Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(1009,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5040.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.t (of order \(2\), degree \(1\), not 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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.5 | ||
Root | \(-1.75233 + 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.1009 |
Dual form | 5040.2.t.y.1009.6 |
$q$-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 \(\left(\mathbb{Z}/5040\mathbb{Z}\right)^\times\).
\(n\) | \(2017\) | \(2801\) | \(3151\) | \(3601\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.75233 | − | 1.38900i | 0.783667 | − | 0.621181i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.14134 | 1.55017 | 0.775086 | − | 0.631856i | \(-0.217707\pi\) | ||||
0.775086 | + | 0.631856i | \(0.217707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.64600i | 1.28857i | 0.764786 | + | 0.644284i | \(0.222845\pi\) | ||||
−0.764786 | + | 0.644284i | \(0.777155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.86799i | − | 0.938126i | −0.883165 | − | 0.469063i | \(-0.844592\pi\) | ||
0.883165 | − | 0.469063i | \(-0.155408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.778008 | −0.178487 | −0.0892436 | − | 0.996010i | \(-0.528445\pi\) | ||||
−0.0892436 | + | 0.996010i | \(0.528445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.00933i | − | 1.04452i | −0.852787 | − | 0.522259i | \(-0.825090\pi\) | ||
0.852787 | − | 0.522259i | \(-0.174910\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14134 | − | 4.86799i | 0.228267 | − | 0.973599i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.42401 | 1.74999 | 0.874997 | − | 0.484128i | \(-0.160863\pi\) | ||||
0.874997 | + | 0.484128i | \(0.160863\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.72666 | −0.848933 | −0.424466 | − | 0.905444i | \(-0.639538\pi\) | ||||
−0.424466 | + | 0.905444i | \(0.639538\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.38900 | − | 1.75233i | −0.234785 | − | 0.296198i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00933 | 0.157631 | 0.0788153 | − | 0.996889i | \(-0.474886\pi\) | ||||
0.0788153 | + | 0.996889i | \(0.474886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.00933i | − | 1.06891i | −0.845196 | − | 0.534456i | \(-0.820516\pi\) | ||
0.845196 | − | 0.534456i | \(-0.179484\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.4240i | − | 1.66636i | −0.553000 | − | 0.833181i | \(-0.686517\pi\) | ||
0.553000 | − | 0.833181i | \(-0.313483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.55602i | 1.03790i | 0.854805 | + | 0.518949i | \(0.173677\pi\) | ||||
−0.854805 | + | 0.518949i | \(0.826323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00933 | − | 7.14134i | 1.21482 | − | 0.962938i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.5140 | −1.62918 | −0.814592 | − | 0.580035i | \(-0.803039\pi\) | ||||
−0.814592 | + | 0.580035i | \(0.803039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5047 | 1.47302 | 0.736511 | − | 0.676426i | \(-0.236472\pi\) | ||||
0.736511 | + | 0.676426i | \(0.236472\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.45331 | + | 8.14134i | 0.800435 | + | 1.00981i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7360i | 1.43378i | 0.697187 | + | 0.716889i | \(0.254435\pi\) | ||||
−0.697187 | + | 0.716889i | \(0.745565\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.72666 | 0.323595 | 0.161797 | − | 0.986824i | \(-0.448271\pi\) | ||||
0.161797 | + | 0.986824i | \(0.448271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.00933i | − | 0.586298i | −0.956067 | − | 0.293149i | \(-0.905297\pi\) | ||
0.956067 | − | 0.293149i | \(-0.0947031\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.14134i | − | 0.585910i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.68802 | 0.639953 | 0.319976 | − | 0.947426i | \(-0.396325\pi\) | ||||
0.319976 | + | 0.947426i | \(0.396325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.67531i | 0.513181i | 0.966520 | + | 0.256591i | \(0.0825992\pi\) | ||||
−0.966520 | + | 0.256591i | \(0.917401\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.37266 | − | 6.77801i | −0.582746 | − | 0.735178i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.82936 | −0.299911 | −0.149956 | − | 0.988693i | \(-0.547913\pi\) | ||||
−0.149956 | + | 0.988693i | \(0.547913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.64600 | 0.487033 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.36333 | + | 1.08066i | −0.139875 | + | 0.110873i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.58532i | − | 0.160965i | −0.996756 | − | 0.0804824i | \(-0.974354\pi\) | ||
0.996756 | − | 0.0804824i | \(-0.0256461\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.06068 | 0.901571 | 0.450786 | − | 0.892632i | \(-0.351144\pi\) | ||||
0.450786 | + | 0.892632i | \(0.351144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.14134i | 0.506591i | 0.967389 | + | 0.253295i | \(0.0815145\pi\) | ||||
−0.967389 | + | 0.253295i | \(0.918486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.97070 | 0.380324 | 0.190162 | − | 0.981753i | \(-0.439099\pi\) | ||||
0.190162 | + | 0.981753i | \(0.439099\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.54669i | 0.427716i | 0.976865 | + | 0.213858i | \(0.0686030\pi\) | ||||
−0.976865 | + | 0.213858i | \(0.931397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.95798 | − | 8.77801i | −0.648835 | − | 0.818553i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.86799 | −0.354578 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.4333 | 1.40303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.76166 | − | 10.1157i | −0.425896 | − | 0.904772i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.1214i | − | 1.43054i | −0.698849 | − | 0.715270i | \(-0.746304\pi\) | ||
0.698849 | − | 0.715270i | \(-0.253696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0513514 | 0.00448659 | 0.00224330 | − | 0.999997i | \(-0.499286\pi\) | ||||
0.00224330 | + | 0.999997i | \(0.499286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.778008i | 0.0674618i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.0187i | 1.19769i | 0.800863 | + | 0.598847i | \(0.204374\pi\) | ||||
−0.800863 | + | 0.598847i | \(0.795626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6167 | 1.07013 | 0.535067 | − | 0.844810i | \(-0.320286\pi\) | ||||
0.535067 | + | 0.844810i | \(0.320286\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.8867i | 1.99750i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.5140 | − | 13.0900i | 1.37141 | − | 1.08706i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.4533 | −0.938292 | −0.469146 | − | 0.883121i | \(-0.655438\pi\) | ||||
−0.469146 | + | 0.883121i | \(0.655438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.86799 | −0.477530 | −0.238765 | − | 0.971077i | \(-0.576743\pi\) | ||||
−0.238765 | + | 0.971077i | \(0.576743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.28267 | + | 6.56534i | −0.665280 | + | 0.527341i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.78734i | − | 0.461880i | −0.972968 | − | 0.230940i | \(-0.925820\pi\) | ||
0.972968 | − | 0.230940i | \(-0.0741801\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.00933 | −0.394790 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.27334i | 0.256388i | 0.991749 | + | 0.128194i | \(0.0409180\pi\) | ||||
−0.991749 | + | 0.128194i | \(0.959082\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 24.8773i | − | 1.92506i | −0.271166 | − | 0.962532i | \(-0.587409\pi\) | ||
0.271166 | − | 0.962532i | \(-0.412591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.58532 | −0.660409 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.62734i | 0.503868i | 0.967744 | + | 0.251934i | \(0.0810665\pi\) | ||||
−0.967744 | + | 0.251934i | \(0.918933\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.86799 | − | 1.14134i | −0.367986 | − | 0.0862769i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0187 | 0.748830 | 0.374415 | − | 0.927261i | \(-0.377844\pi\) | ||||
0.374415 | + | 0.927261i | \(0.377844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.78734 | 0.132852 | 0.0664258 | − | 0.997791i | \(-0.478840\pi\) | ||||
0.0664258 | + | 0.997791i | \(0.478840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.33402 | + | 10.5140i | 0.612730 | + | 0.773004i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 19.8867i | − | 1.45426i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.59465 | −0.621887 | −0.310943 | − | 0.950428i | \(-0.600645\pi\) | ||||
−0.310943 | + | 0.950428i | \(0.600645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.17064i | 0.372191i | 0.982532 | + | 0.186095i | \(0.0595834\pi\) | ||||
−0.982532 | + | 0.186095i | \(0.940417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.9160i | − | 1.70394i | −0.523590 | − | 0.851971i | \(-0.675407\pi\) | ||
0.523590 | − | 0.851971i | \(-0.324593\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3107 | −1.08534 | −0.542672 | − | 0.839945i | \(-0.682587\pi\) | ||||
−0.542672 | + | 0.839945i | \(0.682587\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.42401i | − | 0.661436i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.76868 | − | 1.40196i | 0.123530 | − | 0.0979172i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03863 | 0.0715025 | 0.0357512 | − | 0.999361i | \(-0.488618\pi\) | ||||
0.0357512 | + | 0.999361i | \(0.488618\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.73599 | − | 12.2827i | −0.663989 | − | 0.837671i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.72666i | 0.320866i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9707 | 1.20884 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.86799i | − | 0.660810i | −0.943839 | − | 0.330405i | \(-0.892815\pi\) | ||
0.943839 | − | 0.330405i | \(-0.107185\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 21.6553i | − | 1.43731i | −0.695364 | − | 0.718657i | \(-0.744757\pi\) | ||
0.695364 | − | 0.718657i | \(-0.255243\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.2313 | −1.33692 | −0.668462 | − | 0.743747i | \(-0.733047\pi\) | ||||
−0.668462 | + | 0.743747i | \(0.733047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.45331i | − | 0.357258i | −0.983916 | − | 0.178629i | \(-0.942834\pi\) | ||
0.983916 | − | 0.178629i | \(-0.0571663\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8680 | − | 20.0187i | −1.03511 | − | 1.30587i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.5853 | 0.749392 | 0.374696 | − | 0.927148i | \(-0.377747\pi\) | ||||
0.374696 | + | 0.927148i | \(0.377747\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00933 | −0.322679 | −0.161340 | − | 0.986899i | \(-0.551581\pi\) | ||||
−0.161340 | + | 0.986899i | \(0.551581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.75233 | + | 1.38900i | −0.111952 | + | 0.0887402i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.61462i | − | 0.229993i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4206 | −1.47830 | −0.739148 | − | 0.673543i | \(-0.764772\pi\) | ||||
−0.739148 | + | 0.673543i | \(0.764772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 25.7546i | − | 1.61918i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.0093i | − | 0.811500i | −0.913984 | − | 0.405750i | \(-0.867010\pi\) | ||
0.913984 | − | 0.405750i | \(-0.132990\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6.01866i | − | 0.371126i | −0.982632 | − | 0.185563i | \(-0.940589\pi\) | ||
0.982632 | − | 0.185563i | \(-0.0594109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4953 | + | 13.2406i | 0.644723 | + | 0.813367i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.24065 | 0.197586 | 0.0987929 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987929 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.1307 | 1.76956 | 0.884782 | − | 0.466006i | \(-0.154307\pi\) | ||||
0.884782 | + | 0.466006i | \(0.154307\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.86799 | − | 25.0280i | 0.353853 | − | 1.50924i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.44398i | − | 0.267013i | −0.991048 | − | 0.133507i | \(-0.957376\pi\) | ||
0.991048 | − | 0.133507i | \(-0.0426237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6974 | 1.47332 | 0.736660 | − | 0.676263i | \(-0.236402\pi\) | ||||
0.736660 | + | 0.676263i | \(0.236402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.73937i | 0.460058i | 0.973184 | + | 0.230029i | \(0.0738821\pi\) | ||||
−0.973184 | + | 0.230029i | \(0.926118\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.00933i | − | 0.0595788i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.03863 | 0.119920 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.1086i | 1.46686i | 0.679764 | + | 0.733431i | \(0.262082\pi\) | ||||
−0.679764 | + | 0.733431i | \(0.737918\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.9287 | + | 17.3820i | −1.27674 | + | 1.01202i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.2733 | 1.34593 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.00933 | −0.404011 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.1600 | − | 15.9800i | 1.15436 | − | 0.915014i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.9193i | 1.93588i | 0.251183 | + | 0.967940i | \(0.419180\pi\) | ||||
−0.251183 | + | 0.967940i | \(0.580820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.565344 | 0.0320577 | 0.0160289 | − | 0.999872i | \(-0.494898\pi\) | ||||
0.0160289 | + | 0.999872i | \(0.494898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.3400i | 1.54535i | 0.634804 | + | 0.772673i | \(0.281081\pi\) | ||||
−0.634804 | + | 0.772673i | \(0.718919\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 22.7267i | − | 1.27646i | −0.769847 | − | 0.638228i | \(-0.779668\pi\) | ||
0.769847 | − | 0.638228i | \(-0.220332\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.4520 | 2.71279 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00933i | 0.167444i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.6167 | + | 5.30265i | 1.25455 | + | 0.294138i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.4240 | −0.629826 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.462642 | −0.0254291 | −0.0127145 | − | 0.999919i | \(-0.504047\pi\) | ||||
−0.0127145 | + | 0.999919i | \(0.504047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.3013 | + | 20.5653i | 0.890637 | + | 1.12360i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.5653i | − | 0.575531i | −0.957701 | − | 0.287765i | \(-0.907088\pi\) | ||
0.957701 | − | 0.287765i | \(-0.0929124\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.3013 | −1.31599 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.8760i | 1.71119i | 0.517643 | + | 0.855597i | \(0.326810\pi\) | ||||
−0.517643 | + | 0.855597i | \(0.673190\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.62602 | 0.515269 | 0.257635 | − | 0.966242i | \(-0.417057\pi\) | ||||
0.257635 | + | 0.966242i | \(0.417057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.2534i | − | 1.39733i | −0.715451 | − | 0.698663i | \(-0.753779\pi\) | ||
0.715451 | − | 0.698663i | \(-0.246221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.77801 | − | 3.78734i | 0.253590 | − | 0.201011i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.56534 | 0.240950 | 0.120475 | − | 0.992716i | \(-0.461558\pi\) | ||||
0.120475 | + | 0.992716i | \(0.461558\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3947 | −0.968142 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.95798 | − | 8.77801i | −0.364197 | − | 0.459462i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.79073i | − | 0.197874i | −0.995094 | − | 0.0989371i | \(-0.968456\pi\) | ||
0.995094 | − | 0.0989371i | \(-0.0315443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.55602 | 0.392289 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 20.7453i | − | 1.07415i | −0.843534 | − | 0.537076i | \(-0.819529\pi\) | ||
0.843534 | − | 0.537076i | \(-0.180471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.7839i | 2.25499i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.00933 | 0.154579 | 0.0772894 | − | 0.997009i | \(-0.475373\pi\) | ||||
0.0772894 | + | 0.997009i | \(0.475373\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 7.00933i | − | 0.358160i | −0.983835 | − | 0.179080i | \(-0.942688\pi\) | ||
0.983835 | − | 0.179080i | \(-0.0573121\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.14134 | − | 9.00933i | −0.363956 | − | 0.459158i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.7653 | −1.00214 | −0.501070 | − | 0.865407i | \(-0.667060\pi\) | ||||
−0.501070 | + | 0.865407i | \(0.667060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.3760 | −0.979889 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.96731 | − | 7.90069i | 0.501510 | − | 0.397527i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.37266i | − | 0.470400i | −0.971947 | − | 0.235200i | \(-0.924425\pi\) | ||
0.971947 | − | 0.235200i | \(-0.0755745\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.1507 | 0.806526 | 0.403263 | − | 0.915084i | \(-0.367876\pi\) | ||||
0.403263 | + | 0.915084i | \(0.367876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 21.9600i | − | 1.09391i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.8480i | 1.52908i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2920 | −0.756141 | −0.378070 | − | 0.925777i | \(-0.623412\pi\) | ||||
−0.378070 | + | 0.925777i | \(0.623412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.5140i | 0.615773i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.49402 | + | 8.19269i | 0.318779 | + | 0.402163i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.1820 | 1.62105 | 0.810524 | − | 0.585705i | \(-0.199182\pi\) | ||||
0.810524 | + | 0.585705i | \(0.199182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8094 | 1.35535 | 0.677673 | − | 0.735363i | \(-0.262988\pi\) | ||||
0.677673 | + | 0.735363i | \(0.262988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.8294 | − | 4.41468i | −0.913358 | − | 0.214143i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 11.5047i | − | 0.556750i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.5454 | −1.03780 | −0.518902 | − | 0.854834i | \(-0.673659\pi\) | ||||
−0.518902 | + | 0.854834i | \(0.673659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.0187i | 1.73095i | 0.500955 | + | 0.865473i | \(0.332982\pi\) | ||||
−0.500955 | + | 0.865473i | \(0.667018\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.89730i | 0.186433i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.1893 | −1.01131 | −0.505655 | − | 0.862736i | \(-0.668749\pi\) | ||||
−0.505655 | + | 0.862736i | \(0.668749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.1120i | 0.527949i | 0.964530 | + | 0.263974i | \(0.0850334\pi\) | ||||
−0.964530 | + | 0.263974i | \(0.914967\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.95798 | + | 3.92999i | −0.235031 | + | 0.186299i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.961367 | 0.0453697 | 0.0226848 | − | 0.999743i | \(-0.492779\pi\) | ||||
0.0226848 | + | 0.999743i | \(0.492779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.18930 | 0.244355 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.14134 | − | 6.45331i | 0.381672 | − | 0.302536i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2241i | 1.32027i | 0.751149 | + | 0.660133i | \(0.229500\pi\) | ||||
−0.751149 | + | 0.660133i | \(0.770500\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.0887 | −1.21507 | −0.607535 | − | 0.794293i | \(-0.707842\pi\) | ||||
−0.607535 | + | 0.794293i | \(0.707842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.90663i | − | 0.135082i | −0.997716 | − | 0.0675412i | \(-0.978485\pi\) | ||
0.997716 | − | 0.0675412i | \(-0.0215154\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2020i | 0.564642i | 0.959320 | + | 0.282321i | \(0.0911043\pi\) | ||||
−0.959320 | + | 0.282321i | \(0.908896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.7360 | 0.541917 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 36.0373i | − | 1.65700i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.887968 | + | 3.78734i | −0.0407428 | + | 0.173775i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.6519 | 0.806538 | 0.403269 | − | 0.915082i | \(-0.367874\pi\) | ||||
0.403269 | + | 0.915082i | \(0.367874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8760 | −1.27104 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.20202 | − | 2.77801i | −0.0999884 | − | 0.126143i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.57467i | 0.0713553i | 0.999363 | + | 0.0356776i | \(0.0113590\pi\) | ||||
−0.999363 | + | 0.0356776i | \(0.988641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.26270 | −0.147243 | −0.0736217 | − | 0.997286i | \(-0.523456\pi\) | ||||
−0.0736217 | + | 0.997286i | \(0.523456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 36.4520i | − | 1.64172i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.72666i | − | 0.122307i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.5293 | 1.90387 | 0.951936 | − | 0.306298i | \(-0.0990905\pi\) | ||||
0.951936 | + | 0.306298i | \(0.0990905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.6974i | 0.833674i | 0.908981 | + | 0.416837i | \(0.136861\pi\) | ||||
−0.908981 | + | 0.416837i | \(0.863139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.8773 | − | 12.5853i | 0.706532 | − | 0.560039i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2313 | 0.896738 | 0.448369 | − | 0.893849i | \(-0.352005\pi\) | ||||
0.448369 | + | 0.893849i | \(0.352005\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.00933 | −0.221600 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.14134 | + | 9.00933i | 0.314685 | + | 0.396998i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 58.7347i | − | 2.58315i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.8387 | −0.956770 | −0.478385 | − | 0.878150i | \(-0.658778\pi\) | ||||
−0.478385 | + | 0.878150i | \(0.658778\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.4554i | − | 0.894451i | −0.894421 | − | 0.447226i | \(-0.852412\pi\) | ||
0.894421 | − | 0.447226i | \(-0.147588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.2827i | 0.796406i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.09337 | −0.0910163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.68934i | 0.203118i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.14134 | −0.221453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3400 | 1.17544 | 0.587718 | − | 0.809066i | \(-0.300026\pi\) | ||||
0.587718 | + | 0.809066i | \(0.300026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.95798 | − | 5.51531i | 0.298047 | − | 0.236250i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6867i | 0.970013i | 0.874510 | + | 0.485007i | \(0.161183\pi\) | ||||
−0.874510 | + | 0.485007i | \(0.838817\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.33195 | −0.312352 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.68802i | − | 0.241879i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.7453i | 0.540036i | 0.962855 | + | 0.270018i | \(0.0870297\pi\) | ||||
−0.962855 | + | 0.270018i | \(0.912970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.5653 | 1.37737 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.20333i | 0.219294i | 0.993971 | + | 0.109647i | \(0.0349721\pi\) | ||||
−0.993971 | + | 0.109647i | \(0.965028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.31537 | + | 7.96731i | 0.265689 | + | 0.335187i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.37605 | −0.309220 | −0.154610 | − | 0.987976i | \(-0.549412\pi\) | ||||
−0.154610 | + | 0.987976i | \(0.549412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8973 | −0.665281 | −0.332641 | − | 0.943054i | \(-0.607940\pi\) | ||||
−0.332641 | + | 0.943054i | \(0.607940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.3854 | − | 5.71733i | −1.01694 | − | 0.238429i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.9707i | − | 0.831391i | −0.909504 | − | 0.415695i | \(-0.863538\pi\) | ||
0.909504 | − | 0.415695i | \(-0.136462\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.67531 | 0.193964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.8480i | 1.60892i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 13.8060i | − | 0.569834i | −0.958552 | − | 0.284917i | \(-0.908034\pi\) | ||
0.958552 | − | 0.284917i | \(-0.0919661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.67738 | 0.151524 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.0666i | 0.824037i | 0.911175 | + | 0.412019i | \(0.135176\pi\) | ||||
−0.911175 | + | 0.412019i | \(0.864824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.77801 | + | 5.37266i | −0.277871 | + | 0.220257i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.0267 | −1.88060 | −0.940299 | − | 0.340349i | \(-0.889455\pi\) | ||||
−0.940299 | + | 0.340349i | \(0.889455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.37605 | −0.0561301 | −0.0280651 | − | 0.999606i | \(-0.508935\pi\) | ||||
−0.0280651 | + | 0.999606i | \(0.508935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.0443 | − | 21.4370i | 1.09951 | − | 0.871537i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.7933i | − | 0.762796i | −0.924411 | − | 0.381398i | \(-0.875443\pi\) | ||
0.924411 | − | 0.381398i | \(-0.124557\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.0759 | 2.14722 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.8480i | − | 1.00360i | −0.864983 | − | 0.501801i | \(-0.832671\pi\) | ||
0.864983 | − | 0.501801i | \(-0.167329\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 43.1680i | − | 1.73788i | −0.494919 | − | 0.868939i | \(-0.664802\pi\) | ||
0.494919 | − | 0.868939i | \(-0.335198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.9486 | 1.28412 | 0.642062 | − | 0.766652i | \(-0.278079\pi\) | ||||
0.642062 | + | 0.766652i | \(0.278079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.82936i | 0.113356i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.3947 | − | 11.1120i | −0.895788 | − | 0.444481i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.2080 | 0.925362 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.59465 | 0.342148 | 0.171074 | − | 0.985258i | \(-0.445276\pi\) | ||||
0.171074 | + | 0.985258i | \(0.445276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.3926 | − | 28.2500i | −0.888625 | − | 1.12107i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.64600i | − | 0.184081i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.2266 | −1.31237 | −0.656186 | − | 0.754599i | \(-0.727831\pi\) | ||||
−0.656186 | + | 0.754599i | \(0.727831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.4940i | 0.689897i | 0.938622 | + | 0.344948i | \(0.112104\pi\) | ||||
−0.938622 | + | 0.344948i | \(0.887896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.91595i | 0.389836i | 0.980820 | + | 0.194918i | \(0.0624441\pi\) | ||||
−0.980820 | + | 0.194918i | \(0.937556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −64.3386 | −2.52551 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.6240i | 0.572280i | 0.958188 | + | 0.286140i | \(0.0923722\pi\) | ||||
−0.958188 | + | 0.286140i | \(0.907628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0899847 | − | 0.0713273i | 0.00351599 | − | 0.00278699i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.2534 | −0.788959 | −0.394480 | − | 0.918905i | \(-0.629075\pi\) | ||||
−0.394480 | + | 0.918905i | \(0.629075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4299 | −0.483469 | −0.241734 | − | 0.970342i | \(-0.577716\pi\) | ||||
−0.241734 | + | 0.970342i | \(0.577716\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.08066 | + | 1.36333i | 0.0419060 | + | 0.0528676i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 47.2080i | − | 1.82790i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59.1493 | 2.28344 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.6774i | 1.83783i | 0.394458 | + | 0.918914i | \(0.370932\pi\) | ||||
−0.394458 | + | 0.918914i | \(0.629068\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6.00339i | − | 0.230729i | −0.993323 | − | 0.115364i | \(-0.963196\pi\) | ||
0.993323 | − | 0.115364i | \(-0.0368036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.58532 | −0.0608390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.5653i | 1.09302i | 0.837452 | + | 0.546511i | \(0.184044\pi\) | ||||
−0.837452 | + | 0.546511i | \(0.815956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.4720 | + | 24.5653i | 0.743986 | + | 0.938594i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.1053 | −1.33740 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.8247 | −1.81934 | −0.909668 | − | 0.415337i | \(-0.863664\pi\) | ||||
−0.909668 | + | 0.415337i | \(0.863664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.1086 | − | 17.5246i | 0.838629 | − | 0.664747i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.90408i | − | 0.147877i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.80005 | 0.181296 | 0.0906478 | − | 0.995883i | \(-0.471106\pi\) | ||||
0.0906478 | + | 0.995883i | \(0.471106\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.66805i | − | 0.176059i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 9.06068i | − | 0.340762i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.7653 | −0.441855 | −0.220927 | − | 0.975290i | \(-0.570908\pi\) | ||||
−0.220927 | + | 0.975290i | \(0.570908\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.6774i | 0.886725i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.1787 | + | 41.8573i | 1.24081 | + | 1.56538i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.7640 | 1.52024 | 0.760120 | − | 0.649783i | \(-0.225140\pi\) | ||||
0.760120 | + | 0.649783i | \(0.225140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.14134 | 0.191473 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.7560 | − | 45.8760i | 0.399466 | − | 1.70379i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22.1214i | − | 0.820436i | −0.911988 | − | 0.410218i | \(-0.865453\pi\) | ||
0.911988 | − | 0.410218i | \(-0.134547\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.1120 | −1.00277 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 13.0500i | − | 0.482014i | −0.970523 | − | 0.241007i | \(-0.922522\pi\) | ||
0.970523 | − | 0.241007i | \(-0.0774777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 60.3386i | 2.22260i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.5734 | −1.27180 | −0.635901 | − | 0.771771i | \(-0.719371\pi\) | ||||
−0.635901 | + | 0.771771i | \(0.719371\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.55602i | 0.130458i | 0.997870 | + | 0.0652288i | \(0.0207777\pi\) | ||||
−0.997870 | + | 0.0652288i | \(0.979222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0700 | + | 15.9087i | −0.735308 | + | 0.582850i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6226 | 0.862002 | 0.431001 | − | 0.902351i | \(-0.358161\pi\) | ||||
0.431001 | + | 0.902351i | \(0.358161\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.2827 | + | 8.15066i | −0.374225 | + | 0.296633i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1893i | 0.552064i | 0.961148 | + | 0.276032i | \(0.0890196\pi\) | ||||
−0.961148 | + | 0.276032i | \(0.910980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.4626 | −1.24927 | −0.624635 | − | 0.780917i | \(-0.714752\pi\) | ||||
−0.624635 | + | 0.780917i | \(0.714752\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.97070i | − | 0.143749i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 58.1400i | − | 2.09931i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.3854 | −1.45633 | −0.728167 | − | 0.685400i | \(-0.759627\pi\) | ||||
−0.728167 | + | 0.685400i | \(0.759627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 10.7674i | − | 0.387275i | −0.981073 | − | 0.193638i | \(-0.937971\pi\) | ||
0.981073 | − | 0.193638i | \(-0.0620286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.39470 | + | 23.0093i | −0.193783 | + | 0.826519i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.785266 | −0.0281351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0187 | 0.501627 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.03863 | − | 10.1413i | −0.286911 | − | 0.361960i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.19269i | 0.327684i | 0.986487 | + | 0.163842i | \(0.0523887\pi\) | ||||
−0.986487 | + | 0.163842i | \(0.947611\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.54669 | 0.161662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.4507i | 1.89809i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 21.1086i | − | 0.747706i | −0.927488 | − | 0.373853i | \(-0.878036\pi\) | ||
0.927488 | − | 0.373853i | \(-0.121964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.1880 | −1.56326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 25.7546i | − | 0.908862i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.77801 | + | 6.95798i | −0.309384 | + | 0.245236i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.8280 | −0.978382 | −0.489191 | − | 0.872177i | \(-0.662708\pi\) | ||||
−0.489191 | + | 0.872177i | \(0.662708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0607 | 0.388393 | 0.194197 | − | 0.980963i | \(-0.437790\pi\) | ||||
0.194197 | + | 0.980963i | \(0.437790\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.54669 | + | 5.73599i | 0.159264 | + | 0.200923i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.45331i | 0.190787i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.8867 | 0.624248 | 0.312124 | − | 0.950041i | \(-0.398959\pi\) | ||||
0.312124 | + | 0.950041i | \(0.398959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.8667i | 1.84282i | 0.388596 | + | 0.921408i | \(0.372960\pi\) | ||||
−0.388596 | + | 0.921408i | \(0.627040\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.3013i | 1.26232i | 0.775652 | + | 0.631160i | \(0.217421\pi\) | ||||
−0.775652 | + | 0.631160i | \(0.782579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.759350 | 0.0263733 | 0.0131867 | − | 0.999913i | \(-0.495802\pi\) | ||||
0.0131867 | + | 0.999913i | \(0.495802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.86799i | 0.134018i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.5547 | − | 43.5933i | −1.19581 | − | 1.50861i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.3107 | 1.49525 | 0.747625 | − | 0.664121i | \(-0.231194\pi\) | ||||
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.8119 | 2.06248 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.0443 | + | 11.9250i | −0.517541 | + | 0.410234i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.4333i | − | 0.530296i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.0560 | 1.03031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3713i | 1.38229i | 0.722717 | + | 0.691144i | \(0.242893\pi\) | ||||
−0.722717 | + | 0.691144i | \(0.757107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 13.4720i | − | 0.460194i | −0.973168 | − | 0.230097i | \(-0.926096\pi\) | ||
0.973168 | − | 0.230097i | \(-0.0739043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.7313 | −1.18502 | −0.592508 | − | 0.805565i | \(-0.701862\pi\) | ||||
−0.592508 | + | 0.805565i | \(0.701862\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2454i | 0.484918i | 0.970162 | + | 0.242459i | \(0.0779539\pi\) | ||||
−0.970162 | + | 0.242459i | \(0.922046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.20541 | + | 11.6133i | 0.312993 | + | 0.394864i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.2440 | 0.992036 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.5254 | −1.84752 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1157 | + | 4.76166i | −0.341972 | + | 0.160974i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7546i | 0.667067i | 0.942738 | + | 0.333533i | \(0.108241\pi\) | ||||
−0.942738 | + | 0.333533i | \(0.891759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.53058 | 0.321093 | 0.160547 | − | 0.987028i | \(-0.448674\pi\) | ||||
0.160547 | + | 0.987028i | \(0.448674\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.1867i | 1.72257i | 0.508124 | + | 0.861284i | \(0.330339\pi\) | ||||
−0.508124 | + | 0.861284i | \(0.669661\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.4626i | 0.821375i | 0.911776 | + | 0.410688i | \(0.134711\pi\) | ||||
−0.911776 | + | 0.410688i | \(0.865289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.1214 | −0.540693 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.88797i | 0.297425i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.5560 | − | 13.9160i | 0.586833 | − | 0.465159i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −44.5441 | −1.48563 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.2266 | 0.973680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.13201 | − | 2.48262i | 0.104111 | − | 0.0825250i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.09592i | 0.268821i | 0.990926 | + | 0.134410i | \(0.0429140\pi\) | ||||
−0.990926 | + | 0.134410i | \(0.957086\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.5093 | −1.97163 | −0.985815 | − | 0.167834i | \(-0.946323\pi\) | ||||
−0.985815 | + | 0.167834i | \(0.946323\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0373i | 0.795519i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.0513514i | − | 0.00169577i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.7067 | 1.70565 | 0.852823 | − | 0.522200i | \(-0.174889\pi\) | ||||
0.852823 | + | 0.522200i | \(0.174889\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.6680i | 0.416974i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.2080 | + | 6.84802i | 0.960352 | + | 0.225161i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.76142 | −0.123408 | −0.0617041 | − | 0.998094i | \(-0.519654\pi\) | ||||
−0.0617041 | + | 0.998094i | \(0.519654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.778008 | 0.0254982 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.6226 | − | 34.8480i | −0.903357 | − | 1.13965i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.1014i | 0.689352i | 0.938722 | + | 0.344676i | \(0.112011\pi\) | ||||
−0.938722 | + | 0.344676i | \(0.887989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.72873 | 0.0563549 | 0.0281775 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281775 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.05606i | − | 0.164648i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 24.7267i | − | 0.803508i | −0.915748 | − | 0.401754i | \(-0.868401\pi\) | ||
0.915748 | − | 0.401754i | \(-0.131599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.2733 | 0.755485 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.18930i | 0.0385251i | 0.999814 | + | 0.0192626i | \(0.00613185\pi\) | ||||
−0.999814 | + | 0.0192626i | \(0.993868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0607 | + | 11.9380i | −0.487352 | + | 0.386305i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0187 | 0.452686 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.65872 | −0.279314 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.18204 | + | 9.06068i | 0.231198 | + | 0.291674i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3293i | 0.750220i | 0.926980 | + | 0.375110i | \(0.122395\pi\) | ||||
−0.926980 | + | 0.375110i | \(0.877605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.61670 | −0.148157 | −0.0740784 | − | 0.997252i | \(-0.523602\pi\) | ||||
−0.0740784 | + | 0.997252i | \(0.523602\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 12.6167i | − | 0.404473i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.1120i | 0.611448i | 0.952120 | + | 0.305724i | \(0.0988985\pi\) | ||||
−0.952120 | + | 0.305724i | \(0.901102\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.5467 | −0.464914 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.6506i | 1.67929i | 0.543132 | + | 0.839647i | \(0.317238\pi\) | ||||
−0.543132 | + | 0.839647i | \(0.682762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.2194 | − | 41.9087i | −1.05846 | − | 1.33532i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.1120 | −1.11650 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.4227 | −1.66526 | −0.832631 | − | 0.553828i | \(-0.813166\pi\) | ||||
−0.832631 | + | 0.553828i | \(0.813166\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.8294 | + | 21.2666i | −0.850548 | + | 0.674195i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7580i | 0.625743i | 0.949795 | + | 0.312872i | \(0.101291\pi\) | ||||
−0.949795 | + | 0.312872i | \(0.898709\pi\) | |||||||
\(998\) | 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 | 5040.2.t.y.1009.5 | 6 | ||
3.2 | odd | 2 | 560.2.g.f.449.4 | 6 | |||
4.3 | odd | 2 | 2520.2.t.g.1009.5 | 6 | |||
5.4 | even | 2 | inner | 5040.2.t.y.1009.6 | 6 | ||
12.11 | even | 2 | 280.2.g.b.169.3 | ✓ | 6 | ||
15.2 | even | 4 | 2800.2.a.bq.1.2 | 3 | |||
15.8 | even | 4 | 2800.2.a.br.1.2 | 3 | |||
15.14 | odd | 2 | 560.2.g.f.449.3 | 6 | |||
20.19 | odd | 2 | 2520.2.t.g.1009.6 | 6 | |||
24.5 | odd | 2 | 2240.2.g.m.449.3 | 6 | |||
24.11 | even | 2 | 2240.2.g.l.449.4 | 6 | |||
60.23 | odd | 4 | 1400.2.a.s.1.2 | 3 | |||
60.47 | odd | 4 | 1400.2.a.t.1.2 | 3 | |||
60.59 | even | 2 | 280.2.g.b.169.4 | yes | 6 | ||
84.83 | odd | 2 | 1960.2.g.c.1569.4 | 6 | |||
120.29 | odd | 2 | 2240.2.g.m.449.4 | 6 | |||
120.59 | even | 2 | 2240.2.g.l.449.3 | 6 | |||
420.83 | even | 4 | 9800.2.a.cg.1.2 | 3 | |||
420.167 | even | 4 | 9800.2.a.cd.1.2 | 3 | |||
420.419 | odd | 2 | 1960.2.g.c.1569.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.g.b.169.3 | ✓ | 6 | 12.11 | even | 2 | ||
280.2.g.b.169.4 | yes | 6 | 60.59 | even | 2 | ||
560.2.g.f.449.3 | 6 | 15.14 | odd | 2 | |||
560.2.g.f.449.4 | 6 | 3.2 | odd | 2 | |||
1400.2.a.s.1.2 | 3 | 60.23 | odd | 4 | |||
1400.2.a.t.1.2 | 3 | 60.47 | odd | 4 | |||
1960.2.g.c.1569.3 | 6 | 420.419 | odd | 2 | |||
1960.2.g.c.1569.4 | 6 | 84.83 | odd | 2 | |||
2240.2.g.l.449.3 | 6 | 120.59 | even | 2 | |||
2240.2.g.l.449.4 | 6 | 24.11 | even | 2 | |||
2240.2.g.m.449.3 | 6 | 24.5 | odd | 2 | |||
2240.2.g.m.449.4 | 6 | 120.29 | odd | 2 | |||
2520.2.t.g.1009.5 | 6 | 4.3 | odd | 2 | |||
2520.2.t.g.1009.6 | 6 | 20.19 | odd | 2 | |||
2800.2.a.bq.1.2 | 3 | 15.2 | even | 4 | |||
2800.2.a.br.1.2 | 3 | 15.8 | even | 4 | |||
5040.2.t.y.1009.5 | 6 | 1.1 | even | 1 | trivial | ||
5040.2.t.y.1009.6 | 6 | 5.4 | even | 2 | inner | ||
9800.2.a.cd.1.2 | 3 | 420.167 | even | 4 | |||
9800.2.a.cg.1.2 | 3 | 420.83 | even | 4 |