Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.2 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.c.2591.7 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | − 3.14626i | − 1.40705i | −0.710669 | − | 0.703526i | \(-0.751608\pi\) | ||||
0.710669 | − | 0.703526i | \(-0.248392\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.449490 | 0.124666 | 0.0623330 | − | 0.998055i | \(-0.480146\pi\) | ||||
0.0623330 | + | 0.998055i | \(0.480146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.51059i | 0.608907i | 0.952527 | + | 0.304454i | \(0.0984739\pi\) | ||||
−0.952527 | + | 0.304454i | \(0.901526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.44949i | − 0.561951i | −0.959715 | − | 0.280976i | \(-0.909342\pi\) | ||||
0.959715 | − | 0.280976i | \(-0.0906580\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89898 | −0.979796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.34242i | 1.54915i | 0.632483 | + | 0.774574i | \(0.282036\pi\) | ||||
−0.632483 | + | 0.774574i | \(0.717964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.55051i | − 0.278480i | −0.990259 | − | 0.139240i | \(-0.955534\pi\) | ||||
0.990259 | − | 0.139240i | \(-0.0444659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.14626 | 0.531816 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.00000 | 1.47959 | 0.739795 | − | 0.672832i | \(-0.234922\pi\) | ||||
0.739795 | + | 0.672832i | \(0.234922\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0745i | 1.57337i | 0.617356 | + | 0.786684i | \(0.288204\pi\) | ||||
−0.617356 | + | 0.786684i | \(0.711796\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.34847i | − 1.27313i | −0.771223 | − | 0.636565i | \(-0.780355\pi\) | ||||
0.771223 | − | 0.636565i | \(-0.219645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.460702 | 0.0672003 | 0.0336001 | − | 0.999435i | \(-0.489303\pi\) | ||||
0.0336001 | + | 0.999435i | \(0.489303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.02118i | 0.689712i | 0.938656 | + | 0.344856i | \(0.112072\pi\) | ||||
−0.938656 | + | 0.344856i | \(0.887928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.44949i | 0.599969i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.4887 | 1.49570 | 0.747849 | − | 0.663868i | \(-0.231086\pi\) | ||||
0.747849 | + | 0.663868i | \(0.231086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.55051 | −0.710670 | −0.355335 | − | 0.934739i | \(-0.615633\pi\) | ||||
−0.355335 | + | 0.934739i | \(0.615633\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 1.41421i | − 0.175412i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 13.7980i | − 1.68569i | −0.538157 | − | 0.842844i | \(-0.680879\pi\) | ||||
0.538157 | − | 0.842844i | \(-0.319121\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79796 | 1.14676 | 0.573382 | − | 0.819288i | \(-0.305631\pi\) | ||||
0.573382 | + | 0.819288i | \(0.305631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.41421i | − 0.161165i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 0.348469i | − 0.0392059i | −0.999808 | − | 0.0196029i | \(-0.993760\pi\) | ||||
0.999808 | − | 0.0196029i | \(-0.00624020\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.36773 | 0.259892 | 0.129946 | − | 0.991521i | \(-0.458520\pi\) | ||||
0.129946 | + | 0.991521i | \(0.458520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.89898 | 0.856765 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.55708i | − 0.165050i | −0.996589 | − | 0.0825250i | \(-0.973702\pi\) | ||||
0.996589 | − | 0.0825250i | \(-0.0262984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.449490i | 0.0471193i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.70674 | −0.790695 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2474 | 1.04047 | 0.520235 | − | 0.854023i | \(-0.325844\pi\) | ||||
0.520235 | + | 0.854023i | \(0.325844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 5.65685i | − 0.562878i | −0.959579 | − | 0.281439i | \(-0.909188\pi\) | ||||
0.959579 | − | 0.281439i | \(-0.0908117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.79796i | − 0.571290i | −0.958336 | − | 0.285645i | \(-0.907792\pi\) | ||||
0.958336 | − | 0.285645i | \(-0.0922078\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8564 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266391\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.797959 | 0.0764306 | 0.0382153 | − | 0.999270i | \(-0.487833\pi\) | ||||
0.0382153 | + | 0.999270i | \(0.487833\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5352i | 0.991065i | 0.868589 | + | 0.495533i | \(0.165027\pi\) | ||||
−0.868589 | + | 0.495533i | \(0.834973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 17.7980i | − 1.65967i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.51059 | −0.230145 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 0.317837i | − 0.0284282i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5505i | 1.11368i | 0.830621 | + | 0.556839i | \(0.187986\pi\) | ||||
−0.830621 | + | 0.556839i | \(0.812014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.84961 | 0.685823 | 0.342912 | − | 0.939368i | \(-0.388587\pi\) | ||||
0.342912 | + | 0.939368i | \(0.388587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.44949 | 0.212398 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 12.4422i | − 1.06301i | −0.847056 | − | 0.531504i | \(-0.821627\pi\) | ||||
0.847056 | − | 0.531504i | \(-0.178373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.449490i | 0.0381252i | 0.999818 | + | 0.0190626i | \(0.00606819\pi\) | ||||
−0.999818 | + | 0.0190626i | \(0.993932\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.635674 | −0.0531578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.2474 | 2.17973 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 17.4634i | − 1.43066i | −0.698789 | − | 0.715328i | \(-0.746277\pi\) | ||||
0.698789 | − | 0.715328i | \(-0.253723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.34847i | 0.679389i | 0.940536 | + | 0.339694i | \(0.110324\pi\) | ||||
−0.940536 | + | 0.339694i | \(0.889676\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.87832 | −0.391836 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2474 | −0.817835 | −0.408918 | − | 0.912571i | \(-0.634094\pi\) | ||||
−0.408918 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.65685i | 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.550510i | 0.0431193i | 0.999768 | + | 0.0215596i | \(0.00686318\pi\) | ||||
−0.999768 | + | 0.0215596i | \(0.993137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.58166 | 0.741451 | 0.370725 | − | 0.928742i | \(-0.379109\pi\) | ||||
0.370725 | + | 0.928742i | \(0.379109\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7980 | −0.984458 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.84961i | 0.596795i | 0.954442 | + | 0.298397i | \(0.0964520\pi\) | ||||
−0.954442 | + | 0.298397i | \(0.903548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.89898i | − 0.370328i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.1708 | −0.834948 | −0.417474 | − | 0.908689i | \(-0.637085\pi\) | ||||
−0.417474 | + | 0.908689i | \(0.637085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.79796 | 0.282300 | 0.141150 | − | 0.989988i | \(-0.454920\pi\) | ||||
0.141150 | + | 0.989988i | \(0.454920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 28.3164i | − 2.08186i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.55051i | − 0.259639i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.84961 | −0.567978 | −0.283989 | − | 0.958828i | \(-0.591658\pi\) | ||||
−0.283989 | + | 0.958828i | \(0.591658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.5959 | 1.48253 | 0.741263 | − | 0.671214i | \(-0.234227\pi\) | ||||
0.741263 | + | 0.671214i | \(0.234227\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.89949i | 0.705310i | 0.935753 | + | 0.352655i | \(0.114721\pi\) | ||||
−0.935753 | + | 0.352655i | \(0.885279\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 12.6969i | − 0.900062i | −0.893013 | − | 0.450031i | \(-0.851413\pi\) | ||||
0.893013 | − | 0.450031i | \(-0.148587\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.34242 | −0.585523 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.6969 | 2.21381 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.46410i | 0.239617i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 17.5959i | − 1.21135i | −0.795711 | − | 0.605676i | \(-0.792903\pi\) | ||||
0.795711 | − | 0.605676i | \(-0.207097\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −26.2665 | −1.79136 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.55051 | 0.105255 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.12848i | 0.0759101i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 28.2474i | − 1.89159i | −0.324766 | − | 0.945795i | \(-0.605285\pi\) | ||||
0.324766 | − | 0.945795i | \(-0.394715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6848 | 1.10741 | 0.553706 | − | 0.832712i | \(-0.313213\pi\) | ||||
0.553706 | + | 0.832712i | \(0.313213\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.7980 | 1.57261 | 0.786307 | − | 0.617836i | \(-0.211991\pi\) | ||||
0.786307 | + | 0.617836i | \(0.211991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07107i | 0.463241i | 0.972806 | + | 0.231621i | \(0.0744028\pi\) | ||||
−0.972806 | + | 0.231621i | \(0.925597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.44949i | − 0.0945543i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3704 | −1.25297 | −0.626483 | − | 0.779435i | \(-0.715506\pi\) | ||||
−0.626483 | + | 0.779435i | \(0.715506\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.34847 | 0.602188 | 0.301094 | − | 0.953594i | \(-0.402648\pi\) | ||||
0.301094 | + | 0.953594i | \(0.402648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.14626i | 0.201007i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.10102i | − 0.0700563i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.6814 | −0.863564 | −0.431782 | − | 0.901978i | \(-0.642115\pi\) | ||||
−0.431782 | + | 0.901978i | \(0.642115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 14.1421i | − 0.882162i | −0.897467 | − | 0.441081i | \(-0.854595\pi\) | ||||
0.897467 | − | 0.441081i | \(-0.145405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.00000i | 0.559233i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.7347 | −1.15523 | −0.577616 | − | 0.816308i | \(-0.696017\pi\) | ||||
−0.577616 | + | 0.816308i | \(0.696017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.7980 | 0.970461 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 22.9453i | − 1.39900i | −0.714634 | − | 0.699498i | \(-0.753407\pi\) | ||||
0.714634 | − | 0.699498i | \(-0.246593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.69694i | 0.528301i | 0.964481 | + | 0.264151i | \(0.0850916\pi\) | ||||
−0.964481 | + | 0.264151i | \(0.914908\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.92820 | 0.417786 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | −0.0600842 | −0.0300421 | − | 0.999549i | \(-0.509564\pi\) | ||||
−0.0300421 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 4.38551i | − 0.261617i | −0.991408 | − | 0.130809i | \(-0.958243\pi\) | ||||
0.991408 | − | 0.130809i | \(-0.0417574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.65153i | 0.157617i | 0.996890 | + | 0.0788086i | \(0.0251116\pi\) | ||||
−0.996890 | + | 0.0788086i | \(0.974888\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0745 | −0.594677 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.6969 | 0.629232 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 11.6315i | − 0.679522i | −0.940512 | − | 0.339761i | \(-0.889654\pi\) | ||||
0.940512 | − | 0.339761i | \(-0.110346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 36.1464i | − 2.10453i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.54270 | 0.147048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.34847 | 0.481198 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.4634i | 0.999950i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.20204i | − 0.125677i | −0.998024 | − | 0.0628386i | \(-0.979985\pi\) | ||||
0.998024 | − | 0.0628386i | \(-0.0200153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.8954 | 1.18487 | 0.592434 | − | 0.805619i | \(-0.298167\pi\) | ||||
0.592434 | + | 0.805619i | \(0.298167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.5851i | 0.706847i | 0.935463 | + | 0.353424i | \(0.114983\pi\) | ||||
−0.935463 | + | 0.353424i | \(0.885017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 11.7980i | − 0.660559i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.14966 | 0.342176 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.20204 | −0.122147 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.460702i | 0.0253993i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 28.1464i | − 1.54707i | −0.633755 | − | 0.773534i | \(-0.718487\pi\) | ||||
0.633755 | − | 0.773534i | \(-0.281513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43.4120 | −2.37185 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.5959 | −1.12193 | −0.560966 | − | 0.827839i | \(-0.689570\pi\) | ||||
−0.560966 | + | 0.827839i | \(0.689570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.19275i | 0.118744i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.5911 | 1.74958 | 0.874792 | − | 0.484499i | \(-0.160998\pi\) | ||||
0.874792 | + | 0.484499i | \(0.160998\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0000 | −0.856460 | −0.428230 | − | 0.903670i | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 22.6595i | − 1.20604i | −0.797724 | − | 0.603022i | \(-0.793963\pi\) | ||||
0.797724 | − | 0.603022i | \(-0.206037\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7980i | 0.944618i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3923 | −0.548485 | −0.274242 | − | 0.961661i | \(-0.588427\pi\) | ||||
−0.274242 | + | 0.961661i | \(0.588427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 30.8270i | − 1.61356i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1010i | 0.892666i | 0.894867 | + | 0.446333i | \(0.147270\pi\) | ||||
−0.894867 | + | 0.446333i | \(0.852730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.02118 | −0.260687 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.1010 | −0.626567 | −0.313284 | − | 0.949660i | \(-0.601429\pi\) | ||||
−0.313284 | + | 0.949660i | \(0.601429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.74983i | 0.193126i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 11.0454i | − 0.567364i | −0.958918 | − | 0.283682i | \(-0.908444\pi\) | ||||
0.958918 | − | 0.283682i | \(-0.0915561\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.02458 | 0.410037 | 0.205018 | − | 0.978758i | \(-0.434275\pi\) | ||||
0.205018 | + | 0.978758i | \(0.434275\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.44949 | −0.226767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.9487i | 1.31565i | 0.753171 | + | 0.657824i | \(0.228523\pi\) | ||||
−0.753171 | + | 0.657824i | \(0.771477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.2020i | 0.718228i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.09638 | −0.0551647 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.7980 | 1.09401 | 0.547004 | − | 0.837130i | \(-0.315768\pi\) | ||||
0.547004 | + | 0.837130i | \(0.315768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2.47848i | − 0.123769i | −0.998083 | − | 0.0618847i | \(-0.980289\pi\) | ||||
0.998083 | − | 0.0618847i | \(-0.0197111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.696938i | − 0.0347170i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7279 | −0.630900 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.79796 | 0.286691 | 0.143345 | − | 0.989673i | \(-0.454214\pi\) | ||||
0.143345 | + | 0.989673i | \(0.454214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4887i | 0.565321i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 7.44949i | − 0.365681i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.36773 | 0.115671 | 0.0578355 | − | 0.998326i | \(-0.481580\pi\) | ||||
0.0578355 | + | 0.998326i | \(0.481580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8990 | 1.60340 | 0.801699 | − | 0.597728i | \(-0.203930\pi\) | ||||
0.801699 | + | 0.597728i | \(0.203930\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 12.2993i | − 0.596605i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.55051i | − 0.268608i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.92820 | 0.333720 | 0.166860 | − | 0.985981i | \(-0.446637\pi\) | ||||
0.166860 | + | 0.985981i | \(0.446637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4495 | 1.27108 | 0.635541 | − | 0.772067i | \(-0.280777\pi\) | ||||
0.635541 | + | 0.772067i | \(0.280777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 13.8564i | − 0.662842i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.10102i | 0.243458i | 0.992563 | + | 0.121729i | \(0.0388439\pi\) | ||||
−0.992563 | + | 0.121729i | \(0.961156\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.8912 | 1.51520 | 0.757599 | − | 0.652720i | \(-0.226372\pi\) | ||||
0.757599 | + | 0.652720i | \(0.226372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.89898 | −0.232234 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.5843i | 1.25459i | 0.778781 | + | 0.627296i | \(0.215838\pi\) | ||||
−0.778781 | + | 0.627296i | \(0.784162\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 14.2474i | − 0.670886i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.41421 | 0.0662994 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5959 | 0.542434 | 0.271217 | − | 0.962518i | \(-0.412574\pi\) | ||||
0.271217 | + | 0.962518i | \(0.412574\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.5091i | 1.42095i | 0.703721 | + | 0.710476i | \(0.251520\pi\) | ||||
−0.703721 | + | 0.710476i | \(0.748480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 31.2474i | − 1.45219i | −0.687593 | − | 0.726096i | \(-0.741333\pi\) | ||||
0.687593 | − | 0.726096i | \(-0.258667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.2275 | 0.889744 | 0.444872 | − | 0.895594i | \(-0.353249\pi\) | ||||
0.444872 | + | 0.895594i | \(0.353249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7980 | 0.637131 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.8065i | 0.542864i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000i | 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.6028 | 0.667221 | 0.333610 | − | 0.942711i | \(-0.391733\pi\) | ||||
0.333610 | + | 0.942711i | \(0.391733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.04541 | 0.184455 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 32.2412i | − 1.46400i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 19.5959i | − 0.887976i | −0.896033 | − | 0.443988i | \(-0.853563\pi\) | ||||
0.896033 | − | 0.443988i | \(-0.146437\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4634 | 0.788111 | 0.394055 | − | 0.919087i | \(-0.371072\pi\) | ||||
0.394055 | + | 0.919087i | \(0.371072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.9444 | −0.943288 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 5.65685i | − 0.253745i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.2474i | 1.13023i | 0.825012 | + | 0.565116i | \(0.191168\pi\) | ||||
−0.825012 | + | 0.565116i | \(0.808832\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.4169 | −0.821168 | −0.410584 | − | 0.911823i | \(-0.634675\pi\) | ||||
−0.410584 | + | 0.911823i | \(0.634675\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.7980 | −0.791999 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.87492i | − 0.0831042i | −0.999136 | − | 0.0415521i | \(-0.986770\pi\) | ||||
0.999136 | − | 0.0415521i | \(-0.0132302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796i | 0.433436i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.2419 | −0.803835 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.651531 | −0.0286543 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 5.68896i | − 0.249238i | −0.992205 | − | 0.124619i | \(-0.960229\pi\) | ||||
0.992205 | − | 0.124619i | \(-0.0397709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 12.0454i | − 0.526709i | −0.964699 | − | 0.263354i | \(-0.915171\pi\) | ||||
0.964699 | − | 0.263354i | \(-0.0848289\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.89270 | 0.169568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.52837i | 0.196145i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 43.5959i | − 1.88482i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.41421 | 0.0609145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0000 | −1.24681 | −0.623404 | − | 0.781900i | \(-0.714251\pi\) | ||||
−0.623404 | + | 0.781900i | \(0.714251\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 2.51059i | − 0.107542i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.146428i | 0.00626082i | 0.999995 | + | 0.00313041i | \(0.000996442\pi\) | ||||
−0.999995 | + | 0.00313041i | \(0.999004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.4347 | 0.870546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.348469 | 0.0148184 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.7128i | 1.17423i | 0.809504 | + | 0.587115i | \(0.199736\pi\) | ||||
−0.809504 | + | 0.587115i | \(0.800264\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 3.75255i | − 0.158716i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.6698 | 1.37687 | 0.688433 | − | 0.725300i | \(-0.258299\pi\) | ||||
0.688433 | + | 0.725300i | \(0.258299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.1464 | 1.39448 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.38551i | 0.183850i | 0.995766 | + | 0.0919250i | \(0.0293020\pi\) | ||||
−0.995766 | + | 0.0919250i | \(0.970698\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 14.3485i | − 0.600465i | −0.953866 | − | 0.300232i | \(-0.902936\pi\) | ||||
0.953866 | − | 0.300232i | \(-0.0970642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.7128 | −1.15570 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.59592 | −0.0664389 | −0.0332195 | − | 0.999448i | \(-0.510576\pi\) | ||||
−0.0332195 | + | 0.999448i | \(0.510576\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.36773i | 0.0982298i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7.10102i | − 0.294094i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.8844 | 1.02709 | 0.513544 | − | 0.858063i | \(-0.328332\pi\) | ||||
0.513544 | + | 0.858063i | \(0.328332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.79796 | −0.156492 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.603566i | 0.0247855i | 0.999923 | + | 0.0123928i | \(0.00394484\pi\) | ||||
−0.999923 | + | 0.0123928i | \(0.996055\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.89898i | 0.323827i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.1270 | −1.19010 | −0.595049 | − | 0.803689i | \(-0.702867\pi\) | ||||
−0.595049 | + | 0.803689i | \(0.702867\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.7423 | 1.90666 | 0.953330 | − | 0.301930i | \(-0.0976310\pi\) | ||||
0.953330 | + | 0.301930i | \(0.0976310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.3164i | 1.15122i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.75255i | − 0.0711339i | −0.999367 | − | 0.0355669i | \(-0.988676\pi\) | ||||
0.999367 | − | 0.0355669i | \(-0.0113237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.207081 | 0.00837759 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.3939 | −1.67188 | −0.835941 | − | 0.548819i | \(-0.815078\pi\) | ||||
−0.835941 | + | 0.548819i | \(0.815078\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 4.38551i | − 0.176554i | −0.996096 | − | 0.0882769i | \(-0.971864\pi\) | ||||
0.996096 | − | 0.0882769i | \(-0.0281360\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.8434i | 1.92299i | 0.274827 | + | 0.961494i | \(0.411379\pi\) | ||||
−0.274827 | + | 0.961494i | \(0.588621\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.55708 | 0.0623830 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.4949 | −1.01980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.5953i | 0.900934i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 33.7423i | − 1.34326i | −0.740886 | − | 0.671631i | \(-0.765594\pi\) | ||||
0.740886 | − | 0.671631i | \(-0.234406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.4872 | 1.56700 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.449490 | −0.0178094 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9487i | 1.02491i | 0.858714 | + | 0.512455i | \(0.171264\pi\) | ||||
−0.858714 | + | 0.512455i | \(0.828736\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.4949i | 1.51809i | 0.651038 | + | 0.759045i | \(0.274334\pi\) | ||||
−0.651038 | + | 0.759045i | \(0.725666\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.4982 | −1.39558 | −0.697789 | − | 0.716303i | \(-0.745833\pi\) | ||||
−0.697789 | + | 0.716303i | \(0.745833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.2474 | −0.637768 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 6.43539i | − 0.251836i | −0.992041 | − | 0.125918i | \(-0.959812\pi\) | ||||
0.992041 | − | 0.125918i | \(-0.0401877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 24.6969i | − 0.964989i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.2351 | −0.476612 | −0.238306 | − | 0.971190i | \(-0.576592\pi\) | ||||
−0.238306 | + | 0.971190i | \(0.576592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.0454 | 1.63538 | 0.817688 | − | 0.575661i | \(-0.195255\pi\) | ||||
0.817688 | + | 0.575661i | \(0.195255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 7.70674i | − 0.298855i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47.1918i | 1.82728i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.84961 | 0.303031 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8990 | −0.497219 | −0.248610 | − | 0.968604i | \(-0.579974\pi\) | ||||
−0.248610 | + | 0.968604i | \(0.579974\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 0.285729i | − 0.0109815i | −0.999985 | − | 0.00549073i | \(-0.998252\pi\) | ||||
0.999985 | − | 0.00549073i | \(-0.00174776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.2474i | 0.393261i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.1626 | −1.26893 | −0.634466 | − | 0.772951i | \(-0.718780\pi\) | ||||
−0.634466 | + | 0.772951i | \(0.718780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.1464 | −1.49571 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.25697i | 0.0859837i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.9444i | 1.55760i | 0.627274 | + | 0.778799i | \(0.284171\pi\) | ||||
−0.627274 | + | 0.778799i | \(0.715829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.41421 | 0.0536442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.2929 | −0.958035 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.2049i | 1.63183i | 0.578173 | + | 0.815914i | \(0.303766\pi\) | ||||
−0.578173 | + | 0.815914i | \(0.696234\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 22.0454i | − 0.831458i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.65685 | 0.212748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.3939 | 1.96769 | 0.983847 | − | 0.179013i | \(-0.0572905\pi\) | ||||
0.983847 | + | 0.179013i | \(0.0572905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8.77101i | − 0.328477i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000i | 0.0747958i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5590 | 1.21425 | 0.607123 | − | 0.794608i | \(-0.292323\pi\) | ||||
0.607123 | + | 0.794608i | \(0.292323\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.79796 | 0.215927 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 40.8693i | − 1.51785i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0454i | 0.965971i | 0.875628 | + | 0.482985i | \(0.160448\pi\) | ||||
−0.875628 | + | 0.482985i | \(0.839552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.9596 | 0.775218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.5959 | 0.649920 | 0.324960 | − | 0.945728i | \(-0.394649\pi\) | ||||
0.324960 | + | 0.945728i | \(0.394649\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.5133i | 0.718780i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 20.0000i | − 0.735712i | −0.929883 | − | 0.367856i | \(-0.880092\pi\) | ||||
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.8769 | 1.20613 | 0.603067 | − | 0.797690i | \(-0.293945\pi\) | ||||
0.603067 | + | 0.797690i | \(0.293945\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −54.9444 | −2.01301 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.8564i | 0.506302i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.7980i | 0.941381i | 0.882298 | + | 0.470690i | \(0.155995\pi\) | ||||
−0.882298 | + | 0.470690i | \(0.844005\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.2665 | 0.955935 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.6969 | −1.22474 | −0.612368 | − | 0.790573i | \(-0.709783\pi\) | ||||
−0.612368 | + | 0.790573i | \(0.709783\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 19.1954i | − 0.695834i | −0.937525 | − | 0.347917i | \(-0.886889\pi\) | ||||
0.937525 | − | 0.347917i | \(-0.113111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.797959i | 0.0288881i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.16404 | 0.186463 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7980 | 1.29091 | 0.645454 | − | 0.763799i | \(-0.276668\pi\) | ||||
0.645454 | + | 0.763799i | \(0.276668\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 12.5529i | − 0.451498i | −0.974185 | − | 0.225749i | \(-0.927517\pi\) | ||||
0.974185 | − | 0.225749i | \(-0.0724830\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.59592i | 0.272853i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.6773 | 0.884156 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.2412i | 1.15074i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 37.3939i | − 1.33295i | −0.745528 | − | 0.666474i | \(-0.767803\pi\) | ||||
0.745528 | − | 0.666474i | \(-0.232197\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.5352 | −0.374588 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.49490 | −0.0885964 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 40.5836i | − 1.43754i | −0.695245 | − | 0.718772i | \(-0.744704\pi\) | ||||
0.695245 | − | 0.718772i | \(-0.255296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.15663i | 0.0409187i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.8564 | −0.488982 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.7980 | 0.627296 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.13534i | 0.286023i | 0.989721 | + | 0.143012i | \(0.0456786\pi\) | ||||
−0.989721 | + | 0.143012i | \(0.954321\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 16.0454i | − 0.563430i | −0.959498 | − | 0.281715i | \(-0.909097\pi\) | ||||
0.959498 | − | 0.281715i | \(-0.0909033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.73205 | 0.0606711 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.4495 | −0.715437 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 35.9124i | − 1.25335i | −0.779281 | − | 0.626675i | \(-0.784415\pi\) | ||||
0.779281 | − | 0.626675i | \(-0.215585\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.8434i | 1.49343i | 0.665146 | + | 0.746713i | \(0.268369\pi\) | ||||
−0.665146 | + | 0.746713i | \(0.731631\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.1708 | 0.388448 | 0.194224 | − | 0.980957i | \(-0.437781\pi\) | ||||
0.194224 | + | 0.980957i | \(0.437781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.0454 | −1.80761 | −0.903806 | − | 0.427943i | \(-0.859238\pi\) | ||||
−0.903806 | + | 0.427943i | \(0.859238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2.51059i | − 0.0869868i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 30.1464i | − 1.04326i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.56048 | −0.157445 | −0.0787226 | − | 0.996897i | \(-0.525084\pi\) | ||||
−0.0787226 | + | 0.996897i | \(0.525084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40.5959 | −1.39986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.2658i | 1.38518i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 9.00000i | − 0.309244i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.9117 | 1.74523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.2020 | 0.828662 | 0.414331 | − | 0.910126i | \(-0.364016\pi\) | ||||
0.414331 | + | 0.910126i | \(0.364016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.1380i | 0.858698i | 0.903139 | + | 0.429349i | \(0.141257\pi\) | ||||
−0.903139 | + | 0.429349i | \(0.858743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 29.1010i | − 0.992914i | −0.868061 | − | 0.496457i | \(-0.834634\pi\) | ||||
0.868061 | − | 0.496457i | \(-0.165366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.4347 | −0.695604 | −0.347802 | − | 0.937568i | \(-0.613072\pi\) | ||||
−0.347802 | + | 0.937568i | \(0.613072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.6969 | 0.839721 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.492810i | 0.0167174i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 6.20204i | − 0.210148i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.317837 | 0.0107449 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.5959 | 1.30329 | 0.651646 | − | 0.758523i | \(-0.274079\pi\) | ||||
0.651646 | + | 0.758523i | \(0.274079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.4974i | 1.63392i | 0.576695 | + | 0.816960i | \(0.304342\pi\) | ||||
−0.576695 | + | 0.816960i | \(0.695658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 7.65153i | − 0.257495i | −0.991677 | − | 0.128747i | \(-0.958904\pi\) | ||||
0.991677 | − | 0.128747i | \(-0.0410956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.8304 | −1.13591 | −0.567956 | − | 0.823059i | \(-0.692266\pi\) | ||||
−0.567956 | + | 0.823059i | \(0.692266\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5505 | −0.420931 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.12848i | − 0.0377633i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.1464i | 1.17482i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.9350 | 0.431406 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6061 | −0.419971 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 11.9494i | − 0.397211i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.2474i | 0.771919i | 0.922516 | + | 0.385959i | \(0.126130\pi\) | ||||
−0.922516 | + | 0.385959i | \(0.873870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.2117 | −1.63046 | −0.815229 | − | 0.579139i | \(-0.803389\pi\) | ||||
−0.815229 | + | 0.579139i | \(0.803389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.34847 | −0.110818 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.84961i | 0.259217i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.8434i | 0.951455i | 0.879593 | + | 0.475727i | \(0.157815\pi\) | ||||
−0.879593 | + | 0.475727i | \(0.842185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.54270 | −0.0836939 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.0908 | −1.44970 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.14626i | 0.103226i | 0.998667 | + | 0.0516128i | \(0.0164362\pi\) | ||||
−0.998667 | + | 0.0516128i | \(0.983564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.44949i | 0.0802788i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.1708 | −0.365326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.7423 | 1.78835 | 0.894177 | − | 0.447713i | \(-0.147761\pi\) | ||||
0.894177 | + | 0.447713i | \(0.147761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 58.8576i | 1.91870i | 0.282213 | + | 0.959352i | \(0.408932\pi\) | ||||
−0.282213 | + | 0.959352i | \(0.591068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.9898i | 1.85584i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.4120 | −1.41070 | −0.705351 | − | 0.708859i | \(-0.749210\pi\) | ||||
−0.705351 | + | 0.708859i | \(0.749210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.40408 | 0.142963 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.81405i | − 0.123549i | −0.998090 | − | 0.0617745i | \(-0.980324\pi\) | ||||
0.998090 | − | 0.0617745i | \(-0.0196760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.6969i | 0.799174i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.4422 | 0.401779 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5959 | 0.922449 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 64.8002i | − 2.08599i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8990i | 0.414803i | 0.978256 | + | 0.207402i | \(0.0665007\pi\) | ||||
−0.978256 | + | 0.207402i | \(0.933499\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.2015 | −1.25804 | −0.629018 | − | 0.777391i | \(-0.716543\pi\) | ||||
−0.629018 | + | 0.777391i | \(0.716543\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.449490 | −0.0144100 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 31.4626i | − 1.00658i | −0.864118 | − | 0.503290i | \(-0.832123\pi\) | ||||
0.864118 | − | 0.503290i | \(-0.167877\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.20204i | 0.0703775i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.58166 | 0.305607 | 0.152804 | − | 0.988257i | \(-0.451170\pi\) | ||||
0.152804 | + | 0.988257i | \(0.451170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.1464 | 0.992408 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 47.2261i | − 1.50170i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.65153i | 0.243059i | 0.992588 | + | 0.121529i | \(0.0387799\pi\) | ||||
−0.992588 | + | 0.121529i | \(0.961220\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.9479 | −1.26643 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.8434 | −1.32519 | −0.662596 | − | 0.748977i | \(-0.730545\pi\) | ||||
−0.662596 | + | 0.748977i | \(0.730545\pi\) | |||||||
\(998\) | 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 | 6048.2.h.c.2591.2 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.c.2591.8 | yes | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.c.2591.1 | ✓ | 8 | |
12.11 | even | 2 | inner | 6048.2.h.c.2591.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.c.2591.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
6048.2.h.c.2591.2 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.c.2591.7 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.c.2591.8 | yes | 8 | 3.2 | odd | 2 | inner |