Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, 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("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-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 | ||||||||
\(3\) | −2.43348 | −1.40497 | −0.702487 | − | 0.711697i | \(-0.747927\pi\) | ||||
−0.702487 | + | 0.711697i | \(0.747927\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.73446 | −0.775673 | −0.387836 | − | 0.921728i | \(-0.626777\pi\) | ||||
−0.387836 | + | 0.921728i | \(0.626777\pi\) | |||||||
\(6\) | −2.43348 | −0.993466 | ||||||||
\(7\) | −1.67668 | −0.633726 | −0.316863 | − | 0.948471i | \(-0.602630\pi\) | ||||
−0.316863 | + | 0.948471i | \(0.602630\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.92185 | 0.973950 | ||||||||
\(10\) | −1.73446 | −0.548483 | ||||||||
\(11\) | −1.47743 | −0.445463 | −0.222731 | − | 0.974880i | \(-0.571497\pi\) | ||||
−0.222731 | + | 0.974880i | \(0.571497\pi\) | |||||||
\(12\) | −2.43348 | −0.702487 | ||||||||
\(13\) | −2.80106 | −0.776874 | −0.388437 | − | 0.921475i | \(-0.626985\pi\) | ||||
−0.388437 | + | 0.921475i | \(0.626985\pi\) | |||||||
\(14\) | −1.67668 | −0.448112 | ||||||||
\(15\) | 4.22077 | 1.08980 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.61875 | 1.12021 | 0.560106 | − | 0.828421i | \(-0.310760\pi\) | ||||
0.560106 | + | 0.828421i | \(0.310760\pi\) | |||||||
\(18\) | 2.92185 | 0.688686 | ||||||||
\(19\) | −3.67566 | −0.843253 | −0.421627 | − | 0.906770i | \(-0.638541\pi\) | ||||
−0.421627 | + | 0.906770i | \(0.638541\pi\) | |||||||
\(20\) | −1.73446 | −0.387836 | ||||||||
\(21\) | 4.08018 | 0.890368 | ||||||||
\(22\) | −1.47743 | −0.314990 | ||||||||
\(23\) | 4.55945 | 0.950711 | 0.475356 | − | 0.879794i | \(-0.342319\pi\) | ||||
0.475356 | + | 0.879794i | \(0.342319\pi\) | |||||||
\(24\) | −2.43348 | −0.496733 | ||||||||
\(25\) | −1.99166 | −0.398332 | ||||||||
\(26\) | −2.80106 | −0.549333 | ||||||||
\(27\) | 0.190180 | 0.0366002 | ||||||||
\(28\) | −1.67668 | −0.316863 | ||||||||
\(29\) | 7.39932 | 1.37402 | 0.687009 | − | 0.726649i | \(-0.258923\pi\) | ||||
0.687009 | + | 0.726649i | \(0.258923\pi\) | |||||||
\(30\) | 4.22077 | 0.770604 | ||||||||
\(31\) | 8.27128 | 1.48557 | 0.742783 | − | 0.669532i | \(-0.233505\pi\) | ||||
0.742783 | + | 0.669532i | \(0.233505\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.59531 | 0.625863 | ||||||||
\(34\) | 4.61875 | 0.792110 | ||||||||
\(35\) | 2.90813 | 0.491564 | ||||||||
\(36\) | 2.92185 | 0.486975 | ||||||||
\(37\) | −7.95068 | −1.30708 | −0.653542 | − | 0.756890i | \(-0.726718\pi\) | ||||
−0.653542 | + | 0.756890i | \(0.726718\pi\) | |||||||
\(38\) | −3.67566 | −0.596270 | ||||||||
\(39\) | 6.81634 | 1.09149 | ||||||||
\(40\) | −1.73446 | −0.274242 | ||||||||
\(41\) | 10.8781 | 1.69888 | 0.849439 | − | 0.527687i | \(-0.176941\pi\) | ||||
0.849439 | + | 0.527687i | \(0.176941\pi\) | |||||||
\(42\) | 4.08018 | 0.629586 | ||||||||
\(43\) | −8.21581 | −1.25290 | −0.626450 | − | 0.779462i | \(-0.715493\pi\) | ||||
−0.626450 | + | 0.779462i | \(0.715493\pi\) | |||||||
\(44\) | −1.47743 | −0.222731 | ||||||||
\(45\) | −5.06782 | −0.755466 | ||||||||
\(46\) | 4.55945 | 0.672254 | ||||||||
\(47\) | 7.62833 | 1.11271 | 0.556353 | − | 0.830946i | \(-0.312200\pi\) | ||||
0.556353 | + | 0.830946i | \(0.312200\pi\) | |||||||
\(48\) | −2.43348 | −0.351243 | ||||||||
\(49\) | −4.18874 | −0.598391 | ||||||||
\(50\) | −1.99166 | −0.281663 | ||||||||
\(51\) | −11.2397 | −1.57387 | ||||||||
\(52\) | −2.80106 | −0.388437 | ||||||||
\(53\) | 9.29471 | 1.27673 | 0.638363 | − | 0.769735i | \(-0.279612\pi\) | ||||
0.638363 | + | 0.769735i | \(0.279612\pi\) | |||||||
\(54\) | 0.190180 | 0.0258803 | ||||||||
\(55\) | 2.56254 | 0.345533 | ||||||||
\(56\) | −1.67668 | −0.224056 | ||||||||
\(57\) | 8.94465 | 1.18475 | ||||||||
\(58\) | 7.39932 | 0.971578 | ||||||||
\(59\) | −13.8888 | −1.80817 | −0.904087 | − | 0.427349i | \(-0.859447\pi\) | ||||
−0.904087 | + | 0.427349i | \(0.859447\pi\) | |||||||
\(60\) | 4.22077 | 0.544900 | ||||||||
\(61\) | −9.15887 | −1.17267 | −0.586337 | − | 0.810068i | \(-0.699430\pi\) | ||||
−0.586337 | + | 0.810068i | \(0.699430\pi\) | |||||||
\(62\) | 8.27128 | 1.05045 | ||||||||
\(63\) | −4.89901 | −0.617217 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.85832 | 0.602600 | ||||||||
\(66\) | 3.59531 | 0.442552 | ||||||||
\(67\) | −2.71897 | −0.332175 | −0.166087 | − | 0.986111i | \(-0.553113\pi\) | ||||
−0.166087 | + | 0.986111i | \(0.553113\pi\) | |||||||
\(68\) | 4.61875 | 0.560106 | ||||||||
\(69\) | −11.0954 | −1.33572 | ||||||||
\(70\) | 2.90813 | 0.347588 | ||||||||
\(71\) | 5.49990 | 0.652718 | 0.326359 | − | 0.945246i | \(-0.394178\pi\) | ||||
0.326359 | + | 0.945246i | \(0.394178\pi\) | |||||||
\(72\) | 2.92185 | 0.344343 | ||||||||
\(73\) | 0.923118 | 0.108043 | 0.0540214 | − | 0.998540i | \(-0.482796\pi\) | ||||
0.0540214 | + | 0.998540i | \(0.482796\pi\) | |||||||
\(74\) | −7.95068 | −0.924248 | ||||||||
\(75\) | 4.84667 | 0.559646 | ||||||||
\(76\) | −3.67566 | −0.421627 | ||||||||
\(77\) | 2.47718 | 0.282301 | ||||||||
\(78\) | 6.81634 | 0.771798 | ||||||||
\(79\) | 5.33352 | 0.600068 | 0.300034 | − | 0.953929i | \(-0.403002\pi\) | ||||
0.300034 | + | 0.953929i | \(0.403002\pi\) | |||||||
\(80\) | −1.73446 | −0.193918 | ||||||||
\(81\) | −9.22835 | −1.02537 | ||||||||
\(82\) | 10.8781 | 1.20129 | ||||||||
\(83\) | 8.63102 | 0.947377 | 0.473689 | − | 0.880692i | \(-0.342922\pi\) | ||||
0.473689 | + | 0.880692i | \(0.342922\pi\) | |||||||
\(84\) | 4.08018 | 0.445184 | ||||||||
\(85\) | −8.01103 | −0.868918 | ||||||||
\(86\) | −8.21581 | −0.885934 | ||||||||
\(87\) | −18.0061 | −1.93046 | ||||||||
\(88\) | −1.47743 | −0.157495 | ||||||||
\(89\) | −0.766957 | −0.0812973 | −0.0406486 | − | 0.999174i | \(-0.512942\pi\) | ||||
−0.0406486 | + | 0.999174i | \(0.512942\pi\) | |||||||
\(90\) | −5.06782 | −0.534195 | ||||||||
\(91\) | 4.69649 | 0.492326 | ||||||||
\(92\) | 4.55945 | 0.475356 | ||||||||
\(93\) | −20.1280 | −2.08718 | ||||||||
\(94\) | 7.62833 | 0.786803 | ||||||||
\(95\) | 6.37527 | 0.654089 | ||||||||
\(96\) | −2.43348 | −0.248367 | ||||||||
\(97\) | 3.33078 | 0.338189 | 0.169095 | − | 0.985600i | \(-0.445916\pi\) | ||||
0.169095 | + | 0.985600i | \(0.445916\pi\) | |||||||
\(98\) | −4.18874 | −0.423126 | ||||||||
\(99\) | −4.31683 | −0.433858 | ||||||||
\(100\) | −1.99166 | −0.199166 | ||||||||
\(101\) | 4.48831 | 0.446604 | 0.223302 | − | 0.974749i | \(-0.428316\pi\) | ||||
0.223302 | + | 0.974749i | \(0.428316\pi\) | |||||||
\(102\) | −11.2397 | −1.11289 | ||||||||
\(103\) | 2.05394 | 0.202381 | 0.101190 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101190 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(104\) | −2.80106 | −0.274667 | ||||||||
\(105\) | −7.07690 | −0.690634 | ||||||||
\(106\) | 9.29471 | 0.902782 | ||||||||
\(107\) | −15.2769 | −1.47687 | −0.738436 | − | 0.674323i | \(-0.764435\pi\) | ||||
−0.738436 | + | 0.674323i | \(0.764435\pi\) | |||||||
\(108\) | 0.190180 | 0.0183001 | ||||||||
\(109\) | −15.1271 | −1.44891 | −0.724455 | − | 0.689322i | \(-0.757909\pi\) | ||||
−0.724455 | + | 0.689322i | \(0.757909\pi\) | |||||||
\(110\) | 2.56254 | 0.244329 | ||||||||
\(111\) | 19.3479 | 1.83642 | ||||||||
\(112\) | −1.67668 | −0.158432 | ||||||||
\(113\) | 7.89675 | 0.742864 | 0.371432 | − | 0.928460i | \(-0.378867\pi\) | ||||
0.371432 | + | 0.928460i | \(0.378867\pi\) | |||||||
\(114\) | 8.94465 | 0.837744 | ||||||||
\(115\) | −7.90817 | −0.737441 | ||||||||
\(116\) | 7.39932 | 0.687009 | ||||||||
\(117\) | −8.18427 | −0.756636 | ||||||||
\(118\) | −13.8888 | −1.27857 | ||||||||
\(119\) | −7.74418 | −0.709908 | ||||||||
\(120\) | 4.22077 | 0.385302 | ||||||||
\(121\) | −8.81719 | −0.801563 | ||||||||
\(122\) | −9.15887 | −0.829205 | ||||||||
\(123\) | −26.4718 | −2.38688 | ||||||||
\(124\) | 8.27128 | 0.742783 | ||||||||
\(125\) | 12.1267 | 1.08465 | ||||||||
\(126\) | −4.89901 | −0.436439 | ||||||||
\(127\) | −11.2577 | −0.998959 | −0.499479 | − | 0.866326i | \(-0.666475\pi\) | ||||
−0.499479 | + | 0.866326i | \(0.666475\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 19.9930 | 1.76029 | ||||||||
\(130\) | 4.85832 | 0.426103 | ||||||||
\(131\) | −11.8547 | −1.03575 | −0.517875 | − | 0.855456i | \(-0.673277\pi\) | ||||
−0.517875 | + | 0.855456i | \(0.673277\pi\) | |||||||
\(132\) | 3.59531 | 0.312931 | ||||||||
\(133\) | 6.16291 | 0.534392 | ||||||||
\(134\) | −2.71897 | −0.234883 | ||||||||
\(135\) | −0.329860 | −0.0283898 | ||||||||
\(136\) | 4.61875 | 0.396055 | ||||||||
\(137\) | 5.49625 | 0.469576 | 0.234788 | − | 0.972047i | \(-0.424560\pi\) | ||||
0.234788 | + | 0.972047i | \(0.424560\pi\) | |||||||
\(138\) | −11.0954 | −0.944499 | ||||||||
\(139\) | −15.2731 | −1.29545 | −0.647723 | − | 0.761876i | \(-0.724279\pi\) | ||||
−0.647723 | + | 0.761876i | \(0.724279\pi\) | |||||||
\(140\) | 2.90813 | 0.245782 | ||||||||
\(141\) | −18.5634 | −1.56332 | ||||||||
\(142\) | 5.49990 | 0.461541 | ||||||||
\(143\) | 4.13838 | 0.346068 | ||||||||
\(144\) | 2.92185 | 0.243487 | ||||||||
\(145\) | −12.8338 | −1.06579 | ||||||||
\(146\) | 0.923118 | 0.0763978 | ||||||||
\(147\) | 10.1932 | 0.840723 | ||||||||
\(148\) | −7.95068 | −0.653542 | ||||||||
\(149\) | 6.17203 | 0.505633 | 0.252816 | − | 0.967514i | \(-0.418643\pi\) | ||||
0.252816 | + | 0.967514i | \(0.418643\pi\) | |||||||
\(150\) | 4.84667 | 0.395729 | ||||||||
\(151\) | 8.95488 | 0.728738 | 0.364369 | − | 0.931255i | \(-0.381285\pi\) | ||||
0.364369 | + | 0.931255i | \(0.381285\pi\) | |||||||
\(152\) | −3.67566 | −0.298135 | ||||||||
\(153\) | 13.4953 | 1.09103 | ||||||||
\(154\) | 2.47718 | 0.199617 | ||||||||
\(155\) | −14.3462 | −1.15231 | ||||||||
\(156\) | 6.81634 | 0.545744 | ||||||||
\(157\) | 13.6153 | 1.08662 | 0.543312 | − | 0.839531i | \(-0.317170\pi\) | ||||
0.543312 | + | 0.839531i | \(0.317170\pi\) | |||||||
\(158\) | 5.33352 | 0.424312 | ||||||||
\(159\) | −22.6185 | −1.79377 | ||||||||
\(160\) | −1.73446 | −0.137121 | ||||||||
\(161\) | −7.64475 | −0.602491 | ||||||||
\(162\) | −9.22835 | −0.725047 | ||||||||
\(163\) | −20.1208 | −1.57598 | −0.787992 | − | 0.615685i | \(-0.788879\pi\) | ||||
−0.787992 | + | 0.615685i | \(0.788879\pi\) | |||||||
\(164\) | 10.8781 | 0.849439 | ||||||||
\(165\) | −6.23591 | −0.485465 | ||||||||
\(166\) | 8.63102 | 0.669897 | ||||||||
\(167\) | −18.9475 | −1.46620 | −0.733100 | − | 0.680120i | \(-0.761927\pi\) | ||||
−0.733100 | + | 0.680120i | \(0.761927\pi\) | |||||||
\(168\) | 4.08018 | 0.314793 | ||||||||
\(169\) | −5.15406 | −0.396466 | ||||||||
\(170\) | −8.01103 | −0.614418 | ||||||||
\(171\) | −10.7397 | −0.821286 | ||||||||
\(172\) | −8.21581 | −0.626450 | ||||||||
\(173\) | 6.80237 | 0.517175 | 0.258587 | − | 0.965988i | \(-0.416743\pi\) | ||||
0.258587 | + | 0.965988i | \(0.416743\pi\) | |||||||
\(174\) | −18.0061 | −1.36504 | ||||||||
\(175\) | 3.33938 | 0.252433 | ||||||||
\(176\) | −1.47743 | −0.111366 | ||||||||
\(177\) | 33.7983 | 2.54043 | ||||||||
\(178\) | −0.766957 | −0.0574859 | ||||||||
\(179\) | 17.9187 | 1.33931 | 0.669654 | − | 0.742673i | \(-0.266442\pi\) | ||||
0.669654 | + | 0.742673i | \(0.266442\pi\) | |||||||
\(180\) | −5.06782 | −0.377733 | ||||||||
\(181\) | 11.1532 | 0.829012 | 0.414506 | − | 0.910046i | \(-0.363954\pi\) | ||||
0.414506 | + | 0.910046i | \(0.363954\pi\) | |||||||
\(182\) | 4.69649 | 0.348127 | ||||||||
\(183\) | 22.2880 | 1.64757 | ||||||||
\(184\) | 4.55945 | 0.336127 | ||||||||
\(185\) | 13.7901 | 1.01387 | ||||||||
\(186\) | −20.1280 | −1.47586 | ||||||||
\(187\) | −6.82390 | −0.499013 | ||||||||
\(188\) | 7.62833 | 0.556353 | ||||||||
\(189\) | −0.318872 | −0.0231945 | ||||||||
\(190\) | 6.37527 | 0.462510 | ||||||||
\(191\) | −24.6453 | −1.78327 | −0.891636 | − | 0.452753i | \(-0.850442\pi\) | ||||
−0.891636 | + | 0.452753i | \(0.850442\pi\) | |||||||
\(192\) | −2.43348 | −0.175622 | ||||||||
\(193\) | 5.02429 | 0.361656 | 0.180828 | − | 0.983515i | \(-0.442122\pi\) | ||||
0.180828 | + | 0.983515i | \(0.442122\pi\) | |||||||
\(194\) | 3.33078 | 0.239136 | ||||||||
\(195\) | −11.8226 | −0.846637 | ||||||||
\(196\) | −4.18874 | −0.299195 | ||||||||
\(197\) | 11.9986 | 0.854863 | 0.427432 | − | 0.904048i | \(-0.359418\pi\) | ||||
0.427432 | + | 0.904048i | \(0.359418\pi\) | |||||||
\(198\) | −4.31683 | −0.306784 | ||||||||
\(199\) | 15.6396 | 1.10867 | 0.554333 | − | 0.832295i | \(-0.312974\pi\) | ||||
0.554333 | + | 0.832295i | \(0.312974\pi\) | |||||||
\(200\) | −1.99166 | −0.140832 | ||||||||
\(201\) | 6.61656 | 0.466696 | ||||||||
\(202\) | 4.48831 | 0.315796 | ||||||||
\(203\) | −12.4063 | −0.870752 | ||||||||
\(204\) | −11.2397 | −0.786934 | ||||||||
\(205\) | −18.8676 | −1.31777 | ||||||||
\(206\) | 2.05394 | 0.143105 | ||||||||
\(207\) | 13.3220 | 0.925945 | ||||||||
\(208\) | −2.80106 | −0.194219 | ||||||||
\(209\) | 5.43053 | 0.375638 | ||||||||
\(210\) | −7.07690 | −0.488352 | ||||||||
\(211\) | −1.48562 | −0.102274 | −0.0511372 | − | 0.998692i | \(-0.516285\pi\) | ||||
−0.0511372 | + | 0.998692i | \(0.516285\pi\) | |||||||
\(212\) | 9.29471 | 0.638363 | ||||||||
\(213\) | −13.3839 | −0.917051 | ||||||||
\(214\) | −15.2769 | −1.04431 | ||||||||
\(215\) | 14.2500 | 0.971840 | ||||||||
\(216\) | 0.190180 | 0.0129401 | ||||||||
\(217\) | −13.8683 | −0.941442 | ||||||||
\(218\) | −15.1271 | −1.02453 | ||||||||
\(219\) | −2.24639 | −0.151797 | ||||||||
\(220\) | 2.56254 | 0.172767 | ||||||||
\(221\) | −12.9374 | −0.870264 | ||||||||
\(222\) | 19.3479 | 1.29854 | ||||||||
\(223\) | −13.5411 | −0.906780 | −0.453390 | − | 0.891312i | \(-0.649786\pi\) | ||||
−0.453390 | + | 0.891312i | \(0.649786\pi\) | |||||||
\(224\) | −1.67668 | −0.112028 | ||||||||
\(225\) | −5.81933 | −0.387955 | ||||||||
\(226\) | 7.89675 | 0.525284 | ||||||||
\(227\) | −4.86914 | −0.323176 | −0.161588 | − | 0.986858i | \(-0.551662\pi\) | ||||
−0.161588 | + | 0.986858i | \(0.551662\pi\) | |||||||
\(228\) | 8.94465 | 0.592374 | ||||||||
\(229\) | −6.93924 | −0.458558 | −0.229279 | − | 0.973361i | \(-0.573637\pi\) | ||||
−0.229279 | + | 0.973361i | \(0.573637\pi\) | |||||||
\(230\) | −7.90817 | −0.521449 | ||||||||
\(231\) | −6.02819 | −0.396626 | ||||||||
\(232\) | 7.39932 | 0.485789 | ||||||||
\(233\) | 12.6118 | 0.826224 | 0.413112 | − | 0.910680i | \(-0.364442\pi\) | ||||
0.413112 | + | 0.910680i | \(0.364442\pi\) | |||||||
\(234\) | −8.18427 | −0.535023 | ||||||||
\(235\) | −13.2310 | −0.863096 | ||||||||
\(236\) | −13.8888 | −0.904087 | ||||||||
\(237\) | −12.9790 | −0.843079 | ||||||||
\(238\) | −7.74418 | −0.501981 | ||||||||
\(239\) | −25.2641 | −1.63420 | −0.817099 | − | 0.576497i | \(-0.804419\pi\) | ||||
−0.817099 | + | 0.576497i | \(0.804419\pi\) | |||||||
\(240\) | 4.22077 | 0.272450 | ||||||||
\(241\) | 1.81987 | 0.117228 | 0.0586141 | − | 0.998281i | \(-0.481332\pi\) | ||||
0.0586141 | + | 0.998281i | \(0.481332\pi\) | |||||||
\(242\) | −8.81719 | −0.566791 | ||||||||
\(243\) | 21.8865 | 1.40402 | ||||||||
\(244\) | −9.15887 | −0.586337 | ||||||||
\(245\) | 7.26518 | 0.464156 | ||||||||
\(246\) | −26.4718 | −1.68778 | ||||||||
\(247\) | 10.2957 | 0.655102 | ||||||||
\(248\) | 8.27128 | 0.525227 | ||||||||
\(249\) | −21.0035 | −1.33104 | ||||||||
\(250\) | 12.1267 | 0.766962 | ||||||||
\(251\) | 3.84973 | 0.242993 | 0.121496 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121496 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(252\) | −4.89901 | −0.308609 | ||||||||
\(253\) | −6.73628 | −0.423506 | ||||||||
\(254\) | −11.2577 | −0.706371 | ||||||||
\(255\) | 19.4947 | 1.22081 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.0592 | −1.50077 | −0.750385 | − | 0.661001i | \(-0.770132\pi\) | ||||
−0.750385 | + | 0.661001i | \(0.770132\pi\) | |||||||
\(258\) | 19.9930 | 1.24471 | ||||||||
\(259\) | 13.3308 | 0.828334 | ||||||||
\(260\) | 4.85832 | 0.301300 | ||||||||
\(261\) | 21.6197 | 1.33822 | ||||||||
\(262\) | −11.8547 | −0.732386 | ||||||||
\(263\) | −23.0108 | −1.41890 | −0.709452 | − | 0.704753i | \(-0.751058\pi\) | ||||
−0.709452 | + | 0.704753i | \(0.751058\pi\) | |||||||
\(264\) | 3.59531 | 0.221276 | ||||||||
\(265\) | −16.1213 | −0.990321 | ||||||||
\(266\) | 6.16291 | 0.377872 | ||||||||
\(267\) | 1.86638 | 0.114220 | ||||||||
\(268\) | −2.71897 | −0.166087 | ||||||||
\(269\) | −23.4563 | −1.43016 | −0.715079 | − | 0.699043i | \(-0.753609\pi\) | ||||
−0.715079 | + | 0.699043i | \(0.753609\pi\) | |||||||
\(270\) | −0.329860 | −0.0200746 | ||||||||
\(271\) | 17.8028 | 1.08144 | 0.540722 | − | 0.841201i | \(-0.318151\pi\) | ||||
0.540722 | + | 0.841201i | \(0.318151\pi\) | |||||||
\(272\) | 4.61875 | 0.280053 | ||||||||
\(273\) | −11.4288 | −0.691704 | ||||||||
\(274\) | 5.49625 | 0.332041 | ||||||||
\(275\) | 2.94254 | 0.177442 | ||||||||
\(276\) | −11.0954 | −0.667862 | ||||||||
\(277\) | −17.0890 | −1.02678 | −0.513390 | − | 0.858156i | \(-0.671610\pi\) | ||||
−0.513390 | + | 0.858156i | \(0.671610\pi\) | |||||||
\(278\) | −15.2731 | −0.916019 | ||||||||
\(279\) | 24.1674 | 1.44687 | ||||||||
\(280\) | 2.90813 | 0.173794 | ||||||||
\(281\) | −18.1072 | −1.08019 | −0.540094 | − | 0.841605i | \(-0.681611\pi\) | ||||
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(282\) | −18.5634 | −1.10544 | ||||||||
\(283\) | −16.6038 | −0.986995 | −0.493497 | − | 0.869747i | \(-0.664282\pi\) | ||||
−0.493497 | + | 0.869747i | \(0.664282\pi\) | |||||||
\(284\) | 5.49990 | 0.326359 | ||||||||
\(285\) | −15.5141 | −0.918977 | ||||||||
\(286\) | 4.13838 | 0.244707 | ||||||||
\(287\) | −18.2392 | −1.07662 | ||||||||
\(288\) | 2.92185 | 0.172172 | ||||||||
\(289\) | 4.33290 | 0.254876 | ||||||||
\(290\) | −12.8338 | −0.753626 | ||||||||
\(291\) | −8.10540 | −0.475147 | ||||||||
\(292\) | 0.923118 | 0.0540214 | ||||||||
\(293\) | 15.9968 | 0.934541 | 0.467270 | − | 0.884114i | \(-0.345237\pi\) | ||||
0.467270 | + | 0.884114i | \(0.345237\pi\) | |||||||
\(294\) | 10.1932 | 0.594481 | ||||||||
\(295\) | 24.0896 | 1.40255 | ||||||||
\(296\) | −7.95068 | −0.462124 | ||||||||
\(297\) | −0.280979 | −0.0163040 | ||||||||
\(298\) | 6.17203 | 0.357536 | ||||||||
\(299\) | −12.7713 | −0.738583 | ||||||||
\(300\) | 4.84667 | 0.279823 | ||||||||
\(301\) | 13.7753 | 0.793995 | ||||||||
\(302\) | 8.95488 | 0.515295 | ||||||||
\(303\) | −10.9222 | −0.627466 | ||||||||
\(304\) | −3.67566 | −0.210813 | ||||||||
\(305\) | 15.8857 | 0.909610 | ||||||||
\(306\) | 13.4953 | 0.771475 | ||||||||
\(307\) | 5.76038 | 0.328762 | 0.164381 | − | 0.986397i | \(-0.447437\pi\) | ||||
0.164381 | + | 0.986397i | \(0.447437\pi\) | |||||||
\(308\) | 2.47718 | 0.141151 | ||||||||
\(309\) | −4.99824 | −0.284340 | ||||||||
\(310\) | −14.3462 | −0.814808 | ||||||||
\(311\) | −1.95681 | −0.110961 | −0.0554804 | − | 0.998460i | \(-0.517669\pi\) | ||||
−0.0554804 | + | 0.998460i | \(0.517669\pi\) | |||||||
\(312\) | 6.81634 | 0.385899 | ||||||||
\(313\) | 3.37010 | 0.190490 | 0.0952448 | − | 0.995454i | \(-0.469637\pi\) | ||||
0.0952448 | + | 0.995454i | \(0.469637\pi\) | |||||||
\(314\) | 13.6153 | 0.768359 | ||||||||
\(315\) | 8.49712 | 0.478759 | ||||||||
\(316\) | 5.33352 | 0.300034 | ||||||||
\(317\) | −15.8004 | −0.887436 | −0.443718 | − | 0.896166i | \(-0.646341\pi\) | ||||
−0.443718 | + | 0.896166i | \(0.646341\pi\) | |||||||
\(318\) | −22.6185 | −1.26838 | ||||||||
\(319\) | −10.9320 | −0.612074 | ||||||||
\(320\) | −1.73446 | −0.0969591 | ||||||||
\(321\) | 37.1761 | 2.07497 | ||||||||
\(322\) | −7.64475 | −0.426025 | ||||||||
\(323\) | −16.9770 | −0.944623 | ||||||||
\(324\) | −9.22835 | −0.512686 | ||||||||
\(325\) | 5.57876 | 0.309454 | ||||||||
\(326\) | −20.1208 | −1.11439 | ||||||||
\(327\) | 36.8115 | 2.03568 | ||||||||
\(328\) | 10.8781 | 0.600644 | ||||||||
\(329\) | −12.7903 | −0.705152 | ||||||||
\(330\) | −6.23591 | −0.343275 | ||||||||
\(331\) | −27.2807 | −1.49948 | −0.749741 | − | 0.661731i | \(-0.769822\pi\) | ||||
−0.749741 | + | 0.661731i | \(0.769822\pi\) | |||||||
\(332\) | 8.63102 | 0.473689 | ||||||||
\(333\) | −23.2307 | −1.27303 | ||||||||
\(334\) | −18.9475 | −1.03676 | ||||||||
\(335\) | 4.71593 | 0.257659 | ||||||||
\(336\) | 4.08018 | 0.222592 | ||||||||
\(337\) | −5.86743 | −0.319619 | −0.159810 | − | 0.987148i | \(-0.551088\pi\) | ||||
−0.159810 | + | 0.987148i | \(0.551088\pi\) | |||||||
\(338\) | −5.15406 | −0.280344 | ||||||||
\(339\) | −19.2166 | −1.04370 | ||||||||
\(340\) | −8.01103 | −0.434459 | ||||||||
\(341\) | −12.2203 | −0.661764 | ||||||||
\(342\) | −10.7397 | −0.580737 | ||||||||
\(343\) | 18.7600 | 1.01294 | ||||||||
\(344\) | −8.21581 | −0.442967 | ||||||||
\(345\) | 19.2444 | 1.03608 | ||||||||
\(346\) | 6.80237 | 0.365698 | ||||||||
\(347\) | 15.7387 | 0.844899 | 0.422449 | − | 0.906387i | \(-0.361170\pi\) | ||||
0.422449 | + | 0.906387i | \(0.361170\pi\) | |||||||
\(348\) | −18.0061 | −0.965230 | ||||||||
\(349\) | 20.3168 | 1.08754 | 0.543768 | − | 0.839236i | \(-0.316997\pi\) | ||||
0.543768 | + | 0.839236i | \(0.316997\pi\) | |||||||
\(350\) | 3.33938 | 0.178497 | ||||||||
\(351\) | −0.532707 | −0.0284338 | ||||||||
\(352\) | −1.47743 | −0.0787474 | ||||||||
\(353\) | −19.7115 | −1.04914 | −0.524568 | − | 0.851368i | \(-0.675773\pi\) | ||||
−0.524568 | + | 0.851368i | \(0.675773\pi\) | |||||||
\(354\) | 33.7983 | 1.79636 | ||||||||
\(355\) | −9.53933 | −0.506295 | ||||||||
\(356\) | −0.766957 | −0.0406486 | ||||||||
\(357\) | 18.8454 | 0.997402 | ||||||||
\(358\) | 17.9187 | 0.947034 | ||||||||
\(359\) | −9.58105 | −0.505669 | −0.252834 | − | 0.967510i | \(-0.581363\pi\) | ||||
−0.252834 | + | 0.967510i | \(0.581363\pi\) | |||||||
\(360\) | −5.06782 | −0.267098 | ||||||||
\(361\) | −5.48955 | −0.288924 | ||||||||
\(362\) | 11.1532 | 0.586200 | ||||||||
\(363\) | 21.4565 | 1.12617 | ||||||||
\(364\) | 4.69649 | 0.246163 | ||||||||
\(365\) | −1.60111 | −0.0838058 | ||||||||
\(366\) | 22.2880 | 1.16501 | ||||||||
\(367\) | −9.51485 | −0.496671 | −0.248335 | − | 0.968674i | \(-0.579884\pi\) | ||||
−0.248335 | + | 0.968674i | \(0.579884\pi\) | |||||||
\(368\) | 4.55945 | 0.237678 | ||||||||
\(369\) | 31.7842 | 1.65462 | ||||||||
\(370\) | 13.7901 | 0.716914 | ||||||||
\(371\) | −15.5843 | −0.809095 | ||||||||
\(372\) | −20.1280 | −1.04359 | ||||||||
\(373\) | 3.17222 | 0.164252 | 0.0821258 | − | 0.996622i | \(-0.473829\pi\) | ||||
0.0821258 | + | 0.996622i | \(0.473829\pi\) | |||||||
\(374\) | −6.82390 | −0.352855 | ||||||||
\(375\) | −29.5102 | −1.52390 | ||||||||
\(376\) | 7.62833 | 0.393401 | ||||||||
\(377\) | −20.7259 | −1.06744 | ||||||||
\(378\) | −0.318872 | −0.0164010 | ||||||||
\(379\) | −12.2390 | −0.628675 | −0.314338 | − | 0.949311i | \(-0.601782\pi\) | ||||
−0.314338 | + | 0.949311i | \(0.601782\pi\) | |||||||
\(380\) | 6.37527 | 0.327044 | ||||||||
\(381\) | 27.3954 | 1.40351 | ||||||||
\(382\) | −24.6453 | −1.26096 | ||||||||
\(383\) | 31.0014 | 1.58410 | 0.792048 | − | 0.610458i | \(-0.209015\pi\) | ||||
0.792048 | + | 0.610458i | \(0.209015\pi\) | |||||||
\(384\) | −2.43348 | −0.124183 | ||||||||
\(385\) | −4.29657 | −0.218973 | ||||||||
\(386\) | 5.02429 | 0.255729 | ||||||||
\(387\) | −24.0054 | −1.22026 | ||||||||
\(388\) | 3.33078 | 0.169095 | ||||||||
\(389\) | 14.4603 | 0.733165 | 0.366583 | − | 0.930385i | \(-0.380528\pi\) | ||||
0.366583 | + | 0.930385i | \(0.380528\pi\) | |||||||
\(390\) | −11.8226 | −0.598663 | ||||||||
\(391\) | 21.0590 | 1.06500 | ||||||||
\(392\) | −4.18874 | −0.211563 | ||||||||
\(393\) | 28.8483 | 1.45520 | ||||||||
\(394\) | 11.9986 | 0.604480 | ||||||||
\(395\) | −9.25076 | −0.465456 | ||||||||
\(396\) | −4.31683 | −0.216929 | ||||||||
\(397\) | −4.02599 | −0.202058 | −0.101029 | − | 0.994883i | \(-0.532214\pi\) | ||||
−0.101029 | + | 0.994883i | \(0.532214\pi\) | |||||||
\(398\) | 15.6396 | 0.783945 | ||||||||
\(399\) | −14.9973 | −0.750806 | ||||||||
\(400\) | −1.99166 | −0.0995830 | ||||||||
\(401\) | 1.76890 | 0.0883348 | 0.0441674 | − | 0.999024i | \(-0.485937\pi\) | ||||
0.0441674 | + | 0.999024i | \(0.485937\pi\) | |||||||
\(402\) | 6.61656 | 0.330004 | ||||||||
\(403\) | −23.1684 | −1.15410 | ||||||||
\(404\) | 4.48831 | 0.223302 | ||||||||
\(405\) | 16.0062 | 0.795353 | ||||||||
\(406\) | −12.4063 | −0.615714 | ||||||||
\(407\) | 11.7466 | 0.582257 | ||||||||
\(408\) | −11.2397 | −0.556447 | ||||||||
\(409\) | −4.45546 | −0.220308 | −0.110154 | − | 0.993915i | \(-0.535134\pi\) | ||||
−0.110154 | + | 0.993915i | \(0.535134\pi\) | |||||||
\(410\) | −18.8676 | −0.931806 | ||||||||
\(411\) | −13.3750 | −0.659742 | ||||||||
\(412\) | 2.05394 | 0.101190 | ||||||||
\(413\) | 23.2872 | 1.14589 | ||||||||
\(414\) | 13.3220 | 0.654742 | ||||||||
\(415\) | −14.9701 | −0.734855 | ||||||||
\(416\) | −2.80106 | −0.137333 | ||||||||
\(417\) | 37.1668 | 1.82007 | ||||||||
\(418\) | 5.43053 | 0.265616 | ||||||||
\(419\) | −5.29702 | −0.258776 | −0.129388 | − | 0.991594i | \(-0.541301\pi\) | ||||
−0.129388 | + | 0.991594i | \(0.541301\pi\) | |||||||
\(420\) | −7.07690 | −0.345317 | ||||||||
\(421\) | −2.01222 | −0.0980696 | −0.0490348 | − | 0.998797i | \(-0.515615\pi\) | ||||
−0.0490348 | + | 0.998797i | \(0.515615\pi\) | |||||||
\(422\) | −1.48562 | −0.0723189 | ||||||||
\(423\) | 22.2888 | 1.08372 | ||||||||
\(424\) | 9.29471 | 0.451391 | ||||||||
\(425\) | −9.19899 | −0.446216 | ||||||||
\(426\) | −13.3839 | −0.648453 | ||||||||
\(427\) | 15.3565 | 0.743154 | ||||||||
\(428\) | −15.2769 | −0.738436 | ||||||||
\(429\) | −10.0707 | −0.486217 | ||||||||
\(430\) | 14.2500 | 0.687194 | ||||||||
\(431\) | −33.3323 | −1.60556 | −0.802781 | − | 0.596274i | \(-0.796647\pi\) | ||||
−0.802781 | + | 0.596274i | \(0.796647\pi\) | |||||||
\(432\) | 0.190180 | 0.00915006 | ||||||||
\(433\) | −23.8617 | −1.14672 | −0.573360 | − | 0.819303i | \(-0.694360\pi\) | ||||
−0.573360 | + | 0.819303i | \(0.694360\pi\) | |||||||
\(434\) | −13.8683 | −0.665700 | ||||||||
\(435\) | 31.2308 | 1.49740 | ||||||||
\(436\) | −15.1271 | −0.724455 | ||||||||
\(437\) | −16.7590 | −0.801690 | ||||||||
\(438\) | −2.24639 | −0.107337 | ||||||||
\(439\) | −28.6508 | −1.36743 | −0.683714 | − | 0.729750i | \(-0.739636\pi\) | ||||
−0.683714 | + | 0.729750i | \(0.739636\pi\) | |||||||
\(440\) | 2.56254 | 0.122164 | ||||||||
\(441\) | −12.2389 | −0.582803 | ||||||||
\(442\) | −12.9374 | −0.615370 | ||||||||
\(443\) | 12.4509 | 0.591560 | 0.295780 | − | 0.955256i | \(-0.404420\pi\) | ||||
0.295780 | + | 0.955256i | \(0.404420\pi\) | |||||||
\(444\) | 19.3479 | 0.918209 | ||||||||
\(445\) | 1.33025 | 0.0630601 | ||||||||
\(446\) | −13.5411 | −0.641191 | ||||||||
\(447\) | −15.0196 | −0.710400 | ||||||||
\(448\) | −1.67668 | −0.0792158 | ||||||||
\(449\) | 19.1697 | 0.904674 | 0.452337 | − | 0.891847i | \(-0.350590\pi\) | ||||
0.452337 | + | 0.891847i | \(0.350590\pi\) | |||||||
\(450\) | −5.81933 | −0.274326 | ||||||||
\(451\) | −16.0717 | −0.756786 | ||||||||
\(452\) | 7.89675 | 0.371432 | ||||||||
\(453\) | −21.7916 | −1.02386 | ||||||||
\(454\) | −4.86914 | −0.228520 | ||||||||
\(455\) | −8.14586 | −0.381884 | ||||||||
\(456\) | 8.94465 | 0.418872 | ||||||||
\(457\) | −11.1950 | −0.523679 | −0.261839 | − | 0.965111i | \(-0.584329\pi\) | ||||
−0.261839 | + | 0.965111i | \(0.584329\pi\) | |||||||
\(458\) | −6.93924 | −0.324249 | ||||||||
\(459\) | 0.878397 | 0.0410001 | ||||||||
\(460\) | −7.90817 | −0.368720 | ||||||||
\(461\) | 24.9647 | 1.16272 | 0.581362 | − | 0.813645i | \(-0.302520\pi\) | ||||
0.581362 | + | 0.813645i | \(0.302520\pi\) | |||||||
\(462\) | −6.02819 | −0.280457 | ||||||||
\(463\) | 33.4913 | 1.55647 | 0.778236 | − | 0.627972i | \(-0.216115\pi\) | ||||
0.778236 | + | 0.627972i | \(0.216115\pi\) | |||||||
\(464\) | 7.39932 | 0.343505 | ||||||||
\(465\) | 34.9112 | 1.61897 | ||||||||
\(466\) | 12.6118 | 0.584229 | ||||||||
\(467\) | −36.8368 | −1.70460 | −0.852301 | − | 0.523051i | \(-0.824794\pi\) | ||||
−0.852301 | + | 0.523051i | \(0.824794\pi\) | |||||||
\(468\) | −8.18427 | −0.378318 | ||||||||
\(469\) | 4.55884 | 0.210508 | ||||||||
\(470\) | −13.2310 | −0.610301 | ||||||||
\(471\) | −33.1327 | −1.52668 | ||||||||
\(472\) | −13.8888 | −0.639286 | ||||||||
\(473\) | 12.1383 | 0.558120 | ||||||||
\(474\) | −12.9790 | −0.596147 | ||||||||
\(475\) | 7.32066 | 0.335895 | ||||||||
\(476\) | −7.74418 | −0.354954 | ||||||||
\(477\) | 27.1577 | 1.24347 | ||||||||
\(478\) | −25.2641 | −1.15555 | ||||||||
\(479\) | −15.0474 | −0.687535 | −0.343768 | − | 0.939055i | \(-0.611703\pi\) | ||||
−0.343768 | + | 0.939055i | \(0.611703\pi\) | |||||||
\(480\) | 4.22077 | 0.192651 | ||||||||
\(481\) | 22.2703 | 1.01544 | ||||||||
\(482\) | 1.81987 | 0.0828929 | ||||||||
\(483\) | 18.6034 | 0.846483 | ||||||||
\(484\) | −8.81719 | −0.400782 | ||||||||
\(485\) | −5.77709 | −0.262324 | ||||||||
\(486\) | 21.8865 | 0.992792 | ||||||||
\(487\) | −8.18508 | −0.370901 | −0.185451 | − | 0.982654i | \(-0.559374\pi\) | ||||
−0.185451 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(488\) | −9.15887 | −0.414603 | ||||||||
\(489\) | 48.9637 | 2.21422 | ||||||||
\(490\) | 7.26518 | 0.328208 | ||||||||
\(491\) | −32.6516 | −1.47355 | −0.736773 | − | 0.676140i | \(-0.763651\pi\) | ||||
−0.736773 | + | 0.676140i | \(0.763651\pi\) | |||||||
\(492\) | −26.4718 | −1.19344 | ||||||||
\(493\) | 34.1756 | 1.53919 | ||||||||
\(494\) | 10.2957 | 0.463227 | ||||||||
\(495\) | 7.48736 | 0.336532 | ||||||||
\(496\) | 8.27128 | 0.371392 | ||||||||
\(497\) | −9.22158 | −0.413644 | ||||||||
\(498\) | −21.0035 | −0.941187 | ||||||||
\(499\) | −8.22805 | −0.368338 | −0.184169 | − | 0.982895i | \(-0.558959\pi\) | ||||
−0.184169 | + | 0.982895i | \(0.558959\pi\) | |||||||
\(500\) | 12.1267 | 0.542324 | ||||||||
\(501\) | 46.1084 | 2.05997 | ||||||||
\(502\) | 3.84973 | 0.171822 | ||||||||
\(503\) | −9.87075 | −0.440115 | −0.220057 | − | 0.975487i | \(-0.570624\pi\) | ||||
−0.220057 | + | 0.975487i | \(0.570624\pi\) | |||||||
\(504\) | −4.89901 | −0.218219 | ||||||||
\(505\) | −7.78478 | −0.346418 | ||||||||
\(506\) | −6.73628 | −0.299464 | ||||||||
\(507\) | 12.5423 | 0.557024 | ||||||||
\(508\) | −11.2577 | −0.499479 | ||||||||
\(509\) | −23.0106 | −1.01993 | −0.509964 | − | 0.860196i | \(-0.670341\pi\) | ||||
−0.509964 | + | 0.860196i | \(0.670341\pi\) | |||||||
\(510\) | 19.4947 | 0.863241 | ||||||||
\(511\) | −1.54778 | −0.0684696 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.699038 | −0.0308633 | ||||||||
\(514\) | −24.0592 | −1.06121 | ||||||||
\(515\) | −3.56247 | −0.156981 | ||||||||
\(516\) | 19.9930 | 0.880145 | ||||||||
\(517\) | −11.2703 | −0.495669 | ||||||||
\(518\) | 13.3308 | 0.585720 | ||||||||
\(519\) | −16.5535 | −0.726617 | ||||||||
\(520\) | 4.85832 | 0.213051 | ||||||||
\(521\) | 2.21300 | 0.0969534 | 0.0484767 | − | 0.998824i | \(-0.484563\pi\) | ||||
0.0484767 | + | 0.998824i | \(0.484563\pi\) | |||||||
\(522\) | 21.6197 | 0.946268 | ||||||||
\(523\) | 43.6544 | 1.90887 | 0.954436 | − | 0.298415i | \(-0.0964579\pi\) | ||||
0.954436 | + | 0.298415i | \(0.0964579\pi\) | |||||||
\(524\) | −11.8547 | −0.517875 | ||||||||
\(525\) | −8.12633 | −0.354662 | ||||||||
\(526\) | −23.0108 | −1.00332 | ||||||||
\(527\) | 38.2030 | 1.66415 | ||||||||
\(528\) | 3.59531 | 0.156466 | ||||||||
\(529\) | −2.21141 | −0.0961481 | ||||||||
\(530\) | −16.1213 | −0.700263 | ||||||||
\(531\) | −40.5811 | −1.76107 | ||||||||
\(532\) | 6.16291 | 0.267196 | ||||||||
\(533\) | −30.4703 | −1.31981 | ||||||||
\(534\) | 1.86638 | 0.0807661 | ||||||||
\(535\) | 26.4971 | 1.14557 | ||||||||
\(536\) | −2.71897 | −0.117441 | ||||||||
\(537\) | −43.6049 | −1.88169 | ||||||||
\(538\) | −23.4563 | −1.01127 | ||||||||
\(539\) | 6.18857 | 0.266561 | ||||||||
\(540\) | −0.329860 | −0.0141949 | ||||||||
\(541\) | 1.22422 | 0.0526332 | 0.0263166 | − | 0.999654i | \(-0.491622\pi\) | ||||
0.0263166 | + | 0.999654i | \(0.491622\pi\) | |||||||
\(542\) | 17.8028 | 0.764697 | ||||||||
\(543\) | −27.1412 | −1.16474 | ||||||||
\(544\) | 4.61875 | 0.198027 | ||||||||
\(545\) | 26.2373 | 1.12388 | ||||||||
\(546\) | −11.4288 | −0.489109 | ||||||||
\(547\) | 5.84038 | 0.249717 | 0.124858 | − | 0.992175i | \(-0.460152\pi\) | ||||
0.124858 | + | 0.992175i | \(0.460152\pi\) | |||||||
\(548\) | 5.49625 | 0.234788 | ||||||||
\(549\) | −26.7608 | −1.14212 | ||||||||
\(550\) | 2.94254 | 0.125470 | ||||||||
\(551\) | −27.1973 | −1.15865 | ||||||||
\(552\) | −11.0954 | −0.472250 | ||||||||
\(553\) | −8.94261 | −0.380279 | ||||||||
\(554\) | −17.0890 | −0.726043 | ||||||||
\(555\) | −33.5580 | −1.42446 | ||||||||
\(556\) | −15.2731 | −0.647723 | ||||||||
\(557\) | 4.54052 | 0.192388 | 0.0961941 | − | 0.995363i | \(-0.469333\pi\) | ||||
0.0961941 | + | 0.995363i | \(0.469333\pi\) | |||||||
\(558\) | 24.1674 | 1.02309 | ||||||||
\(559\) | 23.0130 | 0.973345 | ||||||||
\(560\) | 2.90813 | 0.122891 | ||||||||
\(561\) | 16.6059 | 0.701100 | ||||||||
\(562\) | −18.1072 | −0.763808 | ||||||||
\(563\) | 37.0810 | 1.56278 | 0.781389 | − | 0.624044i | \(-0.214511\pi\) | ||||
0.781389 | + | 0.624044i | \(0.214511\pi\) | |||||||
\(564\) | −18.5634 | −0.781662 | ||||||||
\(565\) | −13.6966 | −0.576219 | ||||||||
\(566\) | −16.6038 | −0.697911 | ||||||||
\(567\) | 15.4730 | 0.649805 | ||||||||
\(568\) | 5.49990 | 0.230771 | ||||||||
\(569\) | −2.99845 | −0.125702 | −0.0628508 | − | 0.998023i | \(-0.520019\pi\) | ||||
−0.0628508 | + | 0.998023i | \(0.520019\pi\) | |||||||
\(570\) | −15.5141 | −0.649815 | ||||||||
\(571\) | −28.6353 | −1.19835 | −0.599175 | − | 0.800618i | \(-0.704505\pi\) | ||||
−0.599175 | + | 0.800618i | \(0.704505\pi\) | |||||||
\(572\) | 4.13838 | 0.173034 | ||||||||
\(573\) | 59.9740 | 2.50545 | ||||||||
\(574\) | −18.2392 | −0.761288 | ||||||||
\(575\) | −9.08087 | −0.378699 | ||||||||
\(576\) | 2.92185 | 0.121744 | ||||||||
\(577\) | 30.4725 | 1.26859 | 0.634294 | − | 0.773092i | \(-0.281291\pi\) | ||||
0.634294 | + | 0.773092i | \(0.281291\pi\) | |||||||
\(578\) | 4.33290 | 0.180225 | ||||||||
\(579\) | −12.2265 | −0.508117 | ||||||||
\(580\) | −12.8338 | −0.532894 | ||||||||
\(581\) | −14.4715 | −0.600378 | ||||||||
\(582\) | −8.10540 | −0.335980 | ||||||||
\(583\) | −13.7323 | −0.568734 | ||||||||
\(584\) | 0.923118 | 0.0381989 | ||||||||
\(585\) | 14.1953 | 0.586902 | ||||||||
\(586\) | 15.9968 | 0.660820 | ||||||||
\(587\) | −10.6453 | −0.439378 | −0.219689 | − | 0.975570i | \(-0.570504\pi\) | ||||
−0.219689 | + | 0.975570i | \(0.570504\pi\) | |||||||
\(588\) | 10.1932 | 0.420362 | ||||||||
\(589\) | −30.4024 | −1.25271 | ||||||||
\(590\) | 24.0896 | 0.991753 | ||||||||
\(591\) | −29.1984 | −1.20106 | ||||||||
\(592\) | −7.95068 | −0.326771 | ||||||||
\(593\) | −2.33558 | −0.0959107 | −0.0479553 | − | 0.998849i | \(-0.515271\pi\) | ||||
−0.0479553 | + | 0.998849i | \(0.515271\pi\) | |||||||
\(594\) | −0.280979 | −0.0115287 | ||||||||
\(595\) | 13.4320 | 0.550656 | ||||||||
\(596\) | 6.17203 | 0.252816 | ||||||||
\(597\) | −38.0588 | −1.55765 | ||||||||
\(598\) | −12.7713 | −0.522257 | ||||||||
\(599\) | −13.6993 | −0.559738 | −0.279869 | − | 0.960038i | \(-0.590291\pi\) | ||||
−0.279869 | + | 0.960038i | \(0.590291\pi\) | |||||||
\(600\) | 4.84667 | 0.197865 | ||||||||
\(601\) | 18.2452 | 0.744237 | 0.372119 | − | 0.928185i | \(-0.378631\pi\) | ||||
0.372119 | + | 0.928185i | \(0.378631\pi\) | |||||||
\(602\) | 13.7753 | 0.561439 | ||||||||
\(603\) | −7.94441 | −0.323521 | ||||||||
\(604\) | 8.95488 | 0.364369 | ||||||||
\(605\) | 15.2930 | 0.621751 | ||||||||
\(606\) | −10.9222 | −0.443685 | ||||||||
\(607\) | 35.9030 | 1.45726 | 0.728629 | − | 0.684909i | \(-0.240158\pi\) | ||||
0.728629 | + | 0.684909i | \(0.240158\pi\) | |||||||
\(608\) | −3.67566 | −0.149068 | ||||||||
\(609\) | 30.1905 | 1.22338 | ||||||||
\(610\) | 15.8857 | 0.643192 | ||||||||
\(611\) | −21.3674 | −0.864433 | ||||||||
\(612\) | 13.4953 | 0.545515 | ||||||||
\(613\) | 19.0023 | 0.767497 | 0.383749 | − | 0.923438i | \(-0.374633\pi\) | ||||
0.383749 | + | 0.923438i | \(0.374633\pi\) | |||||||
\(614\) | 5.76038 | 0.232470 | ||||||||
\(615\) | 45.9141 | 1.85144 | ||||||||
\(616\) | 2.47718 | 0.0998086 | ||||||||
\(617\) | −11.4829 | −0.462285 | −0.231142 | − | 0.972920i | \(-0.574246\pi\) | ||||
−0.231142 | + | 0.972920i | \(0.574246\pi\) | |||||||
\(618\) | −4.99824 | −0.201059 | ||||||||
\(619\) | 34.8866 | 1.40221 | 0.701105 | − | 0.713058i | \(-0.252690\pi\) | ||||
0.701105 | + | 0.713058i | \(0.252690\pi\) | |||||||
\(620\) | −14.3462 | −0.576157 | ||||||||
\(621\) | 0.867119 | 0.0347963 | ||||||||
\(622\) | −1.95681 | −0.0784611 | ||||||||
\(623\) | 1.28594 | 0.0515202 | ||||||||
\(624\) | 6.81634 | 0.272872 | ||||||||
\(625\) | −11.0750 | −0.443000 | ||||||||
\(626\) | 3.37010 | 0.134696 | ||||||||
\(627\) | −13.2151 | −0.527761 | ||||||||
\(628\) | 13.6153 | 0.543312 | ||||||||
\(629\) | −36.7222 | −1.46421 | ||||||||
\(630\) | 8.49712 | 0.338534 | ||||||||
\(631\) | −43.6184 | −1.73642 | −0.868211 | − | 0.496194i | \(-0.834730\pi\) | ||||
−0.868211 | + | 0.496194i | \(0.834730\pi\) | |||||||
\(632\) | 5.33352 | 0.212156 | ||||||||
\(633\) | 3.61524 | 0.143693 | ||||||||
\(634\) | −15.8004 | −0.627512 | ||||||||
\(635\) | 19.5260 | 0.774865 | ||||||||
\(636\) | −22.6185 | −0.896883 | ||||||||
\(637\) | 11.7329 | 0.464875 | ||||||||
\(638\) | −10.9320 | −0.432802 | ||||||||
\(639\) | 16.0699 | 0.635714 | ||||||||
\(640\) | −1.73446 | −0.0685604 | ||||||||
\(641\) | 7.10126 | 0.280483 | 0.140241 | − | 0.990117i | \(-0.455212\pi\) | ||||
0.140241 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(642\) | 37.1761 | 1.46722 | ||||||||
\(643\) | −7.52088 | −0.296595 | −0.148297 | − | 0.988943i | \(-0.547379\pi\) | ||||
−0.148297 | + | 0.988943i | \(0.547379\pi\) | |||||||
\(644\) | −7.64475 | −0.301245 | ||||||||
\(645\) | −34.6771 | −1.36541 | ||||||||
\(646\) | −16.9770 | −0.667949 | ||||||||
\(647\) | 5.84769 | 0.229896 | 0.114948 | − | 0.993371i | \(-0.463330\pi\) | ||||
0.114948 | + | 0.993371i | \(0.463330\pi\) | |||||||
\(648\) | −9.22835 | −0.362524 | ||||||||
\(649\) | 20.5198 | 0.805474 | ||||||||
\(650\) | 5.57876 | 0.218817 | ||||||||
\(651\) | 33.7483 | 1.32270 | ||||||||
\(652\) | −20.1208 | −0.787992 | ||||||||
\(653\) | 16.4418 | 0.643417 | 0.321708 | − | 0.946839i | \(-0.395743\pi\) | ||||
0.321708 | + | 0.946839i | \(0.395743\pi\) | |||||||
\(654\) | 36.8115 | 1.43944 | ||||||||
\(655\) | 20.5615 | 0.803404 | ||||||||
\(656\) | 10.8781 | 0.424719 | ||||||||
\(657\) | 2.69721 | 0.105228 | ||||||||
\(658\) | −12.7903 | −0.498617 | ||||||||
\(659\) | 39.4782 | 1.53785 | 0.768926 | − | 0.639337i | \(-0.220791\pi\) | ||||
0.768926 | + | 0.639337i | \(0.220791\pi\) | |||||||
\(660\) | −6.23591 | −0.242732 | ||||||||
\(661\) | 16.2491 | 0.632018 | 0.316009 | − | 0.948756i | \(-0.397657\pi\) | ||||
0.316009 | + | 0.948756i | \(0.397657\pi\) | |||||||
\(662\) | −27.2807 | −1.06029 | ||||||||
\(663\) | 31.4830 | 1.22270 | ||||||||
\(664\) | 8.63102 | 0.334948 | ||||||||
\(665\) | −10.6893 | −0.414513 | ||||||||
\(666\) | −23.2307 | −0.900171 | ||||||||
\(667\) | 33.7368 | 1.30629 | ||||||||
\(668\) | −18.9475 | −0.733100 | ||||||||
\(669\) | 32.9521 | 1.27400 | ||||||||
\(670\) | 4.71593 | 0.182192 | ||||||||
\(671\) | 13.5316 | 0.522382 | ||||||||
\(672\) | 4.08018 | 0.157396 | ||||||||
\(673\) | −9.44875 | −0.364223 | −0.182111 | − | 0.983278i | \(-0.558293\pi\) | ||||
−0.182111 | + | 0.983278i | \(0.558293\pi\) | |||||||
\(674\) | −5.86743 | −0.226005 | ||||||||
\(675\) | −0.378775 | −0.0145790 | ||||||||
\(676\) | −5.15406 | −0.198233 | ||||||||
\(677\) | 0.357955 | 0.0137573 | 0.00687866 | − | 0.999976i | \(-0.497810\pi\) | ||||
0.00687866 | + | 0.999976i | \(0.497810\pi\) | |||||||
\(678\) | −19.2166 | −0.738010 | ||||||||
\(679\) | −5.58466 | −0.214320 | ||||||||
\(680\) | −8.01103 | −0.307209 | ||||||||
\(681\) | 11.8490 | 0.454054 | ||||||||
\(682\) | −12.2203 | −0.467938 | ||||||||
\(683\) | 28.0063 | 1.07163 | 0.535815 | − | 0.844335i | \(-0.320004\pi\) | ||||
0.535815 | + | 0.844335i | \(0.320004\pi\) | |||||||
\(684\) | −10.7397 | −0.410643 | ||||||||
\(685\) | −9.53301 | −0.364237 | ||||||||
\(686\) | 18.7600 | 0.716258 | ||||||||
\(687\) | 16.8865 | 0.644261 | ||||||||
\(688\) | −8.21581 | −0.313225 | ||||||||
\(689\) | −26.0350 | −0.991856 | ||||||||
\(690\) | 19.2444 | 0.732622 | ||||||||
\(691\) | 13.4425 | 0.511377 | 0.255688 | − | 0.966759i | \(-0.417698\pi\) | ||||
0.255688 | + | 0.966759i | \(0.417698\pi\) | |||||||
\(692\) | 6.80237 | 0.258587 | ||||||||
\(693\) | 7.23796 | 0.274947 | ||||||||
\(694\) | 15.7387 | 0.597434 | ||||||||
\(695\) | 26.4905 | 1.00484 | ||||||||
\(696\) | −18.0061 | −0.682520 | ||||||||
\(697\) | 50.2434 | 1.90310 | ||||||||
\(698\) | 20.3168 | 0.769004 | ||||||||
\(699\) | −30.6905 | −1.16082 | ||||||||
\(700\) | 3.33938 | 0.126217 | ||||||||
\(701\) | 52.0604 | 1.96630 | 0.983148 | − | 0.182812i | \(-0.0585199\pi\) | ||||
0.983148 | + | 0.182812i | \(0.0585199\pi\) | |||||||
\(702\) | −0.532707 | −0.0201057 | ||||||||
\(703\) | 29.2240 | 1.10220 | ||||||||
\(704\) | −1.47743 | −0.0556828 | ||||||||
\(705\) | 32.1975 | 1.21263 | ||||||||
\(706\) | −19.7115 | −0.741852 | ||||||||
\(707\) | −7.52547 | −0.283024 | ||||||||
\(708\) | 33.7983 | 1.27022 | ||||||||
\(709\) | 17.6982 | 0.664669 | 0.332334 | − | 0.943162i | \(-0.392164\pi\) | ||||
0.332334 | + | 0.943162i | \(0.392164\pi\) | |||||||
\(710\) | −9.53933 | −0.358005 | ||||||||
\(711\) | 15.5837 | 0.584436 | ||||||||
\(712\) | −0.766957 | −0.0287429 | ||||||||
\(713\) | 37.7125 | 1.41234 | ||||||||
\(714\) | 18.8454 | 0.705270 | ||||||||
\(715\) | −7.17784 | −0.268436 | ||||||||
\(716\) | 17.9187 | 0.669654 | ||||||||
\(717\) | 61.4798 | 2.29601 | ||||||||
\(718\) | −9.58105 | −0.357562 | ||||||||
\(719\) | −5.77878 | −0.215512 | −0.107756 | − | 0.994177i | \(-0.534367\pi\) | ||||
−0.107756 | + | 0.994177i | \(0.534367\pi\) | |||||||
\(720\) | −5.06782 | −0.188867 | ||||||||
\(721\) | −3.44381 | −0.128254 | ||||||||
\(722\) | −5.48955 | −0.204300 | ||||||||
\(723\) | −4.42863 | −0.164703 | ||||||||
\(724\) | 11.1532 | 0.414506 | ||||||||
\(725\) | −14.7369 | −0.547315 | ||||||||
\(726\) | 21.4565 | 0.796326 | ||||||||
\(727\) | −43.5348 | −1.61462 | −0.807309 | − | 0.590129i | \(-0.799077\pi\) | ||||
−0.807309 | + | 0.590129i | \(0.799077\pi\) | |||||||
\(728\) | 4.69649 | 0.174063 | ||||||||
\(729\) | −25.5754 | −0.947238 | ||||||||
\(730\) | −1.60111 | −0.0592597 | ||||||||
\(731\) | −37.9468 | −1.40351 | ||||||||
\(732\) | 22.2880 | 0.823787 | ||||||||
\(733\) | 28.4660 | 1.05142 | 0.525708 | − | 0.850665i | \(-0.323800\pi\) | ||||
0.525708 | + | 0.850665i | \(0.323800\pi\) | |||||||
\(734\) | −9.51485 | −0.351199 | ||||||||
\(735\) | −17.6797 | −0.652126 | ||||||||
\(736\) | 4.55945 | 0.168064 | ||||||||
\(737\) | 4.01709 | 0.147971 | ||||||||
\(738\) | 31.7842 | 1.16999 | ||||||||
\(739\) | −30.4590 | −1.12045 | −0.560227 | − | 0.828339i | \(-0.689286\pi\) | ||||
−0.560227 | + | 0.828339i | \(0.689286\pi\) | |||||||
\(740\) | 13.7901 | 0.506935 | ||||||||
\(741\) | −25.0545 | −0.920401 | ||||||||
\(742\) | −15.5843 | −0.572116 | ||||||||
\(743\) | 15.5518 | 0.570539 | 0.285270 | − | 0.958447i | \(-0.407917\pi\) | ||||
0.285270 | + | 0.958447i | \(0.407917\pi\) | |||||||
\(744\) | −20.1280 | −0.737930 | ||||||||
\(745\) | −10.7051 | −0.392205 | ||||||||
\(746\) | 3.17222 | 0.116143 | ||||||||
\(747\) | 25.2185 | 0.922698 | ||||||||
\(748\) | −6.82390 | −0.249506 | ||||||||
\(749\) | 25.6145 | 0.935933 | ||||||||
\(750\) | −29.5102 | −1.07756 | ||||||||
\(751\) | −21.7185 | −0.792519 | −0.396259 | − | 0.918139i | \(-0.629692\pi\) | ||||
−0.396259 | + | 0.918139i | \(0.629692\pi\) | |||||||
\(752\) | 7.62833 | 0.278177 | ||||||||
\(753\) | −9.36826 | −0.341399 | ||||||||
\(754\) | −20.7259 | −0.754794 | ||||||||
\(755\) | −15.5318 | −0.565262 | ||||||||
\(756\) | −0.318872 | −0.0115973 | ||||||||
\(757\) | −25.3717 | −0.922149 | −0.461075 | − | 0.887361i | \(-0.652536\pi\) | ||||
−0.461075 | + | 0.887361i | \(0.652536\pi\) | |||||||
\(758\) | −12.2390 | −0.444541 | ||||||||
\(759\) | 16.3926 | 0.595015 | ||||||||
\(760\) | 6.37527 | 0.231255 | ||||||||
\(761\) | −22.9568 | −0.832185 | −0.416092 | − | 0.909322i | \(-0.636601\pi\) | ||||
−0.416092 | + | 0.909322i | \(0.636601\pi\) | |||||||
\(762\) | 27.3954 | 0.992432 | ||||||||
\(763\) | 25.3633 | 0.918213 | ||||||||
\(764\) | −24.6453 | −0.891636 | ||||||||
\(765\) | −23.4070 | −0.846283 | ||||||||
\(766\) | 31.0014 | 1.12013 | ||||||||
\(767\) | 38.9035 | 1.40472 | ||||||||
\(768\) | −2.43348 | −0.0878108 | ||||||||
\(769\) | 3.48148 | 0.125545 | 0.0627727 | − | 0.998028i | \(-0.480006\pi\) | ||||
0.0627727 | + | 0.998028i | \(0.480006\pi\) | |||||||
\(770\) | −4.29657 | −0.154838 | ||||||||
\(771\) | 58.5477 | 2.10854 | ||||||||
\(772\) | 5.02429 | 0.180828 | ||||||||
\(773\) | 42.1369 | 1.51556 | 0.757780 | − | 0.652511i | \(-0.226284\pi\) | ||||
0.757780 | + | 0.652511i | \(0.226284\pi\) | |||||||
\(774\) | −24.0054 | −0.862855 | ||||||||
\(775\) | −16.4736 | −0.591748 | ||||||||
\(776\) | 3.33078 | 0.119568 | ||||||||
\(777\) | −32.4402 | −1.16379 | ||||||||
\(778\) | 14.4603 | 0.518426 | ||||||||
\(779\) | −39.9842 | −1.43258 | ||||||||
\(780\) | −11.8226 | −0.423319 | ||||||||
\(781\) | −8.12572 | −0.290761 | ||||||||
\(782\) | 21.0590 | 0.753068 | ||||||||
\(783\) | 1.40721 | 0.0502894 | ||||||||
\(784\) | −4.18874 | −0.149598 | ||||||||
\(785\) | −23.6152 | −0.842864 | ||||||||
\(786\) | 28.8483 | 1.02898 | ||||||||
\(787\) | −34.7902 | −1.24014 | −0.620068 | − | 0.784548i | \(-0.712895\pi\) | ||||
−0.620068 | + | 0.784548i | \(0.712895\pi\) | |||||||
\(788\) | 11.9986 | 0.427432 | ||||||||
\(789\) | 55.9964 | 1.99352 | ||||||||
\(790\) | −9.25076 | −0.329127 | ||||||||
\(791\) | −13.2403 | −0.470773 | ||||||||
\(792\) | −4.31683 | −0.153392 | ||||||||
\(793\) | 25.6545 | 0.911020 | ||||||||
\(794\) | −4.02599 | −0.142877 | ||||||||
\(795\) | 39.2309 | 1.39138 | ||||||||
\(796\) | 15.6396 | 0.554333 | ||||||||
\(797\) | −8.19266 | −0.290199 | −0.145099 | − | 0.989417i | \(-0.546350\pi\) | ||||
−0.145099 | + | 0.989417i | \(0.546350\pi\) | |||||||
\(798\) | −14.9973 | −0.530900 | ||||||||
\(799\) | 35.2334 | 1.24647 | ||||||||
\(800\) | −1.99166 | −0.0704158 | ||||||||
\(801\) | −2.24093 | −0.0791794 | ||||||||
\(802\) | 1.76890 | 0.0624621 | ||||||||
\(803\) | −1.36384 | −0.0481290 | ||||||||
\(804\) | 6.61656 | 0.233348 | ||||||||
\(805\) | 13.2595 | 0.467336 | ||||||||
\(806\) | −23.1684 | −0.816071 | ||||||||
\(807\) | 57.0807 | 2.00933 | ||||||||
\(808\) | 4.48831 | 0.157898 | ||||||||
\(809\) | −23.4461 | −0.824322 | −0.412161 | − | 0.911111i | \(-0.635226\pi\) | ||||
−0.412161 | + | 0.911111i | \(0.635226\pi\) | |||||||
\(810\) | 16.0062 | 0.562399 | ||||||||
\(811\) | −34.2710 | −1.20342 | −0.601709 | − | 0.798715i | \(-0.705513\pi\) | ||||
−0.601709 | + | 0.798715i | \(0.705513\pi\) | |||||||
\(812\) | −12.4063 | −0.435376 | ||||||||
\(813\) | −43.3229 | −1.51940 | ||||||||
\(814\) | 11.7466 | 0.411718 | ||||||||
\(815\) | 34.8987 | 1.22245 | ||||||||
\(816\) | −11.2397 | −0.393467 | ||||||||
\(817\) | 30.1985 | 1.05651 | ||||||||
\(818\) | −4.45546 | −0.155781 | ||||||||
\(819\) | 13.7224 | 0.479500 | ||||||||
\(820\) | −18.8676 | −0.658886 | ||||||||
\(821\) | −13.3332 | −0.465331 | −0.232666 | − | 0.972557i | \(-0.574745\pi\) | ||||
−0.232666 | + | 0.972557i | \(0.574745\pi\) | |||||||
\(822\) | −13.3750 | −0.466508 | ||||||||
\(823\) | 15.3048 | 0.533491 | 0.266745 | − | 0.963767i | \(-0.414052\pi\) | ||||
0.266745 | + | 0.963767i | \(0.414052\pi\) | |||||||
\(824\) | 2.05394 | 0.0715525 | ||||||||
\(825\) | −7.16063 | −0.249301 | ||||||||
\(826\) | 23.2872 | 0.810264 | ||||||||
\(827\) | 45.4487 | 1.58041 | 0.790203 | − | 0.612846i | \(-0.209975\pi\) | ||||
0.790203 | + | 0.612846i | \(0.209975\pi\) | |||||||
\(828\) | 13.3220 | 0.462972 | ||||||||
\(829\) | −36.1121 | −1.25423 | −0.627113 | − | 0.778928i | \(-0.715764\pi\) | ||||
−0.627113 | + | 0.778928i | \(0.715764\pi\) | |||||||
\(830\) | −14.9701 | −0.519621 | ||||||||
\(831\) | 41.5859 | 1.44260 | ||||||||
\(832\) | −2.80106 | −0.0971093 | ||||||||
\(833\) | −19.3467 | −0.670325 | ||||||||
\(834\) | 37.1668 | 1.28698 | ||||||||
\(835\) | 32.8636 | 1.13729 | ||||||||
\(836\) | 5.43053 | 0.187819 | ||||||||
\(837\) | 1.57304 | 0.0543721 | ||||||||
\(838\) | −5.29702 | −0.182982 | ||||||||
\(839\) | −22.0689 | −0.761903 | −0.380951 | − | 0.924595i | \(-0.624403\pi\) | ||||
−0.380951 | + | 0.924595i | \(0.624403\pi\) | |||||||
\(840\) | −7.07690 | −0.244176 | ||||||||
\(841\) | 25.7499 | 0.887927 | ||||||||
\(842\) | −2.01222 | −0.0693457 | ||||||||
\(843\) | 44.0637 | 1.51763 | ||||||||
\(844\) | −1.48562 | −0.0511372 | ||||||||
\(845\) | 8.93950 | 0.307528 | ||||||||
\(846\) | 22.2888 | 0.766306 | ||||||||
\(847\) | 14.7836 | 0.507972 | ||||||||
\(848\) | 9.29471 | 0.319181 | ||||||||
\(849\) | 40.4052 | 1.38670 | ||||||||
\(850\) | −9.19899 | −0.315523 | ||||||||
\(851\) | −36.2507 | −1.24266 | ||||||||
\(852\) | −13.3839 | −0.458525 | ||||||||
\(853\) | −24.9379 | −0.853857 | −0.426928 | − | 0.904285i | \(-0.640404\pi\) | ||||
−0.426928 | + | 0.904285i | \(0.640404\pi\) | |||||||
\(854\) | 15.3565 | 0.525489 | ||||||||
\(855\) | 18.6276 | 0.637049 | ||||||||
\(856\) | −15.2769 | −0.522153 | ||||||||
\(857\) | 44.4456 | 1.51823 | 0.759116 | − | 0.650955i | \(-0.225632\pi\) | ||||
0.759116 | + | 0.650955i | \(0.225632\pi\) | |||||||
\(858\) | −10.0707 | −0.343807 | ||||||||
\(859\) | 54.4801 | 1.85884 | 0.929418 | − | 0.369029i | \(-0.120310\pi\) | ||||
0.929418 | + | 0.369029i | \(0.120310\pi\) | |||||||
\(860\) | 14.2500 | 0.485920 | ||||||||
\(861\) | 44.3847 | 1.51263 | ||||||||
\(862\) | −33.3323 | −1.13530 | ||||||||
\(863\) | −21.5393 | −0.733207 | −0.366604 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366604 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(864\) | 0.190180 | 0.00647007 | ||||||||
\(865\) | −11.7984 | −0.401158 | ||||||||
\(866\) | −23.8617 | −0.810854 | ||||||||
\(867\) | −10.5440 | −0.358094 | ||||||||
\(868\) | −13.8683 | −0.470721 | ||||||||
\(869\) | −7.87991 | −0.267308 | ||||||||
\(870\) | 31.2308 | 1.05882 | ||||||||
\(871\) | 7.61599 | 0.258058 | ||||||||
\(872\) | −15.1271 | −0.512267 | ||||||||
\(873\) | 9.73203 | 0.329379 | ||||||||
\(874\) | −16.7590 | −0.566881 | ||||||||
\(875\) | −20.3327 | −0.687370 | ||||||||
\(876\) | −2.24639 | −0.0758986 | ||||||||
\(877\) | −15.1288 | −0.510862 | −0.255431 | − | 0.966827i | \(-0.582217\pi\) | ||||
−0.255431 | + | 0.966827i | \(0.582217\pi\) | |||||||
\(878\) | −28.6508 | −0.966917 | ||||||||
\(879\) | −38.9279 | −1.31300 | ||||||||
\(880\) | 2.56254 | 0.0863833 | ||||||||
\(881\) | −42.9661 | −1.44757 | −0.723783 | − | 0.690027i | \(-0.757598\pi\) | ||||
−0.723783 | + | 0.690027i | \(0.757598\pi\) | |||||||
\(882\) | −12.2389 | −0.412104 | ||||||||
\(883\) | −15.5357 | −0.522818 | −0.261409 | − | 0.965228i | \(-0.584187\pi\) | ||||
−0.261409 | + | 0.965228i | \(0.584187\pi\) | |||||||
\(884\) | −12.9374 | −0.435132 | ||||||||
\(885\) | −58.6217 | −1.97055 | ||||||||
\(886\) | 12.4509 | 0.418296 | ||||||||
\(887\) | −52.4803 | −1.76211 | −0.881057 | − | 0.473009i | \(-0.843168\pi\) | ||||
−0.881057 | + | 0.473009i | \(0.843168\pi\) | |||||||
\(888\) | 19.3479 | 0.649272 | ||||||||
\(889\) | 18.8756 | 0.633067 | ||||||||
\(890\) | 1.33025 | 0.0445902 | ||||||||
\(891\) | 13.6343 | 0.456765 | ||||||||
\(892\) | −13.5411 | −0.453390 | ||||||||
\(893\) | −28.0391 | −0.938294 | ||||||||
\(894\) | −15.0196 | −0.502329 | ||||||||
\(895\) | −31.0792 | −1.03886 | ||||||||
\(896\) | −1.67668 | −0.0560140 | ||||||||
\(897\) | 31.0788 | 1.03769 | ||||||||
\(898\) | 19.1697 | 0.639701 | ||||||||
\(899\) | 61.2018 | 2.04120 | ||||||||
\(900\) | −5.81933 | −0.193978 | ||||||||
\(901\) | 42.9300 | 1.43020 | ||||||||
\(902\) | −16.0717 | −0.535129 | ||||||||
\(903\) | −33.5220 | −1.11554 | ||||||||
\(904\) | 7.89675 | 0.262642 | ||||||||
\(905\) | −19.3448 | −0.643042 | ||||||||
\(906\) | −21.7916 | −0.723976 | ||||||||
\(907\) | −14.1199 | −0.468842 | −0.234421 | − | 0.972135i | \(-0.575319\pi\) | ||||
−0.234421 | + | 0.972135i | \(0.575319\pi\) | |||||||
\(908\) | −4.86914 | −0.161588 | ||||||||
\(909\) | 13.1142 | 0.434969 | ||||||||
\(910\) | −8.14586 | −0.270033 | ||||||||
\(911\) | 12.4258 | 0.411684 | 0.205842 | − | 0.978585i | \(-0.434007\pi\) | ||||
0.205842 | + | 0.978585i | \(0.434007\pi\) | |||||||
\(912\) | 8.94465 | 0.296187 | ||||||||
\(913\) | −12.7517 | −0.422021 | ||||||||
\(914\) | −11.1950 | −0.370297 | ||||||||
\(915\) | −38.6575 | −1.27798 | ||||||||
\(916\) | −6.93924 | −0.229279 | ||||||||
\(917\) | 19.8766 | 0.656383 | ||||||||
\(918\) | 0.878397 | 0.0289914 | ||||||||
\(919\) | −27.9939 | −0.923434 | −0.461717 | − | 0.887027i | \(-0.652767\pi\) | ||||
−0.461717 | + | 0.887027i | \(0.652767\pi\) | |||||||
\(920\) | −7.90817 | −0.260725 | ||||||||
\(921\) | −14.0178 | −0.461902 | ||||||||
\(922\) | 24.9647 | 0.822170 | ||||||||
\(923\) | −15.4055 | −0.507080 | ||||||||
\(924\) | −6.02819 | −0.198313 | ||||||||
\(925\) | 15.8350 | 0.520653 | ||||||||
\(926\) | 33.4913 | 1.10059 | ||||||||
\(927\) | 6.00131 | 0.197109 | ||||||||
\(928\) | 7.39932 | 0.242894 | ||||||||
\(929\) | 56.2352 | 1.84502 | 0.922509 | − | 0.385975i | \(-0.126135\pi\) | ||||
0.922509 | + | 0.385975i | \(0.126135\pi\) | |||||||
\(930\) | 34.9112 | 1.14478 | ||||||||
\(931\) | 15.3964 | 0.504595 | ||||||||
\(932\) | 12.6118 | 0.413112 | ||||||||
\(933\) | 4.76188 | 0.155897 | ||||||||
\(934\) | −36.8368 | −1.20534 | ||||||||
\(935\) | 11.8358 | 0.387071 | ||||||||
\(936\) | −8.18427 | −0.267511 | ||||||||
\(937\) | −19.1665 | −0.626141 | −0.313071 | − | 0.949730i | \(-0.601358\pi\) | ||||
−0.313071 | + | 0.949730i | \(0.601358\pi\) | |||||||
\(938\) | 4.55884 | 0.148851 | ||||||||
\(939\) | −8.20110 | −0.267633 | ||||||||
\(940\) | −13.2310 | −0.431548 | ||||||||
\(941\) | −35.3778 | −1.15328 | −0.576642 | − | 0.816997i | \(-0.695637\pi\) | ||||
−0.576642 | + | 0.816997i | \(0.695637\pi\) | |||||||
\(942\) | −33.1327 | −1.07952 | ||||||||
\(943\) | 49.5983 | 1.61514 | ||||||||
\(944\) | −13.8888 | −0.452043 | ||||||||
\(945\) | 0.553070 | 0.0179914 | ||||||||
\(946\) | 12.1383 | 0.394650 | ||||||||
\(947\) | −52.3783 | −1.70207 | −0.851033 | − | 0.525112i | \(-0.824023\pi\) | ||||
−0.851033 | + | 0.525112i | \(0.824023\pi\) | |||||||
\(948\) | −12.9790 | −0.421539 | ||||||||
\(949\) | −2.58571 | −0.0839357 | ||||||||
\(950\) | 7.32066 | 0.237513 | ||||||||
\(951\) | 38.4499 | 1.24682 | ||||||||
\(952\) | −7.74418 | −0.250990 | ||||||||
\(953\) | 0.881783 | 0.0285638 | 0.0142819 | − | 0.999898i | \(-0.495454\pi\) | ||||
0.0142819 | + | 0.999898i | \(0.495454\pi\) | |||||||
\(954\) | 27.1577 | 0.879264 | ||||||||
\(955\) | 42.7462 | 1.38324 | ||||||||
\(956\) | −25.2641 | −0.817099 | ||||||||
\(957\) | 26.6028 | 0.859947 | ||||||||
\(958\) | −15.0474 | −0.486161 | ||||||||
\(959\) | −9.21546 | −0.297583 | ||||||||
\(960\) | 4.22077 | 0.136225 | ||||||||
\(961\) | 37.4141 | 1.20691 | ||||||||
\(962\) | 22.2703 | 0.718025 | ||||||||
\(963\) | −44.6367 | −1.43840 | ||||||||
\(964\) | 1.81987 | 0.0586141 | ||||||||
\(965\) | −8.71441 | −0.280527 | ||||||||
\(966\) | 18.6034 | 0.598554 | ||||||||
\(967\) | 37.8751 | 1.21798 | 0.608990 | − | 0.793178i | \(-0.291575\pi\) | ||||
0.608990 | + | 0.793178i | \(0.291575\pi\) | |||||||
\(968\) | −8.81719 | −0.283395 | ||||||||
\(969\) | 41.3132 | 1.32717 | ||||||||
\(970\) | −5.77709 | −0.185491 | ||||||||
\(971\) | 14.4797 | 0.464677 | 0.232338 | − | 0.972635i | \(-0.425362\pi\) | ||||
0.232338 | + | 0.972635i | \(0.425362\pi\) | |||||||
\(972\) | 21.8865 | 0.702010 | ||||||||
\(973\) | 25.6081 | 0.820958 | ||||||||
\(974\) | −8.18508 | −0.262267 | ||||||||
\(975\) | −13.5758 | −0.434774 | ||||||||
\(976\) | −9.15887 | −0.293168 | ||||||||
\(977\) | −48.7592 | −1.55994 | −0.779972 | − | 0.625815i | \(-0.784767\pi\) | ||||
−0.779972 | + | 0.625815i | \(0.784767\pi\) | |||||||
\(978\) | 48.9637 | 1.56569 | ||||||||
\(979\) | 1.13313 | 0.0362149 | ||||||||
\(980\) | 7.26518 | 0.232078 | ||||||||
\(981\) | −44.1990 | −1.41117 | ||||||||
\(982\) | −32.6516 | −1.04195 | ||||||||
\(983\) | −6.90072 | −0.220099 | −0.110049 | − | 0.993926i | \(-0.535101\pi\) | ||||
−0.110049 | + | 0.993926i | \(0.535101\pi\) | |||||||
\(984\) | −26.4718 | −0.843889 | ||||||||
\(985\) | −20.8110 | −0.663094 | ||||||||
\(986\) | 34.1756 | 1.08837 | ||||||||
\(987\) | 31.1250 | 0.990719 | ||||||||
\(988\) | 10.2957 | 0.327551 | ||||||||
\(989\) | −37.4596 | −1.19115 | ||||||||
\(990\) | 7.48736 | 0.237964 | ||||||||
\(991\) | −27.7575 | −0.881747 | −0.440874 | − | 0.897569i | \(-0.645331\pi\) | ||||
−0.440874 | + | 0.897569i | \(0.645331\pi\) | |||||||
\(992\) | 8.27128 | 0.262613 | ||||||||
\(993\) | 66.3871 | 2.10673 | ||||||||
\(994\) | −9.22158 | −0.292491 | ||||||||
\(995\) | −27.1263 | −0.859961 | ||||||||
\(996\) | −21.0035 | −0.665520 | ||||||||
\(997\) | −43.4855 | −1.37720 | −0.688600 | − | 0.725142i | \(-0.741774\pi\) | ||||
−0.688600 | + | 0.725142i | \(0.741774\pi\) | |||||||
\(998\) | −8.22805 | −0.260454 | ||||||||
\(999\) | −1.51206 | −0.0478396 |
(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 | 6046.2.a.e.1.10 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.e.1.10 | ✓ | 56 | 1.1 | even | 1 | trivial |