Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 10x^{5} + 7x^{4} + 27x^{3} - 15x^{2} - 20x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.30699\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 | ||||||||
\(3\) | −1.20937 | −0.698232 | −0.349116 | − | 0.937079i | \(-0.613518\pi\) | ||||
−0.349116 | + | 0.937079i | \(0.613518\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.40321 | −1.07475 | −0.537373 | − | 0.843344i | \(-0.680583\pi\) | ||||
−0.537373 | + | 0.843344i | \(0.680583\pi\) | |||||||
\(6\) | 1.20937 | 0.493725 | ||||||||
\(7\) | 1.52017 | 0.574572 | 0.287286 | − | 0.957845i | \(-0.407247\pi\) | ||||
0.287286 | + | 0.957845i | \(0.407247\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.53742 | −0.512472 | ||||||||
\(10\) | 2.40321 | 0.759961 | ||||||||
\(11\) | 5.07638 | 1.53059 | 0.765294 | − | 0.643681i | \(-0.222594\pi\) | ||||
0.765294 | + | 0.643681i | \(0.222594\pi\) | |||||||
\(12\) | −1.20937 | −0.349116 | ||||||||
\(13\) | 5.11021 | 1.41732 | 0.708659 | − | 0.705552i | \(-0.249301\pi\) | ||||
0.708659 | + | 0.705552i | \(0.249301\pi\) | |||||||
\(14\) | −1.52017 | −0.406284 | ||||||||
\(15\) | 2.90637 | 0.750423 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.65764 | −1.61471 | −0.807357 | − | 0.590063i | \(-0.799103\pi\) | ||||
−0.807357 | + | 0.590063i | \(0.799103\pi\) | |||||||
\(18\) | 1.53742 | 0.362372 | ||||||||
\(19\) | −5.71222 | −1.31047 | −0.655236 | − | 0.755424i | \(-0.727431\pi\) | ||||
−0.655236 | + | 0.755424i | \(0.727431\pi\) | |||||||
\(20\) | −2.40321 | −0.537373 | ||||||||
\(21\) | −1.83846 | −0.401184 | ||||||||
\(22\) | −5.07638 | −1.08229 | ||||||||
\(23\) | −6.36685 | −1.32758 | −0.663790 | − | 0.747919i | \(-0.731053\pi\) | ||||
−0.663790 | + | 0.747919i | \(0.731053\pi\) | |||||||
\(24\) | 1.20937 | 0.246862 | ||||||||
\(25\) | 0.775401 | 0.155080 | ||||||||
\(26\) | −5.11021 | −1.00219 | ||||||||
\(27\) | 5.48743 | 1.05606 | ||||||||
\(28\) | 1.52017 | 0.287286 | ||||||||
\(29\) | −6.00511 | −1.11512 | −0.557560 | − | 0.830137i | \(-0.688262\pi\) | ||||
−0.557560 | + | 0.830137i | \(0.688262\pi\) | |||||||
\(30\) | −2.90637 | −0.530629 | ||||||||
\(31\) | 2.77822 | 0.498984 | 0.249492 | − | 0.968377i | \(-0.419736\pi\) | ||||
0.249492 | + | 0.968377i | \(0.419736\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −6.13924 | −1.06871 | ||||||||
\(34\) | 6.65764 | 1.14178 | ||||||||
\(35\) | −3.65329 | −0.617519 | ||||||||
\(36\) | −1.53742 | −0.256236 | ||||||||
\(37\) | −1.59410 | −0.262069 | −0.131034 | − | 0.991378i | \(-0.541830\pi\) | ||||
−0.131034 | + | 0.991378i | \(0.541830\pi\) | |||||||
\(38\) | 5.71222 | 0.926644 | ||||||||
\(39\) | −6.18015 | −0.989616 | ||||||||
\(40\) | 2.40321 | 0.379980 | ||||||||
\(41\) | 9.69619 | 1.51429 | 0.757146 | − | 0.653246i | \(-0.226593\pi\) | ||||
0.757146 | + | 0.653246i | \(0.226593\pi\) | |||||||
\(42\) | 1.83846 | 0.283680 | ||||||||
\(43\) | −9.26120 | −1.41232 | −0.706160 | − | 0.708053i | \(-0.749574\pi\) | ||||
−0.706160 | + | 0.708053i | \(0.749574\pi\) | |||||||
\(44\) | 5.07638 | 0.765294 | ||||||||
\(45\) | 3.69473 | 0.550777 | ||||||||
\(46\) | 6.36685 | 0.938741 | ||||||||
\(47\) | −7.55235 | −1.10162 | −0.550811 | − | 0.834630i | \(-0.685682\pi\) | ||||
−0.550811 | + | 0.834630i | \(0.685682\pi\) | |||||||
\(48\) | −1.20937 | −0.174558 | ||||||||
\(49\) | −4.68907 | −0.669867 | ||||||||
\(50\) | −0.775401 | −0.109658 | ||||||||
\(51\) | 8.05157 | 1.12745 | ||||||||
\(52\) | 5.11021 | 0.708659 | ||||||||
\(53\) | −9.42058 | −1.29402 | −0.647008 | − | 0.762483i | \(-0.723980\pi\) | ||||
−0.647008 | + | 0.762483i | \(0.723980\pi\) | |||||||
\(54\) | −5.48743 | −0.746745 | ||||||||
\(55\) | −12.1996 | −1.64499 | ||||||||
\(56\) | −1.52017 | −0.203142 | ||||||||
\(57\) | 6.90820 | 0.915014 | ||||||||
\(58\) | 6.00511 | 0.788509 | ||||||||
\(59\) | −6.31332 | −0.821924 | −0.410962 | − | 0.911652i | \(-0.634807\pi\) | ||||
−0.410962 | + | 0.911652i | \(0.634807\pi\) | |||||||
\(60\) | 2.90637 | 0.375211 | ||||||||
\(61\) | −7.97918 | −1.02163 | −0.510815 | − | 0.859691i | \(-0.670656\pi\) | ||||
−0.510815 | + | 0.859691i | \(0.670656\pi\) | |||||||
\(62\) | −2.77822 | −0.352835 | ||||||||
\(63\) | −2.33714 | −0.294452 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.2809 | −1.52326 | ||||||||
\(66\) | 6.13924 | 0.755689 | ||||||||
\(67\) | −2.54885 | −0.311392 | −0.155696 | − | 0.987805i | \(-0.549762\pi\) | ||||
−0.155696 | + | 0.987805i | \(0.549762\pi\) | |||||||
\(68\) | −6.65764 | −0.807357 | ||||||||
\(69\) | 7.69990 | 0.926959 | ||||||||
\(70\) | 3.65329 | 0.436652 | ||||||||
\(71\) | 1.98957 | 0.236118 | 0.118059 | − | 0.993007i | \(-0.462333\pi\) | ||||
0.118059 | + | 0.993007i | \(0.462333\pi\) | |||||||
\(72\) | 1.53742 | 0.181186 | ||||||||
\(73\) | 12.7523 | 1.49254 | 0.746269 | − | 0.665644i | \(-0.231843\pi\) | ||||
0.746269 | + | 0.665644i | \(0.231843\pi\) | |||||||
\(74\) | 1.59410 | 0.185311 | ||||||||
\(75\) | −0.937750 | −0.108282 | ||||||||
\(76\) | −5.71222 | −0.655236 | ||||||||
\(77\) | 7.71699 | 0.879432 | ||||||||
\(78\) | 6.18015 | 0.699764 | ||||||||
\(79\) | 3.64283 | 0.409851 | 0.204925 | − | 0.978778i | \(-0.434305\pi\) | ||||
0.204925 | + | 0.978778i | \(0.434305\pi\) | |||||||
\(80\) | −2.40321 | −0.268687 | ||||||||
\(81\) | −2.02411 | −0.224901 | ||||||||
\(82\) | −9.69619 | −1.07077 | ||||||||
\(83\) | −0.689504 | −0.0756829 | −0.0378415 | − | 0.999284i | \(-0.512048\pi\) | ||||
−0.0378415 | + | 0.999284i | \(0.512048\pi\) | |||||||
\(84\) | −1.83846 | −0.200592 | ||||||||
\(85\) | 15.9997 | 1.73541 | ||||||||
\(86\) | 9.26120 | 0.998660 | ||||||||
\(87\) | 7.26242 | 0.778613 | ||||||||
\(88\) | −5.07638 | −0.541144 | ||||||||
\(89\) | 2.78972 | 0.295709 | 0.147855 | − | 0.989009i | \(-0.452763\pi\) | ||||
0.147855 | + | 0.989009i | \(0.452763\pi\) | |||||||
\(90\) | −3.69473 | −0.389458 | ||||||||
\(91\) | 7.76841 | 0.814350 | ||||||||
\(92\) | −6.36685 | −0.663790 | ||||||||
\(93\) | −3.35991 | −0.348407 | ||||||||
\(94\) | 7.55235 | 0.778965 | ||||||||
\(95\) | 13.7276 | 1.40843 | ||||||||
\(96\) | 1.20937 | 0.123431 | ||||||||
\(97\) | 11.9363 | 1.21194 | 0.605972 | − | 0.795486i | \(-0.292784\pi\) | ||||
0.605972 | + | 0.795486i | \(0.292784\pi\) | |||||||
\(98\) | 4.68907 | 0.473668 | ||||||||
\(99\) | −7.80451 | −0.784383 | ||||||||
\(100\) | 0.775401 | 0.0775401 | ||||||||
\(101\) | −14.5273 | −1.44552 | −0.722759 | − | 0.691100i | \(-0.757127\pi\) | ||||
−0.722759 | + | 0.691100i | \(0.757127\pi\) | |||||||
\(102\) | −8.05157 | −0.797224 | ||||||||
\(103\) | −10.1048 | −0.995656 | −0.497828 | − | 0.867276i | \(-0.665869\pi\) | ||||
−0.497828 | + | 0.867276i | \(0.665869\pi\) | |||||||
\(104\) | −5.11021 | −0.501097 | ||||||||
\(105\) | 4.41819 | 0.431172 | ||||||||
\(106\) | 9.42058 | 0.915007 | ||||||||
\(107\) | −12.2725 | −1.18643 | −0.593214 | − | 0.805045i | \(-0.702141\pi\) | ||||
−0.593214 | + | 0.805045i | \(0.702141\pi\) | |||||||
\(108\) | 5.48743 | 0.528028 | ||||||||
\(109\) | 14.2163 | 1.36168 | 0.680838 | − | 0.732434i | \(-0.261616\pi\) | ||||
0.680838 | + | 0.732434i | \(0.261616\pi\) | |||||||
\(110\) | 12.1996 | 1.16319 | ||||||||
\(111\) | 1.92786 | 0.182985 | ||||||||
\(112\) | 1.52017 | 0.143643 | ||||||||
\(113\) | 12.7024 | 1.19494 | 0.597471 | − | 0.801891i | \(-0.296172\pi\) | ||||
0.597471 | + | 0.801891i | \(0.296172\pi\) | |||||||
\(114\) | −6.90820 | −0.647013 | ||||||||
\(115\) | 15.3009 | 1.42681 | ||||||||
\(116\) | −6.00511 | −0.557560 | ||||||||
\(117\) | −7.85652 | −0.726335 | ||||||||
\(118\) | 6.31332 | 0.581188 | ||||||||
\(119\) | −10.1208 | −0.927769 | ||||||||
\(120\) | −2.90637 | −0.265314 | ||||||||
\(121\) | 14.7697 | 1.34270 | ||||||||
\(122\) | 7.97918 | 0.722401 | ||||||||
\(123\) | −11.7263 | −1.05733 | ||||||||
\(124\) | 2.77822 | 0.249492 | ||||||||
\(125\) | 10.1526 | 0.908075 | ||||||||
\(126\) | 2.33714 | 0.208209 | ||||||||
\(127\) | −17.1800 | −1.52448 | −0.762238 | − | 0.647297i | \(-0.775899\pi\) | ||||
−0.762238 | + | 0.647297i | \(0.775899\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.2002 | 0.986127 | ||||||||
\(130\) | 12.2809 | 1.07711 | ||||||||
\(131\) | 5.22919 | 0.456877 | 0.228438 | − | 0.973558i | \(-0.426638\pi\) | ||||
0.228438 | + | 0.973558i | \(0.426638\pi\) | |||||||
\(132\) | −6.13924 | −0.534353 | ||||||||
\(133\) | −8.68356 | −0.752960 | ||||||||
\(134\) | 2.54885 | 0.220187 | ||||||||
\(135\) | −13.1874 | −1.13499 | ||||||||
\(136\) | 6.65764 | 0.570888 | ||||||||
\(137\) | −12.9664 | −1.10779 | −0.553895 | − | 0.832586i | \(-0.686859\pi\) | ||||
−0.553895 | + | 0.832586i | \(0.686859\pi\) | |||||||
\(138\) | −7.69990 | −0.655459 | ||||||||
\(139\) | −0.692646 | −0.0587495 | −0.0293747 | − | 0.999568i | \(-0.509352\pi\) | ||||
−0.0293747 | + | 0.999568i | \(0.509352\pi\) | |||||||
\(140\) | −3.65329 | −0.308759 | ||||||||
\(141\) | 9.13361 | 0.769189 | ||||||||
\(142\) | −1.98957 | −0.166961 | ||||||||
\(143\) | 25.9414 | 2.16933 | ||||||||
\(144\) | −1.53742 | −0.128118 | ||||||||
\(145\) | 14.4315 | 1.19847 | ||||||||
\(146\) | −12.7523 | −1.05538 | ||||||||
\(147\) | 5.67084 | 0.467723 | ||||||||
\(148\) | −1.59410 | −0.131034 | ||||||||
\(149\) | 11.5986 | 0.950197 | 0.475099 | − | 0.879933i | \(-0.342412\pi\) | ||||
0.475099 | + | 0.879933i | \(0.342412\pi\) | |||||||
\(150\) | 0.937750 | 0.0765669 | ||||||||
\(151\) | 1.14291 | 0.0930089 | 0.0465045 | − | 0.998918i | \(-0.485192\pi\) | ||||
0.0465045 | + | 0.998918i | \(0.485192\pi\) | |||||||
\(152\) | 5.71222 | 0.463322 | ||||||||
\(153\) | 10.2356 | 0.827496 | ||||||||
\(154\) | −7.71699 | −0.621852 | ||||||||
\(155\) | −6.67665 | −0.536281 | ||||||||
\(156\) | −6.18015 | −0.494808 | ||||||||
\(157\) | −12.2350 | −0.976460 | −0.488230 | − | 0.872715i | \(-0.662357\pi\) | ||||
−0.488230 | + | 0.872715i | \(0.662357\pi\) | |||||||
\(158\) | −3.64283 | −0.289808 | ||||||||
\(159\) | 11.3930 | 0.903523 | ||||||||
\(160\) | 2.40321 | 0.189990 | ||||||||
\(161\) | −9.67872 | −0.762790 | ||||||||
\(162\) | 2.02411 | 0.159029 | ||||||||
\(163\) | −23.6815 | −1.85488 | −0.927438 | − | 0.373978i | \(-0.877994\pi\) | ||||
−0.927438 | + | 0.373978i | \(0.877994\pi\) | |||||||
\(164\) | 9.69619 | 0.757146 | ||||||||
\(165\) | 14.7539 | 1.14859 | ||||||||
\(166\) | 0.689504 | 0.0535159 | ||||||||
\(167\) | −3.54694 | −0.274470 | −0.137235 | − | 0.990538i | \(-0.543822\pi\) | ||||
−0.137235 | + | 0.990538i | \(0.543822\pi\) | |||||||
\(168\) | 1.83846 | 0.141840 | ||||||||
\(169\) | 13.1142 | 1.00879 | ||||||||
\(170\) | −15.9997 | −1.22712 | ||||||||
\(171\) | 8.78205 | 0.671580 | ||||||||
\(172\) | −9.26120 | −0.706160 | ||||||||
\(173\) | 20.8927 | 1.58844 | 0.794220 | − | 0.607630i | \(-0.207880\pi\) | ||||
0.794220 | + | 0.607630i | \(0.207880\pi\) | |||||||
\(174\) | −7.26242 | −0.550562 | ||||||||
\(175\) | 1.17874 | 0.0891047 | ||||||||
\(176\) | 5.07638 | 0.382647 | ||||||||
\(177\) | 7.63516 | 0.573894 | ||||||||
\(178\) | −2.78972 | −0.209098 | ||||||||
\(179\) | 2.13073 | 0.159258 | 0.0796290 | − | 0.996825i | \(-0.474626\pi\) | ||||
0.0796290 | + | 0.996825i | \(0.474626\pi\) | |||||||
\(180\) | 3.69473 | 0.275389 | ||||||||
\(181\) | 18.5589 | 1.37948 | 0.689738 | − | 0.724059i | \(-0.257726\pi\) | ||||
0.689738 | + | 0.724059i | \(0.257726\pi\) | |||||||
\(182\) | −7.76841 | −0.575833 | ||||||||
\(183\) | 9.64981 | 0.713334 | ||||||||
\(184\) | 6.36685 | 0.469371 | ||||||||
\(185\) | 3.83095 | 0.281657 | ||||||||
\(186\) | 3.35991 | 0.246361 | ||||||||
\(187\) | −33.7967 | −2.47146 | ||||||||
\(188\) | −7.55235 | −0.550811 | ||||||||
\(189\) | 8.34185 | 0.606780 | ||||||||
\(190\) | −13.7276 | −0.995907 | ||||||||
\(191\) | 15.6213 | 1.13032 | 0.565160 | − | 0.824982i | \(-0.308815\pi\) | ||||
0.565160 | + | 0.824982i | \(0.308815\pi\) | |||||||
\(192\) | −1.20937 | −0.0872790 | ||||||||
\(193\) | −18.5417 | −1.33466 | −0.667330 | − | 0.744762i | \(-0.732563\pi\) | ||||
−0.667330 | + | 0.744762i | \(0.732563\pi\) | |||||||
\(194\) | −11.9363 | −0.856974 | ||||||||
\(195\) | 14.8522 | 1.06359 | ||||||||
\(196\) | −4.68907 | −0.334934 | ||||||||
\(197\) | −9.98285 | −0.711249 | −0.355624 | − | 0.934629i | \(-0.615732\pi\) | ||||
−0.355624 | + | 0.934629i | \(0.615732\pi\) | |||||||
\(198\) | 7.80451 | 0.554643 | ||||||||
\(199\) | 5.33431 | 0.378139 | 0.189070 | − | 0.981964i | \(-0.439453\pi\) | ||||
0.189070 | + | 0.981964i | \(0.439453\pi\) | |||||||
\(200\) | −0.775401 | −0.0548292 | ||||||||
\(201\) | 3.08251 | 0.217424 | ||||||||
\(202\) | 14.5273 | 1.02214 | ||||||||
\(203\) | −9.12880 | −0.640716 | ||||||||
\(204\) | 8.05157 | 0.563723 | ||||||||
\(205\) | −23.3020 | −1.62748 | ||||||||
\(206\) | 10.1048 | 0.704035 | ||||||||
\(207\) | 9.78850 | 0.680348 | ||||||||
\(208\) | 5.11021 | 0.354329 | ||||||||
\(209\) | −28.9974 | −2.00579 | ||||||||
\(210\) | −4.41819 | −0.304884 | ||||||||
\(211\) | −19.7945 | −1.36271 | −0.681355 | − | 0.731953i | \(-0.738609\pi\) | ||||
−0.681355 | + | 0.731953i | \(0.738609\pi\) | |||||||
\(212\) | −9.42058 | −0.647008 | ||||||||
\(213\) | −2.40613 | −0.164865 | ||||||||
\(214\) | 12.2725 | 0.838931 | ||||||||
\(215\) | 22.2566 | 1.51789 | ||||||||
\(216\) | −5.48743 | −0.373372 | ||||||||
\(217\) | 4.22338 | 0.286702 | ||||||||
\(218\) | −14.2163 | −0.962850 | ||||||||
\(219\) | −15.4222 | −1.04214 | ||||||||
\(220\) | −12.1996 | −0.822497 | ||||||||
\(221\) | −34.0219 | −2.28856 | ||||||||
\(222\) | −1.92786 | −0.129390 | ||||||||
\(223\) | 29.2824 | 1.96089 | 0.980447 | − | 0.196783i | \(-0.0630495\pi\) | ||||
0.980447 | + | 0.196783i | \(0.0630495\pi\) | |||||||
\(224\) | −1.52017 | −0.101571 | ||||||||
\(225\) | −1.19211 | −0.0794743 | ||||||||
\(226\) | −12.7024 | −0.844951 | ||||||||
\(227\) | −5.90479 | −0.391915 | −0.195957 | − | 0.980612i | \(-0.562781\pi\) | ||||
−0.195957 | + | 0.980612i | \(0.562781\pi\) | |||||||
\(228\) | 6.90820 | 0.457507 | ||||||||
\(229\) | 14.2761 | 0.943391 | 0.471695 | − | 0.881762i | \(-0.343642\pi\) | ||||
0.471695 | + | 0.881762i | \(0.343642\pi\) | |||||||
\(230\) | −15.3009 | −1.00891 | ||||||||
\(231\) | −9.33272 | −0.614048 | ||||||||
\(232\) | 6.00511 | 0.394254 | ||||||||
\(233\) | −27.0850 | −1.77440 | −0.887198 | − | 0.461389i | \(-0.847351\pi\) | ||||
−0.887198 | + | 0.461389i | \(0.847351\pi\) | |||||||
\(234\) | 7.85652 | 0.513597 | ||||||||
\(235\) | 18.1498 | 1.18397 | ||||||||
\(236\) | −6.31332 | −0.410962 | ||||||||
\(237\) | −4.40555 | −0.286171 | ||||||||
\(238\) | 10.1208 | 0.656032 | ||||||||
\(239\) | 7.97200 | 0.515666 | 0.257833 | − | 0.966190i | \(-0.416992\pi\) | ||||
0.257833 | + | 0.966190i | \(0.416992\pi\) | |||||||
\(240\) | 2.90637 | 0.187606 | ||||||||
\(241\) | −2.36516 | −0.152353 | −0.0761767 | − | 0.997094i | \(-0.524271\pi\) | ||||
−0.0761767 | + | 0.997094i | \(0.524271\pi\) | |||||||
\(242\) | −14.7697 | −0.949430 | ||||||||
\(243\) | −14.0144 | −0.899024 | ||||||||
\(244\) | −7.97918 | −0.510815 | ||||||||
\(245\) | 11.2688 | 0.719938 | ||||||||
\(246\) | 11.7263 | 0.747643 | ||||||||
\(247\) | −29.1906 | −1.85735 | ||||||||
\(248\) | −2.77822 | −0.176417 | ||||||||
\(249\) | 0.833868 | 0.0528443 | ||||||||
\(250\) | −10.1526 | −0.642106 | ||||||||
\(251\) | −23.0435 | −1.45449 | −0.727246 | − | 0.686376i | \(-0.759200\pi\) | ||||
−0.727246 | + | 0.686376i | \(0.759200\pi\) | |||||||
\(252\) | −2.33714 | −0.147226 | ||||||||
\(253\) | −32.3206 | −2.03198 | ||||||||
\(254\) | 17.1800 | 1.07797 | ||||||||
\(255\) | −19.3496 | −1.21172 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.2436 | 1.44990 | 0.724948 | − | 0.688803i | \(-0.241864\pi\) | ||||
0.724948 | + | 0.688803i | \(0.241864\pi\) | |||||||
\(258\) | −11.2002 | −0.697297 | ||||||||
\(259\) | −2.42331 | −0.150577 | ||||||||
\(260\) | −12.2809 | −0.761628 | ||||||||
\(261\) | 9.23234 | 0.571468 | ||||||||
\(262\) | −5.22919 | −0.323061 | ||||||||
\(263\) | 4.62308 | 0.285072 | 0.142536 | − | 0.989790i | \(-0.454474\pi\) | ||||
0.142536 | + | 0.989790i | \(0.454474\pi\) | |||||||
\(264\) | 6.13924 | 0.377844 | ||||||||
\(265\) | 22.6396 | 1.39074 | ||||||||
\(266\) | 8.68356 | 0.532423 | ||||||||
\(267\) | −3.37381 | −0.206474 | ||||||||
\(268\) | −2.54885 | −0.155696 | ||||||||
\(269\) | −1.00000 | −0.0609711 | ||||||||
\(270\) | 13.1874 | 0.802561 | ||||||||
\(271\) | 12.4311 | 0.755135 | 0.377568 | − | 0.925982i | \(-0.376761\pi\) | ||||
0.377568 | + | 0.925982i | \(0.376761\pi\) | |||||||
\(272\) | −6.65764 | −0.403679 | ||||||||
\(273\) | −9.39490 | −0.568605 | ||||||||
\(274\) | 12.9664 | 0.783326 | ||||||||
\(275\) | 3.93623 | 0.237364 | ||||||||
\(276\) | 7.69990 | 0.463480 | ||||||||
\(277\) | −4.92762 | −0.296072 | −0.148036 | − | 0.988982i | \(-0.547295\pi\) | ||||
−0.148036 | + | 0.988982i | \(0.547295\pi\) | |||||||
\(278\) | 0.692646 | 0.0415422 | ||||||||
\(279\) | −4.27129 | −0.255715 | ||||||||
\(280\) | 3.65329 | 0.218326 | ||||||||
\(281\) | −21.3194 | −1.27181 | −0.635905 | − | 0.771767i | \(-0.719373\pi\) | ||||
−0.635905 | + | 0.771767i | \(0.719373\pi\) | |||||||
\(282\) | −9.13361 | −0.543898 | ||||||||
\(283\) | −29.9997 | −1.78330 | −0.891649 | − | 0.452728i | \(-0.850451\pi\) | ||||
−0.891649 | + | 0.452728i | \(0.850451\pi\) | |||||||
\(284\) | 1.98957 | 0.118059 | ||||||||
\(285\) | −16.6018 | −0.983408 | ||||||||
\(286\) | −25.9414 | −1.53395 | ||||||||
\(287\) | 14.7399 | 0.870069 | ||||||||
\(288\) | 1.53742 | 0.0905931 | ||||||||
\(289\) | 27.3241 | 1.60730 | ||||||||
\(290\) | −14.4315 | −0.847447 | ||||||||
\(291\) | −14.4354 | −0.846218 | ||||||||
\(292\) | 12.7523 | 0.746269 | ||||||||
\(293\) | 16.9481 | 0.990120 | 0.495060 | − | 0.868859i | \(-0.335146\pi\) | ||||
0.495060 | + | 0.868859i | \(0.335146\pi\) | |||||||
\(294\) | −5.67084 | −0.330730 | ||||||||
\(295\) | 15.1722 | 0.883360 | ||||||||
\(296\) | 1.59410 | 0.0926553 | ||||||||
\(297\) | 27.8563 | 1.61639 | ||||||||
\(298\) | −11.5986 | −0.671891 | ||||||||
\(299\) | −32.5360 | −1.88160 | ||||||||
\(300\) | −0.937750 | −0.0541410 | ||||||||
\(301\) | −14.0786 | −0.811479 | ||||||||
\(302\) | −1.14291 | −0.0657672 | ||||||||
\(303\) | 17.5689 | 1.00931 | ||||||||
\(304\) | −5.71222 | −0.327618 | ||||||||
\(305\) | 19.1756 | 1.09799 | ||||||||
\(306\) | −10.2356 | −0.585128 | ||||||||
\(307\) | 18.4715 | 1.05422 | 0.527112 | − | 0.849796i | \(-0.323275\pi\) | ||||
0.527112 | + | 0.849796i | \(0.323275\pi\) | |||||||
\(308\) | 7.71699 | 0.439716 | ||||||||
\(309\) | 12.2205 | 0.695199 | ||||||||
\(310\) | 6.67665 | 0.379208 | ||||||||
\(311\) | 13.9141 | 0.788995 | 0.394497 | − | 0.918897i | \(-0.370919\pi\) | ||||
0.394497 | + | 0.918897i | \(0.370919\pi\) | |||||||
\(312\) | 6.18015 | 0.349882 | ||||||||
\(313\) | 21.9666 | 1.24162 | 0.620812 | − | 0.783959i | \(-0.286803\pi\) | ||||
0.620812 | + | 0.783959i | \(0.286803\pi\) | |||||||
\(314\) | 12.2350 | 0.690462 | ||||||||
\(315\) | 5.61663 | 0.316461 | ||||||||
\(316\) | 3.64283 | 0.204925 | ||||||||
\(317\) | −3.38070 | −0.189879 | −0.0949395 | − | 0.995483i | \(-0.530266\pi\) | ||||
−0.0949395 | + | 0.995483i | \(0.530266\pi\) | |||||||
\(318\) | −11.3930 | −0.638887 | ||||||||
\(319\) | −30.4842 | −1.70679 | ||||||||
\(320\) | −2.40321 | −0.134343 | ||||||||
\(321\) | 14.8420 | 0.828402 | ||||||||
\(322\) | 9.67872 | 0.539374 | ||||||||
\(323\) | 38.0299 | 2.11604 | ||||||||
\(324\) | −2.02411 | −0.112450 | ||||||||
\(325\) | 3.96246 | 0.219798 | ||||||||
\(326\) | 23.6815 | 1.31159 | ||||||||
\(327\) | −17.1928 | −0.950765 | ||||||||
\(328\) | −9.69619 | −0.535383 | ||||||||
\(329\) | −11.4809 | −0.632961 | ||||||||
\(330\) | −14.7539 | −0.812174 | ||||||||
\(331\) | 21.9585 | 1.20695 | 0.603476 | − | 0.797382i | \(-0.293782\pi\) | ||||
0.603476 | + | 0.797382i | \(0.293782\pi\) | |||||||
\(332\) | −0.689504 | −0.0378415 | ||||||||
\(333\) | 2.45080 | 0.134303 | ||||||||
\(334\) | 3.54694 | 0.194080 | ||||||||
\(335\) | 6.12542 | 0.334667 | ||||||||
\(336\) | −1.83846 | −0.100296 | ||||||||
\(337\) | 3.21883 | 0.175341 | 0.0876705 | − | 0.996150i | \(-0.472058\pi\) | ||||
0.0876705 | + | 0.996150i | \(0.472058\pi\) | |||||||
\(338\) | −13.1142 | −0.713321 | ||||||||
\(339\) | −15.3619 | −0.834346 | ||||||||
\(340\) | 15.9997 | 0.867704 | ||||||||
\(341\) | 14.1033 | 0.763738 | ||||||||
\(342\) | −8.78205 | −0.474879 | ||||||||
\(343\) | −17.7694 | −0.959459 | ||||||||
\(344\) | 9.26120 | 0.499330 | ||||||||
\(345\) | −18.5045 | −0.996246 | ||||||||
\(346\) | −20.8927 | −1.12320 | ||||||||
\(347\) | 15.8474 | 0.850734 | 0.425367 | − | 0.905021i | \(-0.360145\pi\) | ||||
0.425367 | + | 0.905021i | \(0.360145\pi\) | |||||||
\(348\) | 7.26242 | 0.389306 | ||||||||
\(349\) | −17.0834 | −0.914451 | −0.457226 | − | 0.889351i | \(-0.651157\pi\) | ||||
−0.457226 | + | 0.889351i | \(0.651157\pi\) | |||||||
\(350\) | −1.17874 | −0.0630066 | ||||||||
\(351\) | 28.0419 | 1.49677 | ||||||||
\(352\) | −5.07638 | −0.270572 | ||||||||
\(353\) | −4.73633 | −0.252090 | −0.126045 | − | 0.992025i | \(-0.540228\pi\) | ||||
−0.126045 | + | 0.992025i | \(0.540228\pi\) | |||||||
\(354\) | −7.63516 | −0.405804 | ||||||||
\(355\) | −4.78134 | −0.253767 | ||||||||
\(356\) | 2.78972 | 0.147855 | ||||||||
\(357\) | 12.2398 | 0.647798 | ||||||||
\(358\) | −2.13073 | −0.112612 | ||||||||
\(359\) | 18.2662 | 0.964051 | 0.482025 | − | 0.876157i | \(-0.339901\pi\) | ||||
0.482025 | + | 0.876157i | \(0.339901\pi\) | |||||||
\(360\) | −3.69473 | −0.194729 | ||||||||
\(361\) | 13.6294 | 0.717338 | ||||||||
\(362\) | −18.5589 | −0.975437 | ||||||||
\(363\) | −17.8620 | −0.937514 | ||||||||
\(364\) | 7.76841 | 0.407175 | ||||||||
\(365\) | −30.6463 | −1.60410 | ||||||||
\(366\) | −9.64981 | −0.504404 | ||||||||
\(367\) | 5.99172 | 0.312765 | 0.156383 | − | 0.987697i | \(-0.450017\pi\) | ||||
0.156383 | + | 0.987697i | \(0.450017\pi\) | |||||||
\(368\) | −6.36685 | −0.331895 | ||||||||
\(369\) | −14.9071 | −0.776032 | ||||||||
\(370\) | −3.83095 | −0.199162 | ||||||||
\(371\) | −14.3209 | −0.743505 | ||||||||
\(372\) | −3.35991 | −0.174203 | ||||||||
\(373\) | −16.9416 | −0.877203 | −0.438601 | − | 0.898682i | \(-0.644526\pi\) | ||||
−0.438601 | + | 0.898682i | \(0.644526\pi\) | |||||||
\(374\) | 33.7967 | 1.74759 | ||||||||
\(375\) | −12.2783 | −0.634047 | ||||||||
\(376\) | 7.55235 | 0.389483 | ||||||||
\(377\) | −30.6873 | −1.58048 | ||||||||
\(378\) | −8.34185 | −0.429058 | ||||||||
\(379\) | −16.7293 | −0.859325 | −0.429663 | − | 0.902989i | \(-0.641368\pi\) | ||||
−0.429663 | + | 0.902989i | \(0.641368\pi\) | |||||||
\(380\) | 13.7276 | 0.704213 | ||||||||
\(381\) | 20.7770 | 1.06444 | ||||||||
\(382\) | −15.6213 | −0.799257 | ||||||||
\(383\) | −26.8421 | −1.37157 | −0.685785 | − | 0.727804i | \(-0.740541\pi\) | ||||
−0.685785 | + | 0.727804i | \(0.740541\pi\) | |||||||
\(384\) | 1.20937 | 0.0617156 | ||||||||
\(385\) | −18.5455 | −0.945167 | ||||||||
\(386\) | 18.5417 | 0.943747 | ||||||||
\(387\) | 14.2383 | 0.723774 | ||||||||
\(388\) | 11.9363 | 0.605972 | ||||||||
\(389\) | 8.89100 | 0.450792 | 0.225396 | − | 0.974267i | \(-0.427632\pi\) | ||||
0.225396 | + | 0.974267i | \(0.427632\pi\) | |||||||
\(390\) | −14.8522 | −0.752069 | ||||||||
\(391\) | 42.3882 | 2.14366 | ||||||||
\(392\) | 4.68907 | 0.236834 | ||||||||
\(393\) | −6.32405 | −0.319006 | ||||||||
\(394\) | 9.98285 | 0.502929 | ||||||||
\(395\) | −8.75448 | −0.440486 | ||||||||
\(396\) | −7.80451 | −0.392191 | ||||||||
\(397\) | −15.3011 | −0.767939 | −0.383970 | − | 0.923346i | \(-0.625443\pi\) | ||||
−0.383970 | + | 0.923346i | \(0.625443\pi\) | |||||||
\(398\) | −5.33431 | −0.267385 | ||||||||
\(399\) | 10.5017 | 0.525741 | ||||||||
\(400\) | 0.775401 | 0.0387701 | ||||||||
\(401\) | −9.91869 | −0.495316 | −0.247658 | − | 0.968848i | \(-0.579661\pi\) | ||||
−0.247658 | + | 0.968848i | \(0.579661\pi\) | |||||||
\(402\) | −3.08251 | −0.153742 | ||||||||
\(403\) | 14.1973 | 0.707218 | ||||||||
\(404\) | −14.5273 | −0.722759 | ||||||||
\(405\) | 4.86434 | 0.241711 | ||||||||
\(406\) | 9.12880 | 0.453055 | ||||||||
\(407\) | −8.09227 | −0.401119 | ||||||||
\(408\) | −8.05157 | −0.398612 | ||||||||
\(409\) | −13.4737 | −0.666233 | −0.333117 | − | 0.942886i | \(-0.608100\pi\) | ||||
−0.333117 | + | 0.942886i | \(0.608100\pi\) | |||||||
\(410\) | 23.3020 | 1.15080 | ||||||||
\(411\) | 15.6812 | 0.773495 | ||||||||
\(412\) | −10.1048 | −0.497828 | ||||||||
\(413\) | −9.59734 | −0.472254 | ||||||||
\(414\) | −9.78850 | −0.481079 | ||||||||
\(415\) | 1.65702 | 0.0813400 | ||||||||
\(416\) | −5.11021 | −0.250549 | ||||||||
\(417\) | 0.837668 | 0.0410208 | ||||||||
\(418\) | 28.9974 | 1.41831 | ||||||||
\(419\) | −24.5320 | −1.19847 | −0.599233 | − | 0.800574i | \(-0.704528\pi\) | ||||
−0.599233 | + | 0.800574i | \(0.704528\pi\) | |||||||
\(420\) | 4.41819 | 0.215586 | ||||||||
\(421\) | −27.8189 | −1.35581 | −0.677906 | − | 0.735149i | \(-0.737112\pi\) | ||||
−0.677906 | + | 0.735149i | \(0.737112\pi\) | |||||||
\(422\) | 19.7945 | 0.963581 | ||||||||
\(423\) | 11.6111 | 0.564551 | ||||||||
\(424\) | 9.42058 | 0.457504 | ||||||||
\(425\) | −5.16234 | −0.250410 | ||||||||
\(426\) | 2.40613 | 0.116577 | ||||||||
\(427\) | −12.1297 | −0.586999 | ||||||||
\(428\) | −12.2725 | −0.593214 | ||||||||
\(429\) | −31.3728 | −1.51469 | ||||||||
\(430\) | −22.2566 | −1.07331 | ||||||||
\(431\) | 32.5743 | 1.56905 | 0.784525 | − | 0.620097i | \(-0.212907\pi\) | ||||
0.784525 | + | 0.620097i | \(0.212907\pi\) | |||||||
\(432\) | 5.48743 | 0.264014 | ||||||||
\(433\) | −5.11693 | −0.245904 | −0.122952 | − | 0.992413i | \(-0.539236\pi\) | ||||
−0.122952 | + | 0.992413i | \(0.539236\pi\) | |||||||
\(434\) | −4.22338 | −0.202729 | ||||||||
\(435\) | −17.4531 | −0.836811 | ||||||||
\(436\) | 14.2163 | 0.680838 | ||||||||
\(437\) | 36.3688 | 1.73976 | ||||||||
\(438\) | 15.4222 | 0.736903 | ||||||||
\(439\) | 18.8040 | 0.897466 | 0.448733 | − | 0.893666i | \(-0.351875\pi\) | ||||
0.448733 | + | 0.893666i | \(0.351875\pi\) | |||||||
\(440\) | 12.1996 | 0.581593 | ||||||||
\(441\) | 7.20905 | 0.343288 | ||||||||
\(442\) | 34.0219 | 1.61826 | ||||||||
\(443\) | 16.7817 | 0.797325 | 0.398662 | − | 0.917098i | \(-0.369475\pi\) | ||||
0.398662 | + | 0.917098i | \(0.369475\pi\) | |||||||
\(444\) | 1.92786 | 0.0914924 | ||||||||
\(445\) | −6.70426 | −0.317812 | ||||||||
\(446\) | −29.2824 | −1.38656 | ||||||||
\(447\) | −14.0271 | −0.663458 | ||||||||
\(448\) | 1.52017 | 0.0718215 | ||||||||
\(449\) | 29.1983 | 1.37795 | 0.688977 | − | 0.724784i | \(-0.258060\pi\) | ||||
0.688977 | + | 0.724784i | \(0.258060\pi\) | |||||||
\(450\) | 1.19211 | 0.0561968 | ||||||||
\(451\) | 49.2216 | 2.31775 | ||||||||
\(452\) | 12.7024 | 0.597471 | ||||||||
\(453\) | −1.38221 | −0.0649418 | ||||||||
\(454\) | 5.90479 | 0.277126 | ||||||||
\(455\) | −18.6691 | −0.875220 | ||||||||
\(456\) | −6.90820 | −0.323506 | ||||||||
\(457\) | 6.74219 | 0.315387 | 0.157693 | − | 0.987488i | \(-0.449594\pi\) | ||||
0.157693 | + | 0.987488i | \(0.449594\pi\) | |||||||
\(458\) | −14.2761 | −0.667078 | ||||||||
\(459\) | −36.5333 | −1.70523 | ||||||||
\(460\) | 15.3009 | 0.713406 | ||||||||
\(461\) | 17.8901 | 0.833226 | 0.416613 | − | 0.909084i | \(-0.363217\pi\) | ||||
0.416613 | + | 0.909084i | \(0.363217\pi\) | |||||||
\(462\) | 9.33272 | 0.434197 | ||||||||
\(463\) | 17.2936 | 0.803703 | 0.401851 | − | 0.915705i | \(-0.368367\pi\) | ||||
0.401851 | + | 0.915705i | \(0.368367\pi\) | |||||||
\(464\) | −6.00511 | −0.278780 | ||||||||
\(465\) | 8.07456 | 0.374449 | ||||||||
\(466\) | 27.0850 | 1.25469 | ||||||||
\(467\) | −3.00187 | −0.138910 | −0.0694550 | − | 0.997585i | \(-0.522126\pi\) | ||||
−0.0694550 | + | 0.997585i | \(0.522126\pi\) | |||||||
\(468\) | −7.85652 | −0.363168 | ||||||||
\(469\) | −3.87470 | −0.178917 | ||||||||
\(470\) | −18.1498 | −0.837190 | ||||||||
\(471\) | 14.7967 | 0.681796 | ||||||||
\(472\) | 6.31332 | 0.290594 | ||||||||
\(473\) | −47.0134 | −2.16168 | ||||||||
\(474\) | 4.40555 | 0.202354 | ||||||||
\(475\) | −4.42926 | −0.203228 | ||||||||
\(476\) | −10.1208 | −0.463884 | ||||||||
\(477\) | 14.4833 | 0.663147 | ||||||||
\(478\) | −7.97200 | −0.364631 | ||||||||
\(479\) | −25.7701 | −1.17747 | −0.588734 | − | 0.808327i | \(-0.700373\pi\) | ||||
−0.588734 | + | 0.808327i | \(0.700373\pi\) | |||||||
\(480\) | −2.90637 | −0.132657 | ||||||||
\(481\) | −8.14619 | −0.371434 | ||||||||
\(482\) | 2.36516 | 0.107730 | ||||||||
\(483\) | 11.7052 | 0.532605 | ||||||||
\(484\) | 14.7697 | 0.671349 | ||||||||
\(485\) | −28.6853 | −1.30253 | ||||||||
\(486\) | 14.0144 | 0.635706 | ||||||||
\(487\) | 9.85904 | 0.446756 | 0.223378 | − | 0.974732i | \(-0.428292\pi\) | ||||
0.223378 | + | 0.974732i | \(0.428292\pi\) | |||||||
\(488\) | 7.97918 | 0.361200 | ||||||||
\(489\) | 28.6397 | 1.29513 | ||||||||
\(490\) | −11.2688 | −0.509073 | ||||||||
\(491\) | 9.75565 | 0.440266 | 0.220133 | − | 0.975470i | \(-0.429351\pi\) | ||||
0.220133 | + | 0.975470i | \(0.429351\pi\) | |||||||
\(492\) | −11.7263 | −0.528663 | ||||||||
\(493\) | 39.9798 | 1.80060 | ||||||||
\(494\) | 29.1906 | 1.31335 | ||||||||
\(495\) | 18.7559 | 0.843013 | ||||||||
\(496\) | 2.77822 | 0.124746 | ||||||||
\(497\) | 3.02448 | 0.135667 | ||||||||
\(498\) | −0.833868 | −0.0373665 | ||||||||
\(499\) | −3.06163 | −0.137058 | −0.0685288 | − | 0.997649i | \(-0.521830\pi\) | ||||
−0.0685288 | + | 0.997649i | \(0.521830\pi\) | |||||||
\(500\) | 10.1526 | 0.454037 | ||||||||
\(501\) | 4.28957 | 0.191644 | ||||||||
\(502\) | 23.0435 | 1.02848 | ||||||||
\(503\) | −15.0940 | −0.673010 | −0.336505 | − | 0.941682i | \(-0.609245\pi\) | ||||
−0.336505 | + | 0.941682i | \(0.609245\pi\) | |||||||
\(504\) | 2.33714 | 0.104104 | ||||||||
\(505\) | 34.9121 | 1.55357 | ||||||||
\(506\) | 32.3206 | 1.43683 | ||||||||
\(507\) | −15.8600 | −0.704368 | ||||||||
\(508\) | −17.1800 | −0.762238 | ||||||||
\(509\) | 13.2575 | 0.587629 | 0.293814 | − | 0.955863i | \(-0.405075\pi\) | ||||
0.293814 | + | 0.955863i | \(0.405075\pi\) | |||||||
\(510\) | 19.3496 | 0.856814 | ||||||||
\(511\) | 19.3856 | 0.857570 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −31.3454 | −1.38393 | ||||||||
\(514\) | −23.2436 | −1.02523 | ||||||||
\(515\) | 24.2839 | 1.07008 | ||||||||
\(516\) | 11.2002 | 0.493063 | ||||||||
\(517\) | −38.3386 | −1.68613 | ||||||||
\(518\) | 2.42331 | 0.106474 | ||||||||
\(519\) | −25.2670 | −1.10910 | ||||||||
\(520\) | 12.2809 | 0.538553 | ||||||||
\(521\) | 20.2639 | 0.887776 | 0.443888 | − | 0.896082i | \(-0.353599\pi\) | ||||
0.443888 | + | 0.896082i | \(0.353599\pi\) | |||||||
\(522\) | −9.23234 | −0.404089 | ||||||||
\(523\) | −2.18471 | −0.0955307 | −0.0477654 | − | 0.998859i | \(-0.515210\pi\) | ||||
−0.0477654 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(524\) | 5.22919 | 0.228438 | ||||||||
\(525\) | −1.42554 | −0.0622158 | ||||||||
\(526\) | −4.62308 | −0.201576 | ||||||||
\(527\) | −18.4964 | −0.805716 | ||||||||
\(528\) | −6.13924 | −0.267176 | ||||||||
\(529\) | 17.5368 | 0.762470 | ||||||||
\(530\) | −22.6396 | −0.983401 | ||||||||
\(531\) | 9.70620 | 0.421213 | ||||||||
\(532\) | −8.68356 | −0.376480 | ||||||||
\(533\) | 49.5496 | 2.14623 | ||||||||
\(534\) | 3.37381 | 0.145999 | ||||||||
\(535\) | 29.4933 | 1.27511 | ||||||||
\(536\) | 2.54885 | 0.110094 | ||||||||
\(537\) | −2.57685 | −0.111199 | ||||||||
\(538\) | 1.00000 | 0.0431131 | ||||||||
\(539\) | −23.8035 | −1.02529 | ||||||||
\(540\) | −13.1874 | −0.567497 | ||||||||
\(541\) | 21.9779 | 0.944903 | 0.472452 | − | 0.881357i | \(-0.343369\pi\) | ||||
0.472452 | + | 0.881357i | \(0.343369\pi\) | |||||||
\(542\) | −12.4311 | −0.533961 | ||||||||
\(543\) | −22.4447 | −0.963194 | ||||||||
\(544\) | 6.65764 | 0.285444 | ||||||||
\(545\) | −34.1647 | −1.46346 | ||||||||
\(546\) | 9.39490 | 0.402065 | ||||||||
\(547\) | −2.59714 | −0.111046 | −0.0555229 | − | 0.998457i | \(-0.517683\pi\) | ||||
−0.0555229 | + | 0.998457i | \(0.517683\pi\) | |||||||
\(548\) | −12.9664 | −0.553895 | ||||||||
\(549\) | 12.2673 | 0.523556 | ||||||||
\(550\) | −3.93623 | −0.167842 | ||||||||
\(551\) | 34.3025 | 1.46133 | ||||||||
\(552\) | −7.69990 | −0.327730 | ||||||||
\(553\) | 5.53774 | 0.235489 | ||||||||
\(554\) | 4.92762 | 0.209354 | ||||||||
\(555\) | −4.63305 | −0.196662 | ||||||||
\(556\) | −0.692646 | −0.0293747 | ||||||||
\(557\) | 32.9165 | 1.39471 | 0.697357 | − | 0.716724i | \(-0.254359\pi\) | ||||
0.697357 | + | 0.716724i | \(0.254359\pi\) | |||||||
\(558\) | 4.27129 | 0.180818 | ||||||||
\(559\) | −47.3266 | −2.00170 | ||||||||
\(560\) | −3.65329 | −0.154380 | ||||||||
\(561\) | 40.8729 | 1.72565 | ||||||||
\(562\) | 21.3194 | 0.899306 | ||||||||
\(563\) | −16.1700 | −0.681485 | −0.340742 | − | 0.940157i | \(-0.610678\pi\) | ||||
−0.340742 | + | 0.940157i | \(0.610678\pi\) | |||||||
\(564\) | 9.13361 | 0.384594 | ||||||||
\(565\) | −30.5265 | −1.28426 | ||||||||
\(566\) | 29.9997 | 1.26098 | ||||||||
\(567\) | −3.07699 | −0.129222 | ||||||||
\(568\) | −1.98957 | −0.0834803 | ||||||||
\(569\) | −11.9495 | −0.500951 | −0.250476 | − | 0.968123i | \(-0.580587\pi\) | ||||
−0.250476 | + | 0.968123i | \(0.580587\pi\) | |||||||
\(570\) | 16.6018 | 0.695375 | ||||||||
\(571\) | −18.1326 | −0.758824 | −0.379412 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379412 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(572\) | 25.9414 | 1.08466 | ||||||||
\(573\) | −18.8920 | −0.789225 | ||||||||
\(574\) | −14.7399 | −0.615232 | ||||||||
\(575\) | −4.93687 | −0.205882 | ||||||||
\(576\) | −1.53742 | −0.0640590 | ||||||||
\(577\) | 22.5512 | 0.938817 | 0.469408 | − | 0.882981i | \(-0.344467\pi\) | ||||
0.469408 | + | 0.882981i | \(0.344467\pi\) | |||||||
\(578\) | −27.3241 | −1.13653 | ||||||||
\(579\) | 22.4238 | 0.931903 | ||||||||
\(580\) | 14.4315 | 0.599236 | ||||||||
\(581\) | −1.04817 | −0.0434853 | ||||||||
\(582\) | 14.4354 | 0.598367 | ||||||||
\(583\) | −47.8225 | −1.98060 | ||||||||
\(584\) | −12.7523 | −0.527692 | ||||||||
\(585\) | 18.8808 | 0.780626 | ||||||||
\(586\) | −16.9481 | −0.700121 | ||||||||
\(587\) | 22.1880 | 0.915796 | 0.457898 | − | 0.889005i | \(-0.348603\pi\) | ||||
0.457898 | + | 0.889005i | \(0.348603\pi\) | |||||||
\(588\) | 5.67084 | 0.233861 | ||||||||
\(589\) | −15.8698 | −0.653905 | ||||||||
\(590\) | −15.1722 | −0.624630 | ||||||||
\(591\) | 12.0730 | 0.496617 | ||||||||
\(592\) | −1.59410 | −0.0655172 | ||||||||
\(593\) | 30.4282 | 1.24954 | 0.624768 | − | 0.780811i | \(-0.285194\pi\) | ||||
0.624768 | + | 0.780811i | \(0.285194\pi\) | |||||||
\(594\) | −27.8563 | −1.14296 | ||||||||
\(595\) | 24.3223 | 0.997117 | ||||||||
\(596\) | 11.5986 | 0.475099 | ||||||||
\(597\) | −6.45118 | −0.264029 | ||||||||
\(598\) | 32.5360 | 1.33049 | ||||||||
\(599\) | 15.6413 | 0.639086 | 0.319543 | − | 0.947572i | \(-0.396471\pi\) | ||||
0.319543 | + | 0.947572i | \(0.396471\pi\) | |||||||
\(600\) | 0.937750 | 0.0382835 | ||||||||
\(601\) | −19.9435 | −0.813512 | −0.406756 | − | 0.913537i | \(-0.633340\pi\) | ||||
−0.406756 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(602\) | 14.0786 | 0.573802 | ||||||||
\(603\) | 3.91864 | 0.159580 | ||||||||
\(604\) | 1.14291 | 0.0465045 | ||||||||
\(605\) | −35.4946 | −1.44306 | ||||||||
\(606\) | −17.5689 | −0.713688 | ||||||||
\(607\) | −11.4793 | −0.465932 | −0.232966 | − | 0.972485i | \(-0.574843\pi\) | ||||
−0.232966 | + | 0.972485i | \(0.574843\pi\) | |||||||
\(608\) | 5.71222 | 0.231661 | ||||||||
\(609\) | 11.0401 | 0.447369 | ||||||||
\(610\) | −19.1756 | −0.776398 | ||||||||
\(611\) | −38.5941 | −1.56135 | ||||||||
\(612\) | 10.2356 | 0.413748 | ||||||||
\(613\) | 11.2663 | 0.455044 | 0.227522 | − | 0.973773i | \(-0.426938\pi\) | ||||
0.227522 | + | 0.973773i | \(0.426938\pi\) | |||||||
\(614\) | −18.4715 | −0.745449 | ||||||||
\(615\) | 28.1808 | 1.13636 | ||||||||
\(616\) | −7.71699 | −0.310926 | ||||||||
\(617\) | 10.0317 | 0.403861 | 0.201930 | − | 0.979400i | \(-0.435279\pi\) | ||||
0.201930 | + | 0.979400i | \(0.435279\pi\) | |||||||
\(618\) | −12.2205 | −0.491580 | ||||||||
\(619\) | 10.0658 | 0.404579 | 0.202289 | − | 0.979326i | \(-0.435162\pi\) | ||||
0.202289 | + | 0.979326i | \(0.435162\pi\) | |||||||
\(620\) | −6.67665 | −0.268141 | ||||||||
\(621\) | −34.9377 | −1.40200 | ||||||||
\(622\) | −13.9141 | −0.557904 | ||||||||
\(623\) | 4.24085 | 0.169906 | ||||||||
\(624\) | −6.18015 | −0.247404 | ||||||||
\(625\) | −28.2758 | −1.13103 | ||||||||
\(626\) | −21.9666 | −0.877961 | ||||||||
\(627\) | 35.0687 | 1.40051 | ||||||||
\(628\) | −12.2350 | −0.488230 | ||||||||
\(629\) | 10.6129 | 0.423166 | ||||||||
\(630\) | −5.61663 | −0.223772 | ||||||||
\(631\) | −35.3530 | −1.40738 | −0.703691 | − | 0.710506i | \(-0.748466\pi\) | ||||
−0.703691 | + | 0.710506i | \(0.748466\pi\) | |||||||
\(632\) | −3.64283 | −0.144904 | ||||||||
\(633\) | 23.9389 | 0.951488 | ||||||||
\(634\) | 3.38070 | 0.134265 | ||||||||
\(635\) | 41.2870 | 1.63842 | ||||||||
\(636\) | 11.3930 | 0.451762 | ||||||||
\(637\) | −23.9621 | −0.949414 | ||||||||
\(638\) | 30.4842 | 1.20688 | ||||||||
\(639\) | −3.05879 | −0.121004 | ||||||||
\(640\) | 2.40321 | 0.0949951 | ||||||||
\(641\) | 0.166926 | 0.00659316 | 0.00329658 | − | 0.999995i | \(-0.498951\pi\) | ||||
0.00329658 | + | 0.999995i | \(0.498951\pi\) | |||||||
\(642\) | −14.8420 | −0.585768 | ||||||||
\(643\) | −30.9571 | −1.22083 | −0.610415 | − | 0.792082i | \(-0.708997\pi\) | ||||
−0.610415 | + | 0.792082i | \(0.708997\pi\) | |||||||
\(644\) | −9.67872 | −0.381395 | ||||||||
\(645\) | −26.9165 | −1.05984 | ||||||||
\(646\) | −38.0299 | −1.49626 | ||||||||
\(647\) | −0.959927 | −0.0377386 | −0.0188693 | − | 0.999822i | \(-0.506007\pi\) | ||||
−0.0188693 | + | 0.999822i | \(0.506007\pi\) | |||||||
\(648\) | 2.02411 | 0.0795144 | ||||||||
\(649\) | −32.0488 | −1.25803 | ||||||||
\(650\) | −3.96246 | −0.155421 | ||||||||
\(651\) | −5.10765 | −0.200185 | ||||||||
\(652\) | −23.6815 | −0.927438 | ||||||||
\(653\) | 27.5173 | 1.07684 | 0.538418 | − | 0.842678i | \(-0.319022\pi\) | ||||
0.538418 | + | 0.842678i | \(0.319022\pi\) | |||||||
\(654\) | 17.1928 | 0.672293 | ||||||||
\(655\) | −12.5668 | −0.491027 | ||||||||
\(656\) | 9.69619 | 0.378573 | ||||||||
\(657\) | −19.6055 | −0.764884 | ||||||||
\(658\) | 11.4809 | 0.447571 | ||||||||
\(659\) | 3.87281 | 0.150863 | 0.0754316 | − | 0.997151i | \(-0.475967\pi\) | ||||
0.0754316 | + | 0.997151i | \(0.475967\pi\) | |||||||
\(660\) | 14.7539 | 0.574294 | ||||||||
\(661\) | 2.60845 | 0.101457 | 0.0507285 | − | 0.998712i | \(-0.483846\pi\) | ||||
0.0507285 | + | 0.998712i | \(0.483846\pi\) | |||||||
\(662\) | −21.9585 | −0.853443 | ||||||||
\(663\) | 41.1452 | 1.59795 | ||||||||
\(664\) | 0.689504 | 0.0267580 | ||||||||
\(665\) | 20.8684 | 0.809242 | ||||||||
\(666\) | −2.45080 | −0.0949664 | ||||||||
\(667\) | 38.2336 | 1.48041 | ||||||||
\(668\) | −3.54694 | −0.137235 | ||||||||
\(669\) | −35.4134 | −1.36916 | ||||||||
\(670\) | −6.12542 | −0.236645 | ||||||||
\(671\) | −40.5054 | −1.56369 | ||||||||
\(672\) | 1.83846 | 0.0709201 | ||||||||
\(673\) | −12.9907 | −0.500753 | −0.250376 | − | 0.968149i | \(-0.580554\pi\) | ||||
−0.250376 | + | 0.968149i | \(0.580554\pi\) | |||||||
\(674\) | −3.21883 | −0.123985 | ||||||||
\(675\) | 4.25496 | 0.163774 | ||||||||
\(676\) | 13.1142 | 0.504394 | ||||||||
\(677\) | 30.7406 | 1.18146 | 0.590728 | − | 0.806871i | \(-0.298841\pi\) | ||||
0.590728 | + | 0.806871i | \(0.298841\pi\) | |||||||
\(678\) | 15.3619 | 0.589972 | ||||||||
\(679\) | 18.1452 | 0.696349 | ||||||||
\(680\) | −15.9997 | −0.613560 | ||||||||
\(681\) | 7.14110 | 0.273648 | ||||||||
\(682\) | −14.1033 | −0.540045 | ||||||||
\(683\) | −6.20328 | −0.237362 | −0.118681 | − | 0.992932i | \(-0.537867\pi\) | ||||
−0.118681 | + | 0.992932i | \(0.537867\pi\) | |||||||
\(684\) | 8.78205 | 0.335790 | ||||||||
\(685\) | 31.1608 | 1.19059 | ||||||||
\(686\) | 17.7694 | 0.678440 | ||||||||
\(687\) | −17.2651 | −0.658706 | ||||||||
\(688\) | −9.26120 | −0.353080 | ||||||||
\(689\) | −48.1411 | −1.83403 | ||||||||
\(690\) | 18.5045 | 0.704453 | ||||||||
\(691\) | 18.1544 | 0.690626 | 0.345313 | − | 0.938488i | \(-0.387773\pi\) | ||||
0.345313 | + | 0.938488i | \(0.387773\pi\) | |||||||
\(692\) | 20.8927 | 0.794220 | ||||||||
\(693\) | −11.8642 | −0.450684 | ||||||||
\(694\) | −15.8474 | −0.601560 | ||||||||
\(695\) | 1.66457 | 0.0631408 | ||||||||
\(696\) | −7.26242 | −0.275281 | ||||||||
\(697\) | −64.5537 | −2.44515 | ||||||||
\(698\) | 17.0834 | 0.646615 | ||||||||
\(699\) | 32.7559 | 1.23894 | ||||||||
\(700\) | 1.17874 | 0.0445524 | ||||||||
\(701\) | −46.2492 | −1.74681 | −0.873404 | − | 0.486996i | \(-0.838093\pi\) | ||||
−0.873404 | + | 0.486996i | \(0.838093\pi\) | |||||||
\(702\) | −28.0419 | −1.05837 | ||||||||
\(703\) | 9.10585 | 0.343434 | ||||||||
\(704\) | 5.07638 | 0.191323 | ||||||||
\(705\) | −21.9499 | −0.826683 | ||||||||
\(706\) | 4.73633 | 0.178254 | ||||||||
\(707\) | −22.0840 | −0.830554 | ||||||||
\(708\) | 7.63516 | 0.286947 | ||||||||
\(709\) | −35.6219 | −1.33781 | −0.668904 | − | 0.743349i | \(-0.733236\pi\) | ||||
−0.668904 | + | 0.743349i | \(0.733236\pi\) | |||||||
\(710\) | 4.78134 | 0.179440 | ||||||||
\(711\) | −5.60055 | −0.210037 | ||||||||
\(712\) | −2.78972 | −0.104549 | ||||||||
\(713\) | −17.6885 | −0.662441 | ||||||||
\(714\) | −12.2398 | −0.458062 | ||||||||
\(715\) | −62.3425 | −2.33148 | ||||||||
\(716\) | 2.13073 | 0.0796290 | ||||||||
\(717\) | −9.64112 | −0.360054 | ||||||||
\(718\) | −18.2662 | −0.681687 | ||||||||
\(719\) | −37.4220 | −1.39561 | −0.697803 | − | 0.716290i | \(-0.745839\pi\) | ||||
−0.697803 | + | 0.716290i | \(0.745839\pi\) | |||||||
\(720\) | 3.69473 | 0.137694 | ||||||||
\(721\) | −15.3611 | −0.572076 | ||||||||
\(722\) | −13.6294 | −0.507234 | ||||||||
\(723\) | 2.86036 | 0.106378 | ||||||||
\(724\) | 18.5589 | 0.689738 | ||||||||
\(725\) | −4.65637 | −0.172933 | ||||||||
\(726\) | 17.8620 | 0.662923 | ||||||||
\(727\) | −24.4331 | −0.906172 | −0.453086 | − | 0.891467i | \(-0.649677\pi\) | ||||
−0.453086 | + | 0.891467i | \(0.649677\pi\) | |||||||
\(728\) | −7.76841 | −0.287916 | ||||||||
\(729\) | 23.0209 | 0.852628 | ||||||||
\(730\) | 30.6463 | 1.13427 | ||||||||
\(731\) | 61.6577 | 2.28049 | ||||||||
\(732\) | 9.64981 | 0.356667 | ||||||||
\(733\) | 37.4726 | 1.38408 | 0.692042 | − | 0.721857i | \(-0.256711\pi\) | ||||
0.692042 | + | 0.721857i | \(0.256711\pi\) | |||||||
\(734\) | −5.99172 | −0.221159 | ||||||||
\(735\) | −13.6282 | −0.502684 | ||||||||
\(736\) | 6.36685 | 0.234685 | ||||||||
\(737\) | −12.9389 | −0.476612 | ||||||||
\(738\) | 14.9071 | 0.548737 | ||||||||
\(739\) | −18.6134 | −0.684707 | −0.342353 | − | 0.939571i | \(-0.611224\pi\) | ||||
−0.342353 | + | 0.939571i | \(0.611224\pi\) | |||||||
\(740\) | 3.83095 | 0.140829 | ||||||||
\(741\) | 35.3024 | 1.29686 | ||||||||
\(742\) | 14.3209 | 0.525737 | ||||||||
\(743\) | 0.773612 | 0.0283811 | 0.0141905 | − | 0.999899i | \(-0.495483\pi\) | ||||
0.0141905 | + | 0.999899i | \(0.495483\pi\) | |||||||
\(744\) | 3.35991 | 0.123180 | ||||||||
\(745\) | −27.8739 | −1.02122 | ||||||||
\(746\) | 16.9416 | 0.620276 | ||||||||
\(747\) | 1.06005 | 0.0387854 | ||||||||
\(748\) | −33.7967 | −1.23573 | ||||||||
\(749\) | −18.6563 | −0.681688 | ||||||||
\(750\) | 12.2783 | 0.448339 | ||||||||
\(751\) | −11.0543 | −0.403377 | −0.201689 | − | 0.979450i | \(-0.564643\pi\) | ||||
−0.201689 | + | 0.979450i | \(0.564643\pi\) | |||||||
\(752\) | −7.55235 | −0.275406 | ||||||||
\(753\) | 27.8682 | 1.01557 | ||||||||
\(754\) | 30.6873 | 1.11757 | ||||||||
\(755\) | −2.74666 | −0.0999610 | ||||||||
\(756\) | 8.34185 | 0.303390 | ||||||||
\(757\) | 31.9235 | 1.16028 | 0.580140 | − | 0.814517i | \(-0.302998\pi\) | ||||
0.580140 | + | 0.814517i | \(0.302998\pi\) | |||||||
\(758\) | 16.7293 | 0.607635 | ||||||||
\(759\) | 39.0877 | 1.41879 | ||||||||
\(760\) | −13.7276 | −0.497954 | ||||||||
\(761\) | 14.7166 | 0.533477 | 0.266739 | − | 0.963769i | \(-0.414054\pi\) | ||||
0.266739 | + | 0.963769i | \(0.414054\pi\) | |||||||
\(762\) | −20.7770 | −0.752671 | ||||||||
\(763\) | 21.6113 | 0.782380 | ||||||||
\(764\) | 15.6213 | 0.565160 | ||||||||
\(765\) | −24.5982 | −0.889348 | ||||||||
\(766\) | 26.8421 | 0.969846 | ||||||||
\(767\) | −32.2624 | −1.16493 | ||||||||
\(768\) | −1.20937 | −0.0436395 | ||||||||
\(769\) | −18.0186 | −0.649768 | −0.324884 | − | 0.945754i | \(-0.605325\pi\) | ||||
−0.324884 | + | 0.945754i | \(0.605325\pi\) | |||||||
\(770\) | 18.5455 | 0.668334 | ||||||||
\(771\) | −28.1102 | −1.01236 | ||||||||
\(772\) | −18.5417 | −0.667330 | ||||||||
\(773\) | 48.8663 | 1.75760 | 0.878799 | − | 0.477193i | \(-0.158346\pi\) | ||||
0.878799 | + | 0.477193i | \(0.158346\pi\) | |||||||
\(774\) | −14.2383 | −0.511785 | ||||||||
\(775\) | 2.15424 | 0.0773825 | ||||||||
\(776\) | −11.9363 | −0.428487 | ||||||||
\(777\) | 2.93069 | 0.105138 | ||||||||
\(778\) | −8.89100 | −0.318758 | ||||||||
\(779\) | −55.3868 | −1.98444 | ||||||||
\(780\) | 14.8522 | 0.531793 | ||||||||
\(781\) | 10.0998 | 0.361399 | ||||||||
\(782\) | −42.3882 | −1.51580 | ||||||||
\(783\) | −32.9526 | −1.17763 | ||||||||
\(784\) | −4.68907 | −0.167467 | ||||||||
\(785\) | 29.4033 | 1.04945 | ||||||||
\(786\) | 6.32405 | 0.225571 | ||||||||
\(787\) | −31.8942 | −1.13691 | −0.568453 | − | 0.822715i | \(-0.692458\pi\) | ||||
−0.568453 | + | 0.822715i | \(0.692458\pi\) | |||||||
\(788\) | −9.98285 | −0.355624 | ||||||||
\(789\) | −5.59103 | −0.199046 | ||||||||
\(790\) | 8.75448 | 0.311471 | ||||||||
\(791\) | 19.3099 | 0.686579 | ||||||||
\(792\) | 7.80451 | 0.277321 | ||||||||
\(793\) | −40.7753 | −1.44797 | ||||||||
\(794\) | 15.3011 | 0.543015 | ||||||||
\(795\) | −27.3797 | −0.971059 | ||||||||
\(796\) | 5.33431 | 0.189070 | ||||||||
\(797\) | −26.0846 | −0.923964 | −0.461982 | − | 0.886889i | \(-0.652861\pi\) | ||||
−0.461982 | + | 0.886889i | \(0.652861\pi\) | |||||||
\(798\) | −10.5017 | −0.371755 | ||||||||
\(799\) | 50.2808 | 1.77881 | ||||||||
\(800\) | −0.775401 | −0.0274146 | ||||||||
\(801\) | −4.28895 | −0.151543 | ||||||||
\(802\) | 9.91869 | 0.350241 | ||||||||
\(803\) | 64.7353 | 2.28446 | ||||||||
\(804\) | 3.08251 | 0.108712 | ||||||||
\(805\) | 23.2600 | 0.819806 | ||||||||
\(806\) | −14.1973 | −0.500079 | ||||||||
\(807\) | 1.20937 | 0.0425720 | ||||||||
\(808\) | 14.5273 | 0.511068 | ||||||||
\(809\) | −2.45878 | −0.0864461 | −0.0432231 | − | 0.999065i | \(-0.513763\pi\) | ||||
−0.0432231 | + | 0.999065i | \(0.513763\pi\) | |||||||
\(810\) | −4.86434 | −0.170916 | ||||||||
\(811\) | −20.3841 | −0.715783 | −0.357891 | − | 0.933763i | \(-0.616504\pi\) | ||||
−0.357891 | + | 0.933763i | \(0.616504\pi\) | |||||||
\(812\) | −9.12880 | −0.320358 | ||||||||
\(813\) | −15.0338 | −0.527260 | ||||||||
\(814\) | 8.09227 | 0.283634 | ||||||||
\(815\) | 56.9114 | 1.99352 | ||||||||
\(816\) | 8.05157 | 0.281861 | ||||||||
\(817\) | 52.9020 | 1.85081 | ||||||||
\(818\) | 13.4737 | 0.471098 | ||||||||
\(819\) | −11.9433 | −0.417332 | ||||||||
\(820\) | −23.3020 | −0.813740 | ||||||||
\(821\) | −8.31824 | −0.290309 | −0.145154 | − | 0.989409i | \(-0.546368\pi\) | ||||
−0.145154 | + | 0.989409i | \(0.546368\pi\) | |||||||
\(822\) | −15.6812 | −0.546943 | ||||||||
\(823\) | −25.5967 | −0.892244 | −0.446122 | − | 0.894972i | \(-0.647195\pi\) | ||||
−0.446122 | + | 0.894972i | \(0.647195\pi\) | |||||||
\(824\) | 10.1048 | 0.352017 | ||||||||
\(825\) | −4.76038 | −0.165735 | ||||||||
\(826\) | 9.59734 | 0.333934 | ||||||||
\(827\) | 28.4900 | 0.990693 | 0.495347 | − | 0.868695i | \(-0.335041\pi\) | ||||
0.495347 | + | 0.868695i | \(0.335041\pi\) | |||||||
\(828\) | 9.78850 | 0.340174 | ||||||||
\(829\) | −15.2875 | −0.530956 | −0.265478 | − | 0.964117i | \(-0.585530\pi\) | ||||
−0.265478 | + | 0.964117i | \(0.585530\pi\) | |||||||
\(830\) | −1.65702 | −0.0575161 | ||||||||
\(831\) | 5.95933 | 0.206727 | ||||||||
\(832\) | 5.11021 | 0.177165 | ||||||||
\(833\) | 31.2181 | 1.08164 | ||||||||
\(834\) | −0.837668 | −0.0290061 | ||||||||
\(835\) | 8.52403 | 0.294986 | ||||||||
\(836\) | −28.9974 | −1.00290 | ||||||||
\(837\) | 15.2453 | 0.526955 | ||||||||
\(838\) | 24.5320 | 0.847444 | ||||||||
\(839\) | 33.9640 | 1.17257 | 0.586283 | − | 0.810106i | \(-0.300591\pi\) | ||||
0.586283 | + | 0.810106i | \(0.300591\pi\) | |||||||
\(840\) | −4.41819 | −0.152442 | ||||||||
\(841\) | 7.06129 | 0.243493 | ||||||||
\(842\) | 27.8189 | 0.958704 | ||||||||
\(843\) | 25.7832 | 0.888019 | ||||||||
\(844\) | −19.7945 | −0.681355 | ||||||||
\(845\) | −31.5162 | −1.08419 | ||||||||
\(846\) | −11.6111 | −0.399198 | ||||||||
\(847\) | 22.4525 | 0.771476 | ||||||||
\(848\) | −9.42058 | −0.323504 | ||||||||
\(849\) | 36.2808 | 1.24516 | ||||||||
\(850\) | 5.16234 | 0.177067 | ||||||||
\(851\) | 10.1494 | 0.347917 | ||||||||
\(852\) | −2.40613 | −0.0824326 | ||||||||
\(853\) | −18.6395 | −0.638203 | −0.319102 | − | 0.947720i | \(-0.603381\pi\) | ||||
−0.319102 | + | 0.947720i | \(0.603381\pi\) | |||||||
\(854\) | 12.1297 | 0.415071 | ||||||||
\(855\) | −21.1051 | −0.721779 | ||||||||
\(856\) | 12.2725 | 0.419465 | ||||||||
\(857\) | 38.5929 | 1.31831 | 0.659154 | − | 0.752008i | \(-0.270915\pi\) | ||||
0.659154 | + | 0.752008i | \(0.270915\pi\) | |||||||
\(858\) | 31.3728 | 1.07105 | ||||||||
\(859\) | 36.7533 | 1.25400 | 0.627002 | − | 0.779017i | \(-0.284282\pi\) | ||||
0.627002 | + | 0.779017i | \(0.284282\pi\) | |||||||
\(860\) | 22.2566 | 0.758943 | ||||||||
\(861\) | −17.8260 | −0.607510 | ||||||||
\(862\) | −32.5743 | −1.10949 | ||||||||
\(863\) | 39.5677 | 1.34690 | 0.673450 | − | 0.739233i | \(-0.264812\pi\) | ||||
0.673450 | + | 0.739233i | \(0.264812\pi\) | |||||||
\(864\) | −5.48743 | −0.186686 | ||||||||
\(865\) | −50.2094 | −1.70717 | ||||||||
\(866\) | 5.11693 | 0.173880 | ||||||||
\(867\) | −33.0451 | −1.12227 | ||||||||
\(868\) | 4.22338 | 0.143351 | ||||||||
\(869\) | 18.4924 | 0.627313 | ||||||||
\(870\) | 17.4531 | 0.591715 | ||||||||
\(871\) | −13.0252 | −0.441341 | ||||||||
\(872\) | −14.2163 | −0.481425 | ||||||||
\(873\) | −18.3510 | −0.621087 | ||||||||
\(874\) | −36.3688 | −1.23019 | ||||||||
\(875\) | 15.4337 | 0.521754 | ||||||||
\(876\) | −15.4222 | −0.521069 | ||||||||
\(877\) | 4.55367 | 0.153766 | 0.0768832 | − | 0.997040i | \(-0.475503\pi\) | ||||
0.0768832 | + | 0.997040i | \(0.475503\pi\) | |||||||
\(878\) | −18.8040 | −0.634604 | ||||||||
\(879\) | −20.4966 | −0.691334 | ||||||||
\(880\) | −12.1996 | −0.411248 | ||||||||
\(881\) | −16.4979 | −0.555828 | −0.277914 | − | 0.960606i | \(-0.589643\pi\) | ||||
−0.277914 | + | 0.960606i | \(0.589643\pi\) | |||||||
\(882\) | −7.20905 | −0.242741 | ||||||||
\(883\) | −43.4286 | −1.46149 | −0.730744 | − | 0.682652i | \(-0.760827\pi\) | ||||
−0.730744 | + | 0.682652i | \(0.760827\pi\) | |||||||
\(884\) | −34.0219 | −1.14428 | ||||||||
\(885\) | −18.3489 | −0.616790 | ||||||||
\(886\) | −16.7817 | −0.563794 | ||||||||
\(887\) | −9.36355 | −0.314397 | −0.157199 | − | 0.987567i | \(-0.550246\pi\) | ||||
−0.157199 | + | 0.987567i | \(0.550246\pi\) | |||||||
\(888\) | −1.92786 | −0.0646949 | ||||||||
\(889\) | −26.1165 | −0.875920 | ||||||||
\(890\) | 6.70426 | 0.224727 | ||||||||
\(891\) | −10.2751 | −0.344230 | ||||||||
\(892\) | 29.2824 | 0.980447 | ||||||||
\(893\) | 43.1406 | 1.44365 | ||||||||
\(894\) | 14.0271 | 0.469136 | ||||||||
\(895\) | −5.12058 | −0.171162 | ||||||||
\(896\) | −1.52017 | −0.0507854 | ||||||||
\(897\) | 39.3481 | 1.31380 | ||||||||
\(898\) | −29.1983 | −0.974360 | ||||||||
\(899\) | −16.6835 | −0.556427 | ||||||||
\(900\) | −1.19211 | −0.0397371 | ||||||||
\(901\) | 62.7188 | 2.08947 | ||||||||
\(902\) | −49.2216 | −1.63890 | ||||||||
\(903\) | 17.0263 | 0.566600 | ||||||||
\(904\) | −12.7024 | −0.422476 | ||||||||
\(905\) | −44.6010 | −1.48259 | ||||||||
\(906\) | 1.38221 | 0.0459208 | ||||||||
\(907\) | −43.0813 | −1.43049 | −0.715246 | − | 0.698873i | \(-0.753685\pi\) | ||||
−0.715246 | + | 0.698873i | \(0.753685\pi\) | |||||||
\(908\) | −5.90479 | −0.195957 | ||||||||
\(909\) | 22.3345 | 0.740788 | ||||||||
\(910\) | 18.6691 | 0.618874 | ||||||||
\(911\) | −3.70489 | −0.122749 | −0.0613743 | − | 0.998115i | \(-0.519548\pi\) | ||||
−0.0613743 | + | 0.998115i | \(0.519548\pi\) | |||||||
\(912\) | 6.90820 | 0.228753 | ||||||||
\(913\) | −3.50019 | −0.115839 | ||||||||
\(914\) | −6.74219 | −0.223012 | ||||||||
\(915\) | −23.1905 | −0.766654 | ||||||||
\(916\) | 14.2761 | 0.471695 | ||||||||
\(917\) | 7.94928 | 0.262508 | ||||||||
\(918\) | 36.5333 | 1.20578 | ||||||||
\(919\) | 42.2046 | 1.39220 | 0.696101 | − | 0.717944i | \(-0.254917\pi\) | ||||
0.696101 | + | 0.717944i | \(0.254917\pi\) | |||||||
\(920\) | −15.3009 | −0.504454 | ||||||||
\(921\) | −22.3390 | −0.736093 | ||||||||
\(922\) | −17.8901 | −0.589180 | ||||||||
\(923\) | 10.1671 | 0.334654 | ||||||||
\(924\) | −9.33272 | −0.307024 | ||||||||
\(925\) | −1.23607 | −0.0406417 | ||||||||
\(926\) | −17.2936 | −0.568304 | ||||||||
\(927\) | 15.5353 | 0.510246 | ||||||||
\(928\) | 6.00511 | 0.197127 | ||||||||
\(929\) | −40.9616 | −1.34391 | −0.671954 | − | 0.740593i | \(-0.734545\pi\) | ||||
−0.671954 | + | 0.740593i | \(0.734545\pi\) | |||||||
\(930\) | −8.07456 | −0.264775 | ||||||||
\(931\) | 26.7850 | 0.877843 | ||||||||
\(932\) | −27.0850 | −0.887198 | ||||||||
\(933\) | −16.8273 | −0.550901 | ||||||||
\(934\) | 3.00187 | 0.0982243 | ||||||||
\(935\) | 81.2205 | 2.65619 | ||||||||
\(936\) | 7.85652 | 0.256798 | ||||||||
\(937\) | −11.2419 | −0.367258 | −0.183629 | − | 0.982996i | \(-0.558785\pi\) | ||||
−0.183629 | + | 0.982996i | \(0.558785\pi\) | |||||||
\(938\) | 3.87470 | 0.126513 | ||||||||
\(939\) | −26.5658 | −0.866942 | ||||||||
\(940\) | 18.1498 | 0.591983 | ||||||||
\(941\) | 1.14007 | 0.0371652 | 0.0185826 | − | 0.999827i | \(-0.494085\pi\) | ||||
0.0185826 | + | 0.999827i | \(0.494085\pi\) | |||||||
\(942\) | −14.7967 | −0.482102 | ||||||||
\(943\) | −61.7342 | −2.01034 | ||||||||
\(944\) | −6.31332 | −0.205481 | ||||||||
\(945\) | −20.0472 | −0.652135 | ||||||||
\(946\) | 47.0134 | 1.52854 | ||||||||
\(947\) | −20.5389 | −0.667424 | −0.333712 | − | 0.942675i | \(-0.608301\pi\) | ||||
−0.333712 | + | 0.942675i | \(0.608301\pi\) | |||||||
\(948\) | −4.40555 | −0.143086 | ||||||||
\(949\) | 65.1667 | 2.11540 | ||||||||
\(950\) | 4.42926 | 0.143704 | ||||||||
\(951\) | 4.08853 | 0.132580 | ||||||||
\(952\) | 10.1208 | 0.328016 | ||||||||
\(953\) | −18.6016 | −0.602567 | −0.301283 | − | 0.953535i | \(-0.597415\pi\) | ||||
−0.301283 | + | 0.953535i | \(0.597415\pi\) | |||||||
\(954\) | −14.4833 | −0.468916 | ||||||||
\(955\) | −37.5413 | −1.21481 | ||||||||
\(956\) | 7.97200 | 0.257833 | ||||||||
\(957\) | 36.8668 | 1.19173 | ||||||||
\(958\) | 25.7701 | 0.832595 | ||||||||
\(959\) | −19.7111 | −0.636505 | ||||||||
\(960\) | 2.90637 | 0.0938028 | ||||||||
\(961\) | −23.2815 | −0.751015 | ||||||||
\(962\) | 8.14619 | 0.262644 | ||||||||
\(963\) | 18.8679 | 0.608011 | ||||||||
\(964\) | −2.36516 | −0.0761767 | ||||||||
\(965\) | 44.5595 | 1.43442 | ||||||||
\(966\) | −11.7052 | −0.376608 | ||||||||
\(967\) | −21.3331 | −0.686026 | −0.343013 | − | 0.939331i | \(-0.611447\pi\) | ||||
−0.343013 | + | 0.939331i | \(0.611447\pi\) | |||||||
\(968\) | −14.7697 | −0.474715 | ||||||||
\(969\) | −45.9923 | −1.47749 | ||||||||
\(970\) | 28.6853 | 0.921030 | ||||||||
\(971\) | 13.0827 | 0.419844 | 0.209922 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209922 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(972\) | −14.0144 | −0.449512 | ||||||||
\(973\) | −1.05294 | −0.0337558 | ||||||||
\(974\) | −9.85904 | −0.315904 | ||||||||
\(975\) | −4.79210 | −0.153470 | ||||||||
\(976\) | −7.97918 | −0.255407 | ||||||||
\(977\) | −22.6902 | −0.725924 | −0.362962 | − | 0.931804i | \(-0.618234\pi\) | ||||
−0.362962 | + | 0.931804i | \(0.618234\pi\) | |||||||
\(978\) | −28.6397 | −0.915798 | ||||||||
\(979\) | 14.1617 | 0.452609 | ||||||||
\(980\) | 11.2688 | 0.359969 | ||||||||
\(981\) | −21.8564 | −0.697820 | ||||||||
\(982\) | −9.75565 | −0.311315 | ||||||||
\(983\) | −51.3612 | −1.63817 | −0.819084 | − | 0.573674i | \(-0.805518\pi\) | ||||
−0.819084 | + | 0.573674i | \(0.805518\pi\) | |||||||
\(984\) | 11.7263 | 0.373821 | ||||||||
\(985\) | 23.9909 | 0.764412 | ||||||||
\(986\) | −39.9798 | −1.27322 | ||||||||
\(987\) | 13.8847 | 0.441954 | ||||||||
\(988\) | −29.1906 | −0.928677 | ||||||||
\(989\) | 58.9647 | 1.87497 | ||||||||
\(990\) | −18.7559 | −0.596100 | ||||||||
\(991\) | −11.0015 | −0.349475 | −0.174737 | − | 0.984615i | \(-0.555908\pi\) | ||||
−0.174737 | + | 0.984615i | \(0.555908\pi\) | |||||||
\(992\) | −2.77822 | −0.0882087 | ||||||||
\(993\) | −26.5561 | −0.842732 | ||||||||
\(994\) | −3.02448 | −0.0959308 | ||||||||
\(995\) | −12.8195 | −0.406404 | ||||||||
\(996\) | 0.833868 | 0.0264221 | ||||||||
\(997\) | 12.2415 | 0.387693 | 0.193846 | − | 0.981032i | \(-0.437904\pi\) | ||||
0.193846 | + | 0.981032i | \(0.437904\pi\) | |||||||
\(998\) | 3.06163 | 0.0969143 | ||||||||
\(999\) | −8.74752 | −0.276759 |
(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 | 538.2.a.d.1.3 | ✓ | 7 | |
3.2 | odd | 2 | 4842.2.a.o.1.5 | 7 | |||
4.3 | odd | 2 | 4304.2.a.i.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.d.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
4304.2.a.i.1.5 | 7 | 4.3 | odd | 2 | |||
4842.2.a.o.1.5 | 7 | 3.2 | odd | 2 |