Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9216,2,Mod(1,9216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9216 = 2^{10} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9216.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(73.5901305028\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.3288334336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} - 8x^{5} + 24x^{4} + 8x^{3} - 16x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 4608) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.05636\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.78089 | −0.796439 | −0.398219 | − | 0.917290i | \(-0.630372\pi\) | ||||
−0.398219 | + | 0.917290i | \(0.630372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.29066 | −1.24375 | −0.621876 | − | 0.783116i | \(-0.713629\pi\) | ||||
−0.621876 | + | 0.783116i | \(0.713629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.53073 | 0.461534 | 0.230767 | − | 0.973009i | \(-0.425877\pi\) | ||||
0.230767 | + | 0.973009i | \(0.425877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | 0.162468 | 0.0812340 | − | 0.996695i | \(-0.474114\pi\) | ||||
0.0812340 | + | 0.996695i | \(0.474114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.08034 | −1.47470 | −0.737350 | − | 0.675511i | \(-0.763923\pi\) | ||||
−0.737350 | + | 0.675511i | \(0.763923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.92762 | −0.442227 | −0.221113 | − | 0.975248i | \(-0.570969\pi\) | ||||
−0.221113 | + | 0.975248i | \(0.570969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.22625 | 1.08975 | 0.544874 | − | 0.838518i | \(-0.316577\pi\) | ||||
0.544874 | + | 0.838518i | \(0.316577\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.82843 | −0.365685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.81801 | −1.26607 | −0.633036 | − | 0.774122i | \(-0.718192\pi\) | ||||
−0.633036 | + | 0.774122i | \(0.718192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.01673 | 1.08064 | 0.540318 | − | 0.841461i | \(-0.318304\pi\) | ||||
0.540318 | + | 0.841461i | \(0.318304\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.86030 | 0.990572 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.41421 | 0.561293 | 0.280647 | − | 0.959811i | \(-0.409451\pi\) | ||||
0.280647 | + | 0.959811i | \(0.409451\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.04322 | −0.162924 | −0.0814619 | − | 0.996676i | \(-0.525959\pi\) | ||||
−0.0814619 | + | 0.996676i | \(0.525959\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2350 | −1.71332 | −0.856661 | − | 0.515879i | \(-0.827465\pi\) | ||||
−0.856661 | + | 0.515879i | \(0.827465\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.896683 | 0.130795 | 0.0653973 | − | 0.997859i | \(-0.479169\pi\) | ||||
0.0653973 | + | 0.997859i | \(0.479169\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.82843 | 0.546918 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.81801 | 0.936526 | 0.468263 | − | 0.883589i | \(-0.344880\pi\) | ||||
0.468263 | + | 0.883589i | \(0.344880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.72607 | −0.367583 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4525 | −1.36080 | −0.680400 | − | 0.732841i | \(-0.738194\pi\) | ||||
−0.680400 | + | 0.732841i | \(0.738194\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.58579 | 0.587150 | 0.293575 | − | 0.955936i | \(-0.405155\pi\) | ||||
0.293575 | + | 0.955936i | \(0.405155\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.04322 | −0.129396 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.30739 | −1.13708 | −0.568539 | − | 0.822656i | \(-0.692491\pi\) | ||||
−0.568539 | + | 0.822656i | \(0.692491\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.7821 | −1.75431 | −0.877155 | − | 0.480208i | \(-0.840561\pi\) | ||||
−0.877155 | + | 0.480208i | \(0.840561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.48528 | −0.759045 | −0.379522 | − | 0.925183i | \(-0.623912\pi\) | ||||
−0.379522 | + | 0.925183i | \(0.623912\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.03712 | −0.574033 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.29066 | 0.370228 | 0.185114 | − | 0.982717i | \(-0.440735\pi\) | ||||
0.185114 | + | 0.982717i | \(0.440735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.2513 | −1.45452 | −0.727262 | − | 0.686360i | \(-0.759207\pi\) | ||||
−0.727262 | + | 0.686360i | \(0.759207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8284 | 1.17451 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.12356 | −0.755096 | −0.377548 | − | 0.925990i | \(-0.623233\pi\) | ||||
−0.377548 | + | 0.925990i | \(0.623233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.92762 | −0.202070 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.43289 | 0.352207 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.31371 | 0.742595 | 0.371297 | − | 0.928514i | \(-0.378913\pi\) | ||||
0.371297 | + | 0.928514i | \(0.378913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4169 | 1.53404 | 0.767020 | − | 0.641623i | \(-0.221739\pi\) | ||||
0.767020 | + | 0.641623i | \(0.221739\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.01673 | −0.592846 | −0.296423 | − | 0.955057i | \(-0.595794\pi\) | ||||
−0.296423 | + | 0.955057i | \(0.595794\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.5140 | 1.30644 | 0.653222 | − | 0.757166i | \(-0.273417\pi\) | ||||
0.653222 | + | 0.757166i | \(0.273417\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0711 | 1.25198 | 0.625991 | − | 0.779831i | \(-0.284695\pi\) | ||||
0.625991 | + | 0.779831i | \(0.284695\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0742 | 0.947705 | 0.473852 | − | 0.880604i | \(-0.342863\pi\) | ||||
0.473852 | + | 0.880604i | \(0.342863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.30739 | −0.867918 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.0083 | 1.83416 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.65685 | −0.786987 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1607 | 1.08768 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.564588 | 0.0500990 | 0.0250495 | − | 0.999686i | \(-0.492026\pi\) | ||||
0.0250495 | + | 0.999686i | \(0.492026\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7206 | 1.02403 | 0.512017 | − | 0.858975i | \(-0.328898\pi\) | ||||
0.512017 | + | 0.858975i | \(0.328898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.34315 | 0.550020 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.1546 | −1.38018 | −0.690090 | − | 0.723724i | \(-0.742429\pi\) | ||||
−0.690090 | + | 0.723724i | \(0.742429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6148 | 1.57888 | 0.789442 | − | 0.613825i | \(-0.210370\pi\) | ||||
0.789442 | + | 0.613825i | \(0.210370\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.896683 | 0.0749844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.1421 | 1.00835 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.34267 | −0.437689 | −0.218844 | − | 0.975760i | \(-0.570229\pi\) | ||||
−0.218844 | + | 0.975760i | \(0.570229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.564588 | −0.0459455 | −0.0229727 | − | 0.999736i | \(-0.507313\pi\) | ||||
−0.0229727 | + | 0.999736i | \(0.507313\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.7151 | −0.860660 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2426 | 1.13669 | 0.568343 | − | 0.822792i | \(-0.307585\pi\) | ||||
0.568343 | + | 0.822792i | \(0.307585\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.1978 | −1.35538 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6871 | 1.30704 | 0.653519 | − | 0.756910i | \(-0.273292\pi\) | ||||
0.653519 | + | 0.756910i | \(0.273292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.8017 | −1.68707 | −0.843533 | − | 0.537078i | \(-0.819528\pi\) | ||||
−0.843533 | + | 0.537078i | \(0.819528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.25623 | −0.247567 | −0.123783 | − | 0.992309i | \(-0.539503\pi\) | ||||
−0.123783 | + | 0.992309i | \(0.539503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.01673 | 0.454822 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0502 | −1.19965 | −0.599823 | − | 0.800133i | \(-0.704762\pi\) | ||||
−0.599823 | + | 0.800133i | \(0.704762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.27208 | 0.0945528 | 0.0472764 | − | 0.998882i | \(-0.484946\pi\) | ||||
0.0472764 | + | 0.998882i | \(0.484946\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.08034 | −0.447036 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.30739 | −0.680623 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3492 | −0.821198 | −0.410599 | − | 0.911816i | \(-0.634680\pi\) | ||||
−0.410599 | + | 0.911816i | \(0.634680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4853 | 0.898710 | 0.449355 | − | 0.893353i | \(-0.351654\pi\) | ||||
0.449355 | + | 0.893353i | \(0.351654\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.25623 | −0.231997 | −0.115998 | − | 0.993249i | \(-0.537007\pi\) | ||||
−0.115998 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1794 | 1.35959 | 0.679794 | − | 0.733403i | \(-0.262069\pi\) | ||||
0.679794 | + | 0.733403i | \(0.262069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.4357 | 1.57468 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.85786 | 0.129759 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.95068 | −0.204103 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.3253 | 1.81231 | 0.906153 | − | 0.422950i | \(-0.139006\pi\) | ||||
0.906153 | + | 0.422950i | \(0.139006\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.0083 | 1.36456 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.7990 | −1.34404 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.56178 | −0.239591 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.9054 | −1.46690 | −0.733448 | − | 0.679746i | \(-0.762090\pi\) | ||||
−0.733448 | + | 0.679746i | \(0.762090\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.3128 | 1.08272 | 0.541359 | − | 0.840791i | \(-0.317910\pi\) | ||||
0.541359 | + | 0.840791i | \(0.317910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.0711 | 1.65674 | 0.828371 | − | 0.560179i | \(-0.189268\pi\) | ||||
0.828371 | + | 0.560179i | \(0.189268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.2720 | 1.78665 | 0.893326 | − | 0.449410i | \(-0.148366\pi\) | ||||
0.893326 | + | 0.449410i | \(0.148366\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.59689 | −0.104170 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8854 | −0.898171 | −0.449086 | − | 0.893489i | \(-0.648250\pi\) | ||||
−0.449086 | + | 0.893489i | \(0.648250\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1421 | 0.653312 | 0.326656 | − | 0.945143i | \(-0.394078\pi\) | ||||
0.326656 | + | 0.945143i | \(0.394078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.81801 | −0.435587 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.12918 | −0.0718477 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.65367 | −0.483095 | −0.241548 | − | 0.970389i | \(-0.577655\pi\) | ||||
−0.241548 | + | 0.970389i | \(0.577655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.1978 | 1.07277 | 0.536385 | − | 0.843974i | \(-0.319790\pi\) | ||||
0.536385 | + | 0.843974i | \(0.319790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.2350 | −0.698109 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.1116 | −1.17847 | −0.589237 | − | 0.807960i | \(-0.700572\pi\) | ||||
−0.589237 | + | 0.807960i | \(0.700572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.1421 | −0.745885 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.73157 | 0.288489 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4533 | −0.999466 | −0.499733 | − | 0.866179i | \(-0.666569\pi\) | ||||
−0.499733 | + | 0.866179i | \(0.666569\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.79884 | −0.168776 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.3848 | 1.70548 | 0.852738 | − | 0.522339i | \(-0.174940\pi\) | ||||
0.852738 | + | 0.522339i | \(0.174940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.4449 | 1.87585 | 0.937924 | − | 0.346842i | \(-0.112746\pi\) | ||||
0.937924 | + | 0.346842i | \(0.112746\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0179 | 1.01161 | 0.505804 | − | 0.862649i | \(-0.331196\pi\) | ||||
0.505804 | + | 0.862649i | \(0.331196\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.43289 | 0.202637 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.9706 | 1.17474 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.5776 | −1.61110 | −0.805550 | − | 0.592527i | \(-0.798130\pi\) | ||||
−0.805550 | + | 0.592527i | \(0.798130\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.6148 | 1.08379 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.06147 | 0.177049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.9706 | 2.13095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.16679 | −0.467629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.30739 | −0.531201 | −0.265600 | − | 0.964083i | \(-0.585570\pi\) | ||||
−0.265600 | + | 0.964083i | \(0.585570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.4525 | 0.592707 | 0.296354 | − | 0.955078i | \(-0.404229\pi\) | ||||
0.296354 | + | 0.955078i | \(0.404229\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1421 | −0.573267 | −0.286634 | − | 0.958040i | \(-0.592536\pi\) | ||||
−0.286634 | + | 0.958040i | \(0.592536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.1023 | −1.46605 | −0.733024 | − | 0.680202i | \(-0.761892\pi\) | ||||
−0.733024 | + | 0.680202i | \(0.761892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.4366 | −0.584335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.7206 | 0.652152 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.07107 | −0.0594122 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.95068 | −0.162676 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6148 | 1.02316 | 0.511580 | − | 0.859236i | \(-0.329060\pi\) | ||||
0.511580 | + | 0.859236i | \(0.329060\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.5754 | 0.905613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4853 | 0.789064 | 0.394532 | − | 0.918882i | \(-0.370907\pi\) | ||||
0.394532 | + | 0.918882i | \(0.370907\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.21001 | 0.498750 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4366 | 0.563521 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.9719 | −1.34056 | −0.670282 | − | 0.742106i | \(-0.733827\pi\) | ||||
−0.670282 | + | 0.742106i | \(0.733827\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7574 | 1.16464 | 0.582322 | − | 0.812958i | \(-0.302144\pi\) | ||||
0.582322 | + | 0.812958i | \(0.302144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3707 | 1.13745 | 0.568724 | − | 0.822529i | \(-0.307437\pi\) | ||||
0.568724 | + | 0.822529i | \(0.307437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.3253 | 1.39720 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.32957 | −0.228506 | −0.114253 | − | 0.993452i | \(-0.536447\pi\) | ||||
−0.114253 | + | 0.993452i | \(0.536447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2843 | −0.804435 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.5496 | 0.604533 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0502 | −0.942212 | −0.471106 | − | 0.882077i | \(-0.656145\pi\) | ||||
−0.471106 | + | 0.882077i | \(0.656145\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.4357 | −1.16481 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.27208 | 0.272978 | 0.136489 | − | 0.990642i | \(-0.456418\pi\) | ||||
0.136489 | + | 0.990642i | \(0.456418\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.99390 | −0.205696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.37976 | 0.379073 | 0.189536 | − | 0.981874i | \(-0.439301\pi\) | ||||
0.189536 | + | 0.981874i | \(0.439301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.0083 | 1.02238 | 0.511189 | − | 0.859468i | \(-0.329205\pi\) | ||||
0.511189 | + | 0.859468i | \(0.329205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.97056 | 0.457182 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.305553 | −0.0154921 | −0.00774607 | − | 0.999970i | \(-0.502466\pi\) | ||||
−0.00774607 | + | 0.999970i | \(0.502466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.7774 | −1.60705 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.86030 | −0.294864 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3848 | −0.822328 | −0.411164 | − | 0.911561i | \(-0.634878\pi\) | ||||
−0.411164 | + | 0.911561i | \(0.634878\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.0681 | −0.702529 | −0.351265 | − | 0.936276i | \(-0.614248\pi\) | ||||
−0.351265 | + | 0.936276i | \(0.614248\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.52452 | 0.175569 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.22625 | 0.259056 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.65685 | −0.0819262 | −0.0409631 | − | 0.999161i | \(-0.513043\pi\) | ||||
−0.0409631 | + | 0.999161i | \(0.513043\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.3956 | 1.69250 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.5992 | 1.15844 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.7766 | −0.673031 | −0.336516 | − | 0.941678i | \(-0.609248\pi\) | ||||
−0.336516 | + | 0.941678i | \(0.609248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.3848 | 1.38339 | 0.691695 | − | 0.722190i | \(-0.256864\pi\) | ||||
0.691695 | + | 0.722190i | \(0.256864\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.1175 | 0.539276 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0903 | −0.730269 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.6788 | 0.755219 | 0.377610 | − | 0.925965i | \(-0.376746\pi\) | ||||
0.377610 | + | 0.925965i | \(0.376746\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.9706 | 1.39224 | 0.696118 | − | 0.717927i | \(-0.254909\pi\) | ||||
0.696118 | + | 0.717927i | \(0.254909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.0742 | −0.481916 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.3420 | 1.54360 | 0.771799 | − | 0.635866i | \(-0.219357\pi\) | ||||
0.771799 | + | 0.635866i | \(0.219357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.2513 | 0.629590 | 0.314795 | − | 0.949160i | \(-0.398064\pi\) | ||||
0.314795 | + | 0.949160i | \(0.398064\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.6863 | 0.601388 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.1175 | 0.524666 | 0.262333 | − | 0.964977i | \(-0.415508\pi\) | ||||
0.262333 | + | 0.964977i | \(0.415508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.59689 | −0.0751948 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.43289 | 0.160936 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3137 | −0.716345 | −0.358173 | − | 0.933655i | \(-0.616600\pi\) | ||||
−0.358173 | + | 0.933655i | \(0.616600\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6269 | 1.14699 | 0.573495 | − | 0.819209i | \(-0.305587\pi\) | ||||
0.573495 | + | 0.819209i | \(0.305587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.8898 | 1.24968 | 0.624839 | − | 0.780754i | \(-0.285165\pi\) | ||||
0.624839 | + | 0.780754i | \(0.285165\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.1899 | 0.471531 | 0.235766 | − | 0.971810i | \(-0.424240\pi\) | ||||
0.235766 | + | 0.971810i | \(0.424240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.6274 | 1.41424 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.1978 | −0.790756 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.52452 | 0.161716 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.9887 | −0.593469 | −0.296735 | − | 0.954960i | \(-0.595898\pi\) | ||||
−0.296735 | + | 0.954960i | \(0.595898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0249 | −0.591431 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.41983 | −0.200282 | −0.100141 | − | 0.994973i | \(-0.531929\pi\) | ||||
−0.100141 | + | 0.994973i | \(0.531929\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.06147 | 0.138162 | 0.0690810 | − | 0.997611i | \(-0.477993\pi\) | ||||
0.0690810 | + | 0.997611i | \(0.477993\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.4558 | 1.86708 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 48.6427 | 2.18193 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.30739 | 0.416656 | 0.208328 | − | 0.978059i | \(-0.433198\pi\) | ||||
0.208328 | + | 0.978059i | \(0.433198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.32957 | −0.193046 | −0.0965230 | − | 0.995331i | \(-0.530772\pi\) | ||||
−0.0965230 | + | 0.995331i | \(0.530772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.4558 | −1.22177 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.9416 | 0.617949 | 0.308975 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308975 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.3408 | 0.944063 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.7151 | 0.472165 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.37258 | 0.0603661 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.1917 | −0.928425 | −0.464213 | − | 0.885724i | \(-0.653663\pi\) | ||||
−0.464213 | + | 0.885724i | \(0.653663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.5424 | −0.898256 | −0.449128 | − | 0.893467i | \(-0.648265\pi\) | ||||
−0.449128 | + | 0.893467i | \(0.648265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.5838 | −1.59361 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.31371 | 0.187553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.611105 | −0.0264699 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0669 | −1.04050 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.86030 | 0.252421 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.72792 | 0.289256 | 0.144628 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144628 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.2781 | −0.997126 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.7050 | −1.44112 | −0.720561 | − | 0.693391i | \(-0.756116\pi\) | ||||
−0.720561 | + | 0.693391i | \(0.756116\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.1426 | 0.559892 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.8284 | −0.460472 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.78089 | 0.0754588 | 0.0377294 | − | 0.999288i | \(-0.487988\pi\) | ||||
0.0377294 | + | 0.999288i | \(0.487988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.58132 | −0.278360 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.2793 | 1.69757 | 0.848785 | − | 0.528739i | \(-0.177335\pi\) | ||||
0.848785 | + | 0.528739i | \(0.177335\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.9411 | −0.754789 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2039 | 0.553537 | 0.276768 | − | 0.960937i | \(-0.410737\pi\) | ||||
0.276768 | + | 0.960937i | \(0.410737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0179 | 0.712176 | 0.356088 | − | 0.934452i | \(-0.384110\pi\) | ||||
0.356088 | + | 0.934452i | \(0.384110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.55582 | −0.398505 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.1127 | 1.54502 | 0.772511 | − | 0.635001i | \(-0.219001\pi\) | ||||
0.772511 | + | 0.635001i | \(0.219001\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 43.6056 | 1.80907 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4366 | 0.432238 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.7821 | −0.610121 | −0.305061 | − | 0.952333i | \(-0.598677\pi\) | ||||
−0.305061 | + | 0.952333i | \(0.598677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.5980 | −0.477886 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.0742 | 0.413699 | 0.206850 | − | 0.978373i | \(-0.433679\pi\) | ||||
0.206850 | + | 0.978373i | \(0.433679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.6326 | −1.46080 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8854 | −0.567342 | −0.283671 | − | 0.958922i | \(-0.591552\pi\) | ||||
−0.283671 | + | 0.958922i | \(0.591552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.8284 | −0.849609 | −0.424805 | − | 0.905285i | \(-0.639657\pi\) | ||||
−0.424805 | + | 0.905285i | \(0.639657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.4169 | 0.626787 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.69376 | −0.0687477 | −0.0343739 | − | 0.999409i | \(-0.510944\pi\) | ||||
−0.0343739 | + | 0.999409i | \(0.510944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.525265 | 0.0212499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8995 | 0.803733 | 0.401867 | − | 0.915698i | \(-0.368362\pi\) | ||||
0.401867 | + | 0.915698i | \(0.368362\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3253 | −1.05810 | −0.529051 | − | 0.848590i | \(-0.677452\pi\) | ||||
−0.529051 | + | 0.848590i | \(0.677452\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.4412 | 0.939152 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5147 | −0.500589 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.7596 | −0.827739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.6494 | −1.65804 | −0.829018 | − | 0.559222i | \(-0.811100\pi\) | ||||
−0.829018 | + | 0.559222i | \(0.811100\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00547 | −0.0399008 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.24264 | 0.0888567 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.08034 | −0.240159 | −0.120080 | − | 0.992764i | \(-0.538315\pi\) | ||||
−0.120080 | + | 0.992764i | \(0.538315\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.78287 | −0.228054 | −0.114027 | − | 0.993478i | \(-0.536375\pi\) | ||||
−0.114027 | + | 0.993478i | \(0.536375\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.9970 | 1.29725 | 0.648624 | − | 0.761109i | \(-0.275345\pi\) | ||||
0.648624 | + | 0.761109i | \(0.275345\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0000 | −0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.2629 | −1.49734 | −0.748672 | − | 0.662940i | \(-0.769308\pi\) | ||||
−0.748672 | + | 0.662940i | \(0.769308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.8731 | −0.815580 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.06147 | −0.119258 | −0.0596289 | − | 0.998221i | \(-0.518992\pi\) | ||||
−0.0596289 | + | 0.998221i | \(0.518992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.3848 | 1.57079 | 0.785393 | − | 0.618998i | \(-0.212461\pi\) | ||||
0.785393 | + | 0.618998i | \(0.212461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.2965 | −0.438058 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.6326 | −1.37970 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.01962 | 0.270989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.34315 | 0.244510 | 0.122255 | − | 0.992499i | \(-0.460987\pi\) | ||||
0.122255 | + | 0.992499i | \(0.460987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.8058 | 0.569033 | 0.284517 | − | 0.958671i | \(-0.408167\pi\) | ||||
0.284517 | + | 0.958671i | \(0.408167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.0669 | −0.923603 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.8381 | −0.644291 | −0.322145 | − | 0.946690i | \(-0.604404\pi\) | ||||
−0.322145 | + | 0.946690i | \(0.604404\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.7696 | 1.09923 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.99390 | 0.152155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.92762 | −0.0733302 | −0.0366651 | − | 0.999328i | \(-0.511673\pi\) | ||||
−0.0366651 | + | 0.999328i | \(0.511673\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.1509 | −1.25748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.34315 | 0.240264 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.5898 | −0.739897 | −0.369948 | − | 0.929052i | \(-0.620625\pi\) | ||||
−0.369948 | + | 0.929052i | \(0.620625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.58132 | −0.248219 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −50.7318 | −1.90797 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.72792 | −0.252672 | −0.126336 | − | 0.991987i | \(-0.540322\pi\) | ||||
−0.126336 | + | 0.991987i | \(0.540322\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.4449 | 1.17762 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.59689 | −0.0597205 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.12293 | −0.228347 | −0.114173 | − | 0.993461i | \(-0.536422\pi\) | ||||
−0.114173 | + | 0.993461i | \(0.536422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7990 | 0.737353 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.4662 | 0.462984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.4689 | 0.425357 | 0.212678 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212678 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68.3127 | 2.52664 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.5563 | 1.09169 | 0.545844 | − | 0.837887i | \(-0.316209\pi\) | ||||
0.545844 | + | 0.837887i | \(0.316209\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.2471 | −0.524800 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0179 | −0.626013 | −0.313006 | − | 0.949751i | \(-0.601336\pi\) | ||||
−0.313006 | + | 0.949751i | \(0.601336\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.8854 | 0.509406 | 0.254703 | − | 0.967019i | \(-0.418022\pi\) | ||||
0.254703 | + | 0.967019i | \(0.418022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.51472 | 0.348592 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.4699 | −1.62489 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.5537 | 1.91771 | 0.958855 | − | 0.283896i | \(-0.0916271\pi\) | ||||
0.958855 | + | 0.283896i | \(0.0916271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00547 | 0.0365928 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.0416 | −1.81879 | −0.909397 | − | 0.415929i | \(-0.863456\pi\) | ||||
−0.909397 | + | 0.415929i | \(0.863456\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1917 | 0.768199 | 0.384099 | − | 0.923292i | \(-0.374512\pi\) | ||||
0.384099 | + | 0.923292i | \(0.374512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.0124 | −1.55715 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.12293 | −0.221086 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.1716 | −0.907710 | −0.453855 | − | 0.891076i | \(-0.649952\pi\) | ||||
−0.453855 | + | 0.891076i | \(0.649952\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.2258 | −1.19505 | −0.597525 | − | 0.801850i | \(-0.703849\pi\) | ||||
−0.597525 | + | 0.801850i | \(0.703849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.0011 | −0.395173 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.01094 | 0.0720493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.6274 | −0.809673 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.3646 | −0.905301 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.37976 | −0.263060 | −0.131530 | − | 0.991312i | \(-0.541989\pi\) | ||||
−0.131530 | + | 0.991312i | \(0.541989\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.1509 | −1.17871 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.68629 | 0.0953930 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.0529 | −1.02911 | −0.514554 | − | 0.857458i | \(-0.672042\pi\) | ||||
−0.514554 | + | 0.857458i | \(0.672042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.45214 | −0.192883 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.92724 | −0.350325 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.6274 | 1.07947 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.4510 | −0.965127 | −0.482563 | − | 0.875861i | \(-0.660294\pi\) | ||||
−0.482563 | + | 0.875861i | \(0.660294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.4645 | 1.70182 | 0.850910 | − | 0.525311i | \(-0.176051\pi\) | ||||
0.850910 | + | 0.525311i | \(0.176051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −29.7180 | −1.04098 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.6569 | 0.757677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.9294 | 0.765340 | 0.382670 | − | 0.923885i | \(-0.375005\pi\) | ||||
0.382670 | + | 0.923885i | \(0.375005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.29066 | 0.114705 | 0.0573526 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573526 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.79337 | 0.0623615 | 0.0311807 | − | 0.999514i | \(-0.490073\pi\) | ||||
0.0311807 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.55635 | −0.331906 | −0.165953 | − | 0.986134i | \(-0.553070\pi\) | ||||
−0.165953 | + | 0.986134i | \(0.553070\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.2781 | −0.806540 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.8264 | 1.34364 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.3575 | 1.08258 | 0.541291 | − | 0.840835i | \(-0.317936\pi\) | ||||
0.541291 | + | 0.840835i | \(0.317936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.4853 | 0.602941 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.5405 | 0.775416 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.4867 | 0.978816 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.8435 | 0.611669 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.5269 | 1.73001 | 0.865004 | − | 0.501765i | \(-0.167316\pi\) | ||||
0.865004 | + | 0.501765i | \(0.167316\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.99390 | −0.136429 | −0.0682145 | − | 0.997671i | \(-0.521730\pi\) | ||||
−0.0682145 | + | 0.997671i | \(0.521730\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6871 | −0.569358 | −0.284679 | − | 0.958623i | \(-0.591887\pi\) | ||||
−0.284679 | + | 0.958623i | \(0.591887\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.76245 | −0.264237 | −0.132119 | − | 0.991234i | \(-0.542178\pi\) | ||||
−0.132119 | + | 0.991234i | \(0.542178\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.79899 | 0.197172 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.03712 | 0.170873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.45214 | −0.184739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.0166 | −1.35281 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.8406 | 1.41286 | 0.706429 | − | 0.707784i | \(-0.250305\pi\) | ||||
0.706429 | + | 0.707784i | \(0.250305\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.5934 | −1.73823 | −0.869113 | − | 0.494613i | \(-0.835310\pi\) | ||||
−0.869113 | + | 0.494613i | \(0.835310\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.0903 | 0.507827 | 0.253914 | − | 0.967227i | \(-0.418282\pi\) | ||||
0.253914 | + | 0.967227i | \(0.418282\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.5529 | −1.42878 | −0.714392 | − | 0.699745i | \(-0.753297\pi\) | ||||
−0.714392 | + | 0.699745i | \(0.753297\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.85786 | −0.0623108 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.72847 | −0.0578409 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.5836 | 0.955445 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.0221 | −1.36816 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.4558 | −1.38109 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.26543 | −0.0753055 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.3976 | −0.810110 | −0.405055 | − | 0.914292i | \(-0.632748\pi\) | ||||
−0.405055 | + | 0.914292i | \(0.632748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.9020 | 1.78585 | 0.892927 | − | 0.450201i | \(-0.148648\pi\) | ||||
0.892927 | + | 0.450201i | \(0.148648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.2843 | −0.671311 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.5685 | −1.27364 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.1303 | −0.400142 | −0.200071 | − | 0.979781i | \(-0.564117\pi\) | ||||
−0.200071 | + | 0.979781i | \(0.564117\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.65914 | −0.285019 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.24264 | −0.205257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.2781 | 0.763731 | 0.381866 | − | 0.924218i | \(-0.375282\pi\) | ||||
0.381866 | + | 0.924218i | \(0.375282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.37976 | −0.241862 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.5754 | 0.542075 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.9411 | −1.69684 | −0.848421 | − | 0.529322i | \(-0.822447\pi\) | ||||
−0.848421 | + | 0.529322i | \(0.822447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.9483 | 1.59567 | 0.797834 | − | 0.602877i | \(-0.205979\pi\) | ||||
0.797834 | + | 0.602877i | \(0.205979\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.45214 | −0.177546 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.8322 | 1.00191 | 0.500957 | − | 0.865472i | \(-0.332982\pi\) | ||||
0.500957 | + | 0.865472i | \(0.332982\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.79899 | −0.123320 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.4388 | −1.14798 | −0.573988 | − | 0.818864i | \(-0.694604\pi\) | ||||
−0.573988 | + | 0.818864i | \(0.694604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.2117 | 0.654034 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.1592 | 1.71660 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.20101 | 0.167775 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.2349 | −0.715768 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.3599 | 1.58731 | 0.793653 | − | 0.608371i | \(-0.208177\pi\) | ||||
0.793653 | + | 0.608371i | \(0.208177\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.8770 | −1.47226 | −0.736131 | − | 0.676839i | \(-0.763349\pi\) | ||||
−0.736131 | + | 0.676839i | \(0.763349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −61.2548 | −1.96374 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.3646 | −0.811485 | −0.405743 | − | 0.913987i | \(-0.632987\pi\) | ||||
−0.405743 | + | 0.913987i | \(0.632987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.9043 | −0.348502 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.8100 | −1.33353 | −0.666766 | − | 0.745267i | \(-0.732322\pi\) | ||||
−0.666766 | + | 0.745267i | \(0.732322\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.79899 | 0.184771 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −58.7170 | −1.86709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.1638 | −0.767588 | −0.383794 | − | 0.923419i | \(-0.625383\pi\) | ||||
−0.383794 | + | 0.923419i | \(0.625383\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.1563 | −1.08283 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.0416 | 0.318022 | 0.159011 | − | 0.987277i | \(-0.449170\pi\) | ||||
0.159011 | + | 0.987277i | \(0.449170\pi\) | |||||||
\(998\) | 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 | 9216.2.a.bs.1.3 | 8 | ||
3.2 | odd | 2 | inner | 9216.2.a.bs.1.5 | 8 | ||
4.3 | odd | 2 | inner | 9216.2.a.bs.1.4 | 8 | ||
8.3 | odd | 2 | 9216.2.a.br.1.6 | 8 | |||
8.5 | even | 2 | 9216.2.a.br.1.5 | 8 | |||
12.11 | even | 2 | inner | 9216.2.a.bs.1.6 | 8 | ||
24.5 | odd | 2 | 9216.2.a.br.1.3 | 8 | |||
24.11 | even | 2 | 9216.2.a.br.1.4 | 8 | |||
32.3 | odd | 8 | 4608.2.k.bl.1153.5 | yes | 16 | ||
32.5 | even | 8 | 4608.2.k.bk.3457.3 | yes | 16 | ||
32.11 | odd | 8 | 4608.2.k.bl.3457.6 | yes | 16 | ||
32.13 | even | 8 | 4608.2.k.bk.1153.4 | yes | 16 | ||
32.19 | odd | 8 | 4608.2.k.bk.1153.3 | ✓ | 16 | ||
32.21 | even | 8 | 4608.2.k.bl.3457.5 | yes | 16 | ||
32.27 | odd | 8 | 4608.2.k.bk.3457.4 | yes | 16 | ||
32.29 | even | 8 | 4608.2.k.bl.1153.6 | yes | 16 | ||
96.5 | odd | 8 | 4608.2.k.bk.3457.5 | yes | 16 | ||
96.11 | even | 8 | 4608.2.k.bl.3457.4 | yes | 16 | ||
96.29 | odd | 8 | 4608.2.k.bl.1153.4 | yes | 16 | ||
96.35 | even | 8 | 4608.2.k.bl.1153.3 | yes | 16 | ||
96.53 | odd | 8 | 4608.2.k.bl.3457.3 | yes | 16 | ||
96.59 | even | 8 | 4608.2.k.bk.3457.6 | yes | 16 | ||
96.77 | odd | 8 | 4608.2.k.bk.1153.6 | yes | 16 | ||
96.83 | even | 8 | 4608.2.k.bk.1153.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4608.2.k.bk.1153.3 | ✓ | 16 | 32.19 | odd | 8 | ||
4608.2.k.bk.1153.4 | yes | 16 | 32.13 | even | 8 | ||
4608.2.k.bk.1153.5 | yes | 16 | 96.83 | even | 8 | ||
4608.2.k.bk.1153.6 | yes | 16 | 96.77 | odd | 8 | ||
4608.2.k.bk.3457.3 | yes | 16 | 32.5 | even | 8 | ||
4608.2.k.bk.3457.4 | yes | 16 | 32.27 | odd | 8 | ||
4608.2.k.bk.3457.5 | yes | 16 | 96.5 | odd | 8 | ||
4608.2.k.bk.3457.6 | yes | 16 | 96.59 | even | 8 | ||
4608.2.k.bl.1153.3 | yes | 16 | 96.35 | even | 8 | ||
4608.2.k.bl.1153.4 | yes | 16 | 96.29 | odd | 8 | ||
4608.2.k.bl.1153.5 | yes | 16 | 32.3 | odd | 8 | ||
4608.2.k.bl.1153.6 | yes | 16 | 32.29 | even | 8 | ||
4608.2.k.bl.3457.3 | yes | 16 | 96.53 | odd | 8 | ||
4608.2.k.bl.3457.4 | yes | 16 | 96.11 | even | 8 | ||
4608.2.k.bl.3457.5 | yes | 16 | 32.21 | even | 8 | ||
4608.2.k.bl.3457.6 | yes | 16 | 32.11 | odd | 8 | ||
9216.2.a.br.1.3 | 8 | 24.5 | odd | 2 | |||
9216.2.a.br.1.4 | 8 | 24.11 | even | 2 | |||
9216.2.a.br.1.5 | 8 | 8.5 | even | 2 | |||
9216.2.a.br.1.6 | 8 | 8.3 | odd | 2 | |||
9216.2.a.bs.1.3 | 8 | 1.1 | even | 1 | trivial | ||
9216.2.a.bs.1.4 | 8 | 4.3 | odd | 2 | inner | ||
9216.2.a.bs.1.5 | 8 | 3.2 | odd | 2 | inner | ||
9216.2.a.bs.1.6 | 8 | 12.11 | even | 2 | inner |