Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4416,2,Mod(1,4416)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4416, 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("4416.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4416 = 2^{6} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4416.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: | \(35.2619375326\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 552) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4416.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.07838 | −0.482265 | −0.241133 | − | 0.970492i | \(-0.577519\pi\) | ||||
−0.241133 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.34017 | −1.64043 | −0.820216 | − | 0.572055i | \(-0.806147\pi\) | ||||
−0.820216 | + | 0.572055i | \(0.806147\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.41855 | −1.03073 | −0.515366 | − | 0.856970i | \(-0.672344\pi\) | ||||
−0.515366 | + | 0.856970i | \(0.672344\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.07838 | −0.278436 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.34017 | −0.567575 | −0.283788 | − | 0.958887i | \(-0.591591\pi\) | ||||
−0.283788 | + | 0.958887i | \(0.591591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.921622 | 0.211435 | 0.105717 | − | 0.994396i | \(-0.466286\pi\) | ||||
0.105717 | + | 0.994396i | \(0.466286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.34017 | −0.947103 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.83710 | −0.767420 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.68035 | −1.24051 | −0.620255 | − | 0.784401i | \(-0.712971\pi\) | ||||
−0.620255 | + | 0.784401i | \(0.712971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.68035 | 1.55904 | 0.779518 | − | 0.626380i | \(-0.215464\pi\) | ||||
0.779518 | + | 0.626380i | \(0.215464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.41855 | −0.595093 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.68035 | 0.791123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.26180 | −1.19383 | −0.596916 | − | 0.802304i | \(-0.703607\pi\) | ||||
−0.596916 | + | 0.802304i | \(0.703607\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.83710 | 1.38012 | 0.690062 | − | 0.723751i | \(-0.257583\pi\) | ||||
0.690062 | + | 0.723751i | \(0.257583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.75872 | 1.18319 | 0.591597 | − | 0.806234i | \(-0.298498\pi\) | ||||
0.591597 | + | 0.806234i | \(0.298498\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.07838 | −0.160755 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.6803 | 1.84962 | 0.924809 | − | 0.380431i | \(-0.124224\pi\) | ||||
0.924809 | + | 0.380431i | \(0.124224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.8371 | 1.69101 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.34017 | −0.327690 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9155 | 1.63672 | 0.818358 | − | 0.574708i | \(-0.194884\pi\) | ||||
0.818358 | + | 0.574708i | \(0.194884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.68649 | 0.497086 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.921622 | 0.122072 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.84324 | −0.239970 | −0.119985 | − | 0.992776i | \(-0.538285\pi\) | ||||
−0.119985 | + | 0.992776i | \(0.538285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.73820 | −0.606665 | −0.303332 | − | 0.952885i | \(-0.598099\pi\) | ||||
−0.303332 | + | 0.952885i | \(0.598099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.34017 | −0.546810 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.15676 | 0.267513 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.75872 | −0.947879 | −0.473939 | − | 0.880557i | \(-0.657168\pi\) | ||||
−0.473939 | + | 0.880557i | \(0.657168\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.52359 | −0.299495 | −0.149748 | − | 0.988724i | \(-0.547846\pi\) | ||||
−0.149748 | + | 0.988724i | \(0.547846\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.83710 | −0.443070 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.8371 | 1.69084 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3402 | 1.38838 | 0.694189 | − | 0.719793i | \(-0.255763\pi\) | ||||
0.694189 | + | 0.719793i | \(0.255763\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.894960 | −0.0982347 | −0.0491173 | − | 0.998793i | \(-0.515641\pi\) | ||||
−0.0491173 | + | 0.998793i | \(0.515641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.52359 | 0.273722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.68035 | −0.716208 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.49693 | −0.900673 | −0.450336 | − | 0.892859i | \(-0.648696\pi\) | ||||
−0.450336 | + | 0.892859i | \(0.648696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.68035 | 0.909948 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.68035 | 0.900110 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.993857 | −0.101968 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.15676 | 0.828193 | 0.414097 | − | 0.910233i | \(-0.364098\pi\) | ||||
0.414097 | + | 0.910233i | \(0.364098\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.41855 | −0.343577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.31351 | 0.628218 | 0.314109 | − | 0.949387i | \(-0.398294\pi\) | ||||
0.314109 | + | 0.949387i | \(0.398294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.81658 | 0.178993 | 0.0894966 | − | 0.995987i | \(-0.471474\pi\) | ||||
0.0894966 | + | 0.995987i | \(0.471474\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.68035 | 0.456755 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.94214 | −0.574448 | −0.287224 | − | 0.957863i | \(-0.592732\pi\) | ||||
−0.287224 | + | 0.957863i | \(0.592732\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.7792 | −1.41559 | −0.707797 | − | 0.706416i | \(-0.750311\pi\) | ||||
−0.707797 | + | 0.706416i | \(0.750311\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.26180 | −0.689259 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.18342 | −0.393543 | −0.196771 | − | 0.980449i | \(-0.563046\pi\) | ||||
−0.196771 | + | 0.980449i | \(0.563046\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.07838 | −0.100559 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.1568 | 0.931068 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.686489 | 0.0624081 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.83710 | 0.796815 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.52973 | 0.852365 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9939 | 1.86290 | 0.931452 | − | 0.363865i | \(-0.118543\pi\) | ||||
0.931452 | + | 0.363865i | \(0.118543\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.75872 | 0.683118 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8371 | 0.946842 | 0.473421 | − | 0.880836i | \(-0.343019\pi\) | ||||
0.473421 | + | 0.880836i | \(0.343019\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.07838 | −0.0928120 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.65983 | −0.141809 | −0.0709043 | − | 0.997483i | \(-0.522588\pi\) | ||||
−0.0709043 | + | 0.997483i | \(0.522588\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.6803 | 1.06788 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.83710 | 0.571747 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.20394 | 0.598254 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.8371 | 0.976308 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.23513 | 0.265032 | 0.132516 | − | 0.991181i | \(-0.457694\pi\) | ||||
0.132516 | + | 0.991181i | \(0.457694\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3607 | 1.41279 | 0.706397 | − | 0.707816i | \(-0.250320\pi\) | ||||
0.706397 | + | 0.707816i | \(0.250320\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.34017 | −0.189192 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.36069 | −0.751869 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.78539 | 0.461724 | 0.230862 | − | 0.972986i | \(-0.425845\pi\) | ||||
0.230862 | + | 0.972986i | \(0.425845\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.9155 | 0.944959 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.34017 | −0.342054 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.15676 | 0.168930 | 0.0844651 | − | 0.996426i | \(-0.473082\pi\) | ||||
0.0844651 | + | 0.996426i | \(0.473082\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.68649 | 0.286993 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.47641 | −0.423777 | −0.211889 | − | 0.977294i | \(-0.567961\pi\) | ||||
−0.211889 | + | 0.977294i | \(0.567961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.921622 | 0.0704782 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.31965 | 0.708560 | 0.354280 | − | 0.935139i | \(-0.384726\pi\) | ||||
0.354280 | + | 0.935139i | \(0.384726\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.6537 | 1.25890 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.84324 | −0.138547 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.36683 | −0.326393 | −0.163196 | − | 0.986594i | \(-0.552180\pi\) | ||||
−0.163196 | + | 0.986594i | \(0.552180\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.94214 | 0.293017 | 0.146509 | − | 0.989209i | \(-0.453196\pi\) | ||||
0.146509 | + | 0.989209i | \(0.453196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.73820 | −0.350258 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.83096 | 0.575744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.34017 | −0.315701 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5174 | −1.12280 | −0.561402 | − | 0.827544i | \(-0.689738\pi\) | ||||
−0.561402 | + | 0.827544i | \(0.689738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8371 | −1.21196 | −0.605981 | − | 0.795479i | \(-0.707219\pi\) | ||||
−0.605981 | + | 0.795479i | \(0.707219\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.15676 | 0.154448 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.20394 | −0.655753 | −0.327877 | − | 0.944721i | \(-0.606333\pi\) | ||||
−0.327877 | + | 0.944721i | \(0.606333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.6947 | −1.89234 | −0.946169 | − | 0.323672i | \(-0.895083\pi\) | ||||
−0.946169 | + | 0.323672i | \(0.895083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.75872 | −0.547258 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.9939 | 2.03497 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.52973 | −0.665585 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.15061 | −0.217932 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5174 | 1.34364 | 0.671818 | − | 0.740716i | \(-0.265514\pi\) | ||||
0.671818 | + | 0.740716i | \(0.265514\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.52359 | −0.172914 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.36683 | −0.570613 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.6742 | −2.55749 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.68035 | 0.314834 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.6742 | −1.98713 | −0.993566 | − | 0.113256i | \(-0.963872\pi\) | ||||
−0.993566 | + | 0.113256i | \(0.963872\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.83710 | −0.255807 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2618 | 0.880216 | 0.440108 | − | 0.897945i | \(-0.354940\pi\) | ||||
0.440108 | + | 0.897945i | \(0.354940\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9421 | 0.789159 | 0.394579 | − | 0.918862i | \(-0.370890\pi\) | ||||
0.394579 | + | 0.918862i | \(0.370890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.8371 | 0.976210 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.68649 | 0.372534 | 0.186267 | − | 0.982499i | \(-0.440361\pi\) | ||||
0.186267 | + | 0.982499i | \(0.440361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.6742 | −0.892007 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.3402 | 0.801580 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.6742 | 1.40199 | 0.700994 | − | 0.713167i | \(-0.252740\pi\) | ||||
0.700994 | + | 0.713167i | \(0.252740\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1568 | 1.04075 | 0.520374 | − | 0.853938i | \(-0.325793\pi\) | ||||
0.520374 | + | 0.853938i | \(0.325793\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.7649 | −0.815517 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.84324 | −0.117283 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.894960 | −0.0567158 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.0989 | 1.77359 | 0.886793 | − | 0.462166i | \(-0.152928\pi\) | ||||
0.886793 | + | 0.462166i | \(0.152928\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.41855 | −0.214922 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.52359 | 0.158033 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.523590 | −0.0326607 | −0.0163303 | − | 0.999867i | \(-0.505198\pi\) | ||||
−0.0163303 | + | 0.999867i | \(0.505198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.5174 | 1.95840 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.68035 | −0.413503 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.99386 | −0.307934 | −0.153967 | − | 0.988076i | \(-0.549205\pi\) | ||||
−0.153967 | + | 0.988076i | \(0.549205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.8494 | −0.789332 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.49693 | −0.520004 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.84324 | 0.234327 | 0.117163 | − | 0.993113i | \(-0.462620\pi\) | ||||
0.117163 | + | 0.993113i | \(0.462620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.6803 | 1.49922 | 0.749612 | − | 0.661877i | \(-0.230240\pi\) | ||||
0.749612 | + | 0.661877i | \(0.230240\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.68035 | 0.525358 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1173 | 0.791005 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8843 | −1.55524 | −0.777618 | − | 0.628737i | \(-0.783572\pi\) | ||||
−0.777618 | + | 0.628737i | \(0.783572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.68035 | 0.519679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.1773 | 1.74057 | 0.870285 | − | 0.492548i | \(-0.163934\pi\) | ||||
0.870285 | + | 0.492548i | \(0.163934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.28231 | −0.135669 | −0.0678347 | − | 0.997697i | \(-0.521609\pi\) | ||||
−0.0678347 | + | 0.997697i | \(0.521609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.993857 | −0.0588710 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −38.3545 | −2.26400 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.5236 | −0.677858 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.15676 | 0.478157 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.60197 | 0.444112 | 0.222056 | − | 0.975034i | \(-0.428723\pi\) | ||||
0.222056 | + | 0.975034i | \(0.428723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.98771 | 0.115729 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.41855 | −0.198364 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.6742 | −1.94095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.31351 | 0.362702 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.10957 | 0.292573 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.8904 | −0.621549 | −0.310775 | − | 0.950484i | \(-0.600588\pi\) | ||||
−0.310775 | + | 0.950484i | \(0.600588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.81658 | 0.103342 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5174 | 0.653095 | 0.326547 | − | 0.945181i | \(-0.394115\pi\) | ||||
0.326547 | + | 0.945181i | \(0.394115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.21008 | −0.237968 | −0.118984 | − | 0.992896i | \(-0.537964\pi\) | ||||
−0.118984 | + | 0.992896i | \(0.537964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.68035 | 0.263708 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.3197 | −0.748106 | −0.374053 | − | 0.927407i | \(-0.622032\pi\) | ||||
−0.374053 | + | 0.927407i | \(0.622032\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.8371 | 1.27863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.94214 | −0.331658 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.15676 | −0.120005 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.67420 | 0.425688 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.7792 | −0.817294 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −55.0349 | −3.03417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.15676 | 0.118546 | 0.0592730 | − | 0.998242i | \(-0.481122\pi\) | ||||
0.0592730 | + | 0.998242i | \(0.481122\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.26180 | −0.397944 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.36683 | 0.457129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.3545 | 1.32668 | 0.663338 | − | 0.748320i | \(-0.269139\pi\) | ||||
0.663338 | + | 0.748320i | \(0.269139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.18342 | −0.227212 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.6742 | −1.60695 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.9939 | −1.13356 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.07838 | −0.0580579 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.0410 | 1.39796 | 0.698978 | − | 0.715143i | \(-0.253638\pi\) | ||||
0.698978 | + | 0.715143i | \(0.253638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.523590 | 0.0280272 | 0.0140136 | − | 0.999902i | \(-0.495539\pi\) | ||||
0.0140136 | + | 0.999902i | \(0.495539\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.0410 | 1.49247 | 0.746237 | − | 0.665680i | \(-0.231859\pi\) | ||||
0.746237 | + | 0.665680i | \(0.231859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.72138 | 0.144436 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.1568 | 0.537553 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.84324 | 0.519507 | 0.259753 | − | 0.965675i | \(-0.416359\pi\) | ||||
0.259753 | + | 0.965675i | \(0.416359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1506 | −0.955295 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.686489 | 0.0360313 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.15676 | −0.112890 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.3340 | −0.904829 | −0.452414 | − | 0.891808i | \(-0.649437\pi\) | ||||
−0.452414 | + | 0.891808i | \(0.649437\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.83710 | 0.460041 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −51.7152 | −2.68492 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.2618 | −1.20445 | −0.602225 | − | 0.798326i | \(-0.705719\pi\) | ||||
−0.602225 | + | 0.798326i | \(0.705719\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.52973 | 0.492113 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.3607 | 0.688111 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.7998 | −1.32524 | −0.662622 | − | 0.748954i | \(-0.730557\pi\) | ||||
−0.662622 | + | 0.748954i | \(0.730557\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.9939 | 1.07555 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.35455 | 0.324702 | 0.162351 | − | 0.986733i | \(-0.448092\pi\) | ||||
0.162351 | + | 0.986733i | \(0.448092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.75872 | 0.394398 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.54864 | −0.179923 | −0.0899617 | − | 0.995945i | \(-0.528674\pi\) | ||||
−0.0899617 | + | 0.995945i | \(0.528674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.34017 | −0.118348 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.8371 | 0.546659 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.3074 | −0.669566 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6270 | 0.533355 | 0.266677 | − | 0.963786i | \(-0.414074\pi\) | ||||
0.266677 | + | 0.963786i | \(0.414074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.00000 | −0.200250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.0677 | 1.80113 | 0.900567 | − | 0.434716i | \(-0.143151\pi\) | ||||
0.900567 | + | 0.434716i | \(0.143151\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.3607 | −0.864798 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.07838 | −0.0535850 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.8248 | 1.23052 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.1506 | −1.44141 | −0.720703 | − | 0.693244i | \(-0.756181\pi\) | ||||
−0.720703 | + | 0.693244i | \(0.756181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.65983 | −0.0818732 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.965105 | 0.0473752 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.7792 | 0.624307 | 0.312153 | − | 0.950032i | \(-0.398950\pi\) | ||||
0.312153 | + | 0.950032i | \(0.398950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.2557 | −1.37710 | −0.688548 | − | 0.725191i | \(-0.741752\pi\) | ||||
−0.688548 | + | 0.725191i | \(0.741752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.6803 | 0.616540 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.97948 | 0.435569 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.5646 | 0.995192 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.83710 | 0.330098 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.8720 | −1.82423 | −0.912115 | − | 0.409935i | \(-0.865552\pi\) | ||||
−0.912115 | + | 0.409935i | \(0.865552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.8371 | −0.616912 | −0.308456 | − | 0.951239i | \(-0.599812\pi\) | ||||
−0.308456 | + | 0.951239i | \(0.599812\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.20394 | 0.345402 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.921622 | 0.0440872 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.3607 | 1.21040 | 0.605200 | − | 0.796074i | \(-0.293093\pi\) | ||||
0.605200 | + | 0.796074i | \(0.293093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.8371 | 0.563671 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.9877 | 1.80485 | 0.902425 | − | 0.430846i | \(-0.141785\pi\) | ||||
0.902425 | + | 0.430846i | \(0.141785\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.16290 | 0.434363 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.23513 | 0.153017 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.1978 | −1.80267 | −0.901333 | − | 0.433128i | \(-0.857410\pi\) | ||||
−0.901333 | + | 0.433128i | \(0.857410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.2101 | −1.42254 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.3607 | 0.815676 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.36069 | −0.438836 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.8432 | 0.554004 | 0.277002 | − | 0.960869i | \(-0.410659\pi\) | ||||
0.277002 | + | 0.960869i | \(0.410659\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.34017 | −0.109230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.1917 | 1.82534 | 0.912669 | − | 0.408700i | \(-0.134018\pi\) | ||||
0.912669 | + | 0.408700i | \(0.134018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.3607 | −1.17861 | −0.589306 | − | 0.807910i | \(-0.700599\pi\) | ||||
−0.589306 | + | 0.807910i | \(0.700599\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.36069 | −0.434092 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.2618 | −0.613683 | −0.306841 | − | 0.951761i | \(-0.599272\pi\) | ||||
−0.306841 | + | 0.951761i | \(0.599272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.6742 | 1.55493 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.78539 | 0.266577 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.5236 | −1.21956 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.53636 | −0.162259 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.9155 | 0.545572 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.6865 | 0.533969 | 0.266985 | − | 0.963701i | \(-0.413973\pi\) | ||||
0.266985 | + | 0.963701i | \(0.413973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.5236 | 0.662219 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.34017 | −0.197485 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.79606 | −0.399409 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.04718 | 0.228710 | 0.114355 | − | 0.993440i | \(-0.463520\pi\) | ||||
0.114355 | + | 0.993440i | \(0.463520\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.15676 | 0.0975319 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.680346 | 0.0307036 | 0.0153518 | − | 0.999882i | \(-0.495113\pi\) | ||||
0.0153518 | + | 0.999882i | \(0.495113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.6332 | 0.704082 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.68649 | 0.165695 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9528 | 0.491301 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.1917 | −1.12773 | −0.563867 | − | 0.825866i | \(-0.690687\pi\) | ||||
−0.563867 | + | 0.825866i | \(0.690687\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.47641 | −0.244668 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8843 | 0.886596 | 0.443298 | − | 0.896374i | \(-0.353808\pi\) | ||||
0.443298 | + | 0.896374i | \(0.353808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.80835 | −0.302968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.4017 | −1.48051 | −0.740253 | − | 0.672329i | \(-0.765294\pi\) | ||||
−0.740253 | + | 0.672329i | \(0.765294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.68035 | −0.383996 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.921622 | 0.0406906 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.95896 | −0.0863222 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.3484 | −1.90646 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.31965 | 0.409087 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3874 | 1.19986 | 0.599931 | − | 0.800052i | \(-0.295195\pi\) | ||||
0.599931 | + | 0.800052i | \(0.295195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.0722 | −1.22751 | −0.613757 | − | 0.789495i | \(-0.710342\pi\) | ||||
−0.613757 | + | 0.789495i | \(0.710342\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.6537 | 0.726826 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.3135 | −0.884870 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.84324 | −0.0799900 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.6742 | −0.765555 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.40787 | 0.277036 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.36683 | −0.188443 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −40.4657 | −1.74298 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.8843 | 1.80075 | 0.900373 | − | 0.435119i | \(-0.143294\pi\) | ||||
0.900373 | + | 0.435119i | \(0.143294\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.94214 | 0.169173 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.9376 | 0.682692 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.2039 | −1.33418 | −0.667092 | − | 0.744975i | \(-0.732461\pi\) | ||||
−0.667092 | + | 0.744975i | \(0.732461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.73820 | −0.202222 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.15676 | −0.262287 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.5585 | −2.27754 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.83096 | 0.332406 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.60811 | −0.279995 | −0.139997 | − | 0.990152i | \(-0.544709\pi\) | ||||
−0.139997 | + | 0.990152i | \(0.544709\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.5174 | −0.656318 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.2618 | 1.23324 | 0.616619 | − | 0.787262i | \(-0.288502\pi\) | ||||
0.616619 | + | 0.787262i | \(0.288502\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.51130 | 0.189792 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.34017 | −0.182270 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.3340 | 0.475147 | 0.237574 | − | 0.971370i | \(-0.423648\pi\) | ||||
0.237574 | + | 0.971370i | \(0.423648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.9627 | 1.46314 | 0.731571 | − | 0.681765i | \(-0.238788\pi\) | ||||
0.731571 | + | 0.681765i | \(0.238788\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.5174 | −0.648251 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.83710 | −0.160018 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.15061 | 0.0479006 | 0.0239503 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239503 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.8371 | −0.699726 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.88428 | 0.161147 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.7337 | −1.68702 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.15676 | 0.0891709 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.5113 | 0.681494 | 0.340747 | − | 0.940155i | \(-0.389320\pi\) | ||||
0.340747 | + | 0.940155i | \(0.389320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.20394 | −0.378599 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.1629 | 0.458405 | 0.229203 | − | 0.973379i | \(-0.426388\pi\) | ||||
0.229203 | + | 0.973379i | \(0.426388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.9528 | −0.449022 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.6947 | −1.09254 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0000 | 1.30748 | 0.653742 | − | 0.756717i | \(-0.273198\pi\) | ||||
0.653742 | + | 0.756717i | \(0.273198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.1506 | 1.67857 | 0.839284 | − | 0.543693i | \(-0.182974\pi\) | ||||
0.839284 | + | 0.543693i | \(0.182974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.75872 | −0.315960 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.740294 | −0.0300973 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0000 | 0.974130 | 0.487065 | − | 0.873366i | \(-0.338067\pi\) | ||||
0.487065 | + | 0.873366i | \(0.338067\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.9939 | 1.17489 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.3607 | −1.02598 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.73820 | −0.191374 | −0.0956871 | − | 0.995411i | \(-0.530505\pi\) | ||||
−0.0956871 | + | 0.995411i | \(0.530505\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.52973 | −0.384276 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.4846 | −1.38830 | −0.694150 | − | 0.719831i | \(-0.744219\pi\) | ||||
−0.694150 | + | 0.719831i | \(0.744219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.0661 | 1.65059 | 0.825293 | − | 0.564705i | \(-0.191010\pi\) | ||||
0.825293 | + | 0.564705i | \(0.191010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.8781 | 1.47749 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.90885 | 0.356354 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.15061 | −0.125823 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9939 | 0.677589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8638 | 0.910192 | 0.455096 | − | 0.890442i | \(-0.349605\pi\) | ||||
0.455096 | + | 0.890442i | \(0.349605\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.5174 | 0.775749 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.6393 | −0.898414 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.6742 | −0.938006 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.52359 | −0.0998317 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.7070 | 1.37084 | 0.685422 | − | 0.728146i | \(-0.259618\pi\) | ||||
0.685422 | + | 0.728146i | \(0.259618\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.96266 | −0.116836 | −0.0584180 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584180 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.36683 | −0.329444 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.4703 | 0.568885 | 0.284442 | − | 0.958693i | \(-0.408192\pi\) | ||||
0.284442 | + | 0.958693i | \(0.408192\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.30122 | 0.247345 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.6742 | −1.47657 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.0000 | 0.391330 | 0.195665 | − | 0.980671i | \(-0.437313\pi\) | ||||
0.195665 | + | 0.980671i | \(0.437313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.6865 | −0.456629 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.1338 | 1.36862 | 0.684309 | − | 0.729192i | \(-0.260104\pi\) | ||||
0.684309 | + | 0.729192i | \(0.260104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.2967 | 1.64515 | 0.822575 | − | 0.568656i | \(-0.192537\pi\) | ||||
0.822575 | + | 0.568656i | \(0.192537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.68035 | 0.181770 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.31351 | 0.167271 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.68035 | −0.258664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.6742 | −1.14727 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.1978 | 0.625309 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.15061 | 0.352730 | 0.176365 | − | 0.984325i | \(-0.443566\pi\) | ||||
0.176365 | + | 0.984325i | \(0.443566\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.83710 | −0.147690 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.0037 | 1.65277 | 0.826383 | − | 0.563108i | \(-0.190395\pi\) | ||||
0.826383 | + | 0.563108i | \(0.190395\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.4017 | −1.35859 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.2618 | 0.508193 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.1978 | −1.69118 | −0.845591 | − | 0.533832i | \(-0.820752\pi\) | ||||
−0.845591 | + | 0.533832i | \(0.820752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.78992 | 0.0683893 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.9421 | 0.455621 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.8310 | −0.907887 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.4703 | −0.854809 | −0.427405 | − | 0.904060i | \(-0.640572\pi\) | ||||
−0.427405 | + | 0.904060i | \(0.640572\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.8371 | 0.563615 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.31351 | 0.163621 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.6803 | −0.783324 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.68649 | 0.215083 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.4801 | 0.924601 | 0.462300 | − | 0.886723i | \(-0.347024\pi\) | ||||
0.462300 | + | 0.886723i | \(0.347024\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.69263 | −0.252417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.6742 | −0.515000 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.4017 | −1.03055 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.5692 | −1.22316 | −0.611580 | − | 0.791182i | \(-0.709466\pi\) | ||||
−0.611580 | + | 0.791182i | \(0.709466\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.3402 | 0.462793 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.68035 | 0.325082 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.37298 | −0.275734 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.6742 | 0.809438 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.20394 | −0.268661 | −0.134331 | − | 0.990937i | \(-0.542888\pi\) | ||||
−0.134331 | + | 0.990937i | \(0.542888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.88428 | −0.293626 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.1568 | 0.600876 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.6332 | 0.951992 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.6537 | −0.617651 | −0.308825 | − | 0.951119i | \(-0.599936\pi\) | ||||
−0.308825 | + | 0.951119i | \(0.599936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.1568 | −0.671552 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.2434 | −1.70804 | −0.854019 | − | 0.520242i | \(-0.825842\pi\) | ||||
−0.854019 | + | 0.520242i | \(0.825842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.7649 | −0.470839 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.5236 | 0.977009 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.7337 | 0.468416 | 0.234208 | − | 0.972187i | \(-0.424750\pi\) | ||||
0.234208 | + | 0.972187i | \(0.424750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.84324 | −0.0677133 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.3668 | −0.747187 | −0.373593 | − | 0.927593i | \(-0.621874\pi\) | ||||
−0.373593 | + | 0.927593i | \(0.621874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.48870 | −0.127816 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.894960 | −0.0327449 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.7899 | 0.942343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.85762 | 0.140767 | 0.0703833 | − | 0.997520i | \(-0.477578\pi\) | ||||
0.0703833 | + | 0.997520i | \(0.477578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.0989 | 1.02398 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.7214 | −0.681341 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.61634 | 0.0587470 | 0.0293735 | − | 0.999569i | \(-0.490649\pi\) | ||||
0.0293735 | + | 0.999569i | \(0.490649\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.41855 | −0.124086 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.0410 | 0.726487 | 0.363244 | − | 0.931694i | \(-0.381669\pi\) | ||||
0.363244 | + | 0.931694i | \(0.381669\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 64.1445 | 2.32219 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.52359 | 0.0912406 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.68649 | 0.133111 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.1629 | −0.835275 | −0.417638 | − | 0.908614i | \(-0.637142\pi\) | ||||
−0.417638 | + | 0.908614i | \(0.637142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.523590 | −0.0188566 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.2762 | −1.48460 | −0.742300 | − | 0.670067i | \(-0.766265\pi\) | ||||
−0.742300 | + | 0.670067i | \(0.766265\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.3074 | −1.19644 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31.5174 | 1.13068 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.14447 | 0.291806 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.62702 | 0.308699 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.68035 | −0.238736 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.23883 | −0.222673 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4329 | 0.478832 | 0.239416 | − | 0.970917i | \(-0.423044\pi\) | ||||
0.239416 | + | 0.970917i | \(0.423044\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.99386 | −0.177786 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.1568 | 0.645580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.47641 | 0.336517 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.8494 | −0.455721 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.07838 | 0.179885 | 0.0899427 | − | 0.995947i | \(-0.471332\pi\) | ||||
0.0899427 | + | 0.995947i | \(0.471332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.6742 | −1.04980 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.49693 | −0.300224 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.83710 | −0.241276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.68035 | 0.164961 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.84324 | 0.135289 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.35455 | 0.293730 | 0.146865 | − | 0.989157i | \(-0.453082\pi\) | ||||
0.146865 | + | 0.989157i | \(0.453082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.8781 | 1.57588 | 0.787942 | − | 0.615749i | \(-0.211146\pi\) | ||||
0.787942 | + | 0.615749i | \(0.211146\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.6803 | 0.865578 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.32580 | −0.0814691 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.15061 | 0.250168 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.68035 | 0.303316 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.3484 | −1.72227 | −0.861136 | − | 0.508375i | \(-0.830246\pi\) | ||||
−0.861136 | + | 0.508375i | \(0.830246\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.0410 | −0.350009 | −0.175004 | − | 0.984568i | \(-0.555994\pi\) | ||||
−0.175004 | + | 0.984568i | \(0.555994\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.1173 | 0.456687 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0866 | 1.88078 | 0.940388 | − | 0.340104i | \(-0.110462\pi\) | ||||
0.940388 | + | 0.340104i | \(0.110462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.8371 | 0.723702 | 0.361851 | − | 0.932236i | \(-0.382145\pi\) | ||||
0.361851 | + | 0.932236i | \(0.382145\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.8843 | −0.897916 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.7009 | −0.959778 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.90564 | 0.204373 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.68035 | 0.300037 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.68035 | −0.299679 | −0.149839 | − | 0.988710i | \(-0.547876\pi\) | ||||
−0.149839 | + | 0.988710i | \(0.547876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6270 | 0.538863 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.1773 | 1.00492 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.70540 | 0.333876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.97948 | −0.102376 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.28231 | −0.0783288 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.26180 | −0.248931 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.0000 | −1.30110 | −0.650548 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.993857 | −0.0339892 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38.3545 | −1.30712 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.8432 | −1.01588 | −0.507938 | − | 0.861394i | \(-0.669592\pi\) | ||||
−0.507938 | + | 0.861394i | \(0.669592\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0501 | −0.341714 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.5236 | −0.391362 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.1855 | −1.43105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5174 | 0.525789 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.15676 | 0.276064 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.3607 | −1.39825 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.4764 | −0.387531 | −0.193765 | − | 0.981048i | \(-0.562070\pi\) | ||||
−0.193765 | + | 0.981048i | \(0.562070\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.60197 | 0.256408 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.8227 | −0.903681 | −0.451840 | − | 0.892099i | \(-0.649232\pi\) | ||||
−0.451840 | + | 0.892099i | \(0.649232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.15676 | −0.0725806 | −0.0362903 | − | 0.999341i | \(-0.511554\pi\) | ||||
−0.0362903 | + | 0.999341i | \(0.511554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.98771 | 0.0668163 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.4140 | −0.987626 | −0.493813 | − | 0.869568i | \(-0.664397\pi\) | ||||
−0.493813 | + | 0.869568i | \(0.664397\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −91.1170 | −3.05597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.41855 | −0.114526 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.6865 | 0.391073 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.70910 | 0.157408 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.9877 | −1.93400 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.8843 | −0.928960 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.6742 | −1.12061 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.25112 | −0.141312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.2700 | −1.46996 | −0.734981 | − | 0.678088i | \(-0.762809\pi\) | ||||
−0.734981 | + | 0.678088i | \(0.762809\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.31351 | 0.209406 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5113 | −0.679570 | −0.339785 | − | 0.940503i | \(-0.610354\pi\) | ||||
−0.339785 | + | 0.940503i | \(0.610354\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.05947 | 0.101254 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.10957 | 0.168917 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.0349 | −1.55323 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.01438 | 0.0664481 | 0.0332241 | − | 0.999448i | \(-0.489423\pi\) | ||||
0.0332241 | + | 0.999448i | \(0.489423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.8904 | −0.358852 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.04718 | 0.166130 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.8642 | 0.916171 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.81658 | 0.0596644 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.21008 | −0.138128 | −0.0690641 | − | 0.997612i | \(-0.522001\pi\) | ||||
−0.0690641 | + | 0.997612i | \(0.522001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9093 | 0.357539 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.5174 | 0.377064 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.62702 | −0.282134 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.6393 | −0.674257 | −0.337128 | − | 0.941459i | \(-0.609456\pi\) | ||||
−0.337128 | + | 0.941459i | \(0.609456\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.21008 | −0.137391 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.5958 | 1.71457 | 0.857287 | − | 0.514838i | \(-0.172148\pi\) | ||||
0.857287 | + | 0.514838i | \(0.172148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.83710 | 0.287776 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.68035 | 0.152252 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.0288 | 1.43074 | 0.715371 | − | 0.698745i | \(-0.246258\pi\) | ||||
0.715371 | + | 0.698745i | \(0.246258\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.3197 | −0.431919 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.39350 | 0.207106 | 0.103553 | − | 0.994624i | \(-0.466979\pi\) | ||||
0.103553 | + | 0.994624i | \(0.466979\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.7337 | 0.541489 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.8371 | 0.738219 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.20394 | 0.232627 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.3484 | 1.43059 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.94214 | −0.191483 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.1568 | 0.584487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.0882 | 1.25699 | 0.628496 | − | 0.777813i | \(-0.283671\pi\) | ||||
0.628496 | + | 0.777813i | \(0.283671\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.15676 | −0.0692850 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54.1933 | −1.73914 | −0.869572 | − | 0.493806i | \(-0.835605\pi\) | ||||
−0.869572 | + | 0.493806i | \(0.835605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.3607 | 0.556558 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.67420 | 0.245771 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.7009 | 1.52609 | 0.763043 | − | 0.646348i | \(-0.223704\pi\) | ||||
0.763043 | + | 0.646348i | \(0.223704\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.0472 | 0.928352 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.7792 | −0.471865 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.5585 | −1.58067 | −0.790335 | − | 0.612675i | \(-0.790094\pi\) | ||||
−0.790335 | + | 0.612675i | \(0.790094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.92532 | 0.316247 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −55.0349 | −1.75178 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.75872 | 0.246713 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.2602 | 0.643586 | 0.321793 | − | 0.946810i | \(-0.395714\pi\) | ||||
0.321793 | + | 0.946810i | \(0.395714\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.15676 | 0.0684426 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.7870 | 0.912609 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.57077 | −0.0497468 | −0.0248734 | − | 0.999691i | \(-0.507918\pi\) | ||||
−0.0248734 | + | 0.999691i | \(0.507918\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.26180 | −0.229753 |
(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 | 4416.2.a.bs.1.2 | 3 | ||
4.3 | odd | 2 | 4416.2.a.bp.1.2 | 3 | |||
8.3 | odd | 2 | 552.2.a.g.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 1104.2.a.o.1.2 | 3 | |||
24.5 | odd | 2 | 3312.2.a.bf.1.2 | 3 | |||
24.11 | even | 2 | 1656.2.a.n.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.a.g.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
1104.2.a.o.1.2 | 3 | 8.5 | even | 2 | |||
1656.2.a.n.1.2 | 3 | 24.11 | even | 2 | |||
3312.2.a.bf.1.2 | 3 | 24.5 | odd | 2 | |||
4416.2.a.bp.1.2 | 3 | 4.3 | odd | 2 | |||
4416.2.a.bs.1.2 | 3 | 1.1 | even | 1 | trivial |