Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.01476 | −1.16322 | −0.581611 | − | 0.813467i | \(-0.697577\pi\) | ||||
−0.581611 | + | 0.813467i | \(0.697577\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.07868 | 0.929613 | 0.464806 | − | 0.885412i | \(-0.346124\pi\) | ||||
0.464806 | + | 0.885412i | \(0.346124\pi\) | |||||||
\(6\) | −2.01476 | −0.822522 | ||||||||
\(7\) | −1.64070 | −0.620128 | −0.310064 | − | 0.950716i | \(-0.600351\pi\) | ||||
−0.310064 | + | 0.950716i | \(0.600351\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.05926 | 0.353086 | ||||||||
\(10\) | 2.07868 | 0.657335 | ||||||||
\(11\) | −2.89925 | −0.874156 | −0.437078 | − | 0.899424i | \(-0.643987\pi\) | ||||
−0.437078 | + | 0.899424i | \(0.643987\pi\) | |||||||
\(12\) | −2.01476 | −0.581611 | ||||||||
\(13\) | −2.54576 | −0.706068 | −0.353034 | − | 0.935610i | \(-0.614850\pi\) | ||||
−0.353034 | + | 0.935610i | \(0.614850\pi\) | |||||||
\(14\) | −1.64070 | −0.438497 | ||||||||
\(15\) | −4.18804 | −1.08135 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.07742 | 0.261312 | 0.130656 | − | 0.991428i | \(-0.458292\pi\) | ||||
0.130656 | + | 0.991428i | \(0.458292\pi\) | |||||||
\(18\) | 1.05926 | 0.249670 | ||||||||
\(19\) | 6.85110 | 1.57175 | 0.785875 | − | 0.618386i | \(-0.212213\pi\) | ||||
0.785875 | + | 0.618386i | \(0.212213\pi\) | |||||||
\(20\) | 2.07868 | 0.464806 | ||||||||
\(21\) | 3.30563 | 0.721347 | ||||||||
\(22\) | −2.89925 | −0.618122 | ||||||||
\(23\) | −1.82864 | −0.381298 | −0.190649 | − | 0.981658i | \(-0.561059\pi\) | ||||
−0.190649 | + | 0.981658i | \(0.561059\pi\) | |||||||
\(24\) | −2.01476 | −0.411261 | ||||||||
\(25\) | −0.679103 | −0.135821 | ||||||||
\(26\) | −2.54576 | −0.499265 | ||||||||
\(27\) | 3.91013 | 0.752504 | ||||||||
\(28\) | −1.64070 | −0.310064 | ||||||||
\(29\) | −4.36452 | −0.810470 | −0.405235 | − | 0.914212i | \(-0.632810\pi\) | ||||
−0.405235 | + | 0.914212i | \(0.632810\pi\) | |||||||
\(30\) | −4.18804 | −0.764627 | ||||||||
\(31\) | 1.10436 | 0.198349 | 0.0991743 | − | 0.995070i | \(-0.468380\pi\) | ||||
0.0991743 | + | 0.995070i | \(0.468380\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.84129 | 1.01684 | ||||||||
\(34\) | 1.07742 | 0.184775 | ||||||||
\(35\) | −3.41049 | −0.576479 | ||||||||
\(36\) | 1.05926 | 0.176543 | ||||||||
\(37\) | −3.20421 | −0.526769 | −0.263385 | − | 0.964691i | \(-0.584839\pi\) | ||||
−0.263385 | + | 0.964691i | \(0.584839\pi\) | |||||||
\(38\) | 6.85110 | 1.11139 | ||||||||
\(39\) | 5.12911 | 0.821314 | ||||||||
\(40\) | 2.07868 | 0.328668 | ||||||||
\(41\) | 7.10776 | 1.11005 | 0.555023 | − | 0.831835i | \(-0.312709\pi\) | ||||
0.555023 | + | 0.831835i | \(0.312709\pi\) | |||||||
\(42\) | 3.30563 | 0.510069 | ||||||||
\(43\) | 8.50150 | 1.29647 | 0.648234 | − | 0.761442i | \(-0.275508\pi\) | ||||
0.648234 | + | 0.761442i | \(0.275508\pi\) | |||||||
\(44\) | −2.89925 | −0.437078 | ||||||||
\(45\) | 2.20186 | 0.328234 | ||||||||
\(46\) | −1.82864 | −0.269618 | ||||||||
\(47\) | 1.67093 | 0.243730 | 0.121865 | − | 0.992547i | \(-0.461112\pi\) | ||||
0.121865 | + | 0.992547i | \(0.461112\pi\) | |||||||
\(48\) | −2.01476 | −0.290806 | ||||||||
\(49\) | −4.30809 | −0.615441 | ||||||||
\(50\) | −0.679103 | −0.0960396 | ||||||||
\(51\) | −2.17073 | −0.303964 | ||||||||
\(52\) | −2.54576 | −0.353034 | ||||||||
\(53\) | 11.9804 | 1.64563 | 0.822816 | − | 0.568308i | \(-0.192402\pi\) | ||||
0.822816 | + | 0.568308i | \(0.192402\pi\) | |||||||
\(54\) | 3.91013 | 0.532101 | ||||||||
\(55\) | −6.02660 | −0.812627 | ||||||||
\(56\) | −1.64070 | −0.219248 | ||||||||
\(57\) | −13.8033 | −1.82829 | ||||||||
\(58\) | −4.36452 | −0.573089 | ||||||||
\(59\) | 0.216612 | 0.0282005 | 0.0141002 | − | 0.999901i | \(-0.495512\pi\) | ||||
0.0141002 | + | 0.999901i | \(0.495512\pi\) | |||||||
\(60\) | −4.18804 | −0.540673 | ||||||||
\(61\) | −10.0683 | −1.28912 | −0.644558 | − | 0.764555i | \(-0.722959\pi\) | ||||
−0.644558 | + | 0.764555i | \(0.722959\pi\) | |||||||
\(62\) | 1.10436 | 0.140254 | ||||||||
\(63\) | −1.73793 | −0.218959 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.29182 | −0.656370 | ||||||||
\(66\) | 5.84129 | 0.719013 | ||||||||
\(67\) | −5.57966 | −0.681664 | −0.340832 | − | 0.940124i | \(-0.610709\pi\) | ||||
−0.340832 | + | 0.940124i | \(0.610709\pi\) | |||||||
\(68\) | 1.07742 | 0.130656 | ||||||||
\(69\) | 3.68427 | 0.443534 | ||||||||
\(70\) | −3.41049 | −0.407632 | ||||||||
\(71\) | −1.16943 | −0.138785 | −0.0693926 | − | 0.997589i | \(-0.522106\pi\) | ||||
−0.0693926 | + | 0.997589i | \(0.522106\pi\) | |||||||
\(72\) | 1.05926 | 0.124835 | ||||||||
\(73\) | −13.4122 | −1.56977 | −0.784887 | − | 0.619638i | \(-0.787279\pi\) | ||||
−0.784887 | + | 0.619638i | \(0.787279\pi\) | |||||||
\(74\) | −3.20421 | −0.372482 | ||||||||
\(75\) | 1.36823 | 0.157990 | ||||||||
\(76\) | 6.85110 | 0.785875 | ||||||||
\(77\) | 4.75681 | 0.542089 | ||||||||
\(78\) | 5.12911 | 0.580757 | ||||||||
\(79\) | −1.87728 | −0.211210 | −0.105605 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105605 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(80\) | 2.07868 | 0.232403 | ||||||||
\(81\) | −11.0557 | −1.22842 | ||||||||
\(82\) | 7.10776 | 0.784921 | ||||||||
\(83\) | −2.72604 | −0.299222 | −0.149611 | − | 0.988745i | \(-0.547802\pi\) | ||||
−0.149611 | + | 0.988745i | \(0.547802\pi\) | |||||||
\(84\) | 3.30563 | 0.360673 | ||||||||
\(85\) | 2.23960 | 0.242919 | ||||||||
\(86\) | 8.50150 | 0.916741 | ||||||||
\(87\) | 8.79346 | 0.942757 | ||||||||
\(88\) | −2.89925 | −0.309061 | ||||||||
\(89\) | 10.9186 | 1.15737 | 0.578684 | − | 0.815552i | \(-0.303567\pi\) | ||||
0.578684 | + | 0.815552i | \(0.303567\pi\) | |||||||
\(90\) | 2.20186 | 0.232096 | ||||||||
\(91\) | 4.17685 | 0.437853 | ||||||||
\(92\) | −1.82864 | −0.190649 | ||||||||
\(93\) | −2.22502 | −0.230723 | ||||||||
\(94\) | 1.67093 | 0.172343 | ||||||||
\(95\) | 14.2412 | 1.46112 | ||||||||
\(96\) | −2.01476 | −0.205631 | ||||||||
\(97\) | 15.4145 | 1.56510 | 0.782551 | − | 0.622587i | \(-0.213918\pi\) | ||||
0.782551 | + | 0.622587i | \(0.213918\pi\) | |||||||
\(98\) | −4.30809 | −0.435183 | ||||||||
\(99\) | −3.07106 | −0.308653 | ||||||||
\(100\) | −0.679103 | −0.0679103 | ||||||||
\(101\) | −16.3718 | −1.62906 | −0.814529 | − | 0.580124i | \(-0.803004\pi\) | ||||
−0.814529 | + | 0.580124i | \(0.803004\pi\) | |||||||
\(102\) | −2.17073 | −0.214935 | ||||||||
\(103\) | 3.26015 | 0.321232 | 0.160616 | − | 0.987017i | \(-0.448652\pi\) | ||||
0.160616 | + | 0.987017i | \(0.448652\pi\) | |||||||
\(104\) | −2.54576 | −0.249633 | ||||||||
\(105\) | 6.87133 | 0.670573 | ||||||||
\(106\) | 11.9804 | 1.16364 | ||||||||
\(107\) | −17.7447 | −1.71544 | −0.857722 | − | 0.514114i | \(-0.828121\pi\) | ||||
−0.857722 | + | 0.514114i | \(0.828121\pi\) | |||||||
\(108\) | 3.91013 | 0.376252 | ||||||||
\(109\) | −14.0053 | −1.34146 | −0.670732 | − | 0.741700i | \(-0.734020\pi\) | ||||
−0.670732 | + | 0.741700i | \(0.734020\pi\) | |||||||
\(110\) | −6.02660 | −0.574614 | ||||||||
\(111\) | 6.45572 | 0.612750 | ||||||||
\(112\) | −1.64070 | −0.155032 | ||||||||
\(113\) | −5.42204 | −0.510062 | −0.255031 | − | 0.966933i | \(-0.582086\pi\) | ||||
−0.255031 | + | 0.966933i | \(0.582086\pi\) | |||||||
\(114\) | −13.8033 | −1.29280 | ||||||||
\(115\) | −3.80115 | −0.354459 | ||||||||
\(116\) | −4.36452 | −0.405235 | ||||||||
\(117\) | −2.69662 | −0.249303 | ||||||||
\(118\) | 0.216612 | 0.0199407 | ||||||||
\(119\) | −1.76772 | −0.162047 | ||||||||
\(120\) | −4.18804 | −0.382314 | ||||||||
\(121\) | −2.59436 | −0.235851 | ||||||||
\(122\) | −10.0683 | −0.911543 | ||||||||
\(123\) | −14.3204 | −1.29123 | ||||||||
\(124\) | 1.10436 | 0.0991743 | ||||||||
\(125\) | −11.8050 | −1.05587 | ||||||||
\(126\) | −1.73793 | −0.154827 | ||||||||
\(127\) | −20.4551 | −1.81510 | −0.907549 | − | 0.419947i | \(-0.862049\pi\) | ||||
−0.907549 | + | 0.419947i | \(0.862049\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −17.1285 | −1.50808 | ||||||||
\(130\) | −5.29182 | −0.464123 | ||||||||
\(131\) | −7.14967 | −0.624669 | −0.312335 | − | 0.949972i | \(-0.601111\pi\) | ||||
−0.312335 | + | 0.949972i | \(0.601111\pi\) | |||||||
\(132\) | 5.84129 | 0.508419 | ||||||||
\(133\) | −11.2406 | −0.974686 | ||||||||
\(134\) | −5.57966 | −0.482009 | ||||||||
\(135\) | 8.12789 | 0.699537 | ||||||||
\(136\) | 1.07742 | 0.0923876 | ||||||||
\(137\) | 0.872289 | 0.0745247 | 0.0372624 | − | 0.999306i | \(-0.488136\pi\) | ||||
0.0372624 | + | 0.999306i | \(0.488136\pi\) | |||||||
\(138\) | 3.68427 | 0.313626 | ||||||||
\(139\) | 1.66686 | 0.141381 | 0.0706906 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706906 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(140\) | −3.41049 | −0.288239 | ||||||||
\(141\) | −3.36652 | −0.283513 | ||||||||
\(142\) | −1.16943 | −0.0981360 | ||||||||
\(143\) | 7.38080 | 0.617214 | ||||||||
\(144\) | 1.05926 | 0.0882716 | ||||||||
\(145\) | −9.07242 | −0.753423 | ||||||||
\(146\) | −13.4122 | −1.11000 | ||||||||
\(147\) | 8.67977 | 0.715895 | ||||||||
\(148\) | −3.20421 | −0.263385 | ||||||||
\(149\) | −6.00583 | −0.492016 | −0.246008 | − | 0.969268i | \(-0.579119\pi\) | ||||
−0.246008 | + | 0.969268i | \(0.579119\pi\) | |||||||
\(150\) | 1.36823 | 0.111715 | ||||||||
\(151\) | −9.22209 | −0.750483 | −0.375241 | − | 0.926927i | \(-0.622440\pi\) | ||||
−0.375241 | + | 0.926927i | \(0.622440\pi\) | |||||||
\(152\) | 6.85110 | 0.555697 | ||||||||
\(153\) | 1.14126 | 0.0922656 | ||||||||
\(154\) | 4.75681 | 0.383315 | ||||||||
\(155\) | 2.29560 | 0.184387 | ||||||||
\(156\) | 5.12911 | 0.410657 | ||||||||
\(157\) | 17.1910 | 1.37199 | 0.685997 | − | 0.727604i | \(-0.259366\pi\) | ||||
0.685997 | + | 0.727604i | \(0.259366\pi\) | |||||||
\(158\) | −1.87728 | −0.149348 | ||||||||
\(159\) | −24.1376 | −1.91424 | ||||||||
\(160\) | 2.07868 | 0.164334 | ||||||||
\(161\) | 3.00026 | 0.236453 | ||||||||
\(162\) | −11.0557 | −0.868622 | ||||||||
\(163\) | −0.156081 | −0.0122252 | −0.00611260 | − | 0.999981i | \(-0.501946\pi\) | ||||
−0.00611260 | + | 0.999981i | \(0.501946\pi\) | |||||||
\(164\) | 7.10776 | 0.555023 | ||||||||
\(165\) | 12.1422 | 0.945265 | ||||||||
\(166\) | −2.72604 | −0.211582 | ||||||||
\(167\) | −3.81756 | −0.295412 | −0.147706 | − | 0.989031i | \(-0.547189\pi\) | ||||
−0.147706 | + | 0.989031i | \(0.547189\pi\) | |||||||
\(168\) | 3.30563 | 0.255035 | ||||||||
\(169\) | −6.51908 | −0.501468 | ||||||||
\(170\) | 2.23960 | 0.171769 | ||||||||
\(171\) | 7.25709 | 0.554964 | ||||||||
\(172\) | 8.50150 | 0.648234 | ||||||||
\(173\) | 3.33903 | 0.253862 | 0.126931 | − | 0.991912i | \(-0.459487\pi\) | ||||
0.126931 | + | 0.991912i | \(0.459487\pi\) | |||||||
\(174\) | 8.79346 | 0.666630 | ||||||||
\(175\) | 1.11421 | 0.0842261 | ||||||||
\(176\) | −2.89925 | −0.218539 | ||||||||
\(177\) | −0.436421 | −0.0328034 | ||||||||
\(178\) | 10.9186 | 0.818382 | ||||||||
\(179\) | 13.2977 | 0.993915 | 0.496958 | − | 0.867775i | \(-0.334450\pi\) | ||||
0.496958 | + | 0.867775i | \(0.334450\pi\) | |||||||
\(180\) | 2.20186 | 0.164117 | ||||||||
\(181\) | −5.73244 | −0.426089 | −0.213044 | − | 0.977043i | \(-0.568338\pi\) | ||||
−0.213044 | + | 0.977043i | \(0.568338\pi\) | |||||||
\(182\) | 4.17685 | 0.309609 | ||||||||
\(183\) | 20.2853 | 1.49953 | ||||||||
\(184\) | −1.82864 | −0.134809 | ||||||||
\(185\) | −6.66052 | −0.489691 | ||||||||
\(186\) | −2.22502 | −0.163146 | ||||||||
\(187\) | −3.12370 | −0.228427 | ||||||||
\(188\) | 1.67093 | 0.121865 | ||||||||
\(189\) | −6.41536 | −0.466649 | ||||||||
\(190\) | 14.2412 | 1.03317 | ||||||||
\(191\) | −6.52684 | −0.472266 | −0.236133 | − | 0.971721i | \(-0.575880\pi\) | ||||
−0.236133 | + | 0.971721i | \(0.575880\pi\) | |||||||
\(192\) | −2.01476 | −0.145403 | ||||||||
\(193\) | −0.0138109 | −0.000994128 0 | −0.000497064 | − | 1.00000i | \(-0.500158\pi\) | ||||
−0.000497064 | 1.00000i | \(0.500158\pi\) | ||||||||
\(194\) | 15.4145 | 1.10669 | ||||||||
\(195\) | 10.6618 | 0.763504 | ||||||||
\(196\) | −4.30809 | −0.307721 | ||||||||
\(197\) | −11.3785 | −0.810687 | −0.405343 | − | 0.914164i | \(-0.632848\pi\) | ||||
−0.405343 | + | 0.914164i | \(0.632848\pi\) | |||||||
\(198\) | −3.07106 | −0.218250 | ||||||||
\(199\) | 22.1964 | 1.57346 | 0.786730 | − | 0.617297i | \(-0.211772\pi\) | ||||
0.786730 | + | 0.617297i | \(0.211772\pi\) | |||||||
\(200\) | −0.679103 | −0.0480198 | ||||||||
\(201\) | 11.2417 | 0.792926 | ||||||||
\(202\) | −16.3718 | −1.15192 | ||||||||
\(203\) | 7.16088 | 0.502595 | ||||||||
\(204\) | −2.17073 | −0.151982 | ||||||||
\(205\) | 14.7747 | 1.03191 | ||||||||
\(206\) | 3.26015 | 0.227145 | ||||||||
\(207\) | −1.93700 | −0.134631 | ||||||||
\(208\) | −2.54576 | −0.176517 | ||||||||
\(209\) | −19.8630 | −1.37395 | ||||||||
\(210\) | 6.87133 | 0.474167 | ||||||||
\(211\) | −6.05237 | −0.416662 | −0.208331 | − | 0.978058i | \(-0.566803\pi\) | ||||
−0.208331 | + | 0.978058i | \(0.566803\pi\) | |||||||
\(212\) | 11.9804 | 0.822816 | ||||||||
\(213\) | 2.35611 | 0.161438 | ||||||||
\(214\) | −17.7447 | −1.21300 | ||||||||
\(215\) | 17.6719 | 1.20521 | ||||||||
\(216\) | 3.91013 | 0.266050 | ||||||||
\(217\) | −1.81193 | −0.123001 | ||||||||
\(218\) | −14.0053 | −0.948558 | ||||||||
\(219\) | 27.0223 | 1.82600 | ||||||||
\(220\) | −6.02660 | −0.406313 | ||||||||
\(221\) | −2.74285 | −0.184504 | ||||||||
\(222\) | 6.45572 | 0.433279 | ||||||||
\(223\) | −9.22732 | −0.617907 | −0.308954 | − | 0.951077i | \(-0.599979\pi\) | ||||
−0.308954 | + | 0.951077i | \(0.599979\pi\) | |||||||
\(224\) | −1.64070 | −0.109624 | ||||||||
\(225\) | −0.719346 | −0.0479564 | ||||||||
\(226\) | −5.42204 | −0.360669 | ||||||||
\(227\) | 6.19976 | 0.411493 | 0.205746 | − | 0.978605i | \(-0.434038\pi\) | ||||
0.205746 | + | 0.978605i | \(0.434038\pi\) | |||||||
\(228\) | −13.8033 | −0.914147 | ||||||||
\(229\) | 6.41997 | 0.424244 | 0.212122 | − | 0.977243i | \(-0.431963\pi\) | ||||
0.212122 | + | 0.977243i | \(0.431963\pi\) | |||||||
\(230\) | −3.80115 | −0.250640 | ||||||||
\(231\) | −9.58383 | −0.630570 | ||||||||
\(232\) | −4.36452 | −0.286545 | ||||||||
\(233\) | −16.2164 | −1.06237 | −0.531187 | − | 0.847254i | \(-0.678254\pi\) | ||||
−0.531187 | + | 0.847254i | \(0.678254\pi\) | |||||||
\(234\) | −2.69662 | −0.176284 | ||||||||
\(235\) | 3.47332 | 0.226575 | ||||||||
\(236\) | 0.216612 | 0.0141002 | ||||||||
\(237\) | 3.78227 | 0.245685 | ||||||||
\(238\) | −1.76772 | −0.114584 | ||||||||
\(239\) | −5.11535 | −0.330885 | −0.165442 | − | 0.986219i | \(-0.552905\pi\) | ||||
−0.165442 | + | 0.986219i | \(0.552905\pi\) | |||||||
\(240\) | −4.18804 | −0.270337 | ||||||||
\(241\) | −18.4665 | −1.18953 | −0.594766 | − | 0.803899i | \(-0.702755\pi\) | ||||
−0.594766 | + | 0.803899i | \(0.702755\pi\) | |||||||
\(242\) | −2.59436 | −0.166772 | ||||||||
\(243\) | 10.5443 | 0.676417 | ||||||||
\(244\) | −10.0683 | −0.644558 | ||||||||
\(245\) | −8.95512 | −0.572122 | ||||||||
\(246\) | −14.3204 | −0.913038 | ||||||||
\(247\) | −17.4413 | −1.10976 | ||||||||
\(248\) | 1.10436 | 0.0701268 | ||||||||
\(249\) | 5.49233 | 0.348062 | ||||||||
\(250\) | −11.8050 | −0.746615 | ||||||||
\(251\) | 23.3686 | 1.47502 | 0.737508 | − | 0.675339i | \(-0.236002\pi\) | ||||
0.737508 | + | 0.675339i | \(0.236002\pi\) | |||||||
\(252\) | −1.73793 | −0.109479 | ||||||||
\(253\) | 5.30168 | 0.333314 | ||||||||
\(254\) | −20.4551 | −1.28347 | ||||||||
\(255\) | −4.51226 | −0.282568 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.2985 | −1.39094 | −0.695470 | − | 0.718555i | \(-0.744804\pi\) | ||||
−0.695470 | + | 0.718555i | \(0.744804\pi\) | |||||||
\(258\) | −17.1285 | −1.06637 | ||||||||
\(259\) | 5.25717 | 0.326664 | ||||||||
\(260\) | −5.29182 | −0.328185 | ||||||||
\(261\) | −4.62316 | −0.286166 | ||||||||
\(262\) | −7.14967 | −0.441708 | ||||||||
\(263\) | −16.1755 | −0.997426 | −0.498713 | − | 0.866767i | \(-0.666194\pi\) | ||||
−0.498713 | + | 0.866767i | \(0.666194\pi\) | |||||||
\(264\) | 5.84129 | 0.359507 | ||||||||
\(265\) | 24.9033 | 1.52980 | ||||||||
\(266\) | −11.2406 | −0.689207 | ||||||||
\(267\) | −21.9983 | −1.34628 | ||||||||
\(268\) | −5.57966 | −0.340832 | ||||||||
\(269\) | −20.6911 | −1.26156 | −0.630780 | − | 0.775962i | \(-0.717265\pi\) | ||||
−0.630780 | + | 0.775962i | \(0.717265\pi\) | |||||||
\(270\) | 8.12789 | 0.494648 | ||||||||
\(271\) | 13.7220 | 0.833550 | 0.416775 | − | 0.909010i | \(-0.363160\pi\) | ||||
0.416775 | + | 0.909010i | \(0.363160\pi\) | |||||||
\(272\) | 1.07742 | 0.0653279 | ||||||||
\(273\) | −8.41535 | −0.509320 | ||||||||
\(274\) | 0.872289 | 0.0526969 | ||||||||
\(275\) | 1.96889 | 0.118728 | ||||||||
\(276\) | 3.68427 | 0.221767 | ||||||||
\(277\) | 21.9010 | 1.31590 | 0.657951 | − | 0.753061i | \(-0.271423\pi\) | ||||
0.657951 | + | 0.753061i | \(0.271423\pi\) | |||||||
\(278\) | 1.66686 | 0.0999717 | ||||||||
\(279\) | 1.16980 | 0.0700342 | ||||||||
\(280\) | −3.41049 | −0.203816 | ||||||||
\(281\) | 18.4307 | 1.09949 | 0.549743 | − | 0.835334i | \(-0.314726\pi\) | ||||
0.549743 | + | 0.835334i | \(0.314726\pi\) | |||||||
\(282\) | −3.36652 | −0.200474 | ||||||||
\(283\) | 10.5955 | 0.629837 | 0.314919 | − | 0.949119i | \(-0.398023\pi\) | ||||
0.314919 | + | 0.949119i | \(0.398023\pi\) | |||||||
\(284\) | −1.16943 | −0.0693926 | ||||||||
\(285\) | −28.6926 | −1.69961 | ||||||||
\(286\) | 7.38080 | 0.436436 | ||||||||
\(287\) | −11.6617 | −0.688371 | ||||||||
\(288\) | 1.05926 | 0.0624175 | ||||||||
\(289\) | −15.8392 | −0.931716 | ||||||||
\(290\) | −9.07242 | −0.532751 | ||||||||
\(291\) | −31.0564 | −1.82056 | ||||||||
\(292\) | −13.4122 | −0.784887 | ||||||||
\(293\) | −19.8676 | −1.16068 | −0.580340 | − | 0.814374i | \(-0.697080\pi\) | ||||
−0.580340 | + | 0.814374i | \(0.697080\pi\) | |||||||
\(294\) | 8.67977 | 0.506214 | ||||||||
\(295\) | 0.450266 | 0.0262155 | ||||||||
\(296\) | −3.20421 | −0.186241 | ||||||||
\(297\) | −11.3364 | −0.657806 | ||||||||
\(298\) | −6.00583 | −0.347908 | ||||||||
\(299\) | 4.65528 | 0.269222 | ||||||||
\(300\) | 1.36823 | 0.0789948 | ||||||||
\(301\) | −13.9485 | −0.803976 | ||||||||
\(302\) | −9.22209 | −0.530671 | ||||||||
\(303\) | 32.9853 | 1.89496 | ||||||||
\(304\) | 6.85110 | 0.392937 | ||||||||
\(305\) | −20.9288 | −1.19838 | ||||||||
\(306\) | 1.14126 | 0.0652417 | ||||||||
\(307\) | −0.768845 | −0.0438803 | −0.0219402 | − | 0.999759i | \(-0.506984\pi\) | ||||
−0.0219402 | + | 0.999759i | \(0.506984\pi\) | |||||||
\(308\) | 4.75681 | 0.271044 | ||||||||
\(309\) | −6.56841 | −0.373664 | ||||||||
\(310\) | 2.29560 | 0.130381 | ||||||||
\(311\) | 7.93499 | 0.449952 | 0.224976 | − | 0.974364i | \(-0.427770\pi\) | ||||
0.224976 | + | 0.974364i | \(0.427770\pi\) | |||||||
\(312\) | 5.12911 | 0.290378 | ||||||||
\(313\) | 13.2254 | 0.747541 | 0.373771 | − | 0.927521i | \(-0.378065\pi\) | ||||
0.373771 | + | 0.927521i | \(0.378065\pi\) | |||||||
\(314\) | 17.1910 | 0.970147 | ||||||||
\(315\) | −3.61260 | −0.203547 | ||||||||
\(316\) | −1.87728 | −0.105605 | ||||||||
\(317\) | −13.3207 | −0.748165 | −0.374083 | − | 0.927395i | \(-0.622042\pi\) | ||||
−0.374083 | + | 0.927395i | \(0.622042\pi\) | |||||||
\(318\) | −24.1376 | −1.35357 | ||||||||
\(319\) | 12.6538 | 0.708478 | ||||||||
\(320\) | 2.07868 | 0.116202 | ||||||||
\(321\) | 35.7513 | 1.99544 | ||||||||
\(322\) | 3.00026 | 0.167198 | ||||||||
\(323\) | 7.38148 | 0.410717 | ||||||||
\(324\) | −11.0557 | −0.614208 | ||||||||
\(325\) | 1.72884 | 0.0958985 | ||||||||
\(326\) | −0.156081 | −0.00864452 | ||||||||
\(327\) | 28.2173 | 1.56042 | ||||||||
\(328\) | 7.10776 | 0.392460 | ||||||||
\(329\) | −2.74150 | −0.151144 | ||||||||
\(330\) | 12.1422 | 0.668404 | ||||||||
\(331\) | 9.68418 | 0.532291 | 0.266145 | − | 0.963933i | \(-0.414250\pi\) | ||||
0.266145 | + | 0.963933i | \(0.414250\pi\) | |||||||
\(332\) | −2.72604 | −0.149611 | ||||||||
\(333\) | −3.39409 | −0.185995 | ||||||||
\(334\) | −3.81756 | −0.208888 | ||||||||
\(335\) | −11.5983 | −0.633683 | ||||||||
\(336\) | 3.30563 | 0.180337 | ||||||||
\(337\) | −13.4565 | −0.733022 | −0.366511 | − | 0.930414i | \(-0.619448\pi\) | ||||
−0.366511 | + | 0.930414i | \(0.619448\pi\) | |||||||
\(338\) | −6.51908 | −0.354591 | ||||||||
\(339\) | 10.9241 | 0.593316 | ||||||||
\(340\) | 2.23960 | 0.121459 | ||||||||
\(341\) | −3.20181 | −0.173388 | ||||||||
\(342\) | 7.25709 | 0.392419 | ||||||||
\(343\) | 18.5532 | 1.00178 | ||||||||
\(344\) | 8.50150 | 0.458370 | ||||||||
\(345\) | 7.65840 | 0.412315 | ||||||||
\(346\) | 3.33903 | 0.179507 | ||||||||
\(347\) | −33.5020 | −1.79848 | −0.899241 | − | 0.437454i | \(-0.855880\pi\) | ||||
−0.899241 | + | 0.437454i | \(0.855880\pi\) | |||||||
\(348\) | 8.79346 | 0.471379 | ||||||||
\(349\) | 22.2490 | 1.19096 | 0.595481 | − | 0.803369i | \(-0.296961\pi\) | ||||
0.595481 | + | 0.803369i | \(0.296961\pi\) | |||||||
\(350\) | 1.11421 | 0.0595569 | ||||||||
\(351\) | −9.95426 | −0.531319 | ||||||||
\(352\) | −2.89925 | −0.154530 | ||||||||
\(353\) | −18.4032 | −0.979504 | −0.489752 | − | 0.871862i | \(-0.662913\pi\) | ||||
−0.489752 | + | 0.871862i | \(0.662913\pi\) | |||||||
\(354\) | −0.436421 | −0.0231955 | ||||||||
\(355\) | −2.43086 | −0.129017 | ||||||||
\(356\) | 10.9186 | 0.578684 | ||||||||
\(357\) | 3.56153 | 0.188496 | ||||||||
\(358\) | 13.2977 | 0.702804 | ||||||||
\(359\) | 17.9357 | 0.946612 | 0.473306 | − | 0.880898i | \(-0.343061\pi\) | ||||
0.473306 | + | 0.880898i | \(0.343061\pi\) | |||||||
\(360\) | 2.20186 | 0.116048 | ||||||||
\(361\) | 27.9376 | 1.47040 | ||||||||
\(362\) | −5.73244 | −0.301290 | ||||||||
\(363\) | 5.22701 | 0.274347 | ||||||||
\(364\) | 4.17685 | 0.218926 | ||||||||
\(365\) | −27.8795 | −1.45928 | ||||||||
\(366\) | 20.2853 | 1.06033 | ||||||||
\(367\) | −28.2557 | −1.47494 | −0.737468 | − | 0.675382i | \(-0.763979\pi\) | ||||
−0.737468 | + | 0.675382i | \(0.763979\pi\) | |||||||
\(368\) | −1.82864 | −0.0953244 | ||||||||
\(369\) | 7.52896 | 0.391942 | ||||||||
\(370\) | −6.66052 | −0.346264 | ||||||||
\(371\) | −19.6563 | −1.02050 | ||||||||
\(372\) | −2.22502 | −0.115362 | ||||||||
\(373\) | −13.7847 | −0.713744 | −0.356872 | − | 0.934153i | \(-0.616157\pi\) | ||||
−0.356872 | + | 0.934153i | \(0.616157\pi\) | |||||||
\(374\) | −3.12370 | −0.161522 | ||||||||
\(375\) | 23.7843 | 1.22822 | ||||||||
\(376\) | 1.67093 | 0.0861717 | ||||||||
\(377\) | 11.1110 | 0.572247 | ||||||||
\(378\) | −6.41536 | −0.329971 | ||||||||
\(379\) | −1.98047 | −0.101730 | −0.0508649 | − | 0.998706i | \(-0.516198\pi\) | ||||
−0.0508649 | + | 0.998706i | \(0.516198\pi\) | |||||||
\(380\) | 14.2412 | 0.730559 | ||||||||
\(381\) | 41.2121 | 2.11136 | ||||||||
\(382\) | −6.52684 | −0.333942 | ||||||||
\(383\) | 1.36202 | 0.0695960 | 0.0347980 | − | 0.999394i | \(-0.488921\pi\) | ||||
0.0347980 | + | 0.999394i | \(0.488921\pi\) | |||||||
\(384\) | −2.01476 | −0.102815 | ||||||||
\(385\) | 9.88787 | 0.503933 | ||||||||
\(386\) | −0.0138109 | −0.000702955 0 | ||||||||
\(387\) | 9.00530 | 0.457765 | ||||||||
\(388\) | 15.4145 | 0.782551 | ||||||||
\(389\) | 9.24189 | 0.468582 | 0.234291 | − | 0.972166i | \(-0.424723\pi\) | ||||
0.234291 | + | 0.972166i | \(0.424723\pi\) | |||||||
\(390\) | 10.6618 | 0.539879 | ||||||||
\(391\) | −1.97020 | −0.0996375 | ||||||||
\(392\) | −4.30809 | −0.217591 | ||||||||
\(393\) | 14.4049 | 0.726630 | ||||||||
\(394\) | −11.3785 | −0.573242 | ||||||||
\(395\) | −3.90225 | −0.196344 | ||||||||
\(396\) | −3.07106 | −0.154326 | ||||||||
\(397\) | −26.7665 | −1.34337 | −0.671685 | − | 0.740837i | \(-0.734429\pi\) | ||||
−0.671685 | + | 0.740837i | \(0.734429\pi\) | |||||||
\(398\) | 22.1964 | 1.11260 | ||||||||
\(399\) | 22.6472 | 1.13378 | ||||||||
\(400\) | −0.679103 | −0.0339551 | ||||||||
\(401\) | −23.6236 | −1.17971 | −0.589854 | − | 0.807510i | \(-0.700815\pi\) | ||||
−0.589854 | + | 0.807510i | \(0.700815\pi\) | |||||||
\(402\) | 11.2417 | 0.560684 | ||||||||
\(403\) | −2.81143 | −0.140048 | ||||||||
\(404\) | −16.3718 | −0.814529 | ||||||||
\(405\) | −22.9813 | −1.14195 | ||||||||
\(406\) | 7.16088 | 0.355389 | ||||||||
\(407\) | 9.28980 | 0.460479 | ||||||||
\(408\) | −2.17073 | −0.107467 | ||||||||
\(409\) | −29.0054 | −1.43422 | −0.717112 | − | 0.696958i | \(-0.754537\pi\) | ||||
−0.717112 | + | 0.696958i | \(0.754537\pi\) | |||||||
\(410\) | 14.7747 | 0.729672 | ||||||||
\(411\) | −1.75745 | −0.0866888 | ||||||||
\(412\) | 3.26015 | 0.160616 | ||||||||
\(413\) | −0.355396 | −0.0174879 | ||||||||
\(414\) | −1.93700 | −0.0951985 | ||||||||
\(415\) | −5.66656 | −0.278161 | ||||||||
\(416\) | −2.54576 | −0.124816 | ||||||||
\(417\) | −3.35832 | −0.164458 | ||||||||
\(418\) | −19.8630 | −0.971533 | ||||||||
\(419\) | −0.958270 | −0.0468146 | −0.0234073 | − | 0.999726i | \(-0.507451\pi\) | ||||
−0.0234073 | + | 0.999726i | \(0.507451\pi\) | |||||||
\(420\) | 6.87133 | 0.335287 | ||||||||
\(421\) | 12.3654 | 0.602651 | 0.301325 | − | 0.953521i | \(-0.402571\pi\) | ||||
0.301325 | + | 0.953521i | \(0.402571\pi\) | |||||||
\(422\) | −6.05237 | −0.294625 | ||||||||
\(423\) | 1.76995 | 0.0860579 | ||||||||
\(424\) | 11.9804 | 0.581819 | ||||||||
\(425\) | −0.731676 | −0.0354915 | ||||||||
\(426\) | 2.35611 | 0.114154 | ||||||||
\(427\) | 16.5191 | 0.799418 | ||||||||
\(428\) | −17.7447 | −0.857722 | ||||||||
\(429\) | −14.8705 | −0.717957 | ||||||||
\(430\) | 17.6719 | 0.852214 | ||||||||
\(431\) | 28.1431 | 1.35561 | 0.677803 | − | 0.735244i | \(-0.262932\pi\) | ||||
0.677803 | + | 0.735244i | \(0.262932\pi\) | |||||||
\(432\) | 3.91013 | 0.188126 | ||||||||
\(433\) | −31.6017 | −1.51868 | −0.759340 | − | 0.650694i | \(-0.774478\pi\) | ||||
−0.759340 | + | 0.650694i | \(0.774478\pi\) | |||||||
\(434\) | −1.81193 | −0.0869752 | ||||||||
\(435\) | 18.2788 | 0.876399 | ||||||||
\(436\) | −14.0053 | −0.670732 | ||||||||
\(437\) | −12.5282 | −0.599304 | ||||||||
\(438\) | 27.0223 | 1.29117 | ||||||||
\(439\) | −21.9805 | −1.04907 | −0.524537 | − | 0.851388i | \(-0.675762\pi\) | ||||
−0.524537 | + | 0.851388i | \(0.675762\pi\) | |||||||
\(440\) | −6.02660 | −0.287307 | ||||||||
\(441\) | −4.56338 | −0.217304 | ||||||||
\(442\) | −2.74285 | −0.130464 | ||||||||
\(443\) | 1.25281 | 0.0595226 | 0.0297613 | − | 0.999557i | \(-0.490525\pi\) | ||||
0.0297613 | + | 0.999557i | \(0.490525\pi\) | |||||||
\(444\) | 6.45572 | 0.306375 | ||||||||
\(445\) | 22.6962 | 1.07590 | ||||||||
\(446\) | −9.22732 | −0.436926 | ||||||||
\(447\) | 12.1003 | 0.572325 | ||||||||
\(448\) | −1.64070 | −0.0775160 | ||||||||
\(449\) | 10.9508 | 0.516799 | 0.258399 | − | 0.966038i | \(-0.416805\pi\) | ||||
0.258399 | + | 0.966038i | \(0.416805\pi\) | |||||||
\(450\) | −0.719346 | −0.0339103 | ||||||||
\(451\) | −20.6072 | −0.970353 | ||||||||
\(452\) | −5.42204 | −0.255031 | ||||||||
\(453\) | 18.5803 | 0.872978 | ||||||||
\(454\) | 6.19976 | 0.290969 | ||||||||
\(455\) | 8.68232 | 0.407033 | ||||||||
\(456\) | −13.8033 | −0.646400 | ||||||||
\(457\) | −23.6447 | −1.10605 | −0.553026 | − | 0.833164i | \(-0.686527\pi\) | ||||
−0.553026 | + | 0.833164i | \(0.686527\pi\) | |||||||
\(458\) | 6.41997 | 0.299986 | ||||||||
\(459\) | 4.21283 | 0.196638 | ||||||||
\(460\) | −3.80115 | −0.177229 | ||||||||
\(461\) | 19.9688 | 0.930041 | 0.465020 | − | 0.885300i | \(-0.346047\pi\) | ||||
0.465020 | + | 0.885300i | \(0.346047\pi\) | |||||||
\(462\) | −9.58383 | −0.445880 | ||||||||
\(463\) | 11.2357 | 0.522169 | 0.261084 | − | 0.965316i | \(-0.415920\pi\) | ||||
0.261084 | + | 0.965316i | \(0.415920\pi\) | |||||||
\(464\) | −4.36452 | −0.202618 | ||||||||
\(465\) | −4.62509 | −0.214483 | ||||||||
\(466\) | −16.2164 | −0.751212 | ||||||||
\(467\) | 25.9897 | 1.20266 | 0.601329 | − | 0.799001i | \(-0.294638\pi\) | ||||
0.601329 | + | 0.799001i | \(0.294638\pi\) | |||||||
\(468\) | −2.69662 | −0.124652 | ||||||||
\(469\) | 9.15457 | 0.422719 | ||||||||
\(470\) | 3.47332 | 0.160213 | ||||||||
\(471\) | −34.6358 | −1.59594 | ||||||||
\(472\) | 0.216612 | 0.00997037 | ||||||||
\(473\) | −24.6480 | −1.13331 | ||||||||
\(474\) | 3.78227 | 0.173725 | ||||||||
\(475\) | −4.65260 | −0.213476 | ||||||||
\(476\) | −1.76772 | −0.0810234 | ||||||||
\(477\) | 12.6903 | 0.581050 | ||||||||
\(478\) | −5.11535 | −0.233971 | ||||||||
\(479\) | −16.5809 | −0.757601 | −0.378801 | − | 0.925478i | \(-0.623663\pi\) | ||||
−0.378801 | + | 0.925478i | \(0.623663\pi\) | |||||||
\(480\) | −4.18804 | −0.191157 | ||||||||
\(481\) | 8.15717 | 0.371935 | ||||||||
\(482\) | −18.4665 | −0.841126 | ||||||||
\(483\) | −6.04480 | −0.275048 | ||||||||
\(484\) | −2.59436 | −0.117925 | ||||||||
\(485\) | 32.0417 | 1.45494 | ||||||||
\(486\) | 10.5443 | 0.478299 | ||||||||
\(487\) | 39.0680 | 1.77034 | 0.885171 | − | 0.465266i | \(-0.154041\pi\) | ||||
0.885171 | + | 0.465266i | \(0.154041\pi\) | |||||||
\(488\) | −10.0683 | −0.455772 | ||||||||
\(489\) | 0.314465 | 0.0142206 | ||||||||
\(490\) | −8.95512 | −0.404551 | ||||||||
\(491\) | 16.4517 | 0.742454 | 0.371227 | − | 0.928542i | \(-0.378937\pi\) | ||||
0.371227 | + | 0.928542i | \(0.378937\pi\) | |||||||
\(492\) | −14.3204 | −0.645615 | ||||||||
\(493\) | −4.70240 | −0.211785 | ||||||||
\(494\) | −17.4413 | −0.784720 | ||||||||
\(495\) | −6.38373 | −0.286927 | ||||||||
\(496\) | 1.10436 | 0.0495871 | ||||||||
\(497\) | 1.91868 | 0.0860647 | ||||||||
\(498\) | 5.49233 | 0.246117 | ||||||||
\(499\) | −21.2789 | −0.952574 | −0.476287 | − | 0.879290i | \(-0.658018\pi\) | ||||
−0.476287 | + | 0.879290i | \(0.658018\pi\) | |||||||
\(500\) | −11.8050 | −0.527937 | ||||||||
\(501\) | 7.69147 | 0.343630 | ||||||||
\(502\) | 23.3686 | 1.04299 | ||||||||
\(503\) | 30.3539 | 1.35341 | 0.676707 | − | 0.736253i | \(-0.263406\pi\) | ||||
0.676707 | + | 0.736253i | \(0.263406\pi\) | |||||||
\(504\) | −1.73793 | −0.0774136 | ||||||||
\(505\) | −34.0317 | −1.51439 | ||||||||
\(506\) | 5.30168 | 0.235688 | ||||||||
\(507\) | 13.1344 | 0.583319 | ||||||||
\(508\) | −20.4551 | −0.907549 | ||||||||
\(509\) | 21.6615 | 0.960129 | 0.480064 | − | 0.877233i | \(-0.340613\pi\) | ||||
0.480064 | + | 0.877233i | \(0.340613\pi\) | |||||||
\(510\) | −4.51226 | −0.199806 | ||||||||
\(511\) | 22.0054 | 0.973461 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 26.7887 | 1.18275 | ||||||||
\(514\) | −22.2985 | −0.983543 | ||||||||
\(515\) | 6.77679 | 0.298621 | ||||||||
\(516\) | −17.1285 | −0.754040 | ||||||||
\(517\) | −4.84444 | −0.213058 | ||||||||
\(518\) | 5.25717 | 0.230987 | ||||||||
\(519\) | −6.72734 | −0.295297 | ||||||||
\(520\) | −5.29182 | −0.232062 | ||||||||
\(521\) | −15.5545 | −0.681455 | −0.340728 | − | 0.940162i | \(-0.610673\pi\) | ||||
−0.340728 | + | 0.940162i | \(0.610673\pi\) | |||||||
\(522\) | −4.62316 | −0.202350 | ||||||||
\(523\) | −22.1847 | −0.970068 | −0.485034 | − | 0.874495i | \(-0.661193\pi\) | ||||
−0.485034 | + | 0.874495i | \(0.661193\pi\) | |||||||
\(524\) | −7.14967 | −0.312335 | ||||||||
\(525\) | −2.24486 | −0.0979737 | ||||||||
\(526\) | −16.1755 | −0.705287 | ||||||||
\(527\) | 1.18985 | 0.0518308 | ||||||||
\(528\) | 5.84129 | 0.254210 | ||||||||
\(529\) | −19.6561 | −0.854612 | ||||||||
\(530\) | 24.9033 | 1.08173 | ||||||||
\(531\) | 0.229448 | 0.00995720 | ||||||||
\(532\) | −11.2406 | −0.487343 | ||||||||
\(533\) | −18.0947 | −0.783768 | ||||||||
\(534\) | −21.9983 | −0.951961 | ||||||||
\(535\) | −36.8855 | −1.59470 | ||||||||
\(536\) | −5.57966 | −0.241004 | ||||||||
\(537\) | −26.7916 | −1.15614 | ||||||||
\(538\) | −20.6911 | −0.892057 | ||||||||
\(539\) | 12.4902 | 0.537992 | ||||||||
\(540\) | 8.12789 | 0.349769 | ||||||||
\(541\) | 37.0805 | 1.59422 | 0.797108 | − | 0.603836i | \(-0.206362\pi\) | ||||
0.797108 | + | 0.603836i | \(0.206362\pi\) | |||||||
\(542\) | 13.7220 | 0.589409 | ||||||||
\(543\) | 11.5495 | 0.495636 | ||||||||
\(544\) | 1.07742 | 0.0461938 | ||||||||
\(545\) | −29.1125 | −1.24704 | ||||||||
\(546\) | −8.41535 | −0.360144 | ||||||||
\(547\) | −22.6540 | −0.968616 | −0.484308 | − | 0.874898i | \(-0.660929\pi\) | ||||
−0.484308 | + | 0.874898i | \(0.660929\pi\) | |||||||
\(548\) | 0.872289 | 0.0372624 | ||||||||
\(549\) | −10.6650 | −0.455170 | ||||||||
\(550\) | 1.96889 | 0.0839536 | ||||||||
\(551\) | −29.9017 | −1.27386 | ||||||||
\(552\) | 3.68427 | 0.156813 | ||||||||
\(553\) | 3.08006 | 0.130977 | ||||||||
\(554\) | 21.9010 | 0.930483 | ||||||||
\(555\) | 13.4194 | 0.569620 | ||||||||
\(556\) | 1.66686 | 0.0706906 | ||||||||
\(557\) | −38.9272 | −1.64940 | −0.824700 | − | 0.565570i | \(-0.808656\pi\) | ||||
−0.824700 | + | 0.565570i | \(0.808656\pi\) | |||||||
\(558\) | 1.16980 | 0.0495216 | ||||||||
\(559\) | −21.6428 | −0.915394 | ||||||||
\(560\) | −3.41049 | −0.144120 | ||||||||
\(561\) | 6.29350 | 0.265712 | ||||||||
\(562\) | 18.4307 | 0.777454 | ||||||||
\(563\) | 21.7304 | 0.915826 | 0.457913 | − | 0.888997i | \(-0.348597\pi\) | ||||
0.457913 | + | 0.888997i | \(0.348597\pi\) | |||||||
\(564\) | −3.36652 | −0.141756 | ||||||||
\(565\) | −11.2707 | −0.474160 | ||||||||
\(566\) | 10.5955 | 0.445362 | ||||||||
\(567\) | 18.1392 | 0.761776 | ||||||||
\(568\) | −1.16943 | −0.0490680 | ||||||||
\(569\) | −0.0195358 | −0.000818983 0 | −0.000409492 | − | 1.00000i | \(-0.500130\pi\) | ||||
−0.000409492 | 1.00000i | \(0.500130\pi\) | ||||||||
\(570\) | −28.6926 | −1.20180 | ||||||||
\(571\) | −33.7804 | −1.41367 | −0.706834 | − | 0.707380i | \(-0.749877\pi\) | ||||
−0.706834 | + | 0.707380i | \(0.749877\pi\) | |||||||
\(572\) | 7.38080 | 0.308607 | ||||||||
\(573\) | 13.1500 | 0.549350 | ||||||||
\(574\) | −11.6617 | −0.486751 | ||||||||
\(575\) | 1.24183 | 0.0517880 | ||||||||
\(576\) | 1.05926 | 0.0441358 | ||||||||
\(577\) | 10.1027 | 0.420583 | 0.210291 | − | 0.977639i | \(-0.432559\pi\) | ||||
0.210291 | + | 0.977639i | \(0.432559\pi\) | |||||||
\(578\) | −15.8392 | −0.658823 | ||||||||
\(579\) | 0.0278256 | 0.00115639 | ||||||||
\(580\) | −9.07242 | −0.376712 | ||||||||
\(581\) | 4.47263 | 0.185556 | ||||||||
\(582\) | −31.0564 | −1.28733 | ||||||||
\(583\) | −34.7341 | −1.43854 | ||||||||
\(584\) | −13.4122 | −0.554999 | ||||||||
\(585\) | −5.60541 | −0.231755 | ||||||||
\(586\) | −19.8676 | −0.820724 | ||||||||
\(587\) | 40.0622 | 1.65354 | 0.826772 | − | 0.562537i | \(-0.190175\pi\) | ||||
0.826772 | + | 0.562537i | \(0.190175\pi\) | |||||||
\(588\) | 8.67977 | 0.357947 | ||||||||
\(589\) | 7.56606 | 0.311754 | ||||||||
\(590\) | 0.450266 | 0.0185372 | ||||||||
\(591\) | 22.9250 | 0.943009 | ||||||||
\(592\) | −3.20421 | −0.131692 | ||||||||
\(593\) | −9.83030 | −0.403682 | −0.201841 | − | 0.979418i | \(-0.564692\pi\) | ||||
−0.201841 | + | 0.979418i | \(0.564692\pi\) | |||||||
\(594\) | −11.3364 | −0.465139 | ||||||||
\(595\) | −3.67452 | −0.150641 | ||||||||
\(596\) | −6.00583 | −0.246008 | ||||||||
\(597\) | −44.7204 | −1.83029 | ||||||||
\(598\) | 4.65528 | 0.190369 | ||||||||
\(599\) | 38.7111 | 1.58169 | 0.790846 | − | 0.612015i | \(-0.209641\pi\) | ||||
0.790846 | + | 0.612015i | \(0.209641\pi\) | |||||||
\(600\) | 1.36823 | 0.0558577 | ||||||||
\(601\) | −37.0042 | −1.50943 | −0.754716 | − | 0.656051i | \(-0.772225\pi\) | ||||
−0.754716 | + | 0.656051i | \(0.772225\pi\) | |||||||
\(602\) | −13.9485 | −0.568497 | ||||||||
\(603\) | −5.91030 | −0.240686 | ||||||||
\(604\) | −9.22209 | −0.375241 | ||||||||
\(605\) | −5.39284 | −0.219250 | ||||||||
\(606\) | 32.9853 | 1.33994 | ||||||||
\(607\) | 35.7322 | 1.45033 | 0.725163 | − | 0.688577i | \(-0.241764\pi\) | ||||
0.725163 | + | 0.688577i | \(0.241764\pi\) | |||||||
\(608\) | 6.85110 | 0.277849 | ||||||||
\(609\) | −14.4275 | −0.584630 | ||||||||
\(610\) | −20.9288 | −0.847382 | ||||||||
\(611\) | −4.25380 | −0.172090 | ||||||||
\(612\) | 1.14126 | 0.0461328 | ||||||||
\(613\) | −1.78866 | −0.0722434 | −0.0361217 | − | 0.999347i | \(-0.511500\pi\) | ||||
−0.0361217 | + | 0.999347i | \(0.511500\pi\) | |||||||
\(614\) | −0.768845 | −0.0310281 | ||||||||
\(615\) | −29.7676 | −1.20034 | ||||||||
\(616\) | 4.75681 | 0.191657 | ||||||||
\(617\) | −46.2330 | −1.86127 | −0.930635 | − | 0.365948i | \(-0.880745\pi\) | ||||
−0.930635 | + | 0.365948i | \(0.880745\pi\) | |||||||
\(618\) | −6.56841 | −0.264220 | ||||||||
\(619\) | 4.35356 | 0.174984 | 0.0874921 | − | 0.996165i | \(-0.472115\pi\) | ||||
0.0874921 | + | 0.996165i | \(0.472115\pi\) | |||||||
\(620\) | 2.29560 | 0.0921936 | ||||||||
\(621\) | −7.15021 | −0.286928 | ||||||||
\(622\) | 7.93499 | 0.318164 | ||||||||
\(623\) | −17.9142 | −0.717716 | ||||||||
\(624\) | 5.12911 | 0.205329 | ||||||||
\(625\) | −21.1433 | −0.845732 | ||||||||
\(626\) | 13.2254 | 0.528591 | ||||||||
\(627\) | 40.0193 | 1.59822 | ||||||||
\(628\) | 17.1910 | 0.685997 | ||||||||
\(629\) | −3.45227 | −0.137651 | ||||||||
\(630\) | −3.61260 | −0.143929 | ||||||||
\(631\) | −10.3924 | −0.413716 | −0.206858 | − | 0.978371i | \(-0.566324\pi\) | ||||
−0.206858 | + | 0.978371i | \(0.566324\pi\) | |||||||
\(632\) | −1.87728 | −0.0746741 | ||||||||
\(633\) | 12.1941 | 0.484671 | ||||||||
\(634\) | −13.3207 | −0.529033 | ||||||||
\(635\) | −42.5196 | −1.68734 | ||||||||
\(636\) | −24.1376 | −0.957118 | ||||||||
\(637\) | 10.9674 | 0.434543 | ||||||||
\(638\) | 12.6538 | 0.500969 | ||||||||
\(639\) | −1.23873 | −0.0490032 | ||||||||
\(640\) | 2.07868 | 0.0821669 | ||||||||
\(641\) | 8.25885 | 0.326205 | 0.163103 | − | 0.986609i | \(-0.447850\pi\) | ||||
0.163103 | + | 0.986609i | \(0.447850\pi\) | |||||||
\(642\) | 35.7513 | 1.41099 | ||||||||
\(643\) | 10.5189 | 0.414826 | 0.207413 | − | 0.978254i | \(-0.433496\pi\) | ||||
0.207413 | + | 0.978254i | \(0.433496\pi\) | |||||||
\(644\) | 3.00026 | 0.118227 | ||||||||
\(645\) | −35.6046 | −1.40193 | ||||||||
\(646\) | 7.38148 | 0.290421 | ||||||||
\(647\) | 0.435539 | 0.0171228 | 0.00856140 | − | 0.999963i | \(-0.497275\pi\) | ||||
0.00856140 | + | 0.999963i | \(0.497275\pi\) | |||||||
\(648\) | −11.0557 | −0.434311 | ||||||||
\(649\) | −0.628011 | −0.0246516 | ||||||||
\(650\) | 1.72884 | 0.0678105 | ||||||||
\(651\) | 3.65060 | 0.143078 | ||||||||
\(652\) | −0.156081 | −0.00611260 | ||||||||
\(653\) | −12.3102 | −0.481734 | −0.240867 | − | 0.970558i | \(-0.577432\pi\) | ||||
−0.240867 | + | 0.970558i | \(0.577432\pi\) | |||||||
\(654\) | 28.2173 | 1.10338 | ||||||||
\(655\) | −14.8618 | −0.580701 | ||||||||
\(656\) | 7.10776 | 0.277511 | ||||||||
\(657\) | −14.2070 | −0.554266 | ||||||||
\(658\) | −2.74150 | −0.106875 | ||||||||
\(659\) | −34.9670 | −1.36212 | −0.681060 | − | 0.732227i | \(-0.738481\pi\) | ||||
−0.681060 | + | 0.732227i | \(0.738481\pi\) | |||||||
\(660\) | 12.1422 | 0.472633 | ||||||||
\(661\) | 8.79554 | 0.342107 | 0.171054 | − | 0.985262i | \(-0.445283\pi\) | ||||
0.171054 | + | 0.985262i | \(0.445283\pi\) | |||||||
\(662\) | 9.68418 | 0.376386 | ||||||||
\(663\) | 5.52618 | 0.214619 | ||||||||
\(664\) | −2.72604 | −0.105791 | ||||||||
\(665\) | −23.3656 | −0.906081 | ||||||||
\(666\) | −3.39409 | −0.131518 | ||||||||
\(667\) | 7.98112 | 0.309030 | ||||||||
\(668\) | −3.81756 | −0.147706 | ||||||||
\(669\) | 18.5908 | 0.718763 | ||||||||
\(670\) | −11.5983 | −0.448082 | ||||||||
\(671\) | 29.1906 | 1.12689 | ||||||||
\(672\) | 3.30563 | 0.127517 | ||||||||
\(673\) | −36.7564 | −1.41686 | −0.708428 | − | 0.705783i | \(-0.750595\pi\) | ||||
−0.708428 | + | 0.705783i | \(0.750595\pi\) | |||||||
\(674\) | −13.4565 | −0.518325 | ||||||||
\(675\) | −2.65538 | −0.102206 | ||||||||
\(676\) | −6.51908 | −0.250734 | ||||||||
\(677\) | −34.7975 | −1.33738 | −0.668688 | − | 0.743543i | \(-0.733144\pi\) | ||||
−0.668688 | + | 0.743543i | \(0.733144\pi\) | |||||||
\(678\) | 10.9241 | 0.419538 | ||||||||
\(679\) | −25.2906 | −0.970563 | ||||||||
\(680\) | 2.23960 | 0.0858847 | ||||||||
\(681\) | −12.4910 | −0.478657 | ||||||||
\(682\) | −3.20181 | −0.122604 | ||||||||
\(683\) | −15.8912 | −0.608058 | −0.304029 | − | 0.952663i | \(-0.598332\pi\) | ||||
−0.304029 | + | 0.952663i | \(0.598332\pi\) | |||||||
\(684\) | 7.25709 | 0.277482 | ||||||||
\(685\) | 1.81321 | 0.0692791 | ||||||||
\(686\) | 18.5532 | 0.708366 | ||||||||
\(687\) | −12.9347 | −0.493490 | ||||||||
\(688\) | 8.50150 | 0.324117 | ||||||||
\(689\) | −30.4992 | −1.16193 | ||||||||
\(690\) | 7.65840 | 0.291550 | ||||||||
\(691\) | −26.6627 | −1.01430 | −0.507148 | − | 0.861859i | \(-0.669300\pi\) | ||||
−0.507148 | + | 0.861859i | \(0.669300\pi\) | |||||||
\(692\) | 3.33903 | 0.126931 | ||||||||
\(693\) | 5.03870 | 0.191404 | ||||||||
\(694\) | −33.5020 | −1.27172 | ||||||||
\(695\) | 3.46486 | 0.131430 | ||||||||
\(696\) | 8.79346 | 0.333315 | ||||||||
\(697\) | 7.65801 | 0.290068 | ||||||||
\(698\) | 22.2490 | 0.842138 | ||||||||
\(699\) | 32.6723 | 1.23578 | ||||||||
\(700\) | 1.11421 | 0.0421131 | ||||||||
\(701\) | 35.0557 | 1.32404 | 0.662018 | − | 0.749488i | \(-0.269700\pi\) | ||||
0.662018 | + | 0.749488i | \(0.269700\pi\) | |||||||
\(702\) | −9.95426 | −0.375699 | ||||||||
\(703\) | −21.9524 | −0.827949 | ||||||||
\(704\) | −2.89925 | −0.109270 | ||||||||
\(705\) | −6.99792 | −0.263557 | ||||||||
\(706\) | −18.4032 | −0.692614 | ||||||||
\(707\) | 26.8613 | 1.01022 | ||||||||
\(708\) | −0.436421 | −0.0164017 | ||||||||
\(709\) | 33.3012 | 1.25065 | 0.625327 | − | 0.780363i | \(-0.284965\pi\) | ||||
0.625327 | + | 0.780363i | \(0.284965\pi\) | |||||||
\(710\) | −2.43086 | −0.0912285 | ||||||||
\(711\) | −1.98852 | −0.0745755 | ||||||||
\(712\) | 10.9186 | 0.409191 | ||||||||
\(713\) | −2.01947 | −0.0756298 | ||||||||
\(714\) | 3.56153 | 0.133287 | ||||||||
\(715\) | 15.3423 | 0.573770 | ||||||||
\(716\) | 13.2977 | 0.496958 | ||||||||
\(717\) | 10.3062 | 0.384892 | ||||||||
\(718\) | 17.9357 | 0.669355 | ||||||||
\(719\) | 24.7119 | 0.921597 | 0.460799 | − | 0.887505i | \(-0.347563\pi\) | ||||
0.460799 | + | 0.887505i | \(0.347563\pi\) | |||||||
\(720\) | 2.20186 | 0.0820584 | ||||||||
\(721\) | −5.34894 | −0.199205 | ||||||||
\(722\) | 27.9376 | 1.03973 | ||||||||
\(723\) | 37.2056 | 1.38369 | ||||||||
\(724\) | −5.73244 | −0.213044 | ||||||||
\(725\) | 2.96396 | 0.110079 | ||||||||
\(726\) | 5.22701 | 0.193993 | ||||||||
\(727\) | 2.74802 | 0.101919 | 0.0509593 | − | 0.998701i | \(-0.483772\pi\) | ||||
0.0509593 | + | 0.998701i | \(0.483772\pi\) | |||||||
\(728\) | 4.17685 | 0.154804 | ||||||||
\(729\) | 11.9230 | 0.441593 | ||||||||
\(730\) | −27.8795 | −1.03187 | ||||||||
\(731\) | 9.15965 | 0.338782 | ||||||||
\(732\) | 20.2853 | 0.749765 | ||||||||
\(733\) | 22.8128 | 0.842609 | 0.421305 | − | 0.906919i | \(-0.361572\pi\) | ||||
0.421305 | + | 0.906919i | \(0.361572\pi\) | |||||||
\(734\) | −28.2557 | −1.04294 | ||||||||
\(735\) | 18.0424 | 0.665505 | ||||||||
\(736\) | −1.82864 | −0.0674045 | ||||||||
\(737\) | 16.1768 | 0.595880 | ||||||||
\(738\) | 7.52896 | 0.277145 | ||||||||
\(739\) | −48.1180 | −1.77005 | −0.885024 | − | 0.465545i | \(-0.845858\pi\) | ||||
−0.885024 | + | 0.465545i | \(0.845858\pi\) | |||||||
\(740\) | −6.66052 | −0.244846 | ||||||||
\(741\) | 35.1400 | 1.29090 | ||||||||
\(742\) | −19.6563 | −0.721604 | ||||||||
\(743\) | 21.9843 | 0.806525 | 0.403263 | − | 0.915084i | \(-0.367876\pi\) | ||||
0.403263 | + | 0.915084i | \(0.367876\pi\) | |||||||
\(744\) | −2.22502 | −0.0815731 | ||||||||
\(745\) | −12.4842 | −0.457385 | ||||||||
\(746\) | −13.7847 | −0.504693 | ||||||||
\(747\) | −2.88759 | −0.105651 | ||||||||
\(748\) | −3.12370 | −0.114214 | ||||||||
\(749\) | 29.1138 | 1.06380 | ||||||||
\(750\) | 23.7843 | 0.868479 | ||||||||
\(751\) | −13.9298 | −0.508305 | −0.254152 | − | 0.967164i | \(-0.581796\pi\) | ||||
−0.254152 | + | 0.967164i | \(0.581796\pi\) | |||||||
\(752\) | 1.67093 | 0.0609326 | ||||||||
\(753\) | −47.0822 | −1.71577 | ||||||||
\(754\) | 11.1110 | 0.404640 | ||||||||
\(755\) | −19.1697 | −0.697658 | ||||||||
\(756\) | −6.41536 | −0.233325 | ||||||||
\(757\) | −36.7228 | −1.33471 | −0.667357 | − | 0.744738i | \(-0.732574\pi\) | ||||
−0.667357 | + | 0.744738i | \(0.732574\pi\) | |||||||
\(758\) | −1.98047 | −0.0719338 | ||||||||
\(759\) | −10.6816 | −0.387718 | ||||||||
\(760\) | 14.2412 | 0.516583 | ||||||||
\(761\) | −15.8787 | −0.575603 | −0.287801 | − | 0.957690i | \(-0.592924\pi\) | ||||
−0.287801 | + | 0.957690i | \(0.592924\pi\) | |||||||
\(762\) | 41.2121 | 1.49296 | ||||||||
\(763\) | 22.9786 | 0.831880 | ||||||||
\(764\) | −6.52684 | −0.236133 | ||||||||
\(765\) | 2.37232 | 0.0857713 | ||||||||
\(766\) | 1.36202 | 0.0492118 | ||||||||
\(767\) | −0.551443 | −0.0199114 | ||||||||
\(768\) | −2.01476 | −0.0727014 | ||||||||
\(769\) | −16.4751 | −0.594107 | −0.297053 | − | 0.954861i | \(-0.596004\pi\) | ||||
−0.297053 | + | 0.954861i | \(0.596004\pi\) | |||||||
\(770\) | 9.88787 | 0.356334 | ||||||||
\(771\) | 44.9261 | 1.61797 | ||||||||
\(772\) | −0.0138109 | −0.000497064 0 | ||||||||
\(773\) | −42.6855 | −1.53529 | −0.767645 | − | 0.640875i | \(-0.778572\pi\) | ||||
−0.767645 | + | 0.640875i | \(0.778572\pi\) | |||||||
\(774\) | 9.00530 | 0.323689 | ||||||||
\(775\) | −0.749973 | −0.0269398 | ||||||||
\(776\) | 15.4145 | 0.553347 | ||||||||
\(777\) | −10.5919 | −0.379983 | ||||||||
\(778\) | 9.24189 | 0.331338 | ||||||||
\(779\) | 48.6960 | 1.74471 | ||||||||
\(780\) | 10.6618 | 0.381752 | ||||||||
\(781\) | 3.39046 | 0.121320 | ||||||||
\(782\) | −1.97020 | −0.0704544 | ||||||||
\(783\) | −17.0658 | −0.609882 | ||||||||
\(784\) | −4.30809 | −0.153860 | ||||||||
\(785\) | 35.7346 | 1.27542 | ||||||||
\(786\) | 14.4049 | 0.513805 | ||||||||
\(787\) | −36.5012 | −1.30113 | −0.650564 | − | 0.759452i | \(-0.725467\pi\) | ||||
−0.650564 | + | 0.759452i | \(0.725467\pi\) | |||||||
\(788\) | −11.3785 | −0.405343 | ||||||||
\(789\) | 32.5898 | 1.16023 | ||||||||
\(790\) | −3.90225 | −0.138836 | ||||||||
\(791\) | 8.89596 | 0.316304 | ||||||||
\(792\) | −3.07106 | −0.109125 | ||||||||
\(793\) | 25.6316 | 0.910204 | ||||||||
\(794\) | −26.7665 | −0.949906 | ||||||||
\(795\) | −50.1743 | −1.77950 | ||||||||
\(796\) | 22.1964 | 0.786730 | ||||||||
\(797\) | −17.7825 | −0.629888 | −0.314944 | − | 0.949110i | \(-0.601986\pi\) | ||||
−0.314944 | + | 0.949110i | \(0.601986\pi\) | |||||||
\(798\) | 22.6472 | 0.801701 | ||||||||
\(799\) | 1.80029 | 0.0636896 | ||||||||
\(800\) | −0.679103 | −0.0240099 | ||||||||
\(801\) | 11.5656 | 0.408651 | ||||||||
\(802\) | −23.6236 | −0.834179 | ||||||||
\(803\) | 38.8852 | 1.37223 | ||||||||
\(804\) | 11.2417 | 0.396463 | ||||||||
\(805\) | 6.23656 | 0.219810 | ||||||||
\(806\) | −2.81143 | −0.0990286 | ||||||||
\(807\) | 41.6876 | 1.46747 | ||||||||
\(808\) | −16.3718 | −0.575959 | ||||||||
\(809\) | 18.1265 | 0.637293 | 0.318647 | − | 0.947874i | \(-0.396772\pi\) | ||||
0.318647 | + | 0.947874i | \(0.396772\pi\) | |||||||
\(810\) | −22.9813 | −0.807481 | ||||||||
\(811\) | 34.3911 | 1.20763 | 0.603817 | − | 0.797123i | \(-0.293646\pi\) | ||||
0.603817 | + | 0.797123i | \(0.293646\pi\) | |||||||
\(812\) | 7.16088 | 0.251298 | ||||||||
\(813\) | −27.6465 | −0.969604 | ||||||||
\(814\) | 9.28980 | 0.325607 | ||||||||
\(815\) | −0.324442 | −0.0113647 | ||||||||
\(816\) | −2.17073 | −0.0759909 | ||||||||
\(817\) | 58.2446 | 2.03772 | ||||||||
\(818\) | −29.0054 | −1.01415 | ||||||||
\(819\) | 4.42437 | 0.154600 | ||||||||
\(820\) | 14.7747 | 0.515956 | ||||||||
\(821\) | −20.6292 | −0.719965 | −0.359982 | − | 0.932959i | \(-0.617217\pi\) | ||||
−0.359982 | + | 0.932959i | \(0.617217\pi\) | |||||||
\(822\) | −1.75745 | −0.0612983 | ||||||||
\(823\) | 2.44475 | 0.0852188 | 0.0426094 | − | 0.999092i | \(-0.486433\pi\) | ||||
0.0426094 | + | 0.999092i | \(0.486433\pi\) | |||||||
\(824\) | 3.26015 | 0.113573 | ||||||||
\(825\) | −3.96684 | −0.138108 | ||||||||
\(826\) | −0.355396 | −0.0123658 | ||||||||
\(827\) | −45.6089 | −1.58598 | −0.792989 | − | 0.609236i | \(-0.791476\pi\) | ||||
−0.792989 | + | 0.609236i | \(0.791476\pi\) | |||||||
\(828\) | −1.93700 | −0.0673155 | ||||||||
\(829\) | 13.6372 | 0.473638 | 0.236819 | − | 0.971554i | \(-0.423895\pi\) | ||||
0.236819 | + | 0.971554i | \(0.423895\pi\) | |||||||
\(830\) | −5.66656 | −0.196689 | ||||||||
\(831\) | −44.1252 | −1.53069 | ||||||||
\(832\) | −2.54576 | −0.0882585 | ||||||||
\(833\) | −4.64160 | −0.160822 | ||||||||
\(834\) | −3.35832 | −0.116289 | ||||||||
\(835\) | −7.93548 | −0.274618 | ||||||||
\(836\) | −19.8630 | −0.686977 | ||||||||
\(837\) | 4.31818 | 0.149258 | ||||||||
\(838\) | −0.958270 | −0.0331029 | ||||||||
\(839\) | 42.3796 | 1.46311 | 0.731554 | − | 0.681784i | \(-0.238796\pi\) | ||||
0.731554 | + | 0.681784i | \(0.238796\pi\) | |||||||
\(840\) | 6.87133 | 0.237083 | ||||||||
\(841\) | −9.95099 | −0.343138 | ||||||||
\(842\) | 12.3654 | 0.426139 | ||||||||
\(843\) | −37.1335 | −1.27895 | ||||||||
\(844\) | −6.05237 | −0.208331 | ||||||||
\(845\) | −13.5511 | −0.466171 | ||||||||
\(846\) | 1.76995 | 0.0608521 | ||||||||
\(847\) | 4.25658 | 0.146258 | ||||||||
\(848\) | 11.9804 | 0.411408 | ||||||||
\(849\) | −21.3474 | −0.732641 | ||||||||
\(850\) | −0.731676 | −0.0250963 | ||||||||
\(851\) | 5.85935 | 0.200856 | ||||||||
\(852\) | 2.35611 | 0.0807191 | ||||||||
\(853\) | −46.9400 | −1.60719 | −0.803597 | − | 0.595173i | \(-0.797083\pi\) | ||||
−0.803597 | + | 0.595173i | \(0.797083\pi\) | |||||||
\(854\) | 16.5191 | 0.565274 | ||||||||
\(855\) | 15.0851 | 0.515901 | ||||||||
\(856\) | −17.7447 | −0.606501 | ||||||||
\(857\) | −9.40426 | −0.321243 | −0.160622 | − | 0.987016i | \(-0.551350\pi\) | ||||
−0.160622 | + | 0.987016i | \(0.551350\pi\) | |||||||
\(858\) | −14.8705 | −0.507672 | ||||||||
\(859\) | 48.6688 | 1.66056 | 0.830280 | − | 0.557347i | \(-0.188181\pi\) | ||||
0.830280 | + | 0.557347i | \(0.188181\pi\) | |||||||
\(860\) | 17.6719 | 0.602606 | ||||||||
\(861\) | 23.4956 | 0.800728 | ||||||||
\(862\) | 28.1431 | 0.958558 | ||||||||
\(863\) | 2.45019 | 0.0834055 | 0.0417027 | − | 0.999130i | \(-0.486722\pi\) | ||||
0.0417027 | + | 0.999130i | \(0.486722\pi\) | |||||||
\(864\) | 3.91013 | 0.133025 | ||||||||
\(865\) | 6.94076 | 0.235993 | ||||||||
\(866\) | −31.6017 | −1.07387 | ||||||||
\(867\) | 31.9121 | 1.08379 | ||||||||
\(868\) | −1.81193 | −0.0615007 | ||||||||
\(869\) | 5.44269 | 0.184631 | ||||||||
\(870\) | 18.2788 | 0.619708 | ||||||||
\(871\) | 14.2045 | 0.481301 | ||||||||
\(872\) | −14.0053 | −0.474279 | ||||||||
\(873\) | 16.3279 | 0.552616 | ||||||||
\(874\) | −12.5282 | −0.423772 | ||||||||
\(875\) | 19.3686 | 0.654777 | ||||||||
\(876\) | 27.0223 | 0.912999 | ||||||||
\(877\) | 29.3592 | 0.991389 | 0.495694 | − | 0.868497i | \(-0.334914\pi\) | ||||
0.495694 | + | 0.868497i | \(0.334914\pi\) | |||||||
\(878\) | −21.9805 | −0.741807 | ||||||||
\(879\) | 40.0285 | 1.35013 | ||||||||
\(880\) | −6.02660 | −0.203157 | ||||||||
\(881\) | 51.1617 | 1.72368 | 0.861841 | − | 0.507178i | \(-0.169311\pi\) | ||||
0.861841 | + | 0.507178i | \(0.169311\pi\) | |||||||
\(882\) | −4.56338 | −0.153657 | ||||||||
\(883\) | 40.4496 | 1.36124 | 0.680619 | − | 0.732638i | \(-0.261711\pi\) | ||||
0.680619 | + | 0.732638i | \(0.261711\pi\) | |||||||
\(884\) | −2.74285 | −0.0922519 | ||||||||
\(885\) | −0.907178 | −0.0304945 | ||||||||
\(886\) | 1.25281 | 0.0420888 | ||||||||
\(887\) | 1.11177 | 0.0373297 | 0.0186648 | − | 0.999826i | \(-0.494058\pi\) | ||||
0.0186648 | + | 0.999826i | \(0.494058\pi\) | |||||||
\(888\) | 6.45572 | 0.216640 | ||||||||
\(889\) | 33.5608 | 1.12559 | ||||||||
\(890\) | 22.6962 | 0.760778 | ||||||||
\(891\) | 32.0534 | 1.07383 | ||||||||
\(892\) | −9.22732 | −0.308954 | ||||||||
\(893\) | 11.4477 | 0.383083 | ||||||||
\(894\) | 12.1003 | 0.404695 | ||||||||
\(895\) | 27.6416 | 0.923956 | ||||||||
\(896\) | −1.64070 | −0.0548121 | ||||||||
\(897\) | −9.37928 | −0.313165 | ||||||||
\(898\) | 10.9508 | 0.365432 | ||||||||
\(899\) | −4.81999 | −0.160756 | ||||||||
\(900\) | −0.719346 | −0.0239782 | ||||||||
\(901\) | 12.9079 | 0.430023 | ||||||||
\(902\) | −20.6072 | −0.686143 | ||||||||
\(903\) | 28.1028 | 0.935203 | ||||||||
\(904\) | −5.42204 | −0.180334 | ||||||||
\(905\) | −11.9159 | −0.396098 | ||||||||
\(906\) | 18.5803 | 0.617289 | ||||||||
\(907\) | −47.6699 | −1.58285 | −0.791427 | − | 0.611263i | \(-0.790662\pi\) | ||||
−0.791427 | + | 0.611263i | \(0.790662\pi\) | |||||||
\(908\) | 6.19976 | 0.205746 | ||||||||
\(909\) | −17.3420 | −0.575198 | ||||||||
\(910\) | 8.68232 | 0.287816 | ||||||||
\(911\) | 10.2555 | 0.339781 | 0.169891 | − | 0.985463i | \(-0.445659\pi\) | ||||
0.169891 | + | 0.985463i | \(0.445659\pi\) | |||||||
\(912\) | −13.8033 | −0.457074 | ||||||||
\(913\) | 7.90348 | 0.261567 | ||||||||
\(914\) | −23.6447 | −0.782096 | ||||||||
\(915\) | 42.1665 | 1.39398 | ||||||||
\(916\) | 6.41997 | 0.212122 | ||||||||
\(917\) | 11.7305 | 0.387375 | ||||||||
\(918\) | 4.21283 | 0.139044 | ||||||||
\(919\) | −28.0002 | −0.923642 | −0.461821 | − | 0.886973i | \(-0.652804\pi\) | ||||
−0.461821 | + | 0.886973i | \(0.652804\pi\) | |||||||
\(920\) | −3.80115 | −0.125320 | ||||||||
\(921\) | 1.54904 | 0.0510426 | ||||||||
\(922\) | 19.9688 | 0.657638 | ||||||||
\(923\) | 2.97708 | 0.0979919 | ||||||||
\(924\) | −9.58383 | −0.315285 | ||||||||
\(925\) | 2.17599 | 0.0715461 | ||||||||
\(926\) | 11.2357 | 0.369229 | ||||||||
\(927\) | 3.45334 | 0.113423 | ||||||||
\(928\) | −4.36452 | −0.143272 | ||||||||
\(929\) | −5.10335 | −0.167435 | −0.0837177 | − | 0.996490i | \(-0.526679\pi\) | ||||
−0.0837177 | + | 0.996490i | \(0.526679\pi\) | |||||||
\(930\) | −4.62509 | −0.151663 | ||||||||
\(931\) | −29.5151 | −0.967319 | ||||||||
\(932\) | −16.2164 | −0.531187 | ||||||||
\(933\) | −15.9871 | −0.523394 | ||||||||
\(934\) | 25.9897 | 0.850408 | ||||||||
\(935\) | −6.49315 | −0.212349 | ||||||||
\(936\) | −2.69662 | −0.0881419 | ||||||||
\(937\) | 2.82938 | 0.0924317 | 0.0462158 | − | 0.998931i | \(-0.485284\pi\) | ||||
0.0462158 | + | 0.998931i | \(0.485284\pi\) | |||||||
\(938\) | 9.15457 | 0.298907 | ||||||||
\(939\) | −26.6459 | −0.869556 | ||||||||
\(940\) | 3.47332 | 0.113287 | ||||||||
\(941\) | 15.6158 | 0.509060 | 0.254530 | − | 0.967065i | \(-0.418079\pi\) | ||||
0.254530 | + | 0.967065i | \(0.418079\pi\) | |||||||
\(942\) | −34.6358 | −1.12850 | ||||||||
\(943\) | −12.9975 | −0.423258 | ||||||||
\(944\) | 0.216612 | 0.00705011 | ||||||||
\(945\) | −13.3355 | −0.433803 | ||||||||
\(946\) | −24.6480 | −0.801375 | ||||||||
\(947\) | 25.3784 | 0.824687 | 0.412344 | − | 0.911028i | \(-0.364710\pi\) | ||||
0.412344 | + | 0.911028i | \(0.364710\pi\) | |||||||
\(948\) | 3.78227 | 0.122842 | ||||||||
\(949\) | 34.1442 | 1.10837 | ||||||||
\(950\) | −4.65260 | −0.150950 | ||||||||
\(951\) | 26.8380 | 0.870283 | ||||||||
\(952\) | −1.76772 | −0.0572922 | ||||||||
\(953\) | −9.28471 | −0.300761 | −0.150381 | − | 0.988628i | \(-0.548050\pi\) | ||||
−0.150381 | + | 0.988628i | \(0.548050\pi\) | |||||||
\(954\) | 12.6903 | 0.410865 | ||||||||
\(955\) | −13.5672 | −0.439024 | ||||||||
\(956\) | −5.11535 | −0.165442 | ||||||||
\(957\) | −25.4944 | −0.824117 | ||||||||
\(958\) | −16.5809 | −0.535705 | ||||||||
\(959\) | −1.43117 | −0.0462149 | ||||||||
\(960\) | −4.18804 | −0.135168 | ||||||||
\(961\) | −29.7804 | −0.960658 | ||||||||
\(962\) | 8.15717 | 0.262998 | ||||||||
\(963\) | −18.7962 | −0.605700 | ||||||||
\(964\) | −18.4665 | −0.594766 | ||||||||
\(965\) | −0.0287083 | −0.000924154 0 | ||||||||
\(966\) | −6.04480 | −0.194488 | ||||||||
\(967\) | 15.8865 | 0.510875 | 0.255438 | − | 0.966826i | \(-0.417780\pi\) | ||||
0.255438 | + | 0.966826i | \(0.417780\pi\) | |||||||
\(968\) | −2.59436 | −0.0833859 | ||||||||
\(969\) | −14.8719 | −0.477755 | ||||||||
\(970\) | 32.0417 | 1.02880 | ||||||||
\(971\) | −26.6849 | −0.856361 | −0.428180 | − | 0.903693i | \(-0.640845\pi\) | ||||
−0.428180 | + | 0.903693i | \(0.640845\pi\) | |||||||
\(972\) | 10.5443 | 0.338209 | ||||||||
\(973\) | −2.73483 | −0.0876745 | ||||||||
\(974\) | 39.0680 | 1.25182 | ||||||||
\(975\) | −3.48319 | −0.111551 | ||||||||
\(976\) | −10.0683 | −0.322279 | ||||||||
\(977\) | 52.6438 | 1.68422 | 0.842111 | − | 0.539304i | \(-0.181312\pi\) | ||||
0.842111 | + | 0.539304i | \(0.181312\pi\) | |||||||
\(978\) | 0.314465 | 0.0100555 | ||||||||
\(979\) | −31.6557 | −1.01172 | ||||||||
\(980\) | −8.95512 | −0.286061 | ||||||||
\(981\) | −14.8352 | −0.473653 | ||||||||
\(982\) | 16.4517 | 0.524994 | ||||||||
\(983\) | −21.1790 | −0.675504 | −0.337752 | − | 0.941235i | \(-0.609667\pi\) | ||||
−0.337752 | + | 0.941235i | \(0.609667\pi\) | |||||||
\(984\) | −14.3204 | −0.456519 | ||||||||
\(985\) | −23.6523 | −0.753625 | ||||||||
\(986\) | −4.70240 | −0.149755 | ||||||||
\(987\) | 5.52347 | 0.175814 | ||||||||
\(988\) | −17.4413 | −0.554881 | ||||||||
\(989\) | −15.5462 | −0.494340 | ||||||||
\(990\) | −6.38373 | −0.202888 | ||||||||
\(991\) | −25.2156 | −0.800999 | −0.400499 | − | 0.916297i | \(-0.631163\pi\) | ||||
−0.400499 | + | 0.916297i | \(0.631163\pi\) | |||||||
\(992\) | 1.10436 | 0.0350634 | ||||||||
\(993\) | −19.5113 | −0.619172 | ||||||||
\(994\) | 1.91868 | 0.0608569 | ||||||||
\(995\) | 46.1391 | 1.46271 | ||||||||
\(996\) | 5.49233 | 0.174031 | ||||||||
\(997\) | 24.1344 | 0.764343 | 0.382171 | − | 0.924091i | \(-0.375176\pi\) | ||||
0.382171 | + | 0.924091i | \(0.375176\pi\) | |||||||
\(998\) | −21.2789 | −0.673572 | ||||||||
\(999\) | −12.5289 | −0.396396 |
(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 | 8002.2.a.d.1.17 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.17 | ✓ | 69 | 1.1 | even | 1 | trivial |