Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3356224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 8x^{4} + 16x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.6 | ||
Root | \(-2.11491i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.q.4049.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.47283i | 1.42769i | 0.700303 | + | 0.713846i | \(0.253048\pi\) | ||||
−0.700303 | + | 0.713846i | \(0.746952\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.527166i | − 0.199250i | −0.995025 | − | 0.0996250i | \(-0.968236\pi\) | ||||
0.995025 | − | 0.0996250i | \(-0.0317643\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.11491 | −1.03830 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.11491 | 0.939180 | 0.469590 | − | 0.882885i | \(-0.344402\pi\) | ||||
0.469590 | + | 0.882885i | \(0.344402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.11491i | 1.14127i | 0.821204 | + | 0.570635i | \(0.193303\pi\) | ||||
−0.821204 | + | 0.570635i | \(0.806697\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.39905i | 1.06693i | 0.845823 | + | 0.533464i | \(0.179110\pi\) | ||||
−0.845823 | + | 0.533464i | \(0.820890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.70265 | 0.849446 | 0.424723 | − | 0.905323i | \(-0.360372\pi\) | ||||
0.424723 | + | 0.905323i | \(0.360372\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30359 | 0.284468 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 0.284147i | − 0.0546842i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.10170 | 1.69014 | 0.845072 | − | 0.534653i | \(-0.179558\pi\) | ||||
0.845072 | + | 0.534653i | \(0.179558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.83076 | 0.867630 | 0.433815 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433815 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.70265i | 1.34086i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.74378i | − 1.60187i | −0.598753 | − | 0.800934i | \(-0.704337\pi\) | ||||
0.598753 | − | 0.800934i | \(-0.295663\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.1755 | −1.62938 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.93246 | 1.08267 | 0.541334 | − | 0.840807i | \(-0.317919\pi\) | ||||
0.541334 | + | 0.840807i | \(0.317919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.45963i | − 0.680087i | −0.940410 | − | 0.340044i | \(-0.889558\pi\) | ||||
0.940410 | − | 0.340044i | \(-0.110442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 0.642074i | − 0.0936561i | −0.998903 | − | 0.0468280i | \(-0.985089\pi\) | ||||
0.998903 | − | 0.0468280i | \(-0.0149113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.72210 | 0.960299 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.8781 | −1.52324 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.89134i | − 0.534516i | −0.963625 | − | 0.267258i | \(-0.913882\pi\) | ||||
0.963625 | − | 0.267258i | \(-0.0861176\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.15604i | 1.21275i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.79811 | −1.14542 | −0.572708 | − | 0.819759i | \(-0.694107\pi\) | ||||
−0.572708 | + | 0.819759i | \(0.694107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.45339 | −0.442161 | −0.221080 | − | 0.975256i | \(-0.570958\pi\) | ||||
−0.221080 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.64207i | 0.206882i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.60719i | 1.05154i | 0.850628 | + | 0.525768i | \(0.176222\pi\) | ||||
−0.850628 | + | 0.525768i | \(0.823778\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.47283 | 0.297694 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3642 | 1.46736 | 0.733678 | − | 0.679497i | \(-0.237802\pi\) | ||||
0.733678 | + | 0.679497i | \(0.237802\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.81756i | − 0.680893i | −0.940264 | − | 0.340447i | \(-0.889422\pi\) | ||||
0.940264 | − | 0.340447i | \(-0.110578\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.64207i | − 0.187132i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.17548 | 0.357270 | 0.178635 | − | 0.983915i | \(-0.442832\pi\) | ||||
0.178635 | + | 0.983915i | \(0.442832\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.64207 | −0.960230 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.71585i | 0.517632i | 0.965927 | + | 0.258816i | \(0.0833323\pi\) | ||||
−0.965927 | + | 0.258816i | \(0.916668\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 22.5070i | 2.41300i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.43171 | 0.575760 | 0.287880 | − | 0.957667i | \(-0.407050\pi\) | ||||
0.287880 | + | 0.957667i | \(0.407050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.16924 | 0.227398 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.9457i | 1.23871i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.06058i | 0.412289i | 0.978522 | + | 0.206144i | \(0.0660917\pi\) | ||||
−0.978522 | + | 0.206144i | \(0.933908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.70265 | −0.975153 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.5529 | −1.54757 | −0.773784 | − | 0.633450i | \(-0.781638\pi\) | ||||
−0.773784 | + | 0.633450i | \(0.781638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9519i | 1.76885i | 0.466678 | + | 0.884427i | \(0.345451\pi\) | ||||
−0.466678 | + | 0.884427i | \(0.654549\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.2298i | 1.18230i | 0.806561 | + | 0.591150i | \(0.201326\pi\) | ||||
−0.806561 | + | 0.591150i | \(0.798674\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.10795 | −0.872383 | −0.436192 | − | 0.899854i | \(-0.643673\pi\) | ||||
−0.436192 | + | 0.899854i | \(0.643673\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0947 | 2.28697 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.1755i | − 1.23945i | −0.784821 | − | 0.619723i | \(-0.787245\pi\) | ||||
0.784821 | − | 0.619723i | \(-0.212755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 12.8176i | − 1.18498i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.31903 | 0.212585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29735 | −0.117941 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.1428i | 1.54572i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 19.5613i | − 1.73579i | −0.496750 | − | 0.867894i | \(-0.665473\pi\) | ||||
0.496750 | − | 0.867894i | \(-0.334527\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.0279 | 0.970955 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.15604 | −0.363115 | −0.181557 | − | 0.983380i | \(-0.558114\pi\) | ||||
−0.181557 | + | 0.983380i | \(0.558114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.95191i | − 0.169252i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1344i | 0.951272i | 0.879642 | + | 0.475636i | \(0.157782\pi\) | ||||
−0.879642 | + | 0.475636i | \(0.842218\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.49452 | 0.550858 | 0.275429 | − | 0.961321i | \(-0.411180\pi\) | ||||
0.275429 | + | 0.961321i | \(0.411180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.58774 | 0.133712 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.8176i | 1.07186i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.6226i | 1.37101i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.47283 | 0.448352 | 0.224176 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224176 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0954606 | −0.00776848 | −0.00388424 | − | 0.999992i | \(-0.501236\pi\) | ||||
−0.00388424 | + | 0.999992i | \(0.501236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 13.7026i | − 1.10779i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.40530i | 0.271772i | 0.990724 | + | 0.135886i | \(0.0433881\pi\) | ||||
−0.990724 | + | 0.135886i | \(0.956612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.62263 | 0.763124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.527166 | −0.0415465 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5745i | 1.45487i | 0.686177 | + | 0.727435i | \(0.259288\pi\) | ||||
−0.686177 | + | 0.727435i | \(0.740712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4596i | 0.964155i | 0.876129 | + | 0.482078i | \(0.160118\pi\) | ||||
−0.876129 | + | 0.482078i | \(0.839882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.93246 | −0.302497 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.5334 | −0.881982 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.49228i | 0.265513i | 0.991149 | + | 0.132757i | \(0.0423829\pi\) | ||||
−0.991149 | + | 0.132757i | \(0.957617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 21.7563i | − 1.63530i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.38585 | −0.477301 | −0.238650 | − | 0.971106i | \(-0.576705\pi\) | ||||
−0.238650 | + | 0.971106i | \(0.576705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8781 | −1.55186 | −0.775930 | − | 0.630819i | \(-0.782719\pi\) | ||||
−0.775930 | + | 0.630819i | \(0.782719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 8.53965i | − 0.631269i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.7026i | 1.00204i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.149793 | −0.0108958 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.83700 | −0.494708 | −0.247354 | − | 0.968925i | \(-0.579561\pi\) | ||||
−0.247354 | + | 0.968925i | \(0.579561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.10170i | 0.511192i | 0.966784 | + | 0.255596i | \(0.0822717\pi\) | ||||
−0.966784 | + | 0.255596i | \(0.917728\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 0.850207i | − 0.0605748i | −0.999541 | − | 0.0302874i | \(-0.990358\pi\) | ||||
0.999541 | − | 0.0302874i | \(-0.00964225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.56829 | −0.607390 | −0.303695 | − | 0.952769i | \(-0.598220\pi\) | ||||
−0.303695 | + | 0.952769i | \(0.598220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.2841 | −1.50127 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.79811i | − 0.336761i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.11491i | 0.216501i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.5334 | 0.797783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.63511 | 0.663309 | 0.331654 | − | 0.943401i | \(-0.392393\pi\) | ||||
0.331654 | + | 0.943401i | \(0.392393\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.5745i | 2.09493i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.54661i | − 0.172875i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.3859 | 0.972106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.1017 | −1.21765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.43171i | 0.631594i | 0.948827 | + | 0.315797i | \(0.102272\pi\) | ||||
−0.948827 | + | 0.315797i | \(0.897728\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.91774i | 0.260030i | 0.991512 | + | 0.130015i | \(0.0415025\pi\) | ||||
−0.991512 | + | 0.130015i | \(0.958497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0947 | 1.46006 | 0.730031 | − | 0.683414i | \(-0.239506\pi\) | ||||
0.730031 | + | 0.683414i | \(0.239506\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.06058 | 0.267166 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 12.5334i | − 0.821091i | −0.911840 | − | 0.410545i | \(-0.865338\pi\) | ||||
0.911840 | − | 0.410545i | \(-0.134662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.85244i | 0.510071i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4123 | 0.802882 | 0.401441 | − | 0.915885i | \(-0.368509\pi\) | ||||
0.401441 | + | 0.915885i | \(0.368509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.74378 | 0.369989 | 0.184995 | − | 0.982740i | \(-0.440773\pi\) | ||||
0.184995 | + | 0.982740i | \(0.440773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 22.2229i | − 1.42560i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.2361i | 0.969447i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6615 | −0.739019 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.33624 | −0.399940 | −0.199970 | − | 0.979802i | \(-0.564085\pi\) | ||||
−0.199970 | + | 0.979802i | \(0.564085\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.11491i | − 0.195833i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 22.2772i | − 1.38961i | −0.719197 | − | 0.694806i | \(-0.755490\pi\) | ||||
0.719197 | − | 0.694806i | \(-0.244510\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.13659 | −0.319172 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.3510 | −1.75488 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 4.66776i | − 0.287827i | −0.989590 | − | 0.143913i | \(-0.954031\pi\) | ||||
0.989590 | − | 0.143913i | \(-0.0459687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4317i | 0.822007i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.70889 | −0.591962 | −0.295981 | − | 0.955194i | \(-0.595646\pi\) | ||||
−0.295981 | + | 0.955194i | \(0.595646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.75698 | −0.410457 | −0.205229 | − | 0.978714i | \(-0.565794\pi\) | ||||
−0.205229 | + | 0.978714i | \(0.565794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.36417i | 0.324654i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 19.0194i | − 1.14277i | −0.820683 | − | 0.571384i | \(-0.806407\pi\) | ||||
0.820683 | − | 0.571384i | \(-0.193593\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.0474 | −0.900863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.8370 | −1.95889 | −0.979446 | − | 0.201708i | \(-0.935351\pi\) | ||||
−0.979446 | + | 0.201708i | \(0.935351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7827i | 0.819295i | 0.912244 | + | 0.409647i | \(0.134348\pi\) | ||||
−0.912244 | + | 0.409647i | \(0.865652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3.65456i | − 0.215722i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.35168 | −0.138334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0411 | −0.588621 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.0668i | 0.880213i | 0.897946 | + | 0.440106i | \(0.145059\pi\) | ||||
−0.897946 | + | 0.440106i | \(0.854941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 0.885092i | − 0.0513583i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.11491 | 0.237971 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.35097 | −0.135507 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 38.4596i | − 2.20945i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.91302i | 0.337474i | 0.985661 | + | 0.168737i | \(0.0539688\pi\) | ||||
−0.985661 | + | 0.168737i | \(0.946031\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −44.3921 | −2.52538 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.7911 | −1.46248 | −0.731241 | − | 0.682119i | \(-0.761058\pi\) | ||||
−0.731241 | + | 0.682119i | \(0.761058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7306i | 0.945668i | 0.881152 | + | 0.472834i | \(0.156769\pi\) | ||||
−0.881152 | + | 0.472834i | \(0.843231\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 28.1623i | − 1.58175i | −0.611977 | − | 0.790876i | \(-0.709625\pi\) | ||||
0.611977 | − | 0.790876i | \(-0.290375\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.3510 | 1.58735 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.2423 | −1.68796 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.2882i | 0.906297i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 22.5224i | − 1.24549i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.338479 | −0.0186610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.8176 | −1.41906 | −0.709531 | − | 0.704675i | \(-0.751093\pi\) | ||||
−0.709531 | + | 0.704675i | \(0.751093\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.3510i | 1.66322i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 33.5676i | − 1.82854i | −0.405103 | − | 0.914271i | \(-0.632764\pi\) | ||||
0.405103 | − | 0.914271i | \(-0.367236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 32.5808 | 1.76955 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0474 | 0.814861 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 7.23382i | − 0.390590i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 7.63984i | − 0.410128i | −0.978749 | − | 0.205064i | \(-0.934260\pi\) | ||||
0.978749 | − | 0.205064i | \(-0.0657403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.01945 | −0.161627 | −0.0808136 | − | 0.996729i | \(-0.525752\pi\) | ||||
−0.0808136 | + | 0.996729i | \(0.525752\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.16924 | 0.0624094 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 25.1840i | − 1.34041i | −0.742177 | − | 0.670203i | \(-0.766207\pi\) | ||||
0.742177 | − | 0.670203i | \(-0.233793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.73458i | 0.303506i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.32304 | 0.280939 | 0.140470 | − | 0.990085i | \(-0.455139\pi\) | ||||
0.140470 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.29039 | −0.278442 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.20813i | − 0.168383i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 8.24230i | − 0.430245i | −0.976587 | − | 0.215122i | \(-0.930985\pi\) | ||||
0.976587 | − | 0.215122i | \(-0.0690150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.5940 | −1.12414 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.05138 | −0.106502 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91774i | 0.0992970i | 0.998767 | + | 0.0496485i | \(0.0158101\pi\) | ||||
−0.998767 | + | 0.0496485i | \(0.984190\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.4527i | 1.92891i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.1692 | −1.54969 | −0.774845 | − | 0.632151i | \(-0.782172\pi\) | ||||
−0.774845 | + | 0.632151i | \(0.782172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 48.3719 | 2.47817 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.64903i | − 0.0842617i | −0.999112 | − | 0.0421309i | \(-0.986585\pi\) | ||||
0.999112 | − | 0.0421309i | \(-0.0134146\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.8913i | 0.706136i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.6414 | 0.843750 | 0.421875 | − | 0.906654i | \(-0.361372\pi\) | ||||
0.421875 | + | 0.906654i | \(0.361372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.39905 | 0.222470 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 10.2772i | − 0.518415i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 36.0257i | − 1.80808i | −0.427450 | − | 0.904039i | \(-0.640588\pi\) | ||||
0.427450 | − | 0.904039i | \(-0.359412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.82675 | 0.241640 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.62263 | −0.280781 | −0.140390 | − | 0.990096i | \(-0.544836\pi\) | ||||
−0.140390 | + | 0.990096i | \(0.544836\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.8781i | 0.990200i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 30.3510i | − 1.50444i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.76546 | 0.136743 | 0.0683716 | − | 0.997660i | \(-0.478220\pi\) | ||||
0.0683716 | + | 0.997660i | \(0.478220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.5334 | −1.35812 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.63807i | 0.228224i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.0599i | 0.786455i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.5962 | 0.859632 | 0.429816 | − | 0.902917i | \(-0.358579\pi\) | ||||
0.429816 | + | 0.902917i | \(0.358579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.5676 | 1.24609 | 0.623044 | − | 0.782187i | \(-0.285896\pi\) | ||||
0.623044 | + | 0.782187i | \(0.285896\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.00000i | 0.0972433i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.82051i | 0.0881006i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.6957 | −1.53028 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.9736 | 0.865757 | 0.432879 | − | 0.901452i | \(-0.357498\pi\) | ||||
0.432879 | + | 0.901452i | \(0.357498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.0382i | 1.77994i | 0.456018 | + | 0.889971i | \(0.349275\pi\) | ||||
−0.456018 | + | 0.889971i | \(0.650725\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.70265i | − 0.177122i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.8168 | −1.85263 | −0.926313 | − | 0.376754i | \(-0.877040\pi\) | ||||
−0.926313 | + | 0.376754i | \(0.877040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.9387 | −0.997081 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3726i | 1.20549i | 0.797934 | + | 0.602745i | \(0.205927\pi\) | ||||
−0.797934 | + | 0.602745i | \(0.794073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.5334i | 0.640108i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.4589 | −1.57902 | −0.789512 | − | 0.613735i | \(-0.789666\pi\) | ||||
−0.789512 | + | 0.613735i | \(0.789666\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.5940 | 1.01682 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 0.236058i | − 0.0110910i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5264i | 1.28763i | 0.765180 | + | 0.643816i | \(0.222650\pi\) | ||||
−0.765180 | + | 0.643816i | \(0.777350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.24998 | 0.0583440 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.3161 | 1.69141 | 0.845704 | − | 0.533652i | \(-0.179181\pi\) | ||||
0.845704 | + | 0.533652i | \(0.179181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 22.5544i | − 1.04819i | −0.851660 | − | 0.524095i | \(-0.824404\pi\) | ||||
0.851660 | − | 0.524095i | \(-0.175596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 22.8370i | − 1.05677i | −0.849005 | − | 0.528385i | \(-0.822798\pi\) | ||||
0.849005 | − | 0.528385i | \(-0.177202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.53742 | 0.209518 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.42074 | −0.388007 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 13.8913i | − 0.638724i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.1212i | 0.554989i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.5264 | 1.62324 | 0.811622 | − | 0.584182i | \(-0.198585\pi\) | ||||
0.811622 | + | 0.584182i | \(0.198585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.0947 | 1.82816 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.30359i | − 0.0593156i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4945i | 0.475552i | 0.971320 | + | 0.237776i | \(0.0764184\pi\) | ||||
−0.971320 | + | 0.237776i | \(0.923582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −45.9317 | −2.07711 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.1685 | 1.90304 | 0.951519 | − | 0.307589i | \(-0.0995221\pi\) | ||||
0.951519 | + | 0.307589i | \(0.0995221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.0389i | 1.80326i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6.51797i | − 0.292371i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.1560 | −1.34997 | −0.674985 | − | 0.737832i | \(-0.735850\pi\) | ||||
−0.674985 | + | 0.737832i | \(0.735850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.8106 | −1.37652 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.9729i | 1.02431i | 0.858893 | + | 0.512155i | \(0.171153\pi\) | ||||
−0.858893 | + | 0.512155i | \(0.828847\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.72433i | − 0.431873i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.8176 | −0.523804 | −0.261902 | − | 0.965094i | \(-0.584350\pi\) | ||||
−0.261902 | + | 0.965094i | \(0.584350\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.06682 | −0.135668 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1.05210i | − 0.0464512i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.00000i | − 0.0879599i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.63583 | −0.379071 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.7438 | −1.56596 | −0.782982 | − | 0.622045i | \(-0.786302\pi\) | ||||
−0.782982 | + | 0.622045i | \(0.786302\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3899i | 0.629225i | 0.949220 | + | 0.314612i | \(0.101875\pi\) | ||||
−0.949220 | + | 0.314612i | \(0.898125\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.2508i | 0.925698i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.4053 | 1.18929 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.5264i | 1.23562i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 15.7911i | − 0.681438i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.9387 | 0.901894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5209 | 0.624303 | 0.312152 | − | 0.950032i | \(-0.398950\pi\) | ||||
0.312152 | + | 0.950032i | \(0.398950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 51.6282i | − 2.21558i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 19.6289i | − 0.839270i | −0.907693 | − | 0.419635i | \(-0.862158\pi\) | ||||
0.907693 | − | 0.419635i | \(-0.137842\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.7570 | 0.459097 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.7004 | 1.43569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.67401i | − 0.0711860i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.13659i | − 0.0481588i | −0.999710 | − | 0.0240794i | \(-0.992335\pi\) | ||||
0.999710 | − | 0.0240794i | \(-0.00766546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.3510 | 0.776163 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.8844 | −1.43060 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.8913i | 1.09119i | 0.838049 | + | 0.545595i | \(0.183696\pi\) | ||||
−0.838049 | + | 0.545595i | \(0.816304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.55581i | 0.191326i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.0558 | 1.84692 | 0.923459 | − | 0.383698i | \(-0.125350\pi\) | ||||
0.923459 | + | 0.383698i | \(0.125350\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.8991 | −1.75342 | −0.876711 | − | 0.481017i | \(-0.840268\pi\) | ||||
−0.876711 | + | 0.481017i | \(0.840268\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 16.9068i | − 0.706291i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1.34544i | − 0.0560114i | −0.999608 | − | 0.0280057i | \(-0.991084\pi\) | ||||
0.999608 | − | 0.0280057i | \(-0.00891566\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.5613 | −0.729824 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.48604 | 0.103138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 12.1212i | − 0.502007i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 25.0411i | − 1.03356i | −0.856119 | − | 0.516779i | \(-0.827131\pi\) | ||||
0.856119 | − | 0.516779i | \(-0.172869\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8866 | 0.737005 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.10242 | 0.0864821 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 22.5947i | − 0.927853i | −0.885874 | − | 0.463927i | \(-0.846440\pi\) | ||||
0.885874 | − | 0.463927i | \(-0.153560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 21.1880i | − 0.867166i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.7111 | −0.601080 | −0.300540 | − | 0.953769i | \(-0.597167\pi\) | ||||
−0.300540 | + | 0.953769i | \(0.597167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2904 | 0.786871 | 0.393436 | − | 0.919352i | \(-0.371286\pi\) | ||||
0.393436 | + | 0.919352i | \(0.371286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 26.8106i | − 1.09181i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.7547i | 0.842409i | 0.906966 | + | 0.421205i | \(0.138393\pi\) | ||||
−0.906966 | + | 0.421205i | \(0.861607\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.8649 | 0.480791 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.64207 | 0.106887 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 43.3091i | − 1.74924i | −0.484810 | − | 0.874619i | \(-0.661111\pi\) | ||||
0.484810 | − | 0.874619i | \(-0.338889\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 13.5621i | − 0.545988i | −0.962016 | − | 0.272994i | \(-0.911986\pi\) | ||||
0.962016 | − | 0.272994i | \(-0.0880139\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.9045 | 0.518677 | 0.259339 | − | 0.965786i | \(-0.416495\pi\) | ||||
0.259339 | + | 0.965786i | \(0.416495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.284147 | −0.0114024 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.86341i | − 0.114720i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28.5202i | 1.13899i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.8634 | 1.70908 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.0404 | 1.79303 | 0.896515 | − | 0.443013i | \(-0.146090\pi\) | ||||
0.896515 | + | 0.443013i | \(0.146090\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.8260i | 0.947000i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.6608i | 1.09596i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.5132 | −1.52356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.08074 | −0.121682 | −0.0608410 | − | 0.998147i | \(-0.519378\pi\) | ||||
−0.0608410 | + | 0.998147i | \(0.519378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.52493i | 0.178446i | 0.996012 | + | 0.0892229i | \(0.0284384\pi\) | ||||
−0.996012 | + | 0.0892229i | \(0.971562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 34.8719i | − 1.37096i | −0.728094 | − | 0.685478i | \(-0.759593\pi\) | ||||
0.728094 | − | 0.685478i | \(-0.240407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.4053 | −1.07575 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.29735 | 0.246813 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 35.3726i | − 1.38424i | −0.721783 | − | 0.692119i | \(-0.756677\pi\) | ||||
0.721783 | − | 0.692119i | \(-0.243323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.1212i | 0.706973i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.10866 | 0.0821419 | 0.0410710 | − | 0.999156i | \(-0.486923\pi\) | ||||
0.0410710 | + | 0.999156i | \(0.486923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0342 | 0.779239 | 0.389619 | − | 0.920976i | \(-0.372607\pi\) | ||||
0.389619 | + | 0.920976i | \(0.372607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 44.7625i | − 1.73843i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.10170i | − 0.352419i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.3230 | −0.901721 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.7570 | −0.415269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 5.07530i | − 0.195638i | −0.995204 | − | 0.0978191i | \(-0.968813\pi\) | ||||
0.995204 | − | 0.0978191i | \(-0.0311867\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.4876i | 0.518369i | 0.965828 | + | 0.259184i | \(0.0834537\pi\) | ||||
−0.965828 | + | 0.259184i | \(0.916546\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.14060 | 0.0821486 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.68793 | −0.371242 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.4379i | 0.973356i | 0.873581 | + | 0.486678i | \(0.161792\pi\) | ||||
−0.873581 | + | 0.486678i | \(0.838208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 54.6366i | 2.08452i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.0125 | 0.610027 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6506 | 0.861668 | 0.430834 | − | 0.902431i | \(-0.358220\pi\) | ||||
0.430834 | + | 0.902431i | \(0.358220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.11491i | 0.194299i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.4963i | 1.15513i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.9930 | 1.17226 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.8099 | −1.57914 | −0.789569 | − | 0.613662i | \(-0.789696\pi\) | ||||
−0.789569 | + | 0.613662i | \(0.789696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 36.0778i | − 1.36070i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.19894i | 0.308353i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.87117 | −0.107829 | −0.0539146 | − | 0.998546i | \(-0.517170\pi\) | ||||
−0.0539146 | + | 0.998546i | \(0.517170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.89134 | −0.370954 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.83076i | − 0.180913i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.6935i | 1.14627i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.1623 | 1.87074 | 0.935369 | − | 0.353674i | \(-0.115068\pi\) | ||||
0.935369 | + | 0.353674i | \(0.115068\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.46364 | 0.352444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.2034i | 0.528230i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.8198i | 0.994691i | 0.867553 | + | 0.497345i | \(0.165692\pi\) | ||||
−0.867553 | + | 0.497345i | \(0.834308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0272 | 1.07508 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.6182 | 0.725604 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9861i | 1.32918i | 0.747210 | + | 0.664588i | \(0.231393\pi\) | ||||
−0.747210 | + | 0.664588i | \(0.768607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8106i | 0.987581i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.84396 | −0.214974 | −0.107487 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107487 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.6762 | −1.38407 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2012i | 0.520991i | 0.965475 | + | 0.260495i | \(0.0838858\pi\) | ||||
−0.965475 | + | 0.260495i | \(0.916114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 14.6894i | − 0.537459i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.44714 | 0.235574 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.0404 | 1.20566 | 0.602831 | − | 0.797869i | \(-0.294039\pi\) | ||||
0.602831 | + | 0.797869i | \(0.294039\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 15.6685i | − 0.570991i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 18.2034i | − 0.661614i | −0.943698 | − | 0.330807i | \(-0.892679\pi\) | ||||
0.943698 | − | 0.330807i | \(-0.107321\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.70265 | 0.279588 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.1010 | 1.23616 | 0.618080 | − | 0.786115i | \(-0.287911\pi\) | ||||
0.618080 | + | 0.786115i | \(0.287911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.80140i | 0.173822i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 36.2034i | − 1.30723i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.1366 | −1.26706 | −0.633529 | − | 0.773719i | \(-0.718394\pi\) | ||||
−0.633529 | + | 0.773719i | \(0.718394\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.0878 | 1.98394 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.13659i | 0.0408803i | 0.999791 | + | 0.0204401i | \(0.00650675\pi\) | ||||
−0.999791 | + | 0.0204401i | \(0.993493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 12.7019i | − 0.455679i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.6685 | 0.919669 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.5132 | 1.37811 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.58622i | − 0.0924241i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.33848i | 0.297235i | 0.988895 | + | 0.148617i | \(0.0474823\pi\) | ||||
−0.988895 | + | 0.148617i | \(0.952518\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.5426 | 0.410928 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.94567 | −0.246960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 14.2104i | − 0.504625i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.190921i | 0.00676278i | 0.999994 | + | 0.00338139i | \(0.00107633\pi\) | ||||
−0.999994 | + | 0.00338139i | \(0.998924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.82452 | 0.0999242 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.9193 | −0.597813 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 18.1212i | − 0.639482i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 24.0085i | − 0.845138i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5202 | 0.510503 | 0.255252 | − | 0.966875i | \(-0.417842\pi\) | ||||
0.255252 | + | 0.966875i | \(0.417842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.5474 | −1.81007 | −0.905037 | − | 0.425332i | \(-0.860157\pi\) | ||||
−0.905037 | + | 0.425332i | \(0.860157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 16.7089i | − 0.586006i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 16.5124i | − 0.577697i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.75698 | −0.236108 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7827 | 0.481019 | 0.240509 | − | 0.970647i | \(-0.422686\pi\) | ||||
0.240509 | + | 0.970647i | \(0.422686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 37.1531i | − 1.29508i | −0.762034 | − | 0.647538i | \(-0.775799\pi\) | ||||
0.762034 | − | 0.647538i | \(-0.224201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.8510i | 1.38576i | 0.721055 | + | 0.692878i | \(0.243657\pi\) | ||||
−0.721055 | + | 0.692878i | \(0.756343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5933 | −0.715234 | −0.357617 | − | 0.933868i | \(-0.616411\pi\) | ||||
−0.357617 | + | 0.933868i | \(0.616411\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 47.0319 | 1.63152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.5709i | 1.02457i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.37265i | − 0.0474456i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.5669 | 1.26243 | 0.631214 | − | 0.775609i | \(-0.282557\pi\) | ||||
0.631214 | + | 0.775609i | \(0.282557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.8410 | 1.85659 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 81.2005i | − 2.79669i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.683919i | 0.0234998i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.0823 | −1.16970 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.74378 | −0.334012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 19.3208i | − 0.661532i | −0.943713 | − | 0.330766i | \(-0.892693\pi\) | ||||
0.943713 | − | 0.330766i | \(-0.107307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 54.6017i | − 1.86516i | −0.360963 | − | 0.932580i | \(-0.617552\pi\) | ||||
0.360963 | − | 0.932580i | \(-0.382448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.9541 | 1.12438 | 0.562190 | − | 0.827008i | \(-0.309959\pi\) | ||||
0.562190 | + | 0.827008i | \(0.309959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.03712 | 0.307984 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 54.6840i | − 1.86147i | −0.365701 | − | 0.930733i | \(-0.619171\pi\) | ||||
0.365701 | − | 0.930733i | \(-0.380829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 5.81532i | − 0.197499i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.89134 | 0.335541 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.4178 | −1.20009 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 12.6483i | − 0.428081i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 16.7500i | − 0.565608i | −0.959178 | − | 0.282804i | \(-0.908735\pi\) | ||||
0.959178 | − | 0.282804i | \(-0.0912646\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.2577 | −1.25667 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.7049 | −1.06816 | −0.534082 | − | 0.845432i | \(-0.679343\pi\) | ||||
−0.534082 | + | 0.845432i | \(0.679343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.9185i | 1.74720i | 0.486646 | + | 0.873599i | \(0.338220\pi\) | ||||
−0.486646 | + | 0.873599i | \(0.661780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 36.2897i | − 1.21849i | −0.792983 | − | 0.609244i | \(-0.791473\pi\) | ||||
0.792983 | − | 0.609244i | \(-0.208527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3121 | −0.345856 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.9193 | −0.901829 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.37737i | − 0.0795558i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.1755i | 0.339749i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.9681 | 1.46642 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.1182 | 0.570290 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 5.81355i | − 0.193463i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.4442i | 0.844861i | 0.906395 | + | 0.422430i | \(0.138823\pi\) | ||||
−0.906395 | + | 0.422430i | \(0.861177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.4457 | 1.60684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.9597 | 1.58897 | 0.794487 | − | 0.607281i | \(-0.207740\pi\) | ||||
0.794487 | + | 0.607281i | \(0.207740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6894i | 0.486150i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.19092i | 0.0723506i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.78562 | −0.0918892 | −0.0459446 | − | 0.998944i | \(-0.514630\pi\) | ||||
−0.0459446 | + | 0.998944i | \(0.514630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.6219 | −0.481808 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.8774i | 1.67465i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 55.9185i | − 1.83661i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.2508 | −1.32059 | −0.660293 | − | 0.751008i | \(-0.729568\pi\) | ||||
−0.660293 | + | 0.751008i | \(0.729568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.8896 | 0.815722 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 63.7772i | − 2.08797i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.9868i | 1.27364i | 0.771011 | + | 0.636822i | \(0.219751\pi\) | ||||
−0.771011 | + | 0.636822i | \(0.780249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.3719 | −1.35012 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.3682 | 1.25077 | 0.625383 | − | 0.780318i | \(-0.284943\pi\) | ||||
0.625383 | + | 0.780318i | \(0.284943\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.93246i | − 0.225752i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 15.0217i | − 0.488139i | −0.969758 | − | 0.244070i | \(-0.921517\pi\) | ||||
0.969758 | − | 0.244070i | \(-0.0784825\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.9387 | 0.777083 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 69.6406 | 2.25825 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 12.1303i | − 0.392940i | −0.980510 | − | 0.196470i | \(-0.937052\pi\) | ||||
0.980510 | − | 0.196470i | \(-0.0629479\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 70.1072i | 2.26624i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.86965 | 0.189541 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.66376 | −0.247218 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 38.0947i | − 1.22759i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 21.2882i | − 0.684581i | −0.939594 | − | 0.342290i | \(-0.888797\pi\) | ||||
0.939594 | − | 0.342290i | \(-0.111203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.2779 | −1.29391 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.4006 | 0.365862 | 0.182931 | − | 0.983126i | \(-0.441442\pi\) | ||||
0.182931 | + | 0.983126i | \(0.441442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.42369i | − 0.109758i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 41.2849i | − 1.32082i | −0.750904 | − | 0.660411i | \(-0.770382\pi\) | ||||
0.750904 | − | 0.660411i | \(-0.229618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9193 | 0.540742 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.3704 | 0.905798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 42.8448i | − 1.36654i | −0.730168 | − | 0.683268i | \(-0.760558\pi\) | ||||
0.730168 | − | 0.683268i | \(-0.239442\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 0.837003i | − 0.0266421i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.45963 | −0.141808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.73307 | 0.277415 | 0.138707 | − | 0.990333i | \(-0.455705\pi\) | ||||
0.138707 | + | 0.990333i | \(0.455705\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 63.8425i | − 2.02598i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0808i | 1.39605i | 0.716072 | + | 0.698027i | \(0.245938\pi\) | ||||
−0.716072 | + | 0.698027i | \(0.754062\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.76867 | −0.0875968 |
(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 | 4600.2.e.q.4049.6 | 6 | ||
5.2 | odd | 4 | 920.2.a.i.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 4600.2.a.v.1.1 | 3 | |||
5.4 | even | 2 | inner | 4600.2.e.q.4049.1 | 6 | ||
15.2 | even | 4 | 8280.2.a.bl.1.1 | 3 | |||
20.3 | even | 4 | 9200.2.a.ci.1.3 | 3 | |||
20.7 | even | 4 | 1840.2.a.q.1.1 | 3 | |||
40.27 | even | 4 | 7360.2.a.cf.1.3 | 3 | |||
40.37 | odd | 4 | 7360.2.a.bw.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.i.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
1840.2.a.q.1.1 | 3 | 20.7 | even | 4 | |||
4600.2.a.v.1.1 | 3 | 5.3 | odd | 4 | |||
4600.2.e.q.4049.1 | 6 | 5.4 | even | 2 | inner | ||
4600.2.e.q.4049.6 | 6 | 1.1 | even | 1 | trivial | ||
7360.2.a.bw.1.1 | 3 | 40.37 | odd | 4 | |||
7360.2.a.cf.1.3 | 3 | 40.27 | even | 4 | |||
8280.2.a.bl.1.1 | 3 | 15.2 | even | 4 | |||
9200.2.a.ci.1.3 | 3 | 20.3 | even | 4 |