Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [717,2,Mod(1,717)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(717, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("717.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 717 = 3 \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 717.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: | \(5.72527382493\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1767625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.267500\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 717.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.12029 | 1.49927 | 0.749635 | − | 0.661852i | \(-0.230229\pi\) | ||||
0.749635 | + | 0.661852i | \(0.230229\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.49562 | 1.24781 | ||||||||
\(5\) | −2.47082 | −1.10499 | −0.552493 | − | 0.833518i | \(-0.686323\pi\) | ||||
−0.552493 | + | 0.833518i | \(0.686323\pi\) | |||||||
\(6\) | −2.12029 | −0.865604 | ||||||||
\(7\) | −2.45271 | −0.927037 | −0.463519 | − | 0.886087i | \(-0.653413\pi\) | ||||
−0.463519 | + | 0.886087i | \(0.653413\pi\) | |||||||
\(8\) | 1.05086 | 0.371534 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.23885 | −1.65667 | ||||||||
\(11\) | −4.01073 | −1.20928 | −0.604641 | − | 0.796498i | \(-0.706683\pi\) | ||||
−0.604641 | + | 0.796498i | \(0.706683\pi\) | |||||||
\(12\) | −2.49562 | −0.720424 | ||||||||
\(13\) | 1.62598 | 0.450966 | 0.225483 | − | 0.974247i | \(-0.427604\pi\) | ||||
0.225483 | + | 0.974247i | \(0.427604\pi\) | |||||||
\(14\) | −5.20045 | −1.38988 | ||||||||
\(15\) | 2.47082 | 0.637964 | ||||||||
\(16\) | −2.76312 | −0.690780 | ||||||||
\(17\) | 4.89570 | 1.18738 | 0.593691 | − | 0.804693i | \(-0.297670\pi\) | ||||
0.593691 | + | 0.804693i | \(0.297670\pi\) | |||||||
\(18\) | 2.12029 | 0.499757 | ||||||||
\(19\) | −6.28561 | −1.44202 | −0.721009 | − | 0.692926i | \(-0.756321\pi\) | ||||
−0.721009 | + | 0.692926i | \(0.756321\pi\) | |||||||
\(20\) | −6.16623 | −1.37881 | ||||||||
\(21\) | 2.45271 | 0.535225 | ||||||||
\(22\) | −8.50391 | −1.81304 | ||||||||
\(23\) | −3.83124 | −0.798868 | −0.399434 | − | 0.916762i | \(-0.630793\pi\) | ||||
−0.399434 | + | 0.916762i | \(0.630793\pi\) | |||||||
\(24\) | −1.05086 | −0.214505 | ||||||||
\(25\) | 1.10496 | 0.220992 | ||||||||
\(26\) | 3.44755 | 0.676120 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −6.12103 | −1.15677 | ||||||||
\(29\) | −0.357168 | −0.0663244 | −0.0331622 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331622 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(30\) | 5.23885 | 0.956479 | ||||||||
\(31\) | −8.44143 | −1.51613 | −0.758063 | − | 0.652181i | \(-0.773854\pi\) | ||||
−0.758063 | + | 0.652181i | \(0.773854\pi\) | |||||||
\(32\) | −7.96032 | −1.40720 | ||||||||
\(33\) | 4.01073 | 0.698179 | ||||||||
\(34\) | 10.3803 | 1.78020 | ||||||||
\(35\) | 6.06021 | 1.02436 | ||||||||
\(36\) | 2.49562 | 0.415937 | ||||||||
\(37\) | −1.81610 | −0.298566 | −0.149283 | − | 0.988795i | \(-0.547696\pi\) | ||||
−0.149283 | + | 0.988795i | \(0.547696\pi\) | |||||||
\(38\) | −13.3273 | −2.16197 | ||||||||
\(39\) | −1.62598 | −0.260365 | ||||||||
\(40\) | −2.59648 | −0.410540 | ||||||||
\(41\) | 10.7403 | 1.67735 | 0.838676 | − | 0.544630i | \(-0.183330\pi\) | ||||
0.838676 | + | 0.544630i | \(0.183330\pi\) | |||||||
\(42\) | 5.20045 | 0.802447 | ||||||||
\(43\) | 9.09255 | 1.38660 | 0.693301 | − | 0.720649i | \(-0.256156\pi\) | ||||
0.693301 | + | 0.720649i | \(0.256156\pi\) | |||||||
\(44\) | −10.0093 | −1.50895 | ||||||||
\(45\) | −2.47082 | −0.368328 | ||||||||
\(46\) | −8.12332 | −1.19772 | ||||||||
\(47\) | 11.0197 | 1.60739 | 0.803693 | − | 0.595044i | \(-0.202866\pi\) | ||||
0.803693 | + | 0.595044i | \(0.202866\pi\) | |||||||
\(48\) | 2.76312 | 0.398822 | ||||||||
\(49\) | −0.984213 | −0.140602 | ||||||||
\(50\) | 2.34284 | 0.331327 | ||||||||
\(51\) | −4.89570 | −0.685535 | ||||||||
\(52\) | 4.05783 | 0.562720 | ||||||||
\(53\) | 5.78427 | 0.794530 | 0.397265 | − | 0.917704i | \(-0.369959\pi\) | ||||
0.397265 | + | 0.917704i | \(0.369959\pi\) | |||||||
\(54\) | −2.12029 | −0.288535 | ||||||||
\(55\) | 9.90981 | 1.33624 | ||||||||
\(56\) | −2.57745 | −0.344426 | ||||||||
\(57\) | 6.28561 | 0.832550 | ||||||||
\(58\) | −0.757299 | −0.0994382 | ||||||||
\(59\) | −1.43742 | −0.187136 | −0.0935678 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935678 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(60\) | 6.16623 | 0.796057 | ||||||||
\(61\) | 2.21862 | 0.284065 | 0.142032 | − | 0.989862i | \(-0.454636\pi\) | ||||
0.142032 | + | 0.989862i | \(0.454636\pi\) | |||||||
\(62\) | −17.8983 | −2.27308 | ||||||||
\(63\) | −2.45271 | −0.309012 | ||||||||
\(64\) | −11.3519 | −1.41899 | ||||||||
\(65\) | −4.01751 | −0.498311 | ||||||||
\(66\) | 8.50391 | 1.04676 | ||||||||
\(67\) | −14.2454 | −1.74036 | −0.870178 | − | 0.492738i | \(-0.835996\pi\) | ||||
−0.870178 | + | 0.492738i | \(0.835996\pi\) | |||||||
\(68\) | 12.2178 | 1.48163 | ||||||||
\(69\) | 3.83124 | 0.461227 | ||||||||
\(70\) | 12.8494 | 1.53580 | ||||||||
\(71\) | −4.12013 | −0.488969 | −0.244485 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244485 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(72\) | 1.05086 | 0.123845 | ||||||||
\(73\) | 2.78648 | 0.326133 | 0.163067 | − | 0.986615i | \(-0.447861\pi\) | ||||
0.163067 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(74\) | −3.85066 | −0.447630 | ||||||||
\(75\) | −1.10496 | −0.127590 | ||||||||
\(76\) | −15.6865 | −1.79936 | ||||||||
\(77\) | 9.83717 | 1.12105 | ||||||||
\(78\) | −3.44755 | −0.390358 | ||||||||
\(79\) | 7.84263 | 0.882365 | 0.441182 | − | 0.897417i | \(-0.354559\pi\) | ||||
0.441182 | + | 0.897417i | \(0.354559\pi\) | |||||||
\(80\) | 6.82718 | 0.763302 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 22.7725 | 2.51480 | ||||||||
\(83\) | −9.91715 | −1.08855 | −0.544274 | − | 0.838907i | \(-0.683195\pi\) | ||||
−0.544274 | + | 0.838907i | \(0.683195\pi\) | |||||||
\(84\) | 6.12103 | 0.667859 | ||||||||
\(85\) | −12.0964 | −1.31204 | ||||||||
\(86\) | 19.2788 | 2.07889 | ||||||||
\(87\) | 0.357168 | 0.0382924 | ||||||||
\(88\) | −4.21471 | −0.449290 | ||||||||
\(89\) | 0.978993 | 0.103773 | 0.0518865 | − | 0.998653i | \(-0.483477\pi\) | ||||
0.0518865 | + | 0.998653i | \(0.483477\pi\) | |||||||
\(90\) | −5.23885 | −0.552224 | ||||||||
\(91\) | −3.98806 | −0.418062 | ||||||||
\(92\) | −9.56131 | −0.996836 | ||||||||
\(93\) | 8.44143 | 0.875336 | ||||||||
\(94\) | 23.3649 | 2.40991 | ||||||||
\(95\) | 15.5306 | 1.59341 | ||||||||
\(96\) | 7.96032 | 0.812447 | ||||||||
\(97\) | −16.8523 | −1.71109 | −0.855545 | − | 0.517728i | \(-0.826778\pi\) | ||||
−0.855545 | + | 0.517728i | \(0.826778\pi\) | |||||||
\(98\) | −2.08682 | −0.210800 | ||||||||
\(99\) | −4.01073 | −0.403094 | ||||||||
\(100\) | 2.75756 | 0.275756 | ||||||||
\(101\) | 3.80431 | 0.378543 | 0.189271 | − | 0.981925i | \(-0.439387\pi\) | ||||
0.189271 | + | 0.981925i | \(0.439387\pi\) | |||||||
\(102\) | −10.3803 | −1.02780 | ||||||||
\(103\) | 8.01017 | 0.789266 | 0.394633 | − | 0.918839i | \(-0.370872\pi\) | ||||
0.394633 | + | 0.918839i | \(0.370872\pi\) | |||||||
\(104\) | 1.70867 | 0.167549 | ||||||||
\(105\) | −6.06021 | −0.591416 | ||||||||
\(106\) | 12.2643 | 1.19122 | ||||||||
\(107\) | −12.6857 | −1.22638 | −0.613188 | − | 0.789937i | \(-0.710113\pi\) | ||||
−0.613188 | + | 0.789937i | \(0.710113\pi\) | |||||||
\(108\) | −2.49562 | −0.240141 | ||||||||
\(109\) | −18.7766 | −1.79847 | −0.899237 | − | 0.437461i | \(-0.855878\pi\) | ||||
−0.899237 | + | 0.437461i | \(0.855878\pi\) | |||||||
\(110\) | 21.0116 | 2.00338 | ||||||||
\(111\) | 1.81610 | 0.172377 | ||||||||
\(112\) | 6.77713 | 0.640379 | ||||||||
\(113\) | −7.61332 | −0.716201 | −0.358101 | − | 0.933683i | \(-0.616575\pi\) | ||||
−0.358101 | + | 0.933683i | \(0.616575\pi\) | |||||||
\(114\) | 13.3273 | 1.24822 | ||||||||
\(115\) | 9.46630 | 0.882737 | ||||||||
\(116\) | −0.891355 | −0.0827603 | ||||||||
\(117\) | 1.62598 | 0.150322 | ||||||||
\(118\) | −3.04774 | −0.280567 | ||||||||
\(119\) | −12.0077 | −1.10075 | ||||||||
\(120\) | 2.59648 | 0.237025 | ||||||||
\(121\) | 5.08598 | 0.462362 | ||||||||
\(122\) | 4.70410 | 0.425890 | ||||||||
\(123\) | −10.7403 | −0.968420 | ||||||||
\(124\) | −21.0666 | −1.89184 | ||||||||
\(125\) | 9.62395 | 0.860792 | ||||||||
\(126\) | −5.20045 | −0.463293 | ||||||||
\(127\) | 14.0067 | 1.24290 | 0.621448 | − | 0.783455i | \(-0.286545\pi\) | ||||
0.621448 | + | 0.783455i | \(0.286545\pi\) | |||||||
\(128\) | −8.14873 | −0.720253 | ||||||||
\(129\) | −9.09255 | −0.800555 | ||||||||
\(130\) | −8.51828 | −0.747102 | ||||||||
\(131\) | −4.05565 | −0.354344 | −0.177172 | − | 0.984180i | \(-0.556695\pi\) | ||||
−0.177172 | + | 0.984180i | \(0.556695\pi\) | |||||||
\(132\) | 10.0093 | 0.871195 | ||||||||
\(133\) | 15.4168 | 1.33680 | ||||||||
\(134\) | −30.2044 | −2.60926 | ||||||||
\(135\) | 2.47082 | 0.212655 | ||||||||
\(136\) | 5.14468 | 0.441153 | ||||||||
\(137\) | −15.5346 | −1.32721 | −0.663604 | − | 0.748084i | \(-0.730974\pi\) | ||||
−0.663604 | + | 0.748084i | \(0.730974\pi\) | |||||||
\(138\) | 8.12332 | 0.691503 | ||||||||
\(139\) | 1.09201 | 0.0926232 | 0.0463116 | − | 0.998927i | \(-0.485253\pi\) | ||||
0.0463116 | + | 0.998927i | \(0.485253\pi\) | |||||||
\(140\) | 15.1240 | 1.27821 | ||||||||
\(141\) | −11.0197 | −0.928025 | ||||||||
\(142\) | −8.73586 | −0.733097 | ||||||||
\(143\) | −6.52138 | −0.545345 | ||||||||
\(144\) | −2.76312 | −0.230260 | ||||||||
\(145\) | 0.882498 | 0.0732875 | ||||||||
\(146\) | 5.90815 | 0.488962 | ||||||||
\(147\) | 0.984213 | 0.0811765 | ||||||||
\(148\) | −4.53230 | −0.372553 | ||||||||
\(149\) | −15.9702 | −1.30833 | −0.654167 | − | 0.756350i | \(-0.726981\pi\) | ||||
−0.654167 | + | 0.756350i | \(0.726981\pi\) | |||||||
\(150\) | −2.34284 | −0.191292 | ||||||||
\(151\) | −8.44617 | −0.687339 | −0.343670 | − | 0.939091i | \(-0.611670\pi\) | ||||
−0.343670 | + | 0.939091i | \(0.611670\pi\) | |||||||
\(152\) | −6.60528 | −0.535759 | ||||||||
\(153\) | 4.89570 | 0.395794 | ||||||||
\(154\) | 20.8576 | 1.68076 | ||||||||
\(155\) | 20.8573 | 1.67530 | ||||||||
\(156\) | −4.05783 | −0.324887 | ||||||||
\(157\) | 8.21810 | 0.655876 | 0.327938 | − | 0.944699i | \(-0.393646\pi\) | ||||
0.327938 | + | 0.944699i | \(0.393646\pi\) | |||||||
\(158\) | 16.6286 | 1.32290 | ||||||||
\(159\) | −5.78427 | −0.458722 | ||||||||
\(160\) | 19.6685 | 1.55494 | ||||||||
\(161\) | 9.39691 | 0.740580 | ||||||||
\(162\) | 2.12029 | 0.166586 | ||||||||
\(163\) | 3.58850 | 0.281073 | 0.140537 | − | 0.990075i | \(-0.455117\pi\) | ||||
0.140537 | + | 0.990075i | \(0.455117\pi\) | |||||||
\(164\) | 26.8037 | 2.09302 | ||||||||
\(165\) | −9.90981 | −0.771478 | ||||||||
\(166\) | −21.0272 | −1.63203 | ||||||||
\(167\) | 14.0773 | 1.08934 | 0.544668 | − | 0.838652i | \(-0.316656\pi\) | ||||
0.544668 | + | 0.838652i | \(0.316656\pi\) | |||||||
\(168\) | 2.57745 | 0.198855 | ||||||||
\(169\) | −10.3562 | −0.796630 | ||||||||
\(170\) | −25.6478 | −1.96710 | ||||||||
\(171\) | −6.28561 | −0.480673 | ||||||||
\(172\) | 22.6916 | 1.73021 | ||||||||
\(173\) | 5.90842 | 0.449208 | 0.224604 | − | 0.974450i | \(-0.427891\pi\) | ||||
0.224604 | + | 0.974450i | \(0.427891\pi\) | |||||||
\(174\) | 0.757299 | 0.0574107 | ||||||||
\(175\) | −2.71015 | −0.204868 | ||||||||
\(176\) | 11.0821 | 0.835348 | ||||||||
\(177\) | 1.43742 | 0.108043 | ||||||||
\(178\) | 2.07575 | 0.155584 | ||||||||
\(179\) | 18.5491 | 1.38642 | 0.693211 | − | 0.720735i | \(-0.256195\pi\) | ||||
0.693211 | + | 0.720735i | \(0.256195\pi\) | |||||||
\(180\) | −6.16623 | −0.459604 | ||||||||
\(181\) | −0.921544 | −0.0684978 | −0.0342489 | − | 0.999413i | \(-0.510904\pi\) | ||||
−0.0342489 | + | 0.999413i | \(0.510904\pi\) | |||||||
\(182\) | −8.45584 | −0.626788 | ||||||||
\(183\) | −2.21862 | −0.164005 | ||||||||
\(184\) | −4.02608 | −0.296807 | ||||||||
\(185\) | 4.48727 | 0.329911 | ||||||||
\(186\) | 17.8983 | 1.31236 | ||||||||
\(187\) | −19.6353 | −1.43588 | ||||||||
\(188\) | 27.5009 | 2.00571 | ||||||||
\(189\) | 2.45271 | 0.178408 | ||||||||
\(190\) | 32.9294 | 2.38895 | ||||||||
\(191\) | 15.1285 | 1.09466 | 0.547329 | − | 0.836918i | \(-0.315645\pi\) | ||||
0.547329 | + | 0.836918i | \(0.315645\pi\) | |||||||
\(192\) | 11.3519 | 0.819256 | ||||||||
\(193\) | −22.7285 | −1.63603 | −0.818015 | − | 0.575197i | \(-0.804925\pi\) | ||||
−0.818015 | + | 0.575197i | \(0.804925\pi\) | |||||||
\(194\) | −35.7317 | −2.56539 | ||||||||
\(195\) | 4.01751 | 0.287700 | ||||||||
\(196\) | −2.45622 | −0.175444 | ||||||||
\(197\) | −2.47078 | −0.176036 | −0.0880179 | − | 0.996119i | \(-0.528053\pi\) | ||||
−0.0880179 | + | 0.996119i | \(0.528053\pi\) | |||||||
\(198\) | −8.50391 | −0.604346 | ||||||||
\(199\) | −5.34461 | −0.378869 | −0.189435 | − | 0.981893i | \(-0.560666\pi\) | ||||
−0.189435 | + | 0.981893i | \(0.560666\pi\) | |||||||
\(200\) | 1.16116 | 0.0821062 | ||||||||
\(201\) | 14.2454 | 1.00479 | ||||||||
\(202\) | 8.06622 | 0.567538 | ||||||||
\(203\) | 0.876029 | 0.0614852 | ||||||||
\(204\) | −12.2178 | −0.855417 | ||||||||
\(205\) | −26.5374 | −1.85345 | ||||||||
\(206\) | 16.9839 | 1.18332 | ||||||||
\(207\) | −3.83124 | −0.266289 | ||||||||
\(208\) | −4.49278 | −0.311518 | ||||||||
\(209\) | 25.2099 | 1.74381 | ||||||||
\(210\) | −12.8494 | −0.886692 | ||||||||
\(211\) | −10.3377 | −0.711676 | −0.355838 | − | 0.934548i | \(-0.615804\pi\) | ||||
−0.355838 | + | 0.934548i | \(0.615804\pi\) | |||||||
\(212\) | 14.4353 | 0.991423 | ||||||||
\(213\) | 4.12013 | 0.282307 | ||||||||
\(214\) | −26.8974 | −1.83867 | ||||||||
\(215\) | −22.4661 | −1.53217 | ||||||||
\(216\) | −1.05086 | −0.0715018 | ||||||||
\(217\) | 20.7044 | 1.40551 | ||||||||
\(218\) | −39.8119 | −2.69640 | ||||||||
\(219\) | −2.78648 | −0.188293 | ||||||||
\(220\) | 24.7311 | 1.66737 | ||||||||
\(221\) | 7.96031 | 0.535469 | ||||||||
\(222\) | 3.85066 | 0.258440 | ||||||||
\(223\) | −10.2702 | −0.687745 | −0.343873 | − | 0.939016i | \(-0.611739\pi\) | ||||
−0.343873 | + | 0.939016i | \(0.611739\pi\) | |||||||
\(224\) | 19.5244 | 1.30453 | ||||||||
\(225\) | 1.10496 | 0.0736641 | ||||||||
\(226\) | −16.1424 | −1.07378 | ||||||||
\(227\) | −16.9467 | −1.12479 | −0.562396 | − | 0.826868i | \(-0.690120\pi\) | ||||
−0.562396 | + | 0.826868i | \(0.690120\pi\) | |||||||
\(228\) | 15.6865 | 1.03886 | ||||||||
\(229\) | −29.0495 | −1.91964 | −0.959822 | − | 0.280609i | \(-0.909464\pi\) | ||||
−0.959822 | + | 0.280609i | \(0.909464\pi\) | |||||||
\(230\) | 20.0713 | 1.32346 | ||||||||
\(231\) | −9.83717 | −0.647238 | ||||||||
\(232\) | −0.375332 | −0.0246418 | ||||||||
\(233\) | −19.7368 | −1.29300 | −0.646500 | − | 0.762914i | \(-0.723768\pi\) | ||||
−0.646500 | + | 0.762914i | \(0.723768\pi\) | |||||||
\(234\) | 3.44755 | 0.225373 | ||||||||
\(235\) | −27.2277 | −1.77614 | ||||||||
\(236\) | −3.58725 | −0.233510 | ||||||||
\(237\) | −7.84263 | −0.509434 | ||||||||
\(238\) | −25.4598 | −1.65032 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | −6.82718 | −0.440692 | ||||||||
\(241\) | 10.4837 | 0.675311 | 0.337656 | − | 0.941270i | \(-0.390366\pi\) | ||||
0.337656 | + | 0.941270i | \(0.390366\pi\) | |||||||
\(242\) | 10.7837 | 0.693205 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.53682 | 0.354459 | ||||||||
\(245\) | 2.43182 | 0.155363 | ||||||||
\(246\) | −22.7725 | −1.45192 | ||||||||
\(247\) | −10.2203 | −0.650301 | ||||||||
\(248\) | −8.87074 | −0.563293 | ||||||||
\(249\) | 9.91715 | 0.628474 | ||||||||
\(250\) | 20.4055 | 1.29056 | ||||||||
\(251\) | 12.1227 | 0.765177 | 0.382588 | − | 0.923919i | \(-0.375033\pi\) | ||||
0.382588 | + | 0.923919i | \(0.375033\pi\) | |||||||
\(252\) | −6.12103 | −0.385589 | ||||||||
\(253\) | 15.3661 | 0.966056 | ||||||||
\(254\) | 29.6983 | 1.86344 | ||||||||
\(255\) | 12.0964 | 0.757506 | ||||||||
\(256\) | 5.42623 | 0.339139 | ||||||||
\(257\) | 28.3873 | 1.77075 | 0.885377 | − | 0.464874i | \(-0.153900\pi\) | ||||
0.885377 | + | 0.464874i | \(0.153900\pi\) | |||||||
\(258\) | −19.2788 | −1.20025 | ||||||||
\(259\) | 4.45438 | 0.276781 | ||||||||
\(260\) | −10.0262 | −0.621797 | ||||||||
\(261\) | −0.357168 | −0.0221081 | ||||||||
\(262\) | −8.59914 | −0.531257 | ||||||||
\(263\) | −14.0844 | −0.868482 | −0.434241 | − | 0.900797i | \(-0.642983\pi\) | ||||
−0.434241 | + | 0.900797i | \(0.642983\pi\) | |||||||
\(264\) | 4.21471 | 0.259397 | ||||||||
\(265\) | −14.2919 | −0.877944 | ||||||||
\(266\) | 32.6880 | 2.00423 | ||||||||
\(267\) | −0.978993 | −0.0599134 | ||||||||
\(268\) | −35.5512 | −2.17163 | ||||||||
\(269\) | 22.1224 | 1.34883 | 0.674415 | − | 0.738353i | \(-0.264396\pi\) | ||||
0.674415 | + | 0.738353i | \(0.264396\pi\) | |||||||
\(270\) | 5.23885 | 0.318826 | ||||||||
\(271\) | −0.185181 | −0.0112490 | −0.00562449 | − | 0.999984i | \(-0.501790\pi\) | ||||
−0.00562449 | + | 0.999984i | \(0.501790\pi\) | |||||||
\(272\) | −13.5274 | −0.820219 | ||||||||
\(273\) | 3.98806 | 0.241368 | ||||||||
\(274\) | −32.9377 | −1.98984 | ||||||||
\(275\) | −4.43171 | −0.267242 | ||||||||
\(276\) | 9.56131 | 0.575523 | ||||||||
\(277\) | −15.8869 | −0.954549 | −0.477274 | − | 0.878754i | \(-0.658375\pi\) | ||||
−0.477274 | + | 0.878754i | \(0.658375\pi\) | |||||||
\(278\) | 2.31538 | 0.138867 | ||||||||
\(279\) | −8.44143 | −0.505375 | ||||||||
\(280\) | 6.36842 | 0.380586 | ||||||||
\(281\) | 19.9963 | 1.19288 | 0.596440 | − | 0.802658i | \(-0.296581\pi\) | ||||
0.596440 | + | 0.802658i | \(0.296581\pi\) | |||||||
\(282\) | −23.3649 | −1.39136 | ||||||||
\(283\) | −30.1737 | −1.79364 | −0.896819 | − | 0.442398i | \(-0.854128\pi\) | ||||
−0.896819 | + | 0.442398i | \(0.854128\pi\) | |||||||
\(284\) | −10.2823 | −0.610141 | ||||||||
\(285\) | −15.5306 | −0.919955 | ||||||||
\(286\) | −13.8272 | −0.817619 | ||||||||
\(287\) | −26.3428 | −1.55497 | ||||||||
\(288\) | −7.96032 | −0.469067 | ||||||||
\(289\) | 6.96786 | 0.409874 | ||||||||
\(290\) | 1.87115 | 0.109878 | ||||||||
\(291\) | 16.8523 | 0.987898 | ||||||||
\(292\) | 6.95401 | 0.406953 | ||||||||
\(293\) | −0.459157 | −0.0268242 | −0.0134121 | − | 0.999910i | \(-0.504269\pi\) | ||||
−0.0134121 | + | 0.999910i | \(0.504269\pi\) | |||||||
\(294\) | 2.08682 | 0.121706 | ||||||||
\(295\) | 3.55160 | 0.206782 | ||||||||
\(296\) | −1.90847 | −0.110927 | ||||||||
\(297\) | 4.01073 | 0.232726 | ||||||||
\(298\) | −33.8615 | −1.96155 | ||||||||
\(299\) | −6.22952 | −0.360262 | ||||||||
\(300\) | −2.75756 | −0.159208 | ||||||||
\(301\) | −22.3014 | −1.28543 | ||||||||
\(302\) | −17.9083 | −1.03051 | ||||||||
\(303\) | −3.80431 | −0.218552 | ||||||||
\(304\) | 17.3679 | 0.996117 | ||||||||
\(305\) | −5.48181 | −0.313887 | ||||||||
\(306\) | 10.3803 | 0.593402 | ||||||||
\(307\) | −11.2133 | −0.639978 | −0.319989 | − | 0.947421i | \(-0.603679\pi\) | ||||
−0.319989 | + | 0.947421i | \(0.603679\pi\) | |||||||
\(308\) | 24.5498 | 1.39886 | ||||||||
\(309\) | −8.01017 | −0.455683 | ||||||||
\(310\) | 44.2234 | 2.51172 | ||||||||
\(311\) | 12.1228 | 0.687423 | 0.343712 | − | 0.939075i | \(-0.388316\pi\) | ||||
0.343712 | + | 0.939075i | \(0.388316\pi\) | |||||||
\(312\) | −1.70867 | −0.0967347 | ||||||||
\(313\) | 12.8050 | 0.723782 | 0.361891 | − | 0.932220i | \(-0.382131\pi\) | ||||
0.361891 | + | 0.932220i | \(0.382131\pi\) | |||||||
\(314\) | 17.4247 | 0.983335 | ||||||||
\(315\) | 6.06021 | 0.341454 | ||||||||
\(316\) | 19.5722 | 1.10102 | ||||||||
\(317\) | −2.96789 | −0.166693 | −0.0833467 | − | 0.996521i | \(-0.526561\pi\) | ||||
−0.0833467 | + | 0.996521i | \(0.526561\pi\) | |||||||
\(318\) | −12.2643 | −0.687748 | ||||||||
\(319\) | 1.43250 | 0.0802049 | ||||||||
\(320\) | 28.0486 | 1.56797 | ||||||||
\(321\) | 12.6857 | 0.708049 | ||||||||
\(322\) | 19.9242 | 1.11033 | ||||||||
\(323\) | −30.7725 | −1.71223 | ||||||||
\(324\) | 2.49562 | 0.138646 | ||||||||
\(325\) | 1.79665 | 0.0996600 | ||||||||
\(326\) | 7.60865 | 0.421404 | ||||||||
\(327\) | 18.7766 | 1.03835 | ||||||||
\(328\) | 11.2865 | 0.623194 | ||||||||
\(329\) | −27.0281 | −1.49011 | ||||||||
\(330\) | −21.0116 | −1.15665 | ||||||||
\(331\) | 35.0721 | 1.92773 | 0.963867 | − | 0.266383i | \(-0.0858286\pi\) | ||||
0.963867 | + | 0.266383i | \(0.0858286\pi\) | |||||||
\(332\) | −24.7494 | −1.35830 | ||||||||
\(333\) | −1.81610 | −0.0995219 | ||||||||
\(334\) | 29.8480 | 1.63321 | ||||||||
\(335\) | 35.1979 | 1.92307 | ||||||||
\(336\) | −6.77713 | −0.369723 | ||||||||
\(337\) | 12.4068 | 0.675840 | 0.337920 | − | 0.941175i | \(-0.390277\pi\) | ||||
0.337920 | + | 0.941175i | \(0.390277\pi\) | |||||||
\(338\) | −21.9581 | −1.19436 | ||||||||
\(339\) | 7.61332 | 0.413499 | ||||||||
\(340\) | −30.1880 | −1.63718 | ||||||||
\(341\) | 33.8563 | 1.83342 | ||||||||
\(342\) | −13.3273 | −0.720658 | ||||||||
\(343\) | 19.5830 | 1.05738 | ||||||||
\(344\) | 9.55498 | 0.515170 | ||||||||
\(345\) | −9.46630 | −0.509649 | ||||||||
\(346\) | 12.5275 | 0.673485 | ||||||||
\(347\) | −25.6920 | −1.37922 | −0.689610 | − | 0.724181i | \(-0.742218\pi\) | ||||
−0.689610 | + | 0.724181i | \(0.742218\pi\) | |||||||
\(348\) | 0.891355 | 0.0477817 | ||||||||
\(349\) | −16.4397 | −0.879996 | −0.439998 | − | 0.897999i | \(-0.645021\pi\) | ||||
−0.439998 | + | 0.897999i | \(0.645021\pi\) | |||||||
\(350\) | −5.74630 | −0.307153 | ||||||||
\(351\) | −1.62598 | −0.0867885 | ||||||||
\(352\) | 31.9267 | 1.70170 | ||||||||
\(353\) | 9.96346 | 0.530302 | 0.265151 | − | 0.964207i | \(-0.414578\pi\) | ||||
0.265151 | + | 0.964207i | \(0.414578\pi\) | |||||||
\(354\) | 3.04774 | 0.161985 | ||||||||
\(355\) | 10.1801 | 0.540304 | ||||||||
\(356\) | 2.44319 | 0.129489 | ||||||||
\(357\) | 12.0077 | 0.635516 | ||||||||
\(358\) | 39.3293 | 2.07862 | ||||||||
\(359\) | 5.08801 | 0.268535 | 0.134267 | − | 0.990945i | \(-0.457132\pi\) | ||||
0.134267 | + | 0.990945i | \(0.457132\pi\) | |||||||
\(360\) | −2.59648 | −0.136847 | ||||||||
\(361\) | 20.5089 | 1.07942 | ||||||||
\(362\) | −1.95394 | −0.102697 | ||||||||
\(363\) | −5.08598 | −0.266945 | ||||||||
\(364\) | −9.95269 | −0.521662 | ||||||||
\(365\) | −6.88491 | −0.360373 | ||||||||
\(366\) | −4.70410 | −0.245887 | ||||||||
\(367\) | 15.5615 | 0.812302 | 0.406151 | − | 0.913806i | \(-0.366871\pi\) | ||||
0.406151 | + | 0.913806i | \(0.366871\pi\) | |||||||
\(368\) | 10.5862 | 0.551842 | ||||||||
\(369\) | 10.7403 | 0.559117 | ||||||||
\(370\) | 9.51430 | 0.494625 | ||||||||
\(371\) | −14.1871 | −0.736559 | ||||||||
\(372\) | 21.0666 | 1.09225 | ||||||||
\(373\) | −17.8554 | −0.924519 | −0.462259 | − | 0.886745i | \(-0.652961\pi\) | ||||
−0.462259 | + | 0.886745i | \(0.652961\pi\) | |||||||
\(374\) | −41.6326 | −2.15277 | ||||||||
\(375\) | −9.62395 | −0.496978 | ||||||||
\(376\) | 11.5801 | 0.597199 | ||||||||
\(377\) | −0.580748 | −0.0299101 | ||||||||
\(378\) | 5.20045 | 0.267482 | ||||||||
\(379\) | 25.1729 | 1.29304 | 0.646522 | − | 0.762896i | \(-0.276223\pi\) | ||||
0.646522 | + | 0.762896i | \(0.276223\pi\) | |||||||
\(380\) | 38.7586 | 1.98827 | ||||||||
\(381\) | −14.0067 | −0.717587 | ||||||||
\(382\) | 32.0767 | 1.64119 | ||||||||
\(383\) | −21.4662 | −1.09687 | −0.548435 | − | 0.836194i | \(-0.684776\pi\) | ||||
−0.548435 | + | 0.836194i | \(0.684776\pi\) | |||||||
\(384\) | 8.14873 | 0.415838 | ||||||||
\(385\) | −24.3059 | −1.23874 | ||||||||
\(386\) | −48.1909 | −2.45285 | ||||||||
\(387\) | 9.09255 | 0.462200 | ||||||||
\(388\) | −42.0569 | −2.13512 | ||||||||
\(389\) | 14.1828 | 0.719096 | 0.359548 | − | 0.933127i | \(-0.382931\pi\) | ||||
0.359548 | + | 0.933127i | \(0.382931\pi\) | |||||||
\(390\) | 8.51828 | 0.431340 | ||||||||
\(391\) | −18.7566 | −0.948561 | ||||||||
\(392\) | −1.03427 | −0.0522384 | ||||||||
\(393\) | 4.05565 | 0.204580 | ||||||||
\(394\) | −5.23877 | −0.263925 | ||||||||
\(395\) | −19.3777 | −0.975000 | ||||||||
\(396\) | −10.0093 | −0.502985 | ||||||||
\(397\) | −8.60119 | −0.431681 | −0.215841 | − | 0.976429i | \(-0.569249\pi\) | ||||
−0.215841 | + | 0.976429i | \(0.569249\pi\) | |||||||
\(398\) | −11.3321 | −0.568027 | ||||||||
\(399\) | −15.4168 | −0.771805 | ||||||||
\(400\) | −3.05314 | −0.152657 | ||||||||
\(401\) | −13.5162 | −0.674969 | −0.337485 | − | 0.941331i | \(-0.609576\pi\) | ||||
−0.337485 | + | 0.941331i | \(0.609576\pi\) | |||||||
\(402\) | 30.2044 | 1.50646 | ||||||||
\(403\) | −13.7256 | −0.683721 | ||||||||
\(404\) | 9.49410 | 0.472349 | ||||||||
\(405\) | −2.47082 | −0.122776 | ||||||||
\(406\) | 1.85743 | 0.0921829 | ||||||||
\(407\) | 7.28391 | 0.361050 | ||||||||
\(408\) | −5.14468 | −0.254700 | ||||||||
\(409\) | 26.6663 | 1.31856 | 0.659281 | − | 0.751896i | \(-0.270861\pi\) | ||||
0.659281 | + | 0.751896i | \(0.270861\pi\) | |||||||
\(410\) | −56.2668 | −2.77882 | ||||||||
\(411\) | 15.5346 | 0.766263 | ||||||||
\(412\) | 19.9904 | 0.984854 | ||||||||
\(413\) | 3.52557 | 0.173482 | ||||||||
\(414\) | −8.12332 | −0.399240 | ||||||||
\(415\) | 24.5035 | 1.20283 | ||||||||
\(416\) | −12.9433 | −0.634599 | ||||||||
\(417\) | −1.09201 | −0.0534760 | ||||||||
\(418\) | 53.4523 | 2.61444 | ||||||||
\(419\) | 7.37267 | 0.360179 | 0.180089 | − | 0.983650i | \(-0.442361\pi\) | ||||
0.180089 | + | 0.983650i | \(0.442361\pi\) | |||||||
\(420\) | −15.1240 | −0.737975 | ||||||||
\(421\) | 36.1603 | 1.76235 | 0.881174 | − | 0.472793i | \(-0.156754\pi\) | ||||
0.881174 | + | 0.472793i | \(0.156754\pi\) | |||||||
\(422\) | −21.9189 | −1.06699 | ||||||||
\(423\) | 11.0197 | 0.535795 | ||||||||
\(424\) | 6.07844 | 0.295195 | ||||||||
\(425\) | 5.40956 | 0.262402 | ||||||||
\(426\) | 8.73586 | 0.423254 | ||||||||
\(427\) | −5.44162 | −0.263339 | ||||||||
\(428\) | −31.6588 | −1.53028 | ||||||||
\(429\) | 6.52138 | 0.314855 | ||||||||
\(430\) | −47.6345 | −2.29714 | ||||||||
\(431\) | −13.4750 | −0.649066 | −0.324533 | − | 0.945874i | \(-0.605207\pi\) | ||||
−0.324533 | + | 0.945874i | \(0.605207\pi\) | |||||||
\(432\) | 2.76312 | 0.132941 | ||||||||
\(433\) | −8.22943 | −0.395481 | −0.197741 | − | 0.980254i | \(-0.563360\pi\) | ||||
−0.197741 | + | 0.980254i | \(0.563360\pi\) | |||||||
\(434\) | 43.8992 | 2.10723 | ||||||||
\(435\) | −0.882498 | −0.0423125 | ||||||||
\(436\) | −46.8593 | −2.24416 | ||||||||
\(437\) | 24.0817 | 1.15198 | ||||||||
\(438\) | −5.90815 | −0.282302 | ||||||||
\(439\) | −1.65529 | −0.0790028 | −0.0395014 | − | 0.999220i | \(-0.512577\pi\) | ||||
−0.0395014 | + | 0.999220i | \(0.512577\pi\) | |||||||
\(440\) | 10.4138 | 0.496458 | ||||||||
\(441\) | −0.984213 | −0.0468673 | ||||||||
\(442\) | 16.8782 | 0.802812 | ||||||||
\(443\) | −15.9770 | −0.759092 | −0.379546 | − | 0.925173i | \(-0.623920\pi\) | ||||
−0.379546 | + | 0.925173i | \(0.623920\pi\) | |||||||
\(444\) | 4.53230 | 0.215094 | ||||||||
\(445\) | −2.41892 | −0.114668 | ||||||||
\(446\) | −21.7758 | −1.03112 | ||||||||
\(447\) | 15.9702 | 0.755367 | ||||||||
\(448\) | 27.8430 | 1.31546 | ||||||||
\(449\) | 13.7005 | 0.646566 | 0.323283 | − | 0.946302i | \(-0.395213\pi\) | ||||
0.323283 | + | 0.946302i | \(0.395213\pi\) | |||||||
\(450\) | 2.34284 | 0.110442 | ||||||||
\(451\) | −43.0765 | −2.02839 | ||||||||
\(452\) | −19.0000 | −0.893683 | ||||||||
\(453\) | 8.44617 | 0.396836 | ||||||||
\(454\) | −35.9319 | −1.68637 | ||||||||
\(455\) | 9.85379 | 0.461953 | ||||||||
\(456\) | 6.60528 | 0.309321 | ||||||||
\(457\) | 34.4962 | 1.61367 | 0.806833 | − | 0.590779i | \(-0.201180\pi\) | ||||
0.806833 | + | 0.590779i | \(0.201180\pi\) | |||||||
\(458\) | −61.5933 | −2.87806 | ||||||||
\(459\) | −4.89570 | −0.228512 | ||||||||
\(460\) | 23.6243 | 1.10149 | ||||||||
\(461\) | −30.3840 | −1.41513 | −0.707563 | − | 0.706651i | \(-0.750205\pi\) | ||||
−0.707563 | + | 0.706651i | \(0.750205\pi\) | |||||||
\(462\) | −20.8576 | −0.970384 | ||||||||
\(463\) | −19.9606 | −0.927648 | −0.463824 | − | 0.885927i | \(-0.653523\pi\) | ||||
−0.463824 | + | 0.885927i | \(0.653523\pi\) | |||||||
\(464\) | 0.986897 | 0.0458156 | ||||||||
\(465\) | −20.8573 | −0.967233 | ||||||||
\(466\) | −41.8477 | −1.93856 | ||||||||
\(467\) | 8.39058 | 0.388270 | 0.194135 | − | 0.980975i | \(-0.437810\pi\) | ||||
0.194135 | + | 0.980975i | \(0.437810\pi\) | |||||||
\(468\) | 4.05783 | 0.187573 | ||||||||
\(469\) | 34.9399 | 1.61337 | ||||||||
\(470\) | −57.7305 | −2.66291 | ||||||||
\(471\) | −8.21810 | −0.378670 | ||||||||
\(472\) | −1.51052 | −0.0695273 | ||||||||
\(473\) | −36.4678 | −1.67679 | ||||||||
\(474\) | −16.6286 | −0.763778 | ||||||||
\(475\) | −6.94536 | −0.318675 | ||||||||
\(476\) | −29.9667 | −1.37352 | ||||||||
\(477\) | 5.78427 | 0.264843 | ||||||||
\(478\) | −2.12029 | −0.0969797 | ||||||||
\(479\) | 21.2295 | 0.969999 | 0.485000 | − | 0.874514i | \(-0.338820\pi\) | ||||
0.485000 | + | 0.874514i | \(0.338820\pi\) | |||||||
\(480\) | −19.6685 | −0.897742 | ||||||||
\(481\) | −2.95295 | −0.134643 | ||||||||
\(482\) | 22.2284 | 1.01247 | ||||||||
\(483\) | −9.39691 | −0.427574 | ||||||||
\(484\) | 12.6927 | 0.576940 | ||||||||
\(485\) | 41.6390 | 1.89073 | ||||||||
\(486\) | −2.12029 | −0.0961782 | ||||||||
\(487\) | 5.32666 | 0.241374 | 0.120687 | − | 0.992691i | \(-0.461490\pi\) | ||||
0.120687 | + | 0.992691i | \(0.461490\pi\) | |||||||
\(488\) | 2.33145 | 0.105540 | ||||||||
\(489\) | −3.58850 | −0.162278 | ||||||||
\(490\) | 5.15615 | 0.232931 | ||||||||
\(491\) | 24.0997 | 1.08760 | 0.543802 | − | 0.839213i | \(-0.316984\pi\) | ||||
0.543802 | + | 0.839213i | \(0.316984\pi\) | |||||||
\(492\) | −26.8037 | −1.20840 | ||||||||
\(493\) | −1.74859 | −0.0787523 | ||||||||
\(494\) | −21.6700 | −0.974977 | ||||||||
\(495\) | 9.90981 | 0.445413 | ||||||||
\(496\) | 23.3247 | 1.04731 | ||||||||
\(497\) | 10.1055 | 0.453293 | ||||||||
\(498\) | 21.0272 | 0.942252 | ||||||||
\(499\) | −34.1034 | −1.52668 | −0.763339 | − | 0.645998i | \(-0.776441\pi\) | ||||
−0.763339 | + | 0.645998i | \(0.776441\pi\) | |||||||
\(500\) | 24.0177 | 1.07410 | ||||||||
\(501\) | −14.0773 | −0.628928 | ||||||||
\(502\) | 25.7036 | 1.14721 | ||||||||
\(503\) | −10.6016 | −0.472704 | −0.236352 | − | 0.971667i | \(-0.575952\pi\) | ||||
−0.236352 | + | 0.971667i | \(0.575952\pi\) | |||||||
\(504\) | −2.57745 | −0.114809 | ||||||||
\(505\) | −9.39976 | −0.418284 | ||||||||
\(506\) | 32.5805 | 1.44838 | ||||||||
\(507\) | 10.3562 | 0.459934 | ||||||||
\(508\) | 34.9555 | 1.55090 | ||||||||
\(509\) | 20.2990 | 0.899736 | 0.449868 | − | 0.893095i | \(-0.351471\pi\) | ||||
0.449868 | + | 0.893095i | \(0.351471\pi\) | |||||||
\(510\) | 25.6478 | 1.13571 | ||||||||
\(511\) | −6.83444 | −0.302338 | ||||||||
\(512\) | 27.8026 | 1.22871 | ||||||||
\(513\) | 6.28561 | 0.277517 | ||||||||
\(514\) | 60.1893 | 2.65484 | ||||||||
\(515\) | −19.7917 | −0.872127 | ||||||||
\(516\) | −22.6916 | −0.998940 | ||||||||
\(517\) | −44.1970 | −1.94378 | ||||||||
\(518\) | 9.44456 | 0.414970 | ||||||||
\(519\) | −5.90842 | −0.259351 | ||||||||
\(520\) | −4.22183 | −0.185140 | ||||||||
\(521\) | −1.16040 | −0.0508378 | −0.0254189 | − | 0.999677i | \(-0.508092\pi\) | ||||
−0.0254189 | + | 0.999677i | \(0.508092\pi\) | |||||||
\(522\) | −0.757299 | −0.0331461 | ||||||||
\(523\) | −19.3796 | −0.847412 | −0.423706 | − | 0.905800i | \(-0.639271\pi\) | ||||
−0.423706 | + | 0.905800i | \(0.639271\pi\) | |||||||
\(524\) | −10.1214 | −0.442154 | ||||||||
\(525\) | 2.71015 | 0.118281 | ||||||||
\(526\) | −29.8630 | −1.30209 | ||||||||
\(527\) | −41.3267 | −1.80022 | ||||||||
\(528\) | −11.0821 | −0.482288 | ||||||||
\(529\) | −8.32163 | −0.361810 | ||||||||
\(530\) | −30.3029 | −1.31628 | ||||||||
\(531\) | −1.43742 | −0.0623786 | ||||||||
\(532\) | 38.4744 | 1.66808 | ||||||||
\(533\) | 17.4635 | 0.756429 | ||||||||
\(534\) | −2.07575 | −0.0898264 | ||||||||
\(535\) | 31.3442 | 1.35513 | ||||||||
\(536\) | −14.9699 | −0.646602 | ||||||||
\(537\) | −18.5491 | −0.800451 | ||||||||
\(538\) | 46.9059 | 2.02226 | ||||||||
\(539\) | 3.94742 | 0.170027 | ||||||||
\(540\) | 6.16623 | 0.265352 | ||||||||
\(541\) | −4.77487 | −0.205288 | −0.102644 | − | 0.994718i | \(-0.532730\pi\) | ||||
−0.102644 | + | 0.994718i | \(0.532730\pi\) | |||||||
\(542\) | −0.392638 | −0.0168652 | ||||||||
\(543\) | 0.921544 | 0.0395472 | ||||||||
\(544\) | −38.9713 | −1.67088 | ||||||||
\(545\) | 46.3937 | 1.98729 | ||||||||
\(546\) | 8.45584 | 0.361876 | ||||||||
\(547\) | −12.9501 | −0.553704 | −0.276852 | − | 0.960913i | \(-0.589291\pi\) | ||||
−0.276852 | + | 0.960913i | \(0.589291\pi\) | |||||||
\(548\) | −38.7684 | −1.65610 | ||||||||
\(549\) | 2.21862 | 0.0946882 | ||||||||
\(550\) | −9.39649 | −0.400668 | ||||||||
\(551\) | 2.24502 | 0.0956410 | ||||||||
\(552\) | 4.02608 | 0.171362 | ||||||||
\(553\) | −19.2357 | −0.817985 | ||||||||
\(554\) | −33.6847 | −1.43113 | ||||||||
\(555\) | −4.48727 | −0.190474 | ||||||||
\(556\) | 2.72525 | 0.115576 | ||||||||
\(557\) | 15.2371 | 0.645618 | 0.322809 | − | 0.946464i | \(-0.395373\pi\) | ||||
0.322809 | + | 0.946464i | \(0.395373\pi\) | |||||||
\(558\) | −17.8983 | −0.757694 | ||||||||
\(559\) | 14.7843 | 0.625310 | ||||||||
\(560\) | −16.7451 | −0.707609 | ||||||||
\(561\) | 19.6353 | 0.829005 | ||||||||
\(562\) | 42.3979 | 1.78845 | ||||||||
\(563\) | −44.4294 | −1.87247 | −0.936237 | − | 0.351368i | \(-0.885716\pi\) | ||||
−0.936237 | + | 0.351368i | \(0.885716\pi\) | |||||||
\(564\) | −27.5009 | −1.15800 | ||||||||
\(565\) | 18.8112 | 0.791392 | ||||||||
\(566\) | −63.9768 | −2.68915 | ||||||||
\(567\) | −2.45271 | −0.103004 | ||||||||
\(568\) | −4.32967 | −0.181669 | ||||||||
\(569\) | −32.3049 | −1.35429 | −0.677146 | − | 0.735848i | \(-0.736784\pi\) | ||||
−0.677146 | + | 0.735848i | \(0.736784\pi\) | |||||||
\(570\) | −32.9294 | −1.37926 | ||||||||
\(571\) | −17.6597 | −0.739036 | −0.369518 | − | 0.929224i | \(-0.620477\pi\) | ||||
−0.369518 | + | 0.929224i | \(0.620477\pi\) | |||||||
\(572\) | −16.2749 | −0.680487 | ||||||||
\(573\) | −15.1285 | −0.632001 | ||||||||
\(574\) | −55.8544 | −2.33132 | ||||||||
\(575\) | −4.23337 | −0.176544 | ||||||||
\(576\) | −11.3519 | −0.472997 | ||||||||
\(577\) | −5.92655 | −0.246726 | −0.123363 | − | 0.992362i | \(-0.539368\pi\) | ||||
−0.123363 | + | 0.992362i | \(0.539368\pi\) | |||||||
\(578\) | 14.7739 | 0.614512 | ||||||||
\(579\) | 22.7285 | 0.944562 | ||||||||
\(580\) | 2.20238 | 0.0914489 | ||||||||
\(581\) | 24.3239 | 1.00913 | ||||||||
\(582\) | 35.7317 | 1.48113 | ||||||||
\(583\) | −23.1992 | −0.960811 | ||||||||
\(584\) | 2.92820 | 0.121170 | ||||||||
\(585\) | −4.01751 | −0.166104 | ||||||||
\(586\) | −0.973544 | −0.0402167 | ||||||||
\(587\) | 25.8268 | 1.06599 | 0.532993 | − | 0.846120i | \(-0.321067\pi\) | ||||
0.532993 | + | 0.846120i | \(0.321067\pi\) | |||||||
\(588\) | 2.45622 | 0.101293 | ||||||||
\(589\) | 53.0596 | 2.18628 | ||||||||
\(590\) | 7.53041 | 0.310022 | ||||||||
\(591\) | 2.47078 | 0.101634 | ||||||||
\(592\) | 5.01811 | 0.206243 | ||||||||
\(593\) | −9.21060 | −0.378234 | −0.189117 | − | 0.981955i | \(-0.560563\pi\) | ||||
−0.189117 | + | 0.981955i | \(0.560563\pi\) | |||||||
\(594\) | 8.50391 | 0.348920 | ||||||||
\(595\) | 29.6690 | 1.21631 | ||||||||
\(596\) | −39.8557 | −1.63255 | ||||||||
\(597\) | 5.34461 | 0.218740 | ||||||||
\(598\) | −13.2084 | −0.540131 | ||||||||
\(599\) | −43.4301 | −1.77450 | −0.887252 | − | 0.461285i | \(-0.847389\pi\) | ||||
−0.887252 | + | 0.461285i | \(0.847389\pi\) | |||||||
\(600\) | −1.16116 | −0.0474041 | ||||||||
\(601\) | −10.2416 | −0.417765 | −0.208883 | − | 0.977941i | \(-0.566983\pi\) | ||||
−0.208883 | + | 0.977941i | \(0.566983\pi\) | |||||||
\(602\) | −47.2854 | −1.92721 | ||||||||
\(603\) | −14.2454 | −0.580118 | ||||||||
\(604\) | −21.0784 | −0.857669 | ||||||||
\(605\) | −12.5666 | −0.510903 | ||||||||
\(606\) | −8.06622 | −0.327668 | ||||||||
\(607\) | 45.2285 | 1.83577 | 0.917884 | − | 0.396849i | \(-0.129896\pi\) | ||||
0.917884 | + | 0.396849i | \(0.129896\pi\) | |||||||
\(608\) | 50.0355 | 2.02921 | ||||||||
\(609\) | −0.876029 | −0.0354985 | ||||||||
\(610\) | −11.6230 | −0.470602 | ||||||||
\(611\) | 17.9178 | 0.724876 | ||||||||
\(612\) | 12.2178 | 0.493875 | ||||||||
\(613\) | 20.4029 | 0.824064 | 0.412032 | − | 0.911169i | \(-0.364819\pi\) | ||||
0.412032 | + | 0.911169i | \(0.364819\pi\) | |||||||
\(614\) | −23.7755 | −0.959500 | ||||||||
\(615\) | 26.5374 | 1.07009 | ||||||||
\(616\) | 10.3375 | 0.416508 | ||||||||
\(617\) | 4.40978 | 0.177531 | 0.0887655 | − | 0.996053i | \(-0.471708\pi\) | ||||
0.0887655 | + | 0.996053i | \(0.471708\pi\) | |||||||
\(618\) | −16.9839 | −0.683192 | ||||||||
\(619\) | 20.8034 | 0.836160 | 0.418080 | − | 0.908410i | \(-0.362703\pi\) | ||||
0.418080 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(620\) | 52.0518 | 2.09045 | ||||||||
\(621\) | 3.83124 | 0.153742 | ||||||||
\(622\) | 25.7039 | 1.03063 | ||||||||
\(623\) | −2.40119 | −0.0962015 | ||||||||
\(624\) | 4.49278 | 0.179855 | ||||||||
\(625\) | −29.3039 | −1.17215 | ||||||||
\(626\) | 27.1503 | 1.08514 | ||||||||
\(627\) | −25.2099 | −1.00679 | ||||||||
\(628\) | 20.5093 | 0.818409 | ||||||||
\(629\) | −8.89109 | −0.354511 | ||||||||
\(630\) | 12.8494 | 0.511932 | ||||||||
\(631\) | 33.5580 | 1.33592 | 0.667962 | − | 0.744196i | \(-0.267167\pi\) | ||||
0.667962 | + | 0.744196i | \(0.267167\pi\) | |||||||
\(632\) | 8.24149 | 0.327829 | ||||||||
\(633\) | 10.3377 | 0.410886 | ||||||||
\(634\) | −6.29278 | −0.249918 | ||||||||
\(635\) | −34.6081 | −1.37338 | ||||||||
\(636\) | −14.4353 | −0.572398 | ||||||||
\(637\) | −1.60031 | −0.0634067 | ||||||||
\(638\) | 3.03732 | 0.120249 | ||||||||
\(639\) | −4.12013 | −0.162990 | ||||||||
\(640\) | 20.1341 | 0.795869 | ||||||||
\(641\) | 24.5383 | 0.969206 | 0.484603 | − | 0.874734i | \(-0.338964\pi\) | ||||
0.484603 | + | 0.874734i | \(0.338964\pi\) | |||||||
\(642\) | 26.8974 | 1.06156 | ||||||||
\(643\) | 9.18123 | 0.362073 | 0.181036 | − | 0.983476i | \(-0.442055\pi\) | ||||
0.181036 | + | 0.983476i | \(0.442055\pi\) | |||||||
\(644\) | 23.4511 | 0.924104 | ||||||||
\(645\) | 22.4661 | 0.884601 | ||||||||
\(646\) | −65.2465 | −2.56709 | ||||||||
\(647\) | 33.3174 | 1.30984 | 0.654922 | − | 0.755697i | \(-0.272702\pi\) | ||||
0.654922 | + | 0.755697i | \(0.272702\pi\) | |||||||
\(648\) | 1.05086 | 0.0412816 | ||||||||
\(649\) | 5.76509 | 0.226300 | ||||||||
\(650\) | 3.80941 | 0.149417 | ||||||||
\(651\) | −20.7044 | −0.811469 | ||||||||
\(652\) | 8.95553 | 0.350726 | ||||||||
\(653\) | −8.78496 | −0.343782 | −0.171891 | − | 0.985116i | \(-0.554988\pi\) | ||||
−0.171891 | + | 0.985116i | \(0.554988\pi\) | |||||||
\(654\) | 39.8119 | 1.55677 | ||||||||
\(655\) | 10.0208 | 0.391545 | ||||||||
\(656\) | −29.6767 | −1.15868 | ||||||||
\(657\) | 2.78648 | 0.108711 | ||||||||
\(658\) | −57.3073 | −2.23407 | ||||||||
\(659\) | −27.9953 | −1.09054 | −0.545270 | − | 0.838260i | \(-0.683573\pi\) | ||||
−0.545270 | + | 0.838260i | \(0.683573\pi\) | |||||||
\(660\) | −24.7311 | −0.962657 | ||||||||
\(661\) | −31.7412 | −1.23459 | −0.617294 | − | 0.786732i | \(-0.711771\pi\) | ||||
−0.617294 | + | 0.786732i | \(0.711771\pi\) | |||||||
\(662\) | 74.3628 | 2.89019 | ||||||||
\(663\) | −7.96031 | −0.309153 | ||||||||
\(664\) | −10.4215 | −0.404433 | ||||||||
\(665\) | −38.0921 | −1.47715 | ||||||||
\(666\) | −3.85066 | −0.149210 | ||||||||
\(667\) | 1.36839 | 0.0529844 | ||||||||
\(668\) | 35.1316 | 1.35928 | ||||||||
\(669\) | 10.2702 | 0.397070 | ||||||||
\(670\) | 74.6297 | 2.88320 | ||||||||
\(671\) | −8.89828 | −0.343514 | ||||||||
\(672\) | −19.5244 | −0.753169 | ||||||||
\(673\) | −0.521763 | −0.0201125 | −0.0100562 | − | 0.999949i | \(-0.503201\pi\) | ||||
−0.0100562 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(674\) | 26.3059 | 1.01327 | ||||||||
\(675\) | −1.10496 | −0.0425300 | ||||||||
\(676\) | −25.8451 | −0.994042 | ||||||||
\(677\) | −2.22663 | −0.0855765 | −0.0427882 | − | 0.999084i | \(-0.513624\pi\) | ||||
−0.0427882 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(678\) | 16.1424 | 0.619946 | ||||||||
\(679\) | 41.3338 | 1.58624 | ||||||||
\(680\) | −12.7116 | −0.487467 | ||||||||
\(681\) | 16.9467 | 0.649398 | ||||||||
\(682\) | 71.7852 | 2.74880 | ||||||||
\(683\) | −18.9101 | −0.723577 | −0.361788 | − | 0.932260i | \(-0.617834\pi\) | ||||
−0.361788 | + | 0.932260i | \(0.617834\pi\) | |||||||
\(684\) | −15.6865 | −0.599788 | ||||||||
\(685\) | 38.3831 | 1.46654 | ||||||||
\(686\) | 41.5215 | 1.58530 | ||||||||
\(687\) | 29.0495 | 1.10831 | ||||||||
\(688\) | −25.1238 | −0.957836 | ||||||||
\(689\) | 9.40511 | 0.358306 | ||||||||
\(690\) | −20.0713 | −0.764101 | ||||||||
\(691\) | −18.7431 | −0.713022 | −0.356511 | − | 0.934291i | \(-0.616034\pi\) | ||||
−0.356511 | + | 0.934291i | \(0.616034\pi\) | |||||||
\(692\) | 14.7452 | 0.560527 | ||||||||
\(693\) | 9.83717 | 0.373683 | ||||||||
\(694\) | −54.4745 | −2.06782 | ||||||||
\(695\) | −2.69817 | −0.102347 | ||||||||
\(696\) | 0.375332 | 0.0142269 | ||||||||
\(697\) | 52.5812 | 1.99166 | ||||||||
\(698\) | −34.8568 | −1.31935 | ||||||||
\(699\) | 19.7368 | 0.746514 | ||||||||
\(700\) | −6.76351 | −0.255637 | ||||||||
\(701\) | 16.1798 | 0.611102 | 0.305551 | − | 0.952176i | \(-0.401159\pi\) | ||||
0.305551 | + | 0.952176i | \(0.401159\pi\) | |||||||
\(702\) | −3.44755 | −0.130119 | ||||||||
\(703\) | 11.4153 | 0.430537 | ||||||||
\(704\) | 45.5296 | 1.71596 | ||||||||
\(705\) | 27.2277 | 1.02545 | ||||||||
\(706\) | 21.1254 | 0.795065 | ||||||||
\(707\) | −9.33086 | −0.350923 | ||||||||
\(708\) | 3.58725 | 0.134817 | ||||||||
\(709\) | −8.57907 | −0.322194 | −0.161097 | − | 0.986939i | \(-0.551503\pi\) | ||||
−0.161097 | + | 0.986939i | \(0.551503\pi\) | |||||||
\(710\) | 21.5848 | 0.810062 | ||||||||
\(711\) | 7.84263 | 0.294122 | ||||||||
\(712\) | 1.02878 | 0.0385552 | ||||||||
\(713\) | 32.3411 | 1.21118 | ||||||||
\(714\) | 25.4598 | 0.952811 | ||||||||
\(715\) | 16.1132 | 0.602598 | ||||||||
\(716\) | 46.2914 | 1.72999 | ||||||||
\(717\) | 1.00000 | 0.0373457 | ||||||||
\(718\) | 10.7880 | 0.402606 | ||||||||
\(719\) | −32.5343 | −1.21333 | −0.606663 | − | 0.794959i | \(-0.707492\pi\) | ||||
−0.606663 | + | 0.794959i | \(0.707492\pi\) | |||||||
\(720\) | 6.82718 | 0.254434 | ||||||||
\(721\) | −19.6466 | −0.731679 | ||||||||
\(722\) | 43.4848 | 1.61834 | ||||||||
\(723\) | −10.4837 | −0.389891 | ||||||||
\(724\) | −2.29982 | −0.0854723 | ||||||||
\(725\) | −0.394657 | −0.0146572 | ||||||||
\(726\) | −10.7837 | −0.400222 | ||||||||
\(727\) | −4.65810 | −0.172759 | −0.0863797 | − | 0.996262i | \(-0.527530\pi\) | ||||
−0.0863797 | + | 0.996262i | \(0.527530\pi\) | |||||||
\(728\) | −4.19088 | −0.155325 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.5980 | −0.540296 | ||||||||
\(731\) | 44.5144 | 1.64642 | ||||||||
\(732\) | −5.53682 | −0.204647 | ||||||||
\(733\) | 8.64374 | 0.319264 | 0.159632 | − | 0.987177i | \(-0.448969\pi\) | ||||
0.159632 | + | 0.987177i | \(0.448969\pi\) | |||||||
\(734\) | 32.9948 | 1.21786 | ||||||||
\(735\) | −2.43182 | −0.0896989 | ||||||||
\(736\) | 30.4979 | 1.12417 | ||||||||
\(737\) | 57.1346 | 2.10458 | ||||||||
\(738\) | 22.7725 | 0.838268 | ||||||||
\(739\) | 42.9217 | 1.57890 | 0.789450 | − | 0.613815i | \(-0.210366\pi\) | ||||
0.789450 | + | 0.613815i | \(0.210366\pi\) | |||||||
\(740\) | 11.1985 | 0.411666 | ||||||||
\(741\) | 10.2203 | 0.375452 | ||||||||
\(742\) | −30.0808 | −1.10430 | ||||||||
\(743\) | 39.0878 | 1.43399 | 0.716997 | − | 0.697076i | \(-0.245516\pi\) | ||||
0.716997 | + | 0.697076i | \(0.245516\pi\) | |||||||
\(744\) | 8.87074 | 0.325217 | ||||||||
\(745\) | 39.4596 | 1.44569 | ||||||||
\(746\) | −37.8586 | −1.38610 | ||||||||
\(747\) | −9.91715 | −0.362850 | ||||||||
\(748\) | −49.0024 | −1.79170 | ||||||||
\(749\) | 31.1144 | 1.13690 | ||||||||
\(750\) | −20.4055 | −0.745105 | ||||||||
\(751\) | 33.4998 | 1.22243 | 0.611213 | − | 0.791466i | \(-0.290682\pi\) | ||||
0.611213 | + | 0.791466i | \(0.290682\pi\) | |||||||
\(752\) | −30.4487 | −1.11035 | ||||||||
\(753\) | −12.1227 | −0.441775 | ||||||||
\(754\) | −1.23135 | −0.0448432 | ||||||||
\(755\) | 20.8690 | 0.759500 | ||||||||
\(756\) | 6.12103 | 0.222620 | ||||||||
\(757\) | 42.7926 | 1.55533 | 0.777663 | − | 0.628682i | \(-0.216405\pi\) | ||||
0.777663 | + | 0.628682i | \(0.216405\pi\) | |||||||
\(758\) | 53.3737 | 1.93862 | ||||||||
\(759\) | −15.3661 | −0.557753 | ||||||||
\(760\) | 16.3205 | 0.592006 | ||||||||
\(761\) | 3.50389 | 0.127016 | 0.0635079 | − | 0.997981i | \(-0.479771\pi\) | ||||
0.0635079 | + | 0.997981i | \(0.479771\pi\) | |||||||
\(762\) | −29.6983 | −1.07586 | ||||||||
\(763\) | 46.0536 | 1.66725 | ||||||||
\(764\) | 37.7549 | 1.36592 | ||||||||
\(765\) | −12.0964 | −0.437346 | ||||||||
\(766\) | −45.5144 | −1.64450 | ||||||||
\(767\) | −2.33721 | −0.0843919 | ||||||||
\(768\) | −5.42623 | −0.195802 | ||||||||
\(769\) | −33.9827 | −1.22545 | −0.612724 | − | 0.790297i | \(-0.709926\pi\) | ||||
−0.612724 | + | 0.790297i | \(0.709926\pi\) | |||||||
\(770\) | −51.5355 | −1.85721 | ||||||||
\(771\) | −28.3873 | −1.02235 | ||||||||
\(772\) | −56.7216 | −2.04146 | ||||||||
\(773\) | 16.2523 | 0.584553 | 0.292277 | − | 0.956334i | \(-0.405587\pi\) | ||||
0.292277 | + | 0.956334i | \(0.405587\pi\) | |||||||
\(774\) | 19.2788 | 0.692963 | ||||||||
\(775\) | −9.32746 | −0.335052 | ||||||||
\(776\) | −17.7094 | −0.635729 | ||||||||
\(777\) | −4.45438 | −0.159800 | ||||||||
\(778\) | 30.0716 | 1.07812 | ||||||||
\(779\) | −67.5093 | −2.41877 | ||||||||
\(780\) | 10.0262 | 0.358995 | ||||||||
\(781\) | 16.5247 | 0.591302 | ||||||||
\(782\) | −39.7693 | −1.42215 | ||||||||
\(783\) | 0.357168 | 0.0127641 | ||||||||
\(784\) | 2.71950 | 0.0971250 | ||||||||
\(785\) | −20.3055 | −0.724733 | ||||||||
\(786\) | 8.59914 | 0.306721 | ||||||||
\(787\) | −10.9298 | −0.389606 | −0.194803 | − | 0.980842i | \(-0.562407\pi\) | ||||
−0.194803 | + | 0.980842i | \(0.562407\pi\) | |||||||
\(788\) | −6.16613 | −0.219659 | ||||||||
\(789\) | 14.0844 | 0.501418 | ||||||||
\(790\) | −41.0864 | −1.46179 | ||||||||
\(791\) | 18.6733 | 0.663945 | ||||||||
\(792\) | −4.21471 | −0.149763 | ||||||||
\(793\) | 3.60743 | 0.128104 | ||||||||
\(794\) | −18.2370 | −0.647207 | ||||||||
\(795\) | 14.2919 | 0.506881 | ||||||||
\(796\) | −13.3381 | −0.472757 | ||||||||
\(797\) | −17.4122 | −0.616772 | −0.308386 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308386 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(798\) | −32.6880 | −1.15714 | ||||||||
\(799\) | 53.9490 | 1.90858 | ||||||||
\(800\) | −8.79585 | −0.310980 | ||||||||
\(801\) | 0.978993 | 0.0345910 | ||||||||
\(802\) | −28.6583 | −1.01196 | ||||||||
\(803\) | −11.1758 | −0.394387 | ||||||||
\(804\) | 35.5512 | 1.25379 | ||||||||
\(805\) | −23.2181 | −0.818330 | ||||||||
\(806\) | −29.1022 | −1.02508 | ||||||||
\(807\) | −22.1224 | −0.778747 | ||||||||
\(808\) | 3.99778 | 0.140642 | ||||||||
\(809\) | −21.8841 | −0.769403 | −0.384702 | − | 0.923041i | \(-0.625696\pi\) | ||||
−0.384702 | + | 0.923041i | \(0.625696\pi\) | |||||||
\(810\) | −5.23885 | −0.184075 | ||||||||
\(811\) | 41.8415 | 1.46925 | 0.734627 | − | 0.678471i | \(-0.237357\pi\) | ||||
0.734627 | + | 0.678471i | \(0.237357\pi\) | |||||||
\(812\) | 2.18624 | 0.0767218 | ||||||||
\(813\) | 0.185181 | 0.00649460 | ||||||||
\(814\) | 15.4440 | 0.541311 | ||||||||
\(815\) | −8.86655 | −0.310582 | ||||||||
\(816\) | 13.5274 | 0.473554 | ||||||||
\(817\) | −57.1522 | −1.99950 | ||||||||
\(818\) | 56.5402 | 1.97688 | ||||||||
\(819\) | −3.98806 | −0.139354 | ||||||||
\(820\) | −66.2272 | −2.31275 | ||||||||
\(821\) | 36.7094 | 1.28117 | 0.640584 | − | 0.767888i | \(-0.278692\pi\) | ||||
0.640584 | + | 0.767888i | \(0.278692\pi\) | |||||||
\(822\) | 32.9377 | 1.14884 | ||||||||
\(823\) | −31.0617 | −1.08274 | −0.541371 | − | 0.840784i | \(-0.682095\pi\) | ||||
−0.541371 | + | 0.840784i | \(0.682095\pi\) | |||||||
\(824\) | 8.41755 | 0.293239 | ||||||||
\(825\) | 4.43171 | 0.154292 | ||||||||
\(826\) | 7.47521 | 0.260096 | ||||||||
\(827\) | 55.1422 | 1.91748 | 0.958741 | − | 0.284281i | \(-0.0917550\pi\) | ||||
0.958741 | + | 0.284281i | \(0.0917550\pi\) | |||||||
\(828\) | −9.56131 | −0.332279 | ||||||||
\(829\) | 11.6426 | 0.404366 | 0.202183 | − | 0.979348i | \(-0.435196\pi\) | ||||
0.202183 | + | 0.979348i | \(0.435196\pi\) | |||||||
\(830\) | 51.9545 | 1.80337 | ||||||||
\(831\) | 15.8869 | 0.551109 | ||||||||
\(832\) | −18.4580 | −0.639917 | ||||||||
\(833\) | −4.81841 | −0.166948 | ||||||||
\(834\) | −2.31538 | −0.0801750 | ||||||||
\(835\) | −34.7825 | −1.20370 | ||||||||
\(836\) | 62.9144 | 2.17594 | ||||||||
\(837\) | 8.44143 | 0.291779 | ||||||||
\(838\) | 15.6322 | 0.540005 | ||||||||
\(839\) | 9.99713 | 0.345139 | 0.172570 | − | 0.984997i | \(-0.444793\pi\) | ||||
0.172570 | + | 0.984997i | \(0.444793\pi\) | |||||||
\(840\) | −6.36842 | −0.219731 | ||||||||
\(841\) | −28.8724 | −0.995601 | ||||||||
\(842\) | 76.6703 | 2.64223 | ||||||||
\(843\) | −19.9963 | −0.688709 | ||||||||
\(844\) | −25.7989 | −0.888036 | ||||||||
\(845\) | 25.5883 | 0.880264 | ||||||||
\(846\) | 23.3649 | 0.803302 | ||||||||
\(847\) | −12.4744 | −0.428627 | ||||||||
\(848\) | −15.9826 | −0.548846 | ||||||||
\(849\) | 30.1737 | 1.03556 | ||||||||
\(850\) | 11.4698 | 0.393412 | ||||||||
\(851\) | 6.95792 | 0.238514 | ||||||||
\(852\) | 10.2823 | 0.352265 | ||||||||
\(853\) | 41.0682 | 1.40615 | 0.703073 | − | 0.711117i | \(-0.251811\pi\) | ||||
0.703073 | + | 0.711117i | \(0.251811\pi\) | |||||||
\(854\) | −11.5378 | −0.394816 | ||||||||
\(855\) | 15.5306 | 0.531136 | ||||||||
\(856\) | −13.3309 | −0.455641 | ||||||||
\(857\) | −22.0503 | −0.753224 | −0.376612 | − | 0.926371i | \(-0.622911\pi\) | ||||
−0.376612 | + | 0.926371i | \(0.622911\pi\) | |||||||
\(858\) | 13.8272 | 0.472053 | ||||||||
\(859\) | 5.68153 | 0.193851 | 0.0969256 | − | 0.995292i | \(-0.469099\pi\) | ||||
0.0969256 | + | 0.995292i | \(0.469099\pi\) | |||||||
\(860\) | −56.0668 | −1.91186 | ||||||||
\(861\) | 26.3428 | 0.897761 | ||||||||
\(862\) | −28.5708 | −0.973125 | ||||||||
\(863\) | 27.0640 | 0.921269 | 0.460635 | − | 0.887590i | \(-0.347622\pi\) | ||||
0.460635 | + | 0.887590i | \(0.347622\pi\) | |||||||
\(864\) | 7.96032 | 0.270816 | ||||||||
\(865\) | −14.5986 | −0.496369 | ||||||||
\(866\) | −17.4488 | −0.592933 | ||||||||
\(867\) | −6.96786 | −0.236641 | ||||||||
\(868\) | 51.6703 | 1.75380 | ||||||||
\(869\) | −31.4547 | −1.06703 | ||||||||
\(870\) | −1.87115 | −0.0634379 | ||||||||
\(871\) | −23.1628 | −0.784841 | ||||||||
\(872\) | −19.7316 | −0.668195 | ||||||||
\(873\) | −16.8523 | −0.570363 | ||||||||
\(874\) | 51.0601 | 1.72713 | ||||||||
\(875\) | −23.6048 | −0.797986 | ||||||||
\(876\) | −6.95401 | −0.234954 | ||||||||
\(877\) | −31.5393 | −1.06501 | −0.532503 | − | 0.846428i | \(-0.678749\pi\) | ||||
−0.532503 | + | 0.846428i | \(0.678749\pi\) | |||||||
\(878\) | −3.50970 | −0.118447 | ||||||||
\(879\) | 0.459157 | 0.0154870 | ||||||||
\(880\) | −27.3820 | −0.923047 | ||||||||
\(881\) | −9.23845 | −0.311251 | −0.155626 | − | 0.987816i | \(-0.549739\pi\) | ||||
−0.155626 | + | 0.987816i | \(0.549739\pi\) | |||||||
\(882\) | −2.08682 | −0.0702667 | ||||||||
\(883\) | −22.5049 | −0.757350 | −0.378675 | − | 0.925530i | \(-0.623620\pi\) | ||||
−0.378675 | + | 0.925530i | \(0.623620\pi\) | |||||||
\(884\) | 19.8659 | 0.668163 | ||||||||
\(885\) | −3.55160 | −0.119386 | ||||||||
\(886\) | −33.8759 | −1.13808 | ||||||||
\(887\) | −30.2960 | −1.01724 | −0.508621 | − | 0.860991i | \(-0.669844\pi\) | ||||
−0.508621 | + | 0.860991i | \(0.669844\pi\) | |||||||
\(888\) | 1.90847 | 0.0640439 | ||||||||
\(889\) | −34.3545 | −1.15221 | ||||||||
\(890\) | −5.12880 | −0.171918 | ||||||||
\(891\) | −4.01073 | −0.134365 | ||||||||
\(892\) | −25.6306 | −0.858176 | ||||||||
\(893\) | −69.2654 | −2.31788 | ||||||||
\(894\) | 33.8615 | 1.13250 | ||||||||
\(895\) | −45.8314 | −1.53198 | ||||||||
\(896\) | 19.9865 | 0.667701 | ||||||||
\(897\) | 6.22952 | 0.207998 | ||||||||
\(898\) | 29.0490 | 0.969377 | ||||||||
\(899\) | 3.01501 | 0.100556 | ||||||||
\(900\) | 2.75756 | 0.0919188 | ||||||||
\(901\) | 28.3180 | 0.943410 | ||||||||
\(902\) | −91.3345 | −3.04111 | ||||||||
\(903\) | 22.3014 | 0.742144 | ||||||||
\(904\) | −8.00052 | −0.266093 | ||||||||
\(905\) | 2.27697 | 0.0756891 | ||||||||
\(906\) | 17.9083 | 0.594964 | ||||||||
\(907\) | −34.6786 | −1.15148 | −0.575742 | − | 0.817632i | \(-0.695287\pi\) | ||||
−0.575742 | + | 0.817632i | \(0.695287\pi\) | |||||||
\(908\) | −42.2925 | −1.40353 | ||||||||
\(909\) | 3.80431 | 0.126181 | ||||||||
\(910\) | 20.8929 | 0.692592 | ||||||||
\(911\) | −29.6688 | −0.982970 | −0.491485 | − | 0.870886i | \(-0.663546\pi\) | ||||
−0.491485 | + | 0.870886i | \(0.663546\pi\) | |||||||
\(912\) | −17.3679 | −0.575109 | ||||||||
\(913\) | 39.7750 | 1.31636 | ||||||||
\(914\) | 73.1420 | 2.41932 | ||||||||
\(915\) | 5.48181 | 0.181223 | ||||||||
\(916\) | −72.4965 | −2.39535 | ||||||||
\(917\) | 9.94733 | 0.328490 | ||||||||
\(918\) | −10.3803 | −0.342601 | ||||||||
\(919\) | 3.41218 | 0.112558 | 0.0562788 | − | 0.998415i | \(-0.482076\pi\) | ||||
0.0562788 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(920\) | 9.94774 | 0.327967 | ||||||||
\(921\) | 11.2133 | 0.369492 | ||||||||
\(922\) | −64.4229 | −2.12165 | ||||||||
\(923\) | −6.69925 | −0.220509 | ||||||||
\(924\) | −24.5498 | −0.807630 | ||||||||
\(925\) | −2.00672 | −0.0659807 | ||||||||
\(926\) | −42.3222 | −1.39079 | ||||||||
\(927\) | 8.01017 | 0.263089 | ||||||||
\(928\) | 2.84317 | 0.0933317 | ||||||||
\(929\) | −5.27469 | −0.173057 | −0.0865285 | − | 0.996249i | \(-0.527577\pi\) | ||||
−0.0865285 | + | 0.996249i | \(0.527577\pi\) | |||||||
\(930\) | −44.2234 | −1.45014 | ||||||||
\(931\) | 6.18638 | 0.202750 | ||||||||
\(932\) | −49.2555 | −1.61342 | ||||||||
\(933\) | −12.1228 | −0.396884 | ||||||||
\(934\) | 17.7905 | 0.582121 | ||||||||
\(935\) | 48.5154 | 1.58662 | ||||||||
\(936\) | 1.70867 | 0.0558498 | ||||||||
\(937\) | −11.6027 | −0.379043 | −0.189521 | − | 0.981877i | \(-0.560694\pi\) | ||||
−0.189521 | + | 0.981877i | \(0.560694\pi\) | |||||||
\(938\) | 74.0826 | 2.41888 | ||||||||
\(939\) | −12.8050 | −0.417876 | ||||||||
\(940\) | −67.9499 | −2.21628 | ||||||||
\(941\) | −28.2271 | −0.920178 | −0.460089 | − | 0.887873i | \(-0.652182\pi\) | ||||
−0.460089 | + | 0.887873i | \(0.652182\pi\) | |||||||
\(942\) | −17.4247 | −0.567729 | ||||||||
\(943\) | −41.1486 | −1.33998 | ||||||||
\(944\) | 3.97175 | 0.129270 | ||||||||
\(945\) | −6.06021 | −0.197139 | ||||||||
\(946\) | −77.3222 | −2.51396 | ||||||||
\(947\) | −41.9537 | −1.36331 | −0.681657 | − | 0.731672i | \(-0.738740\pi\) | ||||
−0.681657 | + | 0.731672i | \(0.738740\pi\) | |||||||
\(948\) | −19.5722 | −0.635676 | ||||||||
\(949\) | 4.53077 | 0.147075 | ||||||||
\(950\) | −14.7262 | −0.477780 | ||||||||
\(951\) | 2.96789 | 0.0962404 | ||||||||
\(952\) | −12.6184 | −0.408965 | ||||||||
\(953\) | −51.3228 | −1.66251 | −0.831255 | − | 0.555892i | \(-0.812377\pi\) | ||||
−0.831255 | + | 0.555892i | \(0.812377\pi\) | |||||||
\(954\) | 12.2643 | 0.397072 | ||||||||
\(955\) | −37.3798 | −1.20958 | ||||||||
\(956\) | −2.49562 | −0.0807141 | ||||||||
\(957\) | −1.43250 | −0.0463063 | ||||||||
\(958\) | 45.0126 | 1.45429 | ||||||||
\(959\) | 38.1018 | 1.23037 | ||||||||
\(960\) | −28.0486 | −0.905265 | ||||||||
\(961\) | 40.2578 | 1.29864 | ||||||||
\(962\) | −6.26111 | −0.201866 | ||||||||
\(963\) | −12.6857 | −0.408792 | ||||||||
\(964\) | 26.1632 | 0.842660 | ||||||||
\(965\) | 56.1580 | 1.80779 | ||||||||
\(966\) | −19.9242 | −0.641049 | ||||||||
\(967\) | −15.0557 | −0.484158 | −0.242079 | − | 0.970257i | \(-0.577829\pi\) | ||||
−0.242079 | + | 0.970257i | \(0.577829\pi\) | |||||||
\(968\) | 5.34464 | 0.171783 | ||||||||
\(969\) | 30.7725 | 0.988554 | ||||||||
\(970\) | 88.2867 | 2.83471 | ||||||||
\(971\) | 18.2675 | 0.586232 | 0.293116 | − | 0.956077i | \(-0.405308\pi\) | ||||
0.293116 | + | 0.956077i | \(0.405308\pi\) | |||||||
\(972\) | −2.49562 | −0.0800471 | ||||||||
\(973\) | −2.67839 | −0.0858651 | ||||||||
\(974\) | 11.2940 | 0.361885 | ||||||||
\(975\) | −1.79665 | −0.0575388 | ||||||||
\(976\) | −6.13030 | −0.196226 | ||||||||
\(977\) | 11.8112 | 0.377873 | 0.188936 | − | 0.981989i | \(-0.439496\pi\) | ||||
0.188936 | + | 0.981989i | \(0.439496\pi\) | |||||||
\(978\) | −7.60865 | −0.243298 | ||||||||
\(979\) | −3.92648 | −0.125491 | ||||||||
\(980\) | 6.06889 | 0.193864 | ||||||||
\(981\) | −18.7766 | −0.599492 | ||||||||
\(982\) | 51.0983 | 1.63061 | ||||||||
\(983\) | −30.4350 | −0.970725 | −0.485363 | − | 0.874313i | \(-0.661312\pi\) | ||||
−0.485363 | + | 0.874313i | \(0.661312\pi\) | |||||||
\(984\) | −11.2865 | −0.359801 | ||||||||
\(985\) | 6.10486 | 0.194517 | ||||||||
\(986\) | −3.70750 | −0.118071 | ||||||||
\(987\) | 27.0281 | 0.860313 | ||||||||
\(988\) | −25.5060 | −0.811453 | ||||||||
\(989\) | −34.8357 | −1.10771 | ||||||||
\(990\) | 21.0116 | 0.667794 | ||||||||
\(991\) | 54.3952 | 1.72792 | 0.863960 | − | 0.503561i | \(-0.167977\pi\) | ||||
0.863960 | + | 0.503561i | \(0.167977\pi\) | |||||||
\(992\) | 67.1965 | 2.13349 | ||||||||
\(993\) | −35.0721 | −1.11298 | ||||||||
\(994\) | 21.4265 | 0.679608 | ||||||||
\(995\) | 13.2056 | 0.418645 | ||||||||
\(996\) | 24.7494 | 0.784216 | ||||||||
\(997\) | 14.6453 | 0.463821 | 0.231910 | − | 0.972737i | \(-0.425502\pi\) | ||||
0.231910 | + | 0.972737i | \(0.425502\pi\) | |||||||
\(998\) | −72.3090 | −2.28890 | ||||||||
\(999\) | 1.81610 | 0.0574590 |
(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 | 717.2.a.d.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 2151.2.a.e.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.2.a.d.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
2151.2.a.e.1.1 | 6 | 3.2 | odd | 2 |