Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,3,Mod(55,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.14987699641\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2355463701504.14 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 79x^{4} + 18x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.8 | ||
Root | \(0.238746 + 0.413520i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.55 |
Dual form | 189.3.d.e.55.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.71106 | 1.85553 | 0.927766 | − | 0.373162i | \(-0.121726\pi\) | ||||
0.927766 | + | 0.373162i | \(0.121726\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 9.77200 | 2.44300 | ||||||||
\(5\) | 8.26535i | 1.65307i | 0.562885 | + | 0.826535i | \(0.309691\pi\) | ||||
−0.562885 | + | 0.826535i | \(0.690309\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.77200 | − | 6.42775i | −0.396000 | − | 0.918250i | ||||
\(8\) | 21.4203 | 2.67753 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 30.6732i | 3.06732i | ||||||||
\(11\) | −10.2871 | −0.935189 | −0.467594 | − | 0.883943i | \(-0.654879\pi\) | ||||
−0.467594 | + | 0.883943i | \(0.654879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.42775i | − | 0.494443i | −0.968959 | − | 0.247221i | \(-0.920483\pi\) | ||
0.968959 | − | 0.247221i | \(-0.0795175\pi\) | |||||||
\(14\) | −10.2871 | − | 23.8538i | −0.734791 | − | 1.70384i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 40.4040 | 2.52525 | ||||||||
\(17\) | − | 15.5885i | − | 0.916968i | −0.888703 | − | 0.458484i | \(-0.848393\pi\) | ||
0.888703 | − | 0.458484i | \(-0.151607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.96224i | − | 0.261170i | −0.991437 | − | 0.130585i | \(-0.958314\pi\) | ||
0.991437 | − | 0.130585i | \(-0.0416856\pi\) | |||||||
\(20\) | 80.7690i | 4.03845i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −38.1760 | −1.73527 | ||||||||
\(23\) | 28.8424 | 1.25402 | 0.627009 | − | 0.779012i | \(-0.284279\pi\) | ||||
0.627009 | + | 0.779012i | \(0.284279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −43.3160 | −1.73264 | ||||||||
\(26\) | − | 23.8538i | − | 0.917454i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −27.0880 | − | 62.8120i | −0.967429 | − | 2.24329i | ||||
\(29\) | −2.01883 | −0.0696149 | −0.0348075 | − | 0.999394i | \(-0.511082\pi\) | ||||
−0.0348075 | + | 0.999394i | \(0.511082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 16.3522i | − | 0.527491i | −0.964592 | − | 0.263746i | \(-0.915042\pi\) | ||
0.964592 | − | 0.263746i | \(-0.0849579\pi\) | |||||||
\(32\) | 64.2608 | 2.00815 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 57.8498i | − | 1.70146i | ||||||
\(35\) | 53.1276 | − | 22.9116i | 1.51793 | − | 0.654616i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.2280 | −0.898054 | −0.449027 | − | 0.893518i | \(-0.648229\pi\) | ||||
−0.449027 | + | 0.893518i | \(0.648229\pi\) | |||||||
\(38\) | − | 18.4152i | − | 0.484610i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 177.046i | 4.42615i | ||||||||
\(41\) | 39.4423i | 0.962006i | 0.876719 | + | 0.481003i | \(0.159727\pi\) | ||||
−0.876719 | + | 0.481003i | \(0.840273\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.91199 | −0.0909766 | −0.0454883 | − | 0.998965i | \(-0.514484\pi\) | ||||
−0.0454883 | + | 0.998965i | \(0.514484\pi\) | |||||||
\(44\) | −100.525 | −2.28467 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 107.036 | 2.32687 | ||||||||
\(47\) | 41.3267i | 0.879293i | 0.898171 | + | 0.439646i | \(0.144896\pi\) | ||||
−0.898171 | + | 0.439646i | \(0.855104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.6320 | + | 35.6355i | −0.686368 | + | 0.727255i | ||||
\(50\) | −160.749 | −3.21497 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 62.8120i | − | 1.20792i | ||||||
\(53\) | −43.6867 | −0.824277 | −0.412138 | − | 0.911121i | \(-0.635218\pi\) | ||||
−0.412138 | + | 0.911121i | \(0.635218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 85.0263i | − | 1.54593i | ||||||
\(56\) | −59.3770 | − | 137.684i | −1.06030 | − | 2.45865i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.49202 | −0.129173 | ||||||||
\(59\) | 30.2347i | 0.512452i | 0.966617 | + | 0.256226i | \(0.0824791\pi\) | ||||
−0.966617 | + | 0.256226i | \(0.917521\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 107.806i | 1.76732i | 0.468133 | + | 0.883658i | \(0.344927\pi\) | ||||
−0.468133 | + | 0.883658i | \(0.655073\pi\) | |||||||
\(62\) | − | 60.6842i | − | 0.978777i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 76.8600 | 1.20094 | ||||||||
\(65\) | 53.1276 | 0.817348 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −36.5800 | −0.545971 | −0.272985 | − | 0.962018i | \(-0.588011\pi\) | ||||
−0.272985 | + | 0.962018i | \(0.588011\pi\) | |||||||
\(68\) | − | 152.330i | − | 2.24015i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 197.160 | − | 85.0263i | 2.81657 | − | 1.21466i | ||||
\(71\) | 79.1051 | 1.11416 | 0.557078 | − | 0.830460i | \(-0.311922\pi\) | ||||
0.557078 | + | 0.830460i | \(0.311922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38.5665i | 0.528308i | 0.964480 | + | 0.264154i | \(0.0850928\pi\) | ||||
−0.964480 | + | 0.264154i | \(0.914907\pi\) | |||||||
\(74\) | −123.311 | −1.66637 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 48.4910i | − | 0.638039i | ||||||
\(77\) | 28.5158 | + | 66.1228i | 0.370335 | + | 0.858738i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 100.316 | 1.26982 | 0.634911 | − | 0.772585i | \(-0.281037\pi\) | ||||
0.634911 | + | 0.772585i | \(0.281037\pi\) | |||||||
\(80\) | 333.953i | 4.17442i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 146.373i | 1.78503i | ||||||||
\(83\) | − | 52.2040i | − | 0.628964i | −0.949263 | − | 0.314482i | \(-0.898169\pi\) | ||
0.949263 | − | 0.314482i | \(-0.101831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 128.844 | 1.51581 | ||||||||
\(86\) | −14.5177 | −0.168810 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −220.352 | −2.50400 | ||||||||
\(89\) | − | 71.5614i | − | 0.804061i | −0.915626 | − | 0.402030i | \(-0.868305\pi\) | ||
0.915626 | − | 0.402030i | \(-0.131695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −41.3160 | + | 17.8177i | −0.454022 | + | 0.195799i | ||||
\(92\) | 281.848 | 3.06357 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 153.366i | 1.63156i | ||||||||
\(95\) | 41.0146 | 0.431733 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 133.517i | − | 1.37647i | −0.725489 | − | 0.688233i | \(-0.758386\pi\) | ||
0.725489 | − | 0.688233i | \(-0.241614\pi\) | |||||||
\(98\) | −124.811 | + | 132.246i | −1.27358 | + | 1.34944i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −423.284 | −4.23284 | ||||||||
\(101\) | 10.8772i | 0.107696i | 0.998549 | + | 0.0538478i | \(0.0171486\pi\) | ||||
−0.998549 | + | 0.0538478i | \(0.982851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 195.429i | − | 1.89737i | −0.316217 | − | 0.948687i | \(-0.602413\pi\) | ||
0.316217 | − | 0.948687i | \(-0.397587\pi\) | |||||||
\(104\) | − | 137.684i | − | 1.32389i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −162.124 | −1.52947 | ||||||||
\(107\) | 103.910 | 0.971120 | 0.485560 | − | 0.874203i | \(-0.338616\pi\) | ||||
0.485560 | + | 0.874203i | \(0.338616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 132.036 | 1.21134 | 0.605670 | − | 0.795716i | \(-0.292905\pi\) | ||||
0.605670 | + | 0.795716i | \(0.292905\pi\) | |||||||
\(110\) | − | 315.538i | − | 2.86853i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −112.000 | − | 259.707i | −1.00000 | − | 2.31881i | ||||
\(113\) | −104.429 | −0.924153 | −0.462077 | − | 0.886840i | \(-0.652896\pi\) | ||||
−0.462077 | + | 0.886840i | \(0.652896\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 238.393i | 2.07298i | ||||||||
\(116\) | −19.7280 | −0.170069 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 112.203i | 0.950871i | ||||||||
\(119\) | −100.199 | + | 43.2112i | −0.842006 | + | 0.363120i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.1760 | −0.125422 | ||||||||
\(122\) | 400.076i | 3.27931i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 159.794i | − | 1.28866i | ||||||
\(125\) | − | 151.388i | − | 1.21111i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 145.580 | 1.14630 | 0.573150 | − | 0.819451i | \(-0.305721\pi\) | ||||
0.573150 | + | 0.819451i | \(0.305721\pi\) | |||||||
\(128\) | 28.1892 | 0.220228 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 197.160 | 1.51662 | ||||||||
\(131\) | 222.222i | 1.69635i | 0.529714 | + | 0.848176i | \(0.322299\pi\) | ||||
−0.529714 | + | 0.848176i | \(0.677701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.8960 | + | 13.7553i | −0.239820 | + | 0.103424i | ||||
\(134\) | −135.751 | −1.01307 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 333.909i | − | 2.45521i | ||||||
\(137\) | 146.884 | 1.07215 | 0.536073 | − | 0.844172i | \(-0.319907\pi\) | ||||
0.536073 | + | 0.844172i | \(0.319907\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 96.0822i | 0.691239i | 0.938375 | + | 0.345619i | \(0.112331\pi\) | ||||
−0.938375 | + | 0.345619i | \(0.887669\pi\) | |||||||
\(140\) | 519.163 | − | 223.892i | 3.70831 | − | 1.59923i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 293.564 | 2.06735 | ||||||||
\(143\) | 66.1228i | 0.462397i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 16.6864i | − | 0.115078i | ||||||
\(146\) | 143.123i | 0.980293i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −324.704 | −2.19395 | ||||||||
\(149\) | −275.599 | −1.84966 | −0.924828 | − | 0.380387i | \(-0.875791\pi\) | ||||
−0.924828 | + | 0.380387i | \(0.875791\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −191.652 | −1.26922 | −0.634610 | − | 0.772833i | \(-0.718839\pi\) | ||||
−0.634610 | + | 0.772833i | \(0.718839\pi\) | |||||||
\(152\) | − | 106.292i | − | 0.699293i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 105.824 | + | 245.386i | 0.687169 | + | 1.59342i | ||||
\(155\) | 135.157 | 0.871980 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 90.5542i | 0.576779i | 0.957513 | + | 0.288389i | \(0.0931197\pi\) | ||||
−0.957513 | + | 0.288389i | \(0.906880\pi\) | |||||||
\(158\) | 372.279 | 2.35620 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 531.138i | 3.31961i | ||||||||
\(161\) | −79.9512 | − | 185.392i | −0.496591 | − | 1.15150i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 189.320 | 1.16147 | 0.580737 | − | 0.814092i | \(-0.302765\pi\) | ||||
0.580737 | + | 0.814092i | \(0.302765\pi\) | |||||||
\(164\) | 385.430i | 2.35018i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 193.732i | − | 1.16706i | ||||||
\(167\) | − | 72.5037i | − | 0.434154i | −0.976155 | − | 0.217077i | \(-0.930348\pi\) | ||
0.976155 | − | 0.217077i | \(-0.0696522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 127.684 | 0.755527 | ||||||||
\(170\) | 478.149 | 2.81264 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −38.2280 | −0.222256 | ||||||||
\(173\) | 172.415i | 0.996620i | 0.866999 | + | 0.498310i | \(0.166046\pi\) | ||||
−0.866999 | + | 0.498310i | \(0.833954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 120.072 | + | 278.425i | 0.686126 | + | 1.59100i | ||||
\(176\) | −415.639 | −2.36159 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 265.569i | − | 1.49196i | ||||||
\(179\) | 158.344 | 0.884602 | 0.442301 | − | 0.896867i | \(-0.354162\pi\) | ||||
0.442301 | + | 0.896867i | \(0.354162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 285.418i | − | 1.57690i | −0.615102 | − | 0.788448i | \(-0.710885\pi\) | ||
0.615102 | − | 0.788448i | \(-0.289115\pi\) | |||||||
\(182\) | −153.326 | + | 66.1228i | −0.842453 | + | 0.363312i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 617.812 | 3.35767 | ||||||||
\(185\) | − | 274.641i | − | 1.48455i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 160.360i | 0.857538i | ||||||||
\(188\) | 403.845i | 2.14811i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 152.208 | 0.801094 | ||||||||
\(191\) | −180.477 | −0.944903 | −0.472452 | − | 0.881357i | \(-0.656631\pi\) | ||||
−0.472452 | + | 0.881357i | \(0.656631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 119.880 | 0.621140 | 0.310570 | − | 0.950550i | \(-0.399480\pi\) | ||||
0.310570 | + | 0.950550i | \(0.399480\pi\) | |||||||
\(194\) | − | 495.491i | − | 2.55408i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −328.652 | + | 348.230i | −1.67680 | + | 1.77668i | ||||
\(197\) | −126.696 | −0.643125 | −0.321563 | − | 0.946888i | \(-0.604208\pi\) | ||||
−0.321563 | + | 0.946888i | \(0.604208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.3210i | − | 0.0719649i | −0.999352 | − | 0.0359825i | \(-0.988544\pi\) | ||
0.999352 | − | 0.0359825i | \(-0.0114560\pi\) | |||||||
\(200\) | −927.841 | −4.63920 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 40.3662i | 0.199833i | ||||||||
\(203\) | 5.59621 | + | 12.9766i | 0.0275675 | + | 0.0639239i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −326.004 | −1.59026 | ||||||||
\(206\) | − | 725.251i | − | 3.52064i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 259.707i | − | 1.24859i | ||||||
\(209\) | 51.0469i | 0.244244i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −332.124 | −1.57405 | −0.787024 | − | 0.616923i | \(-0.788379\pi\) | ||||
−0.787024 | + | 0.616923i | \(0.788379\pi\) | |||||||
\(212\) | −426.906 | −2.01371 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 385.616 | 1.80194 | ||||||||
\(215\) | − | 32.3340i | − | 0.150391i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −105.108 | + | 45.3284i | −0.484369 | + | 0.208887i | ||||
\(218\) | 489.994 | 2.24768 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 830.877i | − | 3.77671i | ||||||
\(221\) | −100.199 | −0.453388 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 193.064i | − | 0.865758i | −0.901452 | − | 0.432879i | \(-0.857498\pi\) | ||
0.901452 | − | 0.432879i | \(-0.142502\pi\) | |||||||
\(224\) | −178.131 | − | 413.053i | −0.795228 | − | 1.84399i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −387.544 | −1.71480 | ||||||||
\(227\) | − | 23.8538i | − | 0.105083i | −0.998619 | − | 0.0525414i | \(-0.983268\pi\) | ||
0.998619 | − | 0.0525414i | \(-0.0167322\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 372.810i | − | 1.62799i | −0.580872 | − | 0.813995i | \(-0.697288\pi\) | ||
0.580872 | − | 0.813995i | \(-0.302712\pi\) | |||||||
\(230\) | 884.690i | 3.84648i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −43.2440 | −0.186396 | ||||||||
\(233\) | −177.612 | −0.762282 | −0.381141 | − | 0.924517i | \(-0.624469\pi\) | ||||
−0.381141 | + | 0.924517i | \(0.624469\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −341.580 | −1.45353 | ||||||||
\(236\) | 295.453i | 1.25192i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −371.844 | + | 160.360i | −1.56237 | + | 0.673780i | ||||
\(239\) | 13.9389 | 0.0583218 | 0.0291609 | − | 0.999575i | \(-0.490716\pi\) | ||||
0.0291609 | + | 0.999575i | \(0.490716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 183.808i | 0.762689i | 0.924433 | + | 0.381344i | \(0.124539\pi\) | ||||
−0.924433 | + | 0.381344i | \(0.875461\pi\) | |||||||
\(242\) | −56.3192 | −0.232724 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1053.48i | 4.31755i | ||||||||
\(245\) | −294.540 | − | 277.980i | −1.20220 | − | 1.13461i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.8960 | −0.129134 | ||||||||
\(248\) | − | 350.269i | − | 1.41238i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 561.811i | − | 2.24725i | ||||||
\(251\) | 191.988i | 0.764891i | 0.923978 | + | 0.382445i | \(0.124918\pi\) | ||||
−0.923978 | + | 0.382445i | \(0.875082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −296.704 | −1.17274 | ||||||||
\(254\) | 540.257 | 2.12700 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −202.828 | −0.792297 | ||||||||
\(257\) | 146.462i | 0.569892i | 0.958544 | + | 0.284946i | \(0.0919756\pi\) | ||||
−0.958544 | + | 0.284946i | \(0.908024\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 92.1081 | + | 213.581i | 0.355630 | + | 0.824638i | ||||
\(260\) | 519.163 | 1.99678 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 824.681i | 3.14764i | ||||||||
\(263\) | 81.3168 | 0.309189 | 0.154595 | − | 0.987978i | \(-0.450593\pi\) | ||||
0.154595 | + | 0.987978i | \(0.450593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 361.086i | − | 1.36259i | ||||||
\(266\) | −118.368 | + | 51.0469i | −0.444993 | + | 0.191906i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −357.460 | −1.33381 | ||||||||
\(269\) | 391.811i | 1.45655i | 0.685287 | + | 0.728273i | \(0.259677\pi\) | ||||
−0.685287 | + | 0.728273i | \(0.740323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 488.175i | − | 1.80138i | −0.434458 | − | 0.900692i | \(-0.643060\pi\) | ||
0.434458 | − | 0.900692i | \(-0.356940\pi\) | |||||||
\(272\) | − | 629.836i | − | 2.31557i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 545.096 | 1.98940 | ||||||||
\(275\) | 445.595 | 1.62035 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 376.004 | 1.35742 | 0.678708 | − | 0.734408i | \(-0.262540\pi\) | ||||
0.678708 | + | 0.734408i | \(0.262540\pi\) | |||||||
\(278\) | 356.567i | 1.28262i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1138.01 | − | 490.772i | 4.06432 | − | 1.75276i | ||||
\(281\) | −113.677 | −0.404546 | −0.202273 | − | 0.979329i | \(-0.564833\pi\) | ||||
−0.202273 | + | 0.979329i | \(0.564833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 65.1774i | 0.230309i | 0.993348 | + | 0.115154i | \(0.0367363\pi\) | ||||
−0.993348 | + | 0.115154i | \(0.963264\pi\) | |||||||
\(284\) | 773.015 | 2.72188 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 245.386i | 0.857993i | ||||||||
\(287\) | 253.525 | − | 109.334i | 0.883363 | − | 0.380955i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.0000 | 0.159170 | ||||||||
\(290\) | − | 61.9242i | − | 0.213532i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 376.872i | 1.29066i | ||||||||
\(293\) | − | 389.926i | − | 1.33081i | −0.746484 | − | 0.665403i | \(-0.768260\pi\) | ||
0.746484 | − | 0.665403i | \(-0.231740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −249.900 | −0.847119 | ||||||||
\(296\) | −711.753 | −2.40457 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1022.76 | −3.43209 | ||||||||
\(299\) | − | 185.392i | − | 0.620040i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8441 | + | 25.1453i | 0.0360267 | + | 0.0835393i | ||||
\(302\) | −711.233 | −2.35508 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 200.494i | − | 0.659521i | ||||||
\(305\) | −891.057 | −2.92150 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 355.892i | − | 1.15926i | −0.814881 | − | 0.579628i | \(-0.803198\pi\) | ||
0.814881 | − | 0.579628i | \(-0.196802\pi\) | |||||||
\(308\) | 278.656 | + | 646.152i | 0.904729 | + | 2.09790i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 501.576 | 1.61799 | ||||||||
\(311\) | − | 90.9188i | − | 0.292344i | −0.989259 | − | 0.146172i | \(-0.953305\pi\) | ||
0.989259 | − | 0.146172i | \(-0.0466952\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.8555i | − | 0.0410719i | −0.999789 | − | 0.0205360i | \(-0.993463\pi\) | ||
0.999789 | − | 0.0205360i | \(-0.00653726\pi\) | |||||||
\(314\) | 336.053i | 1.07023i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 980.288 | 3.10218 | ||||||||
\(317\) | −268.236 | −0.846169 | −0.423085 | − | 0.906090i | \(-0.639053\pi\) | ||||
−0.423085 | + | 0.906090i | \(0.639053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.7679 | 0.0651031 | ||||||||
\(320\) | 635.275i | 1.98523i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −296.704 | − | 688.001i | −0.921441 | − | 2.13665i | ||||
\(323\) | −77.3536 | −0.239485 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 278.425i | 0.856691i | ||||||||
\(326\) | 702.579 | 2.15515 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 844.864i | 2.57581i | ||||||||
\(329\) | 265.638 | − | 114.558i | 0.807411 | − | 0.348200i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −86.5440 | −0.261462 | −0.130731 | − | 0.991418i | \(-0.541732\pi\) | ||||
−0.130731 | + | 0.991418i | \(0.541732\pi\) | |||||||
\(332\) | − | 510.138i | − | 1.53656i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 269.066i | − | 0.805586i | ||||||
\(335\) | − | 302.347i | − | 0.902528i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −77.2800 | −0.229317 | −0.114659 | − | 0.993405i | \(-0.536577\pi\) | ||||
−0.114659 | + | 0.993405i | \(0.536577\pi\) | |||||||
\(338\) | 473.844 | 1.40190 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1259.06 | 3.70313 | ||||||||
\(341\) | 168.217i | 0.493304i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 322.284 | + | 117.397i | 0.939604 | + | 0.342264i | ||||
\(344\) | −83.7959 | −0.243593 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 639.844i | 1.84926i | ||||||||
\(347\) | 50.7822 | 0.146346 | 0.0731732 | − | 0.997319i | \(-0.476687\pi\) | ||||
0.0731732 | + | 0.997319i | \(0.476687\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 129.352i | 0.370637i | 0.982679 | + | 0.185318i | \(0.0593317\pi\) | ||||
−0.982679 | + | 0.185318i | \(0.940668\pi\) | |||||||
\(350\) | 445.595 | + | 1033.25i | 1.27313 | + | 2.95215i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −661.056 | −1.87800 | ||||||||
\(353\) | − | 323.589i | − | 0.916682i | −0.888777 | − | 0.458341i | \(-0.848444\pi\) | ||
0.888777 | − | 0.458341i | \(-0.151556\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 653.831i | 1.84178i | ||||||||
\(356\) | − | 699.298i | − | 1.96432i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 587.624 | 1.64141 | ||||||||
\(359\) | 238.740 | 0.665014 | 0.332507 | − | 0.943101i | \(-0.392105\pi\) | ||||
0.332507 | + | 0.943101i | \(0.392105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 336.376 | 0.931790 | ||||||||
\(362\) | − | 1059.20i | − | 2.92598i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −403.740 | + | 174.115i | −1.10918 | + | 0.478338i | ||||
\(365\) | −318.766 | −0.873331 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 56.9499i | − | 0.155177i | −0.996985 | − | 0.0775885i | \(-0.975278\pi\) | ||
0.996985 | − | 0.0775885i | \(-0.0247220\pi\) | |||||||
\(368\) | 1165.35 | 3.16671 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 1019.21i | − | 2.75462i | ||||||
\(371\) | 121.100 | + | 280.807i | 0.326414 | + | 0.756892i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −367.060 | −0.984076 | −0.492038 | − | 0.870574i | \(-0.663748\pi\) | ||||
−0.492038 | + | 0.870574i | \(0.663748\pi\) | |||||||
\(374\) | 595.105i | 1.59119i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 885.230i | 2.35434i | ||||||||
\(377\) | 12.9766i | 0.0344206i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 51.0839 | 0.134786 | 0.0673930 | − | 0.997727i | \(-0.478532\pi\) | ||||
0.0673930 | + | 0.997727i | \(0.478532\pi\) | |||||||
\(380\) | 400.795 | 1.05472 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −669.760 | −1.75330 | ||||||||
\(383\) | 461.703i | 1.20549i | 0.797934 | + | 0.602745i | \(0.205926\pi\) | ||||
−0.797934 | + | 0.602745i | \(0.794074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −546.528 | + | 235.693i | −1.41955 | + | 0.612190i | ||||
\(386\) | 444.883 | 1.15255 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1304.73i | − | 3.36271i | ||||||
\(389\) | 104.815 | 0.269448 | 0.134724 | − | 0.990883i | \(-0.456985\pi\) | ||||
0.134724 | + | 0.990883i | \(0.456985\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 449.609i | − | 1.14989i | ||||||
\(392\) | −720.407 | + | 763.322i | −1.83777 | + | 1.94725i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −470.176 | −1.19334 | ||||||||
\(395\) | 829.147i | 2.09911i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 598.347i | 1.50717i | 0.657350 | + | 0.753585i | \(0.271677\pi\) | ||||
−0.657350 | + | 0.753585i | \(0.728323\pi\) | |||||||
\(398\) | − | 53.1462i | − | 0.133533i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1750.14 | −4.37535 | ||||||||
\(401\) | 289.730 | 0.722520 | 0.361260 | − | 0.932465i | \(-0.382347\pi\) | ||||
0.361260 | + | 0.932465i | \(0.382347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −105.108 | −0.260814 | ||||||||
\(404\) | 106.292i | 0.263100i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.7679 | + | 48.1569i | 0.0511525 | + | 0.118613i | ||||
\(407\) | 341.819 | 0.839850 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 89.9885i | 0.220021i | 0.993930 | + | 0.110010i | \(0.0350884\pi\) | ||||
−0.993930 | + | 0.110010i | \(0.964912\pi\) | |||||||
\(410\) | −1209.82 | −2.95079 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1909.74i | − | 4.63528i | ||||||
\(413\) | 194.341 | − | 83.8106i | 0.470559 | − | 0.202931i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 431.484 | 1.03972 | ||||||||
\(416\) | − | 413.053i | − | 0.992915i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 189.438i | 0.453202i | ||||||||
\(419\) | − | 661.311i | − | 1.57831i | −0.614196 | − | 0.789154i | \(-0.710519\pi\) | ||
0.614196 | − | 0.789154i | \(-0.289481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 135.056 | 0.320798 | 0.160399 | − | 0.987052i | \(-0.448722\pi\) | ||||
0.160399 | + | 0.987052i | \(0.448722\pi\) | |||||||
\(422\) | −1232.53 | −2.92070 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −935.780 | −2.20703 | ||||||||
\(425\) | 675.230i | 1.58878i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 692.952 | − | 298.839i | 1.62284 | − | 0.699858i | ||||
\(428\) | 1015.41 | 2.37245 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 119.994i | − | 0.279055i | ||||||
\(431\) | −569.812 | −1.32207 | −0.661035 | − | 0.750356i | \(-0.729882\pi\) | ||||
−0.661035 | + | 0.750356i | \(0.729882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 478.816i | 1.10581i | 0.833244 | + | 0.552906i | \(0.186481\pi\) | ||||
−0.833244 | + | 0.552906i | \(0.813519\pi\) | |||||||
\(434\) | −390.063 | + | 168.217i | −0.898762 | + | 0.387596i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1290.26 | 2.95930 | ||||||||
\(437\) | − | 143.123i | − | 0.327512i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 386.462i | − | 0.880324i | −0.897918 | − | 0.440162i | \(-0.854921\pi\) | ||
0.897918 | − | 0.440162i | \(-0.145079\pi\) | |||||||
\(440\) | − | 1821.29i | − | 4.13929i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −371.844 | −0.841276 | ||||||||
\(443\) | −128.002 | −0.288944 | −0.144472 | − | 0.989509i | \(-0.546148\pi\) | ||||
−0.144472 | + | 0.989509i | \(0.546148\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 591.480 | 1.32917 | ||||||||
\(446\) | − | 716.474i | − | 1.60644i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −213.056 | − | 494.037i | −0.475572 | − | 1.10276i | ||||
\(449\) | −3.90398 | −0.00869483 | −0.00434741 | − | 0.999991i | \(-0.501384\pi\) | ||||
−0.00434741 | + | 0.999991i | \(0.501384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 405.746i | − | 0.899658i | ||||||
\(452\) | −1020.48 | −2.25771 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 88.5230i | − | 0.194985i | ||||||
\(455\) | −147.270 | − | 341.491i | −0.323670 | − | 0.750530i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 376.932 | 0.824797 | 0.412398 | − | 0.911004i | \(-0.364691\pi\) | ||||
0.412398 | + | 0.911004i | \(0.364691\pi\) | |||||||
\(458\) | − | 1383.52i | − | 3.02079i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2329.57i | 5.06429i | ||||||||
\(461\) | − | 331.341i | − | 0.718745i | −0.933194 | − | 0.359372i | \(-0.882991\pi\) | ||
0.933194 | − | 0.359372i | \(-0.117009\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.5800 | −0.0595681 | −0.0297840 | − | 0.999556i | \(-0.509482\pi\) | ||||
−0.0297840 | + | 0.999556i | \(0.509482\pi\) | |||||||
\(464\) | −81.5690 | −0.175795 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −659.128 | −1.41444 | ||||||||
\(467\) | 447.784i | 0.958852i | 0.877582 | + | 0.479426i | \(0.159155\pi\) | ||||
−0.877582 | + | 0.479426i | \(0.840845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 101.400 | + | 235.127i | 0.216204 | + | 0.501338i | ||||
\(470\) | −1267.63 | −2.69708 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 647.635i | 1.37211i | ||||||||
\(473\) | 40.2430 | 0.0850803 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 214.944i | 0.452514i | ||||||||
\(476\) | −979.142 | + | 422.260i | −2.05702 | + | 0.887101i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 51.7282 | 0.108218 | ||||||||
\(479\) | 714.457i | 1.49156i | 0.666192 | + | 0.745780i | \(0.267923\pi\) | ||||
−0.666192 | + | 0.745780i | \(0.732077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 213.581i | 0.444036i | ||||||||
\(482\) | 682.123i | 1.41519i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −148.300 | −0.306405 | ||||||||
\(485\) | 1103.57 | 2.27540 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 103.824 | 0.213191 | 0.106595 | − | 0.994302i | \(-0.466005\pi\) | ||||
0.106595 | + | 0.994302i | \(0.466005\pi\) | |||||||
\(488\) | 2309.24i | 4.73205i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1093.06 | − | 1031.60i | −2.23073 | − | 2.10531i | ||||
\(491\) | 629.055 | 1.28117 | 0.640586 | − | 0.767887i | \(-0.278692\pi\) | ||||
0.640586 | + | 0.767887i | \(0.278692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.4705i | 0.0638347i | ||||||||
\(494\) | −118.368 | −0.239612 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 660.696i | − | 1.33205i | ||||||
\(497\) | −219.279 | − | 508.468i | −0.441206 | − | 1.02307i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 184.140 | 0.369018 | 0.184509 | − | 0.982831i | \(-0.440931\pi\) | ||||
0.184509 | + | 0.982831i | \(0.440931\pi\) | |||||||
\(500\) | − | 1479.37i | − | 2.95873i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 712.478i | 1.41928i | ||||||||
\(503\) | − | 224.619i | − | 0.446559i | −0.974754 | − | 0.223280i | \(-0.928324\pi\) | ||
0.974754 | − | 0.223280i | \(-0.0716763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −89.9042 | −0.178028 | ||||||||
\(506\) | −1101.09 | −2.17606 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1422.61 | 2.80041 | ||||||||
\(509\) | − | 643.540i | − | 1.26432i | −0.774837 | − | 0.632161i | \(-0.782168\pi\) | ||
0.774837 | − | 0.632161i | \(-0.217832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 247.896 | − | 106.906i | 0.485119 | − | 0.209210i | ||||
\(512\) | −865.465 | −1.69036 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 543.531i | 1.05745i | ||||||||
\(515\) | 1615.29 | 3.13649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 425.132i | − | 0.822305i | ||||||
\(518\) | 341.819 | + | 792.614i | 0.659882 | + | 1.53014i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1138.01 | 2.18848 | ||||||||
\(521\) | 1.37190i | 0.00263321i | 0.999999 | + | 0.00131660i | \(0.000419088\pi\) | ||||
−0.999999 | + | 0.00131660i | \(0.999581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 130.586i | − | 0.249687i | −0.992176 | − | 0.124843i | \(-0.960157\pi\) | ||
0.992176 | − | 0.124843i | \(-0.0398429\pi\) | |||||||
\(524\) | 2171.56i | 4.14419i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 301.772 | 0.573711 | ||||||||
\(527\) | −254.906 | −0.483693 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 302.884 | 0.572560 | ||||||||
\(530\) | − | 1340.01i | − | 2.52832i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −311.688 | + | 134.417i | −0.585880 | + | 0.252664i | ||||
\(533\) | 253.525 | 0.475657 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 858.851i | 1.60533i | ||||||||
\(536\) | −783.554 | −1.46185 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1454.04i | 2.70267i | ||||||||
\(539\) | 345.975 | − | 366.585i | 0.641883 | − | 0.680121i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −825.484 | −1.52585 | −0.762924 | − | 0.646488i | \(-0.776237\pi\) | ||||
−0.762924 | + | 0.646488i | \(0.776237\pi\) | |||||||
\(542\) | − | 1811.65i | − | 3.34253i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1001.73i | − | 1.84141i | ||||||
\(545\) | 1091.32i | 2.00243i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 700.004 | 1.27972 | 0.639858 | − | 0.768494i | \(-0.278993\pi\) | ||||
0.639858 | + | 0.768494i | \(0.278993\pi\) | |||||||
\(548\) | 1435.35 | 2.61925 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1653.63 | 3.00660 | ||||||||
\(551\) | 10.0179i | 0.0181814i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −278.076 | − | 644.806i | −0.502850 | − | 1.16602i | ||||
\(554\) | 1395.38 | 2.51873 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 938.915i | 1.68870i | ||||||||
\(557\) | 494.626 | 0.888018 | 0.444009 | − | 0.896022i | \(-0.353556\pi\) | ||||
0.444009 | + | 0.896022i | \(0.353556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.1453i | 0.0449827i | ||||||||
\(560\) | 2146.57 | − | 925.719i | 3.83316 | − | 1.65307i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −421.864 | −0.750648 | ||||||||
\(563\) | 64.8828i | 0.115245i | 0.998338 | + | 0.0576224i | \(0.0183519\pi\) | ||||
−0.998338 | + | 0.0576224i | \(0.981648\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 863.145i | − | 1.52769i | ||||||
\(566\) | 241.877i | 0.427345i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1694.45 | 2.98319 | ||||||||
\(569\) | −1007.60 | −1.77082 | −0.885412 | − | 0.464807i | \(-0.846124\pi\) | ||||
−0.885412 | + | 0.464807i | \(0.846124\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −849.328 | −1.48744 | −0.743720 | − | 0.668491i | \(-0.766940\pi\) | ||||
−0.743720 | + | 0.668491i | \(0.766940\pi\) | |||||||
\(572\) | 646.152i | 1.12964i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 940.848 | − | 405.746i | 1.63911 | − | 0.706874i | ||||
\(575\) | −1249.34 | −2.17276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 184.039i | 0.318959i | 0.987201 | + | 0.159480i | \(0.0509816\pi\) | ||||
−0.987201 | + | 0.159480i | \(0.949018\pi\) | |||||||
\(578\) | 170.709 | 0.295344 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 163.059i | − | 0.281136i | ||||||
\(581\) | −335.554 | + | 144.710i | −0.577546 | + | 0.249070i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 449.408 | 0.770854 | ||||||||
\(584\) | 826.105i | 1.41456i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1447.04i | − | 2.46935i | ||||||
\(587\) | 413.912i | 0.705131i | 0.935787 | + | 0.352566i | \(0.114691\pi\) | ||||
−0.935787 | + | 0.352566i | \(0.885309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −81.1436 | −0.137765 | ||||||||
\(590\) | −927.396 | −1.57186 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1342.54 | −2.26781 | ||||||||
\(593\) | 230.273i | 0.388318i | 0.980970 | + | 0.194159i | \(0.0621978\pi\) | ||||
−0.980970 | + | 0.194159i | \(0.937802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −357.156 | − | 828.178i | −0.600262 | − | 1.39190i | ||||
\(596\) | −2693.15 | −4.51871 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 688.001i | − | 1.15050i | ||||||
\(599\) | −540.836 | −0.902898 | −0.451449 | − | 0.892297i | \(-0.649093\pi\) | ||||
−0.451449 | + | 0.892297i | \(0.649093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.8243i | 0.0180105i | 0.999959 | + | 0.00900524i | \(0.00286650\pi\) | ||||
−0.999959 | + | 0.00900524i | \(0.997134\pi\) | |||||||
\(602\) | 40.2430 | + | 93.3159i | 0.0668488 | + | 0.155010i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1872.82 | −3.10070 | ||||||||
\(605\) | − | 125.435i | − | 0.207331i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 980.978i | 1.61611i | 0.589108 | + | 0.808055i | \(0.299479\pi\) | ||||
−0.589108 | + | 0.808055i | \(0.700521\pi\) | |||||||
\(608\) | − | 318.877i | − | 0.524469i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3306.77 | −5.42093 | ||||||||
\(611\) | 265.638 | 0.434760 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −498.640 | −0.813442 | −0.406721 | − | 0.913552i | \(-0.633328\pi\) | ||||
−0.406721 | + | 0.913552i | \(0.633328\pi\) | |||||||
\(614\) | − | 1320.74i | − | 2.15104i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 610.816 | + | 1416.37i | 0.991585 | + | 2.29930i | ||||
\(617\) | 618.501 | 1.00243 | 0.501216 | − | 0.865322i | \(-0.332886\pi\) | ||||
0.501216 | + | 0.865322i | \(0.332886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 153.366i | − | 0.247765i | −0.992297 | − | 0.123882i | \(-0.960465\pi\) | ||
0.992297 | − | 0.123882i | \(-0.0395345\pi\) | |||||||
\(620\) | 1320.75 | 2.13025 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 337.406i | − | 0.542453i | ||||||
\(623\) | −459.979 | + | 198.368i | −0.738329 | + | 0.318408i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 168.376 | 0.269402 | ||||||||
\(626\) | − | 47.7076i | − | 0.0762102i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 884.896i | 1.40907i | ||||||||
\(629\) | 517.973i | 0.823487i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −521.260 | −0.826085 | −0.413043 | − | 0.910712i | \(-0.635534\pi\) | ||||
−0.413043 | + | 0.910712i | \(0.635534\pi\) | |||||||
\(632\) | 2148.80 | 3.39999 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −995.440 | −1.57009 | ||||||||
\(635\) | 1203.27i | 1.89491i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 229.056 | + | 216.178i | 0.359586 | + | 0.339369i | ||||
\(638\) | 77.0710 | 0.120801 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 232.994i | 0.364052i | ||||||||
\(641\) | 1013.31 | 1.58083 | 0.790416 | − | 0.612570i | \(-0.209864\pi\) | ||||
0.790416 | + | 0.612570i | \(0.209864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 752.150i | 1.16975i | 0.811123 | + | 0.584875i | \(0.198857\pi\) | ||||
−0.811123 | + | 0.584875i | \(0.801143\pi\) | |||||||
\(644\) | −781.283 | − | 1811.65i | −1.21317 | − | 2.81312i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −287.064 | −0.444372 | ||||||||
\(647\) | − | 1042.89i | − | 1.61188i | −0.591995 | − | 0.805942i | \(-0.701659\pi\) | ||
0.591995 | − | 0.805942i | \(-0.298341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 311.026i | − | 0.479240i | ||||||
\(650\) | 1033.25i | 1.58962i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1850.04 | 2.83748 | ||||||||
\(653\) | −529.525 | −0.810911 | −0.405455 | − | 0.914115i | \(-0.632887\pi\) | ||||
−0.405455 | + | 0.914115i | \(0.632887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1836.74 | −2.80419 | ||||||||
\(656\) | 1593.63i | 2.42931i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 985.800 | − | 425.132i | 1.49818 | − | 0.646097i | ||||
\(659\) | 392.215 | 0.595168 | 0.297584 | − | 0.954696i | \(-0.403819\pi\) | ||||
0.297584 | + | 0.954696i | \(0.403819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1212.04i | − | 1.83365i | −0.399288 | − | 0.916825i | \(-0.630743\pi\) | ||
0.399288 | − | 0.916825i | \(-0.369257\pi\) | |||||||
\(662\) | −321.170 | −0.485152 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1118.22i | − | 1.68407i | ||||||
\(665\) | −113.693 | − | 263.632i | −0.170966 | − | 0.396439i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −58.2280 | −0.0872983 | ||||||||
\(668\) | − | 708.506i | − | 1.06064i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 1122.03i | − | 1.67467i | ||||||
\(671\) | − | 1109.01i | − | 1.65277i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 376.932 | 0.560077 | 0.280039 | − | 0.959989i | \(-0.409653\pi\) | ||||
0.280039 | + | 0.959989i | \(0.409653\pi\) | |||||||
\(674\) | −286.791 | −0.425506 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1247.73 | 1.84575 | ||||||||
\(677\) | 485.473i | 0.717095i | 0.933511 | + | 0.358548i | \(0.116728\pi\) | ||||
−0.933511 | + | 0.358548i | \(0.883272\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −858.216 | + | 370.110i | −1.26394 | + | 0.545081i | ||||
\(680\) | 2759.87 | 4.05864 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 624.263i | 0.915341i | ||||||||
\(683\) | −223.451 | −0.327161 | −0.163580 | − | 0.986530i | \(-0.552304\pi\) | ||||
−0.163580 | + | 0.986530i | \(0.552304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1214.05i | 1.77233i | ||||||||
\(686\) | 1196.02 | + | 435.666i | 1.74347 | + | 0.635082i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −158.060 | −0.229739 | ||||||||
\(689\) | 280.807i | 0.407557i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 294.314i | − | 0.425924i | −0.977060 | − | 0.212962i | \(-0.931689\pi\) | ||
0.977060 | − | 0.212962i | \(-0.0683111\pi\) | |||||||
\(692\) | 1684.84i | 2.43474i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 188.456 | 0.271550 | ||||||||
\(695\) | −794.153 | −1.14267 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 614.844 | 0.882129 | ||||||||
\(698\) | 480.035i | 0.687729i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1173.34 | + | 2720.77i | 1.67621 | + | 3.88681i | ||||
\(701\) | 1238.74 | 1.76710 | 0.883552 | − | 0.468334i | \(-0.155146\pi\) | ||||
0.883552 | + | 0.468334i | \(0.155146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 164.885i | 0.234545i | ||||||||
\(704\) | −790.665 | −1.12310 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1200.86i | − | 1.70093i | ||||||
\(707\) | 69.9163 | − | 30.1517i | 0.0988914 | − | 0.0426475i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −323.340 | −0.456051 | −0.228026 | − | 0.973655i | \(-0.573227\pi\) | ||||
−0.228026 | + | 0.973655i | \(0.573227\pi\) | |||||||
\(710\) | 2426.41i | 3.41748i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 1532.87i | − | 2.15290i | ||||||
\(713\) | − | 471.638i | − | 0.661483i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −546.528 | −0.764375 | ||||||||
\(716\) | 1547.34 | 2.16108 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 885.980 | 1.23396 | ||||||||
\(719\) | − | 533.479i | − | 0.741973i | −0.928638 | − | 0.370987i | \(-0.879020\pi\) | ||
0.928638 | − | 0.370987i | \(-0.120980\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1256.17 | + | 541.731i | −1.74226 | + | 0.751360i | ||||
\(722\) | 1248.31 | 1.72897 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 2789.11i | − | 3.85236i | ||||||
\(725\) | 87.4478 | 0.120618 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 545.228i | 0.749969i | 0.927031 | + | 0.374985i | \(0.122352\pi\) | ||||
−0.927031 | + | 0.374985i | \(0.877648\pi\) | |||||||
\(728\) | −885.000 | + | 381.661i | −1.21566 | + | 0.524259i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1182.96 | −1.62049 | ||||||||
\(731\) | 60.9819i | 0.0834226i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 112.640i | − | 0.153669i | −0.997044 | − | 0.0768346i | \(-0.975519\pi\) | ||
0.997044 | − | 0.0768346i | \(-0.0244813\pi\) | |||||||
\(734\) | − | 211.345i | − | 0.287936i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1853.44 | 2.51826 | ||||||||
\(737\) | 376.302 | 0.510586 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 764.528 | 1.03454 | 0.517272 | − | 0.855821i | \(-0.326948\pi\) | ||||
0.517272 | + | 0.855821i | \(0.326948\pi\) | |||||||
\(740\) | − | 2683.79i | − | 3.62675i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 449.408 | + | 1042.09i | 0.605671 | + | 1.40444i | ||||
\(743\) | −441.617 | −0.594370 | −0.297185 | − | 0.954820i | \(-0.596048\pi\) | ||||
−0.297185 | + | 0.954820i | \(0.596048\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2277.92i | − | 3.05761i | ||||||
\(746\) | −1362.18 | −1.82598 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1567.04i | 2.09497i | ||||||||
\(749\) | −288.038 | − | 667.907i | −0.384564 | − | 0.891731i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −799.656 | −1.06479 | −0.532394 | − | 0.846497i | \(-0.678708\pi\) | ||||
−0.532394 | + | 0.846497i | \(0.678708\pi\) | |||||||
\(752\) | 1669.77i | 2.22043i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 48.1569i | 0.0638685i | ||||||||
\(755\) | − | 1584.07i | − | 2.09811i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1403.41 | 1.85391 | 0.926957 | − | 0.375169i | \(-0.122415\pi\) | ||||
0.926957 | + | 0.375169i | \(0.122415\pi\) | |||||||
\(758\) | 189.576 | 0.250100 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 878.544 | 1.15598 | ||||||||
\(761\) | − | 40.5164i | − | 0.0532410i | −0.999646 | − | 0.0266205i | \(-0.991525\pi\) | ||
0.999646 | − | 0.0266205i | \(-0.00847457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −366.004 | − | 848.695i | −0.479691 | − | 1.11231i | ||||
\(764\) | −1763.62 | −2.30840 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1713.41i | 2.23682i | ||||||||
\(767\) | 194.341 | 0.253378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 679.542i | 0.883670i | 0.897096 | + | 0.441835i | \(0.145672\pi\) | ||||
−0.897096 | + | 0.441835i | \(0.854328\pi\) | |||||||
\(770\) | −2028.20 | + | 874.672i | −2.63403 | + | 1.13594i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1171.47 | 1.51745 | ||||||||
\(773\) | − | 737.501i | − | 0.954076i | −0.878883 | − | 0.477038i | \(-0.841710\pi\) | ||
0.878883 | − | 0.477038i | \(-0.158290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 708.313i | 0.913952i | ||||||||
\(776\) | − | 2859.98i | − | 3.68554i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 388.976 | 0.499969 | ||||||||
\(779\) | 195.722 | 0.251248 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −813.760 | −1.04195 | ||||||||
\(782\) | − | 1668.53i | − | 2.13367i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1358.87 | + | 1439.82i | −1.73325 | + | 1.83650i | ||||
\(785\) | −748.462 | −0.953455 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 837.871i | − | 1.06464i | −0.846544 | − | 0.532319i | \(-0.821321\pi\) | ||
0.846544 | − | 0.532319i | \(-0.178679\pi\) | |||||||
\(788\) | −1238.07 | −1.57116 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3077.02i | 3.89496i | ||||||||
\(791\) | 289.478 | + | 671.246i | 0.365965 | + | 0.848604i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 692.952 | 0.873836 | ||||||||
\(794\) | 2220.50i | 2.79660i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 139.945i | − | 0.175810i | ||||||
\(797\) | 1387.72i | 1.74118i | 0.492010 | + | 0.870589i | \(0.336262\pi\) | ||||
−0.492010 | + | 0.870589i | \(0.663738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 644.220 | 0.806283 | ||||||||
\(800\) | −2783.52 | −3.47940 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1075.21 | 1.34066 | ||||||||
\(803\) | − | 396.737i | − | 0.494068i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1532.33 | − | 660.825i | 1.90351 | − | 0.820900i | ||||
\(806\) | −390.063 | −0.483949 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 232.994i | 0.288358i | ||||||||
\(809\) | −1281.68 | −1.58428 | −0.792140 | − | 0.610339i | \(-0.791033\pi\) | ||||
−0.792140 | + | 0.610339i | \(0.791033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.7553i | 0.0169610i | 0.999964 | + | 0.00848048i | \(0.00269945\pi\) | ||||
−0.999964 | + | 0.00848048i | \(0.997301\pi\) | |||||||
\(812\) | 54.6862 | + | 126.807i | 0.0673475 | + | 0.156166i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1268.51 | 1.55837 | ||||||||
\(815\) | 1564.80i | 1.92000i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.4122i | 0.0237604i | ||||||||
\(818\) | 333.953i | 0.408256i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3185.71 | −3.88502 | ||||||||
\(821\) | −461.671 | −0.562328 | −0.281164 | − | 0.959660i | \(-0.590721\pi\) | ||||
−0.281164 | + | 0.959660i | \(0.590721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1057.27 | 1.28465 | 0.642326 | − | 0.766432i | \(-0.277970\pi\) | ||||
0.642326 | + | 0.766432i | \(0.277970\pi\) | |||||||
\(824\) | − | 4186.15i | − | 5.08028i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 721.212 | − | 311.026i | 0.873138 | − | 0.376545i | ||||
\(827\) | 73.7018 | 0.0891194 | 0.0445597 | − | 0.999007i | \(-0.485812\pi\) | ||||
0.0445597 | + | 0.999007i | \(0.485812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 134.854i | 0.162670i | 0.996687 | + | 0.0813352i | \(0.0259184\pi\) | ||||
−0.996687 | + | 0.0813352i | \(0.974082\pi\) | |||||||
\(830\) | 1601.27 | 1.92924 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 494.037i | − | 0.593795i | ||||||
\(833\) | 555.502 | + | 524.271i | 0.666869 | + | 0.629377i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 599.268 | 0.717686 | ||||||||
\(836\) | 498.831i | 0.596687i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 2454.17i | − | 2.92860i | ||||||
\(839\) | − | 936.299i | − | 1.11597i | −0.829851 | − | 0.557985i | \(-0.811575\pi\) | ||
0.829851 | − | 0.557985i | \(-0.188425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −836.924 | −0.995154 | ||||||||
\(842\) | 501.202 | 0.595252 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3245.52 | −3.84540 | ||||||||
\(845\) | 1055.35i | 1.24894i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0679 | + | 97.5477i | 0.0496670 | + | 0.115168i | ||||
\(848\) | −1765.12 | −2.08151 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2505.82i | 2.94802i | ||||||||
\(851\) | −958.375 | −1.12618 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.5820i | 0.0299907i | 0.999888 | + | 0.0149953i | \(0.00477334\pi\) | ||||
−0.999888 | + | 0.0149953i | \(0.995227\pi\) | |||||||
\(854\) | 2571.59 | − | 1109.01i | 3.01123 | − | 1.29861i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2225.78 | 2.60021 | ||||||||
\(857\) | 553.564i | 0.645932i | 0.946411 | + | 0.322966i | \(0.104680\pi\) | ||||
−0.946411 | + | 0.322966i | \(0.895320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 647.301i | − | 0.753552i | −0.926304 | − | 0.376776i | \(-0.877033\pi\) | ||
0.926304 | − | 0.376776i | \(-0.122967\pi\) | |||||||
\(860\) | − | 315.968i | − | 0.367404i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2114.61 | −2.45314 | ||||||||
\(863\) | −709.719 | −0.822386 | −0.411193 | − | 0.911548i | \(-0.634888\pi\) | ||||
−0.411193 | + | 0.911548i | \(0.634888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1425.07 | −1.64748 | ||||||||
\(866\) | 1776.92i | 2.05187i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1027.12 | + | 442.949i | −1.18331 | + | 0.510310i | ||||
\(869\) | −1031.96 | −1.18752 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 235.127i | 0.269951i | ||||||||
\(872\) | 2828.25 | 3.24340 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 531.138i | − | 0.607710i | ||||||
\(875\) | −973.086 | + | 419.648i | −1.11210 | + | 0.479598i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −367.996 | −0.419608 | −0.209804 | − | 0.977744i | \(-0.567283\pi\) | ||||
−0.209804 | + | 0.977744i | \(0.567283\pi\) | |||||||
\(878\) | − | 1434.19i | − | 1.63347i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 3435.40i | − | 3.90387i | ||||||
\(881\) | − | 1183.91i | − | 1.34383i | −0.740629 | − | 0.671914i | \(-0.765472\pi\) | ||
0.740629 | − | 0.671914i | \(-0.234528\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 845.784 | 0.957853 | 0.478927 | − | 0.877855i | \(-0.341026\pi\) | ||||
0.478927 | + | 0.877855i | \(0.341026\pi\) | |||||||
\(884\) | −979.142 | −1.10763 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −475.024 | −0.536145 | ||||||||
\(887\) | − | 174.598i | − | 0.196840i | −0.995145 | − | 0.0984202i | \(-0.968621\pi\) | ||
0.995145 | − | 0.0984202i | \(-0.0313789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −403.548 | − | 935.752i | −0.453935 | − | 1.05259i | ||||
\(890\) | 2195.02 | 2.46632 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 1886.62i | − | 2.11505i | ||||||
\(893\) | 205.073 | 0.229645 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1308.77i | 1.46231i | ||||||||
\(896\) | −78.1405 | − | 181.193i | −0.0872104 | − | 0.202225i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.4879 | −0.0161335 | ||||||||
\(899\) | 33.0124i | 0.0367213i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 681.008i | 0.755835i | ||||||||
\(902\) | − | 1505.75i | − | 1.66934i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2236.90 | −2.47445 | ||||||||
\(905\) | 2359.08 | 2.60672 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1055.10 | 1.16329 | 0.581643 | − | 0.813444i | \(-0.302410\pi\) | ||||
0.581643 | + | 0.813444i | \(0.302410\pi\) | |||||||
\(908\) | − | 233.099i | − | 0.256717i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −546.528 | − | 1267.30i | −0.600580 | − | 1.39263i | ||||
\(911\) | −1506.20 | −1.65335 | −0.826676 | − | 0.562679i | \(-0.809771\pi\) | ||||
−0.826676 | + | 0.562679i | \(0.809771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 537.027i | 0.588200i | ||||||||
\(914\) | 1398.82 | 1.53044 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 3643.10i | − | 3.97718i | ||||||
\(917\) | 1428.39 | − | 616.000i | 1.55768 | − | 0.671756i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −69.2280 | −0.0753297 | −0.0376649 | − | 0.999290i | \(-0.511992\pi\) | ||||
−0.0376649 | + | 0.999290i | \(0.511992\pi\) | |||||||
\(920\) | 5106.43i | 5.55047i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1229.63i | − | 1.33365i | ||||||
\(923\) | − | 508.468i | − | 0.550886i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1439.30 | 1.55600 | ||||||||
\(926\) | −102.351 | −0.110531 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −129.732 | −0.139797 | ||||||||
\(929\) | 1289.69i | 1.38826i | 0.719850 | + | 0.694129i | \(0.244210\pi\) | ||||
−0.719850 | + | 0.694129i | \(0.755790\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 176.832 | + | 166.890i | 0.189937 | + | 0.179259i | ||||
\(932\) | −1735.62 | −1.86225 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1661.75i | 1.77918i | ||||||||
\(935\) | −1325.43 | −1.41757 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1061.84i | 1.13323i | 0.823982 | + | 0.566617i | \(0.191748\pi\) | ||||
−0.823982 | + | 0.566617i | \(0.808252\pi\) | |||||||
\(938\) | 376.302 | + | 872.573i | 0.401174 | + | 0.930248i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3337.92 | −3.55098 | ||||||||
\(941\) | − | 653.558i | − | 0.694536i | −0.937766 | − | 0.347268i | \(-0.887109\pi\) | ||
0.937766 | − | 0.347268i | \(-0.112891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1137.61i | 1.20637i | ||||||||
\(944\) | 1221.60i | 1.29407i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 149.344 | 0.157869 | ||||||||
\(947\) | 768.131 | 0.811121 | 0.405560 | − | 0.914068i | \(-0.367076\pi\) | ||||
0.405560 | + | 0.914068i | \(0.367076\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 247.896 | 0.261218 | ||||||||
\(950\) | 797.672i | 0.839655i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2146.28 | + | 925.596i | −2.25450 | + | 0.972265i | ||||
\(953\) | −251.046 | −0.263427 | −0.131714 | − | 0.991288i | \(-0.542048\pi\) | ||||
−0.131714 | + | 0.991288i | \(0.542048\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1491.70i | − | 1.56199i | ||||||
\(956\) | 136.211 | 0.142480 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2651.40i | 2.76764i | ||||||||
\(959\) | −407.163 | − | 944.134i | −0.424570 | − | 0.984499i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 693.605 | 0.721753 | ||||||||
\(962\) | 792.614i | 0.823923i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1796.17i | 1.86325i | ||||||||
\(965\) | 990.851i | 1.02679i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −474.640 | −0.490838 | −0.245419 | − | 0.969417i | \(-0.578926\pi\) | ||||
−0.245419 | + | 0.969417i | \(0.578926\pi\) | |||||||
\(968\) | −325.074 | −0.335821 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4095.41 | 4.22207 | ||||||||
\(971\) | − | 1205.96i | − | 1.24198i | −0.783818 | − | 0.620991i | \(-0.786730\pi\) | ||
0.783818 | − | 0.620991i | \(-0.213270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 617.592 | − | 266.340i | 0.634730 | − | 0.273731i | ||||
\(974\) | 385.298 | 0.395583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4355.81i | 4.46292i | ||||||||
\(977\) | −335.837 | −0.343743 | −0.171872 | − | 0.985119i | \(-0.554981\pi\) | ||||
−0.171872 | + | 0.985119i | \(0.554981\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 736.158i | 0.751949i | ||||||||
\(980\) | −2878.24 | − | 2716.42i | −2.93698 | − | 2.77186i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2334.46 | 2.37725 | ||||||||
\(983\) | − | 1260.83i | − | 1.28263i | −0.767276 | − | 0.641317i | \(-0.778388\pi\) | ||
0.767276 | − | 0.641317i | \(-0.221612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1047.18i | − | 1.06313i | ||||||
\(986\) | 116.789i | 0.118447i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −311.688 | −0.315474 | ||||||||
\(989\) | −112.831 | −0.114086 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 505.836 | 0.510430 | 0.255215 | − | 0.966884i | \(-0.417854\pi\) | ||||
0.255215 | + | 0.966884i | \(0.417854\pi\) | |||||||
\(992\) | − | 1050.81i | − | 1.05928i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −813.760 | − | 1886.96i | −0.818672 | − | 1.89835i | ||||
\(995\) | 118.368 | 0.118963 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1130.51i | 1.13392i | 0.823747 | + | 0.566958i | \(0.191880\pi\) | ||||
−0.823747 | + | 0.566958i | \(0.808120\pi\) | |||||||
\(998\) | 683.355 | 0.684725 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 189.3.d.e.55.8 | yes | 8 | |
3.2 | odd | 2 | inner | 189.3.d.e.55.1 | ✓ | 8 | |
7.6 | odd | 2 | inner | 189.3.d.e.55.7 | yes | 8 | |
21.20 | even | 2 | inner | 189.3.d.e.55.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.3.d.e.55.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
189.3.d.e.55.2 | yes | 8 | 21.20 | even | 2 | inner | |
189.3.d.e.55.7 | yes | 8 | 7.6 | odd | 2 | inner | |
189.3.d.e.55.8 | yes | 8 | 1.1 | even | 1 | trivial |