Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.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: | \(47.9262112932\) |
Analytic rank: | \(1\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-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 | ||||||||
\(3\) | −1.93355 | −1.11634 | −0.558169 | − | 0.829727i | \(-0.688496\pi\) | ||||
−0.558169 | + | 0.829727i | \(0.688496\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.56764 | 1.14828 | 0.574142 | − | 0.818756i | \(-0.305336\pi\) | ||||
0.574142 | + | 0.818756i | \(0.305336\pi\) | |||||||
\(6\) | −1.93355 | −0.789370 | ||||||||
\(7\) | 0.413652 | 0.156346 | 0.0781728 | − | 0.996940i | \(-0.475091\pi\) | ||||
0.0781728 | + | 0.996940i | \(0.475091\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.738635 | 0.246212 | ||||||||
\(10\) | 2.56764 | 0.811959 | ||||||||
\(11\) | −4.92866 | −1.48605 | −0.743023 | − | 0.669265i | \(-0.766609\pi\) | ||||
−0.743023 | + | 0.669265i | \(0.766609\pi\) | |||||||
\(12\) | −1.93355 | −0.558169 | ||||||||
\(13\) | −4.75124 | −1.31776 | −0.658878 | − | 0.752249i | \(-0.728969\pi\) | ||||
−0.658878 | + | 0.752249i | \(0.728969\pi\) | |||||||
\(14\) | 0.413652 | 0.110553 | ||||||||
\(15\) | −4.96467 | −1.28187 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.77589 | 0.673251 | 0.336626 | − | 0.941639i | \(-0.390714\pi\) | ||||
0.336626 | + | 0.941639i | \(0.390714\pi\) | |||||||
\(18\) | 0.738635 | 0.174098 | ||||||||
\(19\) | −3.30404 | −0.757999 | −0.379000 | − | 0.925397i | \(-0.623732\pi\) | ||||
−0.379000 | + | 0.925397i | \(0.623732\pi\) | |||||||
\(20\) | 2.56764 | 0.574142 | ||||||||
\(21\) | −0.799818 | −0.174535 | ||||||||
\(22\) | −4.92866 | −1.05079 | ||||||||
\(23\) | 8.30176 | 1.73104 | 0.865518 | − | 0.500878i | \(-0.166990\pi\) | ||||
0.865518 | + | 0.500878i | \(0.166990\pi\) | |||||||
\(24\) | −1.93355 | −0.394685 | ||||||||
\(25\) | 1.59277 | 0.318554 | ||||||||
\(26\) | −4.75124 | −0.931795 | ||||||||
\(27\) | 4.37247 | 0.841483 | ||||||||
\(28\) | 0.413652 | 0.0781728 | ||||||||
\(29\) | 1.61248 | 0.299430 | 0.149715 | − | 0.988729i | \(-0.452164\pi\) | ||||
0.149715 | + | 0.988729i | \(0.452164\pi\) | |||||||
\(30\) | −4.96467 | −0.906421 | ||||||||
\(31\) | 4.91787 | 0.883276 | 0.441638 | − | 0.897193i | \(-0.354398\pi\) | ||||
0.441638 | + | 0.897193i | \(0.354398\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 9.52983 | 1.65893 | ||||||||
\(34\) | 2.77589 | 0.476061 | ||||||||
\(35\) | 1.06211 | 0.179529 | ||||||||
\(36\) | 0.738635 | 0.123106 | ||||||||
\(37\) | −3.63902 | −0.598251 | −0.299126 | − | 0.954214i | \(-0.596695\pi\) | ||||
−0.299126 | + | 0.954214i | \(0.596695\pi\) | |||||||
\(38\) | −3.30404 | −0.535986 | ||||||||
\(39\) | 9.18678 | 1.47106 | ||||||||
\(40\) | 2.56764 | 0.405979 | ||||||||
\(41\) | −6.36535 | −0.994101 | −0.497051 | − | 0.867722i | \(-0.665584\pi\) | ||||
−0.497051 | + | 0.867722i | \(0.665584\pi\) | |||||||
\(42\) | −0.799818 | −0.123415 | ||||||||
\(43\) | 1.72691 | 0.263351 | 0.131676 | − | 0.991293i | \(-0.457964\pi\) | ||||
0.131676 | + | 0.991293i | \(0.457964\pi\) | |||||||
\(44\) | −4.92866 | −0.743023 | ||||||||
\(45\) | 1.89655 | 0.282721 | ||||||||
\(46\) | 8.30176 | 1.22403 | ||||||||
\(47\) | 9.71136 | 1.41655 | 0.708274 | − | 0.705938i | \(-0.249474\pi\) | ||||
0.708274 | + | 0.705938i | \(0.249474\pi\) | |||||||
\(48\) | −1.93355 | −0.279085 | ||||||||
\(49\) | −6.82889 | −0.975556 | ||||||||
\(50\) | 1.59277 | 0.225252 | ||||||||
\(51\) | −5.36733 | −0.751576 | ||||||||
\(52\) | −4.75124 | −0.658878 | ||||||||
\(53\) | −0.605764 | −0.0832081 | −0.0416041 | − | 0.999134i | \(-0.513247\pi\) | ||||
−0.0416041 | + | 0.999134i | \(0.513247\pi\) | |||||||
\(54\) | 4.37247 | 0.595018 | ||||||||
\(55\) | −12.6550 | −1.70640 | ||||||||
\(56\) | 0.413652 | 0.0552765 | ||||||||
\(57\) | 6.38855 | 0.846184 | ||||||||
\(58\) | 1.61248 | 0.211729 | ||||||||
\(59\) | −9.89689 | −1.28846 | −0.644232 | − | 0.764830i | \(-0.722823\pi\) | ||||
−0.644232 | + | 0.764830i | \(0.722823\pi\) | |||||||
\(60\) | −4.96467 | −0.640936 | ||||||||
\(61\) | 0.612830 | 0.0784648 | 0.0392324 | − | 0.999230i | \(-0.487509\pi\) | ||||
0.0392324 | + | 0.999230i | \(0.487509\pi\) | |||||||
\(62\) | 4.91787 | 0.624570 | ||||||||
\(63\) | 0.305537 | 0.0384941 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.1995 | −1.51316 | ||||||||
\(66\) | 9.52983 | 1.17304 | ||||||||
\(67\) | −5.34629 | −0.653154 | −0.326577 | − | 0.945171i | \(-0.605895\pi\) | ||||
−0.326577 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(68\) | 2.77589 | 0.336626 | ||||||||
\(69\) | −16.0519 | −1.93242 | ||||||||
\(70\) | 1.06211 | 0.126946 | ||||||||
\(71\) | −3.67923 | −0.436644 | −0.218322 | − | 0.975877i | \(-0.570058\pi\) | ||||
−0.218322 | + | 0.975877i | \(0.570058\pi\) | |||||||
\(72\) | 0.738635 | 0.0870489 | ||||||||
\(73\) | −5.61956 | −0.657720 | −0.328860 | − | 0.944379i | \(-0.606664\pi\) | ||||
−0.328860 | + | 0.944379i | \(0.606664\pi\) | |||||||
\(74\) | −3.63902 | −0.423028 | ||||||||
\(75\) | −3.07971 | −0.355614 | ||||||||
\(76\) | −3.30404 | −0.379000 | ||||||||
\(77\) | −2.03875 | −0.232337 | ||||||||
\(78\) | 9.18678 | 1.04020 | ||||||||
\(79\) | −6.22166 | −0.699992 | −0.349996 | − | 0.936751i | \(-0.613817\pi\) | ||||
−0.349996 | + | 0.936751i | \(0.613817\pi\) | |||||||
\(80\) | 2.56764 | 0.287071 | ||||||||
\(81\) | −10.6703 | −1.18559 | ||||||||
\(82\) | −6.36535 | −0.702936 | ||||||||
\(83\) | −2.42115 | −0.265756 | −0.132878 | − | 0.991132i | \(-0.542422\pi\) | ||||
−0.132878 | + | 0.991132i | \(0.542422\pi\) | |||||||
\(84\) | −0.799818 | −0.0872673 | ||||||||
\(85\) | 7.12748 | 0.773083 | ||||||||
\(86\) | 1.72691 | 0.186217 | ||||||||
\(87\) | −3.11781 | −0.334265 | ||||||||
\(88\) | −4.92866 | −0.525397 | ||||||||
\(89\) | −14.5830 | −1.54580 | −0.772900 | − | 0.634528i | \(-0.781194\pi\) | ||||
−0.772900 | + | 0.634528i | \(0.781194\pi\) | |||||||
\(90\) | 1.89655 | 0.199914 | ||||||||
\(91\) | −1.96536 | −0.206026 | ||||||||
\(92\) | 8.30176 | 0.865518 | ||||||||
\(93\) | −9.50897 | −0.986035 | ||||||||
\(94\) | 9.71136 | 1.00165 | ||||||||
\(95\) | −8.48359 | −0.870398 | ||||||||
\(96\) | −1.93355 | −0.197343 | ||||||||
\(97\) | 11.2460 | 1.14186 | 0.570929 | − | 0.821000i | \(-0.306583\pi\) | ||||
0.570929 | + | 0.821000i | \(0.306583\pi\) | |||||||
\(98\) | −6.82889 | −0.689822 | ||||||||
\(99\) | −3.64048 | −0.365882 | ||||||||
\(100\) | 1.59277 | 0.159277 | ||||||||
\(101\) | −5.24995 | −0.522390 | −0.261195 | − | 0.965286i | \(-0.584117\pi\) | ||||
−0.261195 | + | 0.965286i | \(0.584117\pi\) | |||||||
\(102\) | −5.36733 | −0.531445 | ||||||||
\(103\) | −1.90296 | −0.187505 | −0.0937523 | − | 0.995596i | \(-0.529886\pi\) | ||||
−0.0937523 | + | 0.995596i | \(0.529886\pi\) | |||||||
\(104\) | −4.75124 | −0.465897 | ||||||||
\(105\) | −2.05365 | −0.200415 | ||||||||
\(106\) | −0.605764 | −0.0588370 | ||||||||
\(107\) | −18.1159 | −1.75133 | −0.875664 | − | 0.482922i | \(-0.839576\pi\) | ||||
−0.875664 | + | 0.482922i | \(0.839576\pi\) | |||||||
\(108\) | 4.37247 | 0.420742 | ||||||||
\(109\) | 2.69697 | 0.258323 | 0.129161 | − | 0.991624i | \(-0.458772\pi\) | ||||
0.129161 | + | 0.991624i | \(0.458772\pi\) | |||||||
\(110\) | −12.6550 | −1.20661 | ||||||||
\(111\) | 7.03625 | 0.667851 | ||||||||
\(112\) | 0.413652 | 0.0390864 | ||||||||
\(113\) | −14.3092 | −1.34610 | −0.673049 | − | 0.739598i | \(-0.735016\pi\) | ||||
−0.673049 | + | 0.739598i | \(0.735016\pi\) | |||||||
\(114\) | 6.38855 | 0.598342 | ||||||||
\(115\) | 21.3159 | 1.98772 | ||||||||
\(116\) | 1.61248 | 0.149715 | ||||||||
\(117\) | −3.50943 | −0.324447 | ||||||||
\(118\) | −9.89689 | −0.911082 | ||||||||
\(119\) | 1.14825 | 0.105260 | ||||||||
\(120\) | −4.96467 | −0.453210 | ||||||||
\(121\) | 13.2917 | 1.20834 | ||||||||
\(122\) | 0.612830 | 0.0554830 | ||||||||
\(123\) | 12.3078 | 1.10975 | ||||||||
\(124\) | 4.91787 | 0.441638 | ||||||||
\(125\) | −8.74853 | −0.782493 | ||||||||
\(126\) | 0.305537 | 0.0272194 | ||||||||
\(127\) | −9.03404 | −0.801642 | −0.400821 | − | 0.916156i | \(-0.631275\pi\) | ||||
−0.400821 | + | 0.916156i | \(0.631275\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.33907 | −0.293989 | ||||||||
\(130\) | −12.1995 | −1.06996 | ||||||||
\(131\) | −16.6184 | −1.45195 | −0.725977 | − | 0.687719i | \(-0.758612\pi\) | ||||
−0.725977 | + | 0.687719i | \(0.758612\pi\) | |||||||
\(132\) | 9.52983 | 0.829466 | ||||||||
\(133\) | −1.36672 | −0.118510 | ||||||||
\(134\) | −5.34629 | −0.461850 | ||||||||
\(135\) | 11.2269 | 0.966261 | ||||||||
\(136\) | 2.77589 | 0.238030 | ||||||||
\(137\) | 7.48957 | 0.639877 | 0.319939 | − | 0.947438i | \(-0.396338\pi\) | ||||
0.319939 | + | 0.947438i | \(0.396338\pi\) | |||||||
\(138\) | −16.0519 | −1.36643 | ||||||||
\(139\) | 2.34644 | 0.199022 | 0.0995110 | − | 0.995036i | \(-0.468272\pi\) | ||||
0.0995110 | + | 0.995036i | \(0.468272\pi\) | |||||||
\(140\) | 1.06211 | 0.0897645 | ||||||||
\(141\) | −18.7774 | −1.58135 | ||||||||
\(142\) | −3.67923 | −0.308754 | ||||||||
\(143\) | 23.4172 | 1.95825 | ||||||||
\(144\) | 0.738635 | 0.0615529 | ||||||||
\(145\) | 4.14026 | 0.343830 | ||||||||
\(146\) | −5.61956 | −0.465078 | ||||||||
\(147\) | 13.2040 | 1.08905 | ||||||||
\(148\) | −3.63902 | −0.299126 | ||||||||
\(149\) | 2.01065 | 0.164719 | 0.0823593 | − | 0.996603i | \(-0.473754\pi\) | ||||
0.0823593 | + | 0.996603i | \(0.473754\pi\) | |||||||
\(150\) | −3.07971 | −0.251457 | ||||||||
\(151\) | −1.86117 | −0.151460 | −0.0757299 | − | 0.997128i | \(-0.524129\pi\) | ||||
−0.0757299 | + | 0.997128i | \(0.524129\pi\) | |||||||
\(152\) | −3.30404 | −0.267993 | ||||||||
\(153\) | 2.05037 | 0.165762 | ||||||||
\(154\) | −2.03875 | −0.164287 | ||||||||
\(155\) | 12.6273 | 1.01425 | ||||||||
\(156\) | 9.18678 | 0.735531 | ||||||||
\(157\) | −11.3534 | −0.906100 | −0.453050 | − | 0.891485i | \(-0.649664\pi\) | ||||
−0.453050 | + | 0.891485i | \(0.649664\pi\) | |||||||
\(158\) | −6.22166 | −0.494969 | ||||||||
\(159\) | 1.17128 | 0.0928884 | ||||||||
\(160\) | 2.56764 | 0.202990 | ||||||||
\(161\) | 3.43404 | 0.270640 | ||||||||
\(162\) | −10.6703 | −0.838340 | ||||||||
\(163\) | 22.1221 | 1.73274 | 0.866370 | − | 0.499403i | \(-0.166447\pi\) | ||||
0.866370 | + | 0.499403i | \(0.166447\pi\) | |||||||
\(164\) | −6.36535 | −0.497051 | ||||||||
\(165\) | 24.4692 | 1.90492 | ||||||||
\(166\) | −2.42115 | −0.187918 | ||||||||
\(167\) | −13.5895 | −1.05159 | −0.525794 | − | 0.850612i | \(-0.676232\pi\) | ||||
−0.525794 | + | 0.850612i | \(0.676232\pi\) | |||||||
\(168\) | −0.799818 | −0.0617073 | ||||||||
\(169\) | 9.57428 | 0.736483 | ||||||||
\(170\) | 7.12748 | 0.546652 | ||||||||
\(171\) | −2.44048 | −0.186628 | ||||||||
\(172\) | 1.72691 | 0.131676 | ||||||||
\(173\) | 1.63376 | 0.124213 | 0.0621064 | − | 0.998070i | \(-0.480218\pi\) | ||||
0.0621064 | + | 0.998070i | \(0.480218\pi\) | |||||||
\(174\) | −3.11781 | −0.236361 | ||||||||
\(175\) | 0.658853 | 0.0498046 | ||||||||
\(176\) | −4.92866 | −0.371512 | ||||||||
\(177\) | 19.1362 | 1.43836 | ||||||||
\(178\) | −14.5830 | −1.09305 | ||||||||
\(179\) | −3.35613 | −0.250849 | −0.125425 | − | 0.992103i | \(-0.540029\pi\) | ||||
−0.125425 | + | 0.992103i | \(0.540029\pi\) | |||||||
\(180\) | 1.89655 | 0.141360 | ||||||||
\(181\) | −13.6760 | −1.01653 | −0.508264 | − | 0.861201i | \(-0.669713\pi\) | ||||
−0.508264 | + | 0.861201i | \(0.669713\pi\) | |||||||
\(182\) | −1.96536 | −0.145682 | ||||||||
\(183\) | −1.18494 | −0.0875933 | ||||||||
\(184\) | 8.30176 | 0.612014 | ||||||||
\(185\) | −9.34369 | −0.686962 | ||||||||
\(186\) | −9.50897 | −0.697232 | ||||||||
\(187\) | −13.6814 | −1.00048 | ||||||||
\(188\) | 9.71136 | 0.708274 | ||||||||
\(189\) | 1.80868 | 0.131562 | ||||||||
\(190\) | −8.48359 | −0.615464 | ||||||||
\(191\) | −9.74651 | −0.705233 | −0.352616 | − | 0.935768i | \(-0.614708\pi\) | ||||
−0.352616 | + | 0.935768i | \(0.614708\pi\) | |||||||
\(192\) | −1.93355 | −0.139542 | ||||||||
\(193\) | 14.2238 | 1.02385 | 0.511926 | − | 0.859030i | \(-0.328932\pi\) | ||||
0.511926 | + | 0.859030i | \(0.328932\pi\) | |||||||
\(194\) | 11.2460 | 0.807415 | ||||||||
\(195\) | 23.5883 | 1.68920 | ||||||||
\(196\) | −6.82889 | −0.487778 | ||||||||
\(197\) | −14.3214 | −1.02036 | −0.510180 | − | 0.860067i | \(-0.670421\pi\) | ||||
−0.510180 | + | 0.860067i | \(0.670421\pi\) | |||||||
\(198\) | −3.64048 | −0.258718 | ||||||||
\(199\) | 19.3170 | 1.36935 | 0.684673 | − | 0.728851i | \(-0.259945\pi\) | ||||
0.684673 | + | 0.728851i | \(0.259945\pi\) | |||||||
\(200\) | 1.59277 | 0.112626 | ||||||||
\(201\) | 10.3374 | 0.729141 | ||||||||
\(202\) | −5.24995 | −0.369385 | ||||||||
\(203\) | 0.667004 | 0.0468145 | ||||||||
\(204\) | −5.36733 | −0.375788 | ||||||||
\(205\) | −16.3439 | −1.14151 | ||||||||
\(206\) | −1.90296 | −0.132586 | ||||||||
\(207\) | 6.13196 | 0.426201 | ||||||||
\(208\) | −4.75124 | −0.329439 | ||||||||
\(209\) | 16.2845 | 1.12642 | ||||||||
\(210\) | −2.05365 | −0.141715 | ||||||||
\(211\) | −9.72587 | −0.669556 | −0.334778 | − | 0.942297i | \(-0.608661\pi\) | ||||
−0.334778 | + | 0.942297i | \(0.608661\pi\) | |||||||
\(212\) | −0.605764 | −0.0416041 | ||||||||
\(213\) | 7.11399 | 0.487443 | ||||||||
\(214\) | −18.1159 | −1.23838 | ||||||||
\(215\) | 4.43408 | 0.302402 | ||||||||
\(216\) | 4.37247 | 0.297509 | ||||||||
\(217\) | 2.03429 | 0.138096 | ||||||||
\(218\) | 2.69697 | 0.182662 | ||||||||
\(219\) | 10.8657 | 0.734238 | ||||||||
\(220\) | −12.6550 | −0.853201 | ||||||||
\(221\) | −13.1889 | −0.887182 | ||||||||
\(222\) | 7.03625 | 0.472242 | ||||||||
\(223\) | 12.8515 | 0.860597 | 0.430299 | − | 0.902687i | \(-0.358408\pi\) | ||||
0.430299 | + | 0.902687i | \(0.358408\pi\) | |||||||
\(224\) | 0.413652 | 0.0276383 | ||||||||
\(225\) | 1.17648 | 0.0784317 | ||||||||
\(226\) | −14.3092 | −0.951835 | ||||||||
\(227\) | 20.7443 | 1.37685 | 0.688424 | − | 0.725308i | \(-0.258303\pi\) | ||||
0.688424 | + | 0.725308i | \(0.258303\pi\) | |||||||
\(228\) | 6.38855 | 0.423092 | ||||||||
\(229\) | −24.2219 | −1.60063 | −0.800313 | − | 0.599582i | \(-0.795333\pi\) | ||||
−0.800313 | + | 0.599582i | \(0.795333\pi\) | |||||||
\(230\) | 21.3159 | 1.40553 | ||||||||
\(231\) | 3.94203 | 0.259367 | ||||||||
\(232\) | 1.61248 | 0.105864 | ||||||||
\(233\) | −17.6446 | −1.15593 | −0.577967 | − | 0.816060i | \(-0.696154\pi\) | ||||
−0.577967 | + | 0.816060i | \(0.696154\pi\) | |||||||
\(234\) | −3.50943 | −0.229419 | ||||||||
\(235\) | 24.9353 | 1.62660 | ||||||||
\(236\) | −9.89689 | −0.644232 | ||||||||
\(237\) | 12.0299 | 0.781428 | ||||||||
\(238\) | 1.14825 | 0.0744300 | ||||||||
\(239\) | −8.87316 | −0.573957 | −0.286979 | − | 0.957937i | \(-0.592651\pi\) | ||||
−0.286979 | + | 0.957937i | \(0.592651\pi\) | |||||||
\(240\) | −4.96467 | −0.320468 | ||||||||
\(241\) | −4.22672 | −0.272267 | −0.136133 | − | 0.990691i | \(-0.543468\pi\) | ||||
−0.136133 | + | 0.990691i | \(0.543468\pi\) | |||||||
\(242\) | 13.2917 | 0.854422 | ||||||||
\(243\) | 7.51423 | 0.482038 | ||||||||
\(244\) | 0.612830 | 0.0392324 | ||||||||
\(245\) | −17.5341 | −1.12021 | ||||||||
\(246\) | 12.3078 | 0.784714 | ||||||||
\(247\) | 15.6983 | 0.998859 | ||||||||
\(248\) | 4.91787 | 0.312285 | ||||||||
\(249\) | 4.68144 | 0.296674 | ||||||||
\(250\) | −8.74853 | −0.553306 | ||||||||
\(251\) | 23.0729 | 1.45635 | 0.728175 | − | 0.685391i | \(-0.240369\pi\) | ||||
0.728175 | + | 0.685391i | \(0.240369\pi\) | |||||||
\(252\) | 0.305537 | 0.0192471 | ||||||||
\(253\) | −40.9165 | −2.57240 | ||||||||
\(254\) | −9.03404 | −0.566846 | ||||||||
\(255\) | −13.7814 | −0.863023 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.78417 | −0.236050 | −0.118025 | − | 0.993011i | \(-0.537656\pi\) | ||||
−0.118025 | + | 0.993011i | \(0.537656\pi\) | |||||||
\(258\) | −3.33907 | −0.207882 | ||||||||
\(259\) | −1.50529 | −0.0935340 | ||||||||
\(260\) | −12.1995 | −0.756579 | ||||||||
\(261\) | 1.19103 | 0.0737230 | ||||||||
\(262\) | −16.6184 | −1.02669 | ||||||||
\(263\) | 10.2110 | 0.629636 | 0.314818 | − | 0.949152i | \(-0.398057\pi\) | ||||
0.314818 | + | 0.949152i | \(0.398057\pi\) | |||||||
\(264\) | 9.52983 | 0.586521 | ||||||||
\(265\) | −1.55538 | −0.0955465 | ||||||||
\(266\) | −1.36672 | −0.0837992 | ||||||||
\(267\) | 28.1971 | 1.72564 | ||||||||
\(268\) | −5.34629 | −0.326577 | ||||||||
\(269\) | −30.2363 | −1.84354 | −0.921770 | − | 0.387736i | \(-0.873257\pi\) | ||||
−0.921770 | + | 0.387736i | \(0.873257\pi\) | |||||||
\(270\) | 11.2269 | 0.683250 | ||||||||
\(271\) | 15.6754 | 0.952214 | 0.476107 | − | 0.879387i | \(-0.342048\pi\) | ||||
0.476107 | + | 0.879387i | \(0.342048\pi\) | |||||||
\(272\) | 2.77589 | 0.168313 | ||||||||
\(273\) | 3.80013 | 0.229994 | ||||||||
\(274\) | 7.48957 | 0.452462 | ||||||||
\(275\) | −7.85023 | −0.473386 | ||||||||
\(276\) | −16.0519 | −0.966211 | ||||||||
\(277\) | 9.00319 | 0.540949 | 0.270474 | − | 0.962727i | \(-0.412819\pi\) | ||||
0.270474 | + | 0.962727i | \(0.412819\pi\) | |||||||
\(278\) | 2.34644 | 0.140730 | ||||||||
\(279\) | 3.63251 | 0.217473 | ||||||||
\(280\) | 1.06211 | 0.0634731 | ||||||||
\(281\) | 16.8358 | 1.00434 | 0.502171 | − | 0.864768i | \(-0.332535\pi\) | ||||
0.502171 | + | 0.864768i | \(0.332535\pi\) | |||||||
\(282\) | −18.7774 | −1.11818 | ||||||||
\(283\) | −28.0035 | −1.66463 | −0.832316 | − | 0.554301i | \(-0.812986\pi\) | ||||
−0.832316 | + | 0.554301i | \(0.812986\pi\) | |||||||
\(284\) | −3.67923 | −0.218322 | ||||||||
\(285\) | 16.4035 | 0.971659 | ||||||||
\(286\) | 23.4172 | 1.38469 | ||||||||
\(287\) | −2.63304 | −0.155423 | ||||||||
\(288\) | 0.738635 | 0.0435245 | ||||||||
\(289\) | −9.29445 | −0.546732 | ||||||||
\(290\) | 4.14026 | 0.243124 | ||||||||
\(291\) | −21.7447 | −1.27470 | ||||||||
\(292\) | −5.61956 | −0.328860 | ||||||||
\(293\) | 13.2870 | 0.776236 | 0.388118 | − | 0.921610i | \(-0.373125\pi\) | ||||
0.388118 | + | 0.921610i | \(0.373125\pi\) | |||||||
\(294\) | 13.2040 | 0.770075 | ||||||||
\(295\) | −25.4116 | −1.47952 | ||||||||
\(296\) | −3.63902 | −0.211514 | ||||||||
\(297\) | −21.5504 | −1.25048 | ||||||||
\(298\) | 2.01065 | 0.116474 | ||||||||
\(299\) | −39.4436 | −2.28108 | ||||||||
\(300\) | −3.07971 | −0.177807 | ||||||||
\(301\) | 0.714339 | 0.0411738 | ||||||||
\(302\) | −1.86117 | −0.107098 | ||||||||
\(303\) | 10.1511 | 0.583164 | ||||||||
\(304\) | −3.30404 | −0.189500 | ||||||||
\(305\) | 1.57353 | 0.0900998 | ||||||||
\(306\) | 2.05037 | 0.117212 | ||||||||
\(307\) | 24.6758 | 1.40832 | 0.704162 | − | 0.710039i | \(-0.251323\pi\) | ||||
0.704162 | + | 0.710039i | \(0.251323\pi\) | |||||||
\(308\) | −2.03875 | −0.116168 | ||||||||
\(309\) | 3.67948 | 0.209318 | ||||||||
\(310\) | 12.6273 | 0.717183 | ||||||||
\(311\) | 19.7793 | 1.12158 | 0.560790 | − | 0.827958i | \(-0.310498\pi\) | ||||
0.560790 | + | 0.827958i | \(0.310498\pi\) | |||||||
\(312\) | 9.18678 | 0.520099 | ||||||||
\(313\) | 11.4419 | 0.646734 | 0.323367 | − | 0.946274i | \(-0.395185\pi\) | ||||
0.323367 | + | 0.946274i | \(0.395185\pi\) | |||||||
\(314\) | −11.3534 | −0.640710 | ||||||||
\(315\) | 0.784510 | 0.0442021 | ||||||||
\(316\) | −6.22166 | −0.349996 | ||||||||
\(317\) | −4.06866 | −0.228518 | −0.114259 | − | 0.993451i | \(-0.536449\pi\) | ||||
−0.114259 | + | 0.993451i | \(0.536449\pi\) | |||||||
\(318\) | 1.17128 | 0.0656820 | ||||||||
\(319\) | −7.94735 | −0.444966 | ||||||||
\(320\) | 2.56764 | 0.143535 | ||||||||
\(321\) | 35.0280 | 1.95507 | ||||||||
\(322\) | 3.43404 | 0.191371 | ||||||||
\(323\) | −9.17165 | −0.510324 | ||||||||
\(324\) | −10.6703 | −0.592796 | ||||||||
\(325\) | −7.56764 | −0.419777 | ||||||||
\(326\) | 22.1221 | 1.22523 | ||||||||
\(327\) | −5.21473 | −0.288375 | ||||||||
\(328\) | −6.36535 | −0.351468 | ||||||||
\(329\) | 4.01712 | 0.221471 | ||||||||
\(330\) | 24.4692 | 1.34698 | ||||||||
\(331\) | −7.33817 | −0.403342 | −0.201671 | − | 0.979453i | \(-0.564637\pi\) | ||||
−0.201671 | + | 0.979453i | \(0.564637\pi\) | |||||||
\(332\) | −2.42115 | −0.132878 | ||||||||
\(333\) | −2.68791 | −0.147296 | ||||||||
\(334\) | −13.5895 | −0.743585 | ||||||||
\(335\) | −13.7274 | −0.750006 | ||||||||
\(336\) | −0.799818 | −0.0436337 | ||||||||
\(337\) | −16.3019 | −0.888022 | −0.444011 | − | 0.896021i | \(-0.646445\pi\) | ||||
−0.444011 | + | 0.896021i | \(0.646445\pi\) | |||||||
\(338\) | 9.57428 | 0.520772 | ||||||||
\(339\) | 27.6677 | 1.50270 | ||||||||
\(340\) | 7.12748 | 0.386542 | ||||||||
\(341\) | −24.2385 | −1.31259 | ||||||||
\(342\) | −2.44048 | −0.131966 | ||||||||
\(343\) | −5.72035 | −0.308870 | ||||||||
\(344\) | 1.72691 | 0.0931087 | ||||||||
\(345\) | −41.2155 | −2.21897 | ||||||||
\(346\) | 1.63376 | 0.0878317 | ||||||||
\(347\) | 25.2580 | 1.35592 | 0.677960 | − | 0.735099i | \(-0.262864\pi\) | ||||
0.677960 | + | 0.735099i | \(0.262864\pi\) | |||||||
\(348\) | −3.11781 | −0.167132 | ||||||||
\(349\) | −8.44865 | −0.452246 | −0.226123 | − | 0.974099i | \(-0.572605\pi\) | ||||
−0.226123 | + | 0.974099i | \(0.572605\pi\) | |||||||
\(350\) | 0.658853 | 0.0352171 | ||||||||
\(351\) | −20.7747 | −1.10887 | ||||||||
\(352\) | −4.92866 | −0.262698 | ||||||||
\(353\) | −7.06045 | −0.375790 | −0.187895 | − | 0.982189i | \(-0.560166\pi\) | ||||
−0.187895 | + | 0.982189i | \(0.560166\pi\) | |||||||
\(354\) | 19.1362 | 1.01708 | ||||||||
\(355\) | −9.44693 | −0.501391 | ||||||||
\(356\) | −14.5830 | −0.772900 | ||||||||
\(357\) | −2.22021 | −0.117506 | ||||||||
\(358\) | −3.35613 | −0.177377 | ||||||||
\(359\) | 13.4090 | 0.707702 | 0.353851 | − | 0.935302i | \(-0.384872\pi\) | ||||
0.353851 | + | 0.935302i | \(0.384872\pi\) | |||||||
\(360\) | 1.89655 | 0.0999568 | ||||||||
\(361\) | −8.08330 | −0.425437 | ||||||||
\(362\) | −13.6760 | −0.718794 | ||||||||
\(363\) | −25.7002 | −1.34891 | ||||||||
\(364\) | −1.96536 | −0.103013 | ||||||||
\(365\) | −14.4290 | −0.755249 | ||||||||
\(366\) | −1.18494 | −0.0619378 | ||||||||
\(367\) | 0.383791 | 0.0200337 | 0.0100169 | − | 0.999950i | \(-0.496811\pi\) | ||||
0.0100169 | + | 0.999950i | \(0.496811\pi\) | |||||||
\(368\) | 8.30176 | 0.432759 | ||||||||
\(369\) | −4.70167 | −0.244759 | ||||||||
\(370\) | −9.34369 | −0.485755 | ||||||||
\(371\) | −0.250575 | −0.0130092 | ||||||||
\(372\) | −9.50897 | −0.493017 | ||||||||
\(373\) | 25.6861 | 1.32997 | 0.664987 | − | 0.746855i | \(-0.268437\pi\) | ||||
0.664987 | + | 0.746855i | \(0.268437\pi\) | |||||||
\(374\) | −13.6814 | −0.707448 | ||||||||
\(375\) | 16.9158 | 0.873527 | ||||||||
\(376\) | 9.71136 | 0.500825 | ||||||||
\(377\) | −7.66127 | −0.394575 | ||||||||
\(378\) | 1.80868 | 0.0930285 | ||||||||
\(379\) | −9.41195 | −0.483459 | −0.241730 | − | 0.970344i | \(-0.577715\pi\) | ||||
−0.241730 | + | 0.970344i | \(0.577715\pi\) | |||||||
\(380\) | −8.48359 | −0.435199 | ||||||||
\(381\) | 17.4678 | 0.894903 | ||||||||
\(382\) | −9.74651 | −0.498675 | ||||||||
\(383\) | 27.7202 | 1.41644 | 0.708218 | − | 0.705994i | \(-0.249499\pi\) | ||||
0.708218 | + | 0.705994i | \(0.249499\pi\) | |||||||
\(384\) | −1.93355 | −0.0986713 | ||||||||
\(385\) | −5.23477 | −0.266789 | ||||||||
\(386\) | 14.2238 | 0.723972 | ||||||||
\(387\) | 1.27555 | 0.0648401 | ||||||||
\(388\) | 11.2460 | 0.570929 | ||||||||
\(389\) | −23.6989 | −1.20158 | −0.600790 | − | 0.799407i | \(-0.705147\pi\) | ||||
−0.600790 | + | 0.799407i | \(0.705147\pi\) | |||||||
\(390\) | 23.5883 | 1.19444 | ||||||||
\(391\) | 23.0447 | 1.16542 | ||||||||
\(392\) | −6.82889 | −0.344911 | ||||||||
\(393\) | 32.1325 | 1.62087 | ||||||||
\(394\) | −14.3214 | −0.721504 | ||||||||
\(395\) | −15.9750 | −0.803789 | ||||||||
\(396\) | −3.64048 | −0.182941 | ||||||||
\(397\) | −9.01291 | −0.452345 | −0.226172 | − | 0.974087i | \(-0.572621\pi\) | ||||
−0.226172 | + | 0.974087i | \(0.572621\pi\) | |||||||
\(398\) | 19.3170 | 0.968273 | ||||||||
\(399\) | 2.64263 | 0.132297 | ||||||||
\(400\) | 1.59277 | 0.0796386 | ||||||||
\(401\) | −36.5026 | −1.82286 | −0.911428 | − | 0.411460i | \(-0.865019\pi\) | ||||
−0.911428 | + | 0.411460i | \(0.865019\pi\) | |||||||
\(402\) | 10.3374 | 0.515580 | ||||||||
\(403\) | −23.3660 | −1.16394 | ||||||||
\(404\) | −5.24995 | −0.261195 | ||||||||
\(405\) | −27.3975 | −1.36139 | ||||||||
\(406\) | 0.667004 | 0.0331029 | ||||||||
\(407\) | 17.9355 | 0.889029 | ||||||||
\(408\) | −5.36733 | −0.265722 | ||||||||
\(409\) | −28.1491 | −1.39188 | −0.695942 | − | 0.718098i | \(-0.745013\pi\) | ||||
−0.695942 | + | 0.718098i | \(0.745013\pi\) | |||||||
\(410\) | −16.3439 | −0.807169 | ||||||||
\(411\) | −14.4815 | −0.714320 | ||||||||
\(412\) | −1.90296 | −0.0937523 | ||||||||
\(413\) | −4.09386 | −0.201446 | ||||||||
\(414\) | 6.13196 | 0.301370 | ||||||||
\(415\) | −6.21665 | −0.305163 | ||||||||
\(416\) | −4.75124 | −0.232949 | ||||||||
\(417\) | −4.53696 | −0.222176 | ||||||||
\(418\) | 16.2845 | 0.796501 | ||||||||
\(419\) | −1.00405 | −0.0490510 | −0.0245255 | − | 0.999699i | \(-0.507807\pi\) | ||||
−0.0245255 | + | 0.999699i | \(0.507807\pi\) | |||||||
\(420\) | −2.05365 | −0.100208 | ||||||||
\(421\) | −20.3510 | −0.991847 | −0.495924 | − | 0.868366i | \(-0.665170\pi\) | ||||
−0.495924 | + | 0.868366i | \(0.665170\pi\) | |||||||
\(422\) | −9.72587 | −0.473448 | ||||||||
\(423\) | 7.17315 | 0.348770 | ||||||||
\(424\) | −0.605764 | −0.0294185 | ||||||||
\(425\) | 4.42135 | 0.214467 | ||||||||
\(426\) | 7.11399 | 0.344674 | ||||||||
\(427\) | 0.253498 | 0.0122676 | ||||||||
\(428\) | −18.1159 | −0.875664 | ||||||||
\(429\) | −45.2785 | −2.18607 | ||||||||
\(430\) | 4.43408 | 0.213830 | ||||||||
\(431\) | 36.1827 | 1.74286 | 0.871429 | − | 0.490522i | \(-0.163194\pi\) | ||||
0.871429 | + | 0.490522i | \(0.163194\pi\) | |||||||
\(432\) | 4.37247 | 0.210371 | ||||||||
\(433\) | 23.3687 | 1.12303 | 0.561514 | − | 0.827467i | \(-0.310219\pi\) | ||||
0.561514 | + | 0.827467i | \(0.310219\pi\) | |||||||
\(434\) | 2.03429 | 0.0976488 | ||||||||
\(435\) | −8.00542 | −0.383831 | ||||||||
\(436\) | 2.69697 | 0.129161 | ||||||||
\(437\) | −27.4294 | −1.31212 | ||||||||
\(438\) | 10.8657 | 0.519185 | ||||||||
\(439\) | 23.1787 | 1.10626 | 0.553130 | − | 0.833095i | \(-0.313433\pi\) | ||||
0.553130 | + | 0.833095i | \(0.313433\pi\) | |||||||
\(440\) | −12.6550 | −0.603304 | ||||||||
\(441\) | −5.04406 | −0.240193 | ||||||||
\(442\) | −13.1889 | −0.627332 | ||||||||
\(443\) | 7.14042 | 0.339252 | 0.169626 | − | 0.985509i | \(-0.445744\pi\) | ||||
0.169626 | + | 0.985509i | \(0.445744\pi\) | |||||||
\(444\) | 7.03625 | 0.333925 | ||||||||
\(445\) | −37.4440 | −1.77502 | ||||||||
\(446\) | 12.8515 | 0.608534 | ||||||||
\(447\) | −3.88770 | −0.183882 | ||||||||
\(448\) | 0.413652 | 0.0195432 | ||||||||
\(449\) | −33.7316 | −1.59189 | −0.795945 | − | 0.605368i | \(-0.793026\pi\) | ||||
−0.795945 | + | 0.605368i | \(0.793026\pi\) | |||||||
\(450\) | 1.17648 | 0.0554596 | ||||||||
\(451\) | 31.3727 | 1.47728 | ||||||||
\(452\) | −14.3092 | −0.673049 | ||||||||
\(453\) | 3.59867 | 0.169080 | ||||||||
\(454\) | 20.7443 | 0.973579 | ||||||||
\(455\) | −5.04633 | −0.236576 | ||||||||
\(456\) | 6.38855 | 0.299171 | ||||||||
\(457\) | 19.5946 | 0.916599 | 0.458299 | − | 0.888798i | \(-0.348459\pi\) | ||||
0.458299 | + | 0.888798i | \(0.348459\pi\) | |||||||
\(458\) | −24.2219 | −1.13181 | ||||||||
\(459\) | 12.1375 | 0.566530 | ||||||||
\(460\) | 21.3159 | 0.993860 | ||||||||
\(461\) | 28.2593 | 1.31617 | 0.658084 | − | 0.752944i | \(-0.271367\pi\) | ||||
0.658084 | + | 0.752944i | \(0.271367\pi\) | |||||||
\(462\) | 3.94203 | 0.183400 | ||||||||
\(463\) | 22.6776 | 1.05392 | 0.526959 | − | 0.849890i | \(-0.323332\pi\) | ||||
0.526959 | + | 0.849890i | \(0.323332\pi\) | |||||||
\(464\) | 1.61248 | 0.0748574 | ||||||||
\(465\) | −24.4156 | −1.13225 | ||||||||
\(466\) | −17.6446 | −0.817368 | ||||||||
\(467\) | −40.1342 | −1.85719 | −0.928594 | − | 0.371097i | \(-0.878982\pi\) | ||||
−0.928594 | + | 0.371097i | \(0.878982\pi\) | |||||||
\(468\) | −3.50943 | −0.162223 | ||||||||
\(469\) | −2.21150 | −0.102118 | ||||||||
\(470\) | 24.9353 | 1.15018 | ||||||||
\(471\) | 21.9524 | 1.01151 | ||||||||
\(472\) | −9.89689 | −0.455541 | ||||||||
\(473\) | −8.51134 | −0.391352 | ||||||||
\(474\) | 12.0299 | 0.552553 | ||||||||
\(475\) | −5.26258 | −0.241464 | ||||||||
\(476\) | 1.14825 | 0.0526300 | ||||||||
\(477\) | −0.447438 | −0.0204868 | ||||||||
\(478\) | −8.87316 | −0.405849 | ||||||||
\(479\) | −0.525069 | −0.0239910 | −0.0119955 | − | 0.999928i | \(-0.503818\pi\) | ||||
−0.0119955 | + | 0.999928i | \(0.503818\pi\) | |||||||
\(480\) | −4.96467 | −0.226605 | ||||||||
\(481\) | 17.2899 | 0.788350 | ||||||||
\(482\) | −4.22672 | −0.192522 | ||||||||
\(483\) | −6.63990 | −0.302126 | ||||||||
\(484\) | 13.2917 | 0.604168 | ||||||||
\(485\) | 28.8756 | 1.31118 | ||||||||
\(486\) | 7.51423 | 0.340852 | ||||||||
\(487\) | −25.0558 | −1.13539 | −0.567694 | − | 0.823240i | \(-0.692164\pi\) | ||||
−0.567694 | + | 0.823240i | \(0.692164\pi\) | |||||||
\(488\) | 0.612830 | 0.0277415 | ||||||||
\(489\) | −42.7744 | −1.93432 | ||||||||
\(490\) | −17.5341 | −0.792111 | ||||||||
\(491\) | −17.7648 | −0.801715 | −0.400857 | − | 0.916140i | \(-0.631288\pi\) | ||||
−0.400857 | + | 0.916140i | \(0.631288\pi\) | |||||||
\(492\) | 12.3078 | 0.554877 | ||||||||
\(493\) | 4.47605 | 0.201591 | ||||||||
\(494\) | 15.6983 | 0.706300 | ||||||||
\(495\) | −9.34743 | −0.420136 | ||||||||
\(496\) | 4.91787 | 0.220819 | ||||||||
\(497\) | −1.52192 | −0.0682674 | ||||||||
\(498\) | 4.68144 | 0.209780 | ||||||||
\(499\) | 3.09140 | 0.138390 | 0.0691950 | − | 0.997603i | \(-0.477957\pi\) | ||||
0.0691950 | + | 0.997603i | \(0.477957\pi\) | |||||||
\(500\) | −8.74853 | −0.391246 | ||||||||
\(501\) | 26.2761 | 1.17393 | ||||||||
\(502\) | 23.0729 | 1.02980 | ||||||||
\(503\) | −39.7743 | −1.77345 | −0.886725 | − | 0.462298i | \(-0.847025\pi\) | ||||
−0.886725 | + | 0.462298i | \(0.847025\pi\) | |||||||
\(504\) | 0.305537 | 0.0136097 | ||||||||
\(505\) | −13.4800 | −0.599851 | ||||||||
\(506\) | −40.9165 | −1.81896 | ||||||||
\(507\) | −18.5124 | −0.822164 | ||||||||
\(508\) | −9.03404 | −0.400821 | ||||||||
\(509\) | −18.2698 | −0.809795 | −0.404898 | − | 0.914362i | \(-0.632693\pi\) | ||||
−0.404898 | + | 0.914362i | \(0.632693\pi\) | |||||||
\(510\) | −13.7814 | −0.610249 | ||||||||
\(511\) | −2.32454 | −0.102832 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −14.4468 | −0.637844 | ||||||||
\(514\) | −3.78417 | −0.166912 | ||||||||
\(515\) | −4.88612 | −0.215308 | ||||||||
\(516\) | −3.33907 | −0.146994 | ||||||||
\(517\) | −47.8640 | −2.10506 | ||||||||
\(518\) | −1.50529 | −0.0661385 | ||||||||
\(519\) | −3.15897 | −0.138664 | ||||||||
\(520\) | −12.1995 | −0.534982 | ||||||||
\(521\) | −1.09617 | −0.0480243 | −0.0240121 | − | 0.999712i | \(-0.507644\pi\) | ||||
−0.0240121 | + | 0.999712i | \(0.507644\pi\) | |||||||
\(522\) | 1.19103 | 0.0521300 | ||||||||
\(523\) | −29.1966 | −1.27668 | −0.638338 | − | 0.769756i | \(-0.720378\pi\) | ||||
−0.638338 | + | 0.769756i | \(0.720378\pi\) | |||||||
\(524\) | −16.6184 | −0.725977 | ||||||||
\(525\) | −1.27393 | −0.0555988 | ||||||||
\(526\) | 10.2110 | 0.445220 | ||||||||
\(527\) | 13.6515 | 0.594667 | ||||||||
\(528\) | 9.52983 | 0.414733 | ||||||||
\(529\) | 45.9191 | 1.99648 | ||||||||
\(530\) | −1.55538 | −0.0675616 | ||||||||
\(531\) | −7.31018 | −0.317235 | ||||||||
\(532\) | −1.36672 | −0.0592550 | ||||||||
\(533\) | 30.2433 | 1.30998 | ||||||||
\(534\) | 28.1971 | 1.22021 | ||||||||
\(535\) | −46.5150 | −2.01102 | ||||||||
\(536\) | −5.34629 | −0.230925 | ||||||||
\(537\) | 6.48927 | 0.280033 | ||||||||
\(538\) | −30.2363 | −1.30358 | ||||||||
\(539\) | 33.6573 | 1.44972 | ||||||||
\(540\) | 11.2269 | 0.483130 | ||||||||
\(541\) | 34.0157 | 1.46245 | 0.731224 | − | 0.682138i | \(-0.238950\pi\) | ||||
0.731224 | + | 0.682138i | \(0.238950\pi\) | |||||||
\(542\) | 15.6754 | 0.673317 | ||||||||
\(543\) | 26.4433 | 1.13479 | ||||||||
\(544\) | 2.77589 | 0.119015 | ||||||||
\(545\) | 6.92484 | 0.296627 | ||||||||
\(546\) | 3.80013 | 0.162630 | ||||||||
\(547\) | −11.7874 | −0.503991 | −0.251995 | − | 0.967728i | \(-0.581087\pi\) | ||||
−0.251995 | + | 0.967728i | \(0.581087\pi\) | |||||||
\(548\) | 7.48957 | 0.319939 | ||||||||
\(549\) | 0.452657 | 0.0193189 | ||||||||
\(550\) | −7.85023 | −0.334735 | ||||||||
\(551\) | −5.32769 | −0.226967 | ||||||||
\(552\) | −16.0519 | −0.683214 | ||||||||
\(553\) | −2.57360 | −0.109441 | ||||||||
\(554\) | 9.00319 | 0.382509 | ||||||||
\(555\) | 18.0665 | 0.766882 | ||||||||
\(556\) | 2.34644 | 0.0995110 | ||||||||
\(557\) | 0.0686557 | 0.00290904 | 0.00145452 | − | 0.999999i | \(-0.499537\pi\) | ||||
0.00145452 | + | 0.999999i | \(0.499537\pi\) | |||||||
\(558\) | 3.63251 | 0.153776 | ||||||||
\(559\) | −8.20495 | −0.347033 | ||||||||
\(560\) | 1.06211 | 0.0448823 | ||||||||
\(561\) | 26.4537 | 1.11688 | ||||||||
\(562\) | 16.8358 | 0.710177 | ||||||||
\(563\) | 19.2633 | 0.811852 | 0.405926 | − | 0.913906i | \(-0.366949\pi\) | ||||
0.405926 | + | 0.913906i | \(0.366949\pi\) | |||||||
\(564\) | −18.7774 | −0.790673 | ||||||||
\(565\) | −36.7409 | −1.54570 | ||||||||
\(566\) | −28.0035 | −1.17707 | ||||||||
\(567\) | −4.41380 | −0.185362 | ||||||||
\(568\) | −3.67923 | −0.154377 | ||||||||
\(569\) | −24.2099 | −1.01493 | −0.507466 | − | 0.861672i | \(-0.669418\pi\) | ||||
−0.507466 | + | 0.861672i | \(0.669418\pi\) | |||||||
\(570\) | 16.4035 | 0.687066 | ||||||||
\(571\) | 29.7908 | 1.24670 | 0.623352 | − | 0.781941i | \(-0.285770\pi\) | ||||
0.623352 | + | 0.781941i | \(0.285770\pi\) | |||||||
\(572\) | 23.4172 | 0.979124 | ||||||||
\(573\) | 18.8454 | 0.787278 | ||||||||
\(574\) | −2.63304 | −0.109901 | ||||||||
\(575\) | 13.2228 | 0.551429 | ||||||||
\(576\) | 0.738635 | 0.0307764 | ||||||||
\(577\) | −30.5888 | −1.27343 | −0.636713 | − | 0.771101i | \(-0.719707\pi\) | ||||
−0.636713 | + | 0.771101i | \(0.719707\pi\) | |||||||
\(578\) | −9.29445 | −0.386598 | ||||||||
\(579\) | −27.5025 | −1.14296 | ||||||||
\(580\) | 4.14026 | 0.171915 | ||||||||
\(581\) | −1.00151 | −0.0415498 | ||||||||
\(582\) | −21.7447 | −0.901348 | ||||||||
\(583\) | 2.98561 | 0.123651 | ||||||||
\(584\) | −5.61956 | −0.232539 | ||||||||
\(585\) | −9.01095 | −0.372557 | ||||||||
\(586\) | 13.2870 | 0.548882 | ||||||||
\(587\) | 20.7049 | 0.854584 | 0.427292 | − | 0.904114i | \(-0.359468\pi\) | ||||
0.427292 | + | 0.904114i | \(0.359468\pi\) | |||||||
\(588\) | 13.2040 | 0.544525 | ||||||||
\(589\) | −16.2489 | −0.669522 | ||||||||
\(590\) | −25.4116 | −1.04618 | ||||||||
\(591\) | 27.6913 | 1.13907 | ||||||||
\(592\) | −3.63902 | −0.149563 | ||||||||
\(593\) | 35.9861 | 1.47777 | 0.738885 | − | 0.673831i | \(-0.235353\pi\) | ||||
0.738885 | + | 0.673831i | \(0.235353\pi\) | |||||||
\(594\) | −21.5504 | −0.884225 | ||||||||
\(595\) | 2.94829 | 0.120868 | ||||||||
\(596\) | 2.01065 | 0.0823593 | ||||||||
\(597\) | −37.3505 | −1.52865 | ||||||||
\(598\) | −39.4436 | −1.61297 | ||||||||
\(599\) | 21.4359 | 0.875846 | 0.437923 | − | 0.899012i | \(-0.355714\pi\) | ||||
0.437923 | + | 0.899012i | \(0.355714\pi\) | |||||||
\(600\) | −3.07971 | −0.125729 | ||||||||
\(601\) | 44.3471 | 1.80896 | 0.904479 | − | 0.426519i | \(-0.140260\pi\) | ||||
0.904479 | + | 0.426519i | \(0.140260\pi\) | |||||||
\(602\) | 0.714339 | 0.0291143 | ||||||||
\(603\) | −3.94896 | −0.160814 | ||||||||
\(604\) | −1.86117 | −0.0757299 | ||||||||
\(605\) | 34.1283 | 1.38751 | ||||||||
\(606\) | 10.1511 | 0.412359 | ||||||||
\(607\) | 9.18367 | 0.372754 | 0.186377 | − | 0.982478i | \(-0.440325\pi\) | ||||
0.186377 | + | 0.982478i | \(0.440325\pi\) | |||||||
\(608\) | −3.30404 | −0.133997 | ||||||||
\(609\) | −1.28969 | −0.0522608 | ||||||||
\(610\) | 1.57353 | 0.0637102 | ||||||||
\(611\) | −46.1410 | −1.86667 | ||||||||
\(612\) | 2.05037 | 0.0828811 | ||||||||
\(613\) | 30.5892 | 1.23549 | 0.617744 | − | 0.786380i | \(-0.288047\pi\) | ||||
0.617744 | + | 0.786380i | \(0.288047\pi\) | |||||||
\(614\) | 24.6758 | 0.995835 | ||||||||
\(615\) | 31.6019 | 1.27431 | ||||||||
\(616\) | −2.03875 | −0.0821435 | ||||||||
\(617\) | 41.3796 | 1.66588 | 0.832939 | − | 0.553365i | \(-0.186656\pi\) | ||||
0.832939 | + | 0.553365i | \(0.186656\pi\) | |||||||
\(618\) | 3.67948 | 0.148011 | ||||||||
\(619\) | −34.0705 | −1.36941 | −0.684704 | − | 0.728821i | \(-0.740069\pi\) | ||||
−0.684704 | + | 0.728821i | \(0.740069\pi\) | |||||||
\(620\) | 12.6273 | 0.507125 | ||||||||
\(621\) | 36.2992 | 1.45664 | ||||||||
\(622\) | 19.7793 | 0.793077 | ||||||||
\(623\) | −6.03230 | −0.241679 | ||||||||
\(624\) | 9.18678 | 0.367766 | ||||||||
\(625\) | −30.4269 | −1.21708 | ||||||||
\(626\) | 11.4419 | 0.457310 | ||||||||
\(627\) | −31.4870 | −1.25747 | ||||||||
\(628\) | −11.3534 | −0.453050 | ||||||||
\(629\) | −10.1015 | −0.402774 | ||||||||
\(630\) | 0.784510 | 0.0312556 | ||||||||
\(631\) | −20.1027 | −0.800277 | −0.400138 | − | 0.916455i | \(-0.631038\pi\) | ||||
−0.400138 | + | 0.916455i | \(0.631038\pi\) | |||||||
\(632\) | −6.22166 | −0.247484 | ||||||||
\(633\) | 18.8055 | 0.747452 | ||||||||
\(634\) | −4.06866 | −0.161587 | ||||||||
\(635\) | −23.1962 | −0.920512 | ||||||||
\(636\) | 1.17128 | 0.0464442 | ||||||||
\(637\) | 32.4457 | 1.28555 | ||||||||
\(638\) | −7.94735 | −0.314639 | ||||||||
\(639\) | −2.71761 | −0.107507 | ||||||||
\(640\) | 2.56764 | 0.101495 | ||||||||
\(641\) | 17.1231 | 0.676323 | 0.338161 | − | 0.941088i | \(-0.390195\pi\) | ||||
0.338161 | + | 0.941088i | \(0.390195\pi\) | |||||||
\(642\) | 35.0280 | 1.38245 | ||||||||
\(643\) | −40.8807 | −1.61218 | −0.806088 | − | 0.591796i | \(-0.798419\pi\) | ||||
−0.806088 | + | 0.591796i | \(0.798419\pi\) | |||||||
\(644\) | 3.43404 | 0.135320 | ||||||||
\(645\) | −8.57353 | −0.337582 | ||||||||
\(646\) | −9.17165 | −0.360854 | ||||||||
\(647\) | 16.7157 | 0.657164 | 0.328582 | − | 0.944476i | \(-0.393429\pi\) | ||||
0.328582 | + | 0.944476i | \(0.393429\pi\) | |||||||
\(648\) | −10.6703 | −0.419170 | ||||||||
\(649\) | 48.7784 | 1.91472 | ||||||||
\(650\) | −7.56764 | −0.296827 | ||||||||
\(651\) | −3.93340 | −0.154162 | ||||||||
\(652\) | 22.1221 | 0.866370 | ||||||||
\(653\) | 36.8297 | 1.44126 | 0.720629 | − | 0.693321i | \(-0.243853\pi\) | ||||
0.720629 | + | 0.693321i | \(0.243853\pi\) | |||||||
\(654\) | −5.21473 | −0.203912 | ||||||||
\(655\) | −42.6700 | −1.66725 | ||||||||
\(656\) | −6.36535 | −0.248525 | ||||||||
\(657\) | −4.15080 | −0.161938 | ||||||||
\(658\) | 4.01712 | 0.156604 | ||||||||
\(659\) | 30.6710 | 1.19477 | 0.597386 | − | 0.801954i | \(-0.296206\pi\) | ||||
0.597386 | + | 0.801954i | \(0.296206\pi\) | |||||||
\(660\) | 24.4692 | 0.952461 | ||||||||
\(661\) | 10.3495 | 0.402549 | 0.201275 | − | 0.979535i | \(-0.435492\pi\) | ||||
0.201275 | + | 0.979535i | \(0.435492\pi\) | |||||||
\(662\) | −7.33817 | −0.285206 | ||||||||
\(663\) | 25.5015 | 0.990395 | ||||||||
\(664\) | −2.42115 | −0.0939590 | ||||||||
\(665\) | −3.50925 | −0.136083 | ||||||||
\(666\) | −2.68791 | −0.104154 | ||||||||
\(667\) | 13.3864 | 0.518323 | ||||||||
\(668\) | −13.5895 | −0.525794 | ||||||||
\(669\) | −24.8490 | −0.960718 | ||||||||
\(670\) | −13.7274 | −0.530334 | ||||||||
\(671\) | −3.02043 | −0.116602 | ||||||||
\(672\) | −0.799818 | −0.0308537 | ||||||||
\(673\) | −2.79597 | −0.107777 | −0.0538883 | − | 0.998547i | \(-0.517161\pi\) | ||||
−0.0538883 | + | 0.998547i | \(0.517161\pi\) | |||||||
\(674\) | −16.3019 | −0.627926 | ||||||||
\(675\) | 6.96435 | 0.268058 | ||||||||
\(676\) | 9.57428 | 0.368241 | ||||||||
\(677\) | −8.22059 | −0.315943 | −0.157972 | − | 0.987444i | \(-0.550495\pi\) | ||||
−0.157972 | + | 0.987444i | \(0.550495\pi\) | |||||||
\(678\) | 27.6677 | 1.06257 | ||||||||
\(679\) | 4.65192 | 0.178524 | ||||||||
\(680\) | 7.12748 | 0.273326 | ||||||||
\(681\) | −40.1103 | −1.53703 | ||||||||
\(682\) | −24.2385 | −0.928141 | ||||||||
\(683\) | −4.45405 | −0.170430 | −0.0852148 | − | 0.996363i | \(-0.527158\pi\) | ||||
−0.0852148 | + | 0.996363i | \(0.527158\pi\) | |||||||
\(684\) | −2.44048 | −0.0933141 | ||||||||
\(685\) | 19.2305 | 0.734760 | ||||||||
\(686\) | −5.72035 | −0.218404 | ||||||||
\(687\) | 46.8343 | 1.78684 | ||||||||
\(688\) | 1.72691 | 0.0658378 | ||||||||
\(689\) | 2.87813 | 0.109648 | ||||||||
\(690\) | −41.2155 | −1.56905 | ||||||||
\(691\) | 15.3478 | 0.583857 | 0.291928 | − | 0.956440i | \(-0.405703\pi\) | ||||
0.291928 | + | 0.956440i | \(0.405703\pi\) | |||||||
\(692\) | 1.63376 | 0.0621064 | ||||||||
\(693\) | −1.50589 | −0.0572040 | ||||||||
\(694\) | 25.2580 | 0.958780 | ||||||||
\(695\) | 6.02480 | 0.228534 | ||||||||
\(696\) | −3.11781 | −0.118180 | ||||||||
\(697\) | −17.6695 | −0.669280 | ||||||||
\(698\) | −8.44865 | −0.319786 | ||||||||
\(699\) | 34.1167 | 1.29041 | ||||||||
\(700\) | 0.658853 | 0.0249023 | ||||||||
\(701\) | 20.8173 | 0.786260 | 0.393130 | − | 0.919483i | \(-0.371392\pi\) | ||||
0.393130 | + | 0.919483i | \(0.371392\pi\) | |||||||
\(702\) | −20.7747 | −0.784089 | ||||||||
\(703\) | 12.0235 | 0.453474 | ||||||||
\(704\) | −4.92866 | −0.185756 | ||||||||
\(705\) | −48.2137 | −1.81583 | ||||||||
\(706\) | −7.06045 | −0.265724 | ||||||||
\(707\) | −2.17165 | −0.0816734 | ||||||||
\(708\) | 19.1362 | 0.719181 | ||||||||
\(709\) | −42.0190 | −1.57806 | −0.789029 | − | 0.614356i | \(-0.789416\pi\) | ||||
−0.789029 | + | 0.614356i | \(0.789416\pi\) | |||||||
\(710\) | −9.44693 | −0.354537 | ||||||||
\(711\) | −4.59554 | −0.172346 | ||||||||
\(712\) | −14.5830 | −0.546523 | ||||||||
\(713\) | 40.8270 | 1.52898 | ||||||||
\(714\) | −2.22021 | −0.0830891 | ||||||||
\(715\) | 60.1270 | 2.24862 | ||||||||
\(716\) | −3.35613 | −0.125425 | ||||||||
\(717\) | 17.1568 | 0.640731 | ||||||||
\(718\) | 13.4090 | 0.500421 | ||||||||
\(719\) | −3.15233 | −0.117562 | −0.0587810 | − | 0.998271i | \(-0.518721\pi\) | ||||
−0.0587810 | + | 0.998271i | \(0.518721\pi\) | |||||||
\(720\) | 1.89655 | 0.0706801 | ||||||||
\(721\) | −0.787164 | −0.0293155 | ||||||||
\(722\) | −8.08330 | −0.300829 | ||||||||
\(723\) | 8.17259 | 0.303942 | ||||||||
\(724\) | −13.6760 | −0.508264 | ||||||||
\(725\) | 2.56831 | 0.0953845 | ||||||||
\(726\) | −25.7002 | −0.953824 | ||||||||
\(727\) | 0.261421 | 0.00969557 | 0.00484779 | − | 0.999988i | \(-0.498457\pi\) | ||||
0.00484779 | + | 0.999988i | \(0.498457\pi\) | |||||||
\(728\) | −1.96536 | −0.0728410 | ||||||||
\(729\) | 17.4818 | 0.647474 | ||||||||
\(730\) | −14.4290 | −0.534042 | ||||||||
\(731\) | 4.79370 | 0.177301 | ||||||||
\(732\) | −1.18494 | −0.0437966 | ||||||||
\(733\) | −45.3766 | −1.67602 | −0.838011 | − | 0.545653i | \(-0.816282\pi\) | ||||
−0.838011 | + | 0.545653i | \(0.816282\pi\) | |||||||
\(734\) | 0.383791 | 0.0141660 | ||||||||
\(735\) | 33.9032 | 1.25054 | ||||||||
\(736\) | 8.30176 | 0.306007 | ||||||||
\(737\) | 26.3501 | 0.970617 | ||||||||
\(738\) | −4.70167 | −0.173071 | ||||||||
\(739\) | 19.7514 | 0.726567 | 0.363284 | − | 0.931679i | \(-0.381656\pi\) | ||||
0.363284 | + | 0.931679i | \(0.381656\pi\) | |||||||
\(740\) | −9.34369 | −0.343481 | ||||||||
\(741\) | −30.3535 | −1.11506 | ||||||||
\(742\) | −0.250575 | −0.00919891 | ||||||||
\(743\) | −13.0237 | −0.477793 | −0.238896 | − | 0.971045i | \(-0.576786\pi\) | ||||
−0.238896 | + | 0.971045i | \(0.576786\pi\) | |||||||
\(744\) | −9.50897 | −0.348616 | ||||||||
\(745\) | 5.16262 | 0.189144 | ||||||||
\(746\) | 25.6861 | 0.940434 | ||||||||
\(747\) | −1.78835 | −0.0654322 | ||||||||
\(748\) | −13.6814 | −0.500242 | ||||||||
\(749\) | −7.49366 | −0.273812 | ||||||||
\(750\) | 16.9158 | 0.617677 | ||||||||
\(751\) | −20.6835 | −0.754751 | −0.377376 | − | 0.926060i | \(-0.623173\pi\) | ||||
−0.377376 | + | 0.926060i | \(0.623173\pi\) | |||||||
\(752\) | 9.71136 | 0.354137 | ||||||||
\(753\) | −44.6128 | −1.62578 | ||||||||
\(754\) | −7.66127 | −0.279007 | ||||||||
\(755\) | −4.77881 | −0.173919 | ||||||||
\(756\) | 1.80868 | 0.0657811 | ||||||||
\(757\) | 18.8837 | 0.686340 | 0.343170 | − | 0.939273i | \(-0.388499\pi\) | ||||
0.343170 | + | 0.939273i | \(0.388499\pi\) | |||||||
\(758\) | −9.41195 | −0.341857 | ||||||||
\(759\) | 79.1144 | 2.87167 | ||||||||
\(760\) | −8.48359 | −0.307732 | ||||||||
\(761\) | 45.0144 | 1.63177 | 0.815885 | − | 0.578214i | \(-0.196250\pi\) | ||||
0.815885 | + | 0.578214i | \(0.196250\pi\) | |||||||
\(762\) | 17.4678 | 0.632792 | ||||||||
\(763\) | 1.11561 | 0.0403876 | ||||||||
\(764\) | −9.74651 | −0.352616 | ||||||||
\(765\) | 5.26460 | 0.190342 | ||||||||
\(766\) | 27.7202 | 1.00157 | ||||||||
\(767\) | 47.0225 | 1.69788 | ||||||||
\(768\) | −1.93355 | −0.0697712 | ||||||||
\(769\) | 31.4828 | 1.13530 | 0.567649 | − | 0.823271i | \(-0.307853\pi\) | ||||
0.567649 | + | 0.823271i | \(0.307853\pi\) | |||||||
\(770\) | −5.23477 | −0.188648 | ||||||||
\(771\) | 7.31690 | 0.263512 | ||||||||
\(772\) | 14.2238 | 0.511926 | ||||||||
\(773\) | 20.6565 | 0.742963 | 0.371482 | − | 0.928440i | \(-0.378850\pi\) | ||||
0.371482 | + | 0.928440i | \(0.378850\pi\) | |||||||
\(774\) | 1.27555 | 0.0458488 | ||||||||
\(775\) | 7.83304 | 0.281371 | ||||||||
\(776\) | 11.2460 | 0.403707 | ||||||||
\(777\) | 2.91056 | 0.104416 | ||||||||
\(778\) | −23.6989 | −0.849646 | ||||||||
\(779\) | 21.0314 | 0.753528 | ||||||||
\(780\) | 23.5883 | 0.844598 | ||||||||
\(781\) | 18.1337 | 0.648874 | ||||||||
\(782\) | 23.0447 | 0.824078 | ||||||||
\(783\) | 7.05052 | 0.251965 | ||||||||
\(784\) | −6.82889 | −0.243889 | ||||||||
\(785\) | −29.1514 | −1.04046 | ||||||||
\(786\) | 32.1325 | 1.14613 | ||||||||
\(787\) | −17.0863 | −0.609060 | −0.304530 | − | 0.952503i | \(-0.598499\pi\) | ||||
−0.304530 | + | 0.952503i | \(0.598499\pi\) | |||||||
\(788\) | −14.3214 | −0.510180 | ||||||||
\(789\) | −19.7435 | −0.702887 | ||||||||
\(790\) | −15.9750 | −0.568365 | ||||||||
\(791\) | −5.91903 | −0.210457 | ||||||||
\(792\) | −3.64048 | −0.129359 | ||||||||
\(793\) | −2.91170 | −0.103398 | ||||||||
\(794\) | −9.01291 | −0.319856 | ||||||||
\(795\) | 3.00742 | 0.106662 | ||||||||
\(796\) | 19.3170 | 0.684673 | ||||||||
\(797\) | −16.8575 | −0.597122 | −0.298561 | − | 0.954391i | \(-0.596507\pi\) | ||||
−0.298561 | + | 0.954391i | \(0.596507\pi\) | |||||||
\(798\) | 2.64263 | 0.0935482 | ||||||||
\(799\) | 26.9576 | 0.953693 | ||||||||
\(800\) | 1.59277 | 0.0563130 | ||||||||
\(801\) | −10.7715 | −0.380594 | ||||||||
\(802\) | −36.5026 | −1.28895 | ||||||||
\(803\) | 27.6969 | 0.977403 | ||||||||
\(804\) | 10.3374 | 0.364570 | ||||||||
\(805\) | 8.81736 | 0.310771 | ||||||||
\(806\) | −23.3660 | −0.823032 | ||||||||
\(807\) | 58.4636 | 2.05802 | ||||||||
\(808\) | −5.24995 | −0.184693 | ||||||||
\(809\) | 48.2144 | 1.69513 | 0.847564 | − | 0.530693i | \(-0.178068\pi\) | ||||
0.847564 | + | 0.530693i | \(0.178068\pi\) | |||||||
\(810\) | −27.3975 | −0.962651 | ||||||||
\(811\) | 48.9937 | 1.72040 | 0.860200 | − | 0.509956i | \(-0.170338\pi\) | ||||
0.860200 | + | 0.509956i | \(0.170338\pi\) | |||||||
\(812\) | 0.667004 | 0.0234073 | ||||||||
\(813\) | −30.3093 | −1.06299 | ||||||||
\(814\) | 17.9355 | 0.628639 | ||||||||
\(815\) | 56.8017 | 1.98968 | ||||||||
\(816\) | −5.36733 | −0.187894 | ||||||||
\(817\) | −5.70578 | −0.199620 | ||||||||
\(818\) | −28.1491 | −0.984211 | ||||||||
\(819\) | −1.45168 | −0.0507259 | ||||||||
\(820\) | −16.3439 | −0.570755 | ||||||||
\(821\) | 13.5893 | 0.474271 | 0.237136 | − | 0.971477i | \(-0.423791\pi\) | ||||
0.237136 | + | 0.971477i | \(0.423791\pi\) | |||||||
\(822\) | −14.4815 | −0.505100 | ||||||||
\(823\) | −28.7843 | −1.00336 | −0.501679 | − | 0.865054i | \(-0.667284\pi\) | ||||
−0.501679 | + | 0.865054i | \(0.667284\pi\) | |||||||
\(824\) | −1.90296 | −0.0662929 | ||||||||
\(825\) | 15.1788 | 0.528460 | ||||||||
\(826\) | −4.09386 | −0.142444 | ||||||||
\(827\) | 13.4759 | 0.468603 | 0.234301 | − | 0.972164i | \(-0.424720\pi\) | ||||
0.234301 | + | 0.972164i | \(0.424720\pi\) | |||||||
\(828\) | 6.13196 | 0.213100 | ||||||||
\(829\) | −21.3585 | −0.741812 | −0.370906 | − | 0.928670i | \(-0.620953\pi\) | ||||
−0.370906 | + | 0.928670i | \(0.620953\pi\) | |||||||
\(830\) | −6.21665 | −0.215783 | ||||||||
\(831\) | −17.4082 | −0.603882 | ||||||||
\(832\) | −4.75124 | −0.164720 | ||||||||
\(833\) | −18.9562 | −0.656795 | ||||||||
\(834\) | −4.53696 | −0.157102 | ||||||||
\(835\) | −34.8930 | −1.20752 | ||||||||
\(836\) | 16.2845 | 0.563211 | ||||||||
\(837\) | 21.5033 | 0.743261 | ||||||||
\(838\) | −1.00405 | −0.0346843 | ||||||||
\(839\) | −23.8230 | −0.822461 | −0.411231 | − | 0.911531i | \(-0.634901\pi\) | ||||
−0.411231 | + | 0.911531i | \(0.634901\pi\) | |||||||
\(840\) | −2.05365 | −0.0708575 | ||||||||
\(841\) | −26.3999 | −0.910342 | ||||||||
\(842\) | −20.3510 | −0.701342 | ||||||||
\(843\) | −32.5530 | −1.12119 | ||||||||
\(844\) | −9.72587 | −0.334778 | ||||||||
\(845\) | 24.5833 | 0.845691 | ||||||||
\(846\) | 7.17315 | 0.246618 | ||||||||
\(847\) | 5.49813 | 0.188918 | ||||||||
\(848\) | −0.605764 | −0.0208020 | ||||||||
\(849\) | 54.1462 | 1.85829 | ||||||||
\(850\) | 4.42135 | 0.151651 | ||||||||
\(851\) | −30.2103 | −1.03559 | ||||||||
\(852\) | 7.11399 | 0.243721 | ||||||||
\(853\) | −49.1931 | −1.68434 | −0.842170 | − | 0.539212i | \(-0.818722\pi\) | ||||
−0.842170 | + | 0.539212i | \(0.818722\pi\) | |||||||
\(854\) | 0.253498 | 0.00867453 | ||||||||
\(855\) | −6.26627 | −0.214302 | ||||||||
\(856\) | −18.1159 | −0.619188 | ||||||||
\(857\) | 29.9945 | 1.02459 | 0.512296 | − | 0.858809i | \(-0.328795\pi\) | ||||
0.512296 | + | 0.858809i | \(0.328795\pi\) | |||||||
\(858\) | −45.2785 | −1.54578 | ||||||||
\(859\) | −6.64819 | −0.226833 | −0.113417 | − | 0.993548i | \(-0.536179\pi\) | ||||
−0.113417 | + | 0.993548i | \(0.536179\pi\) | |||||||
\(860\) | 4.43408 | 0.151201 | ||||||||
\(861\) | 5.09113 | 0.173505 | ||||||||
\(862\) | 36.1827 | 1.23239 | ||||||||
\(863\) | −36.5616 | −1.24457 | −0.622285 | − | 0.782791i | \(-0.713796\pi\) | ||||
−0.622285 | + | 0.782791i | \(0.713796\pi\) | |||||||
\(864\) | 4.37247 | 0.148755 | ||||||||
\(865\) | 4.19492 | 0.142631 | ||||||||
\(866\) | 23.3687 | 0.794101 | ||||||||
\(867\) | 17.9713 | 0.610338 | ||||||||
\(868\) | 2.03429 | 0.0690482 | ||||||||
\(869\) | 30.6645 | 1.04022 | ||||||||
\(870\) | −8.00542 | −0.271409 | ||||||||
\(871\) | 25.4015 | 0.860698 | ||||||||
\(872\) | 2.69697 | 0.0913308 | ||||||||
\(873\) | 8.30668 | 0.281138 | ||||||||
\(874\) | −27.4294 | −0.927812 | ||||||||
\(875\) | −3.61885 | −0.122339 | ||||||||
\(876\) | 10.8657 | 0.367119 | ||||||||
\(877\) | −48.8766 | −1.65045 | −0.825223 | − | 0.564806i | \(-0.808951\pi\) | ||||
−0.825223 | + | 0.564806i | \(0.808951\pi\) | |||||||
\(878\) | 23.1787 | 0.782244 | ||||||||
\(879\) | −25.6912 | −0.866542 | ||||||||
\(880\) | −12.6550 | −0.426601 | ||||||||
\(881\) | 45.4991 | 1.53290 | 0.766452 | − | 0.642302i | \(-0.222020\pi\) | ||||
0.766452 | + | 0.642302i | \(0.222020\pi\) | |||||||
\(882\) | −5.04406 | −0.169842 | ||||||||
\(883\) | 42.8472 | 1.44192 | 0.720962 | − | 0.692975i | \(-0.243700\pi\) | ||||
0.720962 | + | 0.692975i | \(0.243700\pi\) | |||||||
\(884\) | −13.1889 | −0.443591 | ||||||||
\(885\) | 49.1348 | 1.65165 | ||||||||
\(886\) | 7.14042 | 0.239887 | ||||||||
\(887\) | −25.6534 | −0.861358 | −0.430679 | − | 0.902505i | \(-0.641726\pi\) | ||||
−0.430679 | + | 0.902505i | \(0.641726\pi\) | |||||||
\(888\) | 7.03625 | 0.236121 | ||||||||
\(889\) | −3.73695 | −0.125333 | ||||||||
\(890\) | −37.4440 | −1.25513 | ||||||||
\(891\) | 52.5904 | 1.76184 | ||||||||
\(892\) | 12.8515 | 0.430299 | ||||||||
\(893\) | −32.0867 | −1.07374 | ||||||||
\(894\) | −3.88770 | −0.130024 | ||||||||
\(895\) | −8.61734 | −0.288046 | ||||||||
\(896\) | 0.413652 | 0.0138191 | ||||||||
\(897\) | 76.2664 | 2.54646 | ||||||||
\(898\) | −33.7316 | −1.12564 | ||||||||
\(899\) | 7.92995 | 0.264479 | ||||||||
\(900\) | 1.17648 | 0.0392159 | ||||||||
\(901\) | −1.68153 | −0.0560200 | ||||||||
\(902\) | 31.3727 | 1.04460 | ||||||||
\(903\) | −1.38121 | −0.0459639 | ||||||||
\(904\) | −14.3092 | −0.475917 | ||||||||
\(905\) | −35.1150 | −1.16726 | ||||||||
\(906\) | 3.59867 | 0.119558 | ||||||||
\(907\) | 22.7668 | 0.755958 | 0.377979 | − | 0.925814i | \(-0.376619\pi\) | ||||
0.377979 | + | 0.925814i | \(0.376619\pi\) | |||||||
\(908\) | 20.7443 | 0.688424 | ||||||||
\(909\) | −3.87780 | −0.128618 | ||||||||
\(910\) | −5.04633 | −0.167284 | ||||||||
\(911\) | −17.7160 | −0.586958 | −0.293479 | − | 0.955965i | \(-0.594813\pi\) | ||||
−0.293479 | + | 0.955965i | \(0.594813\pi\) | |||||||
\(912\) | 6.38855 | 0.211546 | ||||||||
\(913\) | 11.9330 | 0.394926 | ||||||||
\(914\) | 19.5946 | 0.648133 | ||||||||
\(915\) | −3.04250 | −0.100582 | ||||||||
\(916\) | −24.2219 | −0.800313 | ||||||||
\(917\) | −6.87422 | −0.227007 | ||||||||
\(918\) | 12.1375 | 0.400597 | ||||||||
\(919\) | −40.9559 | −1.35101 | −0.675506 | − | 0.737354i | \(-0.736075\pi\) | ||||
−0.675506 | + | 0.737354i | \(0.736075\pi\) | |||||||
\(920\) | 21.3159 | 0.702765 | ||||||||
\(921\) | −47.7121 | −1.57217 | ||||||||
\(922\) | 28.2593 | 0.930672 | ||||||||
\(923\) | 17.4809 | 0.575391 | ||||||||
\(924\) | 3.94203 | 0.129683 | ||||||||
\(925\) | −5.79613 | −0.190575 | ||||||||
\(926\) | 22.6776 | 0.745233 | ||||||||
\(927\) | −1.40559 | −0.0461658 | ||||||||
\(928\) | 1.61248 | 0.0529322 | ||||||||
\(929\) | −30.0806 | −0.986913 | −0.493457 | − | 0.869770i | \(-0.664267\pi\) | ||||
−0.493457 | + | 0.869770i | \(0.664267\pi\) | |||||||
\(930\) | −24.4156 | −0.800619 | ||||||||
\(931\) | 22.5630 | 0.739471 | ||||||||
\(932\) | −17.6446 | −0.577967 | ||||||||
\(933\) | −38.2443 | −1.25206 | ||||||||
\(934\) | −40.1342 | −1.31323 | ||||||||
\(935\) | −35.1289 | −1.14884 | ||||||||
\(936\) | −3.50943 | −0.114709 | ||||||||
\(937\) | 33.8861 | 1.10701 | 0.553505 | − | 0.832846i | \(-0.313290\pi\) | ||||
0.553505 | + | 0.832846i | \(0.313290\pi\) | |||||||
\(938\) | −2.21150 | −0.0722082 | ||||||||
\(939\) | −22.1235 | −0.721974 | ||||||||
\(940\) | 24.9353 | 0.813299 | ||||||||
\(941\) | 19.5372 | 0.636896 | 0.318448 | − | 0.947940i | \(-0.396838\pi\) | ||||
0.318448 | + | 0.947940i | \(0.396838\pi\) | |||||||
\(942\) | 21.9524 | 0.715249 | ||||||||
\(943\) | −52.8436 | −1.72082 | ||||||||
\(944\) | −9.89689 | −0.322116 | ||||||||
\(945\) | 4.64404 | 0.151071 | ||||||||
\(946\) | −8.51134 | −0.276728 | ||||||||
\(947\) | −13.4623 | −0.437467 | −0.218734 | − | 0.975785i | \(-0.570193\pi\) | ||||
−0.218734 | + | 0.975785i | \(0.570193\pi\) | |||||||
\(948\) | 12.0299 | 0.390714 | ||||||||
\(949\) | 26.6999 | 0.866715 | ||||||||
\(950\) | −5.26258 | −0.170741 | ||||||||
\(951\) | 7.86697 | 0.255104 | ||||||||
\(952\) | 1.14825 | 0.0372150 | ||||||||
\(953\) | −43.0656 | −1.39503 | −0.697516 | − | 0.716570i | \(-0.745711\pi\) | ||||
−0.697516 | + | 0.716570i | \(0.745711\pi\) | |||||||
\(954\) | −0.447438 | −0.0144864 | ||||||||
\(955\) | −25.0255 | −0.809807 | ||||||||
\(956\) | −8.87316 | −0.286979 | ||||||||
\(957\) | 15.3666 | 0.496733 | ||||||||
\(958\) | −0.525069 | −0.0169642 | ||||||||
\(959\) | 3.09808 | 0.100042 | ||||||||
\(960\) | −4.96467 | −0.160234 | ||||||||
\(961\) | −6.81455 | −0.219824 | ||||||||
\(962\) | 17.2899 | 0.557447 | ||||||||
\(963\) | −13.3810 | −0.431197 | ||||||||
\(964\) | −4.22672 | −0.136133 | ||||||||
\(965\) | 36.5216 | 1.17567 | ||||||||
\(966\) | −6.63990 | −0.213635 | ||||||||
\(967\) | −23.2361 | −0.747222 | −0.373611 | − | 0.927585i | \(-0.621880\pi\) | ||||
−0.373611 | + | 0.927585i | \(0.621880\pi\) | |||||||
\(968\) | 13.2917 | 0.427211 | ||||||||
\(969\) | 17.7339 | 0.569695 | ||||||||
\(970\) | 28.8756 | 0.927141 | ||||||||
\(971\) | −55.8924 | −1.79367 | −0.896837 | − | 0.442362i | \(-0.854141\pi\) | ||||
−0.896837 | + | 0.442362i | \(0.854141\pi\) | |||||||
\(972\) | 7.51423 | 0.241019 | ||||||||
\(973\) | 0.970607 | 0.0311162 | ||||||||
\(974\) | −25.0558 | −0.802841 | ||||||||
\(975\) | 14.6324 | 0.468613 | ||||||||
\(976\) | 0.612830 | 0.0196162 | ||||||||
\(977\) | −35.2286 | −1.12706 | −0.563531 | − | 0.826095i | \(-0.690558\pi\) | ||||
−0.563531 | + | 0.826095i | \(0.690558\pi\) | |||||||
\(978\) | −42.7744 | −1.36777 | ||||||||
\(979\) | 71.8748 | 2.29713 | ||||||||
\(980\) | −17.5341 | −0.560107 | ||||||||
\(981\) | 1.99207 | 0.0636020 | ||||||||
\(982\) | −17.7648 | −0.566898 | ||||||||
\(983\) | −13.5401 | −0.431864 | −0.215932 | − | 0.976408i | \(-0.569279\pi\) | ||||
−0.215932 | + | 0.976408i | \(0.569279\pi\) | |||||||
\(984\) | 12.3078 | 0.392357 | ||||||||
\(985\) | −36.7723 | −1.17166 | ||||||||
\(986\) | 4.47605 | 0.142547 | ||||||||
\(987\) | −7.76732 | −0.247237 | ||||||||
\(988\) | 15.6983 | 0.499429 | ||||||||
\(989\) | 14.3364 | 0.455870 | ||||||||
\(990\) | −9.34743 | −0.297081 | ||||||||
\(991\) | 6.04736 | 0.192101 | 0.0960503 | − | 0.995376i | \(-0.469379\pi\) | ||||
0.0960503 | + | 0.995376i | \(0.469379\pi\) | |||||||
\(992\) | 4.91787 | 0.156143 | ||||||||
\(993\) | 14.1888 | 0.450267 | ||||||||
\(994\) | −1.52192 | −0.0482723 | ||||||||
\(995\) | 49.5991 | 1.57240 | ||||||||
\(996\) | 4.68144 | 0.148337 | ||||||||
\(997\) | 7.88141 | 0.249607 | 0.124803 | − | 0.992181i | \(-0.460170\pi\) | ||||
0.124803 | + | 0.992181i | \(0.460170\pi\) | |||||||
\(998\) | 3.09140 | 0.0978564 | ||||||||
\(999\) | −15.9115 | −0.503418 |
(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 | 6002.2.a.a.1.11 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.a.1.11 | ✓ | 47 | 1.1 | even | 1 | trivial |