Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7674048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.82356\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.823556 | −0.582342 | −0.291171 | − | 0.956671i | \(-0.594045\pi\) | ||||
−0.291171 | + | 0.956671i | \(0.594045\pi\) | |||||||
\(3\) | −2.66029 | −1.53592 | −0.767960 | − | 0.640498i | \(-0.778728\pi\) | ||||
−0.767960 | + | 0.640498i | \(0.778728\pi\) | |||||||
\(4\) | −1.32176 | −0.660878 | ||||||||
\(5\) | −3.16209 | −1.41413 | −0.707065 | − | 0.707148i | \(-0.749981\pi\) | ||||
−0.707065 | + | 0.707148i | \(0.749981\pi\) | |||||||
\(6\) | 2.19090 | 0.894431 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.73565 | 0.967199 | ||||||||
\(9\) | 4.07715 | 1.35905 | ||||||||
\(10\) | 2.60416 | 0.823508 | ||||||||
\(11\) | 5.94270 | 1.79179 | 0.895895 | − | 0.444265i | \(-0.146535\pi\) | ||||
0.895895 | + | 0.444265i | \(0.146535\pi\) | |||||||
\(12\) | 3.51626 | 1.01506 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.41209 | 2.17199 | ||||||||
\(16\) | 0.390549 | 0.0976372 | ||||||||
\(17\) | 2.69964 | 0.654760 | 0.327380 | − | 0.944893i | \(-0.393834\pi\) | ||||
0.327380 | + | 0.944893i | \(0.393834\pi\) | |||||||
\(18\) | −3.35776 | −0.791433 | ||||||||
\(19\) | −1.95705 | −0.448978 | −0.224489 | − | 0.974477i | \(-0.572071\pi\) | ||||
−0.224489 | + | 0.974477i | \(0.572071\pi\) | |||||||
\(20\) | 4.17951 | 0.934568 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.89414 | −1.04343 | ||||||||
\(23\) | −2.72941 | −0.569122 | −0.284561 | − | 0.958658i | \(-0.591848\pi\) | ||||
−0.284561 | + | 0.958658i | \(0.591848\pi\) | |||||||
\(24\) | −7.27763 | −1.48554 | ||||||||
\(25\) | 4.99883 | 0.999766 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.86554 | −0.551474 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.99845 | −1.11388 | −0.556942 | − | 0.830551i | \(-0.688026\pi\) | ||||
−0.556942 | + | 0.830551i | \(0.688026\pi\) | |||||||
\(30\) | −6.92783 | −1.26484 | ||||||||
\(31\) | −1.15155 | −0.206824 | −0.103412 | − | 0.994639i | \(-0.532976\pi\) | ||||
−0.103412 | + | 0.994639i | \(0.532976\pi\) | |||||||
\(32\) | −5.79294 | −1.02406 | ||||||||
\(33\) | −15.8093 | −2.75205 | ||||||||
\(34\) | −2.22331 | −0.381294 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.38900 | −0.898167 | ||||||||
\(37\) | −6.50454 | −1.06934 | −0.534670 | − | 0.845061i | \(-0.679564\pi\) | ||||
−0.534670 | + | 0.845061i | \(0.679564\pi\) | |||||||
\(38\) | 1.61174 | 0.261459 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.65038 | −1.36775 | ||||||||
\(41\) | −3.73374 | −0.583112 | −0.291556 | − | 0.956554i | \(-0.594173\pi\) | ||||
−0.291556 | + | 0.956554i | \(0.594173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.99125 | 1.06616 | 0.533078 | − | 0.846066i | \(-0.321035\pi\) | ||||
0.533078 | + | 0.846066i | \(0.321035\pi\) | |||||||
\(44\) | −7.85479 | −1.18415 | ||||||||
\(45\) | −12.8923 | −1.92188 | ||||||||
\(46\) | 2.24783 | 0.331424 | ||||||||
\(47\) | −0.456071 | −0.0665248 | −0.0332624 | − | 0.999447i | \(-0.510590\pi\) | ||||
−0.0332624 | + | 0.999447i | \(0.510590\pi\) | |||||||
\(48\) | −1.03897 | −0.149963 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.11682 | −0.582206 | ||||||||
\(51\) | −7.18184 | −1.00566 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.399286 | 0.0548462 | 0.0274231 | − | 0.999624i | \(-0.491270\pi\) | ||||
0.0274231 | + | 0.999624i | \(0.491270\pi\) | |||||||
\(54\) | 2.35994 | 0.321146 | ||||||||
\(55\) | −18.7914 | −2.53383 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.20632 | 0.689594 | ||||||||
\(58\) | 4.94006 | 0.648662 | ||||||||
\(59\) | 4.80586 | 0.625670 | 0.312835 | − | 0.949807i | \(-0.398721\pi\) | ||||
0.312835 | + | 0.949807i | \(0.398721\pi\) | |||||||
\(60\) | −11.1187 | −1.43542 | ||||||||
\(61\) | 1.15703 | 0.148142 | 0.0740711 | − | 0.997253i | \(-0.476401\pi\) | ||||
0.0740711 | + | 0.997253i | \(0.476401\pi\) | |||||||
\(62\) | 0.948365 | 0.120442 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.98971 | 0.498714 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.0199 | 1.60263 | ||||||||
\(67\) | 6.27918 | 0.767124 | 0.383562 | − | 0.923515i | \(-0.374697\pi\) | ||||
0.383562 | + | 0.923515i | \(0.374697\pi\) | |||||||
\(68\) | −3.56827 | −0.432716 | ||||||||
\(69\) | 7.26104 | 0.874127 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.50720 | 0.534906 | 0.267453 | − | 0.963571i | \(-0.413818\pi\) | ||||
0.267453 | + | 0.963571i | \(0.413818\pi\) | |||||||
\(72\) | 11.1537 | 1.31447 | ||||||||
\(73\) | −8.30575 | −0.972115 | −0.486057 | − | 0.873927i | \(-0.661565\pi\) | ||||
−0.486057 | + | 0.873927i | \(0.661565\pi\) | |||||||
\(74\) | 5.35685 | 0.622721 | ||||||||
\(75\) | −13.2983 | −1.53556 | ||||||||
\(76\) | 2.58674 | 0.296719 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.91410 | −0.890405 | −0.445203 | − | 0.895430i | \(-0.646868\pi\) | ||||
−0.445203 | + | 0.895430i | \(0.646868\pi\) | |||||||
\(80\) | −1.23495 | −0.138072 | ||||||||
\(81\) | −4.60828 | −0.512031 | ||||||||
\(82\) | 3.07494 | 0.339571 | ||||||||
\(83\) | 6.19795 | 0.680313 | 0.340156 | − | 0.940369i | \(-0.389520\pi\) | ||||
0.340156 | + | 0.940369i | \(0.389520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.53652 | −0.925916 | ||||||||
\(86\) | −5.75769 | −0.620867 | ||||||||
\(87\) | 15.9576 | 1.71084 | ||||||||
\(88\) | 16.2571 | 1.73302 | ||||||||
\(89\) | −3.56136 | −0.377504 | −0.188752 | − | 0.982025i | \(-0.560444\pi\) | ||||
−0.188752 | + | 0.982025i | \(0.560444\pi\) | |||||||
\(90\) | 10.6176 | 1.11919 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.60762 | 0.376120 | ||||||||
\(93\) | 3.06345 | 0.317665 | ||||||||
\(94\) | 0.375600 | 0.0387402 | ||||||||
\(95\) | 6.18837 | 0.634913 | ||||||||
\(96\) | 15.4109 | 1.57287 | ||||||||
\(97\) | 3.42751 | 0.348011 | 0.174005 | − | 0.984745i | \(-0.444329\pi\) | ||||
0.174005 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.2293 | 2.43513 | ||||||||
\(100\) | −6.60723 | −0.660723 | ||||||||
\(101\) | 13.3295 | 1.32633 | 0.663167 | − | 0.748472i | \(-0.269212\pi\) | ||||
0.663167 | + | 0.748472i | \(0.269212\pi\) | |||||||
\(102\) | 5.91465 | 0.585637 | ||||||||
\(103\) | −11.6450 | −1.14741 | −0.573706 | − | 0.819061i | \(-0.694495\pi\) | ||||
−0.573706 | + | 0.819061i | \(0.694495\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.328834 | −0.0319392 | ||||||||
\(107\) | 3.92966 | 0.379894 | 0.189947 | − | 0.981794i | \(-0.439168\pi\) | ||||
0.189947 | + | 0.981794i | \(0.439168\pi\) | |||||||
\(108\) | 3.78755 | 0.364457 | ||||||||
\(109\) | −11.2533 | −1.07787 | −0.538936 | − | 0.842346i | \(-0.681174\pi\) | ||||
−0.538936 | + | 0.842346i | \(0.681174\pi\) | |||||||
\(110\) | 15.4757 | 1.47555 | ||||||||
\(111\) | 17.3040 | 1.64242 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.77418 | −0.543189 | −0.271595 | − | 0.962412i | \(-0.587551\pi\) | ||||
−0.271595 | + | 0.962412i | \(0.587551\pi\) | |||||||
\(114\) | −4.28770 | −0.401579 | ||||||||
\(115\) | 8.63066 | 0.804813 | ||||||||
\(116\) | 7.92849 | 0.736142 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.95790 | −0.364354 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 23.0125 | 2.10075 | ||||||||
\(121\) | 24.3156 | 2.21051 | ||||||||
\(122\) | −0.952877 | −0.0862694 | ||||||||
\(123\) | 9.93284 | 0.895614 | ||||||||
\(124\) | 1.52207 | 0.136686 | ||||||||
\(125\) | 0.00370455 | 0.000331345 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.13117 | 0.544053 | 0.272027 | − | 0.962290i | \(-0.412306\pi\) | ||||
0.272027 | + | 0.962290i | \(0.412306\pi\) | |||||||
\(128\) | 8.30013 | 0.733635 | ||||||||
\(129\) | −18.5988 | −1.63753 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2217 | −0.893073 | −0.446537 | − | 0.894765i | \(-0.647343\pi\) | ||||
−0.446537 | + | 0.894765i | \(0.647343\pi\) | |||||||
\(132\) | 20.8960 | 1.81877 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.17126 | −0.446729 | ||||||||
\(135\) | 9.06111 | 0.779856 | ||||||||
\(136\) | 7.38528 | 0.633283 | ||||||||
\(137\) | 19.9475 | 1.70423 | 0.852116 | − | 0.523353i | \(-0.175319\pi\) | ||||
0.852116 | + | 0.523353i | \(0.175319\pi\) | |||||||
\(138\) | −5.97987 | −0.509041 | ||||||||
\(139\) | 20.3275 | 1.72415 | 0.862077 | − | 0.506777i | \(-0.169163\pi\) | ||||
0.862077 | + | 0.506777i | \(0.169163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.21328 | 0.102177 | ||||||||
\(142\) | −3.71193 | −0.311498 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.59233 | 0.132694 | ||||||||
\(145\) | 18.9677 | 1.57518 | ||||||||
\(146\) | 6.84025 | 0.566103 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.59741 | 0.706703 | ||||||||
\(149\) | −10.7162 | −0.877901 | −0.438951 | − | 0.898511i | \(-0.644650\pi\) | ||||
−0.438951 | + | 0.898511i | \(0.644650\pi\) | |||||||
\(150\) | 10.9519 | 0.894221 | ||||||||
\(151\) | −8.74416 | −0.711590 | −0.355795 | − | 0.934564i | \(-0.615790\pi\) | ||||
−0.355795 | + | 0.934564i | \(0.615790\pi\) | |||||||
\(152\) | −5.35380 | −0.434251 | ||||||||
\(153\) | 11.0069 | 0.889852 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.64130 | 0.292476 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.50734 | −0.519342 | −0.259671 | − | 0.965697i | \(-0.583614\pi\) | ||||
−0.259671 | + | 0.965697i | \(0.583614\pi\) | |||||||
\(158\) | 6.51770 | 0.518520 | ||||||||
\(159\) | −1.06222 | −0.0842393 | ||||||||
\(160\) | 18.3178 | 1.44815 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.79518 | 0.298177 | ||||||||
\(163\) | −2.61267 | −0.204640 | −0.102320 | − | 0.994752i | \(-0.532627\pi\) | ||||
−0.102320 | + | 0.994752i | \(0.532627\pi\) | |||||||
\(164\) | 4.93509 | 0.385366 | ||||||||
\(165\) | 49.9905 | 3.89175 | ||||||||
\(166\) | −5.10436 | −0.396175 | ||||||||
\(167\) | 3.88624 | 0.300726 | 0.150363 | − | 0.988631i | \(-0.451956\pi\) | ||||
0.150363 | + | 0.988631i | \(0.451956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.03030 | 0.539200 | ||||||||
\(171\) | −7.97919 | −0.610184 | ||||||||
\(172\) | −9.24072 | −0.704599 | ||||||||
\(173\) | −13.9768 | −1.06263 | −0.531317 | − | 0.847173i | \(-0.678303\pi\) | ||||
−0.531317 | + | 0.847173i | \(0.678303\pi\) | |||||||
\(174\) | −13.1420 | −0.996293 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.32091 | 0.174945 | ||||||||
\(177\) | −12.7850 | −0.960979 | ||||||||
\(178\) | 2.93298 | 0.219836 | ||||||||
\(179\) | −25.2843 | −1.88984 | −0.944919 | − | 0.327305i | \(-0.893860\pi\) | ||||
−0.944919 | + | 0.327305i | \(0.893860\pi\) | |||||||
\(180\) | 17.0405 | 1.27013 | ||||||||
\(181\) | −0.864474 | −0.0642559 | −0.0321279 | − | 0.999484i | \(-0.510228\pi\) | ||||
−0.0321279 | + | 0.999484i | \(0.510228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.07803 | −0.227535 | ||||||||
\(184\) | −7.46673 | −0.550454 | ||||||||
\(185\) | 20.5680 | 1.51219 | ||||||||
\(186\) | −2.52293 | −0.184990 | ||||||||
\(187\) | 16.0432 | 1.17319 | ||||||||
\(188\) | 0.602814 | 0.0439647 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.09647 | −0.369737 | ||||||||
\(191\) | 14.6676 | 1.06131 | 0.530657 | − | 0.847587i | \(-0.321945\pi\) | ||||
0.530657 | + | 0.847587i | \(0.321945\pi\) | |||||||
\(192\) | −10.6138 | −0.765985 | ||||||||
\(193\) | 16.4959 | 1.18740 | 0.593700 | − | 0.804686i | \(-0.297667\pi\) | ||||
0.593700 | + | 0.804686i | \(0.297667\pi\) | |||||||
\(194\) | −2.82275 | −0.202661 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0102 | −0.784443 | −0.392222 | − | 0.919871i | \(-0.628293\pi\) | ||||
−0.392222 | + | 0.919871i | \(0.628293\pi\) | |||||||
\(198\) | −19.9542 | −1.41808 | ||||||||
\(199\) | 21.2117 | 1.50366 | 0.751829 | − | 0.659358i | \(-0.229172\pi\) | ||||
0.751829 | + | 0.659358i | \(0.229172\pi\) | |||||||
\(200\) | 13.6751 | 0.966972 | ||||||||
\(201\) | −16.7045 | −1.17824 | ||||||||
\(202\) | −10.9776 | −0.772380 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.49264 | 0.664617 | ||||||||
\(205\) | 11.8064 | 0.824597 | ||||||||
\(206\) | 9.59027 | 0.668186 | ||||||||
\(207\) | −11.1282 | −0.773466 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6301 | −0.804474 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.9358 | −1.23475 | −0.617375 | − | 0.786669i | \(-0.711804\pi\) | ||||
−0.617375 | + | 0.786669i | \(0.711804\pi\) | |||||||
\(212\) | −0.527759 | −0.0362466 | ||||||||
\(213\) | −11.9905 | −0.821572 | ||||||||
\(214\) | −3.23629 | −0.221228 | ||||||||
\(215\) | −22.1070 | −1.50768 | ||||||||
\(216\) | −7.83913 | −0.533385 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.26774 | 0.627691 | ||||||||
\(219\) | 22.0957 | 1.49309 | ||||||||
\(220\) | 24.8376 | 1.67455 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −14.2508 | −0.956451 | ||||||||
\(223\) | −16.0312 | −1.07353 | −0.536763 | − | 0.843733i | \(-0.680353\pi\) | ||||
−0.536763 | + | 0.843733i | \(0.680353\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.3810 | 1.35873 | ||||||||
\(226\) | 4.75536 | 0.316322 | ||||||||
\(227\) | 16.3750 | 1.08685 | 0.543424 | − | 0.839458i | \(-0.317127\pi\) | ||||
0.543424 | + | 0.839458i | \(0.317127\pi\) | |||||||
\(228\) | −6.88148 | −0.455737 | ||||||||
\(229\) | −27.0104 | −1.78490 | −0.892449 | − | 0.451148i | \(-0.851015\pi\) | ||||
−0.892449 | + | 0.451148i | \(0.851015\pi\) | |||||||
\(230\) | −7.10783 | −0.468677 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.4097 | −1.07735 | ||||||||
\(233\) | 11.5681 | 0.757853 | 0.378926 | − | 0.925427i | \(-0.376293\pi\) | ||||
0.378926 | + | 0.925427i | \(0.376293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.44214 | 0.0940747 | ||||||||
\(236\) | −6.35217 | −0.413491 | ||||||||
\(237\) | 21.0538 | 1.36759 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6731 | 0.949122 | 0.474561 | − | 0.880223i | \(-0.342607\pi\) | ||||
0.474561 | + | 0.880223i | \(0.342607\pi\) | |||||||
\(240\) | 3.28533 | 0.212067 | ||||||||
\(241\) | 14.3467 | 0.924151 | 0.462076 | − | 0.886841i | \(-0.347105\pi\) | ||||
0.462076 | + | 0.886841i | \(0.347105\pi\) | |||||||
\(242\) | −20.0253 | −1.28727 | ||||||||
\(243\) | 20.8560 | 1.33791 | ||||||||
\(244\) | −1.52931 | −0.0979039 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.18025 | −0.521554 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.15024 | −0.200040 | ||||||||
\(249\) | −16.4883 | −1.04491 | ||||||||
\(250\) | −0.00305091 | −0.000192956 0 | ||||||||
\(251\) | −8.61452 | −0.543744 | −0.271872 | − | 0.962333i | \(-0.587643\pi\) | ||||
−0.271872 | + | 0.962333i | \(0.587643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.2201 | −1.01975 | ||||||||
\(254\) | −5.04936 | −0.316825 | ||||||||
\(255\) | 22.7096 | 1.42213 | ||||||||
\(256\) | −14.8151 | −0.925941 | ||||||||
\(257\) | −10.3639 | −0.646485 | −0.323243 | − | 0.946316i | \(-0.604773\pi\) | ||||
−0.323243 | + | 0.946316i | \(0.604773\pi\) | |||||||
\(258\) | 15.3171 | 0.953603 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.4566 | −1.51383 | ||||||||
\(262\) | 8.41813 | 0.520074 | ||||||||
\(263\) | −22.0826 | −1.36167 | −0.680835 | − | 0.732436i | \(-0.738383\pi\) | ||||
−0.680835 | + | 0.732436i | \(0.738383\pi\) | |||||||
\(264\) | −43.2488 | −2.66178 | ||||||||
\(265\) | −1.26258 | −0.0775596 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.47427 | 0.579816 | ||||||||
\(268\) | −8.29954 | −0.506975 | ||||||||
\(269\) | −12.9399 | −0.788960 | −0.394480 | − | 0.918905i | \(-0.629075\pi\) | ||||
−0.394480 | + | 0.918905i | \(0.629075\pi\) | |||||||
\(270\) | −7.46233 | −0.454143 | ||||||||
\(271\) | 17.6749 | 1.07367 | 0.536837 | − | 0.843686i | \(-0.319619\pi\) | ||||
0.536837 | + | 0.843686i | \(0.319619\pi\) | |||||||
\(272\) | 1.05434 | 0.0639289 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4279 | −0.992446 | ||||||||
\(275\) | 29.7065 | 1.79137 | ||||||||
\(276\) | −9.59732 | −0.577691 | ||||||||
\(277\) | −18.0150 | −1.08242 | −0.541209 | − | 0.840888i | \(-0.682033\pi\) | ||||
−0.541209 | + | 0.840888i | \(0.682033\pi\) | |||||||
\(278\) | −16.7408 | −1.00405 | ||||||||
\(279\) | −4.69504 | −0.281085 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.44178 | 0.145665 | 0.0728323 | − | 0.997344i | \(-0.476796\pi\) | ||||
0.0728323 | + | 0.997344i | \(0.476796\pi\) | |||||||
\(282\) | −0.999205 | −0.0595018 | ||||||||
\(283\) | 28.7240 | 1.70746 | 0.853732 | − | 0.520713i | \(-0.174334\pi\) | ||||
0.853732 | + | 0.520713i | \(0.174334\pi\) | |||||||
\(284\) | −5.95741 | −0.353507 | ||||||||
\(285\) | −16.4629 | −0.975176 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −23.6187 | −1.39175 | ||||||||
\(289\) | −9.71193 | −0.571290 | ||||||||
\(290\) | −15.6209 | −0.917292 | ||||||||
\(291\) | −9.11818 | −0.534517 | ||||||||
\(292\) | 10.9782 | 0.642449 | ||||||||
\(293\) | 29.3309 | 1.71353 | 0.856763 | − | 0.515710i | \(-0.172472\pi\) | ||||
0.856763 | + | 0.515710i | \(0.172472\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.1966 | −0.884779 | ||||||||
\(296\) | −17.7942 | −1.03426 | ||||||||
\(297\) | −17.0291 | −0.988126 | ||||||||
\(298\) | 8.82535 | 0.511239 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 17.5772 | 1.01482 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.20131 | 0.414389 | ||||||||
\(303\) | −35.4603 | −2.03714 | ||||||||
\(304\) | −0.764323 | −0.0438369 | ||||||||
\(305\) | −3.65863 | −0.209492 | ||||||||
\(306\) | −9.06476 | −0.518198 | ||||||||
\(307\) | 7.06910 | 0.403455 | 0.201728 | − | 0.979442i | \(-0.435344\pi\) | ||||
0.201728 | + | 0.979442i | \(0.435344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.9790 | 1.76233 | ||||||||
\(310\) | −2.99882 | −0.170321 | ||||||||
\(311\) | 22.2686 | 1.26274 | 0.631368 | − | 0.775483i | \(-0.282494\pi\) | ||||
0.631368 | + | 0.775483i | \(0.282494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.0840 | 1.58740 | 0.793700 | − | 0.608309i | \(-0.208152\pi\) | ||||
0.793700 | + | 0.608309i | \(0.208152\pi\) | |||||||
\(314\) | 5.35916 | 0.302435 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4605 | 0.588449 | ||||||||
\(317\) | 19.5155 | 1.09610 | 0.548049 | − | 0.836446i | \(-0.315371\pi\) | ||||
0.548049 | + | 0.836446i | \(0.315371\pi\) | |||||||
\(318\) | 0.874796 | 0.0490561 | ||||||||
\(319\) | −35.6470 | −1.99585 | ||||||||
\(320\) | −12.6158 | −0.705247 | ||||||||
\(321\) | −10.4540 | −0.583488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.28333 | −0.293972 | ||||||||
\(324\) | 6.09102 | 0.338390 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.15168 | 0.119171 | ||||||||
\(327\) | 29.9371 | 1.65553 | ||||||||
\(328\) | −10.2142 | −0.563986 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −41.1700 | −2.26633 | ||||||||
\(331\) | 15.6308 | 0.859145 | 0.429573 | − | 0.903032i | \(-0.358664\pi\) | ||||
0.429573 | + | 0.903032i | \(0.358664\pi\) | |||||||
\(332\) | −8.19217 | −0.449604 | ||||||||
\(333\) | −26.5200 | −1.45329 | ||||||||
\(334\) | −3.20053 | −0.175125 | ||||||||
\(335\) | −19.8553 | −1.08481 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.7501 | −1.18480 | −0.592401 | − | 0.805643i | \(-0.701820\pi\) | ||||
−0.592401 | + | 0.805643i | \(0.701820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.3610 | 0.834295 | ||||||||
\(340\) | 11.2832 | 0.611917 | ||||||||
\(341\) | −6.84330 | −0.370586 | ||||||||
\(342\) | 6.57131 | 0.355336 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 19.1256 | 1.03118 | ||||||||
\(345\) | −22.9601 | −1.23613 | ||||||||
\(346\) | 11.5106 | 0.618816 | ||||||||
\(347\) | −15.9590 | −0.856726 | −0.428363 | − | 0.903607i | \(-0.640909\pi\) | ||||
−0.428363 | + | 0.903607i | \(0.640909\pi\) | |||||||
\(348\) | −21.0921 | −1.13065 | ||||||||
\(349\) | −6.81706 | −0.364909 | −0.182455 | − | 0.983214i | \(-0.558404\pi\) | ||||
−0.182455 | + | 0.983214i | \(0.558404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −34.4257 | −1.83490 | ||||||||
\(353\) | 14.0033 | 0.745318 | 0.372659 | − | 0.927968i | \(-0.378446\pi\) | ||||
0.372659 | + | 0.927968i | \(0.378446\pi\) | |||||||
\(354\) | 10.5292 | 0.559619 | ||||||||
\(355\) | −14.2522 | −0.756427 | ||||||||
\(356\) | 4.70725 | 0.249484 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.8230 | 1.10053 | ||||||||
\(359\) | 5.41494 | 0.285789 | 0.142895 | − | 0.989738i | \(-0.454359\pi\) | ||||
0.142895 | + | 0.989738i | \(0.454359\pi\) | |||||||
\(360\) | −35.2689 | −1.85884 | ||||||||
\(361\) | −15.1700 | −0.798419 | ||||||||
\(362\) | 0.711943 | 0.0374189 | ||||||||
\(363\) | −64.6867 | −3.39517 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.2636 | 1.37470 | ||||||||
\(366\) | 2.53493 | 0.132503 | ||||||||
\(367\) | −30.0317 | −1.56764 | −0.783822 | − | 0.620985i | \(-0.786733\pi\) | ||||
−0.783822 | + | 0.620985i | \(0.786733\pi\) | |||||||
\(368\) | −1.06597 | −0.0555675 | ||||||||
\(369\) | −15.2230 | −0.792480 | ||||||||
\(370\) | −16.9389 | −0.880610 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.04914 | −0.209938 | ||||||||
\(373\) | 21.4098 | 1.10856 | 0.554278 | − | 0.832332i | \(-0.312995\pi\) | ||||
0.554278 | + | 0.832332i | \(0.312995\pi\) | |||||||
\(374\) | −13.2124 | −0.683199 | ||||||||
\(375\) | −0.00985519 | −0.000508920 0 | ||||||||
\(376\) | −1.24765 | −0.0643427 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.47655 | 0.486778 | 0.243389 | − | 0.969929i | \(-0.421741\pi\) | ||||
0.243389 | + | 0.969929i | \(0.421741\pi\) | |||||||
\(380\) | −8.17951 | −0.419600 | ||||||||
\(381\) | −16.3107 | −0.835622 | ||||||||
\(382\) | −12.0796 | −0.618048 | ||||||||
\(383\) | 5.43061 | 0.277491 | 0.138746 | − | 0.990328i | \(-0.455693\pi\) | ||||
0.138746 | + | 0.990328i | \(0.455693\pi\) | |||||||
\(384\) | −22.0808 | −1.12680 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.5853 | −0.691473 | ||||||||
\(387\) | 28.5044 | 1.44896 | ||||||||
\(388\) | −4.53033 | −0.229993 | ||||||||
\(389\) | −10.6422 | −0.539580 | −0.269790 | − | 0.962919i | \(-0.586954\pi\) | ||||
−0.269790 | + | 0.962919i | \(0.586954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.36845 | −0.372638 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.1927 | 1.37169 | ||||||||
\(394\) | 9.06750 | 0.456814 | ||||||||
\(395\) | 25.0251 | 1.25915 | ||||||||
\(396\) | −32.0252 | −1.60933 | ||||||||
\(397\) | 37.1854 | 1.86628 | 0.933140 | − | 0.359512i | \(-0.117057\pi\) | ||||
0.933140 | + | 0.359512i | \(0.117057\pi\) | |||||||
\(398\) | −17.4690 | −0.875644 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.95229 | 0.0976143 | ||||||||
\(401\) | −0.896610 | −0.0447746 | −0.0223873 | − | 0.999749i | \(-0.507127\pi\) | ||||
−0.0223873 | + | 0.999749i | \(0.507127\pi\) | |||||||
\(402\) | 13.7571 | 0.686139 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −17.6183 | −0.876545 | ||||||||
\(405\) | 14.5718 | 0.724079 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −38.6545 | −1.91603 | ||||||||
\(408\) | −19.6470 | −0.972672 | ||||||||
\(409\) | −24.5773 | −1.21527 | −0.607635 | − | 0.794217i | \(-0.707881\pi\) | ||||
−0.607635 | + | 0.794217i | \(0.707881\pi\) | |||||||
\(410\) | −9.72326 | −0.480198 | ||||||||
\(411\) | −53.0662 | −2.61756 | ||||||||
\(412\) | 15.3918 | 0.758299 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.16473 | 0.450422 | ||||||||
\(415\) | −19.5985 | −0.962052 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −54.0770 | −2.64816 | ||||||||
\(418\) | 9.57807 | 0.468479 | ||||||||
\(419\) | 7.64558 | 0.373511 | 0.186755 | − | 0.982406i | \(-0.440203\pi\) | ||||
0.186755 | + | 0.982406i | \(0.440203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0780 | −1.22223 | −0.611113 | − | 0.791544i | \(-0.709278\pi\) | ||||
−0.611113 | + | 0.791544i | \(0.709278\pi\) | |||||||
\(422\) | 14.7711 | 0.719046 | ||||||||
\(423\) | −1.85947 | −0.0904106 | ||||||||
\(424\) | 1.09231 | 0.0530471 | ||||||||
\(425\) | 13.4951 | 0.654606 | ||||||||
\(426\) | 9.87481 | 0.478436 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.19405 | −0.251064 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.2063 | 0.877987 | ||||||||
\(431\) | −7.75404 | −0.373499 | −0.186750 | − | 0.982408i | \(-0.559795\pi\) | ||||
−0.186750 | + | 0.982408i | \(0.559795\pi\) | |||||||
\(432\) | −1.11913 | −0.0538444 | ||||||||
\(433\) | −35.9760 | −1.72890 | −0.864448 | − | 0.502722i | \(-0.832332\pi\) | ||||
−0.864448 | + | 0.502722i | \(0.832332\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −50.4595 | −2.41935 | ||||||||
\(436\) | 14.8741 | 0.712342 | ||||||||
\(437\) | 5.34160 | 0.255523 | ||||||||
\(438\) | −18.1971 | −0.869489 | ||||||||
\(439\) | 28.2350 | 1.34758 | 0.673792 | − | 0.738921i | \(-0.264664\pi\) | ||||
0.673792 | + | 0.738921i | \(0.264664\pi\) | |||||||
\(440\) | −51.4066 | −2.45071 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.7918 | 1.36794 | 0.683970 | − | 0.729511i | \(-0.260252\pi\) | ||||
0.683970 | + | 0.729511i | \(0.260252\pi\) | |||||||
\(444\) | −22.8716 | −1.08544 | ||||||||
\(445\) | 11.2614 | 0.533840 | ||||||||
\(446\) | 13.2026 | 0.625159 | ||||||||
\(447\) | 28.5081 | 1.34839 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.1902 | 1.37757 | 0.688785 | − | 0.724965i | \(-0.258144\pi\) | ||||
0.688785 | + | 0.724965i | \(0.258144\pi\) | |||||||
\(450\) | −16.7849 | −0.791247 | ||||||||
\(451\) | −22.1885 | −1.04482 | ||||||||
\(452\) | 7.63205 | 0.358982 | ||||||||
\(453\) | 23.2620 | 1.09295 | ||||||||
\(454\) | −13.4858 | −0.632918 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.2427 | 0.666974 | ||||||||
\(457\) | 31.6848 | 1.48215 | 0.741077 | − | 0.671420i | \(-0.234316\pi\) | ||||
0.741077 | + | 0.671420i | \(0.234316\pi\) | |||||||
\(458\) | 22.2446 | 1.03942 | ||||||||
\(459\) | −7.73594 | −0.361083 | ||||||||
\(460\) | −11.4076 | −0.531883 | ||||||||
\(461\) | 22.1018 | 1.02938 | 0.514691 | − | 0.857376i | \(-0.327907\pi\) | ||||
0.514691 | + | 0.857376i | \(0.327907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.8811 | −1.80696 | −0.903479 | − | 0.428632i | \(-0.858996\pi\) | ||||
−0.903479 | + | 0.428632i | \(0.858996\pi\) | |||||||
\(464\) | −2.34269 | −0.108757 | ||||||||
\(465\) | −9.68693 | −0.449220 | ||||||||
\(466\) | −9.52699 | −0.441329 | ||||||||
\(467\) | −13.2823 | −0.614632 | −0.307316 | − | 0.951607i | \(-0.599431\pi\) | ||||
−0.307316 | + | 0.951607i | \(0.599431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.18768 | −0.0547837 | ||||||||
\(471\) | 17.3114 | 0.797668 | ||||||||
\(472\) | 13.1472 | 0.605147 | ||||||||
\(473\) | 41.5469 | 1.91033 | ||||||||
\(474\) | −17.3390 | −0.796406 | ||||||||
\(475\) | −9.78295 | −0.448872 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.62795 | 0.0745387 | ||||||||
\(478\) | −12.0841 | −0.552714 | ||||||||
\(479\) | −6.63512 | −0.303166 | −0.151583 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151583 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(480\) | −48.7307 | −2.22424 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11.8153 | −0.538172 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −32.1393 | −1.46088 | ||||||||
\(485\) | −10.8381 | −0.492133 | ||||||||
\(486\) | −17.1761 | −0.779123 | ||||||||
\(487\) | 33.4701 | 1.51668 | 0.758338 | − | 0.651861i | \(-0.226012\pi\) | ||||
0.758338 | + | 0.651861i | \(0.226012\pi\) | |||||||
\(488\) | 3.16522 | 0.143283 | ||||||||
\(489\) | 6.95047 | 0.314311 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.3287 | −1.68462 | −0.842310 | − | 0.538993i | \(-0.818805\pi\) | ||||
−0.842310 | + | 0.538993i | \(0.818805\pi\) | |||||||
\(492\) | −13.1288 | −0.591891 | ||||||||
\(493\) | −16.1937 | −0.729327 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −76.6152 | −3.44360 | ||||||||
\(496\) | −0.449736 | −0.0201937 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.5791 | 0.608493 | ||||||||
\(499\) | 34.1327 | 1.52799 | 0.763994 | − | 0.645223i | \(-0.223236\pi\) | ||||
0.763994 | + | 0.645223i | \(0.223236\pi\) | |||||||
\(500\) | −0.00489651 | −0.000218979 0 | ||||||||
\(501\) | −10.3385 | −0.461891 | ||||||||
\(502\) | 7.09454 | 0.316645 | ||||||||
\(503\) | −15.3089 | −0.682592 | −0.341296 | − | 0.939956i | \(-0.610866\pi\) | ||||
−0.341296 | + | 0.939956i | \(0.610866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.1491 | −1.87561 | ||||||||
\(506\) | 13.3581 | 0.593842 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.10390 | −0.359553 | ||||||||
\(509\) | −18.4970 | −0.819866 | −0.409933 | − | 0.912116i | \(-0.634448\pi\) | ||||
−0.409933 | + | 0.912116i | \(0.634448\pi\) | |||||||
\(510\) | −18.7027 | −0.828168 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4.39924 | −0.194421 | ||||||||
\(513\) | 5.60801 | 0.247599 | ||||||||
\(514\) | 8.53529 | 0.376476 | ||||||||
\(515\) | 36.8224 | 1.62259 | ||||||||
\(516\) | 24.5830 | 1.08221 | ||||||||
\(517\) | −2.71029 | −0.119198 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 37.1823 | 1.63212 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.5865 | −1.03334 | −0.516671 | − | 0.856184i | \(-0.672829\pi\) | ||||
−0.516671 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(522\) | 20.1414 | 0.881564 | ||||||||
\(523\) | −12.3059 | −0.538099 | −0.269049 | − | 0.963126i | \(-0.586709\pi\) | ||||
−0.269049 | + | 0.963126i | \(0.586709\pi\) | |||||||
\(524\) | 13.5106 | 0.590212 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.1862 | 0.792958 | ||||||||
\(527\) | −3.10877 | −0.135420 | ||||||||
\(528\) | −6.17431 | −0.268702 | ||||||||
\(529\) | −15.5503 | −0.676100 | ||||||||
\(530\) | 1.03980 | 0.0451662 | ||||||||
\(531\) | 19.5942 | 0.850317 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7.80259 | −0.337651 | ||||||||
\(535\) | −12.4259 | −0.537220 | ||||||||
\(536\) | 17.1777 | 0.741962 | ||||||||
\(537\) | 67.2636 | 2.90264 | ||||||||
\(538\) | 10.6567 | 0.459444 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −11.9766 | −0.515390 | ||||||||
\(541\) | 19.4411 | 0.835838 | 0.417919 | − | 0.908484i | \(-0.362760\pi\) | ||||
0.417919 | + | 0.908484i | \(0.362760\pi\) | |||||||
\(542\) | −14.5563 | −0.625245 | ||||||||
\(543\) | 2.29975 | 0.0986919 | ||||||||
\(544\) | −15.6389 | −0.670511 | ||||||||
\(545\) | 35.5841 | 1.52425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.2163 | 1.71953 | 0.859763 | − | 0.510693i | \(-0.170611\pi\) | ||||
0.859763 | + | 0.510693i | \(0.170611\pi\) | |||||||
\(548\) | −26.3658 | −1.12629 | ||||||||
\(549\) | 4.71738 | 0.201333 | ||||||||
\(550\) | −24.4650 | −1.04319 | ||||||||
\(551\) | 11.7393 | 0.500109 | ||||||||
\(552\) | 19.8637 | 0.845454 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.8364 | 0.630337 | ||||||||
\(555\) | −54.7168 | −2.32260 | ||||||||
\(556\) | −26.8680 | −1.13945 | ||||||||
\(557\) | 7.96399 | 0.337445 | 0.168722 | − | 0.985664i | \(-0.446036\pi\) | ||||
0.168722 | + | 0.985664i | \(0.446036\pi\) | |||||||
\(558\) | 3.86663 | 0.163687 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.6795 | −1.80193 | ||||||||
\(562\) | −2.01095 | −0.0848266 | ||||||||
\(563\) | 1.42396 | 0.0600128 | 0.0300064 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300064 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(564\) | −1.60366 | −0.0675263 | ||||||||
\(565\) | 18.2585 | 0.768140 | ||||||||
\(566\) | −23.6558 | −0.994327 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.3301 | 0.517360 | ||||||||
\(569\) | −18.5189 | −0.776353 | −0.388177 | − | 0.921585i | \(-0.626895\pi\) | ||||
−0.388177 | + | 0.921585i | \(0.626895\pi\) | |||||||
\(570\) | 13.5581 | 0.567886 | ||||||||
\(571\) | 4.35766 | 0.182362 | 0.0911812 | − | 0.995834i | \(-0.470936\pi\) | ||||
0.0911812 | + | 0.995834i | \(0.470936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.0202 | −1.63009 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.6439 | −0.568989 | ||||||||
\(576\) | 16.2667 | 0.677778 | ||||||||
\(577\) | 9.56416 | 0.398161 | 0.199081 | − | 0.979983i | \(-0.436204\pi\) | ||||
0.199081 | + | 0.979983i | \(0.436204\pi\) | |||||||
\(578\) | 7.99832 | 0.332686 | ||||||||
\(579\) | −43.8839 | −1.82375 | ||||||||
\(580\) | −25.0706 | −1.04100 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.50933 | 0.311272 | ||||||||
\(583\) | 2.37284 | 0.0982728 | ||||||||
\(584\) | −22.7216 | −0.940228 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.1556 | −0.997859 | ||||||||
\(587\) | −2.36053 | −0.0974296 | −0.0487148 | − | 0.998813i | \(-0.515513\pi\) | ||||
−0.0487148 | + | 0.998813i | \(0.515513\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.25364 | 0.0928594 | ||||||||
\(590\) | 12.5152 | 0.515244 | ||||||||
\(591\) | 29.2903 | 1.20484 | ||||||||
\(592\) | −2.54034 | −0.104407 | ||||||||
\(593\) | −40.4292 | −1.66023 | −0.830114 | − | 0.557594i | \(-0.811725\pi\) | ||||
−0.830114 | + | 0.557594i | \(0.811725\pi\) | |||||||
\(594\) | 14.0244 | 0.575427 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.1641 | 0.580185 | ||||||||
\(597\) | −56.4294 | −2.30950 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.5873 | −1.57663 | −0.788316 | − | 0.615270i | \(-0.789047\pi\) | ||||
−0.788316 | + | 0.615270i | \(0.789047\pi\) | |||||||
\(600\) | −36.3796 | −1.48519 | ||||||||
\(601\) | −8.16231 | −0.332948 | −0.166474 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166474 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.6012 | 1.04256 | ||||||||
\(604\) | 11.5576 | 0.470274 | ||||||||
\(605\) | −76.8883 | −3.12595 | ||||||||
\(606\) | 29.2036 | 1.18631 | ||||||||
\(607\) | −7.58525 | −0.307876 | −0.153938 | − | 0.988081i | \(-0.549196\pi\) | ||||
−0.153938 | + | 0.988081i | \(0.549196\pi\) | |||||||
\(608\) | 11.3371 | 0.459779 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.01308 | 0.121996 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.5484 | −0.588083 | ||||||||
\(613\) | 15.5778 | 0.629183 | 0.314592 | − | 0.949227i | \(-0.398132\pi\) | ||||
0.314592 | + | 0.949227i | \(0.398132\pi\) | |||||||
\(614\) | −5.82180 | −0.234949 | ||||||||
\(615\) | −31.4086 | −1.26652 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.8687 | 0.960916 | 0.480458 | − | 0.877018i | \(-0.340471\pi\) | ||||
0.480458 | + | 0.877018i | \(0.340471\pi\) | |||||||
\(618\) | −25.5129 | −1.02628 | ||||||||
\(619\) | 19.4963 | 0.783622 | 0.391811 | − | 0.920046i | \(-0.371849\pi\) | ||||
0.391811 | + | 0.920046i | \(0.371849\pi\) | |||||||
\(620\) | −4.81291 | −0.193291 | ||||||||
\(621\) | 7.82126 | 0.313856 | ||||||||
\(622\) | −18.3394 | −0.735344 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0059 | −1.00023 | ||||||||
\(626\) | −23.1287 | −0.924410 | ||||||||
\(627\) | 30.9396 | 1.23561 | ||||||||
\(628\) | 8.60111 | 0.343222 | ||||||||
\(629\) | −17.5599 | −0.700161 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6619 | 1.02158 | 0.510792 | − | 0.859704i | \(-0.329352\pi\) | ||||
0.510792 | + | 0.859704i | \(0.329352\pi\) | |||||||
\(632\) | −21.6502 | −0.861199 | ||||||||
\(633\) | 47.7144 | 1.89648 | ||||||||
\(634\) | −16.0721 | −0.638304 | ||||||||
\(635\) | −19.3873 | −0.769362 | ||||||||
\(636\) | 1.40399 | 0.0556719 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29.3573 | 1.16227 | ||||||||
\(639\) | 18.3765 | 0.726964 | ||||||||
\(640\) | −26.2458 | −1.03746 | ||||||||
\(641\) | −1.10604 | −0.0436860 | −0.0218430 | − | 0.999761i | \(-0.506953\pi\) | ||||
−0.0218430 | + | 0.999761i | \(0.506953\pi\) | |||||||
\(642\) | 8.60949 | 0.339789 | ||||||||
\(643\) | −12.6367 | −0.498341 | −0.249171 | − | 0.968460i | \(-0.580158\pi\) | ||||
−0.249171 | + | 0.968460i | \(0.580158\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 58.8110 | 2.31568 | ||||||||
\(646\) | 4.35112 | 0.171192 | ||||||||
\(647\) | −25.7148 | −1.01095 | −0.505477 | − | 0.862840i | \(-0.668683\pi\) | ||||
−0.505477 | + | 0.862840i | \(0.668683\pi\) | |||||||
\(648\) | −12.6066 | −0.495236 | ||||||||
\(649\) | 28.5598 | 1.12107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.45331 | 0.135242 | ||||||||
\(653\) | 25.2607 | 0.988527 | 0.494263 | − | 0.869312i | \(-0.335438\pi\) | ||||
0.494263 | + | 0.869312i | \(0.335438\pi\) | |||||||
\(654\) | −24.6549 | −0.964083 | ||||||||
\(655\) | 32.3219 | 1.26292 | ||||||||
\(656\) | −1.45821 | −0.0569335 | ||||||||
\(657\) | −33.8638 | −1.32115 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.9764 | 0.895034 | 0.447517 | − | 0.894275i | \(-0.352308\pi\) | ||||
0.447517 | + | 0.894275i | \(0.352308\pi\) | |||||||
\(660\) | −66.0752 | −2.57197 | ||||||||
\(661\) | −30.4326 | −1.18369 | −0.591845 | − | 0.806051i | \(-0.701600\pi\) | ||||
−0.591845 | + | 0.806051i | \(0.701600\pi\) | |||||||
\(662\) | −12.8728 | −0.500316 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.9554 | 0.657998 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.8407 | 0.846310 | ||||||||
\(667\) | 16.3723 | 0.633937 | ||||||||
\(668\) | −5.13665 | −0.198743 | ||||||||
\(669\) | 42.6475 | 1.64885 | ||||||||
\(670\) | 16.3520 | 0.631733 | ||||||||
\(671\) | 6.87586 | 0.265440 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.8387 | 0.417800 | 0.208900 | − | 0.977937i | \(-0.433012\pi\) | ||||
0.208900 | + | 0.977937i | \(0.433012\pi\) | |||||||
\(674\) | 17.9124 | 0.689960 | ||||||||
\(675\) | −14.3244 | −0.551345 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.1209 | 0.696442 | 0.348221 | − | 0.937412i | \(-0.386786\pi\) | ||||
0.348221 | + | 0.937412i | \(0.386786\pi\) | |||||||
\(678\) | −12.6506 | −0.485845 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −23.3529 | −0.895545 | ||||||||
\(681\) | −43.5624 | −1.66931 | ||||||||
\(682\) | 5.63584 | 0.215808 | ||||||||
\(683\) | −37.8352 | −1.44772 | −0.723861 | − | 0.689946i | \(-0.757634\pi\) | ||||
−0.723861 | + | 0.689946i | \(0.757634\pi\) | |||||||
\(684\) | 10.5465 | 0.403257 | ||||||||
\(685\) | −63.0759 | −2.41001 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 71.8556 | 2.74146 | ||||||||
\(688\) | 2.73042 | 0.104096 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.9089 | 0.719850 | ||||||||
\(691\) | 30.0261 | 1.14225 | 0.571124 | − | 0.820864i | \(-0.306508\pi\) | ||||
0.571124 | + | 0.820864i | \(0.306508\pi\) | |||||||
\(692\) | 18.4739 | 0.702271 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.1432 | 0.498907 | ||||||||
\(695\) | −64.2774 | −2.43818 | ||||||||
\(696\) | 43.6545 | 1.65472 | ||||||||
\(697\) | −10.0798 | −0.381798 | ||||||||
\(698\) | 5.61423 | 0.212502 | ||||||||
\(699\) | −30.7746 | −1.16400 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.116177 | −0.00438796 | −0.00219398 | − | 0.999998i | \(-0.500698\pi\) | ||||
−0.00219398 | + | 0.999998i | \(0.500698\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.7297 | 0.480110 | ||||||||
\(704\) | 23.7097 | 0.893591 | ||||||||
\(705\) | −3.83651 | −0.144491 | ||||||||
\(706\) | −11.5325 | −0.434030 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 16.8986 | 0.635090 | ||||||||
\(709\) | −6.72993 | −0.252748 | −0.126374 | − | 0.991983i | \(-0.540334\pi\) | ||||
−0.126374 | + | 0.991983i | \(0.540334\pi\) | |||||||
\(710\) | 11.7375 | 0.440499 | ||||||||
\(711\) | −32.2670 | −1.21011 | ||||||||
\(712\) | −9.74265 | −0.365121 | ||||||||
\(713\) | 3.14305 | 0.117708 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33.4197 | 1.24895 | ||||||||
\(717\) | −39.0347 | −1.45778 | ||||||||
\(718\) | −4.45950 | −0.166427 | ||||||||
\(719\) | −46.8078 | −1.74564 | −0.872818 | − | 0.488046i | \(-0.837710\pi\) | ||||
−0.872818 | + | 0.488046i | \(0.837710\pi\) | |||||||
\(720\) | −5.03509 | −0.187647 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.4933 | 0.464953 | ||||||||
\(723\) | −38.1664 | −1.41942 | ||||||||
\(724\) | 1.14262 | 0.0424653 | ||||||||
\(725\) | −29.9852 | −1.11362 | ||||||||
\(726\) | 53.2731 | 1.97715 | ||||||||
\(727\) | 13.3362 | 0.494611 | 0.247305 | − | 0.968938i | \(-0.420455\pi\) | ||||
0.247305 | + | 0.968938i | \(0.420455\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.6582 | −1.54290 | ||||||||
\(730\) | −21.6295 | −0.800544 | ||||||||
\(731\) | 18.8739 | 0.698076 | ||||||||
\(732\) | 4.06840 | 0.150373 | ||||||||
\(733\) | 29.4612 | 1.08817 | 0.544087 | − | 0.839029i | \(-0.316876\pi\) | ||||
0.544087 | + | 0.839029i | \(0.316876\pi\) | |||||||
\(734\) | 24.7328 | 0.912905 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.8113 | 0.582814 | ||||||||
\(737\) | 37.3153 | 1.37453 | ||||||||
\(738\) | 12.5370 | 0.461494 | ||||||||
\(739\) | −12.0302 | −0.442537 | −0.221269 | − | 0.975213i | \(-0.571020\pi\) | ||||
−0.221269 | + | 0.975213i | \(0.571020\pi\) | |||||||
\(740\) | −27.1858 | −0.999370 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.8826 | 0.802796 | 0.401398 | − | 0.915904i | \(-0.368524\pi\) | ||||
0.401398 | + | 0.915904i | \(0.368524\pi\) | |||||||
\(744\) | 8.38055 | 0.307246 | ||||||||
\(745\) | 33.8855 | 1.24147 | ||||||||
\(746\) | −17.6321 | −0.645558 | ||||||||
\(747\) | 25.2700 | 0.924580 | ||||||||
\(748\) | −21.2051 | −0.775337 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.00811630 | 0.000296365 0 | ||||||||
\(751\) | 34.7492 | 1.26802 | 0.634008 | − | 0.773327i | \(-0.281409\pi\) | ||||
0.634008 | + | 0.773327i | \(0.281409\pi\) | |||||||
\(752\) | −0.178118 | −0.00649529 | ||||||||
\(753\) | 22.9172 | 0.835147 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.6498 | 1.00628 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.9263 | 1.59653 | 0.798265 | − | 0.602307i | \(-0.205752\pi\) | ||||
0.798265 | + | 0.602307i | \(0.205752\pi\) | |||||||
\(758\) | −7.80447 | −0.283471 | ||||||||
\(759\) | 43.1502 | 1.56625 | ||||||||
\(760\) | 16.9292 | 0.614087 | ||||||||
\(761\) | 0.141391 | 0.00512543 | 0.00256272 | − | 0.999997i | \(-0.499184\pi\) | ||||
0.00256272 | + | 0.999997i | \(0.499184\pi\) | |||||||
\(762\) | 13.4328 | 0.486618 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.3870 | −0.701399 | ||||||||
\(765\) | −34.8047 | −1.25837 | ||||||||
\(766\) | −4.47241 | −0.161595 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 39.4124 | 1.42217 | ||||||||
\(769\) | 13.6486 | 0.492180 | 0.246090 | − | 0.969247i | \(-0.420854\pi\) | ||||
0.246090 | + | 0.969247i | \(0.420854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.5711 | 0.992950 | ||||||||
\(772\) | −21.8035 | −0.784726 | ||||||||
\(773\) | −17.5894 | −0.632646 | −0.316323 | − | 0.948652i | \(-0.602448\pi\) | ||||
−0.316323 | + | 0.948652i | \(0.602448\pi\) | |||||||
\(774\) | −23.4750 | −0.843790 | ||||||||
\(775\) | −5.75639 | −0.206776 | ||||||||
\(776\) | 9.37647 | 0.336596 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.76443 | 0.314220 | ||||||||
\(779\) | 7.30711 | 0.261804 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.7849 | 0.958439 | ||||||||
\(782\) | 6.06833 | 0.217003 | ||||||||
\(783\) | 17.1888 | 0.614278 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.5768 | 0.734418 | ||||||||
\(786\) | −22.3947 | −0.798792 | ||||||||
\(787\) | 2.96845 | 0.105814 | 0.0529069 | − | 0.998599i | \(-0.483151\pi\) | ||||
0.0529069 | + | 0.998599i | \(0.483151\pi\) | |||||||
\(788\) | 14.5528 | 0.518421 | ||||||||
\(789\) | 58.7461 | 2.09142 | ||||||||
\(790\) | −20.6096 | −0.733256 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 66.2829 | 2.35526 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −30.6242 | −1.08681 | ||||||||
\(795\) | 3.35883 | 0.119125 | ||||||||
\(796\) | −28.0367 | −0.993735 | ||||||||
\(797\) | −9.45221 | −0.334815 | −0.167407 | − | 0.985888i | \(-0.553539\pi\) | ||||
−0.167407 | + | 0.985888i | \(0.553539\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.23123 | −0.0435577 | ||||||||
\(800\) | −28.9579 | −1.02382 | ||||||||
\(801\) | −14.5202 | −0.513047 | ||||||||
\(802\) | 0.738409 | 0.0260741 | ||||||||
\(803\) | −49.3586 | −1.74183 | ||||||||
\(804\) | 22.0792 | 0.778674 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.4239 | 1.21178 | ||||||||
\(808\) | 36.4648 | 1.28283 | ||||||||
\(809\) | −1.16255 | −0.0408729 | −0.0204365 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204365 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(810\) | −12.0007 | −0.421662 | ||||||||
\(811\) | 19.5561 | 0.686706 | 0.343353 | − | 0.939206i | \(-0.388437\pi\) | ||||
0.343353 | + | 0.939206i | \(0.388437\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −47.0204 | −1.64908 | ||||||||
\(814\) | 31.8342 | 1.11579 | ||||||||
\(815\) | 8.26151 | 0.289388 | ||||||||
\(816\) | −2.80486 | −0.0981897 | ||||||||
\(817\) | −13.6822 | −0.478680 | ||||||||
\(818\) | 20.2408 | 0.707702 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.6052 | −0.544958 | ||||||||
\(821\) | −12.6189 | −0.440403 | −0.220201 | − | 0.975454i | \(-0.570671\pi\) | ||||
−0.220201 | + | 0.975454i | \(0.570671\pi\) | |||||||
\(822\) | 43.7030 | 1.52432 | ||||||||
\(823\) | −6.56808 | −0.228949 | −0.114474 | − | 0.993426i | \(-0.536518\pi\) | ||||
−0.114474 | + | 0.993426i | \(0.536518\pi\) | |||||||
\(824\) | −31.8565 | −1.10978 | ||||||||
\(825\) | −79.0280 | −2.75140 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.3050 | −0.601754 | −0.300877 | − | 0.953663i | \(-0.597279\pi\) | ||||
−0.300877 | + | 0.953663i | \(0.597279\pi\) | |||||||
\(828\) | 14.7088 | 0.511167 | ||||||||
\(829\) | 3.75674 | 0.130477 | 0.0652385 | − | 0.997870i | \(-0.479219\pi\) | ||||
0.0652385 | + | 0.997870i | \(0.479219\pi\) | |||||||
\(830\) | 16.1404 | 0.560243 | ||||||||
\(831\) | 47.9252 | 1.66251 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 44.5355 | 1.54214 | ||||||||
\(835\) | −12.2886 | −0.425266 | ||||||||
\(836\) | 15.3722 | 0.531659 | ||||||||
\(837\) | 3.29981 | 0.114058 | ||||||||
\(838\) | −6.29656 | −0.217511 | ||||||||
\(839\) | −46.3427 | −1.59993 | −0.799965 | − | 0.600047i | \(-0.795148\pi\) | ||||
−0.799965 | + | 0.600047i | \(0.795148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.98142 | 0.240739 | ||||||||
\(842\) | 20.6531 | 0.711753 | ||||||||
\(843\) | −6.49586 | −0.223729 | ||||||||
\(844\) | 23.7067 | 0.816018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.53138 | 0.0526499 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.155941 | 0.00535503 | ||||||||
\(849\) | −76.4142 | −2.62253 | ||||||||
\(850\) | −11.1139 | −0.381205 | ||||||||
\(851\) | 17.7536 | 0.608585 | ||||||||
\(852\) | 15.8485 | 0.542959 | ||||||||
\(853\) | 15.3103 | 0.524215 | 0.262107 | − | 0.965039i | \(-0.415583\pi\) | ||||
0.262107 | + | 0.965039i | \(0.415583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.2309 | 0.862879 | ||||||||
\(856\) | 10.7502 | 0.367433 | ||||||||
\(857\) | −2.59248 | −0.0885574 | −0.0442787 | − | 0.999019i | \(-0.514099\pi\) | ||||
−0.0442787 | + | 0.999019i | \(0.514099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.7738 | 0.469955 | 0.234978 | − | 0.972001i | \(-0.424498\pi\) | ||||
0.234978 | + | 0.972001i | \(0.424498\pi\) | |||||||
\(860\) | 29.2200 | 0.996394 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.38589 | 0.217504 | ||||||||
\(863\) | −29.7592 | −1.01302 | −0.506508 | − | 0.862235i | \(-0.669064\pi\) | ||||
−0.506508 | + | 0.862235i | \(0.669064\pi\) | |||||||
\(864\) | 16.5999 | 0.564741 | ||||||||
\(865\) | 44.1958 | 1.50270 | ||||||||
\(866\) | 29.6282 | 1.00681 | ||||||||
\(867\) | 25.8366 | 0.877456 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.0311 | −1.59542 | ||||||||
\(870\) | 41.5562 | 1.40889 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −30.7852 | −1.04252 | ||||||||
\(873\) | 13.9745 | 0.472965 | ||||||||
\(874\) | −4.39910 | −0.148802 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −29.2051 | −0.986750 | ||||||||
\(877\) | −1.44332 | −0.0487374 | −0.0243687 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243687 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(878\) | −23.2531 | −0.784755 | ||||||||
\(879\) | −78.0286 | −2.63184 | ||||||||
\(880\) | −7.33894 | −0.247396 | ||||||||
\(881\) | 35.8804 | 1.20884 | 0.604420 | − | 0.796666i | \(-0.293405\pi\) | ||||
0.604420 | + | 0.796666i | \(0.293405\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5626 | −0.355458 | −0.177729 | − | 0.984079i | \(-0.556875\pi\) | ||||
−0.177729 | + | 0.984079i | \(0.556875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 40.4273 | 1.35895 | ||||||||
\(886\) | −23.7116 | −0.796608 | ||||||||
\(887\) | −12.2280 | −0.410577 | −0.205288 | − | 0.978702i | \(-0.565813\pi\) | ||||
−0.205288 | + | 0.978702i | \(0.565813\pi\) | |||||||
\(888\) | 47.3377 | 1.58855 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.27436 | −0.310877 | ||||||||
\(891\) | −27.3856 | −0.917452 | ||||||||
\(892\) | 21.1893 | 0.709469 | ||||||||
\(893\) | 0.892553 | 0.0298681 | ||||||||
\(894\) | −23.4780 | −0.785222 | ||||||||
\(895\) | 79.9513 | 2.67248 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.0398 | −0.802217 | ||||||||
\(899\) | 6.90751 | 0.230378 | ||||||||
\(900\) | −26.9387 | −0.897956 | ||||||||
\(901\) | 1.07793 | 0.0359110 | ||||||||
\(902\) | 18.2735 | 0.608440 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.7961 | −0.525372 | ||||||||
\(905\) | 2.73355 | 0.0908662 | ||||||||
\(906\) | −19.1576 | −0.636468 | ||||||||
\(907\) | 4.52555 | 0.150269 | 0.0751343 | − | 0.997173i | \(-0.476061\pi\) | ||||
0.0751343 | + | 0.997173i | \(0.476061\pi\) | |||||||
\(908\) | −21.6438 | −0.718274 | ||||||||
\(909\) | 54.3464 | 1.80256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.2723 | −1.89751 | −0.948757 | − | 0.316006i | \(-0.897658\pi\) | ||||
−0.948757 | + | 0.316006i | \(0.897658\pi\) | |||||||
\(912\) | 2.03332 | 0.0673300 | ||||||||
\(913\) | 36.8325 | 1.21898 | ||||||||
\(914\) | −26.0942 | −0.863120 | ||||||||
\(915\) | 9.73302 | 0.321764 | ||||||||
\(916\) | 35.7012 | 1.17960 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.37098 | 0.210274 | ||||||||
\(919\) | −40.7551 | −1.34439 | −0.672193 | − | 0.740376i | \(-0.734648\pi\) | ||||
−0.672193 | + | 0.740376i | \(0.734648\pi\) | |||||||
\(920\) | 23.6105 | 0.778415 | ||||||||
\(921\) | −18.8059 | −0.619675 | ||||||||
\(922\) | −18.2021 | −0.599453 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.5151 | −1.06909 | ||||||||
\(926\) | 32.0208 | 1.05227 | ||||||||
\(927\) | −47.4783 | −1.55939 | ||||||||
\(928\) | 34.7487 | 1.14068 | ||||||||
\(929\) | −52.2791 | −1.71522 | −0.857611 | − | 0.514298i | \(-0.828052\pi\) | ||||
−0.857611 | + | 0.514298i | \(0.828052\pi\) | |||||||
\(930\) | 7.97773 | 0.261600 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.2902 | −0.500848 | ||||||||
\(933\) | −59.2410 | −1.93946 | ||||||||
\(934\) | 10.9387 | 0.357926 | ||||||||
\(935\) | −50.7300 | −1.65905 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.38634 | 0.208633 | 0.104316 | − | 0.994544i | \(-0.466735\pi\) | ||||
0.104316 | + | 0.994544i | \(0.466735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −74.7116 | −2.43812 | ||||||||
\(940\) | −1.90615 | −0.0621719 | ||||||||
\(941\) | −25.3711 | −0.827073 | −0.413536 | − | 0.910488i | \(-0.635707\pi\) | ||||
−0.413536 | + | 0.910488i | \(0.635707\pi\) | |||||||
\(942\) | −14.2569 | −0.464516 | ||||||||
\(943\) | 10.1909 | 0.331862 | ||||||||
\(944\) | 1.87692 | 0.0610887 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.2162 | −1.11246 | ||||||||
\(947\) | 27.2061 | 0.884080 | 0.442040 | − | 0.896995i | \(-0.354255\pi\) | ||||
0.442040 | + | 0.896995i | \(0.354255\pi\) | |||||||
\(948\) | −27.8280 | −0.903811 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 8.05681 | 0.261397 | ||||||||
\(951\) | −51.9169 | −1.68352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.5879 | 0.861265 | 0.430633 | − | 0.902527i | \(-0.358290\pi\) | ||||
0.430633 | + | 0.902527i | \(0.358290\pi\) | |||||||
\(954\) | −1.34071 | −0.0434070 | ||||||||
\(955\) | −46.3805 | −1.50084 | ||||||||
\(956\) | −19.3942 | −0.627254 | ||||||||
\(957\) | 94.8314 | 3.06546 | ||||||||
\(958\) | 5.46439 | 0.176546 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 33.5618 | 1.08320 | ||||||||
\(961\) | −29.6739 | −0.957224 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0218 | 0.516296 | ||||||||
\(964\) | −18.9628 | −0.610751 | ||||||||
\(965\) | −52.1615 | −1.67914 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.2467 | −1.13346 | −0.566729 | − | 0.823904i | \(-0.691791\pi\) | ||||
−0.566729 | + | 0.823904i | \(0.691791\pi\) | |||||||
\(968\) | 66.5191 | 2.13801 | ||||||||
\(969\) | 14.0552 | 0.451518 | ||||||||
\(970\) | 8.92578 | 0.286590 | ||||||||
\(971\) | −36.9783 | −1.18669 | −0.593344 | − | 0.804949i | \(-0.702193\pi\) | ||||
−0.593344 | + | 0.804949i | \(0.702193\pi\) | |||||||
\(972\) | −27.5665 | −0.884197 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27.5645 | −0.883224 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.451876 | 0.0144642 | ||||||||
\(977\) | 24.7525 | 0.791902 | 0.395951 | − | 0.918272i | \(-0.370415\pi\) | ||||
0.395951 | + | 0.918272i | \(0.370415\pi\) | |||||||
\(978\) | −5.72410 | −0.183036 | ||||||||
\(979\) | −21.1641 | −0.676408 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.8815 | −1.46488 | ||||||||
\(982\) | 30.7423 | 0.981025 | ||||||||
\(983\) | −4.55736 | −0.145357 | −0.0726786 | − | 0.997355i | \(-0.523155\pi\) | ||||
−0.0726786 | + | 0.997355i | \(0.523155\pi\) | |||||||
\(984\) | 27.1728 | 0.866237 | ||||||||
\(985\) | 34.8152 | 1.10930 | ||||||||
\(986\) | 13.3364 | 0.424718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.0820 | −0.606773 | ||||||||
\(990\) | 63.0969 | 2.00535 | ||||||||
\(991\) | −27.1963 | −0.863919 | −0.431960 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431960 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(992\) | 6.67085 | 0.211800 | ||||||||
\(993\) | −41.5824 | −1.31958 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −67.0734 | −2.12637 | ||||||||
\(996\) | 21.7936 | 0.690556 | ||||||||
\(997\) | 30.2274 | 0.957312 | 0.478656 | − | 0.878002i | \(-0.341124\pi\) | ||||
0.478656 | + | 0.878002i | \(0.341124\pi\) | |||||||
\(998\) | −28.1102 | −0.889812 | ||||||||
\(999\) | 18.6390 | 0.589713 |
(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 | 8281.2.a.ch.1.2 | 6 | ||
7.6 | odd | 2 | 1183.2.a.p.1.2 | 6 | |||
13.6 | odd | 12 | 637.2.q.h.491.4 | 12 | |||
13.11 | odd | 12 | 637.2.q.h.589.4 | 12 | |||
13.12 | even | 2 | 8281.2.a.by.1.5 | 6 | |||
91.6 | even | 12 | 91.2.q.a.36.4 | ✓ | 12 | ||
91.11 | odd | 12 | 637.2.u.i.30.3 | 12 | |||
91.19 | even | 12 | 637.2.u.h.361.3 | 12 | |||
91.24 | even | 12 | 637.2.u.h.30.3 | 12 | |||
91.32 | odd | 12 | 637.2.k.g.569.4 | 12 | |||
91.34 | even | 4 | 1183.2.c.i.337.5 | 12 | |||
91.37 | odd | 12 | 637.2.k.g.459.3 | 12 | |||
91.45 | even | 12 | 637.2.k.h.569.4 | 12 | |||
91.58 | odd | 12 | 637.2.u.i.361.3 | 12 | |||
91.76 | even | 12 | 91.2.q.a.43.4 | yes | 12 | ||
91.83 | even | 4 | 1183.2.c.i.337.8 | 12 | |||
91.89 | even | 12 | 637.2.k.h.459.3 | 12 | |||
91.90 | odd | 2 | 1183.2.a.m.1.5 | 6 | |||
273.167 | odd | 12 | 819.2.ct.a.316.3 | 12 | |||
273.188 | odd | 12 | 819.2.ct.a.127.3 | 12 | |||
364.167 | odd | 12 | 1456.2.cc.c.225.6 | 12 | |||
364.279 | odd | 12 | 1456.2.cc.c.673.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.4 | ✓ | 12 | 91.6 | even | 12 | ||
91.2.q.a.43.4 | yes | 12 | 91.76 | even | 12 | ||
637.2.k.g.459.3 | 12 | 91.37 | odd | 12 | |||
637.2.k.g.569.4 | 12 | 91.32 | odd | 12 | |||
637.2.k.h.459.3 | 12 | 91.89 | even | 12 | |||
637.2.k.h.569.4 | 12 | 91.45 | even | 12 | |||
637.2.q.h.491.4 | 12 | 13.6 | odd | 12 | |||
637.2.q.h.589.4 | 12 | 13.11 | odd | 12 | |||
637.2.u.h.30.3 | 12 | 91.24 | even | 12 | |||
637.2.u.h.361.3 | 12 | 91.19 | even | 12 | |||
637.2.u.i.30.3 | 12 | 91.11 | odd | 12 | |||
637.2.u.i.361.3 | 12 | 91.58 | odd | 12 | |||
819.2.ct.a.127.3 | 12 | 273.188 | odd | 12 | |||
819.2.ct.a.316.3 | 12 | 273.167 | odd | 12 | |||
1183.2.a.m.1.5 | 6 | 91.90 | odd | 2 | |||
1183.2.a.p.1.2 | 6 | 7.6 | odd | 2 | |||
1183.2.c.i.337.5 | 12 | 91.34 | even | 4 | |||
1183.2.c.i.337.8 | 12 | 91.83 | even | 4 | |||
1456.2.cc.c.225.6 | 12 | 364.167 | odd | 12 | |||
1456.2.cc.c.673.6 | 12 | 364.279 | odd | 12 | |||
8281.2.a.by.1.5 | 6 | 13.12 | even | 2 | |||
8281.2.a.ch.1.2 | 6 | 1.1 | even | 1 | trivial |