Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.47641 | −1.75108 | −0.875542 | − | 0.483143i | \(-0.839495\pi\) | ||||
−0.875542 | + | 0.483143i | \(0.839495\pi\) | |||||||
\(3\) | 1.36965 | 0.790767 | 0.395384 | − | 0.918516i | \(-0.370612\pi\) | ||||
0.395384 | + | 0.918516i | \(0.370612\pi\) | |||||||
\(4\) | 4.13259 | 2.06629 | ||||||||
\(5\) | −1.36117 | −0.608735 | −0.304367 | − | 0.952555i | \(-0.598445\pi\) | ||||
−0.304367 | + | 0.952555i | \(0.598445\pi\) | |||||||
\(6\) | −3.39181 | −1.38470 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −5.28115 | −1.86717 | ||||||||
\(9\) | −1.12406 | −0.374687 | ||||||||
\(10\) | 3.37081 | 1.06595 | ||||||||
\(11\) | −4.82681 | −1.45534 | −0.727670 | − | 0.685928i | \(-0.759397\pi\) | ||||
−0.727670 | + | 0.685928i | \(0.759397\pi\) | |||||||
\(12\) | 5.66019 | 1.63396 | ||||||||
\(13\) | −3.75983 | −1.04279 | −0.521395 | − | 0.853315i | \(-0.674588\pi\) | ||||
−0.521395 | + | 0.853315i | \(0.674588\pi\) | |||||||
\(14\) | −2.47641 | −0.661847 | ||||||||
\(15\) | −1.86433 | −0.481367 | ||||||||
\(16\) | 4.81310 | 1.20327 | ||||||||
\(17\) | −7.95365 | −1.92904 | −0.964522 | − | 0.264002i | \(-0.914957\pi\) | ||||
−0.964522 | + | 0.264002i | \(0.914957\pi\) | |||||||
\(18\) | 2.78363 | 0.656109 | ||||||||
\(19\) | 3.12881 | 0.717799 | 0.358900 | − | 0.933376i | \(-0.383152\pi\) | ||||
0.358900 | + | 0.933376i | \(0.383152\pi\) | |||||||
\(20\) | −5.62516 | −1.25782 | ||||||||
\(21\) | 1.36965 | 0.298882 | ||||||||
\(22\) | 11.9532 | 2.54842 | ||||||||
\(23\) | −6.41972 | −1.33860 | −0.669302 | − | 0.742991i | \(-0.733407\pi\) | ||||
−0.669302 | + | 0.742991i | \(0.733407\pi\) | |||||||
\(24\) | −7.23332 | −1.47650 | ||||||||
\(25\) | −3.14721 | −0.629442 | ||||||||
\(26\) | 9.31087 | 1.82601 | ||||||||
\(27\) | −5.64852 | −1.08706 | ||||||||
\(28\) | 4.13259 | 0.780985 | ||||||||
\(29\) | 4.44520 | 0.825454 | 0.412727 | − | 0.910855i | \(-0.364576\pi\) | ||||
0.412727 | + | 0.910855i | \(0.364576\pi\) | |||||||
\(30\) | 4.61683 | 0.842914 | ||||||||
\(31\) | 7.80206 | 1.40129 | 0.700646 | − | 0.713509i | \(-0.252895\pi\) | ||||
0.700646 | + | 0.713509i | \(0.252895\pi\) | |||||||
\(32\) | −1.35688 | −0.239865 | ||||||||
\(33\) | −6.61104 | −1.15083 | ||||||||
\(34\) | 19.6965 | 3.37792 | ||||||||
\(35\) | −1.36117 | −0.230080 | ||||||||
\(36\) | −4.64528 | −0.774214 | ||||||||
\(37\) | −8.05339 | −1.32397 | −0.661984 | − | 0.749518i | \(-0.730285\pi\) | ||||
−0.661984 | + | 0.749518i | \(0.730285\pi\) | |||||||
\(38\) | −7.74822 | −1.25693 | ||||||||
\(39\) | −5.14965 | −0.824604 | ||||||||
\(40\) | 7.18855 | 1.13661 | ||||||||
\(41\) | −11.2949 | −1.76397 | −0.881986 | − | 0.471275i | \(-0.843794\pi\) | ||||
−0.881986 | + | 0.471275i | \(0.843794\pi\) | |||||||
\(42\) | −3.39181 | −0.523367 | ||||||||
\(43\) | 2.45552 | 0.374464 | 0.187232 | − | 0.982316i | \(-0.440048\pi\) | ||||
0.187232 | + | 0.982316i | \(0.440048\pi\) | |||||||
\(44\) | −19.9472 | −3.00716 | ||||||||
\(45\) | 1.53004 | 0.228085 | ||||||||
\(46\) | 15.8978 | 2.34401 | ||||||||
\(47\) | 4.92588 | 0.718513 | 0.359257 | − | 0.933239i | \(-0.383030\pi\) | ||||
0.359257 | + | 0.933239i | \(0.383030\pi\) | |||||||
\(48\) | 6.59225 | 0.951510 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.79377 | 1.10221 | ||||||||
\(51\) | −10.8937 | −1.52542 | ||||||||
\(52\) | −15.5378 | −2.15471 | ||||||||
\(53\) | −11.3662 | −1.56127 | −0.780635 | − | 0.624988i | \(-0.785104\pi\) | ||||
−0.780635 | + | 0.624988i | \(0.785104\pi\) | |||||||
\(54\) | 13.9880 | 1.90353 | ||||||||
\(55\) | 6.57012 | 0.885915 | ||||||||
\(56\) | −5.28115 | −0.705723 | ||||||||
\(57\) | 4.28538 | 0.567612 | ||||||||
\(58\) | −11.0081 | −1.44544 | ||||||||
\(59\) | 8.11169 | 1.05605 | 0.528026 | − | 0.849228i | \(-0.322932\pi\) | ||||
0.528026 | + | 0.849228i | \(0.322932\pi\) | |||||||
\(60\) | −7.70449 | −0.994646 | ||||||||
\(61\) | 4.27979 | 0.547971 | 0.273986 | − | 0.961734i | \(-0.411658\pi\) | ||||
0.273986 | + | 0.961734i | \(0.411658\pi\) | |||||||
\(62\) | −19.3211 | −2.45378 | ||||||||
\(63\) | −1.12406 | −0.141619 | ||||||||
\(64\) | −6.26600 | −0.783250 | ||||||||
\(65\) | 5.11778 | 0.634783 | ||||||||
\(66\) | 16.3716 | 2.01521 | ||||||||
\(67\) | −3.83017 | −0.467930 | −0.233965 | − | 0.972245i | \(-0.575170\pi\) | ||||
−0.233965 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(68\) | −32.8692 | −3.98597 | ||||||||
\(69\) | −8.79276 | −1.05852 | ||||||||
\(70\) | 3.37081 | 0.402889 | ||||||||
\(71\) | −13.9578 | −1.65648 | −0.828240 | − | 0.560373i | \(-0.810658\pi\) | ||||
−0.828240 | + | 0.560373i | \(0.810658\pi\) | |||||||
\(72\) | 5.93634 | 0.699604 | ||||||||
\(73\) | 1.34885 | 0.157871 | 0.0789355 | − | 0.996880i | \(-0.474848\pi\) | ||||
0.0789355 | + | 0.996880i | \(0.474848\pi\) | |||||||
\(74\) | 19.9435 | 2.31838 | ||||||||
\(75\) | −4.31057 | −0.497742 | ||||||||
\(76\) | 12.9301 | 1.48318 | ||||||||
\(77\) | −4.82681 | −0.550067 | ||||||||
\(78\) | 12.7526 | 1.44395 | ||||||||
\(79\) | 5.14082 | 0.578388 | 0.289194 | − | 0.957271i | \(-0.406613\pi\) | ||||
0.289194 | + | 0.957271i | \(0.406613\pi\) | |||||||
\(80\) | −6.55145 | −0.732475 | ||||||||
\(81\) | −4.36430 | −0.484922 | ||||||||
\(82\) | 27.9708 | 3.08886 | ||||||||
\(83\) | 10.8767 | 1.19388 | 0.596938 | − | 0.802288i | \(-0.296384\pi\) | ||||
0.596938 | + | 0.802288i | \(0.296384\pi\) | |||||||
\(84\) | 5.66019 | 0.617578 | ||||||||
\(85\) | 10.8263 | 1.17428 | ||||||||
\(86\) | −6.08087 | −0.655717 | ||||||||
\(87\) | 6.08837 | 0.652742 | ||||||||
\(88\) | 25.4911 | 2.71736 | ||||||||
\(89\) | 9.07796 | 0.962262 | 0.481131 | − | 0.876649i | \(-0.340226\pi\) | ||||
0.481131 | + | 0.876649i | \(0.340226\pi\) | |||||||
\(90\) | −3.78900 | −0.399396 | ||||||||
\(91\) | −3.75983 | −0.394138 | ||||||||
\(92\) | −26.5300 | −2.76595 | ||||||||
\(93\) | 10.6861 | 1.10810 | ||||||||
\(94\) | −12.1985 | −1.25818 | ||||||||
\(95\) | −4.25886 | −0.436949 | ||||||||
\(96\) | −1.85845 | −0.189677 | ||||||||
\(97\) | −3.05324 | −0.310009 | −0.155005 | − | 0.987914i | \(-0.549539\pi\) | ||||
−0.155005 | + | 0.987914i | \(0.549539\pi\) | |||||||
\(98\) | −2.47641 | −0.250155 | ||||||||
\(99\) | 5.42564 | 0.545297 | ||||||||
\(100\) | −13.0061 | −1.30061 | ||||||||
\(101\) | 14.7297 | 1.46566 | 0.732830 | − | 0.680411i | \(-0.238199\pi\) | ||||
0.732830 | + | 0.680411i | \(0.238199\pi\) | |||||||
\(102\) | 26.9772 | 2.67115 | ||||||||
\(103\) | 1.07742 | 0.106162 | 0.0530808 | − | 0.998590i | \(-0.483096\pi\) | ||||
0.0530808 | + | 0.998590i | \(0.483096\pi\) | |||||||
\(104\) | 19.8562 | 1.94706 | ||||||||
\(105\) | −1.86433 | −0.181940 | ||||||||
\(106\) | 28.1474 | 2.73391 | ||||||||
\(107\) | −17.4434 | −1.68631 | −0.843157 | − | 0.537668i | \(-0.819305\pi\) | ||||
−0.843157 | + | 0.537668i | \(0.819305\pi\) | |||||||
\(108\) | −23.3430 | −2.24618 | ||||||||
\(109\) | 10.4483 | 1.00076 | 0.500382 | − | 0.865804i | \(-0.333193\pi\) | ||||
0.500382 | + | 0.865804i | \(0.333193\pi\) | |||||||
\(110\) | −16.2703 | −1.55131 | ||||||||
\(111\) | −11.0303 | −1.04695 | ||||||||
\(112\) | 4.81310 | 0.454795 | ||||||||
\(113\) | −4.60337 | −0.433049 | −0.216525 | − | 0.976277i | \(-0.569472\pi\) | ||||
−0.216525 | + | 0.976277i | \(0.569472\pi\) | |||||||
\(114\) | −10.6123 | −0.993936 | ||||||||
\(115\) | 8.73834 | 0.814855 | ||||||||
\(116\) | 18.3702 | 1.70563 | ||||||||
\(117\) | 4.22629 | 0.390720 | ||||||||
\(118\) | −20.0878 | −1.84924 | ||||||||
\(119\) | −7.95365 | −0.729110 | ||||||||
\(120\) | 9.84579 | 0.898794 | ||||||||
\(121\) | 12.2981 | 1.11801 | ||||||||
\(122\) | −10.5985 | −0.959544 | ||||||||
\(123\) | −15.4701 | −1.39489 | ||||||||
\(124\) | 32.2427 | 2.89548 | ||||||||
\(125\) | 11.0898 | 0.991898 | ||||||||
\(126\) | 2.78363 | 0.247986 | ||||||||
\(127\) | −21.2790 | −1.88821 | −0.944103 | − | 0.329650i | \(-0.893069\pi\) | ||||
−0.944103 | + | 0.329650i | \(0.893069\pi\) | |||||||
\(128\) | 18.2309 | 1.61140 | ||||||||
\(129\) | 3.36320 | 0.296114 | ||||||||
\(130\) | −12.6737 | −1.11156 | ||||||||
\(131\) | 6.16387 | 0.538540 | 0.269270 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269270 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(132\) | −27.3207 | −2.37796 | ||||||||
\(133\) | 3.12881 | 0.271303 | ||||||||
\(134\) | 9.48505 | 0.819384 | ||||||||
\(135\) | 7.68860 | 0.661730 | ||||||||
\(136\) | 42.0044 | 3.60185 | ||||||||
\(137\) | 7.65434 | 0.653954 | 0.326977 | − | 0.945032i | \(-0.393970\pi\) | ||||
0.326977 | + | 0.945032i | \(0.393970\pi\) | |||||||
\(138\) | 21.7744 | 1.85356 | ||||||||
\(139\) | 0.167412 | 0.0141997 | 0.00709983 | − | 0.999975i | \(-0.497740\pi\) | ||||
0.00709983 | + | 0.999975i | \(0.497740\pi\) | |||||||
\(140\) | −5.62516 | −0.475413 | ||||||||
\(141\) | 6.74673 | 0.568177 | ||||||||
\(142\) | 34.5651 | 2.90064 | ||||||||
\(143\) | 18.1480 | 1.51761 | ||||||||
\(144\) | −5.41022 | −0.450852 | ||||||||
\(145\) | −6.05069 | −0.502482 | ||||||||
\(146\) | −3.34030 | −0.276445 | ||||||||
\(147\) | 1.36965 | 0.112967 | ||||||||
\(148\) | −33.2813 | −2.73571 | ||||||||
\(149\) | 22.7711 | 1.86548 | 0.932740 | − | 0.360550i | \(-0.117411\pi\) | ||||
0.932740 | + | 0.360550i | \(0.117411\pi\) | |||||||
\(150\) | 10.6747 | 0.871588 | ||||||||
\(151\) | −19.0935 | −1.55381 | −0.776905 | − | 0.629618i | \(-0.783211\pi\) | ||||
−0.776905 | + | 0.629618i | \(0.783211\pi\) | |||||||
\(152\) | −16.5237 | −1.34025 | ||||||||
\(153\) | 8.94040 | 0.722788 | ||||||||
\(154\) | 11.9532 | 0.963212 | ||||||||
\(155\) | −10.6199 | −0.853015 | ||||||||
\(156\) | −21.2814 | −1.70387 | ||||||||
\(157\) | 7.22773 | 0.576836 | 0.288418 | − | 0.957505i | \(-0.406871\pi\) | ||||
0.288418 | + | 0.957505i | \(0.406871\pi\) | |||||||
\(158\) | −12.7308 | −1.01281 | ||||||||
\(159\) | −15.5677 | −1.23460 | ||||||||
\(160\) | 1.84695 | 0.146014 | ||||||||
\(161\) | −6.41972 | −0.505945 | ||||||||
\(162\) | 10.8078 | 0.849139 | ||||||||
\(163\) | 0.0111351 | 0.000872170 0 | 0.000436085 | − | 1.00000i | \(-0.499861\pi\) | ||||
0.000436085 | 1.00000i | \(0.499861\pi\) | ||||||||
\(164\) | −46.6773 | −3.64488 | ||||||||
\(165\) | 8.99876 | 0.700553 | ||||||||
\(166\) | −26.9352 | −2.09058 | ||||||||
\(167\) | −13.3635 | −1.03410 | −0.517048 | − | 0.855956i | \(-0.672969\pi\) | ||||
−0.517048 | + | 0.855956i | \(0.672969\pi\) | |||||||
\(168\) | −7.23332 | −0.558063 | ||||||||
\(169\) | 1.13635 | 0.0874114 | ||||||||
\(170\) | −26.8103 | −2.05626 | ||||||||
\(171\) | −3.51698 | −0.268950 | ||||||||
\(172\) | 10.1477 | 0.773752 | ||||||||
\(173\) | 2.19027 | 0.166523 | 0.0832616 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832616 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(174\) | −15.0773 | −1.14300 | ||||||||
\(175\) | −3.14721 | −0.237907 | ||||||||
\(176\) | −23.2319 | −1.75117 | ||||||||
\(177\) | 11.1102 | 0.835091 | ||||||||
\(178\) | −22.4807 | −1.68500 | ||||||||
\(179\) | 11.3473 | 0.848133 | 0.424067 | − | 0.905631i | \(-0.360602\pi\) | ||||
0.424067 | + | 0.905631i | \(0.360602\pi\) | |||||||
\(180\) | 6.32303 | 0.471291 | ||||||||
\(181\) | 1.98524 | 0.147562 | 0.0737808 | − | 0.997274i | \(-0.476493\pi\) | ||||
0.0737808 | + | 0.997274i | \(0.476493\pi\) | |||||||
\(182\) | 9.31087 | 0.690168 | ||||||||
\(183\) | 5.86181 | 0.433318 | ||||||||
\(184\) | 33.9035 | 2.49940 | ||||||||
\(185\) | 10.9620 | 0.805946 | ||||||||
\(186\) | −26.4631 | −1.94037 | ||||||||
\(187\) | 38.3908 | 2.80741 | ||||||||
\(188\) | 20.3566 | 1.48466 | ||||||||
\(189\) | −5.64852 | −0.410869 | ||||||||
\(190\) | 10.5467 | 0.765135 | ||||||||
\(191\) | 16.8807 | 1.22144 | 0.610722 | − | 0.791845i | \(-0.290879\pi\) | ||||
0.610722 | + | 0.791845i | \(0.290879\pi\) | |||||||
\(192\) | −8.58222 | −0.619369 | ||||||||
\(193\) | 19.1453 | 1.37811 | 0.689055 | − | 0.724709i | \(-0.258026\pi\) | ||||
0.689055 | + | 0.724709i | \(0.258026\pi\) | |||||||
\(194\) | 7.56105 | 0.542852 | ||||||||
\(195\) | 7.00956 | 0.501965 | ||||||||
\(196\) | 4.13259 | 0.295185 | ||||||||
\(197\) | 2.51493 | 0.179181 | 0.0895905 | − | 0.995979i | \(-0.471444\pi\) | ||||
0.0895905 | + | 0.995979i | \(0.471444\pi\) | |||||||
\(198\) | −13.4361 | −0.954861 | ||||||||
\(199\) | 13.2545 | 0.939585 | 0.469793 | − | 0.882777i | \(-0.344329\pi\) | ||||
0.469793 | + | 0.882777i | \(0.344329\pi\) | |||||||
\(200\) | 16.6209 | 1.17527 | ||||||||
\(201\) | −5.24599 | −0.370023 | ||||||||
\(202\) | −36.4767 | −2.56649 | ||||||||
\(203\) | 4.44520 | 0.311992 | ||||||||
\(204\) | −45.0192 | −3.15197 | ||||||||
\(205\) | 15.3744 | 1.07379 | ||||||||
\(206\) | −2.66814 | −0.185898 | ||||||||
\(207\) | 7.21616 | 0.501558 | ||||||||
\(208\) | −18.0964 | −1.25476 | ||||||||
\(209\) | −15.1022 | −1.04464 | ||||||||
\(210\) | 4.61683 | 0.318592 | ||||||||
\(211\) | 17.0722 | 1.17530 | 0.587649 | − | 0.809116i | \(-0.300054\pi\) | ||||
0.587649 | + | 0.809116i | \(0.300054\pi\) | |||||||
\(212\) | −46.9719 | −3.22604 | ||||||||
\(213\) | −19.1172 | −1.30989 | ||||||||
\(214\) | 43.1968 | 2.95288 | ||||||||
\(215\) | −3.34239 | −0.227949 | ||||||||
\(216\) | 29.8307 | 2.02972 | ||||||||
\(217\) | 7.80206 | 0.529638 | ||||||||
\(218\) | −25.8742 | −1.75242 | ||||||||
\(219\) | 1.84745 | 0.124839 | ||||||||
\(220\) | 27.1516 | 1.83056 | ||||||||
\(221\) | 29.9044 | 2.01159 | ||||||||
\(222\) | 27.3155 | 1.83330 | ||||||||
\(223\) | −0.411557 | −0.0275599 | −0.0137800 | − | 0.999905i | \(-0.504386\pi\) | ||||
−0.0137800 | + | 0.999905i | \(0.504386\pi\) | |||||||
\(224\) | −1.35688 | −0.0906605 | ||||||||
\(225\) | 3.53766 | 0.235844 | ||||||||
\(226\) | 11.3998 | 0.758305 | ||||||||
\(227\) | 20.4070 | 1.35446 | 0.677231 | − | 0.735770i | \(-0.263180\pi\) | ||||
0.677231 | + | 0.735770i | \(0.263180\pi\) | |||||||
\(228\) | 17.7097 | 1.17285 | ||||||||
\(229\) | −26.1155 | −1.72576 | −0.862881 | − | 0.505407i | \(-0.831342\pi\) | ||||
−0.862881 | + | 0.505407i | \(0.831342\pi\) | |||||||
\(230\) | −21.6397 | −1.42688 | ||||||||
\(231\) | −6.61104 | −0.434975 | ||||||||
\(232\) | −23.4758 | −1.54126 | ||||||||
\(233\) | 4.09124 | 0.268026 | 0.134013 | − | 0.990980i | \(-0.457214\pi\) | ||||
0.134013 | + | 0.990980i | \(0.457214\pi\) | |||||||
\(234\) | −10.4660 | −0.684184 | ||||||||
\(235\) | −6.70497 | −0.437384 | ||||||||
\(236\) | 33.5223 | 2.18211 | ||||||||
\(237\) | 7.04112 | 0.457370 | ||||||||
\(238\) | 19.6965 | 1.27673 | ||||||||
\(239\) | −27.6539 | −1.78878 | −0.894391 | − | 0.447285i | \(-0.852391\pi\) | ||||
−0.894391 | + | 0.447285i | \(0.852391\pi\) | |||||||
\(240\) | −8.97319 | −0.579217 | ||||||||
\(241\) | −14.8975 | −0.959629 | −0.479815 | − | 0.877370i | \(-0.659296\pi\) | ||||
−0.479815 | + | 0.877370i | \(0.659296\pi\) | |||||||
\(242\) | −30.4552 | −1.95773 | ||||||||
\(243\) | 10.9680 | 0.703597 | ||||||||
\(244\) | 17.6866 | 1.13227 | ||||||||
\(245\) | −1.36117 | −0.0869621 | ||||||||
\(246\) | 38.3102 | 2.44257 | ||||||||
\(247\) | −11.7638 | −0.748514 | ||||||||
\(248\) | −41.2038 | −2.61645 | ||||||||
\(249\) | 14.8973 | 0.944077 | ||||||||
\(250\) | −27.4627 | −1.73690 | ||||||||
\(251\) | −10.6543 | −0.672490 | −0.336245 | − | 0.941774i | \(-0.609157\pi\) | ||||
−0.336245 | + | 0.941774i | \(0.609157\pi\) | |||||||
\(252\) | −4.64528 | −0.292625 | ||||||||
\(253\) | 30.9868 | 1.94812 | ||||||||
\(254\) | 52.6955 | 3.30641 | ||||||||
\(255\) | 14.8282 | 0.928579 | ||||||||
\(256\) | −32.6152 | −2.03845 | ||||||||
\(257\) | 18.9727 | 1.18348 | 0.591741 | − | 0.806128i | \(-0.298441\pi\) | ||||
0.591741 | + | 0.806128i | \(0.298441\pi\) | |||||||
\(258\) | −8.32866 | −0.518519 | ||||||||
\(259\) | −8.05339 | −0.500413 | ||||||||
\(260\) | 21.1497 | 1.31165 | ||||||||
\(261\) | −4.99668 | −0.309287 | ||||||||
\(262\) | −15.2642 | −0.943028 | ||||||||
\(263\) | −10.6016 | −0.653721 | −0.326861 | − | 0.945073i | \(-0.605991\pi\) | ||||
−0.326861 | + | 0.945073i | \(0.605991\pi\) | |||||||
\(264\) | 34.9139 | 2.14880 | ||||||||
\(265\) | 15.4714 | 0.950399 | ||||||||
\(266\) | −7.74822 | −0.475074 | ||||||||
\(267\) | 12.4336 | 0.760925 | ||||||||
\(268\) | −15.8285 | −0.966880 | ||||||||
\(269\) | −13.3866 | −0.816193 | −0.408097 | − | 0.912939i | \(-0.633807\pi\) | ||||
−0.408097 | + | 0.912939i | \(0.633807\pi\) | |||||||
\(270\) | −19.0401 | −1.15874 | ||||||||
\(271\) | −2.05389 | −0.124765 | −0.0623825 | − | 0.998052i | \(-0.519870\pi\) | ||||
−0.0623825 | + | 0.998052i | \(0.519870\pi\) | |||||||
\(272\) | −38.2817 | −2.32117 | ||||||||
\(273\) | −5.14965 | −0.311671 | ||||||||
\(274\) | −18.9552 | −1.14513 | ||||||||
\(275\) | 15.1910 | 0.916052 | ||||||||
\(276\) | −36.3368 | −2.18722 | ||||||||
\(277\) | −20.8842 | −1.25481 | −0.627404 | − | 0.778694i | \(-0.715883\pi\) | ||||
−0.627404 | + | 0.778694i | \(0.715883\pi\) | |||||||
\(278\) | −0.414579 | −0.0248648 | ||||||||
\(279\) | −8.77000 | −0.525046 | ||||||||
\(280\) | 7.18855 | 0.429598 | ||||||||
\(281\) | −22.9131 | −1.36688 | −0.683439 | − | 0.730007i | \(-0.739517\pi\) | ||||
−0.683439 | + | 0.730007i | \(0.739517\pi\) | |||||||
\(282\) | −16.7076 | −0.994925 | ||||||||
\(283\) | −9.87834 | −0.587207 | −0.293603 | − | 0.955927i | \(-0.594854\pi\) | ||||
−0.293603 | + | 0.955927i | \(0.594854\pi\) | |||||||
\(284\) | −57.6816 | −3.42277 | ||||||||
\(285\) | −5.83314 | −0.345525 | ||||||||
\(286\) | −44.9419 | −2.65747 | ||||||||
\(287\) | −11.2949 | −0.666719 | ||||||||
\(288\) | 1.52522 | 0.0898744 | ||||||||
\(289\) | 46.2606 | 2.72121 | ||||||||
\(290\) | 14.9840 | 0.879888 | ||||||||
\(291\) | −4.18186 | −0.245145 | ||||||||
\(292\) | 5.57424 | 0.326208 | ||||||||
\(293\) | −22.2757 | −1.30136 | −0.650681 | − | 0.759351i | \(-0.725517\pi\) | ||||
−0.650681 | + | 0.759351i | \(0.725517\pi\) | |||||||
\(294\) | −3.39181 | −0.197814 | ||||||||
\(295\) | −11.0414 | −0.642855 | ||||||||
\(296\) | 42.5311 | 2.47207 | ||||||||
\(297\) | 27.2643 | 1.58204 | ||||||||
\(298\) | −56.3905 | −3.26661 | ||||||||
\(299\) | 24.1371 | 1.39588 | ||||||||
\(300\) | −17.8138 | −1.02848 | ||||||||
\(301\) | 2.45552 | 0.141534 | ||||||||
\(302\) | 47.2833 | 2.72085 | ||||||||
\(303\) | 20.1745 | 1.15900 | ||||||||
\(304\) | 15.0593 | 0.863709 | ||||||||
\(305\) | −5.82554 | −0.333569 | ||||||||
\(306\) | −22.1401 | −1.26566 | ||||||||
\(307\) | −1.62188 | −0.0925658 | −0.0462829 | − | 0.998928i | \(-0.514738\pi\) | ||||
−0.0462829 | + | 0.998928i | \(0.514738\pi\) | |||||||
\(308\) | −19.9472 | −1.13660 | ||||||||
\(309\) | 1.47569 | 0.0839491 | ||||||||
\(310\) | 26.2993 | 1.49370 | ||||||||
\(311\) | −21.0344 | −1.19275 | −0.596377 | − | 0.802705i | \(-0.703394\pi\) | ||||
−0.596377 | + | 0.802705i | \(0.703394\pi\) | |||||||
\(312\) | 27.1961 | 1.53967 | ||||||||
\(313\) | 32.0980 | 1.81429 | 0.907144 | − | 0.420820i | \(-0.138258\pi\) | ||||
0.907144 | + | 0.420820i | \(0.138258\pi\) | |||||||
\(314\) | −17.8988 | −1.01009 | ||||||||
\(315\) | 1.53004 | 0.0862081 | ||||||||
\(316\) | 21.2449 | 1.19512 | ||||||||
\(317\) | 10.5692 | 0.593627 | 0.296813 | − | 0.954935i | \(-0.404076\pi\) | ||||
0.296813 | + | 0.954935i | \(0.404076\pi\) | |||||||
\(318\) | 38.5520 | 2.16189 | ||||||||
\(319\) | −21.4562 | −1.20132 | ||||||||
\(320\) | 8.52911 | 0.476792 | ||||||||
\(321\) | −23.8913 | −1.33348 | ||||||||
\(322\) | 15.8978 | 0.885951 | ||||||||
\(323\) | −24.8855 | −1.38467 | ||||||||
\(324\) | −18.0358 | −1.00199 | ||||||||
\(325\) | 11.8330 | 0.656376 | ||||||||
\(326\) | −0.0275751 | −0.00152724 | ||||||||
\(327\) | 14.3105 | 0.791372 | ||||||||
\(328\) | 59.6502 | 3.29363 | ||||||||
\(329\) | 4.92588 | 0.271573 | ||||||||
\(330\) | −22.2846 | −1.22673 | ||||||||
\(331\) | −12.7553 | −0.701097 | −0.350548 | − | 0.936545i | \(-0.614005\pi\) | ||||
−0.350548 | + | 0.936545i | \(0.614005\pi\) | |||||||
\(332\) | 44.9490 | 2.46690 | ||||||||
\(333\) | 9.05251 | 0.496074 | ||||||||
\(334\) | 33.0934 | 1.81079 | ||||||||
\(335\) | 5.21352 | 0.284845 | ||||||||
\(336\) | 6.59225 | 0.359637 | ||||||||
\(337\) | −7.69435 | −0.419138 | −0.209569 | − | 0.977794i | \(-0.567206\pi\) | ||||
−0.209569 | + | 0.977794i | \(0.567206\pi\) | |||||||
\(338\) | −2.81406 | −0.153065 | ||||||||
\(339\) | −6.30501 | −0.342441 | ||||||||
\(340\) | 44.7406 | 2.42640 | ||||||||
\(341\) | −37.6591 | −2.03935 | ||||||||
\(342\) | 8.70947 | 0.470954 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.9680 | −0.699187 | ||||||||
\(345\) | 11.9685 | 0.644360 | ||||||||
\(346\) | −5.42400 | −0.291596 | ||||||||
\(347\) | 30.7882 | 1.65280 | 0.826400 | − | 0.563084i | \(-0.190385\pi\) | ||||
0.826400 | + | 0.563084i | \(0.190385\pi\) | |||||||
\(348\) | 25.1607 | 1.34876 | ||||||||
\(349\) | 33.9862 | 1.81924 | 0.909619 | − | 0.415444i | \(-0.136374\pi\) | ||||
0.909619 | + | 0.415444i | \(0.136374\pi\) | |||||||
\(350\) | 7.79377 | 0.416595 | ||||||||
\(351\) | 21.2375 | 1.13357 | ||||||||
\(352\) | 6.54942 | 0.349085 | ||||||||
\(353\) | 19.0638 | 1.01467 | 0.507333 | − | 0.861750i | \(-0.330631\pi\) | ||||
0.507333 | + | 0.861750i | \(0.330631\pi\) | |||||||
\(354\) | −27.5133 | −1.46231 | ||||||||
\(355\) | 18.9989 | 1.00836 | ||||||||
\(356\) | 37.5155 | 1.98832 | ||||||||
\(357\) | −10.8937 | −0.576556 | ||||||||
\(358\) | −28.1004 | −1.48515 | ||||||||
\(359\) | 11.3040 | 0.596601 | 0.298300 | − | 0.954472i | \(-0.403580\pi\) | ||||
0.298300 | + | 0.954472i | \(0.403580\pi\) | |||||||
\(360\) | −8.08038 | −0.425873 | ||||||||
\(361\) | −9.21052 | −0.484764 | ||||||||
\(362\) | −4.91626 | −0.258393 | ||||||||
\(363\) | 16.8441 | 0.884087 | ||||||||
\(364\) | −15.5378 | −0.814404 | ||||||||
\(365\) | −1.83602 | −0.0961016 | ||||||||
\(366\) | −14.5162 | −0.758776 | ||||||||
\(367\) | −18.0988 | −0.944751 | −0.472375 | − | 0.881397i | \(-0.656603\pi\) | ||||
−0.472375 | + | 0.881397i | \(0.656603\pi\) | |||||||
\(368\) | −30.8987 | −1.61071 | ||||||||
\(369\) | 12.6962 | 0.660938 | ||||||||
\(370\) | −27.1465 | −1.41128 | ||||||||
\(371\) | −11.3662 | −0.590104 | ||||||||
\(372\) | 44.1612 | 2.28965 | ||||||||
\(373\) | −3.56325 | −0.184498 | −0.0922491 | − | 0.995736i | \(-0.529406\pi\) | ||||
−0.0922491 | + | 0.995736i | \(0.529406\pi\) | |||||||
\(374\) | −95.0712 | −4.91602 | ||||||||
\(375\) | 15.1891 | 0.784360 | ||||||||
\(376\) | −26.0143 | −1.34159 | ||||||||
\(377\) | −16.7132 | −0.860775 | ||||||||
\(378\) | 13.9880 | 0.719466 | ||||||||
\(379\) | 14.8926 | 0.764982 | 0.382491 | − | 0.923959i | \(-0.375066\pi\) | ||||
0.382491 | + | 0.923959i | \(0.375066\pi\) | |||||||
\(380\) | −17.6001 | −0.902865 | ||||||||
\(381\) | −29.1448 | −1.49313 | ||||||||
\(382\) | −41.8035 | −2.13885 | ||||||||
\(383\) | −16.5812 | −0.847260 | −0.423630 | − | 0.905835i | \(-0.639244\pi\) | ||||
−0.423630 | + | 0.905835i | \(0.639244\pi\) | |||||||
\(384\) | 24.9700 | 1.27424 | ||||||||
\(385\) | 6.57012 | 0.334845 | ||||||||
\(386\) | −47.4116 | −2.41319 | ||||||||
\(387\) | −2.76016 | −0.140307 | ||||||||
\(388\) | −12.6178 | −0.640570 | ||||||||
\(389\) | −21.7981 | −1.10521 | −0.552603 | − | 0.833445i | \(-0.686365\pi\) | ||||
−0.552603 | + | 0.833445i | \(0.686365\pi\) | |||||||
\(390\) | −17.3585 | −0.878983 | ||||||||
\(391\) | 51.0602 | 2.58223 | ||||||||
\(392\) | −5.28115 | −0.266738 | ||||||||
\(393\) | 8.44234 | 0.425860 | ||||||||
\(394\) | −6.22798 | −0.313761 | ||||||||
\(395\) | −6.99755 | −0.352085 | ||||||||
\(396\) | 22.4219 | 1.12674 | ||||||||
\(397\) | −24.8261 | −1.24599 | −0.622994 | − | 0.782226i | \(-0.714084\pi\) | ||||
−0.622994 | + | 0.782226i | \(0.714084\pi\) | |||||||
\(398\) | −32.8235 | −1.64529 | ||||||||
\(399\) | 4.28538 | 0.214537 | ||||||||
\(400\) | −15.1478 | −0.757391 | ||||||||
\(401\) | −15.6648 | −0.782262 | −0.391131 | − | 0.920335i | \(-0.627916\pi\) | ||||
−0.391131 | + | 0.920335i | \(0.627916\pi\) | |||||||
\(402\) | 12.9912 | 0.647942 | ||||||||
\(403\) | −29.3345 | −1.46125 | ||||||||
\(404\) | 60.8718 | 3.02848 | ||||||||
\(405\) | 5.94056 | 0.295189 | ||||||||
\(406\) | −11.0081 | −0.546324 | ||||||||
\(407\) | 38.8722 | 1.92682 | ||||||||
\(408\) | 57.5313 | 2.84822 | ||||||||
\(409\) | −13.3397 | −0.659603 | −0.329802 | − | 0.944050i | \(-0.606982\pi\) | ||||
−0.329802 | + | 0.944050i | \(0.606982\pi\) | |||||||
\(410\) | −38.0731 | −1.88030 | ||||||||
\(411\) | 10.4838 | 0.517126 | ||||||||
\(412\) | 4.45254 | 0.219361 | ||||||||
\(413\) | 8.11169 | 0.399150 | ||||||||
\(414\) | −17.8701 | −0.878270 | ||||||||
\(415\) | −14.8051 | −0.726753 | ||||||||
\(416\) | 5.10165 | 0.250129 | ||||||||
\(417\) | 0.229295 | 0.0112286 | ||||||||
\(418\) | 37.3992 | 1.82925 | ||||||||
\(419\) | −3.53788 | −0.172837 | −0.0864184 | − | 0.996259i | \(-0.527542\pi\) | ||||
−0.0864184 | + | 0.996259i | \(0.527542\pi\) | |||||||
\(420\) | −7.70449 | −0.375941 | ||||||||
\(421\) | −9.69546 | −0.472528 | −0.236264 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236264 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(422\) | −42.2777 | −2.05804 | ||||||||
\(423\) | −5.53700 | −0.269218 | ||||||||
\(424\) | 60.0267 | 2.91515 | ||||||||
\(425\) | 25.0318 | 1.21422 | ||||||||
\(426\) | 47.3420 | 2.29373 | ||||||||
\(427\) | 4.27979 | 0.207114 | ||||||||
\(428\) | −72.0862 | −3.48442 | ||||||||
\(429\) | 24.8564 | 1.20008 | ||||||||
\(430\) | 8.27711 | 0.399158 | ||||||||
\(431\) | −3.83078 | −0.184522 | −0.0922610 | − | 0.995735i | \(-0.529409\pi\) | ||||
−0.0922610 | + | 0.995735i | \(0.529409\pi\) | |||||||
\(432\) | −27.1869 | −1.30803 | ||||||||
\(433\) | −0.324199 | −0.0155800 | −0.00779001 | − | 0.999970i | \(-0.502480\pi\) | ||||
−0.00779001 | + | 0.999970i | \(0.502480\pi\) | |||||||
\(434\) | −19.3211 | −0.927441 | ||||||||
\(435\) | −8.28732 | −0.397346 | ||||||||
\(436\) | 43.1785 | 2.06787 | ||||||||
\(437\) | −20.0861 | −0.960849 | ||||||||
\(438\) | −4.57504 | −0.218604 | ||||||||
\(439\) | 8.19796 | 0.391267 | 0.195634 | − | 0.980677i | \(-0.437324\pi\) | ||||
0.195634 | + | 0.980677i | \(0.437324\pi\) | |||||||
\(440\) | −34.6978 | −1.65415 | ||||||||
\(441\) | −1.12406 | −0.0535268 | ||||||||
\(442\) | −74.0555 | −3.52246 | ||||||||
\(443\) | −18.3580 | −0.872215 | −0.436107 | − | 0.899895i | \(-0.643643\pi\) | ||||
−0.436107 | + | 0.899895i | \(0.643643\pi\) | |||||||
\(444\) | −45.5837 | −2.16331 | ||||||||
\(445\) | −12.3567 | −0.585762 | ||||||||
\(446\) | 1.01918 | 0.0482597 | ||||||||
\(447\) | 31.1884 | 1.47516 | ||||||||
\(448\) | −6.26600 | −0.296041 | ||||||||
\(449\) | 1.88116 | 0.0887775 | 0.0443888 | − | 0.999014i | \(-0.485866\pi\) | ||||
0.0443888 | + | 0.999014i | \(0.485866\pi\) | |||||||
\(450\) | −8.76068 | −0.412983 | ||||||||
\(451\) | 54.5186 | 2.56718 | ||||||||
\(452\) | −19.0238 | −0.894806 | ||||||||
\(453\) | −26.1514 | −1.22870 | ||||||||
\(454\) | −50.5361 | −2.37178 | ||||||||
\(455\) | 5.11778 | 0.239925 | ||||||||
\(456\) | −22.6317 | −1.05983 | ||||||||
\(457\) | −27.0356 | −1.26467 | −0.632335 | − | 0.774695i | \(-0.717904\pi\) | ||||
−0.632335 | + | 0.774695i | \(0.717904\pi\) | |||||||
\(458\) | 64.6726 | 3.02195 | ||||||||
\(459\) | 44.9263 | 2.09698 | ||||||||
\(460\) | 36.1119 | 1.68373 | ||||||||
\(461\) | −28.7063 | −1.33699 | −0.668494 | − | 0.743718i | \(-0.733061\pi\) | ||||
−0.668494 | + | 0.743718i | \(0.733061\pi\) | |||||||
\(462\) | 16.3716 | 0.761677 | ||||||||
\(463\) | −26.1908 | −1.21719 | −0.608594 | − | 0.793482i | \(-0.708266\pi\) | ||||
−0.608594 | + | 0.793482i | \(0.708266\pi\) | |||||||
\(464\) | 21.3952 | 0.993247 | ||||||||
\(465\) | −14.5456 | −0.674536 | ||||||||
\(466\) | −10.1316 | −0.469336 | ||||||||
\(467\) | −14.0623 | −0.650724 | −0.325362 | − | 0.945590i | \(-0.605486\pi\) | ||||
−0.325362 | + | 0.945590i | \(0.605486\pi\) | |||||||
\(468\) | 17.4655 | 0.807343 | ||||||||
\(469\) | −3.83017 | −0.176861 | ||||||||
\(470\) | 16.6042 | 0.765896 | ||||||||
\(471\) | 9.89946 | 0.456143 | ||||||||
\(472\) | −42.8390 | −1.97183 | ||||||||
\(473\) | −11.8523 | −0.544972 | ||||||||
\(474\) | −17.4367 | −0.800893 | ||||||||
\(475\) | −9.84704 | −0.451813 | ||||||||
\(476\) | −32.8692 | −1.50656 | ||||||||
\(477\) | 12.7763 | 0.584988 | ||||||||
\(478\) | 68.4823 | 3.13231 | ||||||||
\(479\) | −9.09674 | −0.415641 | −0.207820 | − | 0.978167i | \(-0.566637\pi\) | ||||
−0.207820 | + | 0.978167i | \(0.566637\pi\) | |||||||
\(480\) | 2.52967 | 0.115463 | ||||||||
\(481\) | 30.2794 | 1.38062 | ||||||||
\(482\) | 36.8921 | 1.68039 | ||||||||
\(483\) | −8.79276 | −0.400084 | ||||||||
\(484\) | 50.8231 | 2.31014 | ||||||||
\(485\) | 4.15598 | 0.188713 | ||||||||
\(486\) | −27.1612 | −1.23206 | ||||||||
\(487\) | 32.8239 | 1.48739 | 0.743696 | − | 0.668518i | \(-0.233071\pi\) | ||||
0.743696 | + | 0.668518i | \(0.233071\pi\) | |||||||
\(488\) | −22.6022 | −1.02315 | ||||||||
\(489\) | 0.0152512 | 0.000689683 0 | ||||||||
\(490\) | 3.37081 | 0.152278 | ||||||||
\(491\) | −8.93039 | −0.403023 | −0.201511 | − | 0.979486i | \(-0.564585\pi\) | ||||
−0.201511 | + | 0.979486i | \(0.564585\pi\) | |||||||
\(492\) | −63.9315 | −2.88225 | ||||||||
\(493\) | −35.3556 | −1.59234 | ||||||||
\(494\) | 29.1320 | 1.31071 | ||||||||
\(495\) | −7.38523 | −0.331941 | ||||||||
\(496\) | 37.5521 | 1.68614 | ||||||||
\(497\) | −13.9578 | −0.626091 | ||||||||
\(498\) | −36.8917 | −1.65316 | ||||||||
\(499\) | 12.7399 | 0.570318 | 0.285159 | − | 0.958480i | \(-0.407954\pi\) | ||||
0.285159 | + | 0.958480i | \(0.407954\pi\) | |||||||
\(500\) | 45.8294 | 2.04955 | ||||||||
\(501\) | −18.3033 | −0.817729 | ||||||||
\(502\) | 26.3842 | 1.17759 | ||||||||
\(503\) | −1.92167 | −0.0856832 | −0.0428416 | − | 0.999082i | \(-0.513641\pi\) | ||||
−0.0428416 | + | 0.999082i | \(0.513641\pi\) | |||||||
\(504\) | 5.93634 | 0.264426 | ||||||||
\(505\) | −20.0497 | −0.892199 | ||||||||
\(506\) | −76.7359 | −3.41133 | ||||||||
\(507\) | 1.55640 | 0.0691221 | ||||||||
\(508\) | −87.9373 | −3.90159 | ||||||||
\(509\) | 20.0363 | 0.888092 | 0.444046 | − | 0.896004i | \(-0.353543\pi\) | ||||
0.444046 | + | 0.896004i | \(0.353543\pi\) | |||||||
\(510\) | −36.7207 | −1.62602 | ||||||||
\(511\) | 1.34885 | 0.0596696 | ||||||||
\(512\) | 44.3066 | 1.95809 | ||||||||
\(513\) | −17.6732 | −0.780289 | ||||||||
\(514\) | −46.9840 | −2.07238 | ||||||||
\(515\) | −1.46656 | −0.0646243 | ||||||||
\(516\) | 13.8987 | 0.611857 | ||||||||
\(517\) | −23.7763 | −1.04568 | ||||||||
\(518\) | 19.9435 | 0.876265 | ||||||||
\(519\) | 2.99990 | 0.131681 | ||||||||
\(520\) | −27.0278 | −1.18525 | ||||||||
\(521\) | −9.10947 | −0.399093 | −0.199547 | − | 0.979888i | \(-0.563947\pi\) | ||||
−0.199547 | + | 0.979888i | \(0.563947\pi\) | |||||||
\(522\) | 12.3738 | 0.541587 | ||||||||
\(523\) | 8.05802 | 0.352352 | 0.176176 | − | 0.984359i | \(-0.443627\pi\) | ||||
0.176176 | + | 0.984359i | \(0.443627\pi\) | |||||||
\(524\) | 25.4727 | 1.11278 | ||||||||
\(525\) | −4.31057 | −0.188129 | ||||||||
\(526\) | 26.2538 | 1.14472 | ||||||||
\(527\) | −62.0549 | −2.70315 | ||||||||
\(528\) | −31.8196 | −1.38477 | ||||||||
\(529\) | 18.2128 | 0.791860 | ||||||||
\(530\) | −38.3134 | −1.66423 | ||||||||
\(531\) | −9.11804 | −0.395689 | ||||||||
\(532\) | 12.9301 | 0.560591 | ||||||||
\(533\) | 42.4671 | 1.83945 | ||||||||
\(534\) | −30.7907 | −1.33244 | ||||||||
\(535\) | 23.7434 | 1.02652 | ||||||||
\(536\) | 20.2277 | 0.873703 | ||||||||
\(537\) | 15.5417 | 0.670676 | ||||||||
\(538\) | 33.1506 | 1.42922 | ||||||||
\(539\) | −4.82681 | −0.207906 | ||||||||
\(540\) | 31.7738 | 1.36733 | ||||||||
\(541\) | −9.61212 | −0.413257 | −0.206629 | − | 0.978419i | \(-0.566249\pi\) | ||||
−0.206629 | + | 0.978419i | \(0.566249\pi\) | |||||||
\(542\) | 5.08627 | 0.218474 | ||||||||
\(543\) | 2.71908 | 0.116687 | ||||||||
\(544\) | 10.7922 | 0.462710 | ||||||||
\(545\) | −14.2219 | −0.609200 | ||||||||
\(546\) | 12.7526 | 0.545762 | ||||||||
\(547\) | −40.6353 | −1.73744 | −0.868721 | − | 0.495302i | \(-0.835057\pi\) | ||||
−0.868721 | + | 0.495302i | \(0.835057\pi\) | |||||||
\(548\) | 31.6322 | 1.35126 | ||||||||
\(549\) | −4.81075 | −0.205318 | ||||||||
\(550\) | −37.6191 | −1.60408 | ||||||||
\(551\) | 13.9082 | 0.592510 | ||||||||
\(552\) | 46.4359 | 1.97644 | ||||||||
\(553\) | 5.14082 | 0.218610 | ||||||||
\(554\) | 51.7177 | 2.19727 | ||||||||
\(555\) | 15.0142 | 0.637315 | ||||||||
\(556\) | 0.691843 | 0.0293407 | ||||||||
\(557\) | −35.3734 | −1.49882 | −0.749410 | − | 0.662107i | \(-0.769663\pi\) | ||||
−0.749410 | + | 0.662107i | \(0.769663\pi\) | |||||||
\(558\) | 21.7181 | 0.919400 | ||||||||
\(559\) | −9.23235 | −0.390487 | ||||||||
\(560\) | −6.55145 | −0.276849 | ||||||||
\(561\) | 52.5819 | 2.22001 | ||||||||
\(562\) | 56.7420 | 2.39352 | ||||||||
\(563\) | 13.1714 | 0.555108 | 0.277554 | − | 0.960710i | \(-0.410476\pi\) | ||||
0.277554 | + | 0.960710i | \(0.410476\pi\) | |||||||
\(564\) | 27.8814 | 1.17402 | ||||||||
\(565\) | 6.26599 | 0.263612 | ||||||||
\(566\) | 24.4628 | 1.02825 | ||||||||
\(567\) | −4.36430 | −0.183283 | ||||||||
\(568\) | 73.7130 | 3.09293 | ||||||||
\(569\) | 7.00486 | 0.293659 | 0.146830 | − | 0.989162i | \(-0.453093\pi\) | ||||
0.146830 | + | 0.989162i | \(0.453093\pi\) | |||||||
\(570\) | 14.4452 | 0.605043 | ||||||||
\(571\) | −12.5623 | −0.525715 | −0.262857 | − | 0.964835i | \(-0.584665\pi\) | ||||
−0.262857 | + | 0.964835i | \(0.584665\pi\) | |||||||
\(572\) | 74.9983 | 3.13583 | ||||||||
\(573\) | 23.1206 | 0.965878 | ||||||||
\(574\) | 27.9708 | 1.16748 | ||||||||
\(575\) | 20.2042 | 0.842574 | ||||||||
\(576\) | 7.04338 | 0.293474 | ||||||||
\(577\) | 27.8537 | 1.15957 | 0.579783 | − | 0.814771i | \(-0.303137\pi\) | ||||
0.579783 | + | 0.814771i | \(0.303137\pi\) | |||||||
\(578\) | −114.560 | −4.76507 | ||||||||
\(579\) | 26.2224 | 1.08976 | ||||||||
\(580\) | −25.0050 | −1.03828 | ||||||||
\(581\) | 10.8767 | 0.451242 | ||||||||
\(582\) | 10.3560 | 0.429269 | ||||||||
\(583\) | 54.8626 | 2.27218 | ||||||||
\(584\) | −7.12348 | −0.294772 | ||||||||
\(585\) | −5.75270 | −0.237845 | ||||||||
\(586\) | 55.1638 | 2.27879 | ||||||||
\(587\) | 26.0642 | 1.07579 | 0.537893 | − | 0.843013i | \(-0.319220\pi\) | ||||
0.537893 | + | 0.843013i | \(0.319220\pi\) | |||||||
\(588\) | 5.66019 | 0.233422 | ||||||||
\(589\) | 24.4112 | 1.00585 | ||||||||
\(590\) | 27.3430 | 1.12569 | ||||||||
\(591\) | 3.44456 | 0.141690 | ||||||||
\(592\) | −38.7617 | −1.59310 | ||||||||
\(593\) | −1.52694 | −0.0627037 | −0.0313519 | − | 0.999508i | \(-0.509981\pi\) | ||||
−0.0313519 | + | 0.999508i | \(0.509981\pi\) | |||||||
\(594\) | −67.5176 | −2.77028 | ||||||||
\(595\) | 10.8263 | 0.443835 | ||||||||
\(596\) | 94.1035 | 3.85463 | ||||||||
\(597\) | 18.1540 | 0.742993 | ||||||||
\(598\) | −59.7732 | −2.44431 | ||||||||
\(599\) | 13.9309 | 0.569202 | 0.284601 | − | 0.958646i | \(-0.408139\pi\) | ||||
0.284601 | + | 0.958646i | \(0.408139\pi\) | |||||||
\(600\) | 22.7648 | 0.929368 | ||||||||
\(601\) | −18.4665 | −0.753264 | −0.376632 | − | 0.926363i | \(-0.622918\pi\) | ||||
−0.376632 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(602\) | −6.08087 | −0.247838 | ||||||||
\(603\) | 4.30535 | 0.175327 | ||||||||
\(604\) | −78.9057 | −3.21063 | ||||||||
\(605\) | −16.7399 | −0.680573 | ||||||||
\(606\) | −49.9603 | −2.02950 | ||||||||
\(607\) | −6.98184 | −0.283384 | −0.141692 | − | 0.989911i | \(-0.545254\pi\) | ||||
−0.141692 | + | 0.989911i | \(0.545254\pi\) | |||||||
\(608\) | −4.24543 | −0.172175 | ||||||||
\(609\) | 6.08837 | 0.246713 | ||||||||
\(610\) | 14.4264 | 0.584107 | ||||||||
\(611\) | −18.5205 | −0.749259 | ||||||||
\(612\) | 36.9470 | 1.49349 | ||||||||
\(613\) | 18.1030 | 0.731174 | 0.365587 | − | 0.930777i | \(-0.380868\pi\) | ||||
0.365587 | + | 0.930777i | \(0.380868\pi\) | |||||||
\(614\) | 4.01644 | 0.162090 | ||||||||
\(615\) | 21.0575 | 0.849119 | ||||||||
\(616\) | 25.4911 | 1.02707 | ||||||||
\(617\) | 47.0623 | 1.89465 | 0.947327 | − | 0.320267i | \(-0.103773\pi\) | ||||
0.947327 | + | 0.320267i | \(0.103773\pi\) | |||||||
\(618\) | −3.65441 | −0.147002 | ||||||||
\(619\) | −8.30274 | −0.333715 | −0.166858 | − | 0.985981i | \(-0.553362\pi\) | ||||
−0.166858 | + | 0.985981i | \(0.553362\pi\) | |||||||
\(620\) | −43.8878 | −1.76258 | ||||||||
\(621\) | 36.2619 | 1.45514 | ||||||||
\(622\) | 52.0898 | 2.08861 | ||||||||
\(623\) | 9.07796 | 0.363701 | ||||||||
\(624\) | −24.7858 | −0.992225 | ||||||||
\(625\) | 0.640988 | 0.0256395 | ||||||||
\(626\) | −79.4878 | −3.17697 | ||||||||
\(627\) | −20.6847 | −0.826068 | ||||||||
\(628\) | 29.8692 | 1.19191 | ||||||||
\(629\) | 64.0538 | 2.55399 | ||||||||
\(630\) | −3.78900 | −0.150958 | ||||||||
\(631\) | 0.859319 | 0.0342090 | 0.0171045 | − | 0.999854i | \(-0.494555\pi\) | ||||
0.0171045 | + | 0.999854i | \(0.494555\pi\) | |||||||
\(632\) | −27.1495 | −1.07995 | ||||||||
\(633\) | 23.3829 | 0.929387 | ||||||||
\(634\) | −26.1737 | −1.03949 | ||||||||
\(635\) | 28.9644 | 1.14942 | ||||||||
\(636\) | −64.3349 | −2.55105 | ||||||||
\(637\) | −3.75983 | −0.148970 | ||||||||
\(638\) | 53.1342 | 2.10360 | ||||||||
\(639\) | 15.6894 | 0.620662 | ||||||||
\(640\) | −24.8154 | −0.980916 | ||||||||
\(641\) | −31.5811 | −1.24738 | −0.623690 | − | 0.781672i | \(-0.714367\pi\) | ||||
−0.623690 | + | 0.781672i | \(0.714367\pi\) | |||||||
\(642\) | 59.1645 | 2.33504 | ||||||||
\(643\) | −31.3747 | −1.23730 | −0.618649 | − | 0.785667i | \(-0.712320\pi\) | ||||
−0.618649 | + | 0.785667i | \(0.712320\pi\) | |||||||
\(644\) | −26.5300 | −1.04543 | ||||||||
\(645\) | −4.57790 | −0.180255 | ||||||||
\(646\) | 61.6266 | 2.42467 | ||||||||
\(647\) | 22.9234 | 0.901213 | 0.450607 | − | 0.892723i | \(-0.351208\pi\) | ||||
0.450607 | + | 0.892723i | \(0.351208\pi\) | |||||||
\(648\) | 23.0485 | 0.905431 | ||||||||
\(649\) | −39.1536 | −1.53691 | ||||||||
\(650\) | −29.3033 | −1.14937 | ||||||||
\(651\) | 10.6861 | 0.418821 | ||||||||
\(652\) | 0.0460168 | 0.00180216 | ||||||||
\(653\) | 30.4719 | 1.19246 | 0.596228 | − | 0.802815i | \(-0.296665\pi\) | ||||
0.596228 | + | 0.802815i | \(0.296665\pi\) | |||||||
\(654\) | −35.4386 | −1.38576 | ||||||||
\(655\) | −8.39009 | −0.327828 | ||||||||
\(656\) | −54.3636 | −2.12254 | ||||||||
\(657\) | −1.51619 | −0.0591523 | ||||||||
\(658\) | −12.1985 | −0.475546 | ||||||||
\(659\) | 12.8567 | 0.500827 | 0.250413 | − | 0.968139i | \(-0.419433\pi\) | ||||
0.250413 | + | 0.968139i | \(0.419433\pi\) | |||||||
\(660\) | 37.1882 | 1.44755 | ||||||||
\(661\) | 10.4601 | 0.406850 | 0.203425 | − | 0.979091i | \(-0.434793\pi\) | ||||
0.203425 | + | 0.979091i | \(0.434793\pi\) | |||||||
\(662\) | 31.5874 | 1.22768 | ||||||||
\(663\) | 40.9585 | 1.59070 | ||||||||
\(664\) | −57.4416 | −2.22917 | ||||||||
\(665\) | −4.25886 | −0.165151 | ||||||||
\(666\) | −22.4177 | −0.868667 | ||||||||
\(667\) | −28.5370 | −1.10496 | ||||||||
\(668\) | −55.2257 | −2.13675 | ||||||||
\(669\) | −0.563689 | −0.0217935 | ||||||||
\(670\) | −12.9108 | −0.498787 | ||||||||
\(671\) | −20.6578 | −0.797484 | ||||||||
\(672\) | −1.85845 | −0.0716913 | ||||||||
\(673\) | 35.9617 | 1.38622 | 0.693111 | − | 0.720831i | \(-0.256240\pi\) | ||||
0.693111 | + | 0.720831i | \(0.256240\pi\) | |||||||
\(674\) | 19.0543 | 0.733946 | ||||||||
\(675\) | 17.7771 | 0.684240 | ||||||||
\(676\) | 4.69606 | 0.180618 | ||||||||
\(677\) | −8.64518 | −0.332261 | −0.166131 | − | 0.986104i | \(-0.553127\pi\) | ||||
−0.166131 | + | 0.986104i | \(0.553127\pi\) | |||||||
\(678\) | 15.6138 | 0.599643 | ||||||||
\(679\) | −3.05324 | −0.117172 | ||||||||
\(680\) | −57.1752 | −2.19257 | ||||||||
\(681\) | 27.9505 | 1.07106 | ||||||||
\(682\) | 93.2592 | 3.57108 | ||||||||
\(683\) | −21.4482 | −0.820691 | −0.410346 | − | 0.911930i | \(-0.634592\pi\) | ||||
−0.410346 | + | 0.911930i | \(0.634592\pi\) | |||||||
\(684\) | −14.5342 | −0.555730 | ||||||||
\(685\) | −10.4189 | −0.398085 | ||||||||
\(686\) | −2.47641 | −0.0945496 | ||||||||
\(687\) | −35.7691 | −1.36468 | ||||||||
\(688\) | 11.8187 | 0.450582 | ||||||||
\(689\) | 42.7351 | 1.62808 | ||||||||
\(690\) | −29.6388 | −1.12833 | ||||||||
\(691\) | −10.0322 | −0.381643 | −0.190821 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190821 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(692\) | 9.05148 | 0.344086 | ||||||||
\(693\) | 5.42564 | 0.206103 | ||||||||
\(694\) | −76.2442 | −2.89419 | ||||||||
\(695\) | −0.227876 | −0.00864383 | ||||||||
\(696\) | −32.1536 | −1.21878 | ||||||||
\(697\) | 89.8360 | 3.40278 | ||||||||
\(698\) | −84.1635 | −3.18564 | ||||||||
\(699\) | 5.60356 | 0.211946 | ||||||||
\(700\) | −13.0061 | −0.491585 | ||||||||
\(701\) | 24.9626 | 0.942826 | 0.471413 | − | 0.881913i | \(-0.343744\pi\) | ||||
0.471413 | + | 0.881913i | \(0.343744\pi\) | |||||||
\(702\) | −52.5926 | −1.98498 | ||||||||
\(703\) | −25.1976 | −0.950344 | ||||||||
\(704\) | 30.2448 | 1.13989 | ||||||||
\(705\) | −9.18346 | −0.345869 | ||||||||
\(706\) | −47.2098 | −1.77676 | ||||||||
\(707\) | 14.7297 | 0.553968 | ||||||||
\(708\) | 45.9137 | 1.72554 | ||||||||
\(709\) | 12.8574 | 0.482871 | 0.241435 | − | 0.970417i | \(-0.422382\pi\) | ||||
0.241435 | + | 0.970417i | \(0.422382\pi\) | |||||||
\(710\) | −47.0490 | −1.76572 | ||||||||
\(711\) | −5.77861 | −0.216715 | ||||||||
\(712\) | −47.9421 | −1.79670 | ||||||||
\(713\) | −50.0870 | −1.87577 | ||||||||
\(714\) | 26.9772 | 1.00960 | ||||||||
\(715\) | −24.7026 | −0.923824 | ||||||||
\(716\) | 46.8935 | 1.75249 | ||||||||
\(717\) | −37.8761 | −1.41451 | ||||||||
\(718\) | −27.9932 | −1.04470 | ||||||||
\(719\) | 49.4280 | 1.84335 | 0.921677 | − | 0.387958i | \(-0.126820\pi\) | ||||
0.921677 | + | 0.387958i | \(0.126820\pi\) | |||||||
\(720\) | 7.36424 | 0.274449 | ||||||||
\(721\) | 1.07742 | 0.0401253 | ||||||||
\(722\) | 22.8090 | 0.848862 | ||||||||
\(723\) | −20.4043 | −0.758843 | ||||||||
\(724\) | 8.20417 | 0.304906 | ||||||||
\(725\) | −13.9900 | −0.519575 | ||||||||
\(726\) | −41.7129 | −1.54811 | ||||||||
\(727\) | −3.07735 | −0.114133 | −0.0570664 | − | 0.998370i | \(-0.518175\pi\) | ||||
−0.0570664 | + | 0.998370i | \(0.518175\pi\) | |||||||
\(728\) | 19.8562 | 0.735921 | ||||||||
\(729\) | 28.1152 | 1.04130 | ||||||||
\(730\) | 4.54672 | 0.168282 | ||||||||
\(731\) | −19.5304 | −0.722357 | ||||||||
\(732\) | 24.2245 | 0.895362 | ||||||||
\(733\) | 51.2910 | 1.89448 | 0.947238 | − | 0.320530i | \(-0.103861\pi\) | ||||
0.947238 | + | 0.320530i | \(0.103861\pi\) | |||||||
\(734\) | 44.8200 | 1.65434 | ||||||||
\(735\) | −1.86433 | −0.0687668 | ||||||||
\(736\) | 8.71080 | 0.321084 | ||||||||
\(737\) | 18.4875 | 0.680996 | ||||||||
\(738\) | −31.4410 | −1.15736 | ||||||||
\(739\) | 7.86046 | 0.289152 | 0.144576 | − | 0.989494i | \(-0.453818\pi\) | ||||
0.144576 | + | 0.989494i | \(0.453818\pi\) | |||||||
\(740\) | 45.3016 | 1.66532 | ||||||||
\(741\) | −16.1123 | −0.591900 | ||||||||
\(742\) | 28.1474 | 1.03332 | ||||||||
\(743\) | 20.1813 | 0.740378 | 0.370189 | − | 0.928956i | \(-0.379293\pi\) | ||||
0.370189 | + | 0.928956i | \(0.379293\pi\) | |||||||
\(744\) | −56.4348 | −2.06900 | ||||||||
\(745\) | −30.9954 | −1.13558 | ||||||||
\(746\) | 8.82406 | 0.323072 | ||||||||
\(747\) | −12.2261 | −0.447330 | ||||||||
\(748\) | 158.653 | 5.80094 | ||||||||
\(749\) | −17.4434 | −0.637366 | ||||||||
\(750\) | −37.6143 | −1.37348 | ||||||||
\(751\) | 24.8078 | 0.905251 | 0.452625 | − | 0.891701i | \(-0.350488\pi\) | ||||
0.452625 | + | 0.891701i | \(0.350488\pi\) | |||||||
\(752\) | 23.7087 | 0.864569 | ||||||||
\(753\) | −14.5926 | −0.531783 | ||||||||
\(754\) | 41.3887 | 1.50729 | ||||||||
\(755\) | 25.9896 | 0.945858 | ||||||||
\(756\) | −23.3430 | −0.848976 | ||||||||
\(757\) | 37.1368 | 1.34976 | 0.674880 | − | 0.737927i | \(-0.264195\pi\) | ||||
0.674880 | + | 0.737927i | \(0.264195\pi\) | |||||||
\(758\) | −36.8802 | −1.33955 | ||||||||
\(759\) | 42.4410 | 1.54051 | ||||||||
\(760\) | 22.4916 | 0.815858 | ||||||||
\(761\) | 9.51244 | 0.344826 | 0.172413 | − | 0.985025i | \(-0.444844\pi\) | ||||
0.172413 | + | 0.985025i | \(0.444844\pi\) | |||||||
\(762\) | 72.1743 | 2.61460 | ||||||||
\(763\) | 10.4483 | 0.378254 | ||||||||
\(764\) | 69.7609 | 2.52386 | ||||||||
\(765\) | −12.1694 | −0.439986 | ||||||||
\(766\) | 41.0618 | 1.48362 | ||||||||
\(767\) | −30.4986 | −1.10124 | ||||||||
\(768\) | −44.6713 | −1.61194 | ||||||||
\(769\) | 9.78969 | 0.353025 | 0.176513 | − | 0.984298i | \(-0.443518\pi\) | ||||
0.176513 | + | 0.984298i | \(0.443518\pi\) | |||||||
\(770\) | −16.2703 | −0.586341 | ||||||||
\(771\) | 25.9859 | 0.935859 | ||||||||
\(772\) | 79.1197 | 2.84758 | ||||||||
\(773\) | 18.4164 | 0.662391 | 0.331196 | − | 0.943562i | \(-0.392548\pi\) | ||||
0.331196 | + | 0.943562i | \(0.392548\pi\) | |||||||
\(774\) | 6.83527 | 0.245689 | ||||||||
\(775\) | −24.5547 | −0.882032 | ||||||||
\(776\) | 16.1246 | 0.578839 | ||||||||
\(777\) | −11.0303 | −0.395710 | ||||||||
\(778\) | 53.9809 | 1.93531 | ||||||||
\(779\) | −35.3398 | −1.26618 | ||||||||
\(780\) | 28.9676 | 1.03721 | ||||||||
\(781\) | 67.3715 | 2.41074 | ||||||||
\(782\) | −126.446 | −4.52169 | ||||||||
\(783\) | −25.1088 | −0.897316 | ||||||||
\(784\) | 4.81310 | 0.171896 | ||||||||
\(785\) | −9.83819 | −0.351140 | ||||||||
\(786\) | −20.9067 | −0.745716 | ||||||||
\(787\) | −47.8941 | −1.70724 | −0.853621 | − | 0.520895i | \(-0.825598\pi\) | ||||
−0.853621 | + | 0.520895i | \(0.825598\pi\) | |||||||
\(788\) | 10.3931 | 0.370240 | ||||||||
\(789\) | −14.5204 | −0.516941 | ||||||||
\(790\) | 17.3288 | 0.616530 | ||||||||
\(791\) | −4.60337 | −0.163677 | ||||||||
\(792\) | −28.6536 | −1.01816 | ||||||||
\(793\) | −16.0913 | −0.571419 | ||||||||
\(794\) | 61.4796 | 2.18183 | ||||||||
\(795\) | 21.1903 | 0.751544 | ||||||||
\(796\) | 54.7753 | 1.94146 | ||||||||
\(797\) | 42.9621 | 1.52180 | 0.760899 | − | 0.648871i | \(-0.224758\pi\) | ||||
0.760899 | + | 0.648871i | \(0.224758\pi\) | |||||||
\(798\) | −10.6123 | −0.375673 | ||||||||
\(799\) | −39.1787 | −1.38604 | ||||||||
\(800\) | 4.27039 | 0.150981 | ||||||||
\(801\) | −10.2042 | −0.360547 | ||||||||
\(802\) | 38.7924 | 1.36981 | ||||||||
\(803\) | −6.51065 | −0.229756 | ||||||||
\(804\) | −21.6795 | −0.764577 | ||||||||
\(805\) | 8.73834 | 0.307986 | ||||||||
\(806\) | 72.6440 | 2.55878 | ||||||||
\(807\) | −18.3349 | −0.645419 | ||||||||
\(808\) | −77.7898 | −2.73664 | ||||||||
\(809\) | −28.9384 | −1.01742 | −0.508710 | − | 0.860938i | \(-0.669878\pi\) | ||||
−0.508710 | + | 0.860938i | \(0.669878\pi\) | |||||||
\(810\) | −14.7112 | −0.516900 | ||||||||
\(811\) | −40.7765 | −1.43186 | −0.715928 | − | 0.698174i | \(-0.753996\pi\) | ||||
−0.715928 | + | 0.698174i | \(0.753996\pi\) | |||||||
\(812\) | 18.3702 | 0.644667 | ||||||||
\(813\) | −2.81311 | −0.0986601 | ||||||||
\(814\) | −96.2633 | −3.37403 | ||||||||
\(815\) | −0.0151568 | −0.000530920 0 | ||||||||
\(816\) | −52.4325 | −1.83550 | ||||||||
\(817\) | 7.68287 | 0.268790 | ||||||||
\(818\) | 33.0344 | 1.15502 | ||||||||
\(819\) | 4.22629 | 0.147678 | ||||||||
\(820\) | 63.5358 | 2.21877 | ||||||||
\(821\) | −17.9268 | −0.625650 | −0.312825 | − | 0.949811i | \(-0.601275\pi\) | ||||
−0.312825 | + | 0.949811i | \(0.601275\pi\) | |||||||
\(822\) | −25.9620 | −0.905530 | ||||||||
\(823\) | 25.5250 | 0.889744 | 0.444872 | − | 0.895594i | \(-0.353249\pi\) | ||||
0.444872 | + | 0.895594i | \(0.353249\pi\) | |||||||
\(824\) | −5.69003 | −0.198222 | ||||||||
\(825\) | 20.8063 | 0.724384 | ||||||||
\(826\) | −20.0878 | −0.698945 | ||||||||
\(827\) | −17.1208 | −0.595350 | −0.297675 | − | 0.954667i | \(-0.596211\pi\) | ||||
−0.297675 | + | 0.954667i | \(0.596211\pi\) | |||||||
\(828\) | 29.8214 | 1.03637 | ||||||||
\(829\) | 38.2548 | 1.32864 | 0.664322 | − | 0.747447i | \(-0.268721\pi\) | ||||
0.664322 | + | 0.747447i | \(0.268721\pi\) | |||||||
\(830\) | 36.6634 | 1.27261 | ||||||||
\(831\) | −28.6040 | −0.992261 | ||||||||
\(832\) | 23.5591 | 0.816766 | ||||||||
\(833\) | −7.95365 | −0.275578 | ||||||||
\(834\) | −0.567828 | −0.0196623 | ||||||||
\(835\) | 18.1900 | 0.629490 | ||||||||
\(836\) | −62.4112 | −2.15854 | ||||||||
\(837\) | −44.0701 | −1.52328 | ||||||||
\(838\) | 8.76123 | 0.302652 | ||||||||
\(839\) | −21.9804 | −0.758847 | −0.379424 | − | 0.925223i | \(-0.623878\pi\) | ||||
−0.379424 | + | 0.925223i | \(0.623878\pi\) | |||||||
\(840\) | 9.84579 | 0.339712 | ||||||||
\(841\) | −9.24016 | −0.318626 | ||||||||
\(842\) | 24.0099 | 0.827435 | ||||||||
\(843\) | −31.3829 | −1.08088 | ||||||||
\(844\) | 70.5523 | 2.42851 | ||||||||
\(845\) | −1.54677 | −0.0532104 | ||||||||
\(846\) | 13.7118 | 0.471423 | ||||||||
\(847\) | 12.2981 | 0.422569 | ||||||||
\(848\) | −54.7067 | −1.87863 | ||||||||
\(849\) | −13.5299 | −0.464344 | ||||||||
\(850\) | −61.9889 | −2.12620 | ||||||||
\(851\) | 51.7005 | 1.77227 | ||||||||
\(852\) | −79.0035 | −2.70662 | ||||||||
\(853\) | −37.0349 | −1.26805 | −0.634025 | − | 0.773313i | \(-0.718598\pi\) | ||||
−0.634025 | + | 0.773313i | \(0.718598\pi\) | |||||||
\(854\) | −10.5985 | −0.362673 | ||||||||
\(855\) | 4.78722 | 0.163719 | ||||||||
\(856\) | 92.1210 | 3.14863 | ||||||||
\(857\) | 53.6104 | 1.83130 | 0.915649 | − | 0.401979i | \(-0.131677\pi\) | ||||
0.915649 | + | 0.401979i | \(0.131677\pi\) | |||||||
\(858\) | −61.5546 | −2.10144 | ||||||||
\(859\) | 20.9489 | 0.714769 | 0.357384 | − | 0.933957i | \(-0.383669\pi\) | ||||
0.357384 | + | 0.933957i | \(0.383669\pi\) | |||||||
\(860\) | −13.8127 | −0.471009 | ||||||||
\(861\) | −15.4701 | −0.527219 | ||||||||
\(862\) | 9.48656 | 0.323113 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | 7.66437 | 0.260747 | ||||||||
\(865\) | −2.98133 | −0.101368 | ||||||||
\(866\) | 0.802849 | 0.0272819 | ||||||||
\(867\) | 63.3608 | 2.15184 | ||||||||
\(868\) | 32.2427 | 1.09439 | ||||||||
\(869\) | −24.8138 | −0.841751 | ||||||||
\(870\) | 20.5228 | 0.695787 | ||||||||
\(871\) | 14.4008 | 0.487952 | ||||||||
\(872\) | −55.1790 | −1.86860 | ||||||||
\(873\) | 3.43203 | 0.116156 | ||||||||
\(874\) | 49.7414 | 1.68253 | ||||||||
\(875\) | 11.0898 | 0.374902 | ||||||||
\(876\) | 7.63475 | 0.257954 | ||||||||
\(877\) | 23.9128 | 0.807477 | 0.403739 | − | 0.914874i | \(-0.367710\pi\) | ||||
0.403739 | + | 0.914874i | \(0.367710\pi\) | |||||||
\(878\) | −20.3015 | −0.685142 | ||||||||
\(879\) | −30.5099 | −1.02907 | ||||||||
\(880\) | 31.6226 | 1.06600 | ||||||||
\(881\) | 43.4188 | 1.46282 | 0.731408 | − | 0.681940i | \(-0.238864\pi\) | ||||
0.731408 | + | 0.681940i | \(0.238864\pi\) | |||||||
\(882\) | 2.78363 | 0.0937298 | ||||||||
\(883\) | 10.7701 | 0.362444 | 0.181222 | − | 0.983442i | \(-0.441995\pi\) | ||||
0.181222 | + | 0.983442i | \(0.441995\pi\) | |||||||
\(884\) | 123.583 | 4.15653 | ||||||||
\(885\) | −15.1228 | −0.508349 | ||||||||
\(886\) | 45.4618 | 1.52732 | ||||||||
\(887\) | −18.4272 | −0.618725 | −0.309362 | − | 0.950944i | \(-0.600116\pi\) | ||||
−0.309362 | + | 0.950944i | \(0.600116\pi\) | |||||||
\(888\) | 58.2527 | 1.95483 | ||||||||
\(889\) | −21.2790 | −0.713675 | ||||||||
\(890\) | 30.6001 | 1.02572 | ||||||||
\(891\) | 21.0657 | 0.705726 | ||||||||
\(892\) | −1.70080 | −0.0569469 | ||||||||
\(893\) | 15.4122 | 0.515749 | ||||||||
\(894\) | −77.2351 | −2.58313 | ||||||||
\(895\) | −15.4456 | −0.516288 | ||||||||
\(896\) | 18.2309 | 0.609053 | ||||||||
\(897\) | 33.0593 | 1.10382 | ||||||||
\(898\) | −4.65852 | −0.155457 | ||||||||
\(899\) | 34.6817 | 1.15670 | ||||||||
\(900\) | 14.6197 | 0.487323 | ||||||||
\(901\) | 90.4029 | 3.01176 | ||||||||
\(902\) | −135.010 | −4.49534 | ||||||||
\(903\) | 3.36320 | 0.111920 | ||||||||
\(904\) | 24.3111 | 0.808575 | ||||||||
\(905\) | −2.70225 | −0.0898259 | ||||||||
\(906\) | 64.7616 | 2.15156 | ||||||||
\(907\) | 24.3751 | 0.809363 | 0.404681 | − | 0.914458i | \(-0.367382\pi\) | ||||
0.404681 | + | 0.914458i | \(0.367382\pi\) | |||||||
\(908\) | 84.3338 | 2.79872 | ||||||||
\(909\) | −16.5571 | −0.549165 | ||||||||
\(910\) | −12.6737 | −0.420129 | ||||||||
\(911\) | 6.28736 | 0.208310 | 0.104155 | − | 0.994561i | \(-0.466786\pi\) | ||||
0.104155 | + | 0.994561i | \(0.466786\pi\) | |||||||
\(912\) | 20.6259 | 0.682993 | ||||||||
\(913\) | −52.4999 | −1.73749 | ||||||||
\(914\) | 66.9510 | 2.21454 | ||||||||
\(915\) | −7.97894 | −0.263776 | ||||||||
\(916\) | −107.925 | −3.56593 | ||||||||
\(917\) | 6.16387 | 0.203549 | ||||||||
\(918\) | −111.256 | −3.67199 | ||||||||
\(919\) | 3.14648 | 0.103793 | 0.0518964 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518964 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(920\) | −46.1485 | −1.52147 | ||||||||
\(921\) | −2.22141 | −0.0731980 | ||||||||
\(922\) | 71.0885 | 2.34118 | ||||||||
\(923\) | 52.4788 | 1.72736 | ||||||||
\(924\) | −27.3207 | −0.898785 | ||||||||
\(925\) | 25.3457 | 0.833362 | ||||||||
\(926\) | 64.8590 | 2.13140 | ||||||||
\(927\) | −1.21109 | −0.0397774 | ||||||||
\(928\) | −6.03162 | −0.197997 | ||||||||
\(929\) | 1.64684 | 0.0540311 | 0.0270156 | − | 0.999635i | \(-0.491400\pi\) | ||||
0.0270156 | + | 0.999635i | \(0.491400\pi\) | |||||||
\(930\) | 36.0208 | 1.18117 | ||||||||
\(931\) | 3.12881 | 0.102543 | ||||||||
\(932\) | 16.9074 | 0.553820 | ||||||||
\(933\) | −28.8098 | −0.943190 | ||||||||
\(934\) | 34.8239 | 1.13947 | ||||||||
\(935\) | −52.2565 | −1.70897 | ||||||||
\(936\) | −22.3196 | −0.729540 | ||||||||
\(937\) | −5.35150 | −0.174826 | −0.0874130 | − | 0.996172i | \(-0.527860\pi\) | ||||
−0.0874130 | + | 0.996172i | \(0.527860\pi\) | |||||||
\(938\) | 9.48505 | 0.309698 | ||||||||
\(939\) | 43.9630 | 1.43468 | ||||||||
\(940\) | −27.7089 | −0.903764 | ||||||||
\(941\) | −16.0695 | −0.523850 | −0.261925 | − | 0.965088i | \(-0.584357\pi\) | ||||
−0.261925 | + | 0.965088i | \(0.584357\pi\) | |||||||
\(942\) | −24.5151 | −0.798744 | ||||||||
\(943\) | 72.5103 | 2.36126 | ||||||||
\(944\) | 39.0423 | 1.27072 | ||||||||
\(945\) | 7.68860 | 0.250110 | ||||||||
\(946\) | 29.3512 | 0.954291 | ||||||||
\(947\) | −38.7591 | −1.25950 | −0.629750 | − | 0.776798i | \(-0.716843\pi\) | ||||
−0.629750 | + | 0.776798i | \(0.716843\pi\) | |||||||
\(948\) | 29.0981 | 0.945061 | ||||||||
\(949\) | −5.07145 | −0.164626 | ||||||||
\(950\) | 24.3853 | 0.791162 | ||||||||
\(951\) | 14.4761 | 0.469421 | ||||||||
\(952\) | 42.0044 | 1.36137 | ||||||||
\(953\) | −34.8226 | −1.12801 | −0.564007 | − | 0.825770i | \(-0.690741\pi\) | ||||
−0.564007 | + | 0.825770i | \(0.690741\pi\) | |||||||
\(954\) | −31.6394 | −1.02436 | ||||||||
\(955\) | −22.9775 | −0.743536 | ||||||||
\(956\) | −114.282 | −3.69615 | ||||||||
\(957\) | −29.3874 | −0.949960 | ||||||||
\(958\) | 22.5272 | 0.727822 | ||||||||
\(959\) | 7.65434 | 0.247171 | ||||||||
\(960\) | 11.6819 | 0.377031 | ||||||||
\(961\) | 29.8722 | 0.963618 | ||||||||
\(962\) | −74.9841 | −2.41758 | ||||||||
\(963\) | 19.6074 | 0.631840 | ||||||||
\(964\) | −61.5650 | −1.98288 | ||||||||
\(965\) | −26.0601 | −0.838903 | ||||||||
\(966\) | 21.7744 | 0.700581 | ||||||||
\(967\) | −27.6286 | −0.888474 | −0.444237 | − | 0.895909i | \(-0.646525\pi\) | ||||
−0.444237 | + | 0.895909i | \(0.646525\pi\) | |||||||
\(968\) | −64.9483 | −2.08752 | ||||||||
\(969\) | −34.0844 | −1.09495 | ||||||||
\(970\) | −10.2919 | −0.330453 | ||||||||
\(971\) | 3.58141 | 0.114933 | 0.0574665 | − | 0.998347i | \(-0.481698\pi\) | ||||
0.0574665 | + | 0.998347i | \(0.481698\pi\) | |||||||
\(972\) | 45.3262 | 1.45384 | ||||||||
\(973\) | 0.167412 | 0.00536697 | ||||||||
\(974\) | −81.2852 | −2.60455 | ||||||||
\(975\) | 16.2070 | 0.519041 | ||||||||
\(976\) | 20.5991 | 0.659360 | ||||||||
\(977\) | −11.9512 | −0.382354 | −0.191177 | − | 0.981556i | \(-0.561230\pi\) | ||||
−0.191177 | + | 0.981556i | \(0.561230\pi\) | |||||||
\(978\) | −0.0377682 | −0.00120769 | ||||||||
\(979\) | −43.8176 | −1.40042 | ||||||||
\(980\) | −5.62516 | −0.179689 | ||||||||
\(981\) | −11.7445 | −0.374974 | ||||||||
\(982\) | 22.1153 | 0.705727 | ||||||||
\(983\) | −6.25902 | −0.199632 | −0.0998159 | − | 0.995006i | \(-0.531825\pi\) | ||||
−0.0998159 | + | 0.995006i | \(0.531825\pi\) | |||||||
\(984\) | 81.6999 | 2.60450 | ||||||||
\(985\) | −3.42325 | −0.109074 | ||||||||
\(986\) | 87.5548 | 2.78831 | ||||||||
\(987\) | 6.74673 | 0.214751 | ||||||||
\(988\) | −48.6150 | −1.54665 | ||||||||
\(989\) | −15.7638 | −0.501258 | ||||||||
\(990\) | 18.2888 | 0.581257 | ||||||||
\(991\) | 41.8783 | 1.33031 | 0.665155 | − | 0.746706i | \(-0.268366\pi\) | ||||
0.665155 | + | 0.746706i | \(0.268366\pi\) | |||||||
\(992\) | −10.5865 | −0.336121 | ||||||||
\(993\) | −17.4703 | −0.554404 | ||||||||
\(994\) | 34.5651 | 1.09634 | ||||||||
\(995\) | −18.0416 | −0.571958 | ||||||||
\(996\) | 61.5643 | 1.95074 | ||||||||
\(997\) | 12.3726 | 0.391845 | 0.195923 | − | 0.980619i | \(-0.437230\pi\) | ||||
0.195923 | + | 0.980619i | \(0.437230\pi\) | |||||||
\(998\) | −31.5493 | −0.998674 | ||||||||
\(999\) | 45.4897 | 1.43923 |
(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 | 6041.2.a.f.1.14 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.14 | ✓ | 132 | 1.1 | even | 1 | trivial |