Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(607,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.607");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.b (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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 607.8 | ||
Root | \(1.09445 + 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.607 |
Dual form | 1216.2.b.d.607.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.64575i | 1.52753i | 0.645497 | + | 0.763763i | \(0.276650\pi\) | ||||
−0.645497 | + | 0.763763i | \(0.723350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | 0.981981 | + | 0.188982i | \(0.0605189\pi\) | ||||
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.00000 | −1.33333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64575 | 0.733799 | 0.366900 | − | 0.930261i | \(-0.380419\pi\) | ||||
0.366900 | + | 0.930261i | \(0.380419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.16515 | −2.36643 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.46410 | + | 2.64575i | −0.794719 | + | 0.606977i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64575 | −0.577350 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000i | 0.625543i | 0.949828 | + | 0.312772i | \(0.101257\pi\) | ||||
−0.949828 | + | 0.312772i | \(0.898743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.64575i | − | 0.509175i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.93725 | 1.47391 | 0.736956 | − | 0.675941i | \(-0.236263\pi\) | ||||
0.736956 | + | 0.675941i | \(0.236263\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.46410 | −0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5830 | 1.73984 | 0.869918 | − | 0.493197i | \(-0.164172\pi\) | ||||
0.869918 | + | 0.493197i | \(0.164172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.00000i | 1.12090i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.16515i | − | 1.43136i | −0.698430 | − | 0.715678i | \(-0.746118\pi\) | ||
0.698430 | − | 0.715678i | \(-0.253882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3923 | −1.58481 | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 13.8564i | − | 2.06559i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 7.93725i | − | 1.11144i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.93725 | −1.09027 | −0.545133 | − | 0.838350i | \(-0.683521\pi\) | ||||
−0.545133 | + | 0.838350i | \(0.683521\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | − | 9.16515i | −0.927173 | − | 1.21395i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.93725i | 1.03334i | 0.856184 | + | 0.516671i | \(0.172829\pi\) | ||||
−0.856184 | + | 0.516671i | \(0.827171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.92820i | − | 0.887066i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4.00000i | − | 0.503953i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.16515i | 1.13680i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.2288i | − | 1.61615i | −0.589080 | − | 0.808075i | \(-0.700510\pi\) | ||
0.589080 | − | 0.808075i | \(-0.299490\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.93725 | −0.955533 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.16515 | 1.08770 | 0.543852 | − | 0.839181i | \(-0.316965\pi\) | ||||
0.543852 | + | 0.839181i | \(0.316965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | 0.819288 | 0.409644 | − | 0.912245i | \(-0.365653\pi\) | ||||
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 18.5203i | − | 2.13854i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.16515 | −1.03116 | −0.515580 | − | 0.856841i | \(-0.672424\pi\) | ||||
−0.515580 | + | 0.856841i | \(0.672424\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.3205 | 1.90117 | 0.950586 | − | 0.310460i | \(-0.100483\pi\) | ||||
0.950586 | + | 0.310460i | \(0.100483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 10.3923i | − | 1.12720i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.0000i | 2.25144i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.16515i | 0.971504i | 0.874097 | + | 0.485752i | \(0.161454\pi\) | ||||
−0.874097 | + | 0.485752i | \(0.838546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.64575i | 0.277350i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.16515 | − | 12.0000i | −0.940325 | − | 1.23117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.16515i | − | 0.930580i | −0.885158 | − | 0.465290i | \(-0.845950\pi\) | ||
0.885158 | − | 0.465290i | \(-0.154050\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8564i | 1.37876i | 0.724398 | + | 0.689382i | \(0.242118\pi\) | ||||
−0.724398 | + | 0.689382i | \(0.757882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.16515 | 0.903069 | 0.451535 | − | 0.892254i | \(-0.350877\pi\) | ||||
0.451535 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 9.16515i | − | 0.894427i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.93725i | 0.767323i | 0.923474 | + | 0.383662i | \(0.125337\pi\) | ||||
−0.923474 | + | 0.383662i | \(0.874663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.64575 | −0.253417 | −0.126709 | − | 0.991940i | \(-0.540441\pi\) | ||||
−0.126709 | + | 0.991940i | \(0.540441\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.0000i | 2.65764i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.16515i | − | 0.862185i | −0.902308 | − | 0.431092i | \(-0.858128\pi\) | ||
0.902308 | − | 0.431092i | \(-0.141872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.3923 | −0.969087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.5830 | −0.978399 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.00000i | − | 0.275010i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.2487 | 2.18643 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 27.4955i | − | 2.42084i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.46410 | −0.302660 | −0.151330 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151330 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.64575 | − | 3.46410i | −0.229416 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.16515 | 0.788811 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | 0.256307 | 0.128154 | − | 0.991754i | \(-0.459095\pi\) | ||||
0.128154 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8564 | −1.17529 | −0.587643 | − | 0.809121i | \(-0.699944\pi\) | ||||
−0.587643 | + | 0.809121i | \(0.699944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.4955i | 2.28337i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.8745i | 1.30931i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3205i | 1.41895i | 0.704730 | + | 0.709476i | \(0.251068\pi\) | ||||
−0.704730 | + | 0.709476i | \(0.748932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.3303 | −1.49170 | −0.745849 | − | 0.666115i | \(-0.767956\pi\) | ||||
−0.745849 | + | 0.666115i | \(0.767956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3923i | 0.829396i | 0.909959 | + | 0.414698i | \(0.136113\pi\) | ||||
−0.909959 | + | 0.414698i | \(0.863887\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 21.0000i | − | 1.66541i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | −0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.92820 | 0.542659 | 0.271329 | − | 0.962487i | \(-0.412537\pi\) | ||||
0.271329 | + | 0.962487i | \(0.412537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.16515 | −0.709221 | −0.354610 | − | 0.935014i | \(-0.615386\pi\) | ||||
−0.354610 | + | 0.935014i | \(0.615386\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | −0.461538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.8564 | − | 10.5830i | 1.05963 | − | 0.809303i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.00000i | − | 0.529150i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.0000 | −1.57846 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.8745i | 1.18652i | 0.805012 | + | 0.593258i | \(0.202159\pi\) | ||||
−0.805012 | + | 0.593258i | \(0.797841\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5830 | 0.786629 | 0.393314 | − | 0.919404i | \(-0.371328\pi\) | ||||
0.393314 | + | 0.919404i | \(0.371328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.3303 | 1.35501 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 36.6606i | 2.69534i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.64575 | 0.192450 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.00000i | − | 0.217072i | −0.994092 | − | 0.108536i | \(-0.965384\pi\) | ||
0.994092 | − | 0.108536i | \(-0.0346163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3303i | 1.31944i | 0.751510 | + | 0.659722i | \(0.229326\pi\) | ||||
−0.751510 | + | 0.659722i | \(0.770674\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.2487 | −1.73649 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.3923i | − | 0.740421i | −0.928948 | − | 0.370211i | \(-0.879286\pi\) | ||
0.928948 | − | 0.370211i | \(-0.120714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.0000i | − | 1.20510i | −0.798082 | − | 0.602549i | \(-0.794152\pi\) | ||
0.798082 | − | 0.602549i | \(-0.205848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35.0000 | 2.46871 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.93725i | 0.557086i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.7490 | 2.21745 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 12.0000i | − | 0.834058i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.64575i | 0.182141i | 0.995844 | + | 0.0910705i | \(0.0290289\pi\) | ||||
−0.995844 | + | 0.0910705i | \(0.970971\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.2487i | 1.66149i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 36.0000i | − | 2.45518i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.5203i | 1.25148i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.93725 | −0.533917 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.4955 | 1.84123 | 0.920616 | − | 0.390469i | \(-0.127687\pi\) | ||||
0.920616 | + | 0.390469i | \(0.127687\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 28.0000 | 1.86667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.93725i | 0.526814i | 0.964685 | + | 0.263407i | \(0.0848462\pi\) | ||||
−0.964685 | + | 0.263407i | \(0.915154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.7846i | 1.37349i | 0.726900 | + | 0.686743i | \(0.240960\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 24.2487i | − | 1.57512i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0000i | 0.970269i | 0.874439 | + | 0.485135i | \(0.161229\pi\) | ||||
−0.874439 | + | 0.485135i | \(0.838771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.16515i | − | 0.590379i | −0.955439 | − | 0.295190i | \(-0.904617\pi\) | ||
0.955439 | − | 0.295190i | \(-0.0953828\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 21.1660i | − | 1.35780i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.7846i | 1.32788i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.16515 | + | 7.00000i | −0.583165 | + | 0.445399i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 45.8258i | 2.90409i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 27.4955 | 1.72183 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.16515i | − | 0.571706i | −0.958273 | − | 0.285853i | \(-0.907723\pi\) | ||
0.958273 | − | 0.285853i | \(-0.0922770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5830i | 0.657596i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −31.7490 | −1.96521 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.0000i | − | 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 27.4955i | − | 1.68903i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.2487 | −1.48400 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.7490 | 1.93577 | 0.967886 | − | 0.251390i | \(-0.0808877\pi\) | ||||
0.967886 | + | 0.251390i | \(0.0808877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.00000i | − | 0.0607457i | −0.999539 | − | 0.0303728i | \(-0.990331\pi\) | ||
0.999539 | − | 0.0303728i | \(-0.00966946\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.00000 | −0.423659 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.3303i | 1.09349i | 0.837298 | + | 0.546747i | \(0.184134\pi\) | ||||
−0.837298 | + | 0.546747i | \(0.815866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3923 | 0.617758 | 0.308879 | − | 0.951101i | \(-0.400046\pi\) | ||||
0.308879 | + | 0.951101i | \(0.400046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 31.7490 | − | 24.2487i | 1.88065 | − | 1.43637i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.16515 | 0.541002 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.2487 | 1.42148 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.8118 | −1.39110 | −0.695549 | − | 0.718479i | \(-0.744839\pi\) | ||||
−0.695549 | + | 0.718479i | \(0.744839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.4955 | −1.60085 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.93725i | 0.459023i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10.3923i | − | 0.599002i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −36.6606 | −2.10610 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.4575i | − | 1.51001i | −0.655719 | − | 0.755005i | \(-0.727634\pi\) | ||
0.655719 | − | 0.755005i | \(-0.272366\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.2487i | 1.37946i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000i | 0.170114i | 0.996376 | + | 0.0850572i | \(0.0271073\pi\) | ||||
−0.996376 | + | 0.0850572i | \(0.972893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0000 | −0.734803 | −0.367402 | − | 0.930062i | \(-0.619753\pi\) | ||||
−0.367402 | + | 0.930062i | \(0.619753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.8564 | 0.780720 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.8118 | −1.33740 | −0.668701 | − | 0.743532i | \(-0.733149\pi\) | ||||
−0.668701 | + | 0.743532i | \(0.733149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.0000 | −1.17211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3923 | − | 7.93725i | 0.578243 | − | 0.441641i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.5203 | −1.02732 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.00000i | − | 0.387101i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.5203i | 1.01797i | 0.860777 | + | 0.508983i | \(0.169978\pi\) | ||||
−0.860777 | + | 0.508983i | \(0.830022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −42.3320 | −2.31978 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 45.8258 | 2.50373 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.16515i | 0.499258i | 0.968342 | + | 0.249629i | \(0.0803086\pi\) | ||||
−0.968342 | + | 0.249629i | \(0.919691\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.2487 | 1.31701 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000i | 0.701934i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 27.4955i | − | 1.48031i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | 1.11578 | 0.557888 | − | 0.829916i | \(-0.311612\pi\) | ||||
0.557888 | + | 0.829916i | \(0.311612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 17.3205i | − | 0.927146i | −0.886059 | − | 0.463573i | \(-0.846567\pi\) | ||
0.886059 | − | 0.463573i | \(-0.153433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 7.00000i | − | 0.373632i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.0000 | 1.11772 | 0.558859 | − | 0.829263i | \(-0.311239\pi\) | ||||
0.558859 | + | 0.829263i | \(0.311239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.7490i | 1.68506i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.93725 | 0.420084 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.0000i | − | 1.42501i | −0.701669 | − | 0.712503i | \(-0.747562\pi\) | ||
0.701669 | − | 0.712503i | \(-0.252438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | − | 18.3303i | 0.263158 | − | 0.964753i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 29.1033i | − | 1.52753i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.2487i | 1.26924i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0000i | 1.46159i | 0.682598 | + | 0.730794i | \(0.260850\pi\) | ||||
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 36.6606i | 1.90847i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.93725i | − | 0.412082i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2288 | −0.684959 | −0.342480 | − | 0.939525i | \(-0.611267\pi\) | ||||
−0.342480 | + | 0.939525i | \(0.611267\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.3303 | 0.946573 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.0000 | 1.08156 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.2288i | 0.679516i | 0.940513 | + | 0.339758i | \(0.110345\pi\) | ||||
−0.940513 | + | 0.339758i | \(0.889655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.4955 | 1.40495 | 0.702476 | − | 0.711707i | \(-0.252078\pi\) | ||||
0.702476 | + | 0.711707i | \(0.252078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 41.5692 | 2.11308 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.7846i | 1.05382i | 0.849921 | + | 0.526911i | \(0.176650\pi\) | ||||
−0.849921 | + | 0.526911i | \(0.823350\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.00000i | − | 0.455150i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 9.16515i | − | 0.462321i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 31.7490i | − | 1.59747i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7846i | 1.04315i | 0.853206 | + | 0.521575i | \(0.174655\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.16515 | − | 7.00000i | 0.458831 | − | 0.350438i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 17.3205i | − | 0.860663i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.3303i | − | 0.906375i | −0.891415 | − | 0.453188i | \(-0.850287\pi\) | ||
0.891415 | − | 0.453188i | \(-0.149713\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.93725i | 0.391516i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.93725 | −0.390567 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 60.0000i | 2.94528i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 36.6606i | − | 1.79528i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1769 | 1.52309 | 0.761546 | − | 0.648111i | \(-0.224441\pi\) | ||||
0.761546 | + | 0.648111i | \(0.224441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.64575 | 0.128946 | 0.0644730 | − | 0.997919i | \(-0.479463\pi\) | ||||
0.0644730 | + | 0.997919i | \(0.479463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.0000 | 1.01865 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.92820 | 0.335279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3303 | 0.882940 | 0.441470 | − | 0.897276i | \(-0.354457\pi\) | ||||
0.441470 | + | 0.897276i | \(0.354457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.4955i | − | 1.32135i | −0.750673 | − | 0.660674i | \(-0.770271\pi\) | ||
0.750673 | − | 0.660674i | \(-0.229729\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −72.7461 | −3.48791 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.93725 | − | 10.3923i | −0.379690 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.0000 | −1.14286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.92820 | −0.329169 | −0.164584 | − | 0.986363i | \(-0.552628\pi\) | ||||
−0.164584 | + | 0.986363i | \(0.552628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.7490 | −1.50505 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −45.8258 | −2.16748 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.6606i | 1.73012i | 0.501668 | + | 0.865060i | \(0.332720\pi\) | ||||
−0.501668 | + | 0.865060i | \(0.667280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 48.4974i | − | 2.27861i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.16515 | −0.429669 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.0000 | −1.35656 | −0.678281 | − | 0.734802i | \(-0.737275\pi\) | ||||
−0.678281 | + | 0.734802i | \(0.737275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.93725i | 0.370479i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.8564i | − | 0.645357i | −0.946509 | − | 0.322679i | \(-0.895417\pi\) | ||
0.946509 | − | 0.322679i | \(-0.104583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.1769 | −1.44270 | −0.721348 | − | 0.692573i | \(-0.756477\pi\) | ||||
−0.721348 | + | 0.692573i | \(0.756477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.2288 | 0.610847 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.4955 | −1.26692 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.2487 | − | 18.5203i | 1.11261 | − | 0.849768i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.7490 | 1.45369 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 24.0000i | − | 1.09659i | −0.836286 | − | 0.548294i | \(-0.815277\pi\) | ||
0.836286 | − | 0.548294i | \(-0.184723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.0000 | 1.27669 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 7.93725i | − | 0.361158i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.7490 | 1.44165 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.16515 | 0.415313 | 0.207656 | − | 0.978202i | \(-0.433416\pi\) | ||||
0.207656 | + | 0.978202i | \(0.433416\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.3303i | 0.828925i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.8564 | 0.625331 | 0.312665 | − | 0.949863i | \(-0.398778\pi\) | ||||
0.312665 | + | 0.949863i | \(0.398778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.8118 | −1.07243 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.16515i | 0.411113i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.1769 | −1.39567 | −0.697835 | − | 0.716258i | \(-0.745853\pi\) | ||||
−0.697835 | + | 0.716258i | \(0.745853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 24.2487i | − | 1.08335i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00000i | 0.401290i | 0.979664 | + | 0.200645i | \(0.0643038\pi\) | ||||
−0.979664 | + | 0.200645i | \(0.935696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −48.0000 | −2.13597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 15.8745i | − | 0.705012i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.7490 | 1.40725 | 0.703625 | − | 0.710571i | \(-0.251563\pi\) | ||||
0.703625 | + | 0.710571i | \(0.251563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.00000i | 0.309662i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.00000 | + | 9.16515i | 0.309058 | + | 0.404651i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.7490i | 1.39903i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.16515i | 0.401533i | 0.979639 | + | 0.200766i | \(0.0643432\pi\) | ||||
−0.979639 | + | 0.200766i | \(0.935657\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 29.1033i | − | 1.27260i | −0.771443 | − | 0.636298i | \(-0.780465\pi\) | ||
0.771443 | − | 0.636298i | \(-0.219535\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.5203 | 0.808290 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0000 | 0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 31.7490i | − | 1.37779i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.2487i | − | 1.05033i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.4955 | −1.18873 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −42.0000 | −1.81243 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3205i | 0.744667i | 0.928099 | + | 0.372333i | \(0.121442\pi\) | ||||
−0.928099 | + | 0.372333i | \(0.878558\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.0000i | 1.20160i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.16515i | − | 0.392592i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.29150i | − | 0.226248i | −0.993581 | − | 0.113124i | \(-0.963914\pi\) | ||
0.993581 | − | 0.113124i | \(-0.0360858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.7128i | 1.18275i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.4955 | + | 21.0000i | −1.17135 | + | 0.894630i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.16515i | − | 0.389742i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −96.9948 | −4.11720 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.46410i | − | 0.146779i | −0.997303 | − | 0.0733893i | \(-0.976618\pi\) | ||
0.997303 | − | 0.0733893i | \(-0.0233816\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.4955 | −1.16293 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.8745i | 0.669031i | 0.942390 | + | 0.334515i | \(0.108573\pi\) | ||||
−0.942390 | + | 0.334515i | \(0.891427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.7490 | 1.33569 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.00000i | − | 0.209980i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.16515i | − | 0.384223i | −0.981373 | − | 0.192112i | \(-0.938466\pi\) | ||
0.981373 | − | 0.192112i | \(-0.0615335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.46410 | −0.144968 | −0.0724841 | − | 0.997370i | \(-0.523093\pi\) | ||||
−0.0724841 | + | 0.997370i | \(0.523093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.93725 | 0.331584 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 21.0000i | − | 0.875761i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −48.4974 | −2.01548 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.3205i | 0.718576i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 36.6606i | − | 1.51573i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.92820 | −0.285958 | −0.142979 | − | 0.989726i | \(-0.545668\pi\) | ||||
−0.142979 | + | 0.989726i | \(0.545668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.4955 | 1.13101 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3923 | 0.426043 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.9778 | 1.84082 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.3303 | 0.748956 | 0.374478 | − | 0.927236i | \(-0.377822\pi\) | ||||
0.374478 | + | 0.927236i | \(0.377822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 52.9150i | 2.15487i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 38.1051i | − | 1.54919i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.16515 | 0.372002 | 0.186001 | − | 0.982550i | \(-0.440447\pi\) | ||||
0.186001 | + | 0.982550i | \(0.440447\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.0000 | −0.850963 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.46410i | 0.139914i | 0.997550 | + | 0.0699569i | \(0.0222862\pi\) | ||||
−0.997550 | + | 0.0699569i | \(0.977714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 84.0000i | 3.38721i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.8564 | 0.556936 | 0.278468 | − | 0.960446i | \(-0.410173\pi\) | ||||
0.278468 | + | 0.960446i | \(0.410173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.93725 | 0.318511 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.16515 | −0.367194 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.7490 | −1.26592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.0000i | − | 0.796187i | −0.917345 | − | 0.398094i | \(-0.869672\pi\) | ||
0.917345 | − | 0.398094i | \(-0.130328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.00000 | −0.278225 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.8745 | 0.628971 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.6606 | −1.45027 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.16515i | 0.362002i | 0.983483 | + | 0.181001i | \(0.0579337\pi\) | ||||
−0.983483 | + | 0.181001i | \(0.942066\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.1769 | 1.22950 | 0.614749 | − | 0.788723i | \(-0.289257\pi\) | ||||
0.614749 | + | 0.788723i | \(0.289257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 95.2470 | 3.75035 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.00000i | 0.117942i | 0.998260 | + | 0.0589711i | \(0.0187820\pi\) | ||||
−0.998260 | + | 0.0589711i | \(0.981218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.92820i | 0.271122i | 0.990769 | + | 0.135561i | \(0.0432836\pi\) | ||||
−0.990769 | + | 0.135561i | \(0.956716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.0000i | − | 0.468879i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.0000 | −1.09238 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7.93725i | − | 0.309192i | −0.987978 | − | 0.154596i | \(-0.950592\pi\) | ||
0.987978 | − | 0.154596i | \(-0.0494075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.9778 | −1.74943 | −0.874716 | − | 0.484635i | \(-0.838952\pi\) | ||||
−0.874716 | + | 0.484635i | \(0.838952\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 21.0000i | − | 0.815572i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | − | 9.16515i | 0.465340 | − | 0.355409i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.8118i | 0.921995i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 72.7461i | 2.81253i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 9.16515i | − | 0.353291i | −0.984275 | − | 0.176645i | \(-0.943475\pi\) | ||
0.984275 | − | 0.176645i | \(-0.0565246\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.5203i | 0.712845i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.8118 | −0.915160 | −0.457580 | − | 0.889168i | \(-0.651284\pi\) | ||||
−0.457580 | + | 0.889168i | \(0.651284\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.16515 | 0.351726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.0000 | −0.804722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.8745i | − | 0.607421i | −0.952764 | − | 0.303711i | \(-0.901774\pi\) | ||
0.952764 | − | 0.303711i | \(-0.0982256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.3923i | 0.397070i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −54.9909 | −2.09803 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.0000 | −0.800036 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7846 | 0.790684 | 0.395342 | − | 0.918534i | \(-0.370626\pi\) | ||||
0.395342 | + | 0.918534i | \(0.370626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 48.0000i | − | 1.82074i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.4955i | 1.04146i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 47.6235i | 1.80129i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.8564i | − | 0.523349i | −0.965156 | − | 0.261675i | \(-0.915725\pi\) | ||
0.965156 | − | 0.261675i | \(-0.0842747\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.6606 | + | 28.0000i | −1.38268 | + | 1.05604i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.8564 | −0.521124 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.92820i | 0.260194i | 0.991501 | + | 0.130097i | \(0.0415289\pi\) | ||||
−0.991501 | + | 0.130097i | \(0.958471\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.6606 | 1.37488 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.6863 | −1.48211 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 15.0000i | − | 0.559406i | −0.960087 | − | 0.279703i | \(-0.909764\pi\) | ||
0.960087 | − | 0.279703i | \(-0.0902359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.16515i | 0.341328i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.2487 | 0.901819 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −55.5608 | −2.06348 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.0000i | 1.74313i | 0.490277 | + | 0.871567i | \(0.336896\pi\) | ||||
−0.490277 | + | 0.871567i | \(0.663104\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.0000 | 1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.1769 | 1.15312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.1769i | − | 1.15155i | −0.817610 | − | 0.575773i | \(-0.804701\pi\) | ||
0.817610 | − | 0.575773i | \(-0.195299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −54.9909 | −2.02837 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.7846 | −0.764574 | −0.382287 | − | 0.924044i | \(-0.624863\pi\) | ||||
−0.382287 | + | 0.924044i | \(0.624863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.5203 | − | 24.2487i | −0.680359 | − | 0.890799i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.3303 | −0.672474 | −0.336237 | − | 0.941777i | \(-0.609154\pi\) | ||||
−0.336237 | + | 0.941777i | \(0.609154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −60.0000 | −2.19823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −69.2820 | −2.53490 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.93725 | −0.290021 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.8258 | 1.67221 | 0.836103 | − | 0.548573i | \(-0.184829\pi\) | ||||
0.836103 | + | 0.548573i | \(0.184829\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 45.8258i | − | 1.66998i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 63.4980i | − | 2.31093i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 48.4974i | − | 1.76267i | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||
0.472493 | − | 0.881334i | \(-0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | 0.543750 | 0.271875 | − | 0.962333i | \(-0.412356\pi\) | ||||
0.271875 | + | 0.962333i | \(0.412356\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.64575i | − | 0.0957826i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41.5692i | 1.50294i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.0000i | 0.758266i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.2487 | 0.873296 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.6863 | 1.42742 | 0.713708 | − | 0.700443i | \(-0.247014\pi\) | ||||
0.713708 | + | 0.700443i | \(0.247014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.0000 | −1.00449 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.2487 | + | 31.7490i | 0.868800 | + | 1.13753i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 21.0000i | − | 0.750479i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.64575i | − | 0.0943108i | −0.998888 | − | 0.0471554i | \(-0.984984\pi\) | ||
0.998888 | − | 0.0471554i | \(-0.0150156\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.7490 | 1.13029 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.16515 | 0.325875 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.3303i | − | 0.650928i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 72.7461 | 2.58004 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.8118 | −0.843456 | −0.421728 | − | 0.906722i | \(-0.638576\pi\) | ||||
−0.421728 | + | 0.906722i | \(0.638576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 36.6606i | − | 1.29534i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 10.3923i | − | 0.366281i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 84.0000i | 2.95694i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.0000 | 1.16022 | 0.580109 | − | 0.814539i | \(-0.303010\pi\) | ||||
0.580109 | + | 0.814539i | \(0.303010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 50.2693i | − | 1.76519i | −0.470131 | − | 0.882596i | \(-0.655793\pi\) | ||
0.470131 | − | 0.882596i | \(-0.344207\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.64575 | 0.0927905 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0000i | 0.840683i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.0000 | − | 27.4955i | 1.25948 | − | 0.961944i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 10.5830i | − | 0.369800i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.4974i | 1.69257i | 0.532729 | + | 0.846286i | \(0.321166\pi\) | ||||
−0.532729 | + | 0.846286i | \(0.678834\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.0000i | 0.871445i | 0.900081 | + | 0.435723i | \(0.143507\pi\) | ||||
−0.900081 | + | 0.435723i | \(0.856493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 39.6863i | − | 1.38003i | −0.723797 | − | 0.690013i | \(-0.757605\pi\) | ||
0.723797 | − | 0.690013i | \(-0.242395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.2288 | −0.459454 | −0.229727 | − | 0.973255i | \(-0.573783\pi\) | ||||
−0.229727 | + | 0.973255i | \(0.573783\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | −0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 31.7490i | − | 1.09872i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.4955 | 0.949248 | 0.474624 | − | 0.880189i | \(-0.342584\pi\) | ||||
0.474624 | + | 0.880189i | \(0.342584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.0000 | 1.17241 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −48.4974 | −1.67034 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 20.7846i | − | 0.715012i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.0000i | − | 0.377964i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.4955i | 0.943642i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.7490i | 1.08834i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.3205i | − | 0.593043i | −0.955026 | − | 0.296521i | \(-0.904173\pi\) | ||
0.955026 | − | 0.296521i | \(-0.0958266\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.6606 | + | 48.0000i | 1.25377 | + | 1.64157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 54.9909i | − | 1.87845i | −0.343297 | − | 0.939227i | \(-0.611544\pi\) | ||
0.343297 | − | 0.939227i | \(-0.388456\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.46410 | 0.118194 | 0.0590968 | − | 0.998252i | \(-0.481178\pi\) | ||||
0.0590968 | + | 0.998252i | \(0.481178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.2487i | 0.826394i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.6606 | 1.24794 | 0.623971 | − | 0.781448i | \(-0.285518\pi\) | ||||
0.623971 | + | 0.781448i | \(0.285518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 21.1660i | − | 0.718835i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 35.0000i | − | 1.18593i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.6606i | 1.24077i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820 | 0.234216 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.2288 | 0.446703 | 0.223352 | − | 0.974738i | \(-0.428300\pi\) | ||||
0.223352 | + | 0.974738i | \(0.428300\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 63.0000i | − | 2.12494i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.6410 | −1.16576 | −0.582882 | − | 0.812557i | \(-0.698075\pi\) | ||||
−0.582882 | + | 0.812557i | \(0.698075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 72.7461i | − | 2.44533i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.6606 | 1.23094 | 0.615471 | − | 0.788159i | \(-0.288966\pi\) | ||||
0.615471 | + | 0.788159i | \(0.288966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54.9909 | −1.83814 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.0000 | −0.701170 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.8118 | 0.793285 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.4955 | 0.914991 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.6606i | 1.21864i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 29.1033i | − | 0.966358i | −0.875522 | − | 0.483179i | \(-0.839482\pi\) | ||
0.875522 | − | 0.483179i | \(-0.160518\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 55.4256i | − | 1.83835i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.16515 | −0.303655 | −0.151828 | − | 0.988407i | \(-0.548516\pi\) | ||||
−0.151828 | + | 0.988407i | \(0.548516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 63.4980i | 2.09918i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3.46410i | − | 0.114395i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0000i | 0.824674i | 0.911031 | + | 0.412337i | \(0.135287\pi\) | ||||
−0.911031 | + | 0.412337i | \(0.864713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 70.0000 | 2.30658 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.2487 | 0.798156 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −74.0810 | −2.43577 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.6606 | −1.20409 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.0000 | 0.885841 | 0.442921 | − | 0.896561i | \(-0.353942\pi\) | ||||
0.442921 | + | 0.896561i | \(0.353942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.7846 | + | 15.8745i | −0.681188 | + | 0.520266i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.93725 | −0.259854 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0000 | 1.20874 | 0.604369 | − | 0.796705i | \(-0.293425\pi\) | ||||
0.604369 | + | 0.796705i | \(0.293425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 34.3948i | − | 1.12243i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.93725 | −0.258747 | −0.129374 | − | 0.991596i | \(-0.541297\pi\) | ||||
−0.129374 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.4955 | 0.895375 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.16515i | 0.298142i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2487 | 0.787977 | 0.393989 | − | 0.919115i | \(-0.371095\pi\) | ||||
0.393989 | + | 0.919115i | \(0.371095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.5203 | 0.601193 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 63.0000i | − | 2.04291i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.4955i | 0.890665i | 0.895365 | + | 0.445333i | \(0.146915\pi\) | ||||
−0.895365 | + | 0.445333i | \(0.853085\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.3923 | 0.336287 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.00000i | 0.0968751i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 31.7490i | − | 1.02310i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −63.4980 | −2.04407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.0000i | − | 0.514525i | −0.966342 | − | 0.257263i | \(-0.917179\pi\) | ||
0.966342 | − | 0.257263i | \(-0.0828206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.0000 | + | 27.4955i | 0.674617 | + | 0.883281i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 15.8745i | − | 0.509437i | −0.967015 | − | 0.254719i | \(-0.918017\pi\) | ||
0.967015 | − | 0.254719i | \(-0.0819828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13.8564i | − | 0.444216i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 49.0000i | − | 1.56926i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 54.9909i | − | 1.75932i | −0.475608 | − | 0.879658i | \(-0.657772\pi\) | ||
0.475608 | − | 0.879658i | \(-0.342228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5830 | 0.337889 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.3303 | −0.584646 | −0.292323 | − | 0.956320i | \(-0.594428\pi\) | ||||
−0.292323 | + | 0.956320i | \(0.594428\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | 1.14706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 31.1769i | − | 0.991368i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.8258 | 1.45570 | 0.727852 | − | 0.685735i | \(-0.240519\pi\) | ||||
0.727852 | + | 0.685735i | \(0.240519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −49.0000 | −1.55497 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 58.8897 | 1.86693 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 62.3538i | − | 1.97477i | −0.158352 | − | 0.987383i | \(-0.550618\pi\) | ||
0.158352 | − | 0.987383i | \(-0.449382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 28.0000i | − | 0.885881i |
(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 | 1216.2.b.d.607.8 | yes | 8 | |
4.3 | odd | 2 | inner | 1216.2.b.d.607.3 | yes | 8 | |
8.3 | odd | 2 | inner | 1216.2.b.d.607.5 | yes | 8 | |
8.5 | even | 2 | inner | 1216.2.b.d.607.2 | yes | 8 | |
19.18 | odd | 2 | inner | 1216.2.b.d.607.4 | yes | 8 | |
76.75 | even | 2 | inner | 1216.2.b.d.607.7 | yes | 8 | |
152.37 | odd | 2 | inner | 1216.2.b.d.607.6 | yes | 8 | |
152.75 | even | 2 | inner | 1216.2.b.d.607.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.b.d.607.1 | ✓ | 8 | 152.75 | even | 2 | inner | |
1216.2.b.d.607.2 | yes | 8 | 8.5 | even | 2 | inner | |
1216.2.b.d.607.3 | yes | 8 | 4.3 | odd | 2 | inner | |
1216.2.b.d.607.4 | yes | 8 | 19.18 | odd | 2 | inner | |
1216.2.b.d.607.5 | yes | 8 | 8.3 | odd | 2 | inner | |
1216.2.b.d.607.6 | yes | 8 | 152.37 | odd | 2 | inner | |
1216.2.b.d.607.7 | yes | 8 | 76.75 | even | 2 | inner | |
1216.2.b.d.607.8 | yes | 8 | 1.1 | even | 1 | trivial |