Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.77462\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.41421 | −1.52688 | −0.763441 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.41421 | −1.07967 | ||||||||
\(11\) | 2.29857 | 0.693046 | 0.346523 | − | 0.938042i | \(-0.387362\pi\) | ||||
0.346523 | + | 0.938042i | \(0.387362\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.54925 | 0.429683 | 0.214842 | − | 0.976649i | \(-0.431076\pi\) | ||||
0.214842 | + | 0.976649i | \(0.431076\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.72082 | 0.659895 | 0.329948 | − | 0.943999i | \(-0.392969\pi\) | ||||
0.329948 | + | 0.943999i | \(0.392969\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.15442 | −1.64134 | −0.820669 | − | 0.571404i | \(-0.806399\pi\) | ||||
−0.820669 | + | 0.571404i | \(0.806399\pi\) | |||||||
\(20\) | −3.41421 | −0.763441 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.29857 | 0.490057 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 1.54925 | 0.303832 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.69564 | −1.80043 | −0.900217 | − | 0.435441i | \(-0.856592\pi\) | ||||
−0.900217 | + | 0.435441i | \(0.856592\pi\) | |||||||
\(30\) | 3.41421 | 0.623347 | ||||||||
\(31\) | −5.15442 | −0.925762 | −0.462881 | − | 0.886420i | \(-0.653184\pi\) | ||||
−0.462881 | + | 0.886420i | \(0.653184\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.29857 | −0.400130 | ||||||||
\(34\) | 2.72082 | 0.466617 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.72082 | 0.447300 | 0.223650 | − | 0.974670i | \(-0.428203\pi\) | ||||
0.223650 | + | 0.974670i | \(0.428203\pi\) | |||||||
\(38\) | −7.15442 | −1.16060 | ||||||||
\(39\) | −1.54925 | −0.248078 | ||||||||
\(40\) | −3.41421 | −0.539835 | ||||||||
\(41\) | 6.01136 | 0.938817 | 0.469408 | − | 0.882981i | \(-0.344467\pi\) | ||||
0.469408 | + | 0.882981i | \(0.344467\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8193 | 1.80243 | 0.901214 | − | 0.433374i | \(-0.142677\pi\) | ||||
0.901214 | + | 0.433374i | \(0.142677\pi\) | |||||||
\(44\) | 2.29857 | 0.346523 | ||||||||
\(45\) | −3.41421 | −0.508961 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 0.557278 | 0.0812874 | 0.0406437 | − | 0.999174i | \(-0.487059\pi\) | ||||
0.0406437 | + | 0.999174i | \(0.487059\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.65685 | 0.941421 | ||||||||
\(51\) | −2.72082 | −0.380991 | ||||||||
\(52\) | 1.54925 | 0.214842 | ||||||||
\(53\) | −3.31796 | −0.455757 | −0.227879 | − | 0.973690i | \(-0.573179\pi\) | ||||
−0.227879 | + | 0.973690i | \(0.573179\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −7.84782 | −1.05820 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.15442 | 0.947627 | ||||||||
\(58\) | −9.69564 | −1.27310 | ||||||||
\(59\) | 7.69564 | 1.00189 | 0.500943 | − | 0.865480i | \(-0.332987\pi\) | ||||
0.500943 | + | 0.865480i | \(0.332987\pi\) | |||||||
\(60\) | 3.41421 | 0.440773 | ||||||||
\(61\) | 0.0113593 | 0.00145441 | 0.000727205 | − | 1.00000i | \(-0.499769\pi\) | ||||
0.000727205 | 1.00000i | \(0.499769\pi\) | ||||||||
\(62\) | −5.15442 | −0.654612 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.28946 | −0.656076 | ||||||||
\(66\) | −2.29857 | −0.282935 | ||||||||
\(67\) | 8.93604 | 1.09171 | 0.545855 | − | 0.837879i | \(-0.316205\pi\) | ||||
0.545855 | + | 0.837879i | \(0.316205\pi\) | |||||||
\(68\) | 2.72082 | 0.329948 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.25067 | −1.09785 | −0.548926 | − | 0.835871i | \(-0.684963\pi\) | ||||
−0.548926 | + | 0.835871i | \(0.684963\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 8.09046 | 0.946917 | 0.473458 | − | 0.880816i | \(-0.343005\pi\) | ||||
0.473458 | + | 0.880816i | \(0.343005\pi\) | |||||||
\(74\) | 2.72082 | 0.316289 | ||||||||
\(75\) | −6.65685 | −0.768667 | ||||||||
\(76\) | −7.15442 | −0.820669 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.54925 | −0.175418 | ||||||||
\(79\) | −10.4062 | −1.17079 | −0.585393 | − | 0.810749i | \(-0.699060\pi\) | ||||
−0.585393 | + | 0.810749i | \(0.699060\pi\) | |||||||
\(80\) | −3.41421 | −0.381721 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.01136 | 0.663844 | ||||||||
\(83\) | −1.71279 | −0.188003 | −0.0940014 | − | 0.995572i | \(-0.529966\pi\) | ||||
−0.0940014 | + | 0.995572i | \(0.529966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.28946 | −1.00758 | ||||||||
\(86\) | 11.8193 | 1.27451 | ||||||||
\(87\) | 9.69564 | 1.03948 | ||||||||
\(88\) | 2.29857 | 0.245029 | ||||||||
\(89\) | −16.0506 | −1.70136 | −0.850680 | − | 0.525684i | \(-0.823809\pi\) | ||||
−0.850680 | + | 0.525684i | \(0.823809\pi\) | |||||||
\(90\) | −3.41421 | −0.359890 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 5.15442 | 0.534489 | ||||||||
\(94\) | 0.557278 | 0.0574788 | ||||||||
\(95\) | 24.4267 | 2.50613 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.76446 | 0.585293 | 0.292646 | − | 0.956221i | \(-0.405464\pi\) | ||||
0.292646 | + | 0.956221i | \(0.405464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.29857 | 0.231015 | ||||||||
\(100\) | 6.65685 | 0.665685 | ||||||||
\(101\) | −13.8193 | −1.37507 | −0.687536 | − | 0.726150i | \(-0.741308\pi\) | ||||
−0.687536 | + | 0.726150i | \(0.741308\pi\) | |||||||
\(102\) | −2.72082 | −0.269401 | ||||||||
\(103\) | −8.86721 | −0.873712 | −0.436856 | − | 0.899531i | \(-0.643908\pi\) | ||||
−0.436856 | + | 0.899531i | \(0.643908\pi\) | |||||||
\(104\) | 1.54925 | 0.151916 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.31796 | −0.322269 | ||||||||
\(107\) | 13.1818 | 1.27434 | 0.637169 | − | 0.770724i | \(-0.280105\pi\) | ||||
0.637169 | + | 0.770724i | \(0.280105\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 3.76446 | 0.360570 | 0.180285 | − | 0.983614i | \(-0.442298\pi\) | ||||
0.180285 | + | 0.983614i | \(0.442298\pi\) | |||||||
\(110\) | −7.84782 | −0.748260 | ||||||||
\(111\) | −2.72082 | −0.258249 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.15218 | −0.578749 | −0.289374 | − | 0.957216i | \(-0.593447\pi\) | ||||
−0.289374 | + | 0.957216i | \(0.593447\pi\) | |||||||
\(114\) | 7.15442 | 0.670073 | ||||||||
\(115\) | −3.41421 | −0.318377 | ||||||||
\(116\) | −9.69564 | −0.900217 | ||||||||
\(117\) | 1.54925 | 0.143228 | ||||||||
\(118\) | 7.69564 | 0.708441 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.41421 | 0.311674 | ||||||||
\(121\) | −5.71656 | −0.519688 | ||||||||
\(122\) | 0.0113593 | 0.00102842 | ||||||||
\(123\) | −6.01136 | −0.542026 | ||||||||
\(124\) | −5.15442 | −0.462881 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0033 | −1.15386 | −0.576929 | − | 0.816794i | \(-0.695749\pi\) | ||||
−0.576929 | + | 0.816794i | \(0.695749\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.8193 | −1.04063 | ||||||||
\(130\) | −5.28946 | −0.463916 | ||||||||
\(131\) | 15.4804 | 1.35253 | 0.676265 | − | 0.736658i | \(-0.263597\pi\) | ||||
0.676265 | + | 0.736658i | \(0.263597\pi\) | |||||||
\(132\) | −2.29857 | −0.200065 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.93604 | 0.771956 | ||||||||
\(135\) | 3.41421 | 0.293849 | ||||||||
\(136\) | 2.72082 | 0.233308 | ||||||||
\(137\) | −15.4416 | −1.31927 | −0.659634 | − | 0.751587i | \(-0.729289\pi\) | ||||
−0.659634 | + | 0.751587i | \(0.729289\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −5.17157 | −0.438647 | −0.219324 | − | 0.975652i | \(-0.570385\pi\) | ||||
−0.219324 | + | 0.975652i | \(0.570385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.557278 | −0.0469313 | ||||||||
\(142\) | −9.25067 | −0.776299 | ||||||||
\(143\) | 3.56105 | 0.297790 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 33.1030 | 2.74905 | ||||||||
\(146\) | 8.09046 | 0.669571 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.72082 | 0.223650 | ||||||||
\(149\) | 6.70475 | 0.549275 | 0.274637 | − | 0.961548i | \(-0.411442\pi\) | ||||
0.274637 | + | 0.961548i | \(0.411442\pi\) | |||||||
\(150\) | −6.65685 | −0.543530 | ||||||||
\(151\) | 8.13395 | 0.661931 | 0.330966 | − | 0.943643i | \(-0.392626\pi\) | ||||
0.330966 | + | 0.943643i | \(0.392626\pi\) | |||||||
\(152\) | −7.15442 | −0.580300 | ||||||||
\(153\) | 2.72082 | 0.219965 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.5983 | 1.41353 | ||||||||
\(156\) | −1.54925 | −0.124039 | ||||||||
\(157\) | 3.64396 | 0.290820 | 0.145410 | − | 0.989372i | \(-0.453550\pi\) | ||||
0.145410 | + | 0.989372i | \(0.453550\pi\) | |||||||
\(158\) | −10.4062 | −0.827871 | ||||||||
\(159\) | 3.31796 | 0.263132 | ||||||||
\(160\) | −3.41421 | −0.269917 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −13.5047 | −1.05777 | −0.528884 | − | 0.848694i | \(-0.677389\pi\) | ||||
−0.528884 | + | 0.848694i | \(0.677389\pi\) | |||||||
\(164\) | 6.01136 | 0.469408 | ||||||||
\(165\) | 7.84782 | 0.610952 | ||||||||
\(166\) | −1.71279 | −0.132938 | ||||||||
\(167\) | −19.6009 | −1.51676 | −0.758382 | − | 0.651810i | \(-0.774010\pi\) | ||||
−0.758382 | + | 0.651810i | \(0.774010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5998 | −0.815372 | ||||||||
\(170\) | −9.28946 | −0.712469 | ||||||||
\(171\) | −7.15442 | −0.547112 | ||||||||
\(172\) | 11.8193 | 0.901214 | ||||||||
\(173\) | −14.6317 | −1.11243 | −0.556213 | − | 0.831040i | \(-0.687746\pi\) | ||||
−0.556213 | + | 0.831040i | \(0.687746\pi\) | |||||||
\(174\) | 9.69564 | 0.735024 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.29857 | 0.173261 | ||||||||
\(177\) | −7.69564 | −0.578440 | ||||||||
\(178\) | −16.0506 | −1.20304 | ||||||||
\(179\) | −6.28613 | −0.469847 | −0.234924 | − | 0.972014i | \(-0.575484\pi\) | ||||
−0.234924 | + | 0.972014i | \(0.575484\pi\) | |||||||
\(180\) | −3.41421 | −0.254480 | ||||||||
\(181\) | −14.8398 | −1.10303 | −0.551516 | − | 0.834164i | \(-0.685951\pi\) | ||||
−0.551516 | + | 0.834164i | \(0.685951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0113593 | −0.000839704 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −9.28946 | −0.682974 | ||||||||
\(186\) | 5.15442 | 0.377941 | ||||||||
\(187\) | 6.25400 | 0.457338 | ||||||||
\(188\) | 0.557278 | 0.0406437 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.4267 | 1.77210 | ||||||||
\(191\) | −18.3492 | −1.32770 | −0.663849 | − | 0.747866i | \(-0.731078\pi\) | ||||
−0.663849 | + | 0.747866i | \(0.731078\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.979075 | −0.0704753 | −0.0352377 | − | 0.999379i | \(-0.511219\pi\) | ||||
−0.0352377 | + | 0.999379i | \(0.511219\pi\) | |||||||
\(194\) | 5.76446 | 0.413864 | ||||||||
\(195\) | 5.28946 | 0.378786 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.65353 | 0.331550 | 0.165775 | − | 0.986164i | \(-0.446987\pi\) | ||||
0.165775 | + | 0.986164i | \(0.446987\pi\) | |||||||
\(198\) | 2.29857 | 0.163352 | ||||||||
\(199\) | −1.46436 | −0.103805 | −0.0519027 | − | 0.998652i | \(-0.516529\pi\) | ||||
−0.0519027 | + | 0.998652i | \(0.516529\pi\) | |||||||
\(200\) | 6.65685 | 0.470711 | ||||||||
\(201\) | −8.93604 | −0.630299 | ||||||||
\(202\) | −13.8193 | −0.972323 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.72082 | −0.190495 | ||||||||
\(205\) | −20.5241 | −1.43346 | ||||||||
\(206\) | −8.86721 | −0.617808 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 1.54925 | 0.107421 | ||||||||
\(209\) | −16.4450 | −1.13752 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9075 | −0.888591 | −0.444295 | − | 0.895880i | \(-0.646546\pi\) | ||||
−0.444295 | + | 0.895880i | \(0.646546\pi\) | |||||||
\(212\) | −3.31796 | −0.227879 | ||||||||
\(213\) | 9.25067 | 0.633846 | ||||||||
\(214\) | 13.1818 | 0.901093 | ||||||||
\(215\) | −40.3536 | −2.75210 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.76446 | 0.254962 | ||||||||
\(219\) | −8.09046 | −0.546703 | ||||||||
\(220\) | −7.84782 | −0.529100 | ||||||||
\(221\) | 4.21522 | 0.283546 | ||||||||
\(222\) | −2.72082 | −0.182609 | ||||||||
\(223\) | −14.4293 | −0.966261 | −0.483130 | − | 0.875548i | \(-0.660500\pi\) | ||||
−0.483130 | + | 0.875548i | \(0.660500\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | −6.15218 | −0.409237 | ||||||||
\(227\) | 14.4133 | 0.956643 | 0.478322 | − | 0.878185i | \(-0.341245\pi\) | ||||
0.478322 | + | 0.878185i | \(0.341245\pi\) | |||||||
\(228\) | 7.15442 | 0.473813 | ||||||||
\(229\) | 1.26357 | 0.0834988 | 0.0417494 | − | 0.999128i | \(-0.486707\pi\) | ||||
0.0417494 | + | 0.999128i | \(0.486707\pi\) | |||||||
\(230\) | −3.41421 | −0.225127 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.69564 | −0.636550 | ||||||||
\(233\) | −16.7166 | −1.09514 | −0.547569 | − | 0.836760i | \(-0.684447\pi\) | ||||
−0.547569 | + | 0.836760i | \(0.684447\pi\) | |||||||
\(234\) | 1.54925 | 0.101277 | ||||||||
\(235\) | −1.90267 | −0.124116 | ||||||||
\(236\) | 7.69564 | 0.500943 | ||||||||
\(237\) | 10.4062 | 0.675954 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6923 | −1.46784 | −0.733922 | − | 0.679234i | \(-0.762312\pi\) | ||||
−0.733922 | + | 0.679234i | \(0.762312\pi\) | |||||||
\(240\) | 3.41421 | 0.220387 | ||||||||
\(241\) | −20.6705 | −1.33150 | −0.665751 | − | 0.746174i | \(-0.731889\pi\) | ||||
−0.665751 | + | 0.746174i | \(0.731889\pi\) | |||||||
\(242\) | −5.71656 | −0.367475 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.0113593 | 0.000727205 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.01136 | −0.383270 | ||||||||
\(247\) | −11.0840 | −0.705256 | ||||||||
\(248\) | −5.15442 | −0.327306 | ||||||||
\(249\) | 1.71279 | 0.108543 | ||||||||
\(250\) | −5.65685 | −0.357771 | ||||||||
\(251\) | −27.6397 | −1.74460 | −0.872301 | − | 0.488969i | \(-0.837373\pi\) | ||||
−0.872301 | + | 0.488969i | \(0.837373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.29857 | 0.144510 | ||||||||
\(254\) | −13.0033 | −0.815901 | ||||||||
\(255\) | 9.28946 | 0.581728 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.9383 | 0.744689 | 0.372345 | − | 0.928095i | \(-0.378554\pi\) | ||||
0.372345 | + | 0.928095i | \(0.378554\pi\) | |||||||
\(258\) | −11.8193 | −0.735838 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.28946 | −0.328038 | ||||||||
\(261\) | −9.69564 | −0.600145 | ||||||||
\(262\) | 15.4804 | 0.956384 | ||||||||
\(263\) | −8.68629 | −0.535620 | −0.267810 | − | 0.963472i | \(-0.586300\pi\) | ||||
−0.267810 | + | 0.963472i | \(0.586300\pi\) | |||||||
\(264\) | −2.29857 | −0.141467 | ||||||||
\(265\) | 11.3282 | 0.695888 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0506 | 0.982280 | ||||||||
\(268\) | 8.93604 | 0.545855 | ||||||||
\(269\) | 20.6134 | 1.25682 | 0.628412 | − | 0.777881i | \(-0.283705\pi\) | ||||
0.628412 | + | 0.777881i | \(0.283705\pi\) | |||||||
\(270\) | 3.41421 | 0.207782 | ||||||||
\(271\) | 3.53789 | 0.214911 | 0.107456 | − | 0.994210i | \(-0.465730\pi\) | ||||
0.107456 | + | 0.994210i | \(0.465730\pi\) | |||||||
\(272\) | 2.72082 | 0.164974 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4416 | −0.932863 | ||||||||
\(275\) | 15.3013 | 0.922701 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 24.4898 | 1.47145 | 0.735724 | − | 0.677282i | \(-0.236842\pi\) | ||||
0.735724 | + | 0.677282i | \(0.236842\pi\) | |||||||
\(278\) | −5.17157 | −0.310170 | ||||||||
\(279\) | −5.15442 | −0.308587 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.1582 | −0.605987 | −0.302994 | − | 0.952993i | \(-0.597986\pi\) | ||||
−0.302994 | + | 0.952993i | \(0.597986\pi\) | |||||||
\(282\) | −0.557278 | −0.0331854 | ||||||||
\(283\) | 16.6042 | 0.987020 | 0.493510 | − | 0.869740i | \(-0.335714\pi\) | ||||
0.493510 | + | 0.869740i | \(0.335714\pi\) | |||||||
\(284\) | −9.25067 | −0.548926 | ||||||||
\(285\) | −24.4267 | −1.44691 | ||||||||
\(286\) | 3.56105 | 0.210570 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −9.59715 | −0.564538 | ||||||||
\(290\) | 33.1030 | 1.94387 | ||||||||
\(291\) | −5.76446 | −0.337919 | ||||||||
\(292\) | 8.09046 | 0.473458 | ||||||||
\(293\) | −24.9737 | −1.45898 | −0.729491 | − | 0.683991i | \(-0.760243\pi\) | ||||
−0.729491 | + | 0.683991i | \(0.760243\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.2745 | −1.52976 | ||||||||
\(296\) | 2.72082 | 0.158144 | ||||||||
\(297\) | −2.29857 | −0.133377 | ||||||||
\(298\) | 6.70475 | 0.388396 | ||||||||
\(299\) | 1.54925 | 0.0895952 | ||||||||
\(300\) | −6.65685 | −0.384334 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.13395 | 0.468056 | ||||||||
\(303\) | 13.8193 | 0.793899 | ||||||||
\(304\) | −7.15442 | −0.410334 | ||||||||
\(305\) | −0.0387831 | −0.00222071 | ||||||||
\(306\) | 2.72082 | 0.155539 | ||||||||
\(307\) | 32.1239 | 1.83341 | 0.916704 | − | 0.399567i | \(-0.130840\pi\) | ||||
0.916704 | + | 0.399567i | \(0.130840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.86721 | 0.504438 | ||||||||
\(310\) | 17.5983 | 0.999516 | ||||||||
\(311\) | −29.0571 | −1.64768 | −0.823838 | − | 0.566825i | \(-0.808172\pi\) | ||||
−0.823838 | + | 0.566825i | \(0.808172\pi\) | |||||||
\(312\) | −1.54925 | −0.0877088 | ||||||||
\(313\) | 1.74174 | 0.0984492 | 0.0492246 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492246 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(314\) | 3.64396 | 0.205641 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.4062 | −0.585393 | ||||||||
\(317\) | −12.7796 | −0.717774 | −0.358887 | − | 0.933381i | \(-0.616844\pi\) | ||||
−0.358887 | + | 0.933381i | \(0.616844\pi\) | |||||||
\(318\) | 3.31796 | 0.186062 | ||||||||
\(319\) | −22.2861 | −1.24778 | ||||||||
\(320\) | −3.41421 | −0.190860 | ||||||||
\(321\) | −13.1818 | −0.735739 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.4659 | −1.08311 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 10.3131 | 0.572068 | ||||||||
\(326\) | −13.5047 | −0.747955 | ||||||||
\(327\) | −3.76446 | −0.208175 | ||||||||
\(328\) | 6.01136 | 0.331922 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.84782 | 0.432008 | ||||||||
\(331\) | 6.34315 | 0.348651 | 0.174325 | − | 0.984688i | \(-0.444226\pi\) | ||||
0.174325 | + | 0.984688i | \(0.444226\pi\) | |||||||
\(332\) | −1.71279 | −0.0940014 | ||||||||
\(333\) | 2.72082 | 0.149100 | ||||||||
\(334\) | −19.6009 | −1.07251 | ||||||||
\(335\) | −30.5095 | −1.66691 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.8866 | 0.865398 | 0.432699 | − | 0.901538i | \(-0.357561\pi\) | ||||
0.432699 | + | 0.901538i | \(0.357561\pi\) | |||||||
\(338\) | −10.5998 | −0.576555 | ||||||||
\(339\) | 6.15218 | 0.334141 | ||||||||
\(340\) | −9.28946 | −0.503791 | ||||||||
\(341\) | −11.8478 | −0.641595 | ||||||||
\(342\) | −7.15442 | −0.386867 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.8193 | 0.637255 | ||||||||
\(345\) | 3.41421 | 0.183815 | ||||||||
\(346\) | −14.6317 | −0.786604 | ||||||||
\(347\) | −28.7699 | −1.54445 | −0.772224 | − | 0.635350i | \(-0.780856\pi\) | ||||
−0.772224 | + | 0.635350i | \(0.780856\pi\) | |||||||
\(348\) | 9.69564 | 0.519741 | ||||||||
\(349\) | −14.6638 | −0.784935 | −0.392468 | − | 0.919766i | \(-0.628379\pi\) | ||||
−0.392468 | + | 0.919766i | \(0.628379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.54925 | −0.0826926 | ||||||||
\(352\) | 2.29857 | 0.122514 | ||||||||
\(353\) | 12.6079 | 0.671049 | 0.335525 | − | 0.942031i | \(-0.391086\pi\) | ||||
0.335525 | + | 0.942031i | \(0.391086\pi\) | |||||||
\(354\) | −7.69564 | −0.409019 | ||||||||
\(355\) | 31.5838 | 1.67629 | ||||||||
\(356\) | −16.0506 | −0.850680 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.28613 | −0.332232 | ||||||||
\(359\) | −13.5047 | −0.712749 | −0.356375 | − | 0.934343i | \(-0.615987\pi\) | ||||
−0.356375 | + | 0.934343i | \(0.615987\pi\) | |||||||
\(360\) | −3.41421 | −0.179945 | ||||||||
\(361\) | 32.1858 | 1.69399 | ||||||||
\(362\) | −14.8398 | −0.779962 | ||||||||
\(363\) | 5.71656 | 0.300042 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.6226 | −1.44583 | ||||||||
\(366\) | −0.0113593 | −0.000593760 0 | ||||||||
\(367\) | −3.04364 | −0.158877 | −0.0794385 | − | 0.996840i | \(-0.525313\pi\) | ||||
−0.0794385 | + | 0.996840i | \(0.525313\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 6.01136 | 0.312939 | ||||||||
\(370\) | −9.28946 | −0.482936 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.15442 | 0.267244 | ||||||||
\(373\) | −37.2752 | −1.93003 | −0.965017 | − | 0.262187i | \(-0.915556\pi\) | ||||
−0.965017 | + | 0.262187i | \(0.915556\pi\) | |||||||
\(374\) | 6.25400 | 0.323387 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0.557278 | 0.0287394 | ||||||||
\(377\) | −15.0209 | −0.773617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.6720 | 1.16458 | 0.582291 | − | 0.812980i | \(-0.302156\pi\) | ||||
0.582291 | + | 0.812980i | \(0.302156\pi\) | |||||||
\(380\) | 24.4267 | 1.25306 | ||||||||
\(381\) | 13.0033 | 0.666181 | ||||||||
\(382\) | −18.3492 | −0.938825 | ||||||||
\(383\) | 11.7278 | 0.599261 | 0.299630 | − | 0.954055i | \(-0.403137\pi\) | ||||
0.299630 | + | 0.954055i | \(0.403137\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.979075 | −0.0498336 | ||||||||
\(387\) | 11.8193 | 0.600809 | ||||||||
\(388\) | 5.76446 | 0.292646 | ||||||||
\(389\) | 7.49223 | 0.379871 | 0.189936 | − | 0.981797i | \(-0.439172\pi\) | ||||
0.189936 | + | 0.981797i | \(0.439172\pi\) | |||||||
\(390\) | 5.28946 | 0.267842 | ||||||||
\(391\) | 2.72082 | 0.137598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.4804 | −0.780884 | ||||||||
\(394\) | 4.65353 | 0.234441 | ||||||||
\(395\) | 35.5289 | 1.78765 | ||||||||
\(396\) | 2.29857 | 0.115508 | ||||||||
\(397\) | 22.3616 | 1.12230 | 0.561148 | − | 0.827715i | \(-0.310360\pi\) | ||||
0.561148 | + | 0.827715i | \(0.310360\pi\) | |||||||
\(398\) | −1.46436 | −0.0734015 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.65685 | 0.332843 | ||||||||
\(401\) | −4.09580 | −0.204534 | −0.102267 | − | 0.994757i | \(-0.532610\pi\) | ||||
−0.102267 | + | 0.994757i | \(0.532610\pi\) | |||||||
\(402\) | −8.93604 | −0.445689 | ||||||||
\(403\) | −7.98547 | −0.397785 | ||||||||
\(404\) | −13.8193 | −0.687536 | ||||||||
\(405\) | −3.41421 | −0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.25400 | 0.309999 | ||||||||
\(408\) | −2.72082 | −0.134701 | ||||||||
\(409\) | −19.5336 | −0.965876 | −0.482938 | − | 0.875655i | \(-0.660430\pi\) | ||||
−0.482938 | + | 0.875655i | \(0.660430\pi\) | |||||||
\(410\) | −20.5241 | −1.01361 | ||||||||
\(411\) | 15.4416 | 0.761680 | ||||||||
\(412\) | −8.86721 | −0.436856 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 5.84782 | 0.287058 | ||||||||
\(416\) | 1.54925 | 0.0759580 | ||||||||
\(417\) | 5.17157 | 0.253253 | ||||||||
\(418\) | −16.4450 | −0.804350 | ||||||||
\(419\) | 5.44055 | 0.265788 | 0.132894 | − | 0.991130i | \(-0.457573\pi\) | ||||
0.132894 | + | 0.991130i | \(0.457573\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.5149 | 1.82837 | 0.914183 | − | 0.405301i | \(-0.132833\pi\) | ||||
0.914183 | + | 0.405301i | \(0.132833\pi\) | |||||||
\(422\) | −12.9075 | −0.628329 | ||||||||
\(423\) | 0.557278 | 0.0270958 | ||||||||
\(424\) | −3.31796 | −0.161135 | ||||||||
\(425\) | 18.1121 | 0.878566 | ||||||||
\(426\) | 9.25067 | 0.448197 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.1818 | 0.637169 | ||||||||
\(429\) | −3.56105 | −0.171929 | ||||||||
\(430\) | −40.3536 | −1.94603 | ||||||||
\(431\) | 18.0303 | 0.868488 | 0.434244 | − | 0.900795i | \(-0.357016\pi\) | ||||
0.434244 | + | 0.900795i | \(0.357016\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 25.4031 | 1.22079 | 0.610397 | − | 0.792096i | \(-0.291010\pi\) | ||||
0.610397 | + | 0.792096i | \(0.291010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −33.1030 | −1.58717 | ||||||||
\(436\) | 3.76446 | 0.180285 | ||||||||
\(437\) | −7.15442 | −0.342243 | ||||||||
\(438\) | −8.09046 | −0.386577 | ||||||||
\(439\) | 4.19205 | 0.200076 | 0.100038 | − | 0.994984i | \(-0.468104\pi\) | ||||
0.100038 | + | 0.994984i | \(0.468104\pi\) | |||||||
\(440\) | −7.84782 | −0.374130 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.21522 | 0.200497 | ||||||||
\(443\) | −24.0836 | −1.14425 | −0.572123 | − | 0.820168i | \(-0.693880\pi\) | ||||
−0.572123 | + | 0.820168i | \(0.693880\pi\) | |||||||
\(444\) | −2.72082 | −0.129124 | ||||||||
\(445\) | 54.8001 | 2.59778 | ||||||||
\(446\) | −14.4293 | −0.683249 | ||||||||
\(447\) | −6.70475 | −0.317124 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.89262 | 0.278090 | 0.139045 | − | 0.990286i | \(-0.455597\pi\) | ||||
0.139045 | + | 0.990286i | \(0.455597\pi\) | |||||||
\(450\) | 6.65685 | 0.313807 | ||||||||
\(451\) | 13.8175 | 0.650643 | ||||||||
\(452\) | −6.15218 | −0.289374 | ||||||||
\(453\) | −8.13395 | −0.382166 | ||||||||
\(454\) | 14.4133 | 0.676449 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.15442 | 0.335037 | ||||||||
\(457\) | −9.40285 | −0.439847 | −0.219923 | − | 0.975517i | \(-0.570581\pi\) | ||||
−0.219923 | + | 0.975517i | \(0.570581\pi\) | |||||||
\(458\) | 1.26357 | 0.0590426 | ||||||||
\(459\) | −2.72082 | −0.126997 | ||||||||
\(460\) | −3.41421 | −0.159189 | ||||||||
\(461\) | −13.5720 | −0.632109 | −0.316055 | − | 0.948741i | \(-0.602358\pi\) | ||||
−0.316055 | + | 0.948741i | \(0.602358\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.7759 | 1.52323 | 0.761613 | − | 0.648033i | \(-0.224408\pi\) | ||||
0.761613 | + | 0.648033i | \(0.224408\pi\) | |||||||
\(464\) | −9.69564 | −0.450109 | ||||||||
\(465\) | −17.5983 | −0.816102 | ||||||||
\(466\) | −16.7166 | −0.774380 | ||||||||
\(467\) | −1.53789 | −0.0711649 | −0.0355824 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355824 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(468\) | 1.54925 | 0.0716139 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.90267 | −0.0877634 | ||||||||
\(471\) | −3.64396 | −0.167905 | ||||||||
\(472\) | 7.69564 | 0.354220 | ||||||||
\(473\) | 27.1675 | 1.24917 | ||||||||
\(474\) | 10.4062 | 0.477972 | ||||||||
\(475\) | −47.6260 | −2.18523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.31796 | −0.151919 | ||||||||
\(478\) | −22.6923 | −1.03792 | ||||||||
\(479\) | 25.6547 | 1.17219 | 0.586096 | − | 0.810241i | \(-0.300664\pi\) | ||||
0.586096 | + | 0.810241i | \(0.300664\pi\) | |||||||
\(480\) | 3.41421 | 0.155837 | ||||||||
\(481\) | 4.21522 | 0.192197 | ||||||||
\(482\) | −20.6705 | −0.941513 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.71656 | −0.259844 | ||||||||
\(485\) | −19.6811 | −0.893673 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −17.8151 | −0.807277 | −0.403639 | − | 0.914919i | \(-0.632255\pi\) | ||||
−0.403639 | + | 0.914919i | \(0.632255\pi\) | |||||||
\(488\) | 0.0113593 | 0.000514212 0 | ||||||||
\(489\) | 13.5047 | 0.610702 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.3973 | −1.77797 | −0.888987 | − | 0.457931i | \(-0.848590\pi\) | ||||
−0.888987 | + | 0.457931i | \(0.848590\pi\) | |||||||
\(492\) | −6.01136 | −0.271013 | ||||||||
\(493\) | −26.3801 | −1.18810 | ||||||||
\(494\) | −11.0840 | −0.498691 | ||||||||
\(495\) | −7.84782 | −0.352733 | ||||||||
\(496\) | −5.15442 | −0.231440 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.71279 | 0.0767518 | ||||||||
\(499\) | 20.2297 | 0.905608 | 0.452804 | − | 0.891610i | \(-0.350424\pi\) | ||||
0.452804 | + | 0.891610i | \(0.350424\pi\) | |||||||
\(500\) | −5.65685 | −0.252982 | ||||||||
\(501\) | 19.6009 | 0.875705 | ||||||||
\(502\) | −27.6397 | −1.23362 | ||||||||
\(503\) | 12.9791 | 0.578708 | 0.289354 | − | 0.957222i | \(-0.406559\pi\) | ||||
0.289354 | + | 0.957222i | \(0.406559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47.1821 | 2.09957 | ||||||||
\(506\) | 2.29857 | 0.102184 | ||||||||
\(507\) | 10.5998 | 0.470755 | ||||||||
\(508\) | −13.0033 | −0.576929 | ||||||||
\(509\) | −15.9151 | −0.705425 | −0.352712 | − | 0.935732i | \(-0.614741\pi\) | ||||
−0.352712 | + | 0.935732i | \(0.614741\pi\) | |||||||
\(510\) | 9.28946 | 0.411344 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.15442 | 0.315876 | ||||||||
\(514\) | 11.9383 | 0.526575 | ||||||||
\(515\) | 30.2745 | 1.33406 | ||||||||
\(516\) | −11.8193 | −0.520316 | ||||||||
\(517\) | 1.28094 | 0.0563359 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.6317 | 0.642259 | ||||||||
\(520\) | −5.28946 | −0.231958 | ||||||||
\(521\) | −1.16732 | −0.0511411 | −0.0255705 | − | 0.999673i | \(-0.508140\pi\) | ||||
−0.0255705 | + | 0.999673i | \(0.508140\pi\) | |||||||
\(522\) | −9.69564 | −0.424367 | ||||||||
\(523\) | −16.5412 | −0.723297 | −0.361648 | − | 0.932315i | \(-0.617786\pi\) | ||||
−0.361648 | + | 0.932315i | \(0.617786\pi\) | |||||||
\(524\) | 15.4804 | 0.676265 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.68629 | −0.378740 | ||||||||
\(527\) | −14.0243 | −0.610906 | ||||||||
\(528\) | −2.29857 | −0.100033 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 11.3282 | 0.492067 | ||||||||
\(531\) | 7.69564 | 0.333962 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.31307 | 0.403394 | ||||||||
\(534\) | 16.0506 | 0.694577 | ||||||||
\(535\) | −45.0056 | −1.94576 | ||||||||
\(536\) | 8.93604 | 0.385978 | ||||||||
\(537\) | 6.28613 | 0.271266 | ||||||||
\(538\) | 20.6134 | 0.888708 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.41421 | 0.146924 | ||||||||
\(541\) | −32.1400 | −1.38181 | −0.690903 | − | 0.722948i | \(-0.742787\pi\) | ||||
−0.690903 | + | 0.722948i | \(0.742787\pi\) | |||||||
\(542\) | 3.53789 | 0.151965 | ||||||||
\(543\) | 14.8398 | 0.636836 | ||||||||
\(544\) | 2.72082 | 0.116654 | ||||||||
\(545\) | −12.8527 | −0.550548 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.7371 | 1.65628 | 0.828140 | − | 0.560522i | \(-0.189399\pi\) | ||||
0.828140 | + | 0.560522i | \(0.189399\pi\) | |||||||
\(548\) | −15.4416 | −0.659634 | ||||||||
\(549\) | 0.0113593 | 0.000484803 0 | ||||||||
\(550\) | 15.3013 | 0.652448 | ||||||||
\(551\) | 69.3667 | 2.95512 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.4898 | 1.04047 | ||||||||
\(555\) | 9.28946 | 0.394315 | ||||||||
\(556\) | −5.17157 | −0.219324 | ||||||||
\(557\) | 19.1879 | 0.813016 | 0.406508 | − | 0.913647i | \(-0.366746\pi\) | ||||
0.406508 | + | 0.913647i | \(0.366746\pi\) | |||||||
\(558\) | −5.15442 | −0.218204 | ||||||||
\(559\) | 18.3110 | 0.774473 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.25400 | −0.264044 | ||||||||
\(562\) | −10.1582 | −0.428498 | ||||||||
\(563\) | −9.61852 | −0.405372 | −0.202686 | − | 0.979244i | \(-0.564967\pi\) | ||||
−0.202686 | + | 0.979244i | \(0.564967\pi\) | |||||||
\(564\) | −0.557278 | −0.0234656 | ||||||||
\(565\) | 21.0049 | 0.883681 | ||||||||
\(566\) | 16.6042 | 0.697929 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.25067 | −0.388150 | ||||||||
\(569\) | −10.0570 | −0.421612 | −0.210806 | − | 0.977528i | \(-0.567609\pi\) | ||||
−0.210806 | + | 0.977528i | \(0.567609\pi\) | |||||||
\(570\) | −24.4267 | −1.02312 | ||||||||
\(571\) | −14.4552 | −0.604933 | −0.302466 | − | 0.953160i | \(-0.597810\pi\) | ||||
−0.302466 | + | 0.953160i | \(0.597810\pi\) | |||||||
\(572\) | 3.56105 | 0.148895 | ||||||||
\(573\) | 18.3492 | 0.766547 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.65685 | 0.277610 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −34.4456 | −1.43399 | −0.716995 | − | 0.697078i | \(-0.754483\pi\) | ||||
−0.716995 | + | 0.697078i | \(0.754483\pi\) | |||||||
\(578\) | −9.59715 | −0.399189 | ||||||||
\(579\) | 0.979075 | 0.0406890 | ||||||||
\(580\) | 33.1030 | 1.37453 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.76446 | −0.238945 | ||||||||
\(583\) | −7.62658 | −0.315861 | ||||||||
\(584\) | 8.09046 | 0.334786 | ||||||||
\(585\) | −5.28946 | −0.218692 | ||||||||
\(586\) | −24.9737 | −1.03166 | ||||||||
\(587\) | −0.135481 | −0.00559192 | −0.00279596 | − | 0.999996i | \(-0.500890\pi\) | ||||
−0.00279596 | + | 0.999996i | \(0.500890\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.8769 | 1.51949 | ||||||||
\(590\) | −26.2745 | −1.08171 | ||||||||
\(591\) | −4.65353 | −0.191421 | ||||||||
\(592\) | 2.72082 | 0.111825 | ||||||||
\(593\) | −28.1286 | −1.15510 | −0.577552 | − | 0.816354i | \(-0.695992\pi\) | ||||
−0.577552 | + | 0.816354i | \(0.695992\pi\) | |||||||
\(594\) | −2.29857 | −0.0943116 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.70475 | 0.274637 | ||||||||
\(597\) | 1.46436 | 0.0599321 | ||||||||
\(598\) | 1.54925 | 0.0633534 | ||||||||
\(599\) | −6.31102 | −0.257861 | −0.128931 | − | 0.991654i | \(-0.541154\pi\) | ||||
−0.128931 | + | 0.991654i | \(0.541154\pi\) | |||||||
\(600\) | −6.65685 | −0.271765 | ||||||||
\(601\) | 27.0450 | 1.10319 | 0.551593 | − | 0.834113i | \(-0.314020\pi\) | ||||
0.551593 | + | 0.834113i | \(0.314020\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.93604 | 0.363904 | ||||||||
\(604\) | 8.13395 | 0.330966 | ||||||||
\(605\) | 19.5176 | 0.793502 | ||||||||
\(606\) | 13.8193 | 0.561371 | ||||||||
\(607\) | 42.1683 | 1.71156 | 0.855778 | − | 0.517343i | \(-0.173079\pi\) | ||||
0.855778 | + | 0.517343i | \(0.173079\pi\) | |||||||
\(608\) | −7.15442 | −0.290150 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.0387831 | −0.00157028 | ||||||||
\(611\) | 0.863361 | 0.0349278 | ||||||||
\(612\) | 2.72082 | 0.109983 | ||||||||
\(613\) | 26.4325 | 1.06760 | 0.533800 | − | 0.845611i | \(-0.320764\pi\) | ||||
0.533800 | + | 0.845611i | \(0.320764\pi\) | |||||||
\(614\) | 32.1239 | 1.29642 | ||||||||
\(615\) | 20.5241 | 0.827610 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.8833 | −1.00176 | −0.500881 | − | 0.865516i | \(-0.666991\pi\) | ||||
−0.500881 | + | 0.865516i | \(0.666991\pi\) | |||||||
\(618\) | 8.86721 | 0.356692 | ||||||||
\(619\) | 34.1496 | 1.37259 | 0.686293 | − | 0.727325i | \(-0.259237\pi\) | ||||
0.686293 | + | 0.727325i | \(0.259237\pi\) | |||||||
\(620\) | 17.5983 | 0.706765 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −29.0571 | −1.16508 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.54925 | −0.0620195 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 1.74174 | 0.0696141 | ||||||||
\(627\) | 16.4450 | 0.656749 | ||||||||
\(628\) | 3.64396 | 0.145410 | ||||||||
\(629\) | 7.40285 | 0.295171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5783 | −0.978446 | −0.489223 | − | 0.872159i | \(-0.662720\pi\) | ||||
−0.489223 | + | 0.872159i | \(0.662720\pi\) | |||||||
\(632\) | −10.4062 | −0.413936 | ||||||||
\(633\) | 12.9075 | 0.513028 | ||||||||
\(634\) | −12.7796 | −0.507543 | ||||||||
\(635\) | 44.3961 | 1.76181 | ||||||||
\(636\) | 3.31796 | 0.131566 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.2861 | −0.882316 | ||||||||
\(639\) | −9.25067 | −0.365951 | ||||||||
\(640\) | −3.41421 | −0.134959 | ||||||||
\(641\) | −27.5998 | −1.09013 | −0.545064 | − | 0.838394i | \(-0.683495\pi\) | ||||
−0.545064 | + | 0.838394i | \(0.683495\pi\) | |||||||
\(642\) | −13.1818 | −0.520246 | ||||||||
\(643\) | −4.81128 | −0.189738 | −0.0948691 | − | 0.995490i | \(-0.530243\pi\) | ||||
−0.0948691 | + | 0.995490i | \(0.530243\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 40.3536 | 1.58892 | ||||||||
\(646\) | −19.4659 | −0.765875 | ||||||||
\(647\) | −32.4514 | −1.27580 | −0.637899 | − | 0.770120i | \(-0.720196\pi\) | ||||
−0.637899 | + | 0.770120i | \(0.720196\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 17.6890 | 0.694353 | ||||||||
\(650\) | 10.3131 | 0.404513 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.5047 | −0.528884 | ||||||||
\(653\) | 11.5192 | 0.450781 | 0.225391 | − | 0.974268i | \(-0.427634\pi\) | ||||
0.225391 | + | 0.974268i | \(0.427634\pi\) | |||||||
\(654\) | −3.76446 | −0.147202 | ||||||||
\(655\) | −52.8535 | −2.06516 | ||||||||
\(656\) | 6.01136 | 0.234704 | ||||||||
\(657\) | 8.09046 | 0.315639 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.2288 | 1.29441 | 0.647205 | − | 0.762316i | \(-0.275938\pi\) | ||||
0.647205 | + | 0.762316i | \(0.275938\pi\) | |||||||
\(660\) | 7.84782 | 0.305476 | ||||||||
\(661\) | 11.6358 | 0.452579 | 0.226290 | − | 0.974060i | \(-0.427340\pi\) | ||||
0.226290 | + | 0.974060i | \(0.427340\pi\) | |||||||
\(662\) | 6.34315 | 0.246533 | ||||||||
\(663\) | −4.21522 | −0.163705 | ||||||||
\(664\) | −1.71279 | −0.0664690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.72082 | 0.105430 | ||||||||
\(667\) | −9.69564 | −0.375417 | ||||||||
\(668\) | −19.6009 | −0.758382 | ||||||||
\(669\) | 14.4293 | 0.557871 | ||||||||
\(670\) | −30.5095 | −1.17869 | ||||||||
\(671\) | 0.0261102 | 0.00100797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.2745 | −0.781526 | −0.390763 | − | 0.920491i | \(-0.627789\pi\) | ||||
−0.390763 | + | 0.920491i | \(0.627789\pi\) | |||||||
\(674\) | 15.8866 | 0.611929 | ||||||||
\(675\) | −6.65685 | −0.256222 | ||||||||
\(676\) | −10.5998 | −0.407686 | ||||||||
\(677\) | 2.87408 | 0.110460 | 0.0552300 | − | 0.998474i | \(-0.482411\pi\) | ||||
0.0552300 | + | 0.998474i | \(0.482411\pi\) | |||||||
\(678\) | 6.15218 | 0.236273 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.28946 | −0.356234 | ||||||||
\(681\) | −14.4133 | −0.552318 | ||||||||
\(682\) | −11.8478 | −0.453676 | ||||||||
\(683\) | 32.5710 | 1.24630 | 0.623148 | − | 0.782104i | \(-0.285853\pi\) | ||||
0.623148 | + | 0.782104i | \(0.285853\pi\) | |||||||
\(684\) | −7.15442 | −0.273556 | ||||||||
\(685\) | 52.7210 | 2.01437 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.26357 | −0.0482081 | ||||||||
\(688\) | 11.8193 | 0.450607 | ||||||||
\(689\) | −5.14034 | −0.195831 | ||||||||
\(690\) | 3.41421 | 0.129977 | ||||||||
\(691\) | −11.8966 | −0.452570 | −0.226285 | − | 0.974061i | \(-0.572658\pi\) | ||||
−0.226285 | + | 0.974061i | \(0.572658\pi\) | |||||||
\(692\) | −14.6317 | −0.556213 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.7699 | −1.09209 | ||||||||
\(695\) | 17.6569 | 0.669763 | ||||||||
\(696\) | 9.69564 | 0.367512 | ||||||||
\(697\) | 16.3558 | 0.619521 | ||||||||
\(698\) | −14.6638 | −0.555033 | ||||||||
\(699\) | 16.7166 | 0.632278 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.0439 | 1.85236 | 0.926181 | − | 0.377080i | \(-0.123072\pi\) | ||||
0.926181 | + | 0.377080i | \(0.123072\pi\) | |||||||
\(702\) | −1.54925 | −0.0584725 | ||||||||
\(703\) | −19.4659 | −0.734170 | ||||||||
\(704\) | 2.29857 | 0.0866307 | ||||||||
\(705\) | 1.90267 | 0.0716586 | ||||||||
\(706\) | 12.6079 | 0.474503 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.69564 | −0.289220 | ||||||||
\(709\) | 40.4789 | 1.52022 | 0.760108 | − | 0.649797i | \(-0.225146\pi\) | ||||
0.760108 | + | 0.649797i | \(0.225146\pi\) | |||||||
\(710\) | 31.5838 | 1.18532 | ||||||||
\(711\) | −10.4062 | −0.390262 | ||||||||
\(712\) | −16.0506 | −0.601521 | ||||||||
\(713\) | −5.15442 | −0.193035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1582 | −0.454691 | ||||||||
\(716\) | −6.28613 | −0.234924 | ||||||||
\(717\) | 22.6923 | 0.847460 | ||||||||
\(718\) | −13.5047 | −0.503990 | ||||||||
\(719\) | 8.70946 | 0.324808 | 0.162404 | − | 0.986724i | \(-0.448075\pi\) | ||||
0.162404 | + | 0.986724i | \(0.448075\pi\) | |||||||
\(720\) | −3.41421 | −0.127240 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 32.1858 | 1.19783 | ||||||||
\(723\) | 20.6705 | 0.768743 | ||||||||
\(724\) | −14.8398 | −0.551516 | ||||||||
\(725\) | −64.5424 | −2.39705 | ||||||||
\(726\) | 5.71656 | 0.212162 | ||||||||
\(727\) | −3.88814 | −0.144203 | −0.0721015 | − | 0.997397i | \(-0.522971\pi\) | ||||
−0.0721015 | + | 0.997397i | \(0.522971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.6226 | −1.02236 | ||||||||
\(731\) | 32.1582 | 1.18941 | ||||||||
\(732\) | −0.0113593 | −0.000419852 0 | ||||||||
\(733\) | 14.0158 | 0.517687 | 0.258844 | − | 0.965919i | \(-0.416659\pi\) | ||||
0.258844 | + | 0.965919i | \(0.416659\pi\) | |||||||
\(734\) | −3.04364 | −0.112343 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 20.5401 | 0.756605 | ||||||||
\(738\) | 6.01136 | 0.221281 | ||||||||
\(739\) | −38.5528 | −1.41819 | −0.709094 | − | 0.705114i | \(-0.750896\pi\) | ||||
−0.709094 | + | 0.705114i | \(0.750896\pi\) | |||||||
\(740\) | −9.28946 | −0.341487 | ||||||||
\(741\) | 11.0840 | 0.407179 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.86605 | −0.0684588 | −0.0342294 | − | 0.999414i | \(-0.510898\pi\) | ||||
−0.0342294 | + | 0.999414i | \(0.510898\pi\) | |||||||
\(744\) | 5.15442 | 0.188970 | ||||||||
\(745\) | −22.8915 | −0.838678 | ||||||||
\(746\) | −37.2752 | −1.36474 | ||||||||
\(747\) | −1.71279 | −0.0626676 | ||||||||
\(748\) | 6.25400 | 0.228669 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.65685 | 0.206559 | ||||||||
\(751\) | 9.90420 | 0.361409 | 0.180705 | − | 0.983537i | \(-0.442162\pi\) | ||||
0.180705 | + | 0.983537i | \(0.442162\pi\) | |||||||
\(752\) | 0.557278 | 0.0203218 | ||||||||
\(753\) | 27.6397 | 1.00725 | ||||||||
\(754\) | −15.0209 | −0.547030 | ||||||||
\(755\) | −27.7710 | −1.01069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.6059 | 1.18508 | 0.592541 | − | 0.805541i | \(-0.298125\pi\) | ||||
0.592541 | + | 0.805541i | \(0.298125\pi\) | |||||||
\(758\) | 22.6720 | 0.823484 | ||||||||
\(759\) | −2.29857 | −0.0834329 | ||||||||
\(760\) | 24.4267 | 0.886051 | ||||||||
\(761\) | −23.8204 | −0.863489 | −0.431744 | − | 0.901996i | \(-0.642102\pi\) | ||||
−0.431744 | + | 0.901996i | \(0.642102\pi\) | |||||||
\(762\) | 13.0033 | 0.471061 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −18.3492 | −0.663849 | ||||||||
\(765\) | −9.28946 | −0.335861 | ||||||||
\(766\) | 11.7278 | 0.423741 | ||||||||
\(767\) | 11.9224 | 0.430494 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −20.8608 | −0.752259 | −0.376130 | − | 0.926567i | \(-0.622745\pi\) | ||||
−0.376130 | + | 0.926567i | \(0.622745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.9383 | −0.429947 | ||||||||
\(772\) | −0.979075 | −0.0352377 | ||||||||
\(773\) | −50.2919 | −1.80887 | −0.904437 | − | 0.426606i | \(-0.859709\pi\) | ||||
−0.904437 | + | 0.426606i | \(0.859709\pi\) | |||||||
\(774\) | 11.8193 | 0.424836 | ||||||||
\(775\) | −34.3122 | −1.23253 | ||||||||
\(776\) | 5.76446 | 0.206932 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.49223 | 0.268609 | ||||||||
\(779\) | −43.0078 | −1.54091 | ||||||||
\(780\) | 5.28946 | 0.189393 | ||||||||
\(781\) | −21.2633 | −0.760862 | ||||||||
\(782\) | 2.72082 | 0.0972963 | ||||||||
\(783\) | 9.69564 | 0.346494 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.4413 | −0.444048 | ||||||||
\(786\) | −15.4804 | −0.552168 | ||||||||
\(787\) | 2.23020 | 0.0794979 | 0.0397490 | − | 0.999210i | \(-0.487344\pi\) | ||||
0.0397490 | + | 0.999210i | \(0.487344\pi\) | |||||||
\(788\) | 4.65353 | 0.165775 | ||||||||
\(789\) | 8.68629 | 0.309240 | ||||||||
\(790\) | 35.5289 | 1.26406 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.29857 | 0.0816762 | ||||||||
\(793\) | 0.0175984 | 0.000624936 0 | ||||||||
\(794\) | 22.3616 | 0.793584 | ||||||||
\(795\) | −11.3282 | −0.401771 | ||||||||
\(796\) | −1.46436 | −0.0519027 | ||||||||
\(797\) | 10.3151 | 0.365379 | 0.182690 | − | 0.983171i | \(-0.441520\pi\) | ||||
0.182690 | + | 0.983171i | \(0.441520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.51625 | 0.0536412 | ||||||||
\(800\) | 6.65685 | 0.235355 | ||||||||
\(801\) | −16.0506 | −0.567120 | ||||||||
\(802\) | −4.09580 | −0.144628 | ||||||||
\(803\) | 18.5965 | 0.656257 | ||||||||
\(804\) | −8.93604 | −0.315150 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.98547 | −0.281276 | ||||||||
\(807\) | −20.6134 | −0.725627 | ||||||||
\(808\) | −13.8193 | −0.486162 | ||||||||
\(809\) | −23.7763 | −0.835929 | −0.417965 | − | 0.908463i | \(-0.637256\pi\) | ||||
−0.417965 | + | 0.908463i | \(0.637256\pi\) | |||||||
\(810\) | −3.41421 | −0.119963 | ||||||||
\(811\) | 7.77627 | 0.273062 | 0.136531 | − | 0.990636i | \(-0.456405\pi\) | ||||
0.136531 | + | 0.990636i | \(0.456405\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.53789 | −0.124079 | ||||||||
\(814\) | 6.25400 | 0.219203 | ||||||||
\(815\) | 46.1078 | 1.61509 | ||||||||
\(816\) | −2.72082 | −0.0952477 | ||||||||
\(817\) | −84.5604 | −2.95839 | ||||||||
\(818\) | −19.5336 | −0.682977 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.5241 | −0.716731 | ||||||||
\(821\) | −31.9557 | −1.11526 | −0.557630 | − | 0.830090i | \(-0.688289\pi\) | ||||
−0.557630 | + | 0.830090i | \(0.688289\pi\) | |||||||
\(822\) | 15.4416 | 0.538589 | ||||||||
\(823\) | −35.1918 | −1.22671 | −0.613354 | − | 0.789808i | \(-0.710180\pi\) | ||||
−0.613354 | + | 0.789808i | \(0.710180\pi\) | |||||||
\(824\) | −8.86721 | −0.308904 | ||||||||
\(825\) | −15.3013 | −0.532722 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.8868 | −1.10881 | −0.554407 | − | 0.832246i | \(-0.687055\pi\) | ||||
−0.554407 | + | 0.832246i | \(0.687055\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 3.80631 | 0.132199 | 0.0660994 | − | 0.997813i | \(-0.478945\pi\) | ||||
0.0660994 | + | 0.997813i | \(0.478945\pi\) | |||||||
\(830\) | 5.84782 | 0.202981 | ||||||||
\(831\) | −24.4898 | −0.849541 | ||||||||
\(832\) | 1.54925 | 0.0537104 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.17157 | 0.179077 | ||||||||
\(835\) | 66.9217 | 2.31592 | ||||||||
\(836\) | −16.4450 | −0.568761 | ||||||||
\(837\) | 5.15442 | 0.178163 | ||||||||
\(838\) | 5.44055 | 0.187941 | ||||||||
\(839\) | −9.29547 | −0.320915 | −0.160458 | − | 0.987043i | \(-0.551297\pi\) | ||||
−0.160458 | + | 0.987043i | \(0.551297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 65.0054 | 2.24156 | ||||||||
\(842\) | 37.5149 | 1.29285 | ||||||||
\(843\) | 10.1582 | 0.349867 | ||||||||
\(844\) | −12.9075 | −0.444295 | ||||||||
\(845\) | 36.1901 | 1.24498 | ||||||||
\(846\) | 0.557278 | 0.0191596 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.31796 | −0.113939 | ||||||||
\(849\) | −16.6042 | −0.569856 | ||||||||
\(850\) | 18.1121 | 0.621240 | ||||||||
\(851\) | 2.72082 | 0.0932685 | ||||||||
\(852\) | 9.25067 | 0.316923 | ||||||||
\(853\) | 23.4213 | 0.801931 | 0.400965 | − | 0.916093i | \(-0.368675\pi\) | ||||
0.400965 | + | 0.916093i | \(0.368675\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.4267 | 0.835377 | ||||||||
\(856\) | 13.1818 | 0.450546 | ||||||||
\(857\) | −14.6467 | −0.500320 | −0.250160 | − | 0.968204i | \(-0.580483\pi\) | ||||
−0.250160 | + | 0.968204i | \(0.580483\pi\) | |||||||
\(858\) | −3.56105 | −0.121572 | ||||||||
\(859\) | −16.0142 | −0.546398 | −0.273199 | − | 0.961958i | \(-0.588082\pi\) | ||||
−0.273199 | + | 0.961958i | \(0.588082\pi\) | |||||||
\(860\) | −40.3536 | −1.37605 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0303 | 0.614113 | ||||||||
\(863\) | −19.9994 | −0.680786 | −0.340393 | − | 0.940283i | \(-0.610560\pi\) | ||||
−0.340393 | + | 0.940283i | \(0.610560\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 49.9557 | 1.69854 | ||||||||
\(866\) | 25.4031 | 0.863232 | ||||||||
\(867\) | 9.59715 | 0.325936 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.9194 | −0.811409 | ||||||||
\(870\) | −33.1030 | −1.12230 | ||||||||
\(871\) | 13.8441 | 0.469090 | ||||||||
\(872\) | 3.76446 | 0.127481 | ||||||||
\(873\) | 5.76446 | 0.195098 | ||||||||
\(874\) | −7.15442 | −0.242002 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.09046 | −0.273351 | ||||||||
\(877\) | 20.5613 | 0.694306 | 0.347153 | − | 0.937808i | \(-0.387148\pi\) | ||||
0.347153 | + | 0.937808i | \(0.387148\pi\) | |||||||
\(878\) | 4.19205 | 0.141475 | ||||||||
\(879\) | 24.9737 | 0.842343 | ||||||||
\(880\) | −7.84782 | −0.264550 | ||||||||
\(881\) | 57.6246 | 1.94142 | 0.970712 | − | 0.240247i | \(-0.0772285\pi\) | ||||
0.970712 | + | 0.240247i | \(0.0772285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3701 | 0.584550 | 0.292275 | − | 0.956334i | \(-0.405588\pi\) | ||||
0.292275 | + | 0.956334i | \(0.405588\pi\) | |||||||
\(884\) | 4.21522 | 0.141773 | ||||||||
\(885\) | 26.2745 | 0.883209 | ||||||||
\(886\) | −24.0836 | −0.809104 | ||||||||
\(887\) | 35.3772 | 1.18785 | 0.593925 | − | 0.804520i | \(-0.297578\pi\) | ||||
0.593925 | + | 0.804520i | \(0.297578\pi\) | |||||||
\(888\) | −2.72082 | −0.0913047 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 54.8001 | 1.83691 | ||||||||
\(891\) | 2.29857 | 0.0770051 | ||||||||
\(892\) | −14.4293 | −0.483130 | ||||||||
\(893\) | −3.98700 | −0.133420 | ||||||||
\(894\) | −6.70475 | −0.224241 | ||||||||
\(895\) | 21.4622 | 0.717402 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.54925 | −0.0517278 | ||||||||
\(898\) | 5.89262 | 0.196639 | ||||||||
\(899\) | 49.9754 | 1.66677 | ||||||||
\(900\) | 6.65685 | 0.221895 | ||||||||
\(901\) | −9.02758 | −0.300752 | ||||||||
\(902\) | 13.8175 | 0.460074 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.15218 | −0.204619 | ||||||||
\(905\) | 50.6662 | 1.68420 | ||||||||
\(906\) | −8.13395 | −0.270232 | ||||||||
\(907\) | 55.0175 | 1.82682 | 0.913412 | − | 0.407036i | \(-0.133438\pi\) | ||||
0.913412 | + | 0.407036i | \(0.133438\pi\) | |||||||
\(908\) | 14.4133 | 0.478322 | ||||||||
\(909\) | −13.8193 | −0.458358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.43376 | −0.246291 | −0.123146 | − | 0.992389i | \(-0.539298\pi\) | ||||
−0.123146 | + | 0.992389i | \(0.539298\pi\) | |||||||
\(912\) | 7.15442 | 0.236907 | ||||||||
\(913\) | −3.93696 | −0.130295 | ||||||||
\(914\) | −9.40285 | −0.311019 | ||||||||
\(915\) | 0.0387831 | 0.00128213 | ||||||||
\(916\) | 1.26357 | 0.0417494 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.72082 | −0.0898004 | ||||||||
\(919\) | −18.5159 | −0.610782 | −0.305391 | − | 0.952227i | \(-0.598787\pi\) | ||||
−0.305391 | + | 0.952227i | \(0.598787\pi\) | |||||||
\(920\) | −3.41421 | −0.112563 | ||||||||
\(921\) | −32.1239 | −1.05852 | ||||||||
\(922\) | −13.5720 | −0.446969 | ||||||||
\(923\) | −14.3316 | −0.471729 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.1121 | 0.595522 | ||||||||
\(926\) | 32.7759 | 1.07708 | ||||||||
\(927\) | −8.86721 | −0.291237 | ||||||||
\(928\) | −9.69564 | −0.318275 | ||||||||
\(929\) | 9.62943 | 0.315931 | 0.157966 | − | 0.987445i | \(-0.449506\pi\) | ||||
0.157966 | + | 0.987445i | \(0.449506\pi\) | |||||||
\(930\) | −17.5983 | −0.577071 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.7166 | −0.547569 | ||||||||
\(933\) | 29.0571 | 0.951286 | ||||||||
\(934\) | −1.53789 | −0.0503212 | ||||||||
\(935\) | −21.3525 | −0.698301 | ||||||||
\(936\) | 1.54925 | 0.0506387 | ||||||||
\(937\) | 23.5568 | 0.769567 | 0.384784 | − | 0.923007i | \(-0.374276\pi\) | ||||
0.384784 | + | 0.923007i | \(0.374276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.74174 | −0.0568397 | ||||||||
\(940\) | −1.90267 | −0.0620581 | ||||||||
\(941\) | −29.3496 | −0.956771 | −0.478386 | − | 0.878150i | \(-0.658778\pi\) | ||||
−0.478386 | + | 0.878150i | \(0.658778\pi\) | |||||||
\(942\) | −3.64396 | −0.118727 | ||||||||
\(943\) | 6.01136 | 0.195757 | ||||||||
\(944\) | 7.69564 | 0.250472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.1675 | 0.883293 | ||||||||
\(947\) | 23.1615 | 0.752649 | 0.376324 | − | 0.926488i | \(-0.377188\pi\) | ||||
0.376324 | + | 0.926488i | \(0.377188\pi\) | |||||||
\(948\) | 10.4062 | 0.337977 | ||||||||
\(949\) | 12.5341 | 0.406874 | ||||||||
\(950\) | −47.6260 | −1.54519 | ||||||||
\(951\) | 12.7796 | 0.414407 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.2573 | 0.494233 | 0.247117 | − | 0.968986i | \(-0.420517\pi\) | ||||
0.247117 | + | 0.968986i | \(0.420517\pi\) | |||||||
\(954\) | −3.31796 | −0.107423 | ||||||||
\(955\) | 62.6480 | 2.02724 | ||||||||
\(956\) | −22.6923 | −0.733922 | ||||||||
\(957\) | 22.2861 | 0.720408 | ||||||||
\(958\) | 25.6547 | 0.828865 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.41421 | 0.110193 | ||||||||
\(961\) | −4.43192 | −0.142965 | ||||||||
\(962\) | 4.21522 | 0.135904 | ||||||||
\(963\) | 13.1818 | 0.424779 | ||||||||
\(964\) | −20.6705 | −0.665751 | ||||||||
\(965\) | 3.34277 | 0.107608 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.9247 | −0.705052 | −0.352526 | − | 0.935802i | \(-0.614677\pi\) | ||||
−0.352526 | + | 0.935802i | \(0.614677\pi\) | |||||||
\(968\) | −5.71656 | −0.183737 | ||||||||
\(969\) | 19.4659 | 0.625334 | ||||||||
\(970\) | −19.6811 | −0.631922 | ||||||||
\(971\) | −17.3574 | −0.557026 | −0.278513 | − | 0.960432i | \(-0.589842\pi\) | ||||
−0.278513 | + | 0.960432i | \(0.589842\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.8151 | −0.570831 | ||||||||
\(975\) | −10.3131 | −0.330284 | ||||||||
\(976\) | 0.0113593 | 0.000363602 0 | ||||||||
\(977\) | 32.8263 | 1.05021 | 0.525103 | − | 0.851039i | \(-0.324027\pi\) | ||||
0.525103 | + | 0.851039i | \(0.324027\pi\) | |||||||
\(978\) | 13.5047 | 0.431832 | ||||||||
\(979\) | −36.8935 | −1.17912 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.76446 | 0.120190 | ||||||||
\(982\) | −39.3973 | −1.25722 | ||||||||
\(983\) | 34.4371 | 1.09837 | 0.549186 | − | 0.835700i | \(-0.314938\pi\) | ||||
0.549186 | + | 0.835700i | \(0.314938\pi\) | |||||||
\(984\) | −6.01136 | −0.191635 | ||||||||
\(985\) | −15.8881 | −0.506238 | ||||||||
\(986\) | −26.3801 | −0.840113 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.0840 | −0.352628 | ||||||||
\(989\) | 11.8193 | 0.375832 | ||||||||
\(990\) | −7.84782 | −0.249420 | ||||||||
\(991\) | 18.9045 | 0.600520 | 0.300260 | − | 0.953857i | \(-0.402927\pi\) | ||||
0.300260 | + | 0.953857i | \(0.402927\pi\) | |||||||
\(992\) | −5.15442 | −0.163653 | ||||||||
\(993\) | −6.34315 | −0.201294 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.99962 | 0.158499 | ||||||||
\(996\) | 1.71279 | 0.0542717 | ||||||||
\(997\) | −15.4989 | −0.490855 | −0.245427 | − | 0.969415i | \(-0.578928\pi\) | ||||
−0.245427 | + | 0.969415i | \(0.578928\pi\) | |||||||
\(998\) | 20.2297 | 0.640361 | ||||||||
\(999\) | −2.72082 | −0.0860829 |
(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 | 6762.2.a.ci.1.2 | ✓ | 4 | |
7.6 | odd | 2 | 6762.2.a.ct.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.ci.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6762.2.a.ct.1.4 | yes | 4 | 7.6 | odd | 2 |