Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(127,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.d (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: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1997017344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 53x^{4} + 56x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(-1.27733i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.127 |
Dual form | 448.3.d.e.127.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.55467i | − 0.851556i | −0.904828 | − | 0.425778i | \(-0.860000\pi\) | ||||
0.904828 | − | 0.425778i | \(-0.140000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.86836 | −1.97367 | −0.986836 | − | 0.161727i | \(-0.948294\pi\) | ||||
−0.986836 | + | 0.161727i | \(0.948294\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.47367 | 0.274852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.1537i | 1.19579i | 0.801574 | + | 0.597896i | \(0.203996\pi\) | ||||
−0.801574 | + | 0.597896i | \(0.796004\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.86836 | 0.451412 | 0.225706 | − | 0.974195i | \(-0.427531\pi\) | ||||
0.225706 | + | 0.974195i | \(0.427531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.2104i | 1.68069i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.570700 | −0.0335706 | −0.0167853 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167853 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 15.6640i | − 0.824421i | −0.911089 | − | 0.412211i | \(-0.864757\pi\) | ||||
0.911089 | − | 0.412211i | \(-0.135243\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.75902 | 0.321858 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 16.4817i | − 0.716596i | −0.933607 | − | 0.358298i | \(-0.883357\pi\) | ||||
0.933607 | − | 0.358298i | \(-0.116643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 72.3844 | 2.89538 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 29.3114i | − 1.08561i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.7367 | 1.02540 | 0.512702 | − | 0.858567i | \(-0.328645\pi\) | ||||
0.512702 | + | 0.858567i | \(0.328645\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 54.8014i | 1.76779i | 0.467687 | + | 0.883894i | \(0.345087\pi\) | ||||
−0.467687 | + | 0.883894i | \(0.654913\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 33.6034 | 1.01828 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 26.1092i | − 0.745978i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 42.0853 | 1.13744 | 0.568721 | − | 0.822531i | \(-0.307439\pi\) | ||||
0.568721 | + | 0.822531i | \(0.307439\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 14.9917i | − 0.384403i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.773275 | 0.0188604 | 0.00943019 | − | 0.999956i | \(-0.496998\pi\) | ||||
0.00943019 | + | 0.999956i | \(0.496998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.7931i | 0.971933i | 0.873977 | + | 0.485967i | \(0.161532\pi\) | ||||
−0.873977 | + | 0.485967i | \(0.838468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −24.4110 | −0.542467 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 58.4528i | − 1.24368i | −0.783145 | − | 0.621839i | \(-0.786386\pi\) | ||||
0.783145 | − | 0.621839i | \(-0.213614\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.45795i | 0.0285873i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.65139 | −0.106630 | −0.0533150 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533150 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 129.805i | − 2.36010i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −40.0163 | −0.702041 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 42.6434i | 0.722770i | 0.932417 | + | 0.361385i | \(0.117696\pi\) | ||||
−0.932417 | + | 0.361385i | \(0.882304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 95.9371 | 1.57274 | 0.786370 | − | 0.617756i | \(-0.211958\pi\) | ||||
0.786370 | + | 0.617756i | \(0.211958\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.54471i | 0.103884i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −57.9110 | −0.890939 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69.8503i | 1.04254i | 0.853391 | + | 0.521271i | \(0.174542\pi\) | ||||
−0.853391 | + | 0.521271i | \(0.825458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −42.1053 | −0.610222 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 92.0882i | 1.29702i | 0.761207 | + | 0.648509i | \(0.224607\pi\) | ||||
−0.761207 | + | 0.648509i | \(0.775393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.97539 | 0.136649 | 0.0683246 | − | 0.997663i | \(-0.478235\pi\) | ||||
0.0683246 | + | 0.997663i | \(0.478235\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 184.918i | − 2.46558i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −34.8014 | −0.451967 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 20.1780i | 0.255417i | 0.991812 | + | 0.127709i | \(0.0407622\pi\) | ||||
−0.991812 | + | 0.127709i | \(0.959238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −52.6180 | −0.649604 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 151.307i | 1.82298i | 0.411321 | + | 0.911491i | \(0.365068\pi\) | ||||
−0.411321 | + | 0.911491i | \(0.634932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.63187 | 0.0662573 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 75.9674i | − 0.873189i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.79743 | 0.0651396 | 0.0325698 | − | 0.999469i | \(-0.489631\pi\) | ||||
0.0325698 | + | 0.999469i | \(0.489631\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.5262i | 0.170618i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 140.000 | 1.50537 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 154.578i | 1.62714i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 103.696 | 1.06903 | 0.534513 | − | 0.845160i | \(-0.320495\pi\) | ||||
0.534513 | + | 0.845160i | \(0.320495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 32.5379i | 0.328666i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −41.9176 | −0.415025 | −0.207513 | − | 0.978232i | \(-0.566537\pi\) | ||||
−0.207513 | + | 0.978232i | \(0.566537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 18.7378i | − 0.181920i | −0.995855 | − | 0.0909602i | \(-0.971006\pi\) | ||||
0.995855 | − | 0.0909602i | \(-0.0289936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −66.7004 | −0.635242 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 64.8549i | − 0.606121i | −0.952971 | − | 0.303060i | \(-0.901992\pi\) | ||||
0.952971 | − | 0.303060i | \(-0.0980084\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 186.432 | 1.71039 | 0.855195 | − | 0.518307i | \(-0.173437\pi\) | ||||
0.855195 | + | 0.518307i | \(0.173437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 107.514i | − 0.968595i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −84.7530 | −0.750027 | −0.375013 | − | 0.927019i | \(-0.622362\pi\) | ||||
−0.375013 | + | 0.927019i | \(0.622362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 162.647i | 1.41433i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.5164 | 0.124071 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 1.50993i | − 0.0126885i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −52.0200 | −0.429917 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.97546i | − 0.0160607i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −467.606 | −3.74085 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 93.3874i | − 0.735334i | −0.929958 | − | 0.367667i | \(-0.880157\pi\) | ||||
0.929958 | − | 0.367667i | \(-0.119843\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 106.768 | 0.827656 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 58.0857i | − 0.443403i | −0.975115 | − | 0.221701i | \(-0.928839\pi\) | ||||
0.975115 | − | 0.221701i | \(-0.0711610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.4431 | 0.311602 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 289.256i | 2.14263i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 176.420 | 1.28774 | 0.643870 | − | 0.765135i | \(-0.277328\pi\) | ||||
0.643870 | + | 0.765135i | \(0.277328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 12.3041i | − 0.0885185i | −0.999020 | − | 0.0442592i | \(-0.985907\pi\) | ||||
0.999020 | − | 0.0442592i | \(-0.0140928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −149.328 | −1.05906 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 77.1906i | 0.539795i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −293.452 | −2.02381 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.8827i | 0.121651i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −173.782 | −1.16632 | −0.583160 | − | 0.812358i | \(-0.698184\pi\) | ||||
−0.583160 | + | 0.812358i | \(0.698184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 138.433i | − 0.916776i | −0.888752 | − | 0.458388i | \(-0.848427\pi\) | ||||
0.888752 | − | 0.458388i | \(-0.151573\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.41172 | −0.00922695 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 540.800i | − 3.48903i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −189.693 | −1.20824 | −0.604119 | − | 0.796894i | \(-0.706475\pi\) | ||||
−0.604119 | + | 0.796894i | \(0.706475\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.4374i | 0.0908014i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 43.6065 | 0.270848 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 17.7685i | − 0.109009i | −0.998514 | − | 0.0545047i | \(-0.982642\pi\) | ||||
0.998514 | − | 0.0545047i | \(-0.0173580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −331.610 | −2.00976 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 0.0890922i | 0 0.000533486i | −1.00000 | 0.000266743i | \(-0.999915\pi\) | |||||
1.00000 | 0.000266743i | \(-8.49069e-5\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −134.562 | −0.796227 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 38.7475i | − 0.226594i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −43.2891 | −0.250226 | −0.125113 | − | 0.992143i | \(-0.539929\pi\) | ||||
−0.125113 | + | 0.992143i | \(0.539929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 191.511i | 1.09435i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 108.940 | 0.615479 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 190.838i | 1.06614i | 0.846072 | + | 0.533068i | \(0.178961\pi\) | ||||
−0.846072 | + | 0.533068i | \(0.821039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 207.153 | 1.14449 | 0.572246 | − | 0.820082i | \(-0.306072\pi\) | ||||
0.572246 | + | 0.820082i | \(0.306072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 245.087i | − 1.33928i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −415.313 | −2.24493 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 7.50683i | − 0.0401434i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 77.5507 | 0.410321 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 315.489i | 1.65178i | 0.563833 | + | 0.825889i | \(0.309326\pi\) | ||||
−0.563833 | + | 0.825889i | \(0.690674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −30.9403 | −0.160312 | −0.0801561 | − | 0.996782i | \(-0.525542\pi\) | ||||
−0.0801561 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 147.943i | 0.758684i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 264.248 | 1.34136 | 0.670681 | − | 0.741746i | \(-0.266002\pi\) | ||||
0.670681 | + | 0.741746i | \(0.266002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 131.321i | − 0.659903i | −0.943998 | − | 0.329951i | \(-0.892968\pi\) | ||||
0.943998 | − | 0.329951i | \(-0.107032\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 178.444 | 0.887783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 78.6759i | 0.387566i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.63095 | −0.0372242 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 40.7703i | − 0.196958i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 206.040 | 0.985836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 247.994i | − 1.17533i | −0.809105 | − | 0.587664i | \(-0.800048\pi\) | ||||
0.809105 | − | 0.587664i | \(-0.199952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 235.255 | 1.10448 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 412.430i | − 1.91828i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −144.991 | −0.668161 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 25.4838i | − 0.116364i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.34907 | −0.0151542 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 56.7999i | 0.254708i | 0.991857 | + | 0.127354i | \(0.0406484\pi\) | ||||
−0.991857 | + | 0.127354i | \(0.959352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 179.055 | 0.795800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 275.095i | − 1.21187i | −0.795513 | − | 0.605937i | \(-0.792798\pi\) | ||||
0.795513 | − | 0.605937i | \(-0.207202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.29210 | −0.0274764 | −0.0137382 | − | 0.999906i | \(-0.504373\pi\) | ||||
−0.0137382 | + | 0.999906i | \(0.504373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 88.9061i | 0.384875i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −142.049 | −0.609653 | −0.304827 | − | 0.952408i | \(-0.598599\pi\) | ||||
−0.304827 | + | 0.952408i | \(0.598599\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 576.833i | 2.45461i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 51.5480 | 0.217502 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 51.3954i | 0.215043i | 0.994203 | + | 0.107522i | \(0.0342915\pi\) | ||||
−0.994203 | + | 0.107522i | \(0.965708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 93.7048 | 0.388817 | 0.194408 | − | 0.980921i | \(-0.437721\pi\) | ||||
0.194408 | + | 0.980921i | \(0.437721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 129.381i | − 0.532433i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 69.0785 | 0.281953 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 91.9220i | − 0.372154i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 386.540 | 1.55237 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 12.4430i | − 0.0495737i | −0.999693 | − | 0.0247869i | \(-0.992109\pi\) | ||||
0.999693 | − | 0.0247869i | \(-0.00789071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 216.796 | 0.856900 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 14.3876i | − 0.0564219i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 169.884 | 0.661029 | 0.330514 | − | 0.943801i | \(-0.392778\pi\) | ||||
0.330514 | + | 0.943801i | \(0.392778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 111.347i | 0.429912i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 73.5587 | 0.281834 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 118.762i | − 0.451565i | −0.974178 | − | 0.225782i | \(-0.927506\pi\) | ||||
0.974178 | − | 0.225782i | \(-0.0724938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 55.7699 | 0.210452 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 14.8105i | − 0.0554700i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.37496 | 0.0348512 | 0.0174256 | − | 0.999848i | \(-0.494453\pi\) | ||||
0.0174256 | + | 0.999848i | \(0.494453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 203.067i | 0.749324i | 0.927161 | + | 0.374662i | \(0.122241\pi\) | ||||
−0.927161 | + | 0.374662i | \(0.877759\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.6643 | 0.145291 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 952.124i | 3.46227i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −154.419 | −0.557471 | −0.278735 | − | 0.960368i | \(-0.589915\pi\) | ||||
−0.278735 | + | 0.960368i | \(0.589915\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 135.561i | 0.485880i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −217.495 | −0.774005 | −0.387002 | − | 0.922079i | \(-0.626489\pi\) | ||||
−0.387002 | + | 0.922079i | \(0.626489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 431.849i | 1.52597i | 0.646418 | + | 0.762983i | \(0.276266\pi\) | ||||
−0.646418 | + | 0.762983i | \(0.723734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 394.896 | 1.38560 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.04589i | 0.00712855i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.674 | −0.998873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 264.908i | − 0.910336i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 212.019 | 0.723616 | 0.361808 | − | 0.932253i | \(-0.382160\pi\) | ||||
0.361808 | + | 0.932253i | \(0.382160\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 420.820i | − 1.42651i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 385.554 | 1.29816 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 96.7206i | − 0.323480i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −110.574 | −0.367356 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 107.086i | 0.353418i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −946.741 | −3.10407 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 192.868i | − 0.628234i | −0.949384 | − | 0.314117i | \(-0.898292\pi\) | ||||
0.949384 | − | 0.314117i | \(-0.101708\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −47.8689 | −0.154915 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 269.814i | 0.867569i | 0.901017 | + | 0.433785i | \(0.142822\pi\) | ||||
−0.901017 | + | 0.433785i | \(0.857178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −236.490 | −0.755558 | −0.377779 | − | 0.925896i | \(-0.623312\pi\) | ||||
−0.377779 | + | 0.925896i | \(0.623312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 64.5855i | − 0.205033i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 249.012 | 0.785526 | 0.392763 | − | 0.919640i | \(-0.371519\pi\) | ||||
0.392763 | + | 0.919640i | \(0.371519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 391.148i | 1.22617i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −165.683 | −0.516146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.93945i | 0.0276763i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 424.778 | 1.30701 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 476.273i | − 1.45649i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 154.652 | 0.470066 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 465.343i | − 1.40587i | −0.711254 | − | 0.702935i | \(-0.751872\pi\) | ||||
0.711254 | − | 0.702935i | \(-0.248128\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 104.105 | 0.312628 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 689.308i | − 2.05763i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 626.243 | 1.85829 | 0.929144 | − | 0.369718i | \(-0.120546\pi\) | ||||
0.929144 | + | 0.369718i | \(0.120546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 216.516i | 0.638690i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −720.842 | −2.11391 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 415.510 | 1.20438 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 450.576i | − 1.29849i | −0.760580 | − | 0.649245i | \(-0.775085\pi\) | ||||
0.760580 | − | 0.649245i | \(-0.224915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 64.7762 | 0.185605 | 0.0928025 | − | 0.995685i | \(-0.470417\pi\) | ||||
0.0928025 | + | 0.995685i | \(0.470417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 172.010i | − 0.490057i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 589.179 | 1.66906 | 0.834532 | − | 0.550960i | \(-0.185738\pi\) | ||||
0.834532 | + | 0.550960i | \(0.185738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 908.760i | − 2.55989i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.85737 | −0.0108050 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 406.643i | 1.13271i | 0.824161 | + | 0.566355i | \(0.191647\pi\) | ||||
−0.824161 | + | 0.566355i | \(0.808353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 115.639 | 0.320329 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 132.894i | 0.366099i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −98.4407 | −0.269701 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 430.196i | 1.17220i | 0.810240 | + | 0.586098i | \(0.199337\pi\) | ||||
−0.810240 | + | 0.586098i | \(0.800663\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.91283 | 0.00518381 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 14.9522i | − 0.0403023i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.60758 | −0.00699083 | −0.00349542 | − | 0.999994i | \(-0.501113\pi\) | ||||
−0.00349542 | + | 0.999994i | \(0.501113\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1194.58i | 3.18555i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 174.506 | 0.462880 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 359.118i | 0.947541i | 0.880648 | + | 0.473771i | \(0.157107\pi\) | ||||
−0.880648 | + | 0.473771i | \(0.842893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −238.574 | −0.626178 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 470.758i | − 1.22913i | −0.788865 | − | 0.614567i | \(-0.789331\pi\) | ||||
0.788865 | − | 0.614567i | \(-0.210669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 343.433 | 0.892034 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 103.382i | 0.267138i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 180.270 | 0.463418 | 0.231709 | − | 0.972785i | \(-0.425568\pi\) | ||||
0.231709 | + | 0.972785i | \(0.425568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.40612i | 0.0240566i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −148.390 | −0.377582 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 199.123i | − 0.504110i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 248.223 | 0.625248 | 0.312624 | − | 0.949877i | \(-0.398792\pi\) | ||||
0.312624 | + | 0.949877i | \(0.398792\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 105.873i | − 0.265347i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 369.502 | 0.921452 | 0.460726 | − | 0.887542i | \(-0.347589\pi\) | ||||
0.460726 | + | 0.887542i | \(0.347589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 321.594i | 0.798001i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 519.253 | 1.28211 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 553.578i | 1.36014i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 479.494 | 1.17236 | 0.586179 | − | 0.810182i | \(-0.300632\pi\) | ||||
0.586179 | + | 0.810182i | \(0.300632\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 450.695i | − 1.09658i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −112.824 | −0.273181 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1493.16i | − 3.59797i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.4328 | −0.0753785 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 564.644i | − 1.34760i | −0.738914 | − | 0.673800i | \(-0.764661\pi\) | ||||
0.738914 | − | 0.673800i | \(-0.235339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −544.282 | −1.29283 | −0.646415 | − | 0.762986i | \(-0.723733\pi\) | ||||
−0.646415 | + | 0.762986i | \(0.723733\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 144.593i | − 0.341827i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.3098 | −0.0971996 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 253.826i | 0.594440i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 197.196 | 0.459665 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 90.3539i | 0.209638i | 0.994491 | + | 0.104819i | \(0.0334263\pi\) | ||||
−0.994491 | + | 0.104819i | \(0.966574\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −131.383 | −0.303425 | −0.151713 | − | 0.988425i | \(-0.548479\pi\) | ||||
−0.151713 | + | 0.988425i | \(0.548479\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 749.674i | 1.72339i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −258.170 | −0.590777 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 128.655i | − 0.293064i | −0.989206 | − | 0.146532i | \(-0.953189\pi\) | ||||
0.989206 | − | 0.146532i | \(-0.0468111\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.3157 | −0.0392646 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 193.210i | 0.436139i | 0.975933 | + | 0.218070i | \(0.0699760\pi\) | ||||
−0.975933 | + | 0.218070i | \(0.930024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −57.2111 | −0.128564 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 443.954i | 0.993186i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.5046 | −0.0701661 | −0.0350830 | − | 0.999384i | \(-0.511170\pi\) | ||||
−0.0350830 | + | 0.999384i | \(0.511170\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.1714i | 0.0225531i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −353.651 | −0.780686 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 153.218i | − 0.336743i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −426.401 | −0.933043 | −0.466521 | − | 0.884510i | \(-0.654493\pi\) | ||||
−0.466521 | + | 0.884510i | \(0.654493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.7280i | 0.0364445i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −430.182 | −0.933150 | −0.466575 | − | 0.884482i | \(-0.654512\pi\) | ||||
−0.466575 | + | 0.884482i | \(0.654512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 183.454i | 0.396230i | 0.980179 | + | 0.198115i | \(0.0634819\pi\) | ||||
−0.980179 | + | 0.198115i | \(0.936518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1381.56 | −2.97111 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 110.381i | − 0.236362i | −0.992992 | − | 0.118181i | \(-0.962294\pi\) | ||||
0.992992 | − | 0.118181i | \(-0.0377063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −184.807 | −0.394044 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 484.604i | 1.02888i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −549.735 | −1.16223 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1133.83i | − 2.38701i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.9797 | −0.0293075 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 515.593i | 1.07639i | 0.842819 | + | 0.538197i | \(0.180894\pi\) | ||||
−0.842819 | + | 0.538197i | \(0.819106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 246.972 | 0.513455 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 111.400i | − 0.230642i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1023.30 | −2.10991 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 59.2995i | − 0.121765i | −0.998145 | − | 0.0608824i | \(-0.980609\pi\) | ||||
0.998145 | − | 0.0608824i | \(-0.0193915\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −45.3927 | −0.0928276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 556.042i | 1.13247i | 0.824244 | + | 0.566234i | \(0.191600\pi\) | ||||
−0.824244 | + | 0.566234i | \(0.808400\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.9708 | −0.0344234 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 321.096i | − 0.648678i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −243.643 | −0.490227 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 150.429i | − 0.301461i | −0.988575 | − | 0.150730i | \(-0.951837\pi\) | ||||
0.988575 | − | 0.150730i | \(-0.0481626\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.227601 | −0.000454293 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 415.893i | 0.826825i | 0.910544 | + | 0.413412i | \(0.135663\pi\) | ||||
−0.910544 | + | 0.413412i | \(0.864337\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 413.658 | 0.819124 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 343.762i | 0.678032i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −622.234 | −1.22246 | −0.611232 | − | 0.791452i | \(-0.709326\pi\) | ||||
−0.611232 | + | 0.791452i | \(0.709326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.3924i | 0.0516485i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −459.134 | −0.894999 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 184.911i | 0.359051i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 768.871 | 1.48718 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 110.589i | 0.213081i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −644.142 | −1.23636 | −0.618179 | − | 0.786037i | \(-0.712129\pi\) | ||||
−0.618179 | + | 0.786037i | \(0.712129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 889.589i | 1.70093i | 0.526028 | + | 0.850467i | \(0.323681\pi\) | ||||
−0.526028 | + | 0.850467i | \(0.676319\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 489.248 | 0.931900 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 31.2752i | − 0.0593457i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 257.353 | 0.486490 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105.486i | 0.198655i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.53785 | 0.00851380 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 640.012i | 1.19628i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 487.529 | 0.907875 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 92.0759i | − 0.170827i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −832.015 | −1.53792 | −0.768961 | − | 0.639296i | \(-0.779226\pi\) | ||||
−0.768961 | + | 0.639296i | \(0.779226\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 529.207i | − 0.974599i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1839.78 | −3.37575 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1014.85i | − 1.85531i | −0.373441 | − | 0.927654i | \(-0.621822\pi\) | ||||
0.373441 | − | 0.927654i | \(-0.378178\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 237.316 | 0.432270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 465.796i | − 0.845365i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.3859 | −0.0965387 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1060.99i | 1.91169i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −473.280 | −0.849694 | −0.424847 | − | 0.905265i | \(-0.639672\pi\) | ||||
−0.424847 | + | 0.905265i | \(0.639672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 245.257i | 0.438742i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.1775 | −0.0341844 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 102.364i | 0.181818i | 0.995859 | + | 0.0909092i | \(0.0289773\pi\) | ||||
−0.995859 | + | 0.0909092i | \(0.971023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 836.373 | 1.48031 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 139.214i | − 0.245527i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −68.4059 | −0.120221 | −0.0601106 | − | 0.998192i | \(-0.519145\pi\) | ||||
−0.0601106 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 701.419i | 1.22841i | 0.789148 | + | 0.614203i | \(0.210522\pi\) | ||||
−0.789148 | + | 0.614203i | \(0.789478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 805.971 | 1.40658 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1193.02i | − 2.07482i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.4710 | 0.0770727 | 0.0385364 | − | 0.999257i | \(-0.487730\pi\) | ||||
0.0385364 | + | 0.999257i | \(0.487730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 79.0421i | 0.136515i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −400.322 | −0.689022 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 74.3367i | − 0.127507i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −143.253 | −0.244876 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 99.0239i | − 0.168695i | −0.996436 | − | 0.0843475i | \(-0.973119\pi\) | ||||
0.996436 | − | 0.0843475i | \(-0.0268806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 858.410 | 1.45740 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 675.066i | − 1.14224i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −443.870 | −0.748516 | −0.374258 | − | 0.927325i | \(-0.622103\pi\) | ||||
−0.374258 | + | 0.927325i | \(0.622103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9005i | 0.0250429i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −335.481 | −0.561945 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 969.972i | − 1.61932i | −0.586900 | − | 0.809659i | \(-0.699652\pi\) | ||||
0.586900 | − | 0.809659i | \(-0.300348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −58.0231 | −0.0965443 | −0.0482722 | − | 0.998834i | \(-0.515371\pi\) | ||||
−0.0482722 | + | 0.998834i | \(0.515371\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 172.786i | 0.286545i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 513.352 | 0.848515 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 67.3822i | − 0.111009i | −0.998458 | − | 0.0555043i | \(-0.982323\pi\) | ||||
0.998458 | − | 0.0555043i | \(-0.0176767\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 200.991 | 0.330034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 343.022i | − 0.561411i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 521.917 | 0.851415 | 0.425707 | − | 0.904861i | \(-0.360025\pi\) | ||||
0.425707 | + | 0.904861i | \(0.360025\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.4946i | 0.0316985i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 165.257 | 0.267840 | 0.133920 | − | 0.990992i | \(-0.457243\pi\) | ||||
0.133920 | + | 0.990992i | \(0.457243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 205.392i | 0.331812i | 0.986142 | + | 0.165906i | \(0.0530549\pi\) | ||||
−0.986142 | + | 0.165906i | \(0.946945\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −483.103 | −0.777943 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3385i | 0.0246205i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2804.90 | 4.48783 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 526.363i | − 0.839495i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.0181 | −0.0381846 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 631.682i | 1.00108i | 0.865713 | + | 0.500540i | \(0.166865\pi\) | ||||
−0.865713 | + | 0.500540i | \(0.833135\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −633.543 | −1.00086 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 921.580i | 1.45131i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.0785 | −0.0644874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 227.796i | 0.356488i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 817.936 | 1.27603 | 0.638016 | − | 0.770023i | \(-0.279755\pi\) | ||||
0.638016 | + | 0.770023i | \(0.279755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 607.082i | − 0.944140i | −0.881561 | − | 0.472070i | \(-0.843507\pi\) | ||||
0.881561 | − | 0.472070i | \(-0.156493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1053.62 | −1.63352 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 621.063i | − 0.959911i | −0.877293 | − | 0.479956i | \(-0.840653\pi\) | ||||
0.877293 | − | 0.479956i | \(-0.159347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −560.919 | −0.864282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 370.404i | 0.568977i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 850.083 | 1.30181 | 0.650906 | − | 0.759159i | \(-0.274389\pi\) | ||||
0.650906 | + | 0.759159i | \(0.274389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 573.211i | 0.875131i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.6758 | 0.0375583 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 331.172i | 0.502537i | 0.967917 | + | 0.251268i | \(0.0808477\pi\) | ||||
−0.967917 | + | 0.251268i | \(0.919152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −464.323 | −0.702456 | −0.351228 | − | 0.936290i | \(-0.614236\pi\) | ||||
−0.351228 | + | 0.936290i | \(0.614236\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.55577i | 0.0129046i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −408.975 | −0.615000 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 490.112i | − 0.734801i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 145.105 | 0.216898 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1261.93i | 1.88067i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −844.655 | −1.25506 | −0.627529 | − | 0.778593i | \(-0.715934\pi\) | ||||
−0.627529 | + | 0.778593i | \(0.715934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2121.69i | − 3.14325i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 664.414 | 0.981410 | 0.490705 | − | 0.871326i | \(-0.336739\pi\) | ||||
0.490705 | + | 0.871326i | \(0.336739\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 274.353i | 0.404054i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −702.778 | −1.03198 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 601.901i | − 0.881261i | −0.897689 | − | 0.440631i | \(-0.854755\pi\) | ||||
0.897689 | − | 0.440631i | \(-0.145245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1740.98 | −2.54157 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.0742i | 0.0233977i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.1643 | −0.0481340 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 579.981i | 0.839336i | 0.907678 | + | 0.419668i | \(0.137854\pi\) | ||||
−0.907678 | + | 0.419668i | \(0.862146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −86.0872 | −0.124224 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 121.421i | 0.174706i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.441308 | −0.000633154 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 362.889i | 0.519154i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −863.561 | −1.23190 | −0.615949 | − | 0.787786i | \(-0.711227\pi\) | ||||
−0.615949 | + | 0.787786i | \(0.711227\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 659.225i | − 0.937731i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1473.62 | 2.09024 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 110.903i | − 0.156865i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 293.022 | 0.413290 | 0.206645 | − | 0.978416i | \(-0.433746\pi\) | ||||
0.206645 | + | 0.978416i | \(0.433746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 49.9136i | 0.0702019i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 903.222 | 1.26679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 761.744i | − 1.06538i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 131.298 | 0.183122 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 381.821i | 0.531044i | 0.964105 | + | 0.265522i | \(0.0855443\pi\) | ||||
−0.964105 | + | 0.265522i | \(0.914456\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.5756 | 0.0687594 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 239.385i | − 0.331099i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2152.48 | 2.96893 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 387.165i | 0.532552i | 0.963897 | + | 0.266276i | \(0.0857932\pi\) | ||||
−0.963897 | + | 0.266276i | \(0.914207\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −804.088 | −1.10300 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 23.8514i | − 0.0326284i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −59.1034 | −0.0806322 | −0.0403161 | − | 0.999187i | \(-0.512836\pi\) | ||||
−0.0403161 | + | 0.999187i | \(0.512836\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 176.473i | − 0.240099i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −918.790 | −1.24666 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1285.33i | − 1.73928i | −0.493687 | − | 0.869640i | \(-0.664351\pi\) | ||||
0.493687 | − | 0.869640i | \(-0.335649\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −234.830 | −0.316910 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1450.21i | − 1.95183i | −0.218141 | − | 0.975917i | \(-0.569999\pi\) | ||||
0.218141 | − | 0.975917i | \(-0.430001\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1714.94 | 2.30193 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 374.284i | 0.501050i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 171.590 | 0.229092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 190.150i | − 0.253195i | −0.991954 | − | 0.126598i | \(-0.959594\pi\) | ||||
0.991954 | − | 0.126598i | \(-0.0404057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.7878 | −0.0422148 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1366.11i | 1.80941i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −441.225 | −0.582859 | −0.291430 | − | 0.956592i | \(-0.594131\pi\) | ||||
−0.291430 | + | 0.956592i | \(0.594131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 553.841i | − 0.729698i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1044.28 | −1.37225 | −0.686123 | − | 0.727486i | \(-0.740689\pi\) | ||||
−0.686123 | + | 0.727486i | \(0.740689\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 493.254i | 0.646466i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.9314 | 0.0182110 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 250.247i | 0.326267i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1141.60 | −1.48452 | −0.742262 | − | 0.670110i | \(-0.766247\pi\) | ||||
−0.742262 | + | 0.670110i | \(0.766247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 433.998i | − 0.562903i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 211.566 | 0.273694 | 0.136847 | − | 0.990592i | \(-0.456303\pi\) | ||||
0.136847 | + | 0.990592i | \(0.456303\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3966.77i | 5.11841i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 284.455 | 0.366095 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 12.1126i | − 0.0155489i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1211.30 | −1.55096 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 871.625i | − 1.11319i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1871.96 | 2.38466 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 523.213i | 0.664820i | 0.943135 | + | 0.332410i | \(0.107862\pi\) | ||||
−0.943135 | + | 0.332410i | \(0.892138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −303.396 | −0.384533 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 224.235i | − 0.283483i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 562.993 | 0.709953 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 142.474i | − 0.179212i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 503.460 | 0.631693 | 0.315847 | − | 0.948810i | \(-0.397711\pi\) | ||||
0.315847 | + | 0.948810i | \(0.397711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.3590i | 0.0417510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3409 | 0.0179038 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 131.213i | 0.163404i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −430.325 | −0.534565 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 23.9499i | − 0.0296777i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 100.517 | 0.124248 | 0.0621242 | − | 0.998068i | \(-0.480212\pi\) | ||||
0.0621242 | + | 0.998068i | \(0.480212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 759.830i | 0.936905i | 0.883489 | + | 0.468453i | \(0.155188\pi\) | ||||
−0.883489 | + | 0.468453i | \(0.844812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 518.768 | 0.638091 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 175.346i | 0.215149i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 654.648 | 0.801283 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 38.4067i | 0.0468946i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 749.705 | 0.913160 | 0.456580 | − | 0.889682i | \(-0.349074\pi\) | ||||
0.456580 | + | 0.889682i | \(0.349074\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 424.800i | − 0.516160i | −0.966124 | − | 0.258080i | \(-0.916910\pi\) | ||||
0.966124 | − | 0.258080i | \(-0.0830899\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2432.36 | 2.94832 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 575.272i | − 0.695613i | −0.937566 | − | 0.347806i | \(-0.886927\pi\) | ||||
0.937566 | − | 0.347806i | \(-0.113073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −157.635 | −0.190151 | −0.0950756 | − | 0.995470i | \(-0.530309\pi\) | ||||
−0.0950756 | + | 0.995470i | \(0.530309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 394.490i | 0.474718i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.99490 | 0.00479580 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.879193i | 0.00105293i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1606.31 | 1.91913 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 759.895i | 0.905716i | 0.891583 | + | 0.452858i | \(0.149595\pi\) | ||||
−0.891583 | + | 0.452858i | \(0.850405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.2720 | 0.0514530 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 555.628i | 0.659108i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1327.91 | 1.57149 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 137.632i | − 0.162493i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1103.23 | 1.29945 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 693.638i | − 0.815086i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −315.373 | −0.369722 | −0.184861 | − | 0.982765i | \(-0.559183\pi\) | ||||
−0.184861 | + | 0.982765i | \(0.559183\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 382.375i | 0.447222i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1222.53 | 1.42652 | 0.713260 | − | 0.700900i | \(-0.247218\pi\) | ||||
0.713260 | + | 0.700900i | \(0.247218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1008.23i | − 1.17373i | −0.809687 | − | 0.586863i | \(-0.800363\pi\) | ||||
0.809687 | − | 0.586863i | \(-0.199637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.22658 | 0.00607036 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1140.31i | 1.32133i | 0.750679 | + | 0.660667i | \(0.229726\pi\) | ||||
−0.750679 | + | 0.660667i | \(0.770274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 427.192 | 0.493864 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 737.467i | 0.850597i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −265.415 | −0.305426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 409.906i | 0.470616i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 256.508 | 0.293824 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1237.17i | − 1.41391i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 306.788 | 0.349816 | 0.174908 | − | 0.984585i | \(-0.444037\pi\) | ||||
0.174908 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 541.640i | − 0.616200i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −248.968 | −0.282597 | −0.141299 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141299 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 458.136i | 0.518841i | 0.965765 | + | 0.259420i | \(0.0835315\pi\) | ||||
−0.965765 | + | 0.259420i | \(0.916469\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1075.06 | −1.21475 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 312.628i | − 0.352456i | −0.984349 | − | 0.176228i | \(-0.943610\pi\) | ||||
0.984349 | − | 0.176228i | \(-0.0563895\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 247.080 | 0.277930 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 692.121i | − 0.776791i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −915.605 | −1.02531 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1883.26i | − 2.10420i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −247.089 | −0.275462 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1629.61i | 1.81270i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.22525 | 0.00357963 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 282.481i | 0.312825i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2044.26 | −2.25885 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 375.701i | 0.414224i | 0.978317 | + | 0.207112i | \(0.0664064\pi\) | ||||
−0.978317 | + | 0.207112i | \(0.933594\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −103.690 | −0.114071 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 41.9614i | − 0.0460608i | −0.999735 | − | 0.0230304i | \(-0.992669\pi\) | ||||
0.999735 | − | 0.0230304i | \(-0.00733145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1990.25 | −2.17991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2418.61i | 2.64329i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 153.680 | 0.167590 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1770.71i | − 1.92678i | −0.268101 | − | 0.963391i | \(-0.586396\pi\) | ||||
0.268101 | − | 0.963391i | \(-0.413604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −492.713 | −0.534976 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 540.407i | 0.585489i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3046.32 | 3.29332 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 46.3511i | − 0.0500012i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1668.30 | 1.79581 | 0.897903 | − | 0.440193i | \(-0.145090\pi\) | ||||
0.897903 | + | 0.440193i | \(0.145090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 109.648i | 0.117774i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 689.285 | 0.738784 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 74.0800i | 0.0792300i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −183.028 | −0.195334 | −0.0976668 | − | 0.995219i | \(-0.531138\pi\) | ||||
−0.0976668 | + | 0.995219i | \(0.531138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 604.152i | 0.643400i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −255.475 | −0.271493 | −0.135747 | − | 0.990744i | \(-0.543343\pi\) | ||||
−0.135747 | + | 0.990744i | \(0.543343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 12.7449i | − 0.0135153i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −765.298 | −0.809839 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 187.173i | − 0.197648i | −0.995105 | − | 0.0988242i | \(-0.968492\pi\) | ||||
0.995105 | − | 0.0988242i | \(-0.0315082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 58.5391 | 0.0616851 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 636.142i | − 0.668920i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 362.350 | 0.380220 | 0.190110 | − | 0.981763i | \(-0.439115\pi\) | ||||
0.190110 | + | 0.981763i | \(0.439115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3113.36i | − 3.26007i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 999.253 | 1.04415 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 466.764i | 0.486720i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2042.20 | −2.12508 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 160.430i | − 0.166594i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 305.330 | 0.316404 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1473.76i | 1.52406i | 0.647545 | + | 0.762028i | \(0.275796\pi\) | ||||
−0.647545 | + | 0.762028i | \(0.724204\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.8373 | 0.0235680 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 223.833i | − 0.230518i | −0.993335 | − | 0.115259i | \(-0.963230\pi\) | ||||
0.993335 | − | 0.115259i | \(-0.0367698\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.5535 | 0.0334568 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1085.17i | − 1.11299i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 825.305 | 0.844734 | 0.422367 | − | 0.906425i | \(-0.361199\pi\) | ||||
0.422367 | + | 0.906425i | \(0.361199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 76.2576i | 0.0778934i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 461.172 | 0.470104 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 411.945i | − 0.419069i | −0.977801 | − | 0.209535i | \(-0.932805\pi\) | ||||
0.977801 | − | 0.209535i | \(-0.0671949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2607.69 | −2.64741 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 395.084i | − 0.400287i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 688.823 | 0.696484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1607.53i | − 1.62213i | −0.584959 | − | 0.811063i | \(-0.698889\pi\) | ||||
0.584959 | − | 0.811063i | \(-0.301111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1188.80 | −1.19718 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1295.92i | 1.30243i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −701.364 | −0.703474 | −0.351737 | − | 0.936099i | \(-0.614409\pi\) | ||||
−0.351737 | + | 0.936099i | \(0.614409\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1233.58i | − 1.23482i |
(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 | 448.3.d.e.127.3 | 8 | ||
4.3 | odd | 2 | inner | 448.3.d.e.127.6 | 8 | ||
8.3 | odd | 2 | 224.3.d.b.127.3 | ✓ | 8 | ||
8.5 | even | 2 | 224.3.d.b.127.6 | yes | 8 | ||
16.3 | odd | 4 | 1792.3.g.d.127.4 | 8 | |||
16.5 | even | 4 | 1792.3.g.d.127.3 | 8 | |||
16.11 | odd | 4 | 1792.3.g.f.127.5 | 8 | |||
16.13 | even | 4 | 1792.3.g.f.127.6 | 8 | |||
24.5 | odd | 2 | 2016.3.m.c.127.2 | 8 | |||
24.11 | even | 2 | 2016.3.m.c.127.1 | 8 | |||
56.13 | odd | 2 | 1568.3.d.n.1471.3 | 8 | |||
56.27 | even | 2 | 1568.3.d.n.1471.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.d.b.127.3 | ✓ | 8 | 8.3 | odd | 2 | ||
224.3.d.b.127.6 | yes | 8 | 8.5 | even | 2 | ||
448.3.d.e.127.3 | 8 | 1.1 | even | 1 | trivial | ||
448.3.d.e.127.6 | 8 | 4.3 | odd | 2 | inner | ||
1568.3.d.n.1471.3 | 8 | 56.13 | odd | 2 | |||
1568.3.d.n.1471.6 | 8 | 56.27 | even | 2 | |||
1792.3.g.d.127.3 | 8 | 16.5 | even | 4 | |||
1792.3.g.d.127.4 | 8 | 16.3 | odd | 4 | |||
1792.3.g.f.127.5 | 8 | 16.11 | odd | 4 | |||
1792.3.g.f.127.6 | 8 | 16.13 | even | 4 | |||
2016.3.m.c.127.1 | 8 | 24.11 | even | 2 | |||
2016.3.m.c.127.2 | 8 | 24.5 | odd | 2 |