Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2x^{10} - 14x^{9} + 27x^{8} + 66x^{7} - 125x^{6} - 115x^{5} + 227x^{4} + 40x^{3} - 129x^{2} + 26x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.05394\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.05394 | 1.45235 | 0.726176 | − | 0.687508i | \(-0.241296\pi\) | ||||
0.726176 | + | 0.687508i | \(0.241296\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.21866 | 1.10933 | ||||||||
\(5\) | 0.0248942 | 0.0111330 | 0.00556652 | − | 0.999985i | \(-0.498228\pi\) | ||||
0.00556652 | + | 0.999985i | \(0.498228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.52855 | 0.577737 | 0.288868 | − | 0.957369i | \(-0.406721\pi\) | ||||
0.288868 | + | 0.957369i | \(0.406721\pi\) | |||||||
\(8\) | 0.449108 | 0.158784 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0511312 | 0.0161691 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.02531 | −0.561720 | −0.280860 | − | 0.959749i | \(-0.590620\pi\) | ||||
−0.280860 | + | 0.959749i | \(0.590620\pi\) | |||||||
\(14\) | 3.13954 | 0.839078 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.51487 | −0.878719 | ||||||||
\(17\) | −4.80386 | −1.16511 | −0.582554 | − | 0.812792i | \(-0.697947\pi\) | ||||
−0.582554 | + | 0.812792i | \(0.697947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.29218 | −0.755279 | −0.377639 | − | 0.925953i | \(-0.623264\pi\) | ||||
−0.377639 | + | 0.925953i | \(0.623264\pi\) | |||||||
\(20\) | 0.0552317 | 0.0123502 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.05394 | −0.437901 | ||||||||
\(23\) | 1.24741 | 0.260102 | 0.130051 | − | 0.991507i | \(-0.458486\pi\) | ||||
0.130051 | + | 0.991507i | \(0.458486\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99938 | −0.999876 | ||||||||
\(26\) | −4.15986 | −0.815816 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.39132 | 0.640900 | ||||||||
\(29\) | 8.92727 | 1.65775 | 0.828876 | − | 0.559433i | \(-0.188981\pi\) | ||||
0.828876 | + | 0.559433i | \(0.188981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.62645 | 1.01054 | 0.505270 | − | 0.862961i | \(-0.331393\pi\) | ||||
0.505270 | + | 0.862961i | \(0.331393\pi\) | |||||||
\(32\) | −8.11755 | −1.43499 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.86683 | −1.69215 | ||||||||
\(35\) | 0.0380520 | 0.00643197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.88845 | −1.13245 | −0.566227 | − | 0.824249i | \(-0.691597\pi\) | ||||
−0.566227 | + | 0.824249i | \(0.691597\pi\) | |||||||
\(38\) | −6.76194 | −1.09693 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0111802 | 0.00176774 | ||||||||
\(41\) | −8.93150 | −1.39487 | −0.697433 | − | 0.716650i | \(-0.745674\pi\) | ||||
−0.697433 | + | 0.716650i | \(0.745674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.34956 | −0.968298 | −0.484149 | − | 0.874986i | \(-0.660871\pi\) | ||||
−0.484149 | + | 0.874986i | \(0.660871\pi\) | |||||||
\(44\) | −2.21866 | −0.334475 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.56209 | 0.377760 | ||||||||
\(47\) | −4.19274 | −0.611574 | −0.305787 | − | 0.952100i | \(-0.598920\pi\) | ||||
−0.305787 | + | 0.952100i | \(0.598920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.66354 | −0.666220 | ||||||||
\(50\) | −10.2684 | −1.45217 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.49347 | −0.623132 | ||||||||
\(53\) | 3.56791 | 0.490090 | 0.245045 | − | 0.969512i | \(-0.421197\pi\) | ||||
0.245045 | + | 0.969512i | \(0.421197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0248942 | −0.00335674 | ||||||||
\(56\) | 0.686483 | 0.0917352 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.3360 | 2.40764 | ||||||||
\(59\) | −1.96110 | −0.255314 | −0.127657 | − | 0.991818i | \(-0.540746\pi\) | ||||
−0.127657 | + | 0.991818i | \(0.540746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 11.5564 | 1.46766 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.64318 | −1.20540 | ||||||||
\(65\) | −0.0504185 | −0.00625365 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.12656 | −0.259801 | −0.129900 | − | 0.991527i | \(-0.541466\pi\) | ||||
−0.129900 | + | 0.991527i | \(0.541466\pi\) | |||||||
\(68\) | −10.6581 | −1.29249 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0781565 | 0.00934148 | ||||||||
\(71\) | −8.06823 | −0.957523 | −0.478761 | − | 0.877945i | \(-0.658914\pi\) | ||||
−0.478761 | + | 0.877945i | \(0.658914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.798991 | 0.0935148 | 0.0467574 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467574 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(74\) | −14.1484 | −1.64472 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.30423 | −0.837852 | ||||||||
\(77\) | −1.52855 | −0.174194 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.406283 | −0.0457104 | −0.0228552 | − | 0.999739i | \(-0.507276\pi\) | ||||
−0.0228552 | + | 0.999739i | \(0.507276\pi\) | |||||||
\(80\) | −0.0875001 | −0.00978281 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.3447 | −2.02584 | ||||||||
\(83\) | 1.36890 | 0.150256 | 0.0751279 | − | 0.997174i | \(-0.476063\pi\) | ||||
0.0751279 | + | 0.997174i | \(0.476063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.119588 | −0.0129712 | ||||||||
\(86\) | −13.0416 | −1.40631 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.449108 | −0.0478751 | ||||||||
\(89\) | 8.42620 | 0.893175 | 0.446588 | − | 0.894740i | \(-0.352639\pi\) | ||||
0.446588 | + | 0.894740i | \(0.352639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.09579 | −0.324527 | ||||||||
\(92\) | 2.76757 | 0.288539 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.61163 | −0.888221 | ||||||||
\(95\) | −0.0819564 | −0.00840854 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8144 | 1.60571 | 0.802854 | − | 0.596176i | \(-0.203314\pi\) | ||||
0.802854 | + | 0.596176i | \(0.203314\pi\) | |||||||
\(98\) | −9.57862 | −0.967586 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.0919 | −1.10919 | ||||||||
\(101\) | −2.04802 | −0.203785 | −0.101893 | − | 0.994795i | \(-0.532490\pi\) | ||||
−0.101893 | + | 0.994795i | \(0.532490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.41108 | −0.336103 | −0.168052 | − | 0.985778i | \(-0.553748\pi\) | ||||
−0.168052 | + | 0.985778i | \(0.553748\pi\) | |||||||
\(104\) | −0.909584 | −0.0891920 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.32826 | 0.711784 | ||||||||
\(107\) | 13.6931 | 1.32376 | 0.661880 | − | 0.749610i | \(-0.269759\pi\) | ||||
0.661880 | + | 0.749610i | \(0.269759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.997758 | 0.0955679 | 0.0477840 | − | 0.998858i | \(-0.484784\pi\) | ||||
0.0477840 | + | 0.998858i | \(0.484784\pi\) | |||||||
\(110\) | −0.0511312 | −0.00487517 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.37266 | −0.507668 | ||||||||
\(113\) | −11.2280 | −1.05624 | −0.528122 | − | 0.849168i | \(-0.677104\pi\) | ||||
−0.528122 | + | 0.849168i | \(0.677104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0310532 | 0.00289573 | ||||||||
\(116\) | 19.8065 | 1.83899 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.02798 | −0.370806 | ||||||||
\(119\) | −7.34294 | −0.673126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.05394 | 0.185955 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.4832 | 1.12102 | ||||||||
\(125\) | −0.248927 | −0.0222647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.3177 | −1.89164 | −0.945819 | − | 0.324695i | \(-0.894738\pi\) | ||||
−0.945819 | + | 0.324695i | \(0.894738\pi\) | |||||||
\(128\) | −3.57139 | −0.315669 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.103557 | −0.00908251 | ||||||||
\(131\) | 2.47278 | 0.216048 | 0.108024 | − | 0.994148i | \(-0.465548\pi\) | ||||
0.108024 | + | 0.994148i | \(0.465548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.03226 | −0.436352 | ||||||||
\(134\) | −4.36782 | −0.377322 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.15745 | −0.185000 | ||||||||
\(137\) | 3.40578 | 0.290975 | 0.145488 | − | 0.989360i | \(-0.453525\pi\) | ||||
0.145488 | + | 0.989360i | \(0.453525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0352 | −1.69936 | −0.849682 | − | 0.527295i | \(-0.823206\pi\) | ||||
−0.849682 | + | 0.527295i | \(0.823206\pi\) | |||||||
\(140\) | 0.0844244 | 0.00713516 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.5716 | −1.39066 | ||||||||
\(143\) | 2.02531 | 0.169365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.222237 | 0.0184558 | ||||||||
\(146\) | 1.64108 | 0.135817 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.2831 | −1.25626 | ||||||||
\(149\) | −9.57828 | −0.784683 | −0.392341 | − | 0.919820i | \(-0.628335\pi\) | ||||
−0.392341 | + | 0.919820i | \(0.628335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.18531 | 0.421974 | 0.210987 | − | 0.977489i | \(-0.432332\pi\) | ||||
0.210987 | + | 0.977489i | \(0.432332\pi\) | |||||||
\(152\) | −1.47855 | −0.119926 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.13954 | −0.252992 | ||||||||
\(155\) | 0.140066 | 0.0112504 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0899 | −1.12450 | −0.562248 | − | 0.826969i | \(-0.690063\pi\) | ||||
−0.562248 | + | 0.826969i | \(0.690063\pi\) | |||||||
\(158\) | −0.834480 | −0.0663877 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.202080 | −0.0159758 | ||||||||
\(161\) | 1.90672 | 0.150271 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.28468 | −0.648906 | −0.324453 | − | 0.945902i | \(-0.605180\pi\) | ||||
−0.324453 | + | 0.945902i | \(0.605180\pi\) | |||||||
\(164\) | −19.8159 | −1.54736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.81163 | 0.218225 | ||||||||
\(167\) | 1.28807 | 0.0996742 | 0.0498371 | − | 0.998757i | \(-0.484130\pi\) | ||||
0.0498371 | + | 0.998757i | \(0.484130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.89811 | −0.684470 | ||||||||
\(170\) | −0.245627 | −0.0188387 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.0875 | −1.07416 | ||||||||
\(173\) | 9.44976 | 0.718452 | 0.359226 | − | 0.933251i | \(-0.383041\pi\) | ||||
0.359226 | + | 0.933251i | \(0.383041\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.64179 | −0.577665 | ||||||||
\(176\) | 3.51487 | 0.264944 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.3069 | 1.29721 | ||||||||
\(179\) | 2.21840 | 0.165811 | 0.0829057 | − | 0.996557i | \(-0.473580\pi\) | ||||
0.0829057 | + | 0.996557i | \(0.473580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.94663 | 0.219021 | 0.109511 | − | 0.993986i | \(-0.465072\pi\) | ||||
0.109511 | + | 0.993986i | \(0.465072\pi\) | |||||||
\(182\) | −6.35855 | −0.471327 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.560220 | 0.0413000 | ||||||||
\(185\) | −0.171483 | −0.0126076 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.80386 | 0.351293 | ||||||||
\(188\) | −9.30226 | −0.678437 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.168333 | −0.0122122 | ||||||||
\(191\) | 16.3873 | 1.18574 | 0.592870 | − | 0.805298i | \(-0.297995\pi\) | ||||
0.592870 | + | 0.805298i | \(0.297995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.43974 | 0.463543 | 0.231771 | − | 0.972770i | \(-0.425548\pi\) | ||||
0.231771 | + | 0.972770i | \(0.425548\pi\) | |||||||
\(194\) | 32.4817 | 2.33205 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.3468 | −0.739057 | ||||||||
\(197\) | 11.9244 | 0.849576 | 0.424788 | − | 0.905293i | \(-0.360349\pi\) | ||||
0.424788 | + | 0.905293i | \(0.360349\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.99146 | 0.141171 | 0.0705853 | − | 0.997506i | \(-0.477513\pi\) | ||||
0.0705853 | + | 0.997506i | \(0.477513\pi\) | |||||||
\(200\) | −2.24526 | −0.158764 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.20650 | −0.295968 | ||||||||
\(203\) | 13.6458 | 0.957744 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.222343 | −0.0155291 | ||||||||
\(206\) | −7.00613 | −0.488140 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.11871 | 0.493594 | ||||||||
\(209\) | 3.29218 | 0.227725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.541369 | −0.0372694 | −0.0186347 | − | 0.999826i | \(-0.505932\pi\) | ||||
−0.0186347 | + | 0.999826i | \(0.505932\pi\) | |||||||
\(212\) | 7.91597 | 0.543671 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.1247 | 1.92257 | ||||||||
\(215\) | −0.158067 | −0.0107801 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.60030 | 0.583827 | ||||||||
\(218\) | 2.04933 | 0.138798 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0552317 | −0.00372372 | ||||||||
\(221\) | 9.72932 | 0.654465 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3029 | −0.890826 | −0.445413 | − | 0.895325i | \(-0.646943\pi\) | ||||
−0.445413 | + | 0.895325i | \(0.646943\pi\) | |||||||
\(224\) | −12.4081 | −0.829049 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.0617 | −1.53404 | ||||||||
\(227\) | 6.94528 | 0.460974 | 0.230487 | − | 0.973075i | \(-0.425968\pi\) | ||||
0.230487 | + | 0.973075i | \(0.425968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.1019 | 1.19621 | 0.598105 | − | 0.801418i | \(-0.295921\pi\) | ||||
0.598105 | + | 0.801418i | \(0.295921\pi\) | |||||||
\(230\) | 0.0637813 | 0.00420561 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.00931 | 0.263224 | ||||||||
\(233\) | 8.79705 | 0.576314 | 0.288157 | − | 0.957583i | \(-0.406957\pi\) | ||||
0.288157 | + | 0.957583i | \(0.406957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.104375 | −0.00680868 | ||||||||
\(236\) | −4.35102 | −0.283227 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.0819 | −0.977616 | ||||||||
\(239\) | 2.68814 | 0.173881 | 0.0869407 | − | 0.996213i | \(-0.472291\pi\) | ||||
0.0869407 | + | 0.996213i | \(0.472291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9889 | 1.02993 | 0.514967 | − | 0.857210i | \(-0.327804\pi\) | ||||
0.514967 | + | 0.857210i | \(0.327804\pi\) | |||||||
\(242\) | 2.05394 | 0.132032 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.21866 | 0.142035 | ||||||||
\(245\) | −0.116095 | −0.00741705 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.66770 | 0.424255 | ||||||||
\(248\) | 2.52688 | 0.160457 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.511280 | −0.0323362 | ||||||||
\(251\) | 7.34500 | 0.463612 | 0.231806 | − | 0.972762i | \(-0.425537\pi\) | ||||
0.231806 | + | 0.972762i | \(0.425537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.24741 | −0.0784237 | ||||||||
\(254\) | −43.7852 | −2.74733 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.9509 | 0.746934 | ||||||||
\(257\) | 18.7759 | 1.17121 | 0.585604 | − | 0.810597i | \(-0.300857\pi\) | ||||
0.585604 | + | 0.810597i | \(0.300857\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5293 | −0.654260 | ||||||||
\(260\) | −0.111861 | −0.00693735 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.07893 | 0.313777 | ||||||||
\(263\) | 12.4646 | 0.768600 | 0.384300 | − | 0.923208i | \(-0.374443\pi\) | ||||
0.384300 | + | 0.923208i | \(0.374443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0888203 | 0.00545619 | ||||||||
\(266\) | −10.3359 | −0.633738 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.71811 | −0.288204 | ||||||||
\(269\) | −16.3747 | −0.998385 | −0.499192 | − | 0.866491i | \(-0.666370\pi\) | ||||
−0.499192 | + | 0.866491i | \(0.666370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.56788 | −0.520461 | −0.260231 | − | 0.965546i | \(-0.583799\pi\) | ||||
−0.260231 | + | 0.965546i | \(0.583799\pi\) | |||||||
\(272\) | 16.8850 | 1.02380 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.99525 | 0.422598 | ||||||||
\(275\) | 4.99938 | 0.301474 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.0553 | −1.80585 | −0.902923 | − | 0.429803i | \(-0.858583\pi\) | ||||
−0.902923 | + | 0.429803i | \(0.858583\pi\) | |||||||
\(278\) | −41.1511 | −2.46808 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0170895 | 0.00102129 | ||||||||
\(281\) | 19.5195 | 1.16444 | 0.582218 | − | 0.813033i | \(-0.302185\pi\) | ||||
0.582218 | + | 0.813033i | \(0.302185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.5866 | −1.46152 | −0.730762 | − | 0.682632i | \(-0.760835\pi\) | ||||
−0.730762 | + | 0.682632i | \(0.760835\pi\) | |||||||
\(284\) | −17.9006 | −1.06221 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.15986 | 0.245978 | ||||||||
\(287\) | −13.6522 | −0.805865 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.07711 | 0.357477 | ||||||||
\(290\) | 0.456461 | 0.0268043 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.77269 | 0.103739 | ||||||||
\(293\) | 8.52124 | 0.497816 | 0.248908 | − | 0.968527i | \(-0.419928\pi\) | ||||
0.248908 | + | 0.968527i | \(0.419928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0488201 | −0.00284242 | ||||||||
\(296\) | −3.09366 | −0.179815 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.6732 | −1.13964 | ||||||||
\(299\) | −2.52638 | −0.146105 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.70560 | −0.559422 | ||||||||
\(302\) | 10.6503 | 0.612856 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.5716 | 0.663678 | ||||||||
\(305\) | 0.0248942 | 0.00142544 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.29270 | 0.359143 | 0.179572 | − | 0.983745i | \(-0.442529\pi\) | ||||
0.179572 | + | 0.983745i | \(0.442529\pi\) | |||||||
\(308\) | −3.39132 | −0.193239 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.287687 | 0.0163395 | ||||||||
\(311\) | −32.0080 | −1.81500 | −0.907502 | − | 0.420047i | \(-0.862014\pi\) | ||||
−0.907502 | + | 0.420047i | \(0.862014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.08898 | −0.231123 | −0.115561 | − | 0.993300i | \(-0.536867\pi\) | ||||
−0.115561 | + | 0.993300i | \(0.536867\pi\) | |||||||
\(314\) | −28.9398 | −1.63316 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.901403 | −0.0507079 | ||||||||
\(317\) | −17.3234 | −0.972981 | −0.486491 | − | 0.873686i | \(-0.661723\pi\) | ||||
−0.486491 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.92727 | −0.499831 | ||||||||
\(320\) | −0.240059 | −0.0134197 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.91628 | 0.218246 | ||||||||
\(323\) | 15.8152 | 0.879981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1253 | 0.561651 | ||||||||
\(326\) | −17.0162 | −0.942440 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.01121 | −0.221482 | ||||||||
\(329\) | −6.40881 | −0.353329 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.06729 | −0.443419 | −0.221709 | − | 0.975113i | \(-0.571164\pi\) | ||||
−0.221709 | + | 0.975113i | \(0.571164\pi\) | |||||||
\(332\) | 3.03711 | 0.166683 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.64562 | 0.144762 | ||||||||
\(335\) | −0.0529391 | −0.00289237 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.1813 | −1.20829 | −0.604146 | − | 0.796874i | \(-0.706486\pi\) | ||||
−0.604146 | + | 0.796874i | \(0.706486\pi\) | |||||||
\(338\) | −18.2762 | −0.994092 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.265326 | −0.0143893 | ||||||||
\(341\) | −5.62645 | −0.304689 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8283 | −0.962637 | ||||||||
\(344\) | −2.85164 | −0.153750 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.4092 | 1.04345 | ||||||||
\(347\) | −0.647734 | −0.0347722 | −0.0173861 | − | 0.999849i | \(-0.505534\pi\) | ||||
−0.0173861 | + | 0.999849i | \(0.505534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.79589 | −0.524362 | −0.262181 | − | 0.965019i | \(-0.584442\pi\) | ||||
−0.262181 | + | 0.965019i | \(0.584442\pi\) | |||||||
\(350\) | −15.6958 | −0.838974 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.11755 | 0.432667 | ||||||||
\(353\) | 27.1957 | 1.44748 | 0.723740 | − | 0.690073i | \(-0.242422\pi\) | ||||
0.723740 | + | 0.690073i | \(0.242422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.200852 | −0.0106601 | ||||||||
\(356\) | 18.6948 | 0.990825 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.55646 | 0.240817 | ||||||||
\(359\) | 17.1339 | 0.904292 | 0.452146 | − | 0.891944i | \(-0.350659\pi\) | ||||
0.452146 | + | 0.891944i | \(0.350659\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.16153 | −0.429554 | ||||||||
\(362\) | 6.05220 | 0.318096 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.86849 | −0.360007 | ||||||||
\(365\) | 0.0198903 | 0.00104110 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5299 | 1.28045 | 0.640226 | − | 0.768187i | \(-0.278841\pi\) | ||||
0.640226 | + | 0.768187i | \(0.278841\pi\) | |||||||
\(368\) | −4.38447 | −0.228557 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.352214 | −0.0183108 | ||||||||
\(371\) | 5.45372 | 0.283143 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.77613 | −0.402633 | −0.201316 | − | 0.979526i | \(-0.564522\pi\) | ||||
−0.201316 | + | 0.979526i | \(0.564522\pi\) | |||||||
\(374\) | 9.86683 | 0.510202 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.88299 | −0.0971080 | ||||||||
\(377\) | −18.0805 | −0.931193 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.8315 | −1.37824 | −0.689121 | − | 0.724646i | \(-0.742003\pi\) | ||||
−0.689121 | + | 0.724646i | \(0.742003\pi\) | |||||||
\(380\) | −0.181833 | −0.00932784 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 33.6584 | 1.72211 | ||||||||
\(383\) | 1.73648 | 0.0887299 | 0.0443650 | − | 0.999015i | \(-0.485874\pi\) | ||||
0.0443650 | + | 0.999015i | \(0.485874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0380520 | −0.00193931 | ||||||||
\(386\) | 13.2268 | 0.673228 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 35.0867 | 1.78126 | ||||||||
\(389\) | −30.1018 | −1.52622 | −0.763112 | − | 0.646267i | \(-0.776329\pi\) | ||||
−0.763112 | + | 0.646267i | \(0.776329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.99237 | −0.303047 | ||||||||
\(392\) | −2.09443 | −0.105785 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.4919 | 1.23388 | ||||||||
\(395\) | −0.0101141 | −0.000508896 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5205 | 0.929516 | 0.464758 | − | 0.885438i | \(-0.346141\pi\) | ||||
0.464758 | + | 0.885438i | \(0.346141\pi\) | |||||||
\(398\) | 4.09033 | 0.205030 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.5722 | 0.878610 | ||||||||
\(401\) | −11.5890 | −0.578728 | −0.289364 | − | 0.957219i | \(-0.593444\pi\) | ||||
−0.289364 | + | 0.957219i | \(0.593444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3953 | −0.567641 | ||||||||
\(404\) | −4.54385 | −0.226065 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 28.0275 | 1.39098 | ||||||||
\(407\) | 6.88845 | 0.341448 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.09585 | 0.0541861 | 0.0270930 | − | 0.999633i | \(-0.491375\pi\) | ||||
0.0270930 | + | 0.999633i | \(0.491375\pi\) | |||||||
\(410\) | −0.456678 | −0.0225537 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.56801 | −0.372849 | ||||||||
\(413\) | −2.99764 | −0.147504 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0340776 | 0.00167280 | ||||||||
\(416\) | 16.4406 | 0.806065 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.76194 | 0.330737 | ||||||||
\(419\) | −13.1872 | −0.644237 | −0.322118 | − | 0.946699i | \(-0.604395\pi\) | ||||
−0.322118 | + | 0.946699i | \(0.604395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.5730 | 1.05140 | 0.525702 | − | 0.850669i | \(-0.323803\pi\) | ||||
0.525702 | + | 0.850669i | \(0.323803\pi\) | |||||||
\(422\) | −1.11194 | −0.0541283 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.60238 | 0.0778183 | ||||||||
\(425\) | 24.0163 | 1.16496 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.52855 | 0.0739716 | ||||||||
\(428\) | 30.3803 | 1.46848 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.324660 | −0.0156565 | ||||||||
\(431\) | −30.9425 | −1.49045 | −0.745225 | − | 0.666813i | \(-0.767658\pi\) | ||||
−0.745225 | + | 0.666813i | \(0.767658\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.9300 | 0.621375 | 0.310687 | − | 0.950512i | \(-0.399441\pi\) | ||||
0.310687 | + | 0.950512i | \(0.399441\pi\) | |||||||
\(434\) | 17.6645 | 0.847922 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.21368 | 0.106016 | ||||||||
\(437\) | −4.10669 | −0.196450 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.331483 | 0.0158208 | 0.00791041 | − | 0.999969i | \(-0.497482\pi\) | ||||
0.00791041 | + | 0.999969i | \(0.497482\pi\) | |||||||
\(440\) | −0.0111802 | −0.000532995 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.9834 | 0.950514 | ||||||||
\(443\) | −29.5889 | −1.40581 | −0.702905 | − | 0.711284i | \(-0.748114\pi\) | ||||
−0.702905 | + | 0.711284i | \(0.748114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.209764 | 0.00994375 | ||||||||
\(446\) | −27.3232 | −1.29379 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.7401 | −0.696403 | ||||||||
\(449\) | −11.4457 | −0.540155 | −0.270078 | − | 0.962839i | \(-0.587049\pi\) | ||||
−0.270078 | + | 0.962839i | \(0.587049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.93150 | 0.420568 | ||||||||
\(452\) | −24.9112 | −1.17172 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.2652 | 0.669497 | ||||||||
\(455\) | −0.0770672 | −0.00361297 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.4054 | 1.14164 | 0.570818 | − | 0.821076i | \(-0.306626\pi\) | ||||
0.570818 | + | 0.821076i | \(0.306626\pi\) | |||||||
\(458\) | 37.1802 | 1.73732 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.0688964 | 0.00321231 | ||||||||
\(461\) | −15.4119 | −0.717805 | −0.358902 | − | 0.933375i | \(-0.616849\pi\) | ||||
−0.358902 | + | 0.933375i | \(0.616849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.2404 | 1.73071 | 0.865354 | − | 0.501161i | \(-0.167094\pi\) | ||||
0.865354 | + | 0.501161i | \(0.167094\pi\) | |||||||
\(464\) | −31.3782 | −1.45670 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.0686 | 0.837011 | ||||||||
\(467\) | −0.981164 | −0.0454028 | −0.0227014 | − | 0.999742i | \(-0.507227\pi\) | ||||
−0.0227014 | + | 0.999742i | \(0.507227\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.25055 | −0.150096 | ||||||||
\(470\) | −0.214380 | −0.00988860 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.880748 | −0.0405397 | ||||||||
\(473\) | 6.34956 | 0.291953 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.4589 | 0.755185 | ||||||||
\(476\) | −16.2915 | −0.746718 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.52127 | 0.252537 | ||||||||
\(479\) | 13.9754 | 0.638551 | 0.319275 | − | 0.947662i | \(-0.396561\pi\) | ||||
0.319275 | + | 0.947662i | \(0.396561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9512 | 0.636122 | ||||||||
\(482\) | 32.8402 | 1.49583 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.21866 | 0.100848 | ||||||||
\(485\) | 0.393687 | 0.0178764 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.3289 | −1.82748 | −0.913739 | − | 0.406302i | \(-0.866818\pi\) | ||||
−0.913739 | + | 0.406302i | \(0.866818\pi\) | |||||||
\(488\) | 0.449108 | 0.0203302 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.238452 | −0.0107722 | ||||||||
\(491\) | 33.6200 | 1.51725 | 0.758624 | − | 0.651528i | \(-0.225872\pi\) | ||||
0.758624 | + | 0.651528i | \(0.225872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.8854 | −1.93146 | ||||||||
\(494\) | 13.6950 | 0.616168 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.7763 | −0.887981 | ||||||||
\(497\) | −12.3327 | −0.553196 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1473 | 0.678084 | 0.339042 | − | 0.940771i | \(-0.389897\pi\) | ||||
0.339042 | + | 0.940771i | \(0.389897\pi\) | |||||||
\(500\) | −0.552283 | −0.0246989 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.0862 | 0.673328 | ||||||||
\(503\) | 4.36125 | 0.194458 | 0.0972292 | − | 0.995262i | \(-0.469002\pi\) | ||||
0.0972292 | + | 0.995262i | \(0.469002\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0509838 | −0.00226875 | ||||||||
\(506\) | −2.56209 | −0.113899 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −47.2966 | −2.09845 | ||||||||
\(509\) | −35.0017 | −1.55142 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.22130 | 0.0540270 | ||||||||
\(512\) | 31.6893 | 1.40048 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 38.5645 | 1.70101 | ||||||||
\(515\) | −0.0849161 | −0.00374185 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.19274 | 0.184397 | ||||||||
\(518\) | −21.6266 | −0.950217 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0226434 | −0.000992978 0 | ||||||||
\(521\) | 2.82818 | 0.123905 | 0.0619525 | − | 0.998079i | \(-0.480267\pi\) | ||||
0.0619525 | + | 0.998079i | \(0.480267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0491 | 0.876685 | 0.438343 | − | 0.898808i | \(-0.355566\pi\) | ||||
0.438343 | + | 0.898808i | \(0.355566\pi\) | |||||||
\(524\) | 5.48625 | 0.239668 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.6015 | 1.11628 | ||||||||
\(527\) | −27.0287 | −1.17739 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4440 | −0.932347 | ||||||||
\(530\) | 0.182431 | 0.00792431 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.1649 | −0.484058 | ||||||||
\(533\) | 18.0891 | 0.783524 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.340879 | 0.0147375 | ||||||||
\(536\) | −0.955055 | −0.0412521 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −33.6327 | −1.45001 | ||||||||
\(539\) | 4.66354 | 0.200873 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.48400 | −0.364756 | −0.182378 | − | 0.983229i | \(-0.558379\pi\) | ||||
−0.182378 | + | 0.983229i | \(0.558379\pi\) | |||||||
\(542\) | −17.5979 | −0.755894 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 38.9956 | 1.67192 | ||||||||
\(545\) | 0.0248384 | 0.00106396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.2600 | 0.524200 | 0.262100 | − | 0.965041i | \(-0.415585\pi\) | ||||
0.262100 | + | 0.965041i | \(0.415585\pi\) | |||||||
\(548\) | 7.55625 | 0.322787 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.2684 | 0.437847 | ||||||||
\(551\) | −29.3902 | −1.25206 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.621023 | −0.0264086 | ||||||||
\(554\) | −61.7316 | −2.62272 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −44.4513 | −1.88515 | ||||||||
\(557\) | 41.7817 | 1.77035 | 0.885173 | − | 0.465262i | \(-0.154040\pi\) | ||||
0.885173 | + | 0.465262i | \(0.154040\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8598 | 0.543913 | ||||||||
\(560\) | −0.133748 | −0.00565189 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 40.0918 | 1.69117 | ||||||||
\(563\) | 26.3634 | 1.11108 | 0.555542 | − | 0.831489i | \(-0.312511\pi\) | ||||
0.555542 | + | 0.831489i | \(0.312511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.279513 | −0.0117592 | ||||||||
\(566\) | −50.4994 | −2.12265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.62351 | −0.152039 | ||||||||
\(569\) | −24.4218 | −1.02381 | −0.511907 | − | 0.859041i | \(-0.671061\pi\) | ||||
−0.511907 | + | 0.859041i | \(0.671061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8587 | 1.12400 | 0.562001 | − | 0.827137i | \(-0.310032\pi\) | ||||
0.562001 | + | 0.827137i | \(0.310032\pi\) | |||||||
\(572\) | 4.49347 | 0.187881 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.0408 | −1.17040 | ||||||||
\(575\) | −6.23625 | −0.260070 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6001 | −0.482918 | −0.241459 | − | 0.970411i | \(-0.577626\pi\) | ||||
−0.241459 | + | 0.970411i | \(0.577626\pi\) | |||||||
\(578\) | 12.4820 | 0.519182 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.493068 | 0.0204736 | ||||||||
\(581\) | 2.09242 | 0.0868084 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.56791 | −0.147768 | ||||||||
\(584\) | 0.358833 | 0.0148486 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.5021 | 0.723004 | ||||||||
\(587\) | 46.5397 | 1.92090 | 0.960450 | − | 0.278453i | \(-0.0898217\pi\) | ||||
0.960450 | + | 0.278453i | \(0.0898217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.5233 | −0.763240 | ||||||||
\(590\) | −0.100274 | −0.00412819 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24.2120 | 0.995108 | ||||||||
\(593\) | 44.6499 | 1.83355 | 0.916776 | − | 0.399401i | \(-0.130782\pi\) | ||||
0.916776 | + | 0.399401i | \(0.130782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.182797 | −0.00749393 | ||||||||
\(596\) | −21.2509 | −0.870471 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.18903 | −0.212195 | ||||||||
\(599\) | 6.40412 | 0.261665 | 0.130833 | − | 0.991404i | \(-0.458235\pi\) | ||||
0.130833 | + | 0.991404i | \(0.458235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.94428 | 0.242472 | 0.121236 | − | 0.992624i | \(-0.461314\pi\) | ||||
0.121236 | + | 0.992624i | \(0.461314\pi\) | |||||||
\(602\) | −19.9347 | −0.812478 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.5044 | 0.468108 | ||||||||
\(605\) | 0.0248942 | 0.00101209 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.84406 | −0.318380 | −0.159190 | − | 0.987248i | \(-0.550888\pi\) | ||||
−0.159190 | + | 0.987248i | \(0.550888\pi\) | |||||||
\(608\) | 26.7245 | 1.08382 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.0511312 | 0.00207024 | ||||||||
\(611\) | 8.49161 | 0.343534 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.7279 | 0.998749 | 0.499374 | − | 0.866386i | \(-0.333563\pi\) | ||||
0.499374 | + | 0.866386i | \(0.333563\pi\) | |||||||
\(614\) | 12.9248 | 0.521603 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.686483 | −0.0276592 | ||||||||
\(617\) | 19.4795 | 0.784217 | 0.392108 | − | 0.919919i | \(-0.371746\pi\) | ||||
0.392108 | + | 0.919919i | \(0.371746\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5947 | 1.18951 | 0.594755 | − | 0.803907i | \(-0.297249\pi\) | ||||
0.594755 | + | 0.803907i | \(0.297249\pi\) | |||||||
\(620\) | 0.310759 | 0.0124804 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −65.7423 | −2.63603 | ||||||||
\(623\) | 12.8798 | 0.516020 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9907 | 0.999628 | ||||||||
\(626\) | −8.39850 | −0.335672 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31.2606 | −1.24744 | ||||||||
\(629\) | 33.0912 | 1.31943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6873 | −1.18183 | −0.590917 | − | 0.806733i | \(-0.701234\pi\) | ||||
−0.590917 | + | 0.806733i | \(0.701234\pi\) | |||||||
\(632\) | −0.182465 | −0.00725807 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −35.5813 | −1.41311 | ||||||||
\(635\) | −0.530687 | −0.0210597 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.44512 | 0.374229 | ||||||||
\(638\) | −18.3360 | −0.725931 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.0889070 | −0.00351436 | ||||||||
\(641\) | −17.3957 | −0.687087 | −0.343544 | − | 0.939137i | \(-0.611627\pi\) | ||||
−0.343544 | + | 0.939137i | \(0.611627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.6750 | 1.17027 | 0.585133 | − | 0.810937i | \(-0.301042\pi\) | ||||
0.585133 | + | 0.810937i | \(0.301042\pi\) | |||||||
\(644\) | 4.23036 | 0.166699 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.4834 | 1.27804 | ||||||||
\(647\) | 30.7044 | 1.20711 | 0.603557 | − | 0.797320i | \(-0.293750\pi\) | ||||
0.603557 | + | 0.797320i | \(0.293750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.96110 | 0.0769800 | ||||||||
\(650\) | 20.7967 | 0.815715 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.3809 | −0.719850 | ||||||||
\(653\) | −19.0430 | −0.745212 | −0.372606 | − | 0.927990i | \(-0.621536\pi\) | ||||
−0.372606 | + | 0.927990i | \(0.621536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0615579 | 0.00240526 | ||||||||
\(656\) | 31.3931 | 1.22569 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.1633 | −0.513158 | ||||||||
\(659\) | 18.7844 | 0.731738 | 0.365869 | − | 0.930666i | \(-0.380772\pi\) | ||||
0.365869 | + | 0.930666i | \(0.380772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5103 | −0.953340 | −0.476670 | − | 0.879082i | \(-0.658156\pi\) | ||||
−0.476670 | + | 0.879082i | \(0.658156\pi\) | |||||||
\(662\) | −16.5697 | −0.644000 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.614782 | 0.0238582 | ||||||||
\(665\) | −0.125274 | −0.00485793 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1359 | 0.431185 | ||||||||
\(668\) | 2.85780 | 0.110571 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.108733 | −0.00420074 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7336 | −1.22324 | −0.611620 | − | 0.791152i | \(-0.709482\pi\) | ||||
−0.611620 | + | 0.791152i | \(0.709482\pi\) | |||||||
\(674\) | −45.5590 | −1.75487 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.7419 | −0.759303 | ||||||||
\(677\) | −0.989479 | −0.0380288 | −0.0190144 | − | 0.999819i | \(-0.506053\pi\) | ||||
−0.0190144 | + | 0.999819i | \(0.506053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.1730 | 0.927676 | ||||||||
\(680\) | −0.0537081 | −0.00205961 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.5564 | −0.442517 | ||||||||
\(683\) | −9.17009 | −0.350884 | −0.175442 | − | 0.984490i | \(-0.556135\pi\) | ||||
−0.175442 | + | 0.984490i | \(0.556135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0847841 | 0.00323944 | ||||||||
\(686\) | −36.6182 | −1.39809 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.3179 | 0.850862 | ||||||||
\(689\) | −7.22613 | −0.275294 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.4465 | −1.00607 | −0.503037 | − | 0.864265i | \(-0.667784\pi\) | ||||
−0.503037 | + | 0.864265i | \(0.667784\pi\) | |||||||
\(692\) | 20.9658 | 0.796999 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.33041 | −0.0505015 | ||||||||
\(695\) | −0.498761 | −0.0189191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.9057 | 1.62517 | ||||||||
\(698\) | −20.1201 | −0.761559 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −16.9545 | −0.640821 | ||||||||
\(701\) | −0.0832491 | −0.00314428 | −0.00157214 | − | 0.999999i | \(-0.500500\pi\) | ||||
−0.00157214 | + | 0.999999i | \(0.500500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.6780 | 0.855318 | ||||||||
\(704\) | 9.64318 | 0.363441 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 55.8582 | 2.10225 | ||||||||
\(707\) | −3.13049 | −0.117734 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.21742 | 0.0457212 | 0.0228606 | − | 0.999739i | \(-0.492723\pi\) | ||||
0.0228606 | + | 0.999739i | \(0.492723\pi\) | |||||||
\(710\) | −0.412538 | −0.0154823 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.78427 | 0.141822 | ||||||||
\(713\) | 7.01847 | 0.262844 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0504185 | 0.00188555 | ||||||||
\(716\) | 4.92188 | 0.183939 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.1919 | 1.31335 | ||||||||
\(719\) | 32.6735 | 1.21852 | 0.609259 | − | 0.792972i | \(-0.291467\pi\) | ||||
0.609259 | + | 0.792972i | \(0.291467\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.21399 | −0.194179 | ||||||||
\(722\) | −16.7633 | −0.623864 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.53757 | 0.242967 | ||||||||
\(725\) | −44.6308 | −1.65755 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.4836 | −1.83525 | −0.917623 | − | 0.397452i | \(-0.869895\pi\) | ||||
−0.917623 | + | 0.397452i | \(0.869895\pi\) | |||||||
\(728\) | −1.39034 | −0.0515295 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0408534 | 0.00151205 | ||||||||
\(731\) | 30.5024 | 1.12817 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.9962 | −1.84665 | −0.923326 | − | 0.384017i | \(-0.874540\pi\) | ||||
−0.923326 | + | 0.384017i | \(0.874540\pi\) | |||||||
\(734\) | 50.3829 | 1.85967 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.1259 | −0.373245 | ||||||||
\(737\) | 2.12656 | 0.0783328 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.1840 | −0.852837 | −0.426418 | − | 0.904526i | \(-0.640225\pi\) | ||||
−0.426418 | + | 0.904526i | \(0.640225\pi\) | |||||||
\(740\) | −0.380461 | −0.0139860 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.2016 | 0.411224 | ||||||||
\(743\) | −10.5448 | −0.386853 | −0.193426 | − | 0.981115i | \(-0.561960\pi\) | ||||
−0.193426 | + | 0.981115i | \(0.561960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.238444 | −0.00873590 | ||||||||
\(746\) | −15.9717 | −0.584764 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.6581 | 0.389700 | ||||||||
\(749\) | 20.9305 | 0.764785 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.78220 | 0.247486 | 0.123743 | − | 0.992314i | \(-0.460510\pi\) | ||||
0.123743 | + | 0.992314i | \(0.460510\pi\) | |||||||
\(752\) | 14.7370 | 0.537402 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −37.1362 | −1.35242 | ||||||||
\(755\) | 0.129084 | 0.00469786 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.8134 | 0.611092 | 0.305546 | − | 0.952177i | \(-0.401161\pi\) | ||||
0.305546 | + | 0.952177i | \(0.401161\pi\) | |||||||
\(758\) | −55.1102 | −2.00169 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0368073 | −0.00133514 | ||||||||
\(761\) | −18.3728 | −0.666013 | −0.333006 | − | 0.942925i | \(-0.608063\pi\) | ||||
−0.333006 | + | 0.942925i | \(0.608063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.52512 | 0.0552131 | ||||||||
\(764\) | 36.3577 | 1.31538 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.56662 | 0.128867 | ||||||||
\(767\) | 3.97184 | 0.143415 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.84361 | 0.318909 | 0.159454 | − | 0.987205i | \(-0.449026\pi\) | ||||
0.159454 | + | 0.987205i | \(0.449026\pi\) | |||||||
\(770\) | −0.0781565 | −0.00281656 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.2876 | 0.514221 | ||||||||
\(773\) | −2.74567 | −0.0987550 | −0.0493775 | − | 0.998780i | \(-0.515724\pi\) | ||||
−0.0493775 | + | 0.998780i | \(0.515724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.1288 | −1.01042 | ||||||||
\(776\) | 7.10237 | 0.254960 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −61.8273 | −2.21661 | ||||||||
\(779\) | 29.4041 | 1.05351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.06823 | 0.288704 | ||||||||
\(782\) | −12.3079 | −0.440131 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.3918 | 0.585420 | ||||||||
\(785\) | −0.350757 | −0.0125191 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6507 | 0.843056 | 0.421528 | − | 0.906815i | \(-0.361494\pi\) | ||||
0.421528 | + | 0.906815i | \(0.361494\pi\) | |||||||
\(788\) | 26.4561 | 0.942459 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.0207737 | −0.000739096 0 | ||||||||
\(791\) | −17.1626 | −0.610232 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.02531 | −0.0719209 | ||||||||
\(794\) | 38.0399 | 1.34999 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.41836 | 0.156605 | ||||||||
\(797\) | −14.1914 | −0.502685 | −0.251343 | − | 0.967898i | \(-0.580872\pi\) | ||||
−0.251343 | + | 0.967898i | \(0.580872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.1414 | 0.712550 | ||||||||
\(800\) | 40.5827 | 1.43482 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.8031 | −0.840518 | ||||||||
\(803\) | −0.798991 | −0.0281958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0474663 | 0.00167297 | ||||||||
\(806\) | −23.4053 | −0.824415 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.919781 | −0.0323578 | ||||||||
\(809\) | 32.5252 | 1.14353 | 0.571763 | − | 0.820419i | \(-0.306260\pi\) | ||||
0.571763 | + | 0.820419i | \(0.306260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.5530 | −1.00263 | −0.501315 | − | 0.865265i | \(-0.667150\pi\) | ||||
−0.501315 | + | 0.865265i | \(0.667150\pi\) | |||||||
\(812\) | 30.2753 | 1.06245 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.1484 | 0.495902 | ||||||||
\(815\) | −0.206241 | −0.00722429 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.9039 | 0.731335 | ||||||||
\(818\) | 2.25080 | 0.0786973 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.493302 | −0.0172269 | ||||||||
\(821\) | −32.0523 | −1.11863 | −0.559317 | − | 0.828954i | \(-0.688937\pi\) | ||||
−0.559317 | + | 0.828954i | \(0.688937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2285 | −0.391401 | −0.195701 | − | 0.980664i | \(-0.562698\pi\) | ||||
−0.195701 | + | 0.980664i | \(0.562698\pi\) | |||||||
\(824\) | −1.53194 | −0.0533677 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.15697 | −0.214228 | ||||||||
\(827\) | 21.6816 | 0.753942 | 0.376971 | − | 0.926225i | \(-0.376966\pi\) | ||||
0.376971 | + | 0.926225i | \(0.376966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.4695 | 0.884593 | 0.442297 | − | 0.896869i | \(-0.354164\pi\) | ||||
0.442297 | + | 0.896869i | \(0.354164\pi\) | |||||||
\(830\) | 0.0699932 | 0.00242950 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.5304 | 0.677096 | ||||||||
\(833\) | 22.4030 | 0.776218 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0320656 | 0.00110968 | ||||||||
\(836\) | 7.30423 | 0.252622 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.0857 | −0.935659 | ||||||||
\(839\) | 30.6806 | 1.05921 | 0.529606 | − | 0.848244i | \(-0.322340\pi\) | ||||
0.529606 | + | 0.848244i | \(0.322340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.6961 | 1.74814 | ||||||||
\(842\) | 44.3096 | 1.52701 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.20111 | −0.0413440 | ||||||||
\(845\) | −0.221512 | −0.00762023 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.52855 | 0.0525215 | ||||||||
\(848\) | −12.5408 | −0.430651 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 49.3281 | 1.69194 | ||||||||
\(851\) | −8.59269 | −0.294554 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.6407 | 1.18608 | 0.593038 | − | 0.805175i | \(-0.297928\pi\) | ||||
0.593038 | + | 0.805175i | \(0.297928\pi\) | |||||||
\(854\) | 3.13954 | 0.107433 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.14967 | 0.210192 | ||||||||
\(857\) | 11.2033 | 0.382697 | 0.191349 | − | 0.981522i | \(-0.438714\pi\) | ||||
0.191349 | + | 0.981522i | \(0.438714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.97945 | −0.340494 | −0.170247 | − | 0.985401i | \(-0.554457\pi\) | ||||
−0.170247 | + | 0.985401i | \(0.554457\pi\) | |||||||
\(860\) | −0.350697 | −0.0119587 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −63.5540 | −2.16466 | ||||||||
\(863\) | −23.7258 | −0.807635 | −0.403818 | − | 0.914840i | \(-0.632317\pi\) | ||||
−0.403818 | + | 0.914840i | \(0.632317\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.235244 | 0.00799855 | ||||||||
\(866\) | 26.5573 | 0.902455 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.0811 | 0.647656 | ||||||||
\(869\) | 0.406283 | 0.0137822 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.30695 | 0.145935 | ||||||||
\(872\) | 0.448101 | 0.0151746 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.43488 | −0.285314 | ||||||||
\(875\) | −0.380497 | −0.0128631 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.5832 | 1.40417 | 0.702083 | − | 0.712095i | \(-0.252253\pi\) | ||||
0.702083 | + | 0.712095i | \(0.252253\pi\) | |||||||
\(878\) | 0.680845 | 0.0229774 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.0875001 | 0.00294963 | ||||||||
\(881\) | −39.2012 | −1.32072 | −0.660362 | − | 0.750948i | \(-0.729597\pi\) | ||||
−0.660362 | + | 0.750948i | \(0.729597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.8271 | −1.71047 | −0.855235 | − | 0.518241i | \(-0.826587\pi\) | ||||
−0.855235 | + | 0.518241i | \(0.826587\pi\) | |||||||
\(884\) | 21.5860 | 0.726016 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −60.7737 | −2.04173 | ||||||||
\(887\) | 47.9367 | 1.60956 | 0.804779 | − | 0.593575i | \(-0.202284\pi\) | ||||
0.804779 | + | 0.593575i | \(0.202284\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.5851 | −1.09287 | ||||||||
\(890\) | 0.430841 | 0.0144418 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29.5145 | −0.988218 | ||||||||
\(893\) | 13.8033 | 0.461909 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0552255 | 0.00184598 | ||||||||
\(896\) | −5.45905 | −0.182374 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.5087 | −0.784496 | ||||||||
\(899\) | 50.2288 | 1.67523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.1398 | −0.571008 | ||||||||
\(902\) | 18.3447 | 0.610813 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.04260 | −0.167714 | ||||||||
\(905\) | 0.0733541 | 0.00243837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.9393 | 1.55859 | 0.779297 | − | 0.626655i | \(-0.215577\pi\) | ||||
0.779297 | + | 0.626655i | \(0.215577\pi\) | |||||||
\(908\) | 15.4092 | 0.511372 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.158291 | −0.00524730 | ||||||||
\(911\) | 33.9584 | 1.12509 | 0.562546 | − | 0.826766i | \(-0.309822\pi\) | ||||
0.562546 | + | 0.826766i | \(0.309822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.36890 | −0.0453038 | ||||||||
\(914\) | 50.1272 | 1.65806 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 40.1620 | 1.32699 | ||||||||
\(917\) | 3.77976 | 0.124819 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.4841 | −1.59934 | −0.799671 | − | 0.600438i | \(-0.794993\pi\) | ||||
−0.799671 | + | 0.600438i | \(0.794993\pi\) | |||||||
\(920\) | 0.0139462 | 0.000459794 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −31.6551 | −1.04251 | ||||||||
\(923\) | 16.3407 | 0.537860 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.4380 | 1.13231 | ||||||||
\(926\) | 76.4894 | 2.51360 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −72.4675 | −2.37886 | ||||||||
\(929\) | 10.2315 | 0.335685 | 0.167842 | − | 0.985814i | \(-0.446320\pi\) | ||||
0.167842 | + | 0.985814i | \(0.446320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.3532 | 0.503182 | ||||||||
\(932\) | 19.5176 | 0.639322 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.01525 | −0.0659409 | ||||||||
\(935\) | 0.119588 | 0.00391096 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.9700 | −1.27309 | −0.636547 | − | 0.771238i | \(-0.719638\pi\) | ||||
−0.636547 | + | 0.771238i | \(0.719638\pi\) | |||||||
\(938\) | −6.67642 | −0.217993 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.231572 | −0.00755306 | ||||||||
\(941\) | −40.7968 | −1.32994 | −0.664969 | − | 0.746871i | \(-0.731555\pi\) | ||||
−0.664969 | + | 0.746871i | \(0.731555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.1412 | −0.362807 | ||||||||
\(944\) | 6.89303 | 0.224349 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.0416 | 0.424019 | ||||||||
\(947\) | −35.3399 | −1.14839 | −0.574196 | − | 0.818718i | \(-0.694685\pi\) | ||||
−0.574196 | + | 0.818718i | \(0.694685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.61821 | −0.0525292 | ||||||||
\(950\) | 33.8055 | 1.09680 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.29777 | −0.106881 | ||||||||
\(953\) | −34.0800 | −1.10396 | −0.551979 | − | 0.833858i | \(-0.686127\pi\) | ||||
−0.551979 | + | 0.833858i | \(0.686127\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.407948 | 0.0132009 | ||||||||
\(956\) | 5.96406 | 0.192892 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.7045 | 0.927401 | ||||||||
\(959\) | 5.20589 | 0.168107 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.656951 | 0.0211920 | ||||||||
\(962\) | 28.6550 | 0.923874 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.4739 | 1.14254 | ||||||||
\(965\) | 0.160312 | 0.00516064 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.97996 | −0.288776 | −0.144388 | − | 0.989521i | \(-0.546121\pi\) | ||||
−0.144388 | + | 0.989521i | \(0.546121\pi\) | |||||||
\(968\) | 0.449108 | 0.0144349 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.808608 | 0.0259628 | ||||||||
\(971\) | 26.8795 | 0.862604 | 0.431302 | − | 0.902208i | \(-0.358054\pi\) | ||||
0.431302 | + | 0.902208i | \(0.358054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.6248 | −0.981786 | ||||||||
\(974\) | −82.8331 | −2.65414 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.51487 | −0.112508 | ||||||||
\(977\) | 30.1502 | 0.964590 | 0.482295 | − | 0.876009i | \(-0.339803\pi\) | ||||
0.482295 | + | 0.876009i | \(0.339803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.42620 | −0.269302 | ||||||||
\(980\) | −0.257575 | −0.00822795 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 69.0533 | 2.20358 | ||||||||
\(983\) | 15.9793 | 0.509660 | 0.254830 | − | 0.966986i | \(-0.417980\pi\) | ||||
0.254830 | + | 0.966986i | \(0.417980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.296848 | 0.00945836 | ||||||||
\(986\) | −88.0838 | −2.80516 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.7933 | 0.470639 | ||||||||
\(989\) | −7.92047 | −0.251856 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.4827 | −1.34951 | −0.674754 | − | 0.738043i | \(-0.735750\pi\) | ||||
−0.674754 | + | 0.738043i | \(0.735750\pi\) | |||||||
\(992\) | −45.6730 | −1.45012 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.3305 | −0.803436 | ||||||||
\(995\) | 0.0495758 | 0.00157166 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.14096 | −0.0678049 | −0.0339025 | − | 0.999425i | \(-0.510794\pi\) | ||||
−0.0339025 | + | 0.999425i | \(0.510794\pi\) | |||||||
\(998\) | 31.1115 | 0.984817 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.c.1.10 | 11 | ||
3.2 | odd | 2 | 2013.2.a.b.1.2 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.b.1.2 | ✓ | 11 | 3.2 | odd | 2 | ||
6039.2.a.c.1.10 | 11 | 1.1 | even | 1 | trivial |