Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 10x^{5} - x^{4} + 30x^{3} + 7x^{2} - 25x - 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.28109\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35880 | −0.960814 | −0.480407 | − | 0.877046i | \(-0.659511\pi\) | ||||
−0.480407 | + | 0.877046i | \(0.659511\pi\) | |||||||
\(3\) | 0.281095 | 0.162290 | 0.0811451 | − | 0.996702i | \(-0.474142\pi\) | ||||
0.0811451 | + | 0.996702i | \(0.474142\pi\) | |||||||
\(4\) | −0.153673 | −0.0768366 | ||||||||
\(5\) | −3.77273 | −1.68722 | −0.843608 | − | 0.536960i | \(-0.819573\pi\) | ||||
−0.843608 | + | 0.536960i | \(0.819573\pi\) | |||||||
\(6\) | −0.381951 | −0.155931 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.92640 | 1.03464 | ||||||||
\(9\) | −2.92099 | −0.973662 | ||||||||
\(10\) | 5.12637 | 1.62110 | ||||||||
\(11\) | −1.53021 | −0.461375 | −0.230687 | − | 0.973028i | \(-0.574097\pi\) | ||||
−0.230687 | + | 0.973028i | \(0.574097\pi\) | |||||||
\(12\) | −0.0431968 | −0.0124698 | ||||||||
\(13\) | 0.587073 | 0.162825 | 0.0814124 | − | 0.996680i | \(-0.474057\pi\) | ||||
0.0814124 | + | 0.996680i | \(0.474057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.06049 | −0.273819 | ||||||||
\(16\) | −3.66904 | −0.917260 | ||||||||
\(17\) | 6.56030 | 1.59111 | 0.795553 | − | 0.605884i | \(-0.207180\pi\) | ||||
0.795553 | + | 0.605884i | \(0.207180\pi\) | |||||||
\(18\) | 3.96902 | 0.935508 | ||||||||
\(19\) | 0.782214 | 0.179452 | 0.0897261 | − | 0.995966i | \(-0.471401\pi\) | ||||
0.0897261 | + | 0.995966i | \(0.471401\pi\) | |||||||
\(20\) | 0.579768 | 0.129640 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.07924 | 0.443295 | ||||||||
\(23\) | 3.72301 | 0.776301 | 0.388151 | − | 0.921596i | \(-0.373114\pi\) | ||||
0.388151 | + | 0.921596i | \(0.373114\pi\) | |||||||
\(24\) | 0.822597 | 0.167912 | ||||||||
\(25\) | 9.23349 | 1.84670 | ||||||||
\(26\) | −0.797713 | −0.156444 | ||||||||
\(27\) | −1.66436 | −0.320306 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.82177 | 1.45247 | 0.726233 | − | 0.687449i | \(-0.241269\pi\) | ||||
0.726233 | + | 0.687449i | \(0.241269\pi\) | |||||||
\(30\) | 1.44100 | 0.263089 | ||||||||
\(31\) | −5.80820 | −1.04318 | −0.521592 | − | 0.853195i | \(-0.674662\pi\) | ||||
−0.521592 | + | 0.853195i | \(0.674662\pi\) | |||||||
\(32\) | −0.867331 | −0.153324 | ||||||||
\(33\) | −0.430133 | −0.0748766 | ||||||||
\(34\) | −8.91411 | −1.52876 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.448877 | 0.0748129 | ||||||||
\(37\) | 8.38915 | 1.37917 | 0.689584 | − | 0.724206i | \(-0.257793\pi\) | ||||
0.689584 | + | 0.724206i | \(0.257793\pi\) | |||||||
\(38\) | −1.06287 | −0.172420 | ||||||||
\(39\) | 0.165023 | 0.0264249 | ||||||||
\(40\) | −11.0405 | −1.74566 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.36609 | −1.42831 | −0.714157 | − | 0.699985i | \(-0.753190\pi\) | ||||
−0.714157 | + | 0.699985i | \(0.753190\pi\) | |||||||
\(44\) | 0.235152 | 0.0354505 | ||||||||
\(45\) | 11.0201 | 1.64278 | ||||||||
\(46\) | −5.05881 | −0.745881 | ||||||||
\(47\) | −11.9226 | −1.73909 | −0.869547 | − | 0.493851i | \(-0.835589\pi\) | ||||
−0.869547 | + | 0.493851i | \(0.835589\pi\) | |||||||
\(48\) | −1.03135 | −0.148862 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.5464 | −1.77433 | ||||||||
\(51\) | 1.84407 | 0.258221 | ||||||||
\(52\) | −0.0902175 | −0.0125109 | ||||||||
\(53\) | 1.92403 | 0.264286 | 0.132143 | − | 0.991231i | \(-0.457814\pi\) | ||||
0.132143 | + | 0.991231i | \(0.457814\pi\) | |||||||
\(54\) | 2.26152 | 0.307754 | ||||||||
\(55\) | 5.77306 | 0.778439 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.219876 | 0.0291233 | ||||||||
\(58\) | −10.6282 | −1.39555 | ||||||||
\(59\) | −4.28746 | −0.558180 | −0.279090 | − | 0.960265i | \(-0.590033\pi\) | ||||
−0.279090 | + | 0.960265i | \(0.590033\pi\) | |||||||
\(60\) | 0.162970 | 0.0210393 | ||||||||
\(61\) | 8.46897 | 1.08434 | 0.542170 | − | 0.840269i | \(-0.317603\pi\) | ||||
0.542170 | + | 0.840269i | \(0.317603\pi\) | |||||||
\(62\) | 7.89217 | 1.00231 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.51660 | 1.06458 | ||||||||
\(65\) | −2.21487 | −0.274721 | ||||||||
\(66\) | 0.584463 | 0.0719425 | ||||||||
\(67\) | −11.5220 | −1.40764 | −0.703818 | − | 0.710381i | \(-0.748523\pi\) | ||||
−0.703818 | + | 0.710381i | \(0.748523\pi\) | |||||||
\(68\) | −1.00814 | −0.122255 | ||||||||
\(69\) | 1.04652 | 0.125986 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.18700 | 0.971618 | 0.485809 | − | 0.874065i | \(-0.338525\pi\) | ||||
0.485809 | + | 0.874065i | \(0.338525\pi\) | |||||||
\(72\) | −8.54798 | −1.00739 | ||||||||
\(73\) | 1.05736 | 0.123755 | 0.0618774 | − | 0.998084i | \(-0.480291\pi\) | ||||
0.0618774 | + | 0.998084i | \(0.480291\pi\) | |||||||
\(74\) | −11.3991 | −1.32512 | ||||||||
\(75\) | 2.59549 | 0.299701 | ||||||||
\(76\) | −0.120205 | −0.0137885 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.224233 | −0.0253894 | ||||||||
\(79\) | 7.19339 | 0.809319 | 0.404660 | − | 0.914467i | \(-0.367390\pi\) | ||||
0.404660 | + | 0.914467i | \(0.367390\pi\) | |||||||
\(80\) | 13.8423 | 1.54761 | ||||||||
\(81\) | 8.29511 | 0.921679 | ||||||||
\(82\) | −1.35880 | −0.150054 | ||||||||
\(83\) | −8.44048 | −0.926463 | −0.463231 | − | 0.886237i | \(-0.653310\pi\) | ||||
−0.463231 | + | 0.886237i | \(0.653310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.7502 | −2.68454 | ||||||||
\(86\) | 12.7266 | 1.37234 | ||||||||
\(87\) | 2.19866 | 0.235721 | ||||||||
\(88\) | −4.47800 | −0.477357 | ||||||||
\(89\) | −7.83130 | −0.830116 | −0.415058 | − | 0.909795i | \(-0.636239\pi\) | ||||
−0.415058 | + | 0.909795i | \(0.636239\pi\) | |||||||
\(90\) | −14.9741 | −1.57840 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.572127 | −0.0596484 | ||||||||
\(93\) | −1.63266 | −0.169299 | ||||||||
\(94\) | 16.2004 | 1.67095 | ||||||||
\(95\) | −2.95108 | −0.302775 | ||||||||
\(96\) | −0.243802 | −0.0248830 | ||||||||
\(97\) | −13.2606 | −1.34641 | −0.673204 | − | 0.739457i | \(-0.735083\pi\) | ||||
−0.673204 | + | 0.739457i | \(0.735083\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.46971 | 0.449223 | ||||||||
\(100\) | −1.41894 | −0.141894 | ||||||||
\(101\) | 6.44946 | 0.641746 | 0.320873 | − | 0.947122i | \(-0.396024\pi\) | ||||
0.320873 | + | 0.947122i | \(0.396024\pi\) | |||||||
\(102\) | −2.50571 | −0.248102 | ||||||||
\(103\) | −18.0323 | −1.77678 | −0.888388 | − | 0.459094i | \(-0.848174\pi\) | ||||
−0.888388 | + | 0.459094i | \(0.848174\pi\) | |||||||
\(104\) | 1.71801 | 0.168465 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.61436 | −0.253929 | ||||||||
\(107\) | 13.0048 | 1.25722 | 0.628609 | − | 0.777721i | \(-0.283625\pi\) | ||||
0.628609 | + | 0.777721i | \(0.283625\pi\) | |||||||
\(108\) | 0.255767 | 0.0246112 | ||||||||
\(109\) | −10.5419 | −1.00973 | −0.504866 | − | 0.863198i | \(-0.668458\pi\) | ||||
−0.504866 | + | 0.863198i | \(0.668458\pi\) | |||||||
\(110\) | −7.84441 | −0.747935 | ||||||||
\(111\) | 2.35815 | 0.223825 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.782350 | −0.0735973 | −0.0367987 | − | 0.999323i | \(-0.511716\pi\) | ||||
−0.0367987 | + | 0.999323i | \(0.511716\pi\) | |||||||
\(114\) | −0.298767 | −0.0279821 | ||||||||
\(115\) | −14.0459 | −1.30979 | ||||||||
\(116\) | −1.20200 | −0.111603 | ||||||||
\(117\) | −1.71483 | −0.158536 | ||||||||
\(118\) | 5.82578 | 0.536307 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.10343 | −0.283304 | ||||||||
\(121\) | −8.65847 | −0.787133 | ||||||||
\(122\) | −11.5076 | −1.04185 | ||||||||
\(123\) | 0.281095 | 0.0253455 | ||||||||
\(124\) | 0.892566 | 0.0801548 | ||||||||
\(125\) | −15.9718 | −1.42856 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.17842 | −0.282039 | −0.141020 | − | 0.990007i | \(-0.545038\pi\) | ||||
−0.141020 | + | 0.990007i | \(0.545038\pi\) | |||||||
\(128\) | −9.83766 | −0.869535 | ||||||||
\(129\) | −2.63276 | −0.231801 | ||||||||
\(130\) | 3.00956 | 0.263955 | ||||||||
\(131\) | 14.7349 | 1.28739 | 0.643695 | − | 0.765282i | \(-0.277401\pi\) | ||||
0.643695 | + | 0.765282i | \(0.277401\pi\) | |||||||
\(132\) | 0.0661000 | 0.00575326 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.6560 | 1.35248 | ||||||||
\(135\) | 6.27917 | 0.540425 | ||||||||
\(136\) | 19.1981 | 1.64622 | ||||||||
\(137\) | 7.83949 | 0.669772 | 0.334886 | − | 0.942259i | \(-0.391302\pi\) | ||||
0.334886 | + | 0.942259i | \(0.391302\pi\) | |||||||
\(138\) | −1.42201 | −0.121049 | ||||||||
\(139\) | −10.9730 | −0.930716 | −0.465358 | − | 0.885123i | \(-0.654074\pi\) | ||||
−0.465358 | + | 0.885123i | \(0.654074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.35139 | −0.282238 | ||||||||
\(142\) | −11.1245 | −0.933544 | ||||||||
\(143\) | −0.898344 | −0.0751233 | ||||||||
\(144\) | 10.7172 | 0.893101 | ||||||||
\(145\) | −29.5094 | −2.45062 | ||||||||
\(146\) | −1.43674 | −0.118905 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.28919 | −0.105971 | ||||||||
\(149\) | −6.34397 | −0.519718 | −0.259859 | − | 0.965647i | \(-0.583676\pi\) | ||||
−0.259859 | + | 0.965647i | \(0.583676\pi\) | |||||||
\(150\) | −3.52674 | −0.287957 | ||||||||
\(151\) | −0.708131 | −0.0576269 | −0.0288134 | − | 0.999585i | \(-0.509173\pi\) | ||||
−0.0288134 | + | 0.999585i | \(0.509173\pi\) | |||||||
\(152\) | 2.28907 | 0.185668 | ||||||||
\(153\) | −19.1625 | −1.54920 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.9128 | 1.76008 | ||||||||
\(156\) | −0.0253597 | −0.00203040 | ||||||||
\(157\) | −12.2054 | −0.974096 | −0.487048 | − | 0.873375i | \(-0.661926\pi\) | ||||
−0.487048 | + | 0.873375i | \(0.661926\pi\) | |||||||
\(158\) | −9.77435 | −0.777605 | ||||||||
\(159\) | 0.540834 | 0.0428909 | ||||||||
\(160\) | 3.27221 | 0.258691 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.2714 | −0.885562 | ||||||||
\(163\) | 1.01447 | 0.0794595 | 0.0397297 | − | 0.999210i | \(-0.487350\pi\) | ||||
0.0397297 | + | 0.999210i | \(0.487350\pi\) | |||||||
\(164\) | −0.153673 | −0.0119999 | ||||||||
\(165\) | 1.62278 | 0.126333 | ||||||||
\(166\) | 11.4689 | 0.890158 | ||||||||
\(167\) | 5.31016 | 0.410913 | 0.205456 | − | 0.978666i | \(-0.434132\pi\) | ||||
0.205456 | + | 0.978666i | \(0.434132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6553 | −0.973488 | ||||||||
\(170\) | 33.6305 | 2.57934 | ||||||||
\(171\) | −2.28484 | −0.174726 | ||||||||
\(172\) | 1.43932 | 0.109747 | ||||||||
\(173\) | 2.51787 | 0.191430 | 0.0957151 | − | 0.995409i | \(-0.469486\pi\) | ||||
0.0957151 | + | 0.995409i | \(0.469486\pi\) | |||||||
\(174\) | −2.98753 | −0.226484 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.61439 | 0.423200 | ||||||||
\(177\) | −1.20518 | −0.0905871 | ||||||||
\(178\) | 10.6411 | 0.797587 | ||||||||
\(179\) | 13.8227 | 1.03316 | 0.516580 | − | 0.856239i | \(-0.327205\pi\) | ||||
0.516580 | + | 0.856239i | \(0.327205\pi\) | |||||||
\(180\) | −1.69349 | −0.126226 | ||||||||
\(181\) | 3.90137 | 0.289987 | 0.144993 | − | 0.989433i | \(-0.453684\pi\) | ||||
0.144993 | + | 0.989433i | \(0.453684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.38058 | 0.175978 | ||||||||
\(184\) | 10.8950 | 0.803192 | ||||||||
\(185\) | −31.6500 | −2.32695 | ||||||||
\(186\) | 2.21845 | 0.162664 | ||||||||
\(187\) | −10.0386 | −0.734096 | ||||||||
\(188\) | 1.83219 | 0.133626 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00992 | 0.290910 | ||||||||
\(191\) | −15.2024 | −1.10001 | −0.550003 | − | 0.835163i | \(-0.685373\pi\) | ||||
−0.550003 | + | 0.835163i | \(0.685373\pi\) | |||||||
\(192\) | 2.39397 | 0.172770 | ||||||||
\(193\) | 14.7029 | 1.05834 | 0.529168 | − | 0.848517i | \(-0.322504\pi\) | ||||
0.529168 | + | 0.848517i | \(0.322504\pi\) | |||||||
\(194\) | 18.0184 | 1.29365 | ||||||||
\(195\) | −0.622588 | −0.0445845 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4673 | 0.817010 | 0.408505 | − | 0.912756i | \(-0.366050\pi\) | ||||
0.408505 | + | 0.912756i | \(0.366050\pi\) | |||||||
\(198\) | −6.07343 | −0.431620 | ||||||||
\(199\) | −16.6817 | −1.18253 | −0.591266 | − | 0.806476i | \(-0.701372\pi\) | ||||
−0.591266 | + | 0.806476i | \(0.701372\pi\) | |||||||
\(200\) | 27.0209 | 1.91067 | ||||||||
\(201\) | −3.23877 | −0.228445 | ||||||||
\(202\) | −8.76351 | −0.616598 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.283384 | −0.0198408 | ||||||||
\(205\) | −3.77273 | −0.263499 | ||||||||
\(206\) | 24.5022 | 1.70715 | ||||||||
\(207\) | −10.8749 | −0.755855 | ||||||||
\(208\) | −2.15399 | −0.149353 | ||||||||
\(209\) | −1.19695 | −0.0827947 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.81295 | 0.675551 | 0.337776 | − | 0.941227i | \(-0.390325\pi\) | ||||
0.337776 | + | 0.941227i | \(0.390325\pi\) | |||||||
\(212\) | −0.295672 | −0.0203068 | ||||||||
\(213\) | 2.30132 | 0.157684 | ||||||||
\(214\) | −17.6708 | −1.20795 | ||||||||
\(215\) | 35.3357 | 2.40988 | ||||||||
\(216\) | −4.87058 | −0.331401 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.3243 | 0.970164 | ||||||||
\(219\) | 0.297219 | 0.0200842 | ||||||||
\(220\) | −0.887164 | −0.0598126 | ||||||||
\(221\) | 3.85138 | 0.259072 | ||||||||
\(222\) | −3.20424 | −0.215055 | ||||||||
\(223\) | −7.71539 | −0.516661 | −0.258330 | − | 0.966057i | \(-0.583172\pi\) | ||||
−0.258330 | + | 0.966057i | \(0.583172\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.9709 | −1.79806 | ||||||||
\(226\) | 1.06305 | 0.0707133 | ||||||||
\(227\) | −26.8002 | −1.77879 | −0.889396 | − | 0.457137i | \(-0.848875\pi\) | ||||
−0.889396 | + | 0.457137i | \(0.848875\pi\) | |||||||
\(228\) | −0.0337891 | −0.00223774 | ||||||||
\(229\) | −10.8206 | −0.715049 | −0.357524 | − | 0.933904i | \(-0.616379\pi\) | ||||
−0.357524 | + | 0.933904i | \(0.616379\pi\) | |||||||
\(230\) | 19.0855 | 1.25846 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.8896 | 1.50278 | ||||||||
\(233\) | −9.09982 | −0.596149 | −0.298075 | − | 0.954543i | \(-0.596344\pi\) | ||||
−0.298075 | + | 0.954543i | \(0.596344\pi\) | |||||||
\(234\) | 2.33011 | 0.152324 | ||||||||
\(235\) | 44.9808 | 2.93423 | ||||||||
\(236\) | 0.658868 | 0.0428886 | ||||||||
\(237\) | 2.02202 | 0.131345 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.68484 | −0.238353 | −0.119176 | − | 0.992873i | \(-0.538025\pi\) | ||||
−0.119176 | + | 0.992873i | \(0.538025\pi\) | |||||||
\(240\) | 3.89100 | 0.251163 | ||||||||
\(241\) | −8.01651 | −0.516389 | −0.258194 | − | 0.966093i | \(-0.583127\pi\) | ||||
−0.258194 | + | 0.966093i | \(0.583127\pi\) | |||||||
\(242\) | 11.7651 | 0.756289 | ||||||||
\(243\) | 7.32479 | 0.469885 | ||||||||
\(244\) | −1.30145 | −0.0833170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.381951 | −0.0243523 | ||||||||
\(247\) | 0.459217 | 0.0292193 | ||||||||
\(248\) | −16.9971 | −1.07932 | ||||||||
\(249\) | −2.37257 | −0.150356 | ||||||||
\(250\) | 21.7024 | 1.37258 | ||||||||
\(251\) | 1.60958 | 0.101596 | 0.0507979 | − | 0.998709i | \(-0.483824\pi\) | ||||
0.0507979 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.69697 | −0.358166 | ||||||||
\(254\) | 4.31882 | 0.270987 | ||||||||
\(255\) | −6.95716 | −0.435675 | ||||||||
\(256\) | −3.66583 | −0.229114 | ||||||||
\(257\) | 20.1668 | 1.25797 | 0.628986 | − | 0.777417i | \(-0.283470\pi\) | ||||
0.628986 | + | 0.777417i | \(0.283470\pi\) | |||||||
\(258\) | 3.57738 | 0.222718 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.340366 | 0.0211086 | ||||||||
\(261\) | −22.8473 | −1.41421 | ||||||||
\(262\) | −20.0217 | −1.23694 | ||||||||
\(263\) | −24.8290 | −1.53102 | −0.765512 | − | 0.643422i | \(-0.777514\pi\) | ||||
−0.765512 | + | 0.643422i | \(0.777514\pi\) | |||||||
\(264\) | −1.25874 | −0.0774703 | ||||||||
\(265\) | −7.25884 | −0.445907 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.20134 | −0.134720 | ||||||||
\(268\) | 1.77062 | 0.108158 | ||||||||
\(269\) | −30.7089 | −1.87235 | −0.936177 | − | 0.351530i | \(-0.885662\pi\) | ||||
−0.936177 | + | 0.351530i | \(0.885662\pi\) | |||||||
\(270\) | −8.53212 | −0.519248 | ||||||||
\(271\) | −18.2934 | −1.11125 | −0.555624 | − | 0.831434i | \(-0.687520\pi\) | ||||
−0.555624 | + | 0.831434i | \(0.687520\pi\) | |||||||
\(272\) | −24.0700 | −1.45946 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.6523 | −0.643527 | ||||||||
\(275\) | −14.1291 | −0.852020 | ||||||||
\(276\) | −0.160822 | −0.00968034 | ||||||||
\(277\) | 1.06650 | 0.0640798 | 0.0320399 | − | 0.999487i | \(-0.489800\pi\) | ||||
0.0320399 | + | 0.999487i | \(0.489800\pi\) | |||||||
\(278\) | 14.9100 | 0.894245 | ||||||||
\(279\) | 16.9657 | 1.01571 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.32567 | 0.0790828 | 0.0395414 | − | 0.999218i | \(-0.487410\pi\) | ||||
0.0395414 | + | 0.999218i | \(0.487410\pi\) | |||||||
\(282\) | 4.55385 | 0.271178 | ||||||||
\(283\) | 21.5009 | 1.27809 | 0.639047 | − | 0.769168i | \(-0.279329\pi\) | ||||
0.639047 | + | 0.769168i | \(0.279329\pi\) | |||||||
\(284\) | −1.25812 | −0.0746558 | ||||||||
\(285\) | −0.829534 | −0.0491373 | ||||||||
\(286\) | 1.22067 | 0.0721795 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.53346 | 0.149286 | ||||||||
\(289\) | 26.0375 | 1.53162 | ||||||||
\(290\) | 40.0973 | 2.35459 | ||||||||
\(291\) | −3.72748 | −0.218509 | ||||||||
\(292\) | −0.162488 | −0.00950890 | ||||||||
\(293\) | 19.4483 | 1.13618 | 0.568092 | − | 0.822965i | \(-0.307682\pi\) | ||||
0.568092 | + | 0.822965i | \(0.307682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1754 | 0.941770 | ||||||||
\(296\) | 24.5500 | 1.42694 | ||||||||
\(297\) | 2.54681 | 0.147781 | ||||||||
\(298\) | 8.62017 | 0.499353 | ||||||||
\(299\) | 2.18568 | 0.126401 | ||||||||
\(300\) | −0.398857 | −0.0230280 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.962205 | 0.0553687 | ||||||||
\(303\) | 1.81291 | 0.104149 | ||||||||
\(304\) | −2.86997 | −0.164604 | ||||||||
\(305\) | −31.9511 | −1.82952 | ||||||||
\(306\) | 26.0380 | 1.48849 | ||||||||
\(307\) | −28.5378 | −1.62874 | −0.814369 | − | 0.580348i | \(-0.802917\pi\) | ||||
−0.814369 | + | 0.580348i | \(0.802917\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.06879 | −0.288353 | ||||||||
\(310\) | −29.7750 | −1.69111 | ||||||||
\(311\) | −9.63544 | −0.546375 | −0.273188 | − | 0.961961i | \(-0.588078\pi\) | ||||
−0.273188 | + | 0.961961i | \(0.588078\pi\) | |||||||
\(312\) | 0.482925 | 0.0273402 | ||||||||
\(313\) | 33.6028 | 1.89934 | 0.949671 | − | 0.313248i | \(-0.101417\pi\) | ||||
0.949671 | + | 0.313248i | \(0.101417\pi\) | |||||||
\(314\) | 16.5846 | 0.935925 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.10543 | −0.0621854 | ||||||||
\(317\) | −30.9417 | −1.73786 | −0.868931 | − | 0.494934i | \(-0.835192\pi\) | ||||
−0.868931 | + | 0.494934i | \(0.835192\pi\) | |||||||
\(318\) | −0.734884 | −0.0412102 | ||||||||
\(319\) | −11.9689 | −0.670131 | ||||||||
\(320\) | −32.1308 | −1.79617 | ||||||||
\(321\) | 3.65557 | 0.204034 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.13156 | 0.285528 | ||||||||
\(324\) | −1.27474 | −0.0708187 | ||||||||
\(325\) | 5.42073 | 0.300688 | ||||||||
\(326\) | −1.37846 | −0.0763458 | ||||||||
\(327\) | −2.96328 | −0.163870 | ||||||||
\(328\) | 2.92640 | 0.161584 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.20502 | −0.121382 | ||||||||
\(331\) | −10.0239 | −0.550962 | −0.275481 | − | 0.961306i | \(-0.588837\pi\) | ||||
−0.275481 | + | 0.961306i | \(0.588837\pi\) | |||||||
\(332\) | 1.29708 | 0.0711863 | ||||||||
\(333\) | −24.5046 | −1.34284 | ||||||||
\(334\) | −7.21543 | −0.394811 | ||||||||
\(335\) | 43.4694 | 2.37498 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00576 | 0.272681 | 0.136341 | − | 0.990662i | \(-0.456466\pi\) | ||||
0.136341 | + | 0.990662i | \(0.456466\pi\) | |||||||
\(338\) | 17.1960 | 0.935341 | ||||||||
\(339\) | −0.219915 | −0.0119441 | ||||||||
\(340\) | 3.80345 | 0.206271 | ||||||||
\(341\) | 8.88775 | 0.481299 | ||||||||
\(342\) | 3.10463 | 0.167879 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −27.4089 | −1.47779 | ||||||||
\(345\) | −3.94823 | −0.212566 | ||||||||
\(346\) | −3.42127 | −0.183929 | ||||||||
\(347\) | −11.0497 | −0.593177 | −0.296589 | − | 0.955005i | \(-0.595849\pi\) | ||||
−0.296589 | + | 0.955005i | \(0.595849\pi\) | |||||||
\(348\) | −0.337875 | −0.0181120 | ||||||||
\(349\) | −10.7923 | −0.577698 | −0.288849 | − | 0.957375i | \(-0.593273\pi\) | ||||
−0.288849 | + | 0.957375i | \(0.593273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.977100 | −0.0521538 | ||||||||
\(352\) | 1.32720 | 0.0707398 | ||||||||
\(353\) | 21.4959 | 1.14411 | 0.572057 | − | 0.820214i | \(-0.306146\pi\) | ||||
0.572057 | + | 0.820214i | \(0.306146\pi\) | |||||||
\(354\) | 1.63760 | 0.0870373 | ||||||||
\(355\) | −30.8873 | −1.63933 | ||||||||
\(356\) | 1.20346 | 0.0637833 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.7823 | −0.992674 | ||||||||
\(359\) | −9.86289 | −0.520543 | −0.260272 | − | 0.965535i | \(-0.583812\pi\) | ||||
−0.260272 | + | 0.965535i | \(0.583812\pi\) | |||||||
\(360\) | 32.2492 | 1.69968 | ||||||||
\(361\) | −18.3881 | −0.967797 | ||||||||
\(362\) | −5.30117 | −0.278623 | ||||||||
\(363\) | −2.43385 | −0.127744 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.98914 | −0.208801 | ||||||||
\(366\) | −3.23473 | −0.169082 | ||||||||
\(367\) | −27.1347 | −1.41642 | −0.708210 | − | 0.706001i | \(-0.750497\pi\) | ||||
−0.708210 | + | 0.706001i | \(0.750497\pi\) | |||||||
\(368\) | −13.6599 | −0.712070 | ||||||||
\(369\) | −2.92099 | −0.152060 | ||||||||
\(370\) | 43.0059 | 2.23577 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.250896 | 0.0130083 | ||||||||
\(373\) | −2.74716 | −0.142242 | −0.0711212 | − | 0.997468i | \(-0.522658\pi\) | ||||
−0.0711212 | + | 0.997468i | \(0.522658\pi\) | |||||||
\(374\) | 13.6404 | 0.705330 | ||||||||
\(375\) | −4.48959 | −0.231842 | ||||||||
\(376\) | −34.8904 | −1.79934 | ||||||||
\(377\) | 4.59195 | 0.236498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.3984 | 1.51010 | 0.755048 | − | 0.655670i | \(-0.227614\pi\) | ||||
0.755048 | + | 0.655670i | \(0.227614\pi\) | |||||||
\(380\) | 0.453502 | 0.0232642 | ||||||||
\(381\) | −0.893437 | −0.0457722 | ||||||||
\(382\) | 20.6569 | 1.05690 | ||||||||
\(383\) | 6.69629 | 0.342164 | 0.171082 | − | 0.985257i | \(-0.445274\pi\) | ||||
0.171082 | + | 0.985257i | \(0.445274\pi\) | |||||||
\(384\) | −2.76532 | −0.141117 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.9782 | −1.01686 | ||||||||
\(387\) | 27.3582 | 1.39070 | ||||||||
\(388\) | 2.03780 | 0.103453 | ||||||||
\(389\) | 0.478863 | 0.0242793 | 0.0121397 | − | 0.999926i | \(-0.496136\pi\) | ||||
0.0121397 | + | 0.999926i | \(0.496136\pi\) | |||||||
\(390\) | 0.845970 | 0.0428374 | ||||||||
\(391\) | 24.4241 | 1.23518 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.14189 | 0.208931 | ||||||||
\(394\) | −15.5817 | −0.784995 | ||||||||
\(395\) | −27.1387 | −1.36550 | ||||||||
\(396\) | −0.686875 | −0.0345168 | ||||||||
\(397\) | 24.2293 | 1.21603 | 0.608016 | − | 0.793925i | \(-0.291966\pi\) | ||||
0.608016 | + | 0.793925i | \(0.291966\pi\) | |||||||
\(398\) | 22.6670 | 1.13619 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −33.8780 | −1.69390 | ||||||||
\(401\) | 23.2843 | 1.16276 | 0.581381 | − | 0.813631i | \(-0.302512\pi\) | ||||
0.581381 | + | 0.813631i | \(0.302512\pi\) | |||||||
\(402\) | 4.40083 | 0.219493 | ||||||||
\(403\) | −3.40984 | −0.169856 | ||||||||
\(404\) | −0.991110 | −0.0493096 | ||||||||
\(405\) | −31.2952 | −1.55507 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.8371 | −0.636313 | ||||||||
\(408\) | 5.39648 | 0.267166 | ||||||||
\(409\) | −30.6511 | −1.51560 | −0.757800 | − | 0.652487i | \(-0.773726\pi\) | ||||
−0.757800 | + | 0.652487i | \(0.773726\pi\) | |||||||
\(410\) | 5.12637 | 0.253173 | ||||||||
\(411\) | 2.20364 | 0.108697 | ||||||||
\(412\) | 2.77108 | 0.136521 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.7767 | 0.726236 | ||||||||
\(415\) | 31.8436 | 1.56314 | ||||||||
\(416\) | −0.509187 | −0.0249649 | ||||||||
\(417\) | −3.08445 | −0.151046 | ||||||||
\(418\) | 1.62641 | 0.0795503 | ||||||||
\(419\) | −5.54908 | −0.271090 | −0.135545 | − | 0.990771i | \(-0.543279\pi\) | ||||
−0.135545 | + | 0.990771i | \(0.543279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8783 | 0.578913 | 0.289457 | − | 0.957191i | \(-0.406525\pi\) | ||||
0.289457 | + | 0.957191i | \(0.406525\pi\) | |||||||
\(422\) | −13.3338 | −0.649079 | ||||||||
\(423\) | 34.8258 | 1.69329 | ||||||||
\(424\) | 5.63048 | 0.273440 | ||||||||
\(425\) | 60.5745 | 2.93829 | ||||||||
\(426\) | −3.12703 | −0.151505 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.99849 | −0.0966004 | ||||||||
\(429\) | −0.252520 | −0.0121918 | ||||||||
\(430\) | −48.0140 | −2.31544 | ||||||||
\(431\) | −15.8059 | −0.761345 | −0.380673 | − | 0.924710i | \(-0.624307\pi\) | ||||
−0.380673 | + | 0.924710i | \(0.624307\pi\) | |||||||
\(432\) | 6.10659 | 0.293804 | ||||||||
\(433\) | 17.8949 | 0.859976 | 0.429988 | − | 0.902835i | \(-0.358518\pi\) | ||||
0.429988 | + | 0.902835i | \(0.358518\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.29495 | −0.397712 | ||||||||
\(436\) | 1.62001 | 0.0775844 | ||||||||
\(437\) | 2.91219 | 0.139309 | ||||||||
\(438\) | −0.403860 | −0.0192972 | ||||||||
\(439\) | −39.1919 | −1.87053 | −0.935263 | − | 0.353955i | \(-0.884837\pi\) | ||||
−0.935263 | + | 0.353955i | \(0.884837\pi\) | |||||||
\(440\) | 16.8943 | 0.805404 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.23324 | −0.248920 | ||||||||
\(443\) | 37.8749 | 1.79949 | 0.899746 | − | 0.436414i | \(-0.143752\pi\) | ||||
0.899746 | + | 0.436414i | \(0.143752\pi\) | |||||||
\(444\) | −0.362384 | −0.0171980 | ||||||||
\(445\) | 29.5454 | 1.40058 | ||||||||
\(446\) | 10.4836 | 0.496415 | ||||||||
\(447\) | −1.78326 | −0.0843452 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.7250 | 1.07246 | 0.536230 | − | 0.844072i | \(-0.319848\pi\) | ||||
0.536230 | + | 0.844072i | \(0.319848\pi\) | |||||||
\(450\) | 36.6479 | 1.72760 | ||||||||
\(451\) | −1.53021 | −0.0720546 | ||||||||
\(452\) | 0.120226 | 0.00565497 | ||||||||
\(453\) | −0.199052 | −0.00935227 | ||||||||
\(454\) | 36.4160 | 1.70909 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.643447 | 0.0301322 | ||||||||
\(457\) | −24.3084 | −1.13710 | −0.568550 | − | 0.822649i | \(-0.692495\pi\) | ||||
−0.568550 | + | 0.822649i | \(0.692495\pi\) | |||||||
\(458\) | 14.7031 | 0.687029 | ||||||||
\(459\) | −10.9187 | −0.509641 | ||||||||
\(460\) | 2.15848 | 0.100640 | ||||||||
\(461\) | −27.0463 | −1.25967 | −0.629837 | − | 0.776727i | \(-0.716878\pi\) | ||||
−0.629837 | + | 0.776727i | \(0.716878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.77747 | 0.454398 | 0.227199 | − | 0.973848i | \(-0.427043\pi\) | ||||
0.227199 | + | 0.973848i | \(0.427043\pi\) | |||||||
\(464\) | −28.6984 | −1.33229 | ||||||||
\(465\) | 6.15957 | 0.285643 | ||||||||
\(466\) | 12.3648 | 0.572788 | ||||||||
\(467\) | 25.1283 | 1.16280 | 0.581400 | − | 0.813618i | \(-0.302505\pi\) | ||||
0.581400 | + | 0.813618i | \(0.302505\pi\) | |||||||
\(468\) | 0.263524 | 0.0121814 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −61.1198 | −2.81925 | ||||||||
\(471\) | −3.43087 | −0.158086 | ||||||||
\(472\) | −12.5468 | −0.577515 | ||||||||
\(473\) | 14.3320 | 0.658988 | ||||||||
\(474\) | −2.74752 | −0.126198 | ||||||||
\(475\) | 7.22256 | 0.331394 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.62006 | −0.257325 | ||||||||
\(478\) | 5.00695 | 0.229012 | ||||||||
\(479\) | 35.1189 | 1.60462 | 0.802311 | − | 0.596906i | \(-0.203603\pi\) | ||||
0.802311 | + | 0.596906i | \(0.203603\pi\) | |||||||
\(480\) | 0.919800 | 0.0419829 | ||||||||
\(481\) | 4.92505 | 0.224563 | ||||||||
\(482\) | 10.8928 | 0.496153 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.33057 | 0.0604807 | ||||||||
\(485\) | 50.0286 | 2.27168 | ||||||||
\(486\) | −9.95289 | −0.451472 | ||||||||
\(487\) | −19.5496 | −0.885876 | −0.442938 | − | 0.896552i | \(-0.646064\pi\) | ||||
−0.442938 | + | 0.896552i | \(0.646064\pi\) | |||||||
\(488\) | 24.7836 | 1.12190 | ||||||||
\(489\) | 0.285162 | 0.0128955 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2980 | 0.464742 | 0.232371 | − | 0.972627i | \(-0.425352\pi\) | ||||
0.232371 | + | 0.972627i | \(0.425352\pi\) | |||||||
\(492\) | −0.0431968 | −0.00194746 | ||||||||
\(493\) | 51.3132 | 2.31103 | ||||||||
\(494\) | −0.623982 | −0.0280743 | ||||||||
\(495\) | −16.8630 | −0.757936 | ||||||||
\(496\) | 21.3105 | 0.956871 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.22384 | 0.144464 | ||||||||
\(499\) | −21.2111 | −0.949541 | −0.474770 | − | 0.880110i | \(-0.657469\pi\) | ||||
−0.474770 | + | 0.880110i | \(0.657469\pi\) | |||||||
\(500\) | 2.45444 | 0.109766 | ||||||||
\(501\) | 1.49266 | 0.0666871 | ||||||||
\(502\) | −2.18709 | −0.0976146 | ||||||||
\(503\) | −44.6725 | −1.99185 | −0.995923 | − | 0.0902029i | \(-0.971248\pi\) | ||||
−0.995923 | + | 0.0902029i | \(0.971248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.3321 | −1.08276 | ||||||||
\(506\) | 7.74103 | 0.344131 | ||||||||
\(507\) | −3.55735 | −0.157988 | ||||||||
\(508\) | 0.488438 | 0.0216709 | ||||||||
\(509\) | 23.3618 | 1.03549 | 0.517747 | − | 0.855534i | \(-0.326771\pi\) | ||||
0.517747 | + | 0.855534i | \(0.326771\pi\) | |||||||
\(510\) | 9.45337 | 0.418602 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.6564 | 1.08967 | ||||||||
\(513\) | −1.30188 | −0.0574796 | ||||||||
\(514\) | −27.4026 | −1.20868 | ||||||||
\(515\) | 68.0310 | 2.99780 | ||||||||
\(516\) | 0.404585 | 0.0178108 | ||||||||
\(517\) | 18.2441 | 0.802374 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.707761 | 0.0310672 | ||||||||
\(520\) | −6.48160 | −0.284237 | ||||||||
\(521\) | −2.33762 | −0.102413 | −0.0512064 | − | 0.998688i | \(-0.516307\pi\) | ||||
−0.0512064 | + | 0.998688i | \(0.516307\pi\) | |||||||
\(522\) | 31.0448 | 1.35879 | ||||||||
\(523\) | 1.57772 | 0.0689888 | 0.0344944 | − | 0.999405i | \(-0.489018\pi\) | ||||
0.0344944 | + | 0.999405i | \(0.489018\pi\) | |||||||
\(524\) | −2.26435 | −0.0989187 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.7376 | 1.47103 | ||||||||
\(527\) | −38.1036 | −1.65982 | ||||||||
\(528\) | 1.57818 | 0.0686813 | ||||||||
\(529\) | −9.13920 | −0.397357 | ||||||||
\(530\) | 9.86328 | 0.428433 | ||||||||
\(531\) | 12.5236 | 0.543478 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.587073 | 0.0254290 | ||||||||
\(534\) | 2.99117 | 0.129441 | ||||||||
\(535\) | −49.0635 | −2.12120 | ||||||||
\(536\) | −33.7180 | −1.45640 | ||||||||
\(537\) | 3.88550 | 0.167672 | ||||||||
\(538\) | 41.7271 | 1.79898 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.964941 | −0.0415245 | ||||||||
\(541\) | −5.19622 | −0.223403 | −0.111702 | − | 0.993742i | \(-0.535630\pi\) | ||||
−0.111702 | + | 0.993742i | \(0.535630\pi\) | |||||||
\(542\) | 24.8571 | 1.06770 | ||||||||
\(543\) | 1.09666 | 0.0470620 | ||||||||
\(544\) | −5.68995 | −0.243955 | ||||||||
\(545\) | 39.7718 | 1.70364 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6657 | 0.456031 | 0.228016 | − | 0.973657i | \(-0.426776\pi\) | ||||
0.228016 | + | 0.973657i | \(0.426776\pi\) | |||||||
\(548\) | −1.20472 | −0.0514631 | ||||||||
\(549\) | −24.7377 | −1.05578 | ||||||||
\(550\) | 19.1986 | 0.818632 | ||||||||
\(551\) | 6.11830 | 0.260648 | ||||||||
\(552\) | 3.06253 | 0.130350 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.44916 | −0.0615688 | ||||||||
\(555\) | −8.89665 | −0.377642 | ||||||||
\(556\) | 1.68625 | 0.0715131 | ||||||||
\(557\) | −25.3290 | −1.07322 | −0.536611 | − | 0.843830i | \(-0.680296\pi\) | ||||
−0.536611 | + | 0.843830i | \(0.680296\pi\) | |||||||
\(558\) | −23.0529 | −0.975907 | ||||||||
\(559\) | −5.49858 | −0.232565 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.82180 | −0.119137 | ||||||||
\(562\) | −1.80131 | −0.0759839 | ||||||||
\(563\) | 2.64057 | 0.111287 | 0.0556433 | − | 0.998451i | \(-0.482279\pi\) | ||||
0.0556433 | + | 0.998451i | \(0.482279\pi\) | |||||||
\(564\) | 0.515019 | 0.0216862 | ||||||||
\(565\) | 2.95160 | 0.124175 | ||||||||
\(566\) | −29.2153 | −1.22801 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.9585 | 1.00527 | ||||||||
\(569\) | −29.7217 | −1.24600 | −0.622998 | − | 0.782223i | \(-0.714086\pi\) | ||||
−0.622998 | + | 0.782223i | \(0.714086\pi\) | |||||||
\(570\) | 1.12717 | 0.0472118 | ||||||||
\(571\) | 14.4005 | 0.602640 | 0.301320 | − | 0.953523i | \(-0.402573\pi\) | ||||
0.301320 | + | 0.953523i | \(0.402573\pi\) | |||||||
\(572\) | 0.138051 | 0.00577222 | ||||||||
\(573\) | −4.27331 | −0.178520 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.3764 | 1.43359 | ||||||||
\(576\) | −24.8769 | −1.03654 | ||||||||
\(577\) | 7.51404 | 0.312813 | 0.156407 | − | 0.987693i | \(-0.450009\pi\) | ||||
0.156407 | + | 0.987693i | \(0.450009\pi\) | |||||||
\(578\) | −35.3797 | −1.47160 | ||||||||
\(579\) | 4.13290 | 0.171758 | ||||||||
\(580\) | 4.53481 | 0.188298 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.06489 | 0.209946 | ||||||||
\(583\) | −2.94416 | −0.121935 | ||||||||
\(584\) | 3.09426 | 0.128042 | ||||||||
\(585\) | 6.46960 | 0.267485 | ||||||||
\(586\) | −26.4263 | −1.09166 | ||||||||
\(587\) | 45.6741 | 1.88517 | 0.942585 | − | 0.333965i | \(-0.108387\pi\) | ||||
0.942585 | + | 0.333965i | \(0.108387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.54326 | −0.187202 | ||||||||
\(590\) | −21.9791 | −0.904865 | ||||||||
\(591\) | 3.22339 | 0.132593 | ||||||||
\(592\) | −30.7801 | −1.26506 | ||||||||
\(593\) | −24.2450 | −0.995624 | −0.497812 | − | 0.867285i | \(-0.665863\pi\) | ||||
−0.497812 | + | 0.867285i | \(0.665863\pi\) | |||||||
\(594\) | −3.46060 | −0.141990 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.974899 | 0.0399334 | ||||||||
\(597\) | −4.68913 | −0.191913 | ||||||||
\(598\) | −2.96989 | −0.121448 | ||||||||
\(599\) | 6.56723 | 0.268330 | 0.134165 | − | 0.990959i | \(-0.457165\pi\) | ||||
0.134165 | + | 0.990959i | \(0.457165\pi\) | |||||||
\(600\) | 7.59544 | 0.310082 | ||||||||
\(601\) | 22.8645 | 0.932661 | 0.466331 | − | 0.884610i | \(-0.345576\pi\) | ||||
0.466331 | + | 0.884610i | \(0.345576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.6556 | 1.37056 | ||||||||
\(604\) | 0.108821 | 0.00442785 | ||||||||
\(605\) | 32.6661 | 1.32806 | ||||||||
\(606\) | −2.46338 | −0.100068 | ||||||||
\(607\) | −2.13050 | −0.0864744 | −0.0432372 | − | 0.999065i | \(-0.513767\pi\) | ||||
−0.0432372 | + | 0.999065i | \(0.513767\pi\) | |||||||
\(608\) | −0.678439 | −0.0275143 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 43.4151 | 1.75782 | ||||||||
\(611\) | −6.99946 | −0.283168 | ||||||||
\(612\) | 2.94477 | 0.119035 | ||||||||
\(613\) | −13.9256 | −0.562448 | −0.281224 | − | 0.959642i | \(-0.590740\pi\) | ||||
−0.281224 | + | 0.959642i | \(0.590740\pi\) | |||||||
\(614\) | 38.7770 | 1.56491 | ||||||||
\(615\) | −1.06049 | −0.0427633 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.8843 | −1.40439 | −0.702195 | − | 0.711985i | \(-0.747796\pi\) | ||||
−0.702195 | + | 0.711985i | \(0.747796\pi\) | |||||||
\(618\) | 6.88745 | 0.277054 | ||||||||
\(619\) | 31.8727 | 1.28107 | 0.640537 | − | 0.767928i | \(-0.278712\pi\) | ||||
0.640537 | + | 0.767928i | \(0.278712\pi\) | |||||||
\(620\) | −3.36741 | −0.135238 | ||||||||
\(621\) | −6.19642 | −0.248654 | ||||||||
\(622\) | 13.0926 | 0.524965 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.605477 | −0.0242385 | ||||||||
\(625\) | 14.0899 | 0.563594 | ||||||||
\(626\) | −45.6594 | −1.82492 | ||||||||
\(627\) | −0.336456 | −0.0134368 | ||||||||
\(628\) | 1.87564 | 0.0748463 | ||||||||
\(629\) | 55.0354 | 2.19440 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.96929 | 0.396871 | 0.198436 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198436 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(632\) | 21.0508 | 0.837354 | ||||||||
\(633\) | 2.75837 | 0.109635 | ||||||||
\(634\) | 42.0435 | 1.66976 | ||||||||
\(635\) | 11.9913 | 0.475861 | ||||||||
\(636\) | −0.0831118 | −0.00329560 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.2633 | 0.643871 | ||||||||
\(639\) | −23.9141 | −0.946027 | ||||||||
\(640\) | 37.1148 | 1.46709 | ||||||||
\(641\) | 38.8172 | 1.53319 | 0.766594 | − | 0.642133i | \(-0.221950\pi\) | ||||
0.766594 | + | 0.642133i | \(0.221950\pi\) | |||||||
\(642\) | −4.96718 | −0.196039 | ||||||||
\(643\) | 17.9051 | 0.706110 | 0.353055 | − | 0.935603i | \(-0.385143\pi\) | ||||
0.353055 | + | 0.935603i | \(0.385143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.93268 | 0.391099 | ||||||||
\(646\) | −6.97274 | −0.274339 | ||||||||
\(647\) | 6.22800 | 0.244848 | 0.122424 | − | 0.992478i | \(-0.460933\pi\) | ||||
0.122424 | + | 0.992478i | \(0.460933\pi\) | |||||||
\(648\) | 24.2748 | 0.953606 | ||||||||
\(649\) | 6.56070 | 0.257530 | ||||||||
\(650\) | −7.36567 | −0.288905 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.155897 | −0.00610540 | ||||||||
\(653\) | −44.2209 | −1.73050 | −0.865248 | − | 0.501344i | \(-0.832839\pi\) | ||||
−0.865248 | + | 0.501344i | \(0.832839\pi\) | |||||||
\(654\) | 4.02649 | 0.157448 | ||||||||
\(655\) | −55.5906 | −2.17211 | ||||||||
\(656\) | −3.66904 | −0.143252 | ||||||||
\(657\) | −3.08854 | −0.120495 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.3675 | −0.988178 | −0.494089 | − | 0.869411i | \(-0.664498\pi\) | ||||
−0.494089 | + | 0.869411i | \(0.664498\pi\) | |||||||
\(660\) | −0.249377 | −0.00970700 | ||||||||
\(661\) | 27.2889 | 1.06141 | 0.530707 | − | 0.847556i | \(-0.321927\pi\) | ||||
0.530707 | + | 0.847556i | \(0.321927\pi\) | |||||||
\(662\) | 13.6204 | 0.529372 | ||||||||
\(663\) | 1.08260 | 0.0420448 | ||||||||
\(664\) | −24.7002 | −0.958555 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 33.2967 | 1.29022 | ||||||||
\(667\) | 29.1205 | 1.12755 | ||||||||
\(668\) | −0.816030 | −0.0315731 | ||||||||
\(669\) | −2.16876 | −0.0838489 | ||||||||
\(670\) | −59.0660 | −2.28192 | ||||||||
\(671\) | −12.9593 | −0.500287 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.43120 | 0.0937158 | 0.0468579 | − | 0.998902i | \(-0.485079\pi\) | ||||
0.0468579 | + | 0.998902i | \(0.485079\pi\) | |||||||
\(674\) | −6.80181 | −0.261996 | ||||||||
\(675\) | −15.3678 | −0.591508 | ||||||||
\(676\) | 1.94479 | 0.0747995 | ||||||||
\(677\) | 3.98914 | 0.153315 | 0.0766576 | − | 0.997057i | \(-0.475575\pi\) | ||||
0.0766576 | + | 0.997057i | \(0.475575\pi\) | |||||||
\(678\) | 0.298819 | 0.0114761 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −72.4292 | −2.77753 | ||||||||
\(681\) | −7.53340 | −0.288681 | ||||||||
\(682\) | −12.0766 | −0.462439 | ||||||||
\(683\) | 29.9721 | 1.14685 | 0.573426 | − | 0.819257i | \(-0.305614\pi\) | ||||
0.573426 | + | 0.819257i | \(0.305614\pi\) | |||||||
\(684\) | 0.351118 | 0.0134253 | ||||||||
\(685\) | −29.5763 | −1.13005 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.04163 | −0.116045 | ||||||||
\(688\) | 34.3645 | 1.31014 | ||||||||
\(689\) | 1.12955 | 0.0430323 | ||||||||
\(690\) | 5.36484 | 0.204236 | ||||||||
\(691\) | 13.4964 | 0.513425 | 0.256713 | − | 0.966488i | \(-0.417361\pi\) | ||||
0.256713 | + | 0.966488i | \(0.417361\pi\) | |||||||
\(692\) | −0.386929 | −0.0147089 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.0142 | 0.569933 | ||||||||
\(695\) | 41.3981 | 1.57032 | ||||||||
\(696\) | 6.43416 | 0.243886 | ||||||||
\(697\) | 6.56030 | 0.248489 | ||||||||
\(698\) | 14.6645 | 0.555061 | ||||||||
\(699\) | −2.55791 | −0.0967491 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.7642 | −1.61518 | −0.807591 | − | 0.589743i | \(-0.799229\pi\) | ||||
−0.807591 | + | 0.589743i | \(0.799229\pi\) | |||||||
\(702\) | 1.32768 | 0.0501101 | ||||||||
\(703\) | 6.56211 | 0.247495 | ||||||||
\(704\) | −13.0322 | −0.491168 | ||||||||
\(705\) | 12.6439 | 0.476196 | ||||||||
\(706\) | −29.2086 | −1.09928 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.185204 | 0.00696040 | ||||||||
\(709\) | −9.91620 | −0.372411 | −0.186205 | − | 0.982511i | \(-0.559619\pi\) | ||||
−0.186205 | + | 0.982511i | \(0.559619\pi\) | |||||||
\(710\) | 41.9696 | 1.57509 | ||||||||
\(711\) | −21.0118 | −0.788003 | ||||||||
\(712\) | −22.9175 | −0.858871 | ||||||||
\(713\) | −21.6240 | −0.809825 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.38921 | 0.126749 | ||||||||
\(716\) | −2.12418 | −0.0793845 | ||||||||
\(717\) | −1.03579 | −0.0386823 | ||||||||
\(718\) | 13.4017 | 0.500145 | ||||||||
\(719\) | −17.3198 | −0.645919 | −0.322960 | − | 0.946413i | \(-0.604678\pi\) | ||||
−0.322960 | + | 0.946413i | \(0.604678\pi\) | |||||||
\(720\) | −40.4331 | −1.50685 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.9857 | 0.929873 | ||||||||
\(723\) | −2.25340 | −0.0838048 | ||||||||
\(724\) | −0.599537 | −0.0222816 | ||||||||
\(725\) | 72.2222 | 2.68227 | ||||||||
\(726\) | 3.30711 | 0.122738 | ||||||||
\(727\) | −40.4385 | −1.49978 | −0.749891 | − | 0.661561i | \(-0.769894\pi\) | ||||
−0.749891 | + | 0.661561i | \(0.769894\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.8264 | −0.845422 | ||||||||
\(730\) | 5.42042 | 0.200619 | ||||||||
\(731\) | −61.4443 | −2.27260 | ||||||||
\(732\) | −0.365832 | −0.0135215 | ||||||||
\(733\) | −5.25881 | −0.194238 | −0.0971192 | − | 0.995273i | \(-0.530963\pi\) | ||||
−0.0971192 | + | 0.995273i | \(0.530963\pi\) | |||||||
\(734\) | 36.8706 | 1.36092 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.22908 | −0.119026 | ||||||||
\(737\) | 17.6310 | 0.649447 | ||||||||
\(738\) | 3.96902 | 0.146102 | ||||||||
\(739\) | 35.8773 | 1.31977 | 0.659884 | − | 0.751368i | \(-0.270605\pi\) | ||||
0.659884 | + | 0.751368i | \(0.270605\pi\) | |||||||
\(740\) | 4.86376 | 0.178795 | ||||||||
\(741\) | 0.129084 | 0.00474200 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.2113 | −1.10835 | −0.554173 | − | 0.832402i | \(-0.686965\pi\) | ||||
−0.554173 | + | 0.832402i | \(0.686965\pi\) | |||||||
\(744\) | −4.77781 | −0.175163 | ||||||||
\(745\) | 23.9341 | 0.876877 | ||||||||
\(746\) | 3.73282 | 0.136668 | ||||||||
\(747\) | 24.6545 | 0.902061 | ||||||||
\(748\) | 1.54267 | 0.0564055 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.10044 | 0.222757 | ||||||||
\(751\) | 41.2217 | 1.50420 | 0.752101 | − | 0.659047i | \(-0.229040\pi\) | ||||
0.752101 | + | 0.659047i | \(0.229040\pi\) | |||||||
\(752\) | 43.7446 | 1.59520 | ||||||||
\(753\) | 0.452444 | 0.0164880 | ||||||||
\(754\) | −6.23953 | −0.227230 | ||||||||
\(755\) | 2.67159 | 0.0972290 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1279 | −1.05867 | −0.529335 | − | 0.848413i | \(-0.677559\pi\) | ||||
−0.529335 | + | 0.848413i | \(0.677559\pi\) | |||||||
\(758\) | −39.9465 | −1.45092 | ||||||||
\(759\) | −1.60139 | −0.0581268 | ||||||||
\(760\) | −8.63606 | −0.313263 | ||||||||
\(761\) | 10.2126 | 0.370207 | 0.185104 | − | 0.982719i | \(-0.440738\pi\) | ||||
0.185104 | + | 0.982719i | \(0.440738\pi\) | |||||||
\(762\) | 1.21400 | 0.0439785 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.33620 | 0.0845208 | ||||||||
\(765\) | 72.2951 | 2.61383 | ||||||||
\(766\) | −9.09889 | −0.328756 | ||||||||
\(767\) | −2.51705 | −0.0908855 | ||||||||
\(768\) | −1.03044 | −0.0371830 | ||||||||
\(769\) | −44.8525 | −1.61742 | −0.808711 | − | 0.588206i | \(-0.799834\pi\) | ||||
−0.808711 | + | 0.588206i | \(0.799834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.66879 | 0.204157 | ||||||||
\(772\) | −2.25944 | −0.0813190 | ||||||||
\(773\) | −6.80825 | −0.244876 | −0.122438 | − | 0.992476i | \(-0.539071\pi\) | ||||
−0.122438 | + | 0.992476i | \(0.539071\pi\) | |||||||
\(774\) | −37.1742 | −1.33620 | ||||||||
\(775\) | −53.6300 | −1.92645 | ||||||||
\(776\) | −38.8058 | −1.39305 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.650677 | −0.0233279 | ||||||||
\(779\) | 0.782214 | 0.0280257 | ||||||||
\(780\) | 0.0956752 | 0.00342572 | ||||||||
\(781\) | −12.5278 | −0.448280 | ||||||||
\(782\) | −33.1873 | −1.18678 | ||||||||
\(783\) | −13.0182 | −0.465234 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.0476 | 1.64351 | ||||||||
\(786\) | −5.62799 | −0.200744 | ||||||||
\(787\) | −56.0803 | −1.99905 | −0.999524 | − | 0.0308539i | \(-0.990177\pi\) | ||||
−0.999524 | + | 0.0308539i | \(0.990177\pi\) | |||||||
\(788\) | −1.76221 | −0.0627763 | ||||||||
\(789\) | −6.97931 | −0.248470 | ||||||||
\(790\) | 36.8760 | 1.31199 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 13.0802 | 0.464784 | ||||||||
\(793\) | 4.97190 | 0.176557 | ||||||||
\(794\) | −32.9226 | −1.16838 | ||||||||
\(795\) | −2.04042 | −0.0723663 | ||||||||
\(796\) | 2.56353 | 0.0908618 | ||||||||
\(797\) | −48.1716 | −1.70632 | −0.853162 | − | 0.521646i | \(-0.825318\pi\) | ||||
−0.853162 | + | 0.521646i | \(0.825318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −78.2160 | −2.76708 | ||||||||
\(800\) | −8.00849 | −0.283143 | ||||||||
\(801\) | 22.8751 | 0.808252 | ||||||||
\(802\) | −31.6386 | −1.11720 | ||||||||
\(803\) | −1.61798 | −0.0570973 | ||||||||
\(804\) | 0.497713 | 0.0175530 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.63328 | 0.163200 | ||||||||
\(807\) | −8.63211 | −0.303865 | ||||||||
\(808\) | 18.8737 | 0.663975 | ||||||||
\(809\) | −42.4935 | −1.49399 | −0.746997 | − | 0.664828i | \(-0.768505\pi\) | ||||
−0.746997 | + | 0.664828i | \(0.768505\pi\) | |||||||
\(810\) | 42.5238 | 1.49413 | ||||||||
\(811\) | −2.95213 | −0.103663 | −0.0518317 | − | 0.998656i | \(-0.516506\pi\) | ||||
−0.0518317 | + | 0.998656i | \(0.516506\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.14219 | −0.180345 | ||||||||
\(814\) | 17.4431 | 0.611379 | ||||||||
\(815\) | −3.82732 | −0.134065 | ||||||||
\(816\) | −6.76595 | −0.236856 | ||||||||
\(817\) | −7.32628 | −0.256314 | ||||||||
\(818\) | 41.6486 | 1.45621 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.579768 | 0.0202464 | ||||||||
\(821\) | −0.811655 | −0.0283269 | −0.0141635 | − | 0.999900i | \(-0.504509\pi\) | ||||
−0.0141635 | + | 0.999900i | \(0.504509\pi\) | |||||||
\(822\) | −2.99430 | −0.104438 | ||||||||
\(823\) | −4.07214 | −0.141946 | −0.0709729 | − | 0.997478i | \(-0.522610\pi\) | ||||
−0.0709729 | + | 0.997478i | \(0.522610\pi\) | |||||||
\(824\) | −52.7698 | −1.83832 | ||||||||
\(825\) | −3.97163 | −0.138274 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.3822 | −0.708758 | −0.354379 | − | 0.935102i | \(-0.615308\pi\) | ||||
−0.354379 | + | 0.935102i | \(0.615308\pi\) | |||||||
\(828\) | 1.67117 | 0.0580773 | ||||||||
\(829\) | −29.3639 | −1.01985 | −0.509925 | − | 0.860219i | \(-0.670327\pi\) | ||||
−0.509925 | + | 0.860219i | \(0.670327\pi\) | |||||||
\(830\) | −43.2690 | −1.50189 | ||||||||
\(831\) | 0.299788 | 0.0103995 | ||||||||
\(832\) | 4.99987 | 0.173339 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.19114 | 0.145127 | ||||||||
\(835\) | −20.0338 | −0.693298 | ||||||||
\(836\) | 0.183939 | 0.00636167 | ||||||||
\(837\) | 9.66693 | 0.334138 | ||||||||
\(838\) | 7.54007 | 0.260468 | ||||||||
\(839\) | −9.95705 | −0.343756 | −0.171878 | − | 0.985118i | \(-0.554983\pi\) | ||||
−0.171878 | + | 0.985118i | \(0.554983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.1801 | 1.10966 | ||||||||
\(842\) | −16.1402 | −0.556228 | ||||||||
\(843\) | 0.372639 | 0.0128344 | ||||||||
\(844\) | −1.50799 | −0.0519071 | ||||||||
\(845\) | 47.7452 | 1.64248 | ||||||||
\(846\) | −47.3212 | −1.62694 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.05933 | −0.242418 | ||||||||
\(849\) | 6.04378 | 0.207422 | ||||||||
\(850\) | −82.3083 | −2.82315 | ||||||||
\(851\) | 31.2329 | 1.07065 | ||||||||
\(852\) | −0.353652 | −0.0121159 | ||||||||
\(853\) | 12.4050 | 0.424740 | 0.212370 | − | 0.977189i | \(-0.431882\pi\) | ||||
0.212370 | + | 0.977189i | \(0.431882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.62007 | 0.294800 | ||||||||
\(856\) | 38.0572 | 1.30077 | ||||||||
\(857\) | −16.1448 | −0.551494 | −0.275747 | − | 0.961230i | \(-0.588925\pi\) | ||||
−0.275747 | + | 0.961230i | \(0.588925\pi\) | |||||||
\(858\) | 0.343123 | 0.0117140 | ||||||||
\(859\) | −43.8520 | −1.49621 | −0.748106 | − | 0.663580i | \(-0.769036\pi\) | ||||
−0.748106 | + | 0.663580i | \(0.769036\pi\) | |||||||
\(860\) | −5.43015 | −0.185167 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.4770 | 0.731511 | ||||||||
\(863\) | −29.4794 | −1.00349 | −0.501745 | − | 0.865016i | \(-0.667308\pi\) | ||||
−0.501745 | + | 0.865016i | \(0.667308\pi\) | |||||||
\(864\) | 1.44355 | 0.0491106 | ||||||||
\(865\) | −9.49925 | −0.322984 | ||||||||
\(866\) | −24.3156 | −0.826277 | ||||||||
\(867\) | 7.31902 | 0.248567 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.0074 | −0.373399 | ||||||||
\(870\) | 11.2711 | 0.382127 | ||||||||
\(871\) | −6.76425 | −0.229198 | ||||||||
\(872\) | −30.8499 | −1.04471 | ||||||||
\(873\) | 38.7340 | 1.31095 | ||||||||
\(874\) | −3.95707 | −0.133850 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0456746 | −0.00154320 | ||||||||
\(877\) | 33.3689 | 1.12679 | 0.563393 | − | 0.826189i | \(-0.309496\pi\) | ||||
0.563393 | + | 0.826189i | \(0.309496\pi\) | |||||||
\(878\) | 53.2537 | 1.79723 | ||||||||
\(879\) | 5.46683 | 0.184391 | ||||||||
\(880\) | −21.1816 | −0.714030 | ||||||||
\(881\) | −35.4625 | −1.19476 | −0.597381 | − | 0.801958i | \(-0.703792\pi\) | ||||
−0.597381 | + | 0.801958i | \(0.703792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.1635 | −1.85640 | −0.928200 | − | 0.372082i | \(-0.878644\pi\) | ||||
−0.928200 | + | 0.372082i | \(0.878644\pi\) | |||||||
\(884\) | −0.591854 | −0.0199062 | ||||||||
\(885\) | 4.54683 | 0.152840 | ||||||||
\(886\) | −51.4643 | −1.72898 | ||||||||
\(887\) | 10.4949 | 0.352383 | 0.176192 | − | 0.984356i | \(-0.443622\pi\) | ||||
0.176192 | + | 0.984356i | \(0.443622\pi\) | |||||||
\(888\) | 6.90089 | 0.231579 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −40.1461 | −1.34570 | ||||||||
\(891\) | −12.6932 | −0.425240 | ||||||||
\(892\) | 1.18565 | 0.0396985 | ||||||||
\(893\) | −9.32605 | −0.312084 | ||||||||
\(894\) | 2.42308 | 0.0810400 | ||||||||
\(895\) | −52.1494 | −1.74316 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.614383 | 0.0205137 | ||||||||
\(898\) | −30.8786 | −1.03043 | ||||||||
\(899\) | −45.4304 | −1.51519 | ||||||||
\(900\) | 4.14470 | 0.138157 | ||||||||
\(901\) | 12.6222 | 0.420507 | ||||||||
\(902\) | 2.07924 | 0.0692311 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.28947 | −0.0761467 | ||||||||
\(905\) | −14.7188 | −0.489270 | ||||||||
\(906\) | 0.270471 | 0.00898579 | ||||||||
\(907\) | 12.5409 | 0.416415 | 0.208207 | − | 0.978085i | \(-0.433237\pi\) | ||||
0.208207 | + | 0.978085i | \(0.433237\pi\) | |||||||
\(908\) | 4.11848 | 0.136676 | ||||||||
\(909\) | −18.8388 | −0.624843 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.5700 | −1.50980 | −0.754901 | − | 0.655839i | \(-0.772315\pi\) | ||||
−0.754901 | + | 0.655839i | \(0.772315\pi\) | |||||||
\(912\) | −0.806735 | −0.0267137 | ||||||||
\(913\) | 12.9157 | 0.427446 | ||||||||
\(914\) | 33.0302 | 1.09254 | ||||||||
\(915\) | −8.98129 | −0.296912 | ||||||||
\(916\) | 1.66284 | 0.0549419 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 14.8363 | 0.489670 | ||||||||
\(919\) | 52.3114 | 1.72559 | 0.862797 | − | 0.505550i | \(-0.168711\pi\) | ||||
0.862797 | + | 0.505550i | \(0.168711\pi\) | |||||||
\(920\) | −41.1040 | −1.35516 | ||||||||
\(921\) | −8.02182 | −0.264328 | ||||||||
\(922\) | 36.7505 | 1.21031 | ||||||||
\(923\) | 4.80637 | 0.158204 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 77.4611 | 2.54691 | ||||||||
\(926\) | −13.2856 | −0.436592 | ||||||||
\(927\) | 52.6721 | 1.72998 | ||||||||
\(928\) | −6.78406 | −0.222698 | ||||||||
\(929\) | 11.0041 | 0.361034 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(930\) | −8.36960 | −0.274450 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.39840 | 0.0458061 | ||||||||
\(933\) | −2.70847 | −0.0886714 | ||||||||
\(934\) | −34.1442 | −1.11723 | ||||||||
\(935\) | 37.8730 | 1.23858 | ||||||||
\(936\) | −5.01829 | −0.164028 | ||||||||
\(937\) | 8.03703 | 0.262558 | 0.131279 | − | 0.991345i | \(-0.458092\pi\) | ||||
0.131279 | + | 0.991345i | \(0.458092\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.44557 | 0.308245 | ||||||||
\(940\) | −6.91235 | −0.225456 | ||||||||
\(941\) | 23.7694 | 0.774859 | 0.387429 | − | 0.921899i | \(-0.373363\pi\) | ||||
0.387429 | + | 0.921899i | \(0.373363\pi\) | |||||||
\(942\) | 4.66186 | 0.151891 | ||||||||
\(943\) | 3.72301 | 0.121238 | ||||||||
\(944\) | 15.7308 | 0.511996 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19.4743 | −0.633165 | ||||||||
\(947\) | −33.2635 | −1.08092 | −0.540459 | − | 0.841370i | \(-0.681750\pi\) | ||||
−0.540459 | + | 0.841370i | \(0.681750\pi\) | |||||||
\(948\) | −0.310731 | −0.0100921 | ||||||||
\(949\) | 0.620748 | 0.0201503 | ||||||||
\(950\) | −9.81399 | −0.318408 | ||||||||
\(951\) | −8.69756 | −0.282038 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.0945 | 0.942463 | 0.471232 | − | 0.882009i | \(-0.343810\pi\) | ||||
0.471232 | + | 0.882009i | \(0.343810\pi\) | |||||||
\(954\) | 7.63651 | 0.247241 | ||||||||
\(955\) | 57.3545 | 1.85595 | ||||||||
\(956\) | 0.566261 | 0.0183142 | ||||||||
\(957\) | −3.36440 | −0.108756 | ||||||||
\(958\) | −47.7194 | −1.54174 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.03181 | −0.291500 | ||||||||
\(961\) | 2.73524 | 0.0882335 | ||||||||
\(962\) | −6.69213 | −0.215763 | ||||||||
\(963\) | −37.9867 | −1.22411 | ||||||||
\(964\) | 1.23192 | 0.0396776 | ||||||||
\(965\) | −55.4700 | −1.78564 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.2398 | −1.67992 | −0.839959 | − | 0.542650i | \(-0.817421\pi\) | ||||
−0.839959 | + | 0.542650i | \(0.817421\pi\) | |||||||
\(968\) | −25.3382 | −0.814399 | ||||||||
\(969\) | 1.44245 | 0.0463383 | ||||||||
\(970\) | −67.9787 | −2.18266 | ||||||||
\(971\) | 1.75797 | 0.0564159 | 0.0282080 | − | 0.999602i | \(-0.491020\pi\) | ||||
0.0282080 | + | 0.999602i | \(0.491020\pi\) | |||||||
\(972\) | −1.12562 | −0.0361044 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 26.5639 | 0.851162 | ||||||||
\(975\) | 1.52374 | 0.0487987 | ||||||||
\(976\) | −31.0730 | −0.994621 | ||||||||
\(977\) | −37.5188 | −1.20033 | −0.600167 | − | 0.799875i | \(-0.704899\pi\) | ||||
−0.600167 | + | 0.799875i | \(0.704899\pi\) | |||||||
\(978\) | −0.387478 | −0.0123902 | ||||||||
\(979\) | 11.9835 | 0.382995 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.7928 | 0.983137 | ||||||||
\(982\) | −13.9929 | −0.446531 | ||||||||
\(983\) | 32.6951 | 1.04281 | 0.521405 | − | 0.853309i | \(-0.325408\pi\) | ||||
0.521405 | + | 0.853309i | \(0.325408\pi\) | |||||||
\(984\) | 0.822597 | 0.0262234 | ||||||||
\(985\) | −43.2630 | −1.37847 | ||||||||
\(986\) | −69.7241 | −2.22047 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.0705694 | −0.00224511 | ||||||||
\(989\) | −34.8700 | −1.10880 | ||||||||
\(990\) | 22.9134 | 0.728236 | ||||||||
\(991\) | −39.7198 | −1.26174 | −0.630870 | − | 0.775889i | \(-0.717302\pi\) | ||||
−0.630870 | + | 0.775889i | \(0.717302\pi\) | |||||||
\(992\) | 5.03764 | 0.159945 | ||||||||
\(993\) | −2.81766 | −0.0894158 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 62.9354 | 1.99519 | ||||||||
\(996\) | 0.364601 | 0.0115528 | ||||||||
\(997\) | 8.11982 | 0.257157 | 0.128579 | − | 0.991699i | \(-0.458959\pi\) | ||||
0.128579 | + | 0.991699i | \(0.458959\pi\) | |||||||
\(998\) | 28.8216 | 0.912332 | ||||||||
\(999\) | −13.9626 | −0.441756 |
(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 | 2009.2.a.p.1.3 | ✓ | 7 | |
7.6 | odd | 2 | 2009.2.a.q.1.3 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.p.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2009.2.a.q.1.3 | yes | 7 | 7.6 | odd | 2 |