646629i | \(0.223822\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | −9.12605 | −0.603066 | −0.301533 | − | 0.953456i | \(-0.597498\pi\) | ||||
−0.301533 | + | 0.953456i | \(0.597498\pi\) | |||||||
\(230\) | 4.26056 | 0.280933 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.13451 | 0.599710 | ||||||||
\(233\) | 2.06006 | 0.134959 | 0.0674797 | − | 0.997721i | \(-0.478504\pi\) | ||||
0.0674797 | + | 0.997721i | \(0.478504\pi\) | |||||||
\(234\) | 2.26056 | 0.147777 | ||||||||
\(235\) | 39.5311 | 2.57873 | ||||||||
\(236\) | 9.74790 | 0.634534 | ||||||||
\(237\) | −3.01784 | −0.196030 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 4.26056 | 0.275018 | ||||||||
\(241\) | −13.3385 | −0.859206 | −0.429603 | − | 0.903018i | \(-0.641346\pi\) | ||||
−0.429603 | + | 0.903018i | \(0.641346\pi\) | |||||||
\(242\) | 3.20895 | 0.206279 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.12605 | −0.0720880 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.90772 | 0.376663 | ||||||||
\(247\) | −4.52111 | −0.287672 | ||||||||
\(248\) | 7.89179 | 0.501129 | ||||||||
\(249\) | 7.22678 | 0.457979 | ||||||||
\(250\) | −34.7335 | −2.19674 | ||||||||
\(251\) | 14.3613 | 0.906477 | 0.453238 | − | 0.891389i | \(-0.350269\pi\) | ||||
0.453238 | + | 0.891389i | \(0.350269\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.76948 | 0.236985 | ||||||||
\(254\) | −0.680937 | −0.0427258 | ||||||||
\(255\) | −1.50328 | −0.0941388 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.5211 | −1.77910 | −0.889549 | − | 0.456840i | \(-0.848981\pi\) | ||||
−0.889549 | + | 0.456840i | \(0.848981\pi\) | |||||||
\(258\) | −9.67720 | −0.602476 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.63123 | −0.597304 | ||||||||
\(261\) | 9.13451 | 0.565412 | ||||||||
\(262\) | 15.7836 | 0.975112 | ||||||||
\(263\) | −3.13451 | −0.193282 | −0.0966409 | − | 0.995319i | \(-0.530810\pi\) | ||||
−0.0966409 | + | 0.995319i | \(0.530810\pi\) | |||||||
\(264\) | 3.76948 | 0.231995 | ||||||||
\(265\) | 43.8436 | 2.69329 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.35284 | 0.266389 | ||||||||
\(268\) | −8.99626 | −0.549534 | ||||||||
\(269\) | −10.9415 | −0.667115 | −0.333557 | − | 0.942730i | \(-0.608249\pi\) | ||||
−0.333557 | + | 0.942730i | \(0.608249\pi\) | |||||||
\(270\) | 4.26056 | 0.259289 | ||||||||
\(271\) | −7.12605 | −0.432877 | −0.216438 | − | 0.976296i | \(-0.569444\pi\) | ||||
−0.216438 | + | 0.976296i | \(0.569444\pi\) | |||||||
\(272\) | −0.352835 | −0.0213938 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.6735 | −1.00728 | ||||||||
\(275\) | −49.5774 | −2.98963 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −27.9925 | −1.68191 | −0.840954 | − | 0.541107i | \(-0.818005\pi\) | ||||
−0.840954 | + | 0.541107i | \(0.818005\pi\) | |||||||
\(278\) | 2.09228 | 0.125487 | ||||||||
\(279\) | 7.89179 | 0.472469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9434 | −1.07041 | −0.535207 | − | 0.844721i | \(-0.679766\pi\) | ||||
−0.535207 | + | 0.844721i | \(0.679766\pi\) | |||||||
\(282\) | 9.27839 | 0.552520 | ||||||||
\(283\) | 18.3047 | 1.08810 | 0.544050 | − | 0.839053i | \(-0.316890\pi\) | ||||
0.544050 | + | 0.839053i | \(0.316890\pi\) | |||||||
\(284\) | 3.29433 | 0.195482 | ||||||||
\(285\) | −8.52111 | −0.504747 | ||||||||
\(286\) | −8.52111 | −0.503864 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.8755 | −0.992677 | ||||||||
\(290\) | −38.9181 | −2.28535 | ||||||||
\(291\) | 16.8173 | 0.985850 | ||||||||
\(292\) | −3.01784 | −0.176606 | ||||||||
\(293\) | 4.38851 | 0.256380 | 0.128190 | − | 0.991750i | \(-0.459083\pi\) | ||||
0.128190 | + | 0.991750i | \(0.459083\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.5315 | −2.41806 | ||||||||
\(296\) | 3.15608 | 0.183444 | ||||||||
\(297\) | 3.76948 | 0.218727 | ||||||||
\(298\) | −2.50702 | −0.145228 | ||||||||
\(299\) | −2.26056 | −0.130731 | ||||||||
\(300\) | −13.1523 | −0.759351 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.4288 | −0.830286 | ||||||||
\(303\) | 10.1007 | 0.580272 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 4.79760 | 0.274710 | ||||||||
\(306\) | −0.352835 | −0.0201703 | ||||||||
\(307\) | −23.9603 | −1.36749 | −0.683743 | − | 0.729722i | \(-0.739649\pi\) | ||||
−0.683743 | + | 0.729722i | \(0.739649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.90772 | 0.563631 | ||||||||
\(310\) | −33.6234 | −1.90968 | ||||||||
\(311\) | −11.4307 | −0.648178 | −0.324089 | − | 0.946027i | \(-0.605058\pi\) | ||||
−0.324089 | + | 0.946027i | \(0.605058\pi\) | |||||||
\(312\) | −2.26056 | −0.127979 | ||||||||
\(313\) | 11.9519 | 0.675559 | 0.337779 | − | 0.941225i | \(-0.390324\pi\) | ||||
0.337779 | + | 0.941225i | \(0.390324\pi\) | |||||||
\(314\) | 11.3951 | 0.643061 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.01784 | 0.169767 | ||||||||
\(317\) | −17.1345 | −0.962370 | −0.481185 | − | 0.876619i | \(-0.659793\pi\) | ||||
−0.481185 | + | 0.876619i | \(0.659793\pi\) | |||||||
\(318\) | 10.2906 | 0.577068 | ||||||||
\(319\) | −34.4323 | −1.92784 | ||||||||
\(320\) | −4.26056 | −0.238172 | ||||||||
\(321\) | −0.996260 | −0.0556058 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.705671 | 0.0392646 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 29.7316 | 1.64921 | ||||||||
\(326\) | −19.7836 | −1.09571 | ||||||||
\(327\) | −11.4007 | −0.630460 | ||||||||
\(328\) | −5.90772 | −0.326199 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −16.0601 | −0.884077 | ||||||||
\(331\) | −5.04223 | −0.277146 | −0.138573 | − | 0.990352i | \(-0.544252\pi\) | ||||
−0.138573 | + | 0.990352i | \(0.544252\pi\) | |||||||
\(332\) | −7.22678 | −0.396621 | ||||||||
\(333\) | 3.15608 | 0.172952 | ||||||||
\(334\) | −1.85611 | −0.101562 | ||||||||
\(335\) | 38.3291 | 2.09414 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4536 | −0.678389 | −0.339195 | − | 0.940716i | \(-0.610154\pi\) | ||||
−0.339195 | + | 0.940716i | \(0.610154\pi\) | |||||||
\(338\) | −7.88988 | −0.429153 | ||||||||
\(339\) | −3.90772 | −0.212238 | ||||||||
\(340\) | 1.50328 | 0.0815266 | ||||||||
\(341\) | −29.7479 | −1.61094 | ||||||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.67720 | 0.521759 | ||||||||
\(345\) | −4.26056 | −0.229381 | ||||||||
\(346\) | 15.9519 | 0.857577 | ||||||||
\(347\) | 14.4288 | 0.774580 | 0.387290 | − | 0.921958i | \(-0.373411\pi\) | ||||
0.387290 | + | 0.921958i | \(0.373411\pi\) | |||||||
\(348\) | −9.13451 | −0.489661 | ||||||||
\(349\) | 3.12605 | 0.167334 | 0.0836668 | − | 0.996494i | \(-0.473337\pi\) | ||||
0.0836668 | + | 0.996494i | \(0.473337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.26056 | −0.120660 | ||||||||
\(352\) | −3.76948 | −0.200914 | ||||||||
\(353\) | 5.44667 | 0.289897 | 0.144949 | − | 0.989439i | \(-0.453698\pi\) | ||||
0.144949 | + | 0.989439i | \(0.453698\pi\) | |||||||
\(354\) | −9.74790 | −0.518095 | ||||||||
\(355\) | −14.0357 | −0.744936 | ||||||||
\(356\) | −4.35284 | −0.230700 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.6735 | 1.19833 | ||||||||
\(359\) | −21.2021 | −1.11900 | −0.559501 | − | 0.828830i | \(-0.689007\pi\) | ||||
−0.559501 | + | 0.828830i | \(0.689007\pi\) | |||||||
\(360\) | −4.26056 | −0.224551 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 18.6894 | 0.982293 | ||||||||
\(363\) | −3.20895 | −0.168426 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.8577 | 0.673001 | ||||||||
\(366\) | 1.12605 | 0.0588596 | ||||||||
\(367\) | −20.8824 | −1.09005 | −0.545026 | − | 0.838419i | \(-0.683480\pi\) | ||||
−0.545026 | + | 0.838419i | \(0.683480\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −5.90772 | −0.307544 | ||||||||
\(370\) | −13.4467 | −0.699059 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.89179 | −0.409170 | ||||||||
\(373\) | 1.70941 | 0.0885099 | 0.0442550 | − | 0.999020i | \(-0.485909\pi\) | ||||
0.0442550 | + | 0.999020i | \(0.485909\pi\) | |||||||
\(374\) | 1.33000 | 0.0687729 | ||||||||
\(375\) | 34.7335 | 1.79363 | ||||||||
\(376\) | −9.27839 | −0.478497 | ||||||||
\(377\) | 20.6491 | 1.06348 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.13825 | −0.109834 | −0.0549171 | − | 0.998491i | \(-0.517489\pi\) | ||||
−0.0549171 | + | 0.998491i | \(0.517489\pi\) | |||||||
\(380\) | 8.52111 | 0.437124 | ||||||||
\(381\) | 0.680937 | 0.0348855 | ||||||||
\(382\) | −17.7479 | −0.908061 | ||||||||
\(383\) | −30.2690 | −1.54667 | −0.773337 | − | 0.633995i | \(-0.781414\pi\) | ||||
−0.773337 | + | 0.633995i | \(0.781414\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.9678 | −1.21993 | ||||||||
\(387\) | 9.67720 | 0.491920 | ||||||||
\(388\) | −16.8173 | −0.853771 | ||||||||
\(389\) | 28.2831 | 1.43401 | 0.717005 | − | 0.697068i | \(-0.245512\pi\) | ||||
0.717005 | + | 0.697068i | \(0.245512\pi\) | |||||||
\(390\) | 9.63123 | 0.487696 | ||||||||
\(391\) | 0.352835 | 0.0178437 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.7836 | −0.796176 | ||||||||
\(394\) | 1.31906 | 0.0664534 | ||||||||
\(395\) | −12.8577 | −0.646940 | ||||||||
\(396\) | −3.76948 | −0.189423 | ||||||||
\(397\) | 6.20395 | 0.311368 | 0.155684 | − | 0.987807i | \(-0.450242\pi\) | ||||
0.155684 | + | 0.987807i | \(0.450242\pi\) | |||||||
\(398\) | 5.20205 | 0.260755 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.1523 | 0.657617 | ||||||||
\(401\) | −31.9925 | −1.59763 | −0.798815 | − | 0.601577i | \(-0.794539\pi\) | ||||
−0.798815 | + | 0.601577i | \(0.794539\pi\) | |||||||
\(402\) | 8.99626 | 0.448693 | ||||||||
\(403\) | 17.8398 | 0.888665 | ||||||||
\(404\) | −10.1007 | −0.502530 | ||||||||
\(405\) | −4.26056 | −0.211709 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8968 | −0.589701 | ||||||||
\(408\) | 0.352835 | 0.0174680 | ||||||||
\(409\) | −20.3047 | −1.00400 | −0.502001 | − | 0.864867i | \(-0.667403\pi\) | ||||
−0.502001 | + | 0.864867i | \(0.667403\pi\) | |||||||
\(410\) | 25.1702 | 1.24307 | ||||||||
\(411\) | 16.6735 | 0.822441 | ||||||||
\(412\) | −9.90772 | −0.488118 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 30.7901 | 1.51143 | ||||||||
\(416\) | 2.26056 | 0.110833 | ||||||||
\(417\) | −2.09228 | −0.102459 | ||||||||
\(418\) | 7.53895 | 0.368742 | ||||||||
\(419\) | −14.3047 | −0.698830 | −0.349415 | − | 0.936968i | \(-0.613620\pi\) | ||||
−0.349415 | + | 0.936968i | \(0.613620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.1308 | −1.27354 | −0.636768 | − | 0.771056i | \(-0.719729\pi\) | ||||
−0.636768 | + | 0.771056i | \(0.719729\pi\) | |||||||
\(422\) | −0.982162 | −0.0478109 | ||||||||
\(423\) | −9.27839 | −0.451131 | ||||||||
\(424\) | −10.2906 | −0.499755 | ||||||||
\(425\) | −4.64061 | −0.225103 | ||||||||
\(426\) | −3.29433 | −0.159611 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.996260 | 0.0481560 | ||||||||
\(429\) | 8.52111 | 0.411403 | ||||||||
\(430\) | −41.2302 | −1.98830 | ||||||||
\(431\) | −16.7091 | −0.804851 | −0.402425 | − | 0.915453i | \(-0.631833\pi\) | ||||
−0.402425 | + | 0.915453i | \(0.631833\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 10.9981 | 0.528535 | 0.264267 | − | 0.964449i | \(-0.414870\pi\) | ||||
0.264267 | + | 0.964449i | \(0.414870\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 38.9181 | 1.86598 | ||||||||
\(436\) | 11.4007 | 0.545995 | ||||||||
\(437\) | 2.00000 | 0.0956730 | ||||||||
\(438\) | 3.01784 | 0.144198 | ||||||||
\(439\) | 4.35284 | 0.207750 | 0.103875 | − | 0.994590i | \(-0.466876\pi\) | ||||
0.103875 | + | 0.994590i | \(0.466876\pi\) | |||||||
\(440\) | 16.0601 | 0.765634 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.797605 | −0.0379382 | ||||||||
\(443\) | −15.8402 | −0.752589 | −0.376295 | − | 0.926500i | \(-0.622802\pi\) | ||||
−0.376295 | + | 0.926500i | \(0.622802\pi\) | |||||||
\(444\) | −3.15608 | −0.149781 | ||||||||
\(445\) | 18.5455 | 0.879141 | ||||||||
\(446\) | 29.4551 | 1.39474 | ||||||||
\(447\) | 2.50702 | 0.118578 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.0779 | 0.617184 | 0.308592 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308592 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(450\) | 13.1523 | 0.620007 | ||||||||
\(451\) | 22.2690 | 1.04861 | ||||||||
\(452\) | 3.90772 | 0.183804 | ||||||||
\(453\) | 14.4288 | 0.677926 | ||||||||
\(454\) | 22.9856 | 1.07877 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 39.3187 | 1.83925 | 0.919626 | − | 0.392795i | \(-0.128492\pi\) | ||||
0.919626 | + | 0.392795i | \(0.128492\pi\) | |||||||
\(458\) | −9.12605 | −0.426432 | ||||||||
\(459\) | 0.352835 | 0.0164689 | ||||||||
\(460\) | 4.26056 | 0.198649 | ||||||||
\(461\) | 13.6115 | 0.633950 | 0.316975 | − | 0.948434i | \(-0.397333\pi\) | ||||
0.316975 | + | 0.948434i | \(0.397333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.45415 | −0.160528 | −0.0802640 | − | 0.996774i | \(-0.525576\pi\) | ||||
−0.0802640 | + | 0.996774i | \(0.525576\pi\) | |||||||
\(464\) | 9.13451 | 0.424059 | ||||||||
\(465\) | 33.6234 | 1.55925 | ||||||||
\(466\) | 2.06006 | 0.0954307 | ||||||||
\(467\) | −3.41848 | −0.158188 | −0.0790941 | − | 0.996867i | \(-0.525203\pi\) | ||||
−0.0790941 | + | 0.996867i | \(0.525203\pi\) | |||||||
\(468\) | 2.26056 | 0.104494 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 39.5311 | 1.82343 | ||||||||
\(471\) | −11.3951 | −0.525057 | ||||||||
\(472\) | 9.74790 | 0.448683 | ||||||||
\(473\) | −36.4780 | −1.67726 | ||||||||
\(474\) | −3.01784 | −0.138614 | ||||||||
\(475\) | −26.3047 | −1.20694 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.2906 | −0.471174 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | −10.5568 | −0.482352 | −0.241176 | − | 0.970481i | \(-0.577533\pi\) | ||||
−0.241176 | + | 0.970481i | \(0.577533\pi\) | |||||||
\(480\) | 4.26056 | 0.194467 | ||||||||
\(481\) | 7.13451 | 0.325305 | ||||||||
\(482\) | −13.3385 | −0.607550 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.20895 | 0.145861 | ||||||||
\(485\) | 71.6513 | 3.25352 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 34.7017 | 1.57248 | 0.786241 | − | 0.617920i | \(-0.212024\pi\) | ||||
0.786241 | + | 0.617920i | \(0.212024\pi\) | |||||||
\(488\) | −1.12605 | −0.0509739 | ||||||||
\(489\) | 19.7836 | 0.894644 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.3009 | −1.36746 | −0.683730 | − | 0.729735i | \(-0.739643\pi\) | ||||
−0.683730 | + | 0.729735i | \(0.739643\pi\) | |||||||
\(492\) | 5.90772 | 0.266341 | ||||||||
\(493\) | −3.22298 | −0.145156 | ||||||||
\(494\) | −4.52111 | −0.203415 | ||||||||
\(495\) | 16.0601 | 0.721846 | ||||||||
\(496\) | 7.89179 | 0.354352 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.22678 | 0.323840 | ||||||||
\(499\) | −10.9747 | −0.491294 | −0.245647 | − | 0.969359i | \(-0.579000\pi\) | ||||
−0.245647 | + | 0.969359i | \(0.579000\pi\) | |||||||
\(500\) | −34.7335 | −1.55333 | ||||||||
\(501\) | 1.85611 | 0.0829249 | ||||||||
\(502\) | 14.3613 | 0.640976 | ||||||||
\(503\) | −20.8258 | −0.928577 | −0.464288 | − | 0.885684i | \(-0.653690\pi\) | ||||
−0.464288 | + | 0.885684i | \(0.653690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.0347 | 1.91502 | ||||||||
\(506\) | 3.76948 | 0.167574 | ||||||||
\(507\) | 7.88988 | 0.350402 | ||||||||
\(508\) | −0.680937 | −0.0302117 | ||||||||
\(509\) | −31.2462 | −1.38496 | −0.692481 | − | 0.721436i | \(-0.743482\pi\) | ||||
−0.692481 | + | 0.721436i | \(0.743482\pi\) | |||||||
\(510\) | −1.50328 | −0.0665662 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | −28.5211 | −1.25801 | ||||||||
\(515\) | 42.2124 | 1.86010 | ||||||||
\(516\) | −9.67720 | −0.426015 | ||||||||
\(517\) | 34.9747 | 1.53818 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.9519 | −0.700209 | ||||||||
\(520\) | −9.63123 | −0.422357 | ||||||||
\(521\) | 39.1111 | 1.71349 | 0.856744 | − | 0.515742i | \(-0.172484\pi\) | ||||
0.856744 | + | 0.515742i | \(0.172484\pi\) | |||||||
\(522\) | 9.13451 | 0.399806 | ||||||||
\(523\) | 37.0779 | 1.62130 | 0.810652 | − | 0.585529i | \(-0.199113\pi\) | ||||
0.810652 | + | 0.585529i | \(0.199113\pi\) | |||||||
\(524\) | 15.7836 | 0.689509 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.13451 | −0.136671 | ||||||||
\(527\) | −2.78450 | −0.121295 | ||||||||
\(528\) | 3.76948 | 0.164045 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 43.8436 | 1.90445 | ||||||||
\(531\) | 9.74790 | 0.423023 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.3547 | −0.578458 | ||||||||
\(534\) | 4.35284 | 0.188366 | ||||||||
\(535\) | −4.24462 | −0.183511 | ||||||||
\(536\) | −8.99626 | −0.388579 | ||||||||
\(537\) | −22.6735 | −0.978432 | ||||||||
\(538\) | −10.9415 | −0.471721 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.26056 | 0.183345 | ||||||||
\(541\) | 34.2765 | 1.47366 | 0.736831 | − | 0.676077i | \(-0.236321\pi\) | ||||
0.736831 | + | 0.676077i | \(0.236321\pi\) | |||||||
\(542\) | −7.12605 | −0.306090 | ||||||||
\(543\) | −18.6894 | −0.802039 | ||||||||
\(544\) | −0.352835 | −0.0151277 | ||||||||
\(545\) | −48.5734 | −2.08065 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.3469 | −1.42581 | −0.712906 | − | 0.701260i | \(-0.752621\pi\) | ||||
−0.712906 | + | 0.701260i | \(0.752621\pi\) | |||||||
\(548\) | −16.6735 | −0.712255 | ||||||||
\(549\) | −1.12605 | −0.0480587 | ||||||||
\(550\) | −49.5774 | −2.11399 | ||||||||
\(551\) | −18.2690 | −0.778286 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −27.9925 | −1.18929 | ||||||||
\(555\) | 13.4467 | 0.570779 | ||||||||
\(556\) | 2.09228 | 0.0887324 | ||||||||
\(557\) | −13.3084 | −0.563896 | −0.281948 | − | 0.959430i | \(-0.590981\pi\) | ||||
−0.281948 | + | 0.959430i | \(0.590981\pi\) | |||||||
\(558\) | 7.89179 | 0.334086 | ||||||||
\(559\) | 21.8759 | 0.925250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.33000 | −0.0561528 | ||||||||
\(562\) | −17.9434 | −0.756897 | ||||||||
\(563\) | 41.5743 | 1.75215 | 0.876074 | − | 0.482178i | \(-0.160154\pi\) | ||||
0.876074 | + | 0.482178i | \(0.160154\pi\) | |||||||
\(564\) | 9.27839 | 0.390691 | ||||||||
\(565\) | −16.6491 | −0.700432 | ||||||||
\(566\) | 18.3047 | 0.769403 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.29433 | 0.138227 | ||||||||
\(569\) | 34.1336 | 1.43095 | 0.715477 | − | 0.698636i | \(-0.246209\pi\) | ||||
0.715477 | + | 0.698636i | \(0.246209\pi\) | |||||||
\(570\) | −8.52111 | −0.356910 | ||||||||
\(571\) | −18.0385 | −0.754887 | −0.377444 | − | 0.926033i | \(-0.623197\pi\) | ||||
−0.377444 | + | 0.926033i | \(0.623197\pi\) | |||||||
\(572\) | −8.52111 | −0.356286 | ||||||||
\(573\) | 17.7479 | 0.741429 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.1523 | −0.548491 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.01784 | 0.125634 | 0.0628171 | − | 0.998025i | \(-0.479992\pi\) | ||||
0.0628171 | + | 0.998025i | \(0.479992\pi\) | |||||||
\(578\) | −16.8755 | −0.701929 | ||||||||
\(579\) | 23.9678 | 0.996067 | ||||||||
\(580\) | −38.9181 | −1.61599 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16.8173 | 0.697101 | ||||||||
\(583\) | 38.7901 | 1.60652 | ||||||||
\(584\) | −3.01784 | −0.124879 | ||||||||
\(585\) | −9.63123 | −0.398202 | ||||||||
\(586\) | 4.38851 | 0.181288 | ||||||||
\(587\) | 28.8577 | 1.19108 | 0.595542 | − | 0.803324i | \(-0.296937\pi\) | ||||
0.595542 | + | 0.803324i | \(0.296937\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.7836 | −0.650351 | ||||||||
\(590\) | −41.5315 | −1.70982 | ||||||||
\(591\) | −1.31906 | −0.0542590 | ||||||||
\(592\) | 3.15608 | 0.129714 | ||||||||
\(593\) | −8.02473 | −0.329536 | −0.164768 | − | 0.986332i | \(-0.552688\pi\) | ||||
−0.164768 | + | 0.986332i | \(0.552688\pi\) | |||||||
\(594\) | 3.76948 | 0.154663 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.50702 | −0.102691 | ||||||||
\(597\) | −5.20205 | −0.212906 | ||||||||
\(598\) | −2.26056 | −0.0924410 | ||||||||
\(599\) | −3.81544 | −0.155895 | −0.0779474 | − | 0.996957i | \(-0.524837\pi\) | ||||
−0.0779474 | + | 0.996957i | \(0.524837\pi\) | |||||||
\(600\) | −13.1523 | −0.536942 | ||||||||
\(601\) | 4.37971 | 0.178652 | 0.0893261 | − | 0.996002i | \(-0.471529\pi\) | ||||
0.0893261 | + | 0.996002i | \(0.471529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.99626 | −0.366356 | ||||||||
\(604\) | −14.4288 | −0.587101 | ||||||||
\(605\) | −13.6719 | −0.555842 | ||||||||
\(606\) | 10.1007 | 0.410314 | ||||||||
\(607\) | −27.4908 | −1.11582 | −0.557909 | − | 0.829902i | \(-0.688396\pi\) | ||||
−0.557909 | + | 0.829902i | \(0.688396\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.79760 | 0.194249 | ||||||||
\(611\) | −20.9743 | −0.848531 | ||||||||
\(612\) | −0.352835 | −0.0142625 | ||||||||
\(613\) | −22.4504 | −0.906764 | −0.453382 | − | 0.891316i | \(-0.649783\pi\) | ||||
−0.453382 | + | 0.891316i | \(0.649783\pi\) | |||||||
\(614\) | −23.9603 | −0.966959 | ||||||||
\(615\) | −25.1702 | −1.01496 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.6094 | 1.07125 | 0.535627 | − | 0.844455i | \(-0.320075\pi\) | ||||
0.535627 | + | 0.844455i | \(0.320075\pi\) | |||||||
\(618\) | 9.90772 | 0.398547 | ||||||||
\(619\) | −41.9356 | −1.68553 | −0.842766 | − | 0.538279i | \(-0.819075\pi\) | ||||
−0.842766 | + | 0.538279i | \(0.819075\pi\) | |||||||
\(620\) | −33.6234 | −1.35035 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −11.4307 | −0.458331 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.26056 | −0.0904947 | ||||||||
\(625\) | 82.2224 | 3.28890 | ||||||||
\(626\) | 11.9519 | 0.477692 | ||||||||
\(627\) | −7.53895 | −0.301077 | ||||||||
\(628\) | 11.3951 | 0.454712 | ||||||||
\(629\) | −1.11358 | −0.0444013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5633 | 0.858423 | 0.429212 | − | 0.903204i | \(-0.358791\pi\) | ||||
0.429212 | + | 0.903204i | \(0.358791\pi\) | |||||||
\(632\) | 3.01784 | 0.120043 | ||||||||
\(633\) | 0.982162 | 0.0390374 | ||||||||
\(634\) | −17.1345 | −0.680498 | ||||||||
\(635\) | 2.90117 | 0.115129 | ||||||||
\(636\) | 10.2906 | 0.408048 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −34.4323 | −1.36319 | ||||||||
\(639\) | 3.29433 | 0.130322 | ||||||||
\(640\) | −4.26056 | −0.168413 | ||||||||
\(641\) | 26.7091 | 1.05495 | 0.527474 | − | 0.849571i | \(-0.323139\pi\) | ||||
0.527474 | + | 0.849571i | \(0.323139\pi\) | |||||||
\(642\) | −0.996260 | −0.0393192 | ||||||||
\(643\) | −22.1201 | −0.872333 | −0.436166 | − | 0.899866i | \(-0.643664\pi\) | ||||
−0.436166 | + | 0.899866i | \(0.643664\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 41.2302 | 1.62344 | ||||||||
\(646\) | 0.705671 | 0.0277643 | ||||||||
\(647\) | 13.7642 | 0.541126 | 0.270563 | − | 0.962702i | \(-0.412790\pi\) | ||||
0.270563 | + | 0.962702i | \(0.412790\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −36.7445 | −1.44235 | ||||||||
\(650\) | 29.7316 | 1.16617 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.7836 | −0.774785 | ||||||||
\(653\) | 10.0848 | 0.394649 | 0.197324 | − | 0.980338i | \(-0.436775\pi\) | ||||
0.197324 | + | 0.980338i | \(0.436775\pi\) | |||||||
\(654\) | −11.4007 | −0.445803 | ||||||||
\(655\) | −67.2468 | −2.62755 | ||||||||
\(656\) | −5.90772 | −0.230658 | ||||||||
\(657\) | −3.01784 | −0.117737 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.72632 | 0.300975 | 0.150487 | − | 0.988612i | \(-0.451916\pi\) | ||||
0.150487 | + | 0.988612i | \(0.451916\pi\) | |||||||
\(660\) | −16.0601 | −0.625137 | ||||||||
\(661\) | −12.9415 | −0.503366 | −0.251683 | − | 0.967810i | \(-0.580984\pi\) | ||||
−0.251683 | + | 0.967810i | \(0.580984\pi\) | |||||||
\(662\) | −5.04223 | −0.195972 | ||||||||
\(663\) | 0.797605 | 0.0309764 | ||||||||
\(664\) | −7.22678 | −0.280454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.15608 | 0.122296 | ||||||||
\(667\) | −9.13451 | −0.353689 | ||||||||
\(668\) | −1.85611 | −0.0718151 | ||||||||
\(669\) | −29.4551 | −1.13880 | ||||||||
\(670\) | 38.3291 | 1.48078 | ||||||||
\(671\) | 4.24462 | 0.163862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.5236 | 1.98609 | 0.993045 | − | 0.117733i | \(-0.0375627\pi\) | ||||
0.993045 | + | 0.117733i | \(0.0375627\pi\) | |||||||
\(674\) | −12.4536 | −0.479694 | ||||||||
\(675\) | −13.1523 | −0.506234 | ||||||||
\(676\) | −7.88988 | −0.303457 | ||||||||
\(677\) | −0.317160 | −0.0121894 | −0.00609472 | − | 0.999981i | \(-0.501940\pi\) | ||||
−0.00609472 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(678\) | −3.90772 | −0.150075 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.50328 | 0.0576480 | ||||||||
\(681\) | −22.9856 | −0.880811 | ||||||||
\(682\) | −29.7479 | −1.13911 | ||||||||
\(683\) | −24.8690 | −0.951584 | −0.475792 | − | 0.879558i | \(-0.657839\pi\) | ||||
−0.475792 | + | 0.879558i | \(0.657839\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 71.0382 | 2.71423 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.12605 | 0.348181 | ||||||||
\(688\) | 9.67720 | 0.368940 | ||||||||
\(689\) | −23.2625 | −0.886229 | ||||||||
\(690\) | −4.26056 | −0.162197 | ||||||||
\(691\) | −35.7439 | −1.35976 | −0.679881 | − | 0.733323i | \(-0.737968\pi\) | ||||
−0.679881 | + | 0.733323i | \(0.737968\pi\) | |||||||
\(692\) | 15.9519 | 0.606398 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.4288 | 0.547711 | ||||||||
\(695\) | −8.91427 | −0.338138 | ||||||||
\(696\) | −9.13451 | −0.346243 | ||||||||
\(697\) | 2.08445 | 0.0789543 | ||||||||
\(698\) | 3.12605 | 0.118323 | ||||||||
\(699\) | −2.06006 | −0.0779188 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.8896 | −1.27999 | −0.639996 | − | 0.768378i | \(-0.721064\pi\) | ||||
−0.639996 | + | 0.768378i | \(0.721064\pi\) | |||||||
\(702\) | −2.26056 | −0.0853192 | ||||||||
\(703\) | −6.31217 | −0.238068 | ||||||||
\(704\) | −3.76948 | −0.142067 | ||||||||
\(705\) | −39.5311 | −1.48883 | ||||||||
\(706\) | 5.44667 | 0.204988 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.74790 | −0.366348 | ||||||||
\(709\) | 48.3750 | 1.81676 | 0.908381 | − | 0.418143i | \(-0.137319\pi\) | ||||
0.908381 | + | 0.418143i | \(0.137319\pi\) | |||||||
\(710\) | −14.0357 | −0.526750 | ||||||||
\(711\) | 3.01784 | 0.113178 | ||||||||
\(712\) | −4.35284 | −0.163129 | ||||||||
\(713\) | −7.89179 | −0.295550 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.3047 | 1.35772 | ||||||||
\(716\) | 22.6735 | 0.847347 | ||||||||
\(717\) | 8.00000 | 0.298765 | ||||||||
\(718\) | −21.2021 | −0.791253 | ||||||||
\(719\) | 35.3028 | 1.31657 | 0.658286 | − | 0.752768i | \(-0.271282\pi\) | ||||
0.658286 | + | 0.752768i | \(0.271282\pi\) | |||||||
\(720\) | −4.26056 | −0.158782 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 13.3385 | 0.496063 | ||||||||
\(724\) | 18.6894 | 0.694586 | ||||||||
\(725\) | 120.140 | 4.46189 | ||||||||
\(726\) | −3.20895 | −0.119095 | ||||||||
\(727\) | −9.25865 | −0.343384 | −0.171692 | − | 0.985151i | \(-0.554923\pi\) | ||||
−0.171692 | + | 0.985151i | \(0.554923\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.8577 | 0.475884 | ||||||||
\(731\) | −3.41446 | −0.126288 | ||||||||
\(732\) | 1.12605 | 0.0416200 | ||||||||
\(733\) | 46.2565 | 1.70852 | 0.854262 | − | 0.519843i | \(-0.174009\pi\) | ||||
0.854262 | + | 0.519843i | \(0.174009\pi\) | |||||||
\(734\) | −20.8824 | −0.770784 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 33.9112 | 1.24913 | ||||||||
\(738\) | −5.90772 | −0.217466 | ||||||||
\(739\) | 3.29433 | 0.121184 | 0.0605919 | − | 0.998163i | \(-0.480701\pi\) | ||||
0.0605919 | + | 0.998163i | \(0.480701\pi\) | |||||||
\(740\) | −13.4467 | −0.494310 | ||||||||
\(741\) | 4.52111 | 0.166087 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.7976 | −0.616244 | −0.308122 | − | 0.951347i | \(-0.599701\pi\) | ||||
−0.308122 | + | 0.951347i | \(0.599701\pi\) | |||||||
\(744\) | −7.89179 | −0.289327 | ||||||||
\(745\) | 10.6813 | 0.391332 | ||||||||
\(746\) | 1.70941 | 0.0625860 | ||||||||
\(747\) | −7.22678 | −0.264414 | ||||||||
\(748\) | 1.33000 | 0.0486298 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 34.7335 | 1.26829 | ||||||||
\(751\) | −3.35439 | −0.122404 | −0.0612018 | − | 0.998125i | \(-0.519493\pi\) | ||||
−0.0612018 | + | 0.998125i | \(0.519493\pi\) | |||||||
\(752\) | −9.27839 | −0.338348 | ||||||||
\(753\) | −14.3613 | −0.523355 | ||||||||
\(754\) | 20.6491 | 0.751995 | ||||||||
\(755\) | 61.4749 | 2.23730 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.03194 | −0.328271 | −0.164136 | − | 0.986438i | \(-0.552483\pi\) | ||||
−0.164136 | + | 0.986438i | \(0.552483\pi\) | |||||||
\(758\) | −2.13825 | −0.0776646 | ||||||||
\(759\) | −3.76948 | −0.136823 | ||||||||
\(760\) | 8.52111 | 0.309093 | ||||||||
\(761\) | 1.97561 | 0.0716158 | 0.0358079 | − | 0.999359i | \(-0.488600\pi\) | ||||
0.0358079 | + | 0.999359i | \(0.488600\pi\) | |||||||
\(762\) | 0.680937 | 0.0246677 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.7479 | −0.642096 | ||||||||
\(765\) | 1.50328 | 0.0543510 | ||||||||
\(766\) | −30.2690 | −1.09366 | ||||||||
\(767\) | 22.0357 | 0.795662 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 16.0085 | 0.577280 | 0.288640 | − | 0.957438i | \(-0.406797\pi\) | ||||
0.288640 | + | 0.957438i | \(0.406797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.5211 | 1.02716 | ||||||||
\(772\) | −23.9678 | −0.862619 | ||||||||
\(773\) | −38.0085 | −1.36707 | −0.683535 | − | 0.729918i | \(-0.739558\pi\) | ||||
−0.683535 | + | 0.729918i | \(0.739558\pi\) | |||||||
\(774\) | 9.67720 | 0.347840 | ||||||||
\(775\) | 103.795 | 3.72844 | ||||||||
\(776\) | −16.8173 | −0.603708 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.2831 | 1.01400 | ||||||||
\(779\) | 11.8154 | 0.423332 | ||||||||
\(780\) | 9.63123 | 0.344853 | ||||||||
\(781\) | −12.4179 | −0.444347 | ||||||||
\(782\) | 0.352835 | 0.0126174 | ||||||||
\(783\) | −9.13451 | −0.326441 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.5493 | −1.73280 | ||||||||
\(786\) | −15.7836 | −0.562981 | ||||||||
\(787\) | −55.1624 | −1.96633 | −0.983163 | − | 0.182732i | \(-0.941506\pi\) | ||||
−0.983163 | + | 0.182732i | \(0.941506\pi\) | |||||||
\(788\) | 1.31906 | 0.0469897 | ||||||||
\(789\) | 3.13451 | 0.111591 | ||||||||
\(790\) | −12.8577 | −0.457455 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.76948 | −0.133942 | ||||||||
\(793\) | −2.54550 | −0.0903934 | ||||||||
\(794\) | 6.20395 | 0.220170 | ||||||||
\(795\) | −43.8436 | −1.55497 | ||||||||
\(796\) | 5.20205 | 0.184382 | ||||||||
\(797\) | −18.1435 | −0.642677 | −0.321339 | − | 0.946964i | \(-0.604133\pi\) | ||||
−0.321339 | + | 0.946964i | \(0.604133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.27375 | 0.115817 | ||||||||
\(800\) | 13.1523 | 0.465006 | ||||||||
\(801\) | −4.35284 | −0.153800 | ||||||||
\(802\) | −31.9925 | −1.12970 | ||||||||
\(803\) | 11.3757 | 0.401439 | ||||||||
\(804\) | 8.99626 | 0.317274 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.8398 | 0.628381 | ||||||||
\(807\) | 10.9415 | 0.385159 | ||||||||
\(808\) | −10.1007 | −0.355343 | ||||||||
\(809\) | −40.3291 | −1.41789 | −0.708947 | − | 0.705261i | \(-0.750830\pi\) | ||||
−0.708947 | + | 0.705261i | \(0.750830\pi\) | |||||||
\(810\) | −4.26056 | −0.149701 | ||||||||
\(811\) | −7.10264 | −0.249407 | −0.124704 | − | 0.992194i | \(-0.539798\pi\) | ||||
−0.124704 | + | 0.992194i | \(0.539798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.12605 | 0.249922 | ||||||||
\(814\) | −11.8968 | −0.416982 | ||||||||
\(815\) | 84.2890 | 2.95252 | ||||||||
\(816\) | 0.352835 | 0.0123517 | ||||||||
\(817\) | −19.3544 | −0.677125 | ||||||||
\(818\) | −20.3047 | −0.709937 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.1702 | 0.878981 | ||||||||
\(821\) | −36.6169 | −1.27794 | −0.638969 | − | 0.769233i | \(-0.720639\pi\) | ||||
−0.638969 | + | 0.769233i | \(0.720639\pi\) | |||||||
\(822\) | 16.6735 | 0.581554 | ||||||||
\(823\) | 49.3222 | 1.71926 | 0.859632 | − | 0.510914i | \(-0.170693\pi\) | ||||
0.859632 | + | 0.510914i | \(0.170693\pi\) | |||||||
\(824\) | −9.90772 | −0.345152 | ||||||||
\(825\) | 49.5774 | 1.72606 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.8183 | 1.66280 | 0.831402 | − | 0.555672i | \(-0.187539\pi\) | ||||
0.831402 | + | 0.555672i | \(0.187539\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −23.6641 | −0.821887 | −0.410944 | − | 0.911661i | \(-0.634801\pi\) | ||||
−0.410944 | + | 0.911661i | \(0.634801\pi\) | |||||||
\(830\) | 30.7901 | 1.06874 | ||||||||
\(831\) | 27.9925 | 0.971050 | ||||||||
\(832\) | 2.26056 | 0.0783707 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.09228 | −0.0724497 | ||||||||
\(835\) | 7.90807 | 0.273670 | ||||||||
\(836\) | 7.53895 | 0.260740 | ||||||||
\(837\) | −7.89179 | −0.272780 | ||||||||
\(838\) | −14.3047 | −0.494147 | ||||||||
\(839\) | 23.6309 | 0.815829 | 0.407914 | − | 0.913020i | \(-0.366256\pi\) | ||||
0.407914 | + | 0.913020i | \(0.366256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.4392 | 1.87721 | ||||||||
\(842\) | −26.1308 | −0.900526 | ||||||||
\(843\) | 17.9434 | 0.618003 | ||||||||
\(844\) | −0.982162 | −0.0338074 | ||||||||
\(845\) | 33.6153 | 1.15640 | ||||||||
\(846\) | −9.27839 | −0.318998 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.2906 | −0.353380 | ||||||||
\(849\) | −18.3047 | −0.628215 | ||||||||
\(850\) | −4.64061 | −0.159172 | ||||||||
\(851\) | −3.15608 | −0.108189 | ||||||||
\(852\) | −3.29433 | −0.112862 | ||||||||
\(853\) | −34.0441 | −1.16565 | −0.582824 | − | 0.812598i | \(-0.698052\pi\) | ||||
−0.582824 | + | 0.812598i | \(0.698052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.52111 | 0.291416 | ||||||||
\(856\) | 0.996260 | 0.0340515 | ||||||||
\(857\) | −35.4823 | −1.21205 | −0.606027 | − | 0.795444i | \(-0.707238\pi\) | ||||
−0.606027 | + | 0.795444i | \(0.707238\pi\) | |||||||
\(858\) | 8.52111 | 0.290906 | ||||||||
\(859\) | 32.8824 | 1.12193 | 0.560967 | − | 0.827838i | \(-0.310430\pi\) | ||||
0.560967 | + | 0.827838i | \(0.310430\pi\) | |||||||
\(860\) | −41.2302 | −1.40594 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.7091 | −0.569115 | ||||||||
\(863\) | 30.5023 | 1.03831 | 0.519156 | − | 0.854680i | \(-0.326246\pi\) | ||||
0.519156 | + | 0.854680i | \(0.326246\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −67.9638 | −2.31084 | ||||||||
\(866\) | 10.9981 | 0.373731 | ||||||||
\(867\) | 16.8755 | 0.573122 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.3757 | −0.385893 | ||||||||
\(870\) | 38.9181 | 1.31945 | ||||||||
\(871\) | −20.3366 | −0.689078 | ||||||||
\(872\) | 11.4007 | 0.386077 | ||||||||
\(873\) | −16.8173 | −0.569181 | ||||||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.01784 | 0.101963 | ||||||||
\(877\) | −31.8793 | −1.07649 | −0.538244 | − | 0.842789i | \(-0.680912\pi\) | ||||
−0.538244 | + | 0.842789i | \(0.680912\pi\) | |||||||
\(878\) | 4.35284 | 0.146901 | ||||||||
\(879\) | −4.38851 | −0.148021 | ||||||||
\(880\) | 16.0601 | 0.541385 | ||||||||
\(881\) | −37.4120 | −1.26044 | −0.630221 | − | 0.776416i | \(-0.717036\pi\) | ||||
−0.630221 | + | 0.776416i | \(0.717036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.34404 | 0.0788831 | 0.0394415 | − | 0.999222i | \(-0.487442\pi\) | ||||
0.0394415 | + | 0.999222i | \(0.487442\pi\) | |||||||
\(884\) | −0.797605 | −0.0268263 | ||||||||
\(885\) | 41.5315 | 1.39607 | ||||||||
\(886\) | −15.8402 | −0.532161 | ||||||||
\(887\) | 42.6819 | 1.43312 | 0.716559 | − | 0.697526i | \(-0.245716\pi\) | ||||
0.716559 | + | 0.697526i | \(0.245716\pi\) | |||||||
\(888\) | −3.15608 | −0.105911 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.5455 | 0.621647 | ||||||||
\(891\) | −3.76948 | −0.126282 | ||||||||
\(892\) | 29.4551 | 0.986231 | ||||||||
\(893\) | 18.5568 | 0.620979 | ||||||||
\(894\) | 2.50702 | 0.0838471 | ||||||||
\(895\) | −96.6015 | −3.22903 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.26056 | 0.0754778 | ||||||||
\(898\) | 13.0779 | 0.436415 | ||||||||
\(899\) | 72.0876 | 2.40426 | ||||||||
\(900\) | 13.1523 | 0.438411 | ||||||||
\(901\) | 3.63088 | 0.120962 | ||||||||
\(902\) | 22.2690 | 0.741477 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.90772 | 0.129969 | ||||||||
\(905\) | −79.6272 | −2.64690 | ||||||||
\(906\) | 14.4288 | 0.479366 | ||||||||
\(907\) | 46.9322 | 1.55836 | 0.779179 | − | 0.626802i | \(-0.215636\pi\) | ||||
0.779179 | + | 0.626802i | \(0.215636\pi\) | |||||||
\(908\) | 22.9856 | 0.762805 | ||||||||
\(909\) | −10.1007 | −0.335020 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.5067 | 0.580024 | 0.290012 | − | 0.957023i | \(-0.406341\pi\) | ||||
0.290012 | + | 0.957023i | \(0.406341\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | 27.2412 | 0.901552 | ||||||||
\(914\) | 39.3187 | 1.30055 | ||||||||
\(915\) | −4.79760 | −0.158604 | ||||||||
\(916\) | −9.12605 | −0.301533 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.352835 | 0.0116453 | ||||||||
\(919\) | −24.2446 | −0.799756 | −0.399878 | − | 0.916568i | \(-0.630948\pi\) | ||||
−0.399878 | + | 0.916568i | \(0.630948\pi\) | |||||||
\(920\) | 4.26056 | 0.140466 | ||||||||
\(921\) | 23.9603 | 0.789519 | ||||||||
\(922\) | 13.6115 | 0.448271 | ||||||||
\(923\) | 7.44702 | 0.245122 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.5099 | 1.36484 | ||||||||
\(926\) | −3.45415 | −0.113510 | ||||||||
\(927\) | −9.90772 | −0.325412 | ||||||||
\(928\) | 9.13451 | 0.299855 | ||||||||
\(929\) | 36.7297 | 1.20506 | 0.602531 | − | 0.798095i | \(-0.294159\pi\) | ||||
0.602531 | + | 0.798095i | \(0.294159\pi\) | |||||||
\(930\) | 33.6234 | 1.10255 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.06006 | 0.0674797 | ||||||||
\(933\) | 11.4307 | 0.374226 | ||||||||
\(934\) | −3.41848 | −0.111856 | ||||||||
\(935\) | −5.66656 | −0.185316 | ||||||||
\(936\) | 2.26056 | 0.0738886 | ||||||||
\(937\) | −18.3638 | −0.599918 | −0.299959 | − | 0.953952i | \(-0.596973\pi\) | ||||
−0.299959 | + | 0.953952i | \(0.596973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9519 | −0.390034 | ||||||||
\(940\) | 39.5311 | 1.28936 | ||||||||
\(941\) | 47.4417 | 1.54655 | 0.773277 | − | 0.634068i | \(-0.218616\pi\) | ||||
0.773277 | + | 0.634068i | \(0.218616\pi\) | |||||||
\(942\) | −11.3951 | −0.371271 | ||||||||
\(943\) | 5.90772 | 0.192382 | ||||||||
\(944\) | 9.74790 | 0.317267 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.4780 | −1.18600 | ||||||||
\(947\) | 3.16637 | 0.102893 | 0.0514467 | − | 0.998676i | \(-0.483617\pi\) | ||||
0.0514467 | + | 0.998676i | \(0.483617\pi\) | |||||||
\(948\) | −3.01784 | −0.0980148 | ||||||||
\(949\) | −6.82199 | −0.221451 | ||||||||
\(950\) | −26.3047 | −0.853437 | ||||||||
\(951\) | 17.1345 | 0.555624 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.1126 | −1.16980 | −0.584902 | − | 0.811104i | \(-0.698867\pi\) | ||||
−0.584902 | + | 0.811104i | \(0.698867\pi\) | |||||||
\(954\) | −10.2906 | −0.333170 | ||||||||
\(955\) | 75.6159 | 2.44687 | ||||||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | 34.4323 | 1.11304 | ||||||||
\(958\) | −10.5568 | −0.341074 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.26056 | 0.137509 | ||||||||
\(961\) | 31.2803 | 1.00904 | ||||||||
\(962\) | 7.13451 | 0.230026 | ||||||||
\(963\) | 0.996260 | 0.0321040 | ||||||||
\(964\) | −13.3385 | −0.429603 | ||||||||
\(965\) | 102.116 | 3.28723 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.9882 | −1.73614 | −0.868071 | − | 0.496440i | \(-0.834640\pi\) | ||||
−0.868071 | + | 0.496440i | \(0.834640\pi\) | |||||||
\(968\) | 3.20895 | 0.103139 | ||||||||
\(969\) | −0.705671 | −0.0226694 | ||||||||
\(970\) | 71.6513 | 2.30058 | ||||||||
\(971\) | 19.7798 | 0.634763 | 0.317381 | − | 0.948298i | \(-0.397196\pi\) | ||||
0.317381 | + | 0.948298i | \(0.397196\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 34.7017 | 1.11191 | ||||||||
\(975\) | −29.7316 | −0.952174 | ||||||||
\(976\) | −1.12605 | −0.0360440 | ||||||||
\(977\) | −10.1485 | −0.324680 | −0.162340 | − | 0.986735i | \(-0.551904\pi\) | ||||
−0.162340 | + | 0.986735i | \(0.551904\pi\) | |||||||
\(978\) | 19.7836 | 0.632609 | ||||||||
\(979\) | 16.4079 | 0.524399 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4007 | 0.363997 | ||||||||
\(982\) | −30.3009 | −0.966940 | ||||||||
\(983\) | 22.7901 | 0.726892 | 0.363446 | − | 0.931615i | \(-0.381600\pi\) | ||||
0.363446 | + | 0.931615i | \(0.381600\pi\) | |||||||
\(984\) | 5.90772 | 0.188331 | ||||||||
\(985\) | −5.61994 | −0.179066 | ||||||||
\(986\) | −3.22298 | −0.102641 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.52111 | −0.143836 | ||||||||
\(989\) | −9.67720 | −0.307717 | ||||||||
\(990\) | 16.0601 | 0.510422 | ||||||||
\(991\) | 28.3366 | 0.900140 | 0.450070 | − | 0.892993i | \(-0.351399\pi\) | ||||
0.450070 | + | 0.892993i | \(0.351399\pi\) | |||||||
\(992\) | 7.89179 | 0.250564 | ||||||||
\(993\) | 5.04223 | 0.160010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.1636 | −0.702634 | ||||||||
\(996\) | 7.22678 | 0.228989 | ||||||||
\(997\) | −37.2105 | −1.17847 | −0.589234 | − | 0.807962i | \(-0.700570\pi\) | ||||
−0.589234 | + | 0.807962i | \(0.700570\pi\) | |||||||
\(998\) | −10.9747 | −0.347397 | ||||||||
\(999\) | −3.15608 | −0.0998541 |
(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 | 6762.2.a.cj.1.1 | ✓ | 4 | |
7.6 | odd | 2 | 6762.2.a.cs.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.cj.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6762.2.a.cs.1.4 | yes | 4 | 7.6 | odd | 2 |