Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1064,2,Mod(1,1064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1064, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1064.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.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: | \(8.49608277506\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1064.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.61803 | 1.51152 | 0.755761 | − | 0.654847i | \(-0.227267\pi\) | ||||
0.755761 | + | 0.654847i | \(0.227267\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.85410 | −1.76508 | −0.882539 | − | 0.470239i | \(-0.844168\pi\) | ||||
−0.882539 | + | 0.470239i | \(0.844168\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.23607 | 1.45222 | 0.726112 | − | 0.687576i | \(-0.241325\pi\) | ||||
0.726112 | + | 0.687576i | \(0.241325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.47214 | 2.44569 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.47214 | −0.599581 | −0.299791 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.61803 | 0.571302 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.70820 | −1.19024 | −0.595121 | − | 0.803636i | \(-0.702896\pi\) | ||||
−0.595121 | + | 0.803636i | \(0.702896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.09017 | 1.61803 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.854102 | −0.158603 | −0.0793014 | − | 0.996851i | \(-0.525269\pi\) | ||||
−0.0793014 | + | 0.996851i | \(0.525269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47214 | 0.803219 | 0.401610 | − | 0.915811i | \(-0.368451\pi\) | ||||
0.401610 | + | 0.915811i | \(0.368451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.3262 | −2.66796 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.61803 | 0.611559 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0901699 | −0.0148238 | −0.00741192 | − | 0.999973i | \(-0.502359\pi\) | ||||
−0.00741192 | + | 0.999973i | \(0.502359\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.7082 | 2.19507 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.09017 | −0.951125 | −0.475562 | − | 0.879682i | \(-0.657755\pi\) | ||||
−0.475562 | + | 0.879682i | \(0.657755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.85410 | 1.04524 | 0.522620 | − | 0.852566i | \(-0.324955\pi\) | ||||
0.522620 | + | 0.852566i | \(0.324955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.9443 | 2.07869 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.8541 | −1.72910 | −0.864549 | − | 0.502548i | \(-0.832396\pi\) | ||||
−0.864549 | + | 0.502548i | \(0.832396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.47214 | −0.906280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.38197 | −0.464549 | −0.232274 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232274 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.1803 | −2.85596 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.61803 | −0.346767 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.09017 | 0.532495 | 0.266247 | − | 0.963905i | \(-0.414216\pi\) | ||||
0.266247 | + | 0.963905i | \(0.414216\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.85410 | −1.00561 | −0.502807 | − | 0.864398i | \(-0.667699\pi\) | ||||
−0.502807 | + | 0.864398i | \(0.667699\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.85410 | 0.485571 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.9443 | 2.34975 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9443 | −1.82573 | −0.912867 | − | 0.408258i | \(-0.866136\pi\) | ||||
−0.912867 | + | 0.408258i | \(0.866136\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.9443 | −1.79908 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5623 | 1.60955 | 0.804775 | − | 0.593580i | \(-0.202286\pi\) | ||||
0.804775 | + | 0.593580i | \(0.202286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.76393 | 1.02574 | 0.512870 | − | 0.858466i | \(-0.328582\pi\) | ||||
0.512870 | + | 0.858466i | \(0.328582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 21.1803 | 2.44569 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.85410 | −0.667137 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.85410 | −0.771147 | −0.385573 | − | 0.922677i | \(-0.625996\pi\) | ||||
−0.385573 | + | 0.922677i | \(0.625996\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.94427 | −0.970143 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.23607 | −0.239732 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.09017 | 0.115558 | 0.0577789 | − | 0.998329i | \(-0.481598\pi\) | ||||
0.0577789 | + | 0.998329i | \(0.481598\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.23607 | 0.548889 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.7082 | 1.21408 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.61803 | −0.371202 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.56231 | −0.361697 | −0.180849 | − | 0.983511i | \(-0.557884\pi\) | ||||
−0.180849 | + | 0.983511i | \(0.557884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.5623 | −2.26760 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9443 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7082 | 1.35071 | 0.675355 | − | 0.737493i | \(-0.263991\pi\) | ||||
0.675355 | + | 0.737493i | \(0.263991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.47214 | 0.924386 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.1803 | 1.17752 | 0.588759 | − | 0.808309i | \(-0.299617\pi\) | ||||
0.588759 | + | 0.808309i | \(0.299617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.56231 | 0.915903 | 0.457951 | − | 0.888977i | \(-0.348583\pi\) | ||||
0.457951 | + | 0.888977i | \(0.348583\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.236068 | −0.0224066 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.9443 | 1.59398 | 0.796992 | − | 0.603991i | \(-0.206424\pi\) | ||||
0.796992 | + | 0.603991i | \(0.206424\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.6525 | −1.92585 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.1803 | 1.86567 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.47214 | −0.226620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.2705 | 2.11550 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.9443 | −1.43765 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.14590 | 0.190418 | 0.0952088 | − | 0.995457i | \(-0.469648\pi\) | ||||
0.0952088 | + | 0.995457i | \(0.469648\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.9443 | 1.57991 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.1803 | −1.93791 | −0.968953 | − | 0.247246i | \(-0.920474\pi\) | ||||
−0.968953 | + | 0.247246i | \(0.920474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.09017 | 0.696291 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.5623 | 1.58588 | 0.792942 | − | 0.609297i | \(-0.208548\pi\) | ||||
0.792942 | + | 0.609297i | \(0.208548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.47214 | −0.209684 | −0.104842 | − | 0.994489i | \(-0.533434\pi\) | ||||
−0.104842 | + | 0.994489i | \(0.533434\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.0344 | −2.61357 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.6525 | −2.56329 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.09017 | −0.256625 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.61803 | 0.215932 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.94427 | −0.732743 | −0.366372 | − | 0.930469i | \(-0.619400\pi\) | ||||
−0.366372 | + | 0.930469i | \(0.619400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.52786 | −0.770282 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.1803 | 1.29964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6180 | 1.48588 | 0.742940 | − | 0.669358i | \(-0.233431\pi\) | ||||
0.742940 | + | 0.669358i | \(0.233431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.85410 | −0.702176 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.70820 | −0.449869 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.56231 | 0.122369 | 0.0611846 | − | 0.998126i | \(-0.480512\pi\) | ||||
0.0611846 | + | 0.998126i | \(0.480512\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −55.4508 | −4.31684 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.85410 | −0.294731 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.180340 | 0.0137110 | 0.00685549 | − | 0.999977i | \(-0.497818\pi\) | ||||
0.00685549 | + | 0.999977i | \(0.497818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.09017 | 0.611559 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.7082 | 0.804878 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.1246 | 1.57893 | 0.789464 | − | 0.613797i | \(-0.210359\pi\) | ||||
0.789464 | + | 0.613797i | \(0.210359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.23607 | −0.537853 | −0.268926 | − | 0.963161i | \(-0.586669\pi\) | ||||
−0.268926 | + | 0.963161i | \(0.586669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5623 | −1.52001 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.326238 | −0.0239855 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.4721 | 1.05831 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.23607 | 0.162650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.70820 | 0.123601 | 0.0618006 | − | 0.998089i | \(-0.480316\pi\) | ||||
0.0618006 | + | 0.998089i | \(0.480316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.23607 | 0.520864 | 0.260432 | − | 0.965492i | \(-0.416135\pi\) | ||||
0.260432 | + | 0.965492i | \(0.416135\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 49.5967 | 3.55170 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.03444 | 0.0733296 | 0.0366648 | − | 0.999328i | \(-0.488327\pi\) | ||||
0.0366648 | + | 0.999328i | \(0.488327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39.1246 | −2.75964 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.854102 | −0.0599462 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.0344 | −1.53895 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.0000 | −1.52911 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.85410 | 0.404937 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8885 | −0.956127 | −0.478063 | − | 0.878325i | \(-0.658661\pi\) | ||||
−0.478063 | + | 0.878325i | \(0.658661\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 35.5066 | 2.43287 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.7984 | 1.69124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.47214 | 0.303588 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.9443 | 1.55043 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.9443 | −0.870726 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.18034 | 0.146006 | 0.0730032 | − | 0.997332i | \(-0.476742\pi\) | ||||
0.0730032 | + | 0.997332i | \(0.476742\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 31.1803 | 2.07869 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9443 | −0.859142 | −0.429571 | − | 0.903033i | \(-0.641335\pi\) | ||||
−0.429571 | + | 0.903033i | \(0.641335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.32624 | −0.616295 | −0.308148 | − | 0.951339i | \(-0.599709\pi\) | ||||
−0.308148 | + | 0.951339i | \(0.599709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.3262 | −1.00839 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1459 | −0.664680 | −0.332340 | − | 0.943160i | \(-0.607838\pi\) | ||||
−0.332340 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −42.8885 | −2.79774 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.9443 | −1.16561 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.29180 | −0.536352 | −0.268176 | − | 0.963370i | \(-0.586421\pi\) | ||||
−0.268176 | + | 0.963370i | \(0.586421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.56231 | 0.293884 | 0.146942 | − | 0.989145i | \(-0.453057\pi\) | ||||
0.146942 | + | 0.989145i | \(0.453057\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6525 | −1.38901 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.61803 | 0.231148 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.23607 | −0.333163 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.4721 | 0.663645 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.2361 | 1.84536 | 0.922682 | − | 0.385562i | \(-0.125992\pi\) | ||||
0.922682 | + | 0.385562i | \(0.125992\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.4164 | 2.10087 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.4164 | −1.46639 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.67376 | −0.166785 | −0.0833923 | − | 0.996517i | \(-0.526575\pi\) | ||||
−0.0833923 | + | 0.996517i | \(0.526575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0901699 | −0.00560289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.29180 | −0.203757 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.2361 | −1.55612 | −0.778061 | − | 0.628188i | \(-0.783797\pi\) | ||||
−0.778061 | + | 0.628188i | \(0.783797\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2361 | −0.751656 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.85410 | 0.174668 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.4164 | −1.79355 | −0.896775 | − | 0.442487i | \(-0.854096\pi\) | ||||
−0.896775 | + | 0.442487i | \(0.854096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8541 | 1.02381 | 0.511907 | − | 0.859041i | \(-0.328939\pi\) | ||||
0.511907 | + | 0.859041i | \(0.328939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.7082 | 0.829658 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −47.3607 | −2.85596 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2918 | −1.09905 | −0.549524 | − | 0.835478i | \(-0.685191\pi\) | ||||
−0.549524 | + | 0.835478i | \(0.685191\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.2361 | 1.03190 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.8885 | −1.06714 | −0.533571 | − | 0.845756i | \(-0.679150\pi\) | ||||
−0.533571 | + | 0.845756i | \(0.679150\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.52786 | 0.328597 | 0.164299 | − | 0.986411i | \(-0.447464\pi\) | ||||
0.164299 | + | 0.986411i | \(0.447464\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.47214 | −0.561081 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.09017 | −0.359491 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.32624 | −0.546714 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.23607 | 0.305894 | 0.152947 | − | 0.988234i | \(-0.451124\pi\) | ||||
0.152947 | + | 0.988234i | \(0.451124\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7984 | 0.861595 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.0902 | −0.759569 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.8885 | −1.72850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.85410 | 0.395064 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.6525 | −1.64604 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.4164 | −1.62712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.90983 | 0.223146 | 0.111573 | − | 0.993756i | \(-0.464411\pi\) | ||||
0.111573 | + | 0.993756i | \(0.464411\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.8885 | 2.04163 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.4508 | 1.44319 | 0.721593 | − | 0.692318i | \(-0.243410\pi\) | ||||
0.721593 | + | 0.692318i | \(0.243410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.00000 | −0.452187 | −0.226093 | − | 0.974106i | \(-0.572595\pi\) | ||||
−0.226093 | + | 0.974106i | \(0.572595\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.9443 | 0.785671 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.67376 | −0.431001 | −0.215501 | − | 0.976504i | \(-0.569138\pi\) | ||||
−0.215501 | + | 0.976504i | \(0.569138\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.8885 | 1.77984 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.47214 | 0.137553 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42.3607 | 2.34975 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.0344 | 1.38441 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.8541 | −0.653538 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.3050 | −1.50082 | −0.750408 | − | 0.660975i | \(-0.770143\pi\) | ||||
−0.750408 | + | 0.660975i | \(0.770143\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.347524 | −0.0190442 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −54.0689 | −2.95410 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.23607 | −0.503121 | −0.251560 | − | 0.967842i | \(-0.580944\pi\) | ||||
−0.251560 | + | 0.967842i | \(0.580944\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 44.3607 | 2.40934 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.1803 | −1.41774 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −54.0689 | −2.91097 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.47214 | −0.132711 | −0.0663556 | − | 0.997796i | \(-0.521137\pi\) | ||||
−0.0663556 | + | 0.997796i | \(0.521137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.8885 | −0.850494 | −0.425247 | − | 0.905077i | \(-0.639813\pi\) | ||||
−0.425247 | + | 0.905077i | \(0.639813\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.7082 | 0.624938 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.3607 | −1.29659 | −0.648294 | − | 0.761390i | \(-0.724517\pi\) | ||||
−0.648294 | + | 0.761390i | \(0.724517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.0689 | 2.60431 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.47214 | −0.342542 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.7639 | −0.673655 | −0.336827 | − | 0.941566i | \(-0.609354\pi\) | ||||
−0.336827 | + | 0.941566i | \(0.609354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 60.9230 | 3.19763 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.7082 | 1.65968 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.67376 | 0.296168 | 0.148084 | − | 0.988975i | \(-0.452689\pi\) | ||||
0.148084 | + | 0.988975i | \(0.452689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.4721 | −1.22191 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.38197 | −0.175583 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.03444 | 0.467786 | 0.233893 | − | 0.972262i | \(-0.424854\pi\) | ||||
0.233893 | + | 0.972262i | \(0.424854\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.2705 | 1.51152 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.47214 | −0.230327 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.1246 | 1.80423 | 0.902115 | − | 0.431496i | \(-0.142014\pi\) | ||||
0.902115 | + | 0.431496i | \(0.142014\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.61803 | 0.287821 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.0689 | 1.33206 | 0.666029 | − | 0.745926i | \(-0.267993\pi\) | ||||
0.666029 | + | 0.745926i | \(0.267993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.1803 | −1.07945 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.4164 | 1.34282 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.3607 | 1.53935 | 0.769674 | − | 0.638437i | \(-0.220419\pi\) | ||||
0.769674 | + | 0.638437i | \(0.220419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.1115 | 0.713647 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −58.0689 | −2.92919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.7984 | −1.24774 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.5066 | 1.83221 | 0.916106 | − | 0.400935i | \(-0.131315\pi\) | ||||
0.916106 | + | 0.400935i | \(0.131315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.61803 | −0.131066 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.88854 | 0.493810 | 0.246905 | − | 0.969040i | \(-0.420586\pi\) | ||||
0.246905 | + | 0.969040i | \(0.420586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.4164 | 1.16645 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.6525 | −1.02623 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.527864 | 0.0261652 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.09017 | −0.449480 | −0.224740 | − | 0.974419i | \(-0.572153\pi\) | ||||
−0.224740 | + | 0.974419i | \(0.572153\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 48.5967 | 2.39710 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.09017 | 0.201264 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.4721 | 0.710409 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.47214 | −0.316942 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.4721 | 1.39095 | 0.695477 | − | 0.718548i | \(-0.255193\pi\) | ||||
0.695477 | + | 0.718548i | \(0.255193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.4721 | −0.997751 | −0.498875 | − | 0.866674i | \(-0.666253\pi\) | ||||
−0.498875 | + | 0.866674i | \(0.666253\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −45.6869 | −2.22137 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.0000 | −0.970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.85410 | −0.380087 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −80.2492 | −3.87447 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.0902 | −1.11221 | −0.556107 | − | 0.831111i | \(-0.687706\pi\) | ||||
−0.556107 | + | 0.831111i | \(0.687706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2705 | −0.878025 | −0.439012 | − | 0.898481i | \(-0.644672\pi\) | ||||
−0.439012 | + | 0.898481i | \(0.644672\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.09017 | −0.387894 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.70820 | 0.273060 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3050 | −1.11228 | −0.556142 | − | 0.831087i | \(-0.687719\pi\) | ||||
−0.556142 | + | 0.831087i | \(0.687719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.85410 | 0.183529 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.27051 | −0.297921 | −0.148960 | − | 0.988843i | \(-0.547593\pi\) | ||||
−0.148960 | + | 0.988843i | \(0.547593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.94427 | 0.186976 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.4164 | −1.10756 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.1803 | 1.23553 | 0.617763 | − | 0.786364i | \(-0.288039\pi\) | ||||
0.617763 | + | 0.786364i | \(0.288039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.6525 | 1.67881 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −52.3607 | −2.46012 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.9443 | 0.888121 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2705 | 1.36922 | 0.684608 | − | 0.728911i | \(-0.259973\pi\) | ||||
0.684608 | + | 0.728911i | \(0.259973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.52786 | −0.258019 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.0344 | 1.21254 | 0.606272 | − | 0.795257i | \(-0.292664\pi\) | ||||
0.606272 | + | 0.795257i | \(0.292664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.23607 | 0.243341 | 0.121670 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121670 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.3607 | 1.96443 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.18034 | −0.193443 | −0.0967215 | − | 0.995311i | \(-0.530836\pi\) | ||||
−0.0967215 | + | 0.995311i | \(0.530836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.9443 | −0.690062 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.7426 | 2.24594 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.1246 | −1.84493 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.09017 | −0.371202 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.0344 | −0.596806 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.3951 | −1.70863 | −0.854313 | − | 0.519758i | \(-0.826022\pi\) | ||||
−0.854313 | + | 0.519758i | \(0.826022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.472136 | −0.0215275 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.9443 | −0.679988 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.8885 | −0.585239 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1459 | 0.776955 | 0.388477 | − | 0.921458i | \(-0.373001\pi\) | ||||
0.388477 | + | 0.921458i | \(0.373001\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.09017 | 0.184964 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.88854 | −0.265746 | −0.132873 | − | 0.991133i | \(-0.542420\pi\) | ||||
−0.132873 | + | 0.991133i | \(0.542420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.11146 | 0.0950952 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −81.6312 | −3.66905 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.5623 | 0.608353 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.0344 | 1.38929 | 0.694646 | − | 0.719352i | \(-0.255561\pi\) | ||||
0.694646 | + | 0.719352i | \(0.255561\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.23607 | −0.233930 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.14590 | −0.318620 | −0.159310 | − | 0.987229i | \(-0.550927\pi\) | ||||
−0.159310 | + | 0.987229i | \(0.550927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.5967 | −1.76203 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.7426 | 1.67621 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.76393 | 0.211158 | 0.105579 | − | 0.994411i | \(-0.466330\pi\) | ||||
0.105579 | + | 0.994411i | \(0.466330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.76393 | 0.387694 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.23607 | −0.0987248 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 49.5967 | 2.18549 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 69.3951 | 3.05199 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.472136 | 0.0207245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.3050 | 1.02101 | 0.510504 | − | 0.859875i | \(-0.329459\pi\) | ||||
0.510504 | + | 0.859875i | \(0.329459\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.8885 | 1.48184 | 0.740921 | − | 0.671592i | \(-0.234389\pi\) | ||||
0.740921 | + | 0.671592i | \(0.234389\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.1803 | 0.924386 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.0557 | −0.481595 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.7639 | 0.684096 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.8885 | −1.38125 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 44.0689 | 1.90526 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 55.3050 | 2.38658 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.85410 | −0.252154 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.7082 | 0.589362 | 0.294681 | − | 0.955596i | \(-0.404787\pi\) | ||||
0.294681 | + | 0.955596i | \(0.404787\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.9443 | −0.812977 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.5967 | 1.48196 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.7082 | −1.09920 | −0.549602 | − | 0.835427i | \(-0.685221\pi\) | ||||
−0.549602 | + | 0.835427i | \(0.685221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.2705 | −1.29191 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.854102 | 0.0363860 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.85410 | −0.291466 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.854102 | −0.0362546 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.81966 | 0.0771015 | 0.0385507 | − | 0.999257i | \(-0.487726\pi\) | ||||
0.0385507 | + | 0.999257i | \(0.487726\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.8885 | 1.51792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 37.8885 | 1.59966 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.7984 | 0.876547 | 0.438273 | − | 0.898842i | \(-0.355590\pi\) | ||||
0.438273 | + | 0.898842i | \(0.355590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.3050 | 2.57912 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.70820 | −0.239722 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.7082 | 0.574678 | 0.287339 | − | 0.957829i | \(-0.407229\pi\) | ||||
0.287339 | + | 0.957829i | \(0.407229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.2148 | 1.43184 | 0.715922 | − | 0.698180i | \(-0.246007\pi\) | ||||
0.715922 | + | 0.698180i | \(0.246007\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.47214 | 0.186826 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46.1803 | −1.92585 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.9443 | −0.788660 | −0.394330 | − | 0.918969i | \(-0.629023\pi\) | ||||
−0.394330 | + | 0.918969i | \(0.629023\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.9443 | 0.787297 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00000 | 0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.7984 | 0.819965 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 73.0132 | 3.01872 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1246 | 0.871906 | 0.435953 | − | 0.899969i | \(-0.356411\pi\) | ||||
0.435953 | + | 0.899969i | \(0.356411\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.47214 | −0.184271 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 47.1246 | 1.93845 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.1246 | −0.538963 | −0.269482 | − | 0.963006i | \(-0.586852\pi\) | ||||
−0.269482 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.94427 | −0.366679 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.70820 | 0.110839 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.7984 | −1.74869 | −0.874347 | − | 0.485301i | \(-0.838710\pi\) | ||||
−0.874347 | + | 0.485301i | \(0.838710\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.88854 | 0.321780 | 0.160890 | − | 0.986972i | \(-0.448563\pi\) | ||||
0.160890 | + | 0.986972i | \(0.448563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −57.5967 | −2.34552 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 84.1935 | 3.42295 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.23607 | 0.374880 | 0.187440 | − | 0.982276i | \(-0.439981\pi\) | ||||
0.187440 | + | 0.982276i | \(0.439981\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.23607 | −0.0906100 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.0689 | −2.51104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.9443 | 0.684373 | 0.342186 | − | 0.939632i | \(-0.388833\pi\) | ||||
0.342186 | + | 0.939632i | \(0.388833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −57.6869 | −2.32616 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.9098 | 1.28464 | 0.642321 | − | 0.766436i | \(-0.277972\pi\) | ||||
0.642321 | + | 0.766436i | \(0.277972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.2918 | 0.735209 | 0.367605 | − | 0.929982i | \(-0.380178\pi\) | ||||
0.367605 | + | 0.929982i | \(0.380178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.7639 | −0.512199 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.09017 | 0.0436767 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.3262 | 0.612071 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.222912 | 0.00888810 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.3607 | 1.60673 | 0.803367 | − | 0.595485i | \(-0.203040\pi\) | ||||
0.803367 | + | 0.595485i | \(0.203040\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −36.3607 | −1.44521 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.76393 | 0.308102 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.23607 | 0.207461 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 52.2705 | 2.06779 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.6525 | −0.894719 | −0.447360 | − | 0.894354i | \(-0.647636\pi\) | ||||
−0.447360 | + | 0.894354i | \(0.647636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.5279 | 1.47995 | 0.739977 | − | 0.672632i | \(-0.234836\pi\) | ||||
0.739977 | + | 0.672632i | \(0.234836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 64.9230 | 2.55634 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.2705 | −0.796916 | −0.398458 | − | 0.917187i | \(-0.630455\pi\) | ||||
−0.398458 | + | 0.917187i | \(0.630455\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.9443 | −0.939895 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.7082 | 0.458881 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.6525 | −1.27779 | −0.638895 | − | 0.769294i | \(-0.720608\pi\) | ||||
−0.638895 | + | 0.769294i | \(0.720608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −80.2492 | −3.13560 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.7771 | 1.31777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.94427 | −0.348419 | −0.174210 | − | 0.984709i | \(-0.555737\pi\) | ||||
−0.174210 | + | 0.984709i | \(0.555737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.8328 | −0.654721 | −0.327360 | − | 0.944900i | \(-0.606159\pi\) | ||||
−0.327360 | + | 0.944900i | \(0.606159\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.8885 | −1.31612 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.61803 | −0.140301 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.87539 | 0.188776 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.70820 | 0.220692 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.9787 | 1.77499 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.2361 | −0.972779 | −0.486389 | − | 0.873742i | \(-0.661686\pi\) | ||||
−0.486389 | + | 0.873742i | \(0.661686\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0902 | 0.696291 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.56231 | −0.136709 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.8885 | −1.29861 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.8885 | 0.914070 | 0.457035 | − | 0.889449i | \(-0.348911\pi\) | ||||
0.457035 | + | 0.889449i | \(0.348911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 67.1591 | 2.56602 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.4164 | −0.931544 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.7082 | −0.674629 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.6525 | −1.47041 | −0.735205 | − | 0.677845i | \(-0.762914\pi\) | ||||
−0.735205 | + | 0.677845i | \(0.762914\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.5623 | −0.857071 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.94427 | −0.339276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0557 | 0.570276 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.5623 | −1.00468 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.2361 | 1.48193 | 0.740963 | − | 0.671546i | \(-0.234369\pi\) | ||||
0.740963 | + | 0.671546i | \(0.234369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0901699 | 0.00340082 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −112.284 | −4.22885 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9443 | −0.411602 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.1803 | 0.682777 | 0.341388 | − | 0.939922i | \(-0.389103\pi\) | ||||
0.341388 | + | 0.939922i | \(0.389103\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.4164 | −0.990693 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.5279 | −0.956026 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −110.902 | −4.14749 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.7082 | −0.810708 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.8885 | 0.965480 | 0.482740 | − | 0.875764i | \(-0.339642\pi\) | ||||
0.482740 | + | 0.875764i | \(0.339642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.7082 | 0.510520 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.9443 | 0.444212 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.90983 | −0.256625 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5623 | 0.577174 | 0.288587 | − | 0.957454i | \(-0.406815\pi\) | ||||
0.288587 | + | 0.957454i | \(0.406815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.9443 | −0.626707 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4377 | −1.01343 | −0.506717 | − | 0.862112i | \(-0.669141\pi\) | ||||
−0.506717 | + | 0.862112i | \(0.669141\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.47214 | 0.349385 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 87.4853 | 3.22256 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.5623 | −1.19782 | −0.598912 | − | 0.800815i | \(-0.704400\pi\) | ||||
−0.598912 | + | 0.800815i | \(0.704400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.7082 | −0.503583 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.79837 | 0.139349 | 0.0696744 | − | 0.997570i | \(-0.477804\pi\) | ||||
0.0696744 | + | 0.997570i | \(0.477804\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.3607 | −1.18560 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.4164 | 0.564057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.1803 | 0.445060 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.9098 | 0.507577 | 0.253788 | − | 0.967260i | \(-0.418323\pi\) | ||||
0.253788 | + | 0.967260i | \(0.418323\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 76.5410 | 2.78931 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72.3607 | −2.63347 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.5279 | 0.782444 | 0.391222 | − | 0.920296i | \(-0.372053\pi\) | ||||
0.391222 | + | 0.920296i | \(0.372053\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 87.4853 | 3.17551 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.9443 | −0.396730 | −0.198365 | − | 0.980128i | \(-0.563563\pi\) | ||||
−0.198365 | + | 0.980128i | \(0.563563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.56231 | 0.346179 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −34.4721 | −1.24634 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.4164 | 0.773302 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.6525 | 1.10536 | 0.552678 | − | 0.833395i | \(-0.313606\pi\) | ||||
0.552678 | + | 0.833395i | \(0.313606\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.00000 | −0.252099 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.7082 | −1.35627 | −0.678135 | − | 0.734937i | \(-0.737211\pi\) | ||||
−0.678135 | + | 0.734937i | \(0.737211\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.1803 | 1.29964 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.236068 | −0.00846889 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.09017 | 0.218203 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −79.3951 | −2.84098 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.90983 | −0.0682518 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 67.3607 | 2.40421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.6738 | −1.02211 | −0.511055 | − | 0.859548i | \(-0.670745\pi\) | ||||
−0.511055 | + | 0.859548i | \(0.670745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −66.0689 | −2.35211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.9443 | 0.602469 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.1246 | −1.46038 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.0344 | −1.13614 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.7082 | 1.76075 | 0.880377 | − | 0.474274i | \(-0.157289\pi\) | ||||
0.880377 | + | 0.474274i | \(0.157289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.3050 | 1.03673 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.20163 | 0.148457 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51.3050 | −1.81051 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.6525 | −0.727904 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −77.0132 | −2.71099 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.03444 | 0.317634 | 0.158817 | − | 0.987308i | \(-0.449232\pi\) | ||||
0.158817 | + | 0.987308i | \(0.449232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.45085 | −0.191405 | −0.0957026 | − | 0.995410i | \(-0.530510\pi\) | ||||
−0.0957026 | + | 0.995410i | \(0.530510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44.1246 | 1.54752 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.65248 | 0.197998 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.85410 | −0.239795 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.1803 | 0.705158 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.4164 | 1.16624 | 0.583120 | − | 0.812386i | \(-0.301832\pi\) | ||||
0.583120 | + | 0.812386i | \(0.301832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.4164 | −1.02539 | −0.512696 | − | 0.858570i | \(-0.671353\pi\) | ||||
−0.512696 | + | 0.858570i | \(0.671353\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −123.992 | −4.31684 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0689 | 0.628317 | 0.314158 | − | 0.949371i | \(-0.398278\pi\) | ||||
0.314158 | + | 0.949371i | \(0.398278\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.4164 | −1.09114 | −0.545568 | − | 0.838066i | \(-0.683686\pi\) | ||||
−0.545568 | + | 0.838066i | \(0.683686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.8885 | −1.66124 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.47214 | −0.0856544 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.23607 | −0.250414 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0000 | 0.345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0557 | −0.726924 | −0.363462 | − | 0.931609i | \(-0.618405\pi\) | ||||
−0.363462 | + | 0.931609i | \(0.618405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2705 | −0.974845 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −46.8328 | −1.61301 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.1591 | 1.79433 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.2705 | 0.799584 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.4721 | 0.496682 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.514708 | 0.0176440 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.90983 | 0.0653913 | 0.0326957 | − | 0.999465i | \(-0.489591\pi\) | ||||
0.0326957 | + | 0.999465i | \(0.489591\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.9443 | −0.476884 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.0000 | 1.70797 | 0.853984 | − | 0.520300i | \(-0.174180\pi\) | ||||
0.853984 | + | 0.520300i | \(0.174180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.59675 | −0.259198 | −0.129599 | − | 0.991567i | \(-0.541369\pi\) | ||||
−0.129599 | + | 0.991567i | \(0.541369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.9443 | −0.543379 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.27051 | 0.213451 | 0.106725 | − | 0.994289i | \(-0.465963\pi\) | ||||
0.106725 | + | 0.994289i | \(0.465963\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.652476 | 0.0221848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.5066 | −0.968134 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.1246 | 1.36113 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −78.2492 | −2.65137 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.7295 | −0.464673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1803 | 0.377964 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.4377 | −1.16288 | −0.581439 | − | 0.813590i | \(-0.697510\pi\) | ||||
−0.581439 | + | 0.813590i | \(0.697510\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.7082 | 0.462366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.5967 | 0.592849 | 0.296425 | − | 0.955056i | \(-0.404206\pi\) | ||||
0.296425 | + | 0.955056i | \(0.404206\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.9656 | −0.671895 | −0.335947 | − | 0.941881i | \(-0.609056\pi\) | ||||
−0.335947 | + | 0.941881i | \(0.609056\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.7426 | 1.30232 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.4164 | −0.584786 | −0.292393 | − | 0.956298i | \(-0.594451\pi\) | ||||
−0.292393 | + | 0.956298i | \(0.594451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.14590 | 0.0719711 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.4164 | 1.11949 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.8541 | 0.396682 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 76.4296 | 2.55476 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −78.2492 | −2.61267 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.81966 | −0.127393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.36068 | 0.278535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.9443 | 0.597148 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.1803 | −0.870264 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.0132 | 0.963366 | 0.481683 | − | 0.876346i | \(-0.340026\pi\) | ||||
0.481683 | + | 0.876346i | \(0.340026\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42.1803 | −1.39903 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.9787 | −1.45708 | −0.728540 | − | 0.685003i | \(-0.759801\pi\) | ||||
−0.728540 | + | 0.685003i | \(0.759801\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.4164 | −0.774970 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −74.3951 | −2.45943 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.1803 | −0.732459 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.5967 | 1.30618 | 0.653088 | − | 0.757282i | \(-0.273473\pi\) | ||||
0.653088 | + | 0.757282i | \(0.273473\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.2361 | 0.337290 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 71.0132 | 2.33743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.729490 | −0.0239855 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 52.8328 | 1.73526 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.76393 | −0.0906817 | −0.0453408 | − | 0.998972i | \(-0.514437\pi\) | ||||
−0.0453408 | + | 0.998972i | \(0.514437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 66.6312 | 2.18141 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 52.3607 | 1.71238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.8885 | −0.845742 | −0.422871 | − | 0.906190i | \(-0.638978\pi\) | ||||
−0.422871 | + | 0.906190i | \(0.638978\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.9443 | −0.683490 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.5410 | −1.90838 | −0.954191 | − | 0.299197i | \(-0.903281\pi\) | ||||
−0.954191 | + | 0.299197i | \(0.903281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.7639 | 1.13207 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.09017 | 0.263173 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.6869 | 0.412269 | 0.206135 | − | 0.978524i | \(-0.433911\pi\) | ||||
0.206135 | + | 0.978524i | \(0.433911\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.8885 | 1.48961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.0902 | −0.651468 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.4721 | −1.18145 | −0.590724 | − | 0.806874i | \(-0.701158\pi\) | ||||
−0.590724 | + | 0.806874i | \(0.701158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.18034 | 0.199991 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.0902 | 0.423145 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.5623 | 0.599408 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0000 | −0.354839 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.9443 | 1.51276 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.1803 | 0.842775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.4164 | −0.495758 | −0.247879 | − | 0.968791i | \(-0.579734\pi\) | ||||
−0.247879 | + | 0.968791i | \(0.579734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.47214 | 0.207915 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.43769 | −0.142412 | −0.0712062 | − | 0.997462i | \(-0.522685\pi\) | ||||
−0.0712062 | + | 0.997462i | \(0.522685\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.47214 | −0.0792530 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 110.902 | 3.55170 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.06888 | −0.0661895 | −0.0330947 | − | 0.999452i | \(-0.510536\pi\) | ||||
−0.0330947 | + | 0.999452i | \(0.510536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.38197 | −0.203969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.8541 | 1.17666 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.0557 | −0.990524 | −0.495262 | − | 0.868744i | \(-0.664928\pi\) | ||||
−0.495262 | + | 0.868744i | \(0.664928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65.1246 | 2.07504 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.0344 | −0.987837 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.1246 | −1.24409 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6738 | 0.752022 | 0.376011 | − | 0.926615i | \(-0.377296\pi\) | ||||
0.376011 | + | 0.926615i | \(0.377296\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −71.4853 | −2.26852 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.74265 | 0.118650 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.4508 | −0.457663 | −0.228832 | − | 0.973466i | \(-0.573490\pi\) | ||||
−0.228832 | + | 0.973466i | \(0.573490\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.201626 | −0.00637917 |
(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 | 1064.2.a.e.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9576.2.a.bc.1.1 | 2 | |||
4.3 | odd | 2 | 2128.2.a.d.1.1 | 2 | |||
7.6 | odd | 2 | 7448.2.a.y.1.1 | 2 | |||
8.3 | odd | 2 | 8512.2.a.ba.1.2 | 2 | |||
8.5 | even | 2 | 8512.2.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2128.2.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
7448.2.a.y.1.1 | 2 | 7.6 | odd | 2 | |||
8512.2.a.e.1.1 | 2 | 8.5 | even | 2 | |||
8512.2.a.ba.1.2 | 2 | 8.3 | odd | 2 | |||
9576.2.a.bc.1.1 | 2 | 3.2 | odd | 2 |