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 | 1.3 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.77966 | −1.96552 | −0.982759 | − | 0.184891i | \(-0.940807\pi\) | ||||
−0.982759 | + | 0.184891i | \(0.940807\pi\) | |||||||
\(3\) | −1.97929 | −1.14275 | −0.571373 | − | 0.820690i | \(-0.693589\pi\) | ||||
−0.571373 | + | 0.820690i | \(0.693589\pi\) | |||||||
\(4\) | 5.72652 | 2.86326 | ||||||||
\(5\) | −3.34292 | −1.49500 | −0.747499 | − | 0.664263i | \(-0.768745\pi\) | ||||
−0.747499 | + | 0.664263i | \(0.768745\pi\) | |||||||
\(6\) | 5.50177 | 2.24609 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −10.3585 | −3.66227 | ||||||||
\(9\) | 0.917605 | 0.305868 | ||||||||
\(10\) | 9.29218 | 2.93844 | ||||||||
\(11\) | −6.19168 | −1.86686 | −0.933431 | − | 0.358756i | \(-0.883201\pi\) | ||||
−0.933431 | + | 0.358756i | \(0.883201\pi\) | |||||||
\(12\) | −11.3345 | −3.27198 | ||||||||
\(13\) | −4.77059 | −1.32312 | −0.661562 | − | 0.749890i | \(-0.730106\pi\) | ||||
−0.661562 | + | 0.749890i | \(0.730106\pi\) | |||||||
\(14\) | −2.77966 | −0.742896 | ||||||||
\(15\) | 6.61661 | 1.70840 | ||||||||
\(16\) | 17.3400 | 4.33500 | ||||||||
\(17\) | 6.95085 | 1.68583 | 0.842915 | − | 0.538047i | \(-0.180838\pi\) | ||||
0.842915 | + | 0.538047i | \(0.180838\pi\) | |||||||
\(18\) | −2.55063 | −0.601190 | ||||||||
\(19\) | 5.45695 | 1.25191 | 0.625955 | − | 0.779859i | \(-0.284709\pi\) | ||||
0.625955 | + | 0.779859i | \(0.284709\pi\) | |||||||
\(20\) | −19.1433 | −4.28057 | ||||||||
\(21\) | −1.97929 | −0.431917 | ||||||||
\(22\) | 17.2108 | 3.66935 | ||||||||
\(23\) | −5.40623 | −1.12728 | −0.563639 | − | 0.826022i | \(-0.690599\pi\) | ||||
−0.563639 | + | 0.826022i | \(0.690599\pi\) | |||||||
\(24\) | 20.5025 | 4.18505 | ||||||||
\(25\) | 6.17509 | 1.23502 | ||||||||
\(26\) | 13.2606 | 2.60063 | ||||||||
\(27\) | 4.12167 | 0.793216 | ||||||||
\(28\) | 5.72652 | 1.08221 | ||||||||
\(29\) | 1.50514 | 0.279498 | 0.139749 | − | 0.990187i | \(-0.455370\pi\) | ||||
0.139749 | + | 0.990187i | \(0.455370\pi\) | |||||||
\(30\) | −18.3920 | −3.35790 | ||||||||
\(31\) | 6.57683 | 1.18123 | 0.590617 | − | 0.806952i | \(-0.298885\pi\) | ||||
0.590617 | + | 0.806952i | \(0.298885\pi\) | |||||||
\(32\) | −27.4824 | −4.85825 | ||||||||
\(33\) | 12.2552 | 2.13335 | ||||||||
\(34\) | −19.3210 | −3.31353 | ||||||||
\(35\) | −3.34292 | −0.565056 | ||||||||
\(36\) | 5.25469 | 0.875781 | ||||||||
\(37\) | 2.34769 | 0.385958 | 0.192979 | − | 0.981203i | \(-0.438185\pi\) | ||||
0.192979 | + | 0.981203i | \(0.438185\pi\) | |||||||
\(38\) | −15.1685 | −2.46065 | ||||||||
\(39\) | 9.44241 | 1.51200 | ||||||||
\(40\) | 34.6275 | 5.47509 | ||||||||
\(41\) | 3.44238 | 0.537609 | 0.268804 | − | 0.963195i | \(-0.413371\pi\) | ||||
0.268804 | + | 0.963195i | \(0.413371\pi\) | |||||||
\(42\) | 5.50177 | 0.848941 | ||||||||
\(43\) | −10.2289 | −1.55989 | −0.779945 | − | 0.625848i | \(-0.784753\pi\) | ||||
−0.779945 | + | 0.625848i | \(0.784753\pi\) | |||||||
\(44\) | −35.4568 | −5.34531 | ||||||||
\(45\) | −3.06748 | −0.457273 | ||||||||
\(46\) | 15.0275 | 2.21568 | ||||||||
\(47\) | 4.97411 | 0.725548 | 0.362774 | − | 0.931877i | \(-0.381830\pi\) | ||||
0.362774 | + | 0.931877i | \(0.381830\pi\) | |||||||
\(48\) | −34.3210 | −4.95381 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −17.1647 | −2.42745 | ||||||||
\(51\) | −13.7578 | −1.92648 | ||||||||
\(52\) | −27.3189 | −3.78845 | ||||||||
\(53\) | −0.487931 | −0.0670224 | −0.0335112 | − | 0.999438i | \(-0.510669\pi\) | ||||
−0.0335112 | + | 0.999438i | \(0.510669\pi\) | |||||||
\(54\) | −11.4569 | −1.55908 | ||||||||
\(55\) | 20.6983 | 2.79095 | ||||||||
\(56\) | −10.3585 | −1.38421 | ||||||||
\(57\) | −10.8009 | −1.43062 | ||||||||
\(58\) | −4.18379 | −0.549359 | ||||||||
\(59\) | −1.04347 | −0.135848 | −0.0679241 | − | 0.997690i | \(-0.521638\pi\) | ||||
−0.0679241 | + | 0.997690i | \(0.521638\pi\) | |||||||
\(60\) | 37.8902 | 4.89160 | ||||||||
\(61\) | −11.8056 | −1.51156 | −0.755778 | − | 0.654828i | \(-0.772741\pi\) | ||||
−0.755778 | + | 0.654828i | \(0.772741\pi\) | |||||||
\(62\) | −18.2814 | −2.32174 | ||||||||
\(63\) | 0.917605 | 0.115607 | ||||||||
\(64\) | 41.7118 | 5.21398 | ||||||||
\(65\) | 15.9477 | 1.97807 | ||||||||
\(66\) | −34.0652 | −4.19314 | ||||||||
\(67\) | −7.29417 | −0.891125 | −0.445563 | − | 0.895251i | \(-0.646996\pi\) | ||||
−0.445563 | + | 0.895251i | \(0.646996\pi\) | |||||||
\(68\) | 39.8042 | 4.82697 | ||||||||
\(69\) | 10.7005 | 1.28819 | ||||||||
\(70\) | 9.29218 | 1.11063 | ||||||||
\(71\) | −0.563675 | −0.0668959 | −0.0334479 | − | 0.999440i | \(-0.510649\pi\) | ||||
−0.0334479 | + | 0.999440i | \(0.510649\pi\) | |||||||
\(72\) | −9.50499 | −1.12017 | ||||||||
\(73\) | −13.1235 | −1.53599 | −0.767996 | − | 0.640455i | \(-0.778746\pi\) | ||||
−0.767996 | + | 0.640455i | \(0.778746\pi\) | |||||||
\(74\) | −6.52579 | −0.758607 | ||||||||
\(75\) | −12.2223 | −1.41131 | ||||||||
\(76\) | 31.2494 | 3.58455 | ||||||||
\(77\) | −6.19168 | −0.705608 | ||||||||
\(78\) | −26.2467 | −2.97185 | ||||||||
\(79\) | 2.20459 | 0.248036 | 0.124018 | − | 0.992280i | \(-0.460422\pi\) | ||||
0.124018 | + | 0.992280i | \(0.460422\pi\) | |||||||
\(80\) | −57.9662 | −6.48082 | ||||||||
\(81\) | −10.9108 | −1.21231 | ||||||||
\(82\) | −9.56864 | −1.05668 | ||||||||
\(83\) | −16.2511 | −1.78379 | −0.891894 | − | 0.452244i | \(-0.850623\pi\) | ||||
−0.891894 | + | 0.452244i | \(0.850623\pi\) | |||||||
\(84\) | −11.3345 | −1.23669 | ||||||||
\(85\) | −23.2361 | −2.52031 | ||||||||
\(86\) | 28.4328 | 3.06599 | ||||||||
\(87\) | −2.97912 | −0.319396 | ||||||||
\(88\) | 64.1364 | 6.83696 | ||||||||
\(89\) | 1.00906 | 0.106960 | 0.0534800 | − | 0.998569i | \(-0.482969\pi\) | ||||
0.0534800 | + | 0.998569i | \(0.482969\pi\) | |||||||
\(90\) | 8.52655 | 0.898777 | ||||||||
\(91\) | −4.77059 | −0.500094 | ||||||||
\(92\) | −30.9589 | −3.22769 | ||||||||
\(93\) | −13.0175 | −1.34985 | ||||||||
\(94\) | −13.8263 | −1.42608 | ||||||||
\(95\) | −18.2421 | −1.87160 | ||||||||
\(96\) | 54.3958 | 5.55175 | ||||||||
\(97\) | −3.71356 | −0.377055 | −0.188527 | − | 0.982068i | \(-0.560371\pi\) | ||||
−0.188527 | + | 0.982068i | \(0.560371\pi\) | |||||||
\(98\) | −2.77966 | −0.280788 | ||||||||
\(99\) | −5.68152 | −0.571014 | ||||||||
\(100\) | 35.3618 | 3.53618 | ||||||||
\(101\) | −12.4218 | −1.23602 | −0.618009 | − | 0.786171i | \(-0.712060\pi\) | ||||
−0.618009 | + | 0.786171i | \(0.712060\pi\) | |||||||
\(102\) | 38.2420 | 3.78652 | ||||||||
\(103\) | 15.1733 | 1.49507 | 0.747534 | − | 0.664224i | \(-0.231238\pi\) | ||||
0.747534 | + | 0.664224i | \(0.231238\pi\) | |||||||
\(104\) | 49.4161 | 4.84564 | ||||||||
\(105\) | 6.61661 | 0.645715 | ||||||||
\(106\) | 1.35628 | 0.131734 | ||||||||
\(107\) | 3.95507 | 0.382351 | 0.191176 | − | 0.981556i | \(-0.438770\pi\) | ||||
0.191176 | + | 0.981556i | \(0.438770\pi\) | |||||||
\(108\) | 23.6028 | 2.27118 | ||||||||
\(109\) | 0.553679 | 0.0530328 | 0.0265164 | − | 0.999648i | \(-0.491559\pi\) | ||||
0.0265164 | + | 0.999648i | \(0.491559\pi\) | |||||||
\(110\) | −57.5342 | −5.48567 | ||||||||
\(111\) | −4.64677 | −0.441052 | ||||||||
\(112\) | 17.3400 | 1.63848 | ||||||||
\(113\) | −3.96232 | −0.372744 | −0.186372 | − | 0.982479i | \(-0.559673\pi\) | ||||
−0.186372 | + | 0.982479i | \(0.559673\pi\) | |||||||
\(114\) | 30.0229 | 2.81190 | ||||||||
\(115\) | 18.0726 | 1.68528 | ||||||||
\(116\) | 8.61924 | 0.800277 | ||||||||
\(117\) | −4.37752 | −0.404702 | ||||||||
\(118\) | 2.90049 | 0.267012 | ||||||||
\(119\) | 6.95085 | 0.637184 | ||||||||
\(120\) | −68.5380 | −6.25663 | ||||||||
\(121\) | 27.3369 | 2.48518 | ||||||||
\(122\) | 32.8157 | 2.97099 | ||||||||
\(123\) | −6.81347 | −0.614350 | ||||||||
\(124\) | 37.6623 | 3.38218 | ||||||||
\(125\) | −3.92822 | −0.351351 | ||||||||
\(126\) | −2.55063 | −0.227228 | ||||||||
\(127\) | −4.95798 | −0.439949 | −0.219975 | − | 0.975506i | \(-0.570597\pi\) | ||||
−0.219975 | + | 0.975506i | \(0.570597\pi\) | |||||||
\(128\) | −60.9799 | −5.38991 | ||||||||
\(129\) | 20.2460 | 1.78256 | ||||||||
\(130\) | −44.3292 | −3.88793 | ||||||||
\(131\) | 9.81299 | 0.857365 | 0.428682 | − | 0.903455i | \(-0.358978\pi\) | ||||
0.428682 | + | 0.903455i | \(0.358978\pi\) | |||||||
\(132\) | 70.1794 | 6.10834 | ||||||||
\(133\) | 5.45695 | 0.473178 | ||||||||
\(134\) | 20.2753 | 1.75152 | ||||||||
\(135\) | −13.7784 | −1.18586 | ||||||||
\(136\) | −72.0002 | −6.17397 | ||||||||
\(137\) | 6.21435 | 0.530928 | 0.265464 | − | 0.964121i | \(-0.414475\pi\) | ||||
0.265464 | + | 0.964121i | \(0.414475\pi\) | |||||||
\(138\) | −29.7438 | −2.53196 | ||||||||
\(139\) | −19.0566 | −1.61636 | −0.808179 | − | 0.588937i | \(-0.799547\pi\) | ||||
−0.808179 | + | 0.588937i | \(0.799547\pi\) | |||||||
\(140\) | −19.1433 | −1.61790 | ||||||||
\(141\) | −9.84523 | −0.829118 | ||||||||
\(142\) | 1.56682 | 0.131485 | ||||||||
\(143\) | 29.5380 | 2.47009 | ||||||||
\(144\) | 15.9113 | 1.32594 | ||||||||
\(145\) | −5.03157 | −0.417849 | ||||||||
\(146\) | 36.4790 | 3.01902 | ||||||||
\(147\) | −1.97929 | −0.163249 | ||||||||
\(148\) | 13.4441 | 1.10510 | ||||||||
\(149\) | −18.1028 | −1.48304 | −0.741521 | − | 0.670930i | \(-0.765895\pi\) | ||||
−0.741521 | + | 0.670930i | \(0.765895\pi\) | |||||||
\(150\) | 33.9739 | 2.77396 | ||||||||
\(151\) | −6.79550 | −0.553010 | −0.276505 | − | 0.961012i | \(-0.589176\pi\) | ||||
−0.276505 | + | 0.961012i | \(0.589176\pi\) | |||||||
\(152\) | −56.5257 | −4.58484 | ||||||||
\(153\) | 6.37814 | 0.515642 | ||||||||
\(154\) | 17.2108 | 1.38688 | ||||||||
\(155\) | −21.9858 | −1.76594 | ||||||||
\(156\) | 54.0722 | 4.32924 | ||||||||
\(157\) | −7.64318 | −0.609992 | −0.304996 | − | 0.952354i | \(-0.598655\pi\) | ||||
−0.304996 | + | 0.952354i | \(0.598655\pi\) | |||||||
\(158\) | −6.12802 | −0.487519 | ||||||||
\(159\) | 0.965759 | 0.0765896 | ||||||||
\(160\) | 91.8714 | 7.26307 | ||||||||
\(161\) | −5.40623 | −0.426071 | ||||||||
\(162\) | 30.3284 | 2.38282 | ||||||||
\(163\) | 20.1932 | 1.58165 | 0.790826 | − | 0.612042i | \(-0.209651\pi\) | ||||
0.790826 | + | 0.612042i | \(0.209651\pi\) | |||||||
\(164\) | 19.7128 | 1.53931 | ||||||||
\(165\) | −40.9680 | −3.18935 | ||||||||
\(166\) | 45.1725 | 3.50607 | ||||||||
\(167\) | −16.7923 | −1.29943 | −0.649715 | − | 0.760178i | \(-0.725112\pi\) | ||||
−0.649715 | + | 0.760178i | \(0.725112\pi\) | |||||||
\(168\) | 20.5025 | 1.58180 | ||||||||
\(169\) | 9.75857 | 0.750659 | ||||||||
\(170\) | 64.5886 | 4.95372 | ||||||||
\(171\) | 5.00733 | 0.382920 | ||||||||
\(172\) | −58.5759 | −4.46637 | ||||||||
\(173\) | −8.99218 | −0.683663 | −0.341831 | − | 0.939761i | \(-0.611047\pi\) | ||||
−0.341831 | + | 0.939761i | \(0.611047\pi\) | |||||||
\(174\) | 8.28096 | 0.627778 | ||||||||
\(175\) | 6.17509 | 0.466793 | ||||||||
\(176\) | −107.364 | −8.09285 | ||||||||
\(177\) | 2.06533 | 0.155240 | ||||||||
\(178\) | −2.80484 | −0.210232 | ||||||||
\(179\) | 10.2297 | 0.764607 | 0.382303 | − | 0.924037i | \(-0.375131\pi\) | ||||
0.382303 | + | 0.924037i | \(0.375131\pi\) | |||||||
\(180\) | −17.5660 | −1.30929 | ||||||||
\(181\) | 18.1511 | 1.34916 | 0.674581 | − | 0.738201i | \(-0.264324\pi\) | ||||
0.674581 | + | 0.738201i | \(0.264324\pi\) | |||||||
\(182\) | 13.2606 | 0.982944 | ||||||||
\(183\) | 23.3668 | 1.72733 | ||||||||
\(184\) | 56.0003 | 4.12840 | ||||||||
\(185\) | −7.84813 | −0.577006 | ||||||||
\(186\) | 36.1842 | 2.65315 | ||||||||
\(187\) | −43.0375 | −3.14721 | ||||||||
\(188\) | 28.4843 | 2.07743 | ||||||||
\(189\) | 4.12167 | 0.299807 | ||||||||
\(190\) | 50.7070 | 3.67867 | ||||||||
\(191\) | −13.9354 | −1.00833 | −0.504165 | − | 0.863607i | \(-0.668200\pi\) | ||||
−0.504165 | + | 0.863607i | \(0.668200\pi\) | |||||||
\(192\) | −82.5599 | −5.95825 | ||||||||
\(193\) | −15.9732 | −1.14978 | −0.574890 | − | 0.818231i | \(-0.694955\pi\) | ||||
−0.574890 | + | 0.818231i | \(0.694955\pi\) | |||||||
\(194\) | 10.3224 | 0.741108 | ||||||||
\(195\) | −31.5652 | −2.26043 | ||||||||
\(196\) | 5.72652 | 0.409037 | ||||||||
\(197\) | −1.76439 | −0.125708 | −0.0628539 | − | 0.998023i | \(-0.520020\pi\) | ||||
−0.0628539 | + | 0.998023i | \(0.520020\pi\) | |||||||
\(198\) | 15.7927 | 1.12234 | ||||||||
\(199\) | 1.77239 | 0.125641 | 0.0628207 | − | 0.998025i | \(-0.479990\pi\) | ||||
0.0628207 | + | 0.998025i | \(0.479990\pi\) | |||||||
\(200\) | −63.9645 | −4.52297 | ||||||||
\(201\) | 14.4373 | 1.01833 | ||||||||
\(202\) | 34.5285 | 2.42941 | ||||||||
\(203\) | 1.50514 | 0.105640 | ||||||||
\(204\) | −78.7842 | −5.51600 | ||||||||
\(205\) | −11.5076 | −0.803724 | ||||||||
\(206\) | −42.1766 | −2.93858 | ||||||||
\(207\) | −4.96079 | −0.344798 | ||||||||
\(208\) | −82.7221 | −5.73575 | ||||||||
\(209\) | −33.7877 | −2.33715 | ||||||||
\(210\) | −18.3920 | −1.26917 | ||||||||
\(211\) | 5.21318 | 0.358890 | 0.179445 | − | 0.983768i | \(-0.442570\pi\) | ||||
0.179445 | + | 0.983768i | \(0.442570\pi\) | |||||||
\(212\) | −2.79415 | −0.191903 | ||||||||
\(213\) | 1.11568 | 0.0764450 | ||||||||
\(214\) | −10.9938 | −0.751518 | ||||||||
\(215\) | 34.1943 | 2.33203 | ||||||||
\(216\) | −42.6942 | −2.90497 | ||||||||
\(217\) | 6.57683 | 0.446464 | ||||||||
\(218\) | −1.53904 | −0.104237 | ||||||||
\(219\) | 25.9753 | 1.75525 | ||||||||
\(220\) | 118.529 | 7.99123 | ||||||||
\(221\) | −33.1597 | −2.23056 | ||||||||
\(222\) | 12.9165 | 0.866895 | ||||||||
\(223\) | −28.4440 | −1.90475 | −0.952376 | − | 0.304926i | \(-0.901368\pi\) | ||||
−0.952376 | + | 0.304926i | \(0.901368\pi\) | |||||||
\(224\) | −27.4824 | −1.83625 | ||||||||
\(225\) | 5.66629 | 0.377753 | ||||||||
\(226\) | 11.0139 | 0.732635 | ||||||||
\(227\) | −25.5923 | −1.69862 | −0.849312 | − | 0.527892i | \(-0.822983\pi\) | ||||
−0.849312 | + | 0.527892i | \(0.822983\pi\) | |||||||
\(228\) | −61.8517 | −4.09623 | ||||||||
\(229\) | −6.29749 | −0.416150 | −0.208075 | − | 0.978113i | \(-0.566720\pi\) | ||||
−0.208075 | + | 0.978113i | \(0.566720\pi\) | |||||||
\(230\) | −50.2357 | −3.31244 | ||||||||
\(231\) | 12.2552 | 0.806330 | ||||||||
\(232\) | −15.5910 | −1.02360 | ||||||||
\(233\) | 8.65776 | 0.567188 | 0.283594 | − | 0.958944i | \(-0.408473\pi\) | ||||
0.283594 | + | 0.958944i | \(0.408473\pi\) | |||||||
\(234\) | 12.1680 | 0.795449 | ||||||||
\(235\) | −16.6280 | −1.08469 | ||||||||
\(236\) | −5.97545 | −0.388969 | ||||||||
\(237\) | −4.36353 | −0.283442 | ||||||||
\(238\) | −19.3210 | −1.25240 | ||||||||
\(239\) | 13.7734 | 0.890927 | 0.445463 | − | 0.895300i | \(-0.353039\pi\) | ||||
0.445463 | + | 0.895300i | \(0.353039\pi\) | |||||||
\(240\) | 114.732 | 7.40593 | ||||||||
\(241\) | −26.0178 | −1.67595 | −0.837977 | − | 0.545705i | \(-0.816262\pi\) | ||||
−0.837977 | + | 0.545705i | \(0.816262\pi\) | |||||||
\(242\) | −75.9874 | −4.88466 | ||||||||
\(243\) | 9.23070 | 0.592150 | ||||||||
\(244\) | −67.6052 | −4.32798 | ||||||||
\(245\) | −3.34292 | −0.213571 | ||||||||
\(246\) | 18.9392 | 1.20752 | ||||||||
\(247\) | −26.0329 | −1.65643 | ||||||||
\(248\) | −68.1259 | −4.32600 | ||||||||
\(249\) | 32.1657 | 2.03842 | ||||||||
\(250\) | 10.9191 | 0.690586 | ||||||||
\(251\) | −24.2358 | −1.52975 | −0.764877 | − | 0.644177i | \(-0.777200\pi\) | ||||
−0.764877 | + | 0.644177i | \(0.777200\pi\) | |||||||
\(252\) | 5.25469 | 0.331014 | ||||||||
\(253\) | 33.4737 | 2.10447 | ||||||||
\(254\) | 13.7815 | 0.864728 | ||||||||
\(255\) | 45.9911 | 2.88008 | ||||||||
\(256\) | 86.0799 | 5.38000 | ||||||||
\(257\) | 9.51267 | 0.593384 | 0.296692 | − | 0.954973i | \(-0.404117\pi\) | ||||
0.296692 | + | 0.954973i | \(0.404117\pi\) | |||||||
\(258\) | −56.2769 | −3.50365 | ||||||||
\(259\) | 2.34769 | 0.145878 | ||||||||
\(260\) | 91.3248 | 5.66372 | ||||||||
\(261\) | 1.38113 | 0.0854897 | ||||||||
\(262\) | −27.2768 | −1.68517 | ||||||||
\(263\) | 24.7176 | 1.52415 | 0.762076 | − | 0.647488i | \(-0.224180\pi\) | ||||
0.762076 | + | 0.647488i | \(0.224180\pi\) | |||||||
\(264\) | −126.945 | −7.81291 | ||||||||
\(265\) | 1.63111 | 0.100198 | ||||||||
\(266\) | −15.1685 | −0.930039 | ||||||||
\(267\) | −1.99722 | −0.122228 | ||||||||
\(268\) | −41.7702 | −2.55152 | ||||||||
\(269\) | 31.5595 | 1.92422 | 0.962110 | − | 0.272663i | \(-0.0879044\pi\) | ||||
0.962110 | + | 0.272663i | \(0.0879044\pi\) | |||||||
\(270\) | 38.2993 | 2.33082 | ||||||||
\(271\) | −15.9783 | −0.970610 | −0.485305 | − | 0.874345i | \(-0.661292\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661292\pi\) | |||||||
\(272\) | 120.528 | 7.30807 | ||||||||
\(273\) | 9.44241 | 0.571481 | ||||||||
\(274\) | −17.2738 | −1.04355 | ||||||||
\(275\) | −38.2342 | −2.30561 | ||||||||
\(276\) | 61.2768 | 3.68843 | ||||||||
\(277\) | −8.23691 | −0.494908 | −0.247454 | − | 0.968900i | \(-0.579594\pi\) | ||||
−0.247454 | + | 0.968900i | \(0.579594\pi\) | |||||||
\(278\) | 52.9708 | 3.17698 | ||||||||
\(279\) | 6.03493 | 0.361302 | ||||||||
\(280\) | 34.6275 | 2.06939 | ||||||||
\(281\) | 10.1158 | 0.603456 | 0.301728 | − | 0.953394i | \(-0.402437\pi\) | ||||
0.301728 | + | 0.953394i | \(0.402437\pi\) | |||||||
\(282\) | 27.3664 | 1.62965 | ||||||||
\(283\) | 7.96966 | 0.473747 | 0.236873 | − | 0.971541i | \(-0.423877\pi\) | ||||
0.236873 | + | 0.971541i | \(0.423877\pi\) | |||||||
\(284\) | −3.22789 | −0.191540 | ||||||||
\(285\) | 36.1065 | 2.13877 | ||||||||
\(286\) | −82.1057 | −4.85501 | ||||||||
\(287\) | 3.44238 | 0.203197 | ||||||||
\(288\) | −25.2180 | −1.48599 | ||||||||
\(289\) | 31.3144 | 1.84202 | ||||||||
\(290\) | 13.9861 | 0.821290 | ||||||||
\(291\) | 7.35023 | 0.430878 | ||||||||
\(292\) | −75.1521 | −4.39795 | ||||||||
\(293\) | 5.84491 | 0.341464 | 0.170732 | − | 0.985318i | \(-0.445387\pi\) | ||||
0.170732 | + | 0.985318i | \(0.445387\pi\) | |||||||
\(294\) | 5.50177 | 0.320870 | ||||||||
\(295\) | 3.48823 | 0.203093 | ||||||||
\(296\) | −24.3185 | −1.41348 | ||||||||
\(297\) | −25.5201 | −1.48083 | ||||||||
\(298\) | 50.3197 | 2.91494 | ||||||||
\(299\) | 25.7909 | 1.49153 | ||||||||
\(300\) | −69.9913 | −4.04095 | ||||||||
\(301\) | −10.2289 | −0.589583 | ||||||||
\(302\) | 18.8892 | 1.08695 | ||||||||
\(303\) | 24.5864 | 1.41245 | ||||||||
\(304\) | 94.6236 | 5.42703 | ||||||||
\(305\) | 39.4652 | 2.25977 | ||||||||
\(306\) | −17.7291 | −1.01350 | ||||||||
\(307\) | 4.74578 | 0.270856 | 0.135428 | − | 0.990787i | \(-0.456759\pi\) | ||||
0.135428 | + | 0.990787i | \(0.456759\pi\) | |||||||
\(308\) | −35.4568 | −2.02034 | ||||||||
\(309\) | −30.0324 | −1.70848 | ||||||||
\(310\) | 61.1131 | 3.47099 | ||||||||
\(311\) | 27.0039 | 1.53125 | 0.765626 | − | 0.643285i | \(-0.222429\pi\) | ||||
0.765626 | + | 0.643285i | \(0.222429\pi\) | |||||||
\(312\) | −97.8089 | −5.53734 | ||||||||
\(313\) | −4.28084 | −0.241967 | −0.120984 | − | 0.992654i | \(-0.538605\pi\) | ||||
−0.120984 | + | 0.992654i | \(0.538605\pi\) | |||||||
\(314\) | 21.2455 | 1.19895 | ||||||||
\(315\) | −3.06748 | −0.172833 | ||||||||
\(316\) | 12.6246 | 0.710191 | ||||||||
\(317\) | −17.1471 | −0.963078 | −0.481539 | − | 0.876425i | \(-0.659922\pi\) | ||||
−0.481539 | + | 0.876425i | \(0.659922\pi\) | |||||||
\(318\) | −2.68448 | −0.150538 | ||||||||
\(319\) | −9.31938 | −0.521785 | ||||||||
\(320\) | −139.439 | −7.79488 | ||||||||
\(321\) | −7.82825 | −0.436931 | ||||||||
\(322\) | 15.0275 | 0.837450 | ||||||||
\(323\) | 37.9305 | 2.11051 | ||||||||
\(324\) | −62.4810 | −3.47117 | ||||||||
\(325\) | −29.4588 | −1.63408 | ||||||||
\(326\) | −56.1302 | −3.10876 | ||||||||
\(327\) | −1.09589 | −0.0606030 | ||||||||
\(328\) | −35.6578 | −1.96887 | ||||||||
\(329\) | 4.97411 | 0.274232 | ||||||||
\(330\) | 113.877 | 6.26873 | ||||||||
\(331\) | −4.46118 | −0.245209 | −0.122604 | − | 0.992456i | \(-0.539125\pi\) | ||||
−0.122604 | + | 0.992456i | \(0.539125\pi\) | |||||||
\(332\) | −93.0622 | −5.10745 | ||||||||
\(333\) | 2.15425 | 0.118052 | ||||||||
\(334\) | 46.6770 | 2.55405 | ||||||||
\(335\) | 24.3838 | 1.33223 | ||||||||
\(336\) | −34.3210 | −1.87236 | ||||||||
\(337\) | −4.95466 | −0.269898 | −0.134949 | − | 0.990853i | \(-0.543087\pi\) | ||||
−0.134949 | + | 0.990853i | \(0.543087\pi\) | |||||||
\(338\) | −27.1255 | −1.47543 | ||||||||
\(339\) | 7.84260 | 0.425952 | ||||||||
\(340\) | −133.062 | −7.21631 | ||||||||
\(341\) | −40.7216 | −2.20520 | ||||||||
\(342\) | −13.9187 | −0.752636 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 105.956 | 5.71274 | ||||||||
\(345\) | −35.7709 | −1.92584 | ||||||||
\(346\) | 24.9952 | 1.34375 | ||||||||
\(347\) | −5.88572 | −0.315962 | −0.157981 | − | 0.987442i | \(-0.550498\pi\) | ||||
−0.157981 | + | 0.987442i | \(0.550498\pi\) | |||||||
\(348\) | −17.0600 | −0.914513 | ||||||||
\(349\) | 4.55226 | 0.243677 | 0.121838 | − | 0.992550i | \(-0.461121\pi\) | ||||
0.121838 | + | 0.992550i | \(0.461121\pi\) | |||||||
\(350\) | −17.1647 | −0.917489 | ||||||||
\(351\) | −19.6628 | −1.04952 | ||||||||
\(352\) | 170.162 | 9.06968 | ||||||||
\(353\) | −21.2818 | −1.13272 | −0.566359 | − | 0.824159i | \(-0.691648\pi\) | ||||
−0.566359 | + | 0.824159i | \(0.691648\pi\) | |||||||
\(354\) | −5.74093 | −0.305127 | ||||||||
\(355\) | 1.88432 | 0.100009 | ||||||||
\(356\) | 5.77840 | 0.306255 | ||||||||
\(357\) | −13.7578 | −0.728139 | ||||||||
\(358\) | −28.4352 | −1.50285 | ||||||||
\(359\) | 15.0025 | 0.791800 | 0.395900 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395900 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(360\) | 31.7744 | 1.67466 | ||||||||
\(361\) | 10.7783 | 0.567281 | ||||||||
\(362\) | −50.4540 | −2.65180 | ||||||||
\(363\) | −54.1078 | −2.83992 | ||||||||
\(364\) | −27.3189 | −1.43190 | ||||||||
\(365\) | 43.8708 | 2.29630 | ||||||||
\(366\) | −64.9519 | −3.39509 | ||||||||
\(367\) | −12.3509 | −0.644714 | −0.322357 | − | 0.946618i | \(-0.604475\pi\) | ||||
−0.322357 | + | 0.946618i | \(0.604475\pi\) | |||||||
\(368\) | −93.7441 | −4.88675 | ||||||||
\(369\) | 3.15874 | 0.164438 | ||||||||
\(370\) | 21.8152 | 1.13412 | ||||||||
\(371\) | −0.487931 | −0.0253321 | ||||||||
\(372\) | −74.5449 | −3.86497 | ||||||||
\(373\) | 12.0320 | 0.622991 | 0.311496 | − | 0.950248i | \(-0.399170\pi\) | ||||
0.311496 | + | 0.950248i | \(0.399170\pi\) | |||||||
\(374\) | 119.630 | 6.18590 | ||||||||
\(375\) | 7.77510 | 0.401504 | ||||||||
\(376\) | −51.5242 | −2.65716 | ||||||||
\(377\) | −7.18043 | −0.369811 | ||||||||
\(378\) | −11.4569 | −0.589277 | ||||||||
\(379\) | −0.172165 | −0.00884354 | −0.00442177 | − | 0.999990i | \(-0.501407\pi\) | ||||
−0.00442177 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(380\) | −104.464 | −5.35889 | ||||||||
\(381\) | 9.81330 | 0.502750 | ||||||||
\(382\) | 38.7357 | 1.98189 | ||||||||
\(383\) | 2.84338 | 0.145290 | 0.0726450 | − | 0.997358i | \(-0.476856\pi\) | ||||
0.0726450 | + | 0.997358i | \(0.476856\pi\) | |||||||
\(384\) | 120.697 | 6.15930 | ||||||||
\(385\) | 20.6983 | 1.05488 | ||||||||
\(386\) | 44.4002 | 2.25991 | ||||||||
\(387\) | −9.38608 | −0.477121 | ||||||||
\(388\) | −21.2658 | −1.07961 | ||||||||
\(389\) | −30.1133 | −1.52681 | −0.763403 | − | 0.645923i | \(-0.776473\pi\) | ||||
−0.763403 | + | 0.645923i | \(0.776473\pi\) | |||||||
\(390\) | 87.7405 | 4.44291 | ||||||||
\(391\) | −37.5779 | −1.90040 | ||||||||
\(392\) | −10.3585 | −0.523182 | ||||||||
\(393\) | −19.4228 | −0.979750 | ||||||||
\(394\) | 4.90441 | 0.247081 | ||||||||
\(395\) | −7.36976 | −0.370813 | ||||||||
\(396\) | −32.5353 | −1.63496 | ||||||||
\(397\) | −21.5186 | −1.07999 | −0.539995 | − | 0.841668i | \(-0.681574\pi\) | ||||
−0.539995 | + | 0.841668i | \(0.681574\pi\) | |||||||
\(398\) | −4.92665 | −0.246951 | ||||||||
\(399\) | −10.8009 | −0.540722 | ||||||||
\(400\) | 107.076 | 5.35380 | ||||||||
\(401\) | 2.97108 | 0.148368 | 0.0741842 | − | 0.997245i | \(-0.476365\pi\) | ||||
0.0741842 | + | 0.997245i | \(0.476365\pi\) | |||||||
\(402\) | −40.1309 | −2.00155 | ||||||||
\(403\) | −31.3754 | −1.56292 | ||||||||
\(404\) | −71.1338 | −3.53904 | ||||||||
\(405\) | 36.4739 | 1.81240 | ||||||||
\(406\) | −4.18379 | −0.207638 | ||||||||
\(407\) | −14.5362 | −0.720530 | ||||||||
\(408\) | 142.510 | 7.05528 | ||||||||
\(409\) | 5.28633 | 0.261392 | 0.130696 | − | 0.991422i | \(-0.458279\pi\) | ||||
0.130696 | + | 0.991422i | \(0.458279\pi\) | |||||||
\(410\) | 31.9872 | 1.57973 | ||||||||
\(411\) | −12.3000 | −0.606715 | ||||||||
\(412\) | 86.8901 | 4.28077 | ||||||||
\(413\) | −1.04347 | −0.0513458 | ||||||||
\(414\) | 13.7893 | 0.677708 | ||||||||
\(415\) | 54.3260 | 2.66676 | ||||||||
\(416\) | 131.107 | 6.42807 | ||||||||
\(417\) | 37.7186 | 1.84709 | ||||||||
\(418\) | 93.9184 | 4.59370 | ||||||||
\(419\) | −6.47399 | −0.316275 | −0.158138 | − | 0.987417i | \(-0.550549\pi\) | ||||
−0.158138 | + | 0.987417i | \(0.550549\pi\) | |||||||
\(420\) | 37.8902 | 1.84885 | ||||||||
\(421\) | 22.2759 | 1.08566 | 0.542830 | − | 0.839843i | \(-0.317353\pi\) | ||||
0.542830 | + | 0.839843i | \(0.317353\pi\) | |||||||
\(422\) | −14.4909 | −0.705405 | ||||||||
\(423\) | 4.56427 | 0.221922 | ||||||||
\(424\) | 5.05422 | 0.245454 | ||||||||
\(425\) | 42.9221 | 2.08203 | ||||||||
\(426\) | −3.10121 | −0.150254 | ||||||||
\(427\) | −11.8056 | −0.571315 | ||||||||
\(428\) | 22.6488 | 1.09477 | ||||||||
\(429\) | −58.4644 | −2.82269 | ||||||||
\(430\) | −95.0486 | −4.58365 | ||||||||
\(431\) | −30.6431 | −1.47603 | −0.738014 | − | 0.674786i | \(-0.764236\pi\) | ||||
−0.738014 | + | 0.674786i | \(0.764236\pi\) | |||||||
\(432\) | 71.4698 | 3.43859 | ||||||||
\(433\) | −37.4271 | −1.79863 | −0.899316 | − | 0.437299i | \(-0.855935\pi\) | ||||
−0.899316 | + | 0.437299i | \(0.855935\pi\) | |||||||
\(434\) | −18.2814 | −0.877533 | ||||||||
\(435\) | 9.95896 | 0.477496 | ||||||||
\(436\) | 3.17065 | 0.151847 | ||||||||
\(437\) | −29.5015 | −1.41125 | ||||||||
\(438\) | −72.2026 | −3.44997 | ||||||||
\(439\) | 2.97048 | 0.141773 | 0.0708865 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708865 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(440\) | −214.402 | −10.2212 | ||||||||
\(441\) | 0.917605 | 0.0436955 | ||||||||
\(442\) | 92.1728 | 4.38421 | ||||||||
\(443\) | 4.06562 | 0.193163 | 0.0965816 | − | 0.995325i | \(-0.469209\pi\) | ||||
0.0965816 | + | 0.995325i | \(0.469209\pi\) | |||||||
\(444\) | −26.6098 | −1.26285 | ||||||||
\(445\) | −3.37320 | −0.159905 | ||||||||
\(446\) | 79.0648 | 3.74382 | ||||||||
\(447\) | 35.8308 | 1.69474 | ||||||||
\(448\) | 41.7118 | 1.97070 | ||||||||
\(449\) | −22.5341 | −1.06345 | −0.531725 | − | 0.846917i | \(-0.678456\pi\) | ||||
−0.531725 | + | 0.846917i | \(0.678456\pi\) | |||||||
\(450\) | −15.7504 | −0.742480 | ||||||||
\(451\) | −21.3141 | −1.00364 | ||||||||
\(452\) | −22.6903 | −1.06726 | ||||||||
\(453\) | 13.4503 | 0.631950 | ||||||||
\(454\) | 71.1381 | 3.33867 | ||||||||
\(455\) | 15.9477 | 0.747639 | ||||||||
\(456\) | 111.881 | 5.23931 | ||||||||
\(457\) | −1.86633 | −0.0873033 | −0.0436517 | − | 0.999047i | \(-0.513899\pi\) | ||||
−0.0436517 | + | 0.999047i | \(0.513899\pi\) | |||||||
\(458\) | 17.5049 | 0.817950 | ||||||||
\(459\) | 28.6491 | 1.33723 | ||||||||
\(460\) | 103.493 | 4.82539 | ||||||||
\(461\) | 30.9483 | 1.44141 | 0.720703 | − | 0.693244i | \(-0.243819\pi\) | ||||
0.720703 | + | 0.693244i | \(0.243819\pi\) | |||||||
\(462\) | −34.0652 | −1.58486 | ||||||||
\(463\) | 2.28236 | 0.106070 | 0.0530351 | − | 0.998593i | \(-0.483110\pi\) | ||||
0.0530351 | + | 0.998593i | \(0.483110\pi\) | |||||||
\(464\) | 26.0992 | 1.21163 | ||||||||
\(465\) | 43.5163 | 2.01802 | ||||||||
\(466\) | −24.0656 | −1.11482 | ||||||||
\(467\) | 2.09724 | 0.0970489 | 0.0485244 | − | 0.998822i | \(-0.484548\pi\) | ||||
0.0485244 | + | 0.998822i | \(0.484548\pi\) | |||||||
\(468\) | −25.0680 | −1.15877 | ||||||||
\(469\) | −7.29417 | −0.336814 | ||||||||
\(470\) | 46.2203 | 2.13198 | ||||||||
\(471\) | 15.1281 | 0.697066 | ||||||||
\(472\) | 10.8087 | 0.497513 | ||||||||
\(473\) | 63.3340 | 2.91210 | ||||||||
\(474\) | 12.1291 | 0.557110 | ||||||||
\(475\) | 33.6972 | 1.54613 | ||||||||
\(476\) | 39.8042 | 1.82442 | ||||||||
\(477\) | −0.447728 | −0.0205001 | ||||||||
\(478\) | −38.2854 | −1.75113 | ||||||||
\(479\) | −15.4198 | −0.704548 | −0.352274 | − | 0.935897i | \(-0.614592\pi\) | ||||
−0.352274 | + | 0.935897i | \(0.614592\pi\) | |||||||
\(480\) | −181.841 | −8.29985 | ||||||||
\(481\) | −11.1999 | −0.510670 | ||||||||
\(482\) | 72.3207 | 3.29412 | ||||||||
\(483\) | 10.7005 | 0.486891 | ||||||||
\(484\) | 156.546 | 7.11571 | ||||||||
\(485\) | 12.4141 | 0.563696 | ||||||||
\(486\) | −25.6582 | −1.16388 | ||||||||
\(487\) | −34.8612 | −1.57971 | −0.789855 | − | 0.613293i | \(-0.789844\pi\) | ||||
−0.789855 | + | 0.613293i | \(0.789844\pi\) | |||||||
\(488\) | 122.288 | 5.53573 | ||||||||
\(489\) | −39.9682 | −1.80743 | ||||||||
\(490\) | 9.29218 | 0.419778 | ||||||||
\(491\) | 27.5227 | 1.24208 | 0.621042 | − | 0.783777i | \(-0.286710\pi\) | ||||
0.621042 | + | 0.783777i | \(0.286710\pi\) | |||||||
\(492\) | −39.0175 | −1.75905 | ||||||||
\(493\) | 10.4620 | 0.471187 | ||||||||
\(494\) | 72.3627 | 3.25575 | ||||||||
\(495\) | 18.9928 | 0.853665 | ||||||||
\(496\) | 114.042 | 5.12065 | ||||||||
\(497\) | −0.563675 | −0.0252843 | ||||||||
\(498\) | −89.4097 | −4.00654 | ||||||||
\(499\) | 5.96452 | 0.267009 | 0.133504 | − | 0.991048i | \(-0.457377\pi\) | ||||
0.133504 | + | 0.991048i | \(0.457377\pi\) | |||||||
\(500\) | −22.4950 | −1.00601 | ||||||||
\(501\) | 33.2370 | 1.48492 | ||||||||
\(502\) | 67.3675 | 3.00676 | ||||||||
\(503\) | −1.14699 | −0.0511419 | −0.0255709 | − | 0.999673i | \(-0.508140\pi\) | ||||
−0.0255709 | + | 0.999673i | \(0.508140\pi\) | |||||||
\(504\) | −9.50499 | −0.423386 | ||||||||
\(505\) | 41.5251 | 1.84784 | ||||||||
\(506\) | −93.0455 | −4.13638 | ||||||||
\(507\) | −19.3151 | −0.857813 | ||||||||
\(508\) | −28.3920 | −1.25969 | ||||||||
\(509\) | 11.8883 | 0.526939 | 0.263469 | − | 0.964668i | \(-0.415133\pi\) | ||||
0.263469 | + | 0.964668i | \(0.415133\pi\) | |||||||
\(510\) | −127.840 | −5.66084 | ||||||||
\(511\) | −13.1235 | −0.580550 | ||||||||
\(512\) | −117.313 | −5.18456 | ||||||||
\(513\) | 22.4918 | 0.993036 | ||||||||
\(514\) | −26.4420 | −1.16631 | ||||||||
\(515\) | −50.7230 | −2.23512 | ||||||||
\(516\) | 115.939 | 5.10393 | ||||||||
\(517\) | −30.7981 | −1.35450 | ||||||||
\(518\) | −6.52579 | −0.286727 | ||||||||
\(519\) | 17.7982 | 0.781253 | ||||||||
\(520\) | −165.194 | −7.24422 | ||||||||
\(521\) | −4.25156 | −0.186264 | −0.0931321 | − | 0.995654i | \(-0.529688\pi\) | ||||
−0.0931321 | + | 0.995654i | \(0.529688\pi\) | |||||||
\(522\) | −3.83907 | −0.168032 | ||||||||
\(523\) | −17.5335 | −0.766685 | −0.383343 | − | 0.923606i | \(-0.625227\pi\) | ||||
−0.383343 | + | 0.923606i | \(0.625227\pi\) | |||||||
\(524\) | 56.1943 | 2.45486 | ||||||||
\(525\) | −12.2223 | −0.533426 | ||||||||
\(526\) | −68.7065 | −2.99575 | ||||||||
\(527\) | 45.7146 | 1.99136 | ||||||||
\(528\) | 212.505 | 9.24807 | ||||||||
\(529\) | 6.22734 | 0.270754 | ||||||||
\(530\) | −4.53394 | −0.196942 | ||||||||
\(531\) | −0.957493 | −0.0415517 | ||||||||
\(532\) | 31.2494 | 1.35483 | ||||||||
\(533\) | −16.4222 | −0.711324 | ||||||||
\(534\) | 5.55161 | 0.240242 | ||||||||
\(535\) | −13.2215 | −0.571614 | ||||||||
\(536\) | 75.5565 | 3.26354 | ||||||||
\(537\) | −20.2477 | −0.873751 | ||||||||
\(538\) | −87.7249 | −3.78209 | ||||||||
\(539\) | −6.19168 | −0.266695 | ||||||||
\(540\) | −78.9023 | −3.39541 | ||||||||
\(541\) | 45.7987 | 1.96904 | 0.984521 | − | 0.175268i | \(-0.0560790\pi\) | ||||
0.984521 | + | 0.175268i | \(0.0560790\pi\) | |||||||
\(542\) | 44.4142 | 1.90775 | ||||||||
\(543\) | −35.9264 | −1.54175 | ||||||||
\(544\) | −191.026 | −8.19018 | ||||||||
\(545\) | −1.85090 | −0.0792839 | ||||||||
\(546\) | −26.2467 | −1.12326 | ||||||||
\(547\) | −0.206296 | −0.00882059 | −0.00441030 | − | 0.999990i | \(-0.501404\pi\) | ||||
−0.00441030 | + | 0.999990i | \(0.501404\pi\) | |||||||
\(548\) | 35.5866 | 1.52018 | ||||||||
\(549\) | −10.8329 | −0.462337 | ||||||||
\(550\) | 106.278 | 4.53171 | ||||||||
\(551\) | 8.21350 | 0.349907 | ||||||||
\(552\) | −110.841 | −4.71771 | ||||||||
\(553\) | 2.20459 | 0.0937487 | ||||||||
\(554\) | 22.8958 | 0.972750 | ||||||||
\(555\) | 15.5338 | 0.659371 | ||||||||
\(556\) | −109.128 | −4.62805 | ||||||||
\(557\) | −41.0407 | −1.73895 | −0.869476 | − | 0.493975i | \(-0.835543\pi\) | ||||
−0.869476 | + | 0.493975i | \(0.835543\pi\) | |||||||
\(558\) | −16.7751 | −0.710145 | ||||||||
\(559\) | 48.7978 | 2.06393 | ||||||||
\(560\) | −57.9662 | −2.44952 | ||||||||
\(561\) | 85.1838 | 3.59646 | ||||||||
\(562\) | −28.1184 | −1.18610 | ||||||||
\(563\) | 17.9057 | 0.754637 | 0.377318 | − | 0.926084i | \(-0.376846\pi\) | ||||
0.377318 | + | 0.926084i | \(0.376846\pi\) | |||||||
\(564\) | −56.3789 | −2.37398 | ||||||||
\(565\) | 13.2457 | 0.557251 | ||||||||
\(566\) | −22.1530 | −0.931158 | ||||||||
\(567\) | −10.9108 | −0.458211 | ||||||||
\(568\) | 5.83881 | 0.244991 | ||||||||
\(569\) | 20.5517 | 0.861573 | 0.430787 | − | 0.902454i | \(-0.358236\pi\) | ||||
0.430787 | + | 0.902454i | \(0.358236\pi\) | |||||||
\(570\) | −100.364 | −4.20379 | ||||||||
\(571\) | 33.0094 | 1.38140 | 0.690701 | − | 0.723140i | \(-0.257302\pi\) | ||||
0.690701 | + | 0.723140i | \(0.257302\pi\) | |||||||
\(572\) | 169.150 | 7.07252 | ||||||||
\(573\) | 27.5822 | 1.15227 | ||||||||
\(574\) | −9.56864 | −0.399387 | ||||||||
\(575\) | −33.3840 | −1.39221 | ||||||||
\(576\) | 38.2750 | 1.59479 | ||||||||
\(577\) | 29.4541 | 1.22619 | 0.613094 | − | 0.790010i | \(-0.289925\pi\) | ||||
0.613094 | + | 0.790010i | \(0.289925\pi\) | |||||||
\(578\) | −87.0434 | −3.62053 | ||||||||
\(579\) | 31.6157 | 1.31391 | ||||||||
\(580\) | −28.8134 | −1.19641 | ||||||||
\(581\) | −16.2511 | −0.674209 | ||||||||
\(582\) | −20.4312 | −0.846898 | ||||||||
\(583\) | 3.02111 | 0.125122 | ||||||||
\(584\) | 135.940 | 5.62522 | ||||||||
\(585\) | 14.6337 | 0.605029 | ||||||||
\(586\) | −16.2469 | −0.671153 | ||||||||
\(587\) | 36.8284 | 1.52007 | 0.760035 | − | 0.649883i | \(-0.225182\pi\) | ||||
0.760035 | + | 0.649883i | \(0.225182\pi\) | |||||||
\(588\) | −11.3345 | −0.467426 | ||||||||
\(589\) | 35.8894 | 1.47880 | ||||||||
\(590\) | −9.69610 | −0.399182 | ||||||||
\(591\) | 3.49225 | 0.143652 | ||||||||
\(592\) | 40.7090 | 1.67313 | ||||||||
\(593\) | −9.34275 | −0.383661 | −0.191830 | − | 0.981428i | \(-0.561442\pi\) | ||||
−0.191830 | + | 0.981428i | \(0.561442\pi\) | |||||||
\(594\) | 70.9372 | 2.91059 | ||||||||
\(595\) | −23.2361 | −0.952588 | ||||||||
\(596\) | −103.666 | −4.24633 | ||||||||
\(597\) | −3.50808 | −0.143576 | ||||||||
\(598\) | −71.6901 | −2.93163 | ||||||||
\(599\) | 6.60359 | 0.269815 | 0.134908 | − | 0.990858i | \(-0.456926\pi\) | ||||
0.134908 | + | 0.990858i | \(0.456926\pi\) | |||||||
\(600\) | 126.604 | 5.16861 | ||||||||
\(601\) | −33.3652 | −1.36100 | −0.680498 | − | 0.732750i | \(-0.738237\pi\) | ||||
−0.680498 | + | 0.732750i | \(0.738237\pi\) | |||||||
\(602\) | 28.4328 | 1.15884 | ||||||||
\(603\) | −6.69317 | −0.272567 | ||||||||
\(604\) | −38.9146 | −1.58341 | ||||||||
\(605\) | −91.3851 | −3.71533 | ||||||||
\(606\) | −68.3420 | −2.77620 | ||||||||
\(607\) | 9.80090 | 0.397806 | 0.198903 | − | 0.980019i | \(-0.436262\pi\) | ||||
0.198903 | + | 0.980019i | \(0.436262\pi\) | |||||||
\(608\) | −149.970 | −6.08210 | ||||||||
\(609\) | −2.97912 | −0.120720 | ||||||||
\(610\) | −109.700 | −4.44162 | ||||||||
\(611\) | −23.7295 | −0.959991 | ||||||||
\(612\) | 36.5246 | 1.47642 | ||||||||
\(613\) | −2.04850 | −0.0827382 | −0.0413691 | − | 0.999144i | \(-0.513172\pi\) | ||||
−0.0413691 | + | 0.999144i | \(0.513172\pi\) | |||||||
\(614\) | −13.1917 | −0.532372 | ||||||||
\(615\) | 22.7769 | 0.918452 | ||||||||
\(616\) | 64.1364 | 2.58413 | ||||||||
\(617\) | 21.1575 | 0.851768 | 0.425884 | − | 0.904778i | \(-0.359963\pi\) | ||||
0.425884 | + | 0.904778i | \(0.359963\pi\) | |||||||
\(618\) | 83.4799 | 3.35805 | ||||||||
\(619\) | 14.1691 | 0.569506 | 0.284753 | − | 0.958601i | \(-0.408088\pi\) | ||||
0.284753 | + | 0.958601i | \(0.408088\pi\) | |||||||
\(620\) | −125.902 | −5.05635 | ||||||||
\(621\) | −22.2827 | −0.894174 | ||||||||
\(622\) | −75.0618 | −3.00970 | ||||||||
\(623\) | 1.00906 | 0.0404271 | ||||||||
\(624\) | 163.731 | 6.55450 | ||||||||
\(625\) | −17.7437 | −0.709749 | ||||||||
\(626\) | 11.8993 | 0.475591 | ||||||||
\(627\) | 66.8758 | 2.67076 | ||||||||
\(628\) | −43.7688 | −1.74657 | ||||||||
\(629\) | 16.3185 | 0.650659 | ||||||||
\(630\) | 8.52655 | 0.339706 | ||||||||
\(631\) | −22.2323 | −0.885055 | −0.442527 | − | 0.896755i | \(-0.645918\pi\) | ||||
−0.442527 | + | 0.896755i | \(0.645918\pi\) | |||||||
\(632\) | −22.8362 | −0.908375 | ||||||||
\(633\) | −10.3184 | −0.410120 | ||||||||
\(634\) | 47.6632 | 1.89295 | ||||||||
\(635\) | 16.5741 | 0.657723 | ||||||||
\(636\) | 5.53044 | 0.219296 | ||||||||
\(637\) | −4.77059 | −0.189018 | ||||||||
\(638\) | 25.9047 | 1.02558 | ||||||||
\(639\) | −0.517231 | −0.0204613 | ||||||||
\(640\) | 203.851 | 8.05791 | ||||||||
\(641\) | −6.35933 | −0.251178 | −0.125589 | − | 0.992082i | \(-0.540082\pi\) | ||||
−0.125589 | + | 0.992082i | \(0.540082\pi\) | |||||||
\(642\) | 21.7599 | 0.858795 | ||||||||
\(643\) | 11.6601 | 0.459830 | 0.229915 | − | 0.973211i | \(-0.426155\pi\) | ||||
0.229915 | + | 0.973211i | \(0.426155\pi\) | |||||||
\(644\) | −30.9589 | −1.21995 | ||||||||
\(645\) | −67.6806 | −2.66492 | ||||||||
\(646\) | −105.434 | −4.14824 | ||||||||
\(647\) | 10.4861 | 0.412252 | 0.206126 | − | 0.978525i | \(-0.433914\pi\) | ||||
0.206126 | + | 0.978525i | \(0.433914\pi\) | |||||||
\(648\) | 113.019 | 4.43982 | ||||||||
\(649\) | 6.46083 | 0.253610 | ||||||||
\(650\) | 81.8856 | 3.21182 | ||||||||
\(651\) | −13.0175 | −0.510195 | ||||||||
\(652\) | 115.637 | 4.52868 | ||||||||
\(653\) | −12.2095 | −0.477793 | −0.238897 | − | 0.971045i | \(-0.576786\pi\) | ||||
−0.238897 | + | 0.971045i | \(0.576786\pi\) | |||||||
\(654\) | 3.04621 | 0.119116 | ||||||||
\(655\) | −32.8040 | −1.28176 | ||||||||
\(656\) | 59.6908 | 2.33053 | ||||||||
\(657\) | −12.0422 | −0.469812 | ||||||||
\(658\) | −13.8263 | −0.539007 | ||||||||
\(659\) | 32.8898 | 1.28121 | 0.640603 | − | 0.767872i | \(-0.278684\pi\) | ||||
0.640603 | + | 0.767872i | \(0.278684\pi\) | |||||||
\(660\) | −234.604 | −9.13195 | ||||||||
\(661\) | 24.1826 | 0.940595 | 0.470298 | − | 0.882508i | \(-0.344147\pi\) | ||||
0.470298 | + | 0.882508i | \(0.344147\pi\) | |||||||
\(662\) | 12.4006 | 0.481962 | ||||||||
\(663\) | 65.6328 | 2.54897 | ||||||||
\(664\) | 168.336 | 6.53272 | ||||||||
\(665\) | −18.2421 | −0.707400 | ||||||||
\(666\) | −5.98810 | −0.232034 | ||||||||
\(667\) | −8.13716 | −0.315072 | ||||||||
\(668\) | −96.1617 | −3.72061 | ||||||||
\(669\) | 56.2991 | 2.17665 | ||||||||
\(670\) | −67.7788 | −2.61852 | ||||||||
\(671\) | 73.0967 | 2.82187 | ||||||||
\(672\) | 54.3958 | 2.09836 | ||||||||
\(673\) | −1.75396 | −0.0676103 | −0.0338051 | − | 0.999428i | \(-0.510763\pi\) | ||||
−0.0338051 | + | 0.999428i | \(0.510763\pi\) | |||||||
\(674\) | 13.7723 | 0.530489 | ||||||||
\(675\) | 25.4517 | 0.979636 | ||||||||
\(676\) | 55.8826 | 2.14933 | ||||||||
\(677\) | 30.6664 | 1.17860 | 0.589302 | − | 0.807913i | \(-0.299403\pi\) | ||||
0.589302 | + | 0.807913i | \(0.299403\pi\) | |||||||
\(678\) | −21.7998 | −0.837216 | ||||||||
\(679\) | −3.71356 | −0.142513 | ||||||||
\(680\) | 240.691 | 9.23007 | ||||||||
\(681\) | 50.6548 | 1.94110 | ||||||||
\(682\) | 113.192 | 4.33436 | ||||||||
\(683\) | −29.6528 | −1.13463 | −0.567316 | − | 0.823500i | \(-0.692018\pi\) | ||||
−0.567316 | + | 0.823500i | \(0.692018\pi\) | |||||||
\(684\) | 28.6746 | 1.09640 | ||||||||
\(685\) | −20.7740 | −0.793736 | ||||||||
\(686\) | −2.77966 | −0.106128 | ||||||||
\(687\) | 12.4646 | 0.475553 | ||||||||
\(688\) | −177.369 | −6.76212 | ||||||||
\(689\) | 2.32772 | 0.0886791 | ||||||||
\(690\) | 99.4311 | 3.78528 | ||||||||
\(691\) | 32.8988 | 1.25153 | 0.625765 | − | 0.780012i | \(-0.284787\pi\) | ||||
0.625765 | + | 0.780012i | \(0.284787\pi\) | |||||||
\(692\) | −51.4939 | −1.95750 | ||||||||
\(693\) | −5.68152 | −0.215823 | ||||||||
\(694\) | 16.3603 | 0.621029 | ||||||||
\(695\) | 63.7045 | 2.41645 | ||||||||
\(696\) | 30.8592 | 1.16971 | ||||||||
\(697\) | 23.9275 | 0.906317 | ||||||||
\(698\) | −12.6537 | −0.478951 | ||||||||
\(699\) | −17.1362 | −0.648152 | ||||||||
\(700\) | 35.3618 | 1.33655 | ||||||||
\(701\) | 10.3374 | 0.390437 | 0.195218 | − | 0.980760i | \(-0.437458\pi\) | ||||
0.195218 | + | 0.980760i | \(0.437458\pi\) | |||||||
\(702\) | 54.6560 | 2.06286 | ||||||||
\(703\) | 12.8112 | 0.483185 | ||||||||
\(704\) | −258.266 | −9.73378 | ||||||||
\(705\) | 32.9118 | 1.23953 | ||||||||
\(706\) | 59.1563 | 2.22638 | ||||||||
\(707\) | −12.4218 | −0.467171 | ||||||||
\(708\) | 11.8272 | 0.444492 | ||||||||
\(709\) | 46.3400 | 1.74033 | 0.870167 | − | 0.492757i | \(-0.164011\pi\) | ||||
0.870167 | + | 0.492757i | \(0.164011\pi\) | |||||||
\(710\) | −5.23776 | −0.196570 | ||||||||
\(711\) | 2.02294 | 0.0758663 | ||||||||
\(712\) | −10.4523 | −0.391717 | ||||||||
\(713\) | −35.5559 | −1.33158 | ||||||||
\(714\) | 38.2420 | 1.43117 | ||||||||
\(715\) | −98.7431 | −3.69278 | ||||||||
\(716\) | 58.5808 | 2.18927 | ||||||||
\(717\) | −27.2616 | −1.01810 | ||||||||
\(718\) | −41.7018 | −1.55630 | ||||||||
\(719\) | −24.2676 | −0.905030 | −0.452515 | − | 0.891757i | \(-0.649473\pi\) | ||||
−0.452515 | + | 0.891757i | \(0.649473\pi\) | |||||||
\(720\) | −53.1901 | −1.98228 | ||||||||
\(721\) | 15.1733 | 0.565083 | ||||||||
\(722\) | −29.9601 | −1.11500 | ||||||||
\(723\) | 51.4969 | 1.91519 | ||||||||
\(724\) | 103.943 | 3.86300 | ||||||||
\(725\) | 9.29440 | 0.345185 | ||||||||
\(726\) | 150.401 | 5.58192 | ||||||||
\(727\) | −32.4213 | −1.20244 | −0.601220 | − | 0.799083i | \(-0.705319\pi\) | ||||
−0.601220 | + | 0.799083i | \(0.705319\pi\) | |||||||
\(728\) | 49.4161 | 1.83148 | ||||||||
\(729\) | 14.4622 | 0.535636 | ||||||||
\(730\) | −121.946 | −4.51343 | ||||||||
\(731\) | −71.0995 | −2.62971 | ||||||||
\(732\) | 133.811 | 4.94578 | ||||||||
\(733\) | −17.3482 | −0.640770 | −0.320385 | − | 0.947288i | \(-0.603812\pi\) | ||||
−0.320385 | + | 0.947288i | \(0.603812\pi\) | |||||||
\(734\) | 34.3314 | 1.26720 | ||||||||
\(735\) | 6.61661 | 0.244057 | ||||||||
\(736\) | 148.576 | 5.47659 | ||||||||
\(737\) | 45.1632 | 1.66361 | ||||||||
\(738\) | −8.78024 | −0.323205 | ||||||||
\(739\) | −25.6340 | −0.942961 | −0.471481 | − | 0.881876i | \(-0.656280\pi\) | ||||
−0.471481 | + | 0.881876i | \(0.656280\pi\) | |||||||
\(740\) | −44.9425 | −1.65212 | ||||||||
\(741\) | 51.5268 | 1.89288 | ||||||||
\(742\) | 1.35628 | 0.0497907 | ||||||||
\(743\) | −14.1137 | −0.517783 | −0.258891 | − | 0.965906i | \(-0.583357\pi\) | ||||
−0.258891 | + | 0.965906i | \(0.583357\pi\) | |||||||
\(744\) | 134.841 | 4.94352 | ||||||||
\(745\) | 60.5162 | 2.21714 | ||||||||
\(746\) | −33.4448 | −1.22450 | ||||||||
\(747\) | −14.9121 | −0.545604 | ||||||||
\(748\) | −246.455 | −9.01129 | ||||||||
\(749\) | 3.95507 | 0.144515 | ||||||||
\(750\) | −21.6122 | −0.789164 | ||||||||
\(751\) | −18.5451 | −0.676719 | −0.338360 | − | 0.941017i | \(-0.609872\pi\) | ||||
−0.338360 | + | 0.941017i | \(0.609872\pi\) | |||||||
\(752\) | 86.2511 | 3.14525 | ||||||||
\(753\) | 47.9699 | 1.74812 | ||||||||
\(754\) | 19.9592 | 0.726870 | ||||||||
\(755\) | 22.7168 | 0.826749 | ||||||||
\(756\) | 23.6028 | 0.858427 | ||||||||
\(757\) | 28.9796 | 1.05328 | 0.526641 | − | 0.850088i | \(-0.323451\pi\) | ||||
0.526641 | + | 0.850088i | \(0.323451\pi\) | |||||||
\(758\) | 0.478561 | 0.0173821 | ||||||||
\(759\) | −66.2542 | −2.40488 | ||||||||
\(760\) | 188.961 | 6.85432 | ||||||||
\(761\) | −40.7998 | −1.47899 | −0.739495 | − | 0.673162i | \(-0.764936\pi\) | ||||
−0.739495 | + | 0.673162i | \(0.764936\pi\) | |||||||
\(762\) | −27.2776 | −0.988165 | ||||||||
\(763\) | 0.553679 | 0.0200445 | ||||||||
\(764\) | −79.8013 | −2.88711 | ||||||||
\(765\) | −21.3216 | −0.770884 | ||||||||
\(766\) | −7.90364 | −0.285570 | ||||||||
\(767\) | 4.97797 | 0.179744 | ||||||||
\(768\) | −170.378 | −6.14797 | ||||||||
\(769\) | −19.0973 | −0.688668 | −0.344334 | − | 0.938847i | \(-0.611895\pi\) | ||||
−0.344334 | + | 0.938847i | \(0.611895\pi\) | |||||||
\(770\) | −57.5342 | −2.07339 | ||||||||
\(771\) | −18.8284 | −0.678087 | ||||||||
\(772\) | −91.4711 | −3.29212 | ||||||||
\(773\) | −6.93671 | −0.249496 | −0.124748 | − | 0.992188i | \(-0.539812\pi\) | ||||
−0.124748 | + | 0.992188i | \(0.539812\pi\) | |||||||
\(774\) | 26.0901 | 0.937790 | ||||||||
\(775\) | 40.6125 | 1.45884 | ||||||||
\(776\) | 38.4668 | 1.38088 | ||||||||
\(777\) | −4.64677 | −0.166702 | ||||||||
\(778\) | 83.7048 | 3.00096 | ||||||||
\(779\) | 18.7849 | 0.673038 | ||||||||
\(780\) | −180.759 | −6.47220 | ||||||||
\(781\) | 3.49009 | 0.124885 | ||||||||
\(782\) | 104.454 | 3.73526 | ||||||||
\(783\) | 6.20371 | 0.221703 | ||||||||
\(784\) | 17.3400 | 0.619286 | ||||||||
\(785\) | 25.5505 | 0.911937 | ||||||||
\(786\) | 53.9888 | 1.92572 | ||||||||
\(787\) | −39.9308 | −1.42338 | −0.711689 | − | 0.702494i | \(-0.752070\pi\) | ||||
−0.711689 | + | 0.702494i | \(0.752070\pi\) | |||||||
\(788\) | −10.1038 | −0.359934 | ||||||||
\(789\) | −48.9234 | −1.74172 | ||||||||
\(790\) | 20.4854 | 0.728840 | ||||||||
\(791\) | −3.96232 | −0.140884 | ||||||||
\(792\) | 58.8519 | 2.09121 | ||||||||
\(793\) | 56.3199 | 1.99998 | ||||||||
\(794\) | 59.8146 | 2.12274 | ||||||||
\(795\) | −3.22845 | −0.114501 | ||||||||
\(796\) | 10.1496 | 0.359744 | ||||||||
\(797\) | −38.3478 | −1.35835 | −0.679175 | − | 0.733977i | \(-0.737662\pi\) | ||||
−0.679175 | + | 0.733977i | \(0.737662\pi\) | |||||||
\(798\) | 30.0229 | 1.06280 | ||||||||
\(799\) | 34.5743 | 1.22315 | ||||||||
\(800\) | −169.706 | −6.00002 | ||||||||
\(801\) | 0.925918 | 0.0327157 | ||||||||
\(802\) | −8.25859 | −0.291621 | ||||||||
\(803\) | 81.2567 | 2.86749 | ||||||||
\(804\) | 82.6756 | 2.91574 | ||||||||
\(805\) | 18.0726 | 0.636975 | ||||||||
\(806\) | 87.2130 | 3.07195 | ||||||||
\(807\) | −62.4656 | −2.19889 | ||||||||
\(808\) | 128.671 | 4.52663 | ||||||||
\(809\) | −35.0181 | −1.23117 | −0.615585 | − | 0.788071i | \(-0.711080\pi\) | ||||
−0.615585 | + | 0.788071i | \(0.711080\pi\) | |||||||
\(810\) | −101.385 | −3.56231 | ||||||||
\(811\) | −7.23577 | −0.254082 | −0.127041 | − | 0.991897i | \(-0.540548\pi\) | ||||
−0.127041 | + | 0.991897i | \(0.540548\pi\) | |||||||
\(812\) | 8.61924 | 0.302476 | ||||||||
\(813\) | 31.6257 | 1.10916 | ||||||||
\(814\) | 40.4056 | 1.41622 | ||||||||
\(815\) | −67.5041 | −2.36456 | ||||||||
\(816\) | −238.560 | −8.35127 | ||||||||
\(817\) | −55.8185 | −1.95284 | ||||||||
\(818\) | −14.6942 | −0.513772 | ||||||||
\(819\) | −4.37752 | −0.152963 | ||||||||
\(820\) | −65.8984 | −2.30127 | ||||||||
\(821\) | −7.16809 | −0.250168 | −0.125084 | − | 0.992146i | \(-0.539920\pi\) | ||||
−0.125084 | + | 0.992146i | \(0.539920\pi\) | |||||||
\(822\) | 34.1899 | 1.19251 | ||||||||
\(823\) | −10.3114 | −0.359433 | −0.179716 | − | 0.983718i | \(-0.557518\pi\) | ||||
−0.179716 | + | 0.983718i | \(0.557518\pi\) | |||||||
\(824\) | −157.172 | −5.47535 | ||||||||
\(825\) | 75.6767 | 2.63472 | ||||||||
\(826\) | 2.90049 | 0.100921 | ||||||||
\(827\) | −11.5523 | −0.401713 | −0.200857 | − | 0.979621i | \(-0.564373\pi\) | ||||
−0.200857 | + | 0.979621i | \(0.564373\pi\) | |||||||
\(828\) | −28.4080 | −0.987248 | ||||||||
\(829\) | 8.47299 | 0.294279 | 0.147140 | − | 0.989116i | \(-0.452993\pi\) | ||||
0.147140 | + | 0.989116i | \(0.452993\pi\) | |||||||
\(830\) | −151.008 | −5.24156 | ||||||||
\(831\) | 16.3033 | 0.565554 | ||||||||
\(832\) | −198.990 | −6.89874 | ||||||||
\(833\) | 6.95085 | 0.240833 | ||||||||
\(834\) | −104.845 | −3.63048 | ||||||||
\(835\) | 56.1354 | 1.94265 | ||||||||
\(836\) | −193.486 | −6.69186 | ||||||||
\(837\) | 27.1075 | 0.936973 | ||||||||
\(838\) | 17.9955 | 0.621645 | ||||||||
\(839\) | 39.9674 | 1.37983 | 0.689914 | − | 0.723891i | \(-0.257648\pi\) | ||||
0.689914 | + | 0.723891i | \(0.257648\pi\) | |||||||
\(840\) | −68.5380 | −2.36479 | ||||||||
\(841\) | −26.7345 | −0.921881 | ||||||||
\(842\) | −61.9194 | −2.13388 | ||||||||
\(843\) | −20.0221 | −0.689597 | ||||||||
\(844\) | 29.8534 | 1.02760 | ||||||||
\(845\) | −32.6221 | −1.12223 | ||||||||
\(846\) | −12.6871 | −0.436192 | ||||||||
\(847\) | 27.3369 | 0.939308 | ||||||||
\(848\) | −8.46072 | −0.290542 | ||||||||
\(849\) | −15.7743 | −0.541372 | ||||||||
\(850\) | −119.309 | −4.09227 | ||||||||
\(851\) | −12.6922 | −0.435082 | ||||||||
\(852\) | 6.38895 | 0.218882 | ||||||||
\(853\) | 48.7968 | 1.67077 | 0.835385 | − | 0.549665i | \(-0.185245\pi\) | ||||
0.835385 | + | 0.549665i | \(0.185245\pi\) | |||||||
\(854\) | 32.8157 | 1.12293 | ||||||||
\(855\) | −16.7391 | −0.572464 | ||||||||
\(856\) | −40.9685 | −1.40027 | ||||||||
\(857\) | 22.9315 | 0.783325 | 0.391662 | − | 0.920109i | \(-0.371900\pi\) | ||||
0.391662 | + | 0.920109i | \(0.371900\pi\) | |||||||
\(858\) | 162.511 | 5.54804 | ||||||||
\(859\) | 21.8748 | 0.746359 | 0.373179 | − | 0.927759i | \(-0.378268\pi\) | ||||
0.373179 | + | 0.927759i | \(0.378268\pi\) | |||||||
\(860\) | 195.814 | 6.67721 | ||||||||
\(861\) | −6.81347 | −0.232203 | ||||||||
\(862\) | 85.1776 | 2.90116 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −113.273 | −3.85364 | ||||||||
\(865\) | 30.0601 | 1.02207 | ||||||||
\(866\) | 104.035 | 3.53524 | ||||||||
\(867\) | −61.9803 | −2.10496 | ||||||||
\(868\) | 37.6623 | 1.27834 | ||||||||
\(869\) | −13.6501 | −0.463049 | ||||||||
\(870\) | −27.6825 | −0.938526 | ||||||||
\(871\) | 34.7975 | 1.17907 | ||||||||
\(872\) | −5.73527 | −0.194221 | ||||||||
\(873\) | −3.40758 | −0.115329 | ||||||||
\(874\) | 82.0043 | 2.77384 | ||||||||
\(875\) | −3.92822 | −0.132798 | ||||||||
\(876\) | 148.748 | 5.02574 | ||||||||
\(877\) | −24.2205 | −0.817868 | −0.408934 | − | 0.912564i | \(-0.634099\pi\) | ||||
−0.408934 | + | 0.912564i | \(0.634099\pi\) | |||||||
\(878\) | −8.25692 | −0.278658 | ||||||||
\(879\) | −11.5688 | −0.390206 | ||||||||
\(880\) | 358.908 | 12.0988 | ||||||||
\(881\) | 1.47634 | 0.0497390 | 0.0248695 | − | 0.999691i | \(-0.492083\pi\) | ||||
0.0248695 | + | 0.999691i | \(0.492083\pi\) | |||||||
\(882\) | −2.55063 | −0.0858843 | ||||||||
\(883\) | −23.4755 | −0.790013 | −0.395007 | − | 0.918678i | \(-0.629258\pi\) | ||||
−0.395007 | + | 0.918678i | \(0.629258\pi\) | |||||||
\(884\) | −189.890 | −6.38668 | ||||||||
\(885\) | −6.90424 | −0.232083 | ||||||||
\(886\) | −11.3010 | −0.379666 | ||||||||
\(887\) | 47.2922 | 1.58792 | 0.793958 | − | 0.607973i | \(-0.208017\pi\) | ||||
0.793958 | + | 0.607973i | \(0.208017\pi\) | |||||||
\(888\) | 48.1334 | 1.61525 | ||||||||
\(889\) | −4.95798 | −0.166285 | ||||||||
\(890\) | 9.37636 | 0.314296 | ||||||||
\(891\) | 67.5563 | 2.26322 | ||||||||
\(892\) | −162.885 | −5.45380 | ||||||||
\(893\) | 27.1435 | 0.908322 | ||||||||
\(894\) | −99.5976 | −3.33104 | ||||||||
\(895\) | −34.1972 | −1.14309 | ||||||||
\(896\) | −60.9799 | −2.03720 | ||||||||
\(897\) | −51.0478 | −1.70444 | ||||||||
\(898\) | 62.6372 | 2.09023 | ||||||||
\(899\) | 9.89908 | 0.330153 | ||||||||
\(900\) | 32.4481 | 1.08160 | ||||||||
\(901\) | −3.39154 | −0.112988 | ||||||||
\(902\) | 59.2460 | 1.97268 | ||||||||
\(903\) | 20.2460 | 0.673743 | ||||||||
\(904\) | 41.0436 | 1.36509 | ||||||||
\(905\) | −60.6777 | −2.01699 | ||||||||
\(906\) | −37.3873 | −1.24211 | ||||||||
\(907\) | 7.54661 | 0.250581 | 0.125291 | − | 0.992120i | \(-0.460014\pi\) | ||||
0.125291 | + | 0.992120i | \(0.460014\pi\) | |||||||
\(908\) | −146.555 | −4.86360 | ||||||||
\(909\) | −11.3983 | −0.378059 | ||||||||
\(910\) | −44.3292 | −1.46950 | ||||||||
\(911\) | −40.8777 | −1.35434 | −0.677170 | − | 0.735827i | \(-0.736794\pi\) | ||||
−0.677170 | + | 0.735827i | \(0.736794\pi\) | |||||||
\(912\) | −187.288 | −6.20172 | ||||||||
\(913\) | 100.622 | 3.33009 | ||||||||
\(914\) | 5.18777 | 0.171596 | ||||||||
\(915\) | −78.1133 | −2.58235 | ||||||||
\(916\) | −36.0627 | −1.19154 | ||||||||
\(917\) | 9.81299 | 0.324053 | ||||||||
\(918\) | −79.6349 | −2.62834 | ||||||||
\(919\) | −48.0843 | −1.58615 | −0.793077 | − | 0.609121i | \(-0.791522\pi\) | ||||
−0.793077 | + | 0.609121i | \(0.791522\pi\) | |||||||
\(920\) | −187.204 | −6.17194 | ||||||||
\(921\) | −9.39329 | −0.309519 | ||||||||
\(922\) | −86.0258 | −2.83311 | ||||||||
\(923\) | 2.68906 | 0.0885116 | ||||||||
\(924\) | 70.1794 | 2.30873 | ||||||||
\(925\) | 14.4972 | 0.476665 | ||||||||
\(926\) | −6.34419 | −0.208483 | ||||||||
\(927\) | 13.9231 | 0.457294 | ||||||||
\(928\) | −41.3650 | −1.35787 | ||||||||
\(929\) | 0.944216 | 0.0309787 | 0.0154894 | − | 0.999880i | \(-0.495069\pi\) | ||||
0.0154894 | + | 0.999880i | \(0.495069\pi\) | |||||||
\(930\) | −120.961 | −3.96646 | ||||||||
\(931\) | 5.45695 | 0.178844 | ||||||||
\(932\) | 49.5788 | 1.62401 | ||||||||
\(933\) | −53.4487 | −1.74983 | ||||||||
\(934\) | −5.82963 | −0.190751 | ||||||||
\(935\) | 143.871 | 4.70507 | ||||||||
\(936\) | 45.3444 | 1.48213 | ||||||||
\(937\) | 30.4214 | 0.993823 | 0.496912 | − | 0.867801i | \(-0.334467\pi\) | ||||
0.496912 | + | 0.867801i | \(0.334467\pi\) | |||||||
\(938\) | 20.2753 | 0.662013 | ||||||||
\(939\) | 8.47304 | 0.276507 | ||||||||
\(940\) | −95.2208 | −3.10576 | ||||||||
\(941\) | −0.250786 | −0.00817539 | −0.00408769 | − | 0.999992i | \(-0.501301\pi\) | ||||
−0.00408769 | + | 0.999992i | \(0.501301\pi\) | |||||||
\(942\) | −42.0510 | −1.37010 | ||||||||
\(943\) | −18.6103 | −0.606034 | ||||||||
\(944\) | −18.0938 | −0.588902 | ||||||||
\(945\) | −13.7784 | −0.448211 | ||||||||
\(946\) | −176.047 | −5.72378 | ||||||||
\(947\) | 43.2058 | 1.40400 | 0.702001 | − | 0.712176i | \(-0.252290\pi\) | ||||
0.702001 | + | 0.712176i | \(0.252290\pi\) | |||||||
\(948\) | −24.9879 | −0.811568 | ||||||||
\(949\) | 62.6070 | 2.03231 | ||||||||
\(950\) | −93.6667 | −3.03895 | ||||||||
\(951\) | 33.9392 | 1.10055 | ||||||||
\(952\) | −72.0002 | −2.33354 | ||||||||
\(953\) | 12.0748 | 0.391141 | 0.195570 | − | 0.980690i | \(-0.437344\pi\) | ||||
0.195570 | + | 0.980690i | \(0.437344\pi\) | |||||||
\(954\) | 1.24453 | 0.0402932 | ||||||||
\(955\) | 46.5849 | 1.50745 | ||||||||
\(956\) | 78.8736 | 2.55096 | ||||||||
\(957\) | 18.4458 | 0.596268 | ||||||||
\(958\) | 42.8618 | 1.38480 | ||||||||
\(959\) | 6.21435 | 0.200672 | ||||||||
\(960\) | 275.991 | 8.90757 | ||||||||
\(961\) | 12.2547 | 0.395312 | ||||||||
\(962\) | 31.1319 | 1.00373 | ||||||||
\(963\) | 3.62920 | 0.116949 | ||||||||
\(964\) | −148.992 | −4.79870 | ||||||||
\(965\) | 53.3972 | 1.71892 | ||||||||
\(966\) | −29.7438 | −0.956992 | ||||||||
\(967\) | −1.52583 | −0.0490673 | −0.0245336 | − | 0.999699i | \(-0.507810\pi\) | ||||
−0.0245336 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(968\) | −283.169 | −9.10139 | ||||||||
\(969\) | −75.0756 | −2.41177 | ||||||||
\(970\) | −34.5071 | −1.10795 | ||||||||
\(971\) | −16.4589 | −0.528191 | −0.264095 | − | 0.964497i | \(-0.585073\pi\) | ||||
−0.264095 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(972\) | 52.8598 | 1.69548 | ||||||||
\(973\) | −19.0566 | −0.610926 | ||||||||
\(974\) | 96.9023 | 3.10495 | ||||||||
\(975\) | 58.3077 | 1.86734 | ||||||||
\(976\) | −204.710 | −6.55260 | ||||||||
\(977\) | −29.3602 | −0.939315 | −0.469657 | − | 0.882849i | \(-0.655623\pi\) | ||||
−0.469657 | + | 0.882849i | \(0.655623\pi\) | |||||||
\(978\) | 111.098 | 3.55253 | ||||||||
\(979\) | −6.24777 | −0.199680 | ||||||||
\(980\) | −19.1433 | −0.611510 | ||||||||
\(981\) | 0.508059 | 0.0162211 | ||||||||
\(982\) | −76.5039 | −2.44134 | ||||||||
\(983\) | 30.8785 | 0.984872 | 0.492436 | − | 0.870349i | \(-0.336107\pi\) | ||||
0.492436 | + | 0.870349i | \(0.336107\pi\) | |||||||
\(984\) | 70.5772 | 2.24992 | ||||||||
\(985\) | 5.89822 | 0.187933 | ||||||||
\(986\) | −29.0809 | −0.926126 | ||||||||
\(987\) | −9.84523 | −0.313377 | ||||||||
\(988\) | −149.078 | −4.74280 | ||||||||
\(989\) | 55.2997 | 1.75843 | ||||||||
\(990\) | −52.7937 | −1.67789 | ||||||||
\(991\) | 38.0520 | 1.20876 | 0.604381 | − | 0.796695i | \(-0.293420\pi\) | ||||
0.604381 | + | 0.796695i | \(0.293420\pi\) | |||||||
\(992\) | −180.747 | −5.73873 | ||||||||
\(993\) | 8.82999 | 0.280211 | ||||||||
\(994\) | 1.56682 | 0.0496967 | ||||||||
\(995\) | −5.92496 | −0.187834 | ||||||||
\(996\) | 184.197 | 5.83652 | ||||||||
\(997\) | −4.21961 | −0.133636 | −0.0668181 | − | 0.997765i | \(-0.521285\pi\) | ||||
−0.0668181 | + | 0.997765i | \(0.521285\pi\) | |||||||
\(998\) | −16.5794 | −0.524810 | ||||||||
\(999\) | 9.67641 | 0.306148 |
(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.1.3 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.3 | ✓ | 132 | 1.1 | even | 1 | trivial |