Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9360,2,Mod(1,9360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9360.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: | \(74.7399762919\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1560) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9360.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.70156 | 1.39906 | 0.699529 | − | 0.714604i | \(-0.253393\pi\) | ||||
0.699529 | + | 0.714604i | \(0.253393\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.70156 | −1.71909 | −0.859543 | − | 0.511064i | \(-0.829252\pi\) | ||||
−0.859543 | + | 0.511064i | \(0.829252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.70156 | −1.38283 | −0.691416 | − | 0.722457i | \(-0.743013\pi\) | ||||
−0.691416 | + | 0.722457i | \(0.743013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.298438 | 0.0622286 | 0.0311143 | − | 0.999516i | \(-0.490094\pi\) | ||||
0.0311143 | + | 0.999516i | \(0.490094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.40312 | 0.631944 | 0.315972 | − | 0.948768i | \(-0.397669\pi\) | ||||
0.315972 | + | 0.948768i | \(0.397669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.40312 | −0.611219 | −0.305610 | − | 0.952157i | \(-0.598860\pi\) | ||||
−0.305610 | + | 0.952157i | \(0.598860\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.70156 | 0.625678 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.298438 | −0.0490629 | −0.0245314 | − | 0.999699i | \(-0.507809\pi\) | ||||
−0.0245314 | + | 0.999699i | \(0.507809\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.29844 | −0.671303 | −0.335652 | − | 0.941986i | \(-0.608956\pi\) | ||||
−0.335652 | + | 0.941986i | \(0.608956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4031 | 1.66332 | 0.831658 | − | 0.555288i | \(-0.187392\pi\) | ||||
0.831658 | + | 0.555288i | \(0.187392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.70156 | 0.957366 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.29844 | −0.590436 | −0.295218 | − | 0.955430i | \(-0.595392\pi\) | ||||
−0.295218 | + | 0.955430i | \(0.595392\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.70156 | −0.768798 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8062 | 1.40685 | 0.703427 | − | 0.710768i | \(-0.251652\pi\) | ||||
0.703427 | + | 0.710768i | \(0.251652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.70156 | −0.473936 | −0.236968 | − | 0.971517i | \(-0.576154\pi\) | ||||
−0.236968 | + | 0.971517i | \(0.576154\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.5078 | −1.95912 | −0.979558 | − | 0.201160i | \(-0.935529\pi\) | ||||
−0.979558 | + | 0.201160i | \(0.935529\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.596876 | 0.0698590 | 0.0349295 | − | 0.999390i | \(-0.488879\pi\) | ||||
0.0349295 | + | 0.999390i | \(0.488879\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.1047 | −2.40510 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.70156 | 0.191441 | 0.0957203 | − | 0.995408i | \(-0.469485\pi\) | ||||
0.0957203 | + | 0.995408i | \(0.469485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.70156 | −0.618421 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.1047 | 1.17709 | 0.588547 | − | 0.808463i | \(-0.299700\pi\) | ||||
0.588547 | + | 0.808463i | \(0.299700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.70156 | −0.388029 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.10469 | −0.112164 | −0.0560820 | − | 0.998426i | \(-0.517861\pi\) | ||||
−0.0560820 | + | 0.998426i | \(0.517861\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.8062 | −1.87129 | −0.935646 | − | 0.352940i | \(-0.885182\pi\) | ||||
−0.935646 | + | 0.352940i | \(0.885182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0000 | −1.18240 | −0.591198 | − | 0.806527i | \(-0.701345\pi\) | ||||
−0.591198 | + | 0.806527i | \(0.701345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.10469 | −0.106794 | −0.0533970 | − | 0.998573i | \(-0.517005\pi\) | ||||
−0.0533970 | + | 0.998573i | \(0.517005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.8062 | −1.41818 | −0.709091 | − | 0.705117i | \(-0.750894\pi\) | ||||
−0.709091 | + | 0.705117i | \(0.750894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.4031 | −1.82529 | −0.912646 | − | 0.408750i | \(-0.865965\pi\) | ||||
−0.912646 | + | 0.408750i | \(0.865965\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.298438 | 0.0278295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.1047 | −1.93466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.5078 | 1.95526 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.596876 | 0.0529642 | 0.0264821 | − | 0.999649i | \(-0.491570\pi\) | ||||
0.0264821 | + | 0.999649i | \(0.491570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.8062 | 1.11889 | 0.559444 | − | 0.828868i | \(-0.311015\pi\) | ||||
0.559444 | + | 0.828868i | \(0.311015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.40312 | 0.641932 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.70156 | −0.144325 | −0.0721623 | − | 0.997393i | \(-0.522990\pi\) | ||||
−0.0721623 | + | 0.997393i | \(0.522990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.70156 | 0.476789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.40312 | 0.282614 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.70156 | −0.630937 | −0.315468 | − | 0.948936i | \(-0.602162\pi\) | ||||
−0.315468 | + | 0.948936i | \(0.602162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.40312 | −0.273346 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8062 | −1.34128 | −0.670642 | − | 0.741781i | \(-0.733981\pi\) | ||||
−0.670642 | + | 0.741781i | \(0.733981\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.10469 | 0.0870615 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.7016 | −1.38649 | −0.693247 | − | 0.720700i | \(-0.743820\pi\) | ||||
−0.693247 | + | 0.720700i | \(0.743820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.80625 | 0.217154 | 0.108577 | − | 0.994088i | \(-0.465371\pi\) | ||||
0.108577 | + | 0.994088i | \(0.465371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | 0.152057 | 0.0760286 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.70156 | 0.279812 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.0000 | −1.64436 | −0.822179 | − | 0.569230i | \(-0.807242\pi\) | ||||
−0.822179 | + | 0.569230i | \(0.807242\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.70156 | −0.572453 | −0.286226 | − | 0.958162i | \(-0.592401\pi\) | ||||
−0.286226 | + | 0.958162i | \(0.592401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.298438 | −0.0219416 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.5078 | 2.37721 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.89531 | −0.208409 | −0.104205 | − | 0.994556i | \(-0.533230\pi\) | ||||
−0.104205 | + | 0.994556i | \(0.533230\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.2094 | −1.72485 | −0.862423 | − | 0.506188i | \(-0.831054\pi\) | ||||
−0.862423 | + | 0.506188i | \(0.831054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.8062 | 1.61669 | 0.808346 | − | 0.588708i | \(-0.200363\pi\) | ||||
0.808346 | + | 0.588708i | \(0.200363\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.5969 | 0.884127 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.29844 | −0.300216 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.4031 | −0.788771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5969 | −0.855132 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70156 | 0.383529 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.40312 | 0.629680 | 0.314840 | − | 0.949145i | \(-0.398049\pi\) | ||||
0.314840 | + | 0.949145i | \(0.398049\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4031 | −1.55332 | −0.776660 | − | 0.629920i | \(-0.783088\pi\) | ||||
−0.776660 | + | 0.629920i | \(0.783088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5969 | −0.832425 | −0.416212 | − | 0.909267i | \(-0.636643\pi\) | ||||
−0.416212 | + | 0.909267i | \(0.636643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.10469 | −0.596468 | −0.298234 | − | 0.954493i | \(-0.596398\pi\) | ||||
−0.298234 | + | 0.954493i | \(0.596398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4031 | 0.743858 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1047 | 0.847672 | 0.423836 | − | 0.905739i | \(-0.360683\pi\) | ||||
0.423836 | + | 0.905739i | \(0.360683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.70156 | 0.428147 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.2094 | 1.27560 | 0.637802 | − | 0.770200i | \(-0.279844\pi\) | ||||
0.637802 | + | 0.770200i | \(0.279844\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.70156 | −0.106976 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2094 | 1.13587 | 0.567935 | − | 0.823074i | \(-0.307743\pi\) | ||||
0.567935 | + | 0.823074i | \(0.307743\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.10469 | −0.0686419 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.4031 | 1.07312 | 0.536561 | − | 0.843861i | \(-0.319723\pi\) | ||||
0.536561 | + | 0.843861i | \(0.319723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.29844 | −0.264051 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.8062 | −0.658869 | −0.329434 | − | 0.944179i | \(-0.606858\pi\) | ||||
−0.329434 | + | 0.944179i | \(0.606858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4031 | 1.17866 | 0.589328 | − | 0.807894i | \(-0.299393\pi\) | ||||
0.589328 | + | 0.807894i | \(0.299393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.70156 | −0.343817 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.8062 | −1.00979 | −0.504895 | − | 0.863181i | \(-0.668469\pi\) | ||||
−0.504895 | + | 0.863181i | \(0.668469\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.9109 | −0.939193 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5078 | 0.912224 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.59688 | −0.151711 | −0.0758556 | − | 0.997119i | \(-0.524169\pi\) | ||||
−0.0758556 | + | 0.997119i | \(0.524169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8062 | 0.629164 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.298438 | −0.0172591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.8062 | −0.853418 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.70156 | −0.211951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.1047 | 1.88938 | 0.944692 | − | 0.327959i | \(-0.106361\pi\) | ||||
0.944692 | + | 0.327959i | \(0.106361\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.80625 | −0.497759 | −0.248879 | − | 0.968535i | \(-0.580062\pi\) | ||||
−0.248879 | + | 0.968535i | \(0.580062\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.2094 | 1.35973 | 0.679867 | − | 0.733336i | \(-0.262038\pi\) | ||||
0.679867 | + | 0.733336i | \(0.262038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.4031 | −1.08637 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.4031 | −0.634487 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.2094 | 2.32708 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.2094 | −1.33067 | −0.665334 | − | 0.746546i | \(-0.731711\pi\) | ||||
−0.665334 | + | 0.746546i | \(0.731711\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.2094 | 1.75456 | 0.877278 | − | 0.479982i | \(-0.159357\pi\) | ||||
0.877278 | + | 0.479982i | \(0.159357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.4031 | 1.05074 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.10469 | −0.0596475 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.1047 | −0.703496 | −0.351748 | − | 0.936095i | \(-0.614413\pi\) | ||||
−0.351748 | + | 0.936095i | \(0.614413\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.19375 | −0.492130 | −0.246065 | − | 0.969253i | \(-0.579138\pi\) | ||||
−0.246065 | + | 0.969253i | \(0.579138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.8062 | 0.681608 | 0.340804 | − | 0.940134i | \(-0.389301\pi\) | ||||
0.340804 | + | 0.940134i | \(0.389301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.5078 | −0.876144 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.6125 | 1.56289 | 0.781444 | − | 0.623975i | \(-0.214484\pi\) | ||||
0.781444 | + | 0.623975i | \(0.214484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.596876 | 0.0312419 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.8062 | −1.39927 | −0.699637 | − | 0.714498i | \(-0.746655\pi\) | ||||
−0.699637 | + | 0.714498i | \(0.746655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.9109 | −0.826055 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.4031 | −1.10821 | −0.554106 | − | 0.832446i | \(-0.686940\pi\) | ||||
−0.554106 | + | 0.832446i | \(0.686940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.40312 | −0.175270 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.6125 | 1.82929 | 0.914646 | − | 0.404257i | \(-0.132470\pi\) | ||||
0.914646 | + | 0.404257i | \(0.132470\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.40312 | 0.378282 | 0.189141 | − | 0.981950i | \(-0.439430\pi\) | ||||
0.189141 | + | 0.981950i | \(0.439430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.1047 | −1.07559 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.6125 | 1.29861 | 0.649303 | − | 0.760530i | \(-0.275061\pi\) | ||||
0.649303 | + | 0.760530i | \(0.275061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.70156 | −0.0860517 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.70156 | 0.0856149 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.2984 | −0.817995 | −0.408998 | − | 0.912535i | \(-0.634122\pi\) | ||||
−0.408998 | + | 0.912535i | \(0.634122\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.8062 | 1.23876 | 0.619382 | − | 0.785089i | \(-0.287383\pi\) | ||||
0.619382 | + | 0.785089i | \(0.287383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.40312 | 0.169522 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70156 | 0.0843433 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.8062 | 1.02880 | 0.514401 | − | 0.857550i | \(-0.328014\pi\) | ||||
0.514401 | + | 0.857550i | \(0.328014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.0000 | 1.96827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.6125 | −1.15355 | −0.576773 | − | 0.816904i | \(-0.695688\pi\) | ||||
−0.576773 | + | 0.816904i | \(0.695688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.6125 | 1.24828 | 0.624138 | − | 0.781314i | \(-0.285450\pi\) | ||||
0.624138 | + | 0.781314i | \(0.285450\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.70156 | −0.276566 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7016 | −0.663065 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.4031 | 1.22080 | 0.610398 | − | 0.792095i | \(-0.291009\pi\) | ||||
0.610398 | + | 0.792095i | \(0.291009\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.596876 | 0.0285524 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1047 | 1.00727 | 0.503636 | − | 0.863916i | \(-0.331995\pi\) | ||||
0.503636 | + | 0.863916i | \(0.331995\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.3141 | 1.48778 | 0.743888 | − | 0.668304i | \(-0.232980\pi\) | ||||
0.743888 | + | 0.668304i | \(0.232980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.1047 | 0.526413 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1047 | −1.09038 | −0.545189 | − | 0.838313i | \(-0.683542\pi\) | ||||
−0.545189 | + | 0.838313i | \(0.683542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.5078 | 1.15403 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.70156 | −0.173532 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.7016 | 0.640932 | 0.320466 | − | 0.947260i | \(-0.396160\pi\) | ||||
0.320466 | + | 0.947260i | \(0.396160\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.1047 | −1.82129 | −0.910643 | − | 0.413193i | \(-0.864413\pi\) | ||||
−0.910643 | + | 0.413193i | \(0.864413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.1047 | −0.701974 | −0.350987 | − | 0.936380i | \(-0.614154\pi\) | ||||
−0.350987 | + | 0.936380i | \(0.614154\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.10469 | −0.0511188 | −0.0255594 | − | 0.999673i | \(-0.508137\pi\) | ||||
−0.0255594 | + | 0.999673i | \(0.508137\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8062 | 0.683689 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.8062 | 1.04863 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.2984 | −1.01884 | −0.509421 | − | 0.860518i | \(-0.670140\pi\) | ||||
−0.509421 | + | 0.860518i | \(0.670140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.298438 | 0.0136076 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.10469 | −0.0501612 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.3141 | −0.965832 | −0.482916 | − | 0.875667i | \(-0.660422\pi\) | ||||
−0.482916 | + | 0.875667i | \(0.660422\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.2094 | 1.45359 | 0.726794 | − | 0.686855i | \(-0.241009\pi\) | ||||
0.726794 | + | 0.686855i | \(0.241009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.4031 | −0.873873 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −61.1047 | −2.74092 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.8062 | −1.82674 | −0.913369 | − | 0.407132i | \(-0.866529\pi\) | ||||
−0.913369 | + | 0.407132i | \(0.866529\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.5969 | 0.829194 | 0.414597 | − | 0.910005i | \(-0.363923\pi\) | ||||
0.414597 | + | 0.910005i | \(0.363923\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8062 | −0.836867 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.3141 | −1.12203 | −0.561013 | − | 0.827807i | \(-0.689588\pi\) | ||||
−0.561013 | + | 0.827807i | \(0.689588\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.20937 | 0.0977369 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0000 | −0.528783 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −65.0156 | −2.85938 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.4031 | 0.845213 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9109 | −0.996128 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.29844 | 0.186186 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.10469 | −0.0477598 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.2094 | −1.64579 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.79063 | 0.0769851 | 0.0384925 | − | 0.999259i | \(-0.487744\pi\) | ||||
0.0384925 | + | 0.999259i | \(0.487744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8062 | −0.634230 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.6125 | −1.09511 | −0.547556 | − | 0.836769i | \(-0.684442\pi\) | ||||
−0.547556 | + | 0.836769i | \(0.684442\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.80625 | 0.289956 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.29844 | 0.267837 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.00000 | −0.0847427 | −0.0423714 | − | 0.999102i | \(-0.513491\pi\) | ||||
−0.0423714 | + | 0.999102i | \(0.513491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.89531 | 0.122023 | 0.0610115 | − | 0.998137i | \(-0.480567\pi\) | ||||
0.0610115 | + | 0.998137i | \(0.480567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.4031 | −0.816296 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.5969 | 0.611933 | 0.305966 | − | 0.952042i | \(-0.401020\pi\) | ||||
0.305966 | + | 0.952042i | \(0.401020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.3141 | 1.31045 | 0.655226 | − | 0.755433i | \(-0.272573\pi\) | ||||
0.655226 | + | 0.755433i | \(0.272573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.298438 | 0.0124457 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.507811 | 0.0211404 | 0.0105702 | − | 0.999944i | \(-0.496635\pi\) | ||||
0.0105702 | + | 0.999944i | \(0.496635\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8062 | 0.614267 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.5078 | 1.01501 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.2094 | 0.586484 | 0.293242 | − | 0.956038i | \(-0.405266\pi\) | ||||
0.293242 | + | 0.956038i | \(0.405266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.80625 | −0.280447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.40312 | −0.386140 | −0.193070 | − | 0.981185i | \(-0.561844\pi\) | ||||
−0.193070 | + | 0.981185i | \(0.561844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.1047 | −0.865208 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.1938 | −0.702518 | −0.351259 | − | 0.936278i | \(-0.614246\pi\) | ||||
−0.351259 | + | 0.936278i | \(0.614246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7016 | 0.640480 | 0.320240 | − | 0.947336i | \(-0.396236\pi\) | ||||
0.320240 | + | 0.947336i | \(0.396236\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.5078 | 0.874417 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.61250 | −0.390159 | −0.195080 | − | 0.980787i | \(-0.562497\pi\) | ||||
−0.195080 | + | 0.980787i | \(0.562497\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.4031 | −0.461321 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.7172 | 0.998318 | 0.499159 | − | 0.866511i | \(-0.333642\pi\) | ||||
0.499159 | + | 0.866511i | \(0.333642\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6125 | 0.466746 | 0.233373 | − | 0.972387i | \(-0.425024\pi\) | ||||
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41.1047 | 1.64682 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.70156 | 0.0678457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.596876 | 0.0236863 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.70156 | −0.265526 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.2094 | −1.11420 | −0.557102 | − | 0.830444i | \(-0.688087\pi\) | ||||
−0.557102 | + | 0.830444i | \(0.688087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.7016 | −1.48680 | −0.743402 | − | 0.668845i | \(-0.766789\pi\) | ||||
−0.743402 | + | 0.668845i | \(0.766789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.895314 | 0.0351984 | 0.0175992 | − | 0.999845i | \(-0.494398\pi\) | ||||
0.0175992 | + | 0.999845i | \(0.494398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −61.6125 | −2.41850 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.6125 | 1.39362 | 0.696812 | − | 0.717253i | \(-0.254601\pi\) | ||||
0.696812 | + | 0.717253i | \(0.254601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.8062 | 0.500382 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5969 | −0.568614 | −0.284307 | − | 0.958733i | \(-0.591763\pi\) | ||||
−0.284307 | + | 0.958733i | \(0.591763\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0000 | −0.466746 | −0.233373 | − | 0.972387i | \(-0.574976\pi\) | ||||
−0.233373 | + | 0.972387i | \(0.574976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.40312 | 0.287081 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.01562 | 0.0393250 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1047 | 0.814737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.8062 | −1.11040 | −0.555200 | − | 0.831717i | \(-0.687358\pi\) | ||||
−0.555200 | + | 0.831717i | \(0.687358\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.1047 | −0.580520 | −0.290260 | − | 0.956948i | \(-0.593742\pi\) | ||||
−0.290260 | + | 0.956948i | \(0.593742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.08907 | −0.156924 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.0000 | 1.07139 | 0.535695 | − | 0.844411i | \(-0.320050\pi\) | ||||
0.535695 | + | 0.844411i | \(0.320050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.29844 | 0.163757 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.70156 | −0.0645439 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.5078 | 0.928300 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.6125 | −0.967371 | −0.483685 | − | 0.875242i | \(-0.660702\pi\) | ||||
−0.483685 | + | 0.875242i | \(0.660702\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.596876 | −0.0225116 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −69.6125 | −2.61805 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.1938 | 0.645725 | 0.322862 | − | 0.946446i | \(-0.395355\pi\) | ||||
0.322862 | + | 0.946446i | \(0.395355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.01562 | −0.0380353 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.70156 | 0.213226 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.8062 | 1.29805 | 0.649027 | − | 0.760765i | \(-0.275176\pi\) | ||||
0.649027 | + | 0.760765i | \(0.275176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.4187 | −1.65424 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.40312 | 0.126389 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.40312 | −0.126215 | −0.0631074 | − | 0.998007i | \(-0.520101\pi\) | ||||
−0.0631074 | + | 0.998007i | \(0.520101\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.8062 | 0.843520 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.7172 | −1.06069 | −0.530347 | − | 0.847781i | \(-0.677938\pi\) | ||||
−0.530347 | + | 0.847781i | \(0.677938\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.8062 | −0.840079 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8062 | −0.618228 | −0.309114 | − | 0.951025i | \(-0.600032\pi\) | ||||
−0.309114 | + | 0.951025i | \(0.600032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.4031 | −0.858577 | −0.429289 | − | 0.903167i | \(-0.641236\pi\) | ||||
−0.429289 | + | 0.903167i | \(0.641236\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.70156 | −0.282163 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.08907 | −0.149411 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.3141 | −0.558818 | −0.279409 | − | 0.960172i | \(-0.590139\pi\) | ||||
−0.279409 | + | 0.960172i | \(0.590139\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.5969 | −1.25744 | −0.628722 | − | 0.777630i | \(-0.716422\pi\) | ||||
−0.628722 | + | 0.777630i | \(0.716422\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −54.8062 | −1.98412 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.8062 | −0.390191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.5969 | 1.39184 | 0.695919 | − | 0.718120i | \(-0.254997\pi\) | ||||
0.695919 | + | 0.718120i | \(0.254997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.4031 | 1.63304 | 0.816518 | − | 0.577319i | \(-0.195901\pi\) | ||||
0.816518 | + | 0.577319i | \(0.195901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.40312 | −0.122244 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.59688 | −0.308015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 94.1203 | 3.36789 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.8062 | −0.599841 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.8062 | −1.09812 | −0.549062 | − | 0.835782i | \(-0.685015\pi\) | ||||
−0.549062 | + | 0.835782i | \(0.685015\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −71.8219 | −2.55369 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.70156 | 0.131446 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.29844 | 0.293946 | 0.146973 | − | 0.989141i | \(-0.453047\pi\) | ||||
0.146973 | + | 0.989141i | \(0.453047\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −65.0156 | −2.30009 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.40312 | −0.120094 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.10469 | 0.0389351 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.8062 | −0.872141 | −0.436071 | − | 0.899912i | \(-0.643630\pi\) | ||||
−0.436071 | + | 0.899912i | \(0.643630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.2094 | −0.850106 | −0.425053 | − | 0.905168i | \(-0.639745\pi\) | ||||
−0.425053 | + | 0.905168i | \(0.639745\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.7016 | −0.620059 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.5078 | 1.20433 | 0.602165 | − | 0.798371i | \(-0.294305\pi\) | ||||
0.602165 | + | 0.798371i | \(0.294305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.4031 | 1.64837 | 0.824184 | − | 0.566322i | \(-0.191634\pi\) | ||||
0.824184 | + | 0.566322i | \(0.191634\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.61250 | 0.125467 | 0.0627336 | − | 0.998030i | \(-0.480018\pi\) | ||||
0.0627336 | + | 0.998030i | \(0.480018\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.2094 | −1.32388 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.80625 | 0.0971142 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.1203 | −1.31606 | −0.658030 | − | 0.752992i | \(-0.728610\pi\) | ||||
−0.658030 | + | 0.752992i | \(0.728610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.4187 | −0.600646 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 79.6125 | 2.73552 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0890652 | −0.00305311 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.7172 | 1.66804 | 0.834022 | − | 0.551731i | \(-0.186032\pi\) | ||||
0.834022 | + | 0.551731i | \(0.186032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.29844 | −0.215151 | −0.107575 | − | 0.994197i | \(-0.534309\pi\) | ||||
−0.107575 | + | 0.994197i | \(0.534309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.7016 | −1.28636 | −0.643180 | − | 0.765715i | \(-0.722385\pi\) | ||||
−0.643180 | + | 0.765715i | \(0.722385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.596876 | 0.0203179 | 0.0101589 | − | 0.999948i | \(-0.496766\pi\) | ||||
0.0101589 | + | 0.999948i | \(0.496766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.70156 | −0.329103 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.00000 | −0.135535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.70156 | 0.125136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.6125 | 1.60776 | 0.803880 | − | 0.594792i | \(-0.202765\pi\) | ||||
0.803880 | + | 0.594792i | \(0.202765\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.8062 | −0.431453 | −0.215727 | − | 0.976454i | \(-0.569212\pi\) | ||||
−0.215727 | + | 0.976454i | \(0.569212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.6125 | −1.13115 | −0.565575 | − | 0.824697i | \(-0.691346\pi\) | ||||
−0.565575 | + | 0.824697i | \(0.691346\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.5078 | 1.69589 | 0.847943 | − | 0.530087i | \(-0.177841\pi\) | ||||
0.847943 | + | 0.530087i | \(0.177841\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.20937 | 0.0741000 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.8062 | 0.763182 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.0000 | −0.735379 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.5813 | −0.386256 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.5078 | 0.816474 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.70156 | −0.256009 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.2094 | −0.737450 | −0.368725 | − | 0.929539i | \(-0.620206\pi\) | ||||
−0.368725 | + | 0.929539i | \(0.620206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8062 | −0.623079 | −0.311539 | − | 0.950233i | \(-0.600845\pi\) | ||||
−0.311539 | + | 0.950233i | \(0.600845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.8062 | −0.754777 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.4031 | 1.56539 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.9109 | −1.71238 | −0.856192 | − | 0.516658i | \(-0.827176\pi\) | ||||
−0.856192 | + | 0.516658i | \(0.827176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5078 | 0.543361 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.298438 | −0.00981258 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1047 | 0.364333 | 0.182166 | − | 0.983268i | \(-0.441689\pi\) | ||||
0.182166 | + | 0.983268i | \(0.441689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.4031 | 0.439270 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.5078 | 1.06312 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1938 | 0.888381 | 0.444191 | − | 0.895932i | \(-0.353491\pi\) | ||||
0.444191 | + | 0.895932i | \(0.353491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.2984 | 1.57448 | 0.787242 | − | 0.616644i | \(-0.211508\pi\) | ||||
0.787242 | + | 0.616644i | \(0.211508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.28282 | −0.0417743 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.6125 | 1.35222 | 0.676112 | − | 0.736799i | \(-0.263663\pi\) | ||||
0.676112 | + | 0.736799i | \(0.263663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.596876 | −0.0193754 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.9109 | 1.29284 | 0.646421 | − | 0.762981i | \(-0.276265\pi\) | ||||
0.646421 | + | 0.762981i | \(0.276265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −66.6281 | −2.15153 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.4187 | −0.626411 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.89531 | −0.0932034 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.8219 | 1.60216 | 0.801082 | − | 0.598555i | \(-0.204258\pi\) | ||||
0.801082 | + | 0.598555i | \(0.204258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.01562 | −0.225142 | −0.112571 | − | 0.993644i | \(-0.535909\pi\) | ||||
−0.112571 | + | 0.993644i | \(0.535909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.29844 | −0.201919 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.2094 | 0.390612 | 0.195306 | − | 0.980742i | \(-0.437430\pi\) | ||||
0.195306 | + | 0.980742i | \(0.437430\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63.3141 | −2.02353 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.0000 | −0.637901 | −0.318950 | − | 0.947771i | \(-0.603330\pi\) | ||||
−0.318950 | + | 0.947771i | \(0.603330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.2094 | −0.771375 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.19375 | −0.0379591 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.7172 | 1.35696 | 0.678478 | − | 0.734621i | \(-0.262640\pi\) | ||||
0.678478 | + | 0.734621i | \(0.262640\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.8062 | 0.723007 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.5969 | −1.22238 | −0.611188 | − | 0.791486i | \(-0.709308\pi\) | ||||
−0.611188 | + | 0.791486i | \(0.709308\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 9360.2.a.ct.1.2 | 2 | ||
3.2 | odd | 2 | 3120.2.a.bf.1.2 | 2 | |||
4.3 | odd | 2 | 4680.2.a.bb.1.1 | 2 | |||
12.11 | even | 2 | 1560.2.a.m.1.1 | ✓ | 2 | ||
60.59 | even | 2 | 7800.2.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.m.1.1 | ✓ | 2 | 12.11 | even | 2 | ||
3120.2.a.bf.1.2 | 2 | 3.2 | odd | 2 | |||
4680.2.a.bb.1.1 | 2 | 4.3 | odd | 2 | |||
7800.2.a.be.1.2 | 2 | 60.59 | even | 2 | |||
9360.2.a.ct.1.2 | 2 | 1.1 | even | 1 | trivial |