Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.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: | \(9.16682615204\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.470117.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 8x^{2} + 7x + 1 \) |
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 | 1.4 | ||
Root | \(-0.475832\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1 |
$q$-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 | ||||||||
\(3\) | 0.475832 | 0.274722 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.19617 | 0.534944 | 0.267472 | − | 0.963566i | \(-0.413812\pi\) | ||||
0.267472 | + | 0.963566i | \(0.413812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.77358 | −0.924528 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.51385 | −1.36098 | −0.680488 | − | 0.732759i | \(-0.738232\pi\) | ||||
−0.680488 | + | 0.732759i | \(0.738232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.46760 | 0.407038 | 0.203519 | − | 0.979071i | \(-0.434762\pi\) | ||||
0.203519 | + | 0.979071i | \(0.434762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.569176 | 0.146961 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.96975 | −1.20534 | −0.602671 | − | 0.797990i | \(-0.705897\pi\) | ||||
−0.602671 | + | 0.797990i | \(0.705897\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.69193 | −0.846987 | −0.423493 | − | 0.905899i | \(-0.639196\pi\) | ||||
−0.423493 | + | 0.905899i | \(0.639196\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.475832 | −0.103835 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.36269 | 0.909683 | 0.454842 | − | 0.890572i | \(-0.349696\pi\) | ||||
0.454842 | + | 0.890572i | \(0.349696\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.56918 | −0.713835 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.74726 | −0.528710 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.12850 | −0.580948 | −0.290474 | − | 0.956883i | \(-0.593813\pi\) | ||||
−0.290474 | + | 0.956883i | \(0.593813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.79167 | −1.39943 | −0.699713 | − | 0.714424i | \(-0.746689\pi\) | ||||
−0.699713 | + | 0.714424i | \(0.746689\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.14783 | −0.373890 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.19617 | −0.202190 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.52861 | 1.56649 | 0.783247 | − | 0.621711i | \(-0.213562\pi\) | ||||
0.783247 | + | 0.621711i | \(0.213562\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.698329 | 0.111822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7158 | −1.78664 | −0.893319 | − | 0.449424i | \(-0.851629\pi\) | ||||
−0.893319 | + | 0.449424i | \(0.851629\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.31768 | −0.494570 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.93311 | 1.01130 | 0.505649 | − | 0.862739i | \(-0.331253\pi\) | ||||
0.505649 | + | 0.862739i | \(0.331253\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.36477 | −0.331134 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.63019 | 1.18545 | 0.592724 | − | 0.805406i | \(-0.298052\pi\) | ||||
0.592724 | + | 0.805406i | \(0.298052\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.39933 | −0.728046 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.75674 | −0.232686 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.99301 | −0.389656 | −0.194828 | − | 0.980837i | \(-0.562415\pi\) | ||||
−0.194828 | + | 0.980837i | \(0.562415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.624504 | 0.0799595 | 0.0399798 | − | 0.999200i | \(-0.487271\pi\) | ||||
0.0399798 | + | 0.999200i | \(0.487271\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.77358 | 0.349439 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75549 | 0.217742 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3304 | 1.26205 | 0.631027 | − | 0.775761i | \(-0.282634\pi\) | ||||
0.631027 | + | 0.775761i | \(0.282634\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.07591 | 0.249910 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26235 | 0.149814 | 0.0749068 | − | 0.997191i | \(-0.476134\pi\) | ||||
0.0749068 | + | 0.997191i | \(0.476134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.30820 | −0.738319 | −0.369159 | − | 0.929366i | \(-0.620354\pi\) | ||||
−0.369159 | + | 0.929366i | \(0.620354\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.69833 | −0.196106 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.51385 | 0.514401 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4848 | −1.17964 | −0.589819 | − | 0.807536i | \(-0.700801\pi\) | ||||
−0.589819 | + | 0.807536i | \(0.700801\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.01352 | 0.779280 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.11184 | −0.780626 | −0.390313 | − | 0.920682i | \(-0.627633\pi\) | ||||
−0.390313 | + | 0.920682i | \(0.627633\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.94467 | −0.644790 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.48864 | −0.159599 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.5356 | −1.11677 | −0.558386 | − | 0.829581i | \(-0.688579\pi\) | ||||
−0.558386 | + | 0.829581i | \(0.688579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.46760 | −0.153846 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.70753 | −0.384453 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.41618 | −0.453090 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6608 | 1.48858 | 0.744292 | − | 0.667855i | \(-0.232787\pi\) | ||||
0.744292 | + | 0.667855i | \(0.232787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.5195 | 1.25826 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.56697 | 0.155919 | 0.0779596 | − | 0.996957i | \(-0.475159\pi\) | ||||
0.0779596 | + | 0.996957i | \(0.475159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.719686 | −0.0709127 | −0.0354564 | − | 0.999371i | \(-0.511288\pi\) | ||||
−0.0354564 | + | 0.999371i | \(0.511288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.569176 | −0.0555459 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.62861 | −0.254117 | −0.127059 | − | 0.991895i | \(-0.540554\pi\) | ||||
−0.127059 | + | 0.991895i | \(0.540554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6880 | −1.21529 | −0.607645 | − | 0.794208i | \(-0.707886\pi\) | ||||
−0.607645 | + | 0.794208i | \(0.707886\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.53402 | 0.430350 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.7838 | −1.01446 | −0.507229 | − | 0.861811i | \(-0.669330\pi\) | ||||
−0.507229 | + | 0.861811i | \(0.669330\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.21852 | 0.486629 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.07050 | −0.376318 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.96975 | 0.455577 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.37483 | 0.852258 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.475832 | 0.0429043 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2502 | −0.916805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1678 | −0.990979 | −0.495489 | − | 0.868614i | \(-0.665011\pi\) | ||||
−0.495489 | + | 0.868614i | \(0.665011\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.57474 | −0.490828 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.60067 | 0.401962 | 0.200981 | − | 0.979595i | \(-0.435587\pi\) | ||||
0.200981 | + | 0.979595i | \(0.435587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.69193 | 0.320131 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.28619 | −0.282830 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.44168 | 0.294042 | 0.147021 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147021 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.13549 | −0.181130 | −0.0905650 | − | 0.995891i | \(-0.528867\pi\) | ||||
−0.0905650 | + | 0.995891i | \(0.528867\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.29900 | 0.277826 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.62450 | −0.553969 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.74222 | −0.310774 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.475832 | 0.0392460 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.58702 | 0.621553 | 0.310777 | − | 0.950483i | \(-0.399411\pi\) | ||||
0.310777 | + | 0.950483i | \(0.399411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.7612 | −0.957112 | −0.478556 | − | 0.878057i | \(-0.658840\pi\) | ||||
−0.478556 | + | 0.878057i | \(0.658840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.7840 | 1.11437 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.32017 | −0.748614 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3221 | 0.983412 | 0.491706 | − | 0.870761i | \(-0.336373\pi\) | ||||
0.491706 | + | 0.870761i | \(0.336373\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.10652 | 0.325669 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.36269 | −0.343828 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.3974 | −1.59765 | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.56918 | −0.200010 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.37176 | 0.493062 | 0.246531 | − | 0.969135i | \(-0.420709\pi\) | ||||
0.246531 | + | 0.969135i | \(0.420709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8462 | −0.834320 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.2399 | 0.783063 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.9841 | 1.67142 | 0.835708 | − | 0.549174i | \(-0.185057\pi\) | ||||
0.835708 | + | 0.549174i | \(0.185057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.56918 | 0.269804 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.42417 | −0.107047 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.33452 | −0.323977 | −0.161989 | − | 0.986793i | \(-0.551791\pi\) | ||||
−0.161989 | + | 0.986793i | \(0.551791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8399 | 1.84633 | 0.923167 | − | 0.384399i | \(-0.125591\pi\) | ||||
0.923167 | + | 0.384399i | \(0.125591\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.297159 | 0.0219666 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.3978 | 0.837986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.4327 | 1.64044 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.74726 | 0.199834 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5998 | 1.41819 | 0.709097 | − | 0.705111i | \(-0.249103\pi\) | ||||
0.709097 | + | 0.705111i | \(0.249103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.0722 | 1.37285 | 0.686425 | − | 0.727201i | \(-0.259179\pi\) | ||||
0.686425 | + | 0.727201i | \(0.259179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.835321 | 0.0598186 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.9686 | −0.995224 | −0.497612 | − | 0.867400i | \(-0.665790\pi\) | ||||
−0.497612 | + | 0.867400i | \(0.665790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.6845 | 0.757402 | 0.378701 | − | 0.925519i | \(-0.376371\pi\) | ||||
0.378701 | + | 0.925519i | \(0.376371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.91552 | 0.346714 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.12850 | 0.219578 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.19617 | 0.0835442 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.1003 | −0.841027 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.6648 | 1.15273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.39554 | 0.577973 | 0.288986 | − | 0.957333i | \(-0.406682\pi\) | ||||
0.288986 | + | 0.957333i | \(0.406682\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.600667 | 0.0411571 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0141 | −0.955750 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.79167 | 0.528933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.00164 | −0.202832 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.29359 | −0.490620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0262 | −0.872299 | −0.436150 | − | 0.899874i | \(-0.643658\pi\) | ||||
−0.436150 | + | 0.899874i | \(0.643658\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.89941 | 0.659961 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5789 | −0.768519 | −0.384260 | − | 0.923225i | \(-0.625543\pi\) | ||||
−0.384260 | + | 0.923225i | \(0.625543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.8025 | −0.978178 | −0.489089 | − | 0.872234i | \(-0.662671\pi\) | ||||
−0.489089 | + | 0.872234i | \(0.662671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.14783 | 0.141317 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2130 | 1.06215 | 0.531075 | − | 0.847325i | \(-0.321788\pi\) | ||||
0.531075 | + | 0.847325i | \(0.321788\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.29318 | 0.540987 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.98903 | −0.324072 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.1097 | −1.04205 | −0.521025 | − | 0.853542i | \(-0.674450\pi\) | ||||
−0.521025 | + | 0.853542i | \(0.674450\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.3504 | −1.63296 | −0.816482 | − | 0.577372i | \(-0.804078\pi\) | ||||
−0.816482 | + | 0.577372i | \(0.804078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.5790 | 0.742795 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.19617 | 0.0764205 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.41826 | −0.344756 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.38404 | −0.214455 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.4484 | −0.911973 | −0.455987 | − | 0.889987i | \(-0.650714\pi\) | ||||
−0.455987 | + | 0.889987i | \(0.650714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.6925 | −1.23806 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.82867 | −0.177138 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.2527 | 1.88711 | 0.943557 | − | 0.331210i | \(-0.107457\pi\) | ||||
0.943557 | + | 0.331210i | \(0.107457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.52861 | −0.592079 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.67716 | 0.537103 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.36884 | −0.331057 | −0.165529 | − | 0.986205i | \(-0.552933\pi\) | ||||
−0.165529 | + | 0.986205i | \(0.552933\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3232 | 0.634148 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.01318 | −0.306802 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.9910 | 0.914020 | 0.457010 | − | 0.889462i | \(-0.348920\pi\) | ||||
0.457010 | + | 0.889462i | \(0.348920\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8762 | 0.903662 | 0.451831 | − | 0.892104i | \(-0.350771\pi\) | ||||
0.451831 | + | 0.892104i | \(0.350771\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.698329 | −0.0422648 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.1107 | 0.971513 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7649 | −1.00730 | −0.503652 | − | 0.863907i | \(-0.668011\pi\) | ||||
−0.503652 | + | 0.863907i | \(0.668011\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.6109 | 1.29381 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.48615 | 0.565896 | 0.282948 | − | 0.959135i | \(-0.408688\pi\) | ||||
0.282948 | + | 0.959135i | \(0.408688\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.3364 | 1.38721 | 0.693603 | − | 0.720357i | \(-0.256022\pi\) | ||||
0.693603 | + | 0.720357i | \(0.256022\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.10136 | −0.124474 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.00000 | −0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.69846 | 0.452850 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.97610 | 0.408946 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.24146 | 0.306209 | 0.153105 | − | 0.988210i | \(-0.451073\pi\) | ||||
0.153105 | + | 0.988210i | \(0.451073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.58015 | −0.208444 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.4007 | 0.719562 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.40266 | 0.370275 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7158 | 0.675286 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.745614 | 0.0428344 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.747013 | 0.0427738 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.8756 | −0.734851 | −0.367426 | − | 0.930053i | \(-0.619761\pi\) | ||||
−0.367426 | + | 0.930053i | \(0.619761\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.342450 | −0.0194813 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.5225 | −1.90089 | −0.950443 | − | 0.310899i | \(-0.899370\pi\) | ||||
−0.950443 | + | 0.310899i | \(0.899370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.48895 | −0.479824 | −0.239912 | − | 0.970795i | \(-0.577119\pi\) | ||||
−0.239912 | + | 0.970795i | \(0.577119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.31768 | 0.186930 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.70236 | −0.544939 | −0.272470 | − | 0.962164i | \(-0.587840\pi\) | ||||
−0.272470 | + | 0.962164i | \(0.587840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.1216 | 0.790657 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.25078 | −0.0698116 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.3480 | 1.02091 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.23811 | −0.290558 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.03736 | −0.333867 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.93311 | −0.382235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.58702 | 0.0872306 | 0.0436153 | − | 0.999048i | \(-0.486112\pi\) | ||||
0.0436153 | + | 0.999048i | \(0.486112\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.4284 | −1.44827 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.3569 | 0.675128 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.97001 | −0.270734 | −0.135367 | − | 0.990796i | \(-0.543221\pi\) | ||||
−0.135367 | + | 0.990796i | \(0.543221\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.13130 | −0.278694 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.1704 | 1.90459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.48314 | 0.133688 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.3942 | 0.719037 | 0.359518 | − | 0.933138i | \(-0.382941\pi\) | ||||
0.359518 | + | 0.933138i | \(0.382941\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.6258 | 0.836432 | 0.418216 | − | 0.908348i | \(-0.362655\pi\) | ||||
0.418216 | + | 0.908348i | \(0.362655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.03186 | −0.215205 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.1802 | 1.55310 | 0.776552 | − | 0.630053i | \(-0.216967\pi\) | ||||
0.776552 | + | 0.630053i | \(0.216967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50999 | 0.0801418 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.36477 | 0.125157 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.2780 | 1.86190 | 0.930951 | − | 0.365144i | \(-0.118980\pi\) | ||||
0.930951 | + | 0.365144i | \(0.118980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.36965 | −0.282613 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.46085 | 0.234134 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.54568 | −0.394959 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.0756 | −1.88313 | −0.941564 | − | 0.336833i | \(-0.890644\pi\) | ||||
−0.941564 | + | 0.336833i | \(0.890644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.77358 | −0.144387 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.63019 | −0.448057 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.34975 | −0.173444 | −0.0867218 | − | 0.996233i | \(-0.527639\pi\) | ||||
−0.0867218 | + | 0.996233i | \(0.527639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.87737 | −0.251866 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.59137 | −0.236468 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.2304 | −1.65556 | −0.827782 | − | 0.561050i | \(-0.810398\pi\) | ||||
−0.827782 | + | 0.561050i | \(0.810398\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.31398 | −0.272243 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.81598 | 0.450475 | 0.225238 | − | 0.974304i | \(-0.427684\pi\) | ||||
0.225238 | + | 0.974304i | \(0.427684\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.39933 | 0.275175 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32.4947 | 1.65180 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.4606 | −1.03739 | −0.518697 | − | 0.854958i | \(-0.673583\pi\) | ||||
−0.518697 | + | 0.854958i | \(0.673583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.6815 | −1.09648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.18915 | 0.110428 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.5417 | −0.631040 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4021 | −0.672631 | −0.336315 | − | 0.941749i | \(-0.609181\pi\) | ||||
−0.336315 | + | 0.941749i | \(0.609181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.75674 | 0.0879470 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.6935 | 1.18320 | 0.591598 | − | 0.806233i | \(-0.298497\pi\) | ||||
0.591598 | + | 0.806233i | \(0.298497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.4350 | −0.569619 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.38936 | 0.416871 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −43.0107 | −2.13196 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.63250 | −0.0807218 | −0.0403609 | − | 0.999185i | \(-0.512851\pi\) | ||||
−0.0403609 | + | 0.999185i | \(0.512851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.63766 | 0.0807799 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.99301 | 0.147276 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.50698 | −0.417591 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.01614 | −0.0497604 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.3900 | 0.849559 | 0.424779 | − | 0.905297i | \(-0.360352\pi\) | ||||
0.424779 | + | 0.905297i | \(0.360352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.25998 | −0.305093 | −0.152546 | − | 0.988296i | \(-0.548747\pi\) | ||||
−0.152546 | + | 0.988296i | \(0.548747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.2296 | −0.934973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.7379 | 0.860416 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.624504 | −0.0302219 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.15215 | −0.152187 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3389 | 1.36504 | 0.682519 | − | 0.730868i | \(-0.260885\pi\) | ||||
0.682519 | + | 0.730868i | \(0.260885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.51273 | −0.457153 | −0.228576 | − | 0.973526i | \(-0.573407\pi\) | ||||
−0.228576 | + | 0.973526i | \(0.573407\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.78067 | −0.0853765 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.1067 | −0.770490 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5414 | −0.837203 | −0.418601 | − | 0.908170i | \(-0.637480\pi\) | ||||
−0.418601 | + | 0.908170i | \(0.637480\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.77358 | −0.132075 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.6698 | −1.02956 | −0.514781 | − | 0.857321i | \(-0.672127\pi\) | ||||
−0.514781 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.6024 | −0.597410 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.61015 | 0.170754 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9887 | 0.896133 | 0.448066 | − | 0.894000i | \(-0.352113\pi\) | ||||
0.448066 | + | 0.894000i | \(0.352113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.51385 | −0.212549 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.59635 | −0.262939 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.75549 | −0.0822988 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.9902 | −1.02866 | −0.514329 | − | 0.857593i | \(-0.671959\pi\) | ||||
−0.514329 | + | 0.857593i | \(0.671959\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.6532 | 0.637276 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8535 | 0.878097 | 0.439048 | − | 0.898463i | \(-0.355316\pi\) | ||||
0.439048 | + | 0.898463i | \(0.355316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.20547 | −0.148971 | −0.0744853 | − | 0.997222i | \(-0.523731\pi\) | ||||
−0.0744853 | + | 0.997222i | \(0.523731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.43484 | −0.205661 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.96252 | 0.322187 | 0.161093 | − | 0.986939i | \(-0.448498\pi\) | ||||
0.161093 | + | 0.986939i | \(0.448498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.3304 | −0.477012 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.86326 | 0.270165 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.8832 | 2.43157 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.1771 | 0.604609 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.9366 | −1.09598 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.8629 | 0.907560 | 0.453780 | − | 0.891114i | \(-0.350075\pi\) | ||||
0.453780 | + | 0.891114i | \(0.350075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9841 | 0.637622 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.07591 | −0.0944570 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.5369 | 0.796308 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.40158 | −0.380712 | −0.190356 | − | 0.981715i | \(-0.560964\pi\) | ||||
−0.190356 | + | 0.981715i | \(0.560964\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.70573 | −0.438908 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9454 | −0.584218 | −0.292109 | − | 0.956385i | \(-0.594357\pi\) | ||||
−0.292109 | + | 0.956385i | \(0.594357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5479 | 0.700241 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.9755 | 0.673099 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.26235 | −0.0566242 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7557 | −0.794853 | −0.397427 | − | 0.917634i | \(-0.630097\pi\) | ||||
−0.397427 | + | 0.917634i | \(0.630097\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.03189 | 0.135455 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.42005 | 0.375431 | 0.187716 | − | 0.982223i | \(-0.439892\pi\) | ||||
0.187716 | + | 0.982223i | \(0.439892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.87436 | 0.0834080 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.16095 | −0.229206 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.1793 | −1.20470 | −0.602351 | − | 0.798231i | \(-0.705769\pi\) | ||||
−0.602351 | + | 0.798231i | \(0.705769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.30820 | 0.279058 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.1427 | 0.447810 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.860867 | −0.0379343 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.2950 | −1.37635 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.4607 | 0.459175 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.4643 | −1.68515 | −0.842576 | − | 0.538578i | \(-0.818962\pi\) | ||||
−0.842576 | + | 0.538578i | \(0.818962\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.7671 | −1.69517 | −0.847583 | − | 0.530664i | \(-0.821943\pi\) | ||||
−0.847583 | + | 0.530664i | \(0.821943\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.69833 | 0.0741212 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.7227 | 1.68679 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.96696 | −0.172476 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.30136 | 0.360248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.46760 | 0.0635686 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.14427 | −0.135938 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.06251 | −0.0890037 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.51385 | −0.194425 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.22511 | −0.0526717 | −0.0263359 | − | 0.999653i | \(-0.508384\pi\) | ||||
−0.0263359 | + | 0.999653i | \(0.508384\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.8196 | 0.507228 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.1770 | −0.650112 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.3496 | −1.12663 | −0.563314 | − | 0.826243i | \(-0.690474\pi\) | ||||
−0.563314 | + | 0.826243i | \(0.690474\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.73211 | −0.0739248 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5502 | 0.492055 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.4848 | 0.445861 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.42346 | 0.230213 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.8215 | −0.839864 | −0.419932 | − | 0.907556i | \(-0.637946\pi\) | ||||
−0.419932 | + | 0.907556i | \(0.637946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.1940 | −0.727229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.6742 | 0.450666 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.7443 | −0.663543 | −0.331772 | − | 0.943360i | \(-0.607646\pi\) | ||||
−0.331772 | + | 0.943360i | \(0.607646\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.8993 | −0.542678 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.01352 | −0.294540 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.3943 | −1.81918 | −0.909592 | − | 0.415502i | \(-0.863606\pi\) | ||||
−0.909592 | + | 0.415502i | \(0.863606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9825 | −1.42212 | −0.711062 | − | 0.703129i | \(-0.751786\pi\) | ||||
−0.711062 | + | 0.703129i | \(0.751786\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.32623 | 0.389609 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.5712 | −0.649364 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1670 | 0.881195 | 0.440598 | − | 0.897705i | \(-0.354767\pi\) | ||||
0.440598 | + | 0.897705i | \(0.354767\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.07519 | 0.377152 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.11184 | 0.295049 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −38.9554 | −1.61337 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.86901 | −0.201309 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.78343 | 0.114885 | 0.0574423 | − | 0.998349i | \(-0.481705\pi\) | ||||
0.0574423 | + | 0.998349i | \(0.481705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.7663 | 1.18530 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.64673 | −0.273410 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.5233 | 0.965985 | 0.482992 | − | 0.875625i | \(-0.339550\pi\) | ||||
0.482992 | + | 0.875625i | \(0.339550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.94467 | 0.243708 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.08402 | 0.208075 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8380 | −0.851417 | −0.425709 | − | 0.904860i | \(-0.639975\pi\) | ||||
−0.425709 | + | 0.904860i | \(0.639975\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.5628 | 1.04273 | 0.521365 | − | 0.853334i | \(-0.325423\pi\) | ||||
0.521365 | + | 0.853334i | \(0.325423\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.6521 | −1.16680 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2139 | 0.455910 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.2169 | 1.51059 | 0.755294 | − | 0.655386i | \(-0.227494\pi\) | ||||
0.755294 | + | 0.655386i | \(0.227494\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.48864 | 0.0603228 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.1750 | 0.411636 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.6927 | −1.28006 | −0.640028 | − | 0.768351i | \(-0.721077\pi\) | ||||
−0.640028 | + | 0.768351i | \(0.721077\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.569176 | 0.0229514 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.4239 | −0.983270 | −0.491635 | − | 0.870801i | \(-0.663601\pi\) | ||||
−0.491635 | + | 0.870801i | \(0.663601\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.01600 | −0.241803 | −0.120902 | − | 0.992664i | \(-0.538579\pi\) | ||||
−0.120902 | + | 0.992664i | \(0.538579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.9854 | −0.480958 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.5356 | 0.422100 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.58490 | 0.223396 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.92966 | 0.316680 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47.3549 | −1.88816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3588 | 0.491995 | 0.245997 | − | 0.969270i | \(-0.420885\pi\) | ||||
0.245997 | + | 0.969270i | \(0.420885\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.99487 | 0.158782 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.3585 | −0.530118 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.46760 | 0.0581482 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.50124 | −0.138507 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.58897 | −0.378741 | −0.189371 | − | 0.981906i | \(-0.560645\pi\) | ||||
−0.189371 | + | 0.981906i | \(0.560645\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.27552 | −0.0897379 | −0.0448689 | − | 0.998993i | \(-0.514287\pi\) | ||||
−0.0448689 | + | 0.998993i | \(0.514287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.66834 | −0.262566 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.3295 | −0.445408 | −0.222704 | − | 0.974886i | \(-0.571488\pi\) | ||||
−0.222704 | + | 0.974886i | \(0.571488\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5100 | 0.530313 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.70753 | 0.145310 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.7539 | −1.20349 | −0.601747 | − | 0.798687i | \(-0.705528\pi\) | ||||
−0.601747 | + | 0.798687i | \(0.705528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.50318 | 0.215027 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.4963 | 0.682596 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.8574 | −1.04622 | −0.523109 | − | 0.852266i | \(-0.675228\pi\) | ||||
−0.523109 | + | 0.852266i | \(0.675228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9154 | 0.735723 | 0.367861 | − | 0.929881i | \(-0.380090\pi\) | ||||
0.367861 | + | 0.929881i | \(0.380090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.47052 | −0.134784 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.41618 | 0.171252 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.6487 | −0.528479 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.19829 | −0.239640 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.81892 | −0.108823 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.5337 | −0.598780 | −0.299390 | − | 0.954131i | \(-0.596783\pi\) | ||||
−0.299390 | + | 0.954131i | \(0.596783\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.80545 | 0.377412 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.8789 | −1.03304 | −0.516521 | − | 0.856275i | \(-0.672773\pi\) | ||||
−0.516521 | + | 0.856275i | \(0.672773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.6608 | −0.562632 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.50962 | −0.211129 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.7859 | −1.56063 | −0.780314 | − | 0.625388i | \(-0.784941\pi\) | ||||
−0.780314 | + | 0.625388i | \(0.784941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.11683 | 0.157296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.04351 | −0.268727 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.6656 | 0.482522 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.5508 | 1.73283 | 0.866417 | − | 0.499322i | \(-0.166417\pi\) | ||||
0.866417 | + | 0.499322i | \(0.166417\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.5195 | −0.475578 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.55441 | −0.0968944 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.96975 | −0.188243 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.71467 | 0.291796 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1849 | 0.460218 | 0.230109 | − | 0.973165i | \(-0.426092\pi\) | ||||
0.230109 | + | 0.973165i | \(0.426092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.1790 | −1.32680 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.94616 | 0.148621 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.56697 | −0.0589319 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.4995 | −1.25810 | −0.629050 | − | 0.777365i | \(-0.716556\pi\) | ||||
−0.629050 | + | 0.777365i | \(0.716556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.0806 | 1.09061 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.9926 | −1.27303 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.92404 | −0.296342 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.66551 | −0.286274 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.3346 | 1.09399 | 0.546997 | − | 0.837134i | \(-0.315771\pi\) | ||||
0.546997 | + | 0.837134i | \(0.315771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.719686 | 0.0268025 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.0625 | −0.448611 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.1662 | 0.414701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.9297 | 1.44382 | 0.721912 | − | 0.691985i | \(-0.243264\pi\) | ||||
0.721912 | + | 0.691985i | \(0.243264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.5309 | −0.575218 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.2245 | 2.15351 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.3084 | −1.00866 | −0.504328 | − | 0.863512i | \(-0.668260\pi\) | ||||
−0.504328 | + | 0.863512i | \(0.668260\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.569176 | 0.0209944 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −46.6297 | −1.71763 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6677 | 0.760273 | 0.380137 | − | 0.924930i | \(-0.375877\pi\) | ||||
0.380137 | + | 0.924930i | \(0.375877\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.57818 | −0.0947119 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.1654 | 1.43684 | 0.718420 | − | 0.695610i | \(-0.244866\pi\) | ||||
0.718420 | + | 0.695610i | \(0.244866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.07537 | 0.332496 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.7253 | 0.721711 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.62861 | 0.0960473 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.61890 | 0.168546 | 0.0842731 | − | 0.996443i | \(-0.473143\pi\) | ||||
0.0842731 | + | 0.996443i | \(0.473143\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.87500 | −0.250539 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.0684 | −0.512001 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.91662 | −0.142352 | −0.0711759 | − | 0.997464i | \(-0.522675\pi\) | ||||
−0.0711759 | + | 0.997464i | \(0.522675\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.37033 | −0.340121 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.08928 | −0.148236 | −0.0741181 | − | 0.997249i | \(-0.523614\pi\) | ||||
−0.0741181 | + | 0.997249i | \(0.523614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6880 | 0.459337 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.4880 | 0.596127 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.39252 | −0.158605 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.41895 | −0.0872297 | −0.0436148 | − | 0.999048i | \(-0.513887\pi\) | ||||
−0.0436148 | + | 0.999048i | \(0.513887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3952 | 0.518432 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.8874 | −0.823204 | −0.411602 | − | 0.911364i | \(-0.635031\pi\) | ||||
−0.411602 | + | 0.911364i | \(0.635031\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.8099 | 0.998960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.53402 | −0.162657 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.69193 | −0.132277 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.69806 | −0.203893 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.59479 | 0.307153 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.7394 | 0.526070 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.2149 | −1.68303 | −0.841516 | − | 0.540233i | \(-0.818336\pi\) | ||||
−0.841516 | + | 0.540233i | \(0.818336\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.55467 | −0.0909486 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7838 | 0.383429 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.916519 | 0.0325465 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.91210 | 0.174214 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.4571 | 1.78728 | 0.893642 | − | 0.448781i | \(-0.148142\pi\) | ||||
0.893642 | + | 0.448781i | \(0.148142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.4558 | −1.21896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.2214 | 1.03249 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.4742 | 1.00483 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.21852 | −0.183929 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.13322 | 0.251101 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.8477 | −1.01423 | −0.507116 | − | 0.861878i | \(-0.669288\pi\) | ||||
−0.507116 | + | 0.861878i | \(0.669288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.2208 | −0.885623 | −0.442811 | − | 0.896615i | \(-0.646019\pi\) | ||||
−0.442811 | + | 0.896615i | \(0.646019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.07855 | 0.248256 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.3987 | −0.854651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.2538 | 1.51326 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.07050 | 0.142235 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.10919 | 0.317913 | 0.158957 | − | 0.987286i | \(-0.449187\pi\) | ||||
0.158957 | + | 0.987286i | \(0.449187\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5664 | 0.682042 | 0.341021 | − | 0.940056i | \(-0.389227\pi\) | ||||
0.341021 | + | 0.940056i | \(0.389227\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.66600 | 0.266896 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.8177 | 0.828224 | 0.414112 | − | 0.910226i | \(-0.364092\pi\) | ||||
0.414112 | + | 0.910226i | \(0.364092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.2073 | −1.63958 | −0.819789 | − | 0.572666i | \(-0.805909\pi\) | ||||
−0.819789 | + | 0.572666i | \(0.805909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.97727 | −0.276728 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.96975 | −0.172192 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.62171 | 0.263760 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.4057 | 0.739890 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.02383 | −0.311537 | −0.155769 | − | 0.987794i | \(-0.549785\pi\) | ||||
−0.155769 | + | 0.987794i | \(0.549785\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2125 | −0.662500 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.51382 | 0.155464 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9739 | −0.446314 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.37483 | −0.322123 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.1042 | 0.381096 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.5704 | 1.42501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.32467 | −0.113835 | −0.0569173 | − | 0.998379i | \(-0.518127\pi\) | ||||
−0.0569173 | + | 0.998379i | \(0.518127\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.2486 | 0.418895 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.2358 | −1.03283 | −0.516417 | − | 0.856337i | \(-0.672735\pi\) | ||||
−0.516417 | + | 0.856337i | \(0.672735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.7343 | 1.66279 | 0.831397 | − | 0.555679i | \(-0.187542\pi\) | ||||
0.831397 | + | 0.555679i | \(0.187542\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.475832 | −0.0162163 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.35784 | 0.318544 | 0.159272 | − | 0.987235i | \(-0.449085\pi\) | ||||
0.159272 | + | 0.987235i | \(0.449085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.2967 | 0.894114 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66317 | 0.124408 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.3270 | 1.60546 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1608 | 0.513704 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −40.6631 | −1.37624 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.2502 | 0.346520 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.4956 | −1.63758 | −0.818790 | − | 0.574094i | \(-0.805354\pi\) | ||||
−0.818790 | + | 0.574094i | \(0.805354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.49406 | 0.0841224 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.12371 | 0.0715495 | 0.0357747 | − | 0.999360i | \(-0.488610\pi\) | ||||
0.0357747 | + | 0.999360i | \(0.488610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.6435 | 1.77159 | 0.885797 | − | 0.464072i | \(-0.153612\pi\) | ||||
0.885797 | + | 0.464072i | \(0.153612\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.70355 | −0.0572642 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.6617 | −1.39886 | −0.699432 | − | 0.714699i | \(-0.746564\pi\) | ||||
−0.699432 | + | 0.714699i | \(0.746564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.1678 | 0.374555 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.6580 | −1.06058 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.5966 | −0.856556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.18483 | −0.173310 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.04659 | 0.101723 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.3763 | 0.812993 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.8899 | −1.42887 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.57474 | 0.185516 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.7127 | 0.987685 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5547 | −0.848530 | −0.424265 | − | 0.905538i | \(-0.639467\pi\) | ||||
−0.424265 | + | 0.905538i | \(0.639467\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.34612 | −0.144152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.2918 | 1.76564 | 0.882818 | − | 0.469715i | \(-0.155643\pi\) | ||||
0.882818 | + | 0.469715i | \(0.155643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.1018 | 1.06241 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.355453 | 0.0117509 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.60067 | −0.151927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.0164 | 1.81482 | 0.907412 | − | 0.420242i | \(-0.138055\pi\) | ||||
0.907412 | + | 0.420242i | \(0.138055\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.12664 | −0.201880 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.85262 | 0.0609798 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.0093 | −1.11822 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.99611 | 0.0655608 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.6341 | −1.66125 | −0.830625 | − | 0.556832i | \(-0.812017\pi\) | ||||
−0.830625 | + | 0.556832i | \(0.812017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.69193 | −0.120998 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.9511 | −0.522215 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.8334 | 0.877545 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.64462 | 0.282407 | 0.141204 | − | 0.989981i | \(-0.454903\pi\) | ||||
0.141204 | + | 0.989981i | \(0.454903\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.03932 | −0.131818 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.76003 | −0.318168 | −0.159084 | − | 0.987265i | \(-0.550854\pi\) | ||||
−0.159084 | + | 0.987265i | \(0.550854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.36269 | 0.142069 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.28619 | 0.106900 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.9190 | 1.23220 | 0.616100 | − | 0.787668i | \(-0.288712\pi\) | ||||
0.616100 | + | 0.787668i | \(0.288712\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.25788 | −0.300523 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.61670 | −0.149707 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.2393 | 0.526042 | 0.263021 | − | 0.964790i | \(-0.415281\pi\) | ||||
0.263021 | + | 0.964790i | \(0.415281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.4447 | 0.758653 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.71950 | 0.217211 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.44168 | −0.111138 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.7102 | 0.958393 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.29067 | 0.234939 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8136 | 0.734397 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.32778 | 0.0426987 | 0.0213493 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213493 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.73056 | 0.280466 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.4967 | −1.26751 | −0.633755 | − | 0.773534i | \(-0.718487\pi\) | ||||
−0.633755 | + | 0.773534i | \(0.718487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.13549 | 0.0684607 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.49246 | −0.0798226 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.3135 | −0.969814 | −0.484907 | − | 0.874566i | \(-0.661147\pi\) | ||||
−0.484907 | + | 0.874566i | \(0.661147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.5561 | 1.51990 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.1913 | 1.12357 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.7778 | 0.343757 | 0.171879 | − | 0.985118i | \(-0.445016\pi\) | ||||
0.171879 | + | 0.985118i | \(0.445016\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.7089 | −0.532389 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.29900 | −0.105008 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.1122 | −1.62527 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.6428 | −0.846336 | −0.423168 | − | 0.906051i | \(-0.639082\pi\) | ||||
−0.423168 | + | 0.906051i | \(0.639082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.755156 | 0.0239642 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.7804 | 0.405167 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.8206 | 0.342693 | 0.171346 | − | 0.985211i | \(-0.445188\pi\) | ||||
0.171346 | + | 0.985211i | \(0.445188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.1775 | −0.828221 |
(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 | 1148.2.a.c.1.4 | ✓ | 5 | |
4.3 | odd | 2 | 4592.2.a.be.1.2 | 5 | |||
7.6 | odd | 2 | 8036.2.a.l.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.c.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4592.2.a.be.1.2 | 5 | 4.3 | odd | 2 | |||
8036.2.a.l.1.2 | 5 | 7.6 | odd | 2 |