Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.62997 | −1.51841 | −0.759207 | − | 0.650849i | \(-0.774413\pi\) | ||||
−0.759207 | + | 0.650849i | \(0.774413\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.133179 | −0.0595596 | −0.0297798 | − | 0.999556i | \(-0.509481\pi\) | ||||
−0.0297798 | + | 0.999556i | \(0.509481\pi\) | |||||||
\(6\) | −2.62997 | −1.07368 | ||||||||
\(7\) | −2.98290 | −1.12743 | −0.563714 | − | 0.825970i | \(-0.690628\pi\) | ||||
−0.563714 | + | 0.825970i | \(0.690628\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.91674 | 1.30558 | ||||||||
\(10\) | −0.133179 | −0.0421150 | ||||||||
\(11\) | −3.21116 | −0.968203 | −0.484101 | − | 0.875012i | \(-0.660853\pi\) | ||||
−0.484101 | + | 0.875012i | \(0.660853\pi\) | |||||||
\(12\) | −2.62997 | −0.759207 | ||||||||
\(13\) | 6.39878 | 1.77470 | 0.887351 | − | 0.461095i | \(-0.152543\pi\) | ||||
0.887351 | + | 0.461095i | \(0.152543\pi\) | |||||||
\(14\) | −2.98290 | −0.797212 | ||||||||
\(15\) | 0.350258 | 0.0904361 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.30489 | −0.801553 | −0.400776 | − | 0.916176i | \(-0.631260\pi\) | ||||
−0.400776 | + | 0.916176i | \(0.631260\pi\) | |||||||
\(18\) | 3.91674 | 0.923185 | ||||||||
\(19\) | 4.41196 | 1.01217 | 0.506087 | − | 0.862482i | \(-0.331091\pi\) | ||||
0.506087 | + | 0.862482i | \(0.331091\pi\) | |||||||
\(20\) | −0.133179 | −0.0297798 | ||||||||
\(21\) | 7.84493 | 1.71190 | ||||||||
\(22\) | −3.21116 | −0.684623 | ||||||||
\(23\) | −1.70409 | −0.355327 | −0.177663 | − | 0.984091i | \(-0.556854\pi\) | ||||
−0.177663 | + | 0.984091i | \(0.556854\pi\) | |||||||
\(24\) | −2.62997 | −0.536840 | ||||||||
\(25\) | −4.98226 | −0.996453 | ||||||||
\(26\) | 6.39878 | 1.25490 | ||||||||
\(27\) | −2.41100 | −0.463998 | ||||||||
\(28\) | −2.98290 | −0.563714 | ||||||||
\(29\) | −4.05713 | −0.753390 | −0.376695 | − | 0.926337i | \(-0.622939\pi\) | ||||
−0.376695 | + | 0.926337i | \(0.622939\pi\) | |||||||
\(30\) | 0.350258 | 0.0639480 | ||||||||
\(31\) | 9.35394 | 1.68002 | 0.840009 | − | 0.542573i | \(-0.182550\pi\) | ||||
0.840009 | + | 0.542573i | \(0.182550\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.44527 | 1.47013 | ||||||||
\(34\) | −3.30489 | −0.566783 | ||||||||
\(35\) | 0.397260 | 0.0671492 | ||||||||
\(36\) | 3.91674 | 0.652790 | ||||||||
\(37\) | −11.1712 | −1.83653 | −0.918267 | − | 0.395961i | \(-0.870411\pi\) | ||||
−0.918267 | + | 0.395961i | \(0.870411\pi\) | |||||||
\(38\) | 4.41196 | 0.715715 | ||||||||
\(39\) | −16.8286 | −2.69473 | ||||||||
\(40\) | −0.133179 | −0.0210575 | ||||||||
\(41\) | −9.01963 | −1.40863 | −0.704315 | − | 0.709888i | \(-0.748746\pi\) | ||||
−0.704315 | + | 0.709888i | \(0.748746\pi\) | |||||||
\(42\) | 7.84493 | 1.21050 | ||||||||
\(43\) | 7.51380 | 1.14584 | 0.572922 | − | 0.819610i | \(-0.305810\pi\) | ||||
0.572922 | + | 0.819610i | \(0.305810\pi\) | |||||||
\(44\) | −3.21116 | −0.484101 | ||||||||
\(45\) | −0.521629 | −0.0777599 | ||||||||
\(46\) | −1.70409 | −0.251254 | ||||||||
\(47\) | 7.66372 | 1.11787 | 0.558934 | − | 0.829212i | \(-0.311211\pi\) | ||||
0.558934 | + | 0.829212i | \(0.311211\pi\) | |||||||
\(48\) | −2.62997 | −0.379603 | ||||||||
\(49\) | 1.89767 | 0.271095 | ||||||||
\(50\) | −4.98226 | −0.704598 | ||||||||
\(51\) | 8.69175 | 1.21709 | ||||||||
\(52\) | 6.39878 | 0.887351 | ||||||||
\(53\) | −3.41893 | −0.469626 | −0.234813 | − | 0.972041i | \(-0.575448\pi\) | ||||
−0.234813 | + | 0.972041i | \(0.575448\pi\) | |||||||
\(54\) | −2.41100 | −0.328096 | ||||||||
\(55\) | 0.427661 | 0.0576658 | ||||||||
\(56\) | −2.98290 | −0.398606 | ||||||||
\(57\) | −11.6033 | −1.53690 | ||||||||
\(58\) | −4.05713 | −0.532727 | ||||||||
\(59\) | 6.87216 | 0.894679 | 0.447339 | − | 0.894364i | \(-0.352372\pi\) | ||||
0.447339 | + | 0.894364i | \(0.352372\pi\) | |||||||
\(60\) | 0.350258 | 0.0452181 | ||||||||
\(61\) | 12.8840 | 1.64963 | 0.824813 | − | 0.565405i | \(-0.191280\pi\) | ||||
0.824813 | + | 0.565405i | \(0.191280\pi\) | |||||||
\(62\) | 9.35394 | 1.18795 | ||||||||
\(63\) | −11.6832 | −1.47195 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.852185 | −0.105701 | ||||||||
\(66\) | 8.44527 | 1.03954 | ||||||||
\(67\) | 6.96556 | 0.850978 | 0.425489 | − | 0.904964i | \(-0.360102\pi\) | ||||
0.425489 | + | 0.904964i | \(0.360102\pi\) | |||||||
\(68\) | −3.30489 | −0.400776 | ||||||||
\(69\) | 4.48170 | 0.539533 | ||||||||
\(70\) | 0.397260 | 0.0474817 | ||||||||
\(71\) | −3.36425 | −0.399263 | −0.199632 | − | 0.979871i | \(-0.563975\pi\) | ||||
−0.199632 | + | 0.979871i | \(0.563975\pi\) | |||||||
\(72\) | 3.91674 | 0.461592 | ||||||||
\(73\) | 8.97955 | 1.05098 | 0.525488 | − | 0.850801i | \(-0.323883\pi\) | ||||
0.525488 | + | 0.850801i | \(0.323883\pi\) | |||||||
\(74\) | −11.1712 | −1.29863 | ||||||||
\(75\) | 13.1032 | 1.51303 | ||||||||
\(76\) | 4.41196 | 0.506087 | ||||||||
\(77\) | 9.57857 | 1.09158 | ||||||||
\(78\) | −16.8286 | −1.90546 | ||||||||
\(79\) | −6.45762 | −0.726539 | −0.363269 | − | 0.931684i | \(-0.618340\pi\) | ||||
−0.363269 | + | 0.931684i | \(0.618340\pi\) | |||||||
\(80\) | −0.133179 | −0.0148899 | ||||||||
\(81\) | −5.40936 | −0.601040 | ||||||||
\(82\) | −9.01963 | −0.996051 | ||||||||
\(83\) | −2.50616 | −0.275087 | −0.137543 | − | 0.990496i | \(-0.543921\pi\) | ||||
−0.137543 | + | 0.990496i | \(0.543921\pi\) | |||||||
\(84\) | 7.84493 | 0.855952 | ||||||||
\(85\) | 0.440142 | 0.0477402 | ||||||||
\(86\) | 7.51380 | 0.810234 | ||||||||
\(87\) | 10.6701 | 1.14396 | ||||||||
\(88\) | −3.21116 | −0.342311 | ||||||||
\(89\) | 6.26390 | 0.663972 | 0.331986 | − | 0.943284i | \(-0.392281\pi\) | ||||
0.331986 | + | 0.943284i | \(0.392281\pi\) | |||||||
\(90\) | −0.521629 | −0.0549845 | ||||||||
\(91\) | −19.0869 | −2.00085 | ||||||||
\(92\) | −1.70409 | −0.177663 | ||||||||
\(93\) | −24.6006 | −2.55096 | ||||||||
\(94\) | 7.66372 | 0.790452 | ||||||||
\(95\) | −0.587583 | −0.0602847 | ||||||||
\(96\) | −2.62997 | −0.268420 | ||||||||
\(97\) | 4.35742 | 0.442429 | 0.221215 | − | 0.975225i | \(-0.428998\pi\) | ||||
0.221215 | + | 0.975225i | \(0.428998\pi\) | |||||||
\(98\) | 1.89767 | 0.191693 | ||||||||
\(99\) | −12.5773 | −1.26407 | ||||||||
\(100\) | −4.98226 | −0.498226 | ||||||||
\(101\) | −5.87049 | −0.584135 | −0.292068 | − | 0.956398i | \(-0.594343\pi\) | ||||
−0.292068 | + | 0.956398i | \(0.594343\pi\) | |||||||
\(102\) | 8.69175 | 0.860612 | ||||||||
\(103\) | 2.77219 | 0.273152 | 0.136576 | − | 0.990630i | \(-0.456390\pi\) | ||||
0.136576 | + | 0.990630i | \(0.456390\pi\) | |||||||
\(104\) | 6.39878 | 0.627452 | ||||||||
\(105\) | −1.04478 | −0.101960 | ||||||||
\(106\) | −3.41893 | −0.332076 | ||||||||
\(107\) | 4.07490 | 0.393936 | 0.196968 | − | 0.980410i | \(-0.436891\pi\) | ||||
0.196968 | + | 0.980410i | \(0.436891\pi\) | |||||||
\(108\) | −2.41100 | −0.231999 | ||||||||
\(109\) | 12.3408 | 1.18203 | 0.591015 | − | 0.806661i | \(-0.298727\pi\) | ||||
0.591015 | + | 0.806661i | \(0.298727\pi\) | |||||||
\(110\) | 0.427661 | 0.0407759 | ||||||||
\(111\) | 29.3799 | 2.78862 | ||||||||
\(112\) | −2.98290 | −0.281857 | ||||||||
\(113\) | −10.3693 | −0.975458 | −0.487729 | − | 0.872995i | \(-0.662175\pi\) | ||||
−0.487729 | + | 0.872995i | \(0.662175\pi\) | |||||||
\(114\) | −11.6033 | −1.08675 | ||||||||
\(115\) | 0.226949 | 0.0211631 | ||||||||
\(116\) | −4.05713 | −0.376695 | ||||||||
\(117\) | 25.0624 | 2.31702 | ||||||||
\(118\) | 6.87216 | 0.632633 | ||||||||
\(119\) | 9.85813 | 0.903693 | ||||||||
\(120\) | 0.350258 | 0.0319740 | ||||||||
\(121\) | −0.688423 | −0.0625839 | ||||||||
\(122\) | 12.8840 | 1.16646 | ||||||||
\(123\) | 23.7214 | 2.13888 | ||||||||
\(124\) | 9.35394 | 0.840009 | ||||||||
\(125\) | 1.32943 | 0.118908 | ||||||||
\(126\) | −11.6832 | −1.04083 | ||||||||
\(127\) | 4.89366 | 0.434242 | 0.217121 | − | 0.976145i | \(-0.430333\pi\) | ||||
0.217121 | + | 0.976145i | \(0.430333\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −19.7611 | −1.73987 | ||||||||
\(130\) | −0.852185 | −0.0747416 | ||||||||
\(131\) | −15.7955 | −1.38006 | −0.690029 | − | 0.723781i | \(-0.742402\pi\) | ||||
−0.690029 | + | 0.723781i | \(0.742402\pi\) | |||||||
\(132\) | 8.44527 | 0.735066 | ||||||||
\(133\) | −13.1604 | −1.14115 | ||||||||
\(134\) | 6.96556 | 0.601732 | ||||||||
\(135\) | 0.321096 | 0.0276355 | ||||||||
\(136\) | −3.30489 | −0.283392 | ||||||||
\(137\) | −10.6305 | −0.908226 | −0.454113 | − | 0.890944i | \(-0.650044\pi\) | ||||
−0.454113 | + | 0.890944i | \(0.650044\pi\) | |||||||
\(138\) | 4.48170 | 0.381508 | ||||||||
\(139\) | 7.14185 | 0.605764 | 0.302882 | − | 0.953028i | \(-0.402051\pi\) | ||||
0.302882 | + | 0.953028i | \(0.402051\pi\) | |||||||
\(140\) | 0.397260 | 0.0335746 | ||||||||
\(141\) | −20.1553 | −1.69739 | ||||||||
\(142\) | −3.36425 | −0.282322 | ||||||||
\(143\) | −20.5475 | −1.71827 | ||||||||
\(144\) | 3.91674 | 0.326395 | ||||||||
\(145\) | 0.540326 | 0.0448716 | ||||||||
\(146\) | 8.97955 | 0.743153 | ||||||||
\(147\) | −4.99080 | −0.411635 | ||||||||
\(148\) | −11.1712 | −0.918267 | ||||||||
\(149\) | 3.29780 | 0.270166 | 0.135083 | − | 0.990834i | \(-0.456870\pi\) | ||||
0.135083 | + | 0.990834i | \(0.456870\pi\) | |||||||
\(150\) | 13.1032 | 1.06987 | ||||||||
\(151\) | −4.60869 | −0.375050 | −0.187525 | − | 0.982260i | \(-0.560047\pi\) | ||||
−0.187525 | + | 0.982260i | \(0.560047\pi\) | |||||||
\(152\) | 4.41196 | 0.357858 | ||||||||
\(153\) | −12.9444 | −1.04649 | ||||||||
\(154\) | 9.57857 | 0.771863 | ||||||||
\(155\) | −1.24575 | −0.100061 | ||||||||
\(156\) | −16.8286 | −1.34737 | ||||||||
\(157\) | −19.9945 | −1.59573 | −0.797867 | − | 0.602833i | \(-0.794038\pi\) | ||||
−0.797867 | + | 0.602833i | \(0.794038\pi\) | |||||||
\(158\) | −6.45762 | −0.513740 | ||||||||
\(159\) | 8.99168 | 0.713087 | ||||||||
\(160\) | −0.133179 | −0.0105288 | ||||||||
\(161\) | 5.08312 | 0.400606 | ||||||||
\(162\) | −5.40936 | −0.424999 | ||||||||
\(163\) | 8.64548 | 0.677166 | 0.338583 | − | 0.940936i | \(-0.390052\pi\) | ||||
0.338583 | + | 0.940936i | \(0.390052\pi\) | |||||||
\(164\) | −9.01963 | −0.704315 | ||||||||
\(165\) | −1.12473 | −0.0875605 | ||||||||
\(166\) | −2.50616 | −0.194516 | ||||||||
\(167\) | −1.48837 | −0.115173 | −0.0575866 | − | 0.998341i | \(-0.518341\pi\) | ||||
−0.0575866 | + | 0.998341i | \(0.518341\pi\) | |||||||
\(168\) | 7.84493 | 0.605249 | ||||||||
\(169\) | 27.9444 | 2.14957 | ||||||||
\(170\) | 0.440142 | 0.0337574 | ||||||||
\(171\) | 17.2805 | 1.32147 | ||||||||
\(172\) | 7.51380 | 0.572922 | ||||||||
\(173\) | −22.2013 | −1.68793 | −0.843965 | − | 0.536398i | \(-0.819785\pi\) | ||||
−0.843965 | + | 0.536398i | \(0.819785\pi\) | |||||||
\(174\) | 10.6701 | 0.808900 | ||||||||
\(175\) | 14.8616 | 1.12343 | ||||||||
\(176\) | −3.21116 | −0.242051 | ||||||||
\(177\) | −18.0736 | −1.35849 | ||||||||
\(178\) | 6.26390 | 0.469499 | ||||||||
\(179\) | 15.6212 | 1.16758 | 0.583792 | − | 0.811903i | \(-0.301568\pi\) | ||||
0.583792 | + | 0.811903i | \(0.301568\pi\) | |||||||
\(180\) | −0.521629 | −0.0388799 | ||||||||
\(181\) | 20.7058 | 1.53905 | 0.769526 | − | 0.638615i | \(-0.220492\pi\) | ||||
0.769526 | + | 0.638615i | \(0.220492\pi\) | |||||||
\(182\) | −19.0869 | −1.41481 | ||||||||
\(183\) | −33.8845 | −2.50482 | ||||||||
\(184\) | −1.70409 | −0.125627 | ||||||||
\(185\) | 1.48777 | 0.109383 | ||||||||
\(186\) | −24.6006 | −1.80380 | ||||||||
\(187\) | 10.6125 | 0.776065 | ||||||||
\(188\) | 7.66372 | 0.558934 | ||||||||
\(189\) | 7.19177 | 0.523125 | ||||||||
\(190\) | −0.587583 | −0.0426277 | ||||||||
\(191\) | −10.5596 | −0.764067 | −0.382034 | − | 0.924148i | \(-0.624776\pi\) | ||||
−0.382034 | + | 0.924148i | \(0.624776\pi\) | |||||||
\(192\) | −2.62997 | −0.189802 | ||||||||
\(193\) | −24.0218 | −1.72912 | −0.864562 | − | 0.502526i | \(-0.832404\pi\) | ||||
−0.864562 | + | 0.502526i | \(0.832404\pi\) | |||||||
\(194\) | 4.35742 | 0.312845 | ||||||||
\(195\) | 2.24122 | 0.160497 | ||||||||
\(196\) | 1.89767 | 0.135548 | ||||||||
\(197\) | −9.67603 | −0.689388 | −0.344694 | − | 0.938715i | \(-0.612017\pi\) | ||||
−0.344694 | + | 0.938715i | \(0.612017\pi\) | |||||||
\(198\) | −12.5773 | −0.893830 | ||||||||
\(199\) | −19.0908 | −1.35331 | −0.676656 | − | 0.736300i | \(-0.736571\pi\) | ||||
−0.676656 | + | 0.736300i | \(0.736571\pi\) | |||||||
\(200\) | −4.98226 | −0.352299 | ||||||||
\(201\) | −18.3192 | −1.29214 | ||||||||
\(202\) | −5.87049 | −0.413046 | ||||||||
\(203\) | 12.1020 | 0.849393 | ||||||||
\(204\) | 8.69175 | 0.608544 | ||||||||
\(205\) | 1.20123 | 0.0838974 | ||||||||
\(206\) | 2.77219 | 0.193147 | ||||||||
\(207\) | −6.67447 | −0.463908 | ||||||||
\(208\) | 6.39878 | 0.443675 | ||||||||
\(209\) | −14.1675 | −0.979989 | ||||||||
\(210\) | −1.04478 | −0.0720968 | ||||||||
\(211\) | −6.74610 | −0.464421 | −0.232210 | − | 0.972666i | \(-0.574596\pi\) | ||||
−0.232210 | + | 0.972666i | \(0.574596\pi\) | |||||||
\(212\) | −3.41893 | −0.234813 | ||||||||
\(213\) | 8.84788 | 0.606247 | ||||||||
\(214\) | 4.07490 | 0.278555 | ||||||||
\(215\) | −1.00068 | −0.0682460 | ||||||||
\(216\) | −2.41100 | −0.164048 | ||||||||
\(217\) | −27.9018 | −1.89410 | ||||||||
\(218\) | 12.3408 | 0.835821 | ||||||||
\(219\) | −23.6159 | −1.59582 | ||||||||
\(220\) | 0.427661 | 0.0288329 | ||||||||
\(221\) | −21.1472 | −1.42252 | ||||||||
\(222\) | 29.3799 | 1.97185 | ||||||||
\(223\) | −9.99394 | −0.669244 | −0.334622 | − | 0.942352i | \(-0.608609\pi\) | ||||
−0.334622 | + | 0.942352i | \(0.608609\pi\) | |||||||
\(224\) | −2.98290 | −0.199303 | ||||||||
\(225\) | −19.5142 | −1.30095 | ||||||||
\(226\) | −10.3693 | −0.689753 | ||||||||
\(227\) | −26.2775 | −1.74410 | −0.872051 | − | 0.489416i | \(-0.837210\pi\) | ||||
−0.872051 | + | 0.489416i | \(0.837210\pi\) | |||||||
\(228\) | −11.6033 | −0.768450 | ||||||||
\(229\) | −8.88024 | −0.586823 | −0.293412 | − | 0.955986i | \(-0.594791\pi\) | ||||
−0.293412 | + | 0.955986i | \(0.594791\pi\) | |||||||
\(230\) | 0.226949 | 0.0149646 | ||||||||
\(231\) | −25.1913 | −1.65747 | ||||||||
\(232\) | −4.05713 | −0.266363 | ||||||||
\(233\) | −14.2979 | −0.936687 | −0.468343 | − | 0.883547i | \(-0.655149\pi\) | ||||
−0.468343 | + | 0.883547i | \(0.655149\pi\) | |||||||
\(234\) | 25.0624 | 1.63838 | ||||||||
\(235\) | −1.02065 | −0.0665798 | ||||||||
\(236\) | 6.87216 | 0.447339 | ||||||||
\(237\) | 16.9833 | 1.10319 | ||||||||
\(238\) | 9.85813 | 0.639008 | ||||||||
\(239\) | 0.234563 | 0.0151726 | 0.00758631 | − | 0.999971i | \(-0.497585\pi\) | ||||
0.00758631 | + | 0.999971i | \(0.497585\pi\) | |||||||
\(240\) | 0.350258 | 0.0226090 | ||||||||
\(241\) | −18.6942 | −1.20420 | −0.602101 | − | 0.798420i | \(-0.705670\pi\) | ||||
−0.602101 | + | 0.798420i | \(0.705670\pi\) | |||||||
\(242\) | −0.688423 | −0.0442535 | ||||||||
\(243\) | 21.4595 | 1.37663 | ||||||||
\(244\) | 12.8840 | 0.824813 | ||||||||
\(245\) | −0.252730 | −0.0161463 | ||||||||
\(246\) | 23.7214 | 1.51242 | ||||||||
\(247\) | 28.2312 | 1.79631 | ||||||||
\(248\) | 9.35394 | 0.593976 | ||||||||
\(249\) | 6.59112 | 0.417695 | ||||||||
\(250\) | 1.32943 | 0.0840806 | ||||||||
\(251\) | −16.5827 | −1.04669 | −0.523344 | − | 0.852122i | \(-0.675316\pi\) | ||||
−0.523344 | + | 0.852122i | \(0.675316\pi\) | |||||||
\(252\) | −11.6832 | −0.735974 | ||||||||
\(253\) | 5.47211 | 0.344028 | ||||||||
\(254\) | 4.89366 | 0.307056 | ||||||||
\(255\) | −1.15756 | −0.0724893 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.577994 | −0.0360543 | −0.0180271 | − | 0.999837i | \(-0.505739\pi\) | ||||
−0.0180271 | + | 0.999837i | \(0.505739\pi\) | |||||||
\(258\) | −19.7611 | −1.23027 | ||||||||
\(259\) | 33.3225 | 2.07056 | ||||||||
\(260\) | −0.852185 | −0.0528503 | ||||||||
\(261\) | −15.8907 | −0.983611 | ||||||||
\(262\) | −15.7955 | −0.975849 | ||||||||
\(263\) | −9.09976 | −0.561115 | −0.280558 | − | 0.959837i | \(-0.590519\pi\) | ||||
−0.280558 | + | 0.959837i | \(0.590519\pi\) | |||||||
\(264\) | 8.44527 | 0.519770 | ||||||||
\(265\) | 0.455331 | 0.0279707 | ||||||||
\(266\) | −13.1604 | −0.806918 | ||||||||
\(267\) | −16.4739 | −1.00818 | ||||||||
\(268\) | 6.96556 | 0.425489 | ||||||||
\(269\) | 6.92422 | 0.422177 | 0.211089 | − | 0.977467i | \(-0.432299\pi\) | ||||
0.211089 | + | 0.977467i | \(0.432299\pi\) | |||||||
\(270\) | 0.321096 | 0.0195413 | ||||||||
\(271\) | 3.32939 | 0.202246 | 0.101123 | − | 0.994874i | \(-0.467756\pi\) | ||||
0.101123 | + | 0.994874i | \(0.467756\pi\) | |||||||
\(272\) | −3.30489 | −0.200388 | ||||||||
\(273\) | 50.1979 | 3.03812 | ||||||||
\(274\) | −10.6305 | −0.642212 | ||||||||
\(275\) | 15.9989 | 0.964768 | ||||||||
\(276\) | 4.48170 | 0.269767 | ||||||||
\(277\) | 0.190648 | 0.0114549 | 0.00572747 | − | 0.999984i | \(-0.498177\pi\) | ||||
0.00572747 | + | 0.999984i | \(0.498177\pi\) | |||||||
\(278\) | 7.14185 | 0.428340 | ||||||||
\(279\) | 36.6370 | 2.19340 | ||||||||
\(280\) | 0.397260 | 0.0237408 | ||||||||
\(281\) | −8.34937 | −0.498081 | −0.249041 | − | 0.968493i | \(-0.580115\pi\) | ||||
−0.249041 | + | 0.968493i | \(0.580115\pi\) | |||||||
\(282\) | −20.1553 | −1.20023 | ||||||||
\(283\) | −12.0914 | −0.718758 | −0.359379 | − | 0.933192i | \(-0.617011\pi\) | ||||
−0.359379 | + | 0.933192i | \(0.617011\pi\) | |||||||
\(284\) | −3.36425 | −0.199632 | ||||||||
\(285\) | 1.54532 | 0.0915371 | ||||||||
\(286\) | −20.5475 | −1.21500 | ||||||||
\(287\) | 26.9046 | 1.58813 | ||||||||
\(288\) | 3.91674 | 0.230796 | ||||||||
\(289\) | −6.07773 | −0.357514 | ||||||||
\(290\) | 0.540326 | 0.0317290 | ||||||||
\(291\) | −11.4599 | −0.671791 | ||||||||
\(292\) | 8.97955 | 0.525488 | ||||||||
\(293\) | 22.0633 | 1.28895 | 0.644477 | − | 0.764624i | \(-0.277075\pi\) | ||||
0.644477 | + | 0.764624i | \(0.277075\pi\) | |||||||
\(294\) | −4.99080 | −0.291070 | ||||||||
\(295\) | −0.915230 | −0.0532867 | ||||||||
\(296\) | −11.1712 | −0.649313 | ||||||||
\(297\) | 7.74213 | 0.449244 | ||||||||
\(298\) | 3.29780 | 0.191036 | ||||||||
\(299\) | −10.9041 | −0.630599 | ||||||||
\(300\) | 13.1032 | 0.756514 | ||||||||
\(301\) | −22.4129 | −1.29186 | ||||||||
\(302\) | −4.60869 | −0.265200 | ||||||||
\(303\) | 15.4392 | 0.886959 | ||||||||
\(304\) | 4.41196 | 0.253044 | ||||||||
\(305\) | −1.71588 | −0.0982511 | ||||||||
\(306\) | −12.9444 | −0.739981 | ||||||||
\(307\) | 5.65068 | 0.322501 | 0.161251 | − | 0.986913i | \(-0.448447\pi\) | ||||
0.161251 | + | 0.986913i | \(0.448447\pi\) | |||||||
\(308\) | 9.57857 | 0.545790 | ||||||||
\(309\) | −7.29077 | −0.414757 | ||||||||
\(310\) | −1.24575 | −0.0707539 | ||||||||
\(311\) | −17.5752 | −0.996597 | −0.498299 | − | 0.867006i | \(-0.666042\pi\) | ||||
−0.498299 | + | 0.867006i | \(0.666042\pi\) | |||||||
\(312\) | −16.8286 | −0.952732 | ||||||||
\(313\) | −10.6930 | −0.604403 | −0.302201 | − | 0.953244i | \(-0.597722\pi\) | ||||
−0.302201 | + | 0.953244i | \(0.597722\pi\) | |||||||
\(314\) | −19.9945 | −1.12835 | ||||||||
\(315\) | 1.55597 | 0.0876687 | ||||||||
\(316\) | −6.45762 | −0.363269 | ||||||||
\(317\) | 7.51322 | 0.421985 | 0.210992 | − | 0.977488i | \(-0.432331\pi\) | ||||
0.210992 | + | 0.977488i | \(0.432331\pi\) | |||||||
\(318\) | 8.99168 | 0.504228 | ||||||||
\(319\) | 13.0281 | 0.729434 | ||||||||
\(320\) | −0.133179 | −0.00744495 | ||||||||
\(321\) | −10.7169 | −0.598158 | ||||||||
\(322\) | 5.08312 | 0.283271 | ||||||||
\(323\) | −14.5810 | −0.811311 | ||||||||
\(324\) | −5.40936 | −0.300520 | ||||||||
\(325\) | −31.8804 | −1.76841 | ||||||||
\(326\) | 8.64548 | 0.478829 | ||||||||
\(327\) | −32.4558 | −1.79481 | ||||||||
\(328\) | −9.01963 | −0.498026 | ||||||||
\(329\) | −22.8601 | −1.26032 | ||||||||
\(330\) | −1.12473 | −0.0619146 | ||||||||
\(331\) | −1.19105 | −0.0654659 | −0.0327330 | − | 0.999464i | \(-0.510421\pi\) | ||||
−0.0327330 | + | 0.999464i | \(0.510421\pi\) | |||||||
\(332\) | −2.50616 | −0.137543 | ||||||||
\(333\) | −43.7547 | −2.39774 | ||||||||
\(334\) | −1.48837 | −0.0814398 | ||||||||
\(335\) | −0.927668 | −0.0506839 | ||||||||
\(336\) | 7.84493 | 0.427976 | ||||||||
\(337\) | −15.7956 | −0.860441 | −0.430220 | − | 0.902724i | \(-0.641564\pi\) | ||||
−0.430220 | + | 0.902724i | \(0.641564\pi\) | |||||||
\(338\) | 27.9444 | 1.51997 | ||||||||
\(339\) | 27.2709 | 1.48115 | ||||||||
\(340\) | 0.440142 | 0.0238701 | ||||||||
\(341\) | −30.0370 | −1.62660 | ||||||||
\(342\) | 17.2805 | 0.934424 | ||||||||
\(343\) | 15.2197 | 0.821788 | ||||||||
\(344\) | 7.51380 | 0.405117 | ||||||||
\(345\) | −0.596870 | −0.0321344 | ||||||||
\(346\) | −22.2013 | −1.19355 | ||||||||
\(347\) | −29.3425 | −1.57519 | −0.787593 | − | 0.616196i | \(-0.788673\pi\) | ||||
−0.787593 | + | 0.616196i | \(0.788673\pi\) | |||||||
\(348\) | 10.6701 | 0.571979 | ||||||||
\(349\) | −11.1330 | −0.595936 | −0.297968 | − | 0.954576i | \(-0.596309\pi\) | ||||
−0.297968 | + | 0.954576i | \(0.596309\pi\) | |||||||
\(350\) | 14.8616 | 0.794384 | ||||||||
\(351\) | −15.4275 | −0.823458 | ||||||||
\(352\) | −3.21116 | −0.171156 | ||||||||
\(353\) | −11.1144 | −0.591559 | −0.295780 | − | 0.955256i | \(-0.595579\pi\) | ||||
−0.295780 | + | 0.955256i | \(0.595579\pi\) | |||||||
\(354\) | −18.0736 | −0.960599 | ||||||||
\(355\) | 0.448049 | 0.0237800 | ||||||||
\(356\) | 6.26390 | 0.331986 | ||||||||
\(357\) | −25.9266 | −1.37218 | ||||||||
\(358\) | 15.6212 | 0.825606 | ||||||||
\(359\) | 26.5411 | 1.40078 | 0.700392 | − | 0.713758i | \(-0.253009\pi\) | ||||
0.700392 | + | 0.713758i | \(0.253009\pi\) | |||||||
\(360\) | −0.521629 | −0.0274923 | ||||||||
\(361\) | 0.465431 | 0.0244964 | ||||||||
\(362\) | 20.7058 | 1.08827 | ||||||||
\(363\) | 1.81053 | 0.0950283 | ||||||||
\(364\) | −19.0869 | −1.00042 | ||||||||
\(365\) | −1.19589 | −0.0625958 | ||||||||
\(366\) | −33.8845 | −1.77117 | ||||||||
\(367\) | 16.7371 | 0.873668 | 0.436834 | − | 0.899542i | \(-0.356100\pi\) | ||||
0.436834 | + | 0.899542i | \(0.356100\pi\) | |||||||
\(368\) | −1.70409 | −0.0888317 | ||||||||
\(369\) | −35.3276 | −1.83908 | ||||||||
\(370\) | 1.48777 | 0.0773457 | ||||||||
\(371\) | 10.1983 | 0.529470 | ||||||||
\(372\) | −24.6006 | −1.27548 | ||||||||
\(373\) | −20.5677 | −1.06496 | −0.532478 | − | 0.846444i | \(-0.678739\pi\) | ||||
−0.532478 | + | 0.846444i | \(0.678739\pi\) | |||||||
\(374\) | 10.6125 | 0.548761 | ||||||||
\(375\) | −3.49636 | −0.180551 | ||||||||
\(376\) | 7.66372 | 0.395226 | ||||||||
\(377\) | −25.9607 | −1.33704 | ||||||||
\(378\) | 7.19177 | 0.369905 | ||||||||
\(379\) | 6.19803 | 0.318371 | 0.159186 | − | 0.987249i | \(-0.449113\pi\) | ||||
0.159186 | + | 0.987249i | \(0.449113\pi\) | |||||||
\(380\) | −0.587583 | −0.0301423 | ||||||||
\(381\) | −12.8702 | −0.659359 | ||||||||
\(382\) | −10.5596 | −0.540277 | ||||||||
\(383\) | −0.542879 | −0.0277398 | −0.0138699 | − | 0.999904i | \(-0.504415\pi\) | ||||
−0.0138699 | + | 0.999904i | \(0.504415\pi\) | |||||||
\(384\) | −2.62997 | −0.134210 | ||||||||
\(385\) | −1.27567 | −0.0650140 | ||||||||
\(386\) | −24.0218 | −1.22268 | ||||||||
\(387\) | 29.4296 | 1.49599 | ||||||||
\(388\) | 4.35742 | 0.221215 | ||||||||
\(389\) | −21.7112 | −1.10080 | −0.550401 | − | 0.834901i | \(-0.685525\pi\) | ||||
−0.550401 | + | 0.834901i | \(0.685525\pi\) | |||||||
\(390\) | 2.24122 | 0.113489 | ||||||||
\(391\) | 5.63182 | 0.284813 | ||||||||
\(392\) | 1.89767 | 0.0958466 | ||||||||
\(393\) | 41.5417 | 2.09550 | ||||||||
\(394\) | −9.67603 | −0.487471 | ||||||||
\(395\) | 0.860021 | 0.0432724 | ||||||||
\(396\) | −12.5773 | −0.632033 | ||||||||
\(397\) | 32.2232 | 1.61724 | 0.808618 | − | 0.588334i | \(-0.200216\pi\) | ||||
0.808618 | + | 0.588334i | \(0.200216\pi\) | |||||||
\(398\) | −19.0908 | −0.956935 | ||||||||
\(399\) | 34.6115 | 1.73274 | ||||||||
\(400\) | −4.98226 | −0.249113 | ||||||||
\(401\) | 34.0790 | 1.70182 | 0.850912 | − | 0.525308i | \(-0.176050\pi\) | ||||
0.850912 | + | 0.525308i | \(0.176050\pi\) | |||||||
\(402\) | −18.3192 | −0.913679 | ||||||||
\(403\) | 59.8538 | 2.98153 | ||||||||
\(404\) | −5.87049 | −0.292068 | ||||||||
\(405\) | 0.720415 | 0.0357977 | ||||||||
\(406\) | 12.1020 | 0.600612 | ||||||||
\(407\) | 35.8726 | 1.77814 | ||||||||
\(408\) | 8.69175 | 0.430306 | ||||||||
\(409\) | −4.18983 | −0.207174 | −0.103587 | − | 0.994620i | \(-0.533032\pi\) | ||||
−0.103587 | + | 0.994620i | \(0.533032\pi\) | |||||||
\(410\) | 1.20123 | 0.0593244 | ||||||||
\(411\) | 27.9579 | 1.37906 | ||||||||
\(412\) | 2.77219 | 0.136576 | ||||||||
\(413\) | −20.4989 | −1.00869 | ||||||||
\(414\) | −6.67447 | −0.328032 | ||||||||
\(415\) | 0.333768 | 0.0163841 | ||||||||
\(416\) | 6.39878 | 0.313726 | ||||||||
\(417\) | −18.7828 | −0.919800 | ||||||||
\(418\) | −14.1675 | −0.692957 | ||||||||
\(419\) | 17.5670 | 0.858203 | 0.429101 | − | 0.903256i | \(-0.358830\pi\) | ||||
0.429101 | + | 0.903256i | \(0.358830\pi\) | |||||||
\(420\) | −1.04478 | −0.0509801 | ||||||||
\(421\) | −25.4373 | −1.23974 | −0.619869 | − | 0.784705i | \(-0.712814\pi\) | ||||
−0.619869 | + | 0.784705i | \(0.712814\pi\) | |||||||
\(422\) | −6.74610 | −0.328395 | ||||||||
\(423\) | 30.0168 | 1.45947 | ||||||||
\(424\) | −3.41893 | −0.166038 | ||||||||
\(425\) | 16.4658 | 0.798709 | ||||||||
\(426\) | 8.84788 | 0.428681 | ||||||||
\(427\) | −38.4316 | −1.85984 | ||||||||
\(428\) | 4.07490 | 0.196968 | ||||||||
\(429\) | 54.0394 | 2.60905 | ||||||||
\(430\) | −1.00068 | −0.0482572 | ||||||||
\(431\) | −7.70426 | −0.371101 | −0.185551 | − | 0.982635i | \(-0.559407\pi\) | ||||
−0.185551 | + | 0.982635i | \(0.559407\pi\) | |||||||
\(432\) | −2.41100 | −0.115999 | ||||||||
\(433\) | 33.2194 | 1.59642 | 0.798211 | − | 0.602378i | \(-0.205780\pi\) | ||||
0.798211 | + | 0.602378i | \(0.205780\pi\) | |||||||
\(434\) | −27.9018 | −1.33933 | ||||||||
\(435\) | −1.42104 | −0.0681337 | ||||||||
\(436\) | 12.3408 | 0.591015 | ||||||||
\(437\) | −7.51838 | −0.359653 | ||||||||
\(438\) | −23.6159 | −1.12841 | ||||||||
\(439\) | −40.5548 | −1.93558 | −0.967788 | − | 0.251767i | \(-0.918988\pi\) | ||||
−0.967788 | + | 0.251767i | \(0.918988\pi\) | |||||||
\(440\) | 0.427661 | 0.0203879 | ||||||||
\(441\) | 7.43267 | 0.353937 | ||||||||
\(442\) | −21.1472 | −1.00587 | ||||||||
\(443\) | −20.2385 | −0.961558 | −0.480779 | − | 0.876842i | \(-0.659646\pi\) | ||||
−0.480779 | + | 0.876842i | \(0.659646\pi\) | |||||||
\(444\) | 29.3799 | 1.39431 | ||||||||
\(445\) | −0.834221 | −0.0395459 | ||||||||
\(446\) | −9.99394 | −0.473227 | ||||||||
\(447\) | −8.67311 | −0.410224 | ||||||||
\(448\) | −2.98290 | −0.140929 | ||||||||
\(449\) | 7.57351 | 0.357416 | 0.178708 | − | 0.983902i | \(-0.442808\pi\) | ||||
0.178708 | + | 0.983902i | \(0.442808\pi\) | |||||||
\(450\) | −19.5142 | −0.919910 | ||||||||
\(451\) | 28.9635 | 1.36384 | ||||||||
\(452\) | −10.3693 | −0.487729 | ||||||||
\(453\) | 12.1207 | 0.569481 | ||||||||
\(454\) | −26.2775 | −1.23327 | ||||||||
\(455\) | 2.54198 | 0.119170 | ||||||||
\(456\) | −11.6033 | −0.543376 | ||||||||
\(457\) | −0.569802 | −0.0266542 | −0.0133271 | − | 0.999911i | \(-0.504242\pi\) | ||||
−0.0133271 | + | 0.999911i | \(0.504242\pi\) | |||||||
\(458\) | −8.88024 | −0.414947 | ||||||||
\(459\) | 7.96809 | 0.371919 | ||||||||
\(460\) | 0.226949 | 0.0105816 | ||||||||
\(461\) | 3.89924 | 0.181606 | 0.0908028 | − | 0.995869i | \(-0.471057\pi\) | ||||
0.0908028 | + | 0.995869i | \(0.471057\pi\) | |||||||
\(462\) | −25.1913 | −1.17201 | ||||||||
\(463\) | 30.2977 | 1.40806 | 0.704028 | − | 0.710173i | \(-0.251383\pi\) | ||||
0.704028 | + | 0.710173i | \(0.251383\pi\) | |||||||
\(464\) | −4.05713 | −0.188347 | ||||||||
\(465\) | 3.27629 | 0.151934 | ||||||||
\(466\) | −14.2979 | −0.662338 | ||||||||
\(467\) | −18.0191 | −0.833825 | −0.416913 | − | 0.908947i | \(-0.636888\pi\) | ||||
−0.416913 | + | 0.908947i | \(0.636888\pi\) | |||||||
\(468\) | 25.0624 | 1.15851 | ||||||||
\(469\) | −20.7775 | −0.959417 | ||||||||
\(470\) | −1.02065 | −0.0470790 | ||||||||
\(471\) | 52.5849 | 2.42299 | ||||||||
\(472\) | 6.87216 | 0.316317 | ||||||||
\(473\) | −24.1280 | −1.10941 | ||||||||
\(474\) | 16.9833 | 0.780071 | ||||||||
\(475\) | −21.9816 | −1.00858 | ||||||||
\(476\) | 9.85813 | 0.451847 | ||||||||
\(477\) | −13.3911 | −0.613135 | ||||||||
\(478\) | 0.234563 | 0.0107287 | ||||||||
\(479\) | −7.99029 | −0.365086 | −0.182543 | − | 0.983198i | \(-0.558433\pi\) | ||||
−0.182543 | + | 0.983198i | \(0.558433\pi\) | |||||||
\(480\) | 0.350258 | 0.0159870 | ||||||||
\(481\) | −71.4821 | −3.25930 | ||||||||
\(482\) | −18.6942 | −0.851500 | ||||||||
\(483\) | −13.3684 | −0.608285 | ||||||||
\(484\) | −0.688423 | −0.0312920 | ||||||||
\(485\) | −0.580319 | −0.0263509 | ||||||||
\(486\) | 21.4595 | 0.973421 | ||||||||
\(487\) | 21.1513 | 0.958455 | 0.479228 | − | 0.877691i | \(-0.340917\pi\) | ||||
0.479228 | + | 0.877691i | \(0.340917\pi\) | |||||||
\(488\) | 12.8840 | 0.583231 | ||||||||
\(489\) | −22.7374 | −1.02822 | ||||||||
\(490\) | −0.252730 | −0.0114172 | ||||||||
\(491\) | 35.1515 | 1.58637 | 0.793183 | − | 0.608983i | \(-0.208422\pi\) | ||||
0.793183 | + | 0.608983i | \(0.208422\pi\) | |||||||
\(492\) | 23.7214 | 1.06944 | ||||||||
\(493\) | 13.4083 | 0.603881 | ||||||||
\(494\) | 28.2312 | 1.27018 | ||||||||
\(495\) | 1.67504 | 0.0752873 | ||||||||
\(496\) | 9.35394 | 0.420004 | ||||||||
\(497\) | 10.0352 | 0.450141 | ||||||||
\(498\) | 6.59112 | 0.295355 | ||||||||
\(499\) | 11.9801 | 0.536303 | 0.268152 | − | 0.963377i | \(-0.413587\pi\) | ||||
0.268152 | + | 0.963377i | \(0.413587\pi\) | |||||||
\(500\) | 1.32943 | 0.0594540 | ||||||||
\(501\) | 3.91436 | 0.174881 | ||||||||
\(502\) | −16.5827 | −0.740120 | ||||||||
\(503\) | −34.3504 | −1.53161 | −0.765805 | − | 0.643073i | \(-0.777659\pi\) | ||||
−0.765805 | + | 0.643073i | \(0.777659\pi\) | |||||||
\(504\) | −11.6832 | −0.520413 | ||||||||
\(505\) | 0.781828 | 0.0347909 | ||||||||
\(506\) | 5.47211 | 0.243265 | ||||||||
\(507\) | −73.4929 | −3.26393 | ||||||||
\(508\) | 4.89366 | 0.217121 | ||||||||
\(509\) | 5.95234 | 0.263833 | 0.131916 | − | 0.991261i | \(-0.457887\pi\) | ||||
0.131916 | + | 0.991261i | \(0.457887\pi\) | |||||||
\(510\) | −1.15756 | −0.0512577 | ||||||||
\(511\) | −26.7851 | −1.18490 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −10.6373 | −0.469647 | ||||||||
\(514\) | −0.577994 | −0.0254942 | ||||||||
\(515\) | −0.369198 | −0.0162688 | ||||||||
\(516\) | −19.7611 | −0.869933 | ||||||||
\(517\) | −24.6095 | −1.08232 | ||||||||
\(518\) | 33.3225 | 1.46411 | ||||||||
\(519\) | 58.3886 | 2.56298 | ||||||||
\(520\) | −0.852185 | −0.0373708 | ||||||||
\(521\) | −4.23233 | −0.185422 | −0.0927109 | − | 0.995693i | \(-0.529553\pi\) | ||||
−0.0927109 | + | 0.995693i | \(0.529553\pi\) | |||||||
\(522\) | −15.8907 | −0.695518 | ||||||||
\(523\) | 25.0692 | 1.09620 | 0.548100 | − | 0.836413i | \(-0.315351\pi\) | ||||
0.548100 | + | 0.836413i | \(0.315351\pi\) | |||||||
\(524\) | −15.7955 | −0.690029 | ||||||||
\(525\) | −39.0855 | −1.70583 | ||||||||
\(526\) | −9.09976 | −0.396768 | ||||||||
\(527\) | −30.9137 | −1.34662 | ||||||||
\(528\) | 8.44527 | 0.367533 | ||||||||
\(529\) | −20.0961 | −0.873743 | ||||||||
\(530\) | 0.455331 | 0.0197783 | ||||||||
\(531\) | 26.9165 | 1.16808 | ||||||||
\(532\) | −13.1604 | −0.570577 | ||||||||
\(533\) | −57.7146 | −2.49990 | ||||||||
\(534\) | −16.4739 | −0.712894 | ||||||||
\(535\) | −0.542693 | −0.0234627 | ||||||||
\(536\) | 6.96556 | 0.300866 | ||||||||
\(537\) | −41.0833 | −1.77288 | ||||||||
\(538\) | 6.92422 | 0.298524 | ||||||||
\(539\) | −6.09372 | −0.262475 | ||||||||
\(540\) | 0.321096 | 0.0138178 | ||||||||
\(541\) | 44.6416 | 1.91929 | 0.959646 | − | 0.281212i | \(-0.0907364\pi\) | ||||
0.959646 | + | 0.281212i | \(0.0907364\pi\) | |||||||
\(542\) | 3.32939 | 0.143010 | ||||||||
\(543\) | −54.4557 | −2.33692 | ||||||||
\(544\) | −3.30489 | −0.141696 | ||||||||
\(545\) | −1.64353 | −0.0704012 | ||||||||
\(546\) | 50.1979 | 2.14827 | ||||||||
\(547\) | −19.2707 | −0.823957 | −0.411978 | − | 0.911194i | \(-0.635162\pi\) | ||||
−0.411978 | + | 0.911194i | \(0.635162\pi\) | |||||||
\(548\) | −10.6305 | −0.454113 | ||||||||
\(549\) | 50.4633 | 2.15372 | ||||||||
\(550\) | 15.9989 | 0.682194 | ||||||||
\(551\) | −17.8999 | −0.762562 | ||||||||
\(552\) | 4.48170 | 0.190754 | ||||||||
\(553\) | 19.2624 | 0.819120 | ||||||||
\(554\) | 0.190648 | 0.00809986 | ||||||||
\(555\) | −3.91280 | −0.166089 | ||||||||
\(556\) | 7.14185 | 0.302882 | ||||||||
\(557\) | −17.2624 | −0.731430 | −0.365715 | − | 0.930727i | \(-0.619175\pi\) | ||||
−0.365715 | + | 0.930727i | \(0.619175\pi\) | |||||||
\(558\) | 36.6370 | 1.55097 | ||||||||
\(559\) | 48.0791 | 2.03353 | ||||||||
\(560\) | 0.397260 | 0.0167873 | ||||||||
\(561\) | −27.9106 | −1.17839 | ||||||||
\(562\) | −8.34937 | −0.352197 | ||||||||
\(563\) | −3.14065 | −0.132363 | −0.0661813 | − | 0.997808i | \(-0.521082\pi\) | ||||
−0.0661813 | + | 0.997808i | \(0.521082\pi\) | |||||||
\(564\) | −20.1553 | −0.848693 | ||||||||
\(565\) | 1.38097 | 0.0580979 | ||||||||
\(566\) | −12.0914 | −0.508238 | ||||||||
\(567\) | 16.1355 | 0.677629 | ||||||||
\(568\) | −3.36425 | −0.141161 | ||||||||
\(569\) | 10.3020 | 0.431881 | 0.215941 | − | 0.976406i | \(-0.430718\pi\) | ||||
0.215941 | + | 0.976406i | \(0.430718\pi\) | |||||||
\(570\) | 1.54532 | 0.0647265 | ||||||||
\(571\) | −35.0932 | −1.46860 | −0.734301 | − | 0.678824i | \(-0.762490\pi\) | ||||
−0.734301 | + | 0.678824i | \(0.762490\pi\) | |||||||
\(572\) | −20.5475 | −0.859135 | ||||||||
\(573\) | 27.7715 | 1.16017 | ||||||||
\(574\) | 26.9046 | 1.12298 | ||||||||
\(575\) | 8.49022 | 0.354066 | ||||||||
\(576\) | 3.91674 | 0.163198 | ||||||||
\(577\) | 15.4046 | 0.641303 | 0.320651 | − | 0.947197i | \(-0.396098\pi\) | ||||
0.320651 | + | 0.947197i | \(0.396098\pi\) | |||||||
\(578\) | −6.07773 | −0.252800 | ||||||||
\(579\) | 63.1765 | 2.62553 | ||||||||
\(580\) | 0.540326 | 0.0224358 | ||||||||
\(581\) | 7.47561 | 0.310140 | ||||||||
\(582\) | −11.4599 | −0.475028 | ||||||||
\(583\) | 10.9787 | 0.454693 | ||||||||
\(584\) | 8.97955 | 0.371576 | ||||||||
\(585\) | −3.33779 | −0.138001 | ||||||||
\(586\) | 22.0633 | 0.911428 | ||||||||
\(587\) | −45.9000 | −1.89450 | −0.947248 | − | 0.320502i | \(-0.896148\pi\) | ||||
−0.947248 | + | 0.320502i | \(0.896148\pi\) | |||||||
\(588\) | −4.99080 | −0.205817 | ||||||||
\(589\) | 41.2693 | 1.70047 | ||||||||
\(590\) | −0.915230 | −0.0376794 | ||||||||
\(591\) | 25.4477 | 1.04678 | ||||||||
\(592\) | −11.1712 | −0.459134 | ||||||||
\(593\) | 3.55411 | 0.145950 | 0.0729749 | − | 0.997334i | \(-0.476751\pi\) | ||||
0.0729749 | + | 0.997334i | \(0.476751\pi\) | |||||||
\(594\) | 7.74213 | 0.317663 | ||||||||
\(595\) | −1.31290 | −0.0538236 | ||||||||
\(596\) | 3.29780 | 0.135083 | ||||||||
\(597\) | 50.2082 | 2.05489 | ||||||||
\(598\) | −10.9041 | −0.445901 | ||||||||
\(599\) | −47.5119 | −1.94128 | −0.970642 | − | 0.240529i | \(-0.922679\pi\) | ||||
−0.970642 | + | 0.240529i | \(0.922679\pi\) | |||||||
\(600\) | 13.1032 | 0.534936 | ||||||||
\(601\) | −42.2330 | −1.72272 | −0.861360 | − | 0.507995i | \(-0.830387\pi\) | ||||
−0.861360 | + | 0.507995i | \(0.830387\pi\) | |||||||
\(602\) | −22.4129 | −0.913481 | ||||||||
\(603\) | 27.2823 | 1.11102 | ||||||||
\(604\) | −4.60869 | −0.187525 | ||||||||
\(605\) | 0.0916837 | 0.00372747 | ||||||||
\(606\) | 15.4392 | 0.627175 | ||||||||
\(607\) | −43.1107 | −1.74981 | −0.874904 | − | 0.484296i | \(-0.839076\pi\) | ||||
−0.874904 | + | 0.484296i | \(0.839076\pi\) | |||||||
\(608\) | 4.41196 | 0.178929 | ||||||||
\(609\) | −31.8279 | −1.28973 | ||||||||
\(610\) | −1.71588 | −0.0694740 | ||||||||
\(611\) | 49.0384 | 1.98388 | ||||||||
\(612\) | −12.9444 | −0.523246 | ||||||||
\(613\) | −20.2861 | −0.819348 | −0.409674 | − | 0.912232i | \(-0.634358\pi\) | ||||
−0.409674 | + | 0.912232i | \(0.634358\pi\) | |||||||
\(614\) | 5.65068 | 0.228043 | ||||||||
\(615\) | −3.15919 | −0.127391 | ||||||||
\(616\) | 9.57857 | 0.385932 | ||||||||
\(617\) | 22.0173 | 0.886384 | 0.443192 | − | 0.896427i | \(-0.353846\pi\) | ||||
0.443192 | + | 0.896427i | \(0.353846\pi\) | |||||||
\(618\) | −7.29077 | −0.293278 | ||||||||
\(619\) | 26.6371 | 1.07063 | 0.535317 | − | 0.844651i | \(-0.320192\pi\) | ||||
0.535317 | + | 0.844651i | \(0.320192\pi\) | |||||||
\(620\) | −1.24575 | −0.0500306 | ||||||||
\(621\) | 4.10856 | 0.164871 | ||||||||
\(622\) | −17.5752 | −0.704701 | ||||||||
\(623\) | −18.6845 | −0.748581 | ||||||||
\(624\) | −16.8286 | −0.673683 | ||||||||
\(625\) | 24.7343 | 0.989371 | ||||||||
\(626\) | −10.6930 | −0.427377 | ||||||||
\(627\) | 37.2602 | 1.48803 | ||||||||
\(628\) | −19.9945 | −0.797867 | ||||||||
\(629\) | 36.9196 | 1.47208 | ||||||||
\(630\) | 1.55597 | 0.0619911 | ||||||||
\(631\) | −23.0720 | −0.918482 | −0.459241 | − | 0.888312i | \(-0.651879\pi\) | ||||
−0.459241 | + | 0.888312i | \(0.651879\pi\) | |||||||
\(632\) | −6.45762 | −0.256870 | ||||||||
\(633\) | 17.7421 | 0.705183 | ||||||||
\(634\) | 7.51322 | 0.298388 | ||||||||
\(635\) | −0.651734 | −0.0258633 | ||||||||
\(636\) | 8.99168 | 0.356543 | ||||||||
\(637\) | 12.1427 | 0.481113 | ||||||||
\(638\) | 13.0281 | 0.515788 | ||||||||
\(639\) | −13.1769 | −0.521270 | ||||||||
\(640\) | −0.133179 | −0.00526438 | ||||||||
\(641\) | −4.86034 | −0.191972 | −0.0959860 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959860 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(642\) | −10.7169 | −0.422961 | ||||||||
\(643\) | −29.0047 | −1.14384 | −0.571918 | − | 0.820311i | \(-0.693800\pi\) | ||||
−0.571918 | + | 0.820311i | \(0.693800\pi\) | |||||||
\(644\) | 5.08312 | 0.200303 | ||||||||
\(645\) | 2.63177 | 0.103626 | ||||||||
\(646\) | −14.5810 | −0.573683 | ||||||||
\(647\) | −43.7061 | −1.71826 | −0.859132 | − | 0.511754i | \(-0.828996\pi\) | ||||
−0.859132 | + | 0.511754i | \(0.828996\pi\) | |||||||
\(648\) | −5.40936 | −0.212500 | ||||||||
\(649\) | −22.0676 | −0.866230 | ||||||||
\(650\) | −31.8804 | −1.25045 | ||||||||
\(651\) | 73.3810 | 2.87603 | ||||||||
\(652\) | 8.64548 | 0.338583 | ||||||||
\(653\) | −23.7803 | −0.930593 | −0.465297 | − | 0.885155i | \(-0.654052\pi\) | ||||
−0.465297 | + | 0.885155i | \(0.654052\pi\) | |||||||
\(654\) | −32.4558 | −1.26912 | ||||||||
\(655\) | 2.10363 | 0.0821958 | ||||||||
\(656\) | −9.01963 | −0.352157 | ||||||||
\(657\) | 35.1706 | 1.37213 | ||||||||
\(658\) | −22.8601 | −0.891178 | ||||||||
\(659\) | 29.1985 | 1.13741 | 0.568705 | − | 0.822541i | \(-0.307444\pi\) | ||||
0.568705 | + | 0.822541i | \(0.307444\pi\) | |||||||
\(660\) | −1.12473 | −0.0437802 | ||||||||
\(661\) | −32.6219 | −1.26884 | −0.634422 | − | 0.772987i | \(-0.718762\pi\) | ||||
−0.634422 | + | 0.772987i | \(0.718762\pi\) | |||||||
\(662\) | −1.19105 | −0.0462914 | ||||||||
\(663\) | 55.6166 | 2.15997 | ||||||||
\(664\) | −2.50616 | −0.0972578 | ||||||||
\(665\) | 1.75270 | 0.0679667 | ||||||||
\(666\) | −43.7547 | −1.69546 | ||||||||
\(667\) | 6.91370 | 0.267700 | ||||||||
\(668\) | −1.48837 | −0.0575866 | ||||||||
\(669\) | 26.2838 | 1.01619 | ||||||||
\(670\) | −0.927668 | −0.0358389 | ||||||||
\(671\) | −41.3726 | −1.59717 | ||||||||
\(672\) | 7.84493 | 0.302625 | ||||||||
\(673\) | −37.4977 | −1.44543 | −0.722715 | − | 0.691146i | \(-0.757106\pi\) | ||||
−0.722715 | + | 0.691146i | \(0.757106\pi\) | |||||||
\(674\) | −15.7956 | −0.608423 | ||||||||
\(675\) | 12.0123 | 0.462352 | ||||||||
\(676\) | 27.9444 | 1.07478 | ||||||||
\(677\) | −22.8796 | −0.879333 | −0.439667 | − | 0.898161i | \(-0.644903\pi\) | ||||
−0.439667 | + | 0.898161i | \(0.644903\pi\) | |||||||
\(678\) | 27.2709 | 1.04733 | ||||||||
\(679\) | −12.9977 | −0.498807 | ||||||||
\(680\) | 0.440142 | 0.0168787 | ||||||||
\(681\) | 69.1091 | 2.64827 | ||||||||
\(682\) | −30.0370 | −1.15018 | ||||||||
\(683\) | 2.77870 | 0.106324 | 0.0531621 | − | 0.998586i | \(-0.483070\pi\) | ||||
0.0531621 | + | 0.998586i | \(0.483070\pi\) | |||||||
\(684\) | 17.2805 | 0.660737 | ||||||||
\(685\) | 1.41576 | 0.0540936 | ||||||||
\(686\) | 15.2197 | 0.581092 | ||||||||
\(687\) | 23.3548 | 0.891040 | ||||||||
\(688\) | 7.51380 | 0.286461 | ||||||||
\(689\) | −21.8770 | −0.833446 | ||||||||
\(690\) | −0.596870 | −0.0227224 | ||||||||
\(691\) | −7.68775 | −0.292456 | −0.146228 | − | 0.989251i | \(-0.546713\pi\) | ||||
−0.146228 | + | 0.989251i | \(0.546713\pi\) | |||||||
\(692\) | −22.2013 | −0.843965 | ||||||||
\(693\) | 37.5168 | 1.42514 | ||||||||
\(694\) | −29.3425 | −1.11382 | ||||||||
\(695\) | −0.951147 | −0.0360791 | ||||||||
\(696\) | 10.6701 | 0.404450 | ||||||||
\(697\) | 29.8088 | 1.12909 | ||||||||
\(698\) | −11.1330 | −0.421391 | ||||||||
\(699\) | 37.6031 | 1.42228 | ||||||||
\(700\) | 14.8616 | 0.561715 | ||||||||
\(701\) | −29.7679 | −1.12432 | −0.562159 | − | 0.827029i | \(-0.690029\pi\) | ||||
−0.562159 | + | 0.827029i | \(0.690029\pi\) | |||||||
\(702\) | −15.4275 | −0.582273 | ||||||||
\(703\) | −49.2870 | −1.85889 | ||||||||
\(704\) | −3.21116 | −0.121025 | ||||||||
\(705\) | 2.68428 | 0.101096 | ||||||||
\(706\) | −11.1144 | −0.418296 | ||||||||
\(707\) | 17.5111 | 0.658571 | ||||||||
\(708\) | −18.0736 | −0.679246 | ||||||||
\(709\) | 3.74967 | 0.140822 | 0.0704109 | − | 0.997518i | \(-0.477569\pi\) | ||||
0.0704109 | + | 0.997518i | \(0.477569\pi\) | |||||||
\(710\) | 0.448049 | 0.0168150 | ||||||||
\(711\) | −25.2928 | −0.948555 | ||||||||
\(712\) | 6.26390 | 0.234749 | ||||||||
\(713\) | −15.9399 | −0.596955 | ||||||||
\(714\) | −25.9266 | −0.970278 | ||||||||
\(715\) | 2.73651 | 0.102340 | ||||||||
\(716\) | 15.6212 | 0.583792 | ||||||||
\(717\) | −0.616894 | −0.0230383 | ||||||||
\(718\) | 26.5411 | 0.990504 | ||||||||
\(719\) | 38.2410 | 1.42615 | 0.713074 | − | 0.701089i | \(-0.247302\pi\) | ||||
0.713074 | + | 0.701089i | \(0.247302\pi\) | |||||||
\(720\) | −0.521629 | −0.0194400 | ||||||||
\(721\) | −8.26915 | −0.307959 | ||||||||
\(722\) | 0.465431 | 0.0173216 | ||||||||
\(723\) | 49.1653 | 1.82848 | ||||||||
\(724\) | 20.7058 | 0.769526 | ||||||||
\(725\) | 20.2137 | 0.750717 | ||||||||
\(726\) | 1.81053 | 0.0671951 | ||||||||
\(727\) | 21.0432 | 0.780450 | 0.390225 | − | 0.920720i | \(-0.372397\pi\) | ||||
0.390225 | + | 0.920720i | \(0.372397\pi\) | |||||||
\(728\) | −19.0869 | −0.707407 | ||||||||
\(729\) | −40.2097 | −1.48925 | ||||||||
\(730\) | −1.19589 | −0.0442619 | ||||||||
\(731\) | −24.8323 | −0.918454 | ||||||||
\(732\) | −33.8845 | −1.25241 | ||||||||
\(733\) | 51.3367 | 1.89616 | 0.948082 | − | 0.318025i | \(-0.103020\pi\) | ||||
0.948082 | + | 0.318025i | \(0.103020\pi\) | |||||||
\(734\) | 16.7371 | 0.617777 | ||||||||
\(735\) | 0.664672 | 0.0245168 | ||||||||
\(736\) | −1.70409 | −0.0628135 | ||||||||
\(737\) | −22.3675 | −0.823919 | ||||||||
\(738\) | −35.3276 | −1.30043 | ||||||||
\(739\) | −41.4344 | −1.52419 | −0.762094 | − | 0.647467i | \(-0.775829\pi\) | ||||
−0.762094 | + | 0.647467i | \(0.775829\pi\) | |||||||
\(740\) | 1.48777 | 0.0546916 | ||||||||
\(741\) | −74.2472 | −2.72754 | ||||||||
\(742\) | 10.1983 | 0.374392 | ||||||||
\(743\) | −4.65789 | −0.170881 | −0.0854406 | − | 0.996343i | \(-0.527230\pi\) | ||||
−0.0854406 | + | 0.996343i | \(0.527230\pi\) | |||||||
\(744\) | −24.6006 | −0.901901 | ||||||||
\(745\) | −0.439198 | −0.0160910 | ||||||||
\(746\) | −20.5677 | −0.753038 | ||||||||
\(747\) | −9.81598 | −0.359148 | ||||||||
\(748\) | 10.6125 | 0.388033 | ||||||||
\(749\) | −12.1550 | −0.444134 | ||||||||
\(750\) | −3.49636 | −0.127669 | ||||||||
\(751\) | 44.7500 | 1.63295 | 0.816476 | − | 0.577380i | \(-0.195925\pi\) | ||||
0.816476 | + | 0.577380i | \(0.195925\pi\) | |||||||
\(752\) | 7.66372 | 0.279467 | ||||||||
\(753\) | 43.6119 | 1.58931 | ||||||||
\(754\) | −25.9607 | −0.945432 | ||||||||
\(755\) | 0.613783 | 0.0223378 | ||||||||
\(756\) | 7.19177 | 0.261562 | ||||||||
\(757\) | −18.1450 | −0.659490 | −0.329745 | − | 0.944070i | \(-0.606963\pi\) | ||||
−0.329745 | + | 0.944070i | \(0.606963\pi\) | |||||||
\(758\) | 6.19803 | 0.225122 | ||||||||
\(759\) | −14.3915 | −0.522378 | ||||||||
\(760\) | −0.587583 | −0.0213139 | ||||||||
\(761\) | 3.29321 | 0.119379 | 0.0596894 | − | 0.998217i | \(-0.480989\pi\) | ||||
0.0596894 | + | 0.998217i | \(0.480989\pi\) | |||||||
\(762\) | −12.8702 | −0.466237 | ||||||||
\(763\) | −36.8112 | −1.33265 | ||||||||
\(764\) | −10.5596 | −0.382034 | ||||||||
\(765\) | 1.72392 | 0.0623286 | ||||||||
\(766\) | −0.542879 | −0.0196150 | ||||||||
\(767\) | 43.9734 | 1.58779 | ||||||||
\(768\) | −2.62997 | −0.0949009 | ||||||||
\(769\) | 31.6709 | 1.14208 | 0.571042 | − | 0.820921i | \(-0.306540\pi\) | ||||
0.571042 | + | 0.820921i | \(0.306540\pi\) | |||||||
\(770\) | −1.27567 | −0.0459719 | ||||||||
\(771\) | 1.52011 | 0.0547453 | ||||||||
\(772\) | −24.0218 | −0.864562 | ||||||||
\(773\) | 25.2491 | 0.908147 | 0.454074 | − | 0.890964i | \(-0.349970\pi\) | ||||
0.454074 | + | 0.890964i | \(0.349970\pi\) | |||||||
\(774\) | 29.4296 | 1.05783 | ||||||||
\(775\) | −46.6038 | −1.67406 | ||||||||
\(776\) | 4.35742 | 0.156422 | ||||||||
\(777\) | −87.6373 | −3.14397 | ||||||||
\(778\) | −21.7112 | −0.778384 | ||||||||
\(779\) | −39.7943 | −1.42578 | ||||||||
\(780\) | 2.24122 | 0.0802486 | ||||||||
\(781\) | 10.8032 | 0.386567 | ||||||||
\(782\) | 5.63182 | 0.201393 | ||||||||
\(783\) | 9.78175 | 0.349571 | ||||||||
\(784\) | 1.89767 | 0.0677738 | ||||||||
\(785\) | 2.66285 | 0.0950413 | ||||||||
\(786\) | 41.5417 | 1.48174 | ||||||||
\(787\) | 19.7923 | 0.705521 | 0.352760 | − | 0.935714i | \(-0.385243\pi\) | ||||
0.352760 | + | 0.935714i | \(0.385243\pi\) | |||||||
\(788\) | −9.67603 | −0.344694 | ||||||||
\(789\) | 23.9321 | 0.852005 | ||||||||
\(790\) | 0.860021 | 0.0305982 | ||||||||
\(791\) | 30.9304 | 1.09976 | ||||||||
\(792\) | −12.5773 | −0.446915 | ||||||||
\(793\) | 82.4418 | 2.92760 | ||||||||
\(794\) | 32.2232 | 1.14356 | ||||||||
\(795\) | −1.19751 | −0.0424712 | ||||||||
\(796\) | −19.0908 | −0.676656 | ||||||||
\(797\) | 15.6704 | 0.555075 | 0.277538 | − | 0.960715i | \(-0.410482\pi\) | ||||
0.277538 | + | 0.960715i | \(0.410482\pi\) | |||||||
\(798\) | 34.6115 | 1.22524 | ||||||||
\(799\) | −25.3277 | −0.896030 | ||||||||
\(800\) | −4.98226 | −0.176150 | ||||||||
\(801\) | 24.5341 | 0.866869 | ||||||||
\(802\) | 34.0790 | 1.20337 | ||||||||
\(803\) | −28.8348 | −1.01756 | ||||||||
\(804\) | −18.3192 | −0.646069 | ||||||||
\(805\) | −0.676966 | −0.0238599 | ||||||||
\(806\) | 59.8538 | 2.10826 | ||||||||
\(807\) | −18.2105 | −0.641039 | ||||||||
\(808\) | −5.87049 | −0.206523 | ||||||||
\(809\) | 33.4793 | 1.17707 | 0.588534 | − | 0.808472i | \(-0.299705\pi\) | ||||
0.588534 | + | 0.808472i | \(0.299705\pi\) | |||||||
\(810\) | 0.720415 | 0.0253128 | ||||||||
\(811\) | 30.9366 | 1.08633 | 0.543166 | − | 0.839626i | \(-0.317226\pi\) | ||||
0.543166 | + | 0.839626i | \(0.317226\pi\) | |||||||
\(812\) | 12.1020 | 0.424697 | ||||||||
\(813\) | −8.75620 | −0.307093 | ||||||||
\(814\) | 35.8726 | 1.25733 | ||||||||
\(815\) | −1.15140 | −0.0403318 | ||||||||
\(816\) | 8.69175 | 0.304272 | ||||||||
\(817\) | 33.1506 | 1.15979 | ||||||||
\(818\) | −4.18983 | −0.146494 | ||||||||
\(819\) | −74.7584 | −2.61227 | ||||||||
\(820\) | 1.20123 | 0.0419487 | ||||||||
\(821\) | −6.18660 | −0.215914 | −0.107957 | − | 0.994156i | \(-0.534431\pi\) | ||||
−0.107957 | + | 0.994156i | \(0.534431\pi\) | |||||||
\(822\) | 27.9579 | 0.975144 | ||||||||
\(823\) | −12.3996 | −0.432224 | −0.216112 | − | 0.976369i | \(-0.569338\pi\) | ||||
−0.216112 | + | 0.976369i | \(0.569338\pi\) | |||||||
\(824\) | 2.77219 | 0.0965737 | ||||||||
\(825\) | −42.0765 | −1.46492 | ||||||||
\(826\) | −20.4989 | −0.713249 | ||||||||
\(827\) | 34.1205 | 1.18649 | 0.593243 | − | 0.805023i | \(-0.297847\pi\) | ||||
0.593243 | + | 0.805023i | \(0.297847\pi\) | |||||||
\(828\) | −6.67447 | −0.231954 | ||||||||
\(829\) | −11.9221 | −0.414070 | −0.207035 | − | 0.978334i | \(-0.566381\pi\) | ||||
−0.207035 | + | 0.978334i | \(0.566381\pi\) | |||||||
\(830\) | 0.333768 | 0.0115853 | ||||||||
\(831\) | −0.501399 | −0.0173933 | ||||||||
\(832\) | 6.39878 | 0.221838 | ||||||||
\(833\) | −6.27157 | −0.217297 | ||||||||
\(834\) | −18.7828 | −0.650397 | ||||||||
\(835\) | 0.198220 | 0.00685967 | ||||||||
\(836\) | −14.1675 | −0.489995 | ||||||||
\(837\) | −22.5524 | −0.779525 | ||||||||
\(838\) | 17.5670 | 0.606841 | ||||||||
\(839\) | 31.2257 | 1.07803 | 0.539016 | − | 0.842296i | \(-0.318796\pi\) | ||||
0.539016 | + | 0.842296i | \(0.318796\pi\) | |||||||
\(840\) | −1.04478 | −0.0360484 | ||||||||
\(841\) | −12.5397 | −0.432404 | ||||||||
\(842\) | −25.4373 | −0.876628 | ||||||||
\(843\) | 21.9586 | 0.756294 | ||||||||
\(844\) | −6.74610 | −0.232210 | ||||||||
\(845\) | −3.72161 | −0.128027 | ||||||||
\(846\) | 30.0168 | 1.03200 | ||||||||
\(847\) | 2.05349 | 0.0705589 | ||||||||
\(848\) | −3.41893 | −0.117407 | ||||||||
\(849\) | 31.7999 | 1.09137 | ||||||||
\(850\) | 16.4658 | 0.564773 | ||||||||
\(851\) | 19.0367 | 0.652570 | ||||||||
\(852\) | 8.84788 | 0.303123 | ||||||||
\(853\) | −31.4513 | −1.07687 | −0.538437 | − | 0.842666i | \(-0.680985\pi\) | ||||
−0.538437 | + | 0.842666i | \(0.680985\pi\) | |||||||
\(854\) | −38.4316 | −1.31510 | ||||||||
\(855\) | −2.30141 | −0.0787065 | ||||||||
\(856\) | 4.07490 | 0.139277 | ||||||||
\(857\) | 42.9199 | 1.46612 | 0.733059 | − | 0.680165i | \(-0.238092\pi\) | ||||
0.733059 | + | 0.680165i | \(0.238092\pi\) | |||||||
\(858\) | 54.0394 | 1.84487 | ||||||||
\(859\) | −35.7822 | −1.22087 | −0.610437 | − | 0.792065i | \(-0.709006\pi\) | ||||
−0.610437 | + | 0.792065i | \(0.709006\pi\) | |||||||
\(860\) | −1.00068 | −0.0341230 | ||||||||
\(861\) | −70.7583 | −2.41144 | ||||||||
\(862\) | −7.70426 | −0.262408 | ||||||||
\(863\) | −10.4621 | −0.356136 | −0.178068 | − | 0.984018i | \(-0.556985\pi\) | ||||
−0.178068 | + | 0.984018i | \(0.556985\pi\) | |||||||
\(864\) | −2.41100 | −0.0820240 | ||||||||
\(865\) | 2.95675 | 0.100532 | ||||||||
\(866\) | 33.2194 | 1.12884 | ||||||||
\(867\) | 15.9842 | 0.542853 | ||||||||
\(868\) | −27.9018 | −0.947050 | ||||||||
\(869\) | 20.7365 | 0.703437 | ||||||||
\(870\) | −1.42104 | −0.0481778 | ||||||||
\(871\) | 44.5711 | 1.51023 | ||||||||
\(872\) | 12.3408 | 0.417911 | ||||||||
\(873\) | 17.0669 | 0.577627 | ||||||||
\(874\) | −7.51838 | −0.254313 | ||||||||
\(875\) | −3.96555 | −0.134060 | ||||||||
\(876\) | −23.6159 | −0.797909 | ||||||||
\(877\) | −36.6331 | −1.23701 | −0.618506 | − | 0.785780i | \(-0.712262\pi\) | ||||
−0.618506 | + | 0.785780i | \(0.712262\pi\) | |||||||
\(878\) | −40.5548 | −1.36866 | ||||||||
\(879\) | −58.0259 | −1.95717 | ||||||||
\(880\) | 0.427661 | 0.0144164 | ||||||||
\(881\) | −6.11592 | −0.206050 | −0.103025 | − | 0.994679i | \(-0.532852\pi\) | ||||
−0.103025 | + | 0.994679i | \(0.532852\pi\) | |||||||
\(882\) | 7.43267 | 0.250271 | ||||||||
\(883\) | −12.4748 | −0.419812 | −0.209906 | − | 0.977722i | \(-0.567316\pi\) | ||||
−0.209906 | + | 0.977722i | \(0.567316\pi\) | |||||||
\(884\) | −21.1472 | −0.711258 | ||||||||
\(885\) | 2.40703 | 0.0809113 | ||||||||
\(886\) | −20.2385 | −0.679924 | ||||||||
\(887\) | −2.96844 | −0.0996705 | −0.0498353 | − | 0.998757i | \(-0.515870\pi\) | ||||
−0.0498353 | + | 0.998757i | \(0.515870\pi\) | |||||||
\(888\) | 29.3799 | 0.985926 | ||||||||
\(889\) | −14.5973 | −0.489577 | ||||||||
\(890\) | −0.834221 | −0.0279632 | ||||||||
\(891\) | 17.3703 | 0.581928 | ||||||||
\(892\) | −9.99394 | −0.334622 | ||||||||
\(893\) | 33.8120 | 1.13148 | ||||||||
\(894\) | −8.67311 | −0.290072 | ||||||||
\(895\) | −2.08042 | −0.0695408 | ||||||||
\(896\) | −2.98290 | −0.0996515 | ||||||||
\(897\) | 28.6774 | 0.957511 | ||||||||
\(898\) | 7.57351 | 0.252731 | ||||||||
\(899\) | −37.9501 | −1.26571 | ||||||||
\(900\) | −19.5142 | −0.650475 | ||||||||
\(901\) | 11.2992 | 0.376430 | ||||||||
\(902\) | 28.9635 | 0.964379 | ||||||||
\(903\) | 58.9452 | 1.96157 | ||||||||
\(904\) | −10.3693 | −0.344877 | ||||||||
\(905\) | −2.75759 | −0.0916654 | ||||||||
\(906\) | 12.1207 | 0.402684 | ||||||||
\(907\) | −31.0898 | −1.03232 | −0.516160 | − | 0.856492i | \(-0.672639\pi\) | ||||
−0.516160 | + | 0.856492i | \(0.672639\pi\) | |||||||
\(908\) | −26.2775 | −0.872051 | ||||||||
\(909\) | −22.9932 | −0.762636 | ||||||||
\(910\) | 2.54198 | 0.0842658 | ||||||||
\(911\) | 40.8917 | 1.35480 | 0.677401 | − | 0.735614i | \(-0.263106\pi\) | ||||
0.677401 | + | 0.735614i | \(0.263106\pi\) | |||||||
\(912\) | −11.6033 | −0.384225 | ||||||||
\(913\) | 8.04769 | 0.266340 | ||||||||
\(914\) | −0.569802 | −0.0188474 | ||||||||
\(915\) | 4.51272 | 0.149186 | ||||||||
\(916\) | −8.88024 | −0.293412 | ||||||||
\(917\) | 47.1163 | 1.55592 | ||||||||
\(918\) | 7.96809 | 0.262986 | ||||||||
\(919\) | −3.20026 | −0.105567 | −0.0527834 | − | 0.998606i | \(-0.516809\pi\) | ||||
−0.0527834 | + | 0.998606i | \(0.516809\pi\) | |||||||
\(920\) | 0.226949 | 0.00748230 | ||||||||
\(921\) | −14.8611 | −0.489690 | ||||||||
\(922\) | 3.89924 | 0.128415 | ||||||||
\(923\) | −21.5271 | −0.708573 | ||||||||
\(924\) | −25.1913 | −0.828734 | ||||||||
\(925\) | 55.6579 | 1.83002 | ||||||||
\(926\) | 30.2977 | 0.995646 | ||||||||
\(927\) | 10.8579 | 0.356622 | ||||||||
\(928\) | −4.05713 | −0.133182 | ||||||||
\(929\) | 34.4417 | 1.12999 | 0.564997 | − | 0.825093i | \(-0.308877\pi\) | ||||
0.564997 | + | 0.825093i | \(0.308877\pi\) | |||||||
\(930\) | 3.27629 | 0.107434 | ||||||||
\(931\) | 8.37244 | 0.274395 | ||||||||
\(932\) | −14.2979 | −0.468343 | ||||||||
\(933\) | 46.2222 | 1.51325 | ||||||||
\(934\) | −18.0191 | −0.589604 | ||||||||
\(935\) | −1.41337 | −0.0462221 | ||||||||
\(936\) | 25.0624 | 0.819189 | ||||||||
\(937\) | 2.20212 | 0.0719402 | 0.0359701 | − | 0.999353i | \(-0.488548\pi\) | ||||
0.0359701 | + | 0.999353i | \(0.488548\pi\) | |||||||
\(938\) | −20.7775 | −0.678410 | ||||||||
\(939\) | 28.1222 | 0.917733 | ||||||||
\(940\) | −1.02065 | −0.0332899 | ||||||||
\(941\) | −1.34998 | −0.0440082 | −0.0220041 | − | 0.999758i | \(-0.507005\pi\) | ||||
−0.0220041 | + | 0.999758i | \(0.507005\pi\) | |||||||
\(942\) | 52.5849 | 1.71331 | ||||||||
\(943\) | 15.3702 | 0.500524 | ||||||||
\(944\) | 6.87216 | 0.223670 | ||||||||
\(945\) | −0.957796 | −0.0311571 | ||||||||
\(946\) | −24.1280 | −0.784471 | ||||||||
\(947\) | 5.09719 | 0.165637 | 0.0828183 | − | 0.996565i | \(-0.473608\pi\) | ||||
0.0828183 | + | 0.996565i | \(0.473608\pi\) | |||||||
\(948\) | 16.9833 | 0.551593 | ||||||||
\(949\) | 57.4581 | 1.86517 | ||||||||
\(950\) | −21.9816 | −0.713176 | ||||||||
\(951\) | −19.7595 | −0.640747 | ||||||||
\(952\) | 9.85813 | 0.319504 | ||||||||
\(953\) | −36.0854 | −1.16892 | −0.584460 | − | 0.811422i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811422i | \(0.698694\pi\) | |||||||
\(954\) | −13.3911 | −0.433552 | ||||||||
\(955\) | 1.40632 | 0.0455075 | ||||||||
\(956\) | 0.234563 | 0.00758631 | ||||||||
\(957\) | −34.2635 | −1.10758 | ||||||||
\(958\) | −7.99029 | −0.258155 | ||||||||
\(959\) | 31.7097 | 1.02396 | ||||||||
\(960\) | 0.350258 | 0.0113045 | ||||||||
\(961\) | 56.4962 | 1.82246 | ||||||||
\(962\) | −71.4821 | −2.30467 | ||||||||
\(963\) | 15.9603 | 0.514315 | ||||||||
\(964\) | −18.6942 | −0.602101 | ||||||||
\(965\) | 3.19920 | 0.102986 | ||||||||
\(966\) | −13.3684 | −0.430123 | ||||||||
\(967\) | −35.7635 | −1.15008 | −0.575039 | − | 0.818126i | \(-0.695013\pi\) | ||||
−0.575039 | + | 0.818126i | \(0.695013\pi\) | |||||||
\(968\) | −0.688423 | −0.0221268 | ||||||||
\(969\) | 38.3477 | 1.23191 | ||||||||
\(970\) | −0.580319 | −0.0186329 | ||||||||
\(971\) | 26.4057 | 0.847400 | 0.423700 | − | 0.905802i | \(-0.360731\pi\) | ||||
0.423700 | + | 0.905802i | \(0.360731\pi\) | |||||||
\(972\) | 21.4595 | 0.688313 | ||||||||
\(973\) | −21.3034 | −0.682955 | ||||||||
\(974\) | 21.1513 | 0.677730 | ||||||||
\(975\) | 83.8445 | 2.68517 | ||||||||
\(976\) | 12.8840 | 0.412407 | ||||||||
\(977\) | 11.2346 | 0.359428 | 0.179714 | − | 0.983719i | \(-0.442483\pi\) | ||||
0.179714 | + | 0.983719i | \(0.442483\pi\) | |||||||
\(978\) | −22.7374 | −0.727061 | ||||||||
\(979\) | −20.1144 | −0.642859 | ||||||||
\(980\) | −0.252730 | −0.00807316 | ||||||||
\(981\) | 48.3355 | 1.54324 | ||||||||
\(982\) | 35.1515 | 1.12173 | ||||||||
\(983\) | −40.6174 | −1.29549 | −0.647746 | − | 0.761856i | \(-0.724288\pi\) | ||||
−0.647746 | + | 0.761856i | \(0.724288\pi\) | |||||||
\(984\) | 23.7214 | 0.756209 | ||||||||
\(985\) | 1.28865 | 0.0410597 | ||||||||
\(986\) | 13.4083 | 0.427009 | ||||||||
\(987\) | 60.1213 | 1.91368 | ||||||||
\(988\) | 28.2312 | 0.898154 | ||||||||
\(989\) | −12.8042 | −0.407149 | ||||||||
\(990\) | 1.67504 | 0.0532362 | ||||||||
\(991\) | −10.5683 | −0.335712 | −0.167856 | − | 0.985811i | \(-0.553684\pi\) | ||||
−0.167856 | + | 0.985811i | \(0.553684\pi\) | |||||||
\(992\) | 9.35394 | 0.296988 | ||||||||
\(993\) | 3.13242 | 0.0994044 | ||||||||
\(994\) | 10.0352 | 0.318297 | ||||||||
\(995\) | 2.54250 | 0.0806027 | ||||||||
\(996\) | 6.59112 | 0.208848 | ||||||||
\(997\) | 10.1443 | 0.321274 | 0.160637 | − | 0.987014i | \(-0.448645\pi\) | ||||
0.160637 | + | 0.987014i | \(0.448645\pi\) | |||||||
\(998\) | 11.9801 | 0.379224 | ||||||||
\(999\) | 26.9338 | 0.852148 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8002.2.a.d.1.12 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.12 | ✓ | 69 | 1.1 | even | 1 | trivial |