Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.174928.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.34440\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34440 | 0.950636 | 0.475318 | − | 0.879814i | \(-0.342333\pi\) | ||||
0.475318 | + | 0.879814i | \(0.342333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.192582 | −0.0962912 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.94771 | −1.04217 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.63652 | 1.69947 | 0.849737 | − | 0.527207i | \(-0.176761\pi\) | ||||
0.849737 | + | 0.527207i | \(0.176761\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.38516 | −1.21623 | −0.608113 | − | 0.793851i | \(-0.708073\pi\) | ||||
−0.608113 | + | 0.793851i | \(0.708073\pi\) | |||||||
\(14\) | −1.34440 | −0.359307 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.57775 | −0.894437 | ||||||||
\(17\) | 2.68880 | 0.652131 | 0.326065 | − | 0.945347i | \(-0.394277\pi\) | ||||
0.326065 | + | 0.945347i | \(0.394277\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.38516 | 1.92369 | 0.961844 | − | 0.273597i | \(-0.0882135\pi\) | ||||
0.961844 | + | 0.273597i | \(0.0882135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.57775 | 1.61558 | ||||||||
\(23\) | 5.63652 | 1.17530 | 0.587648 | − | 0.809117i | \(-0.300054\pi\) | ||||
0.587648 | + | 0.809117i | \(0.300054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.89543 | −1.15619 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.192582 | 0.0363947 | ||||||||
\(29\) | −8.32532 | −1.54597 | −0.772987 | − | 0.634422i | \(-0.781238\pi\) | ||||
−0.772987 | + | 0.634422i | \(0.781238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.08549 | 0.191890 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.61484 | 0.619939 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 11.2730 | 1.82873 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.37761 | 0.839841 | 0.419921 | − | 0.907561i | \(-0.362058\pi\) | ||||
0.419921 | + | 0.907561i | \(0.362058\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.38516 | 0.211236 | 0.105618 | − | 0.994407i | \(-0.466318\pi\) | ||||
0.105618 | + | 0.994407i | \(0.466318\pi\) | |||||||
\(44\) | −1.08549 | −0.163644 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.57775 | 1.11728 | ||||||||
\(47\) | 8.58423 | 1.25214 | 0.626069 | − | 0.779767i | \(-0.284663\pi\) | ||||
0.626069 | + | 0.779767i | \(0.284663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.844506 | 0.117112 | ||||||||
\(53\) | −5.37761 | −0.738671 | −0.369336 | − | 0.929296i | \(-0.620415\pi\) | ||||
−0.369336 | + | 0.929296i | \(0.620415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.94771 | 0.393905 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.1926 | −1.46966 | ||||||||
\(59\) | 8.58423 | 1.11757 | 0.558786 | − | 0.829312i | \(-0.311267\pi\) | ||||
0.558786 | + | 0.829312i | \(0.311267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 8.06641 | 1.02444 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.61484 | 1.07685 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.38516 | 0.169225 | 0.0846124 | − | 0.996414i | \(-0.473035\pi\) | ||||
0.0846124 | + | 0.996414i | \(0.473035\pi\) | |||||||
\(68\) | −0.517816 | −0.0627945 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.258908 | −0.0307268 | −0.0153634 | − | 0.999882i | \(-0.504891\pi\) | ||||
−0.0153634 | + | 0.999882i | \(0.504891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.38516 | −0.747327 | −0.373664 | − | 0.927564i | \(-0.621899\pi\) | ||||
−0.373664 | + | 0.927564i | \(0.621899\pi\) | |||||||
\(74\) | 4.03321 | 0.468851 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.61484 | −0.185234 | ||||||||
\(77\) | −5.63652 | −0.642341 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.38516 | 0.605878 | 0.302939 | − | 0.953010i | \(-0.402032\pi\) | ||||
0.302939 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.22967 | 0.798384 | ||||||||
\(83\) | −16.6506 | −1.82765 | −0.913823 | − | 0.406113i | \(-0.866884\pi\) | ||||
−0.913823 | + | 0.406113i | \(0.866884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.86222 | 0.200808 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −16.6148 | −1.77115 | ||||||||
\(89\) | −13.9618 | −1.47995 | −0.739976 | − | 0.672633i | \(-0.765163\pi\) | ||||
−0.739976 | + | 0.672633i | \(0.765163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.38516 | 0.459690 | ||||||||
\(92\) | −1.08549 | −0.113171 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.5407 | 1.19033 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7703 | 1.09356 | 0.546781 | − | 0.837276i | \(-0.315853\pi\) | ||||
0.546781 | + | 0.837276i | \(0.315853\pi\) | |||||||
\(98\) | 1.34440 | 0.135805 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.68880 | −0.267546 | −0.133773 | − | 0.991012i | \(-0.542709\pi\) | ||||
−0.133773 | + | 0.991012i | \(0.542709\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.3852 | 1.61448 | 0.807239 | − | 0.590225i | \(-0.200961\pi\) | ||||
0.807239 | + | 0.590225i | \(0.200961\pi\) | |||||||
\(104\) | 12.9262 | 1.26752 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.22967 | −0.702208 | ||||||||
\(107\) | −16.6506 | −1.60968 | −0.804839 | − | 0.593493i | \(-0.797749\pi\) | ||||
−0.804839 | + | 0.593493i | \(0.797749\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.57775 | 0.338065 | ||||||||
\(113\) | 8.32532 | 0.783180 | 0.391590 | − | 0.920140i | \(-0.371925\pi\) | ||||
0.391590 | + | 0.920140i | \(0.371925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.60331 | 0.148864 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.5407 | 1.06240 | ||||||||
\(119\) | −2.68880 | −0.246482 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.7703 | 1.88821 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.15549 | −0.103766 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.3852 | −1.36521 | −0.682606 | − | 0.730786i | \(-0.739154\pi\) | ||||
−0.682606 | + | 0.730786i | \(0.739154\pi\) | |||||||
\(128\) | 9.41082 | 0.831806 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.68880 | −0.234922 | −0.117461 | − | 0.993077i | \(-0.537476\pi\) | ||||
−0.117461 | + | 0.993077i | \(0.537476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.38516 | −0.727086 | ||||||||
\(134\) | 1.86222 | 0.160871 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.92582 | −0.679634 | ||||||||
\(137\) | −5.37761 | −0.459440 | −0.229720 | − | 0.973257i | \(-0.573781\pi\) | ||||
−0.229720 | + | 0.973257i | \(0.573781\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.38516 | 0.541583 | 0.270791 | − | 0.962638i | \(-0.412715\pi\) | ||||
0.270791 | + | 0.962638i | \(0.412715\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.348077 | −0.0292100 | ||||||||
\(143\) | −24.7171 | −2.06694 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.58423 | −0.710436 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.577747 | −0.0474905 | ||||||||
\(149\) | −13.7029 | −1.12259 | −0.561294 | − | 0.827617i | \(-0.689696\pi\) | ||||
−0.561294 | + | 0.827617i | \(0.689696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.614835 | 0.0500346 | 0.0250173 | − | 0.999687i | \(-0.492036\pi\) | ||||
0.0250173 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(152\) | −24.7171 | −2.00482 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.57775 | −0.610632 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.77033 | −0.380714 | −0.190357 | − | 0.981715i | \(-0.560965\pi\) | ||||
−0.190357 | + | 0.981715i | \(0.560965\pi\) | |||||||
\(158\) | 7.23983 | 0.575970 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.63652 | −0.444220 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.77033 | −0.373641 | −0.186821 | − | 0.982394i | \(-0.559818\pi\) | ||||
−0.186821 | + | 0.982394i | \(0.559818\pi\) | |||||||
\(164\) | −1.03563 | −0.0808693 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.3852 | −1.73743 | ||||||||
\(167\) | 13.9618 | 1.08040 | 0.540200 | − | 0.841537i | \(-0.318349\pi\) | ||||
0.540200 | + | 0.841537i | \(0.318349\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.22967 | 0.479205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.266758 | −0.0203401 | ||||||||
\(173\) | 3.20662 | 0.243795 | 0.121897 | − | 0.992543i | \(-0.461102\pi\) | ||||
0.121897 | + | 0.992543i | \(0.461102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.1660 | −1.52007 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.7703 | −1.40690 | ||||||||
\(179\) | 16.6506 | 1.24453 | 0.622264 | − | 0.782808i | \(-0.286213\pi\) | ||||
0.622264 | + | 0.782808i | \(0.286213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.61484 | 0.714665 | 0.357333 | − | 0.933977i | \(-0.383686\pi\) | ||||
0.357333 | + | 0.933977i | \(0.383686\pi\) | |||||||
\(182\) | 5.89543 | 0.436998 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.6148 | −1.22486 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.1555 | 1.10828 | ||||||||
\(188\) | −1.65317 | −0.120570 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.2730 | −0.815688 | −0.407844 | − | 0.913052i | \(-0.633719\pi\) | ||||
−0.407844 | + | 0.913052i | \(0.633719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | 0.0719816 | 0.0359908 | − | 0.999352i | \(-0.488541\pi\) | ||||
0.0359908 | + | 0.999352i | \(0.488541\pi\) | |||||||
\(194\) | 14.4797 | 1.03958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.192582 | −0.0137559 | ||||||||
\(197\) | −19.0805 | −1.35943 | −0.679716 | − | 0.733475i | \(-0.737897\pi\) | ||||
−0.679716 | + | 0.733475i | \(0.737897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.7703 | −1.47237 | −0.736185 | − | 0.676781i | \(-0.763375\pi\) | ||||
−0.736185 | + | 0.676781i | \(0.763375\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.61484 | −0.254339 | ||||||||
\(203\) | 8.32532 | 0.584323 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 22.0283 | 1.53478 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.6890 | 1.08784 | ||||||||
\(209\) | 47.2631 | 3.26926 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 1.03563 | 0.0711276 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −22.3852 | −1.53022 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 9.41082 | 0.637381 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.7909 | −0.793139 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.3852 | 0.963302 | 0.481651 | − | 0.876363i | \(-0.340037\pi\) | ||||
0.481651 | + | 0.876363i | \(0.340037\pi\) | |||||||
\(224\) | −1.08549 | −0.0725276 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.1926 | 0.744520 | ||||||||
\(227\) | −8.58423 | −0.569755 | −0.284878 | − | 0.958564i | \(-0.591953\pi\) | ||||
−0.284878 | + | 0.958564i | \(0.591953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.5407 | 1.81994 | 0.909969 | − | 0.414676i | \(-0.136105\pi\) | ||||
0.909969 | + | 0.414676i | \(0.136105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.5407 | 1.61117 | ||||||||
\(233\) | −19.5984 | −1.28393 | −0.641966 | − | 0.766733i | \(-0.721881\pi\) | ||||
−0.641966 | + | 0.766733i | \(0.721881\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.65317 | −0.107612 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.61484 | −0.234315 | ||||||||
\(239\) | −11.2730 | −0.729192 | −0.364596 | − | 0.931166i | \(-0.618793\pi\) | ||||
−0.364596 | + | 0.931166i | \(0.618793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.61484 | 0.490515 | 0.245257 | − | 0.969458i | \(-0.421128\pi\) | ||||
0.245257 | + | 0.969458i | \(0.421128\pi\) | |||||||
\(242\) | 27.9237 | 1.79500 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.7703 | −2.33964 | ||||||||
\(248\) | −17.6863 | −1.12308 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.6125 | 1.93224 | 0.966121 | − | 0.258088i | \(-0.0830924\pi\) | ||||
0.966121 | + | 0.258088i | \(0.0830924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.7703 | 1.99738 | ||||||||
\(254\) | −20.6839 | −1.29782 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.57775 | −0.286109 | ||||||||
\(257\) | −5.89543 | −0.367747 | −0.183873 | − | 0.982950i | \(-0.558864\pi\) | ||||
−0.183873 | + | 0.982950i | \(0.558864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.61484 | −0.223325 | ||||||||
\(263\) | −11.5319 | −0.711090 | −0.355545 | − | 0.934659i | \(-0.615705\pi\) | ||||
−0.355545 | + | 0.934659i | \(0.615705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.2730 | −0.691194 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.266758 | −0.0162949 | ||||||||
\(269\) | −16.6506 | −1.01521 | −0.507604 | − | 0.861591i | \(-0.669469\pi\) | ||||
−0.507604 | + | 0.861591i | \(0.669469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.1555 | −1.04212 | −0.521061 | − | 0.853519i | \(-0.674464\pi\) | ||||
−0.521061 | + | 0.853519i | \(0.674464\pi\) | |||||||
\(272\) | −9.61986 | −0.583290 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.22967 | −0.436760 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.5407 | −1.17408 | −0.587042 | − | 0.809556i | \(-0.699708\pi\) | ||||
−0.587042 | + | 0.809556i | \(0.699708\pi\) | |||||||
\(278\) | 8.58423 | 0.514848 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.2207 | 0.848339 | 0.424169 | − | 0.905583i | \(-0.360566\pi\) | ||||
0.424169 | + | 0.905583i | \(0.360566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0000 | 0.832214 | 0.416107 | − | 0.909316i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909316i | \(0.363394\pi\) | |||||||
\(284\) | 0.0498612 | 0.00295872 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.2297 | −1.96491 | ||||||||
\(287\) | −5.37761 | −0.317430 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.77033 | −0.574725 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.22967 | 0.0719610 | ||||||||
\(293\) | 8.58423 | 0.501496 | 0.250748 | − | 0.968052i | \(-0.419323\pi\) | ||||
0.250748 | + | 0.968052i | \(0.419323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.84314 | −0.513997 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.4223 | −1.06717 | ||||||||
\(299\) | −24.7171 | −1.42942 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.38516 | −0.0798396 | ||||||||
\(302\) | 0.826586 | 0.0475647 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −30.0000 | −1.72062 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1555 | −1.09326 | −0.546631 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546631 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(308\) | 1.08549 | 0.0618518 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4440 | −0.762341 | −0.381170 | − | 0.924505i | \(-0.624479\pi\) | ||||
−0.381170 | + | 0.924505i | \(0.624479\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.9258 | 1.69151 | 0.845754 | − | 0.533573i | \(-0.179151\pi\) | ||||
0.845754 | + | 0.533573i | \(0.179151\pi\) | |||||||
\(314\) | −6.41324 | −0.361920 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.03709 | −0.0583408 | ||||||||
\(317\) | −2.94771 | −0.165560 | −0.0827800 | − | 0.996568i | \(-0.526380\pi\) | ||||
−0.0827800 | + | 0.996568i | \(0.526380\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −46.9258 | −2.62734 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.57775 | −0.422291 | ||||||||
\(323\) | 22.5461 | 1.25450 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.41324 | −0.355197 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.8516 | −0.875261 | ||||||||
\(329\) | −8.58423 | −0.473264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.1555 | −1.21778 | −0.608888 | − | 0.793256i | \(-0.708384\pi\) | ||||
−0.608888 | + | 0.793256i | \(0.708384\pi\) | |||||||
\(332\) | 3.20662 | 0.175986 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.7703 | 1.02707 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7703 | 0.586697 | 0.293349 | − | 0.956006i | \(-0.405230\pi\) | ||||
0.293349 | + | 0.956006i | \(0.405230\pi\) | |||||||
\(338\) | 8.37518 | 0.455550 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.8191 | 1.83141 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −4.08307 | −0.220144 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.31099 | 0.231760 | ||||||||
\(347\) | 5.11870 | 0.274786 | 0.137393 | − | 0.990517i | \(-0.456128\pi\) | ||||
0.137393 | + | 0.990517i | \(0.456128\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.38516 | −0.448848 | −0.224424 | − | 0.974492i | \(-0.572050\pi\) | ||||
−0.224424 | + | 0.974492i | \(0.572050\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.11841 | 0.326112 | ||||||||
\(353\) | 5.89543 | 0.313782 | 0.156891 | − | 0.987616i | \(-0.449853\pi\) | ||||
0.156891 | + | 0.987616i | \(0.449853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.68880 | 0.142506 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.3852 | 1.18309 | ||||||||
\(359\) | −16.3917 | −0.865123 | −0.432561 | − | 0.901604i | \(-0.642390\pi\) | ||||
−0.432561 | + | 0.901604i | \(0.642390\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.3110 | 2.70058 | ||||||||
\(362\) | 12.9262 | 0.679386 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.844506 | −0.0442641 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | −0.208798 | −0.104399 | − | 0.994535i | \(-0.533292\pi\) | ||||
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | −20.1660 | −1.05123 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.37761 | 0.279192 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.0000 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724071\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 20.3751 | 1.05357 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −25.3038 | −1.30495 | ||||||||
\(377\) | 36.5079 | 1.88025 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.614835 | −0.0315820 | −0.0157910 | − | 0.999875i | \(-0.505027\pi\) | ||||
−0.0157910 | + | 0.999875i | \(0.505027\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.1555 | −0.775423 | ||||||||
\(383\) | 19.3394 | 0.988200 | 0.494100 | − | 0.869405i | \(-0.335498\pi\) | ||||
0.494100 | + | 0.869405i | \(0.335498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.34440 | 0.0684283 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.07418 | −0.105300 | ||||||||
\(389\) | 30.8714 | 1.56524 | 0.782621 | − | 0.622499i | \(-0.213882\pi\) | ||||
0.782621 | + | 0.622499i | \(0.213882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.1555 | 0.766446 | ||||||||
\(392\) | −2.94771 | −0.148882 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.6519 | −1.29233 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.7703 | −1.14281 | −0.571405 | − | 0.820668i | \(-0.693601\pi\) | ||||
−0.571405 | + | 0.820668i | \(0.693601\pi\) | |||||||
\(398\) | −27.9237 | −1.39969 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.7029 | −0.684292 | −0.342146 | − | 0.939647i | \(-0.611154\pi\) | ||||
−0.342146 | + | 0.939647i | \(0.611154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.3110 | −1.31064 | ||||||||
\(404\) | 0.517816 | 0.0257623 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.1926 | 0.555479 | ||||||||
\(407\) | 16.9096 | 0.838175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6148 | 0.574317 | 0.287158 | − | 0.957883i | \(-0.407289\pi\) | ||||
0.287158 | + | 0.957883i | \(0.407289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.15549 | −0.155460 | ||||||||
\(413\) | −8.58423 | −0.422402 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.76007 | −0.233382 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 63.5407 | 3.10788 | ||||||||
\(419\) | −5.89543 | −0.288010 | −0.144005 | − | 0.989577i | \(-0.545998\pi\) | ||||
−0.144005 | + | 0.989577i | \(0.545998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.3110 | −1.91590 | −0.957950 | − | 0.286935i | \(-0.907364\pi\) | ||||
−0.957950 | + | 0.286935i | \(0.907364\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.8516 | 0.769824 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.20662 | 0.154998 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.4059 | 1.32009 | 0.660047 | − | 0.751224i | \(-0.270536\pi\) | ||||
0.660047 | + | 0.751224i | \(0.270536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.5407 | 1.61186 | 0.805931 | − | 0.592010i | \(-0.201665\pi\) | ||||
0.805931 | + | 0.592010i | \(0.201665\pi\) | |||||||
\(434\) | −8.06641 | −0.387200 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.34808 | −0.0645612 | ||||||||
\(437\) | 47.2631 | 2.26090 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.1555 | −0.627877 | −0.313939 | − | 0.949443i | \(-0.601649\pi\) | ||||
−0.313939 | + | 0.949443i | \(0.601649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.8516 | −0.753986 | ||||||||
\(443\) | 33.8191 | 1.60679 | 0.803397 | − | 0.595444i | \(-0.203024\pi\) | ||||
0.803397 | + | 0.595444i | \(0.203024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.3394 | 0.915749 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.61484 | −0.407013 | ||||||||
\(449\) | −13.7029 | −0.646681 | −0.323341 | − | 0.946283i | \(-0.604806\pi\) | ||||
−0.323341 | + | 0.946283i | \(0.604806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.3110 | 1.42729 | ||||||||
\(452\) | −1.60331 | −0.0754134 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.5407 | −0.541630 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5407 | 0.680183 | 0.340092 | − | 0.940392i | \(-0.389542\pi\) | ||||
0.340092 | + | 0.940392i | \(0.389542\pi\) | |||||||
\(458\) | 37.0257 | 1.73010 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.9618 | −0.650268 | −0.325134 | − | 0.945668i | \(-0.605409\pi\) | ||||
−0.325134 | + | 0.945668i | \(0.605409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7703 | 0.593488 | 0.296744 | − | 0.954957i | \(-0.404099\pi\) | ||||
0.296744 | + | 0.954957i | \(0.404099\pi\) | |||||||
\(464\) | 29.7859 | 1.38278 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.3481 | −1.22055 | ||||||||
\(467\) | −11.2730 | −0.521654 | −0.260827 | − | 0.965386i | \(-0.583995\pi\) | ||||
−0.260827 | + | 0.965386i | \(0.583995\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.38516 | −0.0639610 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.3038 | −1.16470 | ||||||||
\(473\) | 7.80751 | 0.358989 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.517816 | 0.0237341 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.1555 | −0.693196 | ||||||||
\(479\) | 2.17099 | 0.0991950 | 0.0495975 | − | 0.998769i | \(-0.484206\pi\) | ||||
0.0495975 | + | 0.998769i | \(0.484206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.1555 | −0.599839 | ||||||||
\(482\) | 10.2374 | 0.466301 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.00000 | −0.181818 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.61484 | −0.118489 | −0.0592447 | − | 0.998243i | \(-0.518869\pi\) | ||||
−0.0592447 | + | 0.998243i | \(0.518869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4963 | 0.473692 | 0.236846 | − | 0.971547i | \(-0.423886\pi\) | ||||
0.236846 | + | 0.971547i | \(0.423886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.3852 | −1.00818 | ||||||||
\(494\) | −49.4341 | −2.22415 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.4665 | −0.963874 | ||||||||
\(497\) | 0.258908 | 0.0116136 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5407 | −0.606163 | −0.303082 | − | 0.952965i | \(-0.598015\pi\) | ||||
−0.303082 | + | 0.952965i | \(0.598015\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.1555 | 1.83686 | ||||||||
\(503\) | −23.0639 | −1.02837 | −0.514184 | − | 0.857680i | \(-0.671905\pi\) | ||||
−0.514184 | + | 0.857680i | \(0.671905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 42.7121 | 1.89878 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.96291 | 0.131458 | ||||||||
\(509\) | 19.3394 | 0.857206 | 0.428603 | − | 0.903493i | \(-0.359006\pi\) | ||||
0.428603 | + | 0.903493i | \(0.359006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.38516 | 0.282463 | ||||||||
\(512\) | −24.9760 | −1.10379 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.92582 | −0.349593 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.3852 | 2.12798 | ||||||||
\(518\) | −4.03321 | −0.177209 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.7835 | −1.43627 | −0.718135 | − | 0.695904i | \(-0.755004\pi\) | ||||
−0.718135 | + | 0.695904i | \(0.755004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.7703 | 1.78276 | 0.891381 | − | 0.453255i | \(-0.149737\pi\) | ||||
0.891381 | + | 0.453255i | \(0.149737\pi\) | |||||||
\(524\) | 0.517816 | 0.0226209 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.5036 | −0.675988 | ||||||||
\(527\) | 16.1328 | 0.702757 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.77033 | 0.381319 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.61484 | 0.0700120 | ||||||||
\(533\) | −23.5817 | −1.02144 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.08307 | −0.176362 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.3852 | −0.965093 | ||||||||
\(539\) | 5.63652 | 0.242782 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5407 | 1.22706 | 0.613529 | − | 0.789672i | \(-0.289749\pi\) | ||||
0.613529 | + | 0.789672i | \(0.289749\pi\) | |||||||
\(542\) | −23.0639 | −0.990679 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.91868 | 0.125137 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3852 | −0.999877 | −0.499939 | − | 0.866061i | \(-0.666644\pi\) | ||||
−0.499939 | + | 0.866061i | \(0.666644\pi\) | |||||||
\(548\) | 1.03563 | 0.0442400 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −69.8092 | −2.97397 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.38516 | −0.229001 | ||||||||
\(554\) | −26.2705 | −1.11613 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.22967 | −0.0521496 | ||||||||
\(557\) | 2.94771 | 0.124899 | 0.0624493 | − | 0.998048i | \(-0.480109\pi\) | ||||
0.0624493 | + | 0.998048i | \(0.480109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.07418 | −0.256910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.1184 | 0.806461 | ||||||||
\(563\) | 16.6506 | 0.701741 | 0.350870 | − | 0.936424i | \(-0.385886\pi\) | ||||
0.350870 | + | 0.936424i | \(0.385886\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.8216 | 0.791132 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.763187 | 0.0320226 | ||||||||
\(569\) | −20.1162 | −0.843314 | −0.421657 | − | 0.906755i | \(-0.638551\pi\) | ||||
−0.421657 | + | 0.906755i | \(0.638551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.6148 | 1.03010 | 0.515049 | − | 0.857160i | \(-0.327774\pi\) | ||||
0.515049 | + | 0.857160i | \(0.327774\pi\) | |||||||
\(572\) | 4.76007 | 0.199029 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.22967 | −0.301761 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.8445 | −0.617985 | −0.308992 | − | 0.951064i | \(-0.599992\pi\) | ||||
−0.308992 | + | 0.951064i | \(0.599992\pi\) | |||||||
\(578\) | −13.1353 | −0.546355 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.6506 | 0.690785 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.3110 | −1.25535 | ||||||||
\(584\) | 18.8216 | 0.778845 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.5407 | 0.476740 | ||||||||
\(587\) | −35.9901 | −1.48547 | −0.742735 | − | 0.669585i | \(-0.766472\pi\) | ||||
−0.742735 | + | 0.669585i | \(0.766472\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 50.3110 | 2.07303 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.7332 | −0.441134 | ||||||||
\(593\) | −11.7909 | −0.484192 | −0.242096 | − | 0.970252i | \(-0.577835\pi\) | ||||
−0.242096 | + | 0.970252i | \(0.577835\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.63894 | 0.108095 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −33.2297 | −1.35886 | ||||||||
\(599\) | −22.8050 | −0.931786 | −0.465893 | − | 0.884841i | \(-0.654267\pi\) | ||||
−0.465893 | + | 0.884841i | \(0.654267\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.54066 | −0.0628448 | −0.0314224 | − | 0.999506i | \(-0.510004\pi\) | ||||
−0.0314224 | + | 0.999506i | \(0.510004\pi\) | |||||||
\(602\) | −1.86222 | −0.0758984 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.118406 | −0.00481789 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.15549 | 0.371610 | 0.185805 | − | 0.982587i | \(-0.440511\pi\) | ||||
0.185805 | + | 0.982587i | \(0.440511\pi\) | |||||||
\(608\) | 9.10205 | 0.369137 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.6433 | −1.52288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0000 | −0.928961 | −0.464481 | − | 0.885583i | \(-0.653759\pi\) | ||||
−0.464481 | + | 0.885583i | \(0.653759\pi\) | |||||||
\(614\) | −25.7527 | −1.03929 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.6148 | 0.669431 | ||||||||
\(617\) | −30.8714 | −1.24284 | −0.621418 | − | 0.783479i | \(-0.713443\pi\) | ||||
−0.621418 | + | 0.783479i | \(0.713443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.15549 | 0.207217 | 0.103608 | − | 0.994618i | \(-0.466961\pi\) | ||||
0.103608 | + | 0.994618i | \(0.466961\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.0742 | −0.724708 | ||||||||
\(623\) | 13.9618 | 0.559369 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 40.2323 | 1.60801 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.918682 | 0.0366594 | ||||||||
\(629\) | 8.06641 | 0.321629 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.38516 | 0.214380 | 0.107190 | − | 0.994239i | \(-0.465815\pi\) | ||||
0.107190 | + | 0.994239i | \(0.465815\pi\) | |||||||
\(632\) | −15.8739 | −0.631431 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.96291 | −0.157387 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.38516 | −0.173747 | ||||||||
\(638\) | −63.0872 | −2.49765 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.4938 | 1.00694 | 0.503472 | − | 0.864012i | \(-0.332056\pi\) | ||||
0.503472 | + | 0.864012i | \(0.332056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.5407 | 1.95369 | 0.976846 | − | 0.213942i | \(-0.0686302\pi\) | ||||
0.976846 | + | 0.213942i | \(0.0686302\pi\) | |||||||
\(644\) | 1.08549 | 0.0427745 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30.3110 | 1.19257 | ||||||||
\(647\) | 4.85979 | 0.191058 | 0.0955291 | − | 0.995427i | \(-0.469546\pi\) | ||||
0.0955291 | + | 0.995427i | \(0.469546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.3852 | 1.89928 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.918682 | 0.0359783 | ||||||||
\(653\) | −5.37761 | −0.210442 | −0.105221 | − | 0.994449i | \(-0.533555\pi\) | ||||
−0.105221 | + | 0.994449i | \(0.533555\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −19.2397 | −0.751185 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.5407 | −0.449902 | ||||||||
\(659\) | 38.1611 | 1.48654 | 0.743272 | − | 0.668989i | \(-0.233273\pi\) | ||||
0.743272 | + | 0.668989i | \(0.233273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.9258 | −0.852816 | −0.426408 | − | 0.904531i | \(-0.640221\pi\) | ||||
−0.426408 | + | 0.904531i | \(0.640221\pi\) | |||||||
\(662\) | −29.7859 | −1.15766 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 49.0813 | 1.90472 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.9258 | −1.81698 | ||||||||
\(668\) | −2.68880 | −0.104033 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.5407 | −1.52418 | −0.762090 | − | 0.647471i | \(-0.775827\pi\) | ||||
−0.762090 | + | 0.647471i | \(0.775827\pi\) | |||||||
\(674\) | 14.4797 | 0.557736 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.19972 | −0.0461433 | ||||||||
\(677\) | 11.2730 | 0.433258 | 0.216629 | − | 0.976254i | \(-0.430494\pi\) | ||||
0.216629 | + | 0.976254i | \(0.430494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7703 | −0.413327 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 45.4665 | 1.74100 | ||||||||
\(683\) | 16.9096 | 0.647026 | 0.323513 | − | 0.946224i | \(-0.395136\pi\) | ||||
0.323513 | + | 0.946224i | \(0.395136\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.34440 | −0.0513295 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.95577 | −0.188937 | ||||||||
\(689\) | 23.5817 | 0.898391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.7703 | −1.39881 | −0.699405 | − | 0.714726i | \(-0.746551\pi\) | ||||
−0.699405 | + | 0.714726i | \(0.746551\pi\) | |||||||
\(692\) | −0.617539 | −0.0234753 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.88159 | 0.261222 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.4593 | 0.547687 | ||||||||
\(698\) | −11.2730 | −0.426691 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.41324 | −0.242225 | −0.121112 | − | 0.992639i | \(-0.538646\pi\) | ||||
−0.121112 | + | 0.992639i | \(0.538646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.1555 | 0.948757 | ||||||||
\(704\) | 48.5577 | 1.83009 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.92582 | 0.298292 | ||||||||
\(707\) | 2.68880 | 0.101123 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.54066 | −0.132972 | −0.0664861 | − | 0.997787i | \(-0.521179\pi\) | ||||
−0.0664861 | + | 0.997787i | \(0.521179\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 41.1555 | 1.54237 | ||||||||
\(713\) | 33.8191 | 1.26654 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.20662 | −0.119837 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.0371 | −0.822417 | ||||||||
\(719\) | 38.6789 | 1.44248 | 0.721240 | − | 0.692686i | \(-0.243573\pi\) | ||||
0.721240 | + | 0.692686i | \(0.243573\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.3852 | −0.610215 | ||||||||
\(722\) | 68.9826 | 2.56727 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.85165 | −0.0688160 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6148 | 0.801650 | 0.400825 | − | 0.916155i | \(-0.368724\pi\) | ||||
0.400825 | + | 0.916155i | \(0.368724\pi\) | |||||||
\(728\) | −12.9262 | −0.479077 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.72444 | 0.137753 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.0000 | −1.03420 | −0.517102 | − | 0.855924i | \(-0.672989\pi\) | ||||
−0.517102 | + | 0.855924i | \(0.672989\pi\) | |||||||
\(734\) | −5.37761 | −0.198491 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.11841 | 0.225527 | ||||||||
\(737\) | 7.80751 | 0.287593 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.6148 | −1.19976 | −0.599878 | − | 0.800091i | \(-0.704784\pi\) | ||||
−0.599878 | + | 0.800091i | \(0.704784\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.22967 | 0.265410 | ||||||||
\(743\) | 22.0283 | 0.808138 | 0.404069 | − | 0.914728i | \(-0.367596\pi\) | ||||
0.404069 | + | 0.914728i | \(0.367596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −33.6101 | −1.23055 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.91868 | −0.106718 | ||||||||
\(749\) | 16.6506 | 0.608401 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.22967 | −0.263814 | −0.131907 | − | 0.991262i | \(-0.542110\pi\) | ||||
−0.131907 | + | 0.991262i | \(0.542110\pi\) | |||||||
\(752\) | −30.7122 | −1.11996 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 49.0813 | 1.78744 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.3110 | 1.93762 | 0.968810 | − | 0.247803i | \(-0.0797086\pi\) | ||||
0.968810 | + | 0.247803i | \(0.0797086\pi\) | |||||||
\(758\) | −0.826586 | −0.0300230 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5461 | −0.817294 | −0.408647 | − | 0.912692i | \(-0.633999\pi\) | ||||
−0.408647 | + | 0.912692i | \(0.633999\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.00000 | −0.253417 | ||||||||
\(764\) | 2.17099 | 0.0785436 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.0000 | 0.939418 | ||||||||
\(767\) | −37.6433 | −1.35922 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.2297 | 0.837683 | 0.418842 | − | 0.908059i | \(-0.362436\pi\) | ||||
0.418842 | + | 0.908059i | \(0.362436\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.192582 | −0.00693119 | ||||||||
\(773\) | −22.0283 | −0.792301 | −0.396151 | − | 0.918186i | \(-0.629654\pi\) | ||||
−0.396151 | + | 0.918186i | \(0.629654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −31.7478 | −1.13968 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.5036 | 1.48798 | ||||||||
\(779\) | 45.0921 | 1.61559 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.45934 | −0.0522193 | ||||||||
\(782\) | 20.3751 | 0.728611 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.57775 | −0.127777 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.3852 | 0.370191 | 0.185096 | − | 0.982721i | \(-0.440741\pi\) | ||||
0.185096 | + | 0.982721i | \(0.440741\pi\) | |||||||
\(788\) | 3.67458 | 0.130901 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.32532 | −0.296014 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −30.6125 | −1.08640 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | 0.141776 | ||||||||
\(797\) | −42.4033 | −1.50200 | −0.751002 | − | 0.660300i | \(-0.770429\pi\) | ||||
−0.751002 | + | 0.660300i | \(0.770429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.0813 | 0.816558 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.4223 | −0.650512 | ||||||||
\(803\) | −35.9901 | −1.27006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −35.3726 | −1.24595 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.92582 | 0.278830 | ||||||||
\(809\) | −3.46553 | −0.121842 | −0.0609208 | − | 0.998143i | \(-0.519404\pi\) | ||||
−0.0609208 | + | 0.998143i | \(0.519404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.22967 | 0.324098 | 0.162049 | − | 0.986783i | \(-0.448190\pi\) | ||||
0.162049 | + | 0.986783i | \(0.448190\pi\) | |||||||
\(812\) | −1.60331 | −0.0562652 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.7332 | 0.796800 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6148 | 0.406352 | ||||||||
\(818\) | 15.6150 | 0.545966 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.3369 | 1.19837 | 0.599183 | − | 0.800612i | \(-0.295492\pi\) | ||||
0.599183 | + | 0.800612i | \(0.295492\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.9258 | −1.00829 | −0.504145 | − | 0.863619i | \(-0.668192\pi\) | ||||
−0.504145 | + | 0.863619i | \(0.668192\pi\) | |||||||
\(824\) | −48.2988 | −1.68257 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.5407 | −0.401551 | ||||||||
\(827\) | 0.258908 | 0.00900312 | 0.00450156 | − | 0.999990i | \(-0.498567\pi\) | ||||
0.00450156 | + | 0.999990i | \(0.498567\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.38516 | 0.0828402 | 0.0414201 | − | 0.999142i | \(-0.486812\pi\) | ||||
0.0414201 | + | 0.999142i | \(0.486812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.7775 | −1.30970 | ||||||||
\(833\) | 2.68880 | 0.0931616 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.10205 | −0.314801 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.92582 | −0.273793 | ||||||||
\(839\) | −35.9901 | −1.24252 | −0.621258 | − | 0.783606i | \(-0.713378\pi\) | ||||
−0.621258 | + | 0.783606i | \(0.713378\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.3110 | 1.39003 | ||||||||
\(842\) | −52.8498 | −1.82132 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.7703 | −0.713677 | ||||||||
\(848\) | 19.2397 | 0.660695 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.9096 | 0.579652 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.3110 | −1.17479 | −0.587393 | − | 0.809302i | \(-0.699846\pi\) | ||||
−0.587393 | + | 0.809302i | \(0.699846\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.0813 | 1.67756 | ||||||||
\(857\) | −39.7145 | −1.35662 | −0.678311 | − | 0.734775i | \(-0.737288\pi\) | ||||
−0.678311 | + | 0.734775i | \(0.737288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5407 | 0.530240 | 0.265120 | − | 0.964215i | \(-0.414588\pi\) | ||||
0.265120 | + | 0.964215i | \(0.414588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.8445 | 1.25493 | ||||||||
\(863\) | −22.2872 | −0.758664 | −0.379332 | − | 0.925261i | \(-0.623846\pi\) | ||||
−0.379332 | + | 0.925261i | \(0.623846\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 45.0921 | 1.53229 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.15549 | 0.0392200 | ||||||||
\(869\) | 30.3536 | 1.02967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.07418 | −0.205816 | ||||||||
\(872\) | −20.6340 | −0.698755 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 63.5407 | 2.14929 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.5407 | −0.794912 | −0.397456 | − | 0.917621i | \(-0.630107\pi\) | ||||
−0.397456 | + | 0.917621i | \(0.630107\pi\) | |||||||
\(878\) | −17.6863 | −0.596883 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0639 | −0.777042 | −0.388521 | − | 0.921440i | \(-0.627014\pi\) | ||||
−0.388521 | + | 0.921440i | \(0.627014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.3852 | 0.652363 | 0.326181 | − | 0.945307i | \(-0.394238\pi\) | ||||
0.326181 | + | 0.945307i | \(0.394238\pi\) | |||||||
\(884\) | 2.27071 | 0.0763723 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.4665 | 1.52748 | ||||||||
\(887\) | 5.37761 | 0.180562 | 0.0902812 | − | 0.995916i | \(-0.471223\pi\) | ||||
0.0902812 | + | 0.995916i | \(0.471223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.3852 | 0.516002 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.77033 | −0.0927575 | ||||||||
\(893\) | 71.9802 | 2.40873 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.41082 | −0.314393 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.4223 | −0.614759 | ||||||||
\(899\) | −49.9519 | −1.66599 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4593 | −0.481710 | ||||||||
\(902\) | 40.7502 | 1.35683 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.5407 | −0.816210 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.3110 | 1.40491 | 0.702457 | − | 0.711727i | \(-0.252086\pi\) | ||||
0.702457 | + | 0.711727i | \(0.252086\pi\) | |||||||
\(908\) | 1.65317 | 0.0548624 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.9378 | −1.29007 | −0.645034 | − | 0.764154i | \(-0.723157\pi\) | ||||
−0.645034 | + | 0.764154i | \(0.723157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −93.8516 | −3.10604 | ||||||||
\(914\) | 19.5485 | 0.646607 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.30385 | −0.175244 | ||||||||
\(917\) | 2.68880 | 0.0887922 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.6962 | 0.847638 | 0.423819 | − | 0.905747i | \(-0.360689\pi\) | ||||
0.423819 | + | 0.905747i | \(0.360689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.7703 | −0.618168 | ||||||||
\(923\) | 1.13536 | 0.0373707 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.1685 | 0.564191 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.03709 | −0.296657 | ||||||||
\(929\) | 8.06641 | 0.264650 | 0.132325 | − | 0.991206i | \(-0.457756\pi\) | ||||
0.132325 | + | 0.991206i | \(0.457756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.38516 | 0.274813 | ||||||||
\(932\) | 3.77430 | 0.123631 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.1555 | −0.495903 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7703 | 1.33191 | 0.665954 | − | 0.745993i | \(-0.268025\pi\) | ||||
0.665954 | + | 0.745993i | \(0.268025\pi\) | |||||||
\(938\) | −1.86222 | −0.0608036 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.2374 | −0.333730 | −0.166865 | − | 0.985980i | \(-0.553364\pi\) | ||||
−0.166865 | + | 0.985980i | \(0.553364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.3110 | 0.987062 | ||||||||
\(944\) | −30.7122 | −0.999597 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.4964 | 0.341268 | ||||||||
\(947\) | 50.9876 | 1.65687 | 0.828437 | − | 0.560083i | \(-0.189231\pi\) | ||||
0.828437 | + | 0.560083i | \(0.189231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0000 | 0.908918 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.92582 | 0.256877 | ||||||||
\(953\) | 36.2490 | 1.17422 | 0.587110 | − | 0.809507i | \(-0.300266\pi\) | ||||
0.587110 | + | 0.809507i | \(0.300266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.17099 | 0.0702148 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.91868 | 0.0942983 | ||||||||
\(959\) | 5.37761 | 0.173652 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −17.6863 | −0.570228 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.46648 | −0.0472322 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.54066 | 0.178176 | 0.0890878 | − | 0.996024i | \(-0.471605\pi\) | ||||
0.0890878 | + | 0.996024i | \(0.471605\pi\) | |||||||
\(968\) | −61.2250 | −1.96784 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.8855 | 1.34417 | 0.672085 | − | 0.740474i | \(-0.265399\pi\) | ||||
0.672085 | + | 0.740474i | \(0.265399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.38516 | −0.204699 | ||||||||
\(974\) | −3.51539 | −0.112640 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.0399 | 1.53693 | 0.768466 | − | 0.639891i | \(-0.221021\pi\) | ||||
0.768466 | + | 0.639891i | \(0.221021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78.6962 | −2.51514 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.1113 | 0.450309 | ||||||||
\(983\) | −32.7835 | −1.04563 | −0.522815 | − | 0.852446i | \(-0.675118\pi\) | ||||
−0.522815 | + | 0.852446i | \(0.675118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −30.0947 | −0.958409 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.08132 | 0.225287 | ||||||||
\(989\) | 7.80751 | 0.248264 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.6962 | −1.13393 | −0.566963 | − | 0.823743i | \(-0.691882\pi\) | ||||
−0.566963 | + | 0.823743i | \(0.691882\pi\) | |||||||
\(992\) | 6.51296 | 0.206787 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.348077 | 0.0110403 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.1555 | 1.81013 | 0.905066 | − | 0.425270i | \(-0.139821\pi\) | ||||
0.905066 | + | 0.425270i | \(0.139821\pi\) | |||||||
\(998\) | −18.2041 | −0.576241 | ||||||||
\(999\) | 0 | 0 |
(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 | 1575.2.a.y.1.3 | yes | 4 | |
3.2 | odd | 2 | inner | 1575.2.a.y.1.2 | ✓ | 4 | |
5.2 | odd | 4 | 1575.2.d.l.1324.5 | 8 | |||
5.3 | odd | 4 | 1575.2.d.l.1324.4 | 8 | |||
5.4 | even | 2 | 1575.2.a.z.1.2 | yes | 4 | ||
15.2 | even | 4 | 1575.2.d.l.1324.3 | 8 | |||
15.8 | even | 4 | 1575.2.d.l.1324.6 | 8 | |||
15.14 | odd | 2 | 1575.2.a.z.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.2.a.y.1.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
1575.2.a.y.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1575.2.a.z.1.2 | yes | 4 | 5.4 | even | 2 | ||
1575.2.a.z.1.3 | yes | 4 | 15.14 | odd | 2 | ||
1575.2.d.l.1324.3 | 8 | 15.2 | even | 4 | |||
1575.2.d.l.1324.4 | 8 | 5.3 | odd | 4 | |||
1575.2.d.l.1324.5 | 8 | 5.2 | odd | 4 | |||
1575.2.d.l.1324.6 | 8 | 15.8 | even | 4 |