Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(3.30795\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 | ||||||||
\(3\) | 3.30795 | 1.90984 | 0.954922 | − | 0.296857i | \(-0.0959386\pi\) | ||||
0.954922 | + | 0.296857i | \(0.0959386\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.828943 | −0.370715 | −0.185357 | − | 0.982671i | \(-0.559344\pi\) | ||||
−0.185357 | + | 0.982671i | \(0.559344\pi\) | |||||||
\(6\) | 3.30795 | 1.35046 | ||||||||
\(7\) | 2.22864 | 0.842346 | 0.421173 | − | 0.906980i | \(-0.361619\pi\) | ||||
0.421173 | + | 0.906980i | \(0.361619\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.94251 | 2.64750 | ||||||||
\(10\) | −0.828943 | −0.262135 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.30795 | 0.954922 | ||||||||
\(13\) | 1.20735 | 0.334858 | 0.167429 | − | 0.985884i | \(-0.446454\pi\) | ||||
0.167429 | + | 0.985884i | \(0.446454\pi\) | |||||||
\(14\) | 2.22864 | 0.595629 | ||||||||
\(15\) | −2.74210 | −0.708007 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.58220 | 1.11135 | 0.555673 | − | 0.831401i | \(-0.312461\pi\) | ||||
0.555673 | + | 0.831401i | \(0.312461\pi\) | |||||||
\(18\) | 7.94251 | 1.87207 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.828943 | −0.185357 | ||||||||
\(21\) | 7.37221 | 1.60875 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.76409 | −0.367837 | −0.183919 | − | 0.982941i | \(-0.558878\pi\) | ||||
−0.183919 | + | 0.982941i | \(0.558878\pi\) | |||||||
\(24\) | 3.30795 | 0.675232 | ||||||||
\(25\) | −4.31285 | −0.862571 | ||||||||
\(26\) | 1.20735 | 0.236780 | ||||||||
\(27\) | 16.3495 | 3.14647 | ||||||||
\(28\) | 2.22864 | 0.421173 | ||||||||
\(29\) | 3.91436 | 0.726878 | 0.363439 | − | 0.931618i | \(-0.381603\pi\) | ||||
0.363439 | + | 0.931618i | \(0.381603\pi\) | |||||||
\(30\) | −2.74210 | −0.500637 | ||||||||
\(31\) | −8.68660 | −1.56016 | −0.780080 | − | 0.625680i | \(-0.784822\pi\) | ||||
−0.780080 | + | 0.625680i | \(0.784822\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.58220 | 0.785841 | ||||||||
\(35\) | −1.84741 | −0.312270 | ||||||||
\(36\) | 7.94251 | 1.32375 | ||||||||
\(37\) | −1.36981 | −0.225195 | −0.112597 | − | 0.993641i | \(-0.535917\pi\) | ||||
−0.112597 | + | 0.993641i | \(0.535917\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 3.99384 | 0.639526 | ||||||||
\(40\) | −0.828943 | −0.131067 | ||||||||
\(41\) | −5.91652 | −0.924005 | −0.462003 | − | 0.886879i | \(-0.652869\pi\) | ||||
−0.462003 | + | 0.886879i | \(0.652869\pi\) | |||||||
\(42\) | 7.37221 | 1.13756 | ||||||||
\(43\) | −3.78596 | −0.577353 | −0.288676 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288676 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.58389 | −0.981468 | ||||||||
\(46\) | −1.76409 | −0.260100 | ||||||||
\(47\) | −7.92677 | −1.15624 | −0.578119 | − | 0.815953i | \(-0.696213\pi\) | ||||
−0.578119 | + | 0.815953i | \(0.696213\pi\) | |||||||
\(48\) | 3.30795 | 0.477461 | ||||||||
\(49\) | −2.03317 | −0.290453 | ||||||||
\(50\) | −4.31285 | −0.609930 | ||||||||
\(51\) | 15.1577 | 2.12250 | ||||||||
\(52\) | 1.20735 | 0.167429 | ||||||||
\(53\) | −8.13933 | −1.11802 | −0.559012 | − | 0.829160i | \(-0.688819\pi\) | ||||
−0.559012 | + | 0.829160i | \(0.688819\pi\) | |||||||
\(54\) | 16.3495 | 2.22489 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.22864 | 0.297814 | ||||||||
\(57\) | 3.30795 | 0.438148 | ||||||||
\(58\) | 3.91436 | 0.513980 | ||||||||
\(59\) | −0.104572 | −0.0136142 | −0.00680709 | − | 0.999977i | \(-0.502167\pi\) | ||||
−0.00680709 | + | 0.999977i | \(0.502167\pi\) | |||||||
\(60\) | −2.74210 | −0.354004 | ||||||||
\(61\) | 12.4843 | 1.59846 | 0.799228 | − | 0.601028i | \(-0.205242\pi\) | ||||
0.799228 | + | 0.601028i | \(0.205242\pi\) | |||||||
\(62\) | −8.68660 | −1.10320 | ||||||||
\(63\) | 17.7010 | 2.23011 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00082 | −0.124137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6774 | −1.42662 | −0.713308 | − | 0.700851i | \(-0.752804\pi\) | ||||
−0.713308 | + | 0.700851i | \(0.752804\pi\) | |||||||
\(68\) | 4.58220 | 0.555673 | ||||||||
\(69\) | −5.83550 | −0.702512 | ||||||||
\(70\) | −1.84741 | −0.220808 | ||||||||
\(71\) | 5.40088 | 0.640967 | 0.320483 | − | 0.947254i | \(-0.396155\pi\) | ||||
0.320483 | + | 0.947254i | \(0.396155\pi\) | |||||||
\(72\) | 7.94251 | 0.936034 | ||||||||
\(73\) | −13.2594 | −1.55189 | −0.775946 | − | 0.630799i | \(-0.782727\pi\) | ||||
−0.775946 | + | 0.630799i | \(0.782727\pi\) | |||||||
\(74\) | −1.36981 | −0.159237 | ||||||||
\(75\) | −14.2667 | −1.64737 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.99384 | 0.452213 | ||||||||
\(79\) | −2.32315 | −0.261375 | −0.130688 | − | 0.991424i | \(-0.541719\pi\) | ||||
−0.130688 | + | 0.991424i | \(0.541719\pi\) | |||||||
\(80\) | −0.828943 | −0.0926787 | ||||||||
\(81\) | 30.2559 | 3.36177 | ||||||||
\(82\) | −5.91652 | −0.653370 | ||||||||
\(83\) | −5.98648 | −0.657101 | −0.328551 | − | 0.944486i | \(-0.606560\pi\) | ||||
−0.328551 | + | 0.944486i | \(0.606560\pi\) | |||||||
\(84\) | 7.37221 | 0.804375 | ||||||||
\(85\) | −3.79838 | −0.411992 | ||||||||
\(86\) | −3.78596 | −0.408250 | ||||||||
\(87\) | 12.9485 | 1.38822 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.07639 | −0.644096 | −0.322048 | − | 0.946723i | \(-0.604371\pi\) | ||||
−0.322048 | + | 0.946723i | \(0.604371\pi\) | |||||||
\(90\) | −6.58389 | −0.694003 | ||||||||
\(91\) | 2.69074 | 0.282066 | ||||||||
\(92\) | −1.76409 | −0.183919 | ||||||||
\(93\) | −28.7348 | −2.97966 | ||||||||
\(94\) | −7.92677 | −0.817583 | ||||||||
\(95\) | −0.828943 | −0.0850478 | ||||||||
\(96\) | 3.30795 | 0.337616 | ||||||||
\(97\) | 17.3375 | 1.76036 | 0.880178 | − | 0.474644i | \(-0.157423\pi\) | ||||
0.880178 | + | 0.474644i | \(0.157423\pi\) | |||||||
\(98\) | −2.03317 | −0.205381 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.31285 | −0.431285 | ||||||||
\(101\) | −0.0401979 | −0.00399984 | −0.00199992 | − | 0.999998i | \(-0.500637\pi\) | ||||
−0.00199992 | + | 0.999998i | \(0.500637\pi\) | |||||||
\(102\) | 15.1577 | 1.50083 | ||||||||
\(103\) | 17.2964 | 1.70426 | 0.852132 | − | 0.523327i | \(-0.175309\pi\) | ||||
0.852132 | + | 0.523327i | \(0.175309\pi\) | |||||||
\(104\) | 1.20735 | 0.118390 | ||||||||
\(105\) | −6.11115 | −0.596387 | ||||||||
\(106\) | −8.13933 | −0.790562 | ||||||||
\(107\) | 14.8051 | 1.43126 | 0.715631 | − | 0.698479i | \(-0.246139\pi\) | ||||
0.715631 | + | 0.698479i | \(0.246139\pi\) | |||||||
\(108\) | 16.3495 | 1.57324 | ||||||||
\(109\) | 0.176526 | 0.0169081 | 0.00845407 | − | 0.999964i | \(-0.497309\pi\) | ||||
0.00845407 | + | 0.999964i | \(0.497309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.53125 | −0.430087 | ||||||||
\(112\) | 2.22864 | 0.210587 | ||||||||
\(113\) | 5.63764 | 0.530345 | 0.265172 | − | 0.964201i | \(-0.414571\pi\) | ||||
0.265172 | + | 0.964201i | \(0.414571\pi\) | |||||||
\(114\) | 3.30795 | 0.309818 | ||||||||
\(115\) | 1.46233 | 0.136363 | ||||||||
\(116\) | 3.91436 | 0.363439 | ||||||||
\(117\) | 9.58937 | 0.886537 | ||||||||
\(118\) | −0.104572 | −0.00962667 | ||||||||
\(119\) | 10.2121 | 0.936138 | ||||||||
\(120\) | −2.74210 | −0.250318 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 12.4843 | 1.13028 | ||||||||
\(123\) | −19.5715 | −1.76471 | ||||||||
\(124\) | −8.68660 | −0.780080 | ||||||||
\(125\) | 7.71983 | 0.690482 | ||||||||
\(126\) | 17.7010 | 1.57693 | ||||||||
\(127\) | 15.5597 | 1.38070 | 0.690351 | − | 0.723474i | \(-0.257456\pi\) | ||||
0.690351 | + | 0.723474i | \(0.257456\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.5237 | −1.10265 | ||||||||
\(130\) | −1.00082 | −0.0877780 | ||||||||
\(131\) | 14.8982 | 1.30166 | 0.650829 | − | 0.759224i | \(-0.274421\pi\) | ||||
0.650829 | + | 0.759224i | \(0.274421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.22864 | 0.193247 | ||||||||
\(134\) | −11.6774 | −1.00877 | ||||||||
\(135\) | −13.5528 | −1.16644 | ||||||||
\(136\) | 4.58220 | 0.392920 | ||||||||
\(137\) | 10.1562 | 0.867702 | 0.433851 | − | 0.900985i | \(-0.357154\pi\) | ||||
0.433851 | + | 0.900985i | \(0.357154\pi\) | |||||||
\(138\) | −5.83550 | −0.496751 | ||||||||
\(139\) | 11.3949 | 0.966499 | 0.483250 | − | 0.875483i | \(-0.339456\pi\) | ||||
0.483250 | + | 0.875483i | \(0.339456\pi\) | |||||||
\(140\) | −1.84741 | −0.156135 | ||||||||
\(141\) | −26.2213 | −2.20823 | ||||||||
\(142\) | 5.40088 | 0.453232 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.94251 | 0.661876 | ||||||||
\(145\) | −3.24478 | −0.269464 | ||||||||
\(146\) | −13.2594 | −1.09735 | ||||||||
\(147\) | −6.72562 | −0.554720 | ||||||||
\(148\) | −1.36981 | −0.112597 | ||||||||
\(149\) | −16.6310 | −1.36246 | −0.681231 | − | 0.732068i | \(-0.738555\pi\) | ||||
−0.681231 | + | 0.732068i | \(0.738555\pi\) | |||||||
\(150\) | −14.2667 | −1.16487 | ||||||||
\(151\) | −18.0434 | −1.46835 | −0.734174 | − | 0.678962i | \(-0.762430\pi\) | ||||
−0.734174 | + | 0.678962i | \(0.762430\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 36.3941 | 2.94229 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.20070 | 0.578374 | ||||||||
\(156\) | 3.99384 | 0.319763 | ||||||||
\(157\) | −17.1908 | −1.37198 | −0.685989 | − | 0.727612i | \(-0.740630\pi\) | ||||
−0.685989 | + | 0.727612i | \(0.740630\pi\) | |||||||
\(158\) | −2.32315 | −0.184820 | ||||||||
\(159\) | −26.9245 | −2.13525 | ||||||||
\(160\) | −0.828943 | −0.0655337 | ||||||||
\(161\) | −3.93151 | −0.309846 | ||||||||
\(162\) | 30.2559 | 2.37713 | ||||||||
\(163\) | 9.91065 | 0.776262 | 0.388131 | − | 0.921604i | \(-0.373121\pi\) | ||||
0.388131 | + | 0.921604i | \(0.373121\pi\) | |||||||
\(164\) | −5.91652 | −0.462003 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.98648 | −0.464641 | ||||||||
\(167\) | −13.6271 | −1.05450 | −0.527249 | − | 0.849711i | \(-0.676776\pi\) | ||||
−0.527249 | + | 0.849711i | \(0.676776\pi\) | |||||||
\(168\) | 7.37221 | 0.568779 | ||||||||
\(169\) | −11.5423 | −0.887870 | ||||||||
\(170\) | −3.79838 | −0.291323 | ||||||||
\(171\) | 7.94251 | 0.607379 | ||||||||
\(172\) | −3.78596 | −0.288676 | ||||||||
\(173\) | −11.4678 | −0.871881 | −0.435941 | − | 0.899975i | \(-0.643584\pi\) | ||||
−0.435941 | + | 0.899975i | \(0.643584\pi\) | |||||||
\(174\) | 12.9485 | 0.981622 | ||||||||
\(175\) | −9.61179 | −0.726583 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.345920 | −0.0260009 | ||||||||
\(178\) | −6.07639 | −0.455445 | ||||||||
\(179\) | 0.219190 | 0.0163830 | 0.00819152 | − | 0.999966i | \(-0.497393\pi\) | ||||
0.00819152 | + | 0.999966i | \(0.497393\pi\) | |||||||
\(180\) | −6.58389 | −0.490734 | ||||||||
\(181\) | −24.9347 | −1.85338 | −0.926689 | − | 0.375828i | \(-0.877358\pi\) | ||||
−0.926689 | + | 0.375828i | \(0.877358\pi\) | |||||||
\(182\) | 2.69074 | 0.199451 | ||||||||
\(183\) | 41.2975 | 3.05280 | ||||||||
\(184\) | −1.76409 | −0.130050 | ||||||||
\(185\) | 1.13549 | 0.0834831 | ||||||||
\(186\) | −28.7348 | −2.10694 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.92677 | −0.578119 | ||||||||
\(189\) | 36.4372 | 2.65042 | ||||||||
\(190\) | −0.828943 | −0.0601379 | ||||||||
\(191\) | −9.25309 | −0.669530 | −0.334765 | − | 0.942302i | \(-0.608657\pi\) | ||||
−0.334765 | + | 0.942302i | \(0.608657\pi\) | |||||||
\(192\) | 3.30795 | 0.238730 | ||||||||
\(193\) | 16.1815 | 1.16477 | 0.582384 | − | 0.812914i | \(-0.302120\pi\) | ||||
0.582384 | + | 0.812914i | \(0.302120\pi\) | |||||||
\(194\) | 17.3375 | 1.24476 | ||||||||
\(195\) | −3.31067 | −0.237082 | ||||||||
\(196\) | −2.03317 | −0.145227 | ||||||||
\(197\) | 14.4283 | 1.02797 | 0.513985 | − | 0.857799i | \(-0.328169\pi\) | ||||
0.513985 | + | 0.857799i | \(0.328169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4819 | 0.884821 | 0.442411 | − | 0.896813i | \(-0.354123\pi\) | ||||
0.442411 | + | 0.896813i | \(0.354123\pi\) | |||||||
\(200\) | −4.31285 | −0.304965 | ||||||||
\(201\) | −38.6281 | −2.72461 | ||||||||
\(202\) | −0.0401979 | −0.00282831 | ||||||||
\(203\) | 8.72369 | 0.612283 | ||||||||
\(204\) | 15.1577 | 1.06125 | ||||||||
\(205\) | 4.90446 | 0.342542 | ||||||||
\(206\) | 17.2964 | 1.20510 | ||||||||
\(207\) | −14.0113 | −0.973850 | ||||||||
\(208\) | 1.20735 | 0.0837145 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −6.11115 | −0.421709 | ||||||||
\(211\) | 24.4896 | 1.68593 | 0.842967 | − | 0.537965i | \(-0.180807\pi\) | ||||
0.842967 | + | 0.537965i | \(0.180807\pi\) | |||||||
\(212\) | −8.13933 | −0.559012 | ||||||||
\(213\) | 17.8658 | 1.22415 | ||||||||
\(214\) | 14.8051 | 1.01205 | ||||||||
\(215\) | 3.13834 | 0.214033 | ||||||||
\(216\) | 16.3495 | 1.11245 | ||||||||
\(217\) | −19.3593 | −1.31419 | ||||||||
\(218\) | 0.176526 | 0.0119559 | ||||||||
\(219\) | −43.8613 | −2.96387 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.53231 | 0.372143 | ||||||||
\(222\) | −4.53125 | −0.304118 | ||||||||
\(223\) | −23.0348 | −1.54252 | −0.771262 | − | 0.636518i | \(-0.780374\pi\) | ||||
−0.771262 | + | 0.636518i | \(0.780374\pi\) | |||||||
\(224\) | 2.22864 | 0.148907 | ||||||||
\(225\) | −34.2549 | −2.28366 | ||||||||
\(226\) | 5.63764 | 0.375010 | ||||||||
\(227\) | −11.6050 | −0.770248 | −0.385124 | − | 0.922865i | \(-0.625841\pi\) | ||||
−0.385124 | + | 0.922865i | \(0.625841\pi\) | |||||||
\(228\) | 3.30795 | 0.219074 | ||||||||
\(229\) | 10.8274 | 0.715493 | 0.357746 | − | 0.933819i | \(-0.383545\pi\) | ||||
0.357746 | + | 0.933819i | \(0.383545\pi\) | |||||||
\(230\) | 1.46233 | 0.0964230 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.91436 | 0.256990 | ||||||||
\(233\) | 0.972932 | 0.0637389 | 0.0318694 | − | 0.999492i | \(-0.489854\pi\) | ||||
0.0318694 | + | 0.999492i | \(0.489854\pi\) | |||||||
\(234\) | 9.58937 | 0.626877 | ||||||||
\(235\) | 6.57084 | 0.428634 | ||||||||
\(236\) | −0.104572 | −0.00680709 | ||||||||
\(237\) | −7.68487 | −0.499186 | ||||||||
\(238\) | 10.2121 | 0.661950 | ||||||||
\(239\) | −16.0095 | −1.03557 | −0.517784 | − | 0.855511i | \(-0.673243\pi\) | ||||
−0.517784 | + | 0.855511i | \(0.673243\pi\) | |||||||
\(240\) | −2.74210 | −0.177002 | ||||||||
\(241\) | 11.2997 | 0.727878 | 0.363939 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363939 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 51.0363 | 3.27398 | ||||||||
\(244\) | 12.4843 | 0.799228 | ||||||||
\(245\) | 1.68538 | 0.107675 | ||||||||
\(246\) | −19.5715 | −1.24784 | ||||||||
\(247\) | 1.20735 | 0.0768217 | ||||||||
\(248\) | −8.68660 | −0.551600 | ||||||||
\(249\) | −19.8030 | −1.25496 | ||||||||
\(250\) | 7.71983 | 0.488245 | ||||||||
\(251\) | 24.7199 | 1.56031 | 0.780153 | − | 0.625588i | \(-0.215141\pi\) | ||||
0.780153 | + | 0.625588i | \(0.215141\pi\) | |||||||
\(252\) | 17.7010 | 1.11506 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 15.5597 | 0.976304 | ||||||||
\(255\) | −12.5648 | −0.786841 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.535384 | 0.0333964 | 0.0166982 | − | 0.999861i | \(-0.494685\pi\) | ||||
0.0166982 | + | 0.999861i | \(0.494685\pi\) | |||||||
\(258\) | −12.5237 | −0.779694 | ||||||||
\(259\) | −3.05281 | −0.189692 | ||||||||
\(260\) | −1.00082 | −0.0620684 | ||||||||
\(261\) | 31.0898 | 1.92441 | ||||||||
\(262\) | 14.8982 | 0.920412 | ||||||||
\(263\) | 9.20025 | 0.567312 | 0.283656 | − | 0.958926i | \(-0.408453\pi\) | ||||
0.283656 | + | 0.958926i | \(0.408453\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.74704 | 0.414468 | ||||||||
\(266\) | 2.22864 | 0.136647 | ||||||||
\(267\) | −20.1004 | −1.23012 | ||||||||
\(268\) | −11.6774 | −0.713308 | ||||||||
\(269\) | −11.3073 | −0.689420 | −0.344710 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344710 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(270\) | −13.5528 | −0.824800 | ||||||||
\(271\) | 19.1989 | 1.16625 | 0.583124 | − | 0.812383i | \(-0.301830\pi\) | ||||
0.583124 | + | 0.812383i | \(0.301830\pi\) | |||||||
\(272\) | 4.58220 | 0.277837 | ||||||||
\(273\) | 8.90083 | 0.538703 | ||||||||
\(274\) | 10.1562 | 0.613558 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.83550 | −0.351256 | ||||||||
\(277\) | 5.91887 | 0.355630 | 0.177815 | − | 0.984064i | \(-0.443097\pi\) | ||||
0.177815 | + | 0.984064i | \(0.443097\pi\) | |||||||
\(278\) | 11.3949 | 0.683418 | ||||||||
\(279\) | −68.9934 | −4.13053 | ||||||||
\(280\) | −1.84741 | −0.110404 | ||||||||
\(281\) | −17.5195 | −1.04513 | −0.522563 | − | 0.852600i | \(-0.675024\pi\) | ||||
−0.522563 | + | 0.852600i | \(0.675024\pi\) | |||||||
\(282\) | −26.2213 | −1.56146 | ||||||||
\(283\) | 5.40443 | 0.321260 | 0.160630 | − | 0.987015i | \(-0.448647\pi\) | ||||
0.160630 | + | 0.987015i | \(0.448647\pi\) | |||||||
\(284\) | 5.40088 | 0.320483 | ||||||||
\(285\) | −2.74210 | −0.162428 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.1858 | −0.778332 | ||||||||
\(288\) | 7.94251 | 0.468017 | ||||||||
\(289\) | 3.99655 | 0.235091 | ||||||||
\(290\) | −3.24478 | −0.190540 | ||||||||
\(291\) | 57.3515 | 3.36200 | ||||||||
\(292\) | −13.2594 | −0.775946 | ||||||||
\(293\) | 6.26565 | 0.366043 | 0.183022 | − | 0.983109i | \(-0.441412\pi\) | ||||
0.183022 | + | 0.983109i | \(0.441412\pi\) | |||||||
\(294\) | −6.72562 | −0.392246 | ||||||||
\(295\) | 0.0866846 | 0.00504697 | ||||||||
\(296\) | −1.36981 | −0.0796185 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.6310 | −0.963406 | ||||||||
\(299\) | −2.12986 | −0.123173 | ||||||||
\(300\) | −14.2667 | −0.823687 | ||||||||
\(301\) | −8.43752 | −0.486331 | ||||||||
\(302\) | −18.0434 | −1.03828 | ||||||||
\(303\) | −0.132973 | −0.00763907 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −10.3488 | −0.592571 | ||||||||
\(306\) | 36.3941 | 2.08052 | ||||||||
\(307\) | −0.0433912 | −0.00247647 | −0.00123823 | − | 0.999999i | \(-0.500394\pi\) | ||||
−0.00123823 | + | 0.999999i | \(0.500394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 57.2155 | 3.25488 | ||||||||
\(310\) | 7.20070 | 0.408972 | ||||||||
\(311\) | 2.42902 | 0.137737 | 0.0688687 | − | 0.997626i | \(-0.478061\pi\) | ||||
0.0688687 | + | 0.997626i | \(0.478061\pi\) | |||||||
\(312\) | 3.99384 | 0.226107 | ||||||||
\(313\) | 0.817587 | 0.0462127 | 0.0231064 | − | 0.999733i | \(-0.492644\pi\) | ||||
0.0231064 | + | 0.999733i | \(0.492644\pi\) | |||||||
\(314\) | −17.1908 | −0.970134 | ||||||||
\(315\) | −14.6731 | −0.826736 | ||||||||
\(316\) | −2.32315 | −0.130688 | ||||||||
\(317\) | −18.5495 | −1.04184 | −0.520922 | − | 0.853604i | \(-0.674412\pi\) | ||||
−0.520922 | + | 0.853604i | \(0.674412\pi\) | |||||||
\(318\) | −26.9245 | −1.50985 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.828943 | −0.0463393 | ||||||||
\(321\) | 48.9744 | 2.73349 | ||||||||
\(322\) | −3.93151 | −0.219094 | ||||||||
\(323\) | 4.58220 | 0.254960 | ||||||||
\(324\) | 30.2559 | 1.68088 | ||||||||
\(325\) | −5.20711 | −0.288839 | ||||||||
\(326\) | 9.91065 | 0.548900 | ||||||||
\(327\) | 0.583939 | 0.0322919 | ||||||||
\(328\) | −5.91652 | −0.326685 | ||||||||
\(329\) | −17.6659 | −0.973952 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.31311 | −0.237070 | −0.118535 | − | 0.992950i | \(-0.537820\pi\) | ||||
−0.118535 | + | 0.992950i | \(0.537820\pi\) | |||||||
\(332\) | −5.98648 | −0.328551 | ||||||||
\(333\) | −10.8797 | −0.596204 | ||||||||
\(334\) | −13.6271 | −0.745642 | ||||||||
\(335\) | 9.67987 | 0.528868 | ||||||||
\(336\) | 7.37221 | 0.402187 | ||||||||
\(337\) | 1.35344 | 0.0737266 | 0.0368633 | − | 0.999320i | \(-0.488263\pi\) | ||||
0.0368633 | + | 0.999320i | \(0.488263\pi\) | |||||||
\(338\) | −11.5423 | −0.627819 | ||||||||
\(339\) | 18.6490 | 1.01288 | ||||||||
\(340\) | −3.79838 | −0.205996 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.94251 | 0.429482 | ||||||||
\(343\) | −20.1317 | −1.08701 | ||||||||
\(344\) | −3.78596 | −0.204125 | ||||||||
\(345\) | 4.83730 | 0.260431 | ||||||||
\(346\) | −11.4678 | −0.616513 | ||||||||
\(347\) | −14.9394 | −0.801988 | −0.400994 | − | 0.916081i | \(-0.631335\pi\) | ||||
−0.400994 | + | 0.916081i | \(0.631335\pi\) | |||||||
\(348\) | 12.9485 | 0.694112 | ||||||||
\(349\) | 8.42846 | 0.451165 | 0.225583 | − | 0.974224i | \(-0.427571\pi\) | ||||
0.225583 | + | 0.974224i | \(0.427571\pi\) | |||||||
\(350\) | −9.61179 | −0.513772 | ||||||||
\(351\) | 19.7396 | 1.05362 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.1828 | −1.55324 | −0.776621 | − | 0.629968i | \(-0.783068\pi\) | ||||
−0.776621 | + | 0.629968i | \(0.783068\pi\) | |||||||
\(354\) | −0.345920 | −0.0183854 | ||||||||
\(355\) | −4.47702 | −0.237616 | ||||||||
\(356\) | −6.07639 | −0.322048 | ||||||||
\(357\) | 33.7810 | 1.78788 | ||||||||
\(358\) | 0.219190 | 0.0115846 | ||||||||
\(359\) | −26.4680 | −1.39693 | −0.698465 | − | 0.715644i | \(-0.746133\pi\) | ||||
−0.698465 | + | 0.715644i | \(0.746133\pi\) | |||||||
\(360\) | −6.58389 | −0.347001 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −24.9347 | −1.31054 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.69074 | 0.141033 | ||||||||
\(365\) | 10.9913 | 0.575309 | ||||||||
\(366\) | 41.2975 | 2.15866 | ||||||||
\(367\) | −20.9635 | −1.09429 | −0.547143 | − | 0.837039i | \(-0.684285\pi\) | ||||
−0.547143 | + | 0.837039i | \(0.684285\pi\) | |||||||
\(368\) | −1.76409 | −0.0919593 | ||||||||
\(369\) | −46.9920 | −2.44631 | ||||||||
\(370\) | 1.13549 | 0.0590315 | ||||||||
\(371\) | −18.1396 | −0.941762 | ||||||||
\(372\) | −28.7348 | −1.48983 | ||||||||
\(373\) | −34.2399 | −1.77288 | −0.886438 | − | 0.462847i | \(-0.846828\pi\) | ||||
−0.886438 | + | 0.462847i | \(0.846828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.5368 | 1.31871 | ||||||||
\(376\) | −7.92677 | −0.408792 | ||||||||
\(377\) | 4.72599 | 0.243401 | ||||||||
\(378\) | 36.4372 | 1.87413 | ||||||||
\(379\) | 8.74108 | 0.448999 | 0.224500 | − | 0.974474i | \(-0.427925\pi\) | ||||
0.224500 | + | 0.974474i | \(0.427925\pi\) | |||||||
\(380\) | −0.828943 | −0.0425239 | ||||||||
\(381\) | 51.4707 | 2.63693 | ||||||||
\(382\) | −9.25309 | −0.473429 | ||||||||
\(383\) | 4.17010 | 0.213082 | 0.106541 | − | 0.994308i | \(-0.466022\pi\) | ||||
0.106541 | + | 0.994308i | \(0.466022\pi\) | |||||||
\(384\) | 3.30795 | 0.168808 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.1815 | 0.823615 | ||||||||
\(387\) | −30.0700 | −1.52854 | ||||||||
\(388\) | 17.3375 | 0.880178 | ||||||||
\(389\) | −7.70695 | −0.390758 | −0.195379 | − | 0.980728i | \(-0.562594\pi\) | ||||
−0.195379 | + | 0.980728i | \(0.562594\pi\) | |||||||
\(390\) | −3.31067 | −0.167642 | ||||||||
\(391\) | −8.08339 | −0.408795 | ||||||||
\(392\) | −2.03317 | −0.102691 | ||||||||
\(393\) | 49.2823 | 2.48596 | ||||||||
\(394\) | 14.4283 | 0.726885 | ||||||||
\(395\) | 1.92576 | 0.0968957 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.6939 | 1.38991 | 0.694957 | − | 0.719051i | \(-0.255423\pi\) | ||||
0.694957 | + | 0.719051i | \(0.255423\pi\) | |||||||
\(398\) | 12.4819 | 0.625663 | ||||||||
\(399\) | 7.37221 | 0.369072 | ||||||||
\(400\) | −4.31285 | −0.215643 | ||||||||
\(401\) | −28.3005 | −1.41326 | −0.706630 | − | 0.707583i | \(-0.749786\pi\) | ||||
−0.706630 | + | 0.707583i | \(0.749786\pi\) | |||||||
\(402\) | −38.6281 | −1.92659 | ||||||||
\(403\) | −10.4878 | −0.522432 | ||||||||
\(404\) | −0.0401979 | −0.00199992 | ||||||||
\(405\) | −25.0804 | −1.24626 | ||||||||
\(406\) | 8.72369 | 0.432949 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 15.1577 | 0.750416 | ||||||||
\(409\) | −7.15765 | −0.353923 | −0.176961 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176961 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(410\) | 4.90446 | 0.242214 | ||||||||
\(411\) | 33.5961 | 1.65718 | ||||||||
\(412\) | 17.2964 | 0.852132 | ||||||||
\(413\) | −0.233054 | −0.0114678 | ||||||||
\(414\) | −14.0113 | −0.688616 | ||||||||
\(415\) | 4.96245 | 0.243597 | ||||||||
\(416\) | 1.20735 | 0.0591951 | ||||||||
\(417\) | 37.6936 | 1.84586 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.45181 | 0.461751 | 0.230876 | − | 0.972983i | \(-0.425841\pi\) | ||||
0.230876 | + | 0.972983i | \(0.425841\pi\) | |||||||
\(420\) | −6.11115 | −0.298193 | ||||||||
\(421\) | 27.2670 | 1.32891 | 0.664455 | − | 0.747328i | \(-0.268664\pi\) | ||||
0.664455 | + | 0.747328i | \(0.268664\pi\) | |||||||
\(422\) | 24.4896 | 1.19214 | ||||||||
\(423\) | −62.9584 | −3.06114 | ||||||||
\(424\) | −8.13933 | −0.395281 | ||||||||
\(425\) | −19.7624 | −0.958615 | ||||||||
\(426\) | 17.8658 | 0.865602 | ||||||||
\(427\) | 27.8231 | 1.34645 | ||||||||
\(428\) | 14.8051 | 0.715631 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.13834 | 0.151344 | ||||||||
\(431\) | −1.36032 | −0.0655245 | −0.0327622 | − | 0.999463i | \(-0.510430\pi\) | ||||
−0.0327622 | + | 0.999463i | \(0.510430\pi\) | |||||||
\(432\) | 16.3495 | 0.786618 | ||||||||
\(433\) | 26.1728 | 1.25779 | 0.628893 | − | 0.777492i | \(-0.283508\pi\) | ||||
0.628893 | + | 0.777492i | \(0.283508\pi\) | |||||||
\(434\) | −19.3593 | −0.929276 | ||||||||
\(435\) | −10.7336 | −0.514635 | ||||||||
\(436\) | 0.176526 | 0.00845407 | ||||||||
\(437\) | −1.76409 | −0.0843877 | ||||||||
\(438\) | −43.8613 | −2.09577 | ||||||||
\(439\) | −9.79442 | −0.467462 | −0.233731 | − | 0.972301i | \(-0.575094\pi\) | ||||
−0.233731 | + | 0.972301i | \(0.575094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.1485 | −0.768975 | ||||||||
\(442\) | 5.53231 | 0.263145 | ||||||||
\(443\) | −20.4676 | −0.972447 | −0.486224 | − | 0.873834i | \(-0.661626\pi\) | ||||
−0.486224 | + | 0.873834i | \(0.661626\pi\) | |||||||
\(444\) | −4.53125 | −0.215044 | ||||||||
\(445\) | 5.03699 | 0.238776 | ||||||||
\(446\) | −23.0348 | −1.09073 | ||||||||
\(447\) | −55.0144 | −2.60209 | ||||||||
\(448\) | 2.22864 | 0.105293 | ||||||||
\(449\) | 40.4545 | 1.90917 | 0.954584 | − | 0.297943i | \(-0.0963004\pi\) | ||||
0.954584 | + | 0.297943i | \(0.0963004\pi\) | |||||||
\(450\) | −34.2549 | −1.61479 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5.63764 | 0.265172 | ||||||||
\(453\) | −59.6865 | −2.80431 | ||||||||
\(454\) | −11.6050 | −0.544648 | ||||||||
\(455\) | −2.23047 | −0.104566 | ||||||||
\(456\) | 3.30795 | 0.154909 | ||||||||
\(457\) | 31.1469 | 1.45699 | 0.728495 | − | 0.685051i | \(-0.240220\pi\) | ||||
0.728495 | + | 0.685051i | \(0.240220\pi\) | |||||||
\(458\) | 10.8274 | 0.505930 | ||||||||
\(459\) | 74.9169 | 3.49682 | ||||||||
\(460\) | 1.46233 | 0.0681814 | ||||||||
\(461\) | −28.2437 | −1.31544 | −0.657719 | − | 0.753263i | \(-0.728479\pi\) | ||||
−0.657719 | + | 0.753263i | \(0.728479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0244 | −1.30240 | −0.651201 | − | 0.758905i | \(-0.725735\pi\) | ||||
−0.651201 | + | 0.758905i | \(0.725735\pi\) | |||||||
\(464\) | 3.91436 | 0.181719 | ||||||||
\(465\) | 23.8195 | 1.10460 | ||||||||
\(466\) | 0.972932 | 0.0450702 | ||||||||
\(467\) | −36.0872 | −1.66992 | −0.834959 | − | 0.550312i | \(-0.814509\pi\) | ||||
−0.834959 | + | 0.550312i | \(0.814509\pi\) | |||||||
\(468\) | 9.58937 | 0.443269 | ||||||||
\(469\) | −26.0246 | −1.20170 | ||||||||
\(470\) | 6.57084 | 0.303090 | ||||||||
\(471\) | −56.8663 | −2.62026 | ||||||||
\(472\) | −0.104572 | −0.00481334 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −7.68487 | −0.352978 | ||||||||
\(475\) | −4.31285 | −0.197887 | ||||||||
\(476\) | 10.2121 | 0.468069 | ||||||||
\(477\) | −64.6467 | −2.95997 | ||||||||
\(478\) | −16.0095 | −0.732258 | ||||||||
\(479\) | −26.3357 | −1.20331 | −0.601656 | − | 0.798756i | \(-0.705492\pi\) | ||||
−0.601656 | + | 0.798756i | \(0.705492\pi\) | |||||||
\(480\) | −2.74210 | −0.125159 | ||||||||
\(481\) | −1.65383 | −0.0754083 | ||||||||
\(482\) | 11.2997 | 0.514688 | ||||||||
\(483\) | −13.0052 | −0.591758 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.3718 | −0.652590 | ||||||||
\(486\) | 51.0363 | 2.31505 | ||||||||
\(487\) | −7.80731 | −0.353783 | −0.176891 | − | 0.984230i | \(-0.556604\pi\) | ||||
−0.176891 | + | 0.984230i | \(0.556604\pi\) | |||||||
\(488\) | 12.4843 | 0.565139 | ||||||||
\(489\) | 32.7839 | 1.48254 | ||||||||
\(490\) | 1.68538 | 0.0761379 | ||||||||
\(491\) | −8.97408 | −0.404994 | −0.202497 | − | 0.979283i | \(-0.564906\pi\) | ||||
−0.202497 | + | 0.979283i | \(0.564906\pi\) | |||||||
\(492\) | −19.5715 | −0.882353 | ||||||||
\(493\) | 17.9364 | 0.807813 | ||||||||
\(494\) | 1.20735 | 0.0543211 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.68660 | −0.390040 | ||||||||
\(497\) | 12.0366 | 0.539916 | ||||||||
\(498\) | −19.8030 | −0.887391 | ||||||||
\(499\) | 29.6042 | 1.32527 | 0.662633 | − | 0.748944i | \(-0.269439\pi\) | ||||
0.662633 | + | 0.748944i | \(0.269439\pi\) | |||||||
\(500\) | 7.71983 | 0.345241 | ||||||||
\(501\) | −45.0777 | −2.01393 | ||||||||
\(502\) | 24.7199 | 1.10330 | ||||||||
\(503\) | 5.34001 | 0.238099 | 0.119050 | − | 0.992888i | \(-0.462015\pi\) | ||||
0.119050 | + | 0.992888i | \(0.462015\pi\) | |||||||
\(504\) | 17.7010 | 0.788464 | ||||||||
\(505\) | 0.0333218 | 0.00148280 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.1813 | −1.69569 | ||||||||
\(508\) | 15.5597 | 0.690351 | ||||||||
\(509\) | −21.7883 | −0.965749 | −0.482874 | − | 0.875690i | \(-0.660407\pi\) | ||||
−0.482874 | + | 0.875690i | \(0.660407\pi\) | |||||||
\(510\) | −12.5648 | −0.556381 | ||||||||
\(511\) | −29.5504 | −1.30723 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 16.3495 | 0.721850 | ||||||||
\(514\) | 0.535384 | 0.0236148 | ||||||||
\(515\) | −14.3377 | −0.631796 | ||||||||
\(516\) | −12.5237 | −0.551327 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.05281 | −0.134133 | ||||||||
\(519\) | −37.9349 | −1.66516 | ||||||||
\(520\) | −1.00082 | −0.0438890 | ||||||||
\(521\) | 15.5138 | 0.679674 | 0.339837 | − | 0.940484i | \(-0.389628\pi\) | ||||
0.339837 | + | 0.940484i | \(0.389628\pi\) | |||||||
\(522\) | 31.0898 | 1.36076 | ||||||||
\(523\) | 21.5143 | 0.940757 | 0.470378 | − | 0.882465i | \(-0.344117\pi\) | ||||
0.470378 | + | 0.882465i | \(0.344117\pi\) | |||||||
\(524\) | 14.8982 | 0.650829 | ||||||||
\(525\) | −31.7953 | −1.38766 | ||||||||
\(526\) | 9.20025 | 0.401150 | ||||||||
\(527\) | −39.8037 | −1.73388 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8880 | −0.864696 | ||||||||
\(530\) | 6.74704 | 0.293073 | ||||||||
\(531\) | −0.830567 | −0.0360436 | ||||||||
\(532\) | 2.22864 | 0.0966237 | ||||||||
\(533\) | −7.14330 | −0.309411 | ||||||||
\(534\) | −20.1004 | −0.869829 | ||||||||
\(535\) | −12.2726 | −0.530590 | ||||||||
\(536\) | −11.6774 | −0.504385 | ||||||||
\(537\) | 0.725069 | 0.0312890 | ||||||||
\(538\) | −11.3073 | −0.487494 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −13.5528 | −0.583222 | ||||||||
\(541\) | 13.5322 | 0.581797 | 0.290898 | − | 0.956754i | \(-0.406046\pi\) | ||||
0.290898 | + | 0.956754i | \(0.406046\pi\) | |||||||
\(542\) | 19.1989 | 0.824662 | ||||||||
\(543\) | −82.4825 | −3.53966 | ||||||||
\(544\) | 4.58220 | 0.196460 | ||||||||
\(545\) | −0.146330 | −0.00626810 | ||||||||
\(546\) | 8.90083 | 0.380920 | ||||||||
\(547\) | 29.3177 | 1.25353 | 0.626767 | − | 0.779207i | \(-0.284378\pi\) | ||||
0.626767 | + | 0.779207i | \(0.284378\pi\) | |||||||
\(548\) | 10.1562 | 0.433851 | ||||||||
\(549\) | 99.1569 | 4.23191 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.91436 | 0.166757 | ||||||||
\(552\) | −5.83550 | −0.248375 | ||||||||
\(553\) | −5.17747 | −0.220168 | ||||||||
\(554\) | 5.91887 | 0.251469 | ||||||||
\(555\) | 3.75615 | 0.159440 | ||||||||
\(556\) | 11.3949 | 0.483250 | ||||||||
\(557\) | −3.84810 | −0.163049 | −0.0815246 | − | 0.996671i | \(-0.525979\pi\) | ||||
−0.0815246 | + | 0.996671i | \(0.525979\pi\) | |||||||
\(558\) | −68.9934 | −2.92072 | ||||||||
\(559\) | −4.57096 | −0.193331 | ||||||||
\(560\) | −1.84741 | −0.0780675 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.5195 | −0.739016 | ||||||||
\(563\) | −21.8709 | −0.921750 | −0.460875 | − | 0.887465i | \(-0.652464\pi\) | ||||
−0.460875 | + | 0.887465i | \(0.652464\pi\) | |||||||
\(564\) | −26.2213 | −1.10412 | ||||||||
\(565\) | −4.67329 | −0.196607 | ||||||||
\(566\) | 5.40443 | 0.227165 | ||||||||
\(567\) | 67.4295 | 2.83177 | ||||||||
\(568\) | 5.40088 | 0.226616 | ||||||||
\(569\) | −24.1303 | −1.01159 | −0.505797 | − | 0.862652i | \(-0.668802\pi\) | ||||
−0.505797 | + | 0.862652i | \(0.668802\pi\) | |||||||
\(570\) | −2.74210 | −0.114854 | ||||||||
\(571\) | −24.3325 | −1.01828 | −0.509141 | − | 0.860683i | \(-0.670037\pi\) | ||||
−0.509141 | + | 0.860683i | \(0.670037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.6087 | −1.27870 | ||||||||
\(574\) | −13.1858 | −0.550364 | ||||||||
\(575\) | 7.60824 | 0.317286 | ||||||||
\(576\) | 7.94251 | 0.330938 | ||||||||
\(577\) | 0.513047 | 0.0213584 | 0.0106792 | − | 0.999943i | \(-0.496601\pi\) | ||||
0.0106792 | + | 0.999943i | \(0.496601\pi\) | |||||||
\(578\) | 3.99655 | 0.166234 | ||||||||
\(579\) | 53.5274 | 2.22452 | ||||||||
\(580\) | −3.24478 | −0.134732 | ||||||||
\(581\) | −13.3417 | −0.553507 | ||||||||
\(582\) | 57.3515 | 2.37730 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −13.2594 | −0.548677 | ||||||||
\(585\) | −7.94904 | −0.328652 | ||||||||
\(586\) | 6.26565 | 0.258832 | ||||||||
\(587\) | 9.67182 | 0.399199 | 0.199599 | − | 0.979878i | \(-0.436036\pi\) | ||||
0.199599 | + | 0.979878i | \(0.436036\pi\) | |||||||
\(588\) | −6.72562 | −0.277360 | ||||||||
\(589\) | −8.68660 | −0.357925 | ||||||||
\(590\) | 0.0866846 | 0.00356875 | ||||||||
\(591\) | 47.7279 | 1.96326 | ||||||||
\(592\) | −1.36981 | −0.0562987 | ||||||||
\(593\) | 41.5780 | 1.70740 | 0.853701 | − | 0.520763i | \(-0.174352\pi\) | ||||
0.853701 | + | 0.520763i | \(0.174352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.46522 | −0.347040 | ||||||||
\(596\) | −16.6310 | −0.681231 | ||||||||
\(597\) | 41.2896 | 1.68987 | ||||||||
\(598\) | −2.12986 | −0.0870967 | ||||||||
\(599\) | 9.65115 | 0.394335 | 0.197168 | − | 0.980370i | \(-0.436826\pi\) | ||||
0.197168 | + | 0.980370i | \(0.436826\pi\) | |||||||
\(600\) | −14.2667 | −0.582435 | ||||||||
\(601\) | 10.0551 | 0.410157 | 0.205078 | − | 0.978746i | \(-0.434255\pi\) | ||||
0.205078 | + | 0.978746i | \(0.434255\pi\) | |||||||
\(602\) | −8.43752 | −0.343888 | ||||||||
\(603\) | −92.7475 | −3.77697 | ||||||||
\(604\) | −18.0434 | −0.734174 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.132973 | −0.00540164 | ||||||||
\(607\) | 43.7009 | 1.77377 | 0.886883 | − | 0.461995i | \(-0.152866\pi\) | ||||
0.886883 | + | 0.461995i | \(0.152866\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 28.8575 | 1.16936 | ||||||||
\(610\) | −10.3488 | −0.419011 | ||||||||
\(611\) | −9.57036 | −0.387175 | ||||||||
\(612\) | 36.3941 | 1.47115 | ||||||||
\(613\) | −4.41727 | −0.178412 | −0.0892060 | − | 0.996013i | \(-0.528433\pi\) | ||||
−0.0892060 | + | 0.996013i | \(0.528433\pi\) | |||||||
\(614\) | −0.0433912 | −0.00175113 | ||||||||
\(615\) | 16.2237 | 0.654202 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.7853 | 1.15885 | 0.579427 | − | 0.815024i | \(-0.303277\pi\) | ||||
0.579427 | + | 0.815024i | \(0.303277\pi\) | |||||||
\(618\) | 57.2155 | 2.30155 | ||||||||
\(619\) | −12.6782 | −0.509578 | −0.254789 | − | 0.966997i | \(-0.582006\pi\) | ||||
−0.254789 | + | 0.966997i | \(0.582006\pi\) | |||||||
\(620\) | 7.20070 | 0.289187 | ||||||||
\(621\) | −28.8420 | −1.15739 | ||||||||
\(622\) | 2.42902 | 0.0973950 | ||||||||
\(623\) | −13.5421 | −0.542552 | ||||||||
\(624\) | 3.99384 | 0.159882 | ||||||||
\(625\) | 15.1650 | 0.606599 | ||||||||
\(626\) | 0.817587 | 0.0326773 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.1908 | −0.685989 | ||||||||
\(629\) | −6.27673 | −0.250270 | ||||||||
\(630\) | −14.6731 | −0.584590 | ||||||||
\(631\) | 13.7759 | 0.548411 | 0.274205 | − | 0.961671i | \(-0.411585\pi\) | ||||
0.274205 | + | 0.961671i | \(0.411585\pi\) | |||||||
\(632\) | −2.32315 | −0.0924101 | ||||||||
\(633\) | 81.0103 | 3.21987 | ||||||||
\(634\) | −18.5495 | −0.736695 | ||||||||
\(635\) | −12.8981 | −0.511847 | ||||||||
\(636\) | −26.9245 | −1.06762 | ||||||||
\(637\) | −2.45475 | −0.0972606 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 42.8965 | 1.69696 | ||||||||
\(640\) | −0.828943 | −0.0327669 | ||||||||
\(641\) | −9.65449 | −0.381329 | −0.190665 | − | 0.981655i | \(-0.561064\pi\) | ||||
−0.190665 | + | 0.981655i | \(0.561064\pi\) | |||||||
\(642\) | 48.9744 | 1.93287 | ||||||||
\(643\) | −18.9601 | −0.747713 | −0.373857 | − | 0.927487i | \(-0.621965\pi\) | ||||
−0.373857 | + | 0.927487i | \(0.621965\pi\) | |||||||
\(644\) | −3.93151 | −0.154923 | ||||||||
\(645\) | 10.3815 | 0.408770 | ||||||||
\(646\) | 4.58220 | 0.180284 | ||||||||
\(647\) | −1.35149 | −0.0531325 | −0.0265662 | − | 0.999647i | \(-0.508457\pi\) | ||||
−0.0265662 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(648\) | 30.2559 | 1.18856 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.20711 | −0.204240 | ||||||||
\(651\) | −64.0395 | −2.50991 | ||||||||
\(652\) | 9.91065 | 0.388131 | ||||||||
\(653\) | 26.2017 | 1.02535 | 0.512676 | − | 0.858582i | \(-0.328654\pi\) | ||||
0.512676 | + | 0.858582i | \(0.328654\pi\) | |||||||
\(654\) | 0.583939 | 0.0228338 | ||||||||
\(655\) | −12.3497 | −0.482544 | ||||||||
\(656\) | −5.91652 | −0.231001 | ||||||||
\(657\) | −105.313 | −4.10864 | ||||||||
\(658\) | −17.6659 | −0.688688 | ||||||||
\(659\) | 10.9786 | 0.427666 | 0.213833 | − | 0.976870i | \(-0.431405\pi\) | ||||
0.213833 | + | 0.976870i | \(0.431405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0499 | 0.779851 | 0.389926 | − | 0.920846i | \(-0.372501\pi\) | ||||
0.389926 | + | 0.920846i | \(0.372501\pi\) | |||||||
\(662\) | −4.31311 | −0.167634 | ||||||||
\(663\) | 18.3006 | 0.710735 | ||||||||
\(664\) | −5.98648 | −0.232320 | ||||||||
\(665\) | −1.84741 | −0.0716397 | ||||||||
\(666\) | −10.8797 | −0.421580 | ||||||||
\(667\) | −6.90526 | −0.267373 | ||||||||
\(668\) | −13.6271 | −0.527249 | ||||||||
\(669\) | −76.1978 | −2.94598 | ||||||||
\(670\) | 9.67987 | 0.373966 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 7.37221 | 0.284389 | ||||||||
\(673\) | 1.57266 | 0.0606218 | 0.0303109 | − | 0.999541i | \(-0.490350\pi\) | ||||
0.0303109 | + | 0.999541i | \(0.490350\pi\) | |||||||
\(674\) | 1.35344 | 0.0521326 | ||||||||
\(675\) | −70.5132 | −2.71405 | ||||||||
\(676\) | −11.5423 | −0.443935 | ||||||||
\(677\) | 47.4839 | 1.82495 | 0.912476 | − | 0.409130i | \(-0.134168\pi\) | ||||
0.912476 | + | 0.409130i | \(0.134168\pi\) | |||||||
\(678\) | 18.6490 | 0.716211 | ||||||||
\(679\) | 38.6390 | 1.48283 | ||||||||
\(680\) | −3.79838 | −0.145661 | ||||||||
\(681\) | −38.3886 | −1.47105 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.3311 | 1.16059 | 0.580293 | − | 0.814408i | \(-0.302938\pi\) | ||||
0.580293 | + | 0.814408i | \(0.302938\pi\) | |||||||
\(684\) | 7.94251 | 0.303689 | ||||||||
\(685\) | −8.41891 | −0.321670 | ||||||||
\(686\) | −20.1317 | −0.768631 | ||||||||
\(687\) | 35.8163 | 1.36648 | ||||||||
\(688\) | −3.78596 | −0.144338 | ||||||||
\(689\) | −9.82700 | −0.374379 | ||||||||
\(690\) | 4.83730 | 0.184153 | ||||||||
\(691\) | 11.4962 | 0.437337 | 0.218669 | − | 0.975799i | \(-0.429829\pi\) | ||||
0.218669 | + | 0.975799i | \(0.429829\pi\) | |||||||
\(692\) | −11.4678 | −0.435941 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.9394 | −0.567091 | ||||||||
\(695\) | −9.44569 | −0.358295 | ||||||||
\(696\) | 12.9485 | 0.490811 | ||||||||
\(697\) | −27.1107 | −1.02689 | ||||||||
\(698\) | 8.42846 | 0.319022 | ||||||||
\(699\) | 3.21841 | 0.121731 | ||||||||
\(700\) | −9.61179 | −0.363291 | ||||||||
\(701\) | −42.5115 | −1.60564 | −0.802818 | − | 0.596224i | \(-0.796667\pi\) | ||||
−0.802818 | + | 0.596224i | \(0.796667\pi\) | |||||||
\(702\) | 19.7396 | 0.745023 | ||||||||
\(703\) | −1.36981 | −0.0516633 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.7360 | 0.818624 | ||||||||
\(706\) | −29.1828 | −1.09831 | ||||||||
\(707\) | −0.0895866 | −0.00336925 | ||||||||
\(708\) | −0.345920 | −0.0130005 | ||||||||
\(709\) | 0.138545 | 0.00520315 | 0.00260158 | − | 0.999997i | \(-0.499172\pi\) | ||||
0.00260158 | + | 0.999997i | \(0.499172\pi\) | |||||||
\(710\) | −4.47702 | −0.168020 | ||||||||
\(711\) | −18.4517 | −0.691992 | ||||||||
\(712\) | −6.07639 | −0.227722 | ||||||||
\(713\) | 15.3239 | 0.573885 | ||||||||
\(714\) | 33.7810 | 1.26422 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.219190 | 0.00819152 | ||||||||
\(717\) | −52.9586 | −1.97777 | ||||||||
\(718\) | −26.4680 | −0.987778 | ||||||||
\(719\) | 5.55518 | 0.207173 | 0.103587 | − | 0.994620i | \(-0.466968\pi\) | ||||
0.103587 | + | 0.994620i | \(0.466968\pi\) | |||||||
\(720\) | −6.58389 | −0.245367 | ||||||||
\(721\) | 38.5474 | 1.43558 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 37.3788 | 1.39013 | ||||||||
\(724\) | −24.9347 | −0.926689 | ||||||||
\(725\) | −16.8820 | −0.626984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.2810 | −1.56811 | −0.784057 | − | 0.620688i | \(-0.786853\pi\) | ||||
−0.784057 | + | 0.620688i | \(0.786853\pi\) | |||||||
\(728\) | 2.69074 | 0.0997255 | ||||||||
\(729\) | 78.0575 | 2.89102 | ||||||||
\(730\) | 10.9913 | 0.406805 | ||||||||
\(731\) | −17.3480 | −0.641639 | ||||||||
\(732\) | 41.2975 | 1.52640 | ||||||||
\(733\) | 30.8346 | 1.13890 | 0.569451 | − | 0.822025i | \(-0.307156\pi\) | ||||
0.569451 | + | 0.822025i | \(0.307156\pi\) | |||||||
\(734\) | −20.9635 | −0.773778 | ||||||||
\(735\) | 5.57516 | 0.205643 | ||||||||
\(736\) | −1.76409 | −0.0650251 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −46.9920 | −1.72980 | ||||||||
\(739\) | 3.47185 | 0.127714 | 0.0638569 | − | 0.997959i | \(-0.479660\pi\) | ||||
0.0638569 | + | 0.997959i | \(0.479660\pi\) | |||||||
\(740\) | 1.13549 | 0.0417415 | ||||||||
\(741\) | 3.99384 | 0.146717 | ||||||||
\(742\) | −18.1396 | −0.665926 | ||||||||
\(743\) | 41.6207 | 1.52692 | 0.763458 | − | 0.645857i | \(-0.223500\pi\) | ||||
0.763458 | + | 0.645857i | \(0.223500\pi\) | |||||||
\(744\) | −28.7348 | −1.05347 | ||||||||
\(745\) | 13.7861 | 0.505085 | ||||||||
\(746\) | −34.2399 | −1.25361 | ||||||||
\(747\) | −47.5477 | −1.73968 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.9952 | 1.20562 | ||||||||
\(750\) | 25.5368 | 0.932471 | ||||||||
\(751\) | −21.1375 | −0.771317 | −0.385658 | − | 0.922642i | \(-0.626026\pi\) | ||||
−0.385658 | + | 0.922642i | \(0.626026\pi\) | |||||||
\(752\) | −7.92677 | −0.289059 | ||||||||
\(753\) | 81.7721 | 2.97994 | ||||||||
\(754\) | 4.72599 | 0.172110 | ||||||||
\(755\) | 14.9569 | 0.544338 | ||||||||
\(756\) | 36.4372 | 1.32521 | ||||||||
\(757\) | −0.324892 | −0.0118084 | −0.00590419 | − | 0.999983i | \(-0.501879\pi\) | ||||
−0.00590419 | + | 0.999983i | \(0.501879\pi\) | |||||||
\(758\) | 8.74108 | 0.317490 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.828943 | −0.0300689 | ||||||||
\(761\) | −7.39942 | −0.268229 | −0.134114 | − | 0.990966i | \(-0.542819\pi\) | ||||
−0.134114 | + | 0.990966i | \(0.542819\pi\) | |||||||
\(762\) | 51.4707 | 1.86459 | ||||||||
\(763\) | 0.393413 | 0.0142425 | ||||||||
\(764\) | −9.25309 | −0.334765 | ||||||||
\(765\) | −30.1687 | −1.09075 | ||||||||
\(766\) | 4.17010 | 0.150672 | ||||||||
\(767\) | −0.126255 | −0.00455881 | ||||||||
\(768\) | 3.30795 | 0.119365 | ||||||||
\(769\) | −26.6836 | −0.962235 | −0.481118 | − | 0.876656i | \(-0.659769\pi\) | ||||
−0.481118 | + | 0.876656i | \(0.659769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.77102 | 0.0637818 | ||||||||
\(772\) | 16.1815 | 0.582384 | ||||||||
\(773\) | −27.4993 | −0.989081 | −0.494541 | − | 0.869154i | \(-0.664664\pi\) | ||||
−0.494541 | + | 0.869154i | \(0.664664\pi\) | |||||||
\(774\) | −30.0700 | −1.08084 | ||||||||
\(775\) | 37.4640 | 1.34575 | ||||||||
\(776\) | 17.3375 | 0.622380 | ||||||||
\(777\) | −10.0985 | −0.362282 | ||||||||
\(778\) | −7.70695 | −0.276308 | ||||||||
\(779\) | −5.91652 | −0.211981 | ||||||||
\(780\) | −3.31067 | −0.118541 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.08339 | −0.289062 | ||||||||
\(783\) | 63.9980 | 2.28710 | ||||||||
\(784\) | −2.03317 | −0.0726133 | ||||||||
\(785\) | 14.2502 | 0.508612 | ||||||||
\(786\) | 49.2823 | 1.75784 | ||||||||
\(787\) | 51.3354 | 1.82991 | 0.914956 | − | 0.403555i | \(-0.132225\pi\) | ||||
0.914956 | + | 0.403555i | \(0.132225\pi\) | |||||||
\(788\) | 14.4283 | 0.513985 | ||||||||
\(789\) | 30.4339 | 1.08348 | ||||||||
\(790\) | 1.92576 | 0.0685156 | ||||||||
\(791\) | 12.5643 | 0.446734 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.0729 | 0.535256 | ||||||||
\(794\) | 27.6939 | 0.982818 | ||||||||
\(795\) | 22.3189 | 0.791568 | ||||||||
\(796\) | 12.4819 | 0.442411 | ||||||||
\(797\) | 9.56050 | 0.338650 | 0.169325 | − | 0.985560i | \(-0.445841\pi\) | ||||
0.169325 | + | 0.985560i | \(0.445841\pi\) | |||||||
\(798\) | 7.37221 | 0.260974 | ||||||||
\(799\) | −36.3220 | −1.28498 | ||||||||
\(800\) | −4.31285 | −0.152482 | ||||||||
\(801\) | −48.2618 | −1.70525 | ||||||||
\(802\) | −28.3005 | −0.999326 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −38.6281 | −1.36231 | ||||||||
\(805\) | 3.25900 | 0.114865 | ||||||||
\(806\) | −10.4878 | −0.369415 | ||||||||
\(807\) | −37.4041 | −1.31669 | ||||||||
\(808\) | −0.0401979 | −0.00141416 | ||||||||
\(809\) | −4.69556 | −0.165087 | −0.0825435 | − | 0.996587i | \(-0.526304\pi\) | ||||
−0.0825435 | + | 0.996587i | \(0.526304\pi\) | |||||||
\(810\) | −25.0804 | −0.881236 | ||||||||
\(811\) | 51.9776 | 1.82518 | 0.912590 | − | 0.408876i | \(-0.134079\pi\) | ||||
0.912590 | + | 0.408876i | \(0.134079\pi\) | |||||||
\(812\) | 8.72369 | 0.306141 | ||||||||
\(813\) | 63.5088 | 2.22735 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.21536 | −0.287772 | ||||||||
\(816\) | 15.1577 | 0.530624 | ||||||||
\(817\) | −3.78596 | −0.132454 | ||||||||
\(818\) | −7.15765 | −0.250261 | ||||||||
\(819\) | 21.3712 | 0.746771 | ||||||||
\(820\) | 4.90446 | 0.171271 | ||||||||
\(821\) | 44.9698 | 1.56946 | 0.784728 | − | 0.619840i | \(-0.212802\pi\) | ||||
0.784728 | + | 0.619840i | \(0.212802\pi\) | |||||||
\(822\) | 33.5961 | 1.17180 | ||||||||
\(823\) | 32.8043 | 1.14349 | 0.571744 | − | 0.820432i | \(-0.306267\pi\) | ||||
0.571744 | + | 0.820432i | \(0.306267\pi\) | |||||||
\(824\) | 17.2964 | 0.602548 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.233054 | −0.00810899 | ||||||||
\(827\) | 0.752079 | 0.0261523 | 0.0130762 | − | 0.999915i | \(-0.495838\pi\) | ||||
0.0130762 | + | 0.999915i | \(0.495838\pi\) | |||||||
\(828\) | −14.0113 | −0.486925 | ||||||||
\(829\) | 33.2350 | 1.15430 | 0.577150 | − | 0.816638i | \(-0.304165\pi\) | ||||
0.577150 | + | 0.816638i | \(0.304165\pi\) | |||||||
\(830\) | 4.96245 | 0.172249 | ||||||||
\(831\) | 19.5793 | 0.679199 | ||||||||
\(832\) | 1.20735 | 0.0418572 | ||||||||
\(833\) | −9.31640 | −0.322794 | ||||||||
\(834\) | 37.6936 | 1.30522 | ||||||||
\(835\) | 11.2961 | 0.390918 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −142.022 | −4.90900 | ||||||||
\(838\) | 9.45181 | 0.326507 | ||||||||
\(839\) | 6.91909 | 0.238873 | 0.119437 | − | 0.992842i | \(-0.461891\pi\) | ||||
0.119437 | + | 0.992842i | \(0.461891\pi\) | |||||||
\(840\) | −6.11115 | −0.210855 | ||||||||
\(841\) | −13.6778 | −0.471648 | ||||||||
\(842\) | 27.2670 | 0.939682 | ||||||||
\(843\) | −57.9536 | −1.99603 | ||||||||
\(844\) | 24.4896 | 0.842967 | ||||||||
\(845\) | 9.56792 | 0.329147 | ||||||||
\(846\) | −62.9584 | −2.16455 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.13933 | −0.279506 | ||||||||
\(849\) | 17.8776 | 0.613556 | ||||||||
\(850\) | −19.7624 | −0.677843 | ||||||||
\(851\) | 2.41646 | 0.0828351 | ||||||||
\(852\) | 17.8658 | 0.612073 | ||||||||
\(853\) | −15.7760 | −0.540159 | −0.270079 | − | 0.962838i | \(-0.587050\pi\) | ||||
−0.270079 | + | 0.962838i | \(0.587050\pi\) | |||||||
\(854\) | 27.8231 | 0.952086 | ||||||||
\(855\) | −6.58389 | −0.225164 | ||||||||
\(856\) | 14.8051 | 0.506027 | ||||||||
\(857\) | 16.5727 | 0.566112 | 0.283056 | − | 0.959103i | \(-0.408652\pi\) | ||||
0.283056 | + | 0.959103i | \(0.408652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.87642 | 0.234620 | 0.117310 | − | 0.993095i | \(-0.462573\pi\) | ||||
0.117310 | + | 0.993095i | \(0.462573\pi\) | |||||||
\(860\) | 3.13834 | 0.107017 | ||||||||
\(861\) | −43.6179 | −1.48649 | ||||||||
\(862\) | −1.36032 | −0.0463328 | ||||||||
\(863\) | −40.5236 | −1.37944 | −0.689720 | − | 0.724076i | \(-0.742266\pi\) | ||||
−0.689720 | + | 0.724076i | \(0.742266\pi\) | |||||||
\(864\) | 16.3495 | 0.556223 | ||||||||
\(865\) | 9.50616 | 0.323219 | ||||||||
\(866\) | 26.1728 | 0.889389 | ||||||||
\(867\) | 13.2204 | 0.448987 | ||||||||
\(868\) | −19.3593 | −0.657097 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.7336 | −0.363902 | ||||||||
\(871\) | −14.0986 | −0.477714 | ||||||||
\(872\) | 0.176526 | 0.00597793 | ||||||||
\(873\) | 137.703 | 4.66055 | ||||||||
\(874\) | −1.76409 | −0.0596711 | ||||||||
\(875\) | 17.2047 | 0.581625 | ||||||||
\(876\) | −43.8613 | −1.48194 | ||||||||
\(877\) | −27.9198 | −0.942784 | −0.471392 | − | 0.881924i | \(-0.656248\pi\) | ||||
−0.471392 | + | 0.881924i | \(0.656248\pi\) | |||||||
\(878\) | −9.79442 | −0.330546 | ||||||||
\(879\) | 20.7264 | 0.699086 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.7069 | 0.899780 | 0.449890 | − | 0.893084i | \(-0.351463\pi\) | ||||
0.449890 | + | 0.893084i | \(0.351463\pi\) | |||||||
\(882\) | −16.1485 | −0.543748 | ||||||||
\(883\) | 10.5785 | 0.355997 | 0.177998 | − | 0.984031i | \(-0.443038\pi\) | ||||
0.177998 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(884\) | 5.53231 | 0.186072 | ||||||||
\(885\) | 0.286748 | 0.00963893 | ||||||||
\(886\) | −20.4676 | −0.687624 | ||||||||
\(887\) | −21.3943 | −0.718351 | −0.359176 | − | 0.933270i | \(-0.616942\pi\) | ||||
−0.359176 | + | 0.933270i | \(0.616942\pi\) | |||||||
\(888\) | −4.53125 | −0.152059 | ||||||||
\(889\) | 34.6770 | 1.16303 | ||||||||
\(890\) | 5.03699 | 0.168840 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.0348 | −0.771262 | ||||||||
\(893\) | −7.92677 | −0.265259 | ||||||||
\(894\) | −55.0144 | −1.83996 | ||||||||
\(895\) | −0.181696 | −0.00607343 | ||||||||
\(896\) | 2.22864 | 0.0744536 | ||||||||
\(897\) | −7.04548 | −0.235242 | ||||||||
\(898\) | 40.4545 | 1.34999 | ||||||||
\(899\) | −34.0025 | −1.13405 | ||||||||
\(900\) | −34.2549 | −1.14183 | ||||||||
\(901\) | −37.2960 | −1.24251 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.9109 | −0.928816 | ||||||||
\(904\) | 5.63764 | 0.187505 | ||||||||
\(905\) | 20.6694 | 0.687075 | ||||||||
\(906\) | −59.6865 | −1.98295 | ||||||||
\(907\) | 14.5370 | 0.482694 | 0.241347 | − | 0.970439i | \(-0.422411\pi\) | ||||
0.241347 | + | 0.970439i | \(0.422411\pi\) | |||||||
\(908\) | −11.6050 | −0.385124 | ||||||||
\(909\) | −0.319272 | −0.0105896 | ||||||||
\(910\) | −2.23047 | −0.0739394 | ||||||||
\(911\) | 45.9200 | 1.52140 | 0.760698 | − | 0.649106i | \(-0.224857\pi\) | ||||
0.760698 | + | 0.649106i | \(0.224857\pi\) | |||||||
\(912\) | 3.30795 | 0.109537 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 31.1469 | 1.03025 | ||||||||
\(915\) | −34.2333 | −1.13172 | ||||||||
\(916\) | 10.8274 | 0.357746 | ||||||||
\(917\) | 33.2026 | 1.09645 | ||||||||
\(918\) | 74.9169 | 2.47263 | ||||||||
\(919\) | 10.9057 | 0.359745 | 0.179872 | − | 0.983690i | \(-0.442432\pi\) | ||||
0.179872 | + | 0.983690i | \(0.442432\pi\) | |||||||
\(920\) | 1.46233 | 0.0482115 | ||||||||
\(921\) | −0.143536 | −0.00472966 | ||||||||
\(922\) | −28.2437 | −0.930155 | ||||||||
\(923\) | 6.52074 | 0.214633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.90778 | 0.194247 | ||||||||
\(926\) | −28.0244 | −0.920937 | ||||||||
\(927\) | 137.377 | 4.51204 | ||||||||
\(928\) | 3.91436 | 0.128495 | ||||||||
\(929\) | 8.41320 | 0.276028 | 0.138014 | − | 0.990430i | \(-0.455928\pi\) | ||||
0.138014 | + | 0.990430i | \(0.455928\pi\) | |||||||
\(930\) | 23.8195 | 0.781073 | ||||||||
\(931\) | −2.03317 | −0.0666345 | ||||||||
\(932\) | 0.972932 | 0.0318694 | ||||||||
\(933\) | 8.03508 | 0.263057 | ||||||||
\(934\) | −36.0872 | −1.18081 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.58937 | 0.313438 | ||||||||
\(937\) | −14.6747 | −0.479401 | −0.239701 | − | 0.970847i | \(-0.577049\pi\) | ||||
−0.239701 | + | 0.970847i | \(0.577049\pi\) | |||||||
\(938\) | −26.0246 | −0.849733 | ||||||||
\(939\) | 2.70453 | 0.0882591 | ||||||||
\(940\) | 6.57084 | 0.214317 | ||||||||
\(941\) | 5.44917 | 0.177638 | 0.0888189 | − | 0.996048i | \(-0.471691\pi\) | ||||
0.0888189 | + | 0.996048i | \(0.471691\pi\) | |||||||
\(942\) | −56.8663 | −1.85280 | ||||||||
\(943\) | 10.4372 | 0.339884 | ||||||||
\(944\) | −0.104572 | −0.00340354 | ||||||||
\(945\) | −30.2044 | −0.982549 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.9722 | −0.973964 | −0.486982 | − | 0.873412i | \(-0.661902\pi\) | ||||
−0.486982 | + | 0.873412i | \(0.661902\pi\) | |||||||
\(948\) | −7.68487 | −0.249593 | ||||||||
\(949\) | −16.0087 | −0.519664 | ||||||||
\(950\) | −4.31285 | −0.139927 | ||||||||
\(951\) | −61.3607 | −1.98976 | ||||||||
\(952\) | 10.2121 | 0.330975 | ||||||||
\(953\) | −18.2596 | −0.591487 | −0.295743 | − | 0.955267i | \(-0.595567\pi\) | ||||
−0.295743 | + | 0.955267i | \(0.595567\pi\) | |||||||
\(954\) | −64.6467 | −2.09301 | ||||||||
\(955\) | 7.67029 | 0.248205 | ||||||||
\(956\) | −16.0095 | −0.517784 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.3357 | −0.850869 | ||||||||
\(959\) | 22.6345 | 0.730905 | ||||||||
\(960\) | −2.74210 | −0.0885009 | ||||||||
\(961\) | 44.4571 | 1.43410 | ||||||||
\(962\) | −1.65383 | −0.0533217 | ||||||||
\(963\) | 117.590 | 3.78927 | ||||||||
\(964\) | 11.2997 | 0.363939 | ||||||||
\(965\) | −13.4135 | −0.431796 | ||||||||
\(966\) | −13.0052 | −0.418436 | ||||||||
\(967\) | 29.4143 | 0.945899 | 0.472949 | − | 0.881090i | \(-0.343189\pi\) | ||||
0.472949 | + | 0.881090i | \(0.343189\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.1577 | 0.486934 | ||||||||
\(970\) | −14.3718 | −0.461451 | ||||||||
\(971\) | 14.7085 | 0.472019 | 0.236010 | − | 0.971751i | \(-0.424160\pi\) | ||||
0.236010 | + | 0.971751i | \(0.424160\pi\) | |||||||
\(972\) | 51.0363 | 1.63699 | ||||||||
\(973\) | 25.3950 | 0.814127 | ||||||||
\(974\) | −7.80731 | −0.250162 | ||||||||
\(975\) | −17.2248 | −0.551637 | ||||||||
\(976\) | 12.4843 | 0.399614 | ||||||||
\(977\) | 1.43626 | 0.0459501 | 0.0229751 | − | 0.999736i | \(-0.492686\pi\) | ||||
0.0229751 | + | 0.999736i | \(0.492686\pi\) | |||||||
\(978\) | 32.7839 | 1.04831 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.68538 | 0.0538376 | ||||||||
\(981\) | 1.40206 | 0.0447644 | ||||||||
\(982\) | −8.97408 | −0.286374 | ||||||||
\(983\) | −51.6930 | −1.64875 | −0.824375 | − | 0.566044i | \(-0.808473\pi\) | ||||
−0.824375 | + | 0.566044i | \(0.808473\pi\) | |||||||
\(984\) | −19.5715 | −0.623918 | ||||||||
\(985\) | −11.9602 | −0.381084 | ||||||||
\(986\) | 17.9364 | 0.571210 | ||||||||
\(987\) | −58.4378 | −1.86010 | ||||||||
\(988\) | 1.20735 | 0.0384108 | ||||||||
\(989\) | 6.67875 | 0.212372 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.4491 | 1.12608 | 0.563040 | − | 0.826430i | \(-0.309632\pi\) | ||||
0.563040 | + | 0.826430i | \(0.309632\pi\) | |||||||
\(992\) | −8.68660 | −0.275800 | ||||||||
\(993\) | −14.2675 | −0.452766 | ||||||||
\(994\) | 12.0366 | 0.381778 | ||||||||
\(995\) | −10.3468 | −0.328016 | ||||||||
\(996\) | −19.8030 | −0.627481 | ||||||||
\(997\) | −14.5269 | −0.460071 | −0.230035 | − | 0.973182i | \(-0.573884\pi\) | ||||
−0.230035 | + | 0.973182i | \(0.573884\pi\) | |||||||
\(998\) | 29.6042 | 0.937104 | ||||||||
\(999\) | −22.3957 | −0.708570 |
(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 | 4598.2.a.cd.1.10 | 10 | ||
11.2 | odd | 10 | 418.2.f.h.191.5 | ✓ | 20 | ||
11.6 | odd | 10 | 418.2.f.h.267.5 | yes | 20 | ||
11.10 | odd | 2 | 4598.2.a.cc.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.h.191.5 | ✓ | 20 | 11.2 | odd | 10 | ||
418.2.f.h.267.5 | yes | 20 | 11.6 | odd | 10 | ||
4598.2.a.cc.1.10 | 10 | 11.10 | odd | 2 | |||
4598.2.a.cd.1.10 | 10 | 1.1 | even | 1 | trivial |