Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8030,2,Mod(1,8030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8030, 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("8030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8030.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: | \(64.1198728231\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 4 x^{14} - 23 x^{13} + 99 x^{12} + 191 x^{11} - 922 x^{10} - 702 x^{9} + 4108 x^{8} + 957 x^{7} - 8875 x^{6} + 479 x^{5} + 7698 x^{4} - 1731 x^{3} - 626 x^{2} + 46 x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.82644\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8030.1 |
$q$-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 | ||||||||
\(3\) | −1.82644 | −1.05449 | −0.527247 | − | 0.849712i | \(-0.676776\pi\) | ||||
−0.527247 | + | 0.849712i | \(0.676776\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.82644 | −0.745639 | ||||||||
\(7\) | 3.00453 | 1.13561 | 0.567804 | − | 0.823164i | \(-0.307793\pi\) | ||||
0.567804 | + | 0.823164i | \(0.307793\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.335869 | 0.111956 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.82644 | −0.527247 | ||||||||
\(13\) | −4.32653 | −1.19996 | −0.599982 | − | 0.800013i | \(-0.704826\pi\) | ||||
−0.599982 | + | 0.800013i | \(0.704826\pi\) | |||||||
\(14\) | 3.00453 | 0.802996 | ||||||||
\(15\) | 1.82644 | 0.471584 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.32985 | −0.565072 | −0.282536 | − | 0.959257i | \(-0.591176\pi\) | ||||
−0.282536 | + | 0.959257i | \(0.591176\pi\) | |||||||
\(18\) | 0.335869 | 0.0791651 | ||||||||
\(19\) | −1.98016 | −0.454281 | −0.227140 | − | 0.973862i | \(-0.572938\pi\) | ||||
−0.227140 | + | 0.973862i | \(0.572938\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −5.48759 | −1.19749 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 6.29494 | 1.31259 | 0.656293 | − | 0.754506i | \(-0.272124\pi\) | ||||
0.656293 | + | 0.754506i | \(0.272124\pi\) | |||||||
\(24\) | −1.82644 | −0.372820 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.32653 | −0.848503 | ||||||||
\(27\) | 4.86586 | 0.936436 | ||||||||
\(28\) | 3.00453 | 0.567804 | ||||||||
\(29\) | 3.78974 | 0.703736 | 0.351868 | − | 0.936050i | \(-0.385547\pi\) | ||||
0.351868 | + | 0.936050i | \(0.385547\pi\) | |||||||
\(30\) | 1.82644 | 0.333460 | ||||||||
\(31\) | 2.81506 | 0.505599 | 0.252800 | − | 0.967519i | \(-0.418649\pi\) | ||||
0.252800 | + | 0.967519i | \(0.418649\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.82644 | 0.317942 | ||||||||
\(34\) | −2.32985 | −0.399566 | ||||||||
\(35\) | −3.00453 | −0.507859 | ||||||||
\(36\) | 0.335869 | 0.0559782 | ||||||||
\(37\) | −0.856830 | −0.140862 | −0.0704310 | − | 0.997517i | \(-0.522437\pi\) | ||||
−0.0704310 | + | 0.997517i | \(0.522437\pi\) | |||||||
\(38\) | −1.98016 | −0.321225 | ||||||||
\(39\) | 7.90214 | 1.26535 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.60727 | −0.875708 | −0.437854 | − | 0.899046i | \(-0.644261\pi\) | ||||
−0.437854 | + | 0.899046i | \(0.644261\pi\) | |||||||
\(42\) | −5.48759 | −0.846754 | ||||||||
\(43\) | 8.01229 | 1.22186 | 0.610931 | − | 0.791684i | \(-0.290795\pi\) | ||||
0.610931 | + | 0.791684i | \(0.290795\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −0.335869 | −0.0500684 | ||||||||
\(46\) | 6.29494 | 0.928138 | ||||||||
\(47\) | −6.59031 | −0.961295 | −0.480648 | − | 0.876914i | \(-0.659598\pi\) | ||||
−0.480648 | + | 0.876914i | \(0.659598\pi\) | |||||||
\(48\) | −1.82644 | −0.263623 | ||||||||
\(49\) | 2.02723 | 0.289604 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.25533 | 0.595865 | ||||||||
\(52\) | −4.32653 | −0.599982 | ||||||||
\(53\) | −9.34352 | −1.28343 | −0.641715 | − | 0.766943i | \(-0.721777\pi\) | ||||
−0.641715 | + | 0.766943i | \(0.721777\pi\) | |||||||
\(54\) | 4.86586 | 0.662160 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 3.00453 | 0.401498 | ||||||||
\(57\) | 3.61664 | 0.479036 | ||||||||
\(58\) | 3.78974 | 0.497617 | ||||||||
\(59\) | 7.84290 | 1.02106 | 0.510529 | − | 0.859860i | \(-0.329450\pi\) | ||||
0.510529 | + | 0.859860i | \(0.329450\pi\) | |||||||
\(60\) | 1.82644 | 0.235792 | ||||||||
\(61\) | −2.89353 | −0.370479 | −0.185239 | − | 0.982693i | \(-0.559306\pi\) | ||||
−0.185239 | + | 0.982693i | \(0.559306\pi\) | |||||||
\(62\) | 2.81506 | 0.357513 | ||||||||
\(63\) | 1.00913 | 0.127139 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.32653 | 0.536640 | ||||||||
\(66\) | 1.82644 | 0.224819 | ||||||||
\(67\) | −9.07976 | −1.10927 | −0.554634 | − | 0.832094i | \(-0.687142\pi\) | ||||
−0.554634 | + | 0.832094i | \(0.687142\pi\) | |||||||
\(68\) | −2.32985 | −0.282536 | ||||||||
\(69\) | −11.4973 | −1.38411 | ||||||||
\(70\) | −3.00453 | −0.359111 | ||||||||
\(71\) | 4.45061 | 0.528191 | 0.264095 | − | 0.964497i | \(-0.414927\pi\) | ||||
0.264095 | + | 0.964497i | \(0.414927\pi\) | |||||||
\(72\) | 0.335869 | 0.0395826 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −0.856830 | −0.0996044 | ||||||||
\(75\) | −1.82644 | −0.210899 | ||||||||
\(76\) | −1.98016 | −0.227140 | ||||||||
\(77\) | −3.00453 | −0.342398 | ||||||||
\(78\) | 7.90214 | 0.894741 | ||||||||
\(79\) | 5.72249 | 0.643830 | 0.321915 | − | 0.946769i | \(-0.395673\pi\) | ||||
0.321915 | + | 0.946769i | \(0.395673\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −9.89480 | −1.09942 | ||||||||
\(82\) | −5.60727 | −0.619219 | ||||||||
\(83\) | −5.58265 | −0.612776 | −0.306388 | − | 0.951907i | \(-0.599120\pi\) | ||||
−0.306388 | + | 0.951907i | \(0.599120\pi\) | |||||||
\(84\) | −5.48759 | −0.598745 | ||||||||
\(85\) | 2.32985 | 0.252708 | ||||||||
\(86\) | 8.01229 | 0.863987 | ||||||||
\(87\) | −6.92171 | −0.742085 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −6.01085 | −0.637149 | −0.318575 | − | 0.947898i | \(-0.603204\pi\) | ||||
−0.318575 | + | 0.947898i | \(0.603204\pi\) | |||||||
\(90\) | −0.335869 | −0.0354037 | ||||||||
\(91\) | −12.9992 | −1.36269 | ||||||||
\(92\) | 6.29494 | 0.656293 | ||||||||
\(93\) | −5.14152 | −0.533151 | ||||||||
\(94\) | −6.59031 | −0.679739 | ||||||||
\(95\) | 1.98016 | 0.203161 | ||||||||
\(96\) | −1.82644 | −0.186410 | ||||||||
\(97\) | −7.84684 | −0.796726 | −0.398363 | − | 0.917228i | \(-0.630422\pi\) | ||||
−0.398363 | + | 0.917228i | \(0.630422\pi\) | |||||||
\(98\) | 2.02723 | 0.204781 | ||||||||
\(99\) | −0.335869 | −0.0337561 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −17.0206 | −1.69362 | −0.846809 | − | 0.531897i | \(-0.821479\pi\) | ||||
−0.846809 | + | 0.531897i | \(0.821479\pi\) | |||||||
\(102\) | 4.25533 | 0.421340 | ||||||||
\(103\) | 7.28504 | 0.717816 | 0.358908 | − | 0.933373i | \(-0.383149\pi\) | ||||
0.358908 | + | 0.933373i | \(0.383149\pi\) | |||||||
\(104\) | −4.32653 | −0.424251 | ||||||||
\(105\) | 5.48759 | 0.535534 | ||||||||
\(106\) | −9.34352 | −0.907522 | ||||||||
\(107\) | 4.10876 | 0.397209 | 0.198604 | − | 0.980080i | \(-0.436359\pi\) | ||||
0.198604 | + | 0.980080i | \(0.436359\pi\) | |||||||
\(108\) | 4.86586 | 0.468218 | ||||||||
\(109\) | −15.6780 | −1.50168 | −0.750841 | − | 0.660483i | \(-0.770352\pi\) | ||||
−0.750841 | + | 0.660483i | \(0.770352\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 1.56494 | 0.148538 | ||||||||
\(112\) | 3.00453 | 0.283902 | ||||||||
\(113\) | 14.3410 | 1.34909 | 0.674543 | − | 0.738235i | \(-0.264341\pi\) | ||||
0.674543 | + | 0.738235i | \(0.264341\pi\) | |||||||
\(114\) | 3.61664 | 0.338730 | ||||||||
\(115\) | −6.29494 | −0.587006 | ||||||||
\(116\) | 3.78974 | 0.351868 | ||||||||
\(117\) | −1.45315 | −0.134344 | ||||||||
\(118\) | 7.84290 | 0.721997 | ||||||||
\(119\) | −7.00012 | −0.641700 | ||||||||
\(120\) | 1.82644 | 0.166730 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.89353 | −0.261968 | ||||||||
\(123\) | 10.2413 | 0.923428 | ||||||||
\(124\) | 2.81506 | 0.252800 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.00913 | 0.0899005 | ||||||||
\(127\) | −11.8099 | −1.04795 | −0.523977 | − | 0.851732i | \(-0.675552\pi\) | ||||
−0.523977 | + | 0.851732i | \(0.675552\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −14.6339 | −1.28845 | ||||||||
\(130\) | 4.32653 | 0.379462 | ||||||||
\(131\) | 15.2331 | 1.33093 | 0.665463 | − | 0.746431i | \(-0.268234\pi\) | ||||
0.665463 | + | 0.746431i | \(0.268234\pi\) | |||||||
\(132\) | 1.82644 | 0.158971 | ||||||||
\(133\) | −5.94947 | −0.515885 | ||||||||
\(134\) | −9.07976 | −0.784372 | ||||||||
\(135\) | −4.86586 | −0.418787 | ||||||||
\(136\) | −2.32985 | −0.199783 | ||||||||
\(137\) | 6.96108 | 0.594726 | 0.297363 | − | 0.954765i | \(-0.403893\pi\) | ||||
0.297363 | + | 0.954765i | \(0.403893\pi\) | |||||||
\(138\) | −11.4973 | −0.978716 | ||||||||
\(139\) | 0.0908223 | 0.00770345 | 0.00385172 | − | 0.999993i | \(-0.498774\pi\) | ||||
0.00385172 | + | 0.999993i | \(0.498774\pi\) | |||||||
\(140\) | −3.00453 | −0.253929 | ||||||||
\(141\) | 12.0368 | 1.01368 | ||||||||
\(142\) | 4.45061 | 0.373487 | ||||||||
\(143\) | 4.32653 | 0.361803 | ||||||||
\(144\) | 0.335869 | 0.0279891 | ||||||||
\(145\) | −3.78974 | −0.314720 | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | −3.70260 | −0.305385 | ||||||||
\(148\) | −0.856830 | −0.0704310 | ||||||||
\(149\) | 11.6325 | 0.952970 | 0.476485 | − | 0.879183i | \(-0.341911\pi\) | ||||
0.476485 | + | 0.879183i | \(0.341911\pi\) | |||||||
\(150\) | −1.82644 | −0.149128 | ||||||||
\(151\) | −0.737844 | −0.0600449 | −0.0300224 | − | 0.999549i | \(-0.509558\pi\) | ||||
−0.0300224 | + | 0.999549i | \(0.509558\pi\) | |||||||
\(152\) | −1.98016 | −0.160613 | ||||||||
\(153\) | −0.782526 | −0.0632635 | ||||||||
\(154\) | −3.00453 | −0.242112 | ||||||||
\(155\) | −2.81506 | −0.226111 | ||||||||
\(156\) | 7.90214 | 0.632677 | ||||||||
\(157\) | −4.90260 | −0.391270 | −0.195635 | − | 0.980677i | \(-0.562677\pi\) | ||||
−0.195635 | + | 0.980677i | \(0.562677\pi\) | |||||||
\(158\) | 5.72249 | 0.455257 | ||||||||
\(159\) | 17.0653 | 1.35337 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 18.9134 | 1.49058 | ||||||||
\(162\) | −9.89480 | −0.777409 | ||||||||
\(163\) | −16.7822 | −1.31448 | −0.657241 | − | 0.753681i | \(-0.728276\pi\) | ||||
−0.657241 | + | 0.753681i | \(0.728276\pi\) | |||||||
\(164\) | −5.60727 | −0.437854 | ||||||||
\(165\) | −1.82644 | −0.142188 | ||||||||
\(166\) | −5.58265 | −0.433298 | ||||||||
\(167\) | −11.4368 | −0.885005 | −0.442502 | − | 0.896767i | \(-0.645909\pi\) | ||||
−0.442502 | + | 0.896767i | \(0.645909\pi\) | |||||||
\(168\) | −5.48759 | −0.423377 | ||||||||
\(169\) | 5.71889 | 0.439914 | ||||||||
\(170\) | 2.32985 | 0.178692 | ||||||||
\(171\) | −0.665076 | −0.0508597 | ||||||||
\(172\) | 8.01229 | 0.610931 | ||||||||
\(173\) | −20.2277 | −1.53788 | −0.768941 | − | 0.639319i | \(-0.779216\pi\) | ||||
−0.768941 | + | 0.639319i | \(0.779216\pi\) | |||||||
\(174\) | −6.92171 | −0.524733 | ||||||||
\(175\) | 3.00453 | 0.227121 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −14.3246 | −1.07670 | ||||||||
\(178\) | −6.01085 | −0.450533 | ||||||||
\(179\) | −8.05501 | −0.602060 | −0.301030 | − | 0.953615i | \(-0.597330\pi\) | ||||
−0.301030 | + | 0.953615i | \(0.597330\pi\) | |||||||
\(180\) | −0.335869 | −0.0250342 | ||||||||
\(181\) | −3.96610 | −0.294798 | −0.147399 | − | 0.989077i | \(-0.547090\pi\) | ||||
−0.147399 | + | 0.989077i | \(0.547090\pi\) | |||||||
\(182\) | −12.9992 | −0.963566 | ||||||||
\(183\) | 5.28485 | 0.390667 | ||||||||
\(184\) | 6.29494 | 0.464069 | ||||||||
\(185\) | 0.856830 | 0.0629954 | ||||||||
\(186\) | −5.14152 | −0.376995 | ||||||||
\(187\) | 2.32985 | 0.170376 | ||||||||
\(188\) | −6.59031 | −0.480648 | ||||||||
\(189\) | 14.6197 | 1.06342 | ||||||||
\(190\) | 1.98016 | 0.143656 | ||||||||
\(191\) | 3.49901 | 0.253179 | 0.126590 | − | 0.991955i | \(-0.459597\pi\) | ||||
0.126590 | + | 0.991955i | \(0.459597\pi\) | |||||||
\(192\) | −1.82644 | −0.131812 | ||||||||
\(193\) | −18.0220 | −1.29725 | −0.648627 | − | 0.761106i | \(-0.724657\pi\) | ||||
−0.648627 | + | 0.761106i | \(0.724657\pi\) | |||||||
\(194\) | −7.84684 | −0.563370 | ||||||||
\(195\) | −7.90214 | −0.565884 | ||||||||
\(196\) | 2.02723 | 0.144802 | ||||||||
\(197\) | −14.5436 | −1.03619 | −0.518093 | − | 0.855324i | \(-0.673358\pi\) | ||||
−0.518093 | + | 0.855324i | \(0.673358\pi\) | |||||||
\(198\) | −0.335869 | −0.0238692 | ||||||||
\(199\) | 3.37427 | 0.239196 | 0.119598 | − | 0.992822i | \(-0.461839\pi\) | ||||
0.119598 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 16.5836 | 1.16972 | ||||||||
\(202\) | −17.0206 | −1.19757 | ||||||||
\(203\) | 11.3864 | 0.799168 | ||||||||
\(204\) | 4.25533 | 0.297933 | ||||||||
\(205\) | 5.60727 | 0.391628 | ||||||||
\(206\) | 7.28504 | 0.507572 | ||||||||
\(207\) | 2.11428 | 0.146952 | ||||||||
\(208\) | −4.32653 | −0.299991 | ||||||||
\(209\) | 1.98016 | 0.136971 | ||||||||
\(210\) | 5.48759 | 0.378680 | ||||||||
\(211\) | −21.4525 | −1.47685 | −0.738427 | − | 0.674334i | \(-0.764431\pi\) | ||||
−0.738427 | + | 0.674334i | \(0.764431\pi\) | |||||||
\(212\) | −9.34352 | −0.641715 | ||||||||
\(213\) | −8.12876 | −0.556974 | ||||||||
\(214\) | 4.10876 | 0.280869 | ||||||||
\(215\) | −8.01229 | −0.546433 | ||||||||
\(216\) | 4.86586 | 0.331080 | ||||||||
\(217\) | 8.45794 | 0.574162 | ||||||||
\(218\) | −15.6780 | −1.06185 | ||||||||
\(219\) | −1.82644 | −0.123419 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 10.0802 | 0.678067 | ||||||||
\(222\) | 1.56494 | 0.105032 | ||||||||
\(223\) | 21.6813 | 1.45189 | 0.725944 | − | 0.687753i | \(-0.241403\pi\) | ||||
0.725944 | + | 0.687753i | \(0.241403\pi\) | |||||||
\(224\) | 3.00453 | 0.200749 | ||||||||
\(225\) | 0.335869 | 0.0223913 | ||||||||
\(226\) | 14.3410 | 0.953948 | ||||||||
\(227\) | 16.8342 | 1.11733 | 0.558664 | − | 0.829394i | \(-0.311314\pi\) | ||||
0.558664 | + | 0.829394i | \(0.311314\pi\) | |||||||
\(228\) | 3.61664 | 0.239518 | ||||||||
\(229\) | −20.1367 | −1.33067 | −0.665336 | − | 0.746544i | \(-0.731712\pi\) | ||||
−0.665336 | + | 0.746544i | \(0.731712\pi\) | |||||||
\(230\) | −6.29494 | −0.415076 | ||||||||
\(231\) | 5.48759 | 0.361057 | ||||||||
\(232\) | 3.78974 | 0.248808 | ||||||||
\(233\) | 21.0354 | 1.37808 | 0.689039 | − | 0.724724i | \(-0.258033\pi\) | ||||
0.689039 | + | 0.724724i | \(0.258033\pi\) | |||||||
\(234\) | −1.45315 | −0.0949953 | ||||||||
\(235\) | 6.59031 | 0.429904 | ||||||||
\(236\) | 7.84290 | 0.510529 | ||||||||
\(237\) | −10.4518 | −0.678914 | ||||||||
\(238\) | −7.00012 | −0.453751 | ||||||||
\(239\) | −17.5138 | −1.13288 | −0.566438 | − | 0.824104i | \(-0.691679\pi\) | ||||
−0.566438 | + | 0.824104i | \(0.691679\pi\) | |||||||
\(240\) | 1.82644 | 0.117896 | ||||||||
\(241\) | 4.72871 | 0.304603 | 0.152301 | − | 0.988334i | \(-0.451332\pi\) | ||||
0.152301 | + | 0.988334i | \(0.451332\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 3.47463 | 0.222897 | ||||||||
\(244\) | −2.89353 | −0.185239 | ||||||||
\(245\) | −2.02723 | −0.129515 | ||||||||
\(246\) | 10.2413 | 0.652962 | ||||||||
\(247\) | 8.56725 | 0.545121 | ||||||||
\(248\) | 2.81506 | 0.178756 | ||||||||
\(249\) | 10.1964 | 0.646168 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −13.9460 | −0.880264 | −0.440132 | − | 0.897933i | \(-0.645068\pi\) | ||||
−0.440132 | + | 0.897933i | \(0.645068\pi\) | |||||||
\(252\) | 1.00913 | 0.0635693 | ||||||||
\(253\) | −6.29494 | −0.395760 | ||||||||
\(254\) | −11.8099 | −0.741016 | ||||||||
\(255\) | −4.25533 | −0.266479 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.0521 | −1.87460 | −0.937298 | − | 0.348530i | \(-0.886681\pi\) | ||||
−0.937298 | + | 0.348530i | \(0.886681\pi\) | |||||||
\(258\) | −14.6339 | −0.911069 | ||||||||
\(259\) | −2.57437 | −0.159964 | ||||||||
\(260\) | 4.32653 | 0.268320 | ||||||||
\(261\) | 1.27286 | 0.0787878 | ||||||||
\(262\) | 15.2331 | 0.941107 | ||||||||
\(263\) | 17.1222 | 1.05580 | 0.527901 | − | 0.849306i | \(-0.322979\pi\) | ||||
0.527901 | + | 0.849306i | \(0.322979\pi\) | |||||||
\(264\) | 1.82644 | 0.112409 | ||||||||
\(265\) | 9.34352 | 0.573968 | ||||||||
\(266\) | −5.94947 | −0.364785 | ||||||||
\(267\) | 10.9784 | 0.671870 | ||||||||
\(268\) | −9.07976 | −0.554634 | ||||||||
\(269\) | 13.4766 | 0.821682 | 0.410841 | − | 0.911707i | \(-0.365235\pi\) | ||||
0.410841 | + | 0.911707i | \(0.365235\pi\) | |||||||
\(270\) | −4.86586 | −0.296127 | ||||||||
\(271\) | −26.7041 | −1.62216 | −0.811078 | − | 0.584938i | \(-0.801119\pi\) | ||||
−0.811078 | + | 0.584938i | \(0.801119\pi\) | |||||||
\(272\) | −2.32985 | −0.141268 | ||||||||
\(273\) | 23.7422 | 1.43695 | ||||||||
\(274\) | 6.96108 | 0.420534 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −11.4973 | −0.692057 | ||||||||
\(277\) | 0.768199 | 0.0461566 | 0.0230783 | − | 0.999734i | \(-0.492653\pi\) | ||||
0.0230783 | + | 0.999734i | \(0.492653\pi\) | |||||||
\(278\) | 0.0908223 | 0.00544716 | ||||||||
\(279\) | 0.945491 | 0.0566051 | ||||||||
\(280\) | −3.00453 | −0.179555 | ||||||||
\(281\) | 1.67745 | 0.100068 | 0.0500341 | − | 0.998748i | \(-0.484067\pi\) | ||||
0.0500341 | + | 0.998748i | \(0.484067\pi\) | |||||||
\(282\) | 12.0368 | 0.716780 | ||||||||
\(283\) | 7.32944 | 0.435690 | 0.217845 | − | 0.975983i | \(-0.430097\pi\) | ||||
0.217845 | + | 0.975983i | \(0.430097\pi\) | |||||||
\(284\) | 4.45061 | 0.264095 | ||||||||
\(285\) | −3.61664 | −0.214231 | ||||||||
\(286\) | 4.32653 | 0.255833 | ||||||||
\(287\) | −16.8472 | −0.994460 | ||||||||
\(288\) | 0.335869 | 0.0197913 | ||||||||
\(289\) | −11.5718 | −0.680693 | ||||||||
\(290\) | −3.78974 | −0.222541 | ||||||||
\(291\) | 14.3318 | 0.840142 | ||||||||
\(292\) | 1.00000 | 0.0585206 | ||||||||
\(293\) | −7.57117 | −0.442312 | −0.221156 | − | 0.975238i | \(-0.570983\pi\) | ||||
−0.221156 | + | 0.975238i | \(0.570983\pi\) | |||||||
\(294\) | −3.70260 | −0.215940 | ||||||||
\(295\) | −7.84290 | −0.456631 | ||||||||
\(296\) | −0.856830 | −0.0498022 | ||||||||
\(297\) | −4.86586 | −0.282346 | ||||||||
\(298\) | 11.6325 | 0.673852 | ||||||||
\(299\) | −27.2353 | −1.57506 | ||||||||
\(300\) | −1.82644 | −0.105449 | ||||||||
\(301\) | 24.0732 | 1.38756 | ||||||||
\(302\) | −0.737844 | −0.0424582 | ||||||||
\(303\) | 31.0871 | 1.78591 | ||||||||
\(304\) | −1.98016 | −0.113570 | ||||||||
\(305\) | 2.89353 | 0.165683 | ||||||||
\(306\) | −0.782526 | −0.0447340 | ||||||||
\(307\) | −26.3131 | −1.50177 | −0.750884 | − | 0.660435i | \(-0.770372\pi\) | ||||
−0.750884 | + | 0.660435i | \(0.770372\pi\) | |||||||
\(308\) | −3.00453 | −0.171199 | ||||||||
\(309\) | −13.3057 | −0.756932 | ||||||||
\(310\) | −2.81506 | −0.159885 | ||||||||
\(311\) | 9.91646 | 0.562311 | 0.281155 | − | 0.959662i | \(-0.409282\pi\) | ||||
0.281155 | + | 0.959662i | \(0.409282\pi\) | |||||||
\(312\) | 7.90214 | 0.447370 | ||||||||
\(313\) | 26.8046 | 1.51509 | 0.757544 | − | 0.652784i | \(-0.226399\pi\) | ||||
0.757544 | + | 0.652784i | \(0.226399\pi\) | |||||||
\(314\) | −4.90260 | −0.276670 | ||||||||
\(315\) | −1.00913 | −0.0568581 | ||||||||
\(316\) | 5.72249 | 0.321915 | ||||||||
\(317\) | 18.8464 | 1.05852 | 0.529259 | − | 0.848460i | \(-0.322470\pi\) | ||||
0.529259 | + | 0.848460i | \(0.322470\pi\) | |||||||
\(318\) | 17.0653 | 0.956977 | ||||||||
\(319\) | −3.78974 | −0.212184 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −7.50438 | −0.418854 | ||||||||
\(322\) | 18.9134 | 1.05400 | ||||||||
\(323\) | 4.61349 | 0.256702 | ||||||||
\(324\) | −9.89480 | −0.549711 | ||||||||
\(325\) | −4.32653 | −0.239993 | ||||||||
\(326\) | −16.7822 | −0.929479 | ||||||||
\(327\) | 28.6349 | 1.58351 | ||||||||
\(328\) | −5.60727 | −0.309610 | ||||||||
\(329\) | −19.8008 | −1.09165 | ||||||||
\(330\) | −1.82644 | −0.100542 | ||||||||
\(331\) | 31.9810 | 1.75784 | 0.878918 | − | 0.476973i | \(-0.158266\pi\) | ||||
0.878918 | + | 0.476973i | \(0.158266\pi\) | |||||||
\(332\) | −5.58265 | −0.306388 | ||||||||
\(333\) | −0.287783 | −0.0157704 | ||||||||
\(334\) | −11.4368 | −0.625793 | ||||||||
\(335\) | 9.07976 | 0.496080 | ||||||||
\(336\) | −5.48759 | −0.299373 | ||||||||
\(337\) | −6.25893 | −0.340945 | −0.170473 | − | 0.985362i | \(-0.554529\pi\) | ||||
−0.170473 | + | 0.985362i | \(0.554529\pi\) | |||||||
\(338\) | 5.71889 | 0.311066 | ||||||||
\(339\) | −26.1929 | −1.42260 | ||||||||
\(340\) | 2.32985 | 0.126354 | ||||||||
\(341\) | −2.81506 | −0.152444 | ||||||||
\(342\) | −0.665076 | −0.0359632 | ||||||||
\(343\) | −14.9409 | −0.806731 | ||||||||
\(344\) | 8.01229 | 0.431994 | ||||||||
\(345\) | 11.4973 | 0.618994 | ||||||||
\(346\) | −20.2277 | −1.08745 | ||||||||
\(347\) | −15.9336 | −0.855362 | −0.427681 | − | 0.903930i | \(-0.640669\pi\) | ||||
−0.427681 | + | 0.903930i | \(0.640669\pi\) | |||||||
\(348\) | −6.92171 | −0.371043 | ||||||||
\(349\) | −22.7662 | −1.21865 | −0.609324 | − | 0.792921i | \(-0.708559\pi\) | ||||
−0.609324 | + | 0.792921i | \(0.708559\pi\) | |||||||
\(350\) | 3.00453 | 0.160599 | ||||||||
\(351\) | −21.0523 | −1.12369 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 3.93216 | 0.209288 | 0.104644 | − | 0.994510i | \(-0.466630\pi\) | ||||
0.104644 | + | 0.994510i | \(0.466630\pi\) | |||||||
\(354\) | −14.3246 | −0.761341 | ||||||||
\(355\) | −4.45061 | −0.236214 | ||||||||
\(356\) | −6.01085 | −0.318575 | ||||||||
\(357\) | 12.7853 | 0.676669 | ||||||||
\(358\) | −8.05501 | −0.425720 | ||||||||
\(359\) | −19.6647 | −1.03787 | −0.518933 | − | 0.854815i | \(-0.673670\pi\) | ||||
−0.518933 | + | 0.854815i | \(0.673670\pi\) | |||||||
\(360\) | −0.335869 | −0.0177019 | ||||||||
\(361\) | −15.0789 | −0.793629 | ||||||||
\(362\) | −3.96610 | −0.208454 | ||||||||
\(363\) | −1.82644 | −0.0958630 | ||||||||
\(364\) | −12.9992 | −0.681344 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | 5.28485 | 0.276244 | ||||||||
\(367\) | 14.0691 | 0.734402 | 0.367201 | − | 0.930142i | \(-0.380316\pi\) | ||||
0.367201 | + | 0.930142i | \(0.380316\pi\) | |||||||
\(368\) | 6.29494 | 0.328146 | ||||||||
\(369\) | −1.88331 | −0.0980411 | ||||||||
\(370\) | 0.856830 | 0.0445444 | ||||||||
\(371\) | −28.0729 | −1.45747 | ||||||||
\(372\) | −5.14152 | −0.266576 | ||||||||
\(373\) | 7.03836 | 0.364433 | 0.182216 | − | 0.983258i | \(-0.441673\pi\) | ||||
0.182216 | + | 0.983258i | \(0.441673\pi\) | |||||||
\(374\) | 2.32985 | 0.120474 | ||||||||
\(375\) | 1.82644 | 0.0943168 | ||||||||
\(376\) | −6.59031 | −0.339869 | ||||||||
\(377\) | −16.3964 | −0.844458 | ||||||||
\(378\) | 14.6197 | 0.751954 | ||||||||
\(379\) | 24.9735 | 1.28280 | 0.641402 | − | 0.767205i | \(-0.278353\pi\) | ||||
0.641402 | + | 0.767205i | \(0.278353\pi\) | |||||||
\(380\) | 1.98016 | 0.101580 | ||||||||
\(381\) | 21.5699 | 1.10506 | ||||||||
\(382\) | 3.49901 | 0.179025 | ||||||||
\(383\) | −2.32441 | −0.118772 | −0.0593858 | − | 0.998235i | \(-0.518914\pi\) | ||||
−0.0593858 | + | 0.998235i | \(0.518914\pi\) | |||||||
\(384\) | −1.82644 | −0.0932049 | ||||||||
\(385\) | 3.00453 | 0.153125 | ||||||||
\(386\) | −18.0220 | −0.917297 | ||||||||
\(387\) | 2.69108 | 0.136795 | ||||||||
\(388\) | −7.84684 | −0.398363 | ||||||||
\(389\) | −10.2655 | −0.520483 | −0.260241 | − | 0.965544i | \(-0.583802\pi\) | ||||
−0.260241 | + | 0.965544i | \(0.583802\pi\) | |||||||
\(390\) | −7.90214 | −0.400140 | ||||||||
\(391\) | −14.6663 | −0.741706 | ||||||||
\(392\) | 2.02723 | 0.102390 | ||||||||
\(393\) | −27.8224 | −1.40345 | ||||||||
\(394\) | −14.5436 | −0.732694 | ||||||||
\(395\) | −5.72249 | −0.287929 | ||||||||
\(396\) | −0.335869 | −0.0168781 | ||||||||
\(397\) | −8.96973 | −0.450178 | −0.225089 | − | 0.974338i | \(-0.572267\pi\) | ||||
−0.225089 | + | 0.974338i | \(0.572267\pi\) | |||||||
\(398\) | 3.37427 | 0.169137 | ||||||||
\(399\) | 10.8663 | 0.543997 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −27.9889 | −1.39770 | −0.698849 | − | 0.715269i | \(-0.746304\pi\) | ||||
−0.698849 | + | 0.715269i | \(0.746304\pi\) | |||||||
\(402\) | 16.5836 | 0.827115 | ||||||||
\(403\) | −12.1794 | −0.606701 | ||||||||
\(404\) | −17.0206 | −0.846809 | ||||||||
\(405\) | 9.89480 | 0.491677 | ||||||||
\(406\) | 11.3864 | 0.565097 | ||||||||
\(407\) | 0.856830 | 0.0424715 | ||||||||
\(408\) | 4.25533 | 0.210670 | ||||||||
\(409\) | −19.0794 | −0.943417 | −0.471708 | − | 0.881755i | \(-0.656362\pi\) | ||||
−0.471708 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(410\) | 5.60727 | 0.276923 | ||||||||
\(411\) | −12.7140 | −0.627134 | ||||||||
\(412\) | 7.28504 | 0.358908 | ||||||||
\(413\) | 23.5643 | 1.15952 | ||||||||
\(414\) | 2.11428 | 0.103911 | ||||||||
\(415\) | 5.58265 | 0.274042 | ||||||||
\(416\) | −4.32653 | −0.212126 | ||||||||
\(417\) | −0.165881 | −0.00812324 | ||||||||
\(418\) | 1.98016 | 0.0968530 | ||||||||
\(419\) | −32.8434 | −1.60450 | −0.802251 | − | 0.596986i | \(-0.796365\pi\) | ||||
−0.802251 | + | 0.596986i | \(0.796365\pi\) | |||||||
\(420\) | 5.48759 | 0.267767 | ||||||||
\(421\) | 25.4036 | 1.23809 | 0.619047 | − | 0.785354i | \(-0.287519\pi\) | ||||
0.619047 | + | 0.785354i | \(0.287519\pi\) | |||||||
\(422\) | −21.4525 | −1.04429 | ||||||||
\(423\) | −2.21348 | −0.107623 | ||||||||
\(424\) | −9.34352 | −0.453761 | ||||||||
\(425\) | −2.32985 | −0.113014 | ||||||||
\(426\) | −8.12876 | −0.393840 | ||||||||
\(427\) | −8.69371 | −0.420718 | ||||||||
\(428\) | 4.10876 | 0.198604 | ||||||||
\(429\) | −7.90214 | −0.381519 | ||||||||
\(430\) | −8.01229 | −0.386387 | ||||||||
\(431\) | 28.2811 | 1.36225 | 0.681127 | − | 0.732165i | \(-0.261490\pi\) | ||||
0.681127 | + | 0.732165i | \(0.261490\pi\) | |||||||
\(432\) | 4.86586 | 0.234109 | ||||||||
\(433\) | −11.4205 | −0.548833 | −0.274417 | − | 0.961611i | \(-0.588485\pi\) | ||||
−0.274417 | + | 0.961611i | \(0.588485\pi\) | |||||||
\(434\) | 8.45794 | 0.405994 | ||||||||
\(435\) | 6.92171 | 0.331871 | ||||||||
\(436\) | −15.6780 | −0.750841 | ||||||||
\(437\) | −12.4650 | −0.596283 | ||||||||
\(438\) | −1.82644 | −0.0872705 | ||||||||
\(439\) | −25.6469 | −1.22406 | −0.612030 | − | 0.790835i | \(-0.709647\pi\) | ||||
−0.612030 | + | 0.790835i | \(0.709647\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 0.680883 | 0.0324230 | ||||||||
\(442\) | 10.0802 | 0.479466 | ||||||||
\(443\) | 34.3263 | 1.63089 | 0.815447 | − | 0.578832i | \(-0.196491\pi\) | ||||
0.815447 | + | 0.578832i | \(0.196491\pi\) | |||||||
\(444\) | 1.56494 | 0.0742690 | ||||||||
\(445\) | 6.01085 | 0.284942 | ||||||||
\(446\) | 21.6813 | 1.02664 | ||||||||
\(447\) | −21.2460 | −1.00490 | ||||||||
\(448\) | 3.00453 | 0.141951 | ||||||||
\(449\) | −24.9408 | −1.17703 | −0.588514 | − | 0.808487i | \(-0.700287\pi\) | ||||
−0.588514 | + | 0.808487i | \(0.700287\pi\) | |||||||
\(450\) | 0.335869 | 0.0158330 | ||||||||
\(451\) | 5.60727 | 0.264036 | ||||||||
\(452\) | 14.3410 | 0.674543 | ||||||||
\(453\) | 1.34762 | 0.0633169 | ||||||||
\(454\) | 16.8342 | 0.790070 | ||||||||
\(455\) | 12.9992 | 0.609413 | ||||||||
\(456\) | 3.61664 | 0.169365 | ||||||||
\(457\) | 8.81941 | 0.412554 | 0.206277 | − | 0.978494i | \(-0.433865\pi\) | ||||
0.206277 | + | 0.978494i | \(0.433865\pi\) | |||||||
\(458\) | −20.1367 | −0.940927 | ||||||||
\(459\) | −11.3368 | −0.529154 | ||||||||
\(460\) | −6.29494 | −0.293503 | ||||||||
\(461\) | −16.4185 | −0.764688 | −0.382344 | − | 0.924020i | \(-0.624883\pi\) | ||||
−0.382344 | + | 0.924020i | \(0.624883\pi\) | |||||||
\(462\) | 5.48759 | 0.255306 | ||||||||
\(463\) | −20.3061 | −0.943707 | −0.471853 | − | 0.881677i | \(-0.656415\pi\) | ||||
−0.471853 | + | 0.881677i | \(0.656415\pi\) | |||||||
\(464\) | 3.78974 | 0.175934 | ||||||||
\(465\) | 5.14152 | 0.238432 | ||||||||
\(466\) | 21.0354 | 0.974448 | ||||||||
\(467\) | −20.5992 | −0.953217 | −0.476609 | − | 0.879116i | \(-0.658134\pi\) | ||||
−0.476609 | + | 0.879116i | \(0.658134\pi\) | |||||||
\(468\) | −1.45315 | −0.0671719 | ||||||||
\(469\) | −27.2804 | −1.25969 | ||||||||
\(470\) | 6.59031 | 0.303988 | ||||||||
\(471\) | 8.95430 | 0.412592 | ||||||||
\(472\) | 7.84290 | 0.360999 | ||||||||
\(473\) | −8.01229 | −0.368405 | ||||||||
\(474\) | −10.4518 | −0.480065 | ||||||||
\(475\) | −1.98016 | −0.0908562 | ||||||||
\(476\) | −7.00012 | −0.320850 | ||||||||
\(477\) | −3.13820 | −0.143688 | ||||||||
\(478\) | −17.5138 | −0.801064 | ||||||||
\(479\) | 17.6387 | 0.805932 | 0.402966 | − | 0.915215i | \(-0.367979\pi\) | ||||
0.402966 | + | 0.915215i | \(0.367979\pi\) | |||||||
\(480\) | 1.82644 | 0.0833650 | ||||||||
\(481\) | 3.70710 | 0.169029 | ||||||||
\(482\) | 4.72871 | 0.215387 | ||||||||
\(483\) | −34.5441 | −1.57181 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 7.84684 | 0.356307 | ||||||||
\(486\) | 3.47463 | 0.157612 | ||||||||
\(487\) | −5.31105 | −0.240666 | −0.120333 | − | 0.992734i | \(-0.538396\pi\) | ||||
−0.120333 | + | 0.992734i | \(0.538396\pi\) | |||||||
\(488\) | −2.89353 | −0.130984 | ||||||||
\(489\) | 30.6516 | 1.38611 | ||||||||
\(490\) | −2.02723 | −0.0915807 | ||||||||
\(491\) | −34.1717 | −1.54215 | −0.771073 | − | 0.636747i | \(-0.780280\pi\) | ||||
−0.771073 | + | 0.636747i | \(0.780280\pi\) | |||||||
\(492\) | 10.2413 | 0.461714 | ||||||||
\(493\) | −8.82953 | −0.397662 | ||||||||
\(494\) | 8.56725 | 0.385459 | ||||||||
\(495\) | 0.335869 | 0.0150962 | ||||||||
\(496\) | 2.81506 | 0.126400 | ||||||||
\(497\) | 13.3720 | 0.599817 | ||||||||
\(498\) | 10.1964 | 0.456910 | ||||||||
\(499\) | 3.62548 | 0.162299 | 0.0811494 | − | 0.996702i | \(-0.474141\pi\) | ||||
0.0811494 | + | 0.996702i | \(0.474141\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 20.8885 | 0.933232 | ||||||||
\(502\) | −13.9460 | −0.622440 | ||||||||
\(503\) | −0.419493 | −0.0187043 | −0.00935214 | − | 0.999956i | \(-0.502977\pi\) | ||||
−0.00935214 | + | 0.999956i | \(0.502977\pi\) | |||||||
\(504\) | 1.00913 | 0.0449503 | ||||||||
\(505\) | 17.0206 | 0.757409 | ||||||||
\(506\) | −6.29494 | −0.279844 | ||||||||
\(507\) | −10.4452 | −0.463887 | ||||||||
\(508\) | −11.8099 | −0.523977 | ||||||||
\(509\) | −37.4776 | −1.66116 | −0.830582 | − | 0.556897i | \(-0.811992\pi\) | ||||
−0.830582 | + | 0.556897i | \(0.811992\pi\) | |||||||
\(510\) | −4.25533 | −0.188429 | ||||||||
\(511\) | 3.00453 | 0.132913 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.63521 | −0.425405 | ||||||||
\(514\) | −30.0521 | −1.32554 | ||||||||
\(515\) | −7.28504 | −0.321017 | ||||||||
\(516\) | −14.6339 | −0.644223 | ||||||||
\(517\) | 6.59031 | 0.289841 | ||||||||
\(518\) | −2.57437 | −0.113111 | ||||||||
\(519\) | 36.9446 | 1.62169 | ||||||||
\(520\) | 4.32653 | 0.189731 | ||||||||
\(521\) | −9.01721 | −0.395051 | −0.197526 | − | 0.980298i | \(-0.563291\pi\) | ||||
−0.197526 | + | 0.980298i | \(0.563291\pi\) | |||||||
\(522\) | 1.27286 | 0.0557114 | ||||||||
\(523\) | −38.0175 | −1.66239 | −0.831194 | − | 0.555983i | \(-0.812342\pi\) | ||||
−0.831194 | + | 0.555983i | \(0.812342\pi\) | |||||||
\(524\) | 15.2331 | 0.665463 | ||||||||
\(525\) | −5.48759 | −0.239498 | ||||||||
\(526\) | 17.1222 | 0.746564 | ||||||||
\(527\) | −6.55867 | −0.285700 | ||||||||
\(528\) | 1.82644 | 0.0794854 | ||||||||
\(529\) | 16.6263 | 0.722882 | ||||||||
\(530\) | 9.34352 | 0.405856 | ||||||||
\(531\) | 2.63419 | 0.114314 | ||||||||
\(532\) | −5.94947 | −0.257942 | ||||||||
\(533\) | 24.2600 | 1.05082 | ||||||||
\(534\) | 10.9784 | 0.475084 | ||||||||
\(535\) | −4.10876 | −0.177637 | ||||||||
\(536\) | −9.07976 | −0.392186 | ||||||||
\(537\) | 14.7120 | 0.634868 | ||||||||
\(538\) | 13.4766 | 0.581017 | ||||||||
\(539\) | −2.02723 | −0.0873188 | ||||||||
\(540\) | −4.86586 | −0.209393 | ||||||||
\(541\) | −4.97669 | −0.213965 | −0.106982 | − | 0.994261i | \(-0.534119\pi\) | ||||
−0.106982 | + | 0.994261i | \(0.534119\pi\) | |||||||
\(542\) | −26.7041 | −1.14704 | ||||||||
\(543\) | 7.24383 | 0.310862 | ||||||||
\(544\) | −2.32985 | −0.0998916 | ||||||||
\(545\) | 15.6780 | 0.671573 | ||||||||
\(546\) | 23.7422 | 1.01607 | ||||||||
\(547\) | 14.7387 | 0.630182 | 0.315091 | − | 0.949061i | \(-0.397965\pi\) | ||||
0.315091 | + | 0.949061i | \(0.397965\pi\) | |||||||
\(548\) | 6.96108 | 0.297363 | ||||||||
\(549\) | −0.971848 | −0.0414775 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −7.50430 | −0.319694 | ||||||||
\(552\) | −11.4973 | −0.489358 | ||||||||
\(553\) | 17.1934 | 0.731138 | ||||||||
\(554\) | 0.768199 | 0.0326377 | ||||||||
\(555\) | −1.56494 | −0.0664282 | ||||||||
\(556\) | 0.0908223 | 0.00385172 | ||||||||
\(557\) | −39.2902 | −1.66478 | −0.832389 | − | 0.554192i | \(-0.813027\pi\) | ||||
−0.832389 | + | 0.554192i | \(0.813027\pi\) | |||||||
\(558\) | 0.945491 | 0.0400258 | ||||||||
\(559\) | −34.6654 | −1.46619 | ||||||||
\(560\) | −3.00453 | −0.126965 | ||||||||
\(561\) | −4.25533 | −0.179660 | ||||||||
\(562\) | 1.67745 | 0.0707588 | ||||||||
\(563\) | −12.2878 | −0.517867 | −0.258934 | − | 0.965895i | \(-0.583371\pi\) | ||||
−0.258934 | + | 0.965895i | \(0.583371\pi\) | |||||||
\(564\) | 12.0368 | 0.506840 | ||||||||
\(565\) | −14.3410 | −0.603330 | ||||||||
\(566\) | 7.32944 | 0.308079 | ||||||||
\(567\) | −29.7293 | −1.24851 | ||||||||
\(568\) | 4.45061 | 0.186744 | ||||||||
\(569\) | 31.7088 | 1.32930 | 0.664652 | − | 0.747153i | \(-0.268580\pi\) | ||||
0.664652 | + | 0.747153i | \(0.268580\pi\) | |||||||
\(570\) | −3.61664 | −0.151485 | ||||||||
\(571\) | 6.62363 | 0.277190 | 0.138595 | − | 0.990349i | \(-0.455741\pi\) | ||||
0.138595 | + | 0.990349i | \(0.455741\pi\) | |||||||
\(572\) | 4.32653 | 0.180901 | ||||||||
\(573\) | −6.39072 | −0.266976 | ||||||||
\(574\) | −16.8472 | −0.703190 | ||||||||
\(575\) | 6.29494 | 0.262517 | ||||||||
\(576\) | 0.335869 | 0.0139946 | ||||||||
\(577\) | −31.0460 | −1.29246 | −0.646232 | − | 0.763141i | \(-0.723656\pi\) | ||||
−0.646232 | + | 0.763141i | \(0.723656\pi\) | |||||||
\(578\) | −11.5718 | −0.481323 | ||||||||
\(579\) | 32.9161 | 1.36795 | ||||||||
\(580\) | −3.78974 | −0.157360 | ||||||||
\(581\) | −16.7733 | −0.695872 | ||||||||
\(582\) | 14.3318 | 0.594070 | ||||||||
\(583\) | 9.34352 | 0.386969 | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 1.45315 | 0.0600803 | ||||||||
\(586\) | −7.57117 | −0.312762 | ||||||||
\(587\) | −9.30278 | −0.383967 | −0.191983 | − | 0.981398i | \(-0.561492\pi\) | ||||
−0.191983 | + | 0.981398i | \(0.561492\pi\) | |||||||
\(588\) | −3.70260 | −0.152693 | ||||||||
\(589\) | −5.57428 | −0.229684 | ||||||||
\(590\) | −7.84290 | −0.322887 | ||||||||
\(591\) | 26.5629 | 1.09265 | ||||||||
\(592\) | −0.856830 | −0.0352155 | ||||||||
\(593\) | 43.9366 | 1.80426 | 0.902131 | − | 0.431463i | \(-0.142002\pi\) | ||||
0.902131 | + | 0.431463i | \(0.142002\pi\) | |||||||
\(594\) | −4.86586 | −0.199649 | ||||||||
\(595\) | 7.00012 | 0.286977 | ||||||||
\(596\) | 11.6325 | 0.476485 | ||||||||
\(597\) | −6.16289 | −0.252230 | ||||||||
\(598\) | −27.2353 | −1.11373 | ||||||||
\(599\) | 11.0579 | 0.451815 | 0.225908 | − | 0.974149i | \(-0.427465\pi\) | ||||
0.225908 | + | 0.974149i | \(0.427465\pi\) | |||||||
\(600\) | −1.82644 | −0.0745639 | ||||||||
\(601\) | −16.8549 | −0.687526 | −0.343763 | − | 0.939056i | \(-0.611702\pi\) | ||||
−0.343763 | + | 0.939056i | \(0.611702\pi\) | |||||||
\(602\) | 24.0732 | 0.981150 | ||||||||
\(603\) | −3.04961 | −0.124190 | ||||||||
\(604\) | −0.737844 | −0.0300224 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 31.0871 | 1.26283 | ||||||||
\(607\) | −1.31520 | −0.0533824 | −0.0266912 | − | 0.999644i | \(-0.508497\pi\) | ||||
−0.0266912 | + | 0.999644i | \(0.508497\pi\) | |||||||
\(608\) | −1.98016 | −0.0803063 | ||||||||
\(609\) | −20.7965 | −0.842717 | ||||||||
\(610\) | 2.89353 | 0.117156 | ||||||||
\(611\) | 28.5132 | 1.15352 | ||||||||
\(612\) | −0.782526 | −0.0316317 | ||||||||
\(613\) | −22.4731 | −0.907680 | −0.453840 | − | 0.891083i | \(-0.649946\pi\) | ||||
−0.453840 | + | 0.891083i | \(0.649946\pi\) | |||||||
\(614\) | −26.3131 | −1.06191 | ||||||||
\(615\) | −10.2413 | −0.412970 | ||||||||
\(616\) | −3.00453 | −0.121056 | ||||||||
\(617\) | 32.6429 | 1.31415 | 0.657077 | − | 0.753823i | \(-0.271793\pi\) | ||||
0.657077 | + | 0.753823i | \(0.271793\pi\) | |||||||
\(618\) | −13.3057 | −0.535232 | ||||||||
\(619\) | 21.0286 | 0.845211 | 0.422605 | − | 0.906314i | \(-0.361116\pi\) | ||||
0.422605 | + | 0.906314i | \(0.361116\pi\) | |||||||
\(620\) | −2.81506 | −0.113055 | ||||||||
\(621\) | 30.6303 | 1.22915 | ||||||||
\(622\) | 9.91646 | 0.397614 | ||||||||
\(623\) | −18.0598 | −0.723551 | ||||||||
\(624\) | 7.90214 | 0.316339 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.8046 | 1.07133 | ||||||||
\(627\) | −3.61664 | −0.144435 | ||||||||
\(628\) | −4.90260 | −0.195635 | ||||||||
\(629\) | 1.99629 | 0.0795972 | ||||||||
\(630\) | −1.00913 | −0.0402047 | ||||||||
\(631\) | −5.09926 | −0.202998 | −0.101499 | − | 0.994836i | \(-0.532364\pi\) | ||||
−0.101499 | + | 0.994836i | \(0.532364\pi\) | |||||||
\(632\) | 5.72249 | 0.227628 | ||||||||
\(633\) | 39.1817 | 1.55733 | ||||||||
\(634\) | 18.8464 | 0.748485 | ||||||||
\(635\) | 11.8099 | 0.468660 | ||||||||
\(636\) | 17.0653 | 0.676685 | ||||||||
\(637\) | −8.77086 | −0.347514 | ||||||||
\(638\) | −3.78974 | −0.150037 | ||||||||
\(639\) | 1.49482 | 0.0591343 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −14.1024 | −0.557013 | −0.278506 | − | 0.960434i | \(-0.589839\pi\) | ||||
−0.278506 | + | 0.960434i | \(0.589839\pi\) | |||||||
\(642\) | −7.50438 | −0.296174 | ||||||||
\(643\) | 3.29614 | 0.129987 | 0.0649935 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649935 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(644\) | 18.9134 | 0.745291 | ||||||||
\(645\) | 14.6339 | 0.576211 | ||||||||
\(646\) | 4.61349 | 0.181515 | ||||||||
\(647\) | −46.9087 | −1.84417 | −0.922086 | − | 0.386984i | \(-0.873517\pi\) | ||||
−0.922086 | + | 0.386984i | \(0.873517\pi\) | |||||||
\(648\) | −9.89480 | −0.388704 | ||||||||
\(649\) | −7.84290 | −0.307861 | ||||||||
\(650\) | −4.32653 | −0.169701 | ||||||||
\(651\) | −15.4479 | −0.605450 | ||||||||
\(652\) | −16.7822 | −0.657241 | ||||||||
\(653\) | 28.8352 | 1.12841 | 0.564205 | − | 0.825635i | \(-0.309183\pi\) | ||||
0.564205 | + | 0.825635i | \(0.309183\pi\) | |||||||
\(654\) | 28.6349 | 1.11971 | ||||||||
\(655\) | −15.2331 | −0.595208 | ||||||||
\(656\) | −5.60727 | −0.218927 | ||||||||
\(657\) | 0.335869 | 0.0131035 | ||||||||
\(658\) | −19.8008 | −0.771916 | ||||||||
\(659\) | −40.4273 | −1.57483 | −0.787413 | − | 0.616426i | \(-0.788580\pi\) | ||||
−0.787413 | + | 0.616426i | \(0.788580\pi\) | |||||||
\(660\) | −1.82644 | −0.0710939 | ||||||||
\(661\) | 19.0767 | 0.741998 | 0.370999 | − | 0.928633i | \(-0.379015\pi\) | ||||
0.370999 | + | 0.928633i | \(0.379015\pi\) | |||||||
\(662\) | 31.9810 | 1.24298 | ||||||||
\(663\) | −18.4108 | −0.715017 | ||||||||
\(664\) | −5.58265 | −0.216649 | ||||||||
\(665\) | 5.94947 | 0.230711 | ||||||||
\(666\) | −0.287783 | −0.0111514 | ||||||||
\(667\) | 23.8562 | 0.923714 | ||||||||
\(668\) | −11.4368 | −0.442502 | ||||||||
\(669\) | −39.5996 | −1.53101 | ||||||||
\(670\) | 9.07976 | 0.350782 | ||||||||
\(671\) | 2.89353 | 0.111704 | ||||||||
\(672\) | −5.48759 | −0.211688 | ||||||||
\(673\) | 36.8733 | 1.42136 | 0.710681 | − | 0.703514i | \(-0.248387\pi\) | ||||
0.710681 | + | 0.703514i | \(0.248387\pi\) | |||||||
\(674\) | −6.25893 | −0.241085 | ||||||||
\(675\) | 4.86586 | 0.187287 | ||||||||
\(676\) | 5.71889 | 0.219957 | ||||||||
\(677\) | 31.8011 | 1.22222 | 0.611108 | − | 0.791547i | \(-0.290724\pi\) | ||||
0.611108 | + | 0.791547i | \(0.290724\pi\) | |||||||
\(678\) | −26.1929 | −1.00593 | ||||||||
\(679\) | −23.5761 | −0.904768 | ||||||||
\(680\) | 2.32985 | 0.0893458 | ||||||||
\(681\) | −30.7467 | −1.17822 | ||||||||
\(682\) | −2.81506 | −0.107794 | ||||||||
\(683\) | 5.24583 | 0.200726 | 0.100363 | − | 0.994951i | \(-0.468000\pi\) | ||||
0.100363 | + | 0.994951i | \(0.468000\pi\) | |||||||
\(684\) | −0.665076 | −0.0254298 | ||||||||
\(685\) | −6.96108 | −0.265969 | ||||||||
\(686\) | −14.9409 | −0.570445 | ||||||||
\(687\) | 36.7784 | 1.40318 | ||||||||
\(688\) | 8.01229 | 0.305466 | ||||||||
\(689\) | 40.4250 | 1.54007 | ||||||||
\(690\) | 11.4973 | 0.437695 | ||||||||
\(691\) | −32.3766 | −1.23166 | −0.615832 | − | 0.787877i | \(-0.711180\pi\) | ||||
−0.615832 | + | 0.787877i | \(0.711180\pi\) | |||||||
\(692\) | −20.2277 | −0.768941 | ||||||||
\(693\) | −1.00913 | −0.0383337 | ||||||||
\(694\) | −15.9336 | −0.604832 | ||||||||
\(695\) | −0.0908223 | −0.00344509 | ||||||||
\(696\) | −6.92171 | −0.262367 | ||||||||
\(697\) | 13.0641 | 0.494838 | ||||||||
\(698\) | −22.7662 | −0.861714 | ||||||||
\(699\) | −38.4199 | −1.45317 | ||||||||
\(700\) | 3.00453 | 0.113561 | ||||||||
\(701\) | −17.4489 | −0.659035 | −0.329517 | − | 0.944149i | \(-0.606886\pi\) | ||||
−0.329517 | + | 0.944149i | \(0.606886\pi\) | |||||||
\(702\) | −21.0523 | −0.794569 | ||||||||
\(703\) | 1.69666 | 0.0639909 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −12.0368 | −0.453331 | ||||||||
\(706\) | 3.93216 | 0.147989 | ||||||||
\(707\) | −51.1391 | −1.92328 | ||||||||
\(708\) | −14.3246 | −0.538350 | ||||||||
\(709\) | −11.9616 | −0.449229 | −0.224614 | − | 0.974448i | \(-0.572112\pi\) | ||||
−0.224614 | + | 0.974448i | \(0.572112\pi\) | |||||||
\(710\) | −4.45061 | −0.167029 | ||||||||
\(711\) | 1.92201 | 0.0720809 | ||||||||
\(712\) | −6.01085 | −0.225266 | ||||||||
\(713\) | 17.7206 | 0.663643 | ||||||||
\(714\) | 12.7853 | 0.478477 | ||||||||
\(715\) | −4.32653 | −0.161803 | ||||||||
\(716\) | −8.05501 | −0.301030 | ||||||||
\(717\) | 31.9879 | 1.19461 | ||||||||
\(718\) | −19.6647 | −0.733882 | ||||||||
\(719\) | 45.1017 | 1.68201 | 0.841006 | − | 0.541026i | \(-0.181964\pi\) | ||||
0.841006 | + | 0.541026i | \(0.181964\pi\) | |||||||
\(720\) | −0.335869 | −0.0125171 | ||||||||
\(721\) | 21.8881 | 0.815157 | ||||||||
\(722\) | −15.0789 | −0.561180 | ||||||||
\(723\) | −8.63668 | −0.321202 | ||||||||
\(724\) | −3.96610 | −0.147399 | ||||||||
\(725\) | 3.78974 | 0.140747 | ||||||||
\(726\) | −1.82644 | −0.0677854 | ||||||||
\(727\) | −2.90588 | −0.107773 | −0.0538865 | − | 0.998547i | \(-0.517161\pi\) | ||||
−0.0538865 | + | 0.998547i | \(0.517161\pi\) | |||||||
\(728\) | −12.9992 | −0.481783 | ||||||||
\(729\) | 23.3382 | 0.864378 | ||||||||
\(730\) | −1.00000 | −0.0370117 | ||||||||
\(731\) | −18.6675 | −0.690441 | ||||||||
\(732\) | 5.28485 | 0.195334 | ||||||||
\(733\) | 31.9119 | 1.17869 | 0.589346 | − | 0.807881i | \(-0.299385\pi\) | ||||
0.589346 | + | 0.807881i | \(0.299385\pi\) | |||||||
\(734\) | 14.0691 | 0.519301 | ||||||||
\(735\) | 3.70260 | 0.136572 | ||||||||
\(736\) | 6.29494 | 0.232035 | ||||||||
\(737\) | 9.07976 | 0.334457 | ||||||||
\(738\) | −1.88331 | −0.0693255 | ||||||||
\(739\) | −20.5138 | −0.754614 | −0.377307 | − | 0.926088i | \(-0.623150\pi\) | ||||
−0.377307 | + | 0.926088i | \(0.623150\pi\) | |||||||
\(740\) | 0.856830 | 0.0314977 | ||||||||
\(741\) | −15.6475 | −0.574826 | ||||||||
\(742\) | −28.0729 | −1.03059 | ||||||||
\(743\) | 29.3013 | 1.07496 | 0.537479 | − | 0.843277i | \(-0.319377\pi\) | ||||
0.537479 | + | 0.843277i | \(0.319377\pi\) | |||||||
\(744\) | −5.14152 | −0.188497 | ||||||||
\(745\) | −11.6325 | −0.426181 | ||||||||
\(746\) | 7.03836 | 0.257693 | ||||||||
\(747\) | −1.87504 | −0.0686042 | ||||||||
\(748\) | 2.32985 | 0.0851879 | ||||||||
\(749\) | 12.3449 | 0.451073 | ||||||||
\(750\) | 1.82644 | 0.0666920 | ||||||||
\(751\) | −12.8441 | −0.468687 | −0.234344 | − | 0.972154i | \(-0.575294\pi\) | ||||
−0.234344 | + | 0.972154i | \(0.575294\pi\) | |||||||
\(752\) | −6.59031 | −0.240324 | ||||||||
\(753\) | 25.4715 | 0.928232 | ||||||||
\(754\) | −16.3964 | −0.597122 | ||||||||
\(755\) | 0.737844 | 0.0268529 | ||||||||
\(756\) | 14.6197 | 0.531712 | ||||||||
\(757\) | −44.1602 | −1.60503 | −0.802514 | − | 0.596633i | \(-0.796505\pi\) | ||||
−0.802514 | + | 0.596633i | \(0.796505\pi\) | |||||||
\(758\) | 24.9735 | 0.907079 | ||||||||
\(759\) | 11.4973 | 0.417326 | ||||||||
\(760\) | 1.98016 | 0.0718281 | ||||||||
\(761\) | −5.30498 | −0.192306 | −0.0961528 | − | 0.995367i | \(-0.530654\pi\) | ||||
−0.0961528 | + | 0.995367i | \(0.530654\pi\) | |||||||
\(762\) | 21.5699 | 0.781397 | ||||||||
\(763\) | −47.1052 | −1.70532 | ||||||||
\(764\) | 3.49901 | 0.126590 | ||||||||
\(765\) | 0.782526 | 0.0282923 | ||||||||
\(766\) | −2.32441 | −0.0839842 | ||||||||
\(767\) | −33.9326 | −1.22523 | ||||||||
\(768\) | −1.82644 | −0.0659058 | ||||||||
\(769\) | −37.0814 | −1.33719 | −0.668595 | − | 0.743627i | \(-0.733104\pi\) | ||||
−0.668595 | + | 0.743627i | \(0.733104\pi\) | |||||||
\(770\) | 3.00453 | 0.108276 | ||||||||
\(771\) | 54.8882 | 1.97675 | ||||||||
\(772\) | −18.0220 | −0.648627 | ||||||||
\(773\) | −17.4222 | −0.626634 | −0.313317 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313317 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(774\) | 2.69108 | 0.0967289 | ||||||||
\(775\) | 2.81506 | 0.101120 | ||||||||
\(776\) | −7.84684 | −0.281685 | ||||||||
\(777\) | 4.70193 | 0.168681 | ||||||||
\(778\) | −10.2655 | −0.368037 | ||||||||
\(779\) | 11.1033 | 0.397817 | ||||||||
\(780\) | −7.90214 | −0.282942 | ||||||||
\(781\) | −4.45061 | −0.159255 | ||||||||
\(782\) | −14.6663 | −0.524465 | ||||||||
\(783\) | 18.4403 | 0.659004 | ||||||||
\(784\) | 2.02723 | 0.0724009 | ||||||||
\(785\) | 4.90260 | 0.174981 | ||||||||
\(786\) | −27.8224 | −0.992391 | ||||||||
\(787\) | 53.2897 | 1.89957 | 0.949787 | − | 0.312898i | \(-0.101300\pi\) | ||||
0.949787 | + | 0.312898i | \(0.101300\pi\) | |||||||
\(788\) | −14.5436 | −0.518093 | ||||||||
\(789\) | −31.2726 | −1.11334 | ||||||||
\(790\) | −5.72249 | −0.203597 | ||||||||
\(791\) | 43.0880 | 1.53203 | ||||||||
\(792\) | −0.335869 | −0.0119346 | ||||||||
\(793\) | 12.5190 | 0.444561 | ||||||||
\(794\) | −8.96973 | −0.318324 | ||||||||
\(795\) | −17.0653 | −0.605245 | ||||||||
\(796\) | 3.37427 | 0.119598 | ||||||||
\(797\) | 39.8765 | 1.41250 | 0.706250 | − | 0.707963i | \(-0.250386\pi\) | ||||
0.706250 | + | 0.707963i | \(0.250386\pi\) | |||||||
\(798\) | 10.8663 | 0.384664 | ||||||||
\(799\) | 15.3545 | 0.543202 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −2.01886 | −0.0713330 | ||||||||
\(802\) | −27.9889 | −0.988322 | ||||||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | 16.5836 | 0.584858 | ||||||||
\(805\) | −18.9134 | −0.666609 | ||||||||
\(806\) | −12.1794 | −0.429002 | ||||||||
\(807\) | −24.6141 | −0.866458 | ||||||||
\(808\) | −17.0206 | −0.598784 | ||||||||
\(809\) | −42.9569 | −1.51028 | −0.755142 | − | 0.655562i | \(-0.772432\pi\) | ||||
−0.755142 | + | 0.655562i | \(0.772432\pi\) | |||||||
\(810\) | 9.89480 | 0.347668 | ||||||||
\(811\) | 6.83735 | 0.240092 | 0.120046 | − | 0.992768i | \(-0.461696\pi\) | ||||
0.120046 | + | 0.992768i | \(0.461696\pi\) | |||||||
\(812\) | 11.3864 | 0.399584 | ||||||||
\(813\) | 48.7733 | 1.71055 | ||||||||
\(814\) | 0.856830 | 0.0300319 | ||||||||
\(815\) | 16.7822 | 0.587854 | ||||||||
\(816\) | 4.25533 | 0.148966 | ||||||||
\(817\) | −15.8656 | −0.555069 | ||||||||
\(818\) | −19.0794 | −0.667096 | ||||||||
\(819\) | −4.36604 | −0.152562 | ||||||||
\(820\) | 5.60727 | 0.195814 | ||||||||
\(821\) | 6.83310 | 0.238477 | 0.119238 | − | 0.992866i | \(-0.461955\pi\) | ||||
0.119238 | + | 0.992866i | \(0.461955\pi\) | |||||||
\(822\) | −12.7140 | −0.443451 | ||||||||
\(823\) | −0.603298 | −0.0210296 | −0.0105148 | − | 0.999945i | \(-0.503347\pi\) | ||||
−0.0105148 | + | 0.999945i | \(0.503347\pi\) | |||||||
\(824\) | 7.28504 | 0.253786 | ||||||||
\(825\) | 1.82644 | 0.0635883 | ||||||||
\(826\) | 23.5643 | 0.819905 | ||||||||
\(827\) | 25.3974 | 0.883155 | 0.441577 | − | 0.897223i | \(-0.354419\pi\) | ||||
0.441577 | + | 0.897223i | \(0.354419\pi\) | |||||||
\(828\) | 2.11428 | 0.0734762 | ||||||||
\(829\) | −10.8485 | −0.376784 | −0.188392 | − | 0.982094i | \(-0.560328\pi\) | ||||
−0.188392 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(830\) | 5.58265 | 0.193777 | ||||||||
\(831\) | −1.40307 | −0.0486719 | ||||||||
\(832\) | −4.32653 | −0.149996 | ||||||||
\(833\) | −4.72314 | −0.163647 | ||||||||
\(834\) | −0.165881 | −0.00574400 | ||||||||
\(835\) | 11.4368 | 0.395786 | ||||||||
\(836\) | 1.98016 | 0.0684854 | ||||||||
\(837\) | 13.6977 | 0.473461 | ||||||||
\(838\) | −32.8434 | −1.13455 | ||||||||
\(839\) | 42.3663 | 1.46265 | 0.731324 | − | 0.682030i | \(-0.238903\pi\) | ||||
0.731324 | + | 0.682030i | \(0.238903\pi\) | |||||||
\(840\) | 5.48759 | 0.189340 | ||||||||
\(841\) | −14.6379 | −0.504755 | ||||||||
\(842\) | 25.4036 | 0.875465 | ||||||||
\(843\) | −3.06375 | −0.105521 | ||||||||
\(844\) | −21.4525 | −0.738427 | ||||||||
\(845\) | −5.71889 | −0.196736 | ||||||||
\(846\) | −2.21348 | −0.0761011 | ||||||||
\(847\) | 3.00453 | 0.103237 | ||||||||
\(848\) | −9.34352 | −0.320858 | ||||||||
\(849\) | −13.3868 | −0.459432 | ||||||||
\(850\) | −2.32985 | −0.0799133 | ||||||||
\(851\) | −5.39369 | −0.184893 | ||||||||
\(852\) | −8.12876 | −0.278487 | ||||||||
\(853\) | 40.0418 | 1.37100 | 0.685502 | − | 0.728071i | \(-0.259583\pi\) | ||||
0.685502 | + | 0.728071i | \(0.259583\pi\) | |||||||
\(854\) | −8.69371 | −0.297493 | ||||||||
\(855\) | 0.665076 | 0.0227451 | ||||||||
\(856\) | 4.10876 | 0.140434 | ||||||||
\(857\) | 1.41773 | 0.0484288 | 0.0242144 | − | 0.999707i | \(-0.492292\pi\) | ||||
0.0242144 | + | 0.999707i | \(0.492292\pi\) | |||||||
\(858\) | −7.90214 | −0.269774 | ||||||||
\(859\) | −13.3345 | −0.454967 | −0.227483 | − | 0.973782i | \(-0.573050\pi\) | ||||
−0.227483 | + | 0.973782i | \(0.573050\pi\) | |||||||
\(860\) | −8.01229 | −0.273217 | ||||||||
\(861\) | 30.7704 | 1.04865 | ||||||||
\(862\) | 28.2811 | 0.963260 | ||||||||
\(863\) | 22.3794 | 0.761804 | 0.380902 | − | 0.924615i | \(-0.375614\pi\) | ||||
0.380902 | + | 0.924615i | \(0.375614\pi\) | |||||||
\(864\) | 4.86586 | 0.165540 | ||||||||
\(865\) | 20.2277 | 0.687762 | ||||||||
\(866\) | −11.4205 | −0.388084 | ||||||||
\(867\) | 21.1351 | 0.717787 | ||||||||
\(868\) | 8.45794 | 0.287081 | ||||||||
\(869\) | −5.72249 | −0.194122 | ||||||||
\(870\) | 6.92171 | 0.234668 | ||||||||
\(871\) | 39.2839 | 1.33108 | ||||||||
\(872\) | −15.6780 | −0.530925 | ||||||||
\(873\) | −2.63551 | −0.0891986 | ||||||||
\(874\) | −12.4650 | −0.421635 | ||||||||
\(875\) | −3.00453 | −0.101572 | ||||||||
\(876\) | −1.82644 | −0.0617096 | ||||||||
\(877\) | 5.18944 | 0.175235 | 0.0876175 | − | 0.996154i | \(-0.472075\pi\) | ||||
0.0876175 | + | 0.996154i | \(0.472075\pi\) | |||||||
\(878\) | −25.6469 | −0.865541 | ||||||||
\(879\) | 13.8283 | 0.466415 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 45.0059 | 1.51629 | 0.758144 | − | 0.652087i | \(-0.226106\pi\) | ||||
0.758144 | + | 0.652087i | \(0.226106\pi\) | |||||||
\(882\) | 0.680883 | 0.0229265 | ||||||||
\(883\) | −32.9850 | −1.11003 | −0.555016 | − | 0.831840i | \(-0.687288\pi\) | ||||
−0.555016 | + | 0.831840i | \(0.687288\pi\) | |||||||
\(884\) | 10.0802 | 0.339033 | ||||||||
\(885\) | 14.3246 | 0.481515 | ||||||||
\(886\) | 34.3263 | 1.15322 | ||||||||
\(887\) | −16.0608 | −0.539267 | −0.269634 | − | 0.962963i | \(-0.586903\pi\) | ||||
−0.269634 | + | 0.962963i | \(0.586903\pi\) | |||||||
\(888\) | 1.56494 | 0.0525161 | ||||||||
\(889\) | −35.4831 | −1.19007 | ||||||||
\(890\) | 6.01085 | 0.201484 | ||||||||
\(891\) | 9.89480 | 0.331488 | ||||||||
\(892\) | 21.6813 | 0.725944 | ||||||||
\(893\) | 13.0499 | 0.436698 | ||||||||
\(894\) | −21.2460 | −0.710572 | ||||||||
\(895\) | 8.05501 | 0.269249 | ||||||||
\(896\) | 3.00453 | 0.100374 | ||||||||
\(897\) | 49.7435 | 1.66089 | ||||||||
\(898\) | −24.9408 | −0.832284 | ||||||||
\(899\) | 10.6683 | 0.355809 | ||||||||
\(900\) | 0.335869 | 0.0111956 | ||||||||
\(901\) | 21.7690 | 0.725231 | ||||||||
\(902\) | 5.60727 | 0.186702 | ||||||||
\(903\) | −43.9682 | −1.46317 | ||||||||
\(904\) | 14.3410 | 0.476974 | ||||||||
\(905\) | 3.96610 | 0.131838 | ||||||||
\(906\) | 1.34762 | 0.0447718 | ||||||||
\(907\) | −41.0935 | −1.36449 | −0.682243 | − | 0.731125i | \(-0.738996\pi\) | ||||
−0.682243 | + | 0.731125i | \(0.738996\pi\) | |||||||
\(908\) | 16.8342 | 0.558664 | ||||||||
\(909\) | −5.71671 | −0.189611 | ||||||||
\(910\) | 12.9992 | 0.430920 | ||||||||
\(911\) | 52.6723 | 1.74511 | 0.872555 | − | 0.488515i | \(-0.162461\pi\) | ||||
0.872555 | + | 0.488515i | \(0.162461\pi\) | |||||||
\(912\) | 3.61664 | 0.119759 | ||||||||
\(913\) | 5.58265 | 0.184759 | ||||||||
\(914\) | 8.81941 | 0.291720 | ||||||||
\(915\) | −5.28485 | −0.174712 | ||||||||
\(916\) | −20.1367 | −0.665336 | ||||||||
\(917\) | 45.7685 | 1.51141 | ||||||||
\(918\) | −11.3368 | −0.374169 | ||||||||
\(919\) | 2.69139 | 0.0887808 | 0.0443904 | − | 0.999014i | \(-0.485865\pi\) | ||||
0.0443904 | + | 0.999014i | \(0.485865\pi\) | |||||||
\(920\) | −6.29494 | −0.207538 | ||||||||
\(921\) | 48.0592 | 1.58360 | ||||||||
\(922\) | −16.4185 | −0.540716 | ||||||||
\(923\) | −19.2557 | −0.633810 | ||||||||
\(924\) | 5.48759 | 0.180528 | ||||||||
\(925\) | −0.856830 | −0.0281724 | ||||||||
\(926\) | −20.3061 | −0.667301 | ||||||||
\(927\) | 2.44682 | 0.0803641 | ||||||||
\(928\) | 3.78974 | 0.124404 | ||||||||
\(929\) | −4.03549 | −0.132400 | −0.0662000 | − | 0.997806i | \(-0.521088\pi\) | ||||
−0.0662000 | + | 0.997806i | \(0.521088\pi\) | |||||||
\(930\) | 5.14152 | 0.168597 | ||||||||
\(931\) | −4.01424 | −0.131561 | ||||||||
\(932\) | 21.0354 | 0.689039 | ||||||||
\(933\) | −18.1118 | −0.592953 | ||||||||
\(934\) | −20.5992 | −0.674026 | ||||||||
\(935\) | −2.32985 | −0.0761943 | ||||||||
\(936\) | −1.45315 | −0.0474977 | ||||||||
\(937\) | 36.0105 | 1.17641 | 0.588207 | − | 0.808711i | \(-0.299834\pi\) | ||||
0.588207 | + | 0.808711i | \(0.299834\pi\) | |||||||
\(938\) | −27.2804 | −0.890738 | ||||||||
\(939\) | −48.9570 | −1.59765 | ||||||||
\(940\) | 6.59031 | 0.214952 | ||||||||
\(941\) | −47.8388 | −1.55950 | −0.779750 | − | 0.626091i | \(-0.784654\pi\) | ||||
−0.779750 | + | 0.626091i | \(0.784654\pi\) | |||||||
\(942\) | 8.95430 | 0.291747 | ||||||||
\(943\) | −35.2974 | −1.14944 | ||||||||
\(944\) | 7.84290 | 0.255265 | ||||||||
\(945\) | −14.6197 | −0.475577 | ||||||||
\(946\) | −8.01229 | −0.260502 | ||||||||
\(947\) | 11.9931 | 0.389723 | 0.194862 | − | 0.980831i | \(-0.437574\pi\) | ||||
0.194862 | + | 0.980831i | \(0.437574\pi\) | |||||||
\(948\) | −10.4518 | −0.339457 | ||||||||
\(949\) | −4.32653 | −0.140445 | ||||||||
\(950\) | −1.98016 | −0.0642450 | ||||||||
\(951\) | −34.4217 | −1.11620 | ||||||||
\(952\) | −7.00012 | −0.226875 | ||||||||
\(953\) | 4.31087 | 0.139643 | 0.0698214 | − | 0.997560i | \(-0.477757\pi\) | ||||
0.0698214 | + | 0.997560i | \(0.477757\pi\) | |||||||
\(954\) | −3.13820 | −0.101603 | ||||||||
\(955\) | −3.49901 | −0.113225 | ||||||||
\(956\) | −17.5138 | −0.566438 | ||||||||
\(957\) | 6.92171 | 0.223747 | ||||||||
\(958\) | 17.6387 | 0.569880 | ||||||||
\(959\) | 20.9148 | 0.675375 | ||||||||
\(960\) | 1.82644 | 0.0589480 | ||||||||
\(961\) | −23.0754 | −0.744369 | ||||||||
\(962\) | 3.70710 | 0.119522 | ||||||||
\(963\) | 1.38001 | 0.0444700 | ||||||||
\(964\) | 4.72871 | 0.152301 | ||||||||
\(965\) | 18.0220 | 0.580150 | ||||||||
\(966\) | −34.5441 | −1.11144 | ||||||||
\(967\) | 40.1249 | 1.29033 | 0.645165 | − | 0.764043i | \(-0.276789\pi\) | ||||
0.645165 | + | 0.764043i | \(0.276789\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −8.42625 | −0.270690 | ||||||||
\(970\) | 7.84684 | 0.251947 | ||||||||
\(971\) | −9.22327 | −0.295989 | −0.147994 | − | 0.988988i | \(-0.547282\pi\) | ||||
−0.147994 | + | 0.988988i | \(0.547282\pi\) | |||||||
\(972\) | 3.47463 | 0.111449 | ||||||||
\(973\) | 0.272879 | 0.00874809 | ||||||||
\(974\) | −5.31105 | −0.170177 | ||||||||
\(975\) | 7.90214 | 0.253071 | ||||||||
\(976\) | −2.89353 | −0.0926197 | ||||||||
\(977\) | 1.29895 | 0.0415569 | 0.0207785 | − | 0.999784i | \(-0.493386\pi\) | ||||
0.0207785 | + | 0.999784i | \(0.493386\pi\) | |||||||
\(978\) | 30.6516 | 0.980129 | ||||||||
\(979\) | 6.01085 | 0.192108 | ||||||||
\(980\) | −2.02723 | −0.0647574 | ||||||||
\(981\) | −5.26577 | −0.168123 | ||||||||
\(982\) | −34.1717 | −1.09046 | ||||||||
\(983\) | −21.6788 | −0.691446 | −0.345723 | − | 0.938337i | \(-0.612366\pi\) | ||||
−0.345723 | + | 0.938337i | \(0.612366\pi\) | |||||||
\(984\) | 10.2413 | 0.326481 | ||||||||
\(985\) | 14.5436 | 0.463396 | ||||||||
\(986\) | −8.82953 | −0.281189 | ||||||||
\(987\) | 36.1649 | 1.15114 | ||||||||
\(988\) | 8.56725 | 0.272560 | ||||||||
\(989\) | 50.4369 | 1.60380 | ||||||||
\(990\) | 0.335869 | 0.0106746 | ||||||||
\(991\) | 19.0629 | 0.605554 | 0.302777 | − | 0.953061i | \(-0.402086\pi\) | ||||
0.302777 | + | 0.953061i | \(0.402086\pi\) | |||||||
\(992\) | 2.81506 | 0.0893782 | ||||||||
\(993\) | −58.4113 | −1.85363 | ||||||||
\(994\) | 13.3720 | 0.424135 | ||||||||
\(995\) | −3.37427 | −0.106972 | ||||||||
\(996\) | 10.1964 | 0.323084 | ||||||||
\(997\) | 2.65307 | 0.0840235 | 0.0420118 | − | 0.999117i | \(-0.486623\pi\) | ||||
0.0420118 | + | 0.999117i | \(0.486623\pi\) | |||||||
\(998\) | 3.62548 | 0.114763 | ||||||||
\(999\) | −4.16922 | −0.131908 |
(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 | 8030.2.a.bf.1.5 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8030.2.a.bf.1.5 | ✓ | 15 | 1.1 | even | 1 | trivial |