Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | 1.52105 | 0.878179 | 0.439089 | − | 0.898443i | \(-0.355301\pi\) | ||||
0.439089 | + | 0.898443i | \(0.355301\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.19164 | −1.42734 | −0.713672 | − | 0.700480i | \(-0.752969\pi\) | ||||
−0.713672 | + | 0.700480i | \(0.752969\pi\) | |||||||
\(6\) | −1.52105 | −0.620966 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.686407 | −0.228802 | ||||||||
\(10\) | 3.19164 | 1.00928 | ||||||||
\(11\) | −1.28860 | −0.388529 | −0.194264 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194264 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(12\) | 1.52105 | 0.439089 | ||||||||
\(13\) | 1.34956 | 0.374301 | 0.187150 | − | 0.982331i | \(-0.440075\pi\) | ||||
0.187150 | + | 0.982331i | \(0.440075\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −4.85464 | −1.25346 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.77216 | 1.39995 | 0.699977 | − | 0.714165i | \(-0.253194\pi\) | ||||
0.699977 | + | 0.714165i | \(0.253194\pi\) | |||||||
\(18\) | 0.686407 | 0.161788 | ||||||||
\(19\) | −7.04424 | −1.61606 | −0.808029 | − | 0.589142i | \(-0.799466\pi\) | ||||
−0.808029 | + | 0.589142i | \(0.799466\pi\) | |||||||
\(20\) | −3.19164 | −0.713672 | ||||||||
\(21\) | −1.52105 | −0.331920 | ||||||||
\(22\) | 1.28860 | 0.274731 | ||||||||
\(23\) | −5.21023 | −1.08641 | −0.543204 | − | 0.839601i | \(-0.682789\pi\) | ||||
−0.543204 | + | 0.839601i | \(0.682789\pi\) | |||||||
\(24\) | −1.52105 | −0.310483 | ||||||||
\(25\) | 5.18656 | 1.03731 | ||||||||
\(26\) | −1.34956 | −0.264671 | ||||||||
\(27\) | −5.60721 | −1.07911 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.06455 | −0.383377 | −0.191689 | − | 0.981456i | \(-0.561396\pi\) | ||||
−0.191689 | + | 0.981456i | \(0.561396\pi\) | |||||||
\(30\) | 4.85464 | 0.886332 | ||||||||
\(31\) | −1.05869 | −0.190146 | −0.0950730 | − | 0.995470i | \(-0.530308\pi\) | ||||
−0.0950730 | + | 0.995470i | \(0.530308\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.96003 | −0.341197 | ||||||||
\(34\) | −5.77216 | −0.989917 | ||||||||
\(35\) | 3.19164 | 0.539485 | ||||||||
\(36\) | −0.686407 | −0.114401 | ||||||||
\(37\) | 0.620197 | 0.101960 | 0.0509799 | − | 0.998700i | \(-0.483766\pi\) | ||||
0.0509799 | + | 0.998700i | \(0.483766\pi\) | |||||||
\(38\) | 7.04424 | 1.14273 | ||||||||
\(39\) | 2.05275 | 0.328703 | ||||||||
\(40\) | 3.19164 | 0.504642 | ||||||||
\(41\) | −6.09301 | −0.951569 | −0.475784 | − | 0.879562i | \(-0.657836\pi\) | ||||
−0.475784 | + | 0.879562i | \(0.657836\pi\) | |||||||
\(42\) | 1.52105 | 0.234703 | ||||||||
\(43\) | −9.64795 | −1.47130 | −0.735649 | − | 0.677363i | \(-0.763123\pi\) | ||||
−0.735649 | + | 0.677363i | \(0.763123\pi\) | |||||||
\(44\) | −1.28860 | −0.194264 | ||||||||
\(45\) | 2.19076 | 0.326580 | ||||||||
\(46\) | 5.21023 | 0.768207 | ||||||||
\(47\) | 11.2768 | 1.64489 | 0.822445 | − | 0.568844i | \(-0.192609\pi\) | ||||
0.822445 | + | 0.568844i | \(0.192609\pi\) | |||||||
\(48\) | 1.52105 | 0.219545 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.18656 | −0.733490 | ||||||||
\(51\) | 8.77974 | 1.22941 | ||||||||
\(52\) | 1.34956 | 0.187150 | ||||||||
\(53\) | 11.5691 | 1.58914 | 0.794571 | − | 0.607172i | \(-0.207696\pi\) | ||||
0.794571 | + | 0.607172i | \(0.207696\pi\) | |||||||
\(54\) | 5.60721 | 0.763045 | ||||||||
\(55\) | 4.11276 | 0.554564 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −10.7146 | −1.41919 | ||||||||
\(58\) | 2.06455 | 0.271089 | ||||||||
\(59\) | −2.46795 | −0.321299 | −0.160650 | − | 0.987011i | \(-0.551359\pi\) | ||||
−0.160650 | + | 0.987011i | \(0.551359\pi\) | |||||||
\(60\) | −4.85464 | −0.626732 | ||||||||
\(61\) | −9.99054 | −1.27916 | −0.639579 | − | 0.768726i | \(-0.720891\pi\) | ||||
−0.639579 | + | 0.768726i | \(0.720891\pi\) | |||||||
\(62\) | 1.05869 | 0.134454 | ||||||||
\(63\) | 0.686407 | 0.0864792 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.30731 | −0.534256 | ||||||||
\(66\) | 1.96003 | 0.241263 | ||||||||
\(67\) | 15.7014 | 1.91823 | 0.959114 | − | 0.283019i | \(-0.0913361\pi\) | ||||
0.959114 | + | 0.283019i | \(0.0913361\pi\) | |||||||
\(68\) | 5.77216 | 0.699977 | ||||||||
\(69\) | −7.92502 | −0.954060 | ||||||||
\(70\) | −3.19164 | −0.381474 | ||||||||
\(71\) | 7.43814 | 0.882745 | 0.441373 | − | 0.897324i | \(-0.354492\pi\) | ||||
0.441373 | + | 0.897324i | \(0.354492\pi\) | |||||||
\(72\) | 0.686407 | 0.0808939 | ||||||||
\(73\) | 5.84106 | 0.683645 | 0.341822 | − | 0.939765i | \(-0.388956\pi\) | ||||
0.341822 | + | 0.939765i | \(0.388956\pi\) | |||||||
\(74\) | −0.620197 | −0.0720964 | ||||||||
\(75\) | 7.88902 | 0.910945 | ||||||||
\(76\) | −7.04424 | −0.808029 | ||||||||
\(77\) | 1.28860 | 0.146850 | ||||||||
\(78\) | −2.05275 | −0.232428 | ||||||||
\(79\) | −2.91941 | −0.328459 | −0.164229 | − | 0.986422i | \(-0.552514\pi\) | ||||
−0.164229 | + | 0.986422i | \(0.552514\pi\) | |||||||
\(80\) | −3.19164 | −0.356836 | ||||||||
\(81\) | −6.46962 | −0.718847 | ||||||||
\(82\) | 6.09301 | 0.672861 | ||||||||
\(83\) | −2.31837 | −0.254475 | −0.127237 | − | 0.991872i | \(-0.540611\pi\) | ||||
−0.127237 | + | 0.991872i | \(0.540611\pi\) | |||||||
\(84\) | −1.52105 | −0.165960 | ||||||||
\(85\) | −18.4226 | −1.99822 | ||||||||
\(86\) | 9.64795 | 1.04037 | ||||||||
\(87\) | −3.14028 | −0.336674 | ||||||||
\(88\) | 1.28860 | 0.137366 | ||||||||
\(89\) | 14.5030 | 1.53732 | 0.768658 | − | 0.639660i | \(-0.220925\pi\) | ||||
0.768658 | + | 0.639660i | \(0.220925\pi\) | |||||||
\(90\) | −2.19076 | −0.230927 | ||||||||
\(91\) | −1.34956 | −0.141472 | ||||||||
\(92\) | −5.21023 | −0.543204 | ||||||||
\(93\) | −1.61032 | −0.166982 | ||||||||
\(94\) | −11.2768 | −1.16311 | ||||||||
\(95\) | 22.4827 | 2.30667 | ||||||||
\(96\) | −1.52105 | −0.155242 | ||||||||
\(97\) | 9.65031 | 0.979840 | 0.489920 | − | 0.871767i | \(-0.337026\pi\) | ||||
0.489920 | + | 0.871767i | \(0.337026\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0.884507 | 0.0888963 | ||||||||
\(100\) | 5.18656 | 0.518656 | ||||||||
\(101\) | −17.2580 | −1.71724 | −0.858620 | − | 0.512613i | \(-0.828678\pi\) | ||||
−0.858620 | + | 0.512613i | \(0.828678\pi\) | |||||||
\(102\) | −8.77974 | −0.869324 | ||||||||
\(103\) | 8.12280 | 0.800364 | 0.400182 | − | 0.916436i | \(-0.368947\pi\) | ||||
0.400182 | + | 0.916436i | \(0.368947\pi\) | |||||||
\(104\) | −1.34956 | −0.132335 | ||||||||
\(105\) | 4.85464 | 0.473765 | ||||||||
\(106\) | −11.5691 | −1.12369 | ||||||||
\(107\) | −7.61685 | −0.736349 | −0.368174 | − | 0.929757i | \(-0.620017\pi\) | ||||
−0.368174 | + | 0.929757i | \(0.620017\pi\) | |||||||
\(108\) | −5.60721 | −0.539554 | ||||||||
\(109\) | −14.9452 | −1.43150 | −0.715748 | − | 0.698359i | \(-0.753914\pi\) | ||||
−0.715748 | + | 0.698359i | \(0.753914\pi\) | |||||||
\(110\) | −4.11276 | −0.392136 | ||||||||
\(111\) | 0.943351 | 0.0895389 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 5.90534 | 0.555528 | 0.277764 | − | 0.960649i | \(-0.410407\pi\) | ||||
0.277764 | + | 0.960649i | \(0.410407\pi\) | |||||||
\(114\) | 10.7146 | 1.00352 | ||||||||
\(115\) | 16.6292 | 1.55068 | ||||||||
\(116\) | −2.06455 | −0.191689 | ||||||||
\(117\) | −0.926348 | −0.0856409 | ||||||||
\(118\) | 2.46795 | 0.227193 | ||||||||
\(119\) | −5.77216 | −0.529133 | ||||||||
\(120\) | 4.85464 | 0.443166 | ||||||||
\(121\) | −9.33950 | −0.849046 | ||||||||
\(122\) | 9.99054 | 0.904501 | ||||||||
\(123\) | −9.26778 | −0.835647 | ||||||||
\(124\) | −1.05869 | −0.0950730 | ||||||||
\(125\) | −0.595431 | −0.0532570 | ||||||||
\(126\) | −0.686407 | −0.0611500 | ||||||||
\(127\) | 5.92583 | 0.525833 | 0.262916 | − | 0.964819i | \(-0.415316\pi\) | ||||
0.262916 | + | 0.964819i | \(0.415316\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −14.6750 | −1.29206 | ||||||||
\(130\) | 4.30731 | 0.377776 | ||||||||
\(131\) | −7.13803 | −0.623653 | −0.311826 | − | 0.950139i | \(-0.600941\pi\) | ||||
−0.311826 | + | 0.950139i | \(0.600941\pi\) | |||||||
\(132\) | −1.96003 | −0.170599 | ||||||||
\(133\) | 7.04424 | 0.610813 | ||||||||
\(134\) | −15.7014 | −1.35639 | ||||||||
\(135\) | 17.8962 | 1.54026 | ||||||||
\(136\) | −5.77216 | −0.494958 | ||||||||
\(137\) | 8.51425 | 0.727421 | 0.363711 | − | 0.931512i | \(-0.381510\pi\) | ||||
0.363711 | + | 0.931512i | \(0.381510\pi\) | |||||||
\(138\) | 7.92502 | 0.674623 | ||||||||
\(139\) | −8.10576 | −0.687522 | −0.343761 | − | 0.939057i | \(-0.611701\pi\) | ||||
−0.343761 | + | 0.939057i | \(0.611701\pi\) | |||||||
\(140\) | 3.19164 | 0.269743 | ||||||||
\(141\) | 17.1526 | 1.44451 | ||||||||
\(142\) | −7.43814 | −0.624195 | ||||||||
\(143\) | −1.73905 | −0.145426 | ||||||||
\(144\) | −0.686407 | −0.0572006 | ||||||||
\(145\) | 6.58930 | 0.547211 | ||||||||
\(146\) | −5.84106 | −0.483410 | ||||||||
\(147\) | 1.52105 | 0.125454 | ||||||||
\(148\) | 0.620197 | 0.0509799 | ||||||||
\(149\) | −13.2557 | −1.08595 | −0.542973 | − | 0.839750i | \(-0.682701\pi\) | ||||
−0.542973 | + | 0.839750i | \(0.682701\pi\) | |||||||
\(150\) | −7.88902 | −0.644135 | ||||||||
\(151\) | 11.8253 | 0.962331 | 0.481165 | − | 0.876630i | \(-0.340214\pi\) | ||||
0.481165 | + | 0.876630i | \(0.340214\pi\) | |||||||
\(152\) | 7.04424 | 0.571363 | ||||||||
\(153\) | −3.96205 | −0.320313 | ||||||||
\(154\) | −1.28860 | −0.103839 | ||||||||
\(155\) | 3.37895 | 0.271404 | ||||||||
\(156\) | 2.05275 | 0.164351 | ||||||||
\(157\) | −10.4632 | −0.835057 | −0.417529 | − | 0.908664i | \(-0.637104\pi\) | ||||
−0.417529 | + | 0.908664i | \(0.637104\pi\) | |||||||
\(158\) | 2.91941 | 0.232256 | ||||||||
\(159\) | 17.5972 | 1.39555 | ||||||||
\(160\) | 3.19164 | 0.252321 | ||||||||
\(161\) | 5.21023 | 0.410624 | ||||||||
\(162\) | 6.46962 | 0.508302 | ||||||||
\(163\) | 2.15221 | 0.168574 | 0.0842870 | − | 0.996442i | \(-0.473139\pi\) | ||||
0.0842870 | + | 0.996442i | \(0.473139\pi\) | |||||||
\(164\) | −6.09301 | −0.475784 | ||||||||
\(165\) | 6.25571 | 0.487006 | ||||||||
\(166\) | 2.31837 | 0.179941 | ||||||||
\(167\) | 22.9023 | 1.77224 | 0.886118 | − | 0.463461i | \(-0.153392\pi\) | ||||
0.886118 | + | 0.463461i | \(0.153392\pi\) | |||||||
\(168\) | 1.52105 | 0.117352 | ||||||||
\(169\) | −11.1787 | −0.859899 | ||||||||
\(170\) | 18.4226 | 1.41295 | ||||||||
\(171\) | 4.83522 | 0.369758 | ||||||||
\(172\) | −9.64795 | −0.735649 | ||||||||
\(173\) | 3.05284 | 0.232103 | 0.116051 | − | 0.993243i | \(-0.462976\pi\) | ||||
0.116051 | + | 0.993243i | \(0.462976\pi\) | |||||||
\(174\) | 3.14028 | 0.238064 | ||||||||
\(175\) | −5.18656 | −0.392067 | ||||||||
\(176\) | −1.28860 | −0.0971321 | ||||||||
\(177\) | −3.75387 | −0.282158 | ||||||||
\(178\) | −14.5030 | −1.08705 | ||||||||
\(179\) | 10.9370 | 0.817466 | 0.408733 | − | 0.912654i | \(-0.365971\pi\) | ||||
0.408733 | + | 0.912654i | \(0.365971\pi\) | |||||||
\(180\) | 2.19076 | 0.163290 | ||||||||
\(181\) | −7.20674 | −0.535673 | −0.267836 | − | 0.963464i | \(-0.586309\pi\) | ||||
−0.267836 | + | 0.963464i | \(0.586309\pi\) | |||||||
\(182\) | 1.34956 | 0.100036 | ||||||||
\(183\) | −15.1961 | −1.12333 | ||||||||
\(184\) | 5.21023 | 0.384103 | ||||||||
\(185\) | −1.97944 | −0.145532 | ||||||||
\(186\) | 1.61032 | 0.118074 | ||||||||
\(187\) | −7.43802 | −0.543922 | ||||||||
\(188\) | 11.2768 | 0.822445 | ||||||||
\(189\) | 5.60721 | 0.407864 | ||||||||
\(190\) | −22.4827 | −1.63106 | ||||||||
\(191\) | 4.94052 | 0.357483 | 0.178742 | − | 0.983896i | \(-0.442797\pi\) | ||||
0.178742 | + | 0.983896i | \(0.442797\pi\) | |||||||
\(192\) | 1.52105 | 0.109772 | ||||||||
\(193\) | 0.189080 | 0.0136102 | 0.00680512 | − | 0.999977i | \(-0.497834\pi\) | ||||
0.00680512 | + | 0.999977i | \(0.497834\pi\) | |||||||
\(194\) | −9.65031 | −0.692852 | ||||||||
\(195\) | −6.55163 | −0.469172 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −2.30403 | −0.164155 | −0.0820776 | − | 0.996626i | \(-0.526156\pi\) | ||||
−0.0820776 | + | 0.996626i | \(0.526156\pi\) | |||||||
\(198\) | −0.884507 | −0.0628592 | ||||||||
\(199\) | 22.6764 | 1.60749 | 0.803744 | − | 0.594975i | \(-0.202838\pi\) | ||||
0.803744 | + | 0.594975i | \(0.202838\pi\) | |||||||
\(200\) | −5.18656 | −0.366745 | ||||||||
\(201\) | 23.8826 | 1.68455 | ||||||||
\(202\) | 17.2580 | 1.21427 | ||||||||
\(203\) | 2.06455 | 0.144903 | ||||||||
\(204\) | 8.77974 | 0.614705 | ||||||||
\(205\) | 19.4467 | 1.35822 | ||||||||
\(206\) | −8.12280 | −0.565943 | ||||||||
\(207\) | 3.57634 | 0.248573 | ||||||||
\(208\) | 1.34956 | 0.0935752 | ||||||||
\(209\) | 9.07723 | 0.627885 | ||||||||
\(210\) | −4.85464 | −0.335002 | ||||||||
\(211\) | 12.5303 | 0.862620 | 0.431310 | − | 0.902204i | \(-0.358052\pi\) | ||||
0.431310 | + | 0.902204i | \(0.358052\pi\) | |||||||
\(212\) | 11.5691 | 0.794571 | ||||||||
\(213\) | 11.3138 | 0.775208 | ||||||||
\(214\) | 7.61685 | 0.520677 | ||||||||
\(215\) | 30.7928 | 2.10005 | ||||||||
\(216\) | 5.60721 | 0.381522 | ||||||||
\(217\) | 1.05869 | 0.0718684 | ||||||||
\(218\) | 14.9452 | 1.01222 | ||||||||
\(219\) | 8.88455 | 0.600362 | ||||||||
\(220\) | 4.11276 | 0.277282 | ||||||||
\(221\) | 7.78987 | 0.524004 | ||||||||
\(222\) | −0.943351 | −0.0633135 | ||||||||
\(223\) | −12.9727 | −0.868717 | −0.434359 | − | 0.900740i | \(-0.643025\pi\) | ||||
−0.434359 | + | 0.900740i | \(0.643025\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −3.56009 | −0.237339 | ||||||||
\(226\) | −5.90534 | −0.392817 | ||||||||
\(227\) | 7.24109 | 0.480608 | 0.240304 | − | 0.970698i | \(-0.422753\pi\) | ||||
0.240304 | + | 0.970698i | \(0.422753\pi\) | |||||||
\(228\) | −10.7146 | −0.709594 | ||||||||
\(229\) | 3.79306 | 0.250653 | 0.125326 | − | 0.992116i | \(-0.460002\pi\) | ||||
0.125326 | + | 0.992116i | \(0.460002\pi\) | |||||||
\(230\) | −16.6292 | −1.09650 | ||||||||
\(231\) | 1.96003 | 0.128961 | ||||||||
\(232\) | 2.06455 | 0.135544 | ||||||||
\(233\) | 14.4348 | 0.945656 | 0.472828 | − | 0.881155i | \(-0.343233\pi\) | ||||
0.472828 | + | 0.881155i | \(0.343233\pi\) | |||||||
\(234\) | 0.926348 | 0.0605573 | ||||||||
\(235\) | −35.9915 | −2.34783 | ||||||||
\(236\) | −2.46795 | −0.160650 | ||||||||
\(237\) | −4.44056 | −0.288446 | ||||||||
\(238\) | 5.77216 | 0.374153 | ||||||||
\(239\) | 18.6684 | 1.20756 | 0.603779 | − | 0.797151i | \(-0.293661\pi\) | ||||
0.603779 | + | 0.797151i | \(0.293661\pi\) | |||||||
\(240\) | −4.85464 | −0.313366 | ||||||||
\(241\) | −28.5089 | −1.83642 | −0.918209 | − | 0.396097i | \(-0.870364\pi\) | ||||
−0.918209 | + | 0.396097i | \(0.870364\pi\) | |||||||
\(242\) | 9.33950 | 0.600366 | ||||||||
\(243\) | 6.98101 | 0.447832 | ||||||||
\(244\) | −9.99054 | −0.639579 | ||||||||
\(245\) | −3.19164 | −0.203906 | ||||||||
\(246\) | 9.26778 | 0.590892 | ||||||||
\(247\) | −9.50662 | −0.604892 | ||||||||
\(248\) | 1.05869 | 0.0672268 | ||||||||
\(249\) | −3.52636 | −0.223474 | ||||||||
\(250\) | 0.595431 | 0.0376584 | ||||||||
\(251\) | 26.8629 | 1.69557 | 0.847786 | − | 0.530339i | \(-0.177935\pi\) | ||||
0.847786 | + | 0.530339i | \(0.177935\pi\) | |||||||
\(252\) | 0.686407 | 0.0432396 | ||||||||
\(253\) | 6.71392 | 0.422101 | ||||||||
\(254\) | −5.92583 | −0.371820 | ||||||||
\(255\) | −28.0218 | −1.75479 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.6919 | −0.666943 | −0.333472 | − | 0.942760i | \(-0.608220\pi\) | ||||
−0.333472 | + | 0.942760i | \(0.608220\pi\) | |||||||
\(258\) | 14.6750 | 0.913627 | ||||||||
\(259\) | −0.620197 | −0.0385372 | ||||||||
\(260\) | −4.30731 | −0.267128 | ||||||||
\(261\) | 1.41712 | 0.0877176 | ||||||||
\(262\) | 7.13803 | 0.440989 | ||||||||
\(263\) | 12.9105 | 0.796094 | 0.398047 | − | 0.917365i | \(-0.369688\pi\) | ||||
0.398047 | + | 0.917365i | \(0.369688\pi\) | |||||||
\(264\) | 1.96003 | 0.120632 | ||||||||
\(265\) | −36.9245 | −2.26825 | ||||||||
\(266\) | −7.04424 | −0.431910 | ||||||||
\(267\) | 22.0598 | 1.35004 | ||||||||
\(268\) | 15.7014 | 0.959114 | ||||||||
\(269\) | 12.8847 | 0.785596 | 0.392798 | − | 0.919625i | \(-0.371507\pi\) | ||||
0.392798 | + | 0.919625i | \(0.371507\pi\) | |||||||
\(270\) | −17.8962 | −1.08913 | ||||||||
\(271\) | −6.74674 | −0.409835 | −0.204918 | − | 0.978779i | \(-0.565693\pi\) | ||||
−0.204918 | + | 0.978779i | \(0.565693\pi\) | |||||||
\(272\) | 5.77216 | 0.349988 | ||||||||
\(273\) | −2.05275 | −0.124238 | ||||||||
\(274\) | −8.51425 | −0.514365 | ||||||||
\(275\) | −6.68342 | −0.403025 | ||||||||
\(276\) | −7.92502 | −0.477030 | ||||||||
\(277\) | 6.70796 | 0.403042 | 0.201521 | − | 0.979484i | \(-0.435412\pi\) | ||||
0.201521 | + | 0.979484i | \(0.435412\pi\) | |||||||
\(278\) | 8.10576 | 0.486151 | ||||||||
\(279\) | 0.726691 | 0.0435059 | ||||||||
\(280\) | −3.19164 | −0.190737 | ||||||||
\(281\) | 23.7571 | 1.41723 | 0.708616 | − | 0.705594i | \(-0.249320\pi\) | ||||
0.708616 | + | 0.705594i | \(0.249320\pi\) | |||||||
\(282\) | −17.1526 | −1.02142 | ||||||||
\(283\) | 0.277722 | 0.0165089 | 0.00825444 | − | 0.999966i | \(-0.497373\pi\) | ||||
0.00825444 | + | 0.999966i | \(0.497373\pi\) | |||||||
\(284\) | 7.43814 | 0.441373 | ||||||||
\(285\) | 34.1973 | 2.02567 | ||||||||
\(286\) | 1.73905 | 0.102832 | ||||||||
\(287\) | 6.09301 | 0.359659 | ||||||||
\(288\) | 0.686407 | 0.0404469 | ||||||||
\(289\) | 16.3178 | 0.959871 | ||||||||
\(290\) | −6.58930 | −0.386937 | ||||||||
\(291\) | 14.6786 | 0.860475 | ||||||||
\(292\) | 5.84106 | 0.341822 | ||||||||
\(293\) | 2.33289 | 0.136289 | 0.0681443 | − | 0.997675i | \(-0.478292\pi\) | ||||
0.0681443 | + | 0.997675i | \(0.478292\pi\) | |||||||
\(294\) | −1.52105 | −0.0887094 | ||||||||
\(295\) | 7.87680 | 0.458605 | ||||||||
\(296\) | −0.620197 | −0.0360482 | ||||||||
\(297\) | 7.22547 | 0.419264 | ||||||||
\(298\) | 13.2557 | 0.767880 | ||||||||
\(299\) | −7.03152 | −0.406643 | ||||||||
\(300\) | 7.88902 | 0.455473 | ||||||||
\(301\) | 9.64795 | 0.556099 | ||||||||
\(302\) | −11.8253 | −0.680471 | ||||||||
\(303\) | −26.2503 | −1.50804 | ||||||||
\(304\) | −7.04424 | −0.404015 | ||||||||
\(305\) | 31.8862 | 1.82580 | ||||||||
\(306\) | 3.96205 | 0.226495 | ||||||||
\(307\) | 11.9231 | 0.680488 | 0.340244 | − | 0.940337i | \(-0.389490\pi\) | ||||
0.340244 | + | 0.940337i | \(0.389490\pi\) | |||||||
\(308\) | 1.28860 | 0.0734250 | ||||||||
\(309\) | 12.3552 | 0.702862 | ||||||||
\(310\) | −3.37895 | −0.191912 | ||||||||
\(311\) | 13.8823 | 0.787196 | 0.393598 | − | 0.919283i | \(-0.371230\pi\) | ||||
0.393598 | + | 0.919283i | \(0.371230\pi\) | |||||||
\(312\) | −2.05275 | −0.116214 | ||||||||
\(313\) | −0.493548 | −0.0278970 | −0.0139485 | − | 0.999903i | \(-0.504440\pi\) | ||||
−0.0139485 | + | 0.999903i | \(0.504440\pi\) | |||||||
\(314\) | 10.4632 | 0.590475 | ||||||||
\(315\) | −2.19076 | −0.123436 | ||||||||
\(316\) | −2.91941 | −0.164229 | ||||||||
\(317\) | 5.58340 | 0.313595 | 0.156798 | − | 0.987631i | \(-0.449883\pi\) | ||||
0.156798 | + | 0.987631i | \(0.449883\pi\) | |||||||
\(318\) | −17.5972 | −0.986803 | ||||||||
\(319\) | 2.66039 | 0.148953 | ||||||||
\(320\) | −3.19164 | −0.178418 | ||||||||
\(321\) | −11.5856 | −0.646646 | ||||||||
\(322\) | −5.21023 | −0.290355 | ||||||||
\(323\) | −40.6604 | −2.26241 | ||||||||
\(324\) | −6.46962 | −0.359424 | ||||||||
\(325\) | 6.99957 | 0.388267 | ||||||||
\(326\) | −2.15221 | −0.119200 | ||||||||
\(327\) | −22.7325 | −1.25711 | ||||||||
\(328\) | 6.09301 | 0.336430 | ||||||||
\(329\) | −11.2768 | −0.621710 | ||||||||
\(330\) | −6.25571 | −0.344365 | ||||||||
\(331\) | 20.1655 | 1.10840 | 0.554198 | − | 0.832385i | \(-0.313025\pi\) | ||||
0.554198 | + | 0.832385i | \(0.313025\pi\) | |||||||
\(332\) | −2.31837 | −0.127237 | ||||||||
\(333\) | −0.425708 | −0.0233286 | ||||||||
\(334\) | −22.9023 | −1.25316 | ||||||||
\(335\) | −50.1131 | −2.73797 | ||||||||
\(336\) | −1.52105 | −0.0829801 | ||||||||
\(337\) | −12.4429 | −0.677809 | −0.338904 | − | 0.940821i | \(-0.610056\pi\) | ||||
−0.338904 | + | 0.940821i | \(0.610056\pi\) | |||||||
\(338\) | 11.1787 | 0.608040 | ||||||||
\(339\) | 8.98232 | 0.487852 | ||||||||
\(340\) | −18.4226 | −0.999108 | ||||||||
\(341\) | 1.36423 | 0.0738772 | ||||||||
\(342\) | −4.83522 | −0.261459 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.64795 | 0.520183 | ||||||||
\(345\) | 25.2938 | 1.36177 | ||||||||
\(346\) | −3.05284 | −0.164122 | ||||||||
\(347\) | −4.20130 | −0.225537 | −0.112769 | − | 0.993621i | \(-0.535972\pi\) | ||||
−0.112769 | + | 0.993621i | \(0.535972\pi\) | |||||||
\(348\) | −3.14028 | −0.168337 | ||||||||
\(349\) | 33.7381 | 1.80596 | 0.902981 | − | 0.429681i | \(-0.141374\pi\) | ||||
0.902981 | + | 0.429681i | \(0.141374\pi\) | |||||||
\(350\) | 5.18656 | 0.277233 | ||||||||
\(351\) | −7.56727 | −0.403911 | ||||||||
\(352\) | 1.28860 | 0.0686828 | ||||||||
\(353\) | 25.2469 | 1.34376 | 0.671880 | − | 0.740660i | \(-0.265487\pi\) | ||||
0.671880 | + | 0.740660i | \(0.265487\pi\) | |||||||
\(354\) | 3.75387 | 0.199516 | ||||||||
\(355\) | −23.7399 | −1.25998 | ||||||||
\(356\) | 14.5030 | 0.768658 | ||||||||
\(357\) | −8.77974 | −0.464673 | ||||||||
\(358\) | −10.9370 | −0.578036 | ||||||||
\(359\) | −9.59978 | −0.506657 | −0.253328 | − | 0.967380i | \(-0.581525\pi\) | ||||
−0.253328 | + | 0.967380i | \(0.581525\pi\) | |||||||
\(360\) | −2.19076 | −0.115463 | ||||||||
\(361\) | 30.6213 | 1.61165 | ||||||||
\(362\) | 7.20674 | 0.378778 | ||||||||
\(363\) | −14.2058 | −0.745614 | ||||||||
\(364\) | −1.34956 | −0.0707362 | ||||||||
\(365\) | −18.6426 | −0.975797 | ||||||||
\(366\) | 15.1961 | 0.794313 | ||||||||
\(367\) | 11.8428 | 0.618192 | 0.309096 | − | 0.951031i | \(-0.399974\pi\) | ||||
0.309096 | + | 0.951031i | \(0.399974\pi\) | |||||||
\(368\) | −5.21023 | −0.271602 | ||||||||
\(369\) | 4.18229 | 0.217721 | ||||||||
\(370\) | 1.97944 | 0.102906 | ||||||||
\(371\) | −11.5691 | −0.600639 | ||||||||
\(372\) | −1.61032 | −0.0834911 | ||||||||
\(373\) | 24.7385 | 1.28091 | 0.640456 | − | 0.767995i | \(-0.278745\pi\) | ||||
0.640456 | + | 0.767995i | \(0.278745\pi\) | |||||||
\(374\) | 7.43802 | 0.384611 | ||||||||
\(375\) | −0.905681 | −0.0467692 | ||||||||
\(376\) | −11.2768 | −0.581557 | ||||||||
\(377\) | −2.78623 | −0.143498 | ||||||||
\(378\) | −5.60721 | −0.288404 | ||||||||
\(379\) | 8.42862 | 0.432949 | 0.216475 | − | 0.976288i | \(-0.430544\pi\) | ||||
0.216475 | + | 0.976288i | \(0.430544\pi\) | |||||||
\(380\) | 22.4827 | 1.15334 | ||||||||
\(381\) | 9.01349 | 0.461775 | ||||||||
\(382\) | −4.94052 | −0.252779 | ||||||||
\(383\) | 22.2967 | 1.13931 | 0.569653 | − | 0.821885i | \(-0.307078\pi\) | ||||
0.569653 | + | 0.821885i | \(0.307078\pi\) | |||||||
\(384\) | −1.52105 | −0.0776208 | ||||||||
\(385\) | −4.11276 | −0.209606 | ||||||||
\(386\) | −0.189080 | −0.00962390 | ||||||||
\(387\) | 6.62242 | 0.336637 | ||||||||
\(388\) | 9.65031 | 0.489920 | ||||||||
\(389\) | 6.43268 | 0.326150 | 0.163075 | − | 0.986614i | \(-0.447859\pi\) | ||||
0.163075 | + | 0.986614i | \(0.447859\pi\) | |||||||
\(390\) | 6.55163 | 0.331755 | ||||||||
\(391\) | −30.0743 | −1.52092 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −10.8573 | −0.547678 | ||||||||
\(394\) | 2.30403 | 0.116075 | ||||||||
\(395\) | 9.31769 | 0.468824 | ||||||||
\(396\) | 0.884507 | 0.0444481 | ||||||||
\(397\) | 18.5004 | 0.928509 | 0.464254 | − | 0.885702i | \(-0.346322\pi\) | ||||
0.464254 | + | 0.885702i | \(0.346322\pi\) | |||||||
\(398\) | −22.6764 | −1.13667 | ||||||||
\(399\) | 10.7146 | 0.536403 | ||||||||
\(400\) | 5.18656 | 0.259328 | ||||||||
\(401\) | −9.81363 | −0.490069 | −0.245035 | − | 0.969514i | \(-0.578799\pi\) | ||||
−0.245035 | + | 0.969514i | \(0.578799\pi\) | |||||||
\(402\) | −23.8826 | −1.19115 | ||||||||
\(403\) | −1.42876 | −0.0711718 | ||||||||
\(404\) | −17.2580 | −0.858620 | ||||||||
\(405\) | 20.6487 | 1.02604 | ||||||||
\(406\) | −2.06455 | −0.102462 | ||||||||
\(407\) | −0.799188 | −0.0396143 | ||||||||
\(408\) | −8.77974 | −0.434662 | ||||||||
\(409\) | −21.6181 | −1.06895 | −0.534474 | − | 0.845185i | \(-0.679490\pi\) | ||||
−0.534474 | + | 0.845185i | \(0.679490\pi\) | |||||||
\(410\) | −19.4467 | −0.960404 | ||||||||
\(411\) | 12.9506 | 0.638806 | ||||||||
\(412\) | 8.12280 | 0.400182 | ||||||||
\(413\) | 2.46795 | 0.121440 | ||||||||
\(414\) | −3.57634 | −0.175768 | ||||||||
\(415\) | 7.39941 | 0.363223 | ||||||||
\(416\) | −1.34956 | −0.0661676 | ||||||||
\(417\) | −12.3293 | −0.603767 | ||||||||
\(418\) | −9.07723 | −0.443982 | ||||||||
\(419\) | 13.3692 | 0.653126 | 0.326563 | − | 0.945175i | \(-0.394109\pi\) | ||||
0.326563 | + | 0.945175i | \(0.394109\pi\) | |||||||
\(420\) | 4.85464 | 0.236882 | ||||||||
\(421\) | 8.21394 | 0.400323 | 0.200162 | − | 0.979763i | \(-0.435853\pi\) | ||||
0.200162 | + | 0.979763i | \(0.435853\pi\) | |||||||
\(422\) | −12.5303 | −0.609964 | ||||||||
\(423\) | −7.74048 | −0.376355 | ||||||||
\(424\) | −11.5691 | −0.561846 | ||||||||
\(425\) | 29.9376 | 1.45219 | ||||||||
\(426\) | −11.3138 | −0.548155 | ||||||||
\(427\) | 9.99054 | 0.483476 | ||||||||
\(428\) | −7.61685 | −0.368174 | ||||||||
\(429\) | −2.64518 | −0.127710 | ||||||||
\(430\) | −30.7928 | −1.48496 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −5.60721 | −0.269777 | ||||||||
\(433\) | −7.69393 | −0.369747 | −0.184873 | − | 0.982762i | \(-0.559187\pi\) | ||||
−0.184873 | + | 0.982762i | \(0.559187\pi\) | |||||||
\(434\) | −1.05869 | −0.0508187 | ||||||||
\(435\) | 10.0226 | 0.480549 | ||||||||
\(436\) | −14.9452 | −0.715748 | ||||||||
\(437\) | 36.7021 | 1.75570 | ||||||||
\(438\) | −8.88455 | −0.424520 | ||||||||
\(439\) | −13.8335 | −0.660236 | −0.330118 | − | 0.943940i | \(-0.607089\pi\) | ||||
−0.330118 | + | 0.943940i | \(0.607089\pi\) | |||||||
\(440\) | −4.11276 | −0.196068 | ||||||||
\(441\) | −0.686407 | −0.0326861 | ||||||||
\(442\) | −7.78987 | −0.370526 | ||||||||
\(443\) | −16.9069 | −0.803271 | −0.401636 | − | 0.915800i | \(-0.631558\pi\) | ||||
−0.401636 | + | 0.915800i | \(0.631558\pi\) | |||||||
\(444\) | 0.943351 | 0.0447694 | ||||||||
\(445\) | −46.2884 | −2.19428 | ||||||||
\(446\) | 12.9727 | 0.614276 | ||||||||
\(447\) | −20.1625 | −0.953655 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −20.4743 | −0.966244 | −0.483122 | − | 0.875553i | \(-0.660497\pi\) | ||||
−0.483122 | + | 0.875553i | \(0.660497\pi\) | |||||||
\(450\) | 3.56009 | 0.167824 | ||||||||
\(451\) | 7.85148 | 0.369712 | ||||||||
\(452\) | 5.90534 | 0.277764 | ||||||||
\(453\) | 17.9869 | 0.845098 | ||||||||
\(454\) | −7.24109 | −0.339841 | ||||||||
\(455\) | 4.30731 | 0.201930 | ||||||||
\(456\) | 10.7146 | 0.501759 | ||||||||
\(457\) | 8.32894 | 0.389611 | 0.194806 | − | 0.980842i | \(-0.437592\pi\) | ||||
0.194806 | + | 0.980842i | \(0.437592\pi\) | |||||||
\(458\) | −3.79306 | −0.177238 | ||||||||
\(459\) | −32.3657 | −1.51070 | ||||||||
\(460\) | 16.6292 | 0.775339 | ||||||||
\(461\) | −30.3206 | −1.41217 | −0.706084 | − | 0.708128i | \(-0.749540\pi\) | ||||
−0.706084 | + | 0.708128i | \(0.749540\pi\) | |||||||
\(462\) | −1.96003 | −0.0911888 | ||||||||
\(463\) | 12.7482 | 0.592461 | 0.296230 | − | 0.955117i | \(-0.404270\pi\) | ||||
0.296230 | + | 0.955117i | \(0.404270\pi\) | |||||||
\(464\) | −2.06455 | −0.0958443 | ||||||||
\(465\) | 5.13955 | 0.238341 | ||||||||
\(466\) | −14.4348 | −0.668680 | ||||||||
\(467\) | 19.7315 | 0.913065 | 0.456533 | − | 0.889707i | \(-0.349091\pi\) | ||||
0.456533 | + | 0.889707i | \(0.349091\pi\) | |||||||
\(468\) | −0.926348 | −0.0428204 | ||||||||
\(469\) | −15.7014 | −0.725022 | ||||||||
\(470\) | 35.9915 | 1.66016 | ||||||||
\(471\) | −15.9151 | −0.733330 | ||||||||
\(472\) | 2.46795 | 0.113596 | ||||||||
\(473\) | 12.4324 | 0.571642 | ||||||||
\(474\) | 4.44056 | 0.203962 | ||||||||
\(475\) | −36.5354 | −1.67636 | ||||||||
\(476\) | −5.77216 | −0.264566 | ||||||||
\(477\) | −7.94113 | −0.363599 | ||||||||
\(478\) | −18.6684 | −0.853873 | ||||||||
\(479\) | −30.1114 | −1.37583 | −0.687913 | − | 0.725793i | \(-0.741473\pi\) | ||||
−0.687913 | + | 0.725793i | \(0.741473\pi\) | |||||||
\(480\) | 4.85464 | 0.221583 | ||||||||
\(481\) | 0.836993 | 0.0381636 | ||||||||
\(482\) | 28.5089 | 1.29854 | ||||||||
\(483\) | 7.92502 | 0.360601 | ||||||||
\(484\) | −9.33950 | −0.424523 | ||||||||
\(485\) | −30.8003 | −1.39857 | ||||||||
\(486\) | −6.98101 | −0.316665 | ||||||||
\(487\) | −1.44157 | −0.0653236 | −0.0326618 | − | 0.999466i | \(-0.510398\pi\) | ||||
−0.0326618 | + | 0.999466i | \(0.510398\pi\) | |||||||
\(488\) | 9.99054 | 0.452250 | ||||||||
\(489\) | 3.27362 | 0.148038 | ||||||||
\(490\) | 3.19164 | 0.144184 | ||||||||
\(491\) | −8.76940 | −0.395757 | −0.197879 | − | 0.980227i | \(-0.563405\pi\) | ||||
−0.197879 | + | 0.980227i | \(0.563405\pi\) | |||||||
\(492\) | −9.26778 | −0.417824 | ||||||||
\(493\) | −11.9169 | −0.536710 | ||||||||
\(494\) | 9.50662 | 0.427723 | ||||||||
\(495\) | −2.82303 | −0.126886 | ||||||||
\(496\) | −1.05869 | −0.0475365 | ||||||||
\(497\) | −7.43814 | −0.333646 | ||||||||
\(498\) | 3.52636 | 0.158020 | ||||||||
\(499\) | −9.82796 | −0.439960 | −0.219980 | − | 0.975504i | \(-0.570599\pi\) | ||||
−0.219980 | + | 0.975504i | \(0.570599\pi\) | |||||||
\(500\) | −0.595431 | −0.0266285 | ||||||||
\(501\) | 34.8356 | 1.55634 | ||||||||
\(502\) | −26.8629 | −1.19895 | ||||||||
\(503\) | 4.66012 | 0.207785 | 0.103892 | − | 0.994589i | \(-0.466870\pi\) | ||||
0.103892 | + | 0.994589i | \(0.466870\pi\) | |||||||
\(504\) | −0.686407 | −0.0305750 | ||||||||
\(505\) | 55.0814 | 2.45109 | ||||||||
\(506\) | −6.71392 | −0.298470 | ||||||||
\(507\) | −17.0033 | −0.755145 | ||||||||
\(508\) | 5.92583 | 0.262916 | ||||||||
\(509\) | 13.4419 | 0.595801 | 0.297900 | − | 0.954597i | \(-0.403714\pi\) | ||||
0.297900 | + | 0.954597i | \(0.403714\pi\) | |||||||
\(510\) | 28.0218 | 1.24082 | ||||||||
\(511\) | −5.84106 | −0.258393 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 39.4985 | 1.74390 | ||||||||
\(514\) | 10.6919 | 0.471600 | ||||||||
\(515\) | −25.9251 | −1.14239 | ||||||||
\(516\) | −14.6750 | −0.646032 | ||||||||
\(517\) | −14.5313 | −0.639087 | ||||||||
\(518\) | 0.620197 | 0.0272499 | ||||||||
\(519\) | 4.64352 | 0.203828 | ||||||||
\(520\) | 4.30731 | 0.188888 | ||||||||
\(521\) | −26.6330 | −1.16681 | −0.583407 | − | 0.812180i | \(-0.698281\pi\) | ||||
−0.583407 | + | 0.812180i | \(0.698281\pi\) | |||||||
\(522\) | −1.41712 | −0.0620257 | ||||||||
\(523\) | −26.6902 | −1.16708 | −0.583540 | − | 0.812085i | \(-0.698333\pi\) | ||||
−0.583540 | + | 0.812085i | \(0.698333\pi\) | |||||||
\(524\) | −7.13803 | −0.311826 | ||||||||
\(525\) | −7.88902 | −0.344305 | ||||||||
\(526\) | −12.9105 | −0.562923 | ||||||||
\(527\) | −6.11092 | −0.266196 | ||||||||
\(528\) | −1.96003 | −0.0852994 | ||||||||
\(529\) | 4.14650 | 0.180283 | ||||||||
\(530\) | 36.9245 | 1.60390 | ||||||||
\(531\) | 1.69402 | 0.0735141 | ||||||||
\(532\) | 7.04424 | 0.305406 | ||||||||
\(533\) | −8.22289 | −0.356173 | ||||||||
\(534\) | −22.0598 | −0.954621 | ||||||||
\(535\) | 24.3102 | 1.05102 | ||||||||
\(536\) | −15.7014 | −0.678196 | ||||||||
\(537\) | 16.6356 | 0.717881 | ||||||||
\(538\) | −12.8847 | −0.555500 | ||||||||
\(539\) | −1.28860 | −0.0555041 | ||||||||
\(540\) | 17.8962 | 0.770129 | ||||||||
\(541\) | 0.262978 | 0.0113063 | 0.00565316 | − | 0.999984i | \(-0.498201\pi\) | ||||
0.00565316 | + | 0.999984i | \(0.498201\pi\) | |||||||
\(542\) | 6.74674 | 0.289797 | ||||||||
\(543\) | −10.9618 | −0.470416 | ||||||||
\(544\) | −5.77216 | −0.247479 | ||||||||
\(545\) | 47.6998 | 2.04324 | ||||||||
\(546\) | 2.05275 | 0.0878495 | ||||||||
\(547\) | −15.6346 | −0.668488 | −0.334244 | − | 0.942487i | \(-0.608481\pi\) | ||||
−0.334244 | + | 0.942487i | \(0.608481\pi\) | |||||||
\(548\) | 8.51425 | 0.363711 | ||||||||
\(549\) | 6.85758 | 0.292674 | ||||||||
\(550\) | 6.68342 | 0.284982 | ||||||||
\(551\) | 14.5432 | 0.619560 | ||||||||
\(552\) | 7.92502 | 0.337311 | ||||||||
\(553\) | 2.91941 | 0.124146 | ||||||||
\(554\) | −6.70796 | −0.284994 | ||||||||
\(555\) | −3.01083 | −0.127803 | ||||||||
\(556\) | −8.10576 | −0.343761 | ||||||||
\(557\) | 33.9298 | 1.43765 | 0.718826 | − | 0.695190i | \(-0.244680\pi\) | ||||
0.718826 | + | 0.695190i | \(0.244680\pi\) | |||||||
\(558\) | −0.726691 | −0.0307633 | ||||||||
\(559\) | −13.0205 | −0.550708 | ||||||||
\(560\) | 3.19164 | 0.134871 | ||||||||
\(561\) | −11.3136 | −0.477661 | ||||||||
\(562\) | −23.7571 | −1.00213 | ||||||||
\(563\) | −12.5560 | −0.529172 | −0.264586 | − | 0.964362i | \(-0.585235\pi\) | ||||
−0.264586 | + | 0.964362i | \(0.585235\pi\) | |||||||
\(564\) | 17.1526 | 0.722254 | ||||||||
\(565\) | −18.8477 | −0.792929 | ||||||||
\(566\) | −0.277722 | −0.0116735 | ||||||||
\(567\) | 6.46962 | 0.271699 | ||||||||
\(568\) | −7.43814 | −0.312098 | ||||||||
\(569\) | −6.75825 | −0.283321 | −0.141660 | − | 0.989915i | \(-0.545244\pi\) | ||||
−0.141660 | + | 0.989915i | \(0.545244\pi\) | |||||||
\(570\) | −34.1973 | −1.43237 | ||||||||
\(571\) | −11.7875 | −0.493292 | −0.246646 | − | 0.969106i | \(-0.579329\pi\) | ||||
−0.246646 | + | 0.969106i | \(0.579329\pi\) | |||||||
\(572\) | −1.73905 | −0.0727132 | ||||||||
\(573\) | 7.51478 | 0.313934 | ||||||||
\(574\) | −6.09301 | −0.254317 | ||||||||
\(575\) | −27.0232 | −1.12694 | ||||||||
\(576\) | −0.686407 | −0.0286003 | ||||||||
\(577\) | −1.79260 | −0.0746270 | −0.0373135 | − | 0.999304i | \(-0.511880\pi\) | ||||
−0.0373135 | + | 0.999304i | \(0.511880\pi\) | |||||||
\(578\) | −16.3178 | −0.678731 | ||||||||
\(579\) | 0.287599 | 0.0119522 | ||||||||
\(580\) | 6.58930 | 0.273606 | ||||||||
\(581\) | 2.31837 | 0.0961824 | ||||||||
\(582\) | −14.6786 | −0.608447 | ||||||||
\(583\) | −14.9080 | −0.617427 | ||||||||
\(584\) | −5.84106 | −0.241705 | ||||||||
\(585\) | 2.95657 | 0.122239 | ||||||||
\(586\) | −2.33289 | −0.0963706 | ||||||||
\(587\) | −22.3933 | −0.924271 | −0.462136 | − | 0.886809i | \(-0.652917\pi\) | ||||
−0.462136 | + | 0.886809i | \(0.652917\pi\) | |||||||
\(588\) | 1.52105 | 0.0627270 | ||||||||
\(589\) | 7.45765 | 0.307287 | ||||||||
\(590\) | −7.87680 | −0.324283 | ||||||||
\(591\) | −3.50454 | −0.144158 | ||||||||
\(592\) | 0.620197 | 0.0254899 | ||||||||
\(593\) | 41.3315 | 1.69728 | 0.848641 | − | 0.528969i | \(-0.177421\pi\) | ||||
0.848641 | + | 0.528969i | \(0.177421\pi\) | |||||||
\(594\) | −7.22547 | −0.296465 | ||||||||
\(595\) | 18.4226 | 0.755255 | ||||||||
\(596\) | −13.2557 | −0.542973 | ||||||||
\(597\) | 34.4920 | 1.41166 | ||||||||
\(598\) | 7.03152 | 0.287540 | ||||||||
\(599\) | 8.37665 | 0.342261 | 0.171130 | − | 0.985248i | \(-0.445258\pi\) | ||||
0.171130 | + | 0.985248i | \(0.445258\pi\) | |||||||
\(600\) | −7.88902 | −0.322068 | ||||||||
\(601\) | −5.47057 | −0.223149 | −0.111575 | − | 0.993756i | \(-0.535589\pi\) | ||||
−0.111575 | + | 0.993756i | \(0.535589\pi\) | |||||||
\(602\) | −9.64795 | −0.393221 | ||||||||
\(603\) | −10.7775 | −0.438895 | ||||||||
\(604\) | 11.8253 | 0.481165 | ||||||||
\(605\) | 29.8083 | 1.21188 | ||||||||
\(606\) | 26.2503 | 1.06635 | ||||||||
\(607\) | −0.587193 | −0.0238334 | −0.0119167 | − | 0.999929i | \(-0.503793\pi\) | ||||
−0.0119167 | + | 0.999929i | \(0.503793\pi\) | |||||||
\(608\) | 7.04424 | 0.285682 | ||||||||
\(609\) | 3.14028 | 0.127251 | ||||||||
\(610\) | −31.8862 | −1.29103 | ||||||||
\(611\) | 15.2187 | 0.615684 | ||||||||
\(612\) | −3.96205 | −0.160156 | ||||||||
\(613\) | −11.6822 | −0.471841 | −0.235920 | − | 0.971772i | \(-0.575810\pi\) | ||||
−0.235920 | + | 0.971772i | \(0.575810\pi\) | |||||||
\(614\) | −11.9231 | −0.481177 | ||||||||
\(615\) | 29.5794 | 1.19276 | ||||||||
\(616\) | −1.28860 | −0.0519193 | ||||||||
\(617\) | −21.9608 | −0.884108 | −0.442054 | − | 0.896988i | \(-0.645750\pi\) | ||||
−0.442054 | + | 0.896988i | \(0.645750\pi\) | |||||||
\(618\) | −12.3552 | −0.496999 | ||||||||
\(619\) | −12.8998 | −0.518485 | −0.259242 | − | 0.965812i | \(-0.583473\pi\) | ||||
−0.259242 | + | 0.965812i | \(0.583473\pi\) | |||||||
\(620\) | 3.37895 | 0.135702 | ||||||||
\(621\) | 29.2149 | 1.17235 | ||||||||
\(622\) | −13.8823 | −0.556631 | ||||||||
\(623\) | −14.5030 | −0.581051 | ||||||||
\(624\) | 2.05275 | 0.0821757 | ||||||||
\(625\) | −24.0324 | −0.961296 | ||||||||
\(626\) | 0.493548 | 0.0197261 | ||||||||
\(627\) | 13.8069 | 0.551395 | ||||||||
\(628\) | −10.4632 | −0.417529 | ||||||||
\(629\) | 3.57987 | 0.142739 | ||||||||
\(630\) | 2.19076 | 0.0872821 | ||||||||
\(631\) | 45.0367 | 1.79288 | 0.896442 | − | 0.443161i | \(-0.146143\pi\) | ||||
0.896442 | + | 0.443161i | \(0.146143\pi\) | |||||||
\(632\) | 2.91941 | 0.116128 | ||||||||
\(633\) | 19.0592 | 0.757534 | ||||||||
\(634\) | −5.58340 | −0.221745 | ||||||||
\(635\) | −18.9131 | −0.750544 | ||||||||
\(636\) | 17.5972 | 0.697775 | ||||||||
\(637\) | 1.34956 | 0.0534715 | ||||||||
\(638\) | −2.66039 | −0.105326 | ||||||||
\(639\) | −5.10560 | −0.201974 | ||||||||
\(640\) | 3.19164 | 0.126161 | ||||||||
\(641\) | 12.6284 | 0.498794 | 0.249397 | − | 0.968401i | \(-0.419768\pi\) | ||||
0.249397 | + | 0.968401i | \(0.419768\pi\) | |||||||
\(642\) | 11.5856 | 0.457248 | ||||||||
\(643\) | 25.7783 | 1.01660 | 0.508299 | − | 0.861181i | \(-0.330274\pi\) | ||||
0.508299 | + | 0.861181i | \(0.330274\pi\) | |||||||
\(644\) | 5.21023 | 0.205312 | ||||||||
\(645\) | 46.8374 | 1.84422 | ||||||||
\(646\) | 40.6604 | 1.59976 | ||||||||
\(647\) | 21.2392 | 0.835000 | 0.417500 | − | 0.908677i | \(-0.362906\pi\) | ||||
0.417500 | + | 0.908677i | \(0.362906\pi\) | |||||||
\(648\) | 6.46962 | 0.254151 | ||||||||
\(649\) | 3.18021 | 0.124834 | ||||||||
\(650\) | −6.99957 | −0.274546 | ||||||||
\(651\) | 1.61032 | 0.0631133 | ||||||||
\(652\) | 2.15221 | 0.0842870 | ||||||||
\(653\) | −22.1599 | −0.867182 | −0.433591 | − | 0.901110i | \(-0.642754\pi\) | ||||
−0.433591 | + | 0.901110i | \(0.642754\pi\) | |||||||
\(654\) | 22.7325 | 0.888910 | ||||||||
\(655\) | 22.7820 | 0.890167 | ||||||||
\(656\) | −6.09301 | −0.237892 | ||||||||
\(657\) | −4.00935 | −0.156420 | ||||||||
\(658\) | 11.2768 | 0.439616 | ||||||||
\(659\) | 32.5969 | 1.26979 | 0.634897 | − | 0.772597i | \(-0.281043\pi\) | ||||
0.634897 | + | 0.772597i | \(0.281043\pi\) | |||||||
\(660\) | 6.25571 | 0.243503 | ||||||||
\(661\) | −28.1812 | −1.09612 | −0.548062 | − | 0.836438i | \(-0.684634\pi\) | ||||
−0.548062 | + | 0.836438i | \(0.684634\pi\) | |||||||
\(662\) | −20.1655 | −0.783754 | ||||||||
\(663\) | 11.8488 | 0.460169 | ||||||||
\(664\) | 2.31837 | 0.0899704 | ||||||||
\(665\) | −22.4827 | −0.871840 | ||||||||
\(666\) | 0.425708 | 0.0164958 | ||||||||
\(667\) | 10.7568 | 0.416504 | ||||||||
\(668\) | 22.9023 | 0.886118 | ||||||||
\(669\) | −19.7321 | −0.762889 | ||||||||
\(670\) | 50.1131 | 1.93604 | ||||||||
\(671\) | 12.8738 | 0.496989 | ||||||||
\(672\) | 1.52105 | 0.0586758 | ||||||||
\(673\) | −28.0463 | −1.08110 | −0.540552 | − | 0.841311i | \(-0.681785\pi\) | ||||
−0.540552 | + | 0.841311i | \(0.681785\pi\) | |||||||
\(674\) | 12.4429 | 0.479283 | ||||||||
\(675\) | −29.0821 | −1.11937 | ||||||||
\(676\) | −11.1787 | −0.429950 | ||||||||
\(677\) | 34.7563 | 1.33579 | 0.667896 | − | 0.744255i | \(-0.267195\pi\) | ||||
0.667896 | + | 0.744255i | \(0.267195\pi\) | |||||||
\(678\) | −8.98232 | −0.344964 | ||||||||
\(679\) | −9.65031 | −0.370345 | ||||||||
\(680\) | 18.4226 | 0.706476 | ||||||||
\(681\) | 11.0141 | 0.422060 | ||||||||
\(682\) | −1.36423 | −0.0522390 | ||||||||
\(683\) | 3.41569 | 0.130698 | 0.0653488 | − | 0.997862i | \(-0.479184\pi\) | ||||
0.0653488 | + | 0.997862i | \(0.479184\pi\) | |||||||
\(684\) | 4.83522 | 0.184879 | ||||||||
\(685\) | −27.1744 | −1.03828 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 5.76944 | 0.220118 | ||||||||
\(688\) | −9.64795 | −0.367825 | ||||||||
\(689\) | 15.6132 | 0.594817 | ||||||||
\(690\) | −25.2938 | −0.962919 | ||||||||
\(691\) | −11.6477 | −0.443100 | −0.221550 | − | 0.975149i | \(-0.571112\pi\) | ||||
−0.221550 | + | 0.975149i | \(0.571112\pi\) | |||||||
\(692\) | 3.05284 | 0.116051 | ||||||||
\(693\) | −0.884507 | −0.0335996 | ||||||||
\(694\) | 4.20130 | 0.159479 | ||||||||
\(695\) | 25.8707 | 0.981330 | ||||||||
\(696\) | 3.14028 | 0.119032 | ||||||||
\(697\) | −35.1698 | −1.33215 | ||||||||
\(698\) | −33.7381 | −1.27701 | ||||||||
\(699\) | 21.9561 | 0.830455 | ||||||||
\(700\) | −5.18656 | −0.196034 | ||||||||
\(701\) | −32.4282 | −1.22480 | −0.612398 | − | 0.790550i | \(-0.709795\pi\) | ||||
−0.612398 | + | 0.790550i | \(0.709795\pi\) | |||||||
\(702\) | 7.56727 | 0.285608 | ||||||||
\(703\) | −4.36881 | −0.164773 | ||||||||
\(704\) | −1.28860 | −0.0485661 | ||||||||
\(705\) | −54.7448 | −2.06181 | ||||||||
\(706\) | −25.2469 | −0.950181 | ||||||||
\(707\) | 17.2580 | 0.649056 | ||||||||
\(708\) | −3.75387 | −0.141079 | ||||||||
\(709\) | −39.0374 | −1.46608 | −0.733040 | − | 0.680186i | \(-0.761899\pi\) | ||||
−0.733040 | + | 0.680186i | \(0.761899\pi\) | |||||||
\(710\) | 23.7399 | 0.890942 | ||||||||
\(711\) | 2.00390 | 0.0751522 | ||||||||
\(712\) | −14.5030 | −0.543523 | ||||||||
\(713\) | 5.51601 | 0.206576 | ||||||||
\(714\) | 8.77974 | 0.328573 | ||||||||
\(715\) | 5.55041 | 0.207574 | ||||||||
\(716\) | 10.9370 | 0.408733 | ||||||||
\(717\) | 28.3956 | 1.06045 | ||||||||
\(718\) | 9.59978 | 0.358261 | ||||||||
\(719\) | 6.43215 | 0.239879 | 0.119939 | − | 0.992781i | \(-0.461730\pi\) | ||||
0.119939 | + | 0.992781i | \(0.461730\pi\) | |||||||
\(720\) | 2.19076 | 0.0816450 | ||||||||
\(721\) | −8.12280 | −0.302509 | ||||||||
\(722\) | −30.6213 | −1.13961 | ||||||||
\(723\) | −43.3634 | −1.61270 | ||||||||
\(724\) | −7.20674 | −0.267836 | ||||||||
\(725\) | −10.7079 | −0.397682 | ||||||||
\(726\) | 14.2058 | 0.527228 | ||||||||
\(727\) | −20.2201 | −0.749920 | −0.374960 | − | 0.927041i | \(-0.622344\pi\) | ||||
−0.374960 | + | 0.927041i | \(0.622344\pi\) | |||||||
\(728\) | 1.34956 | 0.0500180 | ||||||||
\(729\) | 30.0273 | 1.11212 | ||||||||
\(730\) | 18.6426 | 0.689992 | ||||||||
\(731\) | −55.6895 | −2.05975 | ||||||||
\(732\) | −15.1961 | −0.561664 | ||||||||
\(733\) | 4.53382 | 0.167460 | 0.0837302 | − | 0.996488i | \(-0.473317\pi\) | ||||
0.0837302 | + | 0.996488i | \(0.473317\pi\) | |||||||
\(734\) | −11.8428 | −0.437128 | ||||||||
\(735\) | −4.85464 | −0.179066 | ||||||||
\(736\) | 5.21023 | 0.192052 | ||||||||
\(737\) | −20.2328 | −0.745286 | ||||||||
\(738\) | −4.18229 | −0.153952 | ||||||||
\(739\) | −31.3707 | −1.15399 | −0.576996 | − | 0.816747i | \(-0.695775\pi\) | ||||
−0.576996 | + | 0.816747i | \(0.695775\pi\) | |||||||
\(740\) | −1.97944 | −0.0727658 | ||||||||
\(741\) | −14.4600 | −0.531203 | ||||||||
\(742\) | 11.5691 | 0.424716 | ||||||||
\(743\) | 46.7592 | 1.71543 | 0.857714 | − | 0.514127i | \(-0.171884\pi\) | ||||
0.857714 | + | 0.514127i | \(0.171884\pi\) | |||||||
\(744\) | 1.61032 | 0.0590371 | ||||||||
\(745\) | 42.3073 | 1.55002 | ||||||||
\(746\) | −24.7385 | −0.905742 | ||||||||
\(747\) | 1.59135 | 0.0582244 | ||||||||
\(748\) | −7.43802 | −0.271961 | ||||||||
\(749\) | 7.61685 | 0.278314 | ||||||||
\(750\) | 0.905681 | 0.0330708 | ||||||||
\(751\) | −33.0895 | −1.20745 | −0.603727 | − | 0.797191i | \(-0.706318\pi\) | ||||
−0.603727 | + | 0.797191i | \(0.706318\pi\) | |||||||
\(752\) | 11.2768 | 0.411223 | ||||||||
\(753\) | 40.8598 | 1.48901 | ||||||||
\(754\) | 2.78623 | 0.101469 | ||||||||
\(755\) | −37.7421 | −1.37358 | ||||||||
\(756\) | 5.60721 | 0.203932 | ||||||||
\(757\) | −34.1041 | −1.23954 | −0.619768 | − | 0.784785i | \(-0.712773\pi\) | ||||
−0.619768 | + | 0.784785i | \(0.712773\pi\) | |||||||
\(758\) | −8.42862 | −0.306141 | ||||||||
\(759\) | 10.2122 | 0.370680 | ||||||||
\(760\) | −22.4827 | −0.815532 | ||||||||
\(761\) | 44.9328 | 1.62881 | 0.814406 | − | 0.580296i | \(-0.197063\pi\) | ||||
0.814406 | + | 0.580296i | \(0.197063\pi\) | |||||||
\(762\) | −9.01349 | −0.326524 | ||||||||
\(763\) | 14.9452 | 0.541054 | ||||||||
\(764\) | 4.94052 | 0.178742 | ||||||||
\(765\) | 12.6454 | 0.457197 | ||||||||
\(766\) | −22.2967 | −0.805611 | ||||||||
\(767\) | −3.33064 | −0.120263 | ||||||||
\(768\) | 1.52105 | 0.0548862 | ||||||||
\(769\) | −27.4737 | −0.990728 | −0.495364 | − | 0.868686i | \(-0.664965\pi\) | ||||
−0.495364 | + | 0.868686i | \(0.664965\pi\) | |||||||
\(770\) | 4.11276 | 0.148213 | ||||||||
\(771\) | −16.2629 | −0.585695 | ||||||||
\(772\) | 0.189080 | 0.00680512 | ||||||||
\(773\) | 32.8340 | 1.18096 | 0.590479 | − | 0.807053i | \(-0.298939\pi\) | ||||
0.590479 | + | 0.807053i | \(0.298939\pi\) | |||||||
\(774\) | −6.62242 | −0.238038 | ||||||||
\(775\) | −5.49095 | −0.197241 | ||||||||
\(776\) | −9.65031 | −0.346426 | ||||||||
\(777\) | −0.943351 | −0.0338425 | ||||||||
\(778\) | −6.43268 | −0.230623 | ||||||||
\(779\) | 42.9206 | 1.53779 | ||||||||
\(780\) | −6.55163 | −0.234586 | ||||||||
\(781\) | −9.58482 | −0.342972 | ||||||||
\(782\) | 30.0743 | 1.07545 | ||||||||
\(783\) | 11.5764 | 0.413705 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 33.3949 | 1.19191 | ||||||||
\(786\) | 10.8573 | 0.387267 | ||||||||
\(787\) | 31.2988 | 1.11568 | 0.557841 | − | 0.829948i | \(-0.311630\pi\) | ||||
0.557841 | + | 0.829948i | \(0.311630\pi\) | |||||||
\(788\) | −2.30403 | −0.0820776 | ||||||||
\(789\) | 19.6375 | 0.699112 | ||||||||
\(790\) | −9.31769 | −0.331509 | ||||||||
\(791\) | −5.90534 | −0.209970 | ||||||||
\(792\) | −0.884507 | −0.0314296 | ||||||||
\(793\) | −13.4828 | −0.478789 | ||||||||
\(794\) | −18.5004 | −0.656555 | ||||||||
\(795\) | −56.1640 | −1.99193 | ||||||||
\(796\) | 22.6764 | 0.803744 | ||||||||
\(797\) | 46.1067 | 1.63318 | 0.816591 | − | 0.577217i | \(-0.195861\pi\) | ||||
0.816591 | + | 0.577217i | \(0.195861\pi\) | |||||||
\(798\) | −10.7146 | −0.379294 | ||||||||
\(799\) | 65.0915 | 2.30277 | ||||||||
\(800\) | −5.18656 | −0.183373 | ||||||||
\(801\) | −9.95497 | −0.351742 | ||||||||
\(802\) | 9.81363 | 0.346531 | ||||||||
\(803\) | −7.52682 | −0.265616 | ||||||||
\(804\) | 23.8826 | 0.842274 | ||||||||
\(805\) | −16.6292 | −0.586101 | ||||||||
\(806\) | 1.42876 | 0.0503261 | ||||||||
\(807\) | 19.5983 | 0.689894 | ||||||||
\(808\) | 17.2580 | 0.607136 | ||||||||
\(809\) | −35.4448 | −1.24617 | −0.623087 | − | 0.782153i | \(-0.714122\pi\) | ||||
−0.623087 | + | 0.782153i | \(0.714122\pi\) | |||||||
\(810\) | −20.6487 | −0.725521 | ||||||||
\(811\) | 0.677435 | 0.0237880 | 0.0118940 | − | 0.999929i | \(-0.496214\pi\) | ||||
0.0118940 | + | 0.999929i | \(0.496214\pi\) | |||||||
\(812\) | 2.06455 | 0.0724515 | ||||||||
\(813\) | −10.2621 | −0.359908 | ||||||||
\(814\) | 0.799188 | 0.0280115 | ||||||||
\(815\) | −6.86908 | −0.240613 | ||||||||
\(816\) | 8.77974 | 0.307352 | ||||||||
\(817\) | 67.9625 | 2.37771 | ||||||||
\(818\) | 21.6181 | 0.755860 | ||||||||
\(819\) | 0.926348 | 0.0323692 | ||||||||
\(820\) | 19.4467 | 0.679108 | ||||||||
\(821\) | −52.8303 | −1.84379 | −0.921896 | − | 0.387438i | \(-0.873360\pi\) | ||||
−0.921896 | + | 0.387438i | \(0.873360\pi\) | |||||||
\(822\) | −12.9506 | −0.451704 | ||||||||
\(823\) | −12.5107 | −0.436097 | −0.218048 | − | 0.975938i | \(-0.569969\pi\) | ||||
−0.218048 | + | 0.975938i | \(0.569969\pi\) | |||||||
\(824\) | −8.12280 | −0.282971 | ||||||||
\(825\) | −10.1658 | −0.353928 | ||||||||
\(826\) | −2.46795 | −0.0858709 | ||||||||
\(827\) | −44.5300 | −1.54846 | −0.774229 | − | 0.632905i | \(-0.781862\pi\) | ||||
−0.774229 | + | 0.632905i | \(0.781862\pi\) | |||||||
\(828\) | 3.57634 | 0.124286 | ||||||||
\(829\) | 10.3978 | 0.361130 | 0.180565 | − | 0.983563i | \(-0.442207\pi\) | ||||
0.180565 | + | 0.983563i | \(0.442207\pi\) | |||||||
\(830\) | −7.39941 | −0.256837 | ||||||||
\(831\) | 10.2031 | 0.353943 | ||||||||
\(832\) | 1.34956 | 0.0467876 | ||||||||
\(833\) | 5.77216 | 0.199993 | ||||||||
\(834\) | 12.3293 | 0.426928 | ||||||||
\(835\) | −73.0960 | −2.52959 | ||||||||
\(836\) | 9.07723 | 0.313942 | ||||||||
\(837\) | 5.93629 | 0.205188 | ||||||||
\(838\) | −13.3692 | −0.461830 | ||||||||
\(839\) | 25.4430 | 0.878391 | 0.439195 | − | 0.898392i | \(-0.355264\pi\) | ||||
0.439195 | + | 0.898392i | \(0.355264\pi\) | |||||||
\(840\) | −4.85464 | −0.167501 | ||||||||
\(841\) | −24.7376 | −0.853022 | ||||||||
\(842\) | −8.21394 | −0.283071 | ||||||||
\(843\) | 36.1358 | 1.24458 | ||||||||
\(844\) | 12.5303 | 0.431310 | ||||||||
\(845\) | 35.6783 | 1.22737 | ||||||||
\(846\) | 7.74048 | 0.266123 | ||||||||
\(847\) | 9.33950 | 0.320909 | ||||||||
\(848\) | 11.5691 | 0.397285 | ||||||||
\(849\) | 0.422429 | 0.0144977 | ||||||||
\(850\) | −29.9376 | −1.02685 | ||||||||
\(851\) | −3.23137 | −0.110770 | ||||||||
\(852\) | 11.3138 | 0.387604 | ||||||||
\(853\) | 20.1321 | 0.689309 | 0.344655 | − | 0.938730i | \(-0.387996\pi\) | ||||
0.344655 | + | 0.938730i | \(0.387996\pi\) | |||||||
\(854\) | −9.99054 | −0.341869 | ||||||||
\(855\) | −15.4323 | −0.527772 | ||||||||
\(856\) | 7.61685 | 0.260339 | ||||||||
\(857\) | −9.58377 | −0.327375 | −0.163688 | − | 0.986512i | \(-0.552339\pi\) | ||||
−0.163688 | + | 0.986512i | \(0.552339\pi\) | |||||||
\(858\) | 2.64518 | 0.0903049 | ||||||||
\(859\) | 38.3394 | 1.30812 | 0.654061 | − | 0.756442i | \(-0.273064\pi\) | ||||
0.654061 | + | 0.756442i | \(0.273064\pi\) | |||||||
\(860\) | 30.7928 | 1.05003 | ||||||||
\(861\) | 9.26778 | 0.315845 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −20.0896 | −0.683856 | −0.341928 | − | 0.939726i | \(-0.611080\pi\) | ||||
−0.341928 | + | 0.939726i | \(0.611080\pi\) | |||||||
\(864\) | 5.60721 | 0.190761 | ||||||||
\(865\) | −9.74355 | −0.331291 | ||||||||
\(866\) | 7.69393 | 0.261450 | ||||||||
\(867\) | 24.8202 | 0.842938 | ||||||||
\(868\) | 1.05869 | 0.0359342 | ||||||||
\(869\) | 3.76196 | 0.127616 | ||||||||
\(870\) | −10.0226 | −0.339800 | ||||||||
\(871\) | 21.1900 | 0.717994 | ||||||||
\(872\) | 14.9452 | 0.506110 | ||||||||
\(873\) | −6.62404 | −0.224190 | ||||||||
\(874\) | −36.7021 | −1.24147 | ||||||||
\(875\) | 0.595431 | 0.0201293 | ||||||||
\(876\) | 8.88455 | 0.300181 | ||||||||
\(877\) | 3.62986 | 0.122572 | 0.0612859 | − | 0.998120i | \(-0.480480\pi\) | ||||
0.0612859 | + | 0.998120i | \(0.480480\pi\) | |||||||
\(878\) | 13.8335 | 0.466857 | ||||||||
\(879\) | 3.54844 | 0.119686 | ||||||||
\(880\) | 4.11276 | 0.138641 | ||||||||
\(881\) | −12.2916 | −0.414115 | −0.207057 | − | 0.978329i | \(-0.566389\pi\) | ||||
−0.207057 | + | 0.978329i | \(0.566389\pi\) | |||||||
\(882\) | 0.686407 | 0.0231125 | ||||||||
\(883\) | −15.3722 | −0.517316 | −0.258658 | − | 0.965969i | \(-0.583280\pi\) | ||||
−0.258658 | + | 0.965969i | \(0.583280\pi\) | |||||||
\(884\) | 7.78987 | 0.262002 | ||||||||
\(885\) | 11.9810 | 0.402737 | ||||||||
\(886\) | 16.9069 | 0.567999 | ||||||||
\(887\) | 42.0265 | 1.41111 | 0.705556 | − | 0.708654i | \(-0.250697\pi\) | ||||
0.705556 | + | 0.708654i | \(0.250697\pi\) | |||||||
\(888\) | −0.943351 | −0.0316568 | ||||||||
\(889\) | −5.92583 | −0.198746 | ||||||||
\(890\) | 46.2884 | 1.55159 | ||||||||
\(891\) | 8.33678 | 0.279293 | ||||||||
\(892\) | −12.9727 | −0.434359 | ||||||||
\(893\) | −79.4365 | −2.65824 | ||||||||
\(894\) | 20.1625 | 0.674336 | ||||||||
\(895\) | −34.9068 | −1.16681 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −10.6953 | −0.357105 | ||||||||
\(898\) | 20.4743 | 0.683238 | ||||||||
\(899\) | 2.18571 | 0.0728977 | ||||||||
\(900\) | −3.56009 | −0.118670 | ||||||||
\(901\) | 66.7788 | 2.22472 | ||||||||
\(902\) | −7.85148 | −0.261426 | ||||||||
\(903\) | 14.6750 | 0.488354 | ||||||||
\(904\) | −5.90534 | −0.196409 | ||||||||
\(905\) | 23.0013 | 0.764589 | ||||||||
\(906\) | −17.9869 | −0.597575 | ||||||||
\(907\) | −2.58213 | −0.0857381 | −0.0428690 | − | 0.999081i | \(-0.513650\pi\) | ||||
−0.0428690 | + | 0.999081i | \(0.513650\pi\) | |||||||
\(908\) | 7.24109 | 0.240304 | ||||||||
\(909\) | 11.8460 | 0.392909 | ||||||||
\(910\) | −4.30731 | −0.142786 | ||||||||
\(911\) | −27.9289 | −0.925327 | −0.462663 | − | 0.886534i | \(-0.653106\pi\) | ||||
−0.462663 | + | 0.886534i | \(0.653106\pi\) | |||||||
\(912\) | −10.7146 | −0.354797 | ||||||||
\(913\) | 2.98747 | 0.0988707 | ||||||||
\(914\) | −8.32894 | −0.275497 | ||||||||
\(915\) | 48.5005 | 1.60338 | ||||||||
\(916\) | 3.79306 | 0.125326 | ||||||||
\(917\) | 7.13803 | 0.235719 | ||||||||
\(918\) | 32.3657 | 1.06823 | ||||||||
\(919\) | 42.6513 | 1.40694 | 0.703469 | − | 0.710726i | \(-0.251634\pi\) | ||||
0.703469 | + | 0.710726i | \(0.251634\pi\) | |||||||
\(920\) | −16.6292 | −0.548248 | ||||||||
\(921\) | 18.1356 | 0.597590 | ||||||||
\(922\) | 30.3206 | 0.998554 | ||||||||
\(923\) | 10.0382 | 0.330412 | ||||||||
\(924\) | 1.96003 | 0.0644803 | ||||||||
\(925\) | 3.21669 | 0.105764 | ||||||||
\(926\) | −12.7482 | −0.418933 | ||||||||
\(927\) | −5.57555 | −0.183125 | ||||||||
\(928\) | 2.06455 | 0.0677722 | ||||||||
\(929\) | 23.5682 | 0.773248 | 0.386624 | − | 0.922237i | \(-0.373641\pi\) | ||||
0.386624 | + | 0.922237i | \(0.373641\pi\) | |||||||
\(930\) | −5.13955 | −0.168533 | ||||||||
\(931\) | −7.04424 | −0.230866 | ||||||||
\(932\) | 14.4348 | 0.472828 | ||||||||
\(933\) | 21.1157 | 0.691298 | ||||||||
\(934\) | −19.7315 | −0.645635 | ||||||||
\(935\) | 23.7395 | 0.776364 | ||||||||
\(936\) | 0.926348 | 0.0302786 | ||||||||
\(937\) | −35.2042 | −1.15007 | −0.575036 | − | 0.818128i | \(-0.695012\pi\) | ||||
−0.575036 | + | 0.818128i | \(0.695012\pi\) | |||||||
\(938\) | 15.7014 | 0.512668 | ||||||||
\(939\) | −0.750711 | −0.0244985 | ||||||||
\(940\) | −35.9915 | −1.17391 | ||||||||
\(941\) | 4.75056 | 0.154864 | 0.0774319 | − | 0.996998i | \(-0.475328\pi\) | ||||
0.0774319 | + | 0.996998i | \(0.475328\pi\) | |||||||
\(942\) | 15.9151 | 0.518542 | ||||||||
\(943\) | 31.7460 | 1.03379 | ||||||||
\(944\) | −2.46795 | −0.0803248 | ||||||||
\(945\) | −17.8962 | −0.582163 | ||||||||
\(946\) | −12.4324 | −0.404212 | ||||||||
\(947\) | 2.56404 | 0.0833202 | 0.0416601 | − | 0.999132i | \(-0.486735\pi\) | ||||
0.0416601 | + | 0.999132i | \(0.486735\pi\) | |||||||
\(948\) | −4.44056 | −0.144223 | ||||||||
\(949\) | 7.88287 | 0.255889 | ||||||||
\(950\) | 36.5354 | 1.18536 | ||||||||
\(951\) | 8.49263 | 0.275392 | ||||||||
\(952\) | 5.77216 | 0.187077 | ||||||||
\(953\) | 45.1337 | 1.46202 | 0.731012 | − | 0.682365i | \(-0.239048\pi\) | ||||
0.731012 | + | 0.682365i | \(0.239048\pi\) | |||||||
\(954\) | 7.94113 | 0.257104 | ||||||||
\(955\) | −15.7684 | −0.510252 | ||||||||
\(956\) | 18.6684 | 0.603779 | ||||||||
\(957\) | 4.04658 | 0.130807 | ||||||||
\(958\) | 30.1114 | 0.972856 | ||||||||
\(959\) | −8.51425 | −0.274939 | ||||||||
\(960\) | −4.85464 | −0.156683 | ||||||||
\(961\) | −29.8792 | −0.963844 | ||||||||
\(962\) | −0.836993 | −0.0269857 | ||||||||
\(963\) | 5.22826 | 0.168478 | ||||||||
\(964\) | −28.5089 | −0.918209 | ||||||||
\(965\) | −0.603474 | −0.0194265 | ||||||||
\(966\) | −7.92502 | −0.254983 | ||||||||
\(967\) | −2.08878 | −0.0671706 | −0.0335853 | − | 0.999436i | \(-0.510693\pi\) | ||||
−0.0335853 | + | 0.999436i | \(0.510693\pi\) | |||||||
\(968\) | 9.33950 | 0.300183 | ||||||||
\(969\) | −61.8466 | −1.98680 | ||||||||
\(970\) | 30.8003 | 0.988938 | ||||||||
\(971\) | −39.2254 | −1.25880 | −0.629401 | − | 0.777081i | \(-0.716700\pi\) | ||||
−0.629401 | + | 0.777081i | \(0.716700\pi\) | |||||||
\(972\) | 6.98101 | 0.223916 | ||||||||
\(973\) | 8.10576 | 0.259859 | ||||||||
\(974\) | 1.44157 | 0.0461907 | ||||||||
\(975\) | 10.6467 | 0.340967 | ||||||||
\(976\) | −9.99054 | −0.319789 | ||||||||
\(977\) | −49.1802 | −1.57341 | −0.786706 | − | 0.617328i | \(-0.788215\pi\) | ||||
−0.786706 | + | 0.617328i | \(0.788215\pi\) | |||||||
\(978\) | −3.27362 | −0.104679 | ||||||||
\(979\) | −18.6886 | −0.597291 | ||||||||
\(980\) | −3.19164 | −0.101953 | ||||||||
\(981\) | 10.2585 | 0.327530 | ||||||||
\(982\) | 8.76940 | 0.279843 | ||||||||
\(983\) | −25.9768 | −0.828530 | −0.414265 | − | 0.910156i | \(-0.635961\pi\) | ||||
−0.414265 | + | 0.910156i | \(0.635961\pi\) | |||||||
\(984\) | 9.26778 | 0.295446 | ||||||||
\(985\) | 7.35362 | 0.234306 | ||||||||
\(986\) | 11.9169 | 0.379512 | ||||||||
\(987\) | −17.1526 | −0.545973 | ||||||||
\(988\) | −9.50662 | −0.302446 | ||||||||
\(989\) | 50.2681 | 1.59843 | ||||||||
\(990\) | 2.82303 | 0.0897217 | ||||||||
\(991\) | 30.5926 | 0.971805 | 0.485903 | − | 0.874013i | \(-0.338491\pi\) | ||||
0.485903 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(992\) | 1.05869 | 0.0336134 | ||||||||
\(993\) | 30.6727 | 0.973370 | ||||||||
\(994\) | 7.43814 | 0.235924 | ||||||||
\(995\) | −72.3750 | −2.29444 | ||||||||
\(996\) | −3.52636 | −0.111737 | ||||||||
\(997\) | 46.7080 | 1.47926 | 0.739628 | − | 0.673016i | \(-0.235001\pi\) | ||||
0.739628 | + | 0.673016i | \(0.235001\pi\) | |||||||
\(998\) | 9.82796 | 0.311099 | ||||||||
\(999\) | −3.47757 | −0.110026 |
(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 | 6034.2.a.n.1.17 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.17 | ✓ | 24 | 1.1 | even | 1 | trivial |