Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(863,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 863.6 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.863 |
Dual form | 864.2.c.b.863.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 1.03528i | 0.462990i | 0.972836 | + | 0.231495i | \(0.0743616\pi\) | ||||
−0.972836 | + | 0.231495i | \(0.925638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.267949i | 0.101275i | 0.998717 | + | 0.0506376i | \(0.0161254\pi\) | ||||
−0.998717 | + | 0.0506376i | \(0.983875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.86370 | −1.16495 | −0.582475 | − | 0.812848i | \(-0.697916\pi\) | ||||
−0.582475 | + | 0.812848i | \(0.697916\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.46410 | −0.683419 | −0.341709 | − | 0.939806i | \(-0.611006\pi\) | ||||
−0.341709 | + | 0.939806i | \(0.611006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.69213i | 1.62308i | 0.584297 | + | 0.811540i | \(0.301370\pi\) | ||||
−0.584297 | + | 0.811540i | \(0.698630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.93426 | −1.23738 | −0.618689 | − | 0.785636i | \(-0.712336\pi\) | ||||
−0.618689 | + | 0.785636i | \(0.712336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.92820 | 0.785641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.07055i | 0.384492i | 0.981347 | + | 0.192246i | \(0.0615771\pi\) | ||||
−0.981347 | + | 0.192246i | \(0.938423\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.535898i | − 0.0962502i | −0.998841 | − | 0.0481251i | \(-0.984675\pi\) | ||||
0.998841 | − | 0.0481251i | \(-0.0153246\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.277401 | −0.0468894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.46410 | −1.06269 | −0.531346 | − | 0.847155i | \(-0.678314\pi\) | ||||
−0.531346 | + | 0.847155i | \(0.678314\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.07055i | 0.323366i | 0.986843 | + | 0.161683i | \(0.0516922\pi\) | ||||
−0.986843 | + | 0.161683i | \(0.948308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.46410i | − 1.13826i | −0.822246 | − | 0.569132i | \(-0.807279\pi\) | ||||
0.822246 | − | 0.569132i | \(-0.192721\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.52056 | −1.38872 | −0.694358 | − | 0.719630i | \(-0.744312\pi\) | ||||
−0.694358 | + | 0.719630i | \(0.744312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3843i | 1.83847i | 0.393710 | + | 0.919235i | \(0.371192\pi\) | ||||
−0.393710 | + | 0.919235i | \(0.628808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 4.00000i | − 0.539360i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.45001 | −0.969908 | −0.484954 | − | 0.874540i | \(-0.661164\pi\) | ||||
−0.484954 | + | 0.874540i | \(0.661164\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.39230 | −1.20256 | −0.601281 | − | 0.799038i | \(-0.705343\pi\) | ||||
−0.601281 | + | 0.799038i | \(0.705343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 2.55103i | − 0.316416i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.73205i | 1.18896i | 0.804111 | + | 0.594480i | \(0.202642\pi\) | ||||
−0.804111 | + | 0.594480i | \(0.797358\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.92820 | 1.16201 | 0.581004 | − | 0.813901i | \(-0.302660\pi\) | ||||
0.581004 | + | 0.813901i | \(0.302660\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.03528i | − 0.117981i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1962i | 1.70970i | 0.518875 | + | 0.854850i | \(0.326351\pi\) | ||||
−0.518875 | + | 0.854850i | \(0.673649\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.72741 | −0.848193 | −0.424097 | − | 0.905617i | \(-0.639408\pi\) | ||||
−0.424097 | + | 0.905617i | \(0.639408\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.92820 | −0.751469 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.69213i | 0.709364i | 0.934987 | + | 0.354682i | \(0.115411\pi\) | ||||
−0.934987 | + | 0.354682i | \(0.884589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.660254i | − 0.0692134i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.79315 | −0.183973 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 15.4548i | − 1.53781i | −0.639362 | − | 0.768906i | \(-0.720802\pi\) | ||||
0.639362 | − | 0.768906i | \(-0.279198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.5885i | − 1.73304i | −0.499140 | − | 0.866521i | \(-0.666351\pi\) | ||||
0.499140 | − | 0.866521i | \(-0.333649\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1774 | 1.46726 | 0.733628 | − | 0.679551i | \(-0.237826\pi\) | ||||
0.733628 | + | 0.679551i | \(0.237826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.928203 | −0.0889057 | −0.0444529 | − | 0.999011i | \(-0.514154\pi\) | ||||
−0.0444529 | + | 0.999011i | \(0.514154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 8.76268i | − 0.824324i | −0.911111 | − | 0.412162i | \(-0.864774\pi\) | ||||
0.911111 | − | 0.412162i | \(-0.135226\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.14359i | − 0.572893i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.79315 | −0.164378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.92820 | 0.357109 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.24316i | 0.826733i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.46410i | 0.307389i | 0.988118 | + | 0.153695i | \(0.0491172\pi\) | ||||
−0.988118 | + | 0.153695i | \(0.950883\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.72741 | 0.675147 | 0.337573 | − | 0.941299i | \(-0.390394\pi\) | ||||
0.337573 | + | 0.941299i | \(0.390394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.464102 | −0.0402427 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 10.8332i | − 0.925546i | −0.886477 | − | 0.462773i | \(-0.846855\pi\) | ||||
0.886477 | − | 0.462773i | \(-0.153145\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.19615i | − 0.101456i | −0.998712 | − | 0.0507282i | \(-0.983846\pi\) | ||||
0.998712 | − | 0.0507282i | \(-0.0161542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.52056 | 0.796149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.14359 | −0.178016 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 11.3137i | − 0.926855i | −0.886135 | − | 0.463428i | \(-0.846619\pi\) | ||||
0.886135 | − | 0.463428i | \(-0.153381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.26795i | 0.672836i | 0.941713 | + | 0.336418i | \(0.109216\pi\) | ||||
−0.941713 | + | 0.336418i | \(0.890784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.554803 | 0.0445628 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.07180 | −0.245156 | −0.122578 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122578 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1.59008i | − 0.125316i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.5885i | 1.22098i | 0.792023 | + | 0.610491i | \(0.209028\pi\) | ||||
−0.792023 | + | 0.610491i | \(0.790972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.34795 | 0.181690 | 0.0908451 | − | 0.995865i | \(-0.471043\pi\) | ||||
0.0908451 | + | 0.995865i | \(0.471043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 9.24316i | − 0.702744i | −0.936236 | − | 0.351372i | \(-0.885715\pi\) | ||||
0.936236 | − | 0.351372i | \(-0.114285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.05256i | 0.0795660i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.5959 | 1.46467 | 0.732334 | − | 0.680946i | \(-0.238431\pi\) | ||||
0.732334 | + | 0.680946i | \(0.238431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.46410 | −0.480473 | −0.240236 | − | 0.970714i | \(-0.577225\pi\) | ||||
−0.240236 | + | 0.970714i | \(0.577225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 6.69213i | − 0.492015i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 25.8564i | − 1.89081i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6617 | 0.988523 | 0.494262 | − | 0.869313i | \(-0.335438\pi\) | ||||
0.494262 | + | 0.869313i | \(0.335438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0717968 | 0.00516804 | 0.00258402 | − | 0.999997i | \(-0.499177\pi\) | ||||
0.00258402 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 14.4195i | − 1.02735i | −0.857985 | − | 0.513675i | \(-0.828284\pi\) | ||||
0.857985 | − | 0.513675i | \(-0.171716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 25.5885i | − 1.81392i | −0.421219 | − | 0.906959i | \(-0.638398\pi\) | ||||
0.421219 | − | 0.906959i | \(-0.361602\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.554803 | −0.0389395 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.14359 | −0.149715 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 6.69213i | − 0.462904i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7321i | 1.49610i | 0.663645 | + | 0.748048i | \(0.269009\pi\) | ||||
−0.663645 | + | 0.748048i | \(0.730991\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.72741 | 0.527005 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.143594 | 0.00974776 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 16.4901i | − 1.10924i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.4641i | 1.57127i | 0.618689 | + | 0.785636i | \(0.287664\pi\) | ||||
−0.618689 | + | 0.785636i | \(0.712336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.14110 | 0.274855 | 0.137427 | − | 0.990512i | \(-0.456117\pi\) | ||||
0.137427 | + | 0.990512i | \(0.456117\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.3137i | 0.741186i | 0.928795 | + | 0.370593i | \(0.120845\pi\) | ||||
−0.928795 | + | 0.370593i | \(0.879155\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 9.85641i | − 0.642961i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4548 | 0.999689 | 0.499844 | − | 0.866115i | \(-0.333391\pi\) | ||||
0.499844 | + | 0.866115i | \(0.333391\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.92820 | 0.381869 | 0.190935 | − | 0.981603i | \(-0.438848\pi\) | ||||
0.190935 | + | 0.981603i | \(0.438848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.17260i | 0.458241i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.26795i | − 0.271563i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.58630 | −0.226365 | −0.113183 | − | 0.993574i | \(-0.536105\pi\) | ||||
−0.113183 | + | 0.993574i | \(0.536105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.9282 | 1.44148 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2.07055i | − 0.129158i | −0.997913 | − | 0.0645788i | \(-0.979430\pi\) | ||||
0.997913 | − | 0.0645788i | \(-0.0205704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.73205i | − 0.107624i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.4548 | −0.952985 | −0.476492 | − | 0.879179i | \(-0.658092\pi\) | ||||
−0.476492 | + | 0.879179i | \(0.658092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.8564 | −0.851192 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3.10583i | − 0.189366i | −0.995507 | − | 0.0946829i | \(-0.969816\pi\) | ||||
0.995507 | − | 0.0946829i | \(-0.0301837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0526i | 0.792886i | 0.918059 | + | 0.396443i | \(0.129756\pi\) | ||||
−0.918059 | + | 0.396443i | \(0.870244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.1774 | −0.915232 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9282 | 1.25745 | 0.628727 | − | 0.777626i | \(-0.283576\pi\) | ||||
0.628727 | + | 0.777626i | \(0.283576\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 17.5254i | − 1.04548i | −0.852493 | − | 0.522738i | \(-0.824911\pi\) | ||||
0.852493 | − | 0.522738i | \(-0.175089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.535898i | 0.0318559i | 0.999873 | + | 0.0159279i | \(0.00507023\pi\) | ||||
−0.999873 | + | 0.0159279i | \(0.994930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.554803 | −0.0327490 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.7846 | −1.63439 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.8038i | 1.62432i | 0.583438 | + | 0.812158i | \(0.301707\pi\) | ||||
−0.583438 | + | 0.812158i | \(0.698293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 7.71281i | − 0.449057i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.6226 | 0.845647 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 9.72363i | − 0.556773i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3923i | 1.27800i | 0.769208 | + | 0.638998i | \(0.220651\pi\) | ||||
−0.769208 | + | 0.638998i | \(0.779349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0754 | 0.571321 | 0.285661 | − | 0.958331i | \(-0.407787\pi\) | ||||
0.285661 | + | 0.958331i | \(0.407787\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.9282 | −1.12641 | −0.563204 | − | 0.826318i | \(-0.690432\pi\) | ||||
−0.563204 | + | 0.826318i | \(0.690432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.07055i | 0.116294i | 0.998308 | + | 0.0581469i | \(0.0185192\pi\) | ||||
−0.998308 | + | 0.0581469i | \(0.981481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 8.00000i | − 0.447914i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.5911 | −0.644947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.67949 | −0.536922 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 2.55103i | − 0.140643i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 25.1962i | − 1.38491i | −0.721463 | − | 0.692453i | \(-0.756530\pi\) | ||||
0.721463 | − | 0.692453i | \(-0.243470\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0754 | −0.550476 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8564 | −0.809280 | −0.404640 | − | 0.914476i | \(-0.632603\pi\) | ||||
−0.404640 | + | 0.914476i | \(0.632603\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.07055i | 0.112127i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.73205i | 0.201512i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4548 | 0.829658 | 0.414829 | − | 0.909899i | \(-0.363841\pi\) | ||||
0.414829 | + | 0.909899i | \(0.363841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3205 | 0.552444 | 0.276222 | − | 0.961094i | \(-0.410917\pi\) | ||||
0.276222 | + | 0.961094i | \(0.410917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.0507i | 1.86556i | 0.360443 | + | 0.932781i | \(0.382625\pi\) | ||||
−0.360443 | + | 0.932781i | \(0.617375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.7128i | 0.621652i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.1480 | −1.69671 | −0.848353 | − | 0.529432i | \(-0.822405\pi\) | ||||
−0.848353 | + | 0.529432i | \(0.822405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2784i | 0.537998i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0526i | 0.890136i | 0.895497 | + | 0.445068i | \(0.146821\pi\) | ||||
−0.895497 | + | 0.445068i | \(0.853179\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.58630 | −0.186192 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.2487 | 0.685992 | 0.342996 | − | 0.939337i | \(-0.388558\pi\) | ||||
0.342996 | + | 0.939337i | \(0.388558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 5.10205i | − 0.262769i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 9.19615i | − 0.472375i | −0.971708 | − | 0.236187i | \(-0.924102\pi\) | ||||
0.971708 | − | 0.236187i | \(-0.0758979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.0507 | −1.79101 | −0.895504 | − | 0.445053i | \(-0.853185\pi\) | ||||
−0.895504 | + | 0.445053i | \(0.853185\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.07180 | 0.0546238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4195i | 0.731100i | 0.930792 | + | 0.365550i | \(0.119119\pi\) | ||||
−0.930792 | + | 0.365550i | \(0.880881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 39.7128i | − 2.00836i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.7322 | −0.791574 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.7846 | 1.34428 | 0.672141 | − | 0.740424i | \(-0.265375\pi\) | ||||
0.672141 | + | 0.740424i | \(0.265375\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6274i | 1.12996i | 0.825105 | + | 0.564980i | \(0.191116\pi\) | ||||
−0.825105 | + | 0.564980i | \(0.808884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.32051i | 0.0657792i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.9754 | 1.23798 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | −0.642809 | −0.321404 | − | 0.946942i | \(-0.604155\pi\) | ||||
−0.321404 | + | 0.946942i | \(0.604155\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.99622i | − 0.0982277i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 8.00000i | − 0.392705i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.7322 | −0.768569 | −0.384284 | − | 0.923215i | \(-0.625552\pi\) | ||||
−0.384284 | + | 0.923215i | \(0.625552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.53590 | 0.464751 | 0.232376 | − | 0.972626i | \(-0.425350\pi\) | ||||
0.232376 | + | 0.972626i | \(0.425350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.2880i | 1.27516i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.51666i | − 0.121790i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.37945 | −0.259119 | −0.129560 | − | 0.991572i | \(-0.541356\pi\) | ||||
−0.129560 | + | 0.991572i | \(0.541356\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.7846 | −1.28719 | −0.643593 | − | 0.765368i | \(-0.722557\pi\) | ||||
−0.643593 | + | 0.765368i | \(0.722557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 10.2784i | − 0.491684i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3205i | 1.01757i | 0.860893 | + | 0.508786i | \(0.169906\pi\) | ||||
−0.860893 | + | 0.508786i | \(0.830094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.3233 | −1.29817 | −0.649085 | − | 0.760716i | \(-0.724848\pi\) | ||||
−0.649085 | + | 0.760716i | \(0.724848\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.92820 | −0.328428 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 12.9038i | − 0.608967i | −0.952518 | − | 0.304484i | \(-0.901516\pi\) | ||||
0.952518 | − | 0.304484i | \(-0.0984839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 8.00000i | − 0.376705i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.683545 | 0.0320451 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.7846 | −1.62716 | −0.813578 | − | 0.581456i | \(-0.802483\pi\) | ||||
−0.813578 | + | 0.581456i | \(0.802483\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.7332i | 1.19852i | 0.800556 | + | 0.599258i | \(0.204538\pi\) | ||||
−0.800556 | + | 0.599258i | \(0.795462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1962i | 1.44981i | 0.688850 | + | 0.724904i | \(0.258116\pi\) | ||||
−0.688850 | + | 0.724904i | \(0.741884\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.3596 | −1.77507 | −0.887536 | − | 0.460738i | \(-0.847585\pi\) | ||||
−0.887536 | + | 0.460738i | \(0.847585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.60770 | −0.120412 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.8391i | 1.32602i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.80385i | 0.312182i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.9000 | 0.680799 | 0.340399 | − | 0.940281i | \(-0.389438\pi\) | ||||
0.340399 | + | 0.940281i | \(0.389438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9282 | 0.726264 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.24693i | 0.329066i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.4449i | − 1.06239i | −0.847250 | − | 0.531194i | \(-0.821743\pi\) | ||||
0.847250 | − | 0.531194i | \(-0.178257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7322 | 0.709985 | 0.354992 | − | 0.934869i | \(-0.384483\pi\) | ||||
0.354992 | + | 0.934869i | \(0.384483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.8564 | −0.624061 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.03150i | 0.135981i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5359i | 0.561184i | 0.959827 | + | 0.280592i | \(0.0905308\pi\) | ||||
−0.959827 | + | 0.280592i | \(0.909469\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.1165 | −1.29824 | −0.649120 | − | 0.760686i | \(-0.724863\pi\) | ||||
−0.649120 | + | 0.760686i | \(0.724863\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | 0.711991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.5606i | 0.822686i | 0.911481 | + | 0.411343i | \(0.134940\pi\) | ||||
−0.911481 | + | 0.411343i | \(0.865060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.66025i | 0.117683i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.2089 | 0.802380 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.7846 | 1.61779 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 37.6018i | − 1.64736i | −0.567053 | − | 0.823681i | \(-0.691916\pi\) | ||||
0.567053 | − | 0.823681i | \(-0.308084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8038i | 0.472419i | 0.971702 | + | 0.236210i | \(0.0759052\pi\) | ||||
−0.971702 | + | 0.236210i | \(0.924095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.58630 | 0.156222 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.2154 | 0.531104 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.10205i | − 0.220994i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7128i | 0.679324i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.7685 | −1.15300 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6077 | 0.628034 | 0.314017 | − | 0.949417i | \(-0.398325\pi\) | ||||
0.314017 | + | 0.949417i | \(0.398325\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 0.960947i | − 0.0411624i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.73205i | 0.245085i | 0.992463 | + | 0.122542i | \(0.0391047\pi\) | ||||
−0.992463 | + | 0.122542i | \(0.960895\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.58630 | −0.152782 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.07180 | −0.173150 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 10.2784i | − 0.435511i | −0.976003 | − | 0.217756i | \(-0.930126\pi\) | ||||
0.976003 | − | 0.217756i | \(-0.0698736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.3923i | 0.777912i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0411 | 0.802487 | 0.401244 | − | 0.915971i | \(-0.368578\pi\) | ||||
0.401244 | + | 0.915971i | \(0.368578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.07180 | 0.381653 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.5627i | 1.61663i | 0.588748 | + | 0.808316i | \(0.299621\pi\) | ||||
−0.588748 | + | 0.808316i | \(0.700379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 23.0526i | − 0.964720i | −0.875973 | − | 0.482360i | \(-0.839780\pi\) | ||||
0.875973 | − | 0.482360i | \(-0.160220\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3110 | −0.972134 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0718 | −1.08538 | −0.542692 | − | 0.839932i | \(-0.682595\pi\) | ||||
−0.542692 | + | 0.839932i | \(0.682595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.07055i | − 0.0859010i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 51.7128i | − 2.14173i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.277401 | 0.0114496 | 0.00572479 | − | 0.999984i | \(-0.498178\pi\) | ||||
0.00572479 | + | 0.999984i | \(0.498178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.928203 | 0.0382459 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.8076i | 1.05979i | 0.848063 | + | 0.529895i | \(0.177769\pi\) | ||||
−0.848063 | + | 0.529895i | \(0.822231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.85641i | − 0.0761052i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.8685 | −0.484934 | −0.242467 | − | 0.970160i | \(-0.577957\pi\) | ||||
−0.242467 | + | 0.970160i | \(0.577957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.78461 | 0.276750 | 0.138375 | − | 0.990380i | \(-0.455812\pi\) | ||||
0.138375 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.06678i | 0.165338i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 10.6603i | − 0.432686i | −0.976317 | − | 0.216343i | \(-0.930587\pi\) | ||||
0.976317 | − | 0.216343i | \(-0.0694130\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.4596 | 0.949075 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.3923 | −1.51026 | −0.755130 | − | 0.655575i | \(-0.772427\pi\) | ||||
−0.755130 | + | 0.655575i | \(0.772427\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.72363i | 0.391459i | 0.980658 | + | 0.195729i | \(0.0627074\pi\) | ||||
−0.980658 | + | 0.195729i | \(0.937293\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.660254i | 0.0265379i | 0.999912 | + | 0.0132689i | \(0.00422375\pi\) | ||||
−0.999912 | + | 0.0132689i | \(0.995776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.79315 | −0.0718411 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 43.2586i | − 1.72483i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9808i | 0.795422i | 0.917511 | + | 0.397711i | \(0.130195\pi\) | ||||
−0.917511 | + | 0.397711i | \(0.869805\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.58630 | −0.142318 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.0718 | −0.676409 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 42.2233i | − 1.66772i | −0.551975 | − | 0.833861i | \(-0.686126\pi\) | ||||
0.551975 | − | 0.833861i | \(-0.313874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 17.6077i | − 0.694380i | −0.937795 | − | 0.347190i | \(-0.887136\pi\) | ||||
0.937795 | − | 0.347190i | \(-0.112864\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.1822 | 0.911387 | 0.455694 | − | 0.890137i | \(-0.349391\pi\) | ||||
0.455694 | + | 0.890137i | \(0.349391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.7846 | 1.12989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3528i | 0.405135i | 0.979268 | + | 0.202567i | \(0.0649285\pi\) | ||||
−0.979268 | + | 0.202567i | \(0.935071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000i | 0.312586i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.4959 | 1.34377 | 0.671885 | − | 0.740655i | \(-0.265485\pi\) | ||||
0.671885 | + | 0.740655i | \(0.265485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.2487 | −1.68218 | −0.841090 | − | 0.540895i | \(-0.818086\pi\) | ||||
−0.841090 | + | 0.540895i | \(0.818086\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 0.480473i | − 0.0186320i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 12.2872i | − 0.475762i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.2891 | 1.40092 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.8564 | 0.803955 | 0.401978 | − | 0.915649i | \(-0.368323\pi\) | ||||
0.401978 | + | 0.915649i | \(0.368323\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.5921i | 0.829853i | 0.909855 | + | 0.414927i | \(0.136193\pi\) | ||||
−0.909855 | + | 0.414927i | \(0.863807\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.87564i | 0.0719806i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9411 | −1.29872 | −0.649361 | − | 0.760481i | \(-0.724963\pi\) | ||||
−0.649361 | + | 0.760481i | \(0.724963\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2154 | 0.428518 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 32.9802i | − 1.25644i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3923i | 1.15618i | 0.815974 | + | 0.578089i | \(0.196201\pi\) | ||||
−0.815974 | + | 0.578089i | \(0.803799\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.23835 | 0.0469732 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.8564 | −0.524849 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 49.4703i | − 1.86847i | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
0.356663 | − | 0.934233i | \(-0.383914\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 11.1962i | − 0.422271i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.14110 | 0.155742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1769 | 0.457314 | 0.228657 | − | 0.973507i | \(-0.426567\pi\) | ||||
0.228657 | + | 0.973507i | \(0.426567\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.18016i | 0.119098i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.85641i | 0.368609i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.58630 | 0.133746 | 0.0668732 | − | 0.997761i | \(-0.478698\pi\) | ||||
0.0668732 | + | 0.997761i | \(0.478698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.71281 | 0.175514 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.13355i | 0.302072i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.3205i | 0.790734i | 0.918523 | + | 0.395367i | \(0.129383\pi\) | ||||
−0.918523 | + | 0.395367i | \(0.870617\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.9507 | 1.84749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.9282 | −1.21623 | −0.608115 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608115 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 37.6018i | − 1.38508i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3923i | 0.529429i | 0.964327 | + | 0.264715i | \(0.0852778\pi\) | ||||
−0.964327 | + | 0.264715i | \(0.914722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.5302 | 0.936611 | 0.468306 | − | 0.883567i | \(-0.344865\pi\) | ||||
0.468306 | + | 0.883567i | \(0.344865\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7128 | 0.429124 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.06678i | 0.148597i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.19615i | 0.116629i | 0.998298 | + | 0.0583146i | \(0.0185727\pi\) | ||||
−0.998298 | + | 0.0583146i | \(0.981427\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.55961 | −0.311516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.39230 | −0.195987 | −0.0979933 | − | 0.995187i | \(-0.531242\pi\) | ||||
−0.0979933 | + | 0.995187i | \(0.531242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 43.8134i | − 1.58824i | −0.607764 | − | 0.794118i | \(-0.707933\pi\) | ||||
0.607764 | − | 0.794118i | \(-0.292067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 0.248711i | − 0.00900395i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.3576 | 0.662853 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.8564 | 0.463614 | 0.231807 | − | 0.972762i | \(-0.425536\pi\) | ||||
0.231807 | + | 0.972762i | \(0.425536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.5569i | 0.739379i | 0.929155 | + | 0.369690i | \(0.120536\pi\) | ||||
−0.929155 | + | 0.369690i | \(0.879464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 2.10512i | − 0.0756181i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.58630 | −0.128493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.7128 | −1.56417 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 3.18016i | − 0.113505i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 30.2679i | − 1.07894i | −0.842006 | − | 0.539468i | \(-0.818625\pi\) | ||||
0.842006 | − | 0.539468i | \(-0.181375\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.34795 | 0.0834836 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.1436 | 0.821853 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.03150i | 0.107381i | 0.998558 | + | 0.0536906i | \(0.0170985\pi\) | ||||
−0.998558 | + | 0.0536906i | \(0.982902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 63.7128i | − 2.25400i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.3596 | −1.35368 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.64617 | 0.0580199 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 19.5959i | − 0.688956i | −0.938794 | − | 0.344478i | \(-0.888056\pi\) | ||||
0.938794 | − | 0.344478i | \(-0.111944\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 15.4641i | − 0.543018i | −0.962436 | − | 0.271509i | \(-0.912477\pi\) | ||||
0.962436 | − | 0.271509i | \(-0.0875227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1384 | −0.565302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9282 | 0.452301 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 21.5921i | − 0.753571i | −0.926301 | − | 0.376785i | \(-0.877029\pi\) | ||||
0.926301 | − | 0.376785i | \(-0.122971\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.9808i | 1.39364i | 0.717245 | + | 0.696821i | \(0.245403\pi\) | ||||
−0.717245 | + | 0.696821i | \(0.754597\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.3692 | 1.89060 | 0.945302 | − | 0.326196i | \(-0.105767\pi\) | ||||
0.945302 | + | 0.326196i | \(0.105767\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6795 | 0.544571 | 0.272286 | − | 0.962216i | \(-0.412220\pi\) | ||||
0.272286 | + | 0.962216i | \(0.412220\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 46.3644i | 1.60643i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.43078i | 0.0841206i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.9822 | 1.82915 | 0.914575 | − | 0.404416i | \(-0.132525\pi\) | ||||
0.914575 | + | 0.404416i | \(0.132525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.7128 | 0.852166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 7.17260i | − 0.246745i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.05256i | 0.0361664i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.3596 | 1.31495 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.6077 | 0.911030 | 0.455515 | − | 0.890228i | \(-0.349455\pi\) | ||||
0.455515 | + | 0.890228i | \(0.349455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 38.0822i | − 1.30086i | −0.759564 | − | 0.650432i | \(-0.774588\pi\) | ||||
0.759564 | − | 0.650432i | \(-0.225412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5167i | 0.631780i | 0.948796 | + | 0.315890i | \(0.102303\pi\) | ||||
−0.948796 | + | 0.315890i | \(0.897697\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.6302 | −0.361855 | −0.180927 | − | 0.983496i | \(-0.557910\pi\) | ||||
−0.180927 | + | 0.983496i | \(0.557910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.56922 | 0.325363 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 58.7134i | − 1.99172i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 23.9808i | − 0.812557i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.47670 | −0.0837276 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.2487 | 0.852588 | 0.426294 | − | 0.904585i | \(-0.359819\pi\) | ||||
0.426294 | + | 0.904585i | \(0.359819\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.9038i | 0.434740i | 0.976089 | + | 0.217370i | \(0.0697478\pi\) | ||||
−0.976089 | + | 0.217370i | \(0.930252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24.1244i | − 0.811849i | −0.913907 | − | 0.405925i | \(-0.866950\pi\) | ||||
0.913907 | − | 0.405925i | \(-0.133050\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.8685 | 0.398506 | 0.199253 | − | 0.979948i | \(-0.436149\pi\) | ||||
0.199253 | + | 0.979948i | \(0.436149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.928203 | −0.0311309 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 16.4901i | − 0.551820i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.2872i | 0.678126i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.10961 | 0.0370074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −89.5692 | −2.98398 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 6.69213i | − 0.222454i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.5167i | 1.81020i | 0.425203 | + | 0.905098i | \(0.360203\pi\) | ||||
−0.425203 | + | 0.905098i | \(0.639797\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.554803 | 0.0183814 | 0.00919072 | − | 0.999958i | \(-0.497074\pi\) | ||||
0.00919072 | + | 0.999958i | \(0.497074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.8564 | 0.988103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.07055i | 0.0683757i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.0333i | 1.88136i | 0.339301 | + | 0.940678i | \(0.389809\pi\) | ||||
−0.339301 | + | 0.940678i | \(0.610191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.8781 | −0.917620 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.3923 | −0.834894 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.6274i | 0.742381i | 0.928557 | + | 0.371191i | \(0.121050\pi\) | ||||
−0.928557 | + | 0.371191i | \(0.878950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000i | 0.393284i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.7685 | 0.875424 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.21539 | 0.203048 | 0.101524 | − | 0.994833i | \(-0.467628\pi\) | ||||
0.101524 | + | 0.994833i | \(0.467628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 31.9449i | − 1.04137i | −0.853748 | − | 0.520687i | \(-0.825676\pi\) | ||||
0.853748 | − | 0.520687i | \(-0.174324\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 12.2872i | − 0.400126i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.277401 | −0.00901433 | −0.00450717 | − | 0.999990i | \(-0.501435\pi\) | ||||
−0.00450717 | + | 0.999990i | \(0.501435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.4641 | −0.794138 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 12.9038i | − 0.417995i | −0.977916 | − | 0.208997i | \(-0.932980\pi\) | ||||
0.977916 | − | 0.208997i | \(-0.0670200\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.1436i | 0.457676i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.90276 | 0.0937349 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7128 | 0.990736 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0743295i | 0.00239275i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 11.7321i | − 0.377277i | −0.982047 | − | 0.188639i | \(-0.939593\pi\) | ||||
0.982047 | − | 0.188639i | \(-0.0604075\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.6418 | 1.49681 | 0.748404 | − | 0.663243i | \(-0.230820\pi\) | ||||
0.748404 | + | 0.663243i | \(0.230820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.320508 | 0.0102750 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 9.24316i | − 0.295715i | −0.989009 | − | 0.147857i | \(-0.952762\pi\) | ||||
0.989009 | − | 0.147857i | \(-0.0472377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 25.8564i | − 0.826374i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.0165 | −1.40391 | −0.701954 | − | 0.712222i | \(-0.747689\pi\) | ||||
−0.701954 | + | 0.712222i | \(0.747689\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.9282 | 0.475652 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.2939i | 1.40846i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.48334i | 0.237716i | 0.992911 | + | 0.118858i | \(0.0379233\pi\) | ||||
−0.992911 | + | 0.118858i | \(0.962077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.4911 | 0.839825 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.78461 | −0.214871 | −0.107435 | − | 0.994212i | \(-0.534264\pi\) | ||||
−0.107435 | + | 0.994212i | \(0.534264\pi\) | |||||||
\(998\) | 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 | 864.2.c.b.863.6 | yes | 8 | |
3.2 | odd | 2 | inner | 864.2.c.b.863.4 | yes | 8 | |
4.3 | odd | 2 | inner | 864.2.c.b.863.5 | yes | 8 | |
8.3 | odd | 2 | 1728.2.c.f.1727.3 | 8 | |||
8.5 | even | 2 | 1728.2.c.f.1727.4 | 8 | |||
9.2 | odd | 6 | 2592.2.s.c.863.3 | 8 | |||
9.4 | even | 3 | 2592.2.s.g.1727.3 | 8 | |||
9.5 | odd | 6 | 2592.2.s.g.1727.2 | 8 | |||
9.7 | even | 3 | 2592.2.s.c.863.2 | 8 | |||
12.11 | even | 2 | inner | 864.2.c.b.863.3 | ✓ | 8 | |
24.5 | odd | 2 | 1728.2.c.f.1727.6 | 8 | |||
24.11 | even | 2 | 1728.2.c.f.1727.5 | 8 | |||
36.7 | odd | 6 | 2592.2.s.g.863.2 | 8 | |||
36.11 | even | 6 | 2592.2.s.g.863.3 | 8 | |||
36.23 | even | 6 | 2592.2.s.c.1727.2 | 8 | |||
36.31 | odd | 6 | 2592.2.s.c.1727.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.c.b.863.3 | ✓ | 8 | 12.11 | even | 2 | inner | |
864.2.c.b.863.4 | yes | 8 | 3.2 | odd | 2 | inner | |
864.2.c.b.863.5 | yes | 8 | 4.3 | odd | 2 | inner | |
864.2.c.b.863.6 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.2.c.f.1727.3 | 8 | 8.3 | odd | 2 | |||
1728.2.c.f.1727.4 | 8 | 8.5 | even | 2 | |||
1728.2.c.f.1727.5 | 8 | 24.11 | even | 2 | |||
1728.2.c.f.1727.6 | 8 | 24.5 | odd | 2 | |||
2592.2.s.c.863.2 | 8 | 9.7 | even | 3 | |||
2592.2.s.c.863.3 | 8 | 9.2 | odd | 6 | |||
2592.2.s.c.1727.2 | 8 | 36.23 | even | 6 | |||
2592.2.s.c.1727.3 | 8 | 36.31 | odd | 6 | |||
2592.2.s.g.863.2 | 8 | 36.7 | odd | 6 | |||
2592.2.s.g.863.3 | 8 | 36.11 | even | 6 | |||
2592.2.s.g.1727.2 | 8 | 9.5 | odd | 6 | |||
2592.2.s.g.1727.3 | 8 | 9.4 | even | 3 |