Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(607,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.607");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.k (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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 607.3 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.607 |
Dual form | 912.2.k.h.607.4 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.37228 | 1.06092 | 0.530458 | − | 0.847711i | \(-0.322020\pi\) | ||||
0.530458 | + | 0.847711i | \(0.322020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.52434i | − | 0.954110i | −0.878873 | − | 0.477055i | \(-0.841704\pi\) | ||
0.878873 | − | 0.477055i | \(-0.158296\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.52434i | − | 0.761116i | −0.924757 | − | 0.380558i | \(-0.875732\pi\) | ||
0.924757 | − | 0.380558i | \(-0.124268\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58457i | 0.439482i | 0.975558 | + | 0.219741i | \(0.0705212\pi\) | ||||
−0.975558 | + | 0.219741i | \(0.929479\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.37228 | 0.612520 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.372281 | −0.0902915 | −0.0451457 | − | 0.998980i | \(-0.514375\pi\) | ||||
−0.0451457 | + | 0.998980i | \(0.514375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.52434i | − | 0.550856i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.87953i | − | 0.391909i | −0.980613 | − | 0.195954i | \(-0.937220\pi\) | ||
0.980613 | − | 0.195954i | \(-0.0627804\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.627719 | 0.125544 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.16915i | − | 0.588496i | −0.955729 | − | 0.294248i | \(-0.904931\pi\) | ||
0.955729 | − | 0.294248i | \(-0.0950692\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.74456 | −0.492938 | −0.246469 | − | 0.969151i | \(-0.579270\pi\) | ||||
−0.246469 | + | 0.969151i | \(0.579270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.52434i | − | 0.439431i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 5.98844i | − | 1.01223i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.58457i | 0.260502i | 0.991481 | + | 0.130251i | \(0.0415784\pi\) | ||||
−0.991481 | + | 0.130251i | \(0.958422\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.58457i | 0.253735i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820i | 1.08200i | 0.841021 | + | 0.541002i | \(0.181955\pi\) | ||||
−0.841021 | + | 0.541002i | \(0.818045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.644810i | 0.0983326i | 0.998791 | + | 0.0491663i | \(0.0156564\pi\) | ||||
−0.998791 | + | 0.0491663i | \(0.984344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.37228 | 0.353639 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.939764i | − | 0.137079i | −0.997648 | − | 0.0685393i | \(-0.978166\pi\) | ||
0.997648 | − | 0.0685393i | \(-0.0218339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.627719 | 0.0896741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.372281 | −0.0521298 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0974i | 1.38698i | 0.720467 | + | 0.693489i | \(0.243927\pi\) | ||||
−0.720467 | + | 0.693489i | \(0.756073\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.98844i | − | 0.807481i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | − | 1.73205i | 0.529813 | − | 0.229416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.372281 | −0.0476657 | −0.0238329 | − | 0.999716i | \(-0.507587\pi\) | ||||
−0.0238329 | + | 0.999716i | \(0.507587\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.52434i | − | 0.318037i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.75906i | 0.466253i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.4891 | 1.64796 | 0.823979 | − | 0.566620i | \(-0.191749\pi\) | ||||
0.823979 | + | 0.566620i | \(0.191749\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.87953i | − | 0.226269i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.1168 | 1.53521 | 0.767605 | − | 0.640923i | \(-0.221448\pi\) | ||||
0.767605 | + | 0.640923i | \(0.221448\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.627719 | 0.0724827 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.37228 | −0.726189 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.74456 | −0.758823 | −0.379411 | − | 0.925228i | \(-0.623873\pi\) | ||||
−0.379411 | + | 0.925228i | \(0.623873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.883156 | −0.0957917 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.16915i | − | 0.339768i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2665i | 1.40625i | 0.711068 | + | 0.703123i | \(0.248212\pi\) | ||||
−0.711068 | + | 0.703123i | \(0.751788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.74456 | −0.284598 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.48913 | − | 4.10891i | 0.973564 | − | 0.421565i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.2665i | − | 1.34701i | −0.739183 | − | 0.673504i | \(-0.764788\pi\) | ||
0.739183 | − | 0.673504i | \(-0.235212\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.52434i | − | 0.253705i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.25544 | −0.323928 | −0.161964 | − | 0.986797i | \(-0.551783\pi\) | ||||
−0.161964 | + | 0.986797i | \(0.551783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.25544 | −0.123702 | −0.0618510 | − | 0.998085i | \(-0.519700\pi\) | ||||
−0.0618510 | + | 0.998085i | \(0.519700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5.98844i | − | 0.584412i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4891 | −1.30404 | −0.652021 | − | 0.758200i | \(-0.726079\pi\) | ||||
−0.652021 | + | 0.758200i | \(0.726079\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.6819i | − | 1.11893i | −0.828855 | − | 0.559463i | \(-0.811007\pi\) | ||
0.828855 | − | 0.559463i | \(-0.188993\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.58457i | 0.150401i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.0256i | 1.60163i | 0.598912 | + | 0.800815i | \(0.295600\pi\) | ||||
−0.598912 | + | 0.800815i | \(0.704400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.45877i | − | 0.415782i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.58457i | 0.146494i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.939764i | 0.0861480i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.62772 | 0.420702 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.92820i | 0.624695i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3723 | −0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.25544 | 0.111402 | 0.0557010 | − | 0.998447i | \(-0.482261\pi\) | ||||
0.0557010 | + | 0.998447i | \(0.482261\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.644810i | 0.0567724i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.57301i | 0.661657i | 0.943691 | + | 0.330829i | \(0.107328\pi\) | ||||
−0.943691 | + | 0.330829i | \(0.892672\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.37228 | − | 10.0974i | −0.379125 | − | 0.875551i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.37228 | 0.204173 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1168 | 1.12065 | 0.560324 | − | 0.828274i | \(-0.310677\pi\) | ||||
0.560324 | + | 0.828274i | \(0.310677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6704i | 1.49878i | 0.662128 | + | 0.749390i | \(0.269653\pi\) | ||||
−0.662128 | + | 0.749390i | \(0.730347\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.939764i | − | 0.0791424i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.51811i | − | 0.624345i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.627719 | 0.0517734 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.1168 | −1.23842 | −0.619210 | − | 0.785225i | \(-0.712547\pi\) | ||||
−0.619210 | + | 0.785225i | \(0.712547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.74456 | 0.223349 | 0.111675 | − | 0.993745i | \(-0.464379\pi\) | ||||
0.111675 | + | 0.993745i | \(0.464379\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.372281 | −0.0300972 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.51087 | −0.522966 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4891 | −1.23617 | −0.618083 | − | 0.786113i | \(-0.712091\pi\) | ||||
−0.618083 | + | 0.786113i | \(0.712091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0974i | 0.800772i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.74456 | −0.373924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.8997i | 1.55867i | 0.626608 | + | 0.779334i | \(0.284443\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.98844i | − | 0.466199i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.48913 | −0.424761 | −0.212381 | − | 0.977187i | \(-0.568122\pi\) | ||||
−0.212381 | + | 0.977187i | \(0.568122\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4891 | 0.806856 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | − | 1.73205i | 0.305888 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.33830i | − | 0.481892i | −0.970539 | − | 0.240946i | \(-0.922542\pi\) | ||
0.970539 | − | 0.240946i | \(-0.0774576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.58457i | − | 0.119783i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.4891 | −1.60617 | −0.803086 | − | 0.595863i | \(-0.796810\pi\) | ||||
−0.803086 | + | 0.595863i | \(0.796810\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 25.5383i | − | 1.89825i | −0.314901 | − | 0.949125i | \(-0.601971\pi\) | ||
0.314901 | − | 0.949125i | \(-0.398029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.372281 | −0.0275198 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.75906i | 0.276371i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.939764i | 0.0687223i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.52434i | − | 0.183619i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.1831i | 1.89455i | 0.320428 | + | 0.947273i | \(0.396173\pi\) | ||||
−0.320428 | + | 0.947273i | \(0.603827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8564i | 0.997406i | 0.866773 | + | 0.498703i | \(0.166190\pi\) | ||||
−0.866773 | + | 0.498703i | \(0.833810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.75906i | 0.269192i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.7446 | −1.19300 | −0.596500 | − | 0.802613i | \(-0.703443\pi\) | ||||
−0.596500 | + | 0.802613i | \(0.703443\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.2603i | 1.29444i | 0.762305 | + | 0.647218i | \(0.224068\pi\) | ||||
−0.762305 | + | 0.647218i | \(0.775932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.4891 | 0.951450 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.00000 | −0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.4356i | 1.14792i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.87953i | − | 0.130636i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.37228 | − | 10.0974i | −0.302437 | − | 0.698448i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.52967i | 0.104323i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.92820i | 0.470317i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.1168 | 0.886354 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.589907i | − | 0.0396815i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7446 | −0.719509 | −0.359755 | − | 0.933047i | \(-0.617140\pi\) | ||||
−0.359755 | + | 0.933047i | \(0.617140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.627719 | 0.0418479 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0000 | −0.796468 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.88316 | −0.454852 | −0.227426 | − | 0.973795i | \(-0.573031\pi\) | ||||
−0.227426 | + | 0.973795i | \(0.573031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.37228 | −0.419265 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.1168 | 0.859313 | 0.429657 | − | 0.902992i | \(-0.358635\pi\) | ||||
0.429657 | + | 0.902992i | \(0.358635\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.22938i | − | 0.145429i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.74456 | −0.438106 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.57835i | 0.425518i | 0.977105 | + | 0.212759i | \(0.0682449\pi\) | ||||
−0.977105 | + | 0.212759i | \(0.931755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.75906i | − | 0.242142i | −0.992644 | − | 0.121071i | \(-0.961367\pi\) | ||
0.992644 | − | 0.121071i | \(-0.0386329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.48913 | 0.0951367 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.74456 | + | 6.33830i | 0.174632 | + | 0.403296i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.46410i | − | 0.219529i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.45254i | − | 0.596639i | −0.954466 | − | 0.298320i | \(-0.903574\pi\) | ||
0.954466 | − | 0.298320i | \(-0.0964261\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.74456 | −0.298288 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.883156 | −0.0553054 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.0256i | − | 1.06202i | −0.847364 | − | 0.531012i | \(-0.821812\pi\) | ||
0.847364 | − | 0.531012i | \(-0.178188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 3.16915i | − | 0.196165i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 14.7962i | − | 0.912371i | −0.889885 | − | 0.456185i | \(-0.849215\pi\) | ||
0.889885 | − | 0.456185i | \(-0.150785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.9538i | 1.47147i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2665i | 0.811897i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.9538i | 1.46049i | 0.683187 | + | 0.730243i | \(0.260593\pi\) | ||||
−0.683187 | + | 0.730243i | \(0.739407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.294954i | 0.0179172i | 0.999960 | + | 0.00895858i | \(0.00285164\pi\) | ||||
−0.999960 | + | 0.00895858i | \(0.997148\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.58457i | − | 0.0955534i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.37228 | −0.503042 | −0.251521 | − | 0.967852i | \(-0.580931\pi\) | ||||
−0.251521 | + | 0.967852i | \(0.580931\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.74456 | −0.164313 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.16915i | − | 0.189056i | −0.995522 | − | 0.0945278i | \(-0.969866\pi\) | ||
0.995522 | − | 0.0945278i | \(-0.0301341\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 29.0573i | − | 1.72728i | −0.504110 | − | 0.863640i | \(-0.668179\pi\) | ||
0.504110 | − | 0.863640i | \(-0.331821\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.48913 | − | 4.10891i | 0.562087 | − | 0.243391i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.4891 | 1.03235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8614 | −0.991847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.2665i | − | 0.777696i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.8564i | 0.809500i | 0.914427 | + | 0.404750i | \(0.132641\pi\) | ||||
−0.914427 | + | 0.404750i | \(0.867359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.48913 | −0.552478 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.52434i | − | 0.146477i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.97825 | 0.172237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.62772 | 0.0938201 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.25544 | −0.187020 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.883156 | −0.0505694 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.48913 | 0.313281 | 0.156640 | − | 0.987656i | \(-0.449934\pi\) | ||||
0.156640 | + | 0.987656i | \(0.449934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.25544 | −0.0714193 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.22938i | 0.126417i | 0.998000 | + | 0.0632084i | \(0.0201333\pi\) | ||||
−0.998000 | + | 0.0632084i | \(0.979867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.48913 | −0.197217 | −0.0986085 | − | 0.995126i | \(-0.531439\pi\) | ||||
−0.0986085 | + | 0.995126i | \(0.531439\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 5.98844i | − | 0.337410i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.9538i | − | 1.34538i | −0.739926 | − | 0.672689i | \(-0.765139\pi\) | ||
0.739926 | − | 0.672689i | \(-0.234861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.4891 | −0.752890 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.48913 | + | 0.644810i | −0.0828571 | + | 0.0358782i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.994667i | 0.0551742i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 11.6819i | − | 0.646012i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.37228 | −0.130788 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4891 | −0.741429 | −0.370715 | − | 0.928747i | \(-0.620887\pi\) | ||||
−0.370715 | + | 0.928747i | \(0.620887\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.58457i | 0.0868341i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.0000 | 1.74835 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.7846i | 1.13221i | 0.824333 | + | 0.566105i | \(0.191550\pi\) | ||||
−0.824333 | + | 0.566105i | \(0.808450\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.0256i | 0.924701i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.92820i | 0.375183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.2549i | − | 1.03967i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 4.45877i | − | 0.240052i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 16.3807i | − | 0.879364i | −0.898153 | − | 0.439682i | \(-0.855091\pi\) | ||
0.898153 | − | 0.439682i | \(-0.144909\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.6060 | 0.781840 | 0.390920 | − | 0.920425i | \(-0.372157\pi\) | ||||
0.390920 | + | 0.920425i | \(0.372157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.58457i | 0.0845783i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.510875 | −0.0271911 | −0.0135956 | − | 0.999908i | \(-0.504328\pi\) | ||||
−0.0135956 | + | 0.999908i | \(0.504328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.48913 | −0.503630 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.939764i | 0.0497376i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.3523i | 1.54915i | 0.632479 | + | 0.774577i | \(0.282037\pi\) | ||||
−0.632479 | + | 0.774577i | \(0.717963\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.62772 | 0.242892 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.1168 | 1.62873 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.9715i | 0.677109i | 0.940947 | + | 0.338555i | \(0.109938\pi\) | ||||
−0.940947 | + | 0.338555i | \(0.890062\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.92820i | 0.360668i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.4891 | 1.32333 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.51278i | − | 0.440775i | −0.975412 | − | 0.220387i | \(-0.929268\pi\) | ||
0.975412 | − | 0.220387i | \(-0.0707322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.3723 | −0.535622 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.02175 | 0.258633 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.9783 | −0.974847 | −0.487424 | − | 0.873166i | \(-0.662063\pi\) | ||||
−0.487424 | + | 0.873166i | \(0.662063\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.25544 | 0.0643180 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.9783 | −0.765353 | −0.382676 | − | 0.923882i | \(-0.624998\pi\) | ||||
−0.382676 | + | 0.923882i | \(0.624998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.1168 | −0.770426 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.644810i | 0.0327775i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.1168 | −0.563646 | −0.281823 | − | 0.959466i | \(-0.590939\pi\) | ||||
−0.281823 | + | 0.959466i | \(0.590939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.699713i | 0.0353860i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.57301i | 0.382008i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.0000 | −0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.1168 | 1.46133 | 0.730666 | − | 0.682735i | \(-0.239210\pi\) | ||||
0.730666 | + | 0.682735i | \(0.239210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.37228 | − | 10.0974i | −0.218888 | − | 0.505500i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.6873i | − | 0.533696i | −0.963739 | − | 0.266848i | \(-0.914018\pi\) | ||
0.963739 | − | 0.266848i | \(-0.0859822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.34896i | − | 0.216637i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.37228 | 0.117880 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.92820i | − | 0.342578i | −0.985221 | − | 0.171289i | \(-0.945207\pi\) | ||
0.985221 | − | 0.171289i | \(-0.0547931\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.1168 | 0.647006 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.0974i | 0.496858i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.21782i | − | 0.403397i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.6704i | 0.865321i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.5615i | 0.662520i | 0.943539 | + | 0.331260i | \(0.107474\pi\) | ||||
−0.943539 | + | 0.331260i | \(0.892526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.1282i | 1.27341i | 0.771106 | + | 0.636706i | \(0.219704\pi\) | ||||
−0.771106 | + | 0.636706i | \(0.780296\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.939764i | − | 0.0456929i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.233688 | −0.0113355 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.939764i | 0.0454784i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 41.4891 | 1.99846 | 0.999230 | − | 0.0392245i | \(-0.0124888\pi\) | ||||
0.999230 | + | 0.0392245i | \(0.0124888\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.3639i | − | 1.12279i | −0.827546 | − | 0.561397i | \(-0.810264\pi\) | ||
0.827546 | − | 0.561397i | \(-0.189736\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 7.51811i | − | 0.360466i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.25544 | − | 7.51811i | −0.155729 | − | 0.359640i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7228 | 0.845864 | 0.422932 | − | 0.906161i | \(-0.361001\pi\) | ||||
0.422932 | + | 0.906161i | \(0.361001\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.627719 | 0.0298914 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.81396i | 0.181207i | 0.995887 | + | 0.0906033i | \(0.0288795\pi\) | ||||
−0.995887 | + | 0.0906033i | \(0.971120\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.4719i | 1.49191i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.1168 | −0.715002 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.8820i | − | 1.45741i | −0.684828 | − | 0.728705i | \(-0.740123\pi\) | ||
0.684828 | − | 0.728705i | \(-0.259877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4891 | 0.823531 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.74456 | 0.128951 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.48913 | 0.444857 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.11684 | 0.426468 | 0.213234 | − | 0.977001i | \(-0.431600\pi\) | ||||
0.213234 | + | 0.977001i | \(0.431600\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.372281 | −0.0173766 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.3723 | 1.78718 | 0.893588 | − | 0.448889i | \(-0.148180\pi\) | ||||
0.893588 | + | 0.448889i | \(0.148180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.6472i | − | 1.37782i | −0.724845 | − | 0.688912i | \(-0.758089\pi\) | ||
0.724845 | − | 0.688912i | \(-0.241911\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.51087 | −0.301935 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.0318i | − | 0.556764i | −0.960470 | − | 0.278382i | \(-0.910202\pi\) | ||
0.960470 | − | 0.278382i | \(-0.0897982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 34.0511i | − | 1.57233i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.4891 | −0.713701 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.62772 | 0.0748426 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.51087 | − | 1.08724i | 0.115207 | − | 0.0498860i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0974i | 0.462326i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 11.3870i | − | 0.520284i | −0.965570 | − | 0.260142i | \(-0.916231\pi\) | ||
0.965570 | − | 0.260142i | \(-0.0837694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.51087 | −0.114486 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.74456 | −0.215885 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 31.4719i | − | 1.42906i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.2337 | 1.82316 | 0.911581 | − | 0.411120i | \(-0.134862\pi\) | ||||
0.911581 | + | 0.411120i | \(0.134862\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8997i | 0.899898i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 34.3461i | − | 1.55002i | −0.631951 | − | 0.775008i | \(-0.717746\pi\) | ||
0.631951 | − | 0.775008i | \(-0.282254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.17981i | 0.0531362i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5.98844i | − | 0.269160i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0974i | 0.452928i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5012i | 0.649164i | 0.945858 | + | 0.324582i | \(0.105224\pi\) | ||||
−0.945858 | + | 0.324582i | \(0.894776\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.48913 | −0.245236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 35.9306i | − | 1.60207i | −0.598619 | − | 0.801034i | \(-0.704284\pi\) | ||
0.598619 | − | 0.801034i | \(-0.295716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.72281 | −0.343661 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.4891 | 0.465838 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 13.2665i | − | 0.588027i | −0.955801 | − | 0.294014i | \(-0.905009\pi\) | ||
0.955801 | − | 0.294014i | \(-0.0949911\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 33.1113i | − | 1.46476i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | − | 1.73205i | 0.176604 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.97825 | −0.131237 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.37228 | −0.104333 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.33830i | − | 0.278220i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0256i | 0.745903i | 0.927851 | + | 0.372952i | \(0.121654\pi\) | ||||
−0.927851 | + | 0.372952i | \(0.878346\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0000 | 1.39926 | 0.699631 | − | 0.714504i | \(-0.253348\pi\) | ||||
0.699631 | + | 0.714504i | \(0.253348\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.58457i | − | 0.0691565i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.02175 | 0.0445081 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4674 | 0.846408 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9783 | −0.475521 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.0000 | −1.38348 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.4891 | −0.927324 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.58457i | − | 0.0682524i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1168 | 0.563937 | 0.281969 | − | 0.959424i | \(-0.409013\pi\) | ||||
0.281969 | + | 0.959424i | \(0.409013\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 25.5383i | − | 1.09595i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 27.7128i | − | 1.18709i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.51087 | −0.278385 | −0.139192 | − | 0.990265i | \(-0.544451\pi\) | ||||
−0.139192 | + | 0.990265i | \(0.544451\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.372281 | −0.0158886 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.48913 | − | 12.6766i | −0.233845 | − | 0.540041i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.0256i | 0.724000i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.75906i | 0.159563i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.8614 | 1.68898 | 0.844491 | − | 0.535570i | \(-0.179903\pi\) | ||||
0.844491 | + | 0.535570i | \(0.179903\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.02175 | −0.0432154 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.939764i | 0.0396769i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.9783 | 0.968418 | 0.484209 | − | 0.874952i | \(-0.339107\pi\) | ||||
0.484209 | + | 0.874952i | \(0.339107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.3894i | 1.69920i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.52434i | − | 0.106012i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.589907i | 0.0247302i | 0.999924 | + | 0.0123651i | \(0.00393603\pi\) | ||||
−0.999924 | + | 0.0123651i | \(0.996064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 23.6588i | − | 0.990090i | −0.868867 | − | 0.495045i | \(-0.835152\pi\) | ||
0.868867 | − | 0.495045i | \(-0.164848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.1831i | 1.09382i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.17981i | − | 0.0492017i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.60597 | 0.108488 | 0.0542440 | − | 0.998528i | \(-0.482725\pi\) | ||||
0.0542440 | + | 0.998528i | \(0.482725\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.8564i | 0.575853i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.74456 | −0.362786 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.4891 | 1.05565 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.75906i | 0.155418i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.5986i | 1.01529i | 0.861566 | + | 0.507646i | \(0.169484\pi\) | ||||
−0.861566 | + | 0.507646i | \(0.830516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.9783 | + | 4.75372i | −0.452351 | + | 0.195874i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.7446 | −0.688779 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.510875 | −0.0209791 | −0.0104896 | − | 0.999945i | \(-0.503339\pi\) | ||||
−0.0104896 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.22938i | 0.0913958i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.2603i | 0.747343i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.4674 | −0.999710 | −0.499855 | − | 0.866109i | \(-0.666613\pi\) | ||||
−0.499855 | + | 0.866109i | \(0.666613\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 33.4612i | − | 1.36491i | −0.730927 | − | 0.682455i | \(-0.760912\pi\) | ||
0.730927 | − | 0.682455i | \(-0.239088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.4891 | 0.549320 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9783 | 0.446329 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.2554 | −1.18744 | −0.593721 | − | 0.804671i | \(-0.702342\pi\) | ||||
−0.593721 | + | 0.804671i | \(0.702342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | −0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.48913 | 0.0602436 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.372281 | −0.0150363 | −0.00751815 | − | 0.999972i | \(-0.502393\pi\) | ||||
−0.00751815 | + | 0.999972i | \(0.502393\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.4356i | 0.662749i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.0951 | 1.77520 | 0.887601 | − | 0.460613i | \(-0.152371\pi\) | ||||
0.887601 | + | 0.460613i | \(0.152371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.3923i | 0.417702i | 0.977947 | + | 0.208851i | \(0.0669724\pi\) | ||||
−0.977947 | + | 0.208851i | \(0.933028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.87953i | − | 0.0754228i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.4891 | 1.34171 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.7446 | −1.10978 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.37228 | − | 10.0974i | −0.174612 | − | 0.403249i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.589907i | − | 0.0235211i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.2496i | 0.806124i | 0.915173 | + | 0.403062i | \(0.132054\pi\) | ||||
−0.915173 | + | 0.403062i | \(0.867946\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.00000 | 0.158986 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.97825 | 0.118188 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.994667i | 0.0394101i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.2665i | 0.523995i | 0.965069 | + | 0.261998i | \(0.0843813\pi\) | ||||
−0.965069 | + | 0.261998i | \(0.915619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.52434i | − | 0.0995502i | −0.998760 | − | 0.0497751i | \(-0.984150\pi\) | ||
0.998760 | − | 0.0497751i | \(-0.0158505\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.52967i | 0.0602307i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.5065i | 0.530997i | 0.964111 | + | 0.265499i | \(0.0855366\pi\) | ||||
−0.964111 | + | 0.265499i | \(0.914463\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0974i | 0.396356i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.92820i | 0.271538i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.88316 | 0.191093 | 0.0955463 | − | 0.995425i | \(-0.469540\pi\) | ||||
0.0955463 | + | 0.995425i | \(0.469540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.9653i | 0.701963i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.1168 | 0.511737 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4891 | −0.525462 | −0.262731 | − | 0.964869i | \(-0.584623\pi\) | ||||
−0.262731 | + | 0.964869i | \(0.584623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8617i | 0.500264i | 0.968212 | + | 0.250132i | \(0.0804740\pi\) | ||||
−0.968212 | + | 0.250132i | \(0.919526\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.589907i | − | 0.0229101i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.3723 | − | 23.9538i | −0.402220 | − | 0.928887i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.95650 | −0.230637 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.7446 | −0.415409 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.939764i | 0.0362792i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.9793i | 1.57964i | 0.613341 | + | 0.789818i | \(0.289825\pi\) | ||||
−0.613341 | + | 0.789818i | \(0.710175\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.627719 | 0.0241609 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 47.9075i | − | 1.84124i | −0.390465 | − | 0.920618i | \(-0.627686\pi\) | ||
0.390465 | − | 0.920618i | \(-0.372314\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.4891 | −1.28519 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.9783 | −1.49146 | −0.745731 | − | 0.666248i | \(-0.767899\pi\) | ||||
−0.745731 | + | 0.666248i | \(0.767899\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.1168 | 1.18891 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.88316 | −0.262609 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.0000 | −0.609551 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.93443i | − | 0.0735892i | −0.999323 | − | 0.0367946i | \(-0.988285\pi\) | ||
0.999323 | − | 0.0367946i | \(-0.0117147\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.37228 | −0.242063 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.9191i | 1.59008i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.57924i | − | 0.0976957i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.1168 | 0.496125 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7228 | −0.744920 | −0.372460 | − | 0.928048i | \(-0.621486\pi\) | ||||
−0.372460 | + | 0.928048i | \(0.621486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.74456 | + | 6.33830i | 0.103513 | + | 0.239053i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.22938i | − | 0.0839635i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.21782i | 0.309063i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.9565 | −1.80104 | −0.900522 | − | 0.434810i | \(-0.856815\pi\) | ||||
−0.900522 | + | 0.434810i | \(0.856815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.74456 | −0.252941 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.15848i | 0.193187i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.48913 | 0.354873 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.57835i | 0.245673i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.3523i | 1.09466i | 0.836918 | + | 0.547328i | \(0.184355\pi\) | ||||
−0.836918 | + | 0.547328i | \(0.815645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.16915i | 0.118025i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 3.75906i | − | 0.139801i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.98933i | − | 0.0738820i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.16292i | 0.302746i | 0.988477 | + | 0.151373i | \(0.0483695\pi\) | ||||
−0.988477 | + | 0.151373i | \(0.951631\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 0.240051i | − | 0.00887860i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.9783 | 0.922593 | 0.461296 | − | 0.887246i | \(-0.347384\pi\) | ||||
0.461296 | + | 0.887246i | \(0.347384\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.48913 | 0.0549272 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 34.0511i | − | 1.25429i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.10358i | − | 0.187738i | −0.995585 | − | 0.0938691i | \(-0.970076\pi\) | ||
0.995585 | − | 0.0938691i | \(-0.0299235\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.74456 | + | 6.33830i | 0.100824 | + | 0.232843i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.9783 | 0.402753 | 0.201376 | − | 0.979514i | \(-0.435459\pi\) | ||||
0.201376 | + | 0.979514i | \(0.435459\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.8614 | −1.31386 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.46410i | − | 0.126745i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.0511i | 1.24420i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.7228 | −1.52249 | −0.761244 | − | 0.648466i | \(-0.775411\pi\) | ||||
−0.761244 | + | 0.648466i | \(0.775411\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9.45254i | − | 0.344470i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.51087 | 0.236955 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8614 | −0.649184 | −0.324592 | − | 0.945854i | \(-0.605227\pi\) | ||||
−0.324592 | + | 0.945854i | \(0.605227\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.74456 | −0.172217 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.8614 | −0.792475 | −0.396238 | − | 0.918148i | \(-0.629684\pi\) | ||||
−0.396238 | + | 0.918148i | \(0.629684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.4891 | −1.06758 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.883156 | −0.0319306 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.33830i | − | 0.228863i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.8614 | −1.36532 | −0.682659 | − | 0.730737i | \(-0.739176\pi\) | ||||
−0.682659 | + | 0.730737i | \(0.739176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 17.0256i | − | 0.613160i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39.7995i | − | 1.43149i | −0.698363 | − | 0.715744i | \(-0.746088\pi\) | ||
0.698363 | − | 0.715744i | \(-0.253912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.72281 | −0.0618853 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | + | 27.7128i | 0.429945 | + | 0.992915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0974i | 0.361312i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.16915i | − | 0.113256i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.7446 | −1.31147 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.9783 | −1.24684 | −0.623420 | − | 0.781887i | \(-0.714257\pi\) | ||||
−0.623420 | + | 0.781887i | \(0.714257\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 14.7962i | − | 0.526758i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.9783 | 1.52813 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.589907i | − | 0.0209482i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.9538i | 0.849552i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.16915i | − | 0.112257i | −0.998424 | − | 0.0561285i | \(-0.982124\pi\) | ||
0.998424 | − | 0.0561285i | \(-0.0178756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.349857i | 0.0123770i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.2665i | 0.468749i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 33.1113i | − | 1.16847i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.2554 | −0.396702 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.9538i | 0.843212i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.8832 | −0.523264 | −0.261632 | − | 0.965168i | \(-0.584261\pi\) | ||||
−0.261632 | + | 0.965168i | \(0.584261\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.4674 | 1.28054 | 0.640271 | − | 0.768149i | \(-0.278822\pi\) | ||||
0.640271 | + | 0.768149i | \(0.278822\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.294954i | 0.0103445i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.2078i | 1.65362i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.11684 | + | 2.57924i | 0.0390734 | + | 0.0902362i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3723 | 0.780798 | 0.390399 | − | 0.920646i | \(-0.372337\pi\) | ||||
0.390399 | + | 0.920646i | \(0.372337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 6.28339i | − | 0.219025i | −0.993985 | − | 0.109513i | \(-0.965071\pi\) | ||
0.993985 | − | 0.109513i | \(-0.0349290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.58457i | − | 0.0551678i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.4891 | 0.747250 | 0.373625 | − | 0.927580i | \(-0.378115\pi\) | ||||
0.373625 | + | 0.927580i | \(0.378115\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 50.0820i | − | 1.73942i | −0.493563 | − | 0.869710i | \(-0.664306\pi\) | ||
0.493563 | − | 0.869710i | \(-0.335694\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.37228 | −0.290431 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.233688 | −0.00809681 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.0217 | −0.450636 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.74456 | −0.0948660 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9565 | 0.653672 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 3.16915i | − | 0.109151i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.8832 | 0.856007 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.6819i | − | 0.401396i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 29.0573i | − | 0.997245i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.97825 | 0.102093 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.48913 | − | 4.10891i | 0.324521 | − | 0.140522i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.74839i | 0.196361i | 0.995169 | + | 0.0981806i | \(0.0313023\pi\) | ||||
−0.995169 | + | 0.0981806i | \(0.968698\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.8757i | 1.22406i | 0.790833 | + | 0.612032i | \(0.209648\pi\) | ||||
−0.790833 | + | 0.612032i | \(0.790352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.4891 | 0.596028 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.4674 | 0.424394 | 0.212197 | − | 0.977227i | \(-0.431938\pi\) | ||||
0.212197 | + | 0.977227i | \(0.431938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 15.0362i | − | 0.511247i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8614 | −0.572643 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.0256i | 0.577552i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.3745i | 0.724248i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.2665i | − | 0.449003i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.1831i | 0.885152i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.2511i | 1.79816i | 0.437781 | + | 0.899082i | \(0.355765\pi\) | ||||
−0.437781 | + | 0.899082i | \(0.644235\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.8564i | 0.467365i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.60597 | 0.222561 | 0.111280 | − | 0.993789i | \(-0.464505\pi\) | ||||
0.111280 | + | 0.993789i | \(0.464505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 9.45254i | − | 0.318103i | −0.987270 | − | 0.159052i | \(-0.949156\pi\) | ||
0.987270 | − | 0.159052i | \(-0.0508436\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.48913 | −0.318973 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.0000 | 0.940148 | 0.470074 | − | 0.882627i | \(-0.344227\pi\) | ||||
0.470074 | + | 0.882627i | \(0.344227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.16915i | − | 0.106290i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.52434i | − | 0.0845685i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.62772 | − | 3.75906i | −0.0544695 | − | 0.125792i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50.9783 | −1.70401 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.97825 | 0.0994409 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.69793i | 0.290092i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.75906i | − | 0.125232i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.62772 | 0.0541671 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 60.5841i | − | 2.01388i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.4674 | 0.679608 | 0.339804 | − | 0.940496i | \(-0.389639\pi\) | ||||
0.339804 | + | 0.940496i | \(0.389639\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.25544 | −0.107976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.51087 | 0.0831890 | 0.0415945 | − | 0.999135i | \(-0.486756\pi\) | ||||
0.0415945 | + | 0.999135i | \(0.486756\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.74456 | −0.289403 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.883156 | −0.0291962 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.1168 | 0.631294 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8386i | 0.819350i | 0.912231 | + | 0.409675i | \(0.134358\pi\) | ||||
−0.912231 | + | 0.409675i | \(0.865642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.48913 | 0.180873 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 6.33830i | − | 0.208628i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.994667i | 0.0327044i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.25544 | −0.0412340 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.5109 | −1.06665 | −0.533324 | − | 0.845911i | \(-0.679057\pi\) | ||||
−0.533324 | + | 0.845911i | \(0.679057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.51087 | − | 1.08724i | 0.0822906 | − | 0.0356329i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.22938i | 0.0729868i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.22938i | 0.0729087i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.6277 | 0.379861 | 0.189931 | − | 0.981798i | \(-0.439174\pi\) | ||||
0.189931 | + | 0.981798i | \(0.439174\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.48913 | −0.113863 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 17.0256i | − | 0.555017i | −0.960723 | − | 0.277509i | \(-0.910491\pi\) | ||
0.960723 | − | 0.277509i | \(-0.0895087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.0217 | 0.424047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 5.98844i | − | 0.194804i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 26.8280i | − | 0.871791i | −0.899997 | − | 0.435896i | \(-0.856432\pi\) | ||
0.899997 | − | 0.435896i | \(-0.143568\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7846i | 0.674697i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 23.9538i | − | 0.776754i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.5437i | 0.795047i | 0.917592 | + | 0.397524i | \(0.130130\pi\) | ||||
−0.917592 | + | 0.397524i | \(0.869870\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.1138i | 2.00995i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.00000 | −0.258603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 33.1113i | − | 1.06922i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4674 | −0.757012 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4891 | −0.434681 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.8713i | 1.05816i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.9253i | − | 1.18744i | −0.804673 | − | 0.593719i | \(-0.797659\pi\) | ||
0.804673 | − | 0.593719i | \(-0.202341\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.48913 | + | 0.644810i | −0.0478376 | + | 0.0207143i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4674 | −0.785195 | −0.392598 | − | 0.919710i | \(-0.628424\pi\) | ||||
−0.392598 | + | 0.919710i | \(0.628424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.6060 | 1.43000 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.994667i | 0.0318548i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.4612i | 1.07052i | 0.844688 | + | 0.535259i | \(0.179786\pi\) | ||||
−0.844688 | + | 0.535259i | \(0.820214\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.4891 | 1.07032 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 11.6819i | − | 0.372975i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.9783 | −1.62595 | −0.812977 | − | 0.582296i | \(-0.802154\pi\) | ||||
−0.812977 | + | 0.582296i | \(0.802154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39.7228 | −1.26567 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.37228 | −0.0755105 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.21194 | 0.0385374 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.74456 | −0.0871839 | −0.0435920 | − | 0.999049i | \(-0.513880\pi\) | ||||
−0.0435920 | + | 0.999049i | \(0.513880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.4891 | −0.428064 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.3185i | 1.37329i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.3940 | −0.424193 | −0.212097 | − | 0.977249i | \(-0.568029\pi\) | ||||
−0.212097 | + | 0.977249i | \(0.568029\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.58457i | 0.0501337i |
(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 | 912.2.k.h.607.3 | yes | 4 | |
3.2 | odd | 2 | 2736.2.k.o.2431.1 | 4 | |||
4.3 | odd | 2 | 912.2.k.g.607.4 | yes | 4 | ||
8.3 | odd | 2 | 3648.2.k.h.2431.2 | 4 | |||
8.5 | even | 2 | 3648.2.k.g.2431.1 | 4 | |||
12.11 | even | 2 | 2736.2.k.n.2431.2 | 4 | |||
19.18 | odd | 2 | 912.2.k.g.607.3 | ✓ | 4 | ||
57.56 | even | 2 | 2736.2.k.n.2431.1 | 4 | |||
76.75 | even | 2 | inner | 912.2.k.h.607.4 | yes | 4 | |
152.37 | odd | 2 | 3648.2.k.h.2431.1 | 4 | |||
152.75 | even | 2 | 3648.2.k.g.2431.2 | 4 | |||
228.227 | odd | 2 | 2736.2.k.o.2431.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.k.g.607.3 | ✓ | 4 | 19.18 | odd | 2 | ||
912.2.k.g.607.4 | yes | 4 | 4.3 | odd | 2 | ||
912.2.k.h.607.3 | yes | 4 | 1.1 | even | 1 | trivial | |
912.2.k.h.607.4 | yes | 4 | 76.75 | even | 2 | inner | |
2736.2.k.n.2431.1 | 4 | 57.56 | even | 2 | |||
2736.2.k.n.2431.2 | 4 | 12.11 | even | 2 | |||
2736.2.k.o.2431.1 | 4 | 3.2 | odd | 2 | |||
2736.2.k.o.2431.2 | 4 | 228.227 | odd | 2 | |||
3648.2.k.g.2431.1 | 4 | 8.5 | even | 2 | |||
3648.2.k.g.2431.2 | 4 | 152.75 | even | 2 | |||
3648.2.k.h.2431.1 | 4 | 152.37 | odd | 2 | |||
3648.2.k.h.2431.2 | 4 | 8.3 | odd | 2 |