Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56595 | −1.81440 | −0.907200 | − | 0.420699i | \(-0.861785\pi\) | ||||
−0.907200 | + | 0.420699i | \(0.861785\pi\) | |||||||
\(3\) | 1.01181 | 0.584170 | 0.292085 | − | 0.956392i | \(-0.405651\pi\) | ||||
0.292085 | + | 0.956392i | \(0.405651\pi\) | |||||||
\(4\) | 4.58410 | 2.29205 | ||||||||
\(5\) | 2.09874 | 0.938584 | 0.469292 | − | 0.883043i | \(-0.344509\pi\) | ||||
0.469292 | + | 0.883043i | \(0.344509\pi\) | |||||||
\(6\) | −2.59626 | −1.05992 | ||||||||
\(7\) | 3.20271 | 1.21051 | 0.605255 | − | 0.796032i | \(-0.293071\pi\) | ||||
0.605255 | + | 0.796032i | \(0.293071\pi\) | |||||||
\(8\) | −6.63067 | −2.34430 | ||||||||
\(9\) | −1.97623 | −0.658745 | ||||||||
\(10\) | −5.38525 | −1.70297 | ||||||||
\(11\) | −3.82268 | −1.15258 | −0.576291 | − | 0.817245i | \(-0.695500\pi\) | ||||
−0.576291 | + | 0.817245i | \(0.695500\pi\) | |||||||
\(12\) | 4.63825 | 1.33895 | ||||||||
\(13\) | 3.94710 | 1.09473 | 0.547364 | − | 0.836894i | \(-0.315631\pi\) | ||||
0.547364 | + | 0.836894i | \(0.315631\pi\) | |||||||
\(14\) | −8.21799 | −2.19635 | ||||||||
\(15\) | 2.12353 | 0.548293 | ||||||||
\(16\) | 7.84578 | 1.96144 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.07092 | 1.19523 | ||||||||
\(19\) | −1.67377 | −0.383990 | −0.191995 | − | 0.981396i | \(-0.561496\pi\) | ||||
−0.191995 | + | 0.981396i | \(0.561496\pi\) | |||||||
\(20\) | 9.62082 | 2.15128 | ||||||||
\(21\) | 3.24054 | 0.707144 | ||||||||
\(22\) | 9.80881 | 2.09125 | ||||||||
\(23\) | −6.51560 | −1.35860 | −0.679298 | − | 0.733862i | \(-0.737716\pi\) | ||||
−0.679298 | + | 0.733862i | \(0.737716\pi\) | |||||||
\(24\) | −6.70900 | −1.36947 | ||||||||
\(25\) | −0.595305 | −0.119061 | ||||||||
\(26\) | −10.1281 | −1.98628 | ||||||||
\(27\) | −5.03502 | −0.968990 | ||||||||
\(28\) | 14.6815 | 2.77455 | ||||||||
\(29\) | −7.47480 | −1.38804 | −0.694018 | − | 0.719958i | \(-0.744161\pi\) | ||||
−0.694018 | + | 0.719958i | \(0.744161\pi\) | |||||||
\(30\) | −5.44887 | −0.994823 | ||||||||
\(31\) | 5.60264 | 1.00626 | 0.503132 | − | 0.864210i | \(-0.332181\pi\) | ||||
0.503132 | + | 0.864210i | \(0.332181\pi\) | |||||||
\(32\) | −6.87052 | −1.21455 | ||||||||
\(33\) | −3.86784 | −0.673304 | ||||||||
\(34\) | −2.56595 | −0.440057 | ||||||||
\(35\) | 6.72164 | 1.13616 | ||||||||
\(36\) | −9.05926 | −1.50988 | ||||||||
\(37\) | −0.965190 | −0.158676 | −0.0793381 | − | 0.996848i | \(-0.525281\pi\) | ||||
−0.0793381 | + | 0.996848i | \(0.525281\pi\) | |||||||
\(38\) | 4.29482 | 0.696711 | ||||||||
\(39\) | 3.99373 | 0.639508 | ||||||||
\(40\) | −13.9160 | −2.20032 | ||||||||
\(41\) | −1.71017 | −0.267083 | −0.133542 | − | 0.991043i | \(-0.542635\pi\) | ||||
−0.133542 | + | 0.991043i | \(0.542635\pi\) | |||||||
\(42\) | −8.31506 | −1.28304 | ||||||||
\(43\) | −5.00992 | −0.764005 | −0.382003 | − | 0.924161i | \(-0.624766\pi\) | ||||
−0.382003 | + | 0.924161i | \(0.624766\pi\) | |||||||
\(44\) | −17.5236 | −2.64178 | ||||||||
\(45\) | −4.14760 | −0.618287 | ||||||||
\(46\) | 16.7187 | 2.46504 | ||||||||
\(47\) | −8.53728 | −1.24529 | −0.622645 | − | 0.782504i | \(-0.713942\pi\) | ||||
−0.622645 | + | 0.782504i | \(0.713942\pi\) | |||||||
\(48\) | 7.93846 | 1.14582 | ||||||||
\(49\) | 3.25733 | 0.465333 | ||||||||
\(50\) | 1.52752 | 0.216024 | ||||||||
\(51\) | 1.01181 | 0.141682 | ||||||||
\(52\) | 18.0939 | 2.50917 | ||||||||
\(53\) | −1.22573 | −0.168367 | −0.0841836 | − | 0.996450i | \(-0.526828\pi\) | ||||
−0.0841836 | + | 0.996450i | \(0.526828\pi\) | |||||||
\(54\) | 12.9196 | 1.75814 | ||||||||
\(55\) | −8.02280 | −1.08179 | ||||||||
\(56\) | −21.2361 | −2.83779 | ||||||||
\(57\) | −1.69354 | −0.224315 | ||||||||
\(58\) | 19.1800 | 2.51845 | ||||||||
\(59\) | 12.4681 | 1.62321 | 0.811605 | − | 0.584207i | \(-0.198594\pi\) | ||||
0.811605 | + | 0.584207i | \(0.198594\pi\) | |||||||
\(60\) | 9.73447 | 1.25671 | ||||||||
\(61\) | −4.75996 | −0.609450 | −0.304725 | − | 0.952440i | \(-0.598565\pi\) | ||||
−0.304725 | + | 0.952440i | \(0.598565\pi\) | |||||||
\(62\) | −14.3761 | −1.82577 | ||||||||
\(63\) | −6.32930 | −0.797417 | ||||||||
\(64\) | 1.93787 | 0.242234 | ||||||||
\(65\) | 8.28392 | 1.02749 | ||||||||
\(66\) | 9.92468 | 1.22164 | ||||||||
\(67\) | 10.3637 | 1.26613 | 0.633063 | − | 0.774101i | \(-0.281798\pi\) | ||||
0.633063 | + | 0.774101i | \(0.281798\pi\) | |||||||
\(68\) | 4.58410 | 0.555904 | ||||||||
\(69\) | −6.59257 | −0.793652 | ||||||||
\(70\) | −17.2474 | −2.06146 | ||||||||
\(71\) | −0.894207 | −0.106123 | −0.0530614 | − | 0.998591i | \(-0.516898\pi\) | ||||
−0.0530614 | + | 0.998591i | \(0.516898\pi\) | |||||||
\(72\) | 13.1038 | 1.54429 | ||||||||
\(73\) | 2.09406 | 0.245091 | 0.122546 | − | 0.992463i | \(-0.460894\pi\) | ||||
0.122546 | + | 0.992463i | \(0.460894\pi\) | |||||||
\(74\) | 2.47663 | 0.287902 | ||||||||
\(75\) | −0.602337 | −0.0695519 | ||||||||
\(76\) | −7.67274 | −0.880124 | ||||||||
\(77\) | −12.2429 | −1.39521 | ||||||||
\(78\) | −10.2477 | −1.16032 | ||||||||
\(79\) | −8.36190 | −0.940788 | −0.470394 | − | 0.882457i | \(-0.655888\pi\) | ||||
−0.470394 | + | 0.882457i | \(0.655888\pi\) | |||||||
\(80\) | 16.4662 | 1.84098 | ||||||||
\(81\) | 0.834207 | 0.0926897 | ||||||||
\(82\) | 4.38820 | 0.484596 | ||||||||
\(83\) | −9.04787 | −0.993133 | −0.496566 | − | 0.867999i | \(-0.665406\pi\) | ||||
−0.496566 | + | 0.867999i | \(0.665406\pi\) | |||||||
\(84\) | 14.8550 | 1.62081 | ||||||||
\(85\) | 2.09874 | 0.227640 | ||||||||
\(86\) | 12.8552 | 1.38621 | ||||||||
\(87\) | −7.56310 | −0.810850 | ||||||||
\(88\) | 25.3470 | 2.70199 | ||||||||
\(89\) | 1.32155 | 0.140084 | 0.0700419 | − | 0.997544i | \(-0.477687\pi\) | ||||
0.0700419 | + | 0.997544i | \(0.477687\pi\) | |||||||
\(90\) | 10.6425 | 1.12182 | ||||||||
\(91\) | 12.6414 | 1.32518 | ||||||||
\(92\) | −29.8682 | −3.11397 | ||||||||
\(93\) | 5.66882 | 0.587830 | ||||||||
\(94\) | 21.9062 | 2.25946 | ||||||||
\(95\) | −3.51281 | −0.360406 | ||||||||
\(96\) | −6.95169 | −0.709503 | ||||||||
\(97\) | −0.597503 | −0.0606672 | −0.0303336 | − | 0.999540i | \(-0.509657\pi\) | ||||
−0.0303336 | + | 0.999540i | \(0.509657\pi\) | |||||||
\(98\) | −8.35814 | −0.844300 | ||||||||
\(99\) | 7.55452 | 0.759257 | ||||||||
\(100\) | −2.72894 | −0.272894 | ||||||||
\(101\) | −7.55936 | −0.752185 | −0.376092 | − | 0.926582i | \(-0.622732\pi\) | ||||
−0.376092 | + | 0.926582i | \(0.622732\pi\) | |||||||
\(102\) | −2.59626 | −0.257068 | ||||||||
\(103\) | −0.360037 | −0.0354755 | −0.0177378 | − | 0.999843i | \(-0.505646\pi\) | ||||
−0.0177378 | + | 0.999843i | \(0.505646\pi\) | |||||||
\(104\) | −26.1719 | −2.56637 | ||||||||
\(105\) | 6.80104 | 0.663713 | ||||||||
\(106\) | 3.14517 | 0.305485 | ||||||||
\(107\) | 6.53257 | 0.631527 | 0.315764 | − | 0.948838i | \(-0.397739\pi\) | ||||
0.315764 | + | 0.948838i | \(0.397739\pi\) | |||||||
\(108\) | −23.0810 | −2.22097 | ||||||||
\(109\) | 15.8041 | 1.51376 | 0.756880 | − | 0.653554i | \(-0.226723\pi\) | ||||
0.756880 | + | 0.653554i | \(0.226723\pi\) | |||||||
\(110\) | 20.5861 | 1.96281 | ||||||||
\(111\) | −0.976592 | −0.0926940 | ||||||||
\(112\) | 25.1277 | 2.37435 | ||||||||
\(113\) | −16.5645 | −1.55826 | −0.779129 | − | 0.626863i | \(-0.784339\pi\) | ||||
−0.779129 | + | 0.626863i | \(0.784339\pi\) | |||||||
\(114\) | 4.34555 | 0.406998 | ||||||||
\(115\) | −13.6745 | −1.27516 | ||||||||
\(116\) | −34.2653 | −3.18145 | ||||||||
\(117\) | −7.80040 | −0.721147 | ||||||||
\(118\) | −31.9926 | −2.94515 | ||||||||
\(119\) | 3.20271 | 0.293592 | ||||||||
\(120\) | −14.0804 | −1.28536 | ||||||||
\(121\) | 3.61290 | 0.328445 | ||||||||
\(122\) | 12.2138 | 1.10579 | ||||||||
\(123\) | −1.73037 | −0.156022 | ||||||||
\(124\) | 25.6831 | 2.30641 | ||||||||
\(125\) | −11.7431 | −1.05033 | ||||||||
\(126\) | 16.2407 | 1.44683 | ||||||||
\(127\) | −17.6884 | −1.56959 | −0.784797 | − | 0.619753i | \(-0.787233\pi\) | ||||
−0.784797 | + | 0.619753i | \(0.787233\pi\) | |||||||
\(128\) | 8.76857 | 0.775039 | ||||||||
\(129\) | −5.06910 | −0.446309 | ||||||||
\(130\) | −21.2561 | −1.86429 | ||||||||
\(131\) | −5.57770 | −0.487326 | −0.243663 | − | 0.969860i | \(-0.578349\pi\) | ||||
−0.243663 | + | 0.969860i | \(0.578349\pi\) | |||||||
\(132\) | −17.7306 | −1.54325 | ||||||||
\(133\) | −5.36060 | −0.464823 | ||||||||
\(134\) | −26.5927 | −2.29726 | ||||||||
\(135\) | −10.5672 | −0.909478 | ||||||||
\(136\) | −6.63067 | −0.568576 | ||||||||
\(137\) | 10.3835 | 0.887121 | 0.443561 | − | 0.896244i | \(-0.353715\pi\) | ||||
0.443561 | + | 0.896244i | \(0.353715\pi\) | |||||||
\(138\) | 16.9162 | 1.44000 | ||||||||
\(139\) | −8.57191 | −0.727060 | −0.363530 | − | 0.931583i | \(-0.618429\pi\) | ||||
−0.363530 | + | 0.931583i | \(0.618429\pi\) | |||||||
\(140\) | 30.8127 | 2.60415 | ||||||||
\(141\) | −8.63813 | −0.727462 | ||||||||
\(142\) | 2.29449 | 0.192549 | ||||||||
\(143\) | −15.0885 | −1.26176 | ||||||||
\(144\) | −15.5051 | −1.29209 | ||||||||
\(145\) | −15.6876 | −1.30279 | ||||||||
\(146\) | −5.37325 | −0.444694 | ||||||||
\(147\) | 3.29581 | 0.271834 | ||||||||
\(148\) | −4.42453 | −0.363694 | ||||||||
\(149\) | 7.17404 | 0.587721 | 0.293860 | − | 0.955848i | \(-0.405060\pi\) | ||||
0.293860 | + | 0.955848i | \(0.405060\pi\) | |||||||
\(150\) | 1.54557 | 0.126195 | ||||||||
\(151\) | −0.183450 | −0.0149289 | −0.00746446 | − | 0.999972i | \(-0.502376\pi\) | ||||
−0.00746446 | + | 0.999972i | \(0.502376\pi\) | |||||||
\(152\) | 11.0982 | 0.900186 | ||||||||
\(153\) | −1.97623 | −0.159769 | ||||||||
\(154\) | 31.4147 | 2.53147 | ||||||||
\(155\) | 11.7585 | 0.944463 | ||||||||
\(156\) | 18.3076 | 1.46578 | ||||||||
\(157\) | −11.8164 | −0.943049 | −0.471524 | − | 0.881853i | \(-0.656296\pi\) | ||||
−0.471524 | + | 0.881853i | \(0.656296\pi\) | |||||||
\(158\) | 21.4562 | 1.70697 | ||||||||
\(159\) | −1.24021 | −0.0983551 | ||||||||
\(160\) | −14.4194 | −1.13996 | ||||||||
\(161\) | −20.8676 | −1.64459 | ||||||||
\(162\) | −2.14053 | −0.168176 | ||||||||
\(163\) | −18.0441 | −1.41333 | −0.706663 | − | 0.707550i | \(-0.749800\pi\) | ||||
−0.706663 | + | 0.707550i | \(0.749800\pi\) | |||||||
\(164\) | −7.83957 | −0.612168 | ||||||||
\(165\) | −8.11757 | −0.631952 | ||||||||
\(166\) | 23.2164 | 1.80194 | ||||||||
\(167\) | −19.9628 | −1.54477 | −0.772383 | − | 0.635157i | \(-0.780935\pi\) | ||||
−0.772383 | + | 0.635157i | \(0.780935\pi\) | |||||||
\(168\) | −21.4870 | −1.65775 | ||||||||
\(169\) | 2.57960 | 0.198431 | ||||||||
\(170\) | −5.38525 | −0.413030 | ||||||||
\(171\) | 3.30777 | 0.252951 | ||||||||
\(172\) | −22.9660 | −1.75114 | ||||||||
\(173\) | −21.5280 | −1.63674 | −0.818372 | − | 0.574689i | \(-0.805123\pi\) | ||||
−0.818372 | + | 0.574689i | \(0.805123\pi\) | |||||||
\(174\) | 19.4065 | 1.47121 | ||||||||
\(175\) | −1.90659 | −0.144124 | ||||||||
\(176\) | −29.9919 | −2.26072 | ||||||||
\(177\) | 12.6154 | 0.948231 | ||||||||
\(178\) | −3.39103 | −0.254168 | ||||||||
\(179\) | 6.95315 | 0.519703 | 0.259851 | − | 0.965649i | \(-0.416326\pi\) | ||||
0.259851 | + | 0.965649i | \(0.416326\pi\) | |||||||
\(180\) | −19.0130 | −1.41715 | ||||||||
\(181\) | −10.9817 | −0.816265 | −0.408133 | − | 0.912923i | \(-0.633820\pi\) | ||||
−0.408133 | + | 0.912923i | \(0.633820\pi\) | |||||||
\(182\) | −32.4372 | −2.40441 | ||||||||
\(183\) | −4.81618 | −0.356023 | ||||||||
\(184\) | 43.2028 | 3.18495 | ||||||||
\(185\) | −2.02568 | −0.148931 | ||||||||
\(186\) | −14.5459 | −1.06656 | ||||||||
\(187\) | −3.82268 | −0.279542 | ||||||||
\(188\) | −39.1358 | −2.85427 | ||||||||
\(189\) | −16.1257 | −1.17297 | ||||||||
\(190\) | 9.01369 | 0.653922 | ||||||||
\(191\) | −8.89162 | −0.643375 | −0.321688 | − | 0.946846i | \(-0.604250\pi\) | ||||
−0.321688 | + | 0.946846i | \(0.604250\pi\) | |||||||
\(192\) | 1.96076 | 0.141506 | ||||||||
\(193\) | −5.65444 | −0.407015 | −0.203508 | − | 0.979073i | \(-0.565234\pi\) | ||||
−0.203508 | + | 0.979073i | \(0.565234\pi\) | |||||||
\(194\) | 1.53316 | 0.110075 | ||||||||
\(195\) | 8.38178 | 0.600232 | ||||||||
\(196\) | 14.9319 | 1.06657 | ||||||||
\(197\) | 12.9768 | 0.924556 | 0.462278 | − | 0.886735i | \(-0.347032\pi\) | ||||
0.462278 | + | 0.886735i | \(0.347032\pi\) | |||||||
\(198\) | −19.3845 | −1.37760 | ||||||||
\(199\) | 17.3327 | 1.22868 | 0.614340 | − | 0.789041i | \(-0.289422\pi\) | ||||
0.614340 | + | 0.789041i | \(0.289422\pi\) | |||||||
\(200\) | 3.94727 | 0.279114 | ||||||||
\(201\) | 10.4861 | 0.739633 | ||||||||
\(202\) | 19.3969 | 1.36476 | ||||||||
\(203\) | −23.9396 | −1.68023 | ||||||||
\(204\) | 4.63825 | 0.324743 | ||||||||
\(205\) | −3.58919 | −0.250680 | ||||||||
\(206\) | 0.923838 | 0.0643669 | ||||||||
\(207\) | 12.8764 | 0.894969 | ||||||||
\(208\) | 30.9681 | 2.14725 | ||||||||
\(209\) | 6.39830 | 0.442580 | ||||||||
\(210\) | −17.4511 | −1.20424 | ||||||||
\(211\) | 11.3135 | 0.778855 | 0.389428 | − | 0.921057i | \(-0.372673\pi\) | ||||
0.389428 | + | 0.921057i | \(0.372673\pi\) | |||||||
\(212\) | −5.61888 | −0.385906 | ||||||||
\(213\) | −0.904770 | −0.0619938 | ||||||||
\(214\) | −16.7622 | −1.14584 | ||||||||
\(215\) | −10.5145 | −0.717083 | ||||||||
\(216\) | 33.3856 | 2.27160 | ||||||||
\(217\) | 17.9436 | 1.21809 | ||||||||
\(218\) | −40.5526 | −2.74657 | ||||||||
\(219\) | 2.11880 | 0.143175 | ||||||||
\(220\) | −36.7773 | −2.47953 | ||||||||
\(221\) | 3.94710 | 0.265511 | ||||||||
\(222\) | 2.50589 | 0.168184 | ||||||||
\(223\) | 11.5423 | 0.772927 | 0.386464 | − | 0.922305i | \(-0.373696\pi\) | ||||
0.386464 | + | 0.922305i | \(0.373696\pi\) | |||||||
\(224\) | −22.0043 | −1.47022 | ||||||||
\(225\) | 1.17646 | 0.0784308 | ||||||||
\(226\) | 42.5037 | 2.82731 | ||||||||
\(227\) | −4.31227 | −0.286215 | −0.143108 | − | 0.989707i | \(-0.545710\pi\) | ||||
−0.143108 | + | 0.989707i | \(0.545710\pi\) | |||||||
\(228\) | −7.76338 | −0.514142 | ||||||||
\(229\) | −23.6117 | −1.56031 | −0.780153 | − | 0.625589i | \(-0.784859\pi\) | ||||
−0.780153 | + | 0.625589i | \(0.784859\pi\) | |||||||
\(230\) | 35.0882 | 2.31364 | ||||||||
\(231\) | −12.3876 | −0.815041 | ||||||||
\(232\) | 49.5630 | 3.25397 | ||||||||
\(233\) | 17.7062 | 1.15997 | 0.579986 | − | 0.814626i | \(-0.303058\pi\) | ||||
0.579986 | + | 0.814626i | \(0.303058\pi\) | |||||||
\(234\) | 20.0154 | 1.30845 | ||||||||
\(235\) | −17.9175 | −1.16881 | ||||||||
\(236\) | 57.1551 | 3.72048 | ||||||||
\(237\) | −8.46068 | −0.549580 | ||||||||
\(238\) | −8.21799 | −0.532693 | ||||||||
\(239\) | 6.24485 | 0.403946 | 0.201973 | − | 0.979391i | \(-0.435265\pi\) | ||||
0.201973 | + | 0.979391i | \(0.435265\pi\) | |||||||
\(240\) | 16.6607 | 1.07545 | ||||||||
\(241\) | 18.3152 | 1.17979 | 0.589894 | − | 0.807481i | \(-0.299169\pi\) | ||||
0.589894 | + | 0.807481i | \(0.299169\pi\) | |||||||
\(242\) | −9.27051 | −0.595931 | ||||||||
\(243\) | 15.9491 | 1.02314 | ||||||||
\(244\) | −21.8201 | −1.39689 | ||||||||
\(245\) | 6.83627 | 0.436754 | ||||||||
\(246\) | 4.44004 | 0.283086 | ||||||||
\(247\) | −6.60655 | −0.420365 | ||||||||
\(248\) | −37.1493 | −2.35898 | ||||||||
\(249\) | −9.15475 | −0.580159 | ||||||||
\(250\) | 30.1321 | 1.90572 | ||||||||
\(251\) | −18.5827 | −1.17293 | −0.586465 | − | 0.809975i | \(-0.699481\pi\) | ||||
−0.586465 | + | 0.809975i | \(0.699481\pi\) | |||||||
\(252\) | −29.0141 | −1.82772 | ||||||||
\(253\) | 24.9071 | 1.56589 | ||||||||
\(254\) | 45.3876 | 2.84787 | ||||||||
\(255\) | 2.12353 | 0.132981 | ||||||||
\(256\) | −26.3754 | −1.64847 | ||||||||
\(257\) | 25.6265 | 1.59854 | 0.799269 | − | 0.600973i | \(-0.205220\pi\) | ||||
0.799269 | + | 0.600973i | \(0.205220\pi\) | |||||||
\(258\) | 13.0071 | 0.809784 | ||||||||
\(259\) | −3.09122 | −0.192079 | ||||||||
\(260\) | 37.9743 | 2.35507 | ||||||||
\(261\) | 14.7720 | 0.914362 | ||||||||
\(262\) | 14.3121 | 0.884204 | ||||||||
\(263\) | 6.44143 | 0.397196 | 0.198598 | − | 0.980081i | \(-0.436361\pi\) | ||||
0.198598 | + | 0.980081i | \(0.436361\pi\) | |||||||
\(264\) | 25.6464 | 1.57843 | ||||||||
\(265\) | −2.57249 | −0.158027 | ||||||||
\(266\) | 13.7550 | 0.843376 | ||||||||
\(267\) | 1.33716 | 0.0818329 | ||||||||
\(268\) | 47.5082 | 2.90202 | ||||||||
\(269\) | −3.96363 | −0.241666 | −0.120833 | − | 0.992673i | \(-0.538557\pi\) | ||||
−0.120833 | + | 0.992673i | \(0.538557\pi\) | |||||||
\(270\) | 27.1149 | 1.65016 | ||||||||
\(271\) | −1.76321 | −0.107107 | −0.0535536 | − | 0.998565i | \(-0.517055\pi\) | ||||
−0.0535536 | + | 0.998565i | \(0.517055\pi\) | |||||||
\(272\) | 7.84578 | 0.475720 | ||||||||
\(273\) | 12.7907 | 0.774131 | ||||||||
\(274\) | −26.6435 | −1.60959 | ||||||||
\(275\) | 2.27566 | 0.137227 | ||||||||
\(276\) | −30.2210 | −1.81909 | ||||||||
\(277\) | −7.39485 | −0.444314 | −0.222157 | − | 0.975011i | \(-0.571310\pi\) | ||||
−0.222157 | + | 0.975011i | \(0.571310\pi\) | |||||||
\(278\) | 21.9951 | 1.31918 | ||||||||
\(279\) | −11.0721 | −0.662871 | ||||||||
\(280\) | −44.5690 | −2.66351 | ||||||||
\(281\) | 6.18579 | 0.369013 | 0.184507 | − | 0.982831i | \(-0.440931\pi\) | ||||
0.184507 | + | 0.982831i | \(0.440931\pi\) | |||||||
\(282\) | 22.1650 | 1.31991 | ||||||||
\(283\) | −19.2937 | −1.14689 | −0.573446 | − | 0.819244i | \(-0.694394\pi\) | ||||
−0.573446 | + | 0.819244i | \(0.694394\pi\) | |||||||
\(284\) | −4.09914 | −0.243239 | ||||||||
\(285\) | −3.55430 | −0.210539 | ||||||||
\(286\) | 38.7164 | 2.28935 | ||||||||
\(287\) | −5.47716 | −0.323306 | ||||||||
\(288\) | 13.5778 | 0.800078 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 40.2537 | 2.36378 | ||||||||
\(291\) | −0.604561 | −0.0354400 | ||||||||
\(292\) | 9.59938 | 0.561761 | ||||||||
\(293\) | 20.8941 | 1.22065 | 0.610324 | − | 0.792152i | \(-0.291039\pi\) | ||||
0.610324 | + | 0.792152i | \(0.291039\pi\) | |||||||
\(294\) | −8.45688 | −0.493215 | ||||||||
\(295\) | 26.1673 | 1.52352 | ||||||||
\(296\) | 6.39986 | 0.371984 | ||||||||
\(297\) | 19.2473 | 1.11684 | ||||||||
\(298\) | −18.4082 | −1.06636 | ||||||||
\(299\) | −25.7177 | −1.48729 | ||||||||
\(300\) | −2.76117 | −0.159416 | ||||||||
\(301\) | −16.0453 | −0.924836 | ||||||||
\(302\) | 0.470723 | 0.0270870 | ||||||||
\(303\) | −7.64866 | −0.439404 | ||||||||
\(304\) | −13.1320 | −0.753174 | ||||||||
\(305\) | −9.98989 | −0.572020 | ||||||||
\(306\) | 5.07092 | 0.289885 | ||||||||
\(307\) | −8.83425 | −0.504198 | −0.252099 | − | 0.967702i | \(-0.581121\pi\) | ||||
−0.252099 | + | 0.967702i | \(0.581121\pi\) | |||||||
\(308\) | −56.1228 | −3.19789 | ||||||||
\(309\) | −0.364291 | −0.0207238 | ||||||||
\(310\) | −30.1716 | −1.71363 | ||||||||
\(311\) | −7.75695 | −0.439857 | −0.219928 | − | 0.975516i | \(-0.570582\pi\) | ||||
−0.219928 | + | 0.975516i | \(0.570582\pi\) | |||||||
\(312\) | −26.4811 | −1.49920 | ||||||||
\(313\) | −17.0734 | −0.965048 | −0.482524 | − | 0.875883i | \(-0.660280\pi\) | ||||
−0.482524 | + | 0.875883i | \(0.660280\pi\) | |||||||
\(314\) | 30.3202 | 1.71107 | ||||||||
\(315\) | −13.2835 | −0.748442 | ||||||||
\(316\) | −38.3318 | −2.15633 | ||||||||
\(317\) | 0.765824 | 0.0430129 | 0.0215065 | − | 0.999769i | \(-0.493154\pi\) | ||||
0.0215065 | + | 0.999769i | \(0.493154\pi\) | |||||||
\(318\) | 3.18232 | 0.178456 | ||||||||
\(319\) | 28.5738 | 1.59983 | ||||||||
\(320\) | 4.06708 | 0.227357 | ||||||||
\(321\) | 6.60974 | 0.368920 | ||||||||
\(322\) | 53.5451 | 2.98395 | ||||||||
\(323\) | −1.67377 | −0.0931312 | ||||||||
\(324\) | 3.82409 | 0.212449 | ||||||||
\(325\) | −2.34973 | −0.130339 | ||||||||
\(326\) | 46.3004 | 2.56434 | ||||||||
\(327\) | 15.9908 | 0.884294 | ||||||||
\(328\) | 11.3396 | 0.626122 | ||||||||
\(329\) | −27.3424 | −1.50744 | ||||||||
\(330\) | 20.8293 | 1.14661 | ||||||||
\(331\) | 23.0643 | 1.26773 | 0.633864 | − | 0.773445i | \(-0.281468\pi\) | ||||
0.633864 | + | 0.773445i | \(0.281468\pi\) | |||||||
\(332\) | −41.4763 | −2.27631 | ||||||||
\(333\) | 1.90744 | 0.104527 | ||||||||
\(334\) | 51.2235 | 2.80283 | ||||||||
\(335\) | 21.7506 | 1.18836 | ||||||||
\(336\) | 25.4245 | 1.38702 | ||||||||
\(337\) | −3.46411 | −0.188702 | −0.0943509 | − | 0.995539i | \(-0.530078\pi\) | ||||
−0.0943509 | + | 0.995539i | \(0.530078\pi\) | |||||||
\(338\) | −6.61914 | −0.360034 | ||||||||
\(339\) | −16.7602 | −0.910289 | ||||||||
\(340\) | 9.62082 | 0.521762 | ||||||||
\(341\) | −21.4171 | −1.15980 | ||||||||
\(342\) | −8.48757 | −0.458955 | ||||||||
\(343\) | −11.9867 | −0.647220 | ||||||||
\(344\) | 33.2191 | 1.79106 | ||||||||
\(345\) | −13.8361 | −0.744909 | ||||||||
\(346\) | 55.2398 | 2.96971 | ||||||||
\(347\) | 27.7595 | 1.49021 | 0.745104 | − | 0.666948i | \(-0.232400\pi\) | ||||
0.745104 | + | 0.666948i | \(0.232400\pi\) | |||||||
\(348\) | −34.6700 | −1.85851 | ||||||||
\(349\) | −3.75441 | −0.200969 | −0.100485 | − | 0.994939i | \(-0.532039\pi\) | ||||
−0.100485 | + | 0.994939i | \(0.532039\pi\) | |||||||
\(350\) | 4.89221 | 0.261499 | ||||||||
\(351\) | −19.8737 | −1.06078 | ||||||||
\(352\) | 26.2638 | 1.39987 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −32.3705 | −1.72047 | ||||||||
\(355\) | −1.87671 | −0.0996052 | ||||||||
\(356\) | 6.05811 | 0.321079 | ||||||||
\(357\) | 3.24054 | 0.171508 | ||||||||
\(358\) | −17.8414 | −0.942949 | ||||||||
\(359\) | 23.5434 | 1.24257 | 0.621287 | − | 0.783583i | \(-0.286610\pi\) | ||||
0.621287 | + | 0.783583i | \(0.286610\pi\) | |||||||
\(360\) | 27.5014 | 1.44945 | ||||||||
\(361\) | −16.1985 | −0.852552 | ||||||||
\(362\) | 28.1786 | 1.48103 | ||||||||
\(363\) | 3.65557 | 0.191868 | ||||||||
\(364\) | 57.9495 | 3.03738 | ||||||||
\(365\) | 4.39488 | 0.230039 | ||||||||
\(366\) | 12.3581 | 0.645968 | ||||||||
\(367\) | −2.59748 | −0.135587 | −0.0677935 | − | 0.997699i | \(-0.521596\pi\) | ||||
−0.0677935 | + | 0.997699i | \(0.521596\pi\) | |||||||
\(368\) | −51.1199 | −2.66481 | ||||||||
\(369\) | 3.37969 | 0.175940 | ||||||||
\(370\) | 5.19779 | 0.270220 | ||||||||
\(371\) | −3.92566 | −0.203810 | ||||||||
\(372\) | 25.9865 | 1.34733 | ||||||||
\(373\) | 13.5699 | 0.702624 | 0.351312 | − | 0.936258i | \(-0.385736\pi\) | ||||
0.351312 | + | 0.936258i | \(0.385736\pi\) | |||||||
\(374\) | 9.80881 | 0.507202 | ||||||||
\(375\) | −11.8818 | −0.613573 | ||||||||
\(376\) | 56.6079 | 2.91933 | ||||||||
\(377\) | −29.5038 | −1.51952 | ||||||||
\(378\) | 41.3777 | 2.12824 | ||||||||
\(379\) | 11.2451 | 0.577620 | 0.288810 | − | 0.957386i | \(-0.406740\pi\) | ||||
0.288810 | + | 0.957386i | \(0.406740\pi\) | |||||||
\(380\) | −16.1031 | −0.826070 | ||||||||
\(381\) | −17.8974 | −0.916911 | ||||||||
\(382\) | 22.8155 | 1.16734 | ||||||||
\(383\) | −18.0813 | −0.923911 | −0.461956 | − | 0.886903i | \(-0.652852\pi\) | ||||
−0.461956 | + | 0.886903i | \(0.652852\pi\) | |||||||
\(384\) | 8.87215 | 0.452755 | ||||||||
\(385\) | −25.6947 | −1.30952 | ||||||||
\(386\) | 14.5090 | 0.738489 | ||||||||
\(387\) | 9.90078 | 0.503285 | ||||||||
\(388\) | −2.73901 | −0.139052 | ||||||||
\(389\) | −30.4014 | −1.54141 | −0.770705 | − | 0.637192i | \(-0.780096\pi\) | ||||
−0.770705 | + | 0.637192i | \(0.780096\pi\) | |||||||
\(390\) | −21.5072 | −1.08906 | ||||||||
\(391\) | −6.51560 | −0.329508 | ||||||||
\(392\) | −21.5983 | −1.09088 | ||||||||
\(393\) | −5.64359 | −0.284681 | ||||||||
\(394\) | −33.2977 | −1.67752 | ||||||||
\(395\) | −17.5494 | −0.883008 | ||||||||
\(396\) | 34.6307 | 1.74026 | ||||||||
\(397\) | 11.9092 | 0.597704 | 0.298852 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298852 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(398\) | −44.4748 | −2.22932 | ||||||||
\(399\) | −5.42393 | −0.271536 | ||||||||
\(400\) | −4.67063 | −0.233531 | ||||||||
\(401\) | 26.7870 | 1.33768 | 0.668840 | − | 0.743406i | \(-0.266791\pi\) | ||||
0.668840 | + | 0.743406i | \(0.266791\pi\) | |||||||
\(402\) | −26.9068 | −1.34199 | ||||||||
\(403\) | 22.1142 | 1.10159 | ||||||||
\(404\) | −34.6529 | −1.72405 | ||||||||
\(405\) | 1.75078 | 0.0869970 | ||||||||
\(406\) | 61.4278 | 3.04861 | ||||||||
\(407\) | 3.68961 | 0.182887 | ||||||||
\(408\) | −6.70900 | −0.332145 | ||||||||
\(409\) | 20.5877 | 1.01800 | 0.508998 | − | 0.860768i | \(-0.330016\pi\) | ||||
0.508998 | + | 0.860768i | \(0.330016\pi\) | |||||||
\(410\) | 9.20968 | 0.454834 | ||||||||
\(411\) | 10.5061 | 0.518230 | ||||||||
\(412\) | −1.65045 | −0.0813117 | ||||||||
\(413\) | 39.9317 | 1.96491 | ||||||||
\(414\) | −33.0401 | −1.62383 | ||||||||
\(415\) | −18.9891 | −0.932138 | ||||||||
\(416\) | −27.1187 | −1.32960 | ||||||||
\(417\) | −8.67317 | −0.424727 | ||||||||
\(418\) | −16.4177 | −0.803017 | ||||||||
\(419\) | 9.73118 | 0.475399 | 0.237700 | − | 0.971339i | \(-0.423607\pi\) | ||||
0.237700 | + | 0.971339i | \(0.423607\pi\) | |||||||
\(420\) | 31.1766 | 1.52126 | ||||||||
\(421\) | 14.9330 | 0.727789 | 0.363895 | − | 0.931440i | \(-0.381447\pi\) | ||||
0.363895 | + | 0.931440i | \(0.381447\pi\) | |||||||
\(422\) | −29.0299 | −1.41316 | ||||||||
\(423\) | 16.8717 | 0.820329 | ||||||||
\(424\) | 8.12742 | 0.394703 | ||||||||
\(425\) | −0.595305 | −0.0288765 | ||||||||
\(426\) | 2.32160 | 0.112482 | ||||||||
\(427\) | −15.2447 | −0.737745 | ||||||||
\(428\) | 29.9460 | 1.44749 | ||||||||
\(429\) | −15.2667 | −0.737086 | ||||||||
\(430\) | 26.9797 | 1.30108 | ||||||||
\(431\) | −32.2126 | −1.55163 | −0.775814 | − | 0.630962i | \(-0.782660\pi\) | ||||
−0.775814 | + | 0.630962i | \(0.782660\pi\) | |||||||
\(432\) | −39.5036 | −1.90062 | ||||||||
\(433\) | 33.4394 | 1.60699 | 0.803497 | − | 0.595309i | \(-0.202970\pi\) | ||||
0.803497 | + | 0.595309i | \(0.202970\pi\) | |||||||
\(434\) | −46.0424 | −2.21011 | ||||||||
\(435\) | −15.8730 | −0.761050 | ||||||||
\(436\) | 72.4477 | 3.46961 | ||||||||
\(437\) | 10.9056 | 0.521687 | ||||||||
\(438\) | −5.43673 | −0.259777 | ||||||||
\(439\) | 1.51622 | 0.0723653 | 0.0361826 | − | 0.999345i | \(-0.488480\pi\) | ||||
0.0361826 | + | 0.999345i | \(0.488480\pi\) | |||||||
\(440\) | 53.1966 | 2.53605 | ||||||||
\(441\) | −6.43725 | −0.306536 | ||||||||
\(442\) | −10.1281 | −0.481743 | ||||||||
\(443\) | −18.9931 | −0.902388 | −0.451194 | − | 0.892426i | \(-0.649002\pi\) | ||||
−0.451194 | + | 0.892426i | \(0.649002\pi\) | |||||||
\(444\) | −4.47679 | −0.212459 | ||||||||
\(445\) | 2.77358 | 0.131480 | ||||||||
\(446\) | −29.6169 | −1.40240 | ||||||||
\(447\) | 7.25879 | 0.343329 | ||||||||
\(448\) | 6.20644 | 0.293227 | ||||||||
\(449\) | 21.6013 | 1.01943 | 0.509715 | − | 0.860343i | \(-0.329751\pi\) | ||||
0.509715 | + | 0.860343i | \(0.329751\pi\) | |||||||
\(450\) | −3.01874 | −0.142305 | ||||||||
\(451\) | 6.53742 | 0.307835 | ||||||||
\(452\) | −75.9334 | −3.57161 | ||||||||
\(453\) | −0.185617 | −0.00872103 | ||||||||
\(454\) | 11.0651 | 0.519309 | ||||||||
\(455\) | 26.5310 | 1.24379 | ||||||||
\(456\) | 11.2293 | 0.525862 | ||||||||
\(457\) | −2.15994 | −0.101038 | −0.0505188 | − | 0.998723i | \(-0.516087\pi\) | ||||
−0.0505188 | + | 0.998723i | \(0.516087\pi\) | |||||||
\(458\) | 60.5865 | 2.83102 | ||||||||
\(459\) | −5.03502 | −0.235015 | ||||||||
\(460\) | −62.6854 | −2.92272 | ||||||||
\(461\) | −2.17997 | −0.101531 | −0.0507657 | − | 0.998711i | \(-0.516166\pi\) | ||||
−0.0507657 | + | 0.998711i | \(0.516166\pi\) | |||||||
\(462\) | 31.7858 | 1.47881 | ||||||||
\(463\) | 17.2753 | 0.802852 | 0.401426 | − | 0.915892i | \(-0.368515\pi\) | ||||
0.401426 | + | 0.915892i | \(0.368515\pi\) | |||||||
\(464\) | −58.6456 | −2.72256 | ||||||||
\(465\) | 11.8974 | 0.551727 | ||||||||
\(466\) | −45.4333 | −2.10466 | ||||||||
\(467\) | 6.33017 | 0.292925 | 0.146463 | − | 0.989216i | \(-0.453211\pi\) | ||||
0.146463 | + | 0.989216i | \(0.453211\pi\) | |||||||
\(468\) | −35.7578 | −1.65291 | ||||||||
\(469\) | 33.1918 | 1.53266 | ||||||||
\(470\) | 45.9754 | 2.12069 | ||||||||
\(471\) | −11.9560 | −0.550901 | ||||||||
\(472\) | −82.6720 | −3.80529 | ||||||||
\(473\) | 19.1513 | 0.880579 | ||||||||
\(474\) | 21.7097 | 0.997159 | ||||||||
\(475\) | 0.996405 | 0.0457182 | ||||||||
\(476\) | 14.6815 | 0.672927 | ||||||||
\(477\) | 2.42233 | 0.110911 | ||||||||
\(478\) | −16.0240 | −0.732920 | ||||||||
\(479\) | −10.1565 | −0.464062 | −0.232031 | − | 0.972708i | \(-0.574537\pi\) | ||||
−0.232031 | + | 0.972708i | \(0.574537\pi\) | |||||||
\(480\) | −14.5898 | −0.665928 | ||||||||
\(481\) | −3.80970 | −0.173707 | ||||||||
\(482\) | −46.9960 | −2.14061 | ||||||||
\(483\) | −21.1141 | −0.960723 | ||||||||
\(484\) | 16.5619 | 0.752813 | ||||||||
\(485\) | −1.25400 | −0.0569413 | ||||||||
\(486\) | −40.9246 | −1.85638 | ||||||||
\(487\) | −14.4559 | −0.655060 | −0.327530 | − | 0.944841i | \(-0.606216\pi\) | ||||
−0.327530 | + | 0.944841i | \(0.606216\pi\) | |||||||
\(488\) | 31.5617 | 1.42873 | ||||||||
\(489\) | −18.2573 | −0.825623 | ||||||||
\(490\) | −17.5415 | −0.792446 | ||||||||
\(491\) | 12.9210 | 0.583118 | 0.291559 | − | 0.956553i | \(-0.405826\pi\) | ||||
0.291559 | + | 0.956553i | \(0.405826\pi\) | |||||||
\(492\) | −7.93218 | −0.357610 | ||||||||
\(493\) | −7.47480 | −0.336648 | ||||||||
\(494\) | 16.9521 | 0.762710 | ||||||||
\(495\) | 15.8549 | 0.712627 | ||||||||
\(496\) | 43.9571 | 1.97373 | ||||||||
\(497\) | −2.86388 | −0.128463 | ||||||||
\(498\) | 23.4906 | 1.05264 | ||||||||
\(499\) | −7.27621 | −0.325728 | −0.162864 | − | 0.986649i | \(-0.552073\pi\) | ||||
−0.162864 | + | 0.986649i | \(0.552073\pi\) | |||||||
\(500\) | −53.8314 | −2.40741 | ||||||||
\(501\) | −20.1986 | −0.902407 | ||||||||
\(502\) | 47.6823 | 2.12817 | ||||||||
\(503\) | −3.94145 | −0.175740 | −0.0878702 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878702 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(504\) | 41.9675 | 1.86938 | ||||||||
\(505\) | −15.8651 | −0.705988 | ||||||||
\(506\) | −63.9103 | −2.84116 | ||||||||
\(507\) | 2.61008 | 0.115918 | ||||||||
\(508\) | −81.0856 | −3.59759 | ||||||||
\(509\) | −3.99573 | −0.177108 | −0.0885539 | − | 0.996071i | \(-0.528225\pi\) | ||||
−0.0885539 | + | 0.996071i | \(0.528225\pi\) | |||||||
\(510\) | −5.44887 | −0.241280 | ||||||||
\(511\) | 6.70666 | 0.296685 | ||||||||
\(512\) | 50.1410 | 2.21594 | ||||||||
\(513\) | 8.42748 | 0.372082 | ||||||||
\(514\) | −65.7564 | −2.90039 | ||||||||
\(515\) | −0.755624 | −0.0332968 | ||||||||
\(516\) | −23.2373 | −1.02296 | ||||||||
\(517\) | 32.6353 | 1.43530 | ||||||||
\(518\) | 7.93192 | 0.348508 | ||||||||
\(519\) | −21.7823 | −0.956138 | ||||||||
\(520\) | −54.9280 | −2.40875 | ||||||||
\(521\) | −24.9472 | −1.09296 | −0.546478 | − | 0.837473i | \(-0.684032\pi\) | ||||
−0.546478 | + | 0.837473i | \(0.684032\pi\) | |||||||
\(522\) | −37.9041 | −1.65902 | ||||||||
\(523\) | −14.6359 | −0.639982 | −0.319991 | − | 0.947421i | \(-0.603680\pi\) | ||||
−0.319991 | + | 0.947421i | \(0.603680\pi\) | |||||||
\(524\) | −25.5687 | −1.11698 | ||||||||
\(525\) | −1.92911 | −0.0841932 | ||||||||
\(526\) | −16.5284 | −0.720672 | ||||||||
\(527\) | 5.60264 | 0.244055 | ||||||||
\(528\) | −30.3462 | −1.32065 | ||||||||
\(529\) | 19.4531 | 0.845785 | ||||||||
\(530\) | 6.60087 | 0.286724 | ||||||||
\(531\) | −24.6399 | −1.06928 | ||||||||
\(532\) | −24.5735 | −1.06540 | ||||||||
\(533\) | −6.75020 | −0.292383 | ||||||||
\(534\) | −3.43109 | −0.148478 | ||||||||
\(535\) | 13.7101 | 0.592741 | ||||||||
\(536\) | −68.7182 | −2.96817 | ||||||||
\(537\) | 7.03528 | 0.303595 | ||||||||
\(538\) | 10.1705 | 0.438480 | ||||||||
\(539\) | −12.4517 | −0.536334 | ||||||||
\(540\) | −48.4410 | −2.08457 | ||||||||
\(541\) | −29.7724 | −1.28002 | −0.640008 | − | 0.768368i | \(-0.721069\pi\) | ||||
−0.640008 | + | 0.768368i | \(0.721069\pi\) | |||||||
\(542\) | 4.52430 | 0.194335 | ||||||||
\(543\) | −11.1114 | −0.476838 | ||||||||
\(544\) | −6.87052 | −0.294571 | ||||||||
\(545\) | 33.1687 | 1.42079 | ||||||||
\(546\) | −32.8204 | −1.40458 | ||||||||
\(547\) | −30.0474 | −1.28473 | −0.642367 | − | 0.766397i | \(-0.722047\pi\) | ||||
−0.642367 | + | 0.766397i | \(0.722047\pi\) | |||||||
\(548\) | 47.5990 | 2.03333 | ||||||||
\(549\) | 9.40679 | 0.401472 | ||||||||
\(550\) | −5.83923 | −0.248986 | ||||||||
\(551\) | 12.5111 | 0.532992 | ||||||||
\(552\) | 43.7132 | 1.86056 | ||||||||
\(553\) | −26.7807 | −1.13883 | ||||||||
\(554\) | 18.9748 | 0.806163 | ||||||||
\(555\) | −2.04961 | −0.0870011 | ||||||||
\(556\) | −39.2945 | −1.66646 | ||||||||
\(557\) | 27.6137 | 1.17003 | 0.585015 | − | 0.811023i | \(-0.301089\pi\) | ||||
0.585015 | + | 0.811023i | \(0.301089\pi\) | |||||||
\(558\) | 28.4105 | 1.20271 | ||||||||
\(559\) | −19.7747 | −0.836379 | ||||||||
\(560\) | 52.7365 | 2.22852 | ||||||||
\(561\) | −3.86784 | −0.163300 | ||||||||
\(562\) | −15.8724 | −0.669538 | ||||||||
\(563\) | −9.37010 | −0.394903 | −0.197451 | − | 0.980313i | \(-0.563266\pi\) | ||||
−0.197451 | + | 0.980313i | \(0.563266\pi\) | |||||||
\(564\) | −39.5981 | −1.66738 | ||||||||
\(565\) | −34.7646 | −1.46256 | ||||||||
\(566\) | 49.5067 | 2.08092 | ||||||||
\(567\) | 2.67172 | 0.112202 | ||||||||
\(568\) | 5.92920 | 0.248784 | ||||||||
\(569\) | −20.7864 | −0.871413 | −0.435706 | − | 0.900089i | \(-0.643501\pi\) | ||||
−0.435706 | + | 0.900089i | \(0.643501\pi\) | |||||||
\(570\) | 9.12017 | 0.382002 | ||||||||
\(571\) | 5.69563 | 0.238355 | 0.119177 | − | 0.992873i | \(-0.461974\pi\) | ||||
0.119177 | + | 0.992873i | \(0.461974\pi\) | |||||||
\(572\) | −69.1672 | −2.89203 | ||||||||
\(573\) | −8.99666 | −0.375841 | ||||||||
\(574\) | 14.0541 | 0.586608 | ||||||||
\(575\) | 3.87877 | 0.161756 | ||||||||
\(576\) | −3.82969 | −0.159570 | ||||||||
\(577\) | 27.9929 | 1.16536 | 0.582680 | − | 0.812702i | \(-0.302004\pi\) | ||||
0.582680 | + | 0.812702i | \(0.302004\pi\) | |||||||
\(578\) | −2.56595 | −0.106729 | ||||||||
\(579\) | −5.72123 | −0.237766 | ||||||||
\(580\) | −71.9137 | −2.98606 | ||||||||
\(581\) | −28.9777 | −1.20220 | ||||||||
\(582\) | 1.55127 | 0.0643024 | ||||||||
\(583\) | 4.68558 | 0.194057 | ||||||||
\(584\) | −13.8850 | −0.574567 | ||||||||
\(585\) | −16.3710 | −0.676857 | ||||||||
\(586\) | −53.6133 | −2.21474 | ||||||||
\(587\) | −23.4527 | −0.967996 | −0.483998 | − | 0.875069i | \(-0.660816\pi\) | ||||
−0.483998 | + | 0.875069i | \(0.660816\pi\) | |||||||
\(588\) | 15.1083 | 0.623056 | ||||||||
\(589\) | −9.37754 | −0.386395 | ||||||||
\(590\) | −67.1439 | −2.76427 | ||||||||
\(591\) | 13.1301 | 0.540098 | ||||||||
\(592\) | −7.57267 | −0.311235 | ||||||||
\(593\) | −3.95682 | −0.162487 | −0.0812436 | − | 0.996694i | \(-0.525889\pi\) | ||||
−0.0812436 | + | 0.996694i | \(0.525889\pi\) | |||||||
\(594\) | −49.3875 | −2.02640 | ||||||||
\(595\) | 6.72164 | 0.275560 | ||||||||
\(596\) | 32.8865 | 1.34709 | ||||||||
\(597\) | 17.5374 | 0.717759 | ||||||||
\(598\) | 65.9904 | 2.69855 | ||||||||
\(599\) | 6.19521 | 0.253129 | 0.126565 | − | 0.991958i | \(-0.459605\pi\) | ||||
0.126565 | + | 0.991958i | \(0.459605\pi\) | |||||||
\(600\) | 3.99390 | 0.163050 | ||||||||
\(601\) | −35.5100 | −1.44849 | −0.724243 | − | 0.689545i | \(-0.757810\pi\) | ||||
−0.724243 | + | 0.689545i | \(0.757810\pi\) | |||||||
\(602\) | 41.1714 | 1.67802 | ||||||||
\(603\) | −20.4811 | −0.834053 | ||||||||
\(604\) | −0.840952 | −0.0342178 | ||||||||
\(605\) | 7.58252 | 0.308273 | ||||||||
\(606\) | 19.6261 | 0.797255 | ||||||||
\(607\) | −21.2741 | −0.863491 | −0.431745 | − | 0.901996i | \(-0.642102\pi\) | ||||
−0.431745 | + | 0.901996i | \(0.642102\pi\) | |||||||
\(608\) | 11.4997 | 0.466374 | ||||||||
\(609\) | −24.2224 | −0.981541 | ||||||||
\(610\) | 25.6336 | 1.03787 | ||||||||
\(611\) | −33.6975 | −1.36326 | ||||||||
\(612\) | −9.05926 | −0.366199 | ||||||||
\(613\) | 48.8542 | 1.97320 | 0.986602 | − | 0.163147i | \(-0.0521646\pi\) | ||||
0.986602 | + | 0.163147i | \(0.0521646\pi\) | |||||||
\(614\) | 22.6683 | 0.914816 | ||||||||
\(615\) | −3.63159 | −0.146440 | ||||||||
\(616\) | 81.1789 | 3.27079 | ||||||||
\(617\) | 22.5379 | 0.907343 | 0.453671 | − | 0.891169i | \(-0.350114\pi\) | ||||
0.453671 | + | 0.891169i | \(0.350114\pi\) | |||||||
\(618\) | 0.934752 | 0.0376012 | ||||||||
\(619\) | −11.6098 | −0.466637 | −0.233319 | − | 0.972400i | \(-0.574959\pi\) | ||||
−0.233319 | + | 0.972400i | \(0.574959\pi\) | |||||||
\(620\) | 53.9020 | 2.16476 | ||||||||
\(621\) | 32.8062 | 1.31647 | ||||||||
\(622\) | 19.9040 | 0.798076 | ||||||||
\(623\) | 4.23253 | 0.169573 | ||||||||
\(624\) | 31.3339 | 1.25436 | ||||||||
\(625\) | −21.6691 | −0.866764 | ||||||||
\(626\) | 43.8096 | 1.75098 | ||||||||
\(627\) | 6.47388 | 0.258542 | ||||||||
\(628\) | −54.1674 | −2.16151 | ||||||||
\(629\) | −0.965190 | −0.0384846 | ||||||||
\(630\) | 34.0849 | 1.35797 | ||||||||
\(631\) | −38.1165 | −1.51739 | −0.758697 | − | 0.651444i | \(-0.774163\pi\) | ||||
−0.758697 | + | 0.651444i | \(0.774163\pi\) | |||||||
\(632\) | 55.4450 | 2.20549 | ||||||||
\(633\) | 11.4472 | 0.454984 | ||||||||
\(634\) | −1.96507 | −0.0780427 | ||||||||
\(635\) | −37.1234 | −1.47320 | ||||||||
\(636\) | −5.68525 | −0.225435 | ||||||||
\(637\) | 12.8570 | 0.509413 | ||||||||
\(638\) | −73.3189 | −2.90272 | ||||||||
\(639\) | 1.76716 | 0.0699079 | ||||||||
\(640\) | 18.4029 | 0.727439 | ||||||||
\(641\) | 5.59627 | 0.221039 | 0.110520 | − | 0.993874i | \(-0.464748\pi\) | ||||
0.110520 | + | 0.993874i | \(0.464748\pi\) | |||||||
\(642\) | −16.9603 | −0.669368 | ||||||||
\(643\) | −4.21122 | −0.166074 | −0.0830372 | − | 0.996546i | \(-0.526462\pi\) | ||||
−0.0830372 | + | 0.996546i | \(0.526462\pi\) | |||||||
\(644\) | −95.6590 | −3.76949 | ||||||||
\(645\) | −10.6387 | −0.418899 | ||||||||
\(646\) | 4.29482 | 0.168977 | ||||||||
\(647\) | −0.395315 | −0.0155414 | −0.00777072 | − | 0.999970i | \(-0.502474\pi\) | ||||
−0.00777072 | + | 0.999970i | \(0.502474\pi\) | |||||||
\(648\) | −5.53136 | −0.217292 | ||||||||
\(649\) | −47.6616 | −1.87088 | ||||||||
\(650\) | 6.02928 | 0.236488 | ||||||||
\(651\) | 18.1556 | 0.711573 | ||||||||
\(652\) | −82.7161 | −3.23941 | ||||||||
\(653\) | 44.0443 | 1.72359 | 0.861794 | − | 0.507259i | \(-0.169341\pi\) | ||||
0.861794 | + | 0.507259i | \(0.169341\pi\) | |||||||
\(654\) | −41.0316 | −1.60446 | ||||||||
\(655\) | −11.7061 | −0.457396 | ||||||||
\(656\) | −13.4176 | −0.523868 | ||||||||
\(657\) | −4.13835 | −0.161453 | ||||||||
\(658\) | 70.1593 | 2.73509 | ||||||||
\(659\) | 17.2824 | 0.673225 | 0.336613 | − | 0.941643i | \(-0.390719\pi\) | ||||
0.336613 | + | 0.941643i | \(0.390719\pi\) | |||||||
\(660\) | −37.2118 | −1.44847 | ||||||||
\(661\) | 21.1771 | 0.823694 | 0.411847 | − | 0.911253i | \(-0.364884\pi\) | ||||
0.411847 | + | 0.911253i | \(0.364884\pi\) | |||||||
\(662\) | −59.1818 | −2.30017 | ||||||||
\(663\) | 3.99373 | 0.155104 | ||||||||
\(664\) | 59.9935 | 2.32820 | ||||||||
\(665\) | −11.2505 | −0.436275 | ||||||||
\(666\) | −4.89440 | −0.189654 | ||||||||
\(667\) | 48.7028 | 1.88578 | ||||||||
\(668\) | −91.5114 | −3.54068 | ||||||||
\(669\) | 11.6786 | 0.451521 | ||||||||
\(670\) | −55.8111 | −2.15617 | ||||||||
\(671\) | 18.1958 | 0.702441 | ||||||||
\(672\) | −22.2642 | −0.858861 | ||||||||
\(673\) | 46.4973 | 1.79234 | 0.896169 | − | 0.443713i | \(-0.146339\pi\) | ||||
0.896169 | + | 0.443713i | \(0.146339\pi\) | |||||||
\(674\) | 8.88872 | 0.342381 | ||||||||
\(675\) | 2.99737 | 0.115369 | ||||||||
\(676\) | 11.8252 | 0.454814 | ||||||||
\(677\) | −13.4314 | −0.516210 | −0.258105 | − | 0.966117i | \(-0.583098\pi\) | ||||
−0.258105 | + | 0.966117i | \(0.583098\pi\) | |||||||
\(678\) | 43.0058 | 1.65163 | ||||||||
\(679\) | −1.91363 | −0.0734382 | ||||||||
\(680\) | −13.9160 | −0.533656 | ||||||||
\(681\) | −4.36321 | −0.167199 | ||||||||
\(682\) | 54.9552 | 2.10434 | ||||||||
\(683\) | −46.8820 | −1.79389 | −0.896944 | − | 0.442144i | \(-0.854218\pi\) | ||||
−0.896944 | + | 0.442144i | \(0.854218\pi\) | |||||||
\(684\) | 15.1631 | 0.579777 | ||||||||
\(685\) | 21.7922 | 0.832637 | ||||||||
\(686\) | 30.7572 | 1.17432 | ||||||||
\(687\) | −23.8906 | −0.911485 | ||||||||
\(688\) | −39.3067 | −1.49855 | ||||||||
\(689\) | −4.83809 | −0.184316 | ||||||||
\(690\) | 35.5027 | 1.35156 | ||||||||
\(691\) | 25.5103 | 0.970458 | 0.485229 | − | 0.874387i | \(-0.338736\pi\) | ||||
0.485229 | + | 0.874387i | \(0.338736\pi\) | |||||||
\(692\) | −98.6866 | −3.75150 | ||||||||
\(693\) | 24.1949 | 0.919088 | ||||||||
\(694\) | −71.2295 | −2.70384 | ||||||||
\(695\) | −17.9902 | −0.682406 | ||||||||
\(696\) | 50.1485 | 1.90087 | ||||||||
\(697\) | −1.71017 | −0.0647771 | ||||||||
\(698\) | 9.63363 | 0.364638 | ||||||||
\(699\) | 17.9154 | 0.677622 | ||||||||
\(700\) | −8.73998 | −0.330340 | ||||||||
\(701\) | 34.9380 | 1.31959 | 0.659796 | − | 0.751445i | \(-0.270643\pi\) | ||||
0.659796 | + | 0.751445i | \(0.270643\pi\) | |||||||
\(702\) | 50.9950 | 1.92468 | ||||||||
\(703\) | 1.61551 | 0.0609301 | ||||||||
\(704\) | −7.40787 | −0.279195 | ||||||||
\(705\) | −18.1292 | −0.682784 | ||||||||
\(706\) | −2.56595 | −0.0965708 | ||||||||
\(707\) | −24.2104 | −0.910527 | ||||||||
\(708\) | 57.8302 | 2.17339 | ||||||||
\(709\) | −52.2985 | −1.96411 | −0.982055 | − | 0.188593i | \(-0.939607\pi\) | ||||
−0.982055 | + | 0.188593i | \(0.939607\pi\) | |||||||
\(710\) | 4.81553 | 0.180724 | ||||||||
\(711\) | 16.5251 | 0.619739 | ||||||||
\(712\) | −8.76276 | −0.328398 | ||||||||
\(713\) | −36.5046 | −1.36711 | ||||||||
\(714\) | −8.31506 | −0.311183 | ||||||||
\(715\) | −31.6668 | −1.18427 | ||||||||
\(716\) | 31.8739 | 1.19118 | ||||||||
\(717\) | 6.31862 | 0.235973 | ||||||||
\(718\) | −60.4113 | −2.25453 | ||||||||
\(719\) | −34.0384 | −1.26942 | −0.634709 | − | 0.772751i | \(-0.718880\pi\) | ||||
−0.634709 | + | 0.772751i | \(0.718880\pi\) | |||||||
\(720\) | −32.5411 | −1.21274 | ||||||||
\(721\) | −1.15309 | −0.0429435 | ||||||||
\(722\) | 41.5645 | 1.54687 | ||||||||
\(723\) | 18.5316 | 0.689197 | ||||||||
\(724\) | −50.3413 | −1.87092 | ||||||||
\(725\) | 4.44979 | 0.165261 | ||||||||
\(726\) | −9.38002 | −0.348125 | ||||||||
\(727\) | 21.3031 | 0.790087 | 0.395043 | − | 0.918662i | \(-0.370730\pi\) | ||||
0.395043 | + | 0.918662i | \(0.370730\pi\) | |||||||
\(728\) | −83.8210 | −3.10661 | ||||||||
\(729\) | 13.6349 | 0.504996 | ||||||||
\(730\) | −11.2770 | −0.417382 | ||||||||
\(731\) | −5.00992 | −0.185299 | ||||||||
\(732\) | −22.0779 | −0.816022 | ||||||||
\(733\) | −11.5023 | −0.424846 | −0.212423 | − | 0.977178i | \(-0.568135\pi\) | ||||
−0.212423 | + | 0.977178i | \(0.568135\pi\) | |||||||
\(734\) | 6.66499 | 0.246009 | ||||||||
\(735\) | 6.91703 | 0.255139 | ||||||||
\(736\) | 44.7656 | 1.65008 | ||||||||
\(737\) | −39.6171 | −1.45931 | ||||||||
\(738\) | −8.67211 | −0.319225 | ||||||||
\(739\) | 0.486775 | 0.0179063 | 0.00895315 | − | 0.999960i | \(-0.497150\pi\) | ||||
0.00895315 | + | 0.999960i | \(0.497150\pi\) | |||||||
\(740\) | −9.28592 | −0.341357 | ||||||||
\(741\) | −6.68459 | −0.245565 | ||||||||
\(742\) | 10.0730 | 0.369793 | ||||||||
\(743\) | 50.4185 | 1.84967 | 0.924837 | − | 0.380363i | \(-0.124201\pi\) | ||||
0.924837 | + | 0.380363i | \(0.124201\pi\) | |||||||
\(744\) | −37.5881 | −1.37805 | ||||||||
\(745\) | 15.0564 | 0.551625 | ||||||||
\(746\) | −34.8198 | −1.27484 | ||||||||
\(747\) | 17.8807 | 0.654221 | ||||||||
\(748\) | −17.5236 | −0.640725 | ||||||||
\(749\) | 20.9219 | 0.764470 | ||||||||
\(750\) | 30.4881 | 1.11327 | ||||||||
\(751\) | 14.6922 | 0.536126 | 0.268063 | − | 0.963401i | \(-0.413616\pi\) | ||||
0.268063 | + | 0.963401i | \(0.413616\pi\) | |||||||
\(752\) | −66.9816 | −2.44257 | ||||||||
\(753\) | −18.8022 | −0.685191 | ||||||||
\(754\) | 75.7053 | 2.75702 | ||||||||
\(755\) | −0.385013 | −0.0140120 | ||||||||
\(756\) | −73.9218 | −2.68851 | ||||||||
\(757\) | 3.74182 | 0.135999 | 0.0679995 | − | 0.997685i | \(-0.478338\pi\) | ||||
0.0679995 | + | 0.997685i | \(0.478338\pi\) | |||||||
\(758\) | −28.8543 | −1.04803 | ||||||||
\(759\) | 25.2013 | 0.914749 | ||||||||
\(760\) | 23.2923 | 0.844900 | ||||||||
\(761\) | −12.8138 | −0.464501 | −0.232251 | − | 0.972656i | \(-0.574609\pi\) | ||||
−0.232251 | + | 0.972656i | \(0.574609\pi\) | |||||||
\(762\) | 45.9238 | 1.66364 | ||||||||
\(763\) | 50.6160 | 1.83242 | ||||||||
\(764\) | −40.7601 | −1.47465 | ||||||||
\(765\) | −4.14760 | −0.149957 | ||||||||
\(766\) | 46.3957 | 1.67635 | ||||||||
\(767\) | 49.2129 | 1.77697 | ||||||||
\(768\) | −26.6870 | −0.962985 | ||||||||
\(769\) | 36.5460 | 1.31788 | 0.658942 | − | 0.752194i | \(-0.271004\pi\) | ||||
0.658942 | + | 0.752194i | \(0.271004\pi\) | |||||||
\(770\) | 65.9313 | 2.37600 | ||||||||
\(771\) | 25.9292 | 0.933819 | ||||||||
\(772\) | −25.9205 | −0.932900 | ||||||||
\(773\) | 14.1080 | 0.507429 | 0.253714 | − | 0.967279i | \(-0.418348\pi\) | ||||
0.253714 | + | 0.967279i | \(0.418348\pi\) | |||||||
\(774\) | −25.4049 | −0.913160 | ||||||||
\(775\) | −3.33528 | −0.119807 | ||||||||
\(776\) | 3.96185 | 0.142222 | ||||||||
\(777\) | −3.12774 | −0.112207 | ||||||||
\(778\) | 78.0084 | 2.79674 | ||||||||
\(779\) | 2.86243 | 0.102557 | ||||||||
\(780\) | 38.4229 | 1.37576 | ||||||||
\(781\) | 3.41827 | 0.122315 | ||||||||
\(782\) | 16.7187 | 0.597860 | ||||||||
\(783\) | 37.6358 | 1.34499 | ||||||||
\(784\) | 25.5563 | 0.912724 | ||||||||
\(785\) | −24.7994 | −0.885130 | ||||||||
\(786\) | 14.4812 | 0.516526 | ||||||||
\(787\) | 4.85838 | 0.173182 | 0.0865912 | − | 0.996244i | \(-0.472403\pi\) | ||||
0.0865912 | + | 0.996244i | \(0.472403\pi\) | |||||||
\(788\) | 59.4868 | 2.11913 | ||||||||
\(789\) | 6.51752 | 0.232030 | ||||||||
\(790\) | 45.0310 | 1.60213 | ||||||||
\(791\) | −53.0513 | −1.88629 | ||||||||
\(792\) | −50.0915 | −1.77992 | ||||||||
\(793\) | −18.7880 | −0.667182 | ||||||||
\(794\) | −30.5583 | −1.08447 | ||||||||
\(795\) | −2.60288 | −0.0923145 | ||||||||
\(796\) | 79.4547 | 2.81620 | ||||||||
\(797\) | −14.1119 | −0.499870 | −0.249935 | − | 0.968263i | \(-0.580409\pi\) | ||||
−0.249935 | + | 0.968263i | \(0.580409\pi\) | |||||||
\(798\) | 13.9175 | 0.492675 | ||||||||
\(799\) | −8.53728 | −0.302027 | ||||||||
\(800\) | 4.09006 | 0.144605 | ||||||||
\(801\) | −2.61169 | −0.0922795 | ||||||||
\(802\) | −68.7342 | −2.42709 | ||||||||
\(803\) | −8.00493 | −0.282488 | ||||||||
\(804\) | 48.0694 | 1.69528 | ||||||||
\(805\) | −43.7955 | −1.54359 | ||||||||
\(806\) | −56.7439 | −1.99872 | ||||||||
\(807\) | −4.01045 | −0.141174 | ||||||||
\(808\) | 50.1237 | 1.76334 | ||||||||
\(809\) | −19.2807 | −0.677875 | −0.338937 | − | 0.940809i | \(-0.610067\pi\) | ||||
−0.338937 | + | 0.940809i | \(0.610067\pi\) | |||||||
\(810\) | −4.49242 | −0.157847 | ||||||||
\(811\) | 14.0200 | 0.492309 | 0.246154 | − | 0.969231i | \(-0.420833\pi\) | ||||
0.246154 | + | 0.969231i | \(0.420833\pi\) | |||||||
\(812\) | −109.742 | −3.85117 | ||||||||
\(813\) | −1.78403 | −0.0625688 | ||||||||
\(814\) | −9.46737 | −0.331831 | ||||||||
\(815\) | −37.8699 | −1.32652 | ||||||||
\(816\) | 7.93846 | 0.277902 | ||||||||
\(817\) | 8.38546 | 0.293370 | ||||||||
\(818\) | −52.8270 | −1.84705 | ||||||||
\(819\) | −24.9824 | −0.872955 | ||||||||
\(820\) | −16.4532 | −0.574571 | ||||||||
\(821\) | −26.1915 | −0.914091 | −0.457046 | − | 0.889443i | \(-0.651092\pi\) | ||||
−0.457046 | + | 0.889443i | \(0.651092\pi\) | |||||||
\(822\) | −26.9583 | −0.940277 | ||||||||
\(823\) | −56.9821 | −1.98627 | −0.993135 | − | 0.116976i | \(-0.962680\pi\) | ||||
−0.993135 | + | 0.116976i | \(0.962680\pi\) | |||||||
\(824\) | 2.38729 | 0.0831652 | ||||||||
\(825\) | 2.30254 | 0.0801642 | ||||||||
\(826\) | −102.463 | −3.56514 | ||||||||
\(827\) | 30.3268 | 1.05457 | 0.527284 | − | 0.849689i | \(-0.323210\pi\) | ||||
0.527284 | + | 0.849689i | \(0.323210\pi\) | |||||||
\(828\) | 59.0265 | 2.05131 | ||||||||
\(829\) | −4.58829 | −0.159358 | −0.0796789 | − | 0.996821i | \(-0.525389\pi\) | ||||
−0.0796789 | + | 0.996821i | \(0.525389\pi\) | |||||||
\(830\) | 48.7251 | 1.69127 | ||||||||
\(831\) | −7.48221 | −0.259555 | ||||||||
\(832\) | 7.64898 | 0.265181 | ||||||||
\(833\) | 3.25733 | 0.112860 | ||||||||
\(834\) | 22.2549 | 0.770625 | ||||||||
\(835\) | −41.8966 | −1.44989 | ||||||||
\(836\) | 29.3304 | 1.01441 | ||||||||
\(837\) | −28.2094 | −0.975059 | ||||||||
\(838\) | −24.9697 | −0.862565 | ||||||||
\(839\) | −10.7495 | −0.371113 | −0.185557 | − | 0.982634i | \(-0.559409\pi\) | ||||
−0.185557 | + | 0.982634i | \(0.559409\pi\) | |||||||
\(840\) | −45.0955 | −1.55594 | ||||||||
\(841\) | 26.8727 | 0.926645 | ||||||||
\(842\) | −38.3173 | −1.32050 | ||||||||
\(843\) | 6.25886 | 0.215567 | ||||||||
\(844\) | 51.8623 | 1.78518 | ||||||||
\(845\) | 5.41391 | 0.186244 | ||||||||
\(846\) | −43.2919 | −1.48841 | ||||||||
\(847\) | 11.5710 | 0.397586 | ||||||||
\(848\) | −9.61681 | −0.330243 | ||||||||
\(849\) | −19.5216 | −0.669980 | ||||||||
\(850\) | 1.52752 | 0.0523936 | ||||||||
\(851\) | 6.28879 | 0.215577 | ||||||||
\(852\) | −4.14756 | −0.142093 | ||||||||
\(853\) | −0.997537 | −0.0341550 | −0.0170775 | − | 0.999854i | \(-0.505436\pi\) | ||||
−0.0170775 | + | 0.999854i | \(0.505436\pi\) | |||||||
\(854\) | 39.1172 | 1.33856 | ||||||||
\(855\) | 6.94213 | 0.237416 | ||||||||
\(856\) | −43.3153 | −1.48049 | ||||||||
\(857\) | −17.0553 | −0.582598 | −0.291299 | − | 0.956632i | \(-0.594088\pi\) | ||||
−0.291299 | + | 0.956632i | \(0.594088\pi\) | |||||||
\(858\) | 39.1737 | 1.33737 | ||||||||
\(859\) | 39.4260 | 1.34520 | 0.672599 | − | 0.740007i | \(-0.265178\pi\) | ||||
0.672599 | + | 0.740007i | \(0.265178\pi\) | |||||||
\(860\) | −48.1995 | −1.64359 | ||||||||
\(861\) | −5.54186 | −0.188866 | ||||||||
\(862\) | 82.6560 | 2.81527 | ||||||||
\(863\) | −2.61746 | −0.0890994 | −0.0445497 | − | 0.999007i | \(-0.514185\pi\) | ||||
−0.0445497 | + | 0.999007i | \(0.514185\pi\) | |||||||
\(864\) | 34.5932 | 1.17689 | ||||||||
\(865\) | −45.1816 | −1.53622 | ||||||||
\(866\) | −85.8037 | −2.91573 | ||||||||
\(867\) | 1.01181 | 0.0343630 | ||||||||
\(868\) | 82.2553 | 2.79193 | ||||||||
\(869\) | 31.9649 | 1.08433 | ||||||||
\(870\) | 40.7292 | 1.38085 | ||||||||
\(871\) | 40.9065 | 1.38606 | ||||||||
\(872\) | −104.792 | −3.54870 | ||||||||
\(873\) | 1.18081 | 0.0399642 | ||||||||
\(874\) | −27.9833 | −0.946550 | ||||||||
\(875\) | −37.6096 | −1.27144 | ||||||||
\(876\) | 9.71278 | 0.328164 | ||||||||
\(877\) | −42.9635 | −1.45077 | −0.725386 | − | 0.688342i | \(-0.758339\pi\) | ||||
−0.725386 | + | 0.688342i | \(0.758339\pi\) | |||||||
\(878\) | −3.89055 | −0.131300 | ||||||||
\(879\) | 21.1409 | 0.713066 | ||||||||
\(880\) | −62.9451 | −2.12188 | ||||||||
\(881\) | −35.3031 | −1.18939 | −0.594696 | − | 0.803951i | \(-0.702727\pi\) | ||||
−0.594696 | + | 0.803951i | \(0.702727\pi\) | |||||||
\(882\) | 16.5177 | 0.556178 | ||||||||
\(883\) | 48.6272 | 1.63644 | 0.818218 | − | 0.574908i | \(-0.194962\pi\) | ||||
0.818218 | + | 0.574908i | \(0.194962\pi\) | |||||||
\(884\) | 18.0939 | 0.608564 | ||||||||
\(885\) | 26.4764 | 0.889994 | ||||||||
\(886\) | 48.7353 | 1.63729 | ||||||||
\(887\) | 52.5407 | 1.76415 | 0.882073 | − | 0.471113i | \(-0.156148\pi\) | ||||
0.882073 | + | 0.471113i | \(0.156148\pi\) | |||||||
\(888\) | 6.47546 | 0.217302 | ||||||||
\(889\) | −56.6509 | −1.90001 | ||||||||
\(890\) | −7.11687 | −0.238558 | ||||||||
\(891\) | −3.18891 | −0.106832 | ||||||||
\(892\) | 52.9109 | 1.77159 | ||||||||
\(893\) | 14.2895 | 0.478179 | ||||||||
\(894\) | −18.6257 | −0.622936 | ||||||||
\(895\) | 14.5928 | 0.487784 | ||||||||
\(896\) | 28.0831 | 0.938192 | ||||||||
\(897\) | −26.0215 | −0.868834 | ||||||||
\(898\) | −55.4280 | −1.84966 | ||||||||
\(899\) | −41.8786 | −1.39673 | ||||||||
\(900\) | 5.39302 | 0.179767 | ||||||||
\(901\) | −1.22573 | −0.0408350 | ||||||||
\(902\) | −16.7747 | −0.558536 | ||||||||
\(903\) | −16.2348 | −0.540262 | ||||||||
\(904\) | 109.834 | 3.65302 | ||||||||
\(905\) | −23.0477 | −0.766133 | ||||||||
\(906\) | 0.476283 | 0.0158235 | ||||||||
\(907\) | −32.6179 | −1.08306 | −0.541530 | − | 0.840681i | \(-0.682155\pi\) | ||||
−0.541530 | + | 0.840681i | \(0.682155\pi\) | |||||||
\(908\) | −19.7679 | −0.656020 | ||||||||
\(909\) | 14.9391 | 0.495498 | ||||||||
\(910\) | −68.0772 | −2.25674 | ||||||||
\(911\) | −36.2740 | −1.20181 | −0.600906 | − | 0.799319i | \(-0.705194\pi\) | ||||
−0.600906 | + | 0.799319i | \(0.705194\pi\) | |||||||
\(912\) | −13.2872 | −0.439982 | ||||||||
\(913\) | 34.5871 | 1.14467 | ||||||||
\(914\) | 5.54229 | 0.183323 | ||||||||
\(915\) | −10.1079 | −0.334157 | ||||||||
\(916\) | −108.238 | −3.57630 | ||||||||
\(917\) | −17.8637 | −0.589912 | ||||||||
\(918\) | 12.9196 | 0.426411 | ||||||||
\(919\) | 14.4055 | 0.475192 | 0.237596 | − | 0.971364i | \(-0.423641\pi\) | ||||
0.237596 | + | 0.971364i | \(0.423641\pi\) | |||||||
\(920\) | 90.6713 | 2.98935 | ||||||||
\(921\) | −8.93861 | −0.294537 | ||||||||
\(922\) | 5.59370 | 0.184219 | ||||||||
\(923\) | −3.52953 | −0.116176 | ||||||||
\(924\) | −56.7858 | −1.86812 | ||||||||
\(925\) | 0.574582 | 0.0188921 | ||||||||
\(926\) | −44.3276 | −1.45669 | ||||||||
\(927\) | 0.711519 | 0.0233693 | ||||||||
\(928\) | 51.3558 | 1.68584 | ||||||||
\(929\) | −25.8026 | −0.846555 | −0.423277 | − | 0.906000i | \(-0.639120\pi\) | ||||
−0.423277 | + | 0.906000i | \(0.639120\pi\) | |||||||
\(930\) | −30.5280 | −1.00105 | ||||||||
\(931\) | −5.45203 | −0.178683 | ||||||||
\(932\) | 81.1671 | 2.65872 | ||||||||
\(933\) | −7.84859 | −0.256951 | ||||||||
\(934\) | −16.2429 | −0.531484 | ||||||||
\(935\) | −8.02280 | −0.262374 | ||||||||
\(936\) | 51.7219 | 1.69058 | ||||||||
\(937\) | −20.1224 | −0.657369 | −0.328685 | − | 0.944440i | \(-0.606605\pi\) | ||||
−0.328685 | + | 0.944440i | \(0.606605\pi\) | |||||||
\(938\) | −85.1686 | −2.78085 | ||||||||
\(939\) | −17.2751 | −0.563752 | ||||||||
\(940\) | −82.1356 | −2.67897 | ||||||||
\(941\) | 42.7336 | 1.39308 | 0.696538 | − | 0.717520i | \(-0.254723\pi\) | ||||
0.696538 | + | 0.717520i | \(0.254723\pi\) | |||||||
\(942\) | 30.6784 | 0.999555 | ||||||||
\(943\) | 11.1428 | 0.362858 | ||||||||
\(944\) | 97.8220 | 3.18384 | ||||||||
\(945\) | −33.8436 | −1.10093 | ||||||||
\(946\) | −49.1413 | −1.59772 | ||||||||
\(947\) | −43.5030 | −1.41366 | −0.706829 | − | 0.707385i | \(-0.749875\pi\) | ||||
−0.706829 | + | 0.707385i | \(0.749875\pi\) | |||||||
\(948\) | −38.7846 | −1.25967 | ||||||||
\(949\) | 8.26547 | 0.268308 | ||||||||
\(950\) | −2.55672 | −0.0829511 | ||||||||
\(951\) | 0.774870 | 0.0251269 | ||||||||
\(952\) | −21.2361 | −0.688266 | ||||||||
\(953\) | −30.5250 | −0.988803 | −0.494401 | − | 0.869234i | \(-0.664613\pi\) | ||||
−0.494401 | + | 0.869234i | \(0.664613\pi\) | |||||||
\(954\) | −6.21559 | −0.201237 | ||||||||
\(955\) | −18.6612 | −0.603861 | ||||||||
\(956\) | 28.6270 | 0.925864 | ||||||||
\(957\) | 28.9113 | 0.934571 | ||||||||
\(958\) | 26.0611 | 0.841995 | ||||||||
\(959\) | 33.2553 | 1.07387 | ||||||||
\(960\) | 4.11513 | 0.132815 | ||||||||
\(961\) | 0.389568 | 0.0125667 | ||||||||
\(962\) | 9.77551 | 0.315175 | ||||||||
\(963\) | −12.9099 | −0.416015 | ||||||||
\(964\) | 83.9589 | 2.70413 | ||||||||
\(965\) | −11.8672 | −0.382018 | ||||||||
\(966\) | 54.1776 | 1.74314 | ||||||||
\(967\) | −0.861347 | −0.0276990 | −0.0138495 | − | 0.999904i | \(-0.504409\pi\) | ||||
−0.0138495 | + | 0.999904i | \(0.504409\pi\) | |||||||
\(968\) | −23.9559 | −0.769973 | ||||||||
\(969\) | −1.69354 | −0.0544045 | ||||||||
\(970\) | 3.21770 | 0.103314 | ||||||||
\(971\) | 19.5290 | 0.626717 | 0.313358 | − | 0.949635i | \(-0.398546\pi\) | ||||
0.313358 | + | 0.949635i | \(0.398546\pi\) | |||||||
\(972\) | 73.1124 | 2.34508 | ||||||||
\(973\) | −27.4533 | −0.880112 | ||||||||
\(974\) | 37.0932 | 1.18854 | ||||||||
\(975\) | −2.37748 | −0.0761404 | ||||||||
\(976\) | −37.3455 | −1.19540 | ||||||||
\(977\) | −35.0890 | −1.12260 | −0.561298 | − | 0.827614i | \(-0.689698\pi\) | ||||
−0.561298 | + | 0.827614i | \(0.689698\pi\) | |||||||
\(978\) | 46.8473 | 1.49801 | ||||||||
\(979\) | −5.05186 | −0.161458 | ||||||||
\(980\) | 31.3382 | 1.00106 | ||||||||
\(981\) | −31.2326 | −0.997182 | ||||||||
\(982\) | −33.1547 | −1.05801 | ||||||||
\(983\) | −32.5329 | −1.03764 | −0.518820 | − | 0.854884i | \(-0.673628\pi\) | ||||
−0.518820 | + | 0.854884i | \(0.673628\pi\) | |||||||
\(984\) | 11.4735 | 0.365762 | ||||||||
\(985\) | 27.2348 | 0.867773 | ||||||||
\(986\) | 19.1800 | 0.610815 | ||||||||
\(987\) | −27.6654 | −0.880599 | ||||||||
\(988\) | −30.2851 | −0.963497 | ||||||||
\(989\) | 32.6426 | 1.03798 | ||||||||
\(990\) | −40.6830 | −1.29299 | ||||||||
\(991\) | −17.9653 | −0.570688 | −0.285344 | − | 0.958425i | \(-0.592108\pi\) | ||||
−0.285344 | + | 0.958425i | \(0.592108\pi\) | |||||||
\(992\) | −38.4931 | −1.22216 | ||||||||
\(993\) | 23.3367 | 0.740569 | ||||||||
\(994\) | 7.34858 | 0.233083 | ||||||||
\(995\) | 36.3767 | 1.15322 | ||||||||
\(996\) | −41.9663 | −1.32975 | ||||||||
\(997\) | 9.94122 | 0.314841 | 0.157421 | − | 0.987532i | \(-0.449682\pi\) | ||||
0.157421 | + | 0.987532i | \(0.449682\pi\) | |||||||
\(998\) | 18.6704 | 0.591001 | ||||||||
\(999\) | 4.85975 | 0.153756 |
(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 | 6001.2.a.b.1.8 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.8 | ✓ | 114 | 1.1 | even | 1 | trivial |