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: | \(0\) |
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: | \( x^{15} - 3 x^{14} - 24 x^{13} + 64 x^{12} + 237 x^{11} - 524 x^{10} - 1225 x^{9} + 2074 x^{8} + 3463 x^{7} - 4142 x^{6} - 5157 x^{5} + 3892 x^{4} + 3622 x^{3} - 1239 x^{2} + \cdots - 52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.51118\) 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 | ||||||||
\(3\) | −1.51118 | −0.872479 | −0.436240 | − | 0.899831i | \(-0.643690\pi\) | ||||
−0.436240 | + | 0.899831i | \(0.643690\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.51118 | 0.616936 | ||||||||
\(7\) | −0.990203 | −0.374262 | −0.187131 | − | 0.982335i | \(-0.559919\pi\) | ||||
−0.187131 | + | 0.982335i | \(0.559919\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.716341 | −0.238780 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.51118 | −0.436240 | ||||||||
\(13\) | −4.51816 | −1.25311 | −0.626557 | − | 0.779376i | \(-0.715536\pi\) | ||||
−0.626557 | + | 0.779376i | \(0.715536\pi\) | |||||||
\(14\) | 0.990203 | 0.264643 | ||||||||
\(15\) | −1.51118 | −0.390184 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.85206 | 1.17680 | 0.588399 | − | 0.808571i | \(-0.299759\pi\) | ||||
0.588399 | + | 0.808571i | \(0.299759\pi\) | |||||||
\(18\) | 0.716341 | 0.168843 | ||||||||
\(19\) | −6.04845 | −1.38761 | −0.693804 | − | 0.720164i | \(-0.744067\pi\) | ||||
−0.693804 | + | 0.720164i | \(0.744067\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.49637 | 0.326535 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 6.91028 | 1.44089 | 0.720446 | − | 0.693511i | \(-0.243937\pi\) | ||||
0.720446 | + | 0.693511i | \(0.243937\pi\) | |||||||
\(24\) | 1.51118 | 0.308468 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.51816 | 0.886085 | ||||||||
\(27\) | 5.61605 | 1.08081 | ||||||||
\(28\) | −0.990203 | −0.187131 | ||||||||
\(29\) | 7.68677 | 1.42740 | 0.713699 | − | 0.700453i | \(-0.247019\pi\) | ||||
0.713699 | + | 0.700453i | \(0.247019\pi\) | |||||||
\(30\) | 1.51118 | 0.275902 | ||||||||
\(31\) | 5.17086 | 0.928714 | 0.464357 | − | 0.885648i | \(-0.346285\pi\) | ||||
0.464357 | + | 0.885648i | \(0.346285\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.51118 | 0.263062 | ||||||||
\(34\) | −4.85206 | −0.832122 | ||||||||
\(35\) | −0.990203 | −0.167375 | ||||||||
\(36\) | −0.716341 | −0.119390 | ||||||||
\(37\) | −5.91021 | −0.971633 | −0.485816 | − | 0.874061i | \(-0.661478\pi\) | ||||
−0.485816 | + | 0.874061i | \(0.661478\pi\) | |||||||
\(38\) | 6.04845 | 0.981188 | ||||||||
\(39\) | 6.82775 | 1.09331 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −6.51071 | −1.01680 | −0.508401 | − | 0.861121i | \(-0.669763\pi\) | ||||
−0.508401 | + | 0.861121i | \(0.669763\pi\) | |||||||
\(42\) | −1.49637 | −0.230895 | ||||||||
\(43\) | −1.00014 | −0.152520 | −0.0762602 | − | 0.997088i | \(-0.524298\pi\) | ||||
−0.0762602 | + | 0.997088i | \(0.524298\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −0.716341 | −0.106786 | ||||||||
\(46\) | −6.91028 | −1.01886 | ||||||||
\(47\) | 1.74147 | 0.254019 | 0.127010 | − | 0.991901i | \(-0.459462\pi\) | ||||
0.127010 | + | 0.991901i | \(0.459462\pi\) | |||||||
\(48\) | −1.51118 | −0.218120 | ||||||||
\(49\) | −6.01950 | −0.859928 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −7.33233 | −1.02673 | ||||||||
\(52\) | −4.51816 | −0.626557 | ||||||||
\(53\) | −7.27787 | −0.999692 | −0.499846 | − | 0.866114i | \(-0.666610\pi\) | ||||
−0.499846 | + | 0.866114i | \(0.666610\pi\) | |||||||
\(54\) | −5.61605 | −0.764248 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0.990203 | 0.132321 | ||||||||
\(57\) | 9.14028 | 1.21066 | ||||||||
\(58\) | −7.68677 | −1.00932 | ||||||||
\(59\) | −6.92339 | −0.901349 | −0.450675 | − | 0.892688i | \(-0.648817\pi\) | ||||
−0.450675 | + | 0.892688i | \(0.648817\pi\) | |||||||
\(60\) | −1.51118 | −0.195092 | ||||||||
\(61\) | 7.09406 | 0.908301 | 0.454150 | − | 0.890925i | \(-0.349943\pi\) | ||||
0.454150 | + | 0.890925i | \(0.349943\pi\) | |||||||
\(62\) | −5.17086 | −0.656700 | ||||||||
\(63\) | 0.709323 | 0.0893663 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.51816 | −0.560409 | ||||||||
\(66\) | −1.51118 | −0.186013 | ||||||||
\(67\) | −8.62196 | −1.05334 | −0.526670 | − | 0.850070i | \(-0.676560\pi\) | ||||
−0.526670 | + | 0.850070i | \(0.676560\pi\) | |||||||
\(68\) | 4.85206 | 0.588399 | ||||||||
\(69\) | −10.4427 | −1.25715 | ||||||||
\(70\) | 0.990203 | 0.118352 | ||||||||
\(71\) | −10.7024 | −1.27014 | −0.635068 | − | 0.772456i | \(-0.719028\pi\) | ||||
−0.635068 | + | 0.772456i | \(0.719028\pi\) | |||||||
\(72\) | 0.716341 | 0.0844216 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | 5.91021 | 0.687048 | ||||||||
\(75\) | −1.51118 | −0.174496 | ||||||||
\(76\) | −6.04845 | −0.693804 | ||||||||
\(77\) | 0.990203 | 0.112844 | ||||||||
\(78\) | −6.82775 | −0.773090 | ||||||||
\(79\) | −1.71773 | −0.193260 | −0.0966299 | − | 0.995320i | \(-0.530806\pi\) | ||||
−0.0966299 | + | 0.995320i | \(0.530806\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −6.33783 | −0.704204 | ||||||||
\(82\) | 6.51071 | 0.718987 | ||||||||
\(83\) | 3.56466 | 0.391272 | 0.195636 | − | 0.980677i | \(-0.437323\pi\) | ||||
0.195636 | + | 0.980677i | \(0.437323\pi\) | |||||||
\(84\) | 1.49637 | 0.163268 | ||||||||
\(85\) | 4.85206 | 0.526280 | ||||||||
\(86\) | 1.00014 | 0.107848 | ||||||||
\(87\) | −11.6161 | −1.24537 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 6.63971 | 0.703808 | 0.351904 | − | 0.936036i | \(-0.385534\pi\) | ||||
0.351904 | + | 0.936036i | \(0.385534\pi\) | |||||||
\(90\) | 0.716341 | 0.0755090 | ||||||||
\(91\) | 4.47390 | 0.468992 | ||||||||
\(92\) | 6.91028 | 0.720446 | ||||||||
\(93\) | −7.81409 | −0.810284 | ||||||||
\(94\) | −1.74147 | −0.179619 | ||||||||
\(95\) | −6.04845 | −0.620557 | ||||||||
\(96\) | 1.51118 | 0.154234 | ||||||||
\(97\) | −2.00346 | −0.203421 | −0.101710 | − | 0.994814i | \(-0.532432\pi\) | ||||
−0.101710 | + | 0.994814i | \(0.532432\pi\) | |||||||
\(98\) | 6.01950 | 0.608061 | ||||||||
\(99\) | 0.716341 | 0.0719950 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.947272 | 0.0942571 | 0.0471285 | − | 0.998889i | \(-0.484993\pi\) | ||||
0.0471285 | + | 0.998889i | \(0.484993\pi\) | |||||||
\(102\) | 7.33233 | 0.726009 | ||||||||
\(103\) | −14.1558 | −1.39482 | −0.697408 | − | 0.716674i | \(-0.745664\pi\) | ||||
−0.697408 | + | 0.716674i | \(0.745664\pi\) | |||||||
\(104\) | 4.51816 | 0.443042 | ||||||||
\(105\) | 1.49637 | 0.146031 | ||||||||
\(106\) | 7.27787 | 0.706889 | ||||||||
\(107\) | 6.31073 | 0.610081 | 0.305040 | − | 0.952339i | \(-0.401330\pi\) | ||||
0.305040 | + | 0.952339i | \(0.401330\pi\) | |||||||
\(108\) | 5.61605 | 0.540405 | ||||||||
\(109\) | −17.9388 | −1.71823 | −0.859115 | − | 0.511783i | \(-0.828985\pi\) | ||||
−0.859115 | + | 0.511783i | \(0.828985\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 8.93138 | 0.847729 | ||||||||
\(112\) | −0.990203 | −0.0935654 | ||||||||
\(113\) | 13.8348 | 1.30147 | 0.650734 | − | 0.759306i | \(-0.274461\pi\) | ||||
0.650734 | + | 0.759306i | \(0.274461\pi\) | |||||||
\(114\) | −9.14028 | −0.856066 | ||||||||
\(115\) | 6.91028 | 0.644387 | ||||||||
\(116\) | 7.68677 | 0.713699 | ||||||||
\(117\) | 3.23655 | 0.299219 | ||||||||
\(118\) | 6.92339 | 0.637350 | ||||||||
\(119\) | −4.80453 | −0.440430 | ||||||||
\(120\) | 1.51118 | 0.137951 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.09406 | −0.642266 | ||||||||
\(123\) | 9.83884 | 0.887138 | ||||||||
\(124\) | 5.17086 | 0.464357 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.709323 | −0.0631915 | ||||||||
\(127\) | 6.19048 | 0.549316 | 0.274658 | − | 0.961542i | \(-0.411435\pi\) | ||||
0.274658 | + | 0.961542i | \(0.411435\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.51139 | 0.133071 | ||||||||
\(130\) | 4.51816 | 0.396269 | ||||||||
\(131\) | −1.73521 | −0.151606 | −0.0758032 | − | 0.997123i | \(-0.524152\pi\) | ||||
−0.0758032 | + | 0.997123i | \(0.524152\pi\) | |||||||
\(132\) | 1.51118 | 0.131531 | ||||||||
\(133\) | 5.98919 | 0.519329 | ||||||||
\(134\) | 8.62196 | 0.744824 | ||||||||
\(135\) | 5.61605 | 0.483353 | ||||||||
\(136\) | −4.85206 | −0.416061 | ||||||||
\(137\) | 5.75063 | 0.491309 | 0.245655 | − | 0.969357i | \(-0.420997\pi\) | ||||
0.245655 | + | 0.969357i | \(0.420997\pi\) | |||||||
\(138\) | 10.4427 | 0.888938 | ||||||||
\(139\) | −22.3773 | −1.89802 | −0.949009 | − | 0.315249i | \(-0.897912\pi\) | ||||
−0.949009 | + | 0.315249i | \(0.897912\pi\) | |||||||
\(140\) | −0.990203 | −0.0836874 | ||||||||
\(141\) | −2.63167 | −0.221626 | ||||||||
\(142\) | 10.7024 | 0.898122 | ||||||||
\(143\) | 4.51816 | 0.377828 | ||||||||
\(144\) | −0.716341 | −0.0596951 | ||||||||
\(145\) | 7.68677 | 0.638351 | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | 9.09653 | 0.750269 | ||||||||
\(148\) | −5.91021 | −0.485816 | ||||||||
\(149\) | 5.81913 | 0.476722 | 0.238361 | − | 0.971177i | \(-0.423390\pi\) | ||||
0.238361 | + | 0.971177i | \(0.423390\pi\) | |||||||
\(150\) | 1.51118 | 0.123387 | ||||||||
\(151\) | 16.6560 | 1.35545 | 0.677725 | − | 0.735316i | \(-0.262966\pi\) | ||||
0.677725 | + | 0.735316i | \(0.262966\pi\) | |||||||
\(152\) | 6.04845 | 0.490594 | ||||||||
\(153\) | −3.47573 | −0.280996 | ||||||||
\(154\) | −0.990203 | −0.0797928 | ||||||||
\(155\) | 5.17086 | 0.415334 | ||||||||
\(156\) | 6.82775 | 0.546657 | ||||||||
\(157\) | 2.55559 | 0.203959 | 0.101979 | − | 0.994787i | \(-0.467482\pi\) | ||||
0.101979 | + | 0.994787i | \(0.467482\pi\) | |||||||
\(158\) | 1.71773 | 0.136655 | ||||||||
\(159\) | 10.9982 | 0.872210 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −6.84258 | −0.539271 | ||||||||
\(162\) | 6.33783 | 0.497947 | ||||||||
\(163\) | −8.37109 | −0.655675 | −0.327837 | − | 0.944734i | \(-0.606320\pi\) | ||||
−0.327837 | + | 0.944734i | \(0.606320\pi\) | |||||||
\(164\) | −6.51071 | −0.508401 | ||||||||
\(165\) | 1.51118 | 0.117645 | ||||||||
\(166\) | −3.56466 | −0.276671 | ||||||||
\(167\) | 23.7180 | 1.83535 | 0.917677 | − | 0.397326i | \(-0.130062\pi\) | ||||
0.917677 | + | 0.397326i | \(0.130062\pi\) | |||||||
\(168\) | −1.49637 | −0.115448 | ||||||||
\(169\) | 7.41380 | 0.570293 | ||||||||
\(170\) | −4.85206 | −0.372136 | ||||||||
\(171\) | 4.33275 | 0.331334 | ||||||||
\(172\) | −1.00014 | −0.0762602 | ||||||||
\(173\) | 20.5031 | 1.55882 | 0.779411 | − | 0.626513i | \(-0.215519\pi\) | ||||
0.779411 | + | 0.626513i | \(0.215519\pi\) | |||||||
\(174\) | 11.6161 | 0.880612 | ||||||||
\(175\) | −0.990203 | −0.0748523 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 10.4625 | 0.786408 | ||||||||
\(178\) | −6.63971 | −0.497667 | ||||||||
\(179\) | −6.97635 | −0.521437 | −0.260719 | − | 0.965415i | \(-0.583959\pi\) | ||||
−0.260719 | + | 0.965415i | \(0.583959\pi\) | |||||||
\(180\) | −0.716341 | −0.0533929 | ||||||||
\(181\) | 13.2575 | 0.985422 | 0.492711 | − | 0.870193i | \(-0.336006\pi\) | ||||
0.492711 | + | 0.870193i | \(0.336006\pi\) | |||||||
\(182\) | −4.47390 | −0.331627 | ||||||||
\(183\) | −10.7204 | −0.792473 | ||||||||
\(184\) | −6.91028 | −0.509432 | ||||||||
\(185\) | −5.91021 | −0.434527 | ||||||||
\(186\) | 7.81409 | 0.572957 | ||||||||
\(187\) | −4.85206 | −0.354818 | ||||||||
\(188\) | 1.74147 | 0.127010 | ||||||||
\(189\) | −5.56103 | −0.404506 | ||||||||
\(190\) | 6.04845 | 0.438800 | ||||||||
\(191\) | −11.9475 | −0.864490 | −0.432245 | − | 0.901756i | \(-0.642279\pi\) | ||||
−0.432245 | + | 0.901756i | \(0.642279\pi\) | |||||||
\(192\) | −1.51118 | −0.109060 | ||||||||
\(193\) | −14.4429 | −1.03962 | −0.519811 | − | 0.854281i | \(-0.673998\pi\) | ||||
−0.519811 | + | 0.854281i | \(0.673998\pi\) | |||||||
\(194\) | 2.00346 | 0.143840 | ||||||||
\(195\) | 6.82775 | 0.488945 | ||||||||
\(196\) | −6.01950 | −0.429964 | ||||||||
\(197\) | 7.88836 | 0.562022 | 0.281011 | − | 0.959704i | \(-0.409330\pi\) | ||||
0.281011 | + | 0.959704i | \(0.409330\pi\) | |||||||
\(198\) | −0.716341 | −0.0509081 | ||||||||
\(199\) | −9.33569 | −0.661790 | −0.330895 | − | 0.943668i | \(-0.607351\pi\) | ||||
−0.330895 | + | 0.943668i | \(0.607351\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 13.0293 | 0.919017 | ||||||||
\(202\) | −0.947272 | −0.0666498 | ||||||||
\(203\) | −7.61146 | −0.534220 | ||||||||
\(204\) | −7.33233 | −0.513366 | ||||||||
\(205\) | −6.51071 | −0.454727 | ||||||||
\(206\) | 14.1558 | 0.986284 | ||||||||
\(207\) | −4.95012 | −0.344057 | ||||||||
\(208\) | −4.51816 | −0.313278 | ||||||||
\(209\) | 6.04845 | 0.418380 | ||||||||
\(210\) | −1.49637 | −0.103260 | ||||||||
\(211\) | 18.7964 | 1.29400 | 0.646998 | − | 0.762491i | \(-0.276024\pi\) | ||||
0.646998 | + | 0.762491i | \(0.276024\pi\) | |||||||
\(212\) | −7.27787 | −0.499846 | ||||||||
\(213\) | 16.1732 | 1.10817 | ||||||||
\(214\) | −6.31073 | −0.431392 | ||||||||
\(215\) | −1.00014 | −0.0682092 | ||||||||
\(216\) | −5.61605 | −0.382124 | ||||||||
\(217\) | −5.12020 | −0.347582 | ||||||||
\(218\) | 17.9388 | 1.21497 | ||||||||
\(219\) | 1.51118 | 0.102116 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −21.9224 | −1.47466 | ||||||||
\(222\) | −8.93138 | −0.599435 | ||||||||
\(223\) | −12.8435 | −0.860061 | −0.430031 | − | 0.902814i | \(-0.641497\pi\) | ||||
−0.430031 | + | 0.902814i | \(0.641497\pi\) | |||||||
\(224\) | 0.990203 | 0.0661607 | ||||||||
\(225\) | −0.716341 | −0.0477561 | ||||||||
\(226\) | −13.8348 | −0.920276 | ||||||||
\(227\) | 22.0558 | 1.46389 | 0.731946 | − | 0.681362i | \(-0.238612\pi\) | ||||
0.731946 | + | 0.681362i | \(0.238612\pi\) | |||||||
\(228\) | 9.14028 | 0.605330 | ||||||||
\(229\) | 3.31830 | 0.219279 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(230\) | −6.91028 | −0.455650 | ||||||||
\(231\) | −1.49637 | −0.0984541 | ||||||||
\(232\) | −7.68677 | −0.504661 | ||||||||
\(233\) | 16.4539 | 1.07793 | 0.538964 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538964 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(234\) | −3.23655 | −0.211580 | ||||||||
\(235\) | 1.74147 | 0.113601 | ||||||||
\(236\) | −6.92339 | −0.450675 | ||||||||
\(237\) | 2.59580 | 0.168615 | ||||||||
\(238\) | 4.80453 | 0.311431 | ||||||||
\(239\) | −6.03920 | −0.390643 | −0.195322 | − | 0.980739i | \(-0.562575\pi\) | ||||
−0.195322 | + | 0.980739i | \(0.562575\pi\) | |||||||
\(240\) | −1.51118 | −0.0975461 | ||||||||
\(241\) | 3.84885 | 0.247926 | 0.123963 | − | 0.992287i | \(-0.460440\pi\) | ||||
0.123963 | + | 0.992287i | \(0.460440\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −7.27057 | −0.466407 | ||||||||
\(244\) | 7.09406 | 0.454150 | ||||||||
\(245\) | −6.01950 | −0.384572 | ||||||||
\(246\) | −9.83884 | −0.627301 | ||||||||
\(247\) | 27.3279 | 1.73883 | ||||||||
\(248\) | −5.17086 | −0.328350 | ||||||||
\(249\) | −5.38683 | −0.341377 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −20.9190 | −1.32040 | −0.660198 | − | 0.751092i | \(-0.729527\pi\) | ||||
−0.660198 | + | 0.751092i | \(0.729527\pi\) | |||||||
\(252\) | 0.709323 | 0.0446832 | ||||||||
\(253\) | −6.91028 | −0.434445 | ||||||||
\(254\) | −6.19048 | −0.388425 | ||||||||
\(255\) | −7.33233 | −0.459168 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.4654 | −1.08946 | −0.544732 | − | 0.838610i | \(-0.683369\pi\) | ||||
−0.544732 | + | 0.838610i | \(0.683369\pi\) | |||||||
\(258\) | −1.51139 | −0.0940953 | ||||||||
\(259\) | 5.85231 | 0.363645 | ||||||||
\(260\) | −4.51816 | −0.280205 | ||||||||
\(261\) | −5.50635 | −0.340834 | ||||||||
\(262\) | 1.73521 | 0.107202 | ||||||||
\(263\) | 26.9377 | 1.66105 | 0.830526 | − | 0.556980i | \(-0.188040\pi\) | ||||
0.830526 | + | 0.556980i | \(0.188040\pi\) | |||||||
\(264\) | −1.51118 | −0.0930066 | ||||||||
\(265\) | −7.27787 | −0.447076 | ||||||||
\(266\) | −5.98919 | −0.367221 | ||||||||
\(267\) | −10.0338 | −0.614057 | ||||||||
\(268\) | −8.62196 | −0.526670 | ||||||||
\(269\) | −10.2138 | −0.622748 | −0.311374 | − | 0.950287i | \(-0.600789\pi\) | ||||
−0.311374 | + | 0.950287i | \(0.600789\pi\) | |||||||
\(270\) | −5.61605 | −0.341782 | ||||||||
\(271\) | −20.8175 | −1.26457 | −0.632286 | − | 0.774735i | \(-0.717883\pi\) | ||||
−0.632286 | + | 0.774735i | \(0.717883\pi\) | |||||||
\(272\) | 4.85206 | 0.294199 | ||||||||
\(273\) | −6.76086 | −0.409186 | ||||||||
\(274\) | −5.75063 | −0.347408 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −10.4427 | −0.628574 | ||||||||
\(277\) | 11.5058 | 0.691319 | 0.345659 | − | 0.938360i | \(-0.387655\pi\) | ||||
0.345659 | + | 0.938360i | \(0.387655\pi\) | |||||||
\(278\) | 22.3773 | 1.34210 | ||||||||
\(279\) | −3.70410 | −0.221759 | ||||||||
\(280\) | 0.990203 | 0.0591759 | ||||||||
\(281\) | 27.8850 | 1.66348 | 0.831739 | − | 0.555167i | \(-0.187346\pi\) | ||||
0.831739 | + | 0.555167i | \(0.187346\pi\) | |||||||
\(282\) | 2.63167 | 0.156714 | ||||||||
\(283\) | 5.13300 | 0.305125 | 0.152562 | − | 0.988294i | \(-0.451247\pi\) | ||||
0.152562 | + | 0.988294i | \(0.451247\pi\) | |||||||
\(284\) | −10.7024 | −0.635068 | ||||||||
\(285\) | 9.14028 | 0.541423 | ||||||||
\(286\) | −4.51816 | −0.267165 | ||||||||
\(287\) | 6.44692 | 0.380550 | ||||||||
\(288\) | 0.716341 | 0.0422108 | ||||||||
\(289\) | 6.54250 | 0.384853 | ||||||||
\(290\) | −7.68677 | −0.451383 | ||||||||
\(291\) | 3.02759 | 0.177480 | ||||||||
\(292\) | −1.00000 | −0.0585206 | ||||||||
\(293\) | 2.28640 | 0.133573 | 0.0667864 | − | 0.997767i | \(-0.478725\pi\) | ||||
0.0667864 | + | 0.997767i | \(0.478725\pi\) | |||||||
\(294\) | −9.09653 | −0.530521 | ||||||||
\(295\) | −6.92339 | −0.403096 | ||||||||
\(296\) | 5.91021 | 0.343524 | ||||||||
\(297\) | −5.61605 | −0.325876 | ||||||||
\(298\) | −5.81913 | −0.337093 | ||||||||
\(299\) | −31.2218 | −1.80560 | ||||||||
\(300\) | −1.51118 | −0.0872479 | ||||||||
\(301\) | 0.990345 | 0.0570825 | ||||||||
\(302\) | −16.6560 | −0.958447 | ||||||||
\(303\) | −1.43150 | −0.0822373 | ||||||||
\(304\) | −6.04845 | −0.346902 | ||||||||
\(305\) | 7.09406 | 0.406205 | ||||||||
\(306\) | 3.47573 | 0.198694 | ||||||||
\(307\) | −21.6710 | −1.23683 | −0.618415 | − | 0.785851i | \(-0.712225\pi\) | ||||
−0.618415 | + | 0.785851i | \(0.712225\pi\) | |||||||
\(308\) | 0.990203 | 0.0564221 | ||||||||
\(309\) | 21.3920 | 1.21695 | ||||||||
\(310\) | −5.17086 | −0.293685 | ||||||||
\(311\) | 12.5364 | 0.710871 | 0.355436 | − | 0.934701i | \(-0.384333\pi\) | ||||
0.355436 | + | 0.934701i | \(0.384333\pi\) | |||||||
\(312\) | −6.82775 | −0.386545 | ||||||||
\(313\) | 25.4308 | 1.43743 | 0.718716 | − | 0.695303i | \(-0.244730\pi\) | ||||
0.718716 | + | 0.695303i | \(0.244730\pi\) | |||||||
\(314\) | −2.55559 | −0.144221 | ||||||||
\(315\) | 0.709323 | 0.0399658 | ||||||||
\(316\) | −1.71773 | −0.0966299 | ||||||||
\(317\) | −5.99644 | −0.336794 | −0.168397 | − | 0.985719i | \(-0.553859\pi\) | ||||
−0.168397 | + | 0.985719i | \(0.553859\pi\) | |||||||
\(318\) | −10.9982 | −0.616746 | ||||||||
\(319\) | −7.68677 | −0.430376 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −9.53663 | −0.532283 | ||||||||
\(322\) | 6.84258 | 0.381322 | ||||||||
\(323\) | −29.3474 | −1.63293 | ||||||||
\(324\) | −6.33783 | −0.352102 | ||||||||
\(325\) | −4.51816 | −0.250623 | ||||||||
\(326\) | 8.37109 | 0.463632 | ||||||||
\(327\) | 27.1088 | 1.49912 | ||||||||
\(328\) | 6.51071 | 0.359494 | ||||||||
\(329\) | −1.72441 | −0.0950696 | ||||||||
\(330\) | −1.51118 | −0.0831876 | ||||||||
\(331\) | −21.5793 | −1.18611 | −0.593053 | − | 0.805163i | \(-0.702078\pi\) | ||||
−0.593053 | + | 0.805163i | \(0.702078\pi\) | |||||||
\(332\) | 3.56466 | 0.195636 | ||||||||
\(333\) | 4.23373 | 0.232007 | ||||||||
\(334\) | −23.7180 | −1.29779 | ||||||||
\(335\) | −8.62196 | −0.471068 | ||||||||
\(336\) | 1.49637 | 0.0816338 | ||||||||
\(337\) | 29.7494 | 1.62055 | 0.810275 | − | 0.586049i | \(-0.199318\pi\) | ||||
0.810275 | + | 0.586049i | \(0.199318\pi\) | |||||||
\(338\) | −7.41380 | −0.403258 | ||||||||
\(339\) | −20.9068 | −1.13550 | ||||||||
\(340\) | 4.85206 | 0.263140 | ||||||||
\(341\) | −5.17086 | −0.280018 | ||||||||
\(342\) | −4.33275 | −0.234288 | ||||||||
\(343\) | 12.8919 | 0.696100 | ||||||||
\(344\) | 1.00014 | 0.0539241 | ||||||||
\(345\) | −10.4427 | −0.562214 | ||||||||
\(346\) | −20.5031 | −1.10225 | ||||||||
\(347\) | 8.44737 | 0.453479 | 0.226739 | − | 0.973955i | \(-0.427193\pi\) | ||||
0.226739 | + | 0.973955i | \(0.427193\pi\) | |||||||
\(348\) | −11.6161 | −0.622687 | ||||||||
\(349\) | 9.34190 | 0.500061 | 0.250030 | − | 0.968238i | \(-0.419559\pi\) | ||||
0.250030 | + | 0.968238i | \(0.419559\pi\) | |||||||
\(350\) | 0.990203 | 0.0529286 | ||||||||
\(351\) | −25.3742 | −1.35438 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 33.4444 | 1.78007 | 0.890033 | − | 0.455895i | \(-0.150681\pi\) | ||||
0.890033 | + | 0.455895i | \(0.150681\pi\) | |||||||
\(354\) | −10.4625 | −0.556075 | ||||||||
\(355\) | −10.7024 | −0.568022 | ||||||||
\(356\) | 6.63971 | 0.351904 | ||||||||
\(357\) | 7.26049 | 0.384266 | ||||||||
\(358\) | 6.97635 | 0.368712 | ||||||||
\(359\) | 16.6322 | 0.877813 | 0.438906 | − | 0.898533i | \(-0.355366\pi\) | ||||
0.438906 | + | 0.898533i | \(0.355366\pi\) | |||||||
\(360\) | 0.716341 | 0.0377545 | ||||||||
\(361\) | 17.5837 | 0.925458 | ||||||||
\(362\) | −13.2575 | −0.696799 | ||||||||
\(363\) | −1.51118 | −0.0793163 | ||||||||
\(364\) | 4.47390 | 0.234496 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | 10.7204 | 0.560363 | ||||||||
\(367\) | 20.0788 | 1.04810 | 0.524052 | − | 0.851686i | \(-0.324420\pi\) | ||||
0.524052 | + | 0.851686i | \(0.324420\pi\) | |||||||
\(368\) | 6.91028 | 0.360223 | ||||||||
\(369\) | 4.66389 | 0.242792 | ||||||||
\(370\) | 5.91021 | 0.307257 | ||||||||
\(371\) | 7.20657 | 0.374146 | ||||||||
\(372\) | −7.81409 | −0.405142 | ||||||||
\(373\) | 5.90606 | 0.305804 | 0.152902 | − | 0.988241i | \(-0.451138\pi\) | ||||
0.152902 | + | 0.988241i | \(0.451138\pi\) | |||||||
\(374\) | 4.85206 | 0.250894 | ||||||||
\(375\) | −1.51118 | −0.0780369 | ||||||||
\(376\) | −1.74147 | −0.0898093 | ||||||||
\(377\) | −34.7301 | −1.78869 | ||||||||
\(378\) | 5.56103 | 0.286029 | ||||||||
\(379\) | 7.88648 | 0.405101 | 0.202551 | − | 0.979272i | \(-0.435077\pi\) | ||||
0.202551 | + | 0.979272i | \(0.435077\pi\) | |||||||
\(380\) | −6.04845 | −0.310279 | ||||||||
\(381\) | −9.35491 | −0.479267 | ||||||||
\(382\) | 11.9475 | 0.611287 | ||||||||
\(383\) | 17.7655 | 0.907776 | 0.453888 | − | 0.891059i | \(-0.350037\pi\) | ||||
0.453888 | + | 0.891059i | \(0.350037\pi\) | |||||||
\(384\) | 1.51118 | 0.0771170 | ||||||||
\(385\) | 0.990203 | 0.0504654 | ||||||||
\(386\) | 14.4429 | 0.735124 | ||||||||
\(387\) | 0.716444 | 0.0364189 | ||||||||
\(388\) | −2.00346 | −0.101710 | ||||||||
\(389\) | 2.64850 | 0.134284 | 0.0671421 | − | 0.997743i | \(-0.478612\pi\) | ||||
0.0671421 | + | 0.997743i | \(0.478612\pi\) | |||||||
\(390\) | −6.82775 | −0.345737 | ||||||||
\(391\) | 33.5291 | 1.69564 | ||||||||
\(392\) | 6.01950 | 0.304031 | ||||||||
\(393\) | 2.62222 | 0.132273 | ||||||||
\(394\) | −7.88836 | −0.397410 | ||||||||
\(395\) | −1.71773 | −0.0864284 | ||||||||
\(396\) | 0.716341 | 0.0359975 | ||||||||
\(397\) | 23.6146 | 1.18518 | 0.592592 | − | 0.805503i | \(-0.298105\pi\) | ||||
0.592592 | + | 0.805503i | \(0.298105\pi\) | |||||||
\(398\) | 9.33569 | 0.467956 | ||||||||
\(399\) | −9.05073 | −0.453103 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −26.8925 | −1.34295 | −0.671474 | − | 0.741029i | \(-0.734338\pi\) | ||||
−0.671474 | + | 0.741029i | \(0.734338\pi\) | |||||||
\(402\) | −13.0293 | −0.649843 | ||||||||
\(403\) | −23.3628 | −1.16378 | ||||||||
\(404\) | 0.947272 | 0.0471285 | ||||||||
\(405\) | −6.33783 | −0.314929 | ||||||||
\(406\) | 7.61146 | 0.377750 | ||||||||
\(407\) | 5.91021 | 0.292958 | ||||||||
\(408\) | 7.33233 | 0.363004 | ||||||||
\(409\) | 9.94490 | 0.491744 | 0.245872 | − | 0.969302i | \(-0.420926\pi\) | ||||
0.245872 | + | 0.969302i | \(0.420926\pi\) | |||||||
\(410\) | 6.51071 | 0.321541 | ||||||||
\(411\) | −8.69022 | −0.428657 | ||||||||
\(412\) | −14.1558 | −0.697408 | ||||||||
\(413\) | 6.85557 | 0.337340 | ||||||||
\(414\) | 4.95012 | 0.243285 | ||||||||
\(415\) | 3.56466 | 0.174982 | ||||||||
\(416\) | 4.51816 | 0.221521 | ||||||||
\(417\) | 33.8161 | 1.65598 | ||||||||
\(418\) | −6.04845 | −0.295839 | ||||||||
\(419\) | −7.37525 | −0.360305 | −0.180152 | − | 0.983639i | \(-0.557659\pi\) | ||||
−0.180152 | + | 0.983639i | \(0.557659\pi\) | |||||||
\(420\) | 1.49637 | 0.0730155 | ||||||||
\(421\) | 15.5669 | 0.758685 | 0.379343 | − | 0.925256i | \(-0.376150\pi\) | ||||
0.379343 | + | 0.925256i | \(0.376150\pi\) | |||||||
\(422\) | −18.7964 | −0.914994 | ||||||||
\(423\) | −1.24748 | −0.0606548 | ||||||||
\(424\) | 7.27787 | 0.353445 | ||||||||
\(425\) | 4.85206 | 0.235360 | ||||||||
\(426\) | −16.1732 | −0.783592 | ||||||||
\(427\) | −7.02456 | −0.339942 | ||||||||
\(428\) | 6.31073 | 0.305040 | ||||||||
\(429\) | −6.82775 | −0.329647 | ||||||||
\(430\) | 1.00014 | 0.0482312 | ||||||||
\(431\) | −3.21997 | −0.155101 | −0.0775503 | − | 0.996988i | \(-0.524710\pi\) | ||||
−0.0775503 | + | 0.996988i | \(0.524710\pi\) | |||||||
\(432\) | 5.61605 | 0.270202 | ||||||||
\(433\) | 5.14929 | 0.247459 | 0.123729 | − | 0.992316i | \(-0.460514\pi\) | ||||
0.123729 | + | 0.992316i | \(0.460514\pi\) | |||||||
\(434\) | 5.12020 | 0.245778 | ||||||||
\(435\) | −11.6161 | −0.556948 | ||||||||
\(436\) | −17.9388 | −0.859115 | ||||||||
\(437\) | −41.7964 | −1.99940 | ||||||||
\(438\) | −1.51118 | −0.0722069 | ||||||||
\(439\) | −11.6466 | −0.555863 | −0.277931 | − | 0.960601i | \(-0.589649\pi\) | ||||
−0.277931 | + | 0.960601i | \(0.589649\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 4.31201 | 0.205334 | ||||||||
\(442\) | 21.9224 | 1.04274 | ||||||||
\(443\) | −19.0393 | −0.904583 | −0.452291 | − | 0.891870i | \(-0.649393\pi\) | ||||
−0.452291 | + | 0.891870i | \(0.649393\pi\) | |||||||
\(444\) | 8.93138 | 0.423865 | ||||||||
\(445\) | 6.63971 | 0.314752 | ||||||||
\(446\) | 12.8435 | 0.608155 | ||||||||
\(447\) | −8.79374 | −0.415930 | ||||||||
\(448\) | −0.990203 | −0.0467827 | ||||||||
\(449\) | 10.8077 | 0.510049 | 0.255025 | − | 0.966935i | \(-0.417916\pi\) | ||||
0.255025 | + | 0.966935i | \(0.417916\pi\) | |||||||
\(450\) | 0.716341 | 0.0337686 | ||||||||
\(451\) | 6.51071 | 0.306577 | ||||||||
\(452\) | 13.8348 | 0.650734 | ||||||||
\(453\) | −25.1702 | −1.18260 | ||||||||
\(454\) | −22.0558 | −1.03513 | ||||||||
\(455\) | 4.47390 | 0.209740 | ||||||||
\(456\) | −9.14028 | −0.428033 | ||||||||
\(457\) | 16.7154 | 0.781914 | 0.390957 | − | 0.920409i | \(-0.372144\pi\) | ||||
0.390957 | + | 0.920409i | \(0.372144\pi\) | |||||||
\(458\) | −3.31830 | −0.155054 | ||||||||
\(459\) | 27.2494 | 1.27189 | ||||||||
\(460\) | 6.91028 | 0.322193 | ||||||||
\(461\) | 9.61907 | 0.448005 | 0.224002 | − | 0.974589i | \(-0.428088\pi\) | ||||
0.224002 | + | 0.974589i | \(0.428088\pi\) | |||||||
\(462\) | 1.49637 | 0.0696176 | ||||||||
\(463\) | 28.1461 | 1.30806 | 0.654029 | − | 0.756469i | \(-0.273077\pi\) | ||||
0.654029 | + | 0.756469i | \(0.273077\pi\) | |||||||
\(464\) | 7.68677 | 0.356849 | ||||||||
\(465\) | −7.81409 | −0.362370 | ||||||||
\(466\) | −16.4539 | −0.762210 | ||||||||
\(467\) | 22.0985 | 1.02260 | 0.511298 | − | 0.859404i | \(-0.329165\pi\) | ||||
0.511298 | + | 0.859404i | \(0.329165\pi\) | |||||||
\(468\) | 3.23655 | 0.149609 | ||||||||
\(469\) | 8.53749 | 0.394225 | ||||||||
\(470\) | −1.74147 | −0.0803279 | ||||||||
\(471\) | −3.86196 | −0.177950 | ||||||||
\(472\) | 6.92339 | 0.318675 | ||||||||
\(473\) | 1.00014 | 0.0459866 | ||||||||
\(474\) | −2.59580 | −0.119229 | ||||||||
\(475\) | −6.04845 | −0.277522 | ||||||||
\(476\) | −4.80453 | −0.220215 | ||||||||
\(477\) | 5.21344 | 0.238707 | ||||||||
\(478\) | 6.03920 | 0.276227 | ||||||||
\(479\) | 27.6449 | 1.26313 | 0.631564 | − | 0.775324i | \(-0.282413\pi\) | ||||
0.631564 | + | 0.775324i | \(0.282413\pi\) | |||||||
\(480\) | 1.51118 | 0.0689755 | ||||||||
\(481\) | 26.7033 | 1.21757 | ||||||||
\(482\) | −3.84885 | −0.175310 | ||||||||
\(483\) | 10.3404 | 0.470502 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −2.00346 | −0.0909726 | ||||||||
\(486\) | 7.27057 | 0.329800 | ||||||||
\(487\) | 5.60480 | 0.253978 | 0.126989 | − | 0.991904i | \(-0.459469\pi\) | ||||
0.126989 | + | 0.991904i | \(0.459469\pi\) | |||||||
\(488\) | −7.09406 | −0.321133 | ||||||||
\(489\) | 12.6502 | 0.572062 | ||||||||
\(490\) | 6.01950 | 0.271933 | ||||||||
\(491\) | −26.4531 | −1.19381 | −0.596905 | − | 0.802312i | \(-0.703603\pi\) | ||||
−0.596905 | + | 0.802312i | \(0.703603\pi\) | |||||||
\(492\) | 9.83884 | 0.443569 | ||||||||
\(493\) | 37.2967 | 1.67976 | ||||||||
\(494\) | −27.3279 | −1.22954 | ||||||||
\(495\) | 0.716341 | 0.0321971 | ||||||||
\(496\) | 5.17086 | 0.232179 | ||||||||
\(497\) | 10.5975 | 0.475363 | ||||||||
\(498\) | 5.38683 | 0.241390 | ||||||||
\(499\) | −8.25403 | −0.369501 | −0.184750 | − | 0.982785i | \(-0.559148\pi\) | ||||
−0.184750 | + | 0.982785i | \(0.559148\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −35.8421 | −1.60131 | ||||||||
\(502\) | 20.9190 | 0.933660 | ||||||||
\(503\) | −28.3431 | −1.26375 | −0.631877 | − | 0.775069i | \(-0.717715\pi\) | ||||
−0.631877 | + | 0.775069i | \(0.717715\pi\) | |||||||
\(504\) | −0.709323 | −0.0315958 | ||||||||
\(505\) | 0.947272 | 0.0421531 | ||||||||
\(506\) | 6.91028 | 0.307199 | ||||||||
\(507\) | −11.2036 | −0.497568 | ||||||||
\(508\) | 6.19048 | 0.274658 | ||||||||
\(509\) | 32.7171 | 1.45016 | 0.725080 | − | 0.688665i | \(-0.241803\pi\) | ||||
0.725080 | + | 0.688665i | \(0.241803\pi\) | |||||||
\(510\) | 7.33233 | 0.324681 | ||||||||
\(511\) | 0.990203 | 0.0438040 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −33.9684 | −1.49974 | ||||||||
\(514\) | 17.4654 | 0.770367 | ||||||||
\(515\) | −14.1558 | −0.623781 | ||||||||
\(516\) | 1.51139 | 0.0665354 | ||||||||
\(517\) | −1.74147 | −0.0765897 | ||||||||
\(518\) | −5.85231 | −0.257136 | ||||||||
\(519\) | −30.9838 | −1.36004 | ||||||||
\(520\) | 4.51816 | 0.198135 | ||||||||
\(521\) | −8.12552 | −0.355986 | −0.177993 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177993 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(522\) | 5.50635 | 0.241006 | ||||||||
\(523\) | 23.5251 | 1.02868 | 0.514340 | − | 0.857586i | \(-0.328037\pi\) | ||||
0.514340 | + | 0.857586i | \(0.328037\pi\) | |||||||
\(524\) | −1.73521 | −0.0758032 | ||||||||
\(525\) | 1.49637 | 0.0653071 | ||||||||
\(526\) | −26.9377 | −1.17454 | ||||||||
\(527\) | 25.0893 | 1.09291 | ||||||||
\(528\) | 1.51118 | 0.0657656 | ||||||||
\(529\) | 24.7519 | 1.07617 | ||||||||
\(530\) | 7.27787 | 0.316130 | ||||||||
\(531\) | 4.95951 | 0.215224 | ||||||||
\(532\) | 5.98919 | 0.259664 | ||||||||
\(533\) | 29.4164 | 1.27417 | ||||||||
\(534\) | 10.0338 | 0.434204 | ||||||||
\(535\) | 6.31073 | 0.272836 | ||||||||
\(536\) | 8.62196 | 0.372412 | ||||||||
\(537\) | 10.5425 | 0.454943 | ||||||||
\(538\) | 10.2138 | 0.440349 | ||||||||
\(539\) | 6.01950 | 0.259278 | ||||||||
\(540\) | 5.61605 | 0.241676 | ||||||||
\(541\) | 16.4866 | 0.708813 | 0.354406 | − | 0.935091i | \(-0.384683\pi\) | ||||
0.354406 | + | 0.935091i | \(0.384683\pi\) | |||||||
\(542\) | 20.8175 | 0.894187 | ||||||||
\(543\) | −20.0344 | −0.859760 | ||||||||
\(544\) | −4.85206 | −0.208030 | ||||||||
\(545\) | −17.9388 | −0.768416 | ||||||||
\(546\) | 6.76086 | 0.289338 | ||||||||
\(547\) | −26.1362 | −1.11750 | −0.558752 | − | 0.829335i | \(-0.688720\pi\) | ||||
−0.558752 | + | 0.829335i | \(0.688720\pi\) | |||||||
\(548\) | 5.75063 | 0.245655 | ||||||||
\(549\) | −5.08176 | −0.216884 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −46.4930 | −1.98067 | ||||||||
\(552\) | 10.4427 | 0.444469 | ||||||||
\(553\) | 1.70090 | 0.0723297 | ||||||||
\(554\) | −11.5058 | −0.488836 | ||||||||
\(555\) | 8.93138 | 0.379116 | ||||||||
\(556\) | −22.3773 | −0.949009 | ||||||||
\(557\) | 10.2298 | 0.433449 | 0.216724 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216724 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(558\) | 3.70410 | 0.156807 | ||||||||
\(559\) | 4.51881 | 0.191125 | ||||||||
\(560\) | −0.990203 | −0.0418437 | ||||||||
\(561\) | 7.33233 | 0.309571 | ||||||||
\(562\) | −27.8850 | −1.17626 | ||||||||
\(563\) | −25.4980 | −1.07461 | −0.537307 | − | 0.843387i | \(-0.680558\pi\) | ||||
−0.537307 | + | 0.843387i | \(0.680558\pi\) | |||||||
\(564\) | −2.63167 | −0.110813 | ||||||||
\(565\) | 13.8348 | 0.582034 | ||||||||
\(566\) | −5.13300 | −0.215756 | ||||||||
\(567\) | 6.27574 | 0.263556 | ||||||||
\(568\) | 10.7024 | 0.449061 | ||||||||
\(569\) | 10.0550 | 0.421528 | 0.210764 | − | 0.977537i | \(-0.432405\pi\) | ||||
0.210764 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(570\) | −9.14028 | −0.382844 | ||||||||
\(571\) | −11.7141 | −0.490218 | −0.245109 | − | 0.969496i | \(-0.578824\pi\) | ||||
−0.245109 | + | 0.969496i | \(0.578824\pi\) | |||||||
\(572\) | 4.51816 | 0.188914 | ||||||||
\(573\) | 18.0548 | 0.754250 | ||||||||
\(574\) | −6.44692 | −0.269089 | ||||||||
\(575\) | 6.91028 | 0.288179 | ||||||||
\(576\) | −0.716341 | −0.0298475 | ||||||||
\(577\) | 8.15872 | 0.339652 | 0.169826 | − | 0.985474i | \(-0.445679\pi\) | ||||
0.169826 | + | 0.985474i | \(0.445679\pi\) | |||||||
\(578\) | −6.54250 | −0.272132 | ||||||||
\(579\) | 21.8258 | 0.907048 | ||||||||
\(580\) | 7.68677 | 0.319176 | ||||||||
\(581\) | −3.52974 | −0.146438 | ||||||||
\(582\) | −3.02759 | −0.125498 | ||||||||
\(583\) | 7.27787 | 0.301419 | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 3.23655 | 0.133815 | ||||||||
\(586\) | −2.28640 | −0.0944502 | ||||||||
\(587\) | −9.99356 | −0.412478 | −0.206239 | − | 0.978502i | \(-0.566122\pi\) | ||||
−0.206239 | + | 0.978502i | \(0.566122\pi\) | |||||||
\(588\) | 9.09653 | 0.375135 | ||||||||
\(589\) | −31.2757 | −1.28869 | ||||||||
\(590\) | 6.92339 | 0.285032 | ||||||||
\(591\) | −11.9207 | −0.490353 | ||||||||
\(592\) | −5.91021 | −0.242908 | ||||||||
\(593\) | −36.9339 | −1.51669 | −0.758346 | − | 0.651852i | \(-0.773992\pi\) | ||||
−0.758346 | + | 0.651852i | \(0.773992\pi\) | |||||||
\(594\) | 5.61605 | 0.230429 | ||||||||
\(595\) | −4.80453 | −0.196966 | ||||||||
\(596\) | 5.81913 | 0.238361 | ||||||||
\(597\) | 14.1079 | 0.577398 | ||||||||
\(598\) | 31.2218 | 1.27675 | ||||||||
\(599\) | −19.5459 | −0.798623 | −0.399311 | − | 0.916815i | \(-0.630751\pi\) | ||||
−0.399311 | + | 0.916815i | \(0.630751\pi\) | |||||||
\(600\) | 1.51118 | 0.0616936 | ||||||||
\(601\) | 30.4933 | 1.24385 | 0.621924 | − | 0.783077i | \(-0.286351\pi\) | ||||
0.621924 | + | 0.783077i | \(0.286351\pi\) | |||||||
\(602\) | −0.990345 | −0.0403635 | ||||||||
\(603\) | 6.17627 | 0.251517 | ||||||||
\(604\) | 16.6560 | 0.677725 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 1.43150 | 0.0581506 | ||||||||
\(607\) | 43.3623 | 1.76002 | 0.880010 | − | 0.474954i | \(-0.157535\pi\) | ||||
0.880010 | + | 0.474954i | \(0.157535\pi\) | |||||||
\(608\) | 6.04845 | 0.245297 | ||||||||
\(609\) | 11.5023 | 0.466096 | ||||||||
\(610\) | −7.09406 | −0.287230 | ||||||||
\(611\) | −7.86824 | −0.318315 | ||||||||
\(612\) | −3.47573 | −0.140498 | ||||||||
\(613\) | 14.4218 | 0.582490 | 0.291245 | − | 0.956649i | \(-0.405931\pi\) | ||||
0.291245 | + | 0.956649i | \(0.405931\pi\) | |||||||
\(614\) | 21.6710 | 0.874571 | ||||||||
\(615\) | 9.83884 | 0.396740 | ||||||||
\(616\) | −0.990203 | −0.0398964 | ||||||||
\(617\) | 8.07656 | 0.325150 | 0.162575 | − | 0.986696i | \(-0.448020\pi\) | ||||
0.162575 | + | 0.986696i | \(0.448020\pi\) | |||||||
\(618\) | −21.3920 | −0.860512 | ||||||||
\(619\) | −20.9320 | −0.841328 | −0.420664 | − | 0.907216i | \(-0.638203\pi\) | ||||
−0.420664 | + | 0.907216i | \(0.638203\pi\) | |||||||
\(620\) | 5.17086 | 0.207667 | ||||||||
\(621\) | 38.8085 | 1.55733 | ||||||||
\(622\) | −12.5364 | −0.502662 | ||||||||
\(623\) | −6.57466 | −0.263408 | ||||||||
\(624\) | 6.82775 | 0.273329 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −25.4308 | −1.01642 | ||||||||
\(627\) | −9.14028 | −0.365028 | ||||||||
\(628\) | 2.55559 | 0.101979 | ||||||||
\(629\) | −28.6767 | −1.14342 | ||||||||
\(630\) | −0.709323 | −0.0282601 | ||||||||
\(631\) | −24.0015 | −0.955485 | −0.477742 | − | 0.878500i | \(-0.658545\pi\) | ||||
−0.477742 | + | 0.878500i | \(0.658545\pi\) | |||||||
\(632\) | 1.71773 | 0.0683277 | ||||||||
\(633\) | −28.4047 | −1.12898 | ||||||||
\(634\) | 5.99644 | 0.238149 | ||||||||
\(635\) | 6.19048 | 0.245662 | ||||||||
\(636\) | 10.9982 | 0.436105 | ||||||||
\(637\) | 27.1971 | 1.07759 | ||||||||
\(638\) | 7.68677 | 0.304322 | ||||||||
\(639\) | 7.66654 | 0.303283 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −28.0727 | −1.10881 | −0.554403 | − | 0.832248i | \(-0.687053\pi\) | ||||
−0.554403 | + | 0.832248i | \(0.687053\pi\) | |||||||
\(642\) | 9.53663 | 0.376381 | ||||||||
\(643\) | 13.5364 | 0.533823 | 0.266912 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266912 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(644\) | −6.84258 | −0.269635 | ||||||||
\(645\) | 1.51139 | 0.0595111 | ||||||||
\(646\) | 29.3474 | 1.15466 | ||||||||
\(647\) | 32.7173 | 1.28625 | 0.643125 | − | 0.765761i | \(-0.277638\pi\) | ||||
0.643125 | + | 0.765761i | \(0.277638\pi\) | |||||||
\(648\) | 6.33783 | 0.248974 | ||||||||
\(649\) | 6.92339 | 0.271767 | ||||||||
\(650\) | 4.51816 | 0.177217 | ||||||||
\(651\) | 7.73754 | 0.303258 | ||||||||
\(652\) | −8.37109 | −0.327837 | ||||||||
\(653\) | 1.52324 | 0.0596089 | 0.0298045 | − | 0.999556i | \(-0.490512\pi\) | ||||
0.0298045 | + | 0.999556i | \(0.490512\pi\) | |||||||
\(654\) | −27.1088 | −1.06004 | ||||||||
\(655\) | −1.73521 | −0.0678005 | ||||||||
\(656\) | −6.51071 | −0.254200 | ||||||||
\(657\) | 0.716341 | 0.0279471 | ||||||||
\(658\) | 1.72441 | 0.0672244 | ||||||||
\(659\) | −47.6697 | −1.85695 | −0.928474 | − | 0.371398i | \(-0.878878\pi\) | ||||
−0.928474 | + | 0.371398i | \(0.878878\pi\) | |||||||
\(660\) | 1.51118 | 0.0588225 | ||||||||
\(661\) | 18.0440 | 0.701831 | 0.350915 | − | 0.936407i | \(-0.385870\pi\) | ||||
0.350915 | + | 0.936407i | \(0.385870\pi\) | |||||||
\(662\) | 21.5793 | 0.838704 | ||||||||
\(663\) | 33.1287 | 1.28661 | ||||||||
\(664\) | −3.56466 | −0.138336 | ||||||||
\(665\) | 5.98919 | 0.232251 | ||||||||
\(666\) | −4.23373 | −0.164054 | ||||||||
\(667\) | 53.1177 | 2.05673 | ||||||||
\(668\) | 23.7180 | 0.917677 | ||||||||
\(669\) | 19.4087 | 0.750385 | ||||||||
\(670\) | 8.62196 | 0.333095 | ||||||||
\(671\) | −7.09406 | −0.273863 | ||||||||
\(672\) | −1.49637 | −0.0577238 | ||||||||
\(673\) | −25.7292 | −0.991789 | −0.495895 | − | 0.868383i | \(-0.665160\pi\) | ||||
−0.495895 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(674\) | −29.7494 | −1.14590 | ||||||||
\(675\) | 5.61605 | 0.216162 | ||||||||
\(676\) | 7.41380 | 0.285146 | ||||||||
\(677\) | 17.9743 | 0.690808 | 0.345404 | − | 0.938454i | \(-0.387742\pi\) | ||||
0.345404 | + | 0.938454i | \(0.387742\pi\) | |||||||
\(678\) | 20.9068 | 0.802922 | ||||||||
\(679\) | 1.98384 | 0.0761326 | ||||||||
\(680\) | −4.85206 | −0.186068 | ||||||||
\(681\) | −33.3302 | −1.27722 | ||||||||
\(682\) | 5.17086 | 0.198003 | ||||||||
\(683\) | 14.6123 | 0.559126 | 0.279563 | − | 0.960127i | \(-0.409810\pi\) | ||||
0.279563 | + | 0.960127i | \(0.409810\pi\) | |||||||
\(684\) | 4.33275 | 0.165667 | ||||||||
\(685\) | 5.75063 | 0.219720 | ||||||||
\(686\) | −12.8919 | −0.492217 | ||||||||
\(687\) | −5.01454 | −0.191317 | ||||||||
\(688\) | −1.00014 | −0.0381301 | ||||||||
\(689\) | 32.8826 | 1.25273 | ||||||||
\(690\) | 10.4427 | 0.397545 | ||||||||
\(691\) | 35.2528 | 1.34108 | 0.670540 | − | 0.741873i | \(-0.266062\pi\) | ||||
0.670540 | + | 0.741873i | \(0.266062\pi\) | |||||||
\(692\) | 20.5031 | 0.779411 | ||||||||
\(693\) | −0.709323 | −0.0269450 | ||||||||
\(694\) | −8.44737 | −0.320658 | ||||||||
\(695\) | −22.3773 | −0.848819 | ||||||||
\(696\) | 11.6161 | 0.440306 | ||||||||
\(697\) | −31.5903 | −1.19657 | ||||||||
\(698\) | −9.34190 | −0.353596 | ||||||||
\(699\) | −24.8647 | −0.940470 | ||||||||
\(700\) | −0.990203 | −0.0374262 | ||||||||
\(701\) | −3.51044 | −0.132587 | −0.0662937 | − | 0.997800i | \(-0.521117\pi\) | ||||
−0.0662937 | + | 0.997800i | \(0.521117\pi\) | |||||||
\(702\) | 25.3742 | 0.957689 | ||||||||
\(703\) | 35.7476 | 1.34825 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −2.63167 | −0.0991143 | ||||||||
\(706\) | −33.4444 | −1.25870 | ||||||||
\(707\) | −0.937992 | −0.0352768 | ||||||||
\(708\) | 10.4625 | 0.393204 | ||||||||
\(709\) | 6.83301 | 0.256619 | 0.128310 | − | 0.991734i | \(-0.459045\pi\) | ||||
0.128310 | + | 0.991734i | \(0.459045\pi\) | |||||||
\(710\) | 10.7024 | 0.401652 | ||||||||
\(711\) | 1.23048 | 0.0461466 | ||||||||
\(712\) | −6.63971 | −0.248834 | ||||||||
\(713\) | 35.7321 | 1.33818 | ||||||||
\(714\) | −7.26049 | −0.271717 | ||||||||
\(715\) | 4.51816 | 0.168970 | ||||||||
\(716\) | −6.97635 | −0.260719 | ||||||||
\(717\) | 9.12631 | 0.340828 | ||||||||
\(718\) | −16.6322 | −0.620707 | ||||||||
\(719\) | −22.0697 | −0.823060 | −0.411530 | − | 0.911396i | \(-0.635005\pi\) | ||||
−0.411530 | + | 0.911396i | \(0.635005\pi\) | |||||||
\(720\) | −0.716341 | −0.0266965 | ||||||||
\(721\) | 14.0172 | 0.522026 | ||||||||
\(722\) | −17.5837 | −0.654398 | ||||||||
\(723\) | −5.81629 | −0.216310 | ||||||||
\(724\) | 13.2575 | 0.492711 | ||||||||
\(725\) | 7.68677 | 0.285479 | ||||||||
\(726\) | 1.51118 | 0.0560851 | ||||||||
\(727\) | 6.99505 | 0.259432 | 0.129716 | − | 0.991551i | \(-0.458593\pi\) | ||||
0.129716 | + | 0.991551i | \(0.458593\pi\) | |||||||
\(728\) | −4.47390 | −0.165814 | ||||||||
\(729\) | 30.0006 | 1.11113 | ||||||||
\(730\) | 1.00000 | 0.0370117 | ||||||||
\(731\) | −4.85276 | −0.179486 | ||||||||
\(732\) | −10.7204 | −0.396237 | ||||||||
\(733\) | −6.06166 | −0.223893 | −0.111946 | − | 0.993714i | \(-0.535708\pi\) | ||||
−0.111946 | + | 0.993714i | \(0.535708\pi\) | |||||||
\(734\) | −20.0788 | −0.741122 | ||||||||
\(735\) | 9.09653 | 0.335531 | ||||||||
\(736\) | −6.91028 | −0.254716 | ||||||||
\(737\) | 8.62196 | 0.317594 | ||||||||
\(738\) | −4.66389 | −0.171680 | ||||||||
\(739\) | 22.4896 | 0.827293 | 0.413646 | − | 0.910438i | \(-0.364255\pi\) | ||||
0.413646 | + | 0.910438i | \(0.364255\pi\) | |||||||
\(740\) | −5.91021 | −0.217264 | ||||||||
\(741\) | −41.2973 | −1.51709 | ||||||||
\(742\) | −7.20657 | −0.264561 | ||||||||
\(743\) | −16.4312 | −0.602804 | −0.301402 | − | 0.953497i | \(-0.597455\pi\) | ||||
−0.301402 | + | 0.953497i | \(0.597455\pi\) | |||||||
\(744\) | 7.81409 | 0.286479 | ||||||||
\(745\) | 5.81913 | 0.213196 | ||||||||
\(746\) | −5.90606 | −0.216236 | ||||||||
\(747\) | −2.55351 | −0.0934281 | ||||||||
\(748\) | −4.85206 | −0.177409 | ||||||||
\(749\) | −6.24890 | −0.228330 | ||||||||
\(750\) | 1.51118 | 0.0551804 | ||||||||
\(751\) | 40.0323 | 1.46080 | 0.730399 | − | 0.683020i | \(-0.239334\pi\) | ||||
0.730399 | + | 0.683020i | \(0.239334\pi\) | |||||||
\(752\) | 1.74147 | 0.0635048 | ||||||||
\(753\) | 31.6123 | 1.15202 | ||||||||
\(754\) | 34.7301 | 1.26479 | ||||||||
\(755\) | 16.6560 | 0.606175 | ||||||||
\(756\) | −5.56103 | −0.202253 | ||||||||
\(757\) | −31.1912 | −1.13367 | −0.566833 | − | 0.823833i | \(-0.691831\pi\) | ||||
−0.566833 | + | 0.823833i | \(0.691831\pi\) | |||||||
\(758\) | −7.88648 | −0.286450 | ||||||||
\(759\) | 10.4427 | 0.379045 | ||||||||
\(760\) | 6.04845 | 0.219400 | ||||||||
\(761\) | −25.7187 | −0.932304 | −0.466152 | − | 0.884705i | \(-0.654360\pi\) | ||||
−0.466152 | + | 0.884705i | \(0.654360\pi\) | |||||||
\(762\) | 9.35491 | 0.338893 | ||||||||
\(763\) | 17.7631 | 0.643067 | ||||||||
\(764\) | −11.9475 | −0.432245 | ||||||||
\(765\) | −3.47573 | −0.125665 | ||||||||
\(766\) | −17.7655 | −0.641894 | ||||||||
\(767\) | 31.2810 | 1.12949 | ||||||||
\(768\) | −1.51118 | −0.0545299 | ||||||||
\(769\) | 17.2208 | 0.620997 | 0.310499 | − | 0.950574i | \(-0.399504\pi\) | ||||
0.310499 | + | 0.950574i | \(0.399504\pi\) | |||||||
\(770\) | −0.990203 | −0.0356844 | ||||||||
\(771\) | 26.3934 | 0.950534 | ||||||||
\(772\) | −14.4429 | −0.519811 | ||||||||
\(773\) | −16.7962 | −0.604118 | −0.302059 | − | 0.953289i | \(-0.597674\pi\) | ||||
−0.302059 | + | 0.953289i | \(0.597674\pi\) | |||||||
\(774\) | −0.716444 | −0.0257520 | ||||||||
\(775\) | 5.17086 | 0.185743 | ||||||||
\(776\) | 2.00346 | 0.0719201 | ||||||||
\(777\) | −8.84388 | −0.317272 | ||||||||
\(778\) | −2.64850 | −0.0949532 | ||||||||
\(779\) | 39.3797 | 1.41092 | ||||||||
\(780\) | 6.82775 | 0.244473 | ||||||||
\(781\) | 10.7024 | 0.382960 | ||||||||
\(782\) | −33.5291 | −1.19900 | ||||||||
\(783\) | 43.1693 | 1.54274 | ||||||||
\(784\) | −6.01950 | −0.214982 | ||||||||
\(785\) | 2.55559 | 0.0912131 | ||||||||
\(786\) | −2.62222 | −0.0935314 | ||||||||
\(787\) | −2.09610 | −0.0747178 | −0.0373589 | − | 0.999302i | \(-0.511894\pi\) | ||||
−0.0373589 | + | 0.999302i | \(0.511894\pi\) | |||||||
\(788\) | 7.88836 | 0.281011 | ||||||||
\(789\) | −40.7077 | −1.44923 | ||||||||
\(790\) | 1.71773 | 0.0611141 | ||||||||
\(791\) | −13.6992 | −0.487089 | ||||||||
\(792\) | −0.716341 | −0.0254541 | ||||||||
\(793\) | −32.0521 | −1.13820 | ||||||||
\(794\) | −23.6146 | −0.838052 | ||||||||
\(795\) | 10.9982 | 0.390064 | ||||||||
\(796\) | −9.33569 | −0.330895 | ||||||||
\(797\) | −5.58804 | −0.197938 | −0.0989692 | − | 0.995090i | \(-0.531555\pi\) | ||||
−0.0989692 | + | 0.995090i | \(0.531555\pi\) | |||||||
\(798\) | 9.05073 | 0.320392 | ||||||||
\(799\) | 8.44971 | 0.298929 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −4.75630 | −0.168055 | ||||||||
\(802\) | 26.8925 | 0.949607 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 13.0293 | 0.459509 | ||||||||
\(805\) | −6.84258 | −0.241169 | ||||||||
\(806\) | 23.3628 | 0.822920 | ||||||||
\(807\) | 15.4349 | 0.543334 | ||||||||
\(808\) | −0.947272 | −0.0333249 | ||||||||
\(809\) | 11.8188 | 0.415527 | 0.207763 | − | 0.978179i | \(-0.433382\pi\) | ||||
0.207763 | + | 0.978179i | \(0.433382\pi\) | |||||||
\(810\) | 6.33783 | 0.222689 | ||||||||
\(811\) | 17.8463 | 0.626667 | 0.313334 | − | 0.949643i | \(-0.398554\pi\) | ||||
0.313334 | + | 0.949643i | \(0.398554\pi\) | |||||||
\(812\) | −7.61146 | −0.267110 | ||||||||
\(813\) | 31.4589 | 1.10331 | ||||||||
\(814\) | −5.91021 | −0.207153 | ||||||||
\(815\) | −8.37109 | −0.293227 | ||||||||
\(816\) | −7.33233 | −0.256683 | ||||||||
\(817\) | 6.04931 | 0.211639 | ||||||||
\(818\) | −9.94490 | −0.347715 | ||||||||
\(819\) | −3.20484 | −0.111986 | ||||||||
\(820\) | −6.51071 | −0.227364 | ||||||||
\(821\) | 36.0498 | 1.25815 | 0.629073 | − | 0.777346i | \(-0.283435\pi\) | ||||
0.629073 | + | 0.777346i | \(0.283435\pi\) | |||||||
\(822\) | 8.69022 | 0.303106 | ||||||||
\(823\) | −4.30228 | −0.149968 | −0.0749841 | − | 0.997185i | \(-0.523891\pi\) | ||||
−0.0749841 | + | 0.997185i | \(0.523891\pi\) | |||||||
\(824\) | 14.1558 | 0.493142 | ||||||||
\(825\) | 1.51118 | 0.0526125 | ||||||||
\(826\) | −6.85557 | −0.238536 | ||||||||
\(827\) | −37.4901 | −1.30366 | −0.651830 | − | 0.758365i | \(-0.725998\pi\) | ||||
−0.651830 | + | 0.758365i | \(0.725998\pi\) | |||||||
\(828\) | −4.95012 | −0.172028 | ||||||||
\(829\) | 19.3863 | 0.673313 | 0.336657 | − | 0.941628i | \(-0.390704\pi\) | ||||
0.336657 | + | 0.941628i | \(0.390704\pi\) | |||||||
\(830\) | −3.56466 | −0.123731 | ||||||||
\(831\) | −17.3874 | −0.603161 | ||||||||
\(832\) | −4.51816 | −0.156639 | ||||||||
\(833\) | −29.2070 | −1.01196 | ||||||||
\(834\) | −33.8161 | −1.17096 | ||||||||
\(835\) | 23.7180 | 0.820796 | ||||||||
\(836\) | 6.04845 | 0.209190 | ||||||||
\(837\) | 29.0398 | 1.00376 | ||||||||
\(838\) | 7.37525 | 0.254774 | ||||||||
\(839\) | −22.1036 | −0.763100 | −0.381550 | − | 0.924348i | \(-0.624610\pi\) | ||||
−0.381550 | + | 0.924348i | \(0.624610\pi\) | |||||||
\(840\) | −1.49637 | −0.0516298 | ||||||||
\(841\) | 30.0864 | 1.03746 | ||||||||
\(842\) | −15.5669 | −0.536471 | ||||||||
\(843\) | −42.1392 | −1.45135 | ||||||||
\(844\) | 18.7964 | 0.646998 | ||||||||
\(845\) | 7.41380 | 0.255043 | ||||||||
\(846\) | 1.24748 | 0.0428894 | ||||||||
\(847\) | −0.990203 | −0.0340238 | ||||||||
\(848\) | −7.27787 | −0.249923 | ||||||||
\(849\) | −7.75687 | −0.266215 | ||||||||
\(850\) | −4.85206 | −0.166424 | ||||||||
\(851\) | −40.8412 | −1.40002 | ||||||||
\(852\) | 16.1732 | 0.554083 | ||||||||
\(853\) | −25.3138 | −0.866730 | −0.433365 | − | 0.901219i | \(-0.642674\pi\) | ||||
−0.433365 | + | 0.901219i | \(0.642674\pi\) | |||||||
\(854\) | 7.02456 | 0.240375 | ||||||||
\(855\) | 4.33275 | 0.148177 | ||||||||
\(856\) | −6.31073 | −0.215696 | ||||||||
\(857\) | −50.4853 | −1.72455 | −0.862273 | − | 0.506444i | \(-0.830960\pi\) | ||||
−0.862273 | + | 0.506444i | \(0.830960\pi\) | |||||||
\(858\) | 6.82775 | 0.233096 | ||||||||
\(859\) | 14.5480 | 0.496372 | 0.248186 | − | 0.968712i | \(-0.420166\pi\) | ||||
0.248186 | + | 0.968712i | \(0.420166\pi\) | |||||||
\(860\) | −1.00014 | −0.0341046 | ||||||||
\(861\) | −9.74245 | −0.332022 | ||||||||
\(862\) | 3.21997 | 0.109673 | ||||||||
\(863\) | 35.0414 | 1.19282 | 0.596412 | − | 0.802678i | \(-0.296592\pi\) | ||||
0.596412 | + | 0.802678i | \(0.296592\pi\) | |||||||
\(864\) | −5.61605 | −0.191062 | ||||||||
\(865\) | 20.5031 | 0.697126 | ||||||||
\(866\) | −5.14929 | −0.174980 | ||||||||
\(867\) | −9.88688 | −0.335776 | ||||||||
\(868\) | −5.12020 | −0.173791 | ||||||||
\(869\) | 1.71773 | 0.0582700 | ||||||||
\(870\) | 11.6161 | 0.393822 | ||||||||
\(871\) | 38.9554 | 1.31995 | ||||||||
\(872\) | 17.9388 | 0.607486 | ||||||||
\(873\) | 1.43516 | 0.0485729 | ||||||||
\(874\) | 41.7964 | 1.41379 | ||||||||
\(875\) | −0.990203 | −0.0334750 | ||||||||
\(876\) | 1.51118 | 0.0510580 | ||||||||
\(877\) | 2.46213 | 0.0831402 | 0.0415701 | − | 0.999136i | \(-0.486764\pi\) | ||||
0.0415701 | + | 0.999136i | \(0.486764\pi\) | |||||||
\(878\) | 11.6466 | 0.393054 | ||||||||
\(879\) | −3.45515 | −0.116539 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 46.7674 | 1.57563 | 0.787817 | − | 0.615909i | \(-0.211211\pi\) | ||||
0.787817 | + | 0.615909i | \(0.211211\pi\) | |||||||
\(882\) | −4.31201 | −0.145193 | ||||||||
\(883\) | −12.8721 | −0.433181 | −0.216591 | − | 0.976262i | \(-0.569494\pi\) | ||||
−0.216591 | + | 0.976262i | \(0.569494\pi\) | |||||||
\(884\) | −21.9224 | −0.737330 | ||||||||
\(885\) | 10.4625 | 0.351692 | ||||||||
\(886\) | 19.0393 | 0.639637 | ||||||||
\(887\) | −2.68379 | −0.0901127 | −0.0450563 | − | 0.998984i | \(-0.514347\pi\) | ||||
−0.0450563 | + | 0.998984i | \(0.514347\pi\) | |||||||
\(888\) | −8.93138 | −0.299718 | ||||||||
\(889\) | −6.12983 | −0.205588 | ||||||||
\(890\) | −6.63971 | −0.222564 | ||||||||
\(891\) | 6.33783 | 0.212325 | ||||||||
\(892\) | −12.8435 | −0.430031 | ||||||||
\(893\) | −10.5332 | −0.352479 | ||||||||
\(894\) | 8.79374 | 0.294107 | ||||||||
\(895\) | −6.97635 | −0.233194 | ||||||||
\(896\) | 0.990203 | 0.0330804 | ||||||||
\(897\) | 47.1816 | 1.57535 | ||||||||
\(898\) | −10.8077 | −0.360659 | ||||||||
\(899\) | 39.7472 | 1.32564 | ||||||||
\(900\) | −0.716341 | −0.0238780 | ||||||||
\(901\) | −35.3127 | −1.17644 | ||||||||
\(902\) | −6.51071 | −0.216783 | ||||||||
\(903\) | −1.49659 | −0.0498033 | ||||||||
\(904\) | −13.8348 | −0.460138 | ||||||||
\(905\) | 13.2575 | 0.440694 | ||||||||
\(906\) | 25.1702 | 0.836225 | ||||||||
\(907\) | 37.4729 | 1.24427 | 0.622134 | − | 0.782910i | \(-0.286266\pi\) | ||||
0.622134 | + | 0.782910i | \(0.286266\pi\) | |||||||
\(908\) | 22.0558 | 0.731946 | ||||||||
\(909\) | −0.678570 | −0.0225067 | ||||||||
\(910\) | −4.47390 | −0.148308 | ||||||||
\(911\) | −22.1590 | −0.734160 | −0.367080 | − | 0.930189i | \(-0.619642\pi\) | ||||
−0.367080 | + | 0.930189i | \(0.619642\pi\) | |||||||
\(912\) | 9.14028 | 0.302665 | ||||||||
\(913\) | −3.56466 | −0.117973 | ||||||||
\(914\) | −16.7154 | −0.552897 | ||||||||
\(915\) | −10.7204 | −0.354405 | ||||||||
\(916\) | 3.31830 | 0.109640 | ||||||||
\(917\) | 1.71821 | 0.0567405 | ||||||||
\(918\) | −27.2494 | −0.899365 | ||||||||
\(919\) | 52.9631 | 1.74709 | 0.873546 | − | 0.486741i | \(-0.161815\pi\) | ||||
0.873546 | + | 0.486741i | \(0.161815\pi\) | |||||||
\(920\) | −6.91028 | −0.227825 | ||||||||
\(921\) | 32.7488 | 1.07911 | ||||||||
\(922\) | −9.61907 | −0.316787 | ||||||||
\(923\) | 48.3550 | 1.59162 | ||||||||
\(924\) | −1.49637 | −0.0492271 | ||||||||
\(925\) | −5.91021 | −0.194327 | ||||||||
\(926\) | −28.1461 | −0.924937 | ||||||||
\(927\) | 10.1404 | 0.333055 | ||||||||
\(928\) | −7.68677 | −0.252331 | ||||||||
\(929\) | 6.89444 | 0.226199 | 0.113100 | − | 0.993584i | \(-0.463922\pi\) | ||||
0.113100 | + | 0.993584i | \(0.463922\pi\) | |||||||
\(930\) | 7.81409 | 0.256234 | ||||||||
\(931\) | 36.4086 | 1.19324 | ||||||||
\(932\) | 16.4539 | 0.538964 | ||||||||
\(933\) | −18.9447 | −0.620220 | ||||||||
\(934\) | −22.0985 | −0.723084 | ||||||||
\(935\) | −4.85206 | −0.158679 | ||||||||
\(936\) | −3.23655 | −0.105790 | ||||||||
\(937\) | 33.0471 | 1.07960 | 0.539800 | − | 0.841793i | \(-0.318500\pi\) | ||||
0.539800 | + | 0.841793i | \(0.318500\pi\) | |||||||
\(938\) | −8.53749 | −0.278759 | ||||||||
\(939\) | −38.4304 | −1.25413 | ||||||||
\(940\) | 1.74147 | 0.0568004 | ||||||||
\(941\) | −3.06232 | −0.0998287 | −0.0499144 | − | 0.998754i | \(-0.515895\pi\) | ||||
−0.0499144 | + | 0.998754i | \(0.515895\pi\) | |||||||
\(942\) | 3.86196 | 0.125829 | ||||||||
\(943\) | −44.9908 | −1.46510 | ||||||||
\(944\) | −6.92339 | −0.225337 | ||||||||
\(945\) | −5.56103 | −0.180900 | ||||||||
\(946\) | −1.00014 | −0.0325175 | ||||||||
\(947\) | 7.60881 | 0.247253 | 0.123627 | − | 0.992329i | \(-0.460548\pi\) | ||||
0.123627 | + | 0.992329i | \(0.460548\pi\) | |||||||
\(948\) | 2.59580 | 0.0843076 | ||||||||
\(949\) | 4.51816 | 0.146666 | ||||||||
\(950\) | 6.04845 | 0.196238 | ||||||||
\(951\) | 9.06169 | 0.293845 | ||||||||
\(952\) | 4.80453 | 0.155716 | ||||||||
\(953\) | −2.91733 | −0.0945017 | −0.0472508 | − | 0.998883i | \(-0.515046\pi\) | ||||
−0.0472508 | + | 0.998883i | \(0.515046\pi\) | |||||||
\(954\) | −5.21344 | −0.168791 | ||||||||
\(955\) | −11.9475 | −0.386612 | ||||||||
\(956\) | −6.03920 | −0.195322 | ||||||||
\(957\) | 11.6161 | 0.375494 | ||||||||
\(958\) | −27.6449 | −0.893166 | ||||||||
\(959\) | −5.69429 | −0.183878 | ||||||||
\(960\) | −1.51118 | −0.0487731 | ||||||||
\(961\) | −4.26217 | −0.137490 | ||||||||
\(962\) | −26.7033 | −0.860949 | ||||||||
\(963\) | −4.52063 | −0.145675 | ||||||||
\(964\) | 3.84885 | 0.123963 | ||||||||
\(965\) | −14.4429 | −0.464933 | ||||||||
\(966\) | −10.3404 | −0.332695 | ||||||||
\(967\) | 29.7568 | 0.956915 | 0.478457 | − | 0.878111i | \(-0.341196\pi\) | ||||
0.478457 | + | 0.878111i | \(0.341196\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 44.3492 | 1.42470 | ||||||||
\(970\) | 2.00346 | 0.0643273 | ||||||||
\(971\) | 53.3495 | 1.71207 | 0.856033 | − | 0.516921i | \(-0.172922\pi\) | ||||
0.856033 | + | 0.516921i | \(0.172922\pi\) | |||||||
\(972\) | −7.27057 | −0.233204 | ||||||||
\(973\) | 22.1581 | 0.710355 | ||||||||
\(974\) | −5.60480 | −0.179589 | ||||||||
\(975\) | 6.82775 | 0.218663 | ||||||||
\(976\) | 7.09406 | 0.227075 | ||||||||
\(977\) | 49.1738 | 1.57321 | 0.786605 | − | 0.617457i | \(-0.211837\pi\) | ||||
0.786605 | + | 0.617457i | \(0.211837\pi\) | |||||||
\(978\) | −12.6502 | −0.404509 | ||||||||
\(979\) | −6.63971 | −0.212206 | ||||||||
\(980\) | −6.01950 | −0.192286 | ||||||||
\(981\) | 12.8503 | 0.410279 | ||||||||
\(982\) | 26.4531 | 0.844152 | ||||||||
\(983\) | −17.0572 | −0.544042 | −0.272021 | − | 0.962291i | \(-0.587692\pi\) | ||||
−0.272021 | + | 0.962291i | \(0.587692\pi\) | |||||||
\(984\) | −9.83884 | −0.313651 | ||||||||
\(985\) | 7.88836 | 0.251344 | ||||||||
\(986\) | −37.2967 | −1.18777 | ||||||||
\(987\) | 2.60589 | 0.0829462 | ||||||||
\(988\) | 27.3279 | 0.869415 | ||||||||
\(989\) | −6.91127 | −0.219766 | ||||||||
\(990\) | −0.716341 | −0.0227668 | ||||||||
\(991\) | −35.9102 | −1.14073 | −0.570363 | − | 0.821393i | \(-0.693198\pi\) | ||||
−0.570363 | + | 0.821393i | \(0.693198\pi\) | |||||||
\(992\) | −5.17086 | −0.164175 | ||||||||
\(993\) | 32.6102 | 1.03485 | ||||||||
\(994\) | −10.5975 | −0.336132 | ||||||||
\(995\) | −9.33569 | −0.295961 | ||||||||
\(996\) | −5.38683 | −0.170688 | ||||||||
\(997\) | 27.2512 | 0.863055 | 0.431527 | − | 0.902100i | \(-0.357975\pi\) | ||||
0.431527 | + | 0.902100i | \(0.357975\pi\) | |||||||
\(998\) | 8.25403 | 0.261277 | ||||||||
\(999\) | −33.1921 | −1.05015 |
(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.be.1.5 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8030.2.a.be.1.5 | ✓ | 15 | 1.1 | even | 1 | trivial |