Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.473.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.201640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.201640 | 0.142581 | 0.0712904 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712904 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.95934 | −0.979671 | ||||||||
\(5\) | 3.75770 | 1.68050 | 0.840248 | − | 0.542203i | \(-0.182410\pi\) | ||||
0.840248 | + | 0.542203i | \(0.182410\pi\) | |||||||
\(6\) | −0.201640 | −0.0823191 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.798360 | −0.282263 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.757702 | 0.239606 | ||||||||
\(11\) | 5.75770 | 1.73601 | 0.868006 | − | 0.496553i | \(-0.165401\pi\) | ||||
0.868006 | + | 0.496553i | \(0.165401\pi\) | |||||||
\(12\) | 1.95934 | 0.565613 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.201640 | 0.0538905 | ||||||||
\(15\) | −3.75770 | −0.970234 | ||||||||
\(16\) | 3.75770 | 0.939425 | ||||||||
\(17\) | 4.20164 | 1.01905 | 0.509524 | − | 0.860457i | \(-0.329822\pi\) | ||||
0.509524 | + | 0.860457i | \(0.329822\pi\) | |||||||
\(18\) | 0.201640 | 0.0475269 | ||||||||
\(19\) | 1.40328 | 0.321934 | 0.160967 | − | 0.986960i | \(-0.448539\pi\) | ||||
0.160967 | + | 0.986960i | \(0.448539\pi\) | |||||||
\(20\) | −7.36262 | −1.64633 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.16098 | 0.247522 | ||||||||
\(23\) | 0.959341 | 0.200037 | 0.100018 | − | 0.994986i | \(-0.468110\pi\) | ||||
0.100018 | + | 0.994986i | \(0.468110\pi\) | |||||||
\(24\) | 0.798360 | 0.162965 | ||||||||
\(25\) | 9.12032 | 1.82406 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.95934 | −0.370281 | ||||||||
\(29\) | 2.79836 | 0.519642 | 0.259821 | − | 0.965657i | \(-0.416336\pi\) | ||||
0.259821 | + | 0.965657i | \(0.416336\pi\) | |||||||
\(30\) | −0.757702 | −0.138337 | ||||||||
\(31\) | 4.35442 | 0.782077 | 0.391039 | − | 0.920374i | \(-0.372116\pi\) | ||||
0.391039 | + | 0.920374i | \(0.372116\pi\) | |||||||
\(32\) | 2.35442 | 0.416207 | ||||||||
\(33\) | −5.75770 | −1.00229 | ||||||||
\(34\) | 0.847217 | 0.145297 | ||||||||
\(35\) | 3.75770 | 0.635168 | ||||||||
\(36\) | −1.95934 | −0.326557 | ||||||||
\(37\) | −10.0797 | −1.65709 | −0.828543 | − | 0.559925i | \(-0.810830\pi\) | ||||
−0.828543 | + | 0.559925i | \(0.810830\pi\) | |||||||
\(38\) | 0.282957 | 0.0459017 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | −0.474342 | ||||||||
\(41\) | 2.80656 | 0.438311 | 0.219155 | − | 0.975690i | \(-0.429670\pi\) | ||||
0.219155 | + | 0.975690i | \(0.429670\pi\) | |||||||
\(42\) | −0.201640 | −0.0311137 | ||||||||
\(43\) | 0.959341 | 0.146298 | 0.0731491 | − | 0.997321i | \(-0.476695\pi\) | ||||
0.0731491 | + | 0.997321i | \(0.476695\pi\) | |||||||
\(44\) | −11.2813 | −1.70072 | ||||||||
\(45\) | 3.75770 | 0.560165 | ||||||||
\(46\) | 0.193441 | 0.0285214 | ||||||||
\(47\) | −6.67638 | −0.973851 | −0.486925 | − | 0.873444i | \(-0.661882\pi\) | ||||
−0.486925 | + | 0.873444i | \(0.661882\pi\) | |||||||
\(48\) | −3.75770 | −0.542378 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.83902 | 0.260077 | ||||||||
\(51\) | −4.20164 | −0.588347 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.9187 | −1.49980 | −0.749898 | − | 0.661553i | \(-0.769898\pi\) | ||||
−0.749898 | + | 0.661553i | \(0.769898\pi\) | |||||||
\(54\) | −0.201640 | −0.0274397 | ||||||||
\(55\) | 21.6357 | 2.91736 | ||||||||
\(56\) | −0.798360 | −0.106685 | ||||||||
\(57\) | −1.40328 | −0.185869 | ||||||||
\(58\) | 0.564260 | 0.0740910 | ||||||||
\(59\) | −12.3934 | −1.61349 | −0.806743 | − | 0.590902i | \(-0.798772\pi\) | ||||
−0.806743 | + | 0.590902i | \(0.798772\pi\) | |||||||
\(60\) | 7.36262 | 0.950510 | ||||||||
\(61\) | 13.3220 | 1.70570 | 0.852851 | − | 0.522154i | \(-0.174871\pi\) | ||||
0.852851 | + | 0.522154i | \(0.174871\pi\) | |||||||
\(62\) | 0.878024 | 0.111509 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −7.04066 | −0.880082 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.16098 | −0.142907 | ||||||||
\(67\) | 7.60492 | 0.929089 | 0.464544 | − | 0.885550i | \(-0.346218\pi\) | ||||
0.464544 | + | 0.885550i | \(0.346218\pi\) | |||||||
\(68\) | −8.23245 | −0.998331 | ||||||||
\(69\) | −0.959341 | −0.115491 | ||||||||
\(70\) | 0.757702 | 0.0905627 | ||||||||
\(71\) | 3.63738 | 0.431677 | 0.215839 | − | 0.976429i | \(-0.430751\pi\) | ||||
0.215839 | + | 0.976429i | \(0.430751\pi\) | |||||||
\(72\) | −0.798360 | −0.0940877 | ||||||||
\(73\) | −7.95934 | −0.931570 | −0.465785 | − | 0.884898i | \(-0.654228\pi\) | ||||
−0.465785 | + | 0.884898i | \(0.654228\pi\) | |||||||
\(74\) | −2.03246 | −0.236269 | ||||||||
\(75\) | −9.12032 | −1.05312 | ||||||||
\(76\) | −2.74950 | −0.315390 | ||||||||
\(77\) | 5.75770 | 0.656151 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.56426 | 0.401011 | 0.200505 | − | 0.979693i | \(-0.435742\pi\) | ||||
0.200505 | + | 0.979693i | \(0.435742\pi\) | |||||||
\(80\) | 14.1203 | 1.57870 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.565914 | 0.0624947 | ||||||||
\(83\) | 14.5643 | 1.59864 | 0.799318 | − | 0.600909i | \(-0.205194\pi\) | ||||
0.799318 | + | 0.600909i | \(0.205194\pi\) | |||||||
\(84\) | 1.95934 | 0.213782 | ||||||||
\(85\) | 15.7885 | 1.71250 | ||||||||
\(86\) | 0.193441 | 0.0208593 | ||||||||
\(87\) | −2.79836 | −0.300016 | ||||||||
\(88\) | −4.59672 | −0.490012 | ||||||||
\(89\) | −1.80656 | −0.191495 | −0.0957474 | − | 0.995406i | \(-0.530524\pi\) | ||||
−0.0957474 | + | 0.995406i | \(0.530524\pi\) | |||||||
\(90\) | 0.757702 | 0.0798688 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.87968 | −0.195970 | ||||||||
\(93\) | −4.35442 | −0.451533 | ||||||||
\(94\) | −1.34622 | −0.138852 | ||||||||
\(95\) | 5.27311 | 0.541009 | ||||||||
\(96\) | −2.35442 | −0.240297 | ||||||||
\(97\) | −16.2731 | −1.65228 | −0.826142 | − | 0.563462i | \(-0.809469\pi\) | ||||
−0.826142 | + | 0.563462i | \(0.809469\pi\) | |||||||
\(98\) | 0.201640 | 0.0203687 | ||||||||
\(99\) | 5.75770 | 0.578671 | ||||||||
\(100\) | −17.8698 | −1.78698 | ||||||||
\(101\) | −2.16918 | −0.215841 | −0.107921 | − | 0.994160i | \(-0.534419\pi\) | ||||
−0.107921 | + | 0.994160i | \(0.534419\pi\) | |||||||
\(102\) | −0.847217 | −0.0838870 | ||||||||
\(103\) | −8.43409 | −0.831035 | −0.415518 | − | 0.909585i | \(-0.636400\pi\) | ||||
−0.415518 | + | 0.909585i | \(0.636400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.75770 | −0.366714 | ||||||||
\(106\) | −2.20164 | −0.213842 | ||||||||
\(107\) | −7.47474 | −0.722611 | −0.361305 | − | 0.932448i | \(-0.617669\pi\) | ||||
−0.361305 | + | 0.932448i | \(0.617669\pi\) | |||||||
\(108\) | 1.95934 | 0.188538 | ||||||||
\(109\) | 9.52360 | 0.912196 | 0.456098 | − | 0.889930i | \(-0.349247\pi\) | ||||
0.456098 | + | 0.889930i | \(0.349247\pi\) | |||||||
\(110\) | 4.36262 | 0.415960 | ||||||||
\(111\) | 10.0797 | 0.956719 | ||||||||
\(112\) | 3.75770 | 0.355069 | ||||||||
\(113\) | −9.86983 | −0.928475 | −0.464238 | − | 0.885711i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885711i | \(0.653672\pi\) | |||||||
\(114\) | −0.282957 | −0.0265013 | ||||||||
\(115\) | 3.60492 | 0.336160 | ||||||||
\(116\) | −5.48294 | −0.509079 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.49901 | −0.230052 | ||||||||
\(119\) | 4.20164 | 0.385164 | ||||||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | 22.1511 | 2.01374 | ||||||||
\(122\) | 2.68624 | 0.243200 | ||||||||
\(123\) | −2.80656 | −0.253059 | ||||||||
\(124\) | −8.53180 | −0.766178 | ||||||||
\(125\) | 15.4829 | 1.38484 | ||||||||
\(126\) | 0.201640 | 0.0179635 | ||||||||
\(127\) | −6.96754 | −0.618269 | −0.309135 | − | 0.951018i | \(-0.600039\pi\) | ||||
−0.309135 | + | 0.951018i | \(0.600039\pi\) | |||||||
\(128\) | −6.12852 | −0.541690 | ||||||||
\(129\) | −0.959341 | −0.0844653 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.75770 | −0.852534 | −0.426267 | − | 0.904597i | \(-0.640172\pi\) | ||||
−0.426267 | + | 0.904597i | \(0.640172\pi\) | |||||||
\(132\) | 11.2813 | 0.981911 | ||||||||
\(133\) | 1.40328 | 0.121680 | ||||||||
\(134\) | 1.53345 | 0.132470 | ||||||||
\(135\) | −3.75770 | −0.323411 | ||||||||
\(136\) | −3.35442 | −0.287639 | ||||||||
\(137\) | −3.32196 | −0.283814 | −0.141907 | − | 0.989880i | \(-0.545323\pi\) | ||||
−0.141907 | + | 0.989880i | \(0.545323\pi\) | |||||||
\(138\) | −0.193441 | −0.0164668 | ||||||||
\(139\) | 0.798360 | 0.0677160 | 0.0338580 | − | 0.999427i | \(-0.489221\pi\) | ||||
0.0338580 | + | 0.999427i | \(0.489221\pi\) | |||||||
\(140\) | −7.36262 | −0.622255 | ||||||||
\(141\) | 6.67638 | 0.562253 | ||||||||
\(142\) | 0.733440 | 0.0615489 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.75770 | 0.313142 | ||||||||
\(145\) | 10.5154 | 0.873257 | ||||||||
\(146\) | −1.60492 | −0.132824 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 19.7495 | 1.62340 | ||||||||
\(149\) | −19.5138 | −1.59863 | −0.799314 | − | 0.600913i | \(-0.794804\pi\) | ||||
−0.799314 | + | 0.600913i | \(0.794804\pi\) | |||||||
\(150\) | −1.83902 | −0.150155 | ||||||||
\(151\) | 9.11212 | 0.741534 | 0.370767 | − | 0.928726i | \(-0.379095\pi\) | ||||
0.370767 | + | 0.928726i | \(0.379095\pi\) | |||||||
\(152\) | −1.12032 | −0.0908702 | ||||||||
\(153\) | 4.20164 | 0.339682 | ||||||||
\(154\) | 1.16098 | 0.0935545 | ||||||||
\(155\) | 16.3626 | 1.31428 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.62918 | −0.130023 | −0.0650114 | − | 0.997885i | \(-0.520708\pi\) | ||||
−0.0650114 | + | 0.997885i | \(0.520708\pi\) | |||||||
\(158\) | 0.718696 | 0.0571764 | ||||||||
\(159\) | 10.9187 | 0.865908 | ||||||||
\(160\) | 8.84722 | 0.699434 | ||||||||
\(161\) | 0.959341 | 0.0756067 | ||||||||
\(162\) | 0.201640 | 0.0158423 | ||||||||
\(163\) | −3.16263 | −0.247717 | −0.123858 | − | 0.992300i | \(-0.539527\pi\) | ||||
−0.123858 | + | 0.992300i | \(0.539527\pi\) | |||||||
\(164\) | −5.49901 | −0.429400 | ||||||||
\(165\) | −21.6357 | −1.68434 | ||||||||
\(166\) | 2.93673 | 0.227935 | ||||||||
\(167\) | 10.8374 | 0.838621 | 0.419310 | − | 0.907843i | \(-0.362272\pi\) | ||||
0.419310 | + | 0.907843i | \(0.362272\pi\) | |||||||
\(168\) | 0.798360 | 0.0615948 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.18359 | 0.244170 | ||||||||
\(171\) | 1.40328 | 0.107311 | ||||||||
\(172\) | −1.87968 | −0.143324 | ||||||||
\(173\) | 8.87802 | 0.674984 | 0.337492 | − | 0.941328i | \(-0.390421\pi\) | ||||
0.337492 | + | 0.941328i | \(0.390421\pi\) | |||||||
\(174\) | −0.564260 | −0.0427765 | ||||||||
\(175\) | 9.12032 | 0.689432 | ||||||||
\(176\) | 21.6357 | 1.63085 | ||||||||
\(177\) | 12.3934 | 0.931547 | ||||||||
\(178\) | −0.364274 | −0.0273035 | ||||||||
\(179\) | −5.10393 | −0.381485 | −0.190743 | − | 0.981640i | \(-0.561090\pi\) | ||||
−0.190743 | + | 0.981640i | \(0.561090\pi\) | |||||||
\(180\) | −7.36262 | −0.548777 | ||||||||
\(181\) | 11.2649 | 0.837314 | 0.418657 | − | 0.908144i | \(-0.362501\pi\) | ||||
0.418657 | + | 0.908144i | \(0.362501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3220 | −0.984788 | ||||||||
\(184\) | −0.765900 | −0.0564629 | ||||||||
\(185\) | −37.8764 | −2.78473 | ||||||||
\(186\) | −0.878024 | −0.0643799 | ||||||||
\(187\) | 24.1918 | 1.76908 | ||||||||
\(188\) | 13.0813 | 0.954053 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 1.06327 | 0.0771375 | ||||||||
\(191\) | 13.7495 | 0.994879 | 0.497440 | − | 0.867499i | \(-0.334274\pi\) | ||||
0.497440 | + | 0.867499i | \(0.334274\pi\) | |||||||
\(192\) | 7.04066 | 0.508116 | ||||||||
\(193\) | 15.9088 | 1.14514 | 0.572571 | − | 0.819855i | \(-0.305946\pi\) | ||||
0.572571 | + | 0.819855i | \(0.305946\pi\) | |||||||
\(194\) | −3.28130 | −0.235584 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.95934 | −0.139953 | ||||||||
\(197\) | −1.71870 | −0.122452 | −0.0612260 | − | 0.998124i | \(-0.519501\pi\) | ||||
−0.0612260 | + | 0.998124i | \(0.519501\pi\) | |||||||
\(198\) | 1.16098 | 0.0825073 | ||||||||
\(199\) | 7.94294 | 0.563060 | 0.281530 | − | 0.959552i | \(-0.409158\pi\) | ||||
0.281530 | + | 0.959552i | \(0.409158\pi\) | |||||||
\(200\) | −7.28130 | −0.514866 | ||||||||
\(201\) | −7.60492 | −0.536410 | ||||||||
\(202\) | −0.437393 | −0.0307748 | ||||||||
\(203\) | 2.79836 | 0.196406 | ||||||||
\(204\) | 8.23245 | 0.576387 | ||||||||
\(205\) | 10.5462 | 0.736579 | ||||||||
\(206\) | −1.70065 | −0.118490 | ||||||||
\(207\) | 0.959341 | 0.0666788 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.07966 | 0.558882 | ||||||||
\(210\) | −0.757702 | −0.0522864 | ||||||||
\(211\) | 25.2000 | 1.73484 | 0.867419 | − | 0.497578i | \(-0.165777\pi\) | ||||
0.867419 | + | 0.497578i | \(0.165777\pi\) | |||||||
\(212\) | 21.3934 | 1.46931 | ||||||||
\(213\) | −3.63738 | −0.249229 | ||||||||
\(214\) | −1.50721 | −0.103030 | ||||||||
\(215\) | 3.60492 | 0.245853 | ||||||||
\(216\) | 0.798360 | 0.0543215 | ||||||||
\(217\) | 4.35442 | 0.295597 | ||||||||
\(218\) | 1.92034 | 0.130062 | ||||||||
\(219\) | 7.95934 | 0.537842 | ||||||||
\(220\) | −42.3918 | −2.85805 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.03246 | 0.136410 | ||||||||
\(223\) | −4.67804 | −0.313265 | −0.156632 | − | 0.987657i | \(-0.550064\pi\) | ||||
−0.156632 | + | 0.987657i | \(0.550064\pi\) | |||||||
\(224\) | 2.35442 | 0.157311 | ||||||||
\(225\) | 9.12032 | 0.608022 | ||||||||
\(226\) | −1.99015 | −0.132383 | ||||||||
\(227\) | 15.7885 | 1.04792 | 0.523960 | − | 0.851743i | \(-0.324454\pi\) | ||||
0.523960 | + | 0.851743i | \(0.324454\pi\) | |||||||
\(228\) | 2.74950 | 0.182090 | ||||||||
\(229\) | 22.3770 | 1.47872 | 0.739358 | − | 0.673313i | \(-0.235129\pi\) | ||||
0.739358 | + | 0.673313i | \(0.235129\pi\) | |||||||
\(230\) | 0.726895 | 0.0479300 | ||||||||
\(231\) | −5.75770 | −0.378829 | ||||||||
\(232\) | −2.23410 | −0.146676 | ||||||||
\(233\) | 7.64392 | 0.500770 | 0.250385 | − | 0.968146i | \(-0.419443\pi\) | ||||
0.250385 | + | 0.968146i | \(0.419443\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.0879 | −1.63655 | ||||||||
\(236\) | 24.2830 | 1.58069 | ||||||||
\(237\) | −3.56426 | −0.231524 | ||||||||
\(238\) | 0.847217 | 0.0549169 | ||||||||
\(239\) | 19.5967 | 1.26761 | 0.633803 | − | 0.773494i | \(-0.281493\pi\) | ||||
0.633803 | + | 0.773494i | \(0.281493\pi\) | |||||||
\(240\) | −14.1203 | −0.911463 | ||||||||
\(241\) | −18.9006 | −1.21750 | −0.608748 | − | 0.793363i | \(-0.708328\pi\) | ||||
−0.608748 | + | 0.793363i | \(0.708328\pi\) | |||||||
\(242\) | 4.46655 | 0.287120 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −26.1023 | −1.67103 | ||||||||
\(245\) | 3.75770 | 0.240071 | ||||||||
\(246\) | −0.565914 | −0.0360813 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.47640 | −0.220751 | ||||||||
\(249\) | −14.5643 | −0.922973 | ||||||||
\(250\) | 3.12198 | 0.197451 | ||||||||
\(251\) | −5.32362 | −0.336024 | −0.168012 | − | 0.985785i | \(-0.553735\pi\) | ||||
−0.168012 | + | 0.985785i | \(0.553735\pi\) | |||||||
\(252\) | −1.95934 | −0.123427 | ||||||||
\(253\) | 5.52360 | 0.347266 | ||||||||
\(254\) | −1.40493 | −0.0881533 | ||||||||
\(255\) | −15.7885 | −0.988715 | ||||||||
\(256\) | 12.8456 | 0.802848 | ||||||||
\(257\) | −11.7967 | −0.735858 | −0.367929 | − | 0.929854i | \(-0.619933\pi\) | ||||
−0.367929 | + | 0.929854i | \(0.619933\pi\) | |||||||
\(258\) | −0.193441 | −0.0120431 | ||||||||
\(259\) | −10.0797 | −0.626320 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.79836 | 0.173214 | ||||||||
\(262\) | −1.96754 | −0.121555 | ||||||||
\(263\) | 14.1836 | 0.874598 | 0.437299 | − | 0.899316i | \(-0.355935\pi\) | ||||
0.437299 | + | 0.899316i | \(0.355935\pi\) | |||||||
\(264\) | 4.59672 | 0.282909 | ||||||||
\(265\) | −41.0292 | −2.52040 | ||||||||
\(266\) | 0.282957 | 0.0173492 | ||||||||
\(267\) | 1.80656 | 0.110560 | ||||||||
\(268\) | −14.9006 | −0.910201 | ||||||||
\(269\) | −20.9983 | −1.28029 | −0.640146 | − | 0.768253i | \(-0.721126\pi\) | ||||
−0.640146 | + | 0.768253i | \(0.721126\pi\) | |||||||
\(270\) | −0.757702 | −0.0461123 | ||||||||
\(271\) | −11.0082 | −0.668700 | −0.334350 | − | 0.942449i | \(-0.608517\pi\) | ||||
−0.334350 | + | 0.942449i | \(0.608517\pi\) | |||||||
\(272\) | 15.7885 | 0.957319 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.669839 | −0.0404665 | ||||||||
\(275\) | 52.5121 | 3.16660 | ||||||||
\(276\) | 1.87968 | 0.113143 | ||||||||
\(277\) | −30.1757 | −1.81308 | −0.906542 | − | 0.422116i | \(-0.861287\pi\) | ||||
−0.906542 | + | 0.422116i | \(0.861287\pi\) | |||||||
\(278\) | 0.160981 | 0.00965501 | ||||||||
\(279\) | 4.35442 | 0.260692 | ||||||||
\(280\) | −3.00000 | −0.179284 | ||||||||
\(281\) | −7.48294 | −0.446395 | −0.223197 | − | 0.974773i | \(-0.571649\pi\) | ||||
−0.223197 | + | 0.974773i | \(0.571649\pi\) | |||||||
\(282\) | 1.34622 | 0.0801665 | ||||||||
\(283\) | 2.07312 | 0.123234 | 0.0616171 | − | 0.998100i | \(-0.480374\pi\) | ||||
0.0616171 | + | 0.998100i | \(0.480374\pi\) | |||||||
\(284\) | −7.12687 | −0.422902 | ||||||||
\(285\) | −5.27311 | −0.312352 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.80656 | 0.165666 | ||||||||
\(288\) | 2.35442 | 0.138736 | ||||||||
\(289\) | 0.653776 | 0.0384574 | ||||||||
\(290\) | 2.12032 | 0.124510 | ||||||||
\(291\) | 16.2731 | 0.953946 | ||||||||
\(292\) | 15.5951 | 0.912632 | ||||||||
\(293\) | 17.7741 | 1.03837 | 0.519187 | − | 0.854661i | \(-0.326235\pi\) | ||||
0.519187 | + | 0.854661i | \(0.326235\pi\) | |||||||
\(294\) | −0.201640 | −0.0117599 | ||||||||
\(295\) | −46.5708 | −2.71146 | ||||||||
\(296\) | 8.04720 | 0.467734 | ||||||||
\(297\) | −5.75770 | −0.334096 | ||||||||
\(298\) | −3.93475 | −0.227934 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 17.8698 | 1.03171 | ||||||||
\(301\) | 0.959341 | 0.0552955 | ||||||||
\(302\) | 1.83737 | 0.105729 | ||||||||
\(303\) | 2.16918 | 0.124616 | ||||||||
\(304\) | 5.27311 | 0.302433 | ||||||||
\(305\) | 50.0600 | 2.86643 | ||||||||
\(306\) | 0.847217 | 0.0484322 | ||||||||
\(307\) | −3.84556 | −0.219478 | −0.109739 | − | 0.993960i | \(-0.535001\pi\) | ||||
−0.109739 | + | 0.993960i | \(0.535001\pi\) | |||||||
\(308\) | −11.2813 | −0.642812 | ||||||||
\(309\) | 8.43409 | 0.479798 | ||||||||
\(310\) | 3.29935 | 0.187391 | ||||||||
\(311\) | −2.52360 | −0.143100 | −0.0715502 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715502 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.2731 | 1.65461 | 0.827307 | − | 0.561750i | \(-0.189872\pi\) | ||||
0.827307 | + | 0.561750i | \(0.189872\pi\) | |||||||
\(314\) | −0.328507 | −0.0185388 | ||||||||
\(315\) | 3.75770 | 0.211723 | ||||||||
\(316\) | −6.98360 | −0.392858 | ||||||||
\(317\) | 9.81476 | 0.551252 | 0.275626 | − | 0.961265i | \(-0.411115\pi\) | ||||
0.275626 | + | 0.961265i | \(0.411115\pi\) | |||||||
\(318\) | 2.20164 | 0.123462 | ||||||||
\(319\) | 16.1121 | 0.902106 | ||||||||
\(320\) | −26.4567 | −1.47897 | ||||||||
\(321\) | 7.47474 | 0.417200 | ||||||||
\(322\) | 0.193441 | 0.0107801 | ||||||||
\(323\) | 5.89607 | 0.328066 | ||||||||
\(324\) | −1.95934 | −0.108852 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.637713 | −0.0353196 | ||||||||
\(327\) | −9.52360 | −0.526656 | ||||||||
\(328\) | −2.24065 | −0.123719 | ||||||||
\(329\) | −6.67638 | −0.368081 | ||||||||
\(330\) | −4.36262 | −0.240154 | ||||||||
\(331\) | 34.7170 | 1.90822 | 0.954111 | − | 0.299454i | \(-0.0968046\pi\) | ||||
0.954111 | + | 0.299454i | \(0.0968046\pi\) | |||||||
\(332\) | −28.5364 | −1.56614 | ||||||||
\(333\) | −10.0797 | −0.552362 | ||||||||
\(334\) | 2.18524 | 0.119571 | ||||||||
\(335\) | 28.5770 | 1.56133 | ||||||||
\(336\) | −3.75770 | −0.204999 | ||||||||
\(337\) | 5.46655 | 0.297782 | 0.148891 | − | 0.988854i | \(-0.452430\pi\) | ||||
0.148891 | + | 0.988854i | \(0.452430\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.86983 | 0.536055 | ||||||||
\(340\) | −30.9351 | −1.67769 | ||||||||
\(341\) | 25.0715 | 1.35770 | ||||||||
\(342\) | 0.282957 | 0.0153006 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.765900 | −0.0412946 | ||||||||
\(345\) | −3.60492 | −0.194082 | ||||||||
\(346\) | 1.79016 | 0.0962397 | ||||||||
\(347\) | 22.0698 | 1.18477 | 0.592385 | − | 0.805655i | \(-0.298187\pi\) | ||||
0.592385 | + | 0.805655i | \(0.298187\pi\) | |||||||
\(348\) | 5.48294 | 0.293917 | ||||||||
\(349\) | −13.3446 | −0.714319 | −0.357159 | − | 0.934044i | \(-0.616255\pi\) | ||||
−0.357159 | + | 0.934044i | \(0.616255\pi\) | |||||||
\(350\) | 1.83902 | 0.0982997 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.5561 | 0.722541 | ||||||||
\(353\) | −27.3203 | −1.45411 | −0.727057 | − | 0.686577i | \(-0.759112\pi\) | ||||
−0.727057 | + | 0.686577i | \(0.759112\pi\) | |||||||
\(354\) | 2.49901 | 0.132821 | ||||||||
\(355\) | 13.6682 | 0.725432 | ||||||||
\(356\) | 3.53967 | 0.187602 | ||||||||
\(357\) | −4.20164 | −0.222374 | ||||||||
\(358\) | −1.02915 | −0.0543925 | ||||||||
\(359\) | 2.16263 | 0.114139 | 0.0570697 | − | 0.998370i | \(-0.481824\pi\) | ||||
0.0570697 | + | 0.998370i | \(0.481824\pi\) | |||||||
\(360\) | −3.00000 | −0.158114 | ||||||||
\(361\) | −17.0308 | −0.896358 | ||||||||
\(362\) | 2.27145 | 0.119385 | ||||||||
\(363\) | −22.1511 | −1.16263 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −29.9088 | −1.56550 | ||||||||
\(366\) | −2.68624 | −0.140412 | ||||||||
\(367\) | −14.7154 | −0.768137 | −0.384069 | − | 0.923305i | \(-0.625477\pi\) | ||||
−0.384069 | + | 0.923305i | \(0.625477\pi\) | |||||||
\(368\) | 3.60492 | 0.187919 | ||||||||
\(369\) | 2.80656 | 0.146104 | ||||||||
\(370\) | −7.63738 | −0.397048 | ||||||||
\(371\) | −10.9187 | −0.566870 | ||||||||
\(372\) | 8.53180 | 0.442353 | ||||||||
\(373\) | −31.8275 | −1.64797 | −0.823983 | − | 0.566614i | \(-0.808253\pi\) | ||||
−0.823983 | + | 0.566614i | \(0.808253\pi\) | |||||||
\(374\) | 4.87802 | 0.252237 | ||||||||
\(375\) | −15.4829 | −0.799536 | ||||||||
\(376\) | 5.33016 | 0.274882 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.201640 | −0.0103712 | ||||||||
\(379\) | −27.6583 | −1.42071 | −0.710357 | − | 0.703842i | \(-0.751466\pi\) | ||||
−0.710357 | + | 0.703842i | \(0.751466\pi\) | |||||||
\(380\) | −10.3318 | −0.530011 | ||||||||
\(381\) | 6.96754 | 0.356958 | ||||||||
\(382\) | 2.77245 | 0.141851 | ||||||||
\(383\) | −23.6747 | −1.20972 | −0.604861 | − | 0.796331i | \(-0.706771\pi\) | ||||
−0.604861 | + | 0.796331i | \(0.706771\pi\) | |||||||
\(384\) | 6.12852 | 0.312745 | ||||||||
\(385\) | 21.6357 | 1.10266 | ||||||||
\(386\) | 3.20785 | 0.163275 | ||||||||
\(387\) | 0.959341 | 0.0487661 | ||||||||
\(388\) | 31.8846 | 1.61869 | ||||||||
\(389\) | 8.79016 | 0.445679 | 0.222839 | − | 0.974855i | \(-0.428467\pi\) | ||||
0.222839 | + | 0.974855i | \(0.428467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.03081 | 0.203847 | ||||||||
\(392\) | −0.798360 | −0.0403233 | ||||||||
\(393\) | 9.75770 | 0.492211 | ||||||||
\(394\) | −0.346557 | −0.0174593 | ||||||||
\(395\) | 13.3934 | 0.673896 | ||||||||
\(396\) | −11.2813 | −0.566907 | ||||||||
\(397\) | −17.1269 | −0.859573 | −0.429786 | − | 0.902931i | \(-0.641411\pi\) | ||||
−0.429786 | + | 0.902931i | \(0.641411\pi\) | |||||||
\(398\) | 1.60161 | 0.0802816 | ||||||||
\(399\) | −1.40328 | −0.0702518 | ||||||||
\(400\) | 34.2715 | 1.71357 | ||||||||
\(401\) | 17.8292 | 0.890346 | 0.445173 | − | 0.895445i | \(-0.353142\pi\) | ||||
0.445173 | + | 0.895445i | \(0.353142\pi\) | |||||||
\(402\) | −1.53345 | −0.0764817 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.25016 | 0.211454 | ||||||||
\(405\) | 3.75770 | 0.186722 | ||||||||
\(406\) | 0.564260 | 0.0280038 | ||||||||
\(407\) | −58.0357 | −2.87672 | ||||||||
\(408\) | 3.35442 | 0.166069 | ||||||||
\(409\) | −17.7479 | −0.877575 | −0.438787 | − | 0.898591i | \(-0.644592\pi\) | ||||
−0.438787 | + | 0.898591i | \(0.644592\pi\) | |||||||
\(410\) | 2.12653 | 0.105022 | ||||||||
\(411\) | 3.32196 | 0.163860 | ||||||||
\(412\) | 16.5253 | 0.814141 | ||||||||
\(413\) | −12.3934 | −0.609841 | ||||||||
\(414\) | 0.193441 | 0.00950712 | ||||||||
\(415\) | 54.7281 | 2.68650 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.798360 | −0.0390959 | ||||||||
\(418\) | 1.62918 | 0.0796858 | ||||||||
\(419\) | 7.99835 | 0.390745 | 0.195372 | − | 0.980729i | \(-0.437408\pi\) | ||||
0.195372 | + | 0.980729i | \(0.437408\pi\) | |||||||
\(420\) | 7.36262 | 0.359259 | ||||||||
\(421\) | −23.7721 | −1.15858 | −0.579291 | − | 0.815121i | \(-0.696670\pi\) | ||||
−0.579291 | + | 0.815121i | \(0.696670\pi\) | |||||||
\(422\) | 5.08132 | 0.247355 | ||||||||
\(423\) | −6.67638 | −0.324617 | ||||||||
\(424\) | 8.71704 | 0.423337 | ||||||||
\(425\) | 38.3203 | 1.85881 | ||||||||
\(426\) | −0.733440 | −0.0355353 | ||||||||
\(427\) | 13.3220 | 0.644695 | ||||||||
\(428\) | 14.6456 | 0.707921 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.726895 | 0.0350540 | ||||||||
\(431\) | 6.03246 | 0.290573 | 0.145287 | − | 0.989390i | \(-0.453590\pi\) | ||||
0.145287 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(432\) | −3.75770 | −0.180793 | ||||||||
\(433\) | 6.29116 | 0.302334 | 0.151167 | − | 0.988508i | \(-0.451697\pi\) | ||||
0.151167 | + | 0.988508i | \(0.451697\pi\) | |||||||
\(434\) | 0.878024 | 0.0421465 | ||||||||
\(435\) | −10.5154 | −0.504175 | ||||||||
\(436\) | −18.6600 | −0.893651 | ||||||||
\(437\) | 1.34622 | 0.0643986 | ||||||||
\(438\) | 1.60492 | 0.0766860 | ||||||||
\(439\) | 29.5039 | 1.40814 | 0.704072 | − | 0.710128i | \(-0.251363\pi\) | ||||
0.704072 | + | 0.710128i | \(0.251363\pi\) | |||||||
\(440\) | −17.2731 | −0.823463 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5318 | −0.690427 | −0.345213 | − | 0.938524i | \(-0.612193\pi\) | ||||
−0.345213 | + | 0.938524i | \(0.612193\pi\) | |||||||
\(444\) | −19.7495 | −0.937270 | ||||||||
\(445\) | −6.78851 | −0.321806 | ||||||||
\(446\) | −0.943278 | −0.0446655 | ||||||||
\(447\) | 19.5138 | 0.922969 | ||||||||
\(448\) | −7.04066 | −0.332640 | ||||||||
\(449\) | 10.0961 | 0.476463 | 0.238231 | − | 0.971208i | \(-0.423432\pi\) | ||||
0.238231 | + | 0.971208i | \(0.423432\pi\) | |||||||
\(450\) | 1.83902 | 0.0866922 | ||||||||
\(451\) | 16.1593 | 0.760913 | ||||||||
\(452\) | 19.3384 | 0.909600 | ||||||||
\(453\) | −9.11212 | −0.428125 | ||||||||
\(454\) | 3.18359 | 0.149413 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.12032 | 0.0524639 | ||||||||
\(457\) | 18.6177 | 0.870898 | 0.435449 | − | 0.900213i | \(-0.356590\pi\) | ||||
0.435449 | + | 0.900213i | \(0.356590\pi\) | |||||||
\(458\) | 4.51210 | 0.210836 | ||||||||
\(459\) | −4.20164 | −0.196116 | ||||||||
\(460\) | −7.06327 | −0.329327 | ||||||||
\(461\) | 30.7380 | 1.43161 | 0.715806 | − | 0.698300i | \(-0.246060\pi\) | ||||
0.715806 | + | 0.698300i | \(0.246060\pi\) | |||||||
\(462\) | −1.16098 | −0.0540137 | ||||||||
\(463\) | −30.4747 | −1.41628 | −0.708141 | − | 0.706071i | \(-0.750466\pi\) | ||||
−0.708141 | + | 0.706071i | \(0.750466\pi\) | |||||||
\(464\) | 10.5154 | 0.488165 | ||||||||
\(465\) | −16.3626 | −0.758798 | ||||||||
\(466\) | 1.54132 | 0.0714002 | ||||||||
\(467\) | −10.7006 | −0.495167 | −0.247583 | − | 0.968867i | \(-0.579636\pi\) | ||||
−0.247583 | + | 0.968867i | \(0.579636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.60492 | 0.351163 | ||||||||
\(470\) | −5.05871 | −0.233341 | ||||||||
\(471\) | 1.62918 | 0.0750687 | ||||||||
\(472\) | 9.89442 | 0.455428 | ||||||||
\(473\) | 5.52360 | 0.253975 | ||||||||
\(474\) | −0.718696 | −0.0330108 | ||||||||
\(475\) | 12.7984 | 0.587229 | ||||||||
\(476\) | −8.23245 | −0.377334 | ||||||||
\(477\) | −10.9187 | −0.499932 | ||||||||
\(478\) | 3.95148 | 0.180736 | ||||||||
\(479\) | −7.15278 | −0.326819 | −0.163409 | − | 0.986558i | \(-0.552249\pi\) | ||||
−0.163409 | + | 0.986558i | \(0.552249\pi\) | |||||||
\(480\) | −8.84722 | −0.403818 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3.81112 | −0.173592 | ||||||||
\(483\) | −0.959341 | −0.0436515 | ||||||||
\(484\) | −43.4016 | −1.97280 | ||||||||
\(485\) | −61.1495 | −2.77665 | ||||||||
\(486\) | −0.201640 | −0.00914656 | ||||||||
\(487\) | −36.2324 | −1.64185 | −0.820924 | − | 0.571037i | \(-0.806541\pi\) | ||||
−0.820924 | + | 0.571037i | \(0.806541\pi\) | |||||||
\(488\) | −10.6357 | −0.481457 | ||||||||
\(489\) | 3.16263 | 0.143019 | ||||||||
\(490\) | 0.757702 | 0.0342295 | ||||||||
\(491\) | −7.12032 | −0.321336 | −0.160668 | − | 0.987009i | \(-0.551365\pi\) | ||||
−0.160668 | + | 0.987009i | \(0.551365\pi\) | |||||||
\(492\) | 5.49901 | 0.247914 | ||||||||
\(493\) | 11.7577 | 0.529540 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.6357 | 0.972454 | ||||||||
\(496\) | 16.3626 | 0.734703 | ||||||||
\(497\) | 3.63738 | 0.163159 | ||||||||
\(498\) | −2.93673 | −0.131598 | ||||||||
\(499\) | −32.2797 | −1.44504 | −0.722518 | − | 0.691352i | \(-0.757015\pi\) | ||||
−0.722518 | + | 0.691352i | \(0.757015\pi\) | |||||||
\(500\) | −30.3364 | −1.35668 | ||||||||
\(501\) | −10.8374 | −0.484178 | ||||||||
\(502\) | −1.07345 | −0.0479105 | ||||||||
\(503\) | 36.2551 | 1.61653 | 0.808267 | − | 0.588817i | \(-0.200406\pi\) | ||||
0.808267 | + | 0.588817i | \(0.200406\pi\) | |||||||
\(504\) | −0.798360 | −0.0355618 | ||||||||
\(505\) | −8.15113 | −0.362721 | ||||||||
\(506\) | 1.11378 | 0.0495134 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.6518 | 0.605700 | ||||||||
\(509\) | −12.5462 | −0.556101 | −0.278051 | − | 0.960566i | \(-0.589688\pi\) | ||||
−0.278051 | + | 0.960566i | \(0.589688\pi\) | |||||||
\(510\) | −3.18359 | −0.140972 | ||||||||
\(511\) | −7.95934 | −0.352101 | ||||||||
\(512\) | 14.8472 | 0.656161 | ||||||||
\(513\) | −1.40328 | −0.0619563 | ||||||||
\(514\) | −2.37868 | −0.104919 | ||||||||
\(515\) | −31.6928 | −1.39655 | ||||||||
\(516\) | 1.87968 | 0.0827482 | ||||||||
\(517\) | −38.4406 | −1.69062 | ||||||||
\(518\) | −2.03246 | −0.0893012 | ||||||||
\(519\) | −8.87802 | −0.389702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0390 | −1.18460 | −0.592300 | − | 0.805717i | \(-0.701780\pi\) | ||||
−0.592300 | + | 0.805717i | \(0.701780\pi\) | |||||||
\(522\) | 0.564260 | 0.0246970 | ||||||||
\(523\) | 10.6600 | 0.466129 | 0.233064 | − | 0.972461i | \(-0.425125\pi\) | ||||
0.233064 | + | 0.972461i | \(0.425125\pi\) | |||||||
\(524\) | 19.1187 | 0.835203 | ||||||||
\(525\) | −9.12032 | −0.398044 | ||||||||
\(526\) | 2.85997 | 0.124701 | ||||||||
\(527\) | 18.2957 | 0.796974 | ||||||||
\(528\) | −21.6357 | −0.941574 | ||||||||
\(529\) | −22.0797 | −0.959985 | ||||||||
\(530\) | −8.27311 | −0.359361 | ||||||||
\(531\) | −12.3934 | −0.537829 | ||||||||
\(532\) | −2.74950 | −0.119206 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.364274 | 0.0157637 | ||||||||
\(535\) | −28.0879 | −1.21434 | ||||||||
\(536\) | −6.07147 | −0.262247 | ||||||||
\(537\) | 5.10393 | 0.220251 | ||||||||
\(538\) | −4.23410 | −0.182545 | ||||||||
\(539\) | 5.75770 | 0.248002 | ||||||||
\(540\) | 7.36262 | 0.316837 | ||||||||
\(541\) | −5.20164 | −0.223636 | −0.111818 | − | 0.993729i | \(-0.535667\pi\) | ||||
−0.111818 | + | 0.993729i | \(0.535667\pi\) | |||||||
\(542\) | −2.21969 | −0.0953438 | ||||||||
\(543\) | −11.2649 | −0.483423 | ||||||||
\(544\) | 9.89243 | 0.424135 | ||||||||
\(545\) | 35.7869 | 1.53294 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.4567 | −1.17396 | −0.586982 | − | 0.809600i | \(-0.699684\pi\) | ||||
−0.586982 | + | 0.809600i | \(0.699684\pi\) | |||||||
\(548\) | 6.50886 | 0.278045 | ||||||||
\(549\) | 13.3220 | 0.568567 | ||||||||
\(550\) | 10.5885 | 0.451496 | ||||||||
\(551\) | 3.92688 | 0.167291 | ||||||||
\(552\) | 0.765900 | 0.0325989 | ||||||||
\(553\) | 3.56426 | 0.151568 | ||||||||
\(554\) | −6.08462 | −0.258511 | ||||||||
\(555\) | 37.8764 | 1.60776 | ||||||||
\(556\) | −1.56426 | −0.0663394 | ||||||||
\(557\) | 14.3951 | 0.609939 | 0.304970 | − | 0.952362i | \(-0.401354\pi\) | ||||
0.304970 | + | 0.952362i | \(0.401354\pi\) | |||||||
\(558\) | 0.878024 | 0.0371697 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14.1203 | 0.596693 | ||||||||
\(561\) | −24.1918 | −1.02138 | ||||||||
\(562\) | −1.50886 | −0.0636473 | ||||||||
\(563\) | 10.6213 | 0.447635 | 0.223818 | − | 0.974631i | \(-0.428148\pi\) | ||||
0.223818 | + | 0.974631i | \(0.428148\pi\) | |||||||
\(564\) | −13.0813 | −0.550823 | ||||||||
\(565\) | −37.0879 | −1.56030 | ||||||||
\(566\) | 0.418023 | 0.0175708 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −2.90394 | −0.121847 | ||||||||
\(569\) | −18.4098 | −0.771780 | −0.385890 | − | 0.922545i | \(-0.626106\pi\) | ||||
−0.385890 | + | 0.922545i | \(0.626106\pi\) | |||||||
\(570\) | −1.06327 | −0.0445354 | ||||||||
\(571\) | −17.0698 | −0.714349 | −0.357175 | − | 0.934038i | \(-0.616260\pi\) | ||||
−0.357175 | + | 0.934038i | \(0.616260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.7495 | −0.574394 | ||||||||
\(574\) | 0.565914 | 0.0236208 | ||||||||
\(575\) | 8.74950 | 0.364880 | ||||||||
\(576\) | −7.04066 | −0.293361 | ||||||||
\(577\) | −5.84722 | −0.243423 | −0.121711 | − | 0.992566i | \(-0.538838\pi\) | ||||
−0.121711 | + | 0.992566i | \(0.538838\pi\) | |||||||
\(578\) | 0.131827 | 0.00548329 | ||||||||
\(579\) | −15.9088 | −0.661148 | ||||||||
\(580\) | −20.6033 | −0.855504 | ||||||||
\(581\) | 14.5643 | 0.604227 | ||||||||
\(582\) | 3.28130 | 0.136014 | ||||||||
\(583\) | −62.8665 | −2.60367 | ||||||||
\(584\) | 6.35442 | 0.262948 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.58396 | 0.148052 | ||||||||
\(587\) | 32.0489 | 1.32280 | 0.661399 | − | 0.750034i | \(-0.269963\pi\) | ||||
0.661399 | + | 0.750034i | \(0.269963\pi\) | |||||||
\(588\) | 1.95934 | 0.0808019 | ||||||||
\(589\) | 6.11047 | 0.251778 | ||||||||
\(590\) | −9.39052 | −0.386602 | ||||||||
\(591\) | 1.71870 | 0.0706977 | ||||||||
\(592\) | −37.8764 | −1.55671 | ||||||||
\(593\) | 14.1347 | 0.580444 | 0.290222 | − | 0.956959i | \(-0.406271\pi\) | ||||
0.290222 | + | 0.956959i | \(0.406271\pi\) | |||||||
\(594\) | −1.16098 | −0.0476356 | ||||||||
\(595\) | 15.7885 | 0.647266 | ||||||||
\(596\) | 38.2341 | 1.56613 | ||||||||
\(597\) | −7.94294 | −0.325083 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.5154 | −0.674801 | −0.337401 | − | 0.941361i | \(-0.609548\pi\) | ||||
−0.337401 | + | 0.941361i | \(0.609548\pi\) | |||||||
\(600\) | 7.28130 | 0.297258 | ||||||||
\(601\) | −3.75770 | −0.153280 | −0.0766399 | − | 0.997059i | \(-0.524419\pi\) | ||||
−0.0766399 | + | 0.997059i | \(0.524419\pi\) | |||||||
\(602\) | 0.193441 | 0.00788408 | ||||||||
\(603\) | 7.60492 | 0.309696 | ||||||||
\(604\) | −17.8538 | −0.726459 | ||||||||
\(605\) | 83.2373 | 3.38408 | ||||||||
\(606\) | 0.437393 | 0.0177679 | ||||||||
\(607\) | 10.7026 | 0.434406 | 0.217203 | − | 0.976126i | \(-0.430307\pi\) | ||||
0.217203 | + | 0.976126i | \(0.430307\pi\) | |||||||
\(608\) | 3.30391 | 0.133991 | ||||||||
\(609\) | −2.79836 | −0.113395 | ||||||||
\(610\) | 10.0941 | 0.408697 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8.23245 | −0.332777 | ||||||||
\(613\) | −8.34001 | −0.336850 | −0.168425 | − | 0.985714i | \(-0.553868\pi\) | ||||
−0.168425 | + | 0.985714i | \(0.553868\pi\) | |||||||
\(614\) | −0.775418 | −0.0312933 | ||||||||
\(615\) | −10.5462 | −0.425264 | ||||||||
\(616\) | −4.59672 | −0.185207 | ||||||||
\(617\) | −0.951143 | −0.0382916 | −0.0191458 | − | 0.999817i | \(-0.506095\pi\) | ||||
−0.0191458 | + | 0.999817i | \(0.506095\pi\) | |||||||
\(618\) | 1.70065 | 0.0684100 | ||||||||
\(619\) | 13.2098 | 0.530948 | 0.265474 | − | 0.964118i | \(-0.414472\pi\) | ||||
0.265474 | + | 0.964118i | \(0.414472\pi\) | |||||||
\(620\) | −32.0600 | −1.28756 | ||||||||
\(621\) | −0.959341 | −0.0384970 | ||||||||
\(622\) | −0.508858 | −0.0204034 | ||||||||
\(623\) | −1.80656 | −0.0723782 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5787 | 0.503147 | ||||||||
\(626\) | 5.90262 | 0.235916 | ||||||||
\(627\) | −8.07966 | −0.322671 | ||||||||
\(628\) | 3.19212 | 0.127380 | ||||||||
\(629\) | −42.3511 | −1.68865 | ||||||||
\(630\) | 0.757702 | 0.0301876 | ||||||||
\(631\) | 37.1511 | 1.47896 | 0.739482 | − | 0.673177i | \(-0.235071\pi\) | ||||
0.739482 | + | 0.673177i | \(0.235071\pi\) | |||||||
\(632\) | −2.84556 | −0.113190 | ||||||||
\(633\) | −25.2000 | −1.00161 | ||||||||
\(634\) | 1.97904 | 0.0785979 | ||||||||
\(635\) | −26.1819 | −1.03900 | ||||||||
\(636\) | −21.3934 | −0.848305 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.24884 | 0.128623 | ||||||||
\(639\) | 3.63738 | 0.143892 | ||||||||
\(640\) | −23.0292 | −0.910307 | ||||||||
\(641\) | −16.9593 | −0.669854 | −0.334927 | − | 0.942244i | \(-0.608712\pi\) | ||||
−0.334927 | + | 0.942244i | \(0.608712\pi\) | |||||||
\(642\) | 1.50721 | 0.0594846 | ||||||||
\(643\) | 22.6131 | 0.891774 | 0.445887 | − | 0.895089i | \(-0.352888\pi\) | ||||
0.445887 | + | 0.895089i | \(0.352888\pi\) | |||||||
\(644\) | −1.87968 | −0.0740697 | ||||||||
\(645\) | −3.60492 | −0.141944 | ||||||||
\(646\) | 1.18888 | 0.0467760 | ||||||||
\(647\) | 1.28296 | 0.0504382 | 0.0252191 | − | 0.999682i | \(-0.491972\pi\) | ||||
0.0252191 | + | 0.999682i | \(0.491972\pi\) | |||||||
\(648\) | −0.798360 | −0.0313626 | ||||||||
\(649\) | −71.3577 | −2.80103 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.35442 | −0.170663 | ||||||||
\(652\) | 6.19668 | 0.242681 | ||||||||
\(653\) | −48.9803 | −1.91675 | −0.958374 | − | 0.285517i | \(-0.907835\pi\) | ||||
−0.958374 | + | 0.285517i | \(0.907835\pi\) | |||||||
\(654\) | −1.92034 | −0.0750911 | ||||||||
\(655\) | −36.6665 | −1.43268 | ||||||||
\(656\) | 10.5462 | 0.411760 | ||||||||
\(657\) | −7.95934 | −0.310523 | ||||||||
\(658\) | −1.34622 | −0.0524813 | ||||||||
\(659\) | 10.2115 | 0.397783 | 0.198892 | − | 0.980021i | \(-0.436266\pi\) | ||||
0.198892 | + | 0.980021i | \(0.436266\pi\) | |||||||
\(660\) | 42.3918 | 1.65010 | ||||||||
\(661\) | 25.7072 | 0.999894 | 0.499947 | − | 0.866056i | \(-0.333353\pi\) | ||||
0.499947 | + | 0.866056i | \(0.333353\pi\) | |||||||
\(662\) | 7.00033 | 0.272076 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.6275 | −0.451236 | ||||||||
\(665\) | 5.27311 | 0.204482 | ||||||||
\(666\) | −2.03246 | −0.0787562 | ||||||||
\(667\) | 2.68458 | 0.103947 | ||||||||
\(668\) | −21.2341 | −0.821572 | ||||||||
\(669\) | 4.67804 | 0.180863 | ||||||||
\(670\) | 5.76226 | 0.222616 | ||||||||
\(671\) | 76.7039 | 2.96112 | ||||||||
\(672\) | −2.35442 | −0.0908238 | ||||||||
\(673\) | 8.58886 | 0.331076 | 0.165538 | − | 0.986203i | \(-0.447064\pi\) | ||||
0.165538 | + | 0.986203i | \(0.447064\pi\) | |||||||
\(674\) | 1.10227 | 0.0424580 | ||||||||
\(675\) | −9.12032 | −0.351041 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.70065 | 0.334393 | 0.167197 | − | 0.985924i | \(-0.446529\pi\) | ||||
0.167197 | + | 0.985924i | \(0.446529\pi\) | |||||||
\(678\) | 1.99015 | 0.0764312 | ||||||||
\(679\) | −16.2731 | −0.624504 | ||||||||
\(680\) | −12.6049 | −0.483377 | ||||||||
\(681\) | −15.7885 | −0.605017 | ||||||||
\(682\) | 5.05540 | 0.193581 | ||||||||
\(683\) | 22.4747 | 0.859972 | 0.429986 | − | 0.902836i | \(-0.358518\pi\) | ||||
0.429986 | + | 0.902836i | \(0.358518\pi\) | |||||||
\(684\) | −2.74950 | −0.105130 | ||||||||
\(685\) | −12.4829 | −0.476949 | ||||||||
\(686\) | 0.201640 | 0.00769864 | ||||||||
\(687\) | −22.3770 | −0.853737 | ||||||||
\(688\) | 3.60492 | 0.137436 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.726895 | −0.0276724 | ||||||||
\(691\) | −23.8275 | −0.906441 | −0.453221 | − | 0.891398i | \(-0.649725\pi\) | ||||
−0.453221 | + | 0.891398i | \(0.649725\pi\) | |||||||
\(692\) | −17.3951 | −0.661262 | ||||||||
\(693\) | 5.75770 | 0.218717 | ||||||||
\(694\) | 4.45015 | 0.168925 | ||||||||
\(695\) | 3.00000 | 0.113796 | ||||||||
\(696\) | 2.23410 | 0.0846833 | ||||||||
\(697\) | 11.7921 | 0.446659 | ||||||||
\(698\) | −2.69079 | −0.101848 | ||||||||
\(699\) | −7.64392 | −0.289120 | ||||||||
\(700\) | −17.8698 | −0.675416 | ||||||||
\(701\) | −51.9885 | −1.96358 | −0.981789 | − | 0.189974i | \(-0.939160\pi\) | ||||
−0.981789 | + | 0.189974i | \(0.939160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.1446 | −0.533473 | ||||||||
\(704\) | −40.5380 | −1.52783 | ||||||||
\(705\) | 25.0879 | 0.944864 | ||||||||
\(706\) | −5.50886 | −0.207329 | ||||||||
\(707\) | −2.16918 | −0.0815804 | ||||||||
\(708\) | −24.2830 | −0.912609 | ||||||||
\(709\) | −7.63407 | −0.286704 | −0.143352 | − | 0.989672i | \(-0.545788\pi\) | ||||
−0.143352 | + | 0.989672i | \(0.545788\pi\) | |||||||
\(710\) | 2.75605 | 0.103433 | ||||||||
\(711\) | 3.56426 | 0.133670 | ||||||||
\(712\) | 1.44228 | 0.0540519 | ||||||||
\(713\) | 4.17738 | 0.156444 | ||||||||
\(714\) | −0.847217 | −0.0317063 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.0003 | 0.373730 | ||||||||
\(717\) | −19.5967 | −0.731853 | ||||||||
\(718\) | 0.436073 | 0.0162741 | ||||||||
\(719\) | −29.1043 | −1.08541 | −0.542703 | − | 0.839925i | \(-0.682599\pi\) | ||||
−0.542703 | + | 0.839925i | \(0.682599\pi\) | |||||||
\(720\) | 14.1203 | 0.526233 | ||||||||
\(721\) | −8.43409 | −0.314102 | ||||||||
\(722\) | −3.43409 | −0.127803 | ||||||||
\(723\) | 18.9006 | 0.702922 | ||||||||
\(724\) | −22.0718 | −0.820292 | ||||||||
\(725\) | 25.5219 | 0.947861 | ||||||||
\(726\) | −4.46655 | −0.165769 | ||||||||
\(727\) | −4.23245 | −0.156973 | −0.0784864 | − | 0.996915i | \(-0.525009\pi\) | ||||
−0.0784864 | + | 0.996915i | \(0.525009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.03081 | −0.223210 | ||||||||
\(731\) | 4.03081 | 0.149085 | ||||||||
\(732\) | 26.1023 | 0.964768 | ||||||||
\(733\) | −28.6993 | −1.06003 | −0.530017 | − | 0.847987i | \(-0.677814\pi\) | ||||
−0.530017 | + | 0.847987i | \(0.677814\pi\) | |||||||
\(734\) | −2.96721 | −0.109522 | ||||||||
\(735\) | −3.75770 | −0.138605 | ||||||||
\(736\) | 2.25869 | 0.0832566 | ||||||||
\(737\) | 43.7869 | 1.61291 | ||||||||
\(738\) | 0.565914 | 0.0208316 | ||||||||
\(739\) | 2.52327 | 0.0928199 | 0.0464100 | − | 0.998922i | \(-0.485222\pi\) | ||||
0.0464100 | + | 0.998922i | \(0.485222\pi\) | |||||||
\(740\) | 74.2127 | 2.72811 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.20164 | −0.0808247 | ||||||||
\(743\) | −26.7170 | −0.980153 | −0.490077 | − | 0.871679i | \(-0.663031\pi\) | ||||
−0.490077 | + | 0.871679i | \(0.663031\pi\) | |||||||
\(744\) | 3.47640 | 0.127451 | ||||||||
\(745\) | −73.3269 | −2.68649 | ||||||||
\(746\) | −6.41769 | −0.234968 | ||||||||
\(747\) | 14.5643 | 0.532878 | ||||||||
\(748\) | −47.4000 | −1.73311 | ||||||||
\(749\) | −7.47474 | −0.273121 | ||||||||
\(750\) | −3.12198 | −0.113998 | ||||||||
\(751\) | −37.6829 | −1.37507 | −0.687535 | − | 0.726151i | \(-0.741307\pi\) | ||||
−0.687535 | + | 0.726151i | \(0.741307\pi\) | |||||||
\(752\) | −25.0879 | −0.914860 | ||||||||
\(753\) | 5.32362 | 0.194003 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.2406 | 1.24614 | ||||||||
\(756\) | 1.95934 | 0.0712606 | ||||||||
\(757\) | −6.40982 | −0.232969 | −0.116485 | − | 0.993193i | \(-0.537163\pi\) | ||||
−0.116485 | + | 0.993193i | \(0.537163\pi\) | |||||||
\(758\) | −5.57702 | −0.202566 | ||||||||
\(759\) | −5.52360 | −0.200494 | ||||||||
\(760\) | −4.20984 | −0.152707 | ||||||||
\(761\) | −4.21149 | −0.152666 | −0.0763332 | − | 0.997082i | \(-0.524321\pi\) | ||||
−0.0763332 | + | 0.997082i | \(0.524321\pi\) | |||||||
\(762\) | 1.40493 | 0.0508953 | ||||||||
\(763\) | 9.52360 | 0.344778 | ||||||||
\(764\) | −26.9400 | −0.974654 | ||||||||
\(765\) | 15.7885 | 0.570835 | ||||||||
\(766\) | −4.77377 | −0.172483 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.8456 | −0.463524 | ||||||||
\(769\) | 27.3856 | 0.987549 | 0.493774 | − | 0.869590i | \(-0.335617\pi\) | ||||
0.493774 | + | 0.869590i | \(0.335617\pi\) | |||||||
\(770\) | 4.36262 | 0.157218 | ||||||||
\(771\) | 11.7967 | 0.424848 | ||||||||
\(772\) | −31.1708 | −1.12186 | ||||||||
\(773\) | −8.78395 | −0.315937 | −0.157968 | − | 0.987444i | \(-0.550494\pi\) | ||||
−0.157968 | + | 0.987444i | \(0.550494\pi\) | |||||||
\(774\) | 0.193441 | 0.00695310 | ||||||||
\(775\) | 39.7137 | 1.42656 | ||||||||
\(776\) | 12.9918 | 0.466378 | ||||||||
\(777\) | 10.0797 | 0.361606 | ||||||||
\(778\) | 1.77245 | 0.0635452 | ||||||||
\(779\) | 3.93839 | 0.141107 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.9429 | 0.749397 | ||||||||
\(782\) | 0.812771 | 0.0290646 | ||||||||
\(783\) | −2.79836 | −0.100005 | ||||||||
\(784\) | 3.75770 | 0.134204 | ||||||||
\(785\) | −6.12198 | −0.218503 | ||||||||
\(786\) | 1.96754 | 0.0701798 | ||||||||
\(787\) | 31.5039 | 1.12299 | 0.561496 | − | 0.827479i | \(-0.310226\pi\) | ||||
0.561496 | + | 0.827479i | \(0.310226\pi\) | |||||||
\(788\) | 3.36751 | 0.119963 | ||||||||
\(789\) | −14.1836 | −0.504949 | ||||||||
\(790\) | 2.70065 | 0.0960847 | ||||||||
\(791\) | −9.86983 | −0.350931 | ||||||||
\(792\) | −4.59672 | −0.163337 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.45346 | −0.122559 | ||||||||
\(795\) | 41.0292 | 1.45515 | ||||||||
\(796\) | −15.5629 | −0.551614 | ||||||||
\(797\) | 28.4570 | 1.00800 | 0.504000 | − | 0.863704i | \(-0.331861\pi\) | ||||
0.504000 | + | 0.863704i | \(0.331861\pi\) | |||||||
\(798\) | −0.282957 | −0.0100166 | ||||||||
\(799\) | −28.0518 | −0.992400 | ||||||||
\(800\) | 21.4731 | 0.759188 | ||||||||
\(801\) | −1.80656 | −0.0638316 | ||||||||
\(802\) | 3.59507 | 0.126946 | ||||||||
\(803\) | −45.8275 | −1.61722 | ||||||||
\(804\) | 14.9006 | 0.525505 | ||||||||
\(805\) | 3.60492 | 0.127057 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.9983 | 0.739177 | ||||||||
\(808\) | 1.73179 | 0.0609240 | ||||||||
\(809\) | −22.2994 | −0.784004 | −0.392002 | − | 0.919964i | \(-0.628217\pi\) | ||||
−0.392002 | + | 0.919964i | \(0.628217\pi\) | |||||||
\(810\) | 0.757702 | 0.0266229 | ||||||||
\(811\) | 40.2616 | 1.41378 | 0.706888 | − | 0.707325i | \(-0.250098\pi\) | ||||
0.706888 | + | 0.707325i | \(0.250098\pi\) | |||||||
\(812\) | −5.48294 | −0.192414 | ||||||||
\(813\) | 11.0082 | 0.386074 | ||||||||
\(814\) | −11.7023 | −0.410165 | ||||||||
\(815\) | −11.8842 | −0.416287 | ||||||||
\(816\) | −15.7885 | −0.552708 | ||||||||
\(817\) | 1.34622 | 0.0470984 | ||||||||
\(818\) | −3.57867 | −0.125125 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.6636 | −0.721605 | ||||||||
\(821\) | −16.0649 | −0.560670 | −0.280335 | − | 0.959902i | \(-0.590445\pi\) | ||||
−0.280335 | + | 0.959902i | \(0.590445\pi\) | |||||||
\(822\) | 0.669839 | 0.0233633 | ||||||||
\(823\) | −7.40328 | −0.258062 | −0.129031 | − | 0.991641i | \(-0.541187\pi\) | ||||
−0.129031 | + | 0.991641i | \(0.541187\pi\) | |||||||
\(824\) | 6.73344 | 0.234570 | ||||||||
\(825\) | −52.5121 | −1.82824 | ||||||||
\(826\) | −2.49901 | −0.0869516 | ||||||||
\(827\) | −52.4226 | −1.82291 | −0.911456 | − | 0.411398i | \(-0.865041\pi\) | ||||
−0.911456 | + | 0.411398i | \(0.865041\pi\) | |||||||
\(828\) | −1.87968 | −0.0653233 | ||||||||
\(829\) | 9.41769 | 0.327090 | 0.163545 | − | 0.986536i | \(-0.447707\pi\) | ||||
0.163545 | + | 0.986536i | \(0.447707\pi\) | |||||||
\(830\) | 11.0354 | 0.383043 | ||||||||
\(831\) | 30.1757 | 1.04678 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.20164 | 0.145578 | ||||||||
\(834\) | −0.160981 | −0.00557432 | ||||||||
\(835\) | 40.7236 | 1.40930 | ||||||||
\(836\) | −15.8308 | −0.547520 | ||||||||
\(837\) | −4.35442 | −0.150511 | ||||||||
\(838\) | 1.61278 | 0.0557127 | ||||||||
\(839\) | −44.7301 | −1.54426 | −0.772128 | − | 0.635467i | \(-0.780808\pi\) | ||||
−0.772128 | + | 0.635467i | \(0.780808\pi\) | |||||||
\(840\) | 3.00000 | 0.103510 | ||||||||
\(841\) | −21.1692 | −0.729972 | ||||||||
\(842\) | −4.79340 | −0.165192 | ||||||||
\(843\) | 7.48294 | 0.257726 | ||||||||
\(844\) | −49.3754 | −1.69957 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.34622 | −0.0462841 | ||||||||
\(847\) | 22.1511 | 0.761122 | ||||||||
\(848\) | −41.0292 | −1.40895 | ||||||||
\(849\) | −2.07312 | −0.0711493 | ||||||||
\(850\) | 7.72689 | 0.265030 | ||||||||
\(851\) | −9.66984 | −0.331478 | ||||||||
\(852\) | 7.12687 | 0.244162 | ||||||||
\(853\) | −41.4550 | −1.41939 | −0.709697 | − | 0.704507i | \(-0.751168\pi\) | ||||
−0.709697 | + | 0.704507i | \(0.751168\pi\) | |||||||
\(854\) | 2.68624 | 0.0919211 | ||||||||
\(855\) | 5.27311 | 0.180336 | ||||||||
\(856\) | 5.96754 | 0.203966 | ||||||||
\(857\) | 19.9885 | 0.682794 | 0.341397 | − | 0.939919i | \(-0.389100\pi\) | ||||
0.341397 | + | 0.939919i | \(0.389100\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.9642 | 1.02237 | 0.511183 | − | 0.859472i | \(-0.329207\pi\) | ||||
0.511183 | + | 0.859472i | \(0.329207\pi\) | |||||||
\(860\) | −7.06327 | −0.240855 | ||||||||
\(861\) | −2.80656 | −0.0956473 | ||||||||
\(862\) | 1.21638 | 0.0414302 | ||||||||
\(863\) | 25.1351 | 0.855608 | 0.427804 | − | 0.903872i | \(-0.359287\pi\) | ||||
0.427804 | + | 0.903872i | \(0.359287\pi\) | |||||||
\(864\) | −2.35442 | −0.0800991 | ||||||||
\(865\) | 33.3610 | 1.13431 | ||||||||
\(866\) | 1.26855 | 0.0431070 | ||||||||
\(867\) | −0.653776 | −0.0222034 | ||||||||
\(868\) | −8.53180 | −0.289588 | ||||||||
\(869\) | 20.5219 | 0.696159 | ||||||||
\(870\) | −2.12032 | −0.0718857 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −7.60327 | −0.257479 | ||||||||
\(873\) | −16.2731 | −0.550761 | ||||||||
\(874\) | 0.271452 | 0.00918201 | ||||||||
\(875\) | 15.4829 | 0.523419 | ||||||||
\(876\) | −15.5951 | −0.526909 | ||||||||
\(877\) | 25.7445 | 0.869331 | 0.434666 | − | 0.900592i | \(-0.356867\pi\) | ||||
0.434666 | + | 0.900592i | \(0.356867\pi\) | |||||||
\(878\) | 5.94916 | 0.200774 | ||||||||
\(879\) | −17.7741 | −0.599505 | ||||||||
\(880\) | 81.3006 | 2.74064 | ||||||||
\(881\) | 51.1006 | 1.72162 | 0.860812 | − | 0.508923i | \(-0.169956\pi\) | ||||
0.860812 | + | 0.508923i | \(0.169956\pi\) | |||||||
\(882\) | 0.201640 | 0.00678956 | ||||||||
\(883\) | −26.6115 | −0.895547 | −0.447774 | − | 0.894147i | \(-0.647783\pi\) | ||||
−0.447774 | + | 0.894147i | \(0.647783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.5708 | 1.56546 | ||||||||
\(886\) | −2.93019 | −0.0984416 | ||||||||
\(887\) | −25.0308 | −0.840452 | −0.420226 | − | 0.907419i | \(-0.638049\pi\) | ||||
−0.420226 | + | 0.907419i | \(0.638049\pi\) | |||||||
\(888\) | −8.04720 | −0.270046 | ||||||||
\(889\) | −6.96754 | −0.233684 | ||||||||
\(890\) | −1.36883 | −0.0458834 | ||||||||
\(891\) | 5.75770 | 0.192890 | ||||||||
\(892\) | 9.16587 | 0.306896 | ||||||||
\(893\) | −9.36883 | −0.313516 | ||||||||
\(894\) | 3.93475 | 0.131598 | ||||||||
\(895\) | −19.1790 | −0.641084 | ||||||||
\(896\) | −6.12852 | −0.204740 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.03577 | 0.0679344 | ||||||||
\(899\) | 12.1852 | 0.406401 | ||||||||
\(900\) | −17.8698 | −0.595661 | ||||||||
\(901\) | −45.8764 | −1.52836 | ||||||||
\(902\) | 3.25836 | 0.108492 | ||||||||
\(903\) | −0.959341 | −0.0319249 | ||||||||
\(904\) | 7.87968 | 0.262074 | ||||||||
\(905\) | 42.3302 | 1.40710 | ||||||||
\(906\) | −1.83737 | −0.0610424 | ||||||||
\(907\) | 16.7072 | 0.554753 | 0.277377 | − | 0.960761i | \(-0.410535\pi\) | ||||
0.277377 | + | 0.960761i | \(0.410535\pi\) | |||||||
\(908\) | −30.9351 | −1.02662 | ||||||||
\(909\) | −2.16918 | −0.0719471 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.5593 | 1.90702 | 0.953512 | − | 0.301354i | \(-0.0974386\pi\) | ||||
0.953512 | + | 0.301354i | \(0.0974386\pi\) | |||||||
\(912\) | −5.27311 | −0.174610 | ||||||||
\(913\) | 83.8567 | 2.77525 | ||||||||
\(914\) | 3.75406 | 0.124173 | ||||||||
\(915\) | −50.0600 | −1.65493 | ||||||||
\(916\) | −43.8442 | −1.44865 | ||||||||
\(917\) | −9.75770 | −0.322228 | ||||||||
\(918\) | −0.847217 | −0.0279623 | ||||||||
\(919\) | −14.2731 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(920\) | −2.87802 | −0.0948857 | ||||||||
\(921\) | 3.84556 | 0.126716 | ||||||||
\(922\) | 6.19800 | 0.204120 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 11.2813 | 0.371128 | ||||||||
\(925\) | −91.9298 | −3.02263 | ||||||||
\(926\) | −6.14492 | −0.201935 | ||||||||
\(927\) | −8.43409 | −0.277012 | ||||||||
\(928\) | 6.58852 | 0.216279 | ||||||||
\(929\) | 53.8131 | 1.76555 | 0.882775 | − | 0.469795i | \(-0.155672\pi\) | ||||
0.882775 | + | 0.469795i | \(0.155672\pi\) | |||||||
\(930\) | −3.29935 | −0.108190 | ||||||||
\(931\) | 1.40328 | 0.0459906 | ||||||||
\(932\) | −14.9771 | −0.490590 | ||||||||
\(933\) | 2.52360 | 0.0826190 | ||||||||
\(934\) | −2.15767 | −0.0706013 | ||||||||
\(935\) | 90.9055 | 2.97293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 59.2715 | 1.93631 | 0.968157 | − | 0.250344i | \(-0.0805437\pi\) | ||||
0.968157 | + | 0.250344i | \(0.0805437\pi\) | |||||||
\(938\) | 1.53345 | 0.0500690 | ||||||||
\(939\) | −29.2731 | −0.955292 | ||||||||
\(940\) | 49.1557 | 1.60328 | ||||||||
\(941\) | −16.3367 | −0.532561 | −0.266281 | − | 0.963896i | \(-0.585795\pi\) | ||||
−0.266281 | + | 0.963896i | \(0.585795\pi\) | |||||||
\(942\) | 0.328507 | 0.0107034 | ||||||||
\(943\) | 2.69245 | 0.0876782 | ||||||||
\(944\) | −46.5708 | −1.51575 | ||||||||
\(945\) | −3.75770 | −0.122238 | ||||||||
\(946\) | 1.11378 | 0.0362120 | ||||||||
\(947\) | 57.4180 | 1.86584 | 0.932918 | − | 0.360090i | \(-0.117254\pi\) | ||||
0.932918 | + | 0.360090i | \(0.117254\pi\) | |||||||
\(948\) | 6.98360 | 0.226817 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.58066 | 0.0837276 | ||||||||
\(951\) | −9.81476 | −0.318265 | ||||||||
\(952\) | −3.35442 | −0.108717 | ||||||||
\(953\) | 24.6829 | 0.799559 | 0.399779 | − | 0.916611i | \(-0.369087\pi\) | ||||
0.399779 | + | 0.916611i | \(0.369087\pi\) | |||||||
\(954\) | −2.20164 | −0.0712807 | ||||||||
\(955\) | 51.6665 | 1.67189 | ||||||||
\(956\) | −38.3967 | −1.24184 | ||||||||
\(957\) | −16.1121 | −0.520831 | ||||||||
\(958\) | −1.44228 | −0.0465981 | ||||||||
\(959\) | −3.32196 | −0.107272 | ||||||||
\(960\) | 26.4567 | 0.853886 | ||||||||
\(961\) | −12.0390 | −0.388355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.47474 | −0.240870 | ||||||||
\(964\) | 37.0328 | 1.19275 | ||||||||
\(965\) | 59.7806 | 1.92441 | ||||||||
\(966\) | −0.193441 | −0.00622387 | ||||||||
\(967\) | 18.2098 | 0.585589 | 0.292794 | − | 0.956175i | \(-0.405415\pi\) | ||||
0.292794 | + | 0.956175i | \(0.405415\pi\) | |||||||
\(968\) | −17.6846 | −0.568404 | ||||||||
\(969\) | −5.89607 | −0.189409 | ||||||||
\(970\) | −12.3302 | −0.395898 | ||||||||
\(971\) | 9.24395 | 0.296653 | 0.148326 | − | 0.988938i | \(-0.452611\pi\) | ||||
0.148326 | + | 0.988938i | \(0.452611\pi\) | |||||||
\(972\) | 1.95934 | 0.0628459 | ||||||||
\(973\) | 0.798360 | 0.0255943 | ||||||||
\(974\) | −7.30590 | −0.234096 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 50.0600 | 1.60238 | ||||||||
\(977\) | 11.7495 | 0.375900 | 0.187950 | − | 0.982179i | \(-0.439816\pi\) | ||||
0.187950 | + | 0.982179i | \(0.439816\pi\) | |||||||
\(978\) | 0.637713 | 0.0203918 | ||||||||
\(979\) | −10.4016 | −0.332437 | ||||||||
\(980\) | −7.36262 | −0.235190 | ||||||||
\(981\) | 9.52360 | 0.304065 | ||||||||
\(982\) | −1.43574 | −0.0458163 | ||||||||
\(983\) | 24.1121 | 0.769057 | 0.384529 | − | 0.923113i | \(-0.374364\pi\) | ||||
0.384529 | + | 0.923113i | \(0.374364\pi\) | |||||||
\(984\) | 2.24065 | 0.0714292 | ||||||||
\(985\) | −6.45835 | −0.205780 | ||||||||
\(986\) | 2.37082 | 0.0755023 | ||||||||
\(987\) | 6.67638 | 0.212512 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.920336 | 0.0292650 | ||||||||
\(990\) | 4.36262 | 0.138653 | ||||||||
\(991\) | −25.0226 | −0.794869 | −0.397435 | − | 0.917630i | \(-0.630099\pi\) | ||||
−0.397435 | + | 0.917630i | \(0.630099\pi\) | |||||||
\(992\) | 10.2521 | 0.325506 | ||||||||
\(993\) | −34.7170 | −1.10171 | ||||||||
\(994\) | 0.733440 | 0.0232633 | ||||||||
\(995\) | 29.8472 | 0.946220 | ||||||||
\(996\) | 28.5364 | 0.904209 | ||||||||
\(997\) | 45.8990 | 1.45364 | 0.726818 | − | 0.686830i | \(-0.240999\pi\) | ||||
0.726818 | + | 0.686830i | \(0.240999\pi\) | |||||||
\(998\) | −6.50886 | −0.206034 | ||||||||
\(999\) | 10.0797 | 0.318906 |
(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 | 3549.2.a.m.1.2 | 3 | ||
13.3 | even | 3 | 273.2.k.b.22.2 | ✓ | 6 | ||
13.9 | even | 3 | 273.2.k.b.211.2 | yes | 6 | ||
13.12 | even | 2 | 3549.2.a.l.1.2 | 3 | |||
39.29 | odd | 6 | 819.2.o.f.568.2 | 6 | |||
39.35 | odd | 6 | 819.2.o.f.757.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.k.b.22.2 | ✓ | 6 | 13.3 | even | 3 | ||
273.2.k.b.211.2 | yes | 6 | 13.9 | even | 3 | ||
819.2.o.f.568.2 | 6 | 39.29 | odd | 6 | |||
819.2.o.f.757.2 | 6 | 39.35 | odd | 6 | |||
3549.2.a.l.1.2 | 3 | 13.12 | even | 2 | |||
3549.2.a.m.1.2 | 3 | 1.1 | even | 1 | trivial |